[duxuser] Re: literart brf to nemeth
- From: Sherry Castro <scastro5@xxxxxxxxxxxxxxxxxxxxxx>
- To: duxuser@xxxxxxxxxxxxx
- Date: Fri, 1 Jun 2012 13:30:27 -0700
Here is the book.
On 6/1/12, David Holladay <david@xxxxxxxxxx> wrote:
>
>
> To all:
>
> I am curious what an Algebra book done in literary braille looks like.
> Could you e-mail one volume or a fragment of this item so I can see what
> this is like?
>
> Send this directly to my e-mail (not to the whole list)
> david@xxxxxxxxxx
>
> -- David Holladay
> Duxbury Systems
>
>
>
>
> At 02:38 PM 6/1/2012, you wrote:
>
>
>>Hello-
>>We have downloaded an algebra book from nimac in a BRF; unfortunately,
>>it is in literary Braille, and we need it in Nemeth. how do we convert
>>it from literary to Nemeth when it has already been translated.
>>We are using 11.1 SR3.
>>
>>We are also concerned with the translating of spanish coursework. In
>>10.7 we used english amer/stand/lit then alt-4; however, with 11.1 it
>>is not working out the same. We are getting the translation in grade-2
>>when it should be grade-1 with contractions for the accents.
>>Help please, Sherry
>>* * *
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SIMPLIFY+ FUNC;NS4
-----------------------------------;VIII
..,,*APT] #A ,EQU,NS & .,9EQUALITIES
,UNIT #A ,L9E> ,EQU,NS1 ,9EQUALITIES1
,FUNC;NS1 & ,SY/EM
,PICTURE3 .,"W .,RATES1 P4 #BJ
,PICTURE3 .;T @+ .;T .K .#G
,PREREQUISITE ,SKILLS
XXIV
#A.A ,APPLY ,PROP]TIES ( ,R1L ,NUMB]S
#B
#A.B ,EVALUATE & ,SIMPLIFY ,ALGEBRAIC
,EXPRES.NS
#AJ
..,GRAPH+ ,CALCULATOR ,ACTIV;Y ,EVALUATE
.,EXPRES.NS #AG
#A.C ,SOLVE ,L9E> ,EQU,NS
#AH
..,GRAPH+ ,CALCULATOR ,ACTIV;Y ,USE
,TA#S 6,SOLVE .,EQU,NS #BE
#A.D ,REWRITE ,=MULAS & ,EQU,NS
#BF
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+ #CC
#A.E ,USE ,PRO#M ,SOLV+ ,/RATEGIES &
,MODELS
#CD
#A.F ,SOLVE ,L9E> ,9EQUALITIES
#DA
,PRO#M ,SOLV+ ,"W%OP #DH
#A.G ,SOLVE ,ABSOLUTE ,VALUE ,EQU,NS &
,9EQUALITIES
#EA
..,9VE/IGAT+ ,ALGEBRA3 ,ABSOLUTE ,VALUE
,EQU,NS & .,9EQUALITIES #EJ
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+ #EI
.,,ASSESS;T
,QUIZZES
#AF @1 #DJ @1 #EH
,*APT] ,SUMM>Y & ,REVIEW
#FJ
,*APT] ,TE/
#FE
..,/&>DIZ$ ,TE/ ,PREP>,N & .,PRACTICE
#FF
.,ANIMAT$ .,ALGEBRA _+CLASSZONE.COM_:
.,ACTIVITIES
#A @1 #E @1 #AA @1 #BJ @1 #BG @1 #CD @1
#DB @1 #EC
,*APT] #A ,HI<LI<TS
,SIDEB>3
,PRO#M ,SOLV+
99 ..,MIX$ ,REVIEW ( ,PRO#M .,SOLV+ @1
#CC @1 #EI
99 .,MULTIPLE .,REPRES5T,NS @1 #AE @1
#BD @1 #CE @1 #CI @1 #DH @1 #EG
99 .,MULTI-.,/EP .,PRO#MS @1 #H @1 #BC
@1 #CB @1 #CC @1 #CI @1 #DG @1 #EG @1
#EI
99 .,US+ .,ALT]NATIVE .,ME?ODS @1 #DH
99 ..,R1L-,_W ,PRO#M ,SOLV+ .,EXAMPLES
@1 #C @1 #E @1 #AA @1 #AC @1 #AI @1 #BJ
@1 #BI @1 #CE @1 #CF @1 #DB @1 #DD @1
#ED
,SIDEB>3
,ASSESS;T
99 ..,/&>DIZ$ ,TE/ ,PRACTICE
.,EXAMPLES @1 #C @1 #AI @1 #CF
99 .,MULTIPLE .,*OICE @1 #F @1 #AD @1
#BA @1 #BD @1 #CJ @1 #CG @1 #CH @1 #DE
@1 #DF @1 #EF
99 .,%ORT .,RESPONSE_/.,EXT5D$
.,RESPONSE @1 #H @1 #I @1 #AE @1 #BC @1
#CA @1 #CB @1 #CC @1 #CG @1 #CH @1 #DG
@1 #EE @1 #EI @1 #FF
99 .,WRIT9G_/.,OP5-.,5D$ @1 #F @1 #AC
@1 #BA @1 #CJ @1 #CB @1 #CC @1 #CG @1
#DD @1 #EE @1 #EI
,SIDEB>3
,TE*NOLOGY
,AT _+CLASSZONE.COM:_:
99 .,ANIMAT$ .,ALGEBRA @1 #A @1 #E @1
#AA @1 #BJ @1 #BG @1 #CD @1 #DB @1 #EC
99 @A .,HOME .,TUTOR @1 XXIV @1 #H @1
#AE @1 #AG @1 #BC @1 #BE @1 #CA @1 #CH
@1 #DF @1 #EG @1 #FA
99 .,ONL9E .,QUIZ @1 #I @1 #AF @1 #BD
@1 #CB @1 #DJ @1 #DG @1 #EH
99 .,/ATE .,TE/ .,PRACTICE @1 #CC @1
#EI @1 #FI
-------------------------------------;IX
..,,*APT] #B ,L9E> ,EQU,NS & .,FUNC;NS
,UNIT #A ,L9E> ,EQU,NS1 ,9EQUALITIES1
,FUNC;NS1 & ,SY/EM
,PICTURE3 .,L9E> .,FUNC;NS1 P4 #GF
,PICTURE3 .;,P7.;D7 .K #A @+ #J.JC .;D
,PREREQUISITE ,SKILLS
#GJ
#B.A ,REPRES5T ,REL,NS & ,FUNC;NS
#GB
#B.B ,F9D ,SLOPE & ,RATE ( ,*ANGE
#HB
#B.C ,GRAPH ,EQU,NS ( ,L9ES
#HI
..,GRAPH+ ,CALCULATOR ,ACTIV;Y ,GRAPH
.,EQU,NS #IG
#B.D ,WRITE ,EQU,NS ( ,L9ES
#IH
,PRO#M ,SOLV+ ,"W%OP #AJE
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+ #AJF
#B.E ,MODEL ,DIRECT ,V>I,N
#AJG
#B.F ,DRAW ,SCATT] ,PLOTS & ,BE/-,FITT+
,L9ES
#AAC
..,9VE/IGAT+ ,ALGEBRA3 ,FITT+ A ,L9E
6.,DATA #AAB
#B.G ,USE ,ABSOLUTE ,VALUE ,FUNC;NS &
,TRANS=M,NS
#ABC
..,9VE/IGAT+ ,ALGEBRA3 ,EXPLOR+
.,TRANS=M,NS #ABA
#B.H ,GRAPH ,L9E> ,9EQUALITIES 9 ,TWO
,V>IA#S
#ACB
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+ #ACI
.,,ASSESS;T
,QUIZZES
#IF @1 #ABJ @1 #ACH
,*APT] ,SUMM>Y & ,REVIEW
#ADJ
,*APT] ,TE/
#ADE
..,/&>DIZ$ ,TE/ ,PREP>,N & .,PRACTICE
#ADF
.,ANIMAT$ .,ALGEBRA _+CLASSZONE.COM_:
.,ACTIVITIES
#GA @1 #GC @1 #HF @1 #IJ @1 #IH @1 #AJB
@1 #AJG @1 #AAA @1 #AAE @1 #ACC
,*APT] #B ,HI<LI<TS
,SIDEB>3
,PRO#M ,SOLV+
99 ..,MIX$ ,REVIEW ( ,PRO#M .,SOLV+ @1
#AJF @1 #ACI
99 .,MULTIPLE .,REPRES5T,NS @1 #IE @1
#AJD @1 #AJE @1 #AAI @1 #ABI
99 .,MULTI-.,/EP .,PRO#MS @1 #GH @1
#HH @1 #IE @1 #AJC @1 #AJF @1 #ACG @1
#ACI
99 .,US+ .,ALT]NATIVE .,ME?ODS @1 #AJE
99 ..,R1L-,_W ,PRO#M ,SOLV+ .,EXAMPLES
@1 #GD @1 #GF @1 #HE @1 #IA @1 #AJJ @1
#AJH @1 #AAE @1 #ABE @1 #ACD
,SIDEB>3
,ASSESS;T
99 ..,/&>DIZ$ ,TE/ ,PRACTICE
.,EXAMPLES @1 #HB @1 #ACB
99 .,MULTIPLE .,*OICE @1 #GG @1 #HF @1
#HG @1 #IC @1 #AJB @1 #AJI @1 #AAJ @1
#AAH @1 #ABG @1 #ABH @1 #ACF
99 .,%ORT .,RESPONSE_/.,EXT5D$
.,RESPONSE @1 #GG @1 #GH @1 #GI @1 #HG
@1 #HH @1 #ID @1 #IE @1 #AJC @1 #AJF @1
#AAA @1 #AAI @1 #ABH @1 #ABI @1 #ACF @1
#ACG @1 #ACI @1 #ADF
99 .,WRIT9G_/.,OP5-.,5D$ @1 #GF @1 #HF
@1 #HG @1 #IC @1 #ID @1 #AJA @1 #AJC @1
#AJF @1 #AJI @1 #AAJ @1 #AAG @1 #AAH @1
#ABG @1 #ABH @1 #ACE @1 #ACF @1 #ACI
,SIDEB>3
,TE*NOLOGY
,AT _+CLASSZONE.COM:_:
99 .,ANIMAT$ .,ALGEBRA @1 #GA @1 #GC
@1 #HF @1 #IJ @1 #IE @1 #IH @1 #AJB @1
#AJG @1 #AAE @1 #ACC
99 @A .,HOME .,TUTOR @1 #GJ @1 #GH @1
#HG @1 #ID @1 #IG @1 #AJC @1 #AAJ @1
#AAI @1 #ABA @1 #ABH @1 #ACG @1 #ADA
99 .,ONL9E .,QUIZ @1 #GI @1 #HH @1 #IF
@1 #AJD @1 #AAA @1 #ABJ @1 #ABI @1 #ACH
99 .,ELECTRONIC .,FUNC;N .,LIBR>Y @1
#ADJ
99 .,/ATE .,TE/ .,PRACTICE @1 #AJF @1
#ACI @1 #ADI
--------------------------------------;X
..,,*APT] #C ,L9E> ,SY/EMS & .,MATRICES
,UNIT #A ,L9E> ,EQU,NS1 ,9EQUALITIES1
,FUNC;NS1 & ,SY/EM
,PICTURE3 .,L9E> .,SY/EMS1 P4 #AEE
,PICTURE3 ..;Y .K ;X @+ #CJ2 ;Y .K
#B.E .;X
,PREREQUISITE ,SKILLS
#AEJ
#C.A ,SOLVE ,L9E> ,SY/EMS 0,GRAPH+
#AEC
..,9VE/IGAT+ ,ALGEBRA3 ,SOLV+ ,L9E>
,SY/EMS ,US+ .,TA#S #AEB
..,GRAPH+ ,CALCULATOR ,ACTIV;Y ,GRAPH
,SY/EMS ( .,EQU,NS #AEI
#C.B ,SOLVE ,L9E> ,SY/EMS ,ALGEBRAIC,Y
#AFJ
#C.C ,GRAPH ,SY/EMS ( ,L9E> ,9EQUALITIES
#AFH
#C.D ,SOLVE ,SY/EMS ( ,L9E> ,EQU,NS 9
,?REE ,V>IA#S
#AGH
..,9VE/IGAT+ ,ALGEBRA3 ,GRAPH+ ,L9E>
,EQU,NS 9 ,?REE .,V>IA#S #AGG
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+ #AHF
#C.E ,P]=M ,BASIC ,MATRIX ,OP],NS
#AHG
..,GRAPH+ ,CALCULATOR ,ACTIV;Y ,USE
,MATRIX .,OP],NS #AID
#C.F ,MULTIPLY ,MATRICES
#AIE
#C.G ,EVALUATE ,DET]M9ANTS & ,APPLY
,CRAM]'S ,RULE
#BJC
#C.H ,USE ,9V]SE ,MATRICES 6,SOLVE ,L9E>
,SY/EMS
#BAJ
,PRO#M ,SOLV+ ,"W%OP #BAH
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+ #BBJ
.,,ASSESS;T
,QUIZZES
#AFG @1 #AIC @1 #BAG
,*APT] ,SUMM>Y & ,REVIEW
#BBA
,*APT] ,TE/
#BBG
..,/&>DIZ$ ,TE/ ,PREP>,N & .,PRACTICE
#BBH
,CUMULATIVE ,REVIEW1 ,*APT]S #A-C
#BCB
.,ANIMAT$ .,ALGEBRA _+CLASSZONE.COM_:
.,ACTIVITIES
#AEA @1 #AEC @1 #AEE @1 #AFA @1 #AFH @1
#AIF @1 #BAA
,*APT] #C ,HI<LI<TS
,SIDEB>3
,PRO#M ,SOLV+
99 ..,MIX$ ,REVIEW ( ,PRO#M .,SOLV+ @1
#AHF @1 #BBJ
99 .,MULTIPLE .,REPRES5T,NS @1 #AEG @1
#AGC @1 #BAF @1 #BAH
99 .,MULTI-.,/EP .,PRO#MS @1 #AHD @1
#AHF @1 #BJJ @1 #BJA @1 #BJI @1 #BAF @1
#BBJ
99 .,US+ .,ALT]NATIVE .,ME?ODS @1 #BAH
99 ..,R1L-,_W ,PRO#M ,SOLV+ .,EXAMPLES
@1 #AEE @1 #AFB @1 #AGJ @1 #AHA @1 #AHI
@1 #AIH @1 #BJF @1 #BAC
,SIDEB>3
,ASSESS;T
99 ..,/&>DIZ$ ,TE/ ,PRACTICE
.,EXAMPLES @1 #AEE @1 #AFB
99 .,MULTIPLE .,*OICE @1 #AEF @1 #AEG
@1 #AFE @1 #AFF @1 #AGA @1 #AGB @1 #AHC
@1 #AIA @1 #AII @1 #BJG @1 #BJH @1 #BAD
@1 #BAE @1 #BBH
99 .,%ORT .,RESPONSE_/.,EXT5D$
.,RESPONSE @1 #AEG @1 #AEH @1 #AFF @1
#AGB @1 #AGC @1 #AHD @1 #AHE @1 #AHF @1
#AIB @1 #BJA @1 #BJB @1 #BJH @1 #BJI @1
#BAF @1 #BBJ
99 .,WRIT9G_/.,OP5-.,5D$ @1 #AEF @1
#AFD @1 #AGA @1 #AHB @1 #AHF @1 #AIJ @1
#AII @1 #BJJ @1 #BJG @1 #BJH @1 #BAD @1
#BBJ @1 #BBB
,SIDEB>3
,TE*NOLOGY
,AT _+CLASSZONE.COM:_:
99 .,ANIMAT$ .,ALGEBRA @1 #AEA @1 #AEC
@1 #AEE @1 #AFA @1 #AFH @1 #AIF @1 #BAA
99 @A .,HOME .,TUTOR @1 #AEJ @1 #AEB
@1 #AEG @1 #AEI @1 #AFE @1 #AGB @1 #AHD
@1 #AIB @1 #AID @1 #BJJ @1 #BJH @1 #BAE
@1 #BBB
99 .,ONL9E .,QUIZ @1 #AEH @1 #AFG @1
#AGC @1 #AHE @1 #AIC @1 #BJB @1 #BJI @1
#BAG
99 .,/ATE .,TE/ .,PRACTICE @1 #AHF @1
#BBJ @1 #BCA
-------------------------------------;XI
..,,*APT] #D ,QUADRATIC ,FUNC;NS &
.,FACTOR+ ,UNIT #B ,QUADRATIC1
,POLYNOMIAL1 & ,RADICAL ,FUNC;NS
,PICTURE3 .,-PLEX .,NUMB]S1 P4 #BHA
,PICTURE3 .;F7.;Z7 .K .;Z #B @+ .;C
,PREREQUISITE ,SKILLS
#BCD
#D.A ,GRAPH ,QUADRATIC ,FUNC;NS 9 ,/&>D
,=M
#BCF
..,GRAPH+ ,CALCULATOR ,ACTIV;Y ,F9D
,MAXIMUM & ,M9IMUM .,VALUES #BDD
#D.B ,GRAPH ,QUADRATIC ,FUNC;NS 9 ,V]TEX
OR ,9T]CEPT ,=M
#BDE
#D.C ,SOLVE .;X #B @+ .BX @+ .;C .K #J
0,FACTOR+
#BEB
#D.D ,SOLVE .AX #B @+ .BX @+ .;C .K #J
0,FACTOR+
#BEI
#D.E ,SOLVE ,QUADRATIC ,EQU,NS 0,F9D+
,SQU>E ,ROOTS
#BFF
,PRO#M ,SOLV+ ,"W%OP #BGB
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+ #BGD
#D.F ,P]=M ,OP],NS ) ,-PLEX ,NUMB]S
#BGE
#D.G ,-PLETE ! ,SQU>E
#BHD
..,9VE/IGAT+ ,ALGEBRA3 ,US+ ,ALGEBRA
,TILES 6,-PLETE ! .,SQU>E #BHC
#D.H ,USE ! ,QUADRATIC ,=MULA &!
,4CRIM9ANT
#BIB
#D.I ,GRAPH & ,SOLVE ,QUADRATIC
,9EQUALITIES
#CJJ
#D.AJ ,WRITE ,QUADRATIC ,FUNC;NS &
,MODELS
#CJI
..,9VE/IGAT+ ,ALGEBRA3 ,MODEL+ ,DATA )A
,QUADRATIC .,FUNC;N #CJH
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+ #CAF
.,,ASSESS;T
,QUIZZES
#BFE @1 #BIA @1 #CAE
,*APT] ,SUMM>Y & ,REVIEW
#CAG
,*APT] ,TE/
#CBC
..,/&>DIZ$ ,TE/ ,PREP>,N & .,PRACTICE
#CBD
.,ANIMAT$ .,ALGEBRA _+CLASSZONE.COM_:
.,ACTIVITIES
#BCE @1 #BCH @1 #BDG @1 #BFI @1 #BGI @1
#BHG @1 #CJJ
,SIDEB>3
,PRO#M ,SOLV+
99 ..,MIX$ ,REVIEW ( ,PRO#M .,SOLV+ @1
#BGD @1 #CAF
99 .,MULTIPLE .,REPRES5T,NS @1 #BDB @1
#BEH @1 #BGB @1 #BIJ @1 #CJF @1 #CAD
99 .,MULTI-.,/EP .,PRO#MS @1 #BEJ @1
#BEG @1 #BGD @1 #BIH @1 #CJG @1 #CAD @1
#CAF
99 .,US+ .,ALT]NATIVE .,ME?ODS @1 #BGB
99 ..,R1L-,_W ,PRO#M ,SOLV+ .,EXAMPLES
@1 #BCI @1 #BDF @1 #BED @1 #BFB @1 #BGG
@1 #BHG @1 #BIE @1 #CJC @1 #CAA
,SIDEB>3
,ASSESS;T
99 ..,/&>DIZ$ ,TE/ ,PRACTICE
.,EXAMPLES @1 #BED @1 #BFH @1 #BHF
99 .,MULTIPLE .,*OICE @1 #BDA1 #BDI1
#BEF1 #BFC1 #BGJ1 #BHJ1 #BHH1 #BIF1
#BIH1 #CJE1 #CAB1 #CAE1 #CBD
99 .,%ORT .,RESPONSE_/.,EXT5D$
.,RESPONSE @1 #BDA1 #BDB1BEA1BEF1 #BEH1
#BFD1BGA1 #BGD1 #BHA1 #BHB1 #BHI1BIJ1
#BIG1 #BII1CJF1 #CAC1 #CAF
99 .,WRIT9G_/.,OP5-.,5D$ @1 #BDJ1
#BEJ1BEE1 #BEG1 #BFC1 #BFI1 #BGI1 #BHI1
#BIF1 #CJD1 #CAB1 #CAF
,SIDEB>3
,TE*NOLOGY
,AT _+CLASSZONE.COM:_:
99 .,ANIMAT$ .,ALGEBRA @1 #BCE @1 #BCH
@1 #BDG @1 #BFI @1 #BGI @1 #BHG @1 #CJJ
99 @A .,HOME .,TUTOR @1 #BCD @1 #BDB
@1 #BDD @1 #BEJ @1 #BEG @1 #BFD @1 #BGJ
@1 #BHA @1 #BIJ @1 #BIH @1 #CJF @1 #CJH
@1 #CAD @1 #CAH @1
99 .,ONL9E .,QUIZ @1 #BDC @1 #BEA @1
#BEH @1 #BFE @1 #BGA @1 #BHB @1 #BIA @1
#BII @1 #CJG @1 #CAE
99 .,ELECTRONIC .,FUNC;N .,LIBR>Y @1
#CAG
99 .,/ATE .,TE/ .,PRACTICE @1 #BGD @1
#CAF @1 #CBG
------------------------------------;XII
..,,*APT] #E ,POLYNOMIALS & ,POLYNOMIAL
.,FUNC;NS ,UNIT #B ,QUADRATIC1
,POLYNOMIAL1 & ,RADICAL ,FUNC;NS
,PICTURE3 .,POLYNOMIAL .,FUNC;NS1 P4
#CDJ
,PICTURE3 .;,E .K #J.JJBI .;S #D
,PREREQUISITE ,SKILLS
#CBH
#E.A ,USE ,PROP]TIES ( ,EXPON5TS
#CCJ
#E.B ,EVALUATE & ,GRAPH ,POLYNOMIAL
,FUNC;NS
#CCG
..,9VE/IGAT+ ,ALGEBRA3 ,5D ,2HAVIOR (
,POLYNOMIAL .,FUNC;NS #CCF
..,GRAPH+ ,CALCULATOR ,ACTIV;Y ,SET A
,GD ,VIEW+ .,W9D[ #CDE
#E.C ,ADD1 ,SUBTRACT1 & ,MULTIPLY
,POLYNOMIALS
#CDF
#E.D ,FACTOR & ,SOLVE ,POLYNOMIAL
,EQU,NS
#CEC
,PRO#M ,SOLV+ ,"W%OP #CFJ
#E.E ,APPLY ! ,REMA9D] & ,FACTOR ,!OREMS
#CFB
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+ #CFI
#E.F ,F9D ,R,NAL ,Z]OS
#CGJ
..,SPR1D%EET ,ACTIV;Y ,USE ! ,LOC,N
.,PR9CIPLE #CGH
#E.G ,APPLY ! ,FUNDA;TAL ,!OREM (
,ALGEBRA
#CGI
#E.H ,ANALYZE ,GRAPHS ( ,POLYNOMIAL
,FUNC;NS
#CHG
#E.I ,WRITE ,POLYNOMIAL ,FUNC;NS &
,MODELS
#CIC
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+ #DJJ
.,,ASSESS;T
,QUIZZES
#CEB @1 #CGG @1 #CII
,*APT] ,SUMM>Y & ,REVIEW
#DJA
,*APT] ,TE/
#DJG
..,/&>DIZ$ ,TE/ ,PREP>,N & .,PRACTICE
#DJH
.,ANIMAT$ .,ALGEBRA _+CLASSZONE.COM_:
.,ACTIVITIES
#CBI @1 #CCA @1 #CDJ @1 #CEA @1 #CGA @1
#CHH @1 #CIF
,SIDEB>3
,PRO#M ,SOLV+
99 ..,MIX$ ,REVIEW ( ,PRO#M .,SOLV+ @1
#CFI @1 #DJJ
99 .,MULTIPLE .,REPRES5T,NS @1 #CDC @1
#CFG @1 #CIB
99 .,MULTI-.,/EP .,PRO#MS @1 #CCE @1
#CDD @1 #CEA @1 #CEH @1 #CFI @1 #CGF @1
#CIH @1 #DJJ
99 .,US+ .,ALT]NATIVE .,ME?ODS @1 #CFJ
99 ..,R1L-,_W ,PRO#M ,SOLV+ .,EXAMPLES
@1 #CCA @1 #CCC @1 #CDJ @1 #CDH @1 #CEF
@1 #CFE @1 #CGC @1 #CHC @1 #CHI @1 #CIF
,SIDEB>3
,ASSESS;T
99 ..,/&>DIZ$ ,TE/ ,PRACTICE
.,EXAMPLES @1 #CCB @1 #CCI @1 #CEE @1
#CFE
99 .,MULTIPLE .,*OICE @1 #CCC @1 #CDB
@1 #CDI @1 #CEJ @1 #CEF @1 #CEG @1 #CFG
@1 #CGE @1 #CHC @1 #CHD @1 #CIA @1 #CIG
99 .,%ORT .,RESPONSE_/.,EXT5D$
.,RESPONSE @1 #CCE @1 #CDD @1 #CEJ @1
#CEI @1 #CFH @1 #CFI @1 #CGE @1 #CGF @1
#CHD @1 #CHF @1 #CIA @1 #CIB @1 #CIH @1
#DJJ @1 #DJH
99 .,WRIT9G_/.,OP5-.,5D$ @1 #CCC @1
#CCD @1 #CDA @1 #CDB @1 #CDI @1 #CEF @1
#CFF @1 #CGD @1 #CHC @1 #CIJ @1 #CIG
,SIDEB>3
,TE*NOLOGY
,AT _+CLASSZONE.COM:_:
99 .,ANIMAT$ .,ALGEBRA @1 #CBI @1 #CCA
@1 #CDJ @1 #CEA @1 #CGA @1 #CHH @1 #CIF
99 @A .,HOME .,TUTOR @1 #CBH @1 #CCD
@1 #CDC @1 #CDE @1 #CEA @1 #CEH @1 #CFG
@1 #CGF @1 #CGH @1 #CHE @1 #CIA @1 #CIH
@1 #DJB
99 .,ONL9E .,QUIZ @1 #CCE @1 #CDD @1
#CEB @1 #CEI @1 #CFH @1 #CGG @1 #CHF @1
#CIB @1 #CII
99 .,ELECTRONIC .,FUNC;N .,LIBR>Y @1
#DJA
99 .,/ATE .,TE/ .,PRACTICE @1 #CFI @1
#DJJ @1 #DAA
-----------------------------------;XIII
..,,*APT] #F ,R,NAL ,EXPON5TS & ,RADICAL
.,FUNC;NS ,UNIT #B ,QUADRATIC1
,POLYNOMIAL1 & ,RADICAL ,FUNC;NS
,PICTURE3 .,SQU>E .,ROOT .,FUNC;NS1 P4
#DEA
,PREREQUISITE ,SKILLS
#DAB
#F.A ,EVALUATE N? ,ROOTS & ,USE ,R,NAL
,EXPON5TS
#DAD
#F.B ,APPLY ,PROP]TIES ( ,R,NAL
,EXPON5TS
#DBJ
#F.C ,P]=M ,FUNC;N ,OP],NS & ,-POSI;N
#DBH
..,GRAPH+ ,CALCULATOR ,ACTIV;Y ,USE
,OP],NS ) .,FUNC;NS #DCE
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+ #DCF
#F.D ,USE ,9V]SE ,FUNC;NS
#DCH
..,9VE/IGAT+ ,ALGEBRA3 ,EXPLOR+ ,9V]SE
.,FUNC;NS #DCG
#F.E ,GRAPH ,SQU>E ,ROOT & ,CUBE ,ROOT
,FUNC;NS
#DDF
#F.F ,SOLVE ,RADICAL ,EQU,NS
#DEB
,PRO#M ,SOLV+ ,"W%OP #DFJ
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+ #DFD
.,,ASSESS;T
,QUIZZES
#DBG @1 #DDE @1 #DEI
,*APT] ,SUMM>Y & ,REVIEW
#DFE
,*APT] ,TE/
#DFI
..,/&>DIZ$ ,TE/ ,PREP>,N & .,PRACTICE
#DGJ
,CUMULATIVE ,REVIEW1 ,*APT]S #A-F
#DGD
.,ANIMAT$ .,ALGEBRA _+CLASSZONE.COM_:
.,ACTIVITIES
#DAC @1 #DCA @1 #DDD @1 #DDH @1 #DEH
,*APT] #F ,HI<LI<TS
,SIDEB>3
,PRO#M ,SOLV+
99 ..,MIX$ ,REVIEW ( ,PRO#M .,SOLV+ @1
#DCF @1 #DFD
99 .,MULTIPLE .,REPRES5T,NS @1 #DCD @1
#DEA @1 #DFJ
99 .,MULTI-.,/EP .,PRO#MS @1 #DAH @1
#DCC @1 #DCF @1 #DDD @1 #DEH @1 #DFD
99 .,US+ .,ALT]NATIVE .,ME?ODS @1 #DFJ
99 ..,R1L-,_W ,PRO#M ,SOLV+ .,EXAMPLES
@1 #DAF @1 #DBA @1 #DBI @1 #DDA @1 #DDG
@1 #DEC
,SIDEB>3
,ASSESS;T
99 ..,/&>DIZ$ ,TE/ ,PRACTICE
.,EXAMPLES @1 #DCJ @1 #DEC
99 .,MULTIPLE .,*OICE @1 #DAG @1 #DBD
@1 #DBE @1 #DCB @1 #DCC @1 #DDC @1 #DDI
@1 #DEJ @1 #DEF @1 #DEG
99 .,%ORT .,RESPONSE_/.,EXT5D$
.,RESPONSE @1 #DAI @1 #DBF @1 #DBG @1
#DCC @1 #DCF @1 #DDD @1 #DDI @1 #DEJ @1
#DEG @1 #DEH @1 #DFD @1 #DGJ
99 .,WRIT9G_/.,OP5-.,5D$ @1 #DAG @1
#DBD @1 #DBE @1 #DCB @1 #DCC @1 #DCF @1
#DDB @1 #DDC @1 #DDI @1 #DEF @1 #DFD
,SIDEB>3
,TE*NOLOGY
,AT _+CLASSZONE.COM:_:
99 .,ANIMAT$ .,ALGEBRA @1 #DAC @1 #DCA
@1 #DDD @1 #DDH @1 #DEH
99 @A .,HOME .,TUTOR @1 #DAB @1 #DAH
@1 #DBF @1 #DCC @1 #DCE @1 #DDD @1 #DEJ
@1 #DEG @1 #DEH @1 #DFF
99 .,ONL9E .,QUIZ @1 #DAI @1 #DBG @1
#DCD @1 #DDE @1 #DEA @1 #DEI
99 .,ELECTRONIC .,FUNC;N .,LIBR>Y @1
#DFE
99 .,/ATE .,TE/ .,PRACTICE @1 #DCF @1
#DFD @1 #DGC
------------------------------------;XIV
..,,*APT] #G ,EXPON5TIAL & ,LOG>I?MIC
.,FUNC;NS ,UNIT #C ,O!R ,NONL9E>
,FUNC;NS & ,REL,NS
,PICTURE3 .,P[] .,FUNC;NS1 P4 #ECB
,PICTURE3 .;Y .K #J.JGHD .;X #B.E
,PREREQUISITE ,SKILLS
#DGF
#G.A ,GRAPH ,EXPON5TIAL ,GR[? ,FUNC;NS
#DGH
#G.B ,GRAPH ,EXPON5TIAL ,DECAY ,FUNC;NS
#DHF
#G.C ,USE ,FUNC;NS ,9VOLV+ .;E
#DIB
#G.D ,EVALUATE ,LOG>I?MS & ,GRAPH
,LOG>I?MIC ,FUNC;NS
#DII
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+ #EJF
#G.E ,APPLY ,PROP]TIES ( ,LOG>I?MS
#EJG
..,GRAPH+ ,CALCULATOR ,ACTIV;Y ,GRAPH
,LOG>I?MIC .,FUNC;NS #EAD
#G.F ,SOLVE ,EXPON5TIAL & ,LOG>I?MIC
,EQU,NS
#EAE
,PRO#M ,SOLV+ ,"W%OP #EBC
..,9VE/IGAT+ ,ALGEBRA3 ,MODEL ,DATA ) AN
,EXPON5TIAL .,FUNC;N #EBH
#G.G ,WRITE & ,APPLY ,EXPON5TIAL & ,P[]
,FUNC;NS
#EBI
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+ #ECG
.,,ASSESS;T
,QUIZZES
#DIH @1 #EAC @1 #ECF
,*APT] ,SUMM>Y & ,REVIEW
#ECH
,*APT] ,TE/
#EDC
..,/&>DIZ$ ,TE/ ,PREP>,N & .,PRACTICE
#EDD
.,ANIMAT$ .,ALGEBRA _+CLASSZONE.COM_:
.,ACTIVITIES
#DGG @1 #DHJ @1 #DHG @1 #EJB @1 #EAI
,*APT] #G ,HI<LI<TS
,SIDEB>3
,PRO#M ,SOLV+
99 ..,MIX$ ,REVIEW ( ,PRO#M .,SOLV+ @1
#EJF @1 #ECG
99 .,MULTIPLE .,REPRES5T,NS @1 #DHE @1
#EBA @1 #EBC
99 .,MULTI-.,/EP .,PRO#MS @1 #DHD @1
#DIA @1 #DIG @1 #EJE @1 #EJF @1 #ECE @1
#ECG @1
99 .,US+ .,ALT]NATIVE .,ME?ODS @1 #EBC
99 ..,R1L-,_W ,PRO#M ,SOLV+ .,EXAMPLES
@1 #DHJ @1 #DHH @1 #DID @1 #EJJ @1 #EJI
@1 #EAF @1 #ECJ
,SIDEB>3
,ASSESS;T
99 ..,/&>DIZ$ ,TE/ ,PRACTICE
.,EXAMPLES @1 #EJH @1 #EAH
99 .,MULTIPLE .,*OICE @1 #DHB @1 #DHI
@1 #DIJ @1 #DIE @1 #EJD @1 #EAJ @1 #EAA
@1 #EBJ @1 #EBA @1 #ECD @1 #EDD
99 .,%ORT .,RESPONSE_/.,EXT5D$
.,RESPONSE @1 #DHD @1 #DHE @1 #DIA @1
#DIF @1 #DIG @1 #EJE @1 #EJF @1 #EAB @1
#EBB @1 #ECE @1 #ECG
99 .,WRIT9G_/.,OP5-.,5D$ @1 #DHB @1
#DHC @1 #DHI @1 #DIJ @1 #DIE @1 #DIF @1
#EJC @1 #EJF @1 #EAJ @1 #EAA @1 #EAI @1
#EBJ @1 #ECC @1 #ECG
,SIDEB>3
,TE*NOLOGY
,AT _+CLASSZONE.COM:_:
99 .,ANIMAT$ .,ALGEBRA @1 #DGG @1 #DHJ
@1 #DHG @1 #EJB @1 #EAI
99 @A .,HOME .,TUTOR @1 #DGF @1 #DHD
@1 #DIJ @1 #DIG @1 #EJD @1 #EAB @1 #EAD
@1 #EBA @1 #EBH @1 #ECD @1 #ECE @1 #ECI
99 .,ONL9E .,QUIZ @1 #DHE @1 #DIA @1
#DIH @1 #EJE @1 #EAC @1 #EBB @1 #ECF
99 .,ELECTRONIC .,FUNC;N .,LIBR>Y @1
#ECH
99 .,/ATE .,TE/ .,PRACTICE @1 #EJF @1
#ECG @1 #EDG
-------------------------------------;XV
..,,*APT] #H ,R,NAL .,FUNC;NS ,UNIT #C
,O!R ,NONL9E> ,FUNC;NS & ,REL,NS
,PICTURE3 .,R,NAL .,EQU,NS1 P4 #EFB
,PREREQUISITE ,SKILLS
#EDH
#H.A ,MODEL ,9V]SE & ,JO9T ,V>I,N
#EEA
..,9VE/IGAT+ ,ALGEBRA3 ,9VE/IGAT+ ,9V]SE
.,V>I,N #EEJ
#H.B ,GRAPH ,SIMPLE ,R,NAL ,FUNC;NS
#EEH
..,GRAPH+ ,CALCULATOR ,ACTIV;Y ,GRAPH
,R,NAL .,FUNC;NS #EFD
#H.C ,GRAPH ,G5]AL ,R,NAL ,FUNC;NS
#EFE
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+ #EGB
#H.D ,MULTIPLY & ,DIVIDE ,R,NAL
,EXPRES.NS
#EGC
..,GRAPH+ ,CALCULATOR ,ACTIV;Y ,V]IFY
.,OP],NS #EHA
#H.E ,ADD & ,SUBTRACT ,R,NAL ,EXPRES.NS
#EHB
#H.F ,SOLVE ,R,NAL ,EQU,NS
#EHI
,PRO#M ,SOLV+ ,"W%OP #EIF
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+ #FJA
.,,ASSESS;T
,QUIZZES
#EGA @1 #EIE
,*APT] ,SUMM>Y & ,REVIEW
#FJB
,*APT] ,TE/
#FJG
..,/&>DIZ$ ,TE/ ,PREP>,N & .,PRACTICE
#FJH
.,ANIMAT$ .,ALGEBRA _+CLASSZONE.COM_:
.,ACTIVITIES
#EDI @1 #EED @1 #EEI @1 #EFH @1 #EHG
,*APT] #H ,HI<LI<TS
,SIDEB>3
,PRO#M ,SOLV+
99 ..,MIX$ ,REVIEW ( ,PRO#M .,SOLV+ @1
#EGB @1 #FJA
99 .,MULTIPLE .,REPRES5T,NS @1 #EFB @1
#EGJ
99 .,MULTI-.,/EP .,PRO#MS @1 #EEF @1
#EGJ @1 #EGB @1 #EHJ @1 #FJA
99 .,US+ .,ALT]NATIVE .,ME?ODS @1 #EIF
99 ..,R1L-,_W ,PRO#M ,SOLV+ .,EXAMPLES
@1 #EEB @1 #EFJ @1 #EFG @1 #EGD @1 #EHE
@1 #EIB
,SIDEB>3
,ASSESS;T
99 ..,/&>DIZ$ ,TE/ ,PRACTICE
.,EXAMPLES @1 #EGE @1 #EIJ
99 .,MULTIPLE .,*OICE @1 #EEE @1 #EFA
@1 #EFH @1 #EFI @1 #EGH @1 #EHF @1 #EIC
@1 #FJH
99 .,%ORT .,RESPONSE_/.,EXT5D$
.,RESPONSE @1 #EEG @1 #EFC @1 #EGJ @1
#EGB @1 #EGH @1 #EGI @1 #EHJ @1 #EHH @1
#EID @1 #FJA
99 .,WRIT9G_/.,OP5-.,5D$ @1 #EEE @1
#EEF @1 #EFA @1 #EFB @1 #EFH @1 #EFI @1
#EGB @1 #EGG @1 #EHF @1 #EHG @1 #EIB @1
#EIC @1 #FJA
,SIDEB>3
,TE*NOLOGY
,AT _+CLASSZONE.COM:_:
99 .,ANIMAT$ .,ALGEBRA @1 #EDI @1 #EED
@1 #EEI @1 #EFH @1 #EHG
99 @A .,HOME .,TUTOR @1 #EDH @1 #EEF
@1 #EFB @1 #EFD @1 #EFI @1 #EGJ @1 #EGI
@1 #EHA @1 #EHG @1 #EID @1 #FJC
99 .,ONL9E .,QUIZ @1 #EEG @1 #EFC @1
#EGA @1 #EHJ @1 #EHH @1 #EIE
99 .,ELECTRONIC .,FUNC;N .,LIBR>Y @1
#FJB
99 .,/ATE .,TE/ .,PRACTICE @1 #EGB @1
#FJA @1 #FAA
------------------------------------;XVI
..,,*APT] #I ,QUADRATIC ,REL,NS & ,3IC
.,SEC;NS ,UNIT #C ,O!R ,NONL9E>
,FUNC;NS & ,REL,NS
,PICTURE3 .,CLASSIFY .,3IC .,SEC;NS1
P4 #FEF
,PICTURE3 #BA .;Y #B -- #BAJ .;Y -- #D
.;X #B .K --#DDA
,PREREQUISITE ,SKILLS
#FAB
#I.A ,APPLY ! ,4T.E & ,MIDPO9T ,=MULAS
#FAD
#I.B ,GRAPH & ,WRITE ,EQU,NS ( ,P>ABOLAS
#FBJ
#I.C ,GRAPH & ,WRITE ,EQU,NS ( ,CIRCLES
#FBF
..,GRAPH+ ,CALCULATOR ,ACTIV;Y ,GRAPH
,EQU,NS ( .,CIRCLES #FCC
#I.D ,GRAPH & ,WRITE ,EQU,NS ( ,ELLIPSES
#FCD
,PRO#M ,SOLV+ ,"W%OP #FDJ
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+ #FDA
#I.E ,GRAPH & ,WRITE ,EQU,NS (
,HYP]BOLAS
#FDB
#I.F ,TRANSLATE & ,CLASSIFY ,3IC ,SEC;NS
#FEJ
..,9VE/IGAT+ ,ALGEBRA3 ,EXPLOR+
,9T]SEC;NS ( ,PLANES & .,C"OS #FDI
#I.G ,SOLVE ,QUADRATIC ,SY/EMS
#FEH
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+ #FFG
.,,ASSESS;T
,QUIZZES
#FCB @1 #FDH @1 #FFD
,*APT] ,SUMM>Y & ,REVIEW
#FFH
,*APT] ,TE/
#FGC
..,/&>DIZ$ ,TE/ ,PREP>,N & .,PRACTICE
#FGD
,CUMULATIVE ,REVIEW1 ,*APT]S #A-I
#FGH
.,ANIMAT$ .,ALGEBRA _+CLASSZONE.COM_:
.,ACTIVITIES
#FAC @1 #FAE @1 #FBA @1 #FBE @1 #FBF @1
#FCE @1 #FDC @1 #FDI @1 #FEA
,*APT] #I ,HI<LI<TS
,SIDEB>3
,PRO#M ,SOLV+
99 ..,MIX$ ,REVIEW ( ,PRO#M .,SOLV+ @1
#FDA @1 #FFG
99 .,MULTIPLE .,REPRES5T,NS @1 #FCA @1
#FDJ @1 #FDG
99 .,MULTI-.,/EP .,PRO#MS @1 #FAI @1
#FBE @1 #FCA @1 #FDA @1 #FDG @1 #FFC @1
#FFG
99 .,US+ .,ALT]NATIVE .,ME?ODS @1 #FDJ
99 ..,R1L-,_W ,PRO#M ,SOLV+ .,EXAMPLES
@1 #FAF @1 #FBB @1 #FBH @1 #FCF @1 #FDD
@1 #FED @1 #FFJ
,SIDEB>3
,ASSESS;T
99 ..,/&>DIZ$ ,TE/ ,PRACTICE
.,EXAMPLES @1 #FAD @1 #FBG
99 .,MULTIPLE .,*OICE @1 #FAG @1 #FBC
@1 #FBD @1 #FBI @1 #FCJ @1 #FCA @1 #FCH
@1 #FDE @1 #FDF @1 #FEE @1 #FEF @1 #FFA
@1 #FFB
99 .,%ORT .,RESPONSE_/.,EXT5D$
.,RESPONSE @1 #FAI @1 #FBD @1 #FBE @1
#FCA @1 #FCH @1 #FCI @1 #FDA @1 #FDF @1
#FDG @1 #FEF @1 #FEG @1 #FFC @1 #FFG @1
#FGD
99 .,WRIT9G_/.,OP5-.,5D$ @1 #FAG @1
#FBC @1 #FBD @1 #FBI @1 #FCJ @1 #FCG @1
#FCH @1 #FDA @1 #FDE @1 #FDF @1 #FEE @1
#FFA @1 #FFG
,SIDEB>3
,TE*NOLOGY
,AT _+CLASSZONE.COM:_:
99 .,ANIMAT$ .,ALGEBRA @1 #FAC @1 #FAE
@1 #FBA @1 #FBE @1 #FBF @1 #FCE @1 #FDC
@1 #FDI @1 #FEA
99 @A .,HOME .,TUTOR @1 #FAB @1 #FAH
@1 #FBD @1 #FCJ @1 #FCC @1 #FCH @1 #FDF
@1 #FEF @1 #FFB @1 #FFC @1 #FFI
99 .,ONL9E .,QUIZ @1 #FAI @1 #FBE @1
#FCB @1 #FCI @1 #FDH @1 #FEG @1 #FFD
99 .,/ATE .,TE/ .,PRACTICE @1 #FDA @1
#FFG @1 #FGG
-----------------------------------;XVII
..,,*APT] #AJ ,C.T+ ,ME?ODS &
.,PROBABIL;Y ,UNIT #D ,PROBABIL;Y1
,DATA ,ANALYSIS1 & ,4CRETE ,MA?
,PICTURE3 .,9DEP5D5T .,EV5TS1 P4 #GAH
,PREREQUISITE ,SKILLS
#FHJ
#AJ.A ,APPLY ! ,C.T+ ,PR9CIPLE &
,P]MUT,NS
#FHB
#AJ.B ,USE ,-B9,NS &! ,BINOMIAL ,!OREM
#FIJ
#AJ.C ,DEF9E & ,USE ,PROBABIL;Y
#FIH
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+ #GJE
#AJ.D ,F9D ,PROBABILITIES ( ,4JO9T &
,OV]LAPP+ ,EV5TS
#GJG
..,9VE/IGAT+ ,ALGEBRA3 ,F9D
,PROBABILITIES ,US+ ,V5N .,DIAGRAMS
#GJF
,PRO#M ,SOLV+ ,"W%OP #GAD
#AJ.E ,F9D ,PROBABILITIES ( ,9DEP5D5T &
,DEP5D5T ,EV5TS
#GAG
#AJ.F ,3/RUCT & ,9T]PRET ,BINOMIAL
,4TRIBU;NS
#GBD
..,GRAPH+ ,CALCULATOR ,ACTIV;Y ,CR1TE A
,BINOMIAL .,4TRIBU;N #GCA
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+ #GCB
.,,ASSESS;T
,QUIZZES
#FIG @1 #GAC @1 #GCJ
,*APT] ,SUMM>Y & ,REVIEW
#GCC
,*APT] ,TE/
#GCG
..,/&>DIZ$ ,TE/ ,PREP>,N & .,PRACTICE
#GCH
.,ANIMAT$ .,ALGEBRA _+CLASSZONE.COM_:
.,ACTIVITIES
#FHA @1 #FHI @1 #GJA @1 #GAA @1 #GAF @1
#GBB @1 #GBF
,*APT] #AJ ,HI<LI<TS
,SIDEB>3
,PRO#M ,SOLV+
99 ..,MIX$ ,REVIEW ( ,PRO#M .,SOLV+ @1
#GJE @1 #GCB
99 .,MULTIPLE .,REPRES5T,NS @1 #GJC @1
#GAD @1 #GBI
99 .,MULTI-.,/EP .,PRO#MS @1 #FHH @1
#FIF @1 #GJE @1 #GAB @1 #GCB
99 .,US+ .,ALT]NATIVE .,ME?ODS @1 #GAD
99 ..,R1L-,_W ,PRO#M ,SOLV+ .,EXAMPLES
@1 #FHC @1 #FHE @1 #FIA @1 #FII @1 #GJJ
@1 #GJH @1 #GJI @1 #GAI @1 #GBJ @1 #GBF
,SIDEB>3
,ASSESS;T
99 ..,/&>DIZ$ ,TE/ ,PRACTICE
.,EXAMPLES @1 #GJH @1 #GAG
99 .,MULTIPLE .,*OICE @1 #FHG @1 #FIE
@1 #GJB @1 #GAJ @1 #GAA @1 #GAB @1 #GBA
@1 #GBB @1 #GBH
99 .,%ORT .,RESPONSE_/.,EXT5D$
.,RESPONSE @1 #FHG @1 #FHH @1 #FIE @1
#FIF @1 #GJB @1 #GJD @1 #GJE @1 #GAA @1
#GAB @1 #GBC @1 #GCJ @1 #GCB @1 #GCH
99 .,WRIT9G_/.,OP5-.,5D$ @1 #FHF @1
#FID @1 #GJA @1 #GJB @1 #GJE @1 #GAJ @1
#GAA @1 #GBA @1 #GBB @1 #GBG @1 #GBH @1
#GCB
,SIDEB>3
,TE*NOLOGY
,AT _+CLASSZONE.COM:_:
99 .,ANIMAT$ .,ALGEBRA @1 #FHA @1 #FHI
@1 #GJA @1 #GAA @1 #GAF @1 #GBB @1 #GBF
99 @A .,HOME .,TUTOR @1 #FHJ @1 #FHH
@1 #FIF @1 #GJC @1 #GAA @1 #GBB @1 #GBI
@1 #GCA @1 #GCD
99 .,ONL9E .,QUIZ @1 #FHI @1 #FIG @1
#GJD @1 #GAC @1 #GBC @1 #GCJ
99 .,/ATE .,TE/ .,PRACTICE @1 #GJE @1
#GCB @1 #GDA
----------------------------------;XVIII
..,,*APT] #AA ,DATA ,ANALYSIS &
.,/ATI/ICS ,UNIT #D ,PROBABIL;Y1 ,DATA
,ANALYSIS1 & ,4CRETE ,MA?
,PICTURE3 .,/&>D .,DEVI,N4 P4 #GEB
,PREREQUISITE ,SKILLS
#GDB
#AA.A ,F9D ,M1SURES ( ,C5TRAL ,T5D5CY &
,4P].N
#GDD
..,GRAPH+ ,CALCULATOR ,ACTIV;Y
,CALCULATE ,"O-,V>IA# .,/ATI/ICS #GEJ
#AA.B ,APPLY ,TRANS=M,NS 6,DATA
#GEA
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+ #GEF
#AA.C ,USE ,NORMAL ,4TRIBU;NS
#GEG
#AA.D ,SELECT & ,DRAW ,3CLU.NS F
,SAMPLES
#GFF
#AA.E ,*OOSE ! ,BE/ ,MODEL = ,TWO-,V>IA#
,DATA
#GGE
..,9VE/IGAT+ ,ALGEBRA3 ,FITT+ A ,MODEL
6.,DATA #GGD
,PRO#M ,SOLV+ ,"W%OP #GHA
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+ #GHB
.,,ASSESS;T
,QUIZZES
#GEE @1 #GHJ
,*APT] ,SUMM>Y & ,REVIEW
#GHC
,*APT] ,TE/
#GHG
..,/&>DIZ$ ,TE/ ,PREP>,N & .,PRACTICE
#GHH
.,ANIMAT$ .,ALGEBRA _+CLASSZONE.COM_:
.,ACTIVITIES
#GDC @1 #GDD @1 #GDH @1 #GED @1 #GEG @1
#GGF
,*APT] #AA ,HI<LI<TS
,SIDEB>3
,PRO#M ,SOLV+
99 ..,MIX$ ,REVIEW ( ,PRO#M .,SOLV+ @1
#GEF @1 #GHB
99 .,MULTIPLE .,REPRES5T,NS @1 #GED @1
#GGI @1 #GHA
99 .,MULTI-.,/EP .,PRO#MS @1 #GDH @1
#GEF @1 #GFA @1 #GGA @1 #GHB
99 .,US+ .,ALT]NATIVE .,ME?ODS @1 #GHA
99 ..,R1L-,_W ,PRO#M ,SOLV+ .,EXAMPLES
@1 #GDF @1 #GEB @1 #GEI @1 #GFG @1 #GGF
,SIDEB>3
,ASSESS;T
99 ..,/&>DIZ$ ,TE/ ,PRACTICE .,EXAMPLES
@1 #GDE @1 #GFI
99 .,MULTIPLE .,*OICE @1 #GDG @1 #GEC
@1 #GED @1 #GFJ @1 #GGJ @1 #GGH @1 #GHH
99 .,%ORT .,RESPONSE_/.,EXT5D$
.,RESPONSE @1 #GDH @1 #GDI @1 #GED @1
#GEF @1 #GFA @1 #GFB @1 #GGA @1 #GGI @1
#GHB
99 .,WRIT9G_/.,OP5-.,5D$ @1 #GDG @1
#GDH @1 #GEC @1 #GEF @1 #GFJ @1 #GFI @1
#GGH @1 #GHB @1 #GHD
,SIDEB>3
,TE*NOLOGY
,AT _+CLASSZONE.COM:_:
99 .,ANIMAT$ .,ALGEBRA @1 #GDC @1 #GDD
@1 #GDH @1 #GED @1 #GEG @1 #GGF
99 @A .,HOME .,TUTOR @1 #GDB @1 #GDH
@1 #GEJ @1 #GEC @1 #GFA @1 #GGJ @1 #GGD
@1 #GGI @1 #GHD
99 .,ONL9E .,QUIZ @1 #GDI @1 #GEE @1
#GFB @1 #GGA @1 #GHJ
99 .,/ATE .,TE/ .,PRACTICE @1 #GEF @1
#GHB @1 #GIA
------------------------------------;XIX
..,,*APT] #AB ,SEQU;ES & .,S]IES ,UNIT
#D ,PROBABIL;Y1 ,DATA ,ANALYSIS1 &
,4CRETE ,MA?
,PICTURE3 .,9F9ITE .,S]IES1 P4 #HBE
,PREREQUISITE ,SKILLS
#GIB
#AB.A ,DEF9E & ,USE ,SEQU;ES & ,S]IES
#GID
..,GRAPH+ ,CALCULATOR ,ACTIV;Y ,"W )
.,SEQU;ES #HJA
#AB.B ,ANALYZE ,>I?METIC ,SEQU;ES &
,S]IES
#HJB
#AB.C ,ANALYZE ,GEOMETRIC ,SEQU;ES &
,S]IES
#HAJ
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+ #HAH
#AB.D ,F9D ,SUMS ( ,9F9ITE ,GEOMETRIC
,S]IES
#HBJ
..,9VE/IGAT+ ,ALGEBRA3 ,9VE/IGAT+ AN
,9F9ITE ,GEOMETRIC .,S]IES #HAI
#AB.E ,USE ,RECURSIVE ,RULES ) ,SEQU;ES
& ,FUNC;NS
#HBG
..,9VE/IGAT+ ,ALGEBRA3 ,EXPLOR+
,RECURSIVE .,RULES #HBF
,PRO#M ,SOLV+ ,"W%OP #HCD
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+ #HCH
.,,ASSESS;T
,QUIZZES
#HAG @1 #HCC
,*APT] ,SUMM>Y & ,REVIEW
#HCI
,*APT] ,TE/
#HDC
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,AT _+CLASSZONE.COM:_:
99 .,ANIMAT$ .,ALGEBRA @1 #GIC @1 #HJE
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-----------------------------------;XXII
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;,D @1 #A.E1 --#J.E1 --#J.GE1 --#B
..,,PROP]TIES ,,( ,,R1L .,,NUMB]S ,Y
LE>N$ 9 PREVI\S C\RSES T :5 Y ADD OR
MULTIPLY R1L NUMB]S1 "! >E S"EAL
PROP]TIES Y C USE4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,PROP]TIES ( ,A4I;N & ,MULTIPLIC,N
,LET .A1 .;B @1 & .;C 2 R1L NUMB]S4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,PROP]TY3 ,A4I;N3 ,MULTIPLIC,N
.,CLOSURE @3 .A @+ .;B IS A R1L NUMB]4
@3 .;AB IS A R1L NUMB]4
.,-MUTATIVE @3 .A @+ .;B .K .;B @+ .A
@3 .;AB .K .BA
.,ASSOCIATIVE @3 @7 .A @+ .;B @7 @+
.;C .K .A @+ @7 .;B @+ .;C @7 @3 @7 .;AB
@7 .;C .K .A @7 .BC @7
.,ID5T;Y @3 .A @+ #J .K .A @1 #J @+ .A
.K .A @3 .A @* #A .K .A @1 #A 99 .A .K
.A
.,9V]SE @3 .A @+ @7-- .A @7 .K #J @3
,! FOLL[+ PROP]TY 9VOLVES BO? A4I;N &
MULTIPLIC,N4
,4TRIBUTIVE ..A7;B @+ ;C7 .K ;AB @+
.;AC
--------------------------------------#D
,EXAMPLE #C ,ID5TIFY PROP]TIES ( R1L
NUMB]S
,ID5TIFY ! PROP]TY T ! /ATE;T
ILLU/RATES4
.A4 #G @+ #D .K #D @+ #G
.B4
,SOLU;N
.A4 ,-MUTATIVE PROP]TY ( A4I;N
.B4 ,9V]SE PROP]TY ( MULTIPLIC,N
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,DEF9+ ,SUBTRAC;N & ,DIVI.N
,SUBTRAC;N IS DEF9$ Z .A4+ .!
.OPPOSITE4 ,! .OPPOSITE @1 OR .A4ITIVE
.9V]SE @1 ( ANY NUMB] .;B IS --.B4 ,IF
.;B IS POSITIVE1 !N -.;B IS NEGATIVE4
,IF .;B IS NEGATIVE1 !N --.;B IS
POSITIVE4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.A -- .;B .K .A @+ @7-- .;B @7 @3
.,DEF9I;N .( .SUBTRAC;N
,DIVI.N IS DEF9$ Z ..MULTIPLY+ 0!
.RECIPROCAL4 ,! .RECIPROCAL @1 OR
.MULTIPLICATIVE .9V]SE @1 ( ANY NONZ]O
NUMB] .;B IS @4
,EXAMPLE #D ,USE PROP]TIES & DEF9I;NS
( OP],NS
,USE PROP]TIES & DEF9I;NS ( OP],NS 6%[
T .A @+ 7#B -- .A7 .K #B4 ,JU/IFY EA*
/EP4
,SOLU;N
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
..A @+ 7#B--A7 .K A @+ ,7#B @+ 7-.A77'
@3 .,DEF9I;N .( .SUBTRAC;N
.K ..A @+ ,77-A7 @+ .#B7' @3
..,-MUTATIVE PROP]TY ( .A4I;N
.K @,7 .A @+ 7-.A7 @7' @+ #B @3
..,ASSOCIATIVE PROP]TY ( .A4I;N
.K #J @+ #B3 ..,9V]SE PROP]TY ( .A4I;N
.K #B3 ..,ID5T;Y PROP]TY ( .A4I;N
..,,GUID$ ,,PRACTICE = ,EXAMPLES #C &
.#D
,ID5TIFY ! PROP]TY T ! /ATE;T
ILLU/RATES4
.#C4 7#B 99 #C7 99 #I .K #B 99 7#C 99
#I7
.#D4 #AE @+ #J .K #AE
.#E4 #D7#E @+ #BE7 .K #D7#E7 @+
#D7#BE7
.#F4 #A 99 #EJJ .K #EJJ
,USE PROP]TIES & DEF9I;NS ( OP],NS 6%[
T ! /ATE;T IS TRUE4 .,JU/IFY EA* /EP4
.#G4 .;B 99 7#D @/ .;B7 .K #D :5 .;B
@6.K #J
.#H4 #C .;X @+ 7#F @+ #D ..;X7 .K
.#G;X @+ #F
--------------------------------------#E
.,,UNIT .,,ANALYSIS ,:5 Y USE OP],NS 9
R1L-LIFE PRO#MS1 Y %D USE .UNIT
.ANALYSIS 6*ECK T ! UNITS 9 YR CALCUL,NS
MAKE S5SE4
,,EXAMPLE #E ,USE UNIT ANALYSIS )
OP],NS
A4 ,Y "W #D H\RS & E>N 4#CF4 ,:AT IS
YR E>N+ RATE8
B4 ,Y TRAVEL = #B.E H\RS AT #EJ MILES
P] H\R4 ,H[ F> D Y G8
C4 ,Y DRIVE #DE MILES P] H\R4 ,:AT IS
YR SPE$ 9 FEET P] SECOND8
,SOLU;N
A4
B4
C4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
,,EXAMPLE #F ,USE UNIT ANALYSIS )
3V].NS
.,,DRIV+ .,,4T.E ,! 4T.E F ,MONTPELI]1
,V]MONT1 6,MONTR1L1 ,CANADA1 IS AB #ACB
MILES4 ,! 4T.E F ,MONTR1L 6,QUEBEC ,C;Y
IS AB #BEC KILOMET]S4
A4 ,3V]T ! 4T.E F ,MONTPELI] 6,MONTR1L
6KILOMET]S4
B4 ,3V]T ! 4T.E F ,MONTR1L 6,QUEBEC
,C;Y 6MILES4
,SOLU;N
A4
B4
,,REVIEW ,,M1SURES
,= HELP ) 3V]T+ UNITS1 SEE ! ,TA# (
,M1SURES ON P4 #AJBE @4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #E &
.#F
,SOLVE ! PRO#M4 ,USE UNIT ANALYSIS
6*ECK YR "W4
.#I4 ,Y "W #F H\RS & E>N 4#FI4 ,:AT IS
YR E>N+ RATE8
.#AJ4 ,H[ L;G DOES X TAKE 6TRAVEL #AHJ
MILES AT #DJ MILES P] H\R8
.#AA4 ,Y DRIVE #FJ KILOMET]S P] H\R4
,:AT IS YR SPE$ 9 MILES P] H\R8
,P]=M ! 9DICAT$ 3V].N4
.#AB4 #AEJ Y>DS 6FEET
.#AC4 #D GALLONS 6P9TS
.#AD4 #AF YE>S 6SECONDS
--------------------------------------#F
#A.A ,EX]CISES
,HOME"W ,KEY
.K .,,"W-.,,\ .,,SOLU;NS
ON P4 ,,WS#A = ,EXS4 #BA1 #CA1 & #EI
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 #B1I1AJ1 #BC1 #BD1 #FJ1 & #FA
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,!
@8 ( ANY NONZ]O NUMB] .;B IS @4
.#B4 .,,WRIT+ ,EXPRESS ! ASSOCIATIVE
PROP]TY ( A4I;N 9 ^WS4
,,EXAMPLE #A
ON P4 #B = ,EXS4 #C--#H
,,GRAPH+ ,,NUMB]S ,GRAPH ! NUMB]S ON A
NUMB] L9E4
.#C4
.#D4
.#E4
.#F4
.#G4
.#H4
,,EXAMPLE #B
ON P4 #C = ,EXS4 #I-AJ
,,ORD]+ ,,NUMB]S ,9 ,EX]CISES #I &
#AJ1 USE ! TA# ( ELEV,NS 2L4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,/ATE @3 ,ALABAMA3 ,CALI=NIA3
,K5TUCKY3 --@3 ,L\ISIANA3 ,T5;SEE
.,HI<E/ .ELEV,N @3 #BDJG FT3 #AD1DID
FT3 #DADE FT3 --@3 #ECE FT3 #FFDC FT
.,L[E/ .ELEV,N @3 #J FT3 --#BHB FT3
#BEG FT3 --@3 --#H FT3 #AGH FT
,PICTURE3 .,L\ISIANA .BAY\
#I4 .,,MULTIPLE .,,*OICE ,: LI/ %[S !
HI<E/ ELEV,NS 9 ORD] F L1/ 6GRTE/8
,A #BDJG2 #AD1DID2 #DADE2 #ECE2 #FFDC
;,B #ECE2 #BDJG2 #DADE2 #FFDC2 #AD1DID
;,C #AD1DID2 #BDJG2 #DADE2 #ECE2 #FFDC
;,D #AD1DID2 #FFDC2 #DADE2 #BDJG2 #ECE
#AJ4 .,,MULTIPLE .,,*OICE ,: LI/ %[S !
L[E/ ELEV,NS 9 ORD] F GRTE/ 6L1/8
,A #J1 --#H1 #AGH1 #BEG1 --#BHB
;,B --#BHB1 --#H1 #J1 #AGH1 #BEG
;,C --#BHB1 #BEG1 #AGH1 --#H1 #J
;,D #BEG1 #AGH1 #J1 --#H1 --#BHB
,,EXAMPLE #C
ON P4 #D = ,EXS4 #AA-AF
,,ID5TIFY+ ,,PROP]TIES ,ID5TIFY !
PROP]TY T ! /ATE;T ILLU/RATES4
.#AA4 7#D @+ #I7 @+ #C .K #D @+ 7#I @+
#C7
.#AB4 #AE 99 #A .K #AE
.#AC4 #F 99 #D .K #D 99 #F
.#AD4 #E @+ 7--#E7 .K #J
.#AE4 #G7#B @+ #H7 .K #G7#B7 @+ #G7#H7
.#AF4 7#F 99 #E7 99 #G .K #F 99 7#E 99
#G7
,,EXAMPLE #D
ON P4 #D = ,EXS4 #AG-BB
,,US+ ,,PROP]TIES ,USE PROP]TIES &
DEF9I;NS ( OP],NS 6%[ T ! /ATE;T IS
TRUE4 .,JU/IFY EA* /EP4
.#AG4 #F 99 @7 .A @+ #C7 .K .#B;A
.#AH4 #AE 99 7#C @/ .;B @7 .K #DE @/
.;B
.#AI4 @7 .;C -- #C7 @+ #C .K .;C
.#BJ4 @7 ..A @+ ;B7--.;C .K ..A @+
7;B--.;C @7
.#BA4 #G .A @+ 7#D @+ #E .A @7 .K #AB
.A @+ #D
.#BB4 7#AB .;B @+ #AE7--#C ..;B .K #AE
@+ .#I;B
.#BC4 .,,OP5-.,,5D$ .,,MA? ,F9D VALUES
( .A & .;B S* T .A IS A :OLE NUMB]1 .;B
IS A R,NAL NUMB] B N AN 9TEG]1 & .A @/
.;B .K --#H4
.#BD4 .,,OP5-.,,5D$ .,,MA? ,WRITE ?REE
EQU,NS US+ 9TEG]S 6ILLU/RATE !
4TRIBUTIVE PROP]TY4
--------------------------------------#G
,,EXAMPLE #E
ON P4 #E = ,EXS4 #BE-CJ
,,OP],NS ,,& ,,UNIT ,,ANALYSIS ,SOLVE
! PRO#M4 ,USE UNIT ANALYSIS 6*ECK YR "W4
#BE4 ,Y "W #AJ H\RS & E>N 4#HE4 ,:AT
IS YR E>N+ RATE8
#BF4 ,Y TRAVEL #FJ KILOMET]S 9 #A.E
H\RS4 ,:AT IS YR AV]AGE SPE$8
#BG4 ,Y "W = #E H\RS AT 4#G.BE P] H\R4
,H[ M* D Y E>N8
#BH4 ,Y BUY #F GALLONS ( JUICE AT
4#A.BE P] GALLON4 ,:AT IS YR TOTAL CO/8
#BI4 ,Y DRIVE = #C H\RS AT #FE MILES
P] H\R4 ,H[ F> D Y G8
#CJ4 ,Y RIDE 9 A TRA9 = #AGE MILES AT
AN AV]AGE SPE$ ( #EJ MILES P] H\R4 ,H[
_M H\RS DOES ! TRIP TAKE8
,,EXAMPLE #F
ON P4 #E = ,EXS4 #CA-DJ
,,3V].N ,,( ,,M1SURE;TS ,P]=M !
9DICAT$ 3V].N4
#CA4 #CEJ FEET 6Y>DS
#CB4 #AE MET]S 6MILLIMET]S
#CC4 #B.B KILOGRAMS 6GRAMS
#CD4 #E H\RS 6M9UTES
#CE4 #G QU>TS 6GALLONS
#CF4 #C.E TONS 6P.DS
#CG4 #EF \NCES 6TONS
#CH4 #FHJJ SECONDS 6H\RS
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 ! 3V].N4
.#CI4
.#DJ4
,,3V].N ,,( ,,RATES ,3V]T ! RATE 96!
GIV5 UNITS4
#DA4 #BJ MI_/;H 6FEET P] SECOND
#DB4 #F FT_/SEC 6MILES P] H\R
#DC4 #EJ KM_/;H 6MILES P] H\R
#DD4 #DJ MI_/;H 6KILOMET]S P] H\R
#DE4 #A GAL_/;H 6\NCES P] SECOND
#DF4 #F OZ_/SEC 6GALLONS P] H\R
#DG4 .,,ROCKET .,,SL$ ,ON A TRACK AT
AN ,AIR ,=CE BASE 9 ,NEW ,MEXICO1 A
ROCKET SL$ TRAVELS #C MILES 9 #F
SECONDS4 ,:AT IS ! AV]AGE SPE$ 9 MILES
P] H\R8
#DH4 .,,ELEVATOR .,,SPE$ ,! ELEVATOR 9
! ,WA%+TON ,MONU;T TAKES #FJ SECONDS
6RISE #EJJ FEET4 ,:AT IS ! AV]AGE SPE$ 9
MILES P] H\R8
,,R1SON+ ,TELL :E!R ! /ATE;T IS .ALW1
."S"TS @1 OR .N"E TRUE = R1L NUMB]S .A
;Y .;B @1 & .C4 .,EXPLA9 YR ANSW]4
#DI4 @7 .A @+ .;B @7 @+ .;C .K .A @+
@7 .;B @+ .;C @7
#EJ4 @7 .A 99 .;B @7 99 .;C .K .A 99
@7 .;B 99 .;C @7
#EA4 @7 .A--.;B @7 -- .;C .K .A -- @7
.;B--.;C @7
#EB4 @7 ..A @/ .;B @7 @/ .;C .K .A @/
@7 ..;B @/ .;C @7
#EC4 ..A7;B--;C7 .K ;AB--.;AC
#ED4 ..A7;B @/ ;C7 .K ;AB @/ .;AC
#EE4 .,,R1SON+ ,%[ T = NONZ]O R1L
NUMB]S .A1 .;B1 .;C @1 & .D4 .,JU/IFY
EA* /EP 9 YR R1SON+4
#EF4 .,,*ALL5GE ,LET & 2 TWO 4T9CT
R,NAL NUMB]S4 ,F9D ! R,NAL NUMB] T LIES
EXACTLY HALFWAY 2T & ON A NUMB] L9E4
--------------------------------------#H
,,PRO#M ,,SOLV+
,,EXAMPLE #B
ON P4 #C = ,EXS4 #EG-EI
#EG4 .,,M9IATURE .,,GOLF ,! TA# %[S !
SCORES ( P PLAY+ #I HOLES ( M9IATURE
GOLF4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,L.E @3 @+#B3 @+#A3 #J3 #J3 --#A3
@+#A3 @+#C3 #J3 #J
.,D>CY @3 --#A3 @+#C3 #J3 --#A3 @+#A3
#J3 #J3 @+#A3 --#A
.,JAVI] @3 @+#A3 #J3 @+#A3 #J3 #J3
--#A3 @+#A3 #J3 @+#A
.,S&RA @3 --#A3 --#A3 #J3 #J3 @+#A3
--#A3 #J3 #J3 #J
A4 ,F9D ! SUM (! SCORES = EA* PLAY]4
B4 ,LI/ ! PLAY]S F BE/ 7L[E/7 6WOR/
7HI<E/7 TOTAL SCORE4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#EH4 .,,VOLCANOES ,! FOLL[+ LI/ %[S !
ELEV,NS 7IN FEET7 ( S"EAL VOLCANO
SUMMITS ABV OR 2L SEA LEVEL4
#FDA1 #CIGF1 #FAJ1 --#EI1 #AGAH1
#AGCC1 --#ACG
,ORD] ! ELEV,NS F L[E/ 6HI<E/4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#EI4 .,,MULTI-.,,/EP .,,PRO#M ,! *>T
%[S ! AV]AGE "D"T SURFACE TEMP]ATURES ON
! PLANETS 9 \R SOL> SY/EM4
A4 .,SORT .0.,TEMP]ATURE ,LI/ !
PLANETS 9 ORD] F L1/ 6GRTE/ "D"T SURFACE
TEMP]ATURE4
B4 .,SORT .0.,4T.E ,LI/ ! PLANETS 9
ORD] F L1/ 6GRTE/ 4T.E F ! SUN4
C4 .,F9D .,PATT]NS ,:AT PATT]N D Y
NOTICE 2T SURFACE TEMP]ATURE & 4T.E F !
SUN8
D4 .,ANALYZE ,: PLANET DOES N FOLL[ !
G5]AL PATT]N Y F.D 9 "P 7;C78
,PICTURE3 .,"D"T .,SURFACE
.,TEMP]ATURES
,,EXAMPLES
#E & #F
ON P4 #E = ,EXS4 #FJ-FA
#FJ4 .,,EXT5D$ .,,RESPONSE ,! AV]AGE
WEI<T (! BLUE :ALE 7! L>GE/ MAMMAL7 IS
#ABJ TONS1 &! AV]AGE WEI<T (! BUM#BEE
BAT 7! SMALLE/ MAMMAL7 IS #J.JG \NCE4
A4 .,3V]T ,3V]T ! WEI<T (! BLUE :ALE F
TONS 6P.DS4 ,3V]T ! WEI<T (! BUM#BEE BAT
F \NCES 6P.DS4
B4 .,-P>E ,AB H[ _M "TS Z H1VY Z ! BAT
IS ! BLUE :ALE8
C4 .,F9D .A .,ME?OD ,2SS 3V]T+ !
WEI<TS 6P.DS1 :AT IS ANO!R ME?OD = -P>+
! WEI<TS (! MAMMALS8
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
--------------------------------------#I
#FA4 .,,%ORT .,,RESPONSE ,! TA# %[S !
MAXIMUM SPE$S ( V>I\S ANIMALS 9 MILES P]
H\R OR FEET P] SECOND4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,ANIMAL3 ,SPE$ 7MI_/;H73 ,SPE$
7FT_/;S7
,*EETAH3 #GJ3 @8
,?REE-TO$ SLO?3 @8@3 #J.BB
,SQUIRREL3 #AB3 @8
,GRIZZLY BE>3 @8@3 #DD
,PICTURE3 ,?REE-TO$ SLO?
A4 ,COPY & -PLETE ! TA#4
B4 .,-P>E ! SPE$S (! FA/E/ & SL[E/
ANIMALS 9 ! TA#4
#FB4 .,,*ALL5GE ,A NEWSPAP] GIVES !
EX*ANGE RATES ( "S CURR5CIES )! ,U4,S4
DOLL>1 Z %[N 2L4 ,COPY & -PLETE !
/ATE;TS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 .#A .,,USD @3 .9 .,,USD
,AU/RALIAN DOLL>3 #A.CABCD3 #J.GFAIIH
,? R[ 9DICATES T 4#A ,U4,S4 4#A.CA
,AU/RALIAN & 4#A ,AU/RALIAN @4#.GF
,U4,S4
,CANADIAN DOLL>3 #A.AIHA3 #J.HCDFEE
,H;G ,K;G DOLL>3 #G.GGAH3 #J.ABHFG
,NEW ,Z1L& DOLL>3 #A.DCIBF3 #J.FIDHJA
,S+APORE DOLL>3 #A.FECD3 #J.FJDHAD
A4 #A ,S+APORE DOLL> @8 ,CANADIAN
DOLL>7;S7
B4 #A ,H;G ,K;G DOLL> @8 ,NEW ,Z1L&
DOLL>7;S7
,MIX$ ,REVIEW
.,,PREVIEW ,PREP>E = ,LESSON #A.B 9
,EXS4 #FC-GD4
,P]=M ! 9DICAT$ OP],N1 @7 P4 #IGE @7
.#FC4 #C--#AA
.#FD4 --#D7--#H7
.#FE4 #DE @/ 7--#I7
.#FF4 --#F @+ #AC
.#FG4 --#C7#G7
.#FH4 #E--7--#B7
,WRITE ! PHRASE Z AN ALGEBRAIC
EXPRES.N1 @7 P4 #IHD @7
.#FI4 #I M ?AN A NUMB]
.#GJ4 #E LESS ?AN A NUMB]
.#GA4 #GE@3P (A NUMB]
.#GB4 #G "TS A NUMB]
.#GC4 ,HALF (A NUMB]
.#GD4 ,! SQU>E (A NUMB]
,F9D ! P]IMET] (! FIGURE1 @7 P4 #IIA
@7
.#GE4
.#GF4
.#GG4
,F9D ! >EA (! FIGURE1 @7 P4 #IIA @7
.#GH4
.#GI4
.#HJ4
.,,EXTRA .,,PRACTICE = ,LESSON #A.A1
P4 #AJAJ
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
-------------------------------------#AJ
#A.B ,EVALUATE & ,SIMPLIFY
,ALGEBRAIC ,EXPRES.NS
.,2F ,Y /UDI$ PROP]TIES ( R1L NUMB]S4
.,N[ ,Y W EVALUATE & SIMPLIFY
EXPRES.NS 9VOLV+ R1L NUMB]S4
.,:Y8 ,S Y C E/IMATE CALORIE USE1 Z 9
,EX4 #FJ4
,KEY ,VOCABUL>Y
99 P[]
99 V>IA#
99T]M
99 COE6ICI5T
99 ID5T;Y
,SIDEB>3
,/&>DS
.,PREP>E .= .#A..J ..,/UD5TS SOLVE
EQU,NS & .9EQUALITIES 9VOLV+ ABSOLUTE
VALUE4
,A NUM]ICAL EXPRES.N 3SI/S ( NUMB]S1
OP],NS1 & GR\P+ SYMBOLS4 ,AN EXPRES.N
=M$ 0REP1T$ MULTIPLIC,N (! SAME FACTOR
IS A .P[] @4
,A P[] HAS TWO "PS3 AN .EXPON5T &A
.BASE4 ,! .EXPON5T REPRES5TS ! NUMB] (
"TS ! .BASE IS US$ Z A FACTOR4 ,9 ! P[]
%[N 2L1 ! BASE #G IS US$ Z A FACTOR #C
"TS4
,Y D N USU,Y WRITE ! EXPON5T :5 X IS
#A4 ,= 9/.E1 Y C WRITE #H #A SIMPLY Z
#H4
,,EXAMPLE #A ,EVALUATE P[]S
A4 7--#E7 #D .K 7--#E7 99 7--#E7 99
7--#E7 99 7--#E7 .K #FBE
B4 --#E #D .K --7#E 99 #E 99 #E 99 #E7
.K --#FBE
,9 ,EXAMPLE #A1 NOTICE H[ P>5!SES >E
US$ 9 "P 7A7 69DICATE T ! BASE IS --#E4
,9 "P 7;B71 ! BASE (! P[] IS #E1 N --#E4
,AN .ORD] .( .OP],NS HELPS AVOID 3FU.N
:5 EVALUAT+ EXPRES.NS4
,,KEY ,,3CEPT
,= ,YR NOTEBOOK
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,ORD] .( .,OP],NS @3 --
,/EPS3 ,EXAMPLE
.,,/EP .#A ,F/.' @1 D OP],NS T O3UR )9
GR\P+ SYMBOLS4 @3 #A @+ #G #B 99
7#E--#C7
.,,/EP .#B ,NEXT.' @1 EVALUATE P[]S4
@3 .K #A @+ #G #B 99 #B
.,,/EP .#C ,!N.' @1 D MULTIPLIC,NS &
DIVI.NS F LEFT 6"R4 @3 .K #A @+ #DI 99
#B
.,,/EP .#D ,F9,Y.' @1 D A4I;NS &
SUBTRAC;NS F LEFT 6"R4 @3 .K #A @+ #IH
--@3 .K #II
-------------------------------------#AA
.,,V>IA#S ,A .V>IA# IS A LR T IS US$
6REPRES5T "O OR M NUMB]S4 ,AN EXPRES.N
9VOLV+ V>IA#S IS CALL$ AN .ALGEBRAIC
.EXPRES.N @4 ,:5 Y SUB/ITUTE A NUMB] =
EA* V>IA# 9 AN ALGEBRAIC EXPRES.N &
SIMPLIFY1 Y >E .EVALUAT+ ! ALGEBRAIC
EXPRES.N4
,,EXAMPLE #B ,EVALUATE AN ALGEBRAIC
EXPRES.N
,EVALUATE --#D .;X #B -- #F .;X @+ #AA
:5 .;X .K --#C4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--#D;X.' #B -- #F;X.' @+ #AA @3 .K
--#D7--#C7 #B -- #F7--#C7 @+ #AA @3
,SUB/ITUTE --#C = X4
--@3 .K --#D7#I7--#F7--#C7 @+ #AA3
,EVALUATE P[]4
--@3 .K --#CF @+ #AH @+ #AA3
,MULTIPLY4
--@3 .K --#G3 ,ADD4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
,,EXAMPLE #C ,USE A V]BAL MODEL 6SOLVE
A PRO#M
.,,CRAFT .,,FAIR ,Y >E SELL+ HOMEMADE
C&LES AT A CRAFT FAIR = 4#C EA*4 ,Y SP5D
4#ABJ 6R5T ! BOO? & BUY MAT]IALS =!
C&LES4
99 ,WRITE AN EXPRES.N T %[S YR PR(IT F
SELL+ .;C C&LES4
99 ,F9D YR PR(IT IF Y SELL #GE C&LES4
,SOLU;N
.,,/EP .#A .,WRITE A V]BAL MODEL4 ,!N
WRITE AN ALGEBRAIC EXPRES.N4 ,USE ! FACT
T PR(IT IS ! DI6];E 2T 9COME & EXP5SES4
,AN EXPRES.N T %[S YR PR(IT IS #C .;C
-- #ABJ4
.,,/EP .#B .,EVALUATE ! EXPRES.N 9
,/EP #A :5 .;C .K #GE4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#C .;C -- #ABJ @3 .K #C7#GE7--#ABJ3
,SUB/ITUTE #GE = .;C @4
--@3 .K #BBE--#ABJ3 ,MULTIPLY4
--@3 .K #AJE3 ,SUBTRACT4
,YR PR(IT IS 4#AJE4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #A1B1
& .#C
,EVALUATE ! EXPRES.N4
#A4 #F #C
#B4 --#B #F
#C4 7--#B7 #F
#D4 #E .;X @7 .;X -- #B7 :5 .;X .K #F
#E4 #C .;Y #B -- #D .;Y :5 .;Y .K --#B
#F4 @7 .;Z @+ #C7 #C :5 .;Z .K #A
#G4 .,,:AT .,,IF8 ,9 ,EXAMPLE #C1 F9D
YR PR(IT IF Y SELL #ACE C&LES4
-------------------------------------#AB
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,T]MS & ,COE6ICI5TS
,9 AN EXPRES.N T C 2 WRITT5 Z A SUM1 !
"PS A4$ TGR >E CALL$ .T]MS @4
,A T]M T HAS A V>IA# "P IS CALL$ A
.V>IA# .T]M @4 ,A T]M T HAS NO V>IA# "P
IS CALL$ A .3/ANT .T]M @4
,:5 A T]M IS A PRODUCT (A NUMB] &A P[]
(A V>IA#1 ! NUMB] IS CALL$ ! .COE6ICI5T
(! P[]4
.,,SIMPLIFY+ ,AN EXPRES.N IS SIMPLIFI$
IF X 3TA9S NO GR\P+ SYMBOLS & ALL .L
.T]MS >E -B9$4 .,L .T]MS >E T]MS T H !
SAME V>IA# "PS4 7,3/ANT T]MS >E AL
3SID]$ L T]MS47 ,! 4TRIBUTIVE PROP]TY
ALL[S Y 6.-B9E .L .T]MS 0A4+ COE6ICI5TS4
,,EXAMPLE #D ,SIMPLIFY 0-B9+ L T]MS
,,AVOID ,,]RORS
,! T]MS #C .;P #B & .;P >E N L T]MS4
,!Y USE ! SAME V>IA# B DI6]5T EXPON5TS1
S ! T]MS _C 2 -B9$4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.A4 #H .;X @+ #C .;X @3 .K 7#H @+ #C7
.;X @3 .,4TRIBUTIVE .PROP]TY
--@3 .K #AA .;X @3 .,ADD .COE6ICI5TS4
.B4 #E .;P #B @+ .;P -- #B .;P #B @3
.K 7#E .;P #B -- #B .;P #B @7 @+ .;P @3
.,GR\P .L .T]MS4
--@3 .K #C .;P #B @+ .;P @3 .,-B9E .L
.T]MS4
.C4 #C7 .;Y @+ #B7--#D7 .;Y -- #G7 @3
.K #C .;Y @+ #F--#D .;Y @+ #BH @3
.,4TRIBUTIVE .PROP]TY
--@3 .K 7#C .;Y -- #D .;Y @7 @+ 7#F @+
#BH7 @3 .,GR\P .L .T]MS4
--@3 .K -- .;Y @+ #CD @3 .,-B9E .L
.T]MS4
.D4 #B .;X -- #C .;Y -- #I .;X @+ .;Y
@3 .K 7#B .;X -- #I .;X @7 @+ 7--#C .;Y
@+ .;Y @7 @3 .,GR\P .L .T]MS4
--@3 .K --#G .;X -- #B .;Y @3 .,-B9E
.L .T]MS4
.,,ID5TITIES ,TWO ALGEBRAIC EXPRES.NS
>E .EQUIVAL5T .EXPRES.NS IF !Y H ! SAME
VALUE = ALL VALUES ( _! V>IA# 7;S74 ,=
9/.E1 9 "P 7A7 ( ,EXAMPLE #D1 !
EXPRES.NS #H .;X @+ #C .;X & #AA .;X >E
EQUIVAL5T4 ,A /ATE;T S* Z #H .;X @+ #C
.;X .K #AA .;X T EQUATES TWO EQUIVAL5T
EXPRES.NS IS CALL$ AN .ID5T;Y4
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#D
#H4 ,ID5TIFY ! T]MS1 COE6ICI5TS1 L
T]MS1 & 3/ANT T]MS 9 ! EXPRES.N #B @+ #E
.;X -- #F .;X #B @+ #G .;X -- #C4 ,!N
SIMPLIFY ! EXPRES.N4
,SIMPLIFY ! EXPRES.N4
#I4 #AE .;M -- #I .;M
#AJ4 #B .;N -- #A @+ #F .;N @+ #E
#AA4 #C .;P #C @+ #E .;P #B -- .;P #C
#AB4 #B .;Q #B @+ .;Q -- #G .;Q -- #E
.;Q #B
#AC4 #H7 .;X -- #C7--#B7 .;X @+ #F7
#AD4 --#D .;Y -- .;X @+ ;L#J .;X @+
.;Y
-------------------------------------#AC
,,EXAMPLE #E ,SIMPLIFY A MA!MATICAL
MODEL
.,,DIGITAL .,,PHOTO .,,PR9T+ ,Y S5D
#AE DIGITAL IMAGES 6A PR9T+ S]VICE T
*>GES @4#.HJ P] PR9T 9 L>GE =MAT &
@4#.BJ P] PR9T 9 SMALL =MAT4 ,WRITE &
SIMPLIFY AN EXPRES.N T REPRES5TS ! TOTAL
CO/ IF .;N (! #AE PR9TS >E 9 L>GE =MAT4
,!N F9D ! TOTAL CO/ IF #E (! #AE PR9TS
>E 9 L>GE =MAT4
,SOLU;N
,WRITE A V]BAL MODEL4 ,!N WRITE AN
ALGEBRAIC EXPRES.N
,,9T]PRET ,,EXPRES.NS
,! TOTAL NUMB] ( PR9TS IS #AE1 S IF
;R8 >E 9 L>GE =MAT1 !N #AE -- .;N >E 9
SMALL =MAT4
,AN EXPRES.N =! TOTAL CO/ IS .#J..H
.;N @+ #J.B7#AE -- .;N74
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#J.H .;N @+ #J.B7#AE -- .;N @7 @3 .K
#J.H .;N @+ #C--#J.B .;N @3 .,4TRIBUTIVE
.PROP]TY
--@3 .K 7#J.H .;N -- #J.B .;N @7 @+ #C
@3 .,GR\P .L .T]MS4
--@3 .K #J.F .;N @+ #C @3 .,-B9E .L
.T]MS4
,:5 .;N .K #E1 ! TOTAL CO/ IS #J.F7#E7
@+ #C .K #C @+ #C .K 4#F4
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#E
#AE4 .,,:AT .,,IF8 ,9 ,EXAMPLE #E1
WRITE & SIMPLIFY AN EXPRES.N =! TOTAL
CO/ IF ! PRICE (A L>GE PR9T IS @4#.GE &!
PRICE (A SMALL PR9T IS @4#.BE4
#A.B ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#A = ,EXS4 #BA1BI1 & #EI
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 #B1BD1 #CC1 #EA1 & #EI
.K .,,MULTIPLE .,,REPRES5T,NS
,EX#.FA
,,SKILL ,,PRACTICE
#A4 .,,VOCABUL>Y ,COPY #AB #G & LABEL
! BASE &! EXPON5T4
#B4 .,,WRIT+ .,EXPLA9 :AT X M1NS =
T]MS 6BE L T]MS4
#C4 .,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 EVALUAT+ ! P[] %[N AT !
"R4
,,EXAMPLE #A
ON P4 #AJ = ,EXS4 #D-AE
.,,EVALUAT+ .,,P[]S ,EVALUATE ! P[]4
#D4 #B #C
#E4 #C #D
#F4 #D #C
#G4 #G #B
#H4 --#E #B
#I4 --#B #E
#AJ4 --#H #C
#AA4 --#AJ #D
#AB4 7--#C7 #B
#AC4 7--#D7 #C
#AD4 7--#B7 #H
#AE4 7--#H7 #B
-------------------------------------#AD
,,EXAMPLE #B
ON P4 #AA = ,EXS4 #AF--#BD
,,ORD] ,,( ,,OP],NS ,EVALUATE !
EXPRES.N =! GIV5 VALUE (! V>IA#4
#AF4 #E .;D -- #F :5 .;D .K #G
#AG4 --#AJ .;F @+ #AE :5 .;F .K #B
#AH4 #F .;H @+ #B @+ .;H :5 .;H .K #D
#AI4 #E .;J -- #C .;J 99 #E :5 .;J .K
#AJ
#BJ4 @7 .;K @+ #B7 #B -- #F .;K :5 .;K
.K #E
#BA4 #H .;M @+ 7#B .;M -- #I7 #C :5
.;M .K #F
#BB4 .;N #C -- #D .;N @+ #AJ :5 .;N .K
--#C
#BC4 #B .;X #D -- #D .;X #C :5 .;X .K
--#A
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
#BD4 .,,MULTIPLE .,,*OICE ,:AT IS !
VALUE ( #B .;X #B -- #F .;X @+ #AE :5
.;X .K --#B8
,A #AA
;,B #AI
;,C #CE
;,D #DC
,,EXAMPLE #D
ON P4 #AB = ,EXS4 #BE--#CC
,,SIMPLIFY+ ,,EXPRES.NS ,SIMPLIFY !
EXPRES.N4
#BE4 #I .;X -- #D .;X @+ #E
#BF4 .;Y #B @+ #B .;Y @+ #C .;Y #B
#BG4 #E .;Z #B -- #B .;Z @+ #H .;Z #B
@+ #AJ
#BH4 #AJ .;W #B -- #D .;W @+ #C .;W #B
@+ #AH .;W
#BI4 #G7 .;M -- #C7 @+ #D7 .;M @+ #E7
#CJ4 #AJ7 .;N #B @+ .;N @7--#F7 .;N #B
-- #B7
#CA4 #D .;P #B -- #AB .;P -- #I .;P #B
@+ #C7#D .;P @+ #G7
#CB4 #F7 .;Q -- #B7--#B7 .;Q #B @+ #F
.;Q @7
#CC4 .,,MULTIPLE .,,*OICE ,: T]MS >E L
T]MS8
,A #B .;X @1 #B .;Y
;,B #C .;X #B @1 #D .;X
;,C .;X #B @1 .;Y #B
;,D #AJ .;X #C @1 #B .;X #C
..,,GEOMETRY ,WRITE A SIMPLIFI$
EXPRES.N =! P]IMET] (! FIGURE4 ,!N
EVALUATE ! EXPRES.N =! GIV5 VALUE 7;S7
(! V>IA# 7.;S74
.#CD4 .A .K #C1 .;B .K #AJ
.#CE4 .;N .K #B
.#CF4 .;G .K #E1 .;H .K #D
,,EVALUAT+ ,,EXPRES.NS ,EVALUATE !
EXPRES.N =! GIV5 VALUES ( .;X & .Y4
,,H9T
,FRAC;N B>S >E GR\P+ SYMBOLS4
#CG4 #E .;X @+ #F .;Y :5 .;X .K #AF &
.;Y .K --#I
#CH4 #AF .;X @+ #AA .;Y :5 .;X .K --#B
& .;Y .K --#C
#CI4 .;X #C @+ #E .;Y :5 .;X .K #D &
.;Y .K --#C
#DJ4 7#C .;X @7 #B -- .;Y #C :5 .;X .K
#D & .;Y .K #E
#DA4 :5 .;X .K #AJ & .;Y .K #H
#DB4 :5 .;X .K --#C & .;Y .K #D
,,SIMPLIFY+ ,,EXPRES.NS ,SIMPLIFY !
EXPRES.N4
#DC4 #AF .;C -- ;L#J .;D @+ #C .;D --
#E .;C
#DD4 #I .;J @+ #D .;K -- #B .;J -- #G
.;K
#DE4 #B .;M #B -- #E .;N #B @+ #F .;N
#B -- #H .;M
#DF4 .;P #C @+ #C .;Q #B -- .;Q @+ #C
.;P #C
#DG4 #AJ .;M #B @+ #C .;N -- #H @+ #C
.;M #B -- #C .;N @+ #C
#DH4 #C .;Y #B @+ #E .;X -- #AB .;X @+
#I .;Y #B -- #E
#DI4 #H7 .;S -- .;T @7 @+ #AF7 .;T --
.;S @7
#EJ4 #C7 .;X #B -- .;Y @7 @+ #I7 .;X
#B @+ #B .;Y @7
#EA4 .,,OP5-.,,5D$ .,,MA? ,WRITE AN
ALGEBRAIC EXPRES.N T 9CLUDES ?REE
COE6ICI5TS1 TWO L T]MS1 & "O 3/ANT T]M4
,!N SIMPLIFY ! EXPRES.N4
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
-------------------------------------#AE
.,,GR\P+ .,,SYMBOLS ,ADD P>5!SES 6MAKE
A TRUE /ATE;T4
#EB4 #I @+ #AB @/ #C--#A .K #AE
#EC4 #D @+ #C 99 #E--#B .K #BA
#ED4 #H @+ #E #B -- #F @/ #C .K #I
#EE4 #C 99 #D #B -- #B #C @+ #C #B .K
#BC
#EF4 .,,*ALL5GE ,"U :AT 3DI;NS >E !
EXPRES.NS @7 .;X @+ .;Y @7 #B & .;X #B
@+ .;Y #B EQUAL8 ,>E ! EXPRES.NS
EQUIVAL5T8 .,EXPLA94
,,PRO#M ,,SOLV+
,,EXAMPLE #C
ON P4 #AA = ,EXS4 #EG-EI
.#EG4 .,,MOVIE .,,CO/S ,9 ! ,UNIT$
,/ATES1 ! AV]AGE MOVIE TICKET PRICE 7IN
DOLL>S7 S9CE #AIGD C 2 MODEL$ 0#J.ACA
.;X @+ #A.HI ": .;X IS ! NUMB] ( YE>S
S9CE #AIGD4 ,:AT VALUES ( .;X %D Y USE
6F9D ! TICKET PRICES 9 #AIGD1 #AIHD1
#AIID1 & #BJJD8 ,F9D ! TICKET PRICES =
^? YE>S4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#EH4 .,,MILEAGE ,Y />T DRIV+ A US$ C>
:5 ! ODOMET] R1DS #IF1HHB4 ,AF A TYPICAL
MON? ( DRIV+1 ! R1D+ IS #IG1JEG4 ,WRITE
AN EXPRES.N =! R1D+ ON ! ODOMET] AF .;M
MON?S1 ASSUM+ ! AM.T Y DRIVE EA* MON? IS
! SAME4 ,PREDICT ! R1D+ AF #AB MON?S4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#EI4 .,,%ORT .,,RESPONSE ,A /UD5T HAS
A DEBIT C>D )A PREPD AM.T ( 4#BGJ 6USE =
S*OOL LUN*ES4 ,! CAFET]IA *>GES 4#D.EJ
P] LUN*4 ,WRITE AN EXPRES.N =! BAL.E ON
! C>D AF BUY+ .;X LUN*ES4 ,DOES YR
EXPRES.N MAKE S5SE = ALL POSITIVE 9TEG]
VALUES ( ;X8 .,EXPLA94
,,EXAMPLE #E
ON P4 #AC = ,EXS4 #FJ-FB
#FJ4 .,,CROSS-.,,TRA9+ ,Y EX]CISE =
#FJ M9UTES1 SP5D+ .;W M9UTES WALK+ &!
RE/ (! "T RUNN+4 ,USE ! 9=M,N 9 !
DIAGRAM 2L 6WRITE & SIMPLIFY AN EXPRES.N
=! NUMB] ( CALORIES BURN$4 ,F9D !
CALORIES BURN$ IF Y SP5D #BJ M9UTES
WALK+4
#FA4 .,,MULTIPLE .,,REPRES5T,NS ,A
!AT] HAS #CJ R[S ( S1TS ) #BJ S1TS 9 EA*
R[4 ,TICKETS =! S1TS 9 ! .;N R[S CLOSE/
6! /AGE CO/ 4#DE & TICKETS =! O!R R[S
CO/ 4#CE4
A4 .,VISUAL .,?9K+ ,MAKE A SKET* (!
!AT] S1T+4
B4 .,MODEL+ ,WRITE A V]BAL MODEL =!
9COME IF ALL S1TS >E SOLD4
C4 .,SIMPLIFY+ ,WRITE & SIMPLIFY AN
EXPRES.N =! 9COME4
D4 .,MAK+ .A .,TA# ,MAKE A TA# =!
9COME :5 .;N .K #E1 #AJ1 & #AE4
#FB4 .,,-PUT]S ,A -PANY (F]S EA* ( XS
#HJ "W]S EI A DESKTOP -PUT] T CO/S 4#IJJ
OR A LAPTOP T CO/S 4#AEEJ4 ,WRITE &
SIMPLIFY AN EXPRES.N =! CO/ ( ALL !
-PUT]S :5 .;N "W]S *OOSE DESKTOP -PUT]S4
,F9D ! CO/ IF #FE "W]S *OOSE DESKTOP
-PUT]S4
-------------------------------------#AF
#FC4 .,,*ALL5GE ,Y WANT 6BUY #BE FI% =
AN AQU>IUM4 ,Y DECIDE 6BUY DANIOS1
TETRAS1 & RA9B[FI%4
,WRITE & SIMPLIFY AN EXPRES.N =! TOTAL
CO/ ( .;X DANIOS1 .;Y TETRAS1 &! RE/
RA9B[FI%4 ,Y BUY #H DANIOS1 #AJ TETRAS1
&! RE/ RA9B[FI%4 ,:AT IS ! TOTAL CO/8
,MIX$ ,REVIEW
.,,PREVIEW ,PREP>E = ,LESSON #A.C 9
,EXS4 #FD-FG4
,F9D ! L1/ -MON DENOM9ATOR 7,,LCD7 (!
FRAC;NS1 @7 P4 #IGI @7
.#FD4
.#FE4
.#FF4
.#FG4
,ID5TIFY ! PROP]TY T ! /ATE;T
ILLU/RATES1 @7 P4 #B @7
.#FH4 7#G @* #H7 @* #BE .K #G @* 7#H
@* #BE7
.#FI4
,P]=M ! 9DICAT$ 3V].N1 @7 P4 #B @7
.#GJ4 #AE MET]S 6C5TIMET]S
.#GA4 #EJJJ P.DS 6TONS
.#GB4 #AJJ Y>DS 69*ES
.#GC4 #BJ "DS 6M9UTES
,,QUIZ .= .,LESSONS .#A..A-.A..B
,GRAPH ! NUMB]S ON A NUMB] L9E4 @7 P4
#B @7
#A4
#B4 --#F.B1 #E.D1 @1 --#B.E
#C4
,ID5TIFY ! PROP]TY T ! /ATE;T
ILLU/RATES1 @7 P4 #B @7
#D4 #F7#D @+ #I7 .K #F7#D7 @+ #F7#I7
#E4 --#E 99 #H .K #H 99 7--#E7
#F4 #AG @+ 7--#AG7 .K #J
,EVALUATE ! EXPRES.N =! GIV5 VALUE (!
V>IA#4 @7 P4 #AJ @7
#G4 #AJ .;M @+ #CB :5 .;M .K --#E
#H4 #AB @+ 7#H -- .;N @7 #C :5 .;N .K
#E
#I4 .;P #C -- #C .;P #B :5 .;P .K --#B
,SIMPLIFY ! EXPRES.N4 @7 P4 #AJ @7
#AJ4 #H .;X @+ #F .;X #B -- #I .;X #B
-- #D .;X
#AA4 #E7 .;X @+ #I7--#B7#D -- .;X @7
#AB4 #BD .;X -- #F .;Y @+ #AE .;Y --
#AH .;X
#AC4 .;,,CD .,,CO/S ,,CD,'S >E ON SALE
= 4#H EA* & Y H A GIFT C>D WOR? 4#AJJ4
,WRITE AN EXPRES.N =! AM.T ( M"OY LEFT
ON ! GIFT C>D AF PUR*AS+ .;N ,,CD,'S4
,EVALUATE ! EXPRES.N 6F9D ! AM.T ( M"OY
LEFT AF PUR*AS+ #F ,,CD,'S4 @7 P4 #AJ @7
.,,EXTRA .,,PRACTICE = ,LESSON #A.B1
P4 #AJAJ
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
-------------------------------------#AG
,GRAPH+ ,CALCULATOR ,ACTIV;Y3 #A.B
,EVALUATE ,EXPRES.NS
,USE AF LESSON #A.B
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,KEY/ROKES
,,"Q ,H[ C Y USE A CALCULATOR
6EVALUATE EXPRES.NS8
,Y C USE A SCI5TIFIC CALCULATOR OR A
GRAPH+ CALCULATOR 6EVALUATE EXPRES.NS4
,KEY/ROKES = EVALUAT+ S"EAL EXPRES.NS >E
%[N 2L4
,NOTE T 65T] A NEGATIVE NUMB]1 Y USE !
KEY ON A SCI5TIFIC CALCULATOR OR ! KEY
7N ! KEY7 ON A GRAPH+ CALCULATOR4
,,EXAMPLE ,EVALUATE ,EXPRES.NS
,,PRACTICE
,USE A CALCULATOR 6EVALUATE !
EXPRES.N4
#A4 #EJ.B--#AE @/ #C
#B4 --#AA7#BJ7--#FF
#C4 #BA7--#H7 @+ #EA
#D4 7--#D7 #D
#E4 #G7#DD.E--#H #B @7
#F4
,USE A CALCULATOR 6EVALUATE ! EXPRES.N
:5 .;X .K --#C1 .;Y .K #E1 & .;Z .K
--#F4
#G4 #G .;Z @+ .;Y
#H4 .;X #F
#I4 #F .;Y -- .;Z #C
#AJ4
#AA4 @7 .;X @+ .;Y @7 #B @+ #C .;Z
#AB4 7--#D .;X @+ #I7--@7 .;Y @+ #B7
.#AC4 .,,]ROR .,,ANALYSIS ,A /UD5T
EVALUAT$ ! EXPRES.N #G @+ 7--#D7 #C ON A
GRAPH+ CALCULATOR 0PRESS+ #G #D #C @4 ,!
CALCULATOR 4PLAY$ AN ]ROR MESSAGE4
.,DESCRIBE & CORRECT ! ]ROR4
-------------------------------------#AH
#A.C ,SOLVE ,L9E> ,EQU,NS
.,2F ,Y SIMPLIFI$ ALGEBRAIC EXPRES.NS4
.,N[ ,Y W SOLVE L9E> EQU,NS4
.,:Y8 ,S Y C SOLVE PRO#MS AB E>N+S1 Z
9 ,EXAMPLE #B4
,KEY ,VOCABUL>Y
99 .EQU,N
99 .L9E> .EQU,N
99 .SOLU;N
99 .EQUIVAL5T .EQU,NS
,AN .EQU,N IS A /ATE;T T TWO EXPRES.NS
>E EQUAL4 ,A .L9E> .EQU,N 9 "O V>IA# IS
AN EQU,N T C 2 WRITT5 9 ! =M .AX @+ .;B
.K #J ": .A & .;B >E 3/ANTS & .A @6.K
#J4
,A NUMB] IS A .SOLU;N ( AN EQU,N 9 "O
V>IA# IF SUB/ITUT+ ! NUMB] =! V>IA#
RESULTS 9 A TRUE /ATE;T4 ,TWO EQU,NS >E
.EQUIVAL5T .EQU,NS IF !Y H ! SAME SOLU;N
7;S74
,SIDEB>3
,/&>DS
.,PREP>E .= .#A..J ..,/UD5TS SOLVE
EQU,NS & .9EQUALITIES 9VOLV+ ABSOLUTE
VALUE4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,TRANS=M,NS ,T ,PRODUCE ,EQUIVAL5T
,EQU,NS
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
..,A4I;N ,PROP]TY ( .,EQUAL;Y @3 .,ADD
! SAME NUMB] 6EA* SIDE4 @3 ,IF .A .K .;B
@1
!N .A @+ .;C .K .;B @+ .C4
..,SUBTRAC;N ,PROP]TY ( .,EQUAL;Y @3
.,SUBTRACT ! SAME NUMB] F EA* SIDE4 @3
..,IF A .K .;B @1
!N .A -- .;C .K .;B -- .C4
..,MULTIPLIC,N ,PROP]TY ( .,EQUAL;Y @3
.,MULTIPLY EA* SIDE 0! SAME NONZ]O
NUMB]4 @3 ,IF .A .K .;B & .;C @6.K #J1
!N .A 99 .;C .K .;B 99 .C4
..,DIVI.N ,PROP]TY ( .,EQUAL;Y @3
.,DIVIDE EA* SIDE 0! SAME NONZ]O NUMB]4
@3 ,IF .A .K .;B & .;C @6.K #J1 !N .A @/
.;C .K .;B @/ .;C @4
,EXAMPLE #A ,SOLVE AN EQU,N )A V>IA#
ON "O SIDE
,,ANO!R ,,WAY
,Y C AL SOLVE ! EQU,N 9 ,EXAMPLE #A
0MULTIPLY+ EA* SIDE 0#E F/4
.,SOLVE @4
,! SOLU;N IS #AE4
.,,*ECK ,*ECK .;X .K #AE 9 ! ORIG9AL
EQU,N4
-------------------------------------#AI
,,EXAMPLE #B ,WRITE & USE A L9E> EQU,N
.,,RE/AURANT ,DUR+ "O %IFT1 A WAIT]
E>NS WAGES ( 4#CJ & GETS AN A4I;NAL
#AE@3P 9 TIPS ON CU/OM]S' FOOD BILLS4 ,!
WAIT] E>NS 4#AJE4 ,:AT IS ! TOTAL (!
CU/OM]S' FOOD BILLS8
,SOLU;N
,WRITE A V]BAL MODEL4 ,!N WRITE AN
EQU,N4 ,WRITE #AE@3P Z A DECIMAL4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#AJE .K #CJ @+ #J.AE .;X @3 .,WRITE
.EQU,N4
#GE .K #J.AE .;X @3 ..,SUBTRACT #CJ F
EA* .SIDE4
#EJJ .K .;X @3 ..,DIVIDE EA* SIDE
0#J..AE4
,! TOTAL (! CU/OM]S' FOOD BILLS IS
4#EJJ4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #A &
.#B
,SOLVE ! EQU,N4 ,*ECK YR SOLU;N4
#A4 #D .;X @+ #I .K #BA
#B4 #G .;X -- #DA .K --#AC
#C4
.#D4 .,,R1L .,,E/ATE ,A R1L E/ATE
AG5T'S BASE SAL>Y IS 4#BB1JJJ P] YE>4 ,!
AG5T E>NS A #D@3P -MIS.N ON TOTAL SALES4
,H[ M* M/ ! AG5T SELL 6E>N 4#FJ1JJJ 9 "O
YE>8
..,,EXAMPLE #C ,/&>DIZ$ ,TE/
.,PRACTICE
,:AT IS ! SOLU;N ( #G .;P @+ #AC .K #I
.;P -- #E8
,A --#I
;,B --#D
;,C #D
;,D #I
,SOLU;N
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#G .;P @+ #AC .K #I .;P -- #E @3
.,WRITE .ORIG9AL .EQU,N4
#AC .K #B .;P -- #E @3 ,SUBTRACT #G
.;P F EA* SIDE4
#AH .K #B .;P @3 ..,ADD #E 6EA* .SIDE4
#I .K .;P @3 ..,DIVIDE EA* SIDE 0.#B4
,! CORRECT ANSW] IS ,D4 .,A .;,B .;,C
.;,D
,,*ECK
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#G .;P @+ #AC .K #I .;P -- #E @3
.,WRITE .ORIG9AL .EQU,N4
#G7 .#I @7 @+ #AC #I7 .#I @7--#E @3
,SUB/ITUTE #I =.' ;P @4
#FC @+ #AC .K #HA #E @3 .,MULTIPLY4
#GF .K #GF @3 .,SOLU;N .*ECKS4
-------------------------------------#BJ
,,EXAMPLE #D ,SOLVE AN EQU,N US+ !
4TRIBUTIVE PROP]TY
,SOLVE #C7#E .;X -- #H7 .K --#B7-- .;X
@+ #G7--#AB .;X @4
,! SOLU;N IS @4
,,*ECK
,,EXAMPLE #E ,SOLVE A "W PRO#M
.,,C> .,,WA% ,X TAKES Y #H M9UTES 6WA%
A C> & X TAKES A FR #F M9UTES 6WA% A C>4
,H[ L;G DOES X TAKE ! TWO ( Y 6WA% #G
C>S IF Y "W TGR8
,SOLU;N
.,,/EP .#A .,WRITE A V]BAL MODEL4 ,!N
WRITE AN EQU,N4
.,,/EP .#B .,SOLVE ! EQU,N = .T4
,,AVOID ,,]RORS
,2 SURE 6MULTIPLY .BO? SIDES (! EQU,N
0! ,,LCD1 N J "O SIDE4
,X W TAKE #BD M9UTES 6WA% #G C>S IF Y
"W TGR4
.,,*ECK ,Y WA% C>S & YR FR WA%ES C>S 9
#BD M9UTES4 ,TGR1 Y WA% #G C>S4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
-------------------------------------#BA
..,,GUID$ ,,PRACTICE = ,EXAMPLES #C1D1
& .#E
,SOLVE ! EQU,N4 ,*ECK YR SOLU;N4
#E4 -- .#B;X @+ #I .K #B .;X -- #G
#F4 #AJ -- .;X .K --#F .;X @+ #AE
#G4 #C7 .;X @+ #B7 .K #E7 .;X @+ #D7
#H4 --#D7#B .;X @+ #E7 .K #B7-- .;X --
#I7--#D .;X
#I4
#AJ4
#AA4 .,,:AT .,,IF8 ,9 ,EXAMPLE #E1
SUPPOSE X TAKES Y #I M9UTES 6WA% A C> &
X TAKES YR FR #AB M9UTES 6WA% A C>4 ,H[
L;G DOES X TAKE ! TWO ( Y 6WA% #G C>S IF
Y "W TGR8
#A.C ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
.ON P4 ,,WS#A = ,EXS4 .#BC1.DC @1 &
.#GA
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.,EXS4 #B1AI1 #CB1GB1 .& #GG
.K .,,MULTIPLE .,,REPRES5T,NS
,EX#.GD
,,SKILL ,,PRACTICE
#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,IF A
NUMB] IS SUB/ITUT$ =A V>IA# 9 AN EQU,N
&! RESULT+ /ATE;T IS TRUE1 ! NUMB] IS
CALL$ A7;N7 @8 (! EQU,N4
#B4 .,,WRIT+ ,GIVE AN EXAMPLE ( TWO
EQUIVAL5T EQU,NS4 ,H[ D Y "K !Y >E
EQUIVAL5T8
,,EXAMPLE #A
ON P4 #AH = ,EXS4 #C-AI
,,V>IA# ,,ON ,,"O ,,SIDE ,SOLVE !
EQU,N4 ,*ECK YR SOLU;N4
#C4 .;X @+ #H .K #AA
#D4 .;Y -- #D .K #G
#E4 .;Z -- #AC .K --#A
#F4 --#C .K .;W @+ #E
#G4 #E .;D .K #CJ
#H4
#I4
#AJ4 --#AF .;K .K --#H
#AA4 #F .;M -- #C .K #BA
#AB4 #D .;N -- #AJ .K #AB
#AC4 #C .K #B .;P @+ #E
#AD4 --#C .;Q @+ #D .K #AC
#AE4
#AF4
#AG4
#AH4
#AI4 .,,MULTIPLE .,,*OICE ,:AT IS !
SOLU;N ( #D .;X -- #G .K --#AE8
,A --#AB
;,B --#B
;,C #B
;,D
,,EXAMPLE #C
ON P4 #AI = ,EXS4 #BJ-CB
,,V>IA# ,,ON ,,BO? ,,SIDES ,SOLVE !
EQU,N4 ,*ECK YR SOLU;N4
#BJ4 #C .A @+ #D .K #B .A @+ #AE
#BA4 #E .;W @+ #B .K #B .;W @+ #E
#BB4 #F .;X @+ #G .K #B .;X @+ #EI
#BC4 #E .;B -- #D .K #B .;B @+ #H
#BD4 #C .;Y @+ #G .K .;Y -- #C
#BE4 #B .;Z -- #C .K #F .;Z @+ #BE
#BF4 #D .;N -- #G .K #E--#B .;N
#BG4 #B .;C @+ #AD .K #F--#D .;C
#BH4 #E .;M -- #B .K ;R- .;M -- #B
#BI4 .;P @+ #E .K #BE--#D .;P
#CJ4 #F--#E .;Q .K .;Q @+ #I
#CA4 #AG--#F .;R .K #BE--#C .;R
#CB4 .,,MULTIPLE .,,*OICE ,:AT IS !
SOLU;N ( #G .;T -- #E .K #C .;T @+ #AA8
,A
;,B
;,C
;,D #D
-------------------------------------#BB
,,EXAMPLE #D
.ON P4 #BJ = ,EXS4 #CC-DJ
,,! ,,4TRIBUTIVE ,,PROP]TY ,SOLVE !
EQU,N4 ,*ECK YR SOLU;N4
.#CC4 #B7 .;B @+ #C7 .K #D .;B -- #B
.#CD4 #E .;D @+ #AG .K #D7 .;D @+ #C7
.#CE4 #C7 .;M -- #E7 .K #F7 .;M @+ #A7
.#CF4 --#D7 .;N @+ #B7 .K #C7 .;N --
#D7
.#CG4 #AB7 .;R @+ #C7 .K #B7 .;R @+
#E7--#C .;R
.#CH4 #G7 .;T -- #C7 .K #B7 .;T -- #I7
@+ #B .;T
.#CI4 #AJ7 .;W -- #D7 .K #D7 .;W @+
#D7 @+ #D .;W
.#DJ4 #C7#B .;X -- #E7 -- .;X .K --#G7
.;X @+ #C7
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 SOLV+ ! EQU,N4
.#DA4
.#DB4
,,EXAMPLE #E
ON P4 #BJ = ,EXS4 #DC-EJ
,,EQU,NS ,,) ,,FRAC;NS ,SOLVE ! EQU,N4
,*ECK YR SOLU;N4
.#DC4
.#DD4
.#DE4
.#DF4
.#DG4
.#DH4
.#DI4
.#EJ4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,,GEOMETRY ,SOLVE = X4 ,!N F9D !
L5G? ( EA* SIDE (! .FIGURE4
.#EA4 ,P]IMET] .K #DF
.#EB4 ,P]IMET] .K #BF
.#EC4 ,P]IMET] .K#AE
.#ED4 ,P]IMET] .K #BF
,,EQU,NS ,,) ,,DECIMALS ,SOLVE !
EQU,N4 ,*ECK YR SOLU;N4
.#EE4 #J.F .;G @+ #J.E .K #B.I
.#EF4 #A.A .;H @+ #A.C .K #F.H
.#EG4 #J.D .;K -- #J.F .K #A.C .;K @+
#A.B
.#EH4 #F.E .;M @+ #A.E .K #D.C .;M --
#J.G
.#EI4 #C.H .;W @+ #C.B .K #B.C7 .;W @+
#D7
.#FJ4 #A.G7 .;X @+ #E7 .K #B.A .;X @+
#I.G
.#FA4 #B.BE .;B @+ #C.HA .K #A.GE .;B
@+ #E.BF
.#FB4 #AH.AC--#E.AH .;C .K #F.CB .;C
-- #H.CB
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
-------------------------------------#BC
,,SPECIAL ,,EQU,NS ,SOLVE ! EQU,N4 ,IF
"! IS NO SOLU;N1 WRITE .NO .SOLU;N4 ,IF
! EQU,N IS ALW TRUE1 WRITE .ALL .R1L
.NUMB]S4
.#FC4 #E7 .;X -- #D7 .K #E .;X @+ #AB
.#FD4 #C7 .;X @+ #E7 .K #C .;X @+ #AE
.#FE4 #E7#B -- .;X @7 .K #C--#B .;X @+
#G--#C .;X
.#FF4 --#B7#D--#C .;X @7 @+ #G .K #F7
.;X @+ #A7
.#FG4 .,,*ALL5GE ,SOLVE ! EQU,N .AX @+
.;B .K .CX @+ .;D = .;X 9 T]MS ( .A1
.;B1 .;C @1 & .D4 ,"U :AT 3DI;NS IS "!
NO SOLU;N8 ,"U :AT 3DI;NS >E ALL R1L
NUMB]S SOLU;NS8
,,PRO#M ,,SOLV+
,,EXAMPLE #B
ON P4 #AI = ,EXS4 #FH-GA
.#FH4 .,,CATALOG .,,PUR*ASE ,Y >E
ORD]+ ;,T-%IRTS F A CATALOG4 ,EA*
;,T-%IRT CO/S 4#AE4 ,! CO/ ( %IPP+ IS
4#F NO MATT] H[ _M Y ORD]4 ,! TOTAL CO/
IS 4#AAA4 ,H[ _M ;,T-%IRTS DID Y ORD]8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#FI4 .,,BICYCLE .,,REPAIR ,! BILL =!
REPAIR ( YR BICYCLE 0 4#AHJ4 ,! CO/ (
"PS 0 4#AJE4 ,! CO/ ( LABOR 0 4#BE P]
H\R4 ,H[ _M H\RS DID ! REPAIR "W TAKE8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#GJ4 .,,C> .,,SALES ,A SALESP]SON AT
A C> D1L]%IP HAS A BASE SAL>Y ( 4#BE1JJJ
P] YE> & E>NS A #E@3P -MIS.N ON TOTAL
SALES4 ,H[ M* M/ ! SALESP]SON SELL 6E>N
4#EJ1JJJ 9 "O YE>8
#GA4 .,,SUMM] .,,JOBS ,Y H TWO SUMM]
JOBS4 ,9 ! F/ JOB1 Y "W #BE H\RS P] WEEK
& E>N 4#G.GE P] H\R4 ,9 ! SECOND JOB1 Y
E>N 4#F.BE P] H\R & C "W Z _M H\RS Z Y
WANT4 ,Y WANT 6E>N 4#BEJ P] WEEK4 ,H[ _M
H\RS M/ Y "W AT ! SECOND JOB8
.#GB4 .,,%ORT .,,RESPONSE ,YR FR B"\ A
TOTAL ( #AJ ,,CD,'S & ,,DVD,'S Z GIFTS =
4#AII4 ,! PRICE P] ;,,CD 0 4#AE &! PRICE
P] ,,DVD 0 4#BB4 ,WRITE & SOLVE AN EQU,N
6F9D H[ _M ,,CD,'S & H[ _M ,,DVD,'S YR
FR B"\4 ,H[ WD YR ANSW] *ANGE IF ! TOTAL
CO/ (! ,,CD,'S & ,,DVD,'S 0 4#AHE8
.,EXPLA94
#GC4 .,,MULTI-.,,/EP .,,PRO#M ,Y >E
"W+ ON ! LAY\T (A YE>BOOK4 ,! PAGE IS #I
9*ES WIDE1 HAS 9* M>G9S1 & HAS ?REE
COLUMNS ( EQUAL WID?4
A4 ,WRITE & SIMPLIFY AN EQU,N T
RELATES ! COLUMN WID? .;C &! GAP .;G 2T
COLUMNS 6! TOTAL WID? (! PAGE4
B4 ,COPY & -PLETE ! TA# 0SUB/ITUT+ !
GIV5 VALUE 96YR EQU,N F "P 7A7 & SOLV+
6F9D ! UN"KN VALUE4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,GAP1 .;G 7IN47 @3 @3 @8@3 @3 @8
.,COLUMN .WID?1 .;C7.IN47 @3 @8@3 @3
@8@3
-------------------------------------#BD
#GD4 .,,MULTIPLE .,,REPRES5T,NS ,Y
WANT 65L>GE A #D 9* 0#E 9* PHOTO 6FIT
96A #A 9* WIDE FRAME T HAS AN \T]
P]IMET] ( #EC 9*ES4
A4 .,US+ .A .,DIAGRAM ,WRITE AN
EXPRES.N =! \T] P]IMET] (! PICTURE
FRAME4
B4 .,MAK+ .A .,TA# ,EVALUATE ! P]IMET]
EXPRES.N :5 .;X .K #A.E1 #B1 #B.E1 #C1 &
#C.E4 ,MAKE A TA# ( YR RESULTS4 ,= :AT
VALUE ( .;X IS ! P]IMET] #EC 9*ES8
C4 .,US+ .AN .,EQU,N ,WRITE & SOLVE AN
EQU,N 6F9D .X4 .,EXPLA9 :AT ! VALUE (
.;X TELLS Y AB H[ M* Y %D 5L>GE !
ORIG9AL PHOTO4
,,EXAMPLE #E
ON P4 #BJ = ,EXS4 #GE-GG
#GE4 .,,RAK+ .,,L1VES ,X TAKES Y #CJ
M9UTES 6RAKE ! L1VES 9 YR Y>D & X TAKES
YR BRO!R #DE M9UTES4 ,H[ L;G DOES X TAKE
! TWO ( Y 6RAKE ! L1VES :5 "W+ TGR8
#GF4 .,,MURAL .,,PA9T+ ,Y PA9T #B
SQU>E Y>DS (A -MUN;Y MURAL 9 #C H\RS &A
FR PA9TS #D SQU>E Y>DS 9 #E H\RS4 ,H[
L;G DOES X TAKE ! TWO ( Y 6PA9T #AA
SQU>E Y>DS :5 "W+ TGR8
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
#GG4 .,,MULTIPLE .,,*OICE ,?REE /UD5TS
USE CALLIGRAPHY P5S 6WRITE ! "NS (
GRADUAT+ S5IORS ON _! DIPLOMAS4 ,"O
WRITES #G "NS 9 #F M9UTES1 ANO!R WRITES
#AG "NS 9 #AJ M9UTES1 &! ?IRD WRITES #BC
"NS 9 #AE M9UTES4 ,H[ L;G1 6! NE>E/
M9UTE1 W ! /UD5TS TAKE 6WRITE "NS ON
#DDJ DIPLOMAS IF !Y "W TGR8
,A #IG M9UTES
;,B #AJJ M9UTES
;,C #AJC M9UTES
;,D #BIJ M9UTES
#GH4 .,,*ALL5GE ,A CYL9DRICAL !RMOS )
AN 9SIDE DIAMET] ( 9*ES IS FILL$ )
LIQUID 6A HEI<T ( #I 9*ES4 ,IF ! LIQUID
IS P\R$ 96A CYL9DRICAL TRAVEL MUG ) AN
9SIDE DIAMET] ( 9*ES1 :AT W 2 ! HEI<T
.;H (! LIQUID8
,,MIX$ ,,REVIEW
.,,PREVIEW ,PREP>E = ,LESSON #A.D 9
,EXS4 #GI-HB4
,F9D ! >EA (! FIGURE1 @7 P4 #IIA @7
.#GI4 ,SQU>E ) SIDES ( L5G? #AJ ;M
.#HJ4 #D IN4 0#F IN4 RECTANGLE
.#HA4 ,CIRCLE )A RADIUS ( #C IN4
.#HB4 ,CIRCLE )A DIAMET] ( #AE CM
,ID5TIFY ! PROP]TY T ! /ATE;T
ILLU/RATES1 @7 P4 #B @7
.#HC4 7#AJ @* #AC7 @* #B .K #AJ @*
7#AC @* #B7
.#HD4 --#BC @+ #BC .K #J
.#HE4 #F @+ 7#E @+ #D7 .K #F @+ 7#D @+
#E7
.#HF4 #D7#A @+ #J.BE7 .K #D7#A7 @+
#D7#J.BE7
,SIMPLIFY ! EXPRES.N1 @7 P4 #AJ @7
.#HG4 #G .;X #B @+ #H--#C .;X -- #E
.;X #B
.#HH4 #E .;Y -- #C .;Y #C @+ #G
.;Y--.;Y #B
.#HI4 #B7 .;Z -- #E7 @+ #I7 .;Z @+ #B7
.#IJ4 --#E7 .;W @+ #C7--@7 .;W @+ #B7
.,,EXTRA .,,PRACTICE = ,LESSON #A.C1
P4 #AJAJ
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
-------------------------------------#BE
,GRAPH+ ,CALCULATOR ,ACTIV;Y3 #A.C
,USE ,TA#S 6,SOLVE ,EQU,NS
,USE AF ,LESSON #A.C
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,KEY/ROKES
,SIDEB>3
,/&>DS
.,PREP>E .= .#A..J .,/UD5TS .SOLVE
.EQU,NS & 9EQUALITIES 9VOLV+ ABSOLUTE
VALUE4
,,"Q ,H[ C Y USE TA#S 6SOLVE L9E>
EQU,NS8
,Y C USE ! .TA# F1TURE (A GRAPH+
CALCULATOR 6SOLVE L9E> EQU,NS4
,,EXAMPLE ,SOLVE A L9E> EQU,N
,USE ! .TA# F1TURE (A GRAPH+
CALCULATOR 6SOLVE ! EQU,N #C .;X @+ #H
.K #I .;X -- #AF4
,,/EP #A ,5T] ,EXPRES.NS
,PRESS @4 ,5T] ! LEFT SIDE (! EQU,N Z
.;Y #A .K #C .;X @+ #H4 ,5T] ! "R SIDE
(! EQU,N Z .;Y #B .K #I .;X -- #AF4
,,/EP #B ,MAKE A TA#
,PRESS ,7,,TBLSET7'4 ,SET ! />T+
;X-VALUE ,TBL,/>T 6#J &! /EP VALUE ,TBL
7! VALUE 0: ! ;X-VALUES 9CR1SE7 6#A4
,,/EP #C ,ID5TIFY SOLU;N
,PRESS ,7,,TA#7' 64PLAY ! TA#4 ,SCROLL
"? ! TA# UNTIL Y F9D AN ;X-VALUE = : BO?
SIDES (! EQU,N H ! SAME VALUE4
,BO? SIDES (! EQU,N H A VALUE ( #BJ :5
.;X .K #D4 ,S1 ! SOLU;N ( #C .;X @+ #H
.K #I .;X -- #AF IS #D4
,,PRACTICE
,USE ! .TA# F1TURE (A GRAPH+
CALCULATOR 6SOLVE ! EQU,N4
#A4 #G .;X -- #C .K -- .;X @+ #AC
#B4 --#F .;X @+ #H .K #AB--#E .;X
#C4 -- .#B;X -- #AC .K --#C .;X -- #E
#D4 #BB @+ #AE .;X .K --#I .;X -- #B
#E4 #D .;X @+ #BG .K --#H @+ #AA .;X
#F4 #G--#H .;X .K --#I--#AJ .;X
#G4 .,,R1SON+ ,3SID] ! EQU,N #D .;X @+
#AH .K #I .;X -- #I4
A4 ,ATTEMPT 6SOLVE ! EQU,N US+ ! .TA#
F1TURE (A GRAPH+ CALCULATOR ) /EP VALUE
,TBL .K #A4 ,2T :AT TWO 9TEG]S DOES !
SOLU;N LIE8 ,H[ D Y "K8
B4 ,USE A SMALL] VALUE ( ,TBL 6F9D !
EXACT SOLU;N4
#H4 .,,WRIT+ ,SOLVE ! EQU,N #C .;X @+
#H .K #I .;X -- #AF 0WRIT+ X 9 ! =M .AX
@+ .;B .K #J1 5T]+ .;Y #A .K .AX @+ .;B
ON A GRAPH+ CALCULATOR1 & US+ A TA# 6F9D
! .;X -VALUE = : .;Y #A .K #J4 ,:AT >E !
ADVANTAGES & 4ADVANTAGES ( ? ME?OD -P>$
6! ME?OD %[N ABV8
-------------------------------------#BF
#A.D ,REWRITE ,=MULAS & ,EQU,NS
.,2F ,Y SOLV$ EQU,NS4
.,N[ ,Y W REWRITE & EVALUATE =MULAS &
EQU,NS4
.,:Y8 ,S Y C APPLY GEOMETRIC =MULAS1 Z
9 ,EX4 #CF4
,KEY ,VOCABUL>Y
99 .=MULA
99 SOLVE =A V>IA#
,SIDEB>3
,/&>DS
.,PREP>E .= .#A..J .,/UD5TS .SOLVE
.EQU,NS & 9EQUALITIES 9VOLV+ ABSOLUTE
VALUE4
,A .=MULA IS AN EQU,N T RELATES TWO OR
M QUANTITIES1 USU,Y REPRES5T$ 0V>IA#S4
,"S -MON =MULAS >E %[N 2L4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,QUANT;Y3 ,=MULA3 ,M1N+ ( V>IA#S
,4T.E3 .;D .K .RT @3 .;D .K 4T.E1 .;R
.K RATE1 .;T .K "T
,TEMP]ATURE3 @3 .;,F .K DEGREES
,FAHR5HEIT1
.;,C .K DEGREES ,CELSIUS
,>EA (A TRIANGLE3 @3 .,A .K >EA1 .;B
.K BASE1 .;H .K HEI<T
,>EA (A RECTANGLE3 .,A .K .;W @3 .,A
.K >EA1 .K L5G?1 .;W .K WID?
,P]IMET] (A RECTANGLE3 ..;,P .K #B
@+.#B;W @3 .;,P .K P]IMET]1 .K L5G?1 .;W
.K WID?
,>EA (A TRAPEZOID3 @3 .,A .K >EA1 .;B
#A .K "O BASE1 .;B #B .K O!R BASE1 .;H
.K HEI<T
,>EA (A CIRCLE3 .,A .K ;R #B @3 .,A .K
>EA1 .;R .K RADIUS
,CIRCUMF];E (A CIRCLE3 .;,C.K .#B .;R
@3 .;,C .K CIRCUMF];E1 .;R .K RADIUS
,,R1D+
,! V>IA#S .;B #A & .;B #B >E R1D Z
8.;B SUB "O0 & 8.;B SUB TWO40 ,! SMALL
L[]$ NUMB]S >E CALL$ .SUBSCRIPTS4
,6..SOLVE =A .V>IA# M1NS 6REWRITE AN
EQU,N Z AN EQUIVAL5T EQU,N 9 : ! V>IA#
IS ON "O SIDE & DOES N APPE> ON ! O!R
SIDE4
,,EXAMPLE #A ,REWRITE A =MULA ) TWO
V>IA#S
,SOLVE ! =MULA ..;,C .K #B .;R = .;R
@4 ,!N F9D ! RADIUS (A CIRCLE )A
CIRCUMF];E ( #DD 9*ES4
,SOLU;N
.,,/EP .#A .,SOLVE ! =MULA = .R4
.,,/EP .#B .,SUB/ITUTE ! GIV5 VALUE
96! REWRITT5 =MULA4
,! RADIUS (! CIRCLE IS AB #G 9*ES4
-------------------------------------#BG
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#A
#A4 ,F9D ! RADIUS (A CIRCLE )A
CIRCUMF];E ( #BE FEET4
#B4 ,! =MULA =! 4T.E .;D 2T OPPOSITE
V]TICES (A REGUL> HEXAGON IS ": .A IS !
4T.E 2T OPPOSITE SIDES4 ,SOLVE ! =MULA =
.A4 ,!N F9D .A :5 .;D .K #AJ C5TIMET]S4
,,EXAMPLE #B ,REWRITE A =MULA ) ?REE
V>IA#S
,SOLVE ! =MULA .;,P .K .#B @+ #B .;W =
.W4 ,!N F9D ! WID? (A RECTANGLE )A L5G?
( #AB MET]S &A P]IMET] ( #DA MET]S4
,SOLU;N
.,,/EP .#A .,SOLVE ! =MULA = .W4
.,,/EP .#B .,SUB/ITUTE ! GIV5 VALUES
96! REWRITT5 =MULA4
,! WID? (! RECTANGLE IS #H.E MET]S4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#B
#C4 ,SOLVE ! =MULA .;,P .K .#B;L @+ #B
.;W = ,!N F9D ! L5G? (A RECTANGLE )A
WID? ( #G 9*ES &A P]IMET] ( #CJ 9*ES4
#D4 ,SOLVE ! =MULA ,A .K .;W = .W4 ,!N
F9D ! WID? (A RECTANGLE )A L5G? ( #AF
MET]S & AN >EA ( #DJ SQU>E MET]S4
,SOLVE ! =MULA =! V>IA# 9 R$4 ,!N USE
! GIV5 9=M,N 6F9D ! VALUE (! V>IA#4
.#E4
,F9D .;H IF .;B .K #AB ;M & ,A .K #HD
;M #B @4
.#F4
,F9D .;B IF .;H .K .#C CM & .,A .K #I
CM #B @4
.#G4
,F9D .;H IF .;B #A .K #F IN41 .;B #B
.K #H IN41 & .,A .K #GJ IN4 #B
-------------------------------------#BH
.,,REWRIT+ .,,EQU,NS ,! APPROA* Y USE
6SOLVE A =MULA =A V>IA# C 2 APPLI$ 6O!R
ALGEBRAIC EQU,NS4
,,EXAMPLE #C ,REWRITE A L9E> EQU,N
,SOLVE #I .;X -- #D .;Y .K #G = .;Y @4
,!N F9D ! VALUE ( .;Y :5 .;X .K --#E4
,SOLU;N
.,,/EP .#A .,SOLVE ! EQU,N = .Y4
,,AVOID ,,]RORS
,:5 DIVID+ EA* SIDE ( AN EQU,N 0! SAME
NUMB]1 REMEMB] 6DIVIDE E T]M 0! NUMB]4
.,,/EP#B .,SUB/ITUTE ! GIV5 VALUE 96!
REWRITT5 EQU,N4
,,*ECK
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#I .;X -- #D .;Y .K #G @3 .,WRITE
.ORIG9AL .EQU,N4
#I7--#E7--#D7--#AC7 #G @3 ,SUB/ITUTE
--#E =.' ;X .-& --#AC =.' ;Y @4
#G .K #G @3 .,SOLU;N .*ECKS4
,,EXAMPLE #D ,REWRITE A NONL9E> EQU,N
,SOLVE #B .;Y @+ .XY .K #F = .;Y @4
,!N F9D ! VALUE ( .;Y :5 .;X .K --#C4
,SOLU;N
,,AVOID ,,]RORS
,IF Y REWRITE ! EQU,N Z @1 !N Y H N
SOLV$ = .;Y 2C .;Y / APPE>S ON BO? SIDES
(! EQU,N4
.,,/EP .#A .,SOLVE ! EQU,N = .Y4
.,,/EP .#B .,SUB/ITUTE ! GIV5 VALUE
96! REWRITT5 EQU,N4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #C &
.#D
,SOLVE ! EQU,N = .;Y @4 ,!N F9D !
VALUE ( .;Y :5 .;X .K #B4
.#H4 .;Y -- #F .;X .K #G
.#I4 #E .;Y -- .;X .K #AC
.#AJ4 #C .;X @+ #B .;Y .K #AB
.#AA4 #B .;X @+ #E .;Y .K --#A
.#AB4 #C .K #B .XY -- .;X
.#AC4 #D .;Y -- .XY .K #BH
-------------------------------------#BI
,,EXAMPLE #E ,SOLVE A MULTI-/EP PRO#M
.,,MOVIE .,,R5TAL ,A VIDEO /ORE R5TS
NEW MOVIES = "O PRICE & OLD] MOVIES =A
L[] PRICE1 Z %[N AT ! "R4
99 ,WRITE AN EQU,N T REPRES5TS !
/ORE'S MON?LY REV5UE4
99 ,SOLVE ! REV5UE EQU,N =! V>IA#
REPRES5T+ ! NUMB] ( NEW MOVIES R5T$4
99 ,! [N] WANTS 4#AB1JJJ 9 REV5UE P]
MON?4 ,H[ _M NEW MOVIES M/ 2 R5T$ IF !
NUMB] ( OLD] MOVIES R5T$ IS #EJJ8#AJJJ8
,SOLU;N
.,,/EP .#A .,WRITE A V]BAL MODEL4 ,!N
WRITE AN EQU,N4
,AN EQU,N IS .;,R .K #E .;N #A @+ #C
.;N #B @4
.,,/EP#B .,SOLVE ! EQU,N = .;N #A
.,,/EP .#C .,CALCULATE .;N #A =! GIV5
VALUES ( .;,R & .;N #B
,IF .;N #B .K #EJJ1 !N @4
,IF .;N #B .K #AJJJ1 !N @4
,IF #EJJ OLD] MOVIES >E R5T$1 !N #BAJJ
NEW MOVIES M/ 2 R5T$4 ,IF #AJJJ OLD]
MOVIES >E R5T$1 !N #AHJJ NEW MOVIES M/ 2
R5T$4
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#E
#AD4 .,,:AT .,,IF8 ,9 ,EXAMPLE #E1 H[
_M NEW MOVIES M/ 2 R5T$ IF ! NUMB] (
OLD] MOVIES R5T$ IS #AEJJ8
#AE4 .,,:AT .,,IF8 ,9 ,EXAMPLE #E1 H[
_M NEW MOVIES M/ 2 R5T$ IF CU/OM]S R5T
.NO OLD] MOVIES AT ALL8
#AF4 ,SOLVE ! EQU,N 9 ,/EP #A (
,EXAMPLE #E = .;N #B @4
-------------------------------------#CJ
#A.D ,EX]CISES
,HOME"W ,KEY
.K ..,,"W$-,,\ ,,SOLU;NS .ON P4 ,,WS#A
..= ,EXS4 #C1I1 & .#CE
.K ..,,/&>DIZ$ ,,TE/ ,,PRACTICE ,EXS4
#B1 #F1AE1 #BG1 #CF1 & .#CH
,,SKILL ,,PRACTICE
#A4 .,,VOCABUL>Y ,COPY & -PLETE3
,A7;N7 @8 IS AN EQU,N T RELATES TWO OR M
QUANTITIES4
#B4 .,,WRIT+ ,:AT DOES X M1N 6SOLVE =A
V>IA# 9 AN EQU,N8
,,EXAMPLES
#A & #B
ON PP4 #BF-BG = ,EXS4 #C-F
.,,REWRIT+ .,,=MULAS ,SOLVE ! =MULA =!
9DICAT$ V>IA#4 ,!N USE ! GIV5 9=M,N 6F9D
! VALUE (! V>IA#4
#C4 ,SOLVE .,A .K .;W =4 ,!N F9D !
L5G? (A RECTANGLE )A WID? ( #EJ
MILLIMET]S & AN >EA ( #BEJ SQU>E
MILLIMET]S4
#D4 ,SOLVE = .B4 ,!N F9D ! BASE (A
TRIANGLE )A HEI<T ( #F 9*ES & AN >EA (
#BD SQU>E 9*ES4
#E4 ,SOLVE = .H4 ,!N F9D ! HEI<T (A
TRAPEZOID ) BASES ( L5G?S #AJ C5TIMET]S
& #AE C5TIMET]S & AN >EA ( #GE SQU>E
C5TIMET]S4
#F4 .,,MULTIPLE .,,*OICE ,:AT EQU,N D
Y OBTA9 :5 Y SOLVE ! =MULA = .;B #A @8
,A
;,B
;,C .;B #A .K #B .,A -- .;B #B .;H
;,D
,,EXAMPLE #C
ON P4 #BH = ,EXS4 #G-AG
,,REWRIT+ ,,EQU,NS ,SOLVE ! EQU,N =
.Y4 ,!N F9D ! VALUE ( .;Y =! GIV5 VALUE
( .X4
#G4 #C .;X @+ .;Y .K #BF2 .;X .K #G
#H4 #D .;Y @+ .;X .K #BD2 .;X .K #H
#I4 #F .;X @+ #E .;Y .K #CA2 .;X .K
--#D
#AJ4 #AE .;X @+ #D .;Y .K #I2 .;X .K
--#C
#AA4 #I .;X -- #F .;Y .K #FC2 .;X .K
#E
#AB4 #AJ .;X -- #AH .;Y .K #HD2 .;X .K
#F
#AC4 #H .;Y -- #AD .;X .K --#BB2 .;X
.K #E
#AD4 #I .;Y -- #D .;X .K --#CJ2 .;X .K
#H
#AE4 .,,MULTIPLE .,,*OICE ,:AT EQU,N D
Y OBTA9 :5 Y SOLVE ! EQU,N #D .;X -- #E
.;Y .K #BJ = .;Y @8
,A
;,B
;,C
;,D
.,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 SOLV+ ! EQU,N = Y4
#AF4
#AG4
-------------------------------------#CA
..,,GEOMETRY ,SOLVE ! =MULA =! V>IA# 9
R$4 ,!N USE ! GIV5 9=M,N 6F9D ! VALUE (!
V>IA#4 ,R.D 6! NE>E/ .T5?4
#AH4 ,>EA (A CIRCUL> R+
,A .K #B RW
,F9D .;R IF .;W .K #D FT & .,A .K #ABJ
FT #B @4
#AI4 ,LAT]AL SURFACE >EA (A TRUNCAT$
CYL9D]
.;,S .K .;R7.;H @+ .;K @7
,F9D .;H IF .;R .K .#B CM1 .;K .K #C
CM1 & .;,S .K #EJ CM #B @4
#BJ4 ,VOLUME ( AN ELLIPSOID
,F9D .;C IF .A .K #D IN41 .;B .K
#C;941 & .;,V .K #FJ IN4 #C
,,EXAMPLE #D
ON P4 #BH = ,EXS4 #BA-BF
,,REWRIT+ ,,EQU,NS ,SOLVE ! EQU,N =
.Y4 ,!N F9D ! VALUE ( .;Y ..=! GIV5
VALUE ( .X4
#BA4 .XY -- #C .;X .K #DJ2 .;X .K #E
#BB4 #G .;X -- .XY .K --#AH2 .;X .K
--#D
#BC4 #C .XY -- #BH .K #AF .;X2 .;X .K
#D
#BD4 #I .;Y @+ #F .XY .K #CJ2 .;X .K
--#F
#BE4 .;Y -- #B .XY .K #AE2 .;X .K --#A
#BF4 #D .;X @+ #G .;Y @+ #E .XY .K #J2
.;X .K #A
#BG4 .,,%ORT .,,RESPONSE ,3SID] !
EQU,N #AE .;X -- #I;Y .K #BG4 ,6F9D !
VALUE ( .;Y :5 .;X .K #B1 Y C USE TWO
ME?ODS4
,ME?OD #A ..,SOLVE ! ORIG9AL EQU,N =
;Y & !N SUB/ITUTE #B = .;X @4
,ME?OD #B ..,SUB/ITUTE #B = ;X & !N
SOLVE ! RESULT+ EQU,N = .;Y @4
,%[ ! /EPS (! TWO ME?ODS4 ,: ME?OD IS
M E6ICI5T IF Y NE$ 6F9D ! VALUE ( .;Y =
S"EAL VALUES ( .;X @8 .,EXPLA94
,,R1SON+ ,SOLVE =! 9DICAT$ V>IA#4
#BH4 ,SOLVE .XY .K .;X @+ .;Y = .;Y @4
#BI4 ,SOLVE .XYZ .K .;X @+ .;Y @+ .;Z
= .Z4
#CJ4 ,SOLVE = .;Y @4
#CA4 ,SOLVE = .;Z @4
#CB4 .,,*ALL5GE ,WRITE A =MULA GIV+ !
>EA (A CIRCLE 9 T]MS ( XS CIRCUMF];E4
,,PRO#M ,,SOLV+
,,EXAMPLE #E
ON P4 #BI = ,EXS4 #CC-CH
#CC4 .,,TREE .,,DIAMET] ,Y C E/IMATE !
DIAMET] (A TREE )\T BOR+ "? X 0M1SUR+ XS
CIRCUMF];E4 ,SOLVE ! =MULA .;,C .K .;D =
.D4 ,!N F9D ! DIAMET] ( AN OAK T HAS A
CIRCUMF];E ( #AAC 9*ES4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#CD4 .,,DESIGN ,! FABRIC PANELS ON A
KITE >E RHOMBUSES4 ,=! PANEL %[N1 A
=MULA =! L5G? (! L;G DIAGONAL .;D IS ":
.;S IS ! L5G? (A SIDE4 ,SOLVE ! =MULA =
.S4 ,!N F9D ! VALUE ( .;S :5 .;D .K #AE
9*ES4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
-------------------------------------#CB
#CE4 .,,TEMP]ATURE ,! =MULA = 3V]T+
TEMP]ATURES F DEGREES ,CELSIUS 6DEGREES
,FAHR5HEIT IS @4 ,SOLVE ! =MULA = .,C4
,!N F9D ! TEMP]ATURE 9 DEGREES ,CELSIUS
T CORRESPONDS 6#EJ;DG,F4
#CF4 .,,EXT5D$ .,,RESPONSE ,A QU>T]
MILE RUNN+ TRACK IS %AP$ Z %[N4 ,! =MULA
=! 9SIDE P]IMET] IS .;,P .K #B .;R @+ #B
.X4
A4 ,SOLVE ! P]IMET] =MULA = .R4
B4 ,=A QU>T] MILE TRACK1 .;,P .K #DDJ
Y>DS4 ,F9D .;R :5 .;X .K #GE Y>DS1 #AJJ
Y>DS1 #ABJ Y>DS1 & #AEJ Y>DS4
C4 ,:AT >E ! GRTE/ & L1/ POSSI# VALUES
( .;R IF .;,P .K #DDJ Y>DS8 .,EXPLA9 H[
Y F.D ! VALUES1 & SKET* ! TRACK
CORRESPOND+ 6EA* EXTREME VALUE4
#CG4 .,,MULTI-.,,/EP .,,PRO#M ,A TUX$O
%OP R5TS CLASSIC TUX$OS = 4#HJ & DESIGN]
TUX$OS = 4#AEJ4 ,WRITE AN EQU,N T
REPRES5TS ! %OP'S REV5UE4 ,SOLVE ! EQU,N
=! V>IA# REPRES5T+ ! NUMB] ( DESIGN]
TUX$OS R5T$4 ,! %OP [N] WANTS 4#FJ1JJJ 9
REV5UE DUR+ PROM S1SON4 ,H[ _M DESIGN]
TUX$OS M/ 2 R5T$ IF ! NUMB] ( CLASSIC
TUX$OS R5T$ IS #FJJ8 #DEJ8 #CJJ8
#CH4 .,,OP5-.,,5D$ .,,MA? ,! VOLUME (A
DONUT-L %APE CALL$ A .TORUS IS GIV5 0!
=MULA .;,V .K .#B #B .;R #B .;,R ": .;R
& .;,R >E ! RADII %[N & .;R"K.K .,R4
A4 ,SOLVE ! =MULA = .,R4
B4 ,A METAL R+ 9 ! %APE (A TORUS HAS A
VOLUME ( #AJJ CUBIC C5TIMET]S4 ,*OOSE
?REE POSSI# VALUES ( .;R @1 & F9D !
CORRESPOND+ VALUES ( .,R4
#CI4 .,,*ALL5GE ,A RECTANGUL> PIECE (
PAP] ) L5G? ;I & WID? .;W C 2 ROLL$ 6=M
! LAT]AL SURFACE (A CYL9D] 9 TWO WAYS1
ASSUM+ NO OV]LAPP+4 ,WRITE A =MULA =!
VOLUME ( EA* CYL9D] 9 T]MS (& .W4
,,MIX$ ,,REVIEW
.,,PREVIEW ,PREP>E = ,LESSON #A.E 9
,EXS4 #DJ-DG4
,WRITE AN EXPRES.N 6ANSW] ! "Q4 @7 P4
#IHD @7
.#DJ4 ,Y H 4#BEJ 9 A BANK A3.T &
DEPOSIT .;X DOLL>S4 ,:AT IS YR CURR5T
BAL.E8
.#DA4 ,Y BUY .;X ,,CD,'S = 4#AB.II
EA*4 ,H[ M* D Y SP5D8
,EVALUATE ! EXPRES.N =! GIV5 VALUE (!
V>IA#1 @7 P4 #AJ @7
.#DB4 #F .;J @+ #H :5 .;J .K --#C
.#DC4 #F @+ #D .;K @/ #B :5 .;K .K #C
.#DD4 #H .;G -- #H .;G @* #B :5 .;G .K
--#A
.#DE4 --#E .;M #C @+ .;M #B :5 .;M .K
#AJ
.#DF4 @7 .;N @+ #G7 #B -- #D :5 .;N .K
#B
.#DG4 7#C .;P -- #AG7 #C :5 .;P .K #E
,SOLVE ! EQU,N4 ,*ECK YR SOLU;N1 @7 P4
#AH @7
.#DH4 #D .;X @+ #G .K #AJ .;X @+ #BE
.#DI4 #AE--#B .;Y .K #B .;Y -- #DE
.#EJ4 #EF .K #D7#D @+ #B .;Z @7
.#EA4 #I7 .;P @+ #C7 .K #CE .;P @+ #A
.#EB4
.#EB4
.,,EXTRA .,,PRACTICE = ,LESSON #A.D1
P4 #AJAJ
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
-------------------------------------#CC
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,LESSONS #A.A-A.D
#A4 .,,MULTI-.,,/EP .,,PRO#M ,"! IS A
4#EJ ANNUAL MEMB]%IP FEE 6JO9 AN URBAN
C> R5TAL S]VICE4 ,US+ A C> CO/S 4#H.EJ
P] H\R4
.A4 ,WRITE A V]BAL MODEL = ? SITU,N4
,!N USE ! V]BAL MODEL 6WRITE AN
ALGEBRAIC EXPRES.N4
.B4 ,H[ M* W X CO/ 6JO9 ! S]VICE &
DRIVE = #BJ H\RS8
#B4 .,,MULTI-.,,/EP .,,PRO#M ,Y >E
ATT5D+ A MUSEUM4 ,Y H 4#EJ 6SP5D4
,ADMIS.N 6! MUSEUM IS 4#AE4 ,ADMIS.N
6EA* SPECIAL EXHIBIT 9SIDE ! MUSEUM IS
4#AJ4
.A4 ,WRITE AN EQU,N T C 2 US$ 6F9D !
NUMB] ( SPECIAL EXHIBITS Y C 9CLUDE 9 YR
VISIT4
.B4 ,SOLVE ! EQU,N4 ,9T]PRET YR ANSW]
9 T]MS (! PRO#M4
#C4 .,,%ORT .,,RESPONSE ,9 HOCKEY1 EA*
PLAY] HAS A /ATI/IC CALL$ PLUS_/M9US1 :
IS ! DI6];E 2T ! NUMB] ( GOALS SCOR$ 0!
PLAY]'S T1M &! NUMB] ( GOALS SCOR$ 0!
O!R T1M :5 ! PLAY] IS ON ! ICE4 ,LI/ !
PLAY]S %[N 9 ORD] F L1/ 6GRTE/
PLUS_/M9US4 ,^: PLUS_/ M9US SCORE IS
BE/8 .,EXPLA94
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,PLAY]3 ,PLUS_/,M9US
,V9C5T ,LECAVALI]3 .#BC
,DAVE ,&REY*UK3 --.#I
,RUSLAN ,F$OT5KO3 .#AD
,M>T9 ,ST4 ,L\IS3 .#CE
,CORY ,S>I*3 .#E
,TIM ,TAYLOR3 --.#E
#D4 .,,%ORT .,,RESPONSE ,Y >E 9 *>GE (
BUY+ FOOD =A S*OOL PICNIC4 ,Y H 4#DE
6SP5D ON GR.D BEEF & *ICK54 ,GR.D BEEF
CO/S 4#A.HJ P] P.D & *ICK5 CO/S 4#A.JJ
P] P.D4 ,WRITE AN EQU,N REPRES5T+ !
SITU,N4 ,Y WANT 6BUY EQUAL AM.TS ( GR.D
BEEF & *ICK54 ,H[ M* ( EA* C Y BUY8 ,%[
H[ Y F.D YR ANSW]4
#E4 .,,GRI4$ .,,ANSW] ,Y DRIVE F
,*ICAGO 6,ST4 ,L\IS1 A 4T.E ( #BIJ
MILES4 ,YR AV]AGE SPE$ IS #FJ MILES P]
H\R4 ,H[ _M H\RS DOES ! TRIP TAKE8 ,R.D
YR ANSW] 6! NE>E/ T5? ( AN H\R4
#F4 .,,OP5-.,,5D$ ,DESCRIBE A %OPP+
SITU,N T C 2 MODEL$ 0! EQU,N #AJ .;X @+
#BI .;Y .K #GH4
#G4 .,,EXT5D$ .,,RESPONSE ,9 "O YE>1 !
,BUR1U ( ,5GRAV+ & ,PR9T+ PR9T$ 4#AJ &
4#BJ BILLS )A TOTAL VALUE (
4#FF1CFH1JJJ4 ,! TOTAL NUMB] ( 4#AJ &
4#BJ BILLS 0 #C1EGG1FJJ4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 ,NUMB]3 ,VALUE
4#AJ BILLS3 .;X @3 #AJ .;X
4#BJ BILLS3 @8@3 @8
,TOTAL3 #C1EGG1FJJ3 #FF1CFH1JJJ
A4 ,COPY & -PLETE ! TA#4
B4 ,WRITE & SOLVE AN EQU,N 6F9D H[ _M
4#AJ BILLS & H[ _M 4#BJ BILLS 7 PR9T$4
C4 .,-P>E ! TOTAL VALUE (! 4#AJ BILLS
PR9T$ )! TOTAL VALUE (! 4#BJ BILLS
PR9T$4
.#H4 .,,OP5-.,,5D$ ,Y H TWO SUMM]
JOBS4 ,Y M[ LAWNS = 4#BJ P] LAWN4 ,Y AL
"W AT A RE/AURANT = 4#G.EJ P] H\R4
,WRITE AN EQU,N =! TOTAL AM.T ( M"OY Y
E>N4 ,!N F9D ?REE DI6]5T WAYS 6E>N 4#CJJ
DUR+ "O WEEK4
.#I4 .,,GRI4$ .,,ANSW] ,!
LIOPLEURODON1 A SWIMM+ D9OSAUR F ! ,LATE
,JURASSIC P]IOD1 CD GR[ 6#BE MET]S 9
L5G?4 ,USE ! FACT T #A IN4 .K #B.ED CM
63V]T ! L5G? 6FEET4 ,R.D YR ANSW] 6!
NE>E/ FOOT4
.#AJ4 .,,GRI4$ .,,ANSW] ,! =MULA =!
VOLUME (A C"O IS @4 ,F9D .;H 7IN
C5TIMET]S7 IF .;,V .K #AGF;CM #C & .;,B
.K #DJ;CM #B @4
-------------------------------------#CD
#A.E ,USE ,PRO#M ,SOLV+ ,/RATEGIES &
,MODELS
.,2F ,Y WROTE & SOLV$ EQU,NS4
.,N[ ,Y W SOLVE PRO#MS US+ V]BAL
MODELS4
.,:Y8 ,S Y C SOLVE 3/ANT RATE PRO#MS1
Z 9 ,EX4 #BF4
,KEY ,VOCABUL>Y
99 V]BAL MODEL
,SIDEB>3
,/&>DS
.,ALGEBRA .#A3 #E.J ,/UD5TS SOLVE
MULTI/EP PRO#MS1 9CLUD+ ^W PRO#MS1
9VOLV+ L9E> EQU,NS & L9E> 9EQUALITIES 9
"O V>IA# & PROVIDE JU/IFIC,N = EA* /EP4
,Z Y H SE5 9 ? *APT]1 X IS HELP;L :5
SOLV+ R1L-LIFE PRO#MS 6WRITE AN EQU,N 9
^WS .2F Y WRITE X 9 MA!MATICAL SYMBOLS4
,? ^W EQU,N IS CALL$ A .V]BAL .MODEL @4
,"S"TS PRO#M SOLV+ /RATEGIES C 2 US$
6WRITE A V]BAL OR ALGEBRAIC MODEL4
,EXAMPLES ( S* /RATEGIES >E ..USE A
=MULA1 LOOK =A .PATT]N @1 & .DRAW .A
.DIAGRAM4
,,EXAMPLE #A ,USE A =MULA
.,,HI<-.,,SPE$ .,,TRA9 ,! ,ACELA TRA9
TRAVELS 2T ,BO/ON & ,WA%+TON1 A 4T.E (
#DEG MILES4 ,! TRIP TAKES #F.E H\RS4
,:AT IS ! AV]AGE SPE$8
,SOLU;N
,Y C USE ! =MULA = 4T.E TRAVEL$ Z A
V]BAL MODEL4
,AN EQU,N = ? SITU,N IS #DEG .K #F.ER4
,SOLVE = R4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#DEG .K #F.E;R3 .,WRITE .EQU,N4
#GJ.C .;R @3 ..,DIVIDE EA* SIDE
0#F..E4
,! AV]AGE SPE$ (! TRA9 IS AB #GJ.C
MILES P] H\R4
.,,*ECK ,Y C USE UNIT ANALYSIS 6*ECK
YR ANSW]4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#A
.#A4 .,,AVI,N ,A JET FLIES AT AN
AV]AGE SPE$ ( #EDJ MILES P] H\R4 ,H[ L;G
W X TAKE 6FLY F ,NEW ,YORK 6,TOKYO1 A
4T.E ( #FGFJ MILES8
-------------------------------------#CE
,,EXAMPLE #B ,LOOK =A PATT]N
.,,P>AMOTOR+ ,A P>AMOTOR IS A P>A*UTE
PROPELL$ 0A FAN-L MOTOR4 ,! TA# %[S !
HEI<T .;H (A P>AMOTORI/ .;T M9UTES AF
2G9N+ A DESC5T4 ,F9D ! HEI<T (!
P>AMOTORI/ AF #G M9UTES4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--
.,HEI<T 7.FT71 .FT @3 #BJJJ3 #AGEJ3
#AEJJ3 #ABEJ3 #AJJJ
,SOLU;N
,! HEI<T DECR1SES 0#BEJ FEET P] M9UTE4
,Y C USE ? PATT]N 6WRITE A V]BAL MODEL
=! HEI<T4
,AN EQU,N =! HEI<T IS .;H .K
#BJJJ--#BEJ .;T
,S1 ! HEI<T AF #G M9UTES IS .;H .K
#BJJJ--#BEJ7#G7 .K #BEJ FEET4
..,,EXAMPLE #C ,DRAW A .DIAGRAM
.,,BANN]S ,Y >E HANG+ F\R *AMPION%IP
BANN]S ON A WALL 9 YR S*OOL'S GYM4 ,!
BANN]S >E #H FEET WIDE4 ,! WALL IS #FB
FEET L;G4 ,"! %D 2 AN EQUAL AM.T ( SPACE
2T ! 5DS (! WALL &! BANN]S1 & 2T EA*
PAIR ( BANN]S4 ,H[ F> A"P %D ! BANN]S 2
PLAC$8
,SOLU;N
,2G9 0DRAW+ & LABEL+ A DIAGRAM1 Z %[N
2L4
,F ! DIAGRAM1 Y C WRITE & SOLVE AN
EQU,N 6F9D .;X @4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @+ #H @+ .;X @+ #H @+ .;X @+ #H @+
.;X @+ #H @+ .;X .K #FB @3 .,WRITE
.EQU,N4
#E .;X @+ #CB .K #FB @3 ,-B9E L T]MS4
#E .;X .K #CJ @3 ..,SUBTRACT #CB F EA*
.SIDE4
.;X .K #F @3 ,DIVIDE EA* SIDE 0#E4
,! BANN]S %D 2 PLAC$ #F FEET A"P4
,,REVIEW ,,/RATEGIES
,= HELP ) O!R PRO#M SOLV+ /RATEGIES1
SEE P4 #IIH @4
-------------------------------------#CF
..,,EXAMPLE #D ,/&>DIZ$ ,TE/
.,PRACTICE
,A C> US$ #AF GALLONS ( GASOL9E &
TRAVEL$ A TOTAL 4T.E ( #DFJ MILES4 ,!
C>'S FUEL E6ICI5CY IS #CJ MILES P]
GALLON ON ! HI<WAY & #BE MILES P] GALLON
9 ! C;Y4 ,H[ _M GALLONS ( GASOL9E 7 US$
ON ! HI<WAY8
,A #H GALLONS
;,B #AB GALLONS
;,C GALLONS
;,D #AF GALLONS
,SOLU;N
.,,/EP .#A .,WRITE A V]BAL MODEL4 ,!N
WRITE AN EQU,N4
,AN EQU,N =! SITU,N IS #DFJ .K #CJ .;G
@+ #BE7#AF -- .;G @7@4
.,,/EP .#B .,SOLVE = .;G 6F9D ! NUMB]
( GALLONS US$ ON ! HI<WAY4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#DFJ .K #CJ .;G @+ #BE7#AF -- .;G @7
@3 .,WRITE .EQU,N4
#DFJ .K #CJ .;G @+ #DJJ--#BE .;G @3
.,4TRIBUTIVE .PROP]TY
#DFJ .K #E .;G @+ #DJJ @3 .,-B9E .L
.T]MS4
#FJ .K #E .;G @3 ..,SUBTRACT #DJJ F
EA* .SIDE4
#AB .K .;G @3 ..,DIVIDE EA* SIDE 0.#E4
,! C> US$ #AB GALLONS ON ! HI<WAY4
,! CORRECT ANSW] IS ,B4 ,A ;,B ;,C ;,D
.,,*ECK #CJ @* .#AB @+ #BE7#AF --
.#AB7 .K #CFJ @+ #AJJ .K #DFJ
..,,GUID$ ,,PRACTICE = ,EXAMPLES #B1C1
& .#D
#B4 .,,P>AMOTOR+ ,! TA# %[S ! HEI<T
.;H (A P>AMOTORI/ AF .;T M9UTES4 ,F9D !
HEI<T (! P>AMOTORI/ AF #H M9UTES4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,"T 7M971 .;T @3 #J3 #A3 --@3 #B3 #C3
#D
,HEI<T 7FT71 .;H @3 #BDJJ3 #BAIJ3 --@3
#AIHJ3 #AGGJ3 #AEFJ
.#C4 .,,:AT .,,IF8 ,9 ,EXAMPLE #C1 H[
WD YR ANSW] *ANGE IF "! 7 ONLY ?REE
*AMPION%IP BANN]S8
#D4 .,,FUEL .,,E6ICI5CY ,A TRUCK US$
#BH GALLONS ( GASOL9E & TRAVEL$ A TOTAL
4T.E ( #DBH MILES4 ,! TRUCK'S FUEL
E6ICI5CY IS #AF MILES P] GALLON ON !
HI<WAY & #AB MILES P] GALLON 9 ! C;Y4
,H[ _M GALLONS ( GASOL9E 7 US$ 9 ! C;Y8
-------------------------------------#CG
#A.E ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS .ON P4
,,WS#B ..= ,EXS4 #C1AA1 & .#BG
.K ..,,/&>DIZ$ ,,TE/ ,,PRACTICE ,EXS4
#B1AE1AF1BA1 & .#BG
.K ..,,MULTIPLE ,,REPRES5T,NS ,EX#..BH
,,SKILL ,,PRACTICE
#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,A ^W
EQU,N T REPRES5TS A R1L-LIFE PRO#M IS
CALL$ A7;N7 @8 @4
#B4 .,,WRIT+ ,GIVE AN EXAMPLE ( H[ A
PRO#M SOLV+ /RATEGY C HELP Y WRITE AN
EQU,N T MODELS A R1L-LIFE PRO#M4
,,EXAMPLE #A
ON P4 #CD = ,EXS4 #C-AJ
.,,US+ .,A .,,=MULA ,USE ! =MULA .;D.K
.RT = 4T.E TRAVEL$ 6SOLVE =! MISS+
V>IA#4
#C4 .;D .K #BJ MI1 .;R .K #DJ MI_/;H1
.;T .K @8
#D4 .;D .K #CJJ MI1 .;R .K @8 @1 .;T
.K #D ;H
#E4 .;D .K @8 @1 .;R .K #CJ MI_/;H1
.;T .K #C ;H
#F4 .;D .K #BEJ MI1 .;R .K #EJ MI_/;H1
.;T .K @8
.,,GEOMETRY ,USE ! =MULA ;,P .K #B .;L
@+ #B .;W @2 =! P]IMET] (A RECTANGLE
6SOLVE =! MISS+ V>IA#4
#G4 .;,P .K @8 @1 .K #AE FT1 .;W .K
#AB FT
#H4 .;,P .K #DF IN41 .K @8 @1 .;W .K
#D IN4
#I4 .;,P .K #AJJ ;M1 .K #CJ ;M1 .;W .K
@8
#AJ4 .;,P .K #BE CM1 .;W .K #E CM1 .K
@8
,,EXAMPLE #B
ON P4 #CE = ,EXS4 #AA-AE
,,US+ ,,PATT]NS ,LOOK =A PATT]N 9 !
TA#4 ,!N WRITE AN EQU,N T REPRES5TS !
TA#4
#AA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #J3 #A3 #B3 #C
.;Y @3 #AA3 #AE3 #AI3 #BC
#AB4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #J3 #A3 #B3 #C
.;Y @3 #FJ3 #DE3 #CJ3 #AE
#AC4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #J3 #A3 #B3 #C
.;Y @3 #DF3 #CF3 #BF3 #AF
#AD4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #J3 #A3 #B3 #C
.;Y @3 #EG3 #AJG3 #AEG3 #BJG
#AE4 ..,,MULTIPLE ,,*OICE ,: EQU,N
REPRES5TS ! TA# AT ! ."R8
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #J3 #A3 #B3 #C
.;Y @3 #AB3 #AI3 #BF3 #CC
,A .;Y .K #E .;X @+ #G
;,B .;Y .K #G .;X @+ #E
;,C .;Y .K #AB .;X -- #E
;,D .;Y .K #G .;X @+ #AB
#AF4 .,,%ORT .,,RESPONSE ,! F/ /ORY (A
BUILD+ IS #BD FEET HI<1 & EA* A4I;NAL
/ORY IS #AH FEET HI<4 ,WRITE AN EXPRES.N
=! HEI<T 6! TOP (! .N? /ORY4 .,EXPLA9 !
M1N+ ( EA* T]M 9 ! EXPRES.N4
,,EXAMPLE #C
.ON P4 #CE = ,EXS4 #AG-AH
,,US+ ,,DIAGRAMS ,WRITE & SOLVE AN
EQU,N 6F9D .X4
.#AG4
.#AH4
-------------------------------------#CH
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 WRIT+ ! EQU,N4
#AI4
#BJ4
#BA4 .,,MULTIPLE .,,*OICE ,A C> US$
#AE GALLONS ( GASOL9E & TRAVEL$ A TOTAL
4T.E ( #CEJ MILES4 ,! C>'S FUEL E6ICI5CY
IS #BE MILES P] GALLON ON ! HI<WAY & #BJ
MILES P] GALLON 9 ! C;Y4 ,: EQU,N C Y
SOLVE 6F9D .;H @1 ! NUMB] ( GALLONS T 7
US$ ON ! HI<WAY8
,A #CEJ .K #BE7#AE -- .;H @7 @+ .#BJ;H
;,B #BE .;H @+ #BJ7#AE -- .;H @7 .K
#CEJ
;,C
;,D
.,,*ALL5GE ,WRITE AN EQU,N T REPRES5TS
! TA#4
#BB4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #J3 #C3 #F3 #I
.;Y @3 #AB3 #CJ3 #DH3 #FF
#BC4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #D3 #E3 #F3 #G
.;Y @3 #AB3 #AI3 #BF3 #CC
,,PRO#M ,,SOLV+
,,EXAMPLE #A
ON P4 #CD = ,EXS4 #BD-BF
#BD4 .,,"DTONA .#EJJ ,A REC5T ,"DTONA
#EJJ RACE 0 WON 0,DALE ,E>NH>DT1 ,JR4
,HE -PLET$ ! #EJJ MILE RACE 9 #C.B H\RS4
,:AT 0 8 AV]AGE RAC+ SPE$8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#BE4 .,,MAGLEV .,,TRA9 ,A MAGNETIC
LEVIT,N 7MAGLEV7 TRA9 TRAVELS 2T ! C;Y
C5T] ( ,%ANGHAI1 ,*9A1 & ,PUD;G
,9T]N,NAL ,AIRPORT4 ,! TRIP COV]S #CJ
KILOMET]S 9 J #H M9UTES4 ,:AT IS !
AV]AGE SPE$ (! TRA98
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
,,EXAMPLE #B
ON P4 #CE = ,EXS4 #BG-BH
.#BF4 .,,SCUBA .,,DIV+ ,A SCUBA DIV]
IS RETURN+ 6! SURFACE F A DEP? ( #AFE
FEET4 ,! SAFE ASC5T RATE =A DIV] IS #CJ
FEET P] M9UTE4 ,H[ _M M9UTES W X TAKE =!
DIV] 6RETURN 6! SURFACE8
#BG4 .,,%ORT .,,RESPONSE ,! TA# %[S !
HEI<T (A BAMBOO %OOT DUR+ A P]IOD ( FA/
GR[?4 ,USE ! TA# 6WRITE AN EQU,N MODEL+
! GR[?4 ,D Y ?9K X IS R1SONA# 6ASSUME !
PATT]N 9 ! TA# 3T9UES 9DEF9ITELY8
.,EXPLA94
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,"D @3 #J3 #A3 #B3 #C3 #D
.,BAMBOO .HEI<T 7.FT7 @3 #AE3 #AF.E3
#AH3 #AI.E3 #BA
.K ..,,"W$-,,\ ,,SOLU;NS ON P4.,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
-------------------------------------#CI
#BH4 .,,MULTIPLE .,,REPRES5T,NS ,YR
CELL PH"O PLAN CO/S 4#DJ P] MON? PLUS
@4#.AJ P] TEXT MESSAGE4 ,Y RCV A BILL =
4#EC.HJ4
A4 .,MAK+ .A .,TA# ,COPY & -PLETE !
TA# 2L4 ,USE ! TA# 6E/IMATE H[ _M TEXT
MESSAGES Y S5T4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,TEXT .MESSAGES @3 #J3 #EJ3 #AJJ3
#AEJ3 #BJJ
.,MON?LY .BILL @3 4#DJ3 @8@3 @8@3 @8@3
@8
B4 .,WRIT+ .A .,MODEL ,WRITE AN EQU,N
=! SITU,N4 ,SOLVE X 6F9D EXACTLY H[ _M
TEXT MESSAGES Y S5T4
C4 .,-P>+ .,ANSW]S ,IS YR E/IMATE F "P
7A7 -PATI# )! EXACT ANSW] F "P 7;B78
.,EXPLA94
,,EXAMPLE #C
.ON P4 #CE = ,EXS4 #BI-CJ
#BI4 .,,WOOD .,,%OP ,Y H A PIECE (
WOOD T IS #GB 9*ES L;G4 ,Y CUT ! WOOD
96?REE PIECES4 ,! SECOND PIECE IS #F
9*ES L;G] ?AN ! F/ PIECE4 ,! ?IRD PIECE
IS #F 9*ES L;G] ?AN ! SECOND PIECE4
,DRAW A DIAGRAM & !N WRITE & SOLVE AN
EQU,N 6F9D ! L5G?S (! ?REE PIECES4
#CJ4 .,,PO/]S ,Y WANT 6TAPE FIVE PO/]S
ON A WALL S T ! SPACES 2T PO/]S >E !
SAME4 ,Y AL WANT ! SPACES AT ! LEFT & "R
(! GR\P ( PO/]S 6BE ?REE "TS ! SPACE 2T
ANY TWO ADJAC5T PO/]S4 ,! WALL IS #AE
FEET WIDE &! PO/]S >E #A.E FEET WIDE4
,DRAW A DIAGRAM & !N WRITE & SOLVE AN
EQU,N 6F9D H[ 6POSI;N ! PO/]S4
,,EXAMPLE #D
ON P4 #CF
= ,EXS4 #CA-CB
#CA4 .,,PACK+ .,,WEI<T ,A MOV+ -PANY
WEI<S #BJ BOXES Y H PACK$ T 3TA9 EI
BOOKS OR CLO!S & SAYS ! TOTAL WEI<T IS
#DJD P.DS4 ,Y "K T A BOX ( BOOKS WEI<S
#DJ P.DS &A BOX ( CLO!S WEI<S #G P.DS4
,WRITE & SOLVE AN EQU,N 6F9D H[ _M BOXES
( BOOKS & H[ _M BOXES ( CLO!S Y PACK$4
#CB4 .,,MULTI-.,,/EP .,,PRO#M ,A
DUA?LON 3SI/S (A RUN1 A BIKE RIDE1 &A
SECOND RUN4 ,USE ! 9=M,N 2L AB ! AV]AGE
RATES ( "O "PICIPANT :O -PLET$ A #EE
KILOMET] DUA?LON 9 #B H\RS #CE M9UTES4
A4 .,MODEL ,WRITE A V]BAL MODEL T %[S
! RACE 4T.E Z ! SUM (! TOTAL RUNN+ 4T.E
&! BIK+ 4T.E4
B4 .,TRANSLATE ,WRITE AN EQU,N BAS$ ON
! V]BAL MODEL4
C4 .,SOLVE ,SOLVE ! EQU,N 6F9D H[ M*
"T ! "PICIPANT SP5T RUNN+ & H[ M* "T !
"PICIPANT SP5T BIK+4
D4 .,*ECK ,F9D ! TOTAL RUNN+ 4T.E &!
BIK+ 4T.E1 & V]IFY T _! SUM IS #EE
KILOMET]S4
#CC4 .,,*ALL5GE ,Y >E HANG+ FLI]S >.D
A CYL9DRICAL KIOSK T HAS A DIAMET] ( #E
FEET4 ,Y WANT 6HANG #AE FLI]S T >E #H.E
9*ES WIDE S !Y >E EV5LY SPAC$4 ,H[ F>
A"P %D ! FLI]S 2 PLAC$8
-------------------------------------#DJ
,,MIX$ ,,REVIEW
,WRITE AN EXPRES.N 6ANSW] ! "Q4 @7 P4
#IHD @7
.#CD4 ,A VIDEO R5TAL CO/S 4#B.HE & HAS
A LATE FEE ( 4#A.JJ P] "D4 ,:AT IS !
TOTAL CO/ IF Y RETURN ! VIDEO .;D "DS
LATE8
.#CE4 ,Y WANT 6L1VE A #BJ@3P TIP AT A
RE/AURANT4 ,:AT IS ! TOTAL AM.T Y %D PAY
IF YR M1L CO/S .;X DOLL>S8
,GRAPH ! NUMB]S ON A NUMB] L9E4 @7 P4
#B @7
.#CF4
.#CG4
.#CH4
,GRAPH ! NUMB]S ON A NUMB] L9E4 @7 P4
#B @7
.#CI4 #C .;N #D :5 .;N .K #E
.#DJ4 --#B .;P #B :5 .;P .K --#C
.#DA4 .;R #B @+ .;R #C :5 .;R .K --#A
.#DB4 @7 .;B @+ #G7 #B @+ .;B #B :5
.;B .K #B
.#DC4 .;J #C -- #D .;J :5 .;J .K --#C
.#DD4 -- .;M #B @+ .;M #D :5 .;M .K #E
.,,PREVIEW ,PREP>E = ,LESSON #A.F 9
,EXS4 #DE-EC4
,SOLVE ! EQU,N4 ,*ECK YR SOLU;N1 @7 P4
#AH @7
.#DE4 .;X @+ #H .K --#G
.#DF4 --#C .;Y .K #AJB
.#DG4
.#DH4 #D .;B -- #C .K #AG
.#DI4 .;C @+ #BE .K --#BJ
.#EJ4 --#B .;D @+ #H .K --#BB
.#EA4 #D .;J @+ #AB .K #F .;J -- #G
.#EB4 #C .;P -- #AE .K #D .;P -- #A
.#EC4 #G7 .;W @+ #A7 .K #C7 .;W @+ #E7
,,QUIZ .= .,LESSONS .#A..C-.A..E
,SOLVE ! EQU,N4 ,*ECK YR SOLU;N4 @7 P4
#AH @7
#A4 #E .;B -- #B .K #H
#B4 #B .;D -- #C .K #H .;D @+ #AE
#C4 #B7 .;M -- #D7 .K .;M @+ #B
#D4
,SOLVE ! EQU,N = .;Y @4 ,!N F9D !
VALUE ( .;Y =! GIV5 VALUE ( .X4 @7 P4
#BF @7
#E4 #D .;X @+ .;Y .K #AB2 .;X .K #D
#F4 #C .;X -- #B .;Y .K #AD2 .;X .K #F
#G4 #C .XY -- #D .;X .K #AI2 .;X .K #B
#H4 #AA .;Y @+ #B .XY .K #I2 .;X .K
--#E
,LOOK =A PATT]N 9 ! TA#4 ,!N WRITE AN
EQU,N T REPRES5TS ! TA#4 @7 P4 #CD @7
#I4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #J3 #A3 #B3 #C
.;Y @3 #J3 #AC3 #BF3 #CI
#AJ4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #J3 #A3 #B3 #C
.;Y @3 --#E3 --#B3 #A3 #D
#AA4 .,,TUTOR+ .,,FEE ,A *ESS TUTOR
*>GES A FEE =! F/ LESSON T IS #A.E "TS !
FEE = LAT] LESSONS4 ,Y SP5D 4#CAE = #AJ
LESSONS4 ,H[ M* DOES ! F/ LESSON CO/8
,H[ M* DOES A LAT] LESSON CO/8 @7 P4 #CD
@7
#AB4 .,,FL[] .,,PRICES ,Y BUY "S CALLA
LILIES & PEONIES AT A FL[] /ORE4 ,CALLA
LILIES CO/ 4#C.EJ EA* & PEONIES CO/
4#E.EJ EA*4 ,! TOTAL CO/ ( #AB FL[]S IS
4#EB4 ,H[ _M CALLA LILIES & H[ _M
PEONIES DID Y BUY8 @7 P4 #CD @7
.,,EXTRA .,,PRACTICE = ,LESSON #A.E1
P4 #AJAJ
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
-------------------------------------#DA
#A.F ,SOLVE ,L9E> ,9EQUALITIES
.,2F ,Y SOLV$ L9E> EQU,NS4
.,N[ ,Y W SOLVE L9E> 9EQUALITIES4
.,:Y8 ,S Y C DESCRIBE TEMP]ATURE
RANGES1 Z 9 ,EX4 #ED4
,KEY ,VOCABUL>Y
99 .L9E> .9EQUAL;Y
99 .-P.D .9EQUAL;Y
99 .EQUIVAL5T .9EQUALITIES
,SIDEB>3
,/&>DS
.,PREP>E .= .#A..J .,/UD5TS .SOLVE
EQU,NS & .9EQUALITIES 9VOLV+ ABSOLUTE
VALUE4
,A .L9E> .9EQUAL;Y 9 "O V>IA# C 2
WRITT5 9 "O (! FOLL[+ =MS1 ": .A & .;B
>E R1L NUMB]S & .A @6.K #J3
.AX @+ .;B "K #J
.AX @+ .;B .1 #J
.AX @+ .;B "K.K #J
.AX @+ .;B .1.K #J
,A .SOLU;N ( AN 9EQUAL;Y 9 "O V>IA# IS
A VALUE T1 :5 SUB/ITUT$ =! V>IA#1
RESULTS 9 A TRUE /ATE;T4 ,! .GRAPH ( AN
9EQUAL;Y 9 "O V>IA# 3SI/S ( ALL PO9TS ON
A NUMB] L9E T REPRES5T SOLU;NS4
,,EXAMPLE #A ,GRAPH SIMPLE 9EQUALITIES
A4 ,GRAPH .;X "K #B4
,! SOLU;NS >E ALL R1L NUMB]S LESS ?AN
#B4
,AN OP5 DOT IS US$ 9 ! GRAPH 69DICATE
#B IS .N A SOLU;N4
B4 ,GRAPH .;X .1 --#A4
,! SOLU;NS >E ALL R1L NUMB]S GRT] ?AN
OR EQUAL TO --#A4
,A SOLID DOT IS US$ 9 ! GRAPH 69DICATE
--#A .IS A SOLU;N4
.,,-P.D .,,9EQUALITIES ,A .-P.D
.9EQUAL;Y 3SI/S ( TWO SIMPLE 9EQUALITIES
JO9$ BY 8&0 OR 8OR40
,,EXAMPLE #B ,GRAPH -P.D 9EQUALITIES
,,R1D ,,9EQUALITIES
,! -P.D 9EQUAL;Y --#A "K.;X"K.#B IS
ANO!R WAY ( WRIT+ 8.;X .1 --#A .& .;X "K
#B04
A4 ,GRAPH --#A "K .;X "K #B4
,! SOLU;NS >E ALL R1L NUMB]S T >E GRT]
?AN --#A & LESS ?AN #B4
B4 ,GRAPH .;X "K --#B OR .;X .1 #A4
,! SOLU;NS >E ALL R1L NUMB]S T >E LESS
?AN OR EQUAL TO --#B OR GRT] ?AN #A4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #A &
.#B
,GRAPH ! 9EQUAL;Y4
#A4 .;X .1 --#E
#B4 .;X "K.K #C
#C4 --#C "K.K .;X "K #A
#D4 .;X "K #A OR .;X .1.K #B
-------------------------------------#DB
.,,SOLV+ .,,9EQUALITIES ,6SOLVE A L9E>
9EQUAL;Y 9 "O V>IA#1 Y ISOLATE ! V>IA#
US+ TRANS=M,NS T PRODUCE .EQUIVAL5T
.9EQUALITIES @1 : >E 9EQUALITIES T H !
SAME SOLU;NS Z ! ORIG9AL 9EQUAL;Y4
,,KEY ,,3CEPT
,= YR ,NOTEBOOK
,TRANS=M,NS ,T ,PRODUCE ,EQUIVAL5T
,9EQUALITIES
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,TRANS=M,N APPLI$ 69EQUAL;Y3 ,ORIG9AL
9EQUAL;Y3 ,EQUIVAL5T 9EQUAL;Y
.,ADD ! SAME NUMB] 6EA* SIDE4 @3 .;X
-- #G "K #D @3 .;X "K#AA
.,SUBTRACT ! SAME NUMB] F EA* SIDE4 @3
.;X @+ #C.1 --;L @3 .;X .1 --#D
.,MULTIPLY EA* SIDE 0! SAME .POSITIVE
NUMB]4 @3 @3 .;X .1 #BJ
.,DIVIDE EA* SIDE 0! SAME .POSITIVE
NUMB]4 @3 #E .;X "K #AE @3 .;X "K #C
.,MULTIPLY EA* SIDE 0! SAME .NEGATIVE
NUMB] & .REV]SE ! 9EQUAL;Y4 @3 -- .;X "K
#AG @3 .;X .1 --#AG
.,DIVIDE EA* SIDE 0! SAME .NEGATIVE
NUMB] & .REV]SE ! 9EQUAL;Y4 @3 --#I .;X
.1 #DE @3 .;X "K --#E
,,EXAMPLE #C ,SOLVE AN 9EQUAL;Y )A
V>IA# ON "O SIDE
,,ANO!R ,,WAY
,= ALT]NATIVE ME?ODS = SOLV+ ! PRO#M 9
,EXAMPLE #C1 TURN 6PAGE #DH =! ,PRO#M
,SOLV+ ,"W%OP4
.,,FAIR ,Y H 4#EJ 6SP5D AT A C.TY
FAIR4 ,Y SP5D 4#BJ = ADMIS.N4 ,Y WANT
6PLAY A GAME T CO/S 4#A.EJ4 ,DESCRIBE !
POSSI# NUMB]S ( "TS Y C PLAY ! GAME4
,SOLU;N
.,,/EP .#A ,WRITE A V]BAL MODEL4 ,!N
WRITE AN 9EQUAL;Y4
,AN 9EQUAL;Y IS #BJ @+ #A.E;G"K #EJ4
.,,/EP .#B .,SOLVE ! 9EQUAL;Y4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#BJ @+ #A.E .;G "K.K #EJ @3 .,WRITE
.9EQUAL;Y4
#A.E;G "K.K #CJ3 ..,SUBTRACT #BJ F EA*
.SIDE4
.;G "K.K #BJ @3 ..,DIVIDE EA* SIDE
0#A..E4
,Y C PLAY ! GAME #BJ "TS OR FEW]4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
-------------------------------------#DC
,,EXAMPLE #D ,SOLVE AN 9EQUAL;Y )A
V>IA# ON BO? SIDES
,,AVOID ,,]RORS
,DON'T =GET 6REV]SE ! 9EQUAL;Y SYMBOL
IF Y MULTIPLY OR DIVIDE EA* SIDE ( AN
9EQUAL;Y 0A NEGATIVE NUMB]4
,SOLVE #E .;X @+ #B .1 #G .;X -- #D4
,!N GRAPH ! SOLU;N4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#E .;X @+ #B .1 #G .;X -- #D @3
.,WRITE .ORIG9AL .9EQUAL;Y4
-- .#B;X @+ #B .1 --#D @3 ,SUBTRACT #G
.;X F EA* SIDE4
-- #B .;X .1 --#F @3 ..,SUBTRACT #B F
EA* .SIDE4
.;X "K #C @3 ..,DIVIDE EA* SIDE BY
--#B & REV]SE ! .9EQUAL;Y4
,! SOLU;NS >E ALL R1L NUMB]S LESS ?AN
#C4 ,! GRAPH IS %[N 2L4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #C &
.#D
,SOLVE ! 9EQUAL;Y4 ,!N GRAPH ! SOLU;N4
#E4 #D .;X @+ #I "K #BE
#F4 #A--#C .;X .1.K --#AD
#G4 #E .;X -- #G "K.K #F .;X
#H4 #C -- .;X .1 .;X -- #I
,,EXAMPLE #E ,SOLVE AN 8&0 -P.D
9EQUAL;Y
,SOLVE --#D "K #F .;X -- #AJ "K #AD4
,!N GRAPH ! SOLU;N4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--#D "K #F .;X -- #AJ "K #AD @3
.,WRITE .ORIG9AL .9EQUAL;Y4
--#D @+ #AJ "K #F .;X -- #AJ @+ #AJ
"K.K #AD @+ #AJ @3 ..,ADD #AJ 6EA*
.EXPRES.N4
#F "K #F .;X "K.K #BD @3 .,SIMPLIFY4
#A "K .;X "K.K #D @3 ..,DIVIDE EA*
EXPRES.N 0.#F4
,! SOLU;NS >E ALL R1L NUMB]S GRT] ?AN
#A & LESS ?AN OR EQUAL 6#D4 ,! GRAPH IS
%[N 2L4
,,EXAMPLE #F ,SOLVE AN 8OR0' -P.D
9EQUAL;Y
,SOLVE #C .;X @+ #E .1.K #AA OR #E .;X
-- #G "K.K #BC4 ,!N GRAPH ! SOLU;N4
,SOLU;N
,A SOLU;N ( ? -P.D 9EQUAL;Y IS A
SOLU;N ( .EI ( XS "PS4
,F/ ,9EQUAL;Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#C .;X @+ #E "K.K #AA @3 .,WRITE .F/
.9EQUAL;Y4
#C .;X "K.K #F @3 ..,SUBTRACT #E F EA*
.SIDE4
.;X "K.K #B @3 ..,DIVIDE EA* SIDE
0.#C4
,SECOND ,9EQUAL;Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#E .;X -- #G .1.K #BC @3 .,WRITE
.SECOND .9EQUAL;Y4
#E .;X .1.K #CJ @3 ..,ADD #G 6EA*
.SIDE4
.;X .1.K #F @3 ..,DIVIDE EA* SIDE
0.#E4
,! GRAPH IS %[N 2L4 ,! SOLU;NS >E ALL
R1L NUMB]S ..LESS ?AN OR EQUAL 6.#B OR
..GRT] ?AN OR EQUAL 6.#F4
-------------------------------------#DD
,,EXAMPLE #G ,WRITE & USE A -P.D
9EQUAL;Y
.,,BIOLOGY ,A MONITOR LIZ>D HAS A
TEMP]ATURE T RANGES F #AH;DG;,C
6#CD;DG,C4 ,WRITE ! RANGE ( TEMP]ATURES
Z A -P.D 9EQUAL;Y4 ,!N WRITE AN 9EQUAL;Y
GIV+ ! TEMP]ATURE RANGE 9 DEGREES
,FAHR5HEIT4
,SOLU;N
,! RANGE ( TEMP]ATURES ;,C C 2
REPRES5T$ 0! 9EQUAL;Y #AH "K.K .;,C "K.K
#CD4 ,LET .;,F REPRES5T ! TEMP]ATURE 9
DEGREES ,FAHR5HEIT4
,PICTURE3 MONITOR LIZ>D
,,USE ,A ,,=MULA
,9 ,EXAMPLE #G1 USE ! TEMP]ATURE =MULA
@4
,! TEMP]ATURE (! MONITOR LIZ>D RANGES
F #FD.D;DG;,F 6#IC.B;DG,F4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #E1F1
& .#G
,SOLVE ! 9EQUAL;Y4 ,!N GRAPH ! SOLU;N4
#I4 --#A "K #B .;X @+ #G "K #AI
#AJ4 --#H "K --.;X -- #E "K.K #F
#AA4 .;X @+ #D "K.K #I OR .;X -- #C
.1.K #G
#AB4 #C .;X -- #A "K --#A OR #B .;X @+
#E .1.K #AA
.#AC4 .,,:AT .,,IF8 ,9 ,EXAMPLE #G1
WRITE A -P.D 9EQUAL;Y =A LIZ>D ^:
TEMP]ATURE RANGES F #AE;DG;,C 6#CJ;DG,C4
,!N WRITE AN 9EQUAL;Y GIV+ ! TEMP]ATURE
RANGE 9 DEGREES ,FAHR5HEIT4
#A.F ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#B = ,EXS4 #AC1BE1 & #EE
.K .,,/&>DIZ$ .,,TE/ .,,PRACTICE
,EXS4 #B1AE1 #CF1 #EF1 & #EI
,,SKILL ,,PRACTICE
#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,!
SET ( ALL PO9TS ON A NUMB] L9E T
REPRES5T SOLU;NS ( AN 9EQUAL;Y IS CALL$
! @8 (! 9EQUAL;Y4
#B4 .,,WRIT+ ,! F/ TRANS=M,N ON PAGE
#DB C 2 WRITT5 Z FOLL[S3
,IF .A1 .;B @1 & .;C >E R1L NUMB]S &
.A .1 .;B @1 !N .A @+ .;C .1 .;B @+ .;C
@4
,WRITE SIMIL> /ATE;TS =! O!R
TRANS=M,NS LI/$ ON PAGE #DB @4
,,EXAMPLE #A
.ON P4 #DA = ,EXS4 #C-AJ
.,,GRAPH+ .,,9EQUALITIES ,GRAPH !
9EQUAL;Y4
#C4 .;X .1 #D
#D4 .;X "K --#A
#E4 .;X "K.K --#E
#F4 .;X .1.K #C
#G4 #F .1.K .;X
#H4 --#B "K .;X
#I4 .;X .1.K --#C.E
#AJ4 .;X "K #B.E
-------------------------------------#DE
,,EXAMPLE #B
ON P4 #DA = ,EXS4 #AA-BA
,,WRIT+ ,,-P.D ,,9EQUALITIES ,WRITE !
-P.D 9EQUAL;Y T IS REPRES5T$ 0! GRAPH4
.#AA4
.#AB4
;L#C4
.#AD4
#AE4 ..,,MULTIPLE ,,*OICE ,:AT -P.D
9EQUAL;Y IS GRAPH$ .2L8
,A --;L "K .;X "K #C
;,B .;X "K.K --#A OR .;X .1 #C
;,C .;X "K --#A OR .;X .1.K #C
;,D .;X .1 --#A OR .;X "K.K #C
,,GRAPH+ ,,-P.D ,,9EQUALITIES ,GRAPH !
-P.D 9EQUAL;Y4
.#AF4 #B "K.K .;X "K.K #E
.#AG4 --#C "K .;X "K #D
.#AH4 #E "K.K .;X "K #AJ
.#AI4 .;X "K #J OR .;X .1 #B
.#BJ4 .;X "K.K --#A OR .;X .1 #A
.#BA4 .;X .1 --#B OR .;X "K --#E
,,EXAMPLES
#C & #D
ON PP4 #DB-DC = ,EXS4 #BB-CE
,,SOLV+ ,,9EQUALITIES ,SOLVE !
9EQUAL;Y4 ,!N GRAPH ! SOLU;N4
.#BB4 .;X @+ #D .1 #AJ
.#BC4 .;X -- #C "K --#E
.#BD4 #D .;X -- #H .1 --#D
#BE4 #AE--#C .;X .1 #C
.#BF4 #AA @+ #H .;X .1 #G
.#BG4
.#BH4 #B .;X -- #F .1 #C -- .;X
.#BI4 #D .;X @+ #AD "K #C .;X @+ #F
.#CJ4 #E--#H .;X "K.K #AI--;L#J .;X
.#CA4 #BA .;X @+ #G "K #C .;X @+ #AF
.#CB4 #AH @+ #B .;X "K.K #I .;X @+ #D
.#CC4 #B7 .;X -- #D7 .1 #D .;X @+ #F
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 SOLV+ ! 9EQUAL;Y4
.#CD4
.#CE4
.#CF4 ..,,OP5-,,5D$ ,,MA? ,WRITE TWO
DI6]5T 9EQUALITIES (! =M AX @+ ;B .1 ;C
T H A SOLU;N ( ;X .1 .#E4
,,EXAMPLE #E
ON P4 #DC = ,EXS4 #CG-DB
8,,&0 ,,-P.D ,,9EQUALITIES ,SOLVE !
9EQUAL;Y4 ,!N GRAPH ! SOLU;N4
.#CG4 --#E "K .;X @+ #A "K #D
.#CH4 #B "K.K .;X -- #C "K #F
.#CI4 --#C "K #D -- .;X "K #C
.#DJ4 #B "K #C .;X -- #A "K.K #F
.#DA4 --#D "K #B @+ #D .;X "K #J
.#DB4 #J "K.K .;X @+ #C "K.K #D
,,EXAMPLE #F
ON P4 #DC = ,EXS4 #DC-DH
8,,OR0 ,,-P.D ,,9EQUALITIES ,SOLVE !
9EQUAL;Y4 ,!N GRAPH ! SOLU;N4
.#DC4 .;X @+ #A "K --#C OR .;X -- #B
.1 #J
.#DD4 .;X -- #D "K.K --#F OR .;X @+ #B
.1 #E
.#DE4 #B .;X -- #C "K --#D OR #C .;X
@+ #A .1.K #D
.#DF4 #B @+ #C .;X "K --#AC OR #D @+
#B .;X .1 #G
.#DG4 #J.C .;X -- #J.E "K --#A.G OR
#J.D .;X .1.K #B.D
.#DH4 --;X--#D .1.K #A OR #B--#E .;X
"K.K --#H
,,*ALL5GE ,SOLVE ! 9EQUAL;Y4 ,IF "! IS
NO SOLU;N1 WRITE .NO .SOLU;N4 ,IF !
9EQUAL;Y IS ALW TRUE1 WRITE .ALL .R1L
.NUMB]S4
.#DI4 #B7 .;X -- #D7 .1 #B .;X @+ #A
.#EJ4 #D .;X -- #E "K.K #D7 .;X @+ #B7
.#EA4 #B7#C .;X -- #A7 .1 #C7#B .;X @+
#C7
-------------------------------------#DF
,,PRO#M ,,SOLV+
,,EXAMPLE #C
ON P4 #DB = ,EXS4 #EB-EC
#EB4 .,,SWIMM+ ,Y H BUDGET$ 4#AJJ
6IMPROVE YR SWIMM+ OV] ! SUMM]4 ,AT YR
LOCAL POOL1 X CO/S 4#EJ 6JO9 ! SWIM
ASSOCI,N & 4#E = EA* SWIM CLASS4 ,WRITE
& SOLVE AN 9EQUAL;Y 6F9D ! POSSI# NUMB]S
( SWIM CLASSES Y C ATT5D )9 YR BUDGET4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#EC4 .,,VIDEO .,,3TE/ ,Y & "S FRS H
RAIS$ 4#BEJ 6HELP MAKE A VIDEO =A 3TE/4
,Y NE$ 4#CE 6BUY VIDEOTAPES4 ,X CO/S
4#DE P] "D 6R5T ! VIDEO CAM]A4 ,WRITE &
SOLVE AN 9EQUAL;Y 6F9D ! POSSI# NUMB]S (
"DS Y C R5T ! VIDEO CAM]A4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#ED4 .,,WAKEBO>D+ ,:AT Y WE> :5 Y
WAKEBO>D DEP5DS ON ! AIR TEMP]ATURE4
,COPY & -PLETE ! TA# 0WRIT+ AN 9EQUAL;Y
= EA* TEMP]ATURE RANGE4 ,ASSUME EA*
RANGE 9CLUDES ! L[] TEMP]ATURE B N !
HI<] TEMP]ATURE4 7,! F/ 9EQUAL;Y HAS BE5
WRITT5 = Y47
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,TEMP]ATURE3 ,GE>3 ,9EQUAL;Y
#FJ;DG;,F 6#FE;DG;,F3 ,FULL WETSUIT3
#FJ "K.K #G "K #FE
#FE;DG,FTO#GB;DG;,F3 ,FULL LEG
WETSUIT3 @8
#GB;DG;,F 6#HJ;DG;,F3 ,WETSUIT TRUNKS3
@8
#HJ;DG;,F OR W>M]3 ,NO SPECIAL GE>3 @8
#EE4 .,,BOTANY ,9 ,OLYMPIC ,N,NAL ,P>K
9 ,WA%+TON1 DI6]5T PLANTS GR[ DEP5D+ ON
! ELEV,N1 Z %[N 9 ! DIAGRAM4 ,ASSUME EA*
RANGE 9CLUDES ! L[] ELEV,N B N ! HI<]
ELEV,N4
A4 ,WRITE AN 9EQUAL;Y = ELEV,NS 9 !
L[L& Z"O4
B4 ,WRITE AN 9EQUAL;Y = ELEV,NS 9 !
ALP9E & SUBALP9E Z"OS -B9$4
C4 ,WRITE AN 9EQUAL;Y = ELEV,NS .N 9 !
MONTANE Z"O4
#EF4 .,,MULTIPLE .,,*OICE ,CANOE R5TAL
CO/S 4#AH =! F/ TWO H\RS & 4#C P] H\R AF
T4 ,Y WANT 6CANOE = M ?AN #B H\RS B C
SP5D NO M ?AN 4#CJ4 ,: 9EQUAL;Y
REPRES5TS ! SITU,N1 ": .;T IS ! TOTAL
NUMB] ( H\RS Y C CANOE8
,A #AH @+ .;T "K.K #CJ
;,B #AH @+ #C .;T "K.K #CJ
;,C #AH @+ #C7 .;T @+ #B7 "K.K #CJ
;,D #AH @+ #C7 .;T -- #B7 "K.K #CJ
.K ..,,"W$-,,\ ,,SOLU;NS ON P4.,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
-------------------------------------#DG
,,EXAMPLE #G
ON P4 #DD = ,EXS4 #EG--#EH
.#EG4 .,,LAPTOP .,,-PUT]S ,A -PUT]
MANUFACTUR] /ATES T XS LAPTOP -PUT] C
OP]ATE )9 A TEMP]ATURE RANGE ( #EJ;DG;,F
6#IE;DG;,F ,WRITE A -P.D 9EQUAL;Y =!
TEMP]ATURE RANGE4 ,!N REWRITE ! 9EQUAL;Y
9 DEGREES ,CELSIUS4
#EH4 .,,MULTI-.,,/EP .,,PRO#M ,ON A
C]TA9 HI<WAY1 "! IS A M9IMUM SPE$ ( #DE
MILES P] H\R &A MAXIMUM SPE$ ( #GJ MILES
P] H\R4
A4 ,WRITE A -P.D 9EQUAL;Y =! LEGAL
SPE$S ON ! HI<WAY4
B4 ,WRITE A -P.D 9EQUAL;Y =! ILLEGAL
SPE$S ON ! HI<WAY4
C4 ,WRITE EA* -P.D 9EQUAL;Y F "PS 7A7
& 7;B7 S T X EXPRESSES ! SPE$S 9
KILOMET]S P] H\R4 7#A MI #A.FA KM7
#EI4 .,,EXT5D$ .,,RESPONSE ,A MA? T1*]
ANN\NCES T GRADES W 2 CALCULAT$ 0A4+
#FE@3P (A /UD5T'S HOME"W SCORE1 #AE@3P
(! /UD5T'S QUIZ SCORE1 & #BJ@3P (!
/UD5T'S F9AL EXAM SCORE4 ,ALL SCORES
RANGE F #J 6#AJJ PO9TS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,"N3 ,HOME"W3 ,QUIZ3 ,EXAM
,AMY3 .#HD @3 .#HJ @3 .;W
,BRIAN3 .#HJ @3 .#AJJ @3 .;X
,CL>A3 .#GE @3 .#IE @3 .;Y
,DAN3 .#HJ @3 .#IJ @3 .;Z
A4 .,WRITE .,9EQUALITIES ,WRITE AN
9EQUAL;Y = EA* /UD5T T C 2 US$ 6F9D !
POSSI# F9AL EXAM SCORES T RESULT 9 A
GRADE ( #HE OR BETT]4
B4 .,SOLVE ,SOLVE ! 9EQUALITIES F "P
7A74
C4 .,9T]PRET ,= : /UD5TS IS A GRADE (
#HE OR BETT] POSSI#8 .,EXPLA94
#FJ4 .,,*ALL5GE ,Y >E %OPP+ = S+LE-USE
CAM]AS 6H& \ AT A "PY4 ,! "DLI<T CAM]AS
CO/ 4#B.GE &! FLA% CAM]AS CO/ 4#D.BE4 ,Y
M/ BUY EXACTLY #BJ CAM]AS & Y WANT 6SP5D
2T 4#FE & 4#GE1 9CLUSIVE4 ,WRITE & SOLVE
A -P.D 9EQUAL;Y = ? SITU,N4 ,!N LI/ ALL
! SOLU;NS T 9VOLVE :OLE NUMB]S ( CAM]AS4
,,MIX$ ,,REVIEW
.,,PREVIEW ,PREP>E = ,LESSON #A.G 9
,EXS4 #FA-FH4
,F9D ! M1N (! TWO NUMB]S1 @7 P4 #AJJE
@7
.#FA4 #I1 #AE
.#FB4 #BA1 #FC
.#FC4 #HJ1 #ABJ
.#FD4 #AFC1 #ABD
.#FE4 #AAF1 #ACE
.#FF4 #CBG1 #EBE
.#FG4 #E1
.#FH4
,SOLVE = .X4 ,!N F9D ! L5G? ( EA* SIDE
(! FIGURE1 @7 P4 #AH @7
.#FI4 ,P]IMET] .K #AI
.#GJ4 ,P]IMET] .K #CD
.#GA4 ,P]IMET] .K #EJ
,LOOK =A PATT]N 9 ! TA#4 ,!N WRITE AN
EQU,N T REPRES5TS ! TA#1 @7 P4 #CD @7
#GB4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #J3 #A3 #B3 #C
.;Y @3 #AB3 #BJ3 #BH3 #CF
#GC4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #J3 #A3 #B3 #C
.;Y @3 #DBE3 #CBE3 #BBE3 #ABE
.,,EXTRA .,,PRACTICE = ,LESSON #A.F1
P4 #AJAJ
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
-------------------------------------#DH
,PRO#M ,SOLV+ ,"W%OP ,LESSON #A.F3
,US+ ,ALT]NATIVE ,ME?ODS
,ANO!R ,WAY 6,SOLVE ,EXAMPLE #C1 PAGE
#DB
.,,MULTIPLE .,,REPRES5T,NS ,EXAMPLE #C
( ,LESSON #A.F 9VOLV$ SOLV+ AN 9EQUAL;Y
US+ ALGEBRA4 ,Y C AL SOLVE AN 9EQUAL;Y
US+ A TA# OR A GRAPH+ CALCULATOR'S .TE/
F1TURE1 : TELLS :5 AN 9EQUAL;Y IS TRUE
OR FALSE4
,,PRO#M
.,,FAIR ,Y H 4#EJ 6SP5D AT A C.TY
FAIR4 ,Y SP5D 4#BJ = ADMIS.N4 ,Y WANT
6PLAY A GAME T CO/S 4#A.EJ4 ,DESCRIBE !
POSSI# NUMB]S ( "TS Y C PLAY ! GAME4
,,ME?OD #A
.,US+ .A .,TA# ,"O ALT]NATIVE APPROA*
IS 6MAKE A TA# ( VALUES4
,SIDEB>3
,/&>DS
.,PREP>E .= .#A..J ..,/UD5TS SOLVE
EQU,NS & .9EQUALITIES 9VOLV+ ABSOLUTE
VALUE4
.,,/EP .#A .,WRITE AN EXPRES.N =!
TOTAL CO/ ( ADMIS.N & PLAY+ .;X GAMES4
.,,/EP .#B .,5T] ! EQU,N .;Y .K #BJ @+
#A.E4 .;X 96A GRAPH+ CALCULATOR4
.,,/EP .#C .,MAKE A TA# ( VALUES =!
EQU,N4
,PICTURE3 ,USE ,TBL,/>T .K #J & ,TBL
.K #A 6SEE ^! VALUES4
.,,/EP .#D .,SCROLL "? ! TA# ( VALUES
6F9D :5 ! TOTAL CO/ IS 4#EJ4 ,Y C SEE T
.;Y .K #EJ :5 .;X .K #BJ4
,! TA# SU7E/S T #BJ @+ #A.E .;X "K.K
#EJ :5 .;X "K.K #BJ4 ,S1 Y C PLAY ! GAME
AT ! FAIR #BJ "TS OR FEW]4
-------------------------------------#DI
,,ME?OD #B
.,US+ .A .,GRAPH ,ANO!R APPROA* IS
6USE A GRAPH4
,IF YR GRAPH+ CALCULATOR HAS A .TE/
F1TURE1 Y C 5T] ! 9EQUAL;Y & EVALUATE XS
TRU? = V>I\S VALUES ( .X4
99 ,:5 ! 9EQUAL;Y IS .TRUE @1 !
CALCULATOR RETURNS A #A4
99 ,:5 ! 9EQUAL;Y IS .FALSE @1 !
CALCULATOR RETURNS A #J4
.,,/EP .#A .,5T] .;Y .K 7#BJ @+ #A.E
.;X "K.K #EJ7 96A GRAPH+ CALCULATOR4
,PRESS ,7,,TE/7' 65T] ! "K.K SYMBOL4
.,,/EP .#B .,GRAPH ! RESULT4
,PICTURE3 ,! .;Y -VALUE IS #A = ALL
.;X -VALUES T MAKE ! 9EQUAL;Y TRUE4
.,,/EP .#C .,F9D ! PO9T ": ! 9EQUAL;Y
*ANGES F TRUE 6FALSE 0US+ ! .TRACE
F1TURE4
,! GRAPH SU7E/S T ! 9EQUAL;Y IS TRUE
:5 .;X "K #BJ4 ,S1 Y C PLAY ! GAME AT !
FAIR #BJ "TS OR FEW]4
,,PRACTICE
.#A4 .,,R1SON+ ,DET]M9E ! EQU,N T
GIVES ! TA# 2L4 ,= :AT ;X-VALUES IS .;Y
"K --#EJJ8
#B4 .,,GIFT ,Y H 4#AF.EJ 6SP5D =A FR'S
BIR?"D4 ,Y SP5D 4#C ON A C>D & WANT 6BUY
"S *OCOLATES T CO/ @4#.GE EA*4 ,:AT >E !
NUMB]S ( *OCOLATES Y C BUY8 ,SOLVE US+ A
TA# & US+ A GRAPH4
#C4 .,,SALESP]SON ,A SALESP]SON HAS A
WEEKLY SAL>Y ( 4#AEEJ & GETS A #E@3P
-MIS.N ON SALES4 ,:AT >E ! AM.TS !
SALESP]SON C SELL 6E>N AT L1/ 4#AIJJ P]
WEEK8 ,SOLVE US+ A TA# & US+ A GRAPH4
#D4 .,,WRIT+ .,EXPLA9 H[ 6USE A TA# L
! "O 2L 6SOLVE #J.E .;X -- #A.E "K
#C--#J.D .;X @4
-------------------------------------#EJ
,9VE/IGAT+ ,ALGEBRA ,ACTIV;Y3 #A.G
,ABSOLUTE ,VALUE ,EQU,NS & ,9EQUALITIES
,USE 2F LESSON #A.G
.,,MAT]IALS 99 #AC 9DEX C>DS NUMB]$ )!
9TEG]S F --#F 6#F
,,"Q
,:AT DOES ! SOLU;N ( AN ABSOLUTE VALUE
EQU,N OR 9EQUAL;Y LOOK L ON A NUMB] L9E8
,! .ABSOLUTE .VALUE (A NUMB] .;X @1
WRITT5 _\ .;X _\, IS ! 4T.E ! NUMB] IS F
#J ON A NUMB] L9E4 ,2C #B & --#B >E BO?
#B UNITS F #J1 _\#B_\ .K #B & _\--#B_\
.K #B4 ,! ABSOLUTE VALUE (A NUMB] IS N"E
NEGATIVE4
,,EXPLORE ,F9D SOLU;NS ( ABSOLUTE
VALUE EQU,NS & 9EQUALITIES
,"W )A "PN]4 ,PLACE ! NUMB]$ 9DEX C>DS
9 A R[ 6=M A NUMB] L9E4 ,!N TURN ALL !
C>DS FACE D[N4
,,/EP #A
,SOLVE EQU,NS
,TURN OV] C>DS 6REV1L NUMB]S T >E
SOLU;NS (! EQU,NS 2L4
A4 _\ .;X _\ .K #B
B4 _\ .;X -- #B_\ .K #A
C4 _\ .;X @+ #A_\ .K #C
,,/EP #B
,SOLVE 9EQUALITIES ) "K.K
,TURN OV] C>DS 6REV1L NUMB]S T >E
SOLU;NS (! 9EQUALITIES 2L4
D4 _\ .;X _\ "K.K #B
E4 _\ .;X -- #B_\ "K.K #A
F4 _\ .;X @+ #A_\ "K.K #C
,,/EP #C
,SOLVE 9EQUALITIES ) .1.K
,TURN OV] C>DS 6REV1L NUMB]S T >E
SOLU;NS (! 9EQUALITIES 2L4
G4 _\ .;X _\ .1.K #B
H4 _\ .;X -- #B_\ .1.K #A
I4 _\ .;X @+ #A_\ .1.K #C
,,DRAW ,,3CLU.NS ,USE YR OBS]V,NS
6-PLETE ^! EX]CISES
#A4 .,DESCRIBE ! SOLU;NS (! ABSOLUTE
VALUE EQU,NS 9 ,/EP #A4 ,W ALL ABSOLUTE
VALUE EQU,NS H ! SAME NUMB] ( SOLU;NS8
.,EXPLA94
#B4 .,-P>E ! SOLU;NS (! ABSOLUTE VALUE
9EQUALITIES 9 ,/EPS #B & #C4 ,H[ DOES !
9EQUAL;Y SYMBOL 7"K.K OR .1.K7 A6ECT !
PATT]N (! SOLU;NS8
-------------------------------------#EA
#A.G ,SOLVE ,ABSOLUTE ,VALUE ,EQU,NS
& ,9EQUALITIES
.,2F ,Y SOLV$ L9E> EQU,NS &
9EQUALITIES4
.,N[ ,Y W SOLVE ABSOLUTE VALUE EQU,NS
& 9EQUALITIES4
.,:Y8 ,S Y C DESCRIBE HE>+ RANGES (
ANIMALS1 Z 9 ,EX4 #HA4
,KEY ,VOCABUL>Y
99 ABSOLUTE VALUE
99 EXTRANE\S SOLU;N
,RECALL T ! .ABSOLUTE .VALUE (A NUMB]
.;X @1 WRITT5 _\;X_\1 IS ! 4T.E ! NUMB]
IS F #J ON A NUMB] L9E4 ,? "U/&+ (
ABSOLUTE VALUE C 2 EXT5D$ 6APPLY 6SIMPLE
ABSOLUTE VALUE EQU,NS4
,SIDEB>3
,/&>DS
#A.J ,/UD5TS SOLVE EQU,NS &
9EQUALITIES 9VOLV+ ABSOLUTE VALUE4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,9T]PRET+ ,ABSOLUTE ,VALUE ,EQU,NS
,,EXAMPLE #A ,SOLVE A SIMPLE ABSOLUTE
VALUE EQU,N
,SOLVE _\ .;X -- #E_\ .K #G4 ,GRAPH !
SOLU;N4
,SOLU;N
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
_\ .;X -- #E_\ .K #G @3 --@3 --@3
.,WRITE .ORIG9AL .EQU,N4
.;X -- #E .K --#G @3 OR3 .;X -- #E .K
#G @3 .,WRITE .EQUIVAL5T .EQU,NS4
.;X .K #E--#G @3 OR3 .;X .K #E @+ #G
@3 ,SOLVE =.' X4.-
.;X .K --#B @3 OR3 .;X .K #AB @3
.,SIMPLIFY4
,! SOLU;NS >E --#B & #AB4 ,^! >E !
VALUES ( .;X T >E #G UNITS AWAY F #E ON
A NUMB] L9E4 ,! GRAPH IS %[N 2L4
-------------------------------------#EB
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,SOLV+ AN ,ABSOLUTE ,VALUE ,EQU,N
,USE ^! /EPS 6SOLVE AN ABSOLUTE VALUE
EQU,N _\ .AX @+ .;B _\ .K .;C ": .;C .1
#J4
.,,/EP .#A .,WRITE TWO EQU,NS3 .AX @+
.;B .K .;C OR .AX @+ .;B .K -- .;C @4
.,,/EP .#B .,SOLVE EA* EQU,N4
.,,/EP .#C .,*ECK EA* SOLU;N 9 !
ORIG9AL ABSOLUTE VALUE EQU,N4
,,EXAMPLE #B ,SOLVE AN ABSOLUTE VALUE
EQU,N
,SOLVE _\#E .;X -- #AJ_\ .K #DE4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
_\#E .;X -- #AJ_\ .K #DE @3 --@3 --@3
.,WRITE .ORIG9AL .EQU,N4
#E .;X -- #AJ .K #DE @3 OR3 #E .;X --
#AJ .K --#DE @3 ..,EXPRES.N C EQUAL #DE
OR --.#DE4
#E .;X .K #EE @3 OR3 #E .;X .K --#CE
@3 ..,ADD #AJ 6EA* .SIDE4
.;X .K #AA @3 OR3 ;X .K --#G3
..,DIVIDE EA* SIDE 0.#E4
,! SOLU;NS >E #AA & --#G4 ,*ECK ^! 9 !
ORIG9AL EQU,N4
,,*ECK
_\#E .;X -- #AJ_\ .K #DE
_\#E7#AA7--#AJ_\ #DE
_\#DE_\ #DE
#DE .K #DE
_\#E .;X -- #AJ_\ .K #DE
_\#E7--#G7--#AJ_\ #DE
_\--#DE_\ #DE
#DE .K #DE
.,,EXTRANE\S .,,SOLU;NS ,:5 Y SOLVE AN
ABSOLUTE VALUE EQU,N1 X IS POSSI# =A
SOLU;N 6BE .EXTRANE\S4 ,AN .EXTRANE\S
.SOLU;N IS AN APP>5T SOLU;N T M/ 2
REJECT$ 2C X DOES N SATISFY ! ORIG9AL
EQU,N4
,,EXAMPLE #C ,*ECK = EXTRANE\S SOLU;NS
,SOLVE _\#B .;X @+ #AB_\ .K #D .X4
,*ECK = EXTRANE\S SOLU;NS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
_\#B .;X @+ #AB_\ .K #D .;X @3 --@3
--@3 .,WRITE .ORIG9AL .EQU,N4
#B .;X @+ #AB .K #D .;X @3 OR3 #B .;X
@+ #AB .K --#D .;X @3 ,EXPRES.N C EQUAL
#D .;X OR --#D .;X @4
#AB .K #B .;X @3 OR3 #AB .K --#F .;X
@3 ,SUBTRACT #B .;X F EA* SIDE4
#F .K .;X @3 OR3 --#B .K .;X @3 ,SOLVE
=.' ;X @4
,*ECK ! APP>5T SOLU;NS 6SEE IF EI IS
EXTRANE\S4
,,AVOID ,,]RORS
,ALW *ECK YR SOLU;NS 9 ! ORIG9AL EQU,N
6MAKE SURE T !Y >E N EXTRANE\S4
,,*ECK
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
_\#B .;X @+ #AB_\ .K #D .;X @3 _\#B
.;X @+ #AB_\ .K #D .;X
_\#B7#F7 @+ #AB_\ #D7#F7 @3 _\#B7--#B7
@+ #AB_\ #D7--#B7
_\#BD_\ #BD @3 _\#H_\ --#H
#BD .K #BD @3 #H @6.K --#H
,! SOLU;N IS #F4 ,REJECT --#B 2C X IS
AN EXTRANE\S SOLU;N4
-------------------------------------#EC
..,,GUID$ ,,PRACTICE = ,EXAMPLES #A1B1
& .#C
,SOLVE ! EQU,N4 ,*ECK = EXTRANE\S
SOLU;NS4
.#A4 _\ .;X _\ .K #E
.#B4 _\ .;X -- #C_\ .K #AJ
.#C4 _\ .;X @+ #B_\ .K #G
.#D4 _\#C .;X -- #B_\ .K #AC
.#E4 _\#B .;X @+ #E_\ .K #C .;X
.#F4 _\#D .;X -- #A_\ .K #B .;X @+ #I
.,,9EQUALITIES ,Y C SOLVE AN ABSOLUTE
VALUE 9EQUAL;Y 0REWRIT+ X Z A -P.D
9EQUAL;Y & !N SOLV+ EA* "P4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,ABSOLUTE ,VALUE ,9EQUALITIES
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,9EQUAL;Y3 ,EQUIVAL5T =M3 ,GRAPH (
SOLU;N
_\ .AX @+ .;B _\ "K .;C @3 -- .;C "K
.AX @+ .;B "K .;C @3
_\ .AX @+ .;B _\ "K.K .;C @3 -- .;C
"K.K .AX @+ .;B "K.K .;C @3
_\ .AX @+ .;B _\ .1 .;C @3 .AX @+ .;B
"K -- .;C OR .AX @+ .;B .1 .;C @3
_\ .AX @+ .;B _\ .1.K .;C @3 .AX @+
.;B "K.K -- .;C OR .AX @+ .;B .1.K .;C
@3
..,,EXAMPLE #D ,SOLVE AN 9EQUAL;Y (!
=M _\ AX @+ ;B_\ .1 .;C
,SOLVE _\#D .;X @+ #E_\ .1 #AC4 ,!N
GRAPH ! SOLU;N4
,SOLU;N
,! ABSOLUTE VALUE 9EQUAL;Y IS
EQUIVAL5T 6#D .;X @+ #E "K --#AC OR #D
.;X @+ #E .1 #AC4
,! SOLU;NS >E ALL R1L NUMB]S LESS ?AN
--#I OR GRT] ?AN #B4 ,! GRAPH IS %[N 2L4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#D
,SOLVE ! 9EQUAL;Y4 ,!N GRAPH ! SOLU;N4
#G4 _\ .;X @+ #D_\ .1.K #F
#H4 _\#B .;X -- #G_\ .1 #A
#I4 #C_\ .;X @+ #E_\ .1.K #AJ
-------------------------------------#ED
,,EXAMPLE #E ,SOLVE AN 9EQUAL;Y (! =M
_\ .AX @+ .;B _\ "K.K .;C
,,R1D+
.,TOL].E IS ! MAXIMUM A3EPTA# DEVI,N (
AN ITEM F "S ID1L OR M1N M1SURE;T4
.,,BASEBALL ,A PROFES.NAL BASEBALL %D
WEI< #E.ABE \NCES1 )A .TOL].E ( #J.ABE
\NCE4 ,WRITE & SOLVE AN ABSOLUTE VALUE
9EQUAL;Y T DESCRIBES ! A3EPTA# WEI<TS =A
BASEBALL4
,SOLU;N
.,,/EP .#A .,WRITE A V]BAL MODEL4 ,!N
WRITE AN 9EQUAL;Y4
.,,/EP .#B .,SOLVE ! 9EQUAL;Y4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
_\ .;W -- #E.ABE_\ "K.K #J.ABE @3
.,WRITE .9EQUAL;Y4
--#J.ABE "K.K .;W -- #E.ABE "K.K
#J.ABE @3 ..,WRITE EQUIVAL5T -P.D
.9EQUAL;Y4
#E "K.K .;W "K.K #E.BE @3 ..,ADD
#E.ABE 6EA* .EXPRES.N4
,S1 A BASEBALL %D WEI< 2T #E \NCES &
#E.BE \NCES1 9CLUSIVE4 ,! GRAPH IS %[N
2L4
,,EXAMPLE #F ,WRITE A RANGE Z AN
ABSOLUTE VALUE 9EQUAL;Y
.,,GYMNA/ICS ,! ?ICK;S (! MATS US$ 9 !
R+S1 P>ALLEL B>S1 & VAULT EV5TS M/ 2 2T
#G.E 9*ES & #H.BE 9*ES1 9CLUSIVE4 ,WRITE
AN ABSOLUTE VALUE 9EQUAL;Y DESCRIB+ !
A3EPTA# MAT ?ICK;SES4
,,REVIEW ,,M1N
,= HELP ) F9D+ A M1N1 SEE P4 #AJJE @4
,SOLU;N
.,,/EP .#A .,CALCULATE ! M1N (!
EXTREME MAT ?ICK;SES4
.,,/EP .#B .,F9D ! TOL].E 0SUBTRACT+ !
M1N F ! UPP] EXTREME4
,TOL].E .K #H.BE--#G.HGE .K #J.CGE
.,,/EP .#C .,WRITE A V]BAL MODEL4 ,!N
WRITE AN 9EQUAL;Y4
,A MAT IS A3EPTA# IF XS ?ICK;S .;T
SATISFIES _\;T--#G.HGE_\ "K.K #J.CGE4
-------------------------------------#EE
..,,GUID$ ,,PRACTICE = ,EXAMPLES #E &
.#F
,SOLVE ! 9EQUAL;Y4 ,!N GRAPH ! SOLU;N4
#AJ4 .;X @+ #B "K #F
#AA4 _\#B .;X @+ #A_\ "K.K #I
#AB4 _\#G -- .;X _\ "K.K #D
#AC4 .,,GYMNA/ICS ,= ,EXAMPLE #F1
WRITE AN ABSOLUTE VALUE 9EQUAL;Y
DESCRIB+ ! .UNA3EPTA# MAT ?ICK;SES4
#A.G ,EX]CISES
,HOME"W ,KEY
.K ..,,"W$-,,\ ,,SOLU;NS .ON P4 ,,WS#B
..= ,EXS4 #BA1DG1 & .#GG
.K ..,,/&>DIZ$ ,,TE/ ,,PRACTICE ,EXS4
#B1 #CC1DJ1FC1 & .#FD
.K ..,,MULTIPLE ,,REPRES5T,NS ,EX#..GH
,,SKILL ,,PRACTICE
#A4 .,,VOCABUL>Y ,:AT IS AN EXTRANE\S
SOLU;N ( AN EQU,N8
#B4 .,,WRIT+ ,! ABSOLUTE VALUE (A
NUMB] _C 2 NEGATIVE4 ,H[1 !N1 C !
ABSOLUTE VALUE ( .;X 2 -- .;X = C]TA9
VALUES ( .;X @8
,,*ECK+ ,,SOLU;NS ,DECIDE :E!R ! GIV5
NUMB] IS A SOLU;N (! EQU,N4
#C4 _\ .;B -- #A_\ .K #AD2 --#AC
#D4 _\ .;D @+ #F_\ .K #AJ2 --#D
#E4 _\#CB--#F .;F _\ .K #BJ2 --#B
#F4 #B .;M @+ #F .K #AJ2 --#H
#G4 #C .;N -- #G .K #D2 #A
#H4 #AG--#H .;R .K #AE2 #D
,,EXAMPLE #A
ON P4 #EA = ,EXS4 #I-BJ
,,SOLV+ ,,EQU,NS ,SOLVE ! EQU,N4
,GRAPH ! SOLU;N4
.#I4 _\ .;X _\ .K #I
.#AJ4 _\ .;Y _\ .K --#E
.#AA4 _\ .;Z _\ .K #J
.#AB4 _\ .;F -- #E_\ .K #C
.#AC4 _\ .;G -- #B_\ .K #G
.#AD4 _\ .;H -- #D_\ .K #D
.#AE4 _\ .;K @+ #C_\ .K #F
.#AF4 _\ .;M @+ #E_\ .K #A
.#AG4 _\ .;N @+ #I_\ .K #AJ
.#AH4 _\#F -- .;P _\ .K #D
.#AI4 _\#E -- .;Q _\.K #G
.#BJ4 _\--#D -- .;R _\ .K #D
,,EXAMPLE #B
ON P4 #EB = ,EXS4 #BA-CB
,,SOLV+ ,,EQU,NS ,SOLVE ! EQU,N4
#BA4 _\#B .;D -- #E_\ .K #AC
.#BB4 _\#C .;G @+ #AD_\ .K #G
.#BC4 _\#G .;H -- #AJ_\ .K #D
.#BD4 _\#C .;P -- #F_\ .K #BA
.#BE4 _\#B .;Q @+ #C_\ .K #AA
.#BF4 _\#D .;R @+ #G_\ .K #DC
.#BG4 _\#E @+ #B .;J _\ .K #I
.#BH4 _\#F--#C .;K _\ .K #BA
.#BI4 _\#BJ--#I .;M _\ .K #G
.#CJ4
.#CA4
.#CB4
.#CC4 .,,%ORT .,,RESPONSE ,! EQU,N
_\#AE .;X -- #AJ_\ .K #DE 9 ,EXAMPLE #B
HAS TWO SOLU;NS4 ,DOES ! EQU,N _\#E .;X
-- #AJ_\ .K --#DE AL H TWO SOLU;NS8
.,EXPLA94
,,EXAMPLE #C
ON P4 #EB = ,EXS4 #CD--#DB
,,EXTRANE\S ,,SOLU;NS ,SOLVE ! EQU,N4
,*ECK = EXTRANE\S SOLU;NS4
.#CD4 _\#C .;X -- #D_\ .K .;X
.#CE4 _\ .;X @+ #BD_\ .K --#G .;X
.#CF4 _\#H .;X -- #A_\ .K #F .;X
.#CG4 _\#D .;X @+ #E_\ .K #B .;X @+ #D
.#CH4 _\#I--#B .;X _\ .K #AJ @+ #C .;X
.#CI4 _\#H @+ #E .;X _\ .K #G -- .;X
-------------------------------------#EF
#DJ4 .,,MULTIPLE .,,*OICE ,:AT IS 7>E7
! SOLU;N 7;S7 ( _\#C .;X @+ #G_\ .K #E
.;X @8
,A
;,B
;,C
;,D
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 SOLV+ ! EQU,N4
.#DA4
.#DB4
,,EXAMPLES
#D & #E
ON PP4 #EC-ED = ,EXS4 #DC-FC
,,SOLV+ ,,9EQUALITIES ,SOLVE !
9EQUAL;Y4 ,!N GRAPH ! SOLU;N4
.#DC4 _\ .;J _\ "K.K #E
.#DD4 _\ .;K _\ .1 #D
.#DE4 _\ .;M -- #B_\ "K #G
.#DF4 _\ .;N -- #AA_\ .1.K #A
.#DG4 _\ .;D @+ #D_\ .1.K #C
.#DH4 _\ .;F @+ #F_\ "K #B
.#DI4 _\ .;G -- #A_\ .1 #J
.#EJ4 _\ .;H @+ #AJ_\ "K.K #AJ
.#EA4 _\#C .;W -- #AE_\ "K #CJ
.#EB4 _\#B .;X @+ #F_\ .1 #AJ
.#EC4 _\#D .;Y -- #I "K.K #G
.#ED4 _\#E .;Z @+ #A_\ .1 #AD
.#EE4 _\#AF -- .;P _\ .1 #C
.#EF4 _\#BD -- .;Q _\ "K.K #AA
.#EG4 _\#G--#B .;R _\ "K #AI
.#EH4 _\#AI--#E .;T _\ .1 #G
.#EI4
.#FJ4
.#FA4
.#FB4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
#FC4 .,,MULTIPLE .,,*OICE ,:AT IS !
SOLU;N ( _\#F .;X -- #I_\ .1.K #CC8
,A #D "K.K .;X "K.K #G
;,B --#G "K.K .;X "K.K #D
;,C .;X "K.K --#D OR .;X .1.K #G
;,D .;X "K.K --#G OR .;X .1.K #D
#FD4 .,,MULTIPLE .,,*OICE ,: ABSOLUTE
VALUE 9EQUAL;Y REPRES5TS ! GRAPH %[N 2L8
,A --#A "K _\ .;X _\ "K #E
;,B _\ .;X @+ #B_\ "K #C
;,C _\ .;X -- #B_\ "K #C
;,D _\ .;X -- #B_\ "K #E
#FE4 .,,R1SON+ ,=! EQU,N _\ .AX @+ .;B
_\ .K .;C 7": .A1 .;B @1 & .;C >E R1L
NUMB]S & .A @6.K #J71 DESCRIBE ! VALUE
7;S7 ( .;C T YIELD TWO SOLU;NS1 "O
SOLU;N1 & NO SOLU;N4
,,SOLV+ ,,9EQUALITIES ,SOLVE !
9EQUAL;Y4 ,!N GRAPH ! SOLU;N4
.#FF4 _\ .;X @+ #A_\ .1.K --#AF
.#FG4 _\#B .;X -- #A_\ "K --#BE
.#FH4 _\#G .;X @+ #C_\ "K.K #J
.#FI4 _\ .;X -- #I_\ .1 #J
,,*ALL5GE ,SOLVE ! 9EQUAL;Y = .;X 9
T]MS ( .A1 .;B @1 & .C4 ,ASSUME .A1 .;B
@1 & .;C >E R1L NUMB]S & .;C.1 #J4
.#GJ4 _\ .AX @+ .;B _\ "K .;C ": .A .1
#J
.#GA4 _\ .AX @+ .;B _\ .1.K .;C ": .A
.1 #J
.#GB4 _\ .AX @+ .;B _\ "K.K .;C ": .A
"K #J
.#GC4 _\ .AX @+ .;B _\ .1 .;C ": .A "K
#J
.K ..,,"W$-,,\ ,,SOLU;NS ON P4.,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
-------------------------------------#EG
,,PRO#M ,,SOLV+
,,EXAMPLE #E
ON P4 #ED = ,EXS4 #GD-GH
.#GD4 .,,GYMNA/ICS ,! HORIZONTAL B>
US$ 9 GYMNA/ICS EV5TS %D 2 PLAC$ #AAJ.BE
9*ES ABV ! GR.D1 )A TOL].E ( #J.D 9*4
,WRITE AN ABSOLUTE VALUE 9EQUAL;Y =!
A3EPTA# B> HEI<TS4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
..#GE4 ,,SOIL ,,PH .,,LEVELS ,CUCUMB]S
GR[ 9 SOIL HAV+ A P,H LEVEL ( #F.E1 )A
TOL].E ( #A PO9T ON ! P,H SCALE4 ,WRITE
AN ABSOLUTE VALUE 9EQUAL;Y T DESCRIBES !
P,H LEVELS ( SOIL 9 : CUCUMB]S C GR[4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#GF4 .,,MULTI-.,,/EP .,,PRO#M ,A
BASEBALL HAS A CU%ION$ CORK C5T] CALL$ !
.PILL ,! PILL M/ WEI< #J.HE \NCE1 )A
TOL].E ( #J.JE \NCE4
A4 ,WRITE AN ABSOLUTE VALUE 9EQUAL;Y T
DESCRIBES ! A3EPTA# WEI<TS =! PILL (A
BASEBALL4
B4 ,SOLVE ! 9EQUAL;Y 6F9D ! A3EPTA#
WEI<TS =! PILL4
C4 ,LOOK BACK AT ,EXAMPLE #E ON PAGE
#ED @4 ,F9D ! M9IMUM & MAXIMUM P]C5TAGES
(A BASEBALL'S TOTAL WEI<T T ! PILL C
MAKE UP4
#GG4 .,,MANUFACTUR+ ,A REGUL,N
BASKETBALL %D WEI< #BA \NCES1 )A TOL].E
( #A \NCE4 ,WRITE AN ABSOLUTE VALUE
9EQUAL;Y DESCRIB+ ! WEI<TS ( BASKETBALLS
T %D 2 .REJECT$4
#GH4 .,,MULTIPLE .,,REPRES5T,NS ,!
/R5G? ( EYEGLASS L5SES IS M1SUR$ 9 UNITS
CALL$ .DIOPT]S4 ,! DIOPT] NUMB] .;X IS
NEGATIVE = NE>SI<T$ VI.N & POSITIVE =
F>SI<T$ VI.N4
A4 ,WRIT+ ,9EQUALITIES ,WRITE AN
EQUIVAL5T -P.D 9EQUAL;Y = EA* VI.N
CATEGORY %[N ABV4 ,SOLVE ! 9EQUALITIES4
B4 ,MAK+ A ,GRAPH ,ILLU/RATE ! SIX
VI.N CATEGORIES 0GRAPH+ _! RANGES (
DIOPT] NUMB]S ON ! SAME NUMB] L9E4
,LABEL EA* RANGE )! CORRESPOND+ CATEGORY
"N4
,,EXAMPLE #F
ON P4 #ED = ,EXS4 #GI-HA
#GI4 .,,SLEEP+ .,,BAGS ,A MANUFACTUR]
( SLEEP+ BAGS SU7E/S T "O MODEL IS BE/
SUIT$ = TEMP]ATURES 2T #CJ;DG;,F &
#FJ;DG;,F1 9CLUSIVE4 ,WRITE AN ABSOLUTE
VALUE 9EQUAL;Y = ? TEMP]ATURE RANGE4
#HJ4 .,,TEMP]ATURE ,! RECOMM5D$ OV5
SETT+ = COOK+ A PIZZA 9 A PROFES.NAL
BRICK-L9$ OV5 IS 2T #EEJ;DG;,F &
#FEJ;DG;,F1 9CLUSIVE4 ,WRITE AN ABSOLUTE
VALUE 9EQUAL;Y = ? TEMP]ATURE RANGE4
-------------------------------------#EH
.#HA4 .,,AUDI# .,,FREQU5CIES ,AN
ELEPHANT C HE> S.DS ) FREQU5CIES F #AF
H]TZ 6#AB1JJJ H]TZ4 ,A M\SE C HE> S.DS )
FREQU5CIES F #AJJJ H]TZ 6#IA1JJJ H]TZ4
,WRITE AN ABSOLUTE VALUE 9EQUAL;Y =!
HE>+ RANGE ( EA* ANIMAL4
#HB4 .,,*ALL5GE ,! DEP? F9D] ON A FI%+
BOAT GIVES R1D+S T >E )9 #E@3P (! ACTUAL
WAT] DEP?4 ,:5 ! DEP? F9D] R1D+ IS #BEJ
FEET1 ! ACTUAL WAT] DEP? .;X LIES )9 A
RANGE GIV5 0! FOLL[+ 9EQUAL;Y3
_\ .;X -- #BEJ_\ "K.K #J.JE .;X
A4 ,WRITE ! ABSOLUTE VALUE 9EQUAL;Y Z
A -P.D 9EQUAL;Y4
B4 ,SOLVE EA* "P (! -P.D 9EQUAL;Y =
.;X @4 ,:AT >E ! POSSI# ACTUAL WAT]
DEP?S IF ! DEP? F9D]'S R1D+ IS #BEJ
FEET8
,,MIX$ ,,REVIEW
.,,PREVIEW ,PREP>E = ,LESSON #B.A 9
,EXS4 #HC-ID4
,PLOT ! PO9TS 9 ! SAME COORD9ATE
PLANE1 @7 P4 #IHG @7
.#HC4 7#D1 #D7
.#HD4 7#G1 --#H7
.#HE4 7--#C1 #J7
.#HF4 7#J1 --#F7
.#HG4 7--#B1 --#C7
.#HH4 7--#E1 #B7
,EVALUATE ! EXPRES.N =! GIV5 VALUE (!
V>IA#1 @7 P4 #AJ @7
.#HI4 #F;M--#AJ2 .;M .K #D
.#IJ4 --#D .;N @+ #AH2 .;N .K #C
.#IA4 #E;P @+ #AG2 .;P .K #J
.#IB4 #G .;Q @+ #C2 .;Q .K --#D
.#IC4 #B .;R -- #C2 .;R .K #G
.#ID4 #AJ;T--#E2 .;T .K --#C
,SOLVE ! EQU,N = .Y4 ,!N F9D ! VALUE (
.;Y =! GIV5 VALUE ( .;X @4 @7 P4 #BF @7
.#IE4 #E .;X @+ .;Y .K #AD2 .;X .K #H
.#IF4 --#C .;X @+ .;Y .K #AB2 .;X .K
--#I
.#IG4 #H .;X -- #D .;Y .K #CB2 .;X .K
--#C
.#IH4 --#F .;X @+ #AE .;Y .K #CC2 .;X
.K #AJ
,,QUIZ .= .,LESSONS .#A..F-.A..G
,SOLVE ! 9EQUAL;Y4 ,!N GRAPH ! SOLU;N4
@7 P4 #DA @7
.#A4 #D .;K -- #AG "K #BG
.#B4 #AD .;N -- #H .1.K #IJ
.#C4 --#I .;P @+ #AE "K.K #IF
.#D4 --#H;R--#AA .1 #DE
.#E4 #C7 .;X -- #G7 "K #F7#AJ -- .;X
@7
.#F4 --#BE--#D .;Z .1 #FF--#AG .;Z
,SOLVE ! EQU,N OR 9EQUAL;Y1 @7 P4 #EA
@7
.#G4 _\ .;X -- #F_\ .K #I
.#H4 _\#C .;Y @+ #C_\ .K #AB
.#I4 _\#B .;Z @+ #E_\ .K --#I .;Z
.#AJ4 _\ .;P @+ #G_\ .1 #B
.#AA4 _\#B .;Q -- #C_\ "K.K #C
.#AB4 _\#E -- .;R _\ .1 #D
.#AC4 .,,TE/ .,,SCORES ,YR F9AL GRADE
9 A C\RSE IS #HJ@3P ( YR CURR5T GRADE1
PLUS #BJ@3P ( YR F9AL EXAM SCORE4 ,YR
CURR5T GRADE IS #HC & YR GOAL IS 6GET A
F9AL GRADE ( #HE OR BETT]4 ,WRITE &
SOLVE AN 9EQUAL;Y 6F9D ! F9AL EXAM
SCORES T W MEET YR GOAL4 @7 P4 #DA @7
.#AD4 .,,GROC]Y .,,WEI<TS ,A 3TA9] (
POTATO SALAD F YR GROC]'S DELI IS
SUPPOS$ 6WEI< #A.E P.DS1 )A TOL].E (
#J.JBE P.D4 ,WRITE & SOLVE AN ABSOLUTE
VALUE 9EQUAL;Y T DESCRIBES ! A3EPTA#
WEI<TS =! 3TA9] ( POTATO SALAD1 @7 P4
#EA @7
.,,EXTRA .,,PRACTICE = ,LESSON #A.G1
P4 #AJAJ
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
-------------------------------------#EI
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,LESSONS #A.E-A.G
#A4 .,,MULTI-.,,/EP .,,PRO#M ,A HYBRID
C> GETS AB #FJ MILES P] GALLON ( GAS 9 !
C;Y & AB #EA MILES P] GALLON ON !
HI<WAY4 ,DUR+ "O WEEK1 ! HYBRID USES #AB
GALLONS ( GAS & TRAVELS #FGE MILES4
.A4 ,WRITE A V]BAL MODEL =! TOTAL 4T.E
DRIV54 ,!N WRITE AN EQU,N BAS$ ON !
V]BAL MODEL4
.B4 ,SOLVE ! EQU,N 6F9D ! AM.TS ( GAS
US$ 9 ! C;Y & ON ! HI<WAY4
.C4 ,TELL H[ _M MILES 7 DRIV5 9 ! C;Y
& ON ! HI<WAY4
#B4 .,,MULTI-.,,/EP .,,PRO#M ,A
POPCORN MANUFACTUR]'S ID1L WEI<T =A BAG
( MICROWAVE POPCORN IS #C.E \NCES1 )A
TOL].E ( #J.BE \NCE4
.A4 ,WRITE AN ABSOLUTE VALUE 9EQUAL;Y
=! A3EPTA# WEI<TS (A BAG ( POPCORN4
.B4 ,SOLVE ! 9EQUAL;Y4 ,:AT IS ! RANGE
( A3EPTA# WEI<TS8
#C4 .,,EXT5D$ .,,RESPONSE ,Y >E DRA9+
A SWIMM+ POOL4 ,! TA# %[S ! DEP? (! WAT]
AT DI6]5T "TS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,"T 7;H71 .;T @3 #J3 #A3 #B3 #C
,DEP? 7FT71 .;D @3 #AB3 #AJ.E3 .#I @3
#G.E
.A4 ,WRITE AN EQU,N =! DEP?4
.B4 ,USE YR EQU,N 6F9D H[ L;G X W TAKE
=! POOL 6BE EMPTY4
.C4 ,DOES YR EQU,N MAKE S5SE = "TS
GRT] ?AN ! VALUE Y F.D 9 "P 7;B78
.,EXPLA94
#D4 .,,OP5-.,,5D$ ,=A ROPE TRICK1 A
MAGICIAN CUTS A #GB 9* PIECE ( ROPE
96?REE PIECES ( DI6]5T L5G?S4 ,! L5G? (
"O PIECE M/ 2 ! M1N (! L5G?S (! O!R TWO
PIECES4
,F9D ! L5G? (! M$IUM PIECE4 ,!N GIVE
POSSI# L5G?S =! %ORT & L;G PIECES4
#E4 .,,%ORT .,,RESPONSE ,A VIDEO /ORE
R5TS MOVIES = 4#B.IE EA*4 ,REC5TLY1 !
/ORE HAS A4$ A SPECIAL D1L T ALL[S Y
6R5T AN UNLIMIT$ NUMB] ( MOVIES =
4#AE.IE P] MON?4 .,EXPLA9 :5 ! SPECIAL
D1L IS LESS EXP5SIVE ?AN R5T+ MOVIES AT
! USUAL PRICE4 ,WRITE & SOLVE AN
9EQUAL;Y 6JU/IFY YR ANSW]4
#F4 .,,EXT5D$ .,,RESPONSE ,! TRIANGLE
9EQUAL;Y REL,N%IP F GEOMETRY /ATES T !
SUM (! L5G?S ( ANY TWO SIDES (A TRIANGLE
IS GRT] ?AN ! L5G? (! ?IRD SIDE4
.A4 ,WRITE ?REE DI6]5T 9EQUALITIES =!
TRIANGLE4
.B4 ,SOLVE ! ?REE 9EQUALITIES = .;X @4
.C4 ,BAS$ ON YR RESULTS F "P 7;B71 :AT
IS ! RANGE ( POSSI# VALUES = .;X @8
.D4 ,USE YR RESULTS 6DRAW ?REE DI6]5T
TRIANGLES T MEET ! 3DI;NS %[N 9 !
DIAGRAM4
#G4 .,,MULTI-.,,/EP .,,PRO#M ,OXYG5
EXI/S Z A LIQUID 2T --#CFI;DG;,F &
--#BIG;DG;,F1 9CLUSIVE4 ,WRITE !
TEMP]ATURE RANGE = LIQUID OXYG5 Z A -P.D
9EQUAL;Y 9 DEGREES ,FAHR5HEIT4 ,!N
REWRITE ! TEMP]ATURE RANGE 9 DEGREES
,CELSIUS4
#H4 .,,GRI4$ .,,ANSW] ,A FOOTBALL
KICK] SCORES #A PO9T = EA* EXTRA PO9T &
#C PO9TS = EA* FIELD GOAL4 ,"O S1SON1 A
KICK] MADE #CD EXTRA PO9TS & SCOR$ A
TOTAL ( #AAB PO9TS4 ,H[ _M FIELD GOALS
DID ! KICK] MAKE8
-------------------------------------#FJ
#A ,*APT] ,SUMM>Y
,,BIG ,,ID1S
,= ,YR ,NOTEBOOK
,BIG ,IDEA #A
,US+ ,PROP]TIES 6,EVALUATE & ,SIMPLIFY
,EXPRES.NS
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 ,EXAMPLE3 ,ANSW]
,6..EVALUATE A NUM]ICAL .EXPRES.N @1
USE ORD] ( OP],NS & PROP]TIES ( R1L
NUMB]S4 @3 #C @+ 7--#C7 #B @3 #C @+ #I
.K #AB
,6..EVALUATE AN ALGEBRAIC .EXPRES.N @1
SUB/ITUTE ! VALUE7;S7 (! V>IA#7;S7 96!
EXPRES.N1 & !N EVALUATE ! RESULT+
NUM]ICAL EXPRES.N4 @3 #D .;X -- #E :5
.;X .K #A @3 #D7#A7--#E .K --#A
,6..SIMPLIFY AN ALGEBRAIC .EXPRES.N @1
-B9E L T]MS4 @3 #C .;Y -- #D @+ #B .;Y
-- #F @3 #E .;Y -- #AJ
,BIG ,IDEA1 #B
,US+ ,PRO#M ,SOLV+ ,/RATEGIES & ,V]BAL
,MODELS
,Y MAY 2 A# 6WRITE A .V]BAL .MODEL T
DESCRIBES A R1L-_W PRO#M & USE X 6WRITE
AN EQU,N OR 9EQUAL;Y Y C SOLVE4 ,6WRITE
! V]BAL MODEL1 ANALYZE ! 9=M,N Y >E GIV5
& USE A PRO#M SOLV+ /RATEGY IF
APPROPRIATE4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,IF ? IS :AT Y "K'''3 '''TRY ?
/RATEGY4
,A =MULA C 2 APPLI$ 6! SITU,N43 ,USE A
,=MULA
,NUM]ICAL 9=M,N IS GIV5 9 A TA# OR A
LI/43 ,LOOK =A ,PATT]N
,"! IS A GEOMETRIC OR PHYSICAL 3TEXT43
,DRAW A ,DIAGRAM
,BIG ,IDEA #C
,SOLV+ ,L9E> & ,ABSOLUTE ,VALUE
,EQU,NS & ,9EQUALITIES
,USE ! FOLL[+ GUIDEL9ES :5 SOLV+
EQU,NS & 9EQUALITIES4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,L9E> .,EQU,N
.AX @+ .;B .K #J @3 .,L9E> .,9EQUAL;Y
.AX @+ .;B "K.K #J
,USE PROP]TIES ( EQUAL;Y 6ISOLATE .X4
.,ADD OR .SUBTRACT ! SAME NUMB] F EA*
SIDE (! EQU,N1 OR .MULTIPLY OR .DIVIDE
EA* SIDE 0! SAME NONZ]O NUMB]4 @3 ,USE
PROP]TIES SIMIL> 6^? US$ 9 SOLV+ EQU,NS4
,REMEMB] 6.REV]SE .! .9EQUAL;Y :5
MULTIPLY+ OR DIVID+ 0A .NEGATIVE NUMB]4
.,ABSOLUTE .,VALUE .,EQU,N
_\ .AX @+ .;B _\ .K .;C
,REWRITE Z FOLL[S & SOLVE3
.AX @+ .;B .K .;C OR .AX @+ .;B .K --
.;C
,*ECK = .EXTRANE\S SOLU;NS4 @3
.,ABSOLUTE .,VALUE .,9EQUAL;Y
-------------------------------------#FA
#A ,*APT] ,REVIEW
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
99 ,MULTI-,LANGUAGE ,GLOSS>Y
99 ,VOCABUL>Y PRACTICE
,,REVIEW ,,KEY ,,VOCABUL>Y
99 OPPOSITE1 P4 #D
99 RECIPROCAL1 P4 #D
99 NUM]ICAL EXPRES.N1 P4 #AJ
99 P[]1 P4 #AJ
99 EXPON5T1 P4 #AJ
99 BASE1 P4 #AJ
99 V>IA#1 P4 #AA
99 ALGEBRAIC EXPRES.N1 P4 #AA
99 T]M1 P4 #AB
99 V>IA# T]M1 P4 #AB
99 3/ANT T]M1 P4 #AB
99 COE6ICI5T1 P4 #AB
99 L T]MS1 P4 #AB
99 EQUIVAL5T EXPRES.NS1 P4 #AH
99 ID5T;Y1 P4 #AB
99 EQU,N1 P4 #AH
99 L9E> EQU,N1 P4 #AH
99 SOLU;N ( AN EQU,N1 P4 #AH
99 EQUIVAL5T EQU,NS1 P4 #AH
99 =MULA1 P4 #BF
99 SOLVE =A V>IA#1 P4 #BF
99 V]BAL MODEL1 P4 #CD
99 L9E> 9EQUAL;Y1 P4 #DA
99 SOLU;N ( AN 9EQUAL;Y1 P4 #DA
99 GRAPH ( AN 9EQUAL;Y1 P4 #DA
99 -P.D 9EQUAL;Y1 P4 #DA
99 EQUIVAL5T 9EQUALITIES1 P4 #DB
99 ABSOLUTE VALUE1 P4 #EA
99 EXTRANE\S SOLU;N1 P4 #EB
,,VOCABUL>Y ,,EX]CISES
.#A4 ,COPY & -PLETE3 ,9 A P[]1 ! @8
REPRES5TS ! NUMB] ( "TS ! @8 IS US$ Z A
FACTOR4
.#B4 ,COPY & -PLETE3 ,IF SUB/ITUT+ A
NUMB] =A V>IA# 9 AN EQU,N RESULTS 9 A
TRUE /ATE;T1 !N ! NUMB] IS A7;N7 @8 (!
EQU,N4
.#C4 ,COPY & -PLETE3 ,A7;N7 @8 IS AN
APP>5T SOLU;N T M/ 2 REJECT$ 2C X DOES N
SATISFY ! ORIG9AL EQU,N4
.#D4 ,ID5TIFY ! L T]MS 9 ! EXPRES.N
#DJ @+ #C .;X #C @+ #C .;X #B -- #G --
.;X #B @4
.#E4 ,GIVE AN EXAMPLE ( TWO EQUIVAL5T
ALGEBRAIC EXPRES.NS4
.#F4 .,,WRIT+ .,-P>E ! PROC$URES =
SOLV+ A L9E> EQU,N &A L9E> 9EQUAL;Y4 ,H[
>E !Y SIMIL>8 ,H[ >E !Y DI6]5T8
,,REVIEW ,,EXAMPLES ,,& ,,EX]CISES
,USE ! REVIEW EXAMPLES & EX]CISES 2L
6*ECK YR "U/&+ (! 3CEPTS Y H LE>N$ 9 EA*
LESSON ( ,*APT] #A4
#A.A ,APPLY ,PROP]TIES ( ,R1L ,NUMB]S
PP4 #B-I
,,EXAMPLE
,ID5TIFY ! PROP]TY T ! /ATE;T
ILLU/RATES4
A4 #B7 .;W @+ @7 .K #B .;W @+ #B
,4TRIBUTIVE PROP]TY
B4 #F @+ 7#B @+ #D7 .K #F @+ 7#D @+
#B7
,-MUTATIVE PROP]TY ( A4I;N
,,EX]CISES
,ID5TIFY ! PROP]TY T ! /ATE;T
ILLU/RATES4
,,EXAMPLE #C
ON P4 #D = ,EXS4 #G-I
.#G4
.#H4 #FJ @+ #J .K #FJ
.#I4 #C .A @+ #G .A .K _\#C @+ #G_\ .A
-------------------------------------#FB
#A ,,*APT] ,,REVIEW
#A.B ,EVALUATE & ,SIMPLIFY ,ALGEBRAIC
,EXPRES.NS
PP4 #AJ-AF
,,EXAMPLE
,SIMPLIFY ! EXPRES.N4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#E7 .;Y -- #D7--#C7#B .;Y -- #I7 .K #E
.;Y -- #BJ--#F .;Y @+ #BG @3
.,4TRIBUTIVE .PROP]TY
.K 7#E .;Y -- #F .;Y @7 @+ 7--#BJ @+
#BG7 @3 .,GR\P .L .T]MS4
.K -- .;Y @+ #G @3 .,-B9E .L .T]MS4
,,EXAMPLES
#C & #D
ON PP4 #AA-AB = ,EXS4 #AJ-AF
,,EX]CISES
,SIMPLIFY ! EXPRES.N4
.#AJ4 #BE .;X @+ #AD--#AG--#F .;X
.#AA4 #F .;Y @+ #AB .;X ---#AB .;Y --
#I .;X
.#AB4 #F7 .;N -- #B7--#H .;N @+ #DJ
.#AC4 #E7#B .;B @+ #C7 @+ #H7 .;B --
#F7
.#AD4 #C .;G @+ #I .;G #B -- #AB .;G
#B @+ .;G
.#AE4 #G .;T #D @+ #G .;T #B -- #B .;T
#B -- #I .;T #D
.#AF4 .,,TAXI .,,RATES ,A ,NEW ,YORK
,C;Y TAXI *>GES 4#B.EJ1 PLUS @4#.DJ =
EA* FIF? (A MILE IF X IS N DELAY$
0TRA6IC4 ,WRITE AN EXPRES.N =! CO/ (!
RIDE IF Y TRAVEL .;X MILES 9 ! TAXI ) NO
TRA6IC DELAYS4
#A.C ,SOLVE ,L9E> ,EQU,NS
.PP4 #AH-BD
,,EXAMPLE
..,SOLVE --#D7#C ;X @+ #E7 .K --#B7.#E
-- .;X @7@4
,,EXAMPLES #A1 #B1 #C1 & #D
ON PP4 #AH-BJ = ,EXS4 #AG-BD
,,EX]CISES
,SOLVE ! EQU,N4 ,*ECK YR SOLU;N4
.#AG4 #BD .;X @+ #AF .K #AB
.#AH4 --#F .;Y @+ #AE .K --#I
.#AI4 #D7 .;Q -- #E7 .K #AF
.#BJ4 #G .;M @+ #CH .K --#E .;M -- #AF
.#BA4 #DH .;J @+ #BE .K #AB .;J -- #AA
.#BB4 #H7#B .;N -- #E7 .K #C7#F .;N --
#B7
.#BC4 .,,SALES .,,TAX ,Y BUY A JACKET1
&! SALES TAX IS #F@3P4 ,! TOTAL CO/ IS
4#GI.DI4 ,F9D ! CO/ (! JACKET 2F ! TAX4
.#BD4 .,,FOOD .,,%OPP+ ,AT A VEGETA#
/&1 Y B"\ #C P.DS ( PEPP]S = 4#D.EJ4
,GRE5 PEPP]S CO/ 4#A P] P.D & ORANGE
PEPP]S CO/ 4#D P] P.D4 ,F9D H[ _M P.DS (
EA* K9D ( PEPP] Y B"\4
-------------------------------------#FC
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,*APT] ,REVIEW ,PRACTICE
#A.D ,REWRITE ,=MULAS & ,EQU,NS
PP4 #BF-CB
,EXAMPLE
,SOLVE #E .;X -- #AA .;Y .K #G = .;Y
@4 ,!N F9D ! VALUE ( .;Y :5 .;X .K #D4
,,/EP #A
,,/EP #B
,,EXAMPLES #B1 #C1 & #D
ON PP4 #BG-BH = ,EXS4 #BE-CA
,,EX]CISES
,SOLVE ! EQU,N = Y4 ,!N F9D ! VALUE (
.;Y =! GIV5 VALUE ( .X4
.#BE4 #AJ .;X @+ .;Y .K #G2 .;X .K #C
.#BF4 #H .;Y -- #C .;X .K #AH2 .;X .K
#B
.#BG4 .XY -- #F .;Y .K --#AE2 .;X .K
#E
.#BH4 #D .;X .K #F .;Y @+ #I2 .;X .K
#I
.#BI4 #E .;X -- #B .;Y .K #AJ2 .;X .K
--#F
.#CJ4 .;X -- #C .XY .K #A2 .;X .K --#E
.#CA4 .,,GEOMETRY ,! =MULA .;,S .K #B
.RH @+ #B .;R #B GIVES ! SURFACE >EA
.;,S (A CYL9D] ) HEI<T .;H & RADIUS .;R
@4 ,SOLVE ! =MULA = .;H @4 ,F9D .;H IF
.;R .K #E C5TIMET]S & .;,S .K #DJJ SQU>E
C5TIMET]S4
#A.E ,USE ,PRO#M ,SOLV+ ,/RATEGIES &
,MODELS
PP4 #CD-DJ
,EXAMPLE
,F9D ! "T X TAKES 6DRIVE #EBE MILES AT
#EJ MILES P] H\R4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#EBE .K #EJ .;T @3 .,WRITE .EQU,N4
#AJ.E .K .;T @3 ..,DIVIDE EA* SIDE
0.#EJ4
,X TAKES #AJ.E H\RS 6DRIVE #EBE MILES
AT #EJ MILES P] H\R4
,,EXAMPLES #A & #D
ON PP4 #CD-CF = ,EXS4 #CB-CC
,,EX]CISES
.#CB4 .,,AV]AGE .,,SPE$ ,X TAKES #C
H\RS =A TRA9 6TRAVEL #AGE MILES4 ,:AT IS
! AV]AGE SPE$ (! TRA98
.#CC4 .,,C> .,,R5TAL ,:ILE ON VAC,N1
YR FAMILY R5T$ A C> = 4#BIC4 ,! C> R5TAL
CO/ 4#AHJ1 PLUS @4#.BE = E MILE DRIV5
OV] #AEJ MILES4 ,H[ _M MILES DID Y DRIVE
:ILE ON VAC,N8
-------------------------------------#FD
#A ,,*APT] ,,REVIEW
#A.F ,SOLVE ,L9E> ,9EQUALITIES
PP4 #DA-DG
,,EXAMPLE
,SOLVE #BE--#C .;X "K #AJ4 ,!N GRAPH !
SOLU;N4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#BE--#C .;X "K #AJ @3 .,WRITE .ORIG9AL
.9EQUAL;Y4
--#C .;X "K.K --#AE @3 ..,SUBTRACT #BE
F EA* .SIDE4
.;X .1.K #E @3 ..,DIVIDE EA* SIDE BY
--#C & REV]SE ! .9EQUAL;Y4
@3 .,GRAPH .! .SOLU;N4
,,EXAMPLES
#A1B1 #C1 & #D
ON PP4 #DA-DC = ,EXS4 #CD-DJ
,,EX]CISES
,SOLVE ! 9EQUAL;Y4 ,!N GRAPH ! SOLU;N4
.#CD4 #B .;X -- #C "K --#A
.#CE4 #G--#C .;X .1.K --#AA
.#CF4 #AE .;X @+ #H .1 #I .;X -- #BB
.#CG4 #AC .;X @+ #BD "K.K #AF--#C .;X
.#CH4 --#E "K #AJ -- .;X "K #E
.#CI4 --#H "K.K #C .;X @+ #A "K.K #AJ
.#DJ4 .,,GEOMETRY ,A TRIANGLE HAS
SIDES ( L5G?S #AJ1 #B .;X @1 & #C .;X @4
,! SUM (! L5G?S ( ANY TWO SIDES IS GRT]
?AN ! L5G? (! ?IRD SIDE4 ,WRITE & SOLVE
?REE 9EQUALITIES 6F9D ! POSSI# VALUES (
.X4
#A.G ,SOLVE ,ABSOLUTE ,VALUE ,EQU,NS &
,9EQUALITIES
PP4 #EA-EH
,,EXAMPLE
,SOLVE _\#C .;X -- #G_\ .1 #B4 ,!N
GRAPH ! SOLU;N4
,GRAPH ! SOLU;N4
,,EXAMPLES
#B1 #C1 #D1 & #E
ON PP4 #EB-ED = ,EXS4 #DA-DG
,,EX]CISES
,SOLVE ! EQU,N4 ,*ECK = EXTRANE\S
SOLU;NS4
.#DA4 _\#C .;P @+ #B_\ .K #G
.#DB4 _\#I .;Q -- #E_\ .K #B .;Q
.#DC4 _\#H .;R @+ #A_\ .K #C .;R
,SOLVE ! 9EQUAL;Y4 ,!N GRAPH ! SOLU;N4
.#DD4 _\ .;X -- #E_\ .1.K #A
.#DE4 _\#E--#B .;Y _\ .1 #G
.#DF4 _\#F .;Z @+ #E_\ "K.K #BE
.#DG4 .,,VOLLEYBALL ,! CIRCUMF];E (A
VOLLEYBALL %D 2 #BF 9*ES1 )A TOL].E (
#J.E 9*4 ,WRITE & SOLVE AN ABSOLUTE
VALUE 9EQUAL;Y T DESCRIBES ! A3EPTA#
CIRCUMF];ES (A VOLLEYBALL4
-------------------------------------#FE
#A ,*APT] ,TE/
,GRAPH ! NUMB]S ON A NUMB] L9E4
.#A4
.#B4
,USE PROP]TIES & DEF9I;NS ( OP],NS 6%[
T ! /ATE;T IS TRUE4 .,JU/IFY EA* /EP4
.#C4 #E @+ @7 .;X -- #E7 .K .;X
.#D4 7#C .;D @+ #G7 -- .;D @+ #E .K #B
.;D @+ #AB
..,EVALUATE ! EXPRES.N =! GIV5 VALUES
( ;X & .;Y @4
.#E4 #D .;X -- #F .;Y :5 .;X .K #E &
.;Y .K --#C
.#F4 #C .;X #B -- #I .;Y :5 .;X .K #B
& .;Y .K #D
,SIMPLIFY ! EXPRES.N4
.#G4 #E .;N @+ #AJ-- #H .;N @+ #F
.#H4 #AJ .;M -- #D7#C .;M @+ #G7 @+ #F
.;M
.#I4 #AA @+ .;Q -- #C .;Q #B @+ #AH
.;Q #B -- #B
.#AJ4 #I .;T #B @+ #AD--#AG .;T @+ #F
.;T -- #H .;T #B
.#AA4 #E7 .;X -- #C .;Y @7 @+ #B7#D
.;Y -- .;X @7
.#AB4 #E7#B .;U @+ #C .;W @7--#B7#E
.;U -- #G .;W @7
,SOLVE ! EQU,N4 ,*ECK YR SOLU;N4
.#AC4 #E .;N @+ #AA .K --#I
.#AD4 #F .;K @+ #G .K #D @+ #AB .;K
.#AE4 -- .;T -- #B .K #I7 .;T -- #H7
,SOLVE ! EQU,N = Y4 ,!N F9D ! VALUE (
.;Y =! GIV5 VALUE ( .X4
.#AF4 #AB .;X -- #BH .;Y .K #DJ2 .;X
.K #F
.#AG4 .;X @+ #D .;Y .K #AB2 .;X .K #B
.#AH4 #AE .;Y @+ #B .XY .K --#CJ2 .;X
.K #E
,SOLVE ! 9EQUAL;Y4 ,!N GRAPH ! SOLU;N4
.#AI4 --#E .;X -- #F "K #AI
.#BJ4 .;X @+ #BB .1.K --#C .;X -- #AJ
.#BA4 #E "K #B .;X @+ #C "K.K #AA
,SOLVE ! EQU,N4 ,*ECK = EXTRANE\S
SOLU;NS4
.#BB4 _\#C .;D -- #D_\ .K #AD
.#BC4 _\ .;F @+ #C_\ .K #B .;F @+ #D
.#BD4 _\#AJ --#G .;G _\ .K #B .;G
,SOLVE ! 9EQUAL;Y4 ,!N GRAPH ! SOLU;N4
.#BE4 _\ .;X -- #E_\ "K.K #CJ
.#BF4 _\#C .;Y @+ #D_\ .1 #B
.#BG4
.#BH4 .,,WIRE.S .,,NET"W ,6SET UP A
WIRE.S NET"W = ,9T]NET A3ESS AT HOME1 Y
BUY A NET"W R\T] = 4#GE4 ,! FEE = ,,DSL
S]VICE IS 4#AH P] MON?4 ,WRITE AN
EXPRES.N =! AM.T ( M"OY Y SP5D 9 .;N
MON?S4 ,H[ M* M"OY D Y SP5D 9 #AB MON?S8
.#BI4 .,,C> .,,REPAIR ,! BILL =!
REPAIR (A C> 0 4#DBJ4 ,! CO/ ( "PS 0
4#BDJ4 ,! CO/ ( LABOR 0 4#DE P] H\R4 ,H[
_M H\RS DID ! REPAIR TAKE8
.#CJ4 .,,H\SEHOLD .,,*ORES ,Y C WA% "O
W9D[ 9 #AE M9UTES & YR SI/] C WA% "O
W9D[ 9 #BJ M9UTES4 ,H[ _M M9UTES W X
TAKE 6WA% #AB W9D[S IF Y "W TGR8
.#CA4 .,,GEOMETRY ,! =MULA GIVES !
VOLUME .;,V (A C"O ) HEI<T .;H & BASE
RADIUS .;R @4 ,SOLVE ! =MULA = .H4 ,!N
F9D .;H :5 .;R .K #B 9*ES & .;,V .K #DE
CUBIC 9*ES4
-------------------------------------#FF
#A ,/&>DIZ$ ,TE/ ,PREP>,N
,,%ORT ,,RESPONSE ,,"QS
,SCOR+ ,RUBRIC
,FULL ,CR$IT
99 SOLU;N IS -PLETE & CORRECT
,"PIAL ,CR$IT
99 SOLU;N IS -PLETE B HAS ]RORS1
OR
99 SOLU;N IS )\T ]ROR B 9COMPLETE
,NO ,CR$IT
99 NO SOLU;N IS GIV51 .OR
99 SOLU;N MAKES NO S5SE
,,PRO#M
,A N,NAL BANK (F]S A *ECK+ A3.T =A FEE
( 4#C.IJ P] MON?4 ,! F/ #AJ TRANSAC;NS
P] MON? >E FREE1 B E A4I;NAL TRANSAC;N
CO/S @4#.AE4 ,A LOCAL BANK (F]S A *ECK+
A3.T ) NO MON?LY FEE1 B E TRANSAC;N CO/S
@4#.CF4
,2L >E SAMPLE SOLU;NS 6! PRO#M4 ,R1D
EA* SOLU;N &! -;TS ON ! LEFT 6SEE :Y !
SAMPLE REPRES5TS ..FULL CR$IT1 "PIAL
.CR$IT @1 OR .NO .CR$IT4
,SIDEB>3
,/&>DS
.#A..J .,/UD5TS .SOLVE EQU,NS &
.9EQUALITIES 9VOLV+ ABSOLUTE VALUE4
,,SAMPLE #A3 ,FULL CR$IT SOLU;N
,IF Y MAKE #AJ TRANSAC;NS OR FEW] P]
MON?1 ! LOCAL BANK IS LESS EXP5SIVE 2C X
CO/S 4#C.FJ OR LESS1 -P>$ TO 4#C.IJ =!
N,NAL BANK4 ,IF ! NUMB] ( TRANSAC;NS IS
M ?AN #AJ1 Y C USE ! FOLL[+ MODEL1 ":
.;X IS ! NUMB] ( TRANSAC;NS P] MON?4
,! V]BAL MODEL EXPLA9S H[ ! 9EQUAL;Y
IS OBTA9$4
,! 9EQUAL;Y IS SOLV$ CORRECTLY1 /EP
0/EP4
,SOLVE ! 9EQUAL;Y 6F9D :5 X IS LESS
EXP5SIVE 6USE ! N,NAL BANK4
#J.AE7 .;X -- #AJ7 @+ #C.IJ "K #J.CF
.;X
#J.AE .;X -- #A.E @+ #C.IJ "K #J.CF
.;X
#B.D "K #J.BA .;X
#AA.D "K .;X
,! ANSW] IS CORRECT4 ,AN 9TEG] MAKES
S5SE 9 ? 3TEXT4
,A NON9TEG] ANSW] DOES N MAKE S5SE1 S
R.D UP4 ,! N,NAL BANK IS LESS EXP5SIVE
IF Y MAKE #AB OR M TRANSAC;NS P] MON?4
,,SAMPLE #B3 ,"PIAL CR$IT SOLU;N
,! 9EQUAL;Y IS CORRECT :5 .;X .1 #AJ4
,! CASE :5 .;X "K.K #AJ IS N 3SID]$4
#J.AE7 .;X -- #AJ7 @+ #C.IJ "K #J.CF
.;X
#J.AE .;X -- #A.E @+ #C.IJ "K #J.CF
.;X
#B.D "K #J.BA .;X
#B.AI "K .;X
,! /UD5T MADE AN ]ROR 9 ! LA/ /EP4 ,!
ANSW] IS 9CORRECT4
,! N,NAL BANK IS LESS EXP5SIVE IF Y
MAKE #C OR M TRANSAC;NS4
-------------------------------------#FG
,,SAMPLE #C3 ,"PIAL CR$IT SOLU;N
,CALCUL,NS >E %[N = #AB TRANSAC;NS
ONLY4
,F9D ! CO/ = EA* BANK :5 "! >E #AB
TRANSAC;NS4
.,N,NAL .BANK3 4#C.IJ @+ #B7@4#.AE7 .K
4#D.BJ .,LOCAL .BANK3 #AB7@4#.CF7 .K
4#D.CB
,! ANSW] IS CORRECT1 B X IS N JU/IFI$4
,! N,NAL BANK IS LESS EXP5SIVE :5 Y
MAKE #AB OR M TRANSAC;NS4
,,SAMPLE #D3 ,NO CR$IT SOLU;N
,! 9EQUAL;Y IS 9CORRECT4 ,! N,NAL BANK
DOES N *>GE @4#.AE = E TRANSAC;N4
#J.AE .;X @+ #C.IJ "K #J.CF .;X
#C.I "K #J.BA .;X
#AH.F "K .;X
,! ANSW] IS 9CORRECT4
,! N,NAL BANK IS LESS EXP5SIVE :5 Y
MAKE #AI OR M TRANSAC;NS4
,,PRACTICE
,APPLY ! ,SCOR+ ,RUBRIC
,USE ! RUBRIC ON PAGE #FF 6SCORE !
SOLU;N 6! PRO#M 2L ..Z FULL CR$IT1 "PIAL
.CR$IT @1 OR .NO .CR$IT4 .,EXPLA9 YR
R1SON+4
.,,PRO#M ,Y PLANT A #A.E FOOT TALL
SAWTOO? OAK T GR[S #C.E FEET P] YE> &A
#E FOOT TALL *E/NUT OAK T GR[S #B FEET
P] YE>4
A4 ,:5 W ! SAWTOO? OAK 2 TALL] ?AN !
*E/NUT OAK8
B4 ,JU/IFY YR ANSW]4
.#A4 ,! SAWTOO? OAK W 2 TALL] ?AN !
*E/NUT OAK 9 AB #B.CC YE>S4
.#B4 ,LET .;X 2 ! .NUMB] .( YE>S4
,SOLVE ! 9EQUAL;Y = .;X @4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#A.E @+ #C.E .;X .1 #E @+ #B .;X @3 --
#A.E .;X .1 #C.E @3 ,! SAWTOO? OAK W 2
TALL] ?AN ! *E/NUT OAK AF AB #B.CC YE>S4
.;X .1 #B.CC @3 --
.#C4 #AE .;X @+ #C.E .1 #E .;X @+ #B
#A.E .1 #C.E .;X
#J.DC .1 .;X @1 S AF #J.DC YE>1 !
SAWTOO? OAK W 2 TALL]4
-------------------------------------#FH
#A ,/&>DIZ$ ,TE/ ,PRACTICE
,,%ORT ,,RESPONSE
.#A4 ,A T1*] IS BUY+ RUL]S4 ,AT AN
ONL9E SITE1 RUL]S CO/ @4#.HI EA* PLUS
4#E = %IPP+ =! 5TIRE ORD]4 ,AT A /ORE1
EA* RUL] CO/S @4#.IE4 ,"U :AT 3DI;NS IS
! /ORE LESS EXP5SIVE8 ,IF "! IS FREE
%IPP+ = ONL9E ORD]S OV] 4#EJ1 H[ DOES YR
ANSW] *ANGE8
.#B4 ,JESSICA GOES ON A VAC,N
6,MEXICO4 ,%E EX*ANGES 4#AEJ 96PESOS4 ,!
EX*ANGE RATE IS #AA.CGG PESOS P] DOLL>4
,%E SP5DS #ABEJ PESOS4 ,:5 %E EX*ANGES
H] REMA9+ PESOS BACK 96DOLL>S1 H[ M*
DOES %E GET1 6! NE>E/ DOLL>8 .,JU/IFY
ALL ( YR /EPS4
.#C4 ,3SID] ! EQU,N _\ .;X @+ .;H _\
.K .A @4 ,= :AT VALUES ( .;H & .A >E !
SOLU;NS (! EQU,N #H & --#AB8 .,DESCRIBE
! ME?OD Y US$ 6SOLVE ! PRO#M4
.#D4 ,WRITE & SOLVE AN EQU,N 6F9D .;X
@4 ,!N F9D ! >EA (! %AD$ REGION4
.,EXPLA9 YR R1SON+4
.#D4 ,! TA# %[S ! NUMB] ( GOALS .;G &
ASSI/S .A = F\R PLAY]S ON A GIRLS' V>S;Y
SO3] T1M4 ,EA* PLAY] IS ASSIGN$ A PO9T
TOTAL GIV5 0.;P .K #B .;G @+ .A @4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,PLAY]3 ,GOALS1 .;G @3 ,ASSI/S1 .A
,S&RA3 #B3 #F
,KIM3 #C3 #E
,J53 #D3 #A
,MELANIE3 #E3 #B
A4 ,: PLAY] E>N$ ! MO/ PO9TS8
B4 ,IS X POSSI# = TWO PLAY]S 6E>N !
SAME NUMB] ( PO9TS B H DI6]5T NUMB]S (
GOALS & ASSI/S8 .,JU/IFY YR ANSW]4
.#E4 ,! TA# %[S ! NUMB] ( GOALS .;G &
ASSI/S .A = F\R PLAY]S ON A GIRLS' V>S;Y
SO3] T1M4 ,EA* PLAY] IS ASSIGN$ A PO9T
TOTAL GIV5 0.;P .K #B .;G @+ .A @4
.#F4 ,A -MUN;Y IS HAV+ A ,TA/E (! ,T[N
EV5T F1TUR+ ! >EA'S BE/ RE/AURANTS4 ,!
ADMIS.N IS 4#BE 9 ADV.E & 4#CE AT !
DOOR4 ,IF #BBJ P PAY 9 ADV.E &! TOTAL
AM.T COLLECT$ IS 4#GDIE1 H[ _M P PAY AT
! DOOR8 ,H[ M* M M"OY IS COLLECT$ 9
ADV.E ?AN AT ! DOOR8 .,EXPLA9 YR SOLU;N4
.#G4 ,J>$ & #G ( 8 FRS H A B[L+ "PY4
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TOTAL CO/ 6BE AT MO/ 4#HJ4
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,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
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EA* C B[L8 ,H[ DOES YR ANSW] *ANGE IF
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.,EXPLA94
.#H4 ,AT A US$ BOOK SALE1 EA* H>DCOV]
CO/S 4#B & EA* PAP]BACK CO/S 4#A4 ,C>OL
B"\ #AE BOOKS Z GIFTS = 4#BA4 ,H[ _M M
PAP]BACKS ?AN H>DCOV]S DID %E BUY8
.,JU/IFY EA* /EP ( YR SOLU;N4
.#I4 ,A .PICA IS A UNIT ( M1SURE T
EQUALS "O SIX? ( AN 9*4 ,:AT IS ! >EA1 9
SQU>E 9*ES1 (A RECTANGLE T IS #I PICAS
L;G & #H PICAS WIDE8 .,DESCRIBE ! ME?OD
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PRISM )A SQU>E BASE IS GIV5 0.;,V .K .;S
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( "O SIDE (! BASE4
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#AJJJ CUBIC C5TIMET]S4 ,*OOSE ?REE
POSSI# VALUES ( .;S & F9D ! CORRESPOND+
VALUES ( .H4 ,IS "! A MAXIMUM VALUE T
.;S C H8 .,EXPLA94
-------------------------------------#FI
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,,MULTIPLE ,,*OICE
.#AA4 ,: GRAPH REPRES5TS ! SOLU;N (!
9EQUAL;Y #B .;X -- #G "K #AA8
,A
;,B
;,C
;,D
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SECOND8
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,,EXT5D$ ,,RESPONSE
.#BJ4 ,! MELT+ PO9TS & BOIL+ PO9TS (
LI?IUM1 C>BON1 NITROG51 OXYG51 &
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3TA9 TWO DA%ES4
--@3 ,LI3 ;,C3 ;,N3 ,O3 ,MG
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@8@3 --#BIG3 @8
A4 ,COPY ! TA#4 ,USE ! =MULA 63V]T !
,CELSIUS TEMP]ATURES 9 ! TA# 6,FAHR5HEIT
TEMP]ATURES4 ,RECORD ! RESULTS4
B4 ,REWRITE ! =MULA S T X GIVES !
,CELSIUS TEMP]ATURE 9 T]MS (! ,FAHR5HEIT
TEMP]ATURE4 ,JU/IFY EA* /EP4
C4 ,USE ! REWRITT5 =MULA 63V]T !
,FAHR5HEIT TEMP]ATURES 9 ! TA# 6,CELSIUS
TEMP]ATURES4 ,RECORD ! RESULTS4
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AV]AGE 7,,]A7 C 2 CALCULAT$ US+ ? =MULA3
,,]A .K #I @* E>N$ RUNS @/ 9N+S PIT*$4
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GAVE UP #FF E>N$ RUNS 9 #BBH 9N+S PIT*$4
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_H A C>E] ,,]A ( #B.GA4 ,WRITE & SOLVE
AN EQU,N 6F9D ! NUMB] ( E>N$ RUNS HE
ALL[$ 9 ^? 9N+S4 .,EXPLA9 :Y "! >E TWO
POSSI# ANSW]S4
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POSSI# NUMB]S ( E>N$ RUNS HE C ALL[4
.,EXPLA9 H[ Y NE$ 6R.D YR ANSW]4
-------------------------------------#GJ
#B ,L9E> ,EQU,NS & ,FUNC;NS
.#B..A ,REPRES5T ,REL,NS & ,FUNC;NS
.#B..B ,F9D ,SLOPE & ,RATE ( ,*ANGE
.#B..C ,GRAPH ,EQU,NS ( ,L9ES
.#B..D ,WRITE ,EQU,NS ( ,L9ES
.#B..E ,MODEL ,DIRECT ,V>I,N
.#B..F ,DRAW ,SCATT] ,PLOTS &
,BE/-,FITT+ ,L9ES
.#B..G ,USE ,ABSOLUTE ,VALUE ,FUNC;NS
& ,TRANS=M,NS
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,TWO ,V>IA#S
,SIDEB>3
,2F
,9 ,*APT] #A1 Y LE>N$ ! FOLL[+ SKILLS1
: Y'LL USE 9 ,*APT] #B3 EVALUAT+
ALGEBRAIC EXPRES.NS1 SOLV+ L9E> EQU,NS1
& REWRIT+ EQU,NS4
,PREREQUISITE ,SKILLS
,,VOCABUL>Y ,,*ECK
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..#A4 ,A L9E> .EQU,N 9 "O V>IA# IS AN
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IS ! 4T.E ! NUMB] IS F @8 ON A NUMB]
L9E4
,,SKILLS ,,*ECK
,EVALUATE ! EXPRES.N =! GIV5 VALUE (
.;X @7 .,REVIEW P4 #AJ .= .#B..A4 @7
.#C4 --#B7 .;X @+ ;L7 :5 .;X .K --#E
.#D4 #AA .;X -- #AD :5 .;X .K --#C
.#E4 .;X #B @+ .;X @+ #A :5 .;X .K #D
.#F4 -- .;X #B -- #C .;X @+ #G :5 .;X
.K #A
,SOLVE ! EQU,N4 ,*ECK YR SOLU;N4 @7
.,REVIEW P4 #AH .= .#B..C4 @7
.#G4 #E .;X -- #B .K #H
.#H4 --#F .;X -- #AJ .K #BJ
.#I4 -- .;X @+ #I .K #B .;X -- #BG
,SOLVE ! EQU,N = .;Y @4 @7 .,REVIEW P4
#BF .= .#B..D4 @7
.#AJ4 #B .;X @+ #C .;Y .K #F
.#AA4 -- .;X -- .;Y .K #AJ
.#AB4 .;X @+ #D .;Y .K --#E
@A.,HOME,TUTOR ,PREREQUISITE SKILLS
PRACTICE AT _+CLASSZONE.COM_:
-------------------------------------#GA
,SIDEB>3
,N[
,9 ,*APT] #B1 Y W APPLY ! BIG ID1S
LI/$ 2L & REVIEW$ 9 ! ,*APT] ,SUMM>Y ON
PAGE #ADJ @4 ,Y W AL USE ! KEY VOCABUL>Y
LI/$ 2L4
,BIG ,ID1S
.#A ,REPRES5T+ REL,NS & FUNC;NS
.#B ,GRAPH+ L9E> EQU,NS & 9EQUALITIES
9 TWO V>IA#S
.#C ,WRIT+ L9E> EQU,NS & 9EQUALITIES 9
TWO V>IA#S
,KEY ,VOCABUL>Y
99 DOMA91 RANGE1 P4 #GB
99 FUNC;N1 P4 #GC
99 L9E> FUNC;N1 P4 #GE
99 SLOPE1 P4 #HB
99 RATE ( *ANGE1 P4 #HE
99 P>5T FUNC;N1 P4 #HI
99 ;Y-9T]CEPT1 P4 #HI
99 SLOPE-9T]CEPT =M1 P4 #IJ
99 .;X -9T]CEPT1 P4 #IA
99 PO9T-SLOPE =M1 P4 #IH
99 DIRECT V>I,N1 P4 #AJG
99 CORREL,N COE6ICI5T1 P4 #AAD
99 BE/-FITT+ L9E1 P4 #AAD
99 ABSOLUTE VALUE FUNC;N1 P4 #ABC
99 TRANS=M,N1 P4 #ABC
99 L9E> 9EQUAL;Y 9 TWO V>IA#S1 P4 #ACB
,SIDEB>3
,:Y8
,Y C USE RATES ( *ANGE 6F9D L9E>
MODELS4 ,= EXAMPLE1 Y C USE AN AV]AGE
RATE ( *ANGE 6MODEL 4T.E TRAVEL$ Z A
FUNC;N ( "T4
.,ANIMAT$ ,ALGEBRA
,! ANIM,N ILLU/RAT$ 2L = ,EX]CISE #DD
ON PAGE #AAA HELPS Y ANSW] ? "Q3 ,IF A
:ALE MIGRATES AT A GIV5 RATE1 H[ F> W X
TRAVEL 9 DI6]5T P]IODS ( "T8
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,ALASKA4
,PICTURE3 ,*ANGE ! "T ELAPS$ 6F9D H[
F> ! :ALES H TRAVEL$4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,O!R ANIM,NS = ,*APT] .#B3 PAGES #GC
@1 #HF @1 #IJ @1 #IE @1 #IH @1 #AJB @1
#AJG @1 #AAE @1 #ACC @1 & #ADJ
-------------------------------------#GB
#B.A ,REPRES5T ,REL,NS & ,FUNC;NS
.,2F ,Y SOLV$ L9E> EQU,NS4
.,N[ ,Y W REPRES5T REL,NS & GRAPH L9E>
FUNC;NS4
.,:Y8 ,S Y C MODEL *ANGES 9 ELEV,N1 Z
9 ,EX4 #DH4
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99 REL,N
99 DOMA9
99 RANGE
99 FUNC;N
99 EQU,N 9 TWO V>IA#S
99 L9E> FUNC;N
,SIDEB>3
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..,/UD5TS SOLVE PRO#MS 9VOLV+ FUNC;NAL
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FUNC;N & P]=M+ >I?METIC OP],NS ON
FUNC;NS4
,A .REL,N IS A .MAPP+ @1 OR PAIR+1 (
9PUT VALUES ) \TPUT VALUES4 ,! SET (
9PUT VALUES IS ! .DOMA9 @1 &! SET (
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,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,REPRES5T+ ,REL,NS
,A REL,N C 2 REPRES5T$ 9 ! FOLL[+
WAYS4
,ORD]$ ,PAIRS
7--#B1 #B7
7--#B1 --#B7
7#J1A7
7#C1A7
,TA#
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,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 .;Y
--#B3 #B
--#B3 --#B
#J3 #A
#C3 #A
,GRAPH
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,,EXAMPLE #A ,REPRES5T REL,NS
,3SID] ! REL,N GIV5 0! ORD]$ PAIRS
7--#B1 --#C71 7--#A1A71 7#A1 #C71 7#B1
--#B71 & 7#C1A74
.A4 ,ID5TIFY ! DOMA9 & RANGE4
.B4 ,REPRES5T ! REL,N US+ A GRAPH &A
MAPP+ DIAGRAM4
,SOLU;N
.A4 ,! DOMA9 3SI/S ( ALL ! .;X
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--#C1 --#B1 #A1 & #C4
B4 ,GRAPH
,,REVIEW ,,GRAPH+
,= HELP ) PLOTT+ PO9TS 9 A COORD9ATE
PLANE1 SEE P4 #IHG @4
,MAPP+ ,DIAGRAM
-------------------------------------#GC
.,,FUNC;NS ,A FUNC;N IS A REL,N = :
EA* 9PUT HAS EXACTLY "O \TPUT4 ,IF ANY
9PUT (A REL,N HAS M ?AN "O \TPUT1 !
REL,N IS .N A FUNC;N4
,,EXAMPLE #B ,ID5TIFY FUNC;NS
,,AVOID ,,]RORS
,A REL,N C MAP M ?AN "O 9PUT ONTO !
SAME \TPUT & / 2 A FUNC;N4
,TELL :E!R ! REL,N IS A FUNC;N4
,EXPLA94
.A4
.B4
,SOLU;N
.A4 ,! REL,N .IS A FUNC;N 2C EA* 9PUT
IS MAPP$ ONTO EXACTLY "O \TPUT4
.B4 ,! REL,N .IS .N A FUNC;N 2C ! 9PUT
#A IS MAPP$ ONTO BO? --#A & #B4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,,GUID$ ,,PRACTICE = ,EXAMPLES #A &
.#B
#A4 ,3SID] ! REL,N GIV5 0! ORD]$ PAIRS
7--#D1 #C71 7--#B1 #A71 7#J1 #C71 7#A1
--#B71 & 7--#B1 --#D74
A4 ,ID5TIFY ! DOMA9 & RANGE4
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MAPP+ DIAGRAM4
#B4 ,TELL :E!R ! REL,N IS A FUNC;N4
.,EXPLA94
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 --#B3 --#A3 #J3 #A3 #C
.;Y @3 --#D3 --#D3 --#D3 --#D3 --#D
.,,V]TICAL .,,L9E .,,TE/ ,Y C USE !
GRAPH (A REL,N 6DET]M9E :E!R X IS A
FUNC;N 0APPLY+ ! .V]TICAL .L9E .TE/4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,V]TICAL ,L9E ,TE/
,,REVIEW ,,LOGICAL ,,/ATE;TS
,= HELP ) 8,IF & ONLY IF0 /ATE;TS1 SEE
P4 #AJJB @4
,A REL,N IS A FUNC;N IF & ONLY IF NO
V]TICAL L9E 9T]SECTS ! GRAPH (! REL,N AT
M ?AN "O PO9T4
,FUNC;N
,N A FUNC;N
-------------------------------------#GD
,,EXAMPLE #C ,USE ! V]TICAL L9E TE/
.,,BASKETBALL ,! F/ GRAPH 2L PLOTS
AV]AGE PO9TS P] GAME V]SUS AGE AT ! 5D
(! #BJJC-BJJD ,,NBA REGUL> S1SON =! #H
MEMB]S (! ,M9NESOTA ,TIMB]WOLVES )!
HI<E/ AV]AGES4 ,! SECOND GRAPH PLOTS
AV]AGE PO9TS P] GAME V]SUS AGE = "O T1M
MEMB]1 ,KEV9 ,G>NETT1 OV] 8 F/ #I
S1SONS4 ,>E ! REL,NS %[N 0! GRAPHS
FUNC;NS8 ,EXPLA94
,,R1D+ ,,GRAPHS
,! ZIGZAG SYMBOL ON ! HORIZONTAL AXIS
( EA* GRAPH 9DICATES T VALUES ( .;X 7
SKIPP$4
,SOLU;N
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FUNC;N 2C V]TICAL L9ES AT .;X .K #BH &
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REPRES5T A FUNC;N 2C NO V]TICAL L9E
9T]SECTS ! GRAPH AT M ?AN "O PO9T4
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.#C4 .,,:AT .,,IF8 ,9 ,EXAMPLE #C1
SUPPOSE T ,KEV9 ,G>NETT AV]AGES #BD.B
PO9TS P] GAME 9 8 T5? S1SON Z HE DID 9 8
N9?4 ,IF ! REL,N GIV5 0! SECOND GRAPH IS
REVIS$ 69CLUDE ! T5? S1SON1 IS ! REL,N /
A FUNC;N8 .,EXPLA94
..,,EQU,NS ,,9 ,,TWO .,,V>IA#S ,_M
FUNC;NS C 2 DESCRIB$ 0AN ..EQU,N 9 TWO
.V>IA#S @1 S* Z .;Y .K #C .;X -- #E4 ,!
9PUT V>IA# 7IN ? CASE1 .;X @7 IS CALL$ !
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CASE1 .;Y @7 IS CALL$ ! .DEP5D5T .V>IA#
2C XS VALUE .DEP5DS ON ! VALUE (! 9PUT
V>IA#4
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.SOLU;N ( AN EQU,N 9 TWO V>IA#S IF
SUB/ITUT+ .;X & .;Y 9 ! EQU,N PRODUCES A
TRUE /ATE;T4 ,= EXAMPLE1 7#B1A7 IS A
SOLU;N ( .;Y .K #C .;X -- #E 2C #A .K
#C7#B7--#E IS TRUE4 ,! .GRAPH ( AN EQU,N
9 TWO V>IA#S IS ! SET ( ALL PO9TS @7 .;X
@1 .;Y @7 T REPRES5T SOLU;NS (! EQU,N4
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^! /EPS3
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6RECOGNIZE A PATT]N4
.,,/EP#C .,3NECT ! PO9TS )A L9E OR A
CURVE4
-------------------------------------#GE
,,EXAMPLE #D ,GRAPH AN EQU,N 9 TWO
V>IA#S
,GRAPH ! EQU,N .;Y .K --#B .;X -- #A4
,SOLU;N
.,,/EP .#A .,3/RUCT A TA# ( VALUES4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 --#B3 --#A3 #J3 #A3 #B
.;Y @3 #C3 #A3 --#A3 --#C3 --#E
.,,/EP#B .,PLOT ! PO9TS4 ,NOTICE T !Y
ALL LIE ON A L9E4
.,,/EP .#C .,3NECT ! PO9TS )A L9E4
,,R1D+
,! P>5!SES 9 .;F @7 .;X @7 D N 9DICATE
MULTIPLIC,N4 ,! SYMBOL .;F @7 .;X @7
DOES N M1N @8 .;F "TS .;X @4@8
.,,L9E> .,,FUNC;NS ,! FUNC;N .;Y .K
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.FUNC;N 2C X C 2 WRITT5 9 ! =M .;Y .K
.MX @+ .;B ": .;M & .;B >E 3/ANTS4 ,!
GRAPH (A L9E> FUNC;N IS A L9E4 ,0RENAM+
.;Y Z .;F @7 .;X @7@1 Y C WRITE .;Y .K
.MX @+ .;B US+ .FUNC;N .NOT,N4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;Y .K .MX @+ .;B @3 ..,L9E> FUNC;N 9
;X--;Y .NOT,N
.;F @7 .;X @7 .K .MX @+ .;B @3 ..,L9E>
FUNC;N 9 FUNC;N .NOT,N
,! NOT,N .;F @7 .;X @7 IS R1D 8! VALUE
( .;F AT .;X @1@8 OR SIMPLY @8 .;F ( .;X
@1@8 & ID5TIFIES .;X Z ! 9DEP5D5T V>IA#4
,! DOMA9 3SI/S ( ALL VALUES ( .;X = :
.;F @7 .;X @7 IS DEF9$4 ,! RANGE 3SI/S (
ALL VALUES ( .;F @7 .;X @7 ": .;X IS 9 !
DOMA9 ( .;F @4
,,EXAMPLE #E ,CLASSIFY & EVALUATE
FUNC;NS
,,REPRES5T ,,FUNC;NS
,LRS O!R ?AN .;F @1 S* Z .;G OR .;H @1
C AL "N FUNC;NS4
,TELL :E!R ! FUNC;N IS L9E>4 ,!N
EVALUATE ! FUNC;N :5 .;X .K --.#D4
.A4 .;F @7 .;X @7 .K --.;X #B -- #B
.;X @+ #G
.B4 .;G @7 .;X @7 .K #E .;X @+ #H
,SOLU;N
.A4 ,! FUNC;N .;F IS N L9E> 2C X HAS
AN .;X #B -T]M4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;F @7 .;X @7 .K --;X.' #B -- #B;X @+
#G @3 .,WRITE .FUNC;N4
.;F @7 --.#D @7 .K --@7 --.#D @7 #B --
#B7--#D7 @+ #G @3 ,SUB/ITUTE --#D = .;X
@4
.K --#A3 .,SIMPLIFY4
.B4 ,! FUNC;N ;G IS L9E> 2C X HAS ! =M
.;G @7 .;X @7 .K .MX @+ .B4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
;G7 .;X @7 .K #E .;X @+ #H @3 .,WRITE
.FUNC;N4
;G7 --.#D @7 .K #E7 --.#D @7 @+ #H @3
,SUB/ITUTE --#D =.' ;X @4
.K --#AB3 .,SIMPLIFY4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #D &
.#E
.#D4 ,GRAPH ! EQU,N .;Y .K #C .;X --
#B4
,TELL :E!R ! FUNC;N IS L9E>4 ,!N
EVALUATE ! FUNC;N :5 .;X .K --.#B4
.#E4 .;F @7 .;X @7 .K .;X -- #A--;X #C
.#F4 .;G @7 .;X @7 .K --#D--#B .;X
-------------------------------------#GF
..,,DOMA9S ,,9 ,,R1L .,,LIFE ,9
,EXAMPLE #E1 ! DOMA9 ( EA* FUNC;N IS ALL
R1L NUMB]S 2C "! IS AN \TPUT = E R1L
NUMB] .X4 ,9 R1L LIFE1 Y MAY NE$
6RE/RICT ! DOMA9 S T X IS R1SONA# 9 !
GIV5 SITU,N4
,,EXAMPLE #F ,USE A FUNC;N 9 R1L LIFE
.,,DIV+ ,A DIV] US+ A ,DIV] ,PROPUL.N
,VEHICLE 7,,DPV7 DESC5DS 6A DEP? ( #ACJ
FEET4 ,! PRESSURE .;,P 7IN ATMOSPH]ES7
ON ! DIV] IS GIV5 0.;,P7.;D @7 .K #A @+
#J.JC;D ": .;D IS ! DEP? 7IN FEET74
,GRAPH ! FUNC;N1 & DET]M9E A R1SONA#
DOMA9 & RANGE4 ,:AT IS ! PRESSURE ON !
DIV] AT A DEP? ( #CC FEET8
,SOLU;N
,! GRAPH ( .;,P @7 .;D @7 IS %[N4 ,2C
! DEP? V>IES F #J FEET 6#ACJ FEET1 A
R1SONA# DOMA9 IS #J "K.K .;D "K.K #ACJ4
,! M9IMUM VALUE ( .;,P @7 .;D @7 IS
.;,P 7#J7 .K #A1 &! MAXIMUM VALUE ( .;,P
@7 .;D @7 IS .;,P 7#ACJ7 .K #D.I4 ,S1 A
R1SONA# RANGE IS #A "K.K .;,P7.;D7 "K.K
#D.I4
99 ,AT A DEP? ( #CC FEET1 ! PRESSURE
ON ! DIV] IS ;,P7#CC7 .K #A @+
#J.JC7#CC7 #B ATMOSPH]ES1 : Y C V]IFY F
! GRAPH4
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#F
.#G4 .,,OC1N .,,EXPLOR,N ,9 #AIFJ1 !
DEEP-SEA VESSEL .,TRIE/E DESC5D$ 6AN
E/IMAT$ DEP? ( #CE1HJJ FEET4 ,DET]M9E A
R1SONA# DOMA9 & RANGE (! FUNC;N .;,P @7
.;D @7 9 ,EXAMPLE #F = ? TRIP4
#B.A ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#B = ,EXS4 #G1 #AG1 & #DE
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 #B1 #I1 #BJ1 #BD1DJ1DF1 & #DI
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,9 !
EQU,N .;Y .K .;X @+ #E1 .;X IS ! @8
V>IA# & .;Y IS ! @8 V>IA#4
.#B4 .,,WRIT+ .,DESCRIBE H[ 6F9D !
DOMA9 & RANGE (A REL,N GIV5 0A SET (
ORD]$ PAIRS4
,,EXAMPLE #A
ON P4 #GB = ,EXS4 #C-I
,,REPRES5T+ ,,REL,NS ,ID5TIFY ! DOMA9
& RANGE (! GIV5 REL,N4 ,!N REPRES5T !
REL,N US+ A GRAPH &A MAPP+ DIAGRAM4
.#C4 7--#B1 #C71 7#A1 #B71 7#C1 --#A71
7--#D1 --#C7
.#D4 7#E1 --#B71 7--#C1 --#B71 7#C1
#C71 7--#A1 --#A7
.#E4 7#F1 --#A71 7--#B1 --#C71 7#A1
#H71 7--#B1 #E7
.#F4 7--#G1 #D71 7#B1 --#E71 7#A1
--#B71 7--#C1 #F7
.#G 7#E1 #BJ71 7#AJ1 #BJ71 7#AE1 #CJ71
7#BJ1 #CJ7
.#H4 7#D1 --#B71 7#D1 #B71 7#AF1
--#D71 7#AF1 #D7
-------------------------------------#GG
#I4 .,,MULTIPLE .,,*OICE ,:AT IS !
DOMA9 (! REL,N GIV5 0! ORD]$ PAIRS7--#D1
#B71 7--#A1 --#C71 7#A1 #D71 7#A1 --#C71
& 7#B1 #A78
,A --#C1 #A1B1 & #D
;,B --#D1--#A1A1 & #B
;,C --#D1 --#C1 --#A1 & #B
;,D --#D1 --#C1 --#A1 #A1 #B1 & #D
,,EXAMPLE #B
ON P4 #GC = ,EXS4 #AJ--#BJ
.,,ID5TIFY+ .,,FUNC;NS ,TELL :E!R !
REL,N IS A FUNC;N4 .,EXPLA94
.#AJ4
.#AA4
.#AB4
.#AC4
.,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 ! /UD5T'S "W4
.#AD4
.#AE4
.,,ID5TIFY+ .,,FUNC;NS ,TELL :E!R !
REL,N IS A FUNC;N4 .,EXPLA94
.#AF4 7#C1 --#B71 7#J1 #A71 7#A1 #J71
7--#B1 --#A71 7#B1 --#A7
.#AG4 7#B1 --#E71 7--#B1 #E71 7--#A1
#D71 7--#B1 #J71 7#C1 --#D7
.#AH4 7#J1 #A71 7#A1 #J71 7#B1 #C71
7#C1 #B71 7#D1 #D7
.#AI4 7--#A1 --#A71 7#B1 #E71 7#D1
#H71 7--#E1 --#I71 7--#A1 --#E7
#BJ4 .,,MULTIPLE .,,*OICE ,! REL,N
GIV5 0! ORD]$ PAIRS 7--#F1 #C71 7--#B1
#D71 7#A1 #E71 & 7#D1 #J7 IS A FUNC;N4
,: ORD]$ PAIR C 2 9CLUD$ ) ? REL,N 6=M A
NEW REL,N T IS AL A FUNC;N8
,A 7#A1 --#E7
;,B 7#F1 #C7
;,C 7--#B1 #AI7
;,D 7#D1 #D7
,,EXAMPLE #C
ON P4 #GD = ,EXS4 #BA--#BC
.,,V]TICAL .,,L9E .,,TE/ ,USE !
V]TICAL L9E TE/ 6TELL :E!R ! REL,N IS A
FUNC;N4
.#BA4
.#BB4
.#BC4
.#BD4 .,,%ORT .,,RESPONSE .,EXPLA9 :Y
A REL,N IS N A FUNC;N IF A V]TICAL L9E
9T]SECTS ! GRAPH (! REL,N M ?AN ONCE4
,,EXAMPLE #D
ON P4 #GE = ,EXS4 #BE--#CC
.,,GRAPH+ .,,EQU,NS ,GRAPH ! EQU,N4
.#BE4 .;Y .K .;X @+ #B
.#BF4 .;Y .K --.;X @+ #E
.#BG4 .;Y .K #C .;X @+ #A
.#BH4 .;Y .K #E .;X -- #C
.#BI4 .;Y .K #B .;X -- #G
.#CJ4 .;Y .K --.#C;X @+ #B
.#CA4 .;Y .K --.#B;X
.#CB4
.#CC4
-------------------------------------#GH
,,EXAMPLE #E
ON P4 #GE = ,EXS4 #CD-CI
.,,EVALUAT+ .,,FUNC;NS ,TELL :E!R !
FUNC;N IS L9E>4 ,!N EVALUATE ! FUNC;N =!
GIV5 VALUE ( .X4
.#CD4 .;F @7 .;X @7 .K .;X @+ #AE2 .;F
7#H7
.#CE4 .;F @7 .;X @7 .K .;X #B @+ #A2
.;F 7--#C7
.#CF4 .;F @7 .;X @7 .K _\ .;X _\ @+
#AJ2 .;F 7--#D7
.#CG4 .;F @7 .;X @7 .K #F2 .;F 7#B7
.#CH4 .;G @7 .;X @7 .K .;X #C -- #B
.;X #B @+ #E .;X -- #H2 .;G 7--#E7
.#CI4
.#DJ4 .,,%ORT .,,RESPONSE ,:1 IF ANY1
(! REL,NS DESCRIB$ 0! EQU,NS .;Y .K _\
.;X _\, .;X .K _\ .;Y _\, & _\ .;Y _\ .K
_\ .;X _\ REPRES5T FUNC;NS8 .,EXPLA94
.#DA4 .,,*ALL5GE ,LET .;F 2 A FUNC;N
S* T .;F 7A @+ .;B @7 .K .;F @7 .A @7 @+
.;F @7 .;B @7 = ALL R1L NUMB]S .A & .B4
,%[ T .;F 7#B;A7 .K #B 99 .;F @7 .A @7 &
T .;F 7#J7 .K #J4
,,PRO#M ,,SOLV+
.,,EXAMPLE #C
ON P4 #GD = ,EXS4 #DB-DC
.#DB4 .,,BICYCL+ ,! GRAPH %[S ! AGES
(! TOP ?REE F9I%]S 9 ! ,MT4 ,WA%+TON
,AUTO ,ROAD ,BICYCLE ,HILLCLIMB EA* YE>
F #BJJB "? #BJJD4 ,D ! ORD]$ PAIRS 7AGE1
F9I%+ PLACE7 REPRES5T A FUNC;N8
.,EXPLA94
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#DC4 .,,BASEBALL ,! GRAPH %[S ! NUMB]
( GAMES />T$ &! NUMB] ( W9S = EA* />T+
PIT*] ON A BASEBALL T1M DUR+ A REGUL>
S1SON4 ,D ! ORD]$ PAIRS 7/>TS1 W9S7
REPRES5T A FUNC;N8 .,EXPLA94
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#DD4 .,,GEOMETRY ,! VOLUME .;,V (A
CUBE ) $GE L5G? .;S IS GIV5 0! FUNC;N
.;,V7.;S @7 .K .;S #C @4 ,F9D ;,V7#D74
.,EXPLA9 :AT ;,V7#D7 REPRES5TS4
.#DE4 .,,GEOMETRY ,! VOLUME .;,V (A
SPH]E ) RADIUS .;R IS GIV5 0! FUNC;N @4
,F9D .;,V 7#F74 .,EXPLA9 :AT .;,V 7#F7
REPRES5TS4
,,EXAMPLE #F
ON P4 #GF = ,EXS4 #DF-DH
.#DF4 .,,%ORT .,,RESPONSE ,=! P]IOD
#AIII-BJJD1 ! AV]AGE NUMB] ( ACRES .;W
7IN ?\S&S71 US$ 6GR[ WAT]MELONS 9 !
,UNIT$ ,/ATES C 2 MODEL$ 0! FUNC;N .;W
@7 .;T @7 .K --#F.BF .;T @+ #AGB ": .;T
IS ! NUMB] ( YE>S S9CE #AIII4 ,DET]M9E A
R1SONA# DOMA9 & RANGE = .;W @7 .;T @7@4
.,EXPLA9 ! M1N+ (! RANGE4
#DG4 .,,MULTI-.,,/EP .,,PRO#M
,AN?ROPOLOGI/S C E/IMATE A P]SON'S HEI<T
F ! L5G? ( C]TA9 B"OS4 ,! HEI<T .;H 7IN
9*ES7 ( AN ADULT HUMAN FEMALE C 2 MODEL$
0! FUNC;N .;H @7 .;L @7 .K #A.IE6 @+
#BH.G ": .;I IS ! L5G? 7IN 9*ES7 (!
FEMUR1 OR ?I< B"O4 ,! FUNC;N IS VALID =
FEMUR L5G?S 2T #AE 9*ES & #BD 9*ES1
9CLUSIVE4
A4 ,GRAPH ! FUNC;N1 & DET]M9E A
R1SONA# DOMA9 & RANGE4
B4 ,SUPPOSE A FEMALE'S FEMUR IS #AE.E
9*ES L;G4 ,AB H[ TALL 0 %E8
C4 ,IF AN AN?ROPOLOGI/ E/IMATES A
FEMALE'S HEI<T Z #E FEET #AA 9*ES1 AB H[
L;G IS H] FEMUR8
.K .,,"W$-.,,\ .,,SOLU;NS .ON
.P4.,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
-------------------------------------#GI
.#DH4 .,,M.TA9 .,,CLIMB+ ,A CLIMB] ON
,M.T ,RA9I] 9 ,WA%+TON HIKES F AN ELEV,N
( #EDJJ FEET ABV SEA LEVEL 6,CAMP ,MUIR1
: HAS AN ELEV,N ( #AJ1AJJ FEET4 ,!
ELEV,N .;H 7IN FEET7 Z ! CLIMB] ASC5DS C
2 MODEL$ 0.;H @7 .;T @7 .K .#AJJJ;T @+
#EDJJ ": .;T IS ! "T 7IN H\RS74 ,GRAPH !
FUNC;N1 & DET]M9E A R1SONA# DOMA9 &
RANGE4 ,:AT IS ! CLIMB]'S ELEV,N AF HIK+
#C.E H\RS8
#DI4 .,,EXT5D$ .,,RESPONSE ,! TA# %[S
! POPUL,NS ( S"EAL /ATES & _! ELECTORAL
VOTES 9 ! #BJJD & #BJJH ,U4,S4
PRESID5TIAL ELEC;NS4 ,! FIGURES >E BAS$
ON ,U4,S4 C5SUS DATA =! YE> #BJJJ4
A4 ,ID5TIFY ! DOMA9 & RANGE (! REL,N
GIV5 0! ORD]$ PAIRS 7;P1 .;V @7@4
B4 ,IS ! REL,N F "P 7A7 A FUNC;N8
.,EXPLA94
C4 ,IS ! REL,N GIV5 0! ORD]$ PAIRS @7
.;V1 .;P @7 A FUNC;N8 .,EXPLA94
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,/ATE @3 ,POPUL,N 7MILLIONS71 .;P @3
,ELECTORAL VOTES1 .;V
,CALI=NIA3 #CC.HG3 .#EE
,FLORIDA3 #AE.IH3 .#BG
,ILL9OIS3 #AB.DB3 .#BA
,NEW ,YORK3 #AH.IH3 .#CA
,OHIO3 #AA.CE3 .#BJ
,P5NSYLVANIA3 #AB.BH3 .#BA
,TEXAS3 #BJ.HE3 .#CD
#EJ4 .,,*ALL5GE ,! TA# %[S GR.D %IPP+
*>GES = AN ONL9E RETAIL /ORE4
A4 ,IS ! %IPP+ CO/ A FUNC;N (! M]*&ISE
CO/8 .,EXPLA94
B4 ,IS ! M]*&ISE CO/ A FUNC;N (! %IPP+
CO/8 .,EXPLA94
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,M]*&ISE CO/3 ,%IPP+ CO/
@4#.JA-4#CJ.JJ3 4#D.EJ
4#CJ.JA-4#FJ.JJ3 4#G.BE
4#FJ.JA-4#AJJ.JJ3 4#I.EJ
,OV] 4#AJJ.JJ3 4#AB.EJ
,,MIX$ ,,REVIEW
,,PREVIEW
,PREP>E = ,LESSON #B.B 9 ,EXS4 #EA-ED4
,EVALUATE ! EXPRES.N =! GIV5 VALUES (
.;X & .Y4 @7 P4 #AJ @7
.#EA4 :5 .;X .K #F & .;Y .K #B
.#EB4 :5 .;X .K #C & .;Y .K #D
.#EC4 :5 .;X .K --#C & .;Y .K --#C
.#ED4 :5 .;X .K --#AG & .;Y .K #H
,SOLVE ! EQU,N4 ,*ECK YR SOLU;N4 @7 P4
#AH @7
.#EE4 #C .;X @+ #AF .K #CA
.#EF4 --#D .;X -- #G .K #AG
.#EG4 #E .;X @+ #AB .K --#C .;X -- #D
.#EH4 #E--#H .;Z .K #BE @+ #D .;Z
.#EI4
.#FJ4 #F7#D .;W @+ #A7 .K #A.E7#H .;W
@+ #AH7
,SOLVE ! 9EQUAL;Y4 ,!N GRAPH ! SOLU;N4
@7 P4 #DA @7
.#FA4 #B .;X -- #F .1 #H
.#FB4
.#FC4 #AE--#B .;X "K.K #G
.#FD4 #D -- .;X "K #C
.#FE4 --#G "K #F .;X -- #A "K #E
.#FF4 .;X -- #B "K.K #A OR #D .;X @+
#C .1.K #AI
.,,EXTRA .,,PRACTICE = ,LESSON #B.A1
P4 #AJAA
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
-------------------------------------#HJ
,EXT5.N ,USE ,4CRETE & ,3T9U\S
,FUNC;NS
,USE AF ,LESSON #B.A
,KEY ,VOCABUL>Y
99 4CRETE FUNC;N
99 3T9U\S FUNC;N
.,,GOAL ,GRAPH & CLASSIFY 4CRETE &
3T9U\S FUNC;NS4
,! GRAPH (A FUNC;N MAY 3SI/ ( .4CRETE
@1 OR SEP>ATE & UNCONNECT$1 PO9TS 9 A
PLANE4 ,! GRAPH (A FUNC;N MAY AL 2 A
.3T9U\S @1 OR UNBROK51 L9E OR CURVE OR
"P (A L9E OR CURVE4
,SIDEB>3
,/&>DS3 ,PREP>E = #BD.J
..,/UD5TS SOLVE PRO#MS 9VOLV+ FUNC;NAL
.3CEPTS @1 S* Z -POSI;N1 DEF9+ ! 9V]SE
FUNC;N & P]=M+ >I?METIC OP],NS ON
FUNC;NS4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,4CRETE & ,3T9U\S ,FUNC;NS
,! GRAPH (A .4CRETE .FUNC;N 3SI/S (
SEP>ATE PO9TS4
,! GRAPH (A .3T9U\S .FUNC;N IS
UNBROK54
,,EXAMPLE #A ,GRAPH & CLASSIFY FUNC;NS
,GRAPH ! FUNC;N .;F @7 .;X @7 .K #J.E
.;X @+ #A =! GIV5 DOMA94 ,CLASSIFY !
FUNC;N Z .4CRETE OR .3T9U\S =! DOMA94
,!N ID5TIFY ! RANGE4
.A4 ,DOMA93 .;X .K --#B1 #J1 #B1 #D
.B4 ,DOMA93 .;X .1.K --#C
,SOLU;N
.A4 ,MAKE A TA# US+ ! ;X-VALUES 9 !
DOMA94
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 --#B3 #J3 #B3 #D
.;Y @3 #J3 #A@3 #B3 #C
,! GRAPH 3SI/S ( SEP>ATE PO9TS1 S !
FUNC;N IS 4CRETE4 ,XS RANGE IS #J1 #A1
#B1 #C4
.B4 ,NOTE T .;F @7 .;X @7 IS A L9E>
FUNC;N DEF9$ = .;X .1.K --#C1 & T .;F
7--#C7 .K --#J.E4 ,S1 ! GRAPH IS ! RAY )
5DPO9T 7--#C1 --#J.E7 T PASSES "? ALL !
PO9TS F ! TA# 9 "P 7A74
,! GRAPH IS UNBROK51 S ! FUNC;N IS
3T9U\S4 ,XS RANGE IS .;Y .1.K --#J.E4
-------------------------------------#HA
,,EXAMPLE #B ,GRAPH & CLASSIFY R1L-_W
FUNC;NS
,WRITE & GRAPH ! FUNC;N DESCRIB$4
,DET]M9E ! DOMA9 & RANGE4 ,!N TELL :E!R
! FUNC;N IS .4CRETE OR .3T9U\S4
.A4 ,A /UD5T GR\P IS SELL+ *OCOLATE
B>S = 4#B EA*4 ,! FUNC;N .;F @7 .;X @7
GIVES ! AM.T ( M"OY COLLECT$ AF SELL+
.;X *OCOLATE B>S4
.B4 ,A L[-FL[ %[] H1D REL1SES #A.H
GALLONS ( WAT] P] M9UTE4 ,! FUNC;N .;,V
@7 .;X @7 GIVES ! VOLUME ( WAT] REL1S$
AF .;X M9UTES4
,SOLU;N
.A4 ,! FUNC;N IS .;F @7 .;X @7 .K #BX4
,! F/ F\R PO9TS (! GRAPH ( .;F @7 .;X @7
>E %[N4 ,ONLY :OLE *OCOLATE B>S C 2
SOLD1 S ! DOMA9 IS ! SET ( :OLE NUMB]S
#J1 #A1 #B1 #C1'4 ,F ! GRAPH1 Y C SEE T
! RANGE IS #J1 #B1 #D1 #F1'4 ,! GRAPH
3SI/S ( SEP>ATE PO9TS1 S ! FUNC;N IS
4CRETE4
.B4 ,! FUNC;N IS .;,V @7 .;X @7 .K
#A.HX4 ,Y C RUN ! %[] ANY NONNEGATIVE
AM.T ( "T1 S ! DOMA9 IS .;X .1.K #J4 ,F
! GRAPH1 Y C SEE T ! RANGE IS .;Y .1.K
#J4 ,! GRAPH IS UNBROK51 S ! FUNC;N IS
3T9U\S4
,,PRACTICE
,,EXAMPLE #A
ON P4 #HJ = ,EXS4 #A-D
,GRAPH ! FUNC;N =! GIV5 DOMA94
,CLASSIFY ! FUNC;N Z .4CRETE OR .3T9U\S4
,!N ID5TIFY ! RANGE (! FUNC;N4
.#A4 .;Y .K #B .;X @+ #C2 DOMA93 --#B1
--#A1 #J1 #A1 #B
.#B4 .;F @7 .;X @7 .K #J.E .;X -- #D2
DOMA93 --#D1 --#B1 #J1 #B1 #D
.#C4 .;Y .K --#C .;X @+ #I2 DOMA93 .;X
"K #E
.#D4
,,EXAMPLE #B
ON P4 #HA = ,EXS4 #E-H
,WRITE & GRAPH ! FUNC;N DESCRIB$4
,DET]M9E ! DOMA9 & RANGE4 ,!N TELL :E!R
! FUNC;N IS .4CRETE OR .3T9U\S4
.#E4 ,AM&A WALKS AT AN AV]AGE SPE$ (
#C.E MILES P] H\R4 ,! FUNC;N .;D @7 .;X
@7 GIVES ! 4T.E 7IN MILES7 ,AM&A WALKS 9
.;X H\RS4
.#F4 ,A TOK5 6RIDE A SUBWAY CO/S
4#A.BE4 ,! FUNC;N .;S @7 .;X @7 GIVES !
CO/ ( RID+ ! SUBWAY .;X "TS4
.#G4 ,A FAMILY HAS #C GALLONS ( MILK
DELIV]$ E ,?URS"D4 ,! FUNC;N .;M @7 .;X
@7 GIVES ! TOTAL AM.T ( MILK T IS
DELIV]$ 6! FAMILY AF .;X WEEKS4
.#H4 ,/EEL CA# T IS 9* 9 DIAMET] WEI<S
#J.BD P.D P] FOOT4 ,! FUNC;N .;W @7 .;X
@7 GIVES ! WEI<T ( .;X FEET ( /EEL CA#4
.#I4 ,ON A NUMB] L9E1 ! .SIGN$ .4T.E F
A NUMB] .A 6A NUMB] .;B IS GIV5
0.;B--.A4 ,! FUNC;N .;D @7 .;X @7 GIVES
! SIGN$ 4T.E F #C 6ANY NUMB] .X4
-------------------------------------#HB
#B.B ,F9D ,SLOPE & ,RATE ( ,*ANGE
.,2F ,Y GRAPH$ L9E> FUNC;NS4
.,N[ ,Y W F9D SLOPES ( L9ES & RATES (
*ANGE4
.,:Y8 ,S Y C MODEL GR[? RATES1 Z 9
,EX4 #DF4
,KEY ,VOCABUL>Y
99 SLOPE
99 P>ALLEL
99 P]P5DICUL>
99RATE ( *ANGE
99 RECIPROCAL1 P4 #D
,SIDEB>3
,/&>DS3 ,PREP>E = #B.J
..,/UD5TS SOLVE SY/EMS ( L9E> .EQU,NS
& 9EQUALITIES 7IN TWO OR ?REE V>IA#S7
0SUB/ITU;N1 .) .GRAPHS @1 OR ) MATRICES4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,SLOPE (A ,L9E
,^WS
,! .SLOPE .;M (A NONV]TICAL L9E IS !
RATIO ( V]TICAL *ANGE 7! .RISE @7
6HORIZONTAL *ANGE 7! .RUN @7@4
,ALGEBRA
,GRAPH
,,EXAMPLE #A ,F9D SLOPE 9 R1L LIFE
.,,SKATEBO>D+ ,A SKATEBO>D RAMP HAS A
RISE ( #AE 9*ES &A RUN ( #ED 9*ES4 ,:AT
IS XS SLOPE8
,SOLU;N
99 ,! SLOPE (! RAMP IS @4
..,,EXAMPLE #B ,/&>DIZ$ ,TE/
.,PRACTICE
..,:AT IS ! SLOPE (! L9E PASS+ "? !
.PO9TS @7-- ..#A1 #C7 & 7#B1 --.#A78
.,A
.;,B
.;,C
.;,D
,,AVOID ,,]RORS
,:5 CALCULAT+ SLOPE1 2 SURE 6SUBTRACT
! .;X - & .;Y-.COORD 9ATES 9 A 3SI/5T
ORD]4
,SOLU;N
,LET @7 .;X #A @1 .;Y #A @7 .K @7
--.#A1 .#C @7 & @7 .;X #B @1 .;Y #B @7
.K @7 .#B1 --.#A @7@4
99 ,! CORRECT ANSW] IS ,A4 .,A .;,B
.;,C .;,D
-------------------------------------#HC
..,GUID$ ,PRACTICE = ,EXAMPLES #A &
.#B
.#A4 .,,:AT .,,IF8 ,9 ,EXAMPLE #A1
SUPPOSE T ! RISE (! RAMP IS *ANG$ 6#AB
9*ES )\T *ANG+ ! RUN4 ,:AT IS ! SLOPE (!
RAMP8
#B4 ,:AT IS ! SLOPE (! L9E PASS+ "? !
PO9TS 7--#D1 #I7 & 7--#H1 #C78
,A
;,B
;,C
;,D
,F9D ! SLOPE (! L9E PASS+ "? ! GIV5
PO9TS4
.#C4 7#J1 #C71 7#D1 #H7
.#D4 7--#E1 #A71 7#E1 --#D7
.#E4 7--#C1 --#B71 7#F1 #A7
.#F4 7#G1 #C71 7--#A1 #G7
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,CLASSIFIC,N ( ,L9ES 0,SLOPE
,! SLOPE (A L9E 9DICATES :E!R ! L9E
RISES F LEFT 6"R1 FALLS F LEFT 6"R1 IS
HORIZONTAL1 OR IS V]TICAL4
,,R1D+
,A V]TICAL L9E HAS 8UNDEF9$ SLOPE0 2C
= ANY TWO PO9TS1 ! SLOPE =MULA'S
DENOM9ATOR 2COMES #J1 & DIVI.N 0#J IS
UNDEF9$4
,POSITIVE SLOPE
,RISES F LEFT 6"R
,NEGATIVE SLOPE
,FALLS F LEFT 6"R
,Z]O SLOPE
,HORIZONTAL
,UNDEF9$ SLOPE
,V]TICAL
,,EXAMPLE #C ,CLASSIFY L9ES US+ SLOPE
,)\T GRAPH+1 TELL :E!R ! L9E "? ! GIV5
PO9TS ..RISES1 FALLS1 IS .HORIZONTAL @1
OR IS .V]TICAL4
.A4 7--#E1 #A71 7#C1 #A7
.B4 7--#F1J717#B1--#D7
.C4 7--#A1C71 7#E1 #H7
.D4 7#D1 #F71 7#D1--#A7
,SOLU;N
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.A4 @3 ,2C.' ;M .K #J1 ! L9E IS
HORIZONTAL4
.B4 @3 ,2C.' ;M "K #J1 ! L9E FALLS4
.C4 @3 ,2C.' ;M .1 #J1 ! L9E RISES4
.D4 @3 ,2C.' ;M .-IS UNDEF9$1 ! L9E IS
V]TICAL4
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#C
,)\T GRAPH+1 TELL :E!R ! L9E "? ! GIV5
PO9TS ..RISES1 FALLS1 IS .HORIZONTAL @1
OR .IS .V]TICAL4
.#G4 7--#D1 #C71 7#B1--#F7
.#H4 7#G1A71 7#G1--#A7
.#I4 7#C1--#B71 7#E1--#B7
.#AJ4 7#E1 #F71 7#A1--#D7
-------------------------------------#HD
..,,P>ALLEL ,,& ,,P]P5DICUL> .,,L9ES
,RECALL T TWO L9ES 9 A PLANE >E .P>ALLEL
IF !Y D N 9T]SECT4 ,TWO L9ES 9 A PLANE
>E .P]P5DICUL> IF !Y 9T]SECT 6=M A "R
ANGLE4,SLOPE C 2 US$ 6DET]M9E :E!R TWO
DI6]5T NONV]TICAL L9ES >E P>ALLEL OR
P]P5DICUL>4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,SLOPES ( ,P>ALLEL & ,P]P5DICUL> ,L9ES
,3SID] TWO DI6]5T NONV]TICAL L9ES #A &
#B ) SLOPES .;M #A & .;M #B @4
.,P>ALLEL .,L9ES ,! L9ES >E P>ALLEL IF
& ONLY IF !Y H ! SAME SLOPE4
.;M #A .K .;M #B
.,P]P5DICUL> .,L9ES ,! L9ES >E
P]P5DICUL> IF & ONLY IF _! SLOPES >E
NEGATIVE RECIPROCALS ( EA* O!R4
,,EXAMPLE #D ,CLASSIFY P>ALLEL &
P]P5DICUL> L9ES
,TELL :E!R ! L9ES >E .P>ALLEL1
.P]P5DICUL> @1 OR .NEI4
.A4 ,L9E #A3 "? 7--#B1 #B7 & 7#J1
--#A7
,L9E #B3 "? 7--#D1 --#A7 & 7#B1 #C7
.B4 ,L9E #A3 "? 7#A1 #B7 & 7#D1 --#C7
,L9E #B3 "? 7--#D1 #C7 & 7--#A1 --#B7
,SOLU;N
.A4 ,F9D ! SLOPES (! TWO L9ES4
99 ,2C @1 .;M #A & .;M #B >E NEGATIVE
RECIPROCALS ( EA* O!R4 ,S1 ! L9ES >E
P]P5DICUL>4
.B4 ,F9D ! SLOPES (! TWO L9ES4
,2C .;M ;L .K .;M #B 7&! L9ES >E
DI6]5T71 Y C 3CLUDE T ! L9ES >E P>ALLEL4
-------------------------------------#HE
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#D
,TELL :E!R ! L9ES >E .P>ALLEL1
.P]P5DICUL> @1 OR .NEI4
.#AA4 ,L9E #A3 "? 7--#B1 #H7 & 7#B1
--#D7
,L9E #B3 "? 7--#E1 #A7 & 7--#B1 #B7
.#AB4 ,L9E #A3 "? 7--#D1 --#B7 & 7#A1
#G7
,L9E #B3 "? 7--#A1 --#D7 & 7#C1 #E7
.,,RATE .,,( .,,*ANGE ,SLOPE C 2 US$
6REPRES5T AN AV]AGE .RATE .( .*ANGE @1
OR H[ M* "O QUANT;Y *ANGES1 ON AV]AGE1
RELATIVE 6! *ANGE 9 ANO!R QUANT;Y4 ,A
SLOPE T IS A R1L--LIFE RATE ( *ANGE
9VOLVES UNITS ( M1SURE S* Z MILES P] H\R
OR DEGREES P] "D4
,,REVIEW ,,RATES
,REMEMB] T A .RATE IS A RATIO ( TWO
QUANTITIES T H .DI6]5T UNITS4
,,EXAMPLE #E ,SOLVE A MULTI-/EP PRO#M
.,,=E/RY ,USE ! DIAGRAM1 : ILLU/RATES
! GR[? (A GIANT SEQUOIA1 6F9D ! AV]AGE
RATE ( *ANGE 9 ! DIAMET] (! SEQUOIA OV]
"T4 ,!N PREDICT ! SEQUOIA'S DIAMET] 9
#BJFE4
,SOLU;N
.,,/EP .#A .,F9D ! AV]AGE RATE (
*ANGE4
.,,/EP .#B .,PREDICT ! DIAMET] (!
SEQUOIA 9 #BJFE4
,F9D ! NUMB] ( YE>S F #BJJE 6#BJFE4
,MULTIPLY ? NUMB] 0! AV]AGE RATE ( *ANGE
6F9D ! TOTAL 9CR1SE 9 DIAMET] DUR+ !
P]IOD #BJJE-BJFE4
,NUMB] ( YE>S .K #BJFE--#BJJE .K .#FJ
,9CR1SE 9 DIAMET] .K @7 .#FJ YE>S7 @7
.#J..A 9*_/YE>7 .K #F 9*ES
99 ,9 #BJFE1 ! DIAMET] (! SEQUOIA W 2
AB #ADA @+ #F .K #ADG 9*ES4
..,GUID$ ,PRACTICE = ,EXAMPLE .#E
.#AC4 .,,:AT .,,IF8 ,9 ,EXAMPLE #E1
SUPPOSE T ! DIAMET] (! SEQUOIA IS #BDH
9*ES 9 #AIFE & #BEA 9*ES 9 #BJJE4 ,F9D !
AV]AGE RATE ( *ANGE 9 ! DIAMET]1 & USE X
6PREDICT ! DIAMET] 9 #BAJE4
-------------------------------------#HF
#B.B ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
.ON P4 ,,WS#B = ,EXS4 .#I1.AI @1 &
.#DE
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
..,EXS4 #B1AG1 #CE1 #CF1DD1.DE @1 &
.#DH
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,!
@8 (A NONV]TICAL L9E IS ! RATIO (
V]TICAL *ANGE 6HORIZONTAL *ANGE4
.#B4 .,,WRIT+ ,H[ C Y USE SLOPE
6DECIDE :E!R TWO NONV]TICAL L9ES >E
P>ALLEL8 :E!R TWO NONV]TICAL L9ES >E
P]P5DICUL>8
,,EXAMPLES #B & #C
ON PP4 #HB-HC = ,EXS4 #C-AG
,,F9D+ ,,SLOPE ,F9D ! SLOPE (! L9E
PASS+ "? ! GIV5 PO9TS4 ,!N TELL :E!R !
L9E ..RISES1 FALLS1 IS .HORIZONTAL @1 OR
.IS .V]TICAL4
.#C4 7#B1 --#D71 7#D1 --#A7
.#D4 7#H1I71 7--#D1C7
.#E4 7#E1A71 7#H1--#D7
.#F4 7--#C1 --#B71 7#C1 --#B7
.#G4 7--#A1 #D71 7#A1 --#D7
.#H4 7--#F1 #E71 7--#F1 --#E7
.#I4 7--#E1--#D71 7--#A1C7
.#AJ4 7--#C1 #F71 7--#G1 #C7
.#AA4 7#D1 #D71 7#D1 #I7
.#AB4 7#E1E71 7#G1C7
.#AC4 7#J1 --#C71 7#D1 --#C7
.#AD4 7#A1 --#A71 7--#A1 --#D7
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 F9D+ ! SLOPE (! L9E PASS+ "? !
GIV5 PO9TS4
.#AE4
.#AF4
#AG4 .,,MULTIPLE .,,*OICE ,:AT IS TRUE
AB ! L9E "? 7#B1 --#D7 & 7#E1 #A78
,A ,X RISES F LEFT 6"R4
;,B ,X FALLS F LEFT 6"R4
;,C ,X IS HORIZONTAL4
;,D ,X IS V]TICAL4
,,EXAMPLE #D
ON P4 #HD = ,EXS4 #AH-BC
,,CLASSIFY+ ,,L9ES ,TELL :E!R ! L9ES
>E .P>ALLEL1 .P]P5DICUL> @1 OR .NEI4
.#AH4 ,L9E #A3 "? 7#C1 --#A7 & 7#F1
--#D7
,L9E #B3 "? 7--#D1 #E7 & 7--#B1 #G7
.;L#I ,L9E #A3 "? 7#A1 #E7 & 7#C1
--#B7
,L9E #B3 "? 7--#C1 #B7 & 7#D1 #J7
.#BJ4 ,L9E #A3 "? 7--#A1 #D7 & 7#B1
#E7
,L9E #B3 "? 7--#F1 #B7 & 7#J1 #D7
.#BA4 ,L9E #A3 "? 7#E1 #H7 & 7#G1 #B7
,L9E #B3 "? 7--#G1 --#B7 & 7--#D1
--#A7
.#BB4 ,L9E #A3 "? 7--#C1 #B7 & 7#E1
#J7
,L9E #B3 "? 7--#A1 --#D7 & 7#C1 --#C7
.#BC4 ,L9E #A3 "? 7#A1 --#D7 & 7#D1
--#B7
,L9E #B3 "? 7#H1A7 & 7#AD1 #E7
,,EXAMPLE #E
ON P4 #HE = ,EXS4 .#BD--.#BG
,,AV]AGE ,,RATE ,,( ,,*ANGE ,F9D !
AV]AGE RATE ( *ANGE 9 .;Y RELATIVE 6.;X
=! ORD]$ PAIRS4 ,9CLUDE UNITS ( M1SURE 9
YR ANSW]4
.#BD4 7#B1 #AB71 7#E1 #CJ7 .;X IS
M1SUR$ 9 H\RS & .;Y IS M1SUR$ 9 DOLL>S
.#BE4 7#J1 #AA71 7#C1 #EJ7 .;X IS
M1SUR$ 9 GALLONS & .;Y IS M1SUR$ 9 MILES
.#BF4 7#C1 #AJ71 7#E1AH7 .;X IS M1SUR$
9 SECONDS & .;Y IS M1SUR$ 9 FEET
.#BG4 7#A1 #H71 7#G1 #BJ7 .;X IS
M1SUR$ 9 SECONDS & .;Y IS M1SUR$ 9 MET]S
-------------------------------------#HG
.#BH4 .,,R1SON+ ,! ,KEY ,3CEPT BOX ON
PAGE #HD /ATES T L9ES #A & #B M/ 2
NONV]TICAL4 .,EXPLA9 :Y ? 3DI;N IS NEC4
,,F9D+ ,,SLOPE ,F9D ! SLOPE (! L9E
PASS+ "? ! GIV5 PO9TS4
.#BI4
.#CJ4
.#CA4
.#CB4 7--#D.B1 #J.A71 7--#C.B1 #J.A7
.#CC4 7--#J.C1 #B.B71 7#A.G1 --#J.H7
.#CD4 7#C.E1 --#B71 7#D.E1 #J.E7
.#CE4 .,,%ORT .,,RESPONSE ,DOES X MAKE
A DI6];E : TWO PO9TS ON A L9E Y *OOSE :5
F9D+ ! SLOPE8 ,DOES X MAKE A DI6];E :
PO9T IS @7 .;X #A @1 .;Y #A @7 & : PO9T
IS @7 .;X #B @1 .;Y #B @7 9 ! =MULA =
SLOPE8 ,SUPPORT YR ANSW]S US+ ?REE
DI6]5T PAIRS ( PO9TS ON ! L9E %[N4
.#CF4 .,,OP5-.,,5D$ .,,MA? ,F9D TWO
A4I;NAL PO9TS ON ! L9E T PASSES "? 7#J1
#C7 & HAS A SLOPE ( --#D4
,,*ALL5GE ,F9D ! VALUE ( .;K S T ! L9E
"? ! GIV5 PO9TS HAS ! GIV5 SLOPE4 ,*ECK
YR SOLU;N4
.#CG4 7#B1 --#C7 & @7 .;K @1 #G72 .;M
.K --#B
.#CH4 7#J1 .;K @7 & 7#C1 #D72 .;M .K
#A
.#CI4 7--#D1 .#B;K @7 & @7 .;K @1
--#E72 .;M .K --#A
.#DJ4 7--#B1 .;K @7 & 7#B .;K @1 #B72
.;M .K --#J.BE
,,PRO#M ,,SOLV+
,,EXAMPLE #A
ON P4 #HB = ,EXS4 #DA-DD
.#DA4 .,,ESCALATORS ,AN ESCALATOR 9 AN
AIRPORT RISES #BH FEET OV] A HORIZONTAL
4T.E ( #DH FEET4 ,:AT IS ! SLOPE (!
ESCALATOR8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#DB4 .,,9CL9E .,,RAILWAY ,! ,DUQUESNE
,9CL9E1 A CA# C> RAILWAY1 RISES #DJJ
FEET OV] A HORIZONTAL 4T.E ( #FHE FEET
ON XS ASC5T 6AN OV]LOOK ( ,PITTSBUR<1
,P5NSYLVANIA4 ,:AT IS ! SLOPE (! 9CL9E8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#DC4 .,,ROAD .,,GRADE ,A ROAD'S
.GRADE IS XS SLOPE EXPRESS$ Z A P]C5T4
,A ROAD RISES #AIE FEET OV] A HORIZONTAL
4T.E ( #CJJJ FEET4 ,:AT IS ! GRADE (!
ROAD8
.#DD4 .,,%ORT .,,RESPONSE ,! DIAGRAM
%[S A ?REE-SEC;N RAMP 6A BRIDGE4 ,=A
P]SON WALK+ UP ! RAMP1 EA* SEC;N HAS !
SAME POSITIVE SLOPE4 .,-P>E ? SLOPE )!
SLOPE T A S+LE-SEC;N RAMP WD H IF X ROSE
DIRECTLY 6! BRIDGE F ! SAME />T+ PO9T4
.,EXPLA9 ! B5EFITS (A ?REE-SEC;N RAMP 9
? SITU,N4
,,EXAMPLE #E
ON P4 #HE = ,EXS4 #DE-DF
#DE4 .,,MULTIPLE .,,*OICE ,OV] A #CJ
"D P]IOD1 ! AM.T ( PROPANE 9 A TANK T
/ORES PROPANE = H1T+ A HOME DECR1SES F
#DJJ GALLONS 6#BAD GALLONS4 ,:AT IS !
AV]AGE RATE ( *ANGE 9 ! AM.T ( PROPANE8
,A --#F.B GALLONS P] "D
;,B --#F GALLONS P] "D
;,C --#J.AF GALLON P] "D
;,D #F GALLONS P] "D
-------------------------------------#HH
.#DF4 .,,BIOLOGY ,A R$ SEA UR*9 GR[S
XS 5TIRE LIFE1 : C LA/ #BJJ YE>S4 ,!
DIAGRAM GIVES 9=M,N AB ! GR[? 9 !
DIAMET] .;D ( "O R$ SEA UR*94 ,:AT IS !
AV]AGE GR[? RATE ( ? UR*9 OV] ! GIV5
P]IOD8
#DG4 .,,MULTI-.,,/EP .,,PRO#M ,A
BUILD+ CODE REQUIRES ! M9IMUM SLOPE1 OR
.PIT* @1 ( AN ASPHALT-%+LE RO( 6BE A
RISE ( #C FEET = EA* #AB FEET ( RUN4 ,!
ASPHALT-%+LE RO( ( AN A"P;T BUILD+ HAS !
DIM5.NS %[N4
A4 .,CALCULATE ,:AT IS ! SLOPE (! RO(8
B4 .,9T]PRET ,DOES ! RO( SATISFY !
BUILD+ CODE8
C4 .,R1SON+ ,IF Y ANSW]$ 8NO0 6"P
7;B71 0H[ M* M/ ! RISE 2 9CR1S$ 6SATISFY
! CODE8 ,IF Y ANSW]$ 8YES10 0H[ M* DOES
! RISE EXCE$ ! CODE M9IMUM8
#DH4 .,,EXT5D$ .,,RESPONSE ,PLANS =A
NEW WAT] SLIDE 9 AN AMUSE;T P>K CALL =!
SLIDE 6DESC5D F A PLAT=M #HJ FEET TALL4
,! SLIDE W DROP #A FOOT = E #C FEET (
HORIZONTAL 4T.E4
A4 ,:AT HORIZONTAL 4T.E D Y COV] :5
DESC5D+ ! SLIDE8
B4 ,USE ! ,PY?AGOR1N !OREM 6F9D ! L5G?
(! SLIDE4
C4 ,5G9E]S DECIDE 6%ORT5 ! SLIDE
HORIZONT,Y 0#E FEET 6ALL[ =A WID]
WALKWAY AT ! SLIDE'S BASE4 ,! PLANS =!
PLAT=M REMA9 UN*ANG$4 ,H[ W ? A6ECT !
SLOPE (! SLIDE8 .,EXPLA94
#DI4 .,,*ALL5GE ,A C> TRAVELS #CF
MILES P] GALLON ( GASOL9E 9 HI<WAY DRIV+
& #BD MILES P] GALLON 9 C;Y DRIV+4 ,IF Y
DRIVE ! C> EQUAL 4T.ES ON ! HI<WAY & 9 !
C;Y1 H[ _M MILES P] GALLON C Y EXPECT
6AV]AGE8 @7 .,H9T3 ,! AV]AGE FUEL
E6ICI5CY = ALL ! DRIV+ IS ! TOTAL 4T.E
TRAVEL$ DIVID$ 0! TOTAL AM.T ( GASOL9E
US$47
,,MIX$ ,,REVIEW
,ID5TIFY ! PROP]TY T ! /ATE;T
ILLU/RATES4 @7 P4 #B @7
.#EJ4 #E7#H @+ #AB7 .K #E7#H7 @+
#E7#AB7
.#EA4 7#G @+ #I7 @+ #AC .K #G @+ 7#I
@+ #AC7
.#EB4 #D @+ 7--#D7 .K #J
.#EC4 #E 99 #AJ .K #AJ 99 #E
.#ED4
.#EE4
,,PREVIEW
,PREP>E = ,LESSON #B.C 9 ,EXS4 #EF-FA4
,SOLVE ! EQU,N = .Y4 @7 P4 #BF @7
.#EF4 #C .;X @+ .;Y .K #G
.#EG4 #B .;X -- .;Y .K #C
.#EH4 .;Y -- #D .;X .K --#F
.#EI4 #B .;X @+ #C .;Y .K --#AB
.#FJ4 #G .;X -- #D .;Y .K #AJ
.#FA4 -- .;X @+ #B .;Y .K #I
,SOLVE ! EQU,N OR 9EQUAL;Y1 @7 P4 #EA
@7
.#FB4 _\#AE @+ #B .;X _\ .K #G
.#FC4 _\#D .;X -- #I_\ .K #E
.#FD4 _\#F--#E .;X _\ .K #I
.#FE4 ,7#C--#G .;X _\ "K #AJ
.#FF4 _\#C .;X @+ #A_\ .1 #BE
.#FG4 _\#C--#D .;X _\ .1.K #G
.,,EXTRA .,,PRACTICE = ,LESSON #B.B1
P4 #AJAA
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
-------------------------------------#HI
#B.C ,GRAPH ,EQU,NS ( ,L9ES
.,2F ,Y GRAPH$ L9E> EQU,NS 0MAK+ TA#S
( VALUES4
.,N[ ,Y W GRAPH L9E> EQU,NS 9
SLOPE-9T]CEPT OR /&>D =M4
.,:Y8 ,S Y C MODEL MO;N1 Z 9 ,EX4 #FD4
,KEY ,VOCABUL>Y
99 P>5T FUNC;N
99 .;Y -9T]CEPT
99 SLOPE-9T]CEPT =M
99 /&>D =M (A L9E> EQU,N
99 .;X -9T]CEPT
.,A .FAMILY ( FUNC;NS IS A GR\P (
FUNC;NS ) %>$ "*I/ICS4 ,! .P>5T .FUNC;N
IS ! MO/ BASIC FUNC;N 9 A FAMILY4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,P>5T ,FUNC;N = ,L9E> ,FUNC;NS
,! P>5T FUNC;N =! FAMILY ( ALL L9E>
FUNC;NS IS .;F @7 .;X @7 .K .X4 ,! GRAPH
( .;F @7 .;X @7 .K .;X IS %[N4
,9 G5]AL1 A .;Y -.9T]CEPT (A GRAPH IS
! .;Y-.COORD 9ATE (A PO9T ": ! GRAPH
9T]SECTS ! ;Y-AXIS4
,,DEF9E .;,Y -,,9T]CEPT
,A ;Y-9T]CEPT IS "S"TS DEF9$ Z A .PO9T
": A GRAPH 9T]SECTS ! .;Y -AXIS4 ,US+ ?
DEF9I;N1 ! .;Y -9T]CEPT (! L9E .;F @7
.;X @7 .K .;X IS 7#J1 #J71 N #J4
,SIDEB>3
,/&>DS3 ,PREP>E = #B.J
..,/UD5TS SOLVE SY/EMS ( L9E> .EQU,NS
& 9EQUALITIES 7IN TWO OR ?REE V>IA#S7
0SUB/ITU;N1 ) .GRAPHS @1 OR ) MATRICES4
,,EXAMPLE #A ,GRAPH L9E> FUNC;NS
,GRAPH ! EQU,N4 ,-P>E ! GRAPH )! GRAPH
( .;Y .K .X4
A4 .;Y .K .#B;X
B4 .;Y .K .;X @+ #C
,SOLU;N
.A4
,! GRAPHS ( .;Y .K .#B;X & .;Y .K .;X
BO? H A .;Y -9T]CEPT ( #J1 B ! GRAPH (
.;Y .K .#B;X HAS A SLOPE ( #B 9/1D ( #A4
.B4
,! GRAPHS ( .;Y .K .;X @+ #C & .;Y .K
.;X BO? H A SLOPE ( #A1 B ! GRAPH ( .;Y
.K .;X @+ #C HAS A .;Y -9T]CEPT ( #C
9/1D ( #J4
-------------------------------------#IJ
.,,SLOPE-.,,9T]CEPT .,,=M ,IF Y WRITE
! EQU,NS 9 ,EXAMPLE #A Z .;Y .K #B .;X
@+ #J & .;Y .K .,IX @+ #C1 Y C SEE T !
.;X- COE6ICI5TS1 #B & #A1 >E ! SLOPES (!
L9ES1 :ILE ! 3/ANT T]MS1 #J & #C1 >E !
.;Y -9T]CEPTS4 ,9 G5]AL1 A L9E ) EQU,N
..;Y .K MX @+ .;B HAS SLOPE .;M & .;Y
-9T]CEPT .B4 ,! EQU,N .;Y .K .MX @+ .;B
IS SD 6BE 9 .SLOPE-.9T]CEPT .=M4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,US+ ,SLOPE-,9T]CEPT ,=M 6,GRAPH AN
,EQU,N
.,,/EP .#A .,WRITE ! EQU,N 9
SLOPE-9T]CEPT =M 0SOLV+ = .;Y @4
.,,/EP .#B .,ID5TIFY ! .;Y -9T]CEPT
.;B & USE X 6PLOT ! PO9T 7#J1 .;B @7 ":
! L9E CROSSES ! .;Y -AXIS4
.,,/EP .#C .,ID5TIFY ! SLOPE .;M & USE
X 6PLOT A SECOND PO9T ON ! L9E4
.,,/EP .#D .,DRAW A L9E "? ! TWO
PO9TS4
,,EXAMPLE #B ,GRAPH AN EQU,N 9
SLOPE-9T]CEPT =M
.,GRAPH @4
,,ANO!R ,,WAY
,2C @1 Y CD AL PLOT A SECOND PO9T
0MOV+ UP #B UNITS & LEFT #C UNITS4
,SOLU;N
.,,/EP .#A ,! EQU,N IS ALR 9
SLOPE-9T]CEPT =M4
.,,/EP .#B .,ID5TIFY ! .;Y -9T]CEPT4
,! ;Y-9T]CEPT IS --#A1 S PLOT ! PO9T
7#J1 --#A7 ": ! L9E CROSSES ! .;Y -AXIS4
.,,/EP .#C .,ID5TIFY ! SLOPE4 ,! SLOPE
IS @1 S PLOT A SECOND PO9T ON ! L9E
0/>T+ AT 7#J1 --#A7 & !N MOV+ D[N #B
UNITS & "R #C UNITS4 ,! SECOND PO9T IS
7#C1 --#C74
.,,/EP .#D .,DRAW A L9E "? ! TWO
PO9TS4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,GUID$ ,PRACTICE = ,EXAMPLES #A &
.#B
,GRAPH ! EQU,N4 .,-P>E ! GRAPH )!
GRAPH ( .;Y .K .X4
.#A4 .;Y .K -.#B;X
.#B4 .;Y .K .;X -- #B
.#C4 .;Y .K #D .;X
,GRAPH ! EQU,N4
.#D4 .;Y .K -.;X @+ .#B
.#E4
.#F4
.#G4 .;Y .K #E @+ .;X
.#H4 .;F @7 .;X @7 .K #A -- .#C;X
.#I4 .;F @7 .;X @7 .K #AJ -- .;X
-------------------------------------#IA
.,,R1L-.,,LIFE .,,PRO#MS ,9 A R1L-LIFE
3TEXT1 A L9E'S SLOPE C REPRES5T AN
AV]AGE RATE ( *ANGE4 ,! .;Y -9T]CEPT 9 A
R1L-LIFE 3TEXT IS (T5 AN 9ITIAL VALUE4
,,EXAMPLE #C ,SOLVE A MULTI-/EP PRO#M
.,,BIOLOGY ,! BODY L5G? .;Y 7IN 9*ES7
(A WALRUS CALF C 2 MODEL$ 0.;Y .K #E .;X
@+ #DB ": .;X IS ! CALF .;S AGE 7IN
MON?S74
99 ,GRAPH ! EQU,N4
99 ,DESCRIBE :AT ! SLOPE & .;Y
-9T]CEPT REPRES5T 9 ? SITU,N4
99 ,USE ! GRAPH 6E/IMATE ! BODY L5G?
(A CALF T IS #AJ MON?S OLD4
,SOLU;N
.,,/EP .#A .,GRAPH ! EQU,N4
.,,/EP .#B .,9T]PRET ! SLOPE & .;Y
-9T]CEPT4
,! SLOPE1 #E1 REPRES5TS ! CALF'S RATE
( GR[? 9 9*ES P] MON?4 ,! .;Y -9T]CEPT1
#DB1 REPRES5TS A NEWBORN CALF'S BODY
L5G? 9 9*ES4
.,,/EP .#C .,E/IMATE ! BODY L5G? (!
CALF AT AGE #AJ MON?S 0/>T+ AT #AJ ON !
.;X -AXIS & MOV+ UP UNTIL Y R1* ! GRAPH4
,!N MOVE LEFT 6! .;Y -AXIS4 ,AT AGE #AJ
MON?S1 ! BODY L5G? (! CALF IS AB #IB
9*ES4
,,ANO!R ,,WAY
,Y C *ECK ! RESULT Y OBTA9$ F ! GRAPH
0SUB/ITUT+ #AJ = .;X 9 .;Y .K #E .;X @+
#DB & SIMPLIFY+4
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#C
.#AJ4 .,,:AT .,,IF8 ,9 ,EXAMPLE #C1
SUPPOSE T ! BODY L5G? (A FA/-GR[+ CALF
IS MODEL$ 0.;Y .K #F .;X @+ #DH4 ,REP1T
! /EPS (! EXAMPLE =! NEW MODEL4
,,DEF9E .;,X -,,9T]CEPT
,AN .;X -9T]CEPT IS "S"TS DEF9$ Z A
.PO9T ": A GRAPH 9T]SECTS ! .;X -AXIS1 N
! .;X -COORD9ATE ( S* A PO9T4
.,,/&>D .,,=M ,! ./&>D .=M (A L9E>
EQU,N IS .,AX @+ .,BY .K .;,C ": .,A &
.;,B >E N BO? Z]O4 ,Y C GRAPH AN EQU,N 9
/&>D =M 0ID5TIFY+ & PLOTT+ ! .;X - & .;Y
-9T]CEPTS4 ,AN .;X -.9T]CEPT IS ! .;X
-COORD9ATE (A PO9T ": A GRAPH 9T]SECTS !
.;X -AXIS4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,US+ ,/&>D ,=M 6,GRAPH AN ,EQU,N
.,,/EP .#A .,WRITE ! EQU,N 9 /&>D =M4
.,,/EP .#B .,ID5TIFY ! .;X -9T]CEPT
0LETT+ .;Y .K #J & SOLV+ = X4 ,USE ! .;X
-9T]CEPT 6PLOT ! PO9T ": ! L9E CROSSES !
.;X -AXIS4
.,,/EP .#C .,ID5TIFY ! .;Y -9T]CEPT
0LETT+ .;X .K #J & SOLV+ = .;Y @4 ,USE !
.;Y -9T]CEPT 6PLOT ! PO9T ": ! L9E
CROSSES ! .;Y -AXIS4
.,,/EP .#D .,DRAW A L9E "? ! TWO
PO9TS4
-------------------------------------#IB
,EXAMPLE #D ,GRAPH AN EQU,N 9 /&>D =M
,GRAPH #E .;X @+ #B .;Y .K #AJ4
,,ANO!R ,,WAY
,Y C AL GRAPH #E .;X @+ #B .;Y .K #AJ
0F/ SOLV+ = .;Y 6OBTA9 & !N US+ !
PROC$URE = GRAPH+ AN EQU,N 9
SLOPE-9T]CEPT =M4
,SOLU;N
.,,/EP .#A ,! EQU,N IS ALR 9 /&>D =M4
.,,/EP .#B .,ID5TIFY ! .;X -9T]CEPT4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#E .;X @+ #B7 .#J @7 .K #AJ @3 ,LET.'
;Y .K #J4
.;X .K #B @3 ,SOLVE =.' X4.-
,! .;X -9T]CEPT IS #B4 ,S1 PLOT ! PO9T
7#B1 #J74
.,,/EP .#C .,ID5TIFY ! .;Y -9T]CEPT4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#E7 .#J @7 @+ #B .;Y .K #AJ @3 ,LET.'
;X .K #J4
.;Y .K #E @3 ,SOLVE = Y4
,! ;Y-9T]CEPT IS #E4 ,S1 PLOT ! PO9T
7#J1 #E74
.,,/EP .#D .,DRAW A L9E "? ! TWO
PO9TS4
..,,HORIZONTAL ,,& ,,V]TICAL .,,L9ES
,! EQU,N (A V]TICAL L9E _C 2 WRITT5 9
SLOPE-9T]CEPT =M 2C ! SLOPE IS N DEF9$4
,H["E1 E L9E> EQU,N--EV5 T (A V]TICAL
L9E--C 2 WRITT5 9 /&>D =M4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,HORIZONTAL & ,V]TICAL ,L9ES
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,HORIZONTAL .,L9ES @3 ,! GRAPH ( .;Y
.K .;C IS ! HORIZONTAL L9E "? 7#J1 .;C
@7@4
.,V]TICAL .,L9ES @3 ,! GRAPH ( .;X .K
.;C IS ! V]TICAL L9E "? @7 .;C @1 #J74
,,EXAMPLE #E ,GRAPH HORIZONTAL &
V]TICAL L9ES
,GRAPH 7A7 .;Y .K #B & 7;B7 .;X .K
--#C4
,SOLU;N
.A4 ,! GRAPH ( .;Y .K #B IS !
HORIZONTAL L9E T PASSES "? ! PO9T 7#J1
#B74 ,NOTICE T E PO9T ON ! L9E HAS A
.;Y-.COORD 9ATE ( #B4
.B4 ,! GRAPH ( .;X .K --#C IS !
V]TICAL L9E T PASSES "? ! PO9T 7--#C1
#J74 ,NOTICE T E PO9T ON ! L9E HAS AN
.;X-.COORD 9ATE ( --#C4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #D &
.#E
,GRAPH ! EQU,N4
.#AA4 #B .;X @+ #E .;Y .K #AJ
.#AB4 #C .;X -- #B .;Y .K #AB
.#AC4 .;X .K #A
.#AD4 .;Y .K--#D
-------------------------------------#IC
#B.C ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS .ON .P4
,,WS#C = ,EXS4 .#AE1.CG @1 & .#FA
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 #B1 #BC1 #CJ1EE1 #EF1FC1 & #FH
.K .,,MULTIPLE .,,REPRES5T,NS
,EX#.FG
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,!
L9E> EQU,N .;Y .K #B .;X @+ #E IS WRITT5
9 @8 =M4
.#B4 .,,WRIT+ .,DESCRIBE H[ 6GRAPH AN
EQU,N (! =M ..,AX @+ ,BY .K .,C4
,,EXAMPLE #A
ON P4 #HI = ,EXS4 #C-H
.,,GRAPH+ .,,L9E> .,,FUNC;NS ,GRAPH !
EQU,N4 .,-P>E ! GRAPH )! GRAPH ( .;Y .K
.X4
.#C4 .;Y .K #C;X
#D4 .;Y .K --.;X
.#E4 .;Y .K .;X @+ #E
.#F4 .;Y .K .;X -- #B
.#G4 ..;Y .K .#B;X -- #A
.#H4 .;Y .K --#C .;X @+ #B
,,EXAMPLE #B
ON P4 #IJ = ,EXS4 #I-BB
,,SLOPE-,,9T]CEPT ,,=M ,GRAPH ! EQU,N4
.#I4 .;Y .K --.;X -- #C
.#AJ4 .;Y .K .;X -- #F
.#AA4 .;Y .K #B .;X @+ #F
.#AB4 .;Y .K #C .;X -- #D
.#AC4 .;Y .K #D .;X -- #A
.#AD4
.#AE4
.#AF4
.#AG4
.#AH4
.#AI4 .FIX @7 .K --#A.E .;X @+ #B
.#BJ4 .;F @7 .;X @7 .K #C .;X -- #A.E
.,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 GRAPH+ ! EQU,N4
.#BA4 .;Y .K #B .;X @+ #C
.#BB4 .;Y .K #D .;X -- #B
#BC4 .,,MULTIPLE .,,*OICE ,:AT IS !
SLOPE-9T]CEPT =M ( #D .;X -- #C;Y .K
#AH8
,A
;,B
;,C
;,D
,,EXAMPLES #D & #E
.ON P4 #IB = ,EXS4 #BD-D
.,,F9D+ .,,9T]CEPTS ,F9D ! .;X- &
;Y-9T]CEPTS (! L9E )! GIV5 EQU,N4
.#BD4 .;X -- .;Y .K #D
.#BE4 .;X @+ #E;Y .K --#AE
.#BF4 #C .;X -- #D;Y .K --#AB
.#BG4 #B .;X--.;Y .K #AJ
.#BH4 #D .;X -- #E;Y .K #BJ
.#BI4 --#F .;X @+ #H;Y .K --#CF
.#CJ4 .,,MULTIPLE .,,*OICE ,:AT IS !
.;X -9T]CEPT (! GRAPH ( #E .;X -- #F;Y
.K #CJ8
.,A --#E
.;,B
.;,C #F
.;,D #CJ
-------------------------------------#ID
.,,/&>D .,,=M ,GRAPH ! EQU,N4 ,LABEL
ANY 9T]CEPTS4
.#CA4 .;X @+ #D .;Y .K #H
.#CB4 #B .;X -- #F .;Y .K --#AB
.#CC4 .;X .K #D
.#CD4 .;Y .K --#B
.#CE4 #E .;X -- .;Y .K #C
.#CF4 #C .;X @+ #D .;Y .K #AB
.#CG4 --#E .;X @+ ;L#J .;Y .K #BJ
.#CH4 -- .;X -- .;Y .K #F
.#CI4 .;Y .K #A.E
.#DJ4 #B.E .;X -- #E .;Y .K --#AE
.#DA4
.#DB4
.,,*OOS+ .,A .,,ME?OD ,GRAPH ! EQU,N
US+ ANY ME?OD4
.#DC4 #F .;Y .K #C .;X @+ #F
.#DD4 --#C @+ .;X .K #J
.#DE4 .;Y @+ #G .K --#B .;X
.#DF4 #D .;Y .K #AF
.#DG4 #H .;Y .K --#B .;X @+ #BJ
.#DH4
.#DI4 --#D .;X .K #H .;Y @+ #AB
.#EJ4 #C.E .;X .K #AJ.E
.#EA4 .;Y -- #E.E .;X .K #F
.#EB4 #AD--#C .;X .K #G .;Y
.#EC4 #B .;Y -- #E .K #J
.#ED4 #E .;Y .K #G.E--#B.E .;X
.#EE4 .,,OP5--.,,5D$ .,,MA? ,WRITE
EQU,NS ( TWO L9ES1 "O ) AN .;X -9T]CEPT
B NO ;Y-9T]CEPT & "O )A ;Y-9T]CEPT B NO
.;X -9T]CEPT4
.#EF4 .,,%ORT .,,RESPONSE ,SKET* .;Y
.K .MX = S"EAL VALUES ( .;M @1 BO?
POSITIVE & NEGATIVE4 .,DESCRIBE !
REL,N%IP 2T .;M &! /EEP;S (! L9E4
.#EG4 .,,R1SON+ ,3SID] ! GRAPH ( .,AX
@+ .,BY .K .;,C ": .;,B @6.K .#J4 ,:AT
>E ! SLOPE & ;Y-9T]CEPT 9 T]MS ( ,A1
.;,B @1 & .;,C @8
.#EH4 .,,*ALL5GE ,PROVE T ! SLOPE (!
L9E .;Y .K .MX @+ .;B IS .M4 @7 .,H9T3
,F/ F9D TWO PO9TS ON ! L9E 0*OOS+ 3V5I5T
VALUES ( .;X @4@7
,,PRO#M ,,SOLV+
,,EXAMPLE #C
ON P4 #IA = ,EXS4 #EI-FB
.#EI4 .,,FIT;S ,! TOTAL CO/ .;Y 7IN
DOLL>S7 (A GYM MEMB]%IP AF .;X MON?S IS
GIV5 0.;Y .K #DE .;X @+ #GE4 ,GRAPH !
EQU,N4 ,:AT IS ! TOTAL CO/ (! MEMB]%IP
AF #I MON?S8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#FJ4 .,,CAMP+ ,YR ANNUAL MEMB]%IP FEE
6A NATURE SOCIETY LETS Y CAMP AT S"EAL
CAMPGR.DS4 ,YR TOTAL ANNUAL CO/ .;Y 7IN
DOLL>S7 6USE ! CAMPGR.DS IS GIV5 0.;Y .K
#E .;X @+ #CE ": .;X IS ! NUMB] ( NI<TS
Y CAMP4 ,GRAPH ! EQU,N4 ,:AT D ! SLOPE &
;Y-9T]CEPT REPRES5T8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#FA4 .,,SPORTS ,B[L+ ALLEYS (T5 *>GE A
FIX$ FEE 6R5T %OES & !N *>GE = EA* GAME
Y B[L4 ,! FUNC;N .;,C7.;G @7 .K #C .;G
@+ #A.E GIVES ! TOTAL CO/ ;,C 7IN
DOLL>S7 6B[L ;G GAMES4 ,GRAPH ! FUNC;N4
,:AT IS ! CO/ 6R5T %OES8 ,:AT IS ! CO/
P] GAME8
.#FB4 .,,PH"O .,,C>DS ,Y PUR*ASE A
#CJJ M9UTE PH"O C>D4 ,! FUNC;N .;,M @7
.;W @7 .K --.#CJ;W @+ #CJJ MODELS !
NUMB] ;,M ( M9UTES T REMA9 ON ! C>D AF
.;W WEEKS4 .,DESCRIBE H[ 6DET]M9E A
R1SONA# DOMA9 & RANGE4 ,GRAPH ! FUNC;N4
,H[ _M M9UTES P] WEEK D Y USE ! C>D8
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
-------------------------------------#IE
.#FC4 .,,%ORT .,,RESPONSE ,Y RCV A
4#CJ GIFT C>D 6A %OP T SELLS FRUIT
SMOO?IES = 4#C4 ,IF Y GRAPH AN EQU,N (!
L9E T REPRES5TS ! M"OY .;Y REMA9+ ON !
C>D AF Y BUY .;X SMOO?IES1 :AT W ! .;Y
-9T]CEPT BE8 ,W ! L9E RISE OR FALL F
LEFT 6"R8 .,EXPLA94
#FD4 .,,MULTI-.,,/EP .,,PRO#M ,Y &A FR
KAYAK #AHJJ Y>DS D[N A RIV]4 ,Y DRIFT )!
CURR5T "PWAY AT #CJ Y>DS P] M9UTE &
PA4LE "PWAY AT #IJ Y>DS P] M9UTE4 ,!
TRIP IS MODEL$ 0#CJ .;X @+ #IJ .;Y .K
#AHJJ ": .;X IS ! DRIFT+ "T & .;Y IS !
PA4L+ "T 7BO? 9 M9UTES74
A4 ,GRAPH ! EQU,N1 & DET]M9E A R1SONA#
DOMA9 & RANGE4 ,:AT D ! .;X- &
;Y-9T]CEPTS REPRES5T8
B4 ,IF Y PA4LE = #E M9UTES1 :AT IS !
TOTAL TRIP "T8
C4 ,IF Y PA4LE & DRIFT EQUAL AM.TS (
"T1 :AT IS ! TOTAL TRIP "T8
#FE4 .,,VOLUNTE]+ ,Y "PICIPATE 9 A #AD
MILE RUN_/WALK = *>;Y4 ,Y RUN "PWAY AT
#F MILES P] H\R & WALK "PWAY AT #C.E
MILES P] H\R4 ,A MODEL = ? SITU,N IS #F
.;R @+ #C.E .;W .K #AD ": ;R IS ! "T Y
RUN & .;W IS ! "T Y WALK 7BO? 9 H\RS74
,GRAPH ! EQU,N4 ,GIVE ?REE POSSI# -B9,NS
( RUNN+ & WALK+ "TS4
#FF4 .,,TICKETS ,AN HONOR SOCIETY HAS
4#AEJ 6BUY SCI;E MUSEUM & >T MUSEUM
TICKETS = /UD5T AW>DS4 ,! NUMB]S (
TICKETS T C 2 B"\ >E GIV5 0.#E;S @+ .LA
.K #AEJ ": .;S IS ! NUMB] ( SCI;E MUSEUM
TICKETS 7AT 4#E EA*7 & .A IS ! NUMB] (
>T MUSEUM TICKETS 7AT 4#G EA*74 ,GRAPH !
EQU,N4 ,GIVE TWO POSSI# -B9,NS ( TICKETS
T USE ALL 4#AEJ4
#FG4 .,,MULTIPLE .,,REPRES5T,NS ,A HOT
AIR BALLOON IS 9ITI,Y #BJJ FEET ABV !
GR.D4 ,! BURN]S >E !N TURN$ ON1 CAUS+ !
BALLOON 6ASC5D AT A RATE ( #AEJ FEET P]
M9UTE4
A4 .,MAK+ .A .,TA# ,MAKE A TA# %[+ !
HEI<T .;H 7IN FEET7 (! BALLOON .;T
M9UTES AF ! BURN]S >E TURN$ ON ": #J
"K.K .;T "K.K #E4
B4 .,DRAW+ .A .,GRAPH ,PLOT ! PO9TS F
! TA# 9 "P 7A74 ,DRAW A L9E "? ! PO9TS
=! DOMA9 #J "K.K .;T "K.K #E4
C4 .,WRIT+ .AN .,EQU,N ,! BALLOON'S
HEI<T IS XS 9ITIAL HEI<T PLUS ! PRODUCT
(! ASC5T RATE & "T4 ,WRITE AN EQU,N
REPRES5T+ ?4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
#FH4 .,,EXT5D$ .,,RESPONSE ,Y &A FR >E
EA* TYP+ YR RESE>* PAP]S ON -PUT]S4 ,!
FUNC;N .;Y .K #ADJJ--#EJ .;X MODELS !
NUMB] .;Y ( ^WS Y H LEFT 6TYPE AF .;X
M9UTES4 ,= YR FR1 .;Y .K #ABJJ--#EJ;X
MODELS ! NUMB] .;Y ( ^WS LEFT 6TYPE AF
.;X M9UTES4
A4 ,GRAPH ! TWO EQU,NS 9 ! SAME
COORD9ATE PLANE4 .,DESCRIBE H[ ! GRAPHS
>E RELAT$ GEOMETRIC,Y4
B4 ,:AT D ! .;X -9T]CEPTS1
;Y-9T]CEPTS1 & SLOPES REPRES5T8
C4 ,:O W F9I% F/8 .,EXPLA94
-------------------------------------#IF
#FI4 .,,*ALL5GE ,Y WANT 6COV] A
FIVE-BY-FIVE GRID -PLETELY ) .;X
?REE-BY-"O RECTANGLES & .;Y F\R-BY-"O
RECTANGLES T D N OV]LAP OR EXT5D 2Y !
GRID4
A4 .,EXPLA9 :Y .;X & .;Y M/ 2 :OLE
NUMB]S T SATISFY ! EQU,N #C .;X @+ #D
.;Y .K #BE4
B4 ,F9D ALL SOLU;NS @7 .;X1 .;Y @7 (!
EQU,N 9 "P 7A7 S* T .;X & .;Y >E :OLE
NUMB]S4
C4 ,D ALL ! SOLU;NS F "P 7;B7 REPRES5T
-B9,NS ( RECTANGLES T C ACTU,Y COV] !
GRID8 ,USE DIAGRAMS 6SUPPORT YR ANSW]4
,,MIX$ ,,REVIEW
,EVALUATE ! EXPRES.N =! GIV5 VALUE (!
V>IA#4 @7 P4 #AJ @7
.#GJ4 #C .;N -- #AJ :5 .;N .K #E
.#GA4 -- #D .;X @+ #AF :5 .;X .K --#B
.#GB4 #B7#AA--#E .;P @7 :5 .;P .K #D
.#GC4 7#D .;Q @+ #E7 7#B .;Q @7 :5 .;Q
.K --#A
.#GD4 .;M #B -- #D .;M :5 .;M .K --#C
.#GE4 @7 .;D @+ #A7 #B -- .;D :5 .;D
.K #F
,TELL :E!R ! REL,N IS A FUNC;N4
.,EXPLA94 @7 P4 #GB @7
.#GF4 7--#B1 --#G71 7#J1 #C71 7#A1
--#B71 7--#B1 #AC71 7#C1 --#AB7
.#GG4 7#A1 #C71 7#J1 #J71 7#B1 --#B71
7--#C1 #F71 7--#B1 --#B7
,,PREVIEW
,PREP>E = ,LESSON #B.D 9 ,EXS4 #GH-HC4
,F9D ! SLOPE (! L9E PASS+ "? ! GIV5
PO9TS1 @7 P4 #HB @7
.#GH4 7#A1 --#C71 7#E1 #J7
.#GI4 7--#B1 #A71 7#F1 --#G7
.#HJ4 7#D1 #D71 7#H1 #D7
.#HA4 7#B1 #E71 7--#E1 #H7
.#HB4 7#F1 --#C71 7#A1 --#AC7
.#HC4 7#B.E1 #J71 7--#C.E1 --#D7
,,QUIZ .= .,LESSONS .#B..A-.B..C
,TELL :E!R ! REL,N IS A FUNC;N4
.,EXPLA94 @7 P4 #GB @7
.#A4
.#B4
.#C4
,TELL :E!R ! L9ES >E .P>ALLEL1
.P]P5DICUL> @1 OR .NEI @1 @7 P4 #HB @7
.#D4 ,L9E #A3 "? 7--#C1 --#G7 & 7#A1
#I7
,L9E #B3 "? 7--#A1 --#D7 & 7#J1 --#B7
.#E4 ,L9E #A3 "? 7#B1 #G7 & 7--#A1
--#B7
,L9E #B3 "? 7#C1 --#F7 & 7--#F1 --#C7
,GRAPH ! EQU,N4 @7 P4 #HI @7
.#F4 .;Y .K --#E .;X @+ #C
.#G4 .;X .K #AJ
.#H4 #D .;X @+ #C .;Y .K --#BD
.#I4 .,,R[+ .,,SPE$ ,9 #AIII1 ,TORI
,MURD5 2CAME ! F/ WOMAN 6R[ ACR !
,ATLANTIC ,OC1N4 ,%E R[$ A TOTAL ( #CCCC
MILES DUR+ H] CROSS+4 ,! 4T.E .;D R[$
7IN MILES7 C 2 MODEL$ 0.;D .K #DA .;T ":
.;T REPRES5TS ! "T R[$ 7IN "DS7 AT AN
AV]AGE RATE ( #DA MILES P] "D4 ,GRAPH !
FUNC;N1 & DET]M9E A R1SONA# DOMA9 &
RANGE4 ,!N E/IMATE H[ L;G X TOOK ,TORI
,MURD5 6R[ #AJJJ MILES4 @7 P4 #GB @7
,,EXTRA ,,PRACTICE = ,LESSON #B.C1 P4
#AJAA
..,,ONL9E ,,QUIZ AT _+CLASSZONE.COM_:
-------------------------------------#IG
,GRAPH+ ,CALCULATOR ,ACTIV;Y3 #B.C
,GRAPH ,EQU,NS
,USE AF LESSON #B.C
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,KEY/ROKES
,,"Q ,H[ C Y USE A GRAPH+ CALCULATOR
6GRAPH AN EQU,N8
,Y C USE A GRAPH+ CALCULATOR 6GRAPH
EQU,NS 9 TWO V>IA#S4 ,ON MO/
CALCULATORS1 Y M/ F/ WRITE ! EQU,N 9 !
=M .;Y .K .;F7.;X @7@4
,,EXAMPLE ,GRAPH A L9E> EQU,N
,GRAPH ! EQU,N .;X @+ #D .;Y .K #H4
,,/EP #A ,SOLVE = ;Y
,F/1 SOLVE ! EQU,N = .;Y S T X C 2
5T]$ 96! CALCULATOR4
.;X @+ #D;Y .K #H
#D;Y .K -- .;X @+ #H
,,/EP #B ,5T] EQU,N
,= FRAC;NAL COE6ICI5TS1 USE P>5!SES4
,S1 5T] ! EQU,N Z .;Y .K --7;L_/#D7 .;X
@+ #B4
,,/EP #C ,SET VIEW+ W9D[ & GRAPH
,5T] M9IMUM & MAXIMUM .;X- & ;Y-VALUES
& .;X- & ;Y-SCALES4 ,! VIEW+ W9D[ %D %[
! 9T]CEPTS4 ,! ./&>D .VIEW+ .W9D[ SETT+S
&! CORRESPOND+ GRAPH >E %[N 2L4
,,PRACTICE
,GRAPH ! EQU,N 9 A GRAPH+ CALCULATOR'S
/&>D VIEW+ W9D[4
.#A4 .;Y @+ #AD .K #AG--#B .;X
.#B4 #C .;X -- .;Y .K #D
.#C4 #C .;X -- #F .;Y .K --#AH
,GRAPH ! EQU,N US+ A GRAPH+
CALCULATOR4 ,USE A VIEW+ W9D[ T %[S !
.;X- & ;Y-9T]CEPTS4
.#D4 #H .;X .K #E .;Y @+ #AF
.#E4 #D .;X .K #BE .;Y -- #BDJ
.#F4 #A.BE .;X @+ #D.B .;Y .K #BH.G
-------------------------------------#IH
#B.D ,WRITE ,EQU,NS ( ,L9ES
.,2F ,Y GRAPH$ L9E> EQU,NS4
.,N[ ,Y W WRITE L9E> EQU,NS4
.,:Y8 ,S Y C MODEL A /1DY 9CR1SE OR
DECR1SE1 Z 9 ,EX4 #EA4
,KEY ,VOCABUL>Y
99 .PO9T-.SLOPE .=M
,SIDEB>3
,/&>DS ,ALGEBRA #A3 #G.J
,/UD5TS V]IFY T A PO9T LIES ON A L9E1
GIV5 AN EQU,N (! L9E4 ,/UD5TS >E A#
6DERIVE L9E> EQU,NS 0US+ ! PO9T-SLOPE
=MULA4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,WRIT+ AN ,EQU,N (A ,L9E
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,GIV5 SLOPE.' ;M .-&.' ;Y .--9T]CEPT.'
;B @3 ,USE SLOPE-9T]CEPT =M3
.;Y .K .MX @+ .;B
,GIV5 SLOPE ;M &A PO9T @7 .;X #A @1
.;Y #A @7 @3 ,USE .PO9T-.SLOPE .=M3
.;Y -- .;Y #A .K .;M @7 .;X -- .;X #A @7
99 ,GIV5 PO9TS @7 .;X #A @1 .;Y #A @7
& @7 .;X #B @1 .;Y #B @7 @3 ,F/ USE !
SLOPE =MULA 6F9D .M4 ,!N USE PO9T-SLOPE
=M ) EI GIV5 PO9T4
,,EXAMPLE #A ,WRITE AN EQU,N GIV5 !
SLOPE & .;Y -9T]CEPT
,WRITE AN EQU,N (! L9E %[N4
,SOLU;N
,F ! GRAPH1 Y C SEE T ! SLOPE IS &!
.;Y -9T]CEPT IS .;B .K --#B4 ,USE
SLOPE-9T]CEPT =M 6WRITE AN EQU,N (! L9E4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#A
,WRITE AN EQU,N (! L9E T HAS ! GIV5
SLOPE & .;Y -9T]CEPT4
.#A4 .;M .K #C1 .;B .K #A
.#B4 .;M .K --#B1 .;B .K --#D
.#C4
-------------------------------------#II
,,EXAMPLE #B ,WRITE AN EQU,N GIV5 !
SLOPE &A PO9T
,WRITE AN EQU,N (! L9E T PASSES "?
7#E1 #D7 & HAS A SLOPE ( --#C4
,,SIMPLIFY ,,EQU,NS
,9 ? BOOK1 EQU,NS WRITT5 9 PO9T-SLOPE
=M W 2 SIMPLIFI$ 6SLOPE-9T]CEPT =M4
,SOLU;N
,2C Y "K ! SLOPE &A PO9T ON ! L9E1 USE
PO9T-SLOPE =M 6WRITE AN EQU,N (! L9E4
,LET @7 .;X #A @1 .;Y #A @7 .K 7#E1 #D7
& .;M .K --#C4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
;Y -- .;Y #A .K .;M @7 .;X -- .;X #A
@7 @3 .,USE .PO9T-.SLOPE .=M4
.;Y -- #D .K --#C @7 .;X -- #E7 @3
,SUB/ITUTE =.' ;M1 ;X.' #A &.' ;Y.' #A
@4
.;Y -- #D .K --#C .;X @+ #AE @3
.,4TRIBUTIVE .PROP]TY
.;Y .K --#C .;X @+ #AI @3 ..,WRITE 9
SLOPE-9T]CEPT .=M4
,,EXAMPLE #C ,WRITE EQU,NS ( P>ALLEL
OR P]P5DICUL> L9ES
,WRITE AN EQU,N (! L9E T PASSES "?
7--#B1 #C7 & IS 7A7 P>ALLEL TO1 & 7;B7
P]P5DICUL> TO1 ! L9E .;Y .K --#D .;X @+
#A4
,SOLU;N
.A4 ,! GIV5 L9E HAS A SLOPE ( .;M ;L.'
.K --#D4 ,S1 A L9E P>ALLEL 6X HAS A
SLOPE ( .;M #B .K .;M ;L.' .K --#D4 ,Y
"K ! SLOPE &A PO9T ON ! L9E1 S USE !
PO9T-SLOPE =M ) @7 .;X #A @1 .;Y #A @7
.K 7--#B1 #C7 6WRITE AN EQU,N (! L9E4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;Y -- .;Y #A .K .;M #B @7 .;X -- .;X
#A @7 @3 .,USE .PO9T-.SLOPE .=M4
.;Y -- .#C .K --.#D @7 .;X -- @7 --.#B
@7@7 @3 ,SUB/ITUTE = ;M.' #B @1 .;X #A
@1 &.' ;Y #A
;Y--#C .K --#D7 .;X @+ #B7 @3
.,SIMPLIFY4
..;Y--.#C .K --#D .;X --#H @3
.,4TRIBUTIVE .PROP]TY
.;Y .K --#D .;X -- #E @3 ..,WRITE 9
SLOPE-9T]CEPT .=M4
.B4 ,A L9E P]P5DICUL> 6A L9E ) SLOPE
.;M ;L.' .K --#D HAS A SLOPE ( @4 ,USE
PO9T-SLOPE =M ) @7 .;X #A @1 .;Y #A @7
.K 7--#B1 #C7
..,,GUID$ ,,PRACTICE = ,EXAMPLES #B &
.#C
.#D4 ,WRITE AN EQU,N (! L9E T PASSES
"? 7--#A1 #F7 & HAS A SLOPE ( #D4
.#E4 ,WRITE AN EQU,N (! L9E T PASSES
"? 7#D1 --#B7 & IS 7A7 P>ALLEL TO1 &
7;B7 P]P5DICUL> TO1 ! L9E .;Y .K #C .;X
-- #A4
------------------------------------#AJJ
,EXAMPLE #D ,WRITE AN EQU,N GIV5 TWO
PO9TS
,WRITE AN EQU,N (! L9E T PASSES "?
7#E1 --#B7 & 7#B1AJ74
,,ANO!R ,,WAY
,= AN ALT]NATIVE ME?OD = SOLV+ ! PRO#M
9 ,EXAMPLE #D1 TURN 6PAGE #AJE =!
.,PRO#M .,SOLV+ .,"W%OP4
,SOLU;N
,! L9E PASSES "? @7 .;X #A @1 .;Y #A
@7 .K 7#E1 --#B7 & @7 .;X #B @1 .;Y #B
@7 .K 7#B1 #AJ74 ,F9D XS SLOPE4
,Y "K ! SLOPE &A PO9T ON ! L9E1 S USE
PO9T-SLOPE =M ) EI GIV5 PO9T 6WRITE AN
EQU,N (! L9E4 ,*OOSE @7 .;X #A @1 .;Y #A
@7 .K 7#B1 #AJ74
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
;Y -- .;Y #A .K .;M @7 .;X -- .;X #A
@7 @3 .,USE .PO9T-.SLOPE .=M4
.;Y -- .#AJ .K --.#D @7 .;X -- .#B @7
@3 ,SUB/ITUTE =.' ;M1 ;X.' #A &.' ;Y.'
#A @4
.;Y -- #AJ .K --#D .;X @+ #H @3
.,4TRIBUTIVE .PROP]TY
.;Y .K --#D .;X @+ #AH @3 ..,WRITE 9
SLOPE-9T]CEPT .=M4
,EXAMPLE #E ,WRITE A MODEL US+
SLOPE-9T]CEPT =M
.,,SPORTS ,9 ! S*OOL YE> 5D+ 9 #AIIC1
#B.JJ MILLION FEMALES "PICIPAT$ 9 ,U4,S4
HI< S*OOL SPORTS4 ,0#BJJC1 ! NUMB] _H
9CR1S$ 6#B.HF MILLION4 ,WRITE A L9E>
EQU,N T MODELS FEMALE SPORTS "PICIP,N4
,SOLU;N
.,,/EP .#A .,DEF9E ! V>IA#S4 ,LET .;X
REPRES5T ! "T 7IN YE>S7 S9CE #AIIC & LET
.;Y REPRES5T ! NUMB] ( "PICIPANTS 7IN
MILLIONS74
.,,/EP .#B .,ID5TIFY ! 9ITIAL VALUE &
RATE ( *ANGE4 ,! 9ITIAL VALUE IS #B.JJ4
,! RATE ( *ANGE IS ! SLOPE .M4
..,USE 7;X#A1 ;Y#A7 .K 7#J1B.JJ7 & @7
.;X #B @1 .;Y #B @7 .K 7.#AJ1.B..HF74
.,,/EP .#C .,WRITE A V]BAL MODEL4 ,!N
WRITE A L9E> EQU,N4
99 ,9 SLOPE-9T]CEPT =M1 A L9E> MODEL
IS .;Y .K #J.JHF4 .;X @+ #B.JJ4
,,AVOID ,,]RORS
,2C "T IS DEF9$ 9 YE>S S9CE #AIIC 9
,/EP #A1AIIC CORRESPONDS 6.;X #A .K #J &
#BJJC CORRESPONDS 6.;X #B .K #AJ4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #D &
.#E
,WRITE AN EQU,N (! L9E T PASSES "? !
GIV5 PO9TS4
.#F4 7--#B1 #E71 7#D1 --#G7
.#G4 7#F1 #A71 7--#C1 --#H7
.#H4 7--#A1 #B71 7#AJ1 #J7
.#I4 .,,SPORTS ,9 ,EXAMPLE #E1 !
CORRESPOND+ DATA = MALES >E #C.DB
MILLION "PICIPANTS 9 #AIIC & #C.II
MILLION "PICIPANTS 9 #BJJC4 ,WRITE A
L9E> EQU,N T MODELS MALE "PICIP,N 9
,U4,S4 HI< S*OOL SPORTS4
------------------------------------#AJA
,,EXAMPLE #F ,WRITE A MODEL US+ /&>D
=M
.,,ONL9E .,,MUSIC ,Y H 4#CJ 6SP5D ON
D[NLOAD+ S;GS = YR DIGITAL MUSIC PLAY]4
,-PANY ,A *>GES @4#.GI P] S;G1 & -PANY
;,B *>GES @4#.II P] S;G4 ,WRITE AN EQU,N
T MODELS ? SITU,N4
,SOLU;N
,WRITE A V]BAL MODEL4 ,!N WRITE AN
EQU,N4
99 ,AN EQU,N = ? SITU,N IS #J.GI .;X
@+ #J.II .;Y .K #CJ4
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#F
.#AJ4 .,,:AT .,,IF8 ,9 ,EXAMPLE #F1
SUPPOSE T -PANY ,A *>GES @4#.FI P] S;G &
-PANY ;,B *>GES @4#.HI P] S;G4 ,WRITE AN
EQU,N T MODELS ? SITU,N4
#B.D ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#C = ,EXS4 #AE1CE1 & #EC
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 #B1BF1CI1DG1 & #EC
.K .,,MULTIPLE .,,REPRES5T,NS
,EX#.EG
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,!
L9E> EQU,N #F .;X @+ #H .;Y .K #GB IS
WRITT5 9 @8 =M4
.#B4 .,,WRIT+ ,GIV5 TWO PO9TS ON A
L9E1 EXPLA9 H[ Y C USE PO9T-SLOPE =M
6WRITE AN EQU,N (! L9E4
,,EXAMPLE #A
ON P4 #IH = ,EXS4 #C-H
.,,SLOPE-.,,9T]CEPT .,,=M ,WRITE AN
EQU,N (! L9E T HAS ! GIV5 SLOPE & .;Y
-9T]CEPT4
.#C4 .;M .K #J1 .;B .K .#B
.#D4 .;M .K #C1 .;B .K --#D
.#E4 .;M .K #F1 .;B .K #J
.#F4 @1 .;B .K #D
.#G4 @1 .;B .K .#G
#H4 .;M .K --#E1 .;B .K --#A
,,EXAMPLE #B
ON P4 #II = ,EXS4 #I-AI
.,,PO9T-.,,SLOPE .,,=M ,WRITE AN EQU,N
(! L9E T PASSES "? ! GIV5 PO9T & HAS !
GIV5 SLOPE4
.#I4 7#J1--#B71 .;M .K #D
.#AJ4 7#C1 --#A71 .;M .K-#C
.#AA4 7--#D1C71 .;M .K #B
.#AB4 7--#E1 --#F71 .;M .K #J
.#AC4 7#H1 #AC71 .;M .K --#I
.#AD4 7#AB1 #J71
.#AE4 7#G1 --#C71
.#AF4 7--#D1 #B71
.#AG4 7#I1 --#E71
------------------------------------#AJB
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 WRIT+ AN EQU,N (! L9E T PASSES
"? ! GIV5 PO9T & HAS ! GIV5 SLOPE4
.#AH4 7--#D1 #B71 .;M .K #C
.#AI4 7#E1 #A71 .;M .K --.#B
,,EXAMPLE #C
ON P4 #II = ,EXS4 #BJ-BF
,,P>ALLEL ,,& ,,P]P5DICUL> ,,L9ES
,WRITE AN EQU,N (! L9E T PASSES "? !
GIV5 PO9T & SATISFIES ! GIV5 3DI;N4
.#BJ4 7--#C1 --#E72 P>ALLEL 6.;Y .K
--#D .;X @+ #A
.#BA4 7#G1 #A72 P>ALLEL 6..;Y .K --.;X
@+ #C
.#BB4 7#B1 #H72 P>ALLEL 6.;Y .K #C .;X
-- #B
.#BC4 7#D1 #A72 P]P5DICUL> TO
.#BD4 7--#F1 #B72 P]P5DICUL> 6.;Y .K
--#B
.#BE4 7#C1 --#A72 P]P5DICUL> 6.;Y .K
#D .;X @+ #A
#BF4 .,,MULTIPLE .,,*OICE ,:AT IS AN
EQU,N (! L9E T PASSES "? 7#A1 #D7 & IS
P]P5DICUL> 6! L9E .;Y .K #B;X--#C8
,A .;Y .K #B .;X @+ #B
;,B
;,C
;,D
,,EXAMPLE #D
ON P4 #AJJ = ,EXS4 #BG-CH
,,VISUAL ,,?9K+ ,WRITE AN EQU,N (!
L9E4
.#BG4
.#BH4
.#BI4
,,WRIT+ ,,EQU,NS ,WRITE AN EQU,N (!
L9E T PASSES "? ! GIV5 PO9TS4
.#CJ4 7--#A1 #C71 7#B1 #I7
.#CA4 7#D1 --#A71 7#F1 --#G7
.#CB4 7--#B1 --#C71 7#B1 --#A7
.#CC4 7#J1 #G71 7#C1 #E7
.#CD4 7--#A1 #B71 7#C1 --#D7
#CE4 7--#E1 --#B71 7--#C1 #H7
.#CF4 7#AE1 #BJ71 7--#AB1 #BI7
.#CG4 7#C.E1 #G71 7--#A1 #BJ.E7
.#CH4 7#J.F1 #J.I71 7#C.D1 --#B.F7
#CI4 .,,MULTIPLE .,,*OICE ,: PO9T LIES
ON ! L9E T PASSES "? ! PO9T 7#I1 --#E7 &
HAS A SLOPE ( --#F8
,A 7#F1AJ7
;,B 7#F1F7
;,C 7#G1G7
;,D 7#F1--#D7
,,/&>D ,,=M ,WRITE AN EQU,N 9 /&>D =M
.,AX @+ .,BY .K .;,C (! L9E T SATISFIES
! GIV5 3DI;NS4 ,USE 9TEG] VALUES = .,A1
.;,B @1 & .;,C @4
.#DJ4 .;M .K --#C1 .;B .K #E
.#DA4 .;M .K #D1 .;B .K --#C
.#DB4 @1 PASSES "? 7#D1 --#G7
.#DC4 @1 PASSES "? 7#B1 #C7
.#DD4 PASSES "? 7--#A1 #C7 & 7--#F1
--#G7
.#DE4 PASSES "? 7#B1 #H7 & 7--#D1 #AF7
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#A
.K .,,/&>DIZ$ .,,TE/ .,,PRACTICE
------------------------------------#AJC
#DF4 .,,R1SON+ ,WRITE AN EQU,N (! L9E
T PASSES "? 7#C1 #D7 & SATISFIES ! GIV5
3DI;N4
A4 ,P>ALLEL 6.;Y .K --#B
.B4 ,P]P5DICUL> 6.;Y .K --#B
C4 ,P>ALLEL 6.;X .K --#B
D4 ,P]P5DICUL> 6.;X .K --#B
#DG4 .,,OP5-.,,5D$ .,,MA? ,WRITE AN
EQU,N (A L9E ;I S* T .;I &! L9ES .;Y .K
--.#C;X @+ #E & .;Y .K .#B;X @+ #A =M A
"R TRIANGLE4
#DH4 .,,R1SON+ ,3SID] TWO 4T9CT
NONV]TICAL L9ES .,A #A .;X @+ .;,B #A
.;Y .K .;,C #A & .,A #B .;X @+ .;,B #B
.;Y .K .;,C #B @4 ,%[ T ! FOLL[+ /ATE;TS
>E TRUE4
A4 ,IF ! L9ES >E P>ALLEL1 !N .,A #A
.;,B #B .K .,A #B .;,B #A @4
B4 ,IF ! L9ES >E P]P5DICUL>1 !N .,A ;L
.,A #B @+ .;,B ;L .;,B #B .K #J4
#DI4 .,,*ALL5GE ,%[ T AN EQU,N (! L9E
) .;X -9T]CEPT .A & .;Y - 9T]CEPT .;B IS
@4 ,? IS ! .9T]CEPT .=M (A L9E> EQU,N4
,,PRO#M ,,SOLV+
,,EXAMPLE #E
ON P4 #AJJ = ,EXS4 #EJ-EA
.#EJ4 .,,C> .,,EXP5SES ,Y BUY A US$ C>
= 4#FEJJ4 ,! MON?LY CO/ ( [N+ ! C>
79CLUD+ 9SUR.E1 FUEL1 MA9T5.E1 & TAXES7
AV]AGES 4#CEJ4 ,WRITE AN EQU,N T MODELS
! TOTAL CO/ ( BUY+ & [N+ ! C>4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#EA4 .,,H\S+ ,S9CE XS F.D+1 A
VOLUNTE] GR\P HAS RE/OR$ #EJ H\SES4 ,X
PLANS 6RE/ORE #AE H\SES P] YE> 9 !
FUTURE4 ,WRITE AN EQU,N T MODELS ! TOTAL
NUMB] .;N ( RE/OR$ H\SES .;T YE>S F N[4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
,,EXAMPLE #F
ON P4 #AJA = ,EXS4 #EB-ED
.#EB4 .,,G>D5+ ,Y H A RECTANGUL> PLOT
M1SUR+ #AF FEET 0#BE FEET 9 A -MUN;Y
G>D54 ,Y WANT 6GR[ TOMATO PLANTS T EA*
NE$ #H SQU>E FEET ( SPACE & PEPP] PLANTS
T EA* NE$ #E SQU>E FEET4 ,WRITE AN EQU,N
T MODELS H[ _M TOMATO PLANTS & H[ _M
PEPP] PLANTS Y C GR[4 ,H[ _M PEPP]
PLANTS C Y GR[ IF Y GR[ #AE TOMATO
PLANTS8
.#EC .,,%ORT .,,RESPONSE ,3C]T TICKETS
CO/ 4#AE = G5]AL ADMIS.N1 B ONLY 4#I )A
/UD5T ,,ID4 ,TICKET SALES TOTAL 4#DEJJ4
,WRITE & GRAPH AN EQU,N T MODELS ?
SITU,N4 .,EXPLA9 H[ 6USE YR GRAPH 6F9D
H[ _M /UD5T TICKETS 7 SOLD IF #BJJ G5]AL
ADMIS.N TICKETS 7 SOLD4
#ED4 .,,MULTI-.,,/EP .,,PRO#M ,A -PANY
W L1SE (FICE SPACE 9 TWO BUILD+S4 ,!
ANNUAL CO/ IS 4#BA.GE P] SQU>E FOOT 9 !
F/ BUILD+ & 4#AG P] SQU>E FOOT 9 !
SECOND4 ,! -PANY HAS 4#HF1JJJ BUDGET$ =
R5T4
A4 ,WRITE AN EQU,N T MODELS ! POSSI#
AM.TS ( SPACE R5T$ 9 ! BUILD+S4
B4 ,H[ _M SQU>E FEET ( SPACE C 2 R5T$
9 ! F/ BUILD+ IF #BEJJ SQU>E FEET >E
R5T$ 9 ! SECOND8
C4 ,IF ! -PANY WANTS 6R5T EQUAL AM.TS
( SPACE 9 ! BUILD+S1 :AT IS ! TOTAL
NUMB] ( SQU>E FEET T C 2 R5T$8
------------------------------------#AJD
.#EE4 .,,CA# .,,TELEVI.N ,9 #AIID1 !
AV]AGE MON?LY CO/ = EXP&$ BASIC CA#
TELEVI.N S]VICE 0 4#BA.FB4 ,9 #BJJD1 ?
CO/ _H 9CR1S$ TO 4#CH.BC4 ,WRITE A L9E>
EQU,N T MODELS ! MON?LY CO/ Z A FUNC;N
(! NUMB] ( YE>S S9CE #AIID4 ,PREDICT !
AV]AGE MON?LY CO/ ( EXP&$ BASIC CA#
TELEVI.N S]VICE 9 #BJAJ4
.#EF4 .,,TIRE .,,PRESSURE ,AUTOMOBILE
TIRE PRESSURE 9CR1SES AB #A PSI 7P.D P]
SQU>E 9*7 = EA* #AJ;DG;,F 9CR1SE 9 AIR
TEMP]ATURE4 ,AT AN AIR TEMP]ATURE (
#EE;DG;,F1 A TIRE'S PRESSURE IS #CJ PSI4
,WRITE AN EQU,N T MODELS ! TIRE'S
PRESSURE Z A FUNC;N ( AIR TEMP]ATURE4
#EG4 .,,MULTIPLE .,,REPRES5T,NS ,YR
CLASS WANTS 6MAKE A RECTANGUL> _S 4PLAY1
& HAS #BD FEET ( DECORATIVE BORD]
65CLOSE ! 4PLAY
A4 .,WRIT+ .AN .,EQU,N ,WRITE AN EQU,N
9 /&>D =M RELAT+ ! POSSI# L5G?S & WID?S
.;W (! 4PLAY4
B4 .,DRAW+ .A .,GRAPH ,GRAPH ! EQU,N F
"P 7A74
C4 .,MAK+ .A .,TA# ,MAKE A TA# ( AT
L1/ FIVE POSSI# PAIRS ( DIM5.NS =!
4PLAY4
#EH4 .,,*ALL5GE ,Y >E "PICIPAT+ 9 A
D.E-A-?ON 6RAISE M"OY =A CLASS TRIP4
,DONORS C PL$GE AN AM.T ( M"OY = EA* H\R
Y D.E1 A FIX$ AM.T ( M"OY T DOES N DEP5D
ON H[ L;G Y D.E1 OR BO?4 ,! TA# %[S !
AM.TS PL$G$ 0F\R DONORS4 ,WRITE AN EQU,N
T MODELS ! TOTAL AM.T .;Y ( M"OY Y W
RAISE F ! DONORS IF Y D.E = .;X H\RS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,DONOR3 ,H\RLY AM.T3 ,FIX$ AM.T
,CL>E3 4#D3 4#AE
,EMILIA3 4#H3 ,N"O
,JULIO3 ,N"O3 4#CE
,MAX3 4#C3 4#BJ
,,MIX$ ,,REVIEW
,,PREVIEW
,PREP>E = ,LESSON #B.E 9 ,EXS4 #EI-FD4
,SOLVE ! EQU,N4 ,*ECK YR SOLU;N1 @7 P4
#AH @7
.#EI4 #I .;X .K #BG
.#FJ4 #E .;X .K #BJ
.#FA4 --#C .;X .K #BA
.#FB4 #H .;X .K #F
.#FC4 #D .;X .K --#AD
.#FD4 #AJ .;X .K #H
,SOLVE ! 9EQUAL;Y4 ,!N GRAPH ! SOLU;N1
@7 P4 #DA @7
.#FE4 #C .;X @+ #E "K #AG
.#FF4 #B .;X -- #D .1 --#AJ
.#FG4 #F .;X @+ #D .1.K #BB
.#FH4 #E .;X @+ #C "K.K #B .;X -- #AB
.#FI4 #D .;X @+ #E .1.K #B .;X @+ #C
.#GJ4 --#C "K.K #B .;X -- #G "K.K #AC
.#GA4 #AD "K #E -- .;X "K #I
.#GB4 #C .;X -- #E .1.K #G OR -- .;X
--#D .1 #C
.#GC4 #B .;X "K #F OR #E .;X -- #I
.1.K #AF
,GRAPH ! EQU,N1 @7 P4 #GB @7
.#GD4 .;Y .K .;X -- #H
.#GE4 .;Y .K --#B .;X @+#A
.#GF4 .;Y .K #C .;X -- #B
.#GG4 .;Y .K #D .;X @+ #B
.#GH4
.#GI4
.#HJ4 ,,RES]VOIRS ,! SURFACE ELEV,N (A
RES]VOIR IS #IDJ FEET ABV SEA LEVEL4
,WAT] IS REL1S$ OV] A P]IOD ( #AE "DS1
L[]+ ! SURFACE ELEV,N 6#ICD FEET ABV SEA
LEVEL4 ,:AT IS ! AV]AGE RATE ( *ANGE 9 !
RES]VOIR'S SURFACE ELEV,N OV] ! P]IOD8
@7 P4 #HB @7
.,,EXTRA .,,PRACTICE ,,= L,,ESSON
#B.D4 P4 #AJAA
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#AJE
,PRO#M ,SOLV+ ,"W%OP ,LESSON #B.D3
,US+ ,ALT]NATIVE ,ME?ODS
,ANO!R ,WAY 6,SOLVE ,EXAMPLE #D1 PAGE
#AJJ
.,,MULTIPLE .,,REPRES5T,NS ,9 ,EXAMPLE
#D ON PAGE #AJJ @1 Y WROTE AN EQU,N (A
L9E "? TWO GIV5 PO9TS 0F/ WRIT+ ! EQU,N
9 PO9T-SLOPE =M & !N REWRIT+ X 9
SLOPE-9T]CEPT =M4 ,Y C AL WRITE AN EQU,N
(A L9E "? TWO PO9TS 0US+ ! SLOPE-9T]CEPT
=M 6SOLVE =! .;Y -9T]CEPT4
.,,PRO#M ,WRITE AN EQU,N (! L9E T
PASSES "? 7#E1 --#B7 & 7#B1 #AJ74
..,,ME?OD ,SOLV+ =! ;Y -.9T]CEPT
,6WRITE AN EQU,N (A L9E "? TWO PO9TS1 Y
C SUB/ITUTE ! SLOPE &! COORD9ATES ( "O
(! PO9TS 96.;Y .K .MX @+ .;B & SOLVE =!
.;Y -9T]CEPT .;B @4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,,/EP .#A ,F9D.' ! SLOPE (! L9E4 @3
.,,/EP .#B ,SUB/ITUTE.' ! SLOPE &!
COORD9ATES ( "O PO9T 96! SLOPE-9T]CEPT
=M4 ,USE ! PO9T 7#E1 --#B74 @3 .;Y .K
.MX @+ .;B
--#B .K --#D7#E7 @+ .;B
.,,/EP .#C ,SOLVE.' = .B4 @3 --..#B .K
--.#BJ @+ .;B
.#AH .K .;B
.,,/EP .#D ,SUB/ITUTE.' .;M & .;B 96!
SLOPE-9T]CEPT =M4 @3 ;Y .K --#D .;X @+
#AH
,,PRACTICE
..#A4 ,,WRITE ,,AN .,,EQU,N ,USE !
ME?OD ABV 6WRITE AN EQU,N (! L9E T
PASSES "? 7#B1 #AE7 & 7#G1 #CE74
.#B4 .,,FIT;S ,AT A SPE$ ( #DE Y>DS P]
M9UTE1 A #ABJ P.D SWIMM] BURNS #DBJ
CALORIES P] H\R &A #AGB P.D SWIMM] BURNS
#FJJ CALORIES P] H\R4 ,USE TWO DI6]5T
ME?ODS 6WRITE A L9E> EQU,N T MODELS !
NUMB] ( CALORIES BURN$ P] H\R Z A FUNC;N
(A SWIMM]'S WEI<T4
.#C4 .,,SAFETY ,A MOTORI/ LI<TS AN
EM]G5CY FL>E AF HAV+ A FLAT TIRE4 ,AF
BURN+ = #F M9UTES1 ! FL>E IS #AC 9*ES
L;G4 ,AF BURN+ = #BJ M9UTES1 X IS #F
9*ES L;G4 ,USE TWO DI6]5T ME?ODS 6WRITE
A L9E> EQU,N T MODELS ! FL>E'S L5G? Z A
FUNC;N ( "T4
.#D4 .,,SN[FALL ,AF #D H\RS ( SN[FALL1
! SN[ DEP? IS #H 9*ES4 ,AF #F H\RS (
SN[FALL1 ! SN[ DEP? IS #I.E 9*ES4 ,USE
TWO DI6]5T ME?ODS 6WRITE A L9E> EQU,N T
MODELS ! SN[ DEP? Z A FUNC;N ( "T4
.#E4 .,,>*AEOLOGY ,ANCI5T CITIES (T5
ROSE 9 ELEV,N "? "T Z CITIZ5S BUILT ON
TOP ( A3UMULAT+ RUB# & DEBRIS4 ,AN
>*AEOLOGI/ AT A SITE DATES >TIFACTS F A
DEP? ( #ED FEET Z #CEJJ YE>S OLD &
>TIFACTS F A DEP? ( #BF FEET Z #BFJJ
YE>S OLD4
,USE TWO DI6]5T ME?ODS 6WRITE A L9E>
EQU,N T MODELS AN >TIFACT'S AGE Z A
FUNC;N ( DEP?4
.#F4 .,,R1SON+ ,SUPPOSE A L9E HAS
SLOPE .;M & PASSES "? @7 .;X #A @1 .;Y
#A @7@4 ,WRITE AN EXPRES.N =! .;Y
-9T]CEPT .;B 9 T]MS ( .;M1 .;X #A & .;Y
#A @4
------------------------------------#AJF
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,LESSONS #B.A --#B.D
.#A4 .,,MULTI-.,,/EP .,,PRO#M ,F
,JANU>Y 6,JUNE1 ! NUMB] ( VISITORS 6A
NEWS WEBSITE 9CR1S$ 0AN AV]AGE ( #ABJJ
P] MON?4 ,9 ,JANU>Y1 "! 7 #EJ1JJJ
VISITORS 6! WEBSITE4
.A4 ,WRITE AN EQU,N T GIVES ! NUMB]
.;V ( VISITORS 6! WEBSITE Z A FUNC;N (!
NUMB] .;T ( MON?S S9CE ,JANU>Y4
.B4 ,GRAPH ! EQU,N F "P 7A74
.C4 ,USE ! EQU,N F "P 7A7 6PREDICT !
NUMB] ( WEBSITE VISITORS 9 ,OCTOB]4
.#B4 .,,MULTI-.,,/EP .,,PRO#M ,!
(FICIAL POPUL,N ( ,BATON ,R\GE1
,L\ISIANA1 0 #BAI1ECA 9 #AIIJ & #BBG1HAH
9 #BJJJ4
.A4 ,:AT 0 ! AV]AGE RATE ( *ANGE 9 !
POPUL,N F #AIIJ 6#BJJJ8
.B4 ,WRITE A L9E> EQU,N T MODELS !
POPUL,N .;,P ( ,BATON ,R\GE F #AIIJ
6#BJJJ4 ,LET .;T REPRES5T ! NUMB] ( YE>S
S9CE #AIIJ4
.C4 ,USE YR EQU,N F "P 7;B7 6PREDICT !
POPUL,N ( ,BATON ,R\GE 9 #BJAJ4
.#C4 .,,%ORT .,,RESPONSE ,! GRAPH %[S
! NUMB] ( REPRES5TATIVES 9 ! ,U4,S4
,3GRESS GIV5 6,ILL9OIS 0EA* N,NAL C5SUS
F #AIDJ 6#BJJJ4 ,DOES ! GRAPH REPRES5T A
FUNC;N8 .,EXPLA94
.#D4 .,,OP5-.,,5D$ ,WRITE AN EQU,N (A
L9E T IS P>ALLEL 6! L9E .;X @+ #C .;Y .K
#AB & T 3TA9S NO PO9TS 9 ,QUADRANT ,I4
.#E4 .,,EXT5D$ .,,RESPONSE ,G5]AL
ADMIS.N TICKETS 6A HI< S*OOL FOOTBALL
GAME CO/ 4#G1 :ILE /UD5T TICKETS CO/
4#D4 ,TICKET SALES =A GAME TOTAL$
4#AA1BJJ4
.A4 ,WRITE AN EQU,N =! POSSI# NUMB]S (
G5]AL ADMIS.N & /UD5T TICKETS T CD H BE5
SOLD =! GAME4
.B4 ,GRAPH ! EQU,N F "P 7A74
.C4 ,IS X POSSI# T #IEJ G5]AL ADMIS.N
TICKETS 7 SOLD8 .,EXPLA94
.D4 ,F9D ?REE POSSI# -B9,NS ( G5]AL
ADMIS.N & /UD5T TICKETS T CD H BE5 SOLD4
.,EXPLA9 H[ Y F.D YR ANSW]S4
.#F4 .,,GRI4$ .,,ANSW] ,:AT IS ! SLOPE
(A L9E P>ALLEL TO @8
.#G4 .,,GRI4$ .,,ANSW] ,:AT IS ! SLOPE
(A L9E P]P5DICUL> 6! L9E %[N8
.#H4 .,,%ORT .,,RESPONSE ,YR DIGITAL
CAM]A HAS A #EAB MEGABYTE MEMORY C>D4 ,Y
TAKE L[ RESOLU;N PICTURES REQUIR+ #D
MEGABYTES ( MEMORY EA* & HI< RESOLU;N
PICTURES REQUIR+ #H MEGABYTES ( MEMORY
EA*4
.A4 ,WRITE & GRAPH AN EQU,N =! POSSI#
NUMB]S ( L[ & HI< RESOLU;N PICTURES Y C
TAKE4
.B4 .,DESCRIBE ! M1N+ (! SLOPE &
9T]CEPTS 9 ! 3TEXT (! PRO#M4
------------------------------------#AJG
#B.E ,MODEL ,DIRECT ,V>I,N
.,2F ,Y WROTE & GRAPH$ L9E> EQU,NS4
.,N[ ,Y W WRITE & GRAPH DIRECT V>I,N
EQU,NS4
.,:Y8 ,S Y C MODEL ANIMAL MIGR,N1 Z 9
,EX4 #DD4
,KEY ,VOCABUL>Y
99 .DIRECT .V>I,N
99 .3/ANT .( .V>I,N
,SIDEB>3
,/&>DS3 ,PREP>E = #B.J
..,/UD5TS SOLVE SY/EMS ( L9E> .EQU,NS
& 9EQUALITIES 7IN TWO OR ?REE V>IA#S7
0SUB/ITU;N1 .) .GRAPHS @1 OR ) MATRICES4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,DIRECT ,V>I,N
.,EQU,N ,! EQU,N .;Y .K .AX REPRES5TS
.DIRECT .V>I,N 2T .;X & ;Y1 & .;Y IS SD
6.V>Y .DIRECTLY ) .X4 ,! NONZ]O 3/ANT .A
IS CALL$ ! .3/ANT .( .V>I,N4
,GRAPH
,! GRAPH (A DIRECT V>I,N EQU,N .;Y .K
.AX IS A L9E ) SLOPE .A & .;Y -9T]CEPT
#J4
,! FAMILY ( DIRECT V>I,N GRAPHS 3SI/S
( L9ES "? ! ORIG91 S* Z ^? %[N4
..,,EXAMPLE #A ,WRITE & GRAPH A DIRECT
V>I,N .EQU,N
,WRITE & GRAPH A DIRECT V>I,N EQU,N T
HAS 7--#D1H7 Z A SOLU;N4
,SOLU;N
,USE ! GIV5 VALUES ( .;X & .;Y 6F9D !
3/ANT ( V>I,N4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;Y .K .AX @3 ..,WRITE DIRECT V>I,N
.EQU,N4
.#H .K .A @7 --.#D @7 @3 ,SUB/ITUTE #H
= .;Y & --#D = .;X @4
--#B .K .A @3 ,SOLVE =.' A @4
,SUB/ITUT+ --#B = .A 9 .;Y .K .AX
GIVES ! DIRECT V>I,N EQU,N .;Y .K -.#BX4
,XS GRAPH IS %[N4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
.,,GUID$ .,,PRACTICE = ,EXAMPLE #A
,WRITE & GRAPH A DIRECT V>I,N EQU,N T
HAS ! GIV5 ORD]$ PAIR Z A SOLU;N4
.#A4 7#C1 --#I7
.#B4 7--#G1D7
.#C4 7#E1C7
.#D4 7#F1 --#B7
------------------------------------#AJH
,,EXAMPLE #B ,WRITE & APPLY A MODEL =
DIRECT V>I,N
.,,METEOROLOGY ,HAIL/"OS =M :5 /R;G
UPDRAFTS SUPPORT ICE "PICLES HI< 9
CL\DS1 ": WAT] DROPLETS FREEZE ONTO !
"PICLES4 ,! DIAGRAM %[S A HAIL/"O AT TWO
DI6]5T "TS DUR+ XS =M,N4
.A4 ,WRITE AN EQU,N T GIVES !
HAIL/"O'S DIAMET] .;D 7IN 9*ES7 AF .;T
M9UTES IF Y ASSUME ! DIAMET] V>IES
DIRECTLY )! "T ! HAIL/"O TAKES 6=M4
.B4 ,US+ YR EQU,N F "P 7A71 PREDICT !
DIAMET] (! HAIL/"O AF #BJ M9UTES4
,SOLU;N
A4 ,USE ! GIV5 VALUES ( .;T & .;D 6F9D
! 3/ANT ( V>I,N4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;D .K .AT @3 ..,WRITE DIRECT V>I,N
.EQU,N4
.#J..GE .K .A 7.#AB7 @3 ,SUB/ITUTE
#J.GE =.' ;D .-& #AB =.' T4.-
#J.JFBE .K .A @3 ,SOLVE =.' A4.-
,AN EQU,N T RELATES .;T & .;D IS .;D
.K #J.JFBE .;T
B4 ,AF .;T .K #BJ M9UTES1 ! PREDICT$
DIAMET] (! HAIL/"O IS .;D .K
#J.JFBE7#BJ7 .K #A.BE 9*ES4
..,,RATIOS ,,& ,,DIRECT .,,V>I,N ,2C !
DIRECT V>I,N EQU,N .;Y .K .AX C 2 WRITT5
Z @1 A SET ( DATA PAIRS @7 .;X1 .;Y @7
%[S DIRECT V>I,N IF ! RATIO ( .;Y 6.;X
IS 3/ANT4
,,EXAMPLE #C ,USE RATIOS 6ID5TIFY
DIRECT V>I,N
.,,%>KS ,GRT :ITE %>KS H TRIANGUL>
TEE?4 ,! TA# 2L GIVES ! L5G? (A SIDE (A
TOO? &! BODY L5G? = EA* ( SIX GRT :ITE
%>KS4 ,TELL :E!R TOO? L5G? & BODY L5G?
%[ DIRECT V>I,N4 ,IF S1 WRITE AN EQU,N T
RELATES ! QUANTITIES4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,TOO? L5G?1 .;T 7CM7 @3 #A.H3 #B.D3
#B.I3 #C.F3 #D.G3 #E.H
,BODY L5G?1 .;B 7CM7 @3 #BAE3 #BIJ3
#CEJ3 #DCJ3 #EFE3 #FIE
,,AVOID ,,]RORS
,= R1L-_W DATA1 ! RATIOS D N H 6BE
.EXACTLY ! SAME 6%[ T DIRECT V>I,N IS A
PLAUSI# MODEL4
,SOLU;N
,F9D ! RATIO (! BODY L5G? .;B 6! TOO?
L5G? .;T = EA* %>K4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
@3 @3
@3 @3
,2C ! RATIOS >E APPROXIMATELY EQUAL1 !
DATA %[ DIRECT V>I,N4 ,AN EQU,N RELAT+
TOO? L5G? & BODY L5G? IS @1 OR .;B .K
#ABJ .;T @4
------------------------------------#AJI
..,,GUID$ ,,PRACTICE = ,EXAMPLES #B &
.#C
.#E4 .,,:AT .,,IF8 ,9 ,EXAMPLE #B1
SUPPOSE T A HAIL/"O =M+ 9 A CL\D HAS A
RADIUS ( #J.F 9*4 ,PREDICT H[ L;G X HAS
BE5 =M+4
.#F4 .,,%>KS ,9 ,EXAMPLE #C1 !
RESPECTIVE BODY MASSES .;M 7IN
KILOGRAMS7 (! GRT :ITE %>KS >E #HJ1
#BBJ1 #CGE1 #GCJ1 #AFIJ1 & #CAIE4 ,TELL
:E!R TOO? L5G? & BODY MASS %[ DIRECT
V>I,N4 ,IF S1 WRITE AN EQU,N T RELATES !
QUANTITIES4
#B.E ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS .ON .P4
,,WS#C = ,EXS4 .#E1.AE @1 & .#DA
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 #B1AG1 #CJ1DJ1 & #DD
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,DEF9E ! 3/ANT (
V>I,N = TWO V>IA#S .;X & .;Y T V>Y
DIRECTLY4
.#B4 .,,WRIT+ ,GIV5 A TA# ( ORD]$
PAIRS @7 .;X @1 .;Y @7@1 DESCRIBE H[
6DET]M9E :E!R .;X & .;Y %[ DIRECT V>I,N4
,,EXAMPLE #A
ON P4 #AJG = ,EXS4 #C-AJ
,,WRIT+ ,,& ,,GRAPH+ ,WRITE & GRAPH A
DIRECT V>I,N EQU,N T HAS ! GIV5 ORD]$
PAIR Z A SOLU;N4
.#C4 7#B1F7
.#D4 7--#C1AB7
.#E4 7#F1-#BA7
.#F4 7#D1AJ7
.#G4 7--#E1 --#A7
.#H4 7#BD1 --#H7
.#I4
.#AJ4 7#AB.E1 #E7
,,EXAMPLE #B
ON P4 #AJH = ,EXS4 #AA-AG
,,WRIT+ ,,& ,,EVALUAT+ ,! V>IA#S .;X &
.;Y V>Y DIRECTLY4 ,WRITE AN EQU,N T
RELATES .;X & Y4 ,!N F9D .;Y :5 .;X .K
#AB4
.#AA4 .;X .K #D1 .;Y .K #H
.#AB4 .;X .K --#C1 .;Y .K --#E
.#AC4 .;X .K #CE1 .;Y .K --.#G
.#AD4 .;X .K --#AH1 .;Y .K #D
.#AE4 .;X .K --#D.H1 .;Y .K --#A.F
.#AF4
#AG4 .,,MULTIPLE .,,*OICE ,: EQU,N IS
A DIRECT V>I,N EQU,N T HAS 7#C1 #AH7 Z A
SOLU;N8
,A .;Y .K #B .;X #B
;,B
;,C .;Y .K #F .;X
;,D .;Y .K #D .;X @+ #F
,,ID5TIFY+ ,,DIRECT ,,V>I,N ,TELL :E!R
! EQU,N REPRES5TS DIRECT V>I,N4 ,IF S1
GIVE ! 3/ANT ( V>I,N4
.#AH4 .;Y .K --#H .;X
.#AI4 .;Y -- #D .K #C .;X
.#BJ4 #C .;Y -- #G .K ;L#J .;X
.#BA4 #B .;Y -- #E .;X .K #J
.#BB4 #E .;Y .K --#D .;X
.#BC4 #F .;Y .K .;X
,,WRIT+ ,,& ,,SOLV+ ,! V>IA#S .;X &
.;Y V>Y DIRECTLY4 ,WRITE AN EQU,N T
RELATES .;X & Y4 ,!N F9D .;X :5 .;Y .K
--#D4
.#BD4 .;X .K #E1 .;Y .K --#AE
.#BE4 .;X .K --#F1 .;Y .K #H
.#BF4 .;X .K --#AH1 .;Y .K --#B
.#BG4 .;X .K --#AB1 .;Y .K #HD
.#BH4
.#BI4 .;X .K --#J.E1 .;Y .K #C.F
------------------------------------#AAJ
.#CJ4 .,,OP5-.,,5D$ .,,MA? ,GIVE AN
EXAMPLE ( TWO R1L-LIFE QUANTITIES T %[
DIRECT V>I,N4 .,EXPLA9 YR R1SON+4
,,EXAMPLE #C
ON P4 #AJH = ,EXS4 #CA-CD
,,ID5TIFY+ ,,DIRECT ,,V>I,N ,TELL :E!R
! DATA 9 ! TA# %[ DIRECT V>I,N4 ,IF S1
WRITE AN EQU,N RELAT+ .;X & Y4
#CA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #C3 #F3 #I3 #AB3 #AE
.;Y @3 --#A3 --#B3 --#C3 --#D3 --#E
#CB4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #A3 #B3 #C3 #D3 #E
.;Y @3 #G3 #I3 #AA3 #AC3 #AE
#CC4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 --#E3 --#D3 --#C3 --#B3 --#A
.;Y @3 #BJ3 #AF3 #AB3 #H3 #D
#CD4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 --#H3 --#D3 #D3 #H3 #AB
.;Y @3 #H3 #D3 --#D3 --.#H @3 --#AB
.#CE4 .,,]ROR .,,ANALYSIS ,A /UD5T
TRI$ 6DET]M9E :E!R ! DATA PAIRS 7#A1
#BD71 7#B1 #AB71 7#C1 #H71 & 7#D1 #F7 %[
DIRECT V>I,N4 .,DESCRIBE & CORRECT !
]ROR 9 ! /UD5T'S "W4
.#CF4 .,,R1SON+ ,LET 7;X#A1 ;Y#A7 2 A
SOLU;N1 O!R ?AN 7#J1 #J71 (A DIRECT
V>I,N EQU,N4 ,WRITE A SECOND DIRECT
V>I,N EQU,N ^: GRAPH IS P]P5DICUL> 6!
GRAPH (! F/ EQU,N4
.#CG4 .,,*ALL5GE ,LET @7 .;X #A1 .;Y
#A7 & @7 .;X #B @1 .;Y #B @7 2 ANY TWO
4T9CT SOLU;NS (A DIRECT V>I,N EQU,N4 ,%[
T
,,PRO#M ,,SOLV+
,,EXAMPLE #B
ON P4 #AJH = ,EXS4 #CH-DJ
.#CH4 .,,SCUBA .,,DIV+ ,! "T FIT TAKES
A DIV] 6ASC5D SAFELY 6! SURFACE V>IES
DIRECTLY )! DEP? .D4 ,X TAKES A M9IMUM (
#J.GE M9UTE =A SAFE ASC5T F A DEP? ( #DE
FEET4 ,WRITE AN EQU,N T RELATES .;D &
.T4 ,!N PREDICT ! M9IMUM "T =A SAFE
ASC5T F A DEP? ( #AJJ FEET4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#CI4 .,,W1!R ,HAIL #J.E 9* DEEP &
WEI<+ #AHJJ P.DS COV]S A RO(4 ,! HAIL'S
WEI<T .;W V>IES DIRECTLY ) XS DEP? .D4
,WRITE AN EQU,N T RELATES .;D & .W4 ,!N
PREDICT ! WEI<T ON ! RO( ( HAIL T IS
#A.GE 9*ES DEEP4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#DJ4 .,,MULTIPLE .,,*OICE ,YR WEI<T
;,M ON ,M>S V>IES DIRECTLY ) YR WEI<T
.;,E ON ,E>?4 ,IF Y WEI< #AAF P.DS ON
,E>?1 Y WD WEI< #DD P.DS ON ,M>S4 ,:
EQU,N RELATES .;,E & ;,M8
,A .;,M.K.;,E--.#GB
;,B #DD .;,M .K#AAF .;,E
;,C
;,D
#DA4 ,,9T]NET ,,D[NLOADS ,! ORD]$
PAIRS 7#D.E1 #BC71 7#G.H1 #DJ71 &
7#AF.J1 #HB7 >E 9 ! =M @7 .;S1 .;T @7 ":
.;T REPRES5TS ! "T 7IN SECONDS7 NE$$
6D[NLOAD AN ,9T]NET FILE ( SIZE .;S 7IN
MEGABYTES74 ,TELL :E!R ! DATA %[ DIRECT
V>I,N4 ,IF S1 WRITE AN EQU,N T RELATES
.;S & .T4
,,EXAMPLE #C
ON P4 #AJH = ,EXS4 #DA-DC
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#A
.K ,,/&>DIZ$ ,,TE/ ,,PRACTICE
------------------------------------#AAA
..,,GEOMETRY ,9 ,EX]CISES #DB & #DC1
3SID] SQU>ES ) SIDE L5G?S ( #A1 #B1C1 &
#D .C5TIMET]S4
.#DB4 ,COPY & -PLETE ! TA#4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,SIDE L5G?1 ;S 7CM73 #A3 #B3 #C3 #D
.,P]IMET]1 .;,P 7.CM7 @3 @8 @3 @8 @3
@8 @3 @8
,>EA1 .,A 7CM.' #B @7 @3 @8 @3 @8 @3
@8 @3 @8
#DC4 ,TELL :E!R ! GIV5 V>IA#S %[
DIRECT V>I,N4 ,IF S1 WRITE AN EQU,N
RELAT+ ! V>IA#S4 ,IF N1 EXPLA9 :Y N4
A4 .;S & .;,P
B4 .;S & .,A
C4 .;,P & .,A
#DD4 .,,EXT5D$ .,,RESPONSE ,EA* YE>1
GRAY :ALES MIGRATE F ,MEXICO'S ,BAJA
,P59SULA 6FE$+ GR.DS NE> ,ALASKA4 ,A
:ALE MAY TRAVEL #FJJJ MILES AT AN AV]AGE
RATE ( #GE MILES P] "D4
A4 ,WRITE AN EQU,N T GIVES ! 4T.E .;D
#A TRAVEL$ 9 .;T "DS ( MIGR,N4
B4 ,WRITE AN EQU,N T GIVES ! 4T.E .;D
#B T REMA9S 6BE TRAVEL$ AF .;T "DS (
MIGR,N4
C4 ,TELL :E!R ! EQU,NS F "PS 7A7 &
7;B7 REPRES5T DIRECT V>I,N4 .,EXPLA9 YR
ANSW]S4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
#DE4 .,,*ALL5GE ,AT A JEWELRY /ORE1 !
PRICE .;P (A GOLD NECKLACE V>IES
DIRECTLY ) XS L5G? .;,L ,AL1 ! WEI<T .;W
(A NECKLACE V>IES DIRECTLY ) XS L5G?4
,%[ T ! PRICE (A NECKLACE V>IES DIRECTLY
) XS WEI<T4
,,MIX$ ,,REVIEW
,SOLVE ! 9EQUAL;Y4 ,!N GRAPH ! SOLU;N4
@7 P4 #EA @7
.#DF4 _\ .;X -- #E_\ .1.K #AJ
.#DG4 _\#H--#C .;X _\ "K #AC
.#DH4 _\ -- .;X -- #D _\ "K.K #E
.#DI4 _\#D .;X -- #C_\ .1 #C
.#EJ4
.#EA4
,,PREVIEW
,PREP>E = ,LESSON #B.F 9 ,EXS4 #EB-EG4
,F9D ! SLOPE (! L9E PASS+ "? ! GIV5
PO9TS4 @7 P4 #HB @7
.#EB4 7#B1 --#E71 7--#A1 #D7
.#EC4 7--#A1 --#E71 7--#C1 --#B7
.#ED4 7#C1 #AA71 7--#B1 --#D7
.#EE4 7--#B1 --#AJ71 7--#B1 #H7
.#EF4 7--#D1 #I71 7#F1 --#I7
.#EG4 7--#AE1 #A71 7--#F1 #AC7
,GRAPH ! EQU,N4 @7 P4 #HI @7
.#EH4 .;Y .K #A @+ #B .;X
.#EI4
.#FJ4 .;F7.;X7 .K --#D .;X -- #C
.#FA4 #E .;X @+ #H .;Y .K #DJ
.#FB4 .;Y .K --#E
.#FC4 #F .;X -- ;L#J .;Y .K #AE
.#FD4 .,,UTILITIES ,YR JUNE ELECTRIC
BILL IS 4#GH = #GBJ KILOWATT-H\RS (
ELECTRIC;Y4 ,YR ,JULY BILL IS 4#ABJ =
#AADJ KILOWATT-H\RS4 ,WRITE A L9E> EQU,N
T MODELS CO/ Z A FUNC;N ( ELECTRIC;Y
USE4 @7 P4 #IH @7
.,,EXTRA .,,PRACTICE = ,LESSON #B.E1
P4 #AJAA
..,,ONL9E ,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#AAB
,9VE/IGAT+ ,ALGEBRA ,ACTIV;Y3 #B.F
,FITT+ A ,L9E 6,DATA
,USE 2F ,LESSON #B.F
,MAT]IALS
99 OV]H1D PROJECTOR
99 OV]H1D TRANSP>5CY
99 METRIC RUL]
99 MET] /ICK
99 GRAPH PAP]
,,"Q
,H[ C Y APPROXIMATE ! .BE/-.FITT+ .L9E
=A SET ( DATA8
,,EXPLORE
,COLLECT & RECORD DATA
,SIDEB>3
,/&>DS3 ,PROBABIL;Y & /ATI/ICS3 #H.J
,,/EP #A ,SETUP
,POSI;N AN OV]H1D PROJECTOR A 3V5I5T
4T.E F A PROJEC;N SCRE54 ,DRAW A L9E
SEG;T #AE C5TIMET]S L;G ON A TRANSP>5CY1
& PLACE ! TRANSP>5CY ON ! PROJECTOR4
,,/EP #B ,COLLECT DATA
,M1SURE ! 4T.E1 9 C5TIMET]S1 F !
PROJECTOR 6! SCRE5 &! L5G? (! L9E SEG;T
Z X APPE>S ON ! SCRE54 ,REPOSI;N !
PROJECTOR S"EAL "TS1 EA* "T TAK+ ^!
M1SURE;TS4
,,/EP #C ,RECORD DATA
,RECORD YR M1SURE;TS F ,/EP #B 9 A TA#
L ! "O %[N 2L4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,4T.E F PROJECTOR 6SCRE5 7CM71 .;X @3
..,L5G? ( L9E SEG;T .ON SCRE5 7CM71 .;Y
#BJJ3 @8
#BAJ3 @8
#BBJ3 @8
#BCJ3 @8
#BDJ3 @8
#BEJ3 @8
#BFJ3 @8
#BGJ3 @8
#BHJ3 @8
#BIJ3 @8
,,DRAW ,,3CLU.NS
,USE YR OBS]V,NS 6-PLETE ^! EX]CISES
.#A4 ,GRAPH ! DATA PAIRS 7.;X1 .;Y
@7@4 ,:AT PATT]N D Y OBS]VE8
.#B4 ,USE A RUL] 6DRAW A L9E T LIES Z
CLOSE Z POSSI# 6ALL (! PO9TS ON ! GRAPH1
Z %[N AT ! "R4 ,! L9E DOES N H 6PASS "?
ANY (! PO9TS4 ,"! %D 2 AB Z _M PO9TS ABV
! L9E Z 2L X4
.#C4 ,E/IMATE ! COORD9ATES ( TWO PO9TS
ON YR L9E4 ,USE YR PO9TS 6WRITE AN EQU,N
(! L9E4
.#D4 ,US+ YR EQU,N F ,EX]CISE #C1
PREDICT ! L5G? (! L9E SEG;T ON ! SCRE5
=A "PICUL> PROJECTOR-TO-SCRE5 4T.E LESS
?AN ^? 9 YR TA# &=A "PICUL>
PROJECTOR-TO-SCRE5 4T.E GRT] ?AN ^? 9 YR
TA#4
.#E4 ,TE/ YR PREDIC;NS F ,EX]CISE .#D4
,H[ A3URATE 7 !Y8
------------------------------------#AAC
#B.F ,DRAW ,SCATT] ,PLOTS &
,BE/-,FITT+ ,L9ES
.,2F ,Y WROTE EQU,NS ( L9ES4
.,N[ ,Y W FIT L9ES 6DATA 9 SCATT]
PLOTS4
.,:Y3 ,S Y C MODEL SPORTS TR5DS1 Z 9
,EX4 #BG4
,KEY ,VOCABUL>Y
99 SCATT] PLOT
99 POSITIVE CORREL,N
99 NEGATIVE CORREL,N
99 CORREL,N COE6ICI5T
99 BE/-FITT+ L9E
,SIDEB>3
,/&>DS3 ,PROBABIL;Y & ,/ATI/ICS3
#H.J
..,/UD5TS ORGANIZE & DESCRIBE
4TRIBU;NS ( DATA 0.US+ A NUMB] ( DI6]5T
ME?ODS1 9CLUD+ FREQU5CY TA#S1 HI/OGRAMS1
/&>D L9E & B> GRAPHS1 /EM-&-L1F 4PLAYS1
.SCATT]PLOTS @1 & BOX-&-:ISK] PLOTS4
..,ADV.ED ,PLACE;T ,PROBABIL;Y &
,/ATI/ICS3 #AB.J ,/UD5TS F9D ! L9E ( BE/
FIT 6A GIV5 4TRIBU;N ( .DATA 0US+ L1/
SQU>ES REGRES.N
,A .SCATT] .PLOT IS A GRAPH (A SET (
DATA PAIRS @7 .;X1 .;Y @7@4 ,IF .;Y T5DS
69CR1SE Z .;X 9CR1SES1 !N ! DATA H A
.POSITIVE .CORREL,N4 ,IF .;Y T5DS
6DECR1SE Z .;X 9CR1SES1 !N ! DATA H A
.NEGATIVE .CORREL,N4 ,IF ! PO9TS %[ NO
OBVI\S PATT]N1 !N ! DATA H
.APPROXIMATELY .NO .CORREL,N @4
,PICTURE3 .,POSITIVE .CORREL,N
,PICTURE3 .,NEGATIVE .CORREL,N
,PICTURE3 .,APPROXIMATELY .NO
.CORREL,N
,,EXAMPLE #A ,DESCRIBE CORREL,N
.,,TELEPH"OS ,DESCRIBE ! CORREL,N %[N
0EA* SCATT] PLOT4
,SOLU;N
,! F/ SCATT] PLOT %[S A POSITIVE
CORREL,N1 2C Z ! NUMB] ( CELLUL> PH"O
SUBSCRIB]S 9CR1S$1 ! NUMB] ( CELLUL>
S]VICE REGIONS T5D$ 69CR1SE4
,! SECOND SCATT] PLOT %[S A NEGATIVE
CORREL,N1 2C Z ! NUMB] ( CELLUL> PH"O
SUBSCRIB]S 9CR1S$1 CORD$ PH"O SALES T5D$
6DECR1SE4
------------------------------------#AAD
.,,CORREL,N .,,COE6ICI5TS ,A .CORREL,N
.COE6ICI5T @1 DENOT$ 0.;R @1 IS A NUMB]
F --#A 6#A T M1SURES H[ WELL A L9E FITS
A SET ( DATA PAIRS @7 .;X1 .;Y @7@4 ,IF
.;R IS NE> #A1 ! PO9TS LIE CLOSE 6A L9E
) POSITIVE SLOPE4 ,IF .;R IS NE> --#A1 !
PO9TS LIE CLOSE 6A L9E ) NEGATIVE SLOPE4
,IF ;R IS NE> #J1 ! PO9TS D N LIE CLOSE
6ANY L9E4
,,EXAMPLE #B
,E/IMATE CORREL,N COE6ICI5T
,TELL :E!R ! CORREL,N COE6ICI5T =!
DATA IS CLOSE/ TO --#A1 --#J.E1 #J1J.E1
OR #A4
.A4
.B4
.C4
,SOLU;N
.A4 ,! SCATT] PLOT %[S A CLE> B FAIRLY
W1K NEGATIVE CORREL,N4 ,S1 .;R IS 2T #J
& --#A1 B N TOO CLOSE 6EI "O4 ,! BE/
E/IMATE GIV5 IS .;R .K --#J.E4 7,!
ACTUAL VALUE IS .;R --#J.DF47
.B4 ,! SCATT] PLOT %[S APPROXIMATELY
NO CORREL,N4 ,S1 ! BE/ E/IMATE GIV5 IS
.;R .K .#J4 7,! ACTUAL VALUE IS .;R
--#J.JB47
.C4 ,! SCATT] PLOT %[S A /R;G POSITIVE
CORREL,N4 ,S1 ! BE/ E/IMATE GIV5 IS .;R
.K .#A4 7,! ACTUAL VALUE IS .;R #J.IH47
..,,GUID$ ,,PRACTICE = ,EXAMPLES #A &
.#B
,= EA* SCATT] PLOT1 7A7 TELL :E!R !
DATA H A .POSITIVE .CORREL,N @1 A
.NEGATIVE .CORREL,N @1 OR .APPROXIMATELY
.NO .CORREL,N @1 & 7;B7 TELL :E!R !
CORREL,N COE6ICI5T IS CLOSE/ TO --#A1
--#J.E1 #J1 #J.E1 OR #A4
.#A4
.#B4
.#C4
.,,BE/-.,,FITT+ .,,L9ES ,IF ! CORREL,N
COE6ICI5T =A SET ( DATA IS NE> +-#A1 !
DATA C 2 R1SONABLY MODEL$ 0A L9E4 ,!
.BE/-.FITT+ .L9E IS ! L9E T LIES Z CLOSE
Z POSSI# 6ALL ! DATA PO9TS4 ,Y C
APPROXIMATE A BE/-FITT+ L9E 0GRAPH+4
------------------------------------#AAE
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,APPROXIMAT+ A ,BE/-,FITT+ ,L9E
.,,/EP .#A ,DRAW A SCATT] PLOT (!
DATA4
.,,/EP .#B ,SKET* ! L9E T APPE>S
6FOLL[ MO/ CLOSELY ! TR5D GIV5 0! DATA
PO9TS4 ,"! %D 2 AB Z _M PO9TS ABV ! L9E
Z 2L X4
.,,/EP .#C ,*OOSE TWO PO9TS ON ! L9E1
& E/IMATE ! COORD9ATES ( EA* PO9T4 ,^!
PO9TS D N H 6BE ORIG9AL DATA PO9TS4
.,,/EP .#D ,WRITE AN EQU,N (! L9E T
PASSES "? ! TWO PO9TS F ,/EP .#C4 ,?
EQU,N IS A MODEL =! DATA4
..,,EXAMPLE #C ,APPROXIMATE A
BE/-FITT+ .L9E
.,,ALT]NATIVE-.,,FUEL$ .,,VEHICLES ,!
TA# %[S ! NUMB] .;Y 7IN ?\S&S7 (
ALT]NATIVE-FUEL$ VEHICLES 9 USE 9 !
,UNIT$ ,/ATES .;X YE>S AF .#AIIG4
,APPROXIMATE ! BE/-FITT+ L9E =! DATA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #J3 #A3 .#B @3 #C3 #D3 .#E @3
#F3 #G
.;Y @3 #BHJ3 #BIE3 #CBB3 #CIE3 #DBE3
#DGA3 #EAA3 .#EDH
,SOLU;N
.,,/EP .#A ,DRAW A SCATT] PLOT (!
DATA4
.,,/EP .#B ,SKET* ! L9E T APPE>S 6BE/
FIT ! DATA4 ,"O POSSIBIL;Y IS %[N4
.,,/EP .#C ,*OOSE TWO PO9TS T APPE>
6LIE ON ! L9E4 ,=! L9E %[N1 Y MI<T *OOSE
7#A1 #CJJ71 : IS N AN ORIG9AL DATA PO9T1
& 7#G1 #EDH71 : IS AN ORIG9AL DATA PO9T4
.,,/EP .#D ,WRITE AN EQU,N (! L9E4 ,F/
F9D ! SLOPE US+ ! PO9TS 7#A1 #CJJ7 &
7#G1 #EDH74
,USE PO9T-SLOPE =M 6WRITE ! EQU,N4
,*OOSE @7 .;X #A @1 .;Y #A @7 .K 7#A1
#CJJ74
.;Y -- .;Y #A .K .;M @7 .;X -- .;X #A
@7 .,PO9T-.SLOPE .=M
.;Y -- #CJJ .K #DA.C @7 .;X -- #A7
..,SUB/ITUTE = ;M @1 .;X #A @1 .& .;Y #A
@4
.;Y #DA.C .;X @+ #BEI .,SIMPLIFY4
,AN APPROXIM,N (! BE/-FITT+ L9E IS .;Y
.K #DA.C .;X @+ .#BEI4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
------------------------------------#AAF
,,EXAMPLE #D ,USE A L9E ( FIT 6MAKE A
PREDIC;N
,USE ! EQU,N (! L9E ( FIT F ,EXAMPLE
#C 6PREDICT ! NUMB] ( ALT]NATIVE-FUEL$
VEHICLES 9 USE 9 ! ,UNIT$ ,/ATES 9
#BJAJ4
,SOLU;N
,2C #BJAJ IS #AC YE>S AF #AIIG1
SUB/ITUTE #AC = .;X 9 ! EQU,N F ,EXAMPLE
#C4
.;Y .K #DA.C .;X @+ #BEI .K #DA.C7#AC7
@+ #BEI #GIF
,Y C PREDICT T "! W 2 AB #GIF1JJJ
ALT]NATIVE-FUEL$ VEHICLES 9 USE 9 !
,UNIT$ ,/ATES 9 #BJAJ4
.,,L9E> .,,REGRES.N ,_M GRAPH+
CALCULATORS H A .L9E> .REGRES.N F1TURE T
C 2 US$ 6F9D ! BE/-FITT+ L9E =A SET (
DATA4
,,EXAMPLE #E ,USE A GRAPH+ CALCULATOR
6F9D A BE/-FITT+ L9E
,,F9D ,,CORREL,N
,IF YR CALCULATOR DOES N 4PLAY !
CORREL,N COE6ICI5T .;R :5 X 4PLAYS !
REGRES.N EQU,N1 Y MAY NE$ 6SELECT
,DIAGNO/IC,ON F ! ,,CATALOG M5U4
,USE ! .L9E> .REGRES.N F1TURE ON A
GRAPH+ CALCULATOR 6F9D AN EQU,N (!
BE/-FITT+ L9E =! DATA 9 ,EXAMPLE #C4
,SOLU;N
.,,/EP .#A ,5T] ! DATA 96TWO .LI/S @4
,PRESS & !N SELECT ,$IT4 ,5T] YE>S S9CE
#AIIG 9 ;,L #A & NUMB] (
ALT]NATIVE-FUEL$ VEHICLES 9 ;,L #B @4
.,,/EP .#B ,F9D AN EQU,N (! BE/-FITT+
7L9E> REGRES.N7 L9E4 ,PRESS *OOSE !
,,CALC M5U1 & SELECT ,L9,REG7AX@+;B74 ,!
EQU,N C 2 R.D$ 6.;Y .K #DJ.I .;X @+
#BFC4
.,,/EP .#C .,MAKE A SCATT] PLOT (!
DATA PAIRS 6SEE H[ WELL ! REGRES.N EQU,N
MODELS ! DATA4 ,PRESS ,7,,/>T ,,PLOT7'
6SET UP YR PLOT4 ,!N SELECT AN
APPROPRIATE W9D[ =! GRAPH4
.,,/EP .#D .,GRAPH ! REGRES.N EQU,N )!
SCATT] PLOT 05T]+ ! EQU,N .;Y .K #DJ.I
.;X @+ .#BFC4 ,! GRAPH 74PLAY$ 9 ! W9D[
#J "K.K .;X "K.K #H & #BJJ "K.K .;Y "K.K
#FJJ7 %[S T ! L9E FITS ! DATA WELL4
99 ,AN EQU,N (! BE/-FITT+ L9E IS .;Y
.K #DJ.I .;X @+ #BFC4
------------------------------------#AAG
..,,GUID$ ,,PRACTICE = ,EXAMPLES #C1D1
& .#E
.#D4 .,,OIL .,,PRODUC;N ,! TA# %[S !
,U4,S4 DAILY OIL PRODUC;N .;Y 7IN ?\S&S
( B>RELS7 .;X YE>S AF #AIID4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #J3 #A3 .#B @3 #C3 #D3 .#E @3
#F3 #G3 #H
.;Y @3 #FFFJ3 #FEFJ3 #FDGJ3 #FDEJ3
#FBEJ3 #EHHJ3 #EHBJ3 #EHJJ3 .#EGEJ
.A4 ,APPROXIMATE ! BE/-FITT+ L9E =!
DATA4
.B4 ,USE YR EQU,N F "P 7A7 6PREDICT !
DAILY OIL PRODUC;N 9 #BJJI4
.C4 ,USE A GRAPH+ CALCULATOR 6F9D &
GRAPH AN EQU,N (! BE/-FITT+ L9E4 ,REP1T
! PREDIC;N F "P 7;B7 US+ ? EQU,N4
#B.F ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS .ON .P4
,,WS#C = ,EXS4 .#I1.AA @1 & .#BE
.K ,,/&>DIZ$ ,,TE/ ,,PRACTICE
,EXS4 .#B1.AF1.AH1.BA @1 & .#BH
.K .,,MULTIPLE .,,REPRES5T,NS
,EX#.BG
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,A
L9E T LIES Z CLOSE Z POSSI# 6A SET (
DATA PO9TS 7;X1 .;Y @7 IS CALL$ ! @8 =!
DATA PO9TS4
.#B4 .,,WRIT+ .,DESCRIBE H[ 6TELL :E!R
A SET ( DATA PO9TS %[S A POSITIVE
CORREL,N1 A NEGATIVE CORREL,N1 OR
APPROXIMATELY NO CORREL,N4
,,EXAMPLE #A
ON P4 #AAC = ,EXS4 #C-E
.,,DESCRIB+ .,,CORREL,NS ,TELL :E!R !
DATA H A .POSITIVE .CORREL,N @1 A
.NEGATIVE .CORREL,N @1 OR .APPROXIMATELY
.NO .CORREL,N @4
.#C4
.#D4
.#E4
.#F4 .,,R1SON+ .,EXPLA9 H[ Y C DET]M9E
! TYPE ( CORREL,N =A SET ( DATA PAIRS
0EXAM9+ ! DATA 9 A TA# )\T DRAW+ A
SCATT] PLOT4
,,EXAMPLE #B
ON P4 #AAD = ,EXS4 .#G-.I
.,,CORREL,N .,,COE6ICI5TS ,TELL :E!R !
CORREL,N COE6ICI5T =! DATA IS CLOSE/ TO
--#A1 --#J.E1 #J1 #J.E1 OR #A4
.#G4
.#H4
.#I4
------------------------------------#AAH
,,EXAMPLES #C & #D
ON PP4 #AAE--#AAF = ,EXS4 #AJ-AE
,,BE/-,,FITT+ ,,L9ES ,9 ,EX]CISES
#AJ-AE1 7A7 DRAW A SCATT] PLOT (! DATA1
7;B7 APPROXIMATE ! BE/-FITT+ L9E1 & 7;C7
E/IMATE .;Y :5 .;X .K #BJ4
#AJ4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
;X3 #A3 #B3 #C3 #D3 #E
.;Y @3 #AJ3 #BB3 #CE3 #DI3 #FB
#AA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #A3 #B3 #C3 #D3 #E
.;Y @3 #ABJ3 #AJA3 #HG3 #EG3 #DB
#AB4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #AB3 #BE3 #CF3 #EJ3 #FD
.;Y @3 #AJJ3 #GE3 #EB3 #BF3 #I
#AC4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #C3 #G3 #AJ3 #AE3 #AH
.;Y @3 #AF3 #DE3 #HB3 #AJB3 #AAF
#AD4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #E.F3 #F.B3 #G3 #G.C3 #H.D
.;Y @3 #ABJ3 #ACJ3 #ADA3 #AEF3 #AFG
#AE4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #AF3 #BD3 #CI3 #EE3 #FH
.;Y @3 #C.I3 #C.G3 #C.D3 #B.I3 #B.F
#AF4 .,,MULTIPLE .,,*OICE ,: EQU,N BE/
MODELS ! DATA 9 ! SCATT] PLOT8
,A .;Y .K #AE
;,B
;,C
;,D
#AG4 .,,]ROR .,,ANALYSIS ,! GRAPH %[S
"O /UD5T'S APPROXIM,N (! BE/-FITT+ L9E
=! DATA 9 ! SCATT] PLOT4 .,DESCRIBE &
CORRECT ! ]ROR 9 ! /UD5T'S "W4
#AH4 .,,MULTIPLE .,,*OICE ,A SET (
DATA HAS CORREL,N COE6ICI5T .;R @4 ,= :
VALUE ( .;R WD ! DATA PO9TS LIE CLOSE/
6A L9E8
,A ;R.K-#J.IF
;,B ;R.K#J
;,C ;R.K#J.CH
;,D .;R .K #J.E
,,EXAMPLE #E
ON P4 #AAF = ,EXS4 #AI-BJ
,,GRAPH+ ,,CALCULATOR ,9 ,EX]CISES #AI
& #BJ1 USE A GRAPH+ CALCULATOR 6F9D &
GRAPH AN EQU,N (! BE/-FITT+ L9E4
#AI4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #GH3 #GD3 #FH3 #GF3 #HJ3 #HD3
#EJ3 #GF3 #EE3 #IC
.;Y @3 #E.A3 #E.J3 #D.F3 #D.I3 #E.C3
#E.E3 #C.G3 #E.J3 #C.I3 #E.H
#BJ4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #GJJJ3 #GDJJ3 #GHJJ3 #HAJJ3
#HEJJ3 #HHJJ3 #IBJJ3 #IEJJ3 #IHJJ
.;Y @3 #EF.J3 #ED.E3 #EA.I3 #EJ.J3
#DG.C3 #DE.F3 #DC.A3 #DA.F3 #CI.I
.#BA4 .,,OP5-.,,5D$ .,,MA? ,GIVE TWO
R1L-LIFE QUANTITIES T H 7A7 A POSITIVE
CORREL,N1 7;B7 A NEGATIVE CORREL,N1 &
7;C7 APPROXIMATELY NO CORREL,N4
.#BB4 .,,R1SON+ ,A SET ( DATA PAIRS
HAS CORREL,N COE6ICI5T .;R .K #J.A4 ,IS
X LOGICAL 6USE ! BE/-FITT+ L9E 6MAKE
PREDIC;NS F ! DATA8 .,EXPLA9 @4
.#BC4 .,,*ALL5GE ,IF .;X & .;Y H A
POSITIVE CORREL,N & .;Y & .;Z H A
NEGATIVE CORREL,N1 :AT C Y SAY AB !
CORREL,N 2T .;X & ;Z8 .,EXPLA9 @4
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#A
.K ,,/&>DIZ$ ,,TE/ ,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
------------------------------------#AAI
,,PRO#M ,,SOLV+
,,EXAMPLES #C1 #D1 & #E
ON PP4 #AAE-AAF = ,EXS4 #BD-BH
..,,GRAPH+ ,,CALCULATOR ,Y MAY WI%
6USE A GRAPH+ CALCULATOR 6-PLETE !
FOLL[+ ,PRO#M ,SOLV+ .EX]CISES4
.#BD4 .,,POPUL,N ,! DATA PAIRS 7;X1
.;Y @7 GIVE ! POPUL,N .;Y 7IN MILLIONS7
( ,TEXAS .;X YE>S AF .#AIIG4
,APPROXIMATE ! BE/-FITT+ L9E =! DATA4
7#J1 #AI.G71 7#A1 #BJ.B71 7#B1 #BJ.F71
7#C1 #BJ.I71 7#D1 #BA.C71 7#E1 #BA.G71
7#F1 #BB.A71 7#G1 #BB.E7
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#BE4 .,,TUI;N ,! DATA PAIRS 7;X1 ;Y7
GIVE ,U4,S4 AV]AGE ANNUAL PUBLIC COLLEGE
TUI;N .;Y 7IN DOLL>S7 .;X YE>S AF
.#AIIG4 ,APPROXIMATE ! BE/-FITT+ L9E =!
DATA4
7#J1 #BBGA71 7#A1 #BCFJ71 7#B1 #BDCJ71
7#C1 #BEJF71 7#D1 #BEFB71 7#E1 #BGBG71
7#F1 #BIBH7
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#BF4 .,,PHYSICAL .,,SCI;E ,! DIAGRAM
%[S ! BOIL+ PO9T ( WAT] AT V>I\S
ELEV,NS4 ,APPROXIMATE ! BE/-FITT+ L9E =!
DATA PAIRS 7;X1 ;Y7 ": .;X REPRES5TS !
ELEV,N 7IN FEET7 & .;Y REPRES5TS ! BOIL+
PO9T 7IN DEGREES ,FAHR5HEIT74 ,!N USE ?
L9E 6E/IMATE ! BOIL+ PO9T AT AN ELEV,N (
#AD1JJJ FEET4
#BG4 .,,MULTIPLE .,,REPRES5T,NS ,! TA#
%[S ! NUMB]S ( C.TRIES T "PICIPAT$ 9 !
,W9T] ,OLYMPICS F #AIHJ 6#BJJB4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,YE> @3 #AIHJ3 #AIHD3 #AIHH3 #AIIB3
#AIID3 #AIIH3 .#BJJB
.,C.TRIES @3 #CG3 #DI3 #EG3 #FD3 .#FG
@3 #GB3 #GG
A4 .,MAK+ .A .,LI/ ,USE ! TA# 6MAKE A
LI/ ( DATA PAIRS 7;X1 ;Y7 ": .;X
REPRES5TS YE>S S9CE #AIHJ & .;Y
REPRES5TS ! NUMB] ( C.TRIES4
B4 .,DRAW+ .A .,GRAPH ,DRAW A SCATT]
PLOT (! DATA PAIRS F "P 7A74
C4 .,WRIT+ .AN .,EQU,N ,WRITE AN EQU,N
T APPROXIMATES ! BE/-FITT+ L9E1 & USE X
6PREDICT ! NUMB] ( "PICIPAT+ C.TRIES 9
#BJAD4
#BH4 .,,EXT5D$ .,,RESPONSE ,! TA# %[S
MANUFACTUR]S' %IP;TS 7IN MILLIONS7 (
CASSETTES & ,,CD,'S 9 ! ,UNIT$ ,/ATES F
#AIHH 6#BJJB4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,YE> @3 #AIHH3 #AIIJ3 #AIIB3 #AIID3
#AIIF3 #AIIH3 #BJJJ3 #BJJB
.,CASSETTES @3 #DEJ.A3 #DDB.B3 #CCF.D3
#CDE.D3 #BBE.C3 #AEH.E3 #GF.J3 #CA.A
.,,CD,'S @3 #ADI.G3 #BHF.E3 #DJG.E3
#FFB.A3 #GGH.I3 #HDG.J3 #IDB.E3 .#HJC..C
A4 ,DRAW A SCATT] PLOT (! DATA PAIRS
7YE>1 %IP;TS ( CASSETTES74 .,DESCRIBE !
CORREL,N %[N 0! SCATT] PLOT4
B4 ,DRAW A SCATT] PLOT (! DATA PAIRS
7YE>1 %IP;TS ( ,,CD,'S74 .,DESCRIBE !
CORREL,N %[N 0! SCATT] PLOT4
C4 .,DESCRIBE ! CORREL,N 2T CASSETTE
%IP;TS & ;,,CD %IP;TS4 ,:AT R1L-_W
FACTORS MI<T A3.T = ?8
------------------------------------#ABJ
#BI4 .,,*ALL5GE ,DATA F "S C.TRIES 9
,NOR? ,AM]ICA %[ A POSITIVE CORREL,N 2T
! AV]AGE LIFE EXPECTANCY 9 A C.TRY &!
NUMB] ( P]SONAL -PUT]S P] CAPITA 9 T
C.TRY4
A4 ,MAKE A 3JECTURE AB ! R1SON =!
POSITIVE CORREL,N 2T LIFE EXPECTANCY &
NUMB] ( P]SONAL -PUT]S P] CAPITA4
B4 ,IS X R1SONA# 63CLUDE F ! DATA T
GIV+ RESID5TS (A C.TRY M P]SONAL -PUT]S
W L5G!N _! LIVES8 .,EXPLA9 @4
,,MIX$ ,,REVIEW
,SOLVE ! EQU,N = .Y4 ,!N F9D ! VALUE (
.;Y =! GIV5 VALUE ( .;X @4 @7 P4 #BF @7
.#CJ4 #B .;X -- .;Y .K #AJ2 .;X .K #H
.#CA4 #F .;Y @+ .;X .K --#E2 .;X .K #A
.#CB4 .;X -- #D .;Y .K #C2 .;X .K --#C
.#CC4 --#C .;X @+ #D .;Y @+ #E .K #J2
.;X .K --#B
.#CD4 --#J.E .;Y @+ #J.BE .;X .K #B2
.;X .K #D
.#CE4 .XY -- #D .;X .K #I2 .;X .K #F
,,PREVIEW
,PREP>E = ,LESSON #B.G 9 ,EXS4 #CF-DA4
,EVALUATE ! FUNC;N =! GIV5 VALUE ( .X4
@7 P4 #GB @7
.#CF4 .;F7.;X7 .K -- .;X @+ #G2 .;F
7#I7
.#CG4 .;F7.;X7 .K --#D .;X -- #AA2 .;F
7--#E7
.#CH4 .;F7.;X7 .K #AD--_\;X_\2 .;F
7--#B7
.#CI4 .;F7.;X7 .K _\;X--#AJ_\2 .;F
7#AJ7
.#DJ4 .;F7.;X7 .K _\--#F--;X_\2 .;F
7#D7
.#DA4 .;F7.;X7 .K _\#B .;X @+
#H_\--#A2 .;F 7--#C7
,GRAPH ! EQU,N4 @7 P4 #HI @7
.#DB4 .;Y .K .;X @+ #H
.#DC4 .;Y .K -- .;X -- #AD
.#DD4 .;Y .K #E .;X @+ #I
.#DE4 #B .;X @+ .;Y .K #A
.#DF4 #C .;X -- #B .;Y .K --#D
.#DG4 .;X @+ #C .;Y .K #AE
,,QUIZ .= .,LESSONS .#B..D-.B..F
,WRITE AN EQU,N (! L9E T SATISFIES !
GIV5 3DI;NS1 @7 P4 #IH @7
.#A4 .;M .K --#E1 .;B .K #C
.#B4 .;M .K #B1 .;B .K #AB
.#C4 .;M .K .#D @1 PASSES "? 7--#C1
#F7
.#D4 .;M .K --#G1 PASSES "? 7#A1 --#D7
.#E4 PASSES "? 7#J1 #G7 & 7--#C1 --#B7
.#F4 PASSES "? 7--#I1 #I7 & 7--#I1 #J7
,WRITE & GRAPH A DIRECT V>I,N EQU,N T
HAS ! GIV5 ORD]$ PAIR Z A SOLU;N1 @7 P4
#AJG @7
.#G4 7#A1B7
.#H4 7--#B1H7
.#I4 7#E1 --#AF7
.#AJ4 7#AB1D7
,! V>IA#S .;X & .;Y V>Y DIRECTLY4
,WRITE AN EQU,N T RELATES .;X & Y4 ,!N
F9D .;Y :5 .;X .K #H4 @7 P4 #AJG @7
.#AA4 .;X .K #D1 .;Y .K #AB
.#AB4 .;X .K --#C1 .;Y .K --#H
.#AC4 .;X .K #DJ;,Y .K --#E
.#AD4 .;X .K #AB1 .;Y .K #B
.#AE4 .,,3C]T .,,TICKETS ,! TA# %[S !
AV]AGE PRICE (A 3C]T TICKET 6"O (! TOP
#EJ MUSICAL T\R+ ACTS =! YE>S
#AIII-BJJD4 ,WRITE AN EQU,N T
APPROXIMATES ! BE/-FITT+ L9E =! DATA
PAIRS @7 .;X1 .;Y @7@4 ,USE ! EQU,N
6PREDICT ! AV]AGE PRICE (A TICKET 9
.#BJAJ4 @7 P4 #AAC @7
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,YE>S S9CE #AIII;,X3 #J3 #A3 #B3 #C3
#D3 #E
,TICKET PRICE 7DOLL>S71 ;Y3 #CH.EF3
#DD.HJ3 #DF.FI3 #EJ.HA3 #EA.HA3 #EH.GA
.,,EXTRA .,,PRACTICE = ,LESSON #B.F1
P4 #AJAA
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#ABA
,9VE/IGAT+ ,ALGEBRA ,ACTIV;Y3 #B.G
,EXPLOR+ ,TRANS=M,N
,USE 2F LESSON1 #B.G
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,KEY/ROKES
.,,MAT]IALS 99 GRAPH+ CALCULATOR
,,"Q
,H[ >E ! EQU,N &! GRAPH ( AN ABSOLUTE
VALUE FUNC;N RELAT$8
,Y C 9VE/IGATE FAMILIES ( .ABSOLUTE
.VALUE .FUNC;NS ) EQU,NS (! =M ..;Y .K
A_\;X--.;H_\ @+ .;K @2 0V>Y+ ! VALUES (
.A1 .;H @1 & .;K & !N GRAPH+4 ,! RESULT+
GRAPHS >E .TRANS=M,NS (! GRAPH (! P>5T
FUNC;N .;Y .K _\.;X_\ @4
,,EXAMPLE #A
,GRAPH .;Y .K _\.;X_\ @+ .;K
..,GRAPH & DESCRIBE ! FAMILY (
ABSOLUTE VALUE FUNC;NS (! =M .;Y .K
_\.;X_\ @+ .;K @4
,,/EP #A ,V>Y ! VALUE ( ;K
,5T] .;Y .K _\.;X_\ ;,Y .K _\.;X_\
@+#B1 .;Y.K _\.;X_\ @+ #E1 & .;Y .K
_\.;X_\ --#C4
,,/EP #B ,4PLAY GRAPHS
,GRAPH ! EQU,NS 9 ! /&>D VIEW+ W9D[
0PRESS+ @4
,,/EP #C ,-P>E GRAPHS
,DESCRIBE H[ ! FAMILY ( GRAPHS ( .;Y
.K _\.;X_\ @+ .;K IS RELAT$ 6! GRAPH (
.;Y .K _\.;X_\ @4
,! GRAPHS ( ABSOLUTE VALUE FUNC;NS (!
=M .;Y .K _\.;X_\ @+ ;K H ! SAME %APE Z
! GRAPH ( .;Y .K _\.;X_\ @1 B >E %IFT$
;K UNITS V]TIC,Y4
,,EXAMPLE #B
,GRAPH .;Y .K _\ .;X -- ;H_\
..,GRAPH & DESCRIBE ! FAMILY (
ABSOLUTE VALUE FUNC;NS (! =M .;Y .K _\
.;X -- .;H _\.
,,/EP #A ,V>Y ! VALUE ( ;H
,5T] .;Y .K _\ ;X_\1 ;Y.K _\;X-#B_\1
.;Y .K _\ .;X -- #D1 & .;Y .K _\ .;X @+
#E_\4
,,/EP #B ,4PLAY GRAPHS
,GRAPH ! EQU,NS 9 ! /&>D VIEW+ W9D[
0PRESS+ @4
,,/EP #C ,-P>E GRAPHS
,DESCRIBE H[ ! FAMILY ( GRAPHS ( .;Y
.K _\ .;X -- ;H_\ IS RELAT$ 6! GRAPH (
.;Y .K _\ .;X _\.
,! GRAPHS ( .ABSOLUTE VALUE FUNC;NS (!
=M ;Y .K _\;X--;H_\ H ! SAME %APE Z !
GRAPH ( .;Y .K _\.;X_\ @1 B >E %IFT$ ;H
UNITS HORIZONT,Y4
------------------------------------#ABB
,,EXAMPLE #C
,GRAPH .;Y .K .A_\.;X_\ ": .A IS A
POSITIVE NUMB]
,GRAPH & DESCRIBE ! FAMILY ( ABSOLUTE
VALUE FUNC;NS (! =M .;Y .K .A_\.;X_\ ":
.A .1 .#J4
,,/EP #A ,V>Y ! VALUE (A
,5T] .;Y .K _\..;X_\1 ;Y .K #B_\;X_\1
;Y .K #E_\.;X_\ & @4
,,/EP #B ,4PLAY GRAPHS
,GRAPH ! EQU,NS 9 ! /&>D VIEW+ W9D[
0PRESS+
,,/EP #C ,-P>+ GRAPHS
,DESCRIBE H[ ! FAMILY ( GRAPHS ( ..;Y
.K A _\ .;X _\ ": .A .1 #J IS RELAT$ 6!
GRAPH ( .;Y .K _\.;X_\ @4
,Z ) .;Y .K _\.;X_\ @1 ! GRAPH ( .;Y
.K A _\ .;X _\ 7A .1 #J7 HAS XS L[E/
PO9T AT ! ORIG94 ,IF A .1 #A1 ! GRAPH IS
N>R[] ?AN T ( ;Y .K _\.;X_\ @4 ,IF .#J
"K A "K #A1 ! GRAPH IS WID] ?AN T ( .;Y
.K _\.;X_\ @4
,PRACTICE
.#A4 ,GRAPH & DESCRIBE ! FAMILY (
ABSOLUTE VALUE FUNC;NS (! =M .;Y .K
.A_\.;X_\ ": .A .1 .#J4 ,FOLL[ ^! /EPS3
.,,/EP .#A ,5T] .;Y .K _\ ..;X_\1 ;Y
.K--_\;X_\1 ;Y .K--#C_\.;X_\ @1 & @4
.,,/EP .#B ,GRAPH ! EQU,NS 9 ! /&>D
VIEW+ W9D[ 0PRESS+
.,,/EP .#C ,DESCRIBE H[ ! FAMILY (
GRAPHS ( .;Y .K .A_\.;X_\ ": .A "K #J IS
RELAT$ 6! GRAPH ( ;V .K _\.;X_\ @4
.,DESCRIBE H[ ! GRAPH (! GIV5 EQU,N IS
RELAT$ 6! GRAPH ( ..;Y .K _\ .;X_\ @4
,!N GRAPH ! GIV5 EQU,N AL;G ) .;Y .K
_\.;X_\ 63FIRM YR ANSW]4
.#B4 .;Y .K _\.;X_\ @+#F
.#C4 ..;Y .K _\.;X_\ -- #D
.#D4 .;Y .K _\ .;X -- #C_\
.#E4 .;Y .K _\ .;X @+ #B_\
.#F4
#G4 .;Y .K --.#F_\.;X_\
.#H4 .;Y .K _\ .;X -- ;L_\ @+ #B
#I4 ..;Y .K #C_\;X @+ .#B_\
.#AJ4 .;Y .K --#J.E_\ .;X @+ ;L_\ @+
#G
,,DRAW ,,3CLU.NS
,ANSW] ! FOLL[+ "QS AB ! GRAPH ( .;Y
.K .A _\ .;X -- .;H _\ @+ .;K @4
.#AA4 ,H[ DOES ! VALUE ( .;K A6ECT !
GRAPH8
.#AB4 ,H[ DOES ! VALUE ( .;H A6ECT !
GRAPH8
.#AC4 ,H[ D ! SIGN & ABSOLUTE VALUE (
.A A6ECT ! GRAPH8
.#AD4 ,:AT >E ! COORD9ATES (! L[E/ OR
HI<E/ PO9T ON ! GRAPH8 ,H[ C Y TELL :E!R
? PO9T IS ! L[E/ PO9T OR ! HI<E/ PO9T8
------------------------------------#ABC
#B.G ,USE ,ABSOLUTE ,VALUE ,FUNC;NS
& ,TRANS=M,NS
.,2F ,Y GRAPH$ & WROTE L9E> FUNC;NS4
.,N[ ,Y W GRAPH & WRITE ABSOLUTE VALUE
FUNC;NS4
.,:Y8 ,S Y C MODEL /RUCTURES1 Z 9 ,EX4
#CI4
,KEY ,VOCABUL>Y
99 ABSOLUTE VALUE FUNC;N
99 V]TEX ( AN ABSOLUTE VALUE GRAPH
99 TRANS=M,N
99 TRANSL,N
99 REFLEC;N
,SIDEB>3
,/&>DS
,5RI*;T TOPIC2 N REQUIR$ 0! ,CALI=NIA
,/&>DS
,9 ,LESSON #A.G1 Y LE>N$ T ! ABSOLUTE
VALUE (A R1L NUMB] .;X IS DEF9$ Z
FOLL[S4
,Y C AL DEF9E AN ..ABSOLUTE VALUE
FUNC;N ;F @7 ;X @7 .K _\.;X_\ @4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,P>5T ,FUNC;N = ,ABSOLUTE ,VALUE
,FUNC;NS
,! P>5T FUNC;N =! FAMILY ( ALL
ABSOLUTE VALUE FUNC;NS IS_/7;X7 .K
_\.;X_\ ,! GRAPH ( .;F @7 .;X @7 .K
_\.;,X_\ IS ;,V-%AP$ & IS SYMMETRIC AB !
;Y-AXIS4 ,S1 = E PO9T 7;X1 .;Y @7 ON !
GRAPH1 ! PO9T @7 --.;X1 .;Y @7 IS AL ON
! GRAPH4
,! HI<E/ OR L[E/ PO9T ON ! GRAPH ( AN
ABSOLUTE VALUE FUNC;N IS CALL$ ! V]TEX4
,! V]TEX (! GRAPH ( .;F @7 .;X @7 .K
_\.;X_\ IS 7#J1 #J74
,,REVIEW ,,GEOMETRY
,= HELP ) TRANS=M,NS1 SEE P4 #IHH @4
.,,TRANSL,NS ,Y C DERIVE NEW ABSOLUTE
VALUE FUNC;NS F ! P>5T FUNC;N "?
.TRANS=M,NS (! P>5T GRAPH4
,A TRANS=M,N *ANGES A GRAPH'S SIZE1
%APE1 POSI;N1 OR ORI5T,N4 ,A TRANSL,N IS
A TRANS=M,N T %IFTS A GRAPH HORIZONT,Y
&_/OR V]TIC,Y1 B DOES N *ANGE XS SIZE1
%APE1 OR ORI5T,N4
,! GRAPH ( .;Y .K _\.;X-.;H_\ @+ .;K
IS ! GRAPH ( .;Y.K _\.;X_\ TRANSLAT$ .;H
UNITS HORIZONT,Y & .;K UNITS V]TIC,Y1 Z
%[N 9 ! DIAGRAM4 ,! V]TEX ( .;Y.K
_\.;X-.;H_\ @+.;K IS @7 .;H1 .;K @7@4
------------------------------------#ABD
,,EXAMPLE #A
,GRAPH A FUNC;N (! =M ..;Y .K _\;X--;H
_\ @+ .;K
,,9T]PRET ,,FUNC;NS
,6ID5TIFY ! V]TEX1 REWRITE ! GIV5
FUNC;N Z .;Y .K _\ .;X -- 7--#D7_\
@+7--#B74 ,S1 .;H .K --#D & .;K .K --.#B
@4 ,! V]TEX IS 7--#D1 --#B74
,GRAPH ..;Y .K _\.;X @+ #D_\--#B4
,-P>E ! GRAPH )! GRAPH ( .;Y .K _\.;X_\
@4
,SOLU;N
.,,/EP .#A .,ID5TIFY & PLOT ! V]TEX1
@7 .;H1 .;K @7 .K 7--#D1 --#B74
.,,/EP .#B .,PLOT ANO!R PO9T ON !
GRAPH1 S* Z 7--#B1 #J74 ,USE SYMMETRY
6PLOT A ?IRD PO9T1 7--#F1 #J74
.,,/EP .#C .,3NECT ! PO9TS )A ;,V-%AP$
GRAPH4
.,,/EP .#D .,-P>E ) .;Y .K _\.;X_\ @4
,! GRAPH ( .;Y .K _\ .;X @+ #D_\--#B IS
! GRAPH ( .;Y.K _\.;X_\ TRANSLAT$ D[N #B
UNITS & LEFT #D UNITS4
..,,/RET*ES1 ,,%R9KS1 ,,& .,,REFLEC;NS
,:5 _\ .A_\ @6.K #A1 ! GRAPH ( .;Y .K
.A_\.;X_\ IS A V]TICAL ./RET* OR A
V]TICAL .%R9K (! GRAPH ( .;Y .K _\.;X_\
@1 DEP5D+ ON :E!R _\ A _\ IS LESS ?AN OR
GRT] ?AN #A4
,! FOLL[+ TA# IS 9 LI/$
=MAT4 ,= EA* CELL ! H1D+ IS %[N
FOLL[$ 0A COLON1 SPACE &! CELL
3T5TS
,= _\ .A_\ .1 #A @3 ,CELL 3T5TS FOLL[
2T BOX+ L9ES4
99 ,! GRAPH IS V]TIC,Y ./RET*$ @1 OR
EL;GAT$4
99 ,! GRAPH ( .;Y .K .A_\.;X_\ IS
.N>R[] ?AN ! GRAPH ( .;Y .K _\.;X_\ @4
,= _\.A_\ "K#A @3 ,CELL 3T5TS FOLL[ 2T
BOX+ L9ES4
99 ,! GRAPH IS V]TIC,Y .%RUNK @1 OR
-PRESS$4
99 ,! GRAPH ( .;Y .K .A_\.;X_\ IS
.WID] ?AN ! GRAPH ( .;Y .K _\.;X_\ @4
,:5 .A .K --#A1 ! GRAPH ( .;Y .K
.A_\.;X_\ IS A .REFLEC;N 9 ! ;X-AXIS (!
GRAPH ( .;Y .K _\.;X_\ @4 ,:5 A "K #J B
A @6.K --#A1 ! GRAPH ( .;Y .K .A_\.;X_\
IS A V]TICAL /RET* OR %R9K )A REFLEC;N 9
! ;X-AXIS (! GRAPH ( .;Y .K _\.;X_\ @4
,,EXAMPLE #B
,GRAPH FUNC;NS (! =M .;Y.K.A_\.;X_\
,GRAPH 7A7 & 7;B7 .;Y .K --.#C_\.;X_\
@4 ,-P>E EA* GRAPH )! GRAPH .( .;Y.K
_\.;X_\ @4
,SOLU;N
.A4 ,! GRAPH ( .;Y .K _\ .;X _\ IS !
GRAPH ( .;Y .K _\.;X_\ V]TIC,Y %RUNK 0A
FACTOR ( @4 ,! GRAPH HAS V]TEX 7#J1 #J7
& PASSES "? 7--#D1 #B7 & 7#D1 #B74
.B4 ,! GRAPH ( .;Y .K--#C _\.;,X_\ IS
! GRAPH ( .;Y.K _\.;X_\ V]TIC,Y /RET*$
0A FACTOR ( #C & !N REFLECT$ 9 !
;X-AXIS4 ,! GRAPH HAS V]TEX 7#J1 #J7 &
PASSES "? 7--#A1 --#C7 & 7#A1 --#C74
------------------------------------#ABE
.,,MULTIPLE .,,TRANS=M,NS ,9 "P 7;B7 (
,EXAMPLE #B1 GRAPH+ .;Y .K --#C _\.;X_\
9VOLVES BO? V]TIC,Y /RET*+ & REFLECT+ !
GRAPH ( ..;Y .K _\;X_\4 .,A GRAPH MAY 2
RELAT$ 6A P>5T GRAPH 0EV5 M ?AN TWO
TRANS=M,NS4 ,= EXAMPLE1 ! GRAPH ( .;Y .K
.A_\.;X--.;H_\ @+ .;K C 9VOLVE A V]TICAL
/RET* OR %R9K1 A REFLEC;N1 &A TRANSL,N
(! GRAPH ( .;Y .K _\.;X_\
,,EXAMPLE #C
,GRAPH A FUNC;N (! =M .;Y .K .A_\.;X
-- .;H _\ @+ .;K
,GRAPH .;Y .K --#B_\ .;X -- #A_\ @+#C4
,-P>E ! GRAPH )! GRAPH ( .;Y .K _\.;X_\
@4
,SOLU;N
.,,/EP .#A .,ID5TIFY & PLOT ! V]TEX1
@7 .;H1 .;K @7 .K 7#A1 #C74
.,,/EP .#B .,PLOT ANO!R PO9T ON !
GRAPH1 S* Z 7#J1A74 ,USE SYMMETRY 6PLOT
A ?IRD PO9T1 7#B1A74
.,,/EP .#C .,3NECT ! PO9TS )A ;,V-%AP$
GRAPH4
.,,/EP .#D .,-P>E ) .;Y .K _\.;X_\ @4
,! GRAPH ( ;Y.K-#B_\ .;X -;L_\ @+ #C IS
! GRAPH ( .;Y .K_\.;X_\ /RET*$ V]TIC,Y
0A FACTOR ( #B1 !N REFLECT$ 9 ! ;X-AXIS1
& F9,Y TRANSLAT$ "R #A UNIT & UP #C
UNITS4
.,,GUID$ .,,PRACTICE = ,EXAMPLES #A1B1
& #C
,GRAPH ! FUNC;N4 .,-P>E ! GRAPH )!
GRAPH ( .;Y .K _\.;X_\ @4
.#A4 .;Y.K_\.;X-.#B_\ @+#E
.#B4
.#C4 .;F @7 .;X @7 .K --#C_\;X@+ .;L_\
--.#B
,,EXAMPLE #D
,WRITE AN ABSOLUTE VALUE FUNC;N
.,,HOLOGRAMS ,9 HOLOGRAPHY1 LI<T F A
LAS] B1M IS SPLIT 96TWO B1MS1 A REF];E
B1M & AN OBJECT B1M4 ,LI<T F ! OBJECT
B1M REFLECTS (F AN OBJECT & IS RECOMB9$
)! REF];E B1M 6=M IMAGES ON FILM T C 2
US$ 6CR1TE ?REE-DIM5.NAL IMAGES4 ,WRITE
AN EQU,N =! PA? (! REF];E B1M4
,SOLU;N
,! V]TEX (! PA? (! REF];E B1M IS 7#E1
#H74 ,S1 ! EQU,N HAS ! =M .;Y .K .A_\.;X
-- #E_\ @+#H4 ,SUB/ITUTE ! COORD9ATES (!
PO9T 7#J1 #J7 96! EQU,N & SOLVE = .A @4
#J .K .A_\.#J-.E_\ @+#H ,SUB/ITUTE #J
= .;Y & #J = .;X @4
--#A.F .K .A ,SOLVE =A4
,AN EQU,N =! PA? (! REF];E B1M IS .;Y
.K --#A.F _\ .;X -- #E @+#H4
------------------------------------#ABF
..,,TRANS=M,NS ,,( ,,ANY .,,GRAPH ,Y C
P]=M TRANS=M,NS ON ! GRAPH ( .ANY FUNC;N
.;F 9 ! SAME WAY Z = ABSOLUTE VALUE
GRAPHS4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,TRANS=M,NS ( ,G5]AL ,GRAPHS
,! GRAPH ( .;Y .K .A @* .;F @7
.;X--.;H @7 @+ .;K C 2 OBTA9$ F ! GRAPH
( ANY FUNC;N .;Y .K .;F @7 .;X @7 0P]=M+
^! /EPS3
.,,/EP .#A ,/RET* OR %R9K ! GRAPH (
.;Y .K .;F @7 .;X @7 V]TIC,Y 0A FACTOR (
_\ .A _\ IF _\ .A_\ @6.K .#A4 ,IF _\
.A_\ .1 #A1 /RET* ! GRAPH4 ,IF _\ .A_\
"K #A1 %R9K ! GRAPH4
.,,/EP .#B ,REFLECT ! RESULT+ GRAPH F
,/EP #A 9 ! ;X-AXIS IF .A "K #J4
.,,/EP .#C ,TRANSLATE ! RESULT+ GRAPH
F ,/EP #B HORIZONT,Y .;H UNITS & V]TIC,Y
.;K UNITS4
,,EXAMPLE #E ,APPLY TRANS=M,NS 6A
GRAPH
,! GRAPH (A FUNC;N .;Y .K .;F @7 .;X
@7 IS %[N4 ,SKET* ! GRAPH (! GIV5
FUNC;N4
.A4 ..;Y .K #B @* .;F @7 .;X @7
.B4 .;Y .K --.;F @7 .;X @+ #B7 @+ #A
,SOLU;N
.A4 ,! GRAPH ( .;Y .K .#B @* .;F7.;X
@7 IS ! GRAPH ( .;Y .K .;F @7 .;X @7
/RET*$ V]TIC,Y 0A FACTOR ( .#B4 7,"! IS
NO REFLEC;N OR TRANSL,N47 ,6DRAW !
GRAPH1 MULTIPLY ! .;Y-.COORD 9ATE ( EA*
LABEL$ PO9T ON ! GRAPH ( .;Y .K .;F @7
.;X @7 0#B & 3NECT _! IMAGES4
.B4 ,! GRAPH ( .;Y .K --.;F @7 .;X @+
#B7 @+ #A IS ! GRAPH ( .;Y .K .;F @7 .;X
@7 REFLECT$ 9 ! ;X-AXIS1 !N TRANSLAT$
LEFT #B UNITS & UP #A UNIT4 ,6DRAW !
GRAPH1 F/ REFLECT ! LABEL$ PO9TS & 3NECT
_! IMAGES4 ,!N TRANSLATE & 3NECT ^!
PO9TS 6=M ! F9AL IMAGE4
,,AVOID ,,]RORS
,9 ,EXAMPLE #E1 "P 7;B71 ! VALUE ( .;H
IS --#B 2C -.;F @7 .;X @+ #B7 @+ #A .K
-.;F @7 .;X -- 7--#B77 @+ .#A4 ,2C --#B
"K #J1 ! HORIZONTAL TRANSL,N IS 6! LEFT4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #D &
.#E
.#D4 .,,:AT .,,IF8 ,9 ,EXAMPLE #D1
SUPPOSE ! REF];E B1M ORIG9ATES AT 7#C1
#J7 & REFLECTS (F A MIRROR AT 7#E1 #D74
,WRITE AN EQU,N =! PA? (! B1M4
,USE ! GRAPH ( .;Y .K .;F @7 .;X @7 F
,EXAMPLE #E 6GRAPH ! GIV5 FUNC;N4
.#E4 ..;Y.K #J.E +- .;F @7 .;X @7
.#F4 .;Y.K --.;F @7 .;X-.#B @7 -.#E
.#G4 .;Y .K #B @* .;F @7 .;X @+
#C7--#A
------------------------------------#ABG
#B.G ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#D = ,EXS4 #AC1AI1 & .#CI
.K ,,/&>DIZ$ ,,TE/ ,,PRACTICE
,EXS4 #B1BG1 #BH1CA1CB1CC1CH1 & #DJ
.K .,,MULTIPLE .,,REPRES5T,NS
,EX#.DA
,,EXAMPLES #A1 #B1 & #C
ON PP4 #ABD-ABE = ,EXS4 #C-AD
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,! PO9T @7 .;H1 .;K
@7 IS ! @8 (! GRAPH ( ..;Y .KA_\;X-;H_\
@+ .;K @4
.#B4 .,,WRIT+ .,DESCRIBE ?REE DI6]5T
TYPES ( TRANS=M,NS4
,,GRAPH+ ,,FUNC;NS ,GRAPH ! FUNC;N4
.,-P>E ! GRAPH )! GRAPH ( .;Y .K _\.;X_\
@4
.#C4 .;Y .K _\.;X_\ --#G
.#D4 .;Y .K _\ .;,X @+ #B_\
.#E4 .;Y .K _\ .;X @+ #D_\ --#B
.#F4 .;F7.;X @7 .K _\.;X -- #A_\ @+ #D
.#G4 .;F @7 .;X @7 .K .#B_\.;X_\
.#H4 .FIX @7 .K --.#C@\.;X
.#I4
.#AJ4
.#AA4 .;Y .K#B_\ .;X @+#A_\--#F
.#AB4 .;F @7 .;X @7 .K --#D_\ .;X @+
#B_\ --#C
.#AC4
.#AD4
.,,EXAMPLE .#D .ON .P4 #ABE = ,EXS4
#AE-BJ
,,WRIT+ ,,EQU,NS ,WRITE AN EQU,N (!
GRAPH4
.#AE4
.#AF4
.#AG4
.#AH4
.#AI4
.#BJ4
,,EXAMPLE #E
ON P4 #ABF = ,EXS4 #BA-BH
..,,TRANS=M,NS ,USE ! GRAPH ( .;Y .K
.;F @7 .;X @7 .%[N .6.SKET* ! GRAPH ( .!
GIV5 FUNC;N4
.#BA4 .;Y .K .;F @7 .;X @+ #B7--#C
.#BB4 .;Y .K .;F @7 .;X -- #D7 @+ #A
.#BC4 .;Y .K @* .;F @7 .;X @7
.#BD4 ;Y .K --#C @* .;F @7 .;X @7
.#BE4 .;Y .K -.;F @7 .;X -- #A7 @+ #D
.#BF4 .;Y .K #B @* .;F @7 .;X @+
#C7--#A
.#BG4 .,,OP5-.,,5D$ .,,MA? ,CR1TE A
GRAPH (A FUNC;N .;Y .K .;F @7 .;X @7@4
,!N SKET* ! GRAPHS ( 7A7 .;Y .K .;F @7
.;X @+ #C7--#D1 7.;B7 .;Y .K #B @* .;F
@7 .;X @7@1 & 7;C7 .;Y .K -- .;F @7 .;X
@7@4
#BH4 .,,MULTIPLE .,,*OICE ,! HI<E/
PO9T ON ! GRAPH ( .;Y .K .;F @7 .;X @7
IS 7--#A1 #F74 ,:AT IS ! HI<E/ PO9T ON !
GRAPH ( .;Y .K #D @* .;F @7 .;X -- #C7
@+ #E8
,A 7--#AA1 #F7
;,B 7#H1 #AA7
;,C 7--#D1 #BI7
;,D 7#B1 #BI7
------------------------------------#ABH
.,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 GRAPH+ ..;Y .K _\ .;X
@+ #C_\4
.#BI4
.#CJ4
#CA4 .,,MULTIPLE .,,*OICE ,: EQU,N HAS
! GRAPH %[N8
,A
;,B
;,C
;,D
#CB4 .,,WRIT+ .,DESCRIBE H[ ! SIGNS (
.;H & .;K A6ECT H[ 6OBTA9 ! GRAPH ( .;Y
.K .;F @7 .;X--.;H @7 @+ .;K F ! GRAPH (
.;Y .K .;F @7 .;X @7@4
#CC4 .,,%ORT .,,RESPONSE ,! GRAPH (!
REL,N .;X .K AT ! "R4 ,IS ! REL,N A
FUNC;N8 .,EXPLA9 @4
#CD4 .,,R1SON+ ,IS X TRUE 9 G5]AL T _\
.;X @+ .;H _\ .K _\.;X_\@+ _\.;H_\8
.,JU/IFY YR ANSW] 03SID]+ H[ ! GRAPHS (
.;Y .K _\ ..;X @+ .;H _\ & ;Y.K _\.;X_\
@+ _\ .;H_\ >E RELAT$ 6! GRAPH ( .;Y .K
_\.;X_\ @4
#CE4 .,,*ALL5GE ,! GRAPH ( .;Y .K
..A_\;X--;H_\ @+ .;K PASSES "? 7--#B1
#D7 & 7#D1 #D74 .,DESCRIBE ! POSSI#
VALUES ( .;H & .;K @4
,,PRO#M ,,SOLV+
.,,EXAMPLE .#A ON P4 .#ABD .= ,EX4 #CF
.#CF4 .,,SPEEDOMET] ,A C>'S SPEEDOMET]
R1DS #FJ MILES P] H\R4 ,! ]ROR .;,E 9 ?
M1SURE;T IS ..;,E .K _\ .A -- #FJ_\ ":
.A IS ! ACTUAL SPE$4 ,GRAPH ! FUNC;N4 ,=
:AT VALUE 7;S7 ( .A W .;,E 2 #B.E MILES
P] H\R8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
,,EXAMPLE #C
ON P4 #ABE = ,EX4 #CG
.#CG4 .,,SALES ,WEEKLY SALES .;S 7IN
?\S&S7 (A NEW BASKETBALL %OE 9CR1SE
/1DILY =A :ILE & !N DECR1SE Z DESCRIB$
0! FUNC;N .;S .K --#B_\ .;T -- #AE_\
@+#EJ ": .;T IS ! "T 7IN WEEKS74 ,GRAPH
! FUNC;N4 ,:AT IS ! GRTE/ NUMB] ( PAIRS
( %OES SOLD 9 "O WEEK8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
,,EXAMPLE #D
ON P4 #ABE = ,EXS4 #CH-CI
#CH4 ,,%ORT ,,RESPONSE ,ON ! POOL TA#
%[N1 Y BANK ! FIVE BALL (F ! SIDE AT
7--#A.BE1 #E74 ,Y WANT ! BALL 6G 9 !
POCKET AT 7--#E1 #J74
A4 ,WRITE AN EQU,N =! PA? (! BALL4
B4 ,D Y MAKE ! %OT8 .,EXPLA9 H[ Y F.D
YR ANSW]4
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#A
.K ,,/&>DIZ$ ,,TE/ ,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
------------------------------------#ABI
.#CI4 .,,5G9E]+ ,! ,LEON>D ,P4 ,ZAKIM
,BUNK] ,HILL ,BRIDGE SPANS ! ,*>LES
,RIV] 9 ,BO/ON4 ,! BRIDGE IS SUSP5D$ F
TWO T[]S4 ,EA* T[] HAS ! DIM5.NS %[N4
,WRITE AN ABSOLUTE VALUE FUNC;N T
REPRES5TS ! 9V]T$ ;,V-%AP$ POR;N (A T[]4
#DJ4 .,,EXT5D$ .,,RESPONSE ,A SN[/ORM
2G9S ) LI<T SN[ T 9CR1SES 6V H1VY SN[ 2F
DECR1S+ AG4 ,! SN[FALL RATE .;R 7IN 9*ES
P] H\R7 IS GIV5 0.;R @7 .;T @7 .K
--#J.E_\ .;T -- #D_\ @+ #B ": .;T IS !
"T 7IN H\RS74
A4 .,GRAPH ,GRAPH ! FUNC;N4
B4 .,9T]PRET ,:5 IS ! SN[FALL H1VIE/8
,:AT IS ! MAXIMUM SN[FALL RATE8 ,H[ >E
YR ANSW]S RELAT$ 6! FUNC;N'S GRAPH8
C4 .,EXT5D ,! TOTAL SN[FALL IS GIV5 0!
>EA (! TRIANGLE =M$ 0! GRAPH ( .;R @7
.;T @7 &! .;T -AXIS4 ,:AT IS ! TOTAL
SN[FALL8
#DA4 .,,MULTIPLE .,,REPRES5T,NS ,!
DIAGRAM %[S A TRUCK DRIV+ T[>D A RADIO
/,N TRANSMITT] T HAS A BROADCA/+ RANGE (
#EJ MILES4
A4 .,MAK+ .A .,TA# ,MAKE A TA# T %[S !
TRUCK'S 4T.E .;D 7IN MILES7 F !
TRANSMITT] AF .;T .K #J1 #J.E1 #A1 #A.E1
#B1 #B.E1 & #C H\RS4
B4 .,DRAW+ .A .,GRAPH ,USE YR TA# F "P
7A7 6DRAW A GRAPH T %[S .;D Z A FUNC;N (
.;T @4
C4 .,WRIT+ .AN .,EQU,N ,WRITE AN EQU,N
T GIVES .;D Z A FUNC;N ( .;T @4 ,DUR+
:AT DRIV+ "TS IS ! TRUCK )9 RANGE (!
TRANSMITT]8
#DB4 .,,*ALL5GE ,A HIK] WALKS UP & D[N
A HILL4 ,! HILL HAS A CROSS SEC;N T C 2
MODEL$ 0": .;X & .;Y >E M1SUR$ 9 FEET &
#J "K .;X "K .#FJJ4 ,H[ F> DOES ! HIK]
WALK8
,,MIX$ ,,REVIEW
.#DC4 #E .;X -- #AG .1.K #AC
.#DD4 #H--#C .;X .1 --#AC
.#DE4 #B .;X -- #E "K #F .;X @+ #I
.#DF4 #D .;X @+ #F "K .;X -- #AH
.#DG4 #AA "K #B .;X -- #E "K.K #BE
.#DH4 .;X @+ #E "K.K --#A OR .;X -- #C
.1 #D
,GRAPH ! EQU,N4 @7 P4 #HI @7
.#DI4 .;Y .K -- .;X @+ #F
.#EJ4 .;Y .K --#D .;X @+ #C
.#EA4 .;Y .K #B .;X -- #E
.#EB4 .;Y .K --#C
.#EC4 .;Y .K #A.E .;X @+ #B
.#ED4 .;Y .K #C .;X -- #A
.#EE4 .,,DON,NS ,! NUMB] .;D ( DON,NS
A *>;Y RCVS V>IES DIRECTLY )! NUMB] .;R
( REQUE/S X MAILS4 ,! *>;Y S5DS \ #IEJJ
REQUE/S & RCVS #DBJ DON,NS4 ,WRITE AN
EQU,N T RELATES ;R & .D4 @7 P4 #AJG @7
.,,EXTRA .,,PRACTICE = ,LESSON .#B..G
@1 P4 #AJAA
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#ACJ
,EXT5.N ,USE ,PIECEWISE ,FUNC;NS
,USE AF ,LESSON #B.G
,KEY ,VOCABUL>Y
99 .PIECEWISE .FUNC;N
99 ./EP .FUNC;N
,SIDEB>3
,/&>DS
,5RI*;T TOPIC2 N REQUIR$ 0! ,CALI=NIA
,/&>DS
.,,GOAL ,EVALUATE1 GRAPH1 & WRITE
PIECEWISE FUNC;NS4
,A .PIECEWISE .FUNC;N IS DEF9$ 0AT L1/
TWO EQU,NS1 EA* ( : APPLIES 6A DI6]5T "P
(! FUNC;N'S DOMA94 ,"O EXAMPLE (A
PIECEWISE FUNC;N IS ! ABSOLUTE VALUE
FUNC;N .;F @7 .;X @7 .K _\.;X_\ @1 : C 2
DEF9$ 0! EQU,NS .;Y.K --.;X = .;X "K #J
& .;Y .K .;X = .;X .1 .#J4 ,ANO!R
EXAMPLE IS GIV5 2L4
,! EQU,N ..;Y .K .#B;X -- #A GIVES !
VALUE ( .;G @7 .;X @7 :5 .;X IS LESS ?AN
OR EQUAL 6#A1 &! EQU,N .;Y .K #C .;X @+
#A GIVES ! VALUE ( .;G @7 .;X @7 :5 .;X
IS GRT] ?AN #A4
,,EXAMPLE #A
.,EVALUATE .A PIECEWISE .FUNC;N
,EVALUATE ! FUNC;N .;G @7 .;X @7 ABV
:5 7A7 .;X .K #A & 7;B7 .;X .K #E4
,SOLU;N
A4 ..;G @7 ;X @7 .K #B;X -- #A ,2C #A
"K.K #A1 USE F/ .EQU,N4
;G7;L7 .K #B7#A7 --#A .K #A
..,SUB/ITUTE #A = ;X & .SIMPLIFY4
B4 ..;G @7 ;X @7 .K #C;X @+ #A ,2C #E
.1 #A1 USE SECOND .EQU,N4
;G7#E7 .K #C7#E7 @+ #A .K #AF
..,SUB/ITUTE #E = ;X & .SIMPLIFY4
,,EXAMPLE .#B
..,GRAPH A PIECEWISE .FUNC;N
,SOLU;N
.,,/EP .#A ,6! LEFT ( .;X .K --.#B @1
GRAPH @4 ,USE AN OP5 DOT AT 7--#B1B7 2C
! EQU,N DOES N APPLY :5 .;X .K --.#B @4
.,,/EP .#B ,F ..;X .K--.#B 6.;X .K #A1
9CLUSIVE1 GRAPH .;Y .K .;X @+ .#A4 ,USE
SOLID DOTS AT 7--#B1 --#A7 & 7#A1 #B7 2C
! EQU,N .;Y .K .;X @+ #A APPLIES 6BO?
.;X .K --#B & .;X .K #A4
.,,/EP .#C ,6! "R ( .;X .K #A1 GRAPH
.;Y .K
.#C4 ,USE AN OP5 DOT AT 7#A1 #C7 2C !
EQU,N .;Y .K #C DOES N APPLY :5 .;X .K
#A4
------------------------------------#ACA
,,EXAMPLE #C
,WRITE A PIECEWISE FUNC;N
,WRITE A PIECEWISE FUNC;N =! GRAPH
%[N4
,SOLU;N
,= .;X 2T #J & #A1 9CLUD+ .;X .K #J1 !
GRAPH IS ! L9E SEG;T GIV5 0.;Y .K #A4
,= .;X 2T #A & #B1 9CLUD+ .;X .K #A1 !
GRAPH IS ! L9E SEG;T GIV5 0.;Y .K #B4
,= .;X 2T #B & #C1 9CLUD+ .;X .K #B1 !
GRAPH IS ! L9E SEG;T GIV5 0.;Y .K .#C4
,S1 A PIECEWISE FUNC;N =! GRAPH IS Z
FOLL[S3
.,,/EP .,,FUNC;NS ,! PIECEWISE FUNC;N
9 ,EXAMPLE #C IS CALL$ A ./EP .FUNC;N 2C
XS GRAPH RESEM#S A SET ( /AIRS4 ,A /EP
FUNC;N IS DEF9$ 0A 3/ANT VALUE OV] EA*
"P ( XS DOMA94 ,! 3/ANT VALUES C 9CR1SE
) EA* 8/EP0 Z 9 ,EXAMPLE #C1 OR !Y C
DECR1SE ) EA* /EP4
,,PRACTICE
,,EXAMPLE #A
ON P4 #ACJ = ,EXS4 #A-D
,,EVALUAT+ ,,FUNC;NS ,EVALUATE !
FUNC;N 2L =! GIV5 VALUE ( .;X @4
.#A4 .;F 7--#D7
.#B4 .;F 7#B7
.#C4 .;F 7#C7
.#D4 .;F 7#E7
,,EXAMPLE .#B
ON P4 #ACJ = ,EXS4 #E-H
,,GRAPH+ ,,FUNC;NS ,GRAPH ! FUNC;N4
.#E4
.#F4
.#G4
.#H4 .,,PO/AL .,,RATES ,9 #BJJE1 ! CO/
.;,C 7IN DOLL>S7 6S5D ,U4,S4 ,PO/AL
,S]VICE ,EXPRESS ,MAIL UP 6#E P.DS
DEP5D$ ON ! WEI<T .;W 7IN \NCES7 AC 6!
FUNC;N AT ! "R4
.A4 ,GRAPH ! FUNC;N4
.B4 ,:AT IS ! CO/ 6S5D A P>CEL WEI<+
#B P.DS #I \NCES8
,,EXAMPLE #C
ON P4 #ACA = ,EXS4 #I-AJ
.,,SPECIAL .,,/EP .,,FUNC;NS ,WRITE &
GRAPH ! PIECEWISE FUNC;N DESCRIB$ US+ !
DOMA9 --#C "K .;X "K #C4
.#I4 ,R.D+ ,FUNC;N ,! \TPUT .;F @7 .;X
@7 IS ! 9PUT .;X R.D$ 6! NE>E/ 9TEG]4
7,IF ! DECIMAL "P ( .;X IS #J.E1 !N .;X
IS R.D$ UP :5 .;X IS POSITIVE & .;X IS
R.D$ D[N :5 .;X IS NEGATIVE47
.#AJ4 ,GRTE/ ,9TEG] ,FUNC;N ,! \TPUT
.;F @7 .;X @7 IS ! GRTE/ 9TEG] LESS ?AN
OR EQUAL 6! 9PUT X4
------------------------------------#ACB
#B.H ,GRAPH ,L9E> ,9EQUALITIES 9
,TWO ,V>IA#S
.,2F ,Y SOLV$ L9E> 9EQUALITIES 9 "O
V>IA#4
.,N[ ,Y W GRAPH L9E> 9EQUALITIES 9 TWO
V>IA#S4
.,:Y8 ,S Y C MODEL DATA 5COD+1 Z 9
,EXAMPLE #D4
,KEY ,VOCABUL>Y
99 L9E> 9EQUAL;Y 9 TWO V>IA#S
99 SOLU;N (A L9E> 9EQUAL;Y
99 GRAPH (A L9E> 9EQUAL;Y
99 HALF-PLANE
,SIDEB>3
,/&>DS
..,PREP>E = #B.J ,/UD5TS SOLVE SY/EMS
( .L9E> EQU,NS & .9EQUALITIES 7IN TWO OR
?REE V>IA#S7 0SUB/ITU;N1 .) .GRAPHS @1
OR ) MATRICES4
,A L9E> 9EQUAL;Y 9 TWO V>IA#S C 2
WRITT5 9 "O ( ^! =MS3
.,AX @+ .,BY "K .;,C
.,AX @+ .,BY "K.K .;,C
.,AX @+ .,BY .1 .;,C
.,AX @+ .,BY .1.K .;,C
,AN ORD]$ PAIR 7;X1 .;Y @7 IS A SOLU;N
(A L9E> 9EQUAL;Y 9 TWO V>IA#S IF !
9EQUAL;Y IS TRUE :5 ! VALUES ( .;X & .;Y
>E SUB/ITUT$ 96! 9EQUAL;Y4
,,EXAMPLE #A
.,/&>DIZ$ .,TE/ .,PRACTICE
,: ORD]$ PAIR IS A SOLU;N ( .#C;X @+
#D;Y .1 #H8
.,A 7#F1 --#C7
.;,B 7#J1 #B7
.;,C 7--#B1 --#A7
.;,D 7--#C1 #E7
,SOLU;N
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,ORD]$ ,PAIR3 ,SUB/ITUTE3 ,3CLU.N
7#F1 --#C73 #C7#F7 @+ #D 7--#C7 .K #F
#H3 7#F1 --#C7 IS N A SOLU;N4
7#J1 #B73 #C7#J7 @+ #D7#B7 .K #H #H3
7#J1 #B7 IS N A SOLU;N4
7--#B1 --#A73 #C7--#B7 @+ #D7--;L7 .K
--#AJ #H3 7--#B1 --#A7 IS N A SOLU;N4
7--#C1E73 #C7--#C7 @+#D7#E7 .K #AA .1
#H3 7--#C1 #E7 IS A SOLU;N4
,! CORRECT ANSW] IS ,D4 ..,A ;,B ;,C
.;,D
.,,GUID$ .,,PRACTICE = ,EXAMPLE #A
,TELL :E!R ! GIV5 ORD]$ PAIR IS A
SOLU;N ( .#E;X -- .#B;Y "K.K #F4
.#A4 7#J1 --#D7
.#B4 7#B1 #B7
.#C4 7--#C1 #H7
.#D4 7--#A1 --#G7
.,,GRAPH+ .,,9EQUALITIES ,! GRAPH (A
L9E> 9EQUAL;Y 9 TWO V>IA#S IS ! SET (
ALL PO9TS 9 A COORD9ATE PLANE T REPRES5T
SOLU;NS (! 9EQUAL;Y4
,,9T]PRET ,,GRAPHS
,A DA%$ B.D>Y L9E M1NS T PO9TS ON !
L9E >E .N SOLU;NS4 ,A SOLID B.D>Y L9E
M1NS T PO9TS ON ! L9E .>E SOLU;NS4
------------------------------------#ACC
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,GRAPH+ A ,L9E> ,9EQUAL;Y
,6GRAPH A L9E> 9EQUAL;Y 9 TWO V>IA#S1
FOLL[ ^! /EPS3
.,,/EP .#A .,GRAPH ! B.D>Y L9E =!
9EQUAL;Y4 ,USE A DA%$ L9E = "K OR .1 &A
SOLID L9E = "K.K OR .1.K.
.,,/EP .#B .,TE/ A PO9T .N ON ! B.D>Y
L9E 6DET]M9E :E!R X IS A SOLU;N (!
9EQUAL;Y4 ,IF X IS A SOLU;N1 %ADE !
HALF-PLANE 3TA9+ ! PO9T4 ,IF X IS N A
SOLU;N1 %ADE ! O!R HALF-PLANE4
,,EXAMPLE #B
,GRAPH L9E> 9EQUALITIES ) "O V>IA#
,GRAPH 7A7 .;Y "K.K --#C & 7;B7 .;X "K
#B 9 A COORD9ATE PLANE4
.A4 .,GRAPH ! B.D>Y L9E .;Y .K --#C4
,USE A SOLID L9E 2C ! 9EQUAL;Y SYMBOL IS
"K.
.,TE/ ! PO9T 7#J1 #J74 ,2C 7#J1 #J7 IS
.N A SOLU;N (! 9EQUAL;Y1 %ADE !
HALF-PLANE T DOES N 3TA9 7#J1 #J74
.B4 .,GRAPH ! B.D>Y L9E .;X .K .#B4
,USE A DA%$ L9E 2C ! 9EQUAL;Y SYMBOL IS
"K.
.,TE/ ! PO9T 7#J1 #J74 ,2C 7#J1 #J7
.IS A SOLU;N (! 9EQUAL;Y1 %ADE !
HALF-PLANE T 3TA9S 7#J1 #J74
,,EXAMPLE #C
,GRAPH L9E> 9EQUALITIES ) TWO V>IA#S
,,AVOID ,,]RORS
,X IS (T5 3V5I5T 6USE 7#J1 #J7 Z A TE/
PO9T4 ,H["E1 IF 7#J1 #J7 LIES ON ! B.D>Y
L9E1 Y M/ *OOSE A DI6]5T TE/ PO9T4
,GRAPH 7A7 .;Y .1 --.#B;X & 7;B7
..#E;X--.#B;Y "K.K --#D 9 A COORD9ATE
PLANE4
.A4 .,GRAPH ! B.D>Y L9E .;Y .K --.#B;X
@4 ,USE A DA%$ L9E 2C ! 9EQUAL;Y SYMBOL
IS .1.
.,TE/ ! PO9T 7#A1 #A74 ,2C 7#A1 #A7
.IS A SOLU;N (! 9EQUAL;Y1 %ADE !
HALF-PLANE T 3TA9S 7#A1 #A74
.B4 .,GRAPH ! B.D>Y L9E #E .;X--.#B;Y
.K --#D4 ,USE A SOLID L9E 2C ! 9EQUAL;Y
SYMBOL IS "K.
.,TE/ ! PO9T 7#J1 #J74 ,2C 7#J1 #J7 IS
.N A SOLU;N (! 9EQUAL;Y1 %ADE !
HALF-PLANE T DOES N 3TA9 7#J1 #J74
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
------------------------------------#ACD
..,,GUID$ ,,PRACTICE = ,EXAMPLES #B &
.#C
,GRAPH ! 9EQUAL;Y 9 A COORD9ATE PLANE4
#E4 .;Y .1 --;L
.#F4 .;X .1.K --#D
.#G4 .;Y .1.K --#C .;X
#H4 .;Y "K #B .;X @+ #C
.#I4 .;X @+ #C;Y "K #I
.#AJ4 .#B;X -- #F;Y .1 #AB
.,,EXAMPLE .#D
,SOLVE A MULTI-/EP PRO#M
.,,MOVIE .,,RECORD+ ,A FILM CLASS IS
RECORD+ A ,,DVD ( /UD5T-MADE %ORT FILMS4
,EA* /UD5T GR\P IS ALLOTT$ UP 6#CJJ
MEGABYTES 7,,MB7 ( VIDEO SPACE4 ,! FILMS
>E 5COD$ ON ! ,,DVD AT TWO DI6]5T RATES3
A /&>D RATE ( #J.D ,,MB_/SEC = NORMAL
SC5ES &A HI<-QUAL;Y RATE ( #A.B
,,MB_/SEC = -PLEX SC5ES4
99 ,WRITE AN 9EQUAL;Y DESCRIB+ !
POSSI# AM.TS ( "T AVAILA# = /&>D &
HI<-QUAL;Y VIDEO4
99 ,GRAPH ! 9EQUAL;Y4
99 ,ID5TIFY ?REE POSSI# SOLU;NS (!
9EQUAL;Y4
,SOLU;N
.,,/EP .#A .,WRITE AN 9EQUAL;Y4 ,F/
WRITE A V]BAL MODEL4
,AN 9EQUAL;Y IS #J.D .;X @+ #A.B;Y "K
#CJJ4
.,,/EP .#B .,GRAPH ! 9EQUAL;Y4 ,F/
GRAPH ! B.D>Y L9E #J.D .;X @+ #A.B;Y .K
.#CJJ4 ,USE A SOLID L9E 2C ! 9EQUAL;Y
SYMBOL IS "K.K.
,TE/ ! PO9T 7#J1 #J74 ,2C 7#J1 #J7 IS
A SOLU;N (! 9EQUAL;Y1 %ADE ! HALF-PLANE
T 3TA9S 7#J1 #J74 ,2C .;X & .;Y _C 2
NEGATIVE1 %ADE ONLY PO9TS 9 ! F/
QUADRANT4
.,,/EP .#C .,ID5TIFY SOLU;NS4 ,?REE
SOLU;NS >E GIV5 2L & ON ! GRAPH4
7.#AEJ1 .#BJJ7 .#AEJ SECONDS ( /&>D &
.#BJJ SECONDS ( HI< QUAL;Y
7.#CJJ1 .#ABJ7 .#CJJ SECONDS ( /&>D &
.#ABJ SECONDS ( HI< QUAL;Y
7.#FJJ1 .#BE7 .#FJJ SECONDS ( /&>D &
.#BE SECONDS ( HI< QUAL;Y
,=! F/ SOLU;N1 #J.D7#AEJ7 @+
#A.B7#BJJ7 .K #CJJ1 S ALL (! AVAILA#
SPACE IS US$4 ,=! O!R TWO SOLU;NS1 N ALL
(! SPACE IS US$4
------------------------------------#ACE
.,,ABSOLUTE .,,VALUE .,,9EQUALITIES
,GRAPH+ AN ABSOLUTE VALUE 9EQUAL;Y IS
SIMIL> 6GRAPH+ A L9E> 9EQUAL;Y1 B !
B.D>Y IS AN ABSOLUTE VALUE GRAPH4
,,EXAMPLE #E
,GRAPH AN ABSOLUTE VALUE 9EQUAL;Y
,GRAPH .;Y .1 --#B_\ .;X -- #C_\ @+ #D
9 A COORD9ATE PLANE4
,SOLU;N
.,,/EP .#A .,GRAPH ! EQU,N (! B.D>Y1
..;Y .K --#B _\.;X -- #C_\ @+ #D4 ,USE A
DA%$ L9E 2C ! 9EQUAL;Y SYMBOL IS .1.
.,,/EP .#B .,TE/ ! PO9T 7#J1 #J74 ,2C
7#J1 #J7 .IS A SOLU;N (! 9EQUAL;Y1 %ADE
! POR;N (! COORD9ATE PLANE \TSIDE !
ABSOLUTE VALUE GRAPH4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #D &
.#E
.#AA4 .,,:AT .,,IF8 ,REP1T ! /EPS (
,EXAMPLE #D IF EA* /UD5T GR\P IS ALLOTT$
UP 6#DBJ ,,MB ( VIDEO SPACE4
,GRAPH ! 9EQUAL;Y 9 A COORD9ATE PLANE4
#AB4 .;Y "K.K _\ .;X -- #B_\ @+ #A
.#AC4 .;Y .1.K --_\ .;X @+ #C_\--#B
.#AD4 .;Y"K #C_\ .;X -- ;L_\--#C
#B.H ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
ON .P4 ,,WS#D = ,EXS4 .#AE1 .#BE @1 &
.#DE
.K ,,/&>DIZ$ ,,TE/ ,,PRACTICE
,EXS4 #B1 #BA1 #BH1 #CI1 #DJ1 #DA1
#DF1 & #DH
,,SKILL ,,PRACTICE
,,EXAMPLE #A
ON P4 #ACB = ,EXS4 #C-F
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,!
GRAPH (A L9E> 9EQUAL;Y 9 TWO V>IA#S IS
A7;N7 @8 @4
.#B4 .,,WRIT+ .,-P>E ! GRAPH (A L9E>
9EQUAL;Y 9 TWO V>IA#S )! GRAPH (A L9E>
EQU,N 9 TWO V>IA#S4
.,,*ECK+ .,,SOLU;NS ,TELL :E!R ! GIV5
ORD]$ PAIRS >E SOLU;NS (! 9EQUAL;Y4
.#C4 ;X.1 --#G2 7#J1 #AJ71 7--#H1
--#E7
.#D4 .;Y "K.K --.#E;X2 7#C1 #B71
7--#B1 #A7
.#E4 ..;Y .1.K --.#B;X @+ #D2 7#J1
#D71 7--#A1 #H7
.#F4 ..#B;X--.;Y "K #C2 7#J1 #J71 7#B1
--#B7
,,EXAMPLES #B & #C
ON P4 #ACC = ,EXS4 #G-BJ
.,,GRAPH+ .,,9EQUALITIES ,GRAPH !
9EQUAL;Y 9 A COORD9ATE PLANE4
.#G4 ;X"K#C
.#H4 ;X.1.K#F
#I4 .;Y .1 --.#B
.#AJ4 --#B;Y "K.K #H
.;LL4 .;Y "K.K--#B .;X -- ;L
.#AB4 .;Y "K #C .;X @+ #C
.#AC4
.#AD4
.#AE4 #B .;X @+ .;Y "K #F
.#AF4 .;X @+ #D .;Y .1 --#AB
.#AG4 #C .;X--.;Y .1.K #A
.#AH4 #B .;X @+ #E .;Y "K --#AJ
------------------------------------#ACF
,,EXAMPLE #E
ON P4 #ACE = ,EXS4 #BB-BH
.,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 GRAPH+ ! 9EQUAL;Y4
.#AI4 ..;Y "K .#B;X @+ #C
.#BJ4 .;Y .1.K --#C;X--#B
#BA4 99 .,,MULTIPLE .,,*OICE ,: ORD]$
PAIR IS .N A SOLU;N ( #C .;X -- #E .;Y
"K #CJ8
,A 7#J1 #J7
;,B 7--#A1 #G7
;,C 7#A1 --#G7
;,D 7--#E1 --#E7
.,,ABSOLUTE .,,VALUE .,,9EQUALITIES
,GRAPH ! 9EQUAL;Y 9 A COORD9ATE PLANE4
.#BB4 .;Y .1 _\ .;,X -- #A_\
.#BC4 ;Y "K _\.;X_\ @+#E
.#BD4 .;Y .1 _\ .;X @+ #D_\ --#C
.#BE4
.#BF4 .;Y "K #C _\.;,X_\ @+#B
.#BG4 ..;Y .1.K #B_\.;X -- #A_\--#D
#BH4 .,,MULTIPLE .,,*OICE ,! GRAPH ( :
9EQUAL;Y IS %[N8
,A .;Y "K.K --#B_\;X@+#A_\ @+#C
;,B .;Y .1.K --#B_\;X-#A_\ @+#C
;,C .;Y .1 --#B_\ .;X @+ ;L_\ @+#C
;,D .;Y .1.K --#B_\ .;X @+ #A_\ @+#C
.,,*ECK+ .,,SOLU;NS ,TELL :E!R ! GIV5
ORD]$ PAIRS >E SOLU;NS (! 9EQUAL;Y4
.#BI4 @2 7--#F1 #H71 7--#C1 --#C7
.#CJ4 #D.E @+ .;Y "K #A.F;X2 7#J.E1
#A71 7#C.H1 #J7
.#CA4 #J.B .;X @+ #J.G;Y .1 --#A2
7#J.E1 --#A71 7--#C1 --#A.E7
.#CB4
.,,GRAPH+ .,,9EQUALITIES ,GRAPH !
9EQUAL;Y 9 A COORD9ATE PLANE4
.#CC4 #C;Y "K #D.E;X@+#AE
.#CD4 --#A.E;Y-#B .;X .1#C
.#CE4 -.;Y -- #J.B .1 --#J.F .;X
.#CF4
.#CG4
.#CH4 #B;Y--#D "K.K --#C_\ .;X @+ #B_\
.#CI4 .,,OP5-.,,5D$ .,,MA? ,WRITE A
L9E> 9EQUAL;Y 9 TWO V>IA#S T HAS
7--#A1C7 & 7#A1 #F7 Z SOLU;NS1 B DOES N
H 7#D1 #J7 Z A SOLU;N4
.#DJ4 .,,WRIT+ .,EXPLA9 :Y X IS N
HELP;L :5 GRAPH+ A L9E> 9EQUAL;Y 9 TWO
V>IA#S 6*OOSE A TE/ PO9T T LIES ON !
B.D>Y L9E4
.#DA4 .,,%ORT .,,RESPONSE ,WRITE AN
9EQUAL;Y =! GRAPH %[N4 .,EXPLA9 H[ Y
CAME UP )! 9EQUAL;Y4 ,!N DESCRIBE A
R1L-LIFE SITU,N T ! F/-QUADRANT POR;N (!
GRAPH CD REPRES5T4
.#DB4 .,,*ALL5GE ,WRITE AN ABSOLUTE
VALUE 9EQUAL;Y T HAS EXACTLY "O SOLU;N 9
-MON ) .;Y .1.K #B_\ .;X -- #C _\ @+#E4
,! -MON SOLU;N %D N 2 ! V]TEX 7#C1 #E7
(! B.D>Y4 .,EXPLA9 H[ Y F.D YR 9EQUAL;Y4
.K ,,"W$-,,\ ,,SOLU;NS ON P4 .,,WS#A
.K ,,/&>DIZ$ ,,TE/ ,,PRACTICE
------------------------------------#ACG
,,PRO#M ,,SOLV+
,,EXAMPLE #D
ON P4 #ACD = ,EXS4 #DC-DH
.#DC4 .,,CALL+ .,,C>DS ,Y H A 4#BJ
PH"O C>D4 ,CALLS MADE US+ ! C>D CO/
@4#.JC P] M9UTE 6DE/9,NS )9 ! ,UNIT$
,/ATES & @4#.JF P] M9UTE 6DE/9,NS 9
,BRAZIL4 ,WRITE AN 9EQUAL;Y DESCRIB+ !
NUMB]S ( M9UTES Y C USE = CALLS 6,U4,S4
DE/9,NS & 6,BRAZIL4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#DD4 .,,RE/AURANT .,,MANAGE;T ,A
PIZZA %OP HAS #CJJ P.DS 7#DHJJ \NCES7 (
D\<4 ,A SMALL PIZZA USES #AB \NCES ( D\<
&A L>GE PIZZA USES #AH \NCES ( D\<4
,WRITE & GRAPH AN 9EQUAL;Y DESCRIB+ !
POSSI# NUMB]S ( SMALL & L>GE PIZZAS T C
2 MADE4 ,!N GIVE ?REE POSSI# SOLU;NS4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#DE4 .,,CRAFTS ,COTTON LACE CO/S
4#A.EJ P] Y>D & L95 LACE CO/S 4#B.EJ P]
Y>D4 ,Y PLAN 6ORD] AT MO/ 4#GE ( LACE =
CRAFTS4 ,WRITE & GRAPH AN 9EQUAL;Y
DESCRIB+ H[ M* ( EA* TYPE ( LACE Y C
ORD]4 ,IF Y BUY #BD Y>DS ( COTTON LACE1
:AT >E ! AM.TS ( L95 LACE Y C BUY8
.#DF4 .,,%ORT .,,RESPONSE ,Y SELL
;,T-%IRTS = 4#AE EA* & CAPS = 4#AJ EA*4
,WRITE & GRAPH AN 9EQUAL;Y DESCRIB+ H[
_M %IRTS & CAPS Y M/ SELL 6EXCE$ 4#AHJJ
9 SALES4 .,EXPLA9 H[ Y C MODIFY ?
9EQUAL;Y 6DESCRIBE H[ _M %IRTS & CAPS Y
M/ SELL 6EXCE$ 4#FJJ 9 .PR(IT IF Y MAKE
A #DJ@3P PR(IT ON %IRTS &A #CJ@3P PR(IT
ON CAPS4
#DG4 .,,MULTI-.,,/EP .,,PRO#M ,ON A
TWO WEEK VAC,N1 Y & YR BRO!R C R5T "O
CANOE = 4#AA P] "D OR R5T TWO M.TA9
BIKES = 4#AC EA* P] "D4 ,TGR1 Y H 4#ABJ
6SP5D4
A4 ,WRITE & GRAPH AN 9EQUAL;Y DESCRIB+
! POSSI# NUMB]S ( "DS Y & YR BRO!R C
CANOE OR BICYCLE TGR4
B4 ,GIVE ?REE POSSI# SOLU;NS (!
9EQUAL;Y F "P 7A74
C4 ,Y DECIDE T ON "O "D Y W CANOE AL"O
& YR BRO!R W BICYCLE AL"O4 ,REP1T "PS
7A7 & 7;B7 US+ ? NEW 3DI;N4
#DH4 .,,EXT5D$ .,,RESPONSE ,:ILE
CAMP+1 Y &A FR FILT] RIV] WAT] 96TWO
CYL9DRICAL 3TA9]S )! RADII & HEI<TS %[N4
,Y !N USE ^! 3TA9]S 6FILL ! WAT] COOL]
%[N4
A4 ,F9D ! VOLUMES (! 3TA9]S &! COOL] 9
CUBIC 9*ES4
B4 ,US+ YR RESULTS F "P 7A71 WRITE &
GRAPH AN 9EQUAL;Y DESCRIB+ H[ _M "TS !
3TA9]S C 2 FILL$ & EMPTI$ 96! WAT] COOL]
)\T ! COOL] OV]FL[+4
C4 ,3V]T ! VOLUMES F "P 7A7 6GALLONS
7#A IN4 #C #J.JJDCC GAL74 ,!N REWRITE !
9EQUAL;Y F "P 7;B7 9 T]MS ( ^! 3V]T$
VOLUMES4
D4 ,GRAPH ! 9EQUAL;Y F "P 7;C74 .,-P>E
! GRAPH ) YR GRAPH F "P 7;B71 & EXPLA9
:Y ! RESULTS MAKE S5SE4
------------------------------------#ACH
.#DI4 .,,*ALL5GE ,A WIDESCRE5 TELEVI.N
IMAGE HAS A WID? .;W &A HEI<T .;H T
SATISFY ! 9EQUAL;Y @4
.A4 ,DOES ! TELEVI.N SCRE5 %[N AT ! "R
MEET ! REQUIRE;TS (A WIDESCRE5 IMAGE8
.B4 ,LET .;D 2 ! L5G? (A DIAGONAL (A
TELEVI.N IMAGE4 ,WRITE AN 9EQUAL;Y
DESCRIB+ ! POSSI# VALUES ( .;D & .;H =A
WIDESCRE5 IMAGE4
,,MIX$ ,,REVIEW
,LOOK =A PATT]N 9 ! TA#4 ,!N WRITE AN
EQU,N T REPRES5TS ! TA#4 @7 P4 #CD @7
#EJ4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #J3 #A3 #B3 #C
.;Y @3 #AA3 #AE3 #AI3 #BC
#EJ4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #J3 #A3 #B3 #C
.;Y @3 #FJ3 #DE3 #CJ3 #AE
,GRAPH ! EQU,N1 @7 P4 #HI @7
.#EB4 .;X @+ #C .;Y .K --#F
.#EC4 #D .;X -- #C .;Y .K #AE
.#ED4 #H .;X -- #F .;Y .K #AH
.#EE4 #F .;X @+ #I .;Y .K #AH
.#EF4 --#B .;X -- #E .;Y .K #BJ
.#EG4 --#AJ .;X @+ #D .;Y .K #BJ
,WRITE AN EQU,N (! L9E T SATISFIES !
GIV5 3DI;NS4 @7 P4 #IH @7
.#EH4 @1 PASSES "? 7#AJ1 --#B7
.#EI4 .;M .K --#C1 PASSES "? 7#C1 #G7
.#FJ4 PASSES "? 7#J1 #B7 & 7#E1 #H7
.#FA4 PASSES "? 7#D1 --#A7 & 7#G1
--#F7
,,QUIZ .= .,LESSONS .#B..G-.B..H
,GRAPH ! FUNC;N4 .,-P>E ! GRAPH )!
GRAPH ( ..;Y .K _\.;X_\4 @7 P4 #ABC @7
#A.Y.K_\;X @+ #G_\@+#D
#B4 .;Y.K --.#B_\.;X @+ #AJ_\--#A
.#C4
,WRITE AN EQU,N (! GRAPH1 @7 P4 #ABC
@7
.#D4
.#E4
.#F4
,GRAPH ! 9EQUAL;Y 9 A COORD9ATE PLANE4
@7 P4 #ACB @7
#G4 .;Y .1 --.#B
#H4 .;Y "K.#C;X@+.#A
.#I4 #B;X-#E;Y.1#AJ
.#AJ4 .,,M9I-.,,C>S ,Y H A #BJ CR$IT
GIFT PASS 6A M9I-C> RACEWAY4 ,X TAKES #B
CR$ITS 6DRIVE ! C>S ON ! ,R,Y TRACK & #C
CR$ITS 6DRIVE ! C>S ON ! ,GR& ,PRIX
TRACK4 ,WRITE & GRAPH AN 9EQUAL;Y
DESCRIB+ H[ _M "TS Y C RACE ON ! TWO
TRACKS US+ YR GIFT PASS4 ,!N GIVE ?REE
POSSI# SOLU;NS4 @7 P4 #ACB @7
.,,EXTRA .,,PRACTICE = ,LESSON #B.H1
P4 #AJAA
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#ACI
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,LESSONS #B.E-B.H
.#A4 .,,MULTI-.,,/EP .,,PRO#M ,A
GRE5H\SE SELLS M>IGOLDS = 4#B EA* &
DAHLIAS = 4#C EA*4 ,Y H A TOTAL ( 4#CJ
6SP5D4
.A4 ,WRITE AN 9EQUAL;Y DESCRIB+ !
NUMB]S ( M>IGOLDS & DAHLIAS Y C BUY4
.B4 ,GRAPH ! 9EQUAL;Y F "P 7A74
.C4 ,:AT IS ! GRTE/ NUMB] ( M>IGOLDS Y
C BUY IF Y BUY #E DAHLIAS8
.#B4 .,,MULTI-.,,/EP .,,PRO#M ,AN
8,A-FRAME0 H\SE IS %[N 2L4 ,! COORD9ATES
.;X & .;Y >E BO? M1SUR$ 9 FEET4
.A4 ,WRITE AN ABSOLUTE VALUE FUNC;N T
MODELS ! FRONT (! H\SE4
.B4 ,REWRITE YR FUNC;N F "P 7A7 )!
ORIG9 AT ! MIDPO9T (! H\SE'S BASE4
.#C4 .,,%ORT .,,RESPONSE ,TELL :E!R !
DATA PO9TS %[ A POSITIVE CORREL,N1 A
NEGATIVE CORREL,N1 OR APPROXIMATELY NO
CORREL,N4 .,EXPLA9 YR R1SON+4
.#D4 ,,OP5-,,5D$ ,USE ! SYMBOL "K OR
.1 6WRITE A L9E> 9EQUAL;Y 9 TWO V>IA#S T
HAS 7#A1 --#E7 & 7#G1 --#H7 Z SOLU;NS4
.#E4 .,,%ORT .,,RESPONSE ,TELL :E!R !
DATA %[ DIRECT V>I,N4 .,EXPLA94
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,SUBSCRIP;N "T1 .;X 7MON?S7 @3 ,TOTAL
CO/1 .;Y 7DOLL>S7
#A3 #AJ.IE
#B3 #BA.IJ
#C3 #CB.HE
#D3 #DC.HJ
#E3 #ED.GE
.#F4 .,,EXT5D$ .,,RESPONSE ,! TA# %[S
! NUMB] ( DAILY NEWSPAP]S PR9T$ 9 !
,UNIT$ ,/ATES & _! DAILY CIRCUL,N AT #BJ
YE> 9T]VALS F #AIJJ 6#BJJJ4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,YE>3 ,NEWSPAP]S3 ,CIRCUL,N 7MILLIONS7
#AIJJ3 #BBBF3 #AE.A
#AIBJ3 #BJDB3 #BG.H
#AIDJ3 #AHGH3 #DA.A
#AIFJ3 #AGFC3 #EH.I
#AIHJ3 #AGDE3 #FB.B
#BJJJ3 #ADHJ3 #EE.H
.A4 ,DRAW A SCATT] PLOT (! DATA PAIRS
7YE>S S9CE #AIJJ1 NEWSPAP]S74
.B4 ,APPROXIMATE ! BE/-FITT+ L9E =!
SCATT] PLOT F "P 7A74
.C4 ,USE YR MODEL F "P 7;B7 6PREDICT !
NUMB] ( DAILY NEWSPAP]S 9 #BJBJ4
.D4 ,DRAW A SCATT] PLOT (! DATA PAIRS
7YE>S S9CE #AIJJ1 CIRCUL,N74 ,IS X
R1SONA# 6USE A L9E> MODEL 6PREDICT !
CIRCUL,N 9 #BJBJ8 .,EXPLA94
.#G4 .,,GRI4$ .,,ANSW] ,Y >E SELL+
S&WI*ES 6RAISE M"OY =A CLASS TRIP4 ,YR
DAILY SALES ;S 7IN DOLL>S7 9CR1SE /1DILY
=! F/ FEW "DS & !N DECR1SE Z GIV5 0!
FUNC;N .;S7.;T7 .K --#AE_\;T -- #E_\ @+
#AHJ ": .;T IS ! "T 7IN "DS74 ,:AT 0 !
MAXIMUM AM.T ( M"OY Y RAIS$ 9 "O "D8
------------------------------------#ADJ
#B ,*APT] ,SUMM>Y
.,ANIMAT$ ,ALGEBRA
_+CLASSZONE.COM_:
,ELECTRONIC ,FUNC;N ,LIBR>Y
,,BIG ,,ID1S
,= ,YR ,NOTEBOOK
.,BIG .,IDEA .#A ,REPRES5T+ ,REL,NS &
,FUNC;NS
,A REL,N PAIRS 9PUT VALUES ) \TPUT
VALUES4 ,A REL,N IS A FUNC;N IF EA* 9PUT
VALUE IS PAIR$ ) EXACTLY "O \TPUT VALUE4
,PICTURE3 ..,? REL,N IS A FUNC;N 2C
EA* 9PUT HAS EXACTLY "O .\TPUT4
,PICTURE3 ..,? REL,N IS N A FUNC;N 2C
A V]TICAL L9E 9T]SECTS ! GRAPH AT M ?AN
"O .PO9T4
.,BIG .,IDEA .#B ,GRAPH+ ,L9E> ,EQU,NS
& ,9EQUALITIES 9 ,TWO ,V>IA#S
,PICTURE3 .,L9E> .,FUNC;N
,PICTURE3 ..;Y .K MX @+ .;B
,PICTURE3 .,DIRECT .,V>I,N .,EQU,N
,PICTURE3 .;Y .K .AX
,PICTURE3 .,ABSOLUTE .,VALUE .,FUNC;N
,PICTURE3 ..;Y .K A_\;X--;H_\ @+ .;K
,PICTURE3 .,L9E> .,9EQUAL;Y
,PICTURE3 ..,AX @+ ,BY .1 .;,C
.,BIG .,IDEA .#C ,WRIT+ ,L9E> ,EQU,NS
& ,9EQUALITIES 9 ,TWO ,V>IA#S
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,=M3 ,EQU,N3 ,KEY ,FACTS
,SLOPE-9T]CEPT =M3 ;Y .K .MX @+ .;B @3
,! GRAPH IS A L9E ) SLOPE .;M & .;Y
-9T]CEPT .;B @4
,/&>D =M3 ..,AX @+ ,BY .K .;,C @3 ,!
GRAPH IS A L9E ) 9T]CEPTS & @4
,PO9T-SLOPE =M3 ;Y -- .;Y #A .K
.;M7.;X--.;X #A @7 @3 ,! GRAPH IS A L9E
T HAS SLOPE .;M & PASSES "? 7.;X #A .;Y
#A @7@4
,DIRECT V>I,N3 ;Y .K .AX1 .A #J @3 ,!
GRAPH IS A L9E T PASSES "? ! ORIG9 & HAS
SLOPE .A 7! 3/ANT ( V>I,N74
,L9E> 9EQUAL;Y3 .,AX@+.,BY.1.;,C @3 ,!
GRAPH IS A HALF-PLANE ) B.D>Y L9E ..,AX
@+ ,BY .K .;,C @4
------------------------------------#ADA
#B ,*APT] ,REVIEW
,SIDEB>3
@A,HOME,TUTOR
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99 ,MULTI-,LANGUAGE ,GLOSS>Y
99 ,VOCABUL>Y PRACTICE
,,REVIEW ,,KEY ,,VOCABUL>Y
99 REL,N1 P4 #GB
99 DOMA91 RANGE1 P4 #GB
99 FUNC;N1 P4 #GC
99 EQU,N 9 TWO V>IA#S1 P4 #GD
99 SOLU;N1 GRAPH ( AN EQU,N 9 TWO
V>IA#S1 P4 #GD
99 9DEP5D5T V>IA#1 P4 #GD
99 DEP5D5T V>IA#1 P4 #GD
99 L9E> FUNC;N1 P4 #GE
99 FUNC;N NOT,N1 P4 #GE
99 SLOPE1 P4 #HB
99 P>ALLEL1 P]P5DICUL>1 P4 #HD
99 RATE ( *ANGE1 P4 #HE
99 P>5T FUNC;N1 P4 #HI
99 .;Y -9T]CEPT1 P4 #HI
99 SLOPE-9T]CEPT =M1 P4 #IJ
99 .;X -9T]CEPT1 P4 #IA
99 /&>D =M (A L9E> EQU,N1 P4 #IG
99 PO9T-SLOPE =M1 P4 #IH
99 DIRECT V>I,N1 P4 #AJG
99 3/ANT ( V>I,N1 P4 #AJG
99 SCATT] PLOT1 P4 #GGC
99 POSITIVE CORREL,N1 P4 #GGC
99 NEGATIVE CORREL,N1 P4 #GGC
99 CORREL,N COE6ICI5T1 P4 #GGD
99 BE/-FITT+ L9E1 P4 #GGD
99 ABSOLUTE VALUE FUNC;N1 P4 #GBC
99 V]TEX ( AN ABSOLUTE VALUE GRAPH1 P4
#GBC
99 TRANS=M,N1 P4 #GBC
99 TRANSL,N1 P4 #GBC
99 REFLEC;N1 P4 #GBD
99 L9E> 9EQUAL;Y 9 TWO V>IA#S1 .P4
#GCB
99 SOLU;N1 GRAPH (A L9E> 9EQUAL;Y 9
TWO V>IA#S1 P4 #GCB
99 HALF-PLANE1 P4 #GCB
,VOCABUL>Y ,EX]CISES
.#A4 ,COPY & -PLETE3 ,! L9E> EQU,N #E
.;X -- #D .;Y .K #AF IS WRITT5 9 @8 =M4
.#B4 ,COPY & -PLETE3 ,A SET ( DATA
PAIRS @7 .;X1 .;Y7 %[S A @8 CORREL,N IF
.;Y T5DS 6DECR1SE Z .;X 9CR1SES4
.#C4 ,COPY & -PLETE3 ,TWO V>IA#S .;X &
;Y %[ @8 IF .;Y .K .AX & .A @6.K #J4
.#D4 .,,WRIT+ .,EXPLA9 :AT 4T+UI%ES A
FUNC;N F A REL,N4
,,REVIEW ,,EXAMPLES ,,& ,,EX]CISES
,USE ! REVIEW EXAMPLES & EX]CISES 2L
6*ECK YR "U/&+ (! 3CEPTS Y H LE>N$ 9 EA*
LESSON ( ,*APT] #B4
#B.A ,REPRES5T ,REL,NS & ,FUNC;NS PP4
#GB-GI
,,EXAMPLE
,TELL :E!R ! REL,N GIV5 0! ORD]$ PAIRS
7--#F1 #C71 7--#D1 #E71 7--#A1 --#B71
7#B1 --#A71 & 7#B1 #C7 IS A FUNC;N4
,! REL,N IS .N A FUNC;N 2C ! 9PUT #B
IS MAPP$ ONTO BO? --#A & #C1 Z %[N 9 !
MAPP+ DIAGRAM4
,,EX]CISES
,3SID] ! REL,N GIV5 0! ORD]$ PAIRS4
,ID5TIFY ! DOMA9 & RANGE4 ,!N TELL :E!R
! REL,N IS A FUNC;N4
.#E4 7--#B1 --#B71 7--#A1 #J71 7#B1
#F71 7#C1 #H7
.#F4 7--#A1 --#E71 7#A1 #B71 7#C1 #D71
7#A1 --#G7
.#G4 ,TELL :E!R .;F @7 .;X @7 .K #AF
-- .#G;X IS A L9E> FUNC;N4 ,!N F9D .;F
7--#E74
,,EXAMPLES #A1 #B1 & #E
ON PP4 #GB-GE = ,EXS4 #E-G
------------------------------------#ADB
#B ,*APT] ,REVIEW
.#B..B ,F9D ,SLOPE & ,RATE ( ,*ANGE
PP4 #HB-HH
,EXAMPLE
,F9D ! SLOPE .;M (! L9E PASS+ "? !
PO9TS 7--#D1 #AB7 & 7#C1 --#B74
,,EXAMPLE #B
ON P4 #HB = ,EXS4 #H-AA
,,EX]CISES
,F9D ! SLOPE (! L9E PASS+ "? ! GIV5
PO9TS4
.#H4 7--#B1-#A71 7#D1 #C7
.#I4 7#A1-#E71 7#A1B7
.#AJ4 7#E1-#C71 7#A1 #G7
.#AA4 7#F1 #B71 7--#H1 #B7
.#B..C ,GRAPH ,EQU,NS ( ,L9ES PP4
#HI-IF
,,EXAMPLE
,GRAPH #C @+ .;Y .K --.#B;X @4
.,,/EP .#A ,WRITE ! EQU,N 9
SLOPE-9T]CEPT =M1 ..;Y.K --#B;X -- .#C4
.,,/EP .#B ,! .;Y -9T]CEPT IS --#C4
,S1 PLOT ! PO9T 7#J1 --#C74
.,,/EP .#C ,! SLOPE IS --#B4 ,PLOT A
SECOND PO9T 0/>T+ AT 7#J1 --#C7 & !N
MOV+ D[N #B UNITS & "R #A UNIT4
.,,/EP .#D ,DRAW A L9E "? ! TWO PO9TS4
,,EX]CISES
,GRAPH ! EQU,N4
#AB4 .;Y .K #E -- .;X
#AC4 .;Y--.#E;X .K --#D
#AD4 .;X .K #D
#AE4 #F .;X -- #D .;Y .K #AB
,,EXAMPLES #A1B1 & #D
ON PP4 #HI-IB = ,EXS4 #AB-AE
#B.D ,WRITE ,EQU,NS ( ,L9ES PP4
#IH-AJD
,,EXAMPLE
..,WRITE AN EQU,N (! L9E T PASSES "?
7--.#B @1 #E7 .& 7--.#D1 --.#A74
,! SLOPE IS .;R @4 ,USE ! PO9T-SLOPE
=M ) @7 .;X #A .;Y #A @7 .K 7--#B1 #E74
.;Y--.;Y #A .K .;M7.;X--.;X #A @7
.,USE .PO9T-.SLOPE .=M4
.;Y - #E .K #C7;X--7--#B77 .,SUB/ITUTE
.= .;M,.;X #A @1 .& .;Y #A @4
..;Y .K .#C;X @+ #AA ..,WRITE 9
SLOPE-9T]CEPT .=M4
,,EXAMPLE #D
ON P4 #AJJ = ,EXS4 #AF-AH
,,EX]CISES
,WRITE AN EQU,N (! L9E T PASSES "? !
GIV5 PO9TS4
.#AF4 7--#C1 #D71 7#B1 --#F7
.#AG4 7--#D1 #E71 7#AB1 --#G7
.#AH4 7--#D1 #A71 7#C1 --#F7
------------------------------------#ADC
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@A,HOME,TUTOR
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,*APT] ,REVIEW ,PRACTICE
#B.E ,MODEL ,DIRECT ,V>I,N PP4
#AJG-AAA
,,EXAMPLE
,! V>IA#S .;X & ;Y V>Y DIRECTLY1 & .;Y
.K #GF :5 .;X .K -- #H4 ,WRITE AN EQU,N
T RELATES .;X & Y4 ,!N F9D .;Y :5 .;X .K
--#F4
.;Y .K .AX ,WRITE DIRECT V>I,N EQU,N4
.#GF .K .A 7--..#H7 ,SUB/ITUTE #GF =
;Y & --#H = .;X @4
-#I.E .K .A .,SOLVE .= .A4
,AN EQU,N T RELATES .;X & .;Y IS .;Y
.K --#I.EX4 ,:5 ;X.K --#F1 .;Y .K
--#I.E7--#F7 .K #EG4
,,EXAMPLE #B
ON P4 #AJH = ,EXS4 #AI-BB
,,EX]CISES
,! V>IA#S .;X & .;Y V>Y DIRECTLY4
,WRITE AN EQU,N T RELATES .;X & Y4 ,!N
F9D ;Y :5 .;X .K #C4
#AI4 .;X .K #F1 ;Y .K --#DH
#BJ4 ;X .K --#I1 ;Y .K #AE
#BA4 .;X .K --#C1 ;Y .K #B.D
.#BB4 .,,PHYSICS ,*>LES'S ,LAW /ATES T
:5 PRESSURE IS 3/ANT1 ! VOLUME ;,V (A
GAS V>IES DIRECTLY ) XS TEMP]ATURE .;,T
7IN KELV9S74 ,A GAS O3UPIES #D.H LIT]S
AT A TEMP]ATURE ( #CJJ KELV9S4 ,WRITE AN
EQU,N T GIVES .;,V Z A FUNC;N ( .;,T @4
,:AT IS ! VOLUME (! GAS :5 ! TEMP]ATURE
IS #DBJ KELV9S8
#B.F ,DRAW ,SCATT] ,PLOTS &
,BE/-,FITT+ ,L9ES PP4 #AAC-ABJ
,,EXAMPLE
,! TA# %[S ! %OE SIZE .;X & HEI<T .;Y
7IN 9*ES7 = #G M54 ,APPROXIMATE !
BE/-FITT+ L9E =! DATA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #I3 #I.E3 #AJ3 #AJ.E3 #AA3
#AA.E3 #AB
.;Y @3 #FI3 #GJ.E3 #GJ3 #GA.E3 #GB3
#GD3 #GD
,DRAW A SCATT] PLOT & SKET* ! L9E T
APPE>S 6BE/ FIT ! DATA PO9TS4
,*OOSE TWO PO9TS ON ! L9E1 S* Z 7#I1
#FI7 & 7#AB1 #GD74 ,USE ! PO9TS 6F9D AN
EQU,N (! L9E4
,! SLOPE IS @4
,AN EQU,N IS .;Y -- #FI .K #A.FG @7
.;X -- #I71 OR .;Y .K #A.FG .;X @+ #ED4
,,EXAMPLE #C
ON P4 #AAE = ,EX4 #BC
,,EX]CISES
,APPROXIMATE ! BE/-FITT+ L9E =! DATA4
#BC4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 -#B3 -#A3 #J3 #A3 #B3 #C3 #D3
#E
.;Y @3 #D3 #C3 #B.E3 #B3 #J.E3 -#A3
-#B3 -#C
------------------------------------#ADD
#B ,*APT] ,REVIEW
#B.G ,USE ,ABSOLUTE ,VALUE ,FUNC;NS &
,TRANS=M,NS PP4 #ABC-ABI
,,EXAMPLE
,GRAPH .;Y .K #C_\ .;X -- #A_\--#D4
,-P>E ! GRAPH )! GRAPH ( .;Y .K _\.;X_\
@4
.,,/EP .#A .,ID5TIFY & PLOT ! V]TEX1
@7 .;H1 .;K7 .K 7#A1 --#D74
.,,/EP .#B .,PLOT ANO!R PO9T ON !
GRAPH1 S* Z 7#J1 --#A74 ,USE SYMMETRY
6PLOT A ?IRD PO9T1 7#B1 --#A74
.,,/EP#C .,3NECT ! PO9TS )A ;,V-%AP$
GRAPH4
.,,/EP#D .,-P>E ) ;Y .K _\;X_\4 ,!
GRAPH ( .;Y .K #C _\ .;X -- ;L_\ --#D IS
! GRAPH ( .;Y .K _\.;X_\ /RET*$ V]TIC,Y
0A FACTOR ( #C1 !N TRANSLAT$ "R #A UNIT
& D[N #D UNITS4
,,EXAMPLES #A1 #B1 #C1 & #D
ON PP4 #ABC-ABE = ,EXS4 #BD-BG
,,EX]CISES
,GRAPH ! FUNC;N4 .,-P>E ! GRAPH 6!
GRAPH ( .;Y .K _\.;X_\ @4
.#BD4 ..;Y .K _\.;X -- #C_\ @+ #B
.#BE4
.#BF4 .;F7.;X7 .K --#D_\;X @+ ..#B _\
@+ .#C
.#BG4 .,,F9.E ,ANALY/S PREDICT T A
-PANY W REPORT E>N+S ( 4#A.EJ P] %>E 9 !
NEXT QU>T]4 ,! FUNC;N .;D .K _\ .A --
#A.EJ_\ GIVES ! ABSOLUTE DI6];E .;D 2T !
ACTUAL E>N+S .A &! PREDICT$ E>N+S4
,GRAPH ! FUNC;N4 ,= :AT VALUE7;S7 ( .A W
.;D 2 @4#.BE8
.#B..H ,GRAPH ,L9E> ,9EQUALITIES 9
,TWO ,V>IA#S PP4 #ACB-ACH
,,EXAMPLE
,GRAPH #C;X -- .;Y "K.K --.#B 9 A
COORD9ATE PLANE4
.,,/EP .#A .,GRAPH ! B.D>Y L9E
..#C;X--;Y .K --.#B @4 ,USE A SOLID L9E
2C ! 9EQUAL;Y SYMBOL IS "K.K.
.,,/EP .#B .,TE/ ! PO9T 7#J1 #J74 ,2C
7#J1 #J7 IS .N A SOLU;N (! 9EQUAL;Y1
%ADE ! HALF-PLANE T DOES N 3TA9 7#J1
#J74
,,EXAMPLES #B1 #C1 & #D
ON PP4 #ACB-ACD = ,EXS4 #BH-CD
,,EX]CISES
,TELL :E!R ! GIV5 ORD]$ PAIR IS A
SOLU;N (! 9EQUAL;Y4
#BH4 -.;Y "K.K #E;X2 7#J1 #A7
.#BI4 .;Y .1 --.#C;X -- #G2 7--#D1 #F7
.#CJ4 #C;X -- .#D;Y "K --#H2 7--#B1
#J7
,GRAPH ! 9EQUAL;Y 9 A COORD9ATE PLANE4
.#CA4 --#D;Y "K#AF
.#CB4 ;Y-#B;X.1#H
.#CC4 #AB;X-#H;Y "K#BD
.#CD4 .,,W9D .,,5]GY ,AN ELECTRIC
-PANY BUYS 5]GY F 8W9DMILL F>MS0 T H
W9DMILLS ( TWO SIZES1 "O PRODUC+ #A.E
MEGAWATTS ( P[] & "O PRODUC+ #B.E
MEGAWATTS ( P[]4 ,! -PANY WANTS A TOTAL
P[] SUPPLY ( AT L1/ #AHJ MEGAWATTS4
,WRITE & GRAPH AN 9EQUAL;Y DESCRIB+ H[
_M ( EA* SIZE ( W9DMILL X TAKES 6SUPPLY
! ELECTRIC -PANY4
------------------------------------#ADE
#B ,*APT] ,TE/
,9 ,EX]CISES #A & .#B @1 TELL :E!R !
REL,N IS A FUNC;N4 .,EXPLA9 @4
.#A4 7#A1 --#E71 7#J1 #D71 7#B1 #C71
7--#A1 #B71 7#B1 #G71 7#A1 #B7
.#B4 7--#C1 #D71 7#B1 #E71 7#A1 #J71
7#J1 #D71 7--#B1 --#C71 7#C1 #F7
.#C4 ,EVALUATE .;F @7 .;X @7 .K #C;X
#B -- #B;X @+ #AA :5 ;X .K --#F4
,F9D ! SLOPE (! L9E PASS+ "? ! GIV5
PO9TS4 ,!N TELL :E!R ! L9E ..RISES1
FALLS1 IS .HORIZONTAL @1 OR IS .V]TICAL
@4
.#D4 7#C1 --#B71 7#E1 #D7
.#E4 7#F1 --#G71 7#AC1 --#G7
.#F4 7--#B1 #A71 7#A1 --#D7
.#G4 7--#D1 #I71 7--#D1 #H7
,GRAPH ! EQU,N4
.#H4 .;X .K #D
.#I4
.#AJ4 ;X @+ #B;Y .K #F
.#AA4 #C;Y .K #B;X--#AB
,WRITE AN EQU,N (! L9E T PASSES "? !
GIV5 PO9T & SATISFIES ! GIV5 3DI;N4
.#AB4 7#I1 --#A72 P>ALLEL TO
.#AC4 7#AJ1 #B72 P]P5DICUL> 6;Y .K
--#E;X @+ #G
,! V>IA#S ;X & .;Y V>Y DIRECTLY4
,WRITE AN EQU,N T RELATES ;X & .;Y @4
,!N F9D .;X :5 .;Y .K #F4
.#AD4 ;X .K #D1 .;Y .K --#H
.#AE4 ;X .K --#B1 ;Y .K --#A
.#AF4 ;X .K #H1 ;Y .K #AH
.#AG4 ;X .K #AF1 ;Y .K --#F
,9 ,EX]CISES #AH & #AI1 7A7 DRAW A
SCATT] PLOT (! DATA1 7;B7 APPROXIMATE !
BE/-FITT+ L9E =! DATA1 & 7;C7 E/IMATE !
VALUE ( .;Y :5 ;X .K #AJ4
#AH4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #A3 #B3 #C3 #D3 #E
.;Y @3 #AH3 #DJ3 #EE3 #GC3 #IA
#AI4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #A3 #B3 #C3 #D3 #E
.;Y @3 #IG3 #IA3 #HG3 #HA3 #GE
.#BJ4 ,GRAPH ;Y .K --#C_\;X @+ #A_\ @+
#C4 .,-P>E ! GRAPH )! GRAPH ( .;Y .K .;X
@4
,GRAPH ! 9EQUAL;Y 9 A COORD9ATE PLANE4
.#BA4 ;Y.1-#B;X @+ #D #BB4 #B;X-#D;Y
"K#AF
.#BC4 ;Y"K_\;X-#C_\@+;L
#BD4 ..;Y .1-#B_\;X_\--.;C
.#BE4 .,,TIRE .,,WE> ,A NEW SET ( C>
TIRES HAS A TR1D DEP? ( #H MILLIMET]S4
,! TR1D DEP? DECR1SES #J.AB MILLIMET] P]
?\S& MILES DRIV54 ,WRITE AN EQU,N T
GIVES ! TR1D DEP? Z A FUNC;N (! 4T.E
DRIV54 ,!N PREDICT AT :AT 4T.E ! TR1D
DEP? W 2 #B MILLIMET]S4
.#BF4 .,,PA9T+ ,! AM.T ( PA9T AN
ELECTRIC PA9T SPRAY] APPLIES V>IES
DIRECTLY ) "T4 ,A SPRAY] IS SET 6APPLY
#J.E GALLON 9 #B.E M9UTES4 ,WRITE AN
EQU,N T GIVES ! AM.T .;P ( PA9T Z A
FUNC;N (! "T .;T @4 ,H[ M* PA9T IS
APPLI$ IF ! SPRAY] IS OP]AT$ = #BJ
M9UTES8
.#BG4 .,,-PUT] .,,*IPS ,! TA# %[S !
NUMB] ;X ( TRANSI/ORS 7IN MILLIONS7 &!
SPE$Y 7IN GIGAH]TZ7 = S"EAL -PUT]
PROCESSORS4 ,APPROXIMATE ! BE/-FITT+ L9E
=! DATA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #C.A3 #I.E3 #BH3 #CG3 #DB3 #EE3
#AJF3 #ABE
.;Y @3 #J.JF3 #J.DE3 #J.E3 #A.E3 #A.E3
#B3 #B.D3 #C.F
------------------------------------#ADF
#B ,/&>DIZ$ ,TE/ ,PREP>,N
,,EXT5D$ ,,RESPONSE ,,"QS
,SCOR+ ,RUBRIC
,FULL ,CR$IT
99 SOLU;N IS -PLETE & CORRECT
,"PIAL ,CR$IT
99 SOLU;N IS -PLETE B HAS ]RORS1
OR
99 SOLU;N IS )\T ]ROR B 9COMPLETE
,NO ,CR$IT
99 NO SOLU;N IS GIV51
OR
99 SOLU;N MAKES NO S5SE
,,PRO#M
,! TA# %[S ! TOTAL ,U4,S4 EMIS.NS 7IN
MILLIONS ( TONS7 ( .VOLATILE .ORGANIC
.-P.DS 7,,VOC,'S71 A MAJOR AIR
POLLUTANT1 F #AIIE 6#BJJC4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,YE> @3 #AIIE3 #AIIF3 #AIIG3 #AIIH3
#AIII3 #BJJJ3 #BJJA3 #BJJB3 #BJJC
.,,VOC,'S @3 #BB.J3 #BJ.I3 #AI.E3
#AH.H3 #AH.C3 #AG.E3 #AG.A3 #AF.E3 #AF.A
.A4 ,APPROXIMATE ! BE/-FITT+ L9E =!
DATA4
.B4 ,PREDICT ! AM.T ( ,,VOC,'S T W 2
EMITT$ 9 #BJAJ4
.C4 ,IS X R1SONA# 6ASSUME T ! TR5D 9 !
DATA MODEL$ 0! BE/-FITT+ L9E W 3T9UE
9DEF9ITELY8 .,EXPLA94
,2L >E SAMPLE SOLU;NS 6! PRO#M4 ,R1D
EA* SOLU;N &! -;TS 9 BLUE 6SEE :Y !
SAMPLE REPRES5TS FULL CR$IT1 "PIAL
CR$IT1 OR NO CR$IT4
,,SAMPLE #A3 ,FULL CR$IT SOLU;N
,! V>IA#S >E CLE>LY DEF9$4
,! SCATT] PLOT &A L9E FITT+ ! PO9TS >E
CORRECTLY DRAWN4
,! CALCUL,NS >E CORRECT & CLE>LY
EXPLA9$4
,! EQU,N (! L9E ( FIT IS CORRECT4
,! PREDIC;N IS CORRECT4
,! ANSW] IS R1SONA#4
.A4 ,LET ;X REPRES5T YE>S S9CE #AIIE &
LET ;Y REPRES5T MILLIONS ( TONS (
,,VOC,'S EMITT$4 ,!N ! ORD]$ PAIRS >E
7#J1 #BB.J71 7#A1 #BJ.I71 7#B1 #AI.E71
7#C1 #AH.H71 7#D1 #AH.C71 7#E1 #AG.E71
7#F1 #AG.A71 7#G1 #AF.E71 & 7#H1 #AF.A74
,A SCATT] PLOT &A L9E DRAWN 6FIT !
DATA >E %[N4 ,! PO9TS 7#B1 #BJ7 &
7#F1AG.A7 APPE> 6LIE ON ! L9E4
,USE ! PO9TS @7 .;X #A @1 .;Y #A @7 .K
7#B1 #BJ7 & @7 .;X #B @1 .;Y #B @7 .K
7#F1 #AG.A7 6F9D ! SLOPE .;M @4
,N[ USE PO9T-SLOPE =M4
.;Y -- .;Y #A .K .;M @7 .;X -- .;X #A
@7
.;Y -- #BJ .K --#J.GBE7 .;X -- #B7
.;Y -- #BJ .K --#J.GBE .;X @+ #A.DE
.;Y .K --#J.GBE .;X @+ #BA.E
,AN APPROXIM,N (! BE/-FITT+ L9E IS .;Y
.K --#J.GBE .;X @+ #BA.E4
.B4 ,6PREDICT ! AM.T ( EMIS.NS 9
#BJAJ1 USE ! FACT T #BJAJ IS #AE YE>S AF
#AIIE4 ,SUB/ITUTE .;X .K #AE 96! MODEL4
.;Y .K --#J.GBE .;X @+ #BA.E .K
--#J.GBE7#AE7 @+ #BA.E #AJ.F
,Y C PREDICT T #AJ.F MILLION TONS (
,,VOC,'S W 2 EMITT$ 9 #BJAJ4
.C4 ,NO2 ! TR5D CD 3T9UE =A :ILE B N
9DEF9ITELY1 2C ! EQU,N PREDICTS Z]O
EMIS.NS :5 --#J.GBE;X @+ #BA.E .K #J1 OR
:5 .;X -- #CJ4 ,X IS UNR1LI/IC 6PREDICT
T EMIS.NS W 2 REDUC$ 6Z]O4
------------------------------------#ADG
,,SAMPLE #B3 ,"PIAL CR$IT SOLU;N
,A R1SONA# L9E ( FIT IS F.D & ANSW]S
>E CORRECT1 B ! GRAPH IS N LABEL$1 LL "W
IS %[N1 &! EXPLAN,N IS 9COMPLETE4
.A4 ,! ;Y-9T]CEPT IS #BA.E &! L9E
PASSES "? 7#D1AH.E71 S AN APPROXIM,N (!
BE/-FITT+ L9E IS .;Y .K --#J.GE .;X @+
#BA.E4
.B4 .;Y .K --#J.GE7#AE7 @+ #BA.E .K
#AJ.BE
.C4 ,NO2 X WD 2 NEGATIVE4
,SAMPLE #C3 ,NO CR$IT SOLU;N
,! GRAPH IS MISS+ &! EQU,N IS A POOR
*OICE4 ,"PS @7 .;B @7 & @7 .;C @7 >E
9CORRECT4
.A4 .;Y .K --#J.GD .;X @+ #AIIE
.B4 #EJH
.C4 ,YES2 ! L9E ALW KEEPS GO+ D[N4
,,PRACTICE
,APPLY ! ,SCOR+ ,RUBRIC
,SIDEB>3
,/&>DS
..,PROBABIL;Y & ,/ATI/ICS3 #H.J
,/UD5TS ORGANIZE & DESCRIBE 4TRIBU;NS (
DATA 0.US+ A NUMB] ( DI6]5T ME?ODS1
9CLUD+ FREQU5CY TA#S1 HI/OGRAMS1 /&>D
L9E & B> GRAPHS1 /EM-&-L1F 4PLAYS1
.SCATT]PLOTS @1 & BOX-&-:ISK] PLOTS4
..,ADV.ED ,PLACE;T ,PROBABIL;Y &
,/ATI/ICS3 #AB.J ,/UD5TS F9D ! L9E ( BE/
FIT 6A GIV5 4TRIBU;N ( .DATA 0US+ L1/
SQU>ES REGRES.N4
#A4 ,A /UD5T'S SOLU;N 6! PRO#M ON !
PREVI\S PAGE IS GIV5 2L4 ,SCORE ! SOLU;N
..Z FULL CR$IT1 "PIAL .CR$IT @1 OR .NO
.CR$IT4 .,EXPLA9 YR R1SON+4 ,IF Y *OOSE
."PIAL .CR$IT OR .NO .CR$IT @1 EXPLA9 H[
Y WD *ANGE ! SOLU;N S T X E>NS A SCORE (
FULL CR$IT4
A4 ,LET .;X .REPRES5T ! YE>4 ,LET ;Y
REPRES5T .,,VOC,'S .EMITT$ 7MILLIONS .(
.T"O
,A SCATT] PLOT &A L9E ( FIT >E %[N4 ,!
L9E PASSES "? @7 .;X #A @1 .;Y #A @7 .K
7#AIIF1 #BJ.I7 & "? @7 .;X #B @1 .;Y #B
@7 .K 7#BJJA1AG.A74
.;Y -- .;Y #A .K ;M7 .;X -- .;X #A @7
.;Y -- #BJ.I .K --#J.GF7 .;X -- #AIIF7
.;Y --#J.GF .;X @+ #AECH
,AN .APPROXIM,N .( .! BE/-FITT+ L9E IS
.;Y .K --#J.GF .;X @+ #AECH4
B4 ,6PREDICT ! EMIS.NS 9 #BJAJ1
SUB/ITUTE .;X .K #BJAJ 96! MODEL
.;Y .K --#J.GF .;X @+ #AECH .K
--#J.GF7#BJAJ7 @+ #AECE .K #AJ.D
,AB #AJ.D MILLION TONS ( ,,VOC,'S W 2
EMITT$ 9 #BJAJ4
C4 ,NO2 9 #BJBD1 .,,VOC EMIS.NS WD
2COME NEGATIVE 2C --#J.GF7#BJBD7 @+
#AECE .K --#J.BD1 : DOESN'T MAKE S5SE4
------------------------------------#ADH
#B ,/&>DIZ$ ,TE/ ,PRACTICE
,,EXT5D$ ,,RESPONSE
#A4 ,! TA# %[S ! E/IMAT$ BUDGET .;X &!
TOTAL ,U4,S4 BOX (FICE GROSS ;Y 7BO? 9
MILLIONS ( DOLL>S7 =! EI<T HI<E/-E>N+
MOVIES ( ALL "T 7Z ( ,DECEMB]1 #BJJD74
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #BJJ3 #ID3 #ACI3 #AAE3 #AJ.E3
#GJ3 #AA3 #BJJ
.;Y @3 #CGD3 #CGG3 #DJD3 #DCA3 #DCE3
#DDA3 #DFA3 #FJA
A4 ,ID5T;Y ! DOMA9 & RANGE (! REL,N
REPRES5T$ 0! TA#4
B4 ,GRAPH ! REL,N4
C4 ,TELL :E!R ! REL,N IS A FUNC;N4
.,EXPLA94
#B4 ,A P>K TRAIL UP A HILL HAS BE5
IMPROV$ 0BUILD+ /EPS F WOOD5 TIMB]S1 Z
%[N 9 ! DIAGRAM (A SEC;N (! TRAIL4 ,EA*
TIMB] M1SURES #H 9*ES ON A SIDE4
A4 ,:AT IS ! AV]AGE RATE ( *ANGE 9
ELEV,N ON ! TRAIL F PO9T ,A 6PO9T ;,B8
B4 ,IF ! TRAIL 3T9UES Z %[N UP A HILL
T IS #ABJ FEET HI<1 :AT HORIZONTAL 4T.E
D Y COV] CLIMB+ ! TRAIL8
C4 ,IF ! TRAIL _H US$ #F 9* TIMB]S =
EA* /EP 9/1D ( #H 9* TIMB]S1 :AT
HORIZONTAL 4T.E WD EA* /EP COV]8
.,EXPLA94
#C4 ,Y H 4#CJ 6SP5D ON TWO TYPES (
Y>N1 COTTON Y>N T CO/S 4#C.EJ P] BALL &
WOOL Y>N T CO/S 4#D.EJ P] BALL4
A4 ,WRITE AN 9EQUAL;Y T DESCRIBES !
POSSI# AM.TS ( COTTON Y>N & WOOL Y>N Y C
BUY )\T SP5D+ M ?AN 4#CJ4
B4 ,GRAPH ! 9EQUAL;Y F "P 7A74
C4 ,>E ALL PO9TS ON ! B.D>Y L9E
SOLU;NS (! 9EQUAL;Y 9 ? SITU,N8 ,IF N1 :
PO9TS ON ! B.D>Y L9E >E SOLU;NS8 ,:AT
DOES EA* SOLU;N ON ! B.D>Y L9E M1N 9 !
3TEXT (! PRO#M8
#D4 ,! TA# %[S ! TOTAL S*OOL 5ROLL;T
7IN MILLIONS7 AT ALL LEVELS 9 ! ,UNIT$
,/ATES =! YE>S #AIHF 6#BJJA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,YE> @3 #AIHF3 #AIHG3 #AIHH3 #AIHI3
#AIIJ3 #AIIA3 #AIIB3 #AIIC
.,5ROLL;T 7.MILLIONS7 @3 #EG.G3 #EH.C3
#EH.E3 #EI.C3 #FJ.C3 #FA.G3 #FB.F3 #FC.A
.,YE> @3 #AIID3 #AIIE3 #AIIF3 #AIIG3
#AIIH3 #AIII3 #BJJJ3 #BJJA
.,5ROLL;T 7.MILLIONS7 @3 #FC.I3 #FD.H3
#FE.G3 #FF.E3 #FG.J3 #FG.G3 #FH.G3 #FI.H
A4 ,MAKE A SCATT] PLOT (! DATA4 ,LET
.;X REPRES5T YE>S S9CE #AIHF & .;Y
REPRES5T 5ROLL;T 7IN MILLIONS74
B4 .,DESCRIBE ! CORREL,N %[N 0! DATA4
C4 ,APPROXIMATE ! BE/-FITT+ L9E =!
DATA4 ,!N USE ? L9E 6PREDICT TOTAL
5ROLL;T 9 #BJAB4
------------------------------------#ADI
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,,MULTIPLE ,,*OICE
#E4 ,: ORD]$ PAIR IS A SOLU;N (!
9EQUAL;Y -- .;X @+ #B .;Y .1 #AJ8
,A 7--#AJ1 #J7
;,B 7#J1 #E7
;,C 7#E1 #E7
;,D 7#E1 #AJ7
#F4 ,! GRAPH ( : EQU,N PASSES "? !
PO9T 7#A1 --#C7 & IS P]P5DICUL> 6! L9E
.;X @+ .;Y .K #AJ8
,A .;X @+ .;Y .K --#B
;,B .;X -- .;Y .K --#B
;,C .;X @+ .;Y .K #D
;,D .;X -- .;Y .K #D
#G4 ,:AT IS ! SLOPE (! L9E PASS+ "? !
PO9TS 7#J1 --#D7 & 7--#C1 #B78
,A --#B
;,B
;,C
;,D #B
,,GRI4$ ,,ANSW]
.#H4 ,A DIRECT V>I,N EQU,N .;Y .K .AX
HAS 7--#C1 --#F7 Z A SOLU;N4 ,:AT IS !
VALUE (! 3/ANT ( V>I,N8
.#I4 ,:AT IS ! VALUE ( .;F 7#B7 =!
FUNC;N .;F @7 .;X @7 .K #D .;X #B -- #E
.;X @+ #A8
.#AJ4 ,:AT IS ! VALUE ( .;K S T ! L9E
PASS+ "? @7 .;K @1 #B7 & 7#B1 #G7 HAS A
SLOPE ( --#A8
.#AA4 ,:AT IS ! .;X -9T]CEPT (! GRAPH
( #B .;X @+ #C .;Y .K #CF8
.#AB4 ,:AT IS ! ;Y-9T]CEPT (! L9E T
PASSES "? ! PO9T 7#BJ1 #AFH7 & HAS A
SLOPE (-#E8
.#AC4 ,! GRAPH ( .;Y .K --#C @* .;F @7
.;X @7 @+ #E IS OBTA9$ F ! GRAPH ( .;Y
.K .;F @7 .;X @7 "? TRANS=M,NS4 ,! PO9T
7--#G1 --#F7 LIES ON ! GRAPH ( .;Y .K
.;F @7 .;X @7@4 ,:AT IS ! .;Y -VALUE (!
IMAGE ( ? PO9T AF ! TRANS=M,NS8
,,%ORT ,,RESPONSE
.#AD4 ,! NUMB] ( WOM5 ELECT$ 6! ,U4,S4
,H\SE ( ,REPRES5TATIVES HAS 9CR1S$ NE>LY
E ,3GRESS S9CE
#AIHE4 ,9 ! #II? ,3GRESS 2G9N+ 9
#AIHE1 "! 7 #BB FEMALE REPRES5TATIVES4
,9 ! #AJI? ,3GRESS 2G9N+ 9 #BJJE1 "! 7
#FH FEMALE REPRES5TATIVES4
A4 ,WRITE A L9E> EQU,N T MODELS !
NUMB] ;Y ( FEMALE MEMB]S (! ,H\SE (
,REPRES5TATIVES ;X YE>S AF #AIHE4
B4 ,GIV5 T ! NUMB] ( REPRES5TATIVES IS
FIX$ AT #DCE1 IS X R1SONA# 6?9K T !
MODEL CD 2 A FAIRLY A3URATE PREDICTOR (!
NUMB] ( FEMALE REPRES5TATIVES 9 #BJCJ8
.,EXPLA94
#AE4 ,GRAPH .;Y .K --#B _\ .;X @+
#A_\--#C4 .,DESCRIBE H[ ! GRAPH -P>ES )!
GRAPH ( .;Y .K _\ .;X _\. ,IF Y
TRANSLATE ! GRAPH ( .;Y .K --#B _\ .;X
@+ #A_\--#C D[N #B UNITS & LEFT #E
UNITS1 :AT IS AN EQU,N (! NEW GRAPH8
.,EXPLA94
#AF4 ,! SCATT] PLOT %[S ! AGES (!
W9N]S ( PROFES.NAL GOLF'S ANNUAL ,MA/]S
,T\RNA;T =! YE>S #AICD-BJJE4 7,"! 0 NO
T\RNA;T 9 ! YE>S #AIDC-AIDE47 ,:AT TYPE
( CORREL,N DOES ! SCATT] PLOT %[8 ,DOES
YR ANSW] *ANGE IF Y 3SID] ONLY ! DATA F
#AICD 6#AIED8 .,EXPLA94
#AG4 ,Y >E BAK+ COOKIES & SET ! OV5
6#CEJ;DG,F4 ,! OV5 TEMP]ATURE />TS AT
ROOM TEMP]ATURE1 #FH;DG;,F1 & TAKES #H
M9UTES 6R1* #CEJ;DG;,R ,F9D ! AV]AGE
RATE ( *ANGE 9 ! TEMP]ATURE4 ,USE ? RATE
( *ANGE 6E/IMATE H[ M* L;G] X WD TAKE
6H1T ! OV5 6#DBE;DG,F4 .,EXPLA94
------------------------------------#AEJ
#C ,L9E> SY/EMS & ,MATRICES
#C.A SOLVE ,L9E> SY/EMS ,GRAPH+
#C.B SOLVE ,L9E> SY/EMS ,ALGEBRAIC,Y
#C.C ,GRAPH SY/EMS ( ,L9E>
,9EQUALITIES
#C.D SOLVE ,SY/EMS ( ,L9E> ,EQU,NS 9
,?REE ,V>IA#S
#C.E ,P]=M ,BASIC ,MATRIX ,OP],NS
#C.F ,MULTIPLY ,MATRICES
#C.G ,EVALUATE ,DET]M9ANTS ,APPLY
,CRAM]'S ,RULE
#C.H ,USE ,9V]SE ,MATRICES 6,SOLVE
,L9E> ,SY/EMS
,2F
,9 PREVI\S *APT]S1 Y LE>N$ ! FOLL[+
SKILLS1 : Y'LL USE 9 ,*APT] #C3 GRAPH+
EQU,NS1 SOLV+ EQU,NS1 & GRAPH+
9EQUALITIES4
,PREREQUISITE ,SKILLS
,,VOCABUL>Y ,,*ECK
,COPY & -PLETE ! /ATE;T4
.#A4 ,! .L9E> .9EQUAL;Y T REPRES5TS !
GRAPH %[N AT ! "R IS @8 @4
.#B4 ,! ..GRAPH (A L9E> .9EQUAL;Y 9
TWO V>IA#S IS ! SET ( ALL PO9TS 9 A
COORD9ATE PLANE T >E @8 (! 9EQUAL;Y4
,,SKILLS ,,*ECK
,GRAPH ! EQU,N4 7.,REVIEW P4 #HI .=
.#C..A47
.#C4 .;X @+ .;Y .K #D
.#D4 .;Y .K #C .;X -- #C
.#E4 --#B .;X @+ #C .;Y .K --#AB
,SOLVE ! EQU,N4 7..,REVIEW P4 #AH =
#C.B1C..D47
.#F4 #B .;X -- #AB .K #AF
.#G4 --#C .;X -- #G .K #AB
.#H4 --#B .;X @+ #E .K #B .;X -- #E
,GRAPH ! 9EQUAL;Y 9 A COORD9ATE PLANE4
7..,REVIEW P4 #ACB = #C..C47
.#I4 .;Y .1.K -- .;X @+ #B
.#AJ4 .;X @+ #D .;Y "K--#AF
.#AA4 #C .;X @+ #E .;Y .1--#E4
@A.,HOME,TUTOR ,PREREQUISITE SKILLS
PRACTICE AT _+CLASSZONE.COM_:
------------------------------------#AEA
,N[
,9 ,*APT] #C1 Y W APPLY ! BIG ID1S
LI/$ 2L & REVIEW$ 9 ! ,*APT] ,SUMM>Y ON
PAGE #BBA @4 ,Y W AL USE ! KEY VOCABUL>Y
LI/$ 2L4
,BIG ,ID1S
.#A ,SOLV+ SY/EMS ( EQU,NS US+ A
V>IETY ( ME?ODS
.#B ,GRAPH+ SY/EMS ( EQU,NS &
9EQUALITIES
.#C ,US+ MATRICES
,KEY ,VOCABUL>Y
99 SY/EM ( TWO L9E> EQU,NS1 P4 #AEC
99 3SI/5T1 P4 #AED
99 9CONSI/5T1 P4 #GED
99 9DEP5D5T1 P4 #GED
99 DEP5D5T1 P4 #GED
99 SUB/ITU;N ME?OD1 P4 #AFJ
99 ELIM9,N ME?OD1 P4 #AFA
99 SY/EM ( L9E> 9EQUALITIES1 P4 #AFH
99 SY/EM ( ?REE L9E> EQU,NS1 P4 #AGH
99 ORD]$ TRIPLE1 P4 #AGH
99 MATRIX1 P4 #GHG
99 DET]M9ANT1 P4 #BJC
99 ,CRAM]'S RULE1 P4 #BJE
99 ID5T;Y MATRIX1 P4 #BAJ
99 9V]SE MATRICES1 P4 #BAJ
,:Y8
,Y C USE SY/EMS ( L9E> EQU,NS 6SOLVE
R1L-_W PRO#MS4 ,= EXAMPLE1 Y C DET]M9E :
( TWO PAY;T OP;NS = RID+ A BUS IS M
CO/-E6ECTIVE4
,ANIMAT$ ,ALGEBRA
,! ANIM,N ILLU/RAT$ 2L = ,EXAMPLE #D
ON PAGE #AEE HELPS Y ANSW] ? "Q3 ,AF H[
_M BUS RIDES W ! CO/ ( TWO PAY;T OP;NS 2
! SAME8
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,O!R ANIM,NS = ,*APT] .#C3 PAGES
#AEC @1 #AFA @1 #AFH @1 #AIF @1 #BAA @1
& #BAB
------------------------------------#AEB
,9VE/IGAT+ ,ALGEBRA ,ACTIV;Y3 #C.A
,SOLV+ ,L9E> ,SY/EMS ,US+ ,TA#S
,USE 2F ,LESSON #C.A
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,KEY/ROKES
,MAT]IALS
99 GRAPH+ CALCULATOR
,SIDEB>3
,/&>DS
..#B.J ,/UD5TS SOLVE SY/EMS ( L9E>
.EQU,NS & 9EQUALITIES @7 .9 .TWO OR ?REE
.V>IA#S @7 0SUB/ITU;N1 ) GRAPHS1 OR )
MATRICES4
,,"Q ,H[ C Y SOLVE A SY/EM ( L9E>
EQU,NS US+ A TA#8
,AN EXAMPLE (A ..SY/EM ( L9E> .EQU,NS
9 TWO V>IA#S .;X & .;Y IS ! FOLL[+3
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;Y .K #B .;X @+ #D @3 .,EQU,N .#A
.;Y .K --#C .;X @+ #DD @3 .,EQU,N .#B
,A .SOLU;N (A SY/EM ( EQU,NS 9 TWO
V>IA#S IS AN ORD]$ PAIR @7 .;X1 .;Y @7 T
IS A SOLU;N ( BO? EQU,NS4 ,"O WAY 6SOLVE
A SY/EM IS 6USE ! .TA# F1TURE (A GRAPH+
CALCULATOR4
,EXPLORE ,SOLVE A SY/EM
,USE A TA# 6SOLVE ! SY/EM ( EQU,NS
ABV4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
..,,/EP #A ,5T] .EQU,NS @3 ..,,/EP #B
,MAKE A .TA# @3 ..,,/EP #C ,F9D !
.SOLU;N
,PRESS 65T] ! EQU,NS4 ,5T] ,EQU,N #A Z
.;Y #A & ,EQU,N #B Z .;Y #B @4 @3 ,SET !
/>T+ .;X -VALUE (! TA# 6#J &! /EP VALUE
6#A4 ,!N USE ! .TA# F1TURE 6MAKE A TA#4
@3 ,SCROLL "? ! TA# UNTIL Y F9D AN
;X-VALUE = : .;Y #A & .;Y #B >E EQUAL4
,! TA# %[S .;Y #A .K .;Y #B .K #BJ :5
.;X .K #H4
@3 @3
,! SOLU;N (! SY/EM IS 7#H1 #BJ74
,DRAW ,3CLU.NS ,USE YR OBS]V,NS
6-PLETE ^! EX]CISES
,USE A TA# 6SOLVE ! SY/EM4 ,IF Y >E
US+ A GRAPH+ CALCULATOR1 Y MAY NE$ 6F/
SOLVE ! EQU,NS 9 ! SY/EM = .;Y 2F 5T]+
!M4
.#A4 .;Y .K #B .;X @+ #E
.;Y .K -- .;X @+ #B
.#B4 .;Y .K #D .;X @+ #A
.;Y .K #D .;X -- #H
.#C4 .;Y .K #D .;X -- #C
.;Y .K .;X @+ #B
.#D4 #H .;X -- #D .;Y .K #AF
--#F .;X @+ #C .;Y .K #C
.#E4 #F .;X -- #B .;Y .K --#B
--#C .;X -- #G .;Y .K #AG
.#F4 .;X @+ .;Y .K #AA
-- .;X -- .;Y .K --#AA
.#G4 ,BAS$ ON YR RESULTS 9 ,EX]CISES
#A-F1 MAKE A 3JECTURE AB ! NUMB] (
SOLU;NS A SY/EM ( L9E> EQU,NS C H4
------------------------------------#AEC
#C.A ,SOLVE ,L9E> ,SY/EMS 0,GRAPH+
.,2F ,Y SOLV$ L9E> EQU,NS4
.,N[ ,Y W SOLVE SY/EMS ( L9E> EQU,NS4
.,:Y8 ,S Y C -P>E SWIMM+ DATA1 Z 9
,EX4 #CI4
,KEY ,VOCABUL>Y
99 SY/EM ( TWO L9E> EQU,NS
99 SOLU;N (A SY/EM
99 3SI/5T
99 9CONSI/5T
99 9DEP5D5T
99 DEP5D5T
,A ..SY/EM ( TWO L9E> .EQU,NS 9 TWO
V>IA#S .;X & .;Y @1 AL CALL$ A .L9E>
.SY/EM @1 3SI/S ( TWO EQU,NS T C 2
WRITT5 9 ! FOLL[+ =M4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,AX @+ .,BY .K .;,C @3 .,EQU,N .#A
.,DX @+ .,EY .K .;,F @3 .,EQU,N .#B
,A .SOLU;N (A SY/EM ( L9E> EQU,NS 9
TWO V>IA#S IS AN ORD]$ PAIR @7 .;X1 .;Y
@7 T SATISFIES EA* EQU,N4 ,SOLU;NS
CORRESPOND 6PO9TS ": ! GRAPHS (! EQU,NS
9 A SY/EM 9T]SECT4
.,EXAMPLE .#A ..,SOLVE A SY/EM
.GRAPHIC,Y
,SIDEB>3
,/&>DS
..#B.J ,/UD5TS SOLVE SY/EMS ( L9E>
.EQU,NS & 9EQUALITIES @7 .9 .TWO OR ?REE
.V>IA#S @7 0SUB/ITU;N1 .) .GRAPHS @1 OR
) MATRICES4
,GRAPH ! L9E> SY/EM & E/IMATE !
SOLU;N4 ,!N *ECK ! SOLU;N ALGEBRAIC,Y4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#D .;X @+ .;Y .K #H @3 .,EQU,N .#A
#B .;X -- #C .;Y .K #AH @3 .,EQU,N .#B
,SOLU;N
,2G9 0GRAPH+ BO? EQU,NS1 Z %[N AT !
"R4 ,F ! GRAPH1 ! L9ES .APPE> 69T]SECT
AT 7#C1 --#D74 ,Y C *ECK ? ALGEBRAIC,Y Z
FOLL[S4
,,AVOID ,,]RORS
,REMEMB] 6*ECK ! GRAPHICAL SOLU;N 9
.BO? EQU,NS 2F 3CLUD+ T X IS A SOLU;N (!
SY/EM4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,EQU,N #A3 ,EQU,N #B
#D .;X @+ .;Y .K #H @3 #B .;X -- #C
.;Y .K #AH
#D7#C7 @+ 7--#D7 #H3 #B7#C7--#C 7--#D7
#AH
#AB--#D #H3 #F @+ #AB #AH
#H .K #H @3 #AH .K #AH
,! SOLU;N IS 7#C1 --#D74
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,GUID$ ,PRACTICE = ,EXAMPLE .#A
,GRAPH ! L9E> SY/EM & E/IMATE !
SOLU;N4 ,!N *ECK ! SOLU;N ALGEBRAIC,Y4
.#A4 #C .;X @+ #B .;Y .K --#D
.;X @+ #C .;Y .K #A
.#B4 #D .;X -- #E .;Y .K --#AJ
#B .;X -- #G .;Y .K #D
.#C4 #H .;X -- .;Y .K #H
#C .;X @+ #B .;Y .K --#AF
------------------------------------#AED
.,,CLASSIFY+ .,,SY/EMS ,A SY/EM T HAS
AT L1/ "O SOLU;N IS .3SI/5T4 ,IF A SY/EM
HAS NO SOLU;N1 ! SY/EM IS .9CONSI/5T4 ,A
3SI/5T SY/EM T HAS EXACTLY "O SOLU;N IS
.9DEP5D5T @1 &A 3SI/5T SY/EM T HAS
9F9ITELY _M SOLU;NS IS .DEP5D5T @4 ,!
SY/EM 9 ,EXAMPLE #A IS 3SI/5T &
9DEP5D5T4
,,KEY ,,3CEPT .= .,YR .,NOTEBOOK
,NUMB] ( ,SOLU;NS (A ,L9E> ,SY/EM
,! REL,N%IP 2T ! GRAPH (A L9E> SY/EM
&! SY/EM'S NUMB] ( SOLU;NS IS DESCRIB$
2L4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,EXACTLY "O SOLU;N3 ,9F9ITELY _M
SOLU;NS3 ,NO SOLU;N
@3 @3
,L9ES 9T]SECT AT "O PO9T2 3SI/5T &
9DEP5D5T3 ,L9ES CO9CIDE2 3SI/5T &
DEP5D5T3 ,L9ES >E P>ALLEL2 9CONSI/5T
,EXAMPLE #B ,SOLVE A SY/EM ) _M
SOLU;NS
,,*ECK ,,SOLU;N
,6*ECK YR SOLU;N 9 ,EXAMPLE #B1 OBS]VE
T BO? EQU,NS H ! SAME SLOPE-9T]CEPT =M3
,S ! GRAPHS >E ! SAME L9E4
,SOLVE ! SY/EM4 ,!N CLASSIFY ! SY/EM Z
..3SI/5T & 9DEP5D5T1 3SI/5T & .DEP5D5T
@1 OR .9CONSI/5T4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#D .;X -- #C .;Y .K #H @3 .,EQU,N .#A
#H .;X -- #F .;Y .K #AF @3 .,EQU,N .#B
,SOLU;N
,! GRAPHS (! EQU,NS >E ! SAME L9E4 ,S1
EA* PO9T ON ! L9E IS A SOLU;N1 &! SY/EM
HAS 9F9ITELY _M SOLU;NS4 ,"!=E1 ! SY/EM
IS 3SI/5T & DEP5D5T4
,EXAMPLE #C ,SOLVE A SY/EM ) NO SOLU;N
,,*ECK ,,SOLU;N
,6V]IFY T ! GRAPHS 9 ,EXAMPLE #C >E
P>ALLEL L9ES1 WRITE ! EQU,NS 9
SLOPE-9T]CEPT =M & OBS]VE T ! L9ES H !
SAME SLOPE1 --#B1 B DI6]5T ;Y-9T]CEPTS1
#D & #A4
,SOLVE ! SY/EM4 ,!N CLASSIFY ! SY/EM Z
..3SI/5T & 9DEP5D5T1 3SI/5T & .DEP5D5T
@1 OR .9CONSI/5T4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#B .;X @+ .;Y .K #D @3 .,EQU,N .#A
#B .;X @+ .;Y .K #A @3 .,EQU,N .#B
,SOLU;N
,! GRAPHS (! EQU,NS >E TWO P>ALLEL
L9ES4 ,2C ! TWO L9ES H NO PO9T (
9T]SEC;N1 ! SY/EM HAS NO SOLU;N4 ,"!=E1
! SY/EM IS 9CONSI/5T4
------------------------------------#AEE
..,EXAMPLE #D ,/&>DIZ$ ,TE/ .,PRACTICE
,Y RIDE AN EXPRESS BUS F ! C5T] ( T[N
6YR /REET4 ,Y H TWO PAY;T OP;NS4 ,OP;N
,A IS 6BUY A MON?LY PASS & PAY 4#A P]
RIDE4 ,OP;N ;,B IS 6PAY 4#B.EJ P] RIDE4
,A MON?LY PASS CO/S 4#CJ4 ,AF H[ _M
RIDES W ! TOTAL CO/S (! TWO OP;NS 2 !
SAME8
.,A #AB RIDES
.;,B #BJ RIDES
.;,C #BD RIDES
.;,D #BH RIDES
,SOLU;N
,EQU,N #A 7,OP;N ,A7
,EQU,N #B 7,OP;N ;,B7
,6SOLVE ! SY/EM1 GRAPH ! EQU,NS .;Y .K
.;X @+ #CJ & .;Y .K #B.E .;X @1 Z %[N AT
! "R4
,NOTICE T Y NE$ 6GRAPH ! EQU,NS ONLY 9
! F/ QUADRANT 2C ONLY NONNEGATIVE VALUES
( .;X & .;Y MAKE S5SE 9 ? SITU,N4
,! L9ES APPE> 69T]SECT AT AB ! PO9T
7#BJ1 #EJ74 ,Y C *ECK ? ALGEBRAIC,Y Z
FOLL[S4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.#EJ .K .#BJ @+ #CJ @3 .,EQU,N .#A
.*ECKS4
.#EJ .K #B.E7 .#BJ @7 @3 .,EQU,N .#B
.*ECKS4
,! TOTAL CO/S >E EQUAL AF #BJ RIDES4
,! CORRECT ANSW] IS ,B4 ..,A ;,B ;,C
.;,D
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,GUID$ ,PRACTICE = ,EXAMPLES #B1C1 &
.#D
,SOLVE ! SY/EM4 ,!N CLASSIFY ! SY/EM Z
..3SI/5T & 9DEP5D5T1 3SI/5T & .DEP5D5T
@1 OR .9CONSI/5T4
.#D4 #B .;X @+ #E .;Y .K #F
#D .;X @+ #AJ .;Y .K #AB
.#E4 #C .;X -- #B .;Y .K #AJ
#C .;X -- #B .;Y .K #B
.#F4 --#B .;X @+ .;Y .K #E
.;Y .K -- .;X @+ #B
.#G4 .,,:AT .,,IF8 ,9 ,EXAMPLE #D1
SUPPOSE ! CO/ (! MON?LY PASS IS 9CR1S$
TO 4#CF4 ,H[ DOES ? A6ECT ! SOLU;N8
------------------------------------#AEF
#C.A ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#D = ,EXS4 #I1BA1 & #CG
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 #B1AE1 #BI1 #CJ1 #CG1 & #CI
.K .,,MULTIPLE .,,REPRES5T,NS
,EX#.CH
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,A
3SI/5T SY/EM T HAS EXACTLY "O SOLU;N IS
CALL$ @8 @4
.#B4 .,,WRIT+ .,EXPLA9 H[ 6ID5TIFY !
SOLU;N7;S7 (A SY/EM F ! GRAPHS (! EQU,NS
9 ! SY/EM4
,,EXAMPLE #A
ON P4 #AEC = ,EXS4 #C-AF
,,GRAPH ,,& ,,*ECK ,GRAPH ! L9E> SY/EM
& E/IMATE ! SOLU;N4 ,!N *ECK ! SOLU;N
ALGEBRAIC,Y4
.#C4 .;Y .K --#C .;X @+ #B
.;Y .K #B .;X -- #C
.#D4 .;Y .K #E .;X @+ #B
.;Y .K #C .;X
.#E4 .;Y .K -- .;X @+ #C
-- .;X -- #C .;Y .K --#A
.#F4 .;X @+ #B .;Y .K #B
.;X -- #D .;Y .K #AD
.#G4 .;Y .K #B .;X -- #AJ
.;X -- #D .;Y .K #E
.#H4 -- .;X @+ #F .;Y .K --#AB
.;X @+ #F .;Y .K #AB
.#I4 .;Y .K --#C .;X -- #B
#E .;X @+ #B .;Y .K --#B
.#AJ4 .;Y .K --#C .;X -- #AC
-- .;X -- #B .;Y .K --#D
.#AA4 .;X -- #G .;Y .K #F
--#C .;X @+ #BA .;Y .K --#AH
.#AB4 .;Y .K #D .;X @+ #C
#BJ .;X -- #E .;Y .K --#AE
.#AC4 #E .;X -- #D .;Y .K #C
#C .;X @+ #B .;Y .K #AE
.#AD4 #G .;X @+ .;Y .K --#AG
#C .;X -- ;L#J .;Y .K #BD
#AE4 .,,MULTIPLE .,,*OICE ,:AT IS !
SOLU;N (! SY/EM8
--#D .;X -- .;Y .K #B
#G .;X @+ #B .;Y .K --#E
,A 7#B1 --#F7
;,B 7--#A1 #F7
;,C 7#A1 --#F7
;,D 7--#C1 #H7
#AF4 .,,]ROR .,,ANALYSIS ,A /UD5T US$
! *ECK %[N 63CLUDE T 7#J1 --#A7 IS A
SOLU;N ( ? SY/EM3
#C .;X -- #B .;Y .K #B
.;X @+ #B .;Y .K #F
.,DESCRIBE & CORRECT ! /UD5T'S ]ROR4
,,EXAMPLES #B & #C
ON P4 #AED = ,EXS4 #AG--#BI
,,SOLVE ,,& ,,CLASSIFY ,SOLVE ! SY/EM4
,!N CLASSIFY ! SY/EM Z ..3SI/5T &
9DEP5D5T1 3SI/5T & .DEP5D5T @1 OR
.9CONSI/5T4
.#AG4 .;Y .K --#A
#C .;X @+ .;Y .K #E
.#AH4 #B .;X -- .;Y .K #D
.;X -- #B .;Y .K --#A
.#AI4 .;Y .K #C .;X @+ #B
.;Y .K #C .;X -- #B
.#BJ4 .;Y .K #B .;X -- #A
--#F .;X @+ #C .;Y .K --#C
.#BA4 --#BJ .;X @+ #AB .;Y .K --#BD
#E .;X -- #C .;Y .K #F
.#BB4 #D .;X -- #E .;Y .K #J
#C .;X -- #E .;Y .K --#E
.#BC4 #C .;X @+ #G .;Y .K #F
#B .;X @+ #I .;Y .K #D
.#BD4 #D .;X @+ #E .;Y .K #C
#F .;X @+ #I .;Y .K #I
.#BE4 #H .;X @+ #I .;Y .K #AE
#E .;X -- #B .;Y .K #AG
.#BF4
.#BG4
.#BH4
------------------------------------#AEG
#BI4 .,,MULTIPLE .,,*OICE ,H[ WD Y
CLASSIFY ! SY/EM8
--#AB .;X @+ #AF .;Y .K #AJ
#C .;X @+ #D .;Y .K --#F
,A ,3SI/5T & 9DEP5D5T
;,B ,3SI/5T & DEP5D5T
;,C ,9CONSI/5T
;,D ,N"O ( ^!
#CJ4 .,,OP5-.,,5D$ .,,MA? ,WRITE A
SY/EM ( TWO L9E> EQU,NS T HAS ! GIV5
NUMB] ( SOLU;NS4
A4 ,"O SOLU;N
B4 ,NO SOLU;N
C4 ,9F9ITELY _M SOLU;NS
,,GRAPH ,,& ,,*ECK ,GRAPH ! SY/EM &
E/IMATE ! SOLU;N 7;S74 ,!N *ECK ! SOLU;N
7;S7 ALGEBRAIC,Y4
.#CA4 .;Y .K _\ .;X @+ #B_\
.;Y .K .;X
.#CB4 .;Y .K_\ .;X -- ;L_\
.;Y .K -- .;X @+ #D
.#CC4 .;Y .K _\ .;X _\--#B
.;Y .K #B
.#CD4 .,,*ALL5GE ,/ATE ! 3DI;NS ON !
3/ANTS .A1 .;B1 .;C @1 & .;D = : ! SY/EM
2L IS @7 .A @7 3SI/5T & 9DEP5D5T1 @7 .;B
@7 3SI/5T & DEP5D5T1 & @7 .;C @7
9CONSI/5T4
.;Y .K .AX @+ .;B
.;Y .K .CX @+ .;D
,PRO#M ,SOLV+
,,EXAMPLE #D
ON P4 #AEE = ,EXS4 #CE-CI
.#CE4 .,,"W .,,S*$ULE ,Y "W$ #AD H\RS
LA/ WEEK & E>N$ A TOTAL ( 4#IF 2F TAXES4
,YR JOB Z A LIFEGU>D PAYS 4#H P] H\R1 &
YR JOB Z A CA%I] PAYS 4#F P] H\R4 ,H[ _M
H\RS DID Y "W AT EA* JOB8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#CF4 .,,LAW .,,5=CE;T ,DUR+ "O CAL5D>
YE>1 A /ATE TROOP] ISSU$ A TOTAL ( #CGE
CIT,NS = W>N+S & SPE$+ TICKETS4 ,( ^!1
"! 7 #CG M W>N+S ?AN SPE$+ TICKETS4 ,H[
_M W>N+S & H[ _M SPE$+ TICKETS 7 ISSU$8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#CG4 .,,%ORT .,,RESPONSE ,A GYM (F]S
TWO OP;NS = MEMB]%IP PLANS4 ,OP;N ,A
9CLUDES AN 9ITI,N FEE ( 4#ABA & CO/S 4#A
P] "D4 ,OP;N ;,B HAS NO 9ITI,N FEE B
CO/S 4#AB P] "D4 ,AF H[ _M "DS W ! TOTAL
CO/S (! GYM MEMB]%IP PLANS 2 EQUAL8 ,H[
DOES YR ANSW] *ANGE IF ! DAILY CO/ (
,OP;N ;,B 9CR1SES8 .,EXPLA94
#CH4 .,,MULTIPLE .,,REPRES5T,NS ,!
PRICE ( REFRIG]ATOR ,A IS 4#FJJ1 &!
PRICE ( REFRIG]ATOR ;,B IS 4#ABJJ4 ,!
CO/ ( ELECTRIC;Y NE$$ 6OP]ATE !
REFRIG]ATORS IS 4#EJ P] YE> =
REFRIG]ATOR ,A& 4#DJ P] YE> =
REFRIG]ATOR ,B4
A4 .,WRIT+ .,EQU,NS ,WRITE AN EQU,N =!
CO/ ( [N+ REFRIG]ATOR ,A& AN EQU,N =!
CO/ ( [N+ REFRIG]ATOR ,B4
B4 .,GRAPH+ .,EQU,NS ,GRAPH ! EQU,NS F
"P 7A74 ,AF H[ _M YE>S >E ! TOTAL CO/S (
[N+ ! REFRIG]ATORS EQUAL8
C4 .,*ECK+ .,R1SONA#;S ,IS YR SOLU;N F
"P 7;B7 R1SONA# 9 ? SITU,N8 .,EXPLA94
------------------------------------#AEH
#CI4 .,,EXT5D$ .,,RESPONSE ,! TA# 2L
GIVES ! W9N+ "TS 7IN SECONDS7 9 !
,OLYMPIC #AJJ MET] FREE/YLE SWIMM+ EV5T
=! P]IOD #AIGB-BJJJ4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,YE>S S9CE #AIGB1 .;X @3 .#J @3 .#D @3
.#H @3 .#AB @3 .#AF @3 .#BJ @3 .#BD @3
.#BH
,M5'S "T1 .;M @3 .#EA..B @3 .#EJ..J @3
.#EJ..D @3 .#DI..H @3 .#DH..F @3 .#DI..J
@3 .#DH..G @3 .#DH..C
,WOM5'S "T1 .;W @3 .#EH..F @3 .#EE..G
@3 .#ED..H @3 .#EE..I @3 .#ED..I @3
.#ED..F @3 .#ED..D @3 .#EC..H
A4 ,USE A GRAPH+ CALCULATOR 6FIT A L9E
6! DATA PAIRS @7 .;X1 .;M @7@4
B4 ,USE A GRAPH+ CALCULATOR 6FIT A L9E
6! DATA PAIRS @7 .;X1 .;W @7@4
C4 ,GRAPH ! L9ES & PREDICT :5 ! WOM5'S
P]=M.E W CAT* UP 6! M5'S P]=M.E4
D4 ,D Y ?9K YR PREDIC;N F "P 7;C7 IS
R1SONA#8 .,EXPLA94
#DJ4 .,,*ALL5GE ,YR H\SE & YR FR'S
H\SE >E BO? ON A /REET T PASSES 0A P>K1
Z %[N 2L4
,AT #A3JJ ,P4,M41 Y & YR FR L1VE YR
H\SES ON BICYCLES & H1D T[>D ! P>K4 ,Y
TRAVEL AT A SPE$ ( #BE FEET P] SECOND1 &
YR FR AL TRAVELS AT A 3/ANT SPE$4 ,Y BO?
R1* ! P>K AT ! SAME "T4
A4 ,WRITE & GRAPH AN EQU,N GIV+ YR
4T.E .;D 7IN FEET7 F ! P>K AF .;T
SECONDS4
B4 ,AT :AT SPE$ DOES YR FR TRAVEL 6!
P>K8 .,EXPLA9 H[ Y F.D YR ANSW]4
C4 ,WRITE AN EQU,N GIV+ YR FR'S 4T.E
.;D 7IN FEET7 F ! P>K AF .;T SECONDS4
,GRAPH ! EQU,N 9 ! SAME COORD9ATE PLANE
Y US$ = "P 7A74
,MIX$ ,REVIEW
,SOLVE ! EQU,N4
#DA4 #H .;X @+ #A .K #C .;X - #AD @7
P4 #AH @7
#DB4 -#D7 .;X @+ #C7 .K #E .;X @+ #I
@7 P4 #AH @7
#DC4 @7 P4 #AH @7
#DD4 _\ .;X - #AH_\ .K #I @7 P4 #EA @7
#DE4 _\#B .;X @+ #E_\ .K #AB @7 P4 #EA
@7
#DF4 _\#E .;X - #AH_\ .K #AG @7 P4 #EA
@7
..,SOLVE ! EQU,N = ;Y @4 ,!N F9D !
VALUE ( ;Y =! GIV5 VALUE ( .;X @4 @7 P4
#BF @7
.,,PREVIEW ,PREP>E = ,LESSON #C.B 9
,EXS4 #DG-EB4
#DG4 #C .;X - #B .;Y .K #H2 .;X .K -#B
#DH4 -#E .;X @+ .;Y .K -#AB2 .;X .K #I
#DI4 #H .;X - #C .;Y .K #AJ2 .;X .K #H
#EJ4 #H .;X - #B .;Y .K #G2 .;X .K -#A
#EA4 #AF .;X @+ #I .;Y .K -#BD2 .;X .K
-#F
#EB4 -#AB .;X @+ #I .;Y .K -#FJ2 .;X
.K -#G
#EC4 .,,VET]9>Y .,,M$IC9E ,! NORMAL
BODY TEMP]ATURE (A DOG IS #CH;DG,C4 ,YR
DOG'S TEMP]ATURE IS #AJA;DG,F4 ,DOES YR
DOG H A FEV]8 .,EXPLA94 @7 P4 #CF @7
.,,EXTRA .,,PRACTICE = ,LESSON #C.A1
P4 #AJAB
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#AEI
,GRAPH+ ,CALCULATOR ,ACTIV;Y3 #C.A
,GRAPH ,SY/EMS ( ,EQU,NS
,USE AF ,LESSON #C.A
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,KEY/ROKES
,SIDEB>3
,/&>DS
..#B.J ,/UD5TS SOLVE SY/EMS ( L9E>
.EQU,NS & 9EQUALITIES @7 .9 .TWO OR ?REE
.V>IA#S @7 0SUB/ITU;N1 .) .GRAPHS @1 OR
) MATRICES4
,"Q ,H[ C Y SOLVE A SY/EM ( L9E>
EQU,NS US+ A GRAPH+ CALCULATOR8
,9 ,LESSON #C.A1 Y LE>N$ 6.E/IMATE !
SOLU;N (A L9E> SY/EM 0GRAPH+4 ,Y C USE !
.9T]SECT F1TURE (A GRAPH+ CALCULATOR
6GET AN ANSW] T IS V CLOSE TO1 & "S"TS
.EXACTLY EQUAL TO1 ! ACTUAL SOLU;N4
,EXAMPLE ,SOLVE A SY/EM
,USE A GRAPH+ CALCULATOR 6SOLVE !
SY/EM4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#F .;X -- #I .;Y .K --#BJ @3 .,EQU,N
.#A
#B .;X @+ #D .;Y .K --#EB @3 .,EQU,N
.#B
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
..,,/EP #A ,5T] .EQU,NS @3 ..,,/EP #B
,GRAPH .EQU,NS @3 ..,,/EP #C ,F9D !
.SOLU;N
,SOLVE EA* EQU,N = .;Y @4 ,!N 5T] !
REVIS$ EQU,NS 96A GRAPH+ CALCULATOR4 @3
,GRAPH ! EQU,NS 9 ! /&>D VIEW+ W9D[43
,ADJU/ ! VIEW+ W9D[1 & USE ! .9T]SECT
F1TURE 6F9D ! 9T]SEC;N PO9T4
@3 @3
,! SOLU;N IS AB 7--#AC.JE1 --#F.DH74
,PRACTICE
,SOLVE ! L9E> SY/EM US+ A GRAPH+
CALCULATOR4
.#A4 .;Y .K -- .;X @+ #B
.;Y .K #B .;X -- #E
.#B4 .;Y .K --#B .;X @+ #AE
.;Y .K #E .;X -- #D
.#C @4 --#I .;X @+ #G .;Y .K #AD
--#C .;X @+ .;Y .K --#AG
.#D4 --;LL .;X -- #F .;Y .K --#F
#D .;X @+ #B .;Y .K #AJ
.#E4 #E .;X @+ #H .;Y .K --#DH
.;X @+ #C .;Y .K #BG
.#F @4 --#B .;X @+ #AF .;Y .K #EF
#D .;X @+ #G .;Y .K --#CE
.#G4 .,,VAC,N ,YR FAMILY IS PLANN+ A
#G "D TRIP 6,TEXAS4 ,Y E/IMATE T X W CO/
4#BGE P] "D 9 ,SAN ,ANTONIO & 4#DJJ P]
"D 9 ,DALLAS4 ,YR BUDGET =! #G "DS IS
4#BCJJ4 ,H[ _M "DS %D Y SP5D 9 EA* C;Y8
.#H4 .,,MOVIE .,,TICKETS ,9 "O "D1 A
MOVIE !AT] COLLECT$ 4#DFJJ F #HJJ P4 ,!
PRICE ( ADMIS.N IS 4#G = AN ADULT & 4#E
=A *4 ,H[ _M ADULTS & H[ _M *N 7 ADMITT$
6! MOVIE !AT] T "D8
------------------------------------#AFJ
#C.B ,SOLVE ,L9E> ,SY/EMS
,ALGEBRAIC,Y
.,2F ,Y SOLV$ L9E> SY/EMS GRAPHIC,Y4
.,N[ ,Y W SOLVE L9E> SY/EMS
ALGEBRAIC,Y4
.,:Y8 ,S Y C MODEL GUIT> SALES1 Z 9
,EX4 #EE4
,KEY ,VOCABUL>Y
99 .SUB/ITU;N .ME?OD
99 .ELIM9,N .ME?OD
,SIDEB>3
,/&>DS
..#B.J ,/UD5TS SOLVE SY/EMS ( L9E>
.EQU,NS & 9EQUALITIES @7 .9 .TWO OR ?REE
.V>IA#S @7 0SUB/ITU;N1 ) GRAPHS1 OR )
MATRICES4
,9 ? LESSON1 Y W /UDY TWO ALGEBRAIC
ME?ODS = SOLV+ L9E> SY/EMS4 ,! F/ ME?OD
IS CALL$ ! .SUB/ITU;N .ME?OD4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,! ,SUB/ITU;N ,ME?OD
.,,/EP .#A .,SOLVE "O (! EQU,NS = "O (
XS V>IA#S4
.,,/EP .#B .,SUB/ITUTE ! EXPRES.N F
,/EP #A 96! O!R EQU,N & SOLVE =! O!R
V>IA#4
.,,/EP .#C .,SUB/ITUTE ! VALUE F ,/EP
#B 96! REVIS$ EQU,N F ,/EP #A & SOLVE4
,EXAMPLE #A ,USE ! SUB/ITU;N ME?OD
,SOLVE ! SY/EM US+ ! SUB/ITU;N ME?OD4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#B .;X @+ #E .;Y .K --#E @3 .,EQU,N
.#A
.;X @+ #C .;Y .K #C @3 .,EQU,N .#B
,SOLU;N
.,,/EP .#A .,SOLVE ,EQU,N #B = .;X @4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X .K --#C .;Y @+ #C @3 .,REVIS$
.,EQU,N .#B
.,,/EP .#B .,SUB/ITUTE ! EXPRES.N =
.;X 96,EQU,N #A & SOLVE = .;Y @4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#B .;X @+ #E .;Y .K --#E @3 .,WRITE
.,EQU,N .#A4
#B7--#C .;Y @+ #C7 @+ #E .;Y .K --#E
@3 ,SUB/ITUTE --#C .;Y @+ #C =.' ;X @4
.;Y .K #AA @3 ,SOLVE =.' ;Y @4
.,,/EP .#C .,SUB/ITUTE ! VALUE ( .;Y
96REVIS$ ,EQU,N #B & SOLVE = .X4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X .K --#C .;Y @+ #C @3 ..,WRITE
REVIS$ ,EQU,N .#B4
.;X .K --#C7#AA7 @+ #C @3 ,SUB/ITUTE
#AA =.' ;Y @4
.;X .K --#CJ @3 .,SIMPLIFY4
,! SOLU;N IS 7--#CJ1AA74
.,,*ECK ,*ECK ! SOLU;N 0SUB/ITUT+ 96!
ORIG9AL EQU,NS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#B7--#CJ7 @+ #E7#AA7 --#E3 ,SUB/ITUTE
=.' ;X .-&.' ;Y @4 @3 --#CJ @+ #C7#AA7
#C
--#E .K --#E @3 .,SOLU;N .*ECKS4 @3 #C
.K #C
------------------------------------#AFA
.,,ELIM9,N .,,ME?OD ,ANO!R ALGEBRAIC
ME?OD T Y C USE 6SOLVE A SY/EM ( EQU,NS
IS ! .ELIM9,N .ME?OD4 ,! GOAL ( ? ME?OD
IS 6ELIM9ATE "O (! V>IA#S 0A4+ EQU,NS4
,,KEY ,,3CEPT .= .,YR .,NOTEBOOK
,! ,ELIM9,N ,ME?OD
.,,/EP .#A .,MULTIPLY "O OR BO? (!
EQU,NS 0A 3/ANT 6OBTA9 COE6ICI5TS T DI6]
ONLY 9 SIGN = "O (! V>IA#S4
.,,/EP .#B .,ADD ! REVIS$ EQU,NS F
,/EP #A4 ,-B9+ L T]MS W ELIM9ATE "O (!
V>IA#S4 ,SOLVE =! REMA9+ V>IA#4
.,,/EP .#C .,SUB/ITUTE ! VALUE OBTA9$
9 ,/EP #B 96EI (! ORIG9AL EQU,NS & SOLVE
=! O!R V>IA#4
..,EXAMPLE #B ,USE ! ELIM9,N .ME?OD
,SOLVE ! SY/EM US+ ! ELIM9,N ME?OD4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#C .;X -- #G .;Y .K #AJ @3 .,EQU,N .#A
#F .;X -- #H .;Y .K #H @3 .,EQU,N .#B
,,SOLVE ,,SY/EMS
,9 ,EXAMPLE #B1 "O COE6ICI5T ( .;X IS
A MULTIPLE (! O!R4 ,9 ? CASE1 X IS EASI]
6ELIM9ATE ! .;X -T]MS 2C Y NE$ 6MULTIPLY
ONLY "O EQU,N 0A 3/ANT4
,SOLU;N
.,,/EP .#A .,MULTIPLY ,EQU,N #A BY
--.#B S T ! COE6ICI5TS ( .;X DI6] ONLY 9
SIGN4
.,,/EP .#B .,ADD ! REVIS$ EQU,NS &
SOLVE = .Y4
.,,/EP .#C .,SUB/ITUTE ! VALUE ( .;Y
96"O (! ORIG9AL EQU,NS4 ,SOLVE = .X4
,! SOLU;N IS @4
.,,*ECK ,Y C *ECK ! SOLU;N ALGEBRAIC,Y
US+ ! ME?OD %[N 9 ,EXAMPLE #A4 ,Y C AL
USE A GRAPH+ CALCULATOR 6*ECK ! SOLU;N4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,GUID$ ,PRACTICE = ,EXAMPLES #A &
.#B
,SOLVE ! SY/EM US+ ! SUB/ITU;N OR !
ELIM9,N ME?OD4
.#A4 #D .;X @+ #C .;Y .K --#B
.;X @+ #E .;Y .K --#I
.#B4 #C .;X @+ #C .;Y .K --#AE
#E .;X -- #I .;Y .K #C
.#C4 #C .;X -- #F .;Y .K #I
--#D .;X @+ #G .;Y .K --#AF
------------------------------------#AFB
..,EXAMPLE #C ,/&>DIZ$ ,TE/ .,PRACTICE
,6RAISE M"OY = NEW FOOTBALL UNI=MS1 YR
S*OOL SELLS SILK-SCRE5$ ;,T-%IRTS4 ,%ORT
SLEEVE ;,T-%IRTS CO/ ! S*OOL 4#E EA* &
>E SOLD = 4#H EA*4 ,L;G SLEEVE ;,T-%IRTS
CO/ ! S*OOL 4#G EA* & >E SOLD = 4#AB
EA*4 ,! S*OOL SP5DS A TOTAL ( 4#BEJJ ON
;,T-%IRTS & SELLS ALL ( !M = 4#DBJJ4 ,H[
_M (! %ORT SLEEVE ;,T-%IRTS >E SOLD8
.,A #EJ
.;,B #AJJ
.;,C #AEJ
.;,D #BEJ
,SOLU;N
.,,/EP .#A .,WRITE V]BAL MODELS = ?
SITU,N4
,EQU,N #A
,EQU,N #B
.,,/EP .#B .,WRITE A SY/EM ( EQU,NS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,EQU,N .#A @3 #E .;X @+ #G .;Y .K
#BEJJ @3 ..,TOTAL CO/ = ALL ;,T-.%IRTS
.,EQU,N .#B @3 #H .;X @+ #AB .;Y .K
#DBJJ @3 ..,TOTAL REV5UE F ALL ;,T-%IRTS
.SOLD
.,,/EP .#C .,SOLVE ! SY/EM US+ !
ELIM9,N ME?OD4
.,MULTIPLY ,EQU,N #A BY --.#H & ,EQU,N
#B 0.#E S T ! COE6ICI5TS ( .;X DI6] ONLY
9 SIGN4
.,ADD ! REVIS$ EQU,NS & SOLVE = .;Y @4
,,AVOID ,,]RORS
,*OICE ;,D GIVES ! NUMB] ( .L;G SLEEVE
;,T-%IRTS1 B ! "Q ASKS =! NUMB] ( .%ORT
SLEEVE ;,T-%IRTS4 ,S Y / NE$ 6SOLVE =
.;X 9 ,/EP #C4
.,SUB/ITUTE ! VALUE ( .;Y 96"O (!
ORIG9AL EQU,NS & SOLVE = .X4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#E .;X @+ #G .;Y .K #BEJJ @3 .,WRITE
.,EQU,N .#A4
#E .;X @+ #G7#BEJ7 .K #BEJJ @3
,SUB/ITUTE #BEJ =.' ;Y @4
#E .;X @+ #AGEJ .K #BEJJ @3
.,SIMPLIFY4
.;X .K #AEJ @3 ,SOLVE =.' ;X @4
,! S*OOL SOLD #AEJ %ORT SLEEVE
;,T-%IRTS & #BEJ L;G SLEEVE ;,T-%IRTS4
,! CORRECT ANSW] IS ,C4 ..,A ;,B ;,C
.;,D
------------------------------------#AFC
..,GUID$ ,PRACTICE = ,EXAMPLES .#C
.#D4 .,,:AT .,,IF8 ,9 ,EXAMPLE #C1
SUPPOSE ! S*OOL SP5DS A TOTAL ( 4#CGAE
ON ;,T-%IRTS & SELLS ALL ( !M = 4#FAFJ4
,H[ _M ( EA* TYPE ( ;,T-%IRT >E SOLD8
.,,*OOS+ .,A .,,ME?OD ,9 G5]AL1 !
SUB/ITU;N ME?OD IS 3V5I5T :5 "O (!
V>IA#S 9 A SY/EM ( EQU,NS HAS A
COE6ICI5T ( #A OR --#A1 Z 9 ,EXAMPLE #A4
,IF NEI V>IA# 9 A SY/EM HAS A COE6ICI5T
( #A OR --#A1 X IS USU,Y EASI] 6USE !
ELIM9,N ME?OD1 Z 9 ,EXAMPLES #B & #C4
,EXAMPLE #D ,SOLVE L9E> SY/EMS ) _M OR
NO SOLU;NS
,SOLVE ! L9E> SY/EM4
.A4 .;X -- #B .;Y .K #D
#C .;X -- #F .;Y .K #H
.B4 #D .;X -- ;L#J .;Y .K #H
--#AD .;X @+ #CE .;Y .K --#BH
,SOLU;N
.A4 ,2C ! COE6ICI5T ( .;X 9 ! F/ EQU,N
IS #A1 USE ! SUB/ITU;N ME?OD4
.,SOLVE ! F/ EQU,N = .X4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X -- #B .;Y .K #D @3 .,WRITE .F/
.EQU,N4
.;X .K #B .;Y @+ #D @3 ,SOLVE =.' ;X
@4
.,SUB/ITUTE ! EXPRES.N = .;X 96!
SECOND EQU,N4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#C .;X -- #F .;Y .K #H @3 .,WRITE
.SECOND .EQU,N4
#C 7#B .;Y @+ #D7--#F .;Y .K #H @3
,SUB/ITUTE #B .;Y @+ #D =.' ;X @4
#AB .K #H3 .,SIMPLIFY4
,2C ! /ATE;T #AB .K #H IS N"E TRUE1 "!
IS .NO .SOLU;N4
.B4 ,2C NO COE6ICI5T IS #A OR --#A1
USE ! ELIM9,N ME?OD4
.,MULTIPLY ! F/ EQU,N 0#G &! SECOND
EQU,N 0.#B4
.,ADD ! REVIS$ EQU,NS4
,2C ! EQU,N #J .K #J IS ALW TRUE1 "!
>E .9F9ITELY ._M .SOLU;NS4
,,AVOID ,,]RORS
,:5 MULTIPLY+ AN EQU,N 0A 3/ANT1 MAKE
SURE Y MULTIPLY EA* T]M (! EQU,N 0!
3/ANT4
..,GUID$ ,PRACTICE = ,EXAMPLE .#D
,SOLVE ! L9E> SY/EM US+ ANY ALGEBRAIC
ME?OD4
.#E4 #AB .;X -- #C .;Y .K --#I
--#D .;X @+ .;Y .K #C
.#F4 #F .;X @+ #AE .;Y .K --#AB
--#B .;X -- #E .;Y .K #I
.#G4
.#H4 #AB .;X -- #B .;Y .K #BA
#C .;X @+ #AB .;Y .K --#D
.#I4 #H .;X @+ #I .;Y .K #AE
#E .;X -- #B .;Y .K #AG
.#AJ4 #E .;X @+ #E .;Y .K #E
#E .;X @+ #C .;Y .K #D.B
------------------------------------#AFD
#C.B ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#E = ,EXS4 #E1 #BI1 & #EI
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 #B1DJ1 #EJ1 #EG1 #EH1 & #FJ
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3
,6SOLVE A L9E> SY/EM ": "O (! COE6ICI5TS
IS #A OR --#A1 X IS USU,Y EASIE/ 6USE !
@8 ME?OD4
.#B4 .,,WRIT+ .,EXPLA9 H[ 6USE !
ELIM9,N ME?OD 6SOLVE A L9E> SY/EM4
,,EXAMPLES #A & #D
ON PP4 #AFJ-AFC = ,EXS4 #C-AD
,,SUB/ITU;N ,,ME?OD ,SOLVE ! SY/EM US+
! SUB/ITU;N ME?OD4
.#C4 #B .;X @+ #E .;Y .K#G
.;X @+ #D .;Y .K #B
.#D4 #C .;X @+ .;Y .K #AF
#B .;X -- #C .;Y .K --#D
.#E4 #F .;X -- #B .;Y .K #E
--#C .;X @+ .;Y .K #G
.#F4 .;X @+ #D .;Y .K #A
#C .;X @+ #B .;Y .K --#AB
.#G4 #C .;X -- .;Y .K #B
#F .;X @+ #C .;Y .K #AD
.#H4 #C .;X -- #D .;Y .K --#E
-- .;X @+ #C .;Y .K --#E
.#I4 #C .;X @+ #B .;Y .K #F
.;X -- #D .;Y .K --#AB
.#AJ4 #F .;X -- #C .;Y .K #AE
--#B .;X @+ .;Y .K --#E
.#AA4 #C .;X @+ .;Y .K --#A
#B .;X @+ #C .;Y .K #AH
.#AB4 #B .;X -- .;Y .K #A
#H .;X @+ #D .;Y .K #F
.#AC4 #C .;X @+ #G .;Y .K #AC
.;X @+ #C .;Y .K --#G
.#AD4 #B .;X @+ #E .;Y .K #AJ
--#C .;X @+ .;Y .K #CF
,,EXAMPLES #B & #D
ON PP4 #AFA-AFC = ,EXS4 #AE-BG
,,ELIM9,N ,,ME?OD ,SOLVE ! SY/EM US+ !
ELIM9,N ME?OD4
.#AE4 #B .;X @+ #F .;Y .K #AG
#B .;X -- ;L#J .;Y .K #I
.#AF4 #D .;X -- #B .;Y .K --#AF
--#C .;X @+ #D .;Y .K #AB
.#AG4 #C .;X -- #D .;Y .K --#AJ
#F .;X @+ #C .;Y .K --#DB
.#AH4 #D .;X -- #C .;Y .K #AJ
#H .;X -- #F .;Y .K #BJ
.#AI4 #E .;X -- #C .;Y .K --#C
#B .;X @+ #F .;Y .K #J
.#BJ4 ;L#J .;X -- #B .;Y .K #AF
#E .;X @+ #C .;Y .K --#AB
.#BA4 #B .;X @+ #E .;Y .K #AD
#C .;X -- #B .;Y .K --#CF
.#BB4 #G .;X @+ #B .;Y .K #AA
--#B .;X @+ #C .;Y .K #BI
.#BC4 #C .;X @+ #D .;Y .K #AH
#F .;X @+ #H .;Y .K #AH
.#BD4 #B .;X @+ #E .;Y .K #AC
#F .;X @+ #B .;Y .K --#AC
.#BE4 #D .;X -- #E .;Y .K #AC
#F .;X @+ #B .;Y .K #DH
.#BF4 #F .;X -- #D .;Y .K #AD
#B .;X @+ #H .;Y .K #BA
.#BG4 .,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 ! F/ /EP ( SOLV+ !
SY/EM4
#C .;X @+ #B .;Y .K #G
#E .;X @+ #D .;Y .K #AE
,,*OOS+ ,A ,,ME?OD ,SOLVE ! SY/EM US+
ANY ALGEBRAIC ME?OD4
.#BH4 #C .;X @+ #B .;Y .K #AA
#D .;X @+ .;Y .K --#B
.#BI4 #B .;X -- #C .;Y .K #H
--#D .;X @+ #E .;Y .K --#AJ
.#CJ4 #C .;X @+ #G .;Y .K --#A
#B .;X @+ #C .;Y .K #F
.#CA4 #D .;X -- ;L#J .;Y .K #AH
--#B .;X @+ #E .;Y .K --#I
.#CB4 #C .;X -- .;Y .K --#B
#E .;X @+ #B .;Y .K #AE
.#CC4 .;X @+ #B .;Y .K --#H
#C .;X -- #D .;Y .K --#BD
.#CD4 #B .;X @+ #C .;Y .K --#F
#C .;X -- #D .;Y .K #BE
.#CE4 #C .;X @+ .;Y .K #AE
-- .;X @+ #B .;Y .K --#AI
.#CF4 #D .;X -- #C .;Y .K #H
--#H .;X @+ #F .;Y .K #AF
.#CG4 #D .;X -- .;Y .K --#AJ
#F .;X @+ #B .;Y .K --#A
.#CH4 #G .;X @+ #E .;Y .K --#AB
#C .;X -- #D .;Y .K #A
.#CI4 #B .;X @+ .;Y .K --#A
--#D .;X @+ #F .;Y .K #F
------------------------------------#AFE
#DJ4 .,,MULTIPLE .,,*OICE ,:AT IS !
SOLU;N (! L9E> SY/EM8
#C .;X @+ #B .;Y .K #D
#F .;X -- #C .;Y .K --#BG
,A 7--#B1 --#E7
;,B 7--#B1 #E7
;,C 7#B1 --#E7
;,D 7#B1 #E7
..,,GEOMETRY ,F9D ! COORD9ATES (! PO9T
": ! DIAGONALS (! QUADRILAT]AL .9T]SECT4
.#DA4
.#DB4
.#DC4
,,SOLV+ ,,L9E> ,,SY/EMS ,SOLVE ! SY/EM
US+ ANY ALGEBRAIC ME?OD4
.#DD4 #J.JB .;X -- #J.JE .;Y .K
--#J.CH
#J.JC .;X @+ #J.JD .;Y .K #A.JD
.#DE4 #J.JE .;X -- #J.JC .;Y .K #J.BA
#J.JG .;X @+ #J.JB .;Y .K #J.AF
.#DF4
.#DG4
.#DH4
.#DI4
.#EJ4 .,,OP5-.,,5D$ .,,MA? ,WRITE A
SY/EM ( L9E> EQU,NS T HAS 7--#A1 #D7 Z
XS ONLY SOLU;N4 ,V]IFY T 7--#A1 #D7 IS A
SOLU;N US+ EI ! SUB/ITU;N ME?OD OR !
ELIM9,N ME?OD4
,,SOLV+ ,,NONL9E> ,,SY/EMS ,USE !
ELIM9,N ME?OD 6SOLVE ! SY/EM4
.#EA4 #G .;Y @+ #AH .XY .K #CJ
#AC .;Y -- #AH .XY .K #IJ
.#EB4 .XY -- .;X .K #AD
#E -- .XY .K #B .;X
.#EC4 #B .XY @+ .;Y .K #DD
#CB -- .XY .K #C .;Y
#ED4 .,,*ALL5GE ,F9D VALUES ( ;R1 .;S
@1 & .;T T PRODUCE ! 9DICAT$ SOLU;N7;S74
--#C .;X -- #E .;Y .K #I
.RX @+ .SY .K .;T
A4 ,NO SOLU;N
B4 ,9F9ITELY _M SOLU;NS
C4 ,A SOLU;N ( 7#B1 --#C7
,PRO#M ,SOLV+
,,EXAMPLE #C
ON P4 #AFB = ,EXS4 #EE-EI
.#EE4 .,,GUIT> .,,SALES ,9 "O WEEK1 A
MUSIC /ORE SOLD #I GUIT>S =A TOTAL (
4#CFAA4 ,ELECTRIC GUIT>S SOLD = 4#DGI
EA* & AC\/IC GUIT>S SOLD = 4#CCI EA*4
,H[ _M ( EA* TYPE ( GUIT> 7 SOLD8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#EF4 .,,C.TY .,,FAIR ,AN ADULT PASS
=A C.TY FAIR CO/S 4#B M ?AN A *N'S PASS4
,:5 #CGH ADULT & #BAD *N'S PASSES 7
SOLD1 ! TOTAL REV5UE 0 4#BCHD4 ,F9D !
CO/ ( AN ADULT PASS4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
------------------------------------#AFF
.#EG4 .,,%ORT .,,RESPONSE ,A -PANY
PRODUCES GAS M[]S & ELECTRIC M[]S AT TWO
FACTORIES4 ,! -PANY HAS ORD]S = #BBJJ
GAS M[]S & #ADJJ ELECTRIC M[]S4 ,!
PRODUC;N CAPAC;Y ( EA* FACTORY 7IN M[]S
P] WEEK7 IS %[N 9 ! TA#4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 ,FACTORY ,A3 ,FACTORY ;,B
.,GAS .M[]S @3 .#BJJ @3 .#DJJ
.,ELECTRIC .M[]S @3 .#AJJ @3 .#CJJ
.,DESCRIBE H[ ! -PANY C FILL XS ORD]S
0OP]AT+ ! FACTORIES SIMULTANE\SLY AT
FULL CAPAC;Y4 ,WRITE & SOLVE A L9E>
SY/EM 6SUPPORT YR ANSW]4
#EH4 .,,MULTIPLE .,,*OICE ,! CO/ ( #AA
GALLONS ( REGUL> GASOL9E & #AF GALLONS (
PREMIUM GASOL9E IS 4#EH.EE4 ,PREMIUM
CO/S @4#.BJ M P] GALLON ?AN REGUL>4 ,:AT
IS ! CO/ (A GALLON ( PREMIUM GASOL9E8
,A 4#B.JE
;,B 4#B.BE
;,C 4#B.BI
;,D 4#B.EE
.#EI4 .,,TA# .,,T5NIS ,"O EV5+1 #GF P
GA!R$ 6PLAY D\#S & S+LES TA# T5NIS4 ,"!
7 #BF GAMES 9 PROGRESS AT "O "T4 ,A D\#S
GAME REQUIRES #D PLAY]S &A S+LES GAME
REQUIRES #B PLAY]S4 ,H[ _M GAMES ( EA*
K9D 7 9 PROGRESS AT "O "T IF ALL #GF P 7
PLAY+8
#FJ4 .,,EXT5D$ .,,RESPONSE ,A LOCAL
HOSPITAL IS HOLD+ A TWO "D M>A?ON WALK
6RAISE FUNDS =A NEW RESE>* FACIL;Y4 ,!
TOTAL 4T.E (! M>A?ON IS #BF.B MILES4 ,ON
! F/ "D1 ,M>?A />TS WALK+ AT #AJ3JJ A4M4
,%E WALKS #D MILES P] H\R4 ,C>OL />TS
TWO H\RS LAT] ?AN ,M>?A B DECIDES 6RUN
6CAT* UP 6,M>?A4 ,C>OL RUNS AT A SPE$ (
#F MILES P] H\R4
A4 ,WRITE AN EQU,N 6REPRES5T ! 4T.E
,M>?A TRAVELS4
B4 ,WRITE AN EQU,N 6REPRES5T ! 4T.E
,C>OL TRAVELS4
C4 ,SOLVE ! SY/EM ( EQU,NS 6F9D :5
,C>OL W CAT* UP 6,M>?A4
D4 ,C>OL WANTS 6REDUCE ! "T %E TAKES
6CAT* UP 6,M>?A 0#A H\R4 ,H[ C %E D ?
0*ANG+ H] />T+ "T8 ,H[ C %E D ? 0*ANG+
H] SPE$8 .,EXPLA9 :E!R YR ANSW]S >E
R1SONA#4
#FA4 .,,BUSI;S ,A NUT :OLESAL] SELLS A
MIX ( P1NUTS & CA%EWS4 ,! :OLESAL] *>GES
4#B.HJ P] P.D = P1NUTS & 4#E.CJ P] P.D =
CA%EWS4 ,! MIX IS 6SELL = 4#C.CJ P] P.D4
,H[ _M P.DS ( P1NUTS & H[ _M P.DS (
CA%EWS %D 2 US$ 6MAKE #AJJ P.DS (! MIX8
#FB4 .,,AVI,N ,FLY+ )! W9D1 A PLANE
FLEW #AJJJ MILES 9 #E H\RS4 ,FLY+ AG/ !
W9D1 ! PLANE CD FLY ONLY #EJJ MILES 9 !
SAME AM.T ( "T4 ,F9D ! SPE$ (! PLANE 9
CALM AIR &! SPE$ (! W9D4
#FC4 .,,*ALL5GE ,=A REC5T JOB1 AN
ELECTRICIAN E>N$ 4#EJ P] H\R1 &!
ELECTRICIAN'S APPR5TICE E>N$ 4#BJ P]
H\R4 ,! ELECTRICIAN "W$ #D H\RS M ?AN !
APPR5TICE1 & TGR !Y E>N$ A TOTAL (
4#EEJ4 ,H[ M* M"OY DID EA* P]SON E>N8
.K ..,,"W$-,,\ ,,SOLU;NS .ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#AFG
,MIX$ ,REVIEW
,SOLVE ! EQU,N4
#FD4 -#E .;X @+ #D .K #BI @7 P4 #AH @7
#FE4 #F7#B .A - #C7 .K -#CJ @7 P4 #AH
@7
#FF4 #A.B .;M .K #B.C .;M - #B.B @7 P4
#AH @7
#FG4 _\ .;X @+ #C_\ .K #D @7 P4 #EA @7
#FH4 _\#B .;X @+ #AA_\ .K #C @7 P4 #EA
@7
#FI4 _\- .;X @+ #G_\ .K #AC @7 P4 #EA
@7
..,TELL :E!R ! L9ES >E P>ALLEL1
P]P5DICUL> @1 OR .NEI @4 @7 P4 #HB @7
#GJ4 ,L9E #A3 "? 7#B1 #AJ7 & 7#A1 #E7
,L9E #B3 "? 7#C1 -#G7 & 7#H1 -#H7
#GG4 ,L9E #A3 "? 7#D1 #E7 & 7#I1 -#B7
,L9E #B3 "? 7#F1 -#F7 & 7-#B1 -#A7
,WRITE AN EQU,N (! L9E4 @7 P4 #IH @7
#GB4
#GC4
#GD4
,GRAPH ! 9EQUAL;Y 9 A COORD9ATE PLANE4
@7 P4 #ACB @7
.,,PREVIEW ,PREP>E = ,LESSON #C.C 9
,EXS4 #GE-HJ4
#GE4 .;X "K -#C
#GF4 .;Y .1.K #B
#GG4 #B .;X @+ .;Y .1 #A
#GH4 .;Y "K.K - .;X @+ #D
#GI4 #D .;X - .;Y .1.K #E
#HJ4 .;Y "K -#C .;X @+ #B
,,QUIZ .= .,LESSONS .#C..A-.C..B
,GRAPH ! L9E> SY/EM & E/IMATE !
SOLU;N4 ,!N *ECK ! SOLU;N ALGEBRAIC,Y4
@7 P4 #AEC @7
.#A4 #C .;X @+ .;Y .K #AA
.;X -- #B .;Y .K --#H
.#B4 #B .;X @+ .;Y .K --#E
-- .;X @+ #C .;Y .K #F
.#C4 .;X -- #B .;Y .K --#B
#C .;X @+ .;Y .K --#BJ
,SOLVE ! SY/EM4 ,!N CLASSIFY ! SY/EM Z
..3SI/5T & 9DEP5D5T1 3SI/5T & .DEP5D5T
@1 OR .9CONSI/5T4 @7 P4 #AEC @7
.#D4 #D .;X @+ #H .;Y .K #H
.;X @+ #B .;Y .K #F
.#E4
.#F4 .;X -- #B .;Y .K #B
#B .;X -- .;Y .K --#E
,SOLVE ! SY/EM US+ ! SUB/ITU;N ME?OD4
@7 P4 #AFJ @7
.#G4 #C .;X -- .;Y .K --#D
.;X @+ #C .;Y .K --#BH
.#H4 .;X @+ #E .;Y .K #A
--#C .;X @+ #D .;Y .K #AF
.#I4 #F .;X @+ .;Y .K--#F
#D .;X @+ #C .;Y .K #AG
,SOLVE ! SY/EM US+ ! ELIM9,N ME?OD4 @7
P4 #AFJ @7
.#AJ4 #B .;X -- #C .;Y .K --#A
#B .;X @+ #C .;Y .K --#AI
.#AA4 #C .;X -- #B .;Y .K #AJ
--#F .;X @+ #D .;Y .K --#BJ
.#AB4 #B .;X @+ #C .;Y .K #AG
#E .;X @+ #H .;Y .K #BJ
.#AC4 .,,HOME .,,ELECTRONICS ,63NECT A
,,VCR 6A TELEVI.N SET1 Y NE$ A CA# )
SPECIAL 3NECTORS AT BO? 5DS4 ,SUPPOSE Y
BUY A #F FOOT CA# = 4#AE.EJ &A #C FOOT
CA# = 4#AJ.BE4 ,ASSUM+ T ! CO/ (A CA# IS
! SUM (! CO/ (! TWO 3NECTORS &! CO/ (!
CA# XF1 :AT WD Y EXPECT 6PAY =A #D FOOT
CA#8 .,EXPLA9 H[ Y GOT YR ANSW]4
.,,EXTRA .,,PRACTICE = ,LESSON #C.B1
P4 #AJAB
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#AFH
#C.C ,GRAPH ,SY/EMS ( ,L9E>
,9EQUALITIES
.,2F ,Y GRAPH$ L9E> 9EQUALITIES4
.,N[ ,Y W GRAPH SY/EMS ( L9E>
9EQUALITIES4
.,:Y8 ,S Y C MODEL HE>T RATES DUR+
EX]CISE1 Z 9 ,EX4 #CI4
,KEY ,VOCABUL>Y
99 SY/EM ( L9E> 9EQUALITIES
99 SOLU;N (A SY/EM ( 9EQUALITIES
99 GRAPH (A SY/EM ( 9EQUALITIES
,SIDEB>3
,/&>DS
..#B.J ,/UD5TS SOLVE SY/EMS ( L9E>
.EQU,NS & 9EQUALITIES @7 .9 .TWO OR ?REE
.V>IA#S @7 0SUB/ITU;N1 .) .GRAPHS @1 OR
) MATRICES4
,! FOLL[+ IS AN EXAMPLE (A ..SY/EM (
L9E> .9EQUALITIES 9 TWO V>IA#S4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @+ .;Y "K.K #H @3 .,9EQUAL;Y .#A
#D .;X -- .;Y .1 #F @3 .,9EQUAL;Y .#B
,A .SOLU;N (A SY/EM ( 9EQUALITIES IS
AN ORD]$ PAIR T IS A SOLU;N ( EA*
9EQUAL;Y 9 ! SY/EM4 ,= EXAMPLE1 7#E1
--#B7 IS A SOLU;N (! SY/EM ABV4 ,!
.GRAPH (A SY/EM ( 9EQUALITIES IS ! GRAPH
( ALL SOLU;NS (! SY/EM4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,GRAPH+ A ,SY/EM ( ,L9E> ,9EQUALITIES
,6GRAPH A SY/EM ( L9E> 9EQUALITIES1
FOLL[ ^! /EPS3
.,,/EP .#A .,GRAPH EA* 9EQUAL;Y 9 !
SY/EM4 ,Y MAY WANT 6USE COLOR$ P5CILS
64T+UI% ! DI6]5T HALF-PLANES4
.,,/EP .#B .,ID5TIFY ! REGION T IS
-MON 6ALL ! GRAPHS (! 9EQUALITIES4 ,?
REGION IS ! GRAPH (! SY/EM4 ,IF Y US$
COLOR$ P5CILS1 ! GRAPH (! SY/EM IS !
REGION T HAS BE5 %AD$ ) E COLOR4
,EXAMPLE #A ,GRAPH A SY/EM ( TWO
9EQUALITIES
,GRAPH ! SY/EM ( 9EQUALITIES4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;Y .1 --#B .;X -- #E @3 .,9EQUAL;Y
.#A
.;Y "K.K .;X @+ #C @3 .,9EQUAL;Y .#B
,,REVIEW ,,9EQUALITIES
,= HELP ) GRAPH+ L9E> 9EQUALITIES 9
TWO V>IA#S1 SEE P4 #ACB @4
,SOLU;N
.,,/EP .#A .,GRAPH EA* 9EQUAL;Y 9 !
SY/EM4 ,USE .R$ = ..;Y .1 --#B ;X -- .#E
& .BLUE = ..;Y "K.K ;X @+ .#C4
.,,/EP#B .,ID5TIFY ! REGION T IS -MON
6BO? GRAPHS4 ,X IS ! REGION T IS %AD$
.PURPLE4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
------------------------------------#AFI
,EXAMPLE #B ,GRAPH A SY/EM ) NO SOLU;N
,GRAPH ! SY/EM ( 9EQUALITIES4
,SOLU;N
.,,/EP .#A .,GRAPH EA* 9EQUAL;Y 9 !
SY/EM4 ,USE .R$ = ..#B ;X @+ #C ;Y "K
.#F & .BLUE = @4
.,,/EP .#B .,ID5TIFY ! REGION T IS
-MON 6BO? GRAPHS4 ,"! IS NO REGION %AD$
BO? R$ & BLUE4 ,S1 ! SY/EM HAS NO
SOLU;N4
,EXAMPLE #C ,GRAPH A SY/EM ) AN
ABSOLUTE VALUE 9EQUAL;Y
,GRAPH ! SY/EM ( 9EQUALITIES4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;Y "K.K #C @3 .,9EQUAL;Y .#A
.;Y .1 _\ .;X @+ #D_\ @3 .,9EQUAL;Y
.#B
,,REVIEW ,,ABSOLUTE ,,VALUE
,= HELP ) GRAPH+ ABSOLUTE VALUE
9EQUALITIES1 SEE P4 #ACB @4
,SOLU;N
.,,/EP .#A .,GRAPH EA* 9EQUAL;Y 9 !
SY/EM4 ,USE .R$ = .;Y "K.K .#C & .BLUE =
..;Y .1 _\ ;X @+ .#D_\4
.,,/EP .#B .,ID5TIFY ! REGION T IS
-MON 6BO? GRAPHS4 ,X IS ! REGION T IS
%AD$ .PURPLE4
..,GUID$ ,PRACTICE = ,EXAMPLES #A1 #B1
& .#C
,GRAPH ! SY/EM ( 9EQUALITIES4
.#A4 .;Y "K.K #C .;X --#B
.;Y .1 -- .;X @+ #D
.#B4
#D .;X - .;Y "K.K #E
.#C4 .;X @+ .;Y .1 --#C
--#F .;X @+ .;Y "K #A
.#D4 .;Y "K.K #D
.;Y .1.K _\ .;X -- #E_\
.#E4 .;Y .1 --#B
.;Y "K.K --_\ .;X @+ #B_\
.#F4 .;Y .1.K #B_\ .;X @+ #A_\
.;Y "K .;X @+ #A
------------------------------------#AGJ
..,,SY/EMS ,,( ,,?REE ,,OR ,,M
.,,9EQUALITIES ,Y C AL GRAPH A SY/EM (
?REE OR M L9E> 9EQUALITIES1 Z %[N 9
,EXAMPLE #D4
,EXAMPLE #D ,SOLVE A MULTI-/EP PRO#M
.,,%OPP+ ,A 4C.T %OE /ORE IS HAV+ A
SALE1 Z DESCRIB$ 9 ! ADV]TISE;T %[N4
99 ,USE ! 9=M,N 9 ! AD 6WRITE A SY/EM
( 9EQUALITIES =! REGUL> FOOTWE> PRICES &
POSSI# SALE PRICES4
99 ,GRAPH ! SY/EM ( 9EQUALITIES4
99 ,USE ! GRAPH 6E/IMATE ! RANGE (
POSSI# SALE PRICES = FOOTWE> T IS
REGUL>LY PRIC$ AT 4#GJ4
,SOLU;N
.,,/EP .#A .,WRITE A SY/EM (
9EQUALITIES4 ,LET .;X 2 ! REGUL> FOOTWE>
PRICE & LET .;Y 2 ! SALE PRICE4 ,F !
9=M,N 9 ! AD1 Y C WRITE ! FOLL[+ F\R
9EQUALITIES4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X .1.K #BJ @3 ..,REGUL> PRICE M/ 2
AT L1/ 4.#BJ4
.;X "K.K #HJ @3 ..,REGUL> PRICE C 2 AT
MO/ 4.#HJ4
.;Y .1.K #J.D .;X @3 ..,SALE PRICE IS
AT L1/ 7#AJJ--#FJ7@3P .K #DJ@3P ( REGUL>
.PRICE4
.;Y "K.K #J.I .;X @3 ..,SALE PRICE IS
AT MO/ 7#AJJ--#AJ7@3P .K #IJ@3P ( REGUL>
.PRICE4
.,,/EP .#B .,GRAPH EA* 9EQUAL;Y 9 !
SY/EM4 ,!N ID5TIFY ! REGION T IS -MON
6ALL ! GRAPHS4 ,X IS ! REGION T IS %AD$4
.,,/EP .#C .,ID5TIFY ! RANGE ( POSSI#
SALE PRICES = 4#GJ FOOTWE>4 ,F ! GRAPH Y
C SEE T :5 .;X .K #GJ1 ! VALUE ( .;Y IS
2T ^! VALUES3
#J.D7#GJ7 .K #BH & #J.I7#GJ7 .K #FC
,S1 ! VALUE ( .;Y SATISFIES #BH "K.K
.;Y "K.K #FC4
,"!=E1 FOOTWE> REGUL>LY PRIC$ AT 4#GJ
SELLS = 2T 4#BH & 4#FC1 9CLUSIVE1 DUR+ !
SALE4
..,GUID$ ,PRACTICE = ,EXAMPLE .#D
#G4 .,,:AT .,,IF8 ,9 ,EXAMPLE #D1
SUPPOSE ! ADV]TISE;T %[$ A RANGE ( 4C.TS
( #BJ@3P-#EJ@3P &A RANGE ( REGUL> PRICES
( 4#DJ-4#AJJ4
A4 ,WRITE & GRAPH A SY/EM (
9EQUALITIES =! REGUL> FOOTWE> PRICES &
POSSI# SALE PRICES4
B4 ,USE ! GRAPH 6E/IMATE ! RANGE (
POSSI# SALE PRICES = FOOTWE> T IS
REGUL>LY PRIC$ AT 4#FJ4
------------------------------------#AGA
#C.C ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#E = ,EXS4 #I1 #AI1 & #CG
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 #B1C1BF1 #BG1 #CF1 & #CI
.K .,,MULTIPLE .,,REPRES5T,NS
,EX#.CG
,SKILL ,PRACTICE
,,EXAMPLES #A1 #B1 & #C
ON PP4 #AFH-AFI = ,EXS4 #C-AF
.#A4 .,,VOCABUL>Y ,:AT M/ 2 TRUE 9
ORD] = AN ORD]$ PAIR 6BE A SOLU;N (A
SY/EM ( L9E> 9EQUALITIES8
.#B4 .,,WRIT+ .,DESCRIBE H[ 6GRAPH A
SY/EM ( L9E> 9EQUALITIES4
#C4 .,,MULTIPLE .,,*OICE ,: SY/EM (
9EQUALITIES IS REPRES5T$ 0! GRAPH8
,A .;X @+ .;Y .1 #C
-- .;X @+ .;Y "K --#D
;,B -- .;X @+ .;Y .1.K --#D
.;X @+ .;Y "K.K #C
;,C --#B .;X @+ .;Y .1 --#D
#B .;X @+ .;Y "K #C
;,D -- .;X @+ .;Y .1 --#D
.;X @+ .;Y "K #C
,,SY/EMS ,,( ,,TWO ,,9EQUALITIES
,GRAPH ! SY/EM ( 9EQUALITIES4
.#D4 .;X .1 --#A
.;X "K #C
.#E4 .;X "K.K #B
.;Y "K.K #E
.#F4 .;Y .1.K #E
.;Y "K.K #A
.#G4 -- .;X @+ .;Y "K --#C
-- .;X @+ .;Y .1 #D
.#H4 .;Y "K #AJ
.;Y .1 _\ .;X _\
.#I4 #D .;X -- #D .;Y .1.K --#AF
-- .;X @+ #B .;Y .1.K --#D
.#AJ4 -- .;X .1.K .;Y
-- .;X @+ .;Y .1.K --#E
.#AA4 .;Y .1 _\ .;X _\ --#D
#C .;Y "K --#B .;X @+ #I
.#AB4 .;X @+ .;Y .1.K --#C
--#F .;X @+ #D .;Y "K #AD
.#AC4 #B .;Y "K --#E .;X -- #AJ
#E .;X @+ #B .;Y --#B
.#AD4 #C .;X -- .;Y .1 #AB
-- .;X @+ #H .;Y .1 --#D
.#AE4 .;X -- #D .;Y "K.K --#AJ
.;Y "K.K #C_\ .;X -- #A_\
.#AF4 .,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 GRAPH+ ! SY/EM (
9EQUALITIES4
.;Y .1.K --#C
.;Y "K.K #B .;X --#B
,,EXAMPLE #D
ON P4 #AGJ = ,EXS4 #AG-BE
,,SY/EMS ,,( ,,?REE ,,OR ,,M
,,9EQUALITIES ,GRAPH ! SY/EM (
9EQUALITIES4
.#AG4 .;X "K #F
.;Y .1 --#A
.;Y "K .;X
.#AH4 .;X .1.K --#H
.;Y "K.K --#A
.;Y "K --#B .;X -- #D
.#AI4 #C .;X @+ #B .;Y .1 --#F
--#E .;X @+ #B .;Y .1 --#B
.;Y "K #E
.#BJ4 .;X @+ .;Y "K #E
#B .;X -- .;Y .1 #J
-- .;X @+ #E .;Y .1 --#BJ
.#BA4 .;X .1.K #B
--#C .;X @+ .;Y "K --#A
#D .;X @+ #C .;Y "K #AB
.#BB4 .;Y .1.K .;X
.;X @+ #C .;Y "K #E
#B .;X @+ .;Y .1.K --#C
.#BC4 .;Y .1.K #J
.;X .1 #C
.;X @+ .;Y .1.K --#B
.;Y "K #D .;X
.#BD4 .;X @+ .;Y "K #E
.;X @+ .;Y .1 --#E
.;X -- .;Y "K #D
.;X -- .;Y .1 --#B
.#BE4 .;X "K.K #AJ
.;X .1.K --#B
#C .;X @+ #B .;Y "K #F
#F .;X @+ #D .;Y .1 --#AB
------------------------------------#AGB
#BF4 .,,MULTIPLE .,,*OICE ,: QUADRANT
(! COORD9ATE PLANE 3TA9S NO SOLU;NS (!
SY/EM ( 9EQUALITIES8
.;Y "K.K --_\ .;X -- #C_\ @+ #B
#D .;X -- #E .;Y "K.K #BJ
,A ,QUADRANT ,I
;,B ,QUADRANT ,,II
;,C ,QUADRANT ,,III
;,D ,QUADRANT ,,IV
#BG4 .,,OP5-.,,5D$ .,,MA? ,WRITE A
SY/EM ( TWO L9E> 9EQUALITIES T HAS 7#B1
--#A7 Z A SOLU;N4
,,ABSOLUTE ,,VALUE ,,SY/EMS ,GRAPH !
SY/EM ( 9EQUALITIES4
.#BH4 .;Y "K _\ .;X _\
.;Y .1 --_\ .;X _\
.#BI4 .;Y "K.K _\ .;X -- #B_\
.;Y .1.K _\ .;X _\--#B
.#CJ4 .;Y "K.K--_\ .;X -- #C_\ @+ #B
.;Y .1 _\ .;X -- #C_\--#A
,,*ALL5GE ,WRITE A SY/EM ( L9E>
9EQUALITIES =! %AD$ REGION4
.#CA4
.#CB4
.#CC4
,PRO#M ,SOLV+
,,EXAMPLE #D
ON P4 #AGJ = ,EXS4 #CD-CI
.#CD4 .,,SUMM] .,,JOBS ,Y C "W AT MO/
#BJ H\RS NEXT WEEK4 ,Y NE$ 6E>N AT L1/
4#IB 6COV] YR WEEKLY EXP5SES4 ,YR
DOG-WALK+ JOB PAYS 4#G.EJ P] H\R & YR
JOB Z A C> WA% ATT5DANT PAYS 4#F P] H\R4
,WRITE A SY/EM ( L9E> 9EQUALITIES 6MODEL
! SITU,N4
@A,HOME,TUTOR ..= PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
..#CE4 ,,VIDEO ,,GAME .,,SALE ,AN
ONL9E M$IA /ORE IS HAV+ A SALE1 Z
DESCRIB$ 9 ! AD %[N4 ,USE ! 9=M,N 9 ! AD
6WRITE & GRAPH A SY/EM ( 9EQUALITIES =!
REGUL> VIDEO GAME PRICES & POSSI# SALE
PRICES4 ,!N USE ! GRAPH 6E/IMATE ! RANGE
( POSSI# SALE PRICES = GAMES T >E
REGUL>LY PRIC$ AT 4#BJ4
@A,HOME,TUTOR ..= PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#CF4 .,,%ORT .,,RESPONSE ,A BOOK ON !
C>E ( TROPICAL FI% /ATES T ! P,H LEVEL
(! WAT] %D 2 2T #H.J & #H.C P,H UNITS &!
TEMP]ATURE (! WAT] %D 2 2T #GF;DG;,F &
#HJ;DG,F4 ,LET .;X 2 ! P,H LEVEL & .;Y 2
! TEMP]ATURE4 ,WRITE & GRAPH A SY/EM (
9EQUALITIES T DESCRIBES ! PROP] P,H
LEVEL & TEMP]ATURE (! WAT]4 .,-P>E ?
GRAPH 6! GRAPH Y WD OBTA9 IF !
TEMP]ATURES 7 GIV5 9 DEGREES ,CELSIUS4
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
------------------------------------#AGC
.#CG4 .,,MULTIPLE .,,REPRES5T,NS ,!
,JUNIOR-,S5IOR ,PROM ,-MITTEE M/ 3SI/ (
#E 6#H REPRES5TATIVES F ! JUNIOR & S5IOR
CLASSES4 ,! -MITTEE M/ 9CLUDE AT L1/ #B
JUNIORS & AT L1/ #B S5IORS4 ,LET .;X 2 !
NUMB] ( JUNIORS & .;Y 2 ! NUMB] (
S5IORS4
A4 .,WRIT+ .A .,SY/EM ,WRITE A SY/EM (
9EQUALITIES 6DESCRIBE ! SITU,N4
B4 .,GRAPH+ .A .,SY/EM ,GRAPH ! SY/EM
Y WROTE 9 "P 7A74
C4 .,F9D+ .,SOLU;NS ,GIVE TWO POSSI#
SOLU;NS =! NUMB]S ( JUNIORS & S5IORS ON
! PROM -MITTEE4
#CH4 .,,BASEBALL ,9 BASEBALL1 ! /RIKE
Z"O IS A RECTANGLE ! WID? ( HOME PLATE T
EXT5DS F ! BATT]'S KNEES 6A PO9T HALFWAY
2T ! %\LD]S .;,S &! TOP .;,T (! UNI=M
PANTS4 ,! WID? ( HOME PLATE IS #AG 9*ES4
,SUPPOSE A BATT]'S KNEES >E #BJ 9*ES ABV
! GR.D &! PO9T HALFWAY 2T 8 %\LD]S &!
TOP ( 8 PANTS IS #DB 9*ES ABV ! GR.D4
,WRITE & GRAPH A SY/EM ( 9EQUALITIES T
REPRES5TS ! /RIKE Z"O4
#CI4 .,,EXT5D$ .,,RESPONSE ,A P]SON'S
!ORETICAL MAXIMUM HE>T RATE 7IN HE>TB1TS
P] M9UTE7 IS #BBJ -- .;X ": .;X IS !
P]SON'S AGE 9 YE>S 7#BJ "K.K .;X "K.K
#FE74 ,:5 A P]SON EX]CISES1 X IS
RECOMM5D$ T ! P]SON /RIVE =A HE>T RATE T
IS AT L1/ #EJ@3P (! MAXIMUM & AT MO/
#GE@3P (! MAXIMUM4
A4 ,WRITE A SY/EM ( L9E> 9EQUALITIES T
DESCRIBES ! GIV5 9=M,N4
B4 ,GRAPH ! SY/EM Y WROTE 9 "P 7A74
C4 ,A #DJ-YE>-OLD P]SON HAS A HE>T
RATE ( #AEH HE>TB1TS P] M9UTE :5
EX]CIS+4 ,IS ! P]SON'S HE>T RATE 9 !
T>GET Z"O8 .,EXPLA94
#DJ4 .,,*ALL5GE ,Y &A FR >E TRY+
6GUESS ! NUMB] ( P5NIES 9 A J>4 ,Y BO?
AGREE T ! J> 3TA9S AT L1/ #EJJ P5NIES4
,Y GUESS T "! >E .;X P5NIES1 & YR FR
GUESSES T "! >E .;Y P5NIES4 ,! ACTUAL
NUMB] ( P5NIES 9 ! J> IS #AJJJ4 ,WRITE &
GRAPH A SY/EM ( 9EQUALITIES DESCRIB+ !
VALUES (4 .;X & .;Y = : YR GUESS IS
CLOS] ?AN YR FR'S GUESS 6! ACTUAL NUMB]
( P5NIES4
,MIX$ ,REVIEW
,EVALUATE ! EXPRES.N =! GIV5 VALUES (
.;X & .;Y @4 @7 P4 #AJ @7
#DA4 #F .;X - #H .;Y :5 .;X .K #D &
.;Y .K -#A
#DB4 #AB .;X @+ #C .;Y :5 .;X .K #D &
.;Y .K -#E
#DC4 .;X #B - #B .XY @+ #C .;Y :5 .;X
.K -#B & .;Y .K #C
#DD4 #D .;X #B .;Y #B - .XY :5 .;X .K
#E & .;Y .K -#F
,SOLVE ! 9EQUAL;Y4 ,!N GRAPH ! SOLU;N4
@7 P4 #DA @7
#DE4 .;X - #H "K.K -#E
#DF4 #E .;X - #AA .1 - .;X @+ #G
#DG4 #I .;X @+ #B .1.K -#C .;X - #AC
,SOLVE ! SY/EM ( L9E> EQU,NS4 @7 P4
#AFJ @7
.,,PREVIEW ,PREP>E = ,LESSON #C.D 9
,EXS4 #DH-EC4
#DH4 -#E .;X @+ .;Y .K -#AA
#D .;X - .;Y .K #G
#DI4 #I .;X @+ #D .;Y .K -#G
#C .;X - #E .;Y .K -#CD
#EJ4 #D .;X @+ #I .;Y .K -#AJ
#H .;X @+ #AH .;Y .K #BJ
#EA4 .;X - #E .;Y .K #AH
#B .;X @+ #C .;Y .K #AJ
#EB4 #AF .;X - #AB .;Y .K -#H
#H .;X - #F .;Y .K -#D
#EC4 #AF .;X @+ #E .;Y .K -#D
#H .;X - #H .;Y .K #G
.,,EXTRA .,,PRACTICE = ,LESSON #C.C1
P4 #AJAB
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#AGD
,EXT5.N ,USE ,L9E> ,PROGRAMM+
,USE CUTT] ,LESSON #C.C
,KEY ,VOCABUL>Y
99 3/RA9TS
99 OBJECTIVE FUNC;N
99 L9E> PROGRAMM+
99 F1SI# REGION
,SIDEB>3
,/&>DS
..#B.J ,/UD5TS SOLVE SY/EMS ( L9E>
.EQU,NS & 9EQUALITIES @7 .9 .TWO OR ?REE
.V>IA#S @7 0SUB/ITU;N1 .) .GRAPHS @1 OR
) MATRICES4
.,GOAL ,SOLVE L9E> PROGRAMM+ PRO#MS4
.,,BUSI;S ,A POTT] WANTS 6MAKE & SELL
S]V+ B[LS & PLATES4 ,A B[L USES #E P.DS
( CLAY4 ,A PLATE USES #D P.DS ( CLAY4 ,!
POTT] HAS #DJ P.DS ( CLAY & WANTS 6MAKE
AT L1/ #D B[LS4
,LET .;X 2 ! NUMB] ( B[LS MADE & LET
.;Y 2 ! NUMB] ( PLATES MADE4 ,Y C
REPRES5T ! 9=M,N ABV US+ L9E>
9EQUALITIES CALL$ .3/RA9TS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X .1.K #D @3 ..,MAKE AT L1/ #D
.B[LS4
.;Y .1.K #J @3 ..,NUMB] ( PLATES _C 2
.NEGATIVE4
#E .;X @+ #D .;Y "K.K #DJ @3 ..,C USE
UP 6#DJ P.DS ( .CLAY4
,! PR(IT ON A B[L IS 4#CE &! PR(IT ON
A PLATE IS 4#CJ4 ,! POTT]'S TOTAL PR(IT
.;,P IS GIV5 0! EQU,N 2L1 CALL$ !
.OBJECTIVE .FUNC;N4
.;,P .K #CE .;X @+ #CJ .;Y
,X IS R1SONA# =! POTT] 6WANT 6MAXIMIZE
PR(IT SUBJECT 6! GIV5 3/RA9TS4 ,!
PROCESS ( MAXIMIZ+ OR M9IMIZ+ A L9E>
OBJECTIVE FUNC;N SUBJECT 63/RA9TS T >E
L9E> 9EQUALITIES IS CALL$ .L9E>
.PROGRAMM+4
,IF ! 3/RA9TS >E GRAPH$1 ALL (! PO9TS
9 ! 9T]SEC;N >E ! -B9,NS ( B[LS & PLATES
T ! POTT] C MAKE4 ,! 9T]SEC;N (! GRAPHS
IS CALL$ ! .F1SI# .REGION4
,! FOLL[+ RESULT TELLS Y H[ 6DET]M9E !
OPTIMAL SOLU;N (A L9E> PROGRAMM+ PRO#M4
,,R1D+
,A F1SI# REGION IS .B.D$ IF X IS
-PLETELY 5CLOS$ 0L9E SEG;TS4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,OPTIMAL ,SOLU;N (A ,L9E> ,PROGRAMM+
,PRO#M
,IF ! F1SI# REGION =A L9E> PROGRAMM+
PRO#M IS B.D$1 !N ! OBJECTIVE FUNC;N HAS
BO? A MAXIMUM VALUE &A M9IMUM VALUE ON !
REGION4 ,MOREOV]1 ! MAXIMUM & M9IMUM
VALUES EA* O3UR AT A V]TEX (! F1SI#
REGION4
,PICTURE3 .,B.D$ .REGION
,PICTURE3 .,UNB.D$ .REGION
------------------------------------#AGE
,EXAMPLE #A ,USE L9E> PROGRAMM+
6MAXIMIZE PR(IT
.,,BUSI;S ,H[ _M B[LS & H[ _M PLATES
%D ! POTT] DESCRIB$ ON PAGE #AGD MAKE 9
ORD] 6MAXIMIZE PR(IT8
,SOLU;N
.,,/EP .#A .,GRAPH ! SY/EM ( 3/RA9TS3
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X .1.K #D @3 ..,MAKE AT L1/ #D
.B[LS4
.;Y .1.K #J @3 ..,NUMB] ( PLATES _C 2
.NEGATIVE4
#E .;X @+ #D .;Y "K.K #DJ @3 ..,C USE
UP 6#DJ P.DS ( .CLAY4
.,,/EP .#B .,EVALUATE ! PR(IT FUNC;N
.;,P .K #CE .;X @+ #CJ .;Y AT EA* V]TEX
(! F1SI# REGION4
,AT 7#D1 #J73 .;,P .K #CE7#D7 @+
#CJ7#J7--#ADJ
,AT 7#H1 #J73 .;,P .K #CE7#H7 @+
#CJ7#J7--#BHJ
,AT 7#D1 #E73 .;,P .K #CE7#D7 @+
#CJ7#E7 .K #BIJ .,MAXIMUM
,! POTT] C MAXIMIZE PR(IT 0MAK+ #D
B[LS & #E PLATES4
,EXAMPLE #B ,SOLVE A L9E> PROGRAMM+
PRO#M
,F9D ! M9IMUM VALUE &! MAXIMUM VALUE
(! OBJECTIVE FUNC;N .;,C .K #D .;X @+ #E
.;Y SUBJECT 6! FOLL[+ 3/RA9TS4
.;X .1.K #J
.;Y .1.K #J
.;X @+ #B .;Y "K.K #AF
#E .;X @+ .;Y "K.K #CE
,SOLU;N
.,,/EP .#A .,GRAPH ! SY/EM ( 3/RA9TS4
,F9D ! COORD9ATES (! V]TICES (! F1SI#
REGION 0SOLV+ SY/EMS ( TWO L9E> EQU,NS4
,= EXAMPLE1 ! SOLU;N (! SY/EM
.;X @+ #B .;Y .K #AF
#E .;X @+ .;Y .K #CE
GIVES ! V]TEX 7#F1 #E74 ,! O!R ?REE
V]TICES >E 7#J1 #J71 7#G1 #J71 & 7#J1
#H74
.,,/EP .#B .,EVALUATE ! FUNC;N .;,C .K
#D .;X @+ #E .;Y AT EA* (! V]TICES4
,AT 7#J1 #J73 .;,C .K #D7#J7 @+ #E7#J7
.K #J .,M9IMUM
,AT 7#G1J73 .;,C .K #D7#G7 @+ #E7#J7
.K #BH
,AT 7#F1 #E73 .;,C .K #D7#F7 @+ #E7#E7
.K #DI .,MAXIMUM
,AT 7#J1H73 .;,C .K #D7#J7 @+ #E7#H7
.K#DJ
,! M9IMUM VALUE ( .;,C IS #J4 ,X O3URS
:5 .;X .K #J & .;Y .K #J4
,! MAXIMUM VALUE ( .;,C IS #DI4 ,X
O3URS :5 .;X .K #F & .;Y .K #E4
------------------------------------#AGF
,PRACTICE
,,EXAMPLES #A & #B
ON P4 #AGE = ,EXS4 #A-I
,,*ECK+ ,,V]TICES ,F9D ! M9IMUM &
MAXIMUM VALUES (! OBJECTIVE FUNC;N =!
GIV5 F1SI# REGION4
.#A4 .;,C .K .;X @+ #B .;Y
.#B4 .;,C .K #D .;X -- #B .;Y
.#C4 .;,C .K #C .;X @+ #E .;Y
,,F9D+ ,,VALUES ,F9D ! M9IMUM &
MAXIMUM VALUES (! OBJECTIVE FUNC;N
SUBJECT 6! GIV5 3/RA9TS4
#D4 ,OBJECTIVE FUNC;N3
.;,C .K #C .;X @+ #D .;Y
,3/RA9TS3
.;X .1.K #J
.;Y .1.K #J
.;X @+ .;Y "K.K #E
#E4 ,OBJECTIVE FUNC;N3
.;,C .K #B .;X @+ #E .;Y
,3/RA9TS3
.;X "K.K #E
.;Y .1.K #C
--#C .;X @+ #E .;Y "K.K #CJ
#F4 ,OBJECTIVE FUNC;N3
.;,C .K #C .;X @+ .;Y
,3/RA9TS3
.;X .1.K #J
.;Y .1.K --#B
.;Y .1.K -- .;X
.;X -- #D .;Y .1.K --#AF
.#G4 .,,CRAFT .,,FAIR ,PI@NATAS >E
MADE 6SELL AT A CRAFT FAIR4 ,X TAKES #B
H\RS 6MAKE A M9I PI@NATA & #C H\RS 6MAKE
A REGUL>-SIZ$ PI@NATA4 ,! [N] (! CRAFT
BOO? W MAKE A PR(IT ( 4#AB = EA* M9I
PI@NATA SOLD & 4#BD = EA* REGUL>-SIZ$
PI@NATA SOLD4 ,IF ! CRAFT BOO? [N] HAS
NO M ?AN #CJ H\RS AVAILA# 6MAKE4PI@NATAS
& WANTS 6H AT L1/ #AB PI@NATAS 6SELL1 H[
_M ( EA* SIZE PI@NATA %D 2 MADE
6MAXIMIZE PR(IT8
.#H4 .,,MANUFACTUR+ ,A -PANY
MANUFACTURES TWO TYPES ( PR9T]S1 AN
9KJET PR9T] &A LAS] PR9T]4 ,! -PANY C
MAKE A TOTAL ( #FJ PR9T]S P] "D1 & X HAS
#ABJ LABOR-H\RS P] "D AVAILA#4 ,X TAKES
#A LABOR-H\R 6MAKE AN 9KJET PR9T] & #C
LABOR-H\RS 6MAKE A LAS] PR9T]4 ,! PR(IT
IS 4#DJ P] 9KJET PR9T] & 4#FJ P] LAS]
PR9T]4 ,H[ _M ( EA* TYPE ( PR9T] %D !
-PANY MAKE 6MAXIMIZE XS DAILY PR(IT8
..#I4 ,,F>M ,,/& .,,SALES ,Y H #ADJ
TOMATOES & #AC ONIONS LEFT OV] F YR
G>D54 ,Y WANT 6USE ^! 6MAKE J>S ( TOMATO
SAUCE & J>S ( SALSA 6SELL AT A F>M /&4
,A J> ( TOMATO SAUCE REQUIRES #AJ
TOMATOES & #A ONION1 &A J> ( SALSA
REQUIRES #E TOMATOES & ONION4 ,Y W MAKE
A PR(IT ( 4#B ON E J> ( TOMATO SAUCE
SOLD &A PR(IT ( 4#A.EJ ON E J> ( SALSA
SOLD4 ,! [N] (! F>M /& WANTS AT L1/ ?REE
"TS Z _M J>S ( TOMATO SAUCE Z J>S (
SALSA4 ,H[ _M J>S ( EA* %D Y MAKE
6MAXIMIZE PR(IT8
#AJ4 .,,*ALL5GE ,3SID] ! OBJECTIVE
FUNC;N .;,C .K #B .;X @+ #C .;Y @4 ,DRAW
A F1SI# REGION T SATISFIES ! GIV5 3DI;N4
A4 .;,C HAS A MAXIMUM VALUE B NO
M9IMUM VALUE ON ! REGION4
B4 .;,C HAS A M9IMUM VALUE B NO
MAXIMUM VALUE ON ! REGION4
------------------------------------#AGG
,9VE/IGAT+ ,ALGEBRA ,ACTIV;Y3 #C.D
,GRAPH+ ,L9E> ,EQU,NS 9 ,?REE ,V>IA#S
,USE 2F ,LESSON #C.D
,MAT]IALS
99 GRAPH PAP]
99 RUL]
,SIDEB>3
,/&>DS
..#B.J ,/UD5TS SOLVE SY/EMS ( L9E>
.EQU,NS & 9EQUALITIES @7 .9 .TWO OR
.?REE .V>IA#S @7 0SUB/ITU;N1 .) .GRAPHS
@1 OR ) MATRICES4
,"Q ,:AT IS ! GRAPH (A L9E> EQU,N 9
?REE V>IA#S8
,A ..L9E> EQU,N 9 ?REE .V>IA#S HAS !
=M .AX @+ .BY @+ .CZ .K .D4 ,Y C GRAPH ?
TYPE ( EQU,N 9 A ?REE-DIM5.NAL COORD9ATE
SY/EM =M$ 0?REE AXES T DIVIDE SPACE
96EI<T .OCTANTS4 ,EA* PO9T 9 SPACE IS
REPRES5T$ 0AN .ORD]$ .TRIPLE @7 .;X1
.;Y1 .;Z @7@4
,! GRAPH ( ANY EQU,N 9 ?REE V>IA#S IS
! SET ( ALL PO9TS @7 .;X1 .;Y1 .;Z @7 ^:
COORD9ATES MAKE ! EQU,N TRUE4 ,=A L9E>
EQU,N 9 ?REE V>IA#S1 ! GRAPH IS A PLANE4
,EXPLORE ,GRAPH #C .;X @+ #D .;Y @+ #F
.;Z .K #AB
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
..,,/EP #A ,F9D .;X -IUT]CEPT.' @3
..,,/EP #B ,F9D .;Y -9T]CEPT.' @3
..,,/EP #C ,F9D .;Z -9T]CEPT.'.-
,F9D ! .;X -9T]CEPT 0SETT+ .;Y & .;Z
EQUAL 6#J & SOLV+ ! RESULT+ EQU,N1 #C
.;X .K #AB4 ,! .;X -9T]CEPT IS #D1 S
PLOT 7#D1 #J1 #J74 @3 ,F9D ! .;Y
-9T]CEPT 0SETT+ .;X & .;Z EQUAL 6#J &
SOLV+ ! RESULT+ EQU,N1 #D .;Y .K #AB4 ,!
.;Y -9T]CEPT IS #C1 S PLOT 7#J1 #C1 #J74
@3 ,F9D ! .;Z -9T]CEPT 0SETT+ .;X & .;Y
EQUAL 6#J & SOLV+ ! RESULT+ EQU,N1 #F
.;Z .K #AB4 ,! .;Z -9T]CEPT IS #B1 S
PLOT 7#J1 #J1 #B74 ,!N 3NECT ! PO9TS4
@3 @3
,! TRIANGUL> REGION %[N 9 ,/EP #C IS !
POR;N (! GRAPH ( #C .;X @+ #D .;Y @+ #F
.;Z .K #AB T LIES 9 ! F/ OCTANT4
,DRAW ,3CLU.NS ,USE YR OBS]V,NS
6-PLETE ^! EX]CISES
,SKET* ! GRAPH (! EQU,N4
.#A4 #D .;X @+ #C .;Y @+ #B .;Z .K #AB
.#B4 #B .;X @+ #B .;Y @+ #C .;Z .K #F
.#C4 .;X @+ #E .;Y @+ #C .;Z .K #AE
.#D4 #E .;X -- .;Y -- #B .;Z .K #AJ
.#E4 --#G .;X @+ #G .;Y @+ #B .;Z .K
#AD
.#F4 #B .;X @+ #I .;Y -- #C .;Z .K
--#AH
.#G4 ,SUPPOSE ?REE L9E> EQU,NS 9 ?REE
V>IA#S >E GRAPH$ 9 ! SAME COORD9ATE
SY/EM4 ,9 H[ _M DI6]5T WAYS C ! PLANES
9T]SECT8 .,EXPLA9 YR R1SON+4
------------------------------------#AGH
#C.D ,SOLVE ,SY/EMS ( ,L9E> ,EQU,NS
9 ,?REE ,V>IA#S
.,2F ,Y SOLV$ SY/EMS ( EQU,NS 9 TWO
V>IA#S4
.,N[ ,Y W SOLVE SY/EMS ( EQU,NS 9 ?REE
V>IA#S4
.,:Y8 ,S Y C MODEL ! RESULTS (A SPORT+
EV5T1 Z 9 ,EX4 #DE4
,KEY ,VOCABUL>Y
99 L9E> EQU,N 9 ?REE V>IA#S
99 SY/EM ( ?REE L9E> EQU,NS
99 SOLU;N (A SY/EM ( ?REE L9E> EQU,NS
99 ORD]$ TRIPLE
,SIDEB>3
,/&>DS
..#B.J ,/UD5TS SOLVE SY/EMS ( L9E>
.EQU,NS & 9EQUALITIES @7 .9 .TWO OR
.?REE .V>IA#S @7 0SUB/ITU;N1 .) .GRAPHS
@1 OR ) MATRICES4
,A ..L9E> EQU,N 9 ?REE .V>IA#S .;X1
.;Y @1 & .;Z IS AN EQU,N (! =M .AX @+
.BY @+ .CZ .K .;D ": .A1 .;B @1 & .;C >E
N ALL Z]O4
,! FOLL[+ IS AN EXAMPLE (A ..SY/EM (
?REE L9E> .EQU,NS 9 ?REE V>IA#S4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#B .;X @+ .;Y -- .;Z .K #E @3 .,EQU,N
.#A
#C .;X -- #B .;Y @+ .;Z .K #AF @3
.,EQU,N .#B
#D .;X @+ #C .;Y -- #E .;Z .K #C @3
.,EQU,N .#C
,A .SOLU;N ( S* A SY/EM IS AN .ORD]$
.TRIPLE @7 .;X1 .;Y1 .;Z @7 ^:
COORD9ATES MAKE EA* EQU,N TRUE4
,! GRAPH (A L9E> EQU,N 9 ?REE V>IA#S
IS A PLANE 9 ?REE-DIM5.NAL SPACE4 ,!
GRAPHS ( ?REE S* EQU,NS T =M A SY/EM >E
?REE PLANES ^: 9T]SEC;N DET]M9ES ! NUMB]
( SOLU;NS (! SY/EM1 Z %[N 9 ! DIAGRAMS
2L4
,EXACTLY "O SOLU;N
,! PLANES 9T]SECT 9 A S+LE PO9T4
,9F9ITELY _M SOLU;NS
,! PLANES 9T]SECT 9 A L9E OR >E ! SAME
PLANE4
,NO SOLU;N
,! PLANES H NO -MON PO9T ( 9T]SEC;N4
------------------------------------#AGI
.,,ELIM9,N .,,ME?OD ,! ELIM9,N ME?OD Y
/UDI$ 9 ,LESSON #C.B C 2 EXT5D$ 6SOLVE A
SY/EM ( L9E> EQU,NS 9 ?REE V>IA#S4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,! ,ELIM9,N ,ME?OD =A ,?REE-,V>IA#
,SY/EM
.,,/EP .#A .,REWRITE ! L9E> SY/EM 9
?REE V>IA#S Z A L9E> SY/EM 9 TWO V>IA#S
0US+ ! ELIM9,N ME?OD4
.,,/EP .#B .,SOLVE ! NEW L9E> SY/EM =
BO? ( XS V>IA#S4
.,,/EP .#C .,SUB/ITUTE ! VALUES F.D 9
,/EP #B 96"O (! ORIG9AL EQU,NS & SOLVE
=! REMA9+ V>IA#4
,IF Y OBTA9 A FALSE EQU,N1 S* Z #J .K
#A1 9 ANY (! /EPS1 !N ! SY/EM HAS NO
SOLU;N4
,IF Y D N OBTA9 A FALSE EQU,N1 B OBTA9
AN ID5T;Y S* Z #J .K #J1 !N ! SY/EM HAS
9F9ITELY _M SOLU;NS4
,EXAMPLE #A ,USE ! ELIM9,N ME?OD
,SOLVE ! SY/EM4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#D .;X @+ #B .;Y @+ #C .;Z .K #A @3
.,EQU,N .#A
#B .;X -- #C .;Y @+ #E .;Z .K --#AD @3
.,EQU,N .#B
#F .;X -- .;Y @+ #D .;Z .K --#A @3
.,EQU,N .#C
,,ANO!R ,,WAY
,9 ,/EP #A1 Y CD AL ELIM9ATE .;X 6GET
TWO EQU,NS 9 .;Y & .;Z @1 OR Y CD
ELIM9ATE .;Z 6GET TWO EQU,NS 9 .;X &Y4
,SOLU;N
.,,/EP .#A .,REWRITE ! SY/EM Z A L9E>
SY/EM 9 .TWO V>IA#S4
.,,/EP .#B .,SOLVE ! NEW L9E> SY/EM =
BO? ( XS V>IA#S4
.,,/EP .#C .,SUB/ITUTE .;X .K #B & .;Z
.K --#C 96AN ORIG9AL EQU,N & SOLVE = .;Y
@4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#F .;X -- .;Y @+ #D .;Z .K --#A @3
..,WRITE ORIG9AL ,EQU,N .#C4
#F7#B7 -- .;Y @+ #D7--#C7 .K --#A @3
,SUB/ITUTE #B =.' ;X .-& --#C =.' ;Z @4
.;Y .K #A @3 .,SOLVE .= .Y4
,! SOLU;N IS .;X .K #B1 .;Y .K #A1 &
.;Z .K --#C1 OR ! ORD]$ TRIPLE 7#B1 #A1
--#C74 ,*ECK ? SOLU;N 9 EA* (! ORIG9AL
EQU,NS4
------------------------------------#AHJ
,EXAMPLE #B ,SOLVE A ?REE-V>IA# SY/EM
) NO SOLU;N
,SOLVE ! SY/EM4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @+ .;Y @+ .;Z .K #C @3 .,EQU,N .#A
#D .;X @+ #D .;X @+ #D .;Z .K #G @3
.,EQU,N .#B
#C .;X -- .;Y @+ #B .;Z .K #E @3
.,EQU,N .#C
,,REVIEW ,,SY/EMS
,= HELP ) SOLV+ L9E> SY/EMS ) _M
SOLU;NS OR NO SOLU;N1 SEE P4 #AFJ @4
,SOLU;N
,:5 Y MULTIPLY ,EQU,N #A BY --#D & ADD
! RESULT 6,EQU,N #B1 Y OBTA9 A FALSE
EQU,N4
,2C Y OBTA9 A FALSE EQU,N1 Y C 3CLUDE
T ! ORIG9AL SY/EM HAS NO SOLU;N4
,EXAMPLE #C ,SOLVE A ?REE-V>IA# SY/EM
) _M SOLU;NS
,SOLVE ! SY/EM4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @+ .;Y @+ .;Z .K #D @3 .,EQU,N .#A
.;X @+ .;Y -- .;Z .K #D @3 .,EQU,N .#B
#C .;X @+ #C .;Y @+ .;Z .K #AB @3
.,EQU,N .#C
,SOLU;N
.,,/EP .#A .,REWRITE ! SY/EM Z A L9E>
SY/EM 9 .TWO V>IA#S4
.,,/EP .#B .,SOLVE ! NEW L9E> SY/EM =
BO? ( XS V>IA#S4
,2C Y OBTA9 ! ID5TIFY #J .K #J1 !
SY/EM HAS 9F9ITELY _M SOLU;N4
.,,/EP .#C .,DESCRIBE ! SOLU;NS (!
SY/EM4 ,"O WAY 6D ? IS 6DIVIDE NEW
,EQU,N #A 0#B 6GET .;X @+ .;Y .K #D1 OR
.;Y .K -- .;X @+ #D4 ,SUB/ITUT+ ?
96ORIG9AL ,EQU,N #A PRODUCES .;Z .K #J4
,S1 ANY ORD]$ TRIPLE (! =M @7 .;X @1 --
.;X @+ #D1 #J7 IS A SOLU;N (! SY/EM4
..,GUID$ ,PRACTICE = ,EXAMPLE #A1 #B1
& .#C
,SOLVE ! SY/EM4
.#A4 #C .;X @+ .;Y -- #B .;Z .K #AJ
#F .;X -- #B .;Y @+ .;Z .K --#B
.;X @+ #D .;Y @+ #C .;Z .K #G
.#B4 .;X @+ .;Y -- .;Z .K #B
#B .;X @+ #B .;Y -- #B .;Z .K #F
#E .;X @+ .;Y -- #C .;Z .K #H
.#C4 .;X @+ .;Y @+ .;Z .K #C
.;X @+ .;Y -- .;Z .K #C
#B .;X @+ #B .;Y @+ .;Z .K #F
------------------------------------#AHA
,EXAMPLE #D ,SOLVE A SY/EM US+
SUB/ITU;N
.,,M>KET+ ,! M>KET+ DE"P;T (A -PANY
HAS A BUDGET ( 4#CJ1JJJ = ADV]TIS+4 ,A
TELEVI.N AD CO/S 4#AJJJ1 A RADIO AD CO/S
4#BJJ1 &A NEWSPAP] AD CO/S 4#EJJ4 ,!
DE"P;T WANTS 6RUN #FJ ADS P] MON? & H Z
_M RADIO ADS Z TELEVI.N & NEWSPAP] ADS
-B9$4 ,H[ _M ( EA* TYPE ( AD %D ! DE"P;T
RUN EA* MON?8
,SOLU;N
.,,/EP .#A .,WRITE V]BAL MODELS =!
SITU,N4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,,TV ADS @+ ,RADIO ADS @+ ,NEWSPAP]
ADS .K ,TOTAL ADS3 .,EQU,N .#A
.#AJJJ ,,TV ADS @+ .#BJJ ,RADIO ADS @+
.#EJJ ,NEWSPAP] ADS .K ,MON?LY BUDGET @3
.,EQU,N .#B
,RADIO ADS @+ ,,TV ADS @+ ,NEWSPAP]
ADS3 .,EQU,N .#C
.,,/EP .#B .,WRITE A SY/EM ( EQU,NS4
,LET .;X 2 ! NUMB] ( ,,TV ADS1 .;Y 2 !
NUMB] ( RADIO ADS1 & .;Z 2 ! NUMB] (
NEWSPAP] ADS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @+ .;Y @+ .;Z .K #FJ @3 .,EQU,N
.#A
#AJJJ .;X @+ #BJJ .;Y @+ #EJJ .;Z .K
#CJ1JJJ @3 .,EQU,N .#B
.;Y .K .;X @+ .;Z @3 .,EQU,N .#C
.,,/EP .#C .,REWRITE ! SY/EM 9 ,/EP #B
Z A L9E> SY/EM 9 .TWO V>IA#S 0SUB/ITUT+
.;X @+ .;Z = .;Y 9 ,EQU,NS #A & #B4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @+ .;Y @+ .;Z .K #FJ @3 .,WRITE
.,EQU,N .#A4
.;X @+ @7 .;X @+ .;Z @7 @+ .;Z .K #FJ
@3 ,SUB/ITUTE.' ;X @+ .;Z =.' ;Y @4
#B .;X @+ #B .;Z .K #FJ @3 .,NEW
.,EQU,N .#A
#AJJJ .;X @+ #BJJ .;Y @+ #EJJ .;Z .K
#CJ1JJJ @3 .,WRITE .,EQU,N .#B4
;L#JJJ .;X @+ #BJJ7 .;X @+ .;Z @7 @+
#EJJ .;Z .K #CJ1JJJ @3 ,SUB/ITUTE.' ;X
@+ .;Z =.' ;Y @4
#ABJJ .;X @+ #GJJ .;Z .K #CJ1JJJ @3
.,NEW .,EQU,N .#B
,,AVOID ,,]RORS
,9 ,EXAMPLE #D1 2 C>E;L N 6WRITE !
ORD]$ TRIPLE 9 ! ORD] 9 : Y SOLV$ =!
V>IA#S4
7#AB1 #AH1 #CJ7
7#AH1 #CJ1 #AB7
.,,/EP .#D .,SOLVE ! L9E> SY/EM 9 TWO
V>IA#S F ,/EP #C4
,! SOLU;N IS .;X .K #AH1 .;Y .K #CJ1 &
.;Z .K #AB1 OR 7#AH1 #CJ1 #AB74 ,S1 !
DE"P;T %D RUN #AH ,,TV ADS1 #CJ RADIO
ADS1 & #AB NEWSPAP] ADS EA* MON?4
..,GUID$ ,PRACTICE = ,EXAMPLE .#D
.#D4 ,,:AT ,,IF8 ,9 ,EXAMPLE #D1
SUPPOSE ! MON?LY BUDGET IS 4#BE1JJJ4 ,H[
_M ( EA* TYPE ( AD %D ! M>KET+ DE"P;T
RUN EA* MON?8
------------------------------------#AHB
#C.D ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#E = ,EXS4 #AA1BE1 & #DE
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 #B1BC1 #BD1 #CD1DE1 & #DG
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,WRITE A L9E> EQU,N
9 ?REE V>IA#S4 ,:AT IS ! GRAPH ( S* AN
EQU,N8
.#B4 .,,WRIT+ .,EXPLA9 H[ 6USE !
SUB/ITU;N ME?OD 6SOLVE A SY/EM ( ?REE
L9E> EQU,NS 9 ?REE V>IA#S4
,,EXAMPLES #A1B1 & #C
ON PP4 #AGI-AHJ = ,EXS4 #C-AD
,,*ECK+ ,,SOLU;NS ,TELL :E!R ! GIV5
ORD]$ TRIPLE IS A SOLU;N (! SY/EM4
.#C4
.#D4
.#E4
.#F4
.#G4
.#H4
,,ELIM9,N ,,ME?OD ,SOLVE ! SY/EM US+ !
ELIM9,N ME?OD4
.#I4
.#AJ4
.#AA4
.#AB4
.#AC4
.#AD4
,,EXAMPLE #D
ON P4 #AHA = ,EXS4 #AE-BJ
,,SUB/ITU;N ,,ME?OD ,SOLVE ! SY/EM US+
! SUB/ITU;N ME?OD4
.#AE4
.#AF4
.#AG4
.#AH4
.#AI4
.#BJ4
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 ! F/ /EP ( SOLV+ ! SY/EM4
#B .;X @+ .;Y -- #B .;Z .K #BC
#C .;X @+ #B .;Y @+ .;Z .K #AA
.;X -- .;Y @+ .;Z .K --#B
.#BA4
.#BB4
------------------------------------#AHC
#BC4 .,,MULTIPLE .,,*OICE ,: ORD]$
TRIPLE IS A SOLU;N (! SY/EM8
#B .;X @+ #E .;Y @+ #C .;Z .K #AJ
#C .;X -- .;Y @+ #D .;Z .K #H
#E .;X -- #B .;Y @+ #G .;Z .K #AB
,A 7#G1A1--#C7
;,B 7#G1--#A1--#C7
;,C 7#G1A1C7
;,D 7--#G1A1--#C7
#BD4 .,,MULTIPLE .,,*OICE ,: ORD]$
TRIPLE DESCRIBES ALL (! SOLU;NS (!
SY/EM8
#B .;X -- #B .;Y -- .;Z .K #F
-- .;X @+ .;Y @+ #C .;Z .K --#C
#C .;X -- #C .;Y @+ #B .;Z .K #I
,A @7-- .;X1 .;X @+ #B1 #J7
;,B @7 .;X1 .;X -- #C1 #J7
;,C @7 .;X @+ #B1 .;X @1 #J7
;,D 7#J1 .;Y1 .;Y @+ #D7
,,*OOS+ ,A ,,ME?OD ,SOLVE ! SY/EM US+
ANY ALGEBRAIC ME?OD4
.#BE4
.#BF4
.#BG4
.#BH4
.#BI4
.#CJ4
.#CA4
.#CB4
.#CC4
#CD4 .,,OP5-.,,5D$ .,,MA? ,WRITE A
SY/EM ( ?REE L9E> EQU,NS 9 ?REE V>IA#S T
HAS ! GIV5 NUMB] ( SOLU;NS4
A4 ,"O SOLU;N
B4 ,NO SOLU;N
C4 ,9F9ITELY _M SOLU;NS
,,SY/EMS ,,) ,,FRAC;NS ,SOLVE ! SY/EM
US+ ANY ALGEBRAIC ME?OD4
.#CE4
.#CF4
.#CG4 .,,R1SON+ ,= :AT VALUES ( .A1
.;B @1 & .;C DOES ! L9E> SY/EM %[N H
7--#A1 #B1 --#C7 Z XS ONLY SOLU;N8
.,EXPLA9 YR R1SON+4
.;X @+ #B .;Y -- #C .;Z .K .A
-- .;X -- .;Y @+ .;Z .K .;B
#B .;X @+ #C .;Y -- #B .;Z .K .;C
,,*ALL5GE ,SOLVE ! SY/EM ( EQU,NS4
.,DESCRIBE EA* /EP ( YR SOLU;N4
.#CH4
.#CI4
.#DJ4
.#DA4
------------------------------------#AHD
,PRO#M ,SOLV+
,,EXAMPLE #D
ON P4 #AHA = ,EXS4 #DB-DG
.#DB4 .,,PIZZA .,,SPECIALS ,AT A PIZZA
%OP1 TWO SMALL PIZZAS1 A LIT] ( SODA1 &A
SALAD CO/ 4#AD2 "O SMALL PIZZA1 A LIT] (
SODA1 & ?REE SALADS CO/ 4#AE2 & ?REE
SMALL PIZZAS &A LIT] ( SODA CO/ 4#AF4
,:AT IS ! CO/ ( "O SMALL PIZZA8 ( "O
LIT] ( SODA8 ( "O SALAD8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#DC4 .,,H1L? .,,CLUB ,! JUICE B> AT A
H1L? CLUB RCVS A DELIV]Y ( JUICE AT !
2G9N+ ( EA* MON?4 ,OV] A ?REE MON?
P]IOD1 ! H1L? CLUB RCVD #ABJJ GALLONS (
ORANGE JUICE1 #IJJ GALLONS ( P9EAPPLE
JUICE1 & #AJJJ GALLONS ( GRAPEFRUIT
JUICE4 ,! TA# %[S ! -POSI;N ( EA* JUICE
DELIV]Y4 ,H[ _M GALLONS ( JUICE DID !
H1L? CLUB RCV 9 EA* DELIV]Y8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,JUICE3 #A/ DELIV]Y3 #BND DELIV]Y3
#CRD DELIV]Y
.,ORANGE @3 .#GJ@3P @3 .#EJ@3P @3
#CJ@3P
.,P9EAPPLE @3 .#BJ@3P @3 .#CJ@3P @3
#CJ@3P
.,GRAPEFRUIT @3 .#AJ@3P @3 .#BJ@3P @3
#DJ@3P
#DD4 .,,MULTI-.,,/EP .,,PRO#M ,Y MAKE
A TAPE ( YR FR'S ?REE FAVORITE ,,TV %[S3
A -$Y1 A DRAMA1 &A R1L;Y %[4 ,AN EPISODE
(! -$Y LA/S #CJ M9UTES1 :ILE AN EPISODE
(! DRAMA OR ! R1L;Y %[ LA/S #FJ M9UTES4
,! TAPE C HOLD #CFJ M9UTES ( PROGRAMM+4
,Y -PLETELY FILL ! TAPE ) #G EPISODES &
9CLUDE TWICE Z _M EPISODES (! DRAMA Z !
-$Y4
A4 ,WRITE A SY/EM ( EQU,NS 6REPRES5T ?
SITU,N4
B4 ,SOLVE ! SY/EM F "P 7A74 ,H[ _M
EPISODES ( EA* %[ >E ON ! TAPE8
C4 ,H[ WD YR ANSW] 6"P 7;B7 *ANGE IF Y
-PLETELY FILL$ ! TAPE ) ONLY #E EPISODES
B / 9CLUD$ TWICE Z _M EPISODES (! DRAMA
Z ! -$Y8
.#DE4 .,,%ORT .,,RESPONSE ,! FOLL[+
,9T]NET ANN\NCE;T DESCRIBES ! SUITS (A
HI< S*OOL TRACK MEET4
A4 ,WRITE & SOLVE A SY/EM ( EQU,NS
6F9D ! NUMB] ( A?LETES :O F9I%$ 9 F/
PLACE1 9 SECOND PLACE1 & 9 ?IRD PLACE4
B4 ,SUPPOSE ! ANN\NCE;T _H CLAIM$ T !
,MADISON A?LETES SCOR$ A TOTAL ( #GJ
PO9TS 9/1D ( #FH PO9TS4 ,%[ T ? CLAIM M/
2 FALSE 2C ! SOLU;N (! RESULT+ L9E>
SY/EM IS N R1SONA#4
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#AHE
.#DF4 .,,FIELD .,,TRIP ,Y & TWO FRS
BUY SNACKS =A FIELD TRIP4 ,Y SP5D A
TOTAL ( 4#H1 ,JEFF SP5DS 4#I1 & ,CURTIS
SP5DS 4#I4 ,! TA# %[S ! AM.TS ( MIX$
NUTS1 GRANOLA1 & DRI$ FRUIT T EA* P]SON
PUR*AS$4 ,:AT IS ! PRICE P] P.D ( EA*
TYPE ( SNACK8
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 ,MIX$ NUTS3 ,GRANOLA3 ,DRI$ FRUIT
.,Y @3 .#A .LB @3 .#J..E .LB @3 .#A
.LB
.,JEFF @3 .#B .LB @3 .#J..E .#A;B @3
.#J..E .LB
.,CURTIS @3 .#A .LB @3 .#B .#A;B @3
.#J..E .#A;B
#DG4 .,,EXT5D$ .,,RESPONSE ,A FLORI/
M/ MAKE #E ID5TICAL BRIDESMAID B\QUETS
=A W$D+4 ,%E HAS A BUDGET ( 4#AFJ &
WANTS #AB FL[]S = EA* B\QUET4 ,ROSES CO/
4#B.EJ EA*1 LILIES CO/ 4#D EA*1 & IRISES
CO/ 4#B EA*4 ,%E WANTS TWICE Z _M ROSES
Z ! O!R TWO TYPES ( FL[]S -B9$4
A4 .,WRITE ,WRITE A SY/EM ( EQU,NS
6REPRES5T ? SITU,N4
B4 .,SOLVE ,SOLVE ! SY/EM ( EQU,NS4
,H[ _M ( EA* TYPE ( FL[] %D 2 9 EA*
B\QUET8
C4 .,ANALYZE ,SUPPOSE "! IS NO LIMIT,N
ON ! TOTAL CO/ (! B\QUETS4 ,DOES ! PRO#M
/ H A UNIQUE SOLU;N8 ,IF S1 /ATE !
UNIQUE SOLU;N4 ,IF N1 GIVE ?REE POSSI#
SOLU;NS4
#DH4 .,,*ALL5GE ,WRITE A SY/EM (
EQU,NS 6REPRES5T ! F/ ?REE PICTURES 2L4
,USE ! SY/EM 6DET]M9E H[ _M TANG]9ES W
BAL.E ! APPLE 9 ! F9AL PICTURE4 .,NOTE3
,! F/ PICTURE %[S T "O TANG]9E & "O
APPLE BAL.E "O GRAPEFRUIT4
,MIX$ ,REVIEW
#DI4 #AE @+ 7-#H7
#EJ4 -#D--7-#AC7
#EA4 #AE @* #G
#EB4 -#D7-#H7
.,,PREVIEW ,PREP>E = ,LESSON #C.E 9
,EXS4 #DI-EB4
,F9D ! SLOPE (! L9E PASS+ "? ! GIV5
PO9TS4 ,!N TELL :E!R ! L9E ..RISES1
FALLS1 IS .HORIZONTAL @1 OR .IS .V]TICAL
@4 @7 P4 #HB @7
#EC4 7#A1 -#D71 7#B1 #F7
#ED4 7#D1 #B71 7-#AH1 #A7
#EE4 7#F1 -#F71 7-#F1 #F7
#EF4 7-#E1 #B71 7-#E1 #AJ7
#EG4 7-#B1 #D71 7-#F1 #H7
#EH4 7-#G1 #C71 7#E1 #C7
,SOLVE ! SY/EM US+ ANY ALGEBRAIC
ME?OD4 @7 P4 #AFJ @7
#EI4 #C .;X - .;Y .K -#G
#B .;X @+ #C .;Y .K #BA
#FJ4 #C .;X @+ #B .;Y .K -#C
#D .;X - #C .;Y .K--#CH
#FA4 #E .;X @+ .;Y .K #AA
#B .;X @+ #C .;Y .K -#AI
.,,EXTRA .,,PRACTICE = ,LESSON #C.D1
P4 #AJAB
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#AHF
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
..,,/ATE ,,TE/ ,,PRACTICE AT
_+CLASSZONE.COM_:
,LESSONS #C.A-C.D
#A4 .,,MULTI-.,,/EP .,,PRO#M ,Y >E
MAK+ JEWELRY 6SELL AT A CRAFT FAIR4 ,!
CO/ ( MAT]IALS IS 4#C.EJ 6MAKE "O
NECKLACE & 4#B.EJ 6MAKE "O BRACELET4 ,Y
SELL ! NECKLACES = 4#I.JJ EA* &!
BRACELETS = 4#G.EJ EA*4 ,Y SP5D A TOTAL
( 4#ABA ON MAT]IALS & SELL ALL (!
JEWELRY =A TOTAL ( 4#CBD4
A4 ,WRITE A SY/EM ( EQU,NS T REPRES5TS
? SITU,N4
B4 ,SOLVE ! SY/EM 6F9D H[ _M NECKLACES
& H[ _M BRACELETS 7 SOLD4
#B4 .,,MULTI-.,,/EP .,,PRO#M ,Y >E
MAK+ GIFT BASKETS4 ,EA* BASKET W 3TA9
?REE DI6]5T K9DS ( C&LES3 TAP]S1 PILL>S1
& J> C&LES4 ,TAP]S CO/ 4#A EA*1 PILL>S
CO/ 4#D EA*1 & J> C&LES CO/ 4#F EA*4 ,Y
PUT #H C&LES CO/+ A TOTAL ( 4#BD 9 EA*
BASKET1 & Y 9CLUDE Z _M TAP]S Z PILL>S &
J> C&LES -B9$4
A4 ,WRITE A SY/EM ( EQU,NS T REPRES5TS
? SITU,N4
B4 ,SOLVE ! SY/EM ( EQU,NS4 ,H[ _M (
EA* TYPE ( C&LE IS 9 A BASKET8
C4 ,SUPPOSE "! >E NO RE/RIC;NS ON !
VALUE (! C&LES 9CLUD$ 9 EA* BASKET4
,DOES ! PRO#M / H A UNIQUE SOLU;N8 ,IF
S1 /ATE ! UNIQUE SOLU;N4 ,IF N1 GIVE
?REE POSSI# SOLU;NS4
#C4 .,,OP5-.,,5D$ ,WRITE A SY/EM (
L9E> 9EQUALITIES ^: GRAPH IS ! 9T]IOR (A
"R TRIANGLE4
#D4 .,,%ORT .,,RESPONSE ,A RE/AURANT
HAS #BJ TA#S4 ,EA* TA# C S1T EI #D P OR
#F P4 ,! RE/AURANT C S1T A TOTAL ( #IJ
P4
A4 ,H[ _M #D S1T TA#S & H[ _M #F S1T
TA#S DOES ! RE/AURANT H8
B4 .,DESCRIBE ?REE WAYS 9 : !
RE/AURANT C 9CR1SE XS CAPAC;Y 6#ADJ P
0BUY+ A4I;NAL #D S1T & #F S1T TA#S4
#E4 .,,GR#A;,,DD$ .,,ANSW] ,AT A SNACK
BOO?1 "O SODA1 "O PRETZEL1 & TWO HOT
DOGS CO/ 4#G2 TWO SODAS1 "O PRETZEL1 &
TWO HOT DOGS CO/ 4#H2 & "O SODA & F\R
HOT DOGS CO/ 4#AJ4 ,:AT IS ! PRICE 7IN
DOLL>S7 ( "O HOT DOG8
#F4 .,,GRI4$ .,,ANSW] ,YR S*OOL IS
PLANN+ A #E H\R \T+ AT A -MUN;Y P>K4 ,!
P>K R5TS BICYCLES = 4#H P] H\R & 9L9E
SKATES = 4#F P] H\R4 ,! TOTAL BUDGET P]
/UD5T IS 4#CD4 ,A /UD5T BIKES & SKATES !
5TIRE "T & USES ALL ! M"OY BUDGET$4 ,H[
_M H\RS DOES ! /UD5T SP5D 9L9E SKAT+8
#G4 .,,EXT5D$ .,,RESPONSE ,! TA# %[S !
EXPECT$ LIFE SPANS AT BIR? = M5 & WOM5
BORN 9 ! YE>S #AIIF-BJJJ4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,YE>S S9CE #AIIF1 .;X @3 ,M5'S LIFE
SPAN 7YE>S71 .;M @3 ,WOM5'S LIFE SPAN
7YE>S71 .;W
#J3 #GC.J3 #GI.J
#A3 #GC.F3 #GI.D
#B3 #GC.H3 #GI.E
#C3 #GC.I3 #GI.D
#D3 #GD.C3 #GI.G
A4 ,WRITE AN EQU,N (! BE/-FITT+ L9E =!
DATA PAIRS @7 .;X1 .;M @7@4
B4 ,WRITE AN EQU,N (! BE/-FITT+ L9E =!
DATA PAIRS @7 .;X1 .;W @7@4
C4 ,GRAPH ! EQU,NS F "PS 7A7 & 7;B7 &
E/IMATE ! COORD9ATES (! 9T]SEC;N PO9T4
.,EXPLA9 :AT ? PO9T REPRES5TS4
#H4 .,,MULTI-.,,/EP .,,PRO#M ,A /ORE
ORD]S WOOD5 *AIRS1 H& PA9TS !M1 & SELLS
! *AIRS =A PR(IT4 ,A SMALL *AIR CO/S !
/ORE 4#DE & SELLS = 4#HJ4 ,A L>GE *AIR
CO/S ! /ORE 4#GJ & SELLS = 4#AAJ4 ,!
/ORE WANTS 6PAY NO M ?AN 4#BJJJ = XS
NEXT ORD] ( *AIRS & WANTS 6SELL !M ALL =
AT L1/ 4#BGEJ4
A4 ,WRITE & GRAPH A SY/EM (
9EQUALITIES T REPRES5TS ? SITU,N4
B4 ,ID5TIFY ?REE POSSI# -B9,NS ( SMALL
& L>GE WOOD5 *AIRS T ! /ORE C BUY &
SELL4
------------------------------------#AHG
#C.E ,P]=M ,BASIC ,MATRIX ,OP],NS
.,2F ,Y P]=M$ OP],NS ) R1L NUMB]S4
.,N[ ,Y W P]=M OP],NS ) MATRICES4
.,:Y8 ,S Y C ORGANIZE SPORTS DATA1 Z 9
,EX4 #CD4
,KEY ,VOCABUL>Y
99 MATRIX
99 DIM5.NS
99 ELE;TS
99 EQUAL MATRICES
99 SCAL>
99 SCAL> MULTIPLIC,N
,SIDEB>3
,/&>DS
.,PREP>E .#B..J ,/UD5TS SOLVE SY/EMS (
L9E> EQU,NS & 9EQUALITIES 7IN TWO OR
?REE V>IA#S7 0SUB/ITU;N1 ) GRAPHS1 OR )
MATRICES4
,A .MATRIX IS A RECTANGUL> >RANGE;T (
NUMB]S 9 R[S & COLUMNS4 ,= EXAMPLE1
MATRIX ,A 2L HAS TWO R[S & ?REE COLUMNS4
,! .DIM5.NS (A MATRIX ) .;M R[S & .;N
COLUMNS >E .;M * .;N 7R1D @8 .;M 0.;N
@8@7@4 ,S1 ! DIM5.NS ( MATRIX .,A >E #B
* #C4 ,! NUMB]S 9 A MATRIX >E XS
.ELE;TS4
,TWO MATRICES >E .EQUAL IF _! DIM5.NS
>E ! SAME &! ELE;TS 9 CORRESPOND+
POSI;NS >E EQUAL4
,,KEY ,,3CEPT .= .,YR .,NOTEBOOK
,A4+ & ,SUBTRACT+ ,MATRICES
,6ADD OR SUBTRACT TWO MATRICES1 SIMPLY
ADD OR SUBTRACT ELE;TS 9 CORRESPOND+
POSI;NS4 ,Y C ADD OR SUBTRACT MATRICES
ONLY IF !Y H ! SAME DIM5.NS4
.,A4+ .,MATRICES
.,SUBTRACT+ .,MATRICES
,EXAMPLE #A ,ADD & SUBTRACT MATRICES
,,AVOID ,,]RORS
,2 SURE 6V]IFY T ! DIM5.NS ( TWO
MATRICES >E EQUAL 2F A4+ OR SUBTRACT+
!M4
,P]=M ! 9DICAT$ OP],N1 IF POSSI#4
.A4
.B4
------------------------------------#AHH
.,,SCAL> .,,MULTIPLIC,N ,9 MATRIX
ALGEBRA1 A R1L NUMB] IS (T5 CALL$ A
.SCAL>4 ,6MULTIPLY A MATRIX 0A SCAL>1 Y
MULTIPLY EA* ELE;T 9 ! MATRIX 0! SCAL>4
,? PROCESS IS CALL$ .SCAL> .MULTIPLIC,N4
,EXAMPLE #B ,MULTIPLY A MATRIX 0A
SCAL>
,,-P>E ,,ORD] ,,( ,,OP],NS
,! ORD] ( OP],NS = MATRIX EXPRES.NS IS
SIMIL> 6T = R1L NUMB]S4 ,9 "PICUL>1 Y
P]=M SCAL> MULTIPLIC,N 2F MATRIX A4I;N &
SUBTRAC;N4
,P]=M ! 9DICAT$ OP],N1 IF POSSI#4
.A4
.B4
..,GUID$ ,PRACTICE = ,EXAMPLES #A &
.#B
,P]=M ! 9DICAT$ OP],N1 IF POSSI#4
.#A4
.#B4
.#C4
.#D4
.,,MATRIX .,,PROP]TIES ,_M (!
PROP]TIES Y H US$ ) R1L NUMB]S C 2
APPLI$ 6MATRICES Z WELL4
,,3CEPT ,,SUMM>Y .,= .,YR .,NOTEBOOK
,PROP]TIES ( ,MATRIX ,OP],NS
,LET .,A1 .;,B @1 & .;,C 2 MATRICES )!
SAME DIM5.NS1 & LET .;K 2 A SCAL>4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
..,ASSOCIATIVE ,PROP]TY ( .,A4I;N @3
@7 .,A @+ .;,B @7 @+ .;,C .K .,A @+ @7
.;,B @+ .;,C @7
..,-MUTATIVE ,PROP]TY ( .,A4I;N @3 .,A
@+ .;,B .K .;,B @+ .,A
..,4TRIBUTIVE ,PROP]TY ( .,A4I;N @3
.;K @7 .,A @+ .;,B @7 .K .K,A @+ .K,B
..,4TRIBUTIVE ,PROP]TY ( .,SUBTRAC;N
@3 .;K @7 .,A -- .;,B @7 .K .K,A -- .K,B
------------------------------------#AHI
.,,ORGANIZ+ .,,DATA ,MATRICES >E USE;L
= ORGANIZ+ DATA &= P]=M+ ! SAME OP],NS
ON L>GE NUMB]S ( DATA VALUES4
,EXAMPLE #C ,SOLVE A MULTI-/EP PRO#M
.,,MANUFACTUR+ ,A -PANY MANUFACTURES
SMALL & L>GE /EEL ,,DVD RACKS ) WOOD5
BASES4 ,EA* SIZE ( RACK IS AVAILA# 9
?REE TYPES ( WOOD3 WALNUT1 P9E1 & *]RY4
,SALES (! RACKS = LA/ MON? & ? MON? >E
%[N 2L4
,ORGANIZE ! DATA US+ TWO MATRICES1 "O
= LA/ MON?'S SALES & "O = ? MON?'S
SALES4 ,!N WRITE & 9T]PRET A MATRIX GIV+
! AV]AGE MON?LY SALES =! TWO MON? P]IOD4
,SOLU;N
.,,/EP .#A .,ORGANIZE ! DATA US+ TWO
#C * #B MATRICES1 Z %[N4
.,,/EP .#B .,WRITE A MATRIX =! AV]AGE
MON?LY SALES 0F/ A4+ ,A& .;,B 6F9D !
TOTAL SALES & !N MULTIPLY+ ! RESULT BY
@4
.,,/EP .#C .,9T]PRET ! MATRIX F ,/EP
#B4 ,! -PANY SOLD AN AV]AGE ( #AAJ SMALL
WALNUT RACKS1 #AJG L>GE WALNUT RACKS1
#BIG SMALL P9E RACKS1 #BCC L>GE P9E
RACKS1 #BAE SMALL *]RY RACKS1 & #BHE
L>GE *]RY RACKS4
,,ANO!R ,,WAY
,Y C AL EVALUATE 0F/ US+ ! 4TRIBUTIVE
PROP]TY 6REWRITE ! EXPRES.N Z @4
------------------------------------#AIJ
.,,SOLV+ .,,MATRIX .,,EQU,NS ,Y C USE
:AT Y "K AB MATRIX OP],NS & MATRIX
EQUAL;Y 6SOLVE AN EQU,N 9VOLV+ MATRICES4
,EXAMPLE #D ,SOLVE A MATRIX EQU,N
,SOLVE ! MATRIX EQU,N = .;X & .;Y @4
,SOLU;N
.,SIMPLIFY ! LEFT SIDE (! EQU,N4
.,EQUATE CORRESPOND+ ELE;TS & SOLVE !
TWO RESULT+ EQU,NS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#AE .;X @+ #I .K --#BA @3 --#AB --#C
.;Y .K --#BD
.;X .K --#B @3 .;Y .K #D
,! SOLU;N IS .;X .K --#B & .;Y .K #D4
..,GUID$ ,PRACTICE = ,EXAMPLES #C &
.#D
.#E4 ,9 ,EXAMPLE #C1 F9D .;,B -- .,A &
EXPLA9 :AT 9=M,N ? MATRIX GIVES4
.#F4 ,SOLVE = .;X & .;Y @4
#C.E ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#F = ,EXS4 #E1 #BA1 & #CC
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 #B1BH1BI1CC1 & #CD
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,!
@8 (A MATRIX ) #C R[S & #D COLUMNS >E #C
* #D4
.#B4 .,,WRIT+ .,DESCRIBE H[ 6DET]M9E
:E!R TWO MATRICES >E EQUAL4
.#C4 .,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 A4+ ! MATRICES4
,,EXAMPLE #A
ON P4 #AHG = ,EXS4 #C-I
------------------------------------#AIA
,,A4+ ,,& ,,SUBTRACT+ ,,MATRICES ,P]=M
! 9DICAT$ OP],N1 IF POSSI#4 ,IF N
POSSI#1 /ATE ! R1SON4
.#D4
.#E4
.#F4
.#G4
.#H4
.#I4
,,EXAMPLE #B
ON P4 #AHH = ,EXS4 #AJ-AE
,,MULTIPLY+ ,,0,A ,,SCAL> ,P]=M !
9DICAT$ OP],N4
.#AJ4
.#AA4
.#AB4
.#AC4
.#AD4
.#AE4
,,MATRIX ,,OP],NS ,USE MATRICES .,A1
.;,B @1 ;,C1 & .;,D 6EVALUATE ! MATRIX
EXPRES.N4
.#AF4 .,A @+ .;,B
.#AG4 .;,B -- .,A
.#AH4 #D .,A -- .;,B
.#AI4
.#BJ4 .;,C @+ .;,D
.#BA4 .;,C @+ #C .;,D
.#BB4 .;,D -- #B .;,C
.#BC4 #J.E .;,C -- .;,D
,,EXAMPLE #D
ON P4 #AIJ = ,EXS4 #BD--#BG
,,SOLV+ ,,MATRIX ,,EQU,NS ,SOLVE !
MATRIX EQU,N = .;X & .;Y @4
.#BD4
.#BE4
.#BF4
.#BG4
#BH4 .,,MULTIPLE .,,*OICE ,BAS$ ON !
EQU,N 2L1 :AT IS ! VALUE (! EXPRES.N #C
.;X -- #B .;Y @8
,A #G.AE
;,B #I.A
;,C #AJ.A
;,D #BJ.G
#BI4 .,,OP5-.,,5D$ .,,MA? ,F9D TWO
MATRICES .,A & .;,B S* T
#CJ4 .,,*ALL5GE ,F9D ! MATRIX .;,X T
MAKES ! EQU,N TRUE4
A4
B4
C4
D4
------------------------------------#AIB
,PRO#M ,SOLV+
,,EXAMPLE #C
ON P4 #AHI = ,EXS4 #CA-CD
.#CA4 .,,SN[BO>D .,,SALES ,A SPORT+
GDS /ORE SELLS SN[BO>DS 9 S"EAL DI6]5T
/YLES & L5G?S4 ,! MATRICES 2L %[ ! NUMB]
( EA* TYPE ( SN[BO>D SOLD 9 #BJJC &
#BJJD4 ,WRITE A MATRIX GIV+ ! *ANGE 9
SALES = EA* TYPE ( SN[BO>D F #BJJC
6#BJJD4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#CB4 .,,FUEL .,,ECONOMY ,A C> D1L]%IP
SELLS F\R DI6]5T MODELS ( C>S4 ,! FUEL
ECONOMY 7IN MILES P] GALLON7 IS %[N 2L =
EA* MODEL4 ,ORGANIZE ! DATA US+ A
MATRIX4 ,!N WRITE A NEW MATRIX GIV+ !
FUEL ECONOMY FIGURES = NEXT YE>'S MODELS
IF EA* M1SURE ( FUEL ECONOMY 9CR1SES
0#H@3P4
.,ECONOMY .C>3 #CB MPG 9 C;Y DRIV+1
#DJ MPG 9 HI<WAY DRIV+
.,MID-.SIZE .C>3 #BD MPG 9 C;Y DRIV+1
#CD MPG 9 HI<WAY DRIV+
.,M9I-.VAN3 #AH MPG 9 C;Y DRIV+1 #BE
MPG 9 HI<WAY DRIV+
.,,SUV3 #AI MPG 9 C;Y DRIV+1 #BB MPG 9
HI<WAY DRIV+
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#CC4 .,,EXT5D$ .,,RESPONSE ,9 A C]TA9
C;Y1 AN ELECTRONICS *A9 HAS A D[NT[N
/ORE &A /ORE 9 ! MALL4 ,EA* /ORE C>RIES
?REE MODELS ( DIGITAL CAM]A4 ,SALES (!
CAM]AS = ,MAY & ,JUNE >E %[N4
,! FOLL[+ TA# IS 9 LI/$
=MAT4 ,= EA* CELL ! H1D+ IS %[N
FOLL[$ 0A COLON1 SPACE &! CELL
3T5TS
.,MAY @3 ,MALL SALES3 #BB ( MODEL ,A1
#BE ( MODEL ;,B1 #AA ( MODEL ;,C
.,MAY @3 .,JUNE
,D[NT[N SALES3 #CA ( MODEL ,A1 #DB (
MODEL ;,B1 #AH ( MODEL ;,C3 ,D[NT[N
SALES3 #BE ( MODEL ,A1 #CF ( MODEL ;,B1
#AB ( MODEL ;,C
.,MAY @3 .,JUNE
,D[NT[N SALES3 #CA ( MODEL ,A1 #DB (
MODEL ;,B1 #AH ( MODEL ;,C3 ,MALL SALES3
#CH ( MODEL ,A1 #CB ( MODEL ;,B1 #AE (
MODEL ;,C
A4 ,ORGANIZE ! 9=M,N US+ TWO MATRICES
.;,M & ;,J T REPRES5T ! SALES = ,MAY &
,JUNE1 RESPECTIVELY4
B4 ,F9D .;,M @+ .;,J & DESCRIBE :AT ?
MATRIX SUM REPRES5TS4
C4 ,WRITE A MATRIX GIV+ ! AV]AGE
MON?LY SALES =! TWO MON? P]IOD4
#CD4 .,,%ORT .,,RESPONSE ,! MATRICES
2L %[ ! NUMB]S ( FEMALE A?LETES :O
"PICIPAT$ 9 SELECT$ ,,NCAA SPORTS &!
AV]AGE T1M SIZE = EA* SPORT DUR+ !
#BJJJ-BJJA & #BJJA-BJJB S1SONS4 ,DOES !
MATRIX .,A @+ .;,B GIVE M1N+;L 9=M,N8
.,EXPLA94
.K ..,,"W$-,,\ ,,SOLU;NS .ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#AIC
.#CE4 .,,*ALL5GE ,A RECTANGLE HAS
V]TICES 7#A1 #A71 7#A1 #D71 7#E1 #A71 &
7#E1 #D74 ,WRITE A #B * #D MATRIX ,A ^:
COLUMNS >E ! V]TICES (! RECTANGLE4
,MULTIPLY MATRIX .,A 0#C4 ,9 ! SAME
COORD9ATE PLANE1 DRAW ! RECTANGLES
REPRES5T$ 0! MATRICES .,A & #C .,A4 ,H[
>E ! RECTANGLES RELAT$8
,MIX$ ,REVIEW
,P]=M ! 9DICAT$ OP],N4 @7 P4 #IGE @7
.,,PREVIEW ,PREP>E = ,LESSON #C.F 9
,EXS4 #CF-DA4
#CF4 #E @+ 7-#H7
#CG4 -#G @+ #F
#CH4 #H7-#G7
#CI4 -#F--7-#AE7
#DJ4 -#E7-#I7
#DA4 #F--7-#AH7
,WRITE AN EQU,N (! GRAPH %[N4 @7 P4
#ABC @7
#DB4
#DC4
#DD4
,*ECK :E!R ! ORD]$ PAIRS >E SOLU;N (!
9EQUAL;Y4 @7 P4 #ACB @7
#DE4 .;X @+ #B .;Y "K.K -#C2 7#J1 #C71
7-#E1 #A7
#DF4 #E .;X - .;Y .1 #B2 7-#E1 #J71
7#E1 #BC7
#DG4 -#H .;X - #C .;Y "K #E2 7-#A1
#A71 7#C1 -#I7
#DH4 #BA .;X - #AJ .;Y .1 #D2 7#B1
#C717-#A1 #J7
,,QUIZ = .,LESSONS .#C..C-.C..E
,GRAPH ! SY/EM ( 9EQUALITIES1 @7 P4
#AFH @7
.#A4
.#B4
.#C4
.#D4
.#E4
.#F4
,SOLVE ! SY/EM US+ ANY ALGEBRAIC
ME?OD4 7.;P .#AGH7
.#G4
.#H4
.#I4
,USE MATRICES .,A1 .;,B @1 & .;,C
6EVALUATE ! MATRIX EXPRES.N1 IF POSSI#4
,IF N POSSI#1 /ATE ! R1SON1 @7 P4 #AHG
@7
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
@3 @3
.#AJ4 .,A @+ .;,B
.#AA4 .;,B -- #B .,A
.#AB4 #C .,A @+ .;,C
.#AC4 .;,C
.#AD4 .,,APPLES ,Y H 4#BE 6SP5D ON #BA
P.DS ( ?REE TYPES ( APPLES4 ,EMPIRE
APPLES CO/ 4#A.DJ P] P.D1 ,R$ ,DELICI\S
APPLES CO/ 4#A.AJ P] P.D1 & ,GOLD5
,DELICI\S APPLES CO/ 4#A.CJ P] P.D4 ,Y
WANT TWICE Z _M ,R$ ,DELICI\S APPLES Z !
O!R TWO K9DS -B9$4 ,USE A SY/EM ( EQU,NS
6F9D H[ _M P.DS ( EA* TYPE Y %D BUY4 @7
P4 #AGH @7
.,,EXTRA .,,PRACTICE = ,LESSON #C.E1
P4 #AJAB
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#AID
,GRAPH+ ,CALCULATOR ,ACTIV;Y3 #C.E
,USE ,MATRIX ,OP],NS
,USE AF LESSON #C.E
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,KEY/ROKES
,SIDEB>3
,/&>DS
..#B.J ,/UD5TS SOLVE SY/EMS ( L9E>
.EQU,NS & 9EQUALITIES @7 .9 .TWO OR ?REE
.V>IA#S @7 0SUB/ITU;N1 .) .GRAPHS @1 OR
) MATRICES4
,"Q ,H[ C Y USE A GRAPH+ CALCULATOR
6P]=M MATRIX OP],NS8
,EXAMPLE ,P]=M OP],NS ) MATRICES
,US+ MATRICES .,A & .;,B 2L1 F9D .,A
@+ .;,B & .#C;,A -- .#B,B4
,,/EP #A ,5T] MATRIX ,A
,5T] ! DIM5.NS & ELE;TS ( MATRIX .,A4
,,/EP #B ,5T] MATRIX ;,B
,5T] ! DIM5.NS & ELE;TS ( MATRIX .,B4
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99 DIM5.NS1 .P4 .#AHG
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.V>IA#S @7 0SUB/ITU;N1 ) GRAPHS1 OR .)
.MATRICES4
,ASSOCIAT$ ) EA* SQU>E 7.;N * .;N7
MATRIX IS A R1L NUMB] CALL$ XS
.DET]M9ANT4 ,! DET]M9ANT (A MATRIX .,A
IS DENOT$ 0DET .,A OR BY _\ .,A _\.
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,! ,DET]M9ANT (A ,MATRIX
,DET]M9ANT (A #C * #C ,MATRIX
.,,/EP .#A .,REP1T ! F/ TWO COLUMNS 6!
"R (! DET]M9ANT4
.,,/EP .#B .,SUBTRACT ! SUM .( ! .R$
.PRODUCTS F ! SUM (! .BLUE .PRODUCTS4
,EXAMPLE #A ,EVALUATE DET]M9ANTS
,EVALUATE ! DET]M9ANT (! MATRIX4
.A4
.B4
,SOLU;N
.A4
.B4
------------------------------------#BJD
..,,>EA ,,( ,A .,,TRIANGLE ,Y C USE A
DET]M9ANT 6F9D ! >EA (A TRIANGLE ^:
V]TICES >E PO9TS 9 A COORD9ATE PLANE4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,>EA (A ,TRIANGLE
,! >EA (A TRIANGLE ) V]TICES @7 .;X #A
.;Y #A @1 7.;X #B @1 .;Y #B @7 @1 & 7;X
#C @1 ;Y #C @7 IS GIV5 BY
": ! SYMBOL +- 9DICATES T !
APPROPRIATE SIGN %D 2 *OS5 6YIELD A
POSITIVE VALUE4
,EXAMPLE #B ,F9D ! >EA (A TRIANGUL>
REGION
.,,SEA .,,LIONS ,(F ! COA/ ( ,CALI=NIA
LIES A TRIANGUL> REGION (! ,PACIFIC
,OC1N ": HUGE POPUL,NS ( SEA LIONS &
S1LS LIVE4 ,! TRIANGLE IS =M$ 0IMAG9>Y
L9ES 3NECT+ ,BODEGA ,BAY1 ! ,F>ALLON
,ISL&S1 & ,AFIO ,NUEVO ,ISL&1 Z %[N4
7,IN ! MAP1 ! COORD9ATES >E M1SUR$ 9
MILES47 ,USE A DET]M9ANT 6E/IMATE ! >EA
(! REGION4
,SOLU;N
,! APPROXIMATE COORD9ATES (! V]TICES
(! TRIANGUL> REGION >E 7-#A1 #DA71 7#CH1
--#DC71 & 7#J1 #J74 ,S1 ! >EA (! REGION
IS3
,! >EA (! REGION IS AB #GEH SQU>E
MILES4
..,GUID$ ,PRACTICE = ,EXAMPLES #A &
.#B
,EVALUATE ! DET]M9ANT (! MATRIX4
.#A
.#B
.#C
.#D4 ,F9D ! >EA (! TRIANGLE ) V]TICES
.,A 7#E1 #AA71 .;,B 7#I1 #B71 & .;,C
7;L1 #C74
------------------------------------#BJE
.,,CRAM]'S .,,RULE ,Y C USE DET]M9ANTS
6SOLVE A SY/EM ( L9E> EQU,NS4 ,! ME?OD1
CALL$ .,CRAM]'S .RULE & "ND AF ! ,SWISS
MA!MATICIAN ,GABRIEL ,CRAM]
7#AGJD-AGEB71 USES ! .COE6ICI5T .MATRIX
(! L9E> SY/EM4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,CRAM]S ,RULE =A #B * #B ,SY/EM
,LET ,A 2 ! COE6ICI5T MATRIX ( ? L9E>
SY/EM3
.AX @+ .BY .K .;E
.EX @+ .DY .K .;F
,IF DET .,A @6.K #J1 !N ! SY/EM HAS
EXACTLY "O SOLU;N4 ,! SOLU;N IS3
,NOTICE T ! NUM]ATORS = .;X & .;Y >E !
DET]M9ANTS (! MATRICES =M$ 0REPLAC+ !
COE6ICI5TS ( .;X & ;Y1 RESPECTIVELY1 )!
COLUMN ( 3/ANTS4
,EXAMPLE #C ,USE ,CRAM]S RULE =A #B *
#B SY/EM
,USE ,CRAM]'S RULE 6SOLVE ? SY/EM3
#I .;X @+ #D .;Y .K--#F
#C .;X --#E .;Y .K--#BA
,,ANO!R ,,WAY
,Y C AL SOLVE ! SY/EM 9 ,EXAMPLE #C
US+ ! SUB/ITU;N ME?OD OR ! ELIM9,N ME?OD
Y LE>N$ 9 ,LESSON #C.B4
,SOLU;N
.,,/EP .#A .,EVALUATE ! DET]M9ANT (!
COE6ICI5T MATRIX4
.,,/EP#B .,APPLY ,CRAM]'S RULE 2C !
DET]M9ANT IS N #J4
,! SOLU;N IS 7-#B1C74
.,,*ECK ,*ECK ? SOLU;N 9 ! ORIG9AL
EQU,NS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#I .;X @+ #D .;Y .K --#F @3 #C .;X --
#E .;Y .K --#BA
#I7--#B7 @+ #D7#C7 --#F @3
#C7--#B7--#E7#C7 --#BA
--#AH @+ #AB --#F @3 --#F--#AE --#BA
--#F .K --#F @3 --#BA .K --#BA
------------------------------------#BJF
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,CRAM]'S ,RULE =A #C * #C ,SY/EM
,LET .,A 2 ! COE6ICI5T MATRIX (! L9E>
SY/EM %[N 2L4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,L9E> ,SY/EM3 ,COE6ICI5T ,MATRIX
.AX @+ .BY @+ .CZ .K .;J
.DX @+ .EY @+ .FZ .K .;K
.GX @+ .HY @+ .IZ .K .;L @3
,,SOLVE ,,SY/EMS
,Z ) ,CRAM]'S RULE =A #B * #B SY/EM1 !
NUM]ATORS = .;X1 .;Y @1 & .;Z >E !
DET]M9ANTS (! MATRICES =M$ 0REPLAC+ !
COE6ICI5TS ( .;X1 .;Y @1 & ;Z
RESPECTIVELY )! COLUMN ( 3/ANTS4
,IF DET .,A @6.K #J1 !N ! SY/EM HAS
EXACTLY "O SOLU;N4 ,! SOLU;N IS3
,EXAMPLE #D ,SOLVE A MULTI-/EP PRO#M
.,,*EMI/RY ,! ATOMIC WEI<TS ( ?REE
-P.DS >E %[N4 ,USE A L9E> SY/EM &
,CRAM]'S RULE 6F9D ! ATOMIC WEI<TS (
C>BON 7;,C71 HYDROG5 7;,H71 & OXYG5
7,O74
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,-P.D3 ,=MULA3 ,ATOMIC WEI<T
,GLUCOSE3 ;,C #F ;,H #AB ,O #F @3 #AHJ
,C>BON DIOXIDE3 CO #B @3 .#DD
,HYDROG5 P]OXIDE3 ;,H #B ,O #B @3 #CD
,SOLU;N
.,,/EP .#A .,WRITE A L9E> SY/EM US+ !
=MULA = EA* -P.D4 ,LET .;,C1 .;,H @1 &
.,O REPRES5T ! ATOMIC WEI<TS ( C>BON1
HYDROG51 & OXYG54
#F;,C@+ #AB .;,H @+ #F .,O .K #AHJ
;,C @+ #B .#J .K #DD
#B .;,H @+#B .#J .K #CD
.,,/EP#B .,EVALUATE ! DET]M9ANT (!
COE6ICI5T MATRIX4
.,,/EP .#C .,APPLY ,CRAM]'S RULE 2C !
DET]M9ANT IS N #J4
,! ATOMIC WEI<TS ( C>BON1 HYDROG51 &
OXYG5 >E #AB1 #A1 & #AF1 RESPECTIVELY4
------------------------------------#BJG
..,GUID$ ,PRACTICE = ,EXAMPLES #C &
.#D
,USE ,CRAM]'S RULE 6SOLVE ! L9E>
SY/EM4
.#E4 #C;X--#D .;Y .K--#AE
#B .;X @+ #E .;Y .K #AC
.#F4 #D .;X @+ #G .;Y .K #B
--#C .;X -- #B .;Y .K --#H
.#G4 #C .;X -- #D .;Y @+ #B .;Z .K #AH
#D .;X @+ .;Y -- #E .;Z .K --#AC
#B .;X -- #C .;Y @+ .;Z .K #AA
#C.G ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#F = ,EXS4 #AA1BC1 & #DC
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.,EXS4 #B1BA1BH1CH1DB1 .& #DE
,SKILL ,PRACTICE
.#A4 ,,VOCABUL>Y ,COPY & -PLETE3 ,! @8
(A #B * #B MATRIX IS ! DI6];E (!
PRODUCTS (! ELE;TS ON ! DIAGONALS4
.#B4 .,,WRIT+ .,EXPLA9 ,CRAM]'S RULE &
H[ X IS US$4
.,,EXAMPLE .#A .ON .P4 #BJC = ,EXS4
#C-BA
#B*#B ,,DET]M9ANTS ,EVALUATE !
DET]M9ANT (! MATRIX4
.#C
.#D
.#E
.#F
.#G
.#H
.#I
.#AJ
#C*#C ,,DET]M9ANTS ,EVALUATE !
DET]M9ANT (! MATRIX4
.#AA
.#AB
.#AC
.#AD
.#AE
.#AF
.#AG
.#AH
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 EVALUAT+ ! DET]M9ANT4
.#AI
.#BJ
.#BA4 .,,MULTIPLE .,,*OICE ,: MATRIX
HAS ! GRTE/ DET]M9ANT8
,A
;,B
;,C
;,D
------------------------------------#BJH
,,EXAMPLE #B
ON P4 #BJD = ,EXS4 #BB-BH
,,>EA ,,( ,A ,,TRIANGLE ,F9D ! >EA (!
TRIANGLE )! GIV5 V]TICES4
.#BB4 .,A 7#A1 #E71 .;,B 7#D1 #F71
.;,C 7#G1 #C7
.#BC .,A 7#D1 #B71 .;,B 7#D1 #H71 .;,C
7#H1 #E7
.#BD4 .,A 7-#D1 #F71 .;,B 7#J1 #C71
.;,C 7#F1 #F7
.#BE4 .,A 7-#D1 --#D71 .;,B 7-;L1 #B71
.;,C 7#B1 --#F7
.#BF4 .,A 7#E1 --#D71 .;,B 7#F1 #C71
.;,C 7#H1 --#A7
.#BG4 .,A 7--#F1 #A71 .;,B 7--#B1
--#F71 .;,C 7#J1 #C7
.#BH4 .,,MULTIPLE .,,*OICE ,:AT IS !
>EA (! TRIANGLE ) V]TICES 7-#C1 #D71
7#F1 #C71 & 7#B1 --#A78
,A #BJ
;,B #BF
;,C #CJ
;,D #DJ
,,EXAMPLES #C & #D
ON PP4 #BJE-BJF = ,EXS4 #BI-CG
,,US+ ,,CRAM]'S ,,RULE ,USE ,CRAM]'S
RULE 6SOLVE ! L9E> SY/EM4
.#BI4 #C .;X @+ #E .;Y .K #C
-- .;X @+ #B .;Y .K#AJ
.#CJ4 #B .;X -- .;Y .K --#B
.;X @+ #B .;Y .K #AD
.#CA4 #E .;X @+ .;Y .K --#DJ
#B .;X --#E .;Y .K #AA
.#CB4 -- .;X @+ .;Y @+ .;Z .K --#C
#D .;X--.;Y @+ #D;Z .K --#A
.;X @+ #B .;Y -- .;Z .K #I
.#CC4 -- .;X --#B .;Y @+ #D;Z .K --#BH
.;X @+ .;Y @+ #B;Z .K --#AA
#B .;X @+ .;Y --#C;Z .K #CJ
.#CD4 #D .;X @+ .;Y @+ #C;Z .K #G
#B .;X --#E .;Y @+ #D;Z .K --#AI
.;X -- .;Y @+ #B;Z .K --#B
.#CE4 #E .;X -- .;Y --#B;Z .K --#F
.;X @+ #C .;Y @+ #D;Z .K #AF
#B .;X --#D .;Y @+ .;Z .K --#AE
.#CF4 .;X @+ .;Y @+ ;Z .K --#H
#C .;X --#C .;Y @+ #B;Z .K --#BA
- .;X @+ #B .;Y --#B;Z .K #AA
.#CG4 #C .;X -- .;Y @+ .;Z .K #BE
- .;X @+ #B .;Y --#C;Z .K --#AG
.;X @+ .;Y @+ ;Z .K #BA
.#CH4 .,,OP5-.,,5D$ .,,MA? ,WRITE A #B
* #B MATRIX T HAS A DET]M9ANT ( #E4
.#CI4 .,,*ALL5GE ,LET & @4
A4 ,H[ IS DET .;,,AB RELAT$ 6DET .,A &
DET ;,B8
B4 ,H[ IS DET .K,A RELAT$ 6DET1#D IF
.;K IS A SCAL>8 ,GIVE AN ALGEBRAIC
JU/IFIC,N = YR ANSW]4
,PRO#M ,SOLV+
,,EXAMPLE #B
ON P4 #BJD = ,EXS4 #DJ-DA
.#DJ4 .,,B]MUDA .,,TRIANGLE ,! ,B]MUDA
,TRIANGLE IS A L>GE TRIANGUL> REGION 9 !
,ATLANTIC ,OC1N4 ,! TRIANGLE IS =M$
0IMAG9>Y L9ES 3NECT+ ,B]MUDA1 ,PU]TO
,RICO1 & ,MIAMI1 ,FLORIDA4 7,IN ! MAP1 !
COORD9ATES >E M1SUR$ 9 MILES47 ,USE A
DET]M9ANT 6E/IMATE ! >EA (! ,B]MUDA
,TRIANGLE4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#DA4 .,,G>D5+ ,Y >E PLANN+ 6TURN A
TRIANGUL> REGION ( YR Y>D 96A G>D54 ,!
V]TICES (! TRIANGLE >E 7#J1 #J71 7#E1
#B71 & 7#C1 #F7 ": ! COORD9ATES >E
M1SUR$ 9 FEET4 ,F9D ! >EA (! TRIANGUL>
REGION4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
,,EXAMPLES #C & #D
ON PP4 #BJE-BJF = ,EXS4 #DB-DD
.#DB4 .,,%ORT .,,RESPONSE ,! ATT5D.E
AT A ROCK 3C]T 0 #FGJJ P4 ,! TICKETS =!
3C]T CO/ 4#DJ = FLOOR S1TS & 4#BE = ALL
O!R S1TS4 ,! TOTAL 9COME ( TICKET SALES
0 4#AHE1EJJ4 ,WRITE A L9E> SY/EM T
MODELS ? SITU,N4 ,SOLVE ! SY/EM 9 ?REE
WAYS3 US+ ,CRAM]'S RULE1 US+ ! SUB/ITU;N
ME?OD1 & US+ ! ELIM9,N ME?OD4 .,-P>E !
ME?ODS1 & EXPLA9 : "O Y PREF] 9 ?
SITU,N4
.K .,,"W$-.,,\ .,,SOLU;NS .ON
.P4.,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#BJI
.#DC4 .,,MULTI-.,,/EP .,,PRO#M ,AN ICE
CR1M %OP SELLS ! FOLL[+ SIZES ( ICE CR1M
C"OS3 S+LE SCOOP = @4#.IJ1 D\# SCOOP =
4#A.BJ1 & TRIPLE SCOOP = 4#A.FJ4 ,"O "D1
A TOTAL ( #ABJ C"OS >E SOLD = 4#ACD1 Z
_M S+LE-SCOOP C"OS >E SOLD Z D\#-SCOOP &
TRIPLE-SCOOP C"OS -B9$4
A4 ,USE A L9E> SY/EM & ,CRAM]'S RULE
6F9D H[ _M ( EA* SIZE ( C"O >E SOLD4
.;B @4 ,! NEXT "D1 ! %OP RAISES PRICES
0#AJ@3P4 ,Z A RESULT1 ! NUMB] ( EA* SIZE
( C"O SOLD FALLS 0#E@3P4 ,:AT IS !
REV5UE F C"O SALES8
.#DD4 .,,SCI;E ,! ATOMIC WEI<TS ( ?REE
-P.DS >E %[N 9 ! TA#4 ,USE A L9E> SY/EM
& ,CRAM]'S RULE 6F9D ! ATOMIC WEI<TS (
FLUOR9E 7;,F71 SODIUM 7,NA71 & *LOR9E
7,CL74
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,-P.D3 ,=MULA3 ,ATOMIC WEI<T
,SODIUM FLUORIDE3 ,,FN,'A3 #DB
,SODIUM *LORIDE3 ,NA,CL3 #EH.E
,*LOR9E P5TAFLUORIDE3 ,,CIF #E @3
#ACJ.E
.#DE4 .,,EXT5D$ .,,RESPONSE ,9 ,UTAH &
,COLORADO1 AN >EA CALL$ ! ,D9OSAUR
,DIAMOND IS "KN = 3TA9+ _M D9OSAUR
FOSSILS4 ,! MAP AT ! "R %[S ! T[NS AT !
F\R V]TICES (! DIAMOND4 ,! COORD9ATES
GIV5 >E M1SUR$ 9 MILES4
A4 ,F9D ! >EA (! TOP TRIANGUL> REGION4
.;B @4 ,F9D ! >EA (! BOTTOM TRIANGUL>
REGION4
C4 ,:AT IS ! TOTAL >EA (! ,D9OSAUR
,DIAMOND8
.;D @4 .,DESCRIBE ANO!R WAY 9 : Y C
DIVIDE ! ,D9OSAUR ,DIAMOND 96TWO
TRIANGLES 9 ORD] 6F9D XS >EA4
.#DF4 .,,*ALL5GE ,A F>M] IS F5C+ (F A
TRIANGUL> REGION (A PA/URE1 Z %[N4 ,!
>EA (! REGION %D 2 #EJJJ SQU>E FEET4 ,!
F>M] HAS PLANT$ ! F/ TWO F;E PO/S AT
7#J1 #J7 & 7#AJJ1 #EJ74 ,HE WANTS 6PLANT
! F9AL PO/ AL;G 8 NEI<BOR'S F;E1 : LIES
ON ! HORIZONTAL L9E .;Y .K #ABJ4 ,AT :
.TWO PO9TS CD ! F>M] PLANT ! F9AL PO/ S
T ! TRIANGUL> REGION HAS ! DESIR$ >EA8
,,MIX$ ,,REVIEW
,EVALUATE ! FUNC;N =! GIV5 VALUE ( .;X
@4 @7 P4 #GB @7
#DG4 .;F7.;X7 .K .;X - #AB2 .;F7.#H7
#DH4 .;F7.;X7 .K #D .;X @+ #H2
.;F7.#G7
#DI4 .;F7.;X7 .K .;X #B - #AJ2
.;F7-.#E7
#EJ4 .;F7.;X7 .K - .;X #B @+ #B .;X @2
.;F7.#C7
#EA4 .;F7.;X7 .K - .;X #B - .;X @+ #E2
.;F7.#D7
#EB4 .;F7.;X7 .K .;X #B - #B .;X @+
#D2 .;F7-.#B7
,GRAPH ! SY/EM ( L9E> 9EQUALITIES4 @7
P4 #AFH @7
#EC4 .;X @+ .;Y .1.K #C
#D .;X @+ .;Y "K #D
#ED4 #B .;X - .;Y .1.K #B
#E .;X - .;Y .1.K #B
#EE4 #D .;X - #C .;Y .1 #A
- .;X @+ .;Y .1.K #D
#EF4 .;Y "K - .;X - #E
.;Y "K #C .;X @+ #A
.,,PREVIEW ,PREP>E = ,LESSON #C.H 9
,EXS4 #EG-EI4
,F9D ! PRODUCT4 @7 P4 #AIE @7
#EG4
#EH4
#EI4
.,,EXTRA .,,PRACTICE = ,LESSON #C.E1
P4 #AJAB
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#BAJ
#C.H ,USE ,9V]SE ,MATRICES 6,SOLVE
,L9E> ,SY/EMS
.,2F ,Y SOLV$ L9E> SY/EMS US+ ,CRAM]'S
RULE4
.,N[ ,Y W SOLVE L9E> SY/EMS US+ 9V]SE
MATRICES4
.,:Y8 ,S Y C F9D H[ _M BAT*ES (A
RECIPE 6MAKE1 Z 9 ,EX4 #DE4
,KEY ,VOCABUL>Y
99 ID5T;Y MATRIX
99 9V]SE MATRICES
99 MATRIX ( V>IA#S
99 MATRIX ( 3/ANTS
,SIDEB>3
,/&>DS
..#B.J ,/UD5TS SOLVE SY/EMS ( L9E>
.EQU,NS & 9EQUALITIES @7 .9 .TWO OR ?REE
.V>IA#S @7 0SUB/ITU;N1 .) .GRAPHS @1 OR
) MATRICES4
,! .;N * .;N .ID5T;Y .MATRIX IS A
MATRIX ) L'S ON ! MA9 DIAGONAL & #J'S
ELSE":4 ,IF .,A IS ANY .;N * .;N MATRIX
& _/IS ! .;N * .;N ID5T;Y MATRIX1 !N
.,,AI .K .,A & .,,IA .K .,A
,TWO .;N * .;N MATRICES .,A & .;,B >E
.9V]SES ( EA* O!R IF _! PRODUCT 7IN BO?
ORD]S7 IS ! .;N * .;N ID5T;Y MATRIX4 ,T
IS1 .;,,AB .K ,I & .,,BA .K ,I4 ,AN .;N
* .;N MATRIX ,A HAS AN 9V]SE IF & ONLY
IF DET6.K .,A @6.K #J4 ,! SYMBOL =!
9V]SE ( .,A IS .,A #A @4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,! 9V]SE (! MATRIX IS PROVID$ .AD --
.;AB @6.K #J4
,EXAMPLE #A ,F9D ! 9V]SE (A #B * #B
MATRIX
,,*ECK ,,9V]SES
,9 ,EXAMPLE #A1 Y C *ECK ! 9V]SE 0%[+
T .,,AA --#A .K .;L .K .,A --#A .,A @4
,F9D ! 9V]SE ( @4
..,GUID$ ,PRACTICE = ,EXAMPLES .#A
,F9D ! 9V]SE (! MATRIX4
.#A
.#B
.#C
------------------------------------#BAA
,EXAMPLE #B ,SOLVE A MATRIX EQU,N
,SOLVE ! MATRIX EQU,N .,,AX .K .;,B =!
#B * #B MATRIX ,X4
,SOLU;N
,2G9 0F9D+ ! 9V]SE ( .,A @4
,6SOLVE ! EQU,N = .;,X @1 MULTIPLY BO?
SIDES (! EQU,N 0.,A ;L ON ! LEFT4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,GUID$ ,PRACTICE = ,EXAMPLES .#B
.#D4 ,SOLVE ! MATRIX EQU,N
..,,9V]SE ,,( ,A #C * #C ,,MATRIX
.,THE 9V]SE (A #C * #C MATRIX IS
DI6ICULT 6-PUTE 0H&4 ,A CALCULATOR T W
-PUTE 9V]SE MATRICES IS USE;L 9 ? CASE4
,EXAMPLE #C ,F9D ! 9V]SE (A #C * #C
MATRIX
,USE A GRAPH+ CALCULATOR 6F9D ! 9V]SE
( .,A4 ,!N USE ! CALCULATOR 6V]IFY YR
RESULT4
,SOLU;N
,5T] MATRIX .,A 96A GRAPH+ CALCULATOR
& CALCULATE .,A ;L @4 ,!N -PUTE .,,AA ;L
& .,A -;L .,A 6V]IFY T Y OBTA9 ! #C ;,X
#C ID5T;Y MATRIX4
------------------------------------#BAB
..,GUID$ ,PRACTICE = ,EXAMPLES .#C
,USE A GRAPH+ CALCULATOR 6F9D ! 9V]SE
(! MATRIX .,A4 ,*ECK ! RESULT 0%[+ T
.,,AA -;L .K .,I & .,A -;L .,A .K .,I @4
.#E
.#F
.#G
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,US+ AN ,9V]SE ,MATRIX 6,SOLVE A ,L9E>
,SY/EM
.,,/EP .#A ,WRITE ! SY/EM Z A MATRIX
EQU,N .,,AX .K .,B4 ,! MATRIX .,A IS !
COE6ICI5T MATRIX1 .;,X IS ! MATRIX (
V>IA#S1 & .;,B IS ! MATRIX ( 3/ANTS4
.,,/EP .#B ,F9D ! 9V]SE ( MATRIX .,A
@4
.,,/EP .#C ,MULTIPLY EA* SIDE ( .,,AX
.K .;,B 0.,A -;L .ON .! .LEFT 6F9D !
SOLU;N .;,X .K .,A -;L .,B4
,EXAMPLE #D ,SOLVE A L9E> SY/EM
,USE AN 9V]SE MATRIX 6SOLVE ! L9E>
SY/EM4
#B .;X -- #C .;Y .K #AI ,EQU,N #A
.;X @+ #D .;Y .K --#G ,EQU,N #B
,,SOLVE ,,SY/EMS
,Y C USE ! ME?OD %[N 9 ,EXAMPLE #D IF
.,A HAS AN 9V]SE4 ,IF .,A DOES N H AN
9V]SE1 !N ! SY/EM HAS EI NO SOLU;N OR
9F9ITELY _M SOLU;NS4
,SOLU;N
.,,/EP .#A .,WRITE ! L9E> SY/EM Z A
MATRIX EQU,N .,,AX .K .,B4
.,,/EP .#B ,F9D ! 9V]SE ( MATRIX .,A4
.,,/EP .#C ,MULTIPLY ! MATRIX ( 3/ANTS
0.,A -;L.' .-ON ! LEFT4
,! SOLU;N (! SY/EM IS 7#E1 --#C74
.,,*ECK #B7#E7--#C 7-#C7 .K #AJ @+
#I.K #AI #E @+ #D7-#C7 .K #E--#AB .K
--#G
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
------------------------------------#BAC
,EXAMPLE #E ,SOLVE A MULTI-/EP PRO#M
.,,GIFTS ,A -PANY SELLS ?REE TYPES (
MOVIE GIFT BASKETS4 ,A BASIC BASKET ) #B
MOVIE PASSES & #A PACKAGE ( MICROWAVE
POPCORN CO/S 4#AE.EJ4 ,A M$IUM BASKET )
#B MOVIE PASSES1 #B PACKAGES ( POPCORN1
& #A ,,DVD CO/S 4#CG4 ,A SUP] BASKET )
#D MOVIE PASSES1 #C PACKAGES ( POPCORN1
& #B ,,DVD,'S CO/S 4#GB.EJ4 ,F9D ! CO/ (
EA* ITEM 9 ! GIFT BASKETS4
,,ANO!R ,,WAY
,= AN ALT]NATIVE ME?OD = SOLV+ ! PRO#M
9 ,EXAMPLE #E1 TURN 6PAGE #BAH =! ,PRO#M
,SOLV+ ,"W%OP4
,SOLU;N
.,,/EP .#A .,WRITE V]BAL MODELS =!
SITU,N4
.,,/EP .#B .,WRITE A SY/EM ( EQU,NS4
,LET .;M 2 ! CO/ (A MOVIE PASS1 .;P 2 !
CO/ (A PACKAGE ( POPCORN1 & .;D 2 ! CO/
(A ,,DVD4
#B .;M @+ .;P .K #AE.EJ ,EQU,N #A
#B .;M @+ #B .;P @+ .;D .K #CG.JJ
,EQU,N #B
#D .;M @+ #C .;P @+ #B .;D .K #GB.EJ
,EQU,N #C
.,,/EP .#C .,REWRITE ! SY/EM Z A
MATRIX EQU,N4
.,,/EP .#D .,5T] ! COE6ICI5T MATRIX
.,A &! MATRIX ( 3/ANTS .;,B 96A GRAPH+
CALCULATOR4 ,!N F9D ! SOLU;N .;,X .K .,A
-;L .;,B @4
,A MOVIE PASS CO/S 4#G1 A PACKAGE (
POPCORN CO/S 4#A.EJ1 &A ,,DVD CO/S 4#BJ4
..,GUID$ ,PRACTICE = ,EXAMPLES #D &
.#E
,USE AN 9V]SE MATRIX 6SOLVE ! L9E>
SY/EM4
.#H4 #D .;X @+ .;Y .K #AJ
#C .;X @+ #E .;Y .K--#A
.#I4 #B .;X -- .;Y .K --#F
#F .;X -- #C .;Y .K --#AH
.#AJ4 #C .;X -- .;Y .K --#E
--#D .;X @+ #B .;Y .K #H
.#AA4 .,,:AT .,,IF ,9 ,EXAMPLE #E1 H[
DOES ! ANSW] *ANGE IF A BASIC BASKET
CO/S 4#AG1 A M$IUM BASKET CO/S 4#CE1 &A
SUP] BASKET CO/S 4#FI8
------------------------------------#BAD
#C.H ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#G = ,EXS4 #C1BE1 & #DG
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 #B1AB1 #CD1DA1 & #DF
.K .,,MULTIPLE .,,REPRES5T,NS
,EX#.DE
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,ID5TIFY ! MATRIX (
V>IA#S &! MATRIX ( 3/ANTS 9 ! MATRIX
EQU,N4
.#B4 .,,WRIT+ .,EXPLA9 H[ 6F9D ! 9V]SE
(A #B * #B MATRIX ,A ": .DET .,A @6.K#J4
,,EXAMPLE #A
ON P4 #BAJ = ,EXS4 #C-AB
,,F9D+ ,,9V]SES ,F9D ! 9V]SE (!
MATRIX4
.#C
.#D
.#E
.#F
.#G
.#H
.#I
.#AJ
.#AA4 .,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 F9D+ ! 9V]SE (! MATRIX
@4
.#AB .,,MULTIPLE .,,*OICE ,:AT IS !
9V]SE (! MATRIX @8
,A
;,B
;,C
;,D
,,SOLV+ ,,EQU,NS ,SOLVE ! MATRIX
EQU,N4
,,EXAMPLE #B
ON P4 #BAA = ,EXS4 #AC-AH
.#AC
.#AD
.#AE
.#AF
.#AG
.#AH
,,EXAMPLE #C
ON P4 #BAA = ,EXS4 #AI-BD
,,F9D+ ,,9V]SES ,USE A GRAPH+
CALCULATOR 6F9D ! 9V]SE ( MATRIX .,A4
,*ECK ! RESULT 0%[+ T .,,AA -#A .K .,I &
.,A -#A .,A--.,I4
.#AI4
.#BJ
.#BA
.#BB
.#BC
.#BD
------------------------------------#BAE
,,EXAMPLE #D
ON P4 #BAB .= .,EXS4 .#BE-.CD
,,SY/EMS ,,( ,,?REE ,,EQU,NS ,USE AN
9V]SE MATRIX 6SOLVE ! L9E> SY/EM4
.#BE4 #D .;X -- .;Y .K #AJ
--.#G;X --.#B;Y.K --#BE
.#BF4 #D .;X @+ #G .;Y .K --#AF
#B .;X @+ #C .;Y .K --#D
.#BG4 ..#C;X--.#B;Y .K #E
#F .;X -- #E .;Y .K #AD
.#BH4 ..;X--.;Y .K #D
#I .;X -- ;L#J .;Y .K #DE
.#BI4 --#B .;X -- #I .;Y .K --#B
#D .;X @+ #AF .;Y .K #H
.#CJ4 .#B;X-.#G;Y.K --#F
-.;X @+ #E .;Y .K #C
.#CA4 #F .;X @+ .;Y .K --#B
- .;X @+ #C .;Y .K --#BE
#CB4 #B .;X @+ .;Y .K --#B
#B .;X @+ #E .;Y .K #CH
#CC4 #E .;X @+ .#G;Y .K #BJ
#C .;X @+ #E .;Y .K #AF
.#CD4 .,,MULTIPLE .,,*OICE ,:AT IS !
SOLU;N (! SY/EM %[N8
#C .;X -- #E .;Y .K --#BF
- .;X @+ #B .;Y .K #AJ
,A 7#C1 #G7
;,B 7#G1 --#A7
;,C 7-#B1 #D7
;,D 7#FH1 #AAJ7
,,EXAMPLE #E
ON P4 #BAC .= .,EXS4 .#CE-.DJ
,,SY/EMS ,,( ,,?REE ,,EQU,NS ,USE AN
9V]SE MATRIX &A GRAPH+ CALCULATOR 6SOLVE
! L9E> SY/EM4
#CE4 .;X -- .;Y -- .#C;Z .K .#B
#E .;X @+ #B .;Y @+ .;Z .K --#AG
-#C .;X -- .;Y .K #H
#CF4 --#C .;X @+ .;Y -- #H .;Z .K #AH
.;X - .#B;Y @+ .;Z.K --#AA
#B .;X -- #B .;Y @+ #E .;Z .K --#AG
#CG4 #B .;X @+ #D .;Y @+ .#E;Z .K #E
.;X @+ #B .;Y @+ .#C;Z .K #D
#E .;X -- #D .;Y -- .#B;Z .K --#C
#CH4 #D .;X -- .;Y -- .;Z .K --#BJ
#F .;X -- .;Z .K --#BG
- .;X @+ #D .;Y @+ .#E;Z .K #BC
#CI4 #C .;X @+ #B .;Y -- .;Z .K #AD
- .;X -- #E .;Y @+ #D .;Z .K --#DH
#D .;X @+ .;Y @+ .;Z -- #B
#DJ4 #F .;X @+ .;Y @+ #B .;Z .K #AA
.;X -- .;Y @+ .;Z .K --#E -- .;X @+ #D
.;Y -- .;Z .K #AD
.#DA4 .,,OP5-.,,5D$ .,,MA? ,WRITE A #B
;,X #B MATRIX T HAS NO 9V]SE4
.#DB4 .,,*ALL5GE ,SOLVE ! L9E> ;S .;Y
/EM US+ ! GIV5 9V]SE (! COE6ICI5T
MATRIX4
.#B;W @+ #E .;X -- #D .;Y @+ .#F;Z .K
#J
#B .;X @+ .;Y -- #G .;Z .K #EB
#D .;W @+ #H .;X -- #G .;Y @+ #AD .;Z
.K --#BE
#C .;W @+ #F .;X -- #E .;Y @+ ;L#J .;Z
.K --#AF
,PRO#M ,SOLV+
,,EXAMPLES #D & #E
ON PP4 #BAB-BAC = ,EXS4 #DC-DH
.#DC4 .,,AVI,N ,A PILOT HAS #BJJ H\RS
( FLI<T "T 9 S+LE-5G9E AIRPLANES &
TW9-5G9E AIRPLANES4 ,R5T+ A S+LE-5G9E
AIRPLANE CO/S 4#FJ P] H\R1 & R5T+ A
TW9-5G9E AIRPLANE CO/S 4#BDJ P] H\R4 ,!
PILOT HAS SP5T 4#BA1JJJ ON AIRPLANE
R5TALS4 ,USE AN 9V]SE MATRIX 6F9D H[ _M
H\RS ! PILOT HAS FL[N EA* TYPE (
AIRPLANE4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#DD4 .,,BASKETBALL ,DUR+ ! #BJJC-BJJD
,,NBA S1SON1 ,DIRK ,N[ITZKI (! ,DALLAS
,MAV]ICKS MADE A TOTAL ( #IGF %OTS &
SCOR$ #AFHJ PO9TS4 ,8 %OTS 3SI/$ (
#C-PO9T FIELD GOALS1 #B-PO9T FIELD
GOALS1 & #A-PO9T FREE ?R[S4 ,HE MADE
#ACE M #B-PO9T FIELD GOALS ?AN FREE
?R[S4 ,USE AN 9V]SE MATRIX 6F9D H[ _M (
EA* TYPE ( %OT HE MADE4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
------------------------------------#BAF
.#DE4 .,,MULTIPLE .,,REPRES5T,NS ,A
COOK+ CLASS WANTS 6USE UP #H CUPS (
BUTT]MILK & #AA E7S 0BAK+ ROLLS & MU69S
6FREEZE4 ,A BAT* ( ROLLS USES #B CUPS (
BUTT]MILK & #C E7S4 ,A BAT* ( MU69S USES
#A CUP ( BUTT]MILK & #A EGG4
A4 .,WRIT+ .A .,SY/EM ,WRITE A SY/EM (
EQU,NS = ? SITU,N4
B4 ..,WRIT+ A ,MATRIX .,EQU,N ,WRITE !
SY/EM ( EQU,NS F "P 7A7 Z A MATRIX EQU,N
.,,AX .K .,B4
C4 .,SOLV+ .A .,SY/EM ,USE AN 9V]SE
MATRIX 6SOLVE ! SY/EM ( EQU,NS4 ,H[ _M
BAT*ES ( EA* RECIPE %D ! CLASS MAKE8
.#DF4 .,,EXT5D$ .,,RESPONSE ,A -PANY
SELLS "PY PLATT]S ) V>Y+ ASSORT;TS (
M1TS & *EESES4 ,A BASIC PLATT] ) #B
*EESES & #C M1TS CO/S 4#AH1 A M$IUM
PLATT] ) #C *EESES & #E M1TS CO/S 4#BH1
&A SUP] PLATT] ) #G *EESES & #AJ M1TS
CO/S 4#FJ4
A4 ,WRITE & SOLVE A SY/EM ( EQU,NS US+
! 9=M,N AB ! BASIC PLATT] &! M$IUM
PLATT]4
B4 ,WRITE & SOLVE A SY/EM ( EQU,NS US+
! 9=M,N AB ! M$IUM PLATT] &! SUP]
PLATT]4
C4 .,-P>E ! RESULTS F "PS 7A7 & 7;B7 &
MAKE A 3JECTURE AB :Y "! IS A 4CREPANCY4
.#DG4 .,,NUTRI;N ,! TA# %[S !
CALORIES1 FAT1 & C>BOHYDRATES P] \NCE =
?REE BR&S ( C]1L4 ,H[ _M \NCES ( EA* BR&
%D 2 -B9$ 6GET #EJJ CALORIES1 #C GRAMS (
FAT1 & #AJJ GRAMS ( C>BOHYDRATES8 ,R.D
YR ANSW]S 6! NE>E/ T5? ( AN \NCE4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,C]1L3 ,CALORIES3 ,FAT3 ,C>BOHYDRATES
,BRAN ,CRUN*IES3 #GH3 #A ;G3 #BB ;G
,TOA/$ ,OATS3 #AJD3 #J ;G3 #BE.E ;G
,:OLE ,:1T ,FLAKES3 #AIH3 #J.F ;G3
#BC.H ;G
.#DH4 .,,MULTI-.,,/EP .,,PRO#M ,Y NE$
#I SQU>E FEET ( GLASS MOSAIC TILES
6DECORATE A WALL ( YR KIT*54 ,Y WANT !
>EA (! R$ TILES 6EQUAL ! -B9$ >EA (!
YELL[ & BLUE TILES4 ,! CO/ (A %EET (
GLASS TILES HAV+ AN >EA ( #J.GE SQU>E
FOOT IS 4#F.EJ = R$1 4#D.EJ = YELL[1 &
4#H.EJ = BLUE4 ,Y H 4#HJ 6SP5D4
.A @4 ,WRITE A SY/EM ( EQU,NS
6REPRES5T ? SITU,N4
.;B @4 ,REWRITE ! SY/EM Z A MATRIX
EQU,N4
.;C @4 ,USE AN 9V]SE MATRIX 6F9D H[ _M
%EETS ( EA* COLOR TILE Y %D BUY4
.#DI4 .,,GEOMETRY ,! COLUMNS ( MATRIX
.;,T 2L GIVE ! COORD9ATES (! V]TICES (A
TRIANGLE4 ,MATRIX ,A IS A TRANS=M,N
MATRIX4
A4 ,F9D .,,AT & .,,AAT4 ,!N DRAW !
ORIG9AL TRIANGLE &! TWO TRANS=M$
TRIANGLES4 ,:AT TRANS=M,N DOES .,A
REPRES5T8
.;B @4 .,DESCRIBE H[ 6USE MATRICES
6OBTA9 ! ORIG9AL TRIANGLE REPRES5T$ 0;R
F ! TRANS=M$ TRIANGLE REPRES5T$
.0.,,AAT4
.K .,,"W$-.,,\ .,,SOLU;NS
ONP4,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
------------------------------------#BAG
.#EJ4 .,,*ALL5GE ,V]IFY ! =MULA ON
PAGE #BAJ =! 9V]SE (A #B * #B MATRIX
0%[+ T .;,,AB .K .,I & .,,BA .K .,I =!
MATRICES .,A & .;,B GIV5 2L4
,,MIX$ ,,REVIEW
.,,PREVIEW ,PREP>E = ,LESSON #D.A 9
,EXS4 #EA-EF4
,GRAPH ! EQU,N OR 9EQUAL;Y4
.#EA4 .;Y .K --#E .;X @+ #C @7 P4 #HI
@7
.#EB4 @7 P4 #HI @7
.#EC4 @7 P4 #HI @7
.#ED4 .;Y .1.K #B_\ .;X _\ @7 P4 #ACB
@7
.#EE4 .;Y "K _\ .;X -- #B_\ @7 P4 #ACB
@7
.#EF4 .;Y "K.K --#B_\ .;X @+ #A_\ @7
P4 #ACB @7
,TELL :E!R .;X & .;Y H A .POSITIVE
.CORREL,N @1 A .NEGATIVE .CORREL,N @1 OR
.APPROXIMATELY .NO .CORREC;N @4 @7 P4
#AAC @7
.#EG4
.#EH4
.#EI4
,SOLVE ! MATRIX EQU,N = .;X & .;Y @4
@7 P4 #AHG @7
.#FJ4
.#FA4
,,QUIZ .= .,LESSONS .#C..F-.C..H
,US+ ! GIV5 MATRICES1 EVALUATE !
EXPRES.N1 @7 P4 #AIE @7
#A4 .#B,;,AB
.#B4 .;,,AB @+ ;,,AC
.#C4 .,A @7 .;,B @+ .;,C @7
.#D4 @7 .;,B -- .,A @7 .;,C
,EVALUATE ! DET]M9ANT (! MATRIX1 @7 P4
#BJC @7
.#E
.#F
.#G
,USE AN 9V]SE MATRIX 6SOLVE ! L9E>
SY/EM1 @7 P4 #BAJ @7
.#H4 .;X @+ #C .;Y .K --#B
.#B;X @+ .#G;Y.K --#F
.#I4 #C .;X -- .,AY .K #E
#B .;X --#C .;Y .K #C
.#AJ4 --#C .;X @+ #B .;Y .K --#AC
#F .;X --#E .;Y .K #BD
.#AA4 #C .;X - .;Y .K --#D
#B .;X --#B .;Y .K --#H
.#AB4 .#G;X @+ #D .;Y .K #F
#E .;X @+ #C .;Y .K --#BE
.#AC4 .#D;X @+ .;Y .K --#B
--#F .;X @+ .;Y .K #AH
.#AD4 .,,BOAT+ ,Y >E MAK+ A TRIANGUL>
SAIL =A SAILBOAT4 ,! V]TICES (! SAIL >E
7#J1 #B71 7#AB1 #B71 & 7#AB1 #BF7 ": !
COORD9ATES >E M1SUR$ 9 FEET4 ,F9D ! >EA
(! SAIL4 @7 P4 #BJC @7
.,,EXTRA .,,PRACTICE = ,LESSON #C.H1
P4 #AJAB
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#BAH
,PRO#M ,SOLV+ ,"W%OP ,LESSON #C.H3
,US+ ,ALT]NATIVE ,ME?ODS
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#BAC
.,,MULTIPLE .,,REPRES5T,NS ,9 ,EXAMPLE
#E ON PAGE #BAC @1 Y SOLV$ A L9E> SY/EM
US+ AN 9V]SE MATRIX4 ,Y C AL SOLVE
SY/EMS US+ .AUG;T$ .MATRICES4 ,AN AUG;T$
MATRIX =A SY/EM 3TA9S ! SY/EM'S
COE6ICI5T MATRIX & MATRIX ( 3/ANTS4
,SIDEB>3
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..#B.J ,/UD5TS SOLVE SY/EMS ( L9E>
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,RECALL F ,LESSON #C.B T AN EQU,N 9 A
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R[-EQUIVAL5T 6! ORIG9AL3
99 ,9T]*ANGE TWO R[S4
99 ,MULTIPLY A R[ 0A NONZ]O 3/ANT4
99 ,ADD A MULTIPLE ( "O R[ 6ANO!R R[4
,PRO#M
.,,GIFTS ,A -PANY SELLS ?REE TYPES (
MOVIE GIFT BASKETS4 ,A BASIC BASKET ) #B
MOVIE PASSES & #A PACKAGE ( MICROWAVE
POPCORN CO/S 4#AE.EJ4 ,A M$IUM BASKET )
#B MOVIE PASSES1 #B PACKAGES ( POPCORN1
& #A ,,DVD CO/S 4#CG4 ,A SUP] BASKET )
#D MOVIE PASSES1 #C PACKAGES ( POPCORN1
& #B ,,DVD,'S CO/S 4#GB.EJ4 ,F9D ! CO/ (
EA* ITEM 9 ! GIFT BASKETS4
,ME?OD
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6WRITE A L9E> SY/EM1 WRITE ! CORRESPOND+
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! AUG;T$ MATRIX 96A MATRIX ) L'S AL;G !
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,S* A MATRIX IS 9 .TRIANGUL> .=M & C 2
US$ 6SOLVE =! V>IA#S 9 ! SY/EM4
,LET .;M 2 ! CO/ (A MOVIE PASS1 .;P 2
! CO/ (A PACKAGE ( POPCORN1 & .;D 2 !
CO/ (A ,,DVD4
------------------------------------#BAI
.,,/EP .#A .,WRITE A L9E> SY/EM & !N
WRITE AN AUG;T$ MATRIX4
.,,/EP .#B .,ADD --#B "TS ! F/ R[ 6!
?IRD R[4
.,,/EP .#C .,ADD --#A "TS ! F/ R[ 6!
SECOND R[4
.,,/EP .#D .,ADD --#A "TS ! SECOND R[
6! ?IRD R[4
.,,/EP .#E .,MULTIPLY ! F/ R[ 0#J.E4
,! ?IRD R[ (! MATRIX TELLS Y T .;D .K
#BJ4 ,SUB/ITUTE #BJ = .;D 9 ! EQU,N =!
SECOND R[1 ..;P @+ .;D .K #BA.E1 6OBTA9
.;P @+ #BJ .K #BA.E1 OR .;P .K #A.E4 ,!N
SUB/ITUTE #A.E = .;P 9 ! EQU,N =! F/ R[1
.;M @+ .#J..E;P .K #G.GE1 6OBTA9 .;M @+
#J.E7#A.E7 .K #G.GE1 OR .;M .K .#G4
,A MOVIE PASS CO/S 4#G1 A PACKAGE (
POPCORN CO/S 4#A.EJ1 &A ,,DVD CO/S 4#BJ4
,PRACTICE
.#A4 .,,:AT .,,IF8 ,9 ! PRO#M ON PAGE
#BAH @1 SUPPOSE A BASIC BASKET CO/S
4#AG.GE1 A M$IUM BASKET CO/S 4#CD.EJ1 &A
SUP] BASKET CO/S 4#FG.BE4 ,USE AN AUG;T$
MATRIX 6F9D ! CO/ ( EA* ITEM4
.#B4 .,,F9.E ,Y H 4#AH1JJJ 69VE/4 ,Y
WANT AN OV]ALL ANNUAL RETURN ( #H@3P4 ,!
EXPECT$ ANNUAL RETURNS >E #AJ@3P =A /OCK
FUND1 #G@3P =A BOND FUND1 & #E@3P =A
M"OY M>KET FUND4 ,Y WANT 69VE/ Z M* 9
/OCKS Z 9 BONDS &! M"OY M>KET -B9$4 ,USE
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FUND4
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MADE F TWO K9DS ( SE$S1 SUNFL[] SE$S &
?I/LE SE$S4 ,SUNFL[] SE$S CO/ @4#.CD P]
P.D & ?I/LE SE$S CO/ @4#.GI P] P.D4 ,USE
AN AUG;T$ MATRIX 6F9D H[ _M P.DS ( EA*
V>IETY >E 9 ! MIXTURE4
.#D4 .,,R1SON+ ,SOLVE ! GIV5 SY/EM US+
AN AUG;T$ MATRIX4 ,:AT C Y SAY AB !
SY/EM'S SOLU;N7;S78
.;X--.#B;Y @+ #D;Z .K --#AJ
#E .;X @+ .;Y--.;Z .K #BD
#C .;X --#F .;Y @+ #AB .;Z .K---#CJ
------------------------------------#BBJ
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,LESSONS #C.E-C.H
.#A4 .,,MULTI-.,,/EP .,,PRO#M ,! CO/
7IN ?\S&S ( DOLL>S7 (A #CJ SECOND
-M]CIAL ON TWO CA# ,,TV NET"WS IS %[N 2L
= TWO CITIES4 ,! CO/ V>IES BAS$ ON :5 !
-M]CIAL AIRS3 "D"T 7;,D71 PRIME "T
7;,P71 & LATE NI<T 7;,L74
,CO/S 9 ,C;Y ,A
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 .;,D @3 .;,P @3 .;,L
.,NET"W .#A @3 #D.E3 #F3 #B.E
.,NET"W .#B @3 #E.E3 #H3 #B.E
,CO/S 9 ,C;Y ;,B
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 .;,D @3 .;,P @3 .;,L
.,NET"W .#A @3 #D3 #F.E3 #C.BE
.,NET"W .#B @3 #E3 #H.E3 #C.BE
A4 ,ORGANIZE ? 9=M,N US+ TWO MATRICES
.,A & .;,B T GIVE ! CO/S = C;Y ,A& C;Y
;,B1 RESPECTIVELY4
B4 ,F9D .;,B--.,A & DESCRIBE :AT EA*
ELE;T 9 .;,B--.,A REPRES5TS4
C4 ,NEXT YE>1 ALL (! CO/S W 9CR1SE
0#AJ@3P4 ,WRITE TWO MATRICES T GIVE NEXT
YE>'S CO/S =! TWO CITIES4
.#B4 .,,MULTI-.,,/EP .,,PRO#M ,A P]SON
HAS #HE CO9S 9 NICKELS1 DIMES1 & QU>T]S
)A -B9$ VALUE ( 4#AC.BE4 ,"! >E TWICE Z
_M QU>T]S Z DIMES4
A4 ,WRITE A SY/EM ( EQU,NS T MODELS ?
SITU,N4
B4 ,WRITE ! SY/EM F "P 7A7 Z A MATRIX
EQU,N .,,AX .K .,B4
C4 ,USE AN 9V]SE MATRIX 6F9D ! NUMB] (
EA* TYPE ( CO94
.#C4 .,,OP5-.,,5D$ ,3SID] ! FOLL[+
MATRICES4
A4 ,WRITE A #B ;X #B MATRIX ;,C S* T
;,C @6.K .,A B DET ;,C .K DET ,A4
B4 ,WRITE A #C ;,X #C MATRIX .;,D S* T
.;,D @6.K .;,B B DET .;,D .K DET .,B4
.#D4 .,,%ORT .,,RESPONSE ,A /ORE HAS
?REE DE"P;TS3 CLO?+ 7;,C71 H\SEW>ES
7;,H71 & ELECTRONICS 7;,E74 ,MATRIX ,A
%[S ! TOTAL SALES 7IN DOLL>S7 = TWO
SALESPEOPLE1 ,M>Y & ,M>K1 9 EA* DE"P;T4
,MATRIX .;,B %[S ! -MIS.N ON SALES 9 EA*
DE"P;T4 ,: MATRIX IS DEF9$1 .;,,AB OR
.,,BA8 ,F9D ? MATRIX & EXPLA9 :AT XS
ELE;TS REPRES5T4
.#E4 .,,EXT5D$ .,,RESPONSE ,! ATOMIC
WEI<TS ( ?REE -P.DS >E %[N 9 ! TA#4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,-P.D3 ,=MULA3 ,ATOMIC WEI<T
,NITRIC ACID3 ,,HNO #C @3 #FC
,NITR\S OXIDE3 ;,N #B ,O @3 #DD
,WAT]3 ;,H #B ,O @3 #AH
A4 ,WRITE A L9E> SY/EM US+ ! =MULA =
EA* -P.D4 ,LET .;,H1 .;,N @1 & .,O
REPRES5T ! ATOMIC WEI<TS ( HYDROG51
NITROG51 & OXYG51 RESPECTIVELY4
B4 ,WRITE ! COE6ICI5T MATRIX =! SY/EM
& EVALUATE XS DET]M9ANT4
C4 ,C Y USE ,CRAM]'S RULE 6SOLVE !
SY/EM8 ,IF S1 F9D ! ATOMIC WEI<TS (
HYDROG51 NITROG51 & OXYG54 ,IF N1 EXPLA9
:Y N4
.#F4 .,,GRI4$ .,,ANSW] ,A F>M] H>VE/S
8 CROPS & RCVS 4#B.CE P] BU%EL ( CORN1
4#E.DJ P] BU%EL ( SOYB1NS1 & 4#C.FJ P]
BU%EL ( :1T4 ,! F>M] H>VE/S A TOTAL (
#AGJJ BU%ELS ( CROPS & RCVS A TOTAL (
4#DHCG4 ,! AM.T ( CORN H>VE/$ IS #C.BE
"TS ! -B9$ AM.T ( SOYB1NS & :1T H>VE/$4
,H[ _M BU%ELS ( :1T 7 H>VE/$8
------------------------------------#BBA
#C ,*APT] ,SUMM>Y
,,BIG ,,ID1S
,= ,YR ,NOTEBOOK
.,BIG .,IDEA #A ,SOLV+ ,SY/EMS (
,EQU,NS ,US+ A ,V>IETY ( ,ME?ODS
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,ME?OD @3 .,:5 .6.USE
.,GRAPH+3 ,GRAPH EA* EQU,N 9 ! SY/EM4
,A PO9T ": ! GRAPHS 9T]SECT IS A SOLU;N4
@3 ,! EQU,NS H ONLY TWO V>IA#S & >E GIV5
9 A =M T IS EASY 6GRAPH4
.,SUB/ITU;N3 ,SOLVE "O EQU,N = "O (!
V>IA#S & SUB/ITUTE 96! O!R EQU,N7;S74 @3
,"O (! V>IA#S 9 ! SY/EM HAS A COE6ICI5T
( #A OR --#A4
.,ELIM9,N3 ,MULTIPLY EQU,NS 03/ANTS1
!N ADD ! REVIS$ EQU,NS 6ELIM9ATE A
V>IA#4 @3 ,N"O (! V>IA#S 9 ! SY/EM H A
COE6ICI5T ( #A OR --#A4
.,CRAM]'S .RULE3 ,USE DET]M9ANTS 6F9D
! SOLU;N4 @3 ,! DET]M9ANT (! COE6ICI5T
MATRIX IS N Z]O4
.,9V]SE .MATRICES3 ,WRITE ! SY/EM Z A
MATRIX EQU,N .,,AX .K .,B4 ,MULTIPLY EA*
SIDE 0,A -#A ON ! LEFT 6OBTA9 ! SOLU;N
.;,X .K .,A -#A .;,B @4 @3 ,! DET]M9ANT
(! COE6ICI5T MATRIX IS N Z]O4
.,BIG .,IDEA #B ,GRAPH+ ,SY/EMS (
,EQU,NS & ,9EQUALITIES
.,BIG .,IDEA #C ,US+ ,MATRICES
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,A4I;N1 SUBTRAC;N1 & SCAL>
MULTIPLIC,N3 ,MATRIX MULTIPLIC,N3 ,9V]SE
MATRICES
@3 @3
------------------------------------#BBB
#C ,*APT] ,REVIEW
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99 ,MULTI-,LANGUAGE ,GLOSS>Y
99 ,VOCABUL>Y PRACTICE
,,REVIEW ,,KEY ,,VOCABUL>Y
99 SY/EM ( TWO L9E> EQU,NS 9 TWO
V>IA#S1 P4 #AEC
99 SOLU;N (A SY/EM ( L9E> EQU,NS1 P4
#GEC
99 3SI/5T1 9CONSI/5T1 9DEP5D5T1
DEP5D5T1 P4 #GED
99 SUB/ITU;N ME?OD1 P4 MO
99 ELIM9,N ME?OD1 P4 #GFG
99 SY/EM ( L9E> 9EQUALITIES 9 TWO
V>IA#S1 P4 #GFH
99 SOLU;N1 GRAPH (A SY/EM (
9EQUALITIES1 P4 #GFH
99 L9E> EQU,N 9 ?REE V>IA#S1 P4 #GGH
99 SY/EM ( ?REE L9E> EQU,NS 9 ?REE
V>IA#S1 P4 #GGH
99 SOLU;N (A SY/EM ( ?REE L9E> EQU,NS1
P4 #GGH
99 ORD]$ TRIPLE1 P4 #GGH
99 MATRIX1 P4 #GHG
99 DIM5.NS1 ELE;TS (A MATRIX1 P4 #GHG
99 EQUAL MATRICES1 P4 #GHG
99 SCAL>1 P4 #GHH
99 SCAL> MULTIPLIC,N1 P4 #GHH
99 DET]M9ANT1 P4 #BJC
99 ,CRAM]'S RULE1 P4 #BJE
99 COE6ICI5T MATRIX1 P4 #BJE
99 ID5T;Y MATRIX1 9V]SE MATRICES1 P4
#BGJ
99 MATRIX ( V>IA#S1 P4 #BAB
99 MATRIX ( 3/ANTS1 P4 #BGB
,,VOCABUL>Y ,,EX]CISES
.#A4 ,COPY & -PLETE3 ,A SY/EM ( L9E>
EQU,NS ) AT L1/ "O SOLU;N IS @8 ,:ILE A
SY/EM ) NO SOLU;N IS @8 @4
.#B4 ,COPY & -PLETE3 ,A SOLU;N 7.;X1
.;Y1 .;Z7 (A SY/EM ( L9E> EQU,NS 9 ?REE
V>IA#S IS CALL$ A7;N7 @8
.#C4 .,,WRIT+ .,EXPLA9 :5 ! PRODUCT (
TWO MATRICES IS DEF9$4
,,REVIEW ,,EXAMPLES ,,& ,,EX]CISES
,USE ! REVIEW EXAMPLES & EX]CISES 2L
6*ECK YR "U/&+ (! 3CEPTS Y H LE>N$ 9 EA*
LESSON ( ,*APT] #C4
#C.A ,SOLVE ,L9E> ,SY/EMS 0,GRAPH+
.PP#..AEC-.AEH
,EXAMPLE
,GRAPH ! SY/EM & E/IMATE ! SOLU;N4
,*ECK ! SOLU;N ALGEBRAIC,Y4
..#C;X @+ .;Y .K #C ,EQU,N #A
#D;X @+ .#C;Y .K --#A ,EQU,N #B
,GRAPH BO? EQU,NS4 ,F ! GRAPH1 ! L9ES
APPE> 69T]SECT AT 7#B1 --#C74 ,Y C *ECK
? ALGEBRAIC,Y4
#C7#B7 @+ 7-.#C7 .K #C .,EQU,N .#A
.*ECKS4
#D7#B7 @+ #C 7--#C7 .K --#A ,EQU,N #B
*ECKS4
,,EXAMPLE #A
ON P4 #AEC = ,EXS4 #D-F
,,EX]CISES
,GRAPH ! SY/EM & E/IMATE ! SOLU;N4
,*ECK ! SOLU;N ALGEBRAIC,Y4
.#D4 #B .;X -- .;Y .K #I
.;X @+ #C .;Y .K #H
.#E4 #B .;X -#C .;Y .K --#B
.;X @+ .;Y .K --#F
.#F4 #C .;X @+ .;Y .K #F
- .;X @+ #B .;Y .K #AB
------------------------------------#BBC
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,*APT] ,REVIEW ,PRACTICE
#C.B ,SOLVE ,L9E> ,SY/EMS ,ALGEBRAIC,Y
PP4 #AFJ-AFG
,EXAMPLE
,SOLVE ! SY/EM US+ ! ELIM9,N ME?OD4
#B .;X @+ #E .;Y .K #H ,EQU,N #A
#D .;X @+ #C .;Y .K --#AB ,EQU,N #B
,MULTIPLY ,EQU,N #A BY --#B S T !
COE6ICI5TS ( .;X DI6] ONLY 9 SIGN4
,ADD ! REVIS$ EQU,NS & SOLVE = .;Y @4
,SUB/ITUTE ! VALUE ( ;Y 96"O (!
ORIG9AL EQU,NS & SOLVE = .X4
#B .;X @+ #E 7#D7 .K #H ..,SUB/ITUTE
#D = ;Y 9 ,EQU,N .#A4
#B .;X .K --#AB ..,SUBTRACT #E7#D7 .K
#BJ F EA* .SIDE4
.;X .K --#F ..,DIVIDE EA* SIDE 0.#B4
,! SOLU;N IS 7-#F1 #D74
,,EXAMPLES #B & #C
ON PP4 #AFA-AFB = ,EXS4 #G-AJ
,,EX]CISES
,SOLVE ! SY/EM US+ ! ELIM9,N ME?OD4
.#G4 #C .;X @+ #B .;Y .K #E
-#B .;X @+ #C .;Y .K#BG
.#H4 #C .;X @+ #E .;Y .K #E
#B .;X --#C .;Y .K #AF
.#I4 #B .;X @+ #C .;Y .K #I
--#C .;X @+ .;Y .K #BE
.#AJ4 .,,FUEL .,,CO/S ,! CO/ ( #AD
GALLONS ( REGUL> GASOL9E & #AJ GALLONS (
PREMIUM GASOL9E IS 4#DF.FH4 ,PREMIUM
CO/S @4#.CJ M P] GALLON ?AN REGUL>4 ,:AT
IS ! CO/ P] GALLON ( EA* TYPE ( GASOL9E8
#C.C ,GRAPH ,SY/EMS ( ,L9E>
,9EQUALITIES PP4 #AFH-AGC
,EXAMPLE
,GRAPH ! SY/EM ( L9E> 9EQUALITIES4
#C .;X -- .;Y "K.K #D ,9EQUAL;Y #A
.;X @+ .;Y .1 #A ,9EQUAL;Y #B
,GRAPH EA* 9EQUAL;Y 9 ! SY/EM4 ,USE A
DI6]5T COLOR = EA* HALF-PLANE4 ,!N
ID5TIFY ! REGION T IS -MON 6BO? GRAPHS4
,X IS ! REGION T IS %AD$ PURPLE4
,,EXAMPLE #A
ON P4 #AFH = ,EXS4 #AA-AC
,,EX]CISES
,GRAPH ! SY/EM ( L9E> 9EQUALITIES4
.#AA4 #D .;X @+ .;Y "K #A
- .;X @+ #B .;Y "K #E
.#AB4 #B .;X @+ #C .;Y .1 #F
#B .;X -- .;Y "K #H
.#AC4 .;X @+ #C .;Y .1#E
- .;X @+ #B .;Y "K #D
------------------------------------#BBD
#C ,,*APT] ,,REVIEW
.#C..D ,SOLVE ,SY/EMS ( ,L9E> ,EQU,NS
9 ,?REE ,V>IA#S PP4 #AGH-AHE
,,EXAMPLE
,SOLVE ! SY/EM4
#B .;X @+ .;Y @+ #C .;Z .K #E ,EQU,N
#A
--.;X @+ #C .;Y @+ .;Z .K --#AD ,EQU,N
#B
#C .;X -- .;Y -- #B .;Z .K #AA ,EQU,N
#C
,REWRITE ! SY/EM Z A L9E> SY/EM 9 TWO
V>IA#S4 ,ADD --#C "TS ,EQU,N #A 6,EQU,N
#B4 ,!N ADD ,EQU,N #A & ,EQU,N #C4
,SOLVE ! NEW L9E> SY/EM = BO? ( XS
V>IA#S4
,SUB/ITUT+ .;X .K #C & .;Z .K #A 96"O
(! ORIG9AL EQU,NS & SOLV+ = .;Y GIVES
.;Y .K --#D4 ,! SOLU;N IS 7#C1 --#D1
#A74
,,EXAMPLES #A & #D
ON PP4 #AGI-AHA = ,EXS4 #AD-AG
,,EX]CISES
,SOLVE ! SY/EM4
.#AD4 .;X -- .;Y @+ .;Z .K #AJ
#D .;X @+ .;Y -- #B .;Z .K #AE
--#C .;X @+ #E .;Y -- .;Z .K --#AH
.#AE4 #F .;X -- .;Y @+ #D .;Z .K #F
-- .;X -- #C .;Y @+ .;Z .K #CA
#B .;X @+ #B .;Y -- #E .;Z .K --#DB
.#AF4 #E .;X @+ .;Y -- .;Z .K #DJ
.;X @+ #G .;Y @+ #D .;Z .K #DD
-- .;X @+ #C .;Y @+ .;Z .K #AF
.#AG4 .,,MUSIC ,FIFTE5 B& MEMB]S F A
S*OOL 7 SELECT$ 6PLAY 9 ! /ATE OR*E/RA4
,TWICE Z _M /UD5TS :O PLAY A W9D 9/RU;T
7 SELECT$ Z /UD5TS :O PLAY A /R+ OR
P]CUS.N 9/RU;T -B9$4 ,(! /UD5TS SELECT$1
"O FIF? PLAY A /R+ 9/RU;T4 ,H[ _M (!
/UD5TS SELECT$ PLAY EA* TYPE ( 9/RU;T8
#C.E ,P]=M ,BASIC ,MATRIX ,OP],NS PP4
#AHG-AIC
,,EXAMPLE
,P]=M ! 9DICAT$ OP],N4
.A4
.B4
------------------------------------#BBE
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,*APT] ,REVIEW ,PRACTICE
,,EXAMPLES #B & #C
ON PP4 #AHH-AHI = ,EXS4 #AH-BC
,,EX]CISES
,P]=M ! 9DICAT$ OP],N4
.#AH4
.#AI4
.#BJ4
.#BA4
.#BB4
.#BC4
#C.F ,MULTIPLY ,MATRICES PP4 #AIE-BJB
,,EXAMPLES
ON PP4 #AIF-AIH = ,EXS4 #BD-BH
,,EXAMPLE
,F9D .;,,AB IF & @4
,,EX]CISES
,F9D ! PRODUCT4
.#BD4
.#BE4
.#BF4
.#BG4
.#BH4 .,,MANUFACTUR+ ,A -PANY
MANUFACTURES ?REE MODELS ( FLAT-SCRE5
COLOR ,,TV,'S3 A #AI 9* MODEL1 A #BG 9*
MODEL1 &A #CB 9* MODEL4 ,! ,,TV,'S >E
%IPP$ 6TWO W>EH\SES4 ,! NUMB]S ( UNITS
%IPP$ 6EA* W>EH\SE >E GIV5 9 MATRIX .,A
@1 &! PRICES (! MODELS >E GIV5 9 MATRIX
.,B4 ,WRITE A MATRIX T GIVES ! TOTAL
VALUE (! ,,TV,'S 9 EA* W>EH\SE4
------------------------------------#BBF
#C ,*APT] ,REVIEW
#C.G ,EVALUATE ,DET]M9ANTS & ,APPLY
,CRAM]'S ,RULE PP4 #BJC-BJI
,,EXAMPLE
,EVALUATE ! DET]M9ANT ( @4
,,EXAMPLES #A & #B
ON PP4 #BJC-BJD = ,EXS4 #BI-CB
,,EX]CISES
,EVALUATE ! DET]M9ANT (! MATRIX4
.#BI4
.#CJ4
.#CA4
.#CB4 .,,S*OOL .,,_S ,Y >E MAK+ A L>GE
TRIANGUL> P5NANT = YR S*OOL FOOTBALL
T1M4 ,! V]TICES (! TRIANGLE >E 7#J1 #J71
7#J1 #EJ71 & 7#GJ1 #BJ7 ": ! COORD9ATES
>E M1SUR$ 9 9*ES4 ,H[ _M SQU>E .FEET (
MAT]IAL W Y NE$ 6MAKE ! P5NANT8
#C.H ,USE ,9V]SE ,MATRICES 6,SOLVE
,L9E> ,SY/EMS PP4 #BAJ-BAG
,,EXAMPLE
,USE AN 9V]SE MATRIX 6SOLVE ! .;X --
#B .;Y .K #AD
L9E> SY/EM AT ! "R4 #B .;X @+ .;Y .K
#H
,WRITE ! L9E> SY/EM Z A MATRIX EQU,N
.,,AX .K .,B4
,F9D ! 9V]SE (! COE6ICI5T MATRIX .,A
,!N MULTIPLY ! MATRIX ( 3/ANTS 0.,A
--#A ON ! LEFT4
,! SOLU;N (! SY/EM IS 7#F1 --#D74
,,EXAMPLE #D
ON P4 #BAB = ,EXS4 #CC-CE
,,EX]CISES
,USE AN 9V]SE MATRIX 6SOLVE ! L9E>
SY/EM4
.#CC4 .;X @+ #D .;Y .K #AA
#B .;X -- #E .;Y .K #I
.#CD4 #C .;X @+ .;Y .K --#A
- .;X @+ #B .;Y .K #AB
.#CE4 #C .;X @+ #B .;Y .K --#AA
#D .;X -- #C .;Y .K #H
------------------------------------#BBG
#C ,*APT] ,TE/
,GRAPH ! L9E> SY/EM & E/IMATE !
SOLU;N4 ,!N *ECK ! SOLU;N ALGEBRAIC,Y4
.#A4 #D .;X @+ .;Y .K #E
#C .;X -- .;Y .K #B
.#B4 .;X @+ #B .;Y .K --#F
--#F .;X -- #B .;Y .K --#AD
.#C4 #B .;X -- #C .;Y .K #AE
.#D @4 #C .;X -- .;Y .K #AB
-- .;X @+ #H .;Y .K --#D
,GRAPH ! SY/EM ( L9E> 9EQUALITIES4
.#E4 #B .;X @+ .;Y "K #F
.;Y .1 --#B
.#F4
.#G4 .;X -- #B .;Y "K --#AD
.;Y .1.K _\;X_\
.#H4 --#C .;X @+ #D .;Y .1 --#AB
;Y "K --#B_\;X_\ @+ #E
,SOLVE ! SY/EM US+ ANY ALGEBRAIC
ME?OD4
.#I4 #C .;X @+ .;Y .K --#I
.;X -- #B .;Y .K --#AJ
.#AJ4 #B .;X @+ #C .;Y .K --#B
#D .;X @+ #G .;Y .K --#F
.#AA4 .;X @+ #D .;Y .K --#BF
--#E .;X -- #B .;Y .K --#AD
.#AB4 .;X -- .;Y @+ .;Z .K --#C
#B .;X -- .;Y @+ #E .;Z .K #D
#D .;X @+ #B .;Y -- .;Z .K #B
.#AC4 .;X @+ .;Y @+ .;Z .K #C
-- .;X @+ #C .;Y @+ #B .;Z .K --#H
#E .;Y @+ .;Z .K #B
.#AD4 #B .;X -- #E .;Y -- .;Z .K #AG
.;X @+ .;Y @+ #C .;Z .K #AI
--#D .;X @+ #F .;Y @+ .;Z .K --#BJ
,USE ! GIV5 MATRICES 6EVALUATE !
EXPRES.N1 IF POSSI#4 ,IF N POSSI#1 /ATE
! R1SON4
.#AE @4 #B .,A @+ .;,B
.#AF4 .;,C -- #C .;,B
.#AG4 .,A -- #B .;,D
.#AH4 #D .;,D @+ .;,E
#AI4 .;,,AC
#BJ4 .,,DE
.#BA4 @7 .,A @+ .;,B @7 .;,D
.#BB4 .,A @7 .;,C -- .;,B @7
,EVALUATE ! DET]M9ANT (! MATRIX4
.#BC4
.#BD4
.#BE4
.#BF4
,USE AN 9V]SE MATRIX 6SOLVE ! L9E>
SY/EM4
.#BG4 #C .;X @+ #D .;Y .K #F
#D .;X @+ #E .;Y .K #G
.#BH4 #B .;X -- #G .;Y .K --#CF
.;X -- #C .;Y .K --#AF
.#BI4 #E .;X @+ #C .;Y .K --#E
--#I .;X -- #F .;Y .K #AB
.#CJ4 #C .;X @+ #B .;Y .K #AE
- .;X @+ #D .;Y .K --#CC
.#CA4 .,,F9.E ,A TOTAL ( 4#AE1JJJ IS
9VE/$ 9 TWO CORPORATE BONDS T PAY #E@3P
& #G@3P SIMPLE ANNUAL 9T]E/4 ,! 9VE/OR
WANTS 6E>N 4#HHJ 9 9T]E/ P] YE> F !
BONDS4 ,H[ M* %D 2 9VE/$ 9 EA* BOND8
.#CB4 .,,TICKET .,,SALES ,=! OP5+ "D
(A C>NIVAL1 #HJJ ADMIS.N TICKETS 7 SOLD4
,! RECEIPTS TOTAL$ 4#CGGE4 ,TICKETS = *N
CO/ 4#C EA*1 TICKETS = ADULTS CO/ 4#H
EA*1 & TICKETS = S5IOR CITIZ5S CO/ 4#E
EA*4 ,"! 7 TWICE Z _M *N'S TICKETS SOLD
Z ADULT TICKETS4 ,H[ _M ( EA* TYPE (
TICKET 7 SOLD8
.#CC4 .,,BOAT+ ,ON A C]TA9 RIV]1 A
MOTORBOAT C TRAVEL #CD MILES P] H\R )!
CURR5T & #BH MILES P] H\R AG/ ! CURR5T4
,F9D ! SPE$ (! MOTORBOAT 9 / WAT] &!
SPE$ (! CURR5T4
------------------------------------#BBH
#C ,/&>DIZ$ ,TE/ ,PREP>,N
,,MULTIPLE-,,*OICE ,,"QS
,IF Y H DI6ICULTY SOLV+ A MULTIPLE
*OICE PRO#M DIRECTLY1 Y MAY 2 A# 6USE
ANO!R APPROA* 6ELIM9ATE 9CORRECT ANSW]
*OICES & OBTA9 ! CORRECT ANSW]4
,SIDEB>3
,/&>DS
..#B.J ,/UD5TS SOLVE SY/EMS ( L9E>
.EQU,NS & 9EQUALITIES @7 .9 .TWO OR ?REE
.V>IA#S @7 0SUB/ITU;N1 .) .GRAPHS @1 OR
) MATRICES4
,,PRO#M #A
,ON A TR1DMILL1 Y JOG AT #F MILES P]
H\R & SPR9T AT #H MILES P] H\R4 ,Y COV]
MILES 9 H\R4 ,H[ L;G DID Y SP5D AT EA*
ACTIV;Y8
,A4 #BE M9UTES JO7+1 #E M9UTES SPR9T+
,B4 #BJ M9UTES JO7+1 #AJ M9UTES SPR9T+
,C4 #AJ M9UTES JO7+1 #BJ M9UTES SPR9T+
,D4 #E M9UTES JO7+1 #BE M9UTES SPR9T+
,,ME?OD #A
.,,SOLVE .,,DIRECTLY ,WRITE & SOLVE A
L9E> SY/EM4
.,,/EP .#A .,WRITE A SY/EM ( EQU,NS4
,LET .;X 2 ! JO7+ "T & .;Y 2 ! SPR9T+
"T4
.,,/EP .#B .,SOLVE ,EQU,N #B = .;Y
6GET @4
.,,/EP .#C .,SUB/ITUTE = .;Y 9 ,EQU,N
#A & SOLVE = .X4
.,,/EP .#D .,SUB/ITUTE ! VALUE ( .;X
96REVIS$ ,EQU,N #B & SOLVE = .Y4
,HE JOGS = H\R1 OR #BJ M9UTES4 ,HE
SPR9TS = H\R1 OR #AJ M9UTES4
,! CORRECT ANSW] IS ,B4 ..,A ;,B ;,C
.;,D
,,ME?OD #B
.,,ELIM9ATE .,,*OICES ,ANO!R ME?OD IS
6ELIM9ATE 9CORRECT ANSW] *OICES 03SID]+
:AT HAPP5S IF HE JOGS ! 5TIRE "T OR
SPR9TS ! 5TIRE "T4
.,,/EP .#A .,F9D ! 4T.E HE COV]S IF HE
SP5DS ! 5TIRE "T JO7+ OR ! 5TIRE "T
SPR9T+4
,IF HE JOGS ! 5TIRE "T1 !N HE COV]S
MILES4
,IF HE SPR9TS ! 5TIRE "T1 !N HE COV]S
MILES4
,2C IS CLOS] 6#C ?AN 6#D1 HE M/ SP5D M
"T JO7+ ?AN SPR9T+4 ,S1 Y C ELIM9ATE
*OICES ;,C & ,D4
.,,/EP .#B .,CALCULATE ! 4T.ES =!
REMA9+ *OICES4 ,USE ! FACT T @4
,*OICE ,A3
,*OICE ;,B3
,! CORRECT ANSW] IS ,B4 ..,A ;,B ;,C
.;,D
------------------------------------#BBI
,,PRO#M #B
,:AT IS ! 9V]SE ( @8
,A4
,B4
,C4
,D4
,,ME?OD #A
.,,SOLVE .,,DIRECTLY ,F9D ! 9V]SE (
MATRIX ,A 0US+ ! =MULA 2L4
,! 9V]SE ( IS3
,! CORRECT ANSW] IS ,D4 ..,A ;,B ;,C
.;,D
,,ME?OD #B
.,,ELIM9ATE .,,*OICES ,USE ! FACT T
.,A --#A ..,A .K ,I .6ELIM9ATE 9CORRECT
ANSW] *OICES4
,MULTIPLY ! MATRIX 9 EA* ANSW] *OICE
0MATRIX ,A4 ,ELIM9ATE Z SOON Z Y R1LIZE
T ! PRODUCT .,A --#A .,A IS N ! ID5T;Y
MATRIX4
.,*OICE .,A3
.,*OICE .;,B3
.,*OICE .;,C3
.,*OICE .;,D3
,! CORRECT ANSW] IS ,D4 ..,A ;,B ;,C
.;,D
,,PRACTICE
,EXPLA9 :Y Y C ELIM9ATE ! HI<LI<T$
ANSW] *OICE4
#A4 ,:AT IS ! SOLU;N (! SY/EM8
,A4 7#A1-#B1C7
,B4 ;,X 7-#A1 #B1 --#C7
,C4 7#C1 --#B1 #A7
,D4 7#A1 #C1 --#B7
#B4 ,:AT IS ! SOLU;N (! MATRIX EQU,N8
,A4
,B4
,C4
,D4
------------------------------------#BCJ
#C ,/&>DIZ$ ,TE/ ,PRACTICE
,,MULTIPLE-,,*OICE
#A4 ,! TWO TOP-SELL+ ,,DVD,'S ( #BJJC
GROSS$ A -B9$ TOTAL ( 4#FJJ.I MILLION4
,! TOP-SELL+ ,,DVD GROSS$ 4#CI.I MILLION
M ?AN ! ,,DVD RANK$ SECOND4 ,H[ M* DID !
TOP-SELL+ ,,DVD GROSS8
,A4 4#BDJ.F MILLION
,B4 4#BHJ.E MILLION
,C4 4#CBJ.D MILLION
,D4 4#EFA MILLION
#B4 ,: SY/EM HAS 7#J1 #D7 Z A SOLU;N8
,A4 .;X @+ .;Y .K #D
.;X -- .;Y .K #D
,B4 #B .;X @+ .;Y .K --#D
.;X -- #B .;Y .K #H
,C4 #C .;X @+ #B .;Y .K #H
.;X -- #D .;Y .K --#AF
,D4 -- .;X @+ .;Y .K #D
#C .;X -- #B .;Y .K #AB
#C4 ,: SY/EM ( 9EQUALITIES IS GRAPH$
2L8
,A4 .;Y .1 .;X -- #A
#B .;X @+ #C .;Y "K.K #F
,B4 .;Y "K .;X -- ;L
#B .;X @+ #C .;Y .1 #F
,C4 .;Y "K .;X -- #A
#C .;X @+ #B .;Y .1.K #F4
,D4 .;Y .1.K .;X --#A
#C .;X @+ #B .;Y "K #F
#D4 ,JULIA B"\ SC>VES & GLOVES Z GIFTS
= FAMILY MEMB]S4 ,EA* SC>F CO/S 4#C LESS
?AN EA* PAIR ( GLOVES4 ,A PAIR ( GLOVES
CO/S 4#I4 ,JULIA B"\ #H ITEMS = 4#FF4
,H[ _M SC>VES DID %E BUY8
,A4 #B
,B4 #D
,C4 #E
,D4 #F
#E4 ,:AT IS ! SOLU;N (! MATRIX EQU,N8
,A4
,B4
,C4
,D4
#F4 ,A DRIV]'S $UC,N PROGRAM 3SI/S (A
TOTAL ( #DF H\RS ( CLASSROOM 9/RUC;N1
DRIV+1 & OBS]V,N4 ,Y M/ SP5D #C "TS Z M*
"T 9 ! CLASSROOM Z DRIV+1 & #D H\RS L;G]
DRIV+ ?AN OBS]V+4 ,H[ M* "T D Y SP5D
DRIV+8
,A4 #F H\RS
,B4 #AJ H\RS
,C4 #AD H\RS
,D4 #CJ H\RS
#G4 ,:AT IS ! SOLU;N (! L9E> SY/EM8
#B .;X -- #C .;Y .K #I
,A4 7#F1 #F7
,B4 7#I1C7
,C4 ,NO SOLU;N
,D4 ,9F9ITELY _M SOLU;NS
#H4 ,: SET ( V]TICES =MS A TRIANGLE
HAV+ ! SAME >EA Z ! TRIANGLE ) V]TICES
7#A1-#E71 7#B1 #C71 & 7#AB1 #B78
,A4 7-#A1E71 7#B1 #C71 7-#AB1B7
,B4 7#J1 #J71 7#F1 #F71 7#H1 #F7
,C4 7#A1 #A71 7#H1 #A71 7-#B1 --#H7
,D4 7-#A1J71 7#E1I71 7#H1J7
#I4 ,MADEL9E PD 4#AI.DC = #F PACKAGES
( BULBS = H] FL[] G>D54 ,! CO/ ( #A
PACKAGE ( EA* TYPE ( BULB IS %[N4 ,%E
B"\ TWICE Z _M PACKAGES ( PHLOX BULBS Z
LILY BULBS4 ,H[ _M PACKAGES ( LILY BULBS
DID %E BUY8
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,PEONY BULBS3 ,PHLOX BULBS3 ,LILY
BULBS
4#C.II3 4#B.FA3 4#B.BD
,A4 ,N"O
,B4 #A PACKAGE
,C4 #B PACKAGES
,D4 #C PACKAGES
#AJ4 ,: MATRIX HAS .NO 9V]SE8
,A4
,B4
,C4
,D4
------------------------------------#BCA
..,,/ATE ,,TE/ ,,PRACTICE
_+CLASSZONE.COM_:
,,GRI4$ ,,ANSW]
#AA4 ,:AT IS ! ;Y-COORD9ATE (! SOLU;N
(! L9E> SY/EM 2L8
#B .;X -- #E .;Y .K --#AJ
.;X @+ #D .;Y .K #BA
#AB4 ,! SOLU;N (! L9E> SY/EM IS 7--#A1
--#B1 .;Z74 ,:AT IS ! VALUE ( ;Z8
.;X @+ #B .;Y @+ #B .;Z .K #G
#B .;X -- #C .;Y -- .;Z .K --#B
--#D .;X @+ .;Y -- #C .;Z .K --#AF
#AC4 ,:AT IS ! DET]M9ANT (! MATRIX8
#AD4 ,=! MATRIX EQU,N1 :AT IS ! VALUE
( .;X @+ #D;Y8
#AE4 ,! MATRIX GIVES ! RECORDS (! TOP
F\R T1MS 9 ! ,N,NAL ,HOCKEY ,L1GUE =!
#BJJC-BJJD REGUL> S1SON4 ,TWO PO9TS >E
AW>D$ = EA* W9 7;,W71 #A PO9T = EA* TIE
7;,T71 #J PO9TS = EA* LOSS 7;,L71 & #A
PO9T = EA* OV]"T LOSS 7,,OL74 ,H[ _M
PO9TS DID EA* T1M E>N8 .,EXPLA94
#AF4 ,A SECOND-RUN MOVIE !AT] SELLS
MAT9EE TICKETS = 4#D ON WEEK"DS 2F #F
,P4,M4 ,! !AT] SELLS REGUL> TICKETS =
4#F ON WEEK5DS & ON WEEK"DS AF #F ,P4,M4
,9 "O WEEK1 ! !AT] E>N$ 4#FJJJ4 ,! !AT]
SOLD #HIJ M REGUL> TICKETS ?AN MAT9EE
TICKETS1 ,H[ _M ( EA* TYPE ( TICKET 7
SOLD8 .,EXPLA94
,,EXT5D$ ,,RESPONSE
#AG4 ,! TA# %[S ,U4,S4 3SUM] SP5D+ ON
VIDEO GAMES & AT ! BOX (FICE 7IN DOLL>S
P] P]SON P] YE>7 =! YE>S #AIIF 6#BJJB4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 #AIIF3 #AIIG3 #AIIH3 #AIII3
#BJJJ3 #BJJA3 #BJJB
.,VIDEO .GAMES @3 #AA.E3 #AF.E3 #AH.E3
#BD.E3 #BD.G3 #BF.I3 #CJ.E
.,BOX .(FICE @3 #BG.A3 #BH.I3 #CA.B3
#CC.A3 #CB.E3 #CE.E3 #CI.G
A4 ,APPROXIMATE ! BE/-FITT+ L9E =!
VIDEO GAME DATA4
B4 ,APPROXIMATE ! BE/-FITT+ L9E =! BOX
(FICE DATA4
C4 ,USE ! BE/-FITT+ L9ES 6E/IMATE !
YE> :5 3SUM] SP5D+ ON VIDEO GAMES W CAT*
UP 63SUM] SP5D+ AT ! BOX (FICE4 .,EXPLA9
H[ Y F.D YR ANSW]4
#AH4 ,A TRIANGLE HAS AN >EA ( #AJJ
SQU>E UNITS4 ,XS V]TICES >E 7#J1 #J71
7#BJ1 #J71 & @7 .;X1 .;Y @7@4
A4 ,WRITE AN EQU,N 9VOLV+ A DET]M9ANT
T Y C USE 6F9D ! COORD9ATES (! UN"KN
V]TEX4
B4 ,SOLVE ! EQU,N4 ,%[ ALL ( YR /EPS4
C4 ,:AT DOES YR ANSW] TELL Y AB !
COORD9ATES (! UN"KN V]TEX8
------------------------------------#BCB
#C ,CUMULATIVE ,REVIEW
,*APT] #A-C
,SIMPLIFY ! EXPRES.N1 @7 P4 #AJ @7
.#A4 #C .;X #B -- #H .;X @+ #AB .;X --
#E .;X #B @+ #C .;X
.#B4 #AE .;X -- #F .;X @+ #AJ .;Y --
#C .;Y @+ #D .;X
.#C4 #C7 .;X @+ #B7--#D .;X #B @+ #C
.;X @+ #I
,SOLVE ! EQU,N4 ,*ECK YR SOLU;N4
.#D4 #F .;X -- #G .K --#B .;X @+ #I @7
P4 #AH @7
.#E4 #D7 .;X -- #C7 .K #AF .;X @+ #AH
@7 P4 #AH @7
.#F4 P4 #AH @7
.#G4 _\ .;X @+ #C_\ .K #E @7 P4 #EA @7
.#H4 _\#D .;X -- #A_\ .K #BG @7 P4 #EA
@7
.#I4 #AI--#B .;X _\ .K #DA @7 P4 #EA
@7
,SOLVE ! 9EQUAL;Y4 ,!N GRAPH ! SOLU;N4
.#AJ4 #F7 .;X -- #D7 .1 #B .;X @+ #H
@7 P4 #DA @7
.#AA4 #C "K .;X -- #B "K.K #H @7 P4
#DA @7
.#AB4 #B .;X "K --#F OR .;X @+ #B .1
#E @7 P4 #DA @7
.#AC4 _\ .;X -- #D_\ "K #E @7 P4 #EA
@7
.#AD4 _\ .;X @+ #C_\ .1.K #AE @7 P4
#EA @7
.#AE4 _\#F .;X @+ #A_\ "K #BC @7 P4
#EA @7
,F9D ! SLOPE (! L9E PASS+ "? ! GIV5
PO9TS4 ,!N TELL :E!R ! L9E ..RISES1
FALLS1 IS .HORIZONTAL @1 OR IS .V]TICAL1
@7 P4 #HB @7
.#AF4 7#C1 #B71 7--#A1 --#E7
.#AG4 7--#G1 #D71 7#E1 --#C7
.#AH4 7--#D1 --#F71 7--#D1 #D7
.#AI4
,GRAPH ! EQU,N OR 9EQUAL;Y4
.#BJ4 .;Y .K #C .;X @+ #E @7 P4 #HI @7
.#BA4 .;X .K --#F @7 P4 #HI @7
.#BB4 -- .;X @+ #D .;Y .K #AF @7 P4
#HI @7
.#BC4 .;Y .K #B_\ .;X _\ @7 P4 #ABC @7
.#BD4 .;Y .K _\;X--#C_\ @7 P4 #ABC @7
.#BE4 .;Y .K --#D_\ .;X _\ @+ #E @7 P4
#ABC @7
.#BF4 .;Y "K.K .;X -- #G @7 P4 #GCB @7
.#BG4 #B .;X @+ .;Y .1 #A @7 P4 #ACB
@7
.#BH4 #B .;X -- #E .;Y .1.K --#AE @7
P4 #ACB @7
,GRAPH ! REL,N4 ,!N TELL :E!R ! REL,N
IS A FUNC;N1 @7 P4 #GB @7
#BI4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 --#D3 --#B3 #J3 #B3 #D
.;Y @3 --#A3 #J3 #A3 #B3 #C
#CJ4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #D3 --#B3 #A3 #A3 --#C
.;Y @3 --#B3 #J3 #A3 #D3 #C
,SOLVE ! SY/EM US+ ANY ALGEBRAIC
ME?OD4
.#CA4 #D .;X -- #C .;Y .K #CB
-#B .;X @+ .;Y .K --#AD @7 P4 #AFJ @7
.#CB4 #E .;X -- #B .;Y .K --#D
#C .;X @+ #F .;Y .K #CF @7 P4 #GFJ @7
.#CC4 .;X -- .;Y @+ #B .;Z .K --#.D
#C .;X @+ .;Y -- #D .;Z .K --#F
#B .;X @+ #C .;Y @+ .;Z .K #I @7 P4
#GGH @7
,USE ! GIV5 MATRICES 6EVALUATE !
EXPRES.N1 @7 P4 #GIE @7
.#CD4 .;,B -- #C .,A
.#CE4 #B7#D @+ .;,B @7 -- .;,C
.#CF4 @7 .;,C -- .,A @7 .;,B
.#CG4 @7 .;,B @+ .;,C @7 .;,D
,F9D ! 9V]SE (! MATRIX1 @7 P4 #BAJ @7
.#CH4
.#CI4
.#DJ4
.#DA4
.#DB4 .,,C;Y .,,P>K ,A TRIANGUL> SEC;N
(A C;Y P>K IS 2+ TURN$ 96A .PLAYGR.D4 ,!
TRIANGLE'S V]TICES >E 7#J1 #J71 7#AE1
#AJ71 & 7#H1 #BE7 ": ! COORD9ATES >E
M1SUR$ 9 Y>DS4 ,F9D ! >EA (! PLAYGR.D1
@7 P4 #BJC @7
------------------------------------#BCC
#DC4 .,,BASEBALL ,! ,PY?AGOR1N ,!OREM
( ,BASEBALL IS A =MULA = APPROXIMAT+ A
T1M'S RATIO ( W9S 6GAMES PLAY$4 ,LET
.;,R 2 ! NUMB] ( RUNS ! T1M SCORES DUR+
! S1SON1 .,A 2 ! NUMB] ( RUNS ALL[$
6OPPON5TS1 .,WBE ! NUMB] ( W9S1 & .,! !
TOTAL NUMB] ( GAMES PLAY$4 ,!N ! =MULA
2L APPROXIMATES ! T1M'S RATIO ( W9S
6GAMES PLAY$1 @7 P4 #BF @7
A4 ,SOLVE ! =MULA = .,W4
B4 ,9 #BJJD ! ,BO/ON ,R$ ,SOX SCOR$
#IDI RUNS & ALL[$ #GFH RUNS4 ,H[ _M ( XS
#AFB GAMES WD Y E/IMATE ! T1M WON8
.,-P>E YR ANSW] 6! T1M'S ACTUAL NUMB] (
W9S1 : 0 #IH4
#DD4 .,,HI<WAY .,,DRIV+ ,A SPORT
UTIL;Y VEHICLE HAS A #BA GALLON GAS
TANK4 ,ON A L;G HI<WAY TRIP1 GAS IS US$
AT A RATE ( APPROXIMATELY #D GALLONS P]
H\R4 ,ASSUME ! GAS TANK IS FULL AT ! />T
(! TRIP4 @7 P4 #GB @7
A4 ,WRITE A FUNC;N GIV+ ! NUMB] (
GALLONS ;G ( GASOL9E 9 ! TANK AF TRAVEL+
= .;T H\RS4
B4 ,GRAPH ! FUNC;N F "P 7A74
C4 ,ID5TIFY ! DOMA9 & RANGE (! FUNC;N
F "P 7A74
#DE4 .,,-MIS.N ,A R1L E/ATE AG5T'S
-MIS.N .;C V>IES DIRECTLY )! SELL+ PRICE
.;P (A H\SE4 ,AN AG5T MADE 4#CIJJ 9
-MIS.N AF SELL+ A 4#GH1JJJ H\SE4 ,WRITE
AN EQU,N T GIVES .;C Z A FUNC;N ( P4
,PREDICT ! AG5T'S -MIS.N IF ! SELL+
PRICE (A H\SE IS 4#ABE1JJJ4 @7 P4 #AJG
@7
#DF4 .,,WA/E .,,RECOV]Y ,! TA# %[S !
AM.T ( MAT]IAL 7IN MILLIONS ( TONS7
RECOV]$ F SOLID WA/E 9 ! ,UNIT$ ,/ATES F
#AIID 6#BJJA4 ,MAKE A SCATT] PLOT (!
DATA & APPROXIMATE ! BE/-FITT+ L9E4
,PREDICT ! AM.T ( MAT]IAL T W 2 RECOV]$
F SOLID WA/E 9 #BJAJ4 7.P4 .#AAC7
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,YE>S S9CE #AIID1 .;T @3 #J3 #A3 #B3
#C3 #D3 #E3 #F3 #G
.,RECOV]$ .MAT]IAL1 .;M @3 #EJ.F3
#ED.I3 #EG.C3 #EI.D3 #FA.A3 #FD.H3
#FG.G3 #FH.J
#DG4 .,,WEI<TLIFT+ .,,RECORDS ,! M5'S
_W WEI<TLIFT+ RECORDS =! #AJE-KG-&-OV]
WEI<T CATEGORY >E %[N 9 ! TA#4 ,! -B9$
LIFT IS ! SUM (! SNAT* LIFT &! CL1N &
J]K LIFT4 ,LET #E 2 ! WEI<T LIFT$ 9 !
SNAT* & LET7 2 ! WEI<T LIFT$ 9 ! CL1N &
J]K4 ,WRITE & GRAPH A SY/EM (
9EQUALITIES 6DESCRIBE ! WEI<TS AN A?LETE
CD LIFT 6BR1K ! RECORDS = BO? ! SNAT* &
-B9$ LIFTS1 B .N ! CL1N & J]K LIFT4 @7
P4 #AFH @7
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,SNAT*3 ,CL1N & ,J]K3 ,-B9$
#BAC.J3 #BFC.J3 #DGB.E
------------------------------------#BCD
,UNIT #B3 ,QUADRATIC1 ,POLYNOMIAL1 &
,RADICAL ,FUNC;NS
#D ,QUADRATIC ,FUNC;NS & ,FACTOR+
.#D..A ,GRAPH ,QUADRATIC ,FUNC;NS 9
,/&>D ,=M
.#D..B ,GRAPH ,QUADRATIC ,FUNC;NS 9
,V]TEX OR ,9T]CEPT ,=M
.#D..C ,SOLVE ;X #B @+ .BX @+ ;C .K #J
0,FACTOR+
.#D..D ,SOLVE .AX #B @+ ..BX @+ .;C .K
#J 0,FACTOR+
.#D..E ,SOLVE ,QUADRATIC ,EQU,NS
0,F9D+ ,SQU>E ,ROOTS
.#D..F ,P]=M ,OP],NS ) ,-PLEX ,NUMB]S
.#D..G ,-PLETE ! ,SQU>E
.#D..H ,USE ! ,QUADRATIC ,=MULA &!
,4CRIM9ANT
.#D..I ,GRAPH & ,SOLVE ,QUADRATIC
,9EQUALITIES
.#D..AJ ,WRITE ,QUADRATIC ,FUNC;NS &
,MODELS
,SIDEB>3
,2F
,9 PREVI\S *APT]S1 Y LE>N$ ! FOLL[+
SKILLS1 : Y'LL USE 9 ,*APT] #D3 EVALUAT+
EXPRES.NS1 GRAPH+ FUNC;NS1 & SOLV+
EQU,NS1
,PREREQUISITE ,SKILLS
,,VOCABUL>Y ,,*ECK
,COPY & -PLETE ! /ATE;T4
.#A4 ,! .;X -.9T]CEPT (! L9E %[N IS @8
@4
.#B4 ,! .;Y-.9T]CEPT (! L9E %[N IS @8
@4
,,SKILLS ,,*ECK
,EVALUATE ! EXPRES.N :5 .;X--.#C4
7.,REVIEW P4 #AJ .= .#D..A1.D..G47
.#C4 --.#E;X #B @+ #A
.#D4 .;X #B -- .;X -- #H
#E4 @7 .;X @+ #D7 #B
#F4 --#C7 .;X -#G7 #B @+ #B
,GRAPH ! FUNC;N & LABEL ! V]TEX4
7..,REVIEW P4 #ABC = #D..B47
#G4 .;Y .K _\ .;X _\ @+ #B
#H4 .;Y .K _\ .;X -- #C_\
#I4 .;Y.K --.#B_\.;X_\
.#AJ4 .;Y .K _\ .;X -- #E _\ @+#D
,SOLVE ! EQU,N4 7.,REVIEW P4 #AH .=
.#D..C1.D..D47
.#AA4 .;X @+ #H .K #J
.#AB4 #C;X--#E .K #J
.#AC4 .#B;X @+ #A .K .;X
.#AD4 .#D7.;X -- #C7 .K .;X @+ #I
,SIDEB>3
@A .,HOME .,TUTOR ,PREREQUISITE SKILLS
PRACTICE AT _+CLASSZONE.COM_:
------------------------------------#BCE
,SIDEB>3
,N[
,9 ,*APT] #D1 Y W APPLY ! BIG ID1S
LI/$ 2L & REVIEW$ 9 ! ,*APT] ,SUMM>Y ON
PAGE #CAG @4 ,Y W AL USE ! KEY VOCABUL>Y
LI/$ 2L4
,BIG ,ID1S
#A ,GRAPH+ & WRIT+ QUADRATIC FUNC;NS 9
S"EAL =MS
#B ,SOLV+ QUADRATIC EQU,NS US+ A
V>IETY ( ME?ODS
#C ,P]=M+ OP],NS ) SQU>E ROOTS & -PLEX
NUMB]S
,KEY ,VOCABUL>Y
99 /&>D =M (A QUADRATIC FUNC;N1 P4
#BCF
99 P>ABOLA1 P4 #BCF
99 V]TEX =M1 P4 #BDE
99 9T]CEPT =M1 P4 #BDF
99 QUADRATIC EQU,N1 P4 #BEC
99 ROOT ( AN EQU,N1 P4 #BEC
99 Z]O (A FUNC;N1 P4 #BED
99 SQU>E ROOT1 P4 #BFF
99 -PLEX NUMB]1 P4 #BGF
99 IMAG9>Y NUMB]1 P4 #BGF
99 -PLET+ ! SQU>E1 P4 #BHD
99 QUADRATIC =MULA1 P4 #BIB
99 4CRIM9ANT1 P4 #BID
99 BE/-FITT+ QUADRATIC MODEL1 P4 #CAA
,SIDEB>3
,:Y8
,Y C USE QUADRATIC FUNC;NS 6MODEL !
HEI<TS ( PROJECTILES4 ,= EXAMPLE1 !
HEI<T (A BASEBALL HIT 0A BATT] C 2
MODEL$ 0A QUADRATIC FUNC;N4
.,ANIMAT$ ,ALGEBRA
,! ANIM,N ILLU/RAT$ 2L = ,EXAMPLE #G
ON PAGE #BHG HELPS Y ANSW] ? "Q3 ,H[
DOES *ANG+ ! BALL SPE$ & HITT+ ANGLE
A6ECT ! MAXIMUM HEI<T (A BASEBALL8
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,O!R ANIM,NS = ,*APT] .#D3 PAGES
#BCH @1 #BDG @1 #BFI @1 #BGI @1 #CJJ @1
& #CAG
------------------------------------#BCF
#D.A ,GRAPH ,QUADRATIC ,FUNC;NS 9
,/&>D ,=M
.,2F ,Y GRAPH$ L9E> FUNC;NS4
.,N[ ,Y W GRAPH QUADRATIC FUNC;NS4
.,:Y8 ,S Y C MODEL SPORTS REV5UE1 Z 9
,EXAMPLE .#E4
,KEY ,VOCABUL>Y
99 QUADRATIC FUNC;N
99 P>ABOLA
99 V]TEX
99 AXIS ( SYMMETRY
99 M9IMUM VALUE
99 MAXIMUM VALUE
,SIDEB>3
,/&>DS
#AJ.J ,/UD5TS GRAPH QUADRATIC FUNC;NS
& DET]M9E ! MAXIMA1 M9IMA1 & Z]OS (!
FUNC;N4
,A .QUADRATIC .FUNC;N IS A FUNC;N T C
2 WRITT5 9 ! ./&>D .=M .;Y .K .AX #B @+
..BX @+ .;C ": .A @6.K #J4 ,! GRAPH (A
QUADRATIC FUNC;N IS A .P>ABOLA4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,P>5T ,FUNC;N = ,QUADRATIC ,FUNC;NS
,! P>5T FUNC;N =! FAMILY ( ALL
QUADRATIC FUNC;NS IS .;F @7 .;X @7 .K
.;X #B4 ,! GRAPH ( .;F7.;X7 .K .;X #B IS
! P>ABOLA %[N 2L4
,= .;F @7 .;X @7 .K .;X #B @1 &= ANY
QUADRATIC FUNC;N .;G @7 .;X @7 .K .AX #B
@+ .BX @+ .;C ": .;B .K #J1 ! V]TEX LIES
ON ! ;Y-AXIS &! AXIS ( SYMMETRY IS .;X
.K #J4
,,EXAMPLE #A ,GRAPH A FUNC;N (! =M .;Y
.K .AX #B
,GRAPH .;Y .K .#B;X #B4 ,-P>E ! GRAPH
)! GRAPH ( .;Y .K .;X #B4
,SOLU;N
.,,/EP .#A .,MAKE A TA# ( VALUES = .;Y
.K #B .;X #B @4
,,SKET* ,A ,,GRAPH
,*OOSE VALUES ( .;X ON .BO? SIDES (!
AXIS ( SYMMETRY .;X .K #J4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 --#B3 --#A3 #J3 #A3 #B
.;Y @3 #H3 #B3 #J3 #B3 #H
.,,/EP#B .,PLOT ! PO9TS F ! TA#4
.,,/EP#C .,DRAW A SMOO? CURVE "? !
PO9TS4
.,,/EP .#D .,-P>E ! GRAPHS ( .;Y .K
.#B;X #B & .;Y .K .;X #B4 ,BO? OP5 UP &
H ! SAME V]TEX & AXIS ( SYMMETRY4 ,!
GRAPH ( .;Y .K #B;X #B IS N>R[] ?AN !
GRAPH ( .;Y .K .;X #B4
------------------------------------#BCG
,EXAMPLE #B ,GRAPH A FUNC;N (! =M .;Y
.K .AX #B @+ .;C
,GRAPH @4 ,-P>E ! GRAPH )! GRAPH ( .;Y
.K .;X #B
,SOLU;N
.,,/EP .#A ,MAKE A TA# ( VALUES = @4
,,SKET* ,A ,,GRAPH
,*OOSE VALUES ( .;X T >E MULTIPLES (
#B S T ! VALUES ( .;Y W 2 9TEG]S4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X @3 --#D3 --#B3 #J3 #B3 #D
.;Y @3 --#E3 #A3 #C3 #A3 --#E
.,,/EP .#B .,PLOT ! PO9TS F ! TA#
.,,/EP .#C .,DRAW A SMOO? CURVE "? !
PO9TS4
.,,/EP .#D .,-P>E ! GRAPHS ( & .;Y .K
.;X #B @4 ,BO? GRAPHS H ! SAME AXIS (
SYMMETRY4 ,H["E1 ! GRAPH ( OP5S D[N & IS
WID] ?AN ! GRAPH ( .;Y .K .;X #B4 ,AL1
XS V]TEX IS #C UNITS HI<]4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #A &
.#B
,GRAPH ! FUNC;N4 ,-P>E ! GRAPH )!
GRAPH ( .;Y .K .;X #B @4
.#A4 .;Y .K --#D .;X #B
.#B4 .;Y .K -- .;X #B -- #E
.#C4
..,,GRAPH+ ,,ANY ,,QUADRATIC .,,FUNC;N
,Y C USE ! FOLL[+ PROP]TIES 6GRAPH .ANY
QUADRATIC FUNC;N .;Y .K .AX #B @+ .BX @+
.;C @1 9CLUD+ A FUNC;N ": .;B @6.K #J4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,PROP]TIES (! ,GRAPH ( .;Y .K .AX #B
@+ .BX @+ ;C
.;Y .K .AX #B @+ .BX @+ .;C1 .A .1 #J
;Y .K .AX #B @+ .BX @+ .;C1 .A "K #J
,"*I/ICS (! GRAPH ( .;Y .K .AX #B @+
.BX @+ .;C @3
99 ,! GRAPH OP5S UP IF .A .1 #J & OP5S
D[N IF .A "K #J4
99 ,! GRAPH IS N>R[] ?AN ! GRAPH ( .;Y
.K .;X #B IF _\ .A _\ .1 #A & WID] IF _\
.A _\ "K .#A @4
99 ,! AXIS ( SYMMETRY IS &! V]TEX HAS
;X-COORD9ATE @4
99 ,! ;Y-9T]CEPT IS .,C4 ,S1 ! PO9T
7#J1 ;C7 IS ON ! P>ABOLA4
------------------------------------#BCH
,,EXAMPLE #C ,GRAPH A FUNC;N (! =M .;Y
.K .AX #B @+ .BX @+ .;C
,GRAPH .;Y .K #B .;X #B -- #H .;X @+
#F4
,SOLU;N
.,,/EP .#A .,ID5TIFY ! COE6ICI5TS (!
FUNC;N4 ,! COE6ICI5TS >E ..A .K #B1 .;B
.K --#H1 & .;C .K .#F4 ,2C .A .1 #J1 !
P>ABOLA OP5S UP4
.,,/EP .#B .,F9D ! V]TEX4 ,CALCULATE !
.;X -COORD9ATE4
,,AVOID ,,]RORS
,2 SURE 69CLUDE ! NEGATIVE SIGN 2F !
FRAC;N :5 CALCULAT+ ! ;X-COORD9ATE (!
V]TEX4
,!N F9D ! ;Y-COORD9ATE (! V]TEX4
;Y .K #B7 .#B @7 #B --#H7 .#B @7 @+
#F.K --#B
,S1 ! V]TEX IS 7#B1 --#B74 ,PLOT ?
PO9T4
.,,/EP .#C .,DRAW ! AXIS ( SYMMETRY
.;X .K .#B4
.,,/EP .#D .,ID5TIFY ! ;Y-9T]CEPT ;C1
: IS .#F4 ,PLOT ! PO9T 7#J1 #F74 ,!N
REFLECT ? PO9T 9 ! AXIS ( SYMMETRY 6PLOT
ANO!R PO9T1 7#D1 #F74
.,,/EP .#E .,EVALUATE ! FUNC;N = ANO!R
VALUE ( .;X @1 S* Z .;X .K .#A @4
.;Y .K #B7#A7 #B -- #H7#A7 @+ #F .K #J
,PLOT ! PO9T 7#A1 #J7 & XS REFLEC;N
7#C1 #J7 9 ! AXIS ( SYMMETRY4
.,,/EP .#F .,DRAW A P>ABOLA "? !
PLOTT$ PO9TS4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,GUID$ ,PRACTICE = ,EXAMPLE .#C
,GRAPH ! FUNC;N4 ,LABEL ! V]TEX & AXIS
( SYMMETRY4
#D4 .;Y .K .;X #B -- ..#B;X--.#A
#E4 .;Y .K .#B;X #B @+ ..#F;X @+ .#C
.#F4
,,KEY ,,3CEPT .= .,YR .,NOTEBOOK
,M9IMUM & ,MAXIMUM ,VALUES
.,^WS ,= .;Y--.AX #B @+ ..BX @+ .;C @1
! V]TEX'S ;Y-COORD9ATE IS ! .M9IMUM
.VALUE (! FUNC;N IF .A .1 #J &! .MAXIMUM
.VALUE IF .A "K .#J4
,GRAPHS
------------------------------------#BCI
..,,EXAMPLE #D ,F9D ! M9IMUM OR
MAXIMUM .VALUE
,TELL :E!R ! FUNC;N .;Y .K #C .;X #B
-- #AH .;X @+ #BJ HAS A .M9IMUM .VALUE
OR A .MAXIMUM .VALUE4 ,!N F9D ! M9IMUM
OR MAXIMUM VALUE4
,SOLU;N
,2C .A .1 #J1 ! FUNC;N HAS A M9IMUM
VALUE4 ,6F9D X1 CALCULATE ! COORD9ATES
(! V]TEX4
;Y .K #C7 .#C @7 #B -- #AH7 .#C @7
@+#BJ.K --#G
99 ,! M9IMUM VALUE IS .;Y .K -- .#G4
,Y C *ECK ! ANSW] ON A GRAPH+
CALCULATOR4
,,EXAMPLE #E ,SOLVE A MULTI-/EP PRO#M
.,,G-.,,C>TS ,A G-C>T TRACK HAS AB
#CHJ RAC]S P] WEEK & *>GES EA* RAC] 4#CE
6RACE4 ,! [N] E/IMATES T "! W 2 #BJ M
RAC]S P] WEEK = E 4#A REDUC;N 9 ! PRICE
P] RAC]4 ,H[ C ! [N] (! G-C>T TRACK
MAXIMIZE WEEKLY REV5UE8
,SOLU;N
.,,/EP .#A .,DEF9E ! V>IA#S4 ,LET .;X
REPRES5T ! PRICE REDUC;N & .;,R7.;X7
REPRES5T ! WEEKLY REV5UE4
.,,/EP .#B .,WRITE A V]BAL MODEL4 ,!N
WRITE & SIMPLIFY A QUADRATIC FUNC;N4
,,9T]PRET ,,FUNC;NS
,NOTICE T .A .K --#BJ "K#J1 S ! REV5UE
FUNC;N HAS A MAXIMUM VALUE4
.,,/EP .#C .,F9D ! COORD9ATES 7;X1
.;,R7.;X77 (! V]TEX4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
@3 .,F9D .;X-.COORD9AT,E4
;,R7 .#H @7 .K --#BJ7 .#H @7 #B @+
#CBJ7 .#H @7 @+ #AC1CJJ .K #AD1EHJ @3
.,EVALUATE .;,R7.#H74
,! V]TEX IS 7#H1 #AD1EHJ71 : M1NS !
[N] %D REDUCE ! PRICE P] RAC] BY 4#H
69CR1SE ! WEEKLY REV5UE TO 4#AD1EHJ4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #D &
.#E
.#G4 ,F9D ! M9IMUM VALUE ( .;Y .K #D
.;X #B @+ #AF .;X -- #C4
.#H4 .,,:AT .,,IF8 ,9 ,EXAMPLE #E1
SUPPOSE EA* 4#A REDUC;N 9 ! PRICE P]
RAC] BR+S 9 #DJ M RAC]S P] WEEK4 ,H[ C
WEEKLY REV5UE 2 MAXIMIZ$8
------------------------------------#BDJ
#D.A ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS .ON .P4
,,WS#G = ,EXS4 .#AE1 .#CG @1 & .#EG
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
..,EXS4 #B1 #CI1DJ1DC1 #EC1 .#EH @1 &
.#FJ
.K .,,MULTIPLE .,,REPRES5T,NS
,EX#.EI
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,!
GRAPH (A QUADRATIC FUNC;N IS CALL$ A7;N7
@8 @4
.#B4 .,,WRIT+ .,DESCRIBE H[ 6DET]M9E
:E!R A QUADRATIC FUNC;N HAS A M9IMUM
VALUE OR A MAXIMUM VALUE4
,,EXAMPLE #A
ON P4 #BCF = ,EXS4 #C-AB
.,,US+ .,A .,,TA# ,COPY & -PLETE ! TA#
( VALUES =! FUNC;N4
.#C4 .;Y .K #D .;X #B
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 --#B3 --#A3 #J3 #A3 #B
.;Y @3 @8@3 @8@3 @8@3 @8@3 @8
.#D4 .;Y .K --#C .;X #B
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 --#B3 --#A3 #J3 #A3 #B
.;Y @3 @8@3 @8@3 @8@3 @8@3 @8
.#E4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 --#D3 --#B3 #J3 #B3 #D
.;Y @3 @8@3 @8@3 @8@3 @8@3 @8
.#F4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 --#F3 --#C3 #J3 #C3 #F
.;Y @3 @8@3 @8@3 @8@3 @8@3 @8
.,,MAK+ .,A .,,GRAPH ,GRAPH ! FUNC;N4
.,-P>E ! GRAPH )! GRAPH ( .;Y .K .;X #B
@4
.#G4 .;Y .K #C .;X #B
.#H4 .;Y .K #E .;X #B
.#I4 .;Y .K --#B .;X #B
.#AJ4 .;Y .K -- .;X #B
.#AA4
.#AB4
.#AC4 .;Y .K #E .;X #B @+ #A
.#AD4 .;Y .K #D .;X #B @+ #A
.#AE4 .;F @7 .;X @7 .K -- .;X #B @+ #B
.#AF4 ;G7;X7 .K --#B .;X #B -- #E
.#AG4
.#AH4
,,EXAMPLE #B
ON P4 #BCG = ,EXS4 #AC-AH
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 ANALYZ+ ! GRAPH ( .;Y .K #D .;X
#B @+ #BD .;X -- #G4
.#AI4
.#BJ4
.,,EXAMPLE .#C ON P4 #BCH = ,EXS4
#BA-CB
,,MAK+ ,A ,,GRAPH ,GRAPH ! FUNC;N4
,LABEL ! V]TEX & AXIS ( SYMMETRY4
.#BA4 .;Y .K .;X #B @+ #B .;X @+ #A
.#BB4 .;Y .K #C .;X #B -- #F .;X @+ #D
#BC4 .;Y .K --#D .;X #B @+ #H .;X @+
#B
.#BD4 .;Y .K --#B .;X #B -- #F .;X @+
#C
.#BE4 ;G7 .;X @7 .K -- .;X #B -- #B
.;X -- #A
.#BF4 @7 .;X @7 .K --#F .;X #B -- #D
.;X -- #E
.#BG4
.#BH4
.#BI4
.#CJ4
.#CA4
.#CB4
------------------------------------#BDA
.,,EXAMPLE .#D ON P4 #BCI = ,EXS4
#CC-CH
.,,M9#A;,,MUMS .,,OR .,,MAXIMUMS ,TELL
:E!R ! FUNC;N HAS A .M9IMUM .VALUE OR A
.MAXIMUM .VALUE @4 ,!N F9D ! M9IMUM OR
MAXIMUM VALUE4
.#CC4 .;Y .K --#F;X #B - #A
.#CD4 .;Y .K #I;X #B @+ #G
.#CE4 .;F7.;X7 .K .#B;X #B @+ #H;X @+
#G
.#CF4 .;G7.;X7 .K --#C;X #B @+
#AH;X--#E
.#CG4
.#CH4
.#CI4 .,,MULTIPLE .,,*OICE ,:AT IS !
E6ECT ON ! GRAPH (! FUNC;N .;Y .K .;X #B
@+ #B :5 X IS *ANG$ 6.;Y .K .;X #B --
#C8
,A ,! GRAPH WID5S4
;,B ,! GRAPH N>R[S4
;,C ,! GRAPH OP5S D[N4
;,D ,! V]TEX MOVES D[N ! ;Y-AXIS4
.#DJ4 ,,MULTIPLE ,,*OICE ,: FUNC;N HAS
! WIDE/ GRAPH8
,A .;Y .K #B .;X #B
;,B .;Y .K .;X #B
;,C .;Y .K #J.E .;X #B
;,D .;Y .K -- .;X #B
.,,ID5TIFY+ .,,COE6ICI5TS ,9 ,EX]CISES
#DA & #DB1 ID5TIFY ! VALUES ( .A1 .;B @1
& ;C =! QUADRATIC FUNC;N4
.#DA4 ,! PA? (A BASKETBALL ?R[N AT AN
ANGLE ( #DE;DG C 2 MODEL$ 0.;Y .K
--#J.JB .;X #B @+ .;X @+ .#F4
.#DB4 ,! PA? (A %OT PUT REL1S$ AT AN
ANGLE ( #CE;DG C 2 MODEL$ 0.;Y .K
--#J.JA .;X #B @+ #J.G .;X @+ #F4
.#DC4 .,,OP5-.,,5D$ .,,MA? ,WRITE ?REE
DI6]5T QUADRATIC FUNC;NS ^: GRAPHS H !
L9E .;X .K #D Z AN AXIS ( SYMMETRY B H
DI6]5T ;Y-9T]CEPTS4
.,,MAT*+ ,9 ,EX]CISES #DD-DF1 MAT* !
EQU,N ) XS GRAPH4
.#DD4 .;Y .K #J.E .;X #B -- .#B;X
.,A4
.#DE4 .;Y .K #J.E .;X #B @+ #C
.,B4
.#DF4 .;Y .K #J.E .;X #B -- #B .;X @+
#C
.,C4
.,,MAK+ .,A .,,GRAPH ,GRAPH ! FUNC;N4
,LABEL ! V]TEX & AXIS ( SYMMETRY4
.#DG4 .;F @7 .;X @7 .K #J4.L .;X #B @+
#B
.#DH4 .;G7.;X7 .K --#J.E .;X #B -- #E
.#DI4 .;Y .K #J.C .;X #B @+ #C .;X --
#A
.#EJ4 .;Y .K #J.BE .;X #B -- #A.E .;X
@+ #C
.#EA4 .;F7.;X7 .K #D.B .;X #B @+ #F
.;X -- #A
.#EB4 .;G7.;X7 .K #A.GE .;X #B -- #B.E
.#EC4 .,,%ORT .,,RESPONSE ,! PO9TS
7#B1 #C7 & 7--#D1 #C7 LIE ON ! GRAPH (A
QUADRATIC FUNC;N4 .,EXPLA9 H[ ^! PO9TS C
2 US$ 6F9D AN EQU,N (! AXIS ( SYMMETRY4
,!N WRITE AN EQU,N (! AXIS ( SYMMETRY4
.#ED4 .,,*ALL5GE ,=! GRAPH ( .;Y .K
.AX #B @+ .BX @+ .;C @1 %[ T !
;Y-COORD9ATE (! V]TEX IS @4
------------------------------------#BDB
,,PRO#M ,,SOLV+
.,,EXAMPLE .#E ON P4 #BCI = ,EXS4
#EE-EH
.#EE4 .,,ONL9E .,,MUSIC ,AN ONL9E
MUSIC /ORE SELLS AB #DJJJ S;GS EA* "D :5
X *>GES 4#A P] S;G4 ,= EA* @4#.JE 9CR1SE
9 PRICE1 AB #HJ FEW] S;GS P] "D >E SOL
.,D4 ,USE ! V]BAL MODEL & QUADRATIC
FUNC;N 6F9D H[ ! /ORE C MAXIMIZE DAILY
REV5U,E4
@A .,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#EF4 .,,DIGITAL .,,CAM]AS ,AN
ELECTRONICS /ORE SELLS AB #GJ (A NEW
MODEL ( DIGITAL CAM]A P] MON? AT A PRICE
( 4#CBJ EA*4 ,= EA* 4#BJ DECR1SE 9
PRICE1 AB #E M CAM]AS P] MON? >E SOL
.,D4 ,WRITE A FUNC;N T MODELS ! SITU,N4
,!N TELL H[ ! /ORE C MAXIMIZE MON?LY
REV5UE F SALES (! CAM]A4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#EG .,,GOLD5 .,,GATE .,,BRIDGE ,EA*
CA# JO9+ ! TWO T[]S ON ! ,GOLD5 ,GATE
,BRIDGE C 2 MODEL$ 0! FUNC;N
": .;X & .;Y >E M1SUR$ 9 FEET4 ,:AT IS
! HEI<T .;H ABV ! ROAD (A CA# AT XS L[E/
PO9T8
.#EH4 .,,%ORT .,,RESPONSE ,A WOODL&
JUMP+ M\SE HOPS AL;G A P>ABOLIC PA? GIV5
0.;Y .K --#J.B;X #B @+ .#A4 #C;X ": .;X
IS ! M\SE'S HORIZONTAL POSI;N 7IN FEET7
& .;Y IS ! CORRESPOND+ HEI<T 7IN FEET74
,C ! M\SE JUMP OV] A F;E T IS #C FEET
HI<8 .,EXPLA94
#EI4 .,,MULTIPLE .,,REPRES5T,NS ,A
-MUN;Y !AT] SELLS AB #AEJ TICKETS 6A
PLAY EA* WEEK :5 X *>GES 4#BJ P] TICKET4
,= EA* 4#A DECR1SE 9 PRICE1 AB #AJ M
TICKETS P] WEEK >E SOL .,D4 ,! !AT] HAS
FIX$ EXP5SES ( 4#AEJJ P] WEEK4
A4 ,WRIT+ A ,MODEL ,WRITE A V]BAL
MODEL &A QUADRATIC FUNC;N 6REPRES5T !
!AT]'S WEEKLY PR(IT4
B4 ,MAK+ A ,TA# ,MAKE A TA# ( VALUES
=! QUADRATIC FUNC;N4
C4 ,DRAW+ A ,GRAPH ,USE ! TA# 6GRAPH !
QUADRATIC FUNC;N4 ,!N USE ! GRAPH 6F9D
H[ ! !AT] C MAXIMIZE WEEKLY PR(IT4
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
------------------------------------#BDC
#FJ4 .,,EXT5D$ .,,RESPONSE ,9 #AIGA1
A/RONAUT ,ALAN ,%EP>D HIT A GOLF BALL ON
! MOON4 ,! PA? (A GOLF BALL HIT AT AN
ANGLE ( #DE;DG &)A SPE$ ( #AJJ FEET P]
SECOND C 2 MODEL$ BY
": .;X IS ! BALL'S HORIZONTAL POSI;N
7IN FEET71 .;Y IS ! CORRESPOND+ HEI<T
7IN FEET71 & .;G IS ! A3EL],N DUE
6GRAV;Y 7IN FEET P] SECOND SQU>$74
A4 .,MODEL ,USE ! 9=M,N 9 ! DIAGRAM
6WRITE FUNC;NS =! PA?S (A GOLF BALL HIT
ON ,E>? &A GOLF BALL HIT ON ! MOON4
B4 .,GRAPH+ .,CALCULATOR ,GRAPH !
FUNC;NS F "P .,A ON A GRAPH+ CALCULATOR4
,H[ F> DOES ! GOLF BALL TRAVEL ON ,E>?8
ON ! MOON8
C4 .,9T]PRET .,-P>E ! 4T.ES TRAVEL$ 0A
GOLF BALL ON ,E>? & ON ! MOON4 ,YR ANSW]
%D 9CLUDE ! FOLL[+3
99 A CALCUL,N (! RATIO (! 4T.ES
TRAVEL$
99 A 4CUS.N ( H[ ! 4T.ES & VALUES ( ;G
>E RELAT$
,,GRAPH+ ,,CALCULATOR
,9 "P .;,B @1 USE ! CALCULATOR'S .Z]O
F1TURE 6ANSW] ! "QS4
.#FA4 .,,*ALL5GE ,LIFEGU>DS AT A B1*
WANT 6ROPE (F A RECTANGUL> SWIMM+ SEC;N4
,!Y H .;,P FEET ( ROPE ) BUOYS4 ,9 T]MS
( ;,P1 :AT IS ! MAXIMUM >EA T ! SWIMM+
SEC;N C H8
,,MIX$ ,,REVIEW
,,PREVIEW
PREP>E = ,LESSON #D.B 9 ,EXS4 #FH-GC4
,SOLVE ! EQU,N4 @7 P4 #AH @7
.#FB4 .;X -- #C .K #J
.#FC4 #C .;X @+ #D .K #J
.#FD4 --#I .;X @+ #G .K --#D .;X -- #E
.#FE4 #E .;X -- #B .K --#B .;X @+ #AB
.#FF4 #J.G .;X @+ #C .K #J.B .;X -- #B
.#FG4 #J.D .;X .K --#J.E .;X -- #E
,GRAPH ! FUNC;N4 @7 P4 #ABC @7
.#FH4 .;Y .K _\ .;X -- #E_\
.#FI4 .;Y .K --_\ .;X @+ #B_\
.#GJ4 .;Y .K #C_\ .;X -- #A
.#GA4 .;Y .K --#D_\ .;X @+ ;L_\
.#GB4 .;F @7 .;X @7 .K #B_\ .;X --
#C_\ @+ #F
.#GC4 .;G @7 .;X @7 .K --#E_\ .;X @+
#D_\--#A
.#GD4 ,,AV]AGE ,,SPE$ ,Y >E DRIV+ ON A
ROAD TRIP4 ,AT #I3JJ ,A4,M41 Y >E #CDJ
MILES WE/ ( ,NA%VILLE4 ,AT #B3JJ ,P4,M41
Y >E #GJ MILES WE/ ( ,NA%VILLE4 ,F9D YR
AV]AGE SPE$4 @7 P4 #HB @7
.,,EXTRA .,,PRACTICE = ,LESSON #D.A1
P#.AJAC
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#BDD
,GRAPH+ ,CALCULATOR ,ACTIV;Y3 #D.A
,F9D ,MAXIMUM & ,M9IMUM ,VALUES
,USE AF ,LESSON #D.G
,SIDEB>3
@A,HOME,TUTOR
CLASSZ"O4 COM
,KEY/ROKES
,SIDEB>3
,/&>DS
#AJ.J ,/UD5TS GRAPH QUADRATIC FUNC;NS
& DET]M9E ! MAXIMA1 M9IMA1 & Z]OS (!
FUNC;N4
,,"Q ,H[ C Y USE A GRAPH+ CALCULATOR
6F9D ! MAXIMUM OR M9IMUM VALUE (A
FUNC;N8
,,EXAMPLE ,F9D ! MAXIMUM VALUE (A
FUNC;N
,F9D ! MAXIMUM VALUE ( .;Y .K --#B .;X
-- #AJ .;X -- #E &! VALUE ( .;X ": X
O3URS4
,,/EP #A ,GRAPH FUNC;N
,GRAPH ! GIV5 FUNC;N & SELECT !
.MAXIMUM F1TURE4
,,/EP #B ,*OOSE LEFT B.D
,MOVE ! CURSOR 6! LEFT (! MAXIMUM
PO9T4 ,PRESS @4
,,/EP #C ,*OOSE "R B.D
,MOVE ! CURSOR 6! "R (! MAXIMUM PO9T4
,PRESS @4
,,/EP #D .F9D .MAXIMUM
,PUT ! CURSOR APPROXIMATELY ON !
MAXIMUM PO9T4 ,PRESS @4
99 ,! MAXIMUM VALUE (! FUNC;N IS .;Y
.K .#G4 #E & O3URS AT .;X .K -- .#B..E4
,,PRACTICE
,TELL :E!R ! FUNC;N HAS A .MAXIMUM
.VALUE OR A .M9IMUM .VALUE @4 ,!N F9D !
MAXIMUM OR M9IMUM VALUE &! VALUE ( .;X
": X O3URS4
.#A4 .;Y .K .;X #B -- #F .;X @+ #D
.#B4 .;F @7 .;X @7 .K .;X #B -- #C .;X
@+ #C
.#C4 .;Y .K --#C .;X #B @+ #I .;X @+
#B
.#D4 .;Y .K #J.E .;X #B @+ #J.H .;X --
#B
.#E4
.#F4
------------------------------------#BDE
#D.B ,GRAPH ,QUADRATIC ,FUNC;NS 9
,V]TEX OR ,9T]CEPT ,=M
.,2F ,Y GRAPH$ QUADRATIC FUNC;NS 9
/&>D =M4
.,N[ ,Y W GRAPH QUADRATIC FUNC;NS 9
V]TEX =M OR 9T]CEPT =M4
.,:Y8 ,S Y C F9D ! HEI<T (A JUMP1 Z 9
,EX4 #E .#A4
,KEY ,VOCABUL>Y
99 V]TEX =M
99 9T]CEPT =M
,SIDEB>3
,/&>DS
#I.J ,/UD5TS DEMON/RATE & EXPLA9 !
E6ECT T *ANG+ A COE6ICI5T HAS ON ! GRAPH
( QUADRATIC FUNC;NS2 T IS1 /UD5TS C
DET]M9E H[ ! GRAPH (A P>ABOLA *ANGES Z
A1 ;B1 & ;C V>Y 9 ! EQU,N .;Y .K .A @7
.;X -- .;B 7#B @+ .;C @4
,9 ,LESSON #D.A1 Y LE>N$ T ! /&>D =M
(A QUADRATIC FUNC;N IS .;Y .K .AX #B @+
..BX @+ .;C ": .A @+ #J4 ,ANO!R USE;L =M
(A QUADRATIC FUNC;N IS ! .V]TEX .=M @1
..;Y .K A7;X --.;H @7 #B @+ .K4
,,KEY ,,3CEPT
,= YR ,NOTEBOOK
..,GRAPH ( ,V]TEX ,=M .;Y .K .A7.;X --
.;H @7 #B @+ .;K
,! GRAPH ( .;Y .K .A @7 .;X -- .;H @7
#B @+ .;K IS ! P>ABOLA .;Y .K .AX #B
TRANSLAT$ HORIZONT,Y FT UNITS & V]TIC,Y
.;K UNITS4
,"*I/ICS (! GRAPH ( .;Y .K .A @7 .;X
-- .;H @7 #B @+ .;K @3
99 ,! V]TEX IS 7.;H1 .;K74
99 ,! AXIS ( SYMMETRY ..IS ;X .K .H4
99 ,! GRAPH OP5S UP IF .A .1 #J & D[N
IF .A "K #J4
..,,EXAMPLE #A ,GRAPH A .QUADRATIC
FUNC;N .9 .V]TEX .=M
.,GRAPH @4
,SOLU;N
.,,/EP .#A .,ID5TIFY ! 3/ANTS @1 .;H
.K --#B1 & .;K .K .#E4 ,2C .A "K #J1 !
P>ABOLA OP5S D[N4
.,,/EP#B .,PLOT ! V]TEX @7 .;H1 .;K7
.K 7--#B1 #E7 & DRAW ! AXIS ( SYMMETRY
.;X .K -- .#B4
.,,/EP .#C .,EVALUATE ! FUNC;N = TWO
VALUES ( .X4
,PLOT ! PO9TS 7#J1 #D7 & 7#B1 #A7 & _!
REFLEC;NS 9 ! AXIS ( SYMMETRY4
.,,/EP .#D .,DRAW A P>ABOLA "? !
PLOTT$ PO9TS4
------------------------------------#BDF
,,EXAMPLE #B ,USE A QUADRATIC MODEL 9
V]TEX =M
.,,CIVIL .,,5G9E]+ ,! ,TACOMA ,N>R[S
,BRIDGE 9 ,WA%+TON HAS TWO T[]S T EA*
RISE #CJG FEET ABV ! ROADWAY & >E 3NECT$
0SUSP5.N CA#S Z %[N4 ,EA* CA# C 2 MODEL$
0! FUNC;N
": .;X & .;Y >E M1SUR$ 9 FEET4 ,:AT IS
! 4T.E .;D 2T ! TWO T[]S8
,PICTURE3 ..,N DRAWN 6.SCALE
,SOLU;N
,! V]TEX (! P>ABOLA IS 7#ADJJ1 #BG74
,S1 A CA#'S L[E/ PO9T IS #ADJJ FEET F !
LEFT T[] %[N ABV4 ,2C ! HEI<TS (! TWO
T[]S >E ! SAME1 ! SYMMETRY (! P>ABOLA
IMPLIES T ! V]TEX IS AL #ADJJ FEET F !
"R T[]4 ,S1 ! 4T.E 2T ! TWO T[]S IS .;D
.K #B7#ADJJ7 .K #BHJJ FEET4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #A &
.#B
,GRAPH ! FUNC;N4 ,LABEL ! V]TEX & AXIS
( SYMMETRY4
.#A4 .;Y .K @7 .;X @+ #B7 #B -- #C
.#B4 .;Y .K --@7 .;X -- #A7 #B @+ #E
.#C4
.#D4 .,,:AT .,,IF8 ,SUPPOSE AN >*ITECT
DESIGNS A BRIDGE ) CA#S T C 2 MODEL$ 0":
.;X & .;Y >E M1SUR$ 9 FEET4 ,-P>E ?
FUNC;N'S GRAPH 6! GRAPH (! FUNC;N 9
,EXAMPLE .#B4
.,,9T]CEPT .,,=M ,IF ! GRAPH (A
QUADRATIC FUNC;N HAS AT L1/ "O
;X-9T]CEPT1 !N ! FUNC;N C 2 REPRES5T$ 9
9T]CEPT =M1 .;Y .K .A @7 .;X -- .;P @7@7
.;X -- .;Q @7@4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,GRAPH ( ,9T]CEPT ,=M ..;Y .K
A7;X--;P77;X--.;Q7
,"*I/ICS (! GRAPH ( .;Y .K .A @7 .;X
-- .;P @7@7 .;X -- .;Q @7@3
99 ,! ;X-9T]CEPTS >E .;P & .Q4
99 ,! AXIS ( SYMMETRY IS HALFWAY 2T @7
.;P @1 #J7 & @7 .;Q @1 #J74 ,X HAS EQU,N
99 ,! GRAPH OP5S UP IF .A .1 #J & OP5S
D[N IF .A "K #J4
------------------------------------#BDG
,,EXAMPLE #C ,GRAPH A QUADRATIC FUNC;N
9 9T]CEPT =M
,GRAPH .;Y .K #B7 .;X @+ #C7@7 .;X --
#A74
,,AVOID ,,]RORS
,REMEMB] T ! ;X-9T]CEPTS =A QUADRATIC
FUNC;N WRITT5 9 ! =M .;Y .K .A @7 .;X --
.;P @7@7 .;X -- .;Q @7 >E .;P & .;Q @1 N
-- .;P & -- .Q4
,SOLU;N
.,,/EP .#A .,ID5TIFY ! ;X-9T]CEPTS4
,2C .;P .K --#C & .;Q .K .#A @1 !
;X-9T]CEPTS O3UR AT ! PO9TS 7--#C1J7 &
7#A1J74
.,,/EP .#B .,F9D ! COORD9ATES (!
V]TEX4
.;Y .K #B7--#A @+ #C77--#A --#A7 .K
--#H
,S1 ! V]TEX IS 7--#A1 --#H74
.,,/EP .#C .,DRAW A P>ABOLA "? ! V]TEX
&! PO9TS ": ! ;X-9T]CEPTS O3UR4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
,,EXAMPLE #D ,USE A QUADRATIC FUNC;N 9
9T]CEPT =M
.,,FOOTBALL ,! PA? (A PLACEKICK$
FOOTBALL C 2 MODEL$ 0! FUNC;N .;Y .K
--#J.JBF;X7;X--#DF7 ": .;X IS !
HORIZONTAL 4T.E 7IN Y>DS7 & .;Y IS !
CORRESPOND+ HEI<T 7IN Y>DS74
.A4 ,H[ F> IS ! FOOTBALL KICK$8
.B4 ,:AT IS ! FOOTBALL'S MAXIMUM
HEI<T8
,SOLU;N
.A4 ,REWRITE ! FUNC;N Z .;Y .K
--#J.JBF @7 .;X -- #J7@7 .;X -- #DF74
,2C .;P .K #J & .;Q .K #DF1 Y "K ! .;X
-9T]CEPTS >E #J & #D .#F4 ,S1 Y C 3CLUDE
T ! FOOTBALL IS KICK$ A 4T.E ( #DF Y>DS4
.B4 ,6F9D ! FOOTBALL'S MAXIMUM HEI<T1
CALCULATE ! COORD9ATES (! V]TEX4
.;Y .K --#J.JBF7 .#BC @7@7 .#BC --
#DF7 #AC.H
,! MAXIMUM HEI<T IS ! ;Y-COORD9ATE (!
V]TEX1 OR AB .#AC4 #H Y>DS4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #C &
.#D
,GRAPH ! FUNC;N4 ,LABEL ! V]TEX1 AXIS
( SYMMETRY1 & .;X -9T]CEPTS4
#E4 .;Y .K @7 .;X -- #C7@7 .;X -- #G7
.#F4 .;F @7 .;X @7 .K #B7 .;X --#D7@7
.;X @+ #A7
.#G4 .;Y .K --@7 .;X @+ ;L7@7 .;X --
#E7
.#H4 .,,:AT .,,IF8 ,9 ,EXAMPLE #D1 :AT
IS ! MAXIMUM HEI<T (! FOOTBALL IF !
FOOTBALL'S PA? C 2 MODEL$ 0! FUNC;N .;Y
.K --#J.JBE .;X @7 .;X -- #EJ78
------------------------------------#BDH
.,,FOIL .,,ME?OD ,Y C *ANGE QUADRATIC
FUNC;NS F 9T]CEPT =M OR V]TEX =M 6/&>D
=M 0MULTIPLY+ ALGEBRAIC EXPRES.NS4 ,"O
ME?OD = MULTIPLY+ TWO EXPRES.NS EA*
3TA9+ TWO T]MS IS .,,FOIL4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,,FOIL ,ME?OD
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,^WS @3 ,6MULTIPLY TWO EXPRES.NS T
EA* 3TA9 TWO T]MS1 ADD ! PRODUCTS (! ,F/
T]MS1 ! ,\T] T]MS1 ! ,9N] T]MS1 &! ,LA/
T]MS4
.,EXAMPLE @3
,,EXAMPLE #E ,*ANGE F 9T]CEPT =M 6/&>D
=M
,,REVIEW ,,FOIL
,= HELP ) US+ ! ,,FOIL ME?OD1 SEE P4
#IHE @4
,WRITE .;Y .K --#B7 .;X @+ #E7@7 .;X
-- #H7 9 /&>D =M4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;Y .K --#B @7 .;X @+ #E7 @7 .;X --
#H7 @3 ,WRITE ORIG9AL FUNC;N4
.K --#B7 .;X #B -- #H .;X @+ #E .;X --
#DJ7 @3 ,MULTIPLY US+ ,,FOIL4
.K --#B7 .;X #B -- #C .;X -- #DJ7 @3
,-B9E L T]MS4
.K --#B .;X #B @+ #F .;X @+ #HJ @3
,4TRIBUTIVE PROP]TY
,,EXAMPLE #F ,*ANGE F V]TEX =M 6/&>D
=M
,WRITE .;F @7 .;X @7 .K #D7 .;X -- #A7
#B @+ #I 9 /&>D =M4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;F @7 .;X @7 .K #D7 .;X --#A7 #B @+
#I @3 ,WRITE ORIG9AL FUNC;N4
.K #D7 .;X -- ;L7@7 .;X -- #A7 @+ #I
@3 ,REWRITE @7 .;X -- #A7 #B @4
.K #D7 .;X #B -- .;X -- .;X @+ #A7 @+
#I @3 ,MULTIPLY US+ ,,FOIL4
.K #D7 .;X #B -- #B .;X @+ #A7 @+ #I
@3 ,-B9E L T]MS4
.K #D .;X #B -- #H .;X @+ #D @+ #I @3
,4TRIBUTIVE PROP]TY
.K #D .;X #B -- #H .;X @+ #AC @3 ,-B9E
L T]MS4
..,GUID$ ,PRACTICE = ,EXAMPLES #E &
.#F
,WRITE ! QUADRATIC FUNC;N 9 /&>D =M4
.#I4 .;Y .K --@7 .;X --#B7@7 .;X --#G7
.#AJ4 .;Y .K --#D7 .;X -- ;L7@7 .;X @+
#C7
.#AA4 .;F @7 .;X7 @7 .K #B7 .;X @+
#E7@7 .;X @+ #D7
.#AB4 .;Y .K --#G7 .;X --#F7@7 .;X @+
#A7
.#AC4 .;Y .K --#C7 .;X @+ #E7 #B -- #A
.#AD4 .;G @7 .;X @7 .K #F7 .;X -- #D7
#B -- #AJ
.#AE4 .;F @7 .;X @7 .K --@7 .;X @+ #B7
#B @+ #D
.#AF4 .;Y .K #B7 .;X --#C7 #B @+ #I
------------------------------------#BDI
#D.B ,EX]CISES
,,HOME"W ,,KEY
.K .,,"W$-.,,\ .,,SOLU;NS .ON .P4
,,WS#H = ,EXS4 .#AI1.BI @1 & .#EC
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 .#B1.AB1.BB1.DI1.ED @1 & .#EE
,,SKILL ,,PRACTICE
.#A4 ,,VOCABUL>Y ,COPY & -PLETE3 ,A
QUADRATIC FUNC;N 9 ! =M .;Y .K .A @7 .;X
-- .;H @7 #B @+ .;K @3 IS 9 @8 =M4
.#B4 ,,WRIT+ .,EXPLA9 H[ 6F9D A
QUADRATIC FUNC;N'S MAXIMUM VALUE OR
M9IMUM VALUE :5 ! FUNC;N IS GIV5 9
9T]CEPT =M4
,,EXAMPLE #A
ON P4 #BDE = ,EXS4 #C-AB
..,,GRAPH+ ,,) ,,V]TEX .,,=M ,GRAPH !
FUNC;N4 ,LABEL ! V]TEX & AXIS (
SYMMETRY4
.#C4 .;Y .K @7 .;X -- #C7 #B
.#D4 .;Y .K @7 .;X @+ #D7 #B
.#E4 .;F @7 .;X @7 .K --@7 .;X @+ #C7
#B @+ #E
.#F4 .;Y .K #C7 .;X --#G7 #B -- #A
.#G4 .;G @7 .;X @7 .K --#D7 .;X --#B7
#B @+ #D
.#H4 .;Y .K #B7 .;X @+ #A7 #B -- #C
.#I4 .;F @7 .;X @7 .K --#B7 .;X -- #A7
#B --#E
.#AJ4
.#AA4
#AB4 ,,MULTIPLE ,,*OICE ,:AT IS !
V]TEX (! GRAPH (! FUNC;N .;Y .K #C7 .;X
@+ #B7 #B -- #E8
,A 7#B1 --#E7
;,B 7--#B1-#E7
;C 7--#E1B7
;,D 7#E1--#B7
,,EXAMPLE #C
ON P4 #BDG = ,EXS4 #AC-BC
..,,GRAPH+ ,,) ,,9T]CEPT .,,=M ,GRAPH
! FUNC;N4 ,LABEL ! V]TEX1 AXIS (
SYMMETRY1 & .;X -9T]CEPTS4
.#AC4 .;Y .K @7 .;X @+ #C7@7 .;X --
#C7
.#AD4 .;Y .K @7 .;X @+ ;L7@7 .;X --
#C7
.#AE4 .;Y .K #C7 .;X @+ #B7@7 .;X @+
#F7
.#AF4 .;F @7 .;X @7 .K#B7 .;X --#E7@7
.;X -- #A7
.#AG4 .;Y .K --@7 .;X -- .#D7@7 .;X @+
#F7
.#AH4 .;G @7 .;X @7 .K --#D7 .;X @+
#C7@7 .;X @+ #G7
.#AI .;Y .K @7 .;X @+ ;L7@7 .;X @+ #B7
.#BJ4 .;F @7 .;X @7 .K --#B7 .;X
--#C7@7 .;X @+ #D7
.#BA4 .;Y .K #D7 .;X -- #G7@7 .;X @+
#B7
#BB4 .,,MULTIPLE .,,*OICE ,:AT IS !
V]TEX (! GRAPH (! FUNC;N .;Y .K --@7 .;X
--#F7@7 .;X @+ #D78
,A 7#A1BE7
;,B 7--#A1BA7
;,C 7--#F1D7
;,D 7#F1--#D7
#BC4 .,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 ANALYZ+ ! GRAPH (!
FUNC;N .;Y .K #E7 .;X -- #B7@7 .;X @+
#C74
,,EXAMPLES #E & #F
ON P4 #BDH = ,EXS4 #BD-CB
,,WRIT+ ,,9 ,,/&>D ,,=M ,WRITE !
QUADRATIC FUNC;N 9 /&>D =M4
.#BD4 .;Y .K @7 .;X @+ #D7@7 .;X @+
#C7
.#BE4 .;Y .K .;X -- #E7@7 .;X @+ #C7
.#BF4 .;H @7 .;X @7 .K #D7 .;X @+
;L7@7 .;X -- #F7
.#BG4 .;Y .K --#C7 .;X -- #B7@7 .;X
--#D7
.#BH4 .;F @7 .;X @7 .K @7 .;X @+ #E7
#B -- #B
.#BI .;Y .K @7 .;X -- #C7 #B @+ #F
.#CJ4 .;G @7 .;X @7 .K --@7 .;X @+ #F7
#B @+ #AJ
.#CA4 .;Y .K #E7 .;X @+ #C7 #B --#D
.#CB4 .;F @7 .;X @7 .K #AB7 .;X -- #A7
#B @+ #D
..,,M9IMUM ,,OR ,,MAXIMUM .,,VALUES
,F9D ! M9IMUM VALUE OR ! MAXIMUM VALUE
(! FUNC;N4
.#CC4 .;Y .K #C7 .;X -- #C7 #B -- #D
.#CD4 .;G @7 .;X @7 .K --#D7 .;X @+
#F7 #B -- #AB
.#CE4 .;Y .K #AE7 .;X -- #BE7 #B @+
#ACJ
.#CF4 .;F @7 .;X @7 .K#C7 .;X @+
#AJ7@7 .;X --#H7
.#CG4 .;Y .K --@7 .;X --#CF7@7 .;X @+
#AH7
.#CH4 .;Y .K --#AB;X7 .;X -- #I7
.#CI4 .;Y .K #H;X7 .;X @+ #AE7
.#DJ4 .;Y .K #B7 .;X -- #C7@7 .;X --
#F7
.#DA4 .;G @7 .;X @7 .K --#E7 .;X @+
#I7@7 .;X -- #D7
------------------------------------#BEJ
#DB4 .,,GRAPH+ .,,CALCULATOR ,3SID] !
FUNC;N .;Y .K .A @7 .;X -- .;H @7 #B @+
.;K ": .A -- #A1 .;H .K #C1 & .;K
.K--#B4 ,PREDICT ! E6ECT ( EA* *ANGE 9
.A1 .;H @1 OR .;K DESCRIB$ 9 "PS
7A7--7;C74 ,USE A GRAPH+ CALCULATOR
6*ECK YR PREDIC;N 0GRAPH+ ! ORIG9AL &
REVIS$ FUNC;NS 9 ! SAME COORD9ATE PLANE4
A4 .A *ANGES TO --#C
B4 .;H *ANGES TO --#A
C4 .;K *ANGES 6#B
,,MAK+ ,A ,,GRAPH ,GRAPH ! FUNC;N4
,LABEL ! V]TEX & AXIS ( SYMMETRY4
.#DC4 .;Y .K #E7 .;X -- #B.BE7 #B --
#B.GE
.#DD4 .;G @7 .;X @7 .K --#H7 .;,X @+
.#C4 #B7 #B @+ #F.D
.#DE4 .;Y .K --#J.BE7 .;X -- .#E4 #B7
#B @+ #H.E
.#DF4
.#DG4
.#DH4
.#DI4 .,,OP5-.,,5D$ .,,MA? ,WRITE TWO
DI6]5T QUADRATIC FUNC;NS 9 9T]CEPT =M ^:
GRAPHS H AXIS ( SYMMETRY .;X .K .#C4
.#EJ4 .,,*ALL5GE ,WRITE .;Y .K .A @7
.;X -- .;H @7 #B @+ .;K & .;Y .K .A @7
.;X -- .;P @7@7 .;X -- .;Q @7 9 /&>D =M4
,"K+ ! V]TEX (! GRAPH ( .;Y .K .AX #B @+
.BX @+ .;C O3URS AT @1 %[ T ! V]TEX (!
GRAPH ( .;Y .K .A @7 .;X -- .;H @7 #B @+
.;K O3URS AT .;X .K .;H & T ! V]TEX (!
GRAPH ( .;Y .K .A @7 .;X -- .;P @7@7 .;X
-- .;Q @7 O3URS AT @4
,,PRO#M ,,SOLV+
,,EXAMPLES #B & #D
ON PP4 #BDF-BDG = ,EXS4 #EA-ED
.#EA4 .,,BIOLOGY ,! FUNC;N .;Y .K
--#J.JC @7 .;X -- #AD7 #B @+ #F MODELS !
JUMP (A R$ KANG>OO ": .;X IS !
HORIZONTAL 4T.E 7IN FEET7 & .;Y IS !
CORRESPOND+ HEI<T 7IN FEET74 ,:AT IS !
KANG>OO'S MAXIMUM HEI<T8 ,H[ L;G IS !
KANG>OO'S JUMP8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#EB4 .,,CIVIL .,,5G9E]+ ,! >* (!
,GATESH1D ,MILL5NIUM ,BRIDGE =MS A
P>ABOLA ) EQU,N ;Y .K --#J.JAF7 .;X --
#E .#B4 #E7 #B @+ #DE ": .;X IS !
HORIZONTAL 4T.E 7IN MET]S7 F ! >*'S LEFT
5D & .;Y IS ! 4T.E 7IN MET]S7 F ! BASE
(! >*4 ,:AT IS ! WID? (! >*8
@A.,HOTNE,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#EC4 .,,MULTI-.,,/EP .,,PRO#M ,AL? A
FOOTBALL FIELD APPE>S 6BE FLAT1 XS
SURFACE IS ACTU,Y %AP$ L A P>ABOLA S T
RA9 RUNS (F 6BO? SIDES4 ,! CROSS SEC;N
(A FIELD ) SYN!TIC TURF C 2 MODEL$ 0.;Y
.K --#J.JJJBCD .;X @7 .;X -- #AFJ7
": .;X & .;Y >E M1SUR$ 9 FEET4
A4 ,:AT IS ! FIELD'S WID?8
B4 ,:AT IS ! MAXIMUM HEI<T (! FIELD'S
SURFACE8
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#BEA
.#ED4 .,,%ORT .,,RESPONSE ,A JUMP ON A
POGO /ICK )A 3V5;NAL SPR+ C 2 MODEL$
0.;Y .K --#J.E7 .;X -- #F7 #B @+ #AH1 &A
JUMP ON A POGO /ICK )A B[ SPR+ C 2
MODEL$ 0.;Y .K -- .#A4 #AG7 .;X -- #F7
#B @+ #DB1 ": .;X & .;Y >E M1SUR$ 9
9*ES4 .,-P>E ! MAXIMUM HEI<TS (! JUMPS
ON ! TWO POGO /ICKS4 ,: 3/ANTS 9 !
FUNC;NS A6ECT ! MAXIMUM HEI<TS (! JUMPS8
,: D N8
#EE4 .,,EXT5D$ .,,RESPONSE ,A K]NEL (
POPCORN 3TA9S WAT] T EXP&S :5 ! K]NEL IS
H1T$1 CAUS+ X 6POP4 ,! EQU,NS 2L GIVE !
8POPP+ VOLUME0 .;Y 7IN CUBIC C5TIMET]S
P] GRAM7 ( POPCORN ) MOI/URE 3T5T .;X 7Z
A P]C5T (! POPCORN'S WEI<T74
.,HOT-.AIR .POPP+3 .;Y .K --#J.GFA @7
.;X -- #E.EB7 @7 .;X -- #BB.F7
.,HOT-.OIL .POPP+3 .;Y .K --#J.FEB @7
.;X -- #E.CE7 @7 .;X -- #BA.H7
A4 .,9T]PRET ,= HOT-AIR POPP+1 :AT
MOI/URE 3T5T MAXIMIZES POPP+ VOLUME8
,:AT IS ! MAXIMUM VOLUME8
B4 .,9T]PRET ,= HOT-OIL POPP+1 :AT
MOI/URE 3T5T MAXIMIZES POPP+ VOLUME8
,:AT IS ! MAXIMUM VOLUME8
C4 .,GRAPH+ .,CALCULATOR ,GRAPH !
FUNC;NS 9 ! SAME COORD9ATE PLAN .,E4
,:AT >E ! DOMA9 & RANGE ( EA* FUNC;N 9 ?
SITU,N8 .,EXPLA9 H[ Y DET]M9$ ! DOMA9 &
RANGE4
#EF4 .,,*ALL5GE ,FLY+ FI% USE _!
PECTORAL F9S L AIRPLANE W+S 6GLIDE "? !
AIR4 ,SUPPOSE A FLY+ FI% R1*ES A MAXIMUM
HEI<T ( #E FEET AF FLY+ A HORIZONTAL
4T.E ( #CC FEET4 ,WRITE A QUADRATIC
FUNC;N .;Y .K .A @7 .;X -- .;H @7 #B @+
.;K T MODELS ! FLI<T PA?1 ASSUM+ ! FI%
L1VES ! WAT] AT 7#J1 #J74 .,DESCRIBE H[
*ANG+ ! VALUE ( .A1 .;H @1 OR .;K A6ECTS
! FLI<T PA?4
,,MIX$ ,,REVIEW
,,PREVIEW
,PREP>E = ,LESSON #D.C 9 ,EXS4 #EG-FD4
,SOLVE ! EQU,N4
.#EG4 .;X -- #E .K #J @7 P4 #AH @7
.#EI4 #BC .;X -- #AD .K --#E .;X -- #G
@7 P4 #AH @7
.#FJ4 --#E7#C .;X @+ #D7 .K #AG .;X @+
#B @7 P4 #AH @7
.#FA4 _\ .;X -- #I_\ .K #AF7 P4 #EA @7
.#FB4 #D .;X @+ #I .K #BG @7 P4 #EA @7
.#FC4 _\#G --#B .;X _\ .K #A @7 P4 #EG
@7
.#FD4 _\#C--#E .;X _\ .K #G @7 P4 #EA
@7
,USE ! GIV5 MATRICES 6P]=M ! 9DICAT$
OP],N1 IF POSSI#4 ,IF N POSSI#1 /ATE !
R1SON4
.#FE4 #B .,A @+ .;,B @7 P4 #AHG @7
.#FF4 #C @7 .;,B @+ .;,C @7 @7 P4 #AHG
@7
.#FG4 .;,D -- #D .;,E @7 P4 #AHG @7
.#FH4 .;,,AB @7 P4 #AIE @7
.#FI4 .,A @7 .;,B -- .;,C @7 @7 P4
#AIE @7
.#GJ4 #D7 .;,,CD @7 @7 P4 #AIE @7
.,,EXTRA .,,PRACTICE = ,LESSON #D.B1
P4 #AJAC
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#BEB
#D.C ,SOLVE ;X #B @+ BX @+ ;C .K #J
0,FACTOR+
.,2F ,Y GRAPH$ QUADRATIC FUNC;NS4
.,N[ ,Y W SOLVE QUADRATIC EQU,NS4
.,:Y8 ,S Y C D\# ! >EA (A PICNIC SITE1
Z 9 ,EX4 #DB4
,KEY ,VOCABUL>Y
99 MONOMIAL
99 BINOMIAL
99 TRINOMIAL
99 QUADRATIC EQU,N
99 ROOT ( AN EQU,N
99 Z]O (A FUNC;N
,A .MONOMIAL IS AN EXPRES.N T IS EI A
NUMB]1 A V>IA#1 OR ! PRODUCT (A NUMB] &
"O OR M V>IA#S4 ,A .BINOMIAL @1 S* Z .;X
@+ #D1 IS ! SUM ( TWO MONOMIALS4 ,A
.TRINOMIAL @1 S* Z .;X #B @+ #AA .;X @+
#BH1 IS ! SUM ( ?REE MONOMIALS4
,Y "K H[ 6USE ,,FOIL 6WRITE @7 .;X @+
#D7@7 .;X @+ #G7 Z .;X #B @+ #AA .;X @+
#B .#H4 ,Y C USE FACTOR+ 6WRITE A
TRINOMIAL Z A PRODUCT ( BINOMIALS4
,6FACTOR .;X #B @+ .BX @+ .;C @1 F9D
9TEG]S .;M & .;N S* T3
;X #B @+ .BX @+ .;C .K @7 .;X @+ .;M
@7 @7 .;X @+ .;N @7
.K .;X #B @+ @7 .;M @+ .;N @7 .;X @+
.MN
,S1 ! .SUM ( .;M & .;N M/ EQUAL .;B &!
.PRODUCT ( .;M & .;N M/ EQUAL .C4
,,EXAMPLE #A ,FACTOR TRINOMIALS (! =M
.;X #B @+ .BX @+ .;C
,FACTOR ! EXPRES.N4
.A4 .;X #B -- #I .;X @+ #BJ
.B4 .;X #B @+ #C .;X -- #AB
,SOLU;N
.A4 ,Y WANT .;X -- #I .;X @+ #BJ .K @7
.;X @+ ..;M7@7 ;X @+ .;N @7 ": .MN .K
#BJ & .;M @+ .;N .K --#I4
,,AVOID ,,]RORS
,:5 FACTOR+ .;X #B @+ .BX @+ .;C ": ;C
.1 #J1 Y M/ *OOSE FACTORS .;X @+ .;M &
.;X @+ .;N S* T ;M & .;N H ! SAME SIGN4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,FACTORS ( #BJ3 ;M1 .;N @3 #A1BJ3
--#A1--#BJ3 #B1AJ3 --#B1 --#AJ3 #D1E3
--.#D1--.#E
,SUM ( FACTORS3 .;M @+ .;N @3 #BA3
--#BA3 #AB3 --#AB3 #I3 --.#I
99 ,NOTICE T .;M .K --#D & .;N .K --
.#E4 ,S1 ;X #B -- #I .;X @+ #BJ .K @7
.;X -- #D7@7 .;X -- #E74
.B4 ,Y WANT .;X #B @+ #C .;X -- #AB .K
@7 .;X @+ .;M @7@7 .;X @+ .;N @7 ": .MN
.K --#AB & .;M @+ .;N .K #C4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,FACTORS ( --#AB3 .;M1 .;N @3 --#A1AB3
#A1--#AB3 --#B1F3 #B1--#F3 --#C1D3
#C1--#D
,SUM ( FACTORS3 .;M @+ .;N @3 #AA3
-#AA3 #D3 --#D3 #A3 --#A
99 ,NOTICE T "! >E NO FACTORS .;M &
.;N S* T .;M @+ .;N .K .#C4
,S1 .;X #B @+ #C .;X -- #AB _C 2
FACTOR$4
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#A
,FACTOR ! EXPRES.N4 ,IF ! EXPRES.N _C
2 FACTOR$1 SAY S4
.#A4 .;X #B -- #C .;X -- #AH
.#B4 .;N #B -- #C .;N @+ #I
.#C4 .;R #B @+ #B .;R -- #FC
------------------------------------#BEC
,SIDEB>3
,/&>DS
.#H..J .,/UD5TS .SOLVE & GRAPH
..QUADRATIC EQU,NS 0.FACTOR+ @1 -PLET+ !
SQU>E1 OR US+ ! QUADRATIC =MULA4
..,/UD5TS APPLY ^! TE*NIQUES 9 SOLV+ ^W
.PRO#MS4 ,!Y AL SOLVE QUADRATIC EQU,NS 9
! -PLEX NUMB] SY/EM4
.#AJ..J .,/UD5TS GRAPH QUADRATIC
FUNC;NS & .DET]M9E .! MAXIMA1 M9IMA1 &
..Z]OS (! .FUNC;N @4
.,,FACTOR+ .,,SPECIAL .,,PRODUCTS
,FACTOR+ QUADRATIC EXPRES.NS (T5 9VOLVES
TRIAL & ]ROR4 ,H["E1 "S EXPRES.NS >E
EASY 6FACTOR 2C !Y FOLL[ SPECIAL
PATT]NS4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,SPECIAL ,FACTOR+ ,PATT]NS
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,PATT]N ,"N3 ,PATT]N3 ,EXAMPLE
..,DI6];E ( ,TWO .,SQU>ES @3 .A #B --
.;B #B .K @7 .A @+ .;B @7@7 .A -- .;B @7
@3 .;X #B -- #D .K @7 .;X @+ #B7@7 .;X
-- #B7
.,P]FECT .,SQU>E .,TRINOMIAL @3 .A #B
@+ #B .;AB @+ .;B #B .K @7 .A @+ .;B @7
#B
.A #B -- #B .;AB @+ .;B #B .K @7 .A --
.;B @7 #B @3 .;X #B @+ #F .;X @+ #I .K
@7 .;X @+ #C7 #B
.;X #B -- #D .;X @+ #D .K @7 .;X -- #B7
#B
,,EXAMPLE #B ,FACTOR ) SPECIAL PATT]NS
,FACTOR ! EXPRES.N4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.A4 .;X #B -- #DI .K .;X #B -- #G #B
.K @7 .;X @+ #G7@7 .;X -- #G7 @3
..,DI6];E ( TWO .SQU>ES
.B4 .;D #B @+ #AB .;D @+ #CF .K .;D #B
@+ #B7 .;D @77#F7 @+ #F #B
.K @7 .;D @+ #F7 #B @3 .,P]FECT .SQU>E
.TRINOMIAL
.C4 .;Z #B -- #BF .;Z @+ #AFI .K .;Z
#B -- #B7 .;Z @77#AC7 @+ #AC #B
.K @7 .;Z -- #AC7 #B @3 .,P]FECT .SQU>E
.TRINOMIAL
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#B
,FACTOR ! EXPRES.N4
.#D4 .;X #B -- #I
.#E4 .;Q #B -- #AJJ
.#F4 .;Y #B @+ #AF .;Y @+ #FD
.#G4 .;W #B -- #AH .;W @+ #HA
.,,SOLV+ .,,QUADRATIC .,,EQU,NS ,Y C
USE FACTOR+ 6SOLVE C]TA9 .QUADRATIC
.EQU,NS4 .,A .QUADRATIC .EQU,N 9 "O
V>IA# C 2 WRITT5 9 ! =M .AX #B @+ .BX @+
.;C .K #J ": .A6.K .#J4 ,? IS CALL$ !
./&>D .=M (! EQU,N4 ,! SOLU;NS (A
QUADRATIC EQU,N >E CALL$ ! .ROOTS (!
EQU,N4 ,IF ! LEFT SIDE ( AX #B @+ .BX @+
.;C .K #J C 2 FACTOR$1 !N ! EQU,N C 2
SOLV$ US+ ! .Z]O .PRODUCT .PROP]TY4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,Z]O ,PRODUCT ,PROP]TY
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,^WS @3 ,IF ! PRODUCT ( TWO EXPRES.NS
IS Z]O1 !N "O OR BO? (! EXPRES.NS EQUAL
Z]O4
.,ALGEBRA @3 ,IF .,A & .;,B >E
EXPRES.NS & .;,,AB .K #J1 !N ,A .K #J OR
.;,B .K #J4
.,EXAMPLE @3 ,IF @7 .;X @+ #E7@7 .;X
@+ #B7 .K #J1 !N .;X @+ #E .K #J OR ;X
@+ #B .K #J4 ,T IS1 .;X .K --#E OR .;X
.K -- .#B4
------------------------------------#BED
..,,EXAMPLE #C ,/&>DIZ$ ,TE/
.,PRACTICE
,,"U/& ,,ANSW] ,,*OICES
,"S"TS A /&>DIZ$ TE/ "Q MAY ASK =!
.SOLU;N .SET ( AN EQU,N4 ,! ANSW] *OICES
W 2 GIV5 9 ! =MAT @7 .A1 .;B @7@4
,:AT >E ! ROOTS (! EQU,N .;X #B -- #E
.;X -- #CF .K #J8
.,A --#D1--#I
.;,B #D41--#I
.;,C --#D1I
.;,D #D1I
,SOLU;N
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X #B -- #E .;X -- #CF .K #J @3
.,WRITE .ORIG9AL .EQU,N4
@7 .;X -- #I7@7 .;X @+ #D7 .K#J @3
.,FACTOR4
.;X -- #I .K #J OR .;X @+ #D .K #J @3
.,Z]O .PRODUCT .PROP]TY
.;X .K #I OR .;X .K --#D @3 ,SOLVE =.'
X4.-
99 ,! CORRECT ANSW] IS ..,C4 ,A ;,B
;,C .;,D
,,EXAMPLE #D ,USE A QUADRATIC EQU,N Z
A MODEL
.,,NATURE .,,PRES]VE ,A T[N HAS A
NATURE PRES]VE )A RECTANGUL> FIELD T
M1SURES #FJJ MET]S 0#DJJ MET]S4 ,! T[N
WANTS 6D\# ! >EA (! FIELD 0A4+ L& Z %[N4
,F9D ! NEW DIM5.NS (! FIELD4
,SOLU;N
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#DHJ1JJJ .K #BDJ1JJJ @+ ;L#JJJ .;X @+
.;X #B @3 .,MULTIPLY .US+ .,,FOIL4
#J .K ;X.' #B @+ ;L#JJJ .;X --
#BDJ1JJJ @3 ..,WRITE 9 /&>D .=M4
#J .K @7 .;X -- #BJJ7 @7 .;X @+ #ABJJ7
@3 .,FACTOR4
.;X -- #BJJ .K #J OR .;X @+ #ABJJ .K
#J @3 .,Z]O .PRODUCT .PROP]TY
.;X .K #BJJ OR .;X .K-#ABJJ @3 ,SOLVE
=.' ;X @4
99 ,REJECT ! NEGATIVE VALUE1 --#ABJJ4
,! FIELD'S L5G? & WID? %D EA* 2 9CR1S$
0#BJJ MET]S4 ,! NEW DIM5.NS >E #HJJ
MET]S 0#FJJ MET]S4
..,GUID$ ,PRACTICE = ,EXAMPLES #C &
.#D
.#H4 ,SOLVE ! EQU,N .;X #B -- .;X --
#DB .K #J4
.#I4 .,,:AT .,,IF8 ,9 ,EXAMPLE #D1
SUPPOSE ! FIELD 9ITI,Y M1SURES #AJJJ
MET]S 0#CJJ MET]S4 ,F9D ! NEW DIM5.NS (!
FIELD4
..,,Z]OS ,,( ,A .,,FUNC;N ,9 ,LESSON
.#D4 #B1 Y LE>N$ T ! .;X -9T]CEPTS (!
GRAPH ( ..;Y .K A7 ;X--;P7@7 ;X--.;Q @7
>E .;P & .Q4 ,2C ! FUNC;N'S VALUE IS Z]O
:5 .;X .K .;P & :5 .;X .K .;Q @1 !
NUMB]S .;P & .;Q >E AL CALL$ .Z]OS (!
FUNC;N4
------------------------------------#BEE
..,EXAMPLE #E ,F9D ! Z]OS ( QUADRATIC
.FUNC;NS
,,"U/& ,,REPRES5T,NS
,IF A R1L NUMB] .;K IS A Z]O (! FUNC;N
.;Y .K .AX #B @+ .BX @+ ;C1 !N .;K IS AN
.;X -9T]CEPT ( ? FUNC;N'S GRAPH & .;K IS
AL A ROOT (! EQU,N .AX #B @+ .BX @+ ;C
.K #J4
,F9D ! Z]OS (! FUNC;N 0REWRIT+ !
FUNC;N 9 9T]CEPT =M4
.A4 .;Y .K .;X -- .;X -- #AB
.B4 .;Y .K .;X #B @+ #AB .;X @+ #CF
,SOLU;N
A4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;Y .K .;X #B -- .;X --#AB @3 .,WRITE
.ORIG9AL .FUNC;N @4
.K @7 .;X @+ #C7 @7 .;X -- #D7 @3
.,FACTOR @4
,! Z]OS (! FUNC;N >E --#C & .#D4
.,,*ICK ,GRAPH .;Y .K .;X #B -- .;X --
#AB4 ,! GRAPH PASSES "? 7--#C1 #J7 &
7#D1 #J74
B4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;Y .K .;X #B @+ #AB .;X @+ #CF @3
.,WRITE .ORIG9AL .FUNC;N @4
.K @7 .;X @+ #F7 @7 .;X @+ #F7 @3
.,FACTOR @4
,! Z]O (! FUNC;N IS --#F4
.,,*ECK ,GRAPH .;Y .K .;X #B @+ #AB
.;X @+ #C .#F4 ,! GRAPH PASSES "? 7--#F1
#J74
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#E
,F9D ! Z]OS (! FUNC;N 0REWRIT+ !
FUNC;N 9 9T]CEPT =M4
.#AJ4 .;Y .K .;X #B @+ #E .;X -- #AD
#AA4 .;Y .K .;X #B -- #G .;X -- #CJ
.#AB4 .;F @7 .;X @7 .K .;X #B -- ;L#J
.;X @+ #BE
#D.C ,EX]CISES
,,HOME"W ,,KEY
.K .,,"W$-.,,\ .,,SOLU;NS .ON .P4
,,WS#H = ,EXS4 .#CC1.DG @1 & .#FG
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
..,EXS4 #B ,#DA1 #EF1 #EH1.FC @1 &
.#GA
.K .,,MULTIPLE .,,REPRES5T,NS
,EX#.FH
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,:AT IS A Z]O (A
FUNC;N .;Y .K .;F @7 .;X @7@8
.#B4 .,,WRIT+ .,EXPLA9 ! DI6];E 2T A
MONOMIAL1 A BINOMIAL1 &A TRINOMIAL4
,GIVE AN EXAMPLE ( EA* TYPE ( EXPRES.N4
,,EXAMPLE #A
ON P4 #BEB = ,EXS4 #C-AD
.,,FACTOR+ ,FACTOR ! EXPRES.N4 ,IF !
EXPRES.N _C 2 FACTOR$1 SAY S4
.#C4 .;X #B @+ #F .;X @+ #E
.#D4 .;X #B -- #G .;X @+ #AJ
.#E4 .A #B -- #AC .A @+ #BB
.#F4 .;R #B @+ #AE .;R @+ #EF
.#G4 .;P #B @+ #B .;P @+ #D
.#H4 .;Q #B -- #AA .;Q @+ #BH
.#I4 .;B #B @+ #C .;B -- #DJ
#AJ4 .;X #B -- #D .;X -- #AB
.#AA4 .;X #B -- #G .;X -- #AH
.#AB4 .;C #B -- #I .;C -- #AH
.#AC4 .;X #B @+ #I .;X -- #CF
.#AD4 .;M #B @+ #H .;M -- #FE
------------------------------------#BEF
,,EXAMPLE #B
ON P4 #BEC = ,EXS4 #AE-BC
,,FACTOR+ ,,) ,,SPECIAL ,,PATT]NS
,FACTOR ! EXPRES.N4
.#AE4 .;X #B -- #CF
.#AF4 .;B #B -- #H;L
.#AG4 .;X #B -- #BD .;X @+ #ADD
.#AH4 .;T #B -- #AF .;T @+ #FD
.#AI4 .;X #B @+ #H .;X @+ #AF
.#BJ4 .;C #B @+ #BH;C @+ #AIF
.#BA4 .;N #B @+ #AD .;N @+ #DI
.#BB4 .;S #B -- #BF .;S @+ #AFI
.#BC4 .;Z #B -- #ABA
,,EXAMPLE #C
ON P4 #BED = ,EXS4 #BD-DA
,,SOLV+ ,,EQU,NS ,SOLVE ! EQU,N4
.#BD4 .;X #B -- #H .;X @+ #AB .K #J
.#BE4 .;X #B -- #AA .;X @+ #CJ .K #J
.#BF4 .;X #B @+ #B .;X -- #CE .K #J
.#BG4 .A #B -- #DI .K #J
.#BH4 .;B #B -- #F .;B @+ #I .K #J
.#BI4 .;C #B @+ #E .;C @+ #D .K #J
.#CJ4 .;N #B -- #F .;N .K #J
.#CA4 .;T #B @+ #AJ .;T @+ #BE .K #J
.#CB4 .;W #B -- #AF .;W @+ #DH .K #J
.#CC4 .;Z #B -- #C .;Z .K #ED
.#CD4 .;R #B @+ #B .;R .K #HJ
.#CE4 .;U #B .K --#I .;U
.#CF4 .;M #B .K #G .;M
.#CG4 #AD .;X -- #DI .K .;X #B
.#CH4 --#C .;Y @+ #BH .K .;Y #B
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 SOLV+ ! EQU,N4
.#CI4
.#DJ4
#DA4 .,,MULTIPLE .,,*OICE ,:AT >E !
ROOTS (! EQU,N .;X #B @+ #B .;X -- #FC
.K #J8
,A #G1--#I
;,B --#G1--#I
;,C --#G1I
,D4 #G1I
,,EXAMPLE #D
ON P4 #BED = ,EXS4 #DB-DC
,,WRIT+ ,,EQU,NS ,WRITE AN EQU,N T Y C
SOLVE 6F9D ! VALUE ( .X4
.#DB4 ,A RECTANGUL> PICNIC SITE
M1SURES #BD FEET 0#AJ FEET4 ,Y WANT 6D\#
! SITE'S >EA 0A4+ ! SAME 4T.E .;X 6!
L5G? &! WID?4
.#DC4 ,A RECTANGUL> P]=M+ PLAT=M 9 A
P>K M1SURES #AJ FEET 0#AB FEET4 ,Y WANT
6TRIPLE ! PLAT=M'S >EA 0A4+ ! SAME 4T.E
.;X 6! L5G? &! WID?4
,,EXAMPLE #E
ON .P4 #BEE = ,EXS4 #DD-EE
,,F9D+ ,,Z]OS ,F9D ! Z]OS (! FUNC;N
0REWRIT+ ! FUNC;N 9 9T]CEPT =M4
.#DD4 .;Y .K .;X #B @+ #F .;X @+ #H
.#DE4 .;Y .K .;X #B -- #H .;X @+ #AF
.#DF4 .;Y .K .;X #B -- #D .;X -- #CB
.#DG4 .;Y .K .;X #B @+ #G .;X -- #CJ
.#DH4 .;F @7 .;X @7 .K .;X #B @+ #AA
.;X
.#DI4 .;G @7 .;X @7 .K .;X #B -- #H
.;X
.#EJ4 .;Y .K .;X #B -- #FD
.#EA4 .;Y .K .;X #B -- #BE
.#EB4 .;F @7 .;X @7 .K .;X #B -- #AB
.;X -- #DE
.#EC4 .;G @7 .;X @7 .K .;X #B @+ #AI
.;X @+ #HD
.#ED4 .;Y .K .;X #B @+ #BB .;X @+ #ABA
.#EE4 .;Y .K .;X #B @+ #B .;X @+ #A
#EF4 .,,MULTIPLE .,,*OICE ,:AT >E !
Z]OS ( ;F7 .;X @7 .K .;X #B @+ #F .;X --
#EE8
,A --#AA1 --#E
;,B --#AA1E
;,C --#E1AA
;,D #E1AA
#EG4 .,,R1SON+ ,WRITE A QUADRATIC
EQU,N (! =M ;X #B @+ FOX @+ ;C .K #J T
HAS ROOTS #H & #AA4
#EH4 .,,%ORT .,,RESPONSE ,= :AT 9TEG]S
.;B C ! EXPRES.N ;X #B @+ .BX @+ #G 2
FACTOR$8 .,EXPLA94
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#BEG
.,,GEOMETRY ,F9D ! VALUE ( .X4
.#EI4 ,>EA ( RECTANGLE .K #CF
.#FJ4 ,>EA ( RECTANGLE .K #HD
.#FA4 ,>EA ( TRIANGLE .K #DB
.#FB4 ,>EA ( TRAPEZOID .K #CB
.#FC4 .,,OP5-.,,5D$ .,,MA? ,WRITE A
QUADRATIC FUNC;N ) Z]OS T >E EQUIDISTANT
F #AJ ON A NUMB] L9E4
#FD4 .,,*ALL5GE ,IS "! A =MULA =
FACTOR+ ! .SUM ( TWO SQU>ES8 ,Y W
9VE/IGATE ? "Q 9 "PS .,A & .;,B @4
A4 ,3SID] ! SUM ( TWO SQU>ES .;X #B @+
#AF4 ,IF ? SUM C 2 FACTOR$1 !N "! >E
9TEG]S .;M & .;N S* T .;X #B @+ #AF .K
@7 .;X @+ .;M @7@7 .;X @+ .;N @7@4
,WRITE TWO EQU,NS T .;M & .;N M/
SATISFY4
B4 ,%[ T "! >E NO 9TEG]S .;M & .;N T
SATISFY BO? EQU,NS Y WROTE 9 "P7A74 ,:AT
C Y 3CLUDE8
,,PRO#M ,,SOLV+
,,EXAMPLE #D
ON P4 #BED = ,EXS4 #FE-FG
.#FE4 .,,SKATE .,,P>K ,A C;Y'S SKATE
P>K IS A RECTANGLE #AJJ FEET L;G 0#EJ
FEET WIDE4 ,! C;Y WANTS 6TRIPLE ! >EA (!
SKATE P>K 0A4+ ! SAME 4T.E .;X 6! L5G?
&! WID?4 ,WRITE & SOLVE AN EQU,N 6F9D !
VALUE ( .X4 ,:AT >E ! NEW DIM5.NS (!
SKATE P>K8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#FF4 .,,ZOO ,A RECTANGUL> 5CLOSURE AT
A ZOO IS #CE FEET L;G 0#AH FEET WIDE4 ,!
ZOO WANTS 6D\# ! >EA (! 5CLOSURE 0A4+ !
SAME 4T.E .;X 6! L5G? &! WID?4 ,WRITE &
SOLVE AN EQU,N 6F9D ! VALUE ( .X4 ,:AT
>E ! NEW DIM5.NS (! 5CLOSURE8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#FG @4 .,,MULTI-.,,/EP .,,PRO#M ,A
MUSEUM HAS A CAFE )A RECTANGUL> PATIO4
,! MUSEUM WANTS 6ADD #DFD SQU>E FEET 6!
>EA (! PATIO 0EXP&+ ! EXI/+ PATIO Z %[N4
A4 ,F9D ! >EA (! EXI/+ PATIO4
B4 ,WRITE A V]BAL MODEL & AN EQU,N T Y
C USE 6F9D ! VALUE ( .X4
C4 ,SOLVE YR EQU,N4 ,0:AT 4T.E .;X %D
! L5G? &! WID? (! PATIO 2 EXP&$8
------------------------------------#BEH
#FH4 .,,MULTIPLE .,,REPRES5T,NS ,USE !
DIAGRAM %[N4
A4 .,WRIT+ .AN .,EXPRES.N ,WRITE A
QUADRATIC TRINOMIAL T REPRES5TS ! >EA (!
DIAGRAM4
B4 .,DESCRIB+ .A .,MODEL ,FACTOR !
EXPRES.N F "P7A74 .,EXPLA9 H[ ! DIAGRAM
MODELS ! FACTORIZ,N4
C4 .,DRAW+ .A .,DIAGRAM ,DRAW A
DIAGRAM T MODELS ! FACTORIZ,N .;X #B @+
#H .;X @+ #AE.K @7 .;X @+ #E7@7 .;X @+
#C74
#FI4 .,,S*OOL .,,FAIR ,AT LA/ YE>'S
S*OOL FAIR1 AN #AH FOOT 0#AE FOOT
RECTANGUL> SEC;N ( L& 0 ROP$ (F =A DUNK+
BOO?4 ,! L5G? & WID? (! SEC;N W EA* 2
9CR1S$ 0.;X FEET = ? YE>'S FAIR 9 ORD]
6TRIPLE ! ORIG9AL >E .,A4 ,WRITE & SOLVE
AN EQU,N 6F9D ! VALUE ( .X4 ,:AT IS !
L5G? ( ROPE NE$$ 65CLOSE ! NEW SEC;N8
#GJ4 .,,RECRE,N .,,C5T] ,A RECTANGUL>
DECK =A RECRE,N C5T] IS #BA FEET L;G
0#BJ FEET WIDE4 ,XS >EA IS 6BE HALV$
0SUBTRACT+ ! SAME 4T.E .;X F ! L5G? &!
WID?4 ,WRITE & SOLVE AN EQU,N 6F9D !
VALUE ( X4 ,:AT >E ! DECK'S NEW DIM5.NS8
#GA4 .,,%ORT .,,RESPONSE ,A SQU>E G>D5
HAS SIDES T >E #AJ FEET LON .,G4 ,A
G>D5] WANTS 6D\# ! >EA (! G>D5 0A4+ !
SAME 4T.E .;X 6! L5G? &! WID?4 ,WRITE AN
EQU,N T .;X M/ SATISFY4 ,C Y SOLVE !
EQU,N Y WROTE 0FACTOR+8 .,EXPLA9 :Y OR
:Y N4
#GB4 .,,*ALL5GE ,A GROC]Y /ORE WANTS
6D\# ! >EA ( XS P>K+ LOT 0EXP&+ ! EXI/+
LOT Z %[N4 ,0:AT 4T.E .;X %D ! LOT 2
EXP&$8
,,MIX$ ,,REVIEW
,,PREVIEW
,PREP>E = ,LESSON #D.D 9 ,EXS4 #GC-HA4
,SOLVE ! EQU,N4
.#GC4 #B .;X -- #A .K #J @7 P4 #AH @7
.#GD4 #C .;X @+ #D .K #J @7 P4 #AH @7
.#GE4 --#H .;X @+ #G .K #J @7 P4 #GH
@7
.#GF4 #F .;X @+ #E .K #J @7 P4 #AH @7
.#GG4 #D .;X -- #E .K #J @7 P4 #AH @7
.#GH4 #C .;X @+ #A .K #J @7 P4 #AH @7
.#GI4 _\ .;X -- #F_\ .K #G7 P4 #EA @7
.#HJ4 _\#B;X- #E_\ .K #AJ 7P#.EA7
.#HA4 _\#D--#C;X_\ .K #H @7 P4 #EG @7
,GRAPH ! FUNC;N4
.#HB4 .;Y .K #C .;X -- #A @7 P4 #HI @7
.#HC4
.#HD4 .;Y .K _\;X-#D_\--#D @7 P4 #ABC
@7
.#HE4
.#HF4 .;Y .K --#B;X #B @+ #H .;X @+ #G
@7 P4 #BCF @7
.#HG4 .;G @7 .;X @7 .K --#B7 .;X @+
#A7#B--#D @7 P4 #BDE @7
.#HH4 .;F @7 .;X @7 .K @7 .;X @+ #D7
@7 .;X -- #B7 @7 P4 #BDE @7
.#HI4 .;Y .K --@7 .;X -- #C7@7 .;X --
#G7 @7 P4 #BDE @7
.#IJ4 ,,P>K ,,DESIGN ,A C;Y PLANS
6PLACE A PLAYGR.D 9 A TRIANGUL> REGION
(A P>K4 ,! V]TICES (! TRIANGLE >E 7#J1
#J71 7#AD1 #C71 & 7#F1 #BE7 ": !
COORD9ATES >E GIV5 9 FEET4 ,F9D ! >EA (!
TRIANGUL> REGION4 @7 P4 #BJC @7
.,,EXTRA .,,PRACTICE = ,LESSON #D.C1
P4 #AJAC
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#BEI
#D.D ,SOLVE AX #B @+ BX @+ ;C .K #J
0,FACTOR+
.,2F ,Y US$ FACTOR+ 6SOLVE EQU,NS (!
=M .;X #B @+ .BX @+ ;C .K #J4
.,N[ ,Y W USE FACTOR+ 6SOLVE EQU,NS (!
=M .AX #B @+ .BX @+ ;C .K #J4
.,:Y8 ,S Y C MAXIMIZE A %OP'S REV5UE1
Z 9 ,EX4 #F .#D4
,KEY ,VOCABUL>Y
99 .MONOMIAL @1 P4 #BEB
,6FACTOR .AX #B @+ .BX @+ .;C :5
A6.K#A1 F9D 9TEG]S .;K1 .;L,.;M @1 & .;N
S* T3
.A .;X #B @+ .BX @+ .;C .K @7 .KX @+
.;M @7@7 .LX @+ .;N @7 .K .KL .;X #B @+
@7 .KN @+ .LM @7 .;X @+ .MN
,S1 .;K & ;,Z M/ 2 FACTORS ( .A @1 &
.;M & .;N M/ 2 FACTORS ( .,C4
,,EXAMPLE #A ,FACTOR .AX #B @+ .BX @+
.;C ": .;C .1 #J
,FACTOR #E .;X #B -- #AG .;X @+ #F4
,,FACTOR ,,EXPRES.NS
,:5 FACTOR+ .AX #B @+ .BX @+ ;C ": A
.1 #J1 X IS CU/OM>Y 6*OOSE FACTORS .KX
@+ .;M & LX @+ ;N S* T .;K & ;L >E
POSITIVE4
,SOLU;N
,Y WANT #E .;X #B -- #AG .;X @+ #F .K
@7 .KX @+ ;M7 7,ZX @+ .;N @7 ": .;K &
;,Z >E FACTORS ( #E & .;M & .;N >E
FACTORS ( .#F4 ,Y C ASSUME T .;K & .,I
>E POSITIVE & .;K .1.K .,I4 ,2C .MN .1
#J1 .;M & .;N H ! SAME SIGN4 ,S1 .;M &
;N M/ BO? 2 NEGATIVE 2C ! COE6ICI5T (
;X1 --#AG1 IS NEGATIVE4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;K,.;L @3 #E1A3 #E1A3 #E1A3 .#E1.A
.;M,.;N @3 --#F1--#A3 --#A1--#F3
--#C1--#B3 --.#B1--.#C
@7 .KX @+ .;M @7@7 .LX @+ .;N @7 @3
7#E .;X -- #F7@7 .;X -- #A7 @3 7#E .;X
-- #A7@7 .;X -- #F7 @3 7#E .;X -- #C7@7
.;X -- #B7 @3 7#E .;X --#B7@7 .;X --#C7
.AX #B @+ .BX @+ .;C @3 #E .;X #B --
#AA .;X @+ #F @3 #E .;X #B -- #CA .;X @+
#F @3 #E .;X #B -- #AC .;X @+ #F @3 #E
.;X #B -- #AG .;X @+#F
99 ,! CORRECT FACTORIZ,N IS #E .;X #B
-- #AG .;X @+ #F .K 7#E .;X -- #B7@7 .;X
-- #C74
,SIDEB>3
,/&>DS
.#H..J .,/UD5TS .SOLVE & GRAPH
..QUADRATIC EQU,NS 0.FACTOR+ @1 -PLET+ !
SQU>E1 OR US+ ! QUADRATIC =MULA4
..,/UD5TS APPLY ^! TE*NIQUES 9 SOLV+ ^W
.PRO#MS @4 ,!Y AL SOLVE QUADRATIC EQU,NS
9 ! -PLEX NUMB] SY/EM4
.#AJ..J .,/UD5TS GRAPH QUADRATIC
FUNC;NS & .DET]M9E .! MAXIMA1 M9IMA1 &
..Z]OS (! .FUNC;N4
,,EXAMPLE #B ,FACTOR .AX #B @+ .BX @+
.;C ": ;C"K #J
,FACTOR #C .;X #B @+ #BJ .;X -- #G4
,SOLU;N
,Y WANT #C .;X @+ #BJ .;X -- #G .K @7
.KX @+ .;M @7 @7 .LX @+ .;N @7 ": .;K &
;L >E FACTORS ( #C & .;M & .;N >E
FACTORS ( -- .#G4 ,2C MN "K #J1 .;M & ;N
H OPPOSITE SIGNS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;K,.;L @3 #C1A3 #C1A3 .#C1.A @3 #C1A3
#C1A
.;M,.;N @3 #G1--#A3 --.#A1.G @3
--#G1A3 #A1--#G
@7 .KX @+ .;M @7@7 .LX @+ .;N @7 @3
7#C .;X @+ #G7@7 .;X -- #A7 @3 7#C .;X
--#A7@7 .;X @+ #G7 @3 7#C .;X --#G7@7
.;X @+#A7 @3 7#C .;X @+ #A7@7 .;X -- #G7
AX.' #B @+ .BX @+ .;C @3 #C .;X #B @+
#D .;X -- #G @3 #C .;X #B @+ #BJ .;X --
#G @3 #C .;X #B -- #D .;X -- #G @3 #C
.;X #B -- #BJ .;X -- #G
99 ,! CORRECT FACTORIZ,N IS #C .;X #B
@+ #BJ .;X -- #G .K 7#C .;X -- ;L7@7 .;X
@+ #G74
------------------------------------#BFJ
..,,GUID$ ,,PRACTICE = ,EXAMPLES #A &
.#B
,FACTOR ! EXPRES.N4 ,IF ! EXPRES.N _C
2 FACTOR$1 SAY S4
.#A4 #G .;X #B -- #BJ .;X --#C
.#B4 #E .;Z #B @+ #AF .;Z @+ #C
.#C4 #B .;W #B @+ .;W @+ #C
.#D4 #C .;X #B @+ #E .;X -- #AB
.#E4 #D .;U #B @+ #AB .;U @+ #E
.#F4 #D .;X #B -- #I .;X @+ #B
.,,FACTOR+ .,,SPECIAL .,,PRODUCTS ,IF
! VALUES (A& .;C 9 .AX #B @+ .BX @+ .;C
>E P]FECT SQU>ES1 *ECK 6SEE :E!R Y C USE
"O (! SPECIAL FACTOR+ PATT]NS F ,LESSON
.#D4 #C 6FACTOR ! EXPRES.N4
,,EXAMPLE #C ,FACTOR ) SPECIAL PATT]NS
,FACTOR ! EXPRES.N4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.A4 #I .;X #B -- #FD .K 7#C .;X @7 #B
-- #H #B
.K 7#C .;X @+ #H77#C .;X --#H7 @3
..,DI6];E ( TWO .SQU>ES
.B4 #D;Y #B @+ #BJ .;Y @+ #BE .K 7#B
.;Y @7 #B @+ #B7#B .;Y @77#E7 @+ #E #B
.K 7#B .;Y @+ #E7 #B @3 .,P]FECT .SQU>E
.TRINOMIAL
.C4 #CF .;W #B -- #AB .;W @+ #A .K 7#F
.;W @7 #B -- #B7#F .;W @77;L7 @+ #A #B
.K 7#F .;W -- #A7 #B @3 .,P]FECT .SQU>E
.TRINOMIAL
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#C
,FACTOR ! EXPRES.N4
.#G4 #AF .;X #B -- #A
.#H4 #I .;Y #B @+ #AB .;Y @+ #D
.#I4 #D .;R #B -- #BH .;R @+ #DI
.#AJ4 #BE .;S #B -- #HJ .;S @+ #FD
.#AA4 #DI .;Z #B @+ #DB .;Z @+ #I
.#AB4 #CF .;N #B -- #I
.,,FACTOR+ .,,\ .,,MONOMIALS ,:5
FACTOR+ AN EXPRES.N1 F/ *ECK 6SEE :E!R !
T]MS H A -MON MONOMIAL FACTOR4
,,EXAMPLE #D ,FACTOR \ MONOMIALS F/
,,AVOID ,,]RORS
,2 SURE 6FACTOR \ ! -MON MONOMIAL F
ALL (! T]MS (! EXPRES.N1 N J ! F/ T]M4
,FACTOR ! EXPRES.N4
.A4 #E .;X #B -- #DE .K #E7 .;X #B --
#I7
.K #E7 .;X @+ #C7@7 .;X --#C7
.B4 #F .;Q #B -- #AD .;Q @+ #H .K
#B7#C .;Q #B -- #G .;Q @+ #D7
.K #B7#C .;Q -- #D7@7 .;Q -- #A7
.C4 --#E .;Z #B @+ #BJ .;Z .K --#E .;Z
@7 .;Z -- #D7
.D4 #AB .;P #B -- #BA .;P @+ #C .K
#C7#D .;P #B -- #G .;P @+ #A7
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#D
,FACTOR ! EXPRES.N4
.#AC4 #C .;S #B -- #BD
.#AD4 #H .;T #B @+ #CH .;F -- #AJ
.#AE4 #F .;X #B @+ #BD .;X @+ #AE
.#AF4 #AB .;X #B -- #BH .;X -- #BD
.#AG4 --#AF .;N #B @+ #AB .;N
.#AH4 #F .;Z #B @+ #CC .;Z @+ #CF
------------------------------------#BFA
.,,SOLV+ .,,QUADRATIC .,,EQU,NS ,Z Y
SAW 9 ,LESSON .#D4 #C1 IF ! LEFT SIDE (!
QUADRATIC EQU,N .AX #B @+ .BX @+ .;C .K
#J C 2 FACTOR$1 !N ! EQU,N C 2 SOLV$ US+
! Z]O PRODUCT PROP]TY4
,,EXAMPLE #E ,SOLVE QUADRATIC EQU,NS
,SOLVE 7A7 #C .;X #B @+ #AJ .;X -- #H
.K #J & 7;B7 #E .;P #B -- #AF .;P @+ #AE
.K #D .;P -- #E4
A4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#C .;X #B @+ #AJ .;X -- #H .K #J @3
.,WRITE .ORIG9AL .EQU,N4
7#C .;X -- #B7 @7 .;X @+ #D7 .K #J @3
.,FACTOR4
#C .;X -- #B .K #J OR .;X @+ #D .K #J
@3 .,Z]O .PRODUCT .PROP]TY
OR .;X .K --#D @3 ,SOLVE =.' X4.-
,,9T]PRET ,,EQU,NS
,IF ! SQU>E ( AN EXPRES.N IS Z]O1 !N !
EXPRES.N XF M/ 2 Z]O4
B4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#E .;P #B -- #AF .;P @+ #AE .K #D .;P
-- #E @3 .,WRITE .ORIG9AL .EQU,N4
#E .;P #B -- #BJ .;P @+ #BJ .K #J @3
..,WRITE 9 /&>D .=M4
.;P #B -- #D .;P @+ #D .K #J @3
..,DIVIDE EA* SIDE 0.#E4
@7 .;P -- #B7 #B .K #J @3 .,FACTOR4
.;P--.#B .K #J @3 .,Z]O .PRODUCT
.PROP]TY
.;P .K #B @3 .,SOLVE .= .P4
,,EXAMPLE #F ,USE A QUADRATIC EQU,N Z
A MODEL
.,,QUILTS ,Y H MADE A RECTANGUL> QUILT
T IS #E FEET 0#D FEET4 ,Y WANT 6USE !
REMA9+ #AJ SQU>E FEET ( FABRIC 6ADD A
DECORATIVE BORD] ( UNI=M WID? 6! QUILT4
,:AT %D ! WID? (! QUILT'S BORD] BE8
,SOLU;N
,WRITE A V]BAL MODEL4 ,!N WRITE AN
EQU,N4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#AJ .K #BJ @+ #AH .;X @+ #D .;X #B --
#BJ @3 .,MULTIPLY .US+ .,,FOIL4
#J .K #D .;X #B @+ #AH .;X @3 -- ..#AJ
,WRITE 9 /&>D .=M4
#J .K #B;X.' #B @+ #I .;X -- #E @3
..,DIVIDE EA* SIDE 0.#B4
#J .K 7#B .;X -- #A7 @7 .;X @+ #E7 @3
.,FACTOR4
#B .;X -- #A .K #J OR .;X @+ #E .K #J
@3 .,Z]O .PRODUCT .PROP]TY
OR .;X .K --#E @3 .,SOLVE .= .X4
99 ,REJECT ! NEGATIVE VALUE1 --#E4 ,!
BORD]'S WID? %D 2 FT1 OR #F IN4
------------------------------------#BFB
.,,FACTOR+ .,,& .,,Z]OS ,6F9D !
MAXIMUM OR M9IMUM VALUE (A QUADRATIC
FUNC;N1 Y C F/ USE FACTOR+ 6WRITE !
FUNC;N 9 9T]CEPT =M ..;Y .K A7 ;X
--;P7@7 ;X --.;Q74 ,2C ! FUNC;N'S V]TEX
LIES ON ! AXIS ( SYMMETRY
@1 ! MAXIMUM OR M9IMUM O3URS AT !
.AV]AGE (! Z]OS .;P & .Q4
,,EXAMPLE #G ,SOLVE A MULTI-/EP PRO#M
.,,MAGAZ9ES ,A MON?LY TE5 MAGAZ9E HAS
#BH1JJJ SUBSCRIB]S :5 X *>GES 4#AJ P]
ANNUAL SUBSCRIP;N4 ,= EA* 4#A 9CR1SE 9
PRICE1 ! MAGAZ9E LOSES AB #BJJJ
SUBSCRIB]S4 ,H[ M* %D ! MAGAZ9E *>GE
6MAXIMIZE ANNUAL REV5UE8 ,:AT IS !
MAXIMUM ANNUAL REV5UE8
,SOLU;N
.,,/EP .#G .,DEF9E ! V>IA#S4 ,LET .;X
REPRES5T ! PRICE 9CR1SE & .;,R @7 .;X @7
REPRES5T ! ANNUAL REV5UE4
.,,/EP#B .,WRITE A V]BAL MODEL4 ,!N
WRITE & SIMPLIFY A QUADRATIC FUNC;N4
.;,R @7 .;X @7 .K 7--#BJJJ .;X @+
#BH1JJJ7 @7 .;X @+ #AJ7
.;,R @7 .;X @7 .K --#BJJJ @7 .;X --
#AD7@7 .;X @+ #AJ7
.,,/EP .#C .,ID5TIFY ! Z]OS & F9D _!
AV]AGE4 ,F9D H[ M* EA* SUBSCRIP;N %D CO/
6MAXIMIZE ANNUAL REV5UE4
,! Z]OS (! REV5UE FUNC;N >E #AD & --
.#AJ4 ,! AV]AGE (! Z]OS IS @4 ,6MAXIMIZE
REV5UE1 EA* SUBSCRIP;N %D CO/ 4#AJ @+
4.#B .K 4#AB4
.,,/EP .#D ,F9D ! MAXIMUM ANNUAL
REV5UE4
.;,R @7 .#B @7 .K --#BJJJ7 .#B --
#AD7@7 .#B @+ #AJ7 .K 4#BHH1JJJ
99 ,! MAGAZ9E %D *>GE 4#AB P]
SUBSCRIP;N 6MAXIMIZE ANNUAL REV5UE4 ,!
MAXIMUM ANNUAL REV5UE IS 4#BHH1JJJ4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #E1F1
& .#G
,SOLVE ! EQU,N4
.#AI4 #F .;X #B -- #C .;X -- #FC .K #J
.#BJ4 #AB .;X #B @+ #G .;X @+#B .K .;X
@+#H
.#BA4 #G .;X #B @+ #GJ .;X @+ #AGE .K
#J
.#BB4 .,,:AT .,,IF8 ,9 ,EXAMPLE #G1
SUPPOSE ! MAGAZ9E 9ITI,Y *>GES 4#AA P]
ANNUAL SUBSCRIP;N4 ,H[ M* %D ! MAGAZ9E
*>GE 6MAXIMIZE ANNUAL REV5UE8 ,:AT IS !
MAXIMUM ANNUAL REV5UE8
------------------------------------#BFC
#D.D ,EX]CISES
,,HOME"W ,,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
.ON P4 ,,WS#H = ,EXS4 .#BG1.CI @1 &
.#FC
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 #B1AB1FD1FE1 & #FG
,,SKILL ,,PRACTICE
.#A4 ,,VOCABUL>Y ,:AT IS ! GRTE/ -MON
MONOMIAL FACTOR (! T]MS (! EXPRES.N #AB
.;X #B @+ #H .;X @+ #BJ8
.#B4 ,,WRIT+ .,EXPLA9 H[ ! VALUES ( .A
& .;C 9 .AX @+ .BX @+ .;C HELP Y DET]M9E
:E!R Y C USE A P]FECT SQU>E TRINOMIAL
FACTOR+ PATT]N4
,,EXAMPLES #A & #B
ON P4 #BEI = ,EXS4 #C-AB
,,FACTOR+ ,FACTOR ! EXPRES.N4 ,IF !
EXPRES.N _C 2 FACTOR$1 SAY S4
.#C4 #B .;X #B @+ #E .;X @+ #C
.#D4 #C .;N #B @+ #G .;N @+ #D
.#E4 #D .;R #B @+ #E .;R @+ #A
.#F4 #F .;P #B @+ #E .;P @+ #A
.#G4 #AA .;Z #B @+ #B .;Z -#I
.#H4 #AE .;X #B -- #B .;X -- #H
.#I4 #D .;Y #B -- #E .;Y -- #D
.#AJ4 #AD .;M #B @+ .;M -- #C
.#AA4 #I .;D #B -- #AC .;D -- #AJ
#AB4 .,,MULTIPLE .,,*OICE ,:
FACTORIZ,N ( #E .;X #B @+ #AD .;X -- #C
IS CORRECT8
,A 7#E .;X --#C7@7 .;X @+ #A7
;,B 7#E .;X @+ ;L7@7 .;X -- #C7
;,C #E7 .;X -- ;L7@7 .;X @+ #C7
;,D 7#E .;X -- ;L7@7 .;X @+ #C7
,,EXAMPLE #C
ON P4 #BFJ = ,EXS4 #AC-BA
,,FACTOR+ ,,) ,,SPECIAL ,,PATT]NS
,FACTOR ! EXPRES.N4
.#AC4 #I .;X #B -- #A
.#AD4 #D .;R #B -- #BE
.#AE4 .#DI;N #B -- #AF
.#AF4 #AF .;S #B @+ #HE @+ #A
.#AG4 #DI .;X #B @+ #GJ .;X @+ #BE
.#AH4 #FD .;W #B @+ #ADD .;W @+ #HA
#AI4 #I .;P #B -- #AB .;P @+ #D
.#BJ4 #BE .;T #B -- #CJ .;T @+ #I
.#BA4 #CF .;X #B #HD .;X @+ #DI
,,EXAMPLE #D
ON P4 #BFJ ;I = ,EXS4 #BB-CA
,,FACTOR+ ,,MONOMIALS ,,F/ ,FACTOR !
EXPRES.N4
.#BB4 #AB .;X #B -- #D .;X -- #DJ
.#BC4 #AH .;Z #B @+ #CF .;Z @+ #AF
.#BD4 #CB .;V #B -- #B
.#BE4 #F .;U #B -- #BD .;U
.#BF4 #AB .;M #B -- #CF .;M @+ #BG
.#BG #BJ .;X #B @+ #ABD .;X @+ #BD
.#BH4 #BA .;X #B -- #GG .;X -- #BH
.#BI4 --#CF .;N #B @+ #DH .;N -- #AE
.#CJ4 --#H .KY #B @+ #BH .;Y -- #FJ
.#CA4 ,,]ROR ,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 FACTOR+ ! EXPRES.N4
,,EXAMPLE #E
ON P4 #BFA = ,EXS4 #CB-DJ
,,SOLV+ ,,EQU,NS ,SOLVE ! EQU,N4
.#CB4 #AF .;X #B -- #A .K #J
.#CC4 #AA .;Q #B -- #DD .K #J
.#CD4 #AD .;S #B -- #BAE .K #J
.#CE4 #DE .;N #B @+ #AJ .;N .K #J
.#CF4 #D .;X #B -- #BJ .;X @+ #BE .K
#J
.#CG4 #D .;P #B @+ #AB .;P @+ #I .K #J
.#CH4 #AE .;X #B @+ #G .;X -- #B .K #J
.#CI4 #F .;R #B -- #G .;R -- #E .K #J
.#DJ4 #CF;Z #B @+ #IF .;Z @+ #AE .K #J
,,EXAMPLE #G
ON P4 #BFB = ,EXS4 #DA-DI
,,F9D+ ,,Z]OS ,F9D ! Z]OS (! FUNC;N
0REWRIT+ ! FUNC;N 9 9T]CEPT =M4
.#DA4 .;Y .K #D .;X #B -- #AI .;X --
#E
.#DB4 .;G @7 .;X @7 .K #C .;X #B -- #H
.;X @+ #E
.#DC4 .;Y .K #E .;X #B -- #BG .;X --
#AH
.#DD4 .;F @7 .;X @7 .K #C .;X #B -- #C
.;X
.#DE4 .;Y .K #AA;X #B -- #AI .;X -- #F
.#DF4 .;Y .K #AF .;X #B -- #B .;X --
#E
.#DG4 .;Y .K #AE .;X #B -- #E .;X --
#BJ
.#DH4 .;Y .K #AH .;X #B -- #F .;X --
#D
.#DI4 .;G @7 .;X @7 .K #AB .;X #B @+
#E .;X -- #G
------------------------------------#BFD
..,,GEOMETRY ,F9D ! VALUE ( .X4
.#EJ4 ,>EA ( SQU>E .K #CF
.#EA4 ,>EA ( RECTANGLE .K #CJ
.#EB4 ,>EA ( TRIANGLE .K #AAE
.,,SOLV+ .,,EQU,NS ,SOLVE ! EQU,N4
.#EC4 #B .;X #B -- #D .;X -- #H .K --
.;X #B @+ .;X
.#ED4 #BD .;X #B @+ #H .;X @+ #B .K
#E--#F .;X
.#EE4 #AH .;X #B -- #BB .;X .K #BH
.#EF4 #AC .;X #B @+ #BA .;X .K --#E
.;X #B @+ #BB
.#EG4 .;X .K #D .;X #B -- #AE .;X
.#EH4 @7 .;X @+ #H7 #B .K #AF -- .;X
#B @+ #I .;X
.,,*ALL5GE ,FACTOR ! EXPRES.N4
.#EI4 #B .;X #C -- #E .;X #B @+ #C .;X
.#FJ4 #H .;X #D -- #H .;X #C -- #F .;X
#B
.#FA4 #I .;X #C -- #D .;X
,,PRO#M ,,SOLV+
,,EXAMPLE #F
ON P4 #BFA = ,EXS4 #FB-FC
..#FB4 ,,>TS ,,& .,,CRAFTS ,Y H A
RECTANGUL> /A9$ GLASS W9D[ T M1SURES #B
FEET 0#A FOOT4 ,Y H #D SQU>E FEET (
GLASS ) : 6MAKE A BORD] ( UNI=M WID? >.D
! W9D[4 ,:AT %D ! WID? (! BORD] BE8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#FC @4 .,,URBAN .,,PLANN+ ,Y H J
PLANT$ A RECTANGUL> FL[] B$ ( R$ ROSES 9
A C;Y P>K4 ,Y WANT 6PLANT A BORD] (
YELL[ ROSES >.D ! FL[] B$ Z %[N4 ,2C Y
B"\ ! SAME NUMB] ( R$ & YELL[ ROSES1 !
>1S (! BORD] & FL[] B$ W 2 EQUAL4 ,:AT
%D ! WID? (! BORD] ( YELL[ ROSES BE8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
,,EXAMPLE #G
ON P4 #BFB = ,EXS4 #FD-FE
#FD4 .,,MULTIPLE .,,*OICE ,A SURFBO>D
%OP SELLS #DE SURFBO>DS P] MON? :5 X
*>GES 4#EJJ P] SURFBO>D4 ,= EA* 4#BJ
DECR1SE 9 PRICE1 ! /ORE SELLS #E M
SURFBO>DS P] MON?4 ,H[ M* %D ! %OP *>GE
P] SURFBO>D 9 ORD] 6MAXIMIZE MON?LY
REV5UE8
,A 4#CDJ
;,B 4#DIB
;,C 4#EJH
;,D 4#FFJ
#FE4 .,,%ORT .,,RESPONSE ,A RE/AURANT
SELLS AB #CCJ S&WI*ES EA* "D AT A PRICE
( 4#F EA*4 ,= EA* @4#.BE DECR1SE 9
PRICE1 #AE M S&WI*ES >E SOLD P] "D4 ,H[
M* %D ! RE/AURANT *>GE 6MAXIMIZE DAILY
REV5UE8 .,EXPLA9 EA* /EP ( YR SOLU;N4
,:AT IS ! MAXIMUM DAILY REV5UE8
#FF4 .,,PA9T+S ,Y PLACE A MAT >.D A
#BE 9* 0#BA 9* PA9T+ Z %[N4 ,! MAT IS
TWICE Z WIDE AT ! LEFT & "R (! PA9T+ Z X
IS AT ! TOP & BOTTOM (! PA9T+4 ,! >EA (!
MAT IS #GAD SQU>E 9*ES4 ,H[ WIDE IS !
MAT AT ! LEFT & "R (! PA9T+8 AT ! TOP &
BOTTOM (! PA9T+8
.K .,,"W$-.,,\ .,,SOLU;NS .ON .P4
,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#BFE
#FG4 .,,EXT5D$ .,,RESPONSE ,A ,U4,S4
,PO/AL ,S]VICE GUIDEL9E /ATES T =A
RECTANGUL> PACKAGE L ! "O %[N1 ! SUM (!
L5G? &! GIR? _C EXCE$ #AJH 9*ES4
,SUPPOSE T = "O S* PACKAGE1 ! L5G? IS
#CF 9*ES &! GIR? IS Z L>GE Z POSSI#4
A4 ,:AT IS ! GIR? (! PACKAGE8
B4 ,WRITE AN EXPRES.N =! PACKAGE'S
WID? .;W 9 T]MS ( .H4 ,WRITE AN EQU,N
GIV+ ! PACKAGE'S VOLUME .;,V 9 T]MS (
.H4
C4 ,:AT HEI<T & WID? MAXIMIZE ! VOLUME
(! PACKAGE8 ,:AT IS ! MAXIMUM VOLUME8
.,EXPLA9 H[ Y F.D X4
#FH4 .,,*ALL5GE ,RECALL F GEOMETRY !
!OREM AB ! PRODUCTS (! L5G?S ( SEG;TS (
TWO *ORDS T 9T]SECT 9 ! 9T]IOR (A
CIRCLE4 ,USE ? !OREM 6F9D ! VALUE ( .;X
9 ! DIAGRAM4
,,MIX$ ,,REVIEW
,,PREVIEW
,PREP>E = ,LESSON #D.E 9 ,EXS4 #FI-GD4
,SOLVE ! EQU,N4 @7 P4 #AH @7
.#FI4 #AA @+ #AB .;X .K #C7#D .;X @+
#G7
.#GJ4 #F .;X - #AI .K #E7#C @+ #B .;X
@7
.#GA4 --#I7#E .;X @+ #C7 .K #I .;X --
#DB
.#GB4 #F7 .;X -- #G7 .K #AE7#B .;X --
#D7
.#GC4 #I7 .;X -- #C7 .K #C7#E .;X --
#AG7
.#GD4 #D7#C .;X -- #AA7 .K #C7#AA --
.;X @7 @+ .;X
,SOLVE ! SY/EM ( L9E> EQU,NS US+
,CRAM]'S RULE4 @7 P4 #BJC @7
.#GE4 #D .;X @+ #I .;Y .K --#AD
#C .;X @+ #E .;Y .K --#G
.#GF4 #H .;X @+ #E .;Y .K --#B
#B .;X @+ #C .;Y .K #AD
.#GG4 #E .;X -- #H .;Y .K --#EJ
#B .;X -- #C .;Y .K --#BE
,GRAPH ! FUNC;N4
.#GH4 .;Y .K .;X #B--#C .;X -- #AH @7
P4 #BCF @7
.#GI4 .;F @7 .;X @7 .K #B .;X #B @+
;LL .;X @+ #E @7 P4 #BCF @7
.#HJ4 .;Y .K #C7 .;X @+ #F7#B--#B @7
P4 #BDE @7
.#HA4 ;G7 .;X @7 .K @7 .;X @+ #D7@7
.;X -- #E7 @7 P4 #BDE @7
,,QUIZ = ,LESSONS #D.A-D.D
,GRAPH ! FUNC;N4 ,LABEL ! V]TEX & AXIS
( SYMMETRY4 @7 P4 #BCF @7
.#A4 .;Y .K .;X #B--#F .;X @+ #AD
.#B4 .;Y .K #B .;X #B @+ #H .;X @+ #AE
.#C4 .;F @7 .;X @7 .K --#C .;X #B @+
#F .;X -- #E
,WRITE ! QUADRATIC FUNC;N 9 /&>D =M4
@7 P4 #BDE @7
.#D4 .;Y .K @7 .;X -- #D7@7 .;X -- #H7
.#E4 ;G7 .;X @7 .K --#B7 .;X @+ #C7@7
.;X -- #G7
.#F4 .;Y .K #E7 .;X @+ #F7#B--#B
,SOLVE ! EQU,N4
.#G4 .;X #B @+ #I .;X @+ #BJ .K #J @7
P4 #BEB @7
.#H4 ;N#B--LLN @+ #BD .K #J7 P4 #BEB
@7
.#I4 ;Z#B--#C;Z--#DJ .K #J @7 P4 #BEB
@7
.#AJ4 #E;S#B--#ADE--#C .K #J @7 P4
#BEI @7
.#AA4 #G;A#B--#CJ;A @+ #H .K #J @7 P4
#BEI @7
.#AB4 #D .;X #B @+ #BJ .;X @+ #BE .K
#J @7 P4 #BEI @7
.#AC4 ,,DVD ,,PLAY]S ,A /ORE SELLS AB
#EJ (A NEW MODEL ( ,,DVD PLAY] P] MON?
AT A PRICE ( 4#ADJ EA*4 ,= EA* 4#AJ
DECR1SE 9 PRICE1 AB #E M ,,DVD PLAY]S P]
MON? >E SOLD4 ,H[ M* %D ! /ORE *>GE 9
ORD] 6MAXIMIZE MON?LY REV5UE8 ,:AT IS !
MAXIMUM MON?LY REV5UE8 @7 P4 #BEI @7
.,,EXTRA .,,PRACTICE = ,LESSON #D.D1
P4 #AJAC
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#BFF
#D.E ,SOLVE ,QUADRATIC ,EQU,NS
0,F9D+ ,SQU>E ,ROOTS
.,2F ,Y SOLV$ QUADRATIC EQU,NS
0FACTOR+4
.,N[ ,Y W SOLVE QUADRATIC EQU,NS 0F9D+
SQU>E ROOT2
.,:Y8 ,S Y C SOLVE PRO#MS AB A/RONOMY1
Z 9 ,EX4 #CI
,KEY ,VOCABUL>Y
99 SQU>E ROOT
99 RADICAL
99 RADIC&
99 R,NALIZ+ ! DENOM9ATOR
99 3JUGATES
,SIDEB>3
,/&>DS
.#H..J .,/UD5TS .SOLVE & GRAPH
..QUADRATIC EQU,NS 0.FACTOR+ @1 -PLET+ !
SQU>E1 OR US+ ! QUADRATIC =MULA4
..,/UD5TS APPLY ^! TE*NIQUES 9 SOLV+ ^W
.PRO#MS @4 ,!Y AL SOLVE QUADRATIC EQU,NS
9 ! -PLEX NUMB] SY/EM4
,A NUMB] .;R IS A .SQU>E .ROOT (A
NUMB] .;S .IF .;R #B .K .S4.,A POSITIVE
NUMB] #E HAS TWO SQU>E ROOTS1 WRITT5 Z &
@4 ,= EXAMPLE1 2C #C #B .K #I & 7-#C7 #B
.K #I1 ! TWO SQU>E ROOTS ( #I >E @4 ,!
POSITIVE SQU>E ROOT (A NUMB] IS AL CALL$
! .PR9CIPAL SQU>E ROOT4
,! EXPRES.N IS CALL$ A .RADICAL @4 ,!
SYMBOL SQRT IS A .RADICAL .SIGN @1 &!
NUMB] .;S 2N ! RADICAL SIGN IS ! .RADIC&
(! EXPRES.N4
,,KEY ,,3CEPT
,= YR ,NOTEBOOK
,PROP]TIES ( ,SQU>E ,ROOTS 7A .1 #J1
.;B .1 #J7
.,PRODUCT .,PROP]TY
.,EXAMPLE
.,QUOTI5T .,PROP]TY
.,EXAMPLE
.,,SIMPLIFY+ .,,SQU>E .,,ROOTS ,Y C
USE ! PROP]TIES ABV 6SIMPLIFY EXPRES.NS
3TA9+ SQU>E ROOTS4 ,A SQU>E-ROOT
EXPRES.N IS SIMPLIFI$ IF3
99 NO RADIC& HAS A P]FECT-SQU>E FACTOR
O!R ?AN #A1 &
99 "! IS NO RADICAL 9 A DENOM9ATOR
,,EXAMPLE #A
,USE PROP]TIES ( SQU>E ROOTS
,,USE ,A ,,CALCULATOR
,Y C USE A CALCULATOR 6APPROXIMATE :5
;S IS N A P]FECT SQU>E4 ,= EXAMPLE1 @4
,SIMPLIFY ! EXPRES.N4
.A4
.B4
.C4
.D4
.,,GUID$ .,,PRACTICE = ,EXAMPLE #A
,SIMPLIFY ! EXPRES.N4
.#A4
.#B4
.#C4
.#D4
.#E4
.#F4
.#G4
.#H4
------------------------------------#BFG
,,R,NALIZ+ ,,! ,,DENOM9ATOR
,SUPPOSE ! DENOM9ATOR (A FRAC;N
HAS ! =M @1 @1 OR ": .A & .;B >E R,NAL
NUMB]S4 ,! TA# %[S H[ 6ELIM9ATE !
RADICAL F ! DENOM9ATOR4 ,? IS CALL$
.R,NALIZ+ .! .DENOM9ATOR @4
,! EXPRES.NS & >E CALL$ .3JUGATES (
EA* O!R4 ,_! PRODUCT IS ALW A R,NAL
NUMB]4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,=M (! DENOM9ATOR3 ,MULTIPLY NUM]ATOR
& DENOM9ATOR BY3
@3
@3
@3 .A @+
,,EXAMPLE #B
,R,NALIZE DENOM9ATORS ( FRAC;NS
,SIMPLIFY
7.A7 & 7.;B7 @4
,SOLU;N
.A4
.B4
.,,SOLV+ .,,QUADRATIC .,,EQU,NS ,Y C
USE SQU>E ROOTS 6SOLVE "S TYPES (
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#J1 !N ! EQU,N .;X #B .K .;S HAS TWO
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(T5 WRITT5 9 3D5S$ =M Z 7R1D Z 8PLUS OR
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,,EXAMPLE #C
,SOLVE A QUADRATIC EQU,N
,SOLVE .#C;X #B @+ #E .K #DA4
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96! ORIG9AL EQU,N4
------------------------------------#BFH
.,,EXAMPLE .#D
,/&>DIZ$ ,TE/ ,PRACTICE
,:AT >E ! SOLU;NS (! EQU,N @8
.,A --#CH1CB
.;,B
.;,C
.;,D
,SOLU;N
,! SOLU;NS >E & @4
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.;,D
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& #D
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.#I4
.#AJ4
.#AA4
.#AB4
.#AC4
.#AD4
.#AE4
.#AF4
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.#AG4 #E .;X #B .K #HJ
.#AH4 .;Z #B -- #G .K #BI
.#AI4 #C7;X-#B7 #B .K #DJ
.,,MODEL+ .,,DROPP$ .,,OBJECTS ,:5 AN
OBJECT IS DROPP$1 XS HEI<T .;H 7IN FEET7
ABV ! GR.D AF .;T SECONDS C 2 MODEL$ 0!
FUNC;N
;H .K -.#AF;T #B @+ .;H #J
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GRAV;Y1 DI6]5T MODELS >E US$ 7SEE
,EX]CISE #CI74
------------------------------------#BFI
,,EXAMPLE #E
,MODEL A DROPP$ OBJECT )A QUADRATIC
FUNC;N
,,ANO!R ,,WAY
,= ALT]NATIVE ME?ODS = SOLV+ ! PRO#M 9
,EXAMPLE #E1 TURN 6PAGE #BGB =! .,PRO#M
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.,,SCI;E .,,-PETI;N ,=A SCI;E -PETI;N1
/UD5TS M/ DESIGN A 3TA9] T PREV5TS AN
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2C "T M/ 2 POSITIVE4 ,! 3TA9] W FALL =
AB .#A4 #H SECONDS 2F X HITS ! GR.D4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
.,,GUID$ .,,PRACTICE .= .,EXAMPLE .#E
.#BJ4 .,,:AT .,,IF8 ,9 ,EXAMPLE #E1
SUPPOSE ! EGG 3TA9] IS DROPP$ F A HEI<T
( #CJ FEET4 ,H[ L;G DOES ! 3TA9] TAKE
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#D.E ,EX]CISES
,HOME"W ,KEY
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ON P4 ,,WS#H = ,EXS4 #AG1BG1 & #DA
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IS #GB CALL$8
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.#D4
.#E4
.#F4
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.#H4
.#I4
.#AJ4
.#AA4
.#AB4
.#AC4
.#AD4
.#AE4
.#AF4
.#AG4
.#AH4
------------------------------------#BGJ
#AI4 ,:AT IS A -PLETELY SIMPLIFI$
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,A
;,B
;,C
;,D
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
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.#BA4
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#BC4 .A #B .K #EJ
#BD4 .;X #B .K #HD
.#BE4 .#F;Z #B .K #AEJ
.#BF4 #D .;P #B .K #DDH
.#BG -.#C;W #B .K --#BAC
#BH4 #G .;R #B -- #AJ .K #BE
.#BI4
.#CJ4
.#CA4 #D7;X- #A7 #B .K #H
.#CB4 #G7;X--#D7 #B -- #AH .K #AJ
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7IN FEET7 ABV ! WAT] AF .;T SECONDS4 ,H[
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@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
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.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#BGA
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7IN P.DS7 ON A RAC+ CYCLI/ IS GIV5 0!
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BICYCLE'S SPE$ 7IN MILES P] H\R74
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.#DF4 7--#H7 #B
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.#EJ4 --#AE #B
.#EA4 --#G #B
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.,,EXTRA .,,PRACTICE = ,LESSON #D.E1
P4 #AJAC
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#BGB
,PRO#M ,SOLV+ ,"W%OP ,LESSON #D.E3
,US+ ,ALT]NATIVE ,ME?ODS
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#BFI
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EQU,N 0F9D+ SQU>E ROOTS4 ,Y C AL SOLVE A
QUADRATIC EQU,N US+ A TA# OR A GRAPH4
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--#AF;X #B @+ #EJ 96A GRAPH+ CALCULATOR4
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SIGN4
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#H SECONDS AF X IS DROPP$4
------------------------------------#BGC
,,ME?OD #B
.,US+ A .,GRAPH ,ANO!R APPROA* IS
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PROC$URE 6F9D ! APPROXIMATE SOLU;N4
------------------------------------#BGD
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,LESSONS #D.A --#D.E
.#A4 .,,MULTI-.,,/EP .,,PRO#M ,A
P9EC"O FALLS F A TREE BRAN* T IS #BJ
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A V]TEX ( 7-#C1 #B74
------------------------------------#BGE
#D.F ,P]=M ,OP],NS ) ,-PLEX ,NUMB]S
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,KEY ,VOCABUL>Y
99 IMAG9>Y UNIT .;I
99 -PLEX NUMB]
99 IMAG9>Y NUMB]
99 -PLEX 3JUGATES
99 -PLEX PLANE
99 ABSOLUTE VALUE (A -PLEX NUMB]
,SIDEB>3
,/&>DS
#F.J ,/UD5TS ADD1 SUBTRACT MULTIPLY1 &
DIVIDE -PLEX NUMB]S4
#E.J ,/UD5TS DEMON/RATE K ( H[ R1L &
-PLEX NUMB]S >E RELAT$ BO? >I?METIC,Y &
GRAPHIC,Y4 ,9 "PICUL>1 !Y C PLOT -PLEX
NUMB]S Z PO9TS 9 ! PLANE4
,N ALL QUADRATIC EQU,NS H R1L-NUMB]
SOLU;NS4 ,= EXAMPLE1 .;X #B .K --#A HAS
NO R1L-NUMB] SOLU;NS 2C ! SQU>E ( ANY
R1L NUMB] .;X IS N"E A NEGATIVE NUMB]4
,6OV]COME ? PRO#M1 MA!MATICIANS CR1T$
AN EXP&$ SY/EM ( NUMB]S US+ ! .IMAG9>Y
.UNIT .;I @1 DEF9$ Z @4 ,NOTE T .;I #B
.K -- .#A4 ,! IMAG9>Y UNIT .;I C 2 US$
6WRITE ! SQU>E ROOT ( .ANY NEGATIVE
NUMB]4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,! ,SQU>E ,ROOT (A ,NEGATIVE ,NUMB]
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,PROP]TY3 ,EXAMPLE
.#A4 ,IF .;R IS A POSITIVE R1L NUMB]1
!N @4 @3
.#B4 ,0,PROP]TY 7#A71 X FOLL[S T @4 @3
,,EXAMPLE #A
,SOLVE A QUADRATIC EQU,N
.,SOLVE .#B;X #B @+ .#AA .K -.#CG4
,! SOLU;NS >E & @4
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#A
,SOLVE ! EQU,N4
#A4 .;X #B .K --#AC
#B4 .;X #B .K --#CH
#C4 .;X #B @+ #AA .K #C
#D4 .;X #B -- #H .K --#CF
#E4 .#C;X #B -- #G .K --#CA
#F4 #E .;X #B @+ #CC .K #C
------------------------------------#BGF
..,,-PLEX ,,NUMB]S ,A -PLEX .NUMB]
WRITT5 9 ./&>D .=M IS A NUMB] .A @+ .BI
": .A & .;B >E R1L NUMB]S4 ,! NUMB] .A
IS ! .R1L ."P (! -PLEX NUMB]1 &! NUMB]
.BI IS ! .IMAG9>Y ."P4
,IF .;B @6.K #J1 !N .A @+ .BI IS AN
.IMAG9>Y .NUMB]4 ,IF .A .K #J & .;B @6.K
#J1 !N .A @+ .BI IS A .PURE .IMAG9>Y
.NUMB]4 ,! DIAGRAM %[S H[ DI6]5T TYPES (
-PLEX NUMB]S >E RELAT$4
,TWO -PLEX NUMB]S .A @+ .BI & ..;C @+
DI .>E EQUAL IF & ONLY IF .A .K .;C &
.;B .K .,D4 ,= EXAMPLE1 IF ..;X @+ YI .K
#E--.#C;I @1 !N .;X .K #E & .;Y .K --
.#C4
,PICTURE3 ..,-PLEX ,NUMB]S 7A @+ .BI7
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,SUMS & ,DI6];ES ( ,-PLEX ,NUMB]S
,6ADD 7OR SUBTRACT7 TWO -PLEX NUMB]S1
ADD 7OR SUBTRACT7 _! R1L "PS & _!
IMAG9>Y "PS SEP>ATELY4
..,SUM ( -PLEX .NUMB]S3 @7 .A @+ .BI7
@+ 7;C @+ .DI7 .K 7A @+ .;C7 @+ 7.;B @+
.;D7 .;I
..,DI6];E ( -PLEX .NUMB]S3 7A @+ .BI7
-- 7;C @+ ..DI7 .K 7A- .;C7 @+
7.;B--.;D7.;I
,,EXAMPLE #B
,ADD & SUBTRACT -PLEX NUMB]S
,WRITE ! EXPRES.N Z A -PLEX NUMB] 9
/&>D =M4
,A4 7#H -- .;I7 @+ 7#E @+ #D .;Z @7
,B4 7#G--#FJ--7#C--#F .;Z @7
,C4 #AJ--7#F @+ .LI7 @+ .#D .;I
,SOLU;N
A4 7..#H -- ;I7 @+ 7#E @+ #D ;I @7 .K
7#H @+ #E7 @+ 7-#A @+ #D7;I ,DEF9I;N (
-PLEX .A4I;N
.K #AC @+ #C .;I ,WRITE 9 /&>D =M4
B4 7#G--#FJ--7#C--#F .;I @7 .K
7#G--#C7 @+ 7-#F @+ #F7;Z ,DEF9I;N (
-PLEX SUBTRAC;N
.K #D @+ #J .;I ,SIMPLIFY4
.K #D ,WRITE 9 /&>D =M4
,C4 #AJ--7#F @+ #GJ @+ #D .;Z .K
,77.#AJ -- #F7 -- .#G;I7' @+ #D .;I
,DEF9I;N ( -PLEX SUBTRAC;N
.K 7#D--#G .;I @+ #D .;I ,SIMPLIFY4
.K #D @+ 7-#G @+ #D7;I ,DEF9I;N (
-PLEX A4I;N
.K #D--#C .;I ,WRITE 9 /&>D =M4
.,,GUID$ .,,PRACTICE = ,EXAMPLE #B
,WRITE ! EXPRES.N Z A -PLEX NUMB] 9
/&>D =M4
.#G4 7#I--;I7 @+ 7-#F @+ #G7;I
#H4 7#C @+ #G .;I @7--7#H--#B7
#I4 --#D--7#A @+ .;I7 -- 7#E @+ #I .;I
@7
------------------------------------#BGG
,,EXAMPLE #C
,USE ..A4I;N ( -PLEX .NUMB]S 9 R1L
LIFE
.,,ELECTRIC;Y ,CIRCUIT -PON5TS S* Z
RESI/ORS1 9DUCTORS1 & CAPACITORS ALL
OPPOSE ! FL[ ( CURR5T4 ,? OPPOSI;N IS
CALL$ .RESI/.E = RESI/ORS & .REACT.E =
9DUCTORS & CAPACITORS4 ,A CIRCUIT'S
TOTAL OPPOSI;N 6CURR5T FL[ IS .IMP$ANC
.,E4 ,ALL ( ^! QUANTITIES >E M1SUR$ 9
OHMS _+()._:
,,R1D+
,NOTE T :ILE A -PON5T'S RESI/.E OR
REACT.E IS A R1L NUMB]1 XS IMP$.E IS A
-PLEX NUMB]4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,-PON5T .& .SYMBOL @3 ,RESI/OR
@3 ,9DUCTOR
@3 ,CAPACITOR
.,RESI/.E .OR .REACT.E @3 .;,R @3 .;,L
@3 .;,C
.,IMP$.E @3 .;,R @3 .,LI @3 - .,CI
,! TA# %[S ! REL,N%IP 2T A -PON5T'S
RESI/.E OR REACT.E & XS 3TRIBU;N
6IMP$.E4 ,A .S]IES .CIRCUIT IS AL %[N )!
RESI/.E OR REACT.E ( EA* -PON5T LABEL$4
,! IMP$.E =A S]IES CIRCUIT IS ! SUM (!
IMP$.ES =! 9DIVIDUAL -PON5TS4 ,F9D !
IMP$.E (! CIRCUIT %[N ABV4
,SOLU;N
,! RESI/OR HAS A RESI/.E ( #E OHMS1 S
XS IMP$.E IS #E OHMS4 ,! 9DUCTOR HAS A
REACT.E ( #C OHMS1 S XS IMP$.E IS #C .;I
OHMS4 ,! CAPACITOR HAS A REACT.E ( #D
OHMS1 S XS IMP$.E IS --#D;I OHMS4
,IMP$.E ( CIRCUIT .K #E @+ #C .;I @+
7-#D;I7 ,ADD ! 9DIVIDUAL IMP$.ES4
.K #E--;I ,SIMPLIFY4
,! IMP$.E (! CIRCUIT IS #E -- .;I
OHMS4
.,,MULTIPLY+ .,,-PLEX .,,NUMB]S
,6MULTIPLY TWO -PLEX NUMB]S1 USE !
4TRIBUTIVE PROP]TY OR ! ,,FOIL ME?OD J Z
Y D :5 MULTIPLY+ R1L NUMB]S OR ALGEBRAIC
EXPRES.NS4
,,EXAMPLE #D
.,MULTIPLY -PLEX NUMB]S
,WRITE ! EXPRES.N Z A -PLEX NUMB] 9
/&>D =M4
.A4 #D .;I 7-#F @+ .;I7
.B4 7#I --#B;I7 7-#D @+ #G .;I @7
,,AVOID .,,]RORS
,:5 SIMPLIFY+ AN EXPRES.N T 9VOLVES
-PLEX NUMB]S1 2 SURE 6SIMPLIFY .;I #B TO
-- .#A4
,SOLU;N
A4 #D .;I 7-#F @+ .;I7 .K --#BD;I @+
#D .;I #B ,4TRIBUTIVE PROP]TY
.K --#BD;I @+ #D7-;L7 ,USE ;I #B .K --
.#A4
.K --#BD;I--#D ,SIMPLIFY4
.K --#D--#BD;I ,WRITE 9 /&>D =M4
B4 7#I--#B .;I @7 7-#D @+ #G .;I @7 .K
--#CF @+ #FC;I @+ #H .;I -- #AD;I #B
,MULTIPLY US+ ,,FOIL4
.K --#CF @+ #GA;I -- .#AD7-.#A7
,SIMPLIFY & USE ;I #B .K -- .#A4
.K --#CF @+ #GA;I @+ #AD ,SIMPLIFY4
.K --#BB @+ #GA;I ,WRITE 9 /&>D =M4
------------------------------------#BGH
.,,-PLEX .,,3JUGATES ,TWO -PLEX NUMB]S
(! =M .A @+ .BI & .A--.BI >E CALL$ -PLEX
3JUGATES4 ,! PRODUCT ( -PLEX 3JUGATES IS
ALW A R1L NUMB]4 ,= EXAMPLE1 7#B @+ #D
.;I @77#B--#DJ .K #D--#H .;I @+ #H .;Z
@+ #AF .K #BJ4 ,Y C USE ? FACT 6WRITE !
QUOTI5T ( TWO -PLEX NUMB]S 9 /&>D =M4
,,REWRITE ,,QUOTI5TS
,:5 A QUOTI5T HAS AN IMAG9>Y NUMB] 9 !
DENOM9ATOR1 REWRITE ! DENOM9ATOR Z A R1L
NUMB] S Y C EXPRESS ! QUOTI5T 9 /&>D =M4
,,EXAMPLE #E
,DIVIDE -PLEX NUMB]S
,WRITE ! QUOTI5T 9 /&>D =M4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #C1D1
& .#E
.#AJ4 .,,:AT .,,IF8 ,9 ,EXAMPLE #C1
:AT IS ! IMP$.E (! CIRCUIT IF ! GIV5
CAPACITOR IS REPLAC$ ) "O HAV+ A REACT.E
( #G OHMS8
,WRITE ! EXPRES.N Z A -PLEX NUMB] 9
/&>D =M4
.#AA4 .;I 7#I -- .;I @7
.#AB4 7#C @+ .;I @77#E- .;I @7
.#AC4
.#AD4
.,,-PLEX .,,PLANE ,J Z E R1L NUMB]
CORRESPONDS 6A PO9T ON ! R1L NUMB] L9E1
E -PLEX NUMB] CORRESPONDS 6A PO9T 9 !
-PLEX PLANE4 ,Z %[N 9 ! NEXT EXAMPLE1 !
-PLEX PLANE HAS A HORIZONTAL AXIS CALL$
! .R1L .AXIS &A V]TICAL AXIS CALL$ !
.IMAG9>Y .AXIS4
,,EXAMPLE #F
,PLOT -PLEX NUMB]S
,PLOT ! -PLEX NUMB]S 9 ! SAME -PLEX
PLANE4
.A4 #C--#B .;I
.B4 --#B @+ #D .;I
,C4 #C .;I
D4 --#D--#C .;I
,SOLU;N
.A4 ,6PLOT #C -- .#B;I @1 />T AT !
ORIG91 MOVE #C UNITS 6! "R1 & !N MOVE #B
UNITS D[N4
.B4 ,6PLOT --#B @+ #D .;I @1 />T AT !
ORIG91 MOVE #B UNITS 6! LEFT1 & !N MOVE
#D UNITS UP4
.C4 ,6PLOT #C .;I @1 />T AT ! ORIG9 &
MOVE #C UNITS UP4
.D4 ,6PLOT --#D--#C .;I @1 />T AT !
ORIG91 MOVE #D UNITS 6! LEFT1 & !N MOVE
#C UNITS D[N4
------------------------------------#BGI
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,ABSOLUTE ,VALUE (A ,-PLEX ,NUMB]
,! .ABSOLUTE .VALUE (A -PLEX NUMB] .;Z
.K .A @+ .BI @1 DENOT$ _\ .;Z_\ @1 IS A
NONNEGATIVE R1L NUMB] DEF9$ Z @4 ,? IS !
4T.E 2T .;Z &!! ORIG9 9 ! -PLEX PLANE4
,,EXAMPLE #G
,F9D ABSOLUTE VALUES ( -PLEX NUMB]S
,F9D ! ABSOLUTE VALUE ( FA7 --#D @+
.#C;I & .;B --.#C;I
.A4
.B4
.,ANIMAT$ ,ALGEBRA AT
_+CLASSZONE.COM_:
.,,GUID$ .,,PRACTICE = ,EXAMPLES #F &
#G
,PLOT ! -PLEX NUMB]S 9 ! SAME -PLEX
PLANE4 ,!N F9D ! ABSOLUTE VALUE ( EA*
-PLEX NUMB]4
.#AE4 #D -- .;I
.#AF4 --#C--#D .;I
.#AG4 #B @+ #E .;I
.#AH4 --#D .;I
#D.F ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS .ON .P4
,,WS#H = ,EXS4 .#AA1.BI @1 & .#FG
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 .#B1.BA1.EJ1.FJ1.FI @1 & .#GD
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,:AT IS ! -PLEX
3JUGATE ( .A--.BI8
.#B4 .,,WRIT+ ,IS E -PLEX NUMB] AN
IMAG9>Y NUMB]8 .,EXPLA94
,,EXAMPLE #A
ON P4 #BGE = ,EXS4 #C-AA
.,,SOLV+ .,,QUADRATIC .,,EQU,NS ,SOLVE
! EQU,N4
.#C4 ;X #B .K-#BH
.#D4 .;R #B .K --#FBD
.#E4 .;Z #B @+ #H .K #D
.#F4 .;S #B -- #BB .K --#AAB
.#G4 .#B;X #B @+ #CA .K #I
.#H4 #I--#D .;Y #B .K #EG
.#I4 .#F;T #B @+ #E .K #B .;T #B @+ #A
.#AJ4 #C .;P #B @+ #G .K --#I;P #B @+
#D
.#AA --#E7;N--#C7 #B .K #AJ
,,EXAMPLE #B
ON P4 #BGF = ,EXS4 #AB-BA
.,,A4+ .,,& .,,SUBTRACT+ ,WRITE !
EXPRES.N Z A -PLEX NUMB] 9 /&>D =M4
.#AB4 7#F--#C .;I @7 @+ 7#E @+ #D .;I
@7
.#AC4 7#I @+ #H .;I @7 @+ 7#H--#I .;I
@7
.#AD4 7-#B--#F .;I @7--7#D--#F .;I @7
.#AE4 7-#A @+ .;I7 -- 7#G--#E .;I @7
.#AF4 7#H @+ #BJ;I7--7-#H @+ #AB;I7
.#AG4 7#H--#E .;I @7--7-#AA @+ #D .;I
@7
.#AH4 7#AJ--#B .;I @7 @+ 7-#AA--#G .;I
@7
.#AI4 7#AD @+ #C .;I @7 @+ 7#G @+ #F
.;I @7
.#BJ4 7-#A @+ #D .;I @7 @+ 7-#I--#B
.;I @7
------------------------------------#BHJ
.#BA4 ,,MULTIPLE ,,*OICE ,:AT IS !
/&>D =M (! EXPRES.N 7#B @+ #C .;I
@7--7#G @+ #D .;I @7@8
.,A --#D
.;,B --#E @+ #G .;I
.;,C --#E- .;I
.;,D #E @+ .;I
,,EXAMPLES #D & #E
ON PP4 #BGG-BGH = ,EXS4 #BB-CC
.,,MULTIPLY+ .,,& .,,DIVID+ ,WRITE !
EXPRES.N Z A -PLEX NUMB] 9 /&>D =M4
.#BB4 #F .;I 7#C @+ #B .;I @7
.#BC4 --;I7#D--#H .;I @7
.#BD4 7#E-G;I7 7-#D-C;I7
.#BE4 7-#B @+ #E .;I @77-#A @+#D;I7
.#BF4 7-#A--#E .;I @7 7-#A @+ #E .;I
@7
.#BG4 7#H-C .;I @77#H @+ #C .;I @7
.#BH4
.#BI4
.#CJ4
.#CA4
.#CB4
.#CC4
,,EXAMPLE #F
ON P4 #BGH = ,EXS4 #CD-DA
.,,PLOTT+ .,,-PLEX .,,NUMB]S ,PLOT !
NUMB]S 9 ! SAME -PLEX PLANE4
.#CD4 #A @+ #B .;I
.#CE4 --#E @+ #C .;I
.#CF4 --#F .;I
.#CG4 #D .;I
#CH4 --#G -- .;I
#CI4 #E--#E .;I
.#DJ4 #G
.#DA4 --#B
,,EXAMPLE #G
ON P4 #BGI = ,EXS4 #DB-EJ
.,,F9D+ .,,ABSOLUTE .,,VALUE ,F9D !
ABSOLUTE VALUE (! -PLEX NUMB]4
.#DB4 #D @+ #C .;I
.#DC4 --#C @+ #AJ;I
.#DD4 #AJ -- .LI
.#DE4 --#A--#F .;I
.#DF4 --#H;I
.#DG4 #D .;I
#DH4 --#D @+ .;I
#DI4 #G @+ .LI
#EJ4 .,,MULTIPLE .,,*OICE ,:AT IS !
ABSOLUTE VALUE ( #I @+ #AB;I8
,A #G
;,B #AE
;,C #AJH
;,D #BBE
.,,/&>D .,,=M ,WRITE ! EXPRES.N Z A
-PLEX NUMB] 9 /&>D =M4
.#EA4 --#H--7#C @+ #B .;I @7--7#I--#D
.;I @7
.#EB4 7#C @+ #B .;I @7 @+ 7#E--;I7 @+
#F
.#EC4 #E .;I 7#C @+ #B .;I @7 7#H @+
#C .;I @7
.#ED4 7#A --#I .;I @77#A
-.#D;I77.#D-.C;I7
.#EE4
.#EF4
.,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 SIMPLIFY+ ! EXPRES.N4
.#EG4
.#EH4
#EI4 ..,,A4ITIVE ,,& ,,MULTIPLICATIVE
.,,9V]SES ,! A4ITIVE 9V]SE (A -PLEX
NUMB] .;Z IS A -PLEX NUMB] .;Z A.' .-S*
T .;Z @+ .;Z A .K #J4 ,! MULTIPLICATIVE
9V]SE ( .;Z IS A -PLEX NUMB] .;Z ;M.'
.-S* T ..;Z @* ;Z .;M .K #A4 ,F9D !
A4ITIVE & MULTIPLICATIVE 9V]SES ( EA*
-PLEX NUMB]4
A4 .;Z .K .#B @+ .;I
B4 .;Z .K #E -- .;I
C4 .;Z .K --#A @+ #C .;I
#FJ4 .,,OP5-.,,5D$ .,,MA? ,F9D TWO
IMAG9>Y NUMB]S ^: SUM IS A R1L NUMB]4
,H[ >E ! IMAG9>Y NUMB]S RELAT$8
.,,*ALL5GE ,WRITE ! EXPRES.N Z A -PLEX
NUMB] 9 /&>D =M4
.#FA4
.#FB4
.#FC4
.#FD4
.K .,,"W$-.,,\ .,,SOLU;NS
ON .P4 ,,WS#A
.K ,,/&>DIZ$ ,,TE/ ,,PRACTICE
------------------------------------#BHA
,,PRO#M ,,SOLV+
,,EXAMPLE #C
ON P4 #BGG = ,EXS4 #FE-FG
.,,CIRCUITS ,9 ,EX]CISES #FE-FG1 EA*
-PON5T (! CIRCUIT HAS BE5 LABEL$ ) XS
RESI/.E OR REACT.E4 ,F9D ! IMP$.E (!
CIRCUIT4
.#FE4
.#FF4
.#FG4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#FH4 .,,VISUAL .,,?9K+ ,! GRAPH %[S H[
Y C GEOMETRIC,Y ADD TWO -PLEX NUMB]S 7IN
? CASE1 #D @+ .;I & #B @+ #E .;I @7 6F9D
_! SUM 7IN ? CASE1 #F @+ #F .;I @7@4
,F9D EA* (! FOLL[+ SUMS 0DRAW+ A GRAPH4
A4 7#E @+ .;I7 @+ 7#A @+ #DJ
B4 7-#G @+ #CJ @+ 7#B--#BJ
C4 7#C--#BJ @+ 7-#A--#J
D4 7#D @+ #BJ @+ 7-#E--#C .;I @7
#FI4 .,,%ORT .,,RESPONSE ,MAKE A TA# T
%[S ! P[]S ( .;I F ;I #A 6.;I ;S.' .-9 !
F/ R[ &! SIMPLIFI$ =MS ( ^! P[]S 9 !
SECOND R[4 .,DESCRIBE ! PATT]N Y OBS]VE
9 ! TA#4 ,V]IFY T ! PATT]N 3T9UES
0EVALUAT+ ! NEXT F\R P[]S ( .I4
,9 ,EX]CISES #GJ-GC1 USE ! EXAMPLE 2L
6DET]M9E :E!R ! -PLEX NUMB] .;C 2L;GS 6!
,M&ELBROT SET4 .,JU/IFY .YR ANSW]4
,,EXAMPLE
,9VE/IGATE ! ,M&ELBROT SET
,3SID] ! FUNC;NF7;Z7 .K .;Z #B @+ .;C
& ? 9F9ITE LI/ ( -PLEX NUMB]S3 .;Z #J .K
#J1 .;Z #A .K .;F7.;Z #J @7@1 .;Z #B .K
.;F7.;Z #A 7.;Z #C .K .;F 7;Z #B @7@1'
,IF ! ABSOLUTE VALUES ( .;Z #J;T .;Z #A
.;Z #B @1 .;Z #C ''' >E ALL LESS ?AN "S
FIX$ NUMB] .;,N @1 !N .;C 2L;GS 6!
.,M&ELBROT .SET4 ,IF ! ABSOLUTE VALUES
2COME 9F9ITELY L>GE1 !N .;C DOES N 2L;G
6! ,M&ELBROT SET4
,TELL :E!R .;C .K #A @+ ;I 2L;GS 6!
,M&ELBROT SET4
,PICTURE3 ..,! ,M&ELBROT SET IS !
BLACK REGION 9 ! -PLEX PLANE .ABV4
,SOLU;N
,LET .;F7.;Z7 .K.;Z #B @+ 7..#A @+
.;I74
;Z #J .K #J _\.;Z ;O _\.K.#J
;Z #A .K;F7#J7 .K #J #B @+ 7#A @+ ;I7
.K .#A @+ .;I _\;Z #A _\ .#A..DA
.;Z #B .K .;F 7.#A @+ .;I7 -- 7#A @+
.;I7 #B @+ 7;L @+ ;I7 .K ;L @+ .#C .;I
_\ .;Z #B _\ .#C4 #AF
.;Z #C .K .;F 7#A @+ .#C;I7 .K 7#A @+
#C .;I @7 #B @+ 7#A @+ .;I7 .K --#G @+
.#AA _\.;Z #C _\ .#I..IJ
;Z #D .K ;F7-#G @+ .#G;I7 .K 7-#G @+
#G .;I @7 #B @+ 7;L @+ ;I7 .K ;L- #IG;I
_\.;Z #D _\ .#IG..J
,2C ! ABSOLUTE VALUES >E 2COM+
9F9ITELY L>GE1 .;C .K #A @+ ;I DOES N
2L;G 6! ,M&ELBROT SET4
#GJ4 .;C .K .;I
#GA4 .;C .K --.#A @+ .;I
#GB4 .;C .K --#A
.#GC4 ;C .K --#J.E;I
------------------------------------#BHB
.#GD4 .,,%ORT .,,RESPONSE ,EVALUATE @4
,DOES ! RULE ON PAGE #BFF HOLD :5 .A &
.;B >E NEGATIVE NUMB]S8
#GE4 .,,P>ALLEL .,,CIRCUITS ,9 A
.P>ALLEL .CIRCUIT @1 "! IS M ?AN "O
PA?WAY "? : CURR5T C FL[4 ,6F9D ! IMP$.E
.;,Z (A P>ALLEL CIRCUIT ) TWO PA?WAYS1
F/ CALCULATE ! IMP$.ES .;,Z #A & ;,Z #B
(! PA?WAYS SEP>ATELY 0TR1T+ EA* PA?WAY Z
A S]IES CIRCUIT4 ,!N APPLY ? =MULA3
,:AT IS ! IMP$.E ( EA* P>ALLEL CIRCUIT
%[N 2L8
A4
B4
C4
#GF4 .,,*ALL5GE .,JULIA .SETS @1 L !
,M&ELBROT SET %[N ON PAGE #BHA @1 >E
FRACTALS DEF9$ ON ! -PLEX PLANE4 ,= E @'
-PLEX NUMB] .;C @1 "! IS AN ASSOCIAT$
,JULIA SET DET]M9$ 0! FUNC;N ;F7;Z7 .K
.;Z #B @+ .,C4
,= EXAMPLE1 ! ,JULIA SET CORRESPOND+
6.;C .K #A @+ .;I IS DET]M9$ 0! FUNC;N
;F7;Z7 .K ;Z #B @+ #A @+ Z4 ,A NUMB] .;Z
#J IS A MEMB] ( ? ,JULIA SET IF !
ABSOLUTE VALUES (! NUMB]S .;Z #A .K
;F7;Z #J @7;,Z #B .K;F7;Z #A @7;,Z #C
7@+ ;F7;Z #B @7@1' >E ALL LESS ?AN "S
FIX$ NUMB] .;,N @1 & .;Z #J IS N A MEMB]
IF ^! ABSOLUTE VALUES GR[ 9F9ITELY L>GE4
,TELL :E!R ! GIV5 NUMB] ;Z #J 2L;GS 6!
,JULIA SET ASSOCIAT$ )! FUNC;N .;F7.;Z7
.K .;Z #B @+ #A @+ .I4
,PICTURE3 ,A ,JULIA SET
A4 .;Z #J .K .;I
B4 .;Z #J .K #A
C4 .;Z #J .K #B .;I
D4 .;Z ;N .K #B @+ .#C;I
,,MIX$ ,,REVIEW
,TELL :E!R ! REL,N IS A FUNC;N4
,EXPLA94 @7 P4 #GB @7
.#GG4 7#E1 --#C71 7#J1 #C71 7--#B1
#J71 7#B1 #J71 7--#E1 --#C7
.#GH4 7--#C1 #A71 7#B1 --#B71 7#C1
--#A71 7#A1 --#A71 7#C1 #J7
.#GI4 7#J1 --#D71 7#A1 #B71 7--#A1
--#D71 7#B1 #C71 7#A1 --#E7
.#HJ4 7#B1 #F71 7#E1 #F71 7--#A1 #D71
7--#C1 #E71 7--#B1 #C7
,P]=M ! 9DICAT$ OP],N4
.#HA4
.#HB4
.#HC4
.#HD4
,,PREVIEW
,PREP>E = ,LESSON #D.G 9 ,EXS4 #HE-IJ4
,SOLVE ! EQU,N4
.#HE4 #C;X #B -- #C;X--#CF .K #J @7 P4
#BEI @7
.#HF4 #B;X #B -- #I;X @+ #D .K #J @7
P4 #BEI @7
.#HG4 #F;X #B .K #IF @7 P4 #BFF @7
.#HH4 #AD;X #B .K #IA @7 P4 #BFF @7
.#HI4 #B;X #B -- #H .K #DB @7 P4 #BFF
@7
.#IJ4 #C;X #B @+ #AC .K #ABA @7 P4
#BFF @7
.,,EXTRA .,,PRACTICE = ,LESSON #D.F1
P4 #AJAC
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#BHC
,9VE/IGAT+ ,ALGEBRA ,ACTIV;Y3 #D.G
,US+ ,ALGEBRA ,TILES 6,-PLETE ! ,SQU>E
,USE 2F LESSON #D.G
.,,MAT]IALS 99 ALGEBRA TILES
,SIDEB>3
,/&>DS
.#H..J .,/UD5TS .SOLVE & GRAPH
.QUADRATIC .EQU,NS .0FACTOR+1 .-PLET+ .!
.SQU>E @1 OR US+ ! QUADRATIC =MULA4
,/UD5TS APPLY ^! TE*NIQUES 9 SOLV+ ^W
PRO#MS4 ,!Y AL SOLVE QUADRATIC EQU,NS 9
! -PLEX NUMB] SY/EM4
,,"Q
,H[ C Y USE ALGEBRA TILES 6-PLETE !
SQU>E =A QUADRATIC EXPRES.N8
,IF Y >E GIV5 AN EXPRES.N (! =M .;X #B
@+ .BX @1 Y C ADD A 3/ANT .;C 6!
EXPRES.N S T ! RESULT .;X #B @+ .BX @+
.;C IS A P]FECT SQU>E TRINOMIAL4 ,?
PROCESS IS CALL$ .-PLET+ .! .SQU>E .,E4
,,EXPLORE
,-PLETE ! SQU>E =! EXPRES.N .;X #B @+
.#F;X
,PICTURE3 .,MODEL .! .EXPRES.N
,PICTURE3 ,USE ALGEBRA TILES 6MODEL !
EXPRES.N .;X #B @+ .#FX4 ,Y W NE$ 6USE
"O ;X #B -TILE & SIX ;X-TILES = ?
EXPRES.N4
,PICTURE3 .,MAKE .A .SQU>E
,PICTURE3 ,>RANGE ! TILES 9 A SQU>E4
,Y WANT ! L5G? & WID? (! SQU>E 6BE
EQUAL4 ,YR >RANGE;T W 2 9COMPLETE 9 "O
(! CORN]S4
,PICTURE3 .,-PLETE .! .SQU>E
,PICTURE3 ,F9D ! NUMB] ( #A-TILES NE$$
6-PLETE ! SQU>E4 ,0A4+ N9E #A-TILES1 Y C
SEE T .;X #B @+ .#F;X @+ #I IS EQUAL TO
7;X @+ #C7 #B4
,,DRAW ,,3CLU.NS
,USE YR OBS]V,NS 6-PLETE ^! EX]CISES
.#A4 ,COPY & -PLETE ! TA# AT ! "R
0FOLL[+ ! /EPS ABV4
#B4 ,LOOK = PATT]NS 9 ! LA/ COLUMN (
YR TA#4 ,3SID] ! G5]AL /ATE;T .;X #B @+
.BX @+ .;C .K @7 .;X @+ .;D7 #B4
A4 ,H[ IS .;D RELAT$ 6.;B 9 EA* CASE8
B4 ,H[ IS .;C RELAT$ 6.;D 9 EA* CASE8
C4 ,H[ C Y OBTA9 ! NUMB]S 9 ! TA#'S
SECOND COLUMN DIRECTLY F ! COE6ICI5TS (
.;X 9 ! EXPRES.NS F ! F/ COLUMN8
,! FOLL[+ TA# IS 9 LI/$
=MAT4 ,= EA* CELL ! H1D+ IS %[N
FOLL[$ 0A COLON1 SPACE &! CELL
3T5TS
.,-PLET+ .! .,SQU>E @3 ,EXPRES.N
.,-PLET+ .! .,SQU>E @3 ,NUMB] (
#A-TILES NE$$ 6-PLETE ! SQU>E
.,-PLET+ .! .,SQU>E @3 ,EXPRES.N
WRITT5 Z A SQU>E
.,-PLET+ .! .,SQU>E @3 ;X.' #B @+
.#B;X @+ @8
.,-PLET+ .! .,SQU>E @3 @8
.,-PLET+ .! .,SQU>E @3 @8
.,-PLET+ .! .,SQU>E @3 ;X.' #B @+ #D
.;X @+ @8
.,-PLET+ .! .,SQU>E @3 @8
.,-PLET+ .! .,SQU>E @3 @8
.,-PLET+ .! .,SQU>E @3 ;X.' #B @+
.#F;X @+ @8
.,-PLET+ .! .,SQU>E @3 #I
.,-PLET+ .! .,SQU>E @3 ;X.' #B @+ #F
.;X @+ #I .K 7.;X @+ #C7 #B
.,-PLET+ .! .,SQU>E @3 ;X.' #B @+ #H
.;X @+ @8
.,-PLET+ .! .,SQU>E @3 @8
.,-PLET+ .! .,SQU>E @3 @8
.,-PLET+ .! .,SQU>E @3 ;X.' #B @+ #AJ
.;X @+ @8
.,-PLET+ .! .,SQU>E @3 @8
.,-PLET+ .! .,SQU>E @3 @8
------------------------------------#BHD
#D.G ,-PLETE ! ,SQU>E
.,2F ,Y SOLV$ QUADRATIC EQU,NS 0F9D+
SQU>E ROOTS4
.,N[ ,Y W SOLVE QUADRATIC EQU,NS
0-PLET+ ! SQU>E4
.,:Y8 ,S Y C F9D A BASEBALL'S MAXIMUM
HEI<T Z 9 ,EXAMPLE .#G4
,KEY ,VOCABUL>Y
99 .-PLET+ .! .SQU>E
,9 ,LESSON .#D4 #E1 Y SOLV$ EQU,NS (!
=M .;X #B .K .;K 0F9D+ SQU>E ROOTS4 ,?
ME?OD AL "WS IF "O SIDE ( AN EQU,N IS A
P]FECT SQU>E TRINOMIAL4
,,EXAMPLE #A
,SOLVE A QUADRATIC EQU,N 0F9D+ SQU>E
ROOTS
,,ANO!R ,,WAY
,Y C AL F9D ! SOLU;NS 0WRIT+ ! GIV5
EQU,N Z .;X #B -- #H .;X -- #I .K #J &
SOLV+ ? EQU,N 0FACTOR+4
,SIDEB>3
,/&>DS
.#H..J .,/UD5TS .SOLVE & GRAPH
.QUADRATIC .EQU,NS .0FACTOR+1 .-PLET+ .!
.SQU>E @1 OR US+ ! QUADRATIC =MULA4
..,/UD5TS APPLY ^! TE*NIQUES 9 SOLV+ ^W
PRO#MS4 ,!Y AL SOLVE QUADRATIC EQU,NS 9
! -PLEX NUMB] .SY/EM @4
.#AJ..J .,/UD5TS GRAPH QUADRATIC
FUNC;NS & ..DET]M9E ! MAXIMA1 .M9IMA @1
& Z]OS .( .! .FUNC;N4
.,SOLVE .;X #B -- .#H;X @+ .#AF .K
.#BE4
.;X #B -- #H .;X @+ #AF .K #BE .,WRITE
.ORIG9AL .EQU,N4
7.;X -- #D7 #B .K #BE ,WRITE LEFT SIDE
Z A BINOMIAL SQU>$4
.;X -- #D .K +-#E ,TAKE SQU>E ROOTS (
EA* SIDE4
.;X .K #D +- #E ,SOLVE = X4
,! SOLU;NS >E ..#D @+ #E .K .#I &
..#D--#E .K --.#A4
.,,P]FECT .,,SQU>ES ,9 ,EXAMPLE #A1 !
TRINOMIAL .;X #B -- ..#H .;X @+ #AF IS A
P]FECT SQU>E 2C X EQUALS 7;X--#D7 #B4
,"S"TS Y NE$ 6ADD A T]M 6AN EXPRES.N .;X
#B @+ .BX 6MAKE X A SQU>E4 ,? PROCESS IS
CALL$ .-PLET+ .! .SQU>E4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,-PLET+ ! ,SQU>E
.,^WS ,6-PLETE ! SQU>E =! EXPRES.N .;X
@+ .BX @1 ADD @4
.,DIAGRAMS ,9 EA* DIAGRAM1 ! -B9$ >EA
(! %AD$ REGIONS
IS .;X @+ .BX4 ,A4+ -PLETES ! SQU>E 9
! SECOND DIAGRAM4
.,ALGEBRA
------------------------------------#BHE
,,EXAMPLE #B
,MAKE A P]FECT SQU>E TRINOMIAL
,F9D ! VALUE ( .;C T MAKES .;X #B @+
#AF;X @+ .;C A P]FECT SQU>E TRINOMIAL4
,!N WRITE ! EXPRES.N Z ! SQU>E (A
BINOMIAL4
,SOLU;N
.,,/EP .#A .,F9D HALF ! COE6ICI5T ( X4
.,,/EP .#B .,SQU>E ! RESULT ( ,/EP
.#A4 #H #B .K #FD
.,,/EP#C .,REPLACE .;C )! RESULT (
,/EP #B4 ;X #B @+ #AF;X @+ #FD
,! TRINOMIAL .;X #B @+ #AF;X @+ .;C IS
A P]FECT SQU>E :5 ;C .K #F .#D4 ,!N ;X
#B @+ #AF;X @+ #FD .K 7;X @+ #H77;X @+
#H7 .K 7;X @+ #H7 #B4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #A &
.#B
,SOLVE ! EQU,N 0F9D+ SQU>E ROOTS4
#A4 ;X #B @+ #F .;X @+ #I .K #CF
.#B4 .;X #B -- ;L#J;X @+ ..#BE .K .#A
.#C4 .;X #B -- #BD;X @+ #ADD .K .#AJJ
,F9D ! VALUE ( .;C T MAKES ! EXPRES.N
A P]FECT SQU>E TRINOMIAL4 ,!N WRITE !
EXPRES.N Z ! SQU>E (A BINOMIAL4
.#D4 .;X #B @+ #AD;X @+ .;C
.#E4 ;X #B @+ #BB;X @+ .;C
#F4 ;X #B -- #I .;X @+ .;C
.,,SOLV+ .,,EQU,NS ,! ME?OD ( -PLET+ !
SQU>E C 2 US$ 6SOLVE .ANY QUADRATIC
EQU,N4 ,:5 Y -PLETE A SQU>E Z "P ( SOLV+
AN EQU,N1 Y M/ ADD ! SAME NUMB] 6.BO?
SIDES (! EQU,N4
.,,EXAMPLE .#C
,SOLVE .AX #B @+ .BX @+ .;C .K #J :5
.A .K #A
,! SOLU;NS >E & @4
.,,*ECK ,Y C USE ALGEBRA OR A GRAPH4
.,ALGEBRA ,SUB/ITUTE EA* SOLU;N 9 !
ORIG9AL EQU,N 6V]IFY T X IS CORRECT4
.,GRAPH ,USE A GRAPH+ CALCULATOR
6GRAPH .;Y .K .;X #B -- #AB;X @+ #D4 ,!
;X-9T]CEPTS >E AB & @4
,,REVIEW ,,RADICALS
,= HELP ) SIMPLIFY+ SQU>E ROOTS1 SEE
P4 #BFF @4
------------------------------------#BHF
,,EXAMPLE #D
,SOLVE .AX #B @+ ..BX @+ .;C .K #J :5
.A # #A
,SOLVE .#B;X #B @+ .#H;X @+ #AD .K #J
0-PLET+ ! SQU>E4
,! SOLU;NS >E & @4
,,EXAMPLE #E
,/&>DIZ$ ,TE/ ,PRACTICE
,,ELIM9ATE ,,*OICES
,Y C ELIM9ATE *OICES ,A& ;,D 2C ! SIDE
L5G?S >E NEGATIVE :5 .;X .K -- .#F4
,! >EA (! RECTANGLE %[N IS #GB SQU>E
UNITS4 ,:AT IS ! VALUE ( .;X8
.,A --#F
.;,B #D
.;,C #H.DH
;,D --#F OR #D
,SOLU;N
,USE ! =MULA =! >EA (A RECTANGLE
6WRITE AN EQU,N4
#C;X7;X @+ #B7 .K #GB ,L5G? ;X ,WID?
.K ,>EA
#C;X #B @+ #F .;X .K #GB ,4TRIBUTIVE
PROP]TY
;X #B @+ #B .;X .K #BD ,DIVIDE EA*
SIDE 0! COE6ICI5T ( ;X #B4
;X #B @+ #B .;X @+ #A .K #BD @+ #A
,ADD 6EA* SIDE4
7;X @+ #A7 #B .K #BE ,WRITE LEFT SIDE
Z A BINOMIAL SQU>$4
;X @+ #A .K +-#E ,TAKE SQU>E ROOTS (
EA* SIDE4
;X .K --#A +- #E ,SOLVE = X4
,S1 ;X .K --#A @+ #E .K #D OR ;X .K
--#A--#E .K -- .#F4 ,Y C REJECT .;X .K
--#F 2C ! SIDE L5G?S WD 2 --#AH & --#D1
& SIDE L5G?S _C 2 NEGATIVE4
,! VALUE ( ;X IS #D4 ,! CORRECT ANSW]
IS ..,B4 ,A ;,B ;,C .;,D
.,,GUID$ .,,PRACTICE = ,EXAMPLES #C1D1
& #E
,SOLVE ! EQU,N 0-PLET+ ! SQU>E4
#G4 ;X #B @+ #F .;X @+ #D .K #J
.#H4 ;X #B -- ;L#J;X @+ #H .K #J
#I4 .#B;N #B -- #D .;N -- #AD .K #J
.#AJ4 #C .;X #B @+ #AB;X--#AH .K #J
.#AA4 #F .;X 7;X @+ #H7 .K #AB
.#AB4 .#D;P7.;P -- #B7 .K #AJJ
------------------------------------#BHG
.,,V]TEX .,,=M ,RECALL F ,LESSON .#D4
#B T ! V]TEX =M (A QUADRATIC FUNC;N IS
..;Y .K A7;X--.;H7 #B @+ .;K ": @7 .;H1
.;K7 IS ! V]TEX (! FUNC;N'S GRAPH4
,6WRITE A QUADRATIC FUNC;N 9 V]TEX =M1
USE -PLET+ ! SQU>E4
,,EXAMPLE #F
,WRITE A QUADRATIC FUNC;N 9 V]TEX =M
.,WRITE .;Y .K .;X #B -- .#AJ;X @+
..#BB 9 V]TEX =M4 ,!N ID5TIFY ! .V]TEX4
.;Y .K .;X #B -- #AJ .;X @+ ..#BB
,WRITE ORIG9AL .FUNC;N4
..;Y @+ @8 .K 7.;X #B -- ;L#J;X @+
@8@7 @+ ..#BB ,PREP>E 6-PLETE ! .SQU>E4
..;Y @+ #BE .K 7.;X #B -- ;L#J;X @+
..#BE7 @+ #BB .,ADD .6.EA* .SIDE4
.;Y @+ #BE .K 7;X--#E7 #B @+ #BB
,WRITE .;X #B -- #AJ;X @+ #BE Z A
BINOMIAL SQU>$4
.;Y .K 7;X--#E7 #B -- #C ,SOLVE = Y4
,! V]TEX =M (! FUNC;N IS ;Y .K
7;X--#E7 #B -- #C4 ,! V]TEX IS 7#E1
--#C74
,,EXAMPLE #G
,F9D ! MAXIMUM VALUE (A QUADRATIC
FUNC;N
.,,BASEBALL ,! HEI<T .;Y 7IN FEET7 (A
BASEBALL .;T SECONDS AF X IS HIT IS GIV5
0? FUNC;N3
;Y .K -.#AF;T #B @+ ..#IF;T @+ .#C
,F9D ! MAXIMUM HEI<T (! BASEBALL4
,SOLU;N
,! MAXIMUM HEI<T (! BASEBALL IS !
;Y-COORD9ATE (! V]TEX (! P>ABOLA )! GIV5
EQU,N4
;Y .K --#AF;T #B @+ #IF;T@+#C .,WRITE
.ORIG9AL .FUNC;N4
.;Y .K --#AF 7;R #B -- #F .;T @7 @+ #C
,FACTOR --#AF F F/ TWO T]MS4
.;Y @+ 7-#AF7 @7@8@7 .K --#AF @7 .;T
#B -- #F .;T @+ @8@7 @+ #C ,PREP>E
6-PLETE ! SQU>E4
.;Y @+ 7-#AF77#I7 .K --#AF7;T #B --
.#F;T @+ #I7 @+ #C ,ADD 7-#AF77#I7 6EA*
SIDE4
.;Y -- #ADD .K --..#AF7 ;T -- .#C7 #B
@+ ..#C ,WRITE .;T #B -- ..#F ;T @+ #I Z
A BINOMIAL .SQU>$4
..;Y .K --#AF 7;T--.#C7 #B @+ #ADG
.,SOLVE .= .Y4
,! V]TEX IS 7#C1 #ADG71 S ! MAXIMUM
HEI<T (! BASEBALL IS #ADG FEET4
.,ANIMAT$ ,ALGEBRA AT
_+CLASSZONE.COM_:
,,AVOID ,,]RORS
,:5 Y -PLETE ! SQU>E1 2 SURE 6ADD
7--#AF77#I7 .K --#ADD 6EA* SIDE1 N J
.#I4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #F &
.#G
,WRITE ! QUADRATIC FUNC;N 9 V]TEX =M4
,!N ID5TIFY ! V]TEX4
.#AC4 .;Y .K .;X #B -- #H .;X @+ #AG
.#AD4 .;Y .K .;X #B @+ #F .;X @+ #C
#AE4 .;F7.;X7 .K .;X #B -- ..#D ;X --
.#D
.#AF4 .,,:AT .,,IF8 ,9 ,EXAMPLE #G1
SUPPOSE ! HEI<T (! BASEBALL IS GIV5 0.;Y
.K --.,I#F;T #B @+ #HJ;T @+ #B4 ,F9D !
MAXIMUM HEI<T (! BASEBALL4
------------------------------------#BHH
#D.G ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS .ON .P4
,,WS#H = ,EXS4 .#BG1.DE @1 & .#FE
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 .#B1.AB1 .#CD1.EH1 .#EI @1 &
.#FG
.K .,,MULTIPLE .,,REPRES5T,NS
,EX#.FF
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,:AT IS ! DI6];E 2T
A BINOMIAL &A TRINOMIAL8
.#B4 .,,WRIT+ .,DESCRIBE :AT -PLET+ !
SQU>E M1NS = AN EXPRES.N (! =M ;X #B @+
.BX4
,,EXAMPLE #A
ON .P4 #BHD = ,EXS4 #C-AB
,,SOLV+ ,,0,,SQU>E ,,ROOTS ,SOLVE !
EQU,N 0F9D+ SQU>E ROOTS4
.#C4 .;X #B @+ #D .;X @+ #D .K #I
.#D4 .;X #B @+ ;L#J;X @+ #BE .K #FD
.#E4 .;N #B @+ #AF;N @+ #FD .K #CF
.#F4 .;M #B -- .#B;M @+ #A .K #ADD
.#G4 .;X #B -- #BB;X @+ #ABA .K #AC
.#H4 ;X #B -- #AH;X @+ #HA .K #E
.#I4 .;T #B @+ #H .;T @+ #AF .K #DE
.#AJ4 #D .;U #B @+ #D .;U @+ #A .K #GE
.#AA4 #I .;X #B -- #AB;X @+ #D .K --#C
#AB4 .,,MULTIPLE .,,*OICE ,:AT >E !
SOLU;NS ( ;X #B -- #D .;X @+ #D .K --#A8
,A .#B+-.;I
;,B --#B+-;I
;,C --#C1-#A
;,D #A1C
,,EXAMPLE #B
ON P4 #BHE = ,EXS4 #AC-BA
,,F9D+ ;,C ,F9D ! VALUE ( .;C T MAKES
! EXPRES.N A P]FECT SQU>E TRINOMIAL4 ,!N
WRITE ! EXPRES.N Z ! SQU>E (A BINOMIAL4
#AC4 .;X #B @+ #F .;X @+ ;C
.#AD4 .;X #B @+ #AB;X @+ .;C
.#AE4 .;X #B -- #BD;X @+ .;C
.#AF4 .;X #B -- #CJ;X @+ .;C
.#AG4 .;X #B -- #B .;X @+ .;C
.#AH4 .;X #B @+ #EJ;X @+ .;C
#AI4 .;X #B @+ #G .;X @+ .;C
.#BJ4 .;X #B -- #AC;X @+ .;C
#BA4 .;X #B -- .;X @+ .;C
.,,EXAMPLES .#C & .#D ON PP#.BHE-BHF =
,EXS4 #BB-CD
,,-PLET+ ,,! ,,SQU>E ,SOLVE ! EQU,N
0-PLET+ ! SQU>E4
.#BB4 .;X #B @+ #D .;X .K .#AJ
#BC4 ;X #B @+ #H .;X .K --#A
.#BD4 ;X #B @+ #F .;X -- #C .K #J
.#BE4 .;X #B @+ #AB;X @+ ..#AH .K .#J
.#BF4 .;X #B -- #AH;X @+ ..#HF .K .#J
.#BG4 ;X #B -- #B .;X @+ #BE .K #J
.#BH4 .#B;K #B @+ .#AF;K .K --#AB
.#BI4 #C .;X #B @+ #DB;X .K --#BD
.#CJ4 #D .;X #B -- #DJ;X--#AB .K #J
.#CA4 #C .;S #B @+ #FE @+ #I .K #J
.#CB4 #G .;T #B @+ #BH;T @+ #EF .K #J
.#CC4 #F .;R #B @+ #F .;R @+ #AB .K #J
#CD4 .,,MULTIPLE .,,*OICE ,:AT >E !
SOLU;NS ( ;X #B @+ ;L#J;X @+ #H .K --#E8
,A
;,B
;,C
;,D
,,EXAMPLE #E
ON P4 #BHF = ,EXS4 #CE-CH
..,,GEOMETRY ,F9D ! VALUE .( .X4
.#CE4 ,>EA ( RECTANGLE .K #EJ
.#CF4 ,>EA ( P>ALLELOGRAM .K #DH
.#CG4 ,>EA ( TRIANGLE .K #DJ
.#CH4 ,>EA ( TRAPEZOID .K #BJ
------------------------------------#BHI
,,F9D+ ,,! ,,V]TEX ,9 ,EX]CISES #CI &
#DJ1 USE -PLET+ ! SQU>E 6F9D ! V]TEX (!
GIV5 FUNC;N'S GRAPH4 ,!N TELL :AT !
V]TEX REPRES5TS4
.#CI4 ,AT ,BUCK+HAM ,F.TA9 9 ,*ICAGO1
! WAT]'S HEI<T .;H 7IN FEET7 ABV ! MA9
NOZZLE C 2 MODEL$ 0.;H .K --.#AF;T #B @+
#H .#I4 .#F;T ": .;T IS ! "T 7IN
SECONDS7 S9CE ! WAT] HAS LEFT ! NOZZLE4
.#DJ4 ,:5 Y WALK ;X MET]S P] M9UTE1 YR
RATE ;Y ( 5]GY USE 7IN CALORIES P]
M9UTE7 C 2 MODEL$ 0.;Y .K #J.JJHE;X #B
-- #A.E;X @+ #ABJ4
,PICTURE3 .,BUCK+HAM .,F.TA9
,,EXAMPLES #F & #G
ON P4 #BHG = ,EXS4 #DA-DI
,,WRIT+ ,,9 ,,V]TEX ,,=M ,WRITE !
QUADRATIC FUNC;N 9 V]TEX =M4 ,!N ID5TIFY
! V]TEX4
#DA4 .;Y .K .;X #B -- #H .;X @+ #AI
#DB4 ;Y .K ;X #B -- #D .;X -- #A
..#DC4 ;Y .K .;X #B @+ #AB;X @+ .#CG
..#DD4 ;Y .K .;X #B @+ #BJ;X @+ .#IJ
.#DE4 .;F7.;X7 .K .;X #B -- #C .;X @+
#D
.#DF4 ;G7;X7 .K ;X #B @+ #G .;X @+ #B
.#DG4 .;Y .K .#B;X ;Z.' @+ #BD;X @+
#BE
.#DH4 .;Y .K #E .;X #B @+ ;L#J;X @+ #G
.#DI4 .;Y .K #B .;X #B -- #BH;X @+ #II
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 SOLV+ ! EQU,N4
.#EJ4
.#EA4
,,-PLET+ ,,! ,,SQU>E ,SOLVE ! EQU,N
0-PLET+ ! SQU>E4
#EB4 ;X #B @+ #I .;X @+ #BJ .K #J
#EC4 ;X #B @+ #C .;X @+ #AD .K #J
.#ED4 #G .;Q #B @+ .;L#J;Q .K .#B;Q #B
@+ #AEE
#EE4 #C .;X #B @+ ;X .K #B .;X -- #F
.#EF4 #J.A;X #B -- ;X @+ #I .K #J.B;X
.#EG4 .#J..D;V #B @+ #J.G;V2 .K
#J.C;V--#B
.#EH4 .,,OP5-.,,5D$ .,,MA? ,WRITE A
QUADRATIC EQU,N ) R1L-NUMB]
SOLU;NS T C 2 SOLV$ 0-PLET+ ! SQU>E B
N 0FACTOR+4
#EI4 .,,%ORT .,,RESPONSE ,9 ? EX]CISE1
Y W 9VE/IGATE ! GRAPHICAL E6ECT ( -PLET+
! SQU>E4
A4 ,GRAPH EA* PAIR ( FUNC;NS 9 ! SAME
COORD9ATE PLANE4
.;Y .K .;X #B @+ #B .;X
.;Y .K .;X #B @+ #D .;X
;Y .K ..;X--#F .;X
.;Y .K7.;X@+ #A7 #B
.;Y .K 7;X @+ #B7 #B
.;Y .K7.;X- #C7 #B
B4 .,-P>E ! GRAPHS ( .;Y .K .;X @+ .BX
& @4 ,:AT HAPP5S 6! GRAPH ( .;Y .K .;X
#B @+ .BX :5 Y -PLETE ! SQU>E8
#FJ4 ,,R1SON+ ,= :AT VALUE 7;S7 ( .;K
DOES H EXACTLY #A R1L SOLU;N8 #B R1L
SOLU;NS8 #B IMAG9>Y SOLU;NS8
#FA4 ,,*ALL5GE ,SOLVE ;X #B @+ .BX @+
.;C .K #J 0-PLET+ ! SQU>E4 ,YR ANSW] W 2
AN EXPRES.N = ;X 9 T]MS ( .;B & .,C4
------------------------------------#BIJ
,,PRO#M ,,SOLV+
,,EXAMPLE #G
ON P4 #BHG = ,EXS4 #FB-FE
.#FB4 .,,DRUM .,,MAJOR ,:ILE M>*+1 A
DRUM MAJOR TOSSES A BATON 96! AIR &
CAT*ES X4 ,! HEI<T .;H 7IN FEET7 (!
BATON AF .;T SECONDS C 2 MODEL$ 0.;H .K
--#AF;F #B @+ .#CB;T @+ #F4 ,F9D !
MAXIMUM HEI<T (! BATON4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#FC4 .,,VOLLEYBALL ,! HEI<T .;H 7IN
FEET7 (A VOLLEYBALL .;T SECONDS AF X IS
HIT C 2 MODEL$ 0.;H .K --.#AF;T #B @+
.#DH;T @+ #D4 ,F9D ! VOLLEYBALL'S
MAXIMUM HEI<T4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#FD4 .,,SKATEBO>D .,,REV5UE ,A
SKATEBO>D %OP SELLS AB #EJ SKATEBO>DS P]
WEEK =! PRICE ADV]TIS$4 ,= EA* 4#A
DECR1SE 9 PRICE1 AB #A M SKATEBO>D P]
WEEK IS SOLD4 ,! %OP'S REV5UE C 2 MODEL$
0.;Y .K 7#GJ--;X77#EJ @+ ;X74 ,USE V]TEX
=M 6F9D H[ ! %OP C MAXIMIZE WEEKLY
REV5UE4
..#FE4 ,,VIDEO ,,GAME .,,REV5UE ,A
/ORE SELLS AB #DJ VIDEO GAME SY/EMS EA*
MON? :5 X *>GES 4#BJJ P] SY/EM4 ,= EA*
4#AJ 9CR1SE 9 PRICE1 AB #A LESS SY/EM P]
MON? IS SOLD4 ,! /ORE'S REV5UE C 2
MODEL$ 0;Y.K 7#BJJ@+ ;L#J;X7 7#DJ--;X74
,USE V]TEX =M 6F9D H[ ! /ORE C MAXIMIZE
MON?LY REV5UE4
#FF4 .,,MULTIPLE .,,REPRES5T,NS ,! PA?
(A BALL ?R[N 0A ,S(TBALL PLAY] C 2
MODEL$ 0! FUNC;N
;Y .K --#J.JAAJ;X #B @+ .#A4 #BC .;X
@+ .#E4 #EJ
": ;X IS ! ,S(TBALL'S HORIZONTAL
POSI;N 7IN FEET7 & .;Y IS ! CORRESPOND+
HEI<T 7IN FEET74
A4 .,REWRIT+ .A .,FUNC;N ,WRITE ! GIV5
FUNC;N 9 V]TEX =M4
B4 .,MAK+ .A .,TA# ,MAKE A TA# (
VALUES =! FUNC;N4 ,9CLUDE VALUES ( .;X F
#J 6#ABJ 9 9CRE;TS ( .#AJ4
C4 .,DRAW+ .A .,GRAPH ,USE YR TA#
6GRAPH ! FUNC;N4 ,:AT IS ! MAXIMUM HEI<T
(! ,S(TBALL8 ,H[ F> DOES X TRAVEL8
#FG4 .,,EXT5D$ .,,RESPONSE ,YR S*OOL
IS A4+ A RECTANGUL> \TDOOR EAT+ SEC;N
AL;G "P (A #GJ FOOT SIDE (! S*OOL4 ,!
EAT+ SEC;N W 2 5CLOS$ 0A F;E AL;G XS
?REE OP5 SIDES4 ,! S*OOL HAS #ABJ FEET (
F5C+ & PLANS 6USE #AEJJ SQU>E FEET ( L&
=! EAT+ SEC;N4
A4 ,WRITE AN EQU,N =! >EA (! EAT+
SEC;N4
B4 ,SOLVE ! EQU,N4 .,EXPLA9 :Y Y M/
REJECT "O (! SOLU;NS4
C4 ,:AT >E ! DIM5.NS (! EAT+ SEC;N8
.K ..,,"W$-,,\ ,,SOLU;NS ONP4.,,WSI
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
------------------------------------#BIA
,,GEOMETRY ,,REVIEW
,! VOLUME ( CLAY EQUALS ! DI6];E (!
VOLUMES ( TWO CYL9D]S4
.#FH4 .,,*ALL5GE ,9 YR POTT]Y CLASS1 Y
>E GIV5 A LUMP ( CLAY )A VOLUME ( #BJJ
CUBIC C5TIMET]S & >E ASK$ 6MAKE A
CYL9DRICAL P5CIL HOLD]4 ,! P5CIL HOLD]
%D 2 #I C5TIMET]S HI< & H AN 9N] RADIUS
( #C C5TIMET]S4 ,:AT ?ICK;S .;X %D YR
P5CIL HOLD] H IF Y WANT 6USE ALL (!
CLAY8
,,MIX$ ,,REVIEW
,,PREVIEW
,PREP>E = ,LESSON #D.H 9 ,EXS4 #FI-GD4
,EVALUATE ;B #B -- #D;AC =! GIV5
VALUES (A1 ;B1 & C4 @7 P4 #AJ @7
.#FI4 A .K #B1 ;B .K #G1 ;C .K #E
.#GJ4 A .K #A1 ;B .K --#F1 ;C .K #I
.#GA4 A .K #D1 #F .K --#A1 ;C .K #C
.#GB4 A .K #C1 ;B .K #B1 ;C .K --#F
.#GC4 A .K --#D1 ;B .K #B1 ;C .K --#G
.#GD4 A .K --#E1 ;B .K #C1 ;C .K #B
,WRITE AN EQU,N (! L9E T PASSES "? !
GIV5 PO9TS4 @7 P4 #IH @7
.#GE4 7#B1 #E71 7#D1 #I7
.#GF4 7#C1 --#A71 7#F1 --#C7
.#GG4 7--#D1 --#D71 7--#A1 #B7
.#GH4 7--#B1D71 7#A1--#B7
.#GI4 7--#A1 --#E71 7#A1 #A7
.#HJ4 7#F1C71 7#H1D7
,GRAPH ! SY/EM ( 9EQUALITIES4 @7 P4
#AFH @7
.#HA4 ;X.1.K#B
.;Y "K.K #C
.#HB4 ;X.1.K#J
;X @+ ;Y"K#D
.#HC4 #C;X--#B;Y "K #H
#B;X @+ ;Y .1 #J
.#HD4 #D;X @+ ;Y .1.K#C
#B;X--#C;Y "K #F
,,QUIZ = ,LESSONS #D.E-D.G
,SOLVE ! EQU,N4
.#A4 #D;X #B .K #FD @7 P4 #BFF @7
.#B4 #C7;P-- #A7#B .K #AE @7 P4 #BFF
@7
.#C4 #AF7;M @+ #E7#B .K #H @7 P4 #BFF
@7
.#D4 --#B;Z#B .K #DBD @7 P4 #BGE @7
.#E4 ;S#B @+ #AB .K #I @7 P4 #BGE @7
.#F4 #G;X#B--#D.K --#F @7 P4 #BGE @7
,WRITE ! EXPRES.N Z A -PLEX NUMB] 9
/&>D =M4 @7 P4 #BGE @7
.#G4 7#E--#C;I7 @+ 7--#B @+ #E;I7
.#H4 7--#B @+ #I;I7--7#G @+ #H;I7
.#I4 #C;I7#G--#I;I7
.#AJ4 7#H --#C;I77--#F-- #AJ;I7
.#AA4
.#AB4
,WRITE ! QUADRATIC FUNC;N 9 V]TEX =M4
,!N ID5TIFY ! V]TEX4 @7 P4 #BHD @7
.#AC4 ;Y .K ;X #B -- #D;X @+ #I
.#AD4 ;Y .K ;X #B @+ #AD;X @+ #DE
.#AE4 ;F7;X7 .K ;X #B -- #AJ;X @+ #AG
.#AF4 ;G7;X7 .K ;X #B -- #B;X--#G
.#AG4 ;Y .K ;X #B @+ ;X @+ #A
.#AH4 ;Y .K ;X #B @+ #I;X @+ #AI
.#AI4 ,,FALL+ ,,OBJECT ,A /UD5T DROPS
A BALL F A S*OOL RO( #DE FEET ABV GR.D4
,H[ L;G IS ! BALL 9 ! AIR8 @7 P4 #BFF @7
.,,EXTRA .,,PRACTICE = ,LESSON #D.G1
P4 #AJAC
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#BIB
#D.H ,USE ! ,QUADRATIC ,=MULA &!
,4CRIM9ANT
.,2F ,Y SOLV$ QUADRATIC EQU,NS 0-PLET+
! SQU>E4
.,N[ ,Y W SOLVE QUADRATIC EQU,NS US+ !
QUADRATIC =MULA4
.,:Y8 ,S Y C MODEL ! HEI<TS ( ?R[N
OBJECTS1 Z 9 ,EXAMPLE .#E4
,KEY ,VOCABUL>Y
99 .QUADRATIC .=MULA
99 .4CRIM9ANT
,SIDEB>3
,/&>DS
.#H..J .,/UD5TS .SOLVE & GRAPH
.QUADRATIC .EQU,NS .0FACTOR+1 -PLET+ !
SQU>E1 OR ..US+ ! QUADRATIC =MULA4
,/UD5TS APPLY ^! TE*NIQUES 9 SOLV+ ^W
PRO#MS4 ,!Y AL SOLVE QUADRATIC EQU,NS 9
! -PLEX NUMB] .SY/EM @4
,9 ,LESSON .#D4 #G1 Y SOLV$ QUADRATIC
EQU,NS 0-PLET+ ! SQU>E = .EA* .EQU,N
.SEP>ATELY4 ,0-PLET+ ! SQU>E .ONCE =!
G5]AL EQU,N .AX #B @+ ..BX @+ .;C .K #J1
Y C DEVELOP A =MULA T GIVES ! SOLU;NS (
.ANY QUADRATIC EQU,N4 7,SEE ,EX]CISE #F
.#G4 @7 ,! =MULA =! SOLU;NS IS CALL$ !
.QUADRATIC .=MULA4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,! ,QUADRATIC ,=MULA
,LET .A1 .;B @1 & ;C 2 R1L NUMB]S S* T
.A @6.K #J4 ,! SOLU;NS (! QUADRATIC
EQU,N .AX #B @+ ..BX @+ .;C .K #J >E @4
,,AVOID ,,]RORS
,REMEMB] 6WRITE ! QUADRATIC EQU,N 9
/&>D =M 2F APPLY+ ! QUADRATIC =MULA4
.,,EXAMPLE .#A
,SOLVE AN EQU,N ) TWO R1L SOLU;NS
,SOLVE .;X #B @+ ..#C ;X .K .#B4
,! SOLU;NS >E & @4
.,,*ECK ,GRAPH ;Y .K .;X #B @+ .#C;X
-- #B & NOTE T ! ;X-9T]CEPTS >E AB #J.EF
& AB -- .#C..EF4
------------------------------------#BIC
,,ANO!R ,,WAY
,Y C AL USE FACTOR+ 6SOLVE ? EQU,N 2C
! LEFT SIDE FACTORS Z 7#E;X--#C7 #B4
.,,EXAMPLE .#B
,SOLVE AN EQU,N ) "O R1L SOLU;N
.,SOLVE #BE;X #B - .#AH ;X .K #AB;X --
.#I4
,! SOLU;N IS @4
.,,*ECK ,GRAPH .;Y .K #BE;X #B --
#CJ;X @+ #I & NOTE T ! ONLY ;X-9T]CEPT
IS #J.F .K @4
.,,EXAMPLE .#C
,SOLVE AN EQU,N ) IMAG9>Y SOLU;NS
.,SOLVE --.;X #B @+ .#D;X .K .#E4
,! SOLU;NS >E #B @+ .;I & #B -- .I4
.,,*ECK ,GRAPH .;Y .K --.;X #B @+
#D;X--#E4 ,"! >E NO ;X-9T]CEPTS4 ,S1 !
ORIG9AL EQU,N HAS NO R1L SOLU;NS4 ,!
ALGEBRAIC *ECK =! IMAG9>Y SOLU;N #B @+
.;I IS %[N4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #A1
#B1 & .#C
,USE ! QUADRATIC =MULA 6SOLVE ! EQU,N4
#A4 ;X #B .K #F;X--#D
.#B4 .#D;X #B -- ;L#J;X .K ..#B;X--.#I
#C4 #G;X--#E;X #B -- #D .K #B;X @+ #C
------------------------------------#BID
.,,4CRIM9ANT ,9 ! QUADRATIC =MULA1 !
EXPRES.N .;B #B -- .#D;AC IS CALL$ !
.4CRIM9ANT (! ASSOCIAT$ EQU,N .AX #B @+
..BX @+ .;C .K #J4
.,Y C USE ! 4CRIM9ANT (A QUADRATIC
EQU,N 6DET]M9E ! EQU,N'S NUMB] & TYPE (
SOLU;NS4
,,KEY ,,3CEPT .= .,YR .,NOTEBOOK
,US+ ! ,4CRIM9ANT ( .AXR @+ .BX @+ .;C
.K #J
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,VALUE .( .4CRIM9ANT @3 ;B.' #B --
#D;AC.1#J @3 ;B.' #B -- #D;AC .K #J @3
;B.' #B -- #D;AC"K#J
..,NUMB] & TYPE ( .SOLU;NS @3 ,TWO R1L
SOLU;NS3 ,"O R1L SOLU;N3 ,TWO IMAG9>Y
SOLU;NS
,GRAPH ( ;Y .K AX.' #B @+ .BX @+ .;C
@3
,TWO ;X-9T]CEPTS @3
,"O .;X -9T]CEPT @3
,NO ;X-9T]CEPT
,,EXAMPLE #D
,USE ! 4CRIM9ANT
,F9D ! 4CRIM9ANT (! QUADRATIC EQU,N &
GIVE ! NUMB] & TYPE ( SOLU;NS (! EQU,N4
.A4 .;X #B -- .#H;X @+ #AG .K #J
.B4 .;X #B -- #H;X @+ #AF .K #J
.C4 .;X #B -- .#H;X @+ #AE .K #J
,SOLU;N
.,,GUID$ .,,PRACTICE = ,EXAMPLE #D
,F9D ! 4CRIM9ANT (! QUADRATIC EQU,N &
GIVE ! NUMB] & TYPE ( SOLU;NS (! EQU,N4
.#D4 .#B;X #B @+ .#D;X -- #D .K #J
.#E4 .#C;X #B @+ .#AB;X @+ #AB .K #J
.#F4 .#H;X #B .K #I;X--#AA
.#G4 .#G;X #B -- .#B;X .K #E
.#H4 .#D;X #B @+ .#C;X @+ #AB .K #C --
.#C;X
.#I4 .#C;X--.#E;X #B @+ #A .K #F --
.#G;X
------------------------------------#BIE
.,,MODEL+ .,,LAUN*$ .,,OBJECTS ,9
,LESSON #D.E1 ! FUNC;N .;H .K --.#AF;T
#B @+ .;H #J 0 US$ 6MODEL ! HEI<T (A
.DROPP$ OBJECT4 ,= AN OBJECT T IS
.LAUN*$ .OR .?R[N @1 AN EXTRA T]M .;V #J
.;T M/ 2 A4$ 6! MODEL 6A3.T =! OBJECT'S
9ITIAL V]TICAL VELOC;Y .;V #J 7IN FEET
P] SECOND74 ,RECALL T .;H IS ! HEI<T 7IN
FEET71 .TIS ! "T 9 MO;N 7IN SECONDS71 &
.;H #J IS ! 9ITIAL HEI<T 7IN FEET74
.;H .K --.#AF;T #B @+ .;H #J .,OBJECT
.IS .DROPP$4
;H - -.#AF;T #B @+ .;V #J .;T @+ .;H
#J ..,OBJECT IS LAUN*$ OR .?R[N4
,Z %[N 2L1 ! VALUE ( .;V #J C 2
POSITIVE1 NEGATIVE1 OR Z]O DEP5D+ ON
:E!R ! OBJECT IS LAUN*$ UPW>D1 D[NW>D1
OR P>ALLEL 6! GR.D4
,,EXAMPLE #E
,SOLVE A V]TICAL MO;N PRO#M
.,,JU7L+ ,A JU7L] TOSSES A BALL 96!
AIR4 ,! BALL L1VES ! JU7L]'S H& #D FEET
ABV ! GR.D & HAS AN 9ITIAL V]TICAL
VELOC;Y ( #DJ FEET P] SECOND4 ,! JU7L]
CAT*ES ! BALL :5 X FALLS BACK 6A HEI<T (
#C FEET4 ,H[ L;G IS ! BALL 9 ! AIR8
,SOLU;N
,2C ! BALL IS ?R[N1 USE ! MODEL .;H .K
--.,I#F;T #B @+ .;V #J .;T @+ .;H #J @4
,6F9D H[ ,IONS ! BALL IS 9 ! AIR1 SOLVE
= .;T :5 .;H .K .#C4
,REJECT ! SOLU;N --#J.JBE 2C ! BALL'S
"T 9 ! AIR _C 2 NEGATIVE4 ,S1 ! BALL IS
9 ! AIR = AB .#B4 #E SECONDS4
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#E
.#AJ4 .,,:AT .,,IF8 ,9 ,EXAMPLE #E1
SUPPOSE ! BALL L1VES ! JU7L]'S H& ) AN
9ITIAL V]TICAL VELOC;Y ( #EJ FEET P]
SECOND4 ,H[ L;G IS ! BALL 9 ! AIR8
------------------------------------#BIF
#D.H ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#I = ,EXS4 .#AI1.CI @1 &
.#GA
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 .#B1.AB1.EA1.EE1 .#FB1.FI1 .#GB
@1 & .#GC
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,Y C
USE ! @8 (A QUADRATIC EQU,N 6DET]M9E !
EQU,N'S NUMB] & TYPE ( SOLU;NS4
.#B4 .,,WRIT+ .,DESCRIBE A R1L-LIFE
SITU,N 9 : Y C USE ! MODEL .;H .K
--.#AF;T #B @+ .;V ;O .;T @+ .;H ;O .B N
! MODEL .;H .K -.#AF;T #B @+ .;H #J @4
,,EXAMPLES #A1B1 &#C
ON PP4 #BIB-BIC = ,EXS4 #C-CJ
,,EQU,NS ,,9 ,,/&>D ,,=M ,USE !
QUADRATIC =MULA 6SOLVE ! EQU,N4
.#C4 .;X #B -- .#D;X -- #E .K #J
.#D4 .;X #B -- #F;X @+ #G .K #J
.#E4 .;T #B @+ .#H;T @+ #AI .K #J
.#F4 .;X #B -- #AF;X @+ #G .K #J
.#G4 #H .;W #B -- .#H;W @+ #B .K #J
.#H4 #E;P #B -- ;L#J;P @+ #BD .K #J
.#I4 .#D;X #B -- .#H;X @+ #A .K #J
.#AJ4 #F;,M #B @+ #D;W @+ #AA .K #J
.#AA4 .#C;R #B -- .#H;R -- #I .K #J
#AB4 .,,MULTIPLE .,,*OICE ,:AT >E !
-PLEX SOLU;NS (! EQU,N #B;X #B -- #AF;X
@+ #EJ .K #J8
,A #D @+ .#C;I @1 #D--#C;I
;,B #D @+ #AB;I1 #D--#AB;I
;,C #AF @+ .#C;I @1 #AF--#C;I
;,D #AF @+ #AB;I1 #AF--#AB;I
,,EQU,NS ,,N ,,9 ,,/&>D ,,=M ,USE !
QUADRATIC =MULA 6SOLVE ! EQU,N4
.#AC4 #C;W #B -- #A .#B;W .K --#AB
.#AD4 .;X #B @+ #F;X .K --#AE
.#AE4 .;S #B .K --#AD--#C;S
.#AF4 --#C;Y #B .K #F;Y--#AJ
.#AG4 #C -- .#H;V--.#E;V #B .K .#B;V
.#AH4 #G;X--#E @+ #AB;X #B .K --#C;X
.#AI4 #D;X #B @+ #C .K ;X #B -- #G;X
.#BJ4 #F -- .#B;T #B .K #I;R @+ #AE
.#BA4 #D @+ .#I;N--.#C;N #B .K .#B --
.;N
,,SOLV+ ,,US+ ,,TWO ,,ME?ODS ,SOLVE !
EQU,N US+ ! QUADRATIC =MULA4 ,!N SOLVE !
EQU,N 0FACTOR+ 6*ECK YR SOLU;N 7;S74
.#BB4 .;Z #B @+ .#AE;Z @+ #BD .K --#CB
.#BC4 ;X #B -- #E;X @+ #AJ .K #D
.#BD4 .;M #B @+ .#E;M -- #II .K #C;M
.#BE4 .;S #B -- #E--#C .K #E
.#BF4 .;R #B -- #D .;R @+ #H .K #E;R
.#BG4 #C;X #B @+ #G;X--#BD .K #AC;X
.#BH4 #DE;X #B @+ #EG;X @+ #A .K #E
.#BI4 .#E;P #B @+ .#DJ;P @+ #AJJ .K
#BE
.#CJ4 .#I;N #B -- .#DB;N -- #AFB .K
#BA;N
,,EXAMPLE #D
ON P4 #BID = ,EXS4 #CA-CI
,,US+ ,,! ,,4CRIM9ANT ,F9D ! 4CRIM9ANT
(! QUADRATIC EQU,N & GIVE ! NUMB] & TYPE
( SOLU;NS (! EQU,N4
.#CA4 ;X #B -- #H;X @+ #AF .K #J
.#CB4 ;S #B @+ #G;S @+ #AA .K #J
.#CC4 .#H;P #B @+ .#H;P @+ #C .K #J
.#CD4 -.#D;W #B @+ .;W -- #AD .K #J
.#CE4 #E;X #B @+ #BJ;X @+ #BA .K #J
.#CF4 #H;Z--#AJ .K .;Z #B -- .#G;Z @+
#C
.#CG4 .#H;N #B -- .#D;N @+ #B .K
#E;N--#AA
.#CH4 #E;X #B @+ #AF;X .K LLX--#C;X #B
.#CI4 #G;R #B -- #E .K .#B;R @+ #I;R
#B
,,SOLV+ ,,QUADRATIC ,,EQU,NS ,SOLVE !
EQU,N US+ ANY ME?OD4
.#DJ4 #AF;T #B -- #G .;T--.#AG;T -- #I
.#DA4 #G;X--#C;X #B .K #HE @+ #B;X #B
@+ #B;X
.#DB4 #D7;X--#A7 #B .K #F;X @+ #B
.#DC4 #BE--#AF .;V #B .K .#AB;V7.;V @+
#E7
.#DD4
.#DE4
.#DF4 L4L7 .#C4 #D;X -- .#B4 #C7 #B .K
#AE.E
.#DG4 .#AI4 #BE .K --#H.E7#B;R--#A.GE7
#B
.#DH4 #D.E .K #A.E7#C.BE--;S7 #B
------------------------------------#BIG
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 SOLV+ ! EQU,N4
.#DI4
.#EJ4
.#EA4 .,,%ORT .,,RESPONSE ,=A
QUADRATIC EQU,N .AX #B @+ .BX @+ .;C .K
#J ) TWO R1L SOLU;NS1 %[ T ! M1N (!
SOLU;NS IS @4 ,H[ IS ? FACT RELAT$ 6!
SYMMETRY (! GRAPH ( .;Y .K .AX #B @+ .BX
@+ ;C8
..,,VISUAL ,,?9K+ ,9 .,EX]CISES
#EB-ED1 ..! GRAPH (A QUADRATIC FUNC;N ;Y
.K .AX #B @+ ..BX @+ ;C IS %[N4 ,TELL
:E!R ! 4CRIM9ANT ( .AX #B @+ ..BX @+ ;C
.K #J IS POSITIVE1 NEGATIVE @1 .OR .Z]O4
.#EB4
.#EC4
.#ED4
#EE4 .,,MULTIPLE .,,*OICE ,:AT IS !
VALUE ( .;C IF ! 4CRIM9ANT ( .#B;X #B @+
#E;X @+ .;C .K #J IS --#BC8
,A --#BC
;,B --#F
;,C #F
;,D #AD
,,! ,,3/ANT ,,T]M ,USE ! 4CRIM9ANT
6F9D ALL VALUES ( .;C = : ! EQU,N HAS ,A
TWO R1L SOLU;NS1 ;,B "O R1L SOLU;N1 &
;,C TWO IMAG9>Y SOLU;NS4
.#EF4 .;X #B -- #D;X @+ .;C .K #J
.#EG4 .;X #B @+ #H;X @+ .;C .K #J
.#EH4 -.;X #B @+ #AF;X @+ .;C .K #J
.#EI4 #C;X #B @+ #BD;X @+ .;C .K #J
.#FJ4 --#D;X #B -- ;L#J;X @+ .;C .K #J
.#FA4 ;X #B -- ;X @+ .;C .K #J
.#FB4 .,,OP5-.,,5D$ ,,MA? ,WRITE A
QUADRATIC EQU,N 9 /&>D =M T HAS A
4CRIM9ANT ( -- .#AJ4
,,WRIT+ ,,EQU,NS ,WRITE A QUADRATIC
EQU,N 9 ! =M .AX #B @+ .BX @+ .;C .K #J
S* T ;C .K #D &! EQU,N HAS ! GIV5
SOLU;NS4
.#FC4 --#D & #C
.#FD4 & --#A
.#FE4 --#A @+ .;I & --#A -- .;I
.#FF4 .,,R1SON+ ,%[ T "! IS NO
QUADRATIC EQU,N .AX #B @+ .BX @+ .;C .K
#J S* T A1 ;B1 & .;C >E R1L NUMB]S &
#C;I & -.#B;I >E SOLU;NS4
.#FG4 .,,*ALL5GE ,DERIVE ! QUADRATIC
=MULA 0-PLET+ ! SQU>E 6SOLVE ! G5]AL
QUADRATIC EQU,N .AX #B @+ .BX @+ .;C .K
#J4
------------------------------------#BIH
,,PRO#M ,,SOLV+
,,EXAMPLE #E
ON P4 #BIE = ,EXS4 #FH-FI
.#FH4 .,,FOOTBALL ,9 A FOOTBALL GAME1
A DEF5SIVE PLAY] JUMPS UP 6BLOCK A PASS
0! OPPOS+ T1M'S QU>T]BACK4 ,! PLAY] BATS
! BALL D[NW>D ) 8 H& AT AN 9ITIAL
V]TICAL VELOC;Y ( --#EJ FEET P] SECOND
:5 ! BALL IS #G FEET ABV ! GR.D4 ,H[ L;G
D ! DEF5SIVE PLAY]'S T1MMATES H 69T]CEPT
! BALL 2F X HITS ! GR.D8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#FI4 .,,MULTIPLE .,,*OICE ,=! P]IOD
#AIIJ-BJJB1 ! NUMB] .;,S 7IN ?\S&S7 (
CELLUL> TELEPH"O SUBSCRIB]S 9 ! ,UNIT$
,/ATES C 2 MODEL$ 0.;,S .K .#HEH;T #B @+
.#ADAB;T @+ #DIHB ": .TIS ! NUMB] ( YE>S
S9CE #AIIJ4 ,9 :AT YE> DID ! NUMB] (
SUBSCRIB]S R1* #EJ MILLION8
,A #AIIA
;,B #AIIB
;,C #AIIF
;,D #BJJJ
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#GJ4 .,,MULTI-.,,/EP .,,PRO#M ,A /UNT
MOTORCYCLI/ MAKES A JUMP F "O RAMP #BJ
FEET (F ! GR.D 6ANO!R RAMP #BJ FEET (F !
GR.D4 ,! JUMP 2T ! RAMPS C 2 MODEL$ 0":
.;X IS ! HORIZONTAL 4T.E 7IN FEET7 & .;Y
IS ! HEI<T ABV ! GR.D 7IN FEET74
A4 ,:AT IS ! MOTORCYCLE'S HEI<T .;R :5
X L&S ON ! RAMP8
B4 ,:AT IS ! 4T.E .;D 2T ! RAMPS8
C4 ,:AT IS ! HORIZONTAL 4T.E .;H !
MOTORCYCLE HAS TRAVEL$ :5 X R1*ES XS
MAXIMUM HEI<T8
D4 ,:AT IS ! MOTORCYCLE'S MAXIMUM
HEI<T .;K ABV ! GR.D8
.#GA .,,BIOLOGY ,! NUMB] .;,S ( ANT
SPECIES 9 ,KYLE ,CANYON1 ,NEVADA1 C 2
MODEL$ 0! FUNC;N ;,S .K --#J.JJJJAC;,E
#B @+ #J.JDB;,E--#BA ": .;,E IS ! ELEV,N
7IN MET]S74 ,PREDICT ! ELEV,N7;S7 AT : Y
WD EXPECT 6F9D #AJ SPECIES ( ANTS4
#GB4 .,,%ORT .,,RESPONSE ,A C;Y PLANN]
WANTS 6CR1TE ADJAC5T SEC;NS = A?LETICS &
PICNICS 9 ! Y>D (A Y\? C5T]4 ,! SEC;NS W
2 RECTANGUL> & W 2 SURR.D$ 0F5C+ Z %[N4
,"! IS #IJJ FEET ( F5C+ AVAILA#4 ,EA*
SEC;N %D H AN >EA ( #AB1JJJ SQU>E FEET4
A4 ,%[ T @4
B4 ,F9D ! POSSI# DIM5.NS ( EA* SEC;N4
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#BII
#GC4 .,,EXT5D$ .,,RESPONSE ,Y C MODEL
! POSI;N 7;X1 .;Y7 (A MOV+ OBJECT US+ A
PAIR ( .P>AMETRIC .EQU,NS4 ,S* EQU,NS
GIVE ;X & @' .;Y 9 T]MS (A ?IRD V>IA#
.;T T REPRES5TS "T4 ,= EXAMPLE1 SUPPOSE
T :5 A BASKETBALL PLAY] ATTEMPTS A FREE
?R[1 ! PA? (! BASKETBALL C 2 MODEL$ 0!
P>AMETRIC EQU,NS
.;X .K #BJ;T
.;Y .K --#AF;T #B @+ #BA .;T @+ #F
": ;X & ;Y >E M1SUR$ 9 FEET1 .;T IS
M1SUR$ 9 SECONDS1 &! PLAY]'S FEET >E AT
7#J1J74
A4 .,EVALUATE ,MAKE A TA# ( VALUES
GIV+ ! POSI;N 7;X1 .;Y7 (! BASKETBALL AF
#J1 #J.BE1 #J.E1 #J.GE1 & #A SECOND4
B4 .,GRAPH ,USE YR TA# F "P .,A 6GRAPH
! P>AMETRIC EQU,NS4
C4 .,SOLVE ,! POSI;N (! BASKETBALL RIM
IS 7#AE1 #AJ74 ,! TOP (! BACKBO>D IS
7#AE1 #AB74 ,DOES ! PLAY] MAKE ! FREE
?R[8 .,EXPLA94
#GD4 .,,*ALL5GE ,! ,/RATOSPH]E ,T[] 9
,LAS ,VEGAS IS #IBA FEET TALL & HAS A
8NE$LE0 AT XS TOP T EXT5DS EV5 HI<] 96!
AIR4 ,A ?RILL RIDE CALL$ ! ,BIG ,%OT
CATAPULTS RID]S #AFJ FEET UP ! NE$LE &
!N LETS !M FALL BACK 6! LAUN*+ PAD4
A4 ,! HEI<T .;H 7IN FEET7 (A RID] ON !
,BIG ,%OT C 2 MODEL$ 0.;H .K --.,I#F;T
#B @+ .;V #J .;T @+ #IBA ": .TIS !
ELAPS$ "T 7IN SECONDS7 AF LAUN* & .;V #J
IS ! 9ITIAL V]TICAL VELOC;Y 7IN FEET P]
SECOND74 ,F9D .;V #J US+ ! FACT T !
MAXIMUM VALUE ( .;H IS #IBA @+ #AFJ .K
#AJHA FEET4
B4 ,A BRO*URE =! ,BIG ,%OT /ATES T !
RIDE UP ! NE$LE TAKES TWO SECONDS4
.,-P>E ? "T )! "T GIV5 0! MODEL .;H .K
-.#AF;T #B @+ .;V ;O .;T @+ #IBA ": .;V
#J IS ! VALUE Y F.D 9 "P .,A @4 ,4CUSS !
MODEL'S A3URACY4
,,MIX$ ,,REVIEW
,,PREVIEW
,PREP>E = ,LESSON #D.I 9 ,EXS4 #HA-HF4
,F9D ! SLOPE (! L9E PASS+ "? ! GIV5
PO9TS4 ,!N TELL :E!R ! L9E RISES1 FALLS1
IS HORIZONTAL1 OR IS V]TICAL4 @7 P4 #HB
@7
.#GE4 7#B1 --#G71 7#D1 #I7
.#GF4 7--#H1C71 7#D1--#E7
.#GG4 7--#C1 --#B71 7#F1 --#B7
.#GH4
.#GI4 7--#A1 #J71 7--#A1 #E7
.#HJ4
,GRAPH ! 9EQUAL;Y OR EQU,N 9 A
COORD9ATE PLANE4
.#HA4 .;Y "K.K #AJ @7 P4 #ACB @7
.#HB4 #H .;X -- #D .;Y "K --#AF @7 P4
#ACB @7
.#HC4
.#HD4
.#HE4 .;Y .K #C7 .;X @+ #A7@7 .;X @+
#B7 7P#.BDE7
.#HF4 .;Y .K --#B7 .;X -- #C7@7 .;X --
#A7 @7 P4 #BDE @7
.#HG4 ,,HANG-,,GLID+ ,SUPPOSE T ;T
M9UTES AF 2G9N+ A DESC5T1 A HANG GLID]
HAS AN ALTITUDE A 7IN FEET7 GIV5 0!
MODEL A .K #BJJJ--#BEJT4 ,:AT IS ! HEI<T
(! HANG GLID] PRIOR 6! DESC5T8 ,H[ L;G
DOES X TAKE ! HANG GLID] 6R1* ! GR.D8 @7
P4 #GB @7
.,,EXTRA .,,PRACTICE = ,LESSON #D.H1
P4 #AJAC
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#CJJ
#D.I ,GRAPH & ,SOLVE ,QUADRATIC
,9EQUALITIES
.,2F ,Y GRAPH$ & SOLV$ L9E>
9EQUALITIES4
.,N[ ,Y W GRAPH & SOLVE QUADRATIC
9EQUALITIES4
.,:Y8 ,S Y C MODEL ! /R5G? (A ROPE1 Z
9 ,EXAMPLE #B4
,KEY ,VOCABUL>Y
99 QUADRATIC 9EQUAL;Y 9 TWO V>IA#S
99 QUADRATIC 9EQUAL;Y 9 "O V>IA#
,SIDEB>3
,/&>DS
.,5RI*;T .( .#H..J ..,/UD5TS SOLVE &
GRAPH QUADRATIC .EQU,NS 0FACTOR+1 -PLET+
! SQU>E1 OR US+ ! QUADRATIC =MULA4
,/UD5TS APPLY ^! TE*NIQUES 9 SOLV+ ^W
PRO#MS4 ,!Y AL SOLVE QUADRATIC EQU,NS 9
! -PLEX NUMB] SY/EM4
,A ..QUADRATIC 9EQUAL;Y 9 TWO .V>IA#S
C 2 WRITT5 9 "O (! FOLL[+ =MS3
.;Y "K .AX #B @+ .BX @+ .;C
.;Y "K.K .AX #B @+ .BX @+ .;C
.;Y .1 .AX #B @+ .BX @+ .;C
.;Y .1.K .AX #B @+ .BX @+ .;C
,! GRAPH ( ANY S* 9EQUAL;Y 3SI/S ( ALL
SOLU;NS @7 .;X1 .;Y @7 (! 9EQUAL;Y4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,GRAPH+ A ,QUADRATIC ,9EQUAL;Y 9 ,TWO
,V>IA#S
,6GRAPH A QUADRATIC 9EQUAL;Y 9 "O (!
=MS ABV1 FOLL[ ^! /EPS3
.,,/EP .#A ,GRAPH ! P>ABOLA ) EQU,N
.;Y .K .AX #B @+ .BX @+ .;C @4 ,MAKE !
P>ABOLA .DA%$ = 9EQUALITIES ) "K OR .1 &
.SOLID = 9EQUALITIES ) "K.K OR .1.K.
.,,/EP .#B ,TE/ A PO9T @7 .;X1 .;Y @7
9SIDE ! P>ABOLA 6DET]M9E :E!R ! PO9T IS
A SOLU;N (! 9EQUAL;Y4
.,,/EP .#C ,%ADE ! REGION 9SIDE !
P>ABOLA IF ! PO9T F ,/EP #B IS A SOLU;N4
,%ADE ! REGION \TSIDE ! P>ABOLA IF X IS
N A SOLU;N4
,,EXAMPLE #A
,GRAPH A QUADRATIC 9EQUAL;Y
,GRAPH .;Y .1 .;X #B @+ #C .;X -- #D4
,,AVOID ,,]RORS
,2 SURE 6USE A DA%$ P>ABOLA IF !
SYMBOL IS .1 OR "K &A SOLID P>ABOLA IF !
SYMBOL IS .1.K OR "K.K.
,SOLU;N
.,,/EP .#A ,GRAPH .;Y .K .;X #B @+ #C
.;X -- #D4 ,2C ! 9EQUAL;Y SYMBOL IS .1,
MAKE ! P>ABOLA DA%$4
.,,/EP .#B ,TE/ A PO9T 9SIDE !
P>ABOLA1 S* Z 7#J1 #J74
.;Y .1 .;X #B @+ #C .;X -- #D
#J .1 @8 #J #B @+ #C7#J7--#D
#J .1 --#D
,S1 7#J1 #J7 IS A SOLU;N (! 9EQUAL;Y4
.,,/EP .#C .,%ADE ! REGION 9SIDE !
P>ABOL
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
------------------------------------#CJA
,,EXAMPLE #B
,USE A QUADRATIC 9EQUAL;Y 9 R1L LIFE
.,,RAPPELL+ ,A MANILA ROPE US$ =
RAPPELL+ D[N A CLIFF C SAFELY SUPPORT A
WEI<T .;,W 7IN P.DS7 PROVID$
.;,W "K.K #ADHJ .;D #B
": .;D IS ! ROPE'S DIAMET] 7IN 9*ES74
,GRAPH ! 9EQUAL;Y4
,SOLU;N
,GRAPH .;,W .K #ADHJ .;D #B =
NONNEGATIVE VALUES ( .;D @4 ,2C !
9EQUAL;Y SYMBOL IS "K.K, MAKE ! P>ABOLA
SOLID4 ,TE/ A PO9T 9SIDE ! P>ABOLA1 S* Z
7#A1 #BJJJ74
.;,W "K.K #ADHJ .;D #B
.#BJJJ "K.K @8 #ADHJ7 .#A @7 #B
#BJJJ "K.K #ADHJ
,2C 7#A1 #BJJJ7 IS N A SOLU;N1 %ADE !
REGION 2L ! P>ABOLA4
..,,SY/EMS ,,( ,,QUADRATIC
.,,9EQUALITIES ,GRAPH+ A .SY/EM (
QUADRATIC 9EQUALITIES IS SIMIL> 6GRAPH+
A SY/EM ( L9E> 9EQUALITIES4 ,F/ GRAPH
EA* 9EQUAL;Y 9 ! SY/EM4 ,!N ID5TIFY !
REGION 9 ! COORD9ATE PLANE -MON 6ALL (!
GRAPHS4 ,? REGION IS CALL$ ! ..GRAPH (!
.SY/EM4
,,EXAMPLE #C
,GRAPH A SY/EM ( QUADRATIC 9EQUALITIES
.,GRAPH .! SY/EM .( .QUADRATIC
.9EQUALITIES4
.;Y "K --.;X #B @+ #D .,9EQUAL;Y .#A
.;Y .1 .;X #B -- #B .;X -- #C
.,9EQUAL;Y .#B
,SOLU;N
..,,/EP #A ,GRAPH .;Y "K.K -- .;X #B
@+ #D4 ,! GRAPH IS ! R$ REGION 9SIDE &
9CLUD+ ! P>ABOLA .;Y .K --.;X #B @+ #D4
.,,/EP .#B .,GRAPH .;Y .1 .;X #B -- #B
.;X -- #C4 ,! GRAPH IS ! BLUE REGION
9SIDE 7B N 9CLUD+7 ! P>ABOLA .;Y .K .;X
#B -- #B .;X -- #C4
.,,/EP .#C .,ID5TIFY ! .PURPLE .REGION
": ! TWO GRAPHS OV]LAP4 ,? REGION IS !
GRAPH (! SY/EM4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #A1
#B1 & .#C
,GRAPH ! 9EQUAL;Y4
.#A4 .;Y .1 .;X #B @+ #B .;X -- #H
.#B4 .;Y "K.K #B .;X #B --#C .;X @+ #A
.#C4 .;Y "K -- .;X #B @+ #D .;X @+ #B
.#D4 ,GRAPH ! SY/EM ( 9EQUALITIES
3SI/+ ( .;Y .1.K .;X #B & .;Y "K --.;X
#B @+ #E4
------------------------------------#CJB
.,,"O-.,,V>IA# .,,9EQUALITIES ,A
..QUADRATIC 9EQUAL;Y 9 "O .V>IA# C 2
WRITT5 9 "O (! FOLL[+ =MS3
.AX #B @+ .BX @+ .;C "K #J
.AX #B @+ .BX @+ .;C "K.K #J
.AX #B @+ .BX @+ .;C .1 #J
.AX #B @+ .BX @+ .;C .1.K #J
,Y C SOLVE QUADRATIC 9EQUALITIES US+
TA#S1 GRAPHS1 OR ALGEBRAIC ME?ODS4
,,EXAMPLE #D
,SOLVE A QUADRATIC 9EQUAL;Y US+ A TA#
,SOLVE .;X #B @+ .;X "K.K #F US+ A
TA#4
,SOLU;N
,REWRITE ! 9EQUAL;Y Z .;X #B @+ .;X --
#F "K.K #J4 ,!N MAKE A TA# ( VALUES4
,,MAKE ,A ,,TA#
,6GIVE ! EXACT SOLU;N1 YR TA# NE$S
69CLUDE ! .;X -VALUES = : ! VALUE (!
QUADRATIC EXPRES.N IS #J4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 -.#E @3 -.#D @3 -.#C @3 -.#B @3
-.#A @3 .#J @3 .#A @3 .#B @3 .#C @3 .#D
.;X #B @+ .;X - #F @3 .#AD @3 .#F @3
.#J @3 -.#D @3 -.#F @3 -.#F @3 -.#D @3
.#J @3 .#F @3 .#AD
,NOTICE T .;X #B @+ .;X -- #F "K.K #J
:5 ! VALUES ( .;X >E 2T --#C & #B1
9CLUSIVE4
99 ,! SOLU;N (! 9EQUAL;Y IS --#C "K.K
.;X "K.K #B4
..,,GRAPH+ ,,6,,SOLVE .,,9EQUALITIES
,ANO!R WAY 6SOLVE .AX #B @+ .BX @+ .;C
"K #J IS 6F/ GRAPH ! RELAT$ FUNC;N .;Y
.K .AX #B @+ .BX @+ .;C @4 ,!N1 2C !
9EQUAL;Y SYMBOL IS "K, ID5TIFY ! .;X
-VALUES = : ! GRAPH LIES .2L ! .;X
-AXIS4 ,Y C USE A SIMIL> PROC$URE 6SOLVE
QUADRATIC 9EQUALITIES T 9VOLVE "K.K, .1,
OR .1.K.
,,EXAMPLE #E
,SOLVE A QUADRATIC 9EQUAL;Y 0GRAPH+
,SOLVE #B .;X #B @+ .;X -- #D .1.K #J
0GRAPH+4
,SOLU;N
,! SOLU;N 3SI/S (! .;X -VALUES = : !
GRAPH ( .;Y .K #B .;X #B @+ .;X -- #D
LIES ON OR ABV ! .;X -AXIS4 ,F9D !
GRAPH'S .;X -9T]CEPTS 0LETT+ .;Y .K #J &
US+ ! QUADRATIC =MULA 6SOLVE = .;X @4
,SKET* A P>ABOLA T OP5S UP & HAS .#A4
#AI & -- .#A4 #FI Z .;X -9T]CEPTS4 ,!
GRAPH LIES ON OR ABV ! .;X -AXIS 6! LEFT
( 7& 9CLUD+7 .;X .K -- .#A4 #FI & 6! "R
( 7& 9CLUD+7 .;X .K .#A..AI4
,! SOLU;N (! 9EQUAL;Y IS APPROXIMATELY
.;X "K.K --#A.FI OR .;X .1.K #A.AI4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #D &
.#E
.#E4 ,SOLVE ! 9EQUAL;Y #B .;X #B @+ #B
.;X "K.K #C US+ A TA# & US+ A GRAPH4
------------------------------------#CJC
,,EXAMPLE #F
,USE A QUADRATIC 9EQUAL;Y Z A MODEL
.,,ROBOTICS ,! NUMB] .;,T ( T1MS T H
"PICIPAT$ 9 A ROBOT-BUILD+ -PETI;N = HI<
S*OOL /UD5TS C 2 MODEL$ BY
.;,T @7 .;X @7 .K #G.EA .;X #B --
#AF.D .;X @+ #CE.J1 #J "K.K .;X "K.K #I
": .;X IS ! NUMB] ( YE>S S9CE #AII
.#B4 ,= :AT YE>S 0 ! NUMB] ( T1MS GRT]
?AN #AJJ8
,SOLU;N
,Y WANT 6F9D ! VALUES ( .;X = :3
.;,T7.;X7 .1 #AJJ
#G.EA .;X #B -- #AF.D .;X @+ #CE.J .1
#AJJ
#G.EA .;X #B -- #AF.D .;X -- #FE .1 #J
,GRAPH .;Y .K #G.EA .;X #B -- #AF.D
.;X -- #FE ON ! DOMA9 #J "K.K .;X "K.K
#I4 ,! GRAPH'S .;X -9T]CEPT IS AB
.#D..B4 ,! GRAPH LIES ABV ! .;X -AXIS :5
#D.B "K .;X "K.K .#I4
,"! 7 M ?AN #AJJ T1MS "PICIPAT+ 9 !
YE>S #AIIG-BJJA4
,,EXAMPLE #G
,SOLVE A QUADRATIC 9EQUAL;Y
ALGEBRAIC,Y
,SOLVE .;X #B -- #B .;X .1 #AE
ALGEBRAIC,Y4
,SOLU;N
,F/1 WRITE & SOLVE ! EQU,N OBTA9$
0REPLAC+ .1 ) .K.
.;X #B -- #B .;X .K #AE ..,WRITE EQU,N
T CORRESPONDS 6ORIG9AL .9EQUAL;Y4
;X #B -- #B .;X -- #AE .K #J ..,WRITE
9 /&>D .=M4
@7 .;X @+ #C7@7 .;X -- #E7 .K #J
.,FACTOR4
.;X .K --#C OR .;X .K #E .,Z]O
.PRODUCT .PROP]TY
,! NUMB]S --#C & #E >E ! .CRITICAL .;X
-.VALUES (! 9EQUAL;Y .;X #B -- #B .;X .1
#AE4 ,PLOT --#C & #E ON A NUMB] L9E1 US+
OP5 DOTS 2C ! VALUES D N SATISFY !
9EQUAL;Y4 ,! CRITICAL .;X -VALUES "PI;N
! NUMB] L9E 96?REE 9T]VALS4 ,TE/ AN .;X
-VALUE 9 EA* 9T]VAL 6SEE IF X SATISFIES
! 9EQUAL;Y4
,! SOLU;N IS .;X "K --#C OR .;X .1
.#E4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #F &
.#G
.#F4 .,,ROBOTICS ,USE ! 9=M,N 9
,EXAMPLE #F 6DET]M9E 9 :AT YE>S AT L1/
#BJJ T1MS "PICIPAT$ 9 ! ROBOT-BUILD+
-PETI;N4
.#G4 ,SOLVE ! 9EQUAL;Y #B .;X #B -- #G
.;X .1 #D ALGEBRAIC,Y4
------------------------------------#CJD
#D.I ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#I = ,EXS4 #AG1 #CI1 & #GC
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 #B1 #DD1 #DE1 #FH1 & #GC
.K .,,MULTIPLE .,,REPRES5T,NS
,EX4 #GD
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,GIVE AN EXAMPLE (A
QUADRATIC 9EQUAL;Y 9 "O V>IA# & AN
EXAMPLE (A QUADRATIC 9EQUAL;Y 9 TWO
V>IA#S4
.#B4 .,,WRIT+ .,EXPLA9 H[ 6SOLVE .;X
#B @+ #F .;X -- #H "K #J US+ A TA#1
0GRAPH+1 & ALGEBRAIC,Y4
,,EXAMPLE #A
ON P4 #CJJ = ,EXS4 #C-AI
..,,MAT*+ ,,9EQUALITIES ,,) .,,GRAPHS
,MAT* ! 9EQUAL;Y ) XS GRAPH4
.#C4 .;Y "K.K .;X #B @+ ..#D .;X @+ #C
.#D4 .;Y .1 --.;X #B @+ #D .;X -- #C
#E4 .;Y "K .;X #B -- #D .;X @+ #C
,A4
,B4
,C4
.,,GRAPH+ .,,QUADRATIC .,,9EQUALITIES
,GRAPH ! 9EQUAL;Y4
.#F4 .;Y "K --.;X #B
.#G4 .;Y .1.K #D .;X #B
.#H4 .;Y .1 .;X #B -- #I
.#I4 .;Y "K .;X #B @+ #E .;X
.#AJ4 .;Y "K ;X #B @+ #D .;X -- #E
.#AA4 .;Y .1 ;X #B @+ #G .;X @+ #AB
.#AB4 .;Y "K --.;X #B @+ #C .;X @+ #AJ
#AC4 ..;Y .1.K #B .;X #B @+ ..#E ;X
-.#G
#AD4 ..;Y .1 --#B .;X #B
.#AE4 .;Y "K #D .;X #B -#C .;X - #E
.#AF4 .;Y .1 #J.A .;X #B -;X @+ #A.B
.#AG4
.,,]ROR .,,ANALYSIS ,DESCRIBE &
CORRECT ! ]ROR 9 GRAPH+ .;Y .1.K .;X #B
@+ #B4
.#AH4
.#AI4
.,,GRAPH+ .,,SY/EMS ,GRAPH ! SY/EM (
9EQUALITIES4
,,EXAMPLE #C
ON P4 #CJA = ,EXS4 #BJ-BE
.#BJ4 .;Y .1.K #B .;X #B
.;Y "K --;X #B @+ #A
.#BA4 .;Y .1 --#E .;X #B
.;Y .1 #C .;X #B -- #B
.#BB4 .;Y .1.K .;X #B -- #D
.;Y "K.K --#B .;X #B @+ #G .;X @+ #D
.#BC4 .;Y "K.K --;X #B @+ #D .;X -- #D
.;Y "K #B .;X #B @+ .;X -- #H
.#BD4 .;Y .1 #C .;X #B @+ #C .;X -- #E
.;Y "K --;X #B @+ #E .;X @+ #AJ
.#BE4 .;Y .1.K .;X #B -- #C .;X -- #F
.;Y .1.K #B .;X #B @+ #G .;X @+ #F
..,,SOLV+ ,,US+ ,A .,,TA# ,SOLVE !
9EQUAL;Y US+ A TA#4
,,EXAMPLE #D
ON P4 #CJB = ,EXS4 #BF-CD
.#BF4 .;X #B -- #E .;X "K #J
.#BG4 .;X #B @+ #B .;X -- #C .1 #J
.#BH4 .;X #B @+ #C .;X "K.K #AJ
.#BI4 .;X #B -- #B .;X .1.K #H
.#CJ4 -- .;X #B @+ #AE .;X -- #EJ .1
#J
.#CA4 .;X #B -- #AJ .;X "K --#AF
.#CB4 .;X #B -- #D .;X .1 #AB
.#CC4 #C .;X #B -- #F .;X -- #B "K.K
#G
.#CD4 #B .;X #B -- #F .;X -- #I .1.K
#AA
------------------------------------#CJE
,,EXAMPLE #E
ON P4 #CJB = ,EXS4 #CE-DC
.,,SOLV+ .,,0.,,GRAPH+ ,SOLVE !
9EQUAL;Y 0GRAPH+4
.#CE4 .;X #B -- #F .;X "K #J
.#CF4 .;X #B @+ #H .;X "K.K --#G
.#CG4 .;X #B -- #D .;X @+ #B .1 #J
.#CH4 .;X #B @+ #F .;X @+ #C .1 #J
.#CI4 #C .;X #B @+ #B .;X -- #H "K #J
.#DJ4 #C .;X #B @+ #E .;X -- #C "K #A
.#DA4 --#F .;X #B @+ #AI .;X .1.K #AJ
.#DB4
.#DC4 #D .;X #B -- #AJ .;X -- #G "K
#AJ
#DD4 .,,MULTIPLE .,,*OICE ,:AT IS !
SOLU;N ( #C .;X #B -- .;X -- #D .1 #J8
,A
;,B
;,C
;,D
#DE4 .,,MULTIPLE .,,*OICE ,:AT IS !
SOLU;N ( #B .;X #B @+ #I .;X "K #EF8
,A .;X "K.K --#H OR .;X .1.K #C.E
;,B --#H "K.K .;X "K.K #C.E
,C4 .;X "K.K #J OR .;X .1.K #D.E
,D4 #J "K.K .;X "K.K #D.E
,,EXAMPLE #G
ON P4 #CJC = ,EXS4 #DF-EG
.,,SOLV+ .,,ALGEBRAIC,Y ,SOLVE !
9EQUAL;Y ALGEBRAIC,Y4
.#DF4 #D .;X #B "K #BE
.#DG4 .;X #B @+ #AJ .;X @+ #I "K #J
.#DH4 .;X #B -- #AA .;X .1.K --#BH
.#DI4 #C .;X #B -- #AC .;X .1 #AJ
.#EJ4 #B .;X #B -- #E .;X -- #C "K.K
#J
.#EA4 #D .;X #B @+ #H .;X -- #BA .1.K
#J
.#EB4 --#D .;X #B -- .;X @+ #C "K.K #J
.#EC4 #E .;X #B -- #F .;X -- #B "K.K
#J
.#ED4 --#C .;X #B @+ #AJ .;X .1 --#B
.#EE4 --#B .;X #B -- #G .;X .1.K #D
.#EF4 #C .;X #B @+ #A "K #AE .;X
.#EG4 #F .;X #B -- #E .1 #H .;X
#EH4 .,,GRAPH+ .,,CALCULATOR ,9 ?
EX]CISE1 Y W USE A DI6]5T GRAPHICAL
ME?OD 6SOLVE ,EXAMPLE #F ON PAGE #CJC @4
A4 ,5T] ! EQU,NS .;Y .K #G.EA .;X #B
-- #AF.D .;X @+ #CE.J & .;Y .K #AJJ 96A
GRAPH+ CALCULATOR4
B4 ,GRAPH ! EQU,NS F "P .,A = #J "K.K
.;X "K.K #I & #J "K.K .;Y "K.K #CJJ4
C4 ,USE ! .9T]SECT F1TURE 6F9D ! PO9T
": ! GRAPHS 9T]SECT4
D4 ,DUR+ :AT YE>S 0 ! NUMB] (
"PICIPAT+ T1MS GRT] ?AN #AJJ8 .,EXPLA9
YR R1SON+4
.,,*OOS+ .,A .,,ME?OD ,SOLVE !
9EQUAL;Y US+ ANY ME?OD4
.#EI4 #H .;X #B -- #C .;X @+ #A "K #AJ
.#FJ4 #D .;X #B @+ #AA .;X @+ #C .1.K
--#C
.#FA4 --;X #B -- #B .;X -- #A .1 #B
.#FB4 --#C .;X #B @+ #D .;X -- #E "K.K
#B
.#FC4 .;X #B -- #G .;X @+ #D .1 #E .;X
-- #B
.#FD4 #B .;X #B @+ #I .;X -- #A .1.K
--#C .;X @+ #A
.#FE4 #C .;X #B -- #B .;X @+ #A "K.K
--;X #B @+ #A
.#FF4 #E .;X #B @+ .;X -- #G "K #C .;X
#B -- #D .;X
.#FG4 #F .;X #B -- #E .;X @+ #B "K
--#C .;X #B @+ ;X
.#FH4 .,,OP5-.,,5D$ .,,MA? ,WRITE A
QUADRATIC 9EQUAL;Y 9 "O V>IA# T HAS A
SOLU;N ( .;X "K --#B OR .;X .1 .#E4
#FI4 .,,*ALL5GE ,! >EA ,A(! REGION
B.D$ 0A P>ABOLA &A HORIZONTAL L9E IS
GIV5 0": .;B & .;H >E Z DEF9$ 9 !
DIAGRAM4 ,F9D ! >EA (! REGION DET]M9$
0EA* PAIR ( 9EQUALITIES4
A4
B4
------------------------------------#CJF
,,PRO#M ,,SOLV+
,,EXAMPLE #B
ON P4 #CJA = ,EXS4 #GJ-GA
.#GJ4 .,,5G9E]+ ,A WIRE ROPE C SAFELY
SUPPORT A WEI<T .;,W 7IN P.DS7 PROVID$
.;,W "K.K #HJJJ .;D #B ": .;D IS !
ROPE'S DIAMET] 7IN 9*ES74 ,GRAPH !
9EQUAL;Y4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#GA4 .,,WOOD"W+ ,A H>DWOOD %ELF 9 A
WOOD5 BOOKCASE C SAFELY SUPPORT A WEI<T
.;,W 7IN P.DS7 PROVID$ .;,W "K.K #AAE
.;X #B ": .;X IS ! %ELF'S ?ICK;S 7IN
9*ES74 ,GRAPH ! 9EQUAL;Y4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
,,EXAMPLE #F
ON P4 #CJC = ,EXS4 #GB-GD
.#GB4 .,,>*ITECTURE ,! >* (! ,SYDNEY
,H>BOR ,BRIDGE 9 ,SYDNEY1 ,AU/RALIA1 C 2
MODEL$ 0.;Y .K -- #J.JJBAA .;X #B @+
#A.JF .;X ": .;X IS ! 4T.E 7IN MET]S7 F
! LEFT PYLONS & .;Y IS ! HEI<T 7IN
MET]S7 (! >* ABV ! WAT]4 ,= :AT 4T.ES
.;X IS ! >* ABV ! ROAD8
.#GC4 .,,%ORT .,,RESPONSE ,! L5G? .;,L
7IN MILLIMET]S7 (! L>VAE (! BLACK PORGY
FI% C 2 MODEL$ BY
.;,L7.;X @7 .K #J.JJAGJ;,X #B @+
#J.ADE .;X @+ #B.CE1 #J "K.K .;X "K.K
#DJ
": .;X IS ! AGE 7IN "DS7 (! L>VAE4
,WRITE & SOLVE AN 9EQUAL;Y 6F9D AT :AT
AGES A L>VAE'S L5G? T5DS 6BE GRT] ?AN
#AJ MILLIMET]S4 .,EXPLA9 H[ ! GIV5 DOMA9
A6ECTS ! SOLU;N4
#GD4 .,,MULTIPLE .,,REPRES5T,NS ,A
/UDY F.D T A DRIV]'S REAC;N "T .,A7.;X
@7 6AUDIO /IMULI & 8 OR H] REAC;N "T
.;,V7.;X @7 6VISUAL /IMULI 7BO? 9
MILLISECONDS7 C 2 MODEL$ BY
.,A7.;X7 .K #J.JJEA;,X #B -- #J.CAI
.;X @+ #AE1 #AF "K.K .;X "K.K #GJ
.;,V @7 .;X @7 .K #J.JJE .;X #B --
#J.BC .;X @+ #BB1 #AF "K.K .;X "K.K #GJ
": .;X IS ! DRIV]'S AGE 7IN YE>S74
A4 .,WRIT+ .AN .,9EQUAL;Y ,WRITE AN
9EQUAL;Y T Y C USE 6F9D ! .;X -VALUES =
: .,A @7 .;X @7 IS LESS ?AN .;,V @7 .;X
@7@4
B4 .,MAK+ .A .,TA# ,USE A TA# 6F9D !
SOLU;N (! 9EQUAL;Y F "P 7A74 ,YR TA# %D
3TA9 .;X -VALUES F #AF 6#GJ 9 9CRE;TS (
#F4
C4 .,DRAW+ .A .,GRAPH ,*ECK ! SOLU;N Y
F.D 9 "P 7;B7 0US+ A GRAPH+ CALCULATOR
6SOLVE ! 9EQUAL;Y .,A @7 .;X @7
GRAPHIC,Y4 .,DESCRIBE H[ Y US$ ! DOMA9
#AF "K.K .;X "K.K #GJ 6DET]M9E A R1SONA#
SOLU;N4
D4 .,9T]PRET ,BAS$ ON YR RESULTS F "PS
7;B7 & 7;C71 D Y ?9K A DRIV] WD REACT M
QKLY 6A TRA6IC LI<T *ANG+ F GRE5 6YELL[
OR 6! SIR5 ( AN APPROA*+ AMBUL.E8
.,EXPLA94
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
------------------------------------#CJG
#GE4 .,,SO3] ,! PA? (A SO3] BALL KICK$
F ! GR.D C 2 MODEL$ 0.;Y .K --#J.JEDJ
.;X #B @+ #A.DC .;X
": .;X IS ! HORIZONTAL 4T.E 7IN FEET7
F ": ! BALL 0 KICK$ & .;Y IS !
CORRESPOND+ HEI<T 7IN FEET74
A4 ,A SO3] GOAL IS #H FEET HI<4 ,WRITE
& SOLVE AN 9EQUAL;Y 6F9D AT :AT VALUES (
.;X ! BALL IS L[ 5 6G 96! GOAL4
B4 ,A SO3] PLAY] KICKS ! BALL T[>D !
GOAL F A 4T.E ( #AE FEET AWAY4 ,NO "O IS
BLOCK+ ! GOAL4 ,W ! PLAY] SCORE A GOAL8
.,EXPLA9 YR R1SON+4
#GF4 .,,MULTI-.,,/EP .,,PRO#M ,A TRUCK
T IS #AA FEET TALL & #G FEET WIDE IS
TRAVEL+ "U AN >*4 ,! >* C 2 MODEL$ 0.;Y
.K --#J.JFBE .;X #B @+ #A.BE .;X @+
#E.GE
": .;X & .;Y >E M1SUR$ 9 FEET4
A4 ,W ! TRUCK FIT "U ! >*8 .,EXPLA9 YR
R1SON+4
B4 ,:AT IS ! MAXIMUM WID? T A TRUCK
#AA FEET TALL C H & / MAKE X "U ! >*8
C4 ,:AT IS ! MAXIMUM HEI<T T A TRUCK
#G FEET WIDE C H & / MAKE X "U ! >*8
#GG4 .,,*ALL5GE ,= CLE> BLUE ICE ON
LAKES & PONDS1 ! MAXIMUM WEI<T .;W 7IN
TONS7 T ! ICE C SUPPORT IS GIV5 0.;W @7
.;X @7 .K #J.A .;X #B -- #J.E .;X -- #E
": .;X IS ! ?ICK;S (! ICE 7IN 9*ES74
A4 .,CALCULATE ,:AT ?ICK;SES ( ICE C
SUPPORT A WEI<T ( #BJ TONS8
B4 .,9T]PRET .,EXPLA9 H[ Y C USE !
GRAPH ( .;W,7.;X @7 6DET]M9E ! M9IMUM
.;X -VALUE 9 ! DOMA9 = : ! FUNC;N GIVES
M1N+;L RESULTS4
,,MIX$ ,,REVIEW
,,PREVIEW
,PREP>E = ,LESSON #D.AJ 9 ,EXS4
#HG-IB4
,GRAPH ! FUNC;N4
.#GH4 ;Y .K #C .;X @+ #G @7 P4 #HI @7
.#GI4 .;F @7 .;X @7 .K --#D .;X @+ #E
@7 P4 #HI @7
.#HJ4
.#HA4 ;Y .K _\ .;X -- #B_\ @7 P4 #ABC
@7
.#HB4 ;Y .K _\ .;X @+ #F_\--#A @7 P4
#ABC @7
.#HC4 ;G7 .;X @7 .K .;X #B--#H @7 P4
#BCF @7
.#HD4 ;F7 .;X @7 .K .;X #B @+ #D .;X
@+ #C @7 P4 #BCF @7
.#HE4 ;Y .K #B .;X #B--#I .;X @+ #D @7
P4 #BCF @7
.#HF4
,SOLVE ! SY/EM ( EQU,NS4 @7 P4 #AGH @7
.#HG4 .;X @+ ;V @+ ;Z .K --#B
#D .;X @+ #B;Y @+ ;Z .K #C
;Z .K --#C
.#HH4 .;X @+ ;V @+ ;Z .K #C
#B .;X @+ #C;Y--;Z .K --#H
;Z .K #D
.#HI4 #D .;X @+ #B;Y @+ ;Z .K --#F
.;X @+ ;V @+ ;Z .K --#C
#AF .;X @+ #D;Y @+ ;Z .K #J
.#IJ4 .;X @+ ;Y @+ ;Z .K #H
#I .;X -- #C;V @+ ;Z .K #J
#D .;X -- #B;Y @+ ;Z .K --#A
.#IA4 .;X @+ ;V @+ ;Z .K #E
#B .;X -- #C;Y @+ #C;Z .K #I
- .;X @+ #G;Y--;Z .K #AA
.#IB4 .;X @+ ;Y @+ ;Z .K #A
.;X -- ;V @+ ;Z .K #A
#C .;X @+ ;Y @+ #C;Z .K #C
.,,EXTRA .,,PRACTICE = ,LESSON #D.I1
P4 #AJAC
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#CJH
,9VE/IGAT+ ,ALGEBRA ,ACTIV;Y3 #D.AJ
,MODEL+ ,DATA )A ,QUADRATIC ,FUNC;N
,USE 2F LESSON #D.AJ
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,KEY/ROKES
,MAT]IALS
99 -PASS
99 #EJ P5NIES
99 GRAPH+ CALCULATOR
,SIDEB>3
,/&>DS
,5RI*;T ( ..,ADV.ED ,PLACE;T
,PROBABIL;Y & .,/ATI/ICS3 #AB.J
..,/UD5TS F9D ! L9E ( BE/ FIT 6A GIV5
4TRIBU;N ( DATA 0US+ L1/ SQU>ES
.REGRES.N @4
,,"Q ,H[ C Y FIT A QUADRATIC FUNC;N 6A
SET ( DATA8
,,EXPLORE ,COLLECT & MODEL QUADRATIC
DATA
,,/EP #A ,COLLECT DATA
,DRAW FIVE CIRCLES US+ A -PASS4 ,USE
DIAMET]S ( #A 9*1 #B 9*ES1 #C 9*ES1 #D
9*ES1 & #E 9*ES4 ,PLACE Z _M P5NIES Z Y
C 9 EA* CIRCLE1 MAK+ SURE T EA* P5NY IS
-PLETELY )9 ! CIRCLE4
,,/EP #B ,RECORD DATA
,RECORD YR RESULTS F ,/EP #A 9 A TA# L
! "O %[N AT ! "R4 ,AL1 RECORD ! NUMB] (
P5NIES T WD FIT 9 A CIRCLE )A DIAMET] (
#J 9*4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,DIAMET] ( CIRCLE 7IN471 .;X @3 ,NUMB]
( P5NIES1 .;Y
.#J @3 @8
.#A @3 @8
.#B @3 @8
.#C @3 @8
.#D @3 @8
.#E @3 @8
,,/EP #C ,5T] DATA
,5T] ! DATA Y COLLECT$ 96TWO LI/S (A
GRAPH+ CALCULATOR4
,,/EP #D ,4PLAY DATA
,4PLAY ! DATA 9 A SCATT] PLOT4 ,NOTICE
T ! PO9TS APPE> 6LIE ON A P>ABOLA4
,,/EP #E ,F9D MODEL
,USE ! .QUADRATIC .REGRES.N F1TURE
6F9D A QUADRATIC MODEL =! DATA4
,,DRAW ,,3CLU.NS
,USE YR OBS]V,NS 6-PLETE ^! EX]CISES
.#A4 ,GRAPH YR MODEL F ,/EP #E ON !
SAME SCRE5 Z ! SCATT] PLOT4 .,DESCRIBE
H[ WELL ! MODEL FITS ! DATA4
.#B4 ,USE YR MODEL F ,/EP #E 6PREDICT
! NUMB] ( P5NIES T W FIT 9 A CIRCLE )A
DIAMET] ( #F 9*ES4 ,*ECK YR PREDIC;N
0DRAW+ A CIRCLE )A DIAMET] ( #F 9*ES &
FILL+ X ) P5NIES4
.#C4 .,EXPLA9 :Y Y WD EXPECT ! NUMB] (
P5NIES T FIT 9SIDE A CIRCLE 6BE A
QUADRATIC FUNC;N (! CIRCLE'S DIAMET]4
.#D4 ,! DIAMET] (A P5NY IS #J.GE 9*4
,USE ? FACT 6WRITE A QUADRATIC FUNC;N
GIV+ AN UPP] LIMIT .;,L ON ! NUMB] (
P5NIES T C FIT 9SIDE A CIRCLE ) DIAMET]
.;X 9*ES4
------------------------------------#CJI
#D.AJ ,WRITE ,QUADRATIC ,FUNC;NS &
,MODELS
.,2F ,Y WROTE L9E> FUNC;NS & MODELS4
.,N[ ,Y W WRITE QUADRATIC FUNC;NS &
MODELS4
.,:Y8 ,S Y C MODEL ! CROSS SEC;N (
P>ABOLIC DI%ES1 Z 9 ,EX4 #DF
,KEY ,VOCABUL>Y
99 BE/-FITT+ QUADRATIC MODEL
,SIDEB>3
,/&>DS
.,5RI*;T .( #H.J ,/UD5TS SOLVE & GRAPH
QUADRATIC EQU,NS 0FACTOR+1 -PLET+ !
SQU>E1 OR US+ ! QUADRATIC =MULA4
..,/UD5TS APPLY ^! TE*NIQUES 9 SOLV+ ^W
.PRO#MS4 ,!Y AL SOLVE QUADRATIC EQU,NS 9
! -PLEX NUMB] SY/EM4
,9 ,LESSONS #D.A & #D.B1 Y LE>N$ H[
6GRAPH QUADRATIC FUNC;NS4 ,9 ? LESSON1 Y
W WRITE QUADRATIC FUNC;NS GIV5 9=M,N AB
_! GRAPHS4
,,EXAMPLE #A ,WRITE A ,QUADRATIC
FUNC;N 9 V]TEX =M
,WRITE A QUADRATIC FUNC;N =! P>ABOLA
%[N4
,SOLU;N
,USE V]TEX =M 2C ! V]TEX IS GIV54
..;Y .K A7;X--.;H7 #B @+ .;K .,V]TEX
.=M
.;Y .K .A @7 .;X - #A7 #B -- #B
..,SUB/ITUTE #A = ;H & --#B = .K4
,USE ! O!R GIV5 PO9T1 7#C1 #B71 6F9D
.A @4
#B .K .A 7#C - .#A @7 #B -- #B
..,SUB/ITUTE #C = ;X & #B = .;Y @4
#B .K #D .A -- #B ..,SIMPLIFY
COE6ICI5T ( .A @4
#A .K .A ..,SOLVE = .A @4
,A QUADRATIC FUNC;N =! P>ABOLA IS .;Y
.K @7 .;X -- #A7 #B -- #B4
,,EXAMPLE #B
,WRITE A QUADRATIC FUNC;N 9 9T]CEPT =M
,WRITE A QUADRATIC FUNC;N =! P>ABOLA
%[N4
,SOLU;N
,USE 9T]CEPT =M 2C ! .;X -9T]CEPTS >E
GIV54
..;Y .K A7;X--.;P @7 7;X -- .;Q @7
.,9T]CEPT .=M
.;Y .K .A @7 .;X @+ #A7 @7 .;X -- #D7
..,SUB/ITUTE --#A = ;P & #D = .Q4
,,AVOID ,,]RORS
,2 SURE 6SUB/ITUTE ! .;X -9T]CEPTS &!
COORD9ATES (! GIV5 PO9T =! CORRECT LRS 9
..;Y .K A7;X- ;P77;X--.;Q74
,USE ! O!R GIV5 PO9T1 7#C1 #B71 6F9D
.A4
#B .K .A 7#C @+ #A77#C-D7 ..,SUB/ITUTE
#C = ;X & #B = .;Y @4
#B .K --#D .A ..,SIMPLIFY COE6ICI5T (
.A @4
,A QUADRATIC FUNC;N =! P>ABOLA IS
------------------------------------#CAJ
,,EXAMPLE #C
,WRITE A QUADRATIC FUNC;N 9 /&>D =M
,WRITE A QUADRATIC FUNC;N 9 /&>D =M =!
P>ABOLA T PASSES "? ! PO9TS 7-#A1 --#C71
7#J1 --#D71 & 7#B1 #F74
,SOLU;N
.,,/EP .#A .,SUB/ITUTE ! COORD9ATES (
EA* PO9T 96.;Y .K .AX #B @+ .BX @+ .;C
6OBTA9 ! SY/EM ( ?REE L9E> EQU,NS %[N
2L4
-#C .K .A 7-#A7 #B @+ .;B 7-#A7 @+ .;C
..,SUB/ITUTE --#A = ;X & --#C = .;Y @4
-#C .K .A -- .;B @+ .;C .,EQU,N .#A
-#D .K .A 7#J7 #B @+ .;B7.#B7 @+ .;C
..,SUB/ITUTE #J = ;X & --#D = .;Y @4
-#D .K .;C .,EQU,N .#B
#F .K .A 7#B7 #B @+ .;B 7#B7 @+ .;C
..,SUB/ITUTE #B = ;X & #F = .Y4
#F .K #D .A @+ #B .;B @+ .;C .,EQU,N
.#C
,,REVIEW ,,SY/EMS ,,( ,,EQU,NS
,= HELP ) SOLV+ SY/EMS ( L9E> EQU,NS 9
?REE V>IA#S1 SEE P4 #AGH @4
.,,/EP .#B .,REWRITE ! SY/EM ( ?REE
EQU,NS 9 ,/EP #A Z A SY/EM ( TWO EQU,NS
0SUB/ITUT+ --#D = .;C 9 ,EQU,NS #A &
.#C4
.A -- .;B @+ .;C .K --#C .,EQU,N .#A
..A--.;B -- #D .K --#C ..,SUB/ITUTE --#D
= .;C @4 ..A--;B .K .#A .,REVIS$ .,EQU,N
.#A
#D .A @+ #B .;B @+ .;C .K #F .,EQU,N
.#C
#D .A @+ #B .;B - #D .K #F
..,SUB/ITUTE --#D = .;C @4
#D .A @+ #B .;B .K #AJ .,REVIS$
.,EQU,N .#C
.,,/EP .#C .,SOLVE ! SY/EM 3SI/+ (
REVIS$ ,EQU,NS #A & #C4 ,USE ! ELIM9,N
ME?OD4
,S #B -- .;B .K #A1 : M1NS .;B .K #A4
,! SOLU;N IS .A .K #B1 .;B .K #A1 &
.;C .K --#D4
,A QUADRATIC FUNC;N =! P>ABOLA IS .;Y
.K #B .;X #B @+ .;X -- #D4
.,,GUID$ .,,PRACTICE = ,EXAMPLES #A1
#B1 & #C
,WRITE A QUADRATIC FUNC;N ^: GRAPH HAS
! GIV5 "*I/ICS4
.#A4 V]TEX3 7#D1 --#E7
PASSES "?3 7#B1 --#A7
.#B4 V]TEX3 7-#C1 #A7
PASSES "?3 7#J1 --#H7
.#C4 .;X -9T]CEPTS3 --#B1 #E
PASSES "?3 7#F1 #B7
,WRITE A QUADRATIC FUNC;N 9 /&>D =M =!
P>ABOLA T PASSES "? ! GIV5 PO9TS4
.#D4 7-#A1 #E71 7#J1 --#A71 7#B1 #AA7
.#E4 7-#B1 --#A71 7#J1 #C71 7#D1 #A7
.#F4 7-#A1 #J71 7#A1 --#B71 7#B1
--#AE7
------------------------------------#CAA
.,,QUADRATIC .,,REGRES.N ,9 ,*APT] #B1
Y US$ A GRAPH+ CALCULATOR 6P]=M L9E>
REGRES.N ON A DATA SET 9 ORD] 6F9D A
L9E> MODEL =! DATA4 ,A GRAPH+ CALCULATOR
C AL 2 US$ 6P]=M .QUADRATIC .REGRES.N4
,! MODEL GIV5 0QUADRATIC REGRES.N IS
CALL$ ! .BE/-.FITT+ .QUADRATIC .MODEL4
,,EXAMPLE #D
,SOLVE A MULTI-/EP PRO#M
.,,PUMPK9 .,,TOSS+ ,A PUMPK9 TOSS+
3TE/ IS HELD EA* YE> 9 ,MORTON1
,ILL9OIS1 ": P -PETE 6SEE ^: CATAPULT W
S5D PUMPK9S ! F>!/4 ,"O CATAPULT LAUN*ES
PUMPK9S F #BE FEET ABV ! GR.D AT A SPE$
( #ABE FEET P] SECOND4 ,! TA# %[S !
HORIZONTAL 4T.ES 7IN FEET7 ! PUMPK9S
TRAVEL :5 LAUN*$ AT DI6]5T ANGLES4 ,USE
A GRAPH+ CALCULATOR 6F9D ! BE/-FITT+
QUADRATIC MODEL =! DATA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,ANGLE 7.DEGREES7 @3 #BJ3 #CJ3 #DJ3
#EJ3 #FJ3 #GJ
.,4T.E 7.FEET7 @3 #CGB3 #DFB3 #EJI3
#EJA3 #DCG3 #CBC
,SOLU;N
.,,/EP .#A .,5T] ! DATA 96TWO LI/S (A
GRAPH+ CALCULATOR4
.,,/EP .#B .,MAKE A SCATT] PLOT (!
DATA4 ,NOTE T ! PO9TS %[ A P>ABOLIC
TR5D4
.,,/EP .#C .,USE ! QUADRATIC REGRES.N
F1TURE 6F9D ! BE/-FITT+ QUADRATIC MODEL
=! DATA4
.,,/EP .#D .,*ECK H[ WELL ! MODEL FITS
! DATA 0GRAPH+ ! MODEL &! DATA 9 ! SAME
VIEW+ W9D[4
,! BE/-FITT+ QUADRATIC MODEL IS .;Y .K
--#J.BFA .;X #B @+ #BB.F .;X @+ #BC.J4
.,,GUID$ .,,PRACTICE = ,EXAMPLE #D
.#G4 .,,PUMPK9 .,,TOSS+ ,9 ,EXAMPLE
#D1 AT :AT ANGLE DOES ! PUMPK9 TRAVEL !
F>!/8 .,EXPLA9 H[ Y F.D YR ANSW]4
------------------------------------#CAB
#D.AJ ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#I = ,EXS4 #AI1 #CE1 & #DI
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 #B1 #AE1 #AF1 #DC1 #DD1 & #EA
.K .,,MULTIPLE .,,REPRES5T,NS
,EX4 #EJ
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,:5
Y P]=M QUADRATIC REGRES.N ON A SET (
DATA1 ! QUADRATIC MODEL OBTA9$ IS CALL$
! @8 @4
.#B4 .,,WRIT+ .,DESCRIBE .H[ .6WRITE
AN EQU,N (A P>ABOLA IF Y "K ?REE PO9TS
ON ! P>ABOLA T >E N ! V]TEX OR .;X
-9T]CEPTS4
,,EXAMPLE #A
ON P4 #CJI = ,EXS4 #C-AE
..,,WRIT+ ,,9 ,,V]TEX .,,=M ,WRITE A
QUADRATIC FUNC;N 9 V]TEX =M =! P>ABOLA
%[N4
.#C4
.#D4
.#E4
..,,WRIT+ ,,9 ,,V]TEX .,,=M ,WRITE A
QUADRATIC FUNC;N 9 V]TEX =M ^: GRAPH HAS
! GIV5 V]TEX & PASSES "? ! GIV5 PO9T4
.#F4 V]TEX3 7-#D1 #A7
PO9T3 7-#B1 #E7
.#G4 V]TEX3 7#A1 #F7
PO9T3 7-#A1 #B7
.#H4 V]TEX3 7#E1 --#D7
PO9T3 7#A1 #BJ7
.#I4 V]TEX3 7-#C1 #C7
PO9T3 7#A1 --#A7
.#AJ4 V]TEX3 7#E1 #J7
PO9T3 7#B1 --#BG7
.#AA4 V]TEX3 7-#D1 --#B7
PO9T3 7#J1 #CJ7
.#AB4 V]TEX3 7#B1 #A7
PO9T3 7#D1 --#B7
.#AC4 V]TEX3 7-#A1 --#D7
PO9T3 7#B1 --#A7
.#AD4 V]TEX3 7#C1 #E7
PO9T3 7#G1 --#C7
#AE4 .,,MULTIPLE .,,*OICE ,! V]TEX (A
P>ABOLA IS 7#E1 --#C7 & ANO!R PO9T ON !
P>ABOLA IS 7#A1 #E74 ,: PO9T IS AL ON !
P>ABOLA8
,A 7#J1 #C7
;,B 7-#A1 #I7
;,C 7-#A1 #AE7
;,D 7#G1 #G7
,,EXAMPLE #B
ON P4 #CJI = ,EXS4 #AF-BF
#AF4 .,,MULTIPLE .,,*OICE ,! .;X
-9T]CEPTS (A P>ABOLA >E #D & #G & ANO!R
PO9T ON ! P>ABOLA IS 7#B1 --#BJ74 ,:
PO9T IS AL ON ! P>ABOLA8
,A 7#A1 #BA7
;,B 7#H1-#D7
;,C 7#E1-#DJ7
;,D 7#E1 #D7
..,,WRIT+ ,,9 ,,9T]CEPT .,,=M ,WRITE A
QUADRATIC FUNC;N 9 9T]CEPT =M =! P>ABOLA
%[N4
.#AG4
.#AH4
.#AI4
------------------------------------#CAC
..,,WRIT+ ,,9 ,,9T]CEPT .,,=M ,WRITE A
QUADRATIC FUNC;N 9 9T]CEPT =M ^: GRAPH
HAS ! GIV5 .;X -9T]CEPTS & PASSES "? !
GIV5 PO9T4
.#BJ4 .;X -9T]CEPTS3 #B1 #E
PO9T3 7#D1 --#B7
.#BA4 .;X -9T]CEPTS3 --#C1 #J
PO9T3 7#B1 #AJ7
.#BB4 .;X -9T]CEPTS3 --#A1 #D
PO9T3 7#B1 #D7
.#BC4 .;X -9T]CEPTS3 #C1 #G
PO9T3 7#F1 --#I7
.#BD4 .;X -9T]CEPTS3 --#E1 --#A
PO9T3 7-#G1 --#BD7
.#BE4 .;X -9T]CEPTS3 --#F1 #C
PO9T3 7#J1 --#I7
.,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 WRIT+ A QUADRATIC
FUNC;N ^: GRAPH HAS ! GIV5 .;X -9T]CEPTS
OR V]TEX & PASSES "? ! GIV5 PO9T4
.#BF4 .;X -9T]CEPTS3 #D1 --#C2 PO9T3
7#E1 --#E7
.#BG4 .;X -9T]CEPTS3 #D1 --#C2 PO9T3
7#E1 --#E7
,,EXAMPLE #C
ON P4 #CAJ = ,EXS4 #BH-CI
..,,WRIT+ ,,9 ,,/&>D .,,=M ,WRITE A
QUADRATIC FUNC;N 9 /&>D =M =! P>ABOLA
%[N4
.#BH4
.#BI4
.#CJ4
..,,WRIT+ ,,9 ,,/&>D .,,=M ,WRITE A
QUADRATIC FUNC;N 9 /&>D =M =! P>ABOLA T
PASSES "? ! GIV5 PO9TS4
.#CA4 7-#D1 --#C71 7#J1 --#B71 7#A1
#G7
.#CB4 7-#B1 --#D71 7#J1 --#AJ71 7#C1
--#G7
.#CC4 7-#B1 #D71 7#J1 #E71 7#A1 --#AA7
.#CD4 7-#A1 --#A71 7#A1 #AA71 7#C1 #G7
.#CE4 7-#A1 #I71 7#A1 #A71 7#C1 #AG7
.#CF4 7-#F1 --#A71 7-#C1 --#D71 7#C1
#H7
.#CG4 7-#B1 --#AC71 7#B1 #C71 7#D1 #E7
.#CH4 7-#F1 #BI71 7-#D1 #AB71 7#B1
--#C7
.#CI4 7-#C1 --#B71 7#C1 #AJ71 7#F1
--#B7
.,,WRIT+ .,,QUADRATIC .,,FUNC;NS
,WRITE A QUADRATIC FUNC;N ^: GRAPH HAS !
GIV5 "*I/ICS4
.#DJ4 PASSES "?3
7-#J.E1 --#A71 7#B1 #H71 7#AA1 #BE7
.#DA4 .;X -9T]CEPTS3-#AA1 #C
PASSES "?3 7#A1 --#AIB7
.#DB4 V]TEX3 7#D.E1 #G.BE7
PASSES "?3 7#G1 --#C7
.#DC4 .,,OP5-.,,5D$ .,,MA? ,DRAW A
P>ABOLA T PASSES "? 7-#B1 #C74 ,WRITE A
FUNC;N =! P>ABOLA 9 /&>D =M1 9T]CEPT =M1
& V]TEX =M4
.#DD4 .,,%ORT .,,RESPONSE ,SUPPOSE Y
>E GIV5 A SET ( DATA PAIRS @7 .;X1 .;Y
@7@4 .,DESCRIBE H[ Y C USE RATIOS
6DET]M9E :E!R ! DATA C 2 MODEL$ 0A
QUADRATIC FUNC;N (! =M .;Y .K .AX #B @4
.#DE4 .,,*ALL5GE ,F9D A FUNC;N (! =M
.;Y .K .AX #B @+ .BX @+ .;C ^: GRAPH
PASSES "? 7#A1 --#D71 7-#C1 --#AF71 &
7#G1 #AD74 .,EXPLA9 :AT ! MODEL TELLS Y
AB ! PO9TS4
------------------------------------#CAD
,,PRO#M ,,SOLV+
,,EXAMPLES #A & #C
ON PP4 #CJI-CAJ = ,EXS4 #DF-DG
.#DF4 .,,ANT5NA .,,DI% ,?REE PO9TS ON
! P>ABOLA =M$ 0! CROSS SEC;N ( AN ANT5NA
DI% >E 7#J1 #D71 7#B1 #C.BE71 & 7#E1
#C.JFBE74 ,WRITE A QUADRATIC FUNC;N T
MODELS ! CROSS SEC;N4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#DG4 .,,FOOTBALL ,TWO PO9TS ON !
P>ABOLIC PA? (A KICK$ FOOTBALL >E 7#J1
#J7 &! V]TEX 7#BJ1 #AE74 ,WRITE A
QUADRATIC FUNC;N T MODELS ! PA?4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
,,EXAMPLE #D
ON P4 #CAA = ,EXS4 #DH-EJ
#DH4 .,,MULTI-.,,/EP .,,PRO#M ,! B>
GRAPH %[S ! AV]AGE NUMB] ( H\RS P] P]SON
P] YE> SP5T ON ! ,9T]NET 9 ! ,UNIT$
,/ATES =! YE>S #AIIG-BJJA4
A4 ,USE A GRAPH+ CALCULATOR 6CR1TE A
SCATT] PLOT4
B4 ,USE ! QUADRATIC REGRES.N F1TURE (!
CALCULATOR 6F9D ! BE/-FITT+ QUADRATIC
MODEL =! DATA4
C4 ,USE YR MODEL F "P 7;B7 6PREDICT !
AV]AGE NUMB] ( H\RS A P]SON W SP5D ON !
,9T]NET 9 #BJAJ4
.#DI4 .,,RUNN+ ,! TA# %[S H[ W9D
A6ECTS A RUNN]'S P]=M.E 9 ! #BJJ MET]
DA%4 ,POSITIVE W9D SPE$S CORRESPOND
6TAILW9DS1 & NEGATIVE W9D SPE$S
CORRESPOND 6H1DW9DS4 ,! *ANGE F9 F9I%+
"T IS ! DI6];E 2T ! RUNN]'S "T :5 ! W9D
SPE$ IS .;S &! RUNN]'S "T :5 "! IS NO
W9D4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,W9D SPE$ 7;M_/SEC71 .;S @3 -#F3 -#D3
-#B3 #J3 #B3 #D3 #F
,*ANGE 9 F9I%+ "T 7SEC71 .;T @3 #B.BH3
#A.DB3 #J.FG3 #J3 -#J.EG3 -#A.JE3 -#A.DB
A4 ,USE A GRAPH+ CALCULATOR 6F9D !
BE/-FITT+ QUADRATIC MODEL4
B4 ,PREDICT ! *ANGE 9 F9I%+ "T :5 !
W9D SPE$ IS #AJ ;M_/SEC4
#EJ4 .,,MULTIPLE .,,REPRES5T,NS ,! TA#
%[S ! NUMB] ( ,U4,S4 H\SEHOLDS 7IN
MILLIONS7 ) COLOR TELEVI.NS F #AIGJ "?
#BJJJ4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,YE>S .S9CE .#AIGJ @3 #J3 #E3 #AJ3
#AE3 #BJ3 #BE3 #CJ
..,H\SEHOLDS ) COLOR ,,TV,'S
7.MILLIONS7 @3 #BA3 #DG3 #FC3 #GH3 #IJ3
#ID3 #AJA
A4 .,DRAW+ .A .,GRAPH ,MAKE A SCATT]
PLOT (! DATA4 ,DRAW ! P>ABOLA T Y ?9K
BE/ FITS ! DATA4
B4 .,WRIT+ .A .,FUNC;N ,E/IMATE !
COORD9ATES ( ?REE PO9TS ON ! P>ABOLA4
,USE ! PO9TS 6WRITE A QUADRATIC FUNC;N
=! DATA4
C4 .,MAK+ .A .,TA# ,USE YR FUNC;N F "P
7;B7 6MAKE A TA# ( DATA =! YE>S LI/$ 9 !
ORIG9AL TA# ABV4 .,-P>E ! NUMB]S (
H\SEHOLDS GIV5 0YR FUNC;N )! NUMB]S 9 !
ORIG9AL TA#4
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
------------------------------------#CAE
#EA4 .,,MULTIPLE .,,*OICE ,! ,G>ABIT
,VIADUCT 9 ,FR.E HAS A P>ABOLIC >* Z "P
( XS SUPPORT4 ,?REE PO9TS ON ! P>ABOLA T
MODELS ! >* >E 7#J1 #J71 7#DJ1 #CH.B71 &
7#AFE1 #J7 ": .;X & .;Y >E M1SUR$ 9
MET]S4 ,: PO9T IS AL ON ! P>ABOLA8
,A 7#AJ1 --#AA.HD7
;,B 7#BF.GD1 #BE7
;,C 7#HJ1 #EA.IE7
;,D 7#ABE1 #DE7
#EB4 .,,*ALL5GE ,LET .;,R 2 ! MAXIMUM
NUMB] ( REGIONS 96: A CIRCLE C 2 DIVID$
US+ .;N *ORDS4 ,= EXAMPLE1 ! DIAGRAM %[S
T .;,R .K #D :5 .;N .K #B4 ,COPY &
-PLETE ! TA#4 ,!N WRITE A QUADRATIC
MODEL GIV+ .;,R Z A FUNC;N ( .N4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;N @3 #J3 #A3 #B3 #C3 #D3 #E3 #F
.;,R @3 @8@3 @8@3 #D3 @8@3 @8@3 @8@3
@8
,,MIX$ ,,REVIEW
,,PREVIEW
,PREP>E = ,LESSON #E.A 9 ,EXS4 #EC-EH4
,EVALUATE ! EXPRES.N =! GIV5 VALUE (!
V>IA#4 @7 P4 #AJ @7
.#EC4 .;X #B -- #C :5 .;X .K #E
.#ED4 #C;A #E -- #AJ :5 A .K --#A
.#EE4 .;X #D :5 .;X .K --#B
.#EF4 #D;U #C -- #AE :5 ;U .K #C
.#EG4 ;V #B @+ #C;V--#E :5 ;V .K #E
.#EH4 -- .;Y #C @+ #B .;Y @+ #E :5 .;Y
.K #B
,SOLVE ! SY/EM ( L9E> EQU,NS4 @7 P4
#AFJ @7
.#EI4 ,A .;X @+ #E .;Y .K #AH
- .;X @+ #B .;Y .K #AE
.#FJ4 #C .;X @+ #G .;Y .K #A
#D .;X @+ #E .;Y .K #BC
.#FA4 #C .;X @+ ,A .;Y .K --#A
#B .;X @+ #F .;Y .K --#CA
.#FB4 #C .;X @+ .;Y .K #AJ
- .;X @+ #B .;Y .K #BJ
.#FC4 ,A .;X @+ #E .;Y .K #B
-#C .;X @+ #B .;Y .K #CC
.#FD4 #B .;X @+ #C;V .K --#A
#AJ .;X @+ #G .;Y .K --#A
,,QUIZ .= .,LESSONS .#D..H-.D..AJ
,USE ! QUADRATIC =MULA 6SOLVE ! EQU,N1
@7 P4 #BIB @7
.#A4 .;X #B -- #D .;X @+ #E .K #J
.#B4 #B .;X #B -- #H .;X @+ #A .K #J
.#C4 #C .;X #B @+ #E .;X @+ #D .K #J
,GRAPH ! 9EQUAL;Y1 @7 P4 #CJJ @7
.#D4 .;Y "K --#C .;X #B
.#E4 .;Y .1 -- .;X #B @+ #B .;X
.#F4 .;Y .1 -- .;X #B @+ #B .;X @+ #C
,SOLVE ! 9EQUAL;Y1 @7 P4 #CJJ @7
.#G4 #J .1.K .;X #B @+ #E
.#H4 #AB "K.K .;X #B -- #G .;X
.#I4 #B .;X #B @+ #B .1--#E .;X
,WRITE A QUADRATIC FUNC;N ^: GRAPH HAS
! GIV5 "*I/ICS1 @7 P4 #CJI @7
.#AJ4 V]TEX3 7#E1 #G7
PASSES "?3 7#C1 #AA7
.#AA4 .;X -9T]CEPTS3 --#C1 #E
PASSES "?3 7#G1 --#DJ7
.#AB4 PASSES "?3
7-#A1 #B71 7#D1 --#BC71 7#B1 --#G7
.#AC4 .,,SPORTS ,A P]SON ?R[S A
BASEBALL 96! AIR ) AN 9ITIAL V]TICAL
VELOC;Y ( #CJ FEET P] SECOND & !N LETS !
BALL HIT ! GR.D4 ,! BALL IS REL1S$ #E
FEET ABV ! GR.D4 ,H[ L;G IS ! BALL 9 !
AIR8 @7 P4 #BIB @7
.,,EXTRA .,,PRACTICE = ,LESSON #D.AJ1
P4 #AJAC
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#CAF
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,LESSONS #D.F-D.AJ
.#A4 ,,MULTI-,,/EP ,,PRO#M ,Y >E PLAY+
A LAWN V].N ( TIC-TAC-TOE 9 : Y TOSS B1N
BAGS ONTO A L>GE BO>D4 ,"O ( YR TOSSES C
2 MODEL$ 0.;Y .K --#J.AB .;X #B @+ #A.B
.;X @+ #B ": ;X IS ! B1N BAG'S
HORIZONTAL POSI;N 7IN FEET7 & .;Y IS !
CORRESPOND+ HEI<T 7IN FEET74
.A4 ,WRITE ! GIV5 FUNC;N 9 V]TEX =M4
.B4 ,GRAPH ! FUNC;N4
.C4 ,:AT IS ! B1N BAG'S MAXIMUM HEI<T8
.#B4 ,,MULTI-,,/EP ,,PRO#M ,A MUSIC
/ORE SELLS AB #DJ (A NEW MODEL ( DRUM P]
MON? AT A PRICE ( 4#ABJ EA*4 ,= EA* 4#E
DECR1SE 9 PRICE1 AB #B M DRUMS P] MON?
>E SOLD4
.A4 ,WRITE A FUNC;N T MODELS ! /ORE'S
REV5UE F SALES (! NEW DRUM MODEL4
.B4 ,WRITE AN 9EQUAL;Y Y C USE 6F9D !
PRICES T RESULT 9 REV5UES OV] 4#DHCJ4
.C4 ,SOLVE ! 9EQUAL;Y F "P 7;B7
ALGEBRAIC,Y & GRAPHIC,Y4
.#C4 ,,EXT5D$ ,,RESPONSE ,! TA# %[S !
AV]AGE PRICE (A ,,VCR F #AIIH "? #BJJC4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,YE>S S9CE #AIIH1 .;T @3 ,PRICE
7DOLL>S71 .;P
#J3 #ACC
#A3 #AJB
#B3 #HA
#C3 #GA
#D3 #FA
#E3 #FA
.A4 ,USE A GRAPH+ CALCULATOR 6F9D !
BE/-FITT+ QUADRATIC MODEL =! DATA4
.B4 ,GRAPH ! MODEL &! DATA TGR4
.C4 ,D Y ?9K ? MODEL W GIVE A GD
E/IMATE (! PRICE (A ,,VCR 9 #BJAJ8
,EXPLA94
.#D4 ,,OP5-,,5D$ ,"N ?REE DI6]5T -PLEX
NUMB]S ) AN ABSOLUTE VALUE ( #BE4 ,!N
PLOT YR ANSW]S 9 ! SAME -PLEX PLANE4
.#E4 ,,GRI4$ ,,ANSW] ,:AT IS ! PRODUCT
( #E--#I .;I & XS -PLEX 3JUGATE8
.#F4 ,,%ORT ,,RESPONSE ,! DIAGRAM %[S
A DESIGN =A HANG+ GLASS LAMP4 ,WRITE A
QUADRATIC FUNC;N T MODELS ! P>ABOLIC
CROSS SEC;N (! LAMP4 ,EXPLA9 H[ Y C
V]IFY T YR MODEL IS CORRECT4
.#G4 ,,EXT5D$ ,,RESPONSE ,Y ?R[ A BALL
6YR FR4 ,! BALL L1VES YR H& #E FEET ABV
! GR.D & HAS AN 9ITIAL V]TICAL VELOC;Y (
#EJ FEET P] SECOND4 ,YR FR CAT*ES ! BALL
:5 X FALLS 6A HEI<T ( #C FEET4
.A4 ,WRITE A FUNC;N T GIVES ! BALL'S
HEI<T .;H 7IN FEET7 .;T SECONDS AF Y ?R[
X4
.B4 ,H[ L;G IS ! BALL 9 ! AIR8
.C4 ,DESCRIBE ?REE ME?ODS Y CD USE
6F9D ! MAXIMUM HEI<T (! BALL4 ,!N F9D !
MAXIMUM HEI<T US+ EA* ME?OD4
.#H4 ,,%ORT ,,RESPONSE ,Y >E DESIGN+
NOTEPAP] )A SOLID /RIPE AL;G ! PAP]'S
TOP & LEFT SIDES Z %[N4 ,! /RIPES W TAKE
UP "O ?IRD (! >EA (! PAP]4 ,! PAP]
M1SURES #E 9*ES 0#H 9*ES4 ,:AT W ! WID?
;X (! /RIPES BE8 ,EXPLA9 :Y Y M/ REJECT
"O (! SOLU;NS4
.#I4 ,,GRI4$ ,,ANSW] ,:AT IS !
4CRIM9ANT (! EQU,N #C;X#B @+ #E;X--#B .K
#J8
------------------------------------#CAG
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,ELECTRONIC ,FUNC;N ,LIBR>Y
,,BIG ,,ID1S
,= ,YR ,NOTEBOOK
,BIG ,IDEA #A
,GRAPH+ & ,WRIT+ ,QUADRATIC ,FUNC;NS 9
,S"EAL ,=MS
,Y C GRAPH OR WRITE A QUADRATIC FUNC;N
9 /&>D =M1 V]TEX =M1 OR 9T]CEPT =M4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,=M3 ,EQU,N3 ,9=M,N AB QUADRATIC
FUNC;N
,/&>D =M3 .;Y .K .AX #B @+ .BX @+ .;C
@3 99 ,! .;X -COORD9ATE (! V]TEX IS @4
99 ,! AXIS ( SYMMETRY IS @4
,V]TEX =M3 .;Y .K .A7.;X-.;H7 #B @+
.;K @3 99 ,! V]TEX IS 7.;H1 .;K74
99 ,! AXIS ( SYMMETRY IS .;X .K .H4
,9T]CEPT =M3 .;Y .K .A @7 .;X -- .;P
@7@7 .;X - .;Q @7 @3 99 ,! .;X -9T]CEPTS
>E .;P & .Q4
99 ,! AXIS (! SYMMETRY IS @4
,BIG ,IDEA #B
,SOLV+ ,QUADRATIC ,EQU,NS ,US+ A
,V>IETY ( ,ME?ODS
,"! >E S"EAL DI6]5T ME?ODS Y C USE
6SOLVE A QUADRATIC EQU,N4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,EQU,N _+CONTAINS::_: ,EXAMPLE3 ,ME?OD
,BINOMIAL )\T .;X -T]M @3 #E .;X #B --
#DE .K #J @3 ,ISOLATE ! .;X #B -T]M4 ,!N
TAKE SQU>E ROOTS ( EA* SIDE4
,FACTORA# TRINOMIAL3 .;X #B -- #E .;X
@+ #F .K #J @3 ,FACTOR ! TRINOMIAL4 ,!N
USE ! Z]O PRODUCT PROP]TY4
,UNFACTORA# TRINOMIAL3 ;X #B -- #H .;X
@+ #CE .K #J @3 ,-PLETE ! SQU>E1 .OR USE
! QUADRATIC =MULA4
,BIG ,IDEA #C
,P]=M+ ,OP],NS ) ,SQU>E ,ROOTS &
,-PLEX ,NUMB]S
,Y C USE ! FOLL[+ PROP]TIES 6SIMPLIFY
EXPRES.NS 9VOLV+ SQU>E ROOTS OR -PLEX
NUMB]S4
,! FOLL[+ TA# IS 9 LI/$
=MAT4 ,= EA* CELL ! H1D+ IS %[N
FOLL[$ 0A COLON1 SPACE &! CELL
3T5TS
.,SQU>E .ROOTS @3 .,-PLEX .NUMB]S
& @4 @3 ,CELL 3T5TS FOLL[ 2T BOX+
L9ES4
99 ,! IMAG9>Y UNIT .;I IS DEF9$ Z @1 S
T .;I #B .K --#A4
99 ,IF .;R IS A POSITIVE R1L NUMB]1 !N
& @4
99 @7 .A @+ .BI @7 @+ @7 .;C @+ .DI @7
.K @7 .A @+ .;C @7 @+ @7 .;B @+ .;D @7
.;I
99 @7 .A @+ .BI @7--@7 .;C @+ .DI @7
.K @7 .A -- .;C @7 @+ @7 .;B @+ .;D @7
.;I
------------------------------------#CAH
#D ,*APT] ,REVIEW
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99 ,MULTI-,LANGUAGE ,GLOSS>Y
99 ,VOCABUL>Y PRACTICE
,,REVIEW ,,KEY ,,VOCABUL>Y
99 QUADRATIC FUNC;N1 P4 #BCF
99 /&>D =M (A QUADRATIC FUNC;N1 P4
#BCF
99 P>ABOLA1 P4 #BCF
99 V]TEX1 P4 #BCF
99 AXIS ( SYMMETRY1 P4 #BCF
99 M9IMUM1 MAXIMUM VALUE1 P4 #BCH
99 V]TEX =M1 P4 #BDE
99 9T]CEPT =M1 P4 #BDF
99 MONOMIAL1 BINOMIAL1 TRINOMIAL1 P4
#BEB
99 QUADRATIC EQU,N1 P4 #BEC
99 /&>D =M (A QUADRATIC EQU,N1 P4 #BEC
99 ROOT ( AN EQU,N1 P4 #BEC
99 Z]O (A FUNC;N1 P4 #BED
99 SQU>E ROOT1 P4 #BFF
99 RADICAL1 RADIC&1 P4 #BFF
99 R,NALIZ+ ! DENOM9ATOR1 P4 #BFG
99 3JUGATES1 P4 #BFG
99 IMAG9>Y UNIT .;I1 P4 #BGE
99 -PLEX NUMB]1 P4 #BGF
99 /&>D =M (A -PLEX NUMB]1 P4 #BGF
99 IMAG9>Y NUMB]1 P4 #BGF
99 PURE IMAG9>Y NUMB]1 P4 #BGF
99 -PLEX 3JUGATES1 P4 #BGH
99 -PLEX PLANE1 P4 #BGH
99 ABSOLUTE VALUE (A -PLEX NUMB]1 P4
#BGI
99 -PLET+ ! SQU>E1 P4 #BHD
99 QUADRATIC =MULA1 P4 #BIB
99 4CRIM9ANT1 P4 #BID
99 QUADRATIC 9EQUAL;Y 9 TWO V>IA#S1 P4
#CJJ
99 QUADRATIC 9EQUAL;Y 9 "O V>IA#1 P4
#CJB
99 BE/-FITT+ QUADRATIC MODEL1 P4 #CGG
,,VOCABUL>Y ,,EX]CISES
.#A4 .,,WRIT+ ,GIV5 A QUADRATIC FUNC;N
9 /&>D =M1 EXPLA9 H[ 6DET]M9E :E!R !
FUNC;N HAS A MAXIMUM VALUE OR A M9IMUM
VALUE4
.#B4 ,COPY & -PLETE3 ,A7;N7 @8 IS A
-PLEX NUMB] .A @+ .BI ": .A .K #J & .;B
@6.K #J4
.#C4 ,COPY & -PLETE3 ,A FUNC;N (! =M
.;Y .K .A @7 .;X -- .;H @7 #B @+ .;K IS
WRITT5 9 @8 @4
.#D4 ,GIVE AN EXAMPLE (A QUADRATIC
EQU,N T HAS A NEGATIVE 4CRIM9ANT4
,,REVIEW ,,EXAMPLES ,,& ,,EX]CISES
,USE ! REVIEW EXAMPLES & EX]CISES 2L
6*ECK YR "U/&+ (! 3CEPTS Y H LE>N$ 9 EA*
LESSON ( ,*APT] .#D4
#D.A ,GRAPH ,QUADRATIC ,FUNC;NS 9
,/&>D ,=M PP4 #BCF-BDC
,,EXAMPLE
,GRAPH ..;Y .K--.;X #B -- ..#D .;X --
#E4
,2C .A "K #J1 ! P>ABOLA OP5S D[N4 ,F9D
& PLOT ! V]TEX 7-#B1 --#A74 ,DRAW ! AXIS
( SYMMETRY .;X .K -- .#B4 ,PLOT !
;Y-9T]CEPT AT 7#J1 --#E71 & PLOT XS
REFLEC;N 7-#D1 --#E7 9 ! AXIS (
SYMMETRY4 ,PLOT TWO O!R PO9TS3 7-#A1
--#B7 & XS REFLEC;N 7-#C1 --#B7 9 ! AXIS
( SYMMETRY4 ,DRAW A P>ABOLA "? ! PLOTT$
PO9TS4
,,EXAMPLE #C
ON P4 #BCH = ,EXS4 #E-G
,,EX]CISES
,GRAPH ! FUNC;N4 ,LABEL ! V]TEX & AXIS
( SYMMETRY4
.#E4 .;Y .K .;X #B @+ ..#B .;X -- #C
.#F4 .;Y .K --#C .;X #B @+ #AB .;X --
#G
.#G4 .;F @7 .;X @7 .K --;X #B -- #B
.;X -- #F
------------------------------------#CAI
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#D.B ,GRAPH ,QUADRATIC ,FUNC;NS 9
,V]TEX OR ,9T]CEPT ,=M PP4 #BDE-BEA
,,EXAMPLE
.,GRAPH .;Y .K @7 .;X -- #D7@7 .;X @+
#B74
,ID5TIFY ! .;X -9T]CEPTS4 ,! QUADRATIC
FUNC;N IS 9 9T]CEPT =M .;Y .K .A @7 .;X
-- .;P @7@7 .;X -- .;Q @7 ": .A .K #A1
.;P .K #D1 & .;Q .K -- .#B4 ,PLOT ! .;X
-9T]CEPTS AT 7#D1 #J7 & 7-#B1 #J74
,F9D ! COORD9ATES (! V]TEX4
.;Y .K 7#A--#D77#A @+ #B7 .K --#I
,PLOT ! V]TEX AT 7#A1 --#I74 ,DRAW A
P>ABOLA "? ! PLOTT$ PO9TS Z %[N4
,,EXAMPLES #A1 #C1 & #D
ON PP4 #BDE-BDG = ,EXS4 #H-AD
,,EX]CISES
,GRAPH ! FUNC;N4 ,LABEL ! V]TEX & AXIS
( SYMMETRY4
.#H4 .;Y .K @7 .;X -- #A7@7 .;X @+ #E7
.#I4 .;G @7 .;X @7 .K 7.;X @+ #C7@7
.;X -- #B7
.#AJ4 .;Y .K --#C7 .;X @+ #A7@7 .;X --
#F7
.#AA4 .;Y .K @7 .;X--.IF @+ #C
.#AB4 .;F @7 .;X @7 .K @7 .;X @+ #F7
#B @+ #H
.#AC4 .;Y .K --#B7 .;X @+ #H7 #B -- #C
.#AD4 .,,BIOLOGY ,A FLEA'S JUMP C 2
MODEL$ 0! FUNC;N .;Y .K --#J.JGC .;X @7
.;X -- #CC7 ": .;X IS ! HORIZONTAL 4T.E
7IN C5TIMET]S7 & .;Y IS ! CORRESPOND+
HEI<T 7IN C5TIMET]S74 ,H[ F> DID ! FLEA
JUMP8 ,:AT 0 ! FLEA'S MAXIMUM HEI<T8
#D.C ,SOLVE .;X #B @+ .BX @+ .;C .K #J
0,FACTOR+ PP4 #BEB-BEH
,,EXAMPLE
.,SOLVE .;X #B -- #AC .;X -- #DH .K
#J4
,USE FACTOR+ 6SOLVE = .X4
.;X #B -- #AC .;X -- #DH .K #J .,WRITE
.ORIG9AL .EQU,N4
@7 .;X -- #AF7 @7 .;X @+ #C7 .K #J
,FACTOR4
..;X -- #AF .K .#J OR .;X @+ #C .K #J
.,Z]O .PRODUCT .PROP]TY
.;X .K #AF OR .;X .K --#C ..,SOLVE =
.;X @4
,,EXAMPLE #C
ON P4 #BED = ,EXS4 #AE-BA
,,EX]CISES
,SOLVE ! EQU,N4
.#AE4 .;X #B @+ #E .;X .K #J
.#AF4 .;Z #B .K #FC .;Z
.#AG4 .;S #B -- #F .;S -- #BG .K #J
.#AH4 .;K #B @+ #AB .;K -- #DE .K #J
.#AI4 .;X #B @+ #AH .;X .K --#HA
.#BJ4 .;N #B @+ #E .;N .K #BD
.#BA4 .,,URBAN .,,PLANN+ ,A C;Y WANTS
6D\# ! >EA (A RECTANGUL> PLAYGR.D T IS
#GB FEET 0#DH FEET 0A4+ ! SAME 4T.E .;X
6! L5G? &! WID?4 ,WRITE & SOLVE AN EQU,N
6F9D ! VALUE ( .;X @4
------------------------------------#CBJ
#D ,*APT] ,REVIEW
#D.D ,SOLVE .AX #B @+ .BX @+ .;C -- #J
0,FACTOR+ PP4 #BEI-BFD
,,EXAMPLE
,SOLVE --#CJ .;X #B @+ #I .;X @+ #AB
.K #J4
-#CJ .;X #B @+ #I .;X @+ #AB .K #J
.,WRITE .ORIG9AL .EQU,N4
#AJ .;X #B -- #C .;X -- #D .K #J
..,DIVIDE EA* SIDE BY --.#C4
7#E .;X -- #D7 7#B .;X @+ #A7 .K #J
.,FACTOR4
#E .;X -- #D .K #J OR #B .;X @+ #A .K
#J .,Z]O .PRODUCT .PROP]TY
.;X .K OR ..,SOLVE = .;X @4
,,EXAMPLE #E
ON P4 #BFA = ,EXS4 #BB-BD
,,EX]CISES
,SOLVE ! EQU,N4
.#BB4 #AF .K #CH .;R -- #AB .;R #B
.#BC4 #C .;X #B -- #BD .;X -- #DH .K
#J
.#BD4 #BJ .A #B -- #AC .A -- #BA .K #J
#D.E ,SOLVE ,QUADRATIC ,EQU,NS 0,F9D+
,SQU>E ,ROOTS PP4 #BFF-BGA
,,EXAMPLE
,SOLVE #D7 .;X -#G7 #B .K #HJ4
#D7 .;X -- #G7 #B .K #HJ .,WRITE
.ORIG9AL .EQU,N4
@7 .;X -- #G7 #B .K #BJ ..,DIVIDE EA*
SIDE 0.#D4
,,EXAMPLES #C & #D
ON PP4 #BFG-BFH = ,EXS4 #BE-BH
,,EX]CISES
,SOLVE ! EQU,N4
.#BE4 #C .;X #B .K #AJH
.#BF4 #E .;Y #B @+ #D .K #AD
.#BG4 #C7 .;P @+ #A7 #B .K #HA
.#BH4 .,,GEOGRAPHY ,! TOTAL SURFACE
>EA ( ,E>? IS #EAJ1JJJ1JJJ SQU>E
KILOMET]S4 ,USE ! =MULA .;,S .K #D .;R
#B @1 : GIVES ! SURFACE >EA (A SPH]E )
RADIUS .;R @1 6F9D ! RADIUS ( ,E>?4
#D.F ,P]=M ,OP],NS ) ,-PLEX ,NUMB]S
PP4 #BGE-BHB
,,EXAMPLE
,WRITE 7#F--#D .;I @7 7#A--#C .;I @7 Z
A -PLEX NUMB] 9 /&>D =M4
7#F--#D .;I @7@7 .#A -- #C .;I @7 .K
#F--#AH .;I -- #D .;I @+ #AB .;I #B
.,MULTIPLY .US+ .,,FOIL4
.K #F--#BB .;I @+ #AB7-#A7 ..,SIMPLIFY
& USE .;I #B .K --.#A4
.K --#F--#BB .;I ..,WRITE 9 /&>D .=M4
------------------------------------#CBA
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,,EXAMPLES #B1 #D1 & #E
ON PP4 #BGF-BGH = ,EXS4 #BI-CD
,,EX]CISES
,WRITE ! EXPRES.N Z A -PLEX NUMB] 9
/&>D =M4
.#BI4 --#I .;I 7#B -- .;I @7
.#CJ4 7#E @+ .;I @77#D--#B .;I @7
.#CA4 7#B--#E .;I 7#B @+ #E .;I @7
.#CB4 7#H--#F .;I @7 @+ 7#G @+ #D .;I
@7
.#CC4 7#B--#C .;I @7--7#F--#E .;I @7
.#CD4
#D.G ,-PLETE ! ,SQU>E PP4 #BCD-BIA
,,EXAMPLE
,SOLVE .;X #B -- #H .;X @+ #AC .K #J
0-PLET+ ! SQU>E4
,,EXAMPLES #C & #D
ON PP4 #BHE-BHF = ,EXS4 #CE-CG
,,EX]CISES
,SOLVE ! EQU,N 0-PLET+ ! SQU>E4
.#CE4 .;X #B -- #F .;X -- #AE .K #J
.#CF4 #C .;X #B -- #AB .;X @+ #A .K #J
.#CG4 .;X #B @+ #C .;X -- #A .K #J
#D.H ,USE ! ,QUADRATIC ,=MULA &!
,4CRIM9ANT PP4 #BIB-BII
,,EXAMPLE
,SOLVE #C .;X #B @+ #F .;X .K --#B4
,,EXAMPLES #A1 #B1 #C1 & #E
ON PP4 #BIB-BIE = ,EXS4 #CH-DA
,,EX]CISES
,USE ! QUADRATIC =MULA 6SOLVE ! EQU,N4
.#CH4 .;X #B @+ #D .;X -- #C .K #J
.#CI4 #I .;X #B .K --#F .;X -- #A
.#DJ4 #F .;X #B -- #H .;X .K --#C
.#DA4 .,,VOLLEYBALL ,A P]SON SPIKES A
VOLLEYBALL OV] A NET :5 ! BALL IS #I
FEET ABV ! GR.D4 ,! VOLLEYBALL HAS AN
9ITIAL V]TICAL VELOC;Y ( --#DJ FEET P]
SECOND4 ,! VOLLEYBALL IS ALL[$ 6FALL 6!
GR.D4 ,H[ L;G IS ! BALL 9 ! AIR AF X IS
SPIK$8
------------------------------------#CBB
#D ,,*APT] ,,REVIEW
#D.I ,GRAPH & ,SOLVE ,QUADRATIC
,9EQUALITIES PP4 #CJJ-CJG
,,EXAMPLE
.,SOLVE --#B;X #B @+ #B .;X @+ #E "K.K
#J4
,! SOLU;N 3SI/S (! .;X -VALUES = : !
GRAPH ( .;Y .K --#B .;X #B @+ #B .;X @+
#E LIES ON OR 2L ! .;X -AXIS4 ,F9D !
GRAPH'S .;X -9T]CEPTS 0LETT+ .;Y .K #J &
US+ ! QUADRATIC =MULA 6SOLVE = .;X @4
,SKET* A P>ABOLA T OP5S D[N & HAS
--#A.AF & #B.AF Z .;X -9T]CEPTS4 ,!
SOLU;N (! 9EQUAL;Y IS APPROXIMATELY .;X
"K.K --#A.AF OR .;X .1.K #B.AF4
,,EXAMPLE #E
ON P4 #CJB = ,EXS4 #DB-DD
,,EX]CISES
,SOLVE ! 9EQUAL;Y 0GRAPH+4
.#DB4 #B .;X #B -- #AA .;X @+ #E "K #J
.#DC4 -- .;X #B @+ #D .;X @+ #C .1 #J
.#DD4
#D.AJ ,WRITE ,QUADRATIC ,FUNC;NS &
,MODELS PP4 #CJI-CAE
,,EXAMPLE
,WRITE A QUADRATIC FUNC;N =! P>ABOLA
%[N4
,2C Y >E GIV5 ! .;X -9T]CEPTS .;P .K
--#C & .;Q .K #B1 USE ! 9T]CEPT =M .;Y
.K .A @7 .;X -- .;P @7@7 .;X -- .;Q @7
.K .A @7 .;X @+ #C7@7 .;X -- #B74
,USE ! O!R GIV5 PO9T1 7#A1 --#B71 6F9D
.A @4
-#B .K .A 7#A @+ #C77#A--#B7
..,SUB/ITUTE #A = ;X & --#B = .;Y @4
-#B .K --#D .A ..,SIMPLIFY COE6ICI5T (
.A4
.K .A .,SOLVE .= .A4
,A QUADRATIC FUNC;N =! P>ABOLA IS @4
,,EXAMPLES #A & #B
ON P4 #CJI = ,EXS4 #DE-DH
,,EX]CISES
,WRITE A QUADRATIC FUNC;N ^: GRAPH HAS
! GIV5 "*I/ICS4
.#DE4 .;X -9T]CEPTS3 --#C1 #B
PASSES "?3 7#C1 #AB7
.#DF4 PASSES "?3
7#E1 #B71 7#J1 #B71 7#H1 --#F7
.#DG4 V]TEX3 7#B1 #G7
PASSES "?3 7#D1 #B7
.#DH4 .,,SO3] ,! P>ABOLIC PA? (A SO3]
BALL T IS KICK$ F ! GR.D PASSES "? !
PO9T 7#J1 #J7 & HAS V]TEX 7#AB1 #G7 ": !
COORD9ATES >E 9 FEET4 ,WRITE A QUADRATIC
FUNC;N T MODELS ! SO3] BALL'S PA?4
------------------------------------#CBC
#D ,*APT] ,TE/
,GRAPH ! FUNC;N4 ,LABEL ! V]TEX & AXIS
( SYMMETRY4
.#A4 .;Y .K .;X #B -- #H .;X -- #BJ
.#B4 .;Y .K --@7 .;X @+ #C7 #B @+ #E
.#C4 .;F @7 .;X @7 .K #B7 .;X @+ #D7@7
.;X -- #B7
,FACTOR ! EXPRES.N4
.#D4 .;X #B -- #AA .;X @+ #CJ
.#E4 .;Z #B @+ #B .;Z - #AE
.#F4 .;N #B -- #FD
.#G4 #B .;S #B @+ #G .;S -- #AE
.#H4 #I .;X #B @+ #CJ .;X @+ #BE
.#I4 #F .;T #B @+ #BC8 @+ #BJ
,SOLVE ! EQU,N4
.#AJ4 .;X #B -- #C .;X -- #DJ .K #J
.#AA4 .;R #B -- #AC .;R @+ #DB .K #J
.#AB4 #B .;W #B @+ #AC .;W --#G .K #J
.#AC4 #AJ .;Y #B @+ #AA .;Y -- #F .K
#J
.#AD4 #B7 .;M -- #G7 #B .K #AF
.#AE4 @7 .;X @+ #B7 #B -- #AB .K #CF
,WRITE ! EXPRES.N Z A -PLEX NUMB] 9
/&>D =M4
.#AF4 7#C @+ #D .;I @7--7#B--#E .;I @7
.#AG4 7#B--#G .;I @77#A @+ #B .;I @7
.#AH4
,SOLVE ! EQU,N 0-PLET+ ! SQU>E4
.#AI4 .;X #B @+ #D .;X -- #AD--#J
.#BJ4 .;X #B -- #AJ .;X -- #G .K #J
.#BA4 #D .;X #B @+ #H .;X @+ #C .K #J
,USE ! QUADRATIC =MULA 6SOLVE ! EQU,N4
.#BB4 #C .;X #B @+ #AJ .;X -- #E .K #J
.#BC4 #B .;X #B -- .;X @+ #F .K #J
.#BD4 #E .;X #B @+ #B .;X @+ #E .K #J
,GRAPH ! 9EQUAL;Y4
.#BE4 .;Y .1.K .;X #B -- #H
.#BF4 .;Y "K .;X #B @+ #D .;X -- #BA
.#BG4 .;Y .1 -- .;X #B @+ #E .;X @+
#EJ
,WRITE A QUADRATIC FUNC;N ^: GRAPH HAS
! GIV5 "*I/ICS4
.#BH4 .;X -9T]CEPTS3 --#G1 --#C
PASSES "?3 7-#A1 #AB7
.#BI4 V]TEX3 7-#C1 --#B7
PASSES "?3 7#A1 --#AJ7
.#CJ4 PASSES "?3
7#D1 #H71 7#G1 --#D71 7#H1 #J7
.#CA4 .,,ASPECT .,,RATIO ,! .ASPECT
.RATIO (A WIDESCRE5 ,,TV IS ! RATIO (!
SCRE5'S WID? 6XS HEI<T1 OR #AF3I4 ,:AT
>E ! WID? &! HEI<T (A #CB 9* WIDESCRE5
,,TV8 @7 .,H9T3 ,USE ! ,PY?AGOR1N !OREM
&! FACT T ,,TV SIZES S* Z #CB 9*ES REF]
6! L5G? (! SCRE5'S DIAGONAL47
.#CB4 .,,WOOD .,,/R5G? ,! DATA %[ H[ !
/R5G? ( ,D\GLAS FIR WOOD IS RELAT$ 6!
P]C5T MOI/URE 9 ! WOOD4 ,! /R5G? VALUE =
WOOD ) #B@3P MOI/URE IS DEF9$ 6BE #A4
,ALL O!R /R5G? VALUES >E RELATIVE 6?
VALUE4 7,= EXAMPLE1 WOOD ) #D@3P MOI/URE
IS #IG.I@3P Z /R;G Z WOOD ) #B@3P
MOI/URE47 ,USE ! QUADRATIC REGRES.N
F1TURE (A GRAPH+ CALCULATOR 6F9D !
BE/-FITT+ QUADRATIC MODEL =! DATA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,P]C5T MOI/URE1 .;M @3 #B3 #D3 #F3 #H3
#AJ
,/R5G?.' ;S @3 #A3 #J.IGI3 #J.HEJ3
#J.GGD3 #J.GAD
,P]C5T MOI/URE1 .;M @3 #AB3 #AD3 #AF3
#AH3 #BJ
,/R5G?1 .;S @3 #J.FDC3 #J.EHI3 #J.ECE3
#J.DID3 #J.DEH
------------------------------------#CBD
#D ,/&>DIZ$ ,TE/ ,PREP>,N
,,3TEXT-,,BAS$ ,,MULTIPLE-,,*OICE
,,"QS
,SIDEB>3
,/&>DS
.#H..J .,/UD5TS .SOLVE & GRAPH
..QUADRATIC EQU,NS 0.FACTOR+ @1 -PLET+ !
SQU>E1 OR US+ ! QUADRATIC =MULA4
..,/UD5TS APPLY ^! TE*NIQUES 9 SOLV+ ^W
.PRO#MS @4 ,!Y AL SOLVE QUADRATIC EQU,NS
9 ! -PLEX NUMB] SY/EM4
,"S (! 9=M,N Y NE$ 6SOLVE A
MULTIPLE-*OICE "Q MAY APPE> 9 A TA#1 A
DIAGRAM1 OR A GRAPH4
,,PRO#M #A
,! >EA (! %AD$ REGION IS #EF SQU>E
MET]S4 ,:AT IS ! HEI<T (! TRAPEZOID8
,A4 #C MET]S
,B4 #D MET]S
,C4 #F MET]S
,D4 #G.E MET]S
,PLAN
.,,9T]PRET .,,! .,,DIAGRAM ,Y "K ! >EA
(! %AD$ REGION4 ,USE ! DIAGRAM 6F9D !
>EA (! RECTANGLE1 & WRITE AN EXPRES.N =!
>EA (! TRAPEZOID4 ,! DI6];E ( ^! TWO >1S
IS ! >EA (! %AD$ REGION4
,SOLU;N
,,/EP #A
,F9D EXPRES.NS =! TWO >1S4
,>EA OR RECTANGLE3
.,A .K .LW
.K #AC7#H7
.K #AJD ;M #B
,>EA ( TRAPEZOID3
,,/EP #B
,WRITE AN EQU,N =! >EA (! %AD$ REGION
& SOLVE 0FACTOR+4
,>EA ( %AD$ REGION .K ,>EA (
RECTANGLE--,>EA ( TRAPEZOID
#EF .K #AJD--7#D .;X #B @+ #D .;X @7
,SUB/ITUTE4
-#DH .K-#D .;X #B -- #D .;X ,SUBTRACT
#AJD F EA* SIDE4
#D .;X #B @+ #D .;X -- #DH .K #J
,WRITE 9 /&>D =M4
.;X #B @+ .;X -- #AB .K #J ,DIVIDE EA*
SIDE 0#D4
@7 .;X -- #C7@7 .;X @+ #D7 .K #J
,FACTOR4
.;X .K #C OR .;X .K --#D ,Z]O PRODUCT
PROP]TY
,,/EP #C
,F9D ! POSSI# HEI<TS4
,! HEI<T (! TRAPEZOID IS GIV5 0!
EXPRES.N #B .;X @4 ,"!=E1 ! POSSI#
HEI<TS >E #B7#C7 .K #F MET]S & #B7-#D7
.K --#H MET]S4
,,/EP #D
,REJECT ! NEGATIVE HEI<T4
,2C HEI<T _C 2 NEGATIVE1 ! HEI<T (!
TRAPEZOID IS #F MET]S4
,! CORRECT ANSW] IS ,C4 ..,A ;,B ;,C
.;,D
------------------------------------#CBE
,,PRO#M #B
,! HEI<T .;H 7IN FEET7 (A LO2$ T5NIS
BALL AF .;T SECONDS IS %[N 0! GRAPH4
,:AT IS ! 9ITIAL V]TICAL VELOC;Y (!
T5NIS BALL8
,A4 #C FEET_/SECOND
,B4 #AF FEET_/SECOND
,C4 #CG.E FEET_/SECOND
,D4 #DG FEET_/SECOND
,PLAN
.,,9T]PRET .,,! .,,GRAPH ,! GRAPH IS A
P>ABOLA PASS+ "? ! PO9TS 7#J1 #C7 & 7#C1
#J74 ,9 ORD] 6F9D ! 9ITIAL V]TICAL
VELOC;Y (! T5NIS BALL1 Y M/ WRITE AN
EQU,N (! P>ABOLA4
,SOLU;N
,,/EP #A
,WRITE ! MODEL = AN OBJECT T IS LAUN*$
,2C ! T5NIS BALL IS LAUN*$1 ! P>ABOLA
HAS AN EQU,N (! =M .;H .K --#AF .;T #B
@+ .;V #J .;T @+ .;H #J ": .;V #J IS !
9ITIAL V]TICAL VELOC;Y & .;H #J IS !
9ITIAL HEI<TS (! T5NIS BALL4
,,/EP #B
,USE ! 9ITIAL HEI<T 9 YR MODEL4
,! GRAPH PASSES "? 7#J1 #C71 S !
9ITIAL HEI<T (! T5NIS BALL IS #C FEET4
,:5 Y SUB/ITUTE #C = .;H #J 9 ! MODEL1 Y
OBTA9 .;H .K --#AF .;T #B @+ .;V #J .;T
@+ #C4
,,/EP #C
,F9D ! 9ITIAL V]TICAL VELOC;Y
0SUB/ITUT+ A PO9T ON ! P>ABOLA4
,USE ! FACT T ! GRAPH ( .;H .K --#AF
.;T #B @+ .;V #J .;T @+ #C PASSES "?
7#C1 #J7 6F9D ! 9ITIAL V]TICAL VELOC;Y
.;V #J @4
#J .K --#AF7#C7 #B @+ .;V #J 7#C7 @+
#C ,SUB/ITUTE #J = .;H & #C = .;T @4
#J .K --#ADA @+ #C .;V #J ,SIMPLIFY4
#DG .K .;V #J ,SOLVE = .;V #J @4
,! 9ITIAL V]TICAL VELOC;Y IS #DG FEET
P] SECOND4
,! CORRECT ANSW] IS ,D4
,,PRACTICE
,9 ,EX]CISES #A & #B1 USE ! GRAPH 9
,PRO#M #B4
#A4 ,:AT IS ! MAXIMUM HEI<T (! T5NIS
BALL 6! NE>E/ T5? (A FOOT8
,A4 #CF.C FEET
,B4 #CF.H FEET
,C4 #CG.E FEET
,D4 #CH.J FEET
#B4 ,:AT DOES ! .;X -COORD9ATE (!
V]TEX (! GRAPH REPRES5T8
,A4 ,! MAXIMUM HEI<T (! T5NIS BALL
,B4 ,! NUMB] ( SECONDS ! BALL IS 9 !
AIR
,C4 ,! NUMB] ( SECONDS X TAKES ! BALL
6R1* XS MAXIMUM HEI<T
,D4 ,! 9ITIAL HEI<T (! T5NIS BALL
------------------------------------#CBF
#D ,/&>DIZ$ ,TE/ ,PRACTICE
,,3TEXT-,,BAS$ ,,MULTIPLE ,,*OICE
,9 ,EX]CISES #A & #B1 USE ! P>ABOLA
2L4
#A4 ,: /ATE;T IS .N TRUE AB ! P>ABOLA8
,A4 ,! .;X -9T]CEPTS >E --#B & #D4
,B4 ,! ;Y-9T]CEPT IS --#B4
,C4 ,! MAXIMUM VALUE IS #C4
,D4 ,! AXIS ( SYMMETRY IS .;X .K #A4
#B4 ,:AT IS AN EQU,N (! P>ABOLA8
,A4 .;Y .K @7 .;X -- #B7@7 .;X @+ #D7
,B4
,C4 .;Y .K --@7 .;X @+ #B7@7 .;X -#D7
,D4 .;Y .K --#C7 .;X @+ #B7@7 .;X --
#D7
#C4 ,Y >E US+ GLASS TILES 6MAKE A
PICTURE FRAME =A SQU>E PHOTOGRAPH )
SIDES #AJ 9*ES L;G4 ,Y WANT ! FRAME 6=M
A UNI=M BORD] >.D ! PHOTOGRAPH4 ,Y H 5
TILES 6COV] #CJJ SQU>E 9*ES4 ,:AT IS !
L>GE/ POSSI# FRAME WID? .;X @8
,A4 #C.F 9*ES
,B4 #E 9*ES
,C4 #G.C 9*ES
,D4 #AE 9*ES
#D4 ,AT A FLEA M>KET HELD EA* WEEK5D1
AN >TI/ SELLS H&MADE E>R+S4 ,! TA# 2L
%[S ! AV]AGE NUMB] ( PAIRS ( E>R+S SOLD
= S"EAL PRICES4 ,GIV5 ! PATT]N 9 ! TA#1
H[ M* %D ! >TI/ *>GE 6MAXIMIZE REV5UE8
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,PRICE @3 4#AE3 4#AD3 4#AC3 4#AB
.,PAIRS .SOLD @3 #EJ3 #FJ3 #GJ3 #HJ
,A4 4#E
,B4 4#G.EJ
,C4 4#AJ
,D4 4#AE
#E4 ,! GRAPH ( : 9EQUAL;Y IS %[N8
,A4 .;Y .1.K --;X #B -- .;X @+ #F
,B4 .;Y .1.K .;X #B @+ .;X -- #F
,C4 .;Y .1 #B .;X #B @+ #B .;X -- #AB
,D4 .;Y .1.K --#B .;X #B -- #B .;X @+
#AB
,9 ,EX]CISES #F & #G1 USE ! 9=M,N 2L4
,! GRAPH %[S ! HEI<T .;H 7IN FEET7 AF
.;T SECONDS (A HORSE%OE TOSS$ DUR+ A
GAME ( HORSE%OES4 ,! 9ITIAL V]TICAL
VELOC;Y (! HORSE%OE IS #CJ FEET P]
SECOND4
#F4 ,6! NE>E/ T5? (A SECOND1 H[ L;G IS
! HORSE%OE 9 ! AIR8
,A4 #J.A SECOND
,B4 #A.I SECONDS
,C4 #B.A SECONDS
,D4 #C.I SECONDS
#G4 ,6! NE>E/ T5? (A FOOT1 :AT IS !
MAXIMUM HEI<T (! HORSE%OE8
,A4 #A.I FEET
,B4 #H.A FEET
,C4 #AF.A FEET
,D4 #CB.B FEET
#H4 ,! DIAGRAM %[S A CIRCLE 9SCRIB$ 9
A SQU>E4 ,! >EA (! %AD$ REGION IS #BA.E
SQU>E 9*ES4 ,6! NE>E/ T5? ( AN 9*1 H[
L;G IS A SIDE (! SQU>E8
,A4 #D.F 9*ES
,B4 #H.G 9*ES
,C4 #I.G 9*ES
,D4 #AJ.J 9*ES
------------------------------------#CBG
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,,GRI4$ ,,ANSW]
#I4 ,:AT IS ! VALUE ( .;K 9 ! EQU,N #F
.;X #B -- #AA .;X -- #AJ .K 7#C .;X @+
#B77#B .;X -- .;K @7@8
#AJ4 ,:AT IS ! R1L "P (! /&>D =M (!
EXPRES.N 7#E @+ .;I @77#AJ -- .;I @7@8
#AA4 ,= :AT VALUE ( .;C IS .;X #B --
#G .;X @+ .;C A P]FECT SQU>E TRINOMIAL8
#AB4 ,:AT IS ! MAXIMUM VALUE (! FUNC;N
.;Y .K --#C7 .;X -- #B7 #B @+ #F8
#AC4 ,:AT IS ! GRTE/ Z]O (! FUNC;N .;Y
.K .;X #B -- #BE .;X @+ #FF8
#AD4 ,:AT IS ! ABSOLUTE VALUE ( --#E
@+ #AB .;I @8
#AE4 ,:AT IS ! .;X -COORD9ATE (! V]TEX
(! P>ABOLA T PASSES "? ! PO9TS 7#J1
--#BB71 7#B1 --#F71 & 7#E1 --#AB78
#AF4 ,:AT IS ! M9IMUM VALUE (! FUNC;N
.;F @7 .;X @7 .K #D .;X #B @+ #BD .;X @+
#CI8
,,%ORT ,,RESPONSE
.#AG4 ,SOLVE #C;X#B @+ #F;X @+ #AD .K
#J 0-PLET+ ! SQU>E4 ,EXPLA9 ALL ( YR
/EPS4
.#AH4 ,! SURFACE >EA .;Y (A CUBE IS
GIV5 0! FUNC;N .;Y .K #F .;X #B ": ;X IS
AN $GE L5G?4 ,GRAPH ! FUNC;N4 ,-P>E ?
GRAPH 6! GRAPH ( .;Y .K .;X #B @4
.#AI4 ,! HEI<T .;H 7IN FEET7 ( AN
OBJECT AF X IS LAUN*$ IS GIV5 0! FUNC;N
.;H .K --#AF .;T #B @+ ;V #J ;T @+ .;H
#J
": ;V #J IS ! 9ITIAL V]TICAL VELOC;Y1
;H #J IS ! 9ITIAL HEI<T (! OBJECT1 & .;T
IS ! "T 7IN SECONDS7 AF ! OBJECT IS
LAUN*$4 ,EXPLA9 H[ ? FUNC;N IS RELAT$ 6!
G5]AL FUNC;N =A DROPP$ OBJECT4
.#BJ4 ,AT :AT TWO PO9TS D ! GRAPHS (
;Y .K #B;X#B--#E;X--#AB & 9T]SECT8
,EXPLA9 YR R1SON+4
,,EXT5D$ ,,RESPONSE
.#BA4 ,! TA# 2L %[S ! ,NEW ,YORK
,YANKEES' PAYROLL 7IN MILLIONS ( DOLL>S7
F #AIHI "? #BJJD4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,YE>S S9CE #AIHI3 #J3 #A3 #B3 #C3 #D3
#E3 #F3 #G
,PAYROLL3 #BA3 #BA3 #BH3 #CF3 #DA3
#DE3 #DG3 #EB
,YE>S S9CE #AIHI3 #H3 #I3 #AJ3 #AA3
#AB3 #AC3 #AD3 #AE
,PAYROLL3 #EI3 #FC3 #HH3 #IC3 #AAB3
#ABF3 #AEC3 #AHD
.A4 ,MAKE A SCATT] PLOT (! DATA4
.B4 ,DRAW ! P>ABOLA T Y ?9K BE/ FITS !
DATA4
.C4 ,E/IMATE ! COORD9ATES ( ?REE PO9TS
ON ! P>ABOLA F "P 7;B74 ,!N USE A SY/EM
( EQU,NS 6WRITE A QUADRATIC MODEL =!
DATA4
.D4 ,USE YR MODEL F "P 7;C7 6MAKE A
TA# ( DATA =! YE>S LI/$ 9 ! ORIG9AL TA#4
,-P>E ! NUMB]S GIV5 0YR MODEL )! ACTUAL
DATA4 ,ASSESS ! A3URACY ( YR MODEL4
.#BB4 ,A VOLLEYBALL IS HIT UPW>D 0A
PLAY] 9 A GAME4 ,! HEI<T .;H 7IN FEET7
(! VOLLEYBALL AF .;T SECONDS IS GIV5 0!
FUNC;N .;H .K --#AF;T #B @+ #CJ;T @+ #F4
.A4 ,:AT IS ! MAXIMUM HEI<T (!
VOLLEYBALL8 ,EXPLA9 YR R1SON+4
.B4 ,AF H[ _M SECONDS DOES !
VOLLEYBALL R1* XS MAXIMUM HEI<T8
.C4 ,AF H[ _M SECONDS DOES !
VOLLEYBALL HIT ! GR.D8
------------------------------------#CBH
#E ,POLYNOMIALS & ,POLYNOMIAL
,FUNC;NS
,PRODNOTE3 ,PRODUC;N NOTE3 ? IMAGE
CROSSES ! GUTT] 6APPE> BO? ON PAGE #CBH
& PAGE #CBI 9 ! PR9T V].N4
#E.A ,USE ,PROP]TIES ( ,EXPON5TS
#E.B ,EVALUATE & ,GRAPH ,POLYNOMIAL
,FUNC;NS
#E.C ,ADD1 ,SUBTRACT1 & ,MULTIPLY
,POLYNOMIALS
#E.D ,FACTOR & ,SOLVE ,POLYNOMIAL
,EQU,NS
#E.E ,APPLY ! ,REMA9D] & ,FACTOR
,!OREMS
#E.F ,F9D ,R,NAL ,Z]OS
#E.G ,APPLY ! ,FUNDA;TAL ,!OREM (
,ALGEBRA
#E.H ,ANALYZE ,GRAPHS ( ,POLYNOMIAL
,FUNC;NS
#E.I ,WRITE ,POLYNOMIAL ,FUNC;NS &
,MODELS
,SIDEB>3
,2F
,9 PREVI\S *APT]S1 Y LE>N$ ! FOLL[+
SKILLS1 : Y'LL USE 9 ,*APT] #E3 GRAPH+
FUNC;NS1 FACTOR+1 & SOLV+ EQU,NS4
,PREREQUISITE ,SKILLS
,,VOCABUL>Y ,,*ECK
,COPY & -PLETE ! /ATE;T4
.#A4 ,! .Z]OS (! FUNC;N GRAPH$ >E @8
@4
.#B4 ,! .MAXIMUM .VALUE (! FUNC;N
GRAPH$ IS @8 @4
.#C4 ,! ./&>D .=M (A QUADRATIC EQU,N 9
"O V>IA# IS @8 ": .A @6.K #J4
,,SKILLS ,,*ECK
,GRAPH ! FUNC;N4 ,LABEL ! V]TEX &!
AXIS ( SYMMETRY4 7.,REVIEW PP4 #BCF
,.#BDE .= .#E..B47
.#D4 .;Y .K --#B7 .;X -- #A7 #B @+ #D
.#E4 .;Y .K #C7 .;X -- #B7@7 .;X @+
#C7
.#F4 .;Y .K -- .;X #B -- #D .;X @+ #D
,FACTOR ! EXPRES.N4 7.,REVIEW PP4 #BEB
,.#BEI .= .#E..D47
.#G4 .;X #B @+ #I .;X @+ #BJ
.#H4 #B .;X #B @+ #E .;X -- #C
.#I4 #I .;X #B -- #FD
,SOLVE ! EQU,N4 7.,REVIEW PP4 #BEB
,.#BEI .= .#E..D--.#E..G47
.#AJ4 #B .;X #B @+ .;X @+ #F .K #J
.#AA4 ;L#J .;X #B @+ #AC .;X .K #C
.#AB4 .;X #B @+ #F .;X @+ #B .K #BJ
@A.,HOME,TUTOR ,PREREQUISITE SKILLS
PRACTICE AT _+CLASSZONE.COM_:
------------------------------------#CBI
,PRODNOTE3 ,PRODUC;N NOTE3 ? IMAGE
CROSSES ! GUTT] 6APPE> BO? ON PAGE #CBH
& PAGE #CBI 9 ! PR9T V].N4 ,SIDEB>3
,N[
,9 ,*APT] #E1 Y W APPLY ! BIG ID1S
LI/$ 2L & REVIEW$ 9 ! ,*APT] ,SUMM>Y ON
PAGE #DJA @4 ,Y W AL USE ! KEY VOCABUL>Y
LI/$ 2L4
,BIG ,ID1S
#A ,GRAPH+ POLYNOMIAL FUNC;NS
#B ,P]=M+ OP],NS ) POLYNOMIALS
#C ,SOLV+ POLYNOMIAL EQU,NS & F9D+
Z]OS
,KEY ,VOCABUL>Y
99 POLYNOMIAL1 P4 #CCG
99 POLYNOMIAL FUNC;N1 P4 #CCG
99 SYN!TIC SUB/ITU;N1 P4 #CCH
99 5D 2HAVIOR1 P4 #CCI
99 FACTOR$ -PLETELY1 P4 #CEC
99 FACTOR 0GR\P+1 P4 #CED
99 QUADRATIC =M1 P4 #CEE
99 POLYNOMIAL L;G DIVI.N1 P4 #CFB @4
99 SYN!TIC DIVI.N1 P4 #CFC
99 REP1T$ SOLU;N1 P4 #CGI
99 LOCAL MAXIMUM1 P4 #CHH
99 LOCAL M9IMUM1 P4 #CHH
99 F9ITE DI6];ES1 P4 #CIC
,SIDEB>3
,:Y8
,Y C USE POLYNOMIAL FUNC;NS 6MODEL
R1L-LIFE SITU,NS4 ,= EXAMPLE1 Y C USE A
POLYNOMIAL FUNC;N 6MODEL ! REL,N%IP 2T !
SPE$ ( AN OBJECT &! P[] NE$$ 6MA9TA9 T
SPE$4
.,ANIMAT$ ,ALGEBRA
,! ANIM,N ILLU/RAT$ 2L = ,EX]CISE #FA
ON PAGE #CEA HELPS Y ANSW] ? "Q3 ,H[
DOES ! P[] NE$$ 6KEEP A BICYCLE MOV+ AT
A 3/ANT SPE$ *ANGE Z ! 3DI;NS *ANGE8
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,O!R ANIM,NS = ,*APT] .#E3 PAGES
#CCA @1 #CDJ @1 #CGA @1 #CHH @1 #CIF @1
& #DJA
------------------------------------#CCJ
#E.A ,USE ,PROP]TIES ( ,EXPON5TS
.,2F ,Y EVALUAT$ P[]S4
.,N[ ,Y W SIMPLIFY EXPRES.NS 9VOLV+
P[]S4
.,:Y8 ,S Y C -P>E ! VOLUMES ( TWO />S1
Z 9 ,EXAMPLE #E4
,KEY ,VOCABUL>Y
99 .SCI5TIFIC .NOT,N
,3SID] :AT HAPP5S :5 Y MULTIPLY TWO
P[]S T H ! SAME BASE3
#B #C @* #B #E .K 7#B @* #B @* #B7 @*
7#B @* #B @* #B @* #B @* #B7 .K #B #H
,NOTE T ! EXPON5T #H 9 ! PRODUCT IS !
SUM (! EXPON5TS .#C & .#E 9 ! FACTORS4
,? PROP]TY IS "O ( S"EAL PROP]TIES (
EXPON5TS %[N 2L4
,SIDEB>3
,/&>DS
.#G..J .,/UD5TS ADD1 SUBTRACT1
MULTIPLY1 DIVIDE1 .REDUCE @1 & EVALUATE
..R,NAL EXPRES.NS ) .MONOMIAL &
POLYNOMIAL .DENOM9ATORS & SIMPLIFY
-PLICAT$ R,NAL EXPRES.NS1 ..9CLUD+ ^? )
NEGATIVE EXPON5TS 9 ! .DENOM9ATOR4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,PROP]TIES ( ,EXPON5TS
,LET .A & .;B 2 R1L NUMB]S & LET .;M &
.;N 2 9TEG]S4
,,AVOID ,,]RORS
,:5 Y MULTIPLY P[]S1 D N MULTIPLY !
BASES4 ,= EXAMPLE1 #C #B @* #C #E @6.K
#I #G @4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,PROP]TY ,"N3 ,DEF9I;N3 ,EXAMPLE
.,PRODUCT .( .,P[]S @3 .A .;M @* .A
.;N .K .A .;M @+ .;N @3 #E #C @* #E --#A
.K #E #C @+ 7--#A7 .K #E #B .K #BE
..,P[] (A .,P[] @3 @7 .A .;M @7 .;N .K
.A .MN @3 7#C #C @7 #B .K #C #C @* #B .K
#C #F .K #GBI
..,P[] (A .,PRODUCT @3 @7 .;AB @7 .;M
.K .A .;M .;B .;M @3 7#B @* #C7 #D .K #B
#D @* #C #D .K #ABIF
.,NEGATIVE .,EXPON5T @3 @3
.,Z]O .,EXPON5T @3 .A ;DG .K #A1 .A
@6.K #J @3 7--#HI7;DG .K #A
.,QUOTI5T .( .,P[]S @3 @3
..,P[] (A .,QUOTI5T @3 @3
,EXAMPLE #A ,EVALUATE NUM]ICAL
EXPRES.NS
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.A4 7--#D @* #B #E @7 #B @3 .K 7--#D7
#B @* 7#B #E @7 #B @3 ,P[] (A PRODUCT
PROP]TY
--@3 .K #AF @* #B #E @* #B @3 ,P[] (A
P[] PROP]TY
--@3 .K #AF @* #B #AJ .K #AF1CHD @3
,SIMPLIFY & EVALUATE P[]4
.B4
------------------------------------#CCA
.,,SCI5TIFIC .,,NOT,N ,A NUMB] IS
EXPRESS$ 9 .SCI5TIFIC .NOT,N IF X IS 9 !
=M .;C * #AJ0 ": #A "K.K .;C "K #AJ &
.;N IS AN 9TEG]4 ,:5 Y "W ) NUMB]S 9
SCI5TIFIC NOT,N1 ! PROP]TIES ( EXPON5TS
C MAKE CALCUL,NS EASI]4
,EXAMPLE #B ,USE SCI5TIFIC NOT,N 9 R1L
LIFE
.,,LOCU/S ,A SW>M ( LOCU/S MAY 3TA9 Z
_M Z #HE MILLION LOCU/S P] SQU>E
KILOMET] & COV] AN >EA ( #ABJJ SQU>E
KILOMET]S4 ,AB H[ _M LOCU/S >E 9 S* A
SW>M8
,SOLU;N
.,,REVIEW .,,SCI5TIFIC .,,NOT,N ,=
HELP ) SCI5TIFIC NOT,N1 SEE P4 #IHB @4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,NUMB] ( LOCU/S3 .K@3 ,LOCU/S P] SQU>E
KILOMET]3 *@3 ,NUMB] ( SQU>E KILOMET]S
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.K #HE1JJJ1JJJ * #ABJJ3 .,SUB/ITUTE
.VALUES4
.K 7#H.E * #AJ #G @77L#.B * #AJ #C @7
@3 ..,WRITE 9 SCI5TIFIC .NOT,N4
.K 7#H.E * #A.B77;L#J #G * #AJ #C @7
@3 .,USE .MULTIPLIC,N .PROP]TIES4
.K #AJ.B * #AJ #AJ @3 ..,PRODUCT (
P[]S .PROP]TY
.K #A.JB * #AJ #A * #AJ #AJ @3
..,WRITE #AJ.B 9 SCI5TIFIC .NOT,N4
.K #A.JB * #AJ #AA @3 ..,PRODUCT (
P[]S .PROP]TY
,! NUMB] ( LOCU/S IS AB #A.JB * #AJ
#AA @1 OR AB #AJB1JJJ1JJJ1JJJ4
..,GUID$ ,PRACTICE = ,EXAMPLES #A &
.#B
,EVALUATE ! EXPRES.N4 ,TELL :
PROP]TIES ( EXPON5TS Y US$4
.#A4 7#D #B @7 #C
.#B4 7--#H77--#H7 #C
.#C4
.#D4
.,,SIMPLIFY+ .,,EXPRES.NS ,Y C USE !
PROP]TIES ( EXPON5TS 6SIMPLIFY ALGEBRAIC
EXPRES.NS4 ,A SIMPLIFI$ EXPRES.N 3TA9S
ONLY POSITIVE EXPON5TS4
,EXAMPLE #C ,SIMPLIFY EXPRES.NS
,,9T]PRET ,,BASES
,9 ? BOOK1 X IS ASSUM$ T ANY BASE )A
Z]O OR NEGATIVE EXPON5T IS NONZ]O4
.A4 .;B --#D .;B #F .;B #G .K .;B --#D
@+ #F @+ #G .K .;B #I ..,PRODUCT ( P[]S
.PROP]TY
.B4
.C4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
------------------------------------#CCB
..,EXAMPLE #D ,/&>DIZ$ ,TE/ .,PRACTICE
,:AT IS ! SIMPLIFI$ =M ( @8
.,A .;X #AA
.;,B
.;,C
.;,D
,SOLU;N
,! CORRECT ANSW] IS ,B4 .,A .;,B .;,C
.;,D
,EXAMPLE #E ,-P>E R1L-LIFE VOLUMES
.,,A/RONOMY ,2TELGEUSE IS "O (! />S
F.D 9 ! 3/ELL,N ,ORION4 ,XS RADIUS IS AB
#AEJJ "TS ! RADIUS (! SUN4 ,H[ _M "TS Z
GRT Z ! SUN'S VOLUME IS ,2TELGEUSE'S
VOLUME8
,SOLU;N
,LET .;R REPRES5T ! SUN'S RADIUS4 ,!N
#AEJJ;R REPRES5TS ,2TELGEUSE'S RADIUS4
,2TELGEUSE'S VOLUME IS AB #C.D BILLION
"TS Z GRT Z ! SUN'S VOLUME4
------------------------------------#CCC
..,GUID$ ,PRACTICE = ,EXAMPLES #C1D1 &
.#E
,SIMPLIFY ! EXPRES.N4 ,TELL :
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.#E4 .;X --#F .;X #E .;X #C
.#F4 7#G .;Y #B .;Z #E @7@7 .;Y --#D
.;Z --#A @7
.#G4
.#H4
#E.A ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4 ,,WS#I
= ,EXS4 #AG1CA1 & #EA
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE ,EXS4
#B1 #CF1DF1EA1 & #EC
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#A4 .,,VOCABUL>Y ,/ATE ! "N (! PROP]TY
ILLU/RAT$4
A4 .A ;M @* .A ;N .K .A .;M @+ .;N
B4 @1 .A @6.K #J
C4 @7 .;AB @7 ;M .K .A ;M .;B ;M
#B4 .,,WRIT+ ,IS ! NUMB] #BE.B * #AJ
--#C 9 SCI5TIFIC NOT,N8 .,EXPLA94
,,EXAMPLE #A ON P4 #CCJ = ,EXS4 #C-AD
,,EVALUAT+ ,,NUM]ICAL ,,EXPRES.NS
,EVALUATE ! EXPRES.N4 ,TELL : PROP]TIES
( EXPON5TS Y US$4
.#C4 #C #C @* #C #B
.#D4 7#D --#B @7 #C
.#E4 7--#E77--#E7 #D
.#F4 7#B #D @7 #B
.#G4
.#H4
.#I4
.#AJ4 #I #C @* #I --#A
.#AA4
.#AB4
.#AC4 #F #C @* #F #J @* #F --#E
.#AD4
,,EXAMPLE #B ON P4 #CCA = ,EXS4
#AE--#BC
,,SCI5TIFIC ,,NOT,N ,WRITE ! ANSW] 9
SCI5TIFIC NOT,N4
.#AE4 7#D.B * #AJ #C @77L#.E * #AJ #F
@7
.#AF4 7L#.B * #AJ --#C @77#F.G * #AJ
--#G @7
.#AG4 7#F.C * #AJ #E @77#H.I * #AJ
--#AB @7
.#AH4 7#G.B * #AJ #I @77#I.D * #AJ #H
@7
.#AI4 7#B.A * #AJ --#D @7 #C
.#BJ4 7#D.J * #AJ #C @7 #D
.#BA4
.#BB4
.#BC4
,,EXAMPLES #C & #D ON PP4 #CCA-CCB =
,EXS4 #BD-CI
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,SIMPLIFY ! EXPRES.N4 ,TELL : PROP]TIES
( EXPON5TS Y US$4
.#BD4
.#BE4 7#B #B .;Y #C @7 #E
.#BF4 @7 .;P #C .;Q #B @7 --#A
.#BG4 @7 .;W #C .;X --#B @7@7 .;W #F
.;X -#A @7
.#BH4 7#E .;S --#B .;T #D @7 --#C
.#BI4 7#C .A #C .;B #E @7 --#C
.#CJ4
.#CA4
.#CB4
.#CC4
.#CD4
.#CE4
#CF4 .,,MULTIPLE .,,*OICE ,:AT IS !
SIMPLIFI$ =M ( @8
,A
;,B
;,C
;,D
------------------------------------#CCD
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 SIMPLIFY+ ! EXPRES.N4
.#CG4
.#CH4
.#CI4
..,,GEOMETRY ,WRITE AN EXPRES.N =!
FIGURE'S >EA OR VOLUME 9 T]MS ( .;X @4
.#DJ4
.#DA4 .;,V .K .;R #B .;H
.#DB4 .;,V .K .L:
,,R1SON+ ,WRITE AN EXPRES.N T MAKES !
/ATE;T TRUE4
.#DC4 .;X ;L#E .;Y ;L#B .;Z #H .K .;X
#D .;Y #G .;Z #AA @*?
.#DD4
.#DE4 @7 .A #E .;B #D @7 #B .K .A #AD
.;B --#A @*?
.#DF4 .,,OP5-.,,5D$ .,,MA? ,F9D ?REE
DI6]5T WAYS 6-PLETE ! FOLL[+ /ATE;T S T
X IS TRUE3 .;X #AB .;Y #AF .K @7 .;X @8
.;Y @8 @7@7 .;X @8 .;Y @8 @7@4
,,*ALL5GE ,REF] 6! PROP]TIES (
EXPON5TS ON PAGE #CCJ @4
.#DG4 ,%[ H[ ! NEGATIVE EXPON5T
PROP]TY C 2 DERIV$ F ! QUOTI5T ( P[]S
PROP]TY &! Z]O EXPON5T PROP]TY4
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C 2 DERIV$ F ! PRODUCT ( P[]S PROP]TY &!
NEGATIVE EXPON5T PROP]TY4
,PRO#M ,SOLV+
.,,EXAMPLE .#B ON P4 #CCA = ,EXS4
#DI-EJ
.#DI4 .,,OC1N .,,VOLUME ,! TA# %[S !
SURFACE >1S & AV]AGE DEP?S ( F\R OC1NS4
,CALCULATE ! VOLUME ( EA* OC1N
0MULTIPLY+ ! SURFACE >EA ( EA* OC1N 0XS
AV]AGE DEP?4 ,WRITE YR ANSW]S 9
SCI5TIFIC NOT,N4
,! FOLL[+ TA# IS 9 LI/$
=MAT4 ,= EA* CELL ! H1D+ IS %[N
FOLL[$ 0A COLON1 SPACE &! CELL
3T5TS
.,OC1N @3 ,PACIFIC
..,SURFACE >EA 7SQU>E .MET]S7 @3 #A.EF
* #AJ #AD
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#C
.,OC1N @3 ,ATLANTIC
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* #AJ #AC
.,AV]AGE .DEP? 7.MET]S7 @3 #C.IC * #AJ
#C
.,OC1N @3 ,9DIAN
..,SURFACE >EA 7SQU>E .MET]S7 @3 #F.HF
* #AJ #AC
.,AV]AGE .DEP? 7.MET]S7 @3 #C.IF * #AJ
#C
.,OC1N @3 ,>CTIC
..,SURFACE >EA 7SQU>E .MET]S7 @3 #A.DA
* #AJ #AC
.,AV]AGE .DEP? 7.MET]S7 @3 #A.BA * #AJ
#C
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
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MOVE AT A V SL[ RATE4 ,! ,S\? ,AM]ICAN
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YE> =! PA/ #ABE1JJJ1JJJ YE>S4 ,H[ F> HAS
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@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
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.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#CCE
.,,EXAMPLE .#E ON P4 #CCB = ,EXS4
#EA-EB
.#EA4 .,,%ORT .,,RESPONSE ,A TYPICAL
CULTUR$ BLACK PE>L IS MADE 0PLAC+ A B1D
)A DIAMET] ( #F MILLIMET]S 9SIDE AN
OY/]4 ,! RESULT+ PE>L HAS A DIAMET] ( AB
#I MILLIMET]S4 .,-P>E ! VOLUME (!
RESULT+ PE>L )! VOLUME (! B1D4
#EB4 .,,MULTI-.,,/EP .,,PRO#M ,A C (
T5NIS BALLS 3SI/S ( ?REE SPH]ES ( RADIUS
.;R /ACK$ V]TIC,Y 9SIDE A CYL9D] (
RADIUS .;R & HEI<T .;H @4
A4 ,WRITE AN EXPRES.N =! TOTAL VOLUME
(! ?REE T5NIS BALLS 9 T]MS ( .;R @4
B4 ,WRITE AN EXPRES.N =! VOLUME (!
CYL9D] 9 T]MS ( .;R & .;H @4
C4 ,WRITE AN EXPRES.N = .;H 9 T]MS (
.;R US+ ! FACT T ! HEI<T (! CYL9D] IS !
SUM (! DIAMET]S (! ?REE T5NIS BALLS4
D4 ,:AT FRAC;N (! C'S VOLUME IS TAK5
UP 0! T5NIS BALLS8
#EC4 .,,EXT5D$ .,,RESPONSE ,Y C ?9K (A
P5NY Z A CYL9D] )A RADIUS ( AB #I.EC
MILLIMET]S &A HEI<T ( AB #A.EE
MILLIMET]S4
A4 .,CALCULATE ,APPROXIMATE ! VOLUME
(A P5NY4 ,GIVE YR ANSW] 9 CUBIC MET]S4
B4 .,E/IMATE ,APPROXIMATE ! VOLUME (
YR CLASSROOM 9 CUBIC MET]S4 .,EXPLA9 H[
Y OBTA9$ YR ANSW]4
C4 .,9T]PRET ,USE YR RESULTS F "PS 7A7
& 7;B7 6E/IMATE H[ _M P5NIES X WD TAKE
6FILL YR CLASSROOM4 ,D Y ?9K YR ANSW] IS
AN OV]E/IMATE OR AN "UE/IMATE8 .,EXPLA94
#ED4 .,,*ALL5GE ,E>?'S CORE IS
APPROXIMATELY SPH]ICAL 9 %APE & IS
DIVID$ 96A SOLID 9N] CORE 7! YELL[
REGION 9 ! DIAGRAM %[N7 &A LIQUID \T]
CORE 7! D>K ORANGE REGION 9 ! DIAGRAM74
A4 ,E>?'S RADIUS IS AB #E "TS Z GRT Z
! RADIUS ( ,E>?'S 9N] CORE4 ,F9D ! RATIO
( ,E>?'S TOTAL VOLUME 6! VOLUME ( ,E>?'S
9N] CORE4
B4 ,F9D ! RATIO (! VOLUME ( ,E>?'S \T]
CORE 6! VOLUME ( ,E>?'S 9N] CORE4
,MIX$ ,REVIEW
,SIDEB>3
,PREVIEW
,PREP>E = ,LESSON #E.B 9 ,EXS4 #EE-FJ4
,GRAPH ! FUNC;N4
.#EE4 .;Y .K -- .;X @+ #D @7 .P4 #HI
@7
.#EF4 .;Y .K #B .;X -- #E @7 .P4 #HI
@7
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.P4 #BDE @7
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#G .;X @+ #H .;Y .K #BA
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#B ..;X @+ .#H;Y .K @+ #H .;Y .K #A
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#F .;X -- #B .;Y .K #AJ
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/&>D =M4 @7 .P4 #BGE @7
.#FD4 7#H @+ #C .;I @7--7#G @+ #D .;I
@7
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@7
.#FF4 .;I 7#C @+ .;I @7
.#FG4 7#AB @+ #E .;I @7--7#G--#H .;I
@7
.#FH4 7#E @+ #D .;I @77#B @+ #C .;I @7
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..,,ONL9E ,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#CCF
,9VE/IGAT+ ,ALGEBRA ,ACTIV;Y3 #E.B
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@A,HOME,TUTOR
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99 GRAPH+ CALCULATOR
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FUNC;N ON A GRAPH+ CALCULATOR4
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.#A4 .;F @7 .;X @7 .K .;X #E
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.#C4 .;F @7 .;X @7 .K .;X #F
.#D4 .;F @7 .;X @7 .K -- .;X #F
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ODD
B4 .;F @7 .;X @7 .K -- .;X ;N ": .;N
IS ODD
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EV5
D4 .;F @7 .;X @7 .K -- .;X ;N ": .;N
IS EV5
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(! FUNC;N .;F @7 .;X @7 .K .;X #F -- .;X
@4 ,EXPLA9 YR R1SON+4
------------------------------------#CCG
#E.B ,EVALUATE & ,GRAPH ,POLYNOMIAL
,FUNC;NS
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99 .POLYNOMIAL
99 .POLYNOMIAL .FUNC;N
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.;F @7 .;X @7 .K .A ;N .;X ;N @+ .A
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3TA9 TWO DA%ES4
,DEGREE3 ,TYPE3 ,/&>D =M3 ,EXAMPLE
#J3 ,3/ANT3 .;F @7 .;X @7 .K A #J @3
.;F @7 .;X @7 .K --#AD
#A3 ,L9E>3 .;F @7 .;X @7 .K .A #A .;X
@+ .A #J @3 .;F @7 .;X @7 .K #E .;X --
#G
#B3 ,QUADRATIC3 .;F @7 .;X @7 .K .A #B
.;X #B @+ .A #A .;X @+ .A #J @3 .;F @7
.;X @7 .K #B .;X #B @+ .;X -- #I
#C3 ,CUBIC3 .;F @7 .;X @7 .K .A #C .;X
#C @+ .A #B .;X #B @+ .A #A .;X @+ .A #J
@3 .;F @7 .;X @7 .K .;X #C -- .;X #B @+
#C .;X
#D3 ,QU>TIC3 .;F @7 .;X @7 .K .A #D
.;X #D @+ .A #C .;X #C @+ .A #B .;X #B
@+ .A #A .;X @+ .A #J @3 .;F @7 .;X @7
.K .;X #D @+ #B .;X -- #A
,EXAMPLE #A ,ID5TIFY POLYNOMIAL
FUNC;NS
,DECIDE :E!R ! FUNC;N IS A POLYNOMIAL
FUNC;N4 ,IF S1 WRITE X 9 /&>D =M & /ATE
XS DEGREE1 TYPE1 & L1D+ COE6ICI5T4
.A4
.B4
.C4 .;F @7 .;X @7 .K #E .;X #B @+ #C
.;X --#A -- .;X
.D4 .;K @7 .;X @7 .K .;X @+ #B ;X --
#J.F .;X #E
,SOLU;N
.A4 ,! FUNC;N IS A POLYNOMIAL FUNC;N T
IS ALR WRITT5 9 /&>D =M4 ,X HAS DEGREE
#D 7QU>TIC7 &A L1D+ COE6ICI5T ( #A4
.B4 ,! FUNC;N IS A POLYNOMIAL FUNC;N
WRITT5 Z /&>D =M4 ,X HAS DEGREE #B
7QUADRATIC7 &A L1D+ COE6ICI5T (4
.C4 ,! FUNC;N IS N A POLYNOMIAL FUNC;N
2C ! T]M #C .;X --#A HAS AN EXPON5T T IS
N A :OLE NUMB]4
.D4 ,! FUNC;N IS N A POLYNOMIAL FUNC;N
2C ! T]M #B ;X DOES N H A V>IA# BASE &
AN EXPON5T T IS A :OLE NUMB]4
------------------------------------#CCH
,EXAMPLE #B ,EVALUATE 0DIRECT
SUB/ITU;N
,USE DIRECT SUB/ITU;N 6EVALUATE .;F @7
.;X @7 .K #B .;X #D -- #E .;X #C -- #D
.;X @+ #H :5 .;X .K #C4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;F @7 .;X @7 .K #B .;X #D -- #E .;X
#C -- #D .;X @+ #H @3 .,WRITE .ORIG9AL
.FUNC;N4
.;F 7#C7 .K #B7#C7 #D -- #E7#C7 #C --
#D7#C7 @+ #H @3 ,SUB/ITUTE #C =.' ;X @4
.K #AFB--#ACE--#AB @+ #H3 ..,EVALUATE
P[]S & .MULTIPLY4
.K #BC3 .,SIMPLIFY4
..,GUID$ ,PRACTICE = ,EXAMPLES #A &
.#B
,DECIDE :E!R ! FUNC;N IS A POLYNOMIAL
FUNC;N4 ,IF S1 WRITE X 9 /&>D =M & /ATE
XS DEGREE1 TYPE1 & L1D+ COE6ICI5T4
.#A4 .;F @7 .;X @7 .K #AC--#B .;X
.#B4 .;P @7 .;X @7 .K #I .;X #D -- #E
.;X #B @+ #D
.#C4 .;H @7 .;X @7 .K #F .;X #B @+--#C
.;X
,USE DIRECT SUB/ITU;N 6EVALUATE !
POLYNOMIAL FUNC;N =! GIV5 VALUE ( .;X @4
.#D4 .;F @7 .;X @7 .K .;X #D @+ #B .;X
#C @+ #C .;X #B -- #G2 .;X .K --#B
.#E4 .;G @7 .;X @7 .K .;X #C -- #E .;X
#B @+ #F .;X @+ #A2 .;X .K #D
.,,SYN!TIC .,,SUB/ITU;N ,ANO!R WAY
6EVALUATE A POLYNOMIAL FUNC;N IS 6USE
.SYN!TIC .SUB/ITU;N4 ,? ME?OD1 %[N 9 !
NEXT EXAMPLE1 9VOLVES FEW] OP],NS ?AN
DIRECT SUB/ITU;N4
,EXAMPLE #C ,EVALUATE 0SYN!TIC
SUB/ITU;N
,,AVOID ,,]RORS
,! R[ ( COE6ICI5TS = .;F @7 .;X @7 M/
9CLUDE A COE6ICI5T ( #J =! 8MISS+0 .;X
#B -T]M4
,USE SYN!TIC SUB/ITU;N 6EVALUATE .;F
@7 .;X @7 F ,EXAMPLE #B :5 ;X .K #C4
,SOLU;N
.,,/EP .#A .,WRITE ! COE6ICI5TS ( .;F
@7 .;X @7 9 ORD] ( DESC5D+ EXPON5TS4
,WRITE ! VALUE AT : .;F @7 .;X @7 IS 2+
EVALUAT$ 6! LEFT4
..,,/EP #B ,BR+ .D[N ! L1D+ COE6ICI5T4
,MULTIPLY ! L1D+ COE6ICI5T 0! ;X-VALUE4
,WRITE ! PRODUCT "U ! SECOND COE6ICI5T4
.,ADD4
.,,/EP .#C .,MULTIPLY ! PREVI\S SUM 0!
;X-VALUE4 ,WRITE ! PRODUCT "U ! ?IRD
COE6ICI5T4 .,ADD4 ,REP1T = ALL (! REMA9+
COE6ICI5TS4 ,! F9AL SUM IS ! VALUE ( .;F
@7 .;X @7 AT ! GIV5 ;X-VALUE4
,SYN!TIC SUB/ITU;N GIVES ;F7#C7 .K
#BC1 : MAT*ES ! RESULT 9 ,EXAMPLE #B4
------------------------------------#CCI
.,,5D .,,2HAVIOR ,! 5D 2HAVIOR (A
FUNC;N'S GRAPH IS ! 2HAVIOR (! GRAPH Z
.;X APPROA*ES POSITIVE 9F9;Y 7@+#JJ7 OR
NEGATIVE 9F9;Y @7--@7@4 ,=! GRAPH (A
POLYNOMIAL FUNC;N1 ! 5D 2HAVIOR IS
DET]M9$ 0! FUNC;N'S DEGREE &! SIGN ( XS
L1D+ COE6ICI5T4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,5D ,2HAVIOR ( ,POLYNOMIAL ,FUNC;NS
,,R1D+
,! EXPRES.N @8 .;X @+ @8 IS R1D Z @8
.;X APPROA*ES POSITIVE 9F9;Y40
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,DEGREE3 ODD .,L1D+ .COE6ICI5T3
POSITIVE @3 .,DEGREE3 ODD .,L1D+
.COE6ICI5T3 NEGATIVE
@3
.,DEGREE3 EV5 .,L1D+ .COE6ICI5T3
POSITIVE @3 .,DEGREE3 EV5 .,L1D+
.COE6ICI5T3 NEGATIVE
@3
..,EXAMPLE #D ,/&>DIZ$ ,TE/ .,PRACTICE
,:AT IS TRUE AB ! DEGREE & L1D+
COE6ICI5T (! POLYNOMIAL FUNC;N ^: GRAPH
IS %[N8
.,A ,DEGREE IS ODD2 L1D+ COE6ICI5T IS
POSITIVE
.;,B ,DEGREE IS ODD2 L1D+ COE6ICI5T IS
NEGATIVE
.;,C ,DEGREE IS EV52 L1D+ COE6ICI5T IS
POSITIVE
.;,D ,DEGREE IS EV52 L1D+ COE6ICI5T IS
NEGATIVE
,F ! GRAPH1 .;F @7 .;X @7--Z .;X -- &
.;F @7 .;X @7--Z .;X @+ @4 ,S1 ! DEGREE
IS EV5 &! L1D+ COE6ICI5T IS NEGATIVE4
,! CORRECT ANSW] IS ,D4 ..,A ;,B ;,C
.;,D
.,GUID$ .,PRACTICE = ,EXAMPLES #C & #D
,USE SYN!TIC SUB/ITU;N 6EVALUATE !
POLYNOMIAL FUNC;N =! GIV5 VALUE ( .;X @4
.#F4 .;F @7 .;X @7 .K #E .;X #C @+ #C
.;X #B -- .;X @+ #G2 .;X .K #B
.#G4 .;G @7 .;X @7 .K --#B .;X #D --
.;X #C @+ #D .;X -- #E2 .;X .K --#A
.#H4 .,DESCRIBE ! DEGREE & L1D+
COE6ICI5T (! POLYNOMIAL FUNC;N ^: GRAPH
IS %[N4
------------------------------------#CDJ
.,,GRAPH+ .,,POLYNOMIAL .,,FUNC;NS
,6GRAPH A POLYNOMIAL FUNC;N1 F/ PLOT
PO9TS 6DET]M9E ! %APE (! GRAPH'S MI4LE
POR;N4 ,!N USE :AT Y "K AB 5D 2HAVIOR
6SKET* ! 5DS (! GRAPH4
,EXAMPLE #E ,GRAPH POLYNOMIAL FUNC;NS
,GRAPH 7A7 .;F @7 .;X @7 .K -- .;X #C
@+ .;X #B @+ #C .;X -- #C & 7;B7 .;F @7
.;X @7 .K .;X #D -- .;X #C -- #D .;X #B
@+ #D4
,SOLU;N
.A4 ,6GRAPH ! FUNC;N1 MAKE A TA# (
VALUES & PLOT ! CORRESPOND+ PO9TS4
,3NECT ! PO9TS )A SMOO? CURVE & *ECK !
5D 2HAVIOR4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 --#C3 --#B3 --#A3 #J3 #A3 #B3
#C
.;Y @3 #BD3 #C3 --#D3 --#C3 #J3 --#A3
--#AB
,! DEGREE IS ODD & L1D+ COE6ICI5T IS
NEGATIVE4 ,S1 .;F @7 .;X @7 @+ Z .;X --
& .;F @7 .;X @7--Z .;X @+ @4
.B4 ,6GRAPH ! FUNC;N1 MAKE A TA# (
VALUES & PLOT ! CORRESPOND+ PO9TS4
,3NECT ! PO9TS )A SMOO? CURVE & *ECK !
5D 2HAVIOR4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 --#C3 --#B3 --#A3 #J3 #A3 #B3
#C
.;Y @3 #GF3 #AB3 #B3 #D3 #J3 --#D3 #BB
,! DEGREE IS EV5 & L1D+ COE6ICI5T IS
POSITIVE4 ,S1 .;F @7 .;X @7 @+ Z .;X --
& .;F @7 .;X @7 @+ Z .;X @+ @4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,EXAMPLE #F ,SOLVE A MULTI-/EP
.PRO#M
.,,PHYSICAL .,,SCI;E ,! 5]GY .;,E 7IN
FOOT-P.DS7 9 EA* SQU>E FOOT (A WAVE IS
GIV5 0! MODEL .;,E .K #J.JJBI;S #D ":
.;S IS ! W9D SPE$ 7IN KNOTS74 ,GRAPH !
MODEL4 ,USE ! GRAPH 6E/IMATE ! W9D SPE$
NE$$ 6G5]ATE A WAVE ) #AJJJ FOOT-P.DS (
5]GY P] SQU>E FOOT4
,SOLU;N
.,,/EP .#A .,MAKE A TA# ( VALUES4 ,!
MODEL ONLY D1LS ) POSITIVE VALUES ( .;S
@4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;S @3 #J3 #AJ3 #BJ3 #CJ3 #DJ
.;,E @3 #J3 #BI3 #DFD3 #BCDI3 #GDBD
.,,/EP .#B .,PLOT ! PO9TS & 3NECT !M
)A SMOO? CURVE4 ,2C ! L1D+ COE6ICI5T IS
POSITIVE &! DEGREE IS EV51 ! GRAPH RISES
6! "R4
.,,/EP .#C .,EXAM9E ! GRAPH 6SEE T .;S
#BD :5 .;,E .K #AJJJ4
,! W9D SPE$ NE$$ 6G5]ATE ! WAVE IS AB
#BD KNOTS4
------------------------------------#CDA
..,GUID$ ,PRACTICE = ,EXAMPLES #E &
.#F
,GRAPH ! POLYNOMIAL FUNC;N4
.#I4 .;F @7 .;X @7 .K .;X #D @+ #F .;X
#B -- #C
.#AJ4 .;F @7 .;X @7 .K -- .;X #C @+
.;X #B @+ .;X -- #A
.#AA4 .;F @7 .;X @7 .K #D--#B .;X #C
.#AB4 .,,:AT .,,IF8 ,IF W9D SPE$ IS
M1SUR$ 9 MILES P] H\R1 ! MODEL 9
,EXAMPLE #F 2COMES .;,E .K #J.JJEA;S #D
@4 ,GRAPH ? MODEL4 ,:AT W9D SPE$ IS NE$$
6G5]ATE A WAVE ) #BJJJ FOOT--P.DS ( 5]GY
P] SQU>E FOOT8
#E.B ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
,,WS#AJ = ,EXS4 #BA1BG1 & #EG
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE ,EXS4
#B1 #BD1 #CG1 #EJ1 #EB1 & #EI
.K .,,MULTIPLE .,,REPRES5T,NS ,EX#.EF
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,ID5TIFY ! DEGREE1
TYPE1 L1D+ COE6ICI5T1 & 3/ANT T]M (!
POLYNOMIAL FUNC;N .;F @7 .;X @7 .K #F @+
#B .;X #B -- #E .;X #D @4
.#B4 .,,WRIT+ .,EXPLA9 :AT IS M1NT 0!
5D 2HAVIOR (A POLYNOMIAL FUNC;N4
.,,EXAMPLE .#A ON P4 #CCG = ,EXS4 #C-H
.,,POLYNOMIAL .,,FUNC;NS ,DECIDE :E!R
! FUNC;N IS A POLYNOMIAL FUNC;N4 ,IF S1
WRITE X 9 /&>D =M & /ATE XS DEGREE1
TYPE1 & L1D+ COE6ICI5T4
.#C4 .;F @7 .;X @7 .K #H -- .;X #B
.#D4 .;F @7 .;X @7 .K #F .;X @+ #H .;X
#D -- #C
.#E4
.#F4
.#G4
.#H4
.,,EXAMPLE .#B ON P4 #CCH = ,EXS4
#I-AD
.,,DIRECT .,,SUB/ITU;N ,USE DIRECT
SUB/ITU;N 6EVALUATE ! POLYNOMIAL FUNC;N
=! GIV5 VALUE ( .X4
.#I4 .;F @7 .;X @7 .K #E .;X #C -- #B
.;X #B @+ ;L#J .;X -- #AE2 .;X .K --#A
.#AJ4 .;F @7 .;X @7 .K #H .;X @+ #E
.;X #D -- #C .;X #B -- .;X #C @2 .;X .K
#B
.#AA4 .;G @7 .;X @7 .K #D .;X #C -- #B
.;X #E @2 .;X .K --#C
.#AB4 .;H @7 .;X @7 .K #F .;X #C --
#BE .;X @+ #BJ2 .;X .K #E
.#AC4
.#AD4 .;G @7 .;X @7 .K #D .;X #E @+ #F
.;X #C @+ .;X #B -- ;L#J .;X @+ #E2 .;X
.K --#B
.,,EXAMPLE .#C ON P4 #CCH = ,EXS4
#AE-BC
.,,SYN!TIC .,,SUB/ITU;N ,USE SYN!TIC
SUB/ITU;N 6EVALUATE ! POLYNOMIAL FUNC;N
=! GIV5 VALUE ( .;X @4
.#AE4 .;F @7 .;X @7 .K #E .;X #C -- #B
.;X #B -- #H .;X @+ #AF2 .;X .K #C
.#AF4 .;F @7 .;X @7 .K #H .;X #D @+
#AB .;X #C @+ #F .;X #B -- #E .;X @+ #I2
.;X .K --#B
.#AG4 .;G @7 .;X @7 .K .;X #C @+ #H
.;X #B -- #G .;X @+ #CE2 .;X .K --#F
.#AH4 .;H @7 .;X @7 .K --#H .;X #C @+
#AD .;X -- #CE2 .;X .K #D
.#AI4 .;F @7 .;X @7 .K --#B .;X #D @+
#C .;X #C -- #H .;X @+ #AC2 .;X .K #B
.#BJ4 .;G @7 .;X @7 .K #F .;X #E @+
#AJ .;X #C -- #BG2 .;X .K --#C
.#BA4 .;H @7 .;X @7 .K --#G .;X #C @+
#AA .;X #B @+ #D .;X2 .;X .K #C
.#BB4 .;F @7 .;X @7 .K .;X #D @+ #C
.;X -- #BJ2 .;X .K #D
.#BC4 .,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 EVALUAT+ ! POLYNOMIAL
FUNC;N .;F @7 .;X @7 .K --#D .;X #D @+
#I .;X #B -- #BA .;X @+ #G :5 .;X .K
--#B4
------------------------------------#CDB
.,,EXAMPLE .#D ON P4 #CCI = ,EXS4
#BD-BG
#BD4 .,,MULTIPLE .,,*OICE ,! GRAPH (A
POLYNOMIAL FUNC;N IS %[N4 ,:AT IS TRUE
AB ! FUNC;N'S DEGREE & L1D+ COE6ICI5T8
,A ,! DEGREE IS ODD &! L1D+ COE6ICI5T
IS POSITIVE4
;,B ,! DEGREE IS ODD &! L1D+ COE6ICI5T
IS NEGATIVE4
;,C ,! DEGREE IS EV5 &! L1D+ COE6ICI5T
IS POSITIVE4
;,D ,! DEGREE IS EV5 &! L1D+ COE6ICI5T
IS NEGATIVE4
,,US+ ,,5D ,,2HAVIOR .,DESCRIBE !
DEGREE & L1D+ COE6ICI5T (! POLYNOMIAL
FUNC;N ^: GRAPH IS %[N4
.#BE4
.#BF4
.#BG4
.,,DESCRIB+ .,,5D .,,2HAVIOR
.,DESCRIBE ! 5D 2HAVIOR (! GRAPH (!
POLYNOMIAL FUNC;N 0-PLET+ ^! /ATE;TS3
.;F @7 .;X @7 @8 Z .;X -- & .;F @7 .;X
@7 @8 Z .;X @+ @4
.#BH4 .;F7.;X7 .K #AJ .;X #D
.#BI4 .;F @7 .;X @7 .K -- .;X #F @+ #D
.;X #C -- #C .;X
.#CJ4 .;F @7 .;X @7 .K --#B .;X #C @+
#G .;X -- #D
.#CA4 .;F @7 .;X @7 .K .;X #G @+ #C
.;X #D -- .;X #B
.#CB4 .;F @7 .;X @7 .K #C .;X #AJ --
#AF .;X
.#CC4 .;F @7 .;X @7 .K --#F .;X #E @+
#AD .;X #B @+ #BJ
.#CD4 .;F @7 .;X @7 .K #J.B .;X #C --
.;X @+ #DE
.#CE4 .;F @7 .;X @7 .K #E .;X #H @+ #H
.;X #G
.#CF4 .;F @7 .;X @7 .K -- .;X #BGC @+
#EJJ .;X #BGA
.#CG4 .,,OP5-.,,5D$ .,,MA? ,WRITE A
POLYNOMIAL FUNCTION_/( DEGREE #E S* T !
5D 2HAVIOR (! GRAPH (F IS GIV5 0.;F @7
.;X @7 @+ Z .;X -- & .;F @7 .;X @7 --@2
Z .;X @+ @4 ,!N GRAPH ! FUNC;N 6V]IFY YR
ANSW]4
.,,EXAMPLE #E ON P4 #CDJ = ,EXS4
#CH-EJ
.,,GRAPH+ .,,POLYNOMIALS ,GRAPH !
POLYNOMIAL FUNC;N
.#CH4 .;F @7 .;X @7 .K .;X #C
.#CI4 .;F @7 .;X @7 .K -- .;X #D
.#DJ4 .;F @7 .;X @7 .K .;X #E @+ #C
.#DA4 .;F @7 .;X @7 .K .;X #D -- #B
.#DB4 .;F @7 .;X @7 .K -- .;X #C @+ #E
.#DC4 .;F @7 .;X @7 .K .;X #C -- #E
.;X
.#DD4 .;F @7 .;X @7 .K -- .;X #D @+ #H
.;X
.#DE4 .;F @7 .;X @7 .K .;X #E @+ ;,X
.#DF4 .;F @7 .;X @7 .K -- .;X #C @+ #C
.;X #B -- #B .;X @+ #E
.#DG4 .;F @7 .;X @7 .K .;X #E @+ .;X
#B -- #D
.#DH4 .;F @7 .;X @7 .K .;X #D -- #E
.;X #B @+ #F
.#DI4 .;F @7 .;X @7 .K -- .;X #D @+ #C
.;X #C -- .;X @+ #A
#EJ4 .,,MULTIPLE .,,*OICE ,: FUNC;N IS
REPRES5T$ 0! GRAPH %[N8
,A
;,B
;,C
;,D
#EA4 .,,VISUAL .,,?9K+ ,SUPPOSE .;F @7
.;X @7 @+ Z .;X -- & .;F @7 .;X @7--Z
.;X @+ @4 .,DESCRIBE ! 5D 2HAVIOR ( .;G
@7 .;X @7 .K -- .;F @7 .;X @7@4
#EB4 .,,%ORT .,,RESPONSE ,A CUBIC
POLYNOMIAL FUNC;N ;F HAS L1D+ COE6ICI5T
#B & 3/ANT T]M --#E4 ,IF .;F 7#A7 .K #J
& .;F 7#B7 .K #C1 :AT IS .;F 7--#E78
.,EXPLA9 H[ Y F.D YR ANSW]4
.K .,,"W$-.,,\ .,,SOLU;NS ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
------------------------------------#CDC
#EC4 .,,*ALL5GE ,LET .;F @7 .;X @7 .K
.;X #C & .;G @7 .;X @7 .K .;X #C -- #B
.;X #B @+ #D .;X @4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 .;F @7 .;X @7 @3 .;G @7 .;X @7
@3
#AJ3 @8@3 @8@3 @8
#BJ3 @8@3 @8@3 @8
#EJ3 @8@3 @8@3 @8
#AJJ3 @8@3 @8@3 @8
#BJJ3 @8@3 @8@3 @8
A4 ,COPY & -PLETE ! TA#4
B4 ,USE ! NUMB]S 9 ! TA# 6-PLETE ?
/ATE;T3 ,Z @4
C4 .,EXPLA9 H[ ! RESULT F "P 7;B7 %[S
T ! FUNC;NS .;F & ;G H ! SAME 5D 2HAVIOR
Z .;X @+ @4
,PRO#M ,SOLV+
.,,EXAMPLE .#F ON P4 #CDJ = ,EXS4
#ED-EI
.#ED4 .,,DIAMONDS ,! WEI<T ( AN ID1L
R.D-CUT DIAMOND C 2 MODEL$ BY
.;W .K#J.JJGA .;D #C -- #J.JIJ .;D #B
@+ #J.DH .;D
": .;W IS ! DIAMOND'S WEI<T 7IN C>ATS7
& .;D IS XS DIAMET] 7IN MILLIMET]S74 ,AC
6! MODEL1 :AT IS ! WEI<T (A DIAMOND )A
DIAMET] ( #AE MILLIMET]S8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#EE4 .,,SKATEBO>D+ ,F #AIIB 6#BJJC1 !
NUMB] ( P 9 ! ,UNIT$ ,/ATES :O "PICIPAT$
9 SKATEBO>D+ C 2 MODEL$ BY
.;,S .K --#J.JJGF .;T #D @+ #J.AD .;T
#C -- #J.FB .;T #B @+ #J.EB .;T @+ #E.E
": .;,S IS ! NUMB] ( "PICIPANTS 7IN
MILLIONS7 & .;T IS ! NUMB] ( YE>S S9CE
#AIIB4 ,GRAPH ! MODEL4 ,!N USE ! GRAPH
6E/IMATE ! F/ YE> T ! NUMB] ( SKATEBO>D+
"PICIPANTS 0 GRT] ?AN #H MILLION4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#EF4 .,,MULTIPLE .,,REPRES5T,NS ,F
#AIHG 6#BJJC1 ! NUMB] ( 9DOOR MOVIE
SCRE5S ;,M 9 ! ,UNIT$ ,/ATES C 2 MODEL$
BY
.;,M .K --#AA.J .;T #C @+ .#BFG .;T #B
-- #EIB .;T @+ #BA1FJJ
": .;T IS ! NUMB] ( YE>S S9CE #AIHG4
A4 .,CLASSIFY+ .A .,FUNC;N ,/ATE !
DEGREE & TYPE (! FUNC;N4
B4 .,MAK+ .A .,TA# ,MAKE A TA# (
VALUES =! FUNC;N4
C4 .,SKET*+ .A .,GRAPH ,USE YR TA#
6GRAPH ! FUNC;N4
#EG4 .,,SN[BO>D+ ,F #AIIB 6#BJJC1 !
NUMB] ( P 9 ! ,UNIT$ ,/ATES :O "PICIPAT$
9 SN[BO>D+ C 2 MODEL$ BY
.;,S .K #J.JJAC .;T #D -- #J.JBA .;T
#C @+ #J.JHD .;T #B @+ #J.JCG .;T @+
#A.B
": .;,S IS ! NUMB] ( "PICIPANTS 7IN
MILLIONS7 & .;T IS ! NUMB] ( YE>S S9CE
#AIIB4 ,GRAPH ! MODEL4 ,USE ! GRAPH
6E/IMATE ! F/ YE> T ! NUMB] ( SN[BO>D+
"PICIPANTS 0 GRT] ?AN #B MILLION4
------------------------------------#CDD
#EH4 .,,MULTI--.,,/EP .,,PRO#M ,F
#AIHJ 6#BJJB1 ! NUMB] ( QU>T]LY
P]IODICALS .;,P PUBLI%$ 9 ! ,UNIT$
,/ATES C 2 MODEL$ BY
.;,P .K #J.ACH .;T #D -- #F.BD .;T #C
@+ #HF.H .;T #B -- #BCI .;T @+ #ADEJ
": .;T IS ! NUMB] ( YE>S S9CE #AIHJ4
A4 .,DESCRIBE ! 5D 2HAVIOR (! GRAPH (!
MODEL4
B4 ,GRAPH ! MODEL ON ! DOMA9 #J "K .;T
"K #BB4
C4 ,USE ! MODEL 6PREDICT ! NUMB] (
QU>T]LY P]IODICALS 9 ! YE> #BJAJ4 ,IS X
APPROPRIATE 6USE ! MODEL 6MAKE ?
PREDIC;N8 .,EXPLA94
#EI4 .,,EXT5D$ .,,RESPONSE ,! WEI<T (
,S>US CRANE *ICKS .;,S & HOOD$ CRANE
*ICKS .;,H 7BO? 9 GRAMS7 DUR+ ! #AJ "DS
FOLL[+ HAT*+ C 2 MODEL$ 0! FUNC;NS
.;,S .K --#J.ABB .;T #C @+ #C.DI .;T
#B -- #AD.F .;T @+ #ACF
.;,H .K --#J.AAE .;T #C @+ #C.G .;T #B
-- #BJ.F .;T @+ #ABD
": .;T IS ! NUMB] ( "DS AF HAT*+4
A4 .,CALCULATE ,AC 6! MODELS1 :AT IS !
DI6];E 9 WEI<T 2T #E--"D--OLD ,S>US
CRANE *ICKS & HOOD$ CRANE *ICKS8
B4 .,GRAPH ,SKET* ! GRAPHS (! TWO
MODELS4
C4 .,APPLY ,A BIOLOGI/ F9DS T ! WEI<T
(A CRANE *ICK AF #C "DS IS #ACJ GRAMS4
,:AT SPECIES ( CRANE IS ! *ICK M LIKELY
6BE8 .,EXPLA9 H[ Y F.D YR ANSW]4
#FJ4 .,,*ALL5GE ,! WEI<T .;Y 7IN P.DS7
(A RA9B[ TR\T C 2 MODEL$ 0.;Y .K
#J.JJJCJD .;X #C ": .;X IS ! L5G? (!
TR\T 7IN 9*ES74
A4 ,WRITE A FUNC;N T RELATES ! WEI<T
.;Y & L5G? .;X (A RA9B[ TR\T IF .;Y IS
M1SUR$ 9 KILOGRAMS & .;X IS M1SUR$ 9
C5TIMET]S4 ,USE ! FACT T #A KILOGRAM
#B.BJ P.DS & #A C5TIMET] #J.CID 9*4
B4 ,GRAPH ! ORIG9AL FUNC;N &! FUNC;N F
"P 7A7 9 ! SAME COORD9ATE PLANE4 ,:AT
TYPE ( TRANS=M,N C Y APPLY 6! GRAPH (
.;Y .K #J.JJJCJD .;X #C 6PRODUCE ! GRAPH
F "P 7A78
,MIX$ ,REVIEW
,SOLVE ! EQU,N OR 9EQUAL;Y4
.#FA4 #B .;B @+ #AA .K #AE--#F .;B @7
.P4 #AH @7
.#FB4 #B.G .;N @+ #D.C .K #AB.ID @7
.P4 #AH @7
.#FC4 --#G "K #F .;Y -- #A "K #E @7
.P4 #DA @7
.#FD4 .;X #B -- #AD .;X @+ #DH .K #J
@7 .P4 #BEB @7
.#FE4 --#BD .;Q #B -- #IJ .;Q .K #BA
@7 .P4 #BEI @7
.#FF4 .;Z #B @+ #E .;Z "K #CF @7 .P4
#CJJ @7
,! V>IA#S .;X & .;Y V>Y DIRECTLY4
,WRITE AN EQU,N T RELATES .;X & .Y4 ,!N
F9D ! VALUE ( .;X :5 .;Y .K --#C4 @7 .P4
#AJG @7
.#FG4 .;X .K #D1 .;Y .K #AB
.#FH4 .;X .K #C1 .;Y .K --#BA
.#FI4 .;X .K #AJ1 .;Y .K --#D
.#GJ4 .;X .K #J.H1 .;Y .K #J.B
.#GA4 .;X .K --#J.DE1 .;Y .K --#J.CE
.#GB4 .;X .K --#F.E1 .;Y .K #C.I
,SIDEB>3
,PREVIEW
,PREP>E = ,LESSON #E.C 9 ,EXS4 #GC-GH4
,WRITE ! QUADRATIC FUNC;N 9 /&>D =M4
@7 .P4 #BDE @7
.#GC4 .;Y .K @7 .;X @+ #C7@7 .;X --
#G7
.#GD4 .;Y .K #H7 .;X -- #D7@7 .;X @+
#B7
.#GE4 .;Y .K --#C7 .;X -- #E7 #B --
#BE
.#GF4 .;Y .K #B.E7 .;X -- #F7 #B @+
#I.C
.#GG4
.#GH4
,,EXTRA ,,PRACTICE = ,LESSON #E.B1 P4
#AJAD
..,,ONL9E ,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#CDE
,GRAPH+ ,CALCULATOR ,ACTIV;Y3 #E.B
,SET A ,GD ,VIEW+ ,W9D[
,USE AF ,LESSON1 #E.B
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,KEY/ROKES
,,"Q ,:AT IS A GD VIEW+ W9D[ =A
POLYNOMIAL FUNC;N3
,:5 Y GRAPH A FUNC;N )A GRAPH+
CALCULATOR1 Y %D *OOSE A VIEW+ W9D[ T
4PLAYS ! IMPORTANT "*I/ICS (! GRAPH4
,,EXAMPLE ,GRAPH A POLYNOMIAL FUNC;N
,GRAPH .;F @7 .;X @7 .K #J.B .;X #C --
#E .;X #B @+ #CH .;X -- #IG4
.,,/EP .#A ,GRAPH ! FUNC;N
,GRAPH ! FUNC;N 9 ! /&>D VIEW+ W9D[4
--#AJ "K.K .;X "K.K #AJ1 --#AJ "K.K
.;Y "K.K #AJ
.,,/EP .#B ,ADJU/ HORIZONT,Y
,ADJU/ ! HORIZONTAL SCALE S T ! 5D
2HAVIOR (! GRAPH Z .;X @+ IS VISI#4
--#AJ "K.K .;X "K.K #BJ1 --#AJ "K.K
.;Y "K.K #AJ
.,,/EP .#C ,ADJU/ V]TIC,Y
,ADJU/ ! V]TICAL SCALE S T ! TURN+
PO9TS & 5D 2HAVIOR (! GRAPH Z .;X -- >E
VISI#4
--#AJ "K.K .;X "K.K #BJ1 --#BJ "K.K
.;Y "K.K #AJ
,,PRACTICE
,F9D 9T]VALS = .;X & .;Y T DESCRIBE A
GD VIEW+ W9D[ =! GRAPH (! POLYNOMIAL
FUNC;N4
.#A4 .;F @7 .;X @7 .K .;X #C @+ #D .;X
#B -- #H .;X @+ #AA
.#B4 .;F @7 .;X @7 .K -- .;X #C @+ #CF
.;X #B -- #AJ
.#C4 .;F @7 .;X @7 .K .;X #D -- #D .;X
#B @+ #B
.#D4 .;F @7 .;X @7 .K -- .;X #D -- #B
.;X #C @+ #C .;X #B -- #D .;X @+ #E
.#E4 .;F @7 .;X @7 .K--- .;X #D @+ #C
.;X #C @+ #AE .;X
.#F4 .;F @7 .;X @7 .K #B .;X #D -- #G
.;X #C @+ .;X -- #H
.#G4 .;F @7 .;X @7 .K -- .;X #E @+ #I
.;X #C -- #AB .;X @+ #AH
.#H4 .;F @7 .;X @7 .K .;X #E -- #G .;X
#D @+ #BE .;X #C -- #DJ .;X #B @+ #AC
.;X
.#I4 .,,R1SON+ ,LET .;G @7 .;X @7 .K
.;F @7 .;X @7 @+ .;C ": .;F @7 .;X @7 &
.;G @7 .;X @7 >E POLYNOMIAL FUNC;NS &
.;C IS A POSITIVE 3/ANT4 ,H[ IS A GD
VIEW+ W9D[ =! GRAPH ( .;F @7 .;X @7
RELAT$ 6A GD VIEW+ W9D[ =! GRAPH ( .;G
@7 .;X @7@8
.#AJ4 .,,BASEBALL ,F #AIID 6#BJJC1 !
AV]AGE SAL>Y .;,S 7IN ?\S&S ( DOLL>S7 =
MAJOR L1GUE BASEBALL PLAY]S C 2 MODEL$
BY
.;,S @7 .;X @7 .K --#D.AJ .;X #C @+
#FG.D .;X #B -- #ABA .;X @+ #AAGJ
": .;X IS ! NUMB] ( YE>S S9CE #AIID4
,F9D 9T]VALS =! HORIZONTAL & V]TICAL
AXES T DESCRIBE A GD VIEW+ W9D[ =! GRAPH
( .,S4
------------------------------------#CDF
#E.C ,ADD1 ,SUBTRACT & ,MULTIPLY
,POLYNOMIALS
.,2F ,Y EVALUAT$ & GRAPH$ POLYNOMIAL
FUNC;NS4
.,N[ ,Y W ADD1 SUBTRACT1 & MULTIPLY
POLYNOMIALS4
.,:Y8 ,S Y C MODEL COLLEGIATE SPORTS
"PICIP,N1 Z 9 ,EX4 #FC4
,KEY ,VOCABUL>Y
99 L T]MS1 P4 #AB
,SIDEB>3
,/&>DS
..#C.J ,/UD5TS >E ADEPT AT OP],NS ON
.POLYNOMIALS @1 9CLUD+ L;G DIVI.N4
,6ADD OR SUBTRACT POLYNOMIALS1 ADD OR
SUBTRACT ! COE6ICI5TS ( L T]MS ,Y C USE
A V]TICAL OR HORIZONTAL =MAT4
,,EXAMPLE #A ,ADD POLYNOMIALS V]TIC,Y
& HORIZONT,Y
.A4 ,ADD #B .;X #C -- #E .;X #B @+ #C
.;X -- #I & .;X #C @+ #F .;X #B @+ #AA 9
A V]TICAL =MAT4
.B4 ,ADD #C .;Y #C -- #B .;Y #B -- #G
.;Y & --#D .;Y #B @+ #B .;Y -- #E 9 A
HORIZONTAL =MAT4
,,REVIEW ,,SIMPLIFY+
,= HELP ) SIMPLIFY+ EXPRES.NS1 SEE P4
#AJ @4
,SOLU;N
.A4
.B4 7#C .;Y #C -- #B .;Y #B -- #G .;Y
@7 @+ 7--#D .;Y #B @+ #B .;Y -- #E7
.K #C .;Y #C -- #B .;Y #B -- #D .;Y #B
-- #G .;Y @+ #B .;Y -- #E
.K #C .;Y #C -- #F .;Y #B -- #E .;Y --
#E
,,EXAMPLE #B ,SUBTRACT POLYNOMIALS
V]TIC,Y & HORIZONT,Y
.A4 ,SUBTRACT #C .;X #C @+ #B .;X #B
-- .;X @+ #G F #H .;X #C -- .;X #B -- #E
.;X @+ #A 9 A V]TICAL =MAT4
.B4 ,SUBTRACT #E .;Z #B -- .;Z @+ #C F
#D .;Z #B @+ #I .;Z -- #AB 9 A
HORIZONTAL =MAT4
,SOLU;N
.A4 ,ALIGN L T]MS1 !N ADD ! OPPOSITE
(! SUBTRACT$ POLYNOMIAL4
.B4 ,WRITE ! OPPOSITE (! SUBTRACT$
POLYNOMIAL1 !N ADD L T]MS4
7#D .;Z #B @+ #I .;Z -- #AB7--7#E .;Z
#B -- .;Z @+ #C7 .K #D .;Z #B @+ #I .;Z
-- #AB--#E .;Z #B @+ .;Z -- #C
.K #D .;Z #B -- #E .;Z #B @+ #I .;Z @+
.;Z -- #AB--#C
.K -- .;Z #B @+ #AJ .;Z -- #AE
..,,GUID$ ,,PRACTICE = ,EXAMPLES #A &
.#B
,F9D ! SUM OR DI6];E4
.#A4 @7 .;T #B -- #F .;T @+ #B7 @+ 7#E
.;T #B -- .;T -- #H7
.#B4 7#H .;D -- #C @+ #I .;D #C @7--@7
.;D #C -- #AC .;D #B -- #D7
------------------------------------#CDG
.,,MULTIPLY+ .,,POLYNOMIALS ,6MULTIPLY
TWO POLYNOMIALS1 Y MULTIPLY EA* T]M (!
F/ POLYNOMIAL 0EA* T]M (! SECOND
POLYNOMIAL4
,,EXAMPLE #C ,MULTIPLY POLYNOMIALS
V]TIC,Y & HORIZONT,Y
.A4 ,MULTIPLY --#B .;Y #B @+ #C .;Y --
#F & .;Y -- #B 9 A V]TICAL =MAT4
.B4 ,MULTIPLY .;X @+ #C & #C .;X #B --
#B .;X @+ #D 9 A HORIZONTAL =MAT4
,SOLU;N
.A4
.B4 @7 .;X @+ #C77#C .;X #B -- #B .;X
@+ #D7 .K @7 .;X @+ #C7#C .;X #B -- @7
.;X @+ #C7#B .;X @+ @7 .;X @+ #C7#D
.K #C .;X #C @+ #I .;X #B -- #B .;X #B
-- #F .;X @+ #D .;X @+ #AB
.K #C .;X #C @+ #G .;X #B -- #B .;X @+
#AB
,,EXAMPLE #D ,MULTIPLY ?REE BINOMIALS
,MULTIPLY .;X --@2 #E1 .;X @+ #A1 &
.;X @+ #C 9 A HORIZONTAL =MAT4
@7 .;X -- #E7@7 .;X @+ ;L7@7 .;X @+
#C7 .K @7 .;X #B -- #D .;X -- #E7@7 .;X
@+ #C7
.K @7 .;X #B -- #D .;X -- #E7 .;X @+
@7 .;X #B -- #D .;X -- #E7#C
.K .;X #C -- #D .;X #B -- #E .;X @+ #C
.;X #B -- #AB .;X -- #AE
.K .;X #C -- .;X #B -- #AG .;X -- #AE
.,,PRODUCT .,,PATT]NS ,"S BINOMIAL
PRODUCTS O3UR S FREQU5TLY T X IS WOR?
MEMORIZ+ _! PATT]NS4 ,Y C V]IFY ^!
PRODUCT PATT]NS 0MULTIPLY+4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,SPECIAL ,PRODUCT ,PATT]NS
,,AVOID ,,]RORS
,9 G5]AL1 @7 .A +- .;B @7 #B @6.K .A
#B +- .;B #B & @7 .A +- .;B @7 #C @6.K
.A #C +- .;B #C @4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,SUM .& .,DI6];E
@7 .A @+ .;B @7@7 .A -- .;B @7 .K .A #B
-- .;B #B @3 .,EXAMPLE
@7 .;X @+ #D7@7 .;X --#D7 .K .;X #B --
#AF
..,SQU>E (A .,BINOMIAL
@7 A.' @+ ;B.' @7 .K A.' #B @+ #B ;AB.'
@+ ;B.' #B
@7 A.' -- ;B.' @7 .K A.' #B -- #B ;AB.'
@+ .;B #B @3 .,EXAMPLE
@7 .;Y @+ #C7 #B .K .;Y #B @+ #F .;Y @+
#I
7#C .;Z #B -- #E7 #B .K #I .;Z #D -- #CJ
.;Z #B @+ #BE
..,CUBE (A .,BINOMIAL
@7 .A @+ .;B @7 .K .A #C @+ #C .A #B .;B
@+ #C .;AB #B @+ .;B #C
@7 .A -- .;B @7 .K .A #C -- #C .A #B .;B
@+ #C .;AB #B -- .;B #C @3 .,EXAMPLE
@7 .;X @+ #B7 #C .K .;X #C @+ #F .;X #B
@+ #AB .;X @+ #H
@7 .;P -- #C7 #C .K .;P #C -- #I .;P #B
@+ #AG .;P -- #BG
------------------------------------#CDH
,,EXAMPLE #E ,USE SPECIAL PRODUCT
PATT]NS
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.A4 7#C .;T @+ #D77#C .;T -- #D7 .K
7#C .;T @7 #B -- #D #B @3 ,SUM & DI6];E
.K #I .;T #B--#AF @3 --
.B4 7#H .;X -- #C7 #B .K 7#H .;X @7 #B
-- #B7#H .;X @77#C7 @+ #C #B @3 ,SQU>E
(A BINOMIAL
.K #FD .;X #B -- #DH .;X @+ #I @3 --
C4 7.PQ @+ #E7 #C .K @7 .PQ @7 #C @+
#C7 .PQ @7 #B 7#E7 @+ #C7 .PQ @77#E7 #B
@+ #E #C @3 ,CUBE (A BINOMIAL
.K ;P.' #C ;Q.' #C @+ #A #E;P.' #B
;Q.' #B @+ #GE;PQ @+ #ABE @3 --
..,,GUID$ ,,PRACTICE = ,EXAMPLES #C1D1
& .#E
,F9D ! PRODUCT4
.#C4 @7 .;X @+ #B77#C .;X #B -- .;X --
#E7
.#D4 @7 .A -- #E7@7 .A @+ #B7@7 .A @+
#F7
.#E4 @7 .XY -- #D7 #C
,,EXAMPLE #F ,USE POLYNOMIAL MODELS
.,,PETROLEUM ,S9CE #AIHJ1 ! NUMB] .;,W
7IN ?\S&S7 ( ,UNIT$ ,/ATES WELLS PRODUC+
CRUDE OIL &! AV]AGE DAILY OIL \TPUT P]
WELL .,O 7IN B>RELS7 C 2 MODEL$ BY
.;,W .K --#J.EGE .;T #B @+ #AJ.I .;T
@+ #EDH & .,O .K --#J.BDI .;T @+ #AE.D
": .;T IS ! NUMB] ( YE>S S9CE #AIHJ4
,WRITE A MODEL =! AV]AGE .TOTAL AM.T
.;,T ( CRUDE OIL PRODUC$ P] "D4 ,:AT 0 !
AV]AGE TOTAL AM.T ( CRUDE OIL PRODUC$ P]
"D 9 #BJJJ8
,PICTURE3 ,OIL REF9]Y 9 ,L;G ,B1*1
,CALI=NIA
,,DET]M9E ,,SIGNIFICANT ,,DIGITS
,:5 MULTIPLY+ MODELS1 R.D YR RESULT S
T XS T]MS H ! SAME NUMB] ( SIGNIFICANT
DIGITS Z ! MODEL )! FEWE/ NUMB] (
SIGNIFICANT DIGITS4
,SOLU;N
,6F9D A MODEL = .;,T @1 MULTIPLY ! TWO
GIV5 MODELS4
,TOTAL DAILY OIL \TPUT C 2 MODEL$
0.;,T .K #J.ADC .;T #C -- #AA.F .;T #B
@+ #CA.D .;T @+ #HDDJ ": .;,T IS M1SUR$
9 ?\S&S ( B>RELS4 ,0SUB/ITUT+ .;T .K #BJ
96! MODEL1 Y C E/IMATE T ! AV]AGE TOTAL
AM.T ( CRUDE OIL PRODUC$ P] "D 9 #BJJJ 0
AB #EEGJ ?\S& B>RELS1 OR #E1EGJ1JJJ
B>RELS4
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#F
.#F4 .,,9DU/RY ,! MODELS 2L GIVE !
AV]AGE DEP? .;,D 7IN FEET7 ( NEW WELLS
DRILL$ &! AV]AGE CO/ P] FOOT .;,C 7IN
DOLL>S7 ( DRILL+ A NEW WELL4 ,9 BO?
MODELS1 .;T REPRES5TS ! NUMB] ( YE>S
S9CE #AIHJ4 ,WRITE A MODEL =! AV]AGE
.TOTAL CO/ .;,T ( DRILL+ A NEW WELL4
.;,D .K #AJI .;T @+ #DJAJ & .;,C .K
#J.EDB .;T #B -- #G.AF .;T @+ #GI.D
------------------------------------#CDI
#E.C ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
,,WS#AJ = ,EXS4 #AA1 #BA1 & #FA
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE ,EXS4
#B1 #AE1 #DG1 #EF1 & #FC
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,:5 Y ADD OR
SUBTRACT POLYNOMIALS1 Y ADD OR SUBTRACT
! COE6ICI5TS ( @8 @4
.#B4 .,,WRIT+ .,EXPLA9 H[ A POLYNOMIAL
SUBTRAC;N PRO#M IS EQUIVAL5T 6A
POLYNOMIAL A4I;N PRO#M4
.,,EXAMPLES .#A & #B ON P4 #CDF =
,EXS4 #C-AE
..,,A4+ ,,& ,,SUBTRACT+ .,,POLYNOMIALS
,F9D ! SUM OR DI6];E4
.#C4 7#C .;X #B -- #E7 @+ 7#G .;X #B
-- #C7
.#D4 @7 .;X #B -- #C .;X @+ #E7--7--#D
.;X #B @+ #H .;X @+ #I7
.#E4 7#D .;Y #B @+ #I .;Y -- #E7--7#D
.;Y #B -- #E .;Y @+ #C7
.#F4 @7 .;Z #B @+ #E .;Z -- #G7 @+ 7#E
.;Z #B -- #AA .;Z -- #F7
.#G4 7#C .;S #C @+ .;S @7 @+ 7#D .;S
#C -- #B .;S #B @+ #G .;S @+ #AJ7
.#H4 7#B .A #B -- #H7--@7 .A #C @+ #D
.A #B -- #AB .A @+ #D7
.#I4 7#E .;C #B @+ #A .;C @+ #A7 @+
7#B .;C #C -- #F .;C @+ #H7
.#AJ4 7#D .;T #C -- #AA .;T #B @+ #D
.;T @7--7--#G .;T #B -- #E .;T @+ #H7
.#AA4 7#E .;B -- #F .;B #C @+ #B .;B
#D @7--7#I .;B #C @+ #D .;B #D -- #G7
.#AB4 7#C .;Y #B -- #F .;Y #D @+
#E--#F .;Y @7 @+ 7#E .;Y #D -- #F .;Y #C
@+ #D .;Y @7
.#AC4 @7 .;X #D -- .;X #C @+ .;X #B --
.;X @+ #A7 @+ @7 .;X @+ .;X #D -- #A --
.;X #B @7
.#AD4 7#H .;V --#B .;V #B @+ .;V
--#D7--7#C .;V #C -- #AB .;V #B @+ #H
.;V @7
#AE4 .,,MULTIPLE .,,*OICE ,:AT IS !
RESULT :5 #B .;X #D -- #H .;X #B -- .;X
@+ #AJ IS SUBTRACT$ F #H .;X #D -- #D
.;X #C -- .;X @+ #B8
,A --#F .;X #D @+ #D .;X #C -- #H .;X
#B @+ #H
;,B #F .;X #D -- #D .;X #C @+ #H .;X
#B -- #H
;,C #AJ .;X #D -- #H .;X #C -- #D .;X
#B @+#AB
;,D #F .;X #D @+ #D .;X #C -- #B .;X
-- #H
,,EXAMPLE #C
ON P4 #CDG = ,EXS4 #AF-BE
,,MULTIPLY+ ,,POLYNOMIALS ,F9D !
PRODUCT (! POLYNOMIALS4
.#AF4 .;X 7#B .;X #B -- #E .;X @+ #G7
.#AG4 #E .;X #B 7#F .;X @+ #B7
.#AH4 @7 .;Y -- #G7@7 .;Y @+ #F7
.#AI4 7#C .;Z @+ ;L7@7 .;Z -- #C7
.#BJ4 @7 .;W @+ #D7@7 .;W #B @+ #F .;W
-- #AA7
.#BA4 7#B .A -- #C7@7 .A #B -- #AJ .A
-- #B7
.#BB4 7#E .;C #B -- #D7 7#B .;C #B @+
.;C -- #C7
.#BC4 @7-- .;X #B @+ #D .;X @+ #A7@7
.;X #B -- #H .;X @+ #C7
.#BD4 @7-- .;D #B @+ #D .;D @+ #C77#C
.;D #B -- #G .;D @+ #F7
.#BE4 7#C .;Y #B @+ #F .;Y -- ;L77#D
.;Y #B -- #AA .;Y -- #E7
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 SIMPLIFY+ ! EXPRES.N4
.#BF4
.#BG4
,,EXAMPLE #D
ON P4 #CDG = ,EXS4 #BH-CG
,,MULTIPLY+ ,,?REE ,,BINOMIALS ,F9D !
PRODUCT (! BINOMIALS4
.#BH4 @7 .;X @+ #D7@7 .;X -- #F7@7 .;X
-- #E7
.#BI4 @7 .;X @+ ;L7@7 .;X -- #G7@7 .;X
@+ #C7
.#CJ4 @7 .;Z -- #D7@7-- .;Z @+ #B7@7
.;Z @+ #H7
.#CA4 @7 .A -- #F77#B .A @+ #E7@7 .A
@+ #A7
.#CB4 7#C .;P @+ #A7@7 .;P @+ #C7@7
.;P @+ #A7
.#CC4 @7 .;B -- #B7 7#B .;B -- #A7@7--
.;B @+ #A7
.#CD4 7#BE @+ #A77#C .;S --
#B77#DE--#C7
.#CE4 @7 .;W -- #F77#D .;W -- #A77--#C
.;W @+ #E7
.#CF4 7#D .;X -- #A77--#B .;X --
#G77--#E .;X -- #D7
.#CG4 7#C .;Q -- #H77--#I .;Q @+ #B7@7
.;Q -- #B7
------------------------------------#CEJ
.,,EXAMPLE .#E ON P4 #CDH = ,EXS4
#CH-DG
.,,SPECIAL .,,PRODUCTS ,F9D ! PRODUCT4
.#CH4 @7 .;X @+ #E7@7 .;X -- #E7
.#CI4 @7 .;W --#I7 #B
.#DJ4 @7 .;Y @+ #D7 #C
.#DA4 7#B .;C @+ #E7 #B
.#DB4 7#C .;T -- #D7 #C
.#DC4 7#E .;P -- #C77#E .;P @+ #C7
.#DD4 7#G .;X -- .;Y @7 #C
.#DE4 7#B .A @+ #I .;B @7 7#B .A -- #I
.;B @7
.#DF4 7#C .;Z @+ #G .;Y @7 #C
#DG4 .,,MULTIPLE .,,*OICE ,: EXPRES.N
IS EQUIVAL5T TO 7#C .;X -- #B .;Y @7 #B
@8
,A #I .;X #B -- #D .;Y #B
;,B #I .;X #B @+ #D .;Y #B
;,C #I .;X #B @+ #AB .;X ;Y @+ #D .;Y
#B
;,D #I .;X #B -- #AB .;X ;Y @+ #D .;Y
#B
.,,GEOMETRY ,WRITE ! FIGURE'S VOLUME Z
A POLYNOMIAL 9 /&>D =M4
.#DH4 .;,V .K .WH
.#DI4 ;,V.K ;R #B ;H
.#EJ4 .;,V .K .;S #C
.#EA4
.,,SPECIAL .,,PRODUCTS ,V]IFY !
SPECIAL PRODUCT PATT]N 0MULTIPLY+4
.#EB4 @7 .A @+ .;B @7@7 .A -- .;B @7
.K .A #B -- .;B #B
.#EC4 @7 .A @+ .;B @7 #B .K .A #B @+
#B .;AB @+ .;B #B
.#ED4 @7 .A @+ .;B @7 #C .K .A #C @+
#C .A #B .;B @+ #C .;AB #B @+ .;B #C
.#EE4 @7 .A -- .;B @7 #C .K .A #C --
#C .A #B .;B @+ #C .;AB #B -- .;B #C
#EF4 .,,EXT5D$ .,,RESPONSE ,LET
.;P7.;X7 .K .;X #D -- #G .;X @+ #AD &
.;Q7.;X7 .K .;X #B -- #E4
A4 ,:AT IS ! DEGREE (! POLYNOMIAL
.;P7.;X7 @+ .;Q7.;X7 @8
B4 ,:AT IS ! DEGREE (! POLYNOMIAL
.;P7.;X7--.;Q7.;X78
C4 ,:AT IS ! DEGREE (! POLYNOMIAL
.;P7.;X7 @* .;Q7.;X78
D4 ,9 G5]AL1 IF .;P7.;X7 & .;Q7.;X7 >E
POLYNOMIALS S* T ;P7;X7 HAS DEGREE .;M1
.;Q7.;X7 HAS DEGREE .;N @1 & .;M.1 .;N
@1 :AT >E ! DEGREES ( ..;P7;X7 @+
;Q7;X71 ;P7;X7--;Q7.;X7 @1 & ;P7;X7 @*
;G7;X78
#EG4 .,,F9D+ .,A .,,PATT]N ,LOOK AT !
FOLL[+ POLYNOMIAL FACTORIZ,NS4
.;X #B -- #A .K @7 .;X -- ;L7@7 .;X @+
#A7
.;X #C -- #A .K @7 .;X -- #A7@7 .;X #B
@+ .;X @+ #A7
.;X #D -- #A .K @7 .;X -- ;L7@7 .;X #C
@+ .;X #B @+ .;X @+ #A7
A4 ,FACTOR .;X #E -- #A & .;X #F -- #A
96! PRODUCT ( .;X -- #A & ANO!R
POLYNOMIAL4 ,*ECK YR ANSW]S 0MULTIPLY+4
B4 ,9 G5]AL1 H[ C .;X ;N -- #A 2
FACTOR$8 ,%[ T ? FACTORIZ,N "WS
0MULTIPLY+ ! FACTORS4
#EH4 .,,*ALL5GE ,SUPPOSE .;F 7;X7 .K
@7 .;X @+ .A77.;X @+ .;B77.;X @+ ;C7@7
.;X @+ .;D74 ,IF .;F @7 .;X @7 IS WRITT5
9 /&>D =M1 %[ T ! COE6ICI5T ( .;X #C IS
! SUM ( .A1 .;B1 .;C @1 & .;D @1 &!
3/ANT T]M IS ! PRODUCT ..(A1 ;B1 .;C @1
& .D4
.K.,,"W$--.,,\ .,,SOLU;NS ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#CEA
,,PRO#M ,,SOLV+
.,,EXAMPLE .#F ON P4 #CDH = ,EXS4
#EI-FA
.#EI4 .,,HI<] .,,$UC,N ,S9CE #AIGJ1 !
NUMB] 7IN ?\S&S7 ( MALES .;,M & FEMALES
.;,F ATT5D+ 9/ITUTES ( HI<] $UC,N C 2
MODEL$ BY
.;,M -- #J.JIA .;T #C -- #D.H .;T #B
@+ #AAJ .;R @+ #EJJJ & .;,F .K #J.L#I
.;T #C -- #AB .;T #B @+ #CEJ .;T @+
#CFJJ
": .;T IS ! NUMB] ( YE>S S9CE #AIGJ4
,WRITE A MODEL =! TOTAL NUMB] ( P ATT5D+
9/ITUTES ( HI<] $UC,N4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#FJ4 .,,ELECTRONICS ,F #AIII 6#BJJD1
! NUMB] ( ,,DVD PLAY]S .;,D 7IN
MILLIONS7 SOLD 9 ! ,UNIT$ ,/ATES &!
AV]AGE PRICE P] ,,DVD PLAY] .;,P 7IN
DOLL>S7 C 2 MODEL$ BY
.;,D .K #D.AA .;T @+ #D.DD & .;,P .K
.#F..HB .;T #B -- .#FA..GA @+ #BFE
": .;T IS ! NUMB] ( YE>S S9CE #AIII4
,WRITE A MODEL =! TOTAL REV5UE .;,R F
,,DVD SALES4 ,AC 6! MODEL1 :AT 0 ! TOTAL
REV5UE 9 #BJJB8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#FA4 .,,BICYCL+ ,! EQU,N .;,P .K
#J.JJB .#FG .;S .;,F GIVES ! P[] .;,P
7IN HORSEP[]7 NE$$ 6KEEP A C]TA9 BICYCLE
MOV+ AT SPE$ .;S 7IN MILES P] H\R71 ":
;,F IS ! =CE 7IN P.DS7 ( ROAD & AIR
RESI/.E4 ,ON LEVEL GR.D1 ! EQU,N
;,F.K #J.JAAF .;S #B @+ #J.GHI
MODELS ! =CE .,F4 ,WRITE A MODEL 7IN
T]MS ( .;S ONLY7 =! P[] NE$$ 6KEEP !
BICYCLE MOV+ AT SPE$ .;S ON LEVEL GR.D4
,H[ M* P[] IS NE$$ 6KEEP ! BICYCLE MOV+
AT #AJ MILES P] H\R8
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
.#FB4 .,,MULTI--.,,/EP .,,PRO#M ,A
DESS]T IS MADE 0TAK+ A HEMISPH]ICAL M.D
( M>%MALL[ ON A #J.E C5TIMET] ?ICK
COOKIE & COV]+ X )A *OCOLATE %ELL #A
C5TIMET] ?ICK4 ,USE ! DIAGRAMS 6WRITE
TWO POLYNOMIAL FUNC;NS 9 /&>D =M3
.;,M7.;R7 =! -B9$ VOLUME (! M>%MALL[
PLUS COOKIE1 & .;,D7.;R7 =! VOLUME (!
5TIRE DESS]T4 ,!N USE .;,M7.;R7 &
.;,D7.;R7 6WRITE A FUNC;N .;,C7.;F7 =!
VOLUME (! *OCOLATE4
.#FC4 .,,%ORT .,,RESPONSE ,F #AIIG
6#BJJB1 ! NUMB] ( ,,NCAA LACROSSE T1MS =
M5 .;,L & WOM5 .;,L @1 Z WELL Z ! AV]AGE
SIZE (A M5'S T1M .;,S ;M.' @1 &A WOM5'S
T1M .;,S ;W.' @1 C 2 MODEL$ BY
.;,L ;M @1 .K #E.EG .;T @+ #AHB & .;,S
;M .K --#J.ABG .;R #C @+ #J.HBB .;R #B
-- #A.JB;IT @+ #CA.E
.;,L .K #AB.B .;T @+ #AHE & .;,S ;W .K
--#J.JFFB .;T #C @+ #J.DCG .;T #B --
#J.GBE .;T @+ #BB.C
": .;T IS ! NUMB] ( YE>S S9CE #AIIG4
,WRITE A MODEL =! .TOTAL NUMB] ( P .;,N
ON ,,NCAA LACROSSE T1MS4 .,EXPLA9 H[ Y
OBTA9$ YR MODEL4
------------------------------------#CEB
.#FD4 .,,*ALL5GE ,F #AIGJ 6#BJJB1 !
CIRCUL,N .;,C 7IN MILLIONS7 ( ,SUN"D
NEWSPAP]S 9 ! ,UNIT$ ,/ATES C 2 MODEL$
BY
;,C .K --#J.JJAJE .;T #C @+ #J.JBHA
.;T @+ #J.DFE .;T @+ #DH.H
": .;T IS ! NUMB] ( YE>S S9CE #AIGJ4
,REWRITE .;,C Z A FUNC;N ( .;S @1 ": .;S
IS ! NUMB] ( YE>S S9CE #AIGE4
,MIX$ ,REVIEW
,SIDEB>3
,PREVIEW
,PREP>E = ,LESSON #E.D 9 ,EXS4 #FE-GB4
,SOLVE ! EQU,N4
.#FE4 #B .;X -- #G .K #AA @7 .P4 #AH
@7
.#FF4 #AJ--#C .;X .K #BE @7 .P4 #AH @7
.#FG4 #D .;T -- #G .K #B .;T @7 .P4
#AH @7
.#FH4 .;Y #B -- #B .;Y -- #DH .K #J @7
.P4 #BEB @7
.#FI4 .;W #B -- #AE .;W @+ #ED .K #J
@7 .P4 #BEB @7
.#GJ4 .;X #B @+ #I .;X @+ #AD .K #J @7
.P4 #BEB @7
.#GA4 #D .;Z #B @+ #BA .;Z -- #AH .K
#J @7 .P4 #BEI @7
.#GB4 #I .A #B -- #CJ .A @+ #BE .K #J
@7 .P4 #BEI @7
,SOLVE ! SY/EM ( EQU,NS4 @7 .P4 #AGH
@7
.#GC4 .;X @+ .;Y -- #B .;Z .K --#D
#C .;X -- .;Y @+ .;Z .K #BB
-- .;X @+ #B .;Y @+ #C .;Z .K --#I
.#GD4 .;X -- #B .;Y @+ .;Z .K --#AC
-- .;X @+ #D .;Y @+ .;Z .K #CE
#C .;X @+ #B .;Y @+ #D .;Z .K #BH
.#GE4 #C .;X -- .;Y -- #B .;Z .K #BJ
-- .;X @+ #C .;Y -- .;Z .K --#AF
--#B .;X -- .;Y @+ #C .;Z .K --#E
,EVALUATE ! DET]M9ANT (! MATRIX4 @7
.P4 #BJC @7
.#GF4
.#GG4
.#GH4
.#GI4
,,QUIZ .= .,LESSONS .#E..A--.#E..C
,EVALUATE ! EXPRES.N1 @7 P4 #CCJ @7
.#A4 #C #E @* #C-- #A
.#B4 7#B #D @7 #B
.#C4
.#D4
,SIMPLIFY ! EXPRES.N1 @7 P4 #CCJ @7
.#E4 7;X #D ;Y --#B7 7;X --#C ;Y #H @7
.#F4 7A #B ;B-- #E @7 --#C
.#G4
.#H4
,GRAPH ! POLYNOMIAL FUNC;N1 @7 P4 #CCG
@7
.#I4 .;G @7 .;X @7 .K #B .;X #C -- #C
.;X @+ #A
.#AJ4 .;H7.;X7 .K .;X #D -- #D .;X @+
#B
.#AA4 .;F @7 .;X @7 .K --#B .;X #C @+
.;X #B -- #E
,P]=M ! 9DICAT$ OP],N1 @7 P4 #CDF @7
.#AB4 7;X #C @+ .;X #B -- #F7--7#B .;X
#B @+ #D .;X -- #H7
.#AC4 7--#C .;X #B @+ #D .;X -- #AJ7
@+ 7;X #B -- #I .;X @+ #AE7
.#AD4 @7 .;X -- #E77;X #B -- #E .;X @+
#G7
.#AE4 @7 .;X @+ #C7@7 .;X -- #F77#C
.;X -- #A7
.#AF4 .,,N,NAL .,,DEBT ,ON ,JULY #BA1
#BJJD1 ! N,NAL DEBT (! ,UNIT$ ,/ATES 0
AB 4#G1BHB1JJJ1JJJ1JJJ4 ,! POPUL,N (!
,UNIT$ ,/ATES AT T "T 0 AB #BID1JJJ1JJJ4
,SUPPOSE ! N,NAL DEBT 0 DIVID$ EV5LY
AM;G "EY"O 9 ! ,UNIT$ ,/ATES4 ,H[ M* WD
EA* P]SON [E8 @7 P4 #CCJ @7
.,,EXTRA .,,PRACTICE = ,LESSON #E.C1
P4 #AJAD
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#CEC
#E.D ,FACTOR & ,SOLVE ,POLYNOMIAL
,EQU,NS
.,2F ,Y FACTOR$ & SOLV$ QUADRATIC
EQU,NS4
.,N[ ,Y W FACTOR & SOLVE O!R
POLYNOMIAL EQU,NS4
.,:Y8 ,S Y C F9D DIM5.NS (
>*AEOLOGICAL RU9S1 Z 9 ,EX4 #EH4
,KEY ,VOCABUL>Y
99 .FACTOR$ .-PLETELY
99 .FACTOR .0.GR\P+
99 .QUADRATIC .=M
,SIDEB>3
,/&>DS
#D.J ,/UD5TS FACTOR POLYNOMIALS
REPRES5T+ ! DI6];E ( SQU>ES1 P]FECT
SQU>E TRINOMIALS1 &! SUM & DI6];E ( TWO
CUBES4
,9 ,*APT] #D1 Y LE>N$ H[ 6FACTOR !
FOLL[+ TYPES ( QUADRATIC EXPRES.NS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,TYPE3 ,EXAMPLE
,G5]AL TRINOMIAL3 #B .;X #B -- #C .;X
-- #BJ .K 7.#B .;X @+ .#E77.;X -- #D7
,P]FECT SQU>E TRINOMIAL3 .;X #B @+ #H
.;X @+ #AF .K @7 .;X @+ #D7 #B
,DI6];E ( TWO SQU>ES3 #I .;X #B -- #A
.K 7#C .;X @+ #A77#C .;X -- #A7
,-MON MONOMIAL FACTOR3 #H .;X #B @+
#BJ .;X .K #D .;X 7#B .;X @+ #E7
,Y C AL FACTOR POLYNOMIALS ) DEGREE
GRT] ?AN #B4 ,"S ( ^! POLYNOMIALS C .2
.FACTOR$ .-PLETELY US+ TE*NIQUES LE>N$ 9
,*APT] #D4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,FACTOR+ ,POLYNOMIALS
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,DEF9I;N3 ,EXAMPLES
,A FACTORA# POLYNOMIAL ) 9TEG]
COE6ICI5TS IS .FACTOR$ .-PLETELY @2 IF X
IS WRITT5 Z A PRODUCT (2 UNFACTORA#
POLYNOMIALS ) 9TEG] COE6ICI5TS4 @3 #B7
.;X @+ #A7@7 .;X -- #D7 & #E .;X #B @7
.;X #B -- #C7 >E FACTOR$ -PLETELY#.C .;X
@7 .;X #B -- #D7 IS .N FACTOR$ -PLETELY
2C .;X #B -- #D C 2 FACTOR$ Z7 .;X @+
#B7 @7 .;X -- #B74
,,EXAMPLE #A ,F9D A -MON MONOMIAL
FACTOR
,FACTOR ! POLYNOMIAL -PLETELY4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.A4 .;X #C @+ #B .;X #B -- #AE .;X @3
.K .;X @7 .;X #B @+ #B .;X -- #AE7 @3
.,FACTOR .-MON .MONOMIAL4
--@3 .K .;X @7 .;X @+ #E77;X-- #C7 @3
.,FACTOR .TRINOMIAL4
.B4 #B .;Y #E -- #AH .;Y #C @3 .K #B
.;Y #C @7 .;Y #B -- #I7 @3 .,FACTOR
.-MON .MONOMIAL4
--@3 .K #B .;Y #C @7 .;Y @+ #C7@7 .;Y
-- #C7 @3 ..,DI6];E ( TWO .SQU>ES
.C4 #D .;Z #D -- #AF .;Z #C @+ #AF .;Z
#B @3 .K #D .;Z #B 7;Z #B -- #D .;Z @+
#D7 @3 .,FACTOR .-MON .MONOMIAL4
--@3 .K #D .;Z #B @7 .;Z -- #B7 #B @3
.,P]FECT .SQU>E .TRINOMIAL
------------------------------------#CED
.,,FACTOR+ .,,PATT]NS ,9 "P 7;B7 (
,EXAMPLE #A1 ! SPECIAL FACTOR+ PATT]N =!
DI6];E ( TWO SQU>ES IS US$ 6FACTOR !
EXPRES.N -PLETELY4 ,"! >E AL FACTOR+
PATT]NS T Y C USE 6FACTOR ! SUM OR
DI6];E ( TWO .CUBES4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,SPECIAL ,FACTOR+ ,PATT]NS
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,SUM ( ,TWO ,CUBES3 ,EXAMPLE
.A #C @+ ;B #C .K 7A @+ ;B77A.' #B --
;AB @+ ;B.' #B @7 @3 #H .;X #C @+ #BG .K
7#B .;X @7 #C @+ #C #C
.K 7#B .;X @+ #C77#D .;X #B --#F .;X @+
#I7
..,DI6];E ( ,TWO .,CUBES @3 .,EXAMPLE
A.' #C -- ;B.' #C .K 7A -- ;B.' @77A.'
#B @+ ;AB @+ ;B.' #B @7 @3 #FD .;X #C --
#A .K 7#D .;X @7 #C -- #A #C
.K 7#D .;X -- #A77#AF .;X #B @+ #D .;X
@+ #A7
,,EXAMPLE #B ,FACTOR ! SUM OR DI6];E (
TWO CUBES
,FACTOR ! POLYNOMIAL -PLETELY4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.A4 .;X #C @+ #FD @3 .K .;X #C @+ #D
#C .K @7 .;X @+ #D77;X #B --#D .;X @+
#AF7 @3 ..,SUM ( TWO .CUBES
.B4 #AF .;Z #E -- #BEJ .;Z #B @3 .K #B
.;Z #B 7#H .;Z #C -- #ABE7 @3 .,FACTOR
.-MON .MONOMIAL4
--@3 .K #B .;Z #B ,77#B .;Z @7 #C --
#E #C @7' @3 ..,DI6];E ( TWO .CUBES
--@3 .K #B .;Z #B 7#B .;Z -- #E77#D
.;Z #B @+ #AJ .;Z @+ #BE7 @3 --
..,,GUID$ ,,PRACTICE = ,EXAMPLES #A &
.#B
,FACTOR ! POLYNOMIAL -PLETELY4
.#A4 .;X #C -- #G .;X #B @+ ;L#J .;X
.#B4 #C .;Y #E -- #GE .;Y #C
.#C4 #AF .;B #E @+ #FHF .;B #B
.#D4 .;W #C -- #BG
.,,FACTOR+ .,,0.,,GR\P+ ,= "S
POLYNOMIALS1 Y C FACTOR 0GR\P+ PAIRS (
T]MS T H A -MON MONOMIAL FACTOR4 ,!
PATT]N = FACTOR+ 0GR\P+ IS %[N 2L4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
..RA@+ RB @+ SA @+ .SB @3 .K ;R7A @+
;B7 @+ ;S7A @+ .;B7
--@3 .K 7..;R @+ ;S7,7A @+ .;B7
,,EXAMPLE #C ,FACTOR 0GR\P+
,,AVOID ,,]RORS
,AN EXPRES.N IS N FACTOR$ -PLETELY
UNTIL .ALL FACTORS1 S* Z .;X #B -- #AF1
_C 2 FACTOR$ FUR!R4
,FACTOR ! POLYNOMIAL .;X #C -- #C .;X
#B -- #AF .;X @+ #DH -PLETELY4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X #C -- #C .;X #B -- #AF .;X @+ #DH
@3 .K .;X #B7 .;X -- #C7--#AF7 .;X --
#C7 @3 .,FACTOR .0.GR\P+4
--@3 .K7 .;X #B -- #AF7@7 .;X -- #C7
@3 .,4TRIBUTIVE .PROP]TY
--@3 .K @7 .;X @+ #D7@7 .;X -- #D7@7
.;X -- #C7 @3 ..,DI6];E ( TWO .SQU>ES
------------------------------------#CEE
.,,QUADRATIC .,,=M ,AN EXPRES.N (! =M
.AU #B @+ ..BU @+ .;C @1 ": .;U IS ANY
EXPRES.N 9 ;X1 IS SD 6BE 9 .QUADRATIC
.=M4 ,! FACTOR+ TE*NIQUES Y /UDI$ 9
,*APT] #D C "S"TS 2 US$ 6FACTOR S*
EXPRES.NS4
,,EXAMPLE #D ,FACTOR POLYNOMIALS 9
QUADRATIC =M
,,ID5TIFY ,,QUADRATIC ,,=M
,! EXPRES.N #AF .;X #D -- #HA IS 9
QUADRATIC =M 2C X C 2 WRITT5 Z .;U #B --
#HA ": .;U .K #D .;X #B @4
,FACTOR -PLETELY3 7A7 #AF .;X #D --
#HA & 7;B7 #B .;P #H @+ #AJ .;P #E @+
#AB .;P #B @4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.A4 #AF .;X #D -- #HA @3 .K 7#D .;X #B
@7 #B -- #I #B @3 ..,WRITE Z DI6];E (
TWO .SQU>ES4
--@3 .K 7#D .;X #B @+ #I7 7#D .;X #B
-- #I7 @3 ..,DI6];E ( TWO .SQU>ES
--@3 .K 7#D .;X #B @+ #I7 7#B .;X @+
#C7 7#B .;X -- #C7 @3 ..,DI6];E ( TWO
.SQU>ES
.B4 #B .;P #H @+ #AJ .;P #E @+ #AB .;P
#B @3 .K #B .;P #B @7 .;P #F @+ #E .;P
#C @+ #F7 @3 .,FACTOR .-MON .MONOMIAL4
--@3 .K #B .;P #B @7 .;P #C @+ #C7@7
.;P #C @+ #B7 @3 ..,FACTOR TRINOMIAL 9
QUADRATIC .=M4
.,,GUID$ .,,PRACTICE = ,EXAMPLES .#C &
#D
,FACTOR ! POLYNOMIAL -PLETELY4
.#E4 .;X #C @+ #G .;X #B -- #I .;X --
#FC
.#F4 #AF .;G #D -- #FBE
.#G4 #D .;T #F -- #BJ .;T #D @+ #BD
.;T #B
.,,SOLV+ .,,POLYNOMIAL .,,EQU,NS ,9
,*APT] #D1 Y LE>N$ H[ 6USE ! Z]O PRODUCT
PROP]TY 6SOLVE FACTORA# QUADRATIC
EQU,NS4 ,Y C EXT5D ? TE*NIQUE 6SOLVE "S
HI<]--DEGREE POLYNOMIAL EQU,NS4
..,EXAMPLE #E ,/&>DIZ$ ,TE/ .,PRACTICE
,:AT >E ! R1L--NUMB] SOLU;NS (! EQU,N
#C .;X #E @+ #AE .;X .K #AH .;X #C @8
.,A #J1 #A1 #C1 #E
.;,B --#A1 #J1 #A
.;,C
.;,D
,SOLU;N
,,AVOID ,,]RORS
,D N DIVIDE EA* SIDE ( AN EQU,N 0A
V>IA# OR A V>IA# EXPRES.N1 S* Z .#C .;X
@4 ,DO+ S W RESULT 9 ! LOSS ( SOLU;NS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#C .;X #E @+ #AE .;X .K #AH .;X #C @3
.,WRITE .ORIG9AL .EQU,N4
#C .;X #E -- #AH .;X #C @+ #AE .;X .K
#J @3 ..,WRITE 9 /&>D .=M4
#C .;X @7 .;X #D -- #F .;X #B @+ #E7
.K #J @3 .,FACTOR .-MON .MONOMIAL4
#C .;X 7;X #B -- ;L77;X #B --#E7 .K #J
@3 .,FACTOR .TRINOMIAL4
#C .;X 7;X@+ ;L77;X-- ;L77;X #B --#E7
.K #J @3 ..,DI6];E ( TWO .SQU>ES
.;X .K #J1 .;X .K --#A1 .;X .K .#A @1
,OR @3 .,Z]O .PRODUCT .PROP]TY
,! CORRECT ANSW] IS ,D4 ..,A ;,B ;,C
.;,D
.,,GUID$ .,,PRACTICE = ,EXAMPLE #E
,F9D ! R1L--NUMB] SOLU;NS (! EQU,N4
.#H4 #D .;X #E -- #DJ .;X #C @+ #CF
.;X .K #J
.#I4 #B .;X #E @+ #BD .;X .K #AD .;X
#C
.#AJ4 --#BG .;X #C @+ #AE .;X #B .K
--#F .;X #D
------------------------------------#CEF
,,EXAMPLE #F ,SOLVE A POLYNOMIAL EQU,N
.,,C;Y .,,P>K ,Y >E DESIGN+ A M># BAS9
T W HOLD A F.TA9 =A C;Y P>K4 ,! BAS9'S
SIDES & BOTTOM %D 2 #A FOOT ?ICK4 ,XS
\T] L5G? %D 2 TWICE XS \T] WID? & \T]
HEI<T4
,:AT %D ! \T] DIM5.NS (! BAS9 2 IF X
IS 6HOLD #CF CUBIC FEET ( WAT]8
,,ANO!R ,,WAY
,= ALT]NATIVE ME?ODS 6SOLV+ ! PRO#M 9
,EXAMPLE #F1 TURN 6PAGE #CFJ =! ,PRO#M
,SOLV+ ,"W%OP4
,SOLU;N
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#CF .K 7#B .;X --#B77;X--#B77;X-- #A7
@3 .,WRITE .EQU,N4
#J .K #B .;X #C -- #H .;X #B @+ ;L#J
.;X -- #DJ @3 ..,WRITE 9 /&>D .=M4
#J .K #B .;X #B @7 .;X --#D7 @+
#AJ7;X--#D7 @3 .,FACTOR .0.GR\P+4
#J .K 7#B .;X #B @+ #AJ7@7 .;X --#D7
@3 .,4TRIBUTIVE .PROP]TY
,! ONLY R1L SOLU;N IS .;X .K #D4 ,!
BAS9 IS #H FT L;G1 #D FT WIDE1 & #D FT
HI<4
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#F
.#AA4 .,,:AT .,,IF8 ,9 ,EXAMPLE #F1
:AT %D ! BAS9'S DIM5.NS 2 IF X IS 6HOLD
#DJ CUBIC FEET ( WAT] & H \T] L5G? #F
.;X @1 WID? #C .;X @1 & HEI<T ;X8
#E.D ,EX]CISES
,HOME"W ,KEY
.K .,,"W$--.,,\ .,,SOLU;NS ON P4
,,WS#AJ = ,EXS4 #G1 #BC1 & #FA
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE ,EXS4
..#B1 #I1 #DA1 .#FC @1 & .#FD
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,! EXPRES.N #H .;X
#F @+ #AJ .;X #C -- #C IS 9 @8 =M 2C X C
2 WRITT5 Z .#B .;U #B @+ ..#E .;U -- #C
": .;U .K #B .;X #C @4
.#B4 .,,WRIT+ ,:AT 3DI;N M/ !
FACTORIZ,N (A POLYNOMIAL SATISFY 9 ORD]
=! POLYNOMIAL 6BE FACTOR$ -PLETELY8
.,,EXAMPLE .#A ON P4 #CEC = ,EXS4 #C-I
.,,MONOMIAL .,,FACTORS ,FACTOR !
POLYNOMIAL -PLETELY4
.#C4 #AD .;X #B -- #BA .;X
.#D4 #CJ .;B #C -- #ED .;B #B
.#E4 ;C #C @+ #I .;C #B @+ #AH .;C
.#F4 ;Z #C -- #F .;Z #B -- #GB .;Z
7.#G47.#C ;Y #E -- #DH .;Y #C
.#H4 #ED .;M #E @+ #AH .;M #D @+ #I
.;M #C
#I4 .,,MULTIPLE .,,*OICE ,:AT IS !
-PLETE FACTORIZ,N ( #B .;X #G -- #CB .;X
#C @8
,A #B .;X #C @7 .;X @+ #B77;X--#B77;X
#B @+ #D7
;,B #B .;X #C 7;X #B @+ #B77;X #B
--#B7
;,C #B .;X #C 7;X #B @+ #D7 #B
;,D #B .;X #C 7;X@+#B7 #B 7;X--#B7 #B
------------------------------------#CEG
.,,EXAMPLE .#B ON P4 #CED = ,EXS4
#AJ-AG
,,SUM ,,OR ,,DI6];E ,,( ,,CUBES
,FACTOR ! POLYNOMIAL -PLETELY4
.#AJ4 .;X #C @+ #H
.#AA4 ;Y #C -- #FD
.#AB4 #BG .;M #C @+ #A
.#AC4 #ABE .;N #C @+ #BAF
.#AD4 #BG .A #C -- #AJJJ
.#AE4 #H .;C #C @+ #CDC
.#AF4 #AIB .;W #C -- #C
.#AG4 --#E .;Z #C @+ #CBJ
.,,EXAMPLE .#C ON P4 #CED = ,EXS4
#AH-BC
,,FACTOR+ ,,0,,GR\P+ ,FACTOR !
POLYNOMIAL -PLETELY4
.#AH4 .;X #C @+ .;X #B @+ .;X @+ #A
.#AI4 ;Y #C -- #G .;Y #B @+ #D .;Y --
#BH
.#BJ4 .;N #C @+ .#E .;N #B -- ..#I .;N
-- #DE
.#BA4 #C .;M #C -- .;M #B @+ #I .;M --
#C
.#BB4 #BE .;S #C -- #AJJ .;S #B -- .;S
@+ #D
.#BC4 #D .;C #C @+ #H .;C #B -- #I .;C
-- #AH
.,,EXAMPLE .#D ON P4 #CEE = ,EXS4
#BD-BI
,,QUADRATIC ,,=M ,FACTOR ! POLYNOMIAL
-PLETELY4
.#BD4 .;X #D -- #BE
.#BE4 A #D @+ .LA #B @+ #F
.#BF4 #C .;S #D -- .;S #B -- #BD
.#BG4 #CB .;Z #E -- #B .;Z
.#BH4 #CF .;M #F @+ #AB .;M #D @+ ;M
#B
.#BI4 #AE .;X #E -- #GB .;X #C -- #AJH
.;X
.,,EXAMPLE .#E ON P4 #CEE = ,EXS4
#CJ-DA
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 F9D+ ALL R1L--NUMB] SOLU;NS4
.#CJ4
.#CA4
,,SOLV+ ,,EQU,NS ,F9D ! R1L--NUMB]
SOLU;NS (! EQU,N4
.#CB4 ;Y #C -- #E .;Y #B .K #J
.#CC4 #AH .;S #C .K #EJ .;S
.#CD4 ;G #C @+ #C .;G #B -- .;G -- #C
.K #J
.#CE4 ;M #C @+ #F .;M #B -- #D .;M --
#BD .K #J
.#CF4 #D .;W #D @+ #DJ .;W #B -- #DD
.K #J
.#CG4 #D .;Z #E .K #HD .;Z #C
.#CH4 #E .;B #C @+ #AE .;B #B @+ #AB
.;B .K --#CF
.#CI4 .;X #F -- #D .;X #D -- #I .;X #B
@+ #CF .K #J
.#DJ4 #DH .;P #E .K #BG .;P #C
#DA4 .,,MULTIPLE .,,*OICE ,:AT >E !
R1L--NUMB] SOLU;NS (! EQU,N .#C .;X #D
-- #BG .;X #B @+ ..#I ;X .K .;X #C @8
,A --#A1 #J1 #C
;,B --#C1 #J1 #C
;,C --#C1 #J1 #C
;,D
,,*OOS+ ,A ,,ME?OD ,FACTOR !
POLYNOMIAL -PLETELY US+ ANY ME?OD4
.#DB4 #AF .;X #C -- #DD .;X #B -- #DB
.;X
.#DC4 .;N #D -- .,AN #B -- #FJ
.#DD4 --#D .;B #D -- #EJJ .;B
.#DE4 #CF .A #C -- #AE .A #B @+ #HD .A
-- #CE
.#DF4 #AH .;C #D @+ #EG .;C #C -- #AJ
.;C #B
.#DG4 #B .;D #D -- #AC .;D #B -- #DE
.#DH4 #CB .;X #E -- #AJH .;X #B
.#DI4 #H .;Y #F -- #CH .;Y #D -- #AJ
.;Y #B
.#EJ4 .;Z #E -- .#C .;Z #D -- #AF .;Z
@+ #DH
..,,GEOMETRY ,F9D ! POSSI# VALUE 7;S7
( .X4
.#EA4 ,>EA .K #DH
.#EB4 ,VOLUME .K #DJ
.#EC4 ,VOLUME .K #ABE
,,*OOS+ ,A ,,ME?OD ,FACTOR !
POLYNOMIAL -PLETELY US+ ANY ME?OD4
.#ED4 .;X #C ;Y #F -- #BG
.#EE4 #G .;AC #B @+ .BC #B -- #G .AD
#B -- .BD #B
.#EF4 .;X #B .;N --#B .;X ;N @+#A
.#EG4 .,,*ALL5GE ,FACTOR .A #E .;B #B
-- .A #B .;B #D @+ #B .A #D .;B -- #B .A
;B #C @+ .A #C -- .;B #B -PLETELY4
------------------------------------#CEH
,,PRO#M ,,SOLV+
.,,EXAMPLE .#F ON P4 #CEF = ,EXS4
#EH-FC
.#EH4 .,,>*AEOLOGY ,AT ! RU9S (
,CAES>EA1 >*AEOLOGI/S 4COV]$ A HUGE
HYDRAULIC 3CRETE BLOCK )A VOLUME ( #IDE
CUBIC MET]S4 ,! BLOCK'S DIM5.NS >E .;X
MET]S HI< 0#AB .;X -- #AE MET]S L;G
0#AB4 .;X -- #BA MET]S WIDE4 ,:AT IS !
HEI<T (! BLOCK8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#EI4 .,,*OCOLATE .,,MOLD ,Y >E
DESIGN+ A *OCOLATE MOLD %AP$ L A HOLL[
RECTANGUL> PRISM =A C&Y MANUFACTUR]4 ,!
MOLD M/ H A ?ICK;S ( #A C5TIMET] 9 ALL
DIM5.NS4 ,! MOLD'S \T] DIM5.NS %D AL 2 9
! RATIO #A3C3F4 ,:AT %D ! \T] DIM5.NS (!
MOLD 2 IF X IS 6HOLD #AAB CUBIC
C5TIMET]S ( *OCOLATE8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#FJ4 .,,MULTI--.,,/EP .,,PRO#M ,A
PRODUC;N CREW IS ASSEMBL+ A ?REE--LEVEL
PLAT=M 9SIDE A /ADIUM =A P]=M.E4 ,!
PLAT=M HAS ! DIM5.NS %[N 9 ! DIAGRAMS1 &
HAS A TOTAL VOLUME ( #ABEJ CUBIC FEET4
A4 .,WRITE .,EXPRES.NS ,:AT IS !
VOLUME1 9 T]MS ( .;X @1 ( EA* (! ?REE
LEVELS (! PLAT=M8
B4 .,WRITE .AN .,EQU,N ,USE :AT Y "K
AB ! TOTAL VOLUME 6WRITE AN EQU,N 9VOLV+
.;X @4
C4 .,SOLVE ,SOLVE ! EQU,N F "P 7;B74
,USE YR SOLU;N 6CALCULATE ! DIM5.NS (
EA* (! ?REE LEVELS (! PLAT=M4
#FA4 .,,SCULPTURE ,SUPPOSE Y H #BEJ
CUBIC 9*ES ( CLAY ) : 6MAKE A SCULPTURE
%AP$ Z A RECTANGUL> PRISM4 ,Y WANT !
HEI<T & WID? EA* 6BE #E 9*ES LESS ?AN !
L5G?4 ,:AT %D ! DIM5.NS (! PRISM BE8
#FB4 .,,MANUFACTUR+ ,A MANUFACTUR]
WANTS 6BUILD A RECTANGUL> /A9.S /EEL
TANK )A HOLD+ CAPAC;Y ( #FGJ GALLONS1 OR
AB #HI.EH CUBIC FEET4 ,! TANK'S WALLS W
2 "O HALF 9* ?ICK1 & AB #F.DB CUBIC FEET
( /EEL W 2 US$ =! TANK4 ,! MANUFACTUR]
WANTS ! \T] DIM5.NS (! TANK 6BE RELAT$ Z
FOLL[S3
99 ,! WID? %D 2 #B FEET LESS ?AN !
L5G?4
99 ,! HEI<T %D 2 #H FEET M ?AN ! L5G?4
,:AT %D ! \T] DIM5.NS (! TANK BE8
.K ..,,"W$--,,\ ,,SOLU;NS ON P4.,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#CEI
.#FC4 .,,%ORT .,,RESPONSE ,A PLAT=M
%AP$ L A RECTANGUL> PRISM HAS DIM5.NS
.;X -- #B FEET 0#C #B .;X FEET 0#C .;X
@+ #D FEET4 .,EXPLA9 :Y ! VOLUME (!
PLAT=M _C 2 CUBIC FEET4
#FD4 .,,EXT5D$ .,,RESPONSE ,9 #BJJJ
,B4,C41 ! ,BABYLONIANS SOLV$ POLYNOMIAL
EQU,NS US+ TA#S ( VALUES4 ,"O S* TA#
GAVE VALUES ( ;Y #C @+ ;Y #B @4 ,6BE A#
6USE ? TA#1 ! ,BABYLONIANS "S"TS _H
6MANIPULATE ! EQU,N1 Z %[N 2L4
,!Y !N F.D -- 9 ! .;Y #C @+ .;Y #B
COLUMN (! TA#4 ,2C ! CORRESPOND+
;Y--VALUE 0 @1 !Y CD 3CLUDE T @4
A4 ,CALCULATE ;Y #C @+ ;Y #B = .;Y .K
#A1 #B1 #C1'1 #AJ4 ,RECORD ! VALUES 9 A
TA#4
B4 ,USE YR TA# &! ME?OD DESCRIB$ ABV
6SOLVE .;X #C @+ #B .;X #B .K #IF4
C4 ,USE YR TA# &! ME?OD DESCRIB$ ABV
6SOLVE #C .;X #C @+ #B .;X #B .K #EAB4
D4 ,H[ C Y MODIFY ! ME?OD DESCRIB$ ABV
= EQU,NS (! =M .AX #D @+ .BX #C .K ;C8
#FE4 .,,*ALL5GE ,USE ! DIAGRAM 6-PLETE
"PS 7A7--7;C74
A4 .,EXPLA9 :Y .A--.;B IS EQUAL 6! SUM
(! VOLUMES ( SOLID ,I1 SOLID ,,II1 &
SOLID ,,III4
B4 ,WRITE AN ALGEBRAIC EXPRES.N =!
VOLUME ( EA* (! ?REE SOLIDS4 ,L1VE YR
EXPRES.NS 9 FACTOR$ =M4
C4 ,USE ! RESULTS F "PS 7A7 & 7;B7
6DERIVE ! FACTOR+ PATT]N = .A #C -- ;B
#C GIV5 ON PAGE #CED @4
,,MIX$ ,,REVIEW
,GRAPH ! FUNC;N4
.#FF4 .;F @7 .;X @7 .K --#B_\ .;X --
#C_\ @+ #E @7 .P4 #ABC @7
.#FG4 .;Y .K .;X #B @+ #D .;X @+ #E @7
.P4 #BCF @7
.#FH4 .;Y .K #C7 .;X @+ #D7 #B @+ #G
@7 .P4 #BDE @7
.#FI4 .;F @7 .;X @7 .K .;X #C -- #B
.;X -- #E @7 .P4 #CCG @7
,GRAPH ! 9EQUAL;Y 9 A COORD9ATE PLANE4
@7 .P4 #ACB @7
.#GJ4 ;Y "K.K #B .;X -- #C
.#GA4 .;Y .1 --#E -- .;X
.#GB4 .;Y "K #J.E .;X @+ #E
.#GC4 #D .;X @+ #AB .;Y "K.K #D
.#GD4 #I .;X -- #I .;Y .1.K #BG
.#GE4
,SIDEB>3
,PREVIEW
,PREP>E = ,LESSON #E.E 9 ,EXS4 #GF-GI4
,USE SYN!TIC SUB/ITU;N 6EVALUATE !
POLYNOMIAL FUNC;N =! GIV5 VALUE ( .X4 @7
.P4 #CCG @7
.#GF4 .;F @7 .;X @7 .K #E .;X #D -- #C
.;X #C @+ #D .;X #B -- .;X @+ #AJ2 .;X
.K #B
.#GG4 .;F @7 .;X @7 .K --#C .;X #E @+
.;X #C -- #F .;X #B @+ #B .;X @+ #D2 .;X
.K --#C
.#GH4 .;F @7 .;X @7 .K #E .;X #E -- #D
.;X #C @+ #AB .;X #B @+ #BJ2 .;X .K --#B
.#GI4 .;F @7 .;X @7 .K --#F .;X #D @+
#I .;X -- #AE2 .;X .K #D
.,,EXTRA .,,PRACTICE = ,LESSON #E.D1
P4 #AJAD
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#CFJ
,PRO#M ,SOLV+ ,"W%OP ,LESSON #E.D3
,US+ ,ALT]NATIVE ,ME?ODS
,ANO!R ,WAY 6,SOLVE ,EXAMPLE #F1 PAGE
#CEF
.,,MULTIPLE .,,REPRES5T,NS ,9 ,EXAMPLE
#F ON PAGE #CEF @1 Y SOLV$ A POLYNOMIAL
EQU,N 0FACTOR+4 ,Y C AL SOLVE A
POLYNOMIAL EQU,N US+ A TA# OR A GRAPH4
,,PRO#M
,SIDEB>3
,/&>DS
..,PREP>E = ,MA!MATICAL ,ANALYSIS3
#F..J .,/UD5TS F9D ! ROOTS & POLES (A
R,NAL FUNC;N & ..C GRAPH ! .FUNC;N &
LOCATE XS ASYMPTOTES4
.,,C;Y .,,P>K ,Y >E DESIGN+ A M># BAS9
T W HOLD A F.TA9 =A C;Y P>K4 ,! BAS9'S
SIDES & BOTTOM %D 2 #A FOOT ?ICK4 ,XS
\T] L5G? %D 2 TWICE XS \T] WID? & \T]
HEI<T4
,:AT %D ! \T] DIM5.NS (! BAS9 2 IF X
IS 6HOLD #CF CUBIC FEET ( WAT]8
,,ME?OD #A
.,US+ .A .,TA# ,"O ALT]NATIVE APPROA*
IS 6WRITE A FUNC;N =! VOLUME (! BAS9 &
MAKE A TA# ( VALUES =! FUNC;N4 ,US+ !
TA#1 Y C F9D ! VALUE ( .;X T MAKES !
VOLUME (! BAS9 #CF CUBIC FEET4
.,,/EP .#A .,WRITE ! FUNC;N4 ,F !
DIAGRAM1 Y C SEE T ! VOLUME .;Y ( WAT] !
BAS9 C HOLD IS GIV5 0? FUNC;N3
.;Y .K7#B .;X --#B7@7 .;X --#B7@7 .;X
-- #A7
.,,/EP .#B .,MAKE A TA# ( VALUES =!
FUNC;N4 ,USE ONLY POSITIVE VALUES ( .;X
2C ! BAS9'S DIM5.NS M/ 2 POSITIVE4
.,,/EP .#C .,ID5TIFY ! VALUE ( .;X = :
.;Y .K #CF4 ,! TA# %[S T .;Y .K #CF :5
.;X .K #D4
,! VOLUME (! BAS9 IS #CF CUBIC FEET :5
.;X IS #D FEET4 ,S1 ! \T] DIM5.NS (!
BAS9 %D 2 Z FOLL[S3
,L5G? .K #B .;X .K #H FEET
,WID? .K .;X .K #D FEET
,HEI<T .K .;X .K #D FEET
------------------------------------#CFA
,,ME?OD #B
.,US+ .A .,GRAPH ,ANO!R APPROA* IS
6MAKE A GRAPH4 ,Y C USE ! GRAPH 6F9D !
VALUE ( .;X T MAKES ! VOLUME (! BAS9 #CF
CUBIC FEET4
.,,/EP .#A .,WRITE ! FUNC;N4 ,F !
DIAGRAM1 Y C SEE T ! VOLUME .;Y ( WAT] !
BAS9 C HOLD IS GIV5 0? FUNC;N3
.;Y .K 7#B .;X --#B77;X--#B77;X-- #A7
.,,/EP .#B .,GRAPH ! EQU,NS .;Y .K #CF
& .;Y .K @7 .;X -- ;L77#B .;X -- #B7@7
.;X -- #B74 ,*OOSE A VIEW+ W9D[ T %[S !
9T]SEC;N (! GRAPHS4
.,,/EP .#C .,ID5TIFY ! COORD9ATES (!
9T]SEC;N PO9T4 ,ON A GRAPH+ CALCULATOR1
Y C USE ! .9T]SECT F1TURE4 ,! 9T]SEC;N
PO9T IS 7#D1 #CF74
,! VOLUME (! BAS9 IS #CF CUBIC FEET :5
.;X IS #D FEET4 ,S1 ! \T] DIM5.NS (!
BAS9 %D 2 Z FOLL[S3
,L5G? .K #B .;X .K #H FEET
,WID? .K .;X .K #D FEET
,HEI<T .K .;X .K #D FEET
,,PRACTICE
,,SOLV+ ,,EQU,NS ,SOLVE ! POLYNOMIAL
EQU,N US+ A TA# OR US+ A GRAPH4
.#A4 .;X #C @+ #D .;X #B -- #H .;X .K
#IF
.#B4 .;X #C -- #I .;X #B -- #AD .;X @+
#G .K --#CC
.#C4 #B .;X #C -- LLX #B @+ #C .;X @+
#E .K #EI
.#D4 .;X #D @+ .;X #C -- #AE .;X #B --
#H .;X @+ #F .K --#DE
.#E4 -- .;X #D @+ #B .;X #C @+ #F .;X
#B @+ #AG .;X -- #D .K #CB
.#F4 --#C .;X #D @+ #D .;X #C @+ #H
.;X #B @+ #D .;X -- #AA .K #AC
.#G4 #D .;X #D -- #AF .;X #C @+ #BI
.;X #B -- #IE .;X .K --#AEJ
.#H4 .,,:AT .,,IF8 ,9 ! PRO#M ON PAGE
#CFJ @1 SUPPOSE ! BAS9 IS 6HOLD #BJJ
CUBIC FEET ( WAT]4 ,F9D ! \T] DIM5.NS (!
BAS9 US+ A TA# & US+ A GRAPH4
.#I4 .,,PACKAG+ ,A FACTORY NE$S A BOX
T HAS A VOLUME ( #AGBH CUBIC 9*ES4 ,!
WID? %D 2 #D 9*ES LESS ?AN ! HEI<T1 &!
L5G? %D 2 #F 9*ES GRT] ?AN ! HEI<T4 ,F9D
! DIM5.NS (! BOX US+ A TA# & US+ A
GRAPH4
.#AJ4 .,,AGRICULTURE ,F #AIGJ 6#BJJB1
! AV]AGE YE>LY P9EAPPLE 3SUMP;N .;,P 7IN
P.DS7 P] P]SON 9 ! ,UNIT$ ,/ATES C 2
MODEL$ 0! FUNC;N
;,P7;X7 .K #J.JJJJIHD .;X #D --
#J.JJGAB .;X #C @+ #J.AFB .;X #B
--L4LLX,H-- #AB.C
": .;X IS ! NUMB] ( YE>S S9CE #AIGJ4
,9 :AT YE> 0 ! P9EAPPLE 3SUMP;N AB #I.IG
P.DS P] P]SON8 ,SOLVE ! PRO#M US+ A TA#
&A GRAPH4
------------------------------------#CFB
#E.E ,APPLY ! ,REMA9D] & ,FACTOR
,!OREMS
.,2F ,Y US$ SPECIAL PATT]NS 6FACTOR
POLYNOMIALS4
.,N[ ,Y W USE !OREMS 6FACTOR
POLYNOMIALS4
.,:Y8 ,S Y C DET]M9E ATT5D.E AT SPORTS
GAMES1 Z 9 ,EX4 #DC4
,KEY ,VOCABUL>Y
99 .POLYNOMIAL .L;G .DIVI.N
99 .SYN!TIC .DIVI.N
,SIDEB>3
,/&>DS
#C.J ,/UD5TS >E ADEPT AT OP],NS ON
POLYNOMIALS1 9CLUD+ L;G DIVI.N4
,:5 Y DIVIDE A POLYNOMIAL .;F 7;X7 0A
DIVISOR .;D7.;X7 @1 Y GET A QUOTI5T
POLYNOMIAL .;Q7.;X7 &A REMA9D]
POLYNOMIAL .;R7.;X74
,! DEGREE (! REMA9D] M/ 2 LESS ?AN !
DEGREE (! DIVISOR4 ,"O WAY 6DIVIDE
POLYNOMIALS IS CALL$ .POLYNOMIAL .L;G
.DIVI.N4
,,EXAMPLE #A ,USE POLYNOMIAL L;G
DIVI.N
,DIVIDE .;F 7;X7 .K #C .;X #D -- #E
.;X #C @+ #D .;X -- #F 0.;X #B -- ..#C
.;X @+ #E4
,SOLU;N
,WRITE POLYNOMIAL DIVI.N 9 ! SAME =MAT
Y USE :5 DIVID+ NUMB]S4 ,9CLUDE A 8#J0 Z
! COE6ICI5T ( .;X #B 9 ! DIVID5D4 ,AT
EA* /AGE1 DIVIDE ! T]M )! HI<E/ P[] 9
:AT IS LEFT (! DIVID5D 0! F/ T]M (!
DIVISOR4 ,? GIVES ! NEXT T]M (! QUOTI5T4
,,AVOID ,,]RORS
,! EXPRES.N A4$ 6! QUOTI5T 9 ! RESULT
(! L;G DIVI.N PRO#M IS N .;R7.;X74
.,,*ECK ,Y C *ECK ! RESULT (A DIVI.N
PRO#M 0MULTIPLY+ ! QUOTI5T 0! DIVISOR &
A4+ ! REMA9D]4 ,! RESULT %D 2 ! DIVID5D4
7#C .;X #B @+ #D .;X -- #C77;X #B --
#C .;X @+ #E7 @+ 7--#BE .;X @+ #I7
.K #C .;X #B 7;X #B -- #C .;X @+ #E7
@+ #D .;X 7;X #B -- #C .;X @+ #E7--#C7;X
#B -- #C .;X @+ #E7--#BE .;X @+ #I
.K #C .;X #D -- #I .;X #C @+ #AE .;X
#B @+ #D .;X #C -- #AB .;X #B @+ #BJ .;X
-- #C .;X #B @+ #I .;X -- #AE--#BE .;X
@+ #I
.K #C .;X #D -- #E .;X #C @+ #D .;X --
#F @4
------------------------------------#CFC
,,EXAMPLE #B ,USE POIYNOMIA ,H;G
DIVI.N )A L9E> DIVISOR
,DIVIDE .;F @7 .;X @7 .K .;X #C @+ #E
.;X #B -- #G .;X @+ #B .BYX -- #B4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #A &
.#B
,DIVIDE US+ POLYNOMIAL L;G DIVI.N4
.#A4 7#B .;X #D @+ .;X #C @+ .;X --
#A7 @/ 7;X #B @+ #B .;X -- #A7
.#B4 7;X #C -- .;X #B @+ #D .;X --
#AJ7 99 @7 .;X @+ #B7
.,,SYN!TIC .,,DIVI.N ,IF Y USE SYN!TIC
SUB/ITU;N 6EVALUATE .;F 7;X7 9 ,EXAMPLE
#B :5 .;X .K #B1 Z %[N 2L1 Y C SEE
?AT_/7#B7 EQUALS ! REMA9D] :5 .;F @7 .;X
@7 IS DIVID$ 0.;X --#B4 ,AL1 ! O!R
VALUES 2L ! L9E MAT* ! COE6ICI5TS (!
QUOTI5T4 ,= ? R1SON1 SYN!TIC SUB/ITU;N
IS "S"TS CALL$ SYN!TIC DIVI.N4 ,SYN!TIC
DIVI.N C 2 US$ 6DIVIDE ANY POLYNOMIAL 0A
DIVISOR (! =M .;X -- .K4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,REMA9D] ,!OREM
,IF A POLYNOMIAL .;F 7;X7 IS DIVID$
0.;X--.;K @1 !N ! REMA9D] IS .;R .K
.;F7.;K74
,,EXAMPLE #C ,USE SYN!TIC DIVI.N
,DIVIDE .;F @7 .;X7 .K #B .;X #C @+
.;X #B -- #H .;X @+ #E 0.;X @+ #C US+
SYN!TIC DIVI.N4
,,DIVIDE ,,POLYNOMIALS
,2C ! DIVISOR IS .;X @+ #C .K .;X --
7--#C71 EVALUATE ! DIVID5D :5 .;X .K
--#C4
------------------------------------#CFD
.,,FACTOR .,,!OREM ,SUPPOSE ! REMA9D]
IS #J :5 A POLYNOMIAL .;F 7;X7 IS DIVID$
0;X-- .K4 ,!N
": .;Q7.;X7 IS ! QUOTI5T POLYNOMIAL4
,"!=E1 .;F @7 .;X @7 .K @7 .;X -- .;K7
@* .;Q7.;X7 @1 S T .;X--.;K IS A FACTOR
( .;F @7 .;X @7@4 ,? RESULT IS SUMM>IZ$
0! .FACTOR .!OREM4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,FACTOR ,!OREM
,A POLYNOMIA .;F 7;X7 HAS A FACTOR .;X
-- .;K IF & ONLY IF .;F @7 .;K @7 .K #J4
,! FACTOR !OREM C 2 US$ 6SOLVE A
V>IETY ( PRO#MS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,PRO#M3 ,EXAMPLE
,GIV5 "O .FACTOR (A POLYNOMIAL1 F9D !
O!R .FACTORS4 @3 ,SEE ,EXAMPLE #D 2L4
,GIV5 "O .Z]O (A POLYNOMIAL FUNC;N,F9D
! O!R .Z]OS4 @3 ,SEE ,EXAMPLE #E ON PAGE
#CFE @4
,GIV5 "O .SOLU;N (A POLYNOMIAL EQU,N1
F9D ! O!R .SOLU;NS4 @3 ,SEE ,EXAMPLE #F
ON PAGE #CFE @4
,,EXAMPLE #D ,FACTOR A POLYNOMIAL
,FACTOR .;F 7;X7 .K #C .;X #C -- #D
.;X #B -- #BH .;X -- #AF -PLETELY GIV5 T
.;X @+ #B IS A FACTOR4
,SOLU;N
,,AVOID ,,]RORS
,! REMA9D] AF US+ SYN!TIC DIVI.N %D
ALW 2 Z]O :5 Y >E DIVID+ A POLYNOMIAL
0"O ( XS FACTORS4
,2C .;X @+ #B IS A FACTOR ( .;F @7 .;X
@7@1 Y "K ?AT_/7--#B7 .K #J4 ,USE
SYN!TIC DIVI.N 6F9D ! O!R FACTORS4
,USE ! RESULT 6WRITE .;F 7;X7 Z A
PRODUCT ( TWO FACTORS & !N FACTOR
-PLETELY4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;F7.;X7 @3 .K #C .;X #C -- #D .;X #B
-- #BH .;X -- #AF @3 .,WRITE .ORIG9AL
.POLYNOMIAL4
--@3 .K @7 .;X @+ #B77#C .;X #B -- #AJ
.;X --#H7 @3 ..,WRITE Z A PRODUCT ( TWO
.FACTORS4
--@3 .K @7 .;X @+ #B77#C .;X @+
#B77;X--#D7 @3 .,FACTOR .TRINOMIAL4
.,,GUID$ .,,PRACTICE = ,EXAMPLES #C &
#D
,DIVIDE US+ SYN!TIC DIVI.N4
.#C4 7;X #C @+ #D .;X #B --.;X--.#A7
@/ 7..X@+.#C7
.#D4 7#D .;X #C @+ .;X #B -- #C .;X @+
#G7 @/ @7 .;X -- #A7
,FACTOR ! POLYNOMIAL -PLETELY GIV5 T
.;X -- #D IS A FACTOR4
.#E4 .;F @7 .;X @7 .K .;X #C -- #F .;X
#B @+ #E .;X @+ #AB
.#F4 .;F @7 .;X @7 .K .;X #C -- .;X #B
-- #BB .;X @+ #DJ
------------------------------------#CFE
..,EXAMPLE #E ,/&>DIZ$ ,TE/ .,PRACTICE
,"O Z]O ( .;F @7 .;X @7 .K .;X #C --
#B .;X #B -- #BC .;X @+ #FJ IS .;X .K
#C4 ,:AT IS ANO!R Z]O ( .;F @8
.,A --#E
.;,B --#D
.;,C #B
.;,D #E
,SOLU;N
,2C .;F7 #C7 .K #J1 .;X -- #C IS A
FACTOR ..( ;F @7 .;X @7@4 ,USE SYN!TIC
DIVI.N4
,USE ! RESULT 6WRITE .;F 7;X7 Z A
PRODUCT ( TWO FACTORS4 ,!N FACTOR
-PLETELY4
.;F @7 .;X @7 .K .;X #C -- #B .;X #B
-- #BC .;X @+ #FJ .K @7 .;X -- #C77;X #B
@+ .;X -- #BJ7 .K @7 .;X -- #C7@7 .;X @+
#E7@7 .;X -- #D7
,! Z]OS >E #C1 --#E1 & #D4
,! CORRECT ANSW] IS ,A4 .,A ;,B ;,C
;,D
,,EXAMPLE #F ,USE A POLYNOMIAL MODEL
.,,BUSI;S ,! PR(IT .;,P 7IN MILLIONS (
DOLL>S7 =A %OE MANUFACTUR] C 2 MODEL$
0.;,P .K --#BA .;X #C @+ #DF .;X ": .;X
IS ! NUMB] ( %OES PRODUC$ 7IN MILLIONS74
,! -PANY N[ PRODUCES #A MILLION %OES &
MAKES A PR(IT ( 4#BE1JJJ1JJJ1 B WD L
6CUT BACK PRODUC;N4 ,:AT LESS] NUMB] (
%OES CD ! -PANY PRODUCE & / MAKE ! SAME
PR(IT8
,SOLU;N
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#BE .K --#BA .;X #C @+ #DF .;X @3
,SUB/ITUTE #BE = ,P9.' ;,P .K --#BA .;X
#C @+ #DF .;X @4
#J .K #BA .;X #C -- #DF .;X @+ #BE @3
..,WRITE 9 /&>D .=M4
,Y "K T .;X .K #A IS "O SOLU;N (!
EQU,N4 ,? IMPLIES T .;X -- #A IS A
FACTOR ( #BA .;X #C -- #DF .;X @+ #BE4
,USE SYN!TIC DIVI.N 6F9D ! O!R FACTORS4
,S1 @7 .;X -- ;L77#BA .;X #B @+ #BA
.;X -- #BE7 .K #J4 ,USE ! QUADRATIC
=MULA 6F9D T ;X #J.G IS ! O!R POSITIVE
SOLU;N4
,! -PANY CD / MAKE ! SAME PR(IT
PRODUC+ AB #GJJ1JJJ %OES4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #E &
.#F
,F9D ! O!R Z]OS .(F .GIV5 T .;F 7--#B7
.K #J4
.#G4 .;F @7 .;X @7 .K .;X #C @+ #B .;X
#B -- #I .;X -- #AH
.#H4 .;F @7 .;X @7 .K .;X #C @+ #H .;X
#B @+ #E .;X -- #AD
.#I4 .,,:AT .,,IF8 ,9 ,EXAMPLE #F1 H[
DOES ! ANSW] *ANGE IF ! PR(IT =! %OE
MANUFACTUR] IS MODEL$ 0.;,P .K --#AE .;X
#C @+ #DJ .;X @8
------------------------------------#CFF
#E.E ,EX]CISES
,,HOME"W ,,KEY6
.K .,,"W$--.,,\ .,,SOLU;NS ON P4
,,WS#AJ = ,EXS4 #AG1 #BE1 & #DC
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE ,EXS4
.#B1 .#CE1 .#CI1.DD @1 & .#DE
.K .,,MULTIPLE .,,REPRES5T,NS ,EX#.CH
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,/ATE ! REMA9D]
!OREM4
.#B4 .,,WRIT+ ,SYN!TIC DIVI.N HAS BE5
US$ 6DIVIDE .;F @7 .;X @7 .K .;X #D --
#E .;X #B @+ #H .;X -- #B 0.;X @+ #C4
.,EXPLA9 :AT ! COLOR$ NUMB]S REPRES5T 9
! DIVI.N PRO#M4
..,,EXAMPLES #A & .#B ON PP4 #CFB-CFC
= ,EXS4 #C-AJ
.,,US+ .,,L;G .,,DIVI.N ,DIVIDE US+
POLYNOMIAL L;G DIVI.N4
.#C4 7;X #B @+ .;X -- #AG7 --#D-- @7
.;X -- #D7
.#D4 7#C .;X #B -- LLX--#BF7 @/ @7 .;X
-- #E7
.#E4 7;X #C @+ #C .;X #B @+ #C .;X @+
#B7 @/ @7 .;X -- #A7
.#F4 7#H .;X #B @+ #CD .;X -- #A7 @/
7#D .;X -- #A7
.#G4 7#C .;X #C @+ LLX #B @+ #D .;X @+
#A7 --#D-- 7;X #B @+ ;X7
.#H4 7#G .;X #C @+ LLX #B @+ #G .;X @+
#E7 @/ 7;X #B @+ #A7
.#I4 7#E .;X #D -- #B .;X #C -- #G .;X
#B -- #CI7 @/ 7;X #B @+ #B .;X -- #D7
.#AJ4 7#D .;X #D @+ #E .;X -- #D7 @/
7;X #B -- #C .;X -- #B7
.,,EXAMPLE .#C ON P4 #CFC = ,EXS4
#AA-BJ
.,,US+ .,,SYN!TIC .,,DIVI.N ,DIVIDE
US+ SYN!TIC DIVI.N4
.#AA4 7#B .;X #B -- #G .;X @+ #AJ7 @/7
.;X -- #E7
.#AB4 7#D .;X #B -- #AC .;X -- #E7 @/
@7 .;X -- #B7
.#AC4 7;X #B @+ #H .;X @+ #A7 @/ @7
.;X @+ #D7
.#AD4 7;X #B @+ #I7 @/ @7 .;X -- #C7
.#AE4 7;X #C -- #E .;X #B -- #B7 @/ @7
.;X -- #D7
.#AF4 7;X #C -- #D .;X @+ #F7 @/ @7
.;X @+ #C7
.#AG 7;X #D -- #E .;X #C -- #H .;X #B
@+ #AC .;X -- #AB7 @/ @7 .;X -- #F7
.#AH4 7;X #D @+ #D .;X #C @+ #AF .;X
-- #CE7 @/ @7 .;X @+ #E7
.,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 US+ SYN!TIC DIVI.N
6DIVIDE .;X #C -- #E .;X @+ #C 0.;X --
#B4
.#AI4
.#BJ4
.,,EXAMPLE .#D ON P4 #CFD = ,EXS4
#BA-BH
.,,FACTOR ,GIV5 POLYNOMIAL .;F 7;X7 &A
FACTOR ..( ;F @7 .;X @7 @1 FACTOR .;F @7
.;X @7 -PLETELY4
.#BA4 .;F7.;X7 .K .;X #C -- #AJ .;X #B
@+ #AI .;X @+ #CJ2 .;X -- #F
.#BB4 .;F @7 .;X @7 .K .;X #C @+ #F
.;X #B @+ #E .;X -- #AB2 .;X @+ #D
.#BC4 ;F7;X7 .K .;X #C -- #B .;X #B --
#DJ .;X -- #FD2 .;X -- #H
.#BD4 .;F @7 .;X @7 .K .;X #C @+ #AH
.;X #B @+ #IE .;X @+ #AEJ2 .;X @+ #AJ
.#BE4 .;F @7 .;X @7 .K .;X #C @+ #B
.;X #B -- #EA .;X @+ #AJH2 .;X @+ #I
.#BF4 .;F @7 .;X @7 .K .;X #C -- #I
.;X #B @+ #H .;X @+ #FJ2 .;X @+ #B
.#BG4 .;F @7 .;X @7 .K #B .;X #C --
#AE .;X #B @+ #CD .;X -- #BA2 .;X -- #A
.#BH4 .;F @7 .;X @7 .K #C .;X #C -- #B
.;X #B -- #FA .;X -- #BJ2 .;X -- #E
.,,EXAMPLE .#E ON P4 #CFE = ,EXS4
#BI-CE
.,,F9D .,,Z]OS ,GIV5 POLYNOMIAL
.FUNC;N .;F .& A Z]O .(F @1 F9D ! O!R
Z]OS4
.#BI4 .;F @7 .;X @7 .K .;X #C -- #B
.;X #B -- #BA .;X -- #AH2 --#C
.#CJ4 .;F @7 .;X @7 .K #D .;X #C --
#BE .;X #B -- #AED .;X @+ #DJ2 #AJ
.#CA4 .;F,7.;X7 .K #AJ .;X #C -- #HA
.;X #B @+ #GA .;X @+ #DB2 #G
.#CB4 .;F @7 .;X @7 .K #C .;X #C @+
#CD .;X #B @+ #GB .;X -- #FD2 --#D
.#CC4 .;F @7 .;X @7 .K #B .;X #C --
#AJ .;X #B -- #GA .;X -- #I2 #I
.#CD4 .;F @7 .;X @7 .K #E .;X #C --
.;X #B -- #AH .;X @+ #H2 --#B
------------------------------------#CFG
#CE4 .,,MULTIPLE .,,*OICE ,"O Z]O (
.;F @7 .;X @7 .K #D .;X #C @+ #AE .;X #B
-- #FC .;X -- #ED IS .;X .K --#F4 ,:AT
IS ANO!R Z]O ( .;F @8
,A --#I
;,B --#C
;,C --#A
;,D #C
..,,GEOMETRY ,Y >E GIV5 AN EXPRES.N =!
VOLUME (! RECTANGUL> PRISM4 ,F9D AN
EXPRES.N =! MISS+ .DIM5.N4
.#CF4 .;,V .K #B .;X #C @+ #AG .;X #B
@+ #DF .;X @+ #DJ
.#CG4 .;,V .K .;X #C @+ #AC .;X #B @+
#CD .;X -- #DH
#CH4 .,,MULTIPLE .,,REPRES5T,NS ,3SID]
! POLYNOMIAL FUNC;N
.;F @7 .;X @7 .K .;X #C -- #E .;X #B
-- #AB .;X @+ #CF4
A4 ,Z]OS (A ,FUNC;N ,GIV5 ?AT_/7#B7 .K
#J1 F9D ! O!R Z]OS .(F4
B4 ,FACTORS ( AN ,EXPRES.N ,BAS$ ON YR
RESULTS F "P 7A71 :AT >E ! FACTORS (!
POLYNOMIAL .;X #C -- #E .;X #B -- #AB
.;X @+ #CF8
C4 ,SOLU;NS ( AN ,EQU,N ,:AT >E !
SOLU;NS (! POLYNOMIAL EQU,N .;X #C -- #E
.;X #B -- #AB .;X @+ #CF .K #J8
#CI4 .,,MULTIPLE .,,*OICE ,:AT IS !
VALUE ( .;K S* T .;X -- #E IS A FACTOR (
;X #C -- .;X #B @+ .KX -- #CJ8
,A --#AD
;,B --#B
;,C #BF
;,D #CB
#DJ4 .,,*ALL5GE ,X C 2 %[N T #B .;X --
#A IS A FACTOR (! POLYNOMIAL FUNC;N .;F
7;X7 .K #CJ .;X #C @+ #G .;X #B -- #CI
.;X @+ #AD4
A4 ,:AT C Y 3CLUDE IS A Z]O ( .;F @8
B4 ,USE SYN!TIC DIVI.N 6WRITE .;F 7;X7
9 ! =M @7 .;X -- .;K7 @* .;Q7.;X74
C4 ,WRITE .;F 7;X7 Z ! PRODUCT ( L9E>
FACTORS ) 9TEG] COE6ICI5TS4
,PRO#M ,SOLV+
.,,EXAMPLE .#F ON P4 #CFE = ,EXS4
#DA-DC
.#DA4 .,,CLO?+ ,! PR(IT .;,P 7IN
MILLIONS ( DOLL>S7 =A ;,T--%IRT
MANUFACTUR] C 2 MODEL$ 0.;,P .K -- .;X
#C @+ #D .;X #B @+ .;X ": .;X IS ! NUMB]
( ;,T--%IRTS PRODUC$ 7IN MILLIONS74
,CURR5TLY1 ! -PANY PRODUCES #D MILLION
;,T--%IRTS & MAKES A PR(IT (
4#D1JJJ1JJJ4 ,:AT LESS] NUMB] (
;,T--%IRTS CD ! -PANY PRODUCE & / MAKE !
SAME PR(IT8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#DB4 .,,MP#C .,,PLAY]S ,! PR(IT .;,P
7IN MILLIONS ( DOLL>S7 =A MANUFACTUR] (
,,MP#C PLAY]S C 2 MODEL$ 0.;,P .K --#D
.;X #C @+ #AB .;X #B @+ #AF .;X ": .;X
IS ! NUMB] ( ,,MP#C PLAY]S PRODUC$ 7IN
MILLIONS74 ,CURR5TLY1 ! -PANY PRODUCES
#C MILLION ,,MP#C PLAY]S & MAKES A PR(IT
( 4#DH1JJJ1JJJ4 ,:AT LESS] NUMB] (
,,MP#C PLAY]S CD ! -PANY PRODUCE & /
MAKE ! SAME PR(IT8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
------------------------------------#CFH
.#DC4 .,,WOM5'S .,,BASKETBALL ,F #AIHE
6#BJJC1 ! TOTAL ATT5D.E ,A 7IN ?\S&S7 AT
,,NCAA WOM5'S BASKETBALL GAMES &! NUMB]
.;,T ( ,,NCAA WOM5'S BASKETBALL T1MS C 2
MODEL$ BY
.,A .K --#A.IE .;X #C @+ #GJ.A .;X #B
-- #AHH .;X @+ #BAEJ & .;,T .K #AD.H .;X
@+ #GBE
": .;X IS ! NUMB] ( YE>S S9CE #AIHE4
,WRITE A FUNC;N =! AV]AGE ATT5D.E P] T1M
F #AIHE 6#BJJC4
#DD4 .,,EXT5D$ .,,RESPONSE ,! PRICE
.;P 7IN DOLL>S7 T A RADIO MANUFACTUR] IS
A# 6*>GE =A RADIO IS GIV5 0.;P .K
#DJ--#D .;X #B ": .;X IS ! NUMB] 7IN
MILLIONS7 ( RADIOS PRODUC$4 ,X CO/S !
-PANY 4#AE 6MAKE A RADIO4
A4 ,WRITE AN EXPRES.N =! -PANY .;S
TOTAL REV5UE 9 T]MS ( X4
B4 ,WRITE A FUNC;N =! -PANY'S PR(IT
.;,P 0SUBTRACT+ ! TOTAL CO/ 6MAKE .;X
RADIOS F ! EXPRES.N 9 "P 7A74
C4 ,CURR5TLY1 ! -PANY PRODUCES #A.E
MILLION RADIOS & MAKES A PR(IT (
4#BD1JJJ1JJJ4 ,WRITE & SOLVE AN EQU,N
6F9D A LESS] NUMB] ( RADIOS T ! -PANY CD
PRODUCE & / MAKE ! SAME PR(IT4
D4 ,D ALL ! SOLU;NS 9 "P 7;C7 MAKE
S5SE 9 ? SITU,N8 .,EXPLA94
#DE4 .,,%ORT .,,RESPONSE ,S9CE #AIIJ1
OV]NI<T /AYS .;,S & TOTAL VISITS ;,V7BO?
9 MILLIONS7 6N,NAL P>KS C 2 MODEL$ BY
,PICTURE3 ,JO%UA ,TREE ,N,NAL ,P>K1
,CALI=NIA
.;,S .K --#J.JJGBB .;X #D @+ #J.AGF
.;X #C -- #A.DJ .;X #B @+ #C.CI .;X @+
#AG.F ;,V.K#C.AJ .;X @+#BEF
": .;X IS ! NUMB] ( YE>S S9CE #AIIJ4
,WRITE A FUNC;N =! P]C5T ( VISITS 6N,NAL
P>KS T 7 OV]NI<T /AYS4 .,EXPLA9 H[ Y
3/RUCT$ YR FUNC;N4
#DF4 .,,*ALL5GE ,! PR(IT .;,P 7IN
MILLIONS ( DOLL>S7 =A ,,DVD MANUFACTUR]
C 2 MODEL$ 0.;,P .K --#F .;X #C @+ #GB
.;X ": .;X IS ! NUMB] ( ,,DVD,'S PRODUC$
7IN MILLIONS74 ,%[ T #B MILLION ,,DVD,'S
IS ! ONLY PRODUC;N LEVEL =! -PANY T
YIELDS A PR(IT ( 4#IF1JJJ1JJJ4
,MIX$ ,REVIEW
,TELL :E!R ! GIV5 ORD]$ PAIRS >E
SOLU;NS (! 9EQUAL;Y4 7P4 .#GCB @7
.#DG4 .;X -- #D .;Y "K #E2 7#A1 #D71
7#D1 --#A7
.#DH4 #C .;X @+ #B .;Y .1.K #A2 7--#B1
#D71 7#A1 --#C7
.#DI4 #E .;X -- #B .;Y .1 #AJ2 7#D1
#F71 7#H1 #AJ7
.#EJ4 #F .;X @+ #E .;Y "K.K #AE2
7--#E1 #AJ71 7--#A1 #D7
,SIDEB>3
,PREVIEW
,PREP>E = ,LESSON #E.F 9 ,EXS4 #EA-EF4
,SOLVE ! EQU,N4
.#EA4 .;X #B @+ #C .;X -- #DJ .K #J @7
.P4 #BEB @7
.#EB4 #E .;X #B @+ #AC .;X @+ #F .K #J
@7 .P4 #BEI @7
.#EC4 .;X #B @+ #G .;X @+ #B .K #J @7
.P4 #BIB @7
#ED4 #D .;X #B @+ #AE .;X @+ #AJ .K #J
@7 .P4 #BIB @7
.#EE4 #B .;X #B @+ #AE .;X @+ #CA .K
#J @7 .P4 #BIB @7
.#EF4 .;X #B @+ #B .;X @+ #AJ .K #J @7
.P4 #BIB @7
,P]=M ! 9DICAT$ OP],N4 @7 .P4 #CDF @7
.#EG4 @7 .;X #B -- #D .;X @+ #AE7 @+
7--#C .;X #B @+ #F .;X -- #AB7
.#EH4 7#B .;X #B -- #E .;X @+ #H7--7#E
.;X #B -- #G .;X -- #G7
.#EI4 7#C .;X -- #D77#C .;X #C @+ #B
.;X #B -- #H7
.#FJ4 7#C .;X -- #E7 #C
.,,EXTRA .,,PRACTICE = ,LESSON #E.E1
P4 #AJAD
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#CFI
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,LESSONS #E.A --#E.E
.#A4 .,,MULTI-.,,/EP .,,PRO#M ,!
AV]AGE 4T.E 2T ,E>? &! SUN IS
#AFD1JJJ1JJJ1JJJ Y>DS4
.A4 ,WRITE ! 4T.E 9 SCI5TIFIC NOT,N4
.B4 ,! L5G? (A FOOTBALL FIELD1 9CLUD+
! 5D Z"OS1 IS #A.BJ * #AJ #B Y>DS4 ,H[
_M FOOTBALL FIELDS /RET*$ 5D-TO-5D WD X
TAKE 6R1* F ,E>? 6! SUN8
.#B4 .,,MULTI-.,,/EP .,,PRO#M ,Y >E
DESIGN+ A RECTANGUL> PICNIC COOL] ) L5G?
#D "TS XS WID? & HEI<T #B "TS XS WID?4
,! COOL] HAS 9SUL,N T IS #A 9* ?ICK ON
EA* (! F\R SIDES & #B 9*ES ?ICK ON ! TOP
& BOTTOM4
.A4 ,LET .;X REPRES5T ! WID? (! COOL]4
,WRITE A POLYNOMIAL FUNC;N .;,T @7 .;X
@7 9 /&>D =M =! VOLUME (! RECTANGUL>
PRISM =M$ 0! COOL]'S \T] SURFACES4
.B4 ,WRITE A POLYNOMIAL FUNC;N .;,C @7
.;X @7 9 /&>D =M =! VOLUME (! 9SIDE (!
COOL]4
.C4 ,LET .,I @7 .;X @7 2 A POLYNOMIAL
FUNC;N =! VOLUME ( 9SUL,N4 ,H[ IS .,I @7
.;X @7 RELAT$ 6.;,T @7 .;X @7 & ;,C7 .;X
@7@8
.D4 ,WRITE .,I @7 .;X @7 9 /&>D =M4
,:AT IS ! VOLUME (! 9SUL,N :5 .;X .K #H
9*ES8
.#C4 .,,%ORT .,,RESPONSE ,9 BIOLOGY1 A
CELL )A HI<] SURFACE >EA-TO-VOLUME RATIO
C EX*ANGE MAT]IALS ) XS 5VIRON;T FA/]
?AN A CELL )A L[] RATIO4 .,EXPLA9 :E!R A
CUBIC CELL ) SIDE L5G? .;X OR A SPH]ICAL
CELL ) DIAMET] .;X C EX*ANGE MAT]IALS )
XS 5VIRON;T FA/]4
.#D4 .,,OP5-.,,5D$ ,WRITE A POLYNOMIAL
FUNC;N T HAS DEGREE #D & 5D 2HAVIOR GIV5
0.;F @7 .;X @7--Z .;X @+ & .;F @7 .;X @7
@+ Z .;X @+ @4 ,!N GRAPH ! FUNC;N 6*ECK
YR ANSW]4
.#E4 .,,EXT5D$ .,,RESPONSE ,F #AIIE
6#BJJC1 ! AV]AGE MON?LY CELL PH"O BILL
;,C 7IN DOLL>S7 = SUBSCRIB]S 9 ! ,UNIT$
,/ATES C 2 MODEL$ BY
;,C .K --#J.JBG;T #D @+ .#J..CB;T #C
-- .#J..BE;T #B -- #D.I;R @+ #EA
": .;T IS ! NUMB] ( YE>S S9CE #AIIE4
.A4 ,CLASSIFY ! FUNC;N 0DEGREE & TYPE4
.B4 ,MAKE A TA# ( VALUES =! FUNC;N4
.C4 ,SKET* A GRAPH (! FUNC;N4 ,D Y ?9K
! MODEL W A3URATELY PREDICT CELL PH"O
BILLS = YE>S 2Y #BJJC8 .,EXPLA94
.#F4 .,,EXT5D$ .,,RESPONSE ,! PRICE
.;P 7IN DOLL>S7 T A CAM]A MANUFACTUR] IS
A# 6*>GE =A CAM]A IS GIV5 0.;P .K
#AJJ--#AJ .;X #B ": .;X IS ! NUMB] 7IN
MILLIONS7 ( CAM]AS PRODUC$4 ,X CO/S !
-PANY 4#CJ 6MAKE A CAM]A4 ,CURR5TLY1 !
-PANY PRODUCES #B MILLION CAM]AS & MAKES
A PR(IT ( 4#FJ1JJJ1JJJ4
.A4 ,WRITE A FUNC;N T GIVES ! TOTAL
REV5UE .;,R 9 T]MS ( .X4
.B4 ,WRITE A FUNC;N T GIVES ! -PANY'S
PR(IT .;,P 9 T]MS ( .X4
.C4 ,WRITE & SOLVE AN EQU,N 6F9D O!R
VALUES ( .;X T YIELD A PR(IT (
4#FJ1JJJ1JJJ4
.D4 ,D ALL ! SOLU;NS 9 "P 7;C7 MAKE
S5SE 9 ? SITU,N8 .,EXPLA94
.#G4 .,,GRI4$ .,,ANSW] ,=! C;Y P>K
-MIS.N1 Y >E DESIGN+ A M># SCULPTURE 9 !
%APE (A PYRAMID )A SQU>E BASE1 Z %[N 2L4
,! VOLUME (! SCULPTURE IS #DH CUBIC
FEET4 ,:AT IS ! HEI<T .;X 9 FEET (!
SCULPTURE8
------------------------------------#CGJ
#E.F ,F9D ,R,NAL ,Z]OS
.,2F ,Y F.D ! Z]OS (A POLYNOMIAL
FUNC;N GIV5 "O Z]O4
.,N[ ,Y W F9D ALL R1L Z]OS (A
POLYNOMIAL FUNC;N4
.,:Y8 ,S Y C MODEL MANUFACTUR+
PROCESSES1 Z 9 ,EX4 #DE4
,KEY ,VOCABUL>Y
99 ..Z]O (A .FUNC;N @1 P4 #BED
99 .3/ANT .T]M1 .P4 .#CCG
99 L1D+ COE6ICI5T1 P4 #CCG
,SIDEB>3
,/&>DS
..#C.J ,/UD5TS >E ADEPT AT OP],NS ON
.POLYNOMIALS @1 9CLUD+ L;G DIVI.N4
,! POLYNOMIAL FUNC;N .;F @7 .;X @7 .K
#FD .;X #C @+ #AEB .;X #B -- #FB .;X --
#AJE HAS @1 & Z XS Z]OS4 ,NOTICE T !
NUM]ATORS ( ^! Z]OS 7--#E1 --#C1 & #G7
>E FACTORS (! 3/ANT T]M1 --#AJE4 ,AL
NOTICE T ! DENOM9ATORS 7#B1 #D1 & #H7 >E
FACTORS (! L1D+ COE6ICI5T1 #FD4 ,^!
OBS]V,NS >E G5]ALIZ$ 0! .R,NAL .Z]O
.!OREM4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,! ,R,NAL ,Z]O ,!OREM
,IF .;F @7 .;X @7 .K .A ;N .;X ;N.' @+
' @+ .A #A .;X @+ .A #J HAS .9TEG]
COE6ICI5TS1 !N E R,NAL Z]O (_/HAS !
FOLL[+ =M3
,,EXAMPLE #A ,LI/ POSSI# R,NAL Z]OS
,LI/ ! POSSI# R,NAL Z]OS ( .;F US+ !
R,NAL Z]O !OREM4
.A4 .;F @7 .;X @7 .K ;X #C @+ .#B;X #B
-- ;LL .;X @+ #AB
,,AVOID ,,]RORS
,2 SURE YR LI/S 9CLUDE BO? ! POSITIVE
& NEGATIVE FACTORS (! 3/ANT T]M &! L1D+
COE6ICI5T4
,FACTORS (! 3/ANT T]M3 +-#A1 +-#B1
+-#C1 +-#D1 +-#F1 +-#AB
,FACTORS (! L1D+ COE6ICI5T3 +-#A
,POSSI# R,NAL Z]OS3
,SIMPLIFI$ LI/ ( POSSI# Z]OS3
.B4 .;F7.;X7 .K #D .;X #D -- .;X #C --
#C .;X #B @+ #I .;X -- #AJ
,FACTORS (! 3/ANT T]M3 +-#A1 +-#B1
+-#E1 +-#AJ ,FACTORS (! L1D+ COE6ICI5T3
+-#A1 +-#B1 +-#D
,FACTORS (! L1D+ COE6ICI5T3 +-#A1
+-#B1 +-#D
,POSSI# R,NAL Z]OS3
,SIMPLIFI$ LI/ ( POSSI# Z]OS3
------------------------------------#CGA
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#A
,LI/ ! POSSI# R,NAL Z]OS ( .;F US+ !
R,NAL Z]O !OREM4
.#A4 .;F7.;X7 .K .;X #C @+ #I .;X #B
@+ #BC .;X @+ #AE
.#B4 .;F7.;X7 .K #B .;X #C @+ #C .;X
#B -- #AA .;X -- #F
.,,V]IFY+ .,,Z]OS ,9 ,LESSON #E.E1 Y
F.D Z]OS ( POLYNOMIAL FUNC;NS :5 "O Z]O
0 "KN4 ,! R,NAL Z]O !OREM IS A />T+ PO9T
= F9D+ Z]OS :5 NO Z]OS >E "KN4
,H["E1 ! R,NAL Z]O !OREM LI/S ONLY
.POSSI# Z]OS4 ,9 ORD] 6F9D ! .ACTUAL
Z]OS (A POLYNOMIAL FUNC;N .;F @1 Y M/
TE/ VALUES F ! LI/ ( POSSI# Z]OS4 ,Y C
TE/ A VALUE 0EVALUAT+ .;F7 ;X7 US+ ! TE/
VALUE Z .X4
,,EXAMPLE #B ,F9D Z]OS :5 ! L1D+
COE6ICI5T IS #A
,F9D ALL R1L Z]OS ( .;F @7 .;X @7 .K
;X #C -- #H;X #B @+ LLX @+ #BJ4
,SOLU;N
.,,/EP .#A .,LI/ ! POSSI# R,NAL Z]OS4
,! L1D+ COE6ICI5T IS #A &! 3/ANT T]M IS
#BJ4 ,S1 ! POSSI# R,NAL Z]OS >E3
,,AVOID ,,]RORS
,NOTICE T N E .POSSI# Z]O G5]AT$ 0!
R,NAL Z]O !OREM IS AN .ACTUAL Z]O ( .;F
@4
.,,/EP .#B .,TE/ ^! Z]OS US+ SYN!TIC
DIVI.N4
..,TEXT ;X .K .#A @3
..,TEXT ;X .K --.#A @3
,2C --#A IS A Z]O ( .;F @1 Y C WRITE
.;F7.;X7 .K @7 .;X @+ ;L7@7 .;X #B -- #I
.;X @+ #BJ74
.,,/EP .#C .,FACTOR ! TRINOMIAL 9 .;F
@7 .;X @7 & USE ! FACTOR !OREM4
.;F @7 .;X @7 .K @7 .;X @+ ;L7@7 .;X
#B -- #I .;X @+ #BJ7 .K @7 .;X @+ ;L7@7
.;X -- #D7@7 .;X -- #E7
,! Z]OS ( .;F >E --#A1 #D1 & #E4
.,ANIMAT$ ,ALGEBRA AT
_+CLASSZONE.COM_:
.,,GUID$ .,,PRACTICE = ,EXAMPLE #B
,F9D ALL R1L Z]OS (! FUNC;N4
.#C4 .;F7.;X7 .K .;X #C -- #D .;X #B
-- #AE .;X @+ #AH
.#D4 .;F @7 .;X @7 .K .;X #C -- #H .;X
#B @+ #E .;X @+ #AD
..,,LIMIT+ ,,! ,,SE>* ,,= .,,Z]OS ,9
,EXAMPLE #B1 ! L1D+ COE6ICI5T (!
POLYNOMIAL FUNC;N IS #A4 ,:5 ! L1D+
COE6ICI5T IS N #A1 ! LI/ ( POSSI# R,NAL
Z]OS C 9CR1SE DRAMATIC,Y4 ,9 S* CASES1 !
SE>* C 2 %ORT5$ 0SKET*+ ! FUNC;N'S
GRAPH4
------------------------------------#CGB
,,EXAMPLE #C ,F9D Z]OS :5 ! L1D+
COE6ICI5T IS N #A
,F9D ALL R1L Z]OS ( .;F @7 .;X @7 .K
#AJ .;X #D -- ;LL .;X #C -- #DB .;X #B
@+ #G .;X @+ #AB4
,SOLU;N
.,,/EP .#A .,LI/ ! POSSI# R,NAL Z]OS (
.;F @3
.,,/EP .#B .,*OOSE R1SONA# VALUES F !
LI/ ABV 6*ECK US+ ! GRAPH (! FUNC;N4 ,=
.;F @1 ! VALUES
& >E R1SONA# BAS$ ON ! GRAPH %[N AT !
"R4
.,,/EP .#C .,*ECK ! VALUES US+ SYN!TIC
DIVI.N UNTIL A Z]O IS F.D4
.,,/EP .#D .,FACTOR \ A BINOMIAL US+ !
RESULT (! SYN!TIC DIVI.N4
.,,/EP .#E .,REP1T ! /EPS ABV = ;G7
.;X @7 .K #E .;X #C -- #H .;X #B -- .#AG
.;X @+ #AB4 ,ANY Z]O ( .;G W AL 2 A Z]O
( .F4 ,! POSSI# R,NAL Z]OS ( .;G >E3
,! GRAPH ( .;G %[S T MAY 2 A Z]O4
,SYN!TIC DIVI.N %[S T IS A Z]O & @4
,X FOLL[S T3
.;F @7 .;X @7 .K 7#B .;X @+ #A7 99
.;G7.;X7 .K 7#B .;X @+ ;L77#E .;X -- #C7
7;X #B -- .;X -- #D7
.,,/EP .#F .,F9D ! REMA9+ Z]OS ( .;F
0SOLV+ ;X #B -- .;X -- #D .K #J4
,! R1L Z]OS ( .;F >E & @4
------------------------------------#CGC
.,,GUID$ .,,PRACTICE = ,EXAMPLE #C
,F9D ALL R1L Z]OS (! FUNC;N4
.#E4 .;F @7 .;X @7 .K #DH .;X #C @+ #D
.;X #B -- #BJ .;X @+ #C
.#F4 .;F @7 .;X @7 .K #B .;X #D @+ #E
.;X #C -- #AH .;X #B -- #AI .;X @+ #DB
,,EXAMPLE #D ,SOLVE A MULTI--/EP PRO#M
.,,ICE .,,SCULPTURES ,"S ICE
SCULPTURES >E MADE 0FILL+ A MOLD ) WAT]
& !N FREEZ+ X4 ,Y >E MAK+ S* AN ICE
SCULPTURE =A S*OOL D.E4 ,X IS 6BE %AP$ L
A PYRAMID )A HEI<T T IS #A FOOT GRT] ?AN
! L5G? ( EA* SIDE ( XS SQU>E BASE4 ,!
VOLUME (! ICE SCULPTURE IS #D CUBIC
FEET4 ,:AT >E ! DIM5.NS (! MOLD8
,SOLU;N
.,,/EP .#A .,WRITE AN EQU,N =! VOLUME
(! ICE SCULPTURE4
@4.;,T#.;,P#B .,LI/ ! POSSI# R,NAL
SOLU;NS3
.,,/EP .#B .,LI/ ! POSSI# R,NAL
SOLU;NS3
.,,/EP .#C .,TE/ POSSI# SOLU;NS4 ,ONLY
POSITIVE .;X --VALUES MAKE S5SE4
.,,/EP .#D .,*ECK = O!R SOLU;NS4 ,!
O!R TWO SOLU;NS1 : SATISFY .;X #B @+ .#C
.;X @+ #F .K #J1 >E & C 2 4C>D$ 2C !Y >E
IMAG9>Y NUMB]S4
,! ONLY R1SONA# SOLU;N IS .;X .K #B4
,! BASE (! MOLD IS #B FEET 0#B FEET4
,! HEI<T (! MOLD IS #B @+ #A .K #C
FEET4
..,GUID$ ,PRACTICE = ,EXAMPLE .#D
.#G4 .,,:AT .,,IF8 ,9 ,EXAMPLE #D1
SUPPOSE ! BASE (! ICE SCULPTURE HAS
SIDES T >E #A FOOT L;G] ?AN ! HEI<T4 ,!
VOLUME (! ICE SCULPTURE IS #F CUBIC
FEET4 ,:AT >E ! DIM5.NS (! MOLD8
------------------------------------#CGD
#E.F ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
.,,WS#A #A .= .,EXS4 #G1BA1 .& #DG
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE ,EXS4
#B1 #BC1 #CH1CI1DJ1 & #EJ
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,IF
A POLYNOMIAL FUNC;N HAS 9TEG]
COE6ICI5TS1 !N E R,NAL Z]O (! FUNC;N HAS
! =M1 ": .;P IS A FACTOR (! @8 & .;Q IS
A FACTOR (! @8 @4
.#B4 .,,WRIT+ .,DESCRIBE A ME?OD Y C
USE 6%ORT5 ! LI/ ( POSSI# R,NAL Z]OS :5
US+ ! R,NAL Z]O !OREM4
.,,EXAMPLE .#A ON P4 #CGJ = ,EXS4
#C-AJ
.,,LI/+ .,,R,NAL .,,Z]OS ,LI/ ! POSSI#
R,NAL Z]OS (! FUNC;N US+ ! R,NAL Z]O
!OREM4
.#C4 .;F @7 .;X @7 .K .;X #C -- #C .;X
@+ #BH
.#D4 .;G7.;X7 .K .;X #C -- #D .;X #B
@+ .;X -- #AJ
.#E4 .;F @7 .;X @7 .K #B .;X #D @+ #F
.;X #C -- #G .;X @+ #I
.#F4 .;H7.;X7 .K #B .;X #C @+ .;X #B
-- .;X -- #AH
.#G4 .;G7.;X7.K #D .;X #E @+ #C .;X #C
-- #B .;X -- #AD
.#H4 .;F @7 .;X @7 .K #C .;X #D @+ #E
.;X #C -- #C .;X @+ #DB
.#I4 .;H7.;X7 .K #H .;X #D @+ #D .;X
#C -- ;L#J .;X @+ #AE
.#AJ4 .;H @7 .;X @7 .K #F .;X #C -- #C
.;X #B @+ #AB
,,EXAMPLE #B ON P4 #CGA = ,EXS4 #AA-AH
.,,F9D+ .,,R1L .,,Z]OS ,F9D ALL R1L
Z]OS (! FUNC;N4
.#AA4 .;F @7 .;X @7 .K .;X #C -- .#AB
.;X #B @+ .#CE .;X -- #BD
.#AB4 .;F @7 .;X @7 .K .;X #C -- #E
.;X #B -- #BB .;X @+ #EF
.#AC4 .;G @7 .;X @7 .K .;X #C -- .#CA
.;X -- #CJ
.#AD4 .;H7@\.;X7 .K .;X #C @+ #H .;X
#B -- #I .;X -- #GB
.#AE4 .;H7.;X7 .K .;X #D @+ #G .;X #C
@+ .#BF .;X #B @+ .#DD .;X @+ #BD
.#AF4 .;F @7 .;X @7 .K .;X #D -- #B
.;X #C -- #I .;X #B @+ ;L#J .;X -- #BD
.#AG4 .;F @7 .;X @7 .K .;X #D @+ #B
.;X #C -- #I .;X #B -- #B .;X @+ #H
.#AH4 .;G @7 .;X @7 .K .;X #D -- .#AF
.;X #B -- .#DJ .;X -- #BE
.,,EXAMPLE .#C ON P4 #CGB = ,EXS4
#AI-CE
.,,ELIM9AT+ .,,POSSI# .,,Z]OS ,USE !
GRAPH 6%ORT5 ! LI/ ( POSSI# R,NAL Z]OS
(! FUNC;N4 ,!N F9D ALL R1L Z]OS (!
FUNC;N4
.#AI4 .;F @7 .;X @7 .K #D .;X #C --
#BJ .;X @+ #AF
.#BJ4 .;F @7 .;X @7 .K #D .;X #C --
#AB .;X #B -- .;X @+ #AE
.#BA4 7#B .;L @7 .;F @7 .;X @7 .K #F
.;X #C @+ #BE .;X #B @+ #AF .;X -- #AE
.#BB4 .;F @7 .;X @7 .K --#C .;X #C @+
#BJ .;X #B -- #CF .;X @+ #AF
------------------------------------#CGE
#BC4 .,,MULTIPLE .,,*OICE ,AC 6! R,NAL
Z]O !OREM1 : IS .N A POSSI# Z]O (!
FUNC;N .;F @7 .;X @7 .K #B .;X #D -- #E
.;X #C @+ #AJ .;X #B -- #I8
,A --#I
;,B
;,C
;,D #C
.,,F9D+ .,,R1L .,,Z]OS ,F9D ALL R1L
Z]OS (! FUNC;N4
.#BD4 .;F @7 .;X @7 .K #B .;X #C @+ #B
.;X #B -- #H .;X -- #H
.#BE4 .;G @7 .;X @7 .K #B .;X #C -- #G
.;X #B @+ #I
.#BF4 .;H7.;X7 .K #B .;X #C -- #C .;X
#B -- #AD .;X @+ #AE #BG4 .;F7 ;X7 .K #C
.;X #C @+ #D .;X #B -- #CE .;X -- #AB
.#BH4 .;F @7 .;X @7 .K #C .;X #C @+
#AI .;X #B @+ #D .;X -- #AB
.#BI4 .;G @7 .;X @7 .K #B .;X #C @+ #E
.;X #B -- LLX--#AD
.#CJ4 .;G @7 .;X @7 .K #B .;X #D @+ #I
.;X #C @+ #E .;X #B @+ #C .;X -- #D
.#CA4 .;H7.;X7 .K #B .;X #D -- .;X #C
-- #G .;X #B @+ #D .;X -- #D
.#CB4 .;H7.;X7 .K #C .;X #D -- #F .;X
#C -- #CB .;X #B @+ #CE .;X -- #AB
.#CC4 .;F @7 .;X @7 .K #B .;X #D -- #I
.;X #C @+ #CG .;X -- #CJ
.#CD4 .;F @7 .;X @7 .K .;X #E -- #C
.;X #D -- #E .;X #C @+ #AE .;X #B @+ #D
.;X -- #AB
.#CE4 .;H7.;X7 .K #B .;X #E @+ #E .;X
#D -- #C .;X #C -- #B .;X #B -- #E .;X
@+ #C
.,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 LI/+ ! POSSI# R,NAL
Z]OS (! FUNC;N4
.#CF4
.#CG4
.#CH4 .,,OP5--.,,5D$ .,,MA? ,WRITE A
POLYNOMIAL FUNC;N .;F T HAS A L1D+
COE6ICI5T ( #D & HAS #AB POSSI# R,NAL
Z]OS AC 6! R,NAL Z]O !OREM4
#CI4 .,,MULTIPLE .,,*OICE ,: (! FOLL[+
IS .N A Z]O (! FUNC;N .;F @7 .;X @7 .K
#DJ .;X #E -- #DB .;X #D -- #AJG .;X #C
@+ #AJG .;X #B @+ #CC .;X -- #CF8
,A
;,B
;,C
;,D
#DJ4 .,,%ORT .,,RESPONSE ,LET .A ;N 2
! L1D+ COE6ICI5T (A POLYNOMIAL FUNC;N
.;F & .A #J 2 ! 3/ANT T]M4 ,IF .A ;N HAS
.;R FACTORS & .A #J HAS .;S FACTORS1 :AT
IS ! L>GE/ NUMB] ( POSSI# R,NAL Z]OS .(
.;F .T C 2 G5]AT$ 0! R,NAL Z]O !OREM8
.,EXPLA9 YR R1SON+4
.,,MAT*+ ,F9D ALL R1L Z]OS (! FUNC;N4
,!N MAT* EA* FUNC;N ) XS GRAPH4
.#DA4 .;F7.;X7 .K .;X #C -- #B .;X #B
-- .;X @+ #B
.,A4
.#DB4 .;G @7 .;X @7 .K .;X #C -- #C
.;X #B @+ #B
.,B4
.#DC4 .;H @7 .;X @7 .K .;X #C @+ .;X
#B -- .;X @+ #B
.,C4
.#DD4 ,,*ALL5GE ,IS X POSSI# =A CUBIC
FUNC;N 6H M ?AN ?REE R1L Z]OS8 ,IS X
POSSI# =A CUBIC FUNC;N 6H NO R1L Z]OS8
.,EXPLA94
------------------------------------#CGF
,PRO#M ,SOLV+
.,,EXAMPLE .#D ON P4 #CGC = ,EXS4
#DE-DH
.#DE4 .,,MANUFACTUR+ ,AT A FACTORY1
MOLT5 GLASS IS P\R$ 96MOLDS 6MAKE
PAP]WEI<TS4 ,EA* MOLD IS A RECTANGUL>
PRISM )A HEI<T #D 9*ES GRT] ?AN ! L5G? (
EA* SIDE ( XS SQU>E BASE4 ,EA* MOLD
HOLDS #FC CUBIC 9*ES ( MOLT5 GLASS4 ,:AT
>E ! DIM5.NS (! MOLD8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#DF4 .,,SWIMM+ .,,POOL ,Y >E DESIGN+
A RECTANGUL> SWIMM+ POOL T IS 6BE SET
96! GR.D4 ,! WID? (! POOL IS #E FEET M
?AN ! DEP?1 &! L5G? IS #CE FEET M ?AN !
DEP?4 ,! POOL HOLDS #BJJJ CUBIC FEET (
WAT]4 ,:AT >E ! DIM5.NS (! POOL8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
..,,GEOMETRY ,9 ,EX]CISES #DG & #DH1
WRITE A POLYNOMIAL EQU,N 6MODEL !
SITU,N4 ,!N LI/ ! POSSI# R,NAL SOLU;NS
(! .EQU,N4
.#DG4 .,A RECTANGUL> PRISM HAS $GES (
L5G?S .;X @1 .;,X #A1 & .;X--.#B &A
VOLUME ( #BD4
.#DH4 ,A PYRAMID HAS A SQU>E BASE )
SIDES ( L5G? ;X1 A HEI<T ( #B .;X -- #E1
&A VOLUME ( #C4
#DI4 .,,MULTI--.,,/EP .,,PRO#M ,F
#AIID 6#BJJC1 ! AM.T ( A?LETIC EQUIP;T
.;,E 7IN MILLIONS ( DOLL>S7 SOLD
DOME/IC,Y C 2 MODEL$ BY
.;,E @7 .;T @7 .K --#AJ .;T #C @+ #ADJ
.;T #B -- #BJ .;T @+ #AH1AEJ
": .;T IS ! NUMB] ( YE>S S9CE #AIID4
,USE ! FOLL[+ /EPS 6F9D ! YE> :5 AB
4#BJ1CJJ1JJJ1JJJ ( A?LETIC EQUIP;T 0
SOLD4
A4 ,WRITE A POLYNOMIAL EQU,N T C 2 US$
6F9D ! ANSW]4
B4 ,LI/ ! POSSI# :OLE--NUMB] SOLU;NS
(! EQU,N 9 "P 7A7 T >E LESS ?AN #AJ4
C4 ,USE SYN!TIC DIVI.N 6DET]M9E : (!
POSSI# SOLU;NS 9 "P 7;B7 IS AN ACTUAL
SOLU;N4 ,!N CALCULATE ! YE> :
CORRESPONDS 6! SOLU;N4
#EJ4 .,,EXT5D$ .,,RESPONSE ,S9CE
#AIIJ1 ! NUMB] ( ,U4,S4 TRAVEL]S 6=EIGN
C.TRIES .;,F 7IN ?\S&S7 C 2 MODEL$ BY
.;,F7.;T7 .K #AB .;T #D -- #BFD .;T #C
@+ #BJBH .;T #B -- #CIBD .;T @+ #DC1IAF
": .;T .IS @1 ! NUMB] ( YE>S S9CE
#AIIJ4 ,USE ! FOLL[+ /EPS 6F9D ! YE> :5
"! 7 AB #EF1CJJ1JJJ TRAVEL]S4
A4 ,WRITE A POLYNOMIAL EQU,N T C 2 US$
6F9D ! ANSW]4
B4 ,LI/ ! POSSI# :OLE--NUMB] SOLU;NS
(! EQU,N 9 "P 7A7 T >E LESS ?AN OR EQUAL
6#AJ4
C4 ,USE SYN!TIC DIVI.N 6DET]M9E : (!
POSSI# SOLU;NS 9 "P 7;B7 IS AN ACTUAL
SOLU;N4
D4 ,GRAPH ! FUNC;N .;,F7.;T7 & EXPLA9
:Y "! >E NO O!R R1SONA# SOLU;NS4 ,!N
CALCULATE ! YE> : CORRESPONDS 6! SOLU;N4
.K .,,"W$--.,,\ .,,SOLU;NS ON P4
,,WS#A
.K ..,,/&>DIZE ,,TE/ .,,PRACTICE
------------------------------------#CGG
.#EA4 .,,*ALL5GE ,Y >E BUILD+ A PAIR (
RAMPS =A LOAD+ PLAT=M4 ,! LEFT RAMP IS
TWICE Z L;G Z ! "R RAMP4 ,IF #AEJ CUBIC
FEET ( 3CRETE >E US$ 6BUILD ! TWO RAMPS1
:AT >E ! DIM5.NS ( EA* RAMP8
,MIX$ ,REVIEW
,SOLVE ! EQU,N4
.#EB4 #D .;X -- #F .K #AH @7 .P4 #AH
@7
.#EC4 #C .;Y @+ #G .K --#AD @7 .P4 #AH
@7
.#ED4 _\#B .;P @+ #E_\ .K #AE @7 .P4
#EA @7
.#EE4 #DI .;Z #B -- #AD .;Z @+ #A .K
#J @7 .P4 #BEI @7
.#EF4 #H .;X #B -- #CJ .;X @+ #G .K #J
@7 .P4 #BEI @7
.#EG4 --#C7 .;Q @+ #B7 #B .K --#AH @7
.P4 #BFF @7
,SOLVE ! MATRIX EQU,N4 @7 .P4 #BAJ @7
.#EH4
.#EH4
.#EH4
.#EH4
,SIDEB>3
,PREVIEW
,PREP>E = ,LESSON #E.G 9 ,EXS4 #FB-FG4
,,QUIZ .= .,LESSONS .#E..D--.#E..F
,FACTOR ! POLYNOMIAL -PLETELY1 @7 P4
#CEC @7
.#A4 #B .;X #C -- #ED
.#B4 .;X #C -- #C .;X #B @+ #B .;X --
#F
.#C4 .;X #C @+ .;X #B @+ .;X @+ #A
.#D4 #F .;X #E -- #AEJ .;X
.#E4 #C .;X #D -- #BD .;X #B @+ #DH
.#F4 #B .;X #C -- #C .;X #B -- #AB .;X
@+ #AH
,DIVIDE US+ POLYNOMIAL L;G DIVI.N OR
SYN!TIC DIVI.N1 @7 P4 #CFB @7
.#G4 7;X #D @+ .;X #C -- #H .;X #B @+
#E .;X @+ #E7@/ 7;X #B @+ #E .;X -- #B7
.#H4 7#D .;X #C @+ #BG .;X #B @+ #C
.;X @+ #FD7 @/7 .;X @+ #G7
,F9D ALL R1L Z]OS (! FUNC;N1 @7 P4
#CGJ @7
.#I4 .;F7.;X7 .K #B .;X #C -- #AI .;X
#B @+ #EJ .;X @+ #CJ
.#AJ4 .;F @7 .;X @7 .K .;X #C -- #D
.;X #B -- #BE .;X -- #EF
.#AA4 .;F7.;X7 .K .;X #D @+ #D .;X #C
-- #AC .;X #B -- #D .;X @+ #AB
.#AB4 .;F @7 .;X @7 .K #D .;X #D -- #E
.;X #B @+ #DB .;X -- #BJ
.#AC4 .,,L&SCAP+ ,Y >E A L&SCAPE >TI/
DESIGN+ A SQU>E PATIO T IS 6BE MADE F
#ABH CUBIC FEET ( 3CRETE4 ,! ?ICK;S (!
PATIO IS #AE.E FEET LESS ?AN EA* SIDE
L5G?4 ,:AT >E ! DIM5.NS (! PATIO8 @7 P4
#CGJ @7
.,,EXTRA .,,PRACTICE = ,LESSON #E.F1
P4 #AJAD
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#CGH
,SPR1D%EET ,ACTIV;Y3 #E.F ,USE !
,LOC,N ,PR9CIPLE
,USE AF ,LESSON #E.F
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,KEY/ROKES
,SIDEB>3
,/&>DS
..,PREP>E = ,MA!MATICAL ,ANALYSIS3
#F..J ..,/UD5TS F9D ! .ROOTS & POLES
..(A R,NAL .FUNC;N & C GRAPH ! FUNC;N &
LOCATE XS ASYMPTOTES4
.,,"Q ,H[ C Y USE ! ,LOC,N ,PR9CIPLE
6ID5TIFY Z]OS (A POLYNOMIAL FUNC;N8
,Y C USE ! FOLL[+ RESULT1 CALL$ !
.,LOC,N .,PR9CIPLE @1 6HELP Y F9D Z]OS (
POLYNOMIAL FUNC;NS3
,IF .;F IS A POLYNOMIAL FUNC;N & .A &
.;B >E TWO NUMB]S S* T .;F7.A7 "K #J &
.;F7.;B7 .1 #J1 !N .;F HAS AT L1/ "O R1L
Z]O 2T .A & .B4
,,EXAMPLE ,F9D Z]OS (A POLYNOMIAL
FUNC;N
,F9D ALL R1L Z]OS ( .;F7.;X7 .K #F .;X
#C @+ #E .;X #B -- #AG .;X -- #F4
,,/EP #A ..,5T] VALUES = .;X
,5T] 8.;X0 96CELL ,A#A4 ,5T] 8#J0
96CELL ,A#B4 ,TYPE 8.K,A#B@+#A0 96CELL
,A#C4 ,SELECT CELLS ,A#C "? ,A#G1 & USE
! .FILL .D[N -M& 6FILL 9 VALUES ( .X4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 .,A @3 .;,B
.#A @3 .;X @3 --
.#B @3 #J3 --
.#C @3 #A3 --
.#D @3 #B3 --
.#E @3 #C3 --
.#F @3 #D3 --
.#G @3 #E3 --
,,/EP #B ..,5T] VALUES = ;F7.;X7
,5T] 8.;F7.;X70 96CELL ;,BL4 ,5T]
8.K#F99,A#B^C@+#E99,A#B^B--#AG99,A#B--#-
F0 96CELL ;,B#B4 ,SELECT CELLS ;,B#B "?
;,B#G1 & USE ! .FILL .D[N -M& 6FILL 9 !
VALUES ( .;F7.;X7 @4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 .,A @3 .;,B
.#A @3 .;X @3 .;F7.;X7
.#B @3 #J3 --#F
.#C @3 #A3 --#AB
.#D @3 #B3 #BH
.#E @3 #C3 #AEJ
.#F @3 #D3 #CIJ
.#G @3 #E3 #GHD
,,/EP #C ,USE LOC,N ,PR9CIPLE
,! SPR1D%EET 9 ,/EP #B %[S T ;I .;F
7#A7 "K #J & .;F 7#B7 .1 #J4 ,S1 0!
,LOC,N ,PR9CIPLE1 .;F HAS A Z]O 2T #A &
#B4 ,! R,NAL Z]O !OREM %[S T ! ONLY
POSSI# .R,NAL Z]O 2T #A & #B IS @4
,SYN!TIC DIVI.N 3FIRMS T IS A Z]O & T
.;F C 2 FACTOR$ Z3
,! Z]OS ( .;F >E @1 & --#B4
,,PRACTICE
,F9D ALL R1L Z]OS (! FUNC;N4
.#A4 .;F7.;X7 .K #F .;X #C -- #AJ .;X
#B -- #F .;X @+ #AJ
.#B4 .;F7.;X7 .K #BD .;X #D -- #CH .;X
#C -- #AIA .;X #B -- #AEG .;X -- #BH
.#C4 .;F7.;X7 .K #CF .;X #C @+ #AJI
.;X #B -- #CDA .;X @+ #GJ
.#D4 .;F7.;X7 .K #AB .;X #D @+ #BE .;X
#C -- #AFJ .;X #B -- #CJE .;X -- #ACB
------------------------------------#CGI
#E.G ,APPLY ! ,FUNDA;TAL ,!OREM (
,ALGEBRA
.,2F ,Y F.D Z]OS US+ ! R,NAL Z]O
!OREM4
.,N[ ,Y W CLASSIFY ! Z]OS ( POLYNOMIAL
FUNC;NS4
.,:Y8 ,S Y C DET]M9E BOAT SPE$1 Z 9
,EXAMPLE #F4
,KEY ,VOCABUL>Y
99 .REP1T$ .SOLU;N
99 .IRR,NAL .3JUGATES @1 P4 #BFG
99 .-PLEX .3JUGATES @1 P4 #BGH
,SIDEB>3
,/&>DS
.,MA!MATICAL .,ANALYSIS3 .#D..J
,/UD5TS "K ! /ATE;T (1 & C APPLY1 !
FUNDA;TAL !OREM ( ALGEBRA4
,! EQU,N .;X #C -- #E .;X #B -- #H .;X
@+ #DH .K #J1 : 2COMES @7 .;X @+ #C7@7
.;X -- #D7 #B .K #J :5 FACTOR$1 HAS ONLY
TWO 4T9CT SOLU;NS3 --#C & #D4 ,2C !
FACTOR .;X -- #D APPE>S TWICE1 H["E1 Y C
C.T ! SOLU;N #D TWICE4 ,S1 ) #D C.T$ Z A
.REP1T$ .SOLU;N @1 ? .?IRD-.DEGREE EQU,N
HAS .?REE SOLU;NS3 --#C1 #D1 & #D4
,! PREVI\S RESULT IS G5]ALIZ$ 0!
..FUNDA;TAL !OREM ( .ALGEBRA @1 F/ PROV$
0! ,G]MAN MA!MATICIAN ,K>L ,FRI$RI*
,GAUSS 7#AGGG-AHEE74
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,! ,FUNDA;TAL ,!OREM ( ,ALGEBRA
.,!OREM3 ,IF .;F7.;X7 IS A POLYNOMIAL
( DEGREE .;N ": .;N .1 #J1 !N ! EQU,N
.;F7.;X7 .K #J HAS AT L1/ "O SOLU;N 9 !
SET ( -PLEX NUMB]S4
.,COROLL>Y3 ,IF .;F7.;X7 IS A
POLYNOMIAL ( DEGREE .;N ": .;N .1 #J1 !N
! EQU,N .;F7.;X7 .K #J HAS EXACTLY .;N
SOLU;NS PROVID$ EA* SOLU;N REP1T$ TWICE
IS C.T$ Z #B SOLU;NS1 EA* SOLU;N REP1T$
?REE "TS IS C.T$ Z #C SOLU;NS1 & S ON4
,! COROLL>Y 6! FUNDA;TAL !OREM (
ALGEBRA AL IMPLIES T AN N?-DEGREE
POLYNOMIAL FUNC;N .;F HAS EXACTLY .;N
Z]OS4
,,EXAMPLE #A ,F9D ! NUMB] ( SOLU;NS OR
Z]OS
.A4 ,H[ _M SOLU;NS DOES ! EQU,N .;X #C
@+ #E .;X #B @+ #D .;X @+ #BJ .K #J H8
.B4 ,H[ _M Z]OS DOES ! FUNC;N .;F7.;X7
.K .;X #D -- #H .;X #C @+ #AH .;X #B --
#BG H8
,SOLU;N
.A4 ,2C .;X #C @+ #E .;X #B @+ .#D;X
@+ #BJ .K #J IS A POLYNOMIAL EQU,N (
DEGREE #C1 X HAS ?REE SOLU;NS4 7,!
SOLU;NS >E --#E1 --#B .;I @1 & #B .;I
@4@7
.B4 ,2C .;F7.;X7 .K .;X #D -- #H .;X
#C @+ #AH .;X #B -- #BG IS A POLYNOMIAL
FUNC;N ( DEGREE #D1 X HAS F\R Z]OS4 7,!
Z]OS >E --#A1 #C1 #C1 & #C47
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#A
.#A4 ,H[ _M SOLU;NS DOES ! EQU,N .;X
#D @+ #E .;X #B -- #CF .K #J H8
.#B4 ,H[ _M Z]OS DOES ! FUNC;N
.;F7.;X7 .K .;X #C @+ #G .;X #B @+ #H
.;X -- #AF H8
------------------------------------#CHJ
,,EXAMPLE #B ,F9D ! Z]OS (A POLYNOMIAL
FUNC;N
,F9D ALL Z]OS ( .;F7.;X7 .K .;X #E --
#D .;X #D @+ #D .;X #C @+ #AJ .;X #B --
#AC .;X -- #AD4
,SOLU;N
.,,/EP .#A .,F9D ! R,NAL Z]OS ( .;F
,2C .;F IS A POLYNOMIAL FUNC;N ( DEGREE
#E1 X HAS #E Z]OS4 ,! POSSI# R,NAL Z]OS
>E +-#A1 +-#B1 +-#G1 & +-#AD4 ,US+
SYN!TIC DIVI.N1 Y C DET]M9E T --#A IS A
Z]O REP1T$ TWICE & #B IS AL A Z]O4
.,,/EP .#B .,WRITE .;F7.;X7 9 FACTOR$
=M4 ,DIVID+ .;F7.;X7 0XS "KN FACTORS .;X
@+ #A1 .;X @+ #A1 & .;X -- #B GIVES A
QUOTI5T ( .;X #B -- #D .;X @+ #G4 ,"!=E3
.;F7.;X7 .K @7 .;X @+ #A7 #B @7 .;X --
#B7@7 .;X #B -- #D .;X @+ #G7
.,,/EP .#C .,F9D ! -PLEX Z]OS ( .;F @4
,USE ! QUADRATIC =MULA 6FACTOR !
TRINOMIAL 96L9E> FACTORS4
,! Z]OS ( .;F >E @1 &
.,,2HAVIOR .,,NE> .,,Z]OS ,! GRAPH (
.;F 9 ,EXAMPLE #B IS %[N AT ! "R4 ,NOTE
T ONLY ! .R1L Z]OS APPE> Z .;X
-9T]CEPTS4 ,AL NOTE T ! GRAPH IS TANG5T
6! .;X -AXIS AT ! REP1T$ Z]O .;X .K
--#A1 B CROSSES ! .;X -AXIS AT ! Z]O .;X
.K #B4 ,? 3CEPT C 2 G5]ALIZ$ Z FOLL[S3
99 ,:5 A FACTOR .;X -- .;K (A FUNC;N
.;F IS RAIS$ 6AN ODD P[]1 ! GRAPH ( .;F
CROSSES ! .;X -AXIS AT .;X .K .K4
99 ,:5 A FACTOR .;X -- .;K (A FUNC;N
.;F IS RAIS$ 6AN EV5 P[]1 ! GRAPH ( .;F
IS TANG5T 6! .;X -AXIS AT .;X .K .;K @4
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#B
,F9D ALL Z]OS (! POLYNOMIAL FUNC;N4
.#C4 .;F7.;X7 .K .;X #C @+ .#G .;X #B
@+ #AE .;X @+ #I
.#D4 .;F7.;X7 .K .;X #E -- .#B .;X #D
@+ .#H .;X #B -- #AC .;X @+ #F
,,REVIEW ,,-PLEX ,,NUMB]S
,= HELP ) -PLEX 3JUGATES1 SEE P4 #BGH
@4
.,,-PLEX .,,3JUGATES ,AL 9 ,EXAMPLE
#B1 NOTICE T ! Z]OS & >E -PLEX 3JUGATES4
,? ILLU/RATES ! F/ !OREM GIV5 2L4 ,A
SIMIL> RESULT APPLIES 6IRR,NAL Z]OS (
POLYNOMIAL FUNC;NS1 Z %[N 9 ! SECOND
!OREM 2L4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,-PLEX ,3JUGATES ,!OREM
,IF .;F IS A POLYNOMIAL FUNC;N ) R1L
COE6ICI5TS1 & .A @+ .BI IS AN IMAG9>Y
Z]O ( .;F !N .A -- .BI IS AL A Z]O ( .;F
,IRR,NAL ,3JUGATES ,!OREM
,SUPPOSE .;F IS A POLYNOMIAL FUNC;N )
R,NAL COE6ICI5TS1 & .A & .;B >E R,NAL
NUMB]S S* T IS IRR,NAL4 ,IF IS A Z]O (
.;F !N IS AL A Z]O ( .;F
------------------------------------#CHA
,,EXAMPLE #C ,USE Z]OS 6WRITE A
POLYNOMIAL FUNC;N
,WRITE A POLYNOMIAL FUNC;N .;F ( L1/
DEGREE T HAS R,NAL COE6ICI5TS1 A L1D+
COE6ICI5T ( #A1 & #C & Z Z]OS4
,SOLU;N
,2C ! COE6ICI5TS >E R,NAL & IS A Z]O1
M/ AL 2 A Z]O 0! IRR,NAL 3JUGATES !OREM4
,USE ! ?REE Z]OS &! FACTOR !OREM 6WRITE
.;F 7;X7 Z A PRODUCT ( ?REE FACTORS4
.,,*ECK ,Y C *ECK ? RESULT 0EVALUAT+
.;F7.;X7 AT EA* ( XS ?REE Z]OS4
,S9CE @1 0! IRR,NAL 3JUGATES !OREM
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#C
,WRITE A POLYNOMIAL FUNC;N .;F ( L1/
DEGREE T HAS R,NAL COE6ICI5TS1 A L1D+
COE6ICI5T ( #A1 &! GIV5 Z]OS4
.#E4 --#A1 #B1 #D
.#F4
.#G4
.#H4 #C1 #C -- .;I
..,,DESC>TES' ,,RULE ,,( .,,SIGNS
,FR5* MA!MATICIAN ,R5E ,DESC>TES
7#AEIF--#AFEJ7 F.D ! FOLL[+ REL,N%IP 2T
! COE6ICI5TS (A POLYNOMIAL FUNC;N &!
NUMB] ( POSITIVE & NEGATIVE Z]OS (!
FUNC;N4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,DESC>TES' ,RULE ( ,SIGNS
,LET .;F7.;X7 .K .A ;N .;X ;N.' @+ .A
;N--#A .;X ;N--;L.' @+ ' @+ .A #B .;X #B
@+ .A #A .;X @+ .A #J 2 A POLYNOMIAL
FUNC;N ) R1L COE6ICI5TS4
99 ,! NUMB] ( .POSITIVE .R1L .Z]OS (
.;F IS EQUAL 6! NUMB] ( *ANGES 9 SIGN (!
COE6ICI5TS ( .;F7.;X7 OR IS LESS ?AN ?
0AN EV5 NUMB]4
99 ,! NUMB] ( .NEGATIVE .R1L .Z]OS (
.;F IS EQUAL 6! NUMB] ( *ANGES 9 SIGN (!
COE6ICI5TS ( .;F7--.;X7 OR IS LESS ?AN ?
0AN EV5 NUMB]4
------------------------------------#CHB
,,EXAMPLE #D ,USE ,DESC>TES' RULE (
SIGNS
,DET]M9E ! POSSI# NUMB]S ( POSITIVE
R1L Z]OS1 NEGATIVE R1L Z]OS1 & IMAG9>Y
Z]OS = .;F7.;X7 .K .;X #F -- #B .;X #E
@+ #C .;X #D -- #AJ .;X #C -- #F .;X #B
-- #H .;X -- #H4
,SOLU;N
,! COE6ICI5TS 9 .;F7.;X7 H .#C .SIGN
.*ANGES @1 S .;F HAS #C OR #A POSITIVE
R1L Z]O7;S74
,! COE6ICI5TS 9 .;F7--.;X7 H .#C .SIGN
.*ANGES @1 S .;F HAS #C OR #A NEGATIVE
R1L Z]O7;S74 ,! POSSI# NUMB]S ( Z]OS =
.;F >E SUMM>IZ$ 9 ! TA# 2L4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,POSITIVE R1L Z]OS3 ,NEGATIVE R1L
Z]OS3 ,IMAG9>Y Z]OS3 ,TOTAL Z]OS
#C3 #C3 #J3 #F
#C3 #A3 #B3 #F
#A3 #C3 #B3 #F
#A3 #A3 #D3 #F
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#D
,DET]M9E ! POSSI# NUMB]S ( POSITIVE
R1L Z]OS1 NEGATIVE R1L Z]OS1 & IMAG9>Y
Z]OS =! FUNC;N4
.#I4 .;F7.;X7 .K .;X #C @+ #B .;X --
#AA
.#AJ4 .;G7.;X7 .K #B .;X #D -- #H .;X
#C @+ #F .;X #B -- #C .;X @+ #A
.,,APPROXIMAT+ .,,Z]OS ,ALL (! Z]OS (!
FUNC;N 9 ,EXAMPLE #D >E IRR,NAL OR
IMAG9>Y4 ,IRR,NAL Z]OS C 2 APPROXIMAT$
US+ TE*NOLOGY4
,,EXAMPLE #E ,APPROXIMATE R1L Z]OS
,APPROXIMATE ! R1L Z]OS ( .;F7.;X7 .K
.;X #F -- #B .;X #E @+ #C .;X #D -- #AJ
.;X #C -- #F .;X #B -- #H .;X -- #H4
,,ANO!R ,,WAY
,9 ,EXAMPLE #E1 Y C AL APPROXIMATE !
Z]OS ( .;F US+ ! CALCULATOR'S .TRACE
F1TURE4 ,H["E1 ? G5],Y GIVES LESS
PRECISE RESULTS ?AN ! .Z]O 7OR .ROOT @7
F1TURE4
,SOLU;N
,USE ! .Z]O 7OR .ROOT7 F1TURE (A
GRAPH+ CALCULATOR1 Z %[N 2L4
,F ^! SCRE5S1 Y C SEE T ! Z]OS >E .;X
--#J.GC & .;X #B.GC4
------------------------------------#CHC
,,EXAMPLE #F ,APPROXIMATE R1L Z]OS (A
POLYNOMIAL MODEL
.,,TA*OMET] ,A TA*OMET] M1SURES ! SPE$
7IN REVOLU;N2 P] M9UTE1 OR ,,RPM,'S7 AT
: AN 5G9E %AFT ROTATES4 ,=A C]TA9 BOAT1
! SPE$ .;X (! 5G9E %AFT 7IN #AJJ;S (
,,RPM,'S7 &! SPE$ ;S (! BOAT 7IN MILES
P] H\R7 >E MODEL$ 0.;S7.;X7 .K #J.JJEDG
.;X #C -- #J.BBE .;X #B @+ #C.FB .;X --
#AA.J
,:AT IS ! TA*OMET] R1D+ :5 ! BOAT
TRAVELS #AE MILES P] H\R8
,SOLU;N
,SUB/ITUTE #AE = .;S7.;X7 9 ! GIV5
FUNC;N4 ,Y C REWRITE ! RESULT+ EQU,N Z3
#J .K #J.JJEDG .;X #C -- #J.BBE .;X #B
@+ #C.FB .;X -- #BF.J
,!N1 USE A GRAPH+ CALCULATOR
6APPROXIMATE ! R1L Z]OS ( .;F7.;X7 .K
#J.JJEDG .;X #C -- #J.BBE .;X #B @+
#C.FB .;X -- #BF.J4
,F ! GRAPH1 "! IS "O R1L Z]O3 .;X
#AI.I4
,! TA*OMET] R1D+ IS AB #AIIJ ,,RPM,'S4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #E &
.#F
.#AA4 ,APPROXIMATE ! R1L Z]OS (
.;F7.;X7 .K #C .;X #E @+ #B .;X #D -- #H
.;X #C @+ #D .;X #B -- .;X -- #A4
.#AB4 .,,:AT .,,IF8 ,9 ,EXAMPLE #F1
:AT IS ! TA*OMET] R1D+ :5 ! BOAT TRAVELS
#BJ MILES P] H\R8
#E.G ,EX]CISES
,HOME"W ,KEY3
.K ..,,"W$ ,,\ .,,SOLU;NS
ON P4 ,,WS#AA = ,EXS4 #AE1CG1 & #FA
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 #B1I1 #CC1EA1EB1FC1 & #FD
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,=!
EQU,N @7 .;X -- #A7 #B @7 .;X @+ #B7 .K
#J1 A7;N7 @8 SOLU;N IS #A 2C ! FACTOR
.;X -- #A APPE>S TWICE4
.#B4 .,,WRIT+ .,EXPLA9 ! DI6];E 2T
-PLEX 3JUGATES & IRR,NAL 3JUGATES4
,,EXAMPLE #A
ON P4 #CGI = ,EXS4 #C-I
,,NUMB] ,,( ,,SOLU;NS ,,OR ,,Z]OS
,ID5TIFY ! NUMB] ( SOLU;NS OR Z]OS4
.#C4 .;X #D @+ #B .;X #C -- #D .;X #B
@+ .;X -- #AJ .K #J
.#D4 #E .;Y #C -- #C .;Y #B @+ #H .;Y
.K #J
.#E4 #I .;T #F -- #AD .;T #C @+ #D .;T
-- #A .K #J
.#F4 .;F7.;Z7 .K --#G .;Z #D @+ .;Z #B
-- #BE
.#G4 .;G7.;S7 .K #AB .;S #G -- #I .;S
#F @+ #D .;S #E -- .;S #C -- #BJ .;S @+
#EJ
.#H4 .;H7.;X7 .K -- .;X #AB @+ #G .;X
#H @+ #E .;X #D -- #H .;X @+ #F
#I4 .,,MULTIPLE .,,*OICE ,H[ _M Z]OS
DOES ! FUNC;N .;F7.;X7 .K #AF .;X -- #BB
.;X #C @+ #F .;X #F @+ #AI .;X #E -- #C
H8
,A #A
;,B #C
;,C #E
;,D #F
------------------------------------#CHD
,,EXAMPLE #B
ON P4 #CHJ = ,EXS4 #AJ-AI
,,F9D+ ,,Z]OS ,F9D ALL Z]OS (!
POLYNOMIAL FUNC;N4
.#AJ4 .;F7.;X7 .K .;X #D -- #F .;X #C
@+ #G .;X #B @+ #F .;X -- #H
.#AA4 .;F7.;X7 .K .;X #D @+ #E .;X #C
-- #G .;X #B -- #BI .;X @+ #CJ
.#AB4 .;G7.;X7 .K .;X #D -- #I .;X #B
-- #D .;X @+ #AB
.#AC4 .;H7.;X7 .K .;X #C @+ #E .;X #B
-- #D .;X -- #BJ
.#AD4 .;F7.;X7 .K .;X #D @+ #AE .;X #B
-- #AF
.#AE4 .;F7.;X7 .K .;X #D @+ .;X #C @+
#B .;X #B @+ #D .;X -- #H
.#AF4 .;H7.;X7 .K .;X #D @+ #D .;X #C
@+ #G .;X #B @+ #AF .;X @+ #AB
.#AG4 .;G7.;X7 .K .;X #D -- #B .;X #C
-- #C .;X #B @+ #B .;X @+ #B
.#AH4 .;G7.;X7 .K #D .;X #D @+ #D .;X
#C -- ;LL .;X #B -- #AB .;X -- #C
.#AI4 .;H7.;X7 .K #B .;X #D @+ #AC .;X
#C @+ #AI .;X #B -- ;L#J .;X -- #BD
,,EXAMPLE #C
ON P4 #CHA = ,EXS4 #BJ-CB
,,WRIT+ ,,POLYNOMIAL ,,FUNC;NS ,WRITE
A POLYNOMIAL FUNC;N .;F ( L1/ DEGREE T
HAS R,NAL COE6ICI5TS1 A L1D+ COE6ICI5T (
#A1 &! GIV5 Z]OS4
.#BJ4 #A1 #B1 #C
.#BA4 --#B1 #A1 #C
.#BB4 --#E1 --#A1 #B
.#BC4 --#C1 #A1 #F
.#BD4 #B1 -- .;I1 .;I
.#BE4 #C .;I @1 #B -- .;I
.#BF4 --#A1 #B1 --#C .;I
.#BG4 #E1 #E1 #D @+ .;I
.#BH4
.#BI4
.#CJ4
.#CA4
.#CB4 .,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 WRIT+ A POLYNOMIAL
FUNC;N ) R,NAL COE6ICI5TS & Z]OS #B & #A
@+ .I4
.#CC4 .,,OP5-.,,5D$ .,,MA? ,WRITE A
POLYNOMIAL FUNC;N ( DEGREE #E ) Z]OS #A1
#B1 & --.I4
,,EXAMPLE #D
ON P4 #CHB = ,EXS4 #CD-DA
,,CLASSIFY+ ,,Z]OS ,DET]M9E ! POSSI#
NUMB]S ( POSITIVE R1L Z]OS1 NEGATIVE R1L
Z]OS1 & IMAG9>Y Z]OS =! FUNC;N4
.#CD4 .;F7.;X7 .K .;X #D -- .;X #B --
#F
.#CE4 .;G7.;X7 .K -- .;X #C @+ #E .;X
#B @+ #AB
.#CF4 .;G7.;X7 .K .;X #C -- #D .;X #B
@+ #H .;X @+ #G
.#CG4 .;H7.;X7 .K .;X #E -- #B .;X #C
-- .;X #B @+ #F .;X @+ #E
.#CH4 .;H7.;X7 .K .;X #E -- #C .;X #C
@+ #H .;X -- #AJ
.#CI4 .;F7.;X7 .K .;X #E @+ #G .;X #D
-- #D .;X #C -- #C .;X #B @+ #I .;X --
#AE
.#DJ4 .;G7.;X7 .K .;X #F @+ .;X #E --
#C .;X #D @+ .;X #C @+ #E .;X #B @+ #I
.;X -- #AH
.#DA4 .;F7.;X7 .K .;X #G @+ #D .;X #D
-- ;L#J .;X @+ #BE
,,EXAMPLE #E
ON P4 #CHB = ,EXS4 #DB-DI
,,APPROXIMAT+ ,,Z]OS ,USE A GRAPH+
CALCULATOR 6GRAPH ! FUNC;N4 ,!N USE !
.Z]O 7OR .ROOT7 F1TURE 6APPROXIMATE !
R1L Z]OS (! FUNC;N4
.#DB4 .;F7.;X7 .K .;X #C -- .;X #B --
#H .;X @+ #E
.#DC4 .;F7.;X7 .K -- .;X #D -- #D .;X
#B @+ .;X @+ #H
.#DD4 .;G7.;X7 .K .;X #C -- #C .;X #B
@+ .;X @+ #F
.#DE4 .;H7.;X7 .K .;X #D -- #E .;X --
#C
.#DF4 .;H7.;X7 .K #C .;X #C -- .;X #B
-- #E .;X @+ #C
.#DG4 .;G7.;X7 .K .;X #D -- .;X #C @+
#B .;X #B -- #F .;X -- #C
.#DH4 .;F7.;X7 .K #B .;X #F @+ .;X #D
@+ #CA .;X #B -- #CE
.#DI4 .;G7.;X7 .K .;X #E -- #AF .;X #C
-- #C .;X #B @+ #DB .;X @+ #CJ
.#EJ4 .,,R1SON+ ,TWO Z]OS ( .;F7.;X7
.K .;X #C -- #F .;X #B -- #AF .;X @+ #IF
>E #D & --#D4 .,EXPLA9 :Y ! ?IRD Z]O M/
AL 2 A R1L NUMB]4
.#EA4 ,,%ORT ,,RESPONSE .,DESCRIBE !
POSSI# NUMB]S ( POSITIVE R1L1 NEGATIVE
R1L1 & IMAG9>Y Z]OS =A CUBIC FUNC;N )
R,NAL COE6ICI5TS4
#EB4 .,,MULTIPLE .,,*OICE ,: IS .N A
POSSI# CLASSIFIC,N (! Z]OS ( .;F7.;X7 .K
.;X #E -- #D .;X #C @+ #F .;X #B @+ #AB
.;X -- #F AC 6,DESC>TES' RULE ( SIGNS8
,A #C POSITIVE R1L Z]OS1 #B NEGATIVE
R1L Z]OS1 & #J IMAG9>Y Z]OS
;,B #C POSITIVE R1L Z]OS1 #J NEGATIVE
R1L Z]OS1 & #B IMAG9>Y Z]OS
;,C #A POSITIVE R1L Z]O1 #D NEGATIVE
R1L Z]OS1 & #J IMAG9>Y Z]OS
;,D #A POSITIVE R1L Z]O1 #B NEGATIVE
R1L Z]OS1 & #B IMAG9>Y Z]OS
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#CHE
,,CLASSIFY+ ,,Z]OS ,DET]M9E ! NUMB]S (
POSITIVE R1L Z]OS1 NEGATIVE R1L Z]OS1 &
IMAG9>Y Z]OS =! FUNC;N )! GIV5 DEGREE &
GRAPH4 .,EXPLA9 YR R1SON+4
.#EC4 ,DEGREE3 #C
.#ED4 ,DEGREE3 #D
.#EE4 ,DEGREE3 #E
,,*ALL5GE ,%[ T ! GIV5 NUMB] IS A Z]O
(! GIV5 FUNC;N B T ! 3JUGATE (! NUMB] IS
.N A Z]O4
.#EF4 .;F7.;X7 .K .;X #C -- #B .;X #B
@+ #B .;X @+ #E .;Z @2 #B -- .;I
.#EG4 .;G7.;X7 .K .;X #C @+ #B .;X #B
@+ #B .;I -- #B2 --#A @+ .;I
.#EH4 .,EXPLA9 :Y ! RESULTS (
,EX]CISES #EF & #EG D N 3TRADICT ! -PLEX
3JUGATE !OREM ON PAGE #CHJ @4
,,PRO#M ,,SOLV+
,,EXAMPLE #F
ON P4 #CHC = ,EXS4 #EI-FB
.#EI4 .,,BUSI;S ,=! #AB YE>S T A
GROC]Y /ORE HAS BE5 OP51 XS ANNUAL
REV5UE .;,R 7IN MILLIONS ( DOLL>S7 C 2
MODEL$ 0! FUNC;N
.;,R .K #J.JJJA7-- .;T #D @+ #AB .;T
#C -- #GG .;T #B @+ #FJJ .;T @+ #AC1FEJ7
": .;T IS ! NUMB] ( YE>S S9CE ! /ORE
OP5$4 ,9 : YE>7;S7 0 ! REV5UE 4#A.E
MILLION8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#FJ4 .,,5VIRON;T ,F #AIIJ 6#BJJC1 !
NUMB] .;,N ( 9L& LAKES 9 ,MI*IGAN 9FE/$
) ZEBRA MUSSELS C 2 MODEL$ 0! FUNC;N
.;,N .K --#J.JBH .;T #D @+ #J.EI .;T
#C -- #B.E .;T #B @+ #H.C .;T -- #B.E
": .;T IS ! NUMB] ( YE>S S9CE #AIIJ4
,9 : YE> DID ! NUMB] ( 9FE/$ 9L& LAKES
F/ R1* #ABJ8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
,PICTURE3 ..,PIPE CLO7$ ) ZEBRA
.MUSSELS
.#FA4 .,,PHYSIOLOGY ,A /UDY GR\P F.D T
A P]SON'S SCORE .;,S ON A /EP--CLIMB+
EX]CISE TE/ 0 RELAT$ 6HIS OR H] AM.T (
HEMOGLOB9 .;X 7IN GRAMS P] #AJJ
MILLILIT]S ( BLOOD7 0? FUNC;N3
.;,S .K --#J.JAE .;X #C @+ #J.F .;X #B
-- #B.D .;X @+ #AI
,GIV5 T ! NORMAL RANGE ( HEMOGLOB9 IS
#AB-AH GRAMS P] #AJJ MILLILIT]S ( BLOOD1
:AT IS ! MO/ LIKELY AM.T ( HEMOGLOB9 =A
P]SON :O SCORES #GE8
.#FB4 .,,POPUL,N ,F #AHIJ 6#BJJJ1 !
,AM]ICAN ,9DIAN1 ,ESKIMO1 & ,ALEUT
POPUL,N .;,P 7IN ?\S&S7 C 2 MODEL$ 0!
FUNC;N
.;,P .K #J.JJCE .;T #C -- #J.BCE .;T
#B @+ #D.HG .;T @+ #BDC
": .;T IS ! NUMB] ( YE>S S9CE #AHIJ4
,9 : YE> DID ! POPUL,N F/ R1* #GBB1JJJ8
-----------------------------------#CHF
.#FC4 .,,%ORT .,,RESPONSE ,A
#FJ--9*--L;G BOOK%ELF IS W>P$ "U #AHJ
P.DS ( BOOKS4 ,! DEFLEC;N .;D (!
BOOK%ELF 7IN 9*ES7 IS GIV5 0.;D .K
7#B.GBD * #AJ --#G @7 .;X #D -- 7#C.BFI
* #AJ --#E @7 .;X #C @+ 7#I.HJF * #AJ
--#D @7 .;X #B
": .;X IS ! 4T.E 7IN 9*ES7 F !
BOOK%ELF'S LEFT 5D4 ,APPROXIMATE ! R1L
Z]OS (! FUNC;N ON ! DOMA9 #J "K.K .;X
"K.K #FJ4 .,EXPLA9 :Y ALL YR ANSW]S MAKE
S5SE 9 ? SITU,N4
#FD4 .,,EXT5D$ .,,RESPONSE ,Y PLAN
6SAVE 4#AJJJ EA* YE> T[>DS BUY+ A US$ C>
9 F\R YE>S4 ,AT ! 5D ( EA* SUMM]1 Y
DEPOSIT 4#AJJJ E>N$ F SUMM] JOBS 96YR
BANK A3.T4 ,! TA# %[S ! VALUE ( YR
DEPOSITS OV] ! F\R YE> P]IOD4 ,9 ! TA#1
.;G IS ! GR[? FACTOR #A @+ .;R ": .;R IS
! ANNUAL 9T]E/ RATE EXPRESS$ Z A
DECIMAL4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 .,YE> .#A @3 .,YE> .#B @3 .,YE>
.#C @3 .,YE> .#D
,VALUE ( #A/ DEPOSIT3 #AJJJ3 #AJJJ .;G
@3 ;L#JJJ .;G #B @3 ;L#JJJ .;G #C
,VALUE ( #BND DEPOSIT3 --@3 #AJJJ3
@8@3 @8
,VALUE ( #CRD DEPOSIT3 --@3 --@3
#AJJJ3 @8
,VALUE ( #D? DEPOSIT3 --@3 --@3 --@3
#AJJJ
A4 .,APPLY ,COPY & -PLETE ! TA#4
B4 .,MODEL ,WRITE A POLYNOMIAL FUNC;N
T GIVES ! VALUE .;V ( YR A3.T AT ! 5D (!
F\R? SUMM] 9 T]MS ( .;G @4
C4 .,R1SON+ ,Y WANT 6BUY A C> T CO/S
AB 4#DCJJ4 ,:AT GR[? FACTOR D Y NE$
6OBTA9 ? AM.T8 ,:AT ANNUAL 9T]E/ RATE D
Y NE$8 .,EXPLA9 H[ Y F.D YR ANSW]S4
#FE4 .,,*ALL5GE ,A MONU;T )! DIM5.NS
%[N IS 6BE BUILT US+ #AJJJ CUBIC FEET (
M>#4 ,:AT IS ! VALUE ( .;X @8
,MIX$ ,REVIEW
,EVALUATE ! DET]M9ANT (! MATRIX4 @7
.P4 #BJC @7
.#FF4
.#FG4
.#FH4
.#FI4
,SIDEB>3
,PREVIEW
,PREP>E = ,LESSON #E.H 9 ,EXS4 #GJ-GE4
,GRAPH ! FUNC;N4
.#GJ4 .;Y .K #B7 .;X @+ #E7@7 .;X --
#C7 @7 .P4 #BDE @7
.#GA4 .;Y .K @7 .;X -- #B7@7 .;X --
#I7 @7 .P4 #BDE @7
#GB4 .;Y .K #E7 .;X @+ #A7@7 .;X @+
#I7 @7 .P4 #BDE @7
.#GC4 .;Y .K .;X #C -- #E .;X @+ #A @7
.P4 #CCG @7
.#GD4 .;Y .K .;X #D -- #AF @7 .P4 #CCG
@7
.#GE4 .;Y .K .;X #E -- #C 7P4 #CCG @7
,WRITE A QUADRATIC FUNC;N 9 9T]CEPT =M
^: GRAPH HAS ! GIV5 .;X -9T]CEPTS &
PASSES "? ! GIV5 PO9T4 @7 .P4 #CJI @7
.#GH4 .;X -9T]CEPTS3 --#B1 #D PO9T3
7#B1 --#D7
.#GG4 .;X -9T]CEPTS3 --#E1 --#A PO9T3
7--#B1 #F7
.#GF4 .;X -9T]CEPTS3 #B1 #G PO9T3 7#D1
--#B7
.,,EXTRA .,,PRACTICE = ,LESSON #E.G1
P4 #AJAD
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#CHG
#E.H ,ANALYZE ,GRAPHS ( ,POLYNOMIAL
,FUNC;NS
.,2F ,Y GRAPH$ POLYNOMIAL FUNC;NS
0MAK+ TA#S4
.,N[ ,Y W USE 9T]CEPTS 6GRAPH
POLYNOMIAL FUNC;NS4
.,:Y8 ,S Y C MAXIMIZE ! VOLUME (
/RUCTURES1 Z 9 ,EX4 #DB4
,KEY ,VOCABUL>Y
99 .LOCAL .MAXIMUM
99 .LOCAL .M9IMUM
,SIDEB>3
,/&>DS
..,PREP>E = ,MA!MATICAL ,ANALYSIS3
#F..J ..,/UD5TS F9D ! .ROOTS & POLES
..(A R,NAL FUNC;N & C GRAPH ! .FUNC;N &
LOCATE XS ASYMPTOTES4
,9 ? *APT] Y H LE>N$ T Z]OS1 FACTORS1
SOLU;NS1 & ;X--9T]CEPTS >E CLOSELY
RELAT$ 3CEPTS4 ,! REL,N%IPS >E SUMM>IZ$
2L4
,,3CEPT ,,SUMM>Y .,= .,YR .,NOTEBOOK
,Z]OS1 ,FACTORS1 ,SOLU;NS1 & ,9T]CEPTS
,LET .;F7.;X7 .K .A ;N .;X ;N @+ .A
;N--#A .;X ;N--#A @+ ' @+ .A #A .;X @+
.A #J 2 A POLYNOMIAL FUNC;N4 ,! FOLL[+
/ATE;TS >E EQUIVAL5T4
.,Z]O3 .;K IS A Z]O (! POLYNOMIAL
FUNC;N .;F
.,FACTOR3 .;X--.;K IS A FACTOR (!
POLYNOMIAL .;F7.;X7 @4
.,SOLU;N3 .;K IS A SOLU;N (!
POLYNOMIAL EQU,N .;F7.;X7 .K #J4
.;X -.9T]CEPT3 ,IF .;K IS A R1L NUMB]1
.;K IS AN .;X -9T]CEPT (! GRAPH (!
POLYNOMIAL FUNC;N .;F @4 ,! GRAPH ( .;F
PASSES "? @7 .;K @1 #J74
,,EXAMPLE #A ,USE .;X -9T]CEPTS 6GRAPH
A POLYNOMIAL FUNC;N
.,GRAPH .! .FUNC;N
,SOLU;N
.,,/EP .#A .,PLOT ! 9T]CEPTS4 ,2C --#C
& #B >E Z]OS ( .;F PLOT 7--#C1 #J7 &
7#B1 #J74
.,,/EP .#B .,PLOT PO9TS 2T & 2Y ! .;X
-9T]CEPTS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 --#B3 --#A3 #J3 #A3 #C
.;Y @3 @3 #C3 #B3 @3 #A
.,,/EP .#C .,DET]M9E 5D 2HAVIOR4 ,2C
.;F HAS ?REE FACTORS (! =M .;X--.;K &A
3/ANT FACTOR ( @1 X IS A CUBIC FUNC;N )A
POSITIVE L1D+ COE6ICI5T4 ,S1 .;F7.;X7 --
Z .;X -- & .;F7.;X7 @+ Z .;X @+ @4
.,,/EP .#D .,DRAW ! GRAPH S T X PASSES
"? ! PLOTT$ PO9TS & HAS ! APPROPRIATE 5D
2HAVIOR4
------------------------------------#CHH
.,,TURN+ .,,PO9TS ,ANO!R IMPORTANT
"*I/IC ( GRAPHS ( POLYNOMIAL FUNC;NS IS
T !Y H .TURN+ .PO9TS CORRESPOND+ 6LOCAL
MAXIMUM & M9IMUM VALUES4
99 ,! .;Y -COORD9ATE (A TURN+ PO9T IS
A LOCAL MAXIMUM (! FUNC;N IF ! PO9T IS
HI<] ?AN ALL NE>BY PO9TS4
99 ,! .;Y -COORD9ATE (A TURN+ PO9T IS
A LOCAL M9IMUM (! FUNC;N IF ! PO9T IS
L[] ?AN ALL NE>BY PO9TS4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,TURN+ ,PO9TS ( ,POLYNOMIAL ,FUNC;NS
.#A4 ,! GRAPH ( E POLYNOMIAL FUNC;N (
DEGREE .;N HAS .AT .MO/ .;N -- #A TURN+
PO9TS4
.#B4 ,IF A POLYNOMIAL FUNC;N HAS .;N
4T9CT R1L Z]OS1 !N XS GRAPH HAS .EXACTLY
.;N -- #A TURN+ PO9TS4
,,EXAMPLE #B ,F9D TURN+ PO9TS
,GRAPH ! FUNC;N4 ,ID5TIFY ! .;X
-9T]CEPTS &! PO9TS ": ! LOCAL MAXIMUMS &
LOCAL M9IMUMS O3UR4
.A4 .;F7.;X7 .K .;X #C -- #C .;X #B @+
#F
.B4 .;G7.;X7 .K .;X #D -- #F .;X #C @+
#C .;X #B @+ #AJ .;X -- #C
,,F9D ,,MAXIMUMS ,,& ,,M9IMUMS
,= HELP ) US+ ! .MAXIMUM & .M9IMUM
F1TURES (A GRAPH+ CALCULATOR1 SEE P4
#BDD @4
,SOLU;N
.A4 ,USE A GRAPH+ CALCULATOR 6GRAPH !
FUNC;N4
,NOTICE T ! GRAPH ( .;F HAS "O .;X
-9T]CEPT & TWO TURN+ PO9TS4
,Y C USE ! GRAPH+ CALCULATOR'S .Z]O1
.MAXIMUM @1 & .M9IMUM F1TURES
6APPROXIMATE ! COORD9ATES (! PO9TS4
,! .;X -9T]CEPT (! GRAPH IS .;X
--#A.BJ4 ,! FUNC;N HAS A LOCAL MAXIMUM
AT 7.#J1 .#F7 &A LOCAL M9IMUM AT 7.#B1
.#B7 @4
.B4 ,USE A GRAPH+ CALCULATOR 6GRAPH !
FUNC;N4
,NOTICE T ! GRAPH ( .;G HAS F\R .;X
-9T]CEPTS & ?REE TURN+ PO9TS4
,Y C USE ! GRAPH+ CALCULATOR'S .Z]O1
.MAXIMUM @1 & .M9IMUM F1TURES
6APPROXIMATE ! COORD9ATES (! PO9TS4
,! .;X -9T]CEPTS (! GRAPH >E .;X
--#A.AD1 .;X #J.BI1 .;X #A.HB1 & .;X
#E.JC4 ,! FUNC;N HAS A LOCAL MAXIMUM AT
7.#A..AA1 .#E..AA7 & LOCAL M9IMUMS AT
7--.#J..EG1 --.#F..EA7 & 7.#C..IF1
--.#DC..JD7 @4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
------------------------------------#CHI
..,,EXAMPLE #C ,MAXIMIZE A POLYNOMIAL
.MODEL
.,,>TS .,,& .,,CRAFTS ,Y >E MAK+ A
RECTANGUL> BOX \ (A #AF-9*-BY-#BJ-9*
PIECE ( C>DBO>D4 ,! BOX W 2 =M$ 0MAK+ !
CUTS %[N 9 ! DIAGRAM & FOLD+ UP ! SIDES4
,Y WANT ! BOX 6H ! GRTE/ VOLUME POSSI#4
99 ,H[ L;G %D Y MAKE ! CUTS8
99 ,:AT IS ! MAXIMUM VOLUME8
99 ,:AT W ! DIM5.NS (! F9I%$ BOX BE8
,SOLU;N
,WRITE A V]BAL MODEL =! VOLUME4 ,!N
WRITE A FUNC;N4
,6F9D ! MAXIMUM VOLUME1 GRAPH ! VOLUME
FUNC;N ON A GRAPH+ CALCULATOR1 Z %[N AT
! "R4 ,3SID] ONLY ! 9T]VAL #J "K .;X "K
#H 2C ? DESCRIBES ! PHYSICAL RE/RIC;NS
ON ! SIZE (! FLAPS4
,F ! GRAPH1 Y C SEE T ! MAXIMUM VOLUME
IS AB #DBJ & O3URS :5 .;X #B.ID4
,Y %D MAKE ! CUTS AB #C 9*ES L;G4 ,!
MAXIMUM VOLUME IS AB #DBJ CUBIC 9*ES4 ,!
DIM5.NS (! BOX ) ? VOLUME W 2 AB .;X .K
#C 9*ES 0.;X .K #AJ 9*ES 0.;X .K #AD
9*ES4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #A1B1
& .#C
..,GRAPH ! FUNC;N4 ,ID5TIFY ! ;X
-9T]CEPTS &! PO9TS ": ! .LOCAL MAXIMUMS
..& LOCAL M9IMUMS .O3UR4
.#A4 .;F7.;X7 .K #J.BE7 .;X @+ #B7@7
.;X -- ;L7@7 .;X -- #C7
.#B4 .;G7.;X7 .K #B7 .;X -- ;L7 #B @7
.;X -- #D7
.#C4 .;H7.;X7 .K #J.E .;X #C @+ .;X #B
-- .;X @+ #B
.#D4 .;F7.;X7 .K .;X #D @+ #C .;X #C
-- .;X #B -- #D .;X -- #E
.#E4 .,,:AT .,,IF8 ,9 ,EXAMPLE #C1 H[
D ! ANSW]S *ANGE IF ! PIECE ( C>DBO>D IS
#AJ 9*ES 0#AE 9*ES8
------------------------------------#CIJ
#E.H ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#AA = ,EXS4 #C1AI1 & #DA
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 #B1BA1 #CJ1 #CB1 #CC1 & #DC
.K .,,MULTIPLE .,,REPRES5T,NS
,EX#.DB
,,SKILL ,,PRACTICE
.#A4 ,,VOCABUL>Y ,COPY & -PLETE3 ,A
LOCAL MAXIMUM OR LOCAL M9IMUM (A
POLYNOMIAL FUNC;N O3URS AT A @8 PO9T (!
FUNC;N'S GRAPH4
.#B4 ,,WRIT+ .,EXPLA9 :AT A LOCAL
MAXIMUM (A FUNC;N IS & H[ X MAY 2 DI6]5T
F ! MAXIMUM VALUE (! FUNC;N4
,,EXAMPLE #A
ON P4 #CHG = ,EXS4 #C-AD
,,GRAPH+ ,,POLYNOMIAL ,,FUNC;NS ,GRAPH
! FUNC;N4
.#C4 .;F7.;X7 .K @7 .;X -- #B7 #B @7
.;X @+ #A7
.#D4 .;F7.;X7 .K @7 .;X @+ #A7 #B @7
.;X -- #A7@7 .;X -- #C7
.#E4
.#F4
.#G4 .;H7.;X7 .K #D7 .;X @+ #A7@7 .;X
@+ #B7@7 .;X -- #A7
.#H4 .;F7.;X7 .K #J.B7 .;X -- #D7 #B
@7 .;X @+ #A7 #B
.#I4 .;F7.;X7 .K #B7 .;X @+ #B7 #B @7
.;X @+ #D7 #B
.#AJ4 .;H7.;X7 .K #E7 .;X -- ;L7@7 .;X
-- #B7@7 .;X -- #C7
.#AA4 .;G7.;X7 .K @7 .;X -- #C7@7 .;X
#B @+ .;X @+ #A7
.#AB4 .;H7.;X7 .K @7 .;X -- #D77#B .;X
#B -- #B .;X @+ #A7
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 GRAPH+ .F4
.#AC4 .;F7.;X7 .K @7 .;X @+ #B7@7 .;X
-- #A7 #B
.#AD4 .;F7.;X7 .K .;X @7 .;X -- #C7 #C
,,EXAMPLE #B
ON P4 #CHH = ,EXS4 #AE-CJ
,,ANALYZ+ ,,GRAPHS ,E/IMATE !
COORD9ATES ( EA* TURN+ PO9T & /ATE :E!R
EA* CORRESPONDS 6A LOCAL MAXIMUM OR A
LOCAL M9IMUM4 ,!N E/IMATE ALL R1L Z]OS &
DET]M9E ! L1/ DEGREE ! FUNC;N C H4
#AE4
#AF4
#AG4
#AH4
#AI4
#BJ4
----------------------------------#CIA
#BA4 .,,MULTIPLE .,,*OICE ,: PO9T IS A
LOCAL MAXIMUM (! FUNC;N .;F7.;X7 .K
#J.BE7 .;X @+ #B7@7 .;X -- #A7 #B @8
,A 7--#B1 #J7
;,B 7--#A1 #A7
;,C 7#A1 #J7
;,D 7#B1 #A7
,,GRAPH+ ,,CALCULATOR ,USE A GRAPH+
CALCULATOR 6GRAPH ! POLYNOMIAL FUNC;N4
,ID5TIFY ! .;X -9T]CEPTS &! PO9TS ": !
LOCAL MAXIMUMS & LOCAL M9IMUMS O3UR4
.#BB4 .;F7.;X7 .K #B .;X #C @+ #H .;X
#B -- #C
.#BC4 .;G7.;X7 .K #J.E .;X #C -- #B
.;X @+ #B.E
.#BD4 .;H7.;X7 .K -- .;X #D @+ #C .;X
.#BE4 .;F7.;X7 .K .;X #E -- #D .;X #C
@+ .;X #B @+ #B
.#BF4 .;G7.;X7 .K .;X #D -- #C .;X #B
@+ .;X
.#BG4 .;H7.;X7 .K .;X #D -- #E .;X #C
@+ #B .;X #B @+ .;X -- #C
.#BH4 .;H7.;X7 .K .;X #E @+ #B .;X #B
-- #AG .;X -- #D
.#BI4 .;G7.;X7 .K #J.G .;X #D -- #H
.;X #C @+ #E .;X
#CJ4 .,,MULTIPLE .,,*OICE ,:AT IS A
TURN+ PO9T (! GRAPH (! FUNC;N .;G7.;X7
.K .;X #D -- #I .;X #B @+ #D .;X @+ #AB8
,A 7--#C1 #J7
;,B 7--#A1 #J7
;,C 7#J1 #AB7
;,D 7#B1 #J7
#CA4 .,,R1SON+ ,:Y IS ! ADJECTIVE
.LOCAL US$ 6DESCRIBE ! MAXIMUMS &
M9IMUMS ( CUBIC FUNC;NS B N QUADRATIC
FUNC;NS8
#CB4 .,,%ORT .,,RESPONSE ,DOES A CUBIC
FUNC;N .ALW1 ."S"TS @1 OR .N"E H A TURN+
PO9T8 .,JU/IFY YR ANSW]4
#CC4 .,,OP5-.,,5D$ .,,MA? ,WRITE A
CUBIC FUNC;N1 A QU>TIC FUNC;N1 &A
FIF?-DEGREE FUNC;N ^: GRAPHS H .;X
-9T]CEPTS ONLY AT .;X .K --#B1 #J1 & #D4
,,DOMA9 ,,& ,,RANGE ,GRAPH ! FUNC;N4
,!N ID5TIFY XS DOMA9 & RANGE4
.#CD4 .;F7.;X7 .K .;X @7 .;X -- #C7 #B
.#CE4 .;F7.;X7 .K .;X #B @7 .;X --
#B7@7 .;X -- #D7@7 .;X -- #E7
.#CF4 .;F7.;X7 .K @7 .;X @+ #A7 #C @7
.;X -- #A7
.#CG4 .;F7.;X7 .K @7 .;X @+ #B7@7 .;X
@+ #A7@7 .;X -- ;L7 #B @7 .;X -- #B7 #B
.#CH4 .,,*ALL5GE ,9 G5]AL1 :AT C Y SAY
AB ! DOMA9 & RANGE ( ODD-DEGREE
POLYNOMIAL FUNC;NS8 ,:AT C Y SAY AB !
DOMA9 & RANGE ( EV5-DEGREE POLYNOMIAL
FUNC;NS8
,,PRO#M ,,SOLV+
,,EXAMPLE #C
ON P4 #CHI = ,EXS4 #CI-DJ
,9 ,EX]CISES #CI & #DJ1 ASSUME T ! BOX
IS 3/RUCT$ US+ ! ME?OD ILLU/RAT$ 9
,EXAMPLE #C ON PAGE #CHI @4
.#CI4 .,,PO/C>DS ,M>CIE WANTS 6MAKE A
BOX 6HOLD H] PO/C>D COLLEC;N F A PIECE (
C>DBO>D T IS #AJ 9*ES 0#AH 9*ES4 ,:AT >E
! DIM5.NS (! BOX )! MAXIMUM VOLUME8 ,:AT
IS ! MAXIMUM VOLUME (! BOX8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#DJ4 .,,CO9 .,,COLLEC;N ,JORGE IS
MAK+ A BOX = 8 CO9 COLLEC;N F A PIECE (
C>DBO>D T IS #CJ C5TIMET]S 0#DJ
C5TIMET]S4 ,:AT >E ! DIM5.NS (! BOX )!
MAXIMUM VOLUME8 ,:AT IS ! MAXIMUM VOLUME
(! BOX8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
-----------------------------------#CIB
.#DA4 .,,SWIMM+ ,=A SWIMM] DO+ !
BR1//ROKE1 ! FUNC;N
.;,S .K --#BDA .;T #G @+ #AJFJ .;T #F
-- #AHGJ .;T #E @+ #AFEJ .;T #D -- #GCG
.;T #C @+ #ADD .;T #B -- #B.DC .;T
MODELS ! SWIMM]'S SPE$ .;,S 7IN MET]S
P] SECOND7 DUR+ "O -PLETE /ROKE1 ": .;T
.IS ! NUMB] ( SECONDS S9CE ! />T (!
/ROKE4 ,GRAPH ! FUNC;N4 ,AC 6! MODEL1 AT
:AT "T DUR+ ! /ROKE IS ! SWIMM] GO+ !
FA/E/8
#DB4 .,,MULTIPLE .,,REPRES5T,NS ,Y H
#FJJ SQU>E FEET ( MAT]IAL = BUILD+ A
GRE5H\SE T IS %AP$ L HALF A CYL9D]4
A4 .,WRIT+ .AN .,EXPRES.N ,! SURFACE
>EA ;,S (! GRE5H\SE IS GIV5 0.;,S .K .;R
#B @+ .;R ,SUB/ITUTE #FJJ = ;,S & !N
WRITE AN EXPRES.N = 9 T]MS ( .R4
B4 .,WRIT+ .A .,FUNC;N ,! VOLUME .;,V
(! GRE5H\SE IS GIV5 BY @4 ,WRITE AN
EQU,N T GIVES .;,V Z POLYNOMIAL FUNC;N (
.;R AL"O4
C4 .,GRAPH+ .A .,FUNC;N ,GRAPH !
VOLUME FUNC;N F "P 7;B74 ,:AT >E !
DIM5.NS .;R & T MAXIMIZE ! VOLUME (!
GRE5H\SE8 ,:AT IS ! MAXIMUM VOLUME8
.#DC4 .,,EXT5D$ .,,RESPONSE ,F #AIFJ
6#BJJA1 ! NUMB] ( /UD5TS ;,S 7IN ?\S&S7
5ROLL$ 9 PUBLIC S*OOLS 9 ! ,UNIT$ ,/ATES
C 2 MODEL$ 0.;,S .K #A.FD .;X #C -- #AJB
.;X #B @+ #AGAJ .;X @+ #CF1CJJ ": .;X IS
! NUMB] ( YE>S S9CE #AIFJ4
A4 ,GRAPH ! FUNC;N4
B4 ,ID5TIFY ANY TURN+ PO9TS ON ! DOMA9
#J "K.K .;X "K.K #DA4 ,:AT R1L--LIFE
M1N+ D ^! PO9TS H8
C4 ,:AT IS ! RANGE (! FUNC;N8
#DD4 .,,*ALL5GE ,A CYL9D] IS 9SCRIB$ 9
A SPH]E ( RADIUS #H4 ,WRITE AN EQU,N =!
VOLUME (! CYL9D] Z A FUNC;N ( .H4 ,F9D !
VALUE ( .;H T MAXIMIZES ! VOLUME (!
9SCRIB$ CYL9D]4 ,:AT IS ! MAXIMUM VOLUME
(! CYL9D]8
,MIX$ ,REVIEW
,! V>IA#S .;X & .;Y V>Y DIRECTLY4
,WRITE AN EQU,N T RELATES .;X & .Y4 @7
.P4 #AJG @7
.#DE4 .;X .K #A1 .;Y .K #E
.#DF4 .;X .K --#B1 .;Y .K #H
.#DG4 .;X .K #C1 .;Y .K --#E
.#DH4 .;X .K #D1 .;Y .K #F
.#DI4 .;X .K #E1 .;Y .K --#B
.#EJ4 .;X .K --#AB1 .;Y .K --#D
,SIDEB>3
,PREVIEW
,PREP>E = ,LESSON #E.I 9 ,EXS4 #EA-ED4
,WRITE A QUADRATIC FUNC;N ^: GRAPH HAS
! GIV5 "*I/ICS4 @7 .P4 #CJI @7
.#EA4 V]TEX3 7#E1 #D72 PASSES "?3
7#C1AB7
.#EB4 V]TEX3 7--#D1 --#F72 PASSES "?3
7#B1 #C7
.#EC4 PASSES "?3 7--#C1AB71 7--#B1
#C71 7#A1 #J7
.#ED4 PASSES "?3 7--#B1 #AI71 7#B1
--#E71 7#D1 --#AA7
,SIMPLIFY ! EXPRES.N4 ,TELL :
PROP]TIES ( EXPON5TS Y US$4 @7 .P4 #CCJ
@7
.#EE4 7#C #B .;X #C @7 #E
.#EF4 @7 .;X #B .;Y #D @7 --#A
.#EG4 @7 .XY #C @7@7 .;X --#B .;Y @7
--#C
.#EH4 --#D .;X --#C .;Y #J
.#EI4
.#FJ4
.#FA4
.#FB4
.,,EXTRA .,,PRACTICE = ,LESSON #E.H1
P4 #AJAD
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#CIC
#E.I ,WRITE ,POLYNOMIAL ,FUNC;NS &
,MODELS
.,2F ,Y WROTE L9E> & QUADRATIC
FUNC;NS4
.,N[ ,Y W WRITE HI<]-DEGREE POLYNOMIAL
FUNC;NS4
.,:Y8 ,S Y C MODEL LAUN* SPE$1 Z 9
,EXAMPLE #D4
,KEY ,VOCABUL>Y
99 .F9ITE .DI6];ES
,SIDEB>3
,/&>DS
,5RI*;T TOPIC2 N REQUIR$ 0! ,CALI=NIA
,/&>DS
,Y "K T TWO PO9TS DET]M9E A L9E & T
?REE PO9TS DET]M9E A P>ABOLA4 ,9
,EXAMPLE #A1 Y W SEE T F\R PO9TS DET]M9E
! GRAPH (A CUBIC FUNC;N4
,,EXAMPLE #A ,WRITE A CUBIC FUNC;N
,WRITE ! CUBIC FUNC;N ^: GRAPH IS %[N4
,SOLU;N
.,,/EP .#A .,USE ! ?REE GIV5 .;X
-9T]CEPTS 6WRITE ! FUNC;N 9 FACTOR$ =M4
.;F7.;X7 .K .A @7 .;X @+ #D7@7 .;X --
#A7@7 .;X -- #C7
.,,/EP .#B .,F9D ! VALUE ( .A
0SUB/ITUT+ ! COORD9ATES (! F\R? PO9T4
,! FUNC;N IS @4
.,,*ECK ,*ECK ! 5D 2HAVIOR ( .;F @4 ,!
DEGREE ( .;F IS ODD & .A "K #J4
,S .;F7.;X7 @+ Z .;X -- & .;F7.;X7 --
Z .;X @+ @1 : MAT*ES ! GRAPH4
.,,F9ITE .,,DI6];ES ,9 ,EXAMPLE #A1 Y
F.D A FUNC;N GIV5 XS GRAPH4 ,FUNC;NS C
AL 2 WRITT5 F A SET ( DATA .US+ .F9ITE
.DI6];ES4
,:5 ! .;X --VALUES 9 A DATA SET >E
EQU,Y SPAC$1 ! DI6];ES ( 3SECUTIVE .;Y
--VALUES >E CALL$ .F9ITE .DI6];ES4 ,=
EXAMPLE1 "S F9ITE DI6];ES =! FUNC;N
.;F7.;X7 .K .;X #B >E %[N 2L4
,! F9ITE DI6];ES ABV >E CALL$ .F/--
.ORD] .DI6];ES4 ,Y C AL CALCULATE
HI<]--ORD] DI6];ES1 Z %[N 9 ! NEXT
EXAMPLE4
------------------------------------#CID
,,EXAMPLE #B ,F9D F9ITE DI6];ES
,! F/ FIVE TRIANGUL> NUMB]S >E %[N 2L4
,A =MULA =! RA? TRIANGUL> NUMB] IS @4
,%[ T ? FUNC;N HAS 3/ANT SECOND--ORD]
DI6];ES4
,SOLU;N
,WRITE ! F/ S"EAL TRIANGUL> NUMB]S4
,F9D ! F/--ORD] DI6];ES 0SUBTRACT+
3SECUTIVE TRIANGUL> NUMB]S4 ,!N F9D !
SECOND--ORD] DI6];ES 0SUBTRACT+
3SECUTIVE F/--ORD] DI6];ES4
,EA* SECOND--ORD] DI6];E IS #A1 S !
SECOND--ORD] DI6];ES >E 3/ANT4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #A &
.#B
,WRITE A CUBIC FUNC;N ^: GRAPH PASSES
"? ! GIV5 PO9TS4
.#A4 7--#D1 #J71 7#J1 #AJ71 7#B1 #J71
7#E1 #J7
.#B4 7--#A1 #J71 7#J1--#AB71 7#B1 #J71
7#C1 #J7
.#C4 .,,GEOMETRY ,%[ T @1 A =MULA =!
.;N TH P5TAGONAL NUMB]1 HAS 3/ANT
SECOND-ORD] DI6];ES4
..,,PROP]TIES ,,( ,,F9ITE .,,DI6];ES
,9 ,EXAMPLE #B1 NOTICE T ! FUNC;N HAS
DEGREE TWO & T ! SECOND-ORD] DI6];ES >E
3/ANT4 ,? ILLU/RATES ! F/ (! FOLL[+ TWO
PROP]TIES ( F9ITE DI6];ES4
,,KEY ,,3CEPT .= .,YR .,NOTEBOOK
,PROP]TIES ( ,F9ITE ,DI6];ES
.#A4 ,IF A POLYNOMIAL FUNC;N .;F7.;X7
HAS DEGREE .;N @1 !N ! .;N TH-ORD]
DI6];ES ( FUNC;N VALUES = EQU,Y-SPAC$
.;X -VALUES >E NONZ]O & 3/ANT4
.#B4 ,3V]SELY1 IF ! .;N TH-ORD]
DI6];ES ( EQU,Y-SPAC$ DATA >E NONZ]O &
3/ANT1 !N ! DATA C 2 REPRES5T$ 0A
POLYNOMIAL FUNC;N ( DEGREE .N4
,! SECOND PROP]TY ( F9ITE DI6];ES
ALL[S Y 6WRITE A POLYNOMIAL FUNC;N T
MODELS A SET ( EQU,Y-SPAC$ DATA4
------------------------------------#CIE
,,EXAMPLE #C ,MODEL ) F9ITE DI6];ES
,! F/ SEV5 TRIANGUL> PYRAMIDAL NUMB]S
>E %[N 2L4 ,F9D A POLYNOMIAL FUNC;N T
GIVES ! N? TRIANGUL> PYRAMIDAL NUMB]4
,SOLU;N
,2G9 0F9D+ ! F9ITE DI6];ES4
,2C ! ?IRD-ORD] DI6];ES >E 3/ANT1 Y "K
T ! NUMB]S C 2 REPRES5T$ 0A CUBIC FUNC;N
(! =M .;F7.;N7 .K .AN #C @+ .BN #B @+
.CN @+ .;D @4
,0SUB/ITUT+ ! F/ F\R TRIANGUL>
PYRAMIDAL NUMB]S 96! FUNC;N1 Y OBTA9 A
SY/EM ( F\R L9E> EQU,NS 9 F\R V>IA#S4
,,REVIEW ,,SY/EMS
,= HELP ) US+ MATRICES 6SOLVE L9E>
SY/EMS1 SEE P4 #BAJ @4
,WRITE ! L9E> SY/EM Z A MATRIX EQU,N
.,,AX .K .;,B @4 ,5T] ! MATRICES .,A &
.;,B 96A GRAPH+ CALCULATOR1 & !N
CALCULATE ! SOLU;N .;,X .K .,A --#A .;,B
@4
,PICTURE3 ..,CALCULATE ;,X .K .,A --#A
.;,B @4
,! SOLU;N IS @1 & .;D .K #J4 ,S1 ! .;N
TH TRIANGUL> PYRAMIDAL NUMB] IS GIV5 BY
@4
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#C
.#D4 ,USE F9ITE DI6];ES 6F9D A
POLYNOMIAL FUNC;N T FITS ! DATA 9 ! TA#4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #A3 #B3 #C3 #D3 #E3 #F
.;F7.;X7 @3 #F3 #AE3 #BB3 #BA3 #F3
--#BI
------------------------------------#CIF
.,,CUBIC .,,REGRES.N ,9 ,EXAMPLES #A &
#C1 Y F.D A CUBIC MODEL T .EXACTLY FITS
A SET ( DATA PO9TS4 ,9 _M R1L-LIFE
SITU,NS1 Y _C F9D A SIMPLE MODEL 6FIT
DATA PO9TS EXACTLY4 ,9/1D1 Y C USE !
.REGRES.N F1TURE (A GRAPH+ CALCULATOR
6F9D AN .;N TH-DEGREE POLYNOMIAL MODEL T
BE/ FITS ! DATA4
..,,EXAMPLE #D ,SOLVE A MULTI-/EP
.PRO#M
.,,SPACE .,,EXPLOR,N ,! TA# %[S !
TYPICAL SPE$ .;Y 7IN FEET P] SECOND7 (A
SPACE %UTTLE .;X SECONDS AF LAUN*4 ,F9D
A POLYNOMIAL MODEL =! DATA4 ,USE ! MODEL
6PREDICT ! "T :5 ! %UTTLE'S SPE$ R1*ES
#DDJJ FEET P] SECOND1 AT : PO9T XS BOO/]
ROCKETS DETA*4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #AJ3 #BJ3 #CJ3 #DJ3 #EJ3 #FJ3
#GJ3 #HJ
.;Y @3 #BJB.D3 #DFC.C3 #GDH.B3 #IGI.C3
;L#AHFC3 #ADBA.C3 #AGIE.D3 #BBHC.E
,SOLU;N
.,,/EP .#A .,5T] ! DATA 96A GRAPH+
CALCULATOR & MAKE A SCATT] PLOT4 ,!
PO9TS SU7E/ A CUBIC MODEL4
.,,/EP .#B .,USE CUBIC REGRES.N 6OBTA9
? POLYNOMIAL MODEL3
.;Y .K #J.JJFEJ .;X #C -- #J.GCI .;X
#B @+ #DI.J .;X -- #BCF
,,ANO!R ,,WAY
,Y C AL F9D ! VALUE ( .;X = : .;Y .K
#DDJJ 0SUBTRACT+ #DDJJ F ! "R SIDE (!
CUBIC MODEL1 GRAPH+ ! RESULT+ FUNC;N1 &
US+ ! Z]O F1TURE 6F9D ! GRAPH'S .;X
-9T]CEPT4
.,,/EP .#C .,*ECK ! MODEL 0GRAPH+ X &!
DATA 9 ! SAME VIEW+ W9D[4
.,,/EP .#D .,GRAPH ! MODEL & .;Y .K
#DDJJ 9 ! SAME VIEW+ W9D[4 ,USE !
.9T]SECT F1TURE4
,! BOO/] ROCKETS DETA* AB #AJF SECONDS
AF LAUN*4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#D
,USE A GRAPH+ CALCULATOR 6F9D A
POLYNOMIAL FUNC;N T FITS ! DATA4
#E4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #A3 #B3 #C3 #D3 #E3 #F
.;F7.;X7 @3 #E3 #AC3 #AG3 #AA3 #A;L3
#EF
#F4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #J3 #B3 #D3 #F3 #H3 #AJ
.;F7.;X7 @3 #H3 #J3 #A3 #FI3 #IH3 #HG
------------------------------------#CIG
#E.I ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#AA = ,EXS4 #I1AE1 & #BG
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 #B1AJ1BB1BC1 & #BH
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,:5
! .;X -VALUES 9 A DATA SET >E EQU,Y
SPAC$1 ! DI6];ES ( 3SECUTIVE .;Y -VALUES
>E CALL$ @8 @4
.#B4 .,,WRIT+ .,DESCRIBE F/-ORD]
DI6];ES & SECOND-ORD] DI6];ES4
,,EXAMPLE #A
ON P4 #CIC = ,EXS4 #C-AA
,,WRIT+ ,,CUBIC ,,FUNC;NS ,WRITE !
CUBIC FUNC;N ^: GRAPH IS %[N4
#C4
#D4
#E4
,,CUBIC ,,MODELS ,WRITE A CUBIC FUNC;N
^: GRAPH PASSES "? ! PO9TS4
.#F4 7--#C1 #J71 7--#A1 #AJ71 7#J1
#J71 7#D1 #J7
.#G4 7--#B1 #J71 7--#A1 #J71 7#J1
--#H71 7#B1 #J7
.#H4 7--#C1 #J71 7#A1 #J71 7#C1 #B71
7#D1 #J7
.#I4 7--#E1 #J71 7#J1 #J71 7#A1
--#AB71 7#F1 #J7
#AJ4 .,,MULTIPLE .,,*OICE ,: CUBIC
FUNC;N'S GRAPH PASSES "? ! PO9TS
7--#C1J71 7--#A1J71 7#C1J71 & 7#J1C78
,A .;F7.;X7 .K @7 .;X -- #C7@7 .;X @+
#C7@7 .;X -- #A7
.;,B
;,C .;F7.;X7 .K --#B7 .;X -- #C7@7 .;X
@+ #C7@7 .;X -- #A7
;,D .;F7.;X7 .K @7 .;X -- #C7@7 .;X @+
#C7@7 .;X @+ #A7
#AA4 .,,]ROR .,,ANALYSIS ,A /UD5T TRI$
6WRITE A CUBIC FUNC;N ^: GRAPH HAS .;X
-9T]CEPTS --#A1 #B1 & #E1 & PASSES "?
7#A1 #C74 .,DESCRIBE & CORRECT ! ]ROR 9
! /UD5T'S CALCUL,N (! L1D+ COE6ICI5T .A
@4
,,EXAMPLE #B
ON P4 #CID = ,EXS4 #AB-AG
,,F9D+ ,,F9ITE ,,DI6];ES ,%[ T ! .;N
TH-ORD] DI6];ES =! GIV5 FUNC;N ( DEGREE
.;N >E NONZ]O & 3/ANT4
.#AB4 .;F7.;X7 .K #E .;X #C -- #AJ
.#AC4 .;F7.;X7 .K --#B .;X #B @+ #E
.;X
.#AD4 .;F7.;X7 .K .;X #D -- #C .;X #B
@+ #B
.;L#E4 .;F7.;X7 .K #D .;X #B -- #I .;X
@+ #B
.#AF4 .;F7.;X7 .K .;X #C -- #D .;X #B
-- .;X @+ #A
.#AG4 .;F7.;X7 .K #B .;X #E -- #C .;X
#B @+ .;X
,,EXAMPLE #C
ON P4 #CIE = ,EXS4 #AH-BA
,,F9D+ ,A ,,MODEL ,USE F9ITE DI6];ES
&A SY/EM ( EQU,NS 6F9D A POLYNOMIAL
FUNC;N T FITS ! DATA 9 ! TA#4
#AH4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #A3 --@3 #B3 #C3 #D3 #E3 #F
.;F7.;X7 @3 #J3 --#C3 --#H3 --#AE3
--#BD3 --#CE
#AI4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #A3 #B3 #C3 #D3 #E3 #F
.;F7.;X7 @3 #AA3 #AD3 #I3 --#D3 --#BE3
--#ED
#BJ4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #A3 #B3 #C3 #D3 #E3 #F
.;F7.;X7 @3 --#AB3 --#AD3 --#AJ3 #F3
#DJ3 #IH
#BA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #A3 #B3 #C3 #D3 #E3 #F
.;F7.;X7 @3 #E3 #AD3 #BG3 #DA3 #EC3
#FJ
-----------------------------------#CIH
.#BB4 .,,OP5-.,,5D$ .,,MA? ,WRITE TWO
DI6]5T CUBIC FUNC;NS ^: GRAPHS PASS "? !
PO9TS 7--#C1 #J71 7--#A1 #J71 & 7#B1
#F74
.#BC4 .,,%ORT .,,RESPONSE ,H[ _M PO9TS
D Y NE$ 6DET]M9E A QU>TIC FUNC;N8 A
QU9TIC 7FIF?-DEGREE7 FUNC;N8 .,JU/IFY YR
ANSW]S4
.#BD4 .,,*ALL5GE ,SUB/ITUTE !
EXPRES.NS .;K1 .;K @+ #A1 .;K @+ #B1'41
.;K @+ #E = .;X 9 ! FUNC;N .;F7.;X7 .K
.AX #C @+ .BX #B @+ .CX @+ .;D 6G5]ATE
SIX EQU,Y-SPAC$ ORD]$ PAIRS4 ,!N %[ T
?IRD-ORD] DI6];ES >E 3/ANT4
,,PRO#M ,,SOLV+
,,EXAMPLE #C
ON P4 #CIE = ,EX4 #BE
.#BE4 .,,GEOMETRY ,F9D A POLYNOMIAL
FUNC;N T GIVES ! NUMB] ( DIAGONALS .;D
(A POLYGON ) .;N SIDES4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,NUMB] ( SIDES1 .;N @3 #C3 #D3 #E3 #F3
#G3 #H
,NUMB] ( DIAGONALS1 .;D @3 #J3 #B3 #E3
#I3 #AD3 #BJ
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
,,EXAMPLE #D
ON P4 #CIF = ,EXS4 #BF-BH
.#BF4 .,,AVI,N ,! TA# %[S ! NUMB] (
ACTIVE PILOTS 7IN ?\S&S7 ) AIRL9E
TRANSPORT LIC5SES 9 ! ,UNIT$ ,/ATES =!
YE>S #AIIG 6#BJJD4 ,USE A GRAPH+
CALCULATOR 6F9D A POLYNOMIAL MODEL =!
DATA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,YE>S S9CE #AIIG1 .;T @3 #J3 #A3 #B3
#C3 #D3 #E3 #F3 #G
,TRANSPORT PILOTS1 .;P @3 #ACA3 #ACE3
#ACH3 #ADB3 #ADE3 #ADE3 #ADD3 #ADE
@A.,HOITIE,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#BG4 .,,MULTI-.,,/EP .,,PRO#M ,! TA#
%[S ! AV]AGE ,U4,S4 MOVIE TICKET PRICE
7IN DOLL>S7 = V>I\S YE>S F #AIHC 6#BJJC4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,YE>S S9CE #AIHC1 .;T @3 #J3 #D3 #H3
#AB3 #AF3 #BJ
,MOVIE TICKET PRICE1 .;M @3 #C.AE3
#C.IA3 #D.BA3 #D.CE3 #E.JH3 #F.JC
A4 ,USE A GRAPH+ CALCULATOR 6F9D A
POLYNOMIAL MODEL =! DATA4
B4 ,E/IMATE ! AV]AGE ,U4,S4 MOVIE
TICKET PRICE 9 #BJAJ4
C4 ,9 : YE> 0 ! AV]AGE ,U4,S4 MOVIE
TICKET PRICE AB 4#D.EJ8
#BH4 .,,%ORT .,,RESPONSE ,BAS$ ON DATA
COLLECT$ F FRS1 Y E/IMATE ! CUMULATIVE
PR(ITS 7IN DOLL>S7 AF EA* ( SIX MON?S =
TWO POT5TIAL BUSI;SES4 ,F9D A POLYNOMIAL
FUNC;N T MODELS ! PR(IT = EA* BUSI;S4 ,:
BUSI;S W YIELD ! GRTE/ L;G--T]M PR(IT8
,:Y8
,! FOLL[+ TA# IS 9 LI/$
=MAT4 ,= EA* CELL ! H1D+ IS %[N
FOLL[$ 0A COLON1 SPACE &! CELL
3T5TS
.,Y>D ."W @3 ,PR(IT1 .;P
,MON?1 .;T @3 #CJ
#A3 #BAJ
#B3 #DAJ
#C3 #FHJ
#D3 #AJGJ
#E3 #AFCJ
.,Y>D ."W @3 .,PET .C>E
,MON?1 .;T @3 ,MON?1 .;T
#A3 #A
#B3 #B
#C3 #C
#D3 #D
#E3 #E
#F3 #F
.,Y>D ."W @3 .,PET .C>E
,MON?1 .;T @3 ,PR(IT1 .;P
#A3 #CJ
#B3 #EJ
#C3 #BBJ
#D3 #EDJ
#E3 #AJAJ
#F3 #AFCJ
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#CII
.#BI4 .,,GEOMETRY ,! MAXIMUM NUMB] (
REGIONS .;,R 96: SPACE C 2 DIVID$ 0.;N
9T]SECT+ SPH]ES IS GIV5 0,%[ T ? FUNC;N
HAS 3/ANT ?IRD-ORD] DI6];ES4
.#CJ4 .,,*ALL5GE ,A CYL9DRICAL CAKE IS
DIVID$ 96! MAXIMUM NUMB] ( PIECES .;P
0.;C PLANES4 ,:5 .;C .K #A1 #B1 #C1 #D1
#E1 & #F ! VALUES ( .;P7.;C7 >E #B1 #D1
#H1 #AE1 #BF1 & #DB RESPECTIVELY4 ,:AT
IS ! MAXIMUM NUMB] ( PIECES 96: ! CAKE C
2 DIVID$ :5 X IS CUT 0#H PLANES8
,MIX$ ,REVIEW
,DRAW A SCATT] PLOT (! DATA &
APPROXIMATE ! BE/-FITT+ L9E4 @7 .P4 #AAC
@7
#CA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X @3 #J.E3 #A3 #B3 #B.E3 #D3 #E
.;Y @3 #E.E3 #E3 #C.E3 #B3 #J.E3 #J.E
#CB4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 --#D3 --#B3 #J3 #A3 #B3 #B.E3
#C
.;Y @3 --#B3 --#A3 #J.E3 #B3 #B3 #C3
#C
,FACTOR ! POLYNOMIAL4
.#CC4 .;X #B -- #AI .;X @+ #DH @7 .P4
#BEB @7
.#CD4 #AH .;X #B @+ #CJ .;X -- #AB @7
.P4 #BEI @7
.#CE4 #FD .;X #B -- #ADD .;X @+ #HA @7
.P4 #BEI @7
.#CF4 #AH .;X #C @+ #CC .;X #B -- #CJ
.;X @7 .P4 #CEC @7
.#CG4 #FD .;X #C @+ #BG @7 .P4 #CEC @7
.#CH4 #C .;X #E -- #FF .;X #C -- #BBE
.;X @7 .P4 #CEC @7
,SIDEB>3
,PREVIEW
,PREP>E = ,LESSON #F.A 9 ,EXS4 #CI-DD4
,SOLVE ! EQU,N4 @7 .P4 #BFF @7
.#CI4 #E .;X #B .K #AJ
.#DJ4 #BD .;X #B .K #F
.#DA4 #I .;X #B @+ #B .K #F
.#DB4 #G .;X #B -- #D .K #H
.#DC4 -- .;X #B @+ #AF .K #E .;X #B --
#AB
.#DD4 #D .;X #B @+ #C .K --#D .;X #B
@+ #AE
,,QUIZ .= .,LESSONS .#E..G--.#E..I
,F9D ALL Z]OS (! POLYNOMIAL FUNC;N1 @7
P4 #CGI @7
.#A4 .;F7.;X7 .K .;X #C -- #D .;X #B
-- #AA .;X @+ #CJ
.#B4 .;F7.;X7 .K #B .;X #D -- #B .;X
#C -- #DI .;X #B @+ #I .;X @+ #AHJ
,WRITE A POLYNOMIAL FUNC;N .;F ( L1/
DEGREE T HAS R,NAL COE6ICI5TS1 A L1D+
COE6ICI5T ( #A1 &! GIV5 Z]OS1 @7 P4 #CGI
@7
.#C4 --#D1 --#A1 #B
.#D4 #D1 #A @+ .;I
.#E4
.#F4
,GRAPH ! FUNC;N1 @7 P4 #CHG @7
.#G4 .;F7.;X7 .K --@7 .;X -- #C7@7 .;X
-- #B7@7 .;X @+ #B7
.#H4 .;F7.;X7 .K #C7 .;X -- ;L7@7 .;X
@+ #A7@7 .;X -- #D7
.#I4 .;F7.;X7 .K .;X @7 .;X -- #D7@7
.;X -- ;L7@7 .;X @+ #B7
.#AJ4 .;F7.;X7 .K @7 .;X -- #C7@7 .;X
@+ #B7 #B @7 .;X @+ #C7 #B
,WRITE A CUBIC FUNC;N ^: GRAPH PASSES
"? ! GIV5 PO9TS1 @7 P4 #CIC @7
.#AA4 7--#E1 #J71 7--#B1 #J71 7#A1
#I71 7#B1 #J7
.#AB4 7--#A1 #J71 7#J1 #AF71 7#B1 #J71
7#D1 #J7
.#AC4 .,,DRIVE-.,,9S ,! TA# %[S !
NUMB] ( ,U4,S4 DRIVE-IN MOVIE !AT]S =!
YE>S #AIIE 6#BJJB4 ,F9D A POLYNOMIAL
MODEL T FITS ! DATA4 @7 P4 #CIC @7
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,YE>S S9CE #AIIE1 .;T @3 #J3 #A3 #B3
#C3 #D3 #E3 #F3 #G
,DRIVE-IN MOVIE !AT]S1 .;,D @3 #HDH3
#HBF3 #HAE3 #GEJ3 #GCG3 #FFG3 #FFC3 #FCD
.,,EXTRA .,,PRACTICE = ,LESSON #E.I1
P4 #AJAD
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#DJJ
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,LESSONS #E.F--#E.I
.#A4 .,,MULTI-.,,/EP .,,PRO#M ,!
VOLUME (! RECTANGUL> PRISM %[N IS #AHJ
CUBIC 9*ES4
.A4 ,WRITE A POLYNOMIAL EQU,N T Y C
USE 6F9D ! VALUE ( .X4
.B4 ,ID5TIFY ! POSSI# R,NAL SOLU;NS (!
EQU,N 9 "P 7A74
.C4 ,USE SYN!TIC DIVI.N 6F9D A R,NAL
SOLU;N (! EQU,N4 ,%[ T NO O!R R1L
SOLU;NS EXI/4
.D4 ,:AT >E ! DIM5.NS (! PRISM8
.#B4 .,,MULTI-.,,/EP .,,PRO#M ,Y WANT
6MAKE AN OP5 BOX F A PIECE ( C>DBO>D
6HOLD YR S*OOL SUPPLIES4 ,! BOX W 2 =M$
US+ ! ME?OD DESCRIB$ 9 ,EXAMPLE #C ON
PAGE #CHI @4 ,! ORIG9AL PIECE ( C>DBO>D
IS #BJ 9*ES 0#CJ 9*ES4
.A4 ,WRITE A POLYNOMIAL FUNC;N =!
VOLUME (! BOX4
.B4 ,GRAPH ! FUNC;N 9 "P 7A74
.C4 ,:AT >E ! DIM5.NS (! BOX )!
MAXIMUM VOLUME8
.D4 ,:AT IS ! MAXIMUM VOLUME (! BOX8
.#C4 .,,GR#A;,,DD$ .,,ANSW] ,F #AIHJ
6#BJJB1 ! NUMB] .;,R 7IN ?\S&S7 (
RETIREES RCVG ,SOCIAL ,SECUR;Y B5EFITS C
2 MODEL$ 0! FUNC;N
.;,R .K #J.FBI .;T #C -- #BG.H .;T #B
@+ #GDD .;T @+ #AI1FJJ
": .;T IS ! NUMB] ( YE>S S9CE #AIHJ4
,9 : YE> 0 ! NUMB] ( RETIREES RCVG
,SOCIAL ,SECUR;Y B5EFITS AB #BF1IJJ1JJJ8
.#D4 .,,OP5-.,,5D$ ,WRITE A POLYNOMIAL
FUNC;N ) R1L COE6ICI5TS T HAS DEGREE #D
& Z]OS --#B1A1 & #D -- .I4
.#E4 .,,OP5-.,,5D$ ,WRITE A POLYNOMIAL
FUNC;N ) R,NAL COE6ICI5TS T HAS #AF
.POSSI# R,NAL Z]OS AC 6! R,NAL Z]O
!OREM1 B HAS NO ACTUAL R,NAL Z]OS4
.#F4 .,,EXT5D$ .,,RESPONSE ,Y >E MAK+
A SCULPTURE T IS A PYRAMID )A SQU>E
BASE4 ,Y WANT ! HEI<T (! PYRAMID 6BE #D
9*ES LESS ?AN ! L5G? (A SIDE (! BASE4 ,Y
WANT ! VOLUME (! SCULPTURE 6BE #BJJ
CUBIC 9*ES4
.A4 ,LET .;X REPRES5T ! L5G? 7IN 9*ES7
(A SIDE (! SCULPTURE'S BASE4 ,DRAW A
DIAGRAM (! SCULPTURE1 & LABEL ! DIM5.NS
9 T]MS ( .X4
.B4 ,WRITE A FUNC;N T GIVES ! VOLUME
;,V (! SCULPTURE 9 T]MS ( .X4
.C4 ,GRAPH ! FUNC;N 9 "P 7;B74 ,USE !
GRAPH 6E/IMATE ! VALUE ( .;X =!
SCULPTURE4
.D4 ,WRITE & SOLVE AN EQU,N 6F9D !
VALUE ( .X4 .,-P>E YR ANSW] ) YR E/IMATE
F "P 7;C74 ,:AT >E ! DIM5.NS (!
SCULPTURE8
.#G4 .,,%ORT .,,RESPONSE ,YR FR HAS
/>T$ A GOLF CA4Y+ BUSI;S4 ,! TA# %[S !
PR(IT ;P 7IN DOLL>S7 (! BUSI;S 9 ! F/ #E
MON?S4 ,USE F9ITE DI6];ES 6F9D A
POLYNOMIAL MODEL =! DATA4 ,!N USE !
MODEL 6PREDICT ! PR(IT :5 .;T .K #G4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,MON?1 .;T @3 #A3 #B3 #C3 #D3 #E
,PR(IT1 .;P @3 #D3 #B3 #F3 #BB3 #EF
.#H4 .,,%ORT .,,RESPONSE ,! TA# %[S !
AV]AGE REL,N%IP 2T L5G? 7IN 9*ES7 &
WEI<T 7IN P.DS7 = AN ALLIGATOR Z X GR[S4
,USE A GRAPH+ CALCULATOR 6F9D A
POLYNOMIAL MODEL =! DATA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,L5G?3 ,WEI<T
#AB3 #J.B
#BD3 #J.G
#CF3 #H.F
#DH3 #AG.G
#ED3 #BH.J
#FJ3 #CI.F
#FF3 #DE.D
#GB3 #DI.F
------------------------------------#DJA
#E ,*APT] ,SUMM>Y
.,ANIMAT$ .,ALGEBRA _+CLASSZONE.COM_:
,ELECTRONIC ,FUNC;N ,LIBR>Y
,,BIG ,,ID1S ,= ,YR ,NOTEBOOK
.,BIG .,IDEA .#A ,GRAPH+ ,POLYNOMIAL
,FUNC;NS
,! 5D 2HAVIOR (! GRAPH ( .;F7.;X7 IS
.;F7.;X7 @+ Z .;X ---& .;F7.;X7 @+ Z .;X
@+
S .;F7.;X7 IS ( EV5 DEGREE & HAS A
POSITIVE L1D+ COE6ICI5T4
,! GRAPH HAS #C TURN+ PO9TS1 S !
DEGREE ( .;F7.;X7 IS .AT .L1/ .;S #D &
.;F7.;X7 HAS .AT .L1/ .;S #D Z]OS4
.,BIG .IDEA .#B ,P]=M+ ,OP],NS )
,POLYNOMIALS
,Y C ADD1 SUBTRACT1 MULTIPLY1 & DIVIDE
POLYNOMIALS4 ,Y C AL FACTOR POLYNOMIALS
US+ ANY -B9,N (! ME?ODS 2L4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,FACTOR+ ME?OD3 ,EXAMPLE
,G5]AL TRINOMIAL3 #F .;X #B -- #G .;X
-- #C .K 7#C .;X @+ #A77#B .;X -- #C7
,P]FECT SQU>E TRINOMIAL3 .;X #B @+ #AJ
.;X @+ #BE .K @7 .;X @+ #E7 #B
,DI6];E ( TWO SQU>ES3 .;X #B -- #DI .K
@7 .;X @+ #G7@7 .;X -- #G7
,-MON MONOMIAL FACTOR3 #AE .;X #C @+
#I .;X #B .K #C .;X #B 7#E .;X @+ #C7
,SUM OR DI6];E ( TWO CUBES3 #H .;X #C
-- #BG .K 7#B .;X -- #C77#D .;X #B @+ #F
.;X @+ #I7
,FACTOR 0GR\P+3 .;X #C -- #E .;X #B @+
#I .;X -- #DE .K .;X #B @7 .;X -- #E7 @+
#I7 .;X -- #E7 .K @7 .;X #B @+ #I7@7 .;X
-- #E7
.,BIG .,IDEA .#C ,SOLV+ ,POLYNOMIAL
,EQU,NS & ,F9D+ ,Z]OS
,! T]MS .Z]O1 .FACTOR1 .SOLU;N @1 &
.;X-.9T]CEPT >E CLOSELY RELAT$4 ,3SID] !
FUNC;N .;F7.;X7 .K #B .;X #C -- .;X #B
--#AC .;X -- #F4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--#B IS A .Z]O ( .F4 @3 ;F7 --.#B @7
.K #B7 --.#B @7 #C -- @7 --.#B @7 #B
--#AC7 --.#B @7--#F .K #J
.;X @+ #B IS A .FACTOR ( .;F7.;X7 @4
@3 #B .;X #C -- .;X #B -- #AC .;X -- #F
.K @7 .;X @+ #B @7@7 .;X -- #C77#B .;X
@+ #A7
.;X .K --#B IS A .SOLU;N (! EQU,N
.;F7.;X7 .K #J4 @3 #B7 --.#B @7 #C -- @7
--.#B @7 #B -- #AC7 --.#B @7 --#F .K #J
--#B IS AN .;X -9T]CEPT.' (! GRAPH (
.F4 @3
------------------------------------#DJB
#E ,*APT] ,REVIEW
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99 ,MULTI-,LANGUAGE ,GLOSS>Y
99 ,VOCABUL>Y PRACTICE
,,REVIEW ,,KEY ,,VOCABUL>Y
SCI5TIFIC NOT,N1 P4 #CCA
POLYNOMIAL1 P4 #CCG
POLYNOMIAL FUNC;N1 P4 #CCG
L1D+ COE6ICI5T1 P4 #CCG
DEGREE1 P4 #CCG
3/ANT T]M1 P4 #CCG
/&>D =M (A POLYNOMIAL FUNC;N1 P4 #CCG
SYN!TIC SUB/ITU;N1 P4 #CCH
5D 2HAVIOR1 P4 #CCI
FACTOR$ -PLETELY1 P4 #CEC
FACTOR 0GR\P+1 P4 #CED
QUADRATIC =M1 P4 #CEE
POLYNOMIAL L;G DIVI.N1 P4 #CFB
SYN!TIC DIVI.N1 P4 #CFC
REP1T$ SOLU;N1 P4 #CGI
LOCAL MAXIMUM1 P4 #CHH
LOCAL M9IMUM1 P4 #CHH
F9ITE DI6];ES1 P4 #CIC
,,VOCABUL>Y ,,EX]CISES
.#A4 ,COPY & -PLETE3 ,AT EA* ( XS
TURN+ PO9TS1 ! GRAPH (A POLYNOMIAL
FUNC;N HAS A7;N7 @8 OR A7;N7 @8 @4
.#B4 .,,WRIT+ .,EXPLA9 H[ Y C TELL
:E!R A SOLU;N (A POLYNOMIAL EQU,N IS A
REP1T$ SOLU;N :5 ! EQU,N IS WRITT5 9
FACTOR$ =M4
.#C4 .,,WRIT+ .,EXPLA9 H[ Y C TELL
:E!R A NUMB] IS EXPRESS$ 9 SCI5TIFIC
NOT,N4
.#D4 ,LET .;F 2 A F\R?-DEGREE
POLYNOMIAL FUNC;N ) F\R 4T9CT R1L Z]OS4
,H[ _M TURN+ PO9TS DOES ! GRAPH ( .;F H8
,,REVIEW ,,EXAMPLES ,,& ,,EX]CISES
,USE ! REVIEW EXAMPLES & EX]CISES 2L
6*ECK YR "U/&+ (! 3CEPTS Y H LE>N$ 9 EA*
LESSON ( ,*APT] #E4
#E.A ,USE ,PROP]TIES ( ,EXPON5TS PP4
#CCJ-CCE
,,EXAMPLE
,SIMPLIFY ! EXPRES.N4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
@7 .;X #B ;Y #C @7 #C .;X #D .K @7 .;X
#B @7 #C @7 .;Y #C @7 #C .;X #D @3
..,P[] (A PRODUCT .PROP]TY
.K .;X #F .;Y #I .;X #D @3 ..,P[] (A
P[] .PROP]TY
.K .;X #F @+ #D .;Y #I @3 ..,PRODUCT (
P[]S .PROP]TY
.K .;X #AJ .;Y #I @3 .,SIMPLIFY
.EXPON5T4
,,EXAMPLES #A1 #B1C1 & #D
ON PP4 #CCJ --#CCB = ,EXS4 #E-AB
,,EX]CISES
,EVALUATE OR SIMPLIFY ! EXPRES.N4
,TELL : PROP]TIES ( EXPON5TS Y US$4
.#E4 #B #B @* #B #E
.#F4 7#C #B @7 --#C 7#C #C @7
.#G4 @7 .;X #B .;Y #E @7 #B
.#H4 7#C .;X #D .;Y --#B @7 --#C
.#I4
.#AJ4
.#AA4
.#AB4
------------------------------------#DJC
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,*APT] ,REVIEW ,PRACTICE
#E.B ,EVALUATE & ,GRAPH ,POLYNOMIAL
,FUNC;NS PP4 #CCG-CDD
,,EXAMPLE
,GRAPH ! POLYNOMIAL FUNC;N .;F7.;X7 .K
.;X #C -- #B .;X #B @+ #C4
,MAKE A TA# ( VALUES4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 --#B3 --#A3 #J3 #A3 #B3 #C
.;F7.;X7 @3 --#AC3 #J3 #C3 #B3 #C3 #AB
,PLOT ! PO9TS1 3NECT ! PO9TS )A SMOO?
CURVE1 & *ECK ! 5D 2HAVIOR4
,! DEGREE IS ODD &! L1D+ COE6ICI5T IS
POSITIVE1 S .;F7.;X7 -- Z .;F7.;X7 -- &
.;F7.;X7 @+ Z .;X @+ @4
,,EXAMPLES #E & #F
ON P4 #CDJ = ,EXS4 #AC-AF
,,EX]CISES
,GRAPH ! POLYNOMIAL FUNC;N4
.#AC4 .;F7.;X7 .K -- .;X #D
.#AD4 .;F7.;X7 .K .;X #C -- #D
.#AE4 .;F7.;X7 .K .;X #C @+ #B .;X @+
#C
.#AF4 .,,FI% .,,3SUMP;N ,F #AIIJ
6#BJJB1 ! AM.T ( FI% .;,F 7IN MILLIONS (
P.DS7 CAU<T = HUMAN 3SUMP;N 9 ! ,UNIT$
,/ATES C 2 MODEL$ BY
.;,F .K --#J.IJG .;T #D @+ #BH.J .;T
#C -- #BEH .;T #B @+ #IJB .;T @+ #AB1GJJ
": .;T IS ! NUMB] ( YE>S S9CE #AIIJ4
,GRAPH ! FUNC;N4 ,USE ! GRAPH 6E/IMATE !
YE> :5 ! AM.T ( FI% CAU<T F/ 0 GRT] ?AN
#AD.E .BILLION P.DS4
#E.C ,ADD1 ,SUBTRACT & ,MULTIPLY
,POLYNOMIALS PP4 #CDF-CEB
,,EXAMPLE
,P]=M ! 9DICAT$ OP],N4
.A4 7#C .;X #C -- #F .;X #B -- #G .;X
@+ #E7 @+ @7 .;X #C @+ #H .;X @+ #C7 .K
#C .;X #C @+ .;X #C -- #F .;X #B -- #G
.;X @+ #H .;X @+ #E @+ #C
.K #D .;X #C -- #F .;X #B @+ .;X @+ #H
.B4 @7 .;X -- #D77#B .;X #B -- #G .;X
@+ #E7 .K @7 .;X -- #D7#B .;X #B -- @7
.;X -- #D7#G .;X @+ @7 .;X -- #D7#E
.K #B .;X #C -- #H .;X #B -- #G .;X #B
@+ #BH .;X @+ #E .;X -- #BJ
.K #B .;X #C -- #AE .;X #B @+ #CC .;X
-- #BJ
,,EXAMPLES #A1 #B1 #D1 & #E
ON PP4 #CDF --#CDH = ,EXS4 #AG-BJ
,,EX]CISES
,P]=M ! 9DICAT$ OP],N4
.#AG4 7#E .;X #C -- .;X @+ #C7 @+ @7
.;X #C -- #I .;X #B @+ #D .;X @7
.#AH4 @7 .;X #C @+ #D .;X #B -- #E .;X
@7--7#D .;X #C @+ .;X #B -- #G7
.#AI4 @7 .;X -- #F77#E .;X #B @+ .;X
-- #H7
.#BJ4 @7 .;X -- #D7@7 .;X @+ #G77#E
.;X -- #A7
------------------------------------#DJD
#E ,,*APT] ,,REVIEW
#E.D ,FACTOR & ,SOLVE ,POLYNOMIAL
,EQU,NS PP4 #CEC-CEI
,,EXAMPLE
,FACTOR ! POLYNOMIAL -PLETELY4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.A4 .;X #C @+ #ABE .K .;X #C @+ #E #C
.K @7 .;X @+ #E7@7 .;X #B -- #E .;X @+
#BE7 @3 ..,SUM ( TWO .CUBES
.B4 .;X #C @+ #E .;X #B -- #I .;X --
#DE .K .;X #B @7 .;X @+ #E7--#I7 .;X @+
#E7 @3 .,FACTOR .0.GR\P+4
.K @7 .;X #B -- #I7@7 .;X @+ #E7 @3
.,4TRIBUTIVE .PROP]TY
.K @7 .;X @+ #C7@7 .;X --#C7@7 .;X @+
#E7 @3 ..,DI6];E ( TWO .SQU>ES
.C4 #C .;X #F @+ #AB .;X #D -- #IF .;X
#B .K #C .;X #B @7 .;X #D @+ #D .;X #B
-- #CB7 @3 .,FACTOR .-MON .MONOMIAL4
.K #C .;X #B @7 .;X #B -- #D7@7 .;X #B
@+ #H7 @3 ..,FACTOR TRINOMIAL 9
QUADRATIC .=M4
.K #C .;X #B @7 .;X @+ #B7@7 .;X --
#B7@7 .;X #B @+ #H7 @3 ..,DI6];E ( TWO
.SQU>ES
,,EXAMPLES #B1 #C1 #D1 & #F
ON PP4 #CED --#CEF = ,EXS4 #BA-BD
,,EX]CISES
,FACTOR ! POLYNOMIAL -PLETELY4
.#BA4 #FD .;X #C -- #H
.#BB4 #B .;X #E -- #AB .;X #C @+ #AJ
.;X
.#BC4 #B .;X #C -- #G .;X #B -- #H .;X
@+ #BH
.#BD4 .,,SCULPTURE ,Y H #BDJ CUBIC
9*ES ( CLAY ) : 6MAKE A SCULPTURE %AP$ Z
A RECTANGUL> PRISM4 ,Y WANT ! WID? 6BE
#D 9*ES LESS ?AN ! L5G? &! HEI<T 6BE #B
9*ES M ?AN #C "TS ! L5G?4 ,:AT %D !
DIM5.NS (! SCULPTURE BE8
#E.E ,APPLY ! ,REMA9D] & ,FACTOR
,!OREMS PP4 #CFB-CFH
,,EXAMPLE
.,DIVIDE .;F7.;X7 .K #D .;X #D @+ #BI
.;X #C @+ #D .;X #B -- #AD .;X @+ #CG
0.;X @+ #G4
,REWRITE ! DIVISOR 9 ! =M .;X -- .;K
@4 ,2C .;X @+ #G .K .;X -- 7--#G71 .;K
.K --#G4
,S1
,,EXAMPLES #A1C1 & #D
ON PP4 #CFB-CFD = ,EXS4 #BE-CB
,,EX]CISES
,DIVIDE4
.#BE4 @7 .;X #C -- #C .;X #B -- .;X --
#AJ7 @/ @7 .;X #B @+ #C .;X -- #A7
.#BF4 7#D .;X #D -- #AG .;X #B @+ #I
.;X -- #AH7 @/ #B .;X #B -- #B7
.#BG4 7#B .;X #C -- ;LL .;X #B @+ #AC
.;X -- #DD7 @/ @7 .;X -- #E7
.#BH4 7#E .;X #D @+ #B .;X #B -- #AE
.;X @+ #AJ7 @/ @7 .;X @+ #B7
,GIV5 POLYNOMIAL .;F7.;X7 &A FACTOR (
.;F7.;X7 @1 FACTOR .;F7.;X7 -PLETELY4
.#BI4 .;F7.;X7 .K .;X #C -- #E .;X #B
-- #B .;X @+ #BD2 .;X @+ #B
.#CJ4 .;F7.;X7 .K .;X #C -- ;LL .;X #B
@+ #AD .;X @+ #HJ2 .;X -- #H
.#CA4 .;F7.;X7 .K #I .;X #C -- #I .;X
#B -- #D .;X @+ #D2 .;X -- #A
.#CB4 .;F7.;X7 .K #B .;X #C @+ #G .;X
#B -- #CC .;X -- #AH2 .;X @+ #F
------------------------------------#DJE
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,*APT] ,REVIEW ,PRACTICE
#E.F ,F9D ,R,NAL ,Z]OS PP4 #CGJ-CGG
,,EXAMPLE
,F9D ALL R1L Z]OS ( .;F7.;X7 .K .;X #C
@+ #F .;X #B @+ #E .;X -- #AB4
,! L1D+ COE6ICI5T IS #A &! 3/ANT T]M
IS --#AB4
,POSSI# R,NAL Z]OS3
,TE/ ^! Z]OS US+ SYN!TIC DIVI.N4 ,TE/
.;X .K #A3
,Y C WRITE .;F7.;X7 .K @7 .;X -- ;L7@7
.;X #B @+ #G .;X @+ #AB74 ,FACTOR !
TRINOMIAL4
.;F7.;X7 .K @7 .;X -- ;L7@7 .;X #B @+
#G .;X @+ #AB7 .K @7 .;X -- ;L7@7 .;X @+
#C7@7 .;X @+ #D7
,! Z]OS ( .;F >E #A1 --#C1 & --#D4
,,EXAMPLES #B & #C
ON PP4 #CGA --#CGB = ,EXS4 #CC-CD
,,EX]CISES
,F9D ALL R1L Z]OS (! FUNC;N4
.#CC4 .;F7.;X7 .K .;X #C -- #D .;X #B
--#AA .;X @+ #CJ
.#CD4 .;F7.;X7 .K #B .;X #D -- .;X #C
-- #DB .;X #B @+ #AF .;X @+ #AFJ
#E.G ,APPLY ! ,FUNDA;TAL ,!OREM (
,ALGEBRA PP4 #CGI-CHF
,,EXAMPLE
,WRITE A POLYNOMIAL FUNC;N .;F ( L1/
DEGREE T HAS R,NAL COE6ICI5TS1 A L1D+
COE6ICI5T ( #A1 & --#D & Z Z]OS4
,2C IS A Z]O1 M/ AL 2 A Z]O4
,,EXAMPLES #C & #F
ON PP4 #CHA-CHC = ,EXS4 #CE-CH
,,EX]CISES
,WRITE A POLYNOMIAL FUNC;N .;F ( L1/
DEGREE T HAS R,NAL COE6ICI5TS1 A L1D+
COE6ICI5T ( #A1 &! GIV5 Z]OS4
.#CE4 --#D1 #A1 #E
.#CF4 --#A1 --#A1 #F1 #C .;I
.#CG4
.#CH4 .,,ECONOMICS ,=! #AE YE>S T A
-PUT] /ORE HAS BE5 OP51 XS ANNUAL REV5UE
.;,R 7IN MILLIONS ( DOLL>S7 C 2 MODEL$
BY
.;,R .K--#J.JJDJ .;T #D @+ #J.JHH .;T
#C -- #J.CF .;T #B -- #J.EE .;T @+ #E.H
": .;T IS ! NUMB] ( YE>S S9CE ! /ORE
OP5$4 ,9 :AT YE> 0 ! REV5UE F/ GRT] ?AN
4#G MILLION8
------------------------------------#DJF
#E ,,*APT] ,,REVIEW
#E.H ,ANALYZE ,GRAPHS ( ,POLYNOMIAL
,FUNC;NS PP4 #CHG-CIB
,,EXAMPLE
..,GRAPH ! FUNC;N ;F7;X7 .K .;X #C --
..#D ;X @+ .#B @4 ,ID5TIFY ! .;X
-9T]CEPTS &! PO9TS ": ! LOCAL MAXIMUMS &
LOCAL M9IMUMS O3UR4
,USE A GRAPH+ CALCULATOR 6GRAPH !
FUNC;N4
,NOTICE T ! GRAPH HAS ?REE .;X
-9T]CEPTS & TWO TURN+ PO9TS4 ,Y C USE !
GRAPH+ CALCULATOR'S .Z]O1 .MAXIMUM @1 &
.M9IMUM F1TURES 6APPROXIMATE !
COORD9ATES (! PO9TS4
,! .;X -9T]CEPTS (! GRAPH >E AB
--#B.BA1 #J.ED1 & #A.FH4 ,! FUNC;N HAS A
LOCAL MAXIMUM AT 7--#A.AE1 #E.JH7 &A
LOCAL M9IMUM AT 7#A.AE1 --#A.JH74
,,EXAMPLE #B
ON P4 #CHH = ,EXS4 #CI-DJ
,,EX]CISES
,USE A GRAPH+ CALCULATOR 6GRAPH !
FUNC;N4 ,ID5TIFY ! .;X -9T]CEPTS &!
PO9TS ": ! LOCAL MAXIMUMS & LOCAL
M9IMUMS O3UR4
.#CI4 .;F7.;X7 .K --#B .;X #C -- #C
.;X #B -- #A
.#DJ4 .;F7.;X7 .K .;X #D @+ #C .;X #C
-- .;X #B -- #H .;X @+ #B
#E.I ,WRITE ,POLYNOMIAL ,FUNC;NS &
,MODELS PP4 #CIC-CII
,,EXAMPLE
,USE F9ITE DI6];ES &A SY/EM ( EQU,NS
6F9D A POLYNOMIAL FUNC;N T FITS ! DATA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #A3 #B3 #C3 #D3 #E3 #F
.;F7.;X7 @3 #A3 #I3 #BC3 #DC3 #FI3
#AJA
,2C ! SECOND-ORD] DI6];ES >E 3/ANT1 !
DATA C 2 REPRES5T$ 0A FUNC;N (! =M
.;F7.;X7 .K .AX #B @+ .BX @+ .;C @4
,0SUB/ITUT+ ! F/ #C DATA PO9TS 96!
FUNC;N1 Y OBTA9 A SY/EM ( #C L9E> EQU,NS
9 #C V>IA#S4
,SOLVE ! SY/EM4 ,! SOLU;N IS 7#C1
--#A1 --#A71 S .;F7.;X7 .K #C .;X #B --
.;X -- #A4
,,EXAMPLE #C
ON P4 #CIE = ,EX4 #DA
,,EX]CISES
.#DA4 ,USE F9ITE DI6];ES 6F9D A
POLYNOMIAL FUNC;N T FITS ! DATA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #A3 #B3 #C3 #D3 #E3 #F
.;F7.;X7 @3 --#F3 --#BA3 --#DJ3 --#EG3
--#FF3 --#FA
------------------------------------#DJG
#E ,*APT] ,TE/
,SIMPLIFY ! EXPRES.N4 ,TELL :
PROP]TIES ( EXPON5TS Y US$4
.#A4 .;X #C @* .;X #B @* .;X --#D
.#B4 7#B .;X --#B .;Y #C @7 --#E
.#C4
.#D4
,GRAPH ! POLYNOMIAL FUNC;N4
.#E4 .;F7.;X7 .K -- .;X #C
.#F4 .;F7.;X7 .K .;X #D -- #B .;X #B
-- #E .;X @+ #A
.#G4 .;F7.;X7 .K .;X #E -- .;X #D --
#I
,P]=M ! 9DICAT$ OP],N4
.#H4 7#B .;X #C @+ #E .;X #B -- #G .;X
@+ #D7 @+ @7 .;X #C -- #C .;X #B -- #D
.;X @7
.#I4 7#C .;X #C -- #D .;X #B @+ #C .;X
-- #E7--@7 .;X #B @+ #D .;X -- #H7
.#AJ4 7#C .;X -- #B7@7 .;X #B @+ #D
.;X -- #G7
.#AA4 7#C .;X -- #E7 #C
.#AB4 7#C .;X #C -- #AD .;X #B @+ #AF
.;X -- #BB7 @/ @7 .;X -- #D7
.#AC4 7#F .;X #D @+ #G .;X #B @+ #D
.;X -- #AG7 @/ 7#C .;X #B -- #C .;X @+
#B7
,FACTOR ! POLYNOMIAL -PLETELY4
.#AD4 #H .;X #C @+ #BG
.#AE4 .;X #D @+ #E .;X #B -- #F
.#AF4 .;X #C -- #C .;X #B -- #D .;X @+
#AB
,F9D ALL R1L Z]OS (! FUNC;N4
.#AG4 .;F7.;X7 .K .;X #C @+ .;X #B --
#BB .;X -- #DJ
.#AH4 .;F7.;X7 -- #D .;X #D -- #H .;X
#C -- #AI .;X #B @+ #BC .;X -- #F
,WRITE A POLYNOMIAL FUNC;N .;F ( L1/
DEGREE T HAS R,NAL COE6ICI5TS1 A L1D+
COE6ICI5T ( #A1 &! GIV5 Z]OS4
.#AI4 --#A1 #C1 #D
.#BJ4 #F1 #B .;I
.#BA4 --#C1 --#A1
.#BB4 #A @+ #C .;I @1
,USE A GRAPH+ CALCULATOR 6GRAPH !
FUNC;N4 ,ID5TIFY ! .;X -9T]CEPTS &!
PO9TS ": ! LOCAL MAXIMUMS & LOCAL
M9IMUMS O3UR4
.#BC4 .;F7.;X7 .K .;X #C -- #E .;X #B
@+ #C .;X @+ #D
.#BD4 .;F7.;X7 .K .;X #D @+ #C .;X #C
-- .;X #B -- #F .;X @+ #B
,USE F9ITE DI6];ES &A SY/EM ( EQU,NS
6F9D A POLYNOMIAL FUNC;N T FITS ! DATA 9
! TA#4
#BE4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #A3 #B3 #C3 #D3 #E3 #F
.;F7.;X7 @3 #C3 #A3 #A3 #C3 #G3 #AC
#BF4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #A3 #B3 #C3 #D3 #E3 #F
.;F7.;X7 @3 #J3 --#G3 --#D3 #BA3 #HJ3
#AHE
..#BG4 ,,GROSS ,,DOME/IC .,,PRODUCT ,9
#BJJC1 ! GROSS DOME/IC PRODUCT 7,,GDP7
(! ,UNIT$ ,/ATES 0 AB #A.JII * #AJ #AC
DOLL>S4 ,! POPUL,N (! ,U4,S4 9 #BJJC 0
AB #B.IA * #AJ #H @4 ,:AT 0 ! P] CAPITA
,,GDP 9 #BJJC8
.#BH4 .,,TELEVI.N ,F #AIHJ 6#BJJB1 !
NUMB] .;,T 7IN MILLIONS7 ( H\SEHOLDS 9 !
,UNIT$ ,/ATES ) TELEVI.NS &! P]C5T .;,P
( ^? H\SEHOLDS ) ,,VCR,'S C 2 MODEL$ BY
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,T .K #A.BB .;X @+ #GF.I @3 &3 .;,P
.K --#J.BJE .;X #B @+ #H.CF .;X @+ #A.IH
": .;X IS ! NUMB] ( YE>S S9CE #AIHJ4
,WRITE A POLYNOMIAL MODEL =! TOTAL NUMB]
( ,U4,S4 H\SEHOLDS ) BO? TELEVI.NS &
,,VCR,'S4
.#BI4 .,,GEOMETRY ,A RECTANGUL> PRISM
HAS $GES ( L5G?S .;X1 .;X @+ #B1 & #B
.;X -- #C 9*ES4 ,! VOLUME (! PRISM IS
#AJDJ CUBIC 9*ES4 ,WRITE A POLYNOMIAL
EQU,N T MODELS ! PRISM'S VOLUME4 ,:AT >E
! PRISM'S DIM5.NS8
------------------------------------#DJH
#E ,/&>DIZ$ ,TE/ ,PREP>,N
,,%ORT ,,RESPONSE ,,"QS
,,PRO#M
,! WID? (A RECTANGUL> PRISM IS #B
MET]S LESS ?AN XS L5G?1 &! HEI<T IS #A
MET] LESS ?AN XS WID?4 ,! VOLUME (!
PRISM IS #CJ CUBIC MET]S4 ,F9D ! DIM5.NS
(! PRISM4 .,EXPLA9 YR R1SON+4
,SIDEB>3
,SCOR+ ,RUBRIC
99 SOLU;N IS -PLETE & CORRECT
,"PIAL ,CR$IT
99 SOLU;N IS -PLETE B HAS ]RORS1 OR
99 SOLU;N IS )\T ]ROR B 9COMPLETE
,NO ,CR$IT
99 NO SOLU;N IS GIV51 OR
99 SOLU;N MAKES NO S5SE
,2L >E SAMPLE SOLU;NS 6! PRO#M4 ,R1D
EA* SOLU;N &! -;TS 9 BLUE 6SEE :Y !
SAMPLE REPRES5TS FULL CR$IT1 "PIAL
CR$IT1 OR NO CR$IT4
,,SAMPLE #A3 ,FULL CR$IT SOLU;N
,! EXPRES.NS =! DIM5.NS >E CLE>LY
EXPLA9$4
,LET ! L5G? (! PRISM 2 .;X @4
,! WID? IS #B MET]S LESS ?AN ! L5G?1 S
WID? .K .;X -- #B4
,! HEI<T IS #A MET] LESS ?AN ! WID?1 S
HEI<T .K @7 .;X -- #B7--#A .K .;X -- #C4
,! VOLUME (A RECTANGUL> PRISM IS !
PRODUCT ( XS L5G?1 WID?1 & HEI<T4
,! EQU,N IS CORRECT & ALL /EPS >E
CLE>LY %[N4
#CJ .K .;X @7 .;X -- #B7 @7 .;X -- #C7
.,WRITE .EQU,N4
#CJ .K .;X @7 .;X #B -- #E .;X @+ #F7
.,MULTIPLY .BINOMIALS4
#J .K .;X #C -- #E .;X #B @+ #F .;X --
#CJ ..,WRITE 9 /&>D .=M4
#J .K .;X #B @7 .;X -- #E7 @+ #F7 .;X
-- #E7 .,FACTOR .0.GR\P+4
#J .K @7 .;X #B @+ #F7@7 .;X -- #E7
.,4TRIBUTIVE .PROP]TY
,! SOLU;N (! EQU,N IS CORRECT4
,! ONLY R1L SOLU;N IS .;X .K #E4 ,!
FACTOR .;X #B @+ #F DOES N PRODUCE ANY
R1L SOLU;NS4
,USE SUB/ITU;N 6F9D ! DIM5.NS3 L5G? .K
.;X .K #E MET]S
WID? .K .;X -- #B .K #E--#B .K #C
MET]S
HEI<T .K .;X -- #C .K #E--#C .K #B
MET]S
,! DIM5.NS >E CORRECT4
,! PRISM IS #E MET]S L;G1 #C MET]S
WIDE1 & #B MET]S HI<4
,,SAMPLE #B3 ,"PIAL CR$IT SOLU;N
,! EQU,N IS CORRECT4
,LET L5G? .K .;X @1 WID? .K .;X -- #B1
& HEI<T .K .;X -- #C4
#CJ .K .;X @7 .;X -- #B7@7 .;X -- #C7
#J .K .;X #C -- #E .;X #B @+ #F .;X --
#CJ
#J .K @7 .;X #B @+ #F7@7 .;X -- #E7
,IMAG9>Y SOLU;NS %D 2 4C>D$4 ,DIM5.NS
>E N GIV54
------------------------------------#DJI
,SAMPLE #C3 ,NO CR$IT SOLU;N
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,! EQU,N IS 9CORRECT43 ,! VOLUME (A
PRISM IS ! L5G? CUB$4
.;X #C .K #CJ
.;X #C.AA
,! ANSW] IS 9CORRECT43 ,! L5G? (!
PRISM IS #C.AA MET]S4
,SIDEB>3
,/&>DS
#D.J ,/UD5TS FACTOR POLYNOMIALS
REPRES5T+ ! DI6];E ( SQU>ES1 P]FECT
SQU>E TRINOMIALS1 &! SUM & DI6];E ( TWO
CUBES4
.,,PRACTICE ,APPLY ! ,SCOR+ ,RUBRIC
,USE ! RUBRIC ON PAGE #DJH 6SCORE !
SOLU;N 6! PRO#M 2L Z ..FULL CR$IT ;Y
"PIAL .CR$IT @1 OR .NO .CR$IT4 .,EXPLA9
YR R1SON+4
.,,PRO#M ,! VOLUME (A SPH]E ) RADIUS
.;R IS GIV5 0! FUNC;N ,GRAPH ! FUNC;N4
,!N USE ! GRAPH 6E/IMATE ! RADIUS (A
SPH]E )A VOLUME ( #GEJ CUBIC FEET4
.L4 ,! .TA# %[S .! VOLUMES ( SPH]ES )
RADII F ..#J 6#G .FEET4 ,ONLY POSITIVE
;R--VALUES MAKE S5SE4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;R @3 #J3 #A3 #B3 #C3 #D3 #E3 #F3 #G
.;,V @3 #J3 #D.AHI3 #CC.EA3 #AAC.A3
#BFB.A3 #EBC.F3 #IJD.H3 #ADCG
,F ! GRAPH1 Y .C SEE T ! .;R
-COORD9ATE T CORRESPOND ;E 6A .;,V
-COORD9ATE ( #GEJ IS AB #E.F4
,A SPH]E )A VOLUME ( #GEJ CUBIC FEET
HAS A RADIUS ( AB #E.F FEET4
.#B4 ,! TA# %[S ! VOLUME ;,V (A SPH]E
) RADIUS .;R @4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;R @3 #J3 #B3 #D3 #F3 #E3 #AJ
.;,V @3 #J3 #AJ.FG3 #HE.CC3 #BHH.J3
#FEB.G3 #ACCC
,! .;R -COORD9ATE T CORREEPOND ;E 6A
.;,V -COORD9ATE ( #GEJ IS #E.B1 S !
RADIUS (A SPH]E )A VOLUME ( #GEJ CUBIC
FEET IS AB #H.B FEET4
------------------------------------#DAJ
#E ,/&>DIZ$ ,TE/ ,PRACTICE
,,%ORT ,,RESPONSE
.#A4 ,S9CE #AIFJ1 ! NUMB] ( VOT]S .;Y
7IN MILLIONS7 9 ,UNIT$ ,/ATES F$]AL
ELEC;NS C 2 MODEL$ 0! FUNC;N
.;Y .K --#J.JJJF .;X #C @+ #J.JCHC .;X
#B @+ #J.CHC .;X @+ #FH.F
": .;X IS ! NUMB] ( YE>S S9CE #AIFJ4
,AC 6! MODEL1 H[ _M M P VOT$ 9 #AIHJ ?AN
9 #AIFJ8 .,EXPLA9 YR R1SON+4
.#B4 ,%[ TWO DI6]5T WAYS 6EVALUATE !
POLYNOMIAL --#C .;X #D -- #B .;X #C @+
#G .;X #B -- #I :5 .;X .K --#D4
.#C4 ,:AT DOES ! GRAPH (! POLYNOMIAL
FUNC;N TELL Y AB ! SIGN (! L1D+
COE6ICI5T1 ! DEGREE (! FUNC;N1 &! NUMB]
( R1L Z]OS8 .,EXPLA9 YR R1SON+4
.#D4 ,S9CE #AIGJ1 ! AV]AGE FUEL
E6ICI5CY .;,E 7IN MILES P] GALLON7 = ALL
VEHICLES 9 ! ,UNIT$ ,/ATES C 2 MODEL$ 0!
FUNC;N
.;,E .K --#J.JJJG .;T #C @+ #J.JBGH
.;T #B -- #J.JHDC .;T @+ #AB.J
": .;T IS ! NUMB] ( YE>S S9CE #AIGJ4
,USE A GRAPH+ CALCULATOR 6GRAPH !
FUNC;N1 & ID5TIFY ANY TURN+ PO9TS ON !
9T]VAL #J "K.K .;T "K.K #CJ4 ,:AT
R1L-LIFE M1N+ DOES A TURN+ PO9T H 9 ?
SITU,N8
.#E4 ,C Y USE ! R,NAL Z]O !OREM 6F9D !
Z]OS (! POLYNOMIAL FUNC;N .;F @7 .;X @7
.K #C .;X #D -- #B .;X #C @+ #A.E .;X #B
-- #I8 .,EXPLA9 :Y OR :Y N4
.#F4 ,! PR(IT .;,P 7IN MILLIONS (
DOLL>S7 =A MANUFACTUR] ( W9T] COATS C 2
MODEL$ 0.;,P .K -- .;X #C @+ #C .;X #B
@+ #AE .;X ": .;X IS ! NUMB] ( W9T]
COATS PRODUC$ 7IN MILLIONS74 ,CURR5TLY1
! -PANY PRODUCES #E MILLION W9T] COATS &
MAKES A PR(IT ( 4#BE1JJJ1JJJ4 .,EXPLA9
H[ ! -PANY C MAKE ! SAME PR(IT 0PRODUC+
A LESS] NUMB] ( COATS4
.#G4 ,! VOLUME (! RECTANGUL> PRISM %[N
2L IS GIV5 0! EXPRES.N #B .;X #C @+ #E
.;X #B -- #AI .;X -- #DB4
,WRITE A POLYNOMIAL 9 /&>D =M T
REPRES5TS ! >EA (! BASE (! PRISM4 ,%[
ALL ( YR /EPS4
.#H4 ,F #AIIJ 6#BJJC1 ! NUMB] ( ;,,CD
S+LES 7IN MILLIONS7 SOLD 9 ! ,UNIT$
,/ATES C 2 MODEL$ 0! POLYNOMIAL FUNC;N
.;Y .K #J.JAD .;X #E -- #J.DJ .;X #D @+
#C.H;X #C -- #AC .;X #B @+ #AE .;X @+
#A.B ": .;X IS ! NUMB] ( YE>S S9CE
#AIIJ4
.A4 ,USE A GRAPH+ CALCULATOR 6GRAPH !
FUNC;N ON ! DOMA9 #J "K.K .;X "K.K #AC4
,AC 6! MODEL1 9 : YE> 7 ! MO/ ;,,CD
S+LES SOLD8
.B4 ,D Y ?9K T SALES W 3T9UE 6FOLL[ !
MODEL 9DEF9ITELY8 .,EXPLA9 YR R1SON+4
.#I4 ,USE F9ITE DI6];ES &A SY/EM (
EQU,NS 6F9D A POLYNOMIAL FUNC;N T FITS !
DATA 9 EA* TA#4 ,!N F9D .;F @7 .;X @7 @+
.;G @7 .;X @7@4 .,EXPLA9 ALL ( YR /EPS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #A3 #B3 #C3 #D3 #E3 #F
.;F @7 .;X @7 @3 #D3 #I3 #BF3 #EG3
#AJD3 #AFI
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #A3 #B3 #C3 #D3 #E3 #F
.;G @7 .;X @7 @3 --#B3 --#B3 #AB3 #EB3
#ACJ3 #BEH
.#AJ4 ,! POPUL,N (! ,UNIT$ ,/ATES 9
#AHJJ 0 #E.CJH * #AJ #F @1 &! L& >EA 0
#H.FDG * #AJ #E SQU>E MILES4 ,0#BJJJ1 !
POPUL,N _H 9CR1S$ 6#B.HAD * #AJ #H @1 &!
L& >EA 0 #C.ECG * #AJ #F SQU>E MILES4
,0H[ _M P P] SQU>E MILE ( L& DID !
POPUL,N D5S;Y 9CR1SE F #AHJJ 6#BJJJ8
.,EXPLA9 YR R1SON+4
------------------------------------#DAA
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,,MULTIPLE-,,*OICE
#AA4 ,: EXPRES.N IS EQUIVAL5T TO @8
,A4
,B4
C4 @7 .;X --#A .;Y #B .;Z #B @7 #B @7
.;X --#A .;Y #A .;Z #B @7 --#D
,D4
#AB4 ,:AT >E ALL ! R1L SOLU;NS (!
EQU,N .;X #D .K #ABE .;X @8
,A4 #J
,B4 #J1 #E1 --#E
,C4 #J1E
,D4 #J1 #E .;I @1 --#E .;I
#AC4 ,: POLYNOMIAL FUNC;N HAS --#A1
#C1 & --#D .;I Z Z]OS8
,A4 .;F7.;X7 .K .;X #D -- #B .;X #C @+
#AC .;X #B -- #CB .;X -- #DH
,B4 .;F7.;X7 .K .;X #D @+ #B .;X #C @+
#AC .;X #B @+ #CB .;X -- #DH
,C4 .;F7.;X7 .K .;X #D -- #B .;X #C --
#AI .;X #B @+ #CB .;X @+ #DH
,D4 .;F7.;X7 .K .;X #D @+ #B .;X #C @+
#AI .;X #B -- #CB .;X @+ #DH
,,GRI4$ ,,ANSW]
.#AD4 ,GIV5 T .;P @7 .;X @7 IS A
POLYNOMIAL ( DEGREE #F & .;Q @7 .;X @7
IS A POLYNOMIAL ( DEGREE #C1 :AT IS !
DEGREE (! POLYNOMIAL DEF9$ 0#C 99 .;P @7
.;X @7--#B 99 .;Q @7 .;X @7@8
.#AE4 ,H[ _M .R1L Z]OS DOES ! FUNC;N
.;F @7 .;X @7 .K #B .;X #D @+ #C .;X #B
-- #A H8
.#AF4 ,EVALUATE ! EXPRES.N @4
.#AG4 ,:AT IS ! VALUE (! FUNC;N .;F @7
.;X @7 .K #D .;X #D -- .;X #C @+ #B .;X
#B -- #C :5 .;X .K #D8
.#AH4 ,! GRAPH (A QU>TIC FUNC;N IS
%[N4 ,H[ _M IMAG9>Y Z]OS DOES ! FUNC;N
H8
.#AI4 ,USE ! R,NAL Z]O !OREM 6DET]M9E
! NUMB] ( .POSSI# R,NAL Z]OS =! FUNC;N
.;F @7 .;X @7 .K #AE .;X #D @+ #F .;X #C
-- #H .;X #B -- #I4
,,EXT5D$ ,,RESPONSE
#BJ4 ,Y >E MAK+ AN OP5 BOX 6HOLD PAP]
CLIPS \ (A PIECE ( C>DBO>D T IS #E 9*ES
0#H 9*ES4 ,! BOX W 2 =M$ 0MAK+ ! CUTS
%[N 9 ! DIAGRAM & FOLD+ UP ! SIDES4 ,Y
WANT ! BOX 6H ! GRTE/ VOLUME POSSI#4
A4 ,USE A GRAPH+ CALCULATOR 6F9D H[
L;G Y %D MAKE ! CUTS4 .,EXPLA9 YR
R1SON+4
B4 ,:AT IS ! MAXIMUM VOLUME (! BOX8
C4 ,:AT W ! DIM5.NS (! F9I%$ BOX BE8
#BA4 ,F #AIHJ 6#BJJB1 ! NUMB] (
HOSPITALS .;,H 9 ! ,UNIT$ ,/ATES &!
AV]AGE NUMB] ( HOSPITAL B$S .;,B 9 EA*
HOSPITAL C 2 MODEL$ BY
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,H .K --#EH.G .;T @+ #GJGJ @3 &3
.;,B .K #J.JJFF .;T #C -- #J.AIB .;T #B
-- #J.AGD .;T @+ #AIF
": .;T .IS ! NUMB] ( YE>S S9CE #AIHJ4
A4 ,WRITE A MODEL =! TOTAL NUMB] (
HOSPITAL B$S 9 ,U4,S4 HOSPITALS4
B4 ,AC 6! MODEL1 H[ _M B$S 7 9 ,U4,S4
HOSPITALS 9 #AIIE8
C4 ,H[ DOES ! MODEL *ANGE IF Y WANT
6F9D ! NUMB] ( HOSPITAL B$S .9 .?\S&S8
.,EXPLA9 YR R1SON+4
------------------------------------#DAB
#F ,R,NAL ,EXPON5TS & ,RADICAL
,FUNC;NS
#F.A ,EVALUATE N? ,ROOTS & ,USE ,R,NAL
,EXPON5TS
#F.B ,APPLY ,PROP]TIES ( ,R,NAL
,EXPON5TS
#F.C ,P]=M ,FUNC;N ,OP],NS & ,-POSI;N
#F.D ,USE ,9V]SE ,FUNC;NS
#F.E ,GRAPH ,SQU>E ,ROOT & CUBE ROOT
,FUNC;NS
#F.F ,SOLVE ,RADICAL ,EQU,NS
,SIDEB>3
,2F
,9 PREVI\S *APT]S1 Y LE>N$ ! FOLL[+
SKILLS1 : Y'LL USE 9 ,*APT] #F3
SIMPLIFY+ EXPRES.NS 9VOLV+ EXPON5TS1
REWRIT+ EQU,NS1 & GRAPH+ POLYNOMIAL
FUNC;NS4
,PREREQUISITE ,SKILLS
,,VOCABUL>Y ,,*ECK
,COPY & -PLETE ! /ATE;T4
.#A4 ,! .SQU>E .ROOTS ( #HA >E @8 & @8
@4
.#B4 ,9 ! EXPRES.N #B #E @1 ! .EXPON5T
IS @8 @4
#C4 ,=! POLYNOMIAL FUNC;N ^: GRAPH IS
%[N ! SIGN (! .L1D+ .COE6ICI5T IS @8 @4
,,SKILLS ,,*ECK
,SIMPLIFY ! EXPRES.N4 7.,REVIEW P4
#CCJ .= .#F..B47
.#D4
.#E4
.#F4 7#B .;X #E .;Y --#C @7 --#C
,SOLVE ! EQU,N = .Y4 7.,REVIEW P4 #BF
.= .#F..D47
.#G4 --#B .;X -- #E .;Y .K #AJ
.#H4
.#I4 #H .;X -- #D .XY .K #C
,GRAPH ! POLYNOMIAL FUNC;N4 7.,REVIEW
P4 #CCG .= .#F..E47
.#AJ4 .;F7.;X7 .K .;X #C -- #D .;X @+
#F
.#AA4 .;F7.;X7 .K -- .;X #E @+ #G .;X
#B @+ #B
.#AB4 .;F7.;X7 .K .;X #D -- #D .;X #B
@+ .;X
,PRODNOTE3 ,PRODUC;N NOTE3 ? IMAGE
CROSSES ! GUTT] 6APPE> BO? ON PAGE #DAB
& PAGE #DAC 9 ! PR9T V].N4
------------------------------------#DAC
,PRODNOTE3 ,PRODUC;N NOTE3 ? IMAGE
CROSSES ! GUTT] 6APPE> BO? ON PAGE #DAB
& PAGE #DAC 9 ! PR9T V].N4 ,SIDEB>3
,N[
,9 ,*APT] #F1 Y W APPLY ! BIG ID1S
LI/$ 2L & REVIEW$ 9 ! ,*APT] ,SUMM>Y ON
PAGE #DFE @4 ,Y W AL USE ! KEY VOCABUL>Y
LI/$ 2L4
,BIG ,ID1S
#A ,US+ R,NAL EXPON5TS
#B ,P]=M+ FUNC;N OP],NS & F9D+ 9V]SE
FUNC;NS
#C ,GRAPH+ RADICAL FUNC;NS & SOLV+
RADICAL EQU,NS
,KEY ,VOCABUL>Y
99 N? ROOT (A1 P4 #DAD
99 9DEX (A RADICAL1 P4 #DAD
99 SIMPLE/ =M (A RADICAL1 P4 #DBB
99 L RADICALS1 P4 #DBB
99 P[] FUNC;N1 P4 #DBH
99 -POSI;N1 P4 #DCJ
99 9V]SE REL,N1 P4 #DCH
99 9V]SE FUNC;N1 P4 #DCH
99 RADICAL FUNC;N1 P4 #DDF
99 RADICAL EQU,N1 P4 #DEB
,SIDEB>3
,:Y8
,Y C USE A RADICAL FUNC;N 6MODEL ! "T
Y >E SUSP5D$ 9 ! AIR DUR+ A JUMP4 ,=
EXAMPLE1 ! HANG "T (A BASKETBALL PLAY] C
2 MODEL$ 0A RADICAL FUNC;N4
.,ANIMAT$ ,ALGEBRA
,! ANIM,N ILLU/RAT$ 2L = ,EX]CISE #FJ
ON PAGE #DEH HELPS Y ANSW] ? "Q3 ,:AT IS
! REL,N%IP 2T ! HEI<T (A JUMP &! "T !
JUMP] IS SUSP5D$ 9 AIR8
.,ANIMAT$ ,ALGEBRA AT
_+CLASSZONE.COM_:
,O!R ANIM,NS = ,*APT] #F3 PAGES #DCA
@1 #DDD @1 #DDH @1 & #DFE
------------------------------------#DAD
#F.A ,EVALUATE N? ,ROOTS & ,USE
,R,NAL ,EXPON5TS
.,2F ,Y EVALUAT$ SQU>E ROOTS & US$
PROP]TIES ( EXPON5TS4
.,N[ ,Y W EVALUATE N? ROOTS & /UDY
R,NAL EXPON5TS4
.,:Y8 ,S Y C F9D ! RADIUS (A SPH]ICAL
OBJECT1 Z 9 ,EX4 #FJ4
,KEY ,VOCABUL>Y
99 ..RA? ROOT ( .A
99 ..9DEX (A .RADICAL
,SIDEB>3
,/&>DS
..#AB.J ,/UD5TS "K ! LAWS ( FRAC;NAL
.EXPON5TS @1 "U/& EXPON5TIAL FUNC;NS1 &
USE ^! FUNC;NS 9 PRO#MS 9VOLV+
EXPON5TIAL GR[? & DECAY4
,Y C EXT5D ! 3CEPT (A SQU>E ROOT 6O!R
TYPES ( ROOTS4 ,= EXAMPLE1 #B IS A CUBE
ROOT ( #H 2C #B #C .K #H4 ,9 G5]AL1 = AN
9TEG] .;N GRT] ?AN #A1 IF .;B ;N.' .K .A
@1 !N .;B IS AN ..N? ROOT ( .A4 ,AN N?
ROOT (A IS WRITT5 Z ": .;N IS ! .9DEX (!
RADICAL4
,Y C AL WRITE AN .N? ROOT (A Z A P[]
(A4 ,IF Y ASSUME ! P[] (A P[] PROP]TY
APPLIES 6R,NAL EXPON5TS1 !N ! FOLL[+ IS
TRUE3
,2C .A #A/B IS A NUMB] ^: SQU>E IS .A
@1 Y C WRITE @1 ,SIMIL>LY1 & @4 ,9
G5]AL1 = ANY 9TEG] .;N GRT] ?AN #A4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,R1L N? ,ROOTS ( .A
,LET .;N 2 AN 9TEG] @7 .;N .1 #A7 &
LET A 2 A R1L NUMB]4
;N ..IS AN EV5 .9TEG]4
;N ..IS AN ODD .9TEG]4
,EXAMPLE #A ,F9D N? ROOTS
,F9D ! 9DICAT$ R1L RA? ROOT7;S7 (A4
.A4 .;N .K #C1 .A .K --#BAF
.B4 .;N .K #D1 .A .K #HA
,SOLU;N
.A4 ,2C .;N .K #C IS ODD & .A .K
--#BAF "K #J1 --#BAF HAS "O R1L CUBE
ROOT4 ,2C 7--#F7 #C .K --#BAF1 Y C WRITE
@4
.B4 ,2C .;N .K #D IS EV5 & .A .K #HA
.1 #J1 #HA HAS TWO R1L F\R? ROOTS4 ,2C
#C #D .K #HA & 7--#C7 #D .K #HA1 Y C
WRITE @4
------------------------------------#DAE
.,,R,NAL .,,EXPON5TS ,A R,NAL EXPON5T
DOES N H 6BE (! =M @4 ,O!R R,NAL NUMB]S
S* Z & C AL 2 US$ Z EXPON5TS4 ,TWO
PROP]TIES ( R,NAL EXPON5TS >E %[N 2L4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,R,NAL ,EXPON5TS
,LET A #A_/ .;N 2 AN N? ROOT (A1 & LET
.;M 2 A POSITIVE 9TEG]4
,EXAMPLE #B ,EVALUATE EXPRES.NS )
R,NAL EXPON5TS
,EVALUATE 7A7 #AF #C/B & 7;B7 #CB
--#C/E @4
,SOLU;N
,R,NAL ,EXPON5T ,=M
.A4 #AF #C/B .K 7#AF #A/B @7 #C .K #D
#C .K #FD
.B4
,RADICAL ,=M
,SIDEB>3
,AVOID ,]RORS
,2 SURE 6USE P>5!SES 65CLOSE A R,NAL
EXPON5T3 #I_<7#A/E7 #A.EEB4 ,)\T !M1 !
CALCULATOR EVALUATES A P[] & !N DIVIDES3
#I_<8#A/E .K #A.H4
,,EXAMPLE #C ,APPROXIMATE ROOTS )A
CALCULATOR
..,,GUID$ ,,PRACTICE = ,EXAMPLES #A1B1
& .#C
,F9D ! 9DICAT$ R1L N? ROOT7;S7 (A4
.#A4 .;N .K #D1 .A .K #FBE
.#B4 .;N .K #F1 .A .K #FD
.#C4 .;N .K #C1 .A .K --#FD
.#D4 .;N .K #E1 .A .K #BDC
,EVALUATE ! EXPRES.N )\T US+ A
CALCULATOR4
.#E4 #D #E/B
.#F4 #I --#A/B
.#G4 #HA #C/D
.#H4 #A #G/H
,EVALUATE ! EXPRES.N US+ A CALCULATOR4
,R.D ! RESULT 6TWO DECIMAL PLACES :5
APPROPRIATE4
.#I4 #D #B/E
.#AJ4 #FD --#B/C
.#AA4
.#AB4
------------------------------------#DAF
,,EXAMPLE #D ,SOLVE EQU,NS US+ N?
ROOTS
,SOLVE ! EQU,N4
.A4
.B4
,SIDEB>3
,AVOID ,]RORS
,:5 .;N IS EV5 & .A .1 #J1 2 SURE
63SID] BO? ! POSITIVE & NEGATIVE N?
ROOTS ( .A4
,,EXAMPLE #E ,USE N? ROOTS 9 PRO#M
SOLV+
.,,BIOLOGY ,A /UDY DET]M9$ T ! WEI<T
.;W 7IN GRAMS7 ( CORAL COD NE> ,PALAWAN
,ISL&1 ,PHILIPP9ES1 C 2 APPROXIMAT$ US+
! MODEL
.;W .K #J.JAFG .;L #C
": IS ! CORAL COD'S L5G? 7IN
C5TIMET]S74 ,E/IMATE ! L5G? (A CORAL COD
T WEI<S #BJJ GRAMS4
,SOLU;N
,A CORAL COD T WEI<S #BJJ GRAMS IS AB
#BC C5TIMET]S L;G4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #D &
.#E
,SOLVE ! EQU,N4 ,R.D ! RESULT 6TWO
DECIMAL PLACES :5 APPROPRIATE4
.#AC4 .;X #C .K #FD
.#AD4
.#AE4 #C .;X #B .K #AJH
.#AF4
.#AG4 @7 .;X -- #B7 #C .K --#AD
.#AH4 @7 .;X @+ #E7 #D .K #AF
#AI4 .,,:AT .,,IF @8 ,USE ! 9=M,N F
,EXAMPLE #E 6E/IMATE ! L5G? (A CORAL COD
T HAS ! GIV5 WEI<T4
A4 #BGE GRAMS
B4 #CDJ GRAMS
C4 #DEJ GRAMS
------------------------------------#DAG
#F.A ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS .ON P4
,,WS#AB ..= ,EXS4 #I1BE1 & .#FC
.K ..,,/&>DIZ$ ,,TE/ ,,PRACTICE ,EXS4
#B1 #CC1DF1DG1 & .#FE
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,9 !
EXPRES.N @1 ! NUMB] #D IS CALL$ ! @8 @4
.#B4 .,,WRIT+ .,EXPLA9 H[ ! SIGN ( .A
DET]M9ES ! NUMB] ( R1L F\R? ROOTS ( .A
&! NUMB] ( R1L FIF? ROOTS ( .A4
.,,EXAMPLE .#A ON P4 #DAD = ,EXS4
#C-BJ
,,MAT*+ ,,EXPRES.NS ,MAT* ! EXPRES.N 9
R,NAL EXPON5T NOT,N )! EQUIVAL5T
EXPRES.N 9 RADICAL NOT,N4
.#C4 #B #A/C .,A4
.#D4 #B #C/B .,B4
.#E4 #B #B/C .,C4
.#F4 #B #A/B .,D4
,,US+ ,,R,NAL ,,EXPON5T ,,NOT,N
,REWRITE ! EXPRES.N US+ R,NAL EXPON5T
NOT,N4
.#G4
.#H4
.#I4
.#AJ4
,,US+ ,,RADICAL ,,NOT,N ,REWRITE !
EXPRES.N US+ RADICAL NOT,N4
.#AA4 #E #A/D
.#AB4 #G #A/C
.#AC4 #AD #B/E
.#AD4 #BA #I/D
,,F9D+ ,,N? ,,ROOTS ,F9D ! 9DICAT$ R1L
N? ROOT7;S7 .( .A4
.#AE4 .;N .K .#B ;Y .A .K #FD
.#AF4 .;N .K #C1 .A .K --#BG
.#AG4 .;N .K #D1 .A .K #J
.#AH4 .;N .K #C1 .A .K #CDC
.#AI4 .;N .K #D1 .A .K --#AF
.#BJ4 .;N .K #E1 .A .K --#CB
.,,EXAMPLE .#B ON P4 #DAE = ,EXS4
#BA-CC
,,EVALUAT+ ,,EXPRES.NS ,EVALUATE !
EXPRES.N )\T US+ A CALCULATOR4
.#BA4
.#BB4 #H #A/C
.#BC4 #AF #C/B
.#BD4
7#BE7 #BG #B/C
.#BF4 7--#BDC7 #A/E
.#BG4
.#BH4
.#BI4
.#CJ4 #BE #C/B
.#CA4 #FD #B/C
.#CB4
.#CC4 .,,MULTIPLE .,,*OICE ,:AT IS !
VALUE ( #ABH #E/G @8
7.,A7 #H
7.;,B7 #AF
7.;,C7 #CB
7.;,D7 #FD
.,,EXAMPLE .#C ON P4 #DAE = ,EXS4
#CD-DF
,,APPROXIMAT+ ,,ROOTS ,EVALUATE !
EXPRES.N US+ A CALCULATOR4 ,R.D ! RESULT
6TWO DECIMALS PLACES :5 APPROPRIATE4
.#CD4
.#CE4
.#CF4
.#CG4 #HE #A/F
.#CH4 #BE- #A/C
.#CI4 #BJ1GCF #A/D
.#DJ4
.#DA4
.#DB4
.#DC4 #HF-- #E/F
.#DD4 #AIGD #B/G
.#DE4
.#DF4 .,,MULTIPLE .,,*OICE ,: EXPRES.N
HAS ! GRTE/ VALUE8
7,A7 #BG #C/E
7;,B7 #E #C/B
7;,C7
7;,D7
.#DG4 .,,OP5-.,,5D$ .,,MA? ,WRITE TWO
DI6]5T EXPRES.NS (! =M .A#A_/4 ;N.' .-T
EQUAL #C1 ": A IS A R1L NUMB] & .;N IS
AN 9TEG] GRT] ?AN #A4
------------------------------------#DAH
.,,EXAMPLE .#D ON P4 #DAF = ,EXS4
#DH-EH
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 SOLV+ ! EQU,N4
.#DH4
.#DI4
.,,SOLV+ .,,EQU,NS ,SOLVE ! EQU,N4
,R.D ! RESULT 6TWO DECIMAL PLACES :5
APPROPRIATE4
.#EJ4 .;X #C .K #ABE
.#EA4 #E .;X #C .K #AJHJ
.#EB4 .;X #F @+ #CF .K #AJJ
.#EC4 @7 .;X -- #E7 #D .K #BEF
.#ED4 .;X #E .K --#DH
.#EE4 #G .;X #D .K #EF
.#EF4 .;X #C @+ #DJ .K #BE
.#EG4 @7 .;X @+ #AJ7 #E .K #GJ
.#EH4 .;X #F -- #CD .K #AHA
#EI4 .,,*ALL5GE ,! G5]AL %APE (! GRAPH
( .;Y .K .;X ;N.' @1 ": .;N IS A
POSITIVE .EV5 9TEG]1 IS %[N 9 R$4
A4 .,EXPLA9 H[ ! GRAPH JU/IFIES !
RESULTS 9 ! ,KEY ,3CEPT BOX ON PAGE #DAD
:5 .;N IS A POSITIVE .EV5 9TEG]4
B4 ,DRAW A SIMIL> GRAPH T JU/IFIES !
RESULTS 9 ! ,KEY ,3CEPT BOX :5 .;N IS A
POSITIVE .ODD 9TEG]4
,,PRO#M ,,SOLV+
.,,EXAMPLE .#E ON P4 #DAF = ,EXS4
#FJ-FE
.#FJ4 .,,%OT .,,PUT ,! %OT US$ 9 M5'S
%OT PUT HAS A VOLUME ( AB #IJE CUBIC
C5TIMET]S4 ,F9D ! RADIUS (! %OT4 .,H9T3
,USE ! =MULA =! VOLUME (A SPH]E47
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#FA4 .,,B[L+ ,A B[L+ BALL HAS A
SURFACE >EA ( AB #BCB SQU>E 9*ES4 ,F9D !
RADIUS (! B[L+ BALL4 ,7.,H9T3 ,USE !
=MULA .;,S .K .,AVI #B =! SURFACE >EA (A
SPH]E47
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#FB4 .,,9FL,N ,IF ! AV]AGE PRICE ( AN
ITEM 9CR1SES F .;P #A 6.;P #B OV] A
P]IOD ( .;N YE>S1 ! ANNUAL RATE ( 9FL,N
.;R 7EXPRESS$ Z A DECIMAL7 IS GIV5 BY @4
,F9D ! RATE ( 9FL,N = EA* ITEM 9 ! TA#4
,WRITE EA* ANSW] Z A P]C5T R.D$ 6! NE>E/
T5?4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,ITEM3 ,PRICE 9 #AIEJ3 ,PRICE 9 #AIIJ
,BUTT] 7,IB73 @4#.GDBJ3 4#B1AIE
,*ICK5 7,IB73 @4#.DDCJ3 4#A1JHG
,E7S 7DOZ573 @4#.FGAJ3 4#A1CEF
,SUG> 7,IB73 @4#.JICF3 @4#.DEFJ
.#FC .,,MULTI-.,,/EP .,,PRO#M ,! P[]
.;P 7IN HORSEP[]7 US$ 0A FAN ) ROT,NAL
SPE$ .;S 7IN REVOLU;NS P] M9UTE7 C 2
MODEL$ 0! =MULA .;P .K .KS #C = "S 3/ANT
.K4 ,A C]TA9 FAN USES #A.B HORSEP[] :5
XS SPE$ IS #AGJJ REVOLU;NS P] M9UTE4 ,F/
F9D ! VALUE ( .;K = ? FAN4 ,!N F9D !
SPE$ (! FAN IF X USES #A.E HORSEP[]4
.K .,,"W$-.,,\ .,,SOLU;NS ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#DAI
.#FD4 .,,WAT] .,,RATE ,A .WEIR IS A
DAM T IS BUILT ACR A RIV] 6REGULATE !
FL[ ( WAT]4 ,! FL[ RATE ;,Q 7IN CUBIC
FEET P] SECOND7 C 2 CALCULAT$ US+ !
=MULA ;,Q .K #C.CFG;LH #C/B ": ;I IS !
L5G? 7IN FEET7 (! BOTTOM (! SPILLWAY &
.;H IS ! DEP? 7IN FEET7 (! WAT] ON !
SPILLWAY4 ,DET]M9E ! FL[ RATE (A WEIR )A
SPILLWAY T IS #BJ FEET L;G & HAS A WAT]
DEP? ( #E FEET4
#FE4 .,,EXT5D$ .,,RESPONSE ,"S GAMES
USE DICE 9 ! %APE ( REGUL> POLYH$RA4 ,Y
>E DESIGN+ DICE & WANT !M ALL 6H ! SAME
VOLUME Z A CUBE ) AN $GE L5G? ( #AF
MILLIMET]S4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,"N @3 .,TETRAH$RON @3 .,OCTAH$RON @3
.,DODECAH$RON @3 .COSAH$RON
.,NUMB] .( .FACES @3 #D3 #H3 #AB3 #BJ
.,VOLUME .=MULA @3 ;,V .K #J.AAH;X.'
#C @3 ;,V .K #J.DGA;X.' #C @3 .;,V .K
#G.FFC;X #C @3 ;,V .K #B.AHB99 #C
A4 ,F9D ! VOLUME (A CUBE ) AN $GE L5G?
( #AF MILLIMET]S4
B4 ,F9D ! $GE L5G? .;X = EA* (!
POLYH$RA %[N 9 ! TA#4
C4 ,DOES ! POLYH$RON )! GRTE/ NUMB] (
FACES H ! SMALLE/ $GE L5G?8 .,EXPLA94
#FF4 .,,*ALL5GE ,! MASS (! "PICLES T A
RIV] C TRANSPORT IS PROPOR;NAL 6! SIX?
P[] (! SPE$ (! RIV]4 ,A C]TA9 RIV]
NORM,Y FL[S AT A SPE$ ( #A MET] P]
SECOND4 ,:AT M/ XS SPE$ 2 9 ORD]
6TRANSPORT "PICLES T >E TWICE Z MASSIVE
Z USUAL8 #AJ "TS Z MASSIVE8 #AJJ "TS Z
MASSIVE8
,MIX$ ,REVIEW
.#FG4 :5 .;X .K #C & .;Y .K #E
.#FG4 :5 .;X .K #F & .;Y .K --#B
,F9D ALL ! Z]OS (! FUNC;N4
.#FI4 .;F7.;X7 .K .;X #B -- #B .;X --
#CE @7 P4 #BEB @7
.#GJ4 .;F7.;X7 .K .;X #B -- #H .;X @+
#BE @7 P4 #BIB @7
.#GA4 .;F7.;X7 .K .;X #C -- #H .;X #B
@+ #D .;X -- #CB @7 P4 #CGI @7
.#GB4 .;F7.;X7 .K .;X #C -- #D .;X #B
@+ #BE .;X @+ #AJJ @7 P4 #CGI @7
.#GC4 .;F7.;X7 .K .;X #C -- #C .;X #C
-- #CA .;X #C @+ #FC .;X @+ #IJ @7 P4
#CGI @7
.#GD4 .;F7.;X7 .K .;X #D @+ #AJ .;X #C
@+ #BE .;X #B -- #CF @7 P4 #CGI @7
,SIMPLIFY ! EXPRES.N4 ,TELL :
PROP]TIES ( EXPON5TS Y US$4 @7 P4 #CCJ
@7
,,PREVIEW
,PREP>E = ,LESSON #F.B 9 ,EXS4 #GE-HB4
.#GE4
.#GF4 @7 .;X #D @7 --#C
.#GG4 7#C .;X #B .;Y --#C
.#GH4 #D .;X #J .;Y --#D
.#GI4 .;X #F 99 .;X --#C
.#HJ4
.#HA4
.#HB4
,,EXTRA ,,PRACTICE = ,LESSON #F.A1 P4
#AJAE
..,,ONL9E ,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#DBJ
#F.B ,APPLY ,PROP]TIES ( ,R,NAL
,EXPON5TS
.,2F ,Y SIMPLIFI$ EXPRES.NS 9VOLV+
9TEG] EXPON5TS4
.,N[ ,Y W SIMPLIFY EXPRES.NS 9VOLV+
R,NAL EXPON5TS4
.,:Y8 ,S Y C F9D VELOCITIES1 Z 9 ,EX4
#HD4
,KEY ,VOCABUL>Y
99 ..SIMPLE/ =M (A .RADICAL
99 .L .RADICALS
,SIDEB>3
,/&>DS
..#AB.J ,/UD5TS "K ! LAWS ( FRAC;NAL
.EXPON5TS @1 "U/& EXPON5TIAL FUNC;NS1 &
USE ^! FUNC;NS 9 PRO#MS 9VOLV+
EXPON5TIAL GR[? & DECAY4
,! PROP]TIES ( 9TEG] EXPON5TS Y LE>N$
9 ,LESSON #E.A C AL 2 APPLI$ 6R,NAL
EXPON5TS4
,,KEY ,,3CEPT .= .,YR .,NOTEBOOK
,PROP]TIES ( ,R,NAL ,EXPON5TS
,LET .A & .;B 2 R1L NUMB]S & LET .;M &
.;N 2 R,NAL NUMB]S4 ,! FOLL[+ PROP]TIES
H ! SAME "NS Z ^? LI/$ ON PAGE #CCJ @1 B
N[ APPLY 6R,NAL EXPON5TS Z ILLU/RAT$4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,PROP]TY3 ,EXAMPLE
.#A4 A.' ;M.' @* A.' ;N.' .K A.' ;M @+
;N.' @3 #E ;L_/#B @* #E #C/B .K #E
7;L_/#B @+ #C/B7 .K #E #B .K #BE
.#B4 7A.' ;M.' @7 ;N.' .K A.' .-MN.'
@3 7#C #E/B @7 #B .K #C 7#E/B@*#B7 .K #C
#E .K #BDC
.#C4 7;AB7 ;M.' .K A.' ;M.' ;B.' ;M.'
@3 7#AF @* #I7 #A/B .K #AF #A/B @* #I
#A/B .K #D @* #C .K #AB
.#D4 @3
.#E4 @3
.#F4 @3
,,EXAMPLE #A ,USE PROP]TIES ( EXPON5TS
,USE ! PROP]TIES ( R,NAL EXPON5TS
6SIMPLIFY ! EXPRES.N4
.A4 #G ;L_/#D @* #G #A/B .K #G 7#A/D
@+ #A/B7 .K #G #C/D
.B4 7#F #A/B @* #D #A/C @7 #B .K 7#F
#A/B @7 #B @* 7#D #A/C @7 #B .K #F
7#A/B7 @* #B @7 @* #D 7#A/C @* #B7 .K #F
#A @* #D #B/C .K #F @* #D #B/C
.C4
.D4
.E4
------------------------------------#DBA
,,EXAMPLE #B ,APPLY PROP]TIES (
EXPON5TS
.,,BIOLOGY ,A MAMMAL'S SURFACE >EA
.;,S 7IN SQU>E C5TIMET]S7 C 2
APPROXIMAT$ 0! MODEL .;,S .K .KM #BAC ":
.;M IS ! MASS 7IN GRAMS7 (! MAMMAL & ,A3
IS A 3/ANT4 ,! VALUES ( .;K = "S MAMMALS
>E %[N 2L4 ,APPROXIMATE ! SURFACE >EA (A
RA2IT T HAS A MASS ( #C.D KILOGRAMS
7#C.D * #AJ #C GRAMS74
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,MAMMAL @3 ,%EEP3 ,RA2IT3 ,HORSE3
,HUMAN3 ,MONKEY3 ,BAT
.;K @3 #H.D3 #I.GE3 #AJ.J3 #AA.J3
#AA.H3 #EG.E
,SOLU;N
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,S .K KM #B/C @3 .,WRITE .MODEL4
.K #I.GE7#C.D * #AJ #C @7 #B/C @3
,SUB/ITUTE #I.GE =.' ;K .-& #C.D * #AJ
#C =.' M4.-
.K #I.GE7#C.D7 #B/C 7;L#J #C @7 #B/C
@3 ..,P[] (A PRODUCT .PROP]TY
#I.GE 7#B.BF7 7#AJ #B @7 @3 ..,P[] (A
P[] .PROP]TY
#BBJJ3 .,SIMPLIFY4
,! RA2IT'S SURFACE >EA IS AB #BBJJ
SQU>E C5TIMET]S4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #A &
.#B
,SIMPLIFY ! EXPRES.N4
.#A4 7#E #A/C @* #G #A/D @7 #C
.#B4 #B #C/D @* #B #A/B
.#C4
.#D4
.#E4 .,,BIOLOGY ,USE ! 9=M,N 9
,EXAMPLE #B 6APPROXIMATE ! SURFACE >EA
(A %EEP T HAS A MASS ( #IE KILOGRAMS
7#I.E * #AJ #D GRAMS74
.,,PROP]TIES .,,( .,,RADICALS ,! ?IRD
& SIX? PROP]TIES ON PAGE #DBJ C 2
EXPRESS$ US+ RADICAL NOT,N :5 = "S 9TEG]
.;N GRT] ?AN #A4
,,KEY ,,3CEPT .= .,YR .,NOTEBOOK
,PROP]TIES ( ,RADICALS
,PRODUCT PROP]TY ( RADICALS
,QUOTI5T PROP]TY ( RADICALS
,,EXAMPLE #C ,USE PROP]TIES ( RADICALS
,USE ! PROP]TIES ( RADICALS 6SIMPLIFY
! EXPRES.N4
.A4 .,PRODUCT .PROP]TY
.B4 .,QUOTI5T .PROP]TY
------------------------------------#DBB
,SIDEB>3
,REVIEW ,RADICALS
,= HELP ) R,NALIZ+ DENOM9ATORS (
RADICAL EXPRES.NS1 SEE P4 #BFF @4
.,,SIMPLE/ .,,=M ,A RADICAL ) 9DEX .;N
IS 9 .SIMPLE/ .=M IF ! RADIC& HAS NO
P]FECT .N? P[]S Z FACTORS & ANY
DENOM9ATOR HAS BE5 R,NALIZ$4
,,EXAMPLE #D ,WRITE RADICALS 9 SIMPLE/
=M
,WRITE ! EXPRES.N 9 SIMPLE/ =M4
.A4
.B4
.,,L .,,RADICALS ,RADICAL EXPRES.NS )!
SAME 9DEX & RADIC& >E .L .RADICALS4
,6ADD OR SUBTRACT L RADICALS1 USE !
4TRIBUTIVE PROP]TY4
,,EXAMPLE #E ,ADD & SUBTRACT L
RADICALS & ROOTS
,SIMPLIFY ! EXPRES.N4
.A4
.B4 #B7#H #A/E @7 @+ #AJ7#H #A/E @7 .K
7#B @+ #AJ77#H #A/E @7 .K #AB7#H #A/E @7
.C4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #C1D1
& .#E
,SIMPLIFY ! EXPRES.N4
.#F4
.#G4
.#H4
.#I4
.,,V>IA# .,,EXPRES.NS ,! PROP]TIES (
R,NAL EXPON5TS & RADICALS C AL 2 APPLI$
6EXPRES.NS 9VOLV+ V>IA#S4 ,2C A V>IA# C
2 POSITIVE1 NEGATIVE1 OR Z]O1 "S"TS
ABSOLUTE VALUE IS NE$$ :5 SIMPLIFY+ A
V>IA# EXPRES.N4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 .,RULE @3 .,EXAMPLE
..,:5 X IS .ODD @3 @3
..,:5 X IS .EV5 @3 @3
,ABSOLUTE VALUE IS N NE$$ :5 ALL
V>IA#S >E ASSUM$ 6BE POSITIVE4
------------------------------------#DBC
,SIDEB>3
,AVOID ,]RORS
,Y M/ MULTIPLY BO? ! NUM]ATOR .&
DENOM9ATOR (! FRAC;N 0.;Y S T ! VALUE (!
FRAC;N DOES N *ANGE4
,,EXAMPLE #F ,SIMPLIFY EXPRES.NS
9VOLV+ V>IA#S
,SIMPLIFY ! EXPRES.N4 ,ASSUME ALL
V>IA#S >E POSITIVE4
.A4
.B4 7#BG .;P #C .;Q #AB @7 #A/C .K
.#BG #A/C 7.;P #C @7 #A/C 7.;Q #AB @7
#A/C .K #C .;P 7#C @* #A/C7 .;Q 7#AB @*
#A/C7 .K #C .PQ #D
.C4
.D4
,,EXAMPLE #G ,WRITE V>IA# EXPRES.NS 9
SIMPLE/ =M
,WRITE ! EXPRES.N 9 SIMPLE/ =M4
,ASSUME ALL V>IA#S >E POSITIVE4
.A4
.B4
,,EXAMPLE #H ,ADD & SUBTRACT EXPRES.NS
9VOLV+ V>IA#S
,P]=M ! 9DICAT$ OP],N4 ,ASSUME ALL
V>IA#S >E POSITIVE4
.A4
.B4 #C .XY #A/D -- #H .XY #A/D .K --#E
.XY #A/D
.C4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #F1G1
& .#H
,SIMPLIFY ! EXPRES.N4 ,ASSUME ALL
V>IA#S >E POSITIVE4
.#AJ4
.#AA4
.#AB4
.#AC4
------------------------------------#DBD
#F.B ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
,,WS#AB = ,EXS4 #E1BG1 & #HE
.K .,,/&>DIZ$ .,,TE/ .,,PRACTICE ,EXS4
#B1 #BC1 #EA1 #FI1 #HF1 & #HI
,SKILL ,PRACTICE
#A4 .,,VOCABUL>Y ,>E & L RADICALS8
.,EXPLA9 :Y OR :Y N4
#B4 .,,WRIT+ ,"U :AT 3DI;NS IS A
RADICAL EXPRES.N 9 SIMPLE/ =M8
..,,EXAMPLE #A ON .P4 #DBJ = ,EXS4
#C-AD
,,PROP]TIES ,,( ,,R,NAL ,,EXPON5TS
,SIMPLIFY ! EXPRES.N4
.#C4 #E #C/B @* #E #A/B
.#D4 7#F #B/C @7 #A/B
.#E4 #C #A/D @* #BG #A/D
.#F4
.#G4
.#H4
.#I4
.#AJ4 7;L#B #C/E @* #H #C/E @7 #E
.#AA4
.#AB4
.#AC4 7#AF #E/I @* #E #G/I @7 --#C
.#AD4
.,,EXAMPLE .#C ON P4 #DBA = ,EXS4
#AE-BB ;J
.,,PROP]TIES .,,( .,,RADICALS
,SIMPLIFY ! EXPRES.N4
.#AE4
.#AF4
.#AG4
.#AH4
.#AI4
.#BJ4
.#BA4
.#BB4
.,,EXAMPLE .#D ON P4 #DBB = ,EXS4
#BC-CA
#BC4 .,,MULTIPLE .,,*OICE ,:AT IS !
SIMPLE/ =M (! EXPRES.N @8
,A
;,B
;,C
;,D
.,,SIMPLE/ .,,=M ,WRITE ! EXPRES.N 9
SIMPLE/ =M4
.#BD4
.#BE4
.#BF4
.#BG4
.#BH4
.#BI4
.#CJ4
.#CA4
.,,EXAMPLE .#E ON P4 #DBB = ,EXS4
#CB-DA
..,,-B9+ ,,RADICALS ,,& .,,ROOTS
,SIMPLIFY ! EXPRES.N4
.#CB4
.#CC4
.#CD4
.#CE4
.#CF4
.#CG4
.#CH4
.#CI4
.#DJ4
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 SIMPLIFY+ ! EXPRES.N4
.#DA4
.#DB4
------------------------------------#DBE
.,,EXAMPLE .#F ON P4 #DBC = ,EXS4
#DC-EA
,,V>IA# ,,EXPRES.NS ,SIMPLIFY !
EXPRES.N4 ,ASSUME ALL V>IA#S >E
POSITIVE4
.#DC4 .;X #A/D @* .;X #A/C
.#DD4 @7 .;Y #D @7 #A/F
.#DE4
.#DF4
.#DG4
.#DH4
.#DI4
.#EJ4
.#EA4 .,,OP5-.,,5D$ .,,MA? ,WRITE TWO
V>IA# EXPRES.NS ) NON9TEG] EXPON5TS ^:
QUOTI5T IS .;X #C/D @4
.,,EXAMPLE .#G ON P4 #DBC = ,EXS4
#EB-EI
,,SIMPLE/ ,,=M ,WRITE ! EXPRES.N 9
SIMPLE/ =M4 ,ASSUME ALL V>IA#S >E
POSITIVE4
.#EB4
.#EC4
.#ED4
.#EE4
.#EF4
.#EG4
.#EH4
.#EI4
.,,EXAMPLE .#H ON P4 #DBC = ,EXS4
#FJ-FE
,,-B9+ ,,V>IA# ,,EXPRES.NS ,P]=M !
9DICAT$ OP],N4 ,ASSUME ALL V>IA#S >E
POSITIVE4
.#FJ4
.#FA4
.#FB4
.#FC4 @7 .;X #D .;Y @7 #A/B @+ @7 .XY
#A/D @7 #B
.#FD4
.#FE4
..,,GEOMETRY ,F9D SIMPLIFI$ EXPRES.NS
=! P]IMET] & >EA ( .!
.#FF4
.#FG4
.#FH4
#FI4 .,,MULTIPLE .,,*OICE ,:AT IS !
SIMPLIFI$ =M (
,A
;,B
;,C
;,D
,,DECIMAL ,,EXPON5TS ,SIMPLIFY !
EXPRES.N4 ,ASSUME ALL V>IA#S >E ,I
POSITIVE4
.#GJ4 .;X #J.E @* .;X #B
.#GA4 .;Y --#J.F @* .;Y #F
.#GB4 @7 .;X #F .;Y #B @7 --#J.GE
.#GC4
.#GD4 @7 .;X #E ;Y --#C @7 --#J.BE
.#GE4
.#GF4 ;L#J;X #J.F @+ 7#D .;X #J.C @7
#B
.#GG4 #AE;Z #J.C -- 7#B;Z #J.A @7 #C
,,IRR,NAL ,,EXPON5TS ,! PROP]TIES 9 ?
LESSON C AL 2 APPLI$ 6IRR,NAL EXPON5TS4
,SIMPLIFY ! EXPRES.N4 ,ASSUME ALL V>IA#S
>E POSITIVE4
.#GH4
.#GI4
.#HJ4
.#HA4
#HB4 ..,,*ALL5GE ,SOLVE ! EQU,N US+ !
PROP]TIES ( R,NAL .EXPON5TS4
A4
B4
C4 7#D .;X @7 .;X @+ #B .K #FD
------------------------------------#DBF
.,,EXAMPLE .#B ON P4 #DBA = ,EXS4
#HC-HD
,,PRO#M ,,SOLV+
#HC4 .,,BIOLOGY ,LOOK BACK AT ,EXAMPLE
#B ON PAGE #DBA @4 ,USE ! MODEL .;,S .K
.KM #B/C 6APPROXIMATE ! SURFACE >EA (!
MAMMAL GIV5 XS MASS4
A4 ,BAT3 #CB GRAMS
B4 ,HUMAN3 #EI KILOGRAMS
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#HD4 .,,AIRPLANE .,,VELOC;Y ,! VELOC;Y
.;V 7IN FEET P] SECOND7 (A JET C 2
APPROXIMAT$ 0! MODEL
": .,A IS ! >EA (! W+S 7IN SQU>E FEET7
& .;,L IS ! LIFT 7IN ,NEWTONS74 ,F9D !
VELOC;Y (A JET )A W+ >EA ( #E.E * #AJ #C
SQU>E FEET &A LIFT ( #A.D * #AJ #G
,NEWTONS4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#HE4 .,,P9HOLE .,,CAM]A ,! OPTIMUM
DIAMET] .;D 7IN MILLIMET]S7 (! P9HOLE 9
A P9HOLE CAM]A C 2 MODEL$ 0;D.K
#A.I,77#E.E * #AJ --#D @7 @7' #A/B
": IS ! L5G? (! CAM]A BOX 7IN
MILLIMET]S74 ,F9D ! OPTIMUM P9HOLE
DIAMET] =A CAM]A BOX )A L5G? ( #AJ
C5TIMET]S4
#HF4 .,,%ORT .,,RESPONSE ,%[ T !
HYPOT5USE ( AN ISOSCELES "R TRIANGLE )
LEGS ( L5G? .;X IS @4
#HG4 .,,/> .,,MAGNITUDE ,! .APP>5T
.MAGNITUDE (A /> IS A NUMB] T 9DICATES
H[ FA9T ! /> IS 9 REL,N 6O!R />S4 ,!
EXPRES.N TELLS H[ _M "TS FA9T] A /> )
MAGNITUDE .;M @1 IS ?AN A /> ) MAGNITUDE
.;M#B4
A4 ,H[ _M "TS FA9T] IS ,ALTAIR ?AN
,VEGA8
B4 ,H[ _M "TS FA9T] IS ,D5EB ?AN
,ALTAIR8
C4 ,H[ _M "TS FA9T] IS ,D5EB ?AN
,VEGA8
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,/> @3 .,APP>5T .MAGNITUDE @3
.,3/ELL,N
,VEGA3 #J.JC3 ,LYRA
,ALTAIR3 #J.GG3 ,AQUILA
,D5EB3 #A.BE3 ,CYGNUS
#HH4 .,,PHYSICAL .,,SCI;E ,! MAXIMUM
HORIZONTAL 4T.E .;D T AN OBJECT C TRAVEL
:5 LAUN*$ AT AN OPTIMUM ANGLE ( PROJEC;N
IS GIV5 BY
": .;H ;O.' .-IS ! OBJECT'S 9ITIAL
HEI<T1 .;V ;O.' .-IS XS 9ITIAL SPE$1 &
.;G IS ! A3EL],N DUE 6GRAV;Y4 ,SIMPLIFY
! MODEL :5 .;H ;,Q.' .K #J4
.K .,,"W$-.,,\ .,,SOLU;NS .ONP4.,,WSI
.K .,,/&>DIZ$ .,,TE/ .,,PRACTICE
------------------------------------#DBG
#HI4 .,,EXT5D$ .,,RESPONSE ,Y H FILL$
TWO R.D BALLOONS ) WAT]4 ,"O BALLOON
3TA9S TWICE Z M* WAT] Z ! O!R BALLOON4
A4 ,SOLVE ! =MULA =! VOLUME (A SPH]E1
= R4
B4 ,SUB/ITUTE ! EXPRES.N = .;R F "P
7A7 96! =MULA =! SURFACE >EA (A SPH]E1
.;,S .K .#D .;R #B @4 ,SIMPLIFY 6%[ T
.;,S .K 7#D @7 #A/C 7#C .;,V @7 #B/C @4
C4 .,-P>E ! SURFACE >1S (! TWO WAT]
BALLOONS US+ ! =MULA F "P 7;B74
#IJ4 .,,*ALL5GE ,SUB/ITUTE DI6]5T
-B9,NS ( ODD & EV5 POSITIVE 9TEG]S = .;M
& .;N 9 ! EXPRES.N @4 ,IF .;X IS N ALW
POSITIVE1 :5 IS ABSOLUTE VALUE NE$$ 9
SIMPLIFY+ ! EXPRES.N8
,MIX$ ,REVIEW
,SOLVE ! 9EQUAL;Y4
.#IA4 .;X .1.K #AE P4 #DA
.#IB4 #AJ .;X @+ #G "K --#D .;X @+ #I
P4 #DA
.#IC4 #C .;X "K.K --#F .;X --#BJ P4
#DA
.#ID4 .;X #B @+ #G .;X @+ #AJ .1#J P4
#CJJ
.#IE4 -- .;X #B @+ #D .;X .1.K --#CB
P4 #CJJ
.#IF4 #F .;X #B @+ .;X -- "K#E P4 #CJJ
,LET .;F7.;X7 .K .;X #C -- #B .;X #B
-- .;X -- #C.,EVALUATE ! FUNC;N AT !
GIV5 VALUE4 P4 #CCG
.#IG4 .;F 7#C7
.#IH4 .;F 7--#C7
.#II4 .;F 7#E7
.#AJJ4 .;F 7--#D7
,P]=M ! 9DICAT$ OP],N4
,PREVIEW
,PREP>E = ,LESSON #F.C 9 ,EXS4
#AJA-AJF4
.#AJA4 7#AB .;X #B @+ #B .;X @7--7--#H
.;X #C @+ #E .;X #B -- #I .;X P4 #CDF
.#AJB4 7#CE .;X #C -- #AD7 @+ 7--#AE
.;X #B @+ #G .;X @+ #BJ P4 #CDF
.#AJC4 #AH .;X #B @7 .;X @+ #D7 P4
#CDF
.#AJD4 7#H .;X -- #C #B @7 P4 #CDF
.#AJE4 @7 .;X -- #D7@7 .;X @+ #A7@7
.;X @+ #B7 P4 #CDF
.#AJF4 @7 .;X #C @+ .;X #B -- #G .;X
-- #AE7 @+ @7 .;X -- #C7 P4 #CFB
,,QUIZ_/OR .,LESSONS .#F..A-.F..B
,EVALUATE ! EXPRES.N )\T US+ A
CALCULATOR1 @7 P4 #DAD @7
.#A4 #CF #C/B
.#B4 #FD #B/C
.#C4 --7#FBE #C/D @7
.#D4 7--#CB7 #B/E
,SOLVE ! EQU,N4 ,R.D YR ANSW] 6TWO
DECIMAL PLACES :5 APPROPRIATE1 @7 P4
#DAD @7
.#E4 .;X #D .K #BJ
.#F4 .;X #E .K --#AJ
.#G4 .;X #F @+ #E .K #BF
.#H4 @7 .;X @+ #C7 #C .K --#AF
,SIMPLIFY ! EXPRES.N4 ,ASSUME ALL
V>IA#S >E POSITIVE1 @7 P4 #DBJ @7
.#I4
.#AJ4
.#AA4 @7 .;X #F .;Y #D @7 #A/H @+ #B7
.;X #A/C ;Y #A/D @7 #B
.#AB4
.#AC4
.#AD4
.#AE4 .,,GEOMETRY ,F9D A RADICAL
EXPRES.N =! P]IMET] (! R$ TRIANGLE
9SCRIB$ 9 ! SQU>E %[N 6! "R4 ,SIMPLIFY !
EXPRES.N1 7P4 .#DBJ7
.,,EXTRA .,,PRACTICE = ,LESSON #F.B1
P4 #AJAE
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#DBH
#F.C ,P]=M ,FUNC;N ,OP],NS &
,-POSI;N
.,2F ,Y P]=M$ OP],NS ) ALGEBRAIC
EXPRES.NS4
.,N[ ,Y W P]=M OP],NS ) FUNC;NS4
.,:Y8 ,S Y C MODEL BIOLOGICAL
PROCESSES1 Z 9 ,EXAMPLE #C4
,KEY ,VOCABUL>Y
99 .P[] .FUNC;N
99 .-POSI;N
,SIDEB>3
,/&>DS
..#BD.J ,/UD5TS SOLVE PRO#MS 9VOLV+
FUNC;NAL 3CEPTS1 S* Z .-POSI;N @1 DEF9+
! 9V]SE FUNC;N ..& P]=M+ >I?METIC OP],NS
ON .FUNC;NS4
,9 ,*APT] #E Y LE>N$ H[ 6ADD1
SUBTRACT1 MULTIPLY1 & DIVIDE POLYNOMIAL
FUNC;NS4 ,^! OP],NS C 2 DEF9$ = ANY
NUMB] ( FUNC;NS4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,OP],NS ON ,FUNC;NS
,LET ;F & .;G 2 ANY TWO FUNC;NS4 ,A
NEW FUNC;N .;H C 2 DEF9$ 0P]=M+ ANY (!
F\R BASIC OP],NS ON .;F & G4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,OP],N @3 .,DEF9I;N @3 ,EXAMPLE3
.;F7.;X7 .K #E ..;X1 ;G7;X7 .K .;X @+ #B
.,A4I;N @3 .;H7.;X7 .K .;F7.;X7 @+
.;G7.;X7 @3 .;H7.;X7 .K #E .;X @+ @7 .;X
@+ #B7 .K #F .;X @+ #B
.,SUBTRAC;N @3 .;H7.;X7 .K .;F7.;X7 --
;G7;X7 @3 .;H7.;X7 .K #E .;X -- @7 .;X
@+ #B7 .K #D .;X -- #B
.,MULTIPLIC,N @3 .;H7.;X7 .K .;F7.;X7
@* .;G7.;X7 @3 .;H7.;X7 .K #E .;X @7 .;X
@+ #B7 .K #E .;X #B @+ #AJ .;X
.,DIVI.N @3 @3
,! DOMA9 ( .;H 3SI/S (! ;X-VALUES T >E
9 ! DOMA9S ( BO? & G4 ,A4I;N,Y1 ! DOMA9
(! QUOTI5T DOES N 9CLUDE ;X-VALUES = :
;G7;X7 .K #J4
.,,P[] .,,FUNC;NS ,S F> Y H /UDI$
S"EAL TYPES ( FUNC;NS1 9CLUD+ L9E>
FUNC;NS1 QUADRATIC FUNC;NS1 & POLYNOMIAL
FUNC;NS ( HI<] DEGREE4 ,ANO!R -MON TYPE
( FUNC;N IS A .P[] .FUNC;N @1 : HAS ! =M
.;Y .K .AX ;B.' .-": A IS A R1L NUMB] &
.;B IS A R,NAL NUMB]4
,,EXAMPLE #A ,ADD & SUBTRACT FUNC;NS
.,LET .;F7.;X7 .K #D .;X #A/B &
..;G7;X7 .K --#I .;X #A/B @4 ,F9D !
FOLL[+4
.A4 .;F7.;X7 @+ .;G7.;X7
.B4 .;F7.;X7 -- .;G7.;X7
.C4 ! DOMA9S ( .;F @+ .;G & .;F--.;G
,SOLU;N
.A4 .;F7.;X7 @+ .;G7.;X7 .K #D .;X
#A/B @+ 7--#I .;X #A/B @7 .K ,7#D @+
7--#I77' .;X #A/B .K --#E .;X #A/B
.B4 .;F7.;X7 -- .;G7.;X7 .K #D .;X
#A/B -- 7--#I .;X #A/B @7 .K
,7#D--7--#I77' .;X #A/B .K #AC .;X #A/B
C4 ,! FUNC;NS ;F & .;G EA* H ! SAME
DOMA93 ALL NONNEGATIVE R1L NUMB]S4 ,S1 !
DOMA9S ( .;F @+ .;G & .;F -- .;G AL 3SI/
( ALL NONNEGATIVE R1L NUMB]S4
,SIDEB>3
,REVIEW ,DOMA9
,= HELP ) DOMA9S ( FUNC;NS1 SEE P4 #GB
@4
------------------------------------#DBI
,,EXAMPLE #B ,MULTIPLY & DIVIDE
FUNC;NS
,LEF7 .;X @7 .K #F .;C & .;G7.;X7 .K
.;X #C/D ,F9D ! FOLL[+4
.A4 .;F7.;X7 @* .;G7.;X7
.B4
.C4 ! DOMA9S ( .;F @* .;G &
,SOLU;N
.A4 .;F7.;X7 @* .;G7.;X7 .K 7#F .;X
@7@7 .;X #C/D @7 .K #F .;X 7#A @+ #C/D7
.K #F .;X #G/D
.B4
.C4 ,! DOMA9 ( .;F 3SI/S ( ALL R1L
NUMB]S1 &! DOMA9 ( .;G 3SI/S ( ALL
NONNEGATIVE R1L NUMB]S4 ,S1 ! DOMA9 (
.;F @* .;G 3SI/S ( ALL NONNEGATIVE R1L
NUMB]S4 ,2C ;G7#J7 .K #J1 ! DOMA9 ( IS
RE/RICT$ 6ALL .POSITIVE R1L NUMB]S4
,,EXAMPLE #C ,SOLVE A MULTI-/EP PRO#M
.,,RH9OS ,=A :ITE RH9O1 HE>T RATE .;R
7IN B1TS P] M9UTE7 & LIFE SPAN .;S 7IN
M9UTES7 >E RELAT$ 6BODY MASS .;M 7IN
KILOGRAMS7 0^! FUNC;NS3
.;R7.;M7 .K #BD;L .;M --#J.BE
.;S7.;M7 .K 7#F * #AJ #F @7 .;M #J.B
99 ,F9D .;R7.;M7 @* ;S7;M74
99 ,EXPLA9 :AT ? PRODUCT REPRES5TS4
,SOLU;N
.,,/EP .#A .,F9D & SIMPLIFY .;R7.;M7
@* ;S7.M74
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;R7.;M7 @* .;S7.;M7 .K #BD .LM
--#J.BE ,77#F * #AJ #F @7 .;M #J.B @7'
@3 ,WRITE PRODUCT (.' ;R7;M7 .-&.'
;S7;M74.-
.K #BD;L7#F * #AJ #F @7 .;M --#J.BE @+
#J.B7 @3 ..,PRODUCT ( P[]S .PROP]TY
.K 7#ADDF * #AJ #F @7 .;M #J.JE @3
.,SIMPLIFY4
.K 7#A.DDF * #AJ #I @7 .;M #J.JE @3
.,USE .SCI5TIFIC .NOT,N4
.,,/EP#B .,9T]PRET .;R7.;M7 @*
.;S7.;M74
,MULTIPLY+ HE>T RATE 0LIFE SPAN GIVES
! TOTAL NUMB] ( HE>TB1TS =A :ITE RH9O
OV] XS 5TIRE LIFE"T4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #A1
#B1 & .#C
,LET ;F7;X7 .K --.#B;X #B/C & .;G7.;X7
.K .#G;X #B/C ,F9D ! FOLL[+4
#A4 .;F7.;X7 @+ .;G7.;X7
#B4 .;F7.;X7--.;G7.;X7
.#C4 ! DOMA9S ( .;F @+ .;G & .;F --
.;G
.,LET .;F7.;X7 .K .#C;X & .;G7.;X7 .K
.;X #A/E @4 .,F9D .! .FOLL[+4
.#D4 .;F7.;X7 @* .;G7.;X7
.#E4
.#F4 ! DOMA9S ( .;F @* .;G &
.#G4 .,,RH9OS ,USE ! RESULT ( ,EXAMPLE
#C 6F9D A :ITE RH9O'S NUMB] ( HE>TB1TS
OV] XS LIFE"T IF XS BODY MASS IS #A.G *
#AJ #E KILOGRAMS4
------------------------------------#DCJ
,SIDEB>3
,R1D+
,Z ) SUBTRAC;N & DIVI.N ( FUNC;NS1 Y
NE$ 6BE AL]T TO2 ! ORD] ( FUNC;NS :5 !Y
>E -POS$4 ,9 G5]AL1 .;F7.;G7.;X77 IS N
EQUAL 6.;G7.;F7.;X77
.,,-POSI;N .,,( .,,FUNC;NS ,ANO!R
OP],N T C 2 P]=M$ ) TWO FUNC;NS IS
.-POSI;N4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,-POSI;N ( ,FUNC;NS
,! -POSI;N (A FUNC;N .;G )A FUNC;N .;F
IS3 .;H7.;X7 .K .;G7.;F7.;X77
,! DOMA9 ( .;H IS ! SET ( ALL
;X-VALUES S* T .;X IS 9 ! DOMA9 ( .;F &
.;F7.;X7 IS 9 ! DOMA9 ( G4
,EXAMPLE #D ,/&>DIZ$ ,TE/ ,PRACTICE
,LET .;F7.;X7 .K .#B;X -- #G &
.;G7.;X7 .K .;X #B @+ #D4 ,:AT IS !
VALUE ( ;G7;F7#C778
7.,A7 --#E
7.;,B7 --#C
7.;,C7 #C
7.;,D7 #E
,SOLU;N
,6EVALUATE ;G7;F7#C771 Y F/ M/ F9D .;F
7#C74
.;F 7#C7 .K #B7#C7--#G .K --#A
,!N ;G7;F7#C77 .K ;G7--;L7 .K 7--#A7
#B @+ #D .K #A@+#D .K #E4
,S1 ! VALUE ( ;G7;F7#C77 IS #E4
,! CORRECT ANSW] IS ,D4 7..,A7 7;,B7
7;,C7 7.;,D7
,EXAMPLE #E ,F9D -POSI;NS ( FUNC;NS
,LET .;F7.;X7 .K #D .;X --#A &
.;G7.;X7 .K .#E;X -- #B4 ,F9D ! FOLL[+4
A4 .;F7.;G7.;X77
B4 .;G7.;F7.;X77
C4 .;F7.;F7.;X77
.D4 ! DOMA9 ( EA* -POSI;N
,SIDEB>3
,AVOID ,]RORS
,Y _C ALW DET]M9E ! DOMA9 (A -POSI;N F
XS EQU,N4 ,= 9/.E1 ! DOMA9 (
.;F7.;F7.;X77 .K .;X APPE>S 6BE ALL R1L
NUMB]S1 B X IS ACTU,Y ALL R1L NUMB]S
EXCEPT Z]O4
,SOLU;N
.A4
.B4
.C4 .;F,7.;F7.;X77 .K .;F 7#D .;X --#A
@7--#D7#D .;X --#A @7 --#A .K #D7#D -#A
.;X @7 .K #D;DG .;X .K .;X
.D4 ,! DOMA9 ( .;F7.;G7.;X77 3SI/S (
ALL R1L NUMB]S EXCEPT 2C IS N 9 ! DOMA9
( .;F 7,NOTE T @4 : IS UNDEF9$47 ,!
DOMA9S ( ;G7;F7;X77 & ;F7;F7;X77 3SI/ (
ALL R1L NUMB]S EXCEPT .;X .K #J1 AG 2C
#J IS N 9 ! DOMA9 ( .;F @4
------------------------------------#DCA
,,EXAMPLE #F ,SOLVE A MULTI-/EP PRO#M
.,,PA9T .,,/ORE ,Y H A 4#AJ GIFT
C]TIFICATE 6A PA9T /ORE4 ,! /ORE IS (F]+
#AE@3P (F YR 5TIRE PUR*ASE ( ANY PA9TS &
PA9T+ SUPPLIES4 ,Y DECIDE 6PUR*ASE A
4#CJ C ( PA9T & 4#BE WOR? ( PA9T+
SUPPLIES4
,USE -POSI;N ( FUNC;NS 6D ! FOLL[+3
99 ,F9D ! SALE PRICE ( YR PUR*ASE :5 !
4#AJ GIFT C]TIFICATE IS APPLI$ 2F !
#AE@3P 4C.T4
99 ,F9D ! SALE PRICE ( YR PUR*ASE :5 !
#AE@3P 4C.T IS APPLI$ 2F ! 4#AJ GIFT
C]TIFICATE4
,SOLU;N
.,,/EP .#A .,F9D ! TOTAL AM.T ( YR
PUR*ASE4 ,! TOTAL AM.T =! PA9T & PA9T+
SUPPLIES IS 4#CJ @+ 4#BE .K 4#EE4
.,,/EP .#B .,WRITE FUNC;NS =! 4C.TS4
,LET .;X 2 ! REGUL> PRICE1 .;F7.;X7 2 !
PRICE AF ! 4#AJ GIFT C]TIFICATE IS
APPLI$1 & ;G7;X7 2 ! PRICE AF ! #AE@3P
4C.T IS APPLI$4
,FUNC;N = 4#AJ GIFT C]TIFICATE3
.;F7.;X7 .K .;X -- #AJ
,FUNC;N = #AE@3P 4C.T3 .;G7.;X7 .K .;X
-- #J.AE .;X .K #J.HE .;X
.,,/EP .#C .,-POSE ! FUNC;NS4 ,!
-POSI;N ;G7;F7;X77 REPRES5TS ! SALE
PRICE :5 ! 4#AJ GIFT C]TIFICATE IS
APPLI$ 2F ! #AE@3P 4C.T4
;G7;F7;X77 .K .;G7.;X -- #AJ7 .K
#J.HE7 .;X -- #AJ7
,! -POSI;N .;F7.;G7.;X77 REPRES5TS !
SALE PRICE :5 ! #AE@3P 4C.T IS APPLI$ 2F
! 4#AJ GIFT C]TIFICATE4
.;F7.;G7.;X77 .K .;F 7#J.HE .;X @7 .K
#J.HE .;X -- #AJ
.,,/EP .#D .,EVALUATE ! FUNC;NS
.;G7.;F7.;X77 & .;F7.;G7.;X77 :5 .;X .K
#EE4
.;G7.;F 7#EE77 .K #J.HE7#EE--#AJ7 .K
#J.HE7#DE7 .K 4#CH.BE
.;F7.;G 7#EE77 .K #J.HE7#EE--#AJ7 .K
#DF.GE--#AJ--4#CF.GE
,! SALE PRICE IS 4#CH.BE :5 ! 4#AJ
GIFT C]TIFICATE IS APPLI$ 2F ! #AE@3P
4C.T4 ,! SALE PRICE IS 4#CF.GE :5 !
#AE@3P 4C.T IS APPLI$ 2F ! 4#AJ GIFT
C]TIFICATE4
.,ANIMAT$ .,ALGEBRA .AT
_+CLASSZONE.COM_:
..,,GUID$ ,,PRACTICE = ,EXAMPLES #D1E1
& .#F
,LET ;F7;X7 .K .#C;X -- #H & .;G7.;X7
.K #B .;X #B @4 ,F9D ! FOLL[+4
#H4 .;G7.;F7.#E77
#I4 .;F7.;G7.#E77
#AJ4 .;F7.;F7.#E77
#AA4 .;G7.;G7.#E77
.#AB4 ,LET .;F7.;X7 .K #B .;X --#A &
.;G7.;X7 .K .#B;X @+ #G4 ,F9D
.;F7.;G7.;X771 .;G7.;F7.;X77 @1 &
.;F7.;F7.;X77 @4 ,!N /ATE ! DOMA9 ( EA*
-POSI;N4
.#AC4 .,,:AT .,,IF8 ,9 ,EXAMPLE #F1 H[
D YR ANSW]S *ANGE IF ! GIFT C]TIFICATE
6! PA9T /ORE IS 4#AE &! /ORE 4C.T IS
#BJ@3P8
------------------------------------#DCB
#F.C ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
,,WS#AB = ,EXS4 #C1 #AC1 & #DE
.K .,,/&>DIZ$ .,,TE/ .,,PRACTICE ,EXS4
#B1AA1CH1 #CI1 & #DD
.K .,,MULTIPLE .,,REPRES5T,NS
.,EX#..DF
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,!
FUNC;N .;H7.;X7 .K .;G7.;F7.;X77 IS
CALL$ ! @8 (! FUNC;N .;G )! FUNC;N .;F
@4
.#B4 .,,WRIT+ ,TELL :E!R ! SUM ( TWO
P[] FUNC;NS IS ."S"TS1 .ALW @1 OR .N"E A
P[] FUNC;N4 .,EXPLA9 YR R1SON+4
.,,EXAMPLE .#A ON P4 #DBH = ,EXS4
#C-AA
,,ADD ,,& ,,SUBTRACT ,,FUNC;NS ,LET
.;F7.;X7 .K --#C .;X #A/C @+ #D .;X #A/B
& .;G7.;X7 .K #E .;X #A/C @+ #D .;X #A/B
@4 ,P]=M ! 9DICAT$ OP],N & /ATE ! DOMA94
#C4 .;F7.;X7 @+ .;G7.;X7
#D4 .;G7.;X7 @+.;F7.;X7
.#E4 .;F7.;X7 @+ .;F7.;X7
.#F4 .;G7.;X7 @+ .;G7.;X7
#G4 .;F7.;X7--.;G7.;X7
#H4 .;G7.;X7--.;F7.;X7
#I4 .;F7.;X7--.;F7.;X7
#AJ4 .;G7.;X7--.;G7.;X7
.#AA4 .,,MULTIPLE .,,*OICE ,:AT IS
.;F7.;X7 @+ .;G7.;X7 IF .;F7.;X7 .K --#G
.;X #B/C -- #A & .;G7.;X7 .K #B .;X #B/C
@+ #F8
7.,A7 #E .;X #B/C -- #E
7.;,B7 --#E .;X #B/C @+ #E
7.;,C7 #I .;X #B/C @+ #G
7.;,D7 --#I .;X #B/C -- #G
.,,EXAMPLE .#B ON P4 #DBI = ,EXS4
#AB-AI
,,MULTIPLY ,,& ,,DIVIDE ,,FUNC;NS ,LET
.;F7.;X7 .K #D .;X #B/C & .;G7.;X7 .K #E
.;X #A/B @4 ,P]=M ! 9DICAT$ OP],N & /ATE
! DOMA94
.#AB4 .;F7.;X7 @* .;G7.;X7
#AC4 .;G7.;X7 @* .;F7.;X7
.#AD4 .;F7.;X7 -- .;F7.;X7
.#AE4 .;G7.;X7 @* .;G7.;X7
.#AF4
.#AG4
.#AH4
.#AI4
.,,EXAMPLE .#D ON P4 #DCJ = ,EXS4
#BJ-BG
,,EVALUATE ,,-POSI;NS ,,( ,,FUNC;NS
,LET .;F7.;X7 .K #C .;X @+ #B1 .;G7.;X7
.K -- .;X #B @1 & @4 ,F9D ! 9DICAT$
VALUE4
#BJ4 .;F7.;G7--.#C77
#BA4 .;G7.;F7.#B77
#BB4 .;H7.;F7--.#I77
#BC4 .;G7.;H77.#H77
#BD4 .;H7.;G7.#E77
#BE4 .;F7.;F7.#G77
#BF4 .;H7.;H7--.#D77
#BG4 .;G7.;G7--.#E77
.,,EXAMPLE .#E ON P4 #DCJ = ,EXS
#BH-CH
,,F9D ,,-POSI;NS ,,( ,,FUNC;NS ,LET
.;F7.;X7 .K #C .;X --#A @1 .;G7.;X7 .K
#B .;X -- #G1 & @4 ,P]=M ! 9DICAT$ OP],N
& /ATE ! DOMA94
#BH4 .;F7.;G7.;X77
#BI4 .;G7.;F7.;X77
#CJ4 .;H7.;F7.;X77
#CA4 .;G7.;I7.;C77
#CB4 .;H7.;G7.;X77
#CC4 .;F7.;F7.;X77
#CD4 .;H7.;H7.;X77
#CE4 .;G7.;G7.;C77
,,]ROR ,,ANALYSIS ,LET .;F7.;X7 .K .;X
#B -- #C & .;G7.;X7 .K #D .X4 .,DESCRIBE
& CORRECT ! ]ROR 9 ! -POSI;N4
#CF4 .;F7.A7.;X77 .K .;F7.#D;X7
.K @7 .;X #B -- #C77#D .;X @7
.K #D .;X #C -- #AB .;X
.#CG4 ;G7 .;F7.;X7 @7 .K ;G7 .;X #B --
#C7
.K #D .;X #B -- #C
------------------------------------#DCC
.#CH4 .,,MULTIPLE .,,*OICE ,:AT IS
.;G7.;F7.;X77 IF .;F7.;X7 .K #G .;X #B &
.;G7.;X7 .K #C .;X --#B @8
7.,A7
7.;,B7 #BA
7.;,C7 #BA;X #D
7.;,D7
.#CI4 .,,OP5-.,,5D$ .,,MA? ,F9D TWO
DI6]5T FUNC;NS .;F & .;G S* T
.;F7.;G7.;X77 .K .;G7.;F7.;X77 @4
,,*ALL5GE ,F9D FUNC;NS .;F & .;G S* T
.;F7.;G7.;X77 .K ..;H7;X71 ;G7;X7 # ;X1
& ;F7;X7 # .X4
.#DJ4
.#DA4
.#DB4 ;H7;X7 .K _\#B;X @+ #I_\
,,PRO#M ,,SOLV+
.,,EXAMPLE .#C ON P4 #DBI = ,EXS4 #DC1
#DF
#DC4 .,,BIOLOGY ,=A MAMMAL T WEI<S .;W
GRAMS1 ! VOLUME .;B 7IN MILLILIT]S7 (
AIR BR1!D 9 &! VOLUME .;D 7IN
MILLILIT]S7 ( 8D1D SPACE0 7! POR;N (!
LUNGS N FILL$ ) AIR7 C 2 MODEL$ BY3
.;B7.;W7 .K #J.JJG;W .;D7.;W7 .K
#J.JJB;M2
,! BR1?+ RATE .;R 7IN BR1?S P] M9UTE7
(A MAMMAL T WEI<S .;W GRAMS C 2 MODEL$
BY3
,SIMPLIFY .;R7.;W7 & CALCULATE ! BR1?+
RATE = BODY WEI<TS ( #F.E GRAMS1 #CJJ
GRAMS1 & #GJ1JJJ GRAMS4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.,,EXAMPLE .#F ON P4 #DCA = ,EXS4
#DD-DE
.#DD4 .,,%ORT .,,RESPONSE ,! CO/ 7IN
DOLL>S7 ( PRODUC+ .;X SN1K]S 9 A FACTORY
IS GIV5 0;,C7;X7 .K #FJ;X @+ #GEJ4 ,!
NUMB] ( SN1K]S PRODUC$ 9 .;T H\RS IS
GIV5 0.;X7.;T7 .K #EJ#4 ,F9D
.;,C7.;X7.;T774 ,EVALUATE ;,C7;X7#E77 &
EXPLA9 :AT ? NUMB] REPRES5TS4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#DE .,,MULTI-.,,/EP .,,PRO#M ,AN
ONL9E MOVIE /ORE IS HAV+ A SALE4 ,Y
DECIDE 6OP5 A *>GE A3.T & BUY F\R
,,DVD,'S4
A4 ,USE -POSI;N ( FUNC;NS 6F9D ! SALE
PRICE ( 4#HE WOR? ( ,,DVD,'S :5 ! 4#AE
4C.T IS APPLI$ 2F ! #AJ@3P 4C.T4
B4 ,USE -POSI;N ( FUNC;NS 6F9D ! SALE
PRICE ( 4#HE WOR? ( ,,DVD,'S :5 ! #AJ@3P
4C.T IS APPLI$ 2F ! 4#AE 4C.T4
C4 ,: ORD] ( 4C.TS GIVES Y A BETT]
D1L8 .,EXPLA94
------------------------------------#DCD
#DF4 .,,MULTIPLE .,,REPRES5T,NS ,A
MA!MATICIAN AT A LAKE ?R[S A T5NIS BALL
F PO9TS AL;G ! WAT]'S $GE 6PO9T .;,B 9 !
WAT]1 Z %[N4 ,8 DOG1 ,ELVIS1 F/ RUNS
AL;G ! B1* F PO9TS 6PO9T .;,D & !N SWIMS
6FET* ! BALL AT PO9T .,B4
A4 .,US+ .A .,DIAGRAM ,ELVIS'S RUNN+
SPE$ IS AB #F.D MET]S P] SECOND4 ,WRITE
A FUNC;N ;R7;X7 =! "T HE SP5DS RUNN+ F
PO9T .,A 6PO9T .,D4 ,ELVIS'S SWIMM+ SPE$
IS AB #J.I MET] P] SECOND4 ,WRITE A
FUNC;N .;S7.;X7 =! "T HE SP5DS SWIMM+ F
PO9T .;,D 6PO9T .,B4
B4 .,WRIT+ .A .,FUNC;N ,WRITE A FUNC;N
.;T7.;X7 T REPRES5TS ! TOTAL "T ,ELVIS
SP5DS TRAVEL+ F PO9TS 6PO9T .;,D 6PO9T
.,B4
C4 .,US+ .A .,GRAPH ,USE A GRAPH+
CALCULATOR 6GRAPH .;T 7;X74 ,F9D ! VALUE
( .;X T M9IMIZES .;T7.;X74 .,EXPLA9 !
M1N+ ( ? VALUE4
#DG4 .,,*ALL5GE ,6APPROXIMATE ! SQU>E
ROOT (A NUMB] .;N @1 ! ,BABYLONIANS US$
A ME?OD T 9VOLVES />T+ ) AN 9ITIAL GUESS
.;X & CALCULAT+ A SEQU;E ( VALUES T
APPROA*ES ! EXACT ANSW]4 ,_! ME?OD 0
BAS$ ON ! FUNC;N %[N AT ! "R4
A4 ,LET .;N .K #B1 & *OOSE .;X .K #A Z
AN 9ITIAL GUESS = ,CALCULATE ;F7;X71
;F7;F7;X771 ;F7;F7;F7;X7771 &
;F7;F7;F7;F7;X77774
B4 ,H[ _M "TS D Y NE$ 6-POSE ! FUNC;N
9 ORD] =! RESULT 6APPROXIMATE 6?REE
DECIMAL PLACES8 SIX DECIMAL PLACES8
,MIX$ ,REVIEW
,PREVIEW
,PREP>E = ,LESSON #F.D 9 ,EXS4 #DH-EC4
.#DH4 .;Y -- #B .;X .K #AB
.#DI4 #C .;X -- #B .;Y .K #AJ
.#EJ4 .;X .K--#C .;Y @+ #I
.#EA4 #C .;X -- #D .;Y .K #G
.#EB4 .;X -- .;Y .K #AB
.#EC4 .AX @+ .BY .K .;C
,GRAPH ! ORD]$ PAIRS 9 A COORD9ATE
PLANE4 P4 #GB
.#ED4 7--#E1B71 7#A1C71 7#B1--#E74
7#C1A7
.#EE4 7#D1E71 7#E1--#D71 7--#D1E74
7#E1D7
.#EF4 7-#B1 #B71 7#B1 #A71 7#B1-#B71
7#A1 #B7
.#EG4 7#E1 #I71 7#I1-#E71 7-#E1 #I71
7#I1 #E7
,GRAPH ! FUNC;N4
.#EH4 .;Y .K #C .;X -- #E P4 #HI
.#EI4 .;Y .K #G .;X @+ #D P4 #HI
.#FJ4 .;F7.;X7 .K --#D .;X -- #F P4
#HI
.#FA4 .;F7.;X7 .K --#C .;X @+ #I P4
#HI
.#FB4 .;Y .K .;X #B -- .;X -- #B P4
#BCF
.#FC4 .;Y .K #C .;X #B @+ #BJ .;X --
#G P4 #BCF
.#FD4 .;Y .K --#B .;X #B @+ #H .;X @+
#A P4 #BCF
.#FE4 .;F7.;X7 .K @7 .;X -- #C7 #B --
#D P4 #BDE
.#FE4 .;F7.;X7 .K @7 .;X @+ #D7 #B --
#F P4 #BDE
,,EXTRA ,,PRACTICE = ,LESSON #F.C1 P4
#AJAE
..,,ONL9E ,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#DCE
,GRAPH+ ,CALCULATOR ,ACTIV;Y3 #F.C
,USE ,OP],NS ) ,FUNC;NS
,USE AF LESSON #F.C
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,KEY/ROKES
,SIDEB>3
,/&>DS
..#BD.J ,/UD5TS SOLVE PRO#MS 9VOLV+
FUNC;NAL 3CEPTS1 S* Z .-POSI;N @1 DEF9+
! 9V]SE FUNC;N ..& P]=M+ >I?METIC OP],NS
ON .FUNC;NS4
,,"Q ,H[ C Y USE A GRAPH+ CALCULATOR
6P]=M OP],NS ) FUNC;NS8
,,EXAMPLE ,P]=M FUNC;N OP],NS
,LET .;F7.;X7 .K .;X #B -- #C .;X @+
#F & .;G7.;X7 .K .;X -- #D4 ,F9D .;F
7#D7 @+ .;G 7#D7 & .;F7.;G 7--#B774
,,/EP #A ,=M SUM
,5T] ;Y #A .K ;X #B -- #C .;X @+ #F &
;Y #B .K .;X -- #D4 ,! SUM C 2 5T]$ Z ;Y
#C .K .;Y #A @+ .;Y #B @4 ,6D S1 PRESS1
*OOSE ! ;,Y-,V>S M5U1 & SELECT ,FUNC;N4
,,/EP #B .,EVALUATE .SUM
,ON ! HOME SCRE51 5T] ;Y #C 7#D7 &
PRESS @4 ,! SCRE5 %[S T ;Y #C 7#D7 .K
#AJ1 S ;F7#D7 @+ ;G7#D7 .K #AJ4
..,,/EP #C =M .-POSI;N ,! -POSI;N ;F7
.;G7.;X7 @7 C 2 5T]$ Z ;Y #C .K ;Y #A
7;Y #B @7@4
,,/EP #D ,EVALUATE -POSI;N
,ON ! HOME SCRE51 5T] ;Y #C 7--#B7 &
PRESS @4 ,! SCRE5 %[S T ;Y #C 7--#B7 .K
#FJ1 S ;F7;G7--#B77 .K #FJ4
,,PRACTICE
,USE A GRAPH+ CALCULATOR &! FUNC;NS
.;F & .;G 6F9D ! 9DICAT$ VALUE4
.#A4 .;F7.;X7 .K .;X #C @+ #E .;X --
#C1 .;G7.;X7 .K --#C .;X #B -- ;X3
;G7#G7 @+ ;F7#G7
.#B4
.#C4 .;F7.;X7 .K #E .;X #C -- #C .;X
#B @1 .;G7.;X7 -- --#B .;X #B -- #E3
;G7#B7--;F7#B7
.#D4 .;F7.;X7 .K #B .;X #B @+ #G .;X
-- #B1 .;G7.;X7 .K .;X -- #F3 ;F7;G7#E77
------------------------------------#DCF
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,LESSONS #F.A-FC
.#A4 .,,MULTI-.,,/EP .,,PRO#M ,A
CIRCLE IS 9SCRIB$ 9 A SQU>E1 Z %[N4
A4 ,WRITE A FUNC;N .;S7.;X7 =! >EA (!
SQU>E4
B4 ,WRITE A FUNC;N .;C7.;X7 =! >EA (!
CIRCLE4
C4 ,WRITE & SIMPLIFY A FUNC;N ;R7;X7
=! >EA (! %AD$ REGION4
.#B4 .MULTI-.,,/EP .,,PRO#M ,! =MULA
=! VOLUME .;,V (A SPH]E 9 T]MS ( XS
SURFACE >EA ;,S IS .;,V .K #C --#A 7#D
@7 --#A/B 7;,S #C @7 #A/B
A4 ,SIMPLIFY ! "R SIDE (! =MULA4
B4 ,A C&LEP9 B[L+ BALL HAS A SURFACE
>EA ( AB #GI SQU>E 9*ES4 ,:AT IS XS
VOLUME8
C4 ,A #AJ-P9 B[L+ BALL HAS A SURFACE
>EA ( AB #BCB SQU>E 9*ES4 ,:AT IS XS
VOLUME8
,T5-P9 B[L+ BALL
D4 .,-P>E ! SURFACE >1S & VOLUMES (!
TWO B[L+ BALLS4
.#C4 .,,%ORT .,,RESPONSE ,Y >E "W+ Z A
SALES REPRES5TATIVE =A CLO?+
MANUFACTUR]4 ,Y >E PD AN ANNUAL SAL>Y
PLUS A BONUS ( #C@3P ( YR SALES OV]
4#AJJ1JJJ4 ,3SID] ^! TWO FUNC;NS3
.;F7.;X7 .K .;X -- #AJJ1JJJ
.;G7.;X7 .K #J.JC .;X
,: -POSI;N1 .;F7.;G7.;X77 OR
.;G7.;F7.;X77 @1 REPRES5TS YR BONUS IF
.;X .1 #AJJ1JJJ8 .,EXPLA94
.#D4 .,,EXT5D$ .,,RESPONSE ,A
CYL9DRICAL ABV-GR.D POOL HAS A HEI<T (
#E FEET &A RADIUS ( ;X FEET4
A4 ,WRITE AN EQU,N T GIVES ! VOLUME
.;,V (! POOL Z A FUNC;N (! RADIUS .X4
,USE #C.AD =4
B4 ,Y USE A HOSE 6FILL ! POOL ) WAT]4
,WAT] FL[S F ! HOSE AT A RATE ( #ABH
CUBIC FEET P] H\R4 ,AF #H.H H\RS ! POOL
IS HALF FULL4 ,WRITE AN EQU,N T Y C USE
6F9D ! RADIUS .;X (! POOL4
C4 ,:AT IS ! RADIUS (! POOL8
D4 ,A SECOND HOSE T \TPUTS #AJD CUBIC
FEET ( WAT] P] H\R IS A4$ AF ! POOL IS
HALF FULL4 ,F9D ! TOTAL NUMB] ( H\RS X W
TAKE 6FILL (! POOL4 ,YR ANSW] %D 9CLUDE
! #H.H H\RS X TOOK 6FILL ! BOTTOM HALF
(! POOL 9 "P 7;B74
.#E4 .,,OP5-.,,5D$ ,F9D TWO DI6]5T
FUNC;NS .;F7.;X7 S* T .;F7.;F7.;X77 .K
.;X @4
.#F4 .,,%ORT .,,RESPONSE .,DESCRIBE !
/EPS Y WD USE 6SIMPLIFY ? EXPRES.N3
,IS "! ANO!R SET ( /EPS Y CD USE
6SIMPLIFY ! EXPRES.N8 .,EXPLA9 YR
R1SON+4
.#G4 .,,GRI4$ .,,ANSW] ,! VOLUME (A
SPH]E IS #IJJ CUBIC 9*ES4 ,USE ! =MULA
=! VOLUME (A SPH]E1 6F9D ! RADIUS ;R 6!
NE>E/ T5? ( AN 9*4 ,USE #C.AD =4
------------------------------------#DCG
,9VE/IGAT+ ,ALGEBRA ,ACTIV;Y3 #F.D
,EXPLOR+ ,9V]SE ,FUNC;NS
.,,MAT]IALS @* GRAPH PAP] @* /RAI<T$GE
,,"Q ,H[ >E A FUNC;N & XS 9V]SE
RELAT$8
,SIDEB>3
,/&>DS
..#BD.J ,/UD5TS SOLVE PRO#MS .9VOLV+
FUNC;NAL 3CEPTS1 S* Z -POSI;N1 ..DEF9+ !
9V]SE .FUNC;N & P]=M+ >I?METIC OP],NS ON
FUNC;NS4
,,EXPLORE ,F9D ! 9V]SE (
..,,/EP #A ,GRAPH .FUNC;N @1 ,*OOSE
VALUES ( .;X & F9D ! CORRESPOND+ VALUES
( .;Y .K .;F7.;X74 ,PLOT ! PO9TS & DRAW
! L9E T PASSES "? !M4
..,,/EP #B ,9T]*ANGE .COORD9ATES
,9T]*ANGE ! .;X- & ;Y-COORD9ATES (!
ORD]$ PAIRS F.D 9 ,/EP #A4 ,PLOT ! NEW
PO9TS & DRAW ! L9E T PASSES "? !M4
..,,/EP #C ,WRITE .EQU,N ,WRITE AN
EQU,N (! L9E F ,/EP #B4 ,CALL ? FUNC;N
G4
..,,/EP #D ,-P>E .GRAPHS ,FOLD YR
GRAPH PAP] S T ! GRAPHS (_/& .;G
CO9CIDE4 ,H[ >E ! GRAPHS GEOMETRIC,Y
RELAT$8
..,,/EP #E ,DESCRIBE .FUNC;NS ,9 ^WS1
.;F IS ! FUNC;N T SUBTRACTS #C F .;X &
!N DIVIDES ! RESULT 0#B4 ,DESCRIBE !
FUNC;N .;G 9 ^WS4
..,,/EP #F ,F9D .-POSI;NS ,PREDICT :AT
! -POSI;NS .;F7.;G7.;X77 & .;G7.;F7.;X77
W BE4 ,3FIRM YR PREDIC;NS 0F9D+ .;F7
.;G7.;X7 @7 & .;G7.;F7.;X77 @4
,! FUNC;NS .;F & .;G >E CALL$ .9V]SES
( EA* O!R4
,,DRAW ,,3CLU.NS ,USE YR OBS]V,NS
6-PLETE ^! EX]CISES
,-PLETE ,EX]CISES #A-C = EA* FUNC;N
2L4
.;F7.;X7 .K .#C;X @+ #B
#A4 ,-PLETE ,/EPS #A-C ABV 6F9D !
9V]SE (! FUNC;N4
#B4 ,-PLETE ,/EP #D4 ,H[ C Y GRAPH !
9V]SE (A FUNC;N )\T F/ F9D+ ORD]$ PAIRS
7;X1 ;Y78
#C4 ,-PLETE ,/EPS #E & #F4 ,H[ C Y TE/
6SEE IF ! FUNC;N Y F.D 9 ,EX]CISE #A IS
9DE$ ! 9V]SE (! ORIG9AL FUNC;N8
------------------------------------#DCH
#F.D ,USE ,9V]SE ,FUNC;NS
.,2F ,Y P]=M$ OP],NS ) FUNC;NS4
.,N[ ,Y W F9D 9V]SE FUNC;NS4
.,:Y8 ,S Y C 3V]T TEMP]ATURES1 Z 9
,EX4 #DH
,KEY ,VOCABUL>Y
99 9V]SE REL,N
99 9V]SE FUNC;N
,SIDEB>3
,/&>DS
#BD.J ,/UD5TS SOLVE PRO#MS 9VOLV+
FUNC;NAL 3CEPTS1 S* Z -POSI;N1 DEF9+ !
9V]SE FUNC;N & P]=M+ >I?METIC OP],NS ON
FUNC;NS4
,9 ,LESSON #B.A1 Y LE>N$ T A REL,N IS
A PAIR+ ( 9PUT VALUES ) \TPUT VALUES4
,AN .9V]SE .REL,N 9T]*ANGES ! 9PUT &
\TPUT VALUES (! ORIG9AL REL,N4 ,? M1NS T
! DOMA9 & RANGE >E AL 9T]*ANG$4
,ORIG9AL REL,N
,! GRAPH ( AN 9V]SE REL,N IS A
.REFLEC;N (! GRAPH (! ORIG9AL REL,N4 ,!
L9E ( REFLEC;N IS .;Y--.X4 ,6F9D ! 9V]SE
(A REL,N GIV5 0AN EQU,N 9 .;X & .;Y @1
SWIT* ! ROLES ( .;X & .;Y & SOLVE = .Y4
,EXAMPLE #A ,F9D AN 9V]SE REL,N
..,F9D AN EQU,N =! 9V]SE (! .REL,N
..;Y .K .#C;X -- #E4
,9 ,EXAMPLE #A1 BO? ! ORIG9AL REL,N &!
9V]SE REL,N HAPP5 6BE FUNC;NS4 ,9 S*
CASES1 ! TWO FUNC;NS >E CALL$ .9V]SE
.FUNC;NS4
,SIDEB>3
,R1D+
,! SYMBOL --#A 9 .;F --#A IS N 6BE
9T]PRET$ Z AN EXPON5T4 ,9 O!R ^WS1
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,9V]SE ,FUNC;NS
,FUNC;NS .;F & .;G >E 9V]SES ( EA* O!R
PROVID$3
..;F7;G7;X77 .K ;X & ;G7;F7;X77 .K .;X
,! FUNC;N ;G IS DENOT$ 0.;F --#A @1 R1D
Z @8 .;F 9V]SE40
------------------------------------#DCI
,,EXAMPLE #B ,V]IFY T FUNC;NS >E
9V]SES
,V]IFY T .;F7.;X7 .K .#C;X -- #E & >E
9V]SE FUNC;NS4
,SOLU;N
.,/EP .#A ,%[ T .;F7.;F --#A @7@7 .K
.;X @4
.,,/EP .#B .,%[ T .;F --#A 7.;F7.;X77
.K .;X @4
,,EXAMPLE #C ,SOLVE A MULTI-/EP PRO#M
.,,FIT;S ,ELA/IC B&S C 2 US$ 9 EX]CIS+
6PROVIDE A RANGE ( RESI/.E4 ,A B&'S
RESI/.E .;,R 7IN P.DS7 C 2
MODEL$ 0": .;,L IS ! TOTAL L5G? (!
/RET*$ B& 7IN 9*ES74
99 ,F9D ! 9V]SE (! MODEL4
99 ,USE ! 9V]SE FUNC;N 6F9D ! L5G? AT
: ! B& PROVIDES #AI P.DS ( RESI/.E4
,SIDEB>3
,F9D ,9V]SES
,NOTICE T Y D N SWIT* ! V>IA#S :5 Y >E
F9D+ 9V]SES ( MODELS4 ,? WD 2 3FUS+ 2C !
LRS >E *OS5 6REM9D Y (! R1L-LIFE
QUANTITIES !Y REPRES5T4
,SOLU;N
.,,/EP .#A .,F9D ! 9V]SE FUNC;N4
.,,/EP .#B .,EVALUATE ! 9V]SE FUNC;N
:5 .;,R .K #AI4
,! B& PROVIDES #AI P.DS ( RESI/.E :5 X
IS /RET*$ 6#FD 9*ES4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #A1B1
& .#C
,F9D ! 9V]SE (! GIV5 FUNC;N4 ,!N V]IFY
T YR RESULT &! ORIG9AL FUNC;N >E 9V]SES4
.#A4 .;F7.;X7 .K .;X @+ #D
.#B4 .;F7.;X7 .K .#B;X -- #A
.#C4 .;F7.;X7 .K --#C .;X @+ #A
#D4 .,,FIT;S ,USE ! 9V]SE FUNC;N 9
,EXAMPLE #C 6F9D ! L5G? AT : ! B&
PROVIDES #AC P.DS ( RESI/.E4
------------------------------------#DDJ
..,,9V]SES ,,( ,,NONL9E> .,,FUNC;NS ,!
GRAPHS (! P[] FUNC;NS .;F7.;X7 .K .;X #B
& .;G7.;X7 .K .;X #C >E %[N 2L AL;G ) _!
REFLEC;NS 9 ! L9E .;Y .K .X4 ,NOTICE T !
9V]SE ( .;G7.;X7 .K .;X #C IS A FUNC;N1
B T ! 9V]SE ( .;F7.;X7 .K .;X #B IS .N A
FUNC;N4
,IF ! DOMA9 ( .;F7.;X7 .K .;X #B IS
.RE/RICT$ 6ONLY NONNEGATIVE R1L NUMB]S1
!N ! 9V]SE .(F .IS A FUNC;N4
.,EXAMPLE .#D
,F9D ! 9V]SE (A P[] FUNC;N
,F9D ! 9V]SE ( .;F7.;X7 .K ;X #B @1
.;X .1 #J4 ,!N GRAPH .;F & .;F --#A
,SOLU;N
,SIDEB>3
,*ECK ,SOLU;N
,Y C *ECK ! SOLU;N ( ,EXAMPLE #D 0NOT+
T ! GRAPH ( IS ! REFLEC;N (! GRAPH (
.;F7.;X7 .K ;X #B @1 .;X .1 #J1 9 ! L9E
;Y .K .X4
,! DOMA9 ( .;F IS RE/RICT$
6NONNEGATIVE VALUES ( .;X @4 ,S1 ! RANGE
.;F --#A M/ AL 2 RE/RICT$ 6NONNEGATIVE
VALUES1 & "!=E ! 9V]SE IS @4 ,IF ! DOMA9
0 RE/RICT$ 6.;X "K #J1 Y WD *OOSE @4
.,,HORIZONTAL .,,L9E .,,TE/ ,Y C USE !
GRAPH (A FUNCTION_/TO DET]M9E :E!R !
9V]SE ( .;F IS A FUNC;N 0APPLY+ !
.HORIZONTAL .L9E .TE/4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,HORIZONTAL ,L9E ,TE/
,! 9V]SE (A FUNC;N _/ IS AL A FUNC;N
IF & ONLY IF NO HORIZONTAL L9E 9T]SECTS
! GRAPH (_/MORE ?AN ONCE4
,9V]SE IS A FUNC;N
,9V]SE IS N A FUNC;N
------------------------------------#DDA
,,EXAMPLE #E ,F9D ! 9V]SE (A CUBIC
FUNC;N
,3SID] ! FUNC;N .;F7.;X7 .K #B .;X #C
@+ #A4 ,DET]M9E :E!R ! 9V]SE ( .;F IS A
FUNC;N4 ,!N F9D ! 9V]SE4
,SOLU;N
,GRAPH ! FUNC;N .;F ,NOTICE T NO
HORIZONTAL L9E 9T]SECTS ! GRAPH M ?AN
ONCE4 ,S1 ! 9V]SE ( .;F --#A IS XF A
FUNC;N4 ,6F9D AN EQU,N = .;F --#A @1
-PLETE ! FOLL[+ /EPS3
,! 9V]SE ( .;F IS @4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #D &
.#E
,F9D ! 9V]SE (! FUNC;N4 ,!N GRAPH !
FUNC;N & XS 9V]SE4
.#E4 .;F7.;X7 .K ;X #F @1 .;X .1 #J
.#F4
.#G4
.#H4 .;F7.;X7 .K -- .;X #C @+ #D
.#I4 .;F7.;X7 .K #B .;X #E @+ #C
.#AJ4 .;G7.;X7 .K --#G .;X #E @+ #G
,,EXAMPLE #F ,F9D ! 9V]SE (A P[] MODEL
.,,TICKET .,,PRICES ,! AV]AGE PRICE
.;,P 7IN DOLL>S7 =A ,N,NAL ,FOOTBALL
,L1GUE TICKET C 2 MODEL$ BY
;,P .K #CE ;T #J.AIB
": .TIS ! NUMB] ( YE>S S9CE #AIIE4
,F9D ! 9V]SE MODEL T GIVES "T Z A FUNC;N
(! AV]AGE TICKET PRICE4
,SOLU;N
------------------------------------#DDB
,,EXAMPLE #G ,USE AN 9V]SE P[] MODEL
6MAKE A PREDIC;N
,USE ! 9V]SE P[] MODEL F ,EXAMPLE #F
6PREDICT ! YE> :5 ! AV]AGE TICKET PRICE
W R1* 4#EH4
,SOLU;N
,Y C PREDICT T ! AV]AGE TICKET PRICE W
R1* 4#EH AB #AD YE>S AF #AIIE1 OR 9
#BJJI4
..,GUID$ ,PRACTICE = ,EXAMPLES #F &
.#G
.#AA4 .,,TICKET .,,PRICES ,! AV]AGE
PRICE .;,P 7IN DOLL>S7 =A ,MAJOR ,L1GUE
,BASEBALL TICKET C 2 MODEL$ 0.;,P .K
#AJ.G;T #J.BGB ": .;T IS ! NUMB] ( YE>S
S9CE #AIIE4 ,WRITE ! 9V]SE MODEL4 ,!N
USE ! 9V]SE 6PREDICT ! YE> :5 ! AV]AGE
TICKET PRICE W R1* 4#BE4
#F.D ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
,,WS#AB = ,EXS4 #G1AE1 & #DI
.K .,,/&>DIZ$ .,,TE/ .,,PRACTICE ,EXS4
#B1AD1 #BA1 #BH1 & #DH
,,SKILL ,,PRACTICE
#A4 .,,VOCABUL>Y ,/ATE ! DEF9I;N ( AN
9V]SE REL,N4
#B4 .,,WRIT+ .,EXPLA9 H[ 6DET]M9E :E!R
A FUNC;N .;G IS AN 9V]SE .(F4
.,,EXAMPLE .#A ON P4 #DCH = ,EXS4
#C-AC
.,,9V]SE .,,REL,NS ,F9D AN EQU,N =!
9V]SE REL,N4
.#C4 .;Y .K #D;X--#A
.#D4 .;Y .K --#B;X @+#E
.#E4 .;Y .K #G;X--#F
.#F4 .;Y .K #AJ;X--#BH
#G4 .;Y .K #AB .;X @+ #G
.#H4 .;Y .K --#AH .;X -- #E
.#I4
.#AJ4
.#AA4
.,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 F9D+ ! 9V]SE (! REL,N4
.#AB4
.#AC4
------------------------------------#DDC
.,,EXAMPLE .#B ON P4 #DCI = ,EXS4
#AE-BA
.#AD4 .,,OP5-.,,5D$ .,,MA? ,WRITE A
FUNC;N .;F S* T ! GRAPH ( .;F --;L IS A
L9E )A SLOPE ( #C4
,,V]IFY+ ,,9V]SE ,,FUNC;NS ,V]IFY T
.;F & .;G >E 9V]SE FUNC;NS4
.;L#E4 .;F7.;X7 .K .;X @+ #D1 .;G7.;X7
.K .;X -- #D
.#AF4
.#AG4
.#AH4
.#AI4
.#BJ4
#BA4 .,,MULTIPLE .,,*OICE ,:AT IS !
9V]SE (! FUNC;N ^: GRAPH IS %[N8
,A
;,B
;,C
;,D
.,,EXAMPLE .#D ON P4 #DDJ = ,EXS4
#BB-BH
,,9V]SES ,,( ,,P[] ,,FUNC;NS ,F9D !
9V]SE (! P[] FUNC;N4
.#BB4 .;F7.;X7 .K .;X #G
.#BC4 .;F7.;X7 .K #D .;X #D @1 .;X .1
#J
.#BD4 .;F7.;X7 .K --#AJ .;X #F @1 .;X
"K #J
.#BE4 .;F7.;X7 .K #CB .;X #E
.#BF4
.#BG4
.#BH4 ,,MULTIPLE ,,*OICE ,:AT IS !
9V]SE ( @8
7.,A7 .;G7.;X7 .K --#D .;X #C
7.;,B7
7.;,C7
7.;,D7
.,,EXAMPLE .#E ON P4 #DDA = ,EXS4
#BI-DC
.,,HORIZONTAL .,,L9E .,,TE/ ,GRAPH !
FUNC;N .;F @4 ,!N USE ! GRAPH 6DET]M9E
:E!R ! 9V]SE ( .;F IS A FUNC;N4
.#BI4 .;F7.;X7 .K #C .;X @+ #A
.#CJ4 .;F7.;X7 .K -- .;X -- #E
.#CA4
.#CB4 .;F7.;X7 .K --#F .;X #B @1
;X.1#J
.#CC4
.#CD4 .;F7.;X7 .K .;X #C -- #B
.#CE4 .;F7.;X7 .K @7 .;X -- #D7@7 .;X
@+ #A7
.#CF4 .;F7.;X7 .K _\ .;X _\ @+ #D
.#CG4 .;F7.;X7 .K #D .;X #D -- #E .;X
#B -- #F
,,9V]SES ,,( ,,NONL9E> ,,FUNC;NS ,F9D
! 9V]SE (! FUNC;N4
.#CH4
.#CI4 .;F7.;X7 .K .;X #C -- #B
.#DJ4
.#DA4
.#DB4
.#DC4 .;F7.;X7 .K .;X #D -- #I1 .;X .1
#J
#DD4 .,,R1SON+ ,DET]M9E :E!R ! /ATE;T
IS ..TRUE OR FALSE4 .,EXPLA9 YR R1SON+4
A4 ,IF .;F7.;X7 .K .;X ;N ": .;N IS A
POSITIVE EV5 9TEG]1 !N ! 9V]SE ( .;F IS
A FUNC;N4
B4 ,IF .;F7.;X7 .K .;X ;N ": .;N IS A
POSITIVE ODD 9TEG]1 !N ! 9V]SE ( .;F IS
A FUNC;N4
#DE4 .,,*ALL5GE ,%[ T ! 9V]SE ( ANY
L9E> FUNC;N .;F7.;X7 .K .MX @+ .;B @1 ":
.;M # #J1 IS AL A L9E> FUNC;N4 ,GIVE !
SLOPE & .;Y -9T]CEPT (! GRAPH ( .;F --#A
9 T]MS ( .;M & .B4
------------------------------------#DDD
,,PRO#M ,,SOLV+
.,,EXAMPLE .#C @3 ON P4 #DCI = ,EXS4
#DF-DH
.#DF4 .,,EX*ANGE .,,RATES ,! EURO IS !
UNIT ( CURR5CY =! ,EUROP1N ,UNION4 ,ON A
C]TA9 "D1 ! NUMB] .;,E ( EUROS T CD 2
OBTA9$ = .;,D DOLL>S 0 GIV5 0? FUNC;N3
.;,E .K #J.HADAI;,D
,F9D ! 9V]SE (! FUNC;N4 ,!N USE !
9V]SE 6F9D ! NUMB] ( DOLL>S T CD 2
OBTA9$ = #BEJ EUROS ON T "D4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#DG4 .,,MULTI-.,,/EP .,,PRO#M ,:5
CALIBRAT+ A SPR+ SCALE1 Y NE$ 6"K H[ F>
! SPR+ /RET*ES = V>I\S WEI<TS4 ,HOOKE'S
LAW /ATES T ! L5G? A SPR+ /RET*ES IS
PROPOR;NAL 6! WEI<T ATTA*$ 6X4 ,A MODEL
= "O SCALE IS .;L .K .#J..E;W @+ #C ": #
.IS ! TOTAL L5G? 7IN 9*ES7 (! /RET*$
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OBJECT4
A4 ,F9D ! 9V]SE (! GIV5 MODEL4
B4 ,IF Y PLACE A WEI<T ON ! SCALE &!
SPR+ /RET*ES 6A TOTAL L5G? ( #F.E 9*ES1
H[ H1VY IS ! WEI<T8
@A.,HOME,TUTOT = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#DH4 .,,EXT5D$ .,,RESPONSE ,AT ! />T
(A DOG SL$ RACE 9 ,AN*ORAGE1 ,ALASKA1 !
TEMP]ATURE 0 #E;DG,C4 ,0! 5D (! RACE1 !
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.;,F 6DEGREES ,CELSIUS ;,C IS @4
A4 ,F9D ! 9V]SE (! GIV5 MODEL4
.,DESCRIBE :AT 9=M,N Y C OBTA9 F !
9V]SE4
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/>T & 5D (! RACE4
C4 ,USE A GRAPH+ CALCULATOR 6GRAPH !
ORIG9AL FUNC;N & XS 9V]SE4 ,F9D !
TEMP]ATURE T IS ! SAME ON BO? TEMP]ATURE
SCALES4
..,,EXAMPLES #F & .#G ON PP4 #DDA-DDB
= ,EXS4 #DI-EJ
.#DI .,,BOAT .,,SPE$ ,! MAXIMUM HULL
SPE$ .;V 7IN KNOTS7 (A BOAT )A 4PLACE;T
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WAT]L9E4 ,F9D ! 9V]SE (! MODEL4 ,!N F9D
! WAT]L9E L5G? NE$$ 6A*IEVE A MAXIMUM
SPE$ ( #G.E KNOTS4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
.#EJ4 .,,BIOLOGY ,! BODY SURFACE >EA
.,A 7IN SQU>E MET]S7 (A P]SON )A MASS (
#FJ KILOGRAMS C 2 APPROXIMAT$ 0! MODEL
.,A .K #J.BAIE;FT #J.CIFD
": .;H IS ! P]SON'S HEI<T 7IN
C5TIMET]S74 ,F9D ! 9V]SE (! MODEL4 ,!N
E/IMATE ! HEI<T (A #FJ KILOGRAM P]SON :O
HAS A BODY SURFACE >EA ( #A.F SQU>E
MET]S4
.K ..,,"W$-,,\ ,,SOLU;NS .ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#DDE
#EA4 .,,*ALL5GE ,3SID] ! FUNC;N
.;G7.;X7 .K --X4
A4 ,GRAPH ;G7;X7 .K --.;X & EXPLA9 :Y
X IS XS [N 9V]SE4 ,AL V]IFY T ;G7;X7 .K
;G --;L 7;X7 ALGEBRAIC,Y4
B4 ,GRAPH O!R L9E> FUNC;NS T >E _! [N
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C4 ,USE YR RESULTS F "P 7;B7 6WRITE A
G5]AL EQU,N DESCRIB+ ! FAMILY ( L9E>
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,MIX$ ,REVIEW
,PREVIEW
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,GRAPH ! FUNC;N4
.#EB4 .;Y .K _\ .;X _\--#B PP4 #ABC
.#EC4 .;Y .K _\ .;X @+ #A_\ @+ #C PP4
#ABC
.#ED4 .;Y .K --#C_\ .;X _\ PP4 #ABC
.#EE4 .;Y .K #C7 .;X -- #D7@7 .;X @+
#B7 PP4 #BDE
.#EF4 .;Y .K --#B7 .;X @+ #C7 #B --#D
PP4 #BDE
.#EG4
,SOLVE ! SY/EM ( L9E> EQU,NS4 PP4 #CEC
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.;X @+ #B .;Y .K #B
.#EI4 #B .;X -- #D .;Y .K #AC
#D .;X @+ #E .;Y .K #H
.#FJ4 #G .;X -- #AB .;Y .K --#BB
#BE .;X @+ #H .;Y .K #AD
,SOLVE ! EQU,N4 PP4 #CEC
.#FA4 #F .;X #C -- #ED .;X .K #J
.#FB4 #B .;X #C -- #H .;X #B @+ #H .;X
.K #J
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.#FE4 #D .;X #C @+ #H .;X #B -- #BE
.;X -- #EJ .K #J
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,,QUIZ = ,LESSONS #F.C-F.D
.,LET .;F7.;X7 .K .#D;X #B - .;X .&
.;G7.;X7 .K .#B;X #B @4 ..,P]=M !
9DICAT$ OP],N & /ATE ! .DOMA91 @7 P4
#DBH @7
#A4 .;F7.;X7 @+ .;G7.;X7
#B4 .;G7.;X7--.;F7.;X7
#C4 .;F7.;X7 99 .;G7.;X7
#D4
#E4 7.;F7.;G7.;X77
#F4 .;G77.;X77
#G4 .;F7.;F7.;X77
#H4 .;G7.;G7.;X77
,V]IFY T .;F & .;G >E 9V]SE FUNC;NS1
@7 P4 #DCH @7
.#I4 .;F7.;X7 .K .;X -- #I1 .;G7.;X7
.K .;X @+ #I
.#AJ4
.#AA4
.#AB4
,F9D ! 9V]SE (! FUNC;N1 @7 P4 #DCH @7
.#AC4
.#AD4 .;F7.;X7 .K .;X #B -- #AF1 .;X
.1.K #J
.#AE4
#AF4 .;F7.;X7 .K ..#E ;X @+ .#AB
#AG4 .;F7.;X7 .K --.#C .;X #C -- .#D
#AH4 .;F7.;X7 .K .#I;X #D -- ..#DI1 ;X
"K.K .#J
.#AI4 .,,GASOL9E .,,CO/S ,! CO/ 7IN
DOLL>S7 ( ;G GALLONS ( GASOL9E C 2
MODEL$ 0.;,C7.;G7 .K .#B..AEG4 ,! AM.T (
GASOL9E US$ 0A C> C 2 MODEL$ 0.GID7 .K
.#J..JB;D ": .;D IS ! 4T.E 7IN MILES7 T
! C> HAS BE5 DRIV54 ,F9D .,CIGID77 &
;,C7;G7#DJJ774 ,:AT DOES ;,C7;G7#DJJ77
REPRES5T8 7.P4 .#DBH7
,,EXTRA ,,PRACTICE = ,LESSON #F.D #G
P4 #AJAE
..,,ONL9E ,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#DDF
#F.E ,GRAPH ,SQU>E ,ROOT & ,CUBE
,ROOT ,FUNC;NS
.,2F ,Y GRAPH$ POLYNOMIAL FUNC;NS4
.,N[ ,Y W GRAPH SQU>E ROOT & CUBE ROOT
FUNC;NS4
.,:Y8 ,S Y C GRAPH ! SPE$ (A RAC+ C>1
Z 9 ,EX4 #CH4
,KEY ,VOCABUL>Y
99 .RADICAL .FUNC;N
99 .P>5T .FUNC;N @1 P4 #HI
,SIDEB>3
,/&>DS
..#AB.J ,/UD5TS "K ! LAWS ( FRAC;NAL
.EXPON5TS @1 "U/& EXPON5TIAL FUNC;NS1 &
USE ^! FUNC;NS 9 PRO#MS 9VOLV+
EXPON5TIAL GR[? & DECAY4
,9 ,LESSON #F.D1 Y SAW ! GRAPHS ( &
,^! >E EXAMPLES ( .RADICAL .FUNC;NS4 ,9
? LESSON1 Y W LE>N 6GRAPH FUNC;NS (! =M
& @4
,,KEY ,,3CEPT
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,P>5T ,FUNC;NS = ,SQU>E ,ROOT & ,CUBE
,ROOT ,FUNC;NS
,! P>5T FUNC;N =! FAMILY ( SQU>E ROOT
FUNC;NS IS @4
,PICTURE3 ,DOMA93 .;X .1.K #J1 ,RANGE3
.;Y .1.K #J
,! P>5T FUNC;N =! FAMILY ( CUBE ROOT
FUNC;NS IS @4
,PICTURE3 ,DOMA9 & RANGE3 ALL R1L
NUMB]S
,,EXAMPLE #A
,GRAPH A SQU>E ROOT FUNC;N
.,GRAPH @1 ..& /ATE ! DOMA9 & RANGE4
,-P>E ! GRAPH )! GRAPH .( @4
,SOLU;N
,MAKE A TA# ( VALUES & SKET* ! GRAPH4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #J3 #A3 #B3 #C3 #D
.;Y @3 #J3 #J.E3 #J.GA3 #J.HG3 #A
,SIDEB>3
,REVIEW ,DOMA9 ,& ,RANGE
,= HELP )! DOMA9 & RANGE (A FUNC;N1
SEE P4 #GB @4
,! RADIC& (A SQU>E ROOT M/ 2
NONNEGATIVE4 ,S1 ! DOMA9 IS .;X .1.K #J4
,! RANGE IS .;Y .1.K #J4
,! GRAPH ( IS A V]TICAL %R9K (! GRAPH
( 0A FACTOR ( @4
------------------------------------#DDG
,EXAMPLE #B ,GRAPH A CUBE ROOT FUNC;N
.,GRAPH @1 ..& /ATE ! DOMA9 & RANGE4
,-P>E ! GRAPH )! GRAPH .( @4
,SOLU;N
,MAKE A TA# ( VALUES & SKET* ! GRAPH4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 --#B3 --#A3 #J3 #A3 #B
.;Y @3 #C.GH3 #C3 #J3 --#C3 --#C.GH
,! DOMA9 & RANGE >E ALL R1L NUMB]S4
,! GRAPH ( IS A V]TICAL /RET* (! GRAPH
( 0A FACTOR ( #C FOLL[$ 0A REFLEC;N 9 !
;X-AXIS4
,SIDEB>3
,REVIEW ,/RET*ES ,& ,%R9KS
,= HELP ) V]TICAL /RET*ES & %R9KS1 SEE
P4 #ABC @4
,,EXAMPLE #C ,SOLVE A MULTI-/EP PRO#M
.,,P5DULUMS ,! .P]IOD (A P5DULUM IS !
"T ! P5DULUM TAKES 6-PLETE "O BACK-&-=?
SW+4 ,! P]IOD .;,T 7IN SECONDS7 C 2
MODEL$ 0": IS ! P5DULUM'S L5G? 7IN
FEET74
99 ,USE A GRAPH+ CALCULATOR 6GRAPH !
MODEL4
99 ,H[ L;G IS A P5DULUM )A P]IOD ( #C
SECONDS8
,SOLU;N
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EQU,N @4 ,! GRAPH IS %[N 2L4
.,,/EP .#B .,USE ! .TRACE F1TURE 6F9D
! VALUE ( .;X :5 .;Y .K #C4 ,! GRAPH %[S
.;X #G.C4
,A P5DULUM )A P]IOD ( #C SECONDS IS AB
#G.C FEET L;G4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #A1B1
& .#C
,GRAPH ! FUNC;N4 ,!N /ATE ! DOMA9 &
RANGE4
#A4
#B4
#C4
#D4
.#E4 .,,:AT .,,IF8 ,USE ! MODEL 9
,EXAMPLE #C 6F9D ! L5G? (A P5DULUM )A
P]IOD ( #A SECOND4
------------------------------------#DDH
..,,TRANSL,NS ,,( ,,RADICAL .,,FUNC;NS
,! PROC$URE = GRAPH+ FUNC;NS (! =M & IS
DESCRIB$ 2L4
,,KEY ,,3CEPT .= .,YR .,NOTEBOOK
,GRAPHS ( ,RADICAL ,FUNC;NS
,6GRAPH OR @1 FOLL[ ^! /EPS3
.,,/EP .#A .,SKET* ! GRAPH ( OR @4
.,,/EP .#B .,TRANSLATE ! GRAPH
HORIZONT,Y .;H UNITS & V]TIC,Y .;K
UNITS4
,,EXAMPLE #D ,GRAPH A TRANSLAT$ SQU>E
ROOT FUNC;N
.,GRAPH @4 ..,!N /ATE ! DOMA9 &
.RANGE4
,SIDEB>3
,REVIEW ,TRANSL,NS
,= HELP ) TRANSLAT+ GRAPHS1 SEE P4
#ABC @4
,SOLU;N
.,,/EP .#A .,SKET* ! GRAPH ( 7%[N 9
BLUE74 ,NOTICE T X 2G9S AT ! ORIG9 &
PASSES "? ! PO9T 7#A1 --#B74
.,,/EP .#B .,TRANSLATE ! GRAPH4 ,= .;H
.K #C & .;K .K #B4 ,S1 %IFT ! GRAPH ( "R
#C UNITS & UP #B UNITS4 ,! RESULT+ GRAPH
/>TS AT 7#C1 #B7 & PASSES "? 7#D1 #J74
,F ! GRAPH1 Y C SEE T ! DOMA9 (!
FUNC;N IS .;X .1.K #C &! RANGE (! FUNC;N
IS .;Y "K.K #B4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
,,EXAMPLE #E ,GRAPH A TRANSLAT$ CUBE
ROOT FUNC;N
.,GRAPH @4 ..,!N /ATE ! DOMA9 &
.RANGE4
,SOLU;N
.,,/EP .#A .,SKET* ! GRAPH ( 7%[N 9
BLUE74 ,NOTICE T X PASSES "? ! ORIG9 &!
PO9TS 7--#A1 --#C7 & 7#A1C74
.,,/EP .#B .,TRANSLATE ! GRAPH4 ,NOTE
T = & .;K .K --#A4
,S1 ,%IFT ! GRAPH ( LEFT #D UNITS &
D[N #A UNIT4 ,! RESULT+ GRAPH PASSES "?
! PO9TS 7--#E1 --#D71 7--#D1 --#A71 &
7--#C1 #B74
,F ! GRAPH1 Y C SEE T ! DOMA9 & RANGE
(! FUNC;N >E BO? ALL R1L NUMB]S4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
------------------------------------#DDI
..,,GUID$ ,,PRACTICE = ,EXAMPLES #D &
.#E
,GRAPH ! FUNC;N4 ,!N /ATE ! DOMA9 &
RANGE4
#F4
#G4
#H4
#I4
#AJ4
#AA4
#F.E ,EX]CISES
,HOME"W ,KEY
.K ..,,"W$-,,\ ,,SOLU;NS .ON P4
,,WS#AB ..= ,EXS4 #AA1AG1 & .#CG
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE ,EX4
#B1 #I1 #BE1 #BG1 & #CG
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,,SKILL ,,PRACTICE
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>E EXAMPLES ( - @8 - FUNC;NS4
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.A .K #A1 .;H .K #J1 & .;K .K #J4
,PREDICT H[ ! GRAPH ( W *ANGE IF3
A4 .A .K --#C
B4 .;H .K #B
C4 .;K .K #D
..,,EXAMPLE #A ON .P4 #DDF = ,EXS4
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FUNC;N4 ,!N /ATE ! DOMA9 & RANGE4
.#C4
.#D4
.#E4
.#F4
.#G4
.#H4
#I4 .,,MULTIPLE .,,*OICE ,! GRAPH ( :
FUNC;N IS %[N8
,A
;,B
;,C
;,D
.,,EXAMPLE .#B ON P4 #DDG = ,EXS4
#AJ-AE
,,CUBE ,,ROOT ,,FUNC;NS ,GRAPH !
FUNC;N4 ,!N /ATE ! DOMA9 & RANGE4
#AJ4
#AA4
#AB4
#AC4
#AD4
#AE4
,,RADICAL ,,FUNC;NS ,GRAPH ! FUNC;N4
,!N /ATE ! DOMA9 & RANGE4
..,,EXAMPLES #D & .#E ON P4 #DDH =
,EXS4 #AF-BD
#AF4
#AG4 .;Y .K 7;X @+ #A7 #A/B @+#H
#AH4
#AI4
#BJ4
#BA4
.#BB4
.#BC4
.#BD4
.#BE4 .,,%ORT .,,RESPONSE .,EXPLA9 :Y
"! >E LIMIT,NS ON ! DOMA9 & RANGE (!
FUNC;N @4
------------------------------------#DEJ
#BF4 .,,]ROR .,,ANALYSIS ,A /UD5T TRI$
6EXPLA9 H[ ! GRAPHS ( & >E RELAT$4
.,DESCRIBE & CORRECT ! ]ROR4
,! GRAPH ( IS ! GRAPH ( TRANSLAT$ "R
#A UNIT & D[N #C UNITS4
#BG4 .,,MULTIPLE .,,*OICE ,IF ! GRAPH
( IS %IFT$ LEFT #B UNITS1 :AT IS ! EQU,N
(! TRANSLAT$ GRAPH8
,A
;,B
;,C
;,D
.,,R1SON+ ,F9D ! DOMA9 & RANGE (!
FUNC;N )\T GRAPH+4 .,EXPLA9 H[ Y F.D YR
ANSW]S4
.#BH4
.#BI4
.#CJ4
.#CA4
.#CB4
.#CC4
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CALCULATOR4 ,MAKE G5]ALIZ,NS AB ! GRAPH
:5 .;N IS EV5 & :5 .;N IS ODD4
,,PRO#M ,,SOLV+
.,,EXAMPLE .#C ON P4 #DDG = ,EXS4
#CE-CF
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.;D 7IN MILES7 T A PILOT C SEE 6!
HORIZON C 2 MODEL$ 0": .A IS ! PLANE'S
ALTITUDE 7IN FEET ABV SEA LEVEL74 ,GRAPH
! MODEL ON A GRAPH+ CALCULATOR4 ,!N
DET]M9E AT :AT ALTITUDE ! PILOT C SEE #H
MILES4
@A.,HOME,TUT,( = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#CF4 .,,P5DULUMS ,USE ! MODEL =! P]IOD
(A P5DULUM F ,EXAMPLE #C ON PAGE #DDG @4
A4 ,F9D ! P]IOD (A P5DULUM )A L5G? (
#B FEET4
B4 ,F9D ! L5G? (A P5DULUM )A P]IOD (
#B SECONDS4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#CG4 .,,%ORT .,,RESPONSE ,! SPE$ .;V
7IN MET]S P] SECOND7 ( S.D WAVES 9 AIR
DEP5DS ON ! TEMP]ATURE .;,K 7IN KELV9S7
& C 2 MODEL$ BY3
A4 ,KELV9 TEMP]ATURE _,,RT IS RELAT$
6,CELSIUS TEMP]ATURE ;,C 0! =MULA .;,K
.K #BGC.AE @+ ,C4 ,WRITE AN EQU,N T
GIVES ! SPE$ .;V ( S.D WAVES 9 AIR Z A
FUNC;N (! TEMP]ATURE ;,C 9 DEGREES
,CELSIUS4
B4 ,:AT >E A R1SONA# DOMA9 & RANGE =!
FUNC;N F "P 7A78
.K ..,,"W$-,,\ ,,SOLU;NS .ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
------------------------------------#DEA
#CH4 .,,DRAG .,,RAC+ ,=A GIV5 TOTAL
WEI<T1 ! SPE$ (A C> AT ! 5D (A DRAG RACE
IS A FUNC;N (! C>'S P[]4 ,=A C> )A TOTAL
WEI<T ( #CEJJ P.DS1 ! SPE$ .;S 7IN MILES
P] H\R7 C 2 MODEL$ 0": .;P IS ! P[] 7IN
HORSEP[]74 ,GRAPH ! MODEL4 ,!N DET]M9E !
P[] (A #CEJJ P.D C> T R1*ES A SPE$ (
#BJJ MILES P] H\R4
#CI4 .,,MULTIPLE .,,REPRES5T,NS ,"U
C]TA9 3DI;NS1 A SKYDIV]'S T]M9AL VELOC;Y
.;V ;T.' .-7IN FEET P] SECOND7 IS GIV5
BY
": ,,VK IS ! WEI<T (! SKYDIV] 7IN
P.DS7 & ,A IS ! SKYDIV]'S CROSS-SEC;NAL
SURFACE >EA 7IN SQU>E FEET74 ,NOTE T
SKYDIV]S C V>Y _! CROSS-SEC;NAL SURFACE
>EA 0*ANG+ POSI;NS Z !Y FALL4
A4 .,WRIT+ .AN .,EQU,N ,WRITE AN EQU,N
T GIVES .;V ;T.' .-Z A FUNC;N ( ,A=A
SKYDIV] :O WEI<S #AFE P.DS4
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VALUES =! EQU,N F "P 7A74
C4 .,DRAW+ .A .,GRAPH ,USE YR TA#
6GRAPH ! EQU,N4
#DJ4 .,,*ALL5GE ,! SURFACE >EA .;,S (A
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IS GIV5 0": .;R IS ! C"O'S RADIUS4
A4 ,USE -PLET+ ! SQU>E 6%[ ! FOLL[+3
B4 ,GRAPH ! EQU,N F "P 7A7 US+ A
GRAPH+ CALCULATOR4
C4 ,F9D ! RADIUS (A "R CIRCUL> C"O )A
SLANT HEI<T ( #A UNIT &A SURFACE >EA (
SQU>E UNITS4
,MIX$ ,REVIEW
,PREVIEW
,PREP>E = ,LESSON #F.F 9 ,EXS4 #DA-DF4
,SOLVE ! EQU,N4
.#DA4
.#DB4 #I7 .;X -- #C7 #B .K #ACJ PAGE
#BFF
.#DC4 #G .;X #B -- #BJ .K #CF PAGE
#BFF
.#DD4 .;X #B -- #AD .;X @+ #CG .K #J
PAGE #BHD
.#DE4 .;X #B -- #DJ .;X @+ #CHC .K #J
PAGE #BHD
.#DF4 .;X #B -- #BB .;X @+ #IG .K #J
PAGE #BHD
..,F9D ALL ! Z]OS (! POLYNOMIAL
.FUNC;N4 PAGE #CGI
.#DG4 .;F7.;X7 .K .;X #D @+ #E .;X #C
-- .;X #B --#E .;X
.#DH4 .;F7.;X7 .K .;X #D -- #BG .;X #B
-- #AC .;X @+ #DB
.#DI4 .;F7.;X7 .K .;X #D @+ .;X #C @+
#B .;X #B @+ #D .;X -- #H
.#EJ4 .;F7.;X7 .K .;X #D @+ #F .;X #C
@+ #AD .;X #B @+ #ED .;X @+ #DE
,LET .;F7.;X7 .K #E .;X #B/C &
.;G7.;X7 .K #C .;X #A/B @4 ,P]=M !
9DICAT$ OP],N4 PAGE #DBH
.#EA4
.#EB4 .;F7.;X7 99 .;F7.;X7
.#EC4 .;G7.;X7 99 .;G7.;X7
.#ED4 .;F7.;X7 99 .;G7.;X7
#EE4 .;F7.;G7.;X77
#EF4 .;G7.;F7.;X77
#EG4 .;F7.;F7.;X77
#ED4 .;G7.;G7.;X77
.,,EXTRA .,,PRACTICE = ,LESSON #F.E41
P4 #AJAE
..,,ONL9E ,,QUIZ AT _+CLASSZONE.COM_:
.#DEA
------------------------------------#DEB
#F.F ,SOLVE ,RADICAL ,EQU,NS
.,2F ,Y SOLV$ POLYNOMIAL EQU,NS4
.,N[ ,Y W SOLVE RADICAL EQU,NS4
.,:Y8 ,S Y C CALCULATE HANG "T1 Z 9
,EX4 #FJ4
,KEY ,VOCABUL>Y
99 RADICAL EQU,N
99 EXTRANE\S SOLU;N1 P4 #EB
,SIDEB>3
,/&>DS
..#AB.J ,/UD5TS "K ! LAWS ( FRAC;NAL
.EXPON5TS @1 "U/& EXPON5TIAL FUNC;NS1 &
USE ^! FUNC;NS 9 PRO#MS 9VOLV+
EXPON5TIAL GR[? & DECAY4
,EQU,NS ) RADICALS T H V>IA#S 9 _!
RADIC&S >E CALL$ RADICAL EQU,NS4 ,AN
EXAMPLE (A RADICAL EQU,N IS @4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
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/EPS3
.,,/EP .#A ,ISOLATE ! RADICAL ON "O
SIDE (! EQU,N1 IF NEC4
.,,/EP .#B ,RAISE EA* SIDE (! EQU,N 6!
SAME P[] 6ELIM9ATE ! RADICAL & OBTA9 A
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US+ TE*NIQUES Y LE>N$ 9 PREVI\S *APT]S4
,*ECK YR SOLU;N4
,,EXAMPLE #A ,SOLVE A RADICAL EQU,N
.,SOLVE @4
.,,*ECK ,*ECK .;X .K #AJ 9 ! ORIG9AL
EQU,N4
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#A
,SOLVE ! EQU,N4 ,*ECK YR SOLU;N4
.#A4
.#B4
.#C4
------------------------------------#DEC
,,EXAMPLE #B ,SOLVE A RADICAL EQU,N
GIV5 A FUNC;N
.,,W9D .,,VELOC;Y ,9 A HURRICANE1 !
M1N SU/A9$ W9D VELOC;Y .;V 7IN MET]S P]
SECOND7 IS GIV5 BY
": .;P IS ! AIR PRESSURE 7IN MILLIB>S7
AT ! C5T] (! HURRICANE4 ,E/IMATE ! AIR
PRESSURE AT ! C5T] (A HURRICANE :5 ! M1N
SU/A9$ W9D VELOC;Y IS #ED.E MET]S P]
SECOND4
,SOLU;N
,! AIR PRESSURE AT ! C5T] (! HURRICANE
IS AB #ICH MILLIB>S4
,SIDEB>3
,ANO!R ,WAY
,= ,ALT]NATIVE ME?ODS = SOLV+ ! PRO#M
9 EXAMPLE #B1 TURN 6PAGE #DFJ =! PRO#M
SOLV+ "W%OP4
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#B
.#D4 .,,:AT .,,IF8 ,USE ! FUNC;N 9
,EXAMPLE #B 6E/IMATE ! AIR PRESSURE AT !
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------------------------------------#DED
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#F4 --#B .;X #C;,M .K --#AF
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#H4 7;X @+ #C7 #E/B .K #CB
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------------------------------------#DEE
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.#AC4
.#AD4
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#CC4
------------------------------------#DEG
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@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
------------------------------------#DEH
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_+CLASSZONE.COM_:
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------------------------------------#DEI
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.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#DFJ
,PRO#M ,SOLV+ ,"W%OP ,LESSON #F.F3
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#DEC
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#ICH & #ICI MILLIB>S4
------------------------------------#DFA
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#IJJ SQU>E C5TIMET]S4
------------------------------------#DFB
,EXT5.N ,SOLVE ,RADICAL ,9EQUALITIES
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------------------------------------#DFC
,,EXAMPLE #B ,SOLVE A RADICAL 9EQUAL;Y
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6-PETE 9 ! ,AM]ICA'S ,CUP SAILBOAT RACE1
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------------------------------------#DFD
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,LESSONS #F.D-F.F
.#A4 .,,MULTI-.,,/EP .,,PRO#M ,A
MANAG] AT A CLO?+ /ORE IS DET]M9+ !
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PLAC$ ON ! SALES FLOOR4 ,! EQU,N T !
MANAG] USES IS .;,R .K .;,C @+ .,,MC ":
.;,R IS ! RETAIL PRICE1 ;,C IS ! CO/ T !
/ORE PAYS =! ITEM1 & ;,M IS ! P]C5T
7EXPRESS$ Z A DECIMAL7 T ! ITEM IS M>K$
UP4
A4 ,! M>KUP = WOM5'S A?LETIC %OES IS
#DJ@3P4 ,WRITE A FUNC;N T GIVES ! RETAIL
PRICE .;,R 9 T]MS (! CO/ ,C4
B4 ,F9D ! 9V]SE (! FUNC;N F "P 7A74
C4 ,USE ! 9V]SE FUNC;N 6F9D ! CO/ (A
PAIR ( WOM5'S A?LETIC %OES T HAS A
RETAIL PRICE ( 4#FJ4
.#B4 .,,%ORT .,,RESPONSE ,! GRAPH ( IS
%[N 2L4 ,SOLVE ! EQU,N .,EXPLA9 H[ Y C
USE ! GRAPH ( 6V]IFY T YR SOLU;N IS
CORRECT4
.#C4 .,,OP5-.,,5D$ ,WRITE A RADICAL
EQU,N ^: ONLY SOLU;N IS --#E4
.#D4 .,,EXT5D$ .,,RESPONSE ,ON A C]TA9
"D1 ! FUNC;N T GIVES ,SW$I% KRONOR 9
T]MS ( ,U4,S4 DOLL>S IS ;K .K #G.DFC;D
": .;K REPRES5TS KRONOR & .;D REPRES5TS
,U4,S4 DOLL>S4
A4 ,F9D ! 9V]SE FUNC;N4
B4 ,H[ _M ,U4,S4 DOLL>S D Y RCV = #BE
KRONOR8
C4 ,EXPRESS :AT ! 9V]SE FUNC;N M1NS 9
^WS4
.#E4 .,,%ORT .,,RESPONSE ,F9D A SQU>E
ROOT FUNC;N T PASSES "? ! PO9TS 7-#AD1
#J7 & 7-#AC1A74 ,>E "! O!R SQU>E ROOT
FUNC;NS T PASS "? ^! PO9TS8 .,EXPLA94
.#F4 .,,OP5-.,,5D$ ,WRITE TWO FUNC;NS
^: GRAPHS >E TRANSL,NS (! GRAPH ( ,! F/
FUNC;N %D H A DOMA9 ( .;X .1.K #D4 ,!
SECOND FUNC;N %D H A RANGE ( .;Y .1.K
--#B4
.#G4 .,,%ORT .,,RESPONSE ,AN OBJECT IS
LAUN*$ UPW>D F GR.D LEVEL & R1*ES A
MAXIMUM HEI<T ( .;H FEET4 ,! 9ITIAL
VELOC;Y .;V 7IN FEET P] SECOND7 (!
OBJECT IS GIV5 0! FUNC;N
A4 ,F9D ! 9V]SE FUNC;N4
B4 ,WRITE A PRO#M T C 2 SOLV$ US+ !
9V]SE FUNC;N4 ,%[ H[ 6SOLVE ! PRO#M4
.#H4 .,,GRI4$ .,,ANSW] ,YR FR REL1SES
A W1!R BALLOON #EJ FEET F Y4 ,:5 !
BALLOON IS AT HEI<T .;H @1 ! 4T.E .;D 2T
Y &! BALLOON IS GIV5 0": .;H & .;D .>E
M1SUR$ 9 FEET4 ,6! NE>E/ FOOT1 :AT IS !
HEI<T (! BALLOON :5 ! 4T.E 2T Y &!
BALLOON IS #AJJ FEET8
.#I4 .,,%ORT .,,RESPONSE ,Y DROP A
PEB# 96A CALM POND1 CAUS+ RIPPLES (
3C5TRIC CIRCLES4 ,! RADIUS .;R 7IN FEET7
(! \T] RIPPLE IS GIV5 0.;R7.;T7 .K .#F;T
": .;T IS ! "T 7IN SECONDS7 AF ! PEB#
HITS ! WAT]4 ,! >EA .,A 7IN SQU>E FEET7
(! \T] RIPPLE IS GIV5 0.,A7.;R7 .K ;R #B
@4 ,F9D .,A7.;R7.;T77 & EVALUATE
.,A7.;R7.#B774 ,:AT DOES ,A7;R7#B77
REPRES5T8
------------------------------------#DFE
#F ,*APT] ,SUMM>Y
,ANIMAT$ ,ALGEBRA
_+CLASSZONE.COM_: ,ELECTRONIC ,FUNC;N
,LIBR>Y
,,BIG ,,ID1S
,= ,YR ,NOTEBOOK
,BIG ,IDEA #A
,US+ ,R,NAL ,EXPON5TS
,! FOLL[+ >E PROP]TIES ( R,NAL
EXPON5TS4 ,LET .A & .;B 2 R1L NUMB]S &
LET .;M & .;N 2 R,NAL NUMB]S4
,BIG ,IDEA #B
,P]=M+ ,FUNC;N ,OP],NS & ,F9D+ ,9V]SE
,FUNC;NS
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,OP],N @3 .,DEF9I;N @3 ,EXAMPLE3
.;F7.;X7 .K #B .;X1 .;G7.;X7 .K .;X --
#E
,A4I;N3 .;H7.;X7 .K .;F7.;X7 @+
.;G7.;X7 @3 .;H7.;X7 .K #B .;X @+
7;X--#E7 .K #C;X--#E
,SUBTRAC;N3 ..;H7;X7 .K
;F7;X7--;G7.;X7 @3 .;H7.;X7 .K #B .;X --
7.;X -- #E7 .K .;X @+ #E
,MULTIPLIC,N3 .;H7.;X7 .K.;F7.;X7 @*
.;G7.;X7 @3 .;H7.;X7 .K #B .;X @7 .;X --
#E7 .K #B .;X #B -- #AJ .;X
,DIVI.N3 @3
,-POSI;N3 .;H7.;X7 .K .;G7.;F7.;X77 @3
.;H7.;X7 .K #B .;X -- #E
,9V]SE3 .;H7.;X7 .K ;G --#A @7 .;X @7
@3 .;H7.;X7 .K .;X @+ #E
,BIG ,IDEA #C
,GRAPH+ ,RADICAL ,FUNC;NS & ,SOLV+
,RADICAL ,EQU,NS
,6.GRAPH RADICAL FUNC;NS1 USE ! GRAPH
(! P>5T FUNC;NS4 ,= EXAMPLE1 6GRAPH @1
TRANSLATE ! GRAPH (1 LEFT #A UNIT & D[N
#B UNITS4
,6.SOLVE A RADICAL EQU,N1 F/ ISOLATE !
RADICAL4 ,!N RAISE EA* SIDE (! EQU,N 6!
SAME P[] & SOLVE ! ,POLYNOMIAL EQU,N4
------------------------------------#DFF
#F ,*APT] ,REVIEW
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
99 ,MULTI-,LANGUAGE ,GLOSS>Y
99 ,VOCABUL>Y PRACTICE
,,REVIEW ,,KEY ,,VOCABUL>Y
99 N? ROOT ( .A1 .P4 .#D;,U
99 9DEX (A RADICAL1 P4 #DAD
99 SIMPLE/ =M (A RADICAL1 P4 #DBB
99 L RADICALS1 P4 #DBB
99 P[] FUNC;N1 P4 #DBH
99 -POSI;N1 P4 #DCJ
99 9V]SE REL,N1 P4 .#DCH
99 9V]SE FUNC;N1 P4 #DCH
99 RADICAL FUNC;N1 P4 .#DDF
99 RADICAL EQU,N1 P4 #DEB
,,VOCABUL>Y ,,EX]CISES
#A4 ,COPY & -PLETE3 ,! 9DEX (! RADICAL
IS - @8 - @4
#B4 ,LI/ TWO DI6]5T PAIRS ( L
RADICALS4
#C4 ,COPY & -PLETE3 ,A7;N7 - @8 -
FUNC;N HAS ! =M .;Y .K .AX ;B.' .-": A
IS A R1L NUMB] & .;B IS A R,NAL NUMB]4
#D4 .,,WRIT+ .,EXPLA9 H[ ! GRAPH (A
FUNC;N &! GRAPH ( XS 9V]SE >E RELAT$4
#E4 .,,WRIT+ .,EXPLA9 H[ 6USE !
HORIZONTAL L9E TE/ 6DET]M9E :E!R ! 9V]SE
(A FUNCTION_/IS AL A FUNC;N4
#F4 .,,WRIT+ .,DESCRIBE H[ ! GRAPH (
IS RELAT$ 6! GRAPH (! P>5T FUNC;N @4
#G4 .,,R1SON+ ,A /UD5T 2GAN SOLV+ !
EQU,N .;X #B/C .K #E 0CUB+ EA* SIDE4
,:AT W ! /UD5T H 6D NEXT8 ,:AT CD !
/UD5T H D"O 6SOLVE ! EQU,N 9 J "O /EP8
,,REVIEW ,,EXAMPLES ,,& ,,EX]CISES
,USE ! REVIEW EXAMPLES & EX]CISES 2L
6*ECK YR "U/&+ (! 3CEPTS Y H LE>N$ 9 EA*
LESSON ( ,*APT] #F4
#F.A ,EVALUATE N? ,ROOTS & ,USE ,R,NAL
,EXPON5TS PP4 #DAD-DAI
,,EXAMPLE
,EVALUATE ! EXPRES.N4
A4
B4
.,,EXAMPLE .#B ON P4 #DAE = ,EXS4
#H-AE
,,EX]CISES
,EVALUATE ! EXPRES.N )\T US+ A
CALCULATOR4
#H4 #HA #A/D
#I4 #J #A/C
#AJ4
#AA4
#AB4 .#BEF #C/D
#AC4 #BG --#B/C
#AD4
#AE4
------------------------------------#DFG
@A.,HOME,TUTOR _+CLASSZONE.COM_:
,*APT] ,REVIEW ,PRACTICE
#F.B ,APPLY ,PROP]TIES ( ,R,NAL
,EXPON5TS
PP4 #DBJ-DBG
,,EXAMPLE
,WRITE ! EXPRES.N 9 SIMPLE/ =M4
,ASSUME ALL V>IA#S >E POSITIVE4
.A4
.B4
..,,EXAMPLES #D1 #F1 & .#G ON PP4
#DBB-DBC = ,EXS4 #AF-AI
,,EX]CISES
,WRITE ! EXPRES.N 9 SIMPLE/ =M4
,ASSUME ALL V>IA#S >E POSITIVE4
.#AF4
.#AG4 7#C #D @* #E #D @7@8 #A/D
.#AH4 7#BE;A #AJ ;B #AF @7 #A/B
.#AI4
#F.C ,P]=M ,FUNC;N ,OP],NS & ,-POSI;N
,,PP4 #DBH-DCD
,,EXAMPLE
,LET .;F7.;X7 .K #C .;X #B @+ #A &
.;G7.;X7 .K .;X @+ #D4 ,P]=M ! 9DICAT$
OP],N4
A4 .;F7.;X7 @+ .;G7.;X7 .K 7#C;X #B @+
#A7 @+ 7;X @+ #D7 .K #C;X #B @+ .;X @+
#E
B4 .;F7.;X7 99 .;G7.;X7 .K 7#C;X #B @+
;L77;X @+ #D7 .K #C;X #C @+ #AB;X #B @+
.;X @+ #D
C4 .;F7.;G7.;X77 -- .;F7.;X @+ .#D7 .K
#C7 .;X @+ #D7 #B @+ #A .K #C7 .;X #B @+
#H .;X @+ #AF7 @+ #A .K #C .;X #B @+ #BD
.;X @+ #DI
..,,EXAMPLES #A1 #B1 & .#E ON PP4
#DBH-DCJ = ,EXS4 #BJ-BC
,,EX]CISES
,LET .;F7.;X7 .K .#D;X -- #F &
.;G7.;X7 .K .;X @+ #H4 ,P]=M ! 9DICAT$
OP],N4
.#BJ4 .;F7.;X7 @+ .;G7.;X7
#BA4 .;F7.;X7--.;G7.;X7
.#BB4 .;F7.;X7 99 .;G7.;X7
#BC4 7.;G7.;X77
#F.D;,USE ,9V]SE ,FUNC;NS
PP4 #DCH-DDE
,,EXAMPLE
,F9D ! 9V]SE (! FUNC;N ..;Y .K .#C;X
@+ #G4
,,EXAMPLES #A1D1 & #E
ON PP4 #DCH-DDA = ,EXS4 #BD-BF
,,EX]CISES
,F9D ! 9V]SE (! FUNC;N4
#BD4
#BE4 .;Y .K #D .;X #B @+ #I1 .;X .1.K
#J
#BF4 .;F7.;X7 .K .;X #C -- #D
------------------------------------#DFH
#F ,*APT] ,REVIEW
#F.E ,GRAPH ,SQU>E ,ROOT & ,CUBE ,ROOT
,FUNC;NS
,,PP4 #DDF-DEA
,,EXAMPLE
.,GRAPH @4
,SKET* ! GRAPH ( @4 ,NOTICE T X 2G9S
AT ! ORIG9 & PASSES "? ! PO9T 7#A1
--#A74
,= @1 & .;K .K .#B4 ,S1 %IFT ! GRAPH (
"R #C UNITS & UP #B UNITS4 ,! RESULT+
GRAPH 2G9S AT ! PO9T 7#C1 #B7 & PASSES
"? ! PO9T 7#D1 #A74
,,EXAMPLE
.,GRAPH
,SKET* ! GRAPH ( @4 ,NOTICE T X PASSES
"? ! PO9TS 7-#A1 --#A71 7#J1 #J71 & 7#A1
#A74 ,= & .;K .K --#D4 ,S1 %IFT ! GRAPH
( LEFT #B UNITS & D[N #D UNITS4 ,!
RESULT+ GRAPH PASSES "? ! PO9TS 7--#C1
--#E71 7-#B1-#D71 & 7-#A1-#C74
..,,EXAMPLES #D & .#E ON P4 #DDH =
,EXS4 #BG-BI
,,EX]CISES
,GRAPH ! FUNC;N4 ,!N /ATE ! DOMA9 &
RANGE4
.#BG4
.#BH4
.#BI4
#F.F ,SOLVE ,RADICAL ,EQU,NS
PP4 #DEB-DEI
,,EXAMPLE
.,SOLVE @4
.,,*ECK ,*ECK .;X .K #D 9 ! ORIG9AL
EQU,N4
,,EXAMPLES #A1 #C1 & #E
ON PP4 #DEB-DED = ,EXS4 #CJ-CB
,,EX]CISES
,SOLVE ! EQU,N4 ,*ECK = EXTRANE\S
SOLU;NS4
.#CJ4
.#CA4 #C .;X #C/D .K #BD
.#CB4
------------------------------------#DFI
#F ,*APT] ,TE/
,EVALUATE ! EXPRES.N )\T US+ A
CALCULATOR4
.#A4 --#ABE #A/C
.#B4 #CB #A/E
.#C4
.#D4
.#E4 #H #E/C
.#F4 #AF --#C/B
.#G4
.#H4
,WRITE ! EXPRES.N 9 SIMPLE/ =M4
,ASSUME ALL V>IA#S >E POSITIVE4
.#I4
.#AJ4
.#AA4
.#AB4
.#AC4
.#AD4
.#AE4
.#AF4
,LET .;F7.;X7 .K .#B;X @+ #I &
.;G7.;X7 .K .#C;X -- #A4 ,P]=M ! 9DICAT$
OP],N & /ATE ! DOMA94
#AG4 .;F7.;X7 @+ .;G7.;X7
#AH4 .;F7.;X7 -- .;G7.;X7
.#AI4 .;F7.;X7 99 .;G7.;X7
.#BJ4
#BA4 .;F7.;G7.;X77
#BB4 .;G7.;F7.;X77
#BC4 .;F7.;F7.;X77
#BD4 .;G7.;G7.;X77
,F9D ! 9V]SE (! FUNC;N4
.#BE4 .;Y .K --#B .;X @+ #E
.#BF4
.#BG4 .;F7.;X7 .K #E;X--#AB
.#BH4
.#BI4 .;F7.;X7 .K .;X #C @+ #E
.#CJ4 .;F7.;X7 .K --#B .;X #C @+ #A
,GRAPH ! FUNC;N4 ,!N /ATE ! DOMA9 &
RANGE4
.#CA4
.#CB4
.#CC4
,SOLVE ! EQU,N4 ,*ECK = EXTRANE\S
SOLU;NS4
.#CD4
.#CE4
.#CF4
#CG4 .,,K9ETIC .,,5]GY ,! K9ETIC 5]GY
.;,E 7IN J\LES7 (A #ABEJ KILOGRAM -PACT
C> IS GIV5 0! EQU,N .;,E .K .#FBE;S #B
": .;S IS ! SPE$ (! C> 7IN MET]S P]
SECOND74
A4 ,WRITE AN 9V]SE MODEL T GIVES !
SPE$ (! C> Z A FUNC;N ( XS K9ETIC 5]GY4
B4 ,USE ! 9V]SE MODEL 6F9D ! SPE$ (!
C> IF XS K9ETIC 5]GY IS #ABJ1JJJ J\LES4
,GIVE ! SPE$ 9 KILOMET]S P] H\R4
C4 ,IF ! K9ETIC 5]GY D\#S1 W ! SPE$
D\#8 .,EXPLA9 :Y OR :Y N4
#CH4 .,,B[L+ .,,SCORES ,9 B[L+1 A
.H&ICAP IS A *ANGE 9 SCORE 6ADJU/ =
DI6];ES 9 PLAY]S' ABILITIES4 ,Y 2L;G 6A
B[L+ L1GUE 9 : EA* B[L]'S H&ICAP .;H IS
DET]M9$ 0HIS OR H] AV]AGE .A US+ ?
=MULA3
.;H .K #J.I7#BJJ -.A7
,IF A B[L]'S AV]AGE IS OV] #BJJ1 !
H&ICAP IS #J4 ,F9D ! 9V]SE (! MODEL4 ,!N
F9D YR AV]AGE IF YR H&ICAP IS #CF4
------------------------------------#DGJ
#F ,/&>DIZ$ ,TE/ ,PREP>,N
,SCOR+ ,RUBRIC
,FULL ,CR$IT
99 SOLU;N IS -PLETE & CORRECT
,"PIAL ,CR$IT
99 SOLU;N IS -PLETE B HAS ]RORS1 .OR
99 SOLU;N IS )\T ]ROR B 9COMPLETE
,NO ,CR$IT
99 NO SOLU;N IS GIV51 .OR
99 SOLU;N MAKES NO S5SE
,SIDEB>3
,/&>DS
..#BD.J ,/UD5TS SOLVE PRO#MS 9VOLV+
FUNC;NAL 3CEPTS1 S* Z .-POSI;N @1 DEF9+
! 9V]SE FUNC;N ..& P]=M+ >I?METIC OP],NS
ON .FUNC;NS4
,,EXT5D$ ,,RESPONSE ,,"QS
,,PRO#M
,=A TYPE ( D9OSAUR CALL$ A !ROPOD1 !
HEI<T AT ! HIP .;H 7IN C5TIMET]S7 C 2
MODEL$ 0.;H7 @7 .K #C.DI;I #AAD ": # .IS
! L5G? 7IN C5TIMET]S7 (! D9OSAUR'S 9/EP4
,! L5G? (! 9/EP C 2 MODEL$ BY @7 .;P7
.K #A.B;P ": ;P IS ! FOOTPR9T L5G? 7IN
C5TIMET]S74
.A4 ,F9D & SIMPLIFY .;H7 7.;P774
.B4 ,EVALUATE .;H7 7#BJ774
.C4 ,EXPLA9 ! M1N+ ( .;H7 7#BJ774
,2L >E SAMPLE SOLU;NS 6! PRO#M4 ,R1D
EA* SOLU;N &! -;TS 9 BLUE 6SEE :Y !
SAMPLE REPRES5TS FULL CR$IT1 "PIAL
CR$IT1 OR NO CR$IT4
,! -POSI;N IS =M$ & SIMPLIFI$
CORRECTLY4
,! VALUE ( .;H7 7.#BJ77 IS CORRECTLY
DET]M9$1 &A CLE> EXPLAN,N ( XS M1N+ IS
GIV54
,SAMPLE #A3 ,FULL CR$IT SOLU;N
.A4 .;H7 7.;P77 .K .;H7.L#..B;P7
.K #C.DI7#A.B;P7 #AAD
.K #C.DI7#A.B7 #A.AD ;P #A.AD #D.CJ;P
#A.AD
.B4 ,6EVALUATE ;H7 7#BJ771 SUB/ITUTE
#BJ = P4
#D.CJ;P #AAD .K #D.CJ 7#BJ7 #A.AD
#D.CJ7#CJ.D7 #ACA
.C4 ,! -POSI;N .;H7 7;P77 REPRES5TS !
HEI<T AT ! HIP .;H (A !ROPOD Z A FUNC;N
(! FOOTPR9T L5G? P4 ,"!=E1 .;H7 7.#BJ77
#ACA M1NS T A !ROPOD )A FOOTPR9T L5G? (
#BJ C5TIMET]S _H AN APPROXIMATE HEI<T AT
! HIP ( #ACA C5TIMET]S4
,,SAMPLE #B3 ,"PIAL CR$IT SOLU;N
,! /UD5T DOES N APPLY ! P[] (A PRODUCT
PROP]TY CORRECTLY4
,! /UD5T EVALUATES ! -POSI;N CORRECTLY
& EXPLA9S XS M1N+4
A4 ..;H7 7;P77 .K ;H7#A..B;P7
.K #C.DI7#A.B;P7 #A.AD
.K #C.DI7#A.B7;P #A.AD
#D.AI;P #A.AD
.B4 ,6EVALUATE .;H7 7.#BJ77 @1
SUB/ITUTE #BJ = .P4
#D.AI;P #A.AD .K #D.AI7#BJ7 #AAD
#D.AI7#CJ.D7 #ABG
.C4 ,! VALUE ( ;H7 7#BJ77 IS ! HEI<T
AT ! HIP (A !ROPOD )A FOOTPR9T L5G? (
#BJ C5TIMET]S4
------------------------------------#DGA
,SAMPLE #C3 ,NO CR$IT SOLU;N
A4 ..;H7 7;P77 .K .;H 7#C.DI #A.AD @7
.K #A.B7#C.DI #A.AD @7
.K #A.B7#C.DI7 #A.AD #A.AD
#A.B7#D.AF7;I #AAD
#D.II #A.AD
,! -POSI;N IS =M$ & SIMPLIFI$
9CORRECTLY4
B4 ,6EVALUATE ;H @7 7#BJ771 SUB/ITUTE
#BJ =
#D.II #A.AD .K #D.II7#BJ7 #A.AD
#D.II7#CJ.D7
#AEB
,! /UD5T SUB/ITUTES #BJ = R ?AN .P4
.C4 ,! -POSI;N .;H @7 7;P77 REPRES5TS
! HEI<T (A !ROPOD Z A FUNC;N (! 9/EP
L5G?4 ,S1 ;H7 7#BJ77 #AEB M1NS T A
!ROPOD ) AN 9/EP L5G? ( #AEB C5TIMET]S
IS #BJ C5TIMET]S TALL4
,! /UD5T'S DESCRIP;N ( .;H7 7#BJ77 IS
9CORRECT4
,,PRACTICE ,APPLY ! ,SCOR+ ,RUBRIC
,SCORE EA* (! FOLL[+ SOLU;NS 6! PRO#M
ON ! PREVI\S PAGE ..Z FULL CR$IT1 "PIAL
.CR$IT @1 OR .NO .CR$IT4 .,EXPLA9 YR
R1SON+4 ,IF Y *OOSE ."PIAL .CR$IT OR .NO
.CR$IT @1 EXPLA9 H[ Y WD *ANGE ! SOLU;N
S T X E>NS A SCORE ( FULL CR$IT4
#A4
A4 ;H7;I7;P77 .K ;H7#A.B;P7
.K #C.DI7#A.B;P7 #A.AD
.K #C.DI7#A.B7 #A.AD 7;P7 #A.AD
#D.C;P #A.AD
B4 ;H7 7#BJ77 #A.AD
.K #D.C7#BJ7 #A.AD
#D.C7#CJ.D7 #AFJ
C4 ,! VALUE ( ;H7 7#BJ77 M1NS T A
!ROPOD )A .FOOTPR9T .#B..J C5TIMET]S L;G
_H A HEI<T AT ! HIP ( #AFJ C5TIMET]S4
#B4
A4 ;H7;I7;P77 .K ;H7#A.B;P7
.K #C.DI7#A.B;P7
#D.AI;P
B4 ,SUB/ITUTE #AJ = P4
;H7;I7#AJ77 .K #D.AI7#AJ7
.K #DA.I
C4 ,IF A !ROPOD HAS A .FOOTPR9T L5G? (
#DA.I C5TIMET]S1 !N ! !ROPOD 0 #AJ
C5TIMET]S TALL4
------------------------------------#DGB
#F ,/&>DIZ$ ,TE/ ,PRACTICE
,,EXT5D$ ,,RESPONSE
#A4 ,! .GE> .RATIO (A BICYCLE IS !
NUMB] ( TEE? 9 ! *A9:EEL DIVID$ 0! NUMB]
( TEE? 9 ! FREE:EEL4 ,! NUMB] .;W (
RE>-:EEL REVOLU;NS IS EQUAL 6! PRODUCT
(! GE> RATIO &! NUMB] ;P ( P$AL
REVOLU;NS4
A4 ,A BICYCLE 9 F/ GE> HAS #BD TEE? 9
! *A9:EEL & #CB TEE? 9 ! FREE:EEL4
,WRITE A FUNC;N T GIVES .;W 9 T]MS ( P4
B4 ,! 4T.E .;D 7IN 9*ES7 A BICYCLE
TRAVELS AF .;W RE>-:EEL REVOLU;NS IS
GIV5 0! FUNC;N .;D .K .#BBJW4 ,USE
-POSI;N ( FUNC;NS 6F9D A FUNC;N T GIVES
.;D 9 T]MS ( P4
C4 ,! GE> RATIO *ANGES :5 ! GE> IS
%IFT$4 ,COPY & -PLETE ! TA#4 .,EXPLA9 H[
! 4T.E TRAVEL$ P] P$AL REVOLU;N *ANGES Z
Y %IFT GE>S4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,GE>3 #E?3 #AJ?3 #AE?
.,TEE? .9 .*A9:EEL @3 .#BD @3 .#DJ @3
.#EJ
.,TEE? .9 .FREE:EEL @3 .#AI @3 --@3
.#AI
..,4T.E P] P$AL .REVOLU;N @3 @8 @3 @8
@3 @8
#B4 ,9 R[+1 A BOAT'S SPE$ ;S 7IN MET]S
P] SECOND7 C 2 MODEL$ 0! EQU,N IS !
NUMB] ( R[]S4
A4 ,USE A CALCULATOR 6F9D ! SPE$ (A
BOAT = CREWS ( #B P1 #D P1 & #H P4
B4 ,F9D ! "T 7IN M9UTES7 X TAKES EA*
CREW F "P 7A7 6-PLETE A #BJJJ MET] RACE4
C4 ,DOES D\BL+ ! NUMB] ( R[]S D\# !
SPE$8 .,EXPLA94
#C4 ,! TA# %[S VOLUME =MULAS = V>I\S
"R PRISMS T H L5G? ;I & ^: BASES >E
REGUL> POLYGONS ) SIDE L5G? .S4
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3TA9 TWO DA%ES4
.,BASE @3 ,TRIANGLE3 ,P5TAGON3
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.,DIAGRAM @3 @3 @3 @3 @3
.,VOLUME @3 .;,V .K #J.DCC;IS #B @3
;,V.K #A.GB ;S.' #B @3 .;,V .K #B.FJ;IS
#B @3 .;,V .K #D.HC;IS #B @3 .;,V .K
#G.FI;IS #B
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( #D 9*ES4
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SAME VOLUME Z ! CUBE F "P 7A7 & .K .S4
,F9D ! SIDE L5G? .;S = EA* PRISM4
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#D4 ,Y H TWO HEMISPH]ICAL SN[ GLOBES4
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O!R4
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B4 ,SUB/ITUTE ! EXPRES.N = ;R F "P 7A7
96! =MULA =! VOLUME (A HEMISPH]E1 @4
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------------------------------------#DGC
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,,MULTIPLE ,,*OICE
#E4 ,:AT IS ! SOLU;N (! EQU,N @8
,A --#AD
;,B --#D
;,C #A
;,D #AA
#F4 ,! GRAPH ( : FUNC;N IS %[N8
,A
;,B
;,C
;,D
#G4 ,:AT IS ! 9V]SE ( .;Y .K --.#B;X
#E @+ #AJ8
,A
;,B
;,C
;,D
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( ;G7;F7#I778
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99 .;G7.;X7 :5 .;X .K #C8
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ORIG9,Y CO/S 4#BG :5 ! 4#AJ IS SUBTRACT$
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FUNC;NS8 .,EXPLA9 :Y OR :Y N4
------------------------------------#DGD
,CUMULATIVE ,REVIEW ,*APT]S #A-F
,WRITE AN EQU,N (! L9E T PASSES "? !
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#A4 7#C1 #A71 .;M .K #D
#B4 7#D1 .#F7,.;M .K .#G
#C4 7-#C1 #B71 ;M .K --#H
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#E4 7@&#;X#BABBB2#E1 #H7
#F4 7#B1 @&#;X#BABBB2#EAJ7
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#G4 --#B;X @+ #G .K #AE 7P4 .#AH7
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@7
#I4 .;X #B -- #I;X @+ #AD .K #J @7 P4
#BEB @7
#AJ4 #D;X #B -- #F;X @+ #I .K #J @7 P4
#BIB @7
#AA4 ;X #C @+ #C;X #B -- L,OX .K #J @7
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#AB4 @7 P4 #DEB @7
,GRAPH ! EQU,N OR 9EQUAL;Y 9 A
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#AC4 .;Y .K #C;X--#E @7 P4 #HI @7
#AD4 .;Y .K--_\;X @+ #D_\ @+ #C @7 P4
#ABC @7
#AE4 ..;Y "K --.#B;X @+ #E @7 P4 #ACB
@7
#AF4 .;Y .K ;X #B -- #B;X--#D @7 P4
#BCF @7
#AG4 .;Y .K #B7;X--#F7 #B -- #E @7 P4
#BDE @7
#AH4 .;Y .1 ;X #B @+ #B;X @+ #A @7 P4
#CJJ @7
#AI4 .;Y .K .;X #C -- #B @7 P4 #CCG @7
#BJ4 .;Y .K #C7;X @+ #B77;X--,I7 #B @7
P4 #CHG @7
#BA4 @7 P4 #DDF @7
,SOLVE ! SY/EM ( L9E> EQU,NS US+ ANY
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#BB4 #B;X @+ #E;Y .K #A 7P4 .#AFJ7
..#C;X--.#B;Y .K #CJ
#BC4 #C;X -- .;Y .K --#I @7 P4 #AFJ @7
#D;X @+ #C;Y .K #AD
#BD4 #B;X @+ #C;Y .K #DG @7 P4 #AGH @7
#G;X--#H;Y .K --#B
#B;X -- .;Y @+ #C;Z .K --#AI
,WRITE ! EXPRES.N Z A -PLEX NUMB] 9
/&>D =M4 @7 P4 #BGE @7
#BE4 7#D -- .#BA7 @+ 7#E @+ .;I7
#BF4 7#C @+ #D;Z7--7#G @+ .#B;I7
#BG4 7#D--#B_/77#F @+ #E87
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.#BH4 .;Y .K ;X #B @+ #F;X @+ #AF
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#CA4 7#B;X #C ;Y #B @7 #C 7P4 .#CCJ7
#CB4 7;X #H @7 #C/D @7 P4 #DBJ @7
#CC4 @7 P4 #CCJ @7
#CD4 @7 P4 #DBJ @7
,P]=M ! 9DICAT$ OP],N4
#CE4 7;X #B @+ LLX--#I7 @+ 7#D;X #B --
#E;X--#G7 @7 P4 #CDF @7
#CF4 7;X #C @+ #C;X--#AJ7--7#B;X #C @+
#C;X #B @+ #H;X7 7P4 .#CDF7
#CG4 7#B;X--#E77;X #B @+ #D;X--#G7 @7
P4 #CDF @7
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@+ 7;X--#E7 @7 P4 #CFB @7
,FACTOR ! POLYNOMIAL -PLETELY1 @7 P4
#CEC @7
#CI4 ;X #D -- #C;X #B -- #DJ
#DJ4 ;X #C -- #ABE
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#DB4 .;F7.;X7 @+ .;G7.;X7
#DC4 .;F7.;X7 @* .;G7.;X7
#DD4 .;F7.;G7.;X77
#DE4 .;G7.;F7.;X77
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#DF4 .;F7.;X7 .K #D;X @+ #F
#DG4
#DH4
#DI4
#EJ4
#EA4
------------------------------------#DGE
.#EB4 .,,BICYCLE .,,CO/S ,Y WANT 6BUY
A BICYCLE T CO/S 4#CFJ4 ,9 ORD] 6PAY =!
BICYCLE1 Y SAVE 4#CJ P] WEEK4 ,H[ _M
WEEKS W X TAKE 6SAVE 5 M"OY 6BUY !
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#EC4 .,,*>ITA# .,,DON,NS ,! TA# 2L %[S
! AM.TS ( M"OY 7IN MILLIONS ( DOLL>S7
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BE/-FITT+ L9E 6PREDICT ! AM.T ( M"OY !
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#A.GA3 #B.C3 #B.GH3 #C.BB3 #C.FI3 #D.BH
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4#CE = L[]-LEVEL S1TS & 4#BE =
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#AGJ ADULTS1 & #EE S5IOR CITIZ5S 9
ATT5D.E4 ,AT ,SATUR"D NI<T'S 3C]T1 "! 7
#ABF /UD5TS1 #AHH ADULTS1 & #FD S5IOR
CITIZ5S 9 ATT5D.E4 ,ORGANIZE ? 9=M,N US+
MATRICES4 ,!N USE MATRIX MULTIPLIC,N
6F9D ! 9COME F TICKET SALES = ,FRI"D &
,SATUR"D NI<TS' 3C]TS4 7.P4 .#AIE7
#EF4 .,,PHYSICAL .,,SCI;E ,:ILE /&+ AT
! $GE (A CLIFF1 Y DROP A ROCK F A HEI<T
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P>ABOLA =M$ 0?R[+ A BASEBALL >E 7#J1
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PA?4 @7 P4 #CJI @7
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EA* SIDE (! SQU>E BASE4 ,A MA*9E P\RS
#BJJ CUBIC 9*ES ( LIQUID PLA/IC 96EA*
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#CGJ @7
#EI4 .,,PR(IT ,YR FR />TS A H\SEKEEP+
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DOLL>S7 (! BUSI;S DUR+ ! F/ #F MON?S (
XS EXI/;E4 ,USE A GRAPH+ CALCULATOR 6F9D
A POLYNOMIAL MODEL =! DATA4 ,PREDICT !
PR(IT 9 ! N9? MON?1 @7 P4 #CIC @7
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#EJ3 #AJF3 #AIB
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@7 P4 #DAD @7
------------------------------------#DGF
,UNIT #C3 ,O!R ,NONL9E> ,FUNC;NS &
,REL,NS
#G ,EXPON5TIAL & ,LOG>I?MIC ,FUNC;NS
#G.A ,GRAPH ,EXPON5TIAL ,GR[? ,FUNC;NS
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#G.F ,SOLVE ,EXPON5TIAL & ,LOG>I?MIC
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,2F
,9 PREVI\S *APT]S1 Y LE>N$ ! FOLL[+
SKILLS1 : Y'LL USE 9 ,*APT] #G3 GRAPH+
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,PREREQUISITE ,SKILLS
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.#C4 ,! .9V]SE (! FUNC;N IS @8 @4
,PRODNOTE3 ,PRODUC;N NOTE3 ? IMAGE
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& PAGE #DGG 9 ! PR9T V].N4
,,SKILLS ,,*ECK
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.#D4
.#E4
.#F4
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#DCH .= .#G..D47
.#G4 .;Y .K #C .;X @+ #E
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.#I4
,WRITE A QUADRATIC FUNC;N 9 /&>D =M =!
P>ABOLA T PASSES "? ! GIV5 PO9TS4
7.,REVIEW P4 #CJI .= .#G..G47
.#AJ4 7#J1 --#A71 7#A1 #B71 7#C1 #AD7
.#AA4 7#C1 #H71 7#D1 #AG71 7#G1 #EF7
.#AB4 7--#C1 #I71 7#A1 --#G71 7#E1
--#EE7
@A .,HOME .,TUTOR ,PREREQUISITE SKILLS
PRACTICE AT _+CLASSZONE.COM_:
------------------------------------#DGG
,SIDEB>3
,N[
,9 ,*APT] #G1 Y W APPLY ! BIG ID1S
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#B ,SOLV+ EXPON5TIAL & LOG>I?MIC
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#C ,WRIT+ & APPLY+ EXPON5TIAL & P[]
FUNC;NS
,KEY ,VOCABUL>Y
99 EXPON5TIAL FUNC;N1 P4 #DGH
99 EXPON5TIAL GR[? FUNC;N1 P4 #DGH
99 GR[? FACTOR1 P4 #DGH
99 ASYMPTOTE1 P4 #DGH
99 EXPON5TIAL DECAY FUNC;N1 P4 #DHF
99 DECAY FACTOR1 P4 #DHF
99 NATURAL BASE .;E1 P4 #DIB
99 LOG>I?M ( .;Y ) BASE .;B1 P4 #DII
99 -MON LOG>I?M1 P4 #EJJ
99 NATURAL LOG>I?M1 P4 #EJJ
99 EXPON5TIAL EQU,N1 P4 #EGE
99 LOG>I?MIC EQU,N1 P4 #EGG
,PRODNOTE3 ,PRODUC;N NOTE3 ? IMAGE
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& PAGE #DGG 9 ! PR9T V].N4 ,SIDEB>3
,:Y8
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.#DHJ1 .#DHG1 .#EJB @1 & .#ECH
------------------------------------#DGH
#G.A ,GRAPH ,EXPON5TIAL ,GR[?
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FUNC;NS4
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99 .EXPON5TIAL .FUNC;N
99 .EXPON5TIAL .GR[? .FUNC;N
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99 .ASYMPTOTE
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------------------------------------#DGI
,! GRAPH (A FUNC;N .;Y .K .;AB ;X IS A
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,GRAPH .;Y .K .;AB ;X = .;B .1 #A
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.A4
.B4
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6."R @1 DRAW A CURVE T 2G9S J 2L ! .;X
-AXIS1 PASSES "? ! TWO PO9TS1 & MOVES
D[N 6! "R4
,,CLASSIFY ,,FUNC;NS
,NOTE T ! FUNC;N 9 "P 7;B7 ( ,EXAMPLE
#B IS N AN EXPON5TIAL GR[? FUNC;N 2C .A
.K --#A "K #J4
.,,TRANSL,NS ,6GRAPH A FUNC;N (! =M
.;Y .K .;AB .;X -- .;H @+ .;K @1 2G9
0SKET*+ ! GRAPH ( .;Y .K .;AB ;X @4 ,!N
TRANSLATE ! GRAPH HORIZONT,Y 0.;H UNITS
& V]TIC,Y 0.;K UNITS4
,,EXAMPLE #C
,GRAPH .;Y .K .;AB .;X -- .;H @+ .;K =
.;B .1 #A
,GRAPH .;Y .K #D @* #B .;X -- ;L --
#C4 ,/ATE ! DOMA9 & RANGE4
,SOLU;N
,2G9 0SKET*+ ! GRAPH ( .;Y .K #D @* #B
;X @1 : PASSES "? 7#J1 #D7 & 7#A1 #H74
,!N TRANSLATE ! GRAPH "R #A UNIT & D[N
#C UNITS 6OBTA9 ! GRAPH ( .;Y .K #D @*
#B .;X -- #A -- #C4
,! GRAPH'S ASYMPTOTE IS ! L9E .;Y .K
--#C4 ,! DOMA9 IS ALL R1L NUMB]S1 &!
RANGE IS .;Y .1 --#C4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #A1
#B1 & .#C
,GRAPH ! FUNC;N4 ,/ATE ! DOMA9 &
RANGE4
.#A4 .;Y .K #D ;X
.#B4
.#C4 .;F @7 .;X @7 .K #C .;X @+ #A @+
#B
------------------------------------#DHJ
.,,EXPON5TIAL .,,GR[? .,,MODELS ,:5 A
R1L-LIFE QUANT;Y 9CR1SES 0A FIX$ P]C5T
EA* YE> 7OR O!R "T P]IOD71 ! AM.T .;Y (!
QUANT;Y AF .;T YE>S C 2 MODEL$ 0! EQU,N
.;Y .K .A 7#A @+ .;R @7 ;T
": .A IS ! 9ITIAL AM.T & .;R IS !
P]C5T 9CR1SE EXPRESS$ Z A DECIMAL4 ,NOTE
T ! QUANT;Y #A @+ .;R IS ! GR[? FACTOR4
,,EXAMPLE #D
,SOLVE A MULTI-/EP PRO#M
.,,-PUT]S ,9 #AIIF1 "! 7 #BEGC -PUT]
VIRUSES & O!R -PUT] SECUR;Y 9CID5TS4
,DUR+ ! NEXT #G YE>S1 ! NUMB] ( 9CID5TS
9CR1S$ 0AB #IB@3P EA* YE>4
99 ,WRITE AN EXPON5TIAL GR[? MODEL
GIV+ ! NUMB] .;N ( 9CID5TS .;T YE>S AF
#AIIF4 ,AB H[ _M 9CID5TS 7 "! 9 #BJJC8
99 ,GRAPH ! MODEL4
99 ,USE ! GRAPH 6E/IMATE ! YE> :5 "! 7
AB #ABE1JJJ -PUT] SECUR;Y 9CID5TS4
,SOLU;N
.,,/EP .#A ,! 9ITIAL AM.T IS .A .K
#BEGC &! P]C5T 9CR1SE IS .;R .K #J.IB4
,S1 ! EXPON5TIAL GR[? MODEL IS3
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;N @3 .K .A 7;L @+ .;R @7 .;T @3
..,WRITE EXPON5TIAL GR[? .MODEL4
--@3 .K #BEGC7#A @+ #J.IB7 .;T @3
,SUB/ITUTE #BEGC =.' A .-& #J.IB =.' ;R
@4
--@3 .K #BEGC7#A.IB7 .;T @3
.,SIMPLIFY4
,,AVOID ,,]RORS
,NOTICE T ! P]C5T 9CR1SE &! GR[?
FACTOR >E TWO DI6]5T VALUES4 ,AN 9CR1SE
( #IB@3P CORRESPONDS 6A @3 GR[? FACTOR (
#A.IB4
,US+ ? MODEL1 Y C E/IMATE ! NUMB] (
9CID5TS 9 #BJJC @7 .;T .K #G7 6BE .;N .K
#BEGC 7#A.IB7 #G #BDG1DHE4
.,,/EP .#B ,! GRAPH PASSES "? ! PO9TS
7#J1 #BEGC7 & 7#A1 #DIDJ.AF74 ,PLOT A
FEW O!R PO9TS4 ,!N DRAW A SMOO? CURVE "?
! PO9TS4
.,,/EP .#C ,US+ ! GRAPH1 Y C E/IMATE T
! NUMB] ( 9CID5TS 0 AB #ABE1JJJ DUR+
#BJJB @7 .;T #F74
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
.,,GUID$ .,,PRACTICE = ,EXAMPLE #D
.#D4 .,,:AT .,,IF8 ,9 ,EXAMPLE #D1
E/IMATE ! YE> 9 : "! 7 AB #BEJ1JJJ -PUT]
SECUR;Y 9CID5TS4
.#E4 ,9 ! EXPON5TIAL GR[? MODEL .;Y .K
#EBG7#A.CI7 ;X @1 ID5TIFY ! 9ITIAL AM.T1
! GR[? FACTOR1 &! P]C5T 9CR1SE4
------------------------------------#DHA
.,,-P.D .,,9T]E/ ,EXPON5TIAL GR[?
FUNC;NS >E US$ 9 R1L-LIFE SITU,NS 9VOLV+
.-P.D .9T]E/4 ,-P.D 9T]E/ IS 9T]E/ PD ON
! 9ITIAL 9VE/;T1 CALL$ ! .PR9CIPAL @1 &
ON PREVI\SLY E>N$ 9T]E/4 ,9T]E/ PD ONLY
ON ! PR9CIPAL IS CALL$ .SIMPLE .9T]E/4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,-P.D ,9T]E/
,3SID] AN 9ITIAL PR9CIPAL .;,P
DEPOSIT$ 9 AN A3.T T PAYS 9T]E/ AT AN
ANNUAL RATE .;R 7EXPRESS$ Z A DECIMAL71
-P.D$ .;N "TS P] YE>4 ,! AM.T .,A 9 !
A3.T AF .;T YE>S IS GIV5 0? EQU,N3
,,EXAMPLE #E
,F9D ! BAL.E 9 AN A3.T
.,,F9.E ,Y DEPOSIT 4#DJJJ 9 AN A3.T T
PAYS #B.IB@3P ANNUAL 9T]E/4 ,F9D ! BAL.E
AF #A YE> IF ! 9T]E/ IS -P.D$ )! GIV5
FREQU5CY4
.A4 ,QU>T]LY
.B4 ,DAILY
,SOLU;N
.A4 ,) 9T]E/ -P.D$ QU>T]LY1 ! BAL.E AF
#A YE> IS3
,! BAL.E AT ! 5D ( #A YE> IS
4#DAAH.JI4
.B4 ,) 9T]E/ -P.D$ DAILY1 ! BAL.E AF
#A YE> IS3
,! BAL.E AT ! 5D ( #A YE> IS
4#DAAH.EB4
.,,GUID$ .,,PRACTICE = ,EXAMPLE #E
.#F4 .,,F9.E ,Y DEPOSIT 4#BJJJ 9 AN
A3.T T PAYS #D@3P ANNUAL 9T]E/4 ,F9D !
BAL.E AF #C YE>S IF ! 9T]E/ IS -P.D$
DAILY4
------------------------------------#DHB
#G.A ,EX]CISES
,HOME"W ,KEY
.K ..,,"W$-,,\ ,,SOLU;NS .ON P4
,,WS#AC ..= ,EXS4 #AG1 #BI1 & .#CG
.K ..,,/&>DIZ$ ,,TE/ ,,PRACTICE ,EXS4
#B1 #BD1 #BE1CB1DJ1 & .#DA
.K ..,,MULTIPLE ,,REPRES5T,NS ,EX#..DB
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,9 ! EXPON5TIAL GR[?
MODEL .;Y .K #B.D7#A.E7 ;X @1 ID5TIFY !
9ITIAL AM.T1 ! GR[? FACTOR1 &! P]C5T
9CR1SE4
.#B4 .,,WRIT+ ,:AT IS AN ASYMPTOTE8
,,MAT*+ ,,GRAPHS ,MAT* ! FUNC;N ) XS
GRAPH4
,,EXAMPLES #A & #B
ON PP4 #DGH-DGI = ,EXS4 #C-AD
.#C4 .;Y .K #C @* #B ;X
.#D4 .;Y .K --#C @* #B ;X
.#E4 .;Y .K #B @* #C ;X
.,A4
.,B4
.,C4
,,GRAPH+ ,,FUNC;NS ,GRAPH ! FUNC;N4
.#F4 .;Y .K #C ;X
.#G4 .;Y .K --#B ;X
.#H4 .;F @7 .;X @7 .K #E @* #B ;X
.#I4 .;Y .K #E ;X
.#AJ4 .;Y .K #B @* #D ;X
.#AA4 .;G @7 .;X @7 .K --7#A.E7 ;X
.#AB4
.#AC4
.#AD4 .;H @7 .;X @7 .K --#B7#B.E7 ;X
,,EXAMPLE #C
ON P4 #DGI = ,EXS4 #AE-BD
,,TRANSLAT+ ,,GRAPHS ,GRAPH ! FUNC;N4
,/ATE ! DOMA9 & RANGE4
.#AE4 .;Y .K --#C @*#B .;X @+ #B
.#AF4 .;Y .K #E--#D ;X @+ #B
.#AG4 .K #B .;X @+ #A @+ #C
.#AH4 .;Y .K #C .;X -- #B -- #A
.#AI4 .;Y .K #B @* #C .;X -- #B -- #A
.#BJ4 .;Y .K --#C @* #D .;X -- ;L --
#B
.#BA4 .;F @7 .;X @7 .K #F @* #B .;X --
#C @+ #C
.#BB4 .;G @7 .;X @7 .K #E @* #C .;X @+
#B -- #D
.#BC4 .;H @7 .;X @7 .K --#B @* #E .;X
-- #A @+ #A
#BD4 .,,MULTIPLE .,,*OICE ,! GRAPH ( :
FUNC;N IS %[N8
,A .;F @7 .;X @7 .K #B7#A.E7 .;X -- #A
;,B .;F @7 .;X @7 .K #B7#A.E7 .;X @+
#A
;,C .;F @7 .;X @7 .K #C7#A.E7 ;X -- #A
;,D .;F @7 .;X @7--#C7#A.E7 ;X @+ ;L
#BE4 .,,MULTIPLE .,,*OICE ,! /UD5T
5ROLL;T .;,E (A HI< S*OOL 0 #ACAJ 9
#AIIH & HAS 9CR1S$ 0#AJ@3P P] YE> S9CE
!N4 ,: EXPON5TIAL GR[? MODEL GIVES !
S*OOL'S /UD5T 5ROLL;T 9 T]MS ( .;T ":
.;T IS ! NUMB] ( YE>S S9CE #AIIH8
,A .;,E .K #J.A7#ACAJ7 ;T
;,B .;,E .K #ACAJ7#J.A7 ;T
;,C .;,E .K #A.A7#ACAJ7 ;T
;,D .;,E .K #ACAJ7#A.A7 ;T
------------------------------------#DHC
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 GRAPH+ ! FUNC;N4
.#BF4 .;Y .K #B @* #D ;X
.#BG4 .;Y .K #B .;X -- #C @+ #C
,,WRIT+ ,,MODELS ,9 ,EX]CISES #BH-CJ1
WRITE AN EXPON5TIAL GR[? MODEL T
DESCRIBES ! SITU,N4
.#BH4 ,9 #AIIB1 #ABAI MONK P>AKEETS 7
OBS]V$ 9 ! ,UNIT$ ,/ATES4 ,=! NEXT #AA
YE>S1 AB #AB@3P M P>AKEETS 7 OBS]V$ EA*
YE>4
.#BI4 ,Y DEPOSIT 4#HJJ 9 AN A3.T T
PAYS #B@3P ANNUAL 9T]E/ -P.D$ DAILY4
.#CJ4 ,Y PUR*ASE AN ANTIQUE TA# =
4#DEJ4 ,! VALUE (! TA# 9CR1SES 0#F@3P P]
YE>4
#CA4 .,,GRAPH+ .,,CALCULATOR ,Y
DEPOSIT 4#AEJJ 9 A BANK A3.T T PAYS
#C@3P ANNUAL 9T]E/ -P.D$ YE>LY4
A4 ,TYPE #AEJJ 96A GRAPH+ CALCULATOR &
PRESS @4 ,!N 5T] ! =MULA ,,ANS 99 #A.JC1
Z %[N AT ! "R4 ,PRESS SEV5 "TS 6F9D YR
BAL.E AF #G YE>S4
B4 ,F9D ! NUMB] ( YE>S X TAKES = YR
BAL.E 6EXCE$ 4#BEJJ4
#CB4 .,,OP5-.,,5D$ .,,MA? ,WRITE AN
EXPON5TIAL FUNC;N (! =M .;Y .K .;AB .;X
@+ .;H @+ .;K ^: GRAPH HAS AY-9T]CEPT (
#E & AN ASYMPTOTE ( .;Y .K #B4
#CC4 .,,GRAPH+ .,,CALCULATOR ,3SID] !
EXPON5TIAL GR[? FUNC;N .;Y .K .;AB .;X
-- .;H @+ .;K ": .A .K #B1 .;B .K #E1
.;H .K --#D1 & .;K .K #C4 ,PREDICT !
E6ECT ON ! FUNC;N'S GRAPH ( EA* *ANGE 9
.A1 .;B1 .;H @1 OR .;K DESCRIB$ 9 "PS
7A7-7;D74 ,USE A GRAPH+ CALCULATOR 6*ECK
YR PREDIC;N4
A4 .A *ANGES 6#A
B4 .;B *ANGES 6#D
C4 .;H *ANGES 6#C
D4 .;K *ANGES TO --#A
#CD4 .,,*ALL5GE ,3SID] ! EXPON5TIAL
FUNC;N .;F @7 .;X @7 .K .;AB ;X @4
A4 ,%[ T @4
B4 ,USE ! RESULT F "P 7A7 6EXPLA9 :Y
"! IS NO EXPON5TIAL FUNC;N (! =M .;F @7
.;X @7 .K .;AB ;X ^: GRAPH PASSES "? !
PO9TS 9 ! TA# 2L4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #J3 #A3 #B3 #C3 #D
.;Y @3 #D3 #D3 #H3 #BD3 #GB
------------------------------------#DHD
,,PRO#M ,,SOLV+
,,EXAMPLE #D
ON P4 #DHJ = ,EXS4 #CE-CF
#CE4 .,,DVD .,,PLAY]S ,F #AIIG 6#BJJB1
! NUMB] .;N 7IN MILLIONS7 ( ,,DVD PLAY]S
SOLD 9 ! ,UNIT$ ,/ATES C 2 MODEL$ 0.;N
.K #J.DB7#B.DG7 ;T ": .;T IS ! NUMB] (
YE>S S9CE #AIIG4
A4 ,ID5TIFY ! 9ITIAL AM.T1 ! GR[?
FACTOR1 &! ANNUAL P]C5T 9CR1SE4
B4 ,GRAPH ! FUNC;N4 ,E/IMATE ! NUMB] (
,,DVD PLAY]S SOLD 9 #BJJA4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#CF4 .,,9T]NET ,EA* ,M>* F #AIIH
6#BJJC1 A WEBSITE RECORD$ ! NUMB] .;Y (
REF]RALS X RCVD F ,9T]NET SE>* 5G9ES4 ,!
RESULTS C 2 MODEL$ 0.;Y .K #BEJJ
7#A.EJ7;T ": .;T IS ! NUMB] ( YE>S S9CE
#AIIH4
A4 ,ID5TIFY ! 9ITIAL AM.T1 ! GR[?
FACTOR1 &! ANNUAL P]C5T 9CR1SE4
B4 ,GRAPH ! FUNC;N & /ATE ! DOMA9 &
RANGE4 ,E/IMATE ! NUMB] ( REF]RALS !
WEBSITE RCVD F ,9T]NET SE>* 5G9ES 9 ,M>*
( #BJJB4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
,,EXAMPLES #E
ON P4 #DHA = ,EXS4 #CG-CH
#CG4 .,,A3.T .,,BAL.E ,Y DEPOSIT
4#BBJJ 9 A BANK A3.T4 ,F9D ! BAL.E AF #D
YE>S = EA* (! SITU,NS DESCRIB$ 2L4
A4 ,! A3.T PAYS #C@3P ANNUAL 9T]E/
-P.D$ QU>T]LY4
B4 ,! A3.T PAYS #B.BE@3P ANNUAL 9T]E/
-P.D$ MON?LY4
C4 ,! A3.T PAYS #B@3P ANNUAL 9T]E/
-P.D$ DAILY4
#CH4 .,,DEPOSIT+ .,,FUNDS ,Y WANT 6H
4#CJJJ 9 YR SAV+S A3.T AF #C YE>S4 ,F9D
! AM.T Y %D DEPOSIT = EA* (! SITU,NS
DESCRIB$ 2L4
A4 ,! A3.T PAYS #B.BE@3P ANNUAL 9T]E/
-P.D$ QU>T]LY4
B4 ,! A3.T PAYS #C.E@3P ANNUAL 9T]E/
-P.D$ MON?LY4
C4 ,! A3.T PAYS #D@3P ANNUAL 9T]E/
-P.D$ YE>LY4
#CI4 .,,MULTI-.,,/EP .,,PRO#M ,9
#AIIJ1 ! POPUL,N ( ,AU/91 ,TEXAS1 0
#DID1BIJ4 ,DUR+ ! NEXT #AJ YE>S1 !
POPUL,N 9CR1S$ 0AB #C@3P EA* YE>4
A4 ,WRITE A MODEL GIV+ ! POPUL,N .;,P
7IN ?\S&S7 ( ,AU/9 .;T YE>S AF #AIIJ4
,:AT 0 ! POPUL,N 9 #BJJJ8
B4 ,GRAPH ! MODEL & /ATE ! DOMA9 &
RANGE4
C4 ,E/IMATE ! YE> :5 ! POPUL,N 0 AB
#EIJ1JJJ4
,PICTURE3 .,AU/91 .,TEXAS
#DJ4 .,,%ORT .,,RESPONSE ,AT AN ONL9E
AUC;N1 ! OP5+ BID =A PAIR ( IN-L9E
SKATES IS 4#EJ4 ,! PRICE (! SKATES
9CR1SES 0#AJ.E@3P P] BID DUR+ ! NEXT #F
BIDS4
A4 ,WRITE A MODEL GIV+ ! PRICE .;P 7IN
DOLL>S7 (! SKATES AF .;N BIDS4
B4 ,:AT 0 ! PRICE AF #E BIDS8 ,AC 6!
MODEL1 :AT W ! PRICE 2 AF #AJJ BIDS8 ,IS
? PREDICT$ PRICE R1SONA#8 .,EXPLA94
.K ..,,"W$-,,\ ,,SOLU;NS ONO4.,,WS,'L
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
------------------------------------#DHE
#DA4 .,,EXT5D$ .,,RESPONSE ,9 #BJJJ1 !
AV]AGE PRICE (A FOOTBALL TICKET =A
,M9NESOTA ,VIK+'S GAME 0 4#DH.BH4 ,DUR+
! NEXT #D YE>S1 ! PRICE 9CR1S$ AN AV]AGE
( #F@3P EA* YE>4
A4 ,WRITE A MODEL GIV+ ! AV]AGE PRICE
.;P 7IN DOLL>S7 (A TICKET .;T YE>S AF
#BJJJ4
B4 ,GRAPH ! MODEL4 ,E/IMATE ! YE> :5 !
AV]AGE PRICE (A TICKET 0 AB 4#FJ4
C4 .,EXPLA9 H[ Y C USE ! GRAPH (
.;P,7.;T7 6DET]M9E ! M9IMUM & MAXIMUM
.;T -VALUES 9 ! DOMA9 = : ! FUNC;N GIVES
M1N+;L RESULTS4
#DB4 .,,MULTIPLE .,,REPRES5T,NS ,9
#AIGG1 "! 7 #DA BRE$+ PAIRS ( BALD
EAGLES 9 ,M>YL&4 ,OV] ! NEXT #BD YE>S1 !
NUMB] ( BRE$+ PAIRS 9CR1S$ 0AB #H.I@3P
EA* YE>4
A4 .,WRIT+ .AN .,EQU,N ,WRITE A MODEL
GIV+ ! NUMB] .;N ( BRE$+ PAIRS ( BALD
EAGLES 9 ,M>YL& .;T YE>S AF #AIGG4
B4 .,MAK+ .A .,TA# ,MAKE A TA# (
VALUES =! MODEL4
C4 .,DRAW+ .A .,GRAPH ,GRAPH ! MODEL4
D4 .,US+ .A .,GRAPH ,AB H[ _M BRE$+
PAIRS ( BALD EAGLES 7 9 ,M>YL& 9 #BJJA8
#DC4 .,,R1SON+ ,IS 9VE/+ 4#CJJJ AT
#F@3P ANNUAL 9T]E/ & 4#CJJJ AT #H@3P
ANNUAL 9T]E/ EQUIVAL5T 69VE/+ 4#FJJJ 7!
TOTAL (! TWO PR9CIPALS7 AT #G@3P ANNUAL
9T]E/ 7! AV]AGE (! TWO 9T]E/ RATES78
.,EXPLA94
#DD4 .,,*ALL5GE ,! YE>LY CO/ =
RESID5TS 6ATT5D A /ATE UNIV]S;Y HAS
9CR1S$ F 4#EBJJ TO 4#IJJJ 9 ! LA/ #E
YE>S4
A4 ,6! NE>E/ T5? (A P]C5T1 :AT HAS BE5
! AV]AGE ANNUAL GR[? RATE 9 CO/8
B4 ,IF ? GR[? RATE 3T9UES1 :AT W ! CO/
2 9 #E M YE>S8
,,MIX$ ,,REVIEW
.,,PREVIEW ,PREP>E = ,LESSON #G.B 9
,EXS4 #DE-EB4
,EVALUATE ! P[]4
#DE4 7#J.F7 #C @7 P4 #AJ @7
#DF4 7#J.D7 #B @7 P4 #AJ @7
#DG4 7#J.E7 #E @7 P4 #AJ @7
#DH4 7#J.BE7 #C @7 P4 #AJ @7
#DI4 @7 P4 #CCJ @7
#EJ4 @7 P4 #CCJ @7
#EA4 @7 P4 #CCJ @7
#EB4 @7 P4 #CCJ @7
,FACTOR ! EXPRES.N4
#EC4 ;X #B @+ .#G;X-- #CJ @7 P4 #BEB
@7
#ED4 .;X #B @+ #AE;X @+ #ED @7 P4 #BEB
@7
#EE4 .#B;X #B -- #G .;X-- #CJ @7 P4
#BEI @7
#EF4 #AB;X #B -- .#E;X @+ #BE @7 P4
#BEI @7
#EG4 .;X #C -- .#B;X #B -- .#C;X @+ #F
@7 P4 #CEC @7
#EH4 .;X #C -- #FD @7 P4 #CEC @7
,SOLVE ! EQU,N4 @7 P4 #DAD @7
#EI4 .;X #E .K #CABE
#FJ4 #C .;X #C .K #AJBI
#FA4 .;X #G @+ #H .K--#FD
#FB4 @7 .;X @+ #AB7 #D .K #EB
#FC4 --#E .;X #F .K--#AJJJ
#FD4 @7 .;X -- #I7 #H .K #AG
.,,EXTRA .,,PRACTICE = ,LESSON #G.A1
P4 #AJAF
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#DHF
#G.B ,GRAPH ,EXPON5TIAL ,DECAY
,FUNC;NS
.,2F ,Y GRAPH$ & US$ EXPON5TIAL GR[?
FUNC;NS4
.,N[ ,Y W GRAPH & USE EXPON5TIAL DECAY
FUNC;NS4
.,:Y8 ,S Y C MODEL DEPRECI,N1 Z 9 ,EX4
#CA4
,KEY ,VOCABUL>Y
99 .EXPON5TIAL .DECAY .FUNC;N
99 .DECAY .FACTOR
,SIDEB>3
,/&>DS
.#AB..J .,/UD5TS "K ! LAWS ( FRAC;NAL
EXPON5TS1 .."U/& EXPON5TIAL FUNC;NS 9
PRO#MS 9VOLV+ EXPON5TIAL .GR[? & DECAY4
,9 ,LESSON #G.A Y /UDI$ EXPON5TIAL
GR[? FUNC;NS4 ,9 ? LESSON1 Y W /UDY
.EXPON5TIAL .DECAY .FUNC;NS @1 : H ! =M
.;Y .K .;AB ;X ": .A .1 #J & #J "K .;B
"K #A4 ,! BASE .;B ( AN EXPON5TIAL DECAY
FUNC;N IS CALL$ ! DECAY FACTOR4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,P>5T ,FUNC;N = ,EXPON5TIAL ,DECAY
,FUNC;NS
,! FUNC;N .;F @7 .;X @7 .K .;B ;X @1
": #J "K .;B "K #A1 IS ! P>5T FUNC;N =!
FAMILY ( EXPON5TIAL DECAY FUNC;NS ) BASE
.;B @4 ,! G5]AL %APE (! GRAPH ( .;F @7
.;X @7 .K .;B ;X IS %[N 2L4
,! DOMA9 ( .;F @7 .;X @7 .K .;B ;X IS
ALL R1L NUMB]S4 ,! RANGE IS .;Y .1 #J4
,,EXAMPLE #A
,GRAPH .;Y .K .;B ;X = #J "K .;B "K#A
,GRAPH @4
,SOLU;N
.,,/EP .#A .,MAKE A TA# ( VALUES4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 --#C3 --#B3 --#A3 #J3 #A3 #B
.;Y @3 #H3 #D3 #B3 #A3 @3
.,,/EP .#B .,PLOT ! PO9TS F ! TA#4
.,,/EP .#C .,DRAW @1 F ."R 6.LEFT @1 A
SMOO? CURVE T 2G9S J ABV ! .;X -AXIS1
PASSES "? ! PLOTT$ PO9TS1 & MOVES UP 6!
LEFT4
------------------------------------#DHG
.,,TRANS=M,NS ,RECALL F ,LESSON #G.A T
! GRAPH (A FUNC;N .;Y .K .;AB ;X IS A
V]TICAL /RET* OR %R9K (! GRAPH ( .;Y .K
.;B ;X @1 &! GRAPH ( .;Y .K .;AB .;X --
.;H @+ .;K IS A TRANSL,N (! GRAPH ( .;Y
.K .;AB ;X @4
,,EXAMPLE #B
,GRAPH .;Y .K .;AB ;X = #J "K .;B "K
#A
,,CLASSIFY ,,FUNC;NS
,NOTE T ! FUNC;N 9 "P 7;B7 ( ,EXAMPLE
#B IS N AN EXPON5TIAL DECAY FUNC;N 2C .A
.K --#C "K #J4
,GRAPH ! FUNC;N4
.A4
.B4
,SOLU;N
.A4 ,PLOT 7#J1 #B7 & @4 ,!N1 F ."R
6.LEFT @1 DRAW A CURVE T 2G9S J ABV !
.;X -AXIS1 PASSES "? ! TWO PO9TS1 &
MOVES UP 6! LEFT4
.B4 ,PLOT 7#J1 --#C7 & @4 ,!N1 F ."R
6.LEFT @1 DRAW A CURVE T 2G9S J 2L ! .;X
-AXIS1 PASSES "? ! TWO PO9TS1 & MOVES
D[N 6! LEFT4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,,GUID$ ,,PRACTICE = ,EXAMPLES #A &
.#B
,GRAPH ! FUNC;N4
.#A4
.#B4
.#C4
,,EXAMPLE #C
,GRAPH .;Y .K .;AB .;X -- .;H @+ .;K =
#J "K .;B "K ;L
,GRAPH @4 ,/ATE ! DOMA9 & RANGE4
,SOLU;N
,2G9 0SKET*+ ! GRAPH ( @1 : PASSES "?
7#J1 #C7 & @4
,!N TRANSLATE ! GRAPH LEFT #A UNIT &
D[N #B UNITS4 ,NOTICE T ! TRANSLAT$
GRAPH PASSES "? 7--#A1A7 & @4
,! GRAPH'S ASYMPTOTE IS ! L9E .;Y .K
--#B4 ,! DOMA9 IS ALL R1L NUMB]S1 &!
RANGE IS .;Y .1 --#B4
------------------------------------#DHH
.,,EXPON5TIAL .,,DECAY .,,MODELS ,:5 A
R1L-LIFE QUANT;Y DECR1SES 0A FIX$ P]C5T
EA* YE> 7OR O!R "T P]IOD71 ! AM.T .;Y (!
QUANT;Y AF .;T YE>S C 2 MODEL$ 0! EQU,N
.;Y .K .A 7;L -- .;R @7 ;T
": .A IS ! 9ITIAL AM.T & .;R IS !
P]C5T DECR1SE EXPRESS$ Z A DECIMAL4
,NOTE T ! QUANT;Y #A -- .;R IS ! DECAY
FACTOR4
.,,EXAMPLE .#D
,SOLVE A MULTI-/EP PRO#M
.,,SN[MOBILES ,A NEW SN[MOBILE CO/S
4#DBJJ4 ,! VALUE (! SN[MOBILE DECR1SES
0#AJ@3P EA* YE>4
99 ,WRITE AN EXPON5TIAL DECAY MODEL
GIV+ ! SN[MOBILE'S VALUE .;Y 7IN DOLL>S7
AF .;T YE>S4 ,E/IMATE ! VALUE AF #C
YE>S4
99 ,GRAPH ! MODEL4
99 ,USE ! GRAPH 6E/IMATE :5 ! VALUE (!
SN[MOBILE W 2 4#BEJJ4
,SOLU;N
.,,/EP .#A ,! 9ITIAL AM.T IS .A .K
#DBJJ &! P]C5T DECR1SE IS .;R .K #J.AJ4
,S1 ! EXPON5TIAL DECAY MODEL IS3
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;Y @3 .K .A 7#A -- .;R @7 .;T @3
..,WRITE EXPON5TIAL DECAY .MODEL4
--@3 .K .#DBJJ 7#A -- .#J..AJ @7 .;T
@3 ,SUB/ITUTE #DBJJ =.' A .-& #J.AJ =.'
;R @4
--@3 .K #DBJJ7#J.IJ7 .;T @3
.,SIMPLIFY4
,:5 .;T .K #C1 ! SN[MOBILE'S VALUE IS
.;Y .K #DBJJ7#J.IJ7 #C .K 4#CJFA.HJ4
,,AVOID ,,]RORS
,NOTICE T ! P]C5T DECR1SE1 #AJ@3P1
TELLS Y H[ M* VALUE ! SN[MOBILE .LOSES
EA* YE>4 ,! DECAY FACTOR1 #J.IJ1 TELLS Y
:AT FRAC;N (! SN[MOBILE'S VALUE .REMA9S
EA* YE>4
.,,/EP .#B ,! GRAPH PASSES "? ! PO9TS
7#J1 #DBJJ7 & 7#A1 #CGHJ74 ,X HAS ! .;F
-AXIS Z AN ASYMPTOTE4 ,PLOT A FEW O!R
PO9TS4 ,!N DRAW A SMOO? CURVE "? !
PO9TS4
.,,/EP .#C ,US+ ! GRAPH1 Y C E/IMATE T
! VALUE (! SN[MOBILE W 2 4#BEJJ AF AB #E
YE>S4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #C &
.#D
,GRAPH ! FUNC;N4 ,/ATE ! DOMA9 &
RANGE4
.#D4
.#E4
.#F4
.#G4 .,,:AT .,,IF8 ,9 ,EXAMPLE #D1
SUPPOSE ! VALUE (! SN[MOBILE DECR1SES
0#BJ@3P EA* YE>4 ,WRITE & GRAPH AN EQU,N
6MODEL ? SITU,N4 ,USE ! GRAPH 6E/IMATE
:5 ! VALUE (! SN[MOBILE W 2 4#BEJJ4
.#H4 .,,SN[MOBILE ,! VALUE (A
SN[MOBILE HAS BE5 DECR1S+ 0#G@3P EA* YE>
S9CE X 0 NEW4 ,AF #C YE>S1 ! VALUE IS
4#CJJJ4 ,F9D ! ORIG9AL CO/ (! SN[MOBILE4
------------------------------------#DHI
#G.B ,EX]CISES
,HOME"W ,KEY
.K ..,,"W$ ,,\ .,,SOLU;NS ON P4
,,WS#AC = ,EXS4 #I1AI1 & #CC
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE ,EXS4
#B1AE1BG1BH1 #CC1 & #CE
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,9 ! EXPON5TIAL
DECAY MODEL .;Y .K #ABEJ 7#J.HE7 ;T @1
ID5TIFY ! 9ITIAL AM.T1 ! DECAY FACTOR1
&! P]C5T DECR1SE4
.#B4 .,,WRIT+ .,EXPLA9 H[ 6TELL :E!R !
FUNC;N .;Y .K .;B ;X REPRES5TS
EXPON5TIAL GR[? OR EXPON5TIAL DECAY4
,,CLASSIFY+ ,,FUNC;NS ,TELL :E!R !
FUNC;N REPRES5TS .EXPON5TIAL .GR[? OR
.EXPON5TIAL .DECAY4
.#C4
.#D4
.#E4
.#F4 .;F @7 .;X @7 .K #BE7#J.BE7 ;X
..,,EXAMPLES #A & .#B ON PP4 #DHF-DHG
= ,EXS4 #G-AE
,,GRAPH+ ,,FUNC;NS ,GRAPH ! FUNC;N4
.#G4
.#H4
.#I4
.#AJ4 .;Y .K --7#J.B7 ;X
.#AA4
.#AB4 .;G @7 .;X @7 .K #B7#J.GE7 ;X
.#AC4
.#AD4
#AE4 .,,MULTIPLE .,,*OICE ,! GRAPH ( :
FUNC;N IS %[N8
,A
;,B
;,C
;,D
.,,EXAMPLE .#C ON P4 #DHG = ,EXS4
#AF-BE
,,TRANSLAT+ ,,GRAPHS ,GRAPH ! FUNC;N4
,/ATE ! DOMA9 & RANGE4
.#AF4
.#AG4
.#AH4
.#AI4
.#BJ4 .;Y .K #C7#J.BE7 ;X @+ #C
.#BA4
.#BB4
.#BC4
.#BD4
#BE4 .,,GRAPH+ .,,CALCULATOR ,3SID] !
EXPON5TIAL DECAY FUNC;N .;Y .K .;AB .;X
-- .;H @+ .;K ": .A .K #C1 .;B .K #J.D1
.;H .K #B1 & .;K .K --#A4 ,PREDICT !
E6ECT ON ! FUNC;N'S GRAPH ( EA* *ANGE 9
A1 .;B1 .;H @1 OR .;K DESCRIB$ 9 "PS
7A7-7;D74 ,USE A GRAPH+ CALCULATOR 6*ECK
YR PREDIC;N4
A4 .A *ANGES 6#D
B4 .;B *ANGES 6#J.B
C4 .;H *ANGES 6#E
D4 .;K *ANGES 6#C
#BF4 .,,]ROR .,,ANALYSIS ,Y 9VE/ 4#EJJ
9 ! /OCK (A -PANY4 ,! VALUE (! /OCK
DECR1SES #B@3P EA* YE>4 .,DESCRIBE &
CORRECT ! ]ROR 9 WRIT+ A MODEL =! VALUE
(! /OCK AF .;T YE>S4
----------------------------------#DIJ
#BG4 .,,MULTIPLE .,,*OICE ,:AT IS !
ASYMPTOTE (! GRAPH ( @4
,A .;Y .K --#C
;,B .;Y .K --#B
;,C .;Y .K #B
;,D .;Y .K #C
#BH4 .,,OP5-.,,5D$ .,,MA? ,WRITE AN
EXPON5TIAL FUNC;N ^: GRAPH LIES 2T !
GRAPHS ( .;Y .K 7#J.E7 ;X & .;Y .K
7#J.BE7 ;X @+ #C4
#BI4 .,,*ALL5GE ,D .;F @7 .;X @7 .K
#E7#D7 -- .;X & .;G @7 .;X @7 .K
#E7#J.BE7 ;X REPRES5T ! SAME FUNC;N8
.,JU/IFY YR ANSW]4
,,PRO#M ,,SOLV+
,,EXAMPLE #D
ON P4 #DHH = ,EXS4 #CJ-CA
.#CJ4 .,,M$IC9E ,:5 A P]SON TAKES A
DOSAGE ( .,I MILLIGRAMS ( IBUPROF51 !
AM.T .,A 7IN MILLIGRAMS7 ( M$IC,N REMA9+
9 ! P]SON'S BLOOD/R1M AF .;T H\RS C 2
MODEL$ 0! EQU,N .,A .K .,I 7#J.GA7 ;R @4
,F9D ! AM.T ( IBUPROF5 REMA9+ 9 A
P]SON'S BLOOD/R1M =! GIV5 DOSAGE &
ELAPS$ "T S9CE ! M$IC,N 0 TAK54
.A4 ,DOSAGE3 #BJJ MG ,"T3 #A.E H\RS
.B4 ,DOSAGE3 #CBE MG ,"T3 #C.E H\RS
.C4 ,DOSAGE3 #DJJ MG ,"T3 #E H\RS
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#CA4 .,,BIKE .,,CO/S ,Y BUY A NEW
M.TA9 BIKE = 4#BJJ4 ,! VALUE (! BIKE
DECR1SES 0#BE@3P EA* YE>4
A4 ,WRITE A MODEL GIV+ ! M.TA9 BIKE'S
VALUE .;Y 7IN DOLL>S7 AF .;T YE>S4 ,USE
! MODEL 6E/IMATE ! VALUE (! BIKE AF #C
YE>S4
B4 ,GRAPH ! MODEL4
C4 ,E/IMATE :5 ! VALUE (! BIKE W 2
4#AJJ4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#CB4 .,,DEPRECI,N ,! TA# %[S ! AM.T
.;D T A BOAT DEPRECIATES DUR+ EA* YE>
.;T S9CE X 0 NEW4 ,%[ T ! RATIO (
DEPRECI,N AM.TS = 3SECUTIVE YE>S IS
3/ANT4 ,!N WRITE AN EQU,N T GIVES .;D Z
A FUNC;N ( .;T @4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,YE>1 .;T @3 #A3 #B3 #C3 #D3 #E
,DEPRECI,N1 .;D @3 4#AIJF3 4#AHCB3
4#AGFB3 4#AFIB3 4#AFBG
.K ..,,"W$-,,\ ,,SOLU;NS ON P4.,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#DIA
#CC4 .,,%ORT .,,RESPONSE ,! VALUE (A
C> C 2 MODEL$ 0! EQU,N .;Y .K #BD1JJJ
7#J.HDE7;T ": .;T IS ! NUMB] ( YE>S S9CE
! C> 0 PUR*AS$4
A4 ,GRAPH ! MODEL4 ,E/IMATE :5 ! VALUE
(! C> W 2 4#AJ1JJJ4
B4 ,USE ! MODEL 6PREDICT ! VALUE (! C>
AF #EJ YE>S4 ,IS ? A R1SONA# VALUE8
.,EXPLA94
#CD4 .,,MULTI-.,,/EP .,,PRO#M ,:5 A
PLANT OR ANIMAL DIES1 X /OPS ACQUIR+
C>BON-#AD F ! ATMOSPH]E4 ,C>BON-#AD
DECAYS OV] "T )A HALF-LIFE ( AB #EGCJ
YE>S4 ,! P]C5T .;,P (! ORIG9AL AM.T (
C>BON-#AD T REMA9S 9 A SAMPLE AF .;T
YE>S IS GIV5 0? EQU,N3
A4 ,:AT P]C5T (! ORIG9AL C>BON-#AD
REMA9S 9 A SAMPLE AF #BEJJ YE>S8 #EJJJ
YE>S8 #AJ1JJJ YE>S8
B4 ,GRAPH ! MODEL4
C4 ,AN >*AEOLOGI/ F.D A BISON B"O T
3TA9$ AB #CG@3P (! C>BON-#AD PRES5T :5 !
BISON DI$4 ,USE ! GRAPH 6E/IMATE ! AGE
(! B"O :5 X 0 F.D4
#CE4 .,,EXT5D$ .,,RESPONSE ,! NUMB]
.;,E ( E7S A ,LEGHORN *ICK5 PRODUCES P]
YE> C 2 MODEL$ 0! EQU,N .;,E .K #AGI.B
7#J.HI7 .;W _/#EB @4 ": .;W IS ! AGE 7IN
WEEKS7 (! *ICK5 & .;W .1.K #BB4
A4 .,9T]PRET ,ID5TIFY ! DECAY FACTOR
&! P]C5T DECR1SE4
B4 .,GRAPH ,GRAPH ! MODEL4
C4 .,E/IMATE ,E/IMATE ! EGG PRODUC;N
(A *ICK5 T IS #B.E YE>S OLD4
D4 .,R1SON+ .,EXPLA9 H[ Y C REWRITE !
GIV5 EQU,N S T "T IS M1SUR$ 9 YE>S R ?AN
9 WEEKS4
#CF4 .,,*ALL5GE ,Y BUY A NEW /]EO =
4#ACJJ & >E A# 6SELL X #D YE>S LAT] =
4#BGE4 ,ASSUME T ! RESALE VALUE (! /]EO
DECAYS EXPON5TI,Y ) "T4 ,WRITE AN EQU,N
GIV+ ! /]EO'S RESALE VALUE .;,V 7IN
DOLL>S7 Z A FUNC;N (! "T .;T 7IN YE>S7
S9CE Y B"\ X4
,,MIX$ ,,REVIEW
.,,PREVIEW ,PREP>E = ,LESSON #G.B 9
,EXS4 #DE-EB4
,EVALUATE ! P[]4
#CG4 .;Y .K .;X #C @+ #E @7 P4 #CCG @7
#CH4 .;Y .K .;X #D -- #E .;X #B @+ #D
@7 P4 #CCG @7
#CI4 @7 .;Y .K .;X #D -- #I @7 P4 #CCG
@7
#DJ4 @7 P4 #DDF @7
#DA4 @7 P4 #DDF @7
#DB4 @7 P4 #DDF @7
#DC4 .;Y .K #C @* #B ;X @7 P4 #DGH @7
#DD4 @7 P4 #DGH @7
#DE4 @7 P4 #DGH @7
,V]IFY T .;F & .;G >E 9V]SE FUNC;NS4
7.P#..DCH7
#DF4
#DG4
#DH4
#DI4
.,,EXTRA .,,PRACTICE = ,LESSON #G.B1
P4 #AJAF
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#DIB
#G.C ,USE ,FUNC;NS ,9VOLV+ ;E
.,2F ,Y /UDI$ EXPON5TIAL GR[? & DECAY
FUNC;NS4
.,N[ ,Y W /UDY FUNC;NS 9VOLV+ !
NATURAL BASE .E4
.,:Y8 ,S Y C MODEL VISIBIL;Y "UWAT]1 Z
9 ,EX4 #EI4
,KEY ,VOCABUL>Y
99 .NATURAL .BASE .;E
,SIDEB>3
,/&>DS
.#AB..J .,/UD5TS "K ! LAWS ( FRAC;NAL
EXPON5TS1 .."U/& EXPON5TIAL FUNC;NS 9
PRO#MS 9VOLV+ EXPON5TIAL .GR[? & DECAY4
,! HI/ORY ( MA!MATICS IS M>K$ 0!
4COV]Y ( SPECIAL NUMB]S S* Z & .;I @4
,ANO!R SPECIAL NUMB] IS DENOT$ 0! LR .E4
,! NUMB] IS CALL$ ! .NATURAL .BASE .;E
OR ! .,EUL] .NUMB] AF XS 4COV]]1
,LEONH>D ,EUL] 7#AGJG-AGHC74 ,! EXPRES.N
APPROA*ES .;E Z .;N 9CR1SES4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;N @3 #AJ #A @3 #AJ #B @3 #AJ #C @3
#AJ #D @3 #AJ #E @3 #AJ #F
@3 #B.EICGD3 #B.GJDHA3 #B.GAFIB3
#B.GAHAE3 #B.GAHBG3 #B.GAHBH
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,! ,NATURAL ,BASE .;E
,! NATURAL BASE .;E IS IRR,NAL4 ,X IS
DEF9$ Z FOLL[S3
,Z .;N APPROA*ES @+ @1 APPROA*ES .;E
#B.GAHBHAHBH4
,,EXAMPLE #A
,SIMPLIFY NATURAL BASE EXPRES.N
,SIMPLIFY ! EXPRES.N4
,,REVIEW ,,EXPON5TS
,= HELP ) PROP]TIES ( EXPON5TS1 SEE P4
#CCJ @4
A4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;E #B @* .;E #E @3 .K .;E #B @+ #E
--@3 .K .;E #G
.B4
.C4
,,EXAMPLE #B
,EVALUATE NATURAL BASE EXPRES.NS
,USE A CALCULATOR 6EVALUATE !
EXPRES.N4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,EXPRES.N3 ,KEY/ROKES3 ,4PLAY
.A4 .;E #D @3 @3 #ED.EIHAEJJC
.B4 .;E --#J.JI @3 @3 #J.IACICAAHEC
------------------------------------#DIC
..,,GUID$ ,,PRACTICE = ,EXAMPLES #A &
.#B
,SIMPLIFY ! EXPRES.N4
.#A4 .;E #G @* .;E #D
.#B4 #B .;E --#C @* #F .;E #E
.#C4
.#D4 7#AJ .;E --#D .;X @7 #C
.#E4 ,USE A CALCULATOR 6EVALUATE .;E
#C/D @4
,,KEY ,,3CEPT
,= YR .,NOTEBOOK
,NATURAL ,BASE ,FUNC;NS
,A FUNC;N (! =M .;Y .K .AE RX IS CALL$
A ..NATURAL BASE EXPON5TIAL .FUNC;N4
99 ,IF .A .1 #J & .;R .1 #J1 ! FUNC;N
IS AN EXPON5TIAL GR[? FUNC;N4
99 ,IF .A .1 #J & .;R "K #J1 ! FUNC;N
IS AN EXPON5TIAL DECAY FUNC;N4
,! GRAPHS (! BASIC FUNC;NS .;Y .K .;E
;X & .;Y .K .;E -- .;X >E %[N 2L4
,,EXAMPLE #C
,GRAPH NATURAL BASE FUNC;NS
,GRAPH ! FUNC;N4 ,/ATE ! DOMA9 &
RANGE4
.A4 .;Y .K #C .;E #J.BE .;X
.B4 .;Y .K .;E --#J.GE7 .;X -- #B7 @+
#A
,SOLU;N
,,ANO!R ,,WAY
,Y C AL WRITE ! FUNC;N F "P 7A7 9 ! =M
.;Y .K .;AB ;X 9 ORD] 6GRAPH X3
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;Y .K #C .;E #J.BE .;X
.;Y .K #C7 ;E.' #J.BE @7 .;X
.;Y .K #C7#A.BH7 .;X
.A4 ,2C .A .K #C IS POSITIVE & .;R .K
#J.BE IS POSITIVE1 ! FUNC;N IS AN
EXPON5TIAL GR[? FUNC;N4 ,PLOT ! PO9TS
7#J1 #C7 & 7#A1 #C.HE7 & DRAW ! CURVE4
,! DOMA9 IS ALL R1L NUMB]S1 &! RANGE
IS .;Y .1 #J4
.B4 .A .K #A IS POSITIVE & .;R .K
--#J.GE IS NEGATIVE1 S ! FUNC;N IS AN
EXPON5TIAL DECAY FUNC;N4 ,TRANSLATE !
GRAPH ( .;Y .K .;E --#J.GE .;X "R #B
UNITS & UP #A UNIT4
,! DOMA9 IS ALL R1L NUMB]S1 &! RANGE
IS .;Y .1 #A4
------------------------------------#DID
,,EXAMPLE #D
,SOLVE A MULTI-/EP PRO#M
.,,BIOLOGY ,! L5G? .;L 7IN C5TIMET]S7
(A TIG] %>K C 2 MODEL$ 0! FUNC;N
.;L .K #CCG--#BGF .;E --#J.AGH .;T ":
.;T IS ! %>K'S AGE 7IN YE>S74
99 ,GRAPH ! MODEL4
99 ,USE ! GRAPH 6E/IMATE ! L5G? (A
TIG] %>K T IS #C YE>S OLD4
,,9T]PRET ,,V>IA#S
,ON A GRAPH+ CALCULATOR1 5T] ! FUNC;N
.;L .K #CCG--#BGF .;E --#J.AGH .;T US+ !
V>IA#S .;X & .;Y @1 Z %[N 2L .;Y .K
#CCG--#BGF .;E --#J.AGH .;X
,SOLU;N
.,,/EP .#A .,GRAPH ! MODEL1 Z %[N4
.,,/EP .#B .,USE ! .TRACE F1TURE
6DET]M9E T .;L #AGE :5 .;T .K #C4
,! L5G? (A #C-YE>-OLD TIG] %>K IS AB
#AGE C5TIMET]S4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #C &
.#D
,GRAPH ! FUNC;N4 ,/ATE ! DOMA9 &
RANGE4
.#F4 .;Y .K #B .;E #J.E .;X
.#G4
.#H4 .;Y .K#A.E .;E --#J.BE7 .;X --
#A7 -- #B
.#I4 .,,:AT .,,IF8 ,9 ,EXAMPLE #D1 USE
! GIV5 FUNC;N 6E/IMATE ! L5G? (A TIG]
%>K T IS #E YE>S OLD4
.,,3T9U\SLY .,,-P.D$ .,,9T]E/ ,9
,LESSON #G.A1 Y LE>N$ T ! BAL.E ( AN
A3.T E>N+ -P.D 9T]E/ IS GIV5 0? =MULA3
,Z ! FREQU5CY .;N ( -P.D+ APPROA*ES
POSITIVE 9F9;Y1 ! -P.D 9T]E/ =MULA
APPROXIMATES ! FOLL[+ =MULA4
,,KEY ,,3CEPT
,= YR ,NOTEBOOK
,3T9U\SLY ,-P.D$ ,9T]E/
,:5 9T]E/ IS -P.D$ .3T9U\SLY @1 !
AM.TS 9 AN A3.T AF .;T YE>S IS GIV5 0!
=MULA
.,A .K .,PE RT
": .;,P IS ! PR9CIPAL & .;R IS !
ANNUAL 9T]E/ RATE EXPRESS$ Z A DECIMAL4
------------------------------------#DIE
,,EXAMPLE #E
,MODEL 3T9U\SLY -P.D$ 9T]E/
.,,F9.E ,Y DEPOSIT 4#DJJJ 9 AN A3.T T
PAYS #F@3P ANNUAL 9T]E/ -P.D$ 3T9U\SLY4
,:AT IS ! BAL.E AF #A YE>8
,SOLU;N
,USE ! =MULA = 3T9U\SLY -P.D$ 9T]E/4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,A @3 .K .,PE .RT @3 .,WRITE .=MULA4
--@3 .K #DJJJ .;E #J.JF7#A7 @3
,SUB/ITUTE #DJJJ =.' ;,P @1 #J.JF =.' ;R
@1 & #A =.' ;T @4
--@3 #DBDG.CE3 .,USE .A .CALCULATOR4
,! BAL.E AT ! 5D ( #A YE> IS
4#DBDG.CE4
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#E
#AJ4 .,,F9.E ,Y DEPOSIT 4#BEJJ 9 AN
A3.T T PAYS #E@3P ANNUAL 9T]E/ -P.D$
3T9U\SLY4 ,F9D ! BAL.E AF EA* AM.T ( "T4
A4 #B YE>S
B4 #E YE>S
C4 #G.E YE>S
#AA4 .,,F9.E ,F9D ! AM.T ( 9T]E/ E>N$
9 "PS 7A7-7;C7 ( ,EX]CISE #AJ4
#G.C ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
,,WS#AC = ,EXS4 #E1CE1 & #EG
.,,/&>DIZ$ .,,TE/ .,,PRACTICE ,EXS4
#B1AE1AF1EB1EC1 & #FJ
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,!
NUMB] @8 IS AN IRR,NAL NUMB]
APPROXIMATELY EQUAL 6#B.GAHBH4
.#B4 .,,WRIT+ ,TELL :E!R ! FUNC;N IS
AN EXAMPLE ( .EXPON5TIAL .GR[? OR
.EXPON5TIAL .DECAY4 .,EXPLA94
,,SIMPLIFY+ ,,EXPRES.NS ,SIMPLIFY !
EXPRES.N4
.,,EXAMPLE .#A ON P4 #DIB = ,EXS4
#C-AH
.#C4 .;E #C @* .;E #D
.#D4 .;E --#B @* .;E #F
.#E4 7#B .;E #C .;X @7 #C
.#F4 7#B .;E --#B @7-- #D
.#G4 7#C .;E #E .;X @7 --#A
.#H4 .;E ;X @* .;E #C .;X @* .;E #D
.#I4
.#AJ4 .;E ;X @* #E .;E .;X @+ #C
.#AA4
.#AB4
.#AC4
.#AD4
#AE4 .,,MULTIPLE .,,*OICE ,:AT IS !
SIMPLIFI$ =M ( 7#D .;E #B .;X @7 #C @8
,A #D .;E #F .;X
;,B #D .;E #H .;X
;,C #FD .;E #F .;X
;,D #FD .;E #H .;X
#AF4 .,,MULTIPLE .,,*OICE ,:AT IS !
SIMPLIFI$ =M ( @8
,A #F .;E ;L#J .;X
;,B #F .;E #F .;X #D
;,C
;,D #F .;E #C .;X #B
------------------------------------#DIF
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 SIMPLIFY+ ! EXPRES.N4
.#AG4
.#AH4
,,EXAMPLE #B
ON P4 #DIB = ,EXS4 #AI-CJ
,,EVALUAT+ ,,EXPRES.NS ,USE A
CALCULATOR 6EVALUATE ! EXPRES.N4
.#AI4 .;E #C
.#BJ4 .;E --#C/D
.#BA4 .;E #B.B
.#BB4 .;E #A/B
.#BC4 .;E --#B/E
.#BD4 .;E #D @' #C
.#BE4 .;E #G
.#BF4 .;E --#D
.#BG4 #B .;E --#J.C
.#BH4 #E .;E #B/C
.#BI4 --#F .;E #B.D
.#CJ4 #J.D .;E #D.A
,,GR[? ,,OR ,,DECAY ,TELL :E!R !
FUNC;N IS AN EXAMPLE ( .EXPON5TIAL .GR[?
OR .EXPON5TIAL .DECAY4
.#CA4 .;F @7 .;X @7 .K #C .;E -- .;X
.#CB4
.#CC4 .;F @7 .;X @7 .K .;E --#D .;X
.#CD4
.#CE4
.#CF4 .;F @7 .;X @7 .K .;E #C .;X
.#CG4 .;F @7 .;X @7 .K #B .;E #D .;X
.#CH4 .;F @7 .;X @7 .K #D .;E #B .;X
.,,EXAMPLE .#C ON P4 #DIC = ,EXS4
#CI-EJ
,,MAT*+ ,,GRAPHS ,MAT* ! FUNC;N ) XS
GRAPH4
.#CI4 .;Y .K #J.E .;E --#B .;X
.#DJ4 .;Y .K #B .;E #J.E .;X
.#DA4 .;Y .K .;E #J.E .;X @+ #B
.,A4
.,B4
.,C4
,,GRAPH+ ,,FUNC;NS ,GRAPH ! FUNC;N4
,/ATE ! DOMA9 & RANGE4
.#DB4 .;Y .K .;E --#B .;X
.#DC4 .;Y .K #C .;E ;X
.#DD4 .;Y .K #J.E .;E ;X
.#DE4 .;Y .K #B .;E #C .;X -- #A
.#DF4 .;Y .K #B.E .;E --#J.E .;X @+ #B
.#DG4 .;Y .K #J.F .;E .;X -- #B
.#DH4
.#DI4
.#EJ4 .;H @7 .;X .K .;E --#B7 .;X @+
#A7 -- #C
.#EA4 .,,GRAPH+ .,,CALCULATOR ,USE !
.TA# F1TURE (A GRAPH+ CALCULATOR 6F9D !
VALUE ( .;N = : GIVES ! VALUE ( .;E
CORRECT 6#I DECIMAL PLACES4 .,EXPLA9 !
PROCESS Y US$ 6F9D YR ANSW]4
.#EB4 .,,%ORT .,,RESPONSE ,C .;E 2
EXPRESS$ Z A RATIO ( TWO 9TEG]S8
.,EXPLA9 YR R1SON+4
.#EC4 .,,OP5-.,,5D$ .,,MA? ,F9D VALUES
( .A1 .;B1 .;R @1 & .;Q S* T .;F @7 .;X
@7 .K .AE RX & .;G @7 .;X @7 .K .2 QX >E
EXPON5TIAL .DECAY FUNC;NS & IS AN
EXPON5TIAL .GR[? FUNC;N4
.#ED4 .,,*ALL5GE .,EXPLA9 :Y
APPROXIMATES .,A .K .,PE RT Z .;N
APPROA*ES POSITIVE 9F9;Y4 @7 .,H9T3 ,LET
@7@4
.K ..,,"W$-,,\ ,,SOLU;NS .ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#DIG
,,PRO#M ,,SOLV+
,,EXAMPLE #D
ON P4 #DID = ,EXS4 #EE-EF
.#EE4 .,,CAM]A .,,PH"OS ,! NUMB] (
CAM]A PH"OS %IPP$ GLOB,Y C 2 MODEL$ 0!
FUNC;N .;Y .K L#.BH .;E #A.CA .;X ": .;X
IS ! NUMB] ( YE>S S9CE #AIIG & .;Y IS !
NUMB] ( CAM]A PH"OS %IPP$ 7IN MILLIONS74
,H[ _M CAM]A PH"OS 7 %IPP$ 9 #BJJB8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#EF4 .,,BIOLOGY ,SCI5TI/S US$ TRAPS
6/UDY ! ,=MOSAN SUBT]RAN1N T]MITE
POPUL,N 9 ,NEW ,ORL1NS4 ,! M1N NUMB] .;Y
( T]MITES COLLECT$ ANNU,Y C 2 MODEL$
0.;Y .K #GCH;E;DG0' #CDE;R ": ;R IS !
NUMB] ( YE>S S9CE #AIHI4 ,:AT 0 ! M1N
NUMB] ( T]MITES COLLECT$ 9 #AIII8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
,,EXAMPLE #E
ON P4 #DIE = ,EXS4 #EG-EH
.#EG4 .,,F9.E ,Y DEPOSIT 4#BJJJ 9 AN
A3.T T PAYS #D@3P ANNUAL 9T]E/ -P.D$
3T9U\SLY4 ,:AT IS ! BAL.E AF #E YE>S8
.#EH4 .,,F9.E ,Y DEPOSIT 4#HJJ 9 AN
A3.T T PAYS #B.FE@3P ANNUAL 9T]E/ -P.D$
3T9U\SLY4 ,:AT IS ! BAL.E AF #AB.E YE>S8
#EI4 .,,MULTI-.,,/EP .,,PRO#M ,! P]C5T
.;,L ( SURFACE LI<T T FILT]S D[N "?
BODIES ( WAT] C 2 MODEL$ 0! EXPON5TIAL
FUNC;N .;,L @7 .;X @7 .K #AJJ .;E KX ":
.;K IS A M1SURE (! MURKI;S (! WAT] & .;X
IS ! DEP? 2L ! SURFACE 7IN MET]S74
A4 ,A RECRE,NAL SUBM]SI# IS TRAVEL+ 9
CLE> WAT] )A .;K -VALUE ( AB --#J.JB4
,WRITE & GRAPH AN EQU,N GIV+ ! P]C5T (
SURFACE LI<T T FILT]S D[N "? CLE> WAT] Z
A FUNC;N ( DEP?4
B4 ,USE YR GRAPH 6E/IMATE ! P]C5T (
SURFACE LI<T AVAILA# AT A DEP? ( #DJ
MET]S4
C4 ,USE YR GRAPH 6E/IMATE H[ DEEP !
SUBM]SI# C DESC5D 9 CLE> WAT] 2F ONLY
#EJ@3P ( SURFACE LI<T IS AVAILA#4
#FJ4 .,,EXT5D$ .,,RESPONSE ,! GR[? (!
BACT]IA .MYCOBACT]IUM .TUB]CULOSIS C 2
MODEL$ 0! FUNC;N .;,P @7 .;T @7 .K .;,P
#J .;E #J.AAF .;T ": .;,P @7 .;T @7 IS !
POPUL,N AF .;T H\RS & .;,P #J IS !
POPUL,N :5 .;T .K #J4
A4 .,MODEL ,AT #A3JJ ,P4,M41 "! >E #CJ
.MYCOBACT]IUM .TUB]CULOSIS BACT]IA 9 A
SAMPLE4 ,WRITE A FUNC;N =! NUMB] (
BACT]IA AF #A3JJ ,P4,M4
B4 .,GRAPH ,GRAPH ! FUNC;N F "P 7A74
C4 .,E/IMATE ,:AT IS ! POPUL,N AT
#E3JJ ,P4,M48
D4 .,R1SON+ .,DESCRIBE H[ 6F9D !
POPUL,N AT #C3DE ,P4,M4
-----------------------------------#DIH
#FA4 .,,RATE .,,( .,,H1L+ ,! >EA (A
W.D DECR1SES EXPON5TI,Y ) "T4 ,! >EA .,A
(A W.D AF .;T "DS C 2 MODEL$ 0.,A .K .,A
#J .;E #J.JE .;T ": .,A #J IS ! 9ITIAL
W.D >EA4 ,IF ! 9ITIAL W.D >EA IS #D
SQU>E C5TIMET]S1 :AT IS ! >EA AF #AD
"DS8
#FB4 .,,*ALL5GE ,! HEI<T .;Y 7IN FEET7
(! ,GATEWAY ,>* 9 ,ST4 ,L\IS1 ,MISS\RI1
C 2 MODEL$ 0! FUNC;N .;Y .K
#GEG.G--#FC.HE7 .;E .;X _/;L#BG.G @+ .;E
-- .;X _/#ABG.G @7 ": .;X IS !
HORIZONTAL 4T.E 7IN FEET7 F ! C5T] (!
>*4
A4 ,USE A GRAPH+ CALCULATOR 6GRAPH !
FUNC;N4 ,H[ TALL IS ! >* AT XS HI<E/
PO9T8
B4 ,AB H[ F> A"P >E ! 5DS (! >*8
,,MIX$ ,,REVIEW
,SOLVE ! EQU,N4
.#FC4 _\ .;X @+ #H_\ .K #AC 7.P#..EA7
.#FD4 _\#C .;X @+ #AG_\ .K #AF
7.P#..EA7
.#FE4 #B .;X #B --#D .;X @+ #I .K #J
7.P#..BIB7
.#FF4 .;X #B @+#AB .;X -- #C .K #J
7.P#..BIB7
.#FG4 @7 P4 #DEB @7
.#FH4 @7 P4 #DEB @7
.,,PREVIEW ,PREP>E = ,LESSON #G.D 9
,EXS4 #FI-GD4
,F9D ! 9V]SE FUNC;N4 @7 P4 #DCG @7
.#FI4 .;F7.;X7 .K #B .;X
.#GJ4 .;F7.;X7 .K #E .;X -- #C
.#GA4 .;F7.;X7 .K --#D .;X @+#AD
.#GB4
.#GC4 .;F7.;X7 .K --#AB .;X --#F
.#GD4
,,QUIZ .= .,LESSONS .#G..A-.GC
,GRAPH ! FUNC;N4 ,/ATE ! DOMA9 &
RANGE4
.#A4 .;Y .K #B @* #C .;X -- #B @7 P4
#DGH @7
.#B4 @7 P4 #DHF @7
.#C4 @7 P4 #DHF @7
,SIMPLIFY ! EXPRES.N1 @7 P4 #DIB @7
.#D4 #C .;E #D @* .;E #C
.#E4 7--#E .;E #C .;X @7 #C
.#F4
.#G4
,GRAPH ! FUNC;N4 ,/ATE ! DOMA9 &
RANGE1 @7 P4 #DIB @7
.#H4 .;Y .K #B .;E ;X
.#I4 .;Y .K #C .;E --#B .;X
.#AJ4 .;Y .K .;E .;X @+ ;L -- #B
.#AA4 .;G @7 .;X @7 .K #D .;E #C .;X
@+ #A
.#AB4 .,,TV .,,SALES ,F #AIIG 6#BJJA1
! NUMB] .;N 7IN MILLIONS7 ( BLACK-&-:ITE
,,TV,'S SOLD 9 ! ,UNIT$ ,/ATES C 2
MODEL$ 0.;N .K #BF.H 7#J.HE7 ;T ": .;T
IS ! NUMB] ( YE>S S9CE #AIIG4 ,ID5TIFY !
DECAY FACTOR &! P]C5T DECR1SE4 ,GRAPH !
MODEL & /ATE ! DOMA9 & RANGE4 ,E/IMATE !
NUMB] ( BLACK-&-:ITE ,,TV,'S SOLD 9
#AIII4 @7 P4 #DGH @7
.#AC4 .,,F9.E ,Y DEPOSIT 4#ABJJ 9 AN
A3.T T PAYS #D.E@3P ANNUAL 9T]E/ -P.D$
3T9U\SLY4 ,:AT IS ! BAL.E AF #E YE>S8 @7
P4 #DIB @7
.,,EXTRA .,,PRACTICE = ,LESSON #G.C1
P4 #AJAF
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#DII
#G.D ,EVALUATE ,LOG>I?MS & ,GRAPH
,LOG>I?MIC ,FUNC;NS
.,2F ,Y EVALUAT$ & GRAPH$ EXPON5TIAL
FUNC;NS4
.,N[ ,Y W EVALUATE LOG>I?MS & GRAPH
LOG>I?MIC FUNC;NS4
.,:Y8 ,S Y C MODEL ! W9D SPE$ (A
TORNADO1 Z 9 ,EXAMPLE #D4
,KEY ,VOCABUL>Y
99 ..LOG>I?M ( ;Y ) BASE .;B
99 .-MON .LOG>I?M
99 .NATURAL .LOG>I?M
,SIDEB>3
,/&>DS
#AD.J ,/UD5TS "U/& & USE ! PROP]TIES (
LOG>I?MS 6SIMPLIFY LOG>I?MIC NUM]IC
EXPRES.NS & 6ID5TIFY _! APPROXIMATE
VALUES4
,Y "K T #B #B .K #D & #B #C .K #H4
,H["E1 = :AT VALUE ( .;X DOES #B ;X .K
#F8 ,MA!MATICIANS DEF9E ? .;X -VALUE US+
A .LOG>I?M & WRITE .;X .K LOG #B #F4 ,!
DEF9I;N (A LOG>I?M C 2 G5]ALIZ$ Z
FOLL[S4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,DEF9I;N ( ,LOG>I?M ) ,BASE .;B
,LET .;B & .;Y 2 POSITIVE NUMB]S ) .;B
@6.K #A4 ,! ..LOG>I?M ( ;Y ) BASE .;B IS
DENOT$ 0LOG ;B .;Y & IS DEF9$ Z FOLL[S3
LOG ;B .;Y .K .;X IF & ONLY IF .;B ;X
.K .;Y
,! EXPRES.N LOG ;B .;Y IS R1D Z 8LOG
BASE .;B ( .;Y @4@8
,? DEF9I;N TELLS Y T ! EQU,NS LOG ;B
.;Y .K .;X & .;B ;X .K .;Y >E EQUIVAL5T4
,! F/ IS 9 .LOG>I?MIC .=M &! SECOND IS 9
.EXPON5TIAL .=M4
,,EXAMPLE #A
,REWRITE LOG>I?MIC EQU,NS
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,LOG>I?MIC ,=M3 ,EXPON5TIAL ,=M
.A4 LOG #B #H .K #C @3 #B #C .K #H
.B4 LOG #D #A .K #J @3 #D;DG .K #A
.C4 LOG #AB #AB .K #A @3 #AB #A .K #AB
.D4 LOG #A/D #D .K --;L @3
,"PS 7;B7 & 7;C7 ( ,EXAMPLE #A
ILLU/RATE TWO SPECIAL LOG>I?M VALUES T Y
%D LE>N 6RECOGNIZE4 ,LET .;B 2 A
POSITIVE R1L NUMB] S* T .;B @6.K #A4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,LOG>I?M .( .#A @3 ,LOG>I?M (.' ;B
.-) ,BASE.' ;B.-
LOG .;B #A .K #J 2C .;B #J .K #A4 @3
LOG .;B .;B .K #A 2C .;B #A .K .;B @4
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#A
,REWRITE ! EQU,N 9 EXPON5TIAL =M4
.#A4 LOG #C #HA .K #D
.#B4 LOG #G #G .K #A
.#C4 LOG #AD #A .K #J
.#D4 LOG #A/B #CB .K --#E
------------------------------------#EJJ
,,EXAMPLE #B ,EVALUATE LOG>I?MS
,EVALUATE ! LOG>I?M4
.A4 LOG #D #FD
.B4 LOG #E #J.B
.C4 LOG #A/E #ABE
.D4 LOG #CF #F
,SOLU;N
,6HELP Y F9D ! VALUE ( LOG1 .;Y @1 ASK
YRF :AT P[] ( .;B GIVES Y .Y4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.A4 #D 6:AT P[] GIVES #FD8 @3 #D #C .K
#FD1 S LOG #D #FD .K #C4
.B4 #E 6:AT P[] GIVES #J.B8 @3 #E --#A
.K #J.B1 S LOG #E #J.B .K --.#A @4
.C4 6:AT P[] GIVES #ABE8 @3 @1 S LOG
#A/E #ABE .K --.#C @4
.D4 #CF 6:AT P[] GIVES #F8 @3 #CF #A/B
.K #F1 S @4
.,,SPECIAL .,,LOG>I?MS ,A .-MON
.LOG>I?M IS A LOG>I?M ) BASE #AJ4 ,X IS
DENOT$ 0LOG #AJ OR SIMPLY 0LOG4 ,A
.NATURAL .LOG>I?M IS A LOG>I?M ) BASE
.E4 ,X C 2 DENOT$ 0LOG ;E @1 B IS M (T5
DENOT$ 0,IN4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,-MON ,LOG>I?M3 ,NATURAL ,LOG>I?M
LOG #AJ .;X .K LOG .;X @3 LOG .;E .;X
.K ,9 .;X
,MO/ CALCULATORS H KEYS = EVALUAT+
-MON & NATURAL LOG>I?MS4
,EXAMPLE #C ,EVALUATE -MON & NATURAL
LOG>I?MS
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,EXPRES.N3 ,KEY/ROKES3 ,4PLAY3 ,*ECK
.A4 LOG #H @3 @3 #J.IJCJHIIHG3 #AJ
#J.IJC #H
.B4 ,9 #J.C @3 @3 --#A.BJCIGBHJD3 .;E
--#A.BJD #J.C
,,EXAMPLE #D ,EVALUATE A LOG>I?MIC
MODEL
.,,TORNADOES ,! W9D SPE$ #E 7IN MILES
P] H\R7 NE> ! C5T] (A TORNADO C 2 MODEL$
0.;S .K #IC LOG .;D @+ #FE
": .;D IS ! 4T.E 7IN MILES7 T !
TORNADO TRAVELS4 ,9 #AIBE1 A TORNADO
TRAVEL$ #BBJ MILES "? ?REE /ATES4
,E/IMATE ! W9D SPE$ NE> ! TORNADO'S
C5T]4
,SOLU;N
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;S @3 .K #IC LOG .;D @+ #FE @3
.,WRITE .FUNC;N4
--@3 .K #IC LOG .#BBJ @+ #FE @3
,SUB/ITUTE #BBJ =.' D4.-
--@3 #IC7#B.CDB7 @+ #FE3 .,USE .A
.CALCULATOR4
--@3 .K #BHB.HJF3 .,SIMPLIFY4
,! W9D SPE$ NE> ! TORNADO'S C5T] 0 AB
#BHC MILES P] H\R4
------------------------------------#EJA
..,,GUID$ ,,PRACTICE = ,EXAMPLES #B1C1
& .#D
,EVALUATE ! LOG>I?M4 ,USE A CALCULATOR
IF NEC4
.#E4 LOG #B #CB
.#F4 LOG #BG #C
.#G4 LOG #AB
.#H4 ,9 #J.GE
.#I4 .,,:AT .,,IF8 ,USE ! FUNC;N 9
,EXAMPLE #D 6E/IMATE ! W9D SPE$ NE> A
TORNADO'S C5T] IF XS PA? IS #AEJ MILES
L;G4
.,,9V]SE .,,FUNC;NS ,0! DEF9I;N (A
LOG>I?M1 X FOLL[S T ! LOG>I?MIC FUNC;N
.;G @7 .;X @7 .K LOG ;B .;X IS ! 9V]SE
(! EXPON5TIAL FUNC;N .;F @7 .;X @7 .K
.;B ;X @4 ,? M1NS T3
.;G @7 .;F @7 .;X77 .K LOG ;B .;B ;X
.K .;X & .;F @7 .;G @7 .;X @7@7 .K .;B
LOG .;B ;X .K .;X
,,EXAMPLE #E ,USE 9V]SE PROP]TIES
,SIMPLIFY ! EXPRES.N4
.A4 #AJ LOG #D
.B4 LOG #E #BE ;X
,SOLU;N
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.A4 #AJ LOG #D @3 .K #D3 .;B LOG .;B
.;X .K .;X
.B4 LOG #E #BE .;X @3 .K LOG #E 7#E #B
@7 .;X @3 ..,EXPRESS #BE Z A P[] ) BASE
.#E4
--@3 .K LOG #E #E #B .;X @3 ..,P[] (A
P[] .PROP]TY
--@3 .K #B .;X @3 LOG .;B .;B .;X .K
.;X
,,EXAMPLE #F ,F9D 9V]SE FUNC;NS
,F9D ! 9V]SE (! FUNC;N4
.A4 .;Y .K #F ;X
.B4 .;Y .K ,9 @7 .;X @+ #C7
,,REVIEW ,,9V]SES
,= HELP ) F9D+ 9V]SES ( FUNC;NS1 SEE
P4 #DCG @4
,SOLU;N
.A4 ,F ! DEF9I;N ( LOG>I?M1 ! 9V]SE (
.;Y .K #F ;X IS .;Y .K LOG #F .;X @4
B4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;Y @3 .K ,9 @7 .;X @+ #C7 @3 .,WRITE
.ORIG9AL .FUNC;N4
.;X @3 .K ,9 @7 .;Y @+ #C7 @3 ,SWIT*.'
;X .-&.' ;Y @4
.;E .;X @3 .K .;Y @+ #C @3 ..,WRITE 9
EXPON5TIAL .=M4
.;E .;X -- #C @3 .K .;Y @3 .,SOLVE .=
.Y4
,! 9V]SE ( .;Y .K ,9 @7 .;X @+ #C7 IS
.;Y .K .;E ;X -- #C4
,,GUID$ ,,PRACTICE = ,EXAMPLES #E & #F
,SIMPLIFY ! EXPRES.N4
.#AJ4 #H LOG #H .;X
.#AA4 LOG #G #G --#C .;X
.#AB4 LOG #B #FD ;X
.#AC4 .;E LN #BJ
.#AD4 ,F9D ! 9V]SE ( .;Y .K #D ;X @4
.#AE4 ,F9D ! 9V]SE ( .;Y .K ,9 @7 .;X
-- #E74
------------------------------------#EJB
.,,GRAPH+ .,,LOG>I?MIC .,,FUNC;NS ,Y C
USE ! 9V]SE REL,N%IP 2T EXPON5TIAL &
LOG>I?MIC FUNC;NS 6GRAPH LOG>I?MIC
FUNC;NS4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,P>5T ,GRAPHS = ,LOG>I?MIC ,FUNC;NS
,! GRAPH ( .;F @7 .;X @7 .K LOG ;B .;X
IS %[N 2L = .;B .1 #A &= #J "K .;B "K
#A4 ,2C .;F @7 .;X @7 .K LOG ;B .;X &
.;G @7 .;X @7 .K .;B ;X >E 9V]SE
FUNC;NS1 ! GRAPH ( .;F @7 .;X 7.K LOG ;B
.;X IS ! REFLEC;N (! GRAPH ( .;G @7 .;X
@7 .K .;B ;X 9 ! L9E .;Y .K .;X @4
,PICTURE3 ..,GRAPH ( ;F @7 ;X @7 .K
.LOG ;B ..;X = ;B .1 .#A
,PICTURE3 ..,GRAPH ( ;F @7 ;X @7 .K
.LOG ;B ..;X = #J "K ;B "K .#A
,NOTE T ! .;Y -AXIS IS A V]TICAL
ASYMPTOTE (! GRAPH ( .;F @7 .;X @7 .K
LOG ;B .;X @4 ,! DOMA9 ( .;F @7 .;X @7
.K LOG ;X .;X IS .;X .1 #J1 &! RANGE IS
ALL R1L NUMB]S4
,,EXAMPLE #G
,GRAPH LOG>I?MIC FUNC;N
,GRAPH ! FUNC;N4
.A4 .;Y .K LOG #C .;X
.B4 .;Y .K LOG #A/B .;X
,SOLU;N
.A4 ,PLOT S"EAL 3V5I5T PO9TS1 S* Z
7#A1 #J71 7#C1 #A71 & 7#I1 #B74 ,! .;Y
-AXIS IS A V]TICAL ASYMPTOTE4
,F .LEFT 6."R @1 DRAW A CURVE T />TS J
6! "R (! .;Y -AXIS & MOVES UP "? !
PLOTT$ PO9TS1 Z %[N 2L4
.B4 ,PLOT S"EAL 3V5I5T PO9TS1 S* Z
7#A1 #J71 7#B1 --#A71 7#D1 --#B71 & 7#H1
--#C74 ,! .;Y -AXIS IS A V]TICAL
ASYMPTOTE4
,F .LEFT 6."R @1 DRAW A CURVE T />TS J
6! "R (! .;Y -AXIS & MOVES D[N "? !
PLOTT$ PO9TS1 Z %[N 2L4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
------------------------------------#EJC
.,,TRANSL,NS ,Y C GRAPH A LOG>I?MIC
FUNC;N (! =M .;Y .K LOG ;B @7 .;X -- .;H
@7 @+ .;K 0TRANSLAT+ ! GRAPH (! P>5T
FUNC;N .;Y .K LOG ;B .;X @4
,,EXAMPLE #H ,TRANSLATE A LOG>I?MIC
GRAPH
,GRAPH .;Y .K LOG #B @7 .;X @+ #C7 @+
#A4 ,/ATE ! DOMA9 & RANGE4
,SOLU;N
.,,/EP .#A .,SKET* ! GRAPH (! P>5T
FUNC;N .;Y .K LOG #B .;X @1 : PASSES "?
7#A1 #J71 7#B1 #A71 & 7#D1 #B74
.,,/EP .#B .,TRANSLATE ! P>5T GRAPH
LEFT #C UNITS & UP #A UNIT4 ,! TRANSLAT$
GRAPH PASSES "? 7--#B1 #A71 7--#A1 #B71
& 7#A1 #C74 ,! GRAPH'S ASYMPTOTE IS .;X
.K --#C4 ,! DOMA9 IS .;X .1 --#C1 &!
RANGE IS ALL R1L NUMB]S4
.,,GUID$ .,,PRACTICE = ,EXAMPLES #G &
#H
,GRAPH ! FUNC;N4 ,/ATE ! DOMA9 &
RANGE4
.#AF4 .;Y .K LOG #E .;X
.#AG4 .;Y .K LOG #A/C @7 .;X -- #C7
.#AH4 .;F @7 .;X @7 .K LOG #D @7 .;X
@+ #A7--#B
#G.D ,EX]CISES
,HOME"W ,KEY
.K ..,,"W$-,,\ ,,SOLU;NS .ON P4
,,WS#AC ..= ,EXS4 #AC1 #CC1 & .#FA
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE ,EXS4
..#B1 #CF1FA1 & .#FB
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,A
LOG>I?M ) BASE #AJ IS CALL$ A7;N7 @8
LOG>I?M4
.#B4 .,,WRIT+ .,DESCRIBE ! REL,N%IP 2T
.;Y .K #E ;X & .;Y .K LOG #E .;X @4
,,EXAMPLE #A ON P4 #DII = ,EXS4 #C-G
,,EXPON5TIAL ,,=M ,REWRITE ! EQU,N 9
EXPON5TIAL =M4
.#C4 LOG #D #AF .K #B
.#D4 LOG #G #CDC .K #C
.#E4
.#F4 LOG #FD #A .K #J
.#G4 .,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 REWRIT+ ! EQU,N #B --#C
.K 9 LOG>I?MIC =M4
,,EXAMPLE #B
ON P4 #EJJ = ,EXS4 #H-AI
,,EVALUAT+ ,,LOG>I?MS ,EVALUATE !
LOG>I?M )\T US+ A CALCULATOR4
.#H4 LOG #AE #AE
.#I4 LOG #G #DI
.#AJ4 LOG #F #BAF
.#AA4 LOG #B #FD
.#AB4 LOG #I #A
.;L#C4 LOG #A/B #H
.#AD4
.#AE4 LOG #AF
.#AF4 LOG #A/D #AF
.#AG4 LOG #H #EAB
.#AH4 LOG #E #FBE
.#AI4 LOG ;N #ABA
------------------------------------#EJD
,,EXAMPLE #C
ON P4 #EJJ = ,EXS4 #BJ-BG
.,,CALCULAT+ .,,LOG>I?MS ,USE A
CALCULATOR 6EVALUATE ! LOG>I?M4
#BJ4 LOG #AD
#BA4 LN #F
#BB4 ,9 #J.DC
#BC4 LOG #F.BAC
#BD4 LOG #BG
#BE4 ,9 #E.CH
#BF4 LOG #J.GDF
#BG4 ,9 #AAJ
,,EXAMPLE #E
ON P4 #EJA = ,EXS4 #BH-CF
.,,US+ .,,9V]SE .,,PROP]TIES ,SIMPLIFY
! EXPRES.N4
#BH4 #G LOG #G .;X
#BI4 LOG #E #E ;X
#CJ4 #CJ LOG #CJ #D
#CA4 #AJ LOG #H
#CB4 LOG #F #CF ;X
#CC4 #A;OG #C #HA ;X
#CD4 LOG #E #ABE ;X
#CE4 LOG #B #CB ;X
#CF4 .,,MULTIPLE .,,*OICE ,: EXPRES.N
IS EQUIVAL5T 6LOG #AJJ ;X @8
,A .;X
;,B #B .;X
;,C ;L#J .;X
;,D ;L#JJ .;X
,,EXAMPLE #F
ON P4 #EJA = ,EXS4 #CG-DD
.,,F9D+ .,,9V]SES ,F9D ! 9V]SE (!
FUNC;N4
#CG4 .;Y .K LOG #H .;X
#CH4 .;Y .K .#G ;X
#CI4 .;Y .K 7#J.D7 ;X
#DJ4 .;Y .K LOG #A/B .;X
#DA4 .;Y .K .;E .;X @+ #B
#DB4 .;Y .K #B ;X -- #C
#DC4 .;Y .K ,9 @7 .;X @+ #A7
#DD4 .;Y .K #F @+ LOG .;X
,,EXAMPLES #G & #H
ON PP4 #EJB-EJC = ,EXS4 #DE-EC
.,,GRAPH+ .,,FUNC;NS ,GRAPH ! FUNC;N4
,/ATE ! DOMA9 & RANGE4
#DE4 .;Y .K LOG #D .;X
#DF4 .;Y .K LOG #F .;X
#DG4 .;Y .K LOG #A/C .;X
#DH4 .;Y .K LOG #A/E .;X
#DI4 .;Y .K LOG #B @7 .;X -- #C7
#EJ4 .;Y .K LOG #C .;X @+ #D
#EA4 .;F @7 .;X @7 .K LOG #D @7 .;X @+
#B7--#A
#EB4 .;G @7 .;X @7 .K LOG #F @7 .;X --
#D7 @+ #B
#EC4 .;H @7 .;X @7 .K LOG #E @7 .;X @+
#A7--#C
.,,*ALL5GE ,EVALUATE ! LOG>I?M4 @7
.,H9T3 ,= EA* LOG>I?M LOG ;B .;X @1
REWRITE .;B & .;X Z P[]S (! SAME NUMB]47
#ED4 LOG #BG #I
#EE4 LOG #H #CB
#EF4 LOG #ABE #FBE
#EG4 LOG #D #ABH
,,PRO#M ,,SOLV+
,,EXAMPLE #D
ON P4 #EJJ = ,EXS4 #EH-EI
#EH4 .,,ALTIMET] ,SKYDIV]S USE AN
9/RU;T CALL$ AN ALTIMET] 6TRACK _!
ALTITUDE Z !Y FALL4 ,! ALTIMET] DET]M9ES
ALTITUDE 0M1SUR+ AIR PRESSURE4 ,!
ALTITUDE .;H 7IN MET]S7 ABV SEA LEVEL IS
RELAT$ 6! AIR PRESSURE .;,P 7IN PASCALS7
0! FUNC;N 9 ! DIAGRAM 2L4
,:AT IS ! ALTITUDE ABV SEA LEVEL :5 !
AIR PRESSURE IS #EG1JJJ PASCALS8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#EI4 .,,*EMI/RY ,! P,H VALUE =A
SUB/.E M1SURES H[ ACIDIC OR ALKAL9E !
SUB/.E IS4 ,X IS GIV5 0! =MULA P,H .K
--LOG ,7;,H @+ @7' ": ;,H @+ IS !
HYDROG5 ION 3C5TR,N 7IN MOLES P] LIT]74
,LEMON JUICE HAS A HYDROG5 ION 3C5TR,N (
#AJ --#B.C MOLES P] LIT]4 ,:AT IS XS P,H
VALUE8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.K ..,,"W$-,,\ ,,SOLU;NS ON P4.,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#EJE
#FJ4 .,,MULTI-.,,/EP .,,PRO#M
,BIOLOGI/S H F.D T AN ALLIGATOR'S L5G?
.;L 7IN 9*ES7 & WEI<T .;W 7IN P.DS7 >E
RELAT$ 0! FUNC;N .;L .K #BG.A ,9 .;W --
#CB.H4 ,GRAPH ! FUNC;N4 ,USE YR GRAPH
6E/IMATE ! WEI<T ( AN ALLIGATOR T IS #AJ
FEET L;G4
.#FA4 .,,%ORT .,,RESPONSE ,! 5]GY
MAGNITUDE .;,M ( AN E>?QUAKE C 2 MODEL$
0.;,M .K #J.BI7LN .;,E @7 --#I.I
": .;,E IS ! AM.T ( 5]GY REL1S$ 7IN
]GS74
A4 ,9 #BJJA1 A P[];L E>?QUAKE 9 ,P]U1
CAUS$ 0! SLIPPAGE ( TWO TECTONIC PLATES
AL;G A FAULT1 REL1S$ #B.E * #AJ #BD ]GS4
,:AT 0 ! 5]GY MAGNITUDE (! E>?QUAKE8
B4 ,F9D ! 9V]SE (! GIV5 FUNC;N4
.,DESCRIBE :AT X REPRES5TS4
#FB4 .,,EXT5D$ .,,RESPONSE ,A /UDY 9
,FLORIDA F.D T ! NUMB] ( FI% SPECIES #E
9 A POOL OR LAKE C 2 MODEL$ 0! FUNC;N
.;S .K #CJ.F--#BJ.E7LOG .,A @7 @+
#C.H7LOG .,A @7 #B ": .,A IS ! >EA 7IN
SQU>E MET]S7 (! POOL OR LAKE4
A4 .,GRAPH ,USE A GRAPH+ CALCULATOR
6GRAPH ! FUNC;N ON ! DOMA9 #BJJ "K.K .,A
"K.K#CE1JJJ4
B4 .,E/IMATE ,USE YR GRAPH 6E/IMATE !
NUMB] ( FI% SPECIES 9 A LAKE ) AN >EA (
#CJ1JJJ SQU>E MET]S4
C4 .,E/IMATE ,USE YR GRAPH 6E/IMATE !
>EA (A LAKE T 3TA9S #F SPECIES (FI%4
D4 .,R1SON+ .,DESCRIBE :AT HAPP5S 6!
NUMB] ( FI% SPECIES Z ! >EA (A POOL OR
LAKE 9CR1SES4 .,EXPLA9 :Y YR ANSW] MAKES
S5SE4
#FC4 .,,*ALL5GE ,! FUNC;N .;S .K
#J.AEI @+ #J.AAH7LOG .;D @7 GIVES !
SLOPE .;S (A B1* 9 T]MS (! AV]AGE
DIAMET] .;D 7IN MILLIMET]S7 ( S& "PICLES
ON ! B1*4 ,F9D ! 9V]SE ( ? FUNC;N4 ,!N
USE ! 9V]SE 6E/IMATE ! AV]AGE DIAMET] (!
S& "PICLES ON A B1* )A SLOPE ( #J.B4
,,MIX$ ,,REVIEW
.,,PREVIEW ,PREP>E = ,LESSON #G.E 9
,EXS4 #FD-GA4
,EVALUATE ! EXPRES.N4 7.P4 P4 #CCJ7
.#FD4 #B #C @* #B #E
.#FE4 7#E --#C @7 #B
.#FF4 #H #A @* #H #C @* #H --#E
.#FG4
.#FH4
.#FI4 7#F --#B @7 --#A
.#GJ4
.#GA4
,SIMPLIFY ! EXPRES.N4 ,ASSUME ALL
V>IA#S >E POSITIVE4 @7 P4 #DBJ @7
.#GB4 .;X #A/B @* .;X #B/C
.#GC4 7;M #I @7 --#A/F
.#GD4
.#GE4 7;N #D/C @* ;N #B/E @7 #A/F
.#GF4
.#GG4
.#GH4
.#GI4
.,,EXTRA .,,PRACTICE = ,LESSON #G.D1
P4 #AJAF
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#EJF
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,LESSONS #G.A-G.D
#A4 .,,MULTI-.,,/EP .,,PRO#M ,! GRAPH
%[N 2L IS A TRANSL,N (! GRAPH ( ;Y .K
LOG #C .X4
A4 ,WRITE AN EQU,N (! GRAPH4
B4 ,GRAPH ! 9V]SE (! FUNC;N ^: GRAPH
IS %[N ABV4
#B4 .,,MULTI-.,,/EP .,,PRO#M ,:5 A
PIECE ( PAP] IS FOLD$ 9 HALF1 ! PAP] IS
DIVID$ 96TWO REGIONS1 EA* ( : HAS HALF !
>EA (! PAP]4 ,IF ? PROCESS IS REP1T$1 !
NUMB] ( REGIONS 9CR1SES :ILE ! >EA ( EA*
REGION DECR1SES4 ,! TA# 2L %[S ! NUMB] (
REGIONS &! FRAC;NAL >EA ( EA* REGION AF
EA* SU3ESSIVE FOLD4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,FOLD .NUMB] @3 #J3 #A3 #B3 #C3 #D
.,NUMB] .( .REGIONS @3 #A3 #B3 @8@3
@8@3 @8
..,FRAC;NAL >EA ( EA* .REGION @3 #A3
@3 @8@3 @8@3 @8
A4 ,COPY & -PLETE ! TA#4
B4 ,WRITE FUNC;NS GIV+ ! NUMB] (
REGIONS .;,R7.;N7 &! FRAC;NAL >EA ( EA*
REGION .,A7.;N7 AF .;N FOLDS4 ,TELL :E!R
EA* FUNC;N REPRES5TS ..EXPON5TIAL GR[?1
EXPON5TIAL .DECAY @1 OR .NEI4
#C4 .,,OP5-.,,5D$ ,! VALUE ( "O ITEM
.9CR1SES 0;R@3P P] YE> :ILE ! VALUE (
ANO!R ITEM .DECR1SES 0;R@3P P] YE>4 ,AF
#B YE>S1 BO? ITEMS >E WOR? 4#AJJ4 ,*OOSE
A VALUE = .;R & WRITE A FUNC;N GIV+ EA*
ITEM'S VALUE ;Y AF .;T YE>S4 ,GRAPH BO?
FUNC;NS 9 ! SAME COORD9ATE PLANE4
#D4 .,,%ORT .,,RESPONSE ,Y DEPOSIT
4#BJJJ 9 AN A3.T T PAYS #D@3P ANNUAL
9T]E/ -P.D$ 3T9U\SLY4 ,:AT IS YR BAL.E
AF #B YE>S8 ,AF H[ _M FULL YE>S W YR
BAL.E F/ EXCE$ 4#BBEJ8 .,EXPLA9 H[ Y F.D
YR ANSW]S4
#E4 .,,EXT5D$ .,,RESPONSE ,A LOCAL
BANK (F]S C]TIFICATE ( DEPOSIT 7;,,CD7
A3.TS T Y C USE 6SAVE M"OY & E>N 9T]E/4
,Y >E 3SID]+ TWO DI6]5T ,,CD,'S3 A
?REE-YE> ;,,CD T REQUIRES A M9IMUM BAL.E
( 4#AEJJ & PAYS #B@3P ANNUAL 9T]E/1 &A
FIVE-YE> ;,,CD T REQUIRES A M9IMUM BAL.E
( 4#BJJJ & PAYS #C@3P ANNUAL 9T]E/4 ,!
9T]E/ = BO? A3.TS IS -P.D$ MON?LY4
A4 ,IF Y DEPOSIT ! M9IMUM REQUIR$ AM.T
9 EA* ;,,CD1 H[ M* M"OY IS 9 EA* A3.T AT
! 5D ( XS T]M8 ,H[ M* 9T]E/ DOES EA*
A3.T E>N8
B4 ,:AT IS ! DI6];E 9 ! AM.TS ( 9T]E/8
C4 .,DESCRIBE ! B5EFITS & DRAWBACKS (
EA* A3.T4
#F4 .,,GRI4$ .,,ANSW] ,TRITIUM IS A
RADIOACTIVE SUB/.E US$ 6ILLUM9ATE EXIT
SIGNS4 ,! AM.T ( TRITIUM 4APPE>S OV] "T1
A PROCESS CALL$ RADIOACTIVE DECAY4 ,IF Y
/>T )A #AJ MILLIGRAM SAMPLE ( TRITIUM1 !
NUMB] ;Y ( MILLIGRAMS LEFT AF .;T YE>S
IS GIV5 0;Y .K #AJ;E -#JJEFD;T @4 ,H[ _M
MILLIGRAMS ( TRITIUM >E LEFT AF #AJ
YE>S8 ,R.D YR ANSW] 6! NE>E/ HUNDR$?4
#G4 .,,MULTI-.,,/EP .,,PRO#M ,! AM.T
.;Y ( OIL COLLECT$ 0A PETROLEUM -PANY
DRILL+ ON ! ,U4,S4 3T95TAL %ELF C 2
MODEL$ 0;Y .K #AB.BFC ,9 .;X -- #DE.CHA
": ;Y IS M1SUR$ 9 BILLIONS ( B>RELS &
.;X IS ! NUMB] ( WELLS DRILL$4
A4 ,GRAPH ! MODEL4
B4 ,AB H[ _M B>RELS ( OIL WD Y EXPECT
6COLLECT AF DRILL+ #AJJJ WELLS8
C4 ,AB H[ _M WELLS NE$ 6BE DRILL$
6COLLECT #EJ BILLION B>RELS ( OIL8
------------------------------------#EJG
#G.E ,APPLY ,PROP]TIES ( ,LOG>I?MS
.,2F ,Y EVALUAT$ LOG>I?MS4
.,N[ ,Y W REWRITE LOG>I?MIC EXPRES.NS4
.,:Y8 ,S Y C MODEL ! L\D;S ( S.DS1 Z 9
,EX4 #FC4
,KEY ,VOCABUL>Y
99 BASE1 P4 #AJ
,SIDEB>3
,/&>DS
#AD.J ,/UD5TS "U/& & USE ! PROP]TIES (
LOG>I?MS 6SIMPLIFY LOG>I?MIC NUM]IC
EXPRES.NS & 6ID5TIFY _! APPROXIMATE
VALUES4
#AC.J ,/UD5TS USE ! DEF9I;N ( LOG>I?MS
6TRANSLATE 2T LOG>I?MS 9 ANY BASE4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,PROP]TIES ( ,LOG>I?MS
,LET .;B1 .;M @1 & .;N 2 POSITIVE
NUMB]S S* T .;B @6.K #A4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,PRODUCT .,PROP]TY @3 LOG ;B .MN .K
LOG .;B .;M @+ LOG .;B .;N
.,QUOTI5T .,PROP]TY @3
.,P[] .,PROP]TY @3 LOG ;B .;M .;N .K
.;N LOG .;B .;M
,EXAMPLE #A ,USE PROP]TIES ( LOG>I?MS
,,AVOID ,,]RORS
,NOTE T 9 G5]AL & LOG ;B .MN @6.K 7LOG
;B .;M @77LOG ;B .;N @7@4
,USE LOG #D #C #J.GIB & LOG #D #G
#A.DJD 6EVALUATE ! LOG>I?M4
.A4
B4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
LOG #D #BA @3 .K LOG #D 7#C @* #G7 @3
..,WRITE #BA Z #C @* .#G4
--@3 .K LOG #D #C @+ LOG #D #G @3
.,PRODUCT .PROP]TY
--@3 #J.GIB @+ #A.DJD3 ,USE ! GIV5
VALUES ( LOG.' #D #C & LOG.' #D #G4
--@3 .K #B.AIF3 .,SIMPLIFY4
C4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
LOG #D #DI @3 .K LOG #D #G #B @3
,WRITE #DI Z #G #B @4
--@3 .K #B LOG #D #G @3 .,P[] .PROP]TY
--@3 #B7#A.DJD73 ,USE ! GIV5 VALUE (
LOG.' #D #G4
--@3 .K #B.HJH3 .,SIMPLIFY4
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#A
,USE LOG #F #E #J.HIH & LOG #F #H
#A.AFA 6EVALUATE ! LOG>I?M4
.#A4 LOG #F
.#B4 LOG #F #DJ
.#C4 LOG #F #FD
.#D4 LOG #F #ABE
------------------------------------#EJH
.,,REWRIT+ .,,EXPRES.NS ,Y C USE !
PROP]TIES ( LOG>I?MS 6EXP& & 3D5SE
LOG>I?MIC EXPRES.NS4
,,REWRITE ,,EXPRES.NS
,:5 Y >E EXP&+ OR 3D5S+ AN EXPRES.N
9VOLV+ LOG>I?MS1 Y MAY ASSUME ANY V>IA#S
>E POSITIVE4
..,,EXAMPLE #B ,EXP& A LOG>I?MIC
.EXPRES.N
,EXP& @4
,,EXAMPLE #C ,/&>DIZ$ ,TE/ ,PRACTICE
,: (! FOLL[+ IS EQUIVAL5T 6LOG #I @+
#C LOG #B--LOG #C8
.,A LOG #H
.;,B LOG #AD
.;,C LOG #AH
.;,D LOG #BD
,SOLU;N
,! CORRECT ANSW] IS ,D4 ..,A ;,B ;,C
.;,D
.,,GUID$ .,,PRACTICE = ,EXAMPLES #B &
#C
#E4 ,EXP& LOG #C .;X #D @4
#F4 ,3D5SE ,9 #D @+ #C ,9 #C--,9 #AB4
.,,*ANGE-.,,(-.,,BASE .,,=MULA
,LOG>I?MS ) ANY BASE O!R ?AN #AJ OR .;E
C 2 WRITT5 9 T]MS ( -MON OR NATURAL
LOG>I?MS US+ ! .*ANGE-.(-.BASE .=MULA4
,? ALL[S Y 6EVALUATE ANY LOG>I?M US+ A
CALCULATOR4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,*ANGE-(-,BASE ,=MULA
,IF .A1 .;B @1 & .;C >E POSITIVE
NUMB]S ) .;B .;I.K- #A & .;C @6.K #A1
!N3
,9 ,"PICUL>1 & @4
------------------------------------#EJI
,,EXAMPLE #D ,USE ! *ANGE-(-BASE =MULA
,EVALUATE LOG #C #H US+ -MON LOG>I?MS
& NATURAL LOG>I?MS4
,SOLU;N
.,US+ .-MON .LOG>I?MS3
.,US+ .NATURAL .LOG>I?MS3
,,EXAMPLE #E
,USE PROP]TIES ( LOG>I?MS 9 R1L LIFE
.,,S.D .,,9T5S;Y ,=A S.D ) 9T5S;Y .,I
7IN WATTS P] SQU>E MET]71 ! L\D;S .;,L
@7 .,I @7 (! S.D 7IN DECIBELS7 IS GIV5
0! FUNC;N
": .,I #J IS ! 9T5S;Y (A B>ELY AUDI#
S.D 7AB #AJ --#AB WATTS P] SQU>E MET]74
,AN >TI/ 9 A RECORD+ /UDIO TURNS UP !
VOLUME (A TRACK S T ! S.D'S 9T5S;Y D\#S4
,0H[ _M DECIBELS DOES ! L\D;S 9CR1SE8
,SOLU;N
,LET .,I 2 ! ORIG9AL 9T5S;Y1 S T #B
.,I IS ! D\#D 9T5S;Y4
,! L\D;S 9CR1SES 0AB #C DECIBELS4
..,,GUID$ ,,PRACTICE = ,EXAMPLES #D &
.#E
,USE ! *ANGE-(-BASE =MULA 6EVALUATE !
LOG>I?M4
#G4 LOG #E #H
#H4 LOG #H #AD
#I4 LOG #BF #I
#AJ4 LOG #AB #CJ
#AA4 .,,:AT .,,IF8 ,9 ,EXAMPLE #E1
SUPPOSE ! >TI/ TURNS UP ! VOLUME S T !
S.D'S 9T5S;Y TRIPLES4 ,0H[ _M DECIBELS
DOES ! L\D;S 9CR1SE8
------------------------------------#EAJ
#G.E ,EX]CISES
,HOME"W ,KEY
.K ..,,"W$-,,\ ,,SOLU;NS .ON P4
,,WS#AC ..= ,EXS4 #AA1AG1 & .#GA
.K ..,,/&>DIZ$ ,,TE/ ,,PRACTICE ,EXS4
#B1DC1DD1FD1GA1 & .#GC
,,SKILL ,,PRACTICE
#A4 .,,VOCABUL>Y ,COPY & -PLETE3
,63D5SE ! EXPRES.N LOG #C #B .;X @+ LOG
#C .;Y @1 Y NE$ 6USE ! @8 PROP]TY (
LOG>I?MS4
#B4 .,,WRIT+ .,DESCRIBE TWO WAYS
6EVALUATE LOG #G #AB US+ A CALCULATOR4
,,EXAMPLE #A
ON P4 #EJG = ,EXS4 #C-AD
,,MAT*+ ,,EXPRES.NS ,MAT* ! EXPRES.N
)! LOG>I?M T HAS ! SAME VALUE4
#C4 ,9 #F--,9 #B
#D4 #B ,9 #F
#E4 #F ,9 #B
#F4 ,9 #F @+ ,9 #B
,A4 ,9 #FD
,B4 ,9 #C
,C4 ,9 #AB
,D4 ,9 #CF
,,APPROXIMAT+ ,,EXPRES.NS ,USE LOG #D
#J.FJB & LOG #AB #A.JGI 6EVALUATE !
LOG>I?M4
.#G4 LOG #C
.#H4 LOG #DH
.#I4 LOG #AF
.#AJ4 LOG #FD
.#AA4 LOG #ADD
.#AB4
.#AC4
.#AD4
,,EXAMPLE #B
ON P4 #EJH = ,EXS4 #AE-CB
,,EXP&+ ,,EXPRES.NS ,EXP& ! EXPRES.N4
.#AE4 LOG #C #D .;X
.#AF4 ,9 #AE .;X
.;L#G4 LOG #C .;X #D
.#AH4 LOG #E .;X #E
.#AI4
.#BJ4
.#BA4
.#BB4 ,9 #D .;X #B .;Y
.#BC4 LOG #G #E .;X #C .YZ #B
.#BD4 LOG #F #CF .;X #B
.#BE4 LN .;X #B .;Y #A/C
.#BF4 LOG #AJ .;X #C
.#BG4
.#BH4
.#BI4
.#CJ4
.,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 EXP&+ ! LOG>I?MIC
EXPRES.N4
.#CA4
.#CB4 ,9 #H .;X #C .K #C ,9 #H @+ ,9
.;X
,,EXAMPLE#C
ON P4 #EJH = ,EXS4 #CC-DC
,,3D5S+ ,,EXPRES.NS ,3D5SE ! EXPRES.N4
#CC4 LOG #D #G--LOG #D #AJ
#CD4 ,9 #AB--,9 #D
#CE4 #B LOG .;X @+ LOG ;LL
#CF4 #F ,9 .;X @+ #D ,9 .;Y
#CG4 #E LOG .;X -- #D LOG .;Y
#CH4 #E LOG #D #B @+ #G LOG #D .;X @+
#D LOG #D .;Y
#CI4 ,9 #DJ @+ #B ,9 @+ ,9 .;X
#DJ4
#DA4 #F ,9 #B--#D ,9 .;Y
#DB4 #B7LOG #C #BJ--LOG #C #D7 @+ #J.E
LOG #C #D
#DC4 .,,MULTIPLE .,,*OICE ,: (! FOLL[+
IS EQUIVAL5T 6#C LOG #D #F8
,A LOG #D #AH
;,B LOG #D #GB
;,C LOG #D #BAF
;,D LOG #D #BEF
-----------------------------------#EAA
#DD4 .,,MULTIPLE .,,*OICE ,: (! FOLL[+
/ATE;TS IS .N CORRECT8
,A LOG #C #DH .K LOG #C #AF @+ LOG #C
#C
;,B LOG #C #DH .K #C LOG #C #B @+ LOG
#C #F
;,C LOG #C #DH .K #B LOG #C #D @+ LOG
#C #C
;,D LOG #C #DH .K LOG #C #H @+ #B LOG
#C #C
,,EXAMPLE #D
ON P4 #EJI = ,EXS4 #DE-FA
.,,*ANGE-.,,(-.,,BASE .,,=MULA ,USE !
*ANGE-(-BASE =MULA 6EVALUATE ! LOG>I?M4
#DE4 LOG #D #G
#DF4 LOG #E #AC
#DG4 LOG #C #AE
#DH4 LOG #H #BB
#DI4 LOG #C #F
#EJ4 LOG #E #AD
#EA4 LOG #F #AG
#EB4 LOG #B #BH
#EC4 LOG @8 #AI
#ED4 ,IOG #D #DH
#EE4 LOG #I #BG
#EF4 LOG #H #CB
#EG4
#EH4
#EI4
#FJ4
#FA4 .,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 US+ ! *ANGE-(-BASE
=MULA4
,,EXAMPLE #E
ON P4 #EJI = ,EXS4 #FB-FC
.,,S.D .,,9T5S;Y ,9 ,EX]CISES #FB &
#FC1 USE ! FUNC;N 9 ,EXAMPLE #E4
.#FB4 ,F9D ! DECIBEL LEVEL (! S.D MADE
0EA* OBJECT %[N 2L4
A4
,PICTURE3 ..,B>K+ DOG3 ,I .K .#AJ --#D
.;W_/.;M #B
B4
,PICTURE3 ..,AMBUL.E SIR53 ,I .K .#AJ
;DG .;W_/.;M #B
C4
,PICTURE3 ..,BEE3 ,I .K .#AJ -- #F.E
.;W_/.;M #B
#FC4 ,! 9T5S;Y (! S.D (A TRUMPET IS
#AJ #C WATTS P] SQU>E MET]4 ,F9D !
DECIBEL LEVEL (A TRUMPET4
#FD4 .,,OP5-.,,5D$ .,,MA? ,= EA*
/ATE;T1 F9D POSITIVE NUMB]S .;,M1 .;,N
@1 & .;B 7) .;B @6.K #A7 T %[ ! /ATE;T
IS FALSE 9 G5]AL4
A4 LOG ;B @7 .;,M @+ .;,N @7 .K LOG ;B
.;,M @+ LOG ;B .;,N
B4 LOG ;B @7 .;,M -- .;,N @7 .K LOG ;B
.;,M -- LOG ;B .;,N
.,,*ALL5GE ,9 ,EX]CISES #FE-FH1 USE !
GIV5 H9T & PROP]TIES ( EXPON5TS 6PROVE !
PROP]TY ( LOG>I?MS4
.#FE4 .,PRODUCT .PROP]TY LOG ;B .MN .K
LOG ;B .;M @+ LOG ;B .;N
@7 .,H9T3 ,LET .;X .K LOG ;B .;M & LET
.;Y .K LOG ;B .;N @4 ,!N .;N .K .;B ;X &
.;N .K .;B ;Y @4@7
.#FF4 .,QUOTI5T .PROP]TY
7.,H9T3 ,LET .;X .K LOG ;B .;M & LET
.;Y .K LOG .N4 ,!N .;M .K .;B ;X & .;N
.K .;B ;Y @4@7
#FG4 .,P[] .PROP]TY LOG ;B .;M ;N .K
.;N LOG ;B .;M
7.,H9T3 ,LET .;X .K LOG .;M @4 ,!N .;M
.K .;B ;X & .;M ;N .K .;B NX @4@7
#FH4 .,*ANGE-.(-.BASE .=MULA
@7 .,H9T3 ,LET .;X .K LOG ;B .A1 .;Y
.K LOG ;B .;C @1 & .;Z .K LOG ;C .A @4
,!N .A .K .;B ;X @1 .;C .K .;B ;Y @1 &
.A .K .;C ;Z @1 S T .;B ;X .K .;C ;Z
@4@7
------------------------------------#EAB
,,PRO#M ,,SOLV+
,,EXAMPLE #E
ON P4 #EJI = ,EXS4 #FI-GB
.#FI4 .,,3V]S,N ,?REE GR\PS ( P >E
HAV+ SEP>ATE 3V]S,NS 9 A ROOM4 ,! S.D (
EA* 3V]S,N HAS AN 9T5S;Y ( #A.D * #AJ
--#E WATTS P] SQU>E MET]4 ,:AT IS !
DECIBEL LEVEL (! -B9$ 3V]S,NS 9 ! ROOM8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#GJ4 .,,P>K+ .,,G>AGE ,! S.D MADE
0EA* ( FIVE C>S 9 A P>K+ G>AGE HAS AN
9T5S;Y ( #C.B * #AJ --#D WATTS P] SQU>E
MET]4 ,:AT IS ! DECIBEL LEVEL (! S.D
MADE 0ALL FIVE C>S 9 ! P>K+ G>AGE8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#GA4 .,,%ORT .,,RESPONSE ,! 9T5S;Y (!
S.D ,,TV ADS MAKE IS T5 "TS Z GRT Z !
9T5S;Y = AN AV]AGE ,,TV %[4 ,H[ _M
DECIBELS L\D] IS A ,,TV .AD8 .,JU/IFY YR
ANSW] US+ PROP]TIES ( LOG>I?MS4
,9T5S;Y ( ,TELEVI.N ,S.D
,PICTURE3 ,DUR+ %[3 ,9T5S;Y .K .,I
,PICTURE3 ,DUR+ AD3 ,9T5S;Y .K #AJ .,I
#GB4 .,,BIOLOGY ,! L\DE/ ANIMAL ON
,E>? IS ! BLUE :ALE4 ,X C PRODUCE A S.D
) AN 9T5S;Y ( #AJ #FH WATTS P] SQU>E
MET]4 ,! L\DE/ S.D A HUMAN C MAKE HAS AN
9T5S;Y ( #AJ #JH WATTS P] SQU>E MET]4
.,-P>E ! DECIBEL LEVELS (! S.DS MADE 0A
BLUE :ALE &A HUMAN4
#GC4 .,,EXT5D$ .,,RESPONSE ,! ;F-/OPS
ON A #CE MILLIMET] CAM]A 3TROL ! AM.T (
LI<T T 5T]S ! CAM]A4 ,LET .;S 2 A M1SURE
(! AM.T ( LI<T T /RIKES ! FILM & LET .;F
2 ! ;F-/OP4 ,!N .;S & .;F >E RELAT$ 0!
EQU,N3
.;S .K LOG #B .;F #B
A4 .,USE .,PROP]TIES ,EXP& ! EXPRES.N
= .;S @4
B4 .,CALCULATE ,! TA# %[S ! F/ EI<T
;F-/OPS ON A #CE MILLIMET] CAM]A4 ,COPY
& -PLETE ! TA#4 .,DESCRIBE ! PATT]N Y
OBS]VE4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;F @3 #A.DAD3 #B.JJJ3 #B.HBH3 #D.JJJ3
#E.FEG3 #H.JJJ3 #AA.CAD3 #AF.JJJ
.;S @3 @8@3 @8@3 @8@3 @8@3 @8@3 @8@3
@8@3 @8
C4 .,R1SON+ ,_M #CE MILLIMET] CAM]AS H
N9E ;F-/OPS4 ,:AT D Y ?9K ! N9? ;F-/OP
IS8 .,EXPLA9 YR R1SON+4
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
.,,WS#A
.K ..,,/&>DIZE ,,TE/ .,,PRACTICE
------------------------------------#EAC
#GD4 .,,*ALL5GE ,"U C]TA9 3DI;NS1 !
W9D SPE$ .;S 7IN KNOTS7 AT AN ALTITUDE (
.;H MET]S ABV A GRASSY PLA9 C 2 MODEL$
0? FUNC;N3
.;S @7 .;H @7 .K #B ,9 7#AJJ .;H @7
A4 ,0:AT FACTOR DOES ! W9D SPE$ 9CR1SE
:5 ! ALTITUDE D\#S8
B4 ,%[ T ! GIV5 FUNC;N C 2 WRITT5 9
T]MS ( -MON LOG>I?MS Z @4
,,MIX$ ,,REVIEW
,P]=M ! 9DICAT$ OP],N4 @7 P4 #AHG @7
#GE4
#GF4
#GG4
.,,PREVIEW ,PREP>E = ,LESSON #G.F 9
,EXS4 #GH-HC4
#GH4
#GI4
#HJ4
#HA4
#HB4
#HC4
#HD4 .;E #H @7 P4 #DIB @7
#HE4 .;E --#F @7 P4 #DIB @7
#HF4 .;E #C.E @7 P4 #DIB @7
#HG4 .;E --#J.D @7 P4 #DIB @7
#HH4 LOG#AB @7 P4 #DII @7
#HI4 LOG#A.H @7 P4 #DII @7
#IJ4 LN#BD @7 P4 #DII @7
#IA4 LN#H.DI @7 P4 #DII @7
,,QUIZ = ,LESSONS #G.D-G.E
,EVALUATE ! LOG>I?M )\T US+ A
CALCULATOR1 FP4 .#DII7
.#A4 LOG #D #AF
.#B4 LOG #E ;L
.#C4 LOG #H #H
.#D4 LOG #A/B #CB
,GRAPH ! FUNC;N4 ,/ATE ! DOMA9 &
RANGE1 @7 P4 #DII @7
.#E4 .;Y .K LOG #B .;X
.#F4 .;Y .K ,9 .;X @+ #B
.#G4 .;Y .K LOG #C @7 .;X @+ #D7--#A
,EXP& ! EXPRES.N1 @7 P4 #EJG @7
.#H4 LOG #B #E .;X
.#I4 LOG #E .;X #G
.#AJ4 ,9 #E .XY #C
.#AA4
,3D5SE ! EXPRES.N1 7P4 .#EJG7
.#AB4 LOG #C #E--LOG #C #BJ
.#AC4 ,9 #F @+ ,9 #D .;X
.#AD4 LOG #F #E @+ #C LOG #F #B
.#AE4 #D ,9 .;X -- #E ,9 .;X
,USE ! *ANGE-(-BASE =MULA 6EVALUATE !
LOG>I?M1 @7 P4 #EJG @7
.#AF4 LOG #C #AJ
.#AG4 LOG #G #AD
.#AH4 LOG #E #BD
.#AI4 LOG #H #DJ
.#BJ4 .,,S.D .,,9T5S;Y ,! S.D ( AN
AL>M CLOCK HAS AN 9T5S;Y ( .,I .K #AJ
--#D WATTS P] SQU>E MET]4 ,USE ! MODEL
@1 ": .,I #J .K #AJ --#AB WATTS P] SQU>E
MET]1 6F9D ! AL>M CLOCK'S L\D;S .;,L @7
.,I @7@4 @7 P4 #EJG @7
.,,EXTRA .,,PRACTICE = ,LESSON #G.E1
P4 #AJAF
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#EAD
,GRAPH+ ,CALCULATOR ,ACTIV;Y3 #G.E
,GRAPH ,LOG>I?MIC ,FUNC;NS
,USE AF LESS5 #G.E
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,KEY/ROKES
,SIDEB>3
,/&>DS
..#AD.J ,/UD5TS "U/& & USE ! PROP]TIES
( .LOG>I?MS 6SIMPLIFY LOG>I?MIC NUM]IC
EXPRES.NS & ..6ID5TIFY _! APPROXIMATE
.VALUES4
,,"Q
,H[ C Y GRAPH LOG>I?MIC FUNC;NS ON A
GRAPH+ CALCULATOR8
,Y C USE A GRAPH+ CALCULATOR 6GRAPH
LOG>I?MIC FUNC;NS SIMPLY 0US+ ! OR KEY4
,6GRAPH A LOG>I?MIC FUNC;N HAV+ A BASE
O!R ?AN #AJ OR .;E ;Y.' .-Y NE$ 6USE !
*ANGE-(-BASE =MULA 6REWRITE ! FUNC;N 9
T]MS ( -MON OR NATURAL LOG>I?MS4
,,EXAMPLE ,GRAPH LOG>I?MIC FUNC;NS
,USE A GRAPH+ CALCULATOR 6GRAPH .;Y .K
LOG #B .;X & .;Y .K LOG #B @7 .;X -- #C7
@+ #A4
..,,/EP #A ,REWRITE .FUNC;NS ,USE !
*ANGE-(-BASE =MULA 6REWRITE EA* FUNC;N 9
T]MS ( -MON LOG>I?MS4
,,/EP #B ,5T] FUNC;NS
,5T] EA* FUNC;N 96A GRAPH+ CALCULATOR4
,,/EP #C ,GRAPH FUNC;NS
,GRAPH ! FUNC;NS4
,,PRACTICE
,USE A GRAPH+ CALCULATOR 6GRAPH !
FUNC;N4
.#A4 .;Y .K LOG #D .;X
.#B4 .;Y .K LOG #H .;X
.#C4 .;F @7 .;X @7 .K LOG #C .;X
.#D4 .;Y .K LOG #E .;X
.#E4 .;Y .K LOG #AB .;X
.#F4 .;G @7 .;X @7 .K LOG #I .;X
.#G4 .;Y .K LOG #C @7 .;X @+ #B7
.#H4 .;Y .K LOG #E .;X -- #A
.#I4 .;F @7 .;X @7 .K LOG #D @7 .;X --
#E7--#B
.#AJ4 .;Y .K LOG #B @7 .;X @+ #D7--#G
.#AA4 .;Y .K LOG #G @7 .;X -- #E7 @+
#C
.#AB4 .;G @7 .;X @7 .K LOG #C @7 .;X
@+ #F7--#F
.#AC4 .,,R1SON+ ,GRAPH .;Y -- ,9 .;X
@4 ,IF YR CALCULATOR DID N H A NATURAL
LOG>I?M KEY1 EXPLA9 H[ Y CD GRAPH .;Y .K
,9 .;X US+ ! ,,LOG KEY4
------------------------------------#EAE
#G.F ,SOLVE ,EXPON5TIAL & ,LOG>I?MIC
,EQU,NS
.,2F ,Y /UDI$ EXPON5TIAL & LOG>I?MIC
FUNC;NS4
.,N[ ,Y W SOLVE EXPON5TIAL & LOG>I?MIC
EQU,NS4
.,:Y8 ,S Y C SOLVE PRO#MS AB A/RONOMY1
Z 9 ,EXAMPLE #G4
,KEY ,VOCABUL>Y
99 EXPON5TIAL EQU,N
99 LOG>I?MIC EQU,N
99 EXTRANE\S SOLU;N1 P4 #EB
,SIDEB>3
,/&>DS
#AA.A ,/UD5TS "U/& ! 9V]SE REL,N%IP 2T
EXPON5TS & LOG>I?MS & USE ? REL,N%IP
6SOLVE PRO#MS 9VOLV+ LOG>I?MS &
EXPON5TS4
.,EXPON5TIAL .EQU,NS >E EQU,NS 9 :
V>IA# EXPRES.NS O3UR Z EXPON5TS4 ,!
RESULT 2L IS USE;L = SOLV+ C]TA9
EXPON5TIAL EQU,NS4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,PROP]TY ( ,EQUAL;Y = ,EXPON5TIAL
,EQU,NS
.,ALGEBRA ,IF .;B IS A POSITIVE NUMB]
O!R ?AN #A1 !N .;B ;X .K .;B ;Y IF &
ONLY IF .;X .K .;Y @4
.,EXAMPLE ,IF #C ;X .K #C #E @1 !N .;X
.K #E4 ,IF .;X .K #E1 !N .#C ;X .K #C #E
@4
,EXAMPLE #A
,SOLVE 0EQUAT+ EXPON5TS
.,SOLVE @4
,! SOLU;N IS #A4
.,,*ECK ,*ECK ! SOLU;N 0SUB/ITUT+ X
96! ORIG9AL EQU,N4
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#A
,SOLVE ! EQU,N4
.#A4 #I #B .;X .K #BG .;X -- #A
.#B4 #AJJ #G .;X @+ #A .K #AJJJ #C .;X
-- #B
.#C4
------------------------------------#EAF
,:5 X IS N 3V5I5T 6WRITE EA* SIDE ( AN
EXPON5TIAL EQU,N US+ ! SAME BASE1 Y C
SOLVE ! EQU,N 0TAK+ A LOG>I?M ( EA*
SIDE4
,,EXAMPLE #B
,TAKE A LOG>I?M ( EA* SIDE
,,ANO!R ,,WAY
,= AN ALT]NATIVE ME?OD = SOLV+ ! PRO#M
9 ,EXAMPLE #B1 TURN 6PAGE #EBC =!
.,PRO#M .,SOLV+ .,"W%OP @4
,SOLVE #D ;X .K #AA4
,! SOLU;N IS AB #A.GC4 ,*ECK ? 9 !
ORIG9AL EQU,N4
..,,NEWTON'S ,,LAW ,,( .,,COOL+ ,AN
IMPORTANT APPLIC,N ( EXPON5TIAL EQU,NS
IS ..,NEWTON'S LAW ( .COOL+4 ,? LAW
/ATES T =A COOL+ SUB/.E ) 9ITIAL
TEMP]ATURE .;,T #J @1 ! TEMP]ATURE .;,T
AF .;T M9UTES C 2 MODEL$ BY
.;,T .K @7 .;,T #J -- .;,T ;,R @7 .;E
-- .RT @+ .;,T ;,R
": .;,T ;,R IS ! SURR.D+ TEMP]ATURE &
.;R IS ! SUB/.E'S COOL+ RATE4
,,EXAMPLE #C ,USE AN EXPON5TIAL MODEL
.,,C>S ,Y >E DRIV+ ON A HOT "D :5 YR
C> OV]H1TS & /OPS RUNN+4 ,X OV]H1TS AT
#BHJ;DG;,F & C 2 DRIV5 AG AT #BCJ;DG,F4
,IF .;R .K #J.JJDH & X IS #HJ;DG;,F
\TSIDE1 H[ L;G 7IN M9UTES7 D Y H 6WAIT
UNTIL Y C 3T9UE DRIV+8
,SOLU;N
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,T .K @7 .;,T #J -- .;,T .;,R @7 .;E
-- .RT @+ .;,T .;,R @3 ..,NEWTON'S LAW (
.COOL+
#BCJ .K 7#BHJ--#HJ7 .;E --#J.JJDH .;F
@+ #HJ @3 ,SUB/ITUTE =.' ;,T1 ;,T #J @1
.;,T .;,R @1 &.' ;R @4
#AEJ .K #BJJ .;E --#J.JJDH .;T @3
..,SUBTRACT #HJ F EA* .SIDE4
#J.GE .K .;E --#J.JJDH .;T @3
..,DIVIDE EA* SIDE 0.#BJJ4
,9 #J.GE .K LN .;E #J.JJDH .;T @3
..,TAKE NATURAL LOG ( EA* .SIDE4
--#J.BHGG --#J.JJDH .;T @3 ,9.' ;E .;X
.K LOG.' .;E .;E .;X .K .;X
#FJ .;T @3 ..,DIVIDE EA* SIDE BY
--#J..JJDH4
,Y H 6WAIT AB #FJ M9UTES UNTIL Y C
3T9UE DRIV+4
.,,GUID$ .,,PRACTICE = ,EXAMPLES #B &
#C
,SOLVE ! EQU,N4
.#D4 #B ;X .K #E
.#E4 #G #I .;X .K #AE
.#F4 #D .;E --#J.C .;X -- #G .K #AC
------------------------------------#EAG
..,,SOLV+ ,,LOG>I?MIC ,,EQU,NS
,LOG>I?MIC .EQU,NS >E EQU,NS T 9VOLVE
LOG>I?MS ( V>IA# EXPRES.NS4 ,Y C USE !
FOLL[+ PROP]TY 6SOLVE "S TYPES (
LOG>I?MIC EQU,NS4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,PROP]TY ( ,EQUAL;Y = ,LOG>I?MIC
,EQU,NS
.,ALGEBRA ,IF .;B1 .;X @1 & .;Y >E
POSITIVE NUMB]S ) .;B @6.K #A1 !N LOG ;B
.;X .K LOG ;B .;Y IF & ONLY IF .;X .K
.;Y @4
.,EXAMPLE ,IF LOG #B .;X .K LOG #B #G1
!N .;X .K #G4 ,IF .;X .K #G1 !N LOG #B
.;X .K LOG #B #G4
,,EXAMPLE #D ,SOLVE A LOG>I?MIC EQU,N
,SOLVE LOG #E #D .;X -- #G7 .K LOG #E
@7 .;X @+ #E74
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
LOG #E 7#D .;X -- #G7 .K LOG #E @7 .;X
@+ #E7 @3 .,WRITE .ORIG9AL .EQU,N4
#D .;X -- #G .K .;X @+ #E @3
..,PROP]TY ( EQUAL;Y = LOG>I?MIC .EQU,NS
#C .;X -- #G .K #E @3 ,SUBTRACT.' ;X
.-F EA* SIDE4
#C .;X .K #AB @3 ..,ADD #G 6EA* .SIDE4
.;X .K #D @3 ..,DIVIDE EA* SIDE 0.#C4
,! SOLU;N IS #D4
.,,*ECK ,*ECK ! SOLU;N 0SUB/ITUT+ X
96! ORIG9AL EQU,N4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
LOG #E 7#D .;X -- #G7 .K LOG #E @7 .;X
@+ #E7 @3 .,WRITE .ORIG9AL .EQU,N4
LOG #E 7#D @* .#D -- #G7 LOG #E @7 .#D
@+ #E7 @3 ,SUB/ITUTE #D =.' ;X @4
LOG #E #I .K LOG #E #I @3 .,SOLU;N
.*ECKS4
,,EXAMPLE #E ,,EXPON5TIAT+ ,,6,,SOLVE
,,EQU,NS
,! PROP]TY ( EQUAL;Y = EXPON5TIAL
EQU,NS ON PAGE #EAE IMPLIES T IF Y >E
GIV5 AN EQU,N .;X .K .;Y
!N Y C .EXPON5TIATE EA* SIDE 6OBTA9 AN
EQU,N (! =M .;B ;X .K .;B ;Y @4 ,?
TE*NIQUE IS USE;L = SOLV+ "S LOG>I?MIC
EQU,NS4
,,EXAMPLE #E ,EXPON5TIATE EA* SIDE (
AN EQU,N
,SOLVE LOG #D 7#E .;X -- #A7 .K #C4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
LOG #D 7#E .;X -- #A7 .K #C @3 .,WRITE
.ORIG9AL .EQU,N4
#D LOG #D 7#E .;X -- #A7 .K #D #C @3
..,EXPON5TIATE EA* SIDE US+ BASE .#D4
#E .;X -- #A .K #FD @3 .;B LOG .;B .;X
.K .;X
#E .;X .K #FE @3 ..,ADD #A 6EA* .SIDE4
.;X .K #AC @3 ..,DIVIDE EA* SIDE 0.#E4
,! SOLU;N IS .#AC4
.,,*ECK LOG #D 7#E .;X -- #A7 .K LOG
#D 7#E @* #AC--#A7 .K LOG #D #FD
,2C #D #C .K #FD1 LOG #D #FD .K #C4
------------------------------------#EAH
.,,EXTRANE\S .,,SOLU;NS ,2C ! DOMA9 (A
LOG>I?MIC FUNC;N G5],Y DOES N 9CLUDE ALL
R1L NUMB]S1 2 SURE 6*ECK = EXTRANE\S
SOLU;NS ( LOG>I?MIC EQU,NS4 ,Y C D ?
ALGEBRAIC,Y OR GRAPHIC,Y4
,,EXAMPLE #F ,/&>DIZ$ ,TE/ ,PRACTICE
,,ELIM9ATE ,,*OICES
,9/1D ( SOLV+ ! EQU,N 9 ,EXAMPLE #F
DIRECTLY1 Y C SUB/ITUTE EA* POSSI# ANSW]
96! EQU,N 6SEE :E!R X IS A SOLU;N4
,:AT IS 7>E7 ! SOLU;N7;S7 ( LOG #B .;X
@+ LOG @7 .;X -- #E7 .K #B8
.,A --#E1 #AJ
.;,B #E
.;,C #AJ
.;,D #E1AJ
,SOLU;N
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
LOG #B .;X @+ LOG @7 .;X -- #E7 .K #B
@3 .,WRITE .ORIG9AL .EQU,N4
LOG ,7#B .;X @7 .;X -- #E77' .K #B @3
..,PRODUCT PROP]TY ( .LOG>I?MS
#AJ LOG ,7#B .;X @7 .;X -- #E77' .K
#AJ #B @3 ..,EXPON5TIATE EA* SIDE US+
BASE .#AJ4
#B .;X @7 .;X -- #E7 .K #AJJ @3 .;B
LOG .;B .;X .K .;X
#B .;X #B .K ;L#J .;X .K #AJJ @3
.,4TRIBUTIVE .PROP]TY
#B .;X #B -- #AJ .;X -- #AJJ .K #J @3
..,WRITE 9 /&>D .=M4
.;X #B -- #E .;X -- #EJ .K #J @3
..,DIVIDE EA* SIDE 0.#B4
@7 .;X -- #AJ7@7 .;X @+ #E7 .K #J @3
.,FACTOR4
.;X .K #AJ OR .;X .K --#E @3 .,Z]O
.PRODUCT .PROP]TY
.,,*ECK ,*ECK ! APP>5T SOLU;NS #AJ &
--#E US+ ALGEBRA OR A GRAPH4
.,ALGEBRA ,SUB/ITUTE #AJ & --#E = .;X
9 ! ORIG9AL EQU,N4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
LOG #B .;X @+ LOG @7 .;X -- #E7 .K #B
@3 LOG #B .;X @+ LOG @7 .;X -- #E7 .K #B
LOG 7#B @* #AJ7 @+ LOG 7#AJ --#E7 #B
@3 LOG,7#B7--#E77' @+ LOG7--#E --#E7 #B
LOG #BJ @+ LOG #E #B @3 LOG 7--#AJ7 @+
LOG 7--#AJ7 .K #B
LOG #AJJ .K .#B #B #B @3 ,2C LOG
7--#AJ7 IS N DEF9$1 --#E IS .N A SOLU;N4
#B .K #B @3 --
,S1 #AJ IS A SOLU;N4
.,GRAPH ,GRAPH .;Y .K LOG #B .;X @+
LOG @7 .;X -- #E7 &Y .K #B 9 ! SAME
COORD9ATE PLANE4 ,! GRAPHS 9T]SECT ONLY
ONCE1 :5 .;X .K #AJ4 ,S1 #AJ IS ! ONLY
SOLU;N4
,! CORRECT ANSW] IS ,C4 ..,A ;,B ;,C
.;,D
..,,GUID$ ,,PRACTICE = ,EXAMPLES #D1E1
& .#F
,SOLVE ! EQU,N4 ,*ECK = EXTRANE\S
SOLU;NS4
.#G4 ,9 7#G .;X -- #D7 .K ,9 7#B .;X
@+ #AA7
.#H4 LOG #B @7 .;X -- #F7 .K #E
.#I4 LOG #E .;X @+ LOG @7 .;X -- #A7
.K #B
.#AJ4 LOG #D @7 .;X @+ #AB7 @+ LOG #D
.;X .K #C
------------------------------------#EAI
,,EXAMPLE #G ,USE A LOG>I?MIC MODEL
.,,A/RONOMY ,! .APP>5T .MAGNITUDE (A
/> IS A M1SURE (! B"R;S (! /> Z X APPE>S
6OBS]V]S ON ,E>?4 ,! APP>5T MAGNITUDE
.;,M (! DIMME/ /> T C 2 SE5 )A TELESCOPE
IS GIV5 0! FUNC;N
.;,M .K #E LOG .;,D @+ #B
": .;,D IS ! DIAMET] 7IN MILLIMET]S7
(! TELESCOPE'S OBJECTIVE L5S4 ,IF A
TELESCOPE C REV1L />S )A MAGNITUDE (
#AB1 :AT IS ! DIAMET] ( XS OBJECTIVE
L5S8
,,ANO!R ,,WAY
,= AN ALT]NATIVE ME?OD = SOLV+ ! PRO#M
9 ,EXAMPLE #G1 TURN 6PAGE #EBC =! ,PRO#M
,SOLV+ ,"W%OP4
,SOLU;N
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,M .K #E LOG .;,D @+ #B @3 .,WRITE
.ORIG9AL .EQU,N4
.#AB .K #E LOG .;,D @+ #B @3
..,SUB/ITUTE #AB = .,M4
#AJ .K #E LOG .;,D @3 ..,SUBTRACT #B F
EA* .SIDE4
#B .K LOG .;,D @3 ..,DIVIDE EA* SIDE
0.#E4
#AJ #B .K #AJ LOG .;,D @3
..,EXPON5TIATE EA* SIDE US+ BASE .#AJ4
#AJJ .K .;,D @3 .,SIMPLIFY4
,! DIAMET] IS #AJJ MILLIMET]S4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,,GUID$ ,,PRACTICE = ,EXAMPLE .#G
.#AA4 .,,:AT .,,IF8 ,USE ! 9=M,N F
,EXAMPLE #G 6F9D ! DIAMET] (! OBJECTIVE
L5S (A TELESCOPE T C REV1L />S )A
MAGNITUDE ( #G4
#G.F ,EX]CISES
,HOME"W ,KEY
.K ..,,"W$-,,\ ,,SOLU;NS .ON P4
,,WS#AD ..= ,EXS4 #AE1CE1 & .#EG
.K ..,,/&>DIZ$ ,,TE/ ,,PRACTICE ,EXS4
#B1DD1DG1EH1 & .#FJ
.K ..,,MULTIPLE ,,REPRES5T,NS ,EX#..EI
,,SKILL ,,PRACTICE
#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,!
EQU,N #E ;X .K #H IS AN EXAMPLE (A7;N7
@8 EQU,N4
#B4 .,,WRIT+ ,:5 D LOG>I?MIC EQU,NS H
EXTRANE\S SOLU;NS8
.,,EXAMPLE .#A ON .P4 #EAE = ,EXS4
#C-AA
,,SOLV+ ,,EXPON5TIAL ,,EQU,NS ,SOLVE !
EQU,N4
.#C4 #E .;X -- #D .K #BE .;X -- #F
.#D4 #G #C .;X @+ #D .K #DI #B .;X @+
#A
.#E4 #H .;X -- #A .K #CB #C .;X -- #B
.#F4 #BG #D .;X --#A .K #I #C .;X @+
#H
.#G4 #D #B .;X -- #E .K #FD #C .;X
.#H4 #C #C .;X -- #G .K #HA #AB--#C
.;X
.#I4
.#AJ4
.#AA4
------------------------------------#EBJ
,,EXAMPLE #B
ON P4 #EAF = ,EXS4 #AB-BC
,,SOLV+ ,,EXPON5TIAL ,,EQU,NS ,SOLVE !
EQU,N4
.#AB4 #H ;X .K #BJ
.#AC4 .;E -- .;X .K #E
.#AD4 #G #C .;X .K #AH
.;L#E4 #AA #E .;X .K #CC
.#AF4 #G #F .;X .K #AB
.#AG4 #D .;E --#B .;X .K #AG
.#AH4 #AJ #C .;X @+ #D .K #I
.#AI4 --#C .;E #B .;X @+ #AF .K #E
.#BJ4 #J.E--#J.BE .K #D
.#BA4
.#BB4 #B #J.A .;X -- #E .K #G
.#BC4
,,EXAMPLE #D
ON P4 #EAG = ,EXS4 #BD-CA
,,SOLV+ ,,LOG>I?MIC ,,EQU,NS ,SOLVE !
EQU,N4 ,*ECK = EXTRANE\S SOLU;NS4
.#BD4 LOG #E 7#E .;X @+ #I7 .K LOG #E
#F .;X
.#BE4 ,9 7#D .;X -- #G7 .K ,9 @7 .;X
@+ #AA7
.#BF4 ,9 @7 .;X @+ #AI7 .K ,9 7#G .;X
-- #H7
.#BG4 LOG #E 7#B .;X -- #G7 .K LOG #E
7#C .;X -- #I7
.#BH4 LOG 7#AB .;X -- #AA7 .K LOG 7#C
.;X @+ #AC7
.#BI4 LOG #C 7#AH .;X @+ #G7 .K LOG #C
7#C .;X @+ #CH7
.#CJ4 LOG #F 7#C .;X -- #AJ7 .K LOG #F
7#AD--#E .;X @7
.#CA4 LOG #H 7#E--#AB .;X @7 .K LOG #H
7#F .;X -- #A7
,,EXPON5TIAT+ ,,6,,SOLVE ,,EQU,NS
,SOLVE ! EQU,N4 ,*ECK = EXTRANE\S
SOLU;NS4
.#CB4 LOG #D .;X .K --#A
.#CC4 #E ,9 .;X .K #CE
.#CD4
.#CE4 #E.B LOG #D #B .;X .K #AF
.#CF4 LOG #B @7 .;X -- #D7 .K #F
.#CG4 LOG #B .;X @+ LOG #B @7 .;X --
#B7 .K #C
.#CH4 LOG #D @7-- .;X @7 @+ LOG #D @7
.;X @+ #AJ7 .K #B
.#CI4 ,9 @7 .;X @+ #C7 @+ ,9 .;X .K #A
.#DJ4 #D ,9 @7-- .;X @7 @+ #C .K #BA
.#DA4 LOG #E @7 .;X @+ #D7 @+ LOG #E
@7 .;X @+ #A7 .K #B
.#DB4 LOG #F #C .;X @+ LOG #F @7 .;X
-- #A7 .K #C
.#DC4 LOG #C @7 .;X -- #I7 @+ LOG #C
@7 .;X -- #C7 .K #B
#DD4 .,,MULTIPLE .,,*OICE ,:AT IS !
SOLU;N ( #C LOG #H 7#B .;X @+ #G7 @+ #H
.K #AJ8
,A --#A.E
;,B --#A.AGI
;,C #D
;,D #D.FDB
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 SOLV+ ! EQU,N4
#DE4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#C .;X @+#A @3 .K #F .;X
LOG #C #C .;X @+ #A @3 .K LOG #C #F
.;X
.;X @+ #A @3 .K .;X LOG #E #F
.;X @+ #A @3 .K #B .;X
#A3 .K .;X
.#DF4
.#DG4 .,,OP5-.,,5D$ .,,MA? ,GIVE AN
EXAMPLE ( AN EXPON5TIAL EQU,N ^: ONLY
SOLU;N IS #D & AN EXAMPLE (A LOG>I?MIC
EQU,N ^: ONLY SOLU;N IS --#C4
,,*ALL5GE ,SOLVE ! EQU,N4
.#DH4 #C .;X @+ #D .K #F #B .;X -- #E
.#DI4 #AJ #C .;X -- #H .K #B #E -- .;X
.#EJ4 LOG #B @7 .;X @+ #A7 .K LOG #H
#C .;X
.#EA4 LOG #C .;X .K LOG #I #F .;X
.#EB4 #B #B .;X -- #AB @* #B ;X @+ #CB
.K #J
.#EC4 #E #B .;X @+ #BJ @* #E ;X --
#ABE .K #J
.K ..,,"W$-,,\ ,,SOLU;NS .ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
------------------------------------#EBA
,,PRO#M ,,SOLV+
,,EXAMPLE #C
ON .P4 #EAF = ,EXS4 #ED-EH
#ED4 .,,COOK+ ,Y >E COOK+ BEEF /EW4
,:5 Y TAKE ! BEEF /EW (F ! /OVE1 X HAS A
TEMP]ATURE ( #BJJ;DG,F4 ,! ROOM
TEMP]ATURE IS #GE;DG;,F &! COOL+ RATE (!
BEEF /EW IS .;R .K #J.JED4 ,H[ L;G 7IN
M9UTES7 W X TAKE 6COOL ! BEEF /EW 6A
S]V+ TEMP]ATURE ( #AJJ;DG;,F8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#EE4 .,,!RMOMET] ,Z Y >E HANG+ AN
\TDOOR !RMOMET]1 XS R1D+ DROPS F ! 9DOOR
TEMP]ATURE ( #GE;DG;,F 6#CG;DG;,F 9 "O
M9UTE4 ,IF ! COOL+ RATE IS .;R .K #A.CG1
:AT IS ! \TDOOR TEMP]ATURE8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#EF4 .,,-P.D .,,9T]E/ ,Y DEPOSIT 4#AJJ
9 AN A3.T T PAYS #F@3P ANNUAL 9T]E/4 ,H[
L;G W X TAKE =! BAL.E 6R1* 4#AJJJ = EA*
GIV5 FREQU5CY ( -P.D+8
A4 ,ANNUAL
B4 ,QU>T]LY
C4 ,DAILY
#EG4 .,,RADIOACTIVE .,,DECAY ,"O
HUNDR$ GRAMS ( RADIUM >E /OR$ 9 A 3TA9]4
,! AM.T .;,R 7IN GRAMS7 ( RADIUM PRES5T
AF .;T YE>S C 2 MODEL$ 0.;,R .K #AJJ .;E
#J.JJJDC .;R @4 ,AF H[ _M YE>S W ONLY #E
GRAMS ( RADIUM 2 PRES5T8
#EH4 .,,MULTIPLE .,,*OICE ,Y DEPOSIT
4#HJJ 9 AN A3.T T PAYS #B.BE@3P ANNUAL
9T]E/ -P.D$ 3T9U\SLY4 ,AB H[ L;G W X
TAKE =! BAL.E 6TRIPLE8
,A #BD YE>S
;,B #CF YE>S
;,C #DH.H YE>S
;,D #EB.F YE>S
.,,EXAMPLE .#G ON P4 #EAI = ,EX4 #EI
#EI4 .,,MULTIPLE .,,REPRES5T,NS ,!
,RI*T] SCALE IS US$ = M1SUR+ ! MAGNITUDE
( AN E>?QUAKE4 ,! ,RI*T] MAGNITUDE .;,R
IS GIV5 0! FUNC;N
.;,R .K #J.FG LOG 7#J.CG .;,E @7 @+
#A.DF
": .;,E IS ! 5]GY 7IN KILOWATT-H\RS7
REL1S$ 0! E>?QUAKE4
A4 .,MAK+ .A .,GRAPH ,GRAPH ! FUNC;N
US+ A GRAPH+ CALCULATOR4 ,USE YR GRAPH
6APPROXIMATE ! AM.T ( 5]GY REL1S$ 0EA*
E>?QUAKE 9DICAT$ 9 ! DIAGRAM ABV4
B4 .,SOLV+ .,EQU,NS ,WRITE & SOLVE A
LOG>I?MIC EQU,N 6F9D ! AM.T ( 5]GY
REL1S$ 0EA* E>?QUAKE 9 ! DIAGRAM4
-----------------------------------#EBB
#FJ4 .,,EXT5D$ .,,RESPONSE ,IF
;,X-RAYS (A FIX$ WAVEL5G? /RIKE A
MAT]IAL .;X C5TIMET]S ?ICK1 !N ! 9T5S;Y
.,I @7 .;X @7 (! ;,X-RAYS TRANSMITT$ "?
! MAT]IAL IS GIV5 0.,I @7 .;X @7 .K .,I
#J .;E -- .;X ": .,I ;O IS ! 9ITIAL
9T5S;Y & IS A NUMB] T DEP5DS ON ! TYPE (
MAT]IAL &! WAVEL5G? (! ;,X-RAYS4 ,! TA#
%[S ! VALUES (= V>I\S MAT]IALS4 ,^!
-VALUES APPLY 6;,X-RAYS ( M$IUM
WAVEL5G?4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,MAT]IAL @3 .,ALUM9UM @3 .,COPP] @3
.,L1D
.,VALUE .( @3 .#J..DC @3 .#C..B @3
.#DC
A4 ,F9D ! ?ICK;S ( ALUM9UM %IELD+ T
REDUCES ! 9T5S;Y ( ;,X-RAYS 6#CJ@3P ( _!
9ITIAL 9T5S;Y4 @7 .,H9T3 ,F9D ! VALUE (
.;X = : .,I @7 .;X @7 .K #J.C .,I #J
@4@7
B4 ,REP1T "P 7A7 = COPP] %IELD+4
C4 ,REP1T "P 7A7 = L1D %IELD+4
D4 .,R1SON+ ,YR D5TI/ PUTS A L1D APRON
ON Y 2F TAK+ .;X --RAYS ( YR TEE?
6PROTECT Y F H>M;L RADI,N4 ,BAS$ ON YR
RESULTS F "PS 7A7-7;C71 EXPLA9 :Y L1D IS
A BETT] MAT]IAL 6USE ?AN ALUM9UM OR
COPP]4
#FA4 .,,*ALL5GE ,Y PLANT A SUNFL[]
SE$L+ 9 YR G>D54 ,! SE$L+'S HEI<T .;H
7IN C5TIMET]S7 AF .;T WEEKS C 2 MODEL$
0! FUNC;N 2L1 : IS CALL$ A .LOGI/IC
.FUNC;N4
,F9D ! "T X TAKES ! SUNFL[] SE$L+ 6R1*
A HEI<T ( #BJJ C5TIMET]S4
,,MIX$ ,,REVIEW
.,,PREVIEW ,PREP>E = ,LESSON #G.G 9
,EXS4 #FB-FD4
,SOLVE ! SY/EM US+ ANY ALGEBRAIC
ME?OD4 @7 P4 #AFJ @7
#FB4 #C .;X - .;Y .K #G
.;X @+ .#B;Y .K #AD
#FC4 #E .;X -- .;Y .K #G
#B .;X @+ #E .;Y .K --#C
#FD4 .;X @+ .#D;Y .K --#F
-#B .;X @+ .;Y .K #AB
,DET]M9E ! POSSI# NUMB]S ( POSITIVE
R1L Z]OS1 NEGATIVE R1L Z]OS1 & IMAG9>Y
Z]OS =! FUNC;N4 @7 P4 #CGI @7
#FE4 .;F7.;X7 .K ;X #C -- .#B;X #B @+
#E
#FF4 .;F7.;X7 .K .;X #D @+ #F;X #C --
.;X #B @+ .#G;X -- #H
#FG4 .;F 7;X7 .K ;X #E -- #C;X #C @+
#G;X #B @+ #F;X @+ #I
#FH4 .;F7.;X7 .K ;X #G @+ #AJ;X #F --
#E;X #D @+ #AB;X #C -- #AG
,USE F9ITE DI6];ES &A SY/EM ( EQU,NS
6F9D A POLYNOMIAL FUNC;N T FITS ! DATA4
,Y MAY WANT 6USE A GRAPH+ CALCULATOR
6SOLVE ! SY/EM4 @7 P4 #CIC @7
#FI4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #A3 #B3 #C3 #D3 #E3 #F
.;F7.;X7 @3 #AI3 #BH3 #BG3 #AF3 -#E3
-#CF
#GJ4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #A3 #B3 #C3 #D3 #E3 #F
.;F7.;X7 @3 #J3 #B3 #AB3 #CF3 #HJ3
#AEJ
.,,EXTRA .,,PRACTICE = ,LESSON #G.F1
P4 #AJAF
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#EBC
,PRO#M ,SOLV+ ,"W%OP ,LESSON #G.F3
,US+ ,ALT]NATIVE ,ME?ODS
,ANO!R ,WAY 6,SOLVE ,EXAMPLES #B & #G1
PP4 #EAF & #EAI
.,,MULTIPLE .,,REPRES5T,NS ,9
,EXAMPLES #B & #G ON PAGES #EAF & #EAI
@1 RESPECTIVELY1 Y SOLV$ EXPON5TIAL &
LOG>I?MIC EQU,NS ALGEBRAIC,Y4 ,Y C AL
SOLVE S* EQU,NS US+ TA#S & GRAPHS4
.,,PRO#M .#A ,SOLVE ! FOLL[+
EXPON5TIAL EQU,N3 #D ;X .K #AA4
..,,ME?OD #A ,US+ A .,TA# ,"O WAY
6SOLVE ! EQU,N IS 6MAKE A TA# ( VALUES4
,SIDEB>3
,/&>DS
#AA.A ,/UD5TS "U/& ! 9V]SE REL,N%IP 2T
EXPON5TS & LOG>I?MS & USE ? REL,N%IP
6SOLVE PRO#MS 9VOLV+ LOG>I?MS &
EXPON5TS4
.,,/EP .#A .,5T] ! FUNC;N .;Y .K #D ;X
96A GRAPH+ CALCULATOR4
.,,/EP .#B .,CR1TE A TA# ( VALUES =!
FUNC;N4
.,,/EP .#C .,SCROLL "? ! TA# 6F9D :5
.;Y .K #AA4 ,! TA# 9 ,/EP #B %[S T .;Y
.K #AA 2T .;X .K #A.G & .;X .K #A.H4
,! SOLU;N ( #D ;X .K #AA IS 2T #A.G &
#A.H4
..,,ME?OD #B ,US+ A .,GRAPH ,Y C AL
USE A GRAPH 6SOLVE ! EQU,N4
.,,/EP .#A .,5T] ! FUNC;NS .;Y .K #D
;X & .;Y .K #AA 96A GRAPH+ CALCULATOR4
.,,/EP .#B .,GRAPH ! FUNC;NS4 ,USE !
.9T]SECT F1TURE 6F9D ! 9T]SEC;N PO9T (!
GRAPHS4 ,! GRAPHS 9T]SECT AT AB 7#A.GC1
#AA74
,PICTURE3 ,USE A VIEW+ W9D[ ( #J "K.K
.;X "K.K #E & #J "K.K .;Y "K.K#BJ4
,! SOLU;N ( #D ;X .K #AA IS AB #A.GC4
------------------------------------#EBD
,,PRO#M #B
.,,A/RONOMY ,! .APP>5T .MAGNITUDE (A
/> IS A M1SURE (! B"R;S (! /> Z X APPE>S
6OBS]V]S ON ,E>?4 ,! APP>5T MAGNITUDE
.;,M (! DIMME/ /> T C 2 SE5 )A TELESCOPE
IS GIV5 0! FUNC;N
.;,M .K #E LOG .;,D @+ #B
": .;,D IS ! DIAMET] 7IN MILLIMET]S7
(! TELESCOPE'S OBJECTIVE L5S4 ,IF A
TELESCOPE C REV1L />S )A MAGNITUDE (
#AB1 :AT IS ! DIAMET] ( XS OBJECTIVE
L5S8
..,,ME?OD #A ,US+ A .,TA# ,NOTICE T !
PRO#M REQUIRES SOLV+ ! FOLL[+ LOG>I?MIC
EQU,N3
#E LOG .;,D @+ #B .K #AB
,"O WAY 6SOLVE ? EQU,N IS 6MAKE A TA#
( VALUES4 ,Y C USE A GRAPH+ CALCULATOR
6MAKE ! TA#4
.,,/EP .#A .,5T] ! FUNC;N .;Y .K #E
LOG .;X @+ #B 96A GRAPH+ CALCULATOR4
.,,/EP .#B .,CR1TE A TA# ( VALUES =!
FUNC;N4 ,MAKE SURE T ! .;X --VALUES >E 9
! DOMA9 (! FUNC;N @7 .;X .1 #J74
.,,/EP .#C .,SCROLL "? ! TA# ( VALUES
6F9D :5 .;Y .K #AB4
,PICTURE3 ,! TA# %[S T .;Y .K #AB :5
.;X .K #AJJ4
,6REV1L />S )A MAGNITUDE ( #AB1 A
TELESCOPE M/ H AN OBJECTIVE L5S )A
DIAMET] ( #AJJ MILLIMET]S4
------------------------------------#EBE
..,,ME?OD #B ,US+ A .,GRAPH ,Y C AL
USE A GRAPH 6SOLVE ! EQU,N #E LOG .;,D
@+ #B .K #AB4
.,,/EP .#A .,5T] ! FUNC;NS .;Y .K #E
LOG .;X @+ #B & .;Y .K #AB 96A GRAPH+
CALCULATOR4
.,,/EP .#B .,GRAPH ! FUNC;NS4 ,USE !
.9T]SECT F1TURE 6F9D ! 9T]SEC;N PO9T (!
GRAPHS4 ,! GRAPHS 9T]SECT AT 7#AJJ1
#AB74
,PICTURE3 ,USE A VIEW+ W9D[ ( #J "K.K
.;X "K.K #AEJ & #J "K.K .;Y "K.K #BJ4
,6REV1L />S )A MAGNITUDE ( #AB1 A
TELESCOPE M/ H AN OBJECTIVE L5S )A
DIAMET] ( #AJJ MILLIMET]S4
,,PRACTICE
,,EXPON5TIAL ,,EQU,NS ,SOLVE ! EQU,N
US+ A TA# & US+ A GRAPH4
.#A4 #H--#B .;E #C .;X .K --#AD
.#B4 #G--#AJ #E -- .;X .K --#I
.#C4 .;E #E .;X -- #H @+ #C .K #AE
.#D4 #A.F7#C7 --#D .;X @+ #E.F .K #F
,,LOG>I?MIC ,,EQU,NS ,SOLVE ! EQU,N
US+ A TA# & US+ A GRAPH4
#E4 LOG #B #E .;X .K #B
#F4 LOG 7--#C .;X @+ #G7 .K #A
#G4 #D ,9 .;X @+ #F .K #AB
#H4 #AA LOG @7 .;X @+ #I7--#E .K #H
#I4 .,,ECONOMICS ,F #AIIH 6#BJJC1 !
,UNIT$ ,/ATES GROSS N,NAL PRODUCT .;Y
7IN BILLIONS ( DOLL>S7 C 2 MODEL$ 0.;Y
.K #HHHB7#A.JD7 ;X ": .;X IS ! NUMB] (
YE>S S9CE #AIIH4 ,USE A TA# &A GRAPH
6F9D ! YE> :5 ! GROSS N,NAL PRODUCT 0
4#AJ TRILLION4
.#AJ4 .,,WRIT+ ,9 ,ME?OD #A ( ,PRO#M
#A ON PAGE #EBC @1 EXPLA9 H[ Y CD USE A
TA# 6F9D ! SOLU;N ( #D ;X .K #AA M
PRECISELY4
.#AA4 .,,:AT .,,IF8 ,9 ,PRO#M #B ON
PAGE #EBD @1 SUPPOSE ! TELESCOPE C REV1L
/>S ( MAGNITUDE #AD4 ,F9D ! DIAMET] (!
TELESCOPE'S OBJECTIVE L5S US+ A TA# &
US+ A GRAPH4
.#AB4 .,,F9.E ,Y DEPOSIT 4#EJJJ 9 AN
A3.T T PAYS #C@3P ANNUAL 9T]E/ -P.D$
QU>T]LY4 ,H[ L;G W X TAKE =! BAL.E 6R1*
4#FJJJ8 ,SOLVE ! PRO#M US+ A TA# & US+ A
GRAPH4
.#AC4 .,,OC1NOGRAPHY ,! D5S;Y .;D 7IN
GRAMS P] CUBIC C5TIMET]7 ( S1WAT] )A
SAL9;Y ( #CJ "PS P] ?\S& IS RELAT$ 6!
WAT] TEMP]ATURE .;,T 7IN DEGREES
,CELSIUS7 0! FOLL[+ EQU,N3
.;D .K #A.JBDE -- .;E #J.ABBFA--#G.HBH
,= DEEP WAT] 9 ! ,S\? ,ATLANTIC ,OC1N
(F ,ANT>CTICA1 .;D .K #A.JBDA ;G_/CM #C
@4 ,USE A TA# &A GRAPH 6F9D ! WAT]'S
TEMP]ATURE4
------------------------------------#EBF
,EXT5.N ,SOLVE ,EXPON5TIAL &
,LOG>I?MIC ,9EQUALITIES
,USE AF ,LESSON #G.F
.,GOAL ,SOLVE EXPON5TIAL & LOG>I?MIC
9EQUALITIES US+ TA#S & GRAPHS4
,9 ! ,PRO#M ,SOLV+ ,"W%OP ON PAGES
#EBC-EBE @1 Y LE>N$ H[ 6SOLVE EXPON5TIAL
& LOG>I?MIC EQU,NS US+ TA#S & GRAPHS4 ,Y
C USE ^! SAME ME?ODS 6SOLVE EXPON5TIAL &
LOG>I?MIC 9EQUALITIES4
,SIDEB>3
,/&>DS
..,5RI*;T ( #AA.A ,/UD5TS "U/& ! 9V]SE
REL,N%IP 2T EXPON5TS & .LOG>I?MS & USE ?
REL,N%IP 6SOLVE PRO#MS 9VOLV+ LOG>I?MS &
EXPON5TS4
,EXAMPLE #A ,SOLVE AN EXPON5TIAL
9EQUAL;Y
.,,C>S ,YR FAMILY PUR*ASES A NEW C> =
4#BJ1JJJ4 ,XS VALUE DECR1SES 0#AE@3P EA*
YE>4 ,DUR+ :AT 9T]VAL ( "T DOES ! C>'S
VALUE EXCE$ 4#AJ1JJJ8
,SOLU;N
,LET ;Y REPRES5T ! VALUE (! C> 7IN
DOLL>S7 .;X YE>S AF X IS PUR*AS$4 ,A
FUNC;N RELAT+ .;X & .;Y IS .;Y .K
#BJ1JJJ7#A-- #J.AE7 ;X @1 ORY .K #BJ1JJJ
7#J.HE7 ;X @4 ,6F9D ! VALUES ( .;X = :
;Y .1 #AJ1JJJ1 SOLVE ! 9EQUAL;Y
#BJ1JJJ7#J.HE7 ;X .1 #AJ1JJJ4
,,ME?OD #A ,USE A TA#
.,,/EP .#A .,5T] ! FUNC;N ;Y .K
#BJ1JJJ7#J.HE7;X 96A GRAPH+ CALCULATOR4
,SET ! />T+ .;X- VALUE (! TA# 6#J &! /EP
VALUE 6#J.A4
.,,/EP .#B .,USE ! .TA# F1TURE 6CR1TE
A TA# ( VALUES4 ,SCROLL+ "? ! TA# %[S T
;Y .1 #AJ1JJJ :5 #J "K .;X "K #D.B4
,! C> VALUE EXCE$S 4#AJ1JJJ = AB ! F/
#D.B YE>S AF X IS PUR*AS$4
,6*ECK ! SOLU;N'S R1SONA#;S1 NOTE T ;Y
#AJ1DDJ :5 .;X .K #D & .;Y #HHGD :5 .;X
.K #E4 ,S1 #D "K .;X "K #E1 : AGREES )!
SOLU;N OBTA9$ ABV4
,,ME?OD #B ,USE A GRAPH
,GRAPH .;Y .K #BJ1JJJ7#J.HE7;X &Y .K
#AJ1JJJ 9 ! SAME VIEW+ W9D[4 ,SET !
VIEW+ W9D[ 6%[ #J "K .;X "K #H & #J "K
.;Y "K #BE1JJJ4 ,US+ ! .9T]SECT F1TURE1
Y C DET]M9E T ! GRAPHS 9T]SECT :5 .;X
#D.BG4
,! C> VALUE EXCE$S 4#AJ1JJJ = AB ! F/
#D.BG YE>S AF X IS PUR*AS$4
------------------------------------#EBG
,EXAMPLE #B ,SOLVE A LOG>?MIC 9EQUAL;Y
,SOLVE LOG #B .;X "K#B4
,SOLU;N
,,ME?OD #A ,USE A TA#
.,,/EP .#A .,5T] ! FUNC;N .;Y .K LOG
#B ;X 96A
.,,/EP#B .,USE ! .TA# F1TURE 6CR1TE A
TA# ( VALUES4 ,ID5TIFY ! .;X -VALUES = :
.;Y "K #B4 ,^! ;X-VALUES >E GIV5 0#J "K
.;X "K #D4
,! SOLU;N IS #J "K .;X "K #D4
,,ME?OD #B ,USE A GRAPH
,GRAPH .;Y .K LOG #B .;X & .;Y .K #B 9
! SAME VIEW+ W9D[4 ,US+ ! .9T]SECT
F1TURE1 Y C DET]M9E T ! GRAPHS 9T]SECT
:5 .;X .K #D4
,PRACTICE
,,EXAMPLE #A
ON P4 #EB 99#F = ,EXS4 #A-F
,SOLVE ! EXPON5TIAL 9EQUAL;Y US+ A TA#
& US+ A GRAPH4
.#A4 #C ;X "K.K#BJ
.#B4
.#C4 #BDD7#J.CE7 ;X .1.K #EJ
.#D4 --#FC7#J.IF7 ;X "K.K-#BG
.#E4 #IE7#A.F7 ;X "K.K #AFBJ
.#F4
,,EXAMPLE #B
ON P4 #EBG = ,EXS4 #G-AB
,SOLVE ! LOG>I?MIC 9EQUAL;Y US+ A TA#
& US+ A GRAPH4
.#G4 LOG #C .;X .1.K#C
.#H4 LOG #E .;X "K#B
.#I4 LOG #F .;X @+ #I"K.K#AA
.#AJ4 #B;LOG #D .;X -#A.1#D
.#AA4 --#D;LOG #B .;X .1-#BJ
.#AB4 #J"K.KLOG @8 .;X "K.K#A
.#AC4 .,,F9.E ,Y DEPOSIT 4#AJJJ 9 AN
A3.T T PAYS #C.E@3P ANNUAL 9T]E/ -P.D$
MON?LY4 ,:5 IS YR BAL.E AT L1/ 4#ABJJ8
..#AD4 ,,RATES ,,( .,,RETURN ,AN
9VE/;T T E>NS A RATE ( RETURN .;R D\#S 9
VALUE 9 .;T YE>S1 ": & .;R IS EXPRESS$ Z
A DECIMAL4 ,:AT RATES ( RETURN W D\# !
VALUE ( AN 9VE/;T 9 LESS ?AN #AJ YE>S8
------------------------------------#EBH
,9VE/IGAT+ ,ALGEBRA ,ACTIV;Y3 #G.G
,MODEL ,DATA ) AN ,EXPON5TIAL ,FUNC;N
,USE 2F LESSON1 #G.G
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,KEY/ROKES
.,,MAT]IALS 99 #AJJ P5NIES 99 CUP 99
GRAPH+ CALCULATOR
,"Q ,H[ C Y MODEL DATA ) AN EXPON5TIAL
FUNC;N8
,SIDEB>3
,/&>DS
.#AB..J .,/UD5TS "K ! LAWS ( FRAC;NAL
EXPON5TS1 .."U/& EXPON5TIAL FUNC;NS 9
PRO#MS 9VOLV+ EXPON5TIAL .GR[? & DECAY4
,EXPLORE ,COLLECT & RECORD DATA
,,/EP #A ,MAKE A TA#
,MAKE A TA# L ! "O %[N 6RECORD YR
RESULTS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,NUMB] ( TOSS1 .;X @3 .#J @3 .#A @3
.#B @3 .#C @3 .#D @3 .#E @3 .#F @3 .#G
,NUMB] ( P5NIES REMA9+1 .;Y @3 @8 @3
@8 @3 @8 @3 @8 @3 @8 @3 @8 @3 @8 @3 @8
,,/EP #B ,P]=M AN EXP]I;T
,RECORD ! 9ITIAL NUMB] ( P5NIES 9 !
TA#1 & PLACE ! P5NIES 9 A CUP4 ,%AKE !
P5NIES1 & !N SPILL !M ONTO A FLAT
SURFACE4
,REMOVE ALL (! P5NIES %[+ 8H1DS40 ,C.T
! NUMB] ( P5NIES REMA9+1 & RECORD ?
NUMB] 9 ! TA#4
,,/EP #C ,3T9UE COLLECT+ DATA
,REP1T ,/EP #B )! REMA9+ P5NIES UNTIL
"! >E NO P5NIES LEFT 6RETURN 6! CUP4
,DRAW ,3CLU.NS ,USE YR OBS]V,NS
6-PLETE ^! EX]CISES
.#A4 ,:AT IS ! 9ITIAL NUMB] ( P5NIES8
,0:AT P]C5T WD Y EXPECT ! NUMB] ( P5NIES
REMA9+ 6DECR1SE AF EA* TOSS8
.#B4 ,USE YR ANSW]S F ,EX]CISE #A
6WRITE AN EXPON5TIAL FUNC;N T %D MODEL !
DATA 9 ! TA#4
.#C4 ,USE A GRAPH+ CALCULATOR 6MAKE A
SCATT] PLOT (! DATA PAIRS 7;X1 ;Y74 ,9 !
SAME VIEW+ W9D[1 GRAPH YR FUNC;N F
,EX]CISE #B4 ,IS ! FUNC;N A GD MODEL =!
DATA8 .,EXPLA94
.#D4 ,USE ! CALCULATOR'S .EXPON5TIAL
.REGRES.N F1TURE 6F9D AN EXPON5TIAL
FUNC;N T MODELS ! DATA4 .,-P>E ? FUNC;N
)! FUNC;N Y WROTE 9 ,EX]CISE #B4
------------------------------------#EBI
#G.G ,WRITE & ,APPLY ,EXPON5TIAL &
,P[] ,FUNC;NS
.,2F ,Y WROTE L9E>1 QUADRATIC1 & O!R
POLYNOMIAL FUNC;NS4
.,N[ ,Y W WRITE EXPON5TIAL & P[]
FUNC;NS4
.,:Y8 ,S Y C MODEL BIOLOGY PRO#MS1 Z 9
,EXAMPLE #E4
,KEY ,VOCABUL>Y
99 .P[] .FUNC;N @1 P4 #DBH
99 .EXPON5TIAL .FUNC;N @1 P4 #DGH
,SIDEB>3
,/&>DS
.#AB..J .,/UD5TS "K ! LAWS ( FRAC;NAL
EXPON5TS1 .."U/& EXPON5TIAL FUNC;NS 9
PRO#MS 9VOLV+ EXPON5TIAL .GR[? & DECAY4
,9 ,*APT] #B1 Y LE>N$ T TWO PO9TS
DET]M9E A L9E4 ,SIMIL>LY1 TWO PO9TS
DET]M9E AN EXPON5TIAL CURVE4
,EXAMPLE #A ,WRITE AN EXPON5TIAL
FUNC;N
,WRITE AN EXPON5TIAL FUNC;N .;Y .K
.;AB ;X ^: GRAPH PASSES "? 7#A1AB7 &
7#C1AJH74
,SOLU;N
.,,/EP .#A .,SUB/ITUTE ! COORD9ATES (!
TWO GIV5 PO9TS 96.;Y .K .;AB ;X @4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#AB .K .;AB #A @3 ,SUB/ITUTE #AB =.'
;Y .-& #A = X4
#AJH .K .;AB #C @3 ,SUB/ITUTE #AJH =.'
;Y .-& #C = X4
.,,/EP .#B .,SOLVE = .A 9 ! F/ EQU,N
6OBTA9 @1 & SUB/ITUTE ? EXPRES.N = .A 9
! SECOND EQU,N4
.,,/EP .#C ,DET]M9E @1 ,S1 .;Y .K #D
99 #C ;X @4
.,,TRANS=M+ .,,EXPON5TIAL .,,DATA ,A
SET ( M ?AN TWO PO9TS 7;X1 .;Y7 FITS AN
EXPON5TIAL PATT]N IF & ONLY IF ! SET (
TRANS=M$ PO9TS 7;X1 ,9 .;Y7 FITS A L9E>
PATT]N4
,PICTURE3 ..,GRAPH ( PO9TS 7;X1 .;Y7
,PICTURE3 ..,! GRAPH IS AN EXPON5TIAL
.CURVE4
,PICTURE3 ..,GRAPH ( PO9TS 7;X1 ,9
.;Y7
,PICTURE3 ..,! GRAPH IS A .L9E4
------------------------------------#ECJ
..,EXAMPLE #B ,F9D AN EXPON5TIAL
.MODEL
.,,SCOOT]S ,A /ORE SELLS MOTOR
SCOOT]S4 ,! TA# %[S ! NUMB] .;Y (
SCOOT]S SOLD DUR+ ! X? YE> T ! /ORE HAS
BE5 OP54
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,YE>,.;X @3 #A3 #B3 #C3 #D3 #E3 #F3
#G
,NUMB] ( SCOOT]S SOLD1 .;Y @3 #AB3
#AF3 #BE3 #CF3 #EJ3 #FG3 #IF
99 ,DRAW A SCATT] PLOT (! DATA PAIRS
7JC1 ,9 .;Y7 @4 ,IS AN EXPON5TIAL MODEL
A GD FIT =! ORIG9AL DATA PAIRS 7;X1 ;Y78
99 ,F9D AN EXPON5TIAL MODEL =! ORIG9AL
DATA4
,SOLU;N
.,,/EP .#A .,USE A CALCULATOR 6CR1TE A
TA# ( DATA PAIRS 7JT1 ,9 .;Y @7@4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #A3 #B3 #C3 #D3 #E3 #F3 #G
,9.' ;Y @3 #B.DH3 #B.GG3 #C.BB3 #C.EH3
#C.IA3 #D.BJ3 #D.EF
.,,/EP .#B .,PLOT ! NEW PO9TS Z %[N4
,! PO9TS LIE CLOSE 6A L9E1 S AN
EXPON5TIAL MODEL %D 2 A GD FIT =!
ORIG9AL DATA4
.,,/EP .#C .,F9D AN EXPON5TIAL MODEL
.;Y .K .;AB ;X.' .-0*OOS+ TWO PO9TS ON !
L9E1 S* Z 7#A1 #B.DH7 & 7#G1 #D.EF74
,USE ^! PO9TS 6WRITE AN EQU,N (! L9E4
,!N SOLVE = Y4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,9 .;Y -- #B.DH .K #J.CE7 .;X - #A7 @3
.,EQU,N .( .L9E
,9 .;Y .K #J.CE .;X @+ #B.AC @3
.,SIMPLIFY4
.;Y .K ;E #J.CE;X @+ #B.AC @3
..,EXPON5TIATE EA* SIDE US+ BASE .E4
.;Y .K ;E #B.AC 7;E #J.CE @7 ;X @3
..,USE PROP]TIES ( .EXPON5TS4
.;Y .K #H.DA7#A.DB7 ;X @3 .,EXPON5TIAL
.MODEL
,,USE ,,PO9T-,,SLOPE ,,=M
,2C ! AXES >E .;X & ,9 .;Y @1 !
PO9T-SLOPE =M IS REWRITT5 Z ,9 .;Y --
.;Y @1 .K .;M7.;X-- .;X #A @4 ,! SLOPE
(! L9E "? 7#A1 #B.DH7 & 7#G1 #D.EF7 IS3
.,,EXPON5TIAL .,,REGRES.N ,A GRAPH+
CALCULATOR T P]=MS EXPON5TIAL REGRES.N
USES ALL (! ORIG9AL DATA 6F9D !
BE/-FITT+ MODEL4
,EXAMPLE #C ,USE EXPON5TIAL REGRES.N
.,,SCOOT]S ,USE A GRAPH+ CALCULATOR
6F9D AN EXPON5TIAL MODEL =! DATA 9
,EXAMPLE #B4 ,PREDICT ! NUMB] ( SCOOT]S
SOLD 9 ! EI<? YE>4
,SOLU;N
,5T] ! ORIG9AL DATA 96A GRAPH+
CALCULATOR & P]=M AN EXPON5TIAL
REGRES.N4 ,! MODEL IS ;Y.K
#H.DF7#A.DB7994
,SUB/ITUT+ .;X .K #H 7= YE> #H7 96!
MODEL GIVES .;Y .K #H.DF 7#A.DB7 #H #ADJ
SCOOT]S SOLD4
------------------------------------#ECA
..,GUID$ ,PRACTICE = ,EXAMPLES #A1B1 &
.#C
,WRITE AN EXPON5TIAL FUNC;N .;Y .K
.;AB ;X.' .-^: GRAPH PASSES "? ! GIV5
PO9TS4
.#A4 7#A1F71 7#C1BD7
.#B4 7#B1H71 7#C1CB7
.#C4 7#C1 #H71 7#F1 #FD7
.#D4 .,,:AT .,,IF8 ,9 ,EXAMPLES #B &
#C1 H[ WD ! EXPON5TIAL MODELS *ANGE IF !
SCOOT] SALES 7 Z %[N 9 ! TA# 2L8
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,YE>;,X3 #A3 #B3 #C3 #D3 #E3 #F3 #G
,NUMB] ( SCOOT]S SOLD1 .;Y @3 .#AE @3
.#BC @3 .#DJ @3 .#EB @3 .#HJ @3 .#AJE @3
.#ADJ
.,,WRIT+ .,,P[] .,,FUNC;NS ,RECALL F
,LESSON #F.C T A P[] FUNC;N HAS ! =M .;Y
.K .AX ;B @4 ,2C "! >E ONLY TWO 3/ANTS
@7 .A & .;B @7@1 ONLY TWO PO9TS >E NE$$
6DET]M9E A P[] CURVE "? ! PO9TS4
,EXAMPLE #D ,WRITE A P[] FUNC;N
,WRITE A P[] FUNC;N .;Y .K .AX #C ^:
GRAPH PASSES "? 7#C1B7 & 7#F1I74
,SOLU;N
.,,/EP .#A ,SUB/ITUTE ! COORD9ATES (!
TWO GIV5 PO9TS 96.;Y .K .AX ;B @4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#B .K .A @* #C ;B @3 ,SUB/ITUTE #B =.'
;Y .-& #C =.' X4.-
#I .K .A @* #F ;B @3 ,SUB/ITUTE #I =.'
;Y .-& #F =.' X4.-
.,,/EP .#B ,SOLVE = .A 9 ! F/ EQU,N
6OBTA9 & SUB/ITUTE ? EXPRES.N = .A 9 !
SECOND EQU,N4
..,,/EP #C ,DET]M9E .T @4 ,S1 .;Y .K
#J.AHD .;X #B.AG @4
..,GUID$ ,PRACTICE = ,EXAMPLE .#D
,WRITE A P[] FUNC;N .;Y .K .AX ;H.'
.-^: GRAPH PASSES "? ! GIV5 PO9TS4
.#E4 7#B1 #A71 7#G1 #F7
.#F4 7#C1 #D71 7#F1 #AE7
.#G4 7#E1 #H71 7#AJ1 #CD7
.#H4 .,,R1SON+ ,TRY US+ ! ME?OD (
,EXAMPLE #D 6F9D A P[] FUNC;N ^: GRAPH
PASSES "? 7#C1 #E7 & 7#C1 #G74 ,:AT C Y
3CLUDE8
------------------------------------#ECB
.,,TRANS=M+ .,,P[] .,,DATA ,A SET ( M
?AN TWO PO9TS 7;X1 ;Y7 FITS A P[] PATT]N
IF & ONLY IF ! SET ( TRANS=M$ PO9TS 7,IN
.;X @1 ,9 ;Y7 FITS A L9E> PATT]N4
,PICTURE3 ..,GRAPH ( PO9TS 7;X1 .;Y7
,PICTURE3 ..,! GRAPH IS A P[] .CURVE4
,PICTURE3 ..,GRAPH ( PO9TS 7,IN ;X @1
,9 .;Y7
,PICTURE3 ..,! GRAPH IS A .L9E4
,EXAMPLE #E ,F9D A P[] MODEL
.,,BIOLOGY ,! TA# AT ! "R %[S !
TYPICAL W+SPANS .;X 7IN FEET7 &! TYPICAL
WEI<TS .;Y 7IN P.DS7 = S"EAL TYPES (
BIRDS4
99 ,DRAW A SCATT] PLOT (! DATA PAIRS
7,IN .;X @1 ,9 .;Y @7@4 ,IS A P[] MODEL
A GD FIT =! ORIG9AL DATA PAIRS @7 .;X1
.;Y7 @8
99 ,F9D A P[] MODEL =! ORIG9AL DATA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,BIRD99 @3 .,W+SPAN7.FT7 .;X @3
,WEI<T.' 7LB7.-
,CUCKOO3 #A.IJ3 #J.BC
,CR[3 #B.IB3 #A.JD
,CURLEW3 #C.DA3 #A.FI
,GOOSE3 #E.CE3 #F.GF
,VULTURE3 #H.DJ3 #AF.JC
,SOLU;N
.,,/EP .#A .,USE A CALCULATOR 6CR1TE A
TA# ( DATA PAIRS 7,IN .;X @1 ,9 .;Y @7@4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,9.' ;X @3 #J.FDB3 #A.JGB3 #A.BBG3
#A.FGG3 #B.ABH
,9.' ;Y @3 -#A.DGJ3 #J.JCI3 #J.EBE3
#A.IAA3 #B.GGD
.,,/EP .#B .,PLOT ! NEW PO9TS Z %[N4
,! PO9TS LIE CLOSE 6A L9E1 S A P[] MODEL
%D 2 A GD FIT =! ORIG9AL DATA4
.,,/EP .#C .,F9D A P[] MODEL .;Y .K
.AX ;B.' .-0*OOS+ TWO PO9TS ON ! L9E1
SUE7' Z 7#A.BBG1 #J.EBE7 & 7#B.ABH1
#B.GGD74 ,USE ^! PO9TS 6WRITE AN EQU,N
(! L9E4 ,!N SOLVE = Y4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,9 .;Y -- .;Y #A .K .;M 7LN .;X -- .;X
#A @7 @3 ,EQU,N :5 AXES >E ,9.' ;X .-&
,9.' ;Y.-
,9 .;Y -- #B.GGD .K #B.E7LN .;X --
#B.ABH7 @3 .,SUB/ITUTE4
,9 .;Y .K #B.E LN .;X -- #B.EDF @3
.,SIMPLIFY4
,9 .;Y .K LN .;X #B.E -#B.EDF @3
..,P[] PROP]TY ( .LOG>I?MS
.;Y .K ;E LN .;X #B.E -- #B.EDF @3
..,EXPON5TIATE EA* SIDE US+ BASE .E4
.;Y .K ;E -#B.EDF4 99 .;E LN .;X #B.E
@3 ..,PRODUCT ( P[]S .PROP]TY
.;Y .K #J.JGHD .;X #B.E @3 .,SIMPLIFY4
,,USE ,,PO9T-,,SLOPE ,,=M
,! SLOPE (! L9E IS
------------------------------------#ECC
.,,P[] .,,REGRES.N ,A GRAPH+
CALCULATOR T P]=MS P[] REGRES.N USES ALL
(! ORIG9AL DATA 6F9D ! BE/-FITT+ MODEL4
,EXAMPLE #F ,USE P[] REGRES.N
.,,BIOLOGY ,USE A GRAPH+ CALCULATOR
6F9D A P[] MODEL =! DATA 9 ,EXAMPLE #E4
,E/IMATE ! WEI<T (A BIRD )A W+SPAN (
#D.E FEET4
,SOLU;N
,5T] ! ORIG9AL DATA 96A GRAPH+
CALCULATOR & P]=M A P[] REGRES.N4 ,!
MODEL IS .;Y .K #J.JDDB .;X #B.HG @4
,SUB/ITUT+ .;X .K #D.E 96! MODEL GIVES
.;Y .K #J.JDDB7#D.E7 #B.HG #C.CA P.DS4
..,GUID$ ,PRACTICE = ,EXAMPLES #E &
.#F
.#I4 ,! TA# 2L %[S ! ATOMIC NUMB] .;X
&! MELT+ PO9T .;Y 7IN DEGREES ,CELSIUS7
=! ALKALI METALS4 ,F9D A P[] MODEL =!
DATA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,ALKALI .METAL @3 ,LI?IUM3 ,SODIUM3
,POTASSIUM3 ,RUBIDIUM3 ,CESIUM
,ATOMIC NUMB]1 .;X @3 #C3 #AA3 #AI3
#CG3 #EE
,MELT+ PO9TY1 .;Y @3 #AHJ.E3 #IG.H3
#FC.G3 #CH.I3 #BH.E
#G.G ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#AD = ,EXS4 #AA1BC1 & #CC
.K .,,/&>DIZ$ .,,TE/ .,,PRACTICE
,EXS4 #B1BG1 #CC1 & #CE
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3
,GIV5 A SET ( M ?AN TWO DATA PAIRS 7;X1
;Y71 Y C DECIDE :E!R A7;N7 @8 FUNC;N
FITS ! DATA WELL 0MAK+ A SCATT] PLOT (!
PO9TS @7 .;X @1 LN .;Y @7@4
.#B4 .,,WRIT+ .,EXPLA9 H[ Y C DET]M9E
:E!R A P[] FUNC;N IS A GD MODEL =A SET (
DATA PAIRS @7 .;X1 .;Y @7@4
,,EXAMPLE #A
ON P4 #EBI = ,EXS4 #C-AJ
,,WRIT+ ,,EXPON5TIAL ,,FUNC;NS ,WRITE
AN EXPON5TIAL FUNC;N .;Y .K .;AB ;X ^:
GRAPH PASSES "? ! GIV5 PO9TS4
.#C4 7#A1 #C71 7#B1 #AB7
.#D4 7#B1 #BD71 7#C1 #ADD7
.#E4 7#C1 #A71 7#E1 #D7
.#F4 7#C1 #BG71 7#E1 #BDC7
.#G4 7#A1 #B71 7#C1 #EJ7
.#H4 7#A1 #DJ71 7#C1 #FDJ7
.#I4 7-#A1 #AJ71 7#D1 #J.CA7
.#AJ4 7#B1 #F.D71 7#E1 #DJI.F7
,,EXAMPLE #B
ON P4 #ECJ = ,EXS4 #AA-AD
,,F9D+ ,,EXPON5TIAL ,,MODELS ,USE !
PO9TS @7 .;X1 .;Y @7 6DRAW A SCATT] PLOT
(! PO9TS @7 .;X @1 LN .;Y @7@4 ,!N F9D
AN EXPON5TIAL MODEL =! DATA4
.#AA4 7#A1 #AH71 7#B1 #CF71 7#C1 #GB71
7#D1 #ADD71 7#E1 #BHH7
.#AB4 7#A1 #C.C71 7#B1 #AJ.A71 7#C1
#CJ.F71 7#D1 #IB.G71 7#E1 #BHJ.I7
.#AC4 7#A1 #I.H71 7#B1 #AB.B71 7#C1
#AE.B71 7#D1 #AI71 7#E1 #BC.H7
.#AD4 7#A1 #A.D71 7#B1 #F.G71 7#C1
#CB.I71 7#D4 #AFA.D71 7#E1 #GIJ.I7
------------------------------------#ECD
,,EXAMPLE #D
ON P4 #ECA = ,EXS4 #AE-BB
,,WRIT+ ,,P[] ,,FUNC;NS ,WRITE A P[]
FUNC;N .;Y .K .AX ;B ^: GRAPH PASSES "?
! GIV5 PO9TS4
.#AE4 7#D1 #C71 7#H1 #AE7
.#AF4 7#E1 #I71 7#H1 #CD7
.#AG4 7#B1 #C71 7#F1 #AB7
.#AH4 7#C1 #AD71 7#I1 #DD7
.#AI4 7#D1 #H71 7#H1 #CJ7
.#BJ4 7#E1 #AJ71 7#AB1 #HA7
.#BA4 7#D1 #F.B71 7#G1 #BC7
.#BB4 7#C.A1 #E71 7#F.H1 #I.G7
,,EXAMPLE #E
ON P4 #ECB = ,EXS4 #BC-BF
,,F9D+ ,,P[] ,,MODELS ,USE ! GIV5
PO9TS @7 .;X1 .;Y @7 6DRAW A SCATT] PLOT
(! PO9TS 7,IN .;X @1 ,9 .;Y @7@4 ,!N F9D
A P[] MODEL =! DATA4
.#BC4 7#A1 #J.F71 7#B1 #D.A71 7#C1
#AB.D71 7#D1 #BG71 7#E1 #DI.E7
.#BD4 7#A1 #A.E71 7#B1 #D.H71 7#C1
#I.E71 7#D1 #AE.D71 7#E1 #BB.C7
.#BE4 7#A1 #B.E71 7#B1 #C.G71 7#C1
#D.G71 7#D1 #E.E71 7#E1 #F.B7
.#BF4 7#A1 #J.HA71 7#B1 #J.II71 7#C1
#A.AA71 7#D1 #A.BA71 7#E1 #A.BI7
#BG4 .,,MULTIPLE .,,*OICE ,: EQU,N IS
EQUIVAL5T 6LOGY .K #B .;X @+ #A8
,A .;Y .K #AJ7#AJJ7 ;X
;,B .;Y .K #AJ ;X
;,C .;Y .K .;E #B;X@+#A
;,D .;Y .K .;E #B
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 WRIT+ .;Y Z A FUNC;N ( .X4
.#BH4
.#BI4
.#CJ4 .,,*ALL5GE ,TAKE ! NATURAL
LOG>I?M ( BO? SIDES (! EQU,NS .;Y .K
.;AB ;X & .;Y .K .AX ;B @4 ,:AT >E !
SLOPE & .;Y -9T]CEPT (! L9E RELAT+ .;X &
,9 .;Y = .;Y .K .;AB ;X @8 (! L9E RELAT+
,9 .;X & ,9 .;Y = .;Y .K .AX ;B @8
,PRO#M ,SOLV+
..,,GRAPH+ ,,CALCULATOR ,Y MAY WI%
6USE A GRAPH+ CALCULATOR 6-PLETE !
FOLL[+ ,PRO#M ,SOLV+ .EX]CISES4
,,EXAMPLES #B1 #C1 #E1 & #F
ON PP4 #ECJ-ECC = ,EXS4 #CA-CE
#CA4 .,,BIOLOGY ,SCI5TI/S USE !
CIRCUMF];E ( AN ANIMAL'S FEMUR 6E/IMATE
! ANIMAL'S WEI<T4 ,! TA# %[S ! FEMUR
CIRCUMF];E ;,C 7IN MILLIMET]S7 &! WEI<T
.;,W 7IN KILOGRAMS7 = S"EAL ANIMALS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,ANIMAL @3 ,GIRA6E3 ,POL> BE>3 ,LION3
,SQUIRREL3 ,OTT]
.;,C7.MM7 @3 #AGC3 #ACE3 #IC.E3 #AC3
#BH
.;,W 7KG7 @3 #GAJ3 #DDH3 #ADC3 #J.CII3
#I.FH
A4 ,DRAW A SCATT] PLOT (! DATA PAIRS
7,IN ;,C1 ,9 ;,W74
B4 ,F9D A P[] MODEL =! ORIG9AL DATA4
C4 ,PREDICT ! WEI<T (A *EETAH IF !
CIRCUMF];E ( XS FEMUR IS #FH.G
MILLIMET]S4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#A
.K .,,/&>DIZ$ .,,TE/ .,,PRACTICE
------------------------------------#ECE
.#CB4 .,,A/RONOMY ,! TA# %[S ! M1N
4T.E .;X F ! SUN 7IN A/RONOMICAL UNITS7
&! P]IOD .;Y 7IN YE>S7 ( SIX PLANETS4
,DRAW A SCATT] PLOT (! DATA PAIRS 7,IN
;X1 LN .;Y @7@4 ,F9D A P[] MODEL =!
ORIG9AL DATA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,PLANET @3 ,M]CURY3 ,V5US3 ,E>?3
,M>S3 ,JUPIT]3 ,SATURN
.;,X @3 #J.CHG3 #J.GBC3 #A.JJJ3
#A.EBD3 #E.BJC3 #I.ECI
.;Y @3 #J.BDA3 #J.FAE3 #A.JJJ3 #A.HHA3
#AA.HFB3 #BI.DEH
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#CC .,,%ORT .,,RESPONSE ,! TA# %[S !
NUMB]S ( BUSI;S & NON-BUSI;S US]S (
9/ANT MESSAG+ =! YE>S #AIIH-BJJD4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,YE>S S9CE #AIIG3 #A3 #B3 #C3 #D3 #E3
#F3 #G
..,BUSI;S US]S 7IN .MILLIONS7 @3 .#A
@3 .#B @3 .#E @3 .#G @3 .#BJ @3 .#DJ @3
.#HJ
..,NON-BUSI;S US]S 7IN .MILLIONS7 @3
.#EE @3 .#IG @3 .#ADJ @3 .#AFJ @3 .#AIE
@3 .#BCE @3 .#BFJ
A4 ,F9D AN EXPON5TIAL MODEL =! NUMB] (
BUSI;S US]S OV] "T4
B4 .,EXPLA9 H[ 6TELL :E!R A L9E>1
EXPON5TIAL1 OR P[] FUNC;N BE/ MODELS !
NUMB] ( NON-BUSI;S US]S OV] "T4 ,!N F9D
! BE/-FITT+ MODEL4
#CD4 .,,MULTI-.,,/EP .,,PRO#M ,! BOIL+
PO9T ( WAT] 9CR1SES ) ATMOSPH]IC
PRESSURE4 ,AT SEA LEVEL1 ": ! ATMOSPH]IC
PRESSURE IS AB #GFJ MILLIMET]S ( M]CURY1
WAT] BOILS AT #AJJ;DG,C4 ,! TA# %[S !
BOIL+ PO9T .;,T ( WAT] 7IN DEGREES
,CELSIUS7 = S"EAL DI6]5T VALUES (
ATMOSPH]IC PRESSURE .;,P 7IN MILLIMET]S
( M]CURY74
A4 .,GRAPH ,DRAW A SCATT] PLOT (! DATA
PAIRS 7,IN ;,P1 ,9 .;,T7 @4
B4 .,MODEL ,F9D A P[] MODEL =! ORIG9AL
DATA4
C4 .,PREDICT ,:5 ! ATMOSPH]IC PRESSURE
IS #FBJ MILLIMET]S ( M]CURY1 AT :AT
TEMP]ATURE DOES WAT] BOIL8
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;P @3 .;,T
#ADI3 #FJ
#BCD3 #GJ
#CEE3 #HJ
#EBF3 #IJ
#GFJ3 #AJJ
#AJGE3 #AAJ
#CE4 .,,EXT5D$ .,,RESPONSE ,YR VISUAL
.NE> .PO9T IS ! CLOSE/ PO9T AT : YR EYES
C SEE AN OBJECT 4T9CTLY4 ,YR NE> PO9T
MOVES F>!R AWAY F Y Z Y GR[ OLD]4 ,!
DIAGRAM %[S ! NE> PO9TY 7IN C5TIMET]S7
AT AGE .;X 7IN YE>S74
A4 .,GRAPH ,DRAW A SCATT] PLOT (! DATA
PAIRS @7 .;X @1 LN .;Y @7@4
B4 .,GRAPH ,DRAW A SCATT] PLOT (! DATA
PAIRS 7,IN .;X ;Y.' .-LN .;Y @7@4
C4 .,9T]PRET ,BAS$ ON YR SCATT] PLOTS1
DOES AN EXPON5TIAL FUNC;N OR A P[]
FUNC;N BE/ FIT ! ORIG9AL DATA8 .,EXPLA9
YR R1SON+4
D4 .,MODEL ,BAS$ ON YR ANSW] = "P
7;C71 WRITE A MODEL =! ORIG9AL DATA4
,USE YR MODEL 6PREDICT ! NE> PO9T = AN
#HJ-YE>-OLD P]SON4
------------------------------------#ECF
.#CF4 .,,*ALL5GE ,A DOCTOR M1SURES AN
A/RONAUT'S PULSE RATE .;Y 7IN B1TS P]
M9UTE7 AT V>I\S "TS ;X 7IN M9UTES7 AF !
A/RONAUT HAS F9I%$ EX]CIS+4 ,! RESULTS
>E %[N 9 ! TA#4 ,! A/RONAUT'S RE/+ PULSE
RATE IS #GJ B1TS P] M9UTE4 ,WRITE AN
EXPON5TIAL MODEL =! DATA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #J3 #B3 #D3 #F3 #H3 #AJ3 #AB3
#AD
.;Y @3 #AGB3 #ACB3 #AAJ3 #IB3 #HD3
#GH3 #GE3 .#GB
,MIX$ ,REVIEW
.,,PREVIEW ,PREP>E = ,LESSON #H.A 9
,EXS4 #CG-DB4
,! V>IA#S .;X & .;Y V>Y DIRECTLY4
,WRITE AN EQU,N T RELATES .;X & .Y4 @7
P4 #AJG @7
#CG4 .;X .K #F1 .;Y .K #DH
#CH4 .;X .K --#G1 .;Y .K #BH
#CI4 .;X .K #AJ1 .;Y .K #F
#DJ4 .;X .K #CE1 .;Y .K #AE
#DA4 .;X .K #J.C1 .;Y .K #A.B
#DB4 .;X .K #AB1 .;Y .K #AE
,GRAPH ! FUNC;N4 ,/ATE ! DOMA9 &
RANGE4 @7 P4 #DIB @7
#DC4 .;Y .K .;E -#C;X.'.-
#DD4 .;Y .K #D;E ;X
#DE4 .;F7.;X7 .K #B;E #B;X @+ #A
#DF4 .;Y .K ;E -;X -- #D
#DG4 .;Y .K .#B;E ;X -- #B
#DH4 .;G7.;X7 .K #J.E;E ;X@+#A @+ #C
,3D5SE ! EXPRES.N4 @7 P4 #EJG @7
#DI4 #C;LOG #G #D--LOG #G #H
#EJ4 #B;LOG#E @+ LOG#D
#EA4 LN .;X @+ #IA;N .;Y
#EB4 #BA;N #F-C LN .;X
#EC4 LOG #E #G @+ #F LOG #E .;X -- LOG
#E #C
#ED4 LOG #H--#B ,IOG #B @+ #D LOG .;X
#EE4 .,,PIZZA ,A PIZZA CO/S 4#AA PLUS
4#B P] TOPP+4 ,Y H 4#AH4 ,USE AN
9EQUAL;Y 6F9D ! MAXIMUM NUMB] ( TOPP+S Y
C ORD]4 7.P4 .#DA7
,,QUIZ .= .,LESSONS .#G..F-.G..G
,SOLVE ! EQU,N4 ,*ECK = EXTRANE\S
SOLU;NS1 @7 P4 #EAE @7
.#A4 #B ;X @+ #A .K #AF ;X@+ #B
.#B4 ;E -;X .K #D
.#C4 #C #B;X @+ #E .K #AC
.#D4 #C ;X @+ #A -- #E .K #AJ
.#E4 LOG #D 7#D .;X @+ #G7 .K LOG #D
#AA .;X
.#F4 ,9 7#C .;X -- #B7 .K ,9 #F .;X
.#G4 LOG #C .;X .K--#A
.#H4 #F ,9 .;X .K #CJ
.#I4 LOG #B @7 .;X @+ #D7 .K #E
,WRITE AN EXPON5TIAL FUNC;N ..;Y .K
;AB .^: GRAPH PASSES "? ! GIV5 PO9TS1 @7
P4 #EBI @7
.#AJ4 7#A1 #E71 7#B1 #CJ7
.#AA4 7#A1 #D71 7#B1 #CB7
.#AB4 7#B1 #AE71 7#C1 #DE7
,WRITE A P[] FUNC;N .;Y .K .AX ;B ^:
GRAPH PASSES "? ! GIV5 PO9TS4 @7 P4 #EBI
@7
.#AC4 7#D1 #H71 7#I1 #BC7
.#AD4 7#C1 #AB71 7#AJ1 #CF7
.#AE4 7#E1 #D71 7#AA1 #EA7
.#AF4 .,,BIOLOGY ,! AV]AGE WEI<T .;Y
7IN KILOGRAMS7 ( AN ,ATLANTIC COD F !
,GULF ( ,MA9E C 2 MODEL$ 0.;Y .K
#J.EA7#A.DF7 ;X ": ;X IS ! AGE (! COD
7IN YE>S74 ,E/IMATE ! AGE (A COD T WEI<S
#AE KILOGRAMS1 @7 P4 #EAE @7
,,EXTRA ,,PRACTICE = ,LESSON .#G..G @1
P4 #AJAF
..,,ONL9E ,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#ECG
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,LESSONS #G.E-G.G
#A4 .,,MULTI-.,,/EP .,,PRO#M ,! TOTAL
EXP5DITURES 9 ! ,UNIT$ ,/ATES = ELE;T>Y
& SECOND>Y S*OOLS >E %[N 2L4
,A4 ,DRAW A SCATT] PLOT (! DATA PAIRS
@7 .;X @1 ,9 .;Y7 @4
,B4 ,DRAW A SCATT] PLOT (! DATA PAIRS
7LN .;X @1 LN .;Y @7@4
,C4 ,BAS$ ON YR RESULTS F "PS 7A7 &
7;B71 F9D A MODEL =! ORIG9AL DATA4
,D4 ,PREDICT ! TOTAL EXP5DITURES 9
#BJJE4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,YE>S S9CE #AIIG;,X3 ,TOTAL
EXP5DITURES7BILLIONS ( DOLL>S71 ;Y
.#A @3 #CIH
.#B @3 #DAF
.#C @3 #DCC
.#D @3 #DEJ
.#E @3 #DFC
#B4 .,,MULTI-.,,/EP .,,PRO#M ,9 MUSIC1
A .C5T IS A UNIT T IS US$ 6EXPRESS A
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( C5TS 0: TWO NOTES DI6] 9 PIT* IS GIV5
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,A4 ,?REE NOTES ON ! /&>D SCALE >E
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DI6];E 9 ! NUMB] ( C5TS F ;,C#D 6;,E#D
)! DI6];E F ;,E#D 6;,G#D 0EVALUAT+ ?
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,WRITE ! EXPRES.N Z A S+LE LOG>I?M4
,B4 ;,C#D HAS A FREQU5CY ( #BFD H]TZ1
;,E#D HAS A FREQU5CY ( #CCJ H]TZ1 &
;,G#D HAS A FREQU5CY ( #CIF H]TZ4 ,USE ?
9=M,N 6EVALUATE YR EXPRES.N F "P 7A74
#C4 .,,OP5-.,,5D$ ,WRITE AN EXPON5TIAL
FUNC;N ^: GRAPH PASSES "? ! PO9T 7#B1
#G74
#D4 .,,%ORT .,,RESPONSE ,! TOTAL NUMB]
( MILES TRAVEL$ 0MOTOR VEHICLES 9 !
,UNIT$ ,/ATES IS %[N 2L = V>I\S YE>S4
,DOES AN EXPON5TIAL MODEL OR A P[] MODEL
BE/ FIT ! DATA8 .,EXPLA9 YR R1SON+4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,YE>S S9CE #AIIJ;,X3 ,MILES
7BILLIONS71 ;Y
.#G @3 #BEFB
.#H @3 #BFCB
.#I @3 #BFIA
.#AJ @3 #BGDG
.#AA @3 #BGHB
#E4 .,,EXT5D$ .,,RESPONSE ,! .E6ECTIVE
.9T]E/ .RATE IS A RATE ASSOCIAT$ )!
=MULA = 3T9U\SLY -P.D$ 9T]E/4 ,!
E6ECTIVE 9T]E/ RATE TAKES 96A3.T !
E6ECTS ( -P.D+ ON ! .NOM9AL .9T]E/ .RATE
7! 9T]E/ RATE 9 ! =MULA = 3T9U\S -P.D+74
,! REL,N%IP 2T ! E6ECTIVE 9T]E/ RATE
.;,E &! NOM9AL 9T]E/ RATE .;,N IS GIV5
0! EQU,N
.;,N .K ,9 7.;,E @+ #A7 ": .;,E & .;,N
>E EXPRESS$ Z DECIMALS4
,A4 ,:AT IS ! E6ECTIVE 9T]E/ RATE = AN
A3.T T HAS A NOM9AL 9T]E/ RATE ( #E@3P8
,L1VE YR ANSW] 9 T]MS ( .E4
,B4 ,:AT IS ! E6ECTIVE 9T]E/ RATE = AN
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,L1VE YR ANSW] 9 T]MS ( .E4
,C4 ,! E6ECTIVE 9T]E/ RATE F "P 7;B7
IS H[ _M "TS Z GRT Z ! E6ECTIVE 9T]E/
RATE F "P 7A78 ,WRITE YR ANSW] Z A RATIO
9 T]MS ( .E4
,D4 ,%[ T ! RATIO F "P 7;C7 IS EQUAL
TO
#F4 .,,GRI4$ .,,ANSW] ,Y 9VE/ 4#DJJJ 9
AN A3.T T PAYS #B@3P ANNUAL 9T]E/ -P.D$
3T9U\SLY4 ,6! NE>E/ YE>1 H[ L;G W X TAKE
6E>N 4#AJJJ 9T]E/8
------------------------------------#ECH
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,ELECTRONIC ,FUNC;N ,LIBR>Y
,,BIG ,,ID1S
,= ,YR ,NOTEBOOK
,BIG ,IDEA #A
,GRAPH+ ,EXPON5TIAL & ,LOG>I?MIC
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,P>5T FUNC;NS = EXPON5TIAL FUNC;NS H !
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LOG>I?MIC FUNC;NS H ! =M .;Y .K LOGBX4
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COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,SOLV+ AN ,EXPON5TIAL ,EQU,N3 ,SOLV+ A
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BASE1 EQUATE EXPON5TS4
#C ;X @+ #A .K #I .;X
#C ;X @+ #A .K 7#C #B @7 ;X
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.;X .K LOG ;B .;Y @1 USE ! FACT T .;X .K
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LOG #B #C ;X
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BASE1 TAKE A LOG>I?M ( EA* SIDE4 @3 ,IF
A LOG>I?M IS SET ..EQUAL 6A .3/ANT @1
EXPON5TIATE EA* SIDE4
LOG #E @7 .;X @+ #A7 .K #B .;X @+ #A .K
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,FUNC;NS
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,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,WRITE AN ,EXPON5TIAL ,MODEL3 ,WRITE A
,P[] ,MODEL
,AN EXPON5TIAL MODEL FITS A SET ( DATA
PAIRS @7 .;X1 .;Y @7 IF A L9E> MODEL
FITS ! SET ( DATA PAIRS @7 .;X @1 ,9 .;Y
@7@4 @3 ,A P[] MODEL FITS A SET ( DATA
PAIRS @7 .;X1 .;Y @7 IF A L9E> MODEL
FITS ! SET ( DATA PAIRS 7,IN .;X @1 ,9
.;Y @7@4
------------------------------------#ECI
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99 ,MULTI-,LANGUAGE ,GLOSS>Y
99 ,VOCABUL>Y PRACTICE
,,REVIEW ,,KEY ,,VOCABUL>Y
99 EXPON5TIAL FUNC;N1 P4 #DGH
99 EXPON5TIAL GR[? FUNC;N1 P4 #DGH
99 GR[? FACTOR1 P4 #DGH
99 ASYMPTOTE1 P4 #DGH
99 EXPON5TIAL DECAY FUNC;N1 P4 #DHF
99 DECAY FACTOR1 P4 #DHF
99 NATURAL BASE ;E1 P4 #DIB
99 LOG>I?M ( .;Y ) BASE .;B1 P4 #DII
99 -MON LOG>I?M1 P4 #EJJ
99 NATURAL LOG>I?M1 P4 #EJJ
99 EXPON5TIAL EQU,N1 P4 #EGE
99 LOG>I?MIC EQU,N1 P4 #EGG
,VOCABUL>Y ,EX]CISES
.#A4 ,:AT IS ! ASYMPTOTE (! GRAPH (!
FUNC;N
.#B4 ,ID5TIFY ! DECAY FACTOR 9 ! MODEL
.;Y .K #G.B7#J.HI7 X4
.#C4 .,,WRIT+ .,EXPLA9 ! M1N+ ( LOG ;B
.Y4
.#D4 ,COPY & -PLETE3 ,A LOG>I?M ) BASE
.;E IS CALL$ A7;N7 @8 LOG>I?M4
.#E4 ,IS .;Y .K 7#A.D7 ;X AN
.EXPON5TIAL .FUNC;N OR A .P[] .FUNC;N8
.,EXPLA94
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,USE ! REVIEW EXAMPLES & EX]CISES 2L
6*ECK YR "U/&+ (! 3CEPTS Y H LE>N$ 9 EA*
LESSON ( ,*APT] #G4
#G.A ,GRAPH ,EXPON5TIAL ,GR[? ,FUNC;NS
PP4 #DGH-DHE
,EXAMPLE
,GRAPH .;Y .K #B 99 #C ;X-#B @+ #C4
,/ATE ! DOMA9 & RANGE4
,2G9 0SKET*+ ! GRAPH ( .;Y--.#B 99 #C
;,X @1 : PASSES "? 7#J1 #B7 & 7#A1 #F74
,!N TRANSLATE ! GRAPH "R #B UNITS & UP
#C UNITS4 ,NOTICE T ! TRANSLAT$ GRAPH
PASSES "? 7#B1 #E7 & 7#C1 #I74
,! GRAPH'S ASYMPTOTE IS ! L9E .;Y .K
#C4 ,! DOMA9 IS ALL R1L NUMB]S1 &! RANGE
IS .;Y .1 #C4
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ON PP4 #DGH-DHA = ,EXS4 #F-I
,,EX]CISES
,GRAPH ! FUNC;N4 ,/ATE ! DOMA9 &
RANGE4
.#F4 .;Y .K #E ;X
.#G4 .;Y .K #C7#B.E7;X
.#H4 .;F7.;X7 .K--#C 99 #D ;X @+ #A --
#B
.#I4 .,,F9.E ,Y DEPOSIT 4#AEJJ 9 AN
A3.T T PAYS #G@3P ANNUAL 9T]E/ -P.D$
DAILY4 ,F9D ! BAL.E AF #B YE>S4
------------------------------------#EDJ
#G ,*APT] ,REVIEW
#G.B ,GRAPH ,EXPON5TIAL ,DECAY
,FUNC;NS
PP4 #DHF-DIA
,EXAMPLE
,GRAPH ,/ATE ! DOMA9 & RANGE4
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#B UNITS & D[N #B UNITS4 ,NOTICE T !
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#G.C ,USE ,FUNC;NS ,9VOLV+ ;E
PP4 #DIB-DIH
,EXAMPLE
,GRAPH .;Y .K .;E #J.BE7;X-#A7 -- #E4
,/ATE ! DOMA9 & RANGE4
,2C .A .K #A IS POSITIVE & .;R .K
#J.BE IS POSITIVE1 ! FUNC;N IS AN
EXPON5TIAL GR[? FUNC;N4 ,2G9 0SKET*+ !
GRAPH ( .;Y .K ;E #J.BE;X @4 ,TRANSLATE
! GRAPH "R #A UNIT & D[N #E UNITS4
,! DOMA9 IS ALL R1L NUMB]S1 &! RANGE
IS ;Y .1--#E4
,,EXAMPLES #C & #E
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,GRAPH ! FUNC;N4 ,/ATE ! DOMA9 &
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.#AC4 .;Y .K #B .;E -;X
.#AD4 .;Y .K ;E ;X-#B
.#AE4 .;F7.;X7 .K .;E -#J.D7;X @+ #B7
@+ #F
.#AF4 .,,PHYSIOLOGY ,NITROG5-#AC IS A
RADIOACTIVE ISOTOPE ( NITROG5 US$ 9 A
PHYSIOLOGICAL TE/ CALL$ POSITRON EMIS.N
TOMOGRAPH 7,,PET74 ,A TYPICAL ,,PET SCAN
2G9S ) #F.I PICOGRAMS ( NITROG5-#AC 7#A
PICOGRAM .K #AJ -#AB GRAMS74 ,! NUMB]
;,N ( PICOGRAMS ( NITROG5-#AC REMA9+ AF
.;T M9UTES C 2 MODEL$ 0.;,N .K #F.I;E
-#JFIE;R @4 ,H[ _M PICOGRAMS (
NITROG5-#AC REMA9 AF #AJ M9UTES8
------------------------------------#EDA
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,*APT] ,REVIEW ,PRACTICE
#G.D ,F9D ,LOG>I?MS & ,GRAPH
,LOG>I?MIC ,FUNC;NS
PP4 #DII-EJE
,,EXAMPLE
,EVALUATE ! LOG>I?M4
.A4 LOG #E #FBE
.B4 LOG #J.JJA
.C4 LOG #ABE #E
.D4
,6HELP Y F9D ! VALUE ( LOG ;B ;Y1 ASK
YRF :AT P[] ( .;B GIVES Y .Y4
.A4 #E 6:AT P[] GIVES #FBE8
#E #D .K #FBE1 S LOG #E #FBE .K #D4
.B4 #AJ 6:AT P[] GIVES #J.JJA8
#AJ -#C .K #J.JJA1 S LOG #J.JJA
.K--#C4
.C4 #ABE 6:AT P[] GIVES #E8
.D4 #B 6:AT P[] GIVES @8
S
,,EX]CISES
,,EXAMPLES #B1 #D1 #G1 & #H
ON PP4 #EFJ-EFC = ,EXS4 #AG-BD
,EVALUATE ! LOG>I?M )\T US+ A
CALCULATOR4
.#AG4 LOG #C #BDC
.#AH4 LOG #G .#A
.#AI4 LOG #A/F #BAF
.#BJ4
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RANGE4
.#BA4 .;Y .K LOG #A/F .;X
.#BB4 .;Y .K LOG #C .;X -- #D
.#BC4 .;F7.;X7 .K ,9 7;X-- #A7 @+ #C
.#BD4 .,,BIOLOGY ,RESE>*]S H F.D T AF
#BE YE>S ( AGE1 ! AV]AGE SIZE (! PUPIL 9
A P]SON'S EYE DECR1SES4 ,! REL,N%IP 2T
PUPIL DIAMET] .;D 7IN MILLIMET]S7 & AGE
.A 7IN YE>S7 C 2 MODEL$ 0.;D .K--#B.AAEH
,9 .A @+ #AC.FFI4 ,:AT IS ! AV]AGE
DIAMET] (A PUPIL =A P]SON #BE YE>S OLD8
#EJ YE>S OLD8
#G.E ,APPLY ,PROP]TIES ( ,LOG>I?MS
PP4 #EJG-EAC
,EXAMPLES
,EXP& ! EXPRES.N4
,3D5SE ! EXPRES.N4
,,EX]CISES
,,EXAMPLES #B & #C
ON P4 #EJH = ,EXS4 #BE-CA
,EXP& ! EXPRES.N4
.#BE4 LOG #H #C;XY
.#BF4 ,9 #AJ .;X #C ;Y
.#BG4
.#BH4
,3D5SE ! EXPRES.N4
.#BI4 #C LOG #G #D @+ LOG #G #F
.#CJ4 ,9 #AB-- #B ,9 .;X
.#CA4 #B ,9 #C @+ #E ,9 #B-- ,9 #H
------------------------------------#EDB
#G ,,*APT] ,,REVIEW
#G.F ,SOLVE ,EXPON5TIAL & ,LOG>I?MIC
,EQU,NS
PP4 #EAE-EBB
,EXAMPLE
,SOLVE ! EQU,N4
.A4
.B4 LOG #B 7#C .;X -- #G7 .K #E
#B LOG #B 7#C;X-- #G7 .K #B #E
#C;X-- #G .K #CB
.;X .K #AC
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ON PP4 #EAF-EAH = ,EXS4 #CB-CD
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,SOLVE ! EQU,N4 ,*ECK = EXTRANE\S
SOLU;NS4
.#CB4 #E ;X .K #CB
.#CC4 LOG #C 7#B .;X -- #E7 .K #B
.#CD4 ,9 .;X @+ ,9 @7 .;X @+ #B7 .K #C
#G.G ,WRITE & ,APPLY ,EXPON5TIAL &
,P[] ,FUNC;NS
PP4 #EBI-ECF
,,EXAMPLE
,WRITE AN EXPON5TIAL FUNC;N .;Y .K
.;AB ;X ^: GRAPH PASSES "? 7-#A1 #B7 &
7#C1CB74
,SUB/ITUTE ! COORD9ATES (! TWO GIV5
PO9TS 96.;Y .K .;AB ;X @4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#B .K .;AB -#A @3 ,SUB/ITUTE #B =.' ;Y
.-&--#A =.' X4.-
#CB .K .;AB #C @3 ,SUB/ITUTE #CB =.'
;Y .-& #C =.' X4.-
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SECOND EQU,N4
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,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#CB .K 7#BF7 .;B #C @3 ,SUB/ITUTE #B
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#CB .K #BF #D @3 ..,PRODUCT ( P[]S
.PROP]TY
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0.#B4
#B .K .;B @3 ,TAKE ! POSITIVE F\R?
ROOT 2C.' ;B .1 #J4
,2C .;B .K #B1 X FOLL[S T .A .K #B7#B7
.K #D4 ,S1 .;Y .K #D 99 #B ;X @4
,,EXAMPLES #A & #E
ON PP4 #EBI-ECB = ,EXS4 #CE-CH
,,EX]CISES
,WRITE AN EXPON5TIAL FUNC;N72_/ .K ABX
^: GRAPH PASSES "? ! PO9TS4
.#CE4 7#C1 #H71 7#E1 #B7
.#CF4 7-#B1 #B71 7#A1 #J.BE7
.#CG4 7#B1 #I71 7#D1 #CBD7
.#CH4 .,,SPORT+ .,,GDS ,A /ORE 2G9S
SELL+ A NEW TYPE ( BASKETBALL %OE4 ,!
TA# %[S SALES (! %OE OV] "T4 ,F9D A P[]
MODEL =! DATA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,WEEK1 .;X @3 .#A @3 .#B @3 .#C @3 .#D
@3 .#E @3 .#F
,PAIRS SOLD1 .;Y @3 .#BH @3 .#DG @3
.#FD @3 .#GI @3 .#ID @3 .#AJG
------------------------------------#EDC
#G ,*APT] ,TE/
,GRAPH ! FUNC;N4 ,/ATE ! DOMA9 &
RANGE4
.#A4 .;Y .K #C ;X
.#B4 .;Y .K #B 99 #D ;X-#B
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#C
.#D4 .;Y .K #D7#J.BE7 ;X
.#E4
.#F4
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.#AJ4 LOG #E #BE
.#AA4
.#AB4 LOG #F #A
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RANGE4
.#AC4 .;Y .K LOG #B ;X
.#AD4 .;Y .K ,9 .;X -- #C
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,USE ! *ANGE-(-BASE =MULA 6EVALUATE !
LOG>I?M4
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SOLU;NS4
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& 7#B1 #F74
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7#F1AE74
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PRODUCTS AT HOME G>D5+ C5T]S 9CR1S$ 0AB
#D.HE@3P P] YE>4 ,9 #AIIF1 AB #FB
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PRODUCTS4 ,WRITE A FUNC;N GIV+ ! NUMB] (
H\SEHOLDS .;,H 7IN MILLIONS7 T PUR*AS$
LAWN & G>D5 PRODUCTS .;T YE>S AF #AIIF4
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A3.T T PAYS #C.E@3P ANNUAL 9T]E/ -P.D$
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#BI4 .,,E>? .,,SCI;E ,RIV]S & /R1MS
C>RY SMALL "PICLES ( S$I;T D[N/R1M4 ,!
TA# %[S ! DIAMET] .;X 7IN MILLIMET]S7 (
S"EAL "PICLES ( S$I;T &! SPE$ .;Y 7IN
MET]S P] SECOND7 (! CURR5T NE$$ 6C>RY
EA* "PICLE D[N/R1M4
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D[N/R1M4
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COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,TYPE .( .S$I;T @3 .;X @3 .;Y
.,MUD @3 .#J..B @3 .#J..AJ
.,GRAVEL @3 .#E @3 .#J..EJ
.,CO>SE .GRAVEL @3 .#AA @3 .#J..GE
.,PEB#S @3 .#BJ @3 .#A..JJ
.,SMALL ./"OS @3 .#DE @3 .#A..EJ
------------------------------------#EDD
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,IF Y H DI6ICULTY SOLV+ A
MULTIPLE-*OICE PRO#M DIRECTLY1 Y MAY 2
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PO9TS 96.;Y .K .;AB ;X @4
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------------------------------------#EDE
,PRO#M #B
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,A4 ,ALL R1L NUMB]S
,B4
,C4 ,ALL R1L NUMB]S LESS ?AN #J
,D4 ,ALL R1L NUMB]S GRT] ?AN--#E
------------------------------------#EDF
#G ,/&>DIZ$ ,TE/ ,PRACTICE
,,MULTIPLE-,,*OICE
#A4 ,9 #AIII1 ! TUI;N = "O YE> AT
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,B4 #CJI MILLION
,C4 #EGD MILLION
,D4 #DHIA MILLION
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,D4 #B1 #E
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,A4 .;Y .K #D .;X #J.BE
,B4 .;Y .K#D .;X #J-E
,C4
,D4 .;Y -- #B .;X #A/C
------------------------------------#EDG
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,,GRI4$ ,,ANSW]
#AB4 ,Y DEPOSIT 4#EJJ 9 AN A3.T T PAYS
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XS F/ WEEK ( REL1SE4 ,! WEEKLY GROSS .;Y
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#AIGI3 #BI1JJJ
#AIHB3 #ACD1JJJ
#AIHE3 #BGE1JJJ
#AIHI3 #A1BJJ1JJJ
#AIIC3 #C1AJJ1JJJ
#AIIG3 #G1EJJ1JJJ
#AIII3 #I1EJJ1JJJ
#BJJJ3 #DB1JJJ1JJJ
#BJJD3 #ABE1JJJ1JJJ
------------------------------------#EDH
#H ,R,NAL ,FUNC;NS
,PRODNOTE3 ,PRODUC;N NOTE3 ? IMAGE
CROSSES ! GUTT] 6APPE> BO? ON PAGE #EDH
& PAGE #EDI 9 ! PR9T V].N4
.#H..A ,MODEL ,9V]SE & ,JO9T ,V>I,N
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-- .;X7
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@A .,HOME .,TUTOR ,PREREQUISITE SKILLS
PRACTICE AT _+CLASSZONE.COM_:
------------------------------------#EDI
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99 9V]SE V>I,N1 P4 #EEA
99 3/ANT ( V>I,N1 P4 #EEA
99 JO9T V>I,N1 P4 #EEC
99 R,NAL FUNC;N1 P4 #EEH
99 SIMPLIFI$ =M (A R,NAL EXPRES.N1 P4
#EGC
99 -PLEX FRAC;N1 P4 .#EHD
99 CROSS MULTIPLY+1 P4 #EHI
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------------------------------------#EEJ
,9VE/IGAT+ ,ALGEBRA ,ACTIV;Y3 #H.A
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PREDIC;N8
------------------------------------#EEA
#H.A ,MODEL ,9V]SE & ,JO9T ,V>I,N
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V>I,N
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------------------------------------#EEB
,EXAMPLE #C ,WRITE AN 9V]SE V>I,N
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(A S;G IS #B ,,MB1 #B.E ,,MB1 #C ,,MB1 &
#E ,,MB Z %[N 2L4 ,:AT HAPP5S 6! NUMB] (
S;GS Z ! AV]AGE S;G SIZE 9CR1SES8
,SOLU;N
.,,/EP .#A ,WRITE AN 9V]SE V>I,N
MODEL4
,A ,MODEL IS
.,,/EP#B ,MAKE A TA# ( VALUES4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
..,AV]AGE SIZE ( S;G 7,,MB71 .;S @3
#B3 #B.E3 #C3 #E
..,NUMB] ( S;GS1 .;N @3 #EJJJ3 #DJJJ3
#CCCC3 #BJJJ
,F ! TA#1 Y C SEE T ! NUMB] ( S;GS T W
FIT ON ! ,,MP#C PLAY] DECR1SES Z !
AV]AGE S;G SIZE 9CR1SES4
.,GUID$ .,PRACTICE = ,EXAMPLES #A1B1 &
#C
,TELL :E!R .;X & .;Y %[ ..DIRECT
V>I,N1 9V]SE .V>I,N @1 OR .NEI4
.#A4 #C .;X .K .;Y
.#B4 .XY .K .#J..GE
.#C4 ..;Y .K .;X -- #E
,! V>IA#S .;X & .;Y V>Y 9V]SELY4 ,USE
! GIV5 VALUES 6WRITE AN EQU,N RELAT+ .;X
& .Y4 ,!N F9D .;Y :5 .;X -- #B4
.#D4 .;X .K #D1 .;Y .K #C
.#E4 .;X .K #H1 .;Y .K --.#A
.#F4 @1 .;Y .K #AB
.#G4 .,,:AT .,,IF8 ,9 ,EXAMPLE #C1 :AT
IS A MODEL =! ,,MP#C PLAY] IF X /ORES
#CJJJ S;GS :5 ! AV]AGE S;G SIZE IS #E
,,MB8
------------------------------------#EEC
..,,*ECK+ ,,= ,,9V]SE .,,V>I,N ,!
G5]AL EQU,N = 9V]SE V>I,N C 2 REWRITT5 Z
.XY .K .A4 ,? TELLS Y T A SET ( DATA
PAIRS 7;X1 .;Y7 %[S 9V]SE V>I,N IF !
PRODUCTS .XY >E 3/ANT OR APPROXIMATELY
3/ANT4
,EXAMPLE #D ,*ECK DATA = 9V]SE V>I,N
.,,-PUT] .,,*IPS ,! TA# -P>ES ! >EA
.,A 7IN SQU>E MILLIMET]S7 (A -PUT] *IP
)! NUMB] .;C ( *IPS T C 2 OBTA9$ F A
SILICON WAF]4
99 ,WRITE A MODEL T GIVES .;C Z A
FUNC;N ( ,A4
99 ,PREDICT ! NUMB] ( *IPS P] WAF] :5
! >EA (A *IP IS #HA SQU>E MILLIMET]S4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,>EA 7MM.' #B @7@1 ,A.' @3 #EH3 #FB3
#FF3 #GJ
..,NUMB] ( *IPS1 .;,C @3 #DDH3 #DBD3
#CIB3 #CGF
,,AVOID ,,]RORS
,6*ECK DATA PAIRS 7.;X1 .;Y7 = .DIRECT
V>I,N Y F9D ! .QUOTI5TS ,H["E1 6*ECK .;X
DATA PAIRS = .9V]SE V>I,N1 Y F9D !
.PRODUCTS .XY4
,SOLU;N
.,,/EP .#A .,CALCULATE ! PRODUCT ,A 99
.;C = EA* DATA PAIR 9 ! TA#4
#EH7#DDH7 .K #BE1IHD
#FB7#DBD7 .K #BF1BHH
#FF7#CIB7 .K #BE1HGB
#GJ7#CGF7 .K #BF1CBJ
,EA* PRODUCT IS APPROXIMATELY EQUAL
6#BF1JJJ4 ,S1 ! DATA %[ 9V]SE V>I,N4 ,A
MODEL RELAT+ ,A& .;C IS3
.,,/EP#B .,MAKE A PREDIC;N4 ,! NUMB] (
*IPS P] WAF] =A *IP ) AN >EA ( #HA SQU>E
MILLIMET]S IS
..,GUID$ ,PRACTICE = ,EXAMPLE .#D
.#H4 .,,:AT .,,IF8 ,9 ,EXAMPLE #D1
PREDICT ! NUMB] ( *IPS P] WAF] :5 ! >EA
( EA* *IP IS #GI SQU>E MILLIMET]S4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,JO9T ,V>I,N
.,JO9T .V>I,N O3URS :5 A QUANT;Y V>IES
DIRECTLY ) ..! PRODUCT ( TWO OR .M O!R
QUANTITIES4 ,9 ! EQU,NS 2L1 A IS A
NONZ]O 3/ANT4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
..;,Z .K AXY .;Z @3 V>IES JO9TLY ).'
;X .-& Y4
.;P .K .AQRS @3 .;P V>IES JO9TLY ).'
;Q @1 ;R1 & S4
------------------------------------#EED
,EXAMPLE #E ,WRITE A JO9T V>I,N EQU,N
,! V>IA# .;Z V>IES JO9TLY ) .;X & .Y4
,AL1 .;Z .K --#GE :5 .;X -- #C & .;Y .K
--#E4 ,WRITE AN EQU,N T RELATES ;X1 .;Y
@1 & .Z4 ,!N F9D .;Z :5 .;X .K #B & .;Y
.K #F4
,SOLU;N
.,,/EP .#A .,WRITE A G5]AL JO9T V>I,N
EQU,N4
;Z--AXY
.,,/EP .#B .,USE ! GIV5 VALUES ( .;Z1
.;X @1 & .;Y 6F9D ! 3/ANT ( V>I,N A4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
-#GE .K .A 7#C7 7--#E7 @3 ..,SUB/ITUTE
--#GE = ;Z1 #C = ;X1 & --#E = .Y4
-#GE .K --#AE .A @3 .,SIMPLIFY4
#E .K .A @3 ,SOLVE =.' A4.-
.,,/EP .#C .,REWRITE ! JO9T V>I,N
EQU,N )! VALUE (A F ,/EP #B4
.;Z .K #E .XY
.,,/EP .#D .,CALCULATE .;Z :5 .;X .K
.#B & .;Y .K #F US+ SUB/ITU;N4
;Z .K #E .XY .K #E7#B77#F7 .K #FJ
,EXAMPLE #F ,-P>E DI6]5T TYPES ( V>I,N
,WRITE AN EQU,N =! GIV5 REL,N%IP4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,REL,N%IP3 ,EQU,N
.A4 .;Y V>IES 9V]SELY ) X4 @3
.B4 .;Z V>IES JO9TLY ) .;X1 .;Y @1 &
.R4 @3 .;Z .K .AXYR
.C4 .;Y V>IES 9V]SELY )! SQU>E ( .X4
@3
.D4 .;Z V>IES DIRECTLY ) .;Y & 9V]SELY
) X4 @3
.E4 .;X V>IES JO9TLY ) .;T & .;R &
9V]SELY ) S4 @3
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,GUID$ ,PRACTICE = ,EXAMPLES #E &
.#F
,! V>IA# .;Z V>IES JO9TLY ) .;X & .Y4
,USE ! GIV5 VALUES 6WRITE A EQU,N RELAT+
.;X1 .;Y @1 & Z4 ,!N F9D .;Z :5 .;X .K
--#B & .;Y .K #E4
#I4 .;X .K #A1 .;Y .K #B1 .;Z -- #G
..#AJ4 ;X .K .#D @1 .;Y .K --#C1 .;Z
.K #BD
..#AA4 ;X .K --.#B @1 .;Y .K #F1 .;Z
.K #AH
.#AB4 .;X .K --#F1 .;Y .K --#D1 .;Z .K
#EF
,WRITE AN EQU,N =! GIV5 REL,N%IP4
.#AC4 .;X V>IES 9V]SELY ) .;Y &
DIRECTLY ) .W4
.#AD4 .;P V>IES JO9TLY ) .;Q & .;R &
9V]SELY ) #E4
------------------------------------#EEE
#H.A ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
,,WS#AD = ,EXS4 #AE1BA1 & #CI
.K ..,,/&>DIZ$ ,,TE/ ,,PRACTICE ,EXS4
#B1AA1 #CJ1 .#CE @1 & .#DA
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,IF
.;Z V>IES DIRECTLY )! PRODUCT ( .;X &
;Y1 !N .;Z IS SD 6V>Y @8 ) .;X & Y4
.#B4 .,,WRIT+ .,DESCRIBE H[ 6TELL :E!R
A SET ( DATA PAIRS 7;X1 ;Y7 %[S 9V]SE
V>I,N4
.,,EXAMPLE .#A ON P4 #EEA = ,EXS4
#C-AA
.,,DET]M9+ .,,V>I,N ,TELL :E!R .;X &
.;Y %[ ..DIRECT V>I,N1 9V]SE .V>I,N @1
OR .NEI4
.#C4
.#D4 .;Y .K .;X @+ #D
.#E4
.#F4 #D .;X .K .;Y
.#G4
.#H4 .;X @+ .;Y .K #F
.#I4 #H .;Y .K .;X
.#AJ4 .XY .K #AB
.#AA4 .,,MULTIPLE .,,*OICE ,: EQU,N
REPRES5TS 9V]SE V>I,N8
7,A7 .;Y .K #D .;X
7;,B7 .;Y .K .;X -- #A
7.;,C7 XY .K #E
7.;,D7
..,,EXAMPLE #B ON .P4 #EEA = ,EXS4
#AB-AI
.,,US+ .,,9V]SE .,,V>I,N ,! V>IA#S .;X
& .;Y V>Y 9V]SELY4 ,USE ! GIV5 VALUES
6WRITE AN EQU,N RELAT+ .;X & Y4 ,!N F9D
.;Y :5 .;X .K #C4
.#AB4 .;X .K #E1 .;Y .K --#D
.#AC4 .;X .K #A1 .;Y .K #I
.#AD4 .;X .K --#C1 .;Y .K #H
.#AE .Y .;X .K #G1 .;Y .K #B
.#AF4 .;Y .K #BH
.#AG4 .;X .K--#D
.#AH4 .;X .K --#AB
.#AI4 .;Y .K --#G
.,,EXAMPLE .#D ON P4 #EEC = ,EXS4
#BJ-BC
.,,9T]PRET+ .,,DATA ,DET]M9E :E!R .;X
& .;Y %[ ..DIRECT V>I,N1 9V]SE .V>I,N @1
OR .NEI4
#BJ4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 .;Y
#A.E3 #DJ
#B.E3 #BD
#D3 #AE
#G.E3 #H
#AJ3 #F
#BA
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 .;Y
#AB3 #ACB
#AH3 #AIH
#BC3 #BEC
#BI3 #CAI
#CD3 #CGD
#BB4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 .;Y
#D3 #AF
#E3 #AA
#F.B3 #AJ
#G3 #I
#AA3 #F
#BC4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 .;Y
#D3 #BA
#F3 #AD
#H3 #AJ.E
#H.D3 #AJ
#AB3 #G
.,,EXAMPLE .#E ON P4 #EED = ,EXS4
#BD-CJ
.,,US+ .,,JO9T .,,V>I,N ,WRITE AN
EQU,N RELAT+ .;X1 .;Y @1 & .;Z GIV5 T
.;Z V>IES JO9TLY ) .;X & Y4 ,!N F9D .;Z
:5 .;X .K --#D & .;Y .K #E4
.#BD4 .;X .K #B;,Y .K --#F1 .;Z .K #BD
.#BE4 .;X .K #H;,Y .K #F1 .;Z .K #AB
.#BF4 .;Y .K --#C1 .;Z .K #AE
.#BG4 .;X .K #F1 .;Y .K --#G1 .;Z .K
--#C
.#BH4 .;X .K #I1 .;Y .K --#B1 .;Z .K
#F
.#BI4 .;X .K #E1 .;Y .K --#C1 .;Z .K
#GE
.#CJ4 .,,MULTIPLE .,,*OICE ,SUPPOSE
.;Z V>IES JO9TLY ) .;X & ;Y1 & .;Z .K
--#CF :5 .;X .K --#C &Y .K --#D4 ,:AT IS
! 3/ANT ( V>I,N8
7,A7 --#C
7;,B7 --#B
7.;,C7 #C
7;,D7 #AB
------------------------------------#EEF
.,,EXAMPLE .#F ON P4 #EED = ,EXS4
#CA-CC
.,,WRIT+ .,,EQU,NS ,WRITE AN EQU,N =!
GIV5 REL,N%IP4
.#CA4 .;X V>IES DIRECTLY ) .;Y &
9V]SELY ) .Z4
.#CB4 .;Y V>IES JO9TLY ) .;X &! SQU>E
( .Z4
.#CC4 .;W V>IES 9V]SELY ) .;Y & JO9TLY
) .;X & .Z4
.#CD4 .,,]ROR .,,ANALYSIS ,A V>IA# .;Z
V>IES JO9TLY ) .;X &! CUBE ( .;Y &
9V]SELY )! SQU>E ROOT ( .W4 .,DESCRIBE &
CORRECT ! ]ROR 9 WRIT+ AN EQU,N RELAT+ !
V>IA#S4
.#CE4 .,,OP5-.,,5D$ .,,MA? ,LET ;F7;X7
REPRES5T A DIRECT V>I,N FUNC;N1 ;G7;X7
REPRES5T AN 9V]SE V>I,N FUNC;N1 &
.;H7.;X7 2 ! SUM (_/7;X7 & ;G7;X74
,WRITE POSSI# FUNC;NS_/7;X7 & ;G7;X7 S T
.;H7.#B7 .K #E4
.#CF4 .,,*ALL5GE ,SUPPOSE .;X V>IES
9V]SELY ) .;Y & .;Y V>IES 9V]SELY ) .Z4
,H[ DOES .;X V>Y ) .ZL .,JU/IFY YR ANSW]
ALGEBRAIC,Y4
,,PRO#M ,,SOLV+
..,,EXAMPLES #C & .#D ON PP4 #EEB-EEC
= ,EXS4 #CG-CI
.#CG4 .,,DIGITAL .,,CAM]AS ,! NUMB]
.;N ( PHOTOS YR DIGITAL CAM]A C /ORE
V>IES 9V]SELY )! AV]AGE SIZE #E 7IN
MEGAPIXELS7 (! PHOTOS4 ,YR DIGITAL CAM]A
C /ORE #ED PHOTOS :5 ! AV]AGE PHOTO SIZE
IS #A.IB MEGAPIXELS4 ,WRITE A MODEL T
GIVES .;N Z A FUNC;N ( .S4 ,H[ _M PHOTOS
C YR CAM]A /ORE :5 ! AV]AGE PHOTO SIZE
IS #C.HG MEGAPIXELS8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#CH4 .,,ELECTRONICS ,! TA# 2L -P>ES !
CURR5T _/ 7IN MILLIAMPS7 )! RESI/.E .;,R
7IN OHMS7 = S"EAL ELECTRICAL CIRCUITS4
,WRITE A MODEL T GIVES .;,R Z A FUNC;N
.;O .,I @4 ,!N PREDICT .;,R :5 .,I .K
#CD MILLIAMPS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,CURR5T 7.MILLIAMPS71 .,I @3 #G.D3
#H.I3 #AB.A3 #AG.I
,RESI/.E 7OHMS71 .;,R @3 #ABJJ3 #AJJJ3
#GEJ3 #EJJ
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#CI4 .,,SN[%OES ,:5 Y /& ON SN[1 !
AV]AGE PRESSURE .;,P 7IN P.DS P] SQU>E
9*7 T Y EX]T ON ! SN[ V>IES 9V]SELY )!
TOTAL >EA #D 7IN SQU>E 9*ES7 (! SOLES (
YR FOOTWE>4 ,SUPPOSE ! PRESSURE IS #J.DC
P.D P] SQU>E 9* :5 Y WE> ! SN[%OES %[N4
,WRITE AN EQU,N T GIVES .;,P Z A FUNC;N
.( .,A4 ,!N F9D ! PRESSURE IF Y WE> !
BOOTS %[N4
#DJ4 .,,MULTI-.,,/EP .,,PRO#M ,A PIANO
/R+'S FREQU5CY_/7IN H]TZ7 V>IES DIRECTLY
)! SQU>E ROOT (! /R+'S T5.N ;,T7IN
,NEWTONS7 & 9V]SELY ) BO? ! /R+'S L5G?
.;,L & DIAMET] .;D 7EA* 9 C5TIMET]S74
A4 ,! MI4LE ;,C NOTE HAS A FREQU5CY (
#BFB ,HZ4 ,! /R+ PRODUC+ ? NOTE HAS A
T5.N ( #FGJ ;,N1 A L5G? ( #FB CM1 &A
DIAMET] ( #J.AJBE CM4 ,WRITE AN EQU,N
RELAT9G_/ .;,T1 .;,L @1 & .D4
B4 ,F9D ! FREQU5CY (! NOTE PRODUC$ 0A
/R+ )A T5.N ( #AFBI ;,N1 A L5G? ( #BJA.F
CM1 &A DIAMET] ( #J.DI CM4
.K .,,"W$-.,,\ .,,SOLU;NS ON P4 ,,WS#A
.K .,,/&>DIZ$ .,,TE/ .,,PRACTICE
------------------------------------#EEG
#DA4 .,,EXT5D$ .,,RESPONSE ,! ..LAW (
UNIV]SAL .GRAVIT,N /ATES T ! GRAVIT,NAL
=CE .;,F 7IN ,NEWTONS7 2T TWO OBJECTS
V>IES JO9TLY ) _! MASSES .;M ;L.' .-& ;M
#B 7IN KILOGRAMS7 & 9V]SELY )! SQU>E (!
4T.E .;D 7IN MET]S7 2T ! TWO OBJECTS4 ,!
3/ANT ( V>I,N IS DENOT$ 0;,G & IS CALL$
! .UNIV]SAL .GRAVIT,NAL .3/ANT4
A4 .,MODEL ,WRITE AN EQU,N T GIVES ;,F
9 T]MS ( .;M ;V .;M ;V .;D & ,G4
B4 .,APPROXIMATE ,USE ! 9=M,N ABV AB
,E>? &! ,SUN 6APPROXIMATE ! UNIV]SAL
GRAVIT,NAL 3/ANT ,G4
C4 .,R1SON+ .,EXPLA9 :AT HAPP5S 6!
GRAVIT,NAL =CE Z ! MASSES (! TWO OBJECTS
9CR1SE &! 4T.E 2T !M IS HELD 3/ANT4
.,EXPLA9 :AT HAPP5S 6! GRAVIT,NAL =CE Z
! MASSES (! TWO OBJECTS >E HELD 3/ANT &!
4T.E 2T !M 9CR1SES4
#DB4 .,,*ALL5GE ,! LOAD .;,P 7IN P.DS7
T C 2 SAFELY SUPPORT$ 0A HORIZONTAL B1M
V>IES JO9TLY )! B1M'S WID? ,W& ! SQU>E (
XS DEP? .;,D @1 & 9V]SELY ) XS
UNSUPPORT$ L5G? ,L4
A4 ,H[ DOES .;,P *ANGE :5 ! WID? &
L5G? (! B1M >E D\#D8
B4 ,H[ DOES .;,P *ANGE :5 ! WID? &
DEP? (! B1M >E D\#D8
C4 ,H[ DOES .;,P *ANGE :5 ALL ?REE
DIM5.NS >E D\#D8
D4 .,DESCRIBE S"EAL WAYS A B1M C 2
MODIFI$ IF ! SAFE LOAD X IS REQUIR$
6SUPPORT IS 9CR1S$ 0A FACTOR ( #D4
,MIX$ ,REVIEW
.,,PREVIEW ,PREP>E = ,LESSON #H.B 9
,EXS4 #DC-EA4
,GRAPH ! FUNC;N4
.#DC4 .;Y .K .;X #B @+ #H .;X -- #BJ
@7 P4 #BCF @7
.#DD4 .;Y .K -- .;X #B @+ #D .;X @+ #C
@7 P4 #BCF @7
.#DE4 .;F @7 .;X @7 .K .;X #C @+ #A @7
P4 #CCG @7
.#DF4
.#DG4
.#DH4
.#DI4 .;Y .K --#C ;X @7 .P4 #DGH @7
.#EJ4 .;H @7 .;X @7 .K #C .;X @+ #A @+
#B @7 .P4 #DGH @7
.#EA4
,SOLVE ! EQU,N4 ,*ECK = EXTRANE\S
SOLU;NS1 7.P4 #DEB @7
.#EB4
.#EC4
.#ED4 @7 .;X @+ #C7 #E/C .K #CB
.#EE4
.#EF4
.#EG4
.,,EXTRA .,,PRACTICE = ,LESSON #H.A1
P4 #AJAG
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#EEH
#H.B ,GRAPH ,SIMPLE ,R,NAL ,FUNC;NS
.,2F ,Y GRAPH$ POLYNOMIAL FUNC;NS4
.,N[ ,Y W GRAPH R,NAL FUNC;NS4
.,:Y8 ,S Y C F9D AV]AGE MON?LY CO/S1 Z
9 ,EX4 #CH4
,KEY ,VOCABUL>Y
99 R,NAL FUNC;N
99 DOMA91 P4 #GB
99 RANGE1 P4 #GB
99 ASYMPTOTE1 .P4 #DGH
,SIDEB>3
,/&>DS
.#G..J .,/UD5TS ADD1 SUBTRACT1
MULTIPLY1 DIVIDE1 REDUCE1 & ..EVALUATE
R,NAL EXPRES.NS ) MONOMIAL & POLYNOMIAL
.DENOM9ATORS & SIMPLIFY -PLICAT$ R,NAL
EXPRES.NS1 9CLUD+ ^? ) NEGATIVE EXPON5TS
9 ! DENOM9ATOR4
,A .R,NAL .FUNC;N HAS ! =M ": .;P7.;X7
& .;Q7.;X7 >E POLYNOMIALS & .;Q7.;X7
@6.K #J4 ,! 9V]SE V>I,N FUNC;N IS A
R,NAL FUNC;N4 ,! GRAPH ( ? FUNC;N :5 .A
.K #A IS %[N 2L4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,P>5T ,FUNC;N = ,SIMPLE ,R,NAL
,FUNC;NS
,! GRAPH (! P>5T FUNC;N IS A .HYP]BOLA
@1 : 3SI/S ( TWO SYMMETRICAL "PS CALL$
.BRAN*ES4 ,! DOMA9 & RANGE >E ALL NONZ]O
R1L NUMB]S4
,ANY FUNC;N (! =M HAS ! SAME
ASYMPTOTES1 DOMA91 & RANGE Z ! FUNC;N
,EXAMPLE #A ,GRAPH A R,NAL FUNC;N (!
=M
,GRAPH ! FUNC;N ,-P>E ! GRAPH )! GRAPH
(
,,9T]PRET ,,TRANS=M,NS
,! GRAPH ( IS A V]TICAL /RET* (! GRAPH
( 0A FACTOR ( #F4
,SOLU;N
.,,/EP .#A .,DRAW ! ASYMPTOTES .;X .K
#J & .;Y .K #J4
.,,/EP .#B .,PLOT PO9TS 6! LEFT & 6!
"R (! V]TICAL ASYMPTOTE1 S* Z 7--#C1
--#B71 7--#B1 --#C71 7#B1 #C71 & 7#C1
#B74
.,,/EP .#C .,DRAW ! BRAN*ES (!
HYP]BOLA S T !Y PASS "? ! PLOTT$ PO9TS &
APPROA* ! ASYMPTOTES4
,! GRAPH ( LIES F>!R F ! AXES ?AN !
GRAPH (
,BO? GRAPHS LIE 9 ! F/ & ?IRD
QUADRANTS & H ! SAME ASYMPTOTES1 DOMA91
& RANGE4
------------------------------------#EEI
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,GRAPH+ ,TRANSL,NS ( ,SIMPLE ,R,NAL
,FUNC;NS
,6GRAPH A R,NAL FUNC;N (! =M @1 FOLL[
^! /EPS3
.,,/EP .#A .,DRAW ! ASYMPTOTES .;X .K
.;H & .;Y .K .K4
.,,/EP#B .,PLOT PO9TS 6! LEFT & 6! "R
(! V]TICAL ASYMPTOTE4
.,,/EP .#C .,DRAW ! TWO BRAN*ES (!
HYP]BOLA S T !Y PASS "? ! PLOTT$ PO9TS &
APPROA* ! ASYMPTOTES4
,EXAMPLE #B ,GRAPH A R,NAL FUNC;N (!
=M
,GRAPH @4 ,/ATE ! DOMA9 & RANGE4
,,9T]PRET ,,TRANS=M,NS
,! GRAPH ( IS ! GRAPH ( TRANSLAT$ LEFT
#B UNITS & D[N #A UNIT4
,SOLU;N
.,,/EP .#A .,DRAW ! ASYMPTOTES .;X.K
--.#B & .;Y .K --#A4
.,,/EP#B .,PLOT PO9TS 6! LEFT (!
V]TICAL ASYMPTOTE1 S* Z 7--#C1 #C7 &
7--#D1 #A71 & PO9TS 6! "R1 S* Z 7--#A1
--#E7 &7#J1 --#C74
.,,/EP .#C .,DRAW ! TWO BRAN*ES (!
HYP]BOLA S T !Y PASS "? ! PLOTT$ PO9TS &
APPROA* ! ASYMPTOTES4
,! DOMA9 IS ALL R1L NUMB]S EXCEPT
--#B1 &! RANGE IS ALL R1L NUMB]S EXCEPT
--#A4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,GUID$ ,PRACTICE = ,EXAMPLES #A &
.#B
,GRAPH ! FUNC;N4 ,/ATE ! DOMA9 &
RANGE4
.#A4
.#B4
.#C4
.,,O!R .,,R,NAL .,,FUNC;NS ,ALL R,NAL
FUNC;NS (! =M H GRAPHS T >E HYP]BOLAS4
99 ,! V]TICAL ASYMPTOTE (! GRAPH IS !
L9E 2C ! FUNC;N IS UNDEF9$ :5 !
DENOM9ATOR .EX @+ .;D IS Z]O4
99 ,! HORIZONTAL ASYMPTOTE IS ! L9E
------------------------------------#EFJ
,EXAMPLE #C ,GRAPH A R,NAL FUNC;N (!
=M
,GRAPH ,/ATE ! DOMA9 & RANGE4
,SOLU;N
.,,/EP .#A .,DRAW ! ASYMPTOTES4 ,SOLVE
.;X -- #C .K #J = .;X 6F9D ! V]TICAL
ASYMPTOTE .;X .K #C4 ,! HORIZONTAL
ASYMPTOTE IS ! L9E
.,,/EP .#B .,PLOT PO9TS 6! LEFT (!
V]TICAL ASYMPTOTE1 S* Z 7#B1--#E7 & @1 &
PO9TS 6! "R1 S* Z 7#D1 #I7 &7 @4
.,,/EP .#C .,DRAW ! TWO BRAN*ES (!
HYP]BOLA S T !Y PASS "? ! PLOTT$ PO9TS &
APPROA* ! ASYMPTOTES4
,! DOMA9 IS ALL R1L NUMB]S EXCEPT #C4
,! RANGE IS ALL R1L NUMB]S EXCEPT #B4
..,EXAMPLE #D ,SOLVE A MULTI --/EP
.PRO#M
.#C-.;,D .,,MODEL+ ,A #C-;,D PR9T]
BUILDS UP LAY]S ( MAT]IAL 6MAKE
?REE-DIM5.NAL MODELS4 ,EA* DEPOSIT$ LAY]
BONDS 6! LAY] 2L X4 ,A -PANY DECIDES
6MAKE SMALL 4PLAY MODELS ( 5G9E -PON5TS
US+ A #C-;,D PR9T]4 ,! PR9T] CO/S
4#BD1JJJ4 ,! MAT]IAL = EA* MODEL CO/S
4#CJJ4
99 ,WRITE AN EQU,N T GIVES ! AV]AGE
CO/ P] MODEL Z A FUNC;N (! NUMB] (
MODELS PR9T$4
99 ,GRAPH ! FUNC;N4 ,USE ! GRAPH
6E/IMATE H[ _M MODELS M/ 2 PR9T$ =!
AV]AGE CO/ P] MODEL 6FALL TO 4#GJJ4
99 ,:AT HAPP5S 6! AV]AGE CO/ Z M
MODELS >E PR9T$8
,SOLU;N
.,,/EP .#A .,WRITE A FUNC;N4 ,LET .;C
2 ! AV]AGE CO/ & .;M 2 ! NUMB] ( MODELS
PR9T$4
,,DRAW ,,GRAPHS
,2C ! NUMB] ( MODELS & AV]AGE CO/ _C 2
NEGATIVE1 GRAPH ONLY ! BRAN* (! HYP]BOLA
T LIES 9 ! F/ QUADRANT4
.,,/EP#B .,GRAPH ! FUNC;N4 ,!
ASYMPTOTES >E ! L9ES .;M .K #J & .;C .K
#CJJ4 ,! AV]AGE CO/ FALLS TO 4#GJJ P]
MODEL AF #FJ MODELS >E PR9T$4
.,,/EP .#C .,9T]PRET ! GRAPH4 ,Z M
MODELS >E PR9T$1 ! AV]AGE CO/ P] MODEL
APPROA*ES 4#CJJ4
------------------------------------#EFA
..,GUID$ ,PRACTICE = ,EXAMPLES #C &
.#D
,GRAPH ! FUNC;N4 ,/ATE ! DOMA9 &
RANGE4
.#D4
.#E4
.#F4
.#G4 .,,:AT .,,IF8 ,9 ,EXAMPLE #D1 H[
D ! FUNC;N & GRAPH *ANGE IF ! CO/ (!
#C-;,D PR9T] IS 4#BA1JJJ8
#H.B ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
,,WS#AD = ,EXS4 #E1BA1 & #CI
.K .,,/&>DIZ$ .,,TE/ .,,PRACTICE ,EXS4
..#B1 #BC1CE1DJ1 & .#DA
.K .,,MULTIPLE .,,REPRES5T,NS ,EX#.CI
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,!
FUNC;N HAS A7;N7 @8 ( ALL R1L NUMB]S
EXCEPT #C &A7;N7 @8 ( ALL R1L NUMB]S
EXCEPT --#D4
.#B4 .,,WRIT+ ,IS A R,NAL FUNC;N8
.,EXPLA9 YR ANSW]4
..,,EXAMPLE #A ON .P4 #EEH = ,EXS4
#C-AJ
..,,GRAPH+ ,,FUNC;NS ,GRAPH ! FUNC;N4
,-P>E ! GRAPH )! GRAPH .(
.#C4
.#D4
.#E4
.#F4
.#G4
.#H4
.#I4
.#AJ4
.,,EXAMPLE .#B ON P4 #EEI = ,EXS4
#AA-BC
,,GRAPH+ ,,FUNC;NS ,GRAPH ! FUNC;N4
,/ATE ! DOMA9 & RANGE4
.#AA4
.#AB4
.#AC4
.#AD
.#AE4
.#AF4
.#AG4
.#AH
.#AI4
.#BJ4
.#BA
.#BB4
.#BC4 .,,MULTIPLE .,,*OICE ,:AT >E !
ASYMPTOTES (! GRAPH ( @8
7.,A7 .;X .K #H1 .;Y .K #C
7.;,B7 .;X .K #H1 .;Y .K --#C
7.;,C7 .;X .K --#H1 .;Y .K #C
7.;,D7 .;X .K --#H1 .;Y .K --#C
#BD4 .,,GRAPH+ .,,CALCULATOR ,3SID] !
FUNC;N ": .A .K #A1 .;H .K #C1 & .;K .K
--#B4 ,PREDICT ! E6ECT ON ! FUNC;NS
GRAPH ( EA* *ANGE 9 .A1 .;H @1 OR FC
DESCRIB$ 9 "PS 7A7-7;C74 ,USE A GRAPH+
CALCULATOR 6*ECK YR PREDIC;N 0GRAPH+ !
ORIG9AL & REVIS$ FUNC;NS 9 ! SAME
COORD9ATE PLANE4
A4 .A *ANGES TO --#C
B4 .;H *ANGES TO --#A
C4 .;K *ANGES 6#B
------------------------------------#EFB
.,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 ! GRAPH4
.#BE4
.#BF4
.,,EXAMPLE .#C @3 ON P4 #EFJ = ,EXS4
#BG-CD
.,,GRAPH+ .,,FUNC;NS ,GRAPH ! FUNC;N4
,/ATE ! DOMA9 & RANGE4
.#BG4
.#BH4
.#BI4
.#CJ4
.#CA4
.#CB4
.#CC4
.#CD4
.#CE4 .,,OP5-.,,5D$ .,,MA? ,WRITE A
R,NAL FUNC;N S* T ! DOMA9 IS ALL R1L
NUMB]S EXCEPT --#H &! RANGE IS ALL R1L
NUMB]S EXCEPT #C4
.#CF4 .,,*ALL5GE ,%[ T ! EQU,N
REPRES5TS A R,NAL FUNC;N 0WRIT+ ! "R
SIDE Z A QUOTI5T ( POLYNOMIALS4
,,PRO#M ,,SOLV+
.,,EXAMPLE .#D ON P4 #EFJ = ,EXS4
#CG-CH
.#CG4 .,,9T]NET .,,S]VICE ,AN ,9T]NET
S]VICE PROVID] *>GES A 4#EJ 9/ALL,N FEE
&A MON?LY FEE ( 4#DC4 ,WRITE & GRAPH AN
EQU,N T GIVES ! AV]AGE CO/ P] MON? Z A
FUNC;N (! NUMB] ( MON?S ( S]VICE4 ,AF H[
_M MON?S W ! AV]AGE CO/ 2 4#EC8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#CH4 .,,ROCK .,,CLIMB+ .,,GYM ,6JO9 A
ROCK CLIMB+ GYM1 Y M/ PAY AN 9ITIAL FEE
( 4#AJJ &A MON?LY FEE ( 4#EI4 ,WRITE &
GRAPH AN EQU,N T GIVES ! AV]AGE CO/ P]
MON? Z A FUNC;N (! NUMB] ( MON?S (
MEMB]%IP4 ,AF H[ _M MON?S W ! AV]AGE CO/
2 4#FI8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
7.#CI7 .,,MULTIPLE .,,REPRES5T,NS ,!
"T .;T 7IN SECONDS7 X TAKES = S.D
6TRAVEL #A KILOMET] C 2 MODEL$ 0": .;,T
.IS ! AIR TEMP]ATURE 7IN DEGREES
,CELSIUS74
A4 ,EVALUAT+ A ,FUNC;N ,H[ L;G DOES X
TAKE = S.D 6TRAVEL #E KILOMET]S :5 ! AIR
TEMP]ATURE IS #BE;DG;,C8 .,EXPLA94
B4 ,DRAW+ A ,GRAPH ,SUPPOSE Y >E #A
KILOMET] F A LI<TN+ /RIKE1 & X TAKES #C
SECONDS 6HE> ! ?"U4 ,GRAPH ! GIV5
FUNC;N1 & USE ! GRAPH 6E/IMATE ! AIR
TEMP]ATURE4
.K .,,"W$ ,,\ .,,SOLU;NS .ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
------------------------------------#EFC
#DJ4 .,,%ORT .,,RESPONSE ,A BUSI;S IS
/UDY+ ! CO/ 6REMOVE A POLLUTANT F ! GR.D
AT XS SITE4 ,! FUNC;N MODELS ! E/IMAT$
CO/ .;Y 7IN ?\S&S ( DOLL>S7 6REMOVE .;X
P]C5T 7EXPRESS$ Z A DECIMAL7 (!
POLLUTANT4
A4 ,GRAPH ! FUNC;N4 .,DESCRIBE A
R1SONA# DOMA9 & RANGE4
B4 ,H[ M* DOES X CO/ 6REMOVE #BJ@3P (!
POLLUTANT8 #DJ@3P (! POLLUTANT8 #HJ@3P
(! POLLUTANT8 ,DOES D\BL+ ! P]C5T (!
POLLUTANT REMOV$ D\# ! CO/8 .,EXPLA94
#DA4 .,,EXT5D$ .,,RESPONSE ,! .,DOPPL]
.E6ECT O3URS :5 ! S\RCE (A S.D IS MOV+
RELATIVE 6A LI/5]1 S T ! FREQU5CY ;F#A
7IN H]TZ7 HE>D 0! LI/5] IS DI6]5T F !
FREQU5CY FS 7IN H]TZ7 AT ! S\RCE4 ,!
FREQU5CY HE>D DEP5DS ON :E!R ! S.D S\RCE
IS APPROA*+ OR MOV+ AWAY F ! LI/5]4 ,9
BO? EQU,NS 2L1 ;R IS ! SPE$ 7IN MILES P]
H\R7 (! S.D S\RCE4
A4 ,AN AMBUL.E SIR5 HAS A FREQU5CY (
#BJJJ H]TZ4 ,WRITE TWO EQU,NS MODEL+ !
FREQU5CIES Y HE> :5 ! AMBUL.E IS
APPROA*+ & :5 ! AMBUL.E IS MOV+ AWAY4
B4 ,GRAPH ! EQU,NS F "P 7A7 US+ !
DOMA9 #J "K .;R "K #FJ4
C4 ,= ANY SPE$ ;R1 H[ DOES ! FREQU5CY
HE>D = AN APPROA*+ S.D S\RCE -P>E )!
FREQU5CY HE>D :5 ! S\RCE MOVES AWAY8
#DB4 .,,*ALL5GE ,A SAILBOAT TRAVELS AT
A SPE$ ( #AJ KNOTS = #C H\RS4 ,X !N USES
A MOTOR = P[]1 : 9CR1SES XS SPE$ 6#AE
KNOTS4 ,WRITE & GRAPH AN EQU,N GIV+ !
BOAT'S AV]AGE SPE$ .;S 7IN KNOTS7 =!
5TIRE TRIP Z A FUNC;N (! "T .;T 7IN
H\RS7 T X USES ! MOTOR = P[]4
,MIX$ ,REVIEW
.,,PREVIEW ,PREP>E = ,LESSON #H.C 9
,EXS4 #DC-DH4
,FACTOR ! EXPRES.N4 7.P4 #BEB @7
.#DC4 .;M #B @+ #AH .;M @+ #FE
.#DD4 .;P #B @+ #AE .;P @+ #EF
.#DE4 .;Q #B -- #DI
.#DF4 .;R #B -- #BJ .;R @+ #AJJ
.#DG4 .;X #B -- #D .;X -- #BA
.#DH4 .;Z #B -- #I .;Z @+ #BJ
,GRAPH ! POLYNOMIAL FUNC;N4 @7 .P4
#CCG @7
.#DI4 .;F @7 .;X @7 .K #B .;X #D
.#EJ4 .;F @7 .;X @7 .K .;X #C @+ #E
.#EA4 .;F @7 .;X @7 .K .;X #E -- #A
.#EB4 .;F @7 .;X @7 .K #C .;X #D @+ #B
.#EC4 .;F @7 .;X @7 .K -- .;X #F
.#ED4 .;F @7 .;X @7 .K --#B .;X #C @+
#C
,SIMPLIFY ! EXPRES.N1 7.P4 #DIB @7
.#EE4 .;E #E 99 .;E -#I
.#EF4 #C .;E #F 99 .;E ;X
.#EG4 .;E ;X 99 .;E #C .;X @+ #B
.,,EXTRA .,,PRACTICE = ,LESSON #H.B1
P4 #AJAG
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#EFD
,GRAPH+ ,CALCULATOR ,ACTIV;Y3 #H.B
,GRAPH ,R,NAL ,FUNC;NS
,USE AF LESSON #H.B
@A.,HOME,TUTOR _+CLASSZONE.COM_:
,KEY/ROKES
.,,"Q ,H[ C Y USE A GRAPH+ CALCULATOR
6GRAPH R,NAL FUNC;NS8
,MO/ GRAPH+ CALCULATORS H TWO GRAPH+
MODES3 .3NECT$ MODE & .DOT MODE4
.,3NECT$ MODE 4PLAYS ! GRAPH (A R,NAL
FUNC;N Z A SMOO? CURVE1 :ILE .DOT MODE
4PLAYS ! GRAPH Z A S]IES ( DOTS4
,SIDEB>3
,/&>DS
.#G..J .,/UD5TS ADD1 SUBTRACT1
MULTIPLY1 DIVIDE1 REDUCE1 & ..EVALUATE
R,NAL EXPRES.NS ) MONOMIAL & POLYNOMIAL
.DENOM9ATORS & SIMPLIFY -PLICAT$ R,NAL
EXPRES.NS1 9CLUD+ ^? ) NEGATIVE EXPON5TS
9 ! DENOM9ATOR4
.,,EXAMPLE ,GRAPH A R,NAL FUNC;N
,GRAPH
,,/EP #A ,5T] FUNC;N
,5T] ! R,NAL FUNC;N1 US+ P>5!SES4
,,/EP #B ,USE 3NECT$ MODE
,GRAPH ! FUNC;N 9 .3NECT$ MODE4
..,,/EP #C ,USE DOT .MODE ,GRAPH !
FUNC;N 9 .DOT MODE4
,! GRAPH 9 ,/EP #B 9CLUDES A V]TICAL
L9E AT APPROXIMATELY .;X .K #C4 ,? L9E
IS .N "P (! GRAPH4 ,X IS SIMPLY ! GRAPH+
CALCULATOR'S ATTEMPT AT 3NECT+ ! TWO
BRAN*ES (! GRAPH4
,PRACTICE
,USE A GRAPH+ CALCULATOR 6GRAPH !
R,NAL FUNC;N4 ,*OOSE A VIEW+ W9D[ T
4PLAYS ! IMPORTANT "*I/ICS (! GRAPH4
.#A4
.#B4
.#C4
.#D4
.#E4
.#F4
.#G4
.#H4
.#I4 .,,SKATEBO>D+ ,Y >E TRY+ 6DECIDE
:E!R X IS WOR? JO9+ A SKATE P>K4 ,X CO/S
4#AJJ 6JO9 & !N 4#D = EA* VISIT4 ,WRITE
A FUNC;N T GIVES ! AV]AGE CO/ .;Y P]
VISIT AF .;X VISITS4 ,GRAPH ! FUNC;N4
,:AT HAPP5S 6! AV]AGE CO/ Z ! NUMB] (
VISITS 9CR1SES8 ,:AT >E A R1SONA# DOMA9
& RANGE =! FUNC;N8
------------------------------------#EFE
#H.C ,GRAPH ,G5]AL ,R,NAL ,FUNC;NS
.,2F ,Y GRAPH$ R,NAL FUNC;NS 9VOLV+
L9E> POLYNOMIALS4
.,N[ ,Y W GRAPH R,NAL FUNC;NS )
HI<]-DEGREE POLYNOMIALS4
.,:Y8 ,S Y C SOLVE PRO#MS AB ALTITUDE1
Z 9 ,EX4 #CE4
,KEY ,VOCABUL>Y
99 5D 2HAVIOR1 .P4 .#CCI
99 ASYMPTOTE1 .P4 .#DGH
99 R,NAL FUNC;N1 P4 #EEH
,SIDEB>3
,/&>DS
.#G..J .,/UD5TS ADD1 SUBTRACT1
MULTIPLY1 DIVIDE1 REDUCE1 & ..EVALUATE
R,NAL EXPRES.NS ) MONOMIAL & POLYNOMIAL
.DENOM9ATORS & SIMPLIFY -PLICAT$ R,NAL
EXPRES.NS1 9CLUD+ ^? ) NEGATIVE EXPON5TS
9 ! DENOM9ATOR4
,,KEY ,,3CEPT
,= YR ,NOTEBOOK
,GRAPHS ( ,R,NAL ,FUNC;NS
,LET .;P7.;X7 & .;Q7.;X7 2 POLYNOMIALS
) NO -MON FACTORS O!R ?AN +-#A4 ,! GRAPH
(! FOLL[+ R,NAL FUNC;N HAS ! "*I/ICS
LI/$ 2L4
.#A4 ,! ;X-9T]CEPTS (! GRAPH ( .;F >E
! R1L Z]OS ( .;P7.;X74
.#B4 ,! GRAPH ( .;F HAS A V]TICAL
ASYMPTOTE AT EA* R1L Z]O ( .;Q7.;X74
.#C4 ,! GRAPH ( .;F HAS AT MO/ "O
HORIZONTAL ASYMPTOTE1 : IS DET]M9$ 0!
DEGREES .;M & .;N .( .;P7.;X7 &
.;Q7.;X74
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;M"K.;N @3 ,! L9E .;Y .K #J IS A
HORIZONTAL ASYMPTOTE4
.;M .K .;N @3 ,! L9E IS A HORIZONTAL
ASYMPTOTE4
.;M.1.;N @3 ,! GRAPH HAS NO HORIZONTAL
ASYMPTOTE4
,! GRAPH'S 5D 2HAVIOR IS ! SAME Z !
GRAPH (
,EXAMPLE #A;,GRAPH A R,NAL FUNC;N 7.;M
"K .;N7
,GRAPH ,/ATE ! DOMA9 & RANGE4
,SOLU;N
,! NUM]ATOR HAS NO Z]OS1 S "! IS NO
;X-9T]CEPT4 ,! DENOM9ATOR HAS NO R1L
Z]OS1 S "! IS NO V]TICAL ASYMPTOTE4
,! DEGREE (! NUM]ATOR1 #J1 IS LESS ?AN
! DEGREE (! DENOM9ATOR1 #B4 ,S1 ! L9E
.;Y .K #J 7! ;X-AXIS7 IS A HORIZONTAL
ASYMPTOTE4
,! GRAPH PASSES "? ! PO9TS 7--#C1
#J.F71 7--#A1 #C71 7#J1 #F71 7#A1 #C71 &
7#C1 #J.F74 ,! DOMA9 IS ALL R1L NUMB]S1
&! RANGE IS #J "K .;Y "K #F4
------------------------------------#EFF
,EXAMPLE #B ,GRAPH A R,NAL FUNC;N 7.;M
.K ;N7
,GRAPH
,,REVIEW ,,Z]OS ,,( ,,FUNC;NS
,= HELP ) F9D+ Z]OS ( FUNC;NS1 SEE P4
#BEB @4
,SOLU;N
,! Z]O (! NUM]ATOR #B;X #B IS #J1 S #J
IS AN ;X-9T]CEPT4 ,! Z]OS (! DENOM9ATOR
.;X #B -- #I >E +-#C1 S .;X .K #C & .;X
.K --#C >E V]TICAL ASYMPTOTES4
,! NUM]ATOR & DENOM9ATOR H ! SAME
DEGREE1 S ! HORIZONTAL ASYMPTOTE IS
,PLOT PO9TS 2T & 2Y ! V]TICAL
ASYMPTOTES4
,EXAMPLE #C ,GRAPH A R,NAL FUNC;N 7.;M
.1 .;N7
,GRAPH
,SOLU;N
,! NUM]ATOR FACTORS Z 7;X @+
#D77;X--#A71 S ! ;X-9T]CEPTS >E --#D &
#A4 ,! Z]O (! DENOM9ATOR .;X -- #B IS
#B1 S .;X .K #B IS A V]TICAL ASYMPTOTE4
,! DEGREE (! NUM]ATOR1 #B1 IS GRT] ?AN
! DEGREE (! DENOM9ATOR1 #A1 S ! GRAPH
HAS NO HORIZONTAL ASYMPTOTE4 ,! GRAPH
HAS ! SAME 5D 2HAVIOR Z ! GRAPH ( .;Y .K
;X #B -- ;L .K .X4 ,PLOT PO9TS ON EA*
SIDE (! V]TICAL ASYMPTOTE4
------------------------------------#EFG
.,GUID$ .,PRACTICE = ,EXAMPLES #A1B1 &
#C
,GRAPH ! FUNC;N4
.#A4
.#B4
.#C4
.#D4
..,EXAMPLE #D ,SOLVE A MULTI-/EP
.PRO#M
.,,MANUFACTUR+ ,A FOOD MANUFACTUR]
WANTS 6F9D ! MO/ E6ICI5T PACKAG+ =A C (
S\P )A VOLUME ( #CDB CUBIC C5TIMET]S4
,F9D ! DIM5.NS (! C T HAS ? VOLUME &
USES ! L1/ AM.T ( MAT]IAL POSSI#4
,SOLU;N
.,,/EP .#A ,WRITE AN EQU,N T GIVES !
HEI<T .;H (! S\P C 9 T]MS ( XS RADIUS R4
,USE ! =MULA =! VOLUME (A CYL9D] &! FACT
T ! S\P C'S VOLUME IS #CDB CUBIC
C5TIMET]S4
.,,/EP .#B ,WRITE A FUNC;N T GIVES !
SURFACE >EA .;,S (! S\P C 9 T]MS ( ONLY
XS RADIUS R4
,,9T]PRET ,,FUNC;NS
,! FUNC;N =! SURFACE >EA IS A R,NAL
FUNC;N 2C X C 2 WRITT5 Z A QUOTI5T (
POLYNOMIALS3
.,,/EP .#C ,GRAPH ! FUNC;N =! SURFACE
>EA ;,S US+ A GRAPH+ CALCULATOR4 ,!N USE
! .M9IMUM F1TURE 6F9D ! M9IMUM VALUE (
,S4
,Y GET A M9IMUM VALUE ( AB #BGA1 :
O3URS :5
,S1 ! S\P C US+ ! L1/ AM.T ( MAT]IAL
HAS A RADIUS ( AB #C.GI C5TIMET]S &A
HEI<T ( AB #G.EH C5TIMET]S4 ,NOTICE T !
HEI<T &! DIAMET] >E EQUAL = ? C4
..,GUID$ ,PRACTICE = ,EXAMPLE .#D
.#E4 .,,:AT .,,IF8 ,9 ,EXAMPLE #D1
SUPPOSE ! MANUFACTUR] WANTS 6F9D ! MO/
E6ICI5T PACKAG+ =A S\P C )A VOLUME (
#EDD CUBIC C5TIMET]S4 ,F9D ! DIM5.NS ( ?
C4
------------------------------------#EFH
#H.C ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
,,WS#AE = ,EXS4 #G1AE1 & #CC
.K .,,/&>DIZ$ .,,TE/ .,,PRACTICE ,EXS4
#B1F1AD1BD1 & #CE
.K .,,MULTIPLE .,,REPRES5T,NS ,EX#.CC
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,!
GRAPH (A R,NAL FUNC;N .;F HAS NO @8 :5 !
DEGREE (! FUNC;N'S NUM]ATOR IS GRT] ?AN
! DEGREE ( XS DENOM9ATOR4
.#B4 .,,WRIT+ ,LET ": .;P7.;X7 &
.;Q7.;X7 >E POLYNOMIALS ) NO -MON
FACTORS O!R ?AN +-#A4 .,DESCRIBE H[ 6F9D
! ;X-9T]CEPTS &! V]TICAL ASYMPTOTES (!
GRAPH ( .;F @4
,,MAT*+ ,,GRAPHS ,MAT* ! FUNC;N ) XS
GRAPH4
..,,EXAMPLES #A1 #B1 & .#C ON PP4
#EFE-EFF = ,EXS4 #C-BC
.#C4
.#D4
.#E4
.,A4
.,B4
.,C4
.#F4 .,,MULTIPLE .,,*OICE ,! GRAPH ( :
FUNC;N IS %[N8
,A
;,B
;,C
;,D
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
,,ANALYZ+ ,,GRAPHS ,ID5TIFY !
;X-9T]CEPT7;S7 & V]TICAL ASYMPTOTE 7;S7
(! GRAPH (! FUNC;N4
.#G
.#H4
.#I4
.#AJ4
.#AA4
.#AB4
.#AC4 .,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 F9D+ ! V]TICAL
ASYMPTOTE7;S7
------------------------------------#EFI
.#AD4 .,,MULTIPLE .,,*OICE ,:AT IS !
HORIZONTAL ASYMPTOTE (! GRAPH (! FUNC;N
7.,A7 .;Y .K #J
7;,B7
7.;,C7 .;Y .K #D
7.;,D7 .;Y .K #D;X
,,GRAPH+ ,,FUNC;NS ,GRAPH ! FUNC;N4
.#AE4
.#AF4
.#AG4
.#AH4
.#AI4
.#BJ4
.#BA4
.#BB4
.#BC4
.#BD4 .,,OP5-.,,5D$ .,,MA? ,WRITE TWO
DI6]5T R,NAL FUNC;NS ^: GRAPHS H ! SAME
5D 2HAVIOR Z ! GRAPH ( .;Y .K .#C;X #B
@4
,,GRAPH+ ,,CALCULATOR ,USE A GRAPH+
CALCULATOR 6F9D ! RANGE (! R,NAL FUNC;N4
.#BE4
.#BF4
.#BG4
,,*ALL5GE ,! GRAPH (A FUNC;N (! =M IS
%[N4 ,F9D ! VALUES ( .A & .B4
.#BH4
.#BI4
.#CJ4
,,PRO#M ,,SOLV+
,,EXAMPLE #D ON P4 #EFG = ,EXS4 #CA-CB
..,,GRAPH+ ,,CALCULATOR ,Y MAY WI%
6USE A GRAPH+ CALCULATOR 6-PLETE !
FOLL[+ ,PRO#M ,SOLV+ .EX]CISES4
#CA4 .,,AGRICULTURE ,A F>M] MAKES
CYL9DRICAL BALES ( HAY T H A VOLUME (
#AJJ CUBIC FEET4 ,EA* BALE IS 6BE WRAPP$
9 PLA/IC 6KEEP ! HAY DRY4
A4 ,US+ ! =MULA =! VOLUME (A CYL9D]1
WRITE AN EQU,N T GIVES ! L5G? .;I (A
BALE 9 T]MS (! RADIUS .R4
B4 ,WRITE A FUNC;N T GIVES ! SURFACE
>EA (A BALE 9 T]MS ( ONLY ! RADIUS R4
C4 ,F9D ! DIM5.NS (A BALE T HAS ! GIV5
VOLUME & USES ! L1/ AM.T ( PLA/IC POSSI#
:5 ! BALE IS WRAPP$4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
------------------------------------#EGJ
#CB4 .,,AQU>IUM .,,DESIGN ,A
MANUFACTUR] IS DESIGN+ AN AQU>IUM ^:
BASE IS A REGUL> HEXAGON4 ,! AQU>IUM %D
H A VOLUME ( #BD CUBIC FEET & USE ! L1/
AM.T ( MAT]IAL POSSI#4 ,LET .;S 2 ! L5G?
7IN FEET7 (A SIDE (! BASE1 & LET .;H 2 !
HEI<T 7IN FEET74
A4 ,WRITE AN EQU,N T GIVES .;H 9 T]MS
( .S4 7.,H9T3 ,! VOLUME (! AQU>IUM IS
GIV5 BY @7
B4 ,F9D ! DIM5.NS .;S & .;H T M9IMIZE
! AM.T ( MAT]IAL US$4 7.,H9T3 ,! SURFACE
>EA (! AQU>IUM IS GIV5 BY @7
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
7.#CC7 .,,MULTIPLE .,,REPRES5T,NS ,!
M1N TEMP]ATURE .;,T 7IN DEGREES
,CELSIUS7 (! ,ATLANTIC ,OC1N 2T
LATITUDES #DJ;DG;,N & #DJ;DG;,S C 2
MODEL$ 0": .;D IS ! DEP? 7IN MET]S74
A4 ,MAK+ A ,TA# ,MAKE A TA# ( VALUES
%[+ ! M1N TEMP]ATURE = DEP?S F #AJJJ
MET]S 6#ACJJ MET]S 9 #EJ MET] 9T]VALS4
B4 ,US+ A ,GRAPH ,GRAPH ! MODEL4 ,USE
YR GRAPH 6E/IMATE ! DEP? AT : ! M1N
TEMP]ATURE IS #D;DG,C4
#CD4 .,,MULTI-.,,/EP .,,PRO#M ,F #AIIC
6#BJJB1 ! NUMB] .;N 7IN BILLIONS7 ( %>ES
( /OCK SOLD ON ! ,NEW ,YORK ,/OCK
,EX*ANGE C 2 MODEL$ 0": .;T IS ! NUMB] (
YE>S S9CE #AIIC4
A4 ,GRAPH ! MODEL4
B4 .,DESCRIBE ! G5]AL TR5DS %[N 0!
GRAPH4
C4 ,E/IMATE ! YE> :5 ! NUMB] ( %>ES (
/OCK SOLD 0 F/ GRT] ?AN #AJJ BILLION4
#CE4 .,,EXT5D$ .,,RESPONSE ,! A3EL],N
DUE 6GRAV;Y .;G 7IN MET]S P] SECOND
SQU>$7 *ANGES Z ALTITUDE *ANGES & IS
GIV5 0! FUNC;N ": .;H IS ! ALTITUDE 7IN
MET]S7 ABV SEA LEVEL4
A4 ,GRAPH ,GRAPH ! FUNC;N4
B4 ,APPLY ,A M.TA9E] IS CLIMB+ 6A
HEI<T ( #HJJJ MET]S4 ,:AT IS ! VALUE (
.;G AT ? ALTITUDE8
C4 .,APPLY ,A SPACECRAFT R1*ES AN
ALTITUDE ( #AAB KILOMET]S ABV ,E>?4 ,:AT
IS ! VALUE ( .;G AT ? ALTITUDE8
D4 ,EXPLA9 .,DESCRIBE :AT HAPP5S 6!
VALUE ( .;G Z ALTITUDE 9CR1SES4
,PICTURE3 ,? SPACECRAFT R1*$ AN
ALTITUDE ( #AAB KM 9 #BJJD4
.K ..,,"W$-,,\ ,,SOLU;NS ONP4.,,WSI
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
------------------------------------#EGA
#CF4 .,,*ALL5GE ,Y NE$ 6BUILD A
CYL9DRICAL WAT] TANK US+ #AJJ CUBIC FEET
( 3CRETE4 ,! SIDES &! BASE (! TANK M/ 2
#A FOOT ?ICK4
A4 ,WRITE AN EQU,N T GIVES ! TANK'S
9N] HEI<T .;H 9 T]MS ( XS 9N] RADIUS .R4
B4 ,WRITE AN EQU,N T GIVES ! VOLUME
.;,V ( WAT] T ! TANK C HOLD Z A FUNC;N (
.R4
C4 ,GRAPH ! EQU,N F "P 7;B74 ,:AT
VALUES ( .;R & .;H MAXIMIZE ! TANK'S
CAPAC;Y8
,MIX$ ,REVIEW
.,,PREVIEW ,PREP>E = ,LESSON #H.D 9
,EXS4 #CG-DE4
,FACTOR ! EXPRES.N4
.#CG4 .;X #B -- #FD 7.P4 #BEB @7
.#CH4 .;X #B -- #H .;X -- #DH 7.P4
#BEB @7
.#CI4 #AH .;X #B -- #CG .;X -- #BJ
7.P4 #BEI @7
.#DJ4 #AB .;X #B -- #AE .;X -- #AH
7.P4 #BEI @7
.#DA4 #E .;X #B @+ #BB .;X -- #CJ 7.P4
#BEI @7
.#DB4 #E .;X #C @+ #DJ 7.P4 #CEC @7
.#DC4 .;X #C -- #D .;X #B @+ #H .;X --
#CB 7.P4 #CEC @7
.#DD4 .;X #C @+ #B .;X #B -- #CE .;X
7.P4 #CEC @7
.#DE4 .;X #E -- #I .;X #C -- #CF .;X
7.P4 #CEC @7
,SIMPLIFY ! EXPRES.N4 ,TELL :
PROP]TIES ( EXPON5TS Y US$4 7.P4 #CCJ @7
.#DF4
.#DG4
.#DH4
.#DI4
.#EJ4
.#EA4
.#EB4
.#EC4
,,QUIZ .= .,LESSONS .#H..A-.H..C
,! V>IA#S .;X & .;Y V>Y 9V]SELY4 ,USE
! GIV5 VALUES 6WRITE AN EQU,N RELAT+ .;X
& .Y4 ,!N F9D .;Y :5 .;X .K --#D4 @7 P4
#EEA @7
.#A4 .;X .K #H1 .;Y .K #C
.#B4 .;X .K #B1 .;Y .K --#I
.#C4 .;X .K --#E1
.#D4 @1 .;Y .K --.#CB
,GRAPH ! FUNC;N4
.#E4 @7 P4 #EEH @7
.#F4 @7 P4 #EEH @7
.#G4 @7 P4 #EEH @7
.#H4 @7 P4 #EFE @7
.#I4 @7 P4 #EFE @7
.#AJ4 @7 P4 #EFE @7
.#AA4 ,,S(TBALL ,A PIT*] ?R[S #AF
/RIKES 9 H] F/ #CH PIT*ES4 ,! TA# %[S H[
! PIT*]'S /RIKE P]C5TAGE *ANGES IF %E
?R[S .;X 3SECUTIVE /RIKES AF ! F/ #CH
PIT*ES4 ,WRITE A R,NAL FUNC;N =! /RIKE
P]C5TAGE 9 T]MS ( X4 ,GRAPH ! FUNC;N4
,H[ _M 3SECUTIVE /RIKES M/ ! PIT*] ?R[
6R1* A /RIKE P]C5TAGE ( #J.FJ8 @7 P4
#EEH @7
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
;X3 ,TOTAL ,/RIKE3 ,TOTAL PIT*ES3
/RIKES P]C5TAGE
#J3 #AF3 #CH3 #J.DB
#E3 #BA3 #DC3 #J.DI
#AJ3 #BF3 #DH3 #J.ED
.;X @3 ;X@+#AF3 ;X@+#CH3 @8
.,,EXTRA .,,PRACTICE = ,LESSON #H.C1
P4 #AJAG
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#EGB
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
..,,/ATE ,,TE/ ,,PRACTICE
_+CLASSZONE.COM_:
,LESSONS #H.A-HC
.#A4 .,,MULTI-.,,/EP .,,PRO#M ,YR
FAMILY BUYS A PHOTO PR9T] 6PR9T \
DIGITAL PICTURES4 ,! PR9T] CO/S 4#BJJ4
,! 9K & PAP] CO/ AB @4#.FJ = EA* PHOTO Y
PR9T4
.A4 ,WRITE AN EQU,N T GIVES ! AV]AGE
CO/ (A PR9T$ PHOTO Z A FUNC;N (! NUMB] (
PHOTOS PR9T$4
.B4 ,GRAPH ! FUNC;N F "P 7A74 ,USE !
GRAPH 6E/IMATE ! NUMB] ( PHOTOS Y H
6PR9T 2F ! AV]AGE CO/ DROPS TO 4#AJ P]
PR9T$ PHOTO4
.C4 ,:AT HAPP5S 6! AV]AGE CO/ Z !
NUMB] ( PHOTOS PR9T$ 9CR1SES8
.#B4 .,,MULTI-.,,/EP .,,PRO#M ,A FOOD
MANUFACTUR] WANTS 6F9D ! MO/ E6ICI5T
PACKAG+ =A CANI/] ( OATM1L )A VOLUME (
#AFFC CUBIC C5TIMET]S4
.A4 ,USE ! =MULA =! VOLUME (A CYL9D]1
.;,V .K .;R #B .;H @1 6WRITE AN EQU,N T
GIVES ! HEI<T .;H (A POSSI# CANI/] 9
T]MS ( XS RADIUS .R4
.B4 ,WRITE AN EQU,N T GIVES ! CANI/]'S
SURFACE >EA ;,S 9 T]MS ( XS RADIUS .;R
0SUB/ITUT+ ! EXPRES.N = .;H F "P 7A7 96!
=MULA =! SURFACE >EA (A CYL9D]1 ;,S .K
#B ;R #B @+ .#B .RH4
.C4 ,GRAPH ! EQU,N F "P 7;B7 US+ A
GRAPH+ CALCULATOR4 ,:AT >E ! DIM5.NS .;R
& .;H (! CANI/] T USES ! L1/ MAT]IAL
POSSI#8
.#C4 .,,%ORT .,,RESPONSE ,! TA# %[S !
NUMB] .;Y ( C&Y BOXES A MANUFACTUR]
SELLS EA* MON? AT DI6]5T PRICES .;X 7IN
DOLL>S74 ,D ! DATA %[ 9V]SE V>I,N8
.,EXPLA9 YR R1SON+4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #E3 #F3 #G3 #H
.;Y @3 #HJJ3 #FFG3 #EGA3 #EJJ
.#D4 .,,OP5-.,,5D$ ,WRITE A R,NAL
FUNC;N ^: DOMA9 IS ALL R1L NUMB]S EXCEPT
.;X .K #B & .;X .K #C4
.#E4 .,,GR#A;,,DD$ .,,ANSW] ,! V>IA#S
.;X & .;Y V>Y 9V]SELY1 & .;Y .K #D :5
.;X .K #E4 ,:AT IS ! VALUE ( .;Y :5 .;X
.K #AJ8
.#F4 .,,EXT5D$ .,,RESPONSE ,! BODY
MASS 9DEX .;B (A P]SON V>IES DIRECTLY )!
P]SON'S WEI<T .;W & 9V]SELY )! SQU>E (!
P]SON'S HEI<T .H4 ,A P]SON :O IS #A.F
MET]S TALL & WEI<S #EA.B KILOGRAMS HAS A
BODY MASS 9DEX ( #BJ4
.A4 ,WRITE AN EQU,N T RELATES .;B1 .;W
@1 & .H4
.B4 ,USE ! EQU,N F "P 7A7 6-PLETE !
TA# 2L4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,BODY MASS 9DEX3 ,HEI<T 7;M73 ,WEI<T
7KG7
#BJ3 @8@3 #DE
@8@3 #A1D3 #DA
#AI3 #A.E3 @8
.C4 ,SUPPOSE TWO P WEI< ! SAME1 B !
HEI<T ( "O P]SON IS #AJ@3P GRT] ?AN !
HEI<T (! O!R P]SON4 .,-P>E ! BODY MASS
9DICES (! TWO P4
.#G4 .,,GRI4$ .,,ANSW] ,! 9T5S;Y .,I
(A S.D 7IN WATTS P] SQU>E MET]7 V>IES
9V]SELY )! SQU>E (! 4T.E .;D 7IN MET]S7
F ! S\RCE (! S.D4 ,AT A 4T.E ( #A MET] F
! /AGE1 ! S.D 9T5S;Y (A ROCK 3C]T IS AB
#AJ WATTS P] SQU>E MET]4 ,:AT IS !
9T5S;Y (! S.D Y HE> IF Y >E #AE MET]S F
! /AGE8
.#H4 .,,%ORT .,,RESPONSE ,! VALUE ;,M
7IN DOLL>S7 (A MOTORCYCLE .;T YE>S AF X
0 PUR*AS$ NEW C 2 E/IMAT$ US+ ! FUNC;N
.A4 ,E/IMATE ! MOTORCYCLE'S VALUE #E
YE>S AF X 0 PUR*AS$4
.B4 ,:AT DOES ! VALUE (! MOTORCYCLE
APPROA* Z "T PASSES8 .,EXPLA94
------------------------------------#EGC
#H.D ,MULTIPLY & ,DIVIDE ,R,NAL
,EXPRES.NS
.,2F ,Y GRAPH$ R,NAL FUNC;NS4
.,N[ ,Y W MULTIPLY & DIVIDE R,NAL
EXPRES.NS4
.,:Y8 ,S Y C -P>E ! E6ICI5CIES ( TWO
DESIGNS1 Z 9 ,EX4 #EA4
,KEY ,VOCABUL>Y
99 ..SIMPLIFI$ =M (A R,NAL .EXPRES.N
99 RECIPROCAL1 P4 #D
,SIDEB>3
,/&>DS
.#G..J .,/UD5TS ADD1 SUBTRACT1
.MULTIPLY1 .DIVIDE1 .REDUCE @1 &
EVALUATE ..R,NAL EXPRES.NS ) MONOMIAL &
POLYNOMIAL .DENOM9ATORS & SIMPLIFY
-PLICAT$ R,NAL EXPRES.NS1 9CLUD+ ^? )
NEGATIVE EXPON5TS 9 ! DENOM9ATOR4
,A R,NAL EXPRES.N IS 9 .SIMPLIFI$ .=M
IF XS NUM]ATOR & DENOM9ATOR H NO -MON
FACTORS 7O!R ?AN +-#A74 ,6SIMPLIFY A
R,NAL EXPRES.N1 APPLY ! FOLL[+ PROP]TY4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,SIMPLIFY+ ,R,NAL ,EXPRES.NS
,LET .A1 .;B @1 & .;C 2 EXPRES.NS )
.;B .K #J & .;C .K #J4 ,!N ! FOLL[+
PROP]TY APPLIES4
,PROP]TY
,EXAMPLES
,SIMPLIFY+ A R,NAL EXPRES.N USU,Y
REQUIRES TWO /EPS4 ,F/1 FACTOR !
NUM]ATOR & DENOM9ATOR4 ,!N1 DIVIDE \ ANY
FACTORS T >E -MON 6BO? ! NUM]ATOR &
DENOM9ATOR4 ,"H IS AN EXAMPLE3
,NOTICE T Y C DIVIDE \ -MON FACTORS 9
! SECOND EXPRES.N ABV4 ,H["E1 Y _C
DIVIDE \ L T]MS 9 ! ?IRD EXPRES.N4
,EXAMPLE #A ,SIMPLIFY A R,NAL EXPRES.N
,,AVOID ,,]RORS
,D N DIVIDE \ V>IA# T]MS T >E N
FACTORS4
,SIMPLIFY3
------------------------------------#EGD
.,,E6ICI5CY ,MANUFACTUR]S (T5 PACKAGE
_! PRODUCTS 9 A WAY T USES ! L1/ AM.T (
PACKAG+ MAT]IAL4 ,"O M1SURE (! E6ICI5CY
(A PACKAGE IS ! RATIO ( XS SURFACE >EA
6XS VOLUME4 ,! SMALL] ! RATIO1 ! M
E6ICI5T ! PACKAG+4
,EXAMPLE #B ,SOLVE A MULTI-/EP PRO#M
.,,PACKAG+ ,A -PANY MAKES A T9 6HOLD
FLAVOR$ POPCORN4 ,! T9 IS A RECTANGUL>
PRISM )A SQU>E BASE4 ,! -PANY IS DESIGN+
A NEW T9 )! SAME BASE & TWICE ! HEI<T (!
OLD T94
99 ,F9D ! SURFACE >EA & VOLUME ( EA*
T94
99 ,CALCULATE ! RATIO ( SURFACE >EA
6VOLUME = EA* T94
99 ,:AT D ! RATIOS TELL Y AB !
E6ICI5CIES (! TWO T9S8
,SOLU;N
.,,/EP .#C 2C ! LEFT SIDE (! 9EQUAL;Y
HAS A GRT] NUM]ATOR ?AN ! "R SIDE & BO?
H ! SAME 7POSITIVE7 DENOM9ATOR4 ,! RATIO
( SURFACE >EA 6VOLUME IS .GRT] =! OLD T9
?AN =! NEW T94 ,S1 ! OLD T9 IS .LESS
E6ICI5T ?AN ! NEW T94
.,GUID$ .,PRACTICE = ,EXAMPLES #A & #B
,SIMPLIFY ! EXPRES.N1 IF POSSI#4
.#A4
.#B4
.#C4
.#D4
.#E4
.#F4
.#G4 .,,:AT .,,IF8 ,9 ,EXAMPLE #B1
SUPPOSE ! NEW POPCORN T9 IS ! SAME HEI<T
Z ! OLD T9 B HAS A BASE ) SIDES TWICE Z
L;G4 ,:AT IS ! RATIO ( SURFACE >EA
6VOLUME = ? T98
------------------------------------#EGE
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,MULTIPLY+ ,R,NAL ,EXPRES.NS
,! RULE = MULTIPLY+ R,NAL EXPRES.NS IS
! SAME Z ! RULE = MULTIPLY+ NUM]ICAL
FRAC;NS3 MULTIPLY NUM]ATORS1 MULTIPLY
DENOM9ATORS1 & WRITE ! NEW FRAC;N 9
SIMPLIFI$ =M4
,LET .A1 .;B1 .;C @1 & .;D 2 EXPRES.NS
) .;B .K #J & .;D .K #J4
,PROP]TY
,EXAMPLE
..,EXAMPLE #C ,/&>DIZ$ ,TE/ .,PRACTICE
,:AT IS A SIMPLIFI$ =M (
.,A
.;,B #G;X #F ;Y
;C .#G;X #AA .;Y
;,D #G;X #G ;Y #D/C
,,ANO!R ,,WAY
,9 ,EXAMPLE #C1 Y C AL F/ SIMPLIFY EA*
FRAC;N1 !N MULTIPLY1 & F9,Y SIMPLIFY !
RESULT3
,SOLU;N
,! CORRECT ANSW] IS ,B4 7..,A7 7;,B7
7;,C7 7.;,D7
,EXAMPLE #D ,MULTIPLY R,NAL EXPRES.NS
.,MULTIPLY
------------------------------------#EGF
,EXAMPLE #E ,MULTIPLY A R,NAL EXPRES.N
0A POLYNOMIAL
,MULTIPLY
..,GUID$ ,PRACTICE = ,EXAMPLES #C1D1 &
.#E
,MULTIPLY ! EXPRES.NS4 ,SIMPLIFY !
RESULT4
.#H4
.#I4
.#AJ4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,DIVID+ ,R,NAL ,EXPRES.NS
,6DIVIDE "O R,NAL EXPRES.N 0ANO!R1
MULTIPLY ! F/ R,NAL EXPRES.N 0!
RECIPROCAL (! SECOND R,NAL EXPRES.N4
,LET .A1 .;B1 .;C @1 & .;D 2 EXPRES.NS
) .;B @6.K #J1 .;C @6.K #J & .;D @6.K
#J4
,PROP]TY
,EXAMPLES
,EXAMPLE #F ,DIVIDE R,NAL EXPRES.NS
,DIVIDE3
------------------------------------#EGG
,EXAMPLE #G ,DIVIDE A R,NAL EXPRES.N
0A POLYNOMIAL
,DIVIDE3
..,GUID$ ,PRACTICE = ,EXAMPLES #F &
.#G
,DIVIDE ! EXPRES.NS4 ,SIMPLIFY !
RESULT4
.#AA4
.#AB4
#H.D ,EX]CISES
,,HOME"W ,,KEY6
.K ,,"W$-,,\ ,,SOLU;NS .ON P4 ,,WS#AE
..= ,EXS4 #G1BE1 & .#DI
.K ,,/&>DIZ$ ,,TE/ ,,PRACTICE .,EXS4
#B1BJ1 #BC1EJ1 .& #EB
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3
,6DIVIDE "O R,NAL EXPRES.N 0ANO!R1
MULTIPLY ! F/ R,NAL EXPRES.N 0! @8 (!
SECOND R,NAL EXPRES.N4
.#B4 .,,WRIT+ ,H[ D Y "K :5 A R,NAL
EXPRES.N IS SIMPLIFI$8
.,,R1SON+ ,MAT* ! R,NAL EXPRES.N ) XS
SIMPLIFI$ =M4
,,EXAMPLE #A ON P4 #EGC = ,EXS4 #C-BJ
.#C4
.#D4
.#E4
.,A4
.,B4
.,C4
.,,SIMPLIFY+ ,SIMPLIFY ! R,NAL
EXPRES.N1 IF POSSI#4
.#F4
.#G4
.#H4
.#I4
.#AJ4
.#AA4
.#AB4
.#AC4
.#AD4
.#AE4
.#AF4
.#AG4
------------------------------------#EGH
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 SIMPLIFY+ ! R,NAL EXPRES.N4
.#AH4
.#AI4
.#BJ4 .,,MULTIPLE .,,*OICE ,: R,NAL
EXPRES.N IS 9 SIMPLIFI$ =M8
7.,A7
7.;,B7
7.;,C7
7.;,D7
.,,EXAMPLE .#B ON .P4 #EGD = ,EXS4
#BA-BC
..,,GEOMETRY ,A F>M] WANTS 6F;E 9 !
FIELD %[N4 ,WRITE A SIMPLIFI$ R,NAL
EXPRES.N =! RATIO (! FIELD'S P]IMET] 6XS
.>EA4
.#BA
.#BB4
.#BC4 .,,%ORT .,,RESPONSE ,: (! FIELDS
9 ,EX]CISES #BA & #BB HAS ! L[] F5C+ CO/
P] UNIT ( >EA8 .,EXPLA94
..,,EXAMPLES #C1D1 & .#E ON .PP4
#EGE-EGF = ,EXS4 #BD-CC
,,MULTIPLY+ ,MULTIPLY ! EXPRES.NS4
,SIMPLIFY ! RESULT4
.#BD4
.#BE
.#BF4
.#BG4
.#BH4
.#BI4
.#CJ4
.#CA4
.#CB4
.#CC4
..,,EXAMPLES #F & .#G ON PP4 #EGF-EGG
= ,EXS4 #CD-DC
,,DIVID+ ,DIVIDE ! EXPRES.NS4
,SIMPLIFY ! RESULT4
.#CD4
.#CE4
.#CF4
.#CG4
.#CH4
.#CI4
.#DJ4
.#DA4
.#DB4
.#DC4
.K ..,,"W$-,,\ ,,SOLU;NS NN ;N
;,W"K.#AA
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#EGI
.,,PO9T .,,4CONT9U;Y ,9 ,EX]CISES
#DD-DF1 USE ! FOLL[+ 9=M,N4
,! GRAPH (A R,NAL FUNC;N C H A HOLE 9
X1 CALL$ A .PO9T .4CONT9U;Y @1 ": !
FUNC;N IS UNDEF9$4 ,AN EXAMPLE IS %[N
2L4
,! GRAPH ( .;Y IS ! SAME Z ! GRAPH (
.;Y .K .;X -- #D EXCEPT T "! IS A HOLE
AT 7--#D1 --#H7 2C ! R,NAL FUNC;N IS N
DEF9$ :5 .;X .K --#D4
,GRAPH ! R,NAL FUNC;N4 ,USE AN OP5
CIRCLE =A PO9T 4CONT9U;Y4
.#DD4
.#DE4
.#DF4
.#DG4 .,,*ALL5GE ,F9D ! RATIO (!
P]IMET] 6! >EA (! TRIANGLE %[N AT ! "R4
,,PRO#M ,,SOLV+
.,,EXAMPLE#B ON P4 #EGD = ,EXS4 #DH1
#EJ-EB
.#DH .,,GEOMETRY ,F9D ! RATIO (!
VOLUME (! SQU>E PYRAMID 6! VOLUME (!
9SCRIB$ C"O4 ,WRITE YR ANSW] 9 SIMPLIFI$
=M4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#DI .,,5T]TA9;T ,F #AIIB 6#BJJB1 !
GROSS TICKET SALES .;,S 7IN MILLIONS (
DOLL>S7 6,BROADWAY %[S &! TOTAL ATT5D.E
.,A 7IN MILLIONS7 AT ! %[S C 2 MODEL$ BY
&
": .;T IS ! NUMB] ( YE>S S9CE #AIIB4
,WRITE A MODEL =! .AV]AGE DOLL> AM.T A
P]SON PD P] TICKET Z A FUNC;N (! YE>4
,:AT 0 ! AV]AGE AM.T A P]SON PD P]
TICKET 9 #AIII8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#EJ4 .,,%ORT .,,RESPONSE ,ALM ALL (!
5]GY G5]AT$ 0A L;G-4T.E RUNN] IS REL1S$
9 ! =M ( H1T4 ,=A RUNN] ) HEI<T .;,H &
SPE$ .;,V @1 ! RATE .;H ( H1T G5]AT$ &!
RATE .;H ( H1T REL1S$ C 2 MODEL$ 0.;H A
.K .;K,.;,H #C .;,V #B & .;H ;R .K
.;K@:.;,H ": .;K @1 & .;K #J >E 3/ANTS4
A4 ,WRITE ! RATIO ( H1T G5]AT$ 6H1T
REL1S$4 ,SIMPLIFY ! EXPRES.N4
B4 ,:5 ! RATIO ( H1T G5]AT$ 6H1T
REL1S$ EQUALS #A1 H[ IS SPE$ RELAT$
6HEI<T8 ,DOES A TALL] OR %ORT] RUNN] H !
ADVANTAGE8 .,EXPLA94
------------------------------------#EHJ
#EA4 .,,MULTI-.,,/EP .,,PRO#M ,A
MANUFACTUR] IS -P>+ TWO DESIGNS =A WAT]
T[]3 A SPH]E &A CYL9D]4 ,BO? DESIGNS H !
SAME VOLUME &! SAME RADIUS4
A4 ,%[ T ! HEI<T .;H (! CYL9DRICAL
TANK IS .;R @4
B4 ,WRITE AN EXPRES.N =! SURFACE >EA (
EA* TANK 9 T]MS ( .R4
C4 ,F9D ! RATIO (! SURFACE >EA (!
SPH]ICAL TANK 6! SURFACE >EA (!
CYL9DRICAL TANK4 .,EXPLA9 :AT ! RATIO
TELLS Y AB : WAT] T[] WD TAKE LESS
MAT]IAL 6BUILD4
#EB4 .,,EXT5D$ .,,RESPONSE ,! SURFACE
>EA ;,S &! VOLUME .;,V (A CYL9DRICAL C
>E GIV5 0.;,S .K .#B;NR #B @+ .#B;NRH &
.;,V .K .NR #B .;H ": .;R IS ! RADIUS &
.;H IS ! HEI<T4
A4 .,MODEL ,WRITE & SIMPLIFY AN
EXPRES.N =! E6ICI5CY RATIO
B4 .,CALCULATE ,F9D ! E6ICI5CY RATIO =
EA* C LI/$ 9 ! TA#4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 .,S\P .C @3 .,C(FEE .C @3 .,PA9T
.C
.,HEI<T @1 @3 #AJ.B CM3 #AE.I CM3
#AI.D CM
,RADIUS1 .;R @3 #C.D CM3 #G.H CM3 #H.D
CM
C4 .,-P>E ,RANK ! ?REE CANS 9 "P 7;B7
AC 6E6ICI5CY4 .,EXPLA9 YR RANK+4
#EC4 .,,*ALL5GE ,A FUEL /ORAGE 3TA9]
IS %AP$ L A CYL9D] )A HEMISPH]E ON EA*
5D1 Z %[N4 ,! L5G? (! CYL9D] IS ;I &!
RADIUS ( EA* HEMISPH]E IS R4 ,%[ T !
RATIO (! SURFACE >EA 6! VOLUME (! 3TA9]
IS
,MIX$ ,REVIEW
.,,PREVIEW ,PREP>E = ,LESSON #H.E 9
,EXS4 #ED-EI4
,F9D ! GRTE/ -MON FACTOR &! L1/ -MON
MULTIPLE (! PAIR ( NUMB]S1 7.P4 #IGH @7
.#ED4 #DH1 #HJ
.#EE4 #ABJ1 #AEE
.#EF4 #CH1 #IE
.#EG4 #EB1 #IA
.#EH4 #FF1 #AED
.#EI4 #CFJ1 #DEJ
,F9D ! PRODUCT1 7.P4 #CDF @7
.#FJ4 .;X @7 .;X #B @+ #D .;X -- #G7
.#FA4 @7 .;X @+ #I7@7 .;X -- #E7
.#FB4 @7 .;X @+ #AA7 @7 .;X -- #G7
.#FC4 @7 .;X @+ #B7@7 .;X #B -- #F .;X
@+ #AJ7
.#FD4 7#C .;X -- #G7@7 .;X #B -- #E
.;X @7
.#FE4 @7 .;X @+ #E7@7 .;X #C @+ #H .;X
#B @7
.,,EXTRA .,,PRACTICE = ,LESSON #H.D1
P4 #AJAG
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#EHA
,GRAPH+ ,CALCULATOR ,ACTIV;Y3 #H.D
,V]IFY ,OP],NS ) ,R,NAL ,EXPRES.NS
,USE AF ,LESSON #H;,A
@A.,HOME,TUTOR _+CLASSZONE.COM_:
,KEY/ROKES
,,"Q ,H[ C Y USE A GRAPH+ CALCULATOR
6V]IFY ! RESULTS ( OP],NS ON R,NAL
EXPRES.NS8
,EXAMPLE ,*ECK A SIMPLIFI$ R,NAL
EXPRES.N 9 TWO WAYS
,SIDEB>3
,/&>DS
.#G..J .,/UD5TS ADD1 SUBTRACT
MULTIPLY1 DIVIDE1 .REDUCE @1 & EVALUATE
..R,NAL EXPRES.NS ) MONOMIAL &
POLYNOMIAL .DENOM9ATORS & SIMPLIFY
-PLICAT$ R,NAL EXPRES.NS1 9CLUD+ ^? )
NEGATIVE EXPON5TS 9 ! DENOM9ATOR4
,SIMPLIFY @4 ,!N V]IFY ! RESULT
NUM]IC,Y & GRAPHIC,Y4
,,/EP #A ,SIMPLIFY EXPRES.N4
,SIMPLIFY ! R,NAL EXPRES.N 0FACTOR+ !
NUM]ATOR & DENOM9ATOR1 !N DIVID+ \ -MON
FACTORS4
,,/EP #B ,5T] EXPRES.NS
,5T] ! ORIG9AL EXPRES.N Z .;Y ;,Y.'
.-&! SIMPLIFI$ RESULT Z .;Y ;R.' .-,USE
! .?ICK GRAPH /YLE = .;Y ;R.'.-
,,/EP #C ,4PLAY TA#
,USE ! .TA# F1TURE 6EXAM9E CORRESPOND+
VALUES (! TWO EXPRES.NS4
,,/EP #D ,4PLAY GRAPHS
,PUT YR CALCULATOR 9 .3NECT$ MODE4
,4PLAY ! GRAPHS 9 AN APPROPRIATE VIEW+
W9D[4
,PRACTICE
,SIMPLIFY ! EXPRES.N4 ,V]IFY YR RESULT
NUM]IC,Y & GRAPHIC,Y4
.#A4
.#B4
.#C4
,P]=M ! 9DICAT$ OP],N & SIMPLIFY4
,V]IFY YR RESULT NUM]IC,Y & GRAPHIC,Y4
.#D4
.#E4
.#F4
------------------------------------#EHB
#H.E ,ADD & ,SUBTRACT ,R,NAL
,EXPRES.NS
.,2F ,Y MULTIPLI$ & DIVID$ R,NAL
EXPRES.NS4
.,N[ ,Y W ADD & SUBTRACT R,NAL
EXPRES.NS4
.,:Y8 ,S Y C DET]M9E MON?LY C> LOAN
PAY;TS1 Z 9 ,EX4 #DC4
,KEY ,VOCABUL>Y
99 -PLEX FRAC;N
,SIDEB>3
,/&>DS
..#G.J ,/UD5TS ADD1 .SUBTRACT @1
MULTIPLY1 DIVIDE1 REDUCE1 & EVALUATE
..R,NAL EXPRES.NS ) MONOMIAL &
POLYNOMIAL DENOM9ATORS & SIMPLIFY
-PLICAT$ R,NAL .EXPRES.NS @1 9CLUD+ ^? )
NEGATIVE EXPON5TS 9 ! DENOM9ATOR4
,Z ) NUM]ICAL FRAC;NS1 ! PROC$URE US$
6ADD 7OR SUBTRACT7 TWO R,NAL EXPRES.NS
DEP5DS ^U :E!R ! EXPRES.NS H .L OR
.UNLIKE DENOM9ATORS4
,,KEY ,,3CEPT .= .,YR .NOTEBOOK
,A4+ OR ,SUBTRACT+ ) ,L ,DENOM9ATORS
,6ADD 7OR SUBTRACT7 R,NAL EXPRES.NS )
.L DENOM9ATORS1 SIMPLY ADD 7OR SUBTRACT7
_! NUM]ATORS4 ,!N PLACE ! RESULT OV] !
-MON DENOM9ATOR4
,LET .A1 .;B @1 & .;C 2 EXPRES.NS )
.;C @+ #J4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 .,A4I;N @3 .,SUBTRAC;N
.,PROP]TIES @3 @3
.,EXAMPLES @3 @3
,EXAMPLE #A ,ADD OR SUBTRACT ) L
DENOM9ATORS
,P]=M ! 9DICAT$ OP],N4
.A4
.B4
,SOLU;N
.A4
.B4
.,GUID$ .,PRACTICE = .,EXAMPLE .#A
,P]=M ! 9DICAT$ OP],N & SIMPLIFY4
.#A4
.#B
.#C4
.#D4
------------------------------------#EHC
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,A4+ OR ,SUBTRACT+ ) ,UNLIKE
,DENOM9ATORS
,6ADD 7OR SUBTRACT7 TWO R,NAL
EXPRES.NS ) .UNLIKE DENOM9ATORS1 F9D A
-MON DENOM9ATOR4 ,REWRITE EA* R,NAL
EXPRES.N US+ ! -MON DENOM9ATOR4 ,!N ADD
7OR SUBTRACT74
,LET .A1 .;B1 .;C @1 & .;D 2 EXPRES.NS
) .;C .K #J & .;D .K #J4
,A4I;N
,SUBTRAC;N
,Y C ALW F9D A -MON DENOM9ATOR ( TWO
R,NAL EXPRES.NS 0MULTIPLY+ _!
DENOM9ATORS1 Z %[N ABV4 ,H["E1 IF Y USE
! L1/ -MON DENOM9ATOR 7,,LCD71 : IS !
L1/ -MON MULTIPLE 7,,LCM7 (!
DENOM9ATORS1 Y MAY H LESS SIMPLIFY+ 6D4
,EXAMPLE #B ,F9D A L1/ -MON MULTIPLE
7,,LCM7
,F9D ! L1/ -MON MULTIPLE ( #D .;X ;C
#B -- #AF & .#F;X #B -- .#BD;X @+ #BD4
,SOLU;N
.,,/EP .#A ,FACTOR EA* POLYNOMIAL4
,WRITE NUM]ICAL FACTORS Z PRODUCTS (
PRIMES4
#D;X #B -- #AF .K #D7;X #B -- #D7 .K
7#B #B @77;X @+ #B77;X--#B7
.#F;X #B -- .#BD;X @+ #BD .K #F7;X #B
-- #D;X @+ #D7 .K 7#B77#C77JC--#B7 #B
.,,/EP .#B ,=M ! ,,LCM 0WRIT+ EA*
FACTOR 6! HI<E/ P[] X O3URS 9 EI
POLYNOMIAL4
,,LCM .K 7#B #B @77#C77;X @+
#B77;X--#B7 #B .K #AB7;X @+ #B77;X--#B7
#B
,EXAMPLE #C ,ADD ) UNLIKE DENOM9ATORS
.,ADD3
,,REVIEW ,,LCDS
,= HELP ) F9D+ L1/ -MON DENOM9ATORS1
SEE P4 #IHF @4
,SOLU;N
,6F9D ! ,,LCD1 FACTOR EA* DENOM9ATOR &
WRITE EA* FACTOR 6! HI<E/ P[] X O3URS4
,NOTE T #I;X #B .K #C #B ;X #B & #C;X #B
@+ #C;X .K #C;X7;X @+ #A71 S ! ,,LCD IS
#C #B ;X #B 7;X@+ #A7 .K #I;X #B 7;X@+
#A74
------------------------------------#EHD
,,AVOID ,,]RORS
,AF Y SIMPLIFY ! NUM]ATOR1 *ECK 6SEE
IF ! NUM]ATOR HAS A FACTOR 9 -MON )!
DENOM9ATOR4 ,IF S1 ! EXPRES.N C 2
SIMPLIFI$ FUR!R4
,EXAMPLE #D ,SUBTRACT ) UNLIKE
DENOM9ATORS
,SUBTRACT3
,SOLU;N
.,GUID$ .,PRACTICE = ,EXAMPLES #B1C1 &
#D
,F9D ! L1/ -MON MULTIPLE (!
POLYNOMIALS4
.#E4 .#E;X #C & #AJ;X #B - #AE;X
..#F4 #H;X--.#AF & #AB .;X #B @+ #AB
.;X -- #GB
,P]=M ! 9DICAT$ OP],N & SIMPLIFY4
.#G4
.#H4
.#I4
.#AJ4
,,KEY ,,3CEPT .= .,YR .,NOTEBOOK
,SIMPLIFY+ ,-PLEX ,FRAC;NS
.,A .-PLEX .FRAC;N IS A FRAC;N T 3TA9S
A FRAC;N 9 XS NUM]ATOR OR DENOM9ATOR4 ,A
-PLEX FRAC;N C 2 SIMPLIFI$ US+ EI (!
ME?ODS 2L4
.,ME?OD .#A @3 ,IF NEC1 SIMPLIFY !
NUM]ATOR & DENOM9ATOR 0WRIT+ EA* Z A
S+LE FRAC;N4 ,!N DIVIDE ! NUM]ATOR 0!
DENOM9ATOR4
.,ME?OD .#B3 ,MULTIPLY ! NUM]ATOR &!
DENOM9ATOR 0! L1/ -MON DENOM9ATOR
7,,LCD7 ( .E FRAC;N 9 ! NUM]ATOR &
DENOM9ATOR4 ,!N SIMPLIFY4
------------------------------------#EHE
,EXAMPLE #E ,SIMPLIFY A -PLEX FRAC;N
7,ME?OD #A7
.,,PHYSICS ,LET_/BE ! FOCAL L5G? (A ?9
CAM]A L5S1 .;P 2 ! 4T.E 2T AN OBJECT 2+
PHOTOGRAPH$ &! L5S1 & .;Q 2 ! 4T.E 2T !
L5S &! FILM4 ,=! PHOTOGRAPH 6BE 9 FOCUS1
! V>IA#S %D SATISFY ! .L5S .EQU,N 2L4
,SIMPLIFY ! -PLEX FRAC;N4
,L5S .EQU,N3
,SOLU;N
,EXAMPLE #F ,SIMPLIFY A -PLEX FRAC;N
7,ME?OD #B7
.,SIMPLIFY3
,SOLU;N
,! ,,LCD ( ALL ! FRAC;NS 9 ! NUM]ATOR
& DENOM9ATOR IS .;X7.;X @+ #D74
..,GUID$ ,PRACTICE = ,EXAMPLES #E &
.#F
,SIMPLIFY ! -PLEX FRAC;N4
.#AA4
.#AB4
.#AC4
------------------------------------#EHF
#H.E ,EX]CISES
,HOME"W ,KEY
.K ,,"W$-,,\ ,,SOLU;NS
.K ,,/&>DIZ$ ,,TE/ ,,PRACTICE ,EXS4
#B1AE1 #BF1 #CG1 & #DD
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,A
FRAC;N T 3TA9S A FRAC;N 9 XS NUM]ATOR OR
DENOM9ATOR IS CALL$ A7;N7 @8 @4
.#B4 .,,WRIT+ .,EXPLA9 H[ 6ADD R,NAL
EXPRES.NS ) UNLIKE DENOM9ATORS4
.,,EXAMPLE .#A @3 ON P4 #EHB @6 =
,EXS4 #C-H
,,L ,,DENOM9ATORS ,P]=M ! 9DICAT$
OP],N & SIMPLIFY4
.#C4
.#D4
.#E4
.#F4
.#G4
.#H4
,,F9D+ ,,LCMS ,F9D ! L1/ -MON MULTIPLE
(! POLYNOMIALS4
.#I4 #C;X&#C7;X-#B7
.#AJ4 .#B;X #B & #D;X @+ #AB
.#AA4 #B;X&#B;X7;X--#E7
.#AB4 #BD;X #B & #H;X #B -- #AF;X
.#AC4 .;X #B -- #BE1 ;X1 & .;X -- #E
.#AD4 #I;X #B -- #AF & #C;X #B --
#B;X--#H
.,,EXAMPLE #B ON P4 #EHC = ,EXS4 #I-AE
.#AE4 .,,MULTIPLE .,,*OICE ,:AT IS !
L1/ -MON MULTIPLE (! POLYNOMIALS #C;X #B
-- #I;X & #F;X #B @8
7.,A7 #C;X7;X--#C7
7.;,B7 #F;X #B
;,C #F;X7;X--#C7
7.;,D7 #F;X #B 7;X--#C7
.,,EXAMPLES @3 .#C .& .#D ON PP4
#EHC-EHD = ,EXS4 #AF-BF
,,UNLIKE ,,DENOM9ATORS ,P]=M ! 9DICAT$
OP],N & SIMPLIFY4
.#AF4
.#AG
.#AH4
.#AI4
.#BJ4
.#BA4
.#BB
.#BC4
.#BD4
.#BE4 .,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 A4+ ! R,NAL EXPRES.NS4
#BF4 .,,MULTIPLE .,,*OICE ,: EXPRES.N
IS EQUIVAL5T TO
A
;,B
;,C
;,D
,,UNLIKE ,,DENOM9ATORS ,P]=M ! 9DICAT$
OP],N7;S7 & SIMPLIFY4
.#BG4
.#BH4
.#BI4
.#CJ4
------------------------------------#EHG
..,,EXAMPLES #E & .#F ON P4 #EHE =
,EXS4 #CA-CF
.,,SIMPLIFY+ .,,-PLEX .,,FRAC;NS
,SIMPLIFY ! -PLEX FRAC;N4
.#CA4
.#CB4
.#CC4
.#CD4
.#CE4
.#CF4
.#CG4 .,,OP5-.,,5D$ .,,MA? ,WRITE TWO
DI6]5T -PLEX FRAC;NS T EA* SIMPLIFY TO
.,,*ALL5GE ,SIMPLIFY ! -PLEX FRAC;N4
.#CH4
.#CI4
.#DJ
,,PRO#M ,,SOLV+
.,,EXAMPLE .#C #EHC = ,EX4 #DA
.#DA4 .,,JET .,,/R1M ,! TOTAL "T .;,T
7IN H\RS7 NE$$ 6FLY F ,NEW ,YORK 6,LOS
,ANGELES & BACK 7IGNOR+ LAYOV]S7 C 2
MODEL$ 0! EQU,N 9 ! DIAGRAM1 ": .;D IS !
4T.E EA* WAY 7IN MILES71 .A IS ! AV]AGE
AIRPLANE SPE$ 7IN MILES P] H\R71 & .;J
IS ! AV]AGE SPE$ (! JET /R1M 7IN MILES
P] H\R74
,REWRITE ! EQU,N S T ! "R SIDE IS
SIMPLIFI$4 ,!N F9D ! TOTAL "T IF .;D .K
#BDFH MILES1 .A .K #EAJ MI_/;H1 & .;J .K
#AAE MI_/H4
.,ANIMAT$ .,ALGEBRA .AT
_+CLASSZONE.COM_:
..,,EXAMPLES #E & .#F ON P4 #EHE =
,EXS4 #DB-DC
.#DB4 .,,ELECTRONICS ,IF TWO RESI/ORS
9 A P>ALLEL CIRCUIT H RESI/.ES .;,R ;X.'
.-& .;,R #B 7BO? 9 OHMS71 !N ! TOTAL
RESI/.E .;,R 7IN OHMS7 IS GIV5 0! EQU,N
%[N4 ,SIMPLIFY ! -PLEX FRAC;N4 ,!N F9D !
TOTAL RESI/.E IF .;,R ;X.' .K #BJJJ OHMS
& .;,R #B -- #EFJJ OHMS4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
------------------------------------#EHH
#DC4 .,,C> .,,LOANS ,IF Y BORR[ .;,P
DOLL>S 6BUY A C> & AGREE 6REPAY ! LOAN
OV] .;T YE>S AT AN ANNUAL 9T]E/ RATE (
.;I 7EXPRESS$ Z A DECIMAL71 !N YR MON?LY
PAY;T ;,M IS GIV5 0EI =MULA 2L4
.,=MULA .#A3
.,=MULA .#B3
A4 ,%[ T ! =MULAS >E EQUIVAL5T
0SIMPLIFY+ ! F/ =MULA4
B4 ,F9D YR MON?LY PAY;T IF Y BORR[
4#AE1EJJ AT AN ANNUAL 9T]E/ RATE ( #F@3P
& REPAY ! LOAN OV] #D YE>S4
#DD4 .,,EXT5D$ .,,RESPONSE ,! AM.T .,A
7IN MILLIGRAMS7 ( ASPIR9 9 A P]SON'S
BLOOD/R1M C 2 MODEL$ BY
": .;T IS ! "T 7IN H\RS7 AF "O DOSE IS
TAK54
.A4 ,GRAPH ! EQU,N US+ A GRAPH+
CALCULATOR4
.B4 ,A SECOND DOSE (! DRUG IS TAK5 #A
H\R AF ! F/ DOSE4 ,WRITE AN EQU,N 6MODEL
! AM.T (! SECOND DOSE 9 ! BLOOD/R1M4
.C4 ,WRITE & GRAPH A MODEL =! .TOTAL
AM.T ( ASPIR9 9 ! BLOOD/R1M AF ! SECOND
DOSE IS TAK54
.D4 ,AB H[ L;G AF ! SECOND DOSE HAS
BE5 TAK5 IS ! GRTE/ AM.T ( ASPIR9 9 !
BLOOD/R1M8
.#DE4 .,,*ALL5GE ,F9D ! NEXT TWO
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ALL FIVE EXPRES.NS4 ,:AT VALUE D !
EXPRES.NS APPROA*8
,MIX$ ,REVIEW
.,,PREVIEW ,PREP>E = ,LESSON #H.F 9
,EXS4 #DF-ED4
,SOLVE ! EQU,N4
.#DF4 7.P4 #AH @7
.#DG4 7.P4 #AH @7
.#DH4 7.P4 #AH @7
.#DI4 .;X #B @+ #I .;X -- #CF .K #J
7.P4 #BEB @7
.#EJ4 #C .;X #B @+ .;X -- #AD .K #J
7.P4 #BEI @7
.#EA4 #D .;X @7 .;X -- #E7 .K #D .;X
-- #CE 7.P4 #BEI @7
.#EB4 #F .;X #B -- #BE .K .;X #B 7.P4
#BFF @7
.#EC4 #D7 .;X -- #B7 #B .K #ADD 7.P4
#BFF @7
.#ED4 #C7 .;X @+ #E7 #B -- #AJ .K #AHB
7.P4 #BFF @7
,GRAPH ! FUNC;N4
.#EE4 .;Y .K #D ;X 7.P4 #DGH @7
.#EF4 .;Y .K --#B 99 #C ;X 7.P4 #DGH
@7
.#EG4 7.P4 #DGH @7
.#EH4 7.P4 #DHF @7
.#EI4 7.P4 #DHF @7
.#FJ4 7.P4 #DHF @7
.,,EXTRA .,,PRACTICE = ,LESSON #H.E1
P4 #AJAG
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#EHI
#H.F ,SOLVE ,R,NAL ,EQU,NS
.,2F ,Y SOLV$ POLYNOMIAL EQU,NS4
.,N[ ,Y W SOLVE R,NAL EQU,NS4
.,:Y8 ,S Y C MODEL MOBILE PH"O CO/S1 Z
9 ,EX4 #CH4
,KEY ,VOCABUL>Y
99 CROSS MULTIPLY+
99 EXTRANE\S SOLU;N P4 #EB
,SIDEB>3
,/&>DS
..#G.J ,/UD5TS ADD1 SUBTRACT MULTIPLY1
DIVIDE1 REDUCE1 & EVALUATE R,NAL
EXPRES.NS ) MONOMIAL & POLYNOMIAL
DENOM9ATORS & SIMPLIFY -PLICAT$ R,NAL
.EXPRES.NS @1 9CLUD+ ^? ) NEGATIVE
EXPON5TS 9 ! DENOM9ATOR4
,Y C USE CROSS MULTIPLY+ 6SOLVE A
R,NAL EQU,N :5 EA* SIDE (! EQU,N IS A
S+LE R,NAL EXPRES.N4
,,EXAMPLE #A ,SOLVE A R,NAL EQU,N
0CROSS MULTIPLY+
,SOLVE3
,! SOLU;N IS --#B4 ,*ECK ? 9 ! ORIG9AL
EQU,N4
,,EXAMPLE #B ,WRITE & USE A R,NAL
MODEL
.,,ALLOYS ,AN .ALLOY IS =M$ 0MIX+ TWO
OR M METALS4 ,/]L+ SILV] IS AN ALLOY
-POS$ ( #IB.E@3P SILV] & #G.E@3P COPP]
0WEI<T4 ,JEWELRY SILV] IS -POS$ ( #HJ@3P
SILV] & #BJ@3P COPP] 0WEI<T4 ,H[ M* PURE
SILV] %D Y MIX ) #AE \NCES ( JEWELRY
SILV] 6MAKE /]L+ SILV]8
,SOLU;N
,Y %D MIX #BE \NCES ( PURE SILV] )!
JEWELRY SILV]4
------------------------------------#EIJ
.,,GUID$ .,,PRACTICE = ,EXAMPLES #A &
#B
,SOLVE ! EQU,N 0CROSS MULTIPLY+4 ,*ECK
YR SOLU;N7;S74
.#A4
.#B4
.#C4
.#D4 .,,:AT .,,IF8 ,9 ,EXAMPLE #B1
SUPPOSE Y H #AJ \NCES ( JEWELRY SILV]4
,H[ M* PURE SILV] M/ 2 MIX$ )! JEWELRY
SILV] 6MAKE /]L+ SILV]8
.,,US+ .,,LCDS ,:5 A R,NAL EQU,N IS N
EXPRESS$ Z A PROPOR;N1 Y C SOLVE X
0MULTIPLY+ EA* SIDE (! EQU,N 0! L1/ -MON
DENOM9ATOR ( EA* R,NAL EXPRES.N4
..,,EXAMPLE #C ,/&>DIZ$ ,TE/
.,PRACTICE
,,ELIM9ATE ,,*OICES
,Y C ELIM9ATE *OICE ;,D 2C X YIELDS A
POSITIVE VALUE ON ! LEFT SIDE (! EQU,N
&A NEGATIVE VALUE ON ! "R SIDE4
,:AT IS ! SOLU;N ( @8
.,A --#AJ
.;,B --#H
.;,C --#D
.;,D #F
,SOLU;N
,! CORRECT ANSW] IS ,B4 ..,A ;,B ;,C
.;,D
,,EXAMPLE #D ,SOLVE A R,NAL EQU,N )
TWO SOLU;NS
,SOLVE3
,! SOLU;NS >E #A & #AE4 ,*ECK ^! 9 !
ORIG9AL EQU,N4
------------------------------------#EIA
.,,EXTRANE\S .,,SOLU;NS ,:5 SOLV+ A
R,NAL EQU,N1 Y MAY OBTA9 SOLU;NS T >E
EXTRANE\S4 ,2 SURE 6*ECK = EXTRANE\S
SOLU;NS 0SUB/ITUT+ BACK 96! ORIG9AL
EQU,N4
..,,EXAMPLE #E ,*ECK = EXTRANE\S
.SOLU;NS
,SOLVE3
,SOLU;N
,WRITE EA* DENOM9ATOR 9 FACTOR$ =M4 ,!
,,LCD IS @7 .;X @+ #C7@7 .;X -- #C74
,,REVIEW ,,EXTRANE\S ,,SOLU;NS
,= HELP ) EXTRANE\S SOLU;NS1 SEE P4
#EA @4
,Y C USE ALGEBRA OR A GRAPH 6*ECK :E!R
EI (! TWO SOLU;NS IS EXTRANE\S4
.,ALGEBRA ,! SOLU;N *ECKS1 B ! APP>5T
SOLU;N --#C IS EXTRANE\S1 2C SUB/ITUT+ X
9 ! EQU,N RESULTS 9 DIVI.N 0Z]O1 : IS
UNDEF9$4
,PRODNOTE3 ,PRODUC;N NOTE3 CAP;NS
ASSOCIAT$ ) ? IMAGE >E LABELS T
CORRESPOND 6TEXT )9 ! IMAGE4
,PICTURE3 ..,DIVI.N 0Z]O IS .UNDEF9$
.,GRAPH ,GRAPH & @4
,! GRAPHS 9T]SECT :5 @1 B N :5 .;X .K
--#C4
,! SOLU;N IS @4
.,,GUID$ .,,PRACTICE = ,EXAMPLES #C1
#D1 & #E
,SOLVE ! EQU,N 0US+ ! ,,LCD4 ,*ECK =
EXTRANE\S SOLU;NS4
.#E4
.#F4
.#G4
.#H4
.#I4
.#AJ4
------------------------------------#EIB
,,EXAMPLE #F ,SOLVE A R,NAL EQU,N GIV5
A FUNC;N
.,,VIDEO .,,GAME .,,SALES ,F #AIIE "?
#BJJC1 ! ANNUAL SALES .;,S 7IN BILLIONS
( DOLL>S7 ( 5T]TA9;T S(TW>E C 2 MODEL$
BY
": .;T IS ! NUMB] ( YE>S S9CE #AIIE4
,= : YE> 7 ! TOTAL SALES ( 5T]TA9;T
S(TW>E AB 4#E.C BILLION8
,,ANO!R ,,WAY
,= ALT]NATIVE ME?ODS = SOLV+ ! PRO#M 9
,EXAMPLE #F1 TURN 6PAGE #EIF =! .,PRO#M
.,SOLV+ .,"W%OP4
,SOLU;N
,2C--#B.IE IS N 9 ! DOMA9 7#J "K.K .;T
"K.K #H71 ! ONLY SOLU;N IS #B.IE4
,S1 ! TOTAL SALES ( 5T]TA9;T S(TW>E 7
AB 4#E.C BILLION AB #C YE>S AF #AIIE1 OR
9 #AIIH4
.,,GUID$ .,,PRACTICE = ,EXAMPLE #F
.#AA4 .,,:AT .,,IF8 ,USE ! 9=M,N 9
,EXAMPLE #F 6DET]M9E 9 : YE> ! TOTAL
SALES ( 5T]TA9;T S(TW>E 7 AB 4#D.E
BILLION4
#H.F ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS .ON P4
,,WS#AE ..= ,EXS4 #E1 #AE1 & .#CE
.K ..,,/&>DIZ$ ,,TE/ ,,PRACTICE ,EXS4
#B1 #AC1 #BH1 #BI1 #CD1 & .#CF
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,:5
Y WRITE Z #E .;X .K #C7 .;X @+ #B71 Y >E
@8 @4
.#B4 .,,WRIT+ ,A /UD5T SOLV$ ! EQU,N &
GOT ! SOLU;NS #D & #E4 ,:1 IF EI1 ( ^!
IS EXTRANE\S8 .,EXPLA94
.#C4 .,,R1SON+ .,DESCRIBE H[ Y C USE A
GRAPH 6DET]M9E IF AN APP>5T SOLU;N (A
R,NAL EQU,N IS EXTRANE\S4
------------------------------------#EIC
,,EXAMPLE #A
ON P4 #EHI = ,EXS4 #D-AC
,,CROSS ,,MULTIPLY+ ,SOLVE ! EQU,N
0CROSS MULTIPLY+4 ,*ECK = EXTRANE\S
SOLU;NS4
.#D4
.#E4
.#F4
.#G4
.#H4
.#I4
.#AJ4
.#AA4
.#AB4
#AC4 .,,MULTIPLE .,,*OICE ,:AT IS !
SOLU;N ( @8
,A --#E
;,B --#D
;,C --#A
;,D #D
,,EXAMPLES #C1 #D1 & #E
ON PP4 #EIJ-EIA = ,EXS4 #AD-BG
,,L1/ ,,-MON ,,DENOM9ATOR ,SOLVE !
EQU,N 0US+ ! ,,LCD4 ,*ECK = EXTRANE\S
SOLU;NS4
.#AD4
.#AE4
.#AF4
.#AG4
.#AH4
.#AI4
.#BJ4
.#BA4
.#BB4
.#BC4
.#BD4
.#BE4
.,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 ! F/ /EP ( SOLV+ !
EQU,N4
.#BF4
.#BG4
#BH4 .,,MULTIPLE .,,*OICE ,:AT IS 7>E7
! SOLU;N7;S7 ( @8
,A
;,B
;,C
;,D #C
#BI4 .,,OP5-.,,5D$ .,,MA? ,GIVE AN
EXAMPLE (A R,NAL EQU,N T Y WD SOLVE US+
CROSS MULTIPLIC,N4 ,!N GIVE AN EXAMPLE
(A R,NAL EQU,N T Y WD SOLVE 0MULTIPLY+
EA* SIDE 0! ,,LCD (! FRAC;NS4
,,*ALL5GE ,9 ,EX]CISES #CJ-CB1 A IS A
NONZ]O R1L NUMB]4 ,TELL :E!R ! ALGEBRAIC
/ATE;T IS ..ALW TRUE1 "S"TS .TRUE @1 OR
.N"E .TRUE4 .,EXPLA9 YR ANSW]4
.#CJ4 ,=! EQU,N .;X .K .A IS AN
EXTRANE\S SOLU;N4
.#CA4 ,! EQU,N HAS EXACTLY "O SOLU;N4
.#CB4 ,! EQU,N HAS NO SOLU;N4
------------------------------------#EID
,,PRO#M ,,SOLV+
,,EXAMPLE #B
ON P4 #EHI = ,EXS4 #CC-CD
.#CC4 .,,VOLLEYBALL ,S F> 9 YR
VOLLEYBALL MAT*1 Y H PUT 96PLAY #CG (!
#DD S]VES Y H ATTEMPT$4 ,SOLVE ! EQU,N
6F9D ! NUMB] ( 3SECUTIVE S]VES Y NE$
6PUT 96PLAY 9 ORD] 6RAISE YR S]VICE
P]C5TAGE 6#IJ@3P4
@A.,HOM#J;,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#CD4 .,,EXT5D$ .,,RESPONSE ,A SPE$
SKAT] TRAVELS #I KILOMET]S 9 ! SAME AM.T
( "T T X TAKES A SECOND SKAT] 6TRAVEL #H
KILOMET]S4 ,! F/ SKAT] TRAVELS #D.CH
KILOMET]S P] H\R FA/] ?AN ! SECOND
SKAT]4
A4 ,USE ! V]BAL MODEL 2L 6WRITE AN
EQU,N T RELATES ! SKAT+ "TS (! SKAT]S4
B4 ,SOLVE ! EQU,N 9 "P 7A7 6F9D !
SPE$S ( BO? SKAT]S4
C4 ,H[ L;G DID ! SKAT]S SKATE8
.,EXPLA9 YR ANSW]4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
,,EXAMPLE #F
ON P4 #EIB = ,EX4 #CE
.#CE4 .,,MUSIC .,,9DU/RY ,F #AIID "?
#BJJC1 ! NUMB] .;N 7IN MILLIONS7 (
,,CD,'S %IPP$ C 2 MODEL$ BY
": ;R IS ! NUMB] ( YE>S S9CE #AIID4
,DUR+ : YE> 0 ! TOTAL NUMB] ( ,,CD,'S
%IPP$ AB #GBJ MILLION8
#CF4 .,,EXT5D$ .,,RESPONSE ,Y C PA9T A
ROOM 9 #H H\RS4 ,"W+ TGR1 Y & YR FR C
PA9T ! ROOM 9 J #E H\RS4
A4 ,LET .;T 2 ! "T 7IN H\RS7 YR FR WD
TAKE 6PA9T ! ROOM :5 "W+ AL"O4 ,COPY &
-PLETE ! TA#4
,! FOLL[+ TA# IS 9 LI/$
=MAT4 ,= EA* CELL ! H1D+ IS %[N
FOLL[$ 0A COLON1 SPACE &! CELL
3T5TS
@3 ,Y
,"W ,RATE @* ,"T .K ,"W ,D"O3
,"W ,RATE @* ,"T .K ,"W ,D"O3 #E H\RS
,"W ,RATE @* ,"T .K ,"W ,D"O3 @8
@3 ,FR
,"W ,RATE @* ,"T .K ,"W ,D"O3 @8
,"W ,RATE @* ,"T .K ,"W ,D"O3 #E H\RS
,"W ,RATE @* ,"T .K ,"W ,D"O3 @8
B4 ,:AT IS ! SUM (! EXPRES.NS 9 !
TA#'S LA/ COLUMN8 .,EXPLA94
C4 ,WRITE & SOLVE AN EQU,N 6F9D H[ L;G
YR FR WD TAKE 6PA9T ! ROOM :5 "W+ AL"O4
.,EXPLA9 YR ANSW]4
#CG4 .,,GEOMETRY .,GOLD5 .RECTANGLES
>E RECTANGLES = : ! RATIO (! WID? .;W 6!
L5G? IS EQUAL 6! RATIO ( TO @+ .;W @4 ,!
RATIO (! L5G? 6! WID? = ^! RECTANGLES IS
CALL$ ! .GOLD5 .RATIO4 ,F9D ! VALUE (!
GOLD5 RATIO US+ A RECTANGLE )A WID? ( #A
UNIT4
.K .,,"W$-.,,\ .,,SOLU;NS .ON P4
,,WS#A
.K .,,/&>DIZ$ .,,TE/ .,,PRACTICE
------------------------------------#EIE
#CH4 .,,*ALL5GE ,LET .;X 2 ! NUMB] (
YE>S S9CE #AIIH1 LET .;G7.;X7 2 ! AV]AGE
MON?LY BILL 7IN DOLL>S7 = MOBILE PH"O
US]S 9 ! ,UNIT$ ,/ATES1 & LET .;H @7 .;X
@7 2 ! AV]AGE NUMB] ( M9UTES US$ 0,U4,S4
MOBILE PH"O US]S4 ,!N .;G @7 .;X @7 &
.;H @7 .;X @7 >E Z GIV5 2L4
.;G @7 .;X @7 .K --#J.BG .;X #C @+
#A.DJ .;X #B @+ #A.JE .;X @+ #CI.D
.;H @7 .;X @7 .K --#H.BE .;X #C @+
#EC.A .;X #B -- #G.HB .;X @+ #ACH
A4 ,WRITE A R,NAL FUNC;N .;F @7 .;X @7
T GIVES ! AV]AGE PRICE P] M9UTE .;X YE>S
AF #AIIH4
B4 ,F9D ! AV]AGE PRICE P] M9UTE 9
#AIIH4
C4 ,9 :AT YE> DID ! AV]AGE PRICE P]
M9UTE FALL 6#AA C5TS8
,,MIX$ ,,REVIEW
,GRAPH ! FUNC;N4
.#CI4 .;Y .K --#B .;X @+ #G 7.P4 #HI
@7
.#DJ4 .;Y .K .;X #B -- #H .;X @+ #BA
7.P4 #BCF @7
.#DA4 .;F @7 .;X @7 .K .;X #C -- #C
7.P4 #CCG @7
.#DB4 7.P4 #DDF @7
.#DC4 .;Y .K LOG #D .;X 7.P4 #DII @7
.#DD4 7.P4 #EEH @7
.,,PREVIEW ,PREP>E = ,LESSON #I.A 9
,EXS4 #DE-EB4
,SIMPLIFY ! EXPRES.N1 7.P4 #BFF @7
.#DE4
.#DF4
.#DG4
.#DH4
.#DI4
.#EJ4
.#EA4
.#EB4
,,QUIZ = .,LESSONS .#H..D-.H..F
,P]=M ! 9DICAT$ OP],N & SIMPLIFY1 @7
P4 #EGC @7
.#A4
.#B4
.#C4
.#D4
,P]=M ! 9DICAT$ OP],N & SIMPLIFY1 @7
P4 #EHB @7
.#E4
.#F4
.#G4
,SOLVE ! EQU,N4 ,*ECK = EXTRANE\S
SOLU;NS1 @7 P4 #EHI @7
.#H4
.#I4
.#AJ4
.#AA4
.#AB4
.#AC4
.#AD4 .,,BATT+ .,,AV]AGE ,S F> ?
BASEBALL S1SON1 Y H GOTT5 A HIT #AB "TS
\ ( #FJ AT-BATS4 ,SOLVE ! EQU,N 6F9D !
NUMB] ( 3SECUTIVE HITS Y H 6GET 6RAISE
YR BATT+ AV]AGE 6#J.CFJ4 @7 P4 #EHI @7
.,,EXTRA .,,PRACTICE = ,LESSON #H.F1
P4 #AJAG
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#EIF
,PRO#M ,SOLV+ ,"W%OP ,LESSON #H.F3
,US+ ,ALT]NATIVE ,ME?ODS
,ANO!R ,WAY 6,SOLVE ,EXAMPLE #F1 PAGE
#EIB
.,,MULTIPLE .,,REPRES5T,NS ,9 ,EXAMPLE
#F ON PAGE #EIB @1 Y SOLV$ A R,NAL EQU,N
ALGEBRAIC,Y4 ,Y C AL SOLVE R,NAL EQU,NS
US+ TA#S & GRAPHS4
,,PRO#M
.,,VIDEO .,,GAME .,,SALES ,F #AIIE "?
#BJJC1 ! ANNUAL SALES ;,S 7IN BILLIONS (
DOLL>S7 ( 5T]TA9;T S(TW>E C 2 MODEL$ BY
#J "K.K .;T "K.K #H
": .;T IS ! NUMB] ( YE>S S9CE #AIIE4
,= : YE> 7 ! TOTAL SALES ( 5T]TA9;T
S(TW>E AB 4#E.C BILLION8
,,ME?OD #A
.,US+ .A .,TA# ,! PRO#M REQUIRES SOLV+
! FOLL[+ R,NAL EQU,N3
,SIDEB>3
,/&>DS
..#G.J ,/UD5TS ADD1 SUBTRACT1
MULTIPLY1 DIVIDE1 REDUCE1 & EVALUATE
R,NAL EXPRES.NS ) MONOMIAL & POLYNOMIAL
DENOM9ATORS & SIMPLIFY -PLICAT$ R,NAL
.EXPRES.NS @1 9CLUD+ ^? ) NEGATIVE
EXPON5TS 9 ! DENOM9ATOR4
,"O WAY 6SOLVE ? EQU,N IS 6MAKE A TA#
( VALUES4 ,Y C USE A GRAPH+ CALCULATOR
6MAKE ! TA#4
.,,/EP#A .,5T] ! FUNC;N 96A GRAPH+
CALCULATOR4
..,,/EP #B ,SET .UP A TA# ( VALUES =!
FUNC;N4 ,/>T ! TA# AT Z]O S T ! F/ S"EAL
.;X -VALUES 9 ! TA# >E 9 ! DOMA9 (!
FUNC;N4 ,! /EP VALUE 7,TBL7 %D REPRES5T
"O 5TIRE YE>4
.,,/EP .#C .,CR1TE ! TA# ( VALUES4 ,Y
C SEE T .;Y #E.C :5 .;X .K #C4
,2C .;X .K #C REPRES5TS ! NUMB] ( YE>S
AF #AIIE1 TOTAL SALES ( 5T]TA9;T S(TW>E
7 AB 4#E.C BILLION 9 #AIIH4
------------------------------------#EIG
,,ME?OD #B
.,US+ .A .,GRAPH ,Y C AL USE A GRAPH
6SOLVE @4
.,,/EP .#A .,5T] ! FUNC;NS & .;Y .K
#E.C 96A GRAPH+ CALCULATOR4
.,,/EP .#B .,GRAPH ! FUNC;NS4 ,ADJU/ !
VIEW+ W9D[ S T X %[S ! PO9T 9 ! F/
QUADRANT ": ! GRAPHS 9T]SECT4
.,,/EP .#C .,F9D ! 9T]SEC;N PO9T (!
GRAPHS US+ ! CALCULATOR'S .9T]SECT
F1TURE4 ,! GRAPHS 9T]SECT AT AB
7#C.J1E.C74
,TOTAL SALES ( 5T]TA9;T S(TW>E 7 AB
4#E.C BILLION #C YE>S AF #AIIE1 OR 9 !
YE> #AIIH4
,,PRACTICE
,,R,NAL ,,EQU,NS ,SOLVE ! EQU,N US+ A
TA# & US+ A GRAPH4
.#A4
.#B4
.#C4
.#D4
.#E4
.#F4 .,,:AT .,,IF8 ,9 ! PRO#M ON PAGE
#EIF @1 SUPPOSE Y WANT 6F9D ! YE> :5
TOTAL SALES ( 5T]TA9;T S(TW>E 7 4#D.E
BILLION4 ,F9D ? YE> US+ A TA# & US+ A
GRAPH4
#G4 .,,DIV+ ,! RECOMM5D$ P]C5T .;P (
OXYG5 70VOLUME7 9 ! AIR T A DIV] BR1!S
IS GIV5 0": .;D IS ! DEP? 7IN FEET7 (!
DIV]4
A4 ,AT :AT DEP? IS AIR 3TA9+ #E@3P
OXYG5 RECOMM5D$8 ,USE A TA# 6F9D !
ANSW]4
B4 ,AT :AT DEP? IS AIR 3TA9+ #AJ@3P
OXYG5 RECOMM5D$8 ,USE A GRAPH 6F9D !
ANSW]4
------------------------------------#EIH
,EXT5.N ,SOLVE ,R,NAL ,9EQUALITIES
,USE AF LESSON #H.F
.,,GOAL ,F9D SOLU;NS ( R,NAL
9EQUALITIES4
,9 ,LESSON #H.F1 Y SOLV$ R,NAL EQU,NS4
,Y C AL SOLVE R,NAL 9EQUALITIES US+
TA#S1 GRAPHS1 OR ALGEBRAIC ME?ODS4
,SIDEB>3
,/&>DS
..,5RI*;T ( #G.J ,/UD5TS ADD1
SUBTRACT1 MULTIPLY1 DIVIDE1 REDUCE1 &
EVALUATE R,NAL EXPRES.NS ) MONOMIAL &
POLYNOMIAL DENOM9ATORS & SIMPLIFY
-PLICAT$ R,NAL .EXPRES.NS @1 9CLUD+ ^? )
NEGATIVE EXPON5TS 9 ! DENOM9ATOR4
,,EXAMPLE #A ,SOLVE A R,NAL 9EQUAL;Y
US+ A TA#
,USE A TA# 6SOLVE @4
,SOLU;N
,SUBTRACT .;X F EA* SIDE (! 9EQUAL;Y S
T #J IS ON "O SIDE4
,5T] 96A GRAPH+ CALCULATOR4
,USE ! .TA# F1TURE 6F9D VALUES ( .;X =
: .;Y IS POSITIVE4
,! VALUE ( .;Y IS UNDEF9$ :5 .;X .K #B
& APPE>S 6BE POSITIVE :5 .;X .1 #B4 ,USE
A SMALL] /EP VALUE = .;X 63V9CE YRF ( ?4
,! SOLU;N IS .;X .1 #B4
,,EXAMPLE #B ,SOLVE A R,NAL 9EQUAL;Y
0GRAPH+
,F #AIIJ 6#BJJA1 ! NUMB] .;D 7IN
?\S&S7 ( DOCTORS 9 ! ,UNIT$ ,/ATES C 2
MODEL$ 0! FUNC;N ": .;T IS ! NUMB] (
YE>S S9CE #AIIJ4 ,:5 7 "! FEW] ?AN
#HJJ1JJJ DOCTORS8
,SOLU;N
,! PRO#M REQUIRES SOLV+ ? 9EQUAL;Y3
,5T] & .;Y #B .K #HJJ 96A GRAPH+
CALCULATOR4
,GRAPH ! FUNC;NS & USE ! .9T]SECT
F1TURE4 ,! GRAPH ( .;Y #A LIES 2L !
GRAPH ( ;Y #B :5 #J "K.K .;X "K.K #I4
,9 ! YE>S #AIIJ-AIII1 "! 7 FEW] ?AN
#HJJ1JJJ DOCTORS4
------------------------------------#EII
,,EXAMPLE #C ,SOLVE A R,NAL 9EQUAL;Y
ALGEBRAIC,Y
,SOLVE ALGEBRAIC,Y4
,SOLU;N
.,,/EP .#A .,REWRITE ! 9EQUAL;Y S T "O
SIDE IS #J4 ,!N WRITE ! O!R SIDE Z A
SIMPLIFI$ R,NAL EXPRES.N4
,,AVOID ,,]RORS
,D N MULTIPLY EA* SIDE ( AN 9EQUAL;Y
0AN EXPRES.N 9VOLV+ .;X IF ! EXPRES.N C
TAKE ON BO? POSITIVE & NEGATIVE VALUES4
.,,/EP .#B .,ID5TIFY ! .CRITICAL
.;X-.VALUES @1 : >E ! .;X -VALUES T MAKE
! NUM]ATOR OR DENOM9ATOR EQUAL 6#J4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,NUM]ATOR EQUAL TO _+0::_: ,DENOM9ATOR
EQUAL 6#J3
#D .;X -- #B .K #J @3 .;X -- #B .K #J
@3 .;X .K #B
,S1 ! CRITICAL .;X -VALUES >E & .;X .K
#B4
,! CRITICAL .;X -VALUES DIVIDE ! NUMB]
L9E 96?REE 9T]VALS4 ,NOTE T W 2 9CLUD$ 9
! SOLU;N1 B .;X .K #B W N 2C X RESULTS 9
DIVI.N 0Z]O4
.,,/EP .#C .,TE/ AN .;X -VALUE 9 EA*
9T]VAL 6SEE IF X SATISFIES ! ORIG9AL
9EQUAL;Y4 ,IF X DOES1 .E .;X-.VALUE 9 !
9T]VAL W SATISFY ! 9EQUAL;Y4 ,IF X DOES
N1 .NO .;X -VALUE 9 ! 9T]VAL W SATISFY !
9EQUAL;Y4
.,,/EP .#D .,GRAPH ! 9T]VALS ": ! TE/$
.;X -VALUES PRODUCE TRUE /ATE;TS4
.,,/EP .#E .,WRITE 9EQUALITIES
6DESCRIBE ! SOLU;N4
,! SOLU;N IS OR .;X .1 #B4
------------------------------------#FJJ
,,PRACTICE
,,EXAMPLE #A
ON P4 #EIH = ,EXS4 #A-F
,USE A TA# 6SOLVE ! 9EQUAL;Y4
.#A4
.#B4
.#C4
.#D4
.#E4
.#F4
,,EXAMPLE #B
ON P4 #EIH = ,EXS4 #G-AB
,USE A GRAPH 6SOLVE ! 9EQUAL;Y4
.#G4
.#H4
.#I4
.#AJ4
.#AA4
.#AB4
,,EXAMPLE #C
ON P4 #EII = ,EXS4 #AC-AH
,SOLVE ! 9EQUAL;Y ALGEBRAIC,Y4
.#AC4
.#AD4
.#AE4
.#AF4
.#AG4
.#AH4
.#AI4 .,,EGG .,,PRODUC;N ,F #AIID
6#BJJB1 ! TOTAL NUMB] .;,E 7IN BILLIONS7
( E7S PRODUC$ 9 ! ,UNIT$ ,/ATES C 2
MODEL$ BY
": .;T IS ! NUMB] ( YE>S S9CE #AIID4
,= :AT YE>S 0 ! NUMB] ( E7S PRODUC$ GRT]
?AN #HJ BILLION8
.#BJ4 .,,PH"O .,,CO/S ,"O PH"O -PANY
ADV]TISES A FLAT RATE ( @4#.JG P] M9UTE
= L;G--4T.E CALLS4 ,YR L;G--4T.E PLAN
*>GES 4#E.JJ P] MON? PLUS A RATE (
@4#.JE P] M9UTE4 ,H[ _M M9UTES D Y H
6TALK EA* MON? S T YR AV]AGE CO/ IS LESS
?AN @4#.JG P] M9UTE8
.#BA4 .,,SATELLITE .,,TV ,Y SUBSCRIBE
6A SATELLITE TELEVI.N S]VICE4 ,! MON?LY
CO/ = PROGRAMM+ IS 4#DC1 & "! IS A
"O--"T 9/ALL,N FEE ( 4#EJ4 ,! AV]AGE
MON?LY CO/ .;C (! S]VICE IS GIV5 0": .;T
IS ! "T 7IN MON?S7 T Y H SUBSCRIB$ 6!
S]VICE4 ,= :AT SUBSCRIP;N "TS IS !
AV]AGE MON?LY CO/ AT MO/ 4#DG8 ,SOLVE !
PRO#M US+ A TA# & US+ A GRAPH4
#BB4 .,,FUNDRAIS] ,YR S*OOL IS PUBLI%+
A WILDLIFE CAL5D> 6RAISE M"OY =A LOCAL
*>;Y4 ,! TOTAL CO/ ( US+ ! PHOTOS 9 !
CAL5D> IS 4#GAJ4 ,9 A4I;N 6? "O--"T
*>GE1 ! UNIT CO/ ( PR9T+ EA* CAL5D> IS
4#D.EJ4
A4 ,! S*OOL WANTS ! AV]AGE CO/ P]
CAL5D> 6BE 2L 4#AJ4 ,WRITE A R,NAL
9EQUAL;Y RELAT+ ! AV]AGE CO/ P] CAL5D>
6! DESIR$ CO/ P] CAL5D>4
B4 ,SOLVE ! 9EQUAL;Y F "P 7A7 0GRAPH+4
,H[ _M CAL5D>S NE$ 6BE PR9T$ 6BR+ !
AV]AGE CO/ P] CAL5D> 2L 4#AJ8
C4 ,SUPPOSE ! S*OOL WANT$ 6H ! AV]AGE
CO/ P] CAL5D> 2 2L 4#F4 ,H[ _M CAL5D>S
WD !N NE$ 6BE PR9T$8
------------------------------------#FJA
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,LESSONS #H.D-H.F
.#A4 .,,MULTI-.,,/EP .,,PRO#M ,A
CYCLI/ TRAVELS #EJ MILES F H] HOME 6A
/ATE P>K AT A SPE$ ( .;S MILES P] H\R4
,ON ! RETURN TRIP1 %E 9CR1SES H] SPE$
0#E MILES P] H\R4
.A4 ,WRITE AN EXPRES.N 9 T]MS ( .;S =!
"T ! CYCLI/ TAKES 6TRAVEL F H] HOME 6!
/ATE P>K4
.B4 ,WRITE AN EXPRES.N 9 T]MS ( .;S =!
"T ! CYCLI/ TAKES 6RETURN HOME F ! /ATE
P>K4
.C4 ,WRITE AN EXPRES.N 9 SIMPLIFI$ =M
=! .TOTAL "T (! CYCLI/'S R.D TRIP4
.#B4 .,,%ORT .,,RESPONSE ,! SPE$ (A
RIV]'S CURR5T IS #C MILES P] H\R4 ,Y
TRAVEL #B MILES )! CURR5T & !N RETURN
6": Y />T$ 9 A TOTAL "T ( #A.BE H\RS4
,:AT IS YR SPE$ 9 / WAT]8
.#C4 .,,%ORT .,,RESPONSE ,A
MANUFACTUR] ( 9/ANT RICE IS 3SID]+ TWO
DI6]5T /YLES ( PACKAG+4 ,"O IS A
RECTANGUL> 3TA9] )A SQU>E BASE4 ,! O!R
IS A CYL9D]4
.A4 ,F9D ! RATIO ( SURFACE >EA 6VOLUME
= EA* 3TA9]4
.B4 ,US+ ! RATIOS1 :AT C Y DET]M9E AB
! E6ICI5CIES (! 3TA9]S8
.#D4 .,,OP5-.,,5D$ ,WRITE TWO R,NAL
EXPRES.NS .;R7.;X7 & .;S7.;X7 S* T
.;R7.;X7 & .;S7.;X7 EA* 3TA9 A QUADRATIC
POLYNOMIAL &
.#E4 .,,MULTI-.,,/EP .,,PRO#M ,BRASS
IS AN ALLOY -POS$ ( #EE@3P COPP] &
#DE@3P Z9C 0WEI<T4 ,Y H #BE \NCES (
COPP]1 & Y WANT 6DET]M9E H[ _M \NCES (
Z9C Y NE$ 6MAKE BRASS4
.A4 ,LET .;X 2 ! NUMB] ( \NCES ( Z9C Y
NE$4 ,WRITE A V]BAL MODEL & !N A R,NAL
EQU,N T Y C USE 6F9D .X4
.B4 ,SOLVE ! EQU,N F "P 7A7 6F9D !
NUMB] ( \NCES ( Z9C Y NE$ 6MAKE BRASS4
.C4 ,3SID] ! M G5]AL CASE ": Y H .;C
\NCES ( COPP]4 ,9 T]MS ( ;C1 H[ _M \NCES
( Z9C M/ 2 A4$ 6MAKE BRASS8
.#F4 .,,EXT5D$ .,,RESPONSE ,A C>
TRAVELS #ABJ MILES 9 ! SAME AM.T ( "T T
X TAKES A TRUCK 6TRAVEL #AJJ MILES4 ,!
C> TRAVELS #AJ MILES P] H\R FA/] ?AN !
TRUCK4
.A4 ,USE ! V]BAL MODEL 2L 6WRITE AN
EQU,N T RELATES ! SPE$S (! VEHICLES4
.B4 ,SOLVE ! EQU,N F "P 7A7 6F9D !
SPE$S (! C> &! TRUCK4
.C4 ,H[ M* "T DID ! VEHICLES SP5D
TRAVEL+8 .,EXPLA9 YR ANSW]4
.#G4 .,,GRI4$ .,,ANSW] ,F9D ! RATIO (!
VOLUME (! SPH]E 6! VOLUME (! CUBE 9 !
DIAGRAM 2L4
,USE ! =MULA =! VOLUME (A SPH]E &!
=MULA .;,V .K .;S #C =! VOLUME (A CUBE
": .;R IS ! RADIUS (! SPH]E & .;S IS !
SIDE L5G? (! CUBE4 ,WRITE YR ANSW] Z A
DECIMAL R.D$ 6! NE>E/ HUNDR$?4
------------------------------------#FJB
#H ,*APT] ,SUMM>Y
.,ANIMAT$ ,ALGEBRA
_+CLASSZONE.COM_:
,ELECTRONIC ,FUNC;N ,LIBR>Y
,,BIG ,,ID1S ,= ,YR ,NOTEBOOK
,BIG ,IDEA #A
,GRAPH+ ,R,NAL ,FUNC;NS
,USE ! FOLL[+ /EPS 6GRAPH
": .;P @7 .;X @7 & .;Q @7 .;X @7 H NO
-MON FACTORS O!R ?AN +-#A1
.,,/EP .#A .,PLOT ! .;X -9T]CEPTS4 ,!
.;X -9T]CEPTS >E ! R1L Z]OS ( .;P @7 .;X
@7@4
.,,/EP .#B .,DRAW ! V]TICAL ASYMPTOTE
7;S74 ,A V]TICAL ASYMPTOTE O3URS AT EA*
R1L Z]O ( .;Q @7 .;X @7@4
.,,/EP .#C .,DRAW ! HORIZONTAL
ASYMPTOTE1 IF X EXI/S4
,IF .;M "K .;N1 .;Y .K #J IS A
HORIZONTAL ASYMPTOTE4
,IF .;M .K .;N @1 IS A HORIZONTAL
ASYMPTOTE4
,IF .;M .1 .;N @1 "! IS NO HORIZONTAL
ASYMPTOTE4
.,,/EP .#D .,PLOT S"EAL PO9TS ON BO?
SIDES ( EA* V]TICAL ASYMPTOTE4
,BIG IDEA #B
,P]=M+ ,OP],NS ) ,R,NAL ,EXPRES.NS
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,OP],N3 ,EXAMPLE
.,SIMPLIFY ,DIVIDE \ -MON FACTORS F !
NUM]ATOR & DENOM9ATOR4 @3
.,MULTIPLY ,MULTIPLY NUM]ATORS &
DENOM9ATORS4 ,!N SIMPLIFY4 @3
.,DIVIDE ,MULTIPLY ! F/ EXPRES.N 0!
RECIPROCAL (! SECOND EXPRES.N4 ,!N
SIMPLIFY4 @3
.,ADD .OR .,SUBTRACT ,WRITE !
EXPRES.NS ) L DENOM9ATORS4 ,!N ADD OR
SUBTRACT ! NUM]ATORS OV] ! -MON
DENOM9ATOR4 ,LA/LY1 SIMPLIFY4 @3
,BIG ,IDEA #C
,SOLV+ ,R,NAL ,EQU,NS
,SOLVE @4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,,/EP .#A ,F9D.' ! ,,LCD4 @3 ,,LCD IS
@7 .;X @+ #A7@7 .;X @+ #D74
.,,/EP#B ,MULTIPLY.' EA* SIDE (! EQU,N
0! ,,LCD4 @3 .;X @7 .;X @+ #D7 @+ #B7
.;X @+ #A7 .K @7 .;X @+ ;L7@7 .;X @+ #D7
.,,/EP .#C ,SOLVE.' ! RESULT+ EQU,N4
@3 .;X #B @+ #D .;X @+ #B .;X @+ #B .K
.;X #B @+ #E .;X @+ #D
#F .;X @+ #B .K #E .;X @+ #D
.;X .K #B
------------------------------------#FJC
#H ,*APT] ,REVIEW
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
99 ,MULTI-,LANGUAGE ,GLOSS>Y
99 ,VOCABUL>Y PRACTICE
,,REVIEW ,,KEY ,,VOCABUL>Y
99 9V]SE V>I,N1 P4 #EEA
99 3/ANT ( V>I,N1 P4 #EEA
99JO9T V>I,N1 P4 #EEC
99 R,NAL FUNC;N1 P4 #EEH
99 SIMPLIFI$ =M (A R,NAL EXPRES.N1 P4
#EGC
99 -PLEX FRAC;N1 P4 #EHD
99 CROSS MULTIPLY+1 P4 #EHI
,,VOCABUL>Y ,,EX]CISES
.#A4 ,COPY & -PLETE3 ,IF TWO V>IA#S
.;X & .;Y >E RELAT$ 0AN EQU,N (! =M ":
.A @6.K #J1 !N .;X & .;Y %[ @8 @4
.#B4 ,SUPPOSE .;Z V>IES JO9TLY ) .;X &
.;Y @4 ,:AT C Y SAY AB @8
.#C4 ,COPY & -PLETE3 ,A FUNC;N (! =M
": .;P @7 .;X @7 & .;Q @7 .;X @7 >E
POLYNOMIALS & .;Q @7 .;X @7 @6.K #J IS
CALL$ A7;N7 @8 @4
.#D4 ,GIVE TWO EXAMPLES (A -PLEX
FRAC;N4
.#E4 ,COPY & -PLETE3 ,:5 Y REWRITE !
EQU,N Z Z @7 .;X -- #A7 .K #B .;X @1 Y
>E @8 @4
,,REVIEW ,,EXAMPLES ,,& ,,EX]CISES
,USE ! REVIEW EXAMPLES & EX]CISES 2L
6*ECK YR "U/&+ (! 3CEPTS Y H LE>N$ 9 EA*
LESSON ( ,*APT] #H4
#H.A ,MODEL ,9V]SE & ,JO9T ,V>I,N
PP4 #EEA-EEG
,,EXAMPLE
,! V>IA#S .;X & .;Y V>Y 9V]SELY1 & .;Y
.K #AB :5 .;X .K #C4 ,WRITE AN EQU,N T
RELATES .;X & .Y4 ,!N F9D .;Y :5 .;X .K
--#D4
,! 9V]SE V>I,N EQU,N IS @4 ,:5 .;X .K
--#D1 @4
,,EXAMPLE #B
ON P4 #EEA = ,EXS4 #F-I
,,EX]CISES
,! V>IA#S .;X & .;Y V>Y 9V]SELY4 ,USE
! GIV5 VALUES 6WRITE AN EQU,N RELAT+ .;X
& .;Y @4 ,!N F9D .;Y :5 .;X .K --#C4
.#F4 .;X .K #A1 .;Y .K #E
.#G4 .;X .K --#D1 .;Y .K --#F
.#H4 @1 .;Y .K #AH
.#I4 .;X .K --#AB1
------------------------------------#FJD
#H ,,*APT] ,,REVIEW
#H.B ,GRAPH ,SIMPLE ,R,NAL ,FUNC;NS
PP4 #EEH-EFC
,,EXAMPLE
,GRAPH ,/ATE ! DOMA9 & RANGE4
.,,/EP .#A .,DRAW ! ASYMPTOTES4 ,SOLVE
.;X -- #A .K #J = .;X 6F9D ! V]TICAL
ASYMPTOTE .;X .K #A4 ,! HORIZONTAL
ASYMPTOTE IS ! L9E @4
.,,/EP .#B .,PLOT PO9TS 6! LEFT & 6!
"R (! V]TICAL ASYMPTOTE4
.,,/EP .#C .,DRAW ! TWO BRAN*ES (!
HYP]BOLA S T !Y PASS "? ! PLOTT$ PO9TS &
APPROA* ! ASYMPTOTES4
,! DOMA9 IS ALL R1L NUMB]S EXCEPT #A4
,! RANGE IS ALL R1L NUMB]S EXCEPT #B4
,,EXAMPLES #B & #C
ON PP4 #EEI-EFJ = ,EXS4 #AJ-AB
,,EX]CISES
,GRAPH ! FUNC;N4 ,/ATE ! DOMA9 &
RANGE4
.#AJ4
.#AA4
.#AB4
#H.C ,GRAPH ,G5]AL ,R,NAL ,FUNC;NS
PP4 #EFE-EGA
,,EXAMPLE #A
,GRAPH @4
99 ,! NUM]ATOR HAS #J Z XS ONLY Z]O1 S
! GRAPH HAS AN .;X -9T]CEPT AT 7#J1 #J74
99 ,! DENOM9ATOR HAS --#B Z XS ONLY
Z]O1 S ! GRAPH HAS A V]TICAL ASYMPTOTE
AT .;X .K --#B4
99 ,! DEGREE (! NUM]ATOR 7#B7 IS GRT]
?AN ! DEGREE (! DENOM9ATOR 7#A74 ,S1 "!
IS NO HORIZONTAL ASYMPTOTE4 ,! GRAPH HAS
! SAME 5D 2HAVIOR Z ! GRAPH ( @4
,,EX]CISES
,GRAPH ! FUNC;N4
,,EXAMPLES #A1B1 & #C
ON PP4 #EFE-EFF @3 = ,EXS4 #AC-AH
.#AC4
.#AD4
.#AE4
.#AF4
.#AG4
.#AH4
------------------------------------#FJE
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,*APT] ,REVIEW ,PRACTICE
#H.D ,MULTIPLY & ,DIVIDE ,R,NAL
,EXPRES.NS
,,PP4 #EGC-EHJ
,,EXAMPLE
,DIVIDE3
,,EXAMPLES #C1D1 #F1 & #G
ON PP4 #EGE-EGG = ,EXS4 #AI-BB
,,EX]CISES
,P]=M ! 9DICAT$ OP],N4 ,SIMPLIFY !
RESULT4
.#AI4
.#BJ4
.#BA4
.#BB4
#H.E ,ADD & ,SUBTRACT ,R,NAL
,EXPRES.NS
PP4 #EHB-EHH
,,EXAMPLE
,ADD3
,! DENOM9ATORS FACTOR Z #F7 .;X @+ #D7
& @7 .;X @+ #D7@7 .;X @+ #E71 S ! ,,LCD
IS #F7 .;X @+ #D7@7 .;X @+ #E74 ,USE ?
RESULT 6REWRITE EA* EXPRES.N )A -MON
DENOM9ATOR1 & !N ADD4
,,EXAMPLES #C & #D
ON PP4 #EHC-EHD = ,EXS4 #BC-BE
,,EX]CISES
,P]=M ! 9DICAT$ OP],N & SIMPLIFY4
.#BC4
.#BD4
.#BE4
------------------------------------#FJF
#H ,,*APT] ,,REVIEW
#H.F ,SOLVE ,R,NAL ,EQU,NS
PP4 #EHI-EIE
,,EXAMPLE
,SOLVE3
,! L1/ -MON DENOM9ATOR IS #B .;X @7
.;X @+ #A74
,! SOLU;NS >E & #B4 ,*ECK ^! 9 !
ORIG9AL EQU,N 6MAKE SURE NEI SOLU;N IS
EXTRANE\S4
,,EXAMPLES #A1 #D1 & #E
ON PP4 #EHI-EIA = ,EXS4 #BF-CF
,,EX]CISES
,SOLVE ! EQU,N 0CROSS MULTIPLY+4 ,*ECK
YR SOLU;N 7;S74
.#BF4
.#BG4
.#BH4
.#BI4
.#CJ4
.#CA4
,SOLVE ! EQU,N 0US+ ! ,,LCD4 ,*ECK =
EXTRANE\S SOLU;NS4
.#CB4
.#CC4
.#CD4
.#CE4
#CF4 .,,BASKETBALL ,S F> ? S1SON1 A
BASKETBALL PLAY] HAS MADE #FJ ( #GE
FREE-?R[ ATTEMPTS4
A4 ,WRITE A R,NAL EXPRES.N T REPRES5TS
! PLAY]'S FREE--?R[ P]C5TAGE 7EXPRESS$ Z
A DECIMAL7 IF %E MAKES H] NEXT .;X FREE
?R[S4
B4 ,H[ _M 3SECUTIVE FREE ?R[S M/ !
PLAY] MAKE 9 ORD] 6RAISE H] FREE--?R[
P]C5TAGE 6AT L1/ #HB@3P8
------------------------------------#FJG
#H ,*APT] ,TE/
,! V>IA#S .;X & .;Y V>Y 9V]SELY4 ,USE
! GIV5 VALUES 6WRITE AN EQU,N RELAT+ .;X
& .;Y @4 ,!N F9D .;Y :5 .;X .K #D4
.#A4 .;X .K #E1 .;Y .K #B
.#B4 .;X .K --#B1 .;Y .K #H
.#C4 @1 .;Y .K #AJ
.#D4 .;X .K #C1 .;Y .K #F
.#E4 .;X .K --#D1
.#F4
,GRAPH ! FUNC;N4 ,/ATE ! DOMA9 &
RANGE4
.#G4
.#H4
.#I4
,GRAPH ! FUNC;N4
.#AJ4
.#AA4
.#AB4
,F9D ! L1/ -MON MULTIPLE (!
POLYNOMIALS4
.#AC4 @7 .;X -- #C7@7 .;X @+ #E7 & .;X
@7 .;X @+ #E7
.#AD4 #D .;X #B @7 .;X -- #B7 & #H .;X
@7 .;X @+ #B7
.#AE4 .;X #B -- #D .;X & .;X #B -- #B
.;X -- #H
.#AF4 #B .;X @+ #F & .;X #C @+ #AJ .;X
#B @+ #BA .;X
,P]=M ! 9DICAT$ OP],N & SIMPLIFY4
.#AG4
.#AH4
.#AI4
.#BJ4
.#BA4
.#BB4
.#BC4
.#BD4
,SOLVE ! EQU,N4 ,*ECK = EXTRANE\S
SOLU;NS4
.#BE4
.#BF4
.#BG4
.#BH4 .,,S.D .,,9T5S;Y ,! 9T5S;Y .;L
(A S.D V>IES 9V]SELY )! SQU>E (! 4T.E
.;R F ! S\RCE (! S.D4 ,WRITE AN EQU,N
RELAT+ .;L1 .;R @1 &A 3/ANT .A @4
.#BI4 .,,CA# .,,TV ,Y H SUBSCRIB$ 6A
CA# TELEVI.N S]VICE4 ,! CA# -PANY *>GES
Y A "O--"T 9/ALL,N FEE ( 4#CJ &A MON?LY
FEE ( 4#EJ4 ,WRITE & GRAPH A MODEL T
GIVES ! AV]AGE CO/ P] MON? Z A FUNC;N (!
NUMB] ( MON?S Y H SUBSCRIB$ 6! S]VICE4
,AF H[ _M MON?S W ! AV]AGE CO/ 2 4#EF8
.#CJ4 .,,WEB .,,HO/+ ,Y >E BUILD+ A
NEW WEBSITE = YR S*OOL4 ,A -PANY T HO/S
WEBSITES (F]S A D$ICAT$ S]V] =A 4#EJ
SETUP FEE PLUS A MON?LY FEE ( 4#II4 ,H[
_M MON?S WD Y NE$ 6USE ? S]VICE 9 ORD] =
YR AV]AGE MON?LY CO/ 6FALL TO 4#AJJ8
------------------------------------#FJH
#H ,/&>DIZ$ ,TE/ ,PREP>,N
,,3TEXT-,,BAS$ ,,MULTIPLE-,,*OICE
,,"QS
,"S (! 9=M,N Y NE$ 6SOLVE A
MULTIPLE--*OICE "Q MAY APPE> 9 A TA#1 A
DIAGRAM1 OR A GRAPH4
,SIDEB>3
,/&>DS
..#G.J ,/UD5TS ADD1 SUBTRACT1
MULTIPLY1 DIVIDE1 REDUCE1 & EVALUATE
R,NAL EXPRES.NS ) MONOMIAL & POLYNOMIAL
DENOM9ATORS & SIMPLIFY -PLICAT$ R,NAL
.EXPRES.NS @1 9CLUD+ ^? ) NEGATIVE
EXPON5TS 9 ! DENOM9ATOR4
,,PRO#M #A
,: R,NAL EXPRES.N REPRES5TS ! RATIO (!
P]IMET] 6! >EA (! PLAYGR.D %[N 9 !
DIAGRAM8
,A4
,B4
,C4
,D4
,PLAN
.,,9T]PRET .,,! .,,DIAGRAM ,DET]M9E !
MISS+ DIM5.NS ON ! DIAGRAM4 ,!N USE !M
6WRITE EXPRES.NS =! P]IMET] & >EA (!
PLAYGR.D4
,,/EP #A
,F9D ! MISS+ DIM5.NS & WRITE AN
EXPRES.N =! P]IMET]4
,SOLU;N
,COPY ! DIAGRAM4 ,!N F9D & LABEL !
MISS+ DIM5.NS4
,USE SUBTRAC;N & A4I;N 6F9D ! DIM5.NS
T >E N LABEL$ ON ! DIAGRAM4 ,! MISS+
DIM5.NS >E .#D .;X & .#C .;X @4
,P]IMET] .K .#D .;X @+ .;X @+ #B .;X
@+ .#C .;X @+ #F .;X @+ #B .;X
.K #AH .;X
,,/EP #B
,WRITE AN EXPRES.N =! >EA4
,! PLAYGR.D 3SI/S ( TWO RECTANGLES1 "O
) DIM5.NS ..;X 0#B .;X &! O!R ) DIM5.NS
..#B ;X 0#F .;X @4
,6F9D ! >EA (! PLAYGR.D1 ADD ! >1S (!
TWO RECTANGLES4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,>EA3 .K .;X 7#B .;X @7 @+ #B .;X 7#F
.;X @7
--@3 .K #B .;X #B @+ #AB .;X #B
--@3 .K #AD .;X #B
,,/EP #C
,F9D ! RATIO (! P]IMET] 6! >EA4
,! RATIO (! P]IMET] 6! >EA IS3
,! CORRECT ANSW] IS ,A4 7,A7 7;,B7
7;,C7 7;,D7
------------------------------------#FJI
,,PRO#M #B
,! TA# %[S H[ ! =CE .;,F 7IN P.DS7
NE$$ 6LOOS5 A C]TA9 BOLT )A WR5* DEP5DS
ON ! L5G? 7IN 9*ES7 (! WR5*'S H&LE4 ,:
EQU,N RELATES & .;,F @8
,A4 .;,F .K #AEJJ
,B4 .;,F .K #IC.GE
,C4
,D4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
7IN473 .;,F 7LB7
#D3 #CGE
#F3 #BEJ
#AJ3 #AEJ
#AB3 #ABE
,PLAN
.,,9T]PRET .,,! .,,TA# ,! TA# %[S F\R
DATA PAIRS @7 @1 .;,F @7@4 ,6WRITE AN
EQU,N RELAT+ & .;,F @1 Y NE$ 6F9D A
PATT]N 9 ! DATA4
,,/EP #A
,ID5TIFY A PATT]N 9 ! DATA PAIRS @7
.;,F @7@4
,SOLU;N
,F9D ! PRODUCT @* ;,F = EA* DATA PAIR4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#D7#CGE7 .K #AEJJ3 #F7#BEJ7 .K #AEJJ
#AJ7#AEJ7 .K #AEJJ3 #AB7#ABE7 .K #AEJJ
,,/EP #B
,WRITE AN EQU,N T RELATES & .;,F @4
,EA* PRODUCT EQUALS #AEJJ1 S ! DATA %[
9V]SE V>I,N4
,AN EQU,N RELAT+ & .;,F IS ! FOLL[+3
,! CORRECT ANSW] IS ,C4 7,A7 7;,B7
7;,C7 7;,D7
,,PRACTICE
#A4 ,: R,NAL EXPRES.N REPRES5TS !
RATIO (! P]IMET] 6! >EA (! FIGURE %[N8
,A4
,B4
,C4
,D4
#B4 ,: EQU,N REPRES5TS ! ORD]$ PAIRS 9
! TA#8
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #B3 #D3 #F3 #H3 #AJ
.;Y @3 #AHJ3 #IJ3 #FJ3 #DE3 #CF
,A4
,B4
,C4
,D4
------------------------------------#FAJ
#H ,/&>DIZ$ ,TE/ ,PRACTICE
,,MULTIPLE-,,*OICE
,9 ,EX]CISES #A & #B1 USE ! GIV5 GRAPH
(A R,NAL FUNC;N4
#A4 ,:AT IS ! RANGE (! FUNC;N8
,A4 ,ALL R1L NUMB]S
,B4 ,ALL R1L NUMB]S EXCEPT #B
,C4 ,ALL R1L NUMB]S EXCEPT #C
,D4 ,ALL R1L NUMB]S EXCEPT #E
#B4 ,: /ATE;T IS FALSE8
,A4 ,! L9E .;X .K #C IS AN ASYMPTOTE4
,B4 ,! L9E .;Y .K #B IS AN ASYMPTOTE4
,C4 ,! FUNC;N IS UNDEF9$ = .;X .K #B4
,D4 ,! VALUE ( .;Y IS UNB.D$4
,9 ,EX]CISES #C & #D1 USE ! GIV5 TA#4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;P @3 --#AB3 #C3 #CJ3 --#A.E
.;P @3 #B3 #A3 --#E3 --#J.E
.;R @3 --#B3 #A3 --#B3 #A
#C4 ,:AT IS ! REL,N%IP AM;G ! V>IA#S8
,A4 ,! V>IA# .;P V>IES JO9TLY ) .;Q &
.;R @4
,B4 ,! V>IA# .;P V>IES JO9TLY ) .;Q &!
SQU>E ( .;R @4
,C4 ,! V>IA# .;R V>IES 9V]SELY )! SUM
( .;P & .;G @4
,D4 ,! V>IA# .;Q V>IES 9V]SELY )! SUM
( .;P & .;R @4
#D4 ,:AT IS ! VALUE ( .;R :5 .;P .K
#BJ & .;Q .K --#D8
,A4 --#E
,B4
,C4
,D4
,9 ,EX]CISES #E & #F1 USE ! GIV5 GRAPH
(A R,NAL FUNC;N4
#E4 ,:AT >E ! .;X -9T]CEPTS (! GRAPH8
,A4 --#E &--#B.E
,B4 --#B.E & #D
,C4 --#D & #E
,D4 --#E & #D
#F4 ,:AT IS ! HORIZONTAL ASYMPTOTE (!
GRAPH8
,A4 .;X .K --#B
,B4 .;Y .K #J
,C4 .;X .K #A
,D4 .;Y .K #A
#G4 ,3SID] A RECTANGLE ^: DIM5.NS
*ANGE B ^: >EA REMA9S 3/ANT4 ,!
RECTANGLE'S L5G? V>IES 9V]SELY ) XS WID?
.;W @4 ,! DIAGRAM 2L %[S ! RECTANGLE AT
"O MO;T 9 "T4 ,: EQU,N RELATES & .;W @8
,A4 .;W .K #J.FG
,B4 .;W .K #A.AEBD
,C4 .;W .K #A.GB
,D4 .K #A.AEBD .;W
#H4 ,:AT IS ! APPROXIMATE RADIUS (A
CYL9D] T HAS ! SAME VOLUME Z !
RECTANGUL> PRISM 2L & HAS ! L1/ SURFACE
>EA POSSI#8
,A4 #C.FA CM
,B4 #C.HD CM
,C4 #F.JJ CM
,D4 #G.FF CM
------------------------------------#FAA
.,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,,GRI4$ ,,ANSW]
.#I4 ,:AT IS ! SOLU;N (! EQU,N
.#AJ4 ,! V>IA#S .;M & .;N V>Y 9V]SELY1
& .;M .K --#B :5 .;N .K --#H4 ,:AT IS !
VALUE ( .;N :5 .;M .K #E8
.#AA4 ,! V>IA# .;Q V>IES JO9TLY ) .;R
&! SQU>E ( .;S & 9V]SELY )! SQU>E ROOT (
.T4 ,AL1 .;Q .K --#A.GE :5 .;R .K --#B1
.;S .K #A1 & .;T .K #AF4 ,:AT IS ! VALUE
( .;Q :5 .;R .K #E1 .;M .K --#C1 & .;T
.K #BE8
.#AB4 ,:AT NUMB] IS N 9 ! DOMA9 (!
FUNC;N
.#AC4 ,S F> ? QU>T]1 A /UD5T HAS H&$ 9
#AE ( #AG HOME"W ASSIGN;TS4 ,SOLVE !
EQU,N 6DET]M9E ! NUMB] ( 3SECUTIVE
ASSIGN;TS ! /UD5T M/ TURN 9 6RAISE H]
HOME"W P]C5TAGE UP 6#IE@3P4
,,%ORT ,,RESPONSE
.#AD4 ,LISA /EPS ONTO AN ESCALATOR &
2G9S DESC5D+4 ,AF RID+ = #AB FEET1 %E
R1LIZ$ T %E DROPP$ H] KEYS ON ! UPP]
FLOOR & WALKS BACK UP ! ESCALATOR
6RETRIEVE !M4 ,! TOTAL "T .;,T ( H] TRIP
D[N & UP ! ESCALATOR IS GIV5 0! EQU,N ":
.;S IS ! SPE$ (! ESCALATOR & .;W IS
,LISA'S WALK+ SPE$4 ,! TRIP TOOK #I
SECONDS & ,LISA WALKS AT A SPE$ ( #F
FEET P] SECOND4 ,F9D ! SPE$ (!
ESCALATOR4
.#AE4 ,F #AIFJ 6#AIIE 9 ! ,UNIT$
,/ATES1 ! DAILY WAT] 3SUMP;N ;,C 7IN
BILLIONS ( GALLONS7 &! POPUL,N .;,P 7IN
?\S&S7 C 2 MODEL$ 0& .;,P .K #BDFJ .;X
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YE>S S9CE #AIFJ4 ,WRITE A MODEL =! DAILY
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P]SON7 Z A FUNC;N (! YE>4 .,EXPLA9 ALL (
YR /EPS4
,,EXT5D$ ,,RESPONSE
.#AF4 ,F #AIHJ 6#BJJA1 ! NUMB] .;N 7IN
MILLIONS7 ( MALES 5ROLL$ 9 HI< S*OOL 9 !
,UNIT$ ,/ATES C 2 MODEL$ 0": .;X IS !
NUMB] ( YE>S S9CE #AIHJ4
.A4 ,MAKE A TA# ( VALUES %[+ ! 5ROLL;T
AT #B YE> 9T]VALS =! YE>S #AIHJ 6#BJJJ4
.B4 ,GRAPH ! MODEL4
.C4 ,USE YR GRAPH 6E/IMATE ! YE> 9 :
#G.G MILLION MALES 7 5ROLL$ 9 HI< S*OOL4
.D4 ,ANALYZE ! GRAPH'S TR5D4 ,D Y ?9K
X W X 3T9UE 9DEF9ITELY8 .,EXPLA9 YR
ANSW]4
.#AG4 ,A DIGITAL VIDEO RECORD] CO/S
4#II.II1 &A PROGRAMM+ S]VICE =! DIGITAL
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.A4 ,WRITE A MODEL T GIVES ! AV]AGE
CO/ P] MON? ;,C Z A FUNC;N (! NUMB] (
MON?S .;M Y H SUBSCRIB$ 6! S]VICE4
.B4 ,GRAPH ! MODEL4 ,USE ! GRAPH
6E/IMATE ! NUMB] ( MON?S T Y NE$
6SUBSCRIBE 2F ! AV]AGE CO/ DROPS TO 4#AD
P] MON?4
.C4 ,:AT IS ! EQU,N (! HORIZONTAL
ASYMPTOTE8 ,:AT DOES ! ASYMPTOTE
REPRES5T8
------------------------------------#FAB
#I ,QUADRATIC ,REL,NS & ,3IC ,SEC;NS
.#I..A ,APPLY ! ,4T.E & ,MIDPO9T
,=MULAS
.#I..B ,GRAPH & ,WRITE ,EQU,NS (
,P>ABOLAS #I.C ,GRAPH & ,WRITE ,EQU,NS (
,CIRCLES
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,SEC;NS
.#I..G ,SOLVE ,QUADRATIC ,SY/EMS
,SIDEB>3
,2F
,9 PREVI\S *APT]S1 Y LE>N$ ! FOLL[+
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QUADRATIC FUNC;NS1 -PLET+ ! SQU>E1 &
SOLV+ L9E> SY/EMS4
,PREREQUISITE ,SKILLS
,,VOCABUL>Y ,,*ECK
,COPY & -PLETE ! /ATE;T4
.#A4 ,! GRAPH (A7;N7 @8 FUNC;N IS A
.P>ABOLA @4
.#B4 ,! GRAPH (! .R,NAL .FUNC;N @1 %[N
AT ! "R1 IS A @8 @4
.#C4 ,TWO EQU,NS (! =M ..,AX @+ ,BY .K
.;,C & ..,DX @+ ,EY.K .;,F =M A @8
.SY/EM .( .EQU,NS @4
,,SKILLS ,,*ECK
,GRAPH4 ,LABEL ! V]TEX & AXIS (
SYMMETRY4 7.,REVIEW PP4 #BCF ,.#BDE .=
.#I..B47
.#D4 .;Y .K .;X #B -- #C
.#E4 .;Y .K--#J.BE .;X #B
.#F4 .;Y .K#C7 .;X @+;L7 #B
.#G4 .;Y .K #J.E7 .;X -- #B7 #B @+ #D
,SOLVE ! EQU,N 0-PLET+ ! SQU>E4
7.,REVIEW P4 #BHD .= .#I..F47
.#H4 .;X #B -- #D .;X @+ #G .K #J
.#I4 .;X #B -- #H .;X -- #AE .K #J
.#AJ4 #C .;X #B @+ #I .;X -- #AB .K #J
,SOLVE ! SY/EM US+ ANY ALGEBRAIC
ME?OD4 7.,REVIEW P4 #AFJ .= .#I..G47
.#AA4 #B .;X -- .;Y .KLL
-- .;X --#B .;Y .K --#C
.#AB4 .;X @+ #E .;Y .K--#AG
--#B .;X -- #C .;Y .K #AC
.#AC4 --#D .;X @+ #G .;Y .K--#AD
#B .;X -- #F .;Y .K #AB
@A.,HOME,TUTOR ,PREREQUISITE SKILLS
PRACTICE AT _+CLASSZONE.COM_:
------------------------------------#FAC
,N[
,9 ,*APT] #I1 Y W APPLY ! BIG ID1S
LI/$ 2L & REVIEW$ 9 ! ,*APT] ,SUMM>Y ON
PAGE .#FFH4 ,Y W AL USE ! KEY VOCABUL>Y
LI/$ 2L4
,BIG ,ID1S
#A ,WRIT+ EQU,NS ( 3IC SEC;NS
#B ,GRAPH+ EQU,NS ( 3IC SEC;NS
#C ,SOLV+ QUADRATIC SY/EMS
,KEY ,VOCABUL>Y
99 4T.E =MULA1 P4 .#FAD
99 FOCUS1 FOCI1 PP4 #FBJ @1 #FCD @1
#FDB
99 DIRECTRIX1 P4 #FBJ
99 CIRCLE1 P4 #FBF
99 ELLIPSE1 P4 #FCD
99 V]TICES1 PP4 #FCD @1 #FDB
99 MAJOR AXIS1 P4 .#FCD
99 CO--V]TICES1 P4 .#FCD
99 M9OR AXIS1 P4 .#FCD
99 HYP]BOLA1 P4 .#FDB
99 TRANSV]SE AXIS1 P4 .#FDB
99 3IC SEC;NS1 P4 .#FEJ
99 G5]AL SECOND--DEGREE EQU,N1 P4
.#FEC
99 QUADRATIC SY/EM1 P4 .#FEH
,SIDEB>3
,:Y8
,Y C USE 3IC SEC;NS 6DESCRIBE ! %APES
( R1L--_W OBJECTS4 ,= EXAMPLE1 Y C USE A
P>ABOLA 6MODEL ! CROSS SEC;N (A RADIO
TELESCOPE4
.,ANIMAT$ ,ALGEBRA
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DIM5.NS (A RADIO TELESCOPE DET]M9E !
EQU,N T MODELS XS CROSS SEC;N8
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,O!R ANIM,NS = ,*APT] .#I3 PAGES
#FAE @1 #FBA @1 #FCE @1 #FDC @1 #FDI @1
& #FEA
------------------------------------#FAD
#I.A ,APPLY ! ,4T.E & ,MIDPO9T
,=MULAS
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TWO PO9TS4
.,N[ ,Y W F9D ! L5G? & MIDPO9T (A L9E
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.,:Y ,S Y C F9D R1L--_W 4T.ES1 Z 9
,EXS4 #DH--#EA4
,KEY ,VOCABUL>Y
99 4T.E =MULA
99 MIDPO9T =MULA
,SIDEB>3
,/&>DS
..,5RI*;T ( ,GEOMETRY3 #AE.J ,/UD5TS
USE ! PY?AGOR5 !OREM 6DET]M9E .4T.E &
F9D MISS+ L5G?S ( SIDES ( "R TRIANGLES4
,6F9D ! 4T.E .;D 2T .,A @7 .;X #A @1
.;Y #A @7 & .;,B @7 .;X #B @1 .;Y #B
@7@1 APPLY ! ,PY?AGOR1N !OREM 6"R
TRIANGLE .,,ABC4
7;,,AB7 #B .K 7.;,,AC7 #B @+ 7.,,BC7
#B
.;D #B .K @7 .;X #B -- .;X #A @7 #B @+
@7 .;Y #B -- .;Y #A @7 #B
,! F9AL EQU,N IS ! .4T.E .=MULA4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,! ,4T.E ,=MULA
,! 4T.E .;D 2T @7 .;X #A @1@1 .;Y #A &
@7 .;X #B @1 .;Y #B @7 IS
..,EXAMPLE #A ,,/&>DIZ$ ,,TE/
.,,PRACTICE
,:AT IS ! 4T.E 2T 7--#C1 #E7 & 7#D1
--#A78
.,A
.;,B
.;,C
.;,D #AC
,SOLU;N
,LET @7 .;X #A @1 .;Y #A @7 .K @7
--.#C1 .#E @7 & @7 .;X #B @1 .;Y #B @7
.K @7 .#D1 --.#A @7
,! CORRECT ANSW] IS ,C4 ..,A ;,B ;,C
.;,D
,EXAMPLE .#B ,CLASSIFY A TRIANGLE US+
! 4T.E =MULA
,CLASSIFY .,,ABC Z .SCAL5E1 .ISOSCELES
@1 OR .EQUILAT]AL4
,2C .,,BC .K .;,,AC @1 .,,ABC IS
ISOSCELES4
------------------------------------#FAE
..,GUID$ ,PRACTICE = ,EXAMPLES #A &
.#B
.#A4 ,:AT IS ! 4T.E 2T 7#C1 --#C7 &
7--#A1 #E78
.#B4 ,! V]TICES (A TRIANGLE >E .;,R
7--;L1 #C71 ;,S7#E1 #B71 & .;,T 7#C1
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.ISOSCELES @1 OR .EQUILAT]AL4
,,KEY ,,3CEPT
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,! ,MIDPO9T ,=MULA
,A L9E SEG;T'S .MIDPO9T IS EQUIDISTANT
F ! SEG;T'S 5DPO9TS4 ,! .MIDPO9T .=MULA
@1 %[N 2L1 GIVES ! MIDPO9T (! L9E SEG;T
JO9+ .,A @7 .;X #A @1 .;Y #A @7 & .;,B
@7 .;X #B @1 .;Y #B @7@4
,9 ^WS1 EA* COORD9ATE ( ;,M IS ! M1N
(! CORRESPOND+ COORD9ATES ( ,A& .,B4
,EXAMPLE #C ,F9D ! MIDPO9T (A L9E
SEG;T
,F9D ! MIDPO9T (! L9E SEG;T JO9+
7--#E1A7 & 7--#A1 #F74
,SOLU;N
,LET @7 .;X #A @1 .;Y ;L.' @7 .K @7
--.#E1 .#A @7 & @7 .;X #B @1 .;Y #B @7
.K @7 --.#A1 .#F @7@4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
,EXAMPLE #D
,F9D A P]P5DICUL> BISECTOR
,,REVIEW ,,EQU,NS
,= HELP ) WRIT+ EQU,NS ( P]P5DICUL>
L9ES1 SEE P4 #IH @4
,WRITE AN EQU,N =! P]P5DICUL> BISECTOR
(! L9E SEG;T JO9+ .,A 7--#C1D7 & .;,B
7#E1F74
,SOLU;N
.,,/EP .#A .,F9D ! MIDPO9T (! L9E
SEG;T4
.,,/EP .#B .,CALCULATE ! SLOPE ( @4
.,,/EP .#C .,F9D ! SLOPE (! P]P5DICUL>
BISECTOR3
.,,/EP#D .,USE PO9T--SLOPE =M3 .;Y --
.#E .K --.#D @7 .;X -- .#A @7@1 OR .;Y
.K --#D .;X @+ .#I @4
,AN EQU,N =! P]P5DICUL> BISECTOR ( IS
.;Y .K --#D .;X @+ #I4
------------------------------------#FAF
..,,F9D+ ,A ,,CIRCLE'S .,,C5T] ,RECALL
F GEOMETRY T ! P]P5DICUL> BISECTOR ( ANY
*ORD (A CIRCLE PASSES "? ! CIRCLE'S
C5T]4 ,Y C USE ? !OREM 6F9D ! C5T] (A
CIRCLE GIV5 ?REE PO9TS ON ! CIRCLE4
,EXAMPLE #E ,SOLVE A MULTI--/EP PRO#M
.,,A/]OID .,,CRAT] ,_M SCI5TI/S 2LIEVE
T AN A/]OID SLAMM$ 96,E>? AB #FE MILLION
YE>S AGO ON :AT IS N[ ,MEXICO'S ,YUCATAN
P59SULA1 CR1T+ AN ENORM\S CRAT] T IS N[
DEEPLY BURI$ 0S$I;T4 ,USE ! LABEL$ PO9TS
ON ! \TL9E (! CIRCUL> CRAT] 6E/IMATE XS
DIAMET]4 7,EA* UNIT 9 ! COORD9ATE PLANE
REPRES5TS #A MILE47
,SOLU;N
.,,/EP .#A .,WRITE EQU,NS =!
P]P5DICUL> BISECTORS ( US+ ! ME?OD (
,EXAMPLE #D4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;Y .K --;X @+ #CD @3 .,P]P5DICUL>
.BISECTOR .(
.;Y .K #C .;X @+ #AAJ @3 .,P]P5DICUL>
.BISECTOR .(
.,,/EP .#B .,F9D ! COORD9ATES (! C5T]
(! CIRCLE1 ": 9T]SECT1 0SOLV+ ! SY/EM
=M$ 0! TWO EQU,NS 9 ,/EP #A4
,,REVIEW ,,SY/EMS
,= HELP ) SOLV+ SY/EMS ( EQU,NS1 SEE
P4 #AFJ @4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;Y .K -- .;X @+ #CD @3 .,WRITE .F/
.EQU,N @4
#C .;X @+ #AAJ .K --.;X @+ #CD @3
,SUB/ITUTE = .;Y @4
#D .;X .K --#GF @3 .,SIMPLIFY @4
.;X .K --#AI @3 ,SOLVE =.' ;X @4
.;Y .K --7--#AI7 @+ #CD @3 ,SUB/ITUTE
!.' ;X --VALUE 96! F/ EQU,N.' @4
.;Y .K #EC @3 ,SOLVE =.' ;Y @4
,! C5T] (! CIRCLE IS ;,C7--#AI1 #EC74
.,,/EP .#C .,CALCULATE ! RADIUS (!
CIRCLE US+ ! 4T.E =MULA4 ,! RADIUS IS !
4T.E 2T .;,C & ANY (! ?REE GIV5 PO9TS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
@3 ,USE @7 .;X #A @1 .;Y #A @7 .K
7#J1J7 & @7 .;X #B @1 .;Y #B @7 .K
7--#AI1EC7 @4
,! CRAT] HAS A DIAMET] ( AB #B7#EF.C7
.K #AAB.F MILES4
..,GUID$ ,PRACTICE = ,EXAMPLES #C1D1 &
.#E
,=! L9E SEG;T JO9+ ! TWO GIV5 PO9TS1
7A7 F9D ! MIDPO9T & 7;B7 WRITE AN EQU,N
=! P]P5DICUL> BISECTOR4
.#C4 7#J1 #J71 7--#D1 #AB7
.#D4 7--#B1 #A71 7#D1 --#G7
.#E4 7#C1 #H71 7--#E1 --#AJ7
.#F4 ,! PO9TS 7#J1 #J71 7#F1 --#B71 &
7#AF1 #H7 LIE ON A CIRCLE4 ,USE ! ME?OD
GIV5 9 ,EXAMPLE #E 6F9D ! DIAMET] (!
CIRCLE4
------------------------------------#FAG
#I.A ,EX]CISES
,HOME"W ,KEY
.K ..,,"W$--,,\ ,,SOLU;NS .ON P4
,,WS#AE ..= ,EXS4 #G1BG1 & .#EC
.K ..,,/&>DIZ$ ,,TE/ ,,PRACTICE ,EXS4
#B1AH1AI1CG1 & .#EF
,SKILL ,PRACTICE
.#A4 ,,VOCABUL>Y ,/ATE ! 4T.E &
MIDPO9T =MULAS4
.#B4 .,,WRIT+ ,:5 F9D+ ! MIDPO9T (A
L9E SEG;T JO9+ TWO PO9TS1 DOES X MATT] :
PO9T Y *OOSE Z @7 .;X #A @1 .;Y #A @7@8
.,EXPLA94
,,EXAMPLES #A & #C
ON PP4 #FAD --#FAE = ,EXS4 #C--#BA
,,US+ ,,! ,,=MULAS ,F9D ! 4T.E 2T !
TWO PO9TS4 ,!N F9D ! MIDPO9T (! L9E
SEG;T JO9+ ! TWO PO9TS4
.#C4 7#J1 #J71 7#H1 #AE7
.#D4 7#J1 #J71 7#D1 #B7
.#E4 7#J1 #F71 7#E1 --#D7
.#F4 7--#G1 #J71 7#E1 #C7
.#G4 7#B1 --#A71 7#F1 --#E7
.#H4 7--#A1 --#B71 7#H1 #D7
.#I4 7--#D1 #H71 7#H1 --#D7
.#AJ4 7#F1 --#C71 7#AJ1 --#I7
.#AA4 7--#D1 #D71 7#E1 --#D7
.#AB4 7#AA1 --#AB71 7#AH1 #AB7
.#AC4 7--#E1 #A71 7#AE1 #H7
.#AD4 7#I1 #I71 7--#AF1 --#AF7
.#AE4 7--#C.H1 #AE71 7#F.B1 --#AA7
.#AF4 7#A.E1 #D71 7#B.C1 #I7
.#AG4 7--#B.D1 --#F.G71 7#C.A1 --#E.C7
#AH4 .,,MULTIPLE .,,*OICE ,:AT IS !
4T.E 2T 7--#D1 #C7 & 7#F1 #F78
,A
;,B
;,C
;,D
#AI4 .,,MULTIPLE .,,*OICE ,:AT IS !
MIDPO9T (! L9E SEG;T JO9+ 7--#C1 #G7 &
7#E1 --#B78
,A
;,B
;,C
;,D
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 F9D+ ! 4T.E 2T ! TWO PO9TS4
.#BJ4 7#E1--#A71 7#B1 #F7
.#BA4 7--#D1 #C71 7#B1 #H7
,,EXAMPLE #B
ON P4 #FAD = ,EXS4 #BB--#CJ
,,CLASSIFY+ ,,TRIANGLES ,! V]TICES (A
TRIANGLE >E GIV54 ,CLASSIFY ! TRIANGLE Z
.SCAL5E1 .ISOSCELES @1 OR .EQUILAT]AL4
.#BB4 7--#E1 #J71 7#J1 #F71 7#E1 #J7
.#BC4 7#J1 --#C71 7#J1 #C71 7#C1 #J7
.#BD4 7#C1 #E71 7#E1 --#C71 7#G1 --#C7
.#BE4 7--#B1 #E71 7#A1 --#A71 7#D1 #F7
.#BF4 7#A1 #D71 7#D1 #A71 7#G1 #D7
.#BG4 7--#D1 #A71 7--#B1 #F71 7#J1
--#A7
.#BH4 7--#A1 --#F71 7#A1 #A71 7#D1
--#E7
.#BI4 7--#D1 #C71 7#B1 --#A71 7#H1
--#A7
.#CJ4 7#C1 #E71 7#F1 #I71 7#AA1 #I7
,,EXAMPLE #D
ON P4 #FAE = ,EXS4 #CA--#CF
,,WRIT+ ,,EQU,NS ,WRITE AN EQU,N =!
P]P5DICUL> BISECTOR (! L9E SEG;T JO9+ !
TWO PO9TS4
.#CA4 7#C1 #H71 7#G1 #AD7
.#CB4 7--#E1 #F71 7#A1 #H7
.#CC4 7--#C1 --#F71 7--#A1 #B7
.#CD4 7#A1 #D71 7#F1 --#F7
.#CE4 7--#C1 --#E71 7#I1 --#B7
.#CF4 7#E1 #AJ71 7#AJ1 #G7
.#CG4 .,,OP5--.,,5D$ .,,MA? ,F9D TWO
PO9TS N ON ! L9ES .;X .K #D OR .;Y .K #B
S* T ! MIDPO9T (! L9E SEG;T JO9+ ! PO9TS
IS 7#D1 #B74
------------------------------------#FAH
..,,GEOMETRY ,A M$IAN (A TRIANGLE IS A
L9E SEG;T JO9+ A V]TEX &! MIDPO9T (!
OPPOSITE SIDE4 ,! ORD]$ PAIRS REPRES5T
V]TICES (A TRIANGLE4 ,WRITE AN EQU,N (!
L9E 3TA9+ ! M$IAN T JO9S ! F/ V]TEX 6!
SIDE OPPOSITE .X4
.#CH4 7#H1 #D71 7#J1 #J71 7#AJ1 #J7
.#CI4 7#C1 #AJ71 7#D1 #B71 7#AJ1 #H7
.#DJ4 7#B1 #F71 7#C1 #A71 7#G1 #E7
,,F9D+ ,A ,,COORD9ATE ,USE ! GIV5 4T.E
.;D 2T ! TWO PO9TS 6F9D ! VALUE ( .;X OR
.Y4
.#DA4 7#J1 #C71 @7 .;X @1 #E72
.#DB4 7--#C1--#A71 7#B1 .;Y @7@2
.#DC4 @7 .;X @1 #G71 7--#D1 #A72
.#DD4 7;L1 .;Y @7@1 7#H1AC72
.#DE4 .,,R1SON+ ,LET @7 .;X1 .;Y @7 2
ANY PO9T ON ! L9E .;Y .K #B .X4 ,WRITE &
SIMPLIFY AN EQU,N T GIVES ! 4T.E .;D 2T
@7 .;X1 .;Y @7 & 7#B1 #C7 Z A FUNC;N (
.;X AL"O4 ,!N F9D ! COORD9ATES ( TWO
PO9TS ON ! L9E .;Y .K #B .;X T >E EA*
UNITS F 7#B1 #C74
.#DF4 .,,*ALL5GE ,%[ T IS ! MIDPO9T (!
L9E SEG;T ) 5DPO9TS @7 .;X #A @1 .;Y #A
@7 & @7 .;X #B @1 .;Y #B @7@4 ,6D ?1 %[
T ;,M IS EQUIDISTANT F EA* 5DPO9T & T
;,M LIES ON ! L9E 3TA9+ @7 .;X #A @1 .;Y
#A @7 & @7 .;X #B @1 .;Y #B @7@4
,PRO#M ,SOLV+
,,EXAMPLE #A
ON P4 #FAD = ,EXS4 #DG--#EB
#DG4 .,,ROBOTS ,A REMOTE--3TROLL$
ROBOT C 2 9/RUCT$ 6MOVE 05T]+ COORD9ATES
ON A 3TROL PANEL4 ,IF ! ROBOT IS 9/RUCT$
6MOVE F 7#F1 #AA7 /RAI<T TO 7--#B1 #BF71
H[ F> DOES ! ROBOT MOVE8 ,ASSUME !
COORD9ATES >E 9 MET]S4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
,,HELICOPT] ,,RESCUE ,9 ,EX]CISES
#DH--#EA1 USE ! 9=M,N GIV5 6F9D ! 4T.E A
M$ICAL EVACU,N 78M$EVAC07 HELICOPT] WD H
6FLY 6,MEMORIAL ,M$ICAL ,C5T] F EA*
LOC,N4
,! ,HI<WAY ,DE"P;T 9 ,SANGAMON ,C.TY1
,ILL9OIS1 USES A MAP T HAS XS ORIG9 9
C5TRAL ,SPR+FIELD4 ,EA* UNIT ON ! MAP
REPRES5TS #A MILE1 &! LRS ;,N1 ;,S1 ;,E1
& ;,W 9DICATE DIREC;N4 ,= EXAMPLE1 #D;,W
#E.F;,N IS #D MILES WE/ & #E.F MILES
NOR? (! ORIG94 ,ON A COORD9ATE PLANE1
#D;,W #E.F;,N CORRESPONDS 6! PO9T 7--#D1
#E.F74 ,MEMORIAL ,M$ICAL IS AT #J
#J.E;,N1 OR 7#J1 #J.E74
.#DH4 ,CAPITAL ,AIRPORT
.#DI4 ,UNIV]S;Y ( ,ILL9OIS
.#EJ4 ,WA%+TON ,P>K
.#EA4 ,SPAULD+ ,DAM
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#EB4 .,,-MUT+ ,6GET F H] HOME 6H]
(FICE1 ,LI M/ DRIVE >.D A LAKE4 ,IF %E
DRIVES #B MILES NOR?1 !N #E MILES EA/1 &
!N #D MILES S\?1 :AT IS ! /RAI<T--L9E
4T.E 2T ,LI'S HOME & H] (FICE8
.K ..,,"W$--,,\ ,,SOLU;NS ON P4,W
.;,S#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#FAI
,,EXAMPLE #C
ON P4 #FAE = ,EX4 #EC
.#EC4 .,,MULTI--.,,/EP .,,PRO#M ,!
DIAGRAM %[S "P (A TRAIL SY/EM AT A
NATURE PRES]VE4 ,EA* UNIT REPRES5TS #J.A
MILE4 ,SUPPOSE T Y G F ! VISITOR C5T]
.;,V 6! OBS]V,N /& ;,S1 & !N TAKE A BR1K
AT ;,M1 HALFWAY 2T ! OBS]V,N /& &!
PICNIC >EA .,P4
A4 ,:AT >E ! COORD9ATES ( ;,M8
B4 ,:AT IS ! TOTAL 4T.E TRAVEL$ F .;,V
6;,M8
C4 ,:AT IS ! 4T.E F ;,M BACK 6.;,V "?
;,P8
,,EXAMPLE #C
ON P4 #FAF = ,EX4 #ED
.#ED4 .,,>*AEOLOGY ,:ILE ON AN
>*AEOLOGICAL DIG1 Y UNCOV] A PIECE (A
CIRCUL> DI%4 ,Y LAY ! PIECE ON A
COORD9ATE PLANE & M>K ?REE PO9TS ON !
DI%'S $GE AT 7--#D1 #B71 7#J1 #J71 &
7#F1 #D7 ": EA* UNIT REPRES5TS #A 9*4
,:AT 0 ! ORIG9AL DIAMET] (! DI%8
.#EE4 .,,METEOR .,,CRAT]S ,FIVE METEOR
CRAT]S >E CLU/]$ TGR NE> ,ODESSA1
,TEXAS4 ,?REE PO9TS ON ! $GE (! CIRCUL>
MA9 CRAT] C 2 REPRES5T$ BY 7--#BBJ1
#BBJ71 7#J1 #J71 & 7#BJJ1 #DJ7 ": EA*
UNIT REPRES5TS #A FOOT4 ,:AT IS !
DIAMET] (! CRAT] 6! NE>E/ #AJ FEET8
.#EF4 .,,EXT5D$ .,,RESPONSE ,Y >E
ORD]+ A TRIANGUL> SAIL = YR SAILBOAT4
,:5 Y GET ! SAIL1 Y PLAN 6SEW A ?9
DECORATIVE /RIP 3NECT+ ! MIDPO9TS .;,M
#A & ;,M #B ( TWO SIDES (! SAIL1 Z %[N 9
! DIAGRAM4
A4 ,WRITE EXPRES.NS =! COORD9ATES (
.;,M #A & ;,M #B @4
B4 ,WRITE A SIMPLIFI$ EXPRES.N =! L5G?
(! /RIP4 .,-P>E ? L5G? )! L5G? (! SAIL'S
BASE4
C4 ,D YR RESULTS F "P 7;B7 DEP5D ^U !
%APE (! TRIANGUL> SAIL8 .,EXPLA94
.#EG4 .,,*ALL5GE ,AT "T .;T .K #J1 A
C> 2G9S TRAVEL+ EA/ AT #FJ MILES P] H\R
F A PO9T #AJJ MILES WE/ & #DJ MILES NOR?
(A RADIO T[]4 ,! T[] HAS A TRANSMIS.N
RANGE ( #EJ MILES4 ,USE ! 4T.E =MULA
6F9D ! "TS .;T DUR+ : ! C> IS 9 RANGE (!
T[]4
,MIX$ ,REVIEW
.,,PREVIEW ,PREP>E = ,LESSON #I.B 9
,EXS4 #EH-FC4
#EH4 .;Y .K #C .;X #B
#EI4 .;Y .K --#D .;X #B
#FJ4 .;Y .K --#B .;X #B
#FA4 .;Y .K .;X #B
#FB4
#FC4 .;Y .K .;X #B
,FACTOR ! EXPRES.N4
#FD4 .;X #B -- #F .;X -- #AF @7 P4
#BEB @7
#FE4 .;X #B -- #AE .;X @+ #ED @7 P4
#BEB @7
#FF4 #H .;X #B @+ #CG .;X @+ #BJ @7 P4
#BEI @7
#FG4 #AB .;X #B -- #AC .;X @+ #C @7 P4
#BEI @7
#FH4 .;X #C @+ #E .;X #B -- #I .;X --
#DE @7 P4 #CEC @7
#FI4 .;X #C -- #FD @7 P4 #CEC @7
,SOLVE ! EQU,N4 ,*ECK = EXTRANE\S
SOLU;NS4
#GJ4
#GA4
#GB4
#GC4
#GD4
#GE4
.,,EXTRA .,,PRACTICE = ,LESSON #I.A1
P4 #AJAH
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#FBJ
#I.B ,GRAPH & ,WRITE ,EQU,NS (
,P>ABOLAS
.,2F ,Y GRAPH$ & WROTE EQU,NS (
P>ABOLAS T OP5 UP OR D[N4
.,N[ ,Y W GRAPH & WRITE EQU,NS (
P>ABOLAS T OP5 LEFT OR "R4
.,:Y8 S Y C MODEL S.D PROJEC;N1 Z 9
,EX4 #EF4
,KEY ,VOCABUL>Y
99 FOCUS
99 DIRECTRIX
99 P>ABOLA1 .P4 .#BCF
99 .V]TEX @1 P4 #BCF
,SIDEB>3
,/&>DS
#AF.J ,/UD5TS DEMON/RATE & EXPLA9 H[ !
GEOMETRY (! GRAPH (A 3IC SEC;N 7E4G41
ASYMPTOTES1 FOCI1 E35TRIC;Y7 DEP5DS ON !
COE6ICI5TS (! QUADRATIC EQU,N REPRES5T+
X4
,Y "K T ! GRAPH ( .;Y .K .AX #B IS A
P>ABOLA T OP5S UP OR D[N ) V]TEX 7#J1
#J7 & AXIS ( SYMMETRY .;X .K #J4 ,ON ANY
P>ABOLA1 EA* PO9T IS EQUIDISTANT F A
PO9T CALL$ ! .FOCUS &A L9E CALL$ !
.DIRECTRIX4
,PRODNOTE3 ,PRODUC;N NOTE3 CAP;NS
ASSOCIAT$ ) ? IMAGE >E LABELS T
CORRESPOND 6TEXT )9 ! IMAGE4
,PICTURE3 ..,! FOCUS LIES ON ! AXIS (
.SYMMETRY4
,PICTURE3 ..,! V]TEX LIES HALFWAY 2T !
FOCUS &! .DIRECTRIX4
,PICTURE3 ..,! DIRECTRIX IS P]P5DICUL>
6! AXIS ( .SYMMETRY4
,! EQU,N (A P>ABOLA T OP5S UP OR D[N &
HAS V]TEX 7#J1 #J7 C AL 2 WRITT5 9 ! =M
;X #B .K .#D;PY4 ,P>ABOLAS C OP5 LEFT OR
"R Z WELL1 9 : CASE ! EQU,N HAS ! =M .;Y
#B .K #D .PX :5 ! V]TEX IS 7#J1 #J74
,NOTE 2L T = ANY P>ABOLA1 ! FOCUS &
DIRECTRIX EA* LIE @\.;P@\ UNITS F !
V]TEX4
.;X #B .K .#D .PY1 .;P .1 .#J
.;X #B .K .#D .PY1 .;P #J
,,ID5TIFY ,,FUNC;NS
,NOTICE T P>ABOLAS T OP5 LEFT OR "R D
.N REPRES5T FUNC;NS4
;Y #B .K #D .PX,.;P .1 #J
.;Y #B .K #D .PX1 .;P "K #J
------------------------------------#FBA
,,KEY ,,3CEPT
,= YR ,NOTEBOOK
,/&>D ,EQU,N (A ,P>ABOLA ) ,V]TEX AT !
,ORIG9
,! /&>D =M (! EQU,N (A P>ABOLA ) V]TEX
AT 7#J1 #J7 IS Z FOLL[S3
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,EQU,N3 ,FOCUS3 ,DIRECTRIX3 ,AXIS (
,SYMMETRY
.;X #B .K #D .PY @3 7.#J,.;P7 @3
.;Y.K--.;P @3 ,V]TICAL @7 .;X .K #J7
.;Y #B .K #D .PX @3 7.;P1.#J7 @3 .;X
.K --.;P @3 ,HORIZONTAL @7 .;Y .K #J7
,EXAMPLE #A
,GRAPH AN EQU,N (A P>ABOLA
,GRAPH @4 ,ID5TIFY ! FOCUS1 DIRECTRIX1
& AXIS ( SYMMETRY4
,SOLU;N
.,,/EP .#A .,REWRITE ! EQU,N 9 /&>D
=M4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
@3 ,WRITE ORIG9AL EQU,N4
--#H .;X .K .;Y #B @3 ,MULTIPLY EA*
SIDE BY --#H4
.,,/EP .#B ,ID5TIFY ! FOCUS1
DIRECTRIX1 & AXIS ( SYMMETRY4 ,! EQU,N
HAS ! =M .;Y #B .K #D .PX ": .;P .K
--#B4 ,! FOCUS IS 7;P1 #J71 OR 7--#B1
#J74 ,! DIRECTRIX IS ..;X .K--.;P @1 OR
.;X .K .#B4 ,2C .;Y IS SQU>$1 ! AXIS (
SYMMETRY IS ! .;X --AXIS4
.,,/EP .#C ,DRAW ! P>ABOLA 0MAK+ A TA#
( VALUES & PLOTT+ PO9TS4 ,2C .;P "K #J1
! P>ABOLA OP5S 6! LEFT4 ,S1 USE ONLY
NEGATIVE .;X --VALUES4
,,SOLVE ,,= .;,Y
,6FILL 9 ! TA#1 NOTE T 2C --#H .;X .K
.;Y #B @1 @4 ,! VALUE ( .;Y W 2 A R1L
NUMB] ONLY :5 .;X"K.K.#J4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 --#A3 --#B3 --#C3 --#D3 --#E
.;Y @3 +-#B.HC3 +-#D3 +-#D.IJ3
+-#E.FF3 +-#FCB
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
,EXAMPLE #B
,WRITE AN EQU,N (A P>ABOLA
,WRITE AN EQU,N (! P>ABOLA %[N4
,SOLU;N
,! GRAPH %[S T ! V]TEX IS 7#J1 #J7 &!
DIRECTRIX IS ,SUB/ITUTE = .;P 9 ! /&>D
=M (! EQU,N (A P>ABOLA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X #B .K #D .PY @3 ..,/&>D =M1
V]TICAL AXIS ( .SYMMETRY
@3 ,SUB/ITUTE = .P4
.;X #B .K #F .;Y @3 .,SIMPLIFY4
------------------------------------#FBB
..,GUID$ ,PRACTICE = ,EXAMPLES ;L &
.#B
,GRAPH ! EQU,N4 ,ID5TIFY ! FOCUS1
DIRECTRIX1 & AXIS ( SYMMETRY (! P>ABOLA4
#A4 .;Y #B .K --.#F .;X
#B4 ;X #B .K .#B;Y
.#C4
.#D4
,WRITE ! /&>D =M (! EQU,N (! P>ABOLA )
V]TEX AT 7#J1 #J7 &! GIV5 DIRECTRIX OR
FOCUS4
.#E4 ,DIRECTRIX3 .;Y .K #B
.#F4 ,DIRECTRIX3 .;X .K #D
.#G4 ,FOCUS3 7--#B1 #J7
.#H4 ,FOCUS3 7#J1 #C7
.,,P>ABOLIC .,,REFLECTORS .,P>ABOLIC
.REFLECTORS H CROSS SEC;NS T >E
P>ABOLAS4 ,9COM+ S.D1 LI<T1 OR O!R 5]GY
T >RIVES AT A P>ABOLIC REFLECTOR P>ALLEL
6! AXIS ( SYMMETRY IS DIRECT$ 6! FOCUS
7,DIAGRAM #A74 ,SIMIL>LY1 5]GY T IS
EMITT$ F ! FOCUS (A P>ABOLIC REFLECTOR &
!N /RIKES ! REFLECTOR IS DIRECT$ P>ALLEL
6! AXIS ( SYMMETRY 7,DIAGRAM #B74
,EXAMPLE #C
,SOLVE A MULTI--/EP PRO#M
.,,SOL> .,,5]GY ,! ,EURO,DI%1 DEVELOP$
6PROVIDE ELECTRIC;Y 9 REMOTE >1S1 USES A
P>ABOLIC REFLECTOR 63C5TRATE SUNLI<T
ONTO A HI<--E6ICI5CY 5G9E LOCAT$ AT !
REFLECTOR'S FOCUS4 ,! SUNLI<T H1TS
HELIUM 6#FEJ;DG;,C 6P[] ! 5G9E4
99 ,WRITE AN EQU,N =! ,EURO,DI%'S
CROSS SEC;N ) XS V]TEX AT 7#J1 #J74
99 ,H[ DEEP IS ! DI%8
,SOLU;N
.,,/EP .#A .,WRITE AN EQU,N =! CROSS
SEC;N4 ,! 5G9E IS AT ! FOCUS1 : IS _\
.;P _\ .K #D.E MET]S F ! V]TEX4 ,2C !
FOCUS IS ABV ! V]TEX1 .;P IS POSITIVE1 S
.;P .K #D.E4 ,AN EQU,N =! CROSS SEC;N (!
,EURO,DI% ) XS V]TEX AT ! ORIG9 IS Z
FOLL[S3
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X #B .K #D .;P ;Y.' @3 ,/&>D =M1
V]TICAL AXIS ( SYMMETRY
.;X #B .K #D7 .#D..E @7 .;Y @3
,SUB/ITUTE #D.E = P4
.;X #B .K #AH .;Y @3 ,SIMPLIFY4
.,,/EP .#B .,F9D ! DEP? (! ,EURO,DI%4
,! DEP? IS ! .;Y --VALUE AT ! DI%'S
\TSIDE $GE4 ,! DI% EXT5DS MET]S 6EI SIDE
(! V]TEX 7#J1 #J71 S SUB/ITUTE .#D..BE =
.;X 9 ! EQU,N F ,/EP #A4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X #B .K #AH .;Y @3 ..,EQU,N =! CROSS
.SEC;N
@7 #D.BE @7 #B .K #AH .;Y @3
,SUB/ITUTE #D.BE =.' X4.-
.#A..J .;Y @3 ,SOLVE =.' ;Y @4
,! DI% IS AB #A MET] DEEP4
------------------------------------#FBC
..,GUID$ ,PRACTICE = ,EXAMPLE .#C
.#I4 .,,MICROWAVES ,A P>ABOLIC
MICROWAVE ANT5NA IS #AF FEET 9 DIAMET]4
,F9D AN EQU,N =! CROSS SEC;N (! ANT5NA )
XS V]TEX AT ! ORIG9 & XS FOCUS #AJ FEET
6! "R ( XS V]TEX4 ,!N F9D ! ANT5NA'S
DEP?4
#I.B ,EX]CISES
,HOME"W ,KEY
.K .,,"W$--.,,\ .,,SOLU;NS
ON P4 ,,WS#AF = ,EXS4 #AE1BG1 & #EG
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.,EXS4 #B1BE1 #CH1EA1EB1 & #EI
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,A
P>ABOLA IS ! SET ( ALL PO9TS 9 A PLANE
EQUIDISTANT F A PO9T CALL$ ! @8 &A L9E
CALL$ ! @8 @4
.#B4 .,,WRIT+ .,-P>E ! GRAPHS ( .;X #B
.K #D .PY & .;Y #B .K #D .PX @4
,,EXAMPLE #A
ON P4 #FBA = ,EXS4 #C--#BE
.,,GRAPH+ ,GRAPH ! EQU,N4 ,ID5TIFY !
FOCUS1 DIRECTRIX1 & AXIS ( SYMMETRY (!
P>ABOLA4
.#C4 .;Y #B .K #AF .;X
.#D4 .;X #B .K --#F .;Y
.#E4 .;X #B .K #BJ .;Y
.#F4 .;Y #B .K #BH .;X
.#G4 .;Y #B .K --;L#J .;X
.#H4 .;X #B .K #CJ .;Y
#I4 .;Y #B .K --.#B .;X
.#AJ4 .;X #B .K --#CF .;Y
.#AA4 .;X #B .K #AB .;Y
#AB4 --..#B ;Y .K .;X #B
#AC4 .;X .K .#D;Y #B
.#AD4 --.;X #B .K #DH .;Y
.;L#E4 #E .;X #B .K --#AE .;Y
.#AF4 -- .;Y #B .K #AH .;X
.#AG4 --#BD .;X .K #C .;Y #B
.#AH4 #AD .;X .K #F .;Y #B
.#AI4
.#BJ4 #D .;X -- ;LL .;Y #B .K #J
.#BA4 #E .;X #B @+ #AB .;Y .K #J
.#BB4
.,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 GRAPH+ ! P>ABOLA4
.#BC4 --#F .;X @+ .;Y #B .K #J
.#BD4 #J.E .;Y #B @+ .;X .K .#J
#BE4 .,,MULTIPLE .,,*OICE ,:AT IS !
DIRECTRIX (! P>ABOLA #AE .;Y @+ #C .;X
#B .K #J8
,A .;X .K--#E
;,B .;X .K--#A.BE
;,C .;Y .K--#A.BE
;,D .;Y .K #A.BE
,,EXAMPLE #B
ON P4 #FBA = ,EXS4 #BF--#EJ
,,WRIT+ ,,EQU,NS ,WRITE ! /&>D =M (!
EQU,N (! P>ABOLA )! GIV5 FOCUS & V]TEX
AT 7#J1 #J74
.#BF4 7#B1 #J7
.#BG4 7--#E1 #J7
.#BH4 7#C1 #J7 #BI4 7#J1 --#D7
.#CJ4 7#J1 #H7
.#CA4 7#J1 --#AJ7
.#CB4 7#J1 --#F7 #CC4 7--#I1 #J7
.#CD4
.#CE4
.#CF4
.#CG4
------------------------------------#FBD
#CH4 .,,MULTIPLE .,,*OICE ,:AT IS AN
EQU,N (! P>ABOLA ) FOCUS AT 7--#H1J7 &
V]TEX AT 7#J1J78
,A .;Y #B .K --#CB .;X
;,B .;Y #B .K --#J.E .;X
.,C4 .;X #B .K --#H .;Y
;,D .;X #B .K --#CB .;Y
,,WRIT+ ,,EQU,NS ,WRITE ! /&>D =M (!
EQU,N (! P>ABOLA )! GIV5 DIRECTRIX &
V]TEX AT 7#J1 #J74
.#CI4 .;X .K #C
.#DJ4 .;Y .K --#G
.#DA4 .;X .K --#E
.#DB4 .;Y .K #AB
.#DC4 .;Y .K --#D
.#DD4 .;X .K --#B
.#DE4 .;Y .K #F
.#DF4 .;X .K #AA
.#DG4
.#DH4
.#DI4
#EJ4
.#EA4 .,,%ORT .,,RESPONSE ,PREDICT H[
! 9DICAT$ *ANGE 9 .A W A6ECT ! FOCUS1
DIRECTRIX1 & %APE (! GIV5 EQU,N'S GRAPH4
,!N GRAPH BO? ! ORIG9AL & REVIS$ EQU,NS
9 ! SAME COORD9ATE PLANE4
A4 ;X #B .K .AY2 .A *ANGES F #A 6#D
B4 .;Y #B .K .AX2 .A *ANGES F #F TO
#EB4 .,,WRIT+ ,SUPPOSE T .;X #B .K #D
.PY & .;Y .K .AX #B REPRES5T ! SAME
P>ABOLA4 .,EXPLA9 H[ .A & .;P .AXE
RELAT$4
#EC4 .,,VISUAL .,,?9K+ ,Z _\ .;P _\
9CR1SES1 H[ DOES ! WID? (! GRAPH ( .;X
#B .K #D .PY *ANGE8 .,EXPLA94
#ED4 .,,*ALL5GE ,3SID] ! P>ABOLA )
FOCUS 7#J1 .;P @7 & DIRECTRIX .;Y .K
--.P4 ,LET @7 .;X1 .;Y @7 2 ANY PO9T ON
! P>ABOLA4 ,USE ! FACT T @7 .;X1 .;Y @7
IS EQUIDISTANT F ! FOCUS & DIRECTRIX 6%[
T .;X #B .K #D .PY @4
,PRO#M ,SOLV+
,,EXAMPLE #C
ON P4 #FBB = ,EXS4 #EE--#EI
.#EE4 .,,SOL> .,,5]GY ,SOL> 5]GY C 2
3C5TRAT$ US+ L;G TR\<S T H A P>ABOLIC
CROSS SEC;N4 ,! COLLECT$ 5]GY'S USES
9CLUDE H1T+ BUILD+S1 PRODUC+ ELECTRIC;Y1
& PRODUC+ FRE% WAT] F S1WAT]4 ,WRITE AN
EQU,N =! CROSS SEC;N (! TR\< %[N4 ,H[
DEEP IS X8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#EF4 .,,BIOLOGY ,SCI5TI/S /UDY+
DOLPH9 .E*OLOC,N C SIMULATE ! PROJEC;N
(A DOLPH9'S CLICK+ S.DS US+ -PUT]
MODELS4 ,! MODELS ORIG9ATE ! S.DS AT !
FOCUS (A P>ABOLIC REFLECTOR4 ,! P>ABOLA
9 ! GRAPH MODELS ! CROSS SEC;N 7) UNITS
9 9*ES7 (! REFLECTOR US$ 6SIMULATE S.D
PROJEC;N =A BOTTLENOSE DOLPH94 ,:AT IS !
.FOCAL .L5G? 7! 4T.E F ! V]TEX 6!
FOCUS78
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.K .,,"W$--.,,\ .,,SOLU;NS
ON .P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#FBE
#EG4 .,,MULTI--.,,/EP .,,PRO#M ,!
P>ABOLIC ANT5NA US$ 0A TELEVI.N /,N
6TRANSMIT IS #ADF 9*ES 9 DIAMET]4 ,XS
FOCUS IS #DH 9*ES F ! V]TEX4
A4 ,SKET* ! ANT5NA TWICE3 ONCE OP5+
UPW>D & ONCE OP5+ LEFT4
B4 ,USE YR SKET*ES F "P 7A7 6WRITE TWO
EQU,NS =! ANT5NA'S CROSS SEC;N3 "O (! =M
.;X #B .K #D .PY & "O (! =M .;Y #B .K #D
.PX4
C4 ,H[ DEEP IS ! ANT5NA'S DI%8 ,DOES X
MATT] : EQU,N F "P 7;B7 Y USE 6F9D YR
ANSW]8 .,EXPLA94
#EH4 .,,RADIO .,,TELESCOPES ,! ,V
,L>GE ,>RAY 9 ,NEW ,MEXICO 3SI/S ( #BG
RADIO TELESCOPES4 ,= EA* P>ABOLIC
TELESCOPE DI%1 ! DIAMET] IS #BE MET]S &!
4T.E 2T ! V]TEX & FOCUS IS #J.CF "TS !
DIAMET]4 ,WRITE AN EQU,N =! CROSS SEC;N
(A DI% OP5+ UPW>D ) XS V]TEX AT ! ORIG94
,H[ DEEP IS EA* DI%8
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
#EI4 .,,EXT5D$ .,,RESPONSE ,SE>*LI<TS
USE P>ABOLIC REFLECTORS 6PROJECT _!
B1MS4 ,! CROSS SEC;N (A #I.E--9*--DEEP
SE>*LI<T REFLECTOR HAS EQU,N .;X #B .K
#AJ.E .;Y @4
A4 ,H[ WIDE IS ! B1M ( LI<T PROJECT$ F
! SE>*LI<T'S REFLECTOR8
B4 ,WRITE AN EQU,N =! CROSS SEC;N (A
REFLECTOR T HAS ! SAME DEP? Z ! ORIG9AL
REFLECTOR1 B : PROJECTS A WID] B1M4
.,EXPLA9 H[ Y F.D YR ANSW]4 ,H[ WIDE IS
! NEW REFLECTOR'S B1M8
C4 ,REP1T "P 7;B7 =A B1M N>R[] ?AN !
ORIG9AL4
#FJ4 .,,*ALL5GE ,! .LATUS .RECTUM (A
P>ABOLA IS ! L9E SEG;T T IS P>ALLEL 6!
DIRECTRIX1 PASSES "? ! FOCUS1 & HAS
5DPO9TS T LIE ON ! P>ABOLA4 ,F9D ! L5G?
9 T]MS ( .;P (! LATUS RECTUM (A P>ABOLA
) EQU,N .;X #B .K #D .PY4
,MIX$ ,REVIEW
,P]=M ! 9DICAT$ OP],N4
#FA4 @7 .;X #B -- #C7--@7-- .;X #B @+
#D .;X -- #A7 @7 P4 #CDF @7
#FB4 7#B .;X #B -- #B .;X -- #C7 @+
7#G -- .;X -- #C .;X #C @7 @7 P4 #CDF @7
#FC4 @7 .;X #B -- #E .;X @77#B .;X #B
@+ #I .;X -- #C7 @7 P4 #CDF @7
#FD4 @7 .;X @+ #A77#B .;X -- #C7@7 .;X
-- #D7 @7 P4 #CDF @7
#FE4
#FF4
#FG4
#FH4
.,,PREVIEW ,PREP>E = ,LESSON #I.C 9
,EXS4 #FI-GD4
,F9D ! 4T.E 2T ! TWO PO9TS4 @7 P4 #FAD
@7
#FI4 7#B1 #A71 7#H1 #C7
#GJ4 7#H1 --#A717--#B1 #D7
#GA4 7--#C1 #B71 7#E1 #A7
#GB4 7--#AE1 #F71 7--#A1 --#C7
#GC4 7#B1 #C1 #A1 #A71 7--#D1 #F1
--#A1 #D7
#GD4 7#I1 #D1 #F1 #C71 7#H1 #E1 --#C1
#G7
.,,EXTRA .,,PRACTICE = ,LESSON #I.B1
P4 #AJAH
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#FBF
#I.C ,GRAPH & ,WRITE ,EQU,NS (
,CIRCLES
.,2F ,Y GRAPH$ & WROTE EQU,NS (
P>ABOLAS4
.,N[ ,Y W GRAPH & WRITE EQU,NS (
CIRCLES4
.,:Y8 ,S Y C MODEL TRANSMIS.N RANGES1
Z 9 ,EX4 #FB4
,KEY ,VOCABUL>Y
99 CIRCLE
99 C5T]
99 RADIUS
,SIDEB>3
,/&>DS
#AF.J ,/UD5TS DEMON/RATE & EXPLA9 H[ !
GEOMETRY (! GRAPH (A 3IC SEC;N 7E4G41
ASYMPTOTES1 FOCI1 E35TRIC;Y7 DEP5DS ON !
COE6ICI5TS (! QUADRATIC EQU,N REPRES5T+
X4
,A .CIRCLE IS ! SET ( ALL PO9TS @7
.;X1 .;Y @7 9 A PLANE T >E EQUIDISTANT F
A FIX$ PO9T1 CALL$ ! .C5T] (! CIRCLE4 ,!
4T.E .;R 2T ! C5T] & ANY PO9T @7 .;X1
.;Y @7 ON ! CIRCLE IS ! .RADIUS4
,=A CIRCLE ) C5T] AT ! ORIG9 & RADIUS
.;R @1 ! 4T.E 2T ANY PO9T @7 .;X1 .;Y @7
ON ! CIRCLE &! C5T] 7#J1 #J7 IS .;R @1 S
! FOLL[+ IS TRUE3
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
@3 .,4T.E .=MULA
7.;X -- #J7 #B @+ @7 .;Y-- #J7 #B .K
.;R .#B @3 .,SQU>E .EA* .SIDE4
.;X #B @+ .;Y #B .K ;R.' #B @3
.,SIMPLIFY4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,/&>D ,EQU,N (A ,CIRCLE ) ,C5T] AT !
,ORIG9
,! /&>D =M (! EQU,N (A CIRCLE ) C5T]
AT 7#J1 #J7 & RADIUS .;R IS Z FOLL[S3
.;X #B @+ .;Y #B .K .;R #B
,EXAMPLE #A ,GRAPH AN EQU,N (A CIRCLE
,GRAPH .;Y #B .K -- .;X #B @+ #CF4
,ID5TIFY ! RADIUS (! CIRCLE4
,SOLU;N
.,,/EP .#A .,REWRITE ! EQU,N .;Y #B .K
-- .;X #B @+ #CF 9 /&>D =M Z .;X #B @+
.;Y #B .K #CF4
.,,/EP#B .,ID5TIFY ! C5T] & RADIUS4 ,F
! EQU,N1 ! GRAPH IS A CIRCLE C5T]$ AT !
ORIG9 ) RADIUS @4
.,,/EP .#C .,DRAW ! CIRCLE4 ,F/ PLOT
S"EAL 3V5I5T PO9TS T >E #F UNITS F !
ORIG91 S* Z 7#J1 #F71 7#F1 #J71 7#J1
--#F71 & 7--#F1 #J74 ,!N DRAW ! CIRCLE T
PASSES "? ! PO9TS4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
------------------------------------#FBG
,EXAMPLE #B ,WRITE AN EQU,N (A CIRCLE
,! PO9T 7#B1 --#E7 LIES ON A CIRCLE ^:
C5T] IS ! ORIG94 ,WRITE ! /&>D =M (!
EQU,N (! CIRCLE4
,SOLU;N
,2C ! PO9T 7#B1 --#E7 LIES ON !
CIRCLE1 ! CIRCLE'S RADIUS .;R M/ 2 !
4T.E 2T ! C5T] 7#J1 #J7 & 7#B1 --#E74
,USE ! 4T.E =MULA4
,! RADIUS IS @4
,USE ! /&>D =M ) 6WRITE AN EQU,N (!
CIRCLE4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @+ .;Y .K .;R #B @3 .,/&>D .=M
@3 ,SUB/ITUTE.' .-=.' .;R @4
.;X #B @+ .;Y #B .K #BI @3 .,SIMPLIFY4
..,EXAMPLE #C ,/&>DIZ$ ,TE/ .,PRACTICE
,:AT IS AN EQU,N (! L9E TANG5T 6!
CIRCLE .;X #B @+ .;Y #B .K #AC AT 7--#C1
#B78
.,A
.;,B
.;,C
.;,D
,,ELIM9ATE ,,*OICES
,9 ,EXAMPLE #C1 Y C ELIM9ATE *OICE ;,D
2C A QK SKET* (! CIRCLE %[S T ! SLOPE (!
TANG5T L9E AT 7--#C1 #B7 M/ 2 POSITIVE4
,SOLU;N
,A L9E TANG5T 6A CIRCLE IS P]P5DICUL>
6! RADIUS AT ! PO9T ( TANG5CY4 ,2C !
RADIUS 6! PO9T 7--.#C1 .#B7 HAS SLOPE @1
! SLOPE (! TANG5T L9E AT 7--#C1 #B7 IS !
NEGATIVE RECIPROCAL ( @1 OR @4 ,AN EQU,N
(! TANG5T L9E IS Z FOLL[S3
,! CORRECT ANSW] IS ,C4 ..,A ;,B ;,C
.;,D
..,GUID$ ,PRACTICE = ,EXAMPLES #A1B1 &
.#C
,GRAPH ! EQU,N4 ,ID5TIFY ! RADIUS (!
CIRCLE4
.#A4 .;X #B @+ .;Y #B .K #I
.#B4 .;Y #B .K -- .;X #B @+ #DI
.#C4 .;X #B -- #AH .K -- .;Y #B
.#D4 ,WRITE ! /&>D =M (! EQU,N (!
CIRCLE T PASSES "? 7#E1 --#A7 & ^: C5T]
IS ! ORIG94
.#E4 ,WRITE AN EQU,N (! L9E TANG5T 6!
CIRCLE .;X @+ .;Y .K #CG AT 7#F1 #A74
------------------------------------#FBH
.,,CIRCLES .,,& .,,9EQUALITIES ,!
REGIONS 9SIDE & \TSIDE ! CIRCLE .;X #B
@+ .;Y #B .K .;R #B C 2 DESCRIB$
09EQUALITIES1 ) .;X #B @+ .;Y #B "K .;R
#B REPRES5T+ ! REGION 9SIDE ! CIRCLE &
.;X #B @+ .;Y #B .1 .;R #B REPRES5T+ !
REGION \TSIDE ! CIRCLE4
,EXAMPLE #D ,WRITE A CIRCUL> MODEL
.,,CELL .,,PH"OS ,A CELLUL> PH"O T[]
S]VICES A #AJ MILE RADIUS4 ,Y GET A FLAT
TIRE #D MILES EA/ & #I MILES NOR? (!
T[]4 ,>E Y 9 ! T[]'S RANGE8
,PICTURE3 ..,9 ! DIAGRAM ABV1 ! ORIG9
REPRES5TS ! T[] &! POSITIVE ;Y --AXIS
REPRES5TS .NOR?4
,SOLU;N
.,,/EP .#A .,WRITE AN 9EQUAL;Y =!
REGION COV]$ 0! T[]4 ,F ! DIAGRAM1 ?
REGION IS ALL PO9TS T SATISFY ! FOLL[+
9EQUAL;Y3
.;X #B @+ .;Y #B "K #AJ #B
.,,/EP .#B .,SUB/ITUTE ! COORD9ATES
7#D1 #I7 96! 9EQUAL;Y F ,/EP #A4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X #B @+ .;Y #B "K #AJ #B @3
..,9EQUAL;Y F ,/EP .#A
#D #B @+ #I #B #AJ #B @3 ,SUB/ITUTE
=.' ;X .-&.' ;Y @4
#IG "K #AJJ @3 ..,! 9EQUAL;Y IS .TRUE4
,S1 Y >E 9 ! T[]'S RANGE4
,EXAMPLE #E ,APPLY A CIRCUL> MODEL
.,,CELL .,,PH"OS ,9 ,EXAMPLE #D1
SUPPOSE T Y FIX YR TIRE & !N DRIVE S\?4
,= H[ _M M MILES W Y 2 9 RANGE (! T[]8
,SOLU;N
,:5 Y L1VE ! T[]'S RANGE1 Y W 2 AT A
PO9T ON ! CIRCLE .;X #B @+ .;Y #B .K #AJ
#B ^: .;X --COORD9ATE IS #D & ^: .;Y--
COORD9ATE IS NEGATIVE4 ,F9D ! PO9T @7
.#D1 .;Y @7 ": .;Y "K #J ON ! CIRCLE .;X
#B @+ .;Y #B .K #AJ #B @4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X #B @+ .;Y #B .K #AJ #B @3 ..,EQU,N
(! .CIRCLE
.#D #B @+ .;Y #B .K #AJ #B @3
,SUB/ITUTE #D =.' X4.-
@3 ,SOLVE =.' ;Y @4
.;Y +-.#I..B @3 .,USE .A .CALCULATOR4
,2C .;Y "K #J1 .;Y --#I.B4 ,Y W 2 9 !
T[]'S RANGE F 7#D1 #I7 TO 7#D1 --#I.B71
A 4T.E .( _\#I--7--#I.B7 _\ .K #AH.B
MILES4
..,GUID$ ,PRACTICE = ,EXAMPLES #D &
.#E
#F4 .,,:AT .,,IF8 ,9 ,EXAMPLES #D &
#E1 SUPPOSE Y DRIVE WE/ AF FIX+ YR TIRE4
,= H[ _M M MILES W Y 2 9 RANGE (! T[]8
------------------------------------#FBI
#I.C ,EX]CISES
,HOME"W ,KEY
.K .,,"W$--.,,\ .,,SOLU;NS
ON P4 ,,WS#AF = ,EXS4 #AG1CI1 & #FE
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 #B1BA1DC1EI1FD1 & #FF
.K .,,MULTIPLE .,,REPRES5T,NS
,EX#.FH
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,! RADIUS (A CIRCLE
IS ! 4T.E F ANY PO9T ON ! CIRCLE 6A FIX$
PO9T CALL$ ! CIRCLE'S @8 @4
.#B4 .,,WRIT+ ,H[ >E ! SLOPE (A L9E
TANG5T 6A CIRCLE &! SLOPE (! RADIUS AT !
PO9T ( TANG5CY RELAT$8
,,EXAMPLE #A
ON P4 #FBF = ,EXS4 #C--#BA
..,,MAT*+ ,,GRAPHS ,MAT* ! EQU,N ) XS
.GRAPH @1
.#C @4 .;X #B @+ .;Y #B .K #I
.#D4 .;X #B @+ .;Y #B .K #CF
.#E @4 .;X #B @+ .;Y #B .K #D
.#F @4 .;X #B @+ .;Y #B .K #F
.#G @4 .;X #B @+ .;Y #B .K #AF
.#H @4 .;X #B @+ .;Y #B .K #C
.,A4
.,B4
.,C4
.,D4
.,E4
.,F4
,,GRAPH+ ,GRAPH ! EQU,N4 ,ID5TIFY !
RADIUS (! CIRCLE4
.#I @4 .;X #B @+ .;Y #B .K #A
.#AJ @4 .;X #B @+ .;Y #B .K #HA
.#AA @4 .;X #B @+ .;Y #B .K #BE
.#AB @4 ;X #B @+ .;Y #B .K #AB
.#AC @4 .;Y #B .K #BG -- .;X #B
.#AD @4 .;X #B .K -- .;Y #B @+ #DJ
.#AE @4 .;X #B .K #AE -- .;Y #B
.#AF @4 .;Y #B .K -- .;X #B @+ #I
.#AG4 #AE .;X #B @+ #AE .;Y #B .K #FJ
.#AH @4 #G .;X #B @+ #G .;Y #B .K #AAB
.#AI @4 #D .;X #B @+ #D .;Y #B .K #ABH
.#BJ @4 #H .;X #B @+ #H .;Y #B .K #AIB
#BA4 .,,MULTIPLE .,,*OICE ,:AT IS !
RADIUS (! CIRCLE #C .;X #B @+ #C .;Y #B
.K #ED8
,A
;,B
;,C #AH
;,D #ED
,,EXAMPLE #B
ON P4 #FBG = ,EXS4 #BB--#DC
,,WRIT+ ,,EQU,NS ,WRITE ! /&>D =M (!
EQU,N (! CIRCLE )! GIV5 RADIUS & ^: C5T]
IS ! ORIG94
.#BB4 #AB
.#BC4 #H
.#BD4 #B
.#BE4 #AF
.#BF4
.#BG4
.#BH4
.#BI4
.#CJ4 .,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 WRIT+ AN EQU,N (!
CIRCLE )! GIV5 C5T] & RADIUS4
.,C5T]4 7#J1 #J72 ,RADIUS3 #AB ,EQU,N3
;X #B @+ ;Y #B .K #AB
------------------------------------#FCJ
,,WRIT+ ,,EQU,NS ,WRITE ! /&>D =M (!
EQU,N (! CIRCLE T PASSES "? ! GIV5 PO9T
& ^: C5T] IS ! ORIG94
.#CA4 7--#F1 #J7
.#CB4 7#J1 #E7
.#CC4 7--#D1 #C7
.#CD4 7#B1 --#D7
.#CE4 7--#F1 #H7
.#CF4 7--#I1 #B7
.#CG4 7#D1 --#AJ7
.#CH4 7--#H1 --#E7
.#CI4 7--#H1 #AD7
.#DJ4 7#E1--#AB7
.#DA4 7--#AA1--#AA7
.#DB4 7#I1DJ7
#DC4 .,,MULTIPLE .,,*OICE ,:AT IS !
EQU,N 9 /&>D =M (! CIRCLE T PASSES "? !
PO9T 7#D1 --#F7 & ^: C5T] IS ! ORIG98
,A .;X #B @+ .;Y #B .K #E
;,B .;X #B @+ .;Y #B .K #AJ
;,C .;X #B @+ .;Y #B .K #EB
;,D
,,GRAPH+ ,9 ,EX]CISES #DD--#EB1 EQU,NS
( BO? CIRCLES & P>ABOLAS >E GIV54 ,GRAPH
! EQU,N4
.#DD @4 .;Y #B @+ .;X #B .K #DI
.#DE @4 #D .;X #B @+ .;Y .K #J
.#DF @4 #G .;X #B @+ #G .;Y #B .K #FC
.#DG @4 .;Y #B -- #ABA .K -- .;X #B
.#DH @4 .;X #B @+ #AF .;Y .K #J
.#DI @4 #C .;X .K -- .;Y #B
.#EJ4 #AB .;X #B @+ #AB .;Y #B .K #AIB
.#EA4 #B .;X #B @+ #B .;Y #B .K #AF
.#EB4 .#F .;X @+ #F .;Y #B .K #J
,,TANG5T ,,L9ES ,WRITE AN EQU,N (! L9E
TANG5T 6! GIV5 CIRCLE AT ! GIV5 PO9T4
,,EXAMPLE #C
ON P4 #FBG = ,EXS4 #EC--#EH
.#EC4 .;X #B @+ .;Y #B .K #AG2 7#A1
#D7
.#ED4 .;X #B @+ .;Y #B .K #AC2 7#B1
--#C7
.#EE4 .;X #B @+ .;Y #B .K #CD2 7--#E1
#C7
.#EF4 .;X #B @+ .;Y #B .K #DJ2 7--#F1
--#B7
.#EG4 .;X #B @+ .;Y #B .K #AJF2 7--#E1
#I7
.#EH4 .;X #B @+ .;Y #B .K #BEJ2 7#AE1
#E7
.#EI4 .,,OP5--.,,5D$ .,,MA? ,WRITE
EQU,NS 9 /&>D =M = ?REE CIRCLES C5T]$ AT
! ORIG9 S T EA* CIRCLE PASSES 2T 7--#C1
#E7 & 7--#F1 #B74
.#FJ4 .,,R1SON+ ,USE ! DIAGRAM 6%[ T
AN ANGLE 9SCRIB$ 9 A SEMICIRCLE IS A "R
ANGLE4 @7 .,H9T3 ,%[ T ! SEG;TS MEET+ AT
@7 .;X1 .;Y @7 H SLOPES T >E NEGATIVE
RECIPROCALS47
.#FA4 .,,*ALL5GE ,SUPPOSE TWO 3GRU5T
CIRCLES 9T]SECT S T EA* PASSES "? !
O!R'S C5T]1 Z %[N4 ,WRITE AN EQU,N T
GIVES ! L5G? .;I (! *ORD =M$ 0JO9+ !
9T]SEC;N PO9TS 9 T]MS (! RADIUS .;R (
EA* CIRCLE4
,PRO#M ,SOLV+
,,EXAMPLE #D
ON .P4 #FBH = ,EXS4 #FB--#FD
.#FB4 .,,CELL .,,PH"OS ,A CELLUL> PH"O
T[] S]VICES A #AE MILE RADIUS4 ,ON A
HIK+ TRIP1 Y >E #I MILES EA/ & #AA MILES
NOR? (! CELL T[]4 ,>E Y 9 ! REGION S]V$
0! T[]8
@A.,HOTNE,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#FC4 .,,BATS ,DUR+ ! W>M] MON?S1 M
?AN #A MILLION ,MEXICAN FREE--TAIL$ BATS
LIVE "U ! ,3GRESS ,AV5UE ,BRIDGE 9
,AU/91 ,TEXAS4 ,! BATS H AN E/IMAT$ FE$+
RANGE ( #EJ MILES4 ,IS A LOC,N #DJ MILES
NOR? & #BE MILES WE/ (! BRIDGE LOCAT$ )9
? RANGE8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.K .,,"W$--.,,\ .,,SOLU;NS .ON .P4
,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
------------------------------------#FCA
.#FD4 .,,MULTIPLE .,,*OICE ,AN APPLI.E
/ORE CLAIMS 6PROVIDE FREE DELIV]Y UP
6#AJJ MILES F ! /ORE4 ,! FOLL[+ PO9TS
REPRES5T ! LOC,NS ( H\SES1 )! ORIG9
REPRES5T+ ! /ORE4 7,ALL COORD9ATES >E 9
MILES47 ,: H\SE IS LOCAT$ \TSIDE ! FREE
DELIV]Y >EA8
,A 7#IE1CJ7
;,B 7#IJ1CE7
;,C 7#HJ1EE7
;,D 7#GE1GJ7
,,EXAMPLE #E
ON .P4 #FBH = ,EXS4 #FE--#FG
#FE4 .,,MULTI--.,,/EP .,,PRO#M 8,CLASS
;,B0 AIRSPACE "S"TS 3SI/S (A /ACK (
CYL9DRICAL LAY]S Z %[N4 ,SE5 F ABV1 !
AIRSPACE =MS CIRCLES ^: ORIG9 IS ! 3TROL
T[]4 ,A PLANE 9 /RAI<T & LEVEL FLI<T
FLIES "? ! TOO LAV] AL"O ! L9E ;V .K
--#D4 Z %[N4
A4 ,= H[ _M MILES W ! PLANE 2 9 !
TOP--MO/ LAY] ( ,CLASS ;,B AIRSPACE8
B4 ,= H[ _M MILES W ! PLANE 2 ABV !
MI4LE LAY] ( ,CLASS ;,B AIRSPACE8
C4 ,= H[ _M MILES W ! PLANE 2 ABV !
L[E/ LAY] ( ,CLASS ;,B AIRSPACE8
#FF4 .,,%ORT .,,RESPONSE ,A CIRCUL>
UTIL;Y TUNNEL #H FEET 9 DIAMET] HAS A
#F--FOOT--WIDE WALKWAY ACR XS BOTTOM4
,CD A "W] :O IS #F FEET #B 9*ES TALL
WALK D[N ! C5T] (! WALKWAY )\T DUCK+8
.,EXPLA94 7.,H9T3 ,WRITE AN EQU,N (!
TUNNEL'S CROSS SEC;N4 ,F9D ! .;X
--COORD9ATE ( AN 5DPO9T (! WALKWAY &
SUB/ITUTE 6F9D ! .;Y --COORD9ATE47
#FG4 .,,GR.DSKEEP+ ,A R[ ( SPR9KL]S IS
6BE 9/ALL$ P>ALLEL 6& #D.E FEET AWAY F !
BACK $GE (A FL[] B$4 ,EA* SPR9KL] WAT]S
A REGION )A #F FOOT RADIUS4 ,H[ F> A"P
%D ! SPR9KL]S 2 PLAC$ 6WAT] ! 5TIRE FL[]
B$ )! L1/ POSSI# OV]LAP 9 COV]AGE1 Z
%[N8
#FH4 .,,MULTIPLE .,,REPRES5T,NS ,!
,MODIFI$ ,M]CALLI ,9T5S;Y ,SCALE RATES
AN E>?QUAKE'S 8%AK+ /R5G?40 ,9 G5]AL1 !
RAT+ DECR1SES Z 4T.E F ! E>?QUAKE'S
EPIC5T] 9CR1SES4 ,SUPPOSE AN E>?QUAKE
HAS A ,M]CALLI RAT+ ( #F.J AT XS
EPIC5T]1 A #E.G RAT+ #AE MILES AWAY F !
EPIC5T]1 A #E.D RAT+ #BE MILES AWAY1 &A
#E.A RAT+ #CE MILES AWAY4
A4 .,DRAW+ .,GRAPHS ,REPRES5T ! SITU,N
DESCRIB$ ABV US+ CIRCLES 9 A COORD9ATE
PLANE4
B4 .,WRIT+ .,9EQUALITIES ,= EA* CIRCLE
F "P 7A71 WRITE AN 9EQUAL;Y DESCRIB+ !
COORD9ATES ( LOC,NS )A ,M]CALLI RAT+ .AT
.L1/ Z GRT Z ! ,M]CALLI RAT+ REPRES5T$
0! CIRCLE4
C4 .,MAK+ .A .,PREDIC;N ,:AT C Y
PREDICT AB ! ,M]CALLI RAT+ #AB MILES WE/
& #AF MILES S\? (! EPIC5T]8 .,EXPLA94
-----------------------------------#FCB
.#FI4 .,,*ALL5GE ,TWO RADIO
TRANSMITT]S1 "O )A #DJ MILE RANGE & "O
)A #FJ MILE RANGE1 /& #HJ MILES A"P4 ,Y
>E DRIV+ #FJ MILES P] H\R ON A HI<WAY
P>ALLEL 6! L9E SEG;T 3NECT+ ! TWO T[]S4
,H[ L;G W Y 2 )9 RANGE ( .BO?
TRANSMITT]S SIMULTANE\SLY8
,MIX$ ,REVIEW
,SOLVE ! SY/EM US+ ANY ALGEBRAIC
ME?OD4 @7 PP4 #AFJ .& #AGH @7
#GJ4 #C .;X @+ #E .;Y .K #B
--#AB .;X @+ #B .;Y .K --#AI
#GA4 #C .;X -- .;Y .K --#B
#F .;X @+ .;Y .K --#BE
#GB4 #B .;X @+ #E .;Y .K#AC
#C .;X @+ #D .;Y .K #H
#GC4 #B .;X @+ #E .;Y -- .;Z .K --#G
.;X @+ #C .;Y @+#B .;Z .K #AB
-- .;X @+ #B .;Y .K #E
#GD4 .;X @+ #B .;Y -- .;Z .K #AJ
#C .;X -- #B .;Y @+ .;Z .K --#AH
-- .;X @+ #B .;Y .K #E
#GE4 .;X @+ #B .;Y -- .;Z .K #AJ
#C .;X -- #B .;Y @+ .;Z .K --#AH
#B .;X @+ #E .;Y @+ .;Z .K #BG
,F9D ! PRODUCT4 ,IF X IS N DEF9$1 /ATE
! R1SON4 @7 P4 #AIE @7
#GF4
#GG4
#GH4
.,,PREVIEW ,PREP>E = ,LESSON #I.D 9
,EXS4 #GI-HD4
#GI4 .;X #B .K #FJ
#HJ4 .;X #B .K #EJ
#HA4 .;C #B .K #AE #B -- #AB #B
#HB4 .;C #B .K #BJ #B -- #AF #B
#HC4 #CF .K #FD -- .;B #B
#HD4 #AJJ .K #CBD -- .;B #B
,,QUIZ .= .,LESSONS .#I..A--.#I..C
,F9D ! 4T.E 2T ! TWO PO9TS4 ,!N F9D !
MIDPO9T (! L9E SEG;T JO9+ ! TWO PO9TS1
@7 P4 #FAD @7
.#A4 7#D1 --#C71 7#H1 --#G7
.#B4 7--#B1 #E71 7#D1 #I7
.#C4 7--#E1 #A71 7--#D1 #H7
.#D4 7#A1 #B71 7#G1 #A7
.#E4 7--#F1 --#E71 7--#A1 #H7
.#F4 7#C1 --#B71 7#F1 #E7
,WRITE ! /&>D =M (! EQU,N (! P>ABOLA
)! GIV5 FOCUS & V]TEX AT 7#J1 #J74 @7 P4
#FBJ @7
.#G4 7#J1C7
.#H4 7--#B1J7
.#I4 7#F1J7
.#AJ4 7#J1 --#D7
.#AA4 7#J1E7
.#AB4 7--#A1J7
,GRAPH ! EQU,N4 ,ID5TIFY ! RADIUS (!
CIRCLE1 @7 P4 #FBF @7
.#AC4 .;X #B @+ .;Y #B .K #D
.#AD4 .;X #B @+ .;Y #B .K #FD
.#AE4 .;X #B @+ .;Y #B .K #BJ
.#AF4 .;X #B @+ .;Y #B .K #GE
.#AG4 #C .;X #B @+ #C .;Y #B .K #DH
.#AH4 #F .;X #B @+ #F .;Y #B .K #AJH
.#AI4 .,,A/RONOMY ,IF ! PLANE 9 :
,JUPIT] ORBITS ! SUN IS A COORD9ATE
PLANE ) XS ORIG9 AT ! SUN & COORD9ATES 9
MILLIONS ( MILES1 !N A CIRCLE "? ! PO9T
7#CEJ1 #CGJ7 J 5CLOSES ,JUPIT]'S ORBIT4
,IMAG9E REPLAC+ ! SUN )! /> ,,KY ,CYGNI1
^: RADIUS IS AB #FEJ MILLION MILES4 ,WD
,,KY ,CYGNI 3TA9 ,JUPIT]'S ORBIT8
.,EXPLA94 7.P4 .#FBF7
,,EXTRA ,,PRACTICE = ,LESSON #I.C1 P4
#AJAH
..,,ONL9E ,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#FCC
#I.C ,GRAPH ,EQU,NS ( ,CIRCLES
.,GRAPH+ .,CALCULATOR ,,ACTIV;Y
USE AF ,LESSON #I.C
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,KEY/ROKES
,SIDEB>3
,/&>DS
..#AG.J ,GIV5 A QUADRATIC .EQU,N (! =M
.AX #B @+ .0#B @+ .CX @+ .DY @+ .;E .K
#J1 .,/UD5TS C USE ! ME?OD = -PLET+ !
SQU>E 6PUT ! EQU,N 96/&>D =M & ..C
RECOGNIZE :E!R ! GRAPH (! EQU,N IS A
.CIRCLE @1 ELLIPSE1 P>ABOLA1 OR
HYP]BOLA4 ..,/UD5TS C !N GRAPH ! .EQU,N4
,"Q
,H[ C Y USE A GRAPH+ CALCULATOR 6GRAPH
A CIRCLE8
,6GRAPH A CIRCLE ON MO/ GRAPH+
CALCULATORS1 Y M/ F/ REWRITE ! CIRCLE'S
EQU,N Z TWO FUNC;NS T TAK5 TGR REPRES5T
! CIRCLE4
,EXAMPLE ,GRAPH A CIRCLE
,USE A GRAPH+ CALCULATOR 6GRAPH .;X #B
@+ .;Y #B .K #BE4
,,/EP #A
,SOLVE = ;Y
,2G9 0SOLV+ ! EQU,N = ;Y
;X #B @+ ;Y #B .K #BE
;Y #B .K #BE--;X #B
,TGR1 ! FUNC;NS & REPRES5T ! CIRCLE4
,,/EP#B
,5T] FUNC;NS
,5T] ! TWO FUNC;NS Z .;Y #A & .;Y #B
@4 ,Y C 5T] .;Y #B Z -- .;Y #A
,,/EP#C ,GRAPH FUNC;NS
,! GRAPHS >E %[N 9 ! /&>D W9D[ 7--#AJ
"K.K .;X "K.K#AJ & --#AJ "K.K .;Y "K.K
#AJ74 ,2C ! CALCULATOR SCRE5 IS N SQU>E1
A HORIZONTAL 4T.E ( #A UNIT IS L;G] ?AN
A V]TICAL 4T.E ( #A UNIT1 &! CIRCLE IS
/RET*$ 96AN OVAL4
,,/EP #D ,ADJU/ GRAPH
,6%[ ! CIRCLE 9 TRUE PROPOR;N1 SET A
W9D[ S T ! RATIO ( 7,XMAX--,XM97 TO
7,YMAX--,YM97 IS #C3B4 ,S* A 8SQU>E
W9D[0 C AL 2 OBTA9$ 0PRESS+ & SELECT+
,,ZS,'QU>E4
,PRACTICE
,USE A GRAPH+ CALCULATOR 6GRAPH !
EQU,N4 ,GIVE ! VIEW+ W9D[ T Y US$ &
V]IFY T X IS A 8SQU>E W9D[40
.#A4 .;X #B @+ .;Y #B .K #ADD
.#B4 .;X #B @+ .;Y #B .K #HJ
.#C4 .;X #B @+ .;Y #B .K #EGF
.#D4 #J.E .;X #B @+ #J.E .;Y #B .K #AB
.#E4 .#G .;X #B @+ #G .;Y #B .K #AJE
.#F4 #AF .;X #B @+ #AF .;Y #B -- #I
------------------------------------#FCD
#I.D ,GRAPH & ,WRITE ,EQU,NS (
,ELLIPSES
.,2F ,Y GRAPH$ & WROTE EQU,NS (
P>ABOLAS & CIRCLES4
.,N[ ,Y W GRAPH & WRITE EQU,NS (
ELLIPSES4
.,:Y8 ,S Y C MODEL AN ELLIPTICAL
REGION1 Z 9 ,EXAMPLE #C4
,KEY ,VOCABUL>Y
99 ELLIPSE
99FOCI
99 V]TICES
99 MAJOR AXIS
99 C5T]
99 CO--V]TICES
99 M9OR AXIS
,AN .ELLIPSE IS ! SET ( ALL PO9TS .;,P
9 A PLANE S* T ! SUM (! 4T.ES 2T .;,P &
TWO FIX$ PO9TS1 CALL$ ! .FOCI @1 IS A
3/ANT4
,! L9E "? ! FOCI 9T]SECTS ! ELLIPSE AT
! TWO .V]TICES4 ,! .MAJOR .AXIS JO9S !
V]TICES4 ,XS MIDPO9T IS ! ELLIPSE'S
.C5T]4 ,! L9E P]P5DICUL> 6! MAJOR AXIS
AT ! C5T] 9T]SECTS ! ELLIPSE AT ! TWO
.CO--.V]TICES @1 : >E JO9$ 0! .M9OR
.AXIS4 ,9 ? *APT]1 ELLIPSES H A
HORIZONTAL OR A V]TICAL MAJOR AXIS4
,,ID5TIFY ,,AXES
,OBS]VE T ! MAJOR AXIS ( AN ELLIPSE
3TA9S ! FOCI & IS ALW L;G] ?AN ! M9OR
AXIS4
,ELLIPSE ) HORIZONTAL MAJOR AXIS
,ELLIPSE ) V]TICAL MAJOR AXIS
,SIDEB>3
,/&>DS
..#AF.J ,/UD5TS DEMON/RATE & EXPLA9 H[
! .GEOMETRY (! GRAPH (A 3IC SEC;N 7E4G41
ASYMPTOTES1 FOCI1 E35TRIC;Y7 DEP5DS ON !
COE6ICI5TS (! QUADRATIC EQU,N REPRES5T+
X4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,/&>D ,EQU,N ( AN ,ELLIPSE ) ,C5T] AT
! ,ORIG9
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,EQU,N3 ,MAJOR ,AXIS3 ,V]TICES3
,CO--,V]TICES
@3 ,HORIZONTAL3 7+-.A @1 #J7 @3 7#J1
+-.;B7
@3 ,V]TICAL3 7#J1 +- .A @7 @3 7+-.;B
@1 #J7
,! MAJOR & M9OR AXES >E ( L5G?S .#B;A
& .#B;B @1 RESPECTIVELY1 ": .A .1 .;B .1
#J4 ,! FOCI (! ELLIPSE LIE ON ! MAJOR
AXIS AT A 4T.E ( .;C UNITS F ! C5T]1 ":
.;C #B .K .A #B -- .;B #B @4
------------------------------------#FCE
,EXAMPLE #A
,GRAPH AN EQU,N ( AN ELLIPSE
,GRAPH ! EQU,N #D .;X #B @+ #BE .;Y #B
.K #AJJ4 ,ID5TIFY ! V]TICES1
CO--V]TICES1 & FOCI (! ELLIPSE4
,SOLU;N
.,,/EP .#A ,REWRITE ! EQU,N 9 /&>D =M4
.,,/EP .#B ,ID5TIFY ! V]TICES1
CO--V]TICES1 & FOCI4 ,NOTE T .A #B .K
#BE & .;B #B .K #D1 S .A .K #E & .;B .K
#B4 ,! DENOM9ATOR (! .;X #B --T]M IS
GRT] ?AN T (! .;Y --T]M1 S ! MAJOR AXIS
IS HORIZONTAL4
,! V]TICES (! ELLIPSE >E AT 7+- .A @1
#J7 .K 7+-#E1 #J74 ,! CO--V]TICES >E AT
7#J1 +-.;B7 .K 7#J1 +-#B74 ,F9D ! FOCI4
.;C #B .K .A #B -- .;B #B .K .#E #B --
.#B #B .K #BA1 S
,! FOCI >E AT @1 OR AB 7+-#D.F1 #J74
.,,/EP .#C ,DRAW ! ELLIPSE T PASSES "?
EA* V]TEX & CO--V]TEX4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
,,ANO!R ,,WAY
,Y C GRAPH ! ELLIPSE US+ A GRAPH+
CALCULATOR 0SOLV+ = .;Y 6OBTA9 & !N 5T]+
? EQU,N Z TWO SEP>ATE FUNC;NS4
.,GUID$ .,PRACTICE = ,EXAMPLE #A
,GRAPH ! EQU,N4 ,ID5TIFY ! V]TICES1
CO--V]TICES1 & FOCI (! ELLIPSE4
.#A4
.#B4
.#C4 #BE .;X #B @+ #I .;Y #B .K #BBE
..,EXAMPLE #B ,WRITE AN EQU,N GIV5 A
V]TEX &A CO--.V]TEX
,WRITE AN EQU,N (! ELLIPSE T HAS A
V]TEX AT 7#J1D71 A CO--V]TEX AT 7--#C1
#J71 & C5T] AT 7#J1 #J74
,SOLU;N
,SKET* ! ELLIPSE Z A *ECK = YR F9AL
EQU,N4 ,0SYMMETRY1 ! ELLIPSE M/ AL H A
V]TEX AT 7#J1 --#D7 &A CO--V]TEX AT 7#C1
#J74
,2C ! V]TEX IS ON ! .;Y --AXIS &!
CO--V]TEX IS ON ! .;X --AXIS1 ! MAJOR
AXIS IS V]TICAL ) .A .K #D1 &! M9OR AXIS
IS HORIZONTAL ) .;B .K #C4
,AN EQU,N IS @4
------------------------------------#FCF
,EXAMPLE #C ,SOLVE A MULTI--/EP PRO#M
.,,LI<TN+ ,:5 LI<TN+ /RIKES1 AN
ELLIPTICAL REGION ": ! /RIKE MO/ LIKELY
HIT C (T5 2 ID5TIFI$4 ,SUPPOSE X IS
DET]M9$ T "! IS A #EJ@3P *.E T A LI<TN+
/RIKE HIT )9 ! ELLIPTICAL REGION %[N 9 !
DIAGRAM4
99 ,WRITE AN EQU,N (! ELLIPSE4
99 ,! >EA .,A ( AN ELLIPSE IS .,A .K
.;AB4 ,F9D ! >EA (! ELLIPTICAL REGION4
,,ANO!R ,,WAY
,= AN ALT]NATIVE ME?OD = SOLV+ ! PRO#M
9 ,EXAMPLE #C1 TURN 6PAGE #FDJ =!
.,PRO#M .,SOLV+ .,"W%OP @4
,SOLU;N
.,,/EP .#A ,! MAJOR AXIS IS
HORIZONTAL1 )
,AN EQU,N IS
.,,/EP .#B ,! >EA IS .,A .K
7#BJJ77#AJJ7 #FB1HJJ SQU>E MET]S4
..,EXAMPLE #D ,WRITE AN EQU,N GIV5 A
V]TEX &A .FOCUS
,WRITE AN EQU,N (! ELLIPSE T HAS A
V]TEX AT 7--#H1 #J71 A FOCUS AT 7#D1
#J71 & C5T] AT 7#J1 #J74
,SOLU;N
,MAKE A SKET* (! ELLIPSE4 ,2C ! GIV5
V]TEX & FOCUS LIE ON ! .;X --AXIS1 !
MAJOR AXIS IS HORIZONTAL1 ) .A .K #H &
.;C .K #D4 ,6F9D .;B @1 USE ! EQU,N ;C
#B .K .A #B -- .;B #B @4
.#D #B .K .#H #B -- .;B #B
.;B #B .K #H #B --#D #B
,AN EQU,N IS @4
..,GUID$ ,PRACTICE = ,EXAMPLES #B ,#C1
& .#D
,WRITE AN EQU,N (! ELLIPSE )! GIV5
"*I/ICS & C5T] AT 7#J1J74
.#D4 ,V]TEX3 7#G1 #J72 CO--V]TEX3 7#J1
#B7
.#E4 ,V]TEX3 7#J1 #F72 CO--V]TEX3
7--#E1 #J7
.#F4 ,V]TEX3 7#J1 #H72 FOCUS3 7#J1
--#C7
.#G4 ,V]TEX3 7--#E1 #J72 FOCUS3 7#C1
#J7
.#H4 .,,:AT .,,IF8 ,9 ,EXAMPLE #C1
SUPPOSE T ! ELLIPTICAL REGION IS #BEJ
MET]S F EA/ 6WE/ & #CEJ MET]S F NOR?
6S\?4 ,WRITE AN EQU,N (! ELLIPTICAL
B.D>Y & F9D ! >EA (! REGION4
------------------------------------#FCG
#I.D ,EX]CISES
,HOME"W ,KEY
.K .,,"W$--.,,\ .,,SOLU;NS
ON P4 ,,WS#AF = ,EXS4 #AA1BI1 & #DI
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 .#B1 .#CE1.DE1.DF1.EA @1 & .#EB
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,AN
ELLIPSE IS ! SET ( ALL PO9TS .;,P S* T !
SUM (! 4T.ES 2T .;,P & TWO FIX$ PO9TS1
CALL$ ! @8 @1 IS A 3/ANT4
.#B4 .,,WRIT+ .,DESCRIBE H[ 6F9D !
FOCI ( AN ELLIPSE GIV5 ! COORD9ATES ( XS
V]TICES & CO--V]TICES4
.,,EXAMPLE .#A .ON .P4 #FCE = ,EXS4
#C--#AF
.,,GRAPH+ ,GRAPH ! EQU,N4 ,ID5TIFY !
V]TICES1 CO--V]TICES1 & FOCI (! ELLIPSE4
.#C4
.#D4
.#E4
.#F4
.#G4
.#H4
.#I4 #D .;X #B @+ .;Y #B .K #CF
.#AJ4 #I .;X #B @+ .;Y #B .K #I
.#AA4 #AF .;X #B @+ #I .;Y #B .K #ADD
.#AB4 #BE .;X #B @+ #DI .;Y #B .K
#ABBE
.#AC4 #AF .;X #B @+ #BE .;Y #B .K
#AFJJ
.#AD4 #GB .;X #B @+ #H .;Y #B .K #FDH
.,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 GRAPH+ ! ELLIPSE4
.#AE4
.#AF4
,,EXAMPLES #B & #D
ON PP4 #FCE --#FCF = ,EXS4 #AG--#CE
.,,WRIT+ .,,EQU,NS ,WRITE AN EQU,N (!
ELLIPSE )! GIV5 "*I/ICS & C5T] AT 7#J1
#J74
.#AG4 ,V]TEX3 7#E1 #J7
,CO--V]TEX3 7#J1 --#C7
.#AH4 ,V]TEX3 7#J1 --#AJ7
,CO--V]TEX3 7#F1 #J7
.#AI4 ,V]TEX3 7#AD1 #J7
,CO--V]TEX3 7#J1 --#I7
.#BJ4 ,V]TEX3 7#J1 --#F7
,CO--V]TEX3 7#D1 #J7
.#BA4 ,V]TEX3 7#J1 #AB7
,CO--V]TEX3 7#AA1 #J7
.#BB4 ,V]TEX3 7#BJ1 #J7
,CO--V]TEX3 7#J1 --#AF7
.#BC4 ,V]TEX3 7#J1 #H7
,FOCUS3 7#J1 #F7
.#BD4 ,V]TEX3 7#D1 #J7
,FOCUS3 @7 @1 #J7
.#BE4 ,V]TEX3 7#J1 #I7
,FOCUS3
.#BF4 ,V]TEX3 7--#E1 #J7
,FOCUS3 7#C1 #J7
.#BG4 ,V]TEX3 7#J1 --#D7
,FOCUS3
.#BH4 ,V]TEX3 7#AC1 #J7
,FOCUS3
.#BI ,CO--V]TEX3 7#J1 @7
,FOCUS3 7--#C1 #J7
.#CJ4 ,CO--V]TEX3
,FOCUS3 7#J1 #F7
.#CA4 ,CO--V]TEX3
,FOCUS3 7--#AE1 #J7
.#CB4 ,CO--V]TEX3 7#J1 #AE7
,FOCUS3 7--#H1 #J7
.#CC4 ,CO--V]TEX3
,FOCUS3 7#J1 #AD7
.#CD4 ,CO--V]TEX3 7--#CB1 #J7
,FOCUS3 7#J1 #BD7
------------------------------------#FCH
#CE4 .,,MULTIPLE .,,*OICE ,:AT IS AN
EQU,N (! ELLIPSE ) C5T] AT ! ORIG91 A
V]TEX AT 7#J1 --#AB71 &A CO--V]TEX AT
7--#H1 #J78
,A
;,B
;,C
;,D
,,GRAPH+ ,9 ,EX]CISES #CF--#DD1 !
EQU,NS ( P>ABOLAS1 CIRCLES1 & ELLIPSES
>E GIV54 ,GRAPH ! EQU,N4
.#CF4 .;X #B @+ .;Y #B .K #FD
.#CG4 #BE .;X #B @+ #HA .;Y #B .K
#BJBE
.#CH4 #CF .;Y @+ .;X #B .K #J
.#CI4 #FE .;Y #B .K #ACJ .;X #DJ4 #CJ
.;X #B @+ #CJ .;Y #B .K #DHJ
.#DA4
.#DB4
.#DC4
.#DD4 #AF .;X #B @+ #AJ .;Y #B .K #AFJ
.#DE4 .,,%ORT .,,RESPONSE ,3SID] !
GRAPH ( @4 .,DESCRIBE ! E6ECTS ON !
GRAPH ( *ANG+ ! DENOM9ATOR (! .;Y #B
--T]M F/ F #BE 6#I & !N F #I 6#D4 ,GRAPH
! ORIG9AL EQU,N &! TWO REVIS$ EQU,NS 9 !
SAME COORD9ATE PLANE4
.#DF4 .,,OP5--.,,5D$ .,,MA? ,WRITE AN
EQU,N ( AN ELLIPSE 9 /&>D =M4 ,GRAPH !
EQU,N ON A GRAPH+ CALCULATOR 0REWRIT+ X
Z TWO FUNC;NS4 ,GIVE A VIEW+ W9D[ T DOES
N 4TORT ! %APE (! ELLIPSE1 & EXPLA9 H[ Y
F.D YR VIEW+ W9D[4
.#DG4 .,,*ALL5GE ,USE ! DEF9I;N ( AN
ELLIPSE 6%[ T .;C #B .K .A #B -- .;B #B
= ANY ELLIPSE ) EQU,N & FOCI AT @7 .;C
@1 #J7 & @7-- .;C @1 #J74 7.,H9T3 ,DRAW
A DIAGRAM4 ,3SID] ! PO9T .;,P @7 .A @1
#J7 ON ! ELLIPSE47
,PRO#M ,SOLV+
,,EXAMPLE #C
ON P4 #FCF = ,EXS4 #DH--#EJ
.#DH4 .,,M>S ,ON ,JANU>Y #C1 #BJJD1 !
,M>S ROV] ,_S B\NC$ ON XS AIRBAGS 6A L&+
)9 ,GUSEV CRAT]4 ,SCI5TI/S _H E/IMAT$ T
"! 0 A #II@3P *.E ! ROV] WD L& 9SIDE AN
ELLIPSE )A MAJOR AXIS #HA KILOMET]S L;G
&A M9OR AXIS #AB KILOMET]S L;G4 ,WRITE
AN EQU,N (! ELLIPSE4 ,!N F9D XS >EA4
,PICTURE3 ..,>TI/'S R5D]+ ( .L&+
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#DI4 .,,AU/RALIAN .,,FOOTBALL ,!
PLAY+ FIELD = ,AU/RALIAN FOOTBALL IS AN
ELLIPSE T IS 2T #ACE & #AHE MET]S L;G &
2T #AAJ & #AEE MET]S WIDE4 ,WRITE EQU,NS
( ELLIPSES ) V]TICAL MAJOR AXES T MODEL
! L>GE/ & SMALLE/ FIELDS DESCRIB$4 ,!N
WRITE AN 9EQUAL;Y T DESCRIBES ! POSSI#
>1S ( ^! FIELDS4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.K .,,"W$--.,,\ .,,SOLU;NS
ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#FCI
.#EJ4 .,,H1L? .,,C>E ,A .LI?OTRIPT]
USES %OCK WAVES 6BR1K A"P KIDNEY /"OS OR
GALL/"OS 9SIDE ! BODY4 ,%OCK WAVES
G5]AT$ AT "O FOCUS ( AN .ELLIPSOID 7A
?REE--DIM5.NAL %APE ) AN ELLIPTICAL
CROSS SEC;N7 REFLECT 6! /"O POSI;N$ AT !
SECOND FOCUS4 ,WRITE AN EQU,N =! CROSS
SEC;N (! ELLIPSOID )! DIM5.NS %[N4 ,H[
F> A"P >E ! FOCI8
.#EA4 .,,%ORT .,,RESPONSE ,HALLEY'S
-ET RANGES F #J.EI 6#CE.C A/RONOMICAL
UNITS F ! SUN1 : IS AT "O FOCUS (! -ET'S
ELLIPTICAL ORBIT4 7,AN .A/RONOMICAL
.UNIT .IS ,E>?'S M1N 4T.E F ! SUN47
.,EXPLA9 US+ A SKET* H[ 6F9D .A & .C4
,!N WRITE AN EQU,N =! ORBIT4
#EB4 .,,EXT5D$ .,,RESPONSE ,A SMALL
AIRPLANE ) 5 FUEL 6FLY #FJJ MILES SAFELY
W TAKE (F F AIRPORT ,A& L& AT AIRPORT
;,B1 #DEJ MILES AWAY4
A4 .,R1SON ,! REGION 9 : ! AIRPLANE C
FLY IS B.D$ 0AN ELLIPSE4 .,EXPLA9 :Y ?
IS S4
B4 .,CALCULATE ,LET 7#J1 #J7 REPRES5T
! C5T] (! ELLIPSE4 ,F9D ! COORD9ATES (
EA* AIRPORT4
C4 .,APPLY ,SUPPOSE ! PLANE FLIES F
AIRPORT ,A /RAI<T PA/ AIRPORT ;,B 6A
V]TEX (! ELLIPSE & !N /RAI<T BACK
6AIRPORT ,B4 ,H[ F> DOES ! PLANE FLY8
,USE YR ANSW] 6F9D ! COORD9ATES (!
V]TEX4
D4 .,MODEL ,WRITE AN EQU,N (! ELLIPSE4
#EC4 .,,*ALL5GE ,AN >T MUSEUM "W]
L1VES AN #H--FOOT--TALL PA9T+ L1N+ AG/ A
WALL4 ,LAT]1 ! TOP (! PA9T+ SLIDES D[N !
WALL1 &! PA9T+ FALLS 6! FLOOR4 ,USE !
DIAGRAM 6F9D AN EQU,N (! PA? (! PO9T @7
.;X1 .;Y @7 Z ! PA9T+ FALLS4
,MIX$ ,REVIEW
,EVALUATE ! DET]M9ANT (! MATRIX4 @7 P4
#BJC @7
#ED4
#EE4
#EF4
#EG4
,! V>IA#S .;X & .;Y V>Y 9V]SELY4 ,USE
! GIV5 VALUES 6WRITE AN EQU,N RELAT+ .;X
& .;Y @4 ,!N F9D .;Y :5 .;X .K --#D4 @7
P4 #EEA @7
#EH4 .;X .K #C1 .;Y .K --#F
#EI4 .;X .K #H1 .;Y .K #E
#FJ4 .;X .K --#AE1 .;Y .K --#E
#FA4 .;X .K --#F1 .;Y .K
#FB4
#FC4
.,,PREVIEW ,PREP>E = ,LESSON #I.E 9
,EXS4 #FD-FI4
#FD4
#FE4
#FF4
#FG4
#FH4
#FI4
.,,EXTRA .,,PRACTICE = ,LESSON #I.D1
P4 #AJAH
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#FDJ
,PRO#M ,SOLV+ ,"W%OP ,LESSON #I.D3
,US+ ,ALT]NATIVE ,ME?ODS
,ANO!R ,WAY 6,SOLVE ,EXAMPLE #C1 PAGE
#FCF
.,,MULTIPLE .,,REPRES5T,NS ,9 ! SECOND
"P ( ,EXAMPLE #C ON PAGE #FCF @1 Y F.D !
>EA ( AN ELLIPSE US+ A =MULA4 ,Y C AL
APPROXIMATE ! >EA ( AN ELLIPSE 0SUMM+ !
>1S ( RECTANGLES4
,PRO#M
.,,LI<TN+ ,:5 LI<TN+ /RIKES1 AN
ELLIPTICAL REGION ": ! /RIKE MO/ LIKELY
HIT C (T5 2 ID5TIFI$4 ,SUPPOSE X IS
DET]M9$ T "! IS A #EJ@3P *.E T A LI<TN+
/RIKE HIT )9 ! ELLIPTICAL REGION %[N 9 !
DIAGRAM4
99 ,WRITE AN EQU,N (! ELLIPSE4
99 ,F9D ! >EA (! ELLIPTICAL REGION4
,ME?OD
.,SUMM+ .,RECTANGLES ,Z Y SAW ON PAGE
#FCF @1 ! ELLIPSE HAS ! EQU,N @4
,APPROXIMATE ! >EA (! ELLIPSE Z FOLL[S4
,SIDEB>3
,/&>DS
#AF.J ,/UD5TS DEMON/RATE & EXPLA9 H[ !
GEOMETRY (! GRAPH (A 3IC SEC;N 7E4G41
ASYMPTOTES1 FOCI1 E35TRIC;Y7 DEP5DS ON !
COE6ICI5TS (! QUADRATIC EQU,N REPRES5T+
X4
.,,/EP .#A .,GRAPH ! F/--QUADRANT
POR;N (! ELLIPSE4 ,!N DRAW RECTANGLES (
WID? #DJ & HEI<T EQUAL 6! .;Y --VALUE (!
ELLIPSE AT ! RECTANGLE'S LEFT $GE4 ,! F/
RECTANGLE'S HEI<T IS .;Y ;X .K #AJJ4
,6F9D ! O!R .;Y-- VALUES1 SOLVE = .;Y
6OBTA9
@1 ,USE A CALCULATOR 6GET .;Y #B
#IH.J1 .;Y #C #IA.G1 .;Y #D .K #HJ1 &
.;Y #E .K #FJ4
.,,/EP .#B .,CALCULATE ! TOTAL >EA .,A
(! RECTANGLES4
.,A #DJ7#AJJ7 @+ #DJ7#IH.J7 @+
#DJ7#IA.G7 @+ #DJ7#HJ7 @+ #DJ7#FJ7 .K
#AG1AHH ;M #B
.,,/EP .#C .,MULTIPLY ! TOTAL >EA (!
RECTANGLES 0#D 6OBTA9 AN E/IMATE (
#D7#AG1AHH7 #FH1HJJ SQU>E MET]S =! >EA
(! ELLIPSE4
,,PRACTICE
.#A4 ,,SO,'LVE ! PRO#M ABV US+
RECTANGLES ( WID? #BJ4 ,IS ? E/IMATE
BETT] OR WORSE ?AN ! E/IMATE ABV8
.,EXPLA9
.#B4 .,R1SON+ .,EXPLA9 US+ YR RESULTS
F ,EX]CISE #A H[ 6OBTA9 CLOS] & CLOS]
APPROXIM,N (! ELLIPSE'S >1S4
#C4 .,,:AT .,,IF ,SUPPOSE T ! ELLIPSE
9 ! PRO#M _H A HORIZONTAL MAJOR AXIS (
#BEJ MET]S &A M9OR AXIS ( #BJJ MET]S4
A4 ,WRITE AN EQU,N ( ELLIPSE4
B4 ,USE ! ME?OD ABV 6APPROXIMATE ! >EA
(! ELLIPSE4
------------------------------------#FDA
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,LESSONS #I.A--#I.D
#A4 .,,MULTI-.,,/EP .,,PRO#M ,P>ABOLIC
REFLECTORS )A MICROPH"O AT ! FOCUS ALL[
Y 6LI/5 6S.DS F F> AWAY4 ,A P>ABOLIC
MICROPH"O HAS A REFLECTOR T IS #BB.D
9*ES 9 DIAMET] & #H 9*ES DEEP4
A4 ,H[ F> IS ! FOCUS F ! V]TEX8
B4 ,WRITE AN EQU,N =! CROSS SEC;N (!
REFLECTOR S* T ! V]TEX IS AT 7#J1 #J7 &!
REFLECTOR OP5S 6! "R4
C4 ,GRAPH ! EQU,N F "P 7;B74
#B4 .,,MULTI-.,,/EP .,,PRO#M ,A FI%+
BOAT'S RAD> HAS A RANGE ( #AF MILES4 ,A
SECOND BOAT IS #AB MILES WE/ & #AB MILES
S\? (! FI%+ BOAT4
A4 ,WRITE AN 9EQUAL;Y DESCRIB+ !
REGION COV]$ 0! RAD> IF ! FI%+ BOAT IS
AN*OR$ AT ! ORIG94
B4 ,IS ! SECOND BOAT 9 RANGE (! RAD>8
C4 ,A ?IRD BOAT #F MILES NOR? & #D
MILES EA/ (! FI%+ BOAT 2G9S MOV+ WE/W>D4
,= :AT 4T.E W ! ?IRD BOAT 2 9 RAD> RANGE
(! FI%+ BOAT8
#C4 .,,MULTI-.,,/EP .,,PRO#M ,9 XS
ELLIPTICAL ORBIT1 ,M]CURY RANGES F #BI
MILLION MILES 6#DD MILLION MILES F !
SUN1 : IS AT "O FOCUS (! ORBIT4
A4 ,DRAW A SKET* (! SITU,N4
B4 ,F9D ! VALUES ( .A & .C4
C4 ,WRITE AN EQU,N = ,M]CURY'S ORBIT4
#D4 .,,OP5-.,,5D$ ,WRITE AN EQU,N ( AN
ELLIPSE T HAS XS C5T] AT ! ORIG91 A
HORIZONTAL M9OR AXIS1 & LIES -PLETELY 2T
! CIRCLES .;X #B @+ ;Y #B .K #BE & .;X
#B @+ ;Y #B .K #FD4
#E4 .,,EXT5D$ .,,RESPONSE ,A C> SKIDS
:ILE TURN+ 6AVOID AN A3ID5T4 ,! C>'S
SPE$ .;V 7IN MET]S P] SECOND7 C 2
E/IMAT$ US+ ": .;R IS ! RADIUS 7IN
MET]S7 (! CIRCUL> SKID M>K & IS A 3/ANT
T DEP5DS ON ! ROAD SURFACE & W1!R 3DI;NS
7#J "K.K "K.K #A74
A4 ,F9D ! RADIUS (! SKID M>K %[N4
B4 ,E/IMATE H[ FA/ ! C> 0 TRAVEL+ IF X
IS DET]M9$ T .K #J.G4
C4 ,H[ DOES ! C>'S SPE$ :ILE SKI4+
A6ECT ! RADIUS (! CIRCLE8 .,EXPLA94
#F4 .,,%ORT .,,RESPONSE ,TWO L9ES >E
TANG5T 6! CIRCLE ;X #B @+ ;Y #B .K #AC1
"O AT 7--#B1 --#C7 & "O AT 7#C1 --#B74
,:AT IS ! REL,N%IP 2T ! TWO L9ES8
.,EXPLA94
#G4 .,,OP5-.,,5D$ ,WRITE AN EQU,N (A
P>ABOLA T HAS XS V]TEX AT ! ORIG9 &
PASSES 2T 7--#B1 #D7 & 7--#C1 #I74
#H4 .,,GRI4$ .,,ANSW] ,6GET F YR HOME
6! B1*1 Y DRIVE #H MILES S\?1 !N #AF
MILES EA/1 & !N #D MILES S\?4 ,:AT IS !
/RAI<T-L9E 4T.E F YR HOME 6! B1*8
#I4 .,,GRI4$ .,,ANSW] ,Y C MAKE A SOL>
HOT DOG COOK] 0%AP+ FOIL-L9$ C>DBO>D 96A
P>ABOLIC TR\< & PASS+ A WIRE "? ! FOCUS
( EA* 5D PIECE4 ,=! TR\< %[N1 H[ F> F !
BOTTOM1 6! NE>E/ T5? ( AN 9*1 %D ! WIRE
2 PLAC$8
------------------------------------#FDB
#I.E ,GRAPH & ,WRITE ,EQU,NS (
,HYP]BOLAS
.,2F ,Y GRAPH$ & WROTE EQU,NS (
P>ABOLAS1 CIRCLES1 & ELLIPSES4
.,N[ ,Y W GRAPH & WRITE EQU,NS (
HYP]BOLAS4
.,:Y8 ,S Y C MODEL CURV$ MIRRORS1 Z 9
,EXAMPLE #C4
,KEY ,VOCABUL>Y
99 HYP]BOLA
99FOCI
99 V]TICES
99 TRANSV]SE AXIS
99 C5T]
,RECALL T AN ELLIPSE IS ! SET ( ALL
PO9TS .;,P 9 A PLANE S* T ! .SUM (!
4T.ES 2T .;,P & TWO FIX$ PO9TS 7! FOCI7
IS A 3/ANT4
,A .HYP]BOLA IS ! SET ( ALL PO9TS .;,P
S* T ! .DI6];E (! 4T.ES 2T .;,P & TWO
FIX$ PO9TS1 AG CALL$ ! .FOCI @1 IS A
3/ANT4
,! L9E "? ! FOCI 9T]SECTS ! HYP]BOLA
AT ! TWO .V]TICES4 ,! .TRANSV]SE .AXIS
JO9S ! V]TICES4 ,XS MIDPO9T IS !
HYP]BOLA'S .C5T]4 ,A HYP]BOLA HAS TWO
.BRAN*ES @1 & HAS TWO ASYMPTOTES T 3TA9
! DIAGONALS (A RECTANGLE C5T]$ AT !
HYP]BOLA'S C5T]1 Z %[N4
,,ID5TIFY ,,AXES
,IF ! ;X #B --T]M 9 ! EQU,N (A
HYP]BOLA IS POSITIVE1 ! TRANSV]SE AXIS
LIES ON ! .;X --AXIS4 ,IF ! .;Y #B --T]M
IS POSITIVE1 ! TRANSV]SE AXIS LIES ON !
.;Y --AXIS4
,PICTURE3 ..,HYP]BOLA ) HORIZONTAL
TRANSV]SE .AXIS
,PICTURE3 ..,HYP]BOLA ) V]TICAL
TRANSV]SE .AXIS
,SIDEB>3
,/&>DS
#AF.J ,/UD5TS DEMON/RATE & EXPLA9 H[ !
GEOMETRY (! GRAPH (A 3IC SEC;N 7E4G41
ASYMPTOTES1 FOCI1 E35TRIC;Y7 DEP5DS ON !
COE6ICI5TS (! QUADRATIC EQU,N REPRES5T+
X4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,/&>D ,EQU,N (A ,HYP]BOLA ) ,C5T] AT !
,ORIG9
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,EQU,N3 ,TRANSV]SE ,AXIS3 ,ASYMPTOTES3
,V]TICES
@3 ,HORIZONTAL3 @3 7+- .A @2@1 #J7
@3 ,V]TICAL3 @3 7#J1 +-.A @7
,! FOCI LIE ON ! TRANSV]SE AXIS1 .;C
UNITS F ! C5T]1 ": .;C #B .K .A #B @+
.;B #B @4
------------------------------------#FDC
,EXAMPLE #A
..,GRAPH AN EQU,N ( .A HYP]BOLA
,GRAPH #BE .;Y #B -- #D .;X #B .K
#AJJ4 ,ID5TIFY ! V]TICES1 FOCI1 &
ASYMPTOTES (! HYP]BOLA4
,SOLU;N
.,,/EP .#A ,REWRITE ! EQU,N 9 /&>D =M4
.,,/EP .#B ,ID5TIFY ! V]TICES1 FOCI1 &
ASYMPTOTES4 ,NOTE T .A #B .K #D & .;B #B
.K #BE1 S .A .K .#B & .;B .K .#E @4 ,!
.;Y #B --T]M IS POSITIVE1 S ! TRANSV]SE
AXIS IS V]TICAL &! V]TICES >E AT @7 .#J1
+-.#B @7@4 ,F9D ! FOCI4
.;C #B .K .A #B @+ .;B #B .K .#B #B @+
.#E #B .K #BI1 S
,! FOCI >E AT
,! ASYMPTOTES >E
.,,/EP .#C ,DRAW ! HYP]BOLA4 ,F/ DRAW
A RECTANGLE C5T]$ AT ! ORIG9 T IS #B .A
.K #D UNITS HI< & #B .;B .K #AJ UNITS
WIDE4 ,! ASYMPTOTES PASS "? OPPOSITE
CORN]S (! RECTANGLE4 ,!N1 DRAW !
HYP]BOLA PASS+ "? ! V]TICES & APPROA*+ !
ASYMPTOTES4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
,,SOLVE ,,= .;,Y
,6PLOT PO9TS ON ! HYP]BOLA1 SOLVE XS
EQU,N = .;Y 6OBTA9 ,!N MAKE A TA# (
VALUES4
,EXAMPLE #B ,WRITE AN EQU,N (A
HYP]BOLA
,WRITE AN EQU,N (! HYP]BOLA ) FOCI AT
7--#D1J7 & 7#D1 #J7 & V]TICES AT 7--#C1
#J7 & 7#C1 #J74
,SOLU;N
,! FOCI & V]TICES LIE ON ! .;X --AXIS
EQUIDISTANT F ! ORIG91 S ! TRANSV]SE
AXIS IS HORIZONTAL &! C5T] IS ! ORIG94
,! FOCI >E EA* #D UNITS F ! C5T]1 S .;C
.K .#D @4 ,! V]TICES >E EA* #C UNITS F !
C5T]1 S .A .K .#C @4
,2C .;C #B .K .A #B @+ .;B #B @1 Y H
.;B #B .K .;C #B -- .A #B @4 ,F9D .;B #B
@4 .;B #B .K .;C #B -- .A #B .K .#D #B
-- .#C #B .K .#G
,2C ! TRANSV]SE AXIS IS HORIZONTAL1 !
/&>D =M (! EQU,N IS Z FOLL[S3
------------------------------------#FDD
..,GUID$ ,PRACTICE = ,EXAMPLES #A &
.#B
,GRAPH ! EQU,N4 ,ID5TIFY ! V]TICES1
FOCI1 & ASYMPTOTES (! HYP]BOLA4
.#A4
.#B4
.#C #D .;Y #B -- #I .;X #B .K #CF
,WRITE AN EQU,N (! HYP]BOLA )! GIV5
FOCI & V]TICES4
.#D4 ,FOCI3 7--#C1 #J71 7#C1 #J7
,V]TICES3 7--#A1 #J71 7#A1 #J7
.#E4 ,FOCI3 7#J1 --#AJ71 7#J1 #AJ7
,V]TICES3 7#J1 --#F71 7#J1 #F7
,EXAMPLE #C0' ,SOLVE A MULTI--/EP
PRO#M
.,,PHOTOGRAPHY ,Y C TAKE PANORAMIC
PHOTOGRAPHS US+ A HYP]BOLIC MIRROR4
,LI<T RAYS H1D+ T[>D ! FOCUS 2H ! MIRROR
>E REFLECT$ 6A CAM]A POSI;N$ AT ! O!R
FOCUS Z %[N4 ,AF A PHOTOGRAPH IS TAK51
-PUT]S C 8UNW>P0 ! 4TORT$ IMAGE 96A
#CFJ;DG VIEW4
99 ,WRITE AN EQU,N =! CROSS SEC;N (!
MIRROR4
99 ,! MIRROR IS #F C5TIMET]S WIDE4 ,H[
TALL IS X8
,SOLU;N
.,,/EP .#A ,F ! DIAGRAM1 .A .K .#B..HA
& .;C .K .#C..FF4 ,6WRITE AN EQU,N1 F9D
.;B #B @4
.;B #B .K .;C #B -- .A #B .K .#C..FF
#B -- .#B..HA #B .#E..EJ
,2C ! TRANSV]SE AXIS IS V]TICAL1 !
/&>D =M (! EQU,N =! CROSS SEC;N (!
MIRROR IS Z FOLL[S3
.,,/EP#B ,F9D ! .;Y --COORD9ATE AT !
MIRROR'S BOTTOM $GE4 ,2C ! MIRROR IS #F
C5TIMET]S WIDE1 SUB/ITUTE .;X .K #C 96!
EQU,N & SOLVE4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
@3 ..,SUB/ITUTE #C = .;X @4
.;Y #B #BJ.HC @3 ,SOLVE =.' ;Y #B @4
.;Y --#D.EF @3 ,SOLVE =.' Y4.-
,S1 ! MIRROR HAS A HEI<T (
--#B.HA--7--#D.EF7 .K #A.GE C5TIMET]S4
,,AVOID ,,]RORS
,! MIRROR IS 2L ! .;X --AXIS1 S *OOSE
! NEGATIVE SQU>E ROOT4
.,GUID$ .,PRACTICE = ,EXAMPLE #C
.#F4 .,,:AT .,,IF8 ,9 ,EXAMPLE #C1
SUPPOSE T ! MIRROR REMA9S #F C5TIMET]S
WIDE1 B T .A .K #C C5TIMET]S & .;C .K #E
C5TIMET]S4 ,H[ TALL IS ! MIRROR8
------------------------------------#FDE
#I.E ,EX]CISES
,HOME"W ,KEY
.K ,,"W$--,,\ ,,SOLU;NS
ON P4 ,,WS#AG = ,EXS4 #AC1BC1 & #DA
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 #B1AE1 #BF1 #CC1CE1 & #DC
.K ,,MULTIPLE ,,REPRES5T,NS
,EX#.DB
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,!
PO9TS 7--#B1 #J7 & 7#B1 #J7 9 ! GRAPH AT
! "R >E ! @8 (! HYP]BOLA4 ,! L9E SEG;T
JO9+ ^! TWO PO9TS IS ! @8 @4
.#B4 .,,WRIT+ .,-P>E ! DEF9I;NS ( AN
ELLIPSE &A HYP]BOLA4
,,EXAMPLE #A
ON P4 #FDC = ,EXS4 #C--#AG
,,GRAPH+ ,GRAPH ! EQU,N4 ,ID5TIFY !
V]TICES1 FOCI1 & ASYMPTOTES (! HYP]BOLA4
.#C4
.#D4
.#E4
.#F4
.#G4
.#H4
.#I4 #D .;X #B -- .;Y #B .K #BEF
.#AJ4 #DI .;X #B -- #D .;Y #B .K #AIF
.#AA4 #I .;Y #B -- #BE .;X #B .K #BBE
.#AB4 #BE .;Y #B -- #FD .;X #B .K
#AFJJ
.#AC4 #HA .;X #B -- #AF .;Y #B .K
#ABIF
.#AD4 #DI .;Y #B -- #AJJ .;X #B .K
#DIJJ
#AE4 .,,MULTIPLE .,,*OICE ,:AT >E !
FOCI (! HYP]BOLA ) EQU,N #DE .;Y #B --
#BJJ .;X #B .K #AHJJ8
,A
;,B
;,C 7+-#G1J7
;,D 7#J1 +-#G7
.,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 GRAPH+ ! EQU,N4
#AF4
#AG4
,,EXAMPLE #B
ON P4 #FDC = ,EXS4 #AH--#BF
,,WRIT+ ,,EQU,NS ,WRITE AN EQU,N (!
HYP]BOLA )! GIV5 FOCI & V]TICES4
.#AH4 ,FOCI3 7#J1 --#D71 7#J1 #D7
,V]TICES3 7#J1 --#B71 7#J1 #B7
.#AI4 ,FOCI3 7--#F1 #J71 7#F1 #J7
,V]TICES3 7--#B1 #J71 7#B1 #J7
.#BJ4 ,FOCI3 7--#E1 #J71 7#E1 #J7
,V]TICES3 7--#A1 #J71 7#A1 #J7
.#BA4 ,FOCI3 7#J1 --#AB71 7#J1 #AB7
,V]TICES3 7#J1 --#G71 7#J1 #G7
.#BB4 ,FOCI3 7--#AJ1J71 7#AJ1J7
,V]TICES3
.#BC4 ,FOCI3
,V]TICES3 7#J1 --#D71 7#J1D7
.#BD4 ,FOCI3 7#J1 --#C71 7#J1C7
,V]TICES3
.#BE4 ,FOCI3 ,V]TICES3 7--#B1J71
7#B1J7
------------------------------------#FDF
#BF4 .,,MULTIPLE .,,*OICE ,:AT IS AN
EQU,N (! HYP]BOLA ) FOCI AT &) V]TICES
AT 7#J1 --#H7 & 7#J1 #H78
,A
;,B
;,C
;,D
.,,GRAPH+ ,9 ,EX]CISES #BG--#CB1 !
EQU,NS ( P>ABOLAS1 CIRCLES1 ELLIPSES1 &
HYP]BOLAS >E GIV54 ,GRAPH ! EQU,N4
.#BG4
.#BH4 .;Y #B .K #AH .;X
.#BI4 #DH .;X #B @+ #AB .;Y #B .K #DH
.#CJ4
.#CA4
.#CB4 #AH .;X #B @+ #AH .;Y #B .K #BHH
#CC4 .,,%ORT .,,RESPONSE .,DESCRIBE !
E6ECTS (! 9DICAT$ *ANGE ON ! %APE (!
HYP]BOLA & ON ! LOC,NS (! V]TICES &
FOCI4
A4 @2 *ANGE #CF 6#D
B4 @2 *ANGE #D 6#BE
#CD4 .,,GRAPH+ .,,CALCULATOR ,GRAPH
EA* HYP]BOLA US+ A GRAPH+ CALCULATOR4
,TELL :AT TWO FUNC;NS Y 5T]$ 96!
CALCULATOR4
A4
B4
C4 #E .;X #B --.#G..E .;Y #B .K #AB
#CE4 .,,OP5--.,,5D$ .,,MA? ,GIVE
EQU,NS ( ?REE HYP]BOLAS ) HORIZONTAL
TRANSV]SE AXES & ASYMPTOTES .;Y .K +-#B
.X4 .,-P>E ! HYP]BOLAS4
#CF4 .,,R1SON+ ,USE ! DIAGRAM AT ! "R
6%[ T _\ .;D #B -- .;D #A _\ .K #B .A @4
@7 .,H9T3 _\ .;D #B -- .;D #A _\ IS
3/ANT1 S *OOSE A 3V5I5T LOC,N = @7 .;X1
.;Y @7
#CG4 .,,*ALL5GE ,US+ ! 4T.E =MULA &!
DEF9I;N (A HYP]BOLA1 WRITE AN EQU,N 9
/&>D =M (! HYP]BOLA ) FOCI AT 7+-#B1 #J7
IF ! DI6];E 9 ! 4T.ES F A PO9T @7 .;X1
.;Y @7 ON ! HYP]BOLA 6! FOCI IS #B4
,PRO#M ,SOLV+
,,EXAMPLE #C
ON P4 #FDD = ,EXS4 #CH--#DJ
.#CH4 .,,TELESCOPES ,A SATELLITE IS
C>RY+ A TELESCOPE T HAS A HYP]BOLIC
MIRROR = : .A .K #CC & .;C .K #EF 7IN
C5TIMET]S74 ,WRITE AN EQU,N =! CROSS
SEC;N (! MIRROR IF ! TRANSV]SE AXIS IS
HORIZONTAL4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#CI4 .,,SP9N+ .,,CUBE ,! \TL9E (A
CUBE SP9N+ >.D AN AXIS "? A PAIR (
OPPOSITE CORN]S 3TA9S A POR;N (A
HYP]BOLA1 Z %[N4 ,! COORD9ATES GIV5
REPRES5T A V]TEX &A FOCUS (! HYP]BOLA =A
CUBE T M1SURES #A UNIT ON EA* $GE4
,WRITE AN EQU,N T MODELS ? HYP]BOLA4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.K .,,"W$--.,,\ .,,SOLU;NS .ON
.P4.,,WSI
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
------------------------------------#FDG
#DJ4 .,,SUN'S .,,%AD[ ,EA* "D1 EXCEPT
AT ! FALL & SPR+ EQUINOXES1 ! TIP (!
%AD[ (A V]TICAL POLE TRACES A BRAN* (A
HYP]BOLA ACR ! GR.D4 ,! DIAGRAM %[S %AD[
PA?S =A #BJ MET] TALL FLAGPOLE 9
,DALLAS1 ,TEXAS4
A4 ,WRITE AN EQU,N (! HYP]BOLA ) C5T]
AT ! ORIG9 T MODELS ! ,JUNE #BA PA?1
GIV5 T .A .K #AC.C MET]S & .;C .K #BH.B
MET]S4
B4 ,WRITE AN EQU,N (! HYP]BOLA ) C5T]
AT ! ORIG9 T MODELS ! ,SEPTEMB] #A PA?1
GIV5 T .A .K #D.A MET]S & .;C .K #BE.J
MET]S4
#DA4 .,,MULTI--.,,/EP .,,PRO#M ,! RO(
(! ,ST4 ,L\IS ,SCI;E ,C5T] HAS A
HYP]BOLIC CROSS SEC;N )! DIM5.NS %[N4
A4 ,SUPPOSE A COORD9ATE GRID IS
OV]LAID ON ! DIAGRAM ) XS ORIG9 AT ,O1 !
C5T] (! N>R[E/ "P (! RO(4 ,:AT >E !
COORD9ATES (! PO9TS AT .,A & .;,B8
B4 ,USE YR ANSW]S F "P 7A7 6WRITE AN
EQU,N T MODELS ! CROSS SEC;N4
C4 ,F9D ! TOTAL HEI<T .;H (! RO(4
#DB4 .,,MULTIPLE .,,REPRES5T,NS ,A
CIRCUL> WALKWAY IS 6BE BUILT >.D A /ATUE
9 A P>K4 ,"! IS 5 3CRETE AVAILA# =!
WALKWAY 6H AN >EA ( #FJJ SQU>E FEET4
A4 .,WRIT+ .AN .,EQU,N ,LET ! 9SIDE &
\TSIDE RADII (! WALKWAY 2 .;X FEET & .;Y
FEET1 RESPECTIVELY4 ,DRAW A DIAGRAM (!
SITU,N4 ,!N WRITE AN EQU,N RELAT+ .;X &
.Y4
B4 .,MAK+ .A .,TA# ,GIVE F\R POSSI#
PAIRS ( DIM5.NS .;X & .;Y T SATISFY !
EQU,N F "P 7A74
C4 .,DRAW+ .A .,GRAPH ,GRAPH ! EQU,N F
"P 7A74 ,:AT POR;N (! GRAPH REPRES5TS
SOLU;NS T MAKE S5SE 9 ? SITU,N8
D4 .,R1SON+ ,H[ DOES ! WID? (!
WALKWAY1 .;Y--.;X @1 *ANGE Z BO? .;X &
.;Y 9CR1SE8 .,EXPLA9 :Y ? MAKES S5SE4
#DC4 .,,%ORT .,,RESPONSE ,TWO /"OS
DROPP$ AT ! SAME "T 96/ WAT] PRODUCE
CIRCUL> RIPPLES ^: 9T]SEC;N PO9TS =M
HYP]BOLAS ) FOCI ": ! /"OS HIT ! WAT]4
,! GRAPH %[S "O HYP]BOLA =M$ 0/"OS
DROPP$ #AB FEET A"P ) RIPPLES AT #A FOOT
9T]VALS4
A4 ,WRITE AN EQU,N ( ? HYP]BOLA4
B4 ,USE ! DEF9I;N (A HYP]BOLA 6EXPLA9
:Y ! GRAPH %[N IS A HYP]BOLA4 @7 .,H9T3
,EXAM9E ! 4T.ES F EA* 9T]SEC;N PO9T 6!
FOCI47
------------------------------------#FDH
.#DD4 .,,*ALL5GE ,TWO MICROPH"OS PLAC$
#A MILE A"P RECORD ! BUGL+ (A BULL ELK4
,MICROPH"O ,A RCVS ! S.D #B SECONDS AF
MICROPH"O ,B4 ,S.D TRAVELS AT #AAJJ FEET
P] SECOND4 ,IS ? 5 9=M,N 6DET]M9E ": !
ELK IS LOCAT$8 ,IF S1 GIVE ! LOC,N4 ,IF
N1 EXPLA9 :Y N4
,MIX$ ,REVIEW
,P]=M ! 9DICAT$ OP],N1 IF POSSI#4 ,IF
N POSSI#1 /ATE ! R1SON4
#DE4
#DF4
#DG4
#DH4
,WRITE ! QUADRATIC FUNC;N 9 V]TEX =M4
,!N ID5TIFY ! V]TEX4 @7 P4 #BHD @7
.,,PREVIEW ,PREP>E = ,LESSON #I.F 9
,EXS4 #DI-ED4
#DI4 .;Y .K .;X #B -- #D .;X @+ #G
#EJ4 .;Y .K .;X #B -- #B .;X -- #E
#EA4 .;Y .K .;X #B @+ #AD .;X @+ #ED
#EB4 .;Y .K -- .;X #B -- #H .;X -- #BJ
#EC4 .;Y .K .;X #B @+ #I .;X -- #AB
#ED4 .;Y .K --#B .;X #B -- #B .;X --
#I
,,QUIZ .= .,LESSONS .#I..D--.#I..E
,GRAPH ! EQU,N4 ,ID5TIFY ! V]TICES1
CO--V]TICES1 & FOCI (! ELLIPSE4 @7 P4
#FCD @7
.#A4
.#B4
.#C4 #CF .;X #B @+ #I .;Y #B .K #CBD
,WRITE AN EQU,N (! ELLIPSE )! GIV5
"*I/ICS & C5T] AT 7#J1J74 @7 P4 #FCD @7
.#D4 ,V]TEX3 7#J1 #E7
,CO--V]TEX3 7--#D1 #J7
.#E4 ,V]TEX3 7#AJ1 #J7
,FOCUS3 7--#H1 #J7
.#F4 ,CO--V]TEX3
,FOCUS3 7#J1 --#E7
,GRAPH ! EQU,N4 ,ID5TIFY ! V]TICES1
FOCI1 & ASYMPTOTES (! HYP]BOLA1 @7 P4
#FDB @7
.#G4
.#H4 #D .;X #B -- #AF .;Y #B .K #FD
.#I4 #AB .;Y #B -- #BJ .;X #B .K #BDJ
,WRITE AN EQU,N (! HYP]BOLA )! GIV5
FOCI & V]TICES1 .FP4 .#FDB7
.#AJ4 ,FOCI3 7--#E1 #J71 7#E1 #J7
,V]TICES3 7--#B1 #J71 7#B1 #J7
.#AA4 ,FOCI3 7#J1--#C71 7#J1 #C7
,V]TICES3 7#J1 --#A71 7#J1 #A7
.#AB4
.#AC4 .,,A/]OIDS ,! L>GE/ A/]OID1 #A
,C]ES1 RANGES F #B.EE A/RONOMICAL UNITS
6#B.IH A/RONOMICAL UNITS F ! SUN1 : IS
LOCAT$ AT "O FOCUS (! A/]OID'S
ELLIPTICAL ORBIT4 ,F9D .A & C4 ,!N WRITE
AN EQU,N (! ORBIT ( #A ,C]ES1 7.P4
.#FCD7
.,,EXTRA .,,PRACTICE = ,LESSON #I.E1
P4 #AJAH
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#FDI
,9VE/IGAT+ ,ALGEBRA ,ACTIV;Y3 #I.F
,EXPLOR+ ,9T]SEC;NS ( ,PLANES & ,C"OS
,USE 2F ,LESSON1 #I.F
.,ANIMAT$ ,ALGEBRA
_+CLASSZONE.COM_:
,MAT]IALS
99 FLA%LI<T
99 GRAPH PAP]
,SIDEB>3
,/&>DS
#AF.J ,/UD5TS DEMON/RATE & EXPLA9 H[ !
GEOMETRY (! GRAPH (A 3IC SEC;N 7E4G41
ASYMPTOTES1 FOCI1 E35TRIC;Y7 DEP5DS ON !
COE6ICI5TS (! QUADRATIC EQU,N REPRES5T+
X4
,,"Q ,H[ D A PLANE &A D\#--NAPP$ C"O
9T]SECT 6=M DI6]5T 3IC SEC;NS8
,! R1SON T P>ABOLAS1 CIRCLES1
ELLIPSES1 & HYP]BOLAS >E CALL$ .3ICS OR
.3IC .SEC;NS IS T EA* C 2 =M$ 0!
9T]SEC;N (A PLANE &A D\#--NAPP$ C"O1 Z
%[N 2L4
,PICTURE3 .,CIRCLE
,PICTURE3 .,ELLIPSE
,PICTURE3 .,P>ABOLA
,PICTURE3 .,HYP]BOLA
,EXPLORE
,F9D AN EQU,N (A 3IC
,,/EP #A ,DRAW AXES
,"W 9 A GR\P4 ,ON A PIECE ( GRAPH
PAP]1 DRAW .;X-- & .;Y --AXE 6MAKE A
COORD9ATE PLANE4 ,!N TAPE ! PAP] 6A
WALL4
,,/EP #B ,MODEL A CIRCLE
,AIM A FLA%LI<T P]P5DICUL> 6! PAP] S T
! LI<T =MS A CIRCLE C5T]$ ON ! ORIG9 (!
COORD9ATE PLANE4 ,TRACE ! CIRCLE ON !
GRAPH PAP]4 ,F9D ! CIRCLE'S RADIUS1 &
USE X 6WRITE ! /&>D =M (! CIRCLE'S
EQU,N4
,,/EP #C ,MODEL AN ELLIPSE
,TILT ! FLA%LI<T1 & AIM X AT ! PAP]
6=M AN ELLIPSE )A V]TICAL MAJOR AXIS &
C5T] AT ! ORIG94 ,TRACE ! ELLIPSE &
WRITE ! /&>D =M ( XS EQU,N4
,DRAW ,3CLU.NS ,USE YR OBS]V,NS
6-PLETE ^! EX]CISES
.#A4 .,-P>E ! EQU,NS = YR CIRCLE &= YR
ELLIPSE )! EQU,NS ( O!R GR\PS4 ,>E YR
EQU,NS ALL ! SAME8 ,:Y OR :Y N8
.#B4 ,REF] 6! DIAGRAM (A HYP]BOLA
6EXPLA9 H[ Y C ORI5T ! FLA%LI<T B1M 6=M
A BRAN* (A HYP]BOLA ON ! WALL4
------------------------------------#FEJ
#I.F ,TRANSLATE & ,CLASSIFY ,3IC
,SEC;NS
.,2F ,Y GRAPH$ & WROTE EQU,NS ( 3IC
SEC;NS4
.,N[ ,Y W TRANSLATE 3IC SEC;NS4
.,:Y8 ,S Y C MODEL MO;N1 Z 9 ,EX4 #DI4
,KEY ,VOCABUL>Y
99 3IC SEC;NS 73ICS7
99 G5]AL SECOND--DEGREE EQU,N
99 4CRIM9ANT
,SIDEB>3
,/&>DS
#AG.J ,GIV5 A QUADRATIC EQU,N (! =M
.AX #B @+ .0#B @+ ..CX @+ DY @+ ;E .K
.#J @1 ,/UD5TS C USE ! ME?OD = -PLET+ !
SQU>E 6PUT ! EQU,N 96/&>D =M & C
RECOGNIZE :E!R ! GRAPH (! EQU,N IS A
CIRCLE1 ELLIPSE1 P>ABOLA1 OR HYP]POLA4
,/UD5TS C !N GRAPH ! EQU,N4
,2C P>ABOLAS1 CIRCLES1 ELLIPSES1 &
HYP]BOLAS >E =M$ :5 A PLANE 9T]SECTS A
D\#--NAPP$ C"O1 !Y >E CALL$ .3IC .SEC;NS
OR .3ICS4
,PREVI\SLY1 Y /UDI$ EQU,NS ( P>ABOLAS
) V]TICES AT ! ORIG9 & EQU,NS ( CIRCLES1
ELLIPSES1 & HYP]BOLAS ) C5T]S AT !
ORIG94 ,N[ Y W /UDY H[ TRANSLAT+ 3IES 9
! COORD9ATE PLANE A6ECTS _! EQU,NS4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,/&>D ,=M ( ,EQU,NS ( ,TRANSLAT$ ,3IES
,9 ! FOLL[+ EQU,NS1 ! PO9T 7.;H1 .;K7
IS ! .V]TEX (! P>ABOLA &! .C5T] (! O!R
3IES4
.,CIRCLE @7 .;X -- .;H @7 #B @+ @7 .;Y
-- .;K @7 #B .K .;R #B
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 .,HORIZONTAL .AXIS @3 .,V]TICAL
.AXIS
.,P>ABOLA @3 @7 .;Y -- ;K @7 #B .K #D
.;P @7 .;X -- .;H @7 @3 @7 .;X -- .;H @7
#B .K #D .;P @7 .;Y -- .;K @7
.,ELLIPSE @3 @3
.,HYP]BOLA @3 @3
,EXAMPLE #A ,GRAPH ! EQU,N (A
TRANSLAT$ CIRCLE
,GRAPH @7 .;X -- #B7 #B @+ @7 .;Y @+
#C7 #B .K #I4
,SOLU;N
.,,/EP .#A .,-P>E ! GIV5 EQU,N 6! /&>D
=M ( AN EQU,N (A CIRCLE4 ,Y C SEE T !
GRAPH IS A CIRCLE ) C5T] AT @7 .;H1 .;K7
.K 7#B1 --#C7 & RADIUS
.,,/EP .#B .,PLOT ! C5T]4 ,!N PLOT
S"EAL PO9TS T >E EA* .#C UNITS F ! C5T]3
7#B @+ .#C @1 --#C7 .K 7#E1 --#C7 7#B
-- .#C @1 --#C7 .K 7--#A1 --#C7
7#B1 --#C @+ .#C @7 .K 7#B1 #J7 7#B1
--#C -- .#C @7 .K 7#B1 --#F7
.,,/EP .#C .,DRAW A CIRCLE "? ! PO9TS4
------------------------------------#FEA
,EXAMPLE #B ,GRAPH ! EQU,N (A
TRANSLAT$ HYP]BOLA
.,GRAPH @4
,SOLU;N
.,,/EP .#A .,-P>E ! GIV5 EQU,N 6! /&>D
=MS ( EQU,NS ( HYP]BOLAS4 ,! EQU,N'S =M
TELLS Y T ! GRAPH IS A HYP]BOLA )A
V]TICAL TRANSV]SE AXIS4 ,! C5T] IS AT @7
..;H1 ;K @7 .K 7--#A1.C7 @4 ,2C .A #B .K
#D & .;B #B .K #I1 Y "K T .A .K #B & .;B
.K #C4
.,,/EP .#B .,PLOT ! C5T]1 V]TICES1 &
FOCI4 ,! V]TICES LIE .A .K #B UNITS ABV
& 2L ! C5T]1 AT 7--.#A1 .#E7 &
7--.#A1.A7 @4 ,2C .;C #B .K .A #B @+ .;B
#B .K #AC1 ! FOCI LIE UNITS ABV & 2L !
C5T]1 AT 7--.#A1.F..F7 & 7--.#A1
--.#J..F7 @4
,,SOLVE ,,= .;,Y
,6PLOT A4I;NAL PO9TS ON ! HYP]BOLA1
SOLVE = ;Y 6OBTA9 @4 ,!N MAKE A TA# (
VALUES4
.,,/EP .#C .,DRAW ! HYP]BOLA4 ,DRAW A
RECTANGLE C5T]$ AT 7--.#A1 .#C7 T IS
.#B;A .K #D UNITS HI< & .#B;B .K #F
UNITS WIDE4 ,DRAW ! ASYMPTOTES "? !
OPPOSITE CORN]S (! RECTANGLE4 ,!N DRAW !
HYP]BOLA PASS+ "? ! V]TICES & APPROA*+ !
ASYMPTOTES4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,GUID$ ,PRACTICE = ,EXAMPLES #A &
.#B
,GRAPH ! EQU,N4 ,ID5TIFY ! IMPORTANT
"*I/ICS (! GRAPH4
.#A4 @7 .;X @+ #A7 #B @+ @7 .;Y -- #C7
#B -- #D
.#B4 @7 .;X -- #B7 #B .K #H7 .;Y @+
#C7
.#C4
.#D4
,EXAMPLE #C ,WRITE AN EQU,N (A
TRANSLAT$ P>ABOLA
,WRITE AN EQU,N (! P>ABOLA ^: V]TEX IS
AT 7--#B1C7 & ^: FOCUS IS AT 7--#D1 #C74
,SOLU;N
.,,/EP .#A .,DET]M9E ! =M (! EQU,N4
,2G9 0MAK+ A R\< SKET* (! P>ABOLA4 ,2C !
FOCUS IS 6! LEFT (! V]TEX1 ! P>ABOLA
OP5S 6! LEFT1 & XS EQU,N HAS ! =M @7 .;Y
-- .;K @7 #B .K .#D;P7.;X--.;H7 ": .;P
"K #J4
.,,/EP .#B .,ID5TIFY .;H & .K4 ,!
V]TEX IS AT 7--.#B1 .#C7 @1 S .;H .K
--#B & .;K .K #C4
.,,/EP .#C .,F9D .P4 ,! V]TEX
7--.#B1.C7 & FOCUS 7--.#D1 .#C7 BO? LIE
ON ! L9E .;Y .K #C1 S ! 4T.E 2T !M IS _\
.;P _\ .K _\ --.#D -- @7 --.#B 7_\ .K
#B1 & ?US .;P.K +-#B4 ,2C .;P "K #J1 X
FOLL[S T .;P .K --#B1 S #D .;P .K --#H4
,! /&>D =M (! EQU,N IS @7 .;Y -- #C7
#B .K --#H7 .;X @+ #B74
------------------------------------#FEB
..,EXAMPLE #D ,WRITE AN EQU,N (A
TRANSLAT$ .ELLIPSE
,WRITE AN EQU,N (! ELLIPSE ) FOCI AT
7#A1 #B7 & 7#G1 #B7 & CO--V]TICES AT
7#D1J7 & 7#D1 #D74
,SOLU;N
.,,/EP .#A .,DET]M9E ! =M (! EQU,N4
,F/ SKET* ! ELLIPSE4 ,! FOCI LIE ON !
MAJOR AXIS1 S ! AXIS IS HORIZONTAL4 ,!
EQU,N HAS ? =M3
.,,/EP .#B .,ID5TIFY .;H & .;K 0F9D+ !
C5T]1 : IS HALFWAY 2T ! FOCI 7OR !
CO--V]TICES74
.,,/EP .#C .,F9D .;B @1 ! 4T.E 2T A
CO--V]TEX &! C5T] 7#D1 #B71 & .;C @1 !
4T.E 2T A FOCUS &! C5T]4 ,*OOSE !
CO--V]TEX 7#D1 #D7 &! FOCUS 7#A1B73 .;B
.K _\#D--#B_\ .K .#B & .;C .K _\#A--#D_\
.K .#C
,,F9D ,,4T.E
,! CO--V]TICES LIE ON A V]TICAL L9E "?
! C5T] &! FOCI LIE ON A HORIZONTAL L9E
"? ! C5T]1 S Y D N H 6USE ! 4T.E =MULA4
.,,/EP .#D .,F9D .A4 ,= AN ELLIPSE1 .A
#B .K .;B #B @+ .;C #B .K .#B #B @+ .#C
#B .K #AC1 S @4
,! /&>D =M (! EQU,N IS @4
,EXAMPLE #E ,ID5TIFY SYMMETRIES ( 3IC
SEC;NS
,ID5TIFY ! L9E7;S7 ( SYMMETRY = EA*
3IC SEC;N 9 ,EXAMPLES #A--#D4
,SOLU;N
,=! CIRCLE 9 ,EXAMPLE #A1 ANY L9E "? !
C5T] 7#B1 --#C7 IS A L9E ( SYMMETRY4
,=! HYP]BOLA 9 ,EXAMPLE #B1 .;X .K
--#A & .;Y .K #C >E L9ES ( SYMMETRY4
,=! P>ABOLA 9 ,EXAMPLE #C1 .;Y .K #C
IS A L9E ( SYMMETRY4
,=! ELLIPSE 9 ,EXAMPLE #D1 .;X .K #D &
.;Y .K #B >E L9ES ( SYMMETRY4
------------------------------------#FEC
..,GUID$ ,PRACTICE = ,EXAMPLES #C1D1 &
.#E
,WRITE AN EQU,N (! 3IC SEC;N4
.#E4 ,P>ABOLA ) V]TEX AT 7#C1 --#A7 &
FOCUS AT 7#C1 #B7
.#F4 ,HYP]BOLA ) V]TICES AT 7--#G1 #C7
& 7--#A1 #C7 & FOCI AT 7--#I1 #C7 & 7#A1
#C7
,ID5TIFY ! L9E7;S7 ( SYMMETRY =! 3IC
SEC;N4
.#G4
.#H4 @7 .;X @+ #E7 #B .K #H7 .;Y --
#B7
.#I4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,CLASSIFY+ ,3IES ,US+ ,_! ,EQU,NS
,ANY 3IC C 2 DESCRIB$ 0A .G5]AL
.SECOND--.DEGREE .EQU,N 9 .;X & .;Y3
.,AX #B @+ .,BXY @+ .,CY #B @+ .,DX @+
.,BY @+ .;,F .K #J4 ,! EXPRES.N .;,B #B
-- #D .;,,AC IS ! .4CRIM9ANT (! EQU,N &
C 2 US$ 6ID5TIFY ! TYPE ( 3IC4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,4CRIM9ANT3 ,TYPE ( ,3IC
;,B.' #B -- #D .,,AC"K #J1 #E .K #J1 &
.,A .K .;,C @3 ,CIRCLE
;,B.' #B -- #D .;,,AC "K #J & EI .;,B
@6.K #J OR .,A @6.K ;,C @3 ,ELLIPSE
;,B #B -- #D .;,,AC .K #J @3 ,P>ABOLA
;,B #B --#D,;,AC.1#J @3 ,HYP]BOLA
,IF .;,B .K #J1 EA* AXIS (! 3IC IS
HORIZONTAL OR V]TICAL4
,EXAMPLE #F
,CLASSIFY A 3IC
,CLASSIFY ! 3IC GIV5 0#D .;X #B @+ .;Y
#B -- ..#H .;X -- #H .K #J4 ,!N GRAPH !
EQU,N4
,SOLU;N
,NOTE T .,A .K #D1 .;,B .K #J1 & ;,C
.K #A1 S ! VALUE (! 4CRIM9ANT IS3
.;,B #B -- #D .;,,AC .K #J #B --
#D7#D77#A7 .K --#AF
,2C .;,B #B -- #D .;,,AC "K #J & ,A
@6.K ;,C1 ! 3IC IS AN ELLIPSE4
,,-PLETE ,,! ,,SQU>E
,= HELP ) -PLET+ ! SQU>E1 SEE P4 #BHD
@4
,6GRAPH ! ELLIPSE1 F/ -PLETE ! SQU>E 9
.;X @4
.#D;X #B @+ .;Y #B -- #H .;X -- #H .K
#J
7.#D;X #B -- #H .;X @7 @+ .;Y #B .K #H
#D7 .;X #B --#B .;X @7 @+ .;Y #B .K #H
#D7 .;X #B --#B .;X @+ @8 @7 @+ .;Y #B
.K #H @+ #D7 @8 @7
#D7 .;X #B -- #B .;X @+ .#A @7 @+ .;Y
#B .K #H @+ #D7 .#A @7
#D7 .;X -- ;L7 #B @+;Y #B .K #AB
,F ! EQU,N1 Y C SEE T @7 ..;H1 ;K @7
.K 7#A1.J7 @1 @4 ,USE ^! FACTS 6DRAW !
ELLIPSE4
------------------------------------#FED
,,EXAMPLE #G ,SOLVE A MULTI--/EP PRO#M
.,,PHYSICAL .,,SCI;E ,9 A LAB EXP]I;T1
Y RECORD IMAGES (A /EEL BALL ROLL+ PA/ A
MAGNET4 ,! EQU,N #AF .;X #B -- #I .;Y #B
-- #IF .;X @+ #CF .;Y -- #CF .K #J
MODELS ! BALL'S PA?4
99 ,:AT IS ! %APE (! PA?8
99 ,WRITE AN EQU,N =! PA? 9 /&>D =M4
99 ,GRAPH ! EQU,N (! PA?4
,SOLU;N
.,,/EP .#A .,ID5TIFY ! %APE4 ,! EQU,N
IS A G5]AL SECOND--DEGREE EQU,N ) .,A .K
#AF1 .;,B .K #J1 & .;,C .K --#I4 ,F9D !
VALUE (! 4CRIM9ANT4
.;,B #B -- #D .;,,AC .K #J #B --
#D7#AF7 7--#I7 .K #EGF ,2C .;,B #B -- #D
.;,,AC .1 #J1 ! %APE (! PA? IS A
HYP]BOLA4
.,,/EP .#B .,WRITE AN EQU,N4 ,6WRITE
AN EQU,N (! HYP]BOLA1 -PLETE ! SQU>E 9
BO? .;X & .;Y SIMULTANE\SLY4
#AF .;X #B -- #I .;Y #B -- #IF .;X @+
#CF .;Y -- #CF .K #J
7#AF .;X #B -- #IF .;X @7--7#I .;Y #B
-- #CF .;Y @7 .K #CF
#AF7 .;X #B --#F .;X @+ @8 @7 --#I7
.;Y #B --#D .;Y @+ @8 @7 .K #CF @+ #AF7
@8 @7--#I7 @8 @7
#AF7 .;X #B -- #F .;X @+ .#I @7--#I7
.;Y #B -- #D .;Y @+ .#D @7 .K #CF @+
#AF7 .#I @7--#I7 .#D @7
#AF7 .;X --#C7 #B --#I7 .;Y --#B7 #B
.K #ADD
,,AVOID ,,]RORS
,6-PLETE ! SQU>E 9 TWO V>IA#S1 Y M/
ADD A QUANT;Y 6OR SUBTRACT A QUANT;Y F
EA* SIDE = .EA* V>IA#4
.,,/EP .#C .,GRAPH ! EQU,N4 ,F !
EQU,N1 ! TRANSV]SE AXIS IS HORIZONTAL1
@7 ..;H1 ;K @7 .K 7#C1.B7 @1 & @4 ,!
V]TICES >E AT 7#C +- .A @1 #B71 OR
7.#F1.B7 & 7.#J1 .#B7 @4
,PLOT ! C5T] & V]TICES4 ,!N DRAW A
RECTANGLE .#B;A .K #F UNITS WIDE & #B
.;B .K #H UNITS HI< C5T]$ AT 7.#C1 .#B7
@1 DRAW ! ASYMPTOTES1 & DRAW ! HYP]BOLA4
,NOTICE T ! PA? (! BALL IS MODEL$ 0J !
"R--H& BRAN* (! HYP]BOLA4
..,GUID$ ,PRACTICE = ,EXAMPLES #F &
.#G
,CLASSIFY ! 3IC SEC;N & WRITE XS EQU,N
9 /&>D =M4 ,!N GRAPH ! EQU,N4
.#AJ4 .;X #B @+ .;Y #B -- #B .;X @+ #D
.;Y @+ #A .K #J
.#AA4 #B .;X #B @+ .;Y #B -- #D .;X --
#D .K #J
.#AB4 .;Y #B -- #D .;Y -- #B .;X @+ #F
.K #J
.#AC4 #D .;X #B -- .;Y #B -- #AF .;X
-- #D .;Y -- #D .K #J
.#AD4 .,,A/RONOMY ,AN A/]OID'S PA? IS
MODEL$ 0#D .;X #B @+ #F.BE .;Y #B -- #AB
.;X -- #AF .K #J ": .;X & .;Y >E 9
A/RONOMICAL UNITS F ! SUN4 ,CLASSIFY !
PA? & WRITE XS EQU,N 9 /&>D =M4 ,!N
GRAPH ! EQU,N4
------------------------------------#FEE
#I.F ,EX]CISES
,HOME"W ,KEY
.K .,,"W$--.,,\ .,,SOLU;NS
ON P4 ,,WS#AG = ,EXS4 #C1AI1 & #DI
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 #B1AB1 #CF1DE1EA1 & #EB
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y .,EXPLA9 :Y CIRCLES1
ELLIPSES1 P>ABOLAS1 & HYP]BOLAS >E CALL$
3IC SEC;NS4
.#B4 .,,WRIT+ .,EXPLA9 H[ ! 4CRIM9ANT
(A G5]AL SECOND--DEGREE EQU,N C 2 US$
6ID5TIFY :AT 3IC ! EQU,N REPRES5TS4
,,EXAMPLES #A & #B
.ON .PP4 #FEJ--#FEA = ,EXS4 #C--#AB
,,GRAPH+ ,GRAPH ! EQU,N4 ,ID5TIFY !
IMPORTANT "*I/ICS (! GRAPH4
.#C4 @7 .;X @+ #D7 #B .K--#H7 .;Y
--#B7
.#D4 @7 .;X -- #B7 #B @+ @7 .;Y -- #G7
#B .K #I
.#E4
.#F4
.#G4
.#H4 @7 .;X -- #E7 #B @+ @7 .;Y @+ #A7
#B .K #FD
.#I4 7;Y-- ;L7 #B .K #D7 .;X @+ #F7
.#AJ4
.#AA4
#AB4 .,,MULTIPLE .,,*OICE ,:AT >E !
COORD9ATES (! CO--V]TICES (! ELLIPSE )
EQU,N @8
,A 7#J1A71 7#H1A7
;,B 7--#H1A71 7#J1A7
;,C 7#D1C71 7#D1--#A7
;,D 7--#D1 #C71 7--#D1--#A7
,,EXAMPLES #C & #D
ON PP4 #FEA --#FEB = ,EXS4 #AC--#BA
,,WRIT+ ,,EQU,NS ,WRITE AN EQU,N (!
3IC SEC;N4
.#AC4 ,CIRCLE ) C5T] AT 7--#E1 #A7 &
RADIUS #F
.#AD4 ,CIRCLE ) C5T] AT 7#I1 --#A7 &
RADIUS #B
.#AE4 ,P>ABOLA ) V]TEX AT 7--#D1 --#C7
& FOCUS AT 7#A1 --#C7
.#AF4 ,P>ABOLA ) V]TEX AT 7#E1 #C7 &
DIRECTRIX .;Y .K #F
.#AG4 ,ELLIPSE ) V]TICES AT 7--#C1 #D7
& 7#E1 #D7 & FOCI AT 7--#A1 #D7 & 7#C1
#D7
.#AH4 ,ELLIPSE ) V]TICES AT 7--#B1 #A7
& 7--#B1 #I7 & CO--V]TICES AT 7--#D1 #E7
& 7#J1 #E7
.;L#I4 ,HYP]BOLA ) V]TICES AT 7#F1
--#C7 & 7#F1 #A7 & FOCI AT 7#F1 --#F7 &
7#F1 #D7
.#BJ4 ,HYP]BOLA ) V]TICES AT 7#A1 #G7
& 7#G1 #G7 & FOCI AT 7--#A1 #G7 & 7#I1
#G7
.#BA4 .,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 WRIT+ AN EQU,N (!
ELLIPSE ) V]TICES AT 7--#G1 #C7 & 7#C1
#C7 & CO--V]TICES AT 7--#B1 #F7 & 7--#B1
#J74
,AXIS IS HORIZONTAL3 7;H1 ;K7 .K
7--#B1 #C72 ..A .K _\--#G--7--#B7_\ .K
#E2 ;B .K _\#F--#C_\ .K .#C2
.,EQU,N3
.,,EXAMPLE .#E .ON .P4 #FEB = ,EXS4
#BB--#BG
,,L9ES ,,( ,,SYMMETRY ,ID5TIFY ! L9E
7;S7 ( SYMMETRY =! 3IC SEC;N4
.#BB4
.#BC4 7;Y--#D7 #B .K #F7 .;X @+ #F7
.#BD4
.#BE4
.#BF4 @7 .;X @+ #C7 #B .K #AJ 7;Y--
#A7
.#BG4 @7 .;X @+ #B7 #B @+ @7 .;Y @+
#A7 #B .K #ABA
------------------------------------#FEF
,,EXAMPLE #F
ON P4 #FEC = ,EXS4 #BH--#CF
,,CLASSIFY+ ,,CON#A;,,CS ,USE !
4CRIM9ANT 6CLASSIFY ! 3IC SEC;N4
.#BH4 #F .;X #B -- #B .;Y #B @+ #BD
.;X @+ .#B;Y -- #A .K #J
.#BI4 .;X #B @+ .;Y #B -- ;L#J .;X --
#F .;Y @+ #AH .K #J
.#CJ4 .;Y #B -- #AJ .;Y -- #E .;X @+
#EG .K #J
.#CA4 #D .;X #B @+ .;Y #B -- #DH .;X
-- #AD .;Y @+ #AHI .K #J
.#CB4 #I .;X #B @+ #D .;Y #B @+ #H .;Y
@+ #AH .;X -- #DA .K #J
.#CC4 .;X #B -- #AH .;X @+ #F .;Y @+
#II .K #J
.#CD4 .;X #B @+ .;Y #B -- #F .;X @+ #H
.;Y -- #BD .K #J
.#CE4 #H .;X #B -- #I .;Y #B -- #DJ
.;X @+ #D .;Y @+ #ADE .K #J
#CF4 .,,MULTIPLE .,,*OICE ,! EQU,N #D
.;X #B @+ .;Y #B @+ #CB .;X -- ;L#J .;Y
@+ #HE .K #J REPRES5TS :AT 3IC SEC;N8
,A ,CIRCLE
;,B ,ELLIPSE
;,C ,HYP]BOLA
;,D ,P>ABOLA
,,EXAMPLES #F & #G
ON PP4 #FEC --#FED = ,EXS4 #CG--#DD
,,CLASSIFY+ ,,& ,,GRAPH+ ,CLASSIFY !
3IC SEC;N & WRITE XS EQU,N 9 /&>D =M4
,!N GRAPH ! EQU,N4
.#CG4 .;X #B @+ .;Y #B -- #AD .;X @+
#D .;Y -- #AA .K #J
.#CH4 .;X #B @+ #D .;Y #B -- ;L#J .;X
@+ #AF .;Y @+ #CG .K #J
.#CI4 .;X #B -- #AF .;X -- #H .;Y @+
#HJ .K #J
.#DJ4 #I .;Y #B -- .;X #B -- #ED .;Y
@+ #H .;X @+ #EF .K #J
.#DA4 #I .;X #B @+ #D .;Y #B -- #CF
.;X -- #BD .;Y @+ #CF .K #J
.#DB4 .;Y #B @+ #AD .;Y @+ #AF .;X @+
#CC .K #J
.#DC4 .;X #B @+ .;Y #B @+ #AF .;X --
#H .;Y @+ #AF .K #J
.#DD4 .;X #B -- #D .;Y #B @+ #H .;X --
#BD .;Y -- #BD .K #J
.#DE4 .,,%ORT .,,RESPONSE ,3SID] A
G5]AL SECOND--DEGREE EQU,N ": .;,B .K
#J4 .,EXPLA9 H[ Y C CLASSIFY ! EQU,N'S
GRAPH )\T GRAPH+ OR US+ ! 4CRIM9ANT4
.#DF4 .,,R1SON+ ,9 ,*APT] #H1 Y GRAPH$
HYP]BOLAS ) EQU,NS (! =M Z A G5]AL
SECOND--DEGREE EQU,N1 & USE ! 4CRIM9ANT
6%[ T ! GRAPH IS A HYP]BOLA4
.#DG4 .,,*ALL5GE ,F9D EXPRES.NS 9 T]MS
( .;C1 .;H @1 & .;K =! COORD9ATES (!
FOCI (A HYP]BOLA )A V]TICAL TRANSV]SE
AXIS & C5T] @7 .;H1 .;K74 ,!N F9D EQU,NS
(! ASYMPTOTES 9 T]MS (A1 .;B1 .;H @1 &
.K4
,PRO#M ,SOLV+
,,EXAMPLES #C & #D
ON PP4 #FEA --#FEB = ,EX4 #DH
.#DH4 .,,ICE .,,SKAT+ ,A FIGURE SKAT]
PRACTICES SKAT+ FIGURE EI<TS1 : >E =M$
0ET*+ TWO EXT]N,Y TANG5T CIRCLES 9 !
ICE4 ,WRITE EQU,NS =! CIRCLES 9 A FIGURE
EI<T IF EA* IS #H FEET 9 DIAMET]1 !
CIRCLES 9T]SECT AT ! ORIG91 &! C5T]S (!
CIRCLES >E ON ! .;Y --AXIS4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
,,EXAMPLES #F & #G
ON PP4 #FEC --#FED = ,EXS4 #DI--#EJ
.#DI4 .,,JUMP+ .,,/ILTS ,! L1P (A
P]SON WE>+ 8JUMP+ /ILTS0 IS MODEL$ 0.;X
#B -- ;L#J .;X @+ #D .;Y .K #J ": .;X &
.;Y >E 9 FEET &! ORIG9 M>KS ! />T (!
L1P4 ,WRITE AN EQU,N 9 /&>D =M =! PA? (!
L1P4 ,H[ HI< & H[ F> DOES ! P]SON JUMP8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#EJ4 .,,SPACECRAFT ,A SPACECRAFT USES
,SATURN'S GRAVIT,NAL =CE TO 8SL+%OT0 >.D
! PLANET ON ! PA? #BA .;Y #B -- #BAJ .;Y
-- #D .;X #B .K --#DDA1 ": ! ORIG9
REPRES5TS ,SATURN'S C5T] & .;X & .;Y >E
9 HUNDR$S ( ?\S&S ( KILOMET]S4 ,:AT IS !
%APE (! PA?8 ,WRITE AN EQU,N 9 /&>D =M
=! PA?4 ,!N GRAPH ! EQU,N4
.K ..,,"W$--,,\ ,,SOLU;NS ONP4.,,WS,'L
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#FEG
#EA4 .,,EXT5D$ .,,RESPONSE ,Y >E 9 A
P>K SURF+ ! ,9T]NET ON A WIRE.S 3NEC;N4
,A HOTEL'S WIRE.S TRANSMITT] IS LOCAT$
#AJJ Y>DS EA/ & #FJ Y>DS S\? ( Y4 ,X HAS
A RANGE ( #AEJ Y>DS4 ,A CAFE'S
TRANSMITT] IS LOCAT$ #HJ Y>DS WE/ & #GJ
Y>DS S\? ( Y4 ,X HAS A RANGE ( #AJJ
Y>DS4
A4 ,) YR LOC,N Z ! ORIG91 WRITE
9EQUALITIES = CIRCUL> REGIONS >.D !
HOTEL & CAFE 9 : Y C GET WIRE.S ,9T]NET
A3ESS4
B4 ,GRAPH ! 9EQUALITIES4 ,>E Y 9 ONLY
"O REGION OR 9 BO?8 .,EXPLA94
C4 .,EXPLA9 H[ 6DET]M9E :E!R ! REGIONS
OV]LAP )\T GRAPH+4
#EB4 .,,%ORT .,,RESPONSE ,TELL :AT 3IC
SEC;N IS =M$ 9 ! SITU,N DESCRIB$4
.,EXPLA9 YR R1SON+4
A4 ,6USE A NEW TUBE ( CAULK =! F/ "T1
Y CUT ! C"O--%AP$ TIP DIAGON,Y Z %[N4
B4 ,:5 Y %>P5 A P5CIL ) FLAT SIDES1
EA* SIDE 9T]SECTS ! C"O--%AP$ TIP Z %[N4
#EC4 .,,*ALL5GE ,A .DEG5]ATE 3IC
RESULTS :5 ! 9T]SEC;N (A PLANE )A
D\#--NAPP$ C"O IS N A P>ABOLA1 CIRCLE1
ELLIPSE1 OR HYP]BOLA4
A4 ,9 ,DIAGRAM #A1 A PLANE P]P5DICUL>
6! C"O'S AXIS PASSES "? ! C"O1 9T]SECT+
X 9 A CIRCLE ^: RADIUS DECR1SES & !N
9CR1SES4 ,:5 IS ! 9T]SEC;N N A CIRCLE8
,:AT IS X8
B4 ,9 ,DIAGRAM #B1 A PLANE P>ALLEL 6!
C"O'S AXIS PASSES "? ! C"O1 9T]SECT+ X 9
A HYP]BOLA ^: V]TICES GET CLOS] TGR & !N
F>!R A"P4 ,:5 IS ! 9T]SEC;N N A
HYP]BOLA8 ,:AT IS X8
C4 ,9 ,DIAGRAM #C1 A PLANE P>ALLEL 6!
C"O'S NAPPE PASSES "? ! C"O1 9T]SECT+ X
9 A P>ABOLA T F/ GETS N>R[]1 !N FLIPS &
GETS WID]4 ,:5 IS ! 9T]SEC;N N A
P>ABOLA8 ,:AT IS X8
,,MIX$ ,,REVIEW
,SOLVE ! SY/EM US+ ! SUB/ITU;N OR
ELIM9,N ME?OD4 @7 P4 #AFJ @7
.,,PREVIEW ,PREP>E = ,LESSON #I.F 9
,EXS4 #DI-ED4
#ED4 #D .;X @+ #C .;Y .K #G
-- .;X @+ #B .;Y .K #AB
#EE4 .;X @+ #C .;Y .K --#B
#E .;X @+ #G .;Y .K #AD
#EF4 #C .;X -- #B .;Y .K #AC
#E .;X @+ #C .;Y .K --#BI
#EG4 #D .;X -- #E .;Y .K --#AD
#C .;X @+ #B .;Y .K #BD
#EH4 #E .;X @+ #B .;Y .K #E
--#B .;X @+ #C .;Y .K --#BA
#EI4 #B .;X @+ .;Y .K --#G
#E .;X @+ #D .;Y .K --#A
,EXP& ! EXPRES.N4 @7 P4 #EJG @7
#FJ4 ,9 .;X #E .;Y
#FA4
#FB4 LOG #G #DH .;X #C
#FC4
,3D5SE ! EXPRES.N4 @7 P4 #EJG @7
#FD4 #F;LOG #E ;S--#C;LOG #E ;T
#FE4 LOG #BJ @+ LOG #ABE @+ #B;LOG #B
#FF4 #B ,9 .;X -- #B7,IN .;Y @+ #J.BE
,9 .;Y @7
.,,EXTRA .,,PRACTICE = ,LESSON #I.F1
P4 #AJAH
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#FEH
#I.G ,SOLVE ,QUADRATIC ,SY/EMS
.,2F ,Y SOLV$ L9E> SY/EMS4
.,N[ ,Y W SOLVE QUADRATIC SY/EMS4
.,:Y8 ,S Y C F9D 9T]SEC;NS 9VOLV+
3ICS1 Z 9 ,EX4 #DJ4
,KEY ,VOCABUL>Y
99 QUADRATIC SY/EM
,SIDEB>3
,/&>DS
..,5RI*;T ( #B.J ,/UD5TS SOLVE SY/EMS
.( L9E> .EQU,NS & 9EQUALITIES @7 .9 .TWO
OR ?REE .V>IA#S @7 0SUB/ITU;N1 ) GRAPHS1
OR ) MATRICES4
,9 ,*APT] #C1 Y SOLV$ SY/EMS ( L9E>
EQU,NS 0GRAPH+1 SUB/ITU;N1 & ELIM9,N4 ,Y
C USE ! SAME TE*NIQUES 6SOLVE SY/EMS T
9CLUDE "O OR M EQU,NS ( 3ICS4 ,^! SY/EMS
>E CALL$ .QUADRATIC .SY/EMS4
,IF ! GRAPHS (! EQU,NS 9 A SY/EM >E A
L9E &A 3IC SEC;N1 ! GRAPHS C 9T]SECT 9
Z]O1 "O1 OR TWO PO9TS1 & S ! SY/EM C H
Z]O1 "O1 OR TWO SOLU;NS4 ,?REE POSSI#
SC5>IOS >E %[N 2L4
,PICTURE3 .,NO .SOLU;N
,PICTURE3 .,"O .SOLU;N
,PICTURE3 .,TWO .SOLU;NS
,EXAMPLE #A ,SOLVE A L9E>--QUADRATIC
SY/EM 0GRAPH+
,SOLVE ! SY/EM US+ A GRAPH+
CALCULATOR4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;Y #B -- #G .;X @+ #C .K #J @3
.,EQU,N .#A
#B .;X -- .;Y .K #C @3 .,EQU,N .#B
,SOLU;N
.,,/EP .#A .,SOLVE EA* EQU,N = .;Y @4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;Y #B -- .#G .;X @+ #C .K #J @3 #B
.;X -- .;Y .K #C
.;Y #B .K #G .;X -- #C @3 -- .;Y .K
--#B .;X @+ #C
.,EQU,N .#A @3 .;Y .K .#B;X -- #C
,EQU,N #B
,,AVOID ,,]RORS
,6GRAPH ,EQU,N #A1 2 SURE 65T] BO? &
96! GRAPH+ CALCULATOR4
.,,/EP .#B .,GRAPH ! EQU,NS @1 @1 &
.;Y .K #B .;X -- #C4
,USE ! CALCULATOR'S .9T]SECT F1TURE
6F9D ! COORD9ATES (! 9T]SEC;N PO9TS4 ,!
GRAPHS ( & .;Y .K #B .;X -- #C 9T]SECT
AT 7#J.GE1 --#A.E74 ,! GRAPHS ( & .;Y .K
#B .;X -- #C 9T]SECT AT 7#D1 #E74
,! SOLU;NS >E 7#J.GE1 --#A.E7 & 7#D1
#E74 ,*ECK ! SOLU;NS 0SUB/ITUT+ !
COORD9ATES (! PO9TS 96EA* (! ORIG9AL
EQU,NS4
------------------------------------#FEI
..,,EXAMPLE #B ,SOLVE A
L9E>--QUADRATIC SY/EM 0.SUB/ITU;N
,SOLVE ! SY/EM US+ SUB/ITU;N4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X #B @+ .;Y #B .K #AJ @3 .,EQU,N .#A
.;Y .K --#C .;X @+ #AJ @3 .,EQU,N .#B
,SOLU;N
,SUB/ITUTE --.#C;X @+ #AJ = .;Y 9
,EQU,N #A & SOLVE = .X4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X #B @+ .;Y #B .K #AJ @3 .,EQU,N .#A
.;X #B @+ @7 --#C;X @+ #AJ7 #B .K #AJ
@3 ,SUB/ITUTE =.' Y4.-
.;X #B @+ .#I;X #B -- #FJ;X @+ #AJJ .K
#AJ @3 .,EXP& .! .P[]4
#AJ .;X #B -- #FJ .;X @+ #IJ .K #J @3
.,-B9E .L .T]MS4
.;X #B -- #F .;X @+ #I .K #J @3
..,DIVIDE EA* SIDE 0.#AJ4
7.;X -- #C7 #B .K #J @3 .,P]FECT
.SQU>E .TRINOMIAL
.;X .K #C @3 .,Z]O .PRODUCT .PROP]TY
,,AVOID ,,]RORS
,Y C AL SUB/ITUTE .;X .K #C 9 ,EQU,N
#A 6F9D .;Y @4 ,? YIELDS .TWO APP>5T
SOLU;NS1 7#C1A7 & 7#C1 --#A74 ,H["E1
7#C1 --#A7 IS EXTRANE\S 2C X DOES N
SATISFY ,EQU,N #B4
,6F9D !Y--COORD9ATE (! SOLU;N1
SUB/ITUTE .;X .K .#C 9 ,EQU,N #B4
.;Y .K --#C7 .#C @7 @+ #AJ.K #A
,! SOLU;N IS 7#C1 #A74
.,,*ECK ,Y C *ECK ! SOLU;N 0GRAPH+ !
EQU,NS 9 ! SY/EM4 ,Y C SEE F ! GRAPH %[N
T ! L9E &! CIRCLE 9T]SECT ONLY AT ! PO9T
7#C1 #A74
..,GUID$ ,PRACTICE = ,EXAMPLES #A &
.#B
,SOLVE ! SY/EM US+ A GRAPH+
CALCULATOR4
.#A4 .;X #B @+ .;Y #B .K #AC
.;Y .K .;X -- #A
.#B4 .;X #B @+ #H .;Y #B -- #D .K #J
.;Y .K #B .;X @+ #G
.#C4 .;Y #B @+ .#F;X -- #A .K #J
.;Y .K--#J.D .;X @+ #B.F
,SOLVE ! SY/EM US+ SUB/ITU;N4
.#D4 .;Y .K #J.E .;X -- #C
.;X #B @+ #D .;Y #B -- #D .K #J
.#E4 .;Y #B -- #B .;X-- #AJ .K #J
.;Y .K -- .;X -- #A
.#F4 .;Y .K #D .;X -- #H
#I .;X #B -- .;Y #B -- #CF .K #J
.,,QUADRATIC .,,SY/EMS ,TWO 4T9CT 3IC
SEC;NS C H F Z]O 6F\R PO9TS ( 9T]SEC;N4
,S"EAL POSSI# SC5>IOS >E %[N 2L4
,PICTURE3 .,NO .SOLU;N
,PICTURE3 .,"O .SOLU;N
,PICTURE3 .,TWO .SOLU;NS
,PICTURE3 .,?REE .SOLU;NS
,PICTURE3 .,F\R .SOLU;NS
,9 ! EXAMPLES ON ! NEXT PAGE1 Y W USE
ELIM9,N 6SOLVE SY/EMS ( TWO
SECOND--DEGREE EQU,NS4
------------------------------------#FFJ
,,EXAMPLE #C ,SOLVE A QUADRATIC SY/EM
0ELIM9,N
,SOLVE ! SY/EM 0ELIM9,N4
#I .;X #B @+ .;Y #B -- #IJ .;X @+ #BAF
.K #J .,EQU,N .#A
.;X #B -- .;Y #B -- #AF .K #J .,EQU,N
.#B
,,ANO!R ,,WAY
,Y C AL SOLVE 0SUB/ITU;N3 ,SOLVE
,EQU,N #B = .;Y #B @1 !N SUB/ITUTE !
RESULT 9 ,EQU,N #A4
,SOLU;N
,ADD ! EQU,NS 6ELIM9ATE ! .;Y #B --T]M
& OBTA9 A QUADRATIC EQU,N 9 X4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
@3 .,ADD
.;X #B -- #I .;X @+ #BJ .K #J @3
..,DIVIDE EA* SIDE 0.#AJ4
@7 .;X --#D7@7 .;X --#E7 .K #J @3
.,FACTOR4
.;X .K #D OR .;X .K #E @3 .,Z]O
.PRODUCT .PROP]TY
,:5 .;X .K #D1 .;Y .K #J4 ,:5 .;X .K
#E1 .;Y .K +-#C4
,! SOLU;NS >E 7#D1 #J71 7#E1 #C71 &
7#E1 --#C71 Z %[N4
,,EXAMPLE #D ,SOLVE A R1L--LIFE
QUADRATIC SY/EM
.,,NAVIG,N ,A %IP USES ,,LORAN
7L;G--4T.E RADIO NAVIG,N7 6F9D XS
POSI;N4 ,RADIO SIGNALS F /,NS ,A& ;,B
LOCATE ! %IP ON ! BLUE HYP]BOLA1 &
SIGNALS F /,NS ;,B & ;,C LOCATE ! %IP ON
! R$ HYP]BOLA4 ,! EQU,NS (! HYP]BOLAS >E
GIV5 2L4 ,F9D ! %IP'S POSI;N IF X IS EA/
(! .;Y --AXIS4
.;X #B -- .;Y #B -- #AF .;X @+ #CB .K
#J .,EQU,N .#A
--.;X #B @+ .;Y #B -- #H .;Y @+ #H .K
#J .,EQU,N .#B
..,SOLU;N ,,/EP #A .,ADD ! EQU,NS
6ELIM9ATE ! .;X #B -- & .;Y #B --T]MS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
@3 .,ADD
.;Y .K --#B .;X @+ #E @3 ,SOLVE = .;Y
@4
..,,/EP #B ,SUB/ITUTE --#B ;X @+ .#E =
.;Y 9 ,EQU,N #A & SOLVE = .;X @4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X #B -- .;Y #B -- #AF .;X @+ #CB .K
#J @3 ,EQU,N #A
.;X #B -- @7 --#B .;X @+ #E @7 #B --
#AF .;X @+ #CB .K #J @3 ,SUB/ITUTE = .;Y
@4
#C .;X #B -- #D .;X -- #G .K #J @3
,SIMPLIFY4
@7 .;X @+ ;L77#C .;X -- #G7 .K#J @3
,FACTOR4
.;X .K --#A OR @3 ,Z]O PRODUCT PROP]TY
.,,/EP .#C .,SUB/ITUTE = .;X 9 .;Y .K
--#B .;X @+ #E 6F9D ! SOLU;NS 7--#A1 #G7
& @4
,2C ! %IP IS EA/ (! .;Y --AXIS1 X IS
AT @4
------------------------------------#FFA
..,GUID$ ,PRACTICE = ,EXAMPLES #C &
.#D
,SOLVE ! SY/EM4
.#G4 --#B .;Y #B @+ .;X @+ #B .K #J
.;X #B @+ .;Y #B -- #A .K #J
.#H4 .;X #B @+ .;Y #B -- #AF .;X @+
#CI .K #J
.;X #B -- .;Y #B -- #I .K #J
.#I4 .;X #B @+ #D .;Y #B @+ #D .;X @+
#H .;Y .K #H
.;Y #B -- .;X @+ #B .;Y .K #E
.#AJ4 .,,:AT .,,IF8 ,9 ,EXAMPLE #D1
SUPPOSE T A %IP'S ,,LORAN SY/EM LOCATES
! %IP ON ! TWO HYP]BOLAS ^: EQU,NS >E
GIV5 2L4 ,F9D ! %IP'S LOC,N IF X IS S\?
(! .;X --AXIS4
.;X #B -- .;Y #B -- #AB .;X @+ #AH .K
#J .,EQU,N .#A
.;Y #B -- .;X #B -- #D .;Y @+ #B .K #J
.,EQU,N .#B
#I.G ,EX]CISES
,HOME"W ,KEY
.K .,,"W$--.,,\ .,,SOLU;NS
ON P4 ,,WS#AG = ,EXS4 #E1AE1 & #DA
.K .,,/&>DIZ$ .,,TE/ .,,PRACTICE
,EXS4 #B1BA1CD1DB1 & #DD
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,!
EQU,NS ;X #B @+ #E .;X @+ #C .;Y #B .K
#I & #D .;X #B -- #AB .;Y @+ #AF .K #J
=M A7;N7 @8 SY/EM ( EQU,NS4
.#B4 .,,WRIT+ .,EXPLA9 :AT ME?OD Y WD
USE 6SOLVE ! FOLL[+ SY/EM4 ,D N SOLVE !
SY/EM4
#C .;X #B @+ .;Y #B -- #E .;X .K #J
.,EQU,N .#A
#B .;X #B @+ .;Y #B -- #AE .K #J
.,EQU,N .#B
,,EXAMPLE #A
ON P4 #FEH = ,EXS4 #C--#H
.,,SOLV+ .,,0.,,GRAPH+ ,SOLVE ! SY/EM
US+ A GRAPH+ CALCULATOR4
.#C4 .;X #B @+ .;Y #B -- #CB .K #J
.;Y -- .;X .K #J
.#D4 .;Y @+ #B .;X #B -- #I .K #J
.;Y @+ #D .;X @+;L .K #J
.#E4 .;Y -- #C .;X @+ #D .K #J
--#C .;X #B @+ .;Y #B -- #F .K #J
.#F4 .;Y @+ #B .;X .K #F
#C .;X #B @+ .;Y #B .K #AB
.#G4 .;X #B @+ .;Y #B .K #AF
.;Y --#B .;X .K;L
.#H4 #C7;Y @+ #C7 #B @+ #D .;X .K #J
.;Y --#B .;X .KLL
,,EXAMPLE #B
ON P4 #FEI = ,EXS4 #I--#BA
.,,SOLV+ .,,0.,,SUB/ITU;N ,SOLVE !
SY/EM US+ SUB/ITU;N4
.#I4 .;Y #B -- .;X -- #F .K #J
.;Y @+ .;X .K #J
.#AJ4 .;X #B @+ .;Y #B -- #BE .K #J
.;Y .K #B .;X -- #AJ
.#AA4 --#B .;X @+ .;Y -- #H .K #J
.;X #B @+ #D .;Y #B -- #DJ .K #J
.#AB4 -- .;X #B @+ #B .;Y #B .K #H
-- .;X @+ .;Y .K --#B
.#AC4 #F .;X #B @+ #C .;Y #B .K #AB
.;Y .K -- .;X @+ #B
.#AD4 --#C .;X @+ .;Y .K #F
#H .;X @+ .;Y #B @+ #BD .K #J
.#AE4 #D .;X #B -- #E .;Y #B .K --#GF
#B .;X @+ .;Y .K--#F
.#AF4 .;X #B @+ .;Y #B .K #BJ
.;Y .K .;X --#D
.#AG4 #I .;X #B @+ #D .;Y #B .K #CF
-- .;X @+ .;Y .K--#D
.#AH4 .;X #B @+ #F .;X @+ #D .;Y -- #C
.K #J
.;Y @+ #C .;X @+ ;L .K #J
.#AI4 #D .;X #B @+ #B .;Y #B -- .;X --
.;Y .K #F
#C .;X -- .;Y .K#B
.#BJ4 #D .;X #B -- .;Y #B -- #CB .;X
-- #B .;Y .K --#EI
#B .;X @+ .;Y --#G .K #J
#BA4 .,,MULTIPLE .,,*OICE ,: ORD]$
PAIR IS A SOLU;N (! L9E>--QUADRATIC
SY/EM 2L8
#F .;X #B -- #E .;X @+ #H .;Y #B @+
.;Y .K #BC
-- .;X @+ .;Y .K --#A
,A 7--#A1 --#B7
;,B 7#B1 #A7
;,C 7#C1 #B7
;,D 7--#B1 --#C7
------------------------------------#FFB
,,EXAMPLES #C & #D
ON P4 #FFJ = ,EXS4 #BB--#CE
.,,SOLV+ .,,QUADRATIC .,,SY/EMS ,SOLVE
! SY/EM4
.#BB4 #F .;X #B -- .;Y #B -- #AE .K #J
.;X #B @+ .;Y #B -- #AC .K #J
.#BC4 #E .;X #B @+ #BE .;Y #B -- #ABE
.K #J
-- .;X @+ .;Y #B -- #E .K #J
.#BD4 #AJ .;Y .K ;X #B
;X #B -- #F .K --#B
.#BE4 .;X #B -- .;Y #B -- #D .;X @+ #B
.K #J
-- .;X #B @+ .;Y #B -- #D .;Y @+ #B .K
#J
.#BF4 .;X #B -- #B .;Y .K #F
.;X #B -- .;Y #B .K --#BG
.#BG4 .;X #B @+ #B .;Y #B -- #AJ .K #J
#D .;Y #B @+ .;X @+ #D .K #J
.#BH4 .;X #B @+ .;Y #B -- #AF .;X @+
#CI .K #J
.;X #B -- .;Y #B --#I .K #J
.#BI4 .;X #B -- .;Y #B -- #H .;X @+ #H
.;Y .K #BD
.;X #B @+ .;Y #B -- #H .;X -- #H .;Y
.K --#BD
.#CJ4 #AF .;X #B -- .;Y #B @+ #AF .;Y
-- #ABH .K #J
.;Y #B -- #DH .;X -- #AF .;Y -- #CB .K
#J
.#CA4 #D .;X #B -- #EF .;X @+ #I .;Y
#B .K --#AFJ
#D .;X #B @+ .;Y #B -- #FD .K #J
.#CB4 .;X #B -- .;Y #B -- #CB .;X @+
#ABH .K #J
.;Y #B -- .;X #B -- #H .;Y @+ #H .K #J
.#CC4 .;Y #B @+ .;X -- #C .K #J
.;X #B -- #D .;X @+ #C .;Y @+ #A .K #J
#CD4 .,,MULTIPLE .,,*OICE ,H[ _M
SOLU;NS DOES ! SY/EM 3SI/+ (! EQU,NS .;X
#B @+ .;Y #B @+ #F .;X .K #J & .;Y #B @+
.;X -- #F .K #J H8
,A #J
;,B #A
;,C #B
;,D #D
#CE4 .,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 US+ SUB/ITU;N 62G9
SOLV+ ! SY/EM 2L4 ,!N SOLVE ! SY/EM4
.;X #B @+ .;Y #B -- #B .;X -- #B .;Y
.K --#A .,EQU,N .#A
.;Y #B @+ .;X .K #A .,EQU,N .#B
,SOLVE ,EQU,N #B = .;X3 .;X .K #A --
.;Y #B ,SUB/ITUTE = .;X 9 ,EQU,N #A3
7#A -- .;Y #B @7 #B @+ .;Y #B
--#B7#A-- .;Y #B @7--#B .;Y .K--#A
#A--#B .;Y #B @+ .;Y #B @+ .;Y #B --
#B @+ #B .;Y #B -- #B .;Y .K --#A
#B .;Y #B -- #B .;Y .K .#J
#CF4 .,,R1SON+ ,SOLVE ! SY/EM 3SI/+ (!
EQU,NS & #D .;Y #B .K #AF--#H .;X #B @4
,:AT D Y NOTICE8
#CG4 .,,GRAPH+ .,,CALCULATOR ,3SID] !
SY/EM 3SI/+ (! EQU,NS #C .;Y #B @+ .;X
#B @+ #D .;X @+ #AH .;Y .K --#BH & #I
.;Y #B -- #D .;X #B @+ #H .;X @+ #IJ .;Y
.K --#AHE4 ,SOLVE EA* EQU,N = .Y4 ,!N
USE A GRAPH+ CALCULATOR 6SOLVE ! SY/EM4
#CH4 .,,*ALL5GE ,SOLVE ! SY/EM ( ?REE
EQU,NS %[N4
.;X #B @+ .;Y #B .K #A .,EQU,N .#A
.;X #B @+ .;Y #B @+ #D .;X @+ #D .;Y
-- #E .K #J .,EQU,N .#B
.;X @+ .;Y -- #A .K #J .,EQU,N .#C
,,EXAMPLE #B
ON P4 #FEI = ,EXS4 #CI--#DA
,,PRO#M ,,SOLV+
.#CI4 .,,TRA6IC .,,SAFETY ,A C> PASSES
A P>K$ POLICE C> & 3T9UES AT A 3/ANT
SPE$ R4 ,! POLICE C> 2G9S A3EL]AT+ AT A
3/ANT RATE :5 X IS PASS$4 ,! DIAGRAM
9DICATES ! 4T.E ;D 7IN MILES7 ! POLICE
C> TRAVELS Z A FUNC;N ( "T ;T 7IN
M9UTES7 AF 2+ PASS$4 ,WRITE & SOLVE A
SY/EM ( EQU,NS 6F9D H[ L;G X TAKES !
POLICE C> 6CAT* UP 6! O!R C>4
@A .,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.K .,,"W$--.,,\ .,,SOLU;NS
ONP4,,WSI
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#FFC
.#DJ4 .,,BASEBALL ,! PA? (A BASEBALL
HIT =A HOME RUN C 2 MODEL$ 0": .;X & .;Y
>E 9 FEET & HOME PLATE IS ! ORIG94 ,!
BALL L&S 9 ! /&S1 : >E MODEL$ 0.,AY--.;X
.K --#CEB = .;X .1 #DJJ4 ,H[ F>
HORIZONT,Y & V]TIC,Y F HOME PLATE DOES !
BALL L&8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#DA4 .,,MULTI--.,,/EP .,,PRO#M ,6BE
ELIGI# =A P>K+ PASS ON A COLLEGE CAMPUS1
A /UD5T M/ LIVE AT L1/ #A MILE F !
CAMPUS C5T]4
A4 ,WRITE EQU,NS T REPRES5T ! CIRCLE &
,OAK ,LANE4
B4 ,SOLVE ! SY/EM T 3SI/S (! EQU,NS F
"P 7A74
C4 ,= :AT L5G? ( ,OAK ,LANE >E /UD5TS
.N ELIGI# =A P>K+ PASS8
,,EXAMPLES #C & #D
ON P4 #FFJ = ,EXS4 #DB--#DC
.#DB4 .,,%ORT .,,RESPONSE ,A HI< S*OOL
GYM HAS A DOME--%AP$ CEIL+ MODEL$ 0.;X
#B @+ .;Y #B @+ #FJ .;Y -- #CDEF .K #J
": .;X & .;Y >E 9 FEET4 ,A T5NIS PLAY] 9
! GYM HITS A %OT MODEL$ 0.;X #B @+ .;Y
.K #CF ": ! ORIG9 IS LOCAT$ AT ! BASE (!
NET4 ,SOLVE ! SY/EM ( EQU,NS 0BO?
ELIM9,N & SUB/ITU;N4 ,D ANY SOLU;NS
REPRES5T ! BALL HITT+ ! CEIL+8 .,EXPLA94
#DC4 .,,NAVIG,N ,A %IP'S ,,LORAN SY/EM
LOCATES ! %IP ON HYP]BOLAS )! GIV5
EQU,NS4 ,F9D ! %IP'S LOC,N = EA* PAIR (
HYP]BOLAS4 ,9 "P 7;B71 ASSUME ! %IP IS
WE/ (! .;Y --AXIS4
A4 .;X #B -- .;Y #B -- #H .;X @+ #H .K
#J
.;Y #B -- .;X #B --#H .;Y @+ #H .K #J
B4 .XY -- #BD .K #J
.;X #B -- #BE .;Y #B @+ #AJJ .K #J
#DD4 .,,EXT5D$ .,,RESPONSE ,A
.SEISMOGRAPH M1SURES ! 9T5S;Y ( AN
E>?QUAKE4 ,A SEISMOGRAPH C DET]M9E 4T.E
6AN E>?QUAKE'S EPIC5T]1 B N DIREC;N4 ,ON
,JANU>Y #BB1 #BJJC1 A P[];L E>?QUAKE
/RUCK ,MEXICO'S /ATE ( ,COLIMA4 ,!
DIAGRAM %[S APPROXIMATE 4T.ES F ?REE
SEISMIC /,NS 6! EPIC5T]4 ,! RELATIVE
POSI;NS (! SEISMIC /,NS >E DESCRIB$ 2L4
.,MEXICO .,C;Y3 #GJJ MILES S\? & #CJJ
MILES EA/ ( ,LAJITAS
.,LA .,PAZ3 #DJJ MILES S\? & #DJJ
MILES WE/ ( ,LAJITAS
A4 .,MODEL ,US+ ,LAJITAS Z ! ORIG91
WRITE AN EQU,N ( EA* CIRCLE4 ,LET EA*
UNIT REPRES5T #AJJ MILES4
B4 .,ELIM9ATE ,USE ! EQU,N =! CIRCLE
C5T]$ AT ,LAJITAS ) EA* (! O!R TWO
EQU,NS F "P 7A7 6ELIM9ATE ! .;X #B -- &
.;Y #B --T]MS & F9D TWO NEW EQU,NS4
C4 .,SOLVE ,SOLVE ! SY/EM ( L9E>
EQU,NS T RESULTS F "P 7;B7 6F9D !
COORD9ATES (! EPIC5T]4
D4 .,R1SON+ .,EXPLA9 :Y ?REE /,NS >E
REQUIR$ 6LOCATE ! EPIC5T]4
------------------------------------#FFD
.#DE4 .,,*ALL5GE ,:AT IS ! WID? .;W (!
?ICKE/ BOX T W FIT 9 A MAILBOX )!
DIM5.NS %[N8 7.,H9T3 ,USE ! ,PY?AGOR1N
!OREM &! FACT T .,,ABC @: .,,CDE 6WRITE
A SY/EM ( TWO SECOND--DEGREE EQU,NS47
,MIX$ ,REVIEW
.,,PREVIEW ,PREP>E = ,LESSON #AJ.A 9
,EXS4 #DF-EC4
,EVALUATE ! P[]4 @7 P4 #AJ @7
#DF4 #B #E
#DG4 #E #B
#DH4 #C #C
#DI4 #D #F
#EJ4 #F #D
#EA4 #AF #B
#EB4 #AA #C
#EC4 #I #E
,WRITE A POLYNOMIAL FUNC;N .;F ( L1/
DEGREE T HAS R,NAL COE6ICI5TS1 A L1D+
COE6ICI5T ( #A1 &! GIV5 Z]OS4 @7 P4 #CGI
@7
#ED4 #D1 #D1 #A
#EE4 --#C1 --#C1 #J1 #B
#EF4 #B .;I @1 --#B .;I
#EG4
#EH4 --#A1 #B1 --#C .;I
#EI4 --#B1 #J1 #D1
#FJ4 .,,BIOLOGY ,A BEEHIVE IS #E
KILOMET]S S\? & #G KILOMET]S EA/ (A H1!R
PAT*4 ,! BEES W FLY UP 6#I KILOMET]S
6FE$ ON ! H1!R4 ,IS ! PAT* LOCAT$ )9 !
BEES FE$+ RANGE8 @7 P4 #FBF @7
,,QUIZ = .,LESSONS .#I..F--.#I..G
,WRITE AN EQU,N (! 3IC SEC;N4 @7 P4
#FEJ @7
.#A4 ,ELLIPSE ) V]TICES AT 7#C1 --#AJ7
& 7#C1 #F7 & FOCI AT 7#C1 --#G7 & 7#C1
#C7
.#B4 ,P>ABOLA ) V]TEX AT 7--#E1 #B7 &
FOCUS AT 7--#E1 --#A7
.#C4 ,HYP]BOLA ) FOCI AT 7--#C1 #A7 &
7#F1 #A7 & V]TICES AT 7#J1A7 & 7#C1 #A7
,CLASSIFY ! 3IC SEC;N & WRITE XS EQU,N
9 /&>D =M4 ,!N GRAPH ! EQU,N1 @7 P4 #FEJ
@7
.#D4 #I .;X #B -- #D .;Y #B -- #CF .;X
-- #CB .;Y -- #FD .K #J
.#E4 --.;X #B -- .;Y #B -- #D .;X @+
#AB .;Y @+ #ABI .K #J
.#F4 .;X #B @+ #F .;X -- .;Y @+ #AF .K
#J
.#G4 #AB .;X #B @+ #DE .;Y #B @+ #ABJ
.;X @+ #IJ .;Y -- #AEJ .K #J
,SOLVE ! SY/EM1 @7 P4 #FEH @7
.#H4 .;X @+ #B .;Y #B .K --#F
;X @+ #H .;Y .K #J
.#I4 .;X #B @+ #D .;X @+ .;Y #B @+ #F
.;Y .K #AB
#B .;X -- .;Y .K #D
.#AJ4 .;X #B -- .;Y -- #D .K #J
.;X #B @+ #C .;Y #B -- #D .;Y -- #AJ
.K #J
.#AA4 .;Y #B -- #F .;X -- #B .;Y -- #C
.K #J
#B .;Y #B -- #D .;Y @+ .;X @+ #F .K #J
.#AB4 .;Y #B -- #D .;X #B -- #D .;Y .K
#J
.#AC4 #AF .;X #B @+ #I .;Y #B @+ #CB
.;X -- #AH .;Y .K #AAI
.;X #B @+ .;Y #B @+ #B .;X @+ #F .;Y
.K #AE
.#AD4 .,,RAD> ,A RAD> /,N REPORTS T A
%IP IS #AJ MILES AWAY4 ,AT ! SAME "T1 A
SECOND /,N #BJ MILES EA/ & #AE MILES
NOR? (! F/ "O REPORTS T ! %IP IS #AE
MILES AWAY4 ,WRITE & SOLVE A SY/EM (
EQU,NS 6LOCATE ! %IP RELATIVE 6! F/ /,N4
,IS ONLY "O LOC,N POSSI#8 .,EXPLA94 @7
P4 #FEH @7
.,,EXTRA .,,PRACTICE = ,LESSON #I.G1
P4 #AJAH
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#FFE
,EXT5.N
,USE AF ,LESSON #I.G
,DET]M9E ,E35TRIC;Y ( ,3IC ,SEC;NS
.,GOAL ,F9D & APPLY ! E35TRIC;Y (A 3IC
SEC;N4
,KEY ,VOCABUL>Y
99 .E35TRIC;Y
,SIDEB>3
,/&>DS
#AG.J ,GIV5 A QUADRATIC EQU,N (! =M
.AX #B @+ .0#B @+ ..CX @+ DY @+ ;E .K
.#J @1 .,/UD5TS C USE ! ME?OD = -PLET+ !
SQU>E 6PUT ! EQU,N 96/&>D =M & ..C
RECOGNIZE :E!R ! GRAPH (! EQU,N IS A
CIRCLE1 ELLIPSE1 P>ABOLA1 OR HYP]POLA4
,/UD5TS C !N GRAPH ! .EQU,N4
,9 AN ELLIPSE T IS NE>LY CIRCUL>1 !
RATIO .;C3 .A IS CLOSE 6#J4 ,9 A M OVAL
ELLIPSE1 .;C3 .A IS CLOSE 6#A4 ,? RATIO
IS ! .E35TRIC;Y (! ELLIPSE4 ,E 3IC HAS
AN E35TRIC;Y .;E ASSOCIAT$ ) X4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,E35TRIC;Y ( ,3IC ,SEC;NS
,! E35TRIC;Y ( EA* 3IC SEC;N IS DEF9$
2L4 ,= AN ELLIPSE OR HYP]BOLA1 .;C IS !
4T.E F EA* FOCUS 6! C5T]1 & .A IS ! 4T.E
F EA* V]TEX 6! C5T]4
.,CIRCLE3 .;E .K #J
.,ELLIPSE3 & #J "K .;E "K #A
.,P>ABOLA3 .;E .K #A
.,HYP]BOLA3 @1 & .;E .1 #A
,EXAMPLE #A ,F9D E35TRIC;Y
,F9D ! E35TRIC;Y (! 3IC SEC;N
REPRES5T$ 0! EQU,N4
.A4 @7 .;X @+ #C7 #B @+ @7 .;Y -- #A7
#B .K #BE
.B4
,SOLU;N
.A4 ,2C ? EQU,N REPRES5TS A CIRCLE1 !
E35TRIC;Y IS .;E .K #J4
.B4 ,? EQU,N REPRES5TS AN ELLIPSE ) @1
& @4 ,! E35TRIC;Y IS
,EXAMPLE #B ,USE E35TRIC;Y 6WRITE AN
EQU,N
,WRITE AN EQU,N (A HYP]BOLA ) C5T]
7--#B1 #F71 V]TEX 7#F1 #F71 & .;E .K #B4
,SOLU;N
,USE ! =M @4 ,! V]TEX LIES #F--7--#B7
.K #H UNITS F ! C5T]1 S .A .K #H4 ,2C
.;E .K .K #B1 Y "K T @1 OR .;C .K #AF4
,S1 .;B #B .K .;C #B -- .A #B .K
#BEF--#FD .K #AIB4 ,! EQU,N IS
------------------------------------#FFF
,EXAMPLE #C ,USE E35TRIC;Y 6WRITE A
MODEL
.,,A/RONOMY ,PLUTO ORBITS ! SUN 9 AN
ELLIPTICAL PA? )! C5T] (! SUN AT "O
FOCUS4 ,! E35TRIC;Y (! ORBIT IS .;E .K
#J.BDI &! L5G? (! MAJOR AXIS IS AB #GI.J
A/RONOMICAL UNITS4 ,F9D AN EQU,N (
,PLUTO'S ORBIT4 7,ASSUME T ! MAJOR AXIS
IS HORIZONTAL47
,SOLU;N
,! EQU,N (! ORBIT HAS ! =M @4 ,US+ !
L5G? (! MAJOR AXIS1 Y "K T .#B;A .K
#GI.J1 OR .A .K #CI.E4 ,Y C USE !
E35TRIC;Y &! VALUE ( .A 6F9D ! VALUE (
;C1 & !N USE ! VALUES ( .A & .;C 6F9D
.B4 ,S1 AN EQU,N = ,PLUTO'S ORBIT IS @1
": .;X & .;Y >E M1SUR$ 9 A/RONOMICAL
UNITS4
,PRACTICE
,,EXAMPLE #A
ON P4 #FFE = ,EXS4 #A--#F
,F9D ! E35TRIC;Y (! 3IC SEC;N4
.#A4 #G7 .;X -- #C7 #B @+ #G7 .;Y @+
#G7 #B .K #EF
.#B4 #AF7 .;X @+ #A7 #B -- #I7 .;Y --
#E7 #B .K #ADD
.#C4
.#D4
.#E4 @7 .;X -- #E7 #B .K ;L#J .;Y
.#F4 #HA7 .;X @+ #D7 #B @+ @7 .;Y --
#I7 #B .K #HA
,,EXAMPLE #B
ON P4 #FFE = ,EXS4 #G--#AB
,WRITE AN EQU,N (! 3IC SEC;N4
.#G4 ,ELLIPSE ) V]TICES AT 7--#F1 #D7
& 7#F1 #D71 & .;E .K #J.D
.#H4 ,ELLIPSE ) FOCI AT 7--#D1 #B7 &
7--#D1 --#B71 & .;E .K #J.E
.#I4 ,ELLIPSE ) C5T] AT 7#J1 #E71
V]TEX AT 7#G1 #E71 & ;E .K #J.B
.#AJ4 ,HYP]BOLA ) FOCI AT 7#D1 --#E7 &
7#D1 #C71 & .;E .K #B.E
.#AA4 ,HYP]BOLA ) V]TICES AT 7#A1
--#D7 & 7#G1 --#D71 & .;E .K #A.H
.#AB4 ,HYP]BOLA ) C5T] AT 7--#B1 #C71
FOCUS AT 7--#E1 #C71 & .;E .K #D
,,EXAMPLE #C
ON P4 #FFF = ,EXS4 #AC--#AD
.#AC4 .,,A/RONOMY ,N]EID1 A MOON (
,NEPTUNE1 HAS ! MO/ E35TRIC ORBIT ( ANY
MOON 9 ! SOL> SY/EM4 ,! E35TRIC;Y (!
ORBIT IS .;E .K #J.GEA &! L5G? (! MAJOR
AXIS IS AB #AA.J MILLION KILOMET]S4 ,F9D
AN EQU,N ( ,N]EID'S ORBIT4
.#AD4 .,,SATELLITES ,A -MUNIC,NS
SATELLITE IS 9 AN ELLIPTICAL ORBIT >.D
,E>?1 ^: C5T] IS "O FOCUS (! ORBIT4 ,!
E35TRIC;Y (! ORBIT IS .;E .K #J.CID1 &!
SATELLITE IS #AD1CJJ KILOMET]S F ,E>?'S
C5T] AT ! CLOSE/ PO9T 9 XS ORBIT4 ,:AT
IS ! SATELLITE'S 4T.E F ,E>?'S C5T] AT !
F>!/ PO9T 9 XS ORBIT8
.#AE4 .,,R1SON+ .,EXPLA9 :Y ! DEF9I;N
( E35TRIC;Y = ELLIPSES & HYP]BOLAS
IMPLIES T #J "K .;E "K #A = AN ELLIPSE &
;E .1 #A =A HYP]BOLA4
------------------------------------#FFG
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,LESSONS #I.E--#I.G
#A4 .,,MULTI-.,,/EP .,,PRO#M ,A P]SON
AT ! FOCUS ( "O ( TWO FAC+ P>ABOLIC
DI%ES C HE> EV5 A V S(T S.D MADE AT !
FOCUS (! O!R DI%4 ,TWO S* 8:ISP] DI%ES0
>E POSI;N$ ) _! V]TICES #DG FEET A"P4
,EA* DI%'S FOCUS IS #A.E FEET F XS
V]TEX4
A4 ,WRITE AN EQU,N 9 /&>D =M =! CROSS
SEC;N ( EA* DI% IF ! V]TEX ( "O DI% IS
AT ! ORIG9 &! V]TEX (! O!R DI% IS ON !
POSITIVE ;X-AXIS4
B4 ,! DIAMET] ( EA* DI% IS #FG 9*ES4
,H[ DEEP IS EA* DI%8
C4 ,H[ F> A"P >E ! FOCUS & V]TEX =A
DI% #H FEET 9 DIAMET] & #A.BE FEET DEEP8
#B4 .,,MULTI-.,,/EP .,,PRO#M ,A
HYP]BOLIC MIRROR REFLECTS LI<T DIRECT$
T[>D "O FOCUS 6! O!R FOCUS4 ,! HYP]BOLIC
MIRROR %[N HAS FOCI AT 7+-#AB1 #J7 &
V]TICES AT 7+-#H1 #J74
A4 ,WRITE AN EQU,N =! MIRROR4
B4 ,WRITE AN EQU,N =! PA? (! LI<T B1M
ORIG9AT+ AT ! PO9T 7#J1 #I7 2F ! B1M
REFLECTS (F ! MIRROR4
C4 ,AT :AT PO9T DOES ! LI<T B1M 9 "P
7;B7 REFLECT (F ! MIRROR8
#C4 .,,OP5-.,,5D$ ,SKET* FIVE DI6]5T
EXAMPLES ( TWO 3ICS T 9T]SECT 9 EXACTLY
F\R PO9TS4
#D4 .,,EXT5D$ .,,RESPONSE ,:5 A JET
BR1KS ! S.D B>RI]1 S.D WAVES =M A 8,MA*
C"O0 2H ! JET1 &A SONIC BOOM IS HE>D Z !
C"O PASSES4 ,! ,MA* C"O =A JET 9 LEVEL
FLI<T MEETS ! GR.D 9 A HYP]BOLA )! JET
DIRECTLY ABV ! C5T]4 ,SUPPOSE A JET
MAKES A SONIC BOOM HE>D AL;G ": .;X & ;Y
>E 9 MILES4
A4 ,:AT IS ! %ORTE/ POSSI# HORIZONTAL
4T.E Y CD 2 F ! JET :5 Y F/ HE> ! SONIC
BOOM8 .,EXPLA94
B4 ,! JET PASSES A SECOND "T1 CR1T+ A
SONIC BOOM HE>D AL;G @4 ,ANSW] ! "Q F "P
7A7 = ? SONIC BOOM4
C4 .,DESCRIBE ! REL,N%IP 2T ! TWO
HYP]BOLAS4
#E4 .,,%ORT .,,RESPONSE ,! DIAGRAM %[S
! MIRRORS 9 A ,CASSEGRA9 TELESCOPE4 ,!
EQU,NS (! MIRRORS >E GIV5 2L4 ,CLASSIFY
EA* MIRROR Z .P>ABOLIC1 .ELLIPTICAL @1
OR .HYP]BOLIC4 .,EXPLA9 YR R1SON+4
A4 ,MIRROR ,A3 .;Y #B -- .#AB;X --
#DEJ .K #J
B4 ,MIRROR ;,B3 #HH.D;X #B -- #DI.G;Y
#B -- #DCIJ .K #J
#F4 .,,GRI4$ .,,ANSW] ,A LOGO HAS
9T]SECT+ ELLIPSES MODEL$ 0#I .;X #B @+
.;Y #B @+ #H .;Y .K #BJ & .;X #B @+ #D
.;Y #B .K #AF4 ,:AT IS ! ;Y-COORD9ATE (!
UPP]MO/ PO9T ( 9T]SEC;N8
------------------------------------#FFH
#I ,*APT] ,SUMM>Y
,,BIG ,,ID1S
,= ,YR ,NOTEBOOK
.,BIG .,IDEA .#A ,WRIT+ ,EQU,NS ( ,3IC
,SEC;NS
,! FOLL[+ TA# IS 9 LI/$
=MAT4 ,= EA* CELL ! H1D+ IS %[N
FOLL[$ 0A COLON1 SPACE &! CELL
3T5TS
,3IC3 ,CIRCLE
,EQU,N3 .;X #B @+ .;Y #B .K .;R #B
,KEY FACTS3 RADIUS .;R
,KEY FACTS3 RADIUS .;R
,KEY FACTS3 RADIUS .;R
,3IC3 ,P>ABOLA
,EQU,N3 .;X #B .K #D .PY
,KEY FACTS3 .,AXIS .( .SYMMETRY
V]TICAL
,KEY FACTS3 .,FOCUS 7.#J,.;P7
,KEY FACTS3 .,DIRECTRIX .;Y.K --.;P
,3IC3 ,P>ABOLA
,EQU,N3 .;Y #B .K #D .PX
,KEY FACTS3 .,AXIS .( .SYMMETRY
HORIZONTAL
,KEY FACTS3 .,FOCUS 7.;P1.#J7
,KEY FACTS3 .,DIRECTRIX .;X.K --.;P
,3IC3 ,ELLIPSE
,EQU,N3
,KEY FACTS3 .,MAJOR .AXIS HORIZONTAL
,KEY FACTS3 .,V]TICES 7+-.A @1 #J7
,KEY FACTS3 .,CO--.V]TICES 7.#J1
+-.;B7
,3IC3 ,ELLIPSE
,EQU,N3
,KEY FACTS3 .,MAJOR .AXIS V]TICAL
,KEY FACTS3 .,V]TICES 7#J1 +- .A @7
,KEY FACTS3 .,CO--.V]TICES 7+-.;B @1
#J7
,3IC3 ,HYP]BOLA
,EQU,N3
,KEY FACTS3 .,TRANSV]SE .AXIS
HORIZONTAL
,KEY FACTS3 .,ASYMPTOTES
,KEY FACTS3 .,V]TICES 7+-.A @1 #J7
,3IC3 ,HYP]BOLA
,EQU,N3
,KEY FACTS3 .,TRANSV]SE .AXIS V]TICAL
,KEY FACTS3 .,ASYMPTOTES
,KEY FACTS3 .,V]TICES 7#J1 +- .A @7
.,BIG .,IDEA .#B ,GRAPH+ ,EQU,NS (
,3IC ,SEC;NS
,CIRCLE
@7 ;X--;H7 #B @+ 7;Y--;K7 #B .K ;R #B
,P>ABOLA
@7 .;X -- .;H @7 #B .K #D .;P @7 .;Y
-- .;K @7
,ELLIPSE
,HYP]BOLA
.,BIG .,IDEA .#C ,SOLV+ ,QUADRATIC
,SY/EMS
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,ME?OD3 ,DESCRIP;N3 ,:5 6USE
,GRAPH+3 ,GRAPH ! EQU,NS4 ,ID5TIFY ANY
PO9TS ( 9T]SEC;N43 ,:5 GRAPH+ IS EASY OR
:5 US+ A GRAPH+ CALCULATOR
,SUB/ITU;N3 ,SOLVE "O EQU,N = "O (!
V>IA#S & SUB/ITUTE X 96! O!R EQU,N43 ,:5
Y C EASILY SOLVE = "O V>IA# 7OR XS
SQU>E7 9 T]MS (! O!R V>IA#
,ELIM9,N3 ,MULTIPLY "O OR BO? EQU,NS
0A 3/ANT Z NE$$1 & ADD43 ,:5 Y C
ELIM9ATE "O OR M (! V>IA# T]MS
------------------------------------#FFI
#I ,*APT] ,REVIEW
,SIDEB>3
@A,HOME,TUTOR
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99 ,MULTI--,LANGUAGE ,GLOSS>Y
99 ,VOCABUL>Y PRACTICE
,,REVIEW ,,KEY ,,VOCABUL>Y
99 4T.E =MULA1 P4 #FAD
99 MIDPO9T =MULA1 P4 #FAE
99 FOCUS1 FOCI1 PP4 #FBJ @1 #FCD @1
#FDB
99 DIRECTRIX1 P4 #FBJ
99 CIRCLE1 P4 #FBF
99 ,C5T]1 PP4 #FBF @1 #FCD @1 #FDB
99 RADIUS1 P4 #FBF
99 ELLIPSE1 P4 #FCD
99 V]TICES1 PP4 #FCD ,.#FDB
99 MAJOR AXIS1 P4 #FCD
99 CO--V]TICES1 P4 #FCD
99 M9OR AXIS1 P4 #FCD
99 HYP]BOLA1 P4 #FDB
99 TRANSV]SE AXIS1 P4 #FDB
99 3IC SEC;NS1 P4 #FEJ
99 G5]AL SECOND--DEGREE EQU,N1 P4 #FEC
99 4CRIM9ANT1 P4 #FEC
99 QUADRATIC SY/EM1 P4 #FEH
,,VOCABUL>Y ,,EX]CISES
.#A4 ,COPY & -PLETE3 ,A7;N7 @8 IS !
SET ( ALL PO9TS 9 A PLANE EQUIDISTANT F
A PO9T CALL$ ! FOCUS &A L9E CALL$ !
DIRECTRIX4
.#B4 ,COPY & -PLETE3 ,! L9E SEG;T JO9+
! TWO CO--V]TICES ( AN ELLIPSE IS ! @8
@4
.#C4 ,COPY & -PLETE3 ,! L9E SEG;T JO9+
! TWO V]TICES (A HYP]BOLA IS ! @8 @4
.#D4 .,,WRIT+ .,DESCRIBE H[ !
ASYMPTOTES (A HYP]BOLA HELP Y DRAW !
HYP]BOLA4
,,REVIEW ,,EXAMPLES ,,& ,,EX]CISES
,USE ! REVIEW EXAMPLES & EX]CISES 2L
6*ECK YR "U/&+ (! 3CEPTS Y H LE>N$ 9 EA*
LESSON ( ,*APT] #I4
#I.A ,APPLY ! ,4T.E & ,MIDPO9T ,=MULAS
PP4 #FAD --#FAI
,EXAMPLE
,F9D ! 4T.E 2T 7--#E1 #C7 & 7#A1
--#C74 ,!N F9D ! MIDPO9T (! L9E SEG;T
JO9+ ! TWO PO9TS4
,,EXAMPLES #A & #C
ON PP4 #FAD --#FAE = ,EXS4 #E--#H
,,EX]CISES
,F9D ! 4T.E 2T ! TWO PO9TS4 ,!N F9D !
MIDPO9T (! L9E SEG;T JO9+ ! TWO PO9TS4
#E4 7--#F1 --#E71 7#B1 --#C7
#F4 7--#B1 #E71 7#A1 #I7
#G4 7--#C1 --#D71 7#B1 #E7
.#H4 .,,SKYDIV+ ,A SKYDIV] L&S #BJJ
Y>DS WE/ & #DJ Y>DS NOR? (A T>GET4 ,A
SECOND SKYDIV] L&S #CJ Y>DS EA/ & #ADJ
Y>DS S\? (! SAME T>GET4 ,H[ F> F EA* O!R
D ! TWO SKYDIV]S L&8
------------------------------------#FGJ
#I ,,*APT] ,,REVIEW
.#I..B .,GRAPH & ,WRITE .,EQU,NS .(
,P>ABOLAS
PP4 #FBJ --#FBE
,EXAMPLE
.,GRAPH @4 ..,ID5TIFY ! FOCUS1
DIRECTRIX1 & AXIS ( .SYMMETRY @1
.,,/EP .#A .,REWRITE 9 /&>D =M Z .;Y
#B .K #AB .X4
.,,/EP .#B .,ID5TIFY ! FOCUS1
DIRECTRIX1 & AXIS ( SYMMETRY4 ,! EQU,N
HAS ! =M .;Y #B .K #D .PX ) #D .;P .K
#AB1 S .;P .K #C4 ,! FOCUS IS 7;P1 #J71
OR 7#C1 #J71 &! DIRECTRIX IS .;X .K
--.;P @1 OR .;X .K --.#C @4 ,2C .;Y IS
SQU>$1 ! AXIS ( SYMMETRY IS ! .;X
--AXIS4
.,,/EP .#C .,DRAW ! P>ABOLA4 ,2C .;P
.1 #J1 ! P>ABOLA OP5S 6! "R4 ,"S PO9TS
ON ! P>ABOLA >E 7#J1 #J71 7#A1 +-#C.DF71
& 7#B1 +-#D.IJ74
,,EX]CISES
,,EXAMPLES #A & #B
ON .P4 #FBA = ,EXS4 #I--#AD
,GRAPH ! EQU,N4 ,ID5TIFY ! FOCUS1
DIRECTRIX1 & AXIS ( SYMMETRY (! P>ABOLA4
.#I4 .;X #B .K #AF .;Y
#AJ4 .;Y #B .K --.#F .;X
.#AA4 .;X #B @+ #D .;Y .K #J
,WRITE ! /&>D =M (! EQU,N (! P>ABOLA
)! GIV5 FOCUS OR DIRECTRIX & V]TEX AT
7#J1J74
.#AB4 ,FOCUS3 7--#E1 #J7
.#AC4 ,FOCUS3 7#J1 #C7
.#AD4 ,DIRECTRIX3 .;X .K --#F
#I.C ,GRAPH & ,WRITE ,EQU,NS (
,CIRCLES
PP4 #FBF --#FCB
,EXAMPLE
.,GRAPH .;X #B .K #FD -- .;Y #B @4
..,ID5TIFY ! RADIUS (! .CIRCLE4
.,,/EP .#A .,REWRITE .;X #B .K #FD --
.;Y #B 9 /&>D =M Z .;X #B @+ .;Y #B .K
#FD4
.,,/EP .#B .,ID5TIFY ! RADIUS4 ,!
GRAPH IS A CIRCLE ) C5T] AT ! ORIG9 &
RADIUS
.,,/EP .#C .,DRAW A CIRCLE PASS+ "?
PO9TS T >E #H UNITS F ! ORIG91 S* Z 7#H1
#J71 7#J1 #H71 7--#H1 #J71 & 7#J1 --#H74
,,EX]CISES
,GRAPH ! EQU,N4 ,ID5TIFY ! RADIUS (!
CIRCLE4
.#AE4 .;X #B @+ .;Y #B .K #HA
.#AF4 .;X #B .K #DJ -- .;Y #B
.#AG4 .#C;X #B @+ .#C .;Y #B .K #ADG
..,,EXAMPLES #A & .#B ON PP4
.#FBF--.#FBG = .,EXS4 .#AE--.#BJ
,WRITE ! /&>D =M (! EQU,N (! CIRCLE T
PASSES "? ! GIV5 PO9T & ^: C5T] IS !
ORIG94
.#AH4 7#E1 #I7
.#AI4 7--#H1 #B7
.#BJ4 7--#G1 --#D7
------------------------------------#FGA
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,*APT] ,REVIEW ,PRACTICE
#I.D ,GRAPH & ,WRITE ,EQU,NS (
,ELLIPSES
PP4 #FCD --#FCI
,EXAMPLE
,GRAPH #D .;X #B @+ .;Y #B .K #AF4
,ID5TIFY ! V]TICES1 CO--V]TICES1 & FOCI4
.,,/EP .#A .,REWRITE .#D;X #B @+ .;Y
#B .K #AF 9 /&>D =M Z @4
.,,/EP .#B .,ID5TIFY ! V]TICES1
CO--V]TICES1 & FOCI4 ,NOTE T .A #B .K
#AF & .;B #B .K #D1 S .A .K .#D1 .;B .K
.#B @1 & .;C #B .K .A #B -- .;B #B .K
#AB1 OR .;C .#C..E @4 ,! MAJOR AXIS IS
V]TICAL4 ,! V]TICES >E AT @7 .#J1 +-.#D
@7@4 ,! CO--V]TICES >E AT @7 +-.#B1.J
@7@4 ,! FOCI >E AT 7.#J1 +-.#C..E74
.,,/EP .#C ,DRAW ! ELLIPSE4
,,EX]CISES
,GRAPH ! EQU,N4 ,ID5TIFY ! V]TICES1
CO--V]TICES1 & FOCI (! ELLIPSE4
.#BA4 #AF .;X #B @+ #BE .;Y #B .K #DJJ
.#BB4 #HA .;X #B @+ #I .;Y #B .K #GBI
.#BC4 #FD .;X #B @+ #CF .;Y #B .K
#BCJD
,,EXAMPLES #A1B1 & #D
ON PP4 #FCE --#FCF = ,EXS4 #BA--#BE
,WRITE AN EQU,N (! ELLIPSE )! GIV5
"*I/ICS & C5T] AT 7#J1J74
.#BD4 ,V]TEX3 7--#F1 #J72 CO--V]TEX3
7#J1 --#C7
.#BE4 ,V]TEX3 7#J1 --#H72 FOCUS3 7#J1
#E7
#I.E ,GRAPH & ,WRITE ,EQU,NS (
,HYP]BOLAS
PP4 #FDB --#FDH
,EXAMPLE
,GRAPH #D .;X #B -- #I .;Y #B .K #CF4
,ID5TIFY ! V]TICES1 FOCI1 & ASYMPTOTES4
.,,/EP .#A .,REWRITE #D .;X #B -- #I
.;Y #B .K #CF 9 /&>D =M Z @4
.,,/EP .#B .,ID5TIFY ! V]TICES1 FOCI1
& ASYMPTOTES4 ,NOTE T .A #B .K #I & .;B
#B .K #D1 S .A .K .#C1 .;B .K .#B @1 &
.;C #B .K .A #B @+ .;B #B .K #AC1 OR .;C
.#C..F @4 ,! TRANSV]SE AXIS IS
HORIZONTAL4 ,! V]TICES >E AT @7 +-.#C1
.#J @7@4 ,! FOCI >E AT @7 +-.#C..F1.J
@7@4 ,! ASYMPTOTES >E @4
.,,/EP .#C .,DRAW ASYMPTOTES "?
OPPOSITE CORN]S (A RECTANGLE C5T]$ AT
7#J1 #J7 T IS .#B;A .K #F UNITS WIDE &
.#B;B .K #D UNITS HI<4 ,DRAW ! HYP]BOLA4
,,EXAMPLES #A & #B
ON P4 #FDC = ,EXS4 #BF--#CJ
,,EX]CISES
,GRAPH ! EQU,N4 ,ID5TIFY ! V]TICES1
FOCI1 & ASYMPTOTES4
.#BF4 #I .;X #B -- .;Y #B .K #I
.#BG4 #D .;X #B -- #AF .;Y #B .K #FD
.#BH4 #AJJ .;Y #B -- #CF .;X #B .K
#CFJJ
,WRITE AN EQU,N (! HYP]BOLA )! GIV5
FOCI & V]TICES4
.#BI4 ,FOCI3 7#J1 +-#E72 V]TICES3 7#J1
+-#B7
.#CJ4 ,FOCI3 7+-#I1 #J72 V]TICES3
7+-#D1 #J7
------------------------------------#FGB
#I ,,*APT] ,,REVIEW
#I.F ,TRANSLATE & ,CLASSIFY ,3IC
,SEC;NS
PP4 #FEJ --#FEG
,EXAMPLE
,CLASSIFY ! 3IC SEC;N --#D .;X #B @+
.;Y #B @+ #CB .;X -- .,I#B .;Y -- #CB .K
#J & WRITE XS EQU,N 9 /&>D =M4 ,!N GRAPH
! EQU,N4
,2C .,A .K --#D1 .;,B .K #J1 & .;,C .K
#A1 ! 4CRIM9ANT IS .;,B #B -- #D .;,,AC
.K #AF .1 #J1 S ! 3IC IS A HYP]BOLA4
,-PLETE ! SQU>E 6WRITE ! EQU,N 9 /&>D
=M4
--#D .;X #B @+ .;Y #B @+ #CB .;X --
#AB .;Y -- #CB .K #J
@7 .;Y #B -- #AB .;Y @7--#D7 .;X #B --
#H .;X @7 .K #CB
@7 .;Y #B -- #AB .;Y @+ #CF7--#D7 .;X
#B -- #H .;X @+ #AF7 .K #CB @+
#CF--#D7#AF7 @7 .;Y -- #F7 #B -- #D7 .;X
-- #D7 #B .K #D
,F ! EQU,N1 @7 .;H1 .;K7 .K 7#D1F71 &
.;B .K #A4 ,! V]TICES >E 7#D1 #F @+ #B7
.K 7#D1 #H7 & 7#D1 #F--#B7 .K 7#D1 #D74
,! GRAPH IS %[N ABV4
,,EXAMPLE #F
ON P4 #FEC = ,EXS4 #CA--#CD
,,EX]CISES
,CLASSIFY ! 3IC SEC;N & WRITE XS EQU,N
9 /&>D =M4 ,!N GRAPH ! EQU,N4
.#CA4 #D .;X #B @+ #I .;Y #B @+ #DJ
.;X @+ #GB .;Y @+ #BJH .K #J
.#CB4 .;Y #B -- ;L#J .;Y -- #H .;X @+
#A .K #J
.#CC4 #I .;X #B -- ;Y #B -- #AH .;X --
#D .;Y -- #E .K #J
.#CD4 ;X #B @+ ;Y #B @+ #D .;X -- #AD
.;Y @+ #AG .K #J
#I.G ,SOLVE ,QUADRATIC ,SY/EMS
PP4 #FEH --#FFD
,EXAMPLE
,SOLVE ! SY/EM4 #AB .;X #B -- #HA .;Y
#B @+ #AF .K #J
#B .;X #B @+ #I .;Y .K #J
,WRITE ! SECOND EQU,N Z @4 ,!N
SUB/ITUTE 9 ! F/ EQU,N4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
@3 ,SUB/ITUTE =.' ;Y .-9 F/ EQU,N4
#AB .;X #B -- #D .;X #D @+ #AF .K #J
@3 .,SIMPLIFY4
.;X #D -- #C .;X #B -- #D .K #J @3
..,DIVIDE EA* SIDE BY --.#D @4
@7 .;X #B --#D7@7 .;X #B @+ #A7 .K#J
@3 .,FACTOR @4
,0! Z]O PRODUCT PROP]TY1 ..;X .K +-#B4
.,THE SOLU;NS >E
,,EXAMPLES #B & #C
ON PP4 #FEI --#FFJ = ,EXS4 #CE--#CG
,,EX]CISES
,SOLVE ! SY/EM4
.#CE4 .;Y #B .K #D .;X
#B .;X -- #E .;Y .K --#H
.#CF4 .;X #B @+ .;Y #B -- #AJJ .K #J
;X @+ ;Y--#AD .K #J
.#CG4 #AF .;X #B -- #D .;Y #B .K #FD
#D .;X #B @+ #I .;Y #B -- #DJ .;X .K
--#FD
------------------------------------#FGC
#I ,*APT] ,TE/
,F9D ! 4T.E 2T ! TWO PO9TS4 ,!N F9D !
MIDPO9T (! L9E SEG;T JO9+ ! TWO PO9TS4
.#A4 7--#A1 #E71 7#G1 #C7
.#B4 7#D1 #B71 7#H1 #H7
.#C4 7--#A1 --#F71 7#A1 #E7
.#D4 7#B1 --#E71 7#C1 #A7
.#E4 7--#F1 --#B71 7--#C1 #E7
.#F4 7#A1 #I71 7#AJ1 --#B7
,GRAPH ! EQU,N4
.#G4 .;Y #B -- #BD .;X .K #J
.#H4 .;X #B @+ .;Y #B .K #AF
.#I4 #FD .;Y #B -- .;X #B .K .#FD
.#AJ4 #AH .;X #B @+ #B .;Y #B .K #AH
.#AA4 @7 .;X -- #F7 #B @+ @7 .;Y @+
#A7 #B .K #CF
.#AB4 @7 .;X @+ #D7 #B .K #F7 .;Y --
#B7
.#AC4
.#AD4
.#AE4
,WRITE ! /&>D =M (! EQU,N (! 3IC SEC;N
)! GIV5 "*I/ICS4
.#AF4 ,P>ABOLA ) V]TEX AT 7#J1 #J7 &
DIRECTRIX AT ;X .K --#F
.#AG4 ,P>ABOLA ) V]TEX AT 7--#B1 --#A7
& FOCUS AT 7--#B1 #E7
.#AH4 ,CIRCLE ) C5T] AT 7#J1 #J7 &
PASS+ "? 7--#E1 #B7
.#AI4 ,CIRCLE ) C5T] AT 7#A1 --#D7 &
RADIUS #F
.#BJ4 ,ELLIPSE ) C5T] AT 7#J1 #J71
V]TEX AT 7#J1 #F71 & CO--V]TEX AT 7--#C1
#J7
.#BA4 ,ELLIPSE ) V]TICES AT 7--#A1 #D7
& 7#G1 #D7 & FOCI AT 7#A1 #D7 & 7#E1 #D7
.#BB4 ,HYP]BOLA ) V]TICES AT 7#J1
--#F7 & 7#J1 #F7 & FOCI AT 7#J1 --#I7 &
7#J1 #I7
.#BC4 ,HYP]BOLA ) V]TEX AT 7#B1 --#E71
FOCUS AT 7--#A1 --#E71 & C5T] AT 7#E1
--#E7
,CLASSIFY ! 3IC SEC;N & WRITE XS EQU,N
9 /&>D =M4
.#BD4 .;X #B @+.1 #D .;Y #B -- .#F;X
-- #AF .;Y @+ #BA .K #J
.#BE4 .;X #B @+ ;Y #B @+ #H .;X @+ #AB
.;Y @+ #C .K #J
.#BF4 #D .;X #B --.#I .;Y #B -- #DJ
.;X @+ #FD .K #J
.#BG4 ;Y #B -- #AF .;Y -- #AB .;X @+
#DJ .K #J
.#BH4 #BE .;X #B @+ #D .;Y #B @+ #EJ
.;X -- #BD .;Y -- #CI .K #J
.#BI4 ;Y #B -- #AF .;X #B @+ #AD .;Y
@+ #FD .;X -- #CA .K #J
,SOLVE ! SY/EM4
.#CJ4 #D .;X #B @+ ;Y #B .K #AF
.;X @+ .;Y .K #B
.#CA4 ;X #B @+ #D .;Y #B -- #H .;Y .K
#D
;Y #B -- #B .;Y -- #H .;X -- #AF .K #J
.#CB4 ;Y #B -- ;X #B @+ #B .;X -- #E
.K #J
.;X #B @+ .;Y #B -- #B .;X -- #C .K #J
.#CC4 .,,WAT] .,,SURFACE ,A CYL9DRICAL
GLASS ( WAT] HAS A #A.E 9* RADIUS4 ,IF !
GLASS IS TILT$ #FJ;DG1 ! WAT]'S SURFACE
MEETS ! GLASS 9 AN ELLIPSE ) M9OR AXIS
#C 9*ES L;G & MAJOR AXIS #F 9*ES L;G4
,WRITE EQU,NS T MODEL ! WAT]'S SURFACE
)! GLASS UP"R & AF ! GLASS IS TILT$4
,USE ! C5T] (! WAT]'S SURFACE Z ! ORIG94
.#CD4 .,,A/RONOMY ,! ,GRE5 ,BANK
,TELESCOPE 9 ,WE/ ,VIRG9IA HAS A MA9
REFLECTOR ^: CROSS SEC;N IS A POR;N (A
8P>5T0 P>ABOLA4 ,A DIAGRAM (!
REFLECTOR'S CROSS SEC;N &! P>5T P>ABOLA
IS %[N4 ,WRITE AN EQU,N T MODELS ! P>5T
P>ABOLA IF XS V]TEX IS AT 7#J1 #J74 ,:AT
IS ! 4T.E F ! V]TEX 6! FOCUS8
------------------------------------#FGD
#I ,/&>DIZ$ ,TE/ ,PREP>,N
,,%ORT ,,RESPONSE ,,"QS
,SCOR+ ,RUBRIC
,FULL ,CR$IT
99 SOLU;N IS -PLETE & CORRECT
,"PIAL ,CR$IT
99 SOLU;N IS -PLETE B HAS ]RORS1 .OR
99 SOLU;N IS )\T ]ROR B 9COMPLETE
,NO ,CR$IT
99 NO SOLU;N IS GIV51 .OR
99 SOLU;N MAKES NO S5SE
,PRO#M
,TWO V]TICES ( AN EQUILAT]AL TRIANGLE
>E .,A 7#J1 #J7 & ;,B7#F1 #J74 ,WRITE &
SOLVE A SY/EM ( EQU,NS 6F9D ! COORD9ATES
(! ?IRD V]TEX ;,C ( .,,ABC4 ,IS "! ONLY
"O POSSI# POSI;N =! ?IRD V]TEX8
.,EXPLA94
,2L >E SAMPLE SOLU;NS 6! PRO#M4 ,R1D
EA* SOLU;N &! -;TS 9 BLUE 6SEE :Y !
SAMPLE REPRES5TS FULL CR$IT1 "PIAL
CR$IT1 OR NO CR$IT4
,,SAMPLE #A3 ,FULL CR$IT SOLU;N
,! SOLU;N IS SET UP LOGIC,Y & ?OR\<LY4
,2C .;,,AB .K #F--#J .K #F & .,,ABC IS
EQUILAT]AL1 ..;,,AC .K ,,BC .K .#F @4
,LET 7;X1 ;Y7 REPRES5T ! COORD9ATES (
V]TEX ,C4 ,USE ! 4T.E =MULA4
,= .,,BC3
,! CORRECT EQU,NS >E OBTA9$1 &A VALID
ME?OD IS US$ 6SOLVE ! SY/EM4
,SOLVE ! SY/EM 0A4+ --#A "TS ! SECOND
EQU,N 6! F/4
,SUB/ITUTE #C = .;X 9 ! F/ EQU,N3 #C
#B @+ ;Y #B .K #CF1 S ;Y #B .K #BG1 OR
@4
,! SY/EM IS SOLV$ CORRECTLY4 ,A
CORRECT 3CLU.N IS DRAWN4
,! SOLU;NS (! SY/EM >E @4 ,S1 ! ?IRD
V]TEX IS AT .;,C OR @4 ,"! >E TWO
SOLU;NS1 2C ;,C C 2 ABV OR 2L @4
,,SAMPLE #B3 ,"PIAL CR$IT SOLU;N
,! 4T.E 2T .,A & .;,B IS #F4
;,,AC .K#F ;X #B @+ ;Y #B .K #CF
,,BC .K #F ;X #B @+ ;Y #B -- #AB;X .K
#J
,! SY/EM IS CORRECT1 B /EPS >E OMITT$
9 WRIT+ & SOLV+ X4
,SOLVE ! SY/EM 0SUB/ITUT+ #CF = .;X #B
@+ .;Y #B 9 ! SECOND EQU,N4
.;X #B @+ .;Y #B -- .#AB;X .K #J
#CF--#AB .;X -- #J
.;X .K #C
,! A4I;NAL V]TEX IS OMITT$4 ,AN
9CORRECT 3CLU.N IS DRAWN4
,F9D ;Y :5 .;X .K #C3 .;X #B @+ ;Y #B
.K #CF1 S ;Y #B .K #BG1 & @4 ,!
COORD9ATES (! ?IRD V]TEX >E @4 ,? IS !
ONLY POSSI# POSI;N (! V]TEX1 2C !
DIM5.NS (A TRIANGLE M/ 2 POSITIVE4
------------------------------------#FGE
,,SAMPLE #C3 ,"PIAL CR$IT SOLU;N
,A VALID APPROA* IS US$1 &! SOLU;N IS
SET UP LOGIC,Y & ?OR\<LY4
,! 4T.E 2T .,A & .;,B IS #F4 ,S1 ! O!R
TWO SIDES ( .,,ABC H L5G?S ( #F4 ,DRAW
CIRCLES ) RADII ( #F C5T]$ AT .,A & .,B4
,! PO9TS ( 9T]SEC;N (! CIRCLES W 2 !
POSSI# POSI;NS (! ?IRD V]TEX4
,! EQU,NS (! CIRCLES >E CORRECT4
,EQU,N ( CIRCLE .,A3 .;X #B @+ ;Y #B
.K #CF ,EQU,N ( CIRCLE .;,B3 @7 .;X --
#F7 #B @+ ;Y #B .K #CF
,! ANSW] IS CORRECT B "W IS N %[N4
,! SOLU;NS (! SY/EM >E & @1 S ! POSSI#
COORD9ATES (! ?IRD V]TEX >E OR @4
,,SAMPLE #D3 ,NO CR$IT SOLU;N
,! ANSW] %[S A BASIC MIS"U/&+4
,2C .;,,AB .K #F & IS HORIZONTAL1 !
V]TEX AT ;,C IS #F UNITS ABV OR 2L EI ,A
OR .,B4 ,! POSSI# COORD9ATES ( ;,C >E
7#J1 #F71 7#J1 --#F71 7#F1 #F71 OR 7#F1
--#F74
,SIDEB>3
,/&>DS
..,5RI*;T ( #B.J ,/UD5TS SOLVE SY/EMS
.( L9E> .EQU,NS & 9EQUALITIES @7 .9 .TWO
OR ?REE .V>IA#S @7 0SUB/ITU;N1 ) GRAPHS1
OR ) MATRICES4
,,PRACTICE ,APPLY ! ,SCOR+ ,RUBRIC
,USE ! RUBRIC ON PAGE #FGD 6SCORE !
SOLU;N 6! PRO#M 2L ..Z FULL CR$IT1 "PIAL
.CR$IT @1 OR .NO .CR$IT4 .,EXPLA9 YR
R1SON+4
.,,PRO#M .,,R/ IS ISOSCELES ) .,,RT .K
.,,ST & HAS V]TICES AT ;,R7--#B1 #B71
;,S7#D1 --#A71 & ;,T7#B1 .;Y @7@4
,F9D .;Y @4
,IS "! ONLY "O POSSI# VALUE ( .;Y @8
.,EXPLA94
.#A4
.#B4 ,IF ,,R/ IS ISOSCELES .) ,,RT .K
,,ST1 !N ;,T LIES ON ! P]P5DICUL>
BISECTOR ( @4
.,! .P]P5DICUL> BISECTOR ( HAS .A
.ELOPE ( #B1 ! NEGATIVE .RECIPROCAL
(--#J.E4 ,XS .EQU,N IS .;Y -- #J.E .K
#B7 .;X -- #A71 OR .;Y .K #B .;X --
#A.E4 ,SUB/ITUT+ #B = ;X GIVES .;Y .K
#B.E4 ,S9CE .;Y .K #B .;X -- #A.E IS A
FUNC;N1 ? IS ! ONLY VALUE ( .;Y = .;X .K
#B4
------------------------------------#FGF
#I ,/&>DIZ$ ,TE/ ,PRACTICE
,,%ORT ,,RESPONSE
#A4 ,A RHOMBUS IS A QUADRILAT]AL ) F\R
3GRU5T SIDES4 ,! V]TICES ( FIGURE
.,,ABCD >E1 ,A7#F1 #C71 ;,B7--#C1 #E71
;,C7--#E1 --#D71 & ;,D7#D1 --#E74 ,C Y
*ANGE ! COORD9ATES ( "O V]TEX ( .,,ABCD
6MAKE X A RHOMBUS8 ,IF S1 EXPLA9 H[ &
F9D ! COORD9ATES4 ,IF N1 EXPLA9 :Y N4
#B4 ,A LAMP = 9DOOR G>D5+ USES A
P>ABOLIC REFLECTOR )! HEI<T & WID? %[N
63C5TRATE LI<T ON PLANTS4
#C4 ,?REE PO9TS ON ! $GE (! CIRCUL>
,COP]NICUS CRAT] ON ! MOON C 2 REPRES5T$
0! COORD9ATES 7--#CE1 #CE71 7#J1 #J71 &
7#DJ1 #HJ7 ": EA* UNIT REPRES5TS "O
KILOMET]4 ,IS ! PO9T LOCAT$ AT 7#EE1
#BE7 9SIDE ! CRAT] OR \TSIDE ! CRAT]8
.,EXPLA9 YR R1SON+4
#D4 ,= EA* SET ( 3C5TRIC CIRCLES %[N
2L1 ! M1SURES (! RADII >E ! 3SECUTIVE
9TEG]S F #A 6#I4 .,EXPLA9 H[ Y C USE ?
9=M,N 6DEMON/RATE T ! PO9TS %[N 9 R$ LIE
ON AN ELLIPSE ^: FOCI >E ! C5T]S (!
CIRCLES4 ,!N WRITE AN EQU,N (! ELLIPSE4
#E4 ,A SO3] FIELD HAS A P5ALTY-KICK
M>K #AB Y>DS F ! GOAL4 ,F ! M>K'S C5T]1
AN >C )A RADIUS ( #AJ Y>DS IS DRAWN
\TSIDE ! P5ALTY >EA Z %[N 9 ! DIAGRAM4
.,EXPLA9 H[ 6USE AN EQU,N (A CIRCLE 6F9D
! 4T.E .;D AL;G ! $GE (! P5ALTY >EA 2T !
5DPO9TS (! >C4
#F4 ,A COORD9ATE GRID 3TA9S TWO
HYP]BOLAS C5T]$ AT ! ORIG91 "O )A
V]TICAL TRANSV]SE AXIS & "O )A
HORIZONTAL TRANSV]SE AXIS4 ,:AT >E !
POSSI# NUMB]S ( SOLU;NS (! SY/EM T !
HYP]BOLAS REPRES5T8 ,USE SKET*ES 6JU/IFY
YR ANSW]4
#G4 ,! .,TRACTRICI\S SCULPTURE AT !
,F]MI ,N,NAL ,A3EL]ATOR ,LABORATORY 9
,BATAVIA1 ,ILL9OIS1 HAS A HYP]BOLIC
CROSS SEC;N Z %[N 2L4
,USE ! GRAPH 6WRITE AN EQU,N (!
HYP]BOLA T MODELS ! CROSS SEC;N (!
SCULPTURE4 7,EA* UNIT REPRES5TS #A
FOOT47 ,!N EXPLA9 H[ 6MODIFY YR EQU,N S
! ORIG9 IS AT ! BOTTOM LEFT (!
SCULPTURE4
#H4 ,)\T APPLY+ >EA =MULAS1 -P>E ! >1S
(! ELLIPSES REPRES5T$ 0.#D;X #B @+ .#F;Y
#B .K .#DH & @4 .,EXPLA9 H[ Y MADE YR
-P>ISON4
------------------------------------#FGG
,,TE/ ,,PREP>,N
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,,MULTIPLE ,,*OICE
#I4 ,: EQU,N REPRES5TS A HYP]BOLA8
,A4 .;X #B -- .#C;Y @+ #D;X--#AE .K #J
,B4 ;X #B @+ .;Y #B @+
#D;X--#AH;Y--#AE .K #J
,C4 .;X #B -- .;Y #B @+ #D;X -- .#AH;Y
-- #AE .K #J
,D4 --#B;X #B -- ;Y #B @+
#D;X--#AH;Y--#AE .K #J
#AJ4 ,AT :AT PO9T7;S7 D ! GRAPHS
REPRES5T$ 0.;X #B @+ .;Y #B .K #CF &
--.;Y #B @+ .;X .K #F 9T]SECT8
,A4 7#F1 #J7
,B4 7--#F1 #J7
,C4
,D4 7#F1 #J7 & 7--#F1 #J7
#AA4 ,: /ATE;T AB ! GRAPH (! EQU,N #AB
7;X--#F7 .K --7.;Y @+ #D7 #B IS N TRUE8
,A4 ,! V]TEX IS AT 7#F1 --#D74
,B4 ,! AXIS ( SYMMETRY IS .;Y .K --#D4
,C4 ,! FOCUS IS AT 7#F1 --#G74
,D4 ,! GRAPH REPRES5TS A FUNC;N4
,,GRI4$ ,,ANSW]
#AB4 ,! 3IC SEC;N REPRES5T$ 0! EQU,N
#A HAS ! L9E ( SYMMETRY ;X .K .S4 ,:AT
IS ! VALUE ( ;S8
#AC4 ,6! NE>E/ T5?1 :AT IS ! 4T.E 2T
7--#AJ1 #B7 & 7#G1 #G78
#AD4 ,:AT IS ! L5G? (! TRANSV]SE AXIS
(! HYP]BOLA REPRES5T$ 0! EQU,N #I;X #B
-- #D;Y #B .K #CBD8
#AE4 ,:AT IS ! RADIUS (! CIRCLE
REPRES5T$ 0! EQU,N #H;X #B @+ #H;Y #B .K
#GBJ8 ,R.D YR ANSW] 6! NE>E/ T5?4
#AF4 ,EVALUAT+ APPROXIMATES !
CIRCUMF];E ( AN ELLIPSE ) MAJOR AXIS (
L5G? .#B;A & M9OR AXIS ( L5G? .#BB4
,APPROXIMATE ! CIRCUMF];E ( AN ELLIPSE )
C5T] 7#J1 #J71 V]TEX 7#J1 --#E71 & FOCUS
7#J1 #C74 ,R.D YR ANSW] 6! NE>E/ UNIT4
,,EXT5D$ ,,RESPONSE
#AG4 ,A SATELLITE 9 A .GEO/,N>Y ORBIT
APPE>S 6/AY ABV A S+LE PLACE ON ,E>?'S
SURFACE4 ,A SATELLITE ORIG9,Y 9 A L[
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GEO/,N>Y ORBIT4 ,A SATELLITE ORIG9,Y 9 A
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IS BOO/$ 6A CIRCUL> GEO/,N>Y ORBIT
#BB1BDJ MILES F ,E>?'S C5T]4
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ORIG94
B4 ,E>?'S C5T] IS AT "O FOCUS (!
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! TRANSF] ORBIT4 ,USE ,E>?'S C5T] Z !
ORIG91 & *OOSE A HORIZONTAL MAJOR AXIS Z
%[N 9 ! DIAGRAM4
#H4 ,PO9TS "O QU>T] (! WAY AL;G !
SIDES (A SQU>E >E 3NECT$ 6=M A SECOND
SQU>E4 ,! PATT]N 3T9UES4
A4 .,EXPLA9 H[ 6USE ! MIDPO9T =MULA
6F9D ! COORD9ATES (! V]TICES = EA* NEW
SQU>E 9 ! PATT]N4
B4 ,F9D ! COORD9ATES (! V]TICES (!
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C4 ,F9D ! RATIO (! >1S ( SU3ESSIVE
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------------------------------------#FGH
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.#A4 #E .;X @+ #BD .K #AA--#B .;X @7
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.#E4 ;X #C @+ #C .;X #B --#AH .;X .K
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.#F4 @7 P4 #DEB @7
.#G4 #D ;X -- #E .K #C @7 P4 #EAE @7
.#H4 @7 P4 #EHI @7
.#I4 @7 P4 #EHI @7
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#DII @7
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,FACTOR ! EXPRES.N4
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P4 #BEI @7
.#AG4 #F .;X #B @+ #G .;X -- #BJ @7 P4
#BEI @7
.#AH4 ;X #C @+ #H .;X #B -- #D .;X --
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.;Z
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& .Y4 @7 P4 #EEA @7
.#BH4 ;X.K#AH;,Y.K#F
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9 /&>D =M4 ,!N GRAPH ! EQU,N1 @7 P4 #FEJ
@7
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USE ALL (! F5C+1 @7 P4 #CD @7
------------------------------------#FGI
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RIDES Y C TAKE & GAMES Y C PLAY4 ,!N LI/
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6A HI< S*OOL BASKETBALL GAME IS 4#E =
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TICKET SALES 0 4#BEJJ4 ,WRITE & SOLVE A
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MATRIX .;,M #J MODEL ? SITU,N4
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.,EXPLA9 :AT ^! MATRICES REPRES5T4
.,DESCRIBE :AT HAPP5S 6! 4TRIBU;N (
CU/OM]S OV] "T IF ? PATT]N 3T9UES4 @7 P4
#AIE @7
.#DE4 .,,MAPS ,A C.TY MAP USES A
COORD9ATE GRID = : "O UNIT REPRES5TS A
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,! FOLL[+ TA# IS 9 LI/ =MAT4
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#AJFC3 #ABFJ3 #AEEB3 #BAJI3 #BHHG3 #CHID
------------------------------------#FHJ
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& ,4CRETE ,MA?
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& ,DEP5D5T ,EV5TS
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,2F
,9 PREVI\S *APT]S1 Y LE>N$ ! FOLL[+
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@8 @4
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T]MS4
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.= .#AJ..A47
.#D4
.#E4
.#F4
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.#AJ..B47
.#G4 @7 .;X @+ .;Y7 #C
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,F9D ! >EA (! %AD$ REGION4 ,ASSUME ALL
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PP4 #IIA-IIB .= .#AJ..C47
#AJ4
#AA4
#AB4
------------------------------------#FHA
,N[
,9 ,*APT] #AJ1 Y W APPLY ! BIG ID1S
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LI/$ 2L4
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99 P]MUT,N1 P4 #FHD
99 -B9,N1 P4 #FIJ
99 BINOMIAL !OREM1 P4 #FIC
99 PROBABIL;Y1 P4 #FIH
99 -P.D EV5T1 P4 #GJG
99 OV]LAPP+ EV5TS1 P4 #GJG
99 4JO9T EV5TS1 P4 #GJG
99 9DEP5D5T EV5TS1 P#.GGG
99 DEP5D5T EV5TS1 P4 #GAH
99 3DI;NAL PROBABIL;Y1 P4 #GAH
99 R&OM V>IA#1 P4 #GBD
99 BINOMIAL 4TRIBU;N1 P4 #GBE
,:Y8
,Y C USE ! FUNDA;TAL C.T+ PR9CIPLE &
P]MUT,NS 6CALCULATE ! NUMB] ( *OICES =A
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POSSI# \TCOMES ( AN EV5T OR ! NUMB] (
WAYS 6-PLETE A TASK4
.,ANIMAT$ ,ALGEBRA
,! ANIM,N ILLU/RAT$ 2L = ,EX]CISE #FI
ON PAGE #FHI HELPS Y ANSW] ? "Q3 ,H[
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9 A 4PLAY8
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------------------------------------#FHB
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,P]MUT,NS
.,2F ,Y C.T$ ! NUMB] ( DI6]5T WAYS
6P]=M A TASK4
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PR9CIPLE & P]MUT,NS4
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,KEY ,VOCABUL>Y
99 P]MUT,N
99 FACTORIAL
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PR9CIPLES 6-PUTE -B9,NS & P]MUT,NS4
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IS 6USE A .TREE .DIAGRAM4
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EQUIP;T8
,SOLU;N
,DRAW A TREE DIAGRAM & C.T ! NUMB] (
BRAN*ES4
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POSSI# *OICES4
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H #C *OICES =! BO>D & #B *OICES =!
BOOTS1 S ! TOTAL NUMB] ( *OICES IS #C 99
#B .K #F4
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,= ,YR NOTEBOOK
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WAYS & ANO!R EV5T C O3UR 9 .;N WAYS1 !N
! NUMB] ( WAYS T .BO? EV5TS C O3UR IS
.;M 99 .N4
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C.T+ PR9CIPLE C 2 EXT5D$ 6?REE OR M
EV5TS4 ,= EXAMPLE1 IF ?REE EV5TS C O3UR
9 .;M1 .;N @1 & .;P WAYS1 !N ! NUMB] (
WAYS T .ALL ?REE EV5TS C O3UR IS .;M 99
.;N 99 .P4
------------------------------------#FHC
,EXAMPLE #B ,USE ! FUNDA;TAL C.T+
PR9CIPLE
.,,PHOTOGRAPHY ,Y >E FRAM+ A PICTURE4
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AVAILA# 9 #AA DI6]5T %ADES ( BLUE4 ,H[
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,SOLU;N
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6F9D ! TOTAL NUMB] ( WAYS 6FRAME !
PICTURE4 ,MULTIPLY ! NUMB] ( FRAME /YLES
7#AB71 ! NUMB] ( FRAME COLORS 7#EE71 &!
NUMB] ( MAT BO>DS 7#AA74
,NUMB] ( WAYS .K #AB 99 #EE 99 #AA .K
#GBFJ
,! NUMB] ( DI6]5T WAYS Y C FRAME !
PICTURE IS #GBFJ4
,EXAMPLE #C ,USE ! C.T+ PR9CIPLE )
REPETI;N
.,,LIC5SE .,,PLATES ,! /&>D 3FIGUR,N
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0#B DIGITS FOLL[$ 0#C LRS4
.A4 ,H[ _M DI6]5T LIC5SE PLATES >E
POSSI# IF LRS & DIGITS C 2 REP1T$8
.;B @4 ,H[ _M DI6]5T LIC5SE PLATES >E
POSSI# IF LRS & DIGITS _C 2 REP1T$8
,SOLU;N
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,=A GIV5 SITU,N1 ! NUMB] ( *OICES )\T
REPETI;N IS ALW LESS ?AN ! NUMB] (
*OICES ) REPETI;N4
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C.T+ PR9CIPLE 6F9D ! NUMB] ( DI6]5T
PLATES4
,NUMB] ( PLATES .K #BF 99 #AJ 99 #AJ
99 #BF 99 #BF 99 #BF .K #DE1FIG1FJJ
,) REPETI;N1 ! NUMB] ( DI6]5T LIC5SE
PLATES IS #DE1FIG1FJJ4
.B4 ,IF Y _C REP1T LRS "! >E / #BF
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FUNDA;TAL C.T+ PR9CIPLE 6F9D ! NUMB] (
DI6]5T PLATES4
,NUMB] ( PLATES .K #BF 99 #AJ 99 #I 99
#BE 99 #BD 99 #BC .K #CB1BIB1JJJ
,)\T REPETI;N1 ! NUMB] ( DI6]5T LIC5SE
PLATES IS #CB1BIB1JJJ4
.,GUID$ .,PRACTICE = ,EXAMPLES #A1B1 &
#C
#A4 .,,SPORT+ .,,GDS ,! /ORE 9
,EXAMPLE #A AL (F]S #C DI6]5T TYPES (
BICYCLES 7M.TA91 RAC+1 & ,,BMX7 & #C
DI6]5T :EEL SIZES 7#BJ IN41 #BB IN41 &
#BD IN474 ,H[ _M BICYCLE *OICES DOES !
/ORE (F]8
#B4 .,,:AT .,,IF8 ,9 ,EXAMPLE #C1 H[ D
! ANSW]S *ANGE =! /&>D 3FIGUR,N (A ,NEW
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0#D NUMB]S8
------------------------------------#FHD
.,,P]MUT,NS ,AN ORD]+ ( .;N OBJECTS IS
P]MUT,N (! OBJECTS4 ,= 9/.E1 "! >E #F
P]MUT,NS (! LRS .,A1 .;,B @1 & .;,C @3
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,Y C USE ! FUNDA;TAL C.T+ PR9CIPLE
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F/ LR HAS BE5 *OS51 #B *OICES REMA9 =!
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*OS51 "! IS ONLY #A *OICE REMA9+ =! F9AL
LR4 ,S1 ! NUMB] ( P]MUT,NS IS #C 99 #B
99 #A .K #F4
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99' 99 #C 99 #B 99 #A
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OBJECTS IS .;N64
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R.D (! ,OLYMPIC F\R-P]SON BOBSL$D+
-PETI;N4
.A4 ,9 H[ _M DI6]5T WAYS C ! BOBSL$D+
T1MS F9I% ! -PETI;N8 7,ASSUME "! >E NO
TIES47
.B4 ,9 H[ _M DI6]5T WAYS C #C (!
BOBSL$D+ T1MS F9I% F/1 SECOND1 & ?IRD
6W9 ! GOLD1 SILV]1 & BRONZE M$ALS8
,SOLU;N
.A4 ,"! >E #AJ6 DI6]5T WAYS T ! T1MS C
F9I% ! -PETI;N4
#AJ6 .K #AJ@*I@*H@*G@*F@*E@*D@*C@*B@*A
.K #C1FBH1HJJ
.B4 ,ANY (! #AJ T1MS C F9I% F/1 !N ANY
(! REMA9+ #I T1MS C F9I% SECOND1 & F9,Y
ANY (! REMA9+ #H T1MS C F9I% ?IRD4 ,S1 !
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#AJ 99 #I 99 #H .K #GBJ
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WD ! ANSW]S *ANGE IF "! 7 #AB BOBSL$D+
T1MS -PET+ 9 ! F9AL R.D (! -PETI;N8
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CALL$ ! NUMB] ( P]MUT,NS ( #AJ OBJECTS
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FACTORIALS3
,? RESULT IS G5]ALIZ$ AT ! TOP (! NEXT
PAGE4
------------------------------------#FHE
,,KEY ,,3CEPT
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A ,"T
,! NUMB] ( P]MUT,NS ( .;R OBJECTS TAK5
F A GR\P ( .;N 4T9CT OBJECTS IS DENOT$
0;N .;,P ;R.' .-& IS GIV5 0? =MULA3
,EXAMPLE #E ,F9D P]MUT,NS ( .;N
OBJECTS TAK5 .;R AT A "T
.,,MUSIC ,Y >E BURN+ A DEMO ;,,CD = YR
B&4 ,YR B& HAS #AB S;GS /OR$ ON YR
-PUT]4 ,H["E1 Y WANT 6PUT ONLY #D S;GS
ON ! DEMO ;,,CD4 ,9 H[ _M ORD]S C Y BURN
#D (! #AB S;GS ONTO ! ;,,CD8
,SOLU;N
,,EVALUATE ,,P]MUT,NS
,MO/ SCI5TIFIC & GRAPH+ CALCULATORS H
A KEY OR M5U ITEM = EVALUAT+ ;N .;,P R4
,F9D ! NUMB] ( P]MUT,NS ( #AB OBJECTS
TAK5 #D AT A "T4
,Y C BURN #D (! #AB S;GS 9 #AA1HHJ
DI6]5T ORD]S4
..,GUID$ ,PRACTICE = ,EXAMPLE .#E
,F9D ! NUMB] ( P]MUT,NS4
.#D4 #E .;,P #C
.#E4 #D .;,P #A
.#F4 #H .;,P #E
.#G4 #AB .;,P #G
.,,P]MUT,NS .,,) .,,REPETI;N ,IF Y
3SID] ! LRS .;,E & .;,E 6BE .4T9CT @1 "!
>E SIX P]MUT,NS (! LRS .;,E1 .;,E @1 &
.;,Y3
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,,EEY @3 .,,EEY @3 .,,YEE
.,,EYE @3 .,,EYE @3 .,,YEE
,H["E1 IF ! TWO O3URR;ES ( .;,E >E
3SID]$ 9T]*ANGEA#1 !N "! >E ONLY ?REE
4T+UI%A# P]MUT,NS3
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,,EEY @3 .,,EYE @3 .,,YEE
,EA* ( ^! P]MUT,NS CORRESPONDS 6TWO (!
ORIG9AL SIX P]MUT,NS 2C "! >E #B61 OR
#B1 P]MUT,NS ( .;,E & .;,E @4 ,S1 !
NUMB] ( P]MUT,NS ( .;,E1 .;,E @1 & .;,Y
C 2 WRITT5 Z @4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,P]MUT,NS ) ,REPETI;N
,! NUMB] ( 4T+UI%A# P]MUT,NS ( .;N
OBJECTS ": "O OBJECT IS REP1T$ ;S #A
"TS1 ANO!R IS REP1T$ .;S #B "TS1 & S ON1
IS3
------------------------------------#FHF
,EXAMPLE #F ,F9D P]MUT,NS ) REPETI;N
,F9D ! NUMB] ( 4T+UI%A# P]MUT,NS (!
LRS 9 7A7 ,,MIAMI & 7;B7 ,,TALLAHASSEE4
,SOLU;N
.A4 ,,MIAMI HAS #E LRS ( : ;,M & ,I >E
EA* REP1T$ #B "TS4 ,S1 ! NUMB] (
4T+UI%A# P]MUT,NS
.B4 ,,TALLAHASSEE HAS #AA LRS ( : ,A
IS REP1T$ #C "TS1 & ;,L1 ;,S1 & ;,E >E
EA* REP1T$ #B "TS4 ,S1 ! NUMB] (
4T+UI%A# P]MUT,N
.,GUID$ .,PRACTICE = ,EXAMPLE #F
,F9D ! NUMB] ( 4T+UI%A# P]MUT,NS (!
LRS 9 ! ^W4
.#H4 ,,MALL
.#I4 ,,KAYAK
.#AJ4 ,,C9C9NATI
#AJ.A ,EX]CISES
,HOME"W ,KEY
.K ..,,"W$-,,\ ,,SOLU;NS ON P4,,WS#AH
= ,EXS4 #AC1 #CE1 & .#FE
.K ..,,/&>DIZ$ ,,TE/ ,,PRACTICE ,EXS4
#B1AG1DB1EE1EG1 & .#FH
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,:AT IS A P]MUT,N (
.;N OBJECTS8
#B4 .,,WRIT+ ,SIMPLIFY ! =MULA = ;N
.;,P ;R.' .-:5 .;R .K #J4 .,EXPLA9 :Y ?
RESULT MAKES S5SE4
.,,EXAMPLE .#A .ON .P4 #FHB = ,EXS4
.#C-.F
.,,TREE .,,DIAGRAMS ,AN OBJECT HAS AN
ATTRIBUTE F EA* LI/4 ,MAKE A TREE
DIAGRAM T %[S ! NUMB] ( DI6]5T OBJECTS T
C 2 CR1T$4
#C4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
;,T-,%IRTS
..,SIZE3 ;,M1 ;,L1 .,,XL
.,TYPE3 L;G-SLEEV$1 %ORT-SLEEV$
#D4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,TOA/
.,BR1D3 :ITE1 :1T
.,SPR1D3 JAM1 M>G>9E
#E4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,M1L
.,5TREE3 *ICK51 FI%1 PA/A
.,SIDE3 CORN1 GRE5 B1NS1 POTATO
#F4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,FURNITURE
.,WOOD3 *]RY1 MAHOGANY1 OAK1 P9E
.,F9I%3 /A9$1 PA9T$1 UNF9I%$
.,,EXAMPLE .#B .ON .P4 #FHC
= .,EXS @4 #G-AJ
.,,FUNDA;TAL .,,C.T+ .,,PR9CIPLE ,EA*
EV5T C O3UR 9 ! GIV5 NUMB] ( WAYS4 ,F9D
! NUMB] ( WAYS ALL (! EV5TS C O3UR4
.#G4 ,EV5T .,A @3 #B WAYS2 ,EV5T .;,B3
#D WAYS
.#H4 ,EV5T .,A3 #E WAYS2 ,EV5T .;,B3
.#B WAYS
.#I4 ,EV5TS .,A @3 #D WAYS2 ,EV5T
.;,B3 #C WAYS2
.#AJ4 ,EV5TS3 #C WAYS2 ,EV5T .;,B3 #F
WAYS2
,EV5T .;,C @3 #E WAYS ,EV5T .;,C @3 #E
WAYS2 ,EV5T .;,D3 .#B WAYS
------------------------------------#FHG
,,EXAMPLES #C
ON P4 #FHC = ,EXS4 #AA-AG
,,LIC5SE ,,PLATES ,=! GIV5 3FIGUR,N1
DET]M9E H[ _M DI6]5T LIC5SE PLATES >E
POSSI# IF 7A7 DIGITS & LRS C 2 REP1T$1 &
7;B7 DIGITS & LRS _C 2 REP1T$4
.#AA4 #D LRS FOLL[$ 0#C DIGITS
.#AB4 #B LRS FOLL[$ 0#E DIGITS
.#AC4 LRS FOLL[$ 0#B DIGITS
.#AD4 #E DIGITS FOLL[$ 0#C LRS
.#AE4 #A DIGIT FOLL[$ 0#E LRS
.#AF4 #F LRS
#AG4 .,,MULTIPLE .,,*OICE ,H[ _M
DI6]5T LIC5SE PLATES ) #B LRS FOLL[$ 0#D
DIGITS >E POSSI# IF DIGITS & LRS _C 2
REP1T$8
,A #C1BGF1JJJ
;,B #F1GFJ1JJJ
;,C #CB1BIB1JJJ
;,D #DE1FIG1FJJ
,,EXAMPLES #D & #E
ON PP4 #FHD-FHE = ,EXS4 #AH-DA
,,FACTORIALS ,EVALUATE ! EXPRES.N4
.#AH4 #G6
.#AI4 #AA6
.#BJ4 #A6
.#BA4 #H6
.#BB4 #D6
.#BC4 #J6
.#BD4 #AB6
.#BE4 #F6
.#BF4 #C6 99 #D6
.#BG4 #C7#D67
.#BH4
.#BI4
,,P]MUT,NS ,F9D ! NUMB] ( P]MUT,NS4
.#CJ4 #D .;,P #D
#CA4 #F .;,P #B
.#CB4 #AJ .;,P #A
.#CC #H .;,P #G
.#CD4 #G .;,P #D
.#CE4 #I .;,P #B
.#CF4 #AC .;,P #H
.#CG4 #G .;,P #G
.#CH4 #E .;,P #J
.#CI4 #I .;,P #D
.#DJ4 #AA .;P #D
.#DA4 #AE .;,P #J
..#DB4 99 ,,%ORT .,,RESPONSE ,LET .;N
2 A POSITIVE 9TEG]4 ,F9D ! NUMB] (
P]MUT,NS ( .;N OBJECTS TAK5 .;N -- #A AT
A "T4 .,-P>E YR ANSW] )! NUMB] (
P]MUT,NS ( ALL .;N OBJECTS4 ,DOES ? MAKE
S5SE8 .,EXPLA94
,,EXAMPLE #F
ON PP4 #FHF .= .,EXS4 .#DC-.EE
,,P]MUT,NS ,,) ,,REPETI;N ,F9D ! NUMB]
( 4T+UI%A# P]MUT,NS (! LRS 9 ! ^W4
.#DC4 ,,(F
.#DD4 ,,TREE
.#DE4 ,,SKILL
.#DF4 ,,YELL[
.#DG4 ,,GRAVEL
.#DH4 ,,PANAMA
.#DI4 ,,>KANSAS
.#EJ4 ,,FACTORIAL
.#EA4 ,,MAGNETIC
.#EB4 ,,HONOLULU
.#EC4 ,,CLEVEL&
.#ED4 ,,MISSISSIPPI
.#EE4 .,,MULTIPLE .,,*OICE ,:AT IS !
NUMB] ( 4T+UI%A# P]MUT,NS (! LRS 9 ! ^W
,,HAWAII8
.,A #BD
.;,B #AHJ
.;,C #CFJ
.,D4 #GBJ
.#EF4 .,,]ROR .,,ANALYSIS ,9 B+O1
BALLS LABEL$ F #A 6#GE >E DRAWN F A
3TA9] )\T 2+ REPLAC$4 .,DESCRIBE &
CORRECT ! ]ROR 9 F9D+ ! NUMB] ( WAYS !
F/ #D NUMB]S C 2 *OS5 =A GAME ( B+O4
#GE 99 #GE 99 #GE 99 #GE
.K #CA1FDJ1FBE
.#EG4 .,,%ORT .,,RESPONSE .,EXPLA9 H[
! FUNDA;TAL C.T+ PR9CIPLE C 2 US$
6JU/IFY ! =MULA =! NUMB] ( P]MUT,NS (
.;N 4T9CT OBJECTS4
,,SOLV+ ,,EQU,NS ,SOLVE = .N4
.#EH4 ;N .;,P #D .K#H7 ;N .;,P #C @7
.#EI4 ;N .;,P #F .K#E7 ;N .;,P #E @7
.#FJ4 ;N .;,P #E .K .#I7 ;N .;,P #D @7
.#FA4 .,,*ALL5GE ,F9D ! NUMB] (
4T+UI%A# P]MUT,NS ( #F LRS T >E *OS5 F !
LRS 9 ! ^W ,,MANATEE4
------------------------------------#FHH
,PRO#M ,SOLV+
.,,EXAMPLE .#B .ON .P4 #FHC = ,EXS4
#FB-FC
.#FB4 .,,CLASS .,,R+S ,Y WANT 6PUR*ASE
A CLASS R+4 ,! R+ C 2 MADE F #C DI6]5T
METALS4 ,Y C *OOSE F #F DI6]5T SIDE
DESIGNS & #AB DI6]5T /"OS4 ,H[ _M DI6]5T
CLASS R+S >E POSSI#8
,! FOLL[+ TA# IS 9 LI/$
=MAT4 ,= EA* CELL ! H1D+ IS %[N
FOLL[$ 0A COLON1 SPACE &! CELL
3T5TS
,METAL3 ,AURALITE
,SIDE ,DESIGN3 ,ACADEMICS ,LIT]ATURE
,/"O3
,METAL3 ,COLD
,SIDE ,DESIGN3
,/"O3 ,>T ,MUSIC
,METAL3 ,SILV]
,SIDE ,DESIGN3
,/"O3 ,A?LETICS ,TE*NOLOGY
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#FC4 .,,5VIRON;T ,S9CE #AIIJ1 !
,GOLDMAN ,5VIRON;TAL ,PRIZE HAS BE5
AW>D$ ANNU,Y 6#F GRASSROOTS
5VIRON;TALI/S1 "O F EA* ( #F REGIONS4 ,!
REGIONS 3SI/ ( #EB C.TRIES 9 ,AFRICA1
#DG 9 ,EUROPE1 #DE 9 ,ASIA1 #CF 9 ISL&
N,NS1 #AI 9 ,S\? & ,C5TRAL ,AM]ICA1 & #C
9 ,NOR? ,AM]ICA4 ,H[ _M DI6]5T SETS ( #F
C.TRIES C 2 REPRES5T$ 0! PRIZE W9N]S 9 A
GIV5 YE>8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#FD4 .,,PHOTOGRAPHY ,A PHOTOGRAPH]
L9ES UP ! #AE MEMB]S (A FAMILY 9 A S+LE
L9E 9 ORD] 6TAKE A PHOTOGRAPH4 ,H[ _M
DI6]5T WAYS C ! PHOTOGRAPH] >RANGE !
FAMILY MEMB]S =! PICTURE8
,,EXAMPLES
..#D1 #E1 & .#F .ON .PP4 #FHD-FHF =
,EXS4 #FD-FF
.#FE4 .,,S*OOL .,,CLUBS ,A ,SPANI%
CLUB IS ELECT+ A PRESID5T1 VICE
PRESID5T1 & SECRET>Y4 ,! CLUB HAS #I
MEMB]S :O >E ELIGI# = ^! (FICES4 ,H[ _M
DI6]5T WAYS C ! #C (FICES 2 FILL$8
.#FF4 .,,MUSIC ,! W9D[ (A MUSIC /ORE
HAS #H /&S 9 FIX$ POSI;NS ": 9/RU;TS C 2
4PLAY$4 ,9 H[ _M WAYS C #C ID5TICAL
GUIT>S1 #B ID5TICAL KEYBO>DS1 & #C
ID5TICAL VIOL9S 2 4PLAY$8
#FG4 .,,MULTI-.,,/EP .,,PRO#M ,Y >E
DESIGN+ AN 5T]TA9;T C5T]4 ,Y WANT
69CLUDE ?REE AUDIO -PON5TS & ?REE VIDEO
-PON5TS4
A4 ,Y WANT "O ( EA* AUDIO -PON5T LI/$
AT ! "R4 ,H[ _M SELEC;NS ( AUDIO -PON5TS
>E POSSI#8
B4 ,Y WANT "O ( EA* VIDEO -PON5T LI/$
AT ! "R4 ,H[ _M SELEC;NS ( VIDEO -PON5TS
>E POSSI#8
C4 ,H[ _M SELEC;NS ( ALL SIX AUDIO &
VIDEO -PON5TS >E POSSI#8
,! FOLL[+ TA# IS 9 LI/$
=MAT4 ,= EA* CELL ! H1D+ IS %[N
FOLL[$ 0A COLON1 SPACE &! CELL
3T5TS
,5T]TA9;T ,C5T]3 .,AUDIO .,-PON5TS
,5T]TA9;T ,C5T]3 .,VIDEO .,-PON5TS
,5T]TA9;T ,C5T]3 #E RCVRS
,5T]TA9;T ,C5T]3 #G ,,TV SETS
,5T]TA9;T ,C5T]3 #H ;,,CD PLAY]S
,5T]TA9;T ,C5T]3 #I ,,DVD PLAY]S
,5T]TA9;T ,C5T]3 #F SP1K]S
,5T]TA9;T ,C5T]3 #D GAME SY/EMS
#FH4 .,,EXT5D$ .,,RESPONSE ,6KEEP
-PUT] FILES SECURE1 _M PROGRAMS REQUIRE
! US] 65T] A PASS^W4 ,! %ORTE/ ALL[A#
PASS^WS >E TYPIC,Y #F "*S L;G & C 3TA9
BO? LRS & DIGITS4
A4 ,CALCULATE ,H[ _M #F-"* PASS^WS >E
POSSI# IF "*S C 2 REP1T$8
B4 ,CALCULATE ,H[ _M #F-"* PASS^WS >E
POSSI# IF "*S _C 2 REP1T$8
C4 ,DRAW ,3CLU.NS ,: TYPE ( PASS^W IS
M SECURE8 .,EXPLA94
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#FHI
.#FI4 .,,CLO?+ .,,4PLAY ,AN EMPLOYEE
AT A CLO?+ /ORE IS CR1T+ A 4PLAY4 ,!
4PLAY HAS #C DI6]5T MANNEQU9S4 ,EA*
MANNEQU9 IS 6WE> A DI6]5T SW1T] &A
DI6]5T SKIRT4 ,H[ _M DI6]5T 4PLAYS C 2
CR1T$8
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
.#GJ4 .,,CROSS .,,C.TRY ,?REE S*OOLS
>E -PET+ 9 A CROSS C.TRY MEET4 ,S*OOL ,A
HAS #F RUNN]S1 S*OOL ;,B HAS #E RUNN]S1
& S*OOL ;,C HAS #D RUNN]S4 ,= SCOR+
PURPOSES1 ! F9I%+ ORD] (! MEET ONLY
3SID]S ! S*OOL ( EA* RUNN]4 ,H[ _M
DI6]5T F9I%+ ORD]S >E "! = SCOR+
PURPOSES8
#GA4 .,,*ALL5GE ,Y H LE>N$ T .;N6
REPRES5TS ! NUMB] ( WAYS T .;N OBJECTS C
2 PLAC$ 9 A .L9E> ORD]1 ": X MATT]S :
OBJECT IS PLAC$ F/4 ,N[ 3SID] .CIRCUL>
P]MUT,NS 9 : OBJECTS >E PLAC$ 9 A
CIRCLE1 S T X DOES .N MATT] : OBJECT IS
PLAC$ F/4
,PICTURE3 ,! TWO >RANGE;TS %[N
REPRES5T ! SAME P]MUT,N4
A4 ,SUPPOSE Y >E S1T+ #E P AT A
CIRCUL> TA#4 ,H[ _M DI6]5T WAYS C Y
>RANGE ! P >.D ! TA#8
B4 ,F9D A =MULA =! NUMB] ( P]MUT,NS (
.;N OBJECTS PLAC$ 9 CLOCKWISE ORD] >.D A
CIRCLE :5 ONLY ! RELATIVE ORD] (!
OBJECTS MATT]S4 .,EXPLA9 H[ Y DERIV$ YR
=MULA4
,MIX$ ,REVIEW
.,PREVIEW ,PREP>E = ,LESSON #AJ.B 9
,EXS4 #GB-GG
,F9D ! PRODUCT4@7 P#.CDF
.#GB4 @7 .;X -- #H7@7 .;X @+ #H7
.#GC4 7#D .;X -- #E77#D .;X @+ #E7
.#GD4 @7 .;X @+ #G7 #B
.#GE4 7#E .;X -- #F .;Y @7 #B
.#GF4 7#C .;X -- #B7 #C
.#GG4 7#D .;X @+ #C .;Y @7 #C
,F9D ! 9V]SE (! ,FUNC;N4@7 P4 #DCH @7
.#GH4 .;F7.;X7 .K #D .;X -- #I
.#GI4 .;F7.;X7 .K -- .;X @+ #F
.#HJ4 .;F7.;X7 .K #D .;X #E
.#HA4 .;F7.;X7 .K .;X #B @1 .;X .1.K
#J
.#HB4 .;F7.;X7 .K .;X #C @+ #E
.#HC4 .;F7.;X7 .K #C .;X #E -- #A
,GRAPH ! EQU,N4
.#HD4 .;Y #B .K --#BD .;X @7 P#.FBJ @7
.#HE4 .;X #B @+ .;Y #B .K #BJ @7
P#.FBF @7
.#HF4
.#HG4
.#HH4 @7 .;X @+ #C7 #B @+ .;Y #B .K
#AF @7 P4 #FEJ @7
.#HI4
.,,EXTRA .,,PRACTICE = ,LESSON #AJ.A1
P4 #AJAI
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#FIJ
#AJ.B ,USE ,-B9,N &! ,BINOMIAL
,!OREM
.,2F ,Y US$ ! C.T+ PR9CIPLE &
P]MUT,NS4
.,N[ ,Y W USE -B9,NS &! BINOMIAL
!OREM4
.,:Y8 ,S Y C F9D WAYS 6=M A SET1 Z 9
,EXAMPLE #B4
,KEY ,VOCABUL>Y
99 -B9,N
99 ,PASCAL'S TRIANGLE
99 BINOMIAL !OREM
,SIDEB>3
,/&>DS
.#BJ..J ,/UD5TS ,"K ! BINOMIAL !OREM &
USE X 6EXP& BINOMIAL EXPRES.NS T >E
RAIS$ 6POSITIVE 9TEG] ,P[]S4
,9 ,LESSON #AJ.A1 Y LE>N$ T ORD] IS
IMPORTANT = "S C.T+ PRO#MS4 ,= O!R C.T+
PRO#MS1 ORD] IS N IMPORTANT4 ,= 9/.E1 IF
Y PUR*ASE A PACKAGE ( TRAD+ C>DS1 ! ORD]
(! C>DS 9SIDE ! PACKAGE IS N IMPORTANT4
,A -B9,N IS A SELEC;N ( .;R OBJECTS F A
GR\P ( .;N OBJECTS ": ! ORD] IS N
IMPORTANT4
,,KEY ,,3CEPT .= .,YR .,NOTEBOOK
,-B9,NS ( .;N ,OBJECTS ,TAK5 ;R AT A
,"T
,! NUMB] ( -B9,NS ( .;R OBJECTS TAK5 F
A GR\P ( .;N 4T9CT OBJECTS IS DENOT$ 0;N
.;,C ;R.' .-& IS GIV5 0? =MULA3
,EXAMPLE #A ,F9D -B9,NS
.,,C>DS ,A /&>D DECK ( #EB PLAY+ C>DS
HAS #D SUITS ) #AC DI6]5T C>DS 9 EA*
SUIT4
.A4 ,IF ! ORD] 9 : ! C>DS >E D1LT IS N
IMPORTANT1 H[ _M DI6]5T #E-C>D H&S >E
POSSI#8
.B4 ,9 H[ _M #E-C>D H&S >E ALL #E C>DS
(! SAME COLOR8
,SOLU;N
.A4 ,! NUMB] ( WAYS 6*OOSE #E C>DS F A
DECK ( #EB C>DS IS3
.B4 ,= ALL #E C>DS 6BE ! SAME COLOR1 Y
NE$ 6*OOSE #A (! #B COLORS & !N #E (!
#BF C>DS 9 T COLOR4 ,S1 ! NUMB] ( POSSI#
H&S IS3
------------------------------------#FIA
.,,MULTIPLE .,,EV5TS ,:5 F9D+ ! NUMB]
( WAYS BO? AN EV5T .,A .& AN EV5T .;,B C
O3UR1 Y NE$ 6MULTIPLY1 Z 9 "P 7;B7 (
,EXAMPLE #A4 ,:5 F9D+ ! NUMB] ( WAYS T
EV5T .,A .OR EV5T .;,B C O3UR1 Y ADD
9/1D4
,,EXAMPLE #B ,DECIDE 6MULTIPLY OR ADD
-B9,NS
.,,!AT] ,WILLIAM ,%AKESPE>E WROTE #CH
PLAYS T C 2 DIVID$ 96?REE G5RES4 ,(! #CH
PLAYS1 #AH >E -$IES1 #AJ >E HI/ORIES1 &
#AJ >E TRAG$IES4
.A4 ,H[ _M DI6]5T SETS ( .EXACTLY #B
-$IES & #A TRAG$Y C Y R1D8
.B4 ,H[ _M DI6]5T SETS ( .AT .MO/ #C
PLAYS C Y R1D8
,SOLU;N
,,AVOID ,,]RORS
,:5 F9D+ ! NUMB] ( WAYS 6SELECT .AT
.MO/ .;N OBJECTS1 2 SURE 69CLUDE !
POSSIBIL;Y ( SELECT+ #J OBJECTS4
.A4 ,Y C *OOSE #B (! #AH -$IES & #A (!
#AJ TRAG$IES4 ,S1 ! NUMB] ( POSSI# SETS
( PLAYS IS3
.B4 ,Y C R1D #J1 #A1 #B1 OR #C PLAYS4
,2C "! >E #CH PLAYS T C 2 *OS51 ! NUMB]
( POSSI# SETS ( PLAYS IS3
#CH .;,C #J @+ #CH .;,C #A @+ #CH .;,C
#B @+ #CH .;,C #C .K ..#A @+ #CH @+ #GJC
@+ #HDCF .K .#IAGH
.,,SUBTRACT+ .,,POSSIBILITIES ,C.T+
PRO#MS T 9VOLVE PHRASES L 8AT L1/0 OR
8AT MO/0 >E "S"TS EASI] 6SOLVE
0SUBTRACT+ POSSIBILITIES Y D N WANT F !
TOTAL NUMB] ( POSSIBILITIES4
,EXAMPLE #C ,SOLVE A MULTI-/EP PRO#M
.,,BASKETBALL ,DUR+ ! S*OOL YE>1 !
GIRL'S BASKETBALL T1M IS S*$UL$ 6PLAY
#AB HOME GAMES4 ,Y WANT 6ATT5D .AT .L1/
#C (! GAMES4 ,H[ _M DI6]5T -B9,NS (
GAMES C Y ATT5D8
,SOLU;N
,(! #AB HOME GAMES1 Y WANT 6ATT5D #C
GAMES1 OR #D GAMES1 OR #E GAMES1 & S ON4
,S1 ! NUMB] ( -B9,NS ( GAMES Y C ATT5D
IS3
#AB .;,C #C @+ #AB .;,C #D @+ #AB .;,C
#E .@+ 99 99 99 #AB .;,C #AB
,9/1D ( A4+ ^! -B9,NS1 USE ! FOLL[+
R1SON+4 ,= EA* (! #AB GAMES1 Y C *OOSE
6ATT5D OR N ATT5D ! GAME1 S "! >E #B #AB
TOTAL -B9,NS4 ,IF Y ATT5D AT L1/ #C
GAMES1 Y D N ATT5D ONLY A TOTAL ( #J1
#A1 OR #B GAMES4 ,S1 ! NUMB] ( WAYS Y C
ATT5D AT L1/ #C GAMES IS3
#B #AB -- @7 #AB .;,C ;O @+ #AB .;,C
#A @+ #AB .;,C #B @7 .K #DJIF 7#A @+ #AB
@+ #FF7 .K #DJAG
.,GUID$ .,PRACTICE = ,EXAMPLES #A1B1 &
#C
,F9D ! NUMB] ( -B9,NS4
.#A4 #H .;,C #C
.#B #AJ .;,C #F
.#C4 #G .;,C #B
.#D4 #AD ;,C #E
.#E4 .,,:AT .,,IF8 ,9 ,EXAMPLE #B1 H[
_M DI6]5T SETS ( .EXACTLY #C TRAG$IES &
#B HI/ORIES C Y R1D8
------------------------------------#FIB
.,,PASCAL'S .,,TRIANGLE ,IF Y >RANGE !
VALUES ( ;N .;,C ;R.' .-9 A TRIANGUL>
PATT]N 9 : EA* R[ CORRESPONDS 6A VALUE (
.;N @1 Y GET :AT IS CALL$ ,PASCAL'S
TRIANGLE @4 ,PASCAL'S TRIANGLE IS "ND AF
! ,FR5* MA!MATICIAN ,BLAISE ,PASCAL
7#AFBC-AFFB74
KEY 3CEPT
,= ,YR ,NOTEBOOK
,PASCALS ,TRIANGLE
,PASCAL'S TRIANGLE IS %[N 2L ) XS
5TRIES REPRES5T$ 0-B9,NS &) XS 5TRIES
REPRES5T$ 0NUMB]S4 ,! F/ & LA/ NUMB]S 9
EA* R[ >E #A4 ,E NUMB] O!R ?AN #A IS !
SUM (! CLOSE/ TWO NUMB]S 9 ! R[ DIRECTLY
ABV X4
,EXAMPLE #D ,USE ,PASCAL'S TRIANGLE
.,,S*OOL .,,CLUBS ,! #F MEMB]S (A
,MODEL ,,UN CLUB M/ *OOSE #B
REPRES5TATIVES 6ATT5D A /ATE 3V5;N4 ,USE
,PASCAL'S TRIANGLE 6F9D ! NUMB] ( -B9,NS
( #B MEMB]S T C 2 *OS5 Z REPRES5TATIVES4
,SOLU;N
,2C Y NE$ 6F9D #F ;,C #B @1 WRITE !
#F? R[ ( ,PASCAL'S TRIANGLE 0A4+ NUMB]S
F ! PREVI\S R[4
.;N .K #E 7#E? R[7
.;N .K #F 7#F? R[7
,! VALUE ( #F ;,C #B IS ! ?IRD NUMB] 9
! #F? R[ ( ,PASCAL'S TRIANGLE1 Z %[N
ABV4 ,"!=E1 #F ;,C #B .K #AE4 ,"! >E #AE
-B9,NS ( REPRES5TATIVES =! 3V5;N4
.,GUID$ .,PRACTICE = ,EXAMPLE #D
.#F4 .,,:AT .,,IF8 ,9 ,EXAMPLE #D1 USE
,PASCAL'S TRIANGLE 6F9D ! NUMB] ( -B9,NS
( #B MEMB]S T C 2 *OS5 IF ! ,MODEL ,,UN
CLUB HAS #G MEMB]S4
------------------------------------#FIC
.,,BINOMIAL .,,EXPAN.NS ,"! IS AN
IMPORTANT REL,N%IP 2T P[]S ( BINOMIALS &
-B9,NS4 ,! NUMB]S 9 ,PASCAL'S TRIANGLE C
2 US$ 6F9D COE6ICI5TS 9 BINOMIAL
EXPAN.NS4 ,= EXAMPLE1 ! COE6ICI5TS 9 !
EXPAN.N ( 7.A @+ .;B @7 #D >E ! NUMB]S (
-B9,NS 9 ! R[ ( ,PASCAL'S TRIANGLE = .;N
.K #D3
@7 .A @+ .;B7 #D .K #A .A #D @+ #D .A
#C .;B @+ .#F;A #B .;B #B @+ #D .;AB #C
@+ #A .;B #D
#D .;,C ;O #D .;,C #A #D .;,C #B #D
.;,C #C #D .;,C #D
,? RESULT IS G5]ALIZ$ 9 ! BINOMIAL
!OREM @4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,BINOMIAL ,!OREM
,= ANY POSITIVE 9TEG] .;N @1 !
BINOMIAL EXPAN.N ( @7 .A @+ .;B7 ;N .IS3
7.A @+ .;B7 ;N .K ;N.' ;,C #J A ;N .;B
#J @+ ;N .;,C #A .A ;N.' .- ;L .;B ;L @+
;N .;,C #B .A ;N -- #B .;B #B @+ '@+ .;N
.;,C ;N .A #J .;B ;N.'.-
,NOTICE T EA* T]M 9 ! EXPAN.N ( @7 .A
@+ .;B7 ;N.' .-HAS ! =M ;,C .A ;N--;R
.;B ;R.' .-": ;R IS AN 9TEG] F #J 6.N4
,EXAMPLE #E ,EXP& A P[] (A BINOMIAL
SUM
,USE ! BINOMIAL !OREM 6WRITE !
BINOMIAL EXPAN.N4
7;X #B @+ ;Y7 #C .K #C ;C #J ;U #B @7
#C ;Y #J @+ #C ;C #A 7;X #B @7 #B ;Y #A
@+ #C ;C #B 7;X #B @7 #A ;Y #B @+ #C ;C
#C 7;X #B @7 #J ;Y #C
.K 7#A7@7 .;X #F @77;L7 @+ 7#C7@7 .;X
#D @77;Y7 @+ 7#C7@7 .;X #B @7@7 .;Y #B
@7 @+ 7;L77;L7@7 .;Y #C @7
.K .;X #F @+ #C .;X #D .;Y @+ #C .;X
#B .;Y #B @+ .;Y #C
..,,P[]S ,,( ,,BINOMIAL .,,DI6];ES
,6EXP& A P[] (A BINOMIAL DI6];E1 Y C
REWRITE ! BINOMIAL Z A SUM4 ,! RESULT+
EXPAN.N W H T]MS ^: SIGNS ALT]NATE 2T @+
& --@4
,EXAMPLE #F ,EXP& A P[] (A BINOMIAL
DI6];E
,,AVOID ,,]RORS
,:5 A BINOMIAL HAS A T]M OR T]MS )A
COE6ICI5T O!R ?AN #A1 ! COE6ICI5TS (!
BINOMIAL EXPAN.N >E N ! SAME Z !
CORRESPOND+ R[ ( ,PASCAL'S TRIANGLE4
,USE ! BINOMIAL !OREM 6WRITE !
BINOMIAL EXPAN.N4
7.A--.#B;B7 #D .K @,7 .A @+ @7
-.#B;B77' #D
.K #D .;,C #J .A #D @7- #B .;B7;DG @+
#D .;,C #A A #C 7-#B .;B @7 #A @+ #D
.;,C #B .A #B @7- #B .;B7 #B @+ #D .;,C
#C .A ;L @7- #B .;B7 #C @+ #D .;,C #D .A
#J @7- #B .;B7 #D
.K 7#A77A #D @77#A7 @+ 7#D77A #C
@77-#B .;B @7 @+ 7#F7@7 .A #B @77#D .;B
#B @7 @+ 7#D7@7 .A @7@7 - #H .;B #C @7
@+ 7#A77#A77;L#F .;B #D @7
.K .A #D - #H .A #C .;B @+ #BD .A #B
.;B #B - #CB .;AB #C @+ #AF .;B #D
.,GUID$ .,PRACTICE = ,EXAMPLES #E & #F
,USE ! BINOMIAL !OREM 6WRITE !
BINOMIAL EXPAN.N4
.#G4 @7 .;X @+ #C7 #E
.#H4 @7 .A @+ #B .;B @7 #D
.#I4 7#B .;P -- .;Q @7 #D
.#AJ4 7#E--#B .;Y @7 #C
------------------------------------#FID
,EXAMPLE #G ,F9D A COE6ICI5T 9 AN
EXPAN.N
,F9D ! COE6ICI5T ( .;X #D 9 ! EXPAN.N
( 7#C .;X @+ #B7 #AJ @4
,SOLU;N
,F ! BINOMIAL !OREM1 Y "K ! FOLL[+3
7#C .;X @+ #B7 #AJ .K #AJ ;,C #J 7#C
.;X @7 #AJ 7#B7 #J @+ #AJ ;,C #A 7#C .;X
@7 #I 7#B7 #A @+ 99 99 99 @+ #AJ ;,C #AJ
7#C .;X @7 #J 7#B7 #AJ
,EA* T]M 9 ! EXPAN.N HAS ! =M #AJ ;,C
;R 7#C .;X @7 #AJ- .;R 7#B7 ;R @4 ,! T]M
3TA9+ .;X O3URS :5 .;R .K #F3
#AJ ;,C #F 7#C .;X @7 #D 7#B7 #F .K
7#BAJ77#HA .;X #D @77#FD7 .K ;L1#JHH1FDJ
.;X #D
,! COE6ICI5T ( ;X #D IS #A1JHH1FDJ4
.,GUID$ .,PRACTICE = ,EXAMPLE #G
#AA4 ,F9D ! COE6ICI5T ( ;X #E 9 !
EXPAN.N ( 7;X--#C7 #G @4
#AB4 ,F9D ! COE6ICI5T ( ;X #C 9 !
EXPAN.N ( 7#B;X @+ #E7 #H @4
#AJ.B ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#AH = ,EXS4 #AG1 #BI1 & #DI
.K .,,/&>DIZ$ .,,TE/ .,,PRACTICE
,EXS4 #B1 #CE1DJ1DA1 & #EB
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,!
BINOMIAL EXPAN.N ( @7 .A @+ .;B @7 ;N.'
.-IS GIV5 0! @8 @4
.#B4 .,,WRIT+ .,EXPLA9 ! DI6];E 2T
P]MUT,NS & -B9,NS4
.,,-B9,NS ,F9D ! NUMB] ( -B9,NS4
,,EXAMPLES #A1 #B1 & #C
ON PP4 #FIJ-FIA = ,EXS4 #C-AH
.#C4 #E .;,C #B
.#D4 #AJ .;,C #C
.#E4 #I .;,C #F
.#F4 #H ;,C #B
.#G4 #AA .;,C #AA
.#H4 #AB ;,C #D
.#I4 #G .;,C #E
.#AJ4 #AD ;,C #F
.,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 F9D+ ! NUMB] ( -B9,NS4
#AA4
#AB4
.,,C>D .,,H&S ,F9D ! NUMB] ( POSSI#
#E-C>D H&S T 3TA9 ! C>DS SPECIFI$4 ,!
C>DS >E TAK5 F A /&>D #EB-C>D DECK4
.#AC4 #E FACE C>DS 7K+S1 QUE5S1 OR
JACKS7
.#AE4 #A ACE & #D C>DS T >E N ACES
.#AG4 ,AT MO/ #A QUE5
.#AD4 #D K+S & #A O!R C>D
.#AF4 #E HE>TS OR #E DIAMONDS
.#AH4 ,AT L1/ #A SPADE
------------------------------------#FIE
,,EXAMPLE #D
ON P4 #FIB = ,EXS4 #AI-BC
.#AI4 .,,US+ .,,PATT]NS ,COPY
,PASCAL'S TRIANGLE ON PAGE #FIB & ADD
R[S = .;N .K #F1 #G1 #H1 #I1 & #AJ4
,,PASCALS ,,TRIANGLE ,USE ! R[S (
,PASCAL'S TRIANGLE F ,EX]CISE #AI 6WRITE
! BINOMIAL EXPAN.N4
.#BJ4 @7 .;X @+ #C7 #F
.#BA4 @7 .;Y -#C .;Z @7 #AJ
.#BB4 @7 .A @+ .;B #B @7 #H
.#BC4 7#B .;S -- .;T #D @7 #G
,,EXAMPLES #E & #F
ON P4 #FIC = ,EXS4 #BD-CA
,,BINOMIAL ,,!OREM ,USE ! BINOMIAL
!OREM 6WRITE ! BINOMIAL EXPAN.N4
.#BD4 @7 .;X @+ #B7 #C
.#BE4 @7 .;C -#D7 #E
.#BF4 @7 .A @+ #C .;B @7 #D
.#BG4 7#D .;P -- .;Q @7 #F
.#BH4 @7 .;W #C -- #C7 #D
.#BI4 7#B .;S #D @+ #E7 #E
.#CJ4 7#C .;U @+ ;V #B @7 #F
.#CA4 @7 .;X #C -- .;Y #B @7 #D
,,EXAMPLE #G
ON P4 #FID = ,EXS4 #CB-CE
.#CB4 ,F9D ! COE6ICI5T ( ;X #E 9 !
EXPAN.N ( @7 .;X -- #B7 #AJ @4
.#CC4 ,F9D ! COE6ICI5T ( ;X #C 9 !
EXPAN.N ( 7#C .;X @+ #B7 #E @4
.#CD4 ,F9D ! COE6ICI5T ( ;X #F 9 !
EXPAN.N ( @7 .;X #B -- #C7 #H @4
#CE4 .,,MULTIPLE .,,*OICE ,: IS !
COE6ICI5T ( .;X #D 9 ! EXPAN.N (
7;X--#C7 #G @8
,A --#IDE
;,B --#CE
;,C --#BG
;,D #BHCE
,,PASCAL'S ,,TRIANGLE ,9 ,EX]CISES #CF
& #CG1 USE ! DIAGRAMS %[N4
.#CF4 ,:AT IS ! SUM (! NUMB]S 9 EA* (
R[S #J-D ( ,PASCAL'S TRIANGLE8 ,:AT IS !
SUM 9 R[ .;N @8
.#CG4 .,DESCRIBE ! PATT]N =M$ 0! SUMS
(! NUMB]S AL;G ! DIAGONAL SEG;TS (
,PASCAL'S TRIANGLE4
,,R1SON+ ,9 ,EX]CISES #CH & #CI1
DECIDE :E!R ! PRO#M REQUIRES .-B9,NS OR
.P]MUT,NS 6F9D ! ANSW]4 ,!N SOLVE !
PRO#M4
.#CH4 .,,NEWSPAP] ,YR S*OOL NEWSPAP]
HAS AN $ITOR-IN-*IEF & AN ASSI/ANT
$ITOR-IN-*IEF4 ,! /AFF (! NEWSPAP] HAS
#AB /UD5TS4 ,9 H[ _M WAYS C /UD5TS 2
*OS5 = ^! TWO POSI;NS8
#CI4 .,,/UD5T .,,C\NCIL ,FIVE
REPRES5TATIVES F A S5IOR CLASS ( #BHJ
/UD5TS >E 6BE *OS5 =! /UD5T C\NCIL4 ,9
H[ _M WAYS C /UD5TS 2 *OS5 6REPRES5T !
S5IOR CLASS ON ! /UD5T C\NCIL8
#DJ4 .,,MULTIPLE .,,*OICE ,A RELAY
RACE HAS A T1M ( #D RUNN]S :O RUN DI6]5T
"PS (! RACE4 ,"! >E #BJ /UD5TS ON YR
TRACK SQUAD4 ,9 H[ _M WAYS C ! COA*
SELECT /UD5TS 6-PETE ON ! RELAY T1M8
,A #DHDE
;,B #DJ1JJJ
;,C #AAF1BHJ
;,D #AFJ1JJJ
#DA4 .,,%ORT .,,RESPONSE .,EXPLA9 H[ !
=MULA = ;N .;,C ;N SU7E/S ! DEF9I;N #J6
.K #A4
,,*ALL5GE ,V]IFY ! ID5T;Y4 .,JU/IFY
EA* ( YR /EPS4
#DB4 ;N .;,C #J .K ;L
#DC4 ;N .;,C ;N .K #A
#DD ;N .;,C ;R 99 ;N .;,C ;M.' .K ;N
.;,C ;M.' 99 ;N-;M .;,C ;R-;M.'.-
#DE4 ;N .;,C #A .K ;N ;,P.' #A
#DF4 ;N .;,C ;R.' .K ;N .;,C
;N--;R.'.-
#DG4 .;N @+ #A .;,C ;R .K ;N .;,C ;R
@+ ;N .;,C ;R -- #A
------------------------------------#FIF
,PRO#M ,SOLV+
,,EXAMPLES #A1 #B1 & #C
ON PP4 #FIJ-FIA = ,EXS4 #DH-EJ
.#DH4 .,,MUSIC ,Y WANT 6PUR*ASE #C
,,CD,'S F AN ONL9E COLLEC;N T 3TA9S !
TYPES ( MUSIC %[N AT ! "R4 ,Y WANT EA*
;,,CD 63TA9 A DI6]5T TYPE ( MUSIC S* T
#B ,,CD,'S >E DI6]5T TYPES ( 3TEMPOR>Y
MUSIC & #A ;,,CD IS A TYPE ( CLASSICAL
MUSIC4 ,H[ _M DI6]5T SETS ( MUSIC TYPES
C Y *OOSE8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#DI4 .,,FL[]S ,Y >E BUY+ A B\QUET4 ,!
FLORI/ HAS #AH TYPES ( FL[]S T Y C USE
6MAKE ! B\QUET4 ,Y WANT 6USE .EXACTLY #C
TYPES ( FL[]S4 ,H[ _M DI6]5T -B9,NS (
FL[] TYPES C Y USE 9 YR B\QUET8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#EJ4 .,,>CADE .,,GAMES ,AN >CADE HAS
#BJ DI6]5T >CADE GAMES4 ,Y WANT 6PLAY AT
L1/ #AD ( !M4 ,H[ _M DI6]5T -B9,NS (
>CADE GAMES C Y PLAY8
#EA4 .,,MULTI-.,,/EP .,,PRO#M ,A
TELEVIS$ S++ -PETI;N PICKS A W9N] F #BJ
ORIG9AL 3TE/ANTS OV] ! C\RSE ( FIVE
EPISODES4 ,DUR+ EA* (! F/1 SECOND1 &
?IRD EPISODES1 #E S+]S >E ELIM9AT$ 0! 5D
(! EPISODE4 ,! F\R? EPISODE ELIM9ATES #B
M S+]S1 &! W9N] IS SELECT$ AT ! 5D (!
FIF? EPISODE4
A4 ,H[ _M -B9,NS ( #E S+]S \ (!
ORIG9AL #BJ C 2 ELIM9AT$ DUR+ ! F/
EPISODE8
B4 ,H[ _M -B9,NS ( #E S+]S \ (! #AE
S+]S :O />T$ ! SECOND EPISODE C 2
ELIM9AT$ DUR+ ! SECOND EPISODE8
C4 ,H[ _M -B9,NS ( S+]S C 2 ELIM9AT$
DUR+ ! ?IRD EPISODE8 DUR+ ! F\R?
EPISODE8 DUR+ ! FIF? EPISODE8
D4 ,F9D ! TOTAL NUMB] ( WAYS 9 : ! #BJ
ORIG9AL 3TE/ANTS C 2 ELIM9AT$ 6PRODUCE A
W9N]4
#EB4 .,,EXT5D$ .,,RESPONSE ,A GR\P (
#AE HI< S*OOL /UD5TS IS VOLUNTE]+ AT A
LOCAL FIRE /,N4 ,( ^! /UD5TS1 #E W 2
ASSIGN$ 6WA% FIRE TRUCKS1 #G W 2 ASSIGN$
6REPA9T ! /,N'S 9T]IOR1 & #C W 2 ASSIGN$
6D MA9T5.E ON ! /,N'S EXT]IOR4
A4 .,CALCULATE ,"O WAY 6C.T ! NUMB] (
POSSI# JOB ASSIGN;TS IS 6F9D ! NUMB] (
P]MUT,NS ( #E .,W0' ;S 7= 8WA%071 #G
.,R0' ;S 7= 8REPA9T+071 & #C ,M'S 7=
8MA9T5.E074 ,USE ? ME?OD 6WRITE ! NUMB]
( POSSI# JOB ASSIGN;TS F/ Z AN EXPRES.N
9VOLV+ FACTORIALS & !N Z A NUMB]4
B4 .,CALCULATE ,ANO!R WAY 6C.T ! NUMB]
( POSSI# JOB ASSIGN;TS IS 6F/ *OOSE ! #E
.,W'S @1 !N *OOSE ! #G .,R'S @1 & !N
*OOSE ! #C ,M'S4 ,USE ? ME?OD 6WRITE !
NUMB] ( POSSI# JOB ASSIGN;TS F/ Z AN
EXPRES.N 9VOLV+ FACTORIALS & !N Z A
NUMB]4
C4 .,ANALYZE .,-P>E YR RESULTS F "PS
7A7 & 7;B74 .,EXPLA9 :Y !Y MAKE S5SE4
,PICTURE3 ,VOLUNTE]S 9 ,ANIAK1 ,ALASKA
.K ..,,"W$-,,\ ,,SOLU;NS .ON P4 ,,WS#A
.K ,,/&>DIZ$ ,,TE/ ,,PRACTICE
------------------------------------#FIG
.#EC4 .,,*ALL5GE ,A POLYGON IS .3VEX
IF NO L9E T 3TA9S A SIDE (! POLYGON
3TA9S A PO9T 9 ! 9T]IOR (! POLYGON4
,3SID] A 3VEX POLYGON ) .;N SIDES4
.A4 ,USE ! -B9,NS =MULA 6WRITE AN
EXPRES.N =! NUMB] ( L9E SEG;TS T JO9
PAIRS ( V]TICES ON AN ;N-SID$ POLYGON4
.B4 ,USE YR RESULT F "P 7A7 6WRITE A
=MULA =! NUMB] ( DIAGONALS ( AN ;N-SID$
3VEX POLYGON4
,MIX$ ,REVIEW
,F9D ! >EA (! FIGURE4@7 PP4 #IIA-IIB
@7
.#ED4 ,CIRCLE ) RADIUS #AF 9*ES
.#EE4 ,RECTANGLE ) SIDES #H.BE FEET &
#AB.A FEET
.#EF4 ,TRIANGLE ) BASE #AE C5TIMET]S &
HEI<T #AH C5TIMET]S
.#EG4 ,TRAPEZOID ) BASES #AB MET]S &
#AF MET]S1 & HEI<T #I MET]S
,SOLVE ! ,EQU,N4
.#EH4
.#EI4 @7 .;X -- #B7 #C/B .K #BAF7
P#.DEB @7
.#FJ4 ,9 @7 .;X @+ #D7 .K ,9 #E7 P4
#EAE @7
.#FA4 #AJ #D;X -- #E .K #AA7 P4 #EAE
@7
.#FB4
.#FC4
,,QUIZ .= .,LESSONS .#AJ..G-.AJ..B
,=! GIV5 LIC5SE PLATE 3FIGUR,N1 F9D H[
_M PLATES >E POSSI# IF LRS & DIGITS 7A7
C 2 REP1T$ & 7;B7 _C 2 REP1T$1 @7 P4
#FHB @7
.#A4 #B LRS FOLL[$ 0#C DIGITS
.#B4 #C DIGITS FOLL[$ 0#C LRS
,F9D ! NUMB] ( 4T+UI%A# P]MUT,NS (!
LRS 9 ! ^W4 @7 P4 #FHB @7
.#C4 ,,AWAY
.#D4 ,,IDAHO
.#E4 ,,LR
.#F4 ,,T5;SEE
,F9D ! NUMB] ( -B9,NS1 @7 .P4 #FIJ7
.#G4 #H .;,C #F
.#H4 #G .;,C #D
.#I #I .;,C #I
.#AJ4 #AB ;,C ;N
,USE ! BINOMIAL !OREM 6WRITE !
BINOMIAL EXPAN.N1 7.P4 #FIJ7
.#AA4 @7 .;X @+ #E7 #E
.#AB4 7#BE--#C7 #F
.#AC4 7#C .;U @+ .;V @7 #D
.#AD4 7#B .;X #C -- #C .;Y @7 #E
.#AE4 ,F9D ! COE6ICI5T ( ;X #C 9 !
EXPAN.N ( 7;X @+ #B7 #I @4 7.P4 .#FIJ7
.#AF4 .,,M5U .,,*OICES ,A PIZZA P>LOR
RUNS A SPECIAL ": Y C BUY A L>GE PIZZA )
#A *EESE1 #A VEGETA#1 & #B M1TS = 4#AB4
,Y H A *OICE ( #E *EESES1 #AJ VEGETA#S1
& #F M1TS4 ,H[ _M DI6]5T V>I,NS (! PIZZA
SPECIAL >E POSSI#8 7.P4 .#FHB7
.,,EXTRA .,,PRACTICE = ,LESSON #AJ.B1
P4 #AJAI
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#FIH
#AJ.C ,DEF9E & ,USE ,PROBABIL;Y
.,2F ,Y DET]M9$ ! NUMB] ( WAYS AN EV5T
CD O3UR4
.,N[ ,Y W F9D ! LIKELIHOOD T AN EV5T W
O3UR4
.,:Y8 ,S Y C F9D R1L-LIFE GEOMETRIC
PROBABILITIES1 Z 9 ,EX4 #CI
,KEY ,VOCABUL>Y
99 PROBABIL;Y
99 !ORETICAL PROBABIL;Y
99 O4S
99 EXP]I;TAL PROBABIL;Y
99 GEOMETRIC PROBABIL;Y
,SIDEB>3
,/&>DS
.#AI..J ,/UD5TS USE -B9,NS & P]MUT,NS
6-PUTE PROBABILITIES4
,:5 Y ROLL A /&>D SIX-SID$ DIE1 !
POSSI# RESULTS >E CALL$ .\TCOMES4 ,!
\TCOMES ( ROLL+ A DIE >E #A1 #B1 #C1 #D1
#E1 & #F4 ,AN .EV5T IS AN \TCOME OR A
COLLEC;N ( \TCOMES4 ,= EXAMPLE1 ! EV5T
8ROLL+ AN ODD NUMB]0 3SI/S (! \TCOMES
#A1 #C1 & #E4
,! .PROBABIL;Y ( AN EV5T IS A NUMB] F
#J 6#A T 9DICATES ! LIKELIHOOD ! EV5T W
O3UR1 Z %[N ON ! NUMB] L9E 2L4
,PROBABILITIES C 2 WRITT5 Z FRAC;NS1
DECIMALS1 OR P]C5TS4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,!ORETICAL ,PROBABIL;Y ( AN ,EV5T
,:5 ALL \TCOMES >E EQU,Y LIKELY1 !
.!ORETICAL .PROBABIL;Y T AN EV5T ,A W
O3UR IS3
,! !ORETICAL PROBABIL;Y ( AN EV5T IS
(T5 SIMPLY CALL$ ! PROBABIL;Y (! EV5T4
,EXAMPLE #A ,F9D PROBABILITIES ( EV5TS
,Y ROLL A /&>D SIX-SID$ DIE4 ,F9D !
PROBABIL;Y ( 7A7 ROLL+ A #E & 7;B7 ROLL+
AN EV5 NUMB]4
.A4 ,"! >E #F POSSI# \TCOMES4 ,ONLY #A
\TCOME CORRESPONDS 6ROLL+ A #E4
.B4 ,A TOTAL ( #C \TCOMES CORRESPOND
6ROLL+ AN EV5 NUMB]3 A #B1 #D1 OR #F4
------------------------------------#FII
,EXAMPLE #B ,USE P]MUT,NS OR -B9,NS
.,,5T]TA9;T ,A -MUN;Y C5T] HO/S A
TAL5T 3TE/ = LOCAL MUSICIANS4 ,ON A GIV5
EV5+1 #G MUSICIANS >E S*$UL$ 6P]=M4 ,!
ORD] 9 : ! MUSICIANS P]=M IS R&OMLY
SELECT$ DUR+ ! %[4
.A4 ,:AT IS ! PROBABIL;Y T ! MUSICIANS
P]=M 9 ALPHABETICAL ORD] 0_! LA/ "NS8
7,ASSUME T NO TWO MUSICIANS H ! SAME LA/
"N47
.B4 ,Y >E FRS ) #D (! MUSICIANS4 ,:AT
IS ! PROBABIL;Y T ! F/ #B P]=M]S >E YR
FRS8
,SOLU;N
.A4 ,"! >E #G6 DI6]5T .P]MUT,NS (! #G
MUSICIANS4 ,( ^!1 ONLY #A IS 9
ALPHABETICAL ORD] 0LA/ "N4 ,S1 !
PROBABIL;Y IS3
.B4 ,"! >E #G .;,C #B DI6]5T .-B9,NS (
#B MUSICIANS4 ,( ^!1 #D .;,C #B >E #B (
YR FRS4 ,S1 ! PROBABIL;Y IS3
.,GUID$ .,PRACTICE = .,EXAMPLES .#A &
.#B
,Y H AN EQU,Y LIKELY *.E ( *OOS+ ANY
9TEG] F #A "? #BJ4 ,F9D ! PROBABIL;Y (!
GIV5 EV5T4
#A4 ,A P]FECT SQU>E IS *OS54
#B4 ,A FACTOR ( #CJ IS *OS54
#C4 .,,:AT .,,IF8 ,9 ,EXAMPLE #B1 H[ D
YR ANSW]S 6"PS 7A7 & 7;B7 *ANGE IF "! >E
#I MUSICIANS S*$UL$ 6P]=M8
.,,O4S ,Y C AL USE .O4S 6M1SURE !
LIKELIHOOD T AN EV5T W O3UR4 ,O4S M1SURE
! *.ES 9 .FAVOR ( AN EV5T O3URR+ OR !
*.ES .AG/ AN EV5T O3URR+4
,,KEY ,,3CEPT .= .,YR .,NOTEBOOK
,O4S 9 ,FAVOR ( OR ,O4S ,AG/ AN ,EV5T
,:5 ALL \TCOMES >E EQU,Y LIKELY1 ! O4S
9 FAVOR ( AN EV5T ,A&! O4S AG/ AN EV5TS
>E DEF9$ Z FOLL[S3
,Y C WRITE ! O4S 9 FAVOR ( OR AG/ AN
EV5T 9 ! =M OR 9 ! =M .A3 .B4
------------------------------------#GJJ
,EXAMPLE #C ,F9D O4S
,,AVOID ,,]RORS
,NOTE T ! O4S 9 FAVOR ( DRAW+ A #AJ1 :
>E D N EQUAL ! PROBABIL;Y ( DRAW+ A #AJ1
: IS
,A C>D IS DRAWN F A /&>D DECK ( #EB
C>DS4 ,F9D 7A7 ! O4S 9 .FAVOR ( DRAW+ A
#AJ & 7;B7 ! O4S .AG/ DRAW+ A CLUB4
,SOLU;N
.A4
.B4
.,,EXP]I;TAL .,,PROBABIL;Y ,"S"TS X IS
N POSSI# OR 3V5I5T 6F9D ! !ORETICAL
PROBABIL;Y ( AN EV5T4 ,9 S* CASES1 Y MAY
2 A# 6CALCULATE AN .EXP]I;TAL
.PROBABIL;Y 0P]=M+ AN EXP]I;T1 3DUCT+ A
SURVEY1 OR LOOK+ AT ! HI/ORY (! EV5T4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,EXP]I;TAL ,PROBABIL;Y ( AN ,EV5T
,:5 AN EXP]I;T IS P]=M$ T 3SI/S (A
C]TA9 NUMB] ( TRIALS1 ! EXP]I;TAL
PROBABIL;Y ( AN EV5T ,A IS GIV5 BY3
,EXAMPLE #D ,F9D AN EXP]I;TAL
PROBABIL;Y
.,,SURVEY ,! B> GRAPH %[S H[ OLD
ADULTS 9 A SURVEY WD *OOSE 6BE IF !Y CD
*OOSE ANY AGE4 ,F9D ! EXP]I;TAL
PROBABIL;Y T A R&OMLY SELECT$ ADULT WD
PREF] 6BE AT L1/ #DJ YE>S OLD4
,SOLU;N
,! TOTAL NUMB] ( P SURVEY$ IS3
#DFC @+ #AJHE @+ #HGI @+ #EEA @+ #CJJ
@+ #BCH .K #CEAF
,( ^? SURVEY$1 #EEA @+ #CJJ @+ #BCH .K
#AJHI WD PREF] 6BE AT L1/ #DJ4
.,GUID$ .,PRACTICE = ,EXAMPLES #C & #D
,A C>D IS R&OMLY DRAWN F A /&>D DECK4
,F9D ! 9DICAT$ O4S4
.#D4 ,9 FAVOR ( DRAW+ A HE>T
.#E4 ,AG/ DRAW+ A QUE5
.#F4 .,,:AT .,,IF8 ,9 ,EXAMPLE #D1 :AT
IS ! EXP]I;TAL PROBABIL;Y T AN ADULT WD
PREF] 6BE 7A7 AT MO/ #CI YE>S OLD & @7
.;B @7 AT L1/ #CJ YE>S OLD8
------------------------------------#GJA
.,,GEOMETRIC .,,PROBABIL;Y ,"S
PROBABILITIES >E F.D 0CALCULAT+ A RATIO
( TWO L5G?S1 >1S1 OR VOLUMES4 ,S*
PROBABILITIES >E GEOMETRIC PROBABILITIES
@4
,EXAMPLE #E ,F9D A GEOMETRIC
PROBABIL;Y
.,,D>TS ,Y ?R[ A D>T AT ! SQU>E BO>D
%[N4 ,YR D>T IS EQU,Y LIKELY 6HIT ANY
PO9T 9SIDE ! BO>D4 ,>E Y M LIKELY 6GET
#AJ PO9TS OR #J PO9TS8
,SOLU;N
,2C #J.BAE .1 #J.JHGC1 Y >E M LIKELY
6GET #J PO9TS4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
.,GUID$ .,PRACTICE = ,EXAMPLE #E
.#G4 .,,:AT .,,IF8 ,9 ,EXAMPLE #E1 >E
Y M LIKELY 6GET #E PO9TS OR #J PO9TS8
#AJ.C ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;N
ON P4 ,,WS#AH = ,EXS4 #G1AG1 & #CI
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 #B1AI1BF1BG1 #CB1 & #DB
.K .,,MULTIPLE .,,REPRES5T,NS
,EX#.DJ
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,A
PROBABIL;Y T IS ! RATIO ( TWO L5G?S1
>1S1 OR VOLUMES IS CALL$ A7;N7 @8
PROBABIL;Y4
.#B4 .,,WRIT+ .,EXPLA9 ! DI6];E 2T
!ORETICAL PROBABIL;Y & EXP]I;TAL
PROBABIL;Y4 ,GIVE AN EXAMPLE ( EA*4
,,EXAMPLE #A
ON P4 #FIH = ,EXS4 #C-AF
.,,*OOS+ .,,NUMB]S ,Y H AN EQU,Y
LIKELY *.E ( *OOS+ ANY 9TEG] F #A "?
#EJ4 ,F9D ! PROBABIL;Y (! GIV5 EV5T4
.#C4 ,AN EV5 NUMB] IS *OS54
.#D4 ,A NUMB] LESS ?AN #CE IS *OS54
.#E4 ,A P]FECT SQU>E IS *OS54
.#F4 ,A PRIME NUMB] IS *OS54
.#G4 .,A FACTOR ( #AEJ IS *OS54
.#H4 ,A MULTIPLE ( #D IS *OS54
.#I4 ,A TWO-DIGIT NUMB] IS *OS54
.#AJ4 ,A P]FECT CUBE IS *OS54
------------------------------------#GJB
,,*OOS+ ,,C>DS ,A C>D IS R&OMLY DRAWN
F A /&>D DECK ( #EB C>DS4 ,F9D !
PROBABIL;Y ( DRAW+ ! GIV5 C>D4
.#AA4 ,! K+ ( DIAMONDS
.#AB4 ,A K+
.#AC4 ,A SPADE
.#AD4 ,A BLACK C>D
.#AE4 ,A C>D O!R ?AN A #B
.#AF4 ,A FACE C>D 7A K+1 QUE51 OR
JACK7
,,EXAMPLE #B
ON P4 #FII = ,EXS4 #AG-AI
,,LOTT]IES ,9 ,EX]CISES #AG & #AH1 F9D
! PROBABIL;Y ( W9N+ ! LOTT]Y AC 6! GIV5
RULES4 ,ASSUME NUMB]S >E SELECT$ AT
R&OM4
.#AG4 ,Y M/ CORRECTLY SELECT #F \ (
#DH NUMB]S4 ,! ORD] (! NUMB]S IS N
IMPORTANT4
.#AH4 ,Y M/ CORRECTLY SELECT #D
NUMB]S1 EA* AN 9TEG] F #J 6#I4 ,! ORD]
(! NUMB]S IS IMPORTANT4
#AI4 .,,MULTIPLE .,,*OICE ,:AT IS !
PROBABIL;Y 7R.D$ 6?REE DECIMAL PLACES7 T
#B R&OMLY SELECT$ MON?S BO? H #CA "DS8
,A #J.AEI
;,B #J.BBG
;,C #J.CAH
;,D #J.CDJ
,,EXAMPLE #C
ON P4 #GJJ = ,EXS4 #BJ-BE
,,O4S ,Y R&OMLY *OOSE A M># F A BAG4
,! BAG 3TA9S #AJ BLACK1#H R$1 #D :ITE1 &
#F BLUE M>#S4 ,F9D ! 9DICAT$ O4S4
.#BJ4 ,9 FAVOR ( *OOS+ :ITE
.#BA4 ,9 FAVOR ( *OOS+ BLUE
.#BB4 ,AG/ *OOS+ R$
.#BC4 ,AG/ *OOS+ BLACK
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 CALCULAT+ ! O4S AG/ GETT+ A #E
OR #F :5 ROLL+ A SIX-SID$ DIE4
#BD4
#BE4
.#BF4 .,,OP5-.,,5D$ .,,MA? ,FLIP A CO9
#AJ "TS4 ,:AT IS ! EXP]I;TAL PROBABIL;Y
( GETT+ H1DS8
.#BG4 .,,%ORT .,,RESPONSE ,!
PROBABIL;Y ( EV5T ,A IS #J.C4 ,:AT >E !
O4S 9 FAVOR ( EV5T .,A8 .,EXPLA94
,,EXAMPLE #D
ON P4 #GJJ = ,EXS4 #BH-CB
,,ROLL+ ,A ,,DIE ,! RESULTS ( ROLL+ A
SIX-SID$ DIE #AEJ "TS >E %[N4 ,USE ! TA#
6F9D ! EXP]I;TAL PROBABIL;Y (! GIV5
EV5T4 .,-P>E YR ANSW] 6! !ORETICAL
PROBABIL;Y (! EV5T4
.#BH4 ,ROLL+ A #E
.#BI4 ,ROLL+ AN EV5 NUMB]
.#CJ4 ,ROLL+ A NUMB] LESS ?AN #E
.#CA4 ,ROLL+ ANY NUMB] B A #C
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,ROLL @3 @3 @3 @3 @3 @3
.,NUMB] .( .O3URR;ES @3 .#BG @3 #BB3
.#AH @3 .#BF @3 #BG3 .#CJ
#CB4 .,,MULTIPLE .,,*OICE ,Y FLIP A
CO9 #HJ "TS4 ,Y GET H1DS #CG "TS & TAILS
#DC "TS4 ,:AT IS ! EXP]I;TAL PROBABIL;Y
( GETT+ H1DS8
,A #J.DFBE
;,B #J.E
;,C #J.ECGE
;,D #J.HFJE
#CC4 .,,R1SON+ ,F9D ! PROBABIL;Y T !
V]TEX (! GRAPH ( .;Y .K .;X #B -- #F;X
@+ .;C IS ABV ! .;X -AXIS IF .;C IS A
R&OMLY *OS5 9TEG] F #A 6#BJ4
.K ..,,"W$-,,\ ,,SOLU;NS ON P4.,,WSI
.K .,,/&>DIZ$ .,,TE/ .,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
------------------------------------#GJC
#CD4 .,,*ALL5GE ,SUPPOSE Y ?R[ A D>T
AT EA* SQU>E T>GET 2L4 ,ASSUME T ! D>T
IS EQU,Y LIKELY 6HIT ANY PO9T 9SIDE !
T>GET4
,T>GET ,A
,T>GET ;,B
,T>GET ;,C
A4 ,CALCULATE ,:AT IS ! PROBABIL;Y T !
D>T L&S 9SIDE ! CIRCLE 9 T>GET ,A8 9SIDE
A CIRCLE 9 T>GET ;,B8 9SIDE A CIRCLE 9
T>GET ;,C8
B4 ,G5]ALIZE ,3SID] ! G5]AL CASE ": A
SQU>E T>GET ) SIDES #AB 9*ES L;G 3TA9S
.;N #B ID5TICAL CIRCLES >RANG$ 9 .;N R[S
& .;N COLUMNS4 ,MAKE A 3JECTURE AB !
PROBABIL;Y T A D>T L&S 9SIDE "O (!
CIRCLES4 ,!N PROVE YR 3JECTURE4
,PRO#M ,SOLV+
,,EXAMPLE #E
ON P4 #GJA = ,EXS4 #CE-CG
.,,GEOMETRIC .,,PROBABIL;Y ,F9D !
PROBABIL;Y T A D>T ?R[N AT ! GIV5 T>GET
W HIT ! %AD$ REGION4 ,ASSUME ! D>T IS
EQU,Y LIKELY 6HIT ANY PO9T 9SIDE !
T>GET4
#CE4
#CF4
#CG4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#CH4 .,,JURY .,,SELEC;N ,A JURY ( #AB
P IS SELECT$ F A POOL ( #CJ P T 9CLUDES
#AB M5 & #AH WOM54 ,:AT IS ! PROBABIL;Y
T ! JURY W 2 -POS$ ( #AB WOM58
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#CI4 .,,>*]Y ,! /&>D >*]Y T>GET US$ 9
-PETI;N HAS A DIAMET] ( #HJ C5TIMET]S4
,F9D ! PROBABIL;Y T AN >R[ %OT AT !
T>GET W HIT ! C5T] CIRCLE1 : HAS A
DIAMET] ( #AF C5TIMET]S4 ,ASSUME ! >R[
IS EQU,Y LIKELY 6HIT ANY PO9T 9SIDE !
T>GET4
#DJ4 .,,MULTIPLE .,,REPRES5T,NS ,ON A
TYPICAL WEEK"D1 "! >E #A1AHA1AJJ "O-WAY
TRIPS TAK5 ON ! PUBLIC TRANSPORT,N SY/EM
OP]AT$ 0! ,MASSA*USETTS ,BAY ,TRANSIT
,AU?OR;Y4 ,( ^! TRIPS1 #CGF1IJJ >E BUS
RIDES4 ,SUPPOSE A "O-WAY TRIP IS SELECT$
AT R&OM4
A4 ,US+ ,FRAC;NS ,:AT IS ! PROBABIL;Y1
EXPRESS$ Z A FRAC;N1 T ! TRIP 0 TAK5 ON
A BUS8
B4 ,US+ ,DECIMALS ,:AT IS !
PROBABIL;Y1 EXPRESS$ Z A DECIMAL1 T !
TRIP 0 TAK5 ON A BUS8
C4 ,US+ ,P]C5TS ,:AT IS ! PROBABIL;Y1
EXPRESS$ Z A P]C5T1 T ! TRIP 0 TAK5 ON A
BUS8
D4 ,US+ ,O4S ,:AT >E ! O4S 9 FAVOR (!
TRIP HAV+ BE5 ON A BUS8
------------------------------------#GJD
#DA4 .,,GULF .,,COA/ ,! MAP %[S ! L5G?
( %OREL9E 7IN MILES7 AL;G ! ,GULF (
,MEXICO = EA* /ATE T BORD]S ! BODY (
WAT]4 ,:AT IS ! PROBABIL;Y T A %IP -+
A%ORE AT A R&OM PO9T 9 ! ,GULF ( ,MEXICO
L&S 9 ! GIV5 /ATE8
A4 ,TEXAS
B4 ,FLORIDA
C4 ,ALABAMA
#DB4 .,,EXT5D$ .,,RESPONSE ,A MAGICIAN
CLAIMS 6BE A# 6R1D M9DS4 ,6TE/ ? CLAIM1
FIVE C>DS NUMB]$ #A "? #E >E US$4 ,A
SUBJECT SELECTS TWO C>DS F ! FIVE C>DS &
3C5TRATES ON ! NUMB]S4
A4 ,:AT IS ! PROBABIL;Y T ! TWO NUMB]S
*OS5 >E #C & #D8
B4 ,:AT IS ! PROBABIL;Y T ! MAGICIAN C
CORRECTLY ID5TIFY ! TWO NUMB]S 0GUESS+8
C4 ,SUPPOSE ! MAGICIAN IS A# 63SI/5TLY
ID5TIFY ! TWO NUMB]S AB HALF ! "T4 ,DOES
? SUPPORT ! MAGICIAN'S CLAIM 6BE A M9D
R1D]8 .,EXPLA94
#DC4 .,,*ALL5GE ,9 A GUESS+ GAME1 "O
PLAY] SECRETLY PLACES F\R DI6]5T-COLOR$
PEGS ON A BO>D 9 EA* ( F\R POSI;NS3 ,A1
;,B1 ;,C1 OR ,D4 ,A SECOND PLAY] GUESSES
! 3FIGUR,N (! PEGS 0PLAC+ AN ID5TICAL
SET ( PEGS 9 SLOTS ,A1 ;,B1 ;,C1 & ;,D
ON AN ID5TICAL BO>D4 ,! SECOND PLAY] IS
!N TOLD H[ _M (! PEGS >E 9 ! CORRECT
SLOT4
A4 ,:AT IS ! PROBABIL;Y T ! SECOND
PLAY] HAS ALL F\R PEGS CORRECT ON ! F/
GUESS8
B4 ,:AT IS ! PROBABIL;Y T ! SECOND
PLAY] HAS EXACTLY "O PEG CORRECT ON ! F/
GUESS8
C4 ,! SECOND PLAY] IS TOLD %E HAS
PLAC$ TWO PEGS 9 ! CORRECT SLOT4 ,!
PLAY] !N SWIT*ES TWO (! PEGS4 ,:AT IS !
PROBABIL;Y T ! PLAY] N[ HAS ALL F\R PEGS
9 ! CORRECT SLOT8
,MIX$ ,REVIEW
.#DD4 .;Y .K #D7#J.GE7 ;X @7 P4 #DHF
@7
.#DE4 .;F7.;X7 .K #C .;E --#B .;X @7
P#.DIB @7
.#DF4 .;Y .K ,9 .;X @+ #B7 P4 #DII @7
.#DG4
.#DH4
.#DI4
,EVALUATE ! EXPRES.N )\T US+ A
CALCULATOR1 @7 P4 #DII @7
.#EJ4 LOG #D #FD
.#EA4 LN .;E
.#EB4 LOG #F #CF
.#EC4 LOG #B #EAB
.#ED4 ,9 .;E #B.I
.#EE4 LOG #A/C #I
.#EF4 LOG #I #BG
.#EG4
,PREVIEW
,PREP>E = ,LESSON #AJ.D 9 ,EXS4
#EH-FA4
,F9D ! NUMB] ( -B9,NS4 @7 P4 #FIJ @7
.#EH4 #H ;,C #C
.#EI4 #AJ ;,C #I
.#FJ4 #G ;,C #D
.#FA4 #AB ;,C #E
.,,EXTRA .,,PRACTICE = ,LESSON #AJ.C1
P4 #AJAI
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#GJE
,MIX$ ,REVIEW ( PRO#M ,SOLV+
..,,/ATE ,,TE/ ,,PRACTICE
_+CLASSZONE.COM_:
,LESSONS #AJ.A-AJC
#A4 .,,MULTI-.,,/EP .,,PRO#M ,FIVE P
WALK 96A MOVIE !AT] & LOOK = EMPTY S1TS4
,A4 ,F9D ! NUMB] ( WAYS ! P C 2 S1T$
IF "! >E #E EMPTY S1TS4
,B4 ,F9D ! NUMB] ( WAYS ! P C 2 S1T$
IF "! >E #H EMPTY S1TS4
,C4 ,G5]ALIZE YR RESULTS F "PS 7A7 &
7;B7 0WRIT+ AN EXPRES.N 9VOLV+
FACTORIALS =! NUMB] ( WAYS ! P C 2 S1T$
IF "! >E .;N EMPTY S1TS4
,D4 ,:AT IS ! M9IMUM VALUE ( .;N S* T
"! >E AT L1/ #A MILLION WAYS ! P C 2
S1T$8
#B4 .,,MULTI-.,,/EP .,,PRO#M ,Y &A FR
>E MEET+ AT ! GYM 6"W \4 ,Y BO? AGREE
6>RIVE 2T #I3JJ ,A4,M4 & #I3CJ ,A4,M4 ,Y
W WAIT = EA* O!R = UP 6#AJ M9UTES4
,A4 ,LET .;X 2 YR >RIVAL "T 7IN M9UTES
AF #I3JJ A4M471 & LET .;Y 2 YR FR ;S
>RIVAL "T 7IN M9UTES AF #I3JJ ,A4,M474
,WRITE 9EQUALITIES REPRES5T+ ! "T
9T]VALS 9 : Y & YR FR >RIVE4
,B4 ,IF Y & YR FR >E 6MEET1 ! DI6];E
2T YR >RIVAL "TS M/ N EXCE$ #AJ M9UTES4
,WRITE TWO 9EQUALITIES T %[ ? FACT4
,C4 ,GRAPH YR 9EQUALITIES F "PS 7A7 &
7;B7 9 ! SAME COORD9ATE PLANE4
,D4 ,US+ YR GRAPH F "P 7;C71 F9D !
PROBABIL;Y T Y & YR FR W MEET AT ! GYM4
#C4 .,,GRI4$ .,,ANSW] ,Y WANT 6MAKE A
FRUIT SMOO?IE US+ #C (! FRUITS LI/$4 ,H[
_M DI6]5T FRUIT SMOO?IES C Y MAKE8
.#D4 .,,GRI4$ .,,ANSW] ,9 A HI< S*OOL
FA%ION %[1 H[ _M WAYS C #A FRE%MAN1 #B
SOPHOMORES1 #B JUNIORS1 & #C S5IORS L9E
UP 9 FRONT (! JUDGES IF ! 3TE/ANTS 9 !
SAME CLASS >E 3SID]$ ID5TICAL8
.#E4 .,,EXT5D$ .,,RESPONSE ,! GRAPH
%[S ! RESULTS (A SURVEY 9 #BJJD T ASK$
,U4,S4 ADULTS : SPORT !Y WD MO/ L
6"PICIPATE 9 AT ! ,SUMM] ,OLYMPICS4
,SUMM] ,OLYMPICS ,SPORTS
,A4 ,F9D ! PROBABIL;Y T A R&OMLY
SELECT$ ,U4,S4 ADULT WD L 6"PICIPATE 9
TRACK & FIELD4
,B4 ,IS YR ANSW] F "P 7A7 A .!ORETICAL
OR .EXP]I;TAL PROBABIL;Y8 .,EXPLA94
,C4 ,:AT >E ! O4S 9 FAVOR (A R&OMLY
SELECT$ ,U4,S4 ADULT PREF]R+ 6"PICIPATE
9 GYMNA/ICS8
.#F4 .,,%ORT .,,RESPONSE ,Y M/ TAKE
#AH ELECTIVE C\RSES 6MEET YR GRADU,N
REQUIRE;TS = COLLEGE4 ,"! >E #CJ C\RSES
T Y >E 9T]E/$ IN4 ,DOES F9D+ ! NUMB] (
POSSI# C\RSE SELEC;NS 9VOLVE .P]MUT,NS
OR .-B9,NS #G @4 .,EXPLA94 ,H[ _M DI6]5T
C\RSE SELEC;NS >E POSSI#8
.#G4 .,,OP5-.,,5D$ ,GIVE AN EXAMPLE (A
R1L-LIFE PRO#M = : ! ANSW] IS ! SUM (
TWO -B9,NS4 ,%[ H[ 6F9D ! ANSW]4
.#H4 .,,GRI4$ .,,ANSW] ,AN ICE CR1M
%OP (F]S A *OICE ( #CA FLAVORS4 ,H[ _M
DI6]5T ICE CR1M C"OS C 2 MADE ) ?REE
SCOOPS ( ICE CR1M IF EA* SCOOP IS A
DI6]5T FLAVOR &! ORD] (! SCOOPS IS N
IMPORTANT8
------------------------------------#GJF
,9VE/IG,N ,ALGEBRA ,ACTIV;Y3 #AJ.D
,F9D ,PROBABILITIES ,US+ ,V5N ,DIAGRAMS
,USE 2F LESSON #AJ.D
,"Q ,H[ C Y USE A ,V5N DIAGRAM 6F9D
PROBABILITIES 9VOLV+ TWO EV5TS8
,9 ,LESSON #AJ.C1 Y LE>N$ H[ 6-PUTE !
PROBABIL;Y ( "O EV5T4 ,9 "S SITU,NS1
H["E1 Y MI<T 2 9T]E/$ 9 ! PROBABIL;Y T
TWO EV5TS W O3UR SIMULTANE\SLY4 ,Y AL
MI<T 2 9T]E/$ 9 ! PROBABIL;Y T AT L1/ "O
( TWO EV5TS W O3UR4 ,? ACTIV;Y
DEMON/RATES H[ A ,V5N DIAGRAM IS USE;L =
-PUT+ S* PROBABILITIES4
,SIDEB>3
,/&>DS
.,PROBABIL;Y .& .,/ATI/ICS3 #B.J
,/UD5TS "K ! DEF9I;N ( 3DI;NAL
PROBABIL;Y & USE X 6SOLVE =
PROBABILITIES 9 F9ITE SAMPLE SPACES4
,EXPLORE ,USE A ,V5N DIAGRAM 6COLLECT
DATA
,,/EP #A ,-PLETE A ,V5N DIAGRAM
,COPY ! ,V5N DIAGRAM %[N 2L4 ,ASK !
MEMB]S ( YR CLASS IF !Y H A SI/]1 H A
BRO!R1 H BO?1 OR H NEI4 ,WRITE _! "NS 9
! APPROPRIATE "P (! ,V5N DIAGRAM4
,,/EP #B ,-PLETE A TA#
,COPY & -PLETE ! FREQU5CY TA#4 ,:5
DET]M9+ ! FREQU5CY =A CATEGORY1 2 SURE
69CLUDE ALL ! /UD5TS :O >E 9 ! CATEGORY4
,NOTE T A /UD5T C 2L;G 6M ?AN "O
CATEGORY4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,CATEGORY3 ,NUMB] ( /UD5TS
,H A SI/]3 @8
,H A BRO!R3 @8
,H BO? A SI/] & BRO!R3 @8
,D N H A SI/] OR BRO!R3 @8
,DRAW ,3CLU.NS ,USE YR DATA 6-PLETE ^!
EX]CISES
#A4 ,A /UD5T F YR CLASS IS SELECT$ AT
R&OM4 ,F9D ! PROBABIL;Y ( EA* EV5T4
.,EXPLA9 H[ Y F.D YR ANSW]S4
A4 ,! /UD5T HAS A SI/]4
B4 ,! /UD5T HAS A BRO!R4
C4 ,! /UD5T HAS A SI/] &A BRO!R4
D4 ,! /UD5T DOES N H A SI/] OR A
BRO!R4
#B4 ,F9D ! PROBABIL;Y T A R&OMLY
SELECT$ /UD5T F YR CLASS HAS EI A SI/]
OR A BRO!R4 .,EXPLA9 H[ Y F.D YR ANSW]4
#C4 ,H[ CD Y CALCULATE ! ANSW]
6,EX]CISE #B US+ YR ANSW]S F ,EX]CISE
#A8
------------------------------------#GJG
#AJ.D ,F9D ,PROBABILITIES ( ,4JO9T &
,OV]LAPP+ ,EV5TS
,SIDEB>3
.,2F ,Y F.D PROBABILITIES ( SIMPLE
EV5TS4
.,N[ ,Y W F9D PROBABILITIES ( -P.D
EV5TS4
.,:Y8 ,S Y C SOLVE PRO#MS AB
METEOROLOGY1 Z 9 ,EX4 #DD
,KEY ,VOCABUL>Y
99 -P.D EV5T
99 OV]LAPP+ EV5TS
99 4JO9T OR MUTU,Y EXCLUSIVE EV5TS
,SIDEB>3
,/&>DS
,PROBABIL;Y & ,/ATI/ICS3 #B.J ,/UD5TS
"K ! DEF9I;N ( 3DI;NAL PROBABIL;Y & USE
X 6SOLVE = PROBABILITIES 9 F9ITE SAMPLE
SPACES4
,:5 Y 3SID] ALL ! \TCOMES = EI ( TWO
EV5TS .,A & .;,B @1 Y =M ! .UNION ( ,A&
.,B4 ,:5 Y 3SID] ONLY ! \TCOMES %>$ 0BO?
.,A & .;,B @1 Y =M ! .9T]SEC;N .( .,A &
.,B4 ,! UNION OR 9T]SEC;N ( TWO EV5TS IS
CALL$ A .-P.D .EV5T4
,UNION ( .,A & .;,B
,9T]SEC;N ( .,A & .;,B
,9T]SEC;N ( .,A & .;,B IS EMPTY4
,6F9D .;,P7.,A OR .;,B7 Y M/ 3SID] :AT
\TCOMES1 IF ANY1 >E 9 ! 9T]SEC;N ( .,A &
.,B4 ,TWO EV5TS >E .OV]LAPP+ IF !Y H "O
OR M \TCOMES 9 -MON1 Z %[N 9 ! F/
DIAGRAM4 ,TWO EV5TS >E .4JO9T @1 OR
.MUTU,Y .EXCLUSIVE @1 IF !Y H NO \TCOMES
9 -MON1 Z %[N 9 ! ?IRD DIAGRAM4
,,KEY ,,3CEPT .= .,YR .,NOTEBOOK
,PROBABIL;Y ( ,-P.D ,EV5TS
,IF .,A & .;,B >E ANY TWO EV5TS1 !N !
PROBABIL;Y ( .,A OR .;,B IS3
.;,P @7 .,A OR .;,B @7 .K .;,P @7 .,A
@7 @+ .;,P @7 .;,B @7 - .;,P @7 .,A &
.;,B @7
,IF .,A & .;,B >E 4JO9T EV5TS1 !N !
PROBABIL;Y ( .,A OR .;,B IS3
.;,P @7 .,A OR .;,B @7 .K.;,P @7 .,A
@7 @+.;,P @7 .;,B @7
,EXAMPLE #A ,F9D PROBABIL;Y ( 4JO9T
EV5TS
,A C>D IS R&OMLY SELECT$ F A /&>D DECK
( #EB C>DS4 ,:AT IS ! PROBABIL;Y T X IS
A #AJ .OR A FACE C>D8
,SOLU;N
,LET EV5T .,A 2 SELECT+ A #AJ & EV5T
.;,B 2 SELECT+ A FACE C>D4 .,A HAS #D
\TCOMES & .;,B HAS #AB \TCOMES4 ,2C .,A
& .;,B >E 4JO9T1 ! PROBABIL;Y IS3
------------------------------------#GJH
..,EXAMPLE #B ,/&>DIZ$ ,TE/ .,PRACTICE
,A C>D IS R&OMLY SELECT$ F A /&>D DECK
( #EB C>DS4 ,:AT IS ! PROBABIL;Y T X IS
A FACE C>D .OR A SPADE8
.,A
.;,B
.;,C
.;,D
,SOLU;N
,,AVOID ,,]RORS
,:5 TWO EV5TS .,A & .;,B OV]LAP1 Z 9
,EXAMPLE .#B1 .;,P7.,A OR .;,B7 DOES N
EQUAL .;,P7.,A7 @+ .;,P7.;,B74
,LET EV5T .,A 2 SELECT+ A FACE C>D &
EV5T .;,B 2 SELECT+ A SPADE4 .,A HAS #AB
\TCOMES & .;,B HAS #AC \TCOMES4 ,( ^!1
#C \TCOMES >E -MON 6.,A & .,B4 ,S1 !
PROBABIL;Y ( SELECT+ A FACE C>D .OR A
SPADE IS3
,! CORRECT ANSW] IS ,B4 ..,A ;,B ;,C
.;,D
,EXAMPLE #C ,USE A =MULA 6F9D .;,P @7
.,A & .;,B @7
.,,S5IOR .,,CLASS ,\ ( #BJJ /UD5TS 9 A
S5IOR CLASS1 #AAC /UD5TS >E EI V>S;Y
A?LETES .OR ON ! HONOR ROLL4 ,"! >E #GD
S5IORS :O >E V>S;Y A?LETES & #EA S5IORS
:O >E ON ! HONOR ROLL4 ,:AT IS !
PROBABIL;Y T A R&OMLY SELECT$ S5IOR IS
BO? A V>S;Y A?LETE .& ON ! HONOR ROLL8
,SOLU;N
,LET EV5T .,A 2 SELECT+ A S5IOR :O IS
A V>S;Y A?LETE & EV5T .;,B 2 SELECT+ A
S5IOR ON ! HONOR ROLL4 ,F ! GIV5 9=M,N Y
"K T
@4 ,F9D .;,P @7 .,A & .;,B @7@4
..,GUID$ ,PRACTICE = ,EXAMPLES #A1 #B
@1 & .#C
,A C>D IS R&OMLY SELECT$ F A /&>D DECK
( #EB C>DS4 ,F9D ! PROBABIL;Y (! GIV5
EV5T4
.#A4 ,SELECT+ AN ACE .OR AN EI<T
.#B4 ,SELECT+ A #AJ .OR A DIAMOND
.#C4 .,,:AT .,,IF8 ,9 ,EXAMPLE #C1
SUPPOSE #CB S5IORS >E 9 ! B& & #FD
S5IORS >E 9 ! B& .OR ON ! HONOR ROLL4
,:AT IS ! PROBABIL;Y T A R&OMLY SELECT$
S5IOR IS BO? 9 ! B& .& ON ! HONOR ROLL8
------------------------------------#GJI
.,,-PLE;TS ,! EV5T ,A1 CALL$ ! .-PLE;T
( EV5T .,A @1 3SI/S ( ALL \TCOMES T >E N
9 ,A ,! NOT,N .,A IS R1D Z 8.,A B>40
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,PROBABIL;Y (! ,-PLE;T ( AN ,EV5T
,! PROBABIL;Y (! -PLE;T ( .,A IS .;P7
@7 .K #A -- .;,P7.,A7
,EXAMPLE #D ,F9D PROBABILITIES (
-PLE;TS
,,ANO!R ,,WAY
,= AN ALT]NATIVE ME?OD = SOLV+ ! PRO#M
9 ,EXAMPLE #D1 TURN 6PAGE #GAD =! ,PRO#M
,SOLV+ ,"W%OP4
.,,DICE ,:5 TWO SIX-SID$ DICE >E
ROLL$1 "! >E #CF POSSI# \TCOMES1 Z %[N4
,F9D ! PROBABIL;Y (! GIV5 EV5T4
.A4 ,! SUM IS N #F4
.B4 ,! SUM IS LESS ?AN OR EQUAL 6#I4
,SOLU;N
.A4
.B4
,EXAMPLE #E ,USE A -PLE;T 9 R1L LIFE
.,,=TUNE .,,COOKIES ,A RE/AURANT GIVES
A FREE =TUNE COOKIE 6E GUE/4 ,!
RE/AURANT CLAIMS "! >E #EJJ DI6]5T
MESSAGES HI45 9SIDE ! =TUNE COOKIES4
,:AT IS ! PROBABIL;Y T A GR\P ( #E P RCV
AT L1/ #B =TUNE COOKIES )! SAME MESSAGE
9SIDE8
,SOLU;N
,! NUMB] ( WAYS 6GIVE MESSAGES 6! #E P
IS .#EJJ #E @4 ,! NUMB] ( WAYS 6GIVE
.DI6]5T MESSAGES 6! #E P IS #EJJ 99 #DII
99 #DIH 99 #DIG 99 #DIF4 ,S1 !
PROBABIL;Y T AT L1/ #B (! #E P H ! SAME
MESSAGE IS3
.;,P 7AT L1/ #B >E ! SAME7 .K #A --
.;,P 7N"O >E ! SAME7
#JAII
..,GUID$ ,PRACTICE = ,EXAMPLES #D &
.#E
.,F9D .;,P @7 @7@4
.#D4 .;,P @7 .,A @7 .K #J.DE
.#E4
.#F4 .;,P @7 .,A @7 .K #A
.#G4 .;,P @7 .,A @7 .K #J.JC
.#H4 .,,:AT .,,IF8 ,9 ,EXAMPLE #E1 H[
DOES ! ANSW] *ANGE IF "! >E ONLY #AJJ
DI6]5T MESSAGES HI45 9SIDE ! =TUNE
COOKIES8
------------------------------------#GAJ
#AJ.D ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#AH = ,EXS4 #AA1BA1 & #DE
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 #B1AE1CD1 #CI1DJ1DD1 & #DG
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,!
UNION OR 9T]SEC;N ( TWO EV5TS IS CALL$
A7;N7 @8 @4
#B4 .,,WRIT+ ,>E ! EV5TS .,A & .,A
4JO9T8 .,EXPLA94 ,!N GIVE AN EXAMPLE (A
R1L-LIFE EV5T & XS -PLE;T4
,,4JO9T ,EV5TS .,A & .;,B >E 4JO9T4
,F9D .;,P @7 .,A .OR .;,B @7@4
.,,EXAMPLE #A
ON P4 #GJG .= .,EXS4 .#C-.H
.#C4 .;,P @7 .,A @7 .K #J.C1 .;,P @7
.;,B @7 .K #J.A
.#D4 .;,P @7 .,A @7 .K #J.EE1 .;,P @7
.;,B @7 .K #J.B
.#E4 .;,P @7 .,A @7 .K #J.DA1 .;,P @7
.;,B @7 .K #J.BD
.#F4
.#G4
.#H4
,,OV]LAPP+ ,,EV5TS ,F9D ! 9DICAT$
PROBABIL;Y4
,,EXAMPLES #B & #C
ON P4 #GJH = ,EXS4 #I-AE
.#I4 .;,P7.,A7 .K #J.E1 .;,P7.;,B7 .K
#J.CE
.;,P @7 .,A & .;,B @7 .K #J.B
.;,P @7 .,A .OR .;,B @7 .K?
.#AJ4 .;,P 7,A7 .K #J.F1 .;,P @7 .;,B
@7 .K #J.B
.;,P @7 .,A OR .;,B @7 .K #J.G
.;,P 7,A& .;,B @7 .K @8
.#AA4 ;,P7 .,A @7 .K #J.BH1 .;,P @7
.;,B @7 .K #J.FD
.;,P 7,A OR .;,B @7 .K #J.GA
.;,P @7 .,A & .;,B @7 .K @8
.#AB4 .;,P @7 .,A @7 .K #J.DF1 ;,P7
.;,B @7 .K #J.CG
.;,P @7 .,A & .;,B @7 .K #J.CA
.;,P7.,A OR ;,B7 .K @8
.#AC4
.#AD4
#AE4 .,,MULTIPLE .,,*OICE ,:AT IS .;,P
@7 .,A OR .;,B @7 IF @7 .,A @7 .K #J.DA1
;,P7 .;,B7 .K #J.EC1 & .;,P @7 .,A &
.;,B7 .K #J.BG8
,A #J.AB
;,B #J.FG
;,C #J.HJ
;,D #J.ID
,,F9D+ ,,PROBABILITIES ,,( ,,-PLE;TS
,F9D .;P7 @7@4
,,EXAMPLE #D
ON P4 #GJI = ,EXS4 #AF-AI
.#AF4 ;,P7 .,A @7 .K #J.E
.#AG4 ;,P7,A7 .K #J
.#AH4
.#AI4
,,*OOS+ ,,C>DS ,A C>D IS R&OMLY
SELECT$ F A /&>D DECK ( #EB C>DS4 ,F9D !
PROBABIL;Y ( DRAW+ ! GIV5 C>D4
.#BJ4 ,A K+ .& A DIAMOND
.#BA4 ;J ,A K+ .OR A DIAMOND
.#BB4 ,A SPADE .OR A CLUB
.#BC4 ,A #D OR A #E
.#BD4 ,A #F .& A FACE C>D
.#BE4 ,NO8 A HE>T
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 F9D+ ! PROBABIL;Y ( R&OMLY
DRAW+ ! GIV5 C>D F A /&>D DECK ( #EB
C>DS4
#BF4
#BG4
------------------------------------#GAA
.,,F9D+ .,,PROBABILITIES ,F9D !
9DICAT$ PROBABIL;Y4 ,/ATE :E!R .,A &
.;,B >E 4JO9T EV5TS4
.#BH4 .;,P @7 .,A @7 .K #J.BE
.;,P7.;,B7 .K #J.D
.;,P @7 .,A OR .;,B @7 .K #J.EJ
.;,P @7 .,A & #E7 .K @8
.#BI4 .;,P7.,A7 .K #J.F
.;,P @7 .;,B @7 .K #J.CB
.;,P @7 .,A OR #E7 .K @8
;,P7 .,A & .;,B @7 .K #J.BE
.#CJ4 .;,P @7 .,A @7 .K @8
.;,P @7 .;,B @7 .K #J.CH
.;,P @7 .,A OR .;,B @7 .K #J.FE
.;,P @7 .,A & ;,B7 .K #J
.#CA4
.#CB4
.#CC4 ;,P7,A7 .K #AF@3P
.;,P @7 .;,B @7 .K?
;,P7 .,A OR #E7 .K #CB@3P
.;,P @7 .,A & .;,B @7 .K #H@3P
.#CD4 .,,OP5-.,,5D$ .,,MA? .,DESCRIBE
A R1L-LIFE SITU,N T 9VOLVES TWO 4JO9T
EV5TS .,A & .,B4 ,!N DESCRIBE A R1L-LIFE
SITU,N T 9VOLVES TWO OV]LAPP+ EV5TS ;,C
& .,D4
.,,ROLL+ .,,DICE ,TWO SIX-SID$ DICE >E
ROLL$4 ,F9D ! PROBABIL;Y (! GIV5 EV5T4
7,REF] 6,EXAMPLE #D ON PAGE #GJI =!
POSSI# \TCOMES47
.#CE4 ,! SUM IS #C OR #D4
.#CF4 ,! SUM IS N #G4
.#CG4 ,! SUM IS GRT] ?AN OR EQUAL 6#E4
.#CH4 ,! SUM IS LESS ?AN #H OR GRT]
?AN #AA4
#CI4 99 .,,MULTIPLE .,,*OICE ,TWO
SIX-SID$ DICE >E ROLL$4 ,:AT IS !
PROBABIL;Y T ! SUM IS A PRIME NUMB]8
,A
;,B
;,C
;,D
#DJ4 .,,%ORT .,,RESPONSE ,USE ! F/
DIAGRAM AT ! "R 6EXPLA9 :Y ? EQU,N IS
TRUE3
.;,P @7 .,A @7 @+ .;,P @7 .;,B @7 .K
.;,P @7 .,A OR .;,B @7 @+ .;,P @7 .,A &
.;,B @7
,EX#.DJ
,EX#.DA
#DA4 .,,*ALL5GE ,USE ! SECOND DIAGRAM
AT ! "R 6DERIVE A =MULA = .;,P7.,A OR
.;,B OR ;,C74
,PRO#M ,SOLV+
,,EXAMPLES #A1 #B1 & #C
ON PP4 #GJG-GJH = ,EXS4 #DB-DD
.#DB4 .,,CLASS .,,ELEC;NS ,Y & YR BE/
FR >E AM;G S"EAL C&IDATES RUNN+ = CLASS
PRESID5T4 ,Y E/IMATE T "! IS A #DE@3P
*.E Y W W9 &A #BE@3P *.E YR BE/ FR W W94
,:AT IS ! PROBABIL;Y T EI Y OR YR BE/ FR
W9 ! ELEC;N8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#DC4 .,,BIOLOGY ,Y >E P]=M+ AN
EXP]I;T 6DET]M9E H[ WELL PLANTS GR[ "U
DI6]5T LI<T S\RCES4 ,\ (! #CJ PLANTS 9 !
EXP]I;T1 #AB RCV VISI# LI<T1 #AE RCV
ULTRAVIOLET LI<T1 & #F RCV BO? VISI# &
ULTRAVIOLET LI<T4 ,:AT IS ! PROBABIL;Y T
A PLANT 9 ! EXP]I;T RCVS EI VISI# LI<T
OR ULTRAVIOLET LI<T8
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
------------------------------------#GAB
,,EXAMPLES #D & #E
ON .P4 #GJI = ,EXS4 #DD-DF
#DD4 .,,MULTIPLE .,,*OICE ,REF] 6! *>T
2L4 ,: (! FOLL[+ PROBABILITIES IS GRTE/8
,A .;,P 7RA9S ON ,SUN"D7
;,B ;,P7DOES N RA9 ON ,SATUR"D7
;,C .;,P 7RA9S ON ,MON"D7
;,D ;,P7DOES N RA9 ON ,FRI"D7
#DE4 .,,DRAMA .,,CLUB ,! ORGANIZ] (A
CA/ "PY =A DRAMA CLUB ASKS EA* ( #F CA/
MEMB]S 6BR+ "O FOOD ITEM F A LI/ ( #AJ
ITEMS4 ,:AT IS ! PROBABIL;Y T AT L1/ #B
(! #F CA/ MEMB]S BR+ ! SAME ITEM8
#DF4 .,,HOME .,,ELECTRONICS ,A
DEVELOP;T HAS #F H\SES )! SAME MODEL (
G>AGE DOOR OP5]4 ,EA* OP5] HAS #DJIF
POSSI# TRANSMITT] CODES4 ,:AT IS !
PROBABIL;Y T AT L1/ #B (! #F H\SES H !
SAME CODE8
#DG4 .,,EXT5D$ .,,RESPONSE ,USE ! GIV5
9=M,N AB A F>M]'S TOMATO CROP 6-PLETE
"PS 7A7-7;C74
A4 #DJ@3P (! TOMATOES >E "PI,Y ROTT51
#CJ@3P (! TOMATOES H BE5 F$ ON 09SECTS1
& #AB@3P >E "PI,Y ROTT5 .& H BE5 F$ ON
09SECTS4 ,:AT IS ! PROBABIL;Y T A R&OMLY
SELECT$ TOMATO IS "PI,Y ROTT5 .OR HAS
BE5 F$ ON 09SECTS8
B4 #BJ@3P (! TOMATOES H BITE M>KS F A
*IPMUNK & #G@3P H BITE M>KS .& >E "PI,Y
ROTT54 ,:AT IS ! PROBABIL;Y T A R&OMLY
SELECT$ TOMATO HAS BITE M>KS .OR IS
"PI,Y ROTT58
C4 ,SUPPOSE ! F>M] F9DS \ T #F@3P (!
TOMATOES H BITE M>KS .& H BE5 F$ ON
09SECTS4 ,D Y H 5 9=M,N 6DET]M9E !
PROBABIL;Y T A R&OMLY SELECT$ TOMATO HAS
BE5 F$ ON 09SECTS .OR IS "PI,Y ROTT5 .OR
HAS BITE M>KS F A *IPMUNK8 ,IF N1 :AT
O!R 9=M,N D Y REQUIRE8
#DH4 .,,MULTI-.,,/EP .,,PRO#M ,FOLL[ !
/EPS 2L 6EXPLORE A FAM\S PROBABIL;Y
PRO#M CALL$ ! .BIR?"D .PRO#M4 7,ASSUME T
"! >E #CFE POSSI# BIR?"DS47
A4 .,CALCULATE ,SUPPOSE T #F P >E *OS5
AT R&OM4 ,F9D ! PROBABIL;Y T AT L1/ #B
(! P %>E ! SAME BIR?"D4
B4 .,CALCULATE ,SUPPOSE T #AJ P >E
*OS5 AT R&OM4 ,F9D ! PROBABIL;Y T AT L1/
#B (! P %>E ! SAME BIR?"D4
C4 .,MODEL ,G5]ALIZE ! RESULTS F "PS
7A7 & 7;B7 0WRIT+ A =MULA =! PROBABIL;Y
.;,P7.;X7 T AT L1/ #B P 9 A GR\P ( .;X P
%>E ! SAME BIR?"D4 @7 .,H9T3 ,USE ;N
.;,P ;R.' .-NOT,N 9 YR =MULA47
D4 .,ANALYZE ,5T] ! =MULA F "P 7;C7
96A GRAPH+ CALCULATOR4 ,USE ! .TA#
F1TURE 6MAKE A TA# ( VALUES4 ,= :AT GR\P
SIZE DOES ! PROBABIL;Y T AT L1/ #B P %>E
! SAME BIR?"D F/ EXCE$ #EJ@3P8
.K ..,,"W$-,,\ ,,SOLU;NS ONP4.,,WS,'L
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#GAC
.#DI4 .,,PET .,,/ORE ,A PET /ORE HAS
#H BLACK ,LABRADOR RETRIEV] PUPPIES 7#E
FEMALES & #C MALES7 & #AB YELL[
,LABRADOR RETRIEV] PUPPIES 7#D FEMALES &
#H MALES74 ,Y R&OMLY *OOSE "O (!
,LABRADOR RETRIEV] PUPPIES4 ,:AT IS !
PROBABIL;Y T X IS A FEMALE OR A YELL[
,LABRADOR RETRIEV]8
.#EJ4 .,,*ALL5GE ,Y [N #EJ ,,DVD,'S
3SI/+ ( #BE -$IES1 #AE DRAMAS1 & #AJ
?RILL]S4 ,Y R&OMLY PICK #D MOVIES 6WAT*
DUR+ A L;G TRA9 RIDE4 ,:AT IS !
PROBABIL;Y T Y PICK AT L1/ "O ,,DVD (
EA* TYPE ( MOVIE8
,MIX$ ,REVIEW
,USE ! GIV5 VALUES 6WRITE AN EQU,N
RELAT+ .;X & .Y4 ,!N F9D ! VALUE ( ;Y :5
JC .K #H4
.#EA4 .;X1 .;Y V>Y DIRECTLY2 .;X
.K--#E1 .;Y .K #BJ @7 P4 #AJG @7
.#EB4 .;X1 .;Y V>Y DIRECTLY2 .;X .K
#ED1 .;Y .K--#I @7 ;P #AJG @7
.#EC4 .;X1 .;Y V>Y DIRECTLY2 .;X .K
#AB1 .;Y .K--#D @7 ;P #EEA @7
.#ED4 .;X1 .;Y V>Y DIRECTLY2 .;X .K --
#B1 .;Y .K--#C @7 ;P #EEA @7
,F9D ! 9V]SE (! FUNC;N1 @7 P4 #DCG @7
.#EE4 .;F7.;X7 .K .#C;X -- #G
.#EF4 ..;F7;X7 .K--.#E;X @+ #C
.#EG4 .;F7.;X7 .K--#F .;X #B @1 .;X
"K.K #J
.#EH4 .;F7.;X7 .K--#B.E .;X #E
.#EI4 .;F7.;X7 .K .#D;X #B -- #AB1 .;X
.1.K #J
#FJ4 .;F7.;X7 .K .#J..B;X #C @+ .#J..E
,,PREVIEW
,PREP>E = ,LESSON #AJ.E 9 ,EXS4
#FA-FD4
,EA* EV5T C O3UR 9 ! GIV5 NUMB] (
WAYS4 ,F9D ! NUMB] ( WAYS ALL (! EV5TS C
O3UR1 @7 P4 #FHB @7
.#FA4 ,EV5T .,A3 #B WAYS1 ,EV5T .;,B3
#D WAYS
.#FB4 ,EV5T .,A3 #AC WAYS1 ,EV5T .;,B3
#G WAYS
.#FC4 ,EV5T ,A3 #C WAYS1 ,EV5T .;,B3
#E WAYS1 ,EV5T ;,C3 #F WAYS
.#FD4 ,EV5TS3 #AB WAYS1 ,EV5T .;,B3
#AA WAYS1 ,EV5T ;,C3 #H WAYS1 ,EV5T
.;,D3 #AJ WAYS
,,QUIZ .= ,LESSONS .#AJ..C-.AJ..D
,A C>D IS R&OMLY DRAWN F A /&>D DECK (
#EB C>DS4 ,F9D ! PROBABIL;Y ( DRAW+ !
GIV5 C>D4 @7 P4 #FIH @7
.#A4 ,! QUE5 ( HE>TS
.#B4 ,AN ACE
.#C4 ,A DIAMOND
.#D4 ,A R$ C>D
.#E4 ,A C>D O!R ?AN A #AJ
.#F4 ,! #F ( CLUBS
,Y R&OMLY SELECT A M># F A BAG4 ,! BAG
3TA9S #H BLACK1 #AC R$1 #G :ITE1 & #AB
BLUE M>#S4 ,F9D ! 9DICAT$ O4S4 7.P4
#FIH7
.#G4 ,9 FAVOR ( *OOS+ BLUE
.#H4 ,9 FAVOR ( *OOS+ BLACK OR :ITE
.#I4 ,AG/ *OOS+ R$
.#AJ4 ,AG/ *OOS+ R$ OR :ITE
,F9D ! 9DICAT$ PROBABIL;Y1 @7 P4 #GJG
@7
.#AA4 .;,P @7 .,A @7 .K #J.F
.;,P @7 .;,B @7 .K #J.CE
.;,P @7 .,A .OR .;,B @7 .K @8
.;,P @7 .,A & .;,B @7 .K #J.B
.#AB4 .;,P @7 .,A @7 .K @8
.;,P @7 .;,B @7 .K #J.DD
.;,P @7 .,A .OR .;,B @7 --#J.EF
.;,P @7 .,A .& .;,B @7 .K#J.AB
.#AC4 .;,P @7 .,A @7 .K #J.GE
.;,P @7 .;,B @7 .K @8
.;,P @7 .,A .OR .;,B @7 .K#J.HC
.;,P @7 .,A .& .;,B @7 .K #J.BE
#AD4 .;,P7.,A7 .K #H@3P
.;,P7.;,B7 .K #CC@3P
.;,P @7 .,A .OR .;,B @7 .K#DA@3P
.;,P @7 .,A & .;,B @7 .K @8
.#AE4 .,,-PUT]S ,A MANUFACTUR] ( -PUT]
*IPS F9DS T #A@3P (! *IPS PRODUC$ >E
DEFECTIVE4 ,:AT IS ! PROBABIL;Y T \ ( #H
*IPS1 AT L1/ #B >E DEFECTIVE8 @7 P4 #GJG
@7
.,,EXTRA .,,PRACTICE = ,LESSON #AJ.D1
P4 #AJAI
,,ONL9E ,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#GAD
,PRO#M ,SOLV+ ,"W%OP ,LESSON #AJ.D3
,US+ ,ALT]NATIVE ,ME?ODS
..,ANO!R ,WAY 6,SOLVE .,EXAMPLE #D1
PAGE #GJI
.,,MULTIPLE .,,REPRES5T,NS ,9 ,EXAMPLE
#D ON PAGE #GJI @1 Y F.D !ORETICAL
PROBABILITIES 9VOLV+ ! SUM ( TWO DICE4
,Y C AL P]=M A .SIMUL,N 6E/IMATE ^!
PROBABILITIES4
,PRO#M
.,,DICE ,:5 TWO SIX-SID$ DICE >E
ROLL$1 "! >E #CF POSSI# \TCOMES4 ,F9D !
PROBABIL;Y (! GIV5 EV5T4
.A4 ,! SUM IS N #F4
.B4 ,! SUM IS LESS ?AN OR EQUAL 6#I4
,ME?OD
.,US+ .A .,SIMUL,N ,AN ALT]NATIVE
APPROA* IS 6USE ! R&OM NUMB] F1TURE (A
GRAPH+ CALCULATOR 6SIMULATE ROLL+ TWO
DICE4 ,Y C !N USE ! RESULTS (! SIMUL,N
6F9D ! EXP]I;TAL PROBABILITIES =! PRO#M4
,SIDEB>3
,/&>DS
.,PROBABIL;Y .& .,/ATI/ICS3 #B.J
,/UD5TS "K ! DEF9I;N ( 3DI;NAL
PROBABIL;Y & USE X 6SOLVE =
PROBABILITIES 9 F9ITE SAMPLE SPACES4
.,,/EP .#A .,G5]ATE TWO LI/S ( #ABJ
R&OM 9TEG]S F #A 6#F 05T]+ ;R &
LNT7;L1#F1ABJ7 96LI/S ;,L #A & ;,L #B @4
,DEF9E LI/ ;,L #C 6BE ! SUM ( LI/S ;,L
#A & ;,L #B @4
.,,/EP .#B .,SORT ! SUMS 9 LI/ ;,L #C
9 ASC5D+ ORD] US+ ! -M& ,SORT,A7;,L #C
@7@4 ,SCROLL "? ! LI/ & C.T ! FREQU5CY (
EA* SUM4
.,,/EP .#C .,F9D ! PROBABILITIES4
A4 ,DIVIDE ! NUMB] ( "TS ! SUM 0 #F 0!
TOTAL NUMB] ( SIMULAT$ ROLLS1 !N
SUBTRACT ! RESULT F #A4
B4 ,DIVIDE ! NUMB] ( "TS ! SUM 0 GRT]
?AN #I 0! TOTAL NUMB] ( SIMULAT$ ROLLS1
!N SUBTRACT ! RESULT F #A4
,PRACTICE
.#A4 .,,WRIT+ .,-P>E ! PROBABILITIES
F.D 9 ! SIMUL,N ABV )! !ORETICAL
PROBABILITIES F.D 9 ,EXAMPLE #D ON PAGE
#GJI @4
.#B4 .,,SIMUL,NS ,USE ! RESULTS (!
SIMUL,N ABV 6F9D ! EXP]I;TAL PROBABIL;Y
T ! SUM IS GRT] ?AN OR EQUAL 6#D4 .,-P>E
? 6! !ORETICAL PROBABIL;Y (! EV5T4
.#C4 .,,SIMUL,NS ,USE ! RESULTS (!
SIMUL,N ABV 6F9D ! EXP]I;TAL PROBABIL;Y
T ! SUM IS N #H OR #I4 .,-P>E ? 6!
!ORETICAL PROBABIL;Y (! EV5T4
.#D4 .,,R1SON+ ,H[ CD Y *ANGE !
SIMUL,N ABV S T ! RESULTS WD 2 CLOS] 6!
!ORETICAL PROBABILITIES (! EV5TS8
.,EXPLA94
------------------------------------#GAE
,EXT5.N ,APPLY ,SET ,!ORY
,USE AF ,LESSON #AJ.D
,KEY ,VOCABUL>Y
99 SET
99 UNION
99 9T]SEC;N
99 -PLE;T
99 SUBSET
,SIDEB>3
,/&>DS
,5RI*;T TOPIC2 N REQUIR$ 0! ,CALI=NIA
,/&>DS
.,GOAL ,DEF9E ! 3CEPTS ( SETS1 OP],NS
ON SETS1 & SUBSETS4
,A .SET IS A COLLEC;N ( 4T9CT OBJECTS4
,EA* OBJECT 9 A SET IS CALL$ AN .ELE;T
OR .MEMB] (! SET4 ,A SET IS DENOT$
05CLOS+ XS ELE;TS 9 BRACES4 ,= EXAMPLE1
IF .,A IS ! SET ( POSITIVE 9TEG]S LESS
?AN #E1 !N .,A .K 7#A1 #B1 #C1 #D724
,"! >E TWO SPECIAL SETS T >E (T5 US$4
,! SET ) NO ELE;TS IS CALL$ ! .EMPTY
.SET & IS DENOT$ 0#J4 ,! SET ( ALL
ELE;TS "U 3SID],N IS CALL$ ! .UNIV]SAL
.SET & IS DENOT$ 0.,U4
,,KEY ,,3CEPT
,= YR NOTEBOOK
,OP],NS ON ,SETS
,! .UNION ( TWO SETS .,A & .;,B IS
WRITT5 Z .,A .;,B & IS ! SET ( ALL
ELE;TS 9 ..EI ,A OR .,B4
,A ;,B
,! .9T]SEC;N ( TWO SETS .,A & .;,B IS
WRITT5 Z .,A .;,B & IS ! SET ( ALL
ELE;TS 9 .BO? .,A & .,B4
,A ;,B
,! .-PLE;T (A SET .,A IS WRITT5 Z & IS
! SET ( ALL ELE;TS 9 ! UNIV]SAL SET ;,U
T >E .N .9 .,A4
,EXAMPLE #A ,P]=M OP],NS ON SETS
,LET .;,U .2 ! SET ( ALL 9TEG]S F #A
6#AJ4 .,LET .,A .K ;7#A1B1 #D1H72 & LET
.;,B .K ;7#B1D1 #F1H1AJ724 ,F9D !
9DICAT$ SET4
A4 .,A .;,B
B4 .,A .;,B
.C4
.D4
,SOLU;N
.A4 ..,A ;,B .K ;7.#A @1 #B1 #D1 #H72
;,U ;7#B1 #D1 #F1 #H1 #AJ72 .K ;7#A1 #B1
#D1 #F1 #H1 #AJ72
.B4 .,A .;,B .K ;7#A1 #B1 #D1 #H72 ;,H
;7#B1 #D1 #F1 #H1 #AJ72 .K ;7#B1 #D1
#H72
.C4
.D4
------------------------------------#GAF
.,,SUBSETS ,IF E ELE;T (A SET ,A IS AL
AN ELE;T (A SET .;,B @1 !N .,A IS A
.SUBSET ( .;,B @4 ,? REL,N%IP IS WRITT5
.Z .;,,AC .,B4 ,= ANY SET ..,A #J ;,C
,A& .,A ;,C .,A4 ,9 ! DIAGRAM AT ! "R1
.,A IS A SUBSET ( .,B4
,EXAMPLE #B ,ID5TIFY SUBSETS
.,LET ,A .K ;7-#B1A1 @1 @72@1 .;,B .K
;7#A1 @1 #E721 .& .;,C .K ;7-.#B @1 .#A
@1 #C1 @1 #E724
.A4 ,IS ;,B ,A8
.B4 ,IS ;,B ;,C8
.C4 ,IS ;,C 7,A ;,B78
,SOLU;N
.A4 ,N E ELE;T ( .;,B IS AN ELE;T (
,A1 2C #E IS N AN ELE;T ( .,A4 ,S1 .;,B
IS .N .A SUBSET ( .,A4
.B4 ,E ELE;T ( .;,B IS AN ELE;T ( ,C4
,S1 .;,B .IS A SUBSET ( .;,C @4
.C4 ,NOTE T .,A .;,B.K ;7-#B1 #A1 @1
@72 ;7#A1 @1 #E72 .K ;7-#B1 #A1 @1 @1
#E724 ,N E ELE;T ( .;,C IS AN ELE;T (
.,A .;,B @1 2C #C IS N AN ELE;T ( .,A
.;,B @4 ,S1 ;,C IS .N A SUBSET ( .,A
.,B4
,PRACTICE
.,,EXAMPLE .#A ON ;P #GAE = ,EXS4 #A
--#H
,,OP],NS ,,ON ,,SETS ,LET 2 ! SET (
ALL :OLE NUMB]S F #A 6#BJ4 ,LET .,A .K
;7#B1 #C1 #E1 #G1AA1AC1AG721 .;,B .K
;7#A1 #D1 #I1 #AF721 & ;,C .K ;7#B1 #E1
#H1AA1AD1AG1 #BJ724 ,F9D ! 9DICAT$ SET4
.#A4 ,A ;,B
.#B4 ,A ;,B
.#C4
.#D4
.#E4 ,A .;,B ;,C
.#F4
.#G4
.#H4 .;,B 7,A ;,C7
.,,EXAMPLE #B
ON P4 #GAF = ,EXS4 #I-AB
.,,SUBSETS .,LET ,A .K ;7-#E1 @1
.#AJ72 @1 .;,B -- ;7-#E1 .#A @1 ,#AJ721
.& .;,C -- ;7-#E1 #B1 ,#AJ724
.#I4 ,IS ,A ;,B8
.#AJ4 ,IS ,A ;,C8
.#AA4 ,IS @7 .,A .;,B @7 .;,C @8
.#AB4 .,,R1SON+ ,LI/ ALL ! SUBSETS (!
SET ,A .K ;7-#B1 #D1 #I724
,,OP],NS ,,ON ,,SETS ,3SID] ! SETS
DEF9$ 2L4 ,F9D ! 9DICAT$ SET4
.;,U .K ! SET ( ALL #AB MON?S
.;,X .K ! SET ( ALL #CJ "D MON?S
.;,Y .K ! SET ( ALL #CA "D MON?S
.;,Z .K ! SET ( ALL MON?S 5D+ ) @8 OR
@8
#AC4 .;,X .;,Z
#AD4 .;,X .;,Y
.#AE4
.#AF4
.#AG4 .,,R1SON+ ,IS ! SET ( ALL
IRR,NAL NUMB]S A SUBSET (! R1L NUMB]S8
(! 9TEG]S8 .,EXPLA94
.#AH4 .,,RADIO ,TWO RADIO T[]S >E SET
UP AT PO9TS .,A & .;,B ON ! MAP AT ! "R4
,EA* RADIO T[] HAS A SIGNAL T C R1* T[NS
UP 6#EJ MILES AWAY4 ,F9D ! SET ( ALL
T[NS T C RCV A SIGNAL F BO? (! T[]S4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
------------------------------------#GAG
#AJ.E ,F9D ,PROBABILITIES (
,9DEP5D5T & ,DEP5D5T ,EV5TS
,SIDEB>3
.,2F ,Y F.D PROBABILITIES ( -P.D
EV5TS4
.,N[ ,Y W EXAM9E 9DEP5D5T & DEP5D5T
EV5TS4
.,:Y8 ,S Y C =MULATE COA*+ /RATEGIES1
Z 9 ,EX4 #DA4
,KEY ,VOCABUL>Y
99 9DEP5D5T EV5TS
99 DEP5D5T EV5TS
99 3DI;NAL PROBABIL;Y
,SIDEB>3
,/&>DS
#AI.J ,/UD5TS USE -B9,NS & P]MUT,NS
6-PUTE PROBABILITIES4
,TWO EV5TS >E .9DEP5D5T IF ! O3URR;E (
"O HAS NO E6ECT ON ! O3URR;E (! O!R4 ,=
9/.E1 IF A CO9 IS TOSS$ TWICE1 ! \TCOME
(! F/ TOSS 7H1DS OR TAILS7 HAS NO E6ECT
ON ! \TCOME (! SECOND TOSS4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,PROBABIL;Y ( ,9DEP5D5T ,EV5TS
,IF .,A & .;,B >E 9DEP5D5T EV5TS1 !N !
PROBABIL;Y T BO? .,A & .;,B O3UR IS3
.;,P @7 .,A & .;,B @7 .K .;,P @7 .,A
@7 99 .;,P @7 .;,B @7
,M G5],Y1 ! PROBABIL;Y T .;N 9DEP5D5T
EV5TS O3UR IS ! PRODUCT (! .;N
PROBABILITIES (! 9DIVIDUAL EV5TS4
.,EXAMPLE .#A
,/&>DIZ$ ,TE/ ,PRACTICE
,=A FUNDRAIS]1 A CLASS SELLS #AEJ
RA6LE TICKETS =A MALL GIFT C]TIFICATE &
#BJJ RA6LE TICKETS =A BOOKLET ( MOVIE
PASSES4 ,Y BUY #E RA6LE TICKETS = EA*
PRIZE4 ,:AT IS ! PROBABIL;Y T Y W9 BO?
PRIZES8
.,A
.;,B
.;,C
.;,D
,SOLU;N
,LET EV5TS .,A & .;,B 2 GETT+ ! W9N+
TICKET =! GIFT C]TIFICATE & MOVIE
PASSES1 RESPECTIVELY4 ,! EV5TS >E
9DEP5D5T4 ,S1 ! PROBABIL;Y IS3
,! CORRECT ANSW] IS ,B4 ..,A ;,B ;,C
.;,D
.,GUID$ .,PRACTICE = ,EXAMPLE #A
.#A4 .,,:AT .,,IF8 ,9 ,EXAMPLE #A1 :AT
IS ! PROBABIL;Y T Y W9 ! MALL GIFT
C]TIFICATE B N ! BOOKLET ( MOVIE PASSES8
------------------------------------#GAH
,EXAMPLE #B ,F9D PROBABIL;Y ( ?REE
9DEP5D5T EV5TS
.,,RAC+ ,9 A ,,BMX MEET1 EA* H1T 3SI/S
( #H -PETITORS :O >E R&OMLY ASSIGN$
LANES F #A 6#H4 ,:AT IS ! PROBABIL;Y T A
RAC] W DRAW LANE #H 9 ! #C H1TS 9 : !
RAC] "PICIPATES8
,SOLU;N
,LET EV5TS .,A1 .;,B @1 & ;,C 2 DRAW+
LANE #H 9 ! F/1 SECOND1 & ?IRD H1TS1
RESPECTIVELY4 ,! ?REE EV5TS >E 9DEP5D5T4
,S1 ! PROBABIL;Y IS3
,,EXAMPLE #C ,USE A -PLE;T 6F9D A
PROBABIL;Y
.,,MUSIC ,:ILE Y >E RID+ 6S*OOL1 YR
PORTA# ;,,CD PLAY] R&OMLY PLAYS #D
DI6]5T S;GS F A ;,,CD ) #AF S;GS ON X4
,:AT IS ! PROBABIL;Y T Y W HE> YR
FAVORITE S;G ON ! ;,,CD AT L1/ ONCE DUR+
! WEEK 7#E "DS78
,SOLU;N
,= "O "D1 ! PROBABIL;Y ( .N HE>+ YR
FAVORITE S;G IS3
,HE>+ OR N HE>+ YR FAVORITE S;G ON
,MON"D1 ON ,TUES"D1 & S ON >E 9DEP5D5T
EV5TS4 ,S1 ! PROBABIL;Y ( HE>+ ! S;G AT
L1/ ONCE IS3
.,GUID$ .,PRACTICE = ,EXAMPLES #B & #C
.#B4 .,,SP9N] ,A SP9N] IS DIVID$ 96T5
EQUAL REGIONS NUMB]$ #A 6#AJ4 ,:AT IS !
PROBABIL;Y T #C 3SECUTIVE SP9S RESULT 9
P]FECT SQU>ES8
.#C4 .,,:AT .,,IF8 ,9 ,EXAMPLE #C1 H[
DOES YR ANSW] *ANGE IF ! ;,,CD HAS ONLY
#AB S;GS ON X8
,,3DI;NAL ,,PROBABILITIES
,! 3DI;NAL PROBABIL;Y ( .;,B GIV5 .,A
C 2 GRT] ?AN1 LESS ?AN1 OR EQUAL 6!
PROBABIL;Y ( .,B4
.,,DEP5D5T .,,EV5TS ,TWO EV5TS .,A &
.;,B >E DEP5D5T EV5TS IF ! O3URR;E ( "O
A6ECTS ! O3URR;E (! O!R4 ,! PROBABIL;Y T
.;,B W O3UR GIV5 T .,A HAS O3URR$ IS
CALL$ ! 3DI;NAL PROBABIL;Y ( .;,B GIV5
.,A & IS WRITT5 Z .;,P7.;,B _\ .,A74
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,PROBABIL;Y ( ,DEP5D5T ,EV5TS
,IF .,A & .;,B >E DEP5D5T EV5TS1 !N !
PROBABIL;Y T BO? .,A & .;,B O3UR IS3
.;,P @7 .,A & .;,B @7 -- .;,P @7 .,A
@7 99 .;,P @7 .;,B_\.,A @7
------------------------------------#GAI
,EXAMPLE #D ,F9D A 3DI;NAL PROBABIL;Y
.,,W1!R ,! TA# %[S ! NUMB]S ( TROPICAL
CYCL"OS T =M$ DUR+ ! HURRICANE S1SONS F
#AIHH 6#BJJD4 ,USE ! TA# 6E/IMATE 7A7 !
PROBABIL;Y T A FUTURE TROPICAL CYCL"O IS
A HURRICANE & 7.;B7 ! PROBABIL;Y T A
FUTURE TROPICAL CYCL"O 9 ! ,NOR!RN
,HEMISPH]E IS A HURRICANE4
,! FOLL[+ TA# IS 9 LI/$
=MAT4 ,= EA* CELL ! H1D+ IS %[N
FOLL[$ 0A COLON1 SPACE &! CELL
3T5TS
,TYPE ( ,TROPICAL ,CYCL"O3 ,TROPICAL
DEPRES.N
,NOR!RN ,HEMISPH]E3 #AII
,S\!RN ,HEMISPH]E3 #AH
,NO H1D+3
,TYPE ( ,TROPICAL ,CYCL"O3 ,TROPICAL
/ORM
,NOR!RN ,HEMISPH]E3
,S\!RN ,HEMISPH]E3 #CIH
,NO H1D+3 #BJJ
,TYPE ( ,TROPICAL ,CYCL"O3 ,HURRICANE
,NOR!RN ,HEMISPH]E3
,S\!RN ,HEMISPH]E3 #EDE
,NO H1D+3 #BAE
,SOLU;N
.A4
.B4 ;,P7HURRICANE _\ ,NOR!RN
,HEMISPH]E7
,EXAMPLE #E ,-P>+ 9DEP5D5T & DEP5D5T
EV5TS
.,,SELECT+ .,,C>DS ,Y R&OMLY SELECT
TWO C>DS F A /&>D DECK ( #EB C>DS4 ,:AT
IS ! PROBABIL;Y T ! F/ C>D IS N A HE>T
&! SECOND IS A HE>T IF 7A7 Y REPLACE !
F/ C>D 2F SELECT+ ! SECOND1 & 7.;B7 Y D
.N REPLACE ! F/ C>D8
,SOLU;N
,,AVOID ,,]RORS
,X IS IMPORTANT 6F/ DET]M9E :E!R .,A &
.;,B >E 9DEP5D5T OR DEP5D5T 9 ORD]
6CALCULATE .;,P7.,A & .;,B7 CORRECTLY4
,LET .,A 2 8! F/ C>D IS N A HE>T0 &
.;,B 2 8! SECOND C>D IS A HE>T40
.A4 ,IF Y REPLACE ! F/ C>D 2F SELECT+
! SECOND C>D1 !N .,A & .;,B >E 9DEP5D5T
EV5TS4 ,S1 ! PROBABIL;Y IS3
.B4 ,IF Y D N REPLACE ! F/ C>D 2F
SELECT+ ! SECOND C>D1 !N .,A & .;,B >E
DEP5D5T EV5TS4 ,S1 ! PROBABIL;Y IS3
.,GUID$ .,PRACTICE = ,EXAMPLES #D & #E
.#D4 .,,:AT .,,IF8 ,USE ! 9=M,N 9
,EXAMPLE #D 6F9D 7A7 ! PROBABIL;Y T A
FUTURE TROPICAL CYCL"O IS A TROPICAL
/ORM & 7.;B7 ! PROBABIL;Y T A FUTURE
TROPICAL CYCL"O 9 ! ,S\!RN ,HEMISPH]E IS
A TROPICAL /ORM4
,F9D ! PROBABIL;Y ( DRAW+ ! GIV5 C>DS
F A /&>D DECK ( #EB C>DS 7A7 ) REPLACE;T
& 7;B7 )\T REPLACE;T4
.#E4 ,A SPADE1 !N A CLUB
.#F4 ,A JACK1 !N ANO!R JACK
------------------------------------#GBJ
..,,?REE ,,OR ,,M ,,DEP5D5T .,,EV5TS
,! =MULA = F9D+ PROBABILITIES ( DEP5D5T
EV5TS C 2 EXT5D$ 6?REE OR M EV5TS1 Z %[N
2L4
,,ANO!R ,,WAY
,Y C AL USE ! FUNDA;TAL C.T+ PR9CIPLE4
;,P7ALL DI6]5T7
,EXAMPLE #F ,F9D PROBABIL;Y ( ?REE
DEP5D5T EV5TS
.,,CO/UME .,,"PY ,Y & TWO FRS G 6!
SAME /ORE AT DI6]5T "TS 6BUY CO/UMES =A
CO/UME "PY4 ,"! >E #AE DI6]5T CO/UMES AT
! /ORE1 &! /ORE HAS AT L1/ #C DUPLICATES
( EA* CO/UME4 ,:AT IS ! PROBABIL;Y T Y
EA* *OOSE DI6]5T CO/UMES8
,SOLU;N
,LET EV5T .,A 2 T Y *OOSE A CO/UME1
LET EV5T .;,B 2 T "O FR *OOSES A DI6]5T
CO/UME1 & LET EV5T .;,C 2 T YR O!R FR
*OOSES A ?IRD CO/UME4 ,^! EV5TS >E
DEP5D5T4 ,S1 ! PROBABIL;Y IS3
.;,P @7 .,A & .;,B & .;,C @7 .K .;,P
@7 .,A @7 99 .;,P @7 .;,B _\ .,A @7 99
.;,P @7 .;,C _\ .,A & .;,B @7
..,EXAMPLE #G ,SOLVE A MULTI-/EP
.PRO#M
.,,SAFETY ,US+ OBS]V,NS MADE ( DRIV]S
>RIV+ AT A C]TA9 HI< S*OOL1 A /UDY
REPORTS T #FI@3P ( ADULTS WE> S1T BELTS
:ILE DRIV+4 ,A HI< S*OOL /UD5T AL 9 ! C>
WE>S A S1T BELT #FF@3P (! "T :5 ! ADULT
WE>S A S1T BELT1 & #BF@3P (! "T :5 !
ADULT DOES N WE> A S1T BELT4 ,:AT IS !
PROBABIL;Y T A HI< S*OOL /UD5T 9 ! /UDY
WE>S A S1T BELT8
,SOLU;N
,A PROBABIL;Y TREE DIAGRAM1 ": !
PROBABILITIES >E GIV5 AL;G ! BRAN*ES1 C
HELP Y SOLVE ! PRO#M4 ,NOTICE T !
PROBABILITIES = ALL BRAN*ES F ! SAME
PO9T M/ SUM 6#A4
,S1 ! PROBABIL;Y T A HI< S*OOL /UD5T
WE>S A S1T BELT IS3
.;,P @7 .;,C @7 .K .;,P @7 .,A & ;,C
@7 @+ .;,P @7 .;,B & ;,C7
.K .;,P @7 .,A @7 99 .;,P @7 .;,C _\
.,A @7 @+ .;,P @7 .;,B @7 99 .;,P @7
.;,C _\ .;,B @7
.K 7#J.FI77#J.FF7 @+ 7#J.CA7 7#J.BF7
.K #J.ECF
------------------------------------#GBA
.,GUID$ .,PRACTICE = ,EXAMPLES #F & #G
.#G4 .,,:AT .,,IF8 ,9 ,EXAMPLE #F1 :AT
IS ! PROBABIL;Y T Y & YR FRS *OOSE
DI6]5T CO/UMES IF ! /ORE SELLS #BJ
DI6]5T CO/UMES8
.#H4 .,,BASKETBALL ,A HI< S*OOL
BASKETBALL T1M L1DS AT HALF"T 9 #FJ@3P
(! GAMES 9 A S1SON4 ,! T1M W9S #HJ@3P (!
"T :5 !Y H ! HALF"T L1D1 B ONLY #AJ@3P
(! "T :5 !Y D N4 ,:AT IS ! PROBABIL;Y T
! T1M W9S A "PICUL> GAME DUR+ ! S1SON8
#AJ.E ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#AH = ,EXS4 #AC1 #BE1 & #CI
.K ..,,/&>DIZ$ ,,TE/ ,,PRACTICE ,EXS4
#B1AE1CB1CD1 & .#DA
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,!
PROBABIL;Y T .;,B W O3UR GIV5 T .,A HAS
O3URR$ IS CALL$ ! @8 ( .;,B GIV5 .,A4
.#B4 .,,WRIT+ .,EXPLA9 ! DI6];E 2T
DEP5D5T EV5TS & 9DEP5D5T EV5TS1 & GIVE
AN EXAMPLE ( EA*4
,,EXAMPLES #A & #B
ON PP4 #GAG-GAH = ,EXS4 #C-AE
.,,9DEP5D5T .,,EV5TS ,EV5TS .,A & .;,B
>E 9DEP5D5T4 ,F9D ! 9DICAT$ PROBABIL;Y4
.#C4 .;,P @7 .,A @7 .K #J.D
.;,P @7 .;,B @7 .K #J.F
.;,P @7 .,A .& .;,B @7 .K @8
.#D4 .;,P @7 .,A @7 .K #J.C
.;,P7.;,B7 .K #J.D
.;,P @7 .,A .& .;,B @7 .K @8
.#E4 .;,P @7 .,A @7 .K #J.BE
.;,P @7 .;,B @7 .K @8
.;,P @7 .,A & .;,B @7 .K #J.B
.#F4 .;,P @7 .,A @7 .K #J.E
.;,P7.;,B7 .K @8
.;,P @7 .,A & ;,B7 .K #J.A
.#G4 .;,P @7 .,A @7 .K @8
.;,P @7 .;,B @7 .K #J.H
.;,P @7 .,A .& .;,B @7 .K #J.F
.#H4 .;,P7.,A7 .K @8
.;,P @7 .;,B @7 .K #J.I
.;,P @7 .,A & .;,B @7 .K #J.DE
,,SP9N+ ,A ,,:EEL ,Y >E PLAY+ A GAME T
9VOLVES SP9N+ ! :EEL %[N4 ,F9D !
PROBABIL;Y ( SP9N+ ! GIV5 COLORS4
.#I4 GRE51 !N BLUE
.#AJ4 R$1 !N YELL[
.#AA4 BLUE1 !N R$
.#AB4 YELL[1 !N GRE5
.#AC4 BLUE1 !N GRE51 !N R$
.#AD4 GRE51 !N R$1 !N YELL[
#AE4 .,,MULTIPLE .,,*OICE ,EV5TS .,A &
.;,B >E 9DEP5D5T4 ,:AT IS .;,P7.,A &
.;,B7 .IF .;,P @7 .,A @7 .K #J.C & .;,P
@7 .;,B @7 .K #J.B8
,A #J.JF
;,B #J.A
;,C #J.E
;,D #J.F
,,EXAMPLE #D
ON P4 #GAI = ,EXS4 #AF-BE
,,DEP5D5T ,EV5TS .,A & .;,B >E
DEP5D5T4 ,F9D ! 9DICAT$ PROBABIL;Y4
#AF4 .;,P @7 .,A @7 .K #J.C
.;,P @7 .;,B _\ .,A @7 .K #J.F
.;,P @7 .,A .& .;,B @7 .K @8
#AG4 .;,P @7 .,A @7 .K #J.G
.;,P @7 .;,B _\ .,A @7 .K #J.E
.;,P @7 .,A .& .;,B @7 .K @8
#AH4 .;,P @7 .,A @7 .K #J.H
.;,P @7 .;,B _\ .,A @7 .K @8
;,P7 .,A & #E7 .K #J.CB
#AI4 .;,P @7 .,A @7 .K #J.F
.;,P @7 .;,B _\ .,A @7 .K @8
.;,P @7 .,A .& .;,B @7 .K #J.DE
#BJ4 .;,P7.,A7 .K @8
.;,P @7 .;,B _\ .,A @7 .K #J.D
.;,P @7 .,A & .;,B @7 .K #J.B
#BA4 .;,P7.,A7 .K #J.G
.;,P @7 .;,B _\ .,A @7 .K @8
.;,P @7 .,A & #E7 .K #J.FC
------------------------------------#GBB
,,3DI;NAL ,,PROBABIL;Y ,LET .;N 2 A
R&OMLY SELECT$ 9TEG] F #A 6#BJ4 ,F9D !
9DICAT$ PROBABIL;Y4
.#BB4 .;N IS #B GIV5 T X IS EV5
.#BC4 .;N IS #E GIV5 T X IS LESS ?AN
#H
.#BD4 .;N IS PRIME GIV5 T X HAS #B
DIGITS
.#BE4 .;N IS ODD GIV5 T X IS PRIME
,,EXAMPLES #E & #F
ON PP4 #GAI-GBJ = ,EXS4 #BF-CB
,,DRAW+ ,,C>DS ,F9D ! PROBABIL;Y (
DRAW+ ! GIV5 C>DS F A /&>D DECK ( #EB
C>DS 7A7 ) REPLACE;T & 7;B7 )\T
REPLACE;T4
.#BF4 ,A CLUB1 !N A SPADE
.#BG4 ,A QUE51 !N AN ACE
.#BH4 ,A FACE C>D1 !N A #F
.#BI4 ,A #AJ1 !N A #B
.#CJ4 ,A K+1 !N A QUE51 !N A JACK
.#CA4 ,A SPADE1 !N A CLUB1 !N ANO!R
SPADE
#CB4 .,,MULTIPLE .,,*OICE ,:AT IS !
APPROXIMATE PROBABIL;Y ( DRAW+ #C
3SECUTIVE HE>TS F A /&>D DECK ( #EB C>DS
)\T REPLACE;T8
,A #J.JABB
;,B #J.JABI
;,C #J.JAEF
;,D #J.JAFF
#CC4 .,,]ROR .,,ANALYSIS ,EV5TS .,A &
.;,B >E 9DEP5D5T4 .,DESCRIBE & CORRECT !
]ROR 9 F9D+ .;,P @7 .,A & .;,B @7@4
;,P7,A7 .K #J.D1 ;,P7;,B7 .K #J.E
;,P7,A& #C7 .K #J.D @+ #J.E .K #J.I
#CD4 .,,OP5-.,,5D$ .,,MA? ,FLIP A SET
( #C CO9S & RECORD ! NUMB] ( CO9S T -E
UP H1DS4 ,REP1T UNTIL Y H A TOTAL ( #AJ
TRIALS4
A4 ,:AT IS ! EXP]I;TAL PROBABIL;Y T A
TRIAL RESULTS 9 #B H1DS8
B4 .,-P>E YR ANSW] F "P 7A7 )!
!ORETICAL PROBABIL;Y T A TRIAL RESULTS 9
#B H1DS4
.,ANIMAT$ ,ALGEBRA AT
_+CLASSZONE.COM_:
#CE4 .,,R1SON+ ,LET .,A & .;,B 2
9DEP5D5T EV5TS4 ,:AT IS ! REL,N%IP 2T
.;,P @7 .;,B @7 & .;,P @7 .;,B _\ .,A @7
@8 .,EXPLA94
#CF4 .,,*ALL5GE ,H[ _M "TS M/ Y ROLL
TWO SIX-SID$ DICE = "! 6BE AT L1/ A
#EJ@3P *.E T Y ROLL TWO #F'S AT L1/
ONCE8
,PRO#M ,SOLV+
,,EXAMPLES
ON PP4 #GAH-GAI = ,EXS4 #CG-CH
.#CG4 .,,S*OOL .,,BUS ,ANGELA USU,Y
RU%ES 6MAKE X 6! BUS /OP 9 "T 6CAT* #C
.& #D _\ ! S*OOL BUS1 & W (T5 MISS ! BUS
IF X IS E>LY4 ,! BUS -ES E>LY 6,ANGELA'S
/OP #BH@3P (! "T4 ,:AT IS ! PROBABIL;Y T
! BUS W -E E>LY AT L1/ ONCE DUR+ A #E "D
S*OOL WEEK8
@A;.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#CH4 .,,5VIRON;T ,! TA# %[S ! NUMB]S
( SPECIES 9 ! ,UNIT$ ,/ATES LI/$ Z
5DANG]$ OR ?R1T5$ Z ( ,SEPTEMB]1 #BJJD4
,F9D 7.A7 ! PROBABIL;Y T A LI/$ ANIMAL
IS A BIRD & 7.;B7 ! PROBABIL;Y T AN
5DANG]$ ANIMAL IS A BIRD4
@A.,HOTNE,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 .,5DANG]$ @3 .,?R1T5$
.,MAMMALS @3 #FI3 #I
.,BIRDS @3 #GG3 #AD
.,REPTILES @3 #AD3 #BB
.,AMPHIBIANS @3 #AA3 #AJ
.,O!R @3 #BAI3 #GD
.K ..,,"W$-,,\ ,,SOLU;NS ONP4.,,WSI
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#GBC
,,EXAMPLE #G
ON P4 #GBJ = ,EXS4 #CI-DJ
.#CI4 .,,T5NIS ,A T5NIS PLAY] W9S A
MAT* #EE@3P (! "T :5 %E S]VES F/ &
#DG@3P (! "T :5 H] OPPON5T S]VES F/4 ,!
PLAY] :O S]VES F/ IS DET]M9$ 0A CO9 TOSS
2F ! MAT*4 ,:AT IS ! PROBABIL;Y T !
PLAY] W9S A GIV5 MAT*8
.#DJ4 .,,A3ID5T .,,RE5ACT;T ,Y >E A
JUROR =A TRIAL 9VOLV+ A NI<T"T C> A3ID5T
9 A C]TA9 C;Y4 ,USE ! TREE DIAGRAM &!
FACTS 2L 6DET]M9E ! PROBABIL;Y T ! C>
9VOLV$ 9 ! A3ID5T 0 BLUE4
99 ,! MAKE (! C> IS "KN4 ,(! C>S 9 !
C;Y MAT*+ ? MAKE1 #HE@3P >E GRE5 &
#AE@3P >E BLUE4
99 ,A WIT;S (! A3ID5T ID5TIFI$ ! C> Z
BLUE4
99 ,9 RE5ACT;TS (! A3ID5T1 ! WIT;S
CORRECTLY REPORT$ ! COLOR (! C> #HJ@3P
(! "T4
#DA4 .,,EXT5D$ .,,RESPONSE ,A FOOTBALL
T1M IS LOS+ 0#AD PO9TS NE> ! 5D (A GAME4
,! T1M SCORES TWO T\*D[NS 7WOR? #F PO9TS
EA*7 2F ! 5D (! GAME4 ,AF EA* T\*D[N1 !
COA* M/ DECIDE :E!R 6G = #A PO9T )A KICK
7: IS SU3ESS;L #II@3P (! "T7 OR #B PO9TS
)A RUN OR PASS 7: IS SU3ESS;L #DE@3P (!
"T74
A4 .,CALCULATE ,IF ! T1M GOES = #A
PO9T AF EA* T\*D[N1 :AT IS ! PROBABIL;Y
T ! COA*'S T1M W9S8 LOSES8 TIES8
B4 .,CALCULATE ,IF ! T1M GOES = #B
PO9TS AF EA* T\*D[N1 :AT IS ! PROBABIL;Y
T ! COA*'S T1M W9S8 LOSES8 TIES8
C4 .,R1SON+ ,C Y DEVELOP A /RATEGY S T
! COA*'S T1M HAS A PROBABIL;Y ( W9N+ !
GAME T IS GRT] ?AN ! PROBABIL;Y ( LOS+8
,IF S1 EXPLA9 YR /RATEGY & CALCULATE !
PROBABILITIES ( W9N+ & LOS+ US+ YR
/RATEGY4
#DB4 .,,*ALL5GE ,X IS E/IMAT$ T
#E.I@3P ( ,AM]ICANS H DIABETES4 ,SUPPOSE
A M$ICAL LAB USES A TE/ = DIABETES T IS
#IH@3P A3URATE = P :O H ! 41SE & #IE@3P
A3URATE = P :O D N H X4 ,F9D ! 3DI;NAL
PROBABIL;Y T A R&OMLY SELECT$ P]SON
ACTU,Y HAS DIABETES GIV5 T ! LAB TE/
SAYS !Y H X4
,MIX$ ,REVIEW
,USE ! BINOMIAL !OREM 6WRITE !
BINOMIAL EXPAN.N1 @7 P4 #FIJ @7
.#DC4 @7 .;X @+ #A7 #F
.#DD4 @7 .;X -- #C7 #E
.#DE4 7#C .;X @+ #B7 #G
.#DF4 7#E .;X -- #A7 #E
.#DG4 7#D .;X @+ .;Y @7 #F
.#DH4 7#B .;X -- .#C;Y7 #D
.,LET .;F7.;X7 .K .;X #B @+ .#B .&
..;G7;X7 .K .;X -- ..#D4 ,P]=M ! 9DICAT$
OP],N & /ATE ! .DOMA91 @7 P4 #DBH @7
#DI4 .;F7.;X7 @+ .;G7.;X7
.#EJ4 .;F7.;X7 -- .;G7.;X7
#EA4 .;F7.;X7 .;G7.;X7
.#EB4
#EC4 .;F7.;G7.;X77
#ED4 .;G7.;F7.;X77
#EE4 .;F7.;F7.;X77
#EF4 .;G7.;G7.;X77
,SOLVE ! EQU,N4
#EG4 .#D ;X@+;L .K .#H #C;X 7.P#..EAE7
.#EH4 #D ,9 ;X .K #AJ 7.P#..EAE7
.#EI4
.#FJ4
,,EXTRA ,,PRACTICE = ,LESSON #AJ.E1 P4
#AJAI
..,,ONL9E ,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#GBD
#AJ.F ,3/RUCT & ,9T]PRET ,BINOMIAL
,4TRIBU;N
,SIDEB>3
.,2F ,Y F.D PROBABILITIES ( EV5TS4
.,N[ ,Y W /UDY PROBABIL;Y 4TRIBU;NS4
.,:Y8 ,S Y C DESCRIBE 9T]E/ 9 MUSEUMS1
Z 9 ,EX4 #DF4
,KEY ,VOCABUL>Y
99 R&OM V>IA#
99 PROBABIL;Y 4TRIBU;N
99 BINOMIAL 4TRIBU;N
99 BINOMIAL EXP]I;T
99 SYMMETRIC
99 SKEW$
,A .R&OM .V>IA# IS A V>IA# ^: VALUE IS
DET]M9$ 0! \TCOMES (A R&OM EV5T4 ,=
EXAMPLE1 :5 Y ROLL A SIX-SID$ DIE1 Y C
DEF9E A R&OM V>IA# .;,X T REPRES5TS !
NUMB] %[+ ON ! DIE4 ,S1 ! POSSI# VALUES
( .;,X >E #A1 #B1 #C1 #D1 #E1 & #F4 ,= E
R&OM V>IA#1 A .PROBABIL;Y .4TRIBU;N C 2
DEF9$4
,,KEY ,,3CEPT
,= YR ,NOTEBOOK
,PROBABIL;Y ,4TRIBU;NS
.,A .PROBABIL;Y .4TRIBU;N IS A FUNC;N
T GIVES ! PROBABIL;Y ( EA* POSSI# VALUE
(A R&OM V>IA#4 ,! SUM ( ALL !
PROBABILITIES 9 A PROBABIL;Y 4TRIBU;N M/
EQUAL #A4
,! FOLL[+ TA# IS 9 LI/$
=MAT4 ,= EA* CELL ! H1D+ IS %[N
FOLL[$ 0A COLON1 SPACE &! CELL
3T5TS
,PROBABIL;Y ,4TRIBU;N = ,ROLL+ A ,DIE3
.;,X
,PROBABIL;Y ,4TRIBU;N = ,ROLL+ A ,DIE3
#A
,PROBABIL;Y ,4TRIBU;N = ,ROLL+ A ,DIE3
#B
,PROBABIL;Y ,4TRIBU;N = ,ROLL+ A ,DIE3
#C
,PROBABIL;Y ,4TRIBU;N = ,ROLL+ A ,DIE3
#D
,PROBABIL;Y ,4TRIBU;N = ,ROLL+ A ,DIE3
#E
,PROBABIL;Y ,4TRIBU;N = ,ROLL+ A ,DIE3
#F
,PROBABIL;Y ,4TRIBU;N = ,ROLL+ A ,DIE3
.;,P7.;X7
,PROBABIL;Y ,4TRIBU;N = ,ROLL+ A ,DIE3
,PROBABIL;Y ,4TRIBU;N = ,ROLL+ A ,DIE3
,PROBABIL;Y ,4TRIBU;N = ,ROLL+ A ,DIE3
,PROBABIL;Y ,4TRIBU;N = ,ROLL+ A ,DIE3
,PROBABIL;Y ,4TRIBU;N = ,ROLL+ A ,DIE3
,PROBABIL;Y ,4TRIBU;N = ,ROLL+ A ,DIE3
..,EXAMPLE #A ,3/RUCT A PROBABIL;Y
.4TRIBU;N
,LET .;,X 2 A R&OM V>IA# T REPRES5TS !
SUM :5 TWO SIX-SID$ DICE >E ROLL$4 ,MAKE
A TA# &A HI/OGRAM %[+ ! PROBABIL;Y
4TRIBU;N = .,X4
,,REVIEW ,,-P.D ,,EV5TS
,RECALL T "! >E #CF POSSI# \TCOMES :5
ROLL+ TWO SIX-SID$ DICE4 ,^! >E LI/$ 9
,EXAMPLE #D ON PAGE #GJI @4
,SOLU;N
,! POSSI# VALUES ( .;,X >E ! 9TEG]S F
#B 6#AB4 ,! TA# %[S H[ _M \TCOMES (
ROLL+ TWO DICE PRODUCE EA* VALUE ( .,X4
,DIVIDE ! NUMB] ( \TCOMES = .;,X 0#CF
6F9D .;,P @7 .;,X @7@4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X7.SUM7 @3 .#B @3 --@3 #D3 #E3 #F3
--@3 --@3 #I3 #AJ3 #AA3 #AB
.,\TCOMES @3 #A3 #B3 #C3 #D3 #E3 #F3
#E3 #D3 #C3 #B3 #A
.;,P @7 .;,X @7 @3 @3 @3 @3 @3 @3 @3
@3 @3 @3 @3
------------------------------------#GBE
,SIDEB>3
,/&>DS
.,PROBABIL;Y .& .,/ATI/ICS3 #D.J
,/UD5TS >E FAMILI> )! /&>D 4TRIBU;NS
7NORMAL1 BINOMIAL1 & EXPON5TIAL7 & C USE
!M 6SOLVE = EV5TS 9 PRO#MS 9 : !
4TRIBU;N 2L;GS 6^? FAMILIES4
,EXAMPLE #B ,9T]PRET A PROBABIL;Y
4TRIBU;N
,USE ! PROBABIL;Y 4TRIBU;N 9 ,EXAMPLE
#A 6ANSW] EA* "Q4
.A4 ,:AT IS ! MO/ LIKELY SUM :5 ROLL+
TWO SIX-SID$ DICE8
.B4 ,:AT IS ! PROBABIL;Y T ! SUM (!
TWO DICE IS AT L1/ #AJ8
,SOLU;N
.A4 ,! MO/ LIKELY SUM :5 ROLL+ TWO
SIX-SID$ DICE IS ! VALUE ( .;,X = :
.;,P;7.;,X7 IS GRTE/4 ,? PROBABIL;Y IS
GRTE/ = .;,X .K #G4 ,S1 ! MO/ LIKELY SUM
:5 ROLL+ ! TWO DICE IS #G4
.B4 ,! PROBABIL;Y T ! SUM (! TWO DICE
IS AT L1/ #AJ IS3
.,GUID$ .,PRACTICE = ,EXAMPLES #A & #B
,A TETRAH$RAL DIE HAS F\R SIDES NUMB]$
#A "? #D4 ,LET .;,X 2 A R&OM V>IA# T
REPRES5TS ! SUM :5 TWO S* DICE >E ROLL$4
.#A4 ,MAKE A TA# &A HI/OGRAM %[+ !
PROBABIL;Y 4TRIBU;N = ;,X
.#B4 ,:AT IS ! MO/ LIKELY SUM :5 ROLL+
! TWO DICE8 ,:AT IS ! PROBABIL;Y T ! SUM
(! TWO DICE IS AT MO/ #C8
.,,BINOMIAL .,,4TRIBU;NS ,"O TYPE (
PROBABIL;Y 4TRIBU;N IS A BINOMIAL
4TRIBU;N @4 ,A BINOMIAL 4TRIBU;N %[S !
PROBABILITIES (! \TCOMES (A .BINOMIAL
.EXP]I;T4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,BINOMIAL ,EXP]I;TS
,A BINOMIAL EXP]I;T MEETS ! FOLL[+
3DI;NS3
99 ,"! >E .;N 9DEP5D5T TRIALS4
99 ,EA* TRIAL HAS ONLY TWO POSSI#
\TCOMES3 SU3ESS & FAILURE4
99 ,! PROBABIL;Y ( SU3ESS IS ! SAME =
EA* TRIAL4 ,? PROBABIL;Y IS DENOT$ 0.P4
,! PROBABIL;Y ( FAILURE IS GIV5 0#A --
.P4
,=A BINOMIAL EXP]I;T1 ! PROBABIL;Y (
EXACTLY .;K SU3ESSES 9 .;N TRIALS IS3
.;,P @7 .;K SU3ESSES7 .K ;N .;,C ;K
.;P ;K.' 7#A - .;P @7 ;N-;K
------------------------------------#GBF
,EXAMPLE #C ,3/RUCT A BINOMIAL
4TRIBU;N
.,,SPORTS .,,SURVEYS ,AC 6A SURVEY1 AB
#DA@3P ( ,U4,S4 H\SEHOLDS H A SO3] BALL4
,SUPPOSE Y ASK #F R&OMLY *OS5 ,U4,S4
H\SEHOLDS :E!R !Y H A SO3] BALL4 ,DRAW A
HI/OGRAM (! BINOMIAL 4TRIBU;N = YR
SURVEY4
,SOLU;N
,! PROBABIL;Y T A R&OMLY SELECT$
H\SEHOLD HAS A SO3] BALL IS .;P .K
#J.DA4 ,2C Y SURVEY #F H\SEHOLDS1 .;N .K
#F4
,,AVOID ,,]RORS
,Y C *ECK YR CALCUL,NS =A BINOMIAL
4TRIBU;N 0A4+ ALL ! PROBABILITIES4 ,!
SUM %D ALW 2 #A4
.;,P @7 .;K .K #J7 .K #F ;,C #J
7#J.DA7;DG7#J.EI7 #F #J.JDB
.;,P @7 .;K .K #A7 .K #F ;,C #A
7#J.DA7 #A 7#J.EI7 #E #J.AGF
.;,P @7 ..;K .K .#B7 .K #F ;,C #B
7#J.DA7 #B 7#J.EI7 #D #J.CJF
.;,P @7 .;K .K #C7 .K #F ;,C #C
7#J.DA7 #C 7#J.EI7 #C #J.BHC
.;,P @7 .;K .K #D7 .K #F ;,C #D
7#J.DA7 #D 7#J.EI7 #B #J.ADH
.;,P @7 .;K .K #E7 .K #F ;,C #E
7#J.DA7 #E 7#J.EI7 #A 99 #J.JDA
.;,P @7 .;K .K #F7 .K #F ;,C #F
7#J.DA7 #F 7#J.EI7 #J #J.JJE
,A HI/OGRAM (! 4TRIBU;N IS %[N4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
,EXAMPLE #D ,9T]PRET A BINOMIAL
4TRIBU;N
,USE ! BINOMIAL 4TRIBU;N 9 ,EXAMPLE #C
6ANSW] EA* "Q4
.A4 ,:AT IS ! MO/ LIKELY \TCOME (!
SURVEY8
.B4 ,:AT IS ! PROBABIL;Y T AT MO/ #B
H\SEHOLDS H A SO3] BALL8
,SOLU;N
.A4 ,! MO/ LIKELY \TCOME (! SURVEY IS
! VALUE ( .;K = : .;,P @7 .;K @7 IS
GRTE/4 ,? PROBABIL;Y IS GRTE/ = .;K .K
#B4 ,S1 ! MO/ LIKELY \TCOME IS T #B (!
#F H\SEHOLDS H A SO3] BALL4
.B4 ,! PROBABIL;Y T AT MO/ #B
H\SEHOLDS H A SO3] BALL IS3
.;,P @7 .;K"K.#B @7 .K .;,P @7 .;K .K
#B7 @+ .;,P @7 .;K .K #A7 @+ .;,P @7 .;K
.K #J7
#J.CJF @+ #J.AGF @+ #J.JDB
#J.EBD
,S1 ! PROBABIL;Y IS AB #EB@3P4
.,GUID$ .,PRACTICE = ,EXAMPLES #C & #D
,9 ,SW$51 #FA@3P ( H\SEHOLDS H A SO3]
BALL4 ,SUPPOSE Y ASK #F R&OMLY *OS5
,SW$I% H\SEHOLDS :E!R !Y H A SO3] BALL4
.#C4 ,DRAW A HI/OGRAM %[+ ! BINOMIAL
4TRIBU;N = YR SURVEY4
.#D4 ,:AT IS ! MO/ LIKELY \TCOME ( YR
SURVEY8 ,:AT IS ! PROBABIL;Y T AT MO/ #B
H\SEHOLDS Y SURVEY H A SO3] BALL8
------------------------------------#GBG
,,CLASSIFY ,,4TRIBU;NS
,NOTE T ! 4TRIBU;N 9 ,EXAMPLE #A ON P4
#GBD IS SYMMETRIC1 :ILE ! 4TRIBU;N 9
,EXAMPLE #C ON P4 #GBF IS SKEW$4
..,,SYMMETRIC ,,& ,,SKEW$ .,,4TRIBU;NS
,SUPPOSE A PROBABIL;Y 4TRIBU;N IS
REPRES5T$ 0A HI/OGRAM4 ,! 4TRIBU;N IS
SYMMETRIC IF Y C DRAW A V]TICAL L9E T
DIVIDES ! HI/OGRAM 96TWO "PS T >E MIRROR
IMAGES4 ,A 4TRIBU;N T IS .N SYMMETRIC IS
CALL$ SKEW$ @4
,EXAMPLE #E ,CLASSIFY 4TRIBU;NS Z
SYMMETRIC OR SKEW$
,DESCRIBE ! %APE (! BINOMIAL 4TRIBU;N
T %[S ! PROBABIL;Y ( EXACTLY .;K
SU3ESSES 9 #H TRIALS IF 7A7 .;P .K #J.E
& 7;B7 .;P .K #J.I4
,SOLU;N
A4
,SYMMETRIC2 ! LEFT HALF IS A MIRROR
IMAGE (! "R HALF4
B4
,SKEW$2 ! 4TRIBU;N IS N SYMMETRIC AB
ANY V]TICAL L9E4
.,GUID$ .,PRACTICE = ,EXAMPLE #E
.#E4 ,A BINOMIAL EXP]I;T 3SI/S ( #E
TRIALS ) PROBABIL;Y .;P ( SU3ESS ON EA*
TRIAL4 ,DESCRIBE ! %APE (! BINOMIAL
4TRIBU;N T %[S ! PROBABIL;Y ( EXACTLY
.;K SU3ESSES IF 7.A7 .;P .K #J.D & 7.;B7
.;P .K #J.E4
#AJ.F ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#AI = ,EXS4 #E1BA1 & #DE
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 #B1I1 #CB1 #CI1 & #DH
.K .,,MULTIPLE .,,REPRES5T,NS ,EX#.DG
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,A
PROBABIL;Y 4TRIBU;N REPRES5T$ 0A
HI/OGRAM IS @8 IF Y C DRAW A V]TICAL L9E
DIVID+ ! HI/OGRAM 96TWO "PS T >E MIRROR
IMAGES4
.#B4 .,,WRIT+ .,EXPLA9 ! DI6];E 2T A
BINOMIAL EXP]I;T &A BINOMIAL 4TRIBU;N4
,,EXAMPLE #A
ON P4 #GBD = ,EXS4 #C-E
,,3/RUCT+ ,,PROBABIL;Y ,,4TRIBU;NS
,MAKE A TA# &A HI/OGRAM %[+ ! PROBABIL;Y
4TRIBU;N =! R&OM V>IA#4
.#C4 .;,X .K ! NUMB] ON A TA# T5NIS
BALL R&OMLY *OS5 F A BAG T 3TA9S #E
BALLS LABEL$ 8#A10 #C BALLS LABEL$ 8#B10
& #B BALLS LABEL$ 8#C40
.#D4 .;,W .K #A IF A R&OMLY *OS5 LR IS
,A1 ;,E1 ,I1 ,O1 OR ;,U & #B O!RWISE4
.#E4 .;,N .K ! NUMB] ( DIGITS 9 A R&OM
9TEG] F #J "? #III4
------------------------------------#GBH
,,EXAMPLE #B
#F-I1 ON P4 #GBE = ,EXS4 #F-I
.,,9T]PRET+ .,,PROBABIL;Y .,,4TRIBU;NS
,9 ,EX]CISES USE ! GIV5 HI/OGRAM (A
PROBABIL;Y 4TRIBU;N =A= R&OM V>IA# .,X4
.#F4 ,:AT IS ! PROBABIL;Y T .;,X IS
EQUAL 6#A8
.#G4 ,:AT IS ! MO/ LIKELY VALUE = ;,X8
.#H4 ,:AT IS ! PROBABIL;Y T ;,X IS
ODD8
#I4 .,,MULTIPLE .,,*OICE ,:AT IS !
PROBABIL;Y T .;,X IS AT L1/ #C8
,A #J.B
;,B #J.D
;,C #J.F
;,D #J.H
,,EXAMPLE #E & #D
ON P4 #GBF = ,EXS4 #AJ-CB
.,,CALCULAT+ .,,PROBABILITIES
,CALCULATE ! PROBABIL;Y ( TOSS+ A CO9 #C
.& #D ..#BJ "TS & GETT+ ! GIV5 NUMB] (
.H1DS4
.#AJ4 #A
.#AA4 #B
.#AB4 #D
.#AC4 #F
.#AD4 #I
.#AE4 #AB
.#AF4 #AE
.#AG4 #AH
.,,BINOMIAL .,,PROBABILITIES
,CALCULATE ! PROBABIL;Y ( R&OMLY GUESS+
! GIV5 NUMB] ( CORRECT ANSW]S ON A
#CJ-"Q MULTIPLE *OICE EXAM T HAS *OICES
,A1 ;,B1 ;,C1 & ;,D = EA* "Q4
.#AH4 #J
.#AI4 #B
.#BJ4 #F
.#BA4 #AA
.#BB4 #AE
.#BC4 #BA
.#BD4 #BF
.#BE4 #CJ
.,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 CALCULAT+ ! PROBABIL;Y
( ROLL+ A #A EXACTLY #C "TS 9 #E ROLLS
(A SIX-SID$ DIE4
.#BF4
.#BG4
.,,BINOMIAL .,,4TRIBU;NS ,CALCULATE !
PROBABIL;Y ( .;K SU3ESSES =A BINOMIAL
EXP]I;T 3SI/+ ( .;N TRIALS ) PROBABIL;Y
.;P ( SU3ESS ON EA* TRIAL4
.#BH4 .;K "K #C1 .;N .K #G1 .;P .K
#J.C
.#CJ4 ..;K "K #B1 .;N .K .#E1 .;P .K
#J.AB
.#BI4 .;K.1.#E,.;N .K .#H1 .;P .K #J.F
.#CA4 .;K.1.#AJ,.;N.K #AE1 .;P .K
#J.GE
#CB4 .,,MULTIPLE .,,*OICE ,Y P]=M A
BINOMIAL EXP]I;T 3SI/+ ( #AJ TRIALS )A
PROBABIL;Y ( SU3ESS ( #CF@3P ON EA*
TRIAL4 ,:AT IS ! MO/ LIKELY NUMB] (
SU3ESSES8
,A #C
;,B #D
;,C #F
;,D #G
.,,EXAMPLE #E
ON P4 #GBG = ,EXS4 #CC-CH
.,,HI/OGRAMS ,A BINOMIAL EXP]I;T 3SI/S
( .;N TRIALS ) PROBABIL;Y .;P ( SU3ESS
ON EA* TRIAL4 ,DRAW A HI/OGRAM (!
BINOMIAL 4TRIBU;N T %[S ! PROBABIL;Y (
EXACTLY .;K SU3ESSES4 .,DESCRIBE !
4TRIBU;N Z EI .SYMMETRIC OR .SKEW$4 ,!N
F9D ! MO/ LIKELY NUMB] ( SU3ESSES4
.#CC4 ..;N .K #C,.;P .K #J.C
.#CD4 ..;N .K #F,.;P .K #J.E
.#CE4 ..;N .K #D,.;P .K #J.AF
.#CF4 ..;N .K #G,.;P .K #J.HE
.#CG4 .;N .K #H1 .;P .K #J.JBE
.#CH4 ;N .K #AB1 .;P .K #J.E
.#CI4 .,,OP5-.,,5D$ .,,MA? ,3/RUCT A
SYMMETRIC PROBABIL;Y 4TRIBU;N =A R&OM
V>IA# ;,X &A SKEW$ PROBABIL;Y 4TRIBU;N
=A R&OM V>IA# .,Y4 ,MAKE A TA# &A
HI/OGRAM = EA* 4TRIBU;N4
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
------------------------------------#GBI
,9 ,EX]CISES #DJ-DB1 Y W DERIVE !
BINOMIAL PROBABIL;Y =MULA ON PAGE #GBE
@4 ,3SID] A BINOMIAL EXP]I;T ) .;N
TRIALS & PROBABIL;Y .;P ( SU3ESS ON EA*
TRIAL4
.#DJ4 ,= ANY "PICUL> SEQU;E ( .;K
SU3ESSES & .;N--.;K FAILURES1 :AT IS !
PROBABIL;Y T ! SEQU;E O3URS8 .,EXPLA94
.#DA4 ,H[ _M SEQU;ES ( .;K SU3ESSES &
.;N--.;K FAILURES >E "!8 .,EXPLA94
.#DB4 .,,*ALL5GE ,USE YR RESULTS F
,EX]CISES #DJ & #DA 6JU/IFY ! BINOMIAL
PROBABIL;Y =MULA4
,PRO#M ,SOLV+
,,EXAMPLES #C & #D
ON P4 #GBF = ,EXS4 #DC-DF
.#DC4 .,,H1L? ,AB #A@3P ( P >E ALL]GIC
6BEE /+S4 ,:AT IS ! PROBABIL;Y T EXACTLY
#A P]SON 9 A CLASS ( #BE IS ALL]GIC 6BEE
/+S8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#DD4 .,,BASKETBALL ,PREDRAG
,/OJAKOVIC (! ,SACRA;TO ,K+S MADE
#IB.G@3P ( 8 FREE ?R[ ATTEMPTS 9 !
#BJJC-BJJD ,,NBA REGUL> S1SON4 ,:AT IS !
PROBABIL;Y T HE W MAKE EXACTLY #AJ ( 8
NEXT #AE FREE ?R[ ATTEMPTS8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#DE4 .,,BLOOD .,,TYPE ,! *>T %[S !
4TRIBU;N ( BLOOD TYPES 7,O1 ,A1 ;,B1
;,,AB7 & ,RH FACTOR @7 @+ OR @7 = HUMAN
BLOOD4 ,IF1 AT R&OM1 #AJ P DONATE BLOOD
6A BLOOD BANK DUR+ A C]TA9 H\R1 F9D !
PROBABIL;Y ( EA* EV5T4
,! FOLL[+ TA# IS 9 LI/$
=MAT4 ,= EA* CELL ! H1D+ IS %[N
FOLL[$ 0A COLON1 SPACE &! CELL
3T5TS
,P]C5T ( ,POPUL,N 0,BLOOD ,TYPE3 #J @+
,P]C5T ( ,POPUL,N 0,BLOOD ,TYPE3 .#J-
,P]C5T ( ,POPUL,N 0,BLOOD ,TYPE3 ,A.'
@+
,P]C5T ( ,POPUL,N 0,BLOOD ,TYPE3 ,A.'
-
,P]C5T ( ,POPUL,N 0,BLOOD ,TYPE3 ;,B.'
@+
,P]C5T ( ,POPUL,N 0,BLOOD ,TYPE3 .;,B
-
,P]C5T ( ,POPUL,N 0,BLOOD ,TYPE3
;,,AB.' @+
,P]C5T ( ,POPUL,N 0,BLOOD ,TYPE3
.;,,AB -
,P]C5T ( ,POPUL,N 0,BLOOD ,TYPE3
.#CG@3P
,P]C5T ( ,POPUL,N 0,BLOOD ,TYPE3
.#F@3P
,P]C5T ( ,POPUL,N 0,BLOOD ,TYPE3 @\
#CD@3P
,P]C5T ( ,POPUL,N 0,BLOOD ,TYPE3
.#F@3P
,P]C5T ( ,POPUL,N 0,BLOOD ,TYPE3
.#AJ@3P
,P]C5T ( ,POPUL,N 0,BLOOD ,TYPE3
.#B@3P
,P]C5T ( ,POPUL,N 0,BLOOD ,TYPE3
.#D@3P
,P]C5T ( ,POPUL,N 0,BLOOD ,TYPE3
.#A@3P
A4 ,EXACTLY #E (! P >E TYPE ,A @+ @4
B4 ,EXACTLY #B (! P >E ,RH1
C4 ,AT MO/ #B (! P >E TYPE ,O4
D4 ,AT L1/ #E (! P >E ,RH @+ @4
#DF4 .,,F9E .,,>TS ,A SURVEY /ATES T
#CE@3P ( P 9 ! ,UNIT$ ,/ATES VISIT$ AN
>T MUSEUM 9 A C]TA9 YE>4 ,Y R&OMLY
SELECT #AJ ,U4,S4 CITIZ5S4
A4 ,DRAW A HI/OGRAM %[+ ! BINOMIAL
4TRIBU;N (! NUMB] ( P :O VISIT$ AN >T
MUSEUM4
B4 ,:AT IS ! PROBABIL;Y T AT MO/ #D P
VISIT$ AN >T MUSEUM8
#DG4 .,,MULTIPLE .,,REPRES5T,NS ,AN
AV]AGE ( #G GOPH] HOLES APPE> ON ! F>M
%[N EA* WEEK4 ,LET .;,X REPRES5T H[ _M
(! #G GOPH] HOLES APPE> 9 ! C>ROT PAT*4
,ASSUME T A GOPH] HOLE HAS AN EQUAL *.E
( APPE>+ AT ANY PO9T ON ! F>M4
A4 ,CALCULAT+ .,PROBABILITIES ,F9D
.;,P @7 .;,X @7 = .;,X.K #J1A1 #B1'1 #G4
B4 ,MAK+ A ,TA# ,MAKE A TA# %[+ !
PROBABIL;Y 4TRIBU;N = .,X4
C4 ,MAK+ A ,HI/OGRAM ,MAKE A HI/OGRAM
%[+ ! PROBABIL;Y 4TRIBU;N = .,X4
------------------------------------#GCJ
#DH4 .,,EXT5D$ .,,RESPONSE ,ASSUME T
HAV+ A MALE * & HAV+ A FEMALE * >E
9DEP5D5T EV5TS & T ! PROBABIL;Y ( EA* IS
#J.E4
A4 ,A C\PLE HAS #D MALE *N4 ,EVALUATE
! VALID;Y ( ? /ATE;T3 8,! F/ #D KIDS 7
ALL BOYS1 S ! NEXT "O W PROBABLY 2 A
GIRL40
B4 ,:AT IS ! PROBABIL;Y ( HAV+ #D MALE
*N & !N A FEMALE *8
C4 ,LET ;,X 2 A R&OM V>IA# T REPRES5TS
! NUMB] ( *N A C\PLE ALR HAS :5 !Y H _!
F/ FEMALE *4 ,DRAW A HI/OGRAM (!
4TRIBU;N ( .;,P @7 .;,X @7 = #J "K
.;,X"K #AJ & DESCRIBE XS %APE4
#DI4 .,,*ALL5GE ,AN 5T]TA9;T SY/EM HAS
.;N SP1K]S4 ,EA* SP1K] W FUNC;N PROP]LY
) PROBABIL;Y .;P @1 9DEP5D5T ( :E!R !
O!R SP1K]S >E FUNC;N+4 ,! SY/EM W OP]ATE
E6ECTIVELY IF AT L1/ #EJ@3P ( XS SP1K]S
>E FUNC;N+4 ,= :AT VALUES ( .;P IS A
#E-SP1K] SY/EM M LIKELY 6OP]ATE ?AN A
#C-SP1K] SY/EM8
,MIX$ ,REVIEW
,,PREVIEW
,PREP>E = ,LESSON #AA.A 9 ,EXS4
#EJ-EE4
.#EJ4 #H @+ #BD @/ #D
.#EA4 #D 99 #C @+ #BH @/ #G
.#EB4 #CE--#C 99 #B @/ #H
.#EC4 #F--7#AE 99 #B7 #B @/ #I
.#ED4 #B @+ #DH @/ #F 99--#E
.#EE4 #AD--#I @/ #C @+ #DJ @/ #H
,SOLVE ! 9EQUAL;Y ALGEBRAIC,Y4 ,!N
GRAPH ! SOLU;N4
.#EF4 #E--#B;X "K.K #AB @7 P4 #DA @7
.#EG4 #A "K.K #D .;X -- #C "K.K #G @7
P4 #DA @7
.#EH4 --#B "K.K #C .;X -- #E "K.K #D
@7 P4 #DA @7
.#EI4 .#F;X #B .1.K #CF @7 P4 #CJJ @7
.#FJ4 #C .;X #B @+ ;LL .;X -- #D "K.K
#J @7 P4 #CJJ @7
.#FA4 #C .;X #B @+ #I .;X "K.K .;X #B
@+ #D @7 P4 #CJJ @7
,F9D ALL Z]OS (! POLYNOMIAL FUNC;N1 @7
P4 #CGI @7
.#FB4 .;F7.;X7 .K .;X #C -- #D .;X #B
-- #G .;X @+ #AJ
#FC4 .;G7.;X7 .K .#C;X #C -- .#C;X #B
@+ ..#GE;X--.#GE
#FD4 .;H7.;X7 .K .;X #D -- .;X #C --
.#E;X #B -- ..;X--.#F
#FE4 .;F7.;X7 .K .#B;X #D @+ .#E;X #C
@+ .#BI;X #B @+ ..#HJ;X--.#DH
,,QUIZ .= .,LESSONS .#GJ..E-.AJ..F
,F9D ! PROBABIL;Y ( R&OMLY DRAW+ !
GIV5 M>#S F A BAG ( #F R$1 #I GRE51 & #E
BLUE M>#S )\T REPLACE;T1 7.P4 #GAG7
.#A4 R$1 !N GRE5
.#B4 BLUE1 !N R$
.#C4 GRE51 !N GRE5
,CALCULATE ! PROBABIL;Y ( GETT+ ! GIV5
NUMB] ( #F'S :5 ROLL+ A SIX-SID$ DIE #AJ
"TS1 @7 P4 #GBD @7
.#D4 #J
.#E4 #A
.#F4 #D
.#G4 #H
,A ..BINOMIAL EXP]I;T 3SI/S ( ;N
TRIALS ) PROBABIL;Y ;P ( SU3ESS ON EA*
TRIAL4 ,DRAW A HI/OGRAM (! BINOMIAL
4TRIBU;N T %[S ! PROBABIL;Y ( EXACTLY ;K
SU3ESSES1 @7 P4 .#GBD7
.#H4 .;N .K #E1 .;P .K #J.B
.#I4 ..;N .K #H,.;P .K #J.E
.#AJ4 ..;N .K #F,.;P .K #J.GB
.#AA4 .,,M5U .,,*OICES ,Y & #D FRS >E
9 L9E AT LUN* & >E EA* SELECT+ A B"EAGE4
,"! >E #E TYPES ( B"EAGES AVAILA#4 ,:AT
IS ! PROBABIL;Y T ALL ( Y W SELECT
DI6]5T B"EAGES8 @7 .P4 #GAG7
,,EXTRA ,,PRACTICE = ,LESSON #AJ.F1 P4
#AJAI
..,,ONL9E ,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#GCA
,GRAPH+ ,CALCULATOR ,ACTIV;Y3 #AJ.F
,CR1TE A ,BINOMIAL ,4TRIBU;N
,USE AF LESSON #GJ.F
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,KEY/ROKES
,SIDEB>3
,/&>DS
.,PROBABIL;Y .& .,/ATI/ICS3 #D.J
,/UD5TS >E FAMILI> )! /&>D 4TRIBU;NS
7NORMAL1 BINOMIAL1 & EXPON5TIAL7 & C USE
!M 6SOLVE = EV5TS 9 PRO#MS 9 : !
4TRIBU;N 2L;GS 6^? FAMILIES4
,"Q ,H[ C Y USE A GRAPH+ CALCULATOR
6CALCULATE BINOMIAL PROBABILITIES8
,"S CALCULATORS H A BINOMIAL
PROBABIL;Y 4TRIBU;N FUNC;N T Y C USE
6CALCULATE BINOMIAL PROBABILITIES4 ,Y C
!N USE ! CALCULATOR 6DRAW A HI/OGRAM (!
4TRIBU;N4
,EXAMPLE ,CALCULATE BINOMIAL
PROBABILITIES
.,,TV .,,NEWS ,AC 6A SURVEY1 #CH@3P (
,U4,S4 ADULTS GET _! NEWS PRIM>ILY F
TELEVI.N4 ,SUPPOSE Y SURVEY #F ADULTS AT
R&OM4 ,DRAW A HI/OGRAM (! BINOMIAL
4TRIBU;N %[+ ! PROBABIL;Y T TELEVI.N IS
! PRIM>Y NEWS S\RCE = EXACTLY .;K
ADULTS4 ,:AT IS ! MO/ LIKELY NUMB] (
ADULTS 9 YR SURVEY :O GET _! NEWS
PRIM>ILY "? TELEVI.N8
.,,/EP #A ..,CAT] VALUES ( .;K
,LET .;P .K #J.CH 2 ! PROBABIL;Y T
TELEVI.N IS A P]SON'S PRIM>Y NEWS S\RCE4
,5T] ! .;K- VALUES #J "? #F 96LI/ ;,L ON
! GRAPH+ CALCULATOR4
,,/EP #B ,F9D VALUES ( ;,P7;K7
,5T] ! BINOMIAL PROBABIL;Y -M& 6G5]ATE
.;,P7.;K7 = ALL SEV5 .;K -VALUES4 ,/ORE
! RESULTS 9 LI/ ;,L #B @4
,,/EP #C ,DRAW HI/OGRAM
,SET UP ! HI/OGRAM 6USE ! NUMB]S 9 LI/
;,L #A Z .;X -VALUES &! NUMB]S 9 LI/ ;,L
#B Z FREQU5CIES4 ,DRAW ! HI/OGRAM 9 A
SUITA# VIEW+ W9D[4
,F ! HI/OGRAM 9 ,/EP #C1 Y C SEE T .;K
.K .#B IS ! MO/ LIKELY NUMB] (! #F
ADULTS SURVEY$ :O GET _! NEWS PRIM>ILY
"? TELEVI.N4
,PRACTICE
,A ..BINOMIAL EXP]I;T 3SI/S ( ;N
TRIALS ) PROBABIL;Y ;P ( SU3ESS ON EA*
TRIAL4 ,USE A GRAPH+ CALCULATOR 6DRAW A
HI/OGRAM (! BINOMIAL 4TRIBU;N T %[S !
PROBABIL;Y ( EXACTLY ;K SU3ESSES4 ,!N
F9D ! MO/ LIKELY NUMB] ( .SU3ESSES4
.#A4 .;N.K.#AB,.;P .K #J.BI
.#B4 .;N .K #AD1 .;P .K #J.EH
.#C4 .;N .K #AE1 .;P .K #J.HJE
.#D4 .,,:AT .,,IF8 ,9 ! EXAMPLE1 H[ D
YR HI/OGRAM &! MO/ LIKELY NUMB] ( ADULTS
*ANGE IF Y SURVEY #AD ADULTS AT R&OM8
------------------------------------#GCB
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,LESSONS #AJ.D-AJ.F
#A4 .,,MULTI-.,,/EP .,,PRO#M ,Y &A FR
>E PLAY+ A ^W GAME T 9VOLVES LR$ TILES4
,! 4TRIBU;N ( LRS IS %[N 2L4
,A4 ,Y R&OMLY DRAW #A TILE4 ,:AT IS !
PROBABIL;Y ( GETT+ A V[EL8 7,ASSUME T
;,Y IS A 3SONANT47
,B4 ,Y R&OMLY DRAW #B TILES )\T
REPLACE;T4 ,:AT IS ! PROBABIL;Y ( GETT+
#B V[ELS8
,C4 ,AT ! />T (! GAME1 Y R&OMLY *OOSE
#G TILES )\T REPLACE;T4 ,:AT IS !
PROBABIL;Y T ALL (! TILES >E V[ELS8
#B4 .,,MULTI-.,,/EP .,,PRO#M ,AC 6A
SURVEY1 #FB@3P ( ,U4,S4 ADULTS 3SID]
!MVS SPORTS FANS4 ,Y R&OMLY SELECT #AD
ADULTS 6SURVEY4
,A4 ,DRAW A HI/OGRAM (! BINOMIAL
4TRIBU;N %[+ ! PROBABIL;Y T .;K ADULTS
3SID] !MVS SPORTS FANS4
,B4 ,:AT IS ! MO/ LIKELY NUMB] (
ADULTS :O 3SID] !MVS SPORTS FANS8
,C4 ,:AT IS ! PROBABIL;Y T AT L1/ #G
ADULTS 3SID] !MVS SPORTS FANS8
#C4 .,,%ORT .,,RESPONSE ,A MANUFACTUR]
MAKES BRIEFCASES ) NUMB]$ LOCKS4 ,!
LOCKS C 2 SET S T ANY "O ( #AJJJ DI6]5T
CODES W OP5 ! BRIEFCASE4 ,F\R FRS H
BRIEFCASES F ? MANUFACTUR]4 ,:AT IS !
PROBABIL;Y T AT L1/ #B (! #D BRIEFCASES
H ! SAME CODE8 ,IF TWO M FRS BUY ! SAME
BRIEFCASE1 H[ DOES ! PROBABIL;Y T AT L1/
#B (! BRIEFCASES H ! SAME CODE *ANGE8
#D4 .,,OP5-.,,5D$ ,WRITE A R1L-LIFE
PRO#M T Y C SOLVE US+ A TREE DIAGRAM &
3DI;NAL PROBABILITIES4 ,DRAW ! TREE
DIAGRAM & %[ H[ 6SOLVE ! PRO#M4
#E4 .,,GRI4$ .,,ANSW] ,A ,S(TBALL
PLAY] GETS A HIT 9 AB #CA@3P ( H]
AT-BATS4 ,Y R&OMLY SELECT #AE (! PLAY]S
AT-BATS4 ,:AT IS ! MO/ LIKELY NUMB] (
HITS ! PLAY] W H 9 ^? AT BATS8
#F4 .,,EXT5D$ .,,RESPONSE ,! [N] (A
LAWN M[+ BUSI;S [NS ?REE OLD & UNRELIA#
RID+ M[]S4 ,Z L;G Z "O (! M[]S IS "W+1 !
[N] C /AY PRODUCTIVE4 ,F PA/ EXP]I;E1 "O
(! M[]S IS UNUSA# #AJ@3P (! "T1 "O IS
UNUSA# #H@3P (! "T1 & "O IS UNUSA#
#AH@3P (! "T4
A4 ,F9D ! PROBABIL;Y T ALL ?REE M[]S
>E UNUSA# ON A GIV5 "D4
B4 ,F9D ! PROBABIL;Y T AT L1/ "O (!
M[]S IS USA# ON A GIV5 "D4
C4 ,SUPPOSE ! L1/ RELIA# M[] /OPS "W+
-PLETELY4 ,H[ DOES ? A6ECT ! PROBABIL;Y
T ! LAWN M[+ BUSI;S C 2 PRODUCTIVE ON A
GIV5 "D8
#G4 .,,EXT5D$ .,,RESPONSE ,A -PUT]
S(TW>E -PANY IS P]=M+ A M>KET TE/ ON TWO
DESIGNS1 ,A& ;,B1 = XS NEW S(TW>E
PROGRAM4 ,\ ( #BEJ P :O VIEW ! DESIGNS1
#HE L DESIGN ,A1 #ACE L DESIGN ;,B1 &
#DE L BO? DESIGNS4
,A4 ,COPY & -PLETE ! ,V5N DIAGRAM4
,B4 ,:AT IS ! PROBABIL;Y T A P]SON
LIKES DESIGN ,A OR DESIGN ;,B8
,C4 ,:AT IS ! PROBABIL;Y T A P]SON
DOES N L EI DESIGN8
,D4 .,EXPLA9 H[ Y C CALCULATE !
PROBABIL;Y F "P 7;C7 IF Y "K !
PROBABIL;Y F "P 7;B74
------------------------------------#GCC
#AJ ,*APT] ,SUMM>Y
.,BIG .,IDEA #A
,,BIG ,,ID1S
,= ,YR ,NOTEBOOK
,US+ ,P]MUT,NS & ,-B9,NS
,! FOLL[+ TA# IS 9 LI/$
=MAT4 ,= EA* CELL ! H1D+ IS %[N
FOLL[$ 0A COLON1 SPACE &! CELL
3T5TS
..,,P]MUT,NS ,ORD] IS .IMPORTANT @3
,P]MUT,NS ( .;N 4T9CT OBJECTS TAK5 ;R AT
A "T
,P]MUT,NS ( .;N 4T9CT OBJECTS @3
.;N6 @3 ,NUMB] ( WAYS 6>RANGE #H
/UD5TS AT #AJ DESKS3
..,,P]MUT,NS ,ORD] IS .IMPORTANT @3
,P]MUT,NS ( .;N OBJECTS ": "O OBJECT IS
REP1T$ ;S #A "TS1 ANO!R IS REP1T$ ;S #B
"TS1 & S ON
,P]MUT,NS ( .;N 4T9CT OBJECTS @3
.;N6 @3 ,NUMB] ( 4T+UI%A# P]MUT,NS (!
LRS 9 ,,/UD5TS3
..,,P]MUT,NS ,ORD] IS .IMPORTANT @3
..,,-B9,NS ,ORD] IS N .IMPORTANT
,P]MUT,NS ( .;N 4T9CT OBJECTS @3
,-B9,NS ( .;R OBJECTS TAK5 F A GR\P (
.;N 4T9CT OBJECTS
.;N6 @3
,NUMB] ( WAYS 6>RANGE #AJ /UD5TS AT
#AJ DESKS3#AJ6 .K #C1FBH1HJJ3 ,NUMB] (
WAYS 6*OOSE #H /UD5TS F A SET ( #AJ
/UD5TS3
,BIG IDEA #B
,F9D+ ,PROBABILITIES
,! FOLL[+ TA# %[S : =MULA 6USE :5 F9D+
PROBABILITIES 9VOLV+ TWO EV5TS .,A &
.,B4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,OV]LAPP+ ,EV5TS3 ,9DEP5D5T ,EV5TS3
,DEP5D5T ,EV5TS
.;,P @7 .,A OR .;,B @7 .K .;,P @7 .,A
@7 @+ .;,P @7 .;,B @7 - .;,P @7 .,A &
.;,B @7 @3 .;,P7.,A & .;,B7 .K .;,P7.,A7
99 .;,P7.;,B7 @3 .;,P7.,A & .;,B7 .K
.;,P7.,A7 99 .;,P7.;,B .,A7
,BIG ,IDEA #C
,3/RUCT+ ,BINOMIAL ,4TRIBU;NS
,=A BINOMIAL EXP]I;T1 ! PROBABIL;Y (
EXACTLY .;K SU3ESSES 9 .;N TRIALS IS
.;,P7.;K SU3ESSES7 .K ;N .;,C ;K .;P
;K @7 #A --.;P7 ;N-;K.'.-
": ! PROBABIL;Y ( SU3ESS ON EA* TRIAL
IS .P4
,A BINOMIAL 4TRIBU;N %[S !
PROBABILITIES ( ALL POSSI# \TCOMES 9 A
BINOMIAL EXP]I;T4 ,! 4TRIBU;N IS SKEW$
IF .;P .;I.K #J.E4
------------------------------------#GCD
#AJ ,*APT] ,REVIEW
@A.,HOME,TUTOR _+CLASSZONE.COM_:
99 ,MULTI-,LANGUAGE ,GLOSS>Y
99 ,VOCABUL>Y PRACTICE
,,REVIEW ,,KEY ,,VOCABUL>Y
99 P]MUT,N1 P4 #FHD
99 FACTORIAL1 P4 #FHD
99 -B9,N1 P4 #FIJ
99 ,PASCAL'S TRIANGLE1 P4 #FIB
99 BINOMIAL !OREM1 P4 #FIC
99 PROBABIL;Y1 P4 #FIH
99 PROBABIL;Y1 P4 #FIH
99 !ORETICAL PROBABIL;Y1 P4 #FIH
99 O4S1 P4 #FII
99 EXP]I;TAL PROBABIL;Y1 P4 #GJJ
99 GEOMETRIC PROBABIL;Y1 P4 #GJA
99 -P.D EV5T1 P4 #GJG
99 OV]LAPP+ EV5TS1 P4 #GJG
99 4JO9T OR MUTU,Y EXCLUSIVE EV5TS1 P4
#GJG
99 9DEP5D5T EV5TS1 P4 #GGG
99 DEP5D5T EV5TS1 P4 #GGH
99 3DI;NAL PROBABIL;Y1 P4 #G .;,W
99 R&OM V>IA#1 P4 #GBD
99 PROBABIL;Y 4TRIBU;N1 P4 #GBD
99 BINOMIAL 4TRIBU;N1 P4 #GBE
99 BINOMIAL EXP]I;T1 P4 #GBE
99 SYMMETRIC 4TRIBU;N1 P4 #GBG
99 SKEW$ 4TRIBU;N1 P4 #GBG
,,VOCABUL>Y ,,EX]CISES
.#A4 ,COPY & -PLETE3 ,A7;N7 @8 IS A
SELEC;N ( .;R OBJECTS F A GR\P ( .;N
OBJECTS ": ! ORD] (! OBJECTS SELECT$ IS
N IMPORTANT4
.#B4 ,,WRIT+ .,EXPLA9 ! DI6];E 2T !
PROBABIL;Y ( AN EV5T &! O4S 9 FAVOR (!
EV5T4
.#C4 ,,WRIT+ ,Y R&OMLY SELECT #AJ
C>DS1 "O 0"O1 F A /&>D DECK ( #EB C>DS
)\T REPLACE;T4 ,Y RECORD ! NUMB] (
DIAMONDS Y GET4 ,IS ? A BINOMIAL
EXP]I;T8 .,EXPLA94
.#D4 ,,WRIT+ ,LET EV5T .,A 2 R&OMLY
SELECT+ A GRE5 M># F A BAG T 3TA9S R$1
GRE51 & BLUE M>#S4 ,LET EV5T .;,B 2
R&OMLY SELECT+ A M># T IS N R$ F ! SAME
BAG4 ,>E EV5TS .,A & .;,B 4JO9T EV5TS8
.,EXPLA94
,,REVIEW ,,EXAMPLES ,,& ,,EX]CISES
,USE ! REVIEW EXAMPLES & EX]CISES 2L
6*ECK YR "U/&+ (! 3CEPTS Y H LE>N$ 9 EA*
LESSON ( ,*APT] #AJ4
#AJ.A ,APPLY ! ,C.T+ ,PR9CIPLE &
,P]MUT,NS
PP4 #FHB-FHI
,EXAMPLE
,AN ICE SKAT+ -PETI;N F1TURES #H
SKAT]S4 ,H[ _M DI6]5T WAYS C ! SKAT]S
F9I% ! -PETI;N8 ,H[ _M DI6]5T WAYS C #C
(! SKAT]S F9I% F/1 SECOND1 & ?IRD8
,"! >E #H6 WAYS ! SKAT]S C F9I% !
-PETI;N4
#H6 .K #H 99 #G 99 #F-E 99 #D 99 #C 99
#B 99 ;L.K #DJ1CBJ
,"! >E #H .;,P #C WAYS T #C (! SKAT]S
C F9I% F/1 SECOND1 & ?IRD4
------------------------------------#GCE
.,,EXAMPLES .#D & .#E
ON PP4 #FHD-FHE = ,EXS4 #E-I
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,,EX]CISES
.#E4 ,,PHOTOGRAPHY ,Y >E PLAC+ #AB
PICTURES ON SEP>ATE PAGES 9 AN ALBUM4
,H[ _M DI6]5T WAYS C Y ORD] ! #AB
PICTURES 9 ! ALBUM8 ,H[ _M DI6]5T WAYS C
#D (! #AB PICTURES 2 PLAC$ ON ! F/ #D
PAGES8
,F9D ! NUMB] ( P]MUT,NS4
.#F4 #I .;,P #A
.#G4 #E .;,P #E
.#H4 #F .;,P #C
.#I4 #AJ .;,P #B
#AJ.B ,USE ,-B9,NS &! ,BINOMIAL ,!OREM
PP4 #FIJ-FIG
,EXAMPLE
,USE ! BINOMIAL !OREM 6EXP& @7 .;X @+
..#E .;Y @7 #D @4
@7 .;X @+ #E .;Y @7 #D .K #D ;,C #J
.;X #D 7#E .;Y @7 #J @+ #D .;,C #A .;X
#C @7 #E .;Y7 #A @+ #D ;,C #B .;X #B
7#E;Y7 #B @+ #D ;,C #C .;X #A 7#E .;Y @7
#C @+ #D ;,C #D .;X #J 7#E .;Y @7 #D
.K 7#A7@7 .;X #D @77;L7 @+ 7#D7@7 .;X
#C @77#E .;Y @7 @+ 7#F7@7 .;X #B @77#BE
.;Y #B @7 @+ 7#D7@7 .;X @77;L#BE .;Y #C
@7 @+ 7;L77;L77#FBE .;Y #D @7
.K .;X #D @+ #BJ .;X #C .;Y @+ #AEJ
.;X #B .;Y #B @+ #EJJ .XY #C @+ #FBE .;Y
#D
,,EX]CISES
,,EXAMPLES #C1 #E1 & #F
ON PP4 #FIA-FIC = ,EXS4 #AJ-AD
,USE ! BINOMIAL !OREM 6WRITE !
BINOMIAL EXPAN.N4
.#AJ4 @7 .;T @+ #C7 #F
.#AA4 7#B;A @+ .;B #B @7 #D
.#AB4 @7 .;W--.#H;V @7 #D
.#AC4 7;R #C -- #D .;S7 #E
.#AD4 .,,ICE .,,CR1M ,AN ICE CR1M
V5DOR SELLS #AE FLAVORS ( ICE CR1M4 ,Y
WANT 6SAMPLE .AT .L1/S (! FLAVORS4 ,H[
_M DI6]5T -B9,NS ( ICE CR1M FLAVORS C Y
SAMPLE8
#AJ.C ,DEF9E & ,USE ,PROBABIL;Y
PP4 #FIH-GJD
,EXAMPLE
,Y ROLL A /&>D SIX-SID$ DIE4 ,F9D !
PROBABIL;Y ( ROLL+ A NUMB] LESS ?AN #C4
,TWO \TCOMES CORRESPOND 6ROLL+ A NUMB]
LESS ?AN #C3 ROLL+ A #A OR #B4
,,EX]CISES
.,,EXAMPLES #A .& .#D
ON PP4 #FIH-GJJ = ,EXS4 #AE-AI
,Y H AN EQU,Y LIKELY *.E ( *OOS+ ANY
9TEG] F #A "? #CJ4 ,F9D ! PROBABIL;Y (!
GIV5 EV5T4
.#AE4 ,AN EV5 NUMB] IS *OS54
.#AF4 ,A MULTIPLE ( #E IS *OS54
.#AG4 ,A FACTOR ( #FJ IS *OS54
.#AH4 ,A PRIME NUMB] IS *OS54
.#AI4 .,,-MUT+ ,\ ( #BEJ "W "DS1 A
-MUT] >RIV$ AT "W ON "T #DG "TS ON
,MON"DS1 #DC "TS ON ,TUES"DS1 #DH "TS ON
,W$NES"DS1 #CI "TS ON ,?URS"DS1 & #DJ
"TS ON ,FRI"DS4 ,=A R&OMLY SELECT$ "W
"D1 :AT IS ! PROBABIL;Y T ! -MUT] >RIV$
AT "W ON "T8
------------------------------------#GCF
#AJ ,,*APT] ,,REVIEW
#AJ.D ,PROBABILITIES ( ,4JO9T &
,OV]LAPP+ ,EV5TS
PP4 #GJG-GAC
,EXAMPLE
..,LET ,A & ;,B 2 EV5TS S* .T & ,F9D
,,EX]CISES
,,EXAMPLES #B & #D
ON PP4 #GJH-GJI = ,EXS4 #BJ-BB
,LET .,A & .;,B 2 EV5TS S* T .;,P @7
.,A @7 .K #J.CB1 .;,P @7 .;,B @7 .K
#J.DH1 & .;,P @7 .,A & .;,B @7 .K #J.AB4
,F9D ! 9DICAT$ PROBABIL;Y4
.#BJ4 .;,P @7 .,A .OR .;,B @7
.#BA4
.#BB4
#AJ.E ,PROBABILITIES ( ,9DEP5D5T &
,DEP5D5T ,EV5TS
,,PP4 #GAG-GBC
,EXAMPLE
,F9D ! PROBABIL;Y ( SELECT+ A CLUB &
!N ANO!R CLUB F A /&>D DECK ( #EB C>DS
IF 7A7 Y REPLACE ! F/ C>D 2F SELECT+ !
SECOND1 & 7;B7 Y D .N REPLACE ! F/ C>D4
,LET EV5T .,A 2 8! F/ C>D IS A CLUB0 &
.;,B 2 8! SECOND C>D IS A CLUB40
.A4
.B4
,,EX]CISES
,,EXAMPLE #E
ON P4 #GAI = ,EXS4 #BC-BE
,F9D ! PROBABIL;Y ( R&OMLY SELECT+ !
GIV5 M>#S F A BAG ( #E R$1 #H GRE51 & #C
BLUE M>#S IF 7A7 Y REPLACE ! F/ M># 2F
DRAW+ ! SECOND & 7;B7 Y D .N REPLACE !
F/ M>#4
.#BC4 R$1 !N GRE5
.#BD4 BLUE1 !N R$
.#BE4 GRE51 !N GRE5
#AJ.F ,3/RUCT & ,9T]PRET ,BINOMIAL
,4TRIBU;NS
PP4 #GBD-GCJ
,EXAMPLE
,F9D ! PROBABIL;Y ( TOSS+ A CO9 #AB
"TS & GETT+ EXACTLY #D H1DS4
.;,P @7 .;K .K #D7 .K ;N .;,C ;K .;P
;K.' @7 .A --.;P @7 ;N-;K .K #AB ;,C #D
7#J.E7 #D 7;L--#J.E7 #H .K #DIE7#J.E7 #D
7#J.E7 #H #J.ABA
,,EX]CISES
,,EXAMPLE #C
ON P4 #GBF = ,EXS4 #BF-BI
,F9D ! PROBABIL;Y ( TOSS+ A CO9 #H "TS
& GETT+ ! GIV5 NUMB] ( H1DS4
.#BF4 #F
.#BG4 #D
.#BH4 #G
.#BI4 #J
------------------------------------#GCG
#AJ ,*APT] ,TE/
,F9D ! NUMB] ( P]MUT,NS OR -B9,NS4
.#A4 #E .;,P #B
.#B4 #H .;,P #C
.#C4 #AB .;,P #G
.#D4 #AG .;,P #AJ
.#E4 #D ;,C #C
.#F4 #G .;,C #G
.#G4 #AH .;,C #D
.#H4 #I .;,C #E
,USE ! BINOMIAL !OREM 6WRITE !
BINOMIAL EXPAN.N4
.#I4 7;X @+ #E7 #C
.#AJ4 7#C;A--#C7 #E
.#AA4 @7 .;S @+ .;T #B @7 #D
.#AB4 @7 .;C #C -- .#B;D #B @7 #F
,A C>D IS R&OMLY DRAWN F A /&>D DECK (
#EB C>DS4 ,F9D ! PROBABIL;Y ( DRAW+ !
GIV5 C>D4
.#AC4 ,A QUE5
.#AD4 ,A R$ K+
.#AE4 ,A DIAMOND
.#AF4 ,N A CLUB
,F9D ! 9DICAT$ PROBABIL;Y4
.#AG4 .;,P @7 .,A @7 .K #J.C
.;,P @7 .;,B @7 .K #J.F
.;,P @7 .,A OR .;,B @7 .K @8
;,P7 .,A & .;,B @7 .K#J.A
.#AH4 .;,P @7 .,A @7 .K #CE@3P
;,P7;,B7 .K @8
.;,P @7 .,A .OR .;,B @7 .K #HJ@3P
;,P7,A& ;,B7 .K#BJ@3P
.#AI4 ;,P7,A7 .K @8
.#BJ4 .,A & .;,B >E 9DEP5D5T4
.;,P @7 .,A @7 .K #J.AE
.;,P @7 .;,B @7 .K #J.F
;,P @7 ,AAND ;,B7 .K @8
.#BA4 .,A & #E >E DEP5D5T4
.;,P @7 .,A @7 .K #FJ@3P
;,P7;,B _\ ,A7 .K @8
;,P7,A& ;,B7 .K #BE@3P
.#BB4 .,A & .;,B >E DEP5D5T4
.;,P @7 .,A @7 .K @8
.;,P @7 .;,B_\ .,A @7 .K #J.D .;,P @7
.,A & .;,B @7 .K #J.CF
,CALCULATE ! PROBABIL;Y ( .;K SU3ESSES
=A BINOMIAL EXP]I;T 3SI/+ ( .;N TRIALS )
PROBABIL;Y .;P ( SU3ESS ON EA* TRIAL4
.#BC4 .;K .K #D1 ;W .K #AA1 ;P .K #J.D
.#BD4 ..;K"K.K#B;,N .K #E,.;P .K #J.G
.#BE4 ,A.1.K#H1 ;W .K #I1 ;P .K #J.I
.#BF4 .,,TRUE-.,,OR-.,,FALSE .,,QUIZ
,CALCULATE ! PROBABIL;Y ( R&OMLY GUESS+
AT L1/ #H CORRECT ANSW]S ON A #AJ "Q
TRUE-OR-FALSE QUIZ4
.#BG4 .,,GOV]N;T ,"! >E #AE MEMB]S ON
A C;Y C\NCIL4 ,ON A REC5T AG5DA ITEM1 #H
(! C\NCIL MEMB]S VOT$ 9 FAVOR (A BUDGET
9CR1SE = C;Y P>K IMPROVE;TS4 ,H[ _M
-B9,NS ( C\NCIL MEMB]S CD H VOT$ 9 FAVOR
(! BUDGET 9CR1SE8
.#BH4 .,,P>A*UT+ ,A P>A*UT] IS
ATTEMPT+ 6L& )9 A SQU>E 9 ! MI4LE (A
CIRCUL> L&+ >EA4 ,! SQU>E HAS SIDES #BE
FEET L;G1 &! DIAMET] (! L&+ >EA IS #DJ
FEET4 ,IF ! P>A*UT] IS EQU,Y LIKELY 6F/
T\* ! GR.D AT ANY PO9T )9 ! L&+ >EA1 :AT
IS ! PROBABIL;Y T ! P>A*UT] F/ T\*ES !
GR.D )9 ! SQU>E8
.#BI4 .,,$UC,N ,A HI< S*OOL HAS AN
5ROLL;T ( #AHJJ /UD5TS4 ,"! >E #AJEJ
FEMALES 5ROLL$ 9 ! S*OOL4 ,! HI< S*OOL
HAS #ABJJ /UD5TS :O >E 9VOLV$ 9 AN
AF-S*OOL ACTIV;Y1 #GBE ( :OM >E FEMALE4
,:AT IS ! PROBABIL;Y T A R&OMLY SELECT$
/UD5T AT ! S*OOL IS A FEMALE :O IS N
9VOLV$ 9 AN AF-S*OOL ACTIV;Y8
.#CJ4 .,,FI%+ ,A /UDY F.D T #I@3P ( P
CITE FI%+ Z _! FAVORITE LEISURE-"T
ACTIV;Y4 ,SUPPOSE Y R&OMLY SURVEY #H P
AB _! LEISURE-"T ACTIVITIES4 ,:AT IS !
PROBABIL;Y T AT L1/ #B (! P CITE FI%+ Z
_! FAVORITE8
------------------------------------#GCH
#AJ ,/&>DIZ$ ,TE/ ,PREP>,N
,SIDEB>3
,SCOR+ ,RUBRIC
,FULL ,CR$IT
99 SOLU;N IS -PLETE & CORRECT
,"PIAL ,CR$IT
99 SOLU;N IS -PLETE B HAS ]RORS1
OR
99 SOLU;N IS )\T ]ROR B 9COMPLETE
,NO ,CR$IT
99 NO SOLU;N IS GIV51
OR
99 SOLU;N MAKES NO S5SE
,SIDEB>3
,/&>DS
#AI.J ,/UD5TS USE -B9,NS & P]MUT,NS
6-PUTE PROBABILITIES4
,,EXT5D$ ,,RESPONSE ,,"QS
,PRO#M
,A D>T IS ?R[N AT ! SQU>E T>GET %[N4
,ASSUME ! D>T IS EQU,Y LIKELY 6HIT ANY
PO9T 9SIDE ! T>GET4
.A4 ,F9D ! PROBABIL;Y T ! D>T L&S ON
EA* COLOR4
.B4 ,Y GET #E PO9TS = L&+ ON GRE51 #C
PO9TS = BLUE1 & #A PO9T = R$4 ,DOES !
SCOR+ MAKE S5SE BAS$ ON ! PROBABILITIES8
.,EXPLA94
.C4 ,DEVELOP YR [N SY/EM ( SCOR+ BAS$
ON ! PROBABILITIES F "P 7A74 .,EXPLA9 YR
R1SON+4
,2L >E SAMPLE SOLU;NS 6! PRO#M4 ,R1D
EA* SOLU;N &! -;TS 9 BLUE 6SEE :Y !
SAMPLE REPRES5TS FULL CR$IT1 "PIAL
CR$IT1 OR NO CR$IT4
,,SAMPLE #A3 ,FULL CR$IT SOLU;N
,! >1S >E CALCULAT$ CORRECTLY & FULLY
EXPLA9$4
.A4 ,6F9D ! PROBABILITIES1 F/ F9D !
>1S (! DI6]5T SEC;NS4
,6F9D ! >EA (! GRE5 SEC;N1 SPLIT !
GRE5 SQU>E 96TWO TRIANGLES1 Z %[N4
.,GRE5 .>EA .K #J.E7#AB77#F7 @+
#J.E7#AB77#F7 .K #GB IN4 #B
,! >EA (! BLUE SEC;N IS ! DI6];E (!
>1S (! CIRCLE & GRE5 SQU>E4
.,BLUE .>EA .K 7#F7 #B -- #GB .K
#CF--#GB--#DA.A IN4 #B
,! >EA (! R$ SEC;N IS ! DI6];E (! >1S
(! L>GE SQU>E &! CIRCLE4
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------------------------------------#GDJ
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------------------------------------#GDA
.,,/ATE .,,TE/ .,,PRACTICE
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99 M1N1 P4 P4 #GDD
99 M$IAN1 P4 P4 #GDD
99 MODE1 P4 #GDD
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99 /&>D DEVI,N1 P4 P4 #GDE
99 NORMAL 4TRIBU;N1 P4 P4 #GEG
99 NORMAL CURVE1 P4 P4 #GEG
99 /&>D NORMAL 4TRIBU;N1 P4 P4 #GEH
99 ;Z-SCORE1 P4 P4 #GEH
99 SAMPLE1 P4 P4 #GFF
99 UNBIAS$ SAMPLE1 P4 P4 #GFG
99 BIAS$ SAMPLE1 P4 P4 #GFG
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,EXAMPLE #D1 SUPPOSE ! W9N+ SCORE 9 !
NEXT GAME IS #BE 9/1D ( #C4 ,F9D ! NEW
M1N1 M$IAN1 MODE1 RANGE1 & /&>D DEVI,N
(! DATA SET4
------------------------------------#GDG
#AA.A ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#AI = ,EXS4 #E1AE1 & #BI
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
,EXS4 #B1G1H1BC1BD1 & #CJ
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3
,M1SURES ( @8 REPRES5T ! C5T] OR MI4LE
(A DATA SET4 ,M1SURES ( @8 TELL Y H[
SPR1D \ ! VALUES 9 A DATA SET >E4
#B4 .,,WRIT+ ,DEF9E ! M1N1 M$IAN1 &
MODE (A SET ( .;N NUMB]S4
,,M1SURES ,,( ,,C5TRAL ,,T5D5CY ,9
,EX]CISES #C-F1 F9D ! M1N1 M$IAN1 & MODE
(! DATA SET4
#C4 ,! NUMB]S ( MICE BORN 9 N9E DI6]5T
LITT]S3 #E1 #G1 #F1 #C1 #H1 #F1 #D1 #E1
#D
#D4 ,A /UD5T'S QUIZ SCORES =! F/
SEME/] ( AN ALGEBRA CLASS3 #AH1 #BJ1
#AD1 #AE1 #BJ1 #AG1 #AF
#E ,! HEI<TS 7IN 9*ES7 (! MEMB]S (A
M5'S COLLEGE BASKETBALL T1M3 #FI1 #GJ1
#GE1 #HD1 #GC1 #GH1 #GD1 #GC1 #GH1 #GA
#F4 ,! WAIT+ "TS 7IN M9UTES7 ( S"EAL P
AT A DOCTOR'S (FICE3 #BD1 #AI1 #CJ1 #CI1
#BB1 #AI1 #BF1 #CE1 #DB1 #AE1 #BE
#G4 .,,MULTIPLE .,,*OICE ,:AT IS !
M$IAN ( #J.E1 #J.F1 #J.G1 #A.B1 #A.E1 &
#A.E8
,A #J.G
;,B #J.IE
;,C #A
;,D #A.E
#H4 .,,MULTIPLE .,,*OICE ,:AT IS ! M1N
( #B1 #B1 #F1 #G1 #I1 & #AJ8
,A .#B
;,B .#F
;,C .#F..E
;,D .#G..B
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 F9D+ ! M1SURE ( C5TRAL T5D5CY4
.#I4 ,! M$IAN (! .DATA SET 2L IS #E
.2C #E IS ! MI4LE NUMB]4
#AB1 #C1 #I1 #E1AJ1AJ1 #C
#AJ4
,! ONLY ..MODE (! .DATA SET 2L IS #AB
.2C #AB .O3URS .MO/ FREQU5TLY4
#AB1 #I1 #BD1AB1AH1 #I1AB1AA1 #I
.,,EXAMPLE .#A .ON .P4 #GDD = ,EXS4
#C-AJ
,,M1SURES ,,( ,,4P].N ,F9D ! RANGE &
/&>D DEVI,N (! DATA SET4
.#AA4 #G1 #D1 #F1 #H1 #E1 #I1 #E1 #G
.#AB4 #AJ1 #AB1 #G1 #AA1 #BJ1 #G1 #F1
#H1 #I
.#AC4 #C.A1 #B.G1 #F.J1 #E.F1 #B.C1
#B.J1 #A.C
.#AD4 #DD1 #DG1 #DE1 #DH1 #DE1 #DG1
#EJ1 #DD1 #DH1 #DB
#AE #ACE1 #ADB1 #ADH1 #ACF1 #AEB1
#ADJ1 #AEH1 #AED
.#AF4 #CJA1 #CAB1 #CJH1 #CBJ1 #CAH1
#CAE1 #CBE1 #CCF
,,EXAMPLES #B & #C
ON P4 #GDE = ,EXS4 #AA-AF
,,ID5TIFY+ ,,\TLI]S ,ID5TIFY ! \TLI] 9
! DATA SET4 ,!N F9D ! M1N1 M$IAN1 MODE1
RANGE1 & /&>D DEVI,N (! DATA SET :5 !
\TLI] IS 9CLUD$ & :5 X IS N4
.#AG4 #B1B1C1C1D1D1D1F1FH
.#AH4 #J1GB1GE1GE1HC1HC1HC1IA
.#AI4 #AJ.I1 #AB.D1 #J.G1 #AA.F1
#AB.H1 #AA.F
.#BJ4 #BH1 #BJ1 #BE1 #BH1 #AJJ1 #BE1
#BJ
.#BA4 #FJ1 #FH1 #GE1 #GH1 #AEB1 #GA1
#FF1 #GB1 #FF1 #HJ
.#BB4 #AHD1 #AIB1 #AGC1 #AHA1 #AII1
#FE1 #AIJ1 #AHH
99 ,,EXAMPLE #D
ON P4 #GDF = ,EXS4 #AG-BB
------------------------------------#GDH
.#BC4 .,,OP5-.,,5D$ .,,MA? ,CR1TE A
DATA SET )A M1N ( #AJ1 A M$IAN ( #AA1 &A
MODE ( #H4
#BD4 .,,%ORT .,,RESPONSE ,AN \TLI] C 2
DEF9$ Z A VALUE 9 A DATA SET T LIES M
?AN ?REE /&>D DEVI,NS F ! M1N4 ,S1 .;X
IS AN \TLI] IF @4 ,9 "PS 7A7-7;C71 USE ?
DEF9I;N 6ID5TIFY ! \TLI]7;S7 .A 9 ! DATA
SET4 .,JU/IFY YR ANSW]S MA!MATIC,Y4
A4 #GJ1 #EE1 #ED1 #GE1 #FJ1 #EH1 #EE1
#EF1 #F1 #FB1 #FH1 #ID1 #EE1 #HB1 #FI1
#GD
B4 #AH1 #BJ1 #BB1 #BE1 #AF1 #DJ1 #BD1
#AI1 #CH1 #C1 #BA1 #BG1 #HH1 #BD1 #BC1
#BF
C4 #EJ1 #IC1 #HA1 #HD1 #HH1 #HE1 #IJ1
#II1 #IB1 #AII1 #IF1 #HI1 #HG1 #ID1 #CG
#BE4 .,,*ALL5GE ,! =MULA = /&>D DEVI,N
C AL 2 WRITT5 Z3
,= .;N .K #C1 %[ T ? =MULA IS
EQUIVAL5T 6! =MULA GIV5 ON PAGE #GDE @4
7.,H9T3 ,Y W NE$ 6%[ T @4@7
,PRO#M ,SOLV+
,,EXAMPLES #A1B1 & #C
ON PP4 #GDD-GDE = ,EXS4 #BF-BH
#BF4 .,,FOOTBALL ,! DATA SET 2L GIVES
! NUMB]S ( PASS+ T\*D[NS =! #AB
QU>T]BACKS :O ?REW ! MO/ T\*D[NS DUR+ !
#BJJD ,,NFL REGUL> S1SON4 ,F9D ! M1N1
M$IAN1 MODE1 RANGE1 & /&>D DEVI,N4
#DI1 #CI1 #CA1 #CJ1 #BI1 #BH1 #BG1
#BG1 #BG1 #BB1 #BA1 #BA
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#BG4 .,,OLYMPIC .,,S(TBALL ,! DATA SET
2L GIVES ! TOTAL NUMB] ( AT-BATS = EA*
PLAY] ON ! #BJJD ,U4,S4 WOM5'S ,OLYMPIC
S(TBALL T1M4 ,F9D ! M1N1 M$IAN1 & MODE
(! DATA SET4
#B1 #F1 #F1 #AF1 #AI1 #BJ1 #BJ1 #BA1
#BB1 #BE1 #BF1 #CJ
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#BH4 .,,>*]Y ,! DATA SET 2L GIVES !
SCORES (! 3TE/ANTS 9 ! F/ R.D (A JUNIOR
>*]Y -PETI;N4 ,F9D ! M1N1 M$IAN1 MODE1
RANGE1 & /&>D DEVI,N4
,ILL1 #AAD1 #IG1 #AJB1 #ABJ1 #AAC1
#AAF1 #AAD1 #AJF1 #AAJ
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
.#BI4 .,,MULTI-.,,/EP .,,PRO#M ,! DATA
SET 2L GIVES ! NUMB]S ( TRIALS REQUIR$
0#AJ PUPPIES 6LE>N A TRICK4
#BJ1 #BC1 #AI1 #BE1 #BA1 #BC1 #E1 #BD1
#AI1 #BC
A4 .,ANALYZE ,ID5TIFY ! \TLI] (! DATA
SET4
B4 .,CALCULATE ,F9D ! M1N1 M$IAN1
MODE1 RANGE1 & /&>D DEVI,N (! DATA SET
:5 ! \TLI] IS 9CLUD$ & :5 X IS N4
C4 .,R1SON+ .,DESCRIBE ! \TLI]'S E6ECT
ON ! M1SURES ( C5TRAL T5D5CY & 4N].N4
,,EXAMPLE #D
ON P4 #GDF = ,EX4 #BI
.K ..,,"W$-,,\ ,,SOLU;NS .ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#GDI
#CJ4 .,,EXT5D$ .,,RESPONSE ,! TA# %[S
! RESULTS 7IN MET]S7 =! F9AL R.D (!
#BJJD & #AIFD M5'S ,OLYMPIC JAVEL9 ?R[
EV5TS4
,! FOLL[+ TA# IS 9 LI/$
=MAT4 ,= EA* CELL ! H1D+ IS %[N
FOLL[$ 0A COLON1 SPACE &! CELL
3T5TS
,M5'S ,OLYMPIC ,JAVEL9 ,?R[3 .#BJJD
.DATA
,M5'S ,OLYMPIC ,JAVEL9 ,?R[3 .#AIFD
.DATA
,M5'S ,OLYMPIC ,JAVEL9 ,?R[3
#HF.EJ1HD.IE1HD.HD1HD.AC1
#HC.CA1HC.BE1HC.AD1HC.JA1
#HJ.EI1HJ.BH1GI.DC1GD.CF
,M5'S ,OLYMPIC ,JAVEL9 ,?R[3
#HB.FF1HB.CB1HJ.EG1HJ.AG1 #GH.GB1
#GF.ID1 #GD.GB1 #GD.BF
A4 .,CALCULATE ,F9D ! M1N1 M$IAN1
MODE1 RANGE1 & /&>D DEVI,N (! #BJJD
DATA4
B4 .,CALCULATE ,F9D ! M1N1 M$IAN1
MODE1 RANGE1 & /&>D DEVI,N (! #AIFD
DATA4
C4 .,ANALYZE .,-P>E ! /ATI/ICS = EA*
SET ( DATA4 ,DRAW "O OR M 3CLU.NS AB !
DATA4
#CA4 .,,*ALL5GE ,! M1N 4CUSS$ 9 ?
LESSON IS CALL$ ! .>I?METIC .M1N4 ,ANO!R
TYPE ( M1N IS ! .GEOMETRIC .M1N4 ,!
GEOMETRIC M1N ( TWO POSITIVE NUMB]S .A &
.;B IS @4 ,USE ! /EPS 2L 6PROVE T !
>I?METIC M1N ( .A & .;B IS ALW GRT] ?AN
OR EQUAL 6! GEOMETRIC M1N ( .A & .B4
A4 .,EXPLA9 :Y @7 .A -- .;B7 #B .1.K
#J4
B4 ,USE ! 9EQUAL;Y 9 "P 7A7 6%[ T 7.A
@+ .;B7 #B .1.K .#D;AB4
C4 ,USE ! 9EQUAL;Y 9 "P 7;B7 6%[ T !
>I?METIC M1N ( .A & .;B IS GRT] ?AN OR
EQUAL 6! GEOMETRIC M1N ( .A & .;B @1 OR
D4 ,"U :AT 3DI;N IS ! >I?METIC M1N (
.A & .;B EQUAL 6! GEOMETRIC M1N ( .A &
.;B8
,PREVIEW
,PREP>E = ,LESSON #AA.B 9 ,EXS4
#CB-CG4
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
,EVALUATE ! FUNC;N :5 ;X .K #C.H & :5
;X .K #FJJ4 @7 P4 #GB @7
.#CB4 .;F 7;X7 .K ;X @+ #GJI
.#CC4 .;F 7;X7 .K ;X @+ #AA.FH
.#CD4 .;F 7;X7 .K #AE.D;X
.#CE4 .;F 7;X7 .K #BJJ;X
.#CF4 .;F 7;X7 .K #E;X @+ #ACF
.#CG4 .;F 7;X7 .K #BB;X--#DEJ
,WRITE AN EQU,N (! ELLIPSE )! GIV5
"*I/ICS & C5T] AT 7#J1J74 @7 P4 #FCD @7
.#CH4 ,V]TEX3 7#J1E7
,CO-V]TEX3 7#C1J7
.#CI4 ,V]TEX3 7#G1J7
,FOCUS3 7--#C1J7
.#DJ4 ,CO-V]TEX3 7#J1 @7
,FOCUS3 7--#B1J7
.#DA4 .,,OHM'S .,,LAW ,OHM'S LAW /ATES
T ! RESI/.E .;,R 7IN OHMS7 (A 3DUCTOR
V>IES DIRECTLY )! POT5TIAL DI6];E .;,V
7IN VOLTS7 2T TWO PO9TS & 9V]SELY )!
CURR5T .,I 7IN AMP]ES74 ,! 3/ANT ( V>I,N
IS #A4 ,:AT IS ! RESI/.E (A LI<T BULB :5
"! IS A CURR5T ( #J.H AMP]E &A POT5TIAL
DI6];E ( #ABJ VOLTS8 @7 P4 #EEA @7
.#DB..,,DOG .,,%[ ,9 A DOG %[1 H[ _M
WAYS C #C ,G]MAN %EPH]DS1 #E COLLIES1 #D
COCK] SPANIELS1 & #C CORGIS L9E UP 9
FRONT (! JUDGES IF DOGS (! SAME BRE$ >E
3SID]$ ID5TICAL8 @7 P4 #FHB @7
.,,EXTRA .,,PRACTICE = ,LESSON #AA.A1
P4 #AJBJ
..,,ONL9E ,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#GEJ
,GRAPH+ ,CALCULATOR ,ACTIV;Y3 #AA.A
,CALCULATE ,"O-,V>IA# ,/ATI/ICS
,USE AF ,LESSON #AA.A
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,KEY/ROKES
,SIDEB>3
.,/&>DS
,PROBABIL;Y & ,/ATI/ICS3#F.J
,/UD5TS "K ! DEF9I;NS (! M1N1 M$IAN1 &
MODE (A 4TRIBU;N ( DATA & C -PUTE EA* 9
"PICUL> SITU,NS4
,PROBABIL;Y & ,/ATI/ICS3#G.J
./UD5TS .-PUTE .! V>I.E &! ../&>D
DEVI,N (A 4TRIBU;N ( .DATA4
,"Q ,H[ C Y USE A GRAPH+ CALCULATOR
6F9D /ATI/ICS8
,EXAMPLE ,CALCULATE /ATI/ICS =A DATA
SET
,! DATA SET 2L GIVES ! AGES (! F/ #DC
,PRESID5TS (! ,UNIT$ ,/ATES :5 !Y F/
TOOK (FICE4 ,USE A GRAPH+ CALCULATOR
6F9D ! M1N1 M$IAN1 RANGE1 & /&>D DEVI,N
(! DATA SET4
#EG1 #FA1 #EG1 #EG1 #EH1 #EG1 #FA1
#ED1 #FH1 #EA1 #DI1 #FD1 #EJ1 #DH1 #FE1
#EB1 #EF1
#DF1 #ED1 #DI1 #EA1 #DG1 #EE1 #EE1
#ED1 #DB1 #EA1 #EF1 #EE1 #EA1 #ED1 #EA1
#FJ1 #FB1
#DC1 #EE1 #EF1 #FA1 #EB1 #FI1 #FD1
#DF1 #ED
,,/EP #A .,CALCULATE ./ATI/ICS
,5T] ! DATA 9 LI/ .;,L #A ,!N PRESS @1
*OOSE ! ,,CALC M5U1 & SELECT #A-,V>
,/ATS4
,,/EP#B ,R1D /ATI/ICS
,! SCRE5 %[S A LI/ ( /ATI/ICS4 ,! M1N
IS #ED.H4 ,! /&>D DEVI,N IS ;X #F.AE4
,,/EP #C .,SCROLL .D[N
,SCROLL D[N 6F9D T ! M$IAN 7,M$7 IS
#EE4 ,! RANGE IS MAX,X--M9,X1 OR #BG4
,PRACTICE
,USE A GRAPH+ CALCULATOR 6F9D ! M1N1
M$IAN1 RANGE1 & /&>D DEVI,N (! DATA SET4
.#A4 #DC1 #DF1 #DG1 #DH1 #EA1 #ED1
#EH1 #DJ1 #EB
.#B4 #C.A1 #B.G1 #F.J1 #E.F1 #B.C1
#B.J1 #A.C1 #C.D
.#C4 #HH1 #HC1 #IA1 #HB1 #GH1 #HA1
#IA1 #IE1 #IH
.#D4 #AI.D1 #AF.C1 #AB.G1 #BD.H1
#AI.B1 #AE.D
.#E4 #AAJ1 #AJG1 #AJA1 #AJH1 #AJF1
#AAB1 #AJD
.#F4 #BFE1 #BEB1 #BEG1 #BIH1 #BGE1
#BHA1 #BGF
..#G4 ,,VICE ,,PRESID5TS' .,,ACES ,!
DATA SET 2L GIVES ! AGES (! F/ #DF VICE
PRESID5TS (! ,UNIT$ ,/ATES :5 !Y F/ TOOK
(FICE4 ,USE A GRAPH+ CALCULATOR 6F9D !
M1N1 M$IAN1 RANGE1 & /&>D DEVI,N (! DATA
SET4
#EC1 #EC1 #DE1 #FE1 #FH1 #DB1 #DB1
#EJ1 #EF1 #EJ1 #EB1 #DI1 #FF1 #CF1 #EA1
#EF1 #DE1 #FA1
#EG1 #EA1 #FE1 #FD1 #EG1 #EB1 #DB1
#EB1 #EC1 #EH1 #DH1 #EI1 #FI1 #FD1 #EB1
#FJ1 #GA1 #DJ1
#EB1 #EC1 #EA1 #FJ1 #FF1 #DI1 #EF1
#DA1 #DD1 #EI
------------------------------------#GEA
#AA.B ,APPLY ,TRANS=M,NS 6,DATA
.,2F ,Y CALCULAT$ /ATI/ICS = DATA
SETS4
.,N[ ,Y W LE>N H[ TRANS=M,NS ( DATA
A6ECT /ATI/ICS4
.,:Y8 ,S Y C SOLVE PRO#MS AB SPACE
TRAVEL1 Z 9 ,EXAMPLE #A4
,KEY ,VOCABUL>Y
99 M1N1 .P4 .#GDD
99 M$IAN1 .P4 .#GDD
99 MODE1 .P4 .#GDD
99 RANGE1 .P4 .#GDE
99 ./&>D .DEVI,N @1 P4 #GDE
,SIDEB>3
.,/&>DS
,PROBABIL;Y & ,/ATI/ICS3#F.J
,/UD5TS "K ! DEF9I;NS (! M1N1 M$IAN1 &
MODE (A 4TRIBU;N ( DATA & C -PUTE EA* 9
"PICUL> SITU,NS4
,PROBABIL;Y & ,/ATI/ICS3#G.J
./UD5TS .-PUTE .! V>I.E &! ../&>D
DEVI,N (A 4TRIBU;N ( .DATA4
,! FOLL[+ /ATI/ICS DESCRIBE ! DATA SET
#G1 #AB1 #AF1 #BJ1 & #BJ4
.,M1N3 #AE
.,M$IAN3 #AF
.,MODE3 #BJ
.,RANGE3 #AC
.,/D4 .,DEV43 #E.J
,A4+ #AJ 6EA* DATA VALUE PRODUCES !
DATA SET #AG1 #BB1 #BF1 #CJ1 & #CJ4 ,!
/ATI/ICS = ? DATA SET >E %[N 2L4
.,M1N3 #BE
.,M$IAN3 #BF
.,MODE3 #CJ
.,RANGE3 #AC
.,/D4 .,DEV43 #E.J
,NOTICE T ! M1N1 M$IAN1 & MODE H EA*
9CR1S$ 0#AJ1 B ! RANGE & /&>D DEVI,N >E
UN*ANG$4 ,^! RESULTS C 2 G5]ALIZ$4
,,KEY ,,3CEPT .= .,YR .,NOTEBOOK
,A4+ A ,3/ANT 6,DATA ,VALUES
,:5 A 3/ANT IS A4$ 6E VALUE 9 A DATA
SET1 ! FOLL[+ >E TRUE3
99 ,! M1N1 M$IAN1 & MODE (! NEW DATA
SET C 2 OBTA9$ 0A4+ ! SAME 3/ANT 6! M1N1
M$IAN1 & MODE (! ORIG9AL DATA SET4
99 ,! RANGE & /&>D DEVI,N >E UN*ANG$4
,EXAMPLE #A ,ADD A 3/ANT 6DATA VALUES
.,,A/RONAUTS ,! DATA SET 2L GIVES !
WEI<TS 7IN P.DS7 ON ,E>? ( EI<T
A/RONAUTS )\T _! SPACE SUITS4 ,A SPACE
SUIT WEI<S #BEJ P.DS ON ,E>?4 ,F9D !
M1N1 M$IAN1 MODE1 RANGE1 & /&>D DEVI,N
(! WEI<TS (! A/RONAUTS )\T _! SPACE
SUITS &) _! SPACE SUITS4
#ADB1 #AEJ1 #AEE1 #AEF1 #AFJ1 #AFJ1
#AFF1 #AGE
,SOLU;N
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 .,WEI<TS .)\T .SUITS @3 .,WEI<TS
.) .SUITS
.,M1N @3 #AEH3 #AEH @+ .#BEJ .K #DJH
.,M$IAN @3 #AEH3 #AEH @+ .#BEJ .K #DJH
.,MODE @3 #AFJ3 #AFJ @+ .#BEJ .K #DAJ
.,RANGE @3 #CC3 #CC 7UN*ANG$7
.,/&>D .DEVI,N @3 #I.C3 #I.C 7UN*ANG$7
------------------------------------#GEB
..,,TRANS=M+ ,,DATA ,,0.,,MULTIPLIC,N
,ANO!R TYPE ( TRANS=M,N Y C APPLY 6A
DATA SET IS 6.MULTIPLY EA* DATA VALUE 0!
SAME 3/ANT4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,MULTIPLY+ ,DATA ,VALUES 0A ,3/ANT
,:5 EA* VALUE (A DATA SET IS MULTIPLI$
0A 3/ANT1 ! NEW M1N1 M$IAN1 MODE1 RANGE1
& /&>D DEVI,N C 2 F.D 0MULTIPLY+ EA*
ORIG9AL /ATI/IC 0! SAME 3/ANT4
,EXAMPLE #B ,MULTIPLY DATA VALUES 0A
3/ANT
.,,OLYMPICS ,! DATA SET 2L GIVES !
W9N+ 4T.ES 7IN MET]S7 9 ! M5'S ,OLYMPIC
TRIPLE JUMP EV5TS F #AIFD 6#BJJD4 ,F9D !
M1N1 M$IAN1 MODE1 RANGE1 & /&>D DEVI,N
(! 4T.ES 9 MET]S &(! 4T.ES 9 FEET4 @7
.,NOTE3 #A MET] #C.BH FEET47
#AF.HE1 #AG.CI1 #AG.CE1 #AG.BI1
#AG.CE1 #AG.BF1 #AG.FA1 #AH.AG1 #AH.JI1
#AG.GA1 #AG.GI
,SOLU;N
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 ,4T.ES 9 MET]S3 ,4T.ES 9 FEET
.,M1N @3 #AG.EC3 .#C..BH 7#AG.EC7
#EG.EJ
.,M$IAN @3 #AG.CI3 .#C..BH 7#AG.CI7
#EG.JD
.,MODE @3 #AG.CE3 .#C..BH 7#AG.CE7
#EF.IA
.,RANGE @3 #A.CB3 .#C..BH 7#A.CB7
#D.CC
.,/&>D .DEVI,N @3 #J.CG3 .#C..BH
7#J.CG7 #A.BA
.,GUID$ .,PRACTICE = ,EXAMPLES #A & #B
#A4 .,,A/RONAUTS ,! ,MANN$ ,MANEUV]+
,UNIT 7,,MMU7 IS EQUIP;T T LAT*ES ONTO
AN A/RONAUT'S SPACE SUIT & 5A#S !
A/RONAUT 6MOVE >.D \TSIDE ! SPACECRAFT4
,! ,,MMU WEI<S AB #CJJ P.DS ON ,E>?4
,F9D ! M1N1 M$IAN1 MODE1 RANGE1 & /&>D
DEVI,N (! WEI<TS (! A/RONAUTS 9 ,EXAMPLE
#A ) _! SPACE SUITS & ,,MMU,'S4
#B4 .,,:AT .,,IF8 ,9 ,EXAMPLE #B1 F9D
! M1N1 M$IAN1 MODE1 RANGE1 & /&>D DEVI,N
(! 4T.ES 9 Y>DS4 7.,NOTE3 #A MET] #A.JI
Y>DS47
------------------------------------#GEC
#AA.B ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#BJ = ,EXS4 #E1AA1 & #AI
.K .,,/&>DIZ$ .,,TE/ .,,PRACTICE
,EXS4 ..#B1AF1 #BJ1BB1 & .#BC
.K .,,MULTIPLE .,,REPRES5T,NS
,EX#.BA
,SKILL ,PRACTICE
#A4 .,,VOCABUL>Y ,COPY & -PLETE3
,MULTIPLY+ EA* VALUE 9 A DATA SET 0A
3/ANT IS AN EXAMPLE (A7;N7 @8 (! DATA4
#B4 .,,WRIT+ .,DESCRIBE H[ A4+ ! SAME
3/ANT 6E VALUE 9 A DATA SET A6ECTS !
M1N1 M$IAN1 MODE1 RANGE1 & /&>D DEVI,N4
,,EXAMPLE #A
ON P4 #GEA = ,EXS4 #C-I
,,A4+ ,A ,,3/ANT ,F9D ! M1N1 M$IAN1
MODE1 RANGE1 & /&>D DEVI,N (! GIV5 DATA
SET &(! DATA SET OBTA9$ 0A4+ ! GIV5
3/ANT 6EA* DATA VALUE4
.#C4 #AD1 #AE1 #AG1 #AG1 #AI1 #BA1
#BC2 3/ANT3 #F
.#D4 #CA1 #CE1 #CH1 #CI1 #DB1 #DB1
#DH2 3/ANT3 #AH
.#E4 #GF1 #GG1 #GG1 #GH1 #HA1 #HC2
3/ANT3 #AG
.#F4 #AGH1 #AIC1 #BJD1 #BAA1 #BAA1
#BAF2 3/ANT3 #AEE
.#G4 #EC1 #FD1 #EA1 #FJ1 #EC1 #DE1
#FF2 3/ANT3 --#BA
.#H4 #BIE1 #BGI1 #BGH1 #BHB1 #BGI1
#CJA2 3/ANT3 --#DE
#I4 .,,]ROR .,,ANALYSIS ,! /&>D DEVI,N
(A DATA SET IS #AJ4 .,DESCRIBE & CORRECT
! ]ROR 9 F9D+ ! /&>D DEVI,N IF #C IS A4$
6EA* DATA VALUE4
,NEW /&>D .DEVI,N3 #AJ @+ #C .K #AC
,,EXAMPLE #B
ON P4 #GEB = ,EXS4 #AJ-AF
,,MULTIPLY+ ,,0,A ,,3/ANT ,F9D ! M1N1
M$IAN1 MODE1 RANGE1 & /&>D DEVI,N (!
GIV5 DATA SET &(! DATA SET OBTA9$
0MULTIPLY+ EA* DATA VALUE 0! GIV5 3/ANT4
.#AJ4 #AI1 #BC1 #BC1 #BF1 #CJ1 #CA1
#CD2 3/ANT3 #C
.#AA #EH1 #EH1 #EI1 #FB1 #FD1 #FE1
#FG2 3/ANT3 #D
.#AB4 #BH1 #CA1 #CB1 #CE1 #CE1 #CI1
#DJ2 3/ANT3 #A.E
.#AC4 #HH1 #IA1 #II1 #AJB1 #AJB1 #AJG2
3/ANT3 #B.E
.#AD4 #ACJ1 #ABA1 #ACB1 #AAE1 #ACJ1
#AJH2 3/ANT3 #J.E
.#AE4 #BBB1 #BCA1 #BBB1 #BAB1 #BEJ1
#BCE2 3/ANT3 #J.I
#AF4 .,,MULTIPLE .,,*OICE ,! RANGE (A
DATA SET IS #BA4 ,EA* VALUE 9 ! DATA SET
IS MULTIPLI$ 0#C4 ,:AT IS ! NEW RANGE8
,A .#G
;,B .#BA
;,C .#BD
;,D .#FC
#AG4 .,,*ALL5GE ,LET .;X #A .;X #B
@1@4 @4@4@1 .;X ;N.' .-2 ! VALUES 9 A
DATA SET1 & LET 2 ! M1N (! DATA SET4 ,%[
T ! M1N ( .AX #A @1 .AX #B @1'@1 .AX
;N.' .-IS .A @4
,,EXAMPLES #A & #B
ON PP4 #GEA-GEB = ,EXS4 #AH-BB
,PRO#M ,SOLV+
#AH4 .,,SAL>IES ,! DATA SET 2L GIVES !
ANNUAL SAL>IES 7IN ?\S&S ( DOLL>S7 ( N9E
,,DJ,'S "W+ AT A LOCAL RADIO /,N4
#CI1 #BI1 #DB.E1 #BH.E1 #DH1 #DE1 #CH1
#CF.E1 #BH.E
A4 ,F9D ! M1N1 M$IAN1 MODE1 RANGE1 &
/&>D DEVI,N (! SAL>IES4
B4 ,EA* ,,DJ RCVS AN ANNUAL BONUS (
4#ABJJ4 ,F9D ! M1N1 M$IAN1 MODE1 RANGE1
& /&>D DEVI,N (! SAL>IES 9CLUD+ ! BONUS4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
------------------------------------#GED
#AI .,,3/RUC;N ,P :O PLA/] CEIL+S
"S"TS WALK ON /ILTS4 ,? ALL[S !M 6R1*
HI< CEIL+S )\T HAV+ 6MOVE A LA4]4 ,!
DATA SET 2L GIVES ! HEI<TS 7IN 9*ES7 (
N9E PLA/]]S4
#GB1 #GC1 #GA1 #FF1 #GD1 #FH1 #GB1
#FI1 #GB
A4 ,F9D ! M1N1 M$IAN1 MODE1 RANGE1 &
/&>D DEVI,N (! GIV5 HEI<TS4
B4 ,! PLA/]]S USE /ILTS T >E #BH 9*ES
HI<4 ,F9D ! M1N1 M$IAN1 MODE1 RANGE1 &
/&>D DEVI,N (! PLA/]]S' HEI<TS ) /ILTS4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
#BJ4 .,,MULTIPLE .,,*OICE ,A T1*]
GIVES A TE/ = : ! M1N (! SCORES IS #FH
&! /&>D DEVI,N IS #AE4 ,! T1*] DECIDES
6SCALE ! TE/ SCORES 0A4+ #AJ PO9TS 6EA*
SCORE4 ,:AT >E ! M1N & /&>D DEVI,N (!
SCAL$ TE/ SCORES8
,A M1N3 #FH1 /&>D DEVI,N3 #BE
;,B M1N3 #GH1 /&>D DEVI,N3#AE
;,C M1N3 #GH1 /&>D DEVI,N3 #BE
;,D M1N3 #GH1 /&>D DEVI,N3#E
#BA .,,MULTIPLE .,,REPRES5T,NS ,! DATA
SET GIVES ! W9N+ 4T.ES 7IN MET]S7 9 !
WOM5'S ,OLYMPIC L;G JUMP EV5T F #AIEB
6#BJJD4
#F.BD1 #F.CE1 #F.CG1 #F.GF1 #F.HB1
#F.GH1 #F.GB1 #G.JF1 #F.IF1 #G.DJ1
#G.AD1 #G.AB1 #F.II1 #G.JG
A4 ..,F9D ,/ATI/ICS 9 .,MET]S ,F9D !
M1N1 M$IAN1 MODE1 RANGE1 & /&>D DEVI,N
(! 4T.ES 9 MET]S4
B4 ..,F9D ,/ATI/ICS 9 .,FEET ,F9D !
/ATI/ICS LI/$ 9 "P 7A7 =! 4T.ES 9 FEET4
7.,NOTE3 #A MET] #C.BH FEET47
#BB4 .,,%ORT .,,RESPONSE ,! DATA SET
2L GIVES ! WEI<TS 7IN P.DS7 ( EI<T
SMOKEJUMP]S ) _! EQUIP;T4
#BHG1 #BFE1 #BGC1 #BGE1 #BIE1 #BHJ1
#BIJ1 #BHJ
A4 ,F9D ! M1N1 M$IAN1 MODE1 RANGE1 &
/&>D DEVI,N (! GIV5 WEI<TS4
B4 ,! EQUIP;T EA* SMOKEJUMP] C>RIES
WEI<S AB #AAE P.DS4 ,F9D ! M1N1 M$IAN1
MODE1 RANGE1 & /&>D DEVI,N (! WEI<TS (!
SMOKEJUMP]S )\T _! EQUIP;T4 .,EXPLA9 YR
R1SON+4
#BC4 .,,EXT5D$ .,,RESPONSE ,! WAT]
TEMP]ATURE 9 AN \TDOOR POOL IS M1SUR$
#AB "TS DUR+ A C]TA9 WEEK4 ,!
TEMP]ATURES 7IN DEGREES ,FAHR5HEIT7 >E
LI/$ 2L4
#GD.E1 #HA.I1 #GB.E1 #GC.D1 #GH.D1
#GB.F1 #GF.H1 #GD.E1 #GG.F1 #GB.J1
#GI.B1 #GF.B
A4 ,F9D ! M1N1 M$IAN1 MODE1 RANGE1 &
/&>D DEVI,N (! ,FAHR5HEIT TEMP]ATURES4
B4 ,3V]T ALL (! ,FAHR5HEIT TEMP]ATURES
;,F 6,CELSIUS TEMP]ATURES ;,C US+ !
=MULA
C4 ,F9D ! M1N1 M$IAN1 MODE1 RANGE1 &
/&>D DEVI,N (! ,CELSIUS TEMP]ATURES4
D4 .,DESCRIBE ! E6ECTS ( 3V]T+ F
,FAHR5HEIT 6,CELSIUS ON ! M1SURES (
C5TRAL T5D5CY & 4P].N4
.K ..,,"W$-,,\ ,,SOLU;NS ONP4.,,W/
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
------------------------------------#GEE
#BD4 .,,W1!R ,! GRAPH %[S ! AV]AGE
RA9FALL 7IN C5TIMET]S7 = ,NEW ,YORK'S
,C5TRAL ,P>K DUR+ EA* MON? (! YE>4 ,F9D
! M1N1 M$IAN1 MODE1 RANGE1 & /&>D DEVI,N
(! RA9FALL AM.TS 9 C5TIMET]S & 9 9*ES4
7.,NOTE3 #A C5TIMET] #J.CICG 9*47
#BE4 .,,*ALL5GE ,A -PANY HAS #E
EXECUTIVES1 #AE SUP]VISORS1 & #HJ
PRODUC;N "W]S4 ,! SAL>Y RANGES >E
4#AJJ1JJJ-4#ADJ1JJJ =! EXECUTIVES1
4#FJ1JJJ-4#IJ1JJJ =! SUP]VISORS1 &
4#CJ1JJJ-4#EJ1JJJ =! PRODUC;N "W]S4 ,!
M1N ( ALL ! SAL>IES IS 4#DI1EJJ1 &!
M$IAN IS 4#DB1JJJ4 ,EA* SUP]VISOR GETS A
4#EJJJ RAISE & NO "O ELSE GETS A RAISE4
,:AT >E ! NEW M1N & M$IAN8 .,EXPLA94
,PREVIEW
,PREP>E = ,LESSON #AA.C 9 ,EXS4
#CJ-CG4
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
,SOLVE ! EQU,N4
.#BF4 .;X #B -- LLX @+ #BD .K #J @7 P4
#BEB @7
.#BG4 .#C;X #B -- #AC;X @+ #H .K #J @7
P4 #BIB @7
.#BH4 @7 P4 #DEB @7
.#BI4 #B ;X .K #AG @7 P4 #EAE @7
,CALCULATE ! PROBABIL;Y ( TOSS+ A CO9
#CJ "TS & GETT+ ! GIV5 NUMB] ( H1DS4 @7
P4 #GBD @7
.#CJ4 #D
.#CA4 #AG
.#CB4 #BA
.#CC4 #G
.#CD4 #AD
.#CE4 #AA
.#CF4 #BG
.#CG4 #AH
.#CH4 .,,TRADE .,,%[S ,Y >E ATT5D+ A
TRADE %[ T HAS BOO?S F #BJ DI6]5T
V5DORS4 ,Y PLAN 6VISIT AT L1/ #E (!
BOO?S4 ,H[ _M -B9,NS ( BOO?S C Y VISIT8
@7 P4 #FIJ @7
,,QUIZ .= .,LESSONS .#AA..A-.AA..B
,F9D ! M1N1 M$IAN1 MODE1 RANGE1 & /&>D
DEVI,N (! DATA SET4
7P4 .#GDD7
.#A4 #H1 #E1 #E1 #I1 #AA1 #AE1 #G1
#AA1 #AF
.#B4 #AH1 #AI1 #BC1 #AG1 #AI1 #AE1
#AD1 #BD1 #BA
.#C4 #EF1 #DE1 #DH1 #DG1 #EF1 #EE1
#DC1 #DD
.#D4 #FG1 #GJ1 #GC1 #FH1 #GA1 #GC1
#GD1 #GC1 #GJ
.#E4 #ADE1 #AHA1 #AFC1 #AEJ1 #AEH1
#AGB1 #AEI
.#F4 #BDF1 #BCA1 #BFA1 #BDD1 #BEJ1
#BCB1 #BDF1 #BEH
#G4 .,,DIGITAL .,,CAM]AS ,! DATA SET
2L GIVES ! ORIG9AL PRICES ( N9E DI6]5T
DIGITAL CAM]AS AT AN ELECTRONICS /ORE4
,! /ORE IS (F]+ A PROMO;N 9 : ALL
DIGITAL CAM]AS ORD]$ ONL9E >E #BJ@3P (F4
,F9D ! M1N1 M$IAN1 MODE1 RANGE1 & /&>D
DEVI,N (! ORIG9AL PRICES &(! SALE
PRICES1 @7 P4 #GEA @7
4#ABJ1 4#ACJ1 4#AEJ1 4#AHJ1 4#BCJ1
4#BHJ1 4#CBJ1 4#CBJ1 4#CEJ
.,,EXTRA .,,PRACTICE = ,LESSON #AA.B1
P4 #AJBJ
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#GEF
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
.,/ATE .,TE/ .,PRACTICE
_+CLASSZONE.COM_:
,LESSONS #AA.A-AA.B
.#A4 .,MULTI-.,/EP .,PRO#M ,! DATA SET
2L GIVES ! ORIG9AL PRICES ( EI<T #AC-9*
COLOR ,,TV,'S SOLD 0AN ONL9E ELECTRONICS
/ORE4 ,! /ORE IS HAV+ A ?REE-"D SALE 9 :
ALL #AC-9* COLOR ,,TV,'S >E #BE@3P (F4
4#HD1 4#GE1 4#GJ1 4#AJJ1 4#HJ1 4#ABJ1
4#HJ1 4#GE
A4 ,F9D ! M1N1 M$IAN1 MODE1 RANGE1 &
/&>D DEVI,N (! ORIG9AL PRICES &(! SALE
PRICES4
B4 ,SUPPOSE ! /ORE _H 9/1D (F]$ A FIX$
4#BJ 4C.T ON EA* ,,TV4 .,-P>E ! E6ECTS (
? 4C.T ON ! M1SURES ( 5TRAL T5D5CY &
4P].N )! E6ECTS (! #BE@3P 4C.T4
.#B4 .,EXT5D$ .,RESPONSE ,! TA#S 2L %[
! AV]AGE TEMP]ATURE 7IN DEGREES
,FAHR5HEIT7 = EA* MON? (! YE> 9 ,MIAMI1
,FLORIDA1 & 9 ,BU6ALO1 ,NEW ,YORK4
,! FOLL[+ TA# IS 9 LI/$
=MAT4 ,= EA* CELL ! H1D+ IS %[N
FOLL[$ 0A COLON1 SPACE &! CELL
3T5TS
,AV]AGE ,MON?LY ,TEMP]ATURES 9 ,MIAMI1
,,FL3 #FG.F1FH.B1GA.B1 #GD.E1 #GG.I1
#HJ.H1 #HB.B1HB.F1HA.C1 #GG.I1 #GB.I1
#FH.I
,! FOLL[+ TA# IS 9 LI/$
=MAT4 ,= EA* CELL ! H1D+ IS %[N
FOLL[$ 0A COLON1 SPACE &! CELL
3T5TS
,AV]AGE ,MON?LY ,TEMP]ATURES 9
,BU6ALO1 ,,NY3 #BC.G1 #BD.F1 #CC.H1
#DE.A1 #EF.E1 #FE.H1 #GA.A1FH.I1FA.I1
#EA.A1DJ.E1BI.A
A4 ,F9D ! M1N1 M$IAN1 RANGE1 & /&>D
DEVI,N (! AV]AGE TEMP]ATURES 9 ,MIAMI1
,FLORIDA4
B4 ,F9D ! M1N1 M$IAN1 RANGE1 & /&>D
DEVI,N (! AV]AGE TEMP]ATURES 9 ,BU6ALO1
,NEW ,YORK4
C4 .,-P>E ! /ATI/ICS = EA* SET ( DATA4
,:AT IS "O 3CLU.N Y C MAKE AB ! DATA8
.#C4 .,OP5-.,5D$ ,GIVE AN EXAMPLE (A
DATA SET ( FIVE DI6]5T VALUES T HAS A
M1N ( #BJ4 ,APPLY A TRANS=M,N 6! DATA
VALUES T *ANGES ! M1N F #BJ 6#CJ4
.#D4 .,%ORT .,RESPONSE ,TWO
TRACK-&-FIELD T1MMATES RECORD _! "TS 7IN
SECONDS7 = FIVE TRIALS 9 ! #AJJ MET]
SPR9T EV5T4 ,! "TS >E LI/$ 9 ! TA#4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,TRIAL3 ,T1MMATE #A3 ,T1MMATE #B
#A3 #AA.C3 #AA.H
#B3 #AC.D3 #AB.C
#C3 #AA.A3 #AB.E
#D3 #AB.E3 #AA.I
#E3 #AA.C3 #AA.H
A4 ,F9D ! M1N1 M$IAN1 MODE1 RANGE1 &
/&>D DEVI,N ( EA* T1MMATE'S "TS4
B4 ,: T1MMATE HAS ! M 3SI/5T "TS8
.,EXPLA9 YR R1SON+4
.#E4 .,EXT5D$ .,RESPONSE ,! DATA SET
2L GIVES ! PRICES ( #AD M.TA9 BIKES 9 A
SPORT+ GDS /ORE4
4#AIE1 4#BEJ1 4#BIJ1 4#BJJ1 4#BFJ1
4#BJJ1 4#BGJ1 4#FGJ1 4#BEJ1 4#BCJ1
4#BJJ1 4#BAJ1 4#BGJ1 4#HEJ
A4 ,F9D ! M1N1 M$IAN1 MODE1 RANGE1 &
/&>D DEVI,N (! PRICES4
B4 ,: DATA VALUES WD Y 3SID] 6BE
\TLI]S8 .,EXPLA94
C4 ,F9D ! M1N1 M$IAN1 MODE1 RANGE1 &
/&>D DEVI,N (! PRICES :5 ! \TLI]S
ID5TIFI$ 9 "P 7;B7 >E N 9CLUD$4
D4 ,: (! /ATI/ICS IS MO/ A6ECT$ 0!
\TLI]S8 ,: IS L1/ A6ECT$ 0! \TLI]S8
.#F4 .,GRI4$ .,ANSW] ,! DATA SET 2L
GIVES ! SCORE ( EA* MEMB] (A HI< S*OOL
GOLF T1M 9 ! F/ R.D (! S1SON4
#GF1 #HD1 #HA1 #IB1 #HG
,9 ! LA/ R.D (! S1SON1 ALL ! GOLF]S
DECR1S$ _! SCORES 0#B /ROKES4 ,:AT IS !
AV]AGE SCORE 9 ! LA/ R.D8
------------------------------------#GEG
#AA.C ,USE ,NORMAL ,4TRIBU;NS
.,2F ,Y 9T]PRET$ PROBABIL;Y 4TRIBU;NS4
.,N[ ,Y W /UDY NORMAL 4TRIBU;NS4
.,:Y8 ,S Y C MODEL ANIMAL POPUL,NS1 Z
9 ,EXAMPLE #C4
,KEY ,VOCABUL>Y
99 NORMAL 4TRIBU;N
99 NORMAL CURVE
99 /&>D NORMAL 4TRIBU;N
99 ;Z-SCORE
,9 ,LESSON #AJ.F1 Y /UDI$ PROBABIL;Y
4TRIBU;NS4 ,"O TYPE ( PROBABIL;Y
4TRIBU;N IS A .NORMAL .4TRIBU;N4 ,A
.NORMAL .4TRIBU;N IS MODEL$ 0A BELL-%AP$
CURVE CALL$ A .NORMAL .CURVE T IS
SYMMETRIC AB ! M1N4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,>1S ,"U A ,NORMAL ,CURVE
,A NORMAL 4TRIBU;N ) M1N & /&>D DEVI,N
A HAS ! FOLL[+ PROP]TIES3
99 ,! TOTAL >EA "U ! RELAT$ NORMAL
CURVE IS #A4
99 ,AB #FH@3P (! >EA LIES )9 #A /&>D
DEVI,N (! M1N4
99 ,AB #IE@3P (! >EA LIES )9 #B /&>D
DEVI,NS (! M1N4
99 ,AB #II.G@3P (! >EA LIES )9 #C /&>D
DEVI,NS (! M1N4
,,9T]PRET ,,GRAPHS
,AN >EA "U A NORMAL CURVE C 2 9T]PRET$
EI Z A P]C5TAGE (! DATA VALUES 9 !
4TRIBU;N OR Z A PROBABIL;Y4
,SIDEB>3
.,/&>DS
,PROBABIL;Y & ,/ATI/ICS3#D.J
..,/UD5TS >E FAMILI> )! /&>D 4TRIBU;NS
7.NORMAL @1 BINOMIAL1 & EXPON5TIAL7 ..&
C USE !M 6SOLVE = EV5TS 9 PRO#MS 9 : !
4TRIBU;N 2L;GS 6^? .FAMILIES4
,EXAMPLE #A ,F9D A NORMAL PROBABIL;Y
,A ..NORMAL 4TRIBU;N HAS M1N ;X & /&>D
DEVI,N4,=A R&OMLY SELECT$ ;X-VALUE F !
4TRIBU;N1 F9D .;,P7 --..#B "K.K .;X "K.K
@7
,SOLU;N
,! PROBABIL;Y T A R&OMLY SELECT$
;X-VALUE LIES 2T 2T --#B & IS ! %AD$ >EA
"U ! NORMAL CURVE %[N4
.;,P7 --.#B "K.K.;X"K.K @7 .K #J.ACE
@+ #J.CD .K #J.DGE
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
------------------------------------#GEH
,,R1D+
,! A2REVI,N 8MG_/DL0 /&S = 8MILLIGRAMS
P] DECILIT]40
,EXAMPLE #B ,9T]PRET NORM,Y 4TRIBUT$
DATA
.,,H1L? ,! BLOOD *OLE/]OL R1D+S =A
GR\P ( WOM5 >E NORM,Y 4TRIBUT$ )A M1N (
#AGB MG_/DL &A /&>D DEVI,N ( #AD MG_/DL4
A4 ,AB :AT P]C5T (! WOM5 H R1D+S 2T
#AEH & #AHF8
B4 ,R1D+S HI<] ?AN #BJJ >E 3SID]$
UNDESIRA#4 ,AB :AT P]C5T (! R1D+S >E
UNDESIRA#8
,SOLU;N
A4 ,! R1D+S ( #AEH & #AHF REPRES5T "O
/&>D DEVIATIOR ON EI SIDE (! M1N1 Z %[N
2L4 ,S1 #FH@3P (! WOM5 H R1D+S 2T #AEH &
#AHF4
B4 ,A R1D+ ( #BJJ IS TWO /&>D DEVI,NS
6! "R (! M1N1 Z %[N4 ,S1 ! P]C5T ( R1D+S
T >E UNDESIRA# IS #B.CE@3P@+ #J.AE@3P1
OR #B.E@3P4
..,GUID$ ,PRACTICE = ,EXAMPLES #A &
.#B
,A NORMAL 4TRIBU;N HAS M1N & /&>D
DEVI,N4 ,F9D ! 9DICAT$ PROBABIL;Y =A
R&OMLY SELECT$ ;X-VALUE F ! 4TRIBU;N4
#A4 .;,P7.;,X"K.K @7
#B4 .;,P7.;X.1 @7
#C4 ;,P7 "K.K;X"K.K @+ #B @7
#D4 .;,P7 .-- "K.K ..;X "K.K @7
..#E.,P7 .;X "K.K --.#C @7
#F4 .;,P7.;X.1.K @+ @7
#G4 .,,:AT .,,IF8 ,9 ,EXAMPLE #B1 :AT
P]C5T (! WOM5 H R1D+S 2T #AGB & #BJJ8
.,,/&>D .,,NORMAL .,,4TRIBU;N ,! /&>D
NORMAL 4TRIBU;N IS ! NORMAL 4TRIBU;N )
M1N #J & /&>D DEVI,N #A4 ,! =MULA 2L C 2
US$ 6TRANS=M ;X-VALUES F A NORMAL
4TRIBU;N ) M1N & /&>D DEVI,N .A
96;Z-VALUES HAV+ A /&>D NORMAL 4TRIBU;N4
,! ;Z-VALUE =A "PICUL> ;X-VALUE IS
CALL$ ! ;Z-SCORE =! ;X-VALUE & IS !
NUMB] ( /&>D DEVI,NS ! ;X-VALUE LIES ABV
OR 2L ! M1N X4
------------------------------------#GEI
.,,/&>D .,,NORMAL .,,TA# ,IF .;Z IS A
R&OMLY SELECT$ VALUE F A /&>D NORMAL
4TRIBU;N1 Y C USE ! TA# 2L 6F9D !
PROBABIL;Y T .;Z IS LESS ?AN OR EQUAL
6"S GIV5 VALUE4 ,= EXAMPLE1 ! TA# %[S T
.;,P7.;Z "K.K --#J.D7 .K #J.CDDF4 ,Y C
F9D ! VALUE ( .;,P7.;Z "K.K --#J.D7 9 !
TA# 0F9D+ ! VALUE ": R[ --#J & COLUMN#.D
9T]SECT4
,,R1D+
,9 ! TA#1 ! VALUE#.JJJJ@+ M1NS
8SLI<TLY M ?AN #J0 &! VALUE #A.JJJJ-
M1NS 8SLI<TLY LESS ?AN #A40
,Y C AL USE ! /&>D NORMAL TA# 6F9D
PROBABILITIES = .ANY NORMAL 4TRIBU;N 0F/
3V]T+ VALUES F ! 4TRIBU;N 6;Z-SCORES4
,EXAMPLE #C ,USE A ;Z-SCORE &! /&>D
NORMAL TA#
.,,BIOLOGY ,SCI5TI/S 3DUCT$ AERIAL
SURVEYS (A S1L SANCTU>Y & RECORD$ !
NUMB] .;X ( S1LS !Y OBS]V$ DUR+ EA*
SURVEY4 ,! NUMB]S ( S1LS OBS]V$ 7 NORM,Y
4TRIBUT$ )A M1N ( #GC S1LS &A /&>D
DEVI,N ( #AD.A S1LS4 ,F9D ! PROBABIL;Y T
AT MO/ #EJ S1LS 7 OBS]V$ DUR+ A SURVEY4
,SOLU;N
.,,/EP .#A .,F9D ! ;Z-SCORE
CORRESPOND+ 6AN ;X-VALUE ( #EJ4
.,,/EP#B .,USE ! TA# 6F9D .;,P7.;X
"K.K #EJ7 .;,P7.;Z "K.K --#A.F74
,! TA# %[S T .;,P7.;Z "K.K --#A.F7 .K
#J.JEDH4 ,S1 ! PROBABIL;Y T AT MO/ #EJ
S1LS 7 OBS]V$ DUR+ A SURVEY IS AB
#J.JEDH4
..,GUID$ ,PRACTICE = ,EXAMPLE .#C
#H4 .,,:AT .,,IF8 ,9 ,EXAMPLE #C1 F9D
! PROBABIL;Y T AT MO/ #IJ S1LS 7 OBS]V$
DUR+ A SURVEY4
#I4 .,,R1SON+ .,EXPLA9 :Y X MAKES S5SE
T .;,P7.;Z "K.K #J7 .K #J.E4
------------------------------------#GFJ
#AA.C ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
,,WS#BJ = ,EXS4 #C1AA1 & #CC
.K .,,/&>DIZ$ .,,TE/ .,,PRACTICE ,EXS4
.#B1.AG1.AH1 .#BH @1 & .#CE
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3
;,AFN7 @8 IS A BELL-%AP$ CURVE T IS
SYMMETRIC AB ! M1N4
#B4 .,,WRIT+ .,DESCRIBE H[ 6USE ! /&>D
NORMAL TA# 6F9D .;,P7.;Z "K.K #A.D74
,,EXAMPLE #A
ON P4 #GEG = ,EXS4 #C-AJ
,,F9D ,A ,,NORMAL ,,PROBABIL;Y ,A
NORMAL 4TRIBU;N HAS M1N .;X & /&>D
DEVI,N ,F9D ! 9DICAT$ PROBABIL;Y =A
R&OMLY SELECT$ ;X-VALUE F ! 4TRIBU;N4
.#C ;,P7;X"K.K -- @7
.#D4 ;,P7;X.1.K @+ #B @7
.#E4 ;,P7;X"K @+ @7
.#F4 ;,P7;X.1.K -- @7
#G4 ;,P7 - "K "K;X"K @+ @7
#H4 ;,P7 --#C "K.K;X"K.K @7
,,US+ ,A ,,NORMAL ,,CURVE ,GIVE !
P]C5T (! >EA "U ! NORMAL CURVE REPRES5T$
0! %AD$ REGION4
.#I4
.#AJ4
,,EXAMPLE #B
ON P4 #GEH = ,EXS4 #AA-AH
,,NORMAL ,,4TRIBU;NS ,A NORMAL
4TRIBU;N HAS A M1N ( #CC &A /&>D DEVI,N
( #D4 ,F9D ! PROBABIL;Y T A R&OMLY
SELECT$ ;X-VALUE F ! 4TRIBU;N IS 9 !
GIV5 9T]VAL4
.#AA ,2T #BI & #CG
.#AB4 ,2T #CC & #DE
.#AC4 ,2T #BA & #DA
.#AD4 ,AT L1/ #BE
.#AE4 ,AT L1/ #BI
#AF4 ,AT MO/ #CG
#AG4 .,,MULTIPLE .,,*OICE ,A NORMAL
4TRIBU;N HAS A M1N ( #HD &A /&>D DEVI,N
( #E4 ,:AT IS ! PROBABIL;Y T A R&OMLY
SELECT$ ;X-VALUE F ! 4TRIBU;N IS 2T #GD
& #ID8
,A #J.DGE
;,B #J.FH
;,C #J.IE
;,D #J.IIG
.#AH4 .,,MULTIPLE .,,*OICE ,A NORMAL
4TRIBU;N HAS A M1N ( #EA &A /&>D DEVI,N
( #C4 ,:AT IS ! PROBABIL;Y T A R&OMLY
SELECT$ ;X-VALUE F ! 4TRIBU;N IS AT MO/
#DH8
,A #J.JBE
;,B #J.AF
;,C #J.HD
;,D #J.IGE
,,EXAMPLE #C
ON P4 #GEI = ,EXS4 #AI-BG
,,/&>D ,,NORMAL ,,TA# ,A NORMAL
4TRIBU;N HAS A M1N ( #FD &A /&>D DEVI,N
( #G4 ,USE ! /&>D NORMAL TA# ON PAGE
#GEI 6F9D ! 9DICAT$ PROBABIL;Y =A R&OMLY
SELECT$ ;X-VALUE F ! 4TRIBU;N4
.#AI4 ;,P7;X"K.K#FH7
.#BJ4 ;,P7;X"K.K#HJ7
.#BA4 ;,P7;X"K.K#DE7
.#BB4 ;,P7;X"K.K#ED7
.#BC4 ;,P7;X"K.K#FD7
.#BD4 ;,P7;X.1.K#EI7
.#BE4 ;,P7;X.1.K#GE7
.#BF4 ;,P7#FJ"K.K;X"K.K#GE7
.#BG4 ;,P7#DE"K.K;X"K.K#FE7
------------------------------------#GFA
#BH4 ,,%ORT ,,RESPONSE ,LET .;X 2 A
R&OMLY SELECT$ VALUE F A NORMAL 4TRIBU;N
) M1N #HJ & /&>D DEVI,N #AJ4 ,IF
..;,P7;X "K.K .;K7 .K #J.IAIB1 :AT IS !
VALUE ( ;K8 .,EXPLA94
#BI4 ,,]ROR ,,ANALYSIS ,9 A /UDY1 !
:1T YIELDS 7IN BU%ELS7 = S"EAL PLOTS (
L& 7 NORM,Y 4TRIBUT$ )A M1N ( #D BU%ELS
&A /&>D DEVI,N ( #J.BE BU%EL4 .,DESCRIBE
& CORRECT ! ]ROR 9 F9D+ ! PROBABIL;Y T A
PLOT YIELD$ AT L1/ #C.H BU%ELS4
..,F ! /&>D NORMAL .TA# @1 ;,P7;Z .1
--#J.E7 .K #J.BAAI4 ,S1 ! PROBABIL;Y T A
PLOT .YIELD$ AT L1/ #C.F BU%ELS IS
#J.BAAI4
#CJ4 .,,*ALL5GE ,A NORMAL CURVE IS
DEF9$ 0AN EQU,N ( ? =M3
A4 .,GRAPH+ .,CALCULATOR ,GRAPH ?REE
EQU,NS (! GIV5 =M4 ,! EQU,NS %D USE !
SAME M1N B DI6]5T /&>D DEVI,NS4
B4 .,R1SON+ .,DESCRIBE ! E6ECT (! /&>D
DEVI,N ON ! %APE (A NORMAL CURVE4
,,EXAMPLES #B & #C
ON PP4 #GEH-GEI = ,EXS4 #CA-CD
,PRO#M ,SOLV+
#CA4 .,,BIOLOGY ,! ILLU/R,N %[S A
H\SEFLY AT S"EAL "TS XS ACTUAL SIZE &
9DICATES ! FLY'S W+ L5G?4 ,A /UDY F.D T
! W+ L5G?S ( H\SEFLIES >E NORM,Y
4TRIBUT$ )A M1N ( AB #D.F MILLIMET]S &A
/&>D DEVI,N ( AB #J.D MILLIMET]4 ,:AT IS
! PROBABIL;Y T A R&OMLY SELECT$ H\SEFLY
HAS A W+ L5G? ( AT L1/ #E MILLIMET]S8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#CB4 .,,FIRE .,,DE"P;T ,! "T A FIRE
DE"P;T TAKES 6>RIVE AT ! SC5E ( AN
EM]G5CY IS NORM,Y 4TRIBUT$ )A M1N ( #F
M9UTES &A /&>D DEVI,N ( #A M9UTE4
A4 ,:AT IS ! PROBABIL;Y T ! FIRE
DE"P;T TAKES AT MO/ #H M9UTES 6>RIVE AT
! SC5E ( AN EM]G5CY8
B4 ,:AT IS ! PROBABIL;Y T ! FIRE
DE"P;T TAKES 2T #D M9UTES & #G M9UTES
6>RIVE AT ! SC5E ( AN EM]G5CY8
@A .,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#CC .,,MULTI-.,,/EP .,,PRO#M ,BOXES (
C]1L >E FILL$ 0A MA*9E4 ,TE/S (! MA*9E'S
A3URACY %[ T ! AM.T ( C]1L 9 EA* BOX
V>IES4 ,! WEI<TS >E NORM,Y 4TRIBUT$ )A
M1N ( #BJ \NCES &A /&>D DEVI,N ( #J.BE
\NCE4
A4 ,F9D ! ;Z-SCORES = WEI<TS ( #AI.D
\NCES & #BJ.D \NCES4
B4 ,:AT IS ! PROBABIL;Y T A R&OMLY
SELECT$ C]1L BOX WEI<S AT MO/ #AI.D
\NCES8
C4 ,:AT IS ! PROBABIL;Y T A R&OMLY
SELECT$ C]1L BOX WEI<S 2T #AI.D \NCES &
#BJ.D \NCES8 .,EXPLA9 YR R1SON+4
------------------------------------#GFB
#CD4 .,,BOTANY ,! GUAYULE PLANT1 :
GR[S 9 ! S\?WE/]N ,UNIT$ ,/ATES & 9
,MEXICO1 IS "O ( S"EAL PLANTS T C 2 US$
Z A S\RCE ( RU2]4 ,9 A L>GE GR\P (
GUAYULE PLANTS1 ! HEI<TS (! PLANTS >E
NORM,Y 4TRIBUT$ )A M1N ( #AB 9*ES &A
/&>D DEVI,N ( #B 9*ES4
A4 ,:AT P]C5T (! PLANTS >E TALL] ?AN
#AF 9*ES8
B4 ,:AT P]C5T (! PLANTS >E AT MO/ #AC
9*ES8
C4 ,:AT P]C5T (! PLANTS >E 2T #G 9*ES
& #AD 9*ES8
D4 ,:AT P]C5T (! PLANTS >E AT L1/ #C
9*ES TALL] ?AN OR %ORT] ?AN ! M1N HEI<T8
#CE4 @4 .,,EXT5D$ .,,RESPONSE ,LISA &
,ANN TOOK DI6]5T COLLEGE 5TR.E TE/S4 ,!
SCORES ON ! TE/ T ,LISA TOOK >E NORM,Y
4TRIBUT$ )A M1N ( #BJ PO9TS &A /&>D
DEVI,N ( #D.B PO9TS4 ,! SCORES ON ! TE/
T ,ANN TOOK >E NORM,Y 4TRIBUT$ )A M1N (
#EJJ PO9TS &A /&>D DEVI,N ( #IJ PO9TS4
,LISA SCOR$ #CJ ON H] TE/1 & ,ANN SCOR$
#FAJ ON H] TE/4
A4 .,CALCULATE ,F9D ! ;Z-SCORE =
,LISA'S TE/ SCORE4
B4 .,CALCULATE ,F9D ! ;Z-SCORE =
,ANN'S TE/ SCORE4
C4 .,9T]PRET ,: /UD5T SCOR$ BETT] ON
H] COLLEGE 5TR.E TE/8 .,EXPLA9 YR
R1SON+4
#CF4 .,,*ALL5GE ,AC 6A SURVEY 0!
,N,NAL ,C5T] = ,H1L? ,/ATI/ICS1 ! HEI<TS
( ADULT M5 9 ! ,UNIT$ ,/ATES >E NORM,Y
4TRIBUT$ )A M1N ( #FI 9*ES &A /&>D
DEVI,N ( #B.GE 9*ES4
A4 ,IF Y R&OMLY *OOSE #C ADULT M51 :AT
IS ! PROBABIL;Y T ALL ( !M >E M ?AN #F
FEET TALL8
B4 ,:AT IS ! PROBABIL;Y T #E R&OMLY
SELECT$ M5 ALL H HEI<TS 2T #FE 9*ES &
#GE 9*ES8
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
,USE SYN!TIC SUB/ITU;N 6EVALUATE !
POLYNOMIAL FUNC;N =! GIV5 VALUE ( X4 @7
P4 #CCG @7
.#CG4 .;F 7;X7 .K #D;X #C @+ #E;X #B
-- #C;X @+ #G2 ;X .K #B
.#CH4 .;F 7;X7 .K --#C;X #C -- #E;X #B
@+ #AJ2 ;X .K #D
.#CI4 .;F 7;X7 .K #B;X #D @+ ;X #C --
#B;X #B @+ ;X2 ;X .K #B
.#DJ4 .;F 7;X7 .K ;X #D -- #D;X #B @+
#C;X--#F2 ;X .K --#C
,LET .;F 7;X7 .K #D;X--#I & .;G 7;X7
.K #F;X #B @4 ,P]=M ! 9DICAT$ OP],N &
/ATE ! DOMA94 7.P#..DBH7
.#DA4 .;F 7;X7 @+ .;G 7;X7
.#DB4 .;F 7;X7 -- .;G 7;X7
.#DC4 .;G 7;X7 @+ .;F 7;X7
.#DD4 .;F 7;X7 @* .;G 7;X7
.#DE4
.#DF4
.#DG4 .;F7.;G 7;X77
.#DH4 .;G7.;F 7;X77
,SOLVE ! EQU,N4 ,*ECK = EXTRANE\S
SOLU;NS4 7.P#..DEB7
.#DI4
.#EJ4
.#EA4
.#EB4
.#EC4
.#ED4
,PREVIEW
PREP>E = ,LESSON #AA.D 9 ,EXS4 #DI-ED4
.,,EXTRA .,,PRACTICE = ,LESSON #AA.C1
P4 #AJBJ
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#GFC
,EXT5.N
,USE AF LESSON #AA.C
,APPROXIMATE ,BINOMIAL ,4TRIBU;NS &
,TE/ ,HYPO!SES
.,GOAL ,USE NORMAL 4TRIBU;NS
6APPROXIMATE BINOMIAL 4TRIBU;NS4
,9 ,LESSON #AJ.F1 Y F.D PROBABILITIES
RELAT$ 6A BINOMIAL 4TRIBU;N US+ ! =MULA
.;,P7.;K7 .K ;N .;,C ;K .;P ;K
7.;L--.;P7 ;N--;K @4 ,H["E1 X C 2 T$I\S
6USE ? =MULA :5 ! NUMB] ( PROBABILITIES
6-PUTE IS L>GE4 ,9 S* CASES1 Y MAY 2 A#
6USE A NORMAL 4TRIBU;N 6APPROXIMATE !
BINOMIAL 4TRIBU;N4
,,KEY ,,3CEPT .= .,YR .,NOTEBOOK
,NORMAL ,APPROXIM,N (A ,BINOMIAL
,4TRIBU;N
,3SID] ! BINOMIAL 4TRIBU;N 3SI/+ ( .;N
TRIALS ) PROBABIL;Y .;P ( SU3ESS ON EA*
TRIAL4 ,IF .NP .1.K #E & .;N7.#A--.;P7
.1.K #E1 !N ! BINOMIAL 4TRIBU;N C 2
APPROXIMAT$ 0A NORMAL 4TRIBU;N )! FOLL[+
M1N & /&>D DEVI,N4
,M1N3 .K .NP
.,/&>D .,DEVI,N3
,SIDEB>3
.,/&>DS
,PROBABIL;Y & ,/ATI/ICS3#D.J
..,/UD5TS >E FAMILI> )! /&>D 4TRIBU;NS
7.NORMAL @1 BINOMIAL1 & EXPON5TIAL7 ..&
C USE !M 6SOLVE = EV5TS 9 PRO#MS 9 : !
4TRIBU;N 2L;GS 6^? .FAMILIES4
,EXAMPLE #A ,F9D A BINOMIAL PROBABIL;Y
.,,SURVEYS ,AC 6A SURVEY 3DUCT$ 0!
,H>RIS ,POLL1 #BD@3P ( ADULTS 9 ! ,UNIT$
,/ATES SAY T _! FAVORITE LEISURE-"T
ACTIV;Y IS R1D+4 ,Y >E 3DUCT+ A R&OM
SURVEY ( #BEJ ADULTS4 ,:AT IS !
PROBABIL;Y T Y W F9D AT MO/ #EC ADULTS
:O SAY T R1D+ IS _! FAVORITE LEISURE-"T
ACTIV;Y8
,SOLU;N
,! NUMB] .;X ( ADULTS 9 YR SURVEY :O
SAY R1D+ IS _! FAVORITE LEISURE-"T
ACTIV;Y HAS A BINOMIAL 4TRIBU;N ) .;N .K
#BEJ & .;P .K #J.BD4 ,6SOLVE ! PRO#M US+
! BINOMIAL PROBABIL;Y =MULA1 Y WD H
6CALCULATE ! FOLL[+3
.;,P7.;X "K.K #EC7 .K .;,P7.;X .K #J7
@+ .;,P7.;X .K #A7 @+ .;,P7.;X .K #B7 @+
' @+ .;,P 7.;X .K #EC7
,? WD 2 T$I\S4 ,9/1D1 Y C APPROXIMATE
! ANSW] US+ A NORMAL 4TRIBU;N )! M1N &
/&>D DEVI,N GIV5 2L4
.K .NP .K #BEJ7#J.BD7 .K #FJ ,F9D M1N4
.,F9D ./&>D .DEVI,N4
,= ? NORMAL 4TRIBU;N1 #EC IS AB "O
/&>D DEVI,N 6! LEFT (! M1N4 ,"!=E3
.;,P7.;X "K #EC7 #J.JJAE @+ #J.JBCE @+
#J.ACE .K #J.AF
99 ,! PROBABIL;Y T AT MO/ #EC (! P
SURVEY$ SAY R1D+ IS _! FAVORITE
LEISURE-"T ACTIV;Y IS AB #J.AF4
,,*ECK ,,R1SONA#;S
,9 ,EXAMPLE #A1 NOTE T
.NP .K #FJ .1.K #E & T
.;N7.;L--.;P7 .K #AIJ .1.K #E4 ,S1 X
IS R1SONA# 6USE A NORMAL APPROXIM,N4
------------------------------------#GFD
.,,HYPO!SIS .,,TE/+ ,Y C USE ! FOLL[+
PROC$URE 6TE/ A HYPO!SIS AB A /ATI/ICAL
M1SURE =A POPUL,N4
,,*OOSE ,,CRIT]ION
,9 ,/EP #C1 "S /ATI/ICIANS USE .;P
"K#J.A OR .;P "K #J.JA Z A 3DI;N =
REJECT+ A HYPO!SIS4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,HYPO!SIS ,TE/+
.,,/EP .#A .,/ATE ! HYPO!SIS Y >E
TE/+4 ,! HYPO!SIS %D MAKE A /ATE;T AB "S
/ATI/ICAL M1SURE (A POPUL,N 7S* Z !
P]C5T (! POPUL,N T HAS A C]TA9 "*I/IC74
.,,/EP#B .,COLLECT DATA F A R&OM
SAMPLE (! POPUL,N & -PUTE ! /ATI/ICAL
M1SURE (! SAMPLE4
.,,/EP .#C .,ASSUME T ! HYPO!SIS IS
TRUE & CALCULATE ! RESULT+ PROBABIL;Y
.;P ( OBTA9+ ! SAMPLE /ATI/ICAL M1SURE
..OR A M .EXTREME SAMPLE /ATI/ICAL
M1SURE4 ,IF ? PROBABIL;Y IS SMALL
7TYPIC,Y .;P "K #J.JE71 Y %D REJECT !
HYPO!SIS4
,EXAMPLE #B ,TE/ A HYPO!SIS
.,,FIREFI<T+ ,A REC5T ,H>RIS ,POLL
CLAIM$ T #DH@3P ( ADULTS 3SID] FIREFI<T+
6BE A PRE/IGI\S O3UP,N4 ,6TE/ ? F9D+1 Y
SURVEY #DJ ADULTS & F9D T #AE ( !M D
3SID] FIREFI<T+ A PRE/IGI\S O3UP,N4 ,%D
Y REJECT ! ,H>RIS ,POLL'S F9D+S8
.,EXPLA94
,SOLU;N
.,,/EP .#A .,/ATE ! HYPO!SIS4 #DH@3P (
ADULTS 3SID] FIREFI<T+ A PRE/IGI\S
O3UP,N4
.,,/EP#B .,COLLECT DATA & CALCULATE A
/ATI/ICAL M1SURE4 ,9 YR SURVEY1 #AE \ (
#DJ P1 OR #CG.E@3P1 3SID] FIREFI<T+ 6BE
A PRE/IGI\S O3UP,N4
.,,/EP#C .,ASSUME T ! HYPO!SIS 9 ,/EP
#A IS TRUE4 ,F9D ! RESULT+ PROBABIL;Y T
Y CD R&OMLY SELECT #AE .OR .FEW] ADULTS
\ ( #DJ :O 3SID] FIREFI<T+ A PRE/IGI\S
O3UP,N4 ,? PROBABIL;Y IS
.;,P @7 .;X "K.K #AE7 .K .;,P @7 .;X
.K #J7 @+ .;,P @7 .;X .K #A7 @+ .;,P @7
.;X .K #B7 @+ ' @+ .;,P @7 .;X .K #AE7
": EA* T]M 9 ! SUM IS A BINOMIAL
PROBABIL;Y ) .;N .K #DJ & .;P .K #J.DH4
,Y C APPROXIMATE ! BINOMIAL 4TRIBU;N
)A NORMAL 4TRIBU;N HAV+ ! FOLL[+ M1N &
/&>D DEVI,N3
.K .NP .K #DJ7#J.DH7 .K #AI.B
,US+ A ;Z-SCORE &! /&>D NORMAL TA# ON
PAGE #GEI GIVES3
99 ,S1 IF X IS TRUE T #DH@3P ..(
ADULTS 3SID] FIREFI<T+ A PRE/IGI\S
.O3UP,N @1 !N "! IS AB A #AJ@3P
PROBABIL;Y ( F9D+ #AE OR FEW] ADULTS :O
3SID] FIREFI<T+ PRE/IGI\S 9 A R&OM
SAMPLE ( #DJ ADULTS4 ,)A PROBABIL;Y ?
L>GE1 Y %D N REJECT ! HYPO!SIS4
------------------------------------#GFE
,,EXAMPLE #A
ON P4 #GFC = ,EXS4 #A-AH
,PRACTICE
,,APPROXIMAT+ ,,BINOMIAL ,,4TRIBU;NS
,F9D ! M1N & /&>D DEVI,N (A NORMAL
4TRIBU;N T APPROXIMATES ! BINOMIAL
4TRIBU;N ) .;N TRIALS & PROBABIL;Y .;P (
SU3ESS ON EA* TRIAL4
.#A4 ;N .K #BD;,P .K #J.D
.#B4 ;N .K #DJ;,P .K #J.F
.#C4 ;N .K #DF;,P .K #J.C
.#D4 ;N .K #EE;,P .K #J.AE
.#E4 ;N .K #CF;,P .K #J.G
.#F4 ;N .K #FF;,P .K #J.B
.#G4 ;N .K #AAJ;,P .K #J.JH
.#H4 ;N .K #ABE;,P .K #J.CE
.#I4 ;N .K #ADJ;,P .K #J.GE
,,COLORBL9D;S ,USE ! FACT T
APPROXIMATELY #D@3P ( P >E COLORBL9D4
,3SID] A CLASS ( #DFJ /UD5TS4
.#AJ4 ,:AT IS ! PROBABIL;Y T #AE OR
FEW] /UD5TS >E COLORBL9D8
.#AA4 ,:AT IS ! PROBABIL;Y T #AB OR M
/UD5TS >E COLORBL9D8
.#AB4 ,:AT IS ! PROBABIL;Y T 2T #F &
#AH /UD5TS >E COLORBL9D8
,,LEFT-,,H&$;S ,USE ! FACT T
APPROXIMATELY #I@3P ( P >E LEFT-H&$4
,3SID] A HI< S*OOL ) #ABBA /UD5TS4
.#AC4 ,:AT IS ! PROBABIL;Y T AT L1/
#ADJ /UD5TS >E LEFT-H&$8
.#AD4 ,:AT IS ! PROBABIL;Y T AT MO/
#AJJ /UD5TS >E LEFT-H&$8
.#AE4 ,:AT IS ! PROBABIL;Y T 2T #HJ &
#ACJ /UD5TS >E LEFT-H&$8
,,MYOPIA ,USE ! FACT T MYOPIA1 OR
NE>SI<T$;S1 IS A 3DI;N T A6ECTS
APPROXIMATELY #BE@3P (! ADULT POPUL,N 9
! ,UNIT$ ,/ATES4 ,3SID] A R&OM SAMPLE (
#AIB ,U4,S4 ADULTS4
.#AF4 ,:AT IS ! PROBABIL;Y T #DB OR M
P >E NE>SI<T$8
.#AG4 ,:AT IS ! PROBABIL;Y T #FF OR
FEW] P >E NE>SI<T$8
.#AH4 ,:AT IS ! PROBABIL;Y T 2T #CF &
#FJ P >E NE>SI<T$8
#AI4 .,,SURVEYS ,A SURVEY T ASK$ P 9 !
,UNIT$ ,/ATES AB _! FEEL+S ( P]SONAL
WELL-2+ F.D T #HE@3P >E G5],Y HAPPY4
,6TE/ ? F9D+1 Y "Q #GE P AT R&OM & F9D T
#EF 3SID] !MVS G5],Y HAPPY4 ,WD Y REJECT
! SURVEY'S F9D+S8 .,EXPLA94
.#BJ4 .,,CLASS .,,R+S ,Y R1D AN >TICLE
T CLAIMS #CJ@3P ( GRADUAT+ S5IORS W BUY
A CLASS R+4 ,6TE/ ? CLAIM1 Y SURVEY #DE
R&OMLY SELECT$ S5IORS 9 YR S*OOL & F9D T
#I >E PLANN+ 6BUY A CLASS R+4 ,%D Y
REJECT ! >TICLE'S CLAIM8 .,EXPLA94
.#BA4 .,,-PUT]S ,A MANUFACTUR] (
P]SONAL -PUT]S CLAIMS T "U NORMAL "W USE
ONLY #A@3P ( XS -PUT]S W FAIL 6OP]ATE AT
"S PO9T DUR+ A MON?4 ,A BUSI;S USES #FJJ
(! MANUFACTUR]'S -PUT]S "U NORMAL "W USE
& HAS #AB FAILURES 9 A MON?4 ,WD Y
REJECT ! MANUFACTUR]'S CLAIM8 .,EXPLA94
.#BB4 .,,JUICE .,,PREF];ES ,A -PANY T
MAKES BOTTL$ JUICES HAS CR1T$ A NEW BR&
( APPLE JUICE4 ,! -PANY CLAIMS #HJ@3P (
P PREF] ! NEW APPLE JUICE OV] A
-PETITOR'S APPLE JUICE4 ,A TA/E TE/ IS
3DUCT$ 6TE/ ? CLAIM4 ,( #EJ P1 #CD PREF]
! NEW APPLE JUICE4 ,WD Y REJECT !
-PANY'S CLAIM8 .,EXPLA94
,,EXAMPLE #B
ON P4 #GFD = ,EXS4 #AI-BB
------------------------------------#GFF
#AA.D ,SELECT & ,DRAW ,3CLU.NS F
,SAMPLES
.,2F ,Y US$ /ATI/ICS 6DESCRIBE SETS (
DATA4
.,N[ ,Y W /UDY DI6]5T SAMPL+ ME?ODS =
COLLECT+ DATA4
.,:Y8 ,S Y C 9T]PRET ! RESULTS (A
SURVEY1 Z 9 ,EX4 #BG4
,KEY ,VOCABUL>Y
99 POPUL,N
99 SAMPLE
99 UNBIAS$ SAMPLE
99 BIAS$ SAMPLE
99 M>E9 ( ]ROR
,SIDEB>3
.,/&>DS
,ADV.ED ,PLACE;T ,PROBABIL;Y &
,/ATI/ICS3#AG.J
,/UD5TS DET]M9E 3FID;E 9T]VALS =A
SIMPLE R&OM SAMPLE F A NORMAL 4TRIBU;N (
DATA & DET]M9E ! SAMPLE SIZE REQUIR$ =A
DESIR$ M>G9 ( ]ROR4
.,A .POPUL,N IS A GR\P ( P OR OBJECTS
T Y WANT 9=M,N AB4 ,:5 X IS TOO
DI6ICULT1 "T-3SUM+1 OR EXP5SIVE 6SURVEY
"EY"O 9 A POPUL,N1 9=M,N IS GA!R$ F A
.SAMPLE @1 OR SUBSET1 (! POPUL,N4 ,"S
ME?ODS = SELECT+ A SAMPLE >E DESCRIB$
2L4
,PICTURE3 ,9 A .SELF-.SELECT$ .SAMPLE
@1 MEMB]S (A POPUL,N C VOLUNTE] 6BE 9 !
SAMPLE4
,PICTURE3 ,9 A .SY/EMATIC .SAMPLE @1 A
RULE IS US$ 6SELECT MEMB]S (A POPUL,N1
S* Z SELECT+ E O!R P]SON4
,PICTURE3 ,9 A .3V5I;E .SAMPLE @1
EASY-TO-R1* MEMB]S (A POPUL,N >E
SELECT$1 S* Z ^? 9 ! F/ R[4
,PICTURE3 ,9 A .R&OM .SAMPLE @1 EA*
MEMB] (A POPUL,N HAS AN EQUAL *.E ( 2+
SELECT$4
,EXAMPLE #A ,CLASSIFY SAMPLES
.,,BASEBALL ,A SPORTSWRIT] WANTS
6SURVEY COLLEGE BASEBALL COA*ES AB :E!R
!Y ?9K WOOD5 BATS %D 2 M&ATORY "?\T
COLLEGE BASEBALL4 ,ID5TIFY ! TYPE (
SAMPLE DESCRIB$4
A4 ,! SPORTSWRIT] 3TACTS ONLY ! COA*ES
T HE HAS CELL PH"O NUMB]S = 9 ORD] 6GET
QK RESPONSES4
B4 ,! SPORTSWRIT] MAILS \ SURVEYS 6ALL
! COA*ES & USES ONLY ! SURVEYS T >E
RETURN$4
,SOLU;N
A4 ,! SPORTSWRIT] SELECT$ COA*ES T >E
EASILY A3ESSI#4 ,S1 ! SAMPLE IS A 3V5I;E
SAMPLE4
B4 ,! COA*ES C *OOSE :E!R OR N
6RESPOND4 ,S1 ! SAMPLE IS A SELF-SELECT$
SAMPLE4
------------------------------------#GFG
.,,BIAS .,,9 .,,SAMPL+ ,9 ORD] 6DRAW
A3URATE 3CLU.NS AB A POPUL,N F A SAMPLE1
Y %D SELECT AN .UNBIAS$ .SAMPLE4 ,AN
.UNBIAS$ .SAMPLE IS REPRES5TATIVE (!
POPUL,N Y WANT 9=M,N AB4 ,A SAMPLE T
OV]REPRES5TS OR "UREPRES5TS "P (!
POPUL,N IS A .BIAS$ .SAMPLE4
,EXAMPLE #B ,ID5TIFY A BIAS$ SAMPLE
.,,3C]T .,,ATT5D.E ,! MANAG] (A 3C]T
HALL WANTS 6"K H[ (T5 P 9 ! -MUN;Y ATT5D
3C]TS4 ,! MANAG] ASKS #EJ P /&+ 9 L9E =A
ROCK 3C]T H[ _M 3C]TS P] YE> !Y ATT5D4
,TELL :E!R ! SAMPLE IS .BIAS$ OR
.UNBIAS$4 ,EXPLA9 YR R1SON+4
,SOLU;N
,! SAMPLE IS BIAS$ 2C P /&+ 9 L9E =A
ROCK 3C]T >E M ,I LIKELY 6ATT5D 3C]TS
?AN P 9 G5]AL4
.,,*OOS+ .,,UNBIAS$ .,,SAMPLES ,AL? "!
>E _M WAYS ( SAMPL+ A POPUL,N1 A R&OM
SAMPLE IS PREF]R$ 2C X IS MO/ LIKELY 6BE
REPRES5TATIVE (! POPUL,N4
,EXAMPLE #C ,*OOSE AN UNBIAS$ SAMPLE
.,,S5IOR .,,CLASS .,,PROM ,Y >E A
MEMB] (! PROM -MITTEE4 ,Y WANT 6POLL
MEMB]S (! S5IOR CLASS 6F9D \ ": !Y WANT
6HOLD ! PROM4 ,"! >E #CBD /UD5TS 9 !
S5IOR CLASS4 ,DESCRIBE A ME?OD = SELECT+
A R&OM SAMPLE ( #DJ S5IORS 6POLL4
,SOLU;N
.,,/EP .#A .,MAKE A LI/ ( ALL #CBD
S5IORS4 ,ASSIGN EA* S5IOR A DI6]5T 9TEG]
F #A 6#CBD4
.,,/EP .#B .,G5]ATE #DJ UNIQUE R&OM
9TEG]S F #A 6#CBD US+ ! .R&LNT F1TURE (A
GRAPH+ CALCULATOR4 ,! SCRE5 AT ! "R %[S
SIX S* R&OM 9TEG]S4
,IF :ILE G5]AT+ ! 9TEG]S Y OBTA9 A
DUPLICATE1 4C>D X & G5]ATE A NEW1 UNIQUE
9TEG] Z A REPLACE;T4
.,,/EP .#C .,*OOSE ! #DJ /UD5TS T
CORRESPOND 6! #DJ 9TEG]S Y G5]AT$ 9 ,/EP
#B4
..,GUID$ ,PRACTICE = ,EXAMPLES #A1B1 &
.#C
.#A4 .,,S*OOL .,,WEBSITE ,A -PUT]
SCI;E T1*] WANTS 6"K IF /UD5TS WD L !
MORN+ ANN\NCE;TS PO/$ ON ! S*OOL'S
WEBSITE4 ,HE SURVEYS /UD5TS 9 "O ( 8
-PUT] SCI;E CLASSES4 ,ID5TIFY ! TYPE (
SAMPLE DESCRIB$1 & TELL :E!R ! SAMPLE IS
BIAS$4
#B4 .,,:AT .,,IF8 ,9 ,EXAMPLE #C1 :AT
IS ANO!R ME?OD Y CD USE 6G5]ATE A R&OM
SAMPLE ( #DJ /UD5TS8
------------------------------------#GFH
.,,SAMPLE .,,SIZE ,:5 3DUCT+ A SURVEY1
Y NE$ 6MAKE ! SIZE ( YR SAMPLE L>GE 5 S
T X A3URATELY REPRES5TS ! POPUL,N4 ,Z !
SAMPLE SIZE 9CR1SES1 ! .M>G9 .( .]ROR
DECR1SES4
,! .M>G9 .( .]ROR GIVES A LIMIT ON H[
M* ! RESPONSES (! SAMPLE WD DI6] F !
RESPONSES (! POPUL,N4 ,= EXAMPLE1 IF
#DJ@3P (! P 9 A POLL PREF] C&IDATE ,A1
&! M>G9 ( ]ROR IS +-#D@3P1 !N X IS
LIKELY T 2T #CF@3P & #DD@3P (! 5TIRE
POPUL,N PREF] C&IDATE ,A4
,,KEY ,,3CEPT
,= ,YR ,NOTEBOOK
,M>G9 ( ,]ROR ,=MULA
,:5 A R&OM SAMPLE ( SIZE .;N IS TAK5 F
A L>GE POPUL,N1 ! M>G9 ( ]ROR IS
APPROXIMAT$ 0? =MULA3
,? M1NS T IF ! P]C5T (! SAMPLE
RESPOND+ A C]TA9 WAY IS .;P 7EXPRESS$ Z
A DECIMAL71 !N ! P]C5T (! POPUL,N T WD
RESPOND ! SAME WAY IS LIKELY 6BE 2T
,EXAMPLE #D ,F9D A M>G9 ( ]ROR
,,M$IA ,,SURVEY ,9 A SURVEY ( #AJAA P
#EB@3P SD T TELEVI.N IS _! MA9 S\RCE (
NEWS4
A4 ,:AT IS ! M>G9 ( ]ROR =! SURVEY8
B4 ,GIVE AN 9T]VAL T IS LIKELY 63TA9 !
EXACT P]C5T ( ALL P :O USE TELEVI.N Z _!
MA9 S\RCE ( NEWS4
,SOLU;N
A4 ,USE ! M>G9 ( ]ROR =MULA4
99 ,! M>G9 ( ]ROR =! SURVEY IS AB
+-#C.A@3P4
B4 ,6F9D ! 9T]VAL1 SUBTRACT & ADD
#C.A@3P 6! P]C5T ( P SURVEY$ :O SD
TELEVI.N IS _! MA9 S\RCE ( NEWS
7#EB@3P74
#EB@3P--#C.A@3P .K #DH.I@3P #EB@3P @+
#C.A@3P .K #EE.A@3P
99 ,X IS LIKELY T ! EXACT P]C5T ( ALL
P :O USE TELEVI.N Z _! MA9 S\RCE ( NEWS
IS 2T #DH.I@3P & #EE.A@3P4
------------------------------------#GFI
..,EXAMPLE #E ,/&>DIZ$ ,TE/ .,PRACTICE
,A POLL+ -PANY 3DUCTS A POLL =A ,U4,S4
PRESID5TIAL ELEC;N4 ,H[ _M P DID ! -PANY
SURVEY IF ! M>G9 ( ]ROR IS +-#E@3P8
.,A #BE P
.;,B #BEJ P
.;,C #DJJ P
.;,D #FBE P
,REVIEW ,RADICALS
,= HELP ) SOLV+ EQU,NS 9VOLV+ SQU>E
ROOTS1 SEE P4 #DEB @4
,SOLU;N
,USE ! M>G9 ( ]ROR =MULA4
.;N .K #DJJ ,SOLVE = N4
,"! 7 #DJJ P SURVEY$4
,! CORRECT ANSW] IS ,C4 ,A ;,B ;,C ;,D
..,GUID$ ,PRACTICE = ,EXAMPLES #D &
.#E
.#C4 .,,9T]NET ,9 A SURVEY ( #ABJB P1
#AA@3P SD T !Y USE ! ,9T]NET OR ;E-MAIL
M ?AN #AJ H\RS P] WEEK4 ,:AT IS ! M>G9 (
]ROR =! SURVEY8 ,H[ _M P WD NE$ 6BE
SURVEY$ 6REDUCE ! M>G9 ( ]ROR TO
+-#B@3P8
#AA.D ,EX]CISES
,HOME"W ,KEY
.K ..,,"W$-,,\ ,,SOLU;NS .ON P4
,,WS#BJ ..= ,EXS4 #G1AI1 & .#BI
.K .,,/&>DIZ$ .,,TE/ .,,PRACTICE
,EXS4 .#B1.AD1.BC1.BI @1 & .#CA
,SKILL ,PRACTICE
#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,A
SAMPLE = : EA* MEMB] (A POPUL,N HAS AN
EQUAL *.E ( 2+ SELECT$ IS A7;N7 @8
SAMPLE4
#B4 .,,WRIT+ .,DESCRIBE ! DI6];E 2T AN
UNBIAS$ SAMPLE &A BIAS$ SAMPLE4
,,EXAMPLES #A & #B
ON PP4 #GFF-GFG = ,EXS4 #C-E
,CLASSIFY+ ,SAMPLES ,ID5TIFY ! TYPE (
SAMPLE DESCRIB$4 ,!N TELL IF ! SAMPLE IS
BIAS$4 .,EXPLA9 YR R1SON+4
#C4 ,A TAXICAB -PANY WANTS 6"K IF XS
CU/OM]S >E SATISFI$ )! S]VICE4 ,EA*
DRIV] SURVEYS E T5? CU/OM] DUR+ ! "D4
#D4 ,A T[N C\NCIL WANTS 6"K IF
RESID5TS SUPPORT HAV+ AN (F-L1% >EA =
DOGS 9 ! T[N P>K4 ,EI<TY DOG [N]S >E
SURVEY$ AT ! P>K4
#E4 ,AN ,5GLI% T1*] NE$S 6PICK #E
/UD5TS 6PRES5T BOOK REPORTS 6! CLASS4 ,!
T1*] WRITES ! "NS ( ALL /UD5TS 9 ! CLASS
ON PIECES ( PAP]1 PUTS ! PIECES 9 A HAT1
& *OOSES #E "NS )\T LOOK+4
------------------------------------#GGJ
.,,EXAMPLE .#D .ON .P4 #GFH = ,EXS4
#F-AD
,,F9D+ ,,M>G9 ,,( ,,]ROR ,F9D ! M>G9 (
]ROR =A SURVEY T HAS ! GIV5 SAMPLE SIZE4
,R.D YR ANSW] 6! NE>E/ T5? (A P]C5T4
#F4 #BFJ
#G #AJJJ
#H4 #GEJ
#I4 #FDJJ
#AJ4 #CBGE
#AA4 #EBE
#AB4 #BJBD
#AC4 #AJ1JJJ
#AD4 .,,MULTIPLE .,,*OICE ,9 A SURVEY
( #BJJJ VOT]S1 #DE@3P SD !Y PLANN$ 6VOTE
= C&IDATE ,A4 ,:AT IS ! M>G9 ( ]ROR =!
SURVEY8
,A +-#A.H@3P
;,B +-#B.B@3P
;,C +-#C.F@3P
;,D +-#D.E@3P
,,EXAMPLE #E
ON P4 #GFI = ,EXS4 #AE-BC
,,F9D+ ,,SAMPLE ,,SIZES ,F9D ! SAMPLE
SIZE REQUIR$ 6A*IEVE ! GIV5 M>G9 ( ]ROR4
,R.D YR ANSW] 6! NE>E/ :OLE NUMB]4
#AE4 +-#C@3P
#AF4 +-#H@3P
#AG4 +-#AJ@3P
#AH4 +-#D.B@3P
#AI4 +-#E.F@3P
#BJ4 +-#A.E@3P
#BA4 +-#F.E@3P
#BB4 +-#B.E@3P
#BC4 .,,MULTIPLE .,,*OICE ,! M>G9 (
]ROR =A POLL IS +-#B@3P4 ,:AT IS ! SIZE
(! SAMPLE8
,A #BJJ
;,B #DJJ
;,C #AJJJ
;,D #BEJJ
#BD4 .,,]ROR .,,ANALYSIS ,9 A SURVEY (
HI< S*OOL /UD5TS1 #AC@3P SD T !Y PLAY
BASKETBALL REGUL>LY4 ,! M>G9 ( ]ROR IS
+-#D@3P4 .,DESCRIBE & CORRECT ! ]ROR 9
CALCULAT+ ! SAMPLE SIZE4
;N #EI
#BE4 .,,R1SON+ ,A SURVEY CLAIMS !
P]C5T (A C;Y'S RESID5TS T FAVOR BUILD+ A
NEW FOOTBALL /ADIUM IS LIKELY 2T
#EB.C@3P & #FA.G@3P4 ,H[ _M P 7 SURVEY$8
#BF4 .,,*ALL5GE ,SUPPOSE A R&OM SAMPLE
( SIZE .;N IS REQUIR$ 6PRODUCE A M>G9 (
]ROR ( +-.,E4 .,WRITE AN EXPRES.N 9 T]MS
( .;N =! SAMPLE SIZE
NE$$ 6REDUCE ! M>G9 ( ]ROR TO +- ,0H[
_M "TS M/ ! SAMPLE SIZE 2 9CR1S$ 9 ORD]
6CUT ! M>G9 ( ]ROR 9 HALF8
,,EXAMPLES #C1D1 & #E
ON PP4 #GFG-GFI = ,EXS4 #BG-CA
,PRO#M ,SOLV+
#BG4 .,,VAC,N .,,SURVEY ,9 A SURVEY (
#DCI TE5AG]S 9 ! ,UNIT$ ,/ATES1 #AD@3P
SD T !Y "W$ DUR+ _! SUMM] VAC,N4
A4 ,:AT IS ! M>G9 ( ]ROR =! SURVEY8
B4 ,GIVE AN 9T]VAL T IS LIKELY 63TA9 !
EXACT P]C5T ( ALL ,U4,S4 TE5AG]S :O "W$
DUR+ _! SUMM] VAC,N4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#BH4 .,,NEWSLR ,! /AFF =A /UD5T NEWSLR
WANTS 63DUCT A SURVEY ( /UD5TS' FAVORITE
,,TV %[S4 ,"! >E #ABBE /UD5TS 9 ! S*OOL4
,! NEWSLR /AFF WD L 6SURVEY #BEJ /UD5TS4
.,DESCRIBE A ME?OD = SELECT+ AN UNBIAS$1
R&OM SAMPLE ( /UD5TS4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.K .,,"W$-.,,\ .,,SOLU;NS .ONP4.,,WSI
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#GGA
#BI4 .,,%ORT .,,RESPONSE ,BAS$ ON !
NEWSPAP] REPORT %[N 2L1 IS X R1SONA#
6ASSUME T ,KO/A IS C]TA9 6W9 ! ELEC;N8
.,EXPLA94
#CJ4 .,,MULTI-.,,/EP .,,PRO#M ,A
,GALLUP ,Y\? ,SURVEY REPORT$ T #BC@3P (
/UD5TS SURVEY$1 OR AB #AHA /UD5TS1 SAY T
MA? IS _! FAVORITE SUBJECT 9 S*OOL4
A4 ,H[ _M /UD5TS 7 SURVEY$8
B4 ,:AT IS ! M>G9 ( ]ROR =! SURVEY8
C4 ,GIVE AN 9T]VAL T IS LIKELY 63TA9 !
EXACT P]C5T ( ALL /UD5TS :O WD SAY T MA?
IS _! FAVORITE SUBJECT4
#CA4 .,,EXT5D$ .,,RESPONSE ,A SURVEY
REPORT$ T #BCE \ ( #EJJ VOT]S 9 A SAMPLE
VOT$ = C&IDATE ,A&! REMA9D] VOT$ =
C&IDATE ,B4
A4 .,F9D4.,P]C5TS ,:AT P]C5T (! VOT]S
9 ! SAMPLE VOT$ = C&IDATE ,A8 = C&IDATE
;,B8
B4 ..,F9D ,M>G9 ( .,]ROR ,:AT IS !
M>G9 ( ]ROR =! SURVEY8
C4 .,F9D .,9T]VALS ,= EA* C&IDATE1 F9D
AN 9T]VAL T IS LIKELY 63TA9 ! EXACT
P]C5T ( ALL VOT]S :O VOT$ =! C&IDATE4
D4 .,R1SON+ ,BAS$ ON YR 9T]VALS1 C Y 2
3FID5T T C&IDATE ;,B WON8 ,IF N1 H[ _M P
9 ! SAMPLE WD NE$ 6VOTE = C&IDATE ;,B =
Y 6BE 3FID5T ( H] VICTORY8 7.,H9T3 ,F9D
! L1/ NUMB] ( VOT]S = C&IDATE ;,B S* T !
9T]VALS D N OV]LAP47
#CB4 .,,*ALL5GE ,9 A SURVEY1 #EB@3P (!
RESPOND5TS SD !Y PREF] COLA ;,X & #DH@3P
SD !Y PREF] COLA ,Y4 ,H[ _M P WD H 6BE
SURVEY$ = Y 6BE 3FID5T T COLA ;,X IS
TRULY PREF]R$ 0M ?AN HALF ! POPUL,N8
.,EXPLA9 YR R1SON+4
,PREVIEW
,PREP>E = ,LESSON #AA.E 9 ,EXS4
#CC-CH4
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
,GRAPH ! FUNC;N4
.#CC4 @7 P4 #HI @7
.#CD4 ;Y .K ;X #B -- #E;X--#BD @7 P4
#BCF @7
.#CE4 @7 P4 #BDE @7
.#CF4 .;F 7;X7 .K 7;X @+ #A7 7;X #B --
#C;X @+ #C7 @7 P4 #CHG @7
.#CG4 .;G 7;X7 .K #D @* #B ;X @7 P4
#DGH @7
.#CH4 .;H 7;X7 .K--#B7#J.BE7 ;X @7 P4
#DHF @7
.#CI4 ,USE F9ITE DI6];E &A SY/EM (
EQU,NS 6F9D A POLYNOMIAL FUNC;N T FITS !
DATA 9 ! TA#4 @7 P4 #CIC @7
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #A3 #B3 #C3 #D3 #E3 #F
.;F @7 .;X @7 @3 --#I3 --#AJ3 --#G3
#J3 #AA3 #BF
.,,EXTRA .,,PRACTICE = ,LESSON #AA.D1
P4 #AJBJ
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#GGB
,EXT5.N
USE AF ,LESSON #AA.D
,DESIGN ,SURVEYS & ,EXP]I;TS
.,GOAL ,WRITE UNBIAS$ SURVEY "QS &
UNFLAW$ EXP]I;TAL PROC$URES4
,KEY ,VOCABUL>Y
99 BIAS$ "Q
99 EXP]I;TAL GR\P
99 3TROL GR\P
,SIDEB>3
.,/&>DS
,5RI*;T TOPIC2 N REQUIR$ 0! ,CALI=NIA
,/&>DS4
,:5 DESIGN+ A SURVEY1 X IS IMPORTANT T
! SURVEY "QS 2 C>E;LLY WRITT54 ,IF A "Q
IS POORLY WRITT51 !N ! RESPONSES (! P
SURVEY$ MAY N A3URATELY REFLECT _!
OP9IONS OR AC;NS4 ,^! TYPES ( FLAW$ "QS
>E CALL$ .BIAS$ ."QS4
,"! >E S"EAL R1SONS :Y A "Q MAY 2
BIAS$3
99 ,! "Q MAY 5C\RAGE ! RESPOND5T
6ANSW] 9 A "PICUL> WAY4
99 ,! "Q MAY 2 P]CVD Z TOO S5SITIVE
6ANSW] TRU?;LLY4
99 ,! "Q MAY N PROVIDE ! RESPOND5T ) 5
9=M,N 6GIVE AN A3URATE OP9ION4
,BIAS MAY AL 2 9TRODUC$ "? ! ORD] 9 :
! "QS >E ASK$ OR MAY RESULT :5 ! P]SON
3DUCT+ ! 9T]VIEW 9T5;N,Y OR UN9T5;N,Y
9FLU;ES ! RESPONSES ( ^? 9T]VIEW$4
,EXAMPLE #A ,ID5TIFY & CORRECT BIAS 9
SURVEY "QS
,TELL :Y ! "Q MAY 2 BIAS$4 ,DESCRIBE
H[ 6CORRECT ! FLAW4
A4 8..,_M N,NAL P>KS >E 2+ H1VILY
DAMAG$ 0ACID RA94 ,D Y FAVOR GOV]N;T
FUND+ 6HELP PREV5T ACID .RA980
,? IS AN EXAMPLE (A .L1D+ ."Q4
,RESPOND5TS MAY ?9K A 8NO0 RESPONSE M1NS
!Y >E N 9 FAVOR ( SUPPORT+ N,NAL P>KS4
,9 ? WAY1 ! "Q 5C\RAGES ! RESPOND5T
6ANSW] 8YES40
,A BETT] WAY 6ASK ? "Q IS 6ELIM9ATE !
F/ S5T;E & J ASK1 8,D Y FAVOR GOV]N;T
FUND+ 6HELP PREV5T ACID RA980
B4 8..,D Y AGREE )! AM5D;TS 6! ,CL1N
,AIR .,ACT80
,! "Q ASSUMES T ! RESPOND5T IS FAMILI>
)! AM5D;TS 6! ,CL1N ,AIR ,ACT4
,RESPONSES 0P UNFAMILI> )! AM5D;TS CD
L1D 6MISL1D+ 3CLU.NS4
,A BETT] WAY 6ASK ? "Q IS 6F/ /ATE EA*
AM5D;T & !N ASK1 8,D Y AGREE ) ?
AM5D;T80
.C4 ,POLICE (FIC]S ASK MALL VISITORS1
8..,D Y WE> YR S1T BELT .REGUL>LY80
,_M MOTORI/S MAY ANSW] UNTRU?;LLY 2C A
POLICE (FIC] IS ASK+ ! "Q1 ESPECI,Y IF !
LAW REQUIRES S1T BELT USE4 ,! DATA
COLLECT$ MI<T N A3URATELY REPRES5T !
P]C5T ( P :O WE> S1T BELTS REGUL>LY4
,9 ? CASE1 ! CORREC;N IS 6H ! "Q 2
ASK$ 0"S"O N 9VOLV$ 9 LAW 5=CE;T4
------------------------------------#GGC
.,,EXP]I;TS ,AN EXP]I;T IS (T5 3DUCT$
) TWO GR\PS4 ,"O GR\P1 CALL$ !
.EXP]I;TAL .GR\P @1 "UGOES "S PROC$URE
OR TR1T;T4 ,! O!R GR\P1 CALL$ ! .3TROL
.GR\P @1 DOES N "UGO ! PROC$URE OR
TR1T;T4
,9 A WELL-DESIGN$ EXP]I;T1 "EY?+ ELSE
AB ! EXP]I;TAL GR\P &! 3TROL GR\P IS Z
SIMIL> Z POSSI# S T ! E6ECT (! PROC$URE
OR TR1T;T C 2 DET]M9$4
,EXAMPLE #B ,ID5TIFY FLAWS 9 AN
EXP]I;T
.,,RESE>* ,A DRUG -PANY 3DUCTS AN
EXP]I;T 6TE/ :E!R A NEW PA9 RELIEF
M$IC,N IS E6ECTIVE AT RELIEV+ H1DA*ES4
,! EXP]I;TAL GR\P 3SI/S ( COLLEGE /UD5TS
:O >E GIV5 ! M$IC,N4 ,! 3TROL GR\P 3SI/S
( COLLEGE PROFESSORS :O >E N GIV5 !
M$IC,N4
,! -PANY F9DS T ! H1DA*ES ( P 9 !
EXP]I;TAL GR\P >E ( %ORT] DUR,N ?AN ^? (
P 9 ! 3TROL GR\P4 ,Z A RESULT1 ! -PANY
3CLUDES T ! M$IC,N IS E6ECTIVE4 ,ID5TIFY
ANY FLAWS 9 ? EXP]I;T1 & DESCRIBE H[ !Y
C 2 CORRECT$4
,SOLU;N
,ON AV]AGE1 COLLEGE /UD5TS >E LIKELY
6BE "Y] ?AN COLLEGE PROFESSORS4 ,S1 X CD
2 AGE R ?AN ! M$IC,N T EXPLA9S :Y !
EXP]I;TAL GR\P _H %ORT]-LA/+ H1DA*ES ?AN
! 3TROL GR\P4
,6CORRECT ? FLAW1 ! DRUG -PANY CD
REDESIGN ! EXP]I;T S T ! AGES (! P 9 !
EXP]I;TAL GR\P >E SIMIL> 6! AGES (! P 9
! 3TROL GR\P4
,PRACTICE
,,EXAMPLE #A
ON P4 #GGB = ,EXS4 #A-F
,9 ,EX]CISES #A-F1 TELL :Y ! "Q MAY 2
BIAS$4 .,DESCRIBE H[ 6CORRECT ! FLAW4
#A4 8,D Y AGREE T BUILD+ A B1UTI;L NEW
BASEBALL /ADIUM WD 2 A GD 9VE/;T =! C;Y
6MAKE80
#B4 8,A SURVEY (! VOT]S 9 ? /ATE %[S T
#HE@3P FAVOR A TAX CUT4 ,D Y FAVOR A TAX
CUT80
#C4 ,A D5TI/ ASKS H] PATI5TS1 8,D Y
FLOSS E "D80
#D4 8,DON'T Y ?9K T R5OVAT+ ! OLD T[N
HALL WD 2 A MISTAKE80
#E4 8,D Y ?9K ! DEF5DANT 9 ! ,C>T]
CASE 0 GIV5 A FAIR TRIAL80
#F4 8,: C;Y C\NCIL C&IDATE'S PLAT=M D
Y SUPPORT80
#G4 .,,$UC,N ,A RESE>* -PANY 3DUCTS AN
EXP]I;T 6TE/ :E!R A NEW MA!MATICS S(TW>E
PROGRAM W 9CR1SE TE/ SCORES ( /UD5TS4 ,!
EXP]I;TAL GR\P 3SI/S ( /UD5TS 5ROLL$ 9
,ALGEBRA #B :O >E GIV5 ! S(TW>E4 ,!
3TROL GR\P 3SI/S ( /UD5TS 5ROLL$ 9
,ALGEBRA #A :O >E N GIV5 ! S(TW>E4
,! -PANY F9DS T ! /UD5TS 9 ! EXP]I;TAL
GR\P TE/ HI<] ?AN ! /UD5TS 9 ! 3TROL
GR\P & 3CLUDES T ! S(TW>E IS E6ECTIVE AT
9CR1S+ TE/ SCORES4 ,ID5TIFY ANY FLAWS 9
! EXP]I;T1 & DESCRIBE H[ !Y C 2
CORRECT$4
,,EXAMPLE #B
ON P4 #GGC = ,EX4 #G
------------------------------------#GGD
,9VE/IGAT+ ,ALGEBRA ,ACTIV;Y3 #AA.E
,FITT+ A ,MODEL 6,DATA
,USE 2F LESSON1 #AA.E
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,KEY/ROKES
,,MAT]IALS
99 #BJ 9DEX C>DS
99 GRAPH+ CALCULATOR
,"Q ,H[ C Y *OOSE A MA!MATICAL MODEL
=A DATA SET8
,9 ? ACTIV;Y1 Y W M1SURE ! "T X TAKES
6LE>N A NEW TASK Z X 2COMES M FAMILI>4
,Y W !N F9D A FUNC;N T MODELS ! DATA Y
COLLECT4 ,"W )A "PN]4
,EXPLORE ,COLLECT DATA ON LE>N+ "T
,,/EP #A .,P]=M .TASK
,WRITE A DI6]5T ^W ON EA* 9DEX C>D4
,%U6LE ! C>DS1 !N H YR "PN] PUT !M 9
ALPHABETICAL ORD]4 ,M1SURE ! "T YR "PN]
TAKES 6-PLETE ! TASK4
,,/EP #B .,RECORD .DATA
,H YR "PN] REP1T ! TASK DESCRIB$ 9
,/EP #A AT L1/ FIVE M "TS4 ,RECORD YR
"PN]'S -PLE;N "TS 9 A TA# L ! "O %[N 2L4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,TASK NUMB]3 ,"T7SEC7
.#A @3 .#HI
.#B @3 .#GJ
.#C @3 .#FD
.#D @3 .#EH
.#E @3 .#EH
.#F @3 .#EG
,,/EP #C .MAKE .SCATT] .PLOT
,LET .;X 2 ! TASK NUMB] & LET .;Y 2 !
-PLE;N "T4 ,USE A GRAPH+ CALCULATOR
6MAKE A SCATT] PLOT (! DATA PAIRS @7
.;X1 .;Y7 F ! TA# 9 ,/EP #B4
,DRAW ,3CLU.NS ,USE YR OBS]V,NS
6-PLETE ^! EX]CISES
#A4 .,DESCRIBE ! PATT]N %[N 9 YR
SCATT] PLOT F ,/EP #C4 .,EXPLA9 :Y !
PATT]N MAKES S5SE4
#B4 ,F9D A FUNC;N T IS A GD MODEL =!
DATA 9 YR SCATT] PLOT4 ,Y C USE "O (!
GRAPH+ CALCULATOR'S REGRES.N F1TURES
6F9D A MODEL1 OR Y MAY EXP]I;T ) O!R
TYPES ( FUNC;NS T ! REGRES.N F1TURES _C
G5]ATE4
#C4 ,USE ! FUNC;N Y *OSE 9 ,EX]CISE #B
6PREDICT ! "T YR "PN] WD TAKE
6ALPHABETIZE ! 9DEX C>DS ON ! #AJ?
TRIAL4
#D4 ,"W )A SECOND "PN] & REP1T !
EXP]I;T4 ,F9D A MA!MATICAL MODEL
6DESCRIBE ? "PN]'S LE>N+ "TS4 ,D Y GET
SIMIL> OR DI6]5T RESULTS8 .,EXPLA9 :Y Y
MI<T EXPECT SIMIL> OR DI6]5T RESULTS4
------------------------------------#GGE
#AA.E ,*OOSE ! ,BE/ ,MODEL =
,TWO-,V>IA# ,DATA
.,2F ,Y WROTE DI6]5T TYPES ( FUNC;NS
6MODEL SETS ( DATA4
.,N[ ,Y W *OOSE ! BE/ MODEL 6REPRES5T
A SET ( DATA4
.,:Y8 ,S Y C RELATE 5G9E SPE$ &
HORSEP[]1 Z 9 ,EX4 #AD4
,KEY ,VOCABUL>Y
99 .L9E> .FUNC;N @1 P4 #GE
99 QUADRATIC FUNC;N
P4 #BCF
99 .CUBIC .FUNC;N @1 P4 #CCG
99 .EXPON5TIAL .FUNC;N @1 P4 #DGH
99 .P[] .FUNC;N @1 P4 #ECA
,Y H US$ ! FUNC;NS %[N AT ! "R 6MODEL
SETS ( DATA4
,6F9D ! BE/ MODEL =A SET ( DATA PAIRS
7;X1 ;Y71 MAKE A SCATT] PLOT (! DATA &
DET]M9E ! TYPE ( FUNC;N SU7E/$ 0! PATT]N
9 ! DATA PO9TS4 ,!N F9D A MODEL ( ? TYPE
US+ "O (! REGRES.N F1TURES (A GRAPH+
CALCULATOR4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,FUNC;N3 ,G5]AL =M
,L9E>3 ..;Y .K AX @+ .;B
,QUADRATIC3 ;Y .K AX.' #B @+ .BX @+
;C.'.-
,CUBIC3 ;Y .K AX.' #C @+ BX.' #B @+ CX
@+ ;D.'.-
,EXPON5TIAL3 ;Y .K ;AB.' ;X.'.-
,P[]3 ;Y .K AX.' ;B.'.-
,SIDEB>3
.,/&>DS
,ADV.ED ,PLACE;T ,PROBABIL;Y &
,/ATI/ICS3#AB.J
,/UD5TS F9D ! L9E ( BE/ FIT 6A GIV5
4TRIBU;N ( DATA 0US+ L1/ SQU>ES
REGRES.N4
,EXAMPLE #A ,USE A L9E> MODEL
.,,TUI;N ,! TA# %[S ! AV]AGE TUI;N .;Y
7IN DOLL>S7 =A PRIVATE F\R-YE> COLLEGE 9
! ,UNIT$ ,/ATES F #AIIE 6#BJJB1 ": .;X
IS ! NUMB] ( YE>S S9CE #AIIE4 ,USE A
GRAPH+ CALCULATOR 6F9D A MODEL =! DATA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X @3 #J3 #A3 #B3 #C3 #D3 #E3 #F3 #G
.;Y @3 #AD1ECG3 #AE1FJE3 #AF1EEB3
#AG1BBI3 #AH1CDJ3 #AI1CJG3 #BJ1AJF3
#BA1AHC
,SOLU;N
.,,/EP .#A .,MAKE A SCATT] PLOT4 ,!
PO9TS LIE APPROXIMATELY ON A L9E4 ,?
SU7E/S A L9E> MODEL4
.,,/EP#B .,USE ! L9E> REGRES.N F1TURE
6F9D AN EQU,N (! MODEL4
.,,/EP .#C .,GRAPH ! MODEL AL;G )!
DATA 6V]IFY T ! MODEL FITS ! DATA WELL4
99 ,A MODEL =! DATA IS .;Y .K #ICC;X
@+ #AD1FJJ4
------------------------------------#GGF
,EXAMPLE #B ,USE AN EXPON5TIAL MODEL
.,,COOL+ .,,RATES ,Y >E /OR+ LEFTOV]
*ILI 9 A FREEZ]4 ,! TA# %[S ! *ILI'S
TEMP]ATURE .;Y 7IN DEGREES ,FAHR5HEIT7
AF .;X M9UTES 9 ! FREEZ]4 ,USE A GRAPH+
CALCULATOR 6F9D A MODEL =! DATA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X @3 #J3 #AJ3 #BJ3 #CJ3 #DJ3 #EJ3
#FJ
.;Y @3 #AJJ3 #GE3 #EJ3 #CE3 #BH3 #BJ3
#AE
,,ANO!R ,,WAY
,= AN EXT5.N (! PRO#M 9 ,EXAMPLE #B1
TURN 6PAGE #GHA =! .,PRO#M .,SOLV+
.,"W%OP4
,SOLU;N
.,,/EP#A .,MAKE A SCATT] PLOT4 ,!
PO9TS FALL RAPIDLY AT F/ & !N 2G9 6LEVEL
(F4 ,? SU7E/S AN EXPON5TIAL DECAY MODEL4
.,,/EP#B .,USE ! EXPON5TIAL REGRES.N
F1TURE 6F9D AN EQU,N (! MODEL4
.,,/EP#C .,GRAPH ! MODEL AL;G )! DATA
6V]IFY T ! MODEL FITS ! DATA WELL4
99 ,A MODEL =! DATA IS .;Y .K
#IH.B7#J.IFI7 ;X @4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,GUID$ ,PRACTICE = ,EXAMPLES #A &
.#B
,USE A GRAPH+ CALCULATOR 6F9D A MODEL
=! DATA4 ,!N GRAPH ! MODEL &! DATA 9 !
SAME COORD9ATE PLANE4
#A4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X @3 #AJ3 #BJ3 #CJ3 #DJ3 #EJ3 #FJ3
#GJ3 #HJ
.;Y @3 #BC.A3 #BH.I3 #CD.I3 #DC.G3
#EC.B3 #FF.E3 #HJ.H3 #II.C
#B4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X @3 #J3 #A3 #B3 #C3 #D3 #E3 #F3
.#A
.;Y @3 #CC3 #DA3 #EB3 #FH3 #HJ3 #HI3
#AJB3 #AAH
------------------------------------#GGG
,EXAMPLE #C ,USE A QUADRATIC MODEL
.,,FUEL .,,E6ICI5CY ,A /UDY -P>$ !
SPE$ .;X 7IN MILES P] H\R7 &! AV]AGE
FUEL E6ICI5CY 7IN MILES P] GALLON7 (
C>S4 ,! RESULTS >E %[N 9 ! TA#4 ,USE A
GRAPH+ CALCULATOR 6F9D A MODEL =! DATA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X @3 #AE3 #BJ3 #BE3 #CJ3 .#CE @3
.#DJ @3 .#DE @3 .#EJ @3 .#EE @3 .#FJ @3
.#FE
.;Y @3 #BB.C3 #BE.E3 #BG.E3 .#BI..J @3
.#BH..H @3 .#CJ..J @3 .#BI..I @3 .#CJ..B
@3 .#CJ..D @3 .#BH..H @3 #BG.D
,SOLU;N
.,,/EP .#A .,MAKE A SCATT] PLOT4 ,!
PO9TS =M AN 9V]T$ ;,U-%APE4 ,? SU7E/S A
QUADRATIC MODEL4
.,,/EP#B .,USE ! QUADRATIC REGRES.N
F1TURE 6F9D AN EQU,N (! MODEL4
.,,/EP .#C .,GRAPH ! MODEL AL;G )!
DATA 6V]IFY T ! MODEL FITS ! DATA WELL4
99 ,A MODEL =! DATA IS .;Y .K
--#J.JJGIC;X #B @+ #J.GBG;X @+ #AC.H4
,,*OOSE ,A ,,MODEL
,! DATA 9 ,EXAMPLE #C C 2 MODEL$ 0BO?
A QUADRATIC FUNC;N &A CUBIC FUNC;N4 ,:5
? O3URS1 X IS (T5 BETT] 6*OOSE ! SIMPL]
MODEL4
..,GUID$ ,PRACTICE = ,EXAMPLE .#C
.#C4 .,,FUEL .,,E6ICI5CY ,USE ! MODEL
F ,EXAMPLE #C 6PREDICT ! AV]AGE FUEL
E6ICI5CY (A C> TRAVEL+ #GJ MILES P] H\R4
,USE A GRAPH+ CALCULATOR 6F9D A MODEL
=! DATA4 ,!N GRAPH ! MODEL &! DATA 9 !
SAME COORD9ATE PLANE4
#D4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X @3 #AJJ3 #BJJ3 .#CJJ @3 .#DJJ @3
.#EJJ @3 .#FJJ @3 #GJJ
.;Y @3 #AF3 #CE3 .#EE @3 .#GJ @3 .#FH
@3 .#EF @3 #CH
#E4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X @3 -.#E @3 -.#D @3 -.#C @3 -.#B
@3 -.#A @3 .#A @3 .#B
.;Y @3 -.#BJ @3 .#J @3 .#C @3 .#J @3
-.#D @3 .#J @3 .#AH
------------------------------------#GGH
#AA.E ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
,,WS#BJ = ,EXS4 #C & #AA
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE ,EXS4
.#B1 .#E1.F1.H @1 & .#AC
.K .,,MULTIPLE .,,REPRES5T,NS ,EX#.AB
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,A
FUNC;N (! =M ;Y .K .;AB ;X.' .-IS A7;N7
@8 FUNC;N4
.#B4 .,,WRIT+ .,EXPLA9 H[ Y C DET]M9E
:E!R A L9E> FUNC;N OR A QUADRATIC FUNC;N
IS A BETT] MODEL =A SET ( DATA4
,,EXAMPLES #A1B1 & #C
ON PP4 #GGE-GGG = ,EXS4 #C-G
,,MODEL+ ,,DATA ,USE A GRAPH+
CALCULATOR 6F9D A MODEL =! DATA4 ,!N
GRAPH ! MODEL &! DATA 9 ! SAME COORD9ATE
PLANE4
#C
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X @3 #A3 #B3 #C3 #D3 #E3 #F3 #G
.;Y @3 #AF3 #AG3 #AF3 #AD3 #AA3 #I3 #E
#D4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X @3 #A3 #B3 #C3 #D3 #E3 #F3 #G
.;Y @3 #BF3 #CB3 #CD3 #CG3 #DB3 #DE3
#DI
.#E4 .,,MULTIPLE .,,*OICE ,: TYPE (
FUNC;N BE/ MODELS ! DATA PO9TS8
,A ,L9E>
;,B ,QUADRATIC
;,C ,CUBIC
;,D ,EXPON5TIAL
#F4 .,,MULTIPLE .,,*OICE ,: EQU,N BE/
MODELS ! DATA8
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X @3 #J3 #E3 #AJ3 #AE3 #BJ3 #BE3
#CJ3 #CE
.;Y @3 #ABE3 #IJ3 #FC3 #DC3 #BH3 #BJ3
#AF3 #AJ
,A .;Y .K --#C.AD;X @+ #AJD
;,B .;Y .K #ABF7#J.ICA7 ;X
;,C ;Y .K #ABE;X --#J.F
;,D ;Y .K #J.AB;X #B @+ #ABD
#G4 .,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR MADE 9 US+ ! 9=M,N ON A
GRAPH+ CALCULATOR SCRE5 6WRITE A MODEL4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,! ,EXP,REG .SCRE5 .%[S3 @3 ,A .MODEL
.= .! DATA IS3
;Y.KA99;B_<;X3 ;Y .K #I.GA;X #A.EE
A.K#I.GADIFCBGD
;B.K#A.EEJCEEAAF @3
#H4 .,,OP5-.,,5D$ .,,MA? ,WRITE A TA#
( VALUES T C 2 MODEL$ 0A QUADRATIC
FUNC;N4
#I4 .,,*ALL5GE ,! FUNC;N ;Y .K #E;X
#B.C MODELS A TA# ( DATA 9 : ;X-VALUES
>E M1SUR$ 9 9*ES & ;Y-VALUES >E M1SUR$ 9
P.DS4 ,IF ! TA# IS *ANG$ 6GIVE !
;X-VALUES 9 FEET1 :AT FUNC;N MODELS !
REVIS$ DATA8
------------------------------------#GGI
..,,EXAMPLES #A1B1 & .#C ON PP4
.#GGE-.GGG = ,EXS4 #AJ-AC
,PRO#M ,SOLV+
#AJ4 .,,ECONOMICS ,! GROSS DOME/IC
PRODUCT 7,,GDP7 IS ! TOTAL VALUE ( GDS &
S]VICES PRODUC$ 0A C.TRY 9 ANY GIV5 YE>4
,! TA# %[S ! ,,GDP ;Y 7IN BILLIONS (
DOLL>S7 (! ,UNIT$ ,/ATES = SELECT$ YE>S
F #AICJ 6#BJJJ4 ,9 ! TA#1 .;X REPRES5TS
! NUMB] ( YE>S S9CE #AICJ4 ,USE A GRAPH+
CALCULATOR 6F9D A MODEL =! DATA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X @3 #J3 #AJ3 #BJA3 #CJ3 #DJ3 #EJ3
#FJ3 #GJ
.;Y @3 #IAC3 #AJAC3 #BIDC3 #EBG.D3
#AJCI.G3 #BGIE.F3 #EHJC.B3 #IHBD.F
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#AA .,,AGRICULTURE ,! TA# %[S ! AGES
.;X 7IN YE>S7 & TRUNK DIAMET]S .;Y 7IN
9*ES7 ( S"EAL ,TEXAS GRAPEFRUIT TREES4
,USE A GRAPH+ CALCULATOR 6F9D A MODEL =!
DATA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X @3 .#A @3 .#D @3 .#H @3 .#AB @3
.#AF @3 .#BJ @3 .#BD
.;Y @3 .#A..A @3 .#C..I @3 .#F..B @3
.#GF @3 .#I..A @3 .#AA..D @3 .#AE..B
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#AB4 .,,MULTIPLE .,,REPRES5T,NS ,!
GRAPH 2L %[S ! PRICE (A F/-CLASS /AMP 9
! ,UNIT$ ,/ATES = SELECT$ YE>S F #AIGE
6#BJJB4 ,USE A GRAPH+ CALCULATOR 6F9D A
MODEL =! DATA4 ,!N GRAPH ! MODEL &! DATA
9 ! SAME COORD9ATE PLANE4
.#AC4 .,,EXT5D$ .,,RESPONSE ,! MANAG]
(A RE/AURANT KEPT A RECORD (! NUMB] .;Y
( CU/OM]S EA* H\R1 ": .;X .K #C
REPRES5TS #C3JJ ,P4,M4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X @3 .#C @3 .#D @3 .#E @3 .#F @3
.#G @3 .#H @3 .#I @3 .#AJ
.;Y @3 .#I @3 .#BD @3 .#DD @3 .#EF @3
.#DH @3 .#DB @3 .#CH @3 .#BB
A4 ,MAKE A SCATT] PLOT (! DATA &
DET]M9E ! TYPE ( FUNC;N T BE/ MODELS !
DATA4
B4 ,USE A REGRES.N F1TURE (A GRAPH+
CALCULATOR 6F9D A FUNC;N T MODELS !
DATA4
C4 ,GRAPH ! FUNC;N & DATA 6V]IFY T !
FUNC;N IS A GD MODEL4
D4 ,D Y ?9K ! FUNC;N Y F.D WD
A3URATELY PREDICT ! NUMB] ( CU/OM]S AT
#A P4M48 .,EXPLA94
------------------------------------#GHJ
.#AD4 .,,C> .,,5G9ES ,! TA# %[S !
REL,N%IP 2T A C>'S 5G9E SPE$ 7IN
REVOLU;NS P] M9UTE7 &! P[] 7IN HORSEP[]7
T ! 5G9E PRODUCES4 ,USE A GRAPH+
CALCULATOR 6F9D A MODEL =! DATA4 ,:AT
5G9E SPE$ MAXIMIZES ? C>'S 5G9E P[]8
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,5G9E .SPE$ 7.RPM7 @3 #AJJJ3 #BJJJ3
#CJJJ3 #DJJJ3 #EJJJ3 #FJJJ
.,5G9E .P[] 7.HP7 @3 #AF3 #CE3 #EE3
#GB3 #GG3 #FH
.#AE4 .,,*ALL5GE ,Z A *AIR MANUFACTUR]
PRODUCES M *AIRS1 ! PRODUC;N CO/ P] *AIR
DECR1SES4 ,! TA# %[S ! NUMB] ;X ( *AIRS
PRODUC$ &! PRODUC;N CO/ .;Y 7IN DOLL>S7
P] *AIR4 ,MODEL ! DATA )A FUNC;N ^:
GRAPH HAS A HORIZONTAL ASYMPOTE4 ,:AT
DOES ! ASYMPTOTE REPRES5T 9 ? SITU,N8
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X @3 #EJ3 #CJJ3 #HJJ3 #BJJJ3 #CJJJ3
#DJJJ
.;Y @3 #BFJ3 #AHJ3 .#IE @3 #DE3 #CE3
#CJ
,PREVIEW
,PREP>E = ,LESSON #AB.A
,9 ,EXS4 #AF-BA4
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
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.#AF4 #F;X--#B :5 ;X .K #E
.#AG4 #H--#C;X :5 ;X .K --#F
.#AH4 #D ;X--#A :5 ;X .K #C
.#AI4 #H7;X--#B7 :5 ;X .K #H
.#BJ4 #E;X--#G @+ #B;X :5 ;X .K #D
.#BA4 #F;X--7;X @+ #E7 :5 ;X .K--#I
,3D5SE ! EXPRES.N4 @7 P4 #EJG @7
.#BB4 LOG #C #E--LOG #C #H
.#BC4 #B LN #D @+ LN #C
.#BD4 #B LOG ;X--LOG #D;Y
.#BE4 #G;LOG #D ;X @+ #E;LOG #D ;Y
.#BF4
.#BG4
.#BH4 .,RADIO .,SIGNALS ,! SIGNALS (A
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,YR HOME IS #CE MILES EA/ & #EF MILES
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,,QUIZ .= .,LESSONS .#AA..C-.AG..E
,A NORMAL 4TRIBU;N HAS A M1N ( #DG &A
/&>D DEVI,N ( #F4 ,F9D ! PROBABIL;Y T A
R&OMLY SELECT$ .;X -VALUE IS 9 ! GIV5
9T]VAL1 @7 P4 #GEG @7
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.#D4 +-#C@3P
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,OLYMPICS4 ,USE A GRAPH+ CALCULATOR 6F9D
A MODEL =! DATA4 @7 P4 #GGE @7
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.;X @3 #AJJ3 #BJJ3 #DJJ3 #HJJ3 #AEJJ3
#EJJJ3 #AJ1JJJ
.;Y @3 #I.HE3 #AI.GI3 #DD.JJ3 #AJD.DE3
#BAD.AH #A3 #GID.CI3 #AFBE.AJ
.,,EXTRA .,,PRACTICE = ,LESSON #AA.E1
P4 #AJBJ
,,ONL9E ,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#GHA
,PRO#M ,SOLV+ ,"W%OP ,LESSON #AA.E3
,US+ ,ALT]NATIVE ,ME?ODS
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=MY .K .;AB ;X.' .-=A DATA SET4 ,Y C
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=M ;Y .K .;AB ;X.' @+ .C4
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COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X @3 #J3 #AJ3 #BJ3 #CJ43 #DJ3 #EJ3
#FJ
.;Y @3 #AJJ3 #HD3 #GB3 #FC3 #EG3 #EB3
#DI
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4TRIBU;N ( DATA 0US+ L1/ SQU>ES
REGRES.N4
.,ME?OD .,TRANS=M+ .,DATA ,"O APPROA*
6SOLV+ ! PRO#M IS 6P]=M A TRANS=M,N ON !
DATA & !N F9D A MODEL =! TRANS=M$ DATA4
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6#DJ;DG;,R ,S ! MODEL HAS ! =M .;Y .K
.;AB ;X.' @+ #DJ1 OR ;Y--#DJ .K .;AB ;X
@4
.,,/EP#B .,DEF9E A NEW V>IA# .;Y #A
.K.;Y -- #DJ4 ,!N ! DATA PAIRS 7;X1 ;Y
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6F9D A MODEL =! DATA 9 LI/S ;,L #A & ;,L
#C @4 ,! MODEL IS .;Y #A .K
#FJ.B7#J.IFI7 ;X ,S1 A MODEL =! ORIG9AL
DATA ISY.K #FJ.B7#J.IFI7 ;X @+#DJ4
99 ,A MODEL =! ORIG9AL DATA IS .;Y .K
#FJ.B7#J.IFI7 ;X @+ #DJ4 ,GRAPH ! MODEL
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FITS ! DATA WELL4
,PRACTICE
#A4 ,! DATA PAIRS 7;X1 .;Y7 2L GIVE !
TEMP]ATURE .;Y 7IN DEGREES ,FAHR5HEIT7
(A HOT CUP ( S\P AF X SITS = ;X M9UTES
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TEMP]ATURE (! ROOM4 ,!N F9D A MODEL =!
DATA4
7#J1 #ACB.H71 7#AJ1 #AJE.H71 7#CJ1
#IB.C71 7#EJ1 #HD.B71 7#GJ1 #GI.B71
7#IJ1 #GF.A71 7#AAJ1 #GE71 7#ABJ1
#GD.G71 7#ACJ1 #GD.B7
#B4 ,! DATA PAIRS 7;X1 ;Y7 2L GIVE !
TEMP]ATURE .;Y 7IN DEGREES ,CELSIUS7 (A
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DATA4
7#J1 #C.E71 7#BJ1 #H.A71 7#DJ1 #AB.B71
7#FJ1 #AE.D71 7#HJ1 #AG71 7#AJJ1 #AH.B71
7#AAJ1 #AH.F71 7#ABJ1 #AH.I7
------------------------------------#GHB
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,LESSONS #AA.C-AA.E
#A4 .,MULTI-.,/EP .,PRO#M ,A BIOLOGI/
CAU<T1 M1SUR$1 WEI<$1 & !N REL1S$ EI<T
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9*ES7 & WEI<TY 7IN P.DS74
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
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3TA9 TWO DA%ES4
.;,X @3 #AJ.C3 #AE.B3 #AF.B3 #AF.D
.;Y @3 #J.D3 #A.J3 #A.C3 #A.C
.;,X @3 #AG.E3 #AH.A3 #BB3 #BC.F
.;Y @3 #A.G3 #B.J3 #C.E3 #D.B
A4 ,USE A GRAPH+ CALCULATOR 6F9D A
MODEL =! DATA4
B4 ,USE ! MODEL F "P 7A7 6E/IMATE !
WEI<T (A ,MA9E L&LOCK$ SALMON T IS #BJ
9*ES L;G4
#B4 .,MULTI-.,/EP .,PRO#M ,9 A SURVEY
( #AJBB P :O %OP ONL9E1 #GC@3P SD T !Y D
S 2C (! 3V5I;E4
A4 ,:AT IS ! M>G9 ( ]ROR =! SURVEY8
B4 ,GIVE AN 9T]VAL T IS LIKELY 63TA9 !
EXACT P]C5T ( ALL ONL9E %OPP]S :O %OP 2C
(! 3V5I;E4
#C4 .,GRI4$ .,ANSW] ,AT A TREE NURS]Y1
! HEI<TS ( SCOT* P9E TREES >E NORM,Y
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#BBJ C5TIMET]S4 ,R.D YR ANSW] 6! NE>E/
:OLE NUMB]4
#D4 .,,OP5-.,,5D$ ,CR1TE A TA# ( DATA
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#E4 .,EXT5D$ .,RESPONSE ,! TA# %[S !
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3TA9 TWO DA%ES4
.,AGE @3 #F3 #G3 #H3 #AJ
.,%OE .SIZE @3 #E3 #F3 #G3 #I
.,AGE @3 #AB3 #AD3 #AE3 #AF
.,%OE .SIZE @3 #AJ3 #AA3 #AA3 #AB
A4 ,USE A GRAPH+ CALCULATOR 6F9D A
MODEL =! DATA4
B4 ,USE ! MODEL F "P 7A7 6E/IMATE !
BOY'S %OE SIZE :5 HE IS #AG YE>S OLD4
C4 .,DESCRIBE ANY LIMIT,NS ON ! DOMA9
(! MODEL F "P 7A74
#F4 .,%ORT .,RESPONSE ,! AM.T ( JUICE
4P5S$ F A MA*9E IS NORM,Y 4TRIBUT$ )A
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C4 ,GIVE AN 9T]VAL T IS LIKELY 63TA9 !
EXACT P]C5T ( ALL /UD5TS :O WD PREF] 6H
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SPORTS /ADIUM4 ,:AT TYPE ( SAMPLE IS
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YR R1SON+4
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#AA ,*APT] ,SUMM>Y
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6EA* DATA VALUE OR :5 EA* DATA VALUE IS
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,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#A3 ,DATA3 #A1D1D1 #E1H1I1I1AE3 ,ADD
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VALUE 9 DATA SET 0#C
.,M1N @3 #F.HGE3 #F.HGE @+ #E .K
#AA.HGE63 #C7#F.HGE7 .K #BJ.FBE
.,M$IAN @3 #F.E3 #F.E @+ #E--#AA.E3
#C7#F.E7--#AI.E
.,MODE @3 #D & #I3 #D @+ #E .K #I & #I
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.K #DB
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SYMMETRIC1 BELL-%AP$ CURVE4 ,! >EA "U A
NORMAL CURVE IS 4TRIBUT$ Z %[N 2L4 ,A
;Z-SCORE IS ! NUMB] ( /&>D DEVI,NS A
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USE ;Z-SCORES &! /&>D NORMAL TA# ON PAGE
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,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,SELF-.SELECT$ .SAMPLE @3 ,MEMB]S
VOLUNTE]43 ,(T5 BIAS$
.,SY/EMATIC .SAMPLE @3 ,A RULE IS US$
6SELECT MEMB]S43 ,"S"TS BIAS$
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.,R&OM .SAMPLE @3 ,E MEMB] HAS AN
EQUAL *.E ( 2+ SELECT$43 ,UNBIAS$
------------------------------------#GHD
#AA ,*APT] ,REVIEW
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
99 ,MULTI-,LANGUAGE ,GLOSS>Y
99 ,VOCABUL>Y PRACTICE
,,REVIEW ,,KEY ,,VOCABUL>Y
99 /ATI/ICS1 P4 #GDD
99 M1SURE ( C5TRAL T5D5CY1 P4 #GDD
99 M1N1 M$IAN1 MODE1 P4 #GDD
99 M1SURE ( 4P].N1 P4 P4 #GDE
99 RANGE1 P4 #GDE
99 /&>D DEVI,N1 P4 #GDE
99 \TLI]1 P4 #GDF
99 NORMAL 4TRIBU;N1 P4 P4 #GEG
99 NORMAL CURVE1 P4 P4 #GEG
99 /&>D NORMAL 4TRIBU;N1 P4 #GEH
99 ;Z-SCORE1 P4 P4 #GEH
99 POPUL,N1 P4 #GFF
99 SAMPLE1 P4 P4 #GFF
99 UNBIAS$ SAMPLE1 P4 P4 #GFG
99 BIAS$ SAMPLE1 P4 P4 #GFG
99 M>G9 ( ]ROR1 P4 P4 #GFH
,,VOCABUL>Y ,,EX]CISES
#A4 ,COPY & -PLETE3 @8 IS A M1SURE (
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! M1N1 M$IAN1 MODE1 RANGE1 & /&>D
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6*ECK YR "U/&+ (! 3CEPTS Y H LE>N$ 9 EA*
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DEVI,N (! FOLL[+ DATA SET3
#AC1AC1AC1AI1BD1BD1 #BG1 #BH1CD1CE4
,M1N3
,M$IAN3 #BD ,MODE3 #AC ,RANGE .K
#CE--#AC .K #BB
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.#D4 #CE1CF1CF1CH1DA1DB1DE1DH
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.#F4 #GF1 #AJB1 #HG1 #HE1 #IA1 #IB1
#IA1 #IG
.#G4 #AJC1 #AEE1 #ADJ1 #ABE1 #ACJ1
#ADJ1 #AAE
#H4 .,,GAS .,,PRICES ,! LI/ %[S !
AV]AGE PRICE (A GALLON ( GASOL9E EA* YE>
F #AIID 6#BJJD4 ,F9D ! M$IAN & /&>D
DEVI,N (! PRICES4
4#A.JD1 4#A.AC1 4#A.AC1 4#A.BF1
4#A.AC1 @4#.IG1 4#A.CJ1 4#A.DG1 4#A.AD1
4#A.DG1 4#A.EI
,,EXAMPLES #A & #B
ON PP4 #GDD-GDE = ,EXS4 #D-H
------------------------------------#GHE
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,*APT] ,REVIEW ,PRACTICE
#AA.B ,APPLY ,TRANS=M,NS 6,DATA PP4
#GEA-GEE
,EXAMPLE
.,F9D .! M1N1 ..M$IAN1 MODE1 RANGE1 &
/&>D DEVI,N (! DATA SET 2L &(! DATA SET
OBTA9$ 0MULTIPLY+ EA* DATA VALUE 0#J..H4
#BJJ1 #BBJ1 #BHJ1 #BIJ1 #CBJ1 #CBJ1
#CDJ1 #CHJ
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 .,ORIG9AL .DATA @3 .,TRANS=M$
.DATA
.,M1N @3 #BIC.GE3 #J.H7#BIC.GE7 .K
#BCE
.,M$IAN @3 #CJE3 #J.H7#CJE7 .K #BDD
.,MODE @3 #CBJ3 #J.H7#CBJ7 .K #BEF
.,RANGE @3 #AHJ3 #J.H7#AHJ7 .K #ADD
.,/&>D .DEVI,N @3 #EF.CC3 #J.H7#EF.CC7
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,,EXAMPLES #A & #B
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.#I4 #CD1 #CE1 #CG1 #CG1 #CH1 #DA1
#DB1 #DF1 #DH2 ADD --#G 6EA* DATA VALUE
#AJ4 #FB1 #FF1 #FF1 #FH1 #GD1 #GF1
#GH1 #HJ1 #HB2 MULTIPLY EA* DATA VALUE
0#A.B
#AA4 .,,RA9FALL ,! LI/ 2L %[S ! AV]AGE
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=A R&OMLY SELECT$ JC-VALUE F ! 4TRIBU;N4
.#AB4 ;,P7;X"K.K#HI7
.#AC4 ;,P7;X"K.K#HD7
.#AD4 ;,P7#IA"K;X"K.K#AJJ7
.#AE4 ;,P7;X"K.K#EJ7
.#AF4 ;,P7;X.1.K#AJJ7
.#AG4 ;,P7#EJ"K;X"K.K#HJ7
------------------------------------#GHF
#AA ,*APT] ,REVIEW
#AA.D ,SELECT & ,DRAW ,3CLU.NS F
,SAMPLES ,,PP4 #GFF-GGA
,,EXAMPLE
,9 A SURVEY ( #EHB P1 #EG@3P SD T
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3TA9 TWO DA%ES4
.;,X @3 #BJ3 #CJ3 #DJ3 #EJ3 #FJ3 #GJ3
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.;Y @3 #DB3 #DH3 #EC3 #EB3 #DI3 #DJ3
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9V]T$ ;,U-%APE4 ,? SU7E/S A QUADRATIC
MODEL4
.,USE ! QUADRATIC REGRES.N F1TURE 6F9D
AN EQU,N (! MODEL4
.,GRAPH ! MODEL AL;G )! DATA 6V]IFY T
! MODEL FITS ! DATA WELL4
99 ,A MODEL =! DATA IS .;Y .K
--#J.JAGA;X #B @+ #A.ED;X @+ #AH.A4
..,,EXAMPLES #A1B1 & .#C ON PP4
.#GGE-.GGG = .,EX4 .#BC
,,EX]CISES
#BC4 ,USE A GRAPH+ CALCULATOR 6F9D A
MODEL =! DATA4 ,!N GRAPH ! MODEL &! DATA
9 ! SAME COORD9ATE PLANE4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X @3 #A3 #B3 #C3 #D3 #E3 #F3 #G
.;Y @3 #BD3 #BA3 #AG3 #D3 #I3 #E3 #B
------------------------------------#GHG
#AA ,*APT] ,TE/
,F9D ! M1N1 M$IAN1 MODE1 RANGE1 & /&>D
DEVI,N (! GIV5 DATA SET &(! DATA SET
OBTA9$ 0P]=M+ ! GIV5 TRANS=M,N4
.#A4 #DA1 #CH1 #DB1 #DA1 #DE1 #DD1
#DH1 #CE2 MULTIPLY EA* DATA VALUE 0#C
.#B4 #AF1 #BA1 #AI1 #BA1 #AG1 #BE1
#AE1 #AH2 ADD #AD 6EA* DATA VALUE
.#C4 #AJH1 #IB1 #AJB1 #II1 #AAF1 #IB2
MULTIPLY EA* DATA VALUE 0#D.E
,A NORMAL 4TRIBU;N HAS A M1N ( #GB &A
/&>D DEVI,N ( #E4 ,F9D ! PROBABIL;Y T A
R&OMLY SELECT$ JC-VALUE F ! 4TRIBU;N IS
9 ! GIV5 9T]VAL4
.#D4 ,2T #FG & #GG
.#E4 ,2T #EG & #GB
.#F4 ,AT L1/ #FB
,F9D ! M>G9 ( ]ROR =A SURVEY T HAS !
GIV5 SAMPLE SIZE4 ,R.D YR ANSW] 6! NE>E/
T5? (A P]C5T4
.#G4 #CDJ
.#H4 #HABE
.#I4 #ICA
.#AJ4 #AEFJ
#AA4 .,,FOOTBALL ,T1MS 9 ! ,N,NAL
,FOOTBALL ,L1GUE >E DIVID$ 96TWO 3F];ES1
! ,AM]ICAN ,FOOTBALL ,3F];E 7,,AFC7 &!
,N,NAL ,FOOTBALL ,3F];E 7,,NFC74 ,! TA#
2L %[S ! M>G9 ( VICTORY 9 EA* 3F];E'S
*AMPION%IP GAME =! #AIIJ-BJJD S1SONS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,,AFC ,*AMPION%IP M>G9S ( VICTORY3
,,NFC ,*AMPION%IP M>G9S ( VICTORY
.#DH1.C1.AI1.AG1.D1.D1.AD1.C1
.#AC1.AI1.AC1.G1.AG1.AJ1.AD @3
.#B1.CA1.AJ1.AG1.AJ1.AA1.AG1.AC1
.#C1.E1.DA1.E1.AG1.AA1.AG
A4 ,F9D ! M1N1 M$IAN1 MODE1 RANGE1 &
/&>D DEVI,N (! ,,AFC M>G9S ( VICTORY4
B4 ,F9D ! M1N1 M$IAN1 MODE1 RANGE1 &
/&>D DEVI,N (! ,,NFC M>G9S ( VICTORY4
C4 .,-P>E ! /ATI/ICS = EA* SET ( DATA
& MAKE A 3CLU.N AB ! DATA4
#AB4 .,,TE/ .,,SCORES ,! SCORES ON A
/&>DIZ$ TE/ ADM9I/]$ 6#AJ1JJJ /UD5TS H A
M1N ( #EJ &A /&>D DEVI,N ( #AJ4 ,F9D !
;Z-SCORE = EA* /UD5T ^: SCORE IS GIV54
A4 ,KEV93 #EE
B4 ,MANUEL3 #GJ
C4 ,COLBY3 #DJ
D4 ,N1L3 #DG
#AC4 .,,%OPP+ .,,SURVEY ,9 A SURVEY (
#AFJJ ,U4,S4 ADULTS1 #FA@3P SD T !Y H
PUR*AS$ A PRODUCT ONL9E4 ,F9D ! M>G9 (
]ROR =! SURVEY4 ,!N GIVE AN 9T]VAL T IS
LIKELY 63TA9 ! EXACT P]C5T ( ALL ,U4,S4
ADULTS :O H PUR*AS$ A PRODUCT ONL9E4
#AD4 .,,TYP+ .,,]RORS ,! TA# %[S !
AV]AGE NUMB] .;Y ( ]RORS MADE 0/UD5TS 9
A TYP+ C\RSE :5 !Y TOOK TE/S GIV5 .;X
"DS AF ! />T (! C\RSE4 ,USE A GRAPH+
CALCULATOR 6F9D A MODEL =! DATA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X @3 .#B @3 .#AJ @3 .#AD @3 .#BA @3
.#CJ @3 .#DE @3 .#FC @3 .#GJ @3 .#IA
.;Y @3 .#DE..B @3 .#CF..A @3 .#CJ..B
@3 .#BC..A @3 .#AH..G @3 .#AA..J @3
.#E..F @3 .#D..C @3 .#B..D
------------------------------------#GHH
#AA ,/&>DIZ$ ,TE/ ,PREP>,N
,,MULTIPLE-,,*OICE ,,"QS
,IF Y H DI6ICULTY SOLV+ A
MULTIPLE-*OICE PRO#M DIRECTLY1 Y MAY 2
A# 6USE ANO!R APPROA* 6ELIM9ATE 9CORRECT
ANSW] *OICES & OBTA9 ! CORRECT ANSW]4
,SIDEB>3
.,/&>DS
,ADV.ED ,PLACE;T ,PROBABIL;Y &
,/ATI/ICS3#AG.J
,/UD5TS DET]M9E 3FID;E 9T]VALS =A
SIMPLE R&OM SAMPLE F A NORMAL 4TRIBU;N (
DATA & DET]M9E ! SAMPLE SIZE REQUIR$ =A
DESIR$ M>G9 ( ]ROR4
,PRO#M #A
,! ,NIELS5 RAT+S M1SURE H[ _M VIEW]S
WAT* DI6]5T ,,TV PROGRAMS4 ,"! >E #EJJJ
,NIELS5 H\SEHOLDS1 : >E *OS5 R&OMLY F
,U4,S4 H\SEHOLDS ) TELEVI.NS4 ,SUPPOSE !
,NIELS5 RAT+S REPORT T #I.B@3P (
,NEILSON H\SEHOLDS WAT*$ A C]TA9
PROGRAM4 ,:AT 9T]VAL IS LIKELY 63TA9 !
EXACT P]C5T ( ALL ,U4,S4 H\SEHOLDS )
TELEVI.NS T WAT*$ ! PROGRAM8
.,A #D.J@3P 6#AD.J@3P
.;,B #G.H@3P 6#AJ.F@3P
.;,C #H.C@3P 6#AJ.C@3P
.;,D #I.B@3P 6#I.F@3P
,ME?OD #A
.,,SOLVE .,,DIRECTLY ,CALCULATE ! M>G9
( ]ROR4 ,!N USE ! M>G9 ( ]ROR &! P]C5T
GIV5 9 ! PRO#M 6F9D ! 9T]VAL4
.,,/EP .#A .,CALCULATE ! M>G9 ( ]ROR4
+-#J.JAD
.K +-#A.D@3P
.,,/EP#B .,F9D ! L[] B.D =! 9T]VAL4
,L[] B.D .K #I.B@3P--#A.D@3P
.K #G.H@3P
.,,/EP .#C .,F9D ! UPP] B.D =! 9T]VAL4
,UPP] B.D .K #I.B@3P @+ #A.D@3P .K
#AJ.F@3P
.,,/EP .#D .,WRITE ! 9T]VAL4
,! 9T]VAL IS #G.H@3P 6#AJ.F@3P4
99 ,! CORRECT ANSW] IS ,B4 .,A ;,B
.;,C .;,D
,ME?OD #B
.,,ELIM9ATE .,,*OICES ,ANO!R ME?OD IS
6*ECK ! 9T]VALS GIV5 9 ! ANSW] *OICES4
,Y "K T #I.B@3P M/ FALL EXACTLY 9 !
MI4LE (! 9T]VAL4
.,*OICE .,A3 S #I.B@3P DOES N FALL
EXACTLY 9 ! MI4LE (! 9T]VAL4 ,Y C
ELIM9ATE *OICE ,A4
.,*OICE .;,B3 S #I.B@3P FALLS EXACTLY
9 ! MI4LE (! 9T]VAL4
.,*OICE .;,C3 S #I.B@3P DOES N FALL
EXACTLY 9 ! MI4LE (! 9T]VAL4 ,Y C
ELIM9ATE *OICE ,C4
.,*OICE .;,D3 S #I.B@3P DOES N FALL
EXACTLY 9 ! MI4LE (! 9T]VAL4 ,Y C
ELIM9ATE *OICE ,D4
99 ,! CORRECT ANSW] IS ,B4 .,A ;,B
.;,C .;,D
------------------------------------#GHI
.,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,PRO#M #B
,AT A LOCAL BANK1 ! WAIT+ "TS = AN
AVAILA# TELL] >E NORM,Y 4TRIBUT$ )A M1N
( #AJ M9UTES &A /&>D DEVI,N ( #B M9UTES4
,:AT IS ! APPROXIMATE PROBABIL;Y T A
R&OMLY SELECT$ CU/OM] AT ! BANK WAITS NO
M ?AN #AC M9UTES =A TELL]8
,A4 #FJ.G@3P
,B4 #HB.J@3P
,C4 #IC.C@3P
,D4 #IH.E@3P
,ME?OD #A
.,,SOLVE .,,DIRECTLY ,USE A ;Z-SCORE
&! /&>D NORMAL TA# ON PAGE #GEI 6F9D !
DESIR$ PROBABIL;Y4
.,,/EP .#A ,F9D ! ;Z-SCORE =A WAIT+ "T
( #AC M9UTES4
.K #A.E
.,,/EP .#B .,USE ! /&>D NORMAL TA#
6F9D
;,P7;Z"K.K #A.E74
.;,P7.;Z "K.K #A.E7 .K #J.ICCB
#IC.C@3P
,! PROBABIL;Y ( WAIT+ NO M ?AN #AC
M9UTES IS AB #IC.C@3P4
99 ,! CORRECT ANSW] IS ,C4 .,A .;,B
;,C .;,D
,ME?OD #B
.,,ELIM9ATE .,,*OICES ,USE ! FACTS AB
NORMAL 4TRIBU;NS ON PAGE #GEG 6ELIM9ATE
9CORRECT ANSW] *OICES4
,=A R&OMLY SELECT$ CU/OM] )A WAIT+ "T
( ;X M9UTES1 Y "K ! FOLL[+3
;,P7;X "K.K #AB7 .K .;,P7.;X "K.K @+
@7
.K #EJ@3P @+ #CD@3P
.K #HD@3P
;,P7;X "K.K #AD7 .K .;,P7.;X "K.K @+
#B @7
.K #EJ@3P @+ #CD@3P @+ #AC.E@3P
.K #IG.E@3P
,X FOLL[S T .;,P7.;X "K.K #AC7 IS 2T
#HD@3P & #IG.E@3P4 ,ONLY ! PROBABIL;Y (
#IC.C@3P 9 ANSW] *OICE ;,C SATISFIES ?
3DI;N4
99 ,! CORRECT ANSW] IS ,C4 .,A .;,B
;,C .;,D
,PRACTICE
,EXPLA9 :Y Y C ELIM9ATE ! HI<LI<T$
ANSW] *OICE4
#A4 ,A NORMAL 4TRIBU;N HAS A M1N (
#D.JF &A /&>D DEVI,N ( #J.JD4 ,:AT IS !
PROBABIL;Y T A R&OMLY SELECT$ VALUE F !
4TRIBU;N IS 2T #D.JF & #D.AD8
,A4 #J.JA
,B4 #J.DGE
,C4 #J.FH
,D4
#B4 ,IF Y ADD ! SAME NONZ]O 3/ANT 6EA*
VALUE 9 A DATA SET1 : /ATI/IC DOES N
*ANGE8
,A4 ,M1N
,B4 ,M$IAN
,C4
,D4 ,RANGE
#C4 ,: TYPE ( FUNC;N BE/ MODELS ! DATA
REPRES5T$ 0! SCATT] PLOT AT ! "R8
,A4 ,L9E>
,B4 ,QUADRATIC
,C4 ,CUBIC
,D4
------------------------------------#GIJ
#AA ,/&>DIZ$ ,TE/ ,PRACTICE
,MULTIPLE-,*OICE
,9 ,EX]CISES #A & #B1 USE ! DATA 2L
GIV+ ! L5G?S 7IN M9UTES7 (! MOVIES %[+
AT A LOCAL MOVIE !AT]4
#ID1AJI1AFF1ACF1IG1AAJ1AAC1AAD1
#ID1AJA
#A4 ,:AT IS ! M$IAN (! DATA SET8
,A4 #ID;M9
,B4 #AJI.E M9
,C4 #AAJ M9
,D4 #AAA.E M9
#B4 ,6! NE>E/ T5? (A M9UTE1 :AT IS !
/&>D DEVI,N (! DATA SET8
,A4 #G.B M9
,B4 #BA.B M9
,C4 #BE.F M9
,D4 #FG.J M9
#C4 ,AC 6A SURVEY F ! ,N,NAL ,C5T] =
,H1L? ,/ATI/ICS1 ! HEI<TS ( ADULT WOM5 9
! ,UNIT$ ,/ATES >E NORM,Y 4TRIBUT$ )A
M1N ( #FD 9*ES &A /&>D DEVI,N ( #B.G
9*ES4 ,:AT IS ! APPROXIMATE PROBABIL;Y T
#D R&OMLY SELECT$ WOM5 >E ALL 2T #EH.F
9*ES & #FF.G 9*ES TALL8
,A4 #CD@3P
,B4 #DD@3P
,C4 #FH@3P
,D4 #HA.E@3P
#D4 ,:AT IS ! P]C5T (! >EA "U A NORMAL
CURVE T IS REPRES5T$ 0! %AD$ REGION8
,A4 #EJ@3P
,B4 #HA.E@3P
,C4 #HC.HE@3P
,D4 #HD@3P
#E4 ,RA*EL SCOR$ AN #HH ON H] PHYSICS
TE/4 ,! CLASS AV]AGE 0 #GI.C1 &! /&>D
DEVI,N 0 #G.E4 ,:AT IS ! ;Z-SCORE =
,RA*EL'S TE/ SCORE8
,A4 #A.AF
,B4 #A.CJ
,C4 #A.DE
,D4 #A.FJ
#F4 ,! DATA SET 2L GIVES ! NUMB]S (
PAGES 9 FIVE HI< S*OOL TEXTBOOKS4
#CHD1 #DHJ1 #EGF1 #FDJ1 #GFH
,: /ATE;T IS .FALSE8
,A4 ,"! IS NO MODE4
,B4 ,! M1N IS GRT] ?AN ! M$IAN4
,C4 ,! M1N IS #EFI.F PAGES4
,D4 ,! RANGE IS #CHD PAGES4
#G4 ,9 A N,NWIDE POLL ( #AJAE ,U4,S4
ADULTS1 ,TOM ,HANKS 0 VOT$ ,AM]ICA'S
FAVORITE MOVIE />4 ,:AT IS ! APPROXIMATE
M>G9 ( ]ROR =! SURVEY8
,A4 +-#J.JCA@3P
,B4 +-#J.CA@3P
,C4 +-#C.A@3P
,D4 +-#CA@3P
#H4 ,! TA# %[S ! ATT5D.E 7IN MILLIONS7
AT ,BO/ON ,R$ ,SOX GAMES 9 ,F5WAY ,P>K F
#AIIE 6#BJJD4 ,: TYPE ( FUNC;N BE/
MODELS ! DATA8
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,YE>3 ,ATT5D.E3 ,YE>3 ,ATT5D.E
#AIIE3 #B.AF3 #BJJJ3 #B.EI
#AIIF3 #B.CB3 #BJJA3 #B.FC
#AIIG3 #B.BC3 #BJJB3 #B.FE
#AIIH3 #B.CA3 #BJJC3 #B.GB
#AIII3 #B.DE3 #BJJD3 #B.HD
,A4 ,L9E>
,B4 ,QUADRATIC
,C4 ,EXPON5TIAL
,D4 ,P[]
#I4 ,! DELAYS 7IN M9UTES7 =A -M]CIAL
AIRL9E FLI<T >E LI/$ 2L = ,SUN"D "?
,FRI"D (A C]TA9 WEEK4
#BJ1 #AJ1 #J1 #CJ1 #J1 #DE
,ON ,SATUR"D1 ! FLI<T IS DELAY$ #AEJ
M9UTES4 ,: /ATI/IC IS MO/ A6ECT$ :5 ?
\TLI] IS A4$ 6! GIV5 DATA SET8
,A4 ,M1N
,B4 ,M$IAN
,C4 ,MODE
,D4 ,RANGE
------------------------------------#GIA
.,/ATE .,TE/ .,PRACTICE
_+CLASSZONE.COM_:
,GRI4$ ,ANSW]
#AJ4 ,A NORMAL 4TRIBU;N HAS A M1N (
#GG &A /&>D DEVI,N ( #D4 ,:AT IS !
;Z-SCORE CORRESPOND+ 6AN ;X-VALUE ( #HJ8
#AA4 ,! /&>D DEVI,N (A DATA SET IS
#AB.B4 ,A NEW DATA SET IS CR1T$ 0A4+
#E.A 6EA* DATA VALUE4 ,:AT IS ! /&>D
DEVI,N (! NEW DATA SET8
#AB4 ,:AT IS ! M1N (! DATA SET 2L8
#A1 #C1 #E1 #E1 #G1 #AA1 #AC1 #AE1
#AG1 #AI1 #BA1 #BC1 #BD1 #BE
#AC4 ,9 A NORMAL 4TRIBU;N1 AB :AT
P]C5T (! >EA "U ! RELAT$ NORMAL CURVE
LIES )9 #B /&>D DEVI,NS (! M1N8
,,%ORT ,,RESPONSE
#AD4 ,AC 6A C]TA9 POLL1 #EA@3P (
ADULTS 9 ! ,UNIT$ ,/ATES FOLL[
PROFES.NAL FOOTBALL4 ,! M>G9 ( ]ROR IS
+-#B@3P4 ,AB H[ _M P 7 SURVEY$8 .,EXPLA9
:E!R Y "K = C]TA9 T FOOTBALL IS FOLL[$
0! MAJOR;Y ( ADULTS 9 ! ,UNIT$ ,/ATES4
#AE4 ,A /UD5T IS 3DUCT+ A SURVEY AB !
,9T]NET USAGE ( HI< S*OOL /UD5TS4 ,HE
S5DS ! SURVEY 0;E-MAIL 6EA* P]SON 9 8
A4RESS BOOK1 & USES ONLY ! SURVEYS T >E
RETURN$4 ,:AT TYPE ( SAMPLE IS ?8 ,IS !
SAMPLE BIAS$ OR UNBIAS$8 .,EXPLA94
,EXT5D$ ,RESPONSE
#AF4 ,! DATA SET 2L GIVES ! AV]AGE
RA9FALL = EA* MON? 9 ,SAN ,ANTONIO1
,TEXAS1 & ,*ICAGO1 ,ILL9OIS4
,SAN ,ANTONIO1 ,TEXAS 7IN 9*ES73
#A.E1 #A.H1 #A.H1 #B.H1 #C.D1 #C.A1
#B.B1 #B.E1 #C.D1 #B.E1 #B.B1 #A.H
,*ICAGO1 ,ILL9OIS 7IN MILLIMET]S73
#DH.B1 #DA.H1 #GB.B1 #IF.F1 #HB.E1
#AJC.D1 #AJB.G1 #HI.C1 #GH.F1 #FI.G1
#GB.G1 #FD.H
A4 ,F9D ! M1N1 M$IAN1 MODE1 RANGE1 &
/&>D DEVI,N = EA* C;Y'S RA9FALL DATA4
B4 .,-P>E ! /ATI/ICS = EA* C;Y4 ,MAKE
A 3CLU.N AB ! DATA4 7.,H9T3 #A MILLIMET]
#J.JCICG 9*47
#AG4 ,! TA# %[S ! NUMB]S ( P 7IN
MILLIONS7 :O VOT$ 9 ,U4,S4 ,PRESID5TIAL
ELEC;NS S9CE #AIDJ4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,YE>S .S9CE .#AIDJ @3 #J3 #D3 #H3
#AB3 #AF3 #BJ3 #BD3 #BH
.,VOT]S 7.MILLIONS7 @3 #DI.IJ3 #DG.IH3
#DH.GI3 #FA.EE3 #FB.JC3 #FH.HD3 #GJ.JE3
#GC.BA
.,YE>S .S9CE .#AIDJ @3 #CB3 #CF3 #DJ3
#DH3 #DD3 #EB3 #EE3 #FJ
.,VOT]S 7.MILLIONS7 @3 #GG.GB3 #HA.EF3
#HF.EB3 #IB.FE3 #IA.FJ3 #AJD.FC3 #IF.BH3
#AJE.DJ
A4 ,USE A GRAPH+ CALCULATOR 6MAKE A
SCATT] PLOT (! DATA4 ,DET]M9E ! TYPE (
FUNC;N T BE/ FITS ! DATA4
B4 ,USE A REGRES.N F1TURE 6F9D AN
EQU,N (! FUNC;N4
C4 ,GRAPH ! EQU,N AL;G )! DATA 6V]IFY
T ! EQU,N FITS ! DATA WELL4
D4 ,USE YR EQU,N 6PREDICT ! NUMB] ( P
:O VOT$ 9 ! #BJJD ,U4,S4 ,PRESID5TIAL
ELEC;N4 .,-P>E YR PREDIC;N 6! ACTUAL
NUMB] ( VOT]S 9 T ELEC;N1 : 0 #ABB.CJ
MILLION VOT]S4
------------------------------------#GIB
#AB ,SEQU;ES & ,S]IES
#AB.A ,DEF9E & ,USE ,SEQU;ES & ,S]IES
#AB.B ,ANALYZE ,>I?METIC ,SEQU;ES &
,S]IES
#AB.C ,ANALYZE ,GEOMETRIC ,SEQU;ES &
,S]IES
#AB.D ,F9D ,SUMS ( ,9F9ITE ,GEOMETRIC
,S]IES
#AB.E ,USE ,RECURSIVE ,RULES )
,SEQU;ES & ,FUNC;NS
,SIDEB>3
,2F
,9 PREVI\S *APT]S1 Y LE>N$ ! FOLL[+
SKILLS1 : Y'LL USE 9 ,*APT] #AB3 SOLV+
EQU,NS1 SOLV+ SY/EMS ( EQU,NS1 & P]=M+
FUNC;N -POSI;N4
,PREREQUISITE ,SKILLS
,,VOCABUL>Y ,,*ECK
,COPY & -PLETE ! /ATE;T US+ & .;G @7
.;X @7 .K .#D;X @+ #B4
.#A4 ,! .DOMA9 ( .;F7.;X7 IS @8 @4
.#B4 ,! .RANGE ( .;G @7 .;X @7 IS @8
@4
.#C4 ,! ..-POSI;N ;F @7 ;G @7 .;X @7@7
IS .EQUAL TO @8 @4
,,SKILLS ,,*ECK
,SOLVE ! EQU,N4 ,*ECK YR SOLU;N4
7.,REVIEW P4 #AH .= .#AB..B47
.#D4 #G .;X @+ #C .K #CA
.#E4 #I .K #B .;X -- #G
.#F4 #AD .K --#C .;X @+ #H
.#G4 #AJ--#C .;X .K #BH
.#H4 ;LL .;X @+ #I .K #C .;X @+#AG
.#I4 #B .;X @+ #C .K--#F -- .;X
,SOLVE ! SY/EM US+ ANY ALGEBRAIC
ME?OD4 7.,REVIEW P4 #AFJ .= .#AB..C47
.#AJ4 #C .;X @+ .;Y .K #J
--#B .;X -- #D .;Y .K --#CJ
.#AA4 #B .;X --#B .;Y .K #AJ
.;X @+ .;Y .K--#AJ
.#AB4 #D .;X -- #E .;Y .K #BE
#J.E .;X @+ #A.E .;Y .K #AH.E
,LET .;F @7 .;X @7 .K .#B;X -- #A &
.;G @7 .;X @7 .K --.#B .;X --#A @4 ,P]=M
! 9DICAT$ OP],N & /ATE ! DOMA94
7.,REVIEW P4 #DBH .= .#AB..E47
.#AC4 .;F 7;G7 .;X @7@7
.#AD4 .;F @7 .;F 7;X77
.#AE4 .;G @7 .;G @7 .;X @7@7
@A .,HOME .,TUTOR ,PREREQUISITE SKILLS
PRACTICE AT _+CLASSZONE.COM_:
------------------------------------#GIC
,SIDEB>3
,N[
,9 ,*APT] #AB1 Y W APPLY ! BIG ID1S
LI/$ 2L & REVIEW$ 9 ! ,*APT] ,SUMM>Y ON
PAGE #HCI @4 ,Y W AL USE ! KEY VOCABUL>Y
LI/$ 2L4
,BIG ,ID1S
#A4 ,ANALYZE SEQU;ES
#B4 ,F9D SUMS ( S]IES
#C4 ,USE RECURSIVE RULES
,KEY ,VOCABUL>Y
99 SEQU;E1 P4 #GID
99 T]MS (A SEQU;E1 P4 #GID
99 S]IES1 P4 #GIF
99 SUMM,N NOT,N1 P4 #GIF
99 SIGMA NOT,N1 P4 #GIF
99 >I?METIC SEQU;E1 P4 #HJB
99 -MON DI6];E1 P4 #HJB
99 >I?METIC S]IES1 P4 #HJD
99 GEOMETRIC SEQU;E1 P4 #HAJ
99 -MON RATIO1 P4 #HAJ
99 GEOMETRIC S]IES1 P4 #HAB
99 "PIAL SUM1 P4 #HBJ
99 EXPLICIT RULE1 P4 #HBG
99 RECURSIVE RULE1 P4 #HBG
99 IT],N1 P4 #HCJ
,SIDEB>3
,:Y8
,Y C USE SEQU;ES 6DESCRIBE PATT]NS 9 !
R1L _W4 ,= EXAMPLE1 Y C USE ! ,FIBONA3I
SEQU;E 6DESCRIBE PATT]NS 9 NATURE4
,ANIMAT$ ,ALGEBRA
,! ANIM,N ILLU/RAT$ 2L = ,EXAMPLE #C
ON PAGE #HBH HELPS Y ANSW] ? "Q3 ,H[ C Y
G5]ATE ,FIBONA3I NUMB]S8
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,O!R ANIM,NS = ,*APT] .#AB3 PAGES
#HJE @1 #HAA @1 #HBJ @1 & #HCB
------------------------------------#GID
#AB.A ,DEF9E & ,USE ,SEQU;ES &
,S]IES
.,2F ,Y ID5TIFI$ & WROTE FUNC;NS4
.,N[ ,Y W RECOGNIZE & WRITE RULES =
NUMB] PATT]NS4
.,:Y8 ,S Y C F9D ANGLE M1SURES1 Z 9
,EX4 #FC4
,KEY ,VOCABUL>Y
99 SEQU;E
99 T]MS (A SEQU;E
99 S]IES
99 SUMM,N NOT,N
99 SIGMA NOT,N
,SIDEB>3
,/&>DS
..#BB.J ,/UD5TS F9D ! G5]AL T]M &!
SUMS ( >I?METIC .S]IES &( BO? F9ITE &
9F9ITE GEOMETRIC S]IES4
..#BC.J ,/UD5TS DERIVE ! SUMM,N =MULAS
= >I?METIC .S]IES &= BO? F9ITE & 9F9ITE
GEOMETRIC S]IES4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,SEQU;ES
.,A .SEQU;E IS A FUNC;N ^: DOMA9 IS A
SET ( 3SECUTIVE 9TEG]S4 ,IF A DOMA9 IS N
SPECIFI$1 X IS "U/OOD T ! DOMA9 />TS )
#A4 ,! VALUES 9 ! RANGE >E CALL$ ! .T]MS
(! SEQU;E4
.,A .F9ITE .SEQU;E HAS A LIMIT$ NUMB]
( T]MS4 ,AN .9F9ITE .SEQU;E 3T9UES )\T
/OPP+4
.,F9ITE .SEQU;E3 #B1 #D1 #F1 #H
.,9F9ITE .SEQU;E3 #B1 #D1 #F1 #H1'
,A SEQU;E C 2 SPECIFI$ 0AN EQU,N1 OR
.RULE4 ,= EXAMPLE1 BO? SEQU;ES ABV C 2
DESCRIB$ 0! RULE .A ;N.' .K .#B;N OR .;F
@7 .;N @7 .K .#BN4
,EXAMPLE #A
,WRITE T]MS ( SEQU;ES
,WRITE ! F/ SIX T]MS ( 7A7 .A ;N .K
.#B;N @+ #E & 7;B7 .;F @7 .;N @7 .K
7-#C7 ;N--#A @4
,SOLU;N
.A4 .A #A .K #B7#A7 @+#E .K #G
#A/ T]M
A #B .K #B7#B7@+#E .K #I
#BND T]M
.A #C .K #B7#C7 @+ #E .K #AA
#CRD T]M
.A #D .K #B7#D7 @+ #E .K #AC
#D? T]M
.A #E .K #B7#E7 @+ #E .K #AE
#E? T]M
A #F .K #B7#F7 @+ #E .K #AG
#F? T]M
.B4 .;F 7#A7 .K 7-#C7 #A--#A .K #A
#A/ T]M
.;F 7#B7 .K 7-#C7 #B--#A .K --#C
#BND T]M
.;F 7#C7 .K 7-#C7 #C--#A .K #I
#CRD T]M
.;F 7#D7 .K 7-#C7 #D--#A .K --#BG
#D? T]M
.;F 7#E7 .K 7-#C7 #E --#A .K #HA
#E? T]M
.;F 7#F7 .K 7-#C7 #F--#A .K --#BDC
#F? T]M
..,GUID$ ,PRACTICE = ,EXAMPLE .#A
,WRITE ! F/ SIX T]MS (! SEQU;E4
.#A4 .A ;N .K .;N @+ #D
.#B4 .;F @7 .;N @7 .K 7-#B7 ;N--#A
.#C4
------------------------------------#GIE
.,,WRIT+ .,,RULES ,IF ! T]MS (A SEQU;E
H A RECOGNIZA# PATT]N1 !N Y MAY 2 A#
6WRITE A RULE =! .N? T]M (! SEQU;E4
,EXAMPLE #B ,WRITE RULES = SEQU;ES
,,WRITE ,,RULES
,IF Y >E GIV5 ONLY ! F/ S"EAL T]MS3 (A
SEQU;E1 "! IS NO .S+LE RULE =! N? T]M4
,= 9/.E1 ! SEQU;E #B1 #D1 #H1' C 2 GIV5
0.A ;N .K .#B ;N.' .-OR .A ;N .K .;N #B
-- .;N @+ #B4
,DESCRIBE ! PATT]N1 WRITE ! NEXT T]M1
& WRITE A RULE =! .N? T]M (! SEQU;E 7A7
--#A1 --#H1 --#BG1 --#FD1' & 7;B7 #J1
#B1 #F1 #AB1'4
,SOLU;N
.A4 ,Y C WRITE ! T]MS Z 7-#A7 #C @1
7-#B7 #C @1 7-#C7 #C @1 7-#D7 #C @1' ,!
NEXT T]M IS .A #E .K 7-#E7 #C .K --#ABE4
,A RULE =! .N? T]M IS .A ;N .K @7 -.;N
@7 #C @4
.B4 ,Y C WRITE ! T]MS Z #J 7#A71 #A
7#B71 #B 7#C71 #C 7#D71 - ,! NEXT T]M IS
.;F 7#E7 .K #D7#E7 .K #BJ4 ,A RULE =! N?
T]M IS .;F @7 .;N @7 .K @7 .;N -- #A7
.N4
.,,GRAPH+ .,,SEQU;ES ,6GRAPH A SEQU;E1
LET ! HORIZONTAL AXIS REPRES5T ! POSI;N
NUMB]S 7! DOMA97 &! V]TICAL AXIS
REPRES5T ! T]MS 7! RANGE74
.,EXAMPLE .#C
,SOLVE A MULTI-/EP PRO#M
.,,RETAIL .,,4PLAYS ,Y "W 9 A GROC]Y
/ORE & >E /ACK+ APPLES 9 ! %APE (A SQU>E
PYRAMID ) #G LAY]S4 ,WRITE A RULE =!
NUMB] ( APPLES 9 EA* LAY]4 ,!N GRAPH !
SEQU;E4
,PRODNOTE3 ,PRODUC;N NOTE3 CAP;NS
ASSOCIAT$ ) ? IMAGE >E LABELS T
CORRESPOND 6TEXT )9 ! IMAGE4
,PICTURE3 ,F/ LAY]
,AVOID ,]RORS
,AL? ! PLOTT$ PO9TS 9 ,EXAMPLE #C
FOLL[ A CURVE1 D .N DRAW ! CURVE 2C !
SEQU;E IS DEF9$ ONLY = 9TEG] VALUES (
.N4
,SOLU;N
.,,/EP .#A .,MAKE A TA# %[+ ! NUMB] (
FRUIT 9 ! F/ ?REE LAY]S4 ,LET .A ;N.'
.-REPRES5T ! NUMB] ( APPLES 9 LAY] .N4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,LAY]1 .;N @3 #A3 #B3 #C
,NUMB] ( APPLES1 .A ;N.' @3
#A .K #A #B @3
#D .K #B #B @3 #I .K #C #B
.,,/EP .#B .,WRITE A RULE =! NUMB] (
APPLES 9 EA* LAY]4 ,F ! TA#1 Y C SEE T
.A ;N.' .K .;N #B @4
.,,/EP .#C .,PLOT ! PO9TS 7#A1 #A71
7#B1 #D71 7#C1 #I71'1 7#G1 #DI74 ,!
GRAPH IS %[N AT ! "R4
..,GUID$ ,PRACTICE = ,EXAMPLES #B &
.#C
.#D4 ,=! SEQU;E #C1 #H1AE1 #BD1'1
DESCRIBE ! PATT]N1 WRITE ! NEXT T]M1
GRAPH ! F/ FIVE T]MS1 & WRITE A RULE =!
.N? T]M4
.#E4 .,,:AT .,,IF8 ,9 ,EXAMPLE #C1
SUPPOSE "! >E #I LAY]S ( APPLES4 ,H[ _M
APPLES >E 9 ! #I? LAY]8
------------------------------------#GIF
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,S]IES & ,SUMM,N ,NOT,N
,:5 ! T]MS (A SEQU;E >E A4$ TGR1 !
RESULT+ EXPRES.N IS A .S]IES @4 ,A S]IES
C 2 F9ITE OR 9F9ITE4
.,F9ITE .S]IES3 #B @+ #D @+ #F @+ #H
.,9F9ITE .S]IES3 #B @+ #D @+ #F @+ #H@+
,Y C USE .SUMM,N .NOT,N 6WRITE A
S]IES4 ,= EXAMPLE1 ! TWO S]IES ABV C 2
WRITT5 9 SUMM,N NOT,N Z FOLL[S3
,,R1D+
,:5 WRITT5 9 SUMM,N NOT,N1 ? S]IES IS
R1D Z 8! SUM ( #B .;I = VALUES ( .;I F
#A 6#D40
,= BO? S]IES1 ! .9DEX .( .SUMM,N IS
.;I &! ..L[] LIMIT ( .SUMM,N IS #A4 ,!
..UPP] LIMIT ( .SUMM,N IS #D =! F9ITE
S]IES & 79F9;Y7 =! 9F9ITE S]IES4 ,SUMM,N
NOT,N IS AL CALL$ .SIGMA .NOT,N 2C X
USES ! UPP]CASE ,GREEK LR .SIGMA @1
WRITT5 .,X4
,EXAMPLE #D ,WRITE S]IES US+ SUMM,N
NOT,N
,WRITE ! S]IES US+ SUMM,N NOT,N4
.A4 #BE @+ #EJ @+ #GE @+ 99 99 99 @+
#BEJ
.B4
,SOLU;N
.A4 ,NOTICE T ! F/ T]M IS #BE7#A71 !
SECOND IS #BE7#B71 ! ?IRD IS #BE7#C71 &!
LA/ IS #BE7#AJ74 ,S1 ! T]MS (! S]IES C 2
WRITT5 Z3
.A ;I .K #BE .;I ": .;I.K .#A1.B1.C1'1
.#AJ
,! L[] LIMIT ( SUMM,N IS #A &! UPP]
LIMIT ( SUMM,N IS #AJ4
,! SUMM,N NOT,N =! S]IES IS
.B4 ,NOTICE T = EA* T]M ! DENOM9ATOR
(! FRAC;N IS #A M ?AN ! NUM]ATOR4 ,S1 !
T]MS (! S]IES C 2 WRITT5 Z3
,! L[] LIMIT ( SUMM,N IS #A &! UPP]
LIMIT ( SUMM,N IS 9F9;Y4
,! SUMM,N NOT,N =! S]IES IS
..,GUID$ ,PRACTICE = ,EXAMPLE .#D
,WRITE ! S]IES US+ SUMM,N NOT,N4
.#F4 #E @+ #AJ @+ #AE @+ @* @* @* @+
#AJJ
.#G4
.#H4 #F @+ #CF @+ #BAF @+ #ABIF @+ @*
@* @*
.#I4 #E @+ #F @+ #G @+ @* @* @* @+ #AB
------------------------------------#GIG
.,,9DEX .,,( .,,SUMM,N ,! 9DEX (
SUMM,N =A S]IES DOES N H 6BE .;I --ANY
LR C 2 US$4 ,AL1 ! 9DEX DOES N H 62G9 AT
#A4 ,= 9/.E1 ! 9DEX 2G9S AT #D 9 ! NEXT
EXAMPLE4
,EXAMPLE #E
,F9D ! SUM (A S]IES
@3 ,,AVOID ,,]RORS
,2 SURE 6USE ! CORRECT L[] & UPP]
LIMITS ( SUMM,N :5 F9D+ ! SUM (A S]IES4
,F9D ! SUM (! S]IES4
.K #AI @+ #BH @+ #CI @+ #EB @+ #FG
.K #BJE
.,,SPECIAL .,,=MULAS ,= S]IES ) _M
T]MS1 F9D+ ! SUM 0A4+ ! T]MS C 2 T$I\S4
,2L >E =MULAS Y C USE 6F9D ! SUMS ( ?REE
SPECIAL TYPES ( S]IES4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,=MULAS = ,SPECIAL ,S]IES
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,SUM ( .;N T]MS ( #A @3 ,SUM ( F/ .;N
POSITIVE 9TEG]S @3 ,SUM ( SQU>ES ( F/
.;N POSITIVE 9TEG]S
@3 @3
,EXAMPLE #F
,USE A =MULA =A SUM
.,,RETAIL .,,4PLAYS ,H[ _M APPLES >E 9
! /ACK 9 ,EXAMPLE #C ON PAGE #GIE @8
,SOLU;N
,F ,EXAMPLE #C Y "K T ! I? T]M (!
S]IES IS GIV5 0.A ;I .K .;I #B ": .;I --
#A1 #B1 #C1'1 #G4 ,US+ SUMM,N NOT,N &!
?IRD =MULA LI/$ ABV1 Y C F9D ! TOTAL
NUMB] ( APPLES Z FOLL[S3
,"! >E #ADJ APPLES 9 ! /ACK4 ,*ECK ?
0ACTU,Y A4+ ! NUMB] ( APPLES 9 EA* (!
SEV5 LAY]S4
..,GUID$ ,PRACTICE = ,EXAMPLES #E &
.#F
,F9D ! SUM (! S]IES4
.#AJ4
.#AA4
.#AB4
.#AC4
.#AD4 .,,:AT .,,IF8 ,SUPPOSE "! >E #I
LAY]S 9 ! APPLE /ACK 9 ,EXAMPLE #C4 ,H[
_M APPLES >E 9 ! /ACK8
------------------------------------#GIH
#AB.A ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
,,WS#BJ = ,EXS4 #AI1DG1 & #FE
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE ,EXS4
.#B1 .#BG1.EH1 .#FD @1 & .#FG
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3
,ANO!R "N = SUMM,N NOT,N IS @8 @4
.#B4 .,,WRIT+ .,EXPLA9 ! DI6];E 2T A
SEQU;E &A S]IES4
.,,EXAMPLE .#A .ON .P4 #GID = ,EXS4
#C-AD
,WRIT+ ,T]MS ,WRITE ! F/ SIX T]MS (!
SEQU;E4
.#C4 .A ;N.' .K .;N @+ #B
.#D4 .A ;N .K #F- .;N
.#E4 .A ;N .K ;N #B
.#F4 .;F @7 .;N @7 .K .;N #C @+ .#B
.#G4 .A ;N .K #D ;N--#A
.#H4 .A ;N .K -- .;N #B
.#I4 .;F @7 .;N @7 .K .;N #B -- #E
.#AJ4 .A ;N .K @7 .;N @+ #C7 #B
.#AA4
.#AB4
.#AC4
.#AD4
,,EXAMPLE #B
ON P4 #GIE = ,EXS4 #AE-BG
,WRIT+ ,RULES ,=! SEQU;E1 DESCRIBE !
PATT]N1 WRITE ! NEXT T]M1 & WRITE A RULE
=! RA? T]M4
.#AE4 #A1 #F1 #AA1 #AF1'
.#AF4 #A1B1D1H1'
.#AG --#D1H1-#AB1AF1'
.#AH4 #B1I1BH1FE144
.#AI4
.#BJ4
.#BA4
.#BB4
.#BC4 #C.A1 #C.H1 #D.E1 #E.B1'
.#BD4 #D.B1 #B.F1 #A1 --#J.F1 --#B.B1'
.#BE4 #A.B1 #D.B1 #I.B1 #AF.B1'
.#BF4 #I1 #AF.H1 #BD.F1 #CB.D1'
#BG4 .,,MULTIPLE .,,*OICE ,: RULE
GIVES ! TOTAL NUMB] ( SQU>ES 9 ! N?
FIGURE (! PATT]N %[N8
,A .A ;N .K .#C;N-.#C
;,B A ;N .K #D;N-#E
;,C .A ;N .K .;N
,D4
,,EXAMPLE #C
ON P4 #GIE = ,EXS4 #BH-CF
,GRAPH+ ,SEQU;ES ,GRAPH ! SEQU;E4
.#BH4 --#B1 --#E1 --#H1 --#AA1 --#AD
.#BI4 #B1 #D1 #H1 #AF1 #CB1 #FD
.#CJ4 #A1 #E1 #I1 #AC1 '@1 #BI
.#CA4 --#B1 #D1 --#F1 #H1'1 --#BB
.#CB4 #J1 #C1 #H1 #AE1 #BD1 #CE
.#CC4 --#A1 #J1 #A1 #H1 #BG
.#CD4 #D1 --#I1 #AD1 --#AI1 #BD
.#CE4
.#CF4
,,EXAMPLE #D
ON P4 #GIF = ,EXS4 #CG-DD
,WRIT+ ,SUMM,N ,NOT,N ,WRITE ! S]IES
US+ SUMM,N NOT,N4
.#CG4 #G @+ #AJ @+ #AC @+ #AF @+ #AI
.#CH4 #E @+ #AA @+ #AG @+ #BC @+ #BI
.#CI4 --#A @+ #A @+ #C @+ #E @+ #G @+
@* @* @*
.#DJ4 --#B @+ #D--#H @+ #AF--#CB @+ @*
@* @*
.#DA4 #C @+ #AJ @+ #AG @+ #BD @+ #CA
@+ @* @* @*
.#DB4
.#DC4
.#DD4 --#A @+ #B @+ #G @+ #AD @+ #BC
@+ @* @* @*
------------------------------------#GII
.,,EXAMPLES #E .& .#F
ON P4 #GIG = ,EXS4 #DE-EH
,US+ ,SUMM,N ,NOT,N ,F9D ! SUM (!
S]IES4
.#DE4
.#DF4
.#DG4
.#DH4
.#DI4
.#EJ4
.#EA4
.#EB4
.#EC4
.#ED4
.#EE4
.#EF4
#EG4 .,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 F9D+ ! SUM (! S]IES4
.#EH4 .,,MULTIPLE .,,*OICE ,:AT IS !
SUM (! S]IES
,A #BJ
;,B #BAJ
;,C #DBJ
;,D #BHGJ
,,REVIEW ,,LOGIC
,= HELP ) C.T]-EXAMPLES SEE P4 #AJJB
@4
,,*ALL5GE ,TELL :E!R ! /ATE;T AB
SUMM,N NOT,N IS .TRUE OR .FALSE4 ,IF !
/ATE;T IS TRUE1 PROVE X4 ,IF ! /ATE;T IS
FALSE1 GIVE A C.T]EXAMPLE4
.#EI4
.#FJ4
.#FA4
.#FB4
,PRO#M ,SOLV+
,,EXAMPLES #C & #F
ON PP4 #GIE-GIG = ,EXS4 #FC-FD
.#FC4 .,,GEOMETRY ,=A REGUL> .;N -SID$
POLYGON 7.;N .1.K #C71 ! M1SURE .A ;N.'
.-( AN 9T]IOR ANGLE IS GIV5 0? =MULA3
,WRITE ! F/ FIVE T]MS (! SEQU;E4
,WRITE A RULE =! SEQU;E GIV+ ! TOTAL
M1SURE .;,T ;N.' .-(! 9T]IOR ANGLES 9
EA* REGUL> .;N -SID$ POLYGON4 ,USE !
RULE 6F9D ! TOTAL M1SURE (! ANGLES 9 !
,GU75HEIM ,MUSEUM SKYLI<T1 : IS A REGUL>
DODECAGON4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
,PICTURE3 .,GU75HEIM .,MUSEUM
.,SKYLI<T
.#FD4 .,,%ORT .,,RESPONSE ,Y WANT
6SAVE 4#EJJ =A S*OOL TRIP4 ,Y 2G9 0SAV+
A P5NY ON ! F/ "D4 ,Y PLAN 6SAVE AN
A4I;NAL P5NY EA* "D AF T4 ,= EXAMPLE1 Y
W SAVE #B P5NIES ON ! SECOND "D1 #C
P5NIES ON ! ?IRD "D1 & S ON4 ,H[ M* M"OY
W Y H SAV$ AF #AJJ "DS8 ,H[ _M "DS M/ Y
SAVE 6H SAV$ 4#EJJ8 .,EXPLA9 H[ Y US$ A
S]IES 6F9D YR ANSW]4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
------------------------------------#HJJ
#FE4 .,,T[] .,,( .,,HANOI ,9 ! PUZZLE
CALL$ ! ,T[] ( ,HANOI1 ! OBJECT IS 6USE
A S]IES ( MOVES 6TAKE ! R+S F "O PEG &
/ACK !M 9 ORD] ON ANO!R PEG4 ,A MOVE
3SI/S ( MOV+ EXACTLY "O R+1 & NO R+ MAY
2 PLAC$ ON TOP (A SMALL] R+4 ,! M9IMUM
NUMB] .A ;N.' .-( MOVES REQUIR$ 6MOVE
.;N R+S IS #A = #A R+1 #C = #B R+S1 #G =
#C R+S1 #AE = #D R+S1 & #CA = #E R+S4
,F9D A =MULA =! SEQU;E4 ,:AT IS ! M9IMUM
NUMB] ( MOVES REQUIR$ 6MOVE #F R+S8 #G
R+S8 #H R+S8
#FF4 .,,MULTI-.,,/EP .,,PRO#M ,! M1N
4T.E .;D ;N.' .-7IN A/RONOMICAL UNITS7 (
EA* PLANET 7EXCEPT ,NEPTUNE7 F ! SUN IS
APPROXIMAT$ 0! ,TITIUS-,BODE RULE1 .;D
;N .K #J.C7#B7 .;N -- #B @+ #J.D1 ": .;N
IS A POSITIVE 9TEG] REPRES5T+ ! POSI;N
(! PLANET F ! SUN4
A4 .,EVALUATE ,! VALUE ( .;N IS #D =
,M>S4 ,USE ! ,TITIUS-,BODE RULE
6APPROXIMATE ! 4T.E ( ,M>S F ! SUN4
B4 .,3V]T ,"O A/RONOMICAL UNIT IS
EQUAL 6AB #ADI1FJJ1JJJ KILOMET]S4 ,H[ F>
IS ,M>S F ! SUN 9 KILOMET]S8
C4 ,GRAPH ! SEQU;E GIV5 0!
,TITIUS-,BODE RULE4
.#FG @4 99 .,,EXT5D$ .,,RESPONSE ,=A
4PLAY AT A SPORTS /ORE1 Y >E /ACK+ SO3]
BALLS 9 A PYRAMID ^: BASE IS AN
EQUILAT]AL TRIANGLE4 ,! NUMB] .A ;N.'
.-( BALLS P] LAY] IS GIV5 0": .;N .K #A
REPRES5TS ! TOP LAY]4
A4 ,H[ _M BALLS >E 9 ! FIF? LAY]8
B4 ,H[ _M BALLS >E 9 A /ACK ) FIVE
LAY]S8
C4 .,-P>E ! NUMB] ( BALLS 9 A LAY] (A
TRIANGUL> PYRAMID )! NUMB] ( BALLS 9 !
SAME LAY] (A SQU>E PYRAMID4
#FH4 .,,*ALL5GE ,US+ ! TRUE /ATE;TS F
,EX]CISES #EI-FB ON PAGE #GII &! SPECIAL
=MULAS ON PAGE #GIG @1 F9D A =MULA =!
NUMB] ( BALLS 9 ! TOP .;N LAY]S (!
PYRAMID F ,EX]CISE #FG4
,,MIX$ ,,REVIEW
,PREP>E = ,LESSON #AB.B 9 ,EXS4
#FI-GG4
,SOLVE ! EQU,N4 ,*ECK YR SOLU;N4 @7 P4
#AH @7
#FI4 #AH .K #D .;X -- #B
#GJ4 #BC .K #F .;X -- #A
#GA4 #AB .K #B--#E;X
#GB4 #E .K #H .;X -- #E
#GC4 #AG .K #BJ -- .#B;X
#GD4 #AD .K #E .;X @+ #D
#GE4 #G--#C .;X .K #AF
#GF4 #I @+ #H .;X .K #BE
#GG4 ;LL .;X -- #F .K --#CI
,F9D ! 4T.E 2T ! PO9TS4 @7 P4 #FAD @7
#GH4 7#D1 --#E71 7#F1 #A7
#GI4 7-#G1 #D71 7-#B1 --#A7
#HJ4 7#J1 #E71 7#E1 --#B7
#HA4 7-#D1 #F71 7#A1 #I7
#HB4 7#B1 --#E71 7#F1 --#D7
#HC4 7-#E1 --#D71 7-#B1 --#H7
#HD4 7#I1 #G71 7#E1 #F7
#HE4 7-#A1 #H71 7#C1 #B7
#HF4 7#D1 #J71 7-#I1 --#F7
.,,EXTRA .,,PRACTICE = LESSON #AB.A1
P#.AJBA
..,,ONL9E ,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#HJA
,,GRAPH+ ,,CALCULATOR ,,ACTIV;Y USE AF
LESSON #AB.A #AB.A ,"W ) ,SEQU;ES
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,KEY/ROKES
.,"Q ,H[ C Y USE A GRAPH+ CALCULATOR
6P]=M OP],NS .) .SEQU;ES8
,SIDEB>3
,/&>DS
..#BB.J ,/UD5TS F9D ! G5]AL T]M &!
SUMS ( >I?METIC .S]IES &( BO? F9ITE &
9F9ITE GEOMETRIC S]IES4
.,EXAMPLE ,F9D1 GRAPH1 & SUM T]MS (A
SEQU;E
..,USE A GRAPH+ CALCULATOR 6F9D ! F/
EI<T T]MS ( .A ;N .K ..#E;N -- #C4
,GRAPH ! SEQU;E4 ,!N F9D .! SUM ..(! F/
EI<T T]MS (! .SEQU;E4
,,/EP #A ,5T] SEQU;E
,PUT ! GRAPH+ CALCULATOR 9 .SEQU;E
MODE & .DOT MODE4 ,5T] ! SEQU;E4 ,NOTE T
! CALCULATOR USES .;U @7 .;N @7 R ?AN .A
;N @4
,,/EP #B ,CALCULATE T]MS
,USE ! .TA# F1TURE 6VIEW ! T]MS (!
SEQU;E4 ,! F/ EI<T T]MS >E #B1 #G1 #AB1
#AG1 #BB1 #BG1 #CB1 & #CG4
,,/EP#C ,GRAPH SEQU;E
,SET ! VIEW+ W9D[ S T .;L "K.K ;N"K.K
#H1 #J "K.K .;X "K.K #I1 & #J "K.K .;Y
"K.K #DJ4 ,GRAPH ! SEQU;E4 ,USE ! .TRACE
F1TURE 6VIEW ! T]MS (! SEQU;E4
,,/EP #D ,F9D SUM ( T]MS
,USE ! .SUMM,N F1TURE 6F9D ! SUM (! F/
EI<T T]MS (! SEQU;E4 ,! SCRE5 %[S T !
SUM IS #AEF4
,PRACTICE
,USE A GRAPH+ CALCULATOR TO 7A7 F9D !
F/ T5 T]MS (! SEQU;E1 7;B7 GRAPH !
SEQU;E1 & 7;C7 F9D ! SUM (! F/ T5 T]MS
(! SEQU;E4
.#A4 .A ;N.' .K #D;N @+ #A
.#B4 .A ;N.' .K .#C @7 .;N @+ #B7
#C4 .A ;N .K ..#CE--.#C;N
#D4 .A ;N .K ..#AE @+ .#B;N
.#E4 .A ;N.' .K #C @+ .;N #B
#F4 .A ;N .K.#B ;N--#A
------------------------------------#HJB
#AB.B ,ANALYZE ,>I?METIC ,SEQU;ES &
,S]IES
.,2F ,Y "W$ ) G5]AL SEQU;ES & S]IES4
.,N[ ,Y W /UDY >I?METIC SEQU;ES &
S]IES4
.,:Y8 ,S Y C >RANGE A M>*+ B&1 Z 9
,EX4 #FD4
,KEY ,VOCABUL>Y
99 >I?METIC SEQU;E
99 -MON DI6];E
99 >I?METIC S]IES
,SIDEB>3
,/&>DS
..#BB.J ,/UD5TS F9D ! G5]AL T]M &!
SUMS ( >I?METIC .S]IES &( BO? F9ITE &
9F9ITE GEOMETRIC S]IES4
..#BC.J ,/UD5TS DERIVE ! SUMM,N =MULAS
= >I?METIC .S]IES &= BO? F9ITE & 9F9ITE
GEOMETRIC S]IES4
,9 AN .>I?METIC .SEQU;E @1 ! DI6];E (
3SECUTIVE T]MS IS 3/ANT4 ,? 3/ANT DI6];E
IS CALL$ ! .-MON .DI6];E & IS DENOT$
0.D4
,EXAMPLE #A
,ID5TIFY >I?METIC SEQU;ES
,TELL :E!R ! SEQU;E IS >I?METIC4
.A4 --#D1 #A1 #F1 #AA1 #AF1 '
.B4 #C1 #E1 #I1 #AE1 #BC1'
,SOLU;N
,F9D ! DI6];ES ( 3SECUTIVE T]MS4
.A4 .A #B -- .A ;L.' .K #A--7--#D7 .K
#E
.A #C -- .A #B .K #F-A .K #E
A #D -- .A #C .K #AA--#F .K #E
.A #E -- .A #D .K #AF--#AA .K #E
,EA* DI6];E IS #E1 S ! SEQU;E IS
>I?METIC4
.B4 .A #B -- .A #A .K #E--#C .K #B
A #C -- .A #B .K .#I -- #E .K #D
.A #D -- .A #C .K #AE--#I .K #F
.A #E -- A #D .K #BC--#AE .K #H
,! DI6];ES >E N 3/ANT1 S ! SEQU;E IS N
>I?METIC4
..,GUID$ ,PRACTICE = ,EXAMPLE .#A
.#A4 ,TELL :E!R ! SEQU;E #AG1 #AD1
#AA1 #H1 #E1' IS >I?METIC4 .,EXPLA9 :Y
OR :Y N4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,! FOLL[+ TA# IS 9 LI/$
=MAT4 ,= EA* CELL ! H1D+ IS %[N
FOLL[$ 0A COLON1 SPACE &! CELL
3T5TS
,RULE = AN ,>I?METIC ,SEQU;E3
.,ALGEBRA
,RULE = AN ,>I?METIC ,SEQU;E3 ,! N?
T]M ( AN >I?METIC SEQU;E ) F/ T]M A.' #A
& -MON DI6];E .;D IS GIV5 BY3
A.' ;N.' .K A.' #A @+ @7 .;N -- #A7 .;D
,RULE = AN ,>I?METIC ,SEQU;E3
.,EXAMPLE
,RULE = AN ,>I?METIC ,SEQU;E3 ,! N?
T]M ( AN >I?METIC SEQU;E )A F/ T]M ( .#B
& -MON DI6];E #C IS GIV5 BY3
A.' ;N.' .K #B @+ @7 .;N -- #A7#C1 OR
A.' ;N.' .K --#A @+ #C;N.'.-
------------------------------------#HJC
,EXAMPLE #B
,WRITE A RULE =! .;N TH T]M
,WRITE A RULE =! .N? T]M (! SEQU;E4
,!N F9D .A #AE @4
.A4 #D1 #I1 #AD1 #AI1 '
.B4 #FJ1 #EB1 #DD1 #CF1 '
,,AVOID ,,]RORS
,9 ! G5]AL RULE = AN >I?METIC SEQU;E1
NOTE T ! -MON DI6];E .;D IS MULTIPLI$
0.;N -- #A1 N .;N @4
,SOLU;N
.A4 ,! SEQU;E IS >I?METIC ) F/ T]M .A
#A .K #D & -MON DI6];E .;D .K #I--#D .K
#E4 ,S1 A RULE =! .;N TH T]M IS3
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
A ;N A #A .K @+ @7 .;N -- #A7#E @3
.,WRITE .G5]AL .RULE4
.K #D @+ @7 .;N -- #A7#E @3 ,SUB/ITUTE
#D =A.' #A & #E =.' ;D @4
.K --..#A @+ .#E;N @3 .,SIMPLIFY4
,! #AE? T]M IS .A #AE .K --#A @+
#E7#AE7 .K #GD4
.B4 ,! SEQU;E IS >I?METIC ) F/ T]M .A
#A .K #FJ & -MON DI6];E .;D .K #EB--#FJ
.K --#H4 ,S1 A RULE =! .;N TH T]M IS3
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
A.' ;N.' .K A.' #A @+ @7 .;N -- ;L7
.;D @3 .,WRITE .G5]AL .RULE4
.K #FJ @+ @7 .;N - ;L77-#H7 @3
,SUB/ITUTE #FJ =A.' #A & --#H =.' ;D @4
.K #FH--#H;FT3 .,SIMPLIFY4
,! #AE? T]M IS .A ;L#E .K .#FH-
#H7#AE7 .K --#EB4
,EXAMPLE #C
,WRITE A RULE GIV5 A T]M & -MON DI6];E
..,"O T]M ( AN >I?METIC SEQU;E IS .A
#AI .K ..#DH4 ,! -MON DI6];E IS .;D .K
.#C4
.A4 ,WRITE A RULE =! .;N TH T]M4
.B4 ,GRAPH ! SEQU;E4
,SOLU;N
.A4 ,USE ! G5]AL RULE 6F9D ! F/ T]M4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
A.' ;N.' .K A.' #A @+ @7 .;N -- #A7
.;D @3 .,WRITE .G5]AL .RULE4
.A #AI .K A.' #A @+ 7#AI--#A7 .;D @3
.,SUB/ITUTE .#AI = .N4
#DH .K A.' #A @+ #AH7#C7 @3 ,SUB/ITUTE
#DH =A.' #AI & #C =.' D4.-
--#F .K A.' #A @3 ,SOLVE =.' A.' #A @4
,S1 A RULE =! .;N TH T]M IS3
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
A.' ;N.' .K A.' #A @+ @7 .;N--.#A @7
.;D @3 .,WRITE .G5]AL .RULE4
.K -.#F @+ 7FT--#A7#C @3 ,SUB/ITUTE
--#F =.' A #A & #C =.' ;D @4
.K --#I @+ #C;FT3 .,SIMPLIFY4
.B4 ,CR1TE A TA# ( VALUES =! SEQU;E4
,! GRAPH (! F/ #F T]MS (! SEQU;E IS %[N4
,NOTICE T ! PO9TS LIE ON A L9E4 ,? IS
TRUE = .ANY >I?METIC SEQU;E4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;N @3 #A3 #B3 #C3 #D3 #E3 #F
.A .;N @3 -#F3 -#C3 #J3 #C3 #F3 #I
------------------------------------#HJD
,,EXAMPLE #D ,WRITE A RULE GIV5 TWO
T]MS
,TWO T]MS ( AN >I?METIC SEQU;E >E .A
#H .K #BA & .A #BG .K #IG4 ,F9D A RULE
=! RA? T]M4
,SOLU;N
.,,/EP .#A .,WRITE A SY/EM ( EQU,NS
US+ .A ;N .K .A #A @+ @7 .;N--.#A @7 .;D
& SUB/ITUT+ #BG = .;N 7,EQU,N #A7 & !N
.#H = .;N 7,EQU,N #B74
.,,/EP .#B .,SOLVE ! SY/EM4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#D .K .;D @3 ,SOLVE =.' D4.-
#IG .K A.' #A @+ #BF7#D7 @3 ,SUB/ITUTE
=.' ;D .-9 ,EQU,N #A4
-#G .K A.' #A @3 ,SOLVE =.' A #A @4
..,,/EP #C ,F9D .A RULE = .A ;N
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
A.' ;N.' .K A.' #A @+ @7 .;N--.#A @7
.;D @3 .,WRITE .G5]AL .RULE4
.K --.#G @+ @7 .;N -- #A7#D @3
.,SUB/ITUTE .= .A @1 & .D4
.K --#AA @+ .#D;N @3 .,SIMPLIFY4
,,GUID$ ,,PRACTICE = ,EXAMPLES #B1 #C1
& #D
,WRITE A RULE =E TH .;N TH T]M (!
>I?METIC SEQU;E4 ,!N F9D .A #BJ @4
.#B4 #AG1 #AD1 #AA1 #H1'4
.#C4 .A #AA .K --#EG1 ;D .K --#G
.#D4 .A #G .K #BF1 .A #AF .K #GA
.,,>I?METIC .,,S]IES ,! EXPRES.N =M$
0A4+ ! T]MS ( AN >I?METIC SEQU;E IS
CALL$ AN >I?METIC S]IES4 ,! SUM (! F/
.;N T]MS ( AN >I?METIC S]IES IS DENOT$
0.;,S ;N @1 ,6F9D A RULE = .;,S ;N @1 Y
C WRITE .;,S ;N 9 TWO DI6]5T WAYS & ADD
! RESULTS4
,Y C 3CLUDE T #B .;,S ;N .K .;N @7 .A
#A @+ .A ;N @1 : L1DS 6! FOLL[+ RESULTS4
,,KEY ,,3CEPT ,= ,YR ,NOTEBOOK
,! ,SUM (A ,F9ITE ,>I?METIC ,S]IES
,! SUM (! F/ .;N T]MS ( AN >I?METIC
S]IES IS3
,9 ^WS1 .;,S ;N IS ! M1N (! F/ & .;N
TH T]MS4 MULTIPLI$ 0! NUMB] ( T]MS4
------------------------------------#HJE
..,,EXAMPLE #E ,/&>DIZ$ ,TE/
.,PRACTICE
,:AT IS ! SUM (! >I?METIC S]IES
.,A #AJC
.;,B #AAA
.;,C #AAAJ
.;,D #BBBJ
,,CLASSIFY ,,S]IES
,Y C V]IFY T ! S]IES 9 ,EXAMPLE #E IS
>I?METIC 0EVALUAT+ #C @+ #E .;I =! F/
FEW VALUES (! 9DEX .;I @4 ,! RESULT+
T]MS >E #H1 #AC1 #AH1 #BC1'1 : H A -MON
DI6];E ( #E4
,SOLU;N
,! CORRECT ANSW] IS ,C4 ..,A ;,B ;,C
.;,D
,,EXAMPLE #F ,USE AN >I?METIC SEQU;E &
S]IES 9 R1L LIFE
.,,H\SE .,,( .,,C>DS ,Y >E MAK+ A H\SE
( C>DS SIMIL> 6! "O %[N4
.A4 ,WRITE A RULE =! NUMB] ( C>DS 9 !
.N? R[ IF ! TOP R[ IS R[ #A4
.B4 ,:AT IS ! TOTAL NUMB] ( C>DS IF !
H\SE ( C>DS HAS #AD R[S8
,SOLU;N
.A4 ,/>T+ )! TOP R[1 ! NUMB]S ( C>DS 9
! R[S >E #C1 #F1 #I1 #AB1'4 ,^! NUMB]S
=M AN >I?METIC SEQU;E )A F/ T]M ( #C &A
-MON DI6];E ( #C4 ,S1 A RULE =! SEQU;E
IS3
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
A.' #B .K A.' #A @+ 7;N -- #A 7.;D @3
.,WRITE .G5]AL .RULE4
.K #C @+ @7 .;N -- #A7#C @3 ,SUB/ITUTE
#C =A1 & #C =.' D4.-
.K .#C;N @3 .,SIMPLIFY4
.B4 ,F9D ! SUM ( AN >I?METIC S]IES )
F/ T]M .A ;X .K #C & LA/ T]M A #AD .K
#C7#AD7 .K #DB4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,GUID$ ,PRACTICE = .,EXAMPLES #E .&
.#F
.#E4 ,F9D ! SUM (! >I?METIC S]IES
.#F4 .,,:AT .,,IF8 ,9 ,EXAMPLE #F1 :AT
IS ! TOTAL NUMB] ( C>DS IF ! H\SE ( C>DS
HAS #H R[S8
------------------------------------#HJF
#AB.B ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
,,WS#BA = ,EXS4 #AE1DA1 & #FE
.K .,,/&>DIZ$ .,,TE/ .,,PRACTICE ,EXS4
#B1 #BI1 #CI1 #EB1 & #FH
.K .,,MULTIPLE .,,REPRES5T,NS ,EX#.FF
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,!
3/ANT DI6];E 2T 3SECUTIVE T]MS ( AN
>I?METIC SEQU;E IS CALL$ ! @8 @4
.#B4 .,,WRIT+ .,EXPLA9 ! DI6];E 2T AN
>I?METIC SEQU;E & AN >I?METIC S]IES4
.,,EXAMPLE .#A .ON .P4 #HJB = ,EXS4
#C-AA
,,ID5TIFY+ ,,>I?METIC ,,SEQU;ES ,TELL
:E!R ! SEQU;E IS >I?METIC4 .,EXPLA9 :Y
OR :Y N4
.#C4 #A1 --#B1 --#E1 --#H1 --#AA1 '
.#D4 #AF1 #AD1 #AA1 #F1 #C1 '
.#E4 #E1 #AD1 #BC1 #CB1 #DA144
.#F4 --#AJ1 --#G1 --#E1 --#B1 #J1'
.#G4 #J.E1 #A1 #A.E1 #B1 #B.E1 '
.#H4 #BJ1 #AJ1 #E1 #B.E1 #A.BE1'
.#I4
.#AJ4
.#AA4
.,,EXAMPLE .#B ON P4 #HJC = ,EXS4
#AB-BB
,,WRIT+ ,,RULES ,WRITE A RULE =! RA?
T]M (! >I?METIC SEQU;E4 ,!N F9D .A #BJ
@4
.#AB4 #A1 #D1 #G1 #AJ1 #AC1 '
.#AC4 #E1 #AA1 #AG1 #BC1 #BI1'
.#AD4 #H1 #BA1 #CD1 #DG1 #FJ1 '
.#AE4 --#C1 --#A1 #A1 #C1 #E1'
.#AF4 #F1 #B1 --#B1 --#F1 --#AJ1'
.#AG4 #BE1 #AD1 #C1 --#H1 --#AI1'
.#AH4
.#AI4
.#BJ4 #A.E1 #C.F1 #E.G1 #G.H1 #I.I1'
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 WRIT+ ! RULE =! RA? T]M (!
>I?METIC SEQU;E #CG1 #BD1AA1 --#B1
--#AE1'4
#BA4
,USE A #A .K #CG .& .;D .K --#AC4
A ;N .K A #A @+ .ND
A ;N .K #CG@+;N7-#AC7
A ;N .K #CG--#AC;N
#BB4
,! F/ T]M IS #CG &! .-MON .DI6];E IS
--#AC4
A ;N .K --#AC @+ 7;N--#A77#CG7 A ;N .K
-.#EJ @+ #CG;N
.,,EXAMPLE #C
ON P4 #HJC = ,EXS4 #BC-BI
,,WRIT+ ,,RULES ,WRITE A RULE =! N?
T]M (! >I?METIC SEQU;E4 ,!N GRAPH ! F/
SIX T]MS (! SEQU;E4
.#BC4 A #AF .K #EB1 .;D .K #E
.#BD4 .A #F .K --#AF1 .;D .K #I
.#BE4 .A #D .K #IF1 .;D .K --#AD
.#BF4 .A #AB .K --#C1 .;D .K --.#G
.#BG4
.#BH4
#BI4 .,,MULTIPLE .,,*OICE ,=A C]TA9
>I?METIC SEQU;E1 .A #CJ .K #EG & .;D .K
#D4 ,:AT IS A RULE =! .N? T]M (! SEQU;E8
,A .A .K --#FC -.#D;N
;,B .A ;N.' .K--#EI--#D .;N
;,C .A ;N .K --#FC @+ .#D;N
;,D .A ;N .K --#EI @+ .#D;N
------------------------------------#HJG
,,EXAMPLE #D
ON P4 #HJD = ,EXS4 #CJ-CI
,,WRIT+ ,,RULES ,WRITE A RULE =! .N?
T]M (! >I?METIC SEQU;E T HAS ! TWO GIV5
T]MS4
.#CJ4 .A #D .K #CA1 .A ;L#J .K #HE
.#CA4 .A #F .K #CI1 .A ;U .K #GI
.#CB4 .A #C .K --#B1 .A ;L#G .K #DJ
.#CC4 .A #H .K --#AJ1 .A #BJ .K --#EH
.#CD4 .A #I .K #HI1 .A ;L#E .K #ACG
.#CE4 .A #B .K #AG1 .A #AA .K #CE
.#CF4 .A #G .K #D1 A #AB .K --#I
.#CG4 .A #E .K #AE1 .A #I .K #BD
.#CH4 A #F .K #J1 .A #AA .K --#B
#CI4 .,,MULTIPLE .,,*OICE ,=A C]TA9
>I?METIC SEQU;E1 .A #F .K --#F & .A ;L#C
.K --#DH4 ,:AT IS A RULE =! .N? T]M (!
SEQU;E8
,A .A ;N.' .K #AH @+ #F .;N
;,B .A ;N.' .K #CJ -- .#F;N
;,C .A ;N .K --#F @+ #BD .;N
;,D .A ;N .K --#CF--#F .;N
,,EXAMPLE #E
.ON P4 #HJE = ,EXS4 #DJ-DH
,,F9D+ ,,SUMS ,F9D ! SUM (! >I?METIC
S]IES4
.#DJ4
.#DA4
.#DB4
.#DC4
.#DD4
.#DE4
.#DF4 #B @+ #F @+ #AJ @+ 99 99 99 @+
#EH
.#DG4 --#A @+ #D @+ #I @+ 99 99 99 @+
#CD
.#DH4 #DD @+ #CG @+ #CJ @+ 99 99 99 @+
#B
,,US+ ,,GRAPHS ,WRITE A RULE =! SEQU;E
^: GRAPH IS %[N4
.#DI4
.#EJ4
.#EA4
.#EB4 .,,WRIT+ .,-P>E ! GRAPH ( .A ;N
.K .#C;N @+ #B1 ": .;N IS A POSITIVE
9TEG]1 )! GRAPH ( ..;F7;X7 .K #C .;X @+
#B1 ": .;X IS A R1L NUMB]4 ,4CUSS H[ !
GRAPH ( AN >I?METIC SEQU;E IS SIMIL> 6&
DI6]5T F ! GRAPH (A L9E> FUNC;N4
.,,R1SON+ ,TELL :E!R ! /ATE;T IS .TRUE
OR .FALSE4 .,EXPLA9 YR ANSW]4
.#EC4 ,IF ! -MON DI6];E ( AN >I?METIC
S]IES IS D\#D :ILE ! F/ T]M & NUMB] (
T]MS 9 ! S]IES REMA9 UN*ANG$1 !N ! SUM
(! S]IES IS D\#D4
.#ED4 ,IF ! NUMB]S .A1 .;B @1 & .;C >E
! F/ ?REE T]MS ( AN >I?METIC SEQU;E1 !N
.;B IS HALF ! SUM ( .A & .C4
.,,SOLV+ .,,EQU,NS ,F9D ! VALUE ( .N4
.#EE4
.#EF4
.#EG4
.#EH4
.#EI4
.#FJ4
.#FA4 .,,R1SON+ ,F9D ! SUM ( ALL
POSITIVE ODD 9TEG]S LESS ?AN #CJJ4
.#FB4 .,,*ALL5GE ,! NUMB]S #C -- .;X1
.;X @1 & #A -- .#C .;X >E ! F/ ?REE T]MS
9 AN >I?METIC SEQU;E4 ,F9D ! VALUE ( .;X
&! NEXT T]M 9 ! SEQU;E4
------------------------------------#HJH
,PRO#M ,SOLV+
,,EXAMPLE #F
ON .P4 #HJE = ,EXS4 #FC-FE
#FC4 .,,H"OYCOMBS ,DOME/IC BEES MAKE
_! H"OYCOMB 0/>T+ )A S+LE HEXAGONAL
CELL1 !N =M+ R+ AF R+ ( HEXAGONAL CELLS
>.D ! 9ITIAL CELL1 Z %[N4 ,! NUMB]S (
CELLS 9 SU3ESSIVE R+S =M AN >I?METIC
SEQU;E4
A4 ,WRITE A RULE =! NUMB] ( CELLS 9 !
N? R+4
B4 ,:AT IS ! TOTAL NUMB] ( CELLS 9 !
H"OYCOMB AF ! #I? R+ IS =M$8 7.,H9T3 ,D
N =GET 6C.T ! 9ITIAL CELL47
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#FD4 .,,M>*+ .,,B& ,A M>*+ B& IS
>RANG$ 9 #G R[S4 ,! F/ R[ HAS #C B&
MEMB]S1 & EA* R[ AF ! F/ HAS #B M B&
MEMB]S ?AN ! R[ 2F X4 ,WRITE A RULE =!
NUMB] ( B& MEMB]S 9 ! .N? R[4 ,!N F9D !
TOTAL NUMB] ( B& MEMB]S4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#FE4 .,,SCULPTURE ,SOL ,LE,WITT'S
SCULPTURE .,F\R-.,SID$ .,PYRAMID 9 !
,N,NAL ,GALL]Y ( ,>T ,SCULPTURE ,G>D5 IS
MADE ( 3CRETE BLOCKS4 ,Z %[N 9 !
DIAGRAM1 EA* LAY] HAS #H M VISI# BLOCKS
?AN ! LAY] 9 FRONT ( X4
A4 ,WRITE A RULE =! NUMB] ( VISI#
BLOCKS 9 ! N? LAY] ": .;N .K #A
REPRES5TS ! FRONT LAY]4
B4 ,:5 Y VIEW ! PYRAMID F "O CORN]1 A
TOTAL ( #AB LAY]S >E VISI#4 ,H[ _M (!
PYRAMID'S BLOCKS >E VISI#8
.#FF4 .,,MULTIPLE .,,REPRES5T,NS ,!
4T.E .;,D 7IN FEET7 T AN OBJECT FALLS 9
.;T SECONDS C 2 MODEL$ 0.;,D7.;T7 .K #AF
.;T #B @4
.A4.,MAK+ .A .,TA# ,LET .;D7.;N7
REPRES5T ! 4T.E ! OBJECT FALLS 9 ! N?
SECOND4 ,MAKE A TA# ( VALUES %[+ .;D
7#A71 .;D 7#B71 .;D 7#C71 & .;D 7#D74
@7 .,H9T3 ,! 4T.E .;D 7#A7 T ! OBJECT
FALLS 9 ! F/ SECOND IS .;,D 7;L7- .;,D
7#J747
B4 .,WRIT+ .A .,RULE ,WRITE A RULE =!
SEQU;E ( 4T.ES GIV5 0.;D @7 .;N @7@4
C4 .,DRAW+ .A .,GRAPH ,GRAPH ! SEQU;E
F "P 7;B74
.#FG..,,5T]TA9;T ,DUR+ A HI< S*OOL _S
WEEK1 /UD5TS DRESS UP 9 CO/UMES4 ,A CA%
PRIZE IS GIV5 EA* "D 6! /UD5T )! BE/
CO/UME4 ,! ORGANIZ+ -MITTEE HAS 4#AJJJ
6GIVE AWAY OV] FIVE "DS4 ,! -MITTEE
WANTS 69CR1SE ! AM.T (! PRIZE BY 4#EJ
EA* "D4 ,H[ M* %D ! -MITTEE GIVE AWAY ON
! F/ "D8
.K ..,,"W$-,,\ ,,SOLU;NS ON P4.,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
------------------------------------#HJI
.#FH4 .,,EXT5D$ .,,RESPONSE ,A PAP]
T[EL MANUFACTUR] SELLS PAP] T[ELS ROLL$
ONTO C>DBO>D D[ELS4 ,! ?ICK;S (! PAP] IS
#J.JJJD 9*4 ,! DIAMET] (A D[EL IS #B
9*ES1 &! TOTAL DIAMET] (A ROLL IS #E
9*ES4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;N @3 ;D.' ;N.' 7IN47 @3 .;L ;N 7IN47
#A3 #B3 #B
#B3 @8@3 @8
#C3 @8@3 @8
#D3 @8@3 @8
A4 .,CALCULATE ,LET .;N 2 ! NUMB] (
"TS ! PAP] T[EL IS WRAPP$ >.D ! D[EL1
LET .;D ;N.' .-2 ! DIAMET] (! ROLL J 2F
! N? WRAP1 & LET .;L ;N.' .-2 ! L5G? (
PAP] A4$ 9 ! .N? WRAP4 ,COPY & -PLETE !
TA#4
B4 .,MODEL ,:AT K9D ( SEQU;E IS .;L ;P
.;L #B @1 .;L #C @1 .;L #D @1'@8 ,WRITE
A RULE =! .;N TH T]M (! SEQU;E4
C4 .,APPLY ,F9D ! NUMB] ( "TS ! PAP]
M/ 2 WRAPP$ >.D ! D[EL 6CR1TE A ROLL )A
#E 9* DIAMET]4 ,USE YR ANSW] &! RULE F
"P 7;B7 6F9D ! L5G? ( PAP] 9 A ROLL )A
#E 9* DIAMET]4
D4 .,9T]PRET ,SUPPOSE A ROLL )A #E 9*
DIAMET] CO/S 4#A.EJ4 ,H[ M* WD Y EXPECT
6PAY =A ROLL )A #G 9* DIAMET] ^: D[EL AL
HAS A DIAMET] ( #B 9*ES8 .,EXPLA9 YR
R1SON+ & ANY ASSUMP;NS Y MAKE4
#FI4 .,,*ALL5GE ,A !AT] HAS .;N R[S (
S1TS1 & EA* R[ HAS .;D M S1TS ?AN ! R[ 9
FRONT ( X4 ,"! >E .;X S1TS 9 ! LA/ 7N?7
R[ &A TOTAL ( .;Y S1TS 9 ! 5TIRE !AT]4
,H[ _M S1TS >E 9 ! FRONT R[ (! !AT]8
,WRITE YR ANSW] 9 T]MS ( .;N1 .;X @1 &
.;Y @4
,MIX$ ,REVIEW
,PREP>E = ,LESSON #AB.C 9 ,EXS4
#GJ-HA4
#GJ4 .;X #A/E .K .#G @7 P4 #DEB @7
#GA4 ;X #B/C .K #CF @7 P4 #DEB @7
#GB4 #F;X #B/E -- #E .K #AI @7 P4 #DEB
@7
#GC4 #C;X #C/E -- #D .K #E @7 P4 #DEB
@7
#GD4 7.;X @+ #AJ7 #A/D .K #E @7 P4
#DEB @7
#GE4 7.;X -- #C7 #C/D .K #FD @7 P4
#DEB @7
#GF4 .#F ;X .K #BAF @7 P4 #EAE @7
#GG4 #E ;X .K #CB @7 P4 #EGE @7
#GH4 #AJ #D;X --#F .K #AB @7 P4 #EAE
@7
#GI4 #AJ #E;X @+ #A @+ #E .K #AI @7 P4
#EAE @7
#HJ4 #G .;X -- #C .K #DI .;X -- #H @7
P4 #EAE @7
#HA4 .#C #D;X@+#A .K #GBI ;X @7 P4
#EAE @7
,F9D ! M1N1 M$IAN1 & MODE (! DATA SET4
@7 P4 #GDD @7
#HB4 #E1F1F1F1H1I
#HC4 #CB1CF1CH1DC1DC1DE1DF
#HD4 #HB1 #HA1 #IB1 #HJ1 #GE1 #HC1
#IB1 #IB
#HE4 --#C1 --#D1 --#A1 #E1 --#B1 --#E1
#A
#HF4 #C.A1 #A.I1 #B.F1 #A.I1 #B.E1
#B.H1 #C.E
#HG4 #B.E1 #F.G1 #C.H1 #D.B1 #E.B1
#A.H1 #J.I
#HH4 .,,CRAFT .,,FAIR ,Y >E SELL+
H&MADE HATS & SC>VES AT A CRAFT FAIR4 ,Y
*>GE @4 #AF = EA* HAT & @4 #AH = EA*
SC>F4 ,Y SELL A TOTAL ( #DB ITEMS AT !
CRAFT FAIR & YR REV5UE IS @4 #GAJ4 ,H[
_M HATS DID Y SELL8 @7 P4 #AFJ @7
,,EXTRA ,,PRACTICE = ,LESSON #AB.B1 P4
#AJBA
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#HAJ
#AB.C ,ANALYZE ,GEOMETRIC ,SEQU;ES &
,S]IES
.,2F ,Y /UDI$ >I?METIC SEQU;ES &
S]IES4
.,N[ ,Y W /UDY GEOMETRIC SEQU;ES &
S]IES4
.,:Y8 ,S Y C SOLVE PRO#MS AB SPORTS
T\RNA;TS1 Z 9 ,EX4 #EH4
,KEY ,VOCABUL>Y
99 .GEOMETRIC .SEQU;E
99 .-MON .RATIO
99 .GEOMETRIC .S]IES
,SIDEB>3
,/&>DS
..#BB.J ,/UD5TS F9D ! G5]AL T]M &!
SUMS ( >I?METIC .S]IES &( BO? F9ITE &
9F9ITE GEOMETRIC S]IES4
..#BC.J ,/UD5TS DERIVE ! SUMM,N =MULAS
= >I?METIC .S]IES &= BO? F9ITE & 9F9ITE
GEOMETRIC S]IES4
.,9 A .GEOMETRIC .SEQU;E @1 ! RATIO (
ANY T]M 6! PREVI\S T]M IS 3/ANT4 ,?
3/ANT RATIO IS CALL$ ! .-MON .RATIO & IS
DENOT$ 0.R4
,EXAMPLE #A ,ID5TIFY GEOMETRIC SEQU;ES
,TELL :E!R ! SEQU;E IS GEOMETRIC4
.A4 #D1 #AJ1 #AH1 #BH1 #DJ1 '
.B4 #FBE1 #ABE1 #BE1 #E1 #A1 '
,SOLU;N
,6DECIDE :E!R A SEQU;E IS GEOMETRIC1
F9D ! RATIOS ( 3SECUTIVE T]MS4
A4
,! RATIOS >E DI6]5T1 S ! SEQU;E IS N
GEOMETRIC4
B4
,EA* RATIO IS --;I1 S ! SEQU;E IS
GEOMETRIC4
..,GUID$ ,PRACTICE = ,EXAMPLE .#A
,TELL :E!R ! SEQU;E IS GEOMETRIC4
.,EXPLA9 :Y OR :Y N4
.#A4 #HA1 #BG1 #I1 #C1 #A1'
.#B4 #A1 #B1 #F1 #BD1 #ABJ1 '
.#C4 --#D1 #H1 --#AF1 #CB1 --#FD1'
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,RULE =A ,GEOMETRIC ,SEQU;E
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,ALGEBRA @3 ,! .;N TH T]M (A
GEOMETRIC SEQU;E ) F/ T]M A.' #A & -MON
RATIO .;R IS GIV5 BY3
.A .;N .K A.' #A ;R.' ;N--#A
.,EXAMPLE @3 ,! .;N TH T]M (A
GEOMETRIC SEQU;E )A F/ T]M ( #C & -MON
RATIO #B IS GIV5 BY3
.A .;N .K #C7#B7 ;N--#A
------------------------------------#HAA
,EXAMPLE #B
,WRITE A RULE =! N? T]M
,WRITE A RULE =! N? T]M (! SEQU;E4 ,!N
F9D .A #G
.A4 #D1 #BJ1 #AJJ1 #EJJ1'
.B4 #AEB1 --#GF1 #CH1 --#AI1'
,,AVOID ,,]RORS
,9 ! G5]AL RULE =A GEOMETRIC SEQU;E1
NOTE T ! EXPON5T IS .;N -- #A1 N .N4
,SOLU;N
.A4 ,! SEQU;E IS GEOMETRIC ) F/ T]M A
#A .K #D & -MON RATIO
,S1 A RULE =! N? T]M IS3
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
A.' ;N.' .K A.' #A ;R.' ;N--;L.' @3
.,WRITE .G5]AL .RULE4
.K #D7#E7 ;N--#A @3 ,SUB/ITUTE #D =.'
A #A & #E =.' ;R @4
,! #G? T]M IS .A #G .K #D7#E7 #G --
.;L .K #FB1EJJ4
.B4 ,! SEQU;E IS GEOMETRIC ) F/ T]M .A
#A .K #AEB & -MON RATIO
,,EXAMPLE #C ..,WRITE A RULE GIV5 A
T]M & -MON .RATIO
..,"O T]M (A GEOMETRIC SEQU;E IS .A #D
.K ..#AB4 ,! -MON RATIO IS .;R .K .#B4
.A4 ,WRITE A RULE =! .N? T]M4
.B4 ,GRAPH ! SEQU;E4
,SOLU;N
.A4 ,USE ! G5]AL RULE 6F9D ! F/ T]M4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
A.' ;N.' .K A.' #A ;R.' ;N--;L.' @3
.,WRITE .G5]AL .RULE4
A.' #D .K A.' #A ;R.' #D--;L.' @3
,SUB/ITUTE #D =.' N4.-
#AB .K A #A 7#B7 #C @3 ,SUB/ITUTE #AB
=.' A #D &.' #B .-=.' ;R @4
.#A4 #E .K A.' #A @3 ,SOLVE =.' A.' #A
@4
,S1 A RULE =! .;N TH T]M IS3
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
A.' ;N.' .K A.' #A ;R.' ;N--;L.' @3
.,WRITE .G5]AL .RULE4
.K #A.E7#B7 ;N--#A @3 .,SUB/ITUTE
.#A..E .= .A #A @1 & #B =.' ;R @4
.B4 ,CR1TE A TA# ( VALUES =! SEQU;E4
,! GRAPH (! F/ #F T]MS (! SEQU;E IS %[N4
,NOTICE T ! PO9TS LIE ON AN EXPON5TIAL
CURVE4 ,? IS TRUE = .ANY GEOMETRIC
SEQU;E ) ;R .1 #J4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;N @3 #A3 #B3 #C3 #D3 #E3 #F
A.' ;N.' @3 #A.E3 #C3 #F3 #AB3 #BD3
#DH
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
------------------------------------#HAB
,,EXAMPLE #D ,WRITE A RULE GIV5 TWO
T]MS
,TWO T]MS (A GEOMETRIC SEQU;E >E .A #C
.K --#DH & .A #F .K #CJGB4 ,F9D A RULE
=! RA? T]M4
,SOLU;N
.,,/EP .#A .,WRITE A SY/EM ( EQU,NS
US+ .A ;N .K .A #A .;R ;N --#A &
SUB/ITUT+ #C = .;N 7,EQU,N #A7 & !N #F =
.;N 7,EQU,N #B74
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
A.' #C .K A.' #A ;R.' #C--;L.' @3 -#DH
.K A.' #A ;R.' #B @3 .,EQU,N .#A
A.' #F .K A.' #A ;R.' #F--;L.' @3
#CJGB .K A.' #A ;R.' #E @3 .,EQU,N .#B
,,/EP #B
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,,/EP .#C @3 .,F9D A RULE = A.' ;N.'
@4 @3 A.' ;N.' .K A.' #A ;R.' ;N--#A @3
.,WRITE .G5]AL .RULE4
--@3 --@3 A.' ;N.' .K --#C 7-#D7
;N--;L.' @3 ,SUB/ITUTE =.' A #A &.' ;R
@4
..,GUID$ ,PRACTICE = ,EXAMPLES #B1 #C1
& .#D
,WRITE A RULE =! N? T]M (! GEOMETRIC
SEQU;E4 ,!N F9D .A #H @4
.#D4 #C1 #AE1 #GE1 #CGE1'
.#E4 .A #F .K --#IF1 .;R .K #B
.#F4 .A #B .K --#AB1 .A #D .K --#C
.,,GEOMETRIC .,,S]IES ,! EXPRES.N =M$
0A4+ ! T]MS (A GEOMETRIC SEQU;E IS CALL$
A .GEOMETRIC .S]IES @4 ,! SUM (! F/ .;N
T]MS (A GEOMETRIC S]IES IS DENOT$ 0.;,S
;N @4 ,Y C DEVELOP A RULE = .;,S ;N.'
.-Z FOLL[S4
,S1 .;,S ;N 7;L -- .;R7 .K .A #A 7#A
--.;R ;N.' @7@4 ,IF .;R @6.K #A1 Y C
DIVIDE EA* SIDE ( ? EQU,N 0#A -- .;R
6OBTA9 ! FOLL[+ RULE = .;,S ;N @4
,,KEY ,,3CEPT .= .,YR .,NOTEBOOK
,! ,SUM (A ,F9ITE ,GEOMETRIC ,S]IES
,! SUM (! F/ .;N T]MS (A GEOMETRIC
S]IES ) -MON RATIO .;R @6.K #A IS3
------------------------------------#HAC
,,EXAMPLE #E ,F9D ! SUM (A GEOMETRIC
S]IES
,F9D ! SUM (! GEOMETRIC S]IES
,! SUM (! S]IES IS #HF1JIC1DDJ4
,,EXAMPLE #F ,USE A GEOMETRIC SEQU;E &
S]IES 9 R1L LIFE
.,,MOVIE .,,REV5UE ,9 #AIIJ1 ! TOTAL
BOX (FICE REV5UE AT ,U4,S4 MOVIE !AT]S 0
AB 4#E.JB BILLION4 ,F #AIIJ "? #BJJC1 !
TOTAL BOX (FICE REV5UE 9CR1S$ 0AB
#E.I@3P P] YE>4
.A4 ,WRITE A RULE =! TOTAL BOX (FICE
REV5UE .A ;N.' .-7IN BILLIONS ( DOLL>S7
9 T]MS (! YE>4 ,LET .;N .K #A REPRES5T
#AIIJ4
.B4 ,:AT 0 ! TOTAL BOX (FICE REV5UE AT
,U4,S4 MOVIE !AT]S =! 5TIRE P]IOD
#AIIJ-BJJC8
,SOLU;N
.A4 ,2C ! TOTAL BOX (FICE REV5UE
9CR1S$ 0! SAME P]C5T EA* YE>1 ! TOTAL
REV5UES F YE> 6YE> =M A GEOMETRIC
SEQU;E4 ,USE .A #A .K #E.JB & .;R .K #A
@+ #J.JEI .K #A.JEI 6WRITE A RULE =!
SEQU;E4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
A.' #A .K #E.JB7#A.JEI7 ;N--#A @3
,WRITE A RULE = A.' ;N.' @4
.B4 ,"! >E .#AD YE>S 9 ! P]IOD
#AIIJ-BJJC1 S F9D .;,S #AD @4
,! TOTAL MOVIE BOX (FICE REV5UE =!
P]IOD #AIIJ-BJJC 0 AB 4#AJE BILLION4
..,GUID$ ,PRACTICE = ,EXAMPLES #E &
.#F
.#G4 ,F9D ! SUM (! GEOMETRIC S]IES
.#H4 .,,MOVIE .,,REV5UE ,USE ! RULE 9
"P 7A7 ( ,EXAMPLE #F 6E/IMATE ! TOTAL
BOX (FICE REV5UE AT ,U4,S4 MOVIE !AT]S 9
#BJJJ4
------------------------------------#HAD
#AB.C ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
,,WS#BA = ,EXS4 #AI1DI1 & #EI
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE ,EXS4
#B1 #BG1 #ED1EE1 & #EI
.K .,,MULTIPLE .,,REPRES5T,NS ,EX#.FA
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,!
3/ANT RATIO ( 3SECUTIVE T]MS 9 A
GEOMETRIC SEQU;E IS CALL$ ! @8 @4
.#B4 .,,WRIT+ ,H[ C Y DET]M9E :E!R A
SEQU;E IS GEOMETRIC8
,,EXAMPLE #A
ON P4 #HAJ = ,EXS4 #C-AD
.,,ID5TIFY+ .,,GEOMETRIC .,,SEQU;ES
,TELL :E!R ! SEQU;E IS GEOMETRIC4
.,EXPLA9 :Y OR :Y N4
.#C4 #A1 #D1 #H1 #AF1 #CB1'
.#D4 #D1 #AF1 #FD1 #BEF1 #AJBD1 '
.#E4
.#F4
.#G4
.#H4
.#I4 #AJ1 #E1 #B.E1 #A.BE1 #J.FBE1 '
.#AJ4 --#C1 --#F1 #AB1 #BD1 --#DH1 '
.#AA4 --#D1 #AB1 --#CF1 #AJH1 --#CBD1'
.#AB4 #J.B1 #J.F1 #A.H1 #E.D1 #AF.B1 '
.#AC4 --#E1 #AJ1 #BJ1 #DJ1 #HJ1'
.#AD4 #J.GE1 #A.E1 #B.BE1 #C1 #C.GE1'
,,EXAMPLE #B
ON P4 #HAA = ,EXS4 #AE-BG
.,,WRIT+ .,,RULES ,WRITE A RULE =! N?
T]M (! GEOMETRIC SEQU;E4 ,!N F9D .A #G
@4
.#AE4 #A1 --#D1 #AF1 --#FD1'
.#AF4 #F1 #AH1 #ED1 #AFB1 '
.#AG4 #D1 #BD1 #ADD1 #HFD1 '
.#AH4 #G1 --#CE1 #AGE1 --#HGE1'
.#AI4
.#BJ4
.#BA4 #D1 #B1 #A1 #J.E1 '
.#BB4 --#J.C1 #J.F1 --#A.B1 #B.D1 '
.#BC4 --#B1 --#J.H1 --#J.CB1 --#J.ABH1
'
.#BD4 #G1 --#D.B1 #B.EB1 --#A.EAB1 '
.#BE4 #E1 --#AD1 #CI.B1 --#AJI.GF1 '
.#BF4 #ABJ1 #AHJ1 #BGJ1 #DJE1'
#BG4 .,,MULTIPLE .,,*OICE ,:AT IS A
RULE =! .N? T]M (! GEOMETRIC SEQU;E #E1
#BJ1 #HJ1 #CBJ1'8
,A .A ;N .K #E7#B7 .;N -- #A
;,B .A ;N .K #E7#D7 ;N --#A
;,C .A ;N .K #E7-#D7 ;N--#A
;,D .A ;N .K #E7-#B7 ;N--#A
,,EXAMPLE #C
ON P4 #HAA = ,EXS4 #BH-CH
.,,WRIT+ .,,RULES ,WRITE A RULE =! N?
T]M (! GEOMETRIC SEQU;E4 ,!N GRAPH ! F/
SIX T]MS (! SEQU;E4
.#BH4 .A #A .K #E1 .;R .K #C
.#BI4 .A #A .K --#B1 .;R .K #F
.#CJ4 .A #B .K #F1 .;R .K #B
.#CA4
.#CB4
.#CC4
.#CD4 A #C .K #GE1 .;R .K #E
.#CE4 .A #B -- #H1 .;R .K #D
.#CF4 .A #D .K #EJJ1 .;R .K #E
.,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 WRIT+ ! RULE =! N? T]M
(! GEOMETRIC SEQU;E = : .A #A .K #C &
.;R .K #B4
#CG4
A ;N .K .A ;N ;R ;N
A ;N .K #C7#B7 ;N
#CH4
A ;N .K ;R .A #A ;N--#A
A ;N .K #B7#C7 ;N--#A
------------------------------------#HAE
.,,EXAMPLE .#D .ON .P4 #HAB = ,EXS4
#CI-DG
,,WRIT+ ,,RULES ,WRITE A RULE =! N?
T]M (! GEOMETRIC SEQU;E T HAS ! TWO GIV5
T]MS4
.#CI4 .A #A .K #C1 .A #C .K #AB
.#DJ4 .A #A .K #A1 .A #E .K #FBE
.#DA4
.#DB4 A #C .K #AJ1 .A #F .K #BGJ
.#DC4 A #B .K --#DJ1 A #D .K --#AJ
.#DD4 A #B .K --#BD1 .A #E .K #AECF
.#DE4 A #D .K #AFB1 .A #G .K #DCGD
.#DF4
.#DG4
,,EXAMPLE #E
ON .P4 #HAC = ,EXS4 #DH-ED
,,F9D+ ,,SUMS ,F9D ! SUM (! GEOMETRIC
S]IES4
.#DH4
.#DI4
.#EJ4
.#EA4
.#EB4
#EC4
.#ED4 .,,MULTIPLE .,,*OICE ,:AT IS !
SUM (! GEOMETRIC S]IES
.,A #AI1FHJ
;,B #AI1FHA
;,C #AI1FHB
;,D #AI1FHC
#EE4 .,,OP5-.,,5D$ .,,MA? ,WRITE A
GEOMETRIC S]IES ) #E T]MS S* T ! SUM (!
S]IES IS #AJJ4 @7 .,H9T3 ,*OOSE A VALUE
( .;R & !N F9D .A #A @4 @7
#EF4 .,,*ALL5GE ,US+ ! RULE =! SUM (A
F9ITE GEOMETRIC S]IES1 WRITE EA*
POLYNOMIAL Z A R,NAL EXPRES.N4
A4 #A @+ .;X @+ .;X #B @+ .;X #C @+
.;X #D
B4 .#C .;X @+ #F .;X #C @+ #AB .;X #E
@+ #BD .;X #G
,PRO#M ,SOLV+
,,EXAMPLE #F
ON P4 #HAC = ,EXS4 #EG-EI
#EG4 .,,SKYDIV+ ,9 A SKYDIV+ =M,N )
.;,R R+S1 EA* R+ AF ! F/ HAS TWICE Z _M
SKYDIV]S Z ! PREC$+ R+4 ,! =M,N = .;,R
.K .#B IS %[N4
A4 ,LET .A ;N.' .-2 ! NUMB] ( SKYDIV]S
9 ! .N? R+4 ,F9D A RULE = .A ;N @4
B4 ,F9D ! TOTAL NUMB] ( SKYDIV]S IF "!
>E .;,R .K #D R+S4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#EH4 .,,SO3] ,A REGIONAL SO3] T\RNA;T
HAS #FD "PICIPAT+ T1MS4 ,9 ! F/ R.D (!
T\RNA;T1 #CB GAMES >E PLAY$4 ,9 EA*
SU3ESSIVE R.D1 ! NUMB] ( GAMES PLAY$
DECR1SES 0"O HALF4
A4 ,F9D A RULE =! NUMB] ( GAMES PLAY$
9 ! .N? R.D4 ,= :AT VALUES ( .;N DOES YR
RULE MAKE S5SE8
B4 ,F9D ! TOTAL NUMB] ( GAMES PLAY$ 9
! REGIONAL SO3] T\RNA;T4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
------------------------------------#HAF
.#EI4 .,,%ORT .,,RESPONSE ,A .B9>Y
.SE>* TE*NIQUE US$ ON A -PUT] 9VOLVES
JUMP+ 6! MI4LE ( AN ORD]$ LI/ ( DATA 7S*
Z AN ALPHABETICAL LI/ ( "NS7 & DECID+
:E!R ! ITEM 2+ SE>*$ = IS "!4 ,IF N1 !
-PUT] DECIDES :E!R ! ITEM -ES 2F OR AF !
MI4LE4 ,HALF (! LI/ IS IGNOR$ ON ! NEXT
PASS1 &! -PUT] JUMPS 6! MI4LE (! REMA9+
LI/4 ,? IS REP1T$ UNTIL ! ITEM IS F.D4
,PRODNOTE3 ,PRODUC;N NOTE3 CAP;NS
ASSOCIAT$ ) ? IMAGE >E LABELS T
CORRESPOND 6TEXT )9 ! IMAGE4
,PICTURE3 ..,9ITIAL DATA ,F/ PASS
,SECOND PASS ,?IRD .PASS
,PICTURE3 ,ITEMS 6BE SE>*$
,PICTURE3 ,ITEMS 6BE IGNOR$
A4 ,F9D A RULE =! NUMB] ( ITEMS REMA9+
AF ! .N? PASS "? AN ORD]$ LI/ ( #AJBD
ITEMS4
B4 ,9 ! WOR/ CASE1 ! ITEM 6BE F.D IS !
ONLY "O LEFT 9 ! LI/ AF .;N PASSES "? !
LI/4 ,:AT IS ! WOR/-CASE VALUE ( .;N =A
B9>Y SE>* (A LI/ ) #AJBD ITEMS8
.,EXPLA94
#FJ4 .,,FRACTALS ,! .,SI]P9SKI .C>PET
IS A FRACTAL CR1T$ US+ SQU>ES4 ,!
PROCESS 9VOLVES REMOV+ SMALL] SQU>ES F
L>G] SQU>ES4 ,F/1 DIVIDE A L>GE SQU>E
96N9E 3GRU5T SQU>ES4 ,REMOVE ! C5T]
SQU>E4 ,REP1T ^! /EPS = EA* SMALL]
SQU>E1 Z %[N 2L4 ,ASSUME T EA* SIDE (!
9ITIAL SQU>E IS "O UNIT L;G4
A4 ,LET .A ;N.' .-2 ! NUMB] ( SQU>ES
REMOV$ AT ! .N?4 /AGE4 ,F9D A RULE = .A
;N @4 ,!N F9D ! TOTAL NUMB] ( SQU>ES
REMOV$ "? /AGE #H4
B4 ,LET .;B ;N.' .-2 ! REMA9+ >EA (!
ORIG9AL SQU>E AF ! N? /AGE4 ,F9D A RULE
= .;B ;N @4 ,!N F9D ! REMA9+ >EA (!
ORIG9AL SQU>E AF /AGE #AB4
.#FA4 .,,MULTIPLE .,,REPRES5T,NS ,TWO
-PANIES1 -PANY ,A& -PANY ;,B1 (F] ! SAME
/>T+ SAL>Y ( 4#BJ1JJJ P] YE>4 ,-PANY ,A
GIVES A RAISE ( 4#AJJJ EA* YE>4 ,-PANY
;,B GIVES A RAISE ( #D@3P EA* YE>4
A4 .,WRIT+ .,RULES ,WRITE RULES GIV+ !
SAL>IES .A ;N.' .-& .;B ;N.' .-9 ! .N?
YE> AT -PANIES ,A& ;,B1 RESPECTIVELY4
,TELL :E!R ! SEQU;E REPRES5T$ 0EA* RULE
IS .>I?METIC1 .GEOMETRIC @1 OR .NEI4
B4 .,DRAW+ .,GRAPHS ,GRAPH EA* SEQU;E
9 ! SAME COORD9ATE PLANE4
C4 .,F9D+ .,SUMS ,= EA* -PANY1 F9D !
SUM ( WAGES E>N$ DUR+ ! F/ #BJ YE>S (
EMPLOY;T4
D4 .,US+ .,TE*NOLOGY ,USE A GRAPH+
CALCULATOR OR SPR1D%EET 6F9D AF H[ _M
YE>S ! TOTAL AM.T E>N$ AT -PANY ;,B IS
GRT] ?AN ! TOTAL AM.T E>N$ AT -PANY ,A4
.K .,,"W$-.,,\ .,,SOLU;NS ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
------------------------------------#HAG
.#FB4 ,,*ALL5GE ,ON ,JANU>Y #A ( EA*
YE>1 Y DEPOSIT 4#BJJJ 9 AN 9DIVIDUAL
RETIRE;T A3.T 7,,IRA7 T PAYS #E@3P
ANNUAL 9T]E/4 ,Y MAKE A TOTAL ( #CJ
DEPOSITS4 ,H[ M* M"OY D Y H 9 YR ,,IRA
IMMLY AF Y MAKE YR LA/ DEPOSIT8
,,MIX$ ,,REVIEW
,GRAPH ! NUMB] ON A NUMB] L9E4 @7 P4
#B @7
#FC4
#FD4
#FE4
,SOLVE ! EQU,N4 ,*ECK YR SOLU;N4 @7 P4
#EHI @7
#FF4
#FG4
#FH4
#FI4
#GJ4
#GA4
,F9D ! SUM (! S]IES4 @7 P4 #GID @7
.,,PREVIEW ,PREP>E = ,LESSON #AB.D 9
,EXS4 #GB-GG
#GB4
#GC4
#GD4
#GE4
#GF4
#GG4
,,QUIZ = ,LESSONS #GB.G-ABC
,WRITE ! NEXT T]M 9 ! SEQU;E4 ,!N
WRITE A RULE =! .N? T]M4 @7 P4 #GID @7
.#A4 #A1 #C1 #E1 #G1 '
.#B4 --#E1 #AJ1 --#AE1 #BJ1 '
.#C4
.#D4 #D1 #AF1 #FD1 #BEF1 '
.#E4 #B1 #F1 #AB1 #BJ1 '
.#F4 #I1 #CF1 #HA1 #ADD1 '
,F9D ! SUM (! S]IES1 @7 P4 #GID @7
.#G4
.#H4
.#I4
,WRITE A RULE =! N? T]M .A ;N.' .-(!
>I?METIC OR GEOMETRIC SEQU;E4 ,F9D .A
;L#E @1 !N F9D ! SUM (! F/ #AE T]MS (!
SEQU;E4
.#AJ4 #A1G1 #AC1 #AI1 ' 7.P4 .#HJB7
.#AA4
.#AB4 #E1 #B1 --#A1 --#D1 --#G1 ' @7
P4 #HJB @7
.#AC4 #B1H1CB1 #ABH1 '''@7 P4 #HAJ @7
.#AD4
.#AE4 --#C1 #AE1 --#GE1 #CGE1 ' @7 P4
#HAJ @7
.#AF4 .,,COLLEGE .,,TUI;N ,9 #AIIE1 !
AV]AGE TUI;N AT A PUBLIC COLLEGE 9 !
,UNIT$ ,/ATES 0 4#BJEG4 ,F #AIIE "?
#BJJB1 ! AV]AGE TUI;N AT PUBLIC COLLEGES
9CR1S$ 0AB #F@3P P] YE>4 ,WRITE A RULE
=! AV]AGE TUI;N .A ;N.' .-9 T]MS (! YE>4
,LET .;N .K #A REPRES5T #AIIE4 ,:AT 0 !
AV]AGE TUI;N AT A PUBLIC COLLEGE 9
#BJJB8 7.P4 .#HAJ7
.,,EXTRA .,,PRACTICE = ,LESSON #AB.C1
P4 #AJBA
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#HAH
,MIX$ ,REVIEW ( ,PREVIEW ,SOLV+
.,,/ATE .,,TE/ .,,PRACTICE AT
_+CLASSZONE.COM_:
,LESSONS #AB.A-AB.C
#A4 .,,MULTI-.,,/EP .,,PRO#M ,Y A3EPT
A JOB Z AN 5VIRON;TAL 5G9E] T PAYS A
SAL>Y ( 4#DE1JJJ 9 ! F/ YE>4 ,AF ! F/
YE>1 YR SAL>Y 9CR1SES 0#C.E@3P P] YE>4
,A4 ,WRITE A RULE GIV+ YR SAL>Y .A
;N.' .-= YR .N? YE> ( EMPLOY;T4
,B4 ,:AT W YR SAL>Y 2 DUR+ YR #E? YE>
( EMPLOY;T8
,C4 ,:AT IS ! TOTAL AM.T Y W E>N IF Y
"W =! -PANY = #CJ YE>S8
#B4 .,,EXT5D$ .,,RESPONSE ,A T>GET HAS
R+S T >E EA* #A FOOT WIDE4
,PICTURE3 ,! #C 9N]MO/ R+S (! T>GET
,A4 ,WRITE A RULE =! >EA (! .N? R+4
,B4 ,USE SUMM,N NOT,N 6WRITE A S]IES T
GIVES ! TOTAL >EA (A T>GET ) .;N R+S4
,C4 ,EVALUATE YR EXPRES.N F "P 7;B7 :5
.;N .K #A1 #B1 #D1 & #H4 ,:AT E6ECT DOES
D\BL+ ! NUMB] ( R+S H ON ! >EA (! T>GET8
#C4 .,,%ORT .,,RESPONSE ,RECTANGUL>
TA#S >E PLAC$ TGR AL;G _! %ORT $GES1 Z
%[N 9 ! DIAGRAM4 ,WRITE A RULE =! NUMB]
( P T C 2 S1T$ >.D .;N TA#S4 .,-P>E !
NUMB] ( P T C 2 S1T$ >.D .;N TA#S 9 ?
>RANGE;T )! NUMB] T C 2 S1T$ >.D .;N
TA#S IF ! SAME TA#S >E PLAC$ TGR AL;G _!
L;G $GES4
#D4 .,,OP5-.,,5D$ ,WRITE AN >I?METIC
S]IES ) EI<T T]MS S* T ! SUM (! S]IES IS
#GJ4
#E4 .,,GRI4$ .,,ANSW] ,PIECES ( *ALK
>E /ACK$ 9 A PILE4 ,"P (! PILE IS %[N
2L4
,! BOTTOM R[ HAS #AE PIECES ( *ALK &!
TOP R[ HAS #F PIECES ( *ALK4 ,EA* R[ HAS
"O LESS PIECE ( *ALK ?AN ! R[ 2L X4 ,H[
_M PIECES ( *ALK >E 9 ! PILE8
#F4 .,,%ORT .,,RESPONSE ,A BUILD] IS
3/RUCT+ A /AIRCASE =A DECK4 ,AT ! FOOT
(! /AIRCASE1 "! IS A 3CRETE SLAB T IS #B
9*ES TALL4 ,EA* /AIR IS #G 9*ES TALL4
,WRITE A RULE =! HEI<T (! TOP (! N?
/AIR4 ,F9D ! HEI<T (! TOP (! #AJ? /AIR4
.,EXPLA9 H[ Y CD MODIFY ! RULE S T X
GIVES ! HEI<T (! BOTTOM (! .N? /AIR4
#G4 .,,EXT5D$ .,,RESPONSE ,A SCI5TI/
IS /UDY+ ! RADIOACTIVE DECAY (
,PLAT9UM-#AIG4 ,! SCI5TI/ />TS )A #FF
GRAM SAMPLE ( ,PLAT9UM-#AIG & M1SURES !
AM.T REMA9+ E TWO H\RS4 ,! AM.TS 7IN
GRAMS7 RECORD$ >E #FF1 #CC1AF.E1 #H.BE1'
,A4 ,IS ? SEQU;E .>I?METIC1 .GEOMETRIC
@1 OR .NEI8 .,EXPLA9 H[ Y "K4
,B4 ,WRITE A RULE =! N? T]M (! SEQU;E4
,C4 ,GRAPH ! SEQU;E4 .,DESCRIBE !
CURVE ON : ! PO9TS LIE4
,D4 ,AF H[ _M H\RS W ! SCI5TI/ F/
M1SURE AN AM.T ( ,PLAT9UM-#AIG T IS LESS
?AN #A GRAM8
#H4 .,,OP5-.,,5D$ ,WRITE AN >I?METIC
S]IES &A GEOMETRIC S]IES S* T BO? S]IES
H FIVE T]MS &! SAME SUM4
------------------------------------#HAI
,9VE/IGAT+ ,ALGEBRA ,ACTIV;Y3 #AB.D
,9VE/IGAT+ AN ,9F9ITE ,GEOMETRIC ,S]IES
,USE 2F LESSON #AB.D
,MAT]IALS
99 SCISSORS
99 PAP]
,SIDEB>3
,/&>DS
..,PREP>E = #BC.J ,/UD5TS DERIVE !
SUMM,N =MULAS .= >I?METIC S]IES &= BO?
F9ITE & .9F9ITE .GEOMETRIC .S]IES @4
,,"Q ,:AT IS ! SUM ( AN 9F9ITE
GEOMETRIC S]IES8
,Y C ILLU/RATE AN 9F9ITE GEOMETRIC
S]IES 0CUTT+ A PIECE ( PAP] 96SMALL] &
SMALL] PIECES4
,,EXPLORE ,MODEL AN 9F9ITE GEOMETRIC
S]IES
,/>T )A RECTANGUL> PIECE ( PAP]4
,DEF9E XS >EA 6BE #A SQU>E UNIT4
,,/EP #A ,CUT PAP] 9 HALF
,FOLD ! PAP] 9 HALF & CUT AL;G ! FOLD4
,PLACE "O HALF ON A DESKTOP & HOLD !
REMA9+ HALF4
,,/EP #B ,CUT PAP] AG
,FOLD ! PIECE ( PAP] Y >E HOLD+ 9 HALF
& CUT AL;G ! FOLD4 ,PLACE "O HALF ON !
DESKTOP & HOLD ! REMA9+ HALF4
,,/EP #C ,REP1T /EPS
,REP1T ,/EPS #A & #B UNTIL Y F9D X TOO
DI6ICULT 6FOLD & CUT ! PIECE ( PAP] Y >E
HOLD+4
..,,/EP #D ,F9D .>1S ,! F/ PIECE (
PAP] ON ! DESKTOP HAS AN >EA ( ;Y SQU>E
UNIT4 ,! SECOND PIECE HAS AN >EA ( SQU>E
UNIT4 ,WRITE ! >1S (! NEXT ?REE PIECES (
PAP]4 ,EXPLA9 :Y ^! >1S =M A GEOMETRIC
SEQU;E4
,,/EP#E ,MAKE A TA#
,COPY & -PLETE ! TA# 0RECORD+ ! NUMB]
( PIECES ( PAP] ON ! DESKTOP &! -B9$ >EA
(! PIECES AT EA* /EP4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,NUMB] .( .PIECES @3 #A3 #B3 #C3 #D3
'''
.,-B9$ .>EA @3 @3 @3 @8@3 @8@3 '''
,,DRAW ,,3CLU.NS ,USE YR OBS]V,NS
6-PLETE ^! EX]CISES
.#A4 ,BAS$ ON YR TA#1 :AT NUMB] DOES !
-B9$ >EA (! PIECES ( PAP] APPE> 6BE
APPROA*+8
.#B4 ,US+ ! =MULA =! SUM (A F9ITE
GEOMETRIC S]IES1 WRITE & SIMPLIFY A RULE
=! -B9$ >EA .,A ;N.' .-(! PIECES ( PAP]
AF .;N CUTS4 ,:AT HAPP5S .6.,A ;N.' .-Z
.;N @8 .,JU/IFY YR ANSW] MA!MATIC,Y4
------------------------------------#HBJ
#AB.D ,F9D ,SUMS ( ,9F9ITE
,GEOMETRIC ,S]IES
.,2F ,Y F.D ! SUMS ( F9ITE GEOMETRIC
S]IES4
.,N[ ,Y W F9D ! SUMS ( 9F9ITE
GEOMETRIC S]IES4
.,:Y8 ,S Y C ANALYZE A FRACTAL1 Z 9
,EX4 #DB4
,KEY ,VOCABUL>Y
99 "PIAL SUM
,SIDEB>3
,/&>DS
..#BB.J ,/UD5TS F9D ! G5]AL T]M &!
SUMS ( >I?METIC .S]IES &( BO? F9ITE &
9F9ITE GEOMETRIC S]IES4
..#BC.J ,/UD5TS DERIVE ! SUMM,N =MULAS
= >I?METIC .S]IES &= BO? F9ITE & 9F9ITE
GEOMETRIC S]IES4
,! SUM .;,S ;N.' .-(! F/ .;N T]MS ( AN
9F9ITE S]IES IS CALL$ A "PIAL SUM @4 ,!
"PIAL SUMS ( AN 9F9ITE GEOMETRIC S]IES
MAY APPROA* A LIMIT+ VALUE4
,,EXAMPLE #A ,F9D "PIAL SUMS
,3SID] ! 9F9ITE GEOMETRIC S]IES @1
,F9D & GRAPH ! "PIAL SUMS .;,S ;N.' .-=
.;N.K .#A1.B ,#C1D1 & #E4 ,!N DESCRIBE
:AT HAPP5S 6.;,S ;N.' .-Z .;N 9CR1SES4
,SOLU;N
,F ! GRAPH1 .;,S ;N.' .-APPE>S
6APPROA* #A Z .;N 9CR1SES4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,,SUMS ,,( ,,9F9ITE .,,S]IES ,9
,EXAMPLE #A1 Y C "U/& :Y .;,S ;N.'
.-APPROA*ES #A Z .;N 9CR1SES 03SID]+ !
RULE = .;,S ;N @3
,Z .;N 9CR1SES1 APPROA*ES #J1 S .;,S
;N.' .-APPROA*ES #A4 ,"!=E1 #A IS DEF9$
6BE ! SUM (! 9F9ITE GEOMETRIC S]IES 9
,EXAMPLE #A4 ,M G5],Y1 Z .;N 9CR1SES =
.ANY 9F9ITE GEOMETRIC S]IES ) -MON RATIO
.;R 2T --#A & #A1 ! VALUE (
------------------------------------#HBA
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,! ,SUM ( AN ,9F9ITE ,GEOMETRIC ,S]IES
,! SUM ( AN 9F9ITE GEOMETRIC S]IES )
F/ T]M .A #A & -MON RATIO .;R IS GIV5 BY
PROVID$ ._\ ..;R _\ "K #A4 ,IF ._\
..;R _\ .1 #A1 ! S]IES HAS NO SUM4
,,EXAMPLE #B ,F9D SUMS ( 9F9ITE
GEOMETRIC S]IES
,F9D ! SUM (! 9F9ITE GEOMETRIC S]IES4
.A4
.B4
,SOLU;N
.A4 ,= ? S]IES1 .A #A .K #E & .;R .K
#J.H4
.B4 ,= ? S]IES1 .A #A .K #A &
..,,EXAMPLE #C ,/&>DIZ$ ,TE/
.,PRACTICE
,,AVOID ,,]RORS
,IF Y SUB/ITUTE #A =A #A & --#C = .;R
9 ! =MULA Y GET AN ANSW] ( =! SUM4
,H["E1 ? ANSW] IS N CORRECT 2C ! SUM
=MULA DOES N APPLY :5 ._\ ..;R _\ .1 #A4
,:AT IS ! SUM (! 9F9ITE GEOMETRIC
S]IES #A--#C @+ #I--#BG @+?
.,A
.;,B
.;,C #C
.;,D ,DOES N EXI/
,SOLU;N
,Y "K T .A ;L .K #A & .A #B .K --#C4
,S1
,2C _\ --#C _\ .1.K #A1 ! SUM DOES N
EXI/4
,! CORRECT ANSW] IS ,D4 ..,A ;,B ;,C
.;,D
..,GUID$ ,PRACTICE = ,EXAMPLES #A1 #B
@1 & .#C
.#A4 ,3SID] ! S]IES ,F9D & GRAPH !
"PIAL SUMS .;,S ;N.' .-= .;N .K #A1 #B1
#C1 #D1 & #E4 ,!N DESCRIBE :AT HAPP5S
6.;,S ;N.' .-Z .;N 9CR1SES4
,F9D ! SUM (! 9F9ITE GEOMETRIC S]IES1
IF X EXI/S4
.#B4
.#C4
.#D4
------------------------------------#HBB
,,EXAMPLE #D ,USE AN 9F9ITE S]IES Z A
MODEL
.,,P5DULUMS ,A P5DULUM T IS REL1S$
6SW+ FREELY TRAVELS #AH 9*ES ON ! F/
SW+4 ,ON EA* SU3ESSIVE SW+1 ! P5DULUM
TRAVELS #HJ@3P (! 4T.E (! PREVI\S SW+4
,:AT IS ! TOTAL 4T.E ! P5DULUM SW+S8
,SOLU;N
,! TOTAL 4T.E TRAVEL$ 0! P5DULUM IS3
,! P5DULUM TRAVELS A TOTAL 4T.E ( #IJ
9*ES1 OR #G.E FEET4
,,EXAMPLE #E ,WRITE A REP1T+ DECIMAL Z
A FRAC;N
,WRITE #J.BDBDBD''' Z A FRAC;N 9 L[E/
T]MS4
#J.BDBDBD''' .K #BD7#J.JA7 @+
#BD7#J.JA7 #B @+ #BD7#J.JA7 #C @+ @* @*
@*
,! REP1T+ DECIMAL #J.BDBDBD''' IS Z A
FRAC;N4
..,GUID$ ,PRACTICE = ,EXAMPLES #D &
.#E
.#E4 .,,:AT .,,IF8 ,9 ,EXAMPLE #D1
SUPPOSE ! P5DULUM TRAVELS #AJ 9*ES ON XS
F/ SW+4 ,:AT IS ! TOTAL 4T.E ! P5DULUM
SW+S8
,WRITE ! REP1T+ DECIMAL Z A FRAC;N 9
L[E/ T]MS4
.#F4 #J.EEE'''
.#G4 #J.GBGBGB'''
.#H4 #J.ACACAC'''
------------------------------------#HBC
#AB.D ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
,,WS#BA = ,EXS4 #AC1 #BG1 & #CI
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE ,EXS4
#B1 #CB1 #CD1 #CI1 #DJ1 & #DA
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,!
SUM .;,S ;N.' .-(! F/ .;N T]MS ( AN
9F9ITE S]IES IS CALL$ A7;N7 @8 @4
.#B4 .,,WRIT+ ,EXPLA9 H[ 6TELL :E!R !
S]IES HAS A SUM
.,,EXAMPLE .#A .ON .P4 #HBJ = ,EXS4
.#C-.F
.,,"PIAL .,,SUMS ,=! GIV5 S]IES1 F9D &
GRAPH ! "PIAL SUMS .;,S ;N.' .-= .;N .K
#A1 #B1 #C1D1 & #E4 .,DESCRIBE :AT
HAPP5S 6.;,S ;N.' .-Z .;N 9CR1SES4
.#C4
.#D4
.#E4
.#F4
,,EXAMPLES #B & #C
ON P4 #HBA .= .,EXS4 .#G-.BC
,,F9D+ ,,SUMS ,F9D ! SUM (! 9F9ITE
GEOMETRIC S]IES1 IF X EXI/S4
.#G4
.#H4
.#I4
.#AJ4
.#AA4
.#AB4
.#AC4
.#AD4
.#AE4
.#AF4
.#AG4
.#AH4
.#AI4 .,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 F9D+ ! SUM (! 9F9ITE
GEOMETRIC S]IES
,= ? S]IES1 A #A .K #A .&
.,,F9D+ .,,SUMS ,F9D ! SUM (! 9F9ITE
GEOMETRIC S]IES1 IF X EXI/S4
.#BJ4
.#BA4
.#BB4
.#BC4
.,,EXAMPLE #E
ON P4 #HBB = ,EXS4 #BD-CB
.,,REWRIT+ .,,DECIMALS ,WRITE ! REP1T+
DECIMAL Z A FRAC;N 9 L[E/ T]MS4
.#BD4 #J.BBB'''
.#BE4 #J.DDD'''
.#BF4 #J.AFAFAF'''
.#BG4 #J.FBEFBEFBE'''
.#BH4 #CB.CBCB'''
.#BI4 #ACJ.ACJACJ'''
.#CJ4 #J.JIJIJI'''
.#CA4 #J.BGGG'''
#CB4 .,,MULTIPLE .,,*OICE ,: FRAC;N IS
EQUAL 6! REP1T+ DECIMAL #AH.AHAH'''8
,A
;,B
;,C
;,D
#CC4 .,,R1SON+ ,%[ T #J.III''' IS
EQUAL 6#A4
------------------------------------#HBD
.#CD4 .,,OP5-.,,5D$ .,,MA? ,F9D TWO
9F9ITE GEOMETRIC S]IES ^: SUMS >E EA*
#E4
.,,*ALL5GE ,SPECIFY ! VALUES ( .;X = :
! GIV5 9F9ITE GEOMETRIC S]IES HAS A SUM4
,!N F9D ! SUM 9 T]MS ( X4
.#CE4 #A @+ .#D .;X @+ #AF .;X #B @+
#FD .;X #C @+ @* @* @*
.#CF4
,,PRO#M ,,SOLV+
.,,EXAMPLE #D
ON P4 #HBB = ,EXS4 #CG-CI
.#CG4 .,,TIRE .,,SW+ ,A P]SON IS GIV5
"O PU% ON A TIRE SW+ & !N ALL[$ 6SW+
FREELY4 ,ON ! F/ SW+1 ! P]SON TRAVELS A
4T.E ( #AD FEET4 ,ON EA* SU3ESSIVE SW+1
! P]SON TRAVELS #HJ@3P (! 4T.E (!
PREVI\S SW+4 ,:AT IS ! TOTAL 4T.E !
P]SON SW+S8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#CH4 .,,BUSI;S ,A -PANY _H A PR(IT (
4#CEJ1JJJ 9 XS F/ YE>4 ,S9CE !N1 !
-PANY'S PR(IT HAS DECR1S$ 0#AB@3P P]
YE>4 ,IF ? TR5D 3T9UES1 :AT IS AN UPP]
LIMIT ON ! TOTAL PR(IT ! -PANY C MAKE
OV] ! C\RSE ( XS LIFE"T8 .,JU/IFY YR
ANSW] US+ AN 9F9ITE GEOMETRIC S]IES4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#CI4 .,,MULTIPLE .,,*OICE ,9 #AIID1 !
NUMB] ( CASSETTE TAPES %IPP$ 9 ! ,UNIT$
,/ATES 0 #CDE MILLION4 ,9 EA* SU3ESSIVE
YE>1 ! NUMB] DECR1S$ 0AB #BA.G@3P4 ,:AT
IS ! TOTAL NUMB] ( CASSETTES T W %IP 9
#AIID & AF IF ? TR5D 3T9UES8
,A #DBJ MILLION
;,B #DDJ MILLION
;,C #FAE MILLION
;,B #A.EI BILLION
#DJ4 .,,%ORT .,,RESPONSE ,C ! ,GREEK
H]O ,A*ILLES1 RUNN+ AT #BJ FEET P]
SECOND1 "E CAT* UP 6A TORTOISE T RUNS
#AJ FEET P] SECOND IF ! TORTOISE HAS A
#BJ FOOT H1D />T8 ,! ,GREEK MA!MATICIAN
,Z5O SD NO4 ,HE R1SON$ Z FOLL[S3
,PICTURE3 ..,:5 ,A*ILLES RUNS #BJ FEET
! TORTOISE W 2 9 A NEW SPOT #AJ FEET
.AWAY4
,PICTURE3 ..,!N1 :5 ,A*ILLES GETS 6T
SPOT ! TORTOISE W 2 #E FEET .AWAY4
,PICTURE3 ..,A*ILLES W KEEP HALV+ !
4T.E B W N"E CAT* UP 6! .TORTOISE4
,9 ACTUAL;Y1 LOOK+ AT ! RACE Z ,Z5O
DID1 Y C SEE T BO? ! 4T.ES &! "TS
,A*ILLES REQUIR$ 6TRAV]SE !M =M 9F9ITE
GEOMETRIC S]IES4 ,US+ ! TA#1 %[ T BO?
S]IES H F9ITE SUMS4 ,DOES ,A*ILLES CAT*
UP 6! TORTOISE8 .,EXPLA94
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,4T.E 7.FT7 @3 #BJ3 #AJ3 #E3 #B.E3
#A.BE3 #J.FBE3 '''
.,"T 7.SEC7 @3 #A3 #J.E3 #J.BE3
#J.ABE3 #J.JFBE3 #J.JCABE3 '''
.K .;,W#J;,,RK$-.,,\ .,,SOLU;NS ON P4
,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#HBE
#DA4 .,,EXT5D$ .,,RESPONSE ,A /UD5T
DROPS A RU2] BALL F A HEI<T ( #H FEET4
,EA* "T ! BALL HITS ! GR.D1 X B\NCES
6#GE@3P ( XS PREVI\S HEI<T4
A4 ,H[ F> DOES ! BALL TRAVEL 2T ! F/ &
SECOND B\NCES8 2T ! SECOND & ?IRD
B\NCES8
B4 ,WRITE AN 9F9ITE S]IES 6MODEL !
TOTAL 4T.E TRAVEL$ 0! BALL1 EXCLUD+ !
4T.E TRAVEL$ 2F ! F/ B\NCE4
C4 ,F9D ! TOTAL 4T.E TRAVEL$ 0! BALL1
9CLUD+ ! 4T.E TRAVEL$ 2F ! F/ B\NCE4
D4 ,%[ T IF ! BALL IS DROPP$ F A HEI<T
( .;H FEET1 !N ! TOTAL 4T.E TRAVEL$ 0!
BALL 79CLUD+ ! 4T.E TRAVEL$ 2F ! F/
B\NCE7 IS .#G;H FEET4
#DB4 .,,*ALL5GE ,! .,SI]P9SKI
.TRIANGLE IS A FRACTAL CR1T$ US+
EQUILAT]AL TRIANGLES4 ,! PROCESS 9VOLVES
REMOV+ SMALL] TRIANGLES F L>G] TRIANGLES
0JO9+ ! MIDPO9TS (! SIDES (! L>G]
TRIANGLES Z %[N 2L4 ,ASSUME T ! 9ITIAL
TRIANGLE HAS AN >EA ( #A SQU>E UNIT4
A4 ,LET .A ;N.' .-2 ! TOTAL >EA ( ALL
! TRIANGLES T >E REMOV$ AT /AGE .N4
,WRITE A RULE = .A ;N.'.-
B4 ,F9D @4 ,:AT DOES YR ANSW] M1N 9 !
3TEXT ( ? PRO#M8
,,MIX$ ,,REVIEW
,F9D ! 9DICAT$ PROBABIL;Y4 @7 P4 #GJG
@7
.#DC4 .;,P7.,A7 .K #CB@3P .;,P7.;,B7
.K? .;,P7.,A .OR .;,B7 .K #HB@3P
.;,P7.,A & .;,B7 .K #AA@3P
.#DD4 .;,P @7 .,A @7 .K? .;,P7.;,B7 .K
#J.AG .;,P7.,A OR #E7 .K #J.F .;,P7.,A &
.;,B @7 .K #J.JC
.#DE4 .;,P7.,A7 .K #J.B .;,P7.;,B7 .K
#J.D ;,P7 .,A OR .;,B @7 .K #J.E
.;,P7.,A & #E7 .K?
.,,PREVIEW ,PREP>E = ,LESSON #AB.E 9
,EXS4 #DF-EG4
,WRITE A RULE =! N? T]M .A (! >I?METIC
SEQU;E ) -MON DI6];E .;D OR ! GEOMETRIC
SEQU;E ) -MON RATIO R4
#DF4 .;D .K #E1 .A #A .K .#B @7 P4
#HJB @7
#DG4 .;D .K #H1 .A #A .K --#BG @7 P4
#HJB @7
#DH4 .;D .K --#AH1 .A #H .K #GB @7 P4
#HJB @7
#DI4 .;D .K --#G1 A #G .K --#H @7 P4
#HJB @7
#EJ4 .;D .K #F.E1 A #E -- #IB @7 P4
#HJB @7
#EA4 ;D .K --#A.E1 A #I .K #D @7 P4
#HJB @7
#EB4 ;R .K #B.E1 .A #C .K #BE 7P4
.#HAJ7
#EC4 ;R .K --#C1 .A #B .K --#AH @7 P4
#HAJ @7
#ED4 .;R .K --#J.BE1 A #E .K #DJ.E @7
P4 #HAJ @7
#EE4 ;R .K #F1 A #D .K #BD @7 P4 #HAJ
@7
#EF4 ;R .K #J.GE1 .A #F .K #CJ @7 P4
#HAJ @7
#EG4 ;R .K #D1 A #D .K #ABH 7P4 .#HAJ7
.,,EXTRA .,,PRACTICE = ,LESSON #AB.D1
P4 #AJBA
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#HBF
,9VE/IGAT+ ,ALGEBRA ,ACTIV;Y3 #AB.E
,EXPLOR+ ,RECURSIVE ,RULES
,USE 2F ,LESSON #AB.E
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,KEY/ROKES
,MAT]IALS
99 -PUT] ) SPR1D%EET PROGRAM
,SIDEB>3
,/&>DS
#BB.J ,/UD5TS F9D ! G5]AL T]M &! SUMS
( >I?METIC S]IES &( BO? F9ITE & 9F9ITE
GEOMETRIC S]IES4
,,"Q ,H[ C Y EVALUATE A RECURSIVE RULE
=A SEQU;E8
,A .RECURSIVE .RULE =A SEQU;E GIVES !
2G9N+ T]M OR T]MS (! SEQU;E & !N AN
EQU,N RELAT+ ! .N? T]M .A ;N.' .-6"O OR
M PREC$+ T]MS4 ,= EXAMPLE1 ! RULE .A #A
.K #D1 .A ;N .K .A ;N _ #A @+ #G DEF9ES
A SEQU;E RECURSIVELY4
,,EXPLORE ,F9D T]MS (A SEQU;E GIV5 0A
RECURSIVE RULE
,F9D ! F/ EI<T T]MS (! SEQU;E DEF9$
.0.A #A .K .#D,.A ;N .K .A ;N _ #A @+
#G4 ,:AT TYPE ( SEQU;E DOES ? RULE
REPRES5T8
..,,/EP #A ,5T] F/ .T]M @1
,5T] ! VALUE ( .A #A 96CELL ;,AL4
,,/EP #B ,9T] RECURSIVE EQU,N
,5T] ! =MULA 8.K,AL@+#G0 96CELL ,A#B4
,,/EP #C ,FILL CELLS
,USE .! .FILL .D[N -M& 6COPY !
RECURSIVE EQU,N 96! RE/ ( COLUMN ,A4
,,/EP #D ,ID5T;Y T]MS & TYPE ( SEQU;E
,! F/ EI<T T]MS (! SEQU;E >E #D1 #AA1
#AH1 #BE1 #CB1 #CI1 #DF1 & #EC4 ,?
SEQU;E IS AN >I?METIC SEQU;E 2C ! DI6];E
( 3SECUTIVE T]MS IS ALW #G4
.,,DRAW .,,3CLU.N ,USE YR OBS]V,NS
6-PLETE ^! EX]CISES
.#A4 ,F9D ! F/ EI<T T]MS (! SEQU;E
DEF9$ 0.A #A .K #D1 .A ;N .K .#G;A
;N--#A ,:AT TYPE ( SEQU;E DOES ? RULE
REPRES5T8
.#B4 ,WRITE A RECURSIVE RULE =! SEQU;E
#AE1 #AA1 #G1 #C1 --#A1 --#E1'4
.#C4 ,WRITE A RECURSIVE RULE =! SEQU;E
.#D4 ,:AT EQU,N RELATES ! .;N TH T]M
.A ;N.' .-6! PREC$+ T]M .A ;N _ #A = AN
>I?METIC SEQU;E ) -MON DI6];E .;D @8 =A
GEOMETRIC SEQU;E ) -MON RATIO .;R @8
------------------------------------#HBG
#AB.E ,USE ,RECURSIVE ,RULES )
,SEQU;ES & ,FUNC;NS
.,2F ,Y US$ EXPLICIT RULES = SEQU;ES4
.,,N[ ,Y W USE RECURSIVE RULES =
SEQU;ES4
.,:Y8 ,S Y C MODEL EVAPOR,N F A POOL1
Z 9 ,EX4 #DD4
,KEY ,VOCABUL>Y
99 EXPLICIT RULE
99 RECURSIVE RULE
99 IT],N
,SIDEB>3
,/&>DS
#BB.J ,/UD5TS F9D ! G5]AL T]M &! SUMS
( >I?METIC S]IES &( BO? F9ITE & 9F9ITE
GEOMETRIC S]IES4
,S F> 9 ? *APT] Y H "W$ ) .EXPLICIT
.RULES =! .N? T]M (A SEQU;E1 S* Z .A
;N.' .K #C .;N -- #B & .A ;N.' .K #C7#B7
;N @4 ,AN .EXPLICIT .RULE GIVES .A ;N.'
.-Z A FUNC;N (! T]M'S POSI;N NUMB] .;N 9
! SEQU;E4
,9 ? LESSON Y W LE>N ANO!R WAY 6DEF9E
A SEQU;E--0A .RECURSIVE .RULE @4 ,A
.RECURSIVE .RULE GIVES ! 2G9N+ T]M OR
T]MS (A SEQU;E & !N A .RECURSIVE .EQU,N
T TELLS H[ .A #A IS RELAT$ 6"O OR M
PREC$+ T]MS4
,,EXAMPLE #A ,EVALUATE RECURSIVE RULES
,WRITE ! F/ SIX T]MS (! SEQU;E4
.A4 .A #J .K #A1 .A ;N .K .A ;N--#A @+
#D
.B4 .A #A .K #A1 .A ;N .K .#C;A
;N--;L.'.-
,SOLU;N
.A4 .A #J .K #A
.A #A .K .A #J @+ #D.K#A @+ #D .K #E
.A #B .K .A #A @+ #D .K #E @+ #D .K #I
.A #C .K .A #B @+ #D .K #I @+ #D .K
#AC
A #D .K .A #C @+ #D .K #AC @+ #D .K
#AG
.A #E .K .A #D @+ #D .K #AG @+ #D .K
#BA
B4 .A #A .K #A
.A #B .K #C .A #A .K #C7#A7 .K#C
.A #C .K #C .A #B .K #C7#C7 .K #I
.A #D .K #C .A #C .K #C7#I7 .K #BG
.A #E .K #C;A #D .K #C7#BG7 .K #HA
.A #F .K .#C .A #E .K #C7#HA7 .K #BDC
..,,>I?METIC ,,& ,,GEOMETRIC
.,,SEQU;ES ,9 "P 7A7 ( ,EXAMPLE #A1
OBS]VE T ! .DI6];ES ( 3SECUTIVE T]MS (!
SEQU;E >E 3/ANT1 S ! SEQU;E IS >I?METIC4
,9 "P 7;B71 ! .RATIOS ( 3SECUTIVE T]MS
>E 3/ANT1 S ! SEQU;E IS GEOMETRIC4 ,9
G5]AL1 RULES = >I?METIC & GEOMETRIC
SEQU;ES C 2 WRITT5 RECURSIVELY Z FOLL[S4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,RECURSIVE ,EQU,NS = ,>I?METIC &
,GEOMETRIC ,SEQU;ES
,>I?METIC ,SEQU;E
.A ;N.' .K .A ;N--#A @+ .;D ": .;D IS
! -MON DI6];E
,GEOMETRIC ,SEQU;E
.A ;N.' .K .;R 99 .A ;N --#A ": .;R IS
! -MON RATIO
------------------------------------#HBH
,,EXAMPLE #B ,WRITE RECURSIVE RULES
,WRITE A RECURSIVE RULE =! SEQU;E4
.A4 #C1 #AC1 #BC1 #CC1 #DC1 '
.B4 #AF1 #DJ1 #AJJ1 #BEJ1 #FBE1 '
,,AVOID ,,]RORS
,A RECURSIVE .EQU,N =A SEQU;E DOES N
9CLUDE ! 9ITIAL T]M4 ,6WRITE A RECURSIVE
.RULE =A SEQU;E1 ! 9ITIAL T]M M/ 2
9CLUD$4
,SOLU;N
.A4 ,! SEQU;E IS >I?METIC ) F/ T]M .A
#A .K #C & -MON DI6];E .;D .K #AC--#C .K
#AJ4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
A.' ;N.' .K A.' ;N--;L.' @+ ;D.' @3
,G5]AL RECURSIVE EQU,N = A.' ;N.'.-
.K A.' ;N.' _ #A @+ #AJ @3 ,SUB/ITUTE
#AJ = .;D @4
,S1 A RECURSIVE RULE =! SEQU;E IS .A
#A .K #C1 .A ;N.' .K .A ;N.' _ #A @+
#AJ4
.B4 ,! SEQU;E IS GEOMETRIC ) F/ T]M .A
#A .K #AF & -MON RATIO
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
A.' ;N.' .K ;R.' @* A.' ;N-#A @3
,G5]AL RECURSIVE EQU,N = A.' ;N.'.-
.K .#B..E A.' ;N-#A @3 ,SUB/ITUTE #B.E
= .;R @4
,S1 A RECURSIVE RULE =! SEQU;E IS .A
#A .K #AF1 .A ;N.' .K #B.E .A ;N _ #A
..,GUID$ ,PRACTICE = ,EXAMPLES #A &
.#B
,WRITE ! F/ FIVE T]MS (! SEQU;E4
#A4 .A ;L .K .#C,.A ;N .K .A ;N _ ;L
--.#G
.#B4 .A #J .K #AFB1 .A ;N.' .K #J.E .A
;N.' _ #A
#C4 .A #A .K .#C,.A ;N .K .A ;N _ #A
@+ .;N
.#D4 .A #A .K #D1 .A ;N .K .#B;A ;N _
#A -- #A
,WRITE A RECURSIVE RULE =! SEQU;E4
.#E4 #B1 #AD1 #IH1 #FHF1 #DHJB1 '
.#F4 #AI1 #AC1 #G1 #A1 --#E1 '
.#G4 #AA1 #BB1 #CC1 #DD1 #EE1'
.#H4 #CBD1 #AJH1 #CF1 #AB1 #D1 '
..,,RECURSIVE ,,RULES ,,= ,,SPECIAL
.,,SEQU;ES ,= "S SEQU;ES1 X IS DI6ICULT
6WRITE AN EXPLICIT RULE B RELATIVELY
EASY 6WRITE A RECURSIVE RULE4
..,,EXAMPLE #C ,WRITE RECURSIVE .RULES
= SPECIAL SEQU;ES
,WRITE A RECURSIVE RULE =! SEQU;E4
.A4 #A1 #A1 #B1 #C1 #E1 '
.B4 #A1 #A1 #B1 #F1 #BD1 '
,,"N ,,SEQU;ES
,! SEQU;E 9 "P 7A7 ( ,EXAMPLE #C IS
CALL$ ! .,FIBONA3I .SEQU;E4 ,! SEQU;E 9
"P 7;B7 ( ,EXAMPLE #C LI/S ! FACTORIAL
NUMB]S Y /UDI$ 9 ,*APT] #AJ4
,SOLU;N
.A4 ,2G9N+ )! ?IRD T]M 9 ! SEQU;E1 EA*
T]M IS ! SUM (! TWO PREVI\S T]MS4
,S1 A RECURSIVE RULE IS .A ;L .K #A1
.A #B .K #A1 .A ;N .K .A ;N _ #B @+ .A
;N _ #A @4
.B4 ,DENOTE ! F/ T]M 0.A #J .K #A4 ,!N
NOTE T .A #A .K #A .K #A 99 .A #J @1@1
.A #B .K #B .K #B 99 .A #A ,.A #C .K #F
.K #C 99 .A #B @1 & S ON4
,S1 A RECURSIVE RULE IS .A #J .K #A1
.A ;N .K ..;N 99 .A ;N.' _ #A
------------------------------------#HBI
,,EXAMPLE #D ,SOLVE A MULTI-/EP PRO#M
.,,MUSIC .,,S]VICE ,AN ONL9E MUSIC
S]VICE 9ITI,Y HAS #EJ1JJJ ANNUAL MEMB]S4
,EA* YE> X LOSES #BJ@3P ( XS CURR5T
MEMB]S & A4S #EJJJ NEW MEMB]S4
99 ,WRITE A RECURSIVE RULE =! NUMB] .A
;N.' .-( MEMB]S AT ! />T (! .N? YE>4
99 ,F9D ! NUMB] ( MEMB]S AT ! />T (!
#E? YE>4
99 ,DESCRIBE :AT HAPP5S 6! NUMB] (
MEMB]S OV] "T4
,,ANO!R ,,WAY
,= ALT]NATIVE ME?ODS 99 = SOLV+ !
PRO#M 9 ,EXAMPLE #D1 TURN 6PAGE #HCD =!
,PRO#M ,SOLV+ ,"W%OP4
,SOLU;N
.,,/EP .#A .,WRITE A RECURSIVE RULE4
,2C ! NUMB] ( MEMB]S DECL9ES #BJ@3P EA*
YE>1 #HJ@3P (! MEMB]S >E RETA9$ F "O YE>
6! NEXT4 ,AL1 #EJJJ NEW MEMB]S >E A4$
EA* YE>4
,A RECURSIVE RULE IS .A #A .K #EJ1JJJ1
.A ;N .K #J.H .A ;N--#A @+ #EJJJ4
.,,/EP .#B .,F9D ! NUMB] ( MEMB]S AT !
/>T (! #E? YE>4 ,5T] #EJ1JJJ 7! VALUE (
.A #A 96A GRAPH+ CALCULATOR4 ,!N 5T] !
RULE #J.H * ,ANS @+ #EJJJ 6F9D .A #B
,PRESS ?REE M "TS 6F9D .A #E @4
,"! >E AB #CE1BDJ MEMB]S AT ! />T (!
#E? YE>4
.,,/EP .#C .,DESCRIBE :AT HAPP5S 6!
NUMB] ( MEMB]S OV] "T4 ,3T9UE PRESS+ ON
! CALCULATOR4 ,Z %[N AT ! "R1 AF _M YE>S
! NUMB] ( MEMB]S APPROA*ES #BE1JJJ4
,! NUMB] ( MEMB]S /ABILIZES AT AB
#BE1JJJ MEMB]S4
..,GUID$ ,PRACTICE = ,EXAMPLES #C &
.#D
.#I4 ,WRITE A RECURSIVE RULE =! SEQU;E
#A1 #B1 #B1 #D1 #H1 #CB1'4
.#AJ4 .,,:AT .,,IF8 ,9 ,EXAMPLE #D1
SUPPOSE #GJ@3P (! MEMB]S >E RETA9$ EA*
YE>4 ,:AT HAPP5S 6! NUMB] ( MEMB]S OV]
"T8
------------------------------------#HCJ
.,,IT]AT+ .,,FUNC;NS .,IT],N 9VOLVES !
REP1T$ -POSI;N (A FUNC;N .;F ) XF4 ,!
RESULT ( "O IT],N IS .;F @7 .;F @7 .;X
@7@7@4 ,! RESULT ( TWO IT],NS IS .;F @7
.;F @7 .;F @7 .;X @7@7@7@4 ,Y C USE
IT],N 6G5]ATE A SEQU;E RECURSIVELY4 ,2G9
) AN 9ITIAL VALUE .;X #J @1 & LET .;X #A
.K .;F @7 .;X #J @7@1 .;X #B .K .;F @7
.;X #A @7 .K .;F @7 .;F @7 .;X #J @7@7@1
& S ON4
,,EXAMPLE #E ,IT]ATE A FUNC;N
.,,R1D+ ,AN .IT]ATE IS A NUMB] T IS !
RESULT ( IT]AT+ A FUNC;N4
..,F9D ! F/ ?REE IT]ATES .;X #A @1 .;X
#B @1 .& .;X #C ..(! FUNC;N ;F 7;X7 .K
--#C ;X @+ #A = AN 9ITIAL VALUE .( .;X
#J .K .#B4
,SOLU;N
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X #A .K .;F @7 .;X #J @7 @3 .;X #B
.K .;F @7 .;X #A @7 @3 .;X #C .K .;F @7
.;X #B @7
.K .;F 7#B7 @3 .K .;F 7--#E7 @3 .K .;F
7#AF7
.K --#C7#B7 @+ #A3 .K --#C7--#E7 @+
#A3 .K --#C7#AF7 @+ #A
.K --#E3 .K #AF3 .K--#DG
,! F/ ?REE IT]ATES >E --#E1 #AF1 &
--#DG4
..,GUID$ ,PRACTICE = ,EXAMPLE .#E
,F9D ! F/ ?REE IT]ATES (! FUNC;N =!
GIV5 9ITIAL VALUE4
.#AA4 .;F7.;X7 .K #D .;X -- #C1 .;X #J
.K #B
.#AB4 .;F7.;X7 .K .;X #B -- #E1 .;X #J
.K --#A
#AB.E ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS P4 ,,WS#BA =
,EXS4 #AE1 #BG1 & #DE
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE ,EXS4
.#B1.AB1.CC1.DJ1.DE1 .& .#DG
,SKILL ,PRACTICE
#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,!
REP1T$ -POSI;N (A FUNC;N ) XF IS CALL$ -
@8 - @4
#B4 99 .,,WRIT+ .,EXPLA9 ! DI6];E 2T
AN EXPLICIT RULE =A SEQU;E &A RECURSIVE
RULE =A SEQU;E4
.,,EXAMPLE .#A ON P4 #HBG = ,EXS4
#C-AB
,,WRIT+ ,,T]MS ,WRITE ! F/ FIVE T]MS
(! SEQU;E4
.#C4 .A #A .K #A
.A ;N .K .A .;N -- #A @+ #C
#D4 .A #J .K #D
A ;N .K #B;A ;N--#A
.#E4 .A #A .K --#A
.A ;N.' .K .A .;N -- #A -- #E
.#F4 .A #J .K #C
.A ;N .K .A .;N -- #A -- .;N #B
.#G4 .A #A .K #B
.A ;N .K @7 .A .;N -- #A @7 #B @+ #A
.#H4 .A #J .K #D
.A ;N .K .A @7 .;N -- #A @7 #B -- #AJ
.#I4 .A #A .K #B
.A ;N .K .;N #B @+ #C .;N -- .A .;N --
#A
.#AJ4 .A #J .K #B .A #A .K #D
.A ;N .K .A .;N -- #A -- .A .;N -- #B
.#AA4 .A #A .K #B1 .A #B .K #C
.A ;N .K .A .;N -- #A @* .A .;N -- #B
#AB4 99 .,,MULTIPLE .,,*OICE ,:AT >E !
F/ F\R T]MS (! SEQU;E = : .A #A .K .;L1
.A #B .K .#D,.& .A ;N.' .K .A .;N -- #A
@* .A .;N #G--#B @8
,A #A1 #D1 #D1 #AF
;,B #A1 #D1 #AF1 #FD
;,C #A1 #D1 #H1 #AF
;,D #A1 #D1 #D1 #H
------------------------------------#HCA
..,,EXAMPLES #B & .#C ON P4 #HBH =
,EXS4 #AC-BC
,,WRIT+ ,,RULES ,WRITE A RECURSIVE
RULE =! SEQU;E4 ,! SEQU;E MAY 2
>I?METIC1 GEOMETRIC1 OR NEI4
.#AC4 #BA1 #AD1 #G1 #J1 --#G1 '
.#AD4 #C1 #AB1 #DH1 #AIB1 #GFH1 '
.;L#E4 #D1 --#AB1 #CF1 --#AJH1 #CBD1 '
.#AF4 #A1 #H1 #AE1 #BB1 #BI1 '
.#AG4
.#AH4 #A1 #D1 #E1 #I1 #AD1 '
.#AI4 #ED1 #DC1 #CB1 #BA1 #AJ1 '
.#BJ4 #C1 #E1 #AE1 #GE1 #AABE1 '
.#BA4 #AF1 #I1 #G1 #B1 #E1 '
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 WRIT+ A RECURSIVE RULE =!
SEQU;E #E1 #B1 #C1 --#A1 #D1'4
.#BB4 ,2G9N+ )! ?IRD T]M 9 ! SEQU;E1
EA* T]M A ;N EQUALS A ;N .K A ;N-#B -- A
;N-#A ,S A RECURSIVE RULE IS GIV5 BY3 .A
;N .K .A ;N--#B -- .A ;N--#A
.#BC4 ,2G9N+ )! SECOND T]M 9 ! SEQU;E1
EA* T]M A ;N IS A ;N _ #A -- #C4 ,S A
.RECURSIVE RULE IS GIV5 BY3 A #A .K #E1
A ;N .K A ;N--#A -- #C
.,,EXAMPLE .#E ON P4 #HCJ = ,EXS4
#BD-CC
,,IT]AT+ ,,FUNC;NS ,F9D ! F/ ?REE
IT]ATES (! FUNC;N =! GIV5 9ITIAL VALUE4
.#BD4 .;F @7 .;X @7 .K #C .;X -- #B1
.;X #J .K #B
.#BE4 .FIX7 .K #E .;X @+ #F1 ;X ;,Q .K
--#B
.#BF4 ;G7;X7 .K --#D .;X @+ #G1 ;X #J
.K #A
.#BG4
.#BH4
.#BI4 .;H @7 .;X @7 .K .;X #B -- #D1
.;X ;,Q .K --#C
.#CJ4 .;F7.;X7 .K #B .;X #B @+ #A1 ;X
#J .K --#A
.#CA4 .;F7.;X7 .K .;X #B -- .;X @+ #B1
;X #J .K #A
.#CB4 ;G7;X7 .K --#C .;X #B @+ #B .;X
@1 ;X #J .K #B
#CC4 99 .,,MULTIPLE .,,*OICE ,:AT >E !
F/ ?REE IT]ATES ;X #A @1 ;X #B @1 & ;X
#C (! FUNC;N .;F7.;X7 .K --#B .;X @+ #C
= AN 9ITIAL VALUE ( ;X #J .K #B8
,A --#A1 #A1 #C
;,B #A1 --#E1 #G
;,C --#A1 #E1 --#G
;,D #A1 --#A1 --#C
,,WRIT+ ,,RULES ,WRITE A RECURSIVE
RULE =! SEQU;E4
.#CD4 #C1 #H1 #AG1 #HA1 #CGJ1 '
.#CE4 #A1 #B1 #AB1 #EF1 #BGB1 '
.#CF4
.#CG4 #B1 #E1 #AA1 #BF1 #EI1 '
.#CH4 #H1 #D1 #B1 #B1 #A1 '
.#CI4 --#C1 --#B1 #E1 --#C1 --#B1 '
..#DJ4 99 ,,OP5-,,5D$ .,,MA? ,GIVE AN
EXAMPLE (A SEQU;E 9 : EA* T]M AF ! ?IRD
T]M IS A FUNC;N (! ?REE T]MS PREC$+ X4
,WRITE A RECURSIVE RULE =! SEQU;E & F9D
XS F/ EI<T T]MS4
.#DA4 .,,R1SON+ .,EXPLA9 :Y "! >E N A
FUNC;N .;F & AN 9ITIAL VALUE .;X #J S* T
! FUNC;N'S F/ ?REE IT]ATES >E .;X #A --
#B1 ;X #B .K #B1 & ;X #C .K #H4
#DB4 .,,*ALL5GE ,Y C DEF9E A SEQU;E
US+ A PIECEWISE RULE4 ,! FOLL[+ IS AN
EXAMPLE (A PIECEWISE-DEF9$ SEQU;E4
A4 ,WRITE ! F/ T5 T]MS (! SEQU;E4
B4 ,*OOSE ?REE DI6]5T POSITIVE 9TEG]
VALUES = .A #A 7O!R ?AN .A #A .K #E74 ,=
EA* VALUE ( .A #A F9D ! F/ T5 T]MS (!
SEQU;E4 ,:AT 3CLU.NS C Y MAKE AB !
2HAVIOR ( ? SEQU;E ( 9TEG]S8
------------------------------------#HCB
,,PRO#M ,,SOLV+
.,,EXAMPLE .#D ON P4 #HBI = ,EXS4
#DC-DE
#DC4 .,,FI% .,,POPUL,N ,A LAKE 9ITI,Y
3TA9S #EJJJ FI%4 ,EA* YE> ! POPUL,N
DECL9ES #BJ@3P DUE 6FI%+ & O!R CAUSES1
&! LAKE IS RE/OCK$ ) #EJJ FI%4
A4 ,WRITE A RECURSIVE RULE =! NUMB] .A
;N.' .-( FI% AT ! 2G9N+ (! N? YE>4 ,H[
_M FI% >E "! AT ! 2G9N+ (! #E? YE>8
B4 ,:AT HAPP5S 6! POPUL,N ( FI% 9 !
LAKE OV] "T8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
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#DD4 .,,POOL .,,C>E ,Y >E A4+ *LOR9E
6A SWIMM+ POOL4 ,Y ADD #CD \NCES (
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POOL EVAPORATES4 ,WRITE A RECURSIVE RULE
=! AM.T ( *LOR9E 9 ! POOL EA* WEEK4 ,:AT
HAPP5S 6! AM.T ( *LOR9E 9 ! POOL OV] "T8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
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#DE4 .,,%ORT .,,RESPONSE ,GLADYS [ES
4#BJJJ 6A CR$IT C>D -PANY T *>GES 9T]E/
AT A RATE ( #A.D@3P P] MON?4 ,AT ! 5D (
EA* MON? %E MAKES A PAY;T ( 4#AJJ4
,WRITE A RECURSIVE RULE =! BAL.E .A ;N.'
.-(! A3.T AT ! 2G9N+ (! N? MON?4 ,H[ L;G
W X TAKE 6PAY (F ! A3.T8 .,EXPLA9 YR
R1SON+4
#DF4 .,,FIBONA3I .,,SEQU;E ,!
,FIBONA3I SEQU;E1 : IS DEF9$ RECURSIVELY
9 ,EXAMPLE #C ON PAGE #HBH @1 O3URS _M
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#DG4 99 .,,EXT5D$ .,,RESPONSE ,A P]SON
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(! DRUG IS REMOV$ F ! BLOOD/R1M E #D
H\RS4
A4 ,WRITE A RECURSIVE RULE =! AM.T (!
DRUG 9 ! BLOOD/R1M AF .;N DOSES4
B4 ,! VALUE T A DRUG LEVEL 9 A P]SON'S
BODY APPROA*ES AF AN EXT5D$ P]IOD ( "T
IS CALL$ ! .MA9T5.E .LEVEL4 ,:AT IS !
MA9T5.E LEVEL ( ? DRUG1 GIV5 A DOSAGE (
#BJ MILLIGRAMS8
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MA9T5.E LEVEL (! DRUG8 .,JU/IFY YR ANSW]
MA!MATIC,Y4
.K .,,"W$-.,,\ .,,SOLU;NS ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#HCC
#DH4 .,,*ALL5GE ,Y >E SAV+ M"OY =
RETIRE;T4 ,Y PLAN 6)DRAW 4#CJ1JJJ AT !
2G9N+ ( EA* YE> = #BJ YE>S AF Y RETIRE4
,BAS$ ON ! TYPE ( 9VE/;T Y >E MAK+1 Y C
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YR SAV+S AF Y RETIRE4
A4 ,LET .A ;N.' .-2 YR BAL.E .;N YE>S
AF RETIR+4 ,WRITE A RECURSIVE EQU,N T
%[S H[ .A ;N.' .-IS RELAT$ 6A ;N-#A @4
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#A ,F9D .A #J @1 ! M9IMUM AM.T ( M"OY Y
%D H 9 YR A3.T :5 Y RETIRE4 7.,H9T3 ,LET
.A #BJ .K #J47
,MIX$ ,REVIEW
.,,PREVIEW ,PREP>E = ,LESSON #AC.A 9
,EXS4 #DI-EA4
,F9D ! VALUE ( .X4 @7 P4 #IIE @7
#DI4
#EJ4
#EA4
,EVALUATE ! EXPRES.N )\T US+ A
CALCULATOR4 @7 P4 #DAD @7
#EB4 #AF #C/B
#DI4 7--#BDC7 #B/E
#DI4 #FD --#A/B
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.#A4
.#B4
.#C4
,WRITE ! REP1T+ DECIMAL Z A FRAC;N 9
L[E/ T]MS1 @7 P4 #HBJ @7
#D4 #J.GGG'''
#E4 #J.CICICI'''
#F4 #ABC.ABCABC'''
,WRITE ! F/ FIVE T]MS (! SEQU;E1 @7 P4
#HBG @7
#G4 .A #A .K .#B
.A ;N .K .A ;N- #A @+ #D
#H4 .A #J .K #C
.A ;N .K @7 .A ;N-#A @7 #B -- .#E
.#I4 .A #A .K #A1 .A #B .K #D
A ;N .K .A ;N--#A - .A ;N-#B
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SEQU;E MAY 2 >I?METIC1 GEOMETRIC1 OR
NEI4 @7 P4 #HBG @7
.#AJ4
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GIV5 9ITIAL VALUE1 @7 P4 #HBG @7
.#AC4 .;F @7 .;X @7 .K --..#C .;X --
#B1 ;X #J .K #A
.#AD4 .;G @7 .;X @7 .K .#D .;X @+ #A1
.;X #J .K .#B
.#AE4 .;F @7 .;X @7 .K --.#B .;X @+
#C1 .;X #J .K --.#B
.#AF4 .;F @7 .;X @7 .K ..#E ;X--#G1
.;X ;O .K --#C
.#AG4 .;H @7 .;X @7 .K .;X #B -- #F1
.;X #J .K --#A
.#AH4 .;F @7 .;X @7 .K .#C .;X #B @+
#B1 .;X #J .K #J
.#AI..,,P5DULUMS ,A P5DULUM T IS
REL1S$ 6SW+ FREELY TRAVELS #BE 9*ES ON !
F/ SW+4 ,ON EA* SU3ESSIVE SW+1 ! P5DULUM
TRAVELS #HE@3P Z F> Z ! PREVI\S SW+4
,:AT IS ! TOTAL 4T.E ! P5DULUM SW+S8 @7
P4 #HBJ @7
.,,EXTRA .,,PRACTICE = ,LESSON #AB.E1
P4 #AJBA
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#HCD
,PRO#M ,SOLV+ ,"W%OP ,LESSON #AB.E3
,US+ ,ALT]NATIVE ,ME?ODS
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PAGE #HBI
.,,MULTIPLE .,,REPRES5T,NS ,9 ,EXAMPLE
#D ON PAGE #HBI @1 Y F.D ! NUMB]4 T A
R1L-LIFE SEQU;E APPROA*ES OV] "T 0US+ A
CALCULATOR 6EVALUATE ! RULE =! SEQU;E4
,Y C AL SOLVE ? PRO#M US+ A GRAPH OR AN
ALGEBRAIC ME?OD4
,PRO#M
.,,MUSIC .,,S]VICE ,AN ONL9E MUSIC
S]VICE 9ITI,Y HAS #EJ1JJJ ANNUAL MEMB]S4
,EA* YE> ! MUSIC S]VICE LOSES #BJ@3P (
XS CURR5T MEMB]S & A4S #EJJJ NEW MEMB]S4
,:AT HAPP5S 6! NUMB] ( MEMB]S OV] "T8
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NUMB] .A ;N.' .-( MEMB]S AT ! 2G9N+ (!
N? YE> IS .A #A .K #EJ1JJJ1 .A ;N .K
.#J..H;A ;N _ #A @+ #EJJJ4 ,"O
ALT]NATIVE ME?OD = F9D+ ! NUMB] ? SEQU;E
APPROA*ES IS 6GRAPH ! SEQU;E ON A GRAPH+
CALCULATOR4
,SIDEB>3
,/&>DS
#BB.J ,/UD5TS F9D ! G5]AL T]M &! SUMS
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GEOMETRIC S]IES4
.,,/EP .#A .,SET ! CALCULATOR 6.SEQU;E
MODE & .DOT .MODE4
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,M9 .K #A1 .;U @7 .;N @7 .K .#J..H;U @7
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,! FOLL[+ TA# IS 9 LI/$
=MAT4 ,= EA* CELL ! H1D+ IS %[N
FOLL[$ 0A COLON1 SPACE &! CELL
3T5TS
.;N ,M9 .K #A @3 .;N ,MAX .K #AJJ
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.;N ,M9 .K #A @3 ,PLOT,/>T .K #A
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.;N ,M9 .K #A @3 ,PLOT,/EP .K #A
,XM9 .K #J3 ,PLOT,/EP .K #A
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.,,/EP .#C .,GRAPH ! SEQU;E4 ,USE !
.TRACE F1TURE 6F9D ! VALUE T ! SEQU;E
APPROA*ES Z .;N 2COMES L>GE4 ,F ! GRAPH1
Y C SEE T ! SEQU;E APPROA*ES #BE1JJJ4
,OV] "T1 ! NUMB] ( MEMB]S (! MUSIC
S]VICE APPROA*ES #BE1JJJ4
------------------------------------#HCE
,ME?OD #B
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6! NUMB] ( MEMB]S OV] "T4
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;N--#A @+ #EJJJ4
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LIMIT ;,L1 : IS ! VALUE T ! SEQU;E
APPROA*ES Z .;N 2COMES L>GE4
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3TA9 TWO DA%ES4
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0#J.B4
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NUMB] ( MEMB]S (! MUSIC S]VICE APPROA*ES
#BE1JJJ4
,PRACTICE
.,DESCRIBE .:AT HAPP5S 6! T]MS (!
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.#A4 .A #A .K #CJJJ1 .A ;N .K
.#J..BE;A ;N.' _ #A @+ #CJJ
.#B4 .A #A .K #AGJJ1 .A ;N .K
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MUSIC S]VICE 9 ! PRO#M ON PAGE #HCD
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.#D4 .,,T[N .,,LIBR>Y ,A T[N LIBR>Y
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6! NUMB] ( BOOKS 9 ! LIBR>Y OV] "T4
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%[N 2L4 .,DESCRIBE & CORRECT ! ]ROR 9 !
/UD5T'S "W4
A #A .K #ED1JJJ1 A ;N .K #J.JB;A ;N _
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SEQU;E4 ,!N3
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#AAEJ ;,L--#AAGC
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LIBR>Y .APPROA*ES .AB #AAGC4
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R1L-LIFE SITU,N : Y C REPRES5T )A
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,WRITE A RECURSIVE RULE T REPRES5TS !
SITU,N4
------------------------------------#HCF
,EXT5.N ,PROVE ,/ATE;TS ,US+
,MA!MATICAL ,9DUC;N
,USE AF LESSON #AB.E
,SIDEB>3
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#BA.J ,/UD5TS APPLY ! ME?OD (
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= .;N .K #A4
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POSITIVE 9TEG]4 ,%[ T ? IMPLIES ! /ATE;T
IS TRUE = .;N .K .;K @+ #A4
,,EXAMPLE #A ,USE MA!MATICAL 9DUC;N
,USE MA!MATICAL 9DUC;N 6PROVE T
,SOLU;N
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.;N .K #A4
.,9DUCTIVE .,/EP3 ,ASSUME T
,"!=E1 = ALL POSITIVE 9TEG]S .;N @4
------------------------------------#HCG
.,,EXAMPLE ,USE MA!MATICAL 9DUC;N
,LET .A ;N.' .K .#E;A ;N _ #A @+ #B )
.A #A .K #B4 ,USE MA!MATICAL 9DUC;N
6PROVE T AN EXPLICIT RULE =! N? T]M IS
,SOLU;N
.,BASIS .,/EP3 ,*ECK T ! =MULA "WS =
.;N .K #A4
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,"!=E1 AN EXPLICIT RULE =! .;N TH T]M
IS = ALL POSITIVE 9TEG]S .N4
,PRACTICE
,,EXAMPLES #A & #B
ON PP4 #HCF-HCG = ,EXS4 #A-H
,USE MA!MATICAL 9DUC;N 6PROVE !
/ATE;T4
.#A4
.#B4
.#C4
.#D4
.#E4
.#F4
.#G4 .,,GEOMETRY ,! NUMB]S #A1 #F1
#AE1 #BH1' >E CALL$ .HEXAGONAL .NUMB]S
2C !Y REPRES5T ! NUMB]S ( DOTS US$ 6MAKE
HEXAGONS1 Z %[N 2L4 ,PROVE T ! .N?
HEXAGONAL NUMB] .;,H ;N.' .-IS GIV5
0.;,H ;N.' .K .;N7.#B;N -- #A74
.#H4 .,,R1SON+ ,LET .;F#A1
.;F#B1',.FN144 .2 ! ,FIBONA3I SEQU;E4
,PROVE T ..;F#A @+ ;F#B @+' @+FN .K ;F
.;N@+#B -- #A =A#AA ,POSITIVE 9TEG]S .;N
@4
------------------------------------#HCH
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,LESSONS #AB.D-AB.E
#A4 .,,MULTI-.,,/EP .,,PRO#M ,A BALL
IS DROPP$ F A HEI<T ( #AB FEET4 ,EA* "T
! BALL HITS ! GR.D1 X B\NCES 6#GJ@3P (
XS PREVI\S HEI<T4
A4 ,WRITE AN 9F9ITE S]IES 6MODEL !
TOTAL 4T.E TRAVEL$ 0! BALL1 EXCLUD+ !
4T.E TRAVEL$ 2F ! F/ B\NCE4
B4 ,F9D ! TOTAL 4T.E TRAVEL$ 0! BALL1
9CLUD+ ! 4T.E TRAVEL$ 2F ! F/ B\NCE4
#B4 .,,MULTI-.,,/EP .,,PRO#M ,A
FRACTAL TREE />TS )A S+LE BRAN* 7!
TRUNK74 ,AT EA* /AGE1 ! NEW BRAN*ES F !
PREVI\S /AGE EA* GR[ TWO M BRAN*ES Z
%[N4
A4 ,LI/ ! NUMB] ( .NEW BRAN*ES 9 EA*
(! F/ SIX /AGES4
B4 ,IS ! SEQU;E ( NUMB]S F "P 7A7
.>I?METIC1 .GEOMETRIC @1 OR .NEI84
C4 ,WRITE AN EXPLICIT RULE &A
RECURSIVE RULE =! SEQU;E F "P 7A74
#C4 .,,GRI4$ .,,ANSW] ,:AT IS ! SUM (!
F/ ?REE IT]ATES (! FUNCTION_/7;X7 .K .;X
#B -- #H :5 ! 9ITIAL VALUE IS .;X #J .K
#B8
#D4 .,,OP5-.,,5D$ ,GIVE AN EXAMPLE (
AN EXPLICIT RULE =A SEQU;E &A RECURSIVE
RULE =! SAME SEQU;E4
#E4 .,,%ORT .,,RESPONSE ,:Y DOES ! SUM
( AN 9F9ITE GEOMETRIC S]IES N EXI/ IF _\
.;R _\ .1.K #A ": .;R IS ! -MON RATIO8
#F4 .,,%ORT .,,RESPONSE ,! L5G? .;L #A
(! F/ LOOP (A SPR+ IS #AF 9*ES4 ,! L5G?
.;L #B (! SECOND LOOP IS #J.I "TS ! L5G?
(! F/ LOOP4 ,! L5G? .;L #C (! ?IRD LOOP
IS #J.I "TS ! L5G? (! SECOND LOOP1 & S
ON4 ,IF ! SPR+ CD H 9F9ITELY _M LOOPS1
WD XS L5G? .2 .F9ITE OR .9F9ITE8
.,EXPLA94 ,IF XS L5G? IS F9ITE1 F9D !
L5G?4
#G4 .,,EXT5D$ .,,RESPONSE ,Y TAKE \ A
FIVE YE> LOAN ( 4#AJ1JJJ 6BUY A C>4 ,!
LOAN HAS AN ANNUAL 9T]E/ RATE ( #F.E@3P
-P.D$ MON?LY4 ,EA* MON? Y MAKE A MON?LY
PAY;T ( 4#AIF 7EXCEPT ! LA/ MON? :5 Y
MAKE A PAY;T ( ONLY 4#AFE74
A4 ,F9D ! MON?LY 9T]E/ RATE4 ,!N WRITE
A RECURSIVE RULE =! AM.T ( M"OY Y [E AF
;N MON?S4
B4 ,H[ M* M"OY D Y [E AF #AB MON?S8
C4 ,SUPPOSE Y _H DECID$ 6PAY AN
A4I;NAL 4#EJ ) EA* MON?LY PAY;T4 ,USE A
GRAPH+ CALCULATOR 6F9D ! NUMB] ( MON?S Y
WD H NE$$ 6REPAY ! LOAN4
D4 ,9 YR OP9ION1 IS X B5EFICIAL 6PAY !
A4I;NAL 4#EJ ) EA* PAY;T8 .,EXPLA9 YR
R1SON+4
#H4 .,,GRI4$ .,,ANSW] ,A TREE F>M
9ITI,Y HAS #HJJJ TREES4 ,EA* YE> #AJ@3P
(! TREES >E H>VE/$ & #EJJ SE$L+S >E
PLANT$4 ,:AT NUMB] ( TREES EV5TU,Y EXI/S
ON ! F>M AF AN EXT5D$ P]IOD ( "T8
#I4 .,,OP5-.,,5D$ ,WRITE AN 9F9ITE
GEOMETRIC S]IES T HAS A SUM ( #D4
------------------------------------#HCI
#AB ,*APT] ,SUMM>Y
,,BIG ,,ID1S ,= ,YR ,NOTEBOOK
.,BIG .,IDEA .#A ,ANALYZE ,SEQU;ES
,! 9=M,N 2L HI<LI<TS ! SIMIL>ITIES &
DI6];ES 2T >I?METIC & GEOMETRIC SEQU;ES4
,PICTURE3 .,>I?METIC .,SEQU;E
.A ;N .K .A #A @+7.;N-- #A7 .;D
,F/ T]M3 .A #A
,-MON DI6];E3 .;D
,GRAPH IS L9E>4
,PICTURE3 .,GEOMETRIC .,SEQU;E
.A ;N.' .K .A #A .;R @7 .;N -- #A7
,F/ T]M3 .A #A
,-MON RATIO3 .;R
,GRAPH IS EXPON5TIAL4
.,BIG .,IDEA .#B ,F9D ,SUMS ( ,S]IES
,! MO/ -MON =MULAS = SUMS ( S]IES >E
%[N 2L4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,>I?METIC ,S]IES3 ,GEOMETRIC ,S]IES3
,9F9ITE ,GEOMETRIC ,S]IES
,SUM (! F/ .;N T]MS3 @3 ,SUM (! F/ .;N
T]MS3 @3 ,SUM (! S]IES3
@3 @3
_+EXAMPLE::_: _+EXAMPLE::_: ,EXAMPLE3
#D @+ #I @+ #AD @+ #AI @+ #BD3 #C @+
#F @+ #AB @+ #BD3 #E @+ #A @+ #J.B @+
#J.JD @+ '''
@3 @3
,O!R -MON SUM =MULAS3
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
@3 @3
.,BIG .,IDEA .#C ,USE ,RECURSIVE
,RULES
,! TA# %[S EXPLICIT & RECURSIVE RULES
= >I?METIC & GEOMETRIC SEQU;ES4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 ,EXPLICIT ,RULE3 ,RECURSIVE ,RULE
.,>I?METIC .,SEQU;E
,EXAMPLE3 #C1 #E1 #G1 #I1AA1''' @3 A.'
;N.' .K A.' #A @+ @7 .;N -- #A7 .;D
.A .;N .K #A @+ #B .;N @3 A.' ;N.' .K
A.' .;N -- #A @+ .;D
.A #A .K #C1 .A .;N .K .A .;N -- #A @+
#B
.,GEOMETRIC .,SEQU;E
,EXAMPLE3 #H1 #D1 #B1A1 #J.E1''' @3 A.'
;N.' .K A.' #A ;R.' ;N--#A
A.' ;N.' .K #H7#J.E7 ;N--#A @3 .A .;N .K
.;R @* A.' ;N--#A
A.' #A .K #H,A.' ;N.' .K #J.E;A.' ;N--#A
------------------------------------#HDJ
#AB ,*APT] ,REVIEW
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
99 ,MULTI-,LANGUAGE ,GLOSS>Y
99 ,VOCABUL>Y PRACTICE
,,REVIEW ,,KEY ,,VOCABUL>Y
99 SEQU;E1 P4 #GID
99 T]MS (A SEQU;E1 P4 #GID
99 S]IES1 P4 .#GIF
99 SUMM,N NOT,N1 P4 .#GIF
99 SIGMA NOT,N1 P4 .#GIF
99 >I?METIC SEQU;E1 P4 .#HJB
99 -MON DI6];E1 P4 #HJB
99 >I?METIC S]IES1 P4 .#HJD
99 GEOMETRIC SEQU;E1 P4 .#HAJ
99 -MON RATIO1 P4 #HAJ
99 GEOMETRIC S]IES1 P4 #HAB
99 "PIAL SUM1 P4 #HBJ
99 EXPLICIT RULE1 P4 #HBG
99 RECURSIVE RULE1 P4 .#HBG
99 IT],N1 P4 .#HCJ
,VOCABUL>Y ,EX]CISES
#A4 ,COPY & -PLETE3 ,! VALUES 9 !
RANGE (A SEQU;E >E CALL$ ! @8 (! SEQU;E4
@8
#B4 .,,WRIT+ ,H[ C Y DET]M9E :E!R A
SEQU;E IS >I?METIC8
#C4 ,COPY & -PLETE3 ,A7;N7 @8 RULE
GIVES .A ;N.' .-Z A FUNC;N (! T]M'S
POSI;N NUMB] .;N 9 ! SEQU;E4
#D4 ,COPY & -PLETE3 ,9 A7;N7 @8
SEQU;E1 ! RATIO ( ANY T]M 6! PREVI\S T]M
IS 3/ANT4
,,REVIEW ,,EXAMPLES ,,& ,,EX]CISES
,USE ! REVIEW EXAMPLES & EX]CISES 2L
6*ECK YR "U/&+ (! 3CEPTS Y H LE>N$ 9 EA*
LESSON ( ,*APT] #AB4
#AB.A ,DEF9E & ,USE ,SEQU;ES & ,S]IES
PP4 #GID-HJJ
,EXAMPLE
,F9D ! SUM (! S]IES @4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
A.' #A .K #A #B -- #D .K --#C @3 .,F/
.T]M
A.' #B .K #B #B -- #D .K #J @3
.,SECOND .T]M
A.' #C .K #C #B -- #D .K #E @3 .,?IRD
.T]M
A.' #D .K #D #B -- #D .K #AB @3 .,F\R?
.T]M
,! SUM (! S]IES IS @4
,,EX]CISES
,F9D ! SUM (! S]IES4
,,EXAMPLES #E & #F
ON P4 #GIG = ,EXS4 #E-H
.#E4
.#F4
.#G4
.#H4
------------------------------------#HDA
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,*APT] ,REVIEW ,PRACTICE
#AB.B ,ANALYZE ,>I?METIC ,SEQU;ES &
,S]IES
PP4 #HJB-HJI
,,EXAMPLE
,WRITE A RULE =! N? T]M (! SEQU;E
#I1AC1AG1 #BA1 #BE1'4
,! SEQU;E IS >I?METIC ) F/ T]M .A #A
.K #I & -MON DI6];E .;D .K #D4 ,S1 A
RULE =! .N? T]M IS3
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
A.' ;N.' .K A.' #A @+ 7;N--#A7;D.' @3
.,WRITE .G5]AL .RULE4
.K #I @+ @7 .;N -- #A77#D7 @3
,SUB/ITUTE #I =.' A.' #A & #D =.' D4.-
.K #E @+ .,AN @3 .,SIMPLIFY4
,,EX]CISES
,,EXAMPLES #B1 #C1 #D1 & #E
ON PP4 #HJC-HJE = ,EXS4 #I-AF
,WRITE A RULE =! .;N TH T]M (!
>I?METIC SEQU;E4
.#I4 #H1 #E1 #B1 --#A1 --#D1'
.#AJ4 .;D .K #G1 .A #H .K #ED
.#AA4 .A #D .K #BG1 .A #AA .K #FI
,F9D ! SUM (! S]IES4
.#AB4
.#AC4
.#AD4
.#AE4
.#AF4 .,,-PUT] ,JOE BUYS A 4#FJJ -PUT]
ON LAYAWAY 0MAK+ A 4#BJJ D[N PAY;T & !N
PAY+ 4#BE P] MON?4 ,WRITE A RULE =!
TOTAL AM.T ( M"OY PD ON ! -PUT] AF .;N
MON?S4
#AB.C ,ANALYZE ,GEOMETRIC ,SEQU;ES &
,S]IES
PP4 #HAJ-HAG
,EXAMPLE
,F9D ! SUM (! S]IES @4
,! S]IES IS GEOMETRIC ) F/ T]M .A #A
.K #E & -MON RATIO .;R .K #C4
,,EX]CISES
..,,EXAMPLES #B1 #C1 #D1 & .#E ON PP4
#HAA-HAC = ,EXS4 #AG-BC
,WRITE A RULE =! .N? T]M (! GEOMETRIC
SEQU;E4
.#AG4 #BEF1 #FD1 #AF1 #D1 #A1 '
.#AH4 .;R .K #E1 .A #B .K #BJJ
.#AI4 .A #A .K #ADD1 .A #C .K #AF
,F9D ! SUM (! S]IES4
.#BJ4
.#BA4
.#BB4
.#BC4
------------------------------------#HDB
#AB ,,*APT] ,,REVIEW
#AB.D ,F9D ,SUMS ( ,9F9ITE ,GEOMETRIC
,S]IES
PP4 #HBJ-HBE
,EXAMPLE
,F9D ! SUM (! S]IES @1 IF X EXI/S4
,= ? S]IES1 .A #A .K #A & @4 ,2C _\
.;R _\ "K #A1 ! SUM ( ? S]IES EXI/S4
,! SUM IS @4
,,EX]CISES
..,,EXAMPLES #B & .#E ON PP4 #HBA-HBB
= ,EXS4 #BD-CA
,F9D ! SUM (! 9F9ITE GEOMETRIC S]IES1
IF X EXI/S4
.#BD4
.#BE4
.#BF4
.#BG4
,WRITE ! REP1T+ DECIMAL Z A FRAC;N 9
L[E/ T]MS4
.#BH4 #J.HHH'''
.#BI4 #J.EDFEDFEDF'''
.#CJ4 #J.CGHGHGH'''
.#CA4 #J.GHCHCHC'''
.#AB..E ,USE ,RECURSIVE ,RULES )
,SEQU;ES & ,FUNC;NS PP4 #HBG-HCC
,EXAMPLE
..,WRITE A RECURSIVE RULE =! SEQU;E
#F1 #AJ1 #AD1 #AH1 .#BB @1'@4
,! SEQU;E IS >I?METIC ) F/ T]M .A #A
.K #F & -MON DI6];E .;D .K #AJ--#F .K
#D4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.A .;N -- #A @+ .;D @3 ,G5]AL
RECURSIVE RULE = A.' ;N.'.-
.K .A .;N -- #A @+ #D @3 ,SUB/ITUTE #D
= .D4
,S1 A RECURSIVE RULE =! SEQU;E IS .A
#A .K #F1 .A ;N.' .K .A .;N -- #A @+ #D4
,,EX]CISES
..,,EXAMPLES #A1 #B1 & .#C ON PP4
#HBG-HBH = ,EXS4 #CB-CH
,WRITE ! F/ FIVE T]MS (! SEQU;E4
.#CB4 .A #A .K #D1 .A ;N.' .K .A .;N
-- #A @+ #I
.#CC4 .A #A .K #H1 .A ;N.' .K #E .A
.;N -- #A
.#CD4 .A #A .K #B1 A ;N .K .;N @* .A
.;N -- #A
,WRITE A RECURSIVE RULE =! SEQU;E4
.#CE4 #F1 #AH1 #ED1 #AFB1 #DHF1 '
.#CF4 #D1 #F1 #I1 #AC1 #AH1 '
.#CG4 #G1 #AC1 #AI1 #BE1 #CA1'
.#CH4 .,,POPUL,N ,A T[N'S POPUL,N
9CR1SES AT A RATE ( AB #A@3P P] YE>4 ,9
#BJJJ1 ! T[N _H A POPUL,N ( #BF1JJJ4
,WRITE A RECURSIVE RULE =! T[N'S POPUL,N
.;,P ;N.' .-9 YE> .N4 ,LET .;N .K #A
REPRES5T #BJJJ4
------------------------------------#HDC
#AB ,*APT] ,TE/
,TELL :E!R ! SEQU;E IS .>I?METIC1
.GEOMETRIC @1 OR .NEI4 .,EXPLA94
.#A4 #E1 #I1 #AC1 #AG1'
.#B4 #C1 #F1 #AB1 #BD1'
.#C4
.#D4 #D1 #G1 #AB1 #AI1 '
,WRITE ! F/ SIX T]MS (! SEQU;E4
.#E4 .A ;N.' .K #F -- .;N #B
.#F4 .A ;N .K #G .;N #C
.#G4 .A #A .K #D
.A ;N .K #E .A .;N -- #A
.#H4 .A #A .K--#A
.A .;N -- #A @+ #F
,WRITE ! NEXT T]M (! SEQU;E1 & !N
WRITE A RULE =! .;N TH T]M4
.#I4 #E1 #AA1 #AG1 #BC1 '
.#AJ4 #C1 #AE1 #GE1 #CGE1 '
.#AA4
.#AB4 #A.F1 #C.B1 #D.H1 #F.D1 '
,F9D ! SUM (! S]IES4
.#AC4
.#AD4
.#AE4
.#AF4
.#AG4
.#AH4
.#AI4
.#BJ4
,WRITE ! REP1T+ DECIMAL Z A FRAC;N 9
L[E/ T]MS4
.#BA4 #J.AAA'''
.#BB4 #J.DFDFDF'''
.#BC4 #J.AHGAHGAHG'''
.#BD4 #J.CBEBEBE'''
,WRITE A RECURSIVE RULE =! SEQU;E4
.#BE4 #B1 #AB1 #GB1 #DCB1 '
.#BF4 #C1 #AJ1 #AG1 #BD1 '
.#BG4 #ACE1 #DE1 #AE1 #E1 '
.#BH4 #A1 --#C1 #I1 --#BG1 '
,F9D ! F/ ?REE IT]ATES (! FUNC;N =!
GIV5 9ITIAL VALUE4
.#BI4 .;F @7 .;X @7 .K #C .;X -- #G1
.;X #J .K #D
.#CJ4 .;F @7 .;X @7 .K #H--#E .;X1 .;X
#J .K #A
.#CA4 .;F @7 .;X @7 .K .;X #B @+ #B1
.;X #J .K --#A
#CB4 .,,QUILTS ,USE ! PATT]N (
*ECK]BO>D QUILTS %[N4 ,PRODNOTE3
,PRODUC;N NOTE3 CAP;NS ASSOCIAT$ ) ?
IMAGE >E LABELS T CORRESPOND 6TEXT )9 !
IMAGE4
,PICTURE3 ..;N .K #A1 .A ;N .K .#A
,PICTURE3 ..;N .K #B1 .A ;N .K .#B
,PICTURE3 ..;N .K #C1 .A ;N .K .#E
,PICTURE3 ..;N .K #D1 .A ;N .K .#H
A4 ,:AT DOES .;N REPRES5T = EA* QUILT8
,:AT DOES .A ;N.' .-REPRES5T8
B4 ,MAKE A TA# T %[S .;N &A ;N = .;N
.K #A1 #B1 #C1 #D1 #E1 #F1 #G1 & #H4
C4 ,USE ! RULE 6F9D .A = .;N .K .#A @1
#B1 #C1 #D1 #E1 #F1 #G1 & #H4 .,-P>E ^!
VALUES )! RESULTS 9 YR TA#4 ,:AT C Y
3CLUDE AB ! SEQU;E DEF9$ 0? RULE8
#CC4 .,,AUDI;NS ,S"EAL R.DS ( AUDI;NS
>E 2+ HELD 6CA/ ! ?REE MA9 "PS 9 A PLAY4
,"! >E #CJGB ACTORS AT ! F/ R.D (
AUDI;NS4 ,9 EA* SU3ESSIVE R.D ( AUDI;NS1
"O F\R? (! ACTORS F ! PREVI\S R.D REMA94
,F9D A RULE =! NUMB] .A ;N.' .-( ACTORS
9 ! .N?4 R.D ( AUDI;NS4 ,= :AT VALUES (
.;N DOES YR RULE MAKE S5SE8
------------------------------------#HDD
#AB ,/&>DIZ$ ,TE/ ,PREP>,N
,SIDEB>3
,/&>DS
#BB.J ,/UD5TS F9D ! G5]AL T]M &! SUMS
( >I?METIC S]IES &( BO? F9ITE & 9F9ITE
GEOMETRIC S]IES4
,,3TEXT-,,BAS$ ,,MULTIPLE-,,*OICE
,,"QS
,"S (! 9=M,N Y NE$ 6SOLVE A
MULTIPLE-*OICE "Q MAY APPE> 9 A TA#1 A
DIAGRAM1 OR A GRAPH4
,PRO#M #A
,! FREQU5CIES 7IN H]TZ7 (! NOTES ON A
PIANO =M A GEOMETRIC SEQU;E4 ,!
FREQU5CIES ( ;,G 7LABEL$ 8#H07 & ,A
7LABEL$ 8#AJ07 >E %[N 9 ! DIAGRAM4 ,:AT
IS ! APPROXIMATE FREQU5CY ( ;,E FLAT
7LABEL$ 8#D078
.,A4 #BDG ,HZ
.,B4 #CAA ,HZ
.,C4 #CCJ ,HZ
.,D4 #EED ,HZ
,PLAN
.,,9T]PRET .,,! .,,DIAGRAM ,! DIAGRAM
GIVES Y ! FREQU5CIES (! #H? & #AJ?
NOTES4 ,USE ^! FREQU5CIES 6F9D !
FREQU5CY (! #D? NOTE4
,SOLU;N
.,,/EP .#A ,WRITE A SY/EM ( EQU,NS4
,LET .A ;N 2 ! FREQU5CY 7IN H]TZ7 (!
.N? NOTE4 ,2C ! FREQU5CIES =M A
GEOMETRIC SEQU;E1 A RULE = .A ;N.' .-HAS
! =M .A ;N.' .K .A #A .;R .;N -- #A @4
,F ! DIAGRAM1 .A #H .K #CIB & .A #AJ .K
#DDJ4 ,USE ^! VALUES 6WRITE A SY/EM (
EQU,NS4
.,,/EP .#B ,SOLVE ! SY/EM ( EQU,NS
6F9D ! VALUES ( R& .A #A @4
,F9D .A #A 0SUB/ITUT+ ! VALUE ( .;R
96REVIS$ ,EQU,N #A4
.,,/EP .#C ,WRITE A RULE =! N? T]M &
F9D .A #D @4
,A RULE =! SEQU;E IS .A .K .A #A .;R
.;N -- #A .K #BFA7#A.JF7 .;N -- #A @4
,S1 .A #D .K #BFA7#A.JF7 #C #CAA4
,! CORRECT ANSW] IS ,B4
------------------------------------#HDE
,PRO#M #B
,! F/ #D T]MS ( AN 9F9ITE >I?METIC
SEQU;E >E %[N 9 ! GRAPH4 ,: RULE
DESCRIBES ! .N? T]M 9 ! SEQU;E8
.,A4 .A ;N .K .#B;N -- #E
.,B4 .A ;N .K .#B;N @+ #E
.,C4 .A ;N .K .#E;N--.#B
.,D4 .A ;N .K .;N @+ #E
,PLAN
.,,9T]PRET .,,! .,,GRAPH ,9 ORD] 6F9D
A RULE =! SEQU;E1 Y M/ F/ USE ! GRAPH
6WRITE ! T]MS (! SEQU;E4
,SOLU;N
,! PO9TS %[N 9 ! GRAPH >E3
.,,/EP .#A ,WRITE ! T]MS (! SEQU;E4
7#A1 --#C71 7#B1 --#A71 7#C1 #A71
7#D1C7
,"!=E1 ! SEQU;E IS --#C1 --#A1 #A1
#C1'4
.,,/EP .#B ,F9D ! F/ T]M &! -MON
DI6];E4
,! F/ T]M .A #A (! SEQU;E IS --#C4
,2C EA* T]M AF ! F/ IS #B M ?AN !
PREVI\S T]M1 ! -MON DI6];E .;D IS #B4
.,,/EP .#C ,WRITE A RULE =! N? T]M4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
A.' ;N.' .K .A #A @+ @7 .;N -- #A7 .;D
@3 ,WRITE G5]AL RULE = AN >I?METIC
SEQU;E4
.K --#C @+ @7 .;N -- #A7#B @3
,SUB/ITUTE --#C =A #A & #B = .D4
.K --#C @+ .#B;N -- #B @3 ,4TRIBUTIVE
PROP]TY
.K #B .;N -- #E @3 ,SIMPLIFY4
,! CORRECT ANSW] IS ,A4
,,PRACTICE
,9 ,EX]CISES #A & #B1 USE ! GRAPH 9
,PRO#M #B4
#A4 ,:AT IS ! VALUE (A #AE @8
,A4 --#CE
,B4 #BE
,C4 #CJ
,D4 #AFE
#B4 ,: /ATE;T IS TRUE AB ! SEQU;E T IS
GRAPH$8
,A4 ,! SUM (! F/ #AD T]MS IS #ADJ4
,B4 ,! VALUE ( .A #BJ IS #DJ4
,C4 ,A RECURSIVE RULE =! SEQU;E IS .A
#A .K #B1 .A ;N .K .A ;N _ #A -- #E4
,D4 ,! RATIO ( ANY T]M 6! PREVI\S T]M
IS 3/ANT4
------------------------------------#HDF
#AB ,/&>DIZ$ ,TE/ ,PRACTICE
,,MULTIPLE-,,*OICE
#A4 ,! DIAGRAM %[S ! B\NCE HEI<TS (A
BASKETBALL &A BASEBALL DROPP$ F A HEI<T
( #AJ FEET4 ,ON EA* B\NCE1 ! BASKETBALL
B\NCES 6#CF@3P ( XS PREVI\S HEI<T1 &!
BASEBALL B\NCES 6#CJ@3P ( XS PREVI\S
HEI<T4 ,IF BO? PATT]NS 3T9UE1
APPROXIMATELY H[ M* GRT] IS ! TOTAL 4T.E
TRAVEL$ 0! BASKETBALL ?AN ! TOTAL 4T.E
TRAVEL$ 0! BASEBALL8
,A4 #A.CD FEET
,B4 #B.JJ FEET
,C4 #B.FB FEET
,D4 #E.FC FEET
#B4 ,! TA# %[S ! DOMA9 & RANGE (A
SEQU;E4 ,: RECURSIVE RULE DESCRIBES !
SEQU;E8
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,DOMA9 @3 #A3 #B3 #C3 #D3 #E
.,RANGE @3 #BJ3 #AJ3 #E3 #B.E3 #A.BE
,A4 .A #A .K #BJ1 .A ;N .K .A ;N--#A
@+ #AJ
,B4 .A #A .K .#BJ1 .A ;N .K .A .;N --
#A --.#AJ
,C4 .A #A .K .#BJ1 .A ;N .K .#J..E;A
;N _ #A
,D4 .A ;L .K .#BJ,.A ;N .K .#B;A
;N--;L.'.-
#C4 ,:AT TYPE ( SEQU;E IS GRAPH$ AT !
"R8
,A4 ,>I?METIC
,B4 ,GEOMETRIC ) #J"K;R"K;L
,C4 ,GEOMETRIC ) ;R .1 #A
,D4 ,NEI >I?METIC NOR GEOMETRIC
,9 ,EX]CISES #D & #E1 USE ! 9=M,N 2L4
,*]YL IS RESE>*+ H] L91GE =A HI/ORY
PROJECT4 ,S F>1 %E HAS CR1T$ A FAMILY
TREE = ?REE G5],NS1 Z %[N 2L4 ,*]YL IS
ONLY 9CLUD+ RELATIVES F :OM %E IS
DIRECTLY DESC5D$4 ,SIBL+S >E N 9CLUD$4
#D4 ,ASSUME T ,*]YL IS 9 G5],N #A1 H]
P>5TS >E 9 G5],N #B1 & S ON4 ,LET .A
;N.' .-2 ! NUMB] ( RELATIVES 9 G5],N .N4
,:AT IS A RULE = .A ;N @8
,A4 .A ;N.' .K .;N @+ #B
,B4 .A ;N .K .#B ;N--#A
,C4 .A ;N .K .#B ;N.'.-
,D4 .A ;N .K .#B ;N @+ #A
#E4 ,*]YL CR1TES A FAMILY TREE ) #H
G5],NS ( H] FAMILY4 ,H[ _M P >E 9 H]
FAMILY TREE8
,A4 #H
,B4 #FD
,C4 #ABH
,D4 #BEE
,9 ,EX]CISES #F & .#G @1 USE ! DIAGRAM
(A /ACK ( BLOCKS4
#F4 ,: RULE DESCRIBES ! NUMB] ( BLOCKS
9 ! .N? LAY]1 ": .;N .K #A REPRES5TS !
TOP LAY]8
,A4 .A ;N .K .;N @+ #A
,B4 .A ;N .K .;N7.;N @+ #A7
,C4 .A ;N .K .#B;N #B
,D4 .A ;N .K .;N #B @+ #A
#G4 ,: SUM GIVES ! NUMB] ( BLOCKS %[N8
,A4
,B4
,C4
,D4
------------------------------------#HDG
,SIDEB>3
,/ATE ,TE/ ,PRACTICE
_+CLASSZONE.COM_:
,,GRI4$ ,,ANSW]
#H4 ,TWO T]MS (A GEOMETRIC SEQU;E >E
.A #C .K #AB & .A #E .K #DH4 ,:AT IS !
VALUE (A #A @8
#I4 ,:AT IS ! EI<? T]M (! SEQU;E 2L8
-#D1AB1-#CF1AJH1'
#AJ4 ,:AT IS ! SUM (! FOLL[+ S]IES8
#AA4 ,WRITE ! REP1T+ DECIMAL
#J.AEAE''' Z A FRAC;N 9 L[E/ T]MS4
#AB4 ,:AT IS ! SUM (! F/ ?REE IT]ATES
(! FUNC;N .;F 7;X7 .K .#B;X -- #A = AN
9ITIAL VALUE ( .;X #J .K #B8
#AC4 ,:AT IS ! EI<? T]M (! SEQU;E GIV5
0! RECURSIVE RULE .A #A .K #J.E1 .A ;N
.K .#B;A ;N.' _ #A @+ #E8
#AD4 ,:AT IS ! SUM (! F/ #AE T]MS (!
SEQU;E .A ;N .K .#F;N @+ #C8
#AE4 ,:AT IS ! -MON DI6];E .;D (!
SEQU;E #C1 #F1 #I1 #AB1'8
,,%ORT ,,RESPONSE
#AF4 ,Y RCV AN ;E-MAIL T Y >E 6=W>D
6#AJ ( YR FRS4 ,"! 7 #AJ RECIPI5TS 9 !
F/ R.D1 #AJJ RECIPI5TS 9 ! SECOND R.D1 &
S ON4 ,0! "T Y RCV ! ;E-MAIL1 X HAS ALR
BE5 S5T 6J OV] #AJJ MILLION P4 ,:AT R.D
( RECIPI5TS M/ Y 2 IN8 .,EXPLA9 YR
R1SON+4
#BJ4 ,! NUMB] ( DIAGONALS 9 A 3VEX
POLYGON IS GIV5 0! =MULA ": .;N IS !
NUMB] ( SIDES (! POLYGON @7 .;N .1.K
#C74 ,WRITE ! F/ SIX T]MS (! SEQU;E GIV5
0! =MULA4 ,!N TELL :E!R ! SEQU;E IS
.>I?METIC1 .GEOMETRIC @1 OR .NEI4
.,EXPLA94
#AH4 ,DUR+ A BASEBALL S1SON1 A -PANY
PL$GES A DON,N 6A *>;Y ( 4#EJJJ PLUS
4#AJJ = E HOME RUN HIT 0! LOCAL T1M4
,DOES X MAKE M S5SE 6REPRES5T ? SITU,N
US+ A SEQU;E OR A S]IES8 .,EXPLA9 YR
R1SON+4
,,EXT5D$ ,,RESPONSE
#AI4 ,A RUNN+ TRACK IS %AP$ L A
RECTANGLE ) TWO SEMICIRCUL> 5DS1 Z %[N4
,! TRACK HAS #H LANES T >E EA* #A.BB
MET]S WIDE4 ,! LANES >E NUMB]$ F #A 6#H
/>T+ F ! 9SIDE LANE4 ,! L5G? ( EA* L9E
SEG;T T EXT5DS F ! C5T] (! LEFT
SEMICIRCLE 6! 9SIDE (A LANE IS CALL$ !
LANE'S CURVE RADIUS4
,PICTURE3 ..,N DRAWN 6.,SCALE
A4 ,IS ! SEQU;E =M$ 0! CURVE RADII
.>I?METIC1 .GEOMETRIC @1 OR .NEI8
.,EXPLA94
B4 ,WRITE A =MULA =! SEQU;E F "P 7A74
C4 ,_W RECORDS M/ 2 SET ON TRACKS T H
A CURVE RADIUS ( AT MO/ #EJ MET]S 9 !
\TSIDE LANE4 ,DOES ! TRACK %[N MEET !
REQUIRE;T8 .,EXPLA94
#BJ4 ,M>K TAKES \ A LOAN = 4#AF1JJJ )
AN 9T]E/ RATE ( #J.GE@3P P] MON?4 ,AT !
5D ( EA* MON? HE MAKES A PAY;T ( 4#CJJ4
A4 ,WRITE A RECURSIVE RULE =! BAL.E .A
;N.' .-(! LOAN AT ! 2G9N+ (! N? MON?4
B4 ,H[ M* W ,M>K [E AT ! 2G9N+ (! #AH?
MON?8
C4 ,H[ L;G W X TAKE ,M>K 6PAY (F !
LOAN8
------------------------------------#HDH
#AB ,CUMULATIVE ,REVIEW ,*APT]S
#A-AB
,GRAPH ! FUNC;N4
.#A4 #C .;X -- .;Y .K #E @7 P4 #HI @7
.#B4
.#C4 .;Y .K _\ .;X @+ #C _\--#H @7 P4
#ABC @7
.#D4 .;Y .K .;X #B -- #F .;X -- #BG @7
P4 #BCF @7
.#E4 .;Y .K --#B7 .;X @+ #F7@7 .;X --
#A7 @7 P4 #BDE @7
.#F4 .;Y .K 7;X--#C7 #B @+ #D @7 P4
#BDE @7
.#G4
.#H4
.#I4 .;Y .K #C @* #D .;X -- #B @7 P4
#DGH @7
.#AJ4
.#AA4
.#AB4
,EVALUATE ! DET]M9ANT (! MATRIX4 @7 P4
#BJC @7
.#AC4
.#AD4
.#AE4
.#AF4
..,! V>IA#S ;X & ;Y V>Y 9V]SELY4 ,USE
! GIV5 VALUES 6WRITE AN EQU,N RELAT+ ;X
& Y4 ,!N F9D ! VALUE ( ;Y :5 .;X --
--.#H4 @7 P4 #EEA @7
.#AG4 .;X .K #C;,Y .K #F
.#AH4 .;X .K --#D1 .;Y .K #I
.#AI4
.#BJ4
,GRAPH ! EQU,N4
.#BA4
.#BB4
.#BC4 @7 .;X -- #C7 #B .K #AF .;Y @7
P4 #FEJ @7
,F9D ! NUMB] ( P]MUT,NS OR -B9,NS4
#BD4 #I .;,P #C @7 P4 #FHB @7
#BE4 #AF .;,P #E @7 P4 #FHB @7
#BF4 #G .;,C #B @7 P4 #FIJ @7
#BG4 #F .;,C #F @7 P4 #FIJ @7
,F9D ! 9DICAT$ PROBABIL;Y4
.#BH4 .;,P7.,A7 .K #J.CB
.;,P7.;,B7 .K #J.F
.;,P7.,A .OR .;,B7 .K #J.HE
;,P7,A& ;,B7 .K @8 @7 P4 #GJG @7
.#BI4 .,A & .;,B >E DEP5D5T EV5TS4
;,P7,A7 .K .#J..E
.;,P7.;,B_\.,A7 .K #J.C
.;,P7.,A .& .;,B7 .K @8 7.P#..G;,T#G;I
.#CJ4 ,A& ;,B >E 9DEP5D5T EV5TS4
.;,P @7 .,A @7 .K #J.BE
.;,P7.;,B7 .K @8
.;,P7.,A & ..;,B7 .K #J..B @7 P4 #GAG
@7
,F9D ! M1N1 M$IAN1 MODE1 RANGE1 & /&>D
DEVI,N (! DATA SET4
7;P- #GDD7
.#CA4 #AI1 #AA1 #H1 #AJ1 #AA1 #AE1 #AF
.#CB4 #ED1 #EH1 #DI1 #FJ1 #FC1 #EH1
#DB
.#CC4 #BAF1 #BJC1 #BBE1 #BAF1 #BAB1
#BBH1 #BJI
.#CD4 --#C1 #E1 --#AA1 #F1 --#C1 #B
.#CE4 #II1IB1IC1HB1HH1GA1IG
.#CF4 #GH1D1BH1EG1HH1BD1EG1CG1FE
,F9D ! SUM (! S]IES4
.#CG4
.#CH4
.#CI4
.#DJ4
,WRITE AN EXPLICIT RULE &A RECURSIVE
RULE =! SEQU;E1 @7 P4 #HBG @7
.#DA4 --#G1 --#C1 #A1 #E1'
.#DB4 #A1 --#AD1 --#BI1 --#DD1 '
.#DC4 #C1 #AB1 #DH1 #AIB1 '
------------------------------------#HDI
#DD4 .,,FUNDRAIS] ,Y >E ORGANIZ+ A
S*OOL FUNDRAIS] T 9VOLVES SELL+ HOLI"D
COOKIES & DECORATIVE CAL5D>S4 ,Y WANT
6RAISE 4#BDJJ4 ,Y *>GE 4#B =A BAG (
COOKIES & 4#G =A CAL5D>4 ,WRITE & GRAPH
AN EQU,N 6REPRES5T ! SITU,N4 ,IF Y SELL
#BJJ CAL5D>S1 H[ _M BAGS ( COOKIES D Y
NE$ 6SELL 9 ORD] 6MEET YR GOAL8 @7 P4
#IH @7
.#DE4 .,,GEOMETRY ,A DESIGN] IS CR1T+
A KIT = MAK+ S& CA/LES4 ,! DESIGN] WANTS
"O (! MOLDS 6BE A C"O T W HOLD #GE CUBIC
9*ES ( S&4 ,:AT %D ! DIM5.NS (! C"O 2 IF
! HEI<T %D 2 #D 9*ES M ?AN ! RADIUS (!
BASE8 @7 P4 #CGJ @7
#DF4 .,,ELECTRIC;Y ,! CURR5T .,I 7IN
AMP]ES7 REQUIR$ = AN ELECTRICAL .;P
APPLI.E IS GIV5 0": .;,P IS ! P[] 7IN
WATTS7 & .;,R IS ! RESI/.E 7IN OHMS74
,F9D ! P[] 3SUM$ 0A PORTA# HAIR DRY] = :
.,I .K #AG AMP]ES & .;,R .K #F.E OHMS4
@7 P4 #DEB @7
#DG4 .,,DEPRECI,N ,RA*EL BUYS A NEW C>
= 4#AH1FJJ4 ,! VALUE (! C> DECR1SES
0#AE.E@3P EA* YE>4 ,E/IMATE :5 ! C> W H
A VALUE ( 4#HJJJ4 @7 P4 #DHF @7
#DH4 .,,GEOMETRY ,/EVE IS A LIFEGU>D
AT A POND4 ,! POND IS APPROXIMATELY
CIRCUL> 9 %APE )A DIAMET] ( #CCJ FEET4
,HE ROPES (F A SEC;N (! POND = SWIMM+4
,! ROPE =MS A *ORD (! CIRCLE & IS A
MAXIMUM 4T.E ( #EJ FEET F ! $GE (! POND4
,:AT IS ! L5G? (! ROPE87P4 .#FBF7
#DI4 .,,D9+ .,,\ ,Y & ?REE FRS G 6A
RE/AURANT = D9N]4 ,"! >E #BJ DI6]5T
ITEMS ON ! M5U4 ,EA* ( Y IS EQU,Y LIKELY
6ORD] ANY ITEM4 ,:AT IS ! PROBABIL;Y T
EA* ( Y ORD]S A DI6]5T ITEM F ! M5U8 @7
P4 #GAG @7
#EJ4 .,,R1L .,,E/ATE .,,-MIS.NS ,!
DATA SET 2L GIVES ! SELL+ PRICES ( SEV5
HOMES T >E 2+ SOLD 0"O R1L E/ATE AG5T4
,! AG5T W RCV #E@3P (! SELL+ PRICE ( EA*
HOME Z A -MIS.N4 @7 PP4 #GDD @1 #GEA @7
,SELL+ ,PRICES ( ,HOMES
4#BJA1IJJ2 4#BJE1BJJ2 4#AIE1HJJ2
4#BAJ1CJJ2 4#AII1IJJ2 4#BAE1EJJ2
4#AIB1AJJ
A4 ,F9D ! M1N1 M$IAN1 MODE1 RANGE1 &
/&>D DEVI,N (! DATA4
B4 ,F9D ! AG5T'S -MIS.N = EA* HOME4
,!N F9D ! M1N1 M$IAN1 MODE1 RANGE1 &
/&>D DEVI,N (! -MIS.NS4
C4 .,-P>E ! /ATI/ICS F "PS 7A7 & 7;B74
#EA4 .,,SAL>Y ,AN A3.TANT TAKES A JOB
T PAYS AN ANNUAL SAL>Y ( 4#CA1JJJ =! F/
YE>4 ,! EMPLOY] (F]S A 4#AFJJ RAISE =
EA* (! NEXT #H YE>S4 ,WRITE A RULE =!
A3.TANT'S SAL>Y 9 ! .N? YE>4 ,:AT W !
A3.TANT'S SAL>Y 2 9 ! #I? YE>8 @7 P4
#HJB @7
------------------------------------#HEJ
,UNIT #E3 ,TRIGONOMETRY
#AC ,TRIGONOMETRIC ,RATIOS & ,FUNC;N
#AC.A ,USE ,TRIGONOMETRY ) ,"R
,TRIANGLES
#AC.B ,DEF9E ,G5]AL ,ANGLES & ,USE
,RADIAN ,M1SURE
#AC.C ,EVALUATE ,TRIGONOMETRIC
,FUNC;NS ( ,ANY ,ANGLE
#AC.D ,EVALUATE ,9V]SE ,TRIGONOMETRIC
,FUNC;NS
#AC.E ,APPLY ! ,LAW ( ,S9ES #C.F
,APPLY ! ,LAW ( ,COS9ES
,SIDEB>3
,2F
,9 PREVI\S C\RSES & 9 PREVI\S *APT]S1
Y LE>N$ ! FOLL[+ SKILLS1 : Y'LL USE 9
,*APT] #AC3 US+ ! ,PY?AGOR1N !OREM1
SOLV+ EQU,NS US+ 9V]SE FUNC;NS1 & F9D+
ANGLE M1SURES 9 TRIANGLES4
,PREREQUISITE ,SKILLS
,,VOCABUL>Y ,,*ECK
,COPY & -PLETE ! /ATE;T4
.#A4 ,! .RECIPROCAL ( IS @8 @4
.#B4 ,FUNC;NS .;F & .;G >E .9V]SES (
EA* O!R IF @8 & @8 @4
.#C4 ,AN EQU,N (! .CIRCLE ) C5T] 7#J1
#J7 &A RADIUS ( #A UNIT IS @8 @4
,,SKILLS ,,*ECK
,A "R TRIANGLE HAS LEGS ) L5G?S .A &
.;B &A HYPOT5USE ) L5G? .C4 ,F9D ! UN"KN
SIDE L5G?4 7.,REVIEW P4 #IIE .=
.#AC..A47
.#D4 .A .K #H1 .;B .K #AJ
.#E4 .A .K #B.E1 .;C .K #F.E
.#F4 .;B .K #I1 .;C .K #AA
,SOLVE ! EQU,N4 7.,REVIEW P4 #EAE .=
.#AC..D47
.#G4 #D ;X -- #E .K #C
.#H4 LOG #B .;X .K --#A
.#I4 --#E @+ #B;LN#C .;X .K #BJ
,! M1SURES (! ANGLES (A TRIANGLE >E
GIV54 ,F9D ! VALUE ( .X4 7.,REVIEW P4
#IIE .= .#AC..E1.AC..F47
.#AJ4 .;X;DG @1 #FE;DG1 #EE;DG
.#AA4 #IJ;DG1 .;X;DG1 .;X;DG
.#AB4 #DA;DG1 #AJG;DG1 .;X;DG
@A.,HOME,TUTOR ,PREREQUISITE SKILLS
PRACTICE AT _+CLASSZONE.COM_:
------------------------------------#HEA
,SIDEB>3
,N[
,9 ,*APT] #AC1 Y W APPLY ! BIG ID1S
LI/$ 2L & REVIEW$ 9 ! ,*APT] ,SUMM>Y ON
PAGE #HIG @4 ,Y W AL USE ! KEY VOCABUL>Y
LI/$ 2L4
,BIG ,ID1S
#A ,US+ TRIGONOMETRIC FUNC;NS
#B ,US+ 9V]SE TRIGONOMETRIC FUNC;NS
#C ,APPLY+ ! LAW ( S9ES & LAW ( COS9ES
,KEY ,VOCABUL>Y
99 S9E1 P4 #HEB
99 COS9E1 P4 #HEB
99 TANG5T1 P4 #HEB
99 COSECANT1 P4 .#HEB
99 SECANT1 P4 #HEB
99 COTANG5T1 P4 #HEB
99 RADIAN1 P4 #HFJ
99 C5TRAL ANGLE1 P4 #HFA
99 UNIT CIRCLE1 P4 #HFG
99 REF];E ANGLE1 P4 #HFH
99 9V]SE S9E1 P4 #HGE
99 9V]SE COS9E1 P4 #HGE
99 9V]SE TANG5T1 P4 #HGE
99 LAW ( S9ES1 P4 #HHB
99 LAW ( COS9ES1 P4 #HHI
,SIDEB>3
,:Y8
,Y C USE ANGLE M1SURES & TRIGONOMETRY
6F9D L5G?S & >1S 9 R1L LIFE4 ,= EXAMPLE1
Y C USE AN ANGLE M1SURE 6F9D ! >EA ( EA*
/EP 9 A SPIRAL /AIRCASE4
.,ANIMAT$ ,ALGEBRA
,! ANIM,N ILLU/RAT$ 2L = ,EX]CISE #EC
ON PAGE #HFD HELPS Y ANSW] ? "Q3 ,H[
DOES ! C5TRAL ANGLE (A /EP 9 A SPIRAL
/AIRCASE A6ECT ! /EP'S >EA8
,PICTURE3 ,! /EPS (A SPIRAL /AIRCASE C
2 APPROXIMAT$ 0SECTORS (A CIRCLE4
,PICTURE3 ,EXAM9E ! E6ECT (! C5TRAL
ANGLE ON ! >C L5G? & >EA ( EA* /EP4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,O!R ANIM,NS = ,*APT] .#AC3 PAGES
#HED @1 #HFG @1 #HHD @1 & #HIG
------------------------------------#HEB
#AC.A ,USE ,TRIGONOMETRY ) ,"R
,TRIANGLES
.,2F ,Y US$ ! ,PY?AGOR1N !OREM 6F9D
L5G?S4
.,N[ ,Y W USE TRIGONOMETRIC FUNC;NS
6F9D L5G?S4
.,:Y8 ,S Y C M1SURE 4T.ES 9DIRECTLY1 Z
9 ,EXAMPLE #E
,KEY ,VOCABUL>Y
99S9E
99 COS9E
99 TANG5T
99 COSECANT
99 SECANT
99 COTANG5T
,3SID] A "R TRIANGLE T HAS AN ACUTE
ANGLE .#J 7! ,GREEK LR .!TA74 ,! ?REE
SIDES (! TRIANGLE >E ! .HYPOT5USE @1 !
SIDE .OPPOSITE .#F @1 &! SIDE .ADJAC5T
6.#F4
,RATIOS (A "R TRIANGLE'S SIDE L5G?S >E
US$ 6DEF9E ! SIX TRIGONOMETRIC FUNC;NS3
..S9E1 COS9E1 TANG5T1 COSECANT1 .SECANT
@1 & .COTANG5T4 ,^! SIX FUNC;NS >E
A2REVIAT$ S91 COS1 TAN1 ESC1 SEC1 & COT1
RESPECTIVELY4
,SIDEB>3
,/&>DS
.,MA!MATICAL .,ANALYSIS3 #AB.J ,/UD5TS
USE ANALYSIS 6DET]M9E UN"KN SIDES OR
ANGLES 9 "R TRIANGLES4
,,KEY ,,3CEPT .= .YR .,NOTEBOOK
,"R ,TRIANGLE ,DEF9I;NS (
,TRIGONOMETRIC ,FUNC;NS
,LET 2 AN ACUTE ANGLE (A "R TRIANGLE4
,! SIX TRIGONOMETRIC FUNC;NS ( >E DEF9$
Z FOLL[S3
,! A2REVI,NS .OPP1 .ADJ @1 & .HYP >E
(T5 US$ 6REPRES5T ! SIDE L5G?S (! "R
TRIANGLE4 ,NOTE T ! RATIOS 9 ! SECOND R[
>E RECIPROCALS (! RATIOS 9 ! F/ R[3
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
@3 @3
,EXAMPLE #A ,EVALUATE TRIGONOMETRIC
FUNC;NS
,EVALUATE ! SIX TRIGONOMETRIC FUNC;NS
(! ANGLE
,SOLU;N
,,REVIEW ,,GEOMETRY
,= HELP )! ,PY?AGOR1N !OREM1 SEE P4
#IIE @4
,F ! ,PY?AGOR1N !OREM1 ! L5G? (!
HYPOT5USE IS
------------------------------------#HEC
,,EXAMPLE #B ,/&>DIZ$ ,TE/ ,PRACTICE
,IF IS AN ACUTE ANGLE (A "R TRIANGLE &
@1 :AT IS TAN8
.,A
.;,B
.;,C
.;,D
,SOLU;N
.,,/EP .#A .,DRAW A "R TRIANGLE )
ACUTE ANGLE S* T ! LEG OPPOSITE HAS L5G?
#D &! HYPOT5USE HAS L5G? #G4 ,0!
,PY?AGOR1N !OREM1 ! L5G? .;X (! O!R LEG
IS
.,,/EP .#B .,F9D ! VALUE ( TAN4
,! CORRECT ANSW] IS ,B4 ..,A ;,B ;,C
.;,D
.,GUID$ .,PRACTICE = ,EXAMPLES #A & #B
,EVALUATE ! SIX TRIGONOMETRIC FUNC;NS
(! ANGLE
.#A4
.#B4
.#C4
.#D4 ,9 A "R TRIANGLE1 IS AN ACUTE
ANGLE & @4 ,:AT IS S98
.,,SPECIAL .,,ANGLES ,! ANGLES #CJ;DG1
#DE;DG1 & #FJ;DG O3UR FREQU5TLY 9
TRIGONOMETRY4 ,Y C USE ! TRIGONOMETRIC
VALUES = ^! ANGLES 6F9D UN"KN SIDE L5G?S
9 SPECIAL "R TRIANGLES4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,TRIGONOMETRIC ,VALUES = ,SPECIAL
,ANGLES
,! TA# 2L GIVES ! VALUES (! SIX
TRIGONOMETRIC FUNC;NS =! ANGLES #CJ;DG1
#DE;DG1 & #FJ;DG4 ,Y C OBTA9 ^! VALUES F
! TRIANGLES %[N4
------------------------------------#HED
,,EXAMPLE #C ,F9D AN UN"KN SIDE L5G?
(A "R TRIANGLE
,F9D ! VALUE (=! "R TRIANGLE %[N4
,SOLU;N
,WRITE AN EQU,N US+ A TRIGONOMETRIC
FUNC;N T 9VOLVES ! RATIO ( .;X & #H4
,SOLVE ! EQU,N = .X4
,! L5G? (! SIDE IS
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
.,,SOLV+ .,A .,,TRIANGLE ,F9D+ .ALL
UN"KN SIDE L5G?S & ANGLE M1SURES (A
TRIANGLE IS CALL$ .SOLV+ ! TRIANGLE4
,SOLV+ "R TRIANGLES T H ACUTE ANGLES O!R
?AN #CJ;DG1 #DE;DG1 & #FJ;DG MAY REQUIRE
! USE (A CALCULATOR4
,6F9D VALUES (! S9E1 COS9E1 & TANG5T
FUNC;NS ON A CALCULATOR1 USE ! KEYS @1
@1 & @4 ,USE ^! KEYS &! RECIPROCAL KEY =
COSECANT1 SECANT1 & COTANG5T4 ,2 SURE !
CALCULATOR IS SET 9 DEGREE MODE4
,,EXAMPLE #D ,USE A CALCULATOR 6SOLVE
A "R TRIANGLE
,SOLVE .,,ABC @4
,SOLU;N
,,R1D+
,"?\T ? *APT]1 A CAPITAL LR IS US$
6DENOTE BO? AN ANGLE (A TRIANGLE & XS
M1SURE4 ,! SAME LR 9 L[]CASE IS US$
6DENOTE ! L5G? (! SIDE OPPOSITE T ANGLE4
.,A & .;,B AXE -PLE;T>Y ANGLES1 S .;,B
.K #IJ;DG--#BH;DG .K #FB;DG4
,S1 .;,B -- #FB;DG1 .A #G.IH1 & ;C
#AG.J4
..,GUID$ ,PRACTICE = ,EXAMPLES #C &
.#D
,SOLVE ,,ABC US+ ! DIAGRAM AT ! "R &!
GIV5 M1SURE;TS4
.#E4 .;,B .K #DE;DG1 .;C .K #E
.#F4 .,A .K #CB;DG1 .;B .K #AJ
.#G4 .,A .K #GA;DG1 .;C .K #BJ
.#H4 .;,B .K #FJ;DG1 .A .K #G
------------------------------------#HEE
,,EXAMPLE #E ,USE 9DIRECT M1SURE;T
.,,GR& .,,CANYON ,:ILE /&+ AT ,YAVAPAI
,PO9T NE> ! ,GR& ,CANYON1 Y M1SURE AN
ANGLE ( #IJ;DG 2T ,P[ELL ,PO9T & ,WID=SS
,PO9T1 Z %[N4 ,Y !N WALK 6,P[ELL ,PO9T &
M1SURE AN ANGLE ( #GF;DG 2T ,YAVAPAI
,PO9T & ,WID=SS ,PO9T4 ,! 4T.E 2T
,YAVAPAI ,PO9T & ,P[ELL ,PO9T IS AB #B
MILES4 ,H[ WIDE IS ! ,GR& ,CANYON 2T
,YAVAPAI ,PO9T & ,WID=SS ,PO9T8
,SOLU;N
,,*OOSE ,,FUNC;NS
,! TANG5T FUNC;N IS US$ 6F9D ! UN"KN
4T.E 2C X 9VOLVES ! RATIO ( .;X & #B4
,! WID? IS AB #H.J MILES4
.,,ANGLES .,,( .,,SI<T ,IF Y LOOK AT A
PO9T ABV Y1 S* Z ! TOP (A BUILD+1 !
ANGLE T YR L9E ( SI<T MAKES )A L9E
P>ALLEL 6! GR.D IS CALL$ ! .ANGLE .(
.ELEV,N @4 ,AT ! TOP (! BUILD+1 ! ANGLE
2T A L9E P>ALLEL 6! GR.D & YR L9E ( SI<T
IS CALL$ ! .ANGLE .( .DEPRES.N @4 ,^!
TWO ANGLES H ! SAME M1SURE4
,,EXAMPLE #F ,USE AN ANGLE ( ELEV,N
.,,P>ASAIL+ ,A P>ASAIL] IS ATTA*$ 6A
BOAT )A ROPE #CJJ FEET L;G4 ,! ANGLE (
ELEV,N F ! BOAT 6! P>ASAIL] IS #DH;DG4
,E/IMATE ! P>ASAIL]'S HEI<T ABV ! BOAT4
,SOLU;N
.,,/EP .#A .,DRAW A DIAGRAM T
REPRES5TS ! SITU,N4
.,,/EP .#B .,WRITE & SOLVE AN EQU,N
6F9D ! HEI<T .;H @4
,! HEI<T (! P>ASAIL] ABV ! BOAT IS AB
#BBC FEET4
..,GUID$ ,PRACTICE = ,EXAMPLES #E &
.#F
.#I4 .,,GR& .,,CANYON ,9 ,EXAMPLE #E1
F9D ! 4T.E 2T ,P[ELL ,PO9T & ,WID=SS
,PO9T4
.#AJ4 .,,:AT .,,IF8 ,9 ,EXAMPLE #F1
E/IMATE ! HEI<T (! P>ASAIL] ABV ! BOAT
IF ! ANGLE ( ELEV,N IS #CH;DG4
------------------------------------#HEF
#AC.A ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
,,WS#BA = ,EXS4 #E1AA1 & #CC
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE ,EXS4
#B1AE1 #BJ1 #CC1 & #CF
.K .,,MULTIPLE .,,REPRES5T,NS ,EX#.CD
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,:AT IS AN ANGLE (
ELEV,N8
.#B4 .,,WRIT+ .,EXPLA9 :AT X M1NS
6SOLVE A "R TRIANGLE4
,,EXAMPLE #A
ON P4 #HEB = ,EXS4 #C-H
,,EVALUAT+ ,,FUNC;NS ,EVALUATE ! SIX
TRIGONOMETRIC FUNC;NS (! ANGLE @4
.#C4
.#D4
.#E4
.#F4
.#G4
.#H4
,,F9D+ ,,VALUES ,LET 2 AN ACUTE ANGLE
(A "R TRIANGLE4 ,F9D ! VALUES (! O!R
FIVE TRIGONOMETRIC FUNC;NS ( @4
,,EXAMPLE #B
ON P4 #HEC = ,EXS4 #I-AF
.#I4
.#AJ4
.#AA4
.#AB4
.#AC4
.#AD4
#AE4 .,,MULTIPLE .,,*OICE ,9 A "R
TRIANGLE1 IS AN ACUTE ANGLE & COS .K @4
,:AT IS ! VALUE ( TAN8
,A
;,B
;,C
;,D
#AF4 .,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 F9D+ CSC1 GIV5 T IS AN
ACUTE
ANGLE (A "R TRIANGLE & @4
,,EXAMPLE #C
ON P4 #HED = ,EXS4 #AG-BJ
,,F9D+ ,,SIDE ,,L5G?S ,F9D ! EXACT
VALUES ( .;X & .;Y @4
.#AG4
.#AH4
.#AI4
#BJ4 .,,MULTIPLE .,,*OICE ,9 A #CJ;DG
--#FJ;DG --#IJ;DG TRIANGLE1 ! L;G] LEG
HAS A L5G? ( #E4 ,:AT IS ! L5G? (! %ORT]
LEG8
,A
;,B
;,C
;,D
------------------------------------#HEG
.,,EXAMPLE #D
ON P4 #HED = ,EXS4 #BA-BH
.,,SOLV+ .,,TRIANGLES ,SOLVE .,,ABC
US+ ! DIAGRAM &! GIV5 M1SURE;TS4
.#BA4 .,A .K #CE;DG1 .;C .K #AF
.#BB4 .;,B .K #EC;DG1 .A .K #AB
.#BC4 .;,B .K #AH;DG1 .;C .K #BD
.#BD4 .,A .K #FG;DG1 .;B .K #G
.#BE4 .;,B .K #GE;DG1 .A .K #AE
.#BF4 .,A .K #DI;DG1 .;C .K #BG
.#BG4 .,A .K #FD;DG1 .;B .K #CB
.#BH4 .;,B .K #BD;DG1 .;C .K #AJ.H
.#BI4 .,,*ALL5GE ,A PROC$URE =
APPROXIMAT+ BAS$ ON ! "W ( ,>*IM$ES IS
69SCRIBE A REGUL> HEXAGON 9 A CIRCLE4
.A4 ,USE ! DIAGRAM AT ! "R 6SOLVE =
.;X @4 ,:AT IS ! P]IMET] (! HEXAGON8
.B4 ,%[ T A REGUL> RC-SID$ POLYGON
9SCRIB$ 9 A CIRCLE ( RADIUS #A HAS A
P]IMET] (
.C4 ,USE ! RESULT F "P 7;B7 6F9D AN
EXPRES.N 9 T]MS ( .;N T APPROXIMATES4
,!N EVALUATE ! EXPRES.N :5 .;N .K #EJ4
,PRO#M ,SOLV+
,,EXAMPLES #E & #F
ON P4 #HEE = ,EXS4 #CJ-CE
,9 ,EX]CISES #CJ & #CA1 USE ! 9=M,N 9
! DIAGRAM 6SOLVE ! PRO#M4
.#CJ4 .,,TREE .,,HEI<T ,A TREE CA/S !
%AD[ %[N4 ,:AT IS ! HEI<T (! TREE8
.#CA4 .,,GR& .,,PIANO ,F9D ! L5G? (!
PROP HOLD+ OP5 ! PIANO4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#CB4 .,,RAILWAY ,! ,FALLS ,9CL9E
,RAILWAY AT ,NIAG>A ,FALLS HAS AN ANGLE
( ELEV,N ( #CF;DG4 ,! RAILWAY EXT5DS A
HORIZONTAL 4T.E ( AB #ACH FEET4 ,F9D !
HEI<T & L5G? (! RAILWAY4
.#CC4 .,,%ORT .,,RESPONSE ,A SUBM]SI#
TRAVEL+ AT A DEP? ( #BEJ FEET DIVES AT
AN ANGLE ( #AE;DG ) RESPECT 6A L9E
P>ALLEL 6! WAT]'S SURFACE4 ,X TRAVELS A
HORIZONTAL 4T.E ( #AEJJ FEET DUR+ !
DIVE4 ,:AT IS ! DEP? (! SUBM]SI# AF !
DIVE8 .,EXPLA9 H[ ! ANGLE (! DIVE A6ECTS
! F9AL DEP?4
#CD4 .,,MULTIPLE .,,REPRES5T,NS ,Y >E
CLIMB+ ,M.T ,MASSIVE 9 ,COLORADO4 ,Y >E
AT AN ALTITUDE ( #AA1BJJ FEET4 ,Y M1SURE
! ANGLE ( ELEV,N 6A RIDGE ABV Y 6BE
#BI.D;DG4 ,! 4T.E 7AL;G ! FACE (! M.TA97
2T Y &! RIDGE IS #FCAE FEET4
A4 .,DRAW+ .A .,DIAGRAM ,DRAW A
DIAGRAM T REPRES5TS ? SITU,N4
B4 .,WRIT+ .AN .,EQU,N ,WRITE & SOLVE
AN EQU,N 6F9D ! ALTITUDE (! RIDGE4
------------------------------------#HEH
#CE4 .,,TROPIC .,,( .,,C.ER ,! ,TROPIC
( ,C.ER IS ! CIRCLE ( LATITUDE F>!/ NOR?
(! EQUATOR ": ! SUN C APPE> DIRECTLY
OV]H1D4 ,X LIES #BC.E;DG NOR? (!
EQUATOR1 Z %[N4
A4 ,F9D ! CIRCUMF];E (! ,TROPIC (
,C.ER US+ #CIFJ MILES Z ,E>?'S
APPROXIMATE RADIUS4
B4 ,:AT IS ! 4T.E 2T TWO PO9TS ON !
,TROPIC ( ,C.ER T LIE DIRECTLY ACR F EA*
O!R8
#CF4 .,,EXT5D$ .,,RESPONSE ,A PASS5G]
9 AN AIRPLANE SEES TWO T[NS DIRECTLY 6!
LEFT (! PLANE4
A4 ,:AT IS ! 4T.E .;D F ! AIRPLANE 6!
F/ T[N8
B4 ,:AT IS ! HORIZONTAL 4T.E .;X F !
AIRPLANE 6! F/ T[N8
C4 ,:AT IS ! 4T.E .;Y 2T ! TWO T[NS8
.,EXPLA9 ! PROCESS Y US$ 6F9D YR ANSW]4
#CG4 .,,*ALL5GE ,Y M1SURE ! ANGLE (
ELEV,N F ! GR.D 6! TOP (A BUILD+ Z
#CB;DG4 ,:5 Y MOVE #EJ MET]S CLOS] 6!
BUILD+1 ! ANGLE ( ELEV,N IS #EC;DG4 ,H[
HI< IS ! BUILD+8
,MIX$ ,REVIEW
,PREVIEW
,PREP>E = ,LESSON #AC.B 9 ,EXS4
#CH-DC4
,P]=M ! 9DICAT$ 3V].N4 7P4 #B
.#CH4 #C YE>S 6SECONDS
.#CI4 #AJ P9TS 6GALLONS
.#DJ4 #EJJ FEET 6SECONDS
.#DA4 #I.D KILOGRAMS 6GRAMS
.#DB4 #B TONS 6\NCES
.#DC4 #E.F MET]S 6MILLIMET]S
,SOLVE ! SY/EM US+ ANY ALGEBRAIC
ME?OD4 7P4 #AFJ
.#DD4 #B .;X -- .;Y .K #H
#C .;X @+ #D .;Y .K #BC
.#DE4 #D .;X @+ #C .;Y .K --#A
--#C .;X @+ .;Y .K #C
.#DF4 #I .;X -- #AB .;Y .K #BJ
--#F .;X @+ #H .;Y .K #AA
.#DG4 #AB .;X @+ #E .;Y .K #D
#C .;X -- #AJ .;Y .K --#H
.#DH4 --#B .;X @+ #G .;Y .K #AF
#C .;X -- #E .;Y .K --#B
.#DI4 #D .;X -- #F .;Y .K #AH
--#B .;X @+ .;Y .K --#C
,CLASSIFY ! 3IC SEC;N & WRITE XS EQU,N
9 /&>D =M4 7P4 #FEJ
.#EJ4 .;X #B @+ .;Y #B @+ #D .;X @+ #F
.;Y -- #AG .K #J
.#EA4 .;X #B -- #D .;Y #B @+ #F .;X @+
#AF .;Y @+ #ACG .K #J
.#EB4 .;Y #B -- #D .;Y @+ #AF .;X @+
#AAF .K #J
.#EC4 #I .;X #B @+ #BE .;Y #B @+ #AFB
.;X @+ #BEJ .;Y @+ #DED .K #J
.#ED4 .;X #B @+ #H .;X @+ #D .;Y @+
#BH .K #J
.#EE4 .;X #B -- .;Y #B @+ #AD .;X @+
#AF .;Y -- #E .K #J
.,,EXTRA .,,PRACTICE = ,LESSON #AC.A1
P4 #AJBB
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#HEI
#AC.B ,DEF9E ,G5]AL ,ANGLES & ,USE
,RADIAN ,M1SURE
.,2F ,Y US$ ACUTE ANGLES M1SUR$ 9
DEGREES4
.,N[ ,Y W USE G5]AL ANGLES T MAY 2
M1SUR$ 9 RADIANS4
.,:Y8 ,S Y C F9D ! >EA (A CURV$ PLAY+
FIELD1 Z 9 ,EXAMPLE #D4
,KEY ,VOCABUL>Y
99 9ITIAL SIDE
99 T]M9AL SIDE
99 /&>D POSI;N
99 COT]M9AL
99 RADIAN
99 SECTOR
99 C5TRAL ANGLE
,SIDEB>3
,/&>DS
.,MA!MATICAL .,ANALYSIS3 #A.J ,/UD5TS
"U/& ! NOT,N ( ANGLE & H[ 6M1SURE X1 9
BO? DEGREES & RADIANS4 ,!Y C 3V]T 2T
DEGREES & RADIANS4
,9 ,LESSON #AC.A1 Y "W$ ONLY ) ACUTE
ANGLES4 ,9 ? LESSON1 Y W /UDY ANGLES )
M1SURES T C 2 ANY R1L NUMB]S4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,ANGLES 9 ,/&>D ,POSI;N
,9 A COORD9ATE PLANE1 AN ANGLE C 2 =M$
0FIX+ "O RAY1 CALL$ ! .9ITIAL .SIDE @1 &
ROTAT+ ! O!R RAY1 CALL$ ! .T]M9AL .SIDE
@1 AB ! V]TEX4
,AN ANGLE IS 9 ./&>D .POSI;N IF XS
V]TEX IS AT ! ORIG9 & XS 9ITIAL SIDE
LIES ON ! POSITIVE .;X -AXIS4
,! M1SURE ( AN ANGLE IS POSITIVE IF !
ROT,N ( XS T]M9AL SIDE IS C.T]CLOCKWISE1
& NEGATIVE IF ! ROT,N IS CLOCKWISE4 ,!
T]M9AL SIDE ( AN ANGLE C MAKE M ?AN "O
-PLETE ROT,N4
,,EXAMPLE #A ,DRAW ANGLES 9 /&>D
POSI;N
,DRAW AN ANGLE )! GIV5 M1SURE 9 /&>D
POSI;N4
.A4 #BDJ;DG
.B4 #EJJ;DG
C4 --#EJ;DG
,SOLU;N
.A4 ,2C #BDJ;DG IS #FJ;DG M ?AN
#AHJ;DG1 ! T]M9AL SIDE IS #FJ;DG
C.T]CLOCKWISE PA/ ! NEGATIVE .;X -AXIS4
.B4 ,2C #EJJ;DG IS #ADJ;DG M ?AN
#CFJ;DG1 ! T]M9AL SIDE MAKES "O :OLE
REVOLU;N C.T]CLOCKWISE PLUS #ADJ;DG M4
.C4 ,2C --#EJ;DG IS NEGATIVE1 ! T]M9AL
SIDE IS #EJ;DG CLOCKWISE F ! POSITIVE
.;X -AXIS4
------------------------------------#HFJ
.,,COT]M9AL .,,ANGLES ,9 ,EXAMPLE #A1
! ANGLES #EJJ;DG & #ADJ;DG >E .COT]M9AL
2C _! T]M9AL SIDES CO9CIDE4 ,AN ANGLE
COT]M9AL )A GIV5 ANGLE C 2 F.D 0A4+ OR
SUBTRACT+ MULTIPLES ( #CFJ;DG4
,,EXAMPLE #B ,F9D COT]M9AL ANGLES
,F9D "O POSITIVE ANGLE & "O NEGATIVE
ANGLE T >E COT]M9AL ) 7A7 --#DE;DG &
7;B7 #CIE;DG4
,SOLU;N
,"! >E _M S* ANGLES1 DEP5D+ ON :AT
MULTIPLE ( #CFJ;DG IS A4$ OR SUBTRACT$4
.A4 --#DE;DG @+ #CFJ;DG .K #CAE;DG
--#DE;DG--#CFJ;DG .K --#DJE;DG
.B4 #CIE;DG--#CFJ;DG .K #CE;DG
#CIE;DG --#B7#CFJ;DG7 .K --#CBE;DG
.,GUID$ .,PRACTICE = ,EXAMPLES #A & #B
,DRAW AN ANGLE )! GIV5 M1SURE 9 /&>D
POSI;N4 ,!N F9D "O POSITIVE COT]M9AL
ANGLE & "O NEGATIVE COT]M9AL ANGLE4
.#A4 #FE;DG
.#B4 #BCJ;DG
.#C4 #CJJ;DG
.#D4 #GDJ;DG
.,,RADIAN .,,M1SURE ,ANGLES C AL 2
M1SUR$ 9 .RADIANS @4 ,6DEF9E A RADIAN1
3SID] A CIRCLE ) RADIUS .;R C5T]$ AT !
ORIG9 Z %[N4 ,"O .RADIAN IS ! M1SURE (
AN ANGLE 9 /&>D POSI;N ^: T]M9AL SIDE
9T]CEPTS AN >C ( L5G? .;R @4
,2C ! CIRCUMF];E (A CIRCLE IS #B1 "!
>E #B RADIANS 9 A FULL CIRCLE4 ,DEGREE
M1SURE & RADIAN M1SURE >E "!=E RELAT$ 0!
EQU,N #CFJ;DG .K .#B RADIANS1 OR #AHJ;DG
.K RADIANS4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,3V]T+ ,2T ,DEGREES & ,RADIANS
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,DEGREES 6RADIANS3 ,RADIANS 6DEGREES
,MULTIPLY DEGREE M1SURE BY @3
,MULTIPLY RADIAN M1SURE BY
------------------------------------#HFA
,,EXAMPLE #C ,3V]T 2T DEGREES &
RADIANS
,3V]T 7A7 #ABE;DG 6RADIANS & 7;B7
RADIANS 6DEGREES4
,,R1D+
,! UNIT 8RADIANS0 IS (T5 OMITT$4 ,=
9/.E1 ! M1SURE RADIANS MAY 2 WRITT5
SIMPLY Z @4
.A4
.B4
,,3CEPT ,,SUMM>Y .,= .,YR .,NOTEBOOK
,DEGREE & ,RADIAN ,M1SURES ( ,SPECIAL
,ANGLES
,! DIAGRAM %[S EQUIVAL5T DEGREE &
RADIAN M1SURES = SPECIAL ANGLES F #J;DG
6#CFJ;DG 7#J RADIANS 6.#B RADIANS74
,Y MAY F9D X HELP;L 6MEMORIZE !
EQUIVAL5T DEGREE & RADIAN M1SURES (
SPECIAL ANGLES 9 ! F/ QUADRANT &= @4
,ALL O!R SPECIAL ANGLES >E J MULTIPLES (
^! ANGLES4
.,GUID$ .,PRACTICE = ,EXAMPLE #C
,3V]T ! DEGREE M1SURE 6RADIANS OR !
RADIAN M1SURE 6DEGREES4
.#E4 #ACE;DG
.#F4 --#EJ;DG
.#G4
.#H4
..,,SECTORS ,,( ,,CIRCLES ,A .SECTOR
IS A REGION (A CIRCLE T IS B.D$ 0TWO
RADII & AN >C (! CIRCLE4 ,! .C5TRAL
.ANGLE (A SECTOR IS ! ANGLE =M$ 0! TWO
RADII4 ,"! >E SIMPLE =MULAS =! >C L5G? &
>EA (A SECTOR :5 ! C5TRAL ANGLE IS
M1SUR$ 9 RADIANS4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,>C ,L5G? & ,>EA (A ,SECTOR
,! >C L5G? #E & >EA .,A (A SECTOR )
RADIUS .;R & C5TRAL ANGLE 7M1SUR$ 9
RADIANS7 >E Z FOLL[S4
.,>C .L5G?3 .;S -- .;R
.,>EA3
------------------------------------#HFB
,,EXAMPLE #D ,SOLVE A MULTI-/EP PRO#M
.,,S(TBALL ,A ,S(TBALL FIELD =MS A
SECTOR )! DIM5.NS %[N4 ,F9D ! L5G? (!
\TFIELD F;E &! >EA (! FIELD4
,SOLU;N
.,,/EP .#A .,3V]T ! M1SURE (! C5TRAL
ANGLE 6RADIANS4
,,AVOID ,,]RORS
,Y M/ WRITE ! M1SURE ( AN ANGLE 9
RADIANS :5 US+ ! =MULAS =! >C L5G? & >EA
(A SECTOR4
.,,/EP .#B .,F9D ! >C L5G? &! >EA (!
SECTOR4
,>C L5G?3
,>EA3
,! L5G? (! \TFIELD F;E IS AB #BHC
FEET4 ,! >EA (! FIELD IS AB #BE1DJJ
SQU>E FEET4
.,GUID$ .,PRACTICE = ,EXAMPLE #D
.#I4 .,,:AT .,,IF8 ,9 ,EXAMPLE #D1
E/IMATE ! L5G? (! \TFIELD F;E &! >EA (!
FIELD IF ! \TFIELD F;E IS #BBJ FEET F
HOME PLATE4
#AC.B ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
,,WS#BB = ,EXS4 #AA1BC1 & #EA
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE ,EXS4
#B1AD1 #CA1 #EJ1 & #EC
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,AN
ANGLE IS 9 /&>D POSI;N IF XS V]TEX IS AT
! @8 & XS @8 LIES ON ! POSITIVE .;X
-AXIS4
.#B4 .,,WRIT+ ,H[ DOES ! SIGN ( AN
ANGLE'S M1SURE DET]M9E XS DIREC;N (
ROT,N8
..,,EXAMPLES #A & .#C ON PP4 #HEI-HFA
= ,EXS4 #C-AD
.,,VISUAL .,,?9K+ ,MAT* ! ANGLE M1SURE
)! ANGLE4
.#C4 --#BDJ;DG
.#D4 #FJJ;DG
.#E4
.,A4
.,B4
.,C4
------------------------------------#HFC
,,DRAW+ ,,ANGLES ,DRAW AN ANGLE )!
GIV5 M1SURE 9 /&>D POSI;N4
.#F4 #AAJ;DG
.#G4 --#AJ;DG
.#H4 #DEJ;DG
.#I4 --#IJJ;DG
.#AJ4 #F
.#AA4
.#AB4
.#AC4
#AD4 .,,MULTIPLE .,,*OICE ,: ANGLE
M1SURE IS %[N 9 ! DIAGRAM8
,A --#AEJ;DG
;,B #BAJ;DG
;,C #EGJ;DG
;,D #ICJ;DG
,,F9D+ ,,COT]M9AL ,,ANGLES ,F9D "O
POSITIVE ANGLE & "O NEGATIVE ANGLE T >E
COT]M9AL )! GIV5 ANGLE4
,,EXAMPLES #B & #C
ON PP4 #HFJ-HFA = ,EXS4 #AE-BB
.#AE4 #GJ;DG
.#AF4 #BEE;DG
.#AG4 --#ABE;DG
.#AH4 #HBJ;DG
.#AI4
.#BJ4
.#BA4
.#BB4
,,3V]T+ ,,M1SURES ,3V]T ! DEGREE
M1SURE 6RADIANS OR ! RADIAN M1SURE
6DEGREES4
,,EXAMPLE #C
ON P4 #HFA = ,EXS4 #BC-CA
.#BC4 #DJ;DG
.#BD4 #CAE;DG
.#BE4 --#BFJ;DG
.#BF4 #EJJ;DG
.#BG4
.#BH4
.#BI4 #E
.#CJ4
#CA4 99 .,,MULTIPLE .,,*OICE ,: ANGLE
M1SURE IS EQUIVAL5T 6RADIANS8
,A #CJ;DG
;,B #CIJ;DG
;,C #GEJ;DG
;,D #AAAJ;DG
,,F9D+ ,,>C ,,L5G? ,,& ,,>EA ,F9D ! >C
L5G? & >EA (A SECTOR )! GIV5 RADIUS .;R
& C5TRAL ANGLE4
,,EXAMPLE #D
ON P4 #HFB = ,EXS4 #CB-CH
.#CB4
.#CC4
.#CD4 .;R .K #AE CM1 .K #DE;DG
.#CE4 .;R .K #AB FT1 .K #AEJ;DG
.#CF4 .;R .K #AH ;M1 .K #BE;DG
.#CG4 .;R .K #BE IN41 .K #BGJ;DG
.#CH4 .,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 F9D+ ! >EA (A SECTOR )A
RADIUS ( #F C5TIMET]S &A C5TRAL ANGLE (
#DJ;DG4
,,EVALUAT+ ,,FUNC;NS ,EVALUATE !
TRIGONOMETRIC FUNC;N US+ A CALCULATOR IF
NEC4 ,IF POSSI#1 GIVE AN EXACT ANSW]4
,,H9T
,= ,EXS4 #CI-DF1 SET YR CALCULATOR 9
RADIAN MODE4
.#CI4
.#DJ4
.#DA4
.#DB4
.#DC4
.#DD4
.#DE4
.#DF4
.#DG4 .,,*ALL5GE ,A ROTAT+ OBJECT T
PASSES "? AN ANGLE DUR+ "T .;T HAS AN
ANGUL> VELOC;Y .;V GIV5 0! =MULA @4 ,F9D
! ANGUL> VELOC;Y (! H\R H&1 ! M9UTE H&1
&! SECOND H& ON A #AB H\R CLOCK4 ,GIVE
ALL ANSW]S 9 DEGREES P] H\R4
------------------------------------#HFD
,PRO#M ,SOLV+
,,EXAMPLES #A & #C
ON PP4 #HEI-HFA = ,EXS4 #DH-EJ
.#DH4 .,,A/RONOMY ,9 A/RONOMY1 !
.T]M9ATOR IS ! "D-NI<T L9E ON A PLANET T
DIVIDES ! PLANET 96"D"T & NI<T"T
REGIONS4 ,! T]M9ATOR MOVES ACR !
PLANET'S SURFACE Z ! PLANET ROTATES4 ,X
TAKES AB #D H\RS = ,E>?'S T]M9ATOR 6MOVE
ACR ! 3T95TAL ,UNIT$ ,/ATES4 ,"? :AT
ANGLE HAS ,E>? ROTAT$ DUR+ ? "T8 ,GIVE !
ANSW] 9 BO? DEGREES & RADIANS4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#DI4 .;,,CD .,,PLAY] ,:5 A ;,,CD
PLAY] R1DS 9=M,N F ! \T] $GE (A ;,,CD1 !
;,,CD SP9S AB #BJJ REVOLU;NS P] M9UTE4
,AT T SPE$1 "? :AT ANGLE DOES A PO9T ON
! ;,,CD SP9 9 "O M9UTE8 ,GIVE ! ANSW] 9
BO? DEGREES & RADIANS4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#EJ4 .,,%ORT .,,RESPONSE ,Y "W E
,SATUR"D F #I3JJ ,A4,M4 6#E3JJ ,P4,M4
,DRAW A DIAGRAM T %[S ! ROT,N -PLET$ 0!
H\R H& (A CLOCK DUR+ ? "T4 ,F9D ! M1SURE
(! ANGLE G5]AT$ 0! H\R H& 9 BO? DEGREES
& RADIANS4 .,-P>E ? ANGLE )! ANGLE
G5]AT$ 0! M9UTE H& F #I3JJ A4M4 6#E3JJ
,P4,M4
,,EXAMPLE #D
ON P4 #HFB = ,EXS4 #EA-EC
.#EA4 .,,MULTI-.,,/EP .,,PRO#M ,A
SCI5TI/ P]=M$ AN EXP]I;T 6/UDY ! E6ECTS
( GRAVIT,NAL =CE ON HUMANS4 ,9 ORD] =
HUMANS 6EXP]I;E TWICE ,E>?'S GRAV;Y1 !Y
7 PLAC$ 9 A C5TRIFUGE #EH FEET L;G &
SPUN AT A RATE ( AB #AE REVOLU;NS P]
M9UTE4
.A4 ,"? H[ _M RADIANS DID ! P ROTATE
EA* SECOND8
.B4 ,F9D ! L5G? (! >C "? : ! P ROTAT$
EA* SECOND4
.#EB4 .,,MULTI-.,,/EP .,,PRO#M ,9 !
%OT PUT EV5T AT ! #BJJD ,SUMM] ,OLYMPIC
,GAMES1 ! W9N+ %OT 0 #BA.AF MET]S4 ,=A
%OT PUT 6BE FAIR1 X M/ L& )9 A SECTOR
HAV+ A C5TRAL ANGLE ( #CD.IB;DG4
.A4 ,IF ! (FICIALS DREW AN >C ACR !
FAIR L&+ >EA M>K+ ! F>!/ ?R[1 H[ L;G WD
! >C BE8
.B4 ,ALL FAIR %OT PUTS 9 ! #BJJD
,OLYMPICS L&$ )9 A SECTOR B.D$ 0! >C F
"P 7.A7 @4 ,:AT IS ! >EA ( ? SECTOR8
.#EC4 .,,EXT5D$ .,,RESPONSE ,A SPIRAL
/AIRCASE HAS #AE /EPS4 ,EA* /EP IS A
SECTOR )A RADIUS ( #DB 9*ES &A C5TRAL
ANGLE ( @4
.A4 ,:AT IS ! L5G? (! >C =M$ 0! \T]
$GE (A /EP8
.B4 ,"? :AT ANGLE WD Y ROTATE 0CLIMB+
! /AIRS8 ,9CLUDE A SIXTE5? TURN = /EPP+
UP ON ! L&+4 .,EXPLA9 YR R1SON+4
.C4 ,H[ _M SQU>E 9*ES ( C>PET+ WD Y
NE$ 6COV] ! #AE /EPS8
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
.K .,,"W$-.,,\ .,,SOLU;NS ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#HFE
.#ED4 ,,*ALL5GE ,A D>TBO>D IS DIVID$
96#BJ SECTORS4 ,EA* SECTOR IS WOR? A
PO9T VALUE F #A 6#BJ & HAS %AD$ REGIONS
T D\# OR TRIPLE ? VALUE4 ,A SECTOR IS
%[N 2L4
.A4 ,F9D ! >1S (! 5TIRE SECTOR1 ! D\#
REGION1 &! TRIPLE REGION4
.B4 ,A D>T Y ?R[ R&OMLY L&S "S": 9SIDE
! SECTOR4 ,:AT IS ! PROBABIL;Y T X L&S 9
! D\# REGION8 9 ! TRIPLE REGION8
,MIX$ ,REVIEW
,PREVIEW
,PREP>E = ,LESSON #AC.C 9 ,EXS4
#EE-FB4
,SIMPLIFY ! EXPRES.N4 7P4 #BFF
.#EE4
.#EF4
.#EG4
.#EH4
.#EI4
.#FJ4
.#FA4
.#FB4
,WRITE AN EQU,N (! L9E TANG5T 6! GIV5
CIRCLE AT ! GIV5 PO9T4 7P4 #FBF
.#FC4 .;X #B @+ .;Y #B .K #EC27#G1B7
.#FD4 .;X #B @+ .;Y #B .K #DJ27#B1F7
.#FE4 .;X #B @+ .;Y #B .K #ADF27#E1AA7
,F9D ! NUMB] ( P]MUT,NS OR -B9,NS4
.#FF4 #H .;P #C 7P4 #FHB
.#FG4 #G .;P #D 7P4 #FHB
.#FH4 #AB .;P #B 7P4 #FHB
.#FI4 #AJ .;P #H 7P4 #FHB
.#GJ4 #I .;,C #E 7P4 #FIJ
.#GA4 #AE .;,C #G 7P4 #FIJ
.#GB4 #F .;,C #E 7P4 #FIJ
.#GC4 #H .;,C #D 7P4 #FIJ
,,QUIZ .= .,LESSONS .#AC..A-.AC..B
,SOLVE ,,ABC US+ ! DIAGRAM &! GIV5
M1SURE;TS1 @7 P4 #HEB @7
.#A4 .,A .K #EJ;DG1 .A .K#AD
.#B4 .,A .K #BE;DG1 .;B .K #AJ
.#C4 .;,B .K #GJ;DG1 .A .K #E
.#D4 .;,B .K #DB;DG1 .;C .K #AH
.#E4 .,A .K #AE;DG1 .A .K #I
.#F4 .;,B .K #CG;DG1 .;C .K #AB
,F9D "O POSITIVE ANGLE & "O NEGATIVE
ANGLE T >E COT]M9AL )! GIV5 ANGLE1 @7 P4
#HEI @7
.#G4 #AAE;DG
.#H4 #BIJ;DG
.#I4
.#AJ4
.#AA4 ,F9D ! >C L5G? & >EA (A SECTOR
)A RADIUS ( #H 9*ES &A C5TRAL ANGLE ( .K
#AAE;DG4 @7 P4 #HEI @7
.#AB4 .,,ESCALATOR ,! ESCALATOR AT !
,WIL%IRE _/ ,V]MONT ,METRO ,RAIL ,/,N 9
,LOS ,ANGELES HAS AN ANGLE ( ELEV,N (
#CJ;DG4 ,! L5G? (! ESCALATOR IS #AEB
FEET4 ,:AT IS ! HEI<T (! ESCALATOR8 7.;P
@4 .#HEB7
.,,EXTRA .,,PRACTICE = ,LESSON #AC.B1
P4 #AJBB
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#HFF
#AC.C ,EVALUATE ,TRIGONOMETRIC
,FUNC;NS ( ,ANY ,ANGLE
.,2F ,Y EVALUAT$ TRIGONOMETRIC FUNC;NS
( AN ACUTE ANGLE4
.,N[ ,Y W EVALUATE TRIGONOMETRIC
FUNC;NS ( ANY ANGLE4
.,:Y8 ,S Y C CALCULATE 4T.ES 9VOLV+
ROTAT+ OBJECTS1 Z 9 ,EX4 #CG4
,KEY ,VOCABUL>Y
99 UNIT CIRCLE
99 QUADRANTAL ANGLE
99 REF];E ANGLE
,SIDEB>3
,/&>DS
..,MA!MATICAL ,ANALYSIS3 #I.J /UD5TS
-PUTE1 0H&1 ! VALUES (! TRIGONOMETRIC
.FUNC;NS &! 9V]SE TRIGONOMETRIC FUNC;NS
..AT V>I\S /&>D .PO9TS4
..,MA!MATICAL ,ANALYSIS3 #B.J ,/UD5TS
"K ! DEF9I;N ( S9E & COS9E Z ;Y- &
;X-COORD9ATES ( PO9TS ON ! UNIT .CIRCLE
& >E FAMILI> )! GRAPHS (! S9E & COS9E
FUNC;NS4
,Y C G5]ALIZE ! "R-TRIANGLE DEF9I;NS (
TRIGONOMETRIC FUNC;NS F ,LESSON #AC.A S
T !Y APPLY 6.ANY ANGLE 9 /&>D POSI;N4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,G5]AL ,DEF9I;NS ( ,TRIGONOMETRIC
,FUNC;NS
,LET 2 AN ANGLE 9 /&>D POSI;N1 & LET
@7 .;X1 .;Y @7 2 ! PO9T ": ! T]M9AL SIDE
( 9T]SECTS ! CIRCLE .;X #B @+ .;Y #B .K
.;R #B @4 ,! SIX TRIGONOMETRIC FUNC;NS (
.#H >E DEF9$ Z FOLL[S3
,^! FUNC;NS >E "S"TS CALL$ .CIRCUL>
.FUNC;NS @4
,EXAMPLE #A ,EVALUATE TRIGONOMETRIC
FUNC;NS GIV5 A PO9T
,LET 7--#D1 #C7 2 A PO9T ON ! T]M9AL
SIDE ( AN ANGLE 9 /&>D POSI;N4 ,EVALUATE
! SIX TRIGONOMETRIC FUNC;NS ( @4
,SOLU;N
,USE ! ,PY?AGOR1N !OREM 6F9D ! VALUE (
.;R @4
,US+ .;X .K --#D1 .;Y .K #C1 & .;R .K
#E1 Y C WRITE ! FOLL[+3
------------------------------------#HFG
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,! ,UNIT ,CIRCLE
,! CIRCLE .;X #B @+ .;Y #B .K #A1 :
HAS C5T] 7#J1 #J7 & RADIUS #A1 IS CALL$
! .UNIT .CIRCLE4 ,! VALUES ( S9 & COS >E
SIMPLY ! .;Y -COORD9ATE & .;X
-COORD9ATE1 RESPECTIVELY1 (! PO9T ": !
T]M9AL SIDE ( 9T]SECTS ! UNIT CIRCLE4
,X IS 3V5I5T 6USE ! UNIT CIRCLE 6F9D
TRIGONOMETRIC FUNC;NS ( .QUADRANTAL
.ANGLES @4 ,A .QUADRANTAL .ANGLE IS AN
ANGLE 9 /&>D POSI;N ^: T]M9AL SIDE LIES
ON AN AXIS4 ,! M1SURE (A QUADRANTAL
ANGLE IS ALW A MULTIPLE ( #IJ;DG1 OR
RADIANS4
,,EXAMPLE #B ,USE ! UNIT CIRCLE
,USE ! UNIT CIRCLE 6EVALUATE ! SIX
TRIGONOMETRIC FUNC;NS ( .K #BGJ;DG4
,,ANO!R ,,WAY
,! G5]AL CIRCLE .;X #B @+ .;Y #B .K
.;R #B C AL 2 US$ 6F9D ! TRIGONOMETRIC
FUNC;NS ( .K .#BGJ;DG @4 ,! T]M9AL SIDE
( 9T]SECTS ! CIRCLE AT 7#J1 -- .;R @7@4
,"!=E3
,! O!R FUNC;NS C @3 2 EVALUAT$
SIMIL>LY4
,SOLU;N
,DRAW ! UNIT CIRCLE1 !N DRAW ! ANGLE
.K #BGJ;DG 9 /&>D POSI;N4 ,! T]M9AL SIDE
( 9T]SECTS ! UNIT CIRCLE AT 7#J1 --#A71
S USE .;X .K #J & .;Y .K --#A 6EVALUATE
! TRIGONOMETRIC FUNC;NS4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,GUID$ ,PRACTICE = ,EXAMPLES #A &
.#B
,EVALUATE ! SIX TRIGONOMETRIC FUNC;NS
( @4
.#A4
.#B4
.#C4
.#D4 ,USE ! UNIT CIRCLE 6EVALUATE !
SIX TRIGONOMETRIC FUNC;NS ( .K #AHJ;DG4
------------------------------------#HFH
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,REF];E ,ANGLE ,REL,N%IPS
,,R1D+
,! SYMBOL @' IS R1D Z 8!TA PRIME40
,LET 2 AN ANGLE 9 /&>D POSI;N4 ,!
.REF];E .ANGLE = IS ! ACUTE ANGLE @' =M$
0! T]M9AL SIDE (&! .;X -AXIS4 ,!
REL,N%IP 2T & @' IS %[N 2L =
NONQUADRANTAL ANGLES S* T
,QUADRANT ,,II
.,DEGREES3 @' .K #AHJ;DG --
,RADIANS3 ..#J0' .K--.#J
,QUADRANT ,,III
.,DEGREES3 @' .K -- #AHJ;DG
,RADIANS3 @' .K --
,QUADRANT ,,IV
.,DEGREES3 @' .K #CFJ;DG --
,RADIANS3 .@' .K ..#B --
,,EXAMPLE #C ,F9D REF];E ANGLES
,F9D ! REF];E ANGLE @' = 7A7 & 7;B7 .K
--#ACJ;DG4
,SOLU;N
.A4 ,! T]M9AL SIDE ( LIES 9 ,QUADRANT
,,IV4 ,S1 @4
.B4 ,NOTE T IS COT]M9AL ) #BCJ;DG1 ^:
T]M9AL SIDE LIES 9 ,QUADRANT ,,III4 ,S1
@' .K #BCJ;DG--#AHJ;DG .K #EJ;DG4
.,,EVALUAT+ .,,TRIGONOMETRIC
.,,FUNC;NS ,REF];E ANGLES ALL[ Y
6EVALUATE A TRIGONOMETRIC FUNC;N = ANY
ANGLE4 ,! SIGN (! TRIGONOMETRIC FUNC;N
VALUE DEP5DS ON ! QUADRANT 9 : LIES4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,EVALUAT+ ,TRIGONOMETRIC ,FUNC;NS
,USE ^! /EPS 6EVALUATE A TRIGONOMETRIC
FUNC;N = ANY ANGLE @3
.,,/EP .#A .,F9D ! REF];E ANGLE @' @4
.,,/EP .#B .,EVALUATE ! TRIGONOMETRIC
FUNC;N = @' @4
.,,/EP .#C .,DET]M9E ! SIGN (!
TRIGONOMETRIC FUNC;N VALUE F ! QUADRANT
9 : LIES4
------------------------------------#HFI
,,EXAMPLE #D ,USE REF];E ANGLES
6EVALUATE FUNC;NS
,EVALUATE 7A7 TAN 7--#BDJ;DG7 & 7;B7
,SOLU;N
.A4 ,! ANGLE --#BDJ;DG IS COT]M9AL )
#ABJ;DG4 ,! REF];E ANGLE IS @' .K
#AHJ;DG--#ABJ;DG .K #FJ;DG4 ,! TANG5T
FUNC;N IS NEGATIVE 9 ,QUADRANT ,,II1 S Y
C WRITE3
.B4 ,! ANGLE IS COT]M9AL ) @4 ,!
REF];E ANGLE IS @4 ,! COSECANT FUNC;N IS
POSITIVE 9 ,QUADRANT ,,II1 S Y C WRITE3
.,GUID$ .,PRACTICE = ,EXAMPLES #C & #D
,SKET* ! ANGLE4 ,!N F9D XS REF];E
ANGLE4
.#E4 #BAJ;DG
.#F4 --#BFJ;DG
.#G4
.#H4
.#I4 ,EVALUATE COS 7--#BAJ;DG7 )\T US+
A CALCULATOR4
,,EXAMPLE #E ,CALCULATE HORIZONTAL
4T.E TRAVEL$
.,,ROBOTICS ,! 8FROGBOT0 IS A ROBOT
DESIGN$ = EXPLOR+ R\< T]RA9 ON O!R
PLANETS4 ,X C JUMP AT A #DE;DG ANGLE &)
AN 9ITIAL SPE$ ( #AF FEET P] SECOND4 ,ON
,E>?1 ! HORIZONTAL 4T.E .;D 7IN FEET7
TRAVEL$ 0A PROJECTILE LAUN*$ AT AN ANGLE
&) AN 9ITIAL SPE$ .;V 7IN FEET P]
SECOND7 IS GIV5 BY3
,PICTURE3 .,FROGBOT
,,9T]PRET ,,MODELS
,? MODEL NEGLECTS AIR RESI/.E &
ASSUMES T ! PROJECTILE'S />T+ & 5D+
HEI<TS >E ! SAME4
,H[ F> C ! FROGBOT JUMP ON ,E>?8
,SOLU;N
,! FROGBOT C JUMP A HORIZONTAL 4T.E (
#H FEET ON ,E>?4
------------------------------------#HGJ
,,EXAMPLE #F ,MODEL )A TRIGONOMETRIC
FUNC;N
.,,ROCK .,,CLIMB+ ,A ROCK CLIMB] IS
US+ A ROCK CLIMB+ TR1DMILL T IS #AJ.E
FEET L;G4 ,! CLIMB] 2G9S TR1DMILL T IS
#AJ.E FEET L;G4 ,! CLIMB] 2G9S 0LY+
HORIZONT,Y ON ! TR1DMILL1 : IS !N ROTAT$
AB XS MIDPO9T 0#AAJ;DG S T ! ROCK CLIMB]
IS CLIMB+ T[>DS ! TOP4 ,IF ! MIDPO9T (!
TR1DMILL IS #F FEET ABV ! GR.D1 H[ HI<
ABV ! GR.D IS ! TOP (! TR1DMILL8
,SOLU;N
,! TOP (! TR1DMILL IS AB #F @+ #D.IH
.K #AJ.I FEET ABV ! GR.D4
.,,GUID$ .,,PRACTICE = ,EXAMPLES #E &
#F
..#AJ4 ,,TRACK ,,& .,,FIELD ,E/IMATE !
HORIZONTAL 4T.E TRAVEL$ 0A TRACK & FIELD
L;G JUMP] :O JUMPS AT AN ANGLE ( #BJ;DG
&) AN 9ITIAL SPE$ ( #BG FEET P] SECOND4
.#AA4 .,,:AT .,,IF8 ,9 ,EXAMPLE #F1
HOE HI< IS ! TOP (! ROCK CLIMB+ TR1DMILL
IF X IS ROTAT$ #AJJ;DG AB XS MIDPO9T8
#AC.C ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
,,WS#BB = ,EXS4 #E1AG1 & #CG
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE ,EXS4
#B1AA1 #CC1CG1 & #CI
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3
,A7;N78 IS AN ANGLE 9 /&>D POSI;N ^:
T]M9AL SIDE LIES ON AN AXIS4
.#B4 .,,WRIT+ ,GIV5 AN ANGLE 9
,QUADRANT ,,III1 EXPLA9 H[ Y C USE A
REF];E ANGLE 6F9D COS4
,,EXAMPLE #A
ON P4 #HFF = ,EXS4 #C-AA
,,US+ ,A ,,PO9T ,USE ! GIV5 PO9T ON !
T]M9AL SIDE ( AN ANGLE 9 /&>D POSI;N
6EVALUATE ! SIX TRIGONOMETRIC FUNC;NS (
@4
.#C4 7#H1 #AE7
.#D4 7--#I1 #AB7
.#E4 7--#G1 --#BD7
.#F4 7#E1 --#AB7
.#G4 7#B1 --#B7
.#H4 7--#F1 #I7
.#I4 7--#C1 --#E7
.#AJ4
#AA4 .,,MULTIPLE .,,*OICE ,LET 7--#G1
--#D7 2 A PO9T ON ! T]M9AL SIDE ( AN
ANGLE 9 /&>D POSI;N4 ,:AT IS ! VALUE (
TAN8
,A
;,B
;,C
;,D
------------------------------------#HGA
,,QUADRANTAL ,,ANGLES ,EVALUATE ! SIX
TRIGONOMETRIC FUNC;NS ( @4
,,EXAMPLE #B
ON P4 #HFG = ,EXS4 #AB-AE
.#AB4 .K #J;DG
.#AC4
.#AD4 .K #EDJ;DG
.#AE4
,,F9D+ ,,REF];E ,,ANGLES ,SKET* !
ANGLE4 ,!N F9D XS REF];E ANGLE4
,,EXAMPLE #C
ON P4 #HFH = ,EXS4 #AF-BC
.#AF4 --#AJJ;DG
.#AG #AEJ;DG
.#AH4 #CBJ;DG
.#AI4 --#CGJ;DG
.#BJ4
.#BA4
.#BB4
.#BC4
,,EVALUAT+ ,,FUNC;NS ,EVALUATE !
FUNC;N )\T US+ A CALCULATOR4
,,EXAMPLE #D
ON P4 #HFI = ,EXS4 #BD-CA
.#BD4 SEC #ACE;DG
.#BE4 TAN #BDJ;DG
.#BF4 S9 7--#AEJ;DG7
.#BG4 ESC 7--#DBJ;DG7
.#BH4
.#BI4
.#CJ4
.#CA4
.#CB4 .,,]ROR .,,ANALYSIS ,LET 7#D1
#C7 2 A PO9T ON ! T]M9AL SIDE ( AN ANGLE
9 /&>D POSI;N4 .,DESCRIBE & CORRECT !
]ROR 9 F9D+ TAN4
.#CC4 .,,%ORT .,,RESPONSE ,WRITE TAN Z
! RATIO ( TWO O!R TRIGONOMETRIC FUNC;NS4
,USE ? RATIO 6EXPLA9 :Y TAN #IJ;DG IS
UNDEF9$ B COT #IJ;DG .K #J4
.#CD4 .,,*ALL5GE ,FIVE (! MO/ FAM\S
NUMB]S 9 MA!MATICS--#J1 #A1 @1 .;E @1 &
.;I -- >E RELAT$ 0! SIMPLE EQU,N .;E
;I.' @+ #A .K #J4 ,DERIVE ? EQU,N US+
,EUL]'S =MULA3 .;E A @+ BI.' .K ;E A
7COS .;B @+ .;I S9 .;B @7@4
,PRO#M ,SOLV+
,9 ,EX]CISES #CE & #CF1 USE ! =MULA 9
,EXAMPLE #E ON PAGE #HFI @4
,,EXAMPLE #E
ON P4 #HFI = ,EXS4 #CE-CF
.#CE4 .,,FOOTBALL ,Y &A FR EA* KICK A
FOOTBALL ) AN 9ITIAL SPE$ ( #DI FEET P]
SECOND4 ,YR KICK IS PROJECT$ AT AN ANGLE
( #DE;DG & YR FR'S KICK IS PROJECT$ AT
AN ANGLE ( #FJ;DG4 ,AB H[ M* F>!R W YR
FOOTBALL TRAVEL ?AN YR FR'S FOOTBALL8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#CF4 .,,IN-.,,L9E .,,SKAT+ ,AT :AT
SPE$ M/ ! IN-L9E SKAT] LAUN* HMF (F !
RAMP 9 ORD] 6L& ON ! O!R SIDE (! RAMP8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
,,EXAMPLE #F
ON P4 #HGJ = ,EXS4 #CG-CH
.#CG4 .,,%ORT .,,RESPONSE ,A ,F]RIS
:EEL HAS A RADIUS ( #GE FEET4 ,Y BO>D A
C> AT ! BOTTOM (! ,F]RIS :EEL1 : IS #AJ
FEET ABV ! GR.D1 & ROTATE #BEE;DG
C.T]CLOCKWISE 2F ! RIDE TEMPOR>ILY /OPS4
,H[ HI< ABV ! GR.D >E Y :5 ! RIDE /OPS8
,IF ! RADIUS (! ,F]RIS :EEL IS D\#D1 IS
YR HEI<T ABV ! GR.D D\#D8 .,EXPLA9 @4
------------------------------------#HGB
#CH4 .,,MULTI-.,,/EP .,,PRO#M ,:5 TWO
ATOMS 9 A MOLECULE >E BOND$ 6A -MON
ATOM1 *EMI/S >E 9T]E/$ 9 BO? ! BOND
ANGLE &! L5G?S (! BONDS4 ,AN OZ"O
MOLECULE 7,O #C @7 IS MADE UP ( TWO
OXYG5 ATOMS BOND$ 6A ?IRD OXYG5 ATOM1 Z
%[N4
A4 ,9 ! DIAGRAM1 COORD9ATES >E GIV5 9
PICOMET]S 7PM74 @7 .,NOTE3 #A PM .K #AJ
--#AB M47 ,F9D ! COORD9ATES @7 .;X1 .;Y7
(! C5T] (! OXYG5 ATOM 9 ,QUADRANT ,,II4
B4 ,F9D ! 4T.E .;D 7IN PICOMET]S7 2T !
C5T]S (! TWO UNBOND$ OXYG5 ATOMS4
#CI4 .,,EXT5D$ .,,RESPONSE ,A SPR9KL]
AT GR.D LEVEL IS US$ 6WAT] A G>D54 ,!
WAT] L1V+ ! SPR9KL] HAS AN 9ITIAL SPE$ (
#BE FEET P] SECOND4
A4 .,CALCULATE ,COPY ! TA# 2L4 ,USE !
=MULA 9 ,EXAMPLE #E ON PAGE #HFI 6-PLETE
! TA#4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,ANGLE .( .SPR9KL]1 @3 #BE;DG3
#CJ;DG3 #CE;DG3 #DJ;DG3 #DE;DG3 #EJ;DG3
#EE;DG3 #FJ;DG3 #FE;DG
,HORIZONTAL 4T.E WAT] TRAVELS1 .;D @3
@8@3 @8@3 @8@3 @8@3 @8@3 @8@3 @8@3 @8@3
@8
B4 .,9T]PRET ,:AT VALUE ( APPE>S
6MAXIMIZE ! HORIZONTAL 4T.E TRAVEL$ 0!
WAT]8 ,USE ! =MULA = HORIZONTAL 4T.E
TRAVEL$ &! UNIT CIRCLE 6EXPLA9 :Y YR
ANSW] MAKES S5SE4
C4 .,-P>E .,-P>E ! HORIZONTAL 4T.E
TRAVEL$ 0! WAT] :5 .K 7#DE -- .;K 7;DG
)! 4T.E :5 .K 7#DE @+ .;K 7;DG.
#DJ4 .,,*ALL5GE ,! LATITUDE (A PO9T ON
,E>? IS ! DEGREE M1SURE (! %ORTE/ >C F T
PO9T 6! EQUATOR4 ,= EXAMPLE1 ! LATITUDE
( PO9T .;,P 9 ! DIAGRAM EQUALS ! DEGREE
M1SURE ( >C .,,PE @4 ,AT :AT LATITUDE IS
! CIRCUMF];E (! CIRCLE ( LATITUDE AT
.;,P HALF ! 4T.E >.D ! EQUATOR8
,MIX$ ,REVIEW
,PREVIEW
,PREP>E = ,LESSON #AC.D 9 ,EXS4
#DA-DF4
,GRAPH ! FUNC;N .;F @4 ,!N USE ! GRAPH
6DET]M9E :E!R ! 9V]SE ( .;F IS A FUNC;N4
7P4 #B
.#DA4 .;F7.;X7 .K #E .;X @+ #B
.#DB4 .;F7.;X7 .K -- .;X @+ #G
.#DC4 .;F7.;X7 .K .;X #B @+ #E
.#DD4 .;F7.;X7 .K #D .;X #B @1 .;X
.1.K#J
.#DE4 .;F7.;X7 .K #J.BE .;X #B
.#DE4 .;F7.;X7 .K _\ .;X -- #G_\
,F9D ! RANG & /&>D DEVI,N (! DATA SET4
7P4 #B
.#DG4 #C1E1B1C1G1AA1H1D
.#DH4 #AH1AB1AE1I1AC1G1D1AG
.#DI4 #E.I1H.B1C.G1F.A1B.I1A.H1E.G
.#EJ4 #ED1FJ1EG1EC1EI1EA1EF1FB
,F9D ! SUM (! S]IES4
.#EA4
.#EB4
.#EC4
.#ED4
.#EE4
.#EF4
.,,EXTRA .,,PRACTICE = ,LESSON #AC.C1
P4 #AJBB
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#HGC
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
,LESSONS #AC.A-ACC
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
.#A4 .,,MULTI-.,,/EP .,,PRO#M ,YR
S*OOL'S M>*+ B& IS P]=M+ AT HALF"T DUR+
A FOOTBALL GAME4 ,9 ! LA/ =M,N1 ! B&
MEMB]S =M A CIRCLE #AJJ FEET WIDE 9 !
C5T] (! FIELD4 ,Y />T AT A PO9T ON !
CIRCLE #AJJ FEET F ! GOAL L9E1 M>*
#CJJ;DG >.D ! CIRCLE1 & !N WALK T[>D !
GOAL L9E 6EXIT ! FIELD4
.A4 ,H[ F> F ! GOAL L9E >E Y AT ! PO9T
": Y L1VE ! CIRCLE8
.B4 ,H[ F> D Y M>* >.D ! CIRCLE8
.#B4 .,,MULTI-.,,/EP .,,PRO#M ,Y >E
FLY+ A KITE AT AN ANGLE ( #GJ;DG4 ,Y H
LET \ A TOTAL ( #DJJ FEET ( /R+ & >E
HOLD+ ! REEL /1DY #D FEET ABV ! GR.D4
.A4 ,H[ HI< ABV ! GR.D IS ! KITE8
.B4 ,A FR WAT*+ ! KITE E/IMATES T !
ANGLE ( ELEV,N 6! KITE IS #HE;DG4 ,H[ F>
F YR FR >E Y /&+8
.#C4 .,,GRI4$ .,,ANSW] ,:AT IS !
REF];E ANGLE1 9 DEGREES1 =! ANGLE .#F .K
#EFJ;DG8
.#D4 .,,OP5-.,,5D$ ,:AT IS ! M1SURE1 9
DEGREES1 ( AN ANGLE = : ! SECANT IS
POSITIVE &! COTANG5T IS NEGATIVE8
.#E4 .,,%ORT .,,RESPONSE ,! TOP (!
,SPACE ,NE$LE 9 ,S1TTLE1 ,WA%+TON1 IS A
REVOLV+1 CIRCUL> RE/AURANT4 ,! RE/AURANT
HAS A RADIUS ( #DG.BE FEET & MAKES "O
-PLETE REVOLU;N 9 AB AN H\R4 ,Y H D9N]
AT A W9D[ TA# F #G3JJ ,P4,M4 6#H3EE
,P4,M4
.A4 ,H[ _M FEET D Y REVOLVE8
.B4 ,D D9]S S1T$ #E FEET AWAY F !
W9D[S REVOLVE ! SAME 4T.E8 .,EXPLA94
.#F4 .,,MULTI-.,,/EP .,,PRO#M ,Y >E
/&+ #AJJ MET]S F ! MA9 5TR.E (! ,SE>S
,T[] 9 ,*ICAGO1 ,ILL9OIS4 ,Y E/IMATE T !
ANGLE ( ELEV,N 6! TOP (! SKYSCRAP] IS
#GG;DG4
.A4 ,:AT IS ! APPROXIMATE HEI<T .;H (!
,SE>S ,T[]8
.B4 ,SUPPOSE "O ( YR FRS IS AT ! TOP
(! ,SE>S ,T[]4 ,:AT IS ! /RAI<T-L9E 4T.E
.;D 2T Y & YR FR8
.#G4 .,,EXT5D$ .,,RESPONSE ,A PIZZA
%OP (F]S TWO *OICES = 9DIVIDUAL PIZZA
SLICES1 Z %[N4
.A4 ,F9D ! >EA ( EA* SLICE ( PIZZA4
.B4 ,: SLICE IS ! BETT] D1L8 .,EXPLA9
YR R1SON+4
.C4 ,H[ CD Y *ANGE ! PRICE (! #G 9*
SLICE S T NEI SLICE (F]S A BETT] D1L ?AN
! O!R8
------------------------------------#HGD
,9VE/IGAT+ ,ALGEBRA ,ACTIV;Y3 #AC.D
,9VE/IGAT+ ,9V]SE ,TRIGONOMETRIC
,FUNC;NS
,USE 2F ,LESSON1 #AC.D
.,,MAT]IALS 99 PAP] & P5CIL
.,,"Q ,D ! S9E & COS9E FUNC;NS H 9V]SE
FUNC;NS8
.,,EXPLORE ,DET]M9E IF A TRIGONOMETRIC
FUNC;N HAS AN 9V]SE FUNC;N
..,,/EP #A ,MAKE A .TA# ,COPY & -PLETE
! TA# 6F9D ! VALUES ( .;F7 @7 .K S9 &
.;G @7 @7 .K COS = EA* (! GIV5 VALUES (4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 -- @3 @3 @3 @3 .#J @3 @3 @3 @3 --
.;F7 @7 .K S9.' @3 @8 @3 @8 @3 @8 @3
@8 @3 @8 @3 @8 @3 @8 @3 @8 @3 @8
.;G7 @7 .K COS.' @3 @8 @3 @8 @3 @8 @3
@8 @3 @8 @3 @8 @3 @8 @3 @8 @3 @8
..,,/EP #B ,ANALYZE .S9E ,USE ! TA#
6EXPLA9 :Y .;F @7 @7 .K S9 DOES N H AN
9V]SE FUNC;N ON ! DOMA9 -- "K "K @4
..,,/EP #C ,ANALYZE .COS9E ,DOES .;G
@7 @7 .K COS H AN 9V]SE FUNC;N ON !
DOMA9--"K "K @8 ,EXPLA9 :Y OR :Y N4
..,,/EP #D ,USE .GRAPHS ,! GRAPHS (
.;F @7 @7 .K S9 & .;G @7 @7 .K COS >E
%[N =! DOMA9 -- "K "K @4 ,EXPLA9 H[ !
GRAPHS JU/IFY YR ANSW]S 9 ,/EPS #B & #C4
,PICTURE3 ..;F7 @7 .K .S9
,PICTURE3 .;G7.#J7 .K .COS
.,,DRAW .,,3CLU.N ,USE YR OBS]V,NS
6-PLETE ^! EX]CISES
.#A4 ,USE ! GRAPH ( .;F @7 @7 .K S9 9
,/EP #D 6*OOSE A RE/RICT$ DOMA9 = : !
S9E FUNC;N DOES H AN 9V]SE FUNC;N4
.,EXPLA9 H[ Y MADE YR *OICE4
.#B4 ,GIVE A RE/RICT$ DOMA9 = : .;G @7
@7 .K COS HAS AN 9V]SE FUNC;N4 .,EXPLA9
H[ Y *OSE ! DOMA94
.#C4 ,>E ! DOMA9S T Y WROTE 9
,EX]CISES #A & #B ! .ONLY DOMA9S = : !
TRIGONOMETRIC FUNC;NS H 9V]SE FUNC;NS8
.,EXPLA9 @4
------------------------------------#HGE
#AC.D ,EVALUATE ,9V]SE
,TRIGONOMETRIC ,FUNC;NS
.,2F ,Y F.D VALUES ( TRIGONOMETRIC
FUNC;NS GIV5 ANGLES4
.,N[ ,Y W F9D ANGLES GIV5 VALUES (
TRIGONOMETRIC FUNC;NS4
.,:Y8 ,S Y C F9D LAUN* ANGLES1 Z 9
,EXAMPLE #D4
,KEY ,VOCABUL>Y
99 9V]SE S9E
99 9V]SE COS9E
99 9V]SE TANG5T
,S F> 9 ? *APT]1 Y H LE>N$ 6EVALUATE
TRIGONOMETRIC FUNC;NS (A GIV5 ANGLE4 ,9
? LESSON1 Y W /UDY ! REV]SE PRO#M--F9D+
AN ANGLE T CORRESPONDS 6A GIV5 VALUE (A
TRIGONOMETRIC FUNC;N4
,SUPPOSE Y 7 ASK$ 6F9D AN ANGLE ^: S9E
IS #J.E4 ,AF 3SID]+ ! PRO#M1 Y WD R1LIZE
._M S* ANGLES EXI/4 ,= 9/.E1 ! ANGLES
ALL H A S9E VALUE ( #J.E4 ,6OBTA9 A
UNIQUE ANGLE S* T S9 .K #J.E1 Y M/
RE/RICT ! DOMA9 (! S9E FUNC;N4 ,DOMA9
RE/RIC;NS ALL[ ! ..9V]SE S9E1 9V]SE
.COS9E @1 & .9V]SE .TANG5T FUNC;NS 6BE
DEF9$4
,SIDEB>3
,/&>DS
..,MA!MATICAL ,ANALYSIS3 #H.J ,/UD5TS
"K ! DEF9I;NS (! 9V]SE TRIONOMETRIC
.FUNC;N & C GRAPH ! FUNC;N
,,KEY ,,3CEPT .= .,YR .,NOTEBOOK
,9V]SE ,TRIGONOMETRIC ,FUNC;NS
,IF --#A "K .A "K #A1 !N ! .9V]SE .S9E
( .A IS AN ANGLE1 WRITT5 .K S9 --#A .A
@1 ":3
7#A7 S9 .K .A
7#B7
,IF --#A "K .A "K #A1 !N ! .9V]SE
.COS9E ( .A IS AN ANGLE1 WRITT5 .K COS
--#A A1 ":3
7#A7 COS .K .A
7#B7 #J "K "K 7OR #J;DG "K "K #AHJ;DG7
,IF .A IS ANY R1L NUMB]1 !N ! .9V]SE
.TANG5T ( .A IS AN ANGLE1 WRITT5 .K TAN
--#A .A @1 ":3
7#A7 TAN .K .A
7#B7
------------------------------------#HGF
,,EXAMPLE #A ,EVALUATE 9V]SE
TRIGONOMETRIC FUNC;NS
,EVALUATE ! EXPRES.N 9 BO? RADIANS &
DEGREES4
.A4
.B4 S9 --#A #B
.C4
,SOLU;N
.A4 ,:5 #J "K "K @1 OR #J;DG "K "K
#AHJ;DG1 ! ANGLE ^: COS9E IS IS3 OR .;B
@4 ,"! IS NO ANGLE ^: S9E IS #B4 ,S1 S9
--#A #B IS UNDEF9$4
.C4 ,:5 @1 ! ANGLE ^: TANG5T IS IS3 OR
,,EXAMPLE #B ,SOLVE A TRIGONOMETRIC
EQU,N
,SOLVE ! EQU,N ": #AHJ;DG "K "K
#BGJ;DG4
,SOLU;N
,,USE ,A ,,CALCULATOR
,ON MO/ CALCULATORS1 Y C EVALUATE
9V]SE TRIGONOMETRIC FUNC;NS US+ ! KEYS
9V]SE S9E1 = 9V]SE COS9E1 & = 9V]SE
TANG5T4
.,,/EP .#A .,USE A CALCULATOR 6DET]M9E
T 9 ! 9T]VAL --#IJ;DG "K "K #IJ;DG1 !
ANGLE ^: S9E IS @4 ,? ANGLE IS 9
,QUADRANT ,,IV1 Z %[N4
.,,/EP .#B .,F9D ! ANGLE 9 ,QUADRANT
,,III 7": #AHJ;DG "K "K #BGJ;DG7 T HAS !
SAME S9E VALUE Z ! ANGLE 9 ,/EP #A4 ,!
ANGLE IS3
#AHJ;DG @+ #CH.G;DG .K #BAH.G;DG
.,,*ECK ,USE A CALCULATOR 6*ECK !
ANSW]4
.,GUID$ .,PRACTICE = ,EXAMPLES #A & #B
,EVALUATE ! EXPRES.N 9 BO? RADIANS &
DEGREES4
.#A4
.#B4
.#C4 TAN --#A 7--#A7
.#D4
,SOLVE ! EQU,N = #J4
.#E4 COS .K #J.D2 #BGJ;DG "K "K
#CFJ;DG
.#F4 TAN .K #B.A2 #AHJ;DG "K "K
#BGJ;DG
.#G4 S9 .K --#J.BC2 #BGJ;DG "K "K
#CFJ;DG
.#H4 TAN .K #D.G2 #AHJ;DG "K "K
#BGJ;DG
.#I4 S9 .K #J.FB2 #IJ;DG "K "K #AHJ;DG
.#AJ4 COS .K --#J.CI2 #AHJ;DG "K "K
#BGJ;DG
------------------------------------#HGG
,EXAMPLE #C ,/&>DIZ$ ,TE/ ,PRACTICE
,:AT IS ! M1SURE (! ANGLE 9 ! TRIANGLE
%[N8
.,A #BH.F;DG
.;,B #CC.A;DG
.;,C #EF.I;DG
.;,D #FA.D;DG
,SOLU;N
,,AVOID ,,]RORS
,ALL ! ANSW] *OICES >E 9 DEGREES4
,"!=E1 *ECK T \R CALCULATOR IS SET 9
DEGREE MODE1 N RADIAN MODE4
,9 ! "R TRIANGLE1 Y >E GIV5 ! L5G?S (!
SIDE ADJAC5T 6&! HYPOT5USE1 S USE !
9V]SE COS9E FUNC;N 6SOLVE = @4
,! CORRECT ANSW] IS ,C4 ..,A ;,B ;,C
.;,D
,EXAMPLE #D ,WRITE & SOLVE A
TRIGONOMETRIC EQU,N
.,,MON/] .,,TRUCKS ,A MON/] TRUCK
DRIVES (F A RAMP 9 ORD] 6JUMP ONTO A R[
( C>S4 ,! RAMP HAS A HEI<T ( #H FEET &A
HORIZONTAL L5G? ( #BJ FEET4 ,:AT IS !
ANGLE (! RAMP8
,SOLU;N
.,,/EP .#A .,DRAW A TRIANGLE T
REPRES5TS ! RAMP4
.,,/EP .#B .,WRITE A TRIGONOMETRIC
EQU,N T 9VOLVES ! RATIO (! RAMP'S HEI<T
& HORIZONTAL L5G?4
.,,/EP .#C .,USE A CALCULATOR 6F9D !
M1SURE (4
,! ANGLE (! RAMP IS AB #BB;DG4
.,GUID$ .,PRACTICE = ,EXAMPLES #C & #D
,F9D ! M1SURE (! ANGLE @4
.#AA4
.#AB4
.#AC4
.#AD4 .,,:AT .,,IF8 ,9 ,EXAMPLE #D1
SUPPOSE A MON/] TRUCK DRIVES #BF FEET ON
A RAMP 2F JUMP+ ONTO A R[ ( C>S4 ,IF !
RAMP IS #AJ FEET HI<1 :AT IS ! ANGLE (!
RAMP8
------------------------------------#HGH
#AC.D ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
,,WS#BB = ,EXS4 #G1 #BC1 & #CG
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE ,EXS4
#B1AA1 #CJ1 #CA1 #CG1 & #CH
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,!
@8 S9E ( IS @1 OR #CJ;DG4
.#B4 .,,WRIT+ .,EXPLA9 :Y TAN --#A #C
IS DEF9$1 B COS --#A #C IS UNDEF9$4
,,EXAMPLE #A
ON P4 #HGF = ,EXS4 #C-AA
,,EVALUAT+ ,,EXPRES.NS ,EVALUATE !
EXPRES.N )\T US+ A CALCULATOR4 ,GIVE YR
ANSW] 9 BO? RADIANS & DEGREES4
.#C4 S9 --#A #A
.#D4 TAN --#A 7--#A7
.#E4 COS --#A #J
.#F4 COS --#A 7--#B7
.#G4
.#H4
.#I4
.#AJ4
#AA4 .,,MULTIPLE .,,*OICE ,:AT IS !
VALUE (! EXPRES.N @8
,A #J;DG
;,B #CJ;DG
;,C #DE;DG
;,D #FJ;DG
,,US+ ,A ,,CALCULATOR ,USE A
CALCULATOR 6EVALUATE ! EXPRES.N 9 BO?
RADIANS & DEGREES4
.#AB4 S9 --#A #J.AH
.#AC4 TAN --#A #B.F
.#AD4 COS --#A #J.CF
.#AE4 COS --#A 7--#J.D7
.#AF4 TAN --#A 7--#J.GE7
.#AG4 S9 --#A 7--#J.B7
.#AH4 S9 --#A #J.H
.#AI4 COS --#A #J.II
,,SOLV+ ,,EQU,NS ,SOLVE ! EQU,N = #J4
,,EXAMPLE #B
ON P4 #HGF = ,EXS4 #BJ-BF
.#BJ4 COS .K --#J.HB2 #AHJ;DG "K "K
#BGJ;DG
.#BA4 S9 .K --#J.DE2 #AHJ;DG "K "K
#BGJ;DG
.#BB4 S9 .K #J.AE2 #IJ;DG "K "K
#AHJ;DG
.#BC4 TAN .K #C.B2 #AHJ;DG "K "K
#BGJ;DG
.#BD4 TAN .K --#E.C2 #IJ;DG "K "K
#AHJ;DG
.#BE4 COS .K #J.BE2 #BGJ;DG "K "K
#CFJ;DG
.#BF4 .,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 SOLV+ ! EQU,N S9 .K
#J.G ": #IJ;DG "K "K #AHJ;DG4
,,F9D+ ,,ANGLES ,F9D ! M1SURE (! ANGLE
@4
,,EXAMPLE #C
ON P4 #HGG = ,EXS4 #BG-BI
.#BG4
.#BH4
.#BI4
.#CJ4 .,,OP5-.,,5D$ .,,MA? ,SUPPOSE
COS .1 #J & S9 "K #J4 ,GIVE A POSSI#
VALUE ( S* T --#CFJ;DG "K "K #J;DG4
.#CA4 .,,OP5-.,,5D$ .,,MA? ,SUPPOSE S9
"K #J & TAN .1 #J4 ,GIVE A POSSI# VALUE
( S* T #CFJ;DG "K "K #GBJ;DG4
,,*ALL5GE ,REWRITE ! EXPRES.N S T X
DOES N 9VOLVE TRIGONOMETRIC FUNC;NS OR
9V]SE TRIGONOMETRIC FUNC;NS4
.#CB4 CSC 7S9 --#A .;X @7
.#CC4 COT 7TAN --#A .;X @7
.#CD4 SEC 7COS --#A .;X @7
------------------------------------#HGI
,PRO#M ,SOLV+
,,EXAMPLE#D
ON P4 #HGG = ,EXS4 #CE-CG
.#CE4 .,,LA4] .,,ANGLE ,A FIRE TRUCK
HAS A #AJJ FOOT LA4] ^: BASE IS #AJ FEET
ABV ! GR.D4 ,A FIREFI<T] EXT5DS A LA4]
T[>D A BURN+ BUILD+ 6R1* A W9D[ #IJ FEET
ABV ! GR.D4 ,DRAW A DIAGRAM 6REPRES5T ?
SITU,N4 ,AT :AT ANGLE %D ! FIREFI<T] SET
! LA4]8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
..#CF4 ,,ANGLE ,,( .,,DESC5T ,AN
AIRPLANE IS FLY+ AT AN ALTITUDE (
#CA1JJJ FEET :5 X 2G9S XS DESC5T = L&+4
,IF ! RUNWAY IS #AJD MILES AWAY1 AT :AT
ANGLE DOES ! AIRPLANE DESC5D8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#CG4 .,,%ORT .,,RESPONSE ,DI6]5T
TYPES ( GRANUL> SUB/.ES NATUR,Y SETTLE
AT DI6]5T ANGLES :5 /OR$ 9 C"O-%AP$
PILES4 ,! ANGLE IS CALL$ ! .ANGLE .(
.REPOSE @4 ,:5 ROCK SALT IS /OR$ 9 A
C"O-%AP$ PILE #AA FEET HI<1 ! DIAMET] (!
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------------------------------------#HHJ
.#DJ4 .,,*ALL5GE ,Y WANT 6PHOTOGRAPH A
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.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#HHA
,GEOMETRY ,S(TW>E ,ACTIV;Y3 #AC.E
,EXPLORE ! ,LAW ( ,S9ES
,USE 2F ,LESSON #AC.E
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,KEY/ROKES
,SIDEB>3
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,,DESCRIBE ,,CASES
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.A"K.K.;B
,NO TRIANGLE @3
.;H.1 .A
,NO TRIANGLE
.;H .K .A
,"O TRIANGLE
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,"O TRIANGLE @3
..;H "K A "K.;B
,TWO TRIANGLES
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#BJ1 & .;B .K #AA4
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SIDE OPPOSITE .,A IS L;G] ?AN ! GIV5
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#AHJ;DG--#AAE;DG--#BI.I;DG .K #CE.A;DG4
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L5G? .;C (! TRIANGLE4
,9 .,,ABC1 .;,B #BI.I;DG1
;,C--#CE.A;DG1 & .;C #AB.G4
------------------------------------#HHD
,,EXAMPLE #C ,EXAM9E ! ,,SSA CASE ) NO
SOLU;N
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#C.E1 & .;B .K #E4
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5D =M A #EA;DG ANGLE @7 .,A @7 & DRAW A
SEG;T #E UNITS L;G @7 .;,,AC @1 OR .;B
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UNITS L;G @7 .A @7@4 ,Y C SEE T .A NE$S
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#AC1 & .;B .K #AF4
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#AF S9 #DJ;DG #AJ.C1 & #AJ.C "K #AC "K
#AF @7 ..;H "K A "K .;B @7@1 TWO
TRIANGLES C 2 =M$4
,TRIANGLE #A
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#AHJ;DG = : S9 .;,B #J.GIAA4 ,"O IS
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,H1D+S & COLUMNS >E SEP>AT$ 0A
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@3
,9 ,TRIANGLE #A1 .;,B #EB.C;DG1 .;,C
#HG.G;DG1 & ;C #BJ.B4 @3 ,9 ,TRIANGLE
#B1 .;,B #ABG.G;DG1 .;,C #AB.C;DG1 & .;C
#D.C4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
------------------------------------#HHE
.,GUID$ .,PRACTICE = ,EXAMPLES #B1 #C1
& #D
,SOLVE ,,ABC4
.#C4 .,A .K #ABB;DG1 .A .K #AH1 .;B .K
#AB
.#E4 .,A .K #EJ;DG1 .A .K #B.H1 .;B .K
#D
.#D4 .,A .K #CF;DG1 .A .K #I1 .;B .K
#AB
.#F4 .;,B .K #AJE;DG1 .;B .K #AC1 .A
.K #F
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MILES4
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,F9D ! >EA ( .,,ABC )! GIV5 SIDE L5G?S
& 9CLUD$ ANGLE4
.#G4 .A .K #AJ1 .;B .K #AD1 .;,C .K
#DF;DG
.#H4 .A .K #AI1 .;C .K #H1 .;,B .K
#GE;DG
.#I4 .;B .K #AA1 .;C .K #G1 .,A .K
#ABJ;DG
.#AJ4 .A .K #BJ1 .;B .K #BD1 .;,C .K
#HG;DG
------------------------------------#HHF
#AC.E ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
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#B1 #BH1DA1DG1 & #DH
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.,A >E GIV5 = .,,ABC ": .,A "K #IJ;DG4
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TRIANGLE8 TWO TRIANGLES8
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GIV5 M1SURE;TS4 ,!N DECIDE :E!R !
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..,,EXAMPLES #A1B1 #C1 & .#D ON PP4
#HHB-HHD = ,EXS4 #C-BH
.#C4 .,A .K #AAB;DG1 .A .K #I1 .;B .K
#D
.#D4 .,A .K #DJ;DG1 .;,C .K #GE;DG1
.;C .K #BJ
.#E4 .,A .K #EB;DG1 .A .K #CB1 .;B .K
#DB
.#F4 .,A .K #CG;DG1 .A .K #H1 .;B .K
#AD
.#G4 .,A .K #BH;DG1 .;,B .K #FD;DG1
.;C .K #EE
.#H4 .,A .K #ADI;DG1 .A .K #G1 .;B .K
#AJ
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#AF
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.K #HH
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#BE
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.K #AJ
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.K #CC
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------------------------------------#HHG
,,F9D+ ,,>EA ,F9D ! >EA ( .,,ABC )!
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.K #G
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.K #CF
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.K #AG
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#E
.#CD4 .;,C .K #IF;DG1 .A .K #G1 .;B .K
#AE
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.K #BJ
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@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
,,EXAMPLE #B
ON P4 #HHC = ,EX4 #DD
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OBS]V,N DECK (! ,EMPIRE ,/ATE ,BUILD+
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,LIB]TY4 ,Y "K T ! ,*RYSL] ,BUILD+ &!
,EMPIRE ,/ATE ,BUILD+ >E AB #J.F MILE
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,LIB]TY >E AB #E.G MILES A"P4 ,E/IMATE !
4T.E 2T ! ,EMPIRE ,/ATE ,BUILD+ &!
,/ATUE ( ,LIB]TY4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
,,EXAMPLE #E
ON P4 #HHE = ,EXS4 #DE-DF
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G>D5 IS #FB FEET L;G & ANO!R SIDE IS #ED
FEET L;G4 ,! ANGLE OPPOSITE ! #FB FOOT
SIDE IS #EH;DG4
..A4 ,DRAW+ A .,DIAGRAM ,DRAW A
DIAGRAM 6REPRES5T ? SITU,N4
..B4 ,SOLV+ A .,TRIANGLE ,USE ! LAW (
S9ES 6SOLVE ! TRIANGLE Y DREW 9 "P 7A74
..C4 ,APPLY+ A .,=MULA ,"O BAG (
F]TILIZ] COV]S AN >EA ( #BJJ SQU>E FEET4
,H[ _M BAGS ( F]TILIZ] W Y NE$ 6COV] !
5TIRE G>D58
------------------------------------#HHH
#DF4 .,,MULTI-.,,/EP .,,PRO#M
,QUADRILAT]AL .,,ABCD %[N AT ! "R IS A
KITE4
A4 ,F9D ! >EA ( .,,ABD @4
B4 ,F9D ! >EA ( .,,BCD @4
C4 ,:AT IS ! >EA (! KITE8
#DG4 .,,%ORT .,,RESPONSE ,A BUILD+ IS
3/RUCT$ ON TOP (A CLIFF T IS #CJJ MET]S
HI<4 ,A P]SON /&+ ON LEVEL GR.D 2L !
CLIFF OBS]VES T ! ANGLE ( ELEV,N 6! TOP
(! BUILD+ IS #GB;DG1 &! ANGLE ( ELEV,N
6! TOP (! CLIFF IS #FC;DG4
A4 ,H[ F> AWAY IS ! P]SON F ! BASE (!
CLIFF8
B4 .,DESCRIBE TWO DI6]5T ME?ODS Y C
USE 6F9D ! HEI<T (! BUILD+4 ,USE "O ( ^!
ME?ODS 6F9D ! BUILD+'S HEI<T4
#DH4 .,,EXT5D$ .,,RESPONSE ,USE A
GRAPH+ CALCULATOR 6EXPLORE H[ ! 9CLUD$
ANGLE 9 ! =MULAS ON PAGE #HHE A6ECTS A
TRIANGLE'S >EA4
A4 .,MODEL ,*OOSE L5G?S = TWO SIDES (!
TRIANGLE4 ,LET .;X REPRES5T ! M1SURE 7IN
DEGREES7 (! 9CLUD$ ANGLE4 ,WRITE AN
EQU,N T GIVES ! TRIANGLE'S >EA .;Y Z A
FUNC;N ( .;X @4
B4 .,GRAPH+ .,CALCULATOR ,5T] ! EQU,N
F "P 7A7 96A GRAPH+ CALCULATOR4 ,USE !
.TA# F1TURE 6EXAM9E VALUES (! >EA =
#J;DG "K .;X;DG "K #AHJ;DG4 ,DOES ! >EA
ALW 9CR1SE Z .;X 9CR1SES8 .,EXPLA9 @4
C4 .,9T]PRET ,:AT VALUE ( .;X
MAXIMIZES ! TRIANGLE'S >EA8 ,:AT IS !
MAXIMUM >EA1 & H[ IS X RELAT$ 6! SIDE
L5G?S Y *OSE 9 "P 7A78
#DI4 .,,*ALL5GE ,! 4T.E 2T ,M]CURY &!
SUN IS APPROXIMATELY #CF MILLION MILES4
,! 4T.E 2T ,E>? &! SUN IS APPROXIMATELY
#IC MILLION MILES4 ,IF ON A C]TA9 "D !
ANGLE 7M1SUR$ F ,E>?7 2T ! SUN & ,M]CURY
IS #BB;DG1 :AT >E ! POSSI# 4T.ES 2T
,M]CURY & ,E>?8
,MIX$ ,REVIEW
,PREVIEW
,PREP>E = ,LESSON #AC.F 9 ,EXS4
#FB-FG4
,P]=M ! 9DICAT$ OP],N4 7P4 #DBJ
.#EJ4
.#EA4
.#EB4
.#EC4
.#ED4
.#EE4
,P]=M ! 9DICAT$ OP],N & SIMPLIFY4 7P4
#EGC
.#EF4
.#EG4
.#EH4
.#EI4
.#FJ4
.#FA4
,SOLVE ! EQU,N4 = @4 7P4 #DBJ
.#FB4 COS .K #J.GE2#BGJ;DG "K
"K#CFJ;DG
.#FC4 COS .K --#J.F2#AHJ;DG "K
"K#BGJ;DG
.#FD4 COS .K --#J.CE2#IJ;DG "K
"K#AHJ;DG
.#FE4 COS .K #J.JB2#BGJ;DG "K
"K#CFJ;DG
.#FF4 COS .K --#J.BH2#AHJ;DG "K
"K#BGJ;DG
.#FG4 COS .K #J.DG2#BGJ;DG "K
"K#CFJ;DG
.,,EXTRA .,,PRACTICE = ,LESSON #AC.E1
P4 #AJBB
..,,ONL9E ,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#HHI
#AC.F ,APPLY ! ,LAW ( ,COS9ES
.,2F ,Y SOLV$ TRIANGLES US+ ! LAW (
S9ES4
.,N[ ,Y W SOLVE TRIANGLES US+ .! .LAW
( .COS9ES @1
.,:Y8 ,S Y C F9D ANGLES =M$ 0TRAPEZE
>TI/S1 Z 9 ,EX4 #DC4
,KEY ,VOCABUL>Y
99 .LAW .( .COS9ES
,SIDEB>3
,/&>DS
,MA!MATICAL ,ANALYSIS3 #AC.J ,/UD5TS
"K ! LAW ( S9ES &! LAW ( COS9ES & APPLY
^? LAWS PRO#MS4
,MA!MATICAL ,ANALYSIS3 #AC.J ,/UD5TS
DET]M9E ! >EA (A TRIANGLE1 GIV5 "O &!
TWO ADJAC5T SIDS4
,9 ,LESSON #AC.E1 Y SOLV$ TRIANGLES =!
,,AAS1 ,,ASA1 & ,,SSA CASES4 ,9 ?
LESSON1 Y W USE ! .LAW .( .COS9ES 6SOLVE
TRIANGLES :5 TWO SIDES &! 9CLUD$ ANGLE
>E "KN 7,,SAS71 OR :5 ALL ?REE SIDES >E
"KN 7,,SSS74
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,LAW ( ,COS9ES
,IF .,,ABC HAS SIDES ( L5G? .A1 .;B @1
& .;C Z %[N1 !N3
.A #B .K .;B #B @+ .;C #B -- #B .BC
COS .,A
.;B #B .K .A #B @+ .;C #B -- #B .;AC
COS .;,B
.;C #B .K .A #B @+ .;B #B -- #B .;AB
COS .;,C
.,,EXAMPLE .#A ,SOLVE A TRIANGLE =!
,,SAS CASE
,SOLVE .,,ABC ) .A .K #AA1 .;C .K #AD1
& .;,B .K #CD;DG4
,SOLU;N
,USE ! LAW ( COS9ES 6F9D SIDE L5G? .;B
@4
,USE ! LAW ( S9ES 6F9D ! M1SURE (
ANGLE .,A @4
,,ANO!R ,,WAY
,:5 Y "K ALL ?REE SIDES & "O ANGLE1 Y
C USE ! LAW ( COS9ES .OR ! LAW ( S9ES
6F9D ! M1SURE (A SECOND ANGLE4
,! ?IRD ANGLE .;,C (! TRIANGLE IS .;,C
-- #AHJ;DG--#CD;DG--#EA.F;DG .K
#ID.D;DG4
,9 .,,ABC1 .;B #G.HE1 .,A #EA.F;DG1 &
.;,C #ID.D;DG4
------------------------------------#HIJ
,,EXAMPLE #B ,SOLVE A TRIANGLE =!
,,SSS CASE
,SOLVE .,,ABC ) .A .K #AB1 .;B .K #BG1
& .;C .K #BJ4
,SOLU;N
,,AVOID ,,]RORS
,9 ,EXAMPLE #B1 ! L>GE/ ANGLE IS F.D
F/ 6MAKE SURE T ! O!R TWO ANGLES >E
ACUTE4 ,? WAY1 :5 Y USE ! LAW ( S9ES
6F9D ANO!R ANGLE M1SURE1 Y W "K T X IS
2T #J;DG & #IJ;DG4
,F/ F9D ! ANGLE OPPOSITE ! L;GE/ SIDE1
@4 ,USE ! LAW ( COS9ES 6SOLVE = .;,B @4
,N[ USE ! LAW ( S9ES 6F9D .,A @4
,! ?IRD ANGLE .;,C (! TRIANGLE IS .;,C
#AHJ;DG--#BD.B;DG--#AAB.G;DG .K
#DC.A;DG4
,9 .,,ABC1 .,A #BD.B;DG1 .;,B
#AAB.G;DG1 & .;,C #DC.A;DG4
,,EXAMPLE #C ,USE ! LAW ( COS9ES 9 R1L
LIFE
.,,SCI;E ,SCI5TI/S C USE A SET (
FOOTPR9TS 6CALCULATE AN ORGANISM'S ./EP
.ANGLE @1 : IS A M1SURE ( WALK+
E6ICI5CY4 ,! CLOS] ! /EP ANGLE IS
6#AHJ;DG1 ! M E6ICI5TLY ! ORGANISM
WALK$4
,! DIAGRAM AT ! "R %[S A SET (
FOOTPR9TS =A D9OSAUR4 ,F9D ! /EP ANGLE
.;,B @4
,SOLU;N
,! /EP ANGLE .;,B IS AB #ABG.C;DG4
------------------------------------#HIA
.,GUID$ .,PRACTICE = ,EXAMPLES #A1B1 &
#C
,SOLVE .,,ABC @4
.#A4 .A .K #H1 .;C .K #AJ1 .;,B .K
#DH;DG
.#B4 .A .K #AD1 .;B .K #AF1 .;C .K #I
.#C4 .,,:AT .,,IF8 ,9 ,EXAMPLE #C1
SUPPOSE T .A .K #AIC CM1 .;B .K #CCE CM1
& .;C .K #AHF CM4 ,F9D ! /EP ANGLE4
.,,H]ON'S .,,>EA .,,=MULA ,! LAW (
COS9ES C 2 US$ 6E/ABLI% ! FOLL[+ =MULA
=! >EA (A TRIANGLE4 ,! =MULA IS CR$IT$
6! ,GREEK MA!MATICIAN ,H]ON 7CIRCA A4D4
#AJJ74
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,H]ON'S ,>EA ,=MULA
,! >EA (! TRIANGLE ) SIDES ( L5G? .A1
.;B @1 & .;C IS ": @4 ,! V>IA# .;S IS
CALL$ ! .SEMIP]IMET] @1 OR HALF-P]IMET]1
(! TRIANGLE4
,,EXAMPLE #D ,SOLVE A MULTI-/EP PRO#M
.,,URBAN .,,PLANN+ ,! 9T]SEC;N ( ?REE
/REETS =MS A PIECE ( L& CALL$ A TRA6IC
TRIANGLE4 ,F9D ! >EA (! TRA6IC TRIANGLE
%[N4
,,ANO!R ,,WAY
,= AN ALT]NATIVE ME?OD = SOLV+ ! PRO#M
9 ,EXAMPLE #D1 TURN 6PAGE #HIE =!
.,PRO#M .,SOLV+ .,"W%OP4
,SOLU;N
.,,/EP .#A .,F9D ! SEMIP]IMET] .;S @4
.,,/EP#B .,USE ,H]ON'S =MULA 6F9D !
>EA ( .,,ABC @4
,! >EA (! TRA6IC TRIANGLE IS AB
#AH1CJJ SQU>E Y>DS4
.,,GUID$ .,,PRACTICE = ,EXAMPLE #D
,F9D ! >EA ( .,,ABC @4
.#D4
.#E4
.#F4
------------------------------------#HIB
#AC.F ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
,,WS#BC = ,EXS4 #AG1BE1 & #DE
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE ,EXS4
#B1 #BJ1CC1 #CD1DE1 & #DG
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,9 A
TRIANGLE ) SIDES ( L5G? .A1 .;B @1 & IS
CALL$ ! @8 @4
.#B4 .,,WRIT+ ,EXPRESS ,H]ON'S =MULA 9
^WS4
,,*OOS+ ,A ,,ME?OD ,=! GIV5 CASE1 TELL
:E!R Y WD USE ! .LAW .( .S9ES OR ! .LAW
.( .COS9ES 6SOLVE ! TRIANGLE4
..,,EXAMPLES #A & .#B ON PP4 #HHI-HIJ
= ,EXS4 #C-BJ
.#C4 ,,SSS
.#D4 ,,ASA
.#E4 ,,SSA
.#F4 ,,SAS
.#G4 ,,AAS
,,SOLV+ ,,TRIANGLES ,SOLVE .,,ABC @4
.#H4
.#I4
.#AJ4
.,,SOLV+ .,,TRIANGLES .,SOLVE .,,ABC
@4
.#AA4 .;,B .K #BE;DG1 .A .K #H1 .;C .K
#F
.#AB4 .,A .K #AJC;DG1 .;B .K #AE1 .;C
.K #BD
.#AC4 .A .K #AH1 .;B .K #BH1 .;C .K
#AC
.#AD4 .A .K #CH1 .;B .K #CA1 .;C .K
#CE
.#AE4 .;,C .K #DH;DG1 .A .K #AG1 .;B
.K #BJ
.#AF4 .;,B .K #FC;DG1 .A .K #BI1 .;C
.K #CH
.#AG4 .A .K #AJ1 .;B .K #C1 .;C .K#AB
.#AH4 .A .K #BC1 .;B .K #BD1 .;C .K
#BJ
.#AI4 .;,C .K #IF;DG1 .A .K #CE1 .;B
.K #DC
#BJ4 .,,MULTIPLE .,,*OICE ,:AT IS !
M1SURE ( ANGLE .;,B 9 .,,ABC IF .A .K
#AG1 .;B .K #BI1 & .;C .K #AD8
,A #AH.G;DG
;,B #BB.I;DG
;,C #AAA.B;DG
;,D #ACH.D;DG
,,EXAMPLE #D
ON P4 #HIA = ,EXS4 #BA-CC
,,F9D+ ,,>EA ,F9D ! >EA ( .,,ABC @4
.#BA4
.#BB4
.#BC4
,,F9D+ ,,>EA ,F9D ! >EA ( .,,ABC )!
GIV5 SIDE L5G?S4
.#BD4 .A .K #AB1 .;B .K #G1 .;C .K #H
.#BE4 .A .K #E1 .;B .K #AA1 .;C .K #AJ
.#BF4 .A .K #BE1 .;B .K #BD1 .;C .K
#AI
.#BG4 .A .K #AD1 .;B .K #BJ1 .;C .K
#BH
.#BH4 .A .K #CA1 .;B .K #BC1 .;C .K
#AG
.#BI4 .A .K #HA1 .;B .K #FG1 .;C .K
#GA
.#CJ4 .A .K #DC1 .;B .K #EI1 .;C .K
#DH
.#CA4 .A .K #EA1 .;B .K #EA1 .;C .K
#DC
.#CB4 .A .K #CH1 .;B .K #BE1 .;C .K
#FA
#CC4 .,,MULTIPLE .,,*OICE ,:AT IS !
>EA ( .,,ABC X .A .K #BA1 .;B .K #AF1 &
.;C .K #AC8
,A #FF UNITS #B
;,B #AJD UNITS #B
;,C #ACEJ UNITS #B
;,D #DCFH UNITS #B
#CD4 .,,%ORT .,,RESPONSE ,USE ! LAW (
COS9ES 6%[ T ! M1SURE ( EA* ANGLE ( AN
EQUILAT]AL TRIANGLE IS #FJ;DG4 .,EXPLA9
YR R1SON+4
------------------------------------#HIC
.#CE4 .,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 F9D+ ! M1SURE ( ANGLE
.,A 9 .,,ABC IF .A .K #AH1 .;B .K #AE1 &
.;C .K #AJ4
..,,*OOS+ ,A ,,ME?OD ,USE ! .LAW (
S9ES1 .! .LAW ( COS9ES1 ..OR !
,PY?AGOR1N !OREM 6SOLVE .,,ABC @4
.#CF4 .,A .K #GB;DG1 .;,B .K #DD;DG1
.;B .K #AD
.#CG4 .;,B .K #IH;DG1 .;,C .K #CG;DG1
.A .K #AH
.#CH4 .;,C .K #FE;DG1 .A .K #AB1 .;B
.K #BA
.#CI4 .;,B .K #IJ;DG1 .A .K #AE1 .;C
.K #F
.#DJ4 .;,C .K #DJ;DG1 .;B .K #CF1 .;C
.K #BG
.#DA4 .A .K #CD1 .;B .K #AI1 .;C .K
#BG
.#DB4 .,,*ALL5GE ,GIV5 .,,ABC ) HEI<T
.;H @1 DERIVE ! LAW ( COS9ES4 .,EXPLA9
H[ ! ,PY?AGOR1N !OREM IS RELAT$ 6! LAW (
COS9ES4
,,PRO#M ,,SOLV+
,,EXAMPLE #C
ON P4 #HIJ = ,EX4 #DC
.#DC4 .,,TRAPEZE .,,>TI/S ,! DIAGRAM
%[S ! PA?S ( TWO TRAPEZE >TI/S :O >E BO?
#E FEET L;G :5 HANG+ 0_! KNEES4 ,!
8FLY]0 ON ! LEFT B> IS PREP>+ 6MAKE
H&-TO-H& 3TACT )! 8CAT*]0 ON ! "R B>4
,AT :AT ANGLE W ! TWO MEET8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
,,EXAMPLE #D
ON P4 #HIA = ,EXS4 #DD-DE
.#DD4 .,,RESE>* .,,TRIANGLE ,RALEI<1
,DURHAM1 & ,*APEL ,HILL >E ?REE CITIES 9
,NOR? ,C>OL9A T =M :AT IS "KN Z !
,RESE>* ,TRIANGLE4 ,X IS AB #AH MILES F
,RALEI< 6,DURHAM1 #BC MILES F ,RALEI<
6,*APEL ,HILL1 & #H MILES F ,*APEL ,HILL
6,DURHAM4 ,F9D ! >EA (! ,RESE>*
,TRIANGLE4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#DE4 .,,%ORT .,,RESPONSE ,! DIAGRAM
%[S ! DIM5.NS (A PLOT ( L&4 ,:AT IS !
>EA (! L& 9 ACRES8 7,USE ! FACT T #A
ACRE .K #DC1EFJ SQU>E FEET47 .,EXPLA9 H[
Y CD AL DET]M9E ! >EA 0F/ F9D+ ! L5G? (
@4
.#DF4 .,,MULTI-.,,/EP .,,PRO#M ,A
GOLF] HITS A DRIVE #BFJ Y>DS ON A HOLE T
IS #DJJ Y>DS L;G4 ,! %OT IS #AE;DG (F
T>GET4
.A4 ,:AT IS ! 4T.E .;X F ! GOLF]'S
BALL 6! HOLE8
.B4 ,ASSUME ! GOLF] IS A# 6HIT ! BALL
PRECISELY ! 4T.E F.D 9 "P 7A74 ,:AT IS !
MAXIMUM ANGLE 0: ! BALL C 2 (F T>GET 9
ORD] 6L& NO M ?AN #AJ Y>DS F ! HOLE8
------------------------------------#HID
#DG4 .,,EXT5D$ .,,RESPONSE ,/>T+ AT !
SAME PO9T 9 A =E/1 TWO HIK]S TAKE DI6]5T
PA?S4 ,! F/ HIK] WALKS DUE NOR? AT A
SPE$ ( #B MILES P] H\R4 ,! SECOND HIK]
WALKS #FJ;DG EA/ ( NOR? AT A SPE$ ( #C
MILES P] H\R4
A4 ,H[ F> A"P >E ! HIK]S AF #A H\R8
B4 ,! TWO HIK]S C>RY WALKIE-TALKIES )A
RANGE ( #AJ MILES4 ,AF H[ M* "T >E !
HIK]S \ ( RANGE ( EA* O!R8
C4 ,SUPPOSE AF TWO H\RS ! F/ HIK] /OPS
& TELLS ! SECOND HIK] 6MEET H]4 ,H[ L;G
W X TAKE ! SECOND HIK] 6MEET ! F/ HIK]8
,9 :AT DIREC;N %D ! SECOND HIK] WALK8
.,EXPLA9 YR R1SON+4
#DH4 .,,*ALL5GE ,AN AIRPLANE FLIES
#EE;DG EA/ ( NOR? F C;Y ,A 6C;Y ;,B1 A
4T.E ( #DGJ MILES4 ,ANO!R AIRPLANE FLIES
#G;DG NOR? ( EA/ F C;Y ,A 6C;Y ;,C1 A
4T.E ( #HIJ MILES4 ,:AT IS ! 4T.E 2T
CITIES ;,B & ;,C8
,MIX$ ,REVIEW
,PREVIEW
,PREP>E = ,LESSON #AD.A 9 ,EXS4
#DI-ED4
,GRAPH ! FUNC;N4
.#DI4 .;Y .K #I--#D .;X 7P4 #HI
.#EJ4 .;Y .K _\#D .;X -- #E_\ 7P4 #ABC
.#EA4 .;F7.;X7 .K .;X #B -- #AJ .;X @+
#AB 7P4 #BCF
.#EB4
.#EC4 .;Y .K #A.E .;E -- .;X 7P4 #DIB
.#ED4 .;G7.;X7 .K LN7 .;X @+ #D7 7P4
#DII
,DIVIDE US+ SYN!TIC DIVI.N4 7P4 #CFB
.#EE4 @7 .;X #C @+ #H .;X #B @+ #AG
.;X @+ #A7 @/ @7 .;X @+ #D7
.#EF4 @7 .;X #C -- #I .;X #B @+ #BF
.;X -- #AG7 @/ @7 .;X @+ #C7
.#EG4 @7 .;X #D @+ .;X #C @+ #C .;X #B
@+ #G .;X @+ #D7 @/ @7 .;X @+ #D7
.#EH4 @7 .;X #D @+ .;X #C -- #CA .;X
#B @+ #H .;X -- #BB7 @/ @7 .;X -- #E7
,P]=M ! 9DICAT$ OP],N & /ATE ! DOMA94
7P4 #DBH
.#EI4 .;F @+ .;G @2 .;F7.;X7 .K .;X @+
#G1 .;G7.;X7 .K #AJ .;X
.#FJ4
.#FA4 .;F .;G @2 .;F7.;X7 .K #C .;X --
#B1 .;G7.;X7 .K #B .;X #C
.#FB4 .;F7.;G7.;X772 .;F7.;X7 .K .;X
#B -- #F1 .;G7.;X7 .K #H .;X @+ #AA
,,QUIZ .= .,LESSONS .#AC..E-.AC..F
,SOLVE .,,ABC4 @7 PP4 #HHB .& #HHI @7
.#A4 .,A .K #EJ;DG1 .;,B .K #GD;DG1
.;C .K #AB
.#B4 .;,C .K #FF;DG1 .A .K #AH1 .;C .K
#AG
.#C4 .A .K #BJ1 .;B .K #AD1 .;C .K #BC
.#D4 .;,C .K #AAH;DG1 .A .K #BF1 .;B
.K #CD
.#E4 .,A .K #AJB;DG1 .;,C .K #BE;DG1
.A .K #CA
.#F4 .A .K #DI1 .;B .K #EB1 .;C .K #CH
.#G4 .;,B .K #EC;DG1 .A .K #DA1 .;C .K
#BI
.#H4 .,A .K #AAB;DG1 .;,B .K #DH;DG1
.;C .K #E
,F9D ! >EA ( .,,ABC4 @7 PP4 #HHB .&
#HHI @7
.#I4 .;,B .K #ID;DG1 .A .K #AC1 .;C .K
#AE
.#AJ4 .;,C .K #AH;DG1 .A .K #AF1 .;B
.K #AA
.#AA4 .A .K #AH1 .;B .K #BE1 .;C .K
#AI
.#AB4 .A .K #BG1 .;B .K #BA1 .;C .K
#CG
.#AC4 .A .K #FB1 .;B .K #DG1 .;C .K
#EC
.#AD4 .,A .K #GJ;DG1 .;B .K #DD1 .;C
.K #CF
.#AE4 .,,GEOMETRY ,! BASE (A "R
TRIANGUL> PRISM HAS SIDES ( L5G? #H
C5TIMET]S1 #AJ C5TIMET]S1 & #AC
C5TIMET]S4 ,! HEI<T (! PRISM IS #E
C5TIMET]S4 ,:AT IS ! VOLUME (! PRISM8 @7
P4 #HHI @7
.,,EXTRA .,,PRACTICE = ,LESSON #AC.F1
P4 #AJBB
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#HIE
,PRO#M ,SOLV+ ,"W%OP ,LESSON #AC.F3
,US+ ,ALT]NATIVE ,ME?ODS
,ANO!R ,WAY 6,SOLVE ,EXAMPLE #D1 PAGE
#HIA
.,,MULTIPLE .,,REPRES5T,NS ,9 ,EXAMPLE
#D ON PAGE #HIA @1 Y F.D ! >EA (A
TRIANGLE GIV5 ! L5G?S ( XS SIDES 0US+
,H]ON'S =MULA4 ,Y C AL F9D ! >EA (!
TRIANGLE 0WRIT+ & SOLV+ A SY/EM (
EQU,NS4
,,PRO#M
.,,URBAN .,,PLANN+ ,! 9T]SEC;N ( ?REE
/REETS =MS A PIECE ( L& CALL$ A TRA6IC
TRIANGLE4 ,F9D ! >EA (! TRA6IC TRIANGLE
%[N4
,,ME?OD
..,US+ A ,SY/EM ( .,EQU,NS ,USE A
SY/EM ( QUADRATIC EQU,NS 6F9D !
TRIANGLE'S HEI<T .;H @4 ,!N F9D ! >EA (!
TRIANGLE US+ ! =MULA @4
.,,/EP .#A .,DRAW A NEW DIAGRAM (!
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.,,/EP .#B .,USE ! ,PY?AGOR1N !OREM
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.;H #B @+ 7#CEJ -- .;X @7 #B .K #BDJ
#B
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6GET .;H #B .K #AGJ #B -- .;X #B @4
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#AGJ #B -- .;X #B @+ 7#CEJ -- .;X @7
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.;X @+ .;X #B .K #EG1FJJ
--#GJJ .;X .K --#IC1HJJ
.;X .K #ACD
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6F9D T @4 ,S ! >EA (! TRIANGLE IS @4
,! >EA (! TRIANGLE IS AB #AH1CJJ SQU>E
Y>DS4
,,PRACTICE
.,,F9D+ .,,>1S ,USE ! ME?OD ABV 6F9D !
>EA ( .,,ABC )! GIV5 SIDE L5G?S4
.#A4 .A .K #AB1 .;B .K #AG1 .;C .K #BF
.#B4 .A .K #FC1 .;B .K #IB1 .;C .K #HG
.#C4 .A .K #AJA1 .;B .K #ID1 .;C .K
#AEC
.#D4 .,,:AT .,,IF8 ,SUPPOSE .A .K #BJJ
YD 9 ! PRO#M ABV4 ,F9D ! >EA (!
TRIANGLE4
.#E4 .,,G>D5 .,,>EA ,A TRIANGUL> G>D5
HAS SIDES ) L5G?S #EJ FEET1 #CH FEET1 &
#DC FEET4 ,USE ! ME?OD ABV 6F9D ! >EA (!
G>D54
------------------------------------#HIF
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,LESSONS #AC.D-AC.F
.#A4 .,,MULTI-.,,/EP .,,PRO#M ,Y >E
BUY+ A TRIANGUL> PIECE ( PROP]TY4 ,TWO
SIDES (! TRIANGLE >E #EDJ Y>DS & #CCJ
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.A4 ,H[ L;G IS ! ?IRD SIDE (! PROP]TY8
.B4 ,! PRICE (! L& IS 4#BEJJ P] ACRE
7#A ACRE .K #DHDJ SQU>E Y>DS74 ,H[ M*
DOES ! L& CO/8
.#B4 .,,MULTI-.,,/EP .,,PRO#M ,!
,,IKONOS SATELLITE TAKES IMAGES ( ,E>?'S
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.#D4 .,,GRI4$ .,,ANSW] ,AF WALK+ #BJ
FEET 96! WAT] AT A B1*1 Y NOTICE T !
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.#F AT : ! B1* SLOPES4 ,R.D YR ANSW] 6!
NE>E/ T5? (A DEGREE4
.#E4 .,,%ORT .,,RESPONSE ,ON A
BASEBALL FIELD1 ! PIT*]'S M.D AT .;,P IS
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HALF & !N 5CLOS+ ! 5DS4 ,! VOLUME ( WAT]
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METAL4
.A4 ,PREDICT ! VALUE ( T W MAXIMIZE !
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.B4 ,F9D ! VOLUME (! TR\< Z A FUNC;N (
.#F4 ;7.,H9T3 ,Y W NE$ 6F9D ! >EA ( "O
(! TRIANGUL> FACES47
.C4 .,DESCRIBE H[ ! VOLUME *ANGES Z
9CR1SES F #J;DG 6#AHJ;DG4
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.#G4 .,,%ORT .,,RESPONSE ,Y >E BUILD+
A TRIANGUL> 3CRETE PATIO T HAS SIDES (
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BAGS ( CE;T D Y NE$ 6BUILD ! PATIO8
.,EXPLA9 YR R1SON+4
------------------------------------#HIG
#AC ,*APT] ,SUMM>Y
,SIDEB>3
,ANIMAT$ ,ALGEBRA
_+CLASSZONE.COM_:
,ELECTRONIC ,FUNC;N ,LIBR>Y
,,BIG ,,ID1S ,= ,YR ,NOTEBOOK
.,BIG .,IDEA .#A ,US+ ,TRIGONOMETRIC
,FUNC;NS
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.S9E @3
.COS9E @3
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.A .K @1 ": COS .K .A & #J "K.K "K.K @4
@3 ,IF .A IS ANY R1L NUMB]1 !N ! 9V]SE
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.A .K @1 ": TAN .K .A & @4
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,S9ES & ,LAW ( ,COS9ES
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ANGLE-ANGLE-SIDE @3 ,LAW ( S9ES3
REMA9+ SIDES99
ANGLE-SIDE-ANGLE @3 ,LAW ( S9ES3
REMA9+ SIDES99
SIDE-SIDE-ANGLE @3 ,LAW ( S9ES3 REMA9+
SIDE & "O ANGLE99
SIDE-ANGLE-SIDE @3 ,LAW ( COS9ES3
REMA9+ SIDE & "O ANGLE99
SIDE-SIDE-SIDE @3 ,LAW ( COS9ES3 TWO
ANGLES99
99 ,F9D ! REMA9+ ANGLE 0US+ ! TRIANGLE
SUM !OREM4
------------------------------------#HIH
#AC ,*APT] ,REVIEW
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
99 ,MULTI-,LANGUAGE ,GLOSS>Y
99 ,VOCABUL>Y PRACTICE
,REVIEW ,KEY ,VOCABUL>Y
99 S9E1 P4 #HEB
99 COS9E1 ,P4 #HEB
99 TANG5T1 P4 #HEB
99 COSECANT1 P4 #HEB
99 SECANT1 P4 #HEB
99 COTANG5T1 P4 #HEB
99 ANGLE ( ELEV,N1 P4 #HEE
99 ANGLE ( DEPRES.N1 P4 #HEE
99 9ITIAL SIDE ( AN ANGLE1 P4 #HEI
99 T]M9AL SIDE ( AN ANGLE1 P4 #HEI
99 /&>D POSI;N ( AN ANGLE1 P4 #HEI
99 COT]M9AL ANGLES1 P4 #HFJ
99 RADIAN1 P4 #HFJ
99 SECTOR1 P4 #HFA
99 C5TRAL ANGLE1 P4 #HFG
99 UNIT CIRCLE1 P4 #HFG
99 QUADRANTAL ANGLE1 P4 #HFG
99 REF];E ANGLE1 P4 #HFH
99 9V]SE S9E1 P4 #HGE
99 9V]SE COS9E1 P4 #HGE
99 9V]SE TANG5T1 P4 #HGE
99 LAW ( S9ES1 P4 #HHB
99 LAW ( COS9ES1 P4 #HHI
,VOCABUL>Y ,EX]CISES
.#A4 .,,WRIT+ .,DESCRIBE AN ANGLE 9
/&>D POSI;N4
.#B4 ,ID5TIFY ! REL,N%IP 2T ! ANGLES
--#BBE;DG & #ACE;DG4
.#C4 ,:AT IS ! "N (A CIRCLE ) C5T] AT
! ORIG9 & RADIUS #A UNIT8
.#D4 ,COPY & -PLETE3 ,IF COS .K .A &
#J "K.K "K.K @1 !N ! @8 ( .A EQUALS4
.#E4 .,,WRIT+ ,/ATE ! LAW ( S9ES 9
^WS4
,,REVIEW ,,EXAMPLES ,,& ,,EX]CISES
,USE ! REVIEW EXAMPLES & EX]CISES 2L
6*ECK YR "U/&+ (! 3CEPTS Y H LE>N$ 9 EA*
LESSON ( ,*APT] #AC4
#AC.A ,USE ,TRIGONOMETRY ) ,"R
,TRIANGLES PP4 #HEB-HEH
,,EXAMPLE
,EVALUATE ! SIX TRIGONOMETRIC FUNC;NS
(! ANGLE @4
,F ! ,PY?AGOR1N !OREM1 ! L5G? (!
HYPOT5USE IS
,,EX]CISES
,,EXAMPLES
ON PP4 #HEB-HED = ,EXS4 #F-G
.#F4 ,9 .,,ABC1 .A .K #D1 .;B .K #E1 &
.;,C .K #IJ;DG4 ,EVALUATE ! SIX
TRIGONOMETRIC FUNC;NS ( ANGLE .;,B @4
..#G4 ,,HOT ,,AIR .,,BALLOON ,Y >E /&+
#EJ MET]S F A HOT AIR BALLOON T IS
PREP>+ 6TAKE (F4 ,! ANGLE ( ELEV,N 6!
TOP (! BALLOON IS #BH;DG4 ,F9D ! HEI<T
(! BALLOON4
------------------------------------#HII
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,*APT] ,REVIEW ,PRACTICE
#AC.B ,DEF9E ,G5]AL ,ANGLES & ,USE
,RADIAN ,M1SURE ,,PP4 #HEI-HFE
,EXAMPLE
,3V]T #AAJ;DG 6RADIANS & RADIANS
6DEGREES4
,,EX]CISES
,,EXAMPLE #C
ON P4 #HFA = ,EXS4 #H-AA
,3V]T ! DEGREE M1SURE 6RADIANS OR !
RADIAN M1SURE 6DEGREES4
.#H4 #ADE;DG
.#I4 --#HJ;DG
.#AJ4
.#AA4
#AC.C ,EVALUATE ,TRIGONOMETRIC
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,EVALUATE SEC #ABJ;DG4
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#AHJ;DG--#ABJ;DG .K #FJ;DG4 ,! SECANT
FUNC;N IS NEGATIVE 9 ,QUADRANT ,,II1 S Y
C WRITE3
SEC #ABJ;DG .K --SEC #FJ;DG .K --#B
,,EX]CISES
,EVALUATE ! FUNC;N )\T US+ A
CALCULATOR4
,,EXAMPLE #D
ON P4 #HFI = ,EXS4 #AB-AE
.#AB4 TAN #CCJ;DG
.#AC4 CSC 7--#DJE;DG7
.#AD4
.#AE4
#AC.D ,EVALUATE ,9V]SE ,TRIGONOMETRIC
,FUNC;NS ,,PP4 #HGE-HHJ
,EVALUATE TAN --#A #A 9 BO? RADIANS &
DEGREES4
,:5 @1 OR --#IJ;DG "K "K #IJ;DG1 !
ANGLE ^: TANG5T IS #A IS3
OR .K TAN --#A #A .K #DE;DG
,,EX]CISES
,,EXAMPLES #A & #D
ON PP4 #HGF-HGG = ,EXS4 #AF-AG
.#AF4 ,EVALUATE S9 --#A 7--#J.E7 9 BO?
RADIANS & DEGREES4
.#AG4 .,,RAMP ,Y USE A #AB FOOT RAMP
6LOAD ITEMS 96A VAN4 ,IF ! FLOOR (! VAN
IS #D FEET (F ! GR.D1 :AT IS ! ANGLE (
ELEV,N (! RAMP8
------------------------------------#IJJ
#AC ,*APT] ,REVIEW
#AC.E ,APPLY ! ,LAW ( ,S9ES PP4
#HHB-HHH
,,EXAMPLE
,SOLVE .,,ABC ) .,A .K #BH;DG1 .;,C .K
#GD;DG1 & .;B .K #BB4
,F9D ANGLE .;,B3 .;,B .K
#AHJ;DG--#BH;DG--#GD;DG .K #GH;DG4
,USE ! LAW ( S9ES 6SOLVE = .A & .;C @4
,= .,,ABC1 .;,B .K #GH;DG1 .A #AJ.F1 &
.;C #BA.F4
,,EX]CISES
,SOLVE .,,ABC4 7.,H9T3 ,"S (!
8TRIANGLES0 MAY H NO SOLU;N & "S MAY H
TWO SOLU;NS47
,,EXAMPLES #A1B1C & #D
ON PP4 #HHB-HHD = ,EXS4 #AH-BA
.#AH4 .,A .K #DC;DG1 .;,C .K #HC;DG1
.;B .K #AB
.#AI4 .;,B .K #AJD;DG1 .;B .K #BE1 .;C
.K #AH
.#BJ4 .;,C .K #EE;DG1 .A .K #AG1 .;C
.K #AE
.#BA4 .;,B .K #FJ;DG1 .;,C .K #GC;DG1
.;B .K #BJ
#AC.F ,APPLY ! ,LAW ( ,COS9ES PP4
#HHI-HID
,,EXAMPLE
,SOLVE .,,ABC ) .,A .K #FF;DG1 .;B .K
#AF1 & .;C .K #BA4
,USE ! LAW ( COS9ES 6F9D ! L5G? .A4
.A #B .K .;B #B @+ .;C #B -- #B .BC
COS .,A
.A #B .K #AF #B @+ #BA #B --
#B7#AF77#BA7 COS #FF;DG
.A #B #DBC.G
.A #BJ.F
,N[ F9D ANGLE .;,B & ANGLE .;,C @4
.;,B .K S9 --#A #J.GJIE #DE.B;DG
.;,C #AHJ;DG--#FF;DG--#DE.B;DG
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#FH.H;DG1 & .A #BJ.F4
,,EXAMPLES #A & #B
ON PP4 #HHI-HIJ = ,EXS4 #BB-BD
,,EX]CISES
,SOLVE .,,ABC @4
.#BB4 .A .K #AI1 .;B .K #AA1 .;C .K
#AD
.#BC4 .;,B .K #GE;DG1 .A .K #BJ1 .;C
.K #AG
.#BD4 .A .K #CJ1 .;B .K #CE1 .;C .K
#CI
------------------------------------#IJA
#AC ,*APT] ,TE/
,EVALUATE ! SIX TRIGONOMETRIC FUNC;NS
(! ANGLE @4
.#A4
.#B4
.#C4
,3V]T ! DEGREE M1SURE 6RADIANS OR !
RADIAN M1SURE 6DEGREES4
.#D4 #BFJ;DG
.#E4 --#EJ;DG
.#F4
.#G4
,EVALUATE ! FUNC;N )\T US+ A
CALCULATOR4
.#H4 TAN #AEJ;DG
.#I4 SEC 7--#DHJ;DG7
.#AJ4
.#AA4
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.#AB4 COS --#A #A
.#AC4
.#AD4
.#AE4
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8TRIANGLES0 MAY H NO SOLU;N & "S MAY H
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.#AF4 .,A .K #DG;DG1 .;,C .K #CB;DG1
.;C .K #AB
.#AG4 .A .K #BD1 .;B .K #AB1 .;C .K
#AG
.#AH4 .;,B .K #FC;DG1 .A .K #AA1 .;B
.K #H
.#AI4 .;,C .K #AJA;DG1 .A .K #BC1 .;B
.K #AI
.#BJ4 .A .K #BD1 .;B .K #CJ1 .;C .K
#BA
.#BA4 .,A .K #BF;DG1 .;,B .K #GG;DG1
.;C .K #EJ
,F9D ! >EA ( .,,ABC @4
.#BB4 .,A .K #HA;DG1 .;B .K #AF1 .;C
.K #AH
.#BC4 .A .K #H1 .;B .K #F1 .;C .K #G
.#BD4 .A .K #BE1 .;B .K #BD1 .;C .K
#CH
.#BE4 .;,C .K #AAA;DG1 .A .K #G1 .;B
.K #AC
.#BF4 .A .K #AF1 .;B .K #CC1 .;C .K
#BD
.#BG4 .;,B .K #FA;DG1 .A .K #AB1 .;C
.K #AH
.#BH4 .,,SURVEY+ ,6M1SURE ! WID? (A
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IS #AFJ FEET HI<4 ,AT :AT ANGLE %D ! >M
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.#CJ4 .,,NAVIG,N ,A BOAT TRAVELS #DJ
MILES DUE WE/ 2F TURN+ #BJ;DG & TRAVEL+
AN A4I;NAL #BE MILES4 ,H[ F> IS ! BOAT F
XS PO9T ( DE"PURE8
------------------------------------#IJB
#AC ,/&>DIZ$ ,TE/ ,PREP>,N
,SCOR+ ,RUBRIC
,FULL ,CR$IT
99 SOLU;N IS -PLETE & CORRECT
,"PIAL ,CR$IT
99 SOLU;N IS -PLETE B HAS ]RORS1 .OR
99 SOLU;N IS )\T ]ROR B 9COMPLETE
,NO ,CR$IT
99 NO SOLU;N IS GIV51 .OR
99 SOLU;N MAKES NO S5SE
,,%ORT ,,RESPONSE ,,"QS
,,PRO#M
,AC 6! ,,ADA ,A3ESSIBIL;Y ,GUIDEL9ES1
! MAXIMUM SLOPE (A :EEL*AIR RAMP IS
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( AN A3EPTA# RAMP8 ,:AT IS ! ANGLE (
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,SIDEB>3
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.,MA!MATICAL .,ANALYSIS3 #AB.J ,/UD5TS
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,SAMPLE #A3 ,FULL CR$IT SOLU;N
,! DIAGRAM1 CALCUL,NS1 & R1SON+ >E
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,A RAMP )! MAXIMUM A3EPTA# SLOPE IS
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,! L5G? (! RAMP GIV5 9 ! PRO#M IS #CJ
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,S1 & @4
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,! ANSW] IS CORRECT4
,! RAMP GIV5 9 ! PRO#M HAS AN ANGLE (
ELEV,N LESS ?AN ! MAXIMUM A3EPTA# ANGLE1
S ! RAMP MEETS ! ,,ADA GUIDEL9ES4
,SAMPLE #B3 ,"PIAL CR$IT SOLU;N
,! MAXIMUM A3EPTA# ANGLE IS CORRECTLY
CALCULAT$4
,! SLOPE ( AN A3EPTA# RAMP C 2 AT MO/
#A3AB1 S ": IS ! MAXIMUM ANGLE4 ,"!=E1
@4 ,! MAXIMUM ANGLE ( ELEV,N =A :EEL*AIR
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,! /UD5T =GOT 6USE ! SAME UNITS :5
CALCULAT+ SLOPE1 S ! RE/ (! ANSW]S >E
9CORRECT4
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S @4 ,"!=E1 @4 ,! RAMP'S ANGLE ( ELEV,N
IS AB #CA;DG4
,! ANGLE ( ELEV,N EXCE$S ! MAXIMUM
A3EPTA# ANGLE ( ELEV,N1 S ! RAMP DOES N
MEET ! GUIDEL9ES4
------------------------------------#IJC
,,SAMPLE #C3 ,"PIAL CR$IT SOLU;N
,! ANSW] IS CORRECT & CLE>LY EXPLA9$1
B ONLY "O (! ?REE "QS IS ANSW]$4
,! RISE IS #AH 9*ES4 ,! RUN IS #CJ
FEET1 OR @4
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DID N ANSW] ! F9AL "Q4
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ELEV,N IS @4 ,! SLOPE (! RAMP %[N 9 !
PRO#M IS #AH IN43 #CJ FT1 OR #A3BJ1 S !
ANGLE ( ELEV,N IS @4
,,PRACTICE ,APPLY ! ,SCOR+ ,RUBRIC
,USE ! RUBRIC ON PAGE #IJB 6SCORE !
SOLU;N 6! PRO#M 2L Z ..FULL CR$IT1 "PIAL
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,,PRO#M ,F9D ! VOLUME (! "R TRIANGUL>
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#CJ7#F77#FG7 .K #AB1JFJ CM #C
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.DIAGRAM4
,! VOLUME (! PRISM IS 7.>EA (
BASE77HEI<T7 .K #AFA.I7#F7 .K #IGA.D .CM
#E @4
------------------------------------#IJD
#AC ,/&>DIZ$ ,TE/ ,PRACTICE
,,%ORT ,,RESPONSE
#A4 ,KEPL]'S SECOND LAW /ATES T AN
IMAG9>Y L9E 3NECT+ ! C5T] (A PLANET &!
C5T] (! SUN SWEEPS \ EQUAL >1S 9 EQUAL
"T 9T]VALS4 ,! DIAGRAM 2L %[S ! LOC,N (
,M>S 9 ORBIT OV] A T5 "D P]IOD4
A4 ,APPROXIMATE ! >EA ,M>S SWEPT \
DUR+ ? "T 0F9D+ ! >EA (! TRIANGLE =M$ 0!
SUN &! />T+ & 5D+ POSI;NS ( ,M>S4 ,GIVE
! ANSW] 9 SQU>E MILES4 7.,H9T3 #A ,,AU
IS #A A/RONOMICAL UNIT1 : IS EQUAL 6AB
#IC MILLION MILES47
B4 ,Z A PLANET MOVES CLOS] 6! SUN AL;G
XS ORBIT1 :AT DOES ,KEPL]'S LAW IMPLY AB
! PLANET'S SPE$8 .,EXPLA94
#B4 ,! :EEL (A UNICYCLE -PLETES #F
FULL REVOLU;NS4
A4 ,"? :AT ANGLE1 9 DEGREES & RADIANS1
HAS ! :EEL ROTAT$8
B4 ,IF ! DIAMET] (! :EEL IS #BD 9*ES1
H[ F> DOES ! UNICYCLE TRAVEL 9 #F :EEL
REVOLU;NS8 .,EXPLA94
#C4 ,! TA# LI/S S"EAL TOOLS US$ 6MAKE
V]TICAL TRANSI;NS F "O PO9T 6A HI<]
PO9T4 ,X AL LI/S ! RECOMM5D$ RANGE (
ANGLES ( ELEV,N = EA* TOOL4 ,IF A C]TA9
TASK REQUIRES MAK+ A V]TICAL TRANSI;N )A
SLOPE ( : TOOL WD 2 APPROPRIATE =! TASK8
.,EXPLA9 YR R1SON+4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,TOOL3 ,RANGE ( ANGLES
,RAMP3 #J;DG-#CJ;DG
,FIX$ /EPS3 #CJ;DG-#CE;DG
,LA4] /AIRS3 #CE;DG-#GE;DG
,PORTA# /AIRS3 #FH;DG-#HJ;DG
,FIX$ LA4]3 #GE;DG-#IJ;DG
#D4 ,A T5NIS PLAY] IS PRACTIC+ H]
S]VE4 ,%E AIMS =A C PLAC$ #EG FEET F H]
9 ! S]VICE BOX4 ,IF %E HITS ! BALL :5 X
IS #I FEET 9 ! AIR1 :AT ANGLE M/ ! PA?
(! BALL MAKE )! GR.D 9 ORD] =! BALL 6HIT
! C'S BASE8 ,ASSUME ! BALL TRAVELS AL;G
A /RAI<T L9E4 .,EXPLA9 YR ANSW]4
#E4 ,! DIAGRAMS 2L %[ ! 4T.ES 2T ATOMS
9 A WAT] MOLECULE 9 LIQUID & ICE =MS4 ,!
M1SURE;TS >E GIV5 9 PICOMET]S 7PM71 ":
#A PM .K #AJ-- #AB M4 ,>E ! OBTUSE
ANGLES 9 ! DIAGRAMS ! SAME8 .,EXPLA94
#F4 ,Y >E /&+ #CJ FEET F ! BASE (A
TREE4 ,! ANGLE ( ELEV,N F YR EYES 6! TOP
(! TREE IS #GJ;DG4 ,IF ! HEI<T AT EYE
LEVEL IS #E FEET1 :AT IS ! HEI<T (! TREE
6! NE>E/ FOOT8 .,EXPLA9 ALL ( YR /EPS4
#G4 ,Y KICK A SO3] BALL ) AN 9ITIAL
VELOC;Y ( #DJ FEET P] SECOND AT AN ANGLE
( #DE;DG4 ,YR T1MMATE KICKS A SO3] BALL
AT AN ANGLE ( #BE;DG4 ,) :AT 9ITIAL
VELOC;Y DOES YR T1MMATE H 6KICK ! BALL 9
ORD] = BO? (! SO3] BALLS 6TRAVEL ! SAME
HORIZONTAL 4T.E8 .,EXPLA9 YR R1SON+4
#H4 ,F9D ! RADIUS ;R 7IN 9*ES7 &!
C5TRAL ANGLE .#J 7IN RADIANS7 (A SECTOR
) AN >C L5G? ( 9*ES & AN >EA ( SQU>E
9*ES4 .,EXPLA9 YR R1SON+4
------------------------------------#IJE
,,MULTIPLE ,,*OICE
#I4 ,: ANGLE M1SURE IS %[N 9 !
DIAGRAM8
,A
;,B
;,C
;,D
#AJ4 ,:AT IS ! APPROXIMATE VALUE ( .A
9 .,,ABC IF .,A .K #HE;DG1 .;,B .K
#BG;DG1 & .;C .K #E.J CM8
,A #A.J CM
;,B #E.D CM
;,C #E.I CM
;,D #AA.J CM
#AA4 ,:AT IS ! REF];E ANGLE = #CJJ;DG8
,A #CJ;DG
;,B #FJ;DG
;,C #ABJ;DG
;,D #BDJ;DG
,,GRI4$ ,,ANSW]
.#AB4 ,IF IS AN ACUTE ANGLE (A "R
TRIANGLE & @1 :AT IS ! VALUE ( COS8
#E
.#AC4 ,:AT ANGLE1 9 DEGREES1 IS
EQUIVAL5T 6RADIANS8
.#AD4 ,:AT IS ! VALUE ( S9 -#A #J.E 9
DEGREES8
.#AE4 ,:AT IS ! >EA (! TRIANGLE1 6!
NE>E/ T5? (A SQU>E UNIT8
.#AF4 ,LET 7#AJ1 #BD7 2 A PO9T ON !
T]M9AL SIDE ( AN ANGLE .#F 9 /&>D
POSI;N4 ,:AT IS ! VALUE ( SEC #J8
.#AG4 ,:AT IS ! DEGREE M1SURE ( ANGLE
.,A 9 .,,ABC .IF .A.K #AC1 .;B .K #I1 &
.;C .K #G8 ,R.D YR ANSW] 6! NE>E/
DEGREE4
,,EXT5D$ ,,RESPONSE
#AH4 ,A BOAT USES #EJ FEET ( ROPE
6DROP AN*OR 9 A LAKE4 ,! ANGLE .#F T !
ROPE MAKES )! BOTTOM (! LAKE IS #BJ;DG4
A4 ,F9D ! DEP? (! WAT]4
B4 ,! BOAT MOVES 6DEEP] WAT] B / LETS
\ ! SAME AM.T ( ROPE :5 DROPP+ AN*OR4
,IF ! HORIZONTAL 4T.E F ! BOAT 6! AN*OR
IS #CG FEET1 :AT ANGLE .#F DOES ! ROPE
MAKE )! LAKE BOTTOM8
C4 .,DESCRIBE H[ .#F *ANGES Z ! BOAT
TRAVELS 6DEEP] WAT] )A 3/ANT L5G? (
AN*OR ROPE LET \4 ,ASSUME ! ROPE IS ALW
TAUT4
#AI4 ,Y >E MAK+ A LAMP%ADE \ ( FABRIC
=! LAMP %[N4 ,! PATT]N =! LAMP%ADE IS
%[N 9 ! DIAGRAM ON ! LEFT4
A4 ,USE ! SMALL] SECTOR 6WRITE AN
EQU,N T RELATES & .X4
B4 ,USE ! L>G] SECTOR 6WRITE AN EQU,N
T RELATES & .;X @+ #AJ4
C4 ,SOLVE ! SY/EM ( EQU,NS F "PS 7A7 &
7;B7 6F9D .;X &4
D4 ,USE ! =MULA =! >EA (A SECTOR 6F9D
! AM.T ( FABRIC 7IN SQU>E 9*ES7 T Y W
USE4
------------------------------------#IJF
#AD ,TRIGONOMETRIC ,GRAPHS1
,ID5TITIES1 & ,EQU,NS
#AD.A ,GRAPH ,S9E1 ,COS9E1 & ,TANG5T
,FUNC;NS
#AD.B ,TRANSLATE & ,REFLECT
,TRIGONOMETRIC ,GRAPHS
#AD.C ,V]IFY ,TRIGONOMETRIC ID5TITIES
#AD.D ,SOLVE ,TRIGONOMETRIC ,EQU,NS
#AD.E ,WRITE ,TRIGONOMETRIC ,FUNC;NS &
,MODELS
#AD.F ,APPLY ,SUM & ,DI6];E ,=MULAS
#AD.G ,APPLY ,D\#-,ANGLE &
,HALF-,ANGLE ,=MULAS
,SIDEB>3
,2F
,9 ,*APT] #AC1 Y LE>N$ ! FOLL[+
SKILLS1 : Y'LL USE 9 ,*APT] #AD3
EVALUAT+ TRIGONOMETRIC FUNC;NS1 F9D+
REF];E ANGLES1 & EVALUAT+ 9V]SE
TRIGONOMETRIC FUNC;NS4
,PREREQUISITE ,SKILLS
,,VOCABUL>Y ,,*ECK
,COPY & -PLETE ! /ATE;T4
.#A4 ,! .S9E ( IS @8 @4
.#B4 ,! .COS9E ( IS @8 @4
.#C4 ,! .TANG5T ( IS @8 @4
,,SKILLS ,,*ECK
,EVALUATE ! EXPRES.N4 7.,REVIEW P4
#HFF .= .#AD..A47
.#D4 S9 #DE;DG
.#E4
.#F4
,SKET* ! ANGLE4 ,!N F9D XS REF];E
ANGLE4 7.,REVIEW P4 #HFF .= .#AD..A47
.#G4 --#AFE;DG
.#H4 #BHE;DG
.#I4
,EVALUATE ! EXPRES.N4 7.,REVIEW P4
#HGE .= .#AD..D47
.#AJ4
.#AA4 COS --#A #A
.#AB4
------------------------------------#IJG
,SIDEB>3
,N[
,9 ,*APT] #AD1 Y W APPLY ! BIG ID1S
LI/$ 2L & REVIEW$ 9 ! ,*APT] ,SUMM>Y ON
PAGE #IFD @4 ,Y W AL USE ! KEY VOCABUL>Y
LI/$ 2L4
,BIG ,ID1S
.#A ,GRAPH+ TRIGONOMETRIC FUNC;NS
.#B ,SOLV+ TRIGONOMETRIC EQU,NS
.#C ,APPLY+ TRIGONOMETRIC =MULAS
,KEY ,VOCABUL>Y
99 AMPLITUDE1 P4 #IJH
99 P]IODIC FUNC;N1 P4 #IJH
99 CYCLE1 P4 #IJH
99 P]IOD1 P4 #IJH
99 FREQU5CY1 P4 #IAJ
99 TRIGONOMETRIC ID5T;Y1 P4 #IBD
99 S9USOID1 P4 #IDA
,SIDEB>3
,:Y8
,Y C USE TRIGONOMETRIC FUNC;NS 6MODEL
"*I/ICS (A PROJECTILE'S PA?4 ,= EXAMPLE1
Y C F9D ! HORIZONTAL 4T.E TRAVEL$ 0A
SO3] BALL US+ TRIGONOMETRIC FUNC;NS4
.,ANIMAT$ ,ALGEBRA
,! ANIM,N ILLU/RAT$ 2L = ,EX]CISE #EA
ON PAGE #IFA HELPS Y ANSW] ? "Q3 ,H[
DOES *ANG+ ! 9ITIAL SPE$ & ANGLE (A SO3]
BALL KICK$ F GR.D LEVEL A6ECT !
HORIZONTAL 4T.E ! BALL TRAVELS8
,PICTURE3 ,! ANGLE & SPE$ AT : A BALL
IS KICK$ 9FLU;E ! 4T.E X TRAVELS4
,PICTURE3 ,GIV5 A SPE$ & 4T.E1 USE !
MO;N EQU,N 6SOLVE =! KICK ANGLE4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
..,O!R ANIM,NS = ,*APT] .#AD3 PAGES
#IAB @1 #IAG @1 & #IFD
------------------------------------#IJH
#AD.A ,GRAPH ,S9E1 ,COS9E1 & ,TANG5T
,FUNC;NS
.,2F ,Y EVALUAT$ S9E1 COS9E1 & TANG5T
FUNC;NS4
.,,N[ ,Y W GRAPH S9E1 COS9E1 & TANG5T
FUNC;NS4
.,:Y8 ,S Y C MODEL OSCILLAT+ MO;N1 Z 9
,EX4 #CA4
,KEY ,VOCABUL>Y
99 AMPLITUDE
99 P]IODIC FUNC;N
99 CYCLE
99 P]IOD
99 FREQU5CY
,SIDEB>3
,/&>DS
.,MA!MATICAL .,ANALYSIS3 #B.J ,/UD5TS
"K ! DEF9I;N ( S9E & COS9E Z .;Y - & .;X
-COORD9ATES ( PO9TS ON ! UNIT CIRCLE &
>E FAMILI> )! GRAPHS (! S9E & COS9E
FUNC;NS4
.,MA!MATICAL .,ANALYSIS3 .#E..J /UD5TS
"K ! DEF9I;NS (! TANG5T & COTANG5T
FUNC;NS & C GRAPH !M4
,9 ? LESSON1 Y W LE>N 6GRAPH FUNC;NS
(! =M .;Y .K .A S9 .BX & .;Y .K .A COS
.BX ": .A & .;B >E POSITIVE 3/ANTS & .;X
IS 9 RADIAN M1SURE4 ,! GRAPHS ( ALL S9E
& COS9E FUNC;NS >E RELAT$ 6! GRAPHS (!
P>5T FUNC;NS .;Y .K S9 .;X & .;Y .K COS
.;X @1 : >E %[N 2L4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,"*I/ICS ( .;Y .K S9 .;X & .;Y .K COS
.;X
99 ,! DOMA9 ( EA* FUNC;N IS ALL R1L
NUMB]S4
99 ,! RANGE ( EA* FUNC;N IS --#A "K.K
.;Y "K.K #A4 ,"!=E1 ! M9IMUM VALUE ( EA*
FUNC;N IS .;M .K -- #A &! MAXIMUM VALUE
IS .;,M .K #A4
99 ,! .AMPLITUDE ( EA* FUNC;N'S GRAPH
IS HALF ! DI6];E (! MAXIMUM .;,M &!
M9IMUM .;M @1 OR
99 ,EA* FUNC;N IS .P]IODIC @1 : M1NS T
XS GRAPH HAS A REP1T+ PATT]N4 ,! %ORTE/
REP1T+ POR;N (! GRAPH IS CALL$ A .CYCLE4
,! HORIZONTAL L5G? ( EA* CYCLE IS CALL$
! .P]IOD4 ,EA* GRAPH %[N ABV HAS A P]IOD
( .#B @4
99 ,! .;X -9T]CEPTS = .;Y .K S9 .;X
O3UR :5 .;X .K .K#J1+- ,+-#B ,+-#C '
99 ,! .;X -9T]CEPTS = .;Y .K COS .;X
O3UR :5
------------------------------------#IJI
,,KEY ,,3CEPT .= .,YR .,NOTEBOOK
,AMPLITUDE & ,P]IOD
,! AMPLITUDE & P]IOD (! GRAPHS ( .;Y
.K .A S9 .BX & .;Y .K .A COS .BX @1 ":
.A & .;B >E NONZ]O R1L NUMB]S1 >E Z
FOLL[S3
,AMPLITUDE .K _\ .A _\
,P]IOD .K
.,,GRAPH+ .,,KEY .,,PO9TS ,EA* GRAPH
2L %[S FIVE KEY .;X -VALUES ON ! 9T]VAL
T Y C USE 6SKET* ! GRAPHS ( .;Y .K .A S9
.BX & .;Y .K .A COS .BX = .A .1 #J & .;B
.1 #J4 ,^! >E ! .;X -VALUES ": ! MAXIMUM
& .M9IMUM VALUES O3UR &! .;X -.9T]CEPTS4
,,EXAMPLE #A ,GRAPH S9E & COS9E
FUNC;NS
..,GRAPH 7A7 ;Y .K #D S9 ;X & 7;B7 ;Y
.K COS #D .;X @4
,,V>Y ,,3/ANTS
,NOTICE H[ *ANGES 9 .A & .;B A6ECT !
GRAPHS ( .;Y .K .A S9 .BX & .;Y .K .A
COS .BX4 ,:5 ! VALUE ( .A 9CR1SES1 !
AMPLITUDE 9CR1SES4 ,:5 ! VALUE ( .;B3
9CR1SES1 ! P]IOD3 DECR1SES4
,SOLU;N
.A4 ,! AMPLITUDE IS .A .K #D &! P]IOD
IS
.,9T]CEPTS3
.,MAXIMUM3
.,M9IMUM3
.B4 ,! AMPLITUDE IS .A .K #A &! P]IOD
IS
.,9T]CEPTS3
.,MAXIMUMS3
.,M9IMUM3
..,GUID$ ,PRACTICE = ,EXAMPLE .#A
,GRAPH ! FUNC;N4
.#A4 .;Y .K #B COS .;X
.#B4 .;Y .K #E S9 .;X
.#C4 .;F7.;X7 .K S9 .;X
.#D4 .;G7.;X7 .K COS #D .;X
------------------------------------#IAJ
,,EXAMPLE #B ,GRAPH A COS9E FUNC;N
,GRAPH
,,SKET* ,A ,,GRAPH
,AF Y H DRAWN "O -PLETE CYCLE (! GRAPH
9 ,EXAMPLE #B ON ! 9T]VAL #J "K.K .;X
"K.K #A,Y C EXT5D ! GRAPH 0COPY+ ! CYCLE
Z _M "TS Z DESIR$ 6! LEFT & "R ( #J "K.K
.;X "K.K #A4
,SOLU;N
,! AMPLITUDE IS &! P]IOD IS
.,9T]CEPTS3
.,MAXIMUMS3
.,M9IMUM3
..,,MODEL+ ,,) ,,TRIGONOMETRIC
.,,FUNC;NS ,! P]IODIC NATURE (
TRIGONOMETRIC FUNC;NS IS USE;L = MODEL+
.OSCILLAT+ MO;NS OR REP1T+ PATT]NS T
O3UR 9 R1L LIFE4 ,"S EXAMPLES >E S.D
WAVES1 ! MO;N (A P5DULUM1 & S1SONS (!
YE>4 ,9 S* APPLIC,NS1 ! RECIPROCAL (!
P]IOD IS CALL$ ! .FREQU5CY @1 : GIVES !
NUMB] ( CYCLES P] UNIT ( "T4
..,,EXAMPLE #C ,MODEL )A S9E .FUNC;N
.,,AUDIO .,,TE/ ,A S.D 3SI/+ (A S+LE
FREQU5CY IS CALL$ A PURE T"O4 ,AN
.AUDIOMET] PRODUCES PURE T"OS 6TE/ A
P]SON'S AUDITORY FUNC;NS4 ,SUPPOSE AN
AUDIOMET] PRODUCES A PURE T"O )A
FREQU5CY .;F ( #BJJJ H]TZ 7CYCLES P]
SECOND74 ,! MAXIMUM PRESSURE .;,P
PRODUC$ F ! PURE T"O IS #B MILLIPASCALS4
,WRITE & GRAPH A S9E MODEL T GIVES !
PRESSURE .;,P Z A FUNC;N (! "T .;T 7IN
SECONDS74
,SOLU;N
.,,/EP .#A .,F9D ! VALUES ( .A & .;B 9
! MODEL .;,P .K .A S9 .BT4 ,! MAXIMUM
PRESSURE IS #B1 S .A .K .#B4 ,Y C USE !
FREQU5CY .;F 6F9D .B4
,! PRESSURE .;,P Z A FUNC;N ( "T .;T
IS GIV5 0.;,P .K .#B S9 #DJJJ .;T @4
.,,/EP .#B .,GRAPH ! MODEL4 ,!
AMPLITUDE IS .A .K .#B &! P]IOD IS
.,9T]CEPTS3 7.#J1.J72
.,MAXIMUM3
.,M9IMUM3
------------------------------------#IAA
..,GUID$ ,PRACTICE = ,EXAMPLES #B &
.#C
,GRAPH ! FUNC;N4
.#E4
.#F4
.#G4 .;F7.;X7 .K #B S9 #C .;X
.#H4 .;G7.;X7 .K #C COS #D .;X
.#I4 .,,:AT .,,IF8 ,9 ,EXAMPLE #C1 H[
WD ! FUNC;N *ANGE IF ! AUDIOMET] PRODUC$
A PURE T"O )A FREQU5CY ( #AJJJ H]TZ8
..,,GRAPH ,,( ;,Y .K ,,TAN .;,X ,!
GRAPHS ( ALL TANG5T FUNC;NS >E RELAT$ 6!
GRAPH (! P>5T FUNC;N .;Y .K TAN .;X @1 :
IS %[N 2L4
,,F9D ,,ODD ,,MULTIPLES
,ODD MULTIPLES ( .;Y >E VALUES S* Z
^!3
,! FUNC;N .;Y .K TAN .;X HAS ! FOLL[+
"*I/ICS3
.#A4 ,! DOMA9 IS ALL R1L NUMB]S EXCEPT
ODD MULTIPLES ( @4 ,AT ^! .;X -VALUES1 !
GRAPH HAS V]TICAL ASYMPTOTES4
.#B4 ,! RANGE IS ALL R1L NUMB]S4 ,S1 !
FUNC;N .;Y .K TAN .;X DOES N H A MAXIMUM
OR M9IMUM VALUE1 & "!=E ! GRAPH ( .;Y .K
TAN .;X DOES N H AN AMPLITUDE4
.#C4 ,! GRAPH HAS A P]IOD ( @4
.#D4 ,! .;X -9T]CEPTS (! GRAPH O3UR :5
.;X .K .#J ,+- ,+-#B ,+-#C1 '
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,"*I/ICS ( .;Y .K .A TAN .BX
,! P]IOD & V]TICAL ASYMPTOTES (! GRAPH
( .;Y .K .A TAN .BX @1 ": .A & .;B >E
NONZ]O R1L NUMB]S1 >E Z FOLL[S3
99 ,! P]IOD IS
99 ,! V]TICAL ASYMPTOTES >E AT ODD
MULTIPLES (
.,,GRAPH+ .,,KEY .,,PO9TS ,! GRAPH AT
! "R %[S FIVE KEY .;X -VALUES T C HELP Y
SKET* ! GRAPH ( .;Y .K .A TAN .BX = .A
.1 #J & .;B .1 #J4 ,^! >E ! .;X
-9T]CEPT1 ! .;X -VALUES ": ! ASYMPTOTES
O3UR1 &! .;X -VALUES HALFWAY 2T ! .;X
-9T]CEPT &! ASYMPTOTES4 ,AT EA* HALFWAY
PO9T1 ! FUNC;N'S VALUE IS EI .A OR --.A
@4
------------------------------------#IAB
,,EXAMPLE #D ,GRAPH A TANG5T FUNC;N
..,GRAPH "O P]IOD (! FUNC;N ;Y .K #B
TAN #C .;X @4
,SOLU;N
,! P]IOD IS
,9T]CEPT3 7#J1J7
.,ASYMPTOTES3
.,HALFWAY .PO9TS3
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
.,GUID$ .,PRACTICE = ,EXAMPLE #D
,GRAPH "O P]IOD (! FUNC;N4
.#AJ4 .;Y .K #C TAN .;X
.#AA4 .;Y .K TAN #B .;X
.#AB4 .;F7.;X7 .K #B TAN #D .;X
.#AC4 .;G7.;X7 .K #E TAN .;X
#AD.A ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
,,WS#BC = ,EXS4 #E1AG1 & #CA
.K .,,/&>DIZ$ .,,TE/ .,,PRACTICE ,EXS4
#B1AE1 #BD1 #BE1 & #CA
.K .,,MULTIPLE .,,REPRES5T,NS ,EX#.CB
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,!
GRAPHS (! FUNC;NS .;Y .K S9 .;X & .;Y .K
COS .;X BO? H A7;N7 @8 ( #B4
#B4 .,,WRIT+ .,-P>E ! DOMA9S & RANGES
(! FUNC;NS .;Y .K .A S9 =1 .;Y .K .A COS
.BX @1 & .;Y .K .A TAN .BX ": .A & .;B
>E POSITIVE 3/ANTS4
,,EXAMPLE #A
ON P4 #IJI = ,EXS4 #C-AD
,,ANALYZ+ ,,FUNC;NS ,ID5TIFY !
AMPLITUDE &! P]IOD (! GRAPH (! FUNC;N4
.#C4
.#D4
.#E4
------------------------------------#IAC
,,GRAPH+ ,GRAPH ! FUNC;N4
.#F4
.#G4 .;Y .K #D;COS .;X
.#H4
.#I4 .;Y .K S9 .;X
.#AJ4
.#AA4
.#AB4
.#AC4 .;F7.;X7 .K COS#BD .;X
.#AD4 .,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 F9D+ ! P]IOD (! FUNC;N
#AE4 .,,MULTIPLE .,,*OICE ,! GRAPH ( :
FUNC;N HAS AN AMPLITUDE ( #D &A P]IOD (
#B8
,A .;Y .K #D COS .#B;X
;,B .;Y .K .#B S9 #D .;X
;,C .;Y .K #D S9 .;X
;,D
,,GRAPH+ ,GRAPH ! FUNC;N4
,,EXAMPLES #B1 #C1 & #D
ON PP4 #IAJ-IAB = ,EXS4 #AF-BD
.#AF4 .;Y .K .#B S9 #H .;X
.#AG4 .;F @7 .;X @7 .K #D TAN .;X
.#AH4 .;Y .K #C COS .;X
.#AI4 .;Y .K #E S9 .#B;X
.#BJ4 .;F7.;X7 .K #B TAN #D .;X
.#BA4
.#BB4 .;F @7 .;X @7 .K #D TAN .;X
.#BC4 .;Y .K COS #D .;X
.#BD4 .,,MULTIPLE .,,*OICE ,: (!
FOLL[+ IS AN ASYMPTOTE (! GRAPH ( .;Y .K
#B TAN #C .;X @8
,A4
,B4 .;X .K --
,C4
,D4
#BE4 .,,OP5-.,,5D$ .,,MA? .,DESCRIBE A
R1L-LIFE SITU,N T C 2 MODEL$ 0A P]IODIC
FUNC;N4
,,*ALL5GE ,SKET* ! GRAPH (! FUNC;N
0PLOTT+ PO9TS4 ,!N /ATE ! FUNC;N'S
DOMA91 RANGE1 & P]IOD4
.#BF4 .;Y .K CSC .;X
.#BG4 .;Y .K SEC .;X
.#BH4 .;Y .K COT .;X
,,PRO#M ,,SOLV+
,,EXAMPLE #C
ON P4 #IAJ = ,EXS4 #BI-CJ
.#BI4 .,,P5DULUMS ,! MO;N (A C]TA9
P5DULUM C 2 MODEL$ 0! FUNC;N .;D .K #D
COS .;T ": .;D IS ! P5DULUM'S HORIZONTAL
4PLACE;T 7IN 9*ES7 RELATIVE 6XS POSI;N
AT RE/ & .;T IS ! "T 7IN SECONDS74
,GRAPH ! FUNC;N4 ,:AT IS ! GRTE/
HORIZONTAL 4T.E ! P5DULUM W TRAVEL F XS
POSI;N AT RE/8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#CJ4 .,,TUN+ .,,=KS ,A TUN+ =K
PRODUCES A S.D PRESSURE WAVE T C 2
MODEL$ BY
.;,P .K #J.JJA S9 #HHJ .;T
": .;,P IS ! PRESSURE 7IN PASCALS7 &
.;T IS ! "T 7IN SECONDS74 ,F9D ! P]IOD &
FREQU5CY ( ? FUNC;N4 ,!N GRAPH ! FUNC;N4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
------------------------------------#IAD
.#CL4 .,,%ORT .,,RESPONSE ,A BUOY
OSCILLATES UP & D[N Z WAVES G PA/4 ,!
BUOY MOVES A TOTAL ( #C.E FEET F XS L[
PO9T 6XS HI< PO9T1 & !N RETURNS 6XS HI<
PO9T E #F SECONDS4
A4 ,WRITE AN EQU,N T GIVES ! BUOY'S
V]TICAL POSI;N .;Y AT "T .;T IF ! BUOY
IS AT XS HI<E/ PO9T :5 .;T.K.#J4
B4 .,EXPLA9 :Y Y *OSE .;Y .K .A S9 .BT
OR .;Y .K .A COS .BT = "P 7A74
#CB4 .,,MULTIPLE .,,REPRES5T,NS ,Y >E
/&+ ON A BRIDGE1 #ADJ FEET ABV ! GR.D4
,Y LOOK D[N AT A C> TRAVEL+ AWAY F !
"UPASS4
A4 .,WRIT+ .AN .,EQU,N ,WRITE AN EQU,N
T GIVES ! C>'S 4T.E .;D F ! BASE (!
BRIDGE Z A FUNC;N (! ANGLE @4
B4 .,DRAW+ .A .,GRAPH ,GRAPH ! FUNC;N
F.D 9 "P 7A74 .,EXPLA9 H[ ! GRAPH
RELATES 6! GIV5 SITU,N4
C4 .,MAK+ .A .,TA# ,MAKE A TA# (
VALUES =! FUNC;N4 ,USE ! TA# 6F9D ! C>'S
4T.E F ! BRIDGE :5 .K #BJ;DG1 #DJ;DG1 &
#FJ;DG4
#CC4 .,,*ALL5GE ,! MO;N (A SPR+ C 2
MODEL$ 0.;Y .K .,A COS .KT ": .;Y IS !
SPR+'S V]TICAL 4PLACE;T 7IN FEET7
RELATIVE 6XS POSI;N AT RE/1 .,A IS !
9ITIAL 4PLACE;T 7IN FEET71 ,A2 IS A
3/ANT T M1SURES ! ELA/IC;Y (! SPR+1 &
.;T IS ! "T 7IN SECONDS74
A4 ,SUPPOSE Y H A SPR+ ^: MO;N C 2
MODEL$ 0! FUNC;N .;Y .K #J.B COS #F .T4
,F9D ! 9ITIAL 4PLACE;T &! P]IOD (! SPR+4
,!N GRAPH ! GIV5 FUNC;N4
B4 .,GRAPH+ .,CALCULATOR ,IF A DAMP+
=CE IS APPLI$ 6! SPR+1 ! MO;N (! SPR+ C
2 MODEL$ 0! FUNC;N .;Y .K #J.B;E --#D.E
.;T COS #D .T4 ,GRAPH ? FUNC;N4 ,:AT
E6ECT DOES DAMP+ H ON ! MO;N8
,,MIX$ ,,REVIEW
,,PREVIEW
,PREP>E = ,LESSON #AD.B 9 ,EXS4
#CD-CI4
,GRAPH ! FUNC;N4 ,LABEL ! V]TEX &!
AXIS ( SYMMETRY4 @7 P4 #BDE @7
.#CD4 ;Y .K --7;X-#B7 #B @+ #A
.#CE4 ;Y .K #E 7;X--#A7 #B @+ #G
.#CF4 ;F7;X7 .K #B7;X @+ #F7#B--#C
.#CG4 ;Y .K --#C7;X @+ #C7 #B @+ #B
.#CH4 ;Y .K #J.E7;X @+ #B7 #B @+ #E
.#CI4 ;G7;X7 .K --#B7;X @+ #D7 #B --
#C
,LET .;F @7 .;X @7 .K ;X #B -- #E1
;G;7;X7 .K --#G;X1 & ;H7;X7 .K ;X #A/C
@4 ,F9D ! 9DICAT$ VALUE4 @7 P4 #DBH @7
.#DJ4 ;G7;F7#I77
.#DA4 ;H7;G7#C77
.#DB4 ;F7;G7-#G77
.#DC4 ;F7;H7#H77
,SKET* ! ANGLE4 ,!N F9D XS REF];E
ANGLE4 @7 P4 #HFF @7
.#DD4 #BEJ;DG
.#DE4 #BIJ;DG
.#DF4 --#ADE;DG
.#DG4 --#DCJ;DG
.#DH4
.#DI4
.#EJ4
.#EA4
.,,EXTRA .,,PRACTICE = ,LESSON #AD.A1
P4 #AJBC
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#IAE
#AD.B ,TRANSLATE & ,REFLECT
,TRIGONOMETRIC ,GRAPHS
.,2F ,Y GRAPH$ S9E1 COS9E1 & TANG5T
FUNC;NS4
.,N[ ,Y W TRANSLATE & REFLECT
TRIGONOMETRIC GRAPHS4
.,:Y8 ,S Y C MODEL PR$ATOR-PREY
POPUL,NS1 Z 9 ,EX4 #ED4
,KEY ,VOCABUL>Y
99 TRANSL,N1 P4 #ABC
99 REFLEC;N1 P4 #ABD
99 AMPLITUDE1 P4 #IJH
99 P]IOD1 P4 #IJH
,SIDEB>3
,/&>DS
,MA!MATICAL ,ANALYSIS3 #D.J ,/UD5TS
GRAPH FUNC;NS (! =M ;F7;T7 .K ,A S9 7,BT
@+ ;,C7 OR ;F7;T7 .K ,A COS 7,BT @+ ;,C7
& 9T]PRET ,A1 ;,B1 & ;,C 9 T]MS (
AMPLITUDE1 FREQU5CY1 P]IOD1 & PHASE
%IFT4
,,KEY ,,3CEPT .,= .YR .,NOTEBOOK
,TRANSL,NS ( ,S9E & ,COS9E ,GRAPHS
,6GRAPH .;Y .K .A S9 .;B7.;X--.;H7 @+
.;K OR .;Y .K .A COS .;B7.;X--.;H7 @+
.;K ": .A .1 #J & .;B .1 #J1 FOLL[ ^!
/EPS3
.,,/EP .#A .,ID5TIFY ! AMPLITUDE .A @1
! P]IOD ! HORIZONTAL %IFT .;H @1 &!
V]TICAL %IFT .;K (! GRAPH4
.,,/EP .#B .,DRAW ! HORIZONTAL L9E .;Y
.K .;K @1 CALL$ ! .MIDL9E (! GRAPH4
.,,/EP .#C .,F9D ! FIVE KEY PO9TS
0TRANSLAT+ ! KEY PO9TS ( .;Y .K .A S9
..BX OR ;Y .K .A COS .BX HORIZONT,Y .;H
UNITS & V]TIC,Y .;K UNITS4
.,,/EP .#D .,DRAW ! GRAPH "? ! FIVE
TRANSLAT$ KEY PO9TS4
,,EXAMPLE #A ,GRAPH A V]TICAL TRANSL,N
,GRAPH .;Y .K .#B S9 #D .;X @+ #C4
,SOLU;N
.,,/EP .#A .,ID5TIFY ! AMPLITUDE1
P]IOD1 HORIZONTAL %IFT1 & V]TICAL %IFT4
,AMPLITUDE3 .A .K #B
,HORIZONTAL %IFT3 .;H .K #J
,P]IOD3
,V]TICAL %IFT3 .;K .K #C
.,,/EP .#B .,DRAW ! MIDL9E (! GRAPH1
.;Y .K #C4
,,F9D ,,KEY ,,PO9TS
,2C ! GRAPH IS %IFT$ UP #C UNITS1 !
.;Y -COORD9ATES (! FIVE KEY PO9TS W 2
9CR1S$ 0#C4
.,,/EP .#C .,F9D ! FIVE KEY PO9TS4
.,ON .;Y.K.;K3 7#J1J @+ #C7 .K 7#J1C72
.,MAXIMUM3
.,M9IMUM3
.,,/EP .#D ,DRAW ! GRAPH "? ! KEY
PO9TS4
------------------------------------#IAF
,,EXAMPLE #B ,GRAPH A HORIZONTAL
TRANSL,N
.,GRAPH .;Y .K ..#E COS #B 7;X -- .#C
@7@4
,SOLU;N
.,,/EP .#A .,ID5TIFY ! AMPLITUDE1
P]IOD1 HORIZONTAL %IFT1 & V]TICAL %IFT4
,AMPLITUDE3 .A .K #E
,HORIZONTAL %IFT3 .;H .K #C
,P]IOD3
,V]TICAL %IFT3 .;K .K #J
.,,/EP .#B .,DRAW ! MIDL9E (! GRAPH4
,2C .;K .K #J1 ! MIDL9E IS ! .;X -AXIS4
,,F9D ,,KEY ,,PO9TS
,2C ! GRAPH IS %IFT$ 6! "R #C UNITS1 !
;X-COORD9ATES (! FIVE KEY PO9TS W 2
9CR1S$ 0#C @4
.,,/EP .#C .,F9D ! FIVE KEY PO9TS4
..,ON ;Y .K .;K
.,MAXIMUMS3 7#J @+ #C1 #J7 .K 7#C1
#E72
@7 @+ #C @1 #E7 .K 7#D @1 #E7
.,M9IMUM3
.,,/EP .#D .,DRAW ! GRAPH "? ! KEY
PO9TS4
,,EXAMPLE #C ,GRAPH A MODEL = CIRCUL>
MO;N
.,,F]RIS .,,:EEL ,SUPPOSE Y >E RID+ A
,F]RIS :EEL T TURNS = #AHJ SECONDS4 ,YR
HEI<T .;H 7IN FEET7 ABV ! GR.D AT ANY "T
.;T 7IN SECONDS7 C 2 MODEL$ 0! EQU,N @4
.A4 ,GRAPH YR HEI<T ABV ! GR.D Z A
FUNC;N ( "T4
.B4 ,:AT >E YR MAXIMUM & M9IMUM
HEI<TS8
,SOLU;N
.A4 ,! AMPLITUDE IS #HE &! P]IOD IS @4
,! :EEL TURNS "TS 9 #AHJ SECONDS1 S !
GRAPH 2L %[S #D.E CYCLES4 ,! FIVE KEY
PO9TS >E 7#AJ1 #IJ71 7#BJ1 #AGE71 7#CJ1
#IJ71 7#DJ1 #E71 & 7#EJ1 #IJ74
.B4 ,YR MAXIMUM HEI<T IS #IJ @+ #HE .K
#AGE FEET & YR M9IMUM HEI<T IS #IJ--#HE
.K #E FEET4
------------------------------------#IAG
..,GUID$ ,PRACTICE = ,EXAMPLES #A1B1 &
.#C
,GRAPH ! FUNC;N4
.#A4 .;Y .K COS .;X @+ #D
.#B4
.#C4 .;F7.;X7 .K S9 @7 .;X @+ @7 - .#A
.,,REFLEC;NS ,Y H GRAPH$ FUNC;NS (! =M
.;Y .K .A S9 ..;B7;X--;H7 @+ .;K & .;Y
.K .A COS ..;B7;X--;H7 @+ .;K ": .A .1
#J4 ,6SEE :AT HAPP5S :5 .A "K #J1 3SID]
! GRAPHS ( .;Y .K --S9 .;X & .;Y .K
--COS .;X @4
,NOTICE T ! GRAPHS >E REFLEC;NS (!
GRAPHS ( .;Y .K S9 .;X & .;Y .K COS .;X
9 ! .;X -AXIS4 ,9 G5]AL1 :5 .A "K #J !
GRAPHS ( .;Y .K .A S9 ..;B7;X--;H7 @+
.;K & .;Y .K A COS ..;B7;X--;H7 @+ .;K
>E REFLEC;NS (! GRAPHS ( .;Y .K _\A_\ S9
..;B7;X--;H7 @+ .;K & .;Y .K _\A_\ COS
..;B7;X--;H7 @+ .;K @1 RESPECTIVELY1 9 !
MIDL9E .;Y .K .K4
,,EXAMPLE #D ,-B9E A TRANSL,N &A
REFLEC;N
.,GRAPH
,SOLU;N
.,,/EP .#A .,ID5TIFY ! AMPLITUDE1
P]IOD1 HORIZONTAL %IFT1 & V]TICAL %IFT4
,AMPLITUDE3 _\ .A _\ .K _\-- #B_\ .K
.#B
,HORIZONTAL %IFT3
,P]IOD3
,V]TICAL %IFT3 .;K .K #J
.,,/EP .#B .,DRAW ! MIDL9E (! GRAPH4
,2C .;K .K #J1 ! MIDL9E IS ! .;X -AXIS4
.,,/EP .#C .,F9D ! FIVE KEY PO9TS (
..,ON ;Y .K .;K @3
.,MAXIMUM3
.,M9IMUM3
,,GRAPH ,,REFLEC;NS
,! MAXIMUM & M9IMUM (! ORIG9AL GRAPH
2COME ! M9IMUM & MAXIMUM1 RESPECTIVELY1
(! REFLECT$ GRAPH4
.,,/EP .#D .,REFLECT ! GRAPH4 ,2C .A
"K #J1 ! GRAPH IS REFLECT$ 9 ! MIDL9E
.;Y .K #J4 ,S1 2COMES & 2COMES @4
.,,/EP .#E .,DRAW ! GRAPH "? ! KEY
PO9TS4
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
------------------------------------#IAH
.,,TANG5T .,,FUNC;NS ,GRAPH+ TANG5T
FUNC;NS US+ TRANSL,NS & REFLEC;NS IS
SIMIL> 6GRAPH+ S9E & COS9E FUNC;NS4
,,EXAMPLE #E ,-B9E A TRANSL,N &A
REFLEC;N
,GRAPH .;Y .K --#C TAN .;X @+ #E4
,SOLU;N
,SOLU;N
.,,/EP .#G .,ID5TIFY ! P]IOD1
HORIZONTAL %IFT1 & V]TICAL %IFT4
,P]IOD3
,HORIZONTAL %IFT3 .;H .K #J
,V]TICAL %IFT3 .;K .K #E
.,,/EP .#B .,DRAW ! MIDL9E (! GRAPH1
.;Y .K #E4
.,,/EP .#C .,F9D ! ASYMPTOTES & KEY
PO9TS ( .;Y .K _\ --#C _\ TAN .;X @+ #E4
,,F9D ,,ASYMPTOTES
,NOTICE T ! ASYMPTOTES >E N %IFT$4 ,?
IS 2C "! IS NO HORIZONTAL %IFT4
.,ASYMPTOTES3
.,ON .;Y .K .;K @3 7#J1 #J @+ #E7 .K
7#J1 #E7
.,HALFWAY .PO9TS3
.,,/EP .#D .,REFLECT ! GRAPH4 ,2C .A
"K #J1 ! GRAPH IS REFLECT$ 9 ! MIDL9E
2COMES & 2COMES @4
.,,/EP .#E .,DRAW ! GRAPH "? ! KEY
PO9TS4
,,EXAMPLE #F ,MODEL )A TANG5T FUNC;N
.,,GLASS .,,ELEVATOR ,Y >E /&+ #ABJ
FEET F ! BASE (A #BFJ FOOT BUILD+4 ,Y
WAT* YR FR G D[N ! SIDE (! BUILD+ 9 A
GLASS ELEVATOR4 ,WRITE & GRAPH A MODEL T
GIVES YR FR'S 4T.E .;D 7IN FEET7 F ! TOP
(! BUILD+ Z A FUNC;N (! ANGLE ( ELEV,N
@4
,SOLU;N
,USE A TANG5T FUNC;N 6WRITE AN EQU,N
RELAT+ .;D & @4
,! GRAPH ( .;D .K --#ABJ TAN @+ #BFJ
IS %[N AT ! "R4
------------------------------------#IAI
..,GUID$ ,PRACTICE = ,EXAMPLES #D1E1 &
.#F
,GRAPH ! FUNC;N4
.#D4
.#E4
.#F4 .;F7.;X7 .K --TAN #B .;X -- #A
.#G4 .,,:AT .,,IF8 ,9 ,EXAMPLE #F1 H[
DOES ! MODEL *ANGE IF Y >E /&+ #AEJ FEET
F A BUILD+ T IS #DJJ FEET TALL8
#AD.B ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
,,WS#BC = ,EXS4 #AA1BC1 & #EC
.K .,,/&>DIZ$ .,,TE/ .,,PRACTICE ,EXS4
#B1 #BA1 #CE1 #DH1 & #ED
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 ,!
GRAPH ( .;Y .K COS #B7;X--#C7 IS ! GRAPH
( .;Y .K COS .#B;X TRANSLAT$ @8 UNITS 6!
"R4
.#B4 .,,WRIT+ .,DESCRIBE ! DI6];E 2T !
GRAPHS ( .;Y .K TAN .;X & .;Y .K --TAN
.X4 ,H[ >E ! GRAPHS RELAT$8
,,EXAMPLES #A & #B
ON PP4 #IAE-IAF = ,EXS4 #C-BA
.,,MAT*+ ,MAT* ! FUNC;N ) XS GRAPH4
.#C4
.#D4 .;F7.;X7 .K COS 7.;X @+ @7
.#E4 .;Y .K COS .;X -- #B
.#F4
.#G4
.#H4
.,A4
.,B4
.,C4
.,D4
.,E4
.,F4
.,,GRAPH+ ,GRAPH ! S9E OR COS9E
FUNC;N4
.#I4 .;Y .K S9 .;X @+ #C
.#AJ4 .;Y .K COS .;X -- #E
.#AA4 .;Y .K #B COS .;X @+ #A
.#AB4 .;Y .K S9 #C .;X -- #D
.#AC4
.#AD4
.#AE4 .;Y .K COS#B7 .;X @+ @7
.#AF4
.#AG4
.#AH4
.#AI4
.#BJ4 .;Y .K S9#B7 .;X @+ #B @7--#C
------------------------------------#IBJ
.#BA4 .,,MULTIPLE .,,*OICE ,! GRAPH (
: FUNC;N IS %[N8
.,A
.;,B .;Y .K COS .;X @+ #C
.;,C .;Y .K COS #B .;X @+ #C
.;,D .;Y .K COS @7 .;X @+ @7 @+ #C
.,,GRAPH+ ,GRAPH ! S9E OR COS9E
FUNC;N4
,,EXAMPLE #D
ON P4 #IAG = ,EXS4 #BB-CC
.#BB4 .;F7.;X7 .K --S9 .;X @+ #B
.#BC4
.#BD4 .;Y .K --COS #B;X--#B
.#BE4
.#BF4 .;F7.;X7 .K --S9 7;X --@7
.#BG4
.#BH4 .;Y .K --#C COS @7 .;X -- @7 @+
#D
.#BI4 .;Y .K --COS @7 .;X @+ @7 @+ #A
.#CJ4 .;F @7 .;X @7 .K #A--#C S9 7;X
@+7
.#CA4
.#CB4
.#CC4
.#CD4 .,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 DET]M9+ ! MAXIMUM PO9T
(! FUNC;N
,MAXIMUM3
.#CE4 .,,MULTIPLE .,,*OICE ,: (!
FOLL[+ IS A MAXIMUM PO9T (! GRAPH (
.,A
.;,B 7#J1D7
.;,C
.;,D @7 @1 #D7
.,,GRAPH+ ,GRAPH ! TANG5T FUNC;N4
,,EXAMPLE #E
ON P4 #IAH = ,EXS4 #CF-DA
.#CF4
.#CG4 .;Y .K TAN #B .;X -- #C
.#CH4 .;Y .K --TAN #D;X @+ #B
.#CI4
.#DJ4
.#DA4
.,,WRIT+ .,,EQU,NS ,9 ,EX]CISES
#DB-DF1 WRITE AN EQU,N (! GRAPH
DESCRIB$4
.#DB4 ,! GRAPH ( .;Y .K COS #B .;X
TRANSLAT$ D[N #D UNITS & LEFT #C UNITS
.#DC4 ,! GRAPH ( .;Y .K #C S9 .;X
TRANSLAT$ UP #B UNITS & "R #GG UNITS
.#DD4 ,! GRAPH ( .;Y .K #E TAN .;X
TRANSLAT$ "R UNIT & !N REFLECT$ 9 ! .;X
-AXIS
.#DE4 ,! GRAPH ( COS .;X TRANSLAT$ D[N
#A UNIT & !N REFLECT$ 9 ! L9E .;Y .K
--#A
.#DF4 ,! GRAPH ( TRANSLAT$ D[N UNITS &
"R #A UNIT1 & !N REFLECT$ 9 ! L9E
.#DG4 .,,R1SON+ .,EXPLA9 H[ Y C OBTA9
! GRAPH ( .;Y .K COS .;X 0TRANSLAT+ !
GRAPH ( .;Y .K S9 X4
.K .,,"W$-.,,\ .,,SOLU;NS ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#IBA
.#DH4 .,,%ORT .,,RESPONSE .,EXPLA9 :Y
"! IS M ?AN "O TANG5T FUNC;N ^: GRAPH
PASSES "? ! ORIG9 & HAS ASYMPTOTES AT
.;X .K -- & .;X .K @4
.#DI4 .,,*ALL5GE ,F9D A TANG5T FUNC;N
^: GRAPH 9T]SECTS ! GRAPH ( .;Y .K .#B
@+ #B S9 .;X ONLY AT M9IMUM PO9TS (! S9E
GRAPH4
,,PRO#M ,,SOLV+
,,EXAMPLE #C
ON P4 #IAF = ,EXS4 #EJ-EA
.#EJ4 .,,WAT] .,,:EEL ,! ,GRT ,LAXEY
:EEL1 LOCAT$ ON ! ,ISLE ( ,MAN1 IS "O (!
L>GE/ "W+ WAT] :EELS 9 ! _W4 ,! :EEL 0
BUILT 9 #AHED 6PUMP WAT] F ! M9ES "UN1?
X4 ,! HEI<T .;H 7IN FEET7 ABV ! VIEW+
PLAT=M (A BUCKET ON ! :EEL C 2
APPROXIMAT$ 0! FUNC;N
": .;T IS "T 7IN SECONDS74 ,GRAPH !
FUNC;N4 ,F9D ! DIAMET] (! :EEL IF ! L[E/
PO9T ON ! :EEL IS #B FEET 2L ! VIEW+
PLAT=M4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#EA4 .,,AUTOMOTIVE .,,ME*ANICS ,!
PI/ONS 9 AN 5G9E =CE ! CRANK P9S 6ROTATE
9 A CIRCLE >.D ! C5T] (! CRANK%AFT4 ,!
GRAPH %[S ! HEI<T .;H 7IN 9*ES7 (A CRANK
P9 RELATIVE 6! AXLE Z A FUNC;N ( "T .;T
7IN SECONDS74 ,WRITE A COS9E FUNC;N =!
HEI<T (! CRANK P94
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#EB4 .,,BLOOD .,,PRESSURE ,=A C]TA9
P]SON AT RE/1 ! BLOOD PRESSURE .;,P 7IN
MILLIMET]S ( M]CURY7 AT "T .;T 7IN
SECONDS7 IS GIV5 0? FUNC;N3
,GRAPH ! FUNC;N4 ,IF "O CYCLE IS
EQUIVAL5T 6"O HE>TB1T1 :AT IS ! P]SON'S
PULSE RATE 9 HE>TB1TS P] M9UTE8
,,EXAMPLE #F
ON P4 #IAH = ,EX4 #EC
.#EC4 .,,MULTI-.,,/EP .,,PRO#M ,Y >E
/&+ #CJJ FEET F ! BASE (A #BJJ FOOT
CLIFF4 ,YR FR IS RAPPELL+
.A4 ,WRITE A MODEL T GIVES ..YR FR'S
4T.E .;D 7IN FEET7 F ! TOP (! CLIFF Z A
.FUNC;N .( ! ANGLE ( ELEV,N4
.B4 ,GRAPH ! FUNC;N F "P 7A74
.C4 ,DET]M9E ! ANGLE ( ELEV,N .IF .YR
.FR HAS RAPPELL$ HALFWAY D[N ! CLIFF4
------------------------------------#IBB
#ED4 .,,EXT5D$ .,,RESPONSE ,9 A
"PICUL> REGION1 ! POPUL,N .;,C ( COYOTES
7! PR$ATOR7 &! POPUL,N .;,R ( RA2ITS 7!
PREY7 C 2 MODEL$ 0& ": .;T IS ! "T 9
MON?S4
A4 ,DET]M9E ! RATIO ( RA2ITS 6COYOTES
:5 .;T .K #J1 #F1AB1 & #AH MON?S4
B4 ,GRAPH BO? FUNC;NS 9 ! SAME
COORD9ATE PLANE4
C4 ,USE ! GRAPHS 6EXPLA9 H[ ! *ANGES 9
! TWO POPUL,NS APPE> 6BE RELAT$4
#EE4 .,,*ALL5GE ,SUPPOSE A ,F]RIS :EEL
HAS A RADIUS ( #BE FEET & OP]ATES AT A
SPE$ ( #B REVOLU;NS P] M9UTE4 ,! BOTTOM
C> IS #E FEET ABV ! GR.D4 ,WRITE A MODEL
=A P]SON'S HEI<T .;H 7IN FEET7 ABV !
GR.D IF ! VALUE ( .;H IS #DD FEET :5 .;T
.K #J4
,,MIX$ ,,REVIEW
,,PREVIEW
,PREP>E = ,LESSON #AD.C 9 ,EXS4
#EF-EI4
,SIMPLIFY ! R,NAL EXPRES.N1 IF POSSI#4
@7 P4 #EGC @7
.#EF4
.#EG4
.#EH4
.#EI4
,F9D ! NUMB] ( -B9,NS4 @7 P4 #FIJ @7
.#FJ4 #AJ .;,C #B
.#FA4 #H .;,C #E
.#FB4 #AA .;,C #C
.#FC4 #AD .;,C #F
,F9D ! >C L5G? & >EA (A SECTOR )! GIV5
RADIUS .;R & C5TRAL ANGLE4 @7 P4 #HEI @7
.#FD4
.#FE4
.#FF4
.#FG4 .;R .K #AJ IN41 .K #ACE;DG
.#FH4 .;R .K #AF CM1 .K #EJ;DG
.#FI4 .;R .K #BD ;M1 .K #BDJ;DG
,,QUIZ .= .,LESSONS .#AD..A-.AD..B
,F9D ! AMPLITUDE &! P]IOD (! GRAPH (!
FUNC;N4 @7 P4 #IJH @7
.#A4 .;Y .K COS#D .;X
.#B4
.#C4
.#D4
.#E4 .;Y .K S9 .;X
.#F4
,GRAPH ! FUNC;N4
.#G4 .;Y .K #D S9 .;X @7 P4 #IJH @7
.#H4 @7 P4 #IJH @7
.#I4 @7 P4 #IJH @7
.#AJ4 .FIX7 .K --.#B S9 #C .;X @+ #D
@7 P4 #IAE @7
.#AA4 .;Y .K COS @7 .;X @+ @7 @+ #B @7
P4 #IAE @7
.#AB4 @7 P4 #IAE @7
.#AC4 .,,W9D[ .,,WA%]S ,Y >E /&+ #GJ
FEET F ! BASE (A #BEJ FOOT BUILD+ WAT*+
A W9D[ WA%] L[] HMF 6! GR.D4 ,WRITE &
GRAPH A MODEL T GIVES ! W9D[ WA%]'S 4T.E
.;D 7IN FEET7 F ! TOP (! BUILD+ Z A
FUNC;N (! ANGLE ( ELEV,N @4 @7 P4 #IAE
@7
.,,EXTRA .,,PRACTICE = ,LESSON #AD.B1
P4 #AJBC
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#IBC
,9VE/IGAT+ ,ALGEBRA ,ACTIV;Y3 #AD.C
,9VE/IGAT+ ,TRIGONOMETRIC ,ID5TITIES
,USE 2F ,LESSON1 #AD.C
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,KEY/ROKES
.,,MAT]IALS 99 GRAPH+ CALCULATOR
,SIDEB>3
,/&>DS
,MA!MATICAL ,ANALYSIS3 #C.J ,/UD5TS "K
! ID5T;Y COS #B 7;X7 @+ S9 #B 7;X7 .K
#A4
,"Q ,H[ C Y USE A GRAPH+ CALCULATOR
6V]IFY TRIGONOMETRIC ID5TITIES8
,EXPLORE ,9VE/IGATE A TRIGONOMETRIC
ID5T;Y
,DET]M9E :E!R ! EQU,N S9 #B .;X @+ COS
#B .;X .K #A IS TRUE = ..NO ;X-VALUES1
"S ;X-.VALUES @1 OR .ALL .;X-.VALUES4
,,/EP #A ,5T] EQU,NS
,5T] ! LEFT SIDE (! EQU,N Z .;Y #A &!
"R SIDE Z .;Y #B @4 ,USE ! 8?ICK0 GRAPH
/YLE = .;Y #B 64T+UI% ! GRAPHS4
,,/EP #B ,SET VIEW+ W9D[
,SET YR CALCULATOR 9 RADIAN MODE4
,ADJU/ ! VIEW+ W9D[ S T ! .;X -AXIS %[S
--#B "K.K .;X "K.K .#B &! .;Y -AXIS %[S
--#B "K.K .;Y "K.K #B4
,,/EP #C ,GRAPH EQU,NS
,GRAPH ! EQU,NS4 ,! CALCULATOR F/
GRAPHS .;Y #A .K S9 #B .;X @+ COS #B .;X
& !N ;Y #B .K #A Z A ?ICK] L9E OV] !
GRAPH ( .;Y #A
,! GRAPHS ( EA* SIDE (! EQU,N S9 #B
.;X @+ COS #B .;X .K #A >E ! SAME4 ,S1 !
EQU,N IS TRUE = ALL .;X -VALUES4
,,DRAW ,,3CLU.NS ,USE YR OBS]V,NS
6-PLETE ^! EX]CISES
,USE A GRAPH+ CALCULATOR 6DET]M9E :E!R
! EQU,N IS TRUE = ..NO ;X-VALUE1 "S
;X-.VALUES @1 OR .ALL .;X-.VALUES4 7,SET
YR CALCULATOR 9 RADIAN MODE & USE -- .#B
"K.K .;X "K.K .#B &--#B "K.K .;Y "K.K #B
=! VIEW+ W9D[47
.#A4
.#B4 S9 .;X .K --COS .;X
.#C4
.#D4 COS 7--#C;X7 .K COS #C;X
.#E4 COS .;X .K #A.E
.#F4 S9 7;X --@7 .K COS ;X
.#G4 S9 @7- .;X @7 .K --S9 .;X
.#H4
.#I4
.#AJ4 .,,R1SON+ ,TRIGONOMETRIC EQU,NS
T >E TRUE = .ALL VALUES ( .;X 7IN _!
DOMA97 >E CALL$ TRIGONOMETRIC ID5TITIES4
,: TRIGONOMETRIC EQU,NS 9 ,EX]CISES #A-I
>E TRIGONOMETRIC ID5TITIES8
------------------------------------#IBD
#AD.C ,V]IFY ,TRIGONOMETRIC
,ID5TITIES
.,2F ,Y GRAPH$ TRIGONOMETRIC FUNC;NS4
.,N[ ,Y W V]IFY TRIGONOMETRIC
ID5TITIES4
.,:Y8 ,S Y C MODEL ! PA? ( ,HALLEY'S
-ET1 Z 9 ,EX4 #DA4
,KEY ,VOCABUL>Y
99 .TRIGONOMETRIC .ID5T;Y
,SIDEB>3
,/&>DS
,MA!MATICAL ,ANALYSIS3 #C.J ,/UD5TS "K
! ID5T;Y COS #B 7;X7 @+ S9 #B 7;X7 .K
#A4
,MA!MATICAL ,ANALYSIS3 #C.B ,/UD5TS
PROVE O!R TRIGONOMETRIC ID5TITIES &
SIMPLIFY O!RS 0US+ ! ID5T;Y COS #B 7;X7
@+ S9 #B 7;X7 .K #A4 ,= EXAMPLE1 /UD5TS
USE ? ID5T;Y 6PROVE T SEC #B 7;X7 .K TAN
#B 7;X7 @+ #A4
,RECALL F ,LESSON #AC.C T IF AN ANGLE
#J IS 9 /&>D POSI;N ) XS T]M9AL SIDE
9T]SECT+ ! UNIT CIRCLE AT 7;X1 .;Y7 @1
!N .;X .K COS & .;Y .K S94 ,2C 7;X1 .;Y7
IS ON A CIRCLE C5T]$ AT ! ORIG9 ) RADIUS
#A1 X FOLL[S T3
;X #B @+ .;Y #B .K #A
COS #B @+ S9 #B .K.#A
,! EQU,N COS #B @+ S9 #B .K #A IS TRUE
= ANY VALUE ( @4 .,A TRIGONOMETRIC EQU,N
T IS TRUE = ALL VALUES ( 7IN XS DOMA97
IS CALL$ A .TRIGONOMETRIC .ID5T;Y4
,S"EAL FUNDA;TAL TRIGONOMETRIC ID5TITIES
>E LI/$ 2L1 "S ( : Y H ALR LE>N$4
,,KEY ,,3CEPT .= .YR .,NOTEBOOK
,FUNDA;TAL ,TRIGONOMETRIC ,ID5TITIES
,RECIPROCAL ,ID5TITIES
,TANG5T & ,COTANG5T ,ID5TITIES
,PY?AGOR1N ,ID5TITIES
S9 #B @+ COS #B .K .#A
.#A @+ TAN #B .K SEC #B
.#A @+ COT #B .K .;C SC #B
,C(UNC;N ,ID5TITIES
,NEGATIVE ,ANGLE ,ID5TITIES
S97- @7 .K --S9
COS @7- @7 .K COS
TAN @7- @7 .K --TAN
,Y C USE TRIGONOMETRIC ID5TITIES
6EVALUATE TRIGONOMETRIC FUNC;NS1
SIMPLIFY TRIGONOMETRIC EXPRES.NS1 &
V]IFY O!R ID5TITIES4
------------------------------------#IBE
,,EXAMPLE #A ,F9D TRIGONOMETRIC VALUES
,GIV5 T @1 F9D ! VALUES (! O!R FIVE
TRIGONOMETRIC FUNC;NS (4
,SOLU;N
.,,/EP .#A ,F9D COS @4
,,REVIEW ,,TRIGONOMETRY
,= HELP ) F9D+ ! SIGN (A TRIGONOMETRIC
FUNC;N VALUE1 SEE P4 #HFF @4
.,,/EP .#B ,F9D ! VALUES (! O!R F\R
TRIGONOMETRIC FUNC;NS ( .#F US+ ! "KN
VALUES ( S9 .#F & COS .#J4
,,EXAMPLE #B ,SIMPLIFY A TRIGONOMETRIC
EXPRES.N
.,SIMPLIFY .! .EXPRES.N
,,EXAMPLE #C ,SIMPLIFY A TRIGONOMETRIC
EXPRES.N
,SIMPLIFY ! EXPRES.N
------------------------------------#IBF
..,GUID$ ,PRACTICE = ,EXAMPLES #A1B1 &
.#C
,F9D ! VALUES (! O!R FIVE
TRIGONOMETRIC FUNC;NS ( @4
.#A4
.#B4
,SIMPLIFY ! EXPRES.N4
.#C4 S9 .;X COT .;X SEC .;X
.#D4
.#E4
.,,V]IFY+ .,,ID5TITIES ,Y C USE !
FUNDA;TAL ID5TITIES ON PAGE #IBD 6V]IFY
NEW TRIGONOMETRIC ID5TITIES4 ,:5 V]IFY+
AN ID5T;Y1 2G9 )! EXPRES.N ON "O SIDE4
,USE ALGEBRA & TRIGONOMETRIC PROP]TIES
6MANIPULATE ! EXPRES.N UNTIL X IS
ID5TICAL 6! O!R SIDE4
,,EXAMPLE #D ,V]IFY A TRIGONOMETRIC
ID5T;Y
.,V]IFY .! .ID5T;Y
,,EXAMPLE #E ,V]IFY A TRIGONOMETRIC
ID5T;Y
.,V]IFY .! .ID5T;Y
,,V]IFY ,,ID5TITIES
,6V]IFY ! ID5T;Y1 Y M/ 9TRODUCE #A--S9
.;X 96! DENOM9ATOR4 ,MULTIPLY ! NUM]ATOR
&! DENOM9ATOR 0#A - S9 .;X S Y GET AN
EQUIVAL5T EXPRES.N4
------------------------------------#IBG
,,EXAMPLE #F ,V A R1L-LIFE
TRIGONOMETRIC ID5T;Y
.,,%AD[ .,,L5G? ,A V]TICAL .GNOMON 7!
"P ( _\ A SUNDIAL T PROJECTS A %AD[7 HAS
HEI<T .H4 ,! L5G? .;S (! %AD[ CA/ 0!
GNOMON @\ :5 ! ANGLE (! SUN ABV !
HORIZON IS C 2 MODEL$ 0! EQU,N 2L4 ,%[ T
! EQU,N IS EQUIVAL5T ..6;S .K .;H COT @4
,SOLU;N
,SIMPLIFY ! EQU,N4
..,GUID$ ,PRACTICE = ,EXAMPLES #D1E1 &
.#F
,V]IFY ! ID5T;Y4
.#F4 COT7- @7 .K --COT
.#G4 CSC #B .;X 7#A--S9 #B .;X7 .K COT
#B .;X
.#H4 COS .;X .;C SC .;X TAN .;X .K #A
.#I4 7TAN #B .;X @+ ;L77COS #B .;X --
#A7 .K --TAN #B ;X
#AD.C ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
,,WS#BD = ,EXS4 #E1AA1 & #DA
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE ,EXS4
#B1I1 #BD1 #DB1 #DC1 & #DD
.K .,,MULTIPLE .,,REPRES5T,NS ,EX#.DA
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,:AT IS A
TRIGONOMETRIC ID5T;Y8
.#B4 .,,WRIT+ ,:AT DOES ! C(UNC;N
ID5T;Y TELL Y AB ! GRAPHS ( .;Y .K S9
.;X & .;Y .K COS .;X @8
.,,EXAMPLE .#A ON P4 #IBE = ,EXS4 #C-I
.,,F9D+ .,,VALUES ,F9D ! VALUES (! O!R
FIVE TRIGONOMETRIC FUNC;NS (
.#C4
.#D4
.#E4
.#F4
.#G4
.#H4
------------------------------------#IBH
#I4 .,,MULTIPLE .,,*OICE ,IF @1 :AT IS
! VALUE ( TAN8
,A
;,B
;,C
;,D
,,EXAMPLES #B & #C
ON P4 #IBE = ,EXS4 #AJ-BD
.,,SIMPLIFY+ .,,EXPRES.NS ,SIMPLIFY !
EXPRES.N4
.#AJ4 S9 .;X COT .;X
.#AA4
.#AB4 CSC S9 @+ COT #B
.#AC4 COS #J 7#A @+ TAN #B #J7 #AD4
.#AD4
.#AE4
.#AF4
.#AG4
.#AH4
.#AI4
.#BJ4
.#BA4
.,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 SIMPLIFY+ ! EXPRES.N4
.#BB4 #A--S9 #B .K #A--7#A--COS #B @7
.K #A--#A--COS #B
.K --COS #B
.#BC4
.#BD4 .,,MULTIPLE .,,*OICE ,: (!
FOLL[+ IS ! SIMPLIFI$ =M (! EXPRES.N COS
SEC8
.,A TAN
.;,B #A
.;,C #B
.;,D #A--S9 #B
,,EXAMPLES #D & #E
ON P4 #IBF = ,EXS4 #BE-CD
.,,V]IFY+ .,,ID5TITIES ,V]IFY !
ID5T;Y4
.#BE4 S9 .;X .;C SC .;X .K #A
.#BF4 TAN .;C SC COS .K .#A
.#BG4
.#BH4
.#BI4
.#CJ4 #B--COS #B #J.K#A @+ S9 #B #J
.#CA4 S9 .;X @+ COS .;X COT .;X .K CSC
.;X
.#CB4
.#CC4
.#CD4
..#CE4 ,,ODD ,,& ,,EV5 .,,FUNC;NS ,A
FUNC;N .;F IS .ODD IF .;F7-.;X7 .K
--.;F7.;X74 ,A FUNC;N .;F IS .EV5 IF .;F
@7- .;X @7 .K .;F7.;X74 ,: (! SIX
TRIGONOMETRIC FUNC;NS >E ODD8 ,: >E EV58
.,,V]IFY+ .,,ID5TITIES ,V]IFY !
ID5T;Y4
.#CF4 ,9 _\SEC _\ .K --LN _\COS _\
.#CG4 LN _\TAN _\ .K LN _\S9 _\ - LN
_\COS _\
.#CH4 .,,*ALL5GE ,USE ! ,PY?AGOR1N
ID5T;Y S9 #B @+ COS #B .K #A 6DERIVE !
O!R ,PY?AGOR1N ID5TITIES1 #A @+ TAN #B
.K SEC #B & #A @+ COT #B .K CSC #B @4
.K .,,"W$-.,,\ .,,SOLU;NS ON P4,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
------------------------------------#IBI
,,PRO#M ,,SOLV+
,,EXAMPLE #F
ON P4 #IBG = ,EXS4 #CI-DA
..#CI4 ,,RATE ,,( .,,*ANGE ,9
CALCULUS1 X C 2 %[N T ! RATE ( *ANGE (!
FUNC;N .;F 7;X7 .K SEC .;X @+ COS .;X IS
GIV5 0? EXPRES.N3
SEC .;X TAN .;X -- S9 .;X
,%[ T ! EXPRES.N =! RATE ( *ANGE C 2
WRITT5 Z S9 .;X TAN #B .X4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#DJ4 .,,PHYSICAL .,,SCI;E ,/ATIC
FRIC;N IS ! AM.T ( =CE NEC 6KEEP A /,N>Y
OBJECT ON A FLAT SURFACE F MOV+4
,SUPPOSE A BOOK WEI<+ .;,W P.DS IS LY+
ON A RAMP 9CL9$ AT AN ANGLE .#J4 ,!
COE6ICI5T ( /ATIC FRIC;N .;U =! BOOK C 2
F.D US+ ? EQU,N3
U,WCOS .K ,WS9
A4 ,SOLVE ! EQU,N = .;U & SIMPLIFY !
RESULT4
B4 ,USE ! EQU,N F "P 7A7 6DET]M9E :AT
HAPP5S 6! VALUE ( .;U Z ! ANGLE 9CR1SES
F #J;DG 6#IJ;DG4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#DA4 .,,MULTIPLE .,,REPRES5T,NS ,! PA?
( ,HALLEY'S -ET IS AN ELLIPSE )! SUN Z A
FOCUS4 ,! EQU,N 2L GIVES ! -ET'S 4T.E
.;R F ! SUN 7IN A/RONOMICAL UNITS7 Z A
FUNC;N (! ANGLE 7IN RADIANS7 2T ! MAJOR
AXIS &! -ET4
A4 .,WRIT+ .AN .,EQU,N ,SIMPLIFY !
EQU,N GIV5 ABV4
B4 .,DRAW+ .A .,GRAPH ,USE A GRAPH+
CALCULATOR 6GRAPH ! EQU,N F "P 7A74
C4 .,MAK+ .A .,TA# ,MAKE A TA# (
VALUES =! EQU,N F "P 7A7 9
: />TS AT #J & 9CR1SES 9 9CRE;TS ( @4
,USE ! TA# 6APPROXIMATE ! CLOSE/ & F>!/
4T.E1 9 MILES1 T ,HALLEY'S -ET IS F !
SUN4 7.,NOTE3 #A A/RONOMICAL UNIT #IC
MILLION MILES47
#DB4 .,,%ORT .,,RESPONSE ,USE A
RECIPROCAL ID5T;Y 6DESCRIBE :AT HAPP5S
6! VALUE ( SEC Z ! VALUE ( COS .#F
9CR1SES4 ,ON :AT 9T]VALS DOES ? HAPP58
#DC4 .,,%ORT .,,RESPONSE ,USE ! TANG5T
ID5T;Y 6DESCRIBE :AT HAPP5S 6! VALUE (
TAN Z ! VALUE ( S9 9CR1SES &! VALUE (
COS DECR1SES4 ,ON :AT 9T]VALS DOES ?
HAPP58
------------------------------------#ICJ
#DD4 .,,EXT5D$ .,,RESPONSE ,:5 LI<T
TRAVEL+ 9 A M$IUM 7S* Z AIR7 /RIKES !
SURFACE (A SECOND M$IUM 7S* Z WAT]7 AT
AN ANGLE #A ,! LI<T 2G9S 6TRAVEL AT A
DI6]5T ANGLE #B @4 ,? *ANGE ( DIREC;N IS
DEF9$ 0,SNELL'S LAW1 .;N #A S9 #A .K .;N
#B S9 #B @1 ": .;N #A & .;N #B >E !
.9DICES .( .REFRAC;N =! TWO M$IUMS4
,SNELL'S LAW C 2 DERIV$ F ! EQU,N3
A4 .,DERIVE ,SIMPLIFY ! EQU,N 6DERIVE
,SNELL'S LAW3 .;N #A S9 #A .K .;N #B S9
#B @4
B4 .,SOLVE ,IF #A .K #EE;DG1 #B @1 .K
#CE;DG1 & .;N #B .K .#B @1 :AT IS !
VALUE ( .;N #A @8
C4 .,9T]PRET ,IF #A .K #B @1 :AT M/ 2
TRUE AB ! VALUES ( .;N #A & .;N #B @8
.,EXPLA9 :5 ? SITU,N WD O3UR4
#DE4 .,,*ALL5GE ,BREW/]'S ANGLE IS !
ANGLE #A @1 AT : LI<T REFLECT$ (F WAT]
IS -PLETELY POL>IZ$1 S T GL>E IS M9IMIZ$
:5 Y LOOK AT ! WAT] ) POL>IZ$
SUNGLASSES4 ,BREW/]'S ANGLE C 2 F.D US+
,SNELL'S LAW 7SEE ,EX]CISE #DD74
A4
,ADD ! TWO EQU,NS 6%[ T
B4 ,%[ T ! EQU,N F "P 7A7 C 2
SIMPLIFI$
C4 ,SOLVE ! EQU,N F "P 7;B7 6F9D
,BREW/]'S ANGLE3
,,MIX$ ,,REVIEW
,,PREVIEW
,PREP>E = ,LESSON #AD.D 9 ,EXS4
#DI-ED4
,F9D ! PRODUCT4 @7 P4 #AIE @7
.#DF4
.#DG4
.#DH4
,SOLVE ! EQU,N4
.#DI4 ;X#B @+ #E;X @+ #D .K #J @7 P4
#BEB @7
.#EJ4 ;X#B--#H;X @+ #AB .K #J @7 P4
#BEB @7
.#EA4 ;X#B @+ #C;X--#AJ .K #J @7 P4
#BEB @7
.#EB4 #B;X #B -- ;X--#A .K #J @7 P4
#BEI @7
.#EC4 #AJ;X #B @+ #AG;X--#F .K #J @7
P4 #BEI @7
.#ED4 #D;X #B -- #AB;X--#BG .K #J @7
P4 #BEI @7
,EVALUATE ! EXPRES.N )\T US+ A
CALCULATOR4 ,GIVE YR ANSW] 9 BO? RADIANS
& DEGREES4 @7 P4 #HGE @7
.#EE4
.#EF4
.#EG4
.#EH4
.#EI4 TAN -#A #A
.#FJ4 COS -#A #J
.,,EXTRA .,,PRACTICE = ,LESSON #AD.C1
P4 #AJBC
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#ICA
#AD.D ,SOLVE ,TRIGONOMETRIC ,EQU,NS
.,2F ,Y V]IFI$ TRIGONOMETRIC
ID5TITIES4
.,N[ ,Y W SOLVE TRIGONOMETRIC EQU,NS4
.,:Y ,S Y C SOLVE SURFACE >EA PRO#MS1
Z 9 ,EX4 #DC4
,KEY ,VOCABUL>Y
99 EXTRANE\S SOLU;N1 P4 #EB
,SIDEB>3
,/&>DS
.,MA!MATICAL .,ANALYSIS3 #C.J ,/UD5TS
"K ! ID5T;Y COS #B 7;X7 @+ S9 #B 7;X7 .K
#A4
,9 ,LESSON #AD.C1 Y V]IFI$
TRIGONOMETRIC ID5TITIES4 ,9 ? LESSON1 Y
W SOLVE TRIGONOMETRIC EQU,NS4 ,6SEE !
DI6];E1 3SID] ! FOLL[+3
S9 #B .;X @+ COS #B .;X .K #A .,EQU,N
.#A
S9 .;X .K #A .,EQU,N .#B
,EQU,N #A IS AN ID5T;Y 2C X IS TRUE =
ALL R1L VALUES ( .X4 ,EQU,N #B1 H["E1 IS
TRUE ONLY = "S VALUES ( .X4 ,:5 Y F9D ^!
VALUES1 Y >E SOLV+ ! EQU,N4
,,EXAMPLE #A ,SOLVE A TRIGONOMETRIC
EQU,N
,SOLVE @4
,SOLU;N
,F/ ISOLATE S9 .;X ON "O SIDE (!
EQU,N4
#B;S9X -- .K #J .,WRITE .ORIG9AL
.EQU,N4
#B;S9X .K .,ADD .6.EA* .SIDE4
..,DIVIDE EA* SIDE 0.#B4
,"O SOLU;N ( 9 ! 9T]VAL #J "K .;X "K
.#B IS @4 ,! O!R SOLU;N 9 ! 9T]VAL IS @4
,MOREOV]1 2C .;Y .K S9 .;X IS P]IODIC1
"! W 2 9F9ITELY _M SOLU;NS4
,Y C USE ! TWO SOLU;NS F.D ABV 6WRITE
! G5]AL SOLU;N3
OR
7": .;N IS ANY 9TEG]7
,,WRITE ,,G5]AL @3 ,,SOLU;N
,6WRITE ! G5]AL SOLU;N (A
TRIGONOMETRIC EQU,N1 Y C ADD MULTIPLES
(! P]IOD 6ALL ! SOLU;NS F "O CYCLE4
.,,*ECK ,Y C *ECK ! ANSW] 0GRAPH+ .;Y
.K S9 .;X & 9 ! SAME COORD9ATE PLANE4
,!N F9D ! PO9TS ": ! GRAPHS 9T]SECT4 ,Y
C SEE T "! >E 9F9ITELY _M S* PO9TS4
------------------------------------#ICB
,,EXAMPLE #B ,SOLVE A TRIGONOMETRIC
EQU,N 9 AN 9T]VAL
,SOLVE #I TAN #B .;X @+ #B .K #C 9 !
9T]VAL #J "K.K .;X "K.K #B4
,,REVIEW ,,9V]SE ,,FUNC;NS
,= HELP ) 9V]SE TRIGONOMETRIC FUNC;NS1
SEE P4 #HGE @4
,US+ A CALCULATOR1 Y F9D T & @4 ,"!=E1
! G5]AL SOLU;N (! EQU,N IS3
.;X #J.CBB @+ .;N OR .;X --#J.CBB @+
.;N
7": .;N IS ANY 9TEG]7
,! SPECIFIC SOLU;NS 9 ! 9T]VAL #J "K.K
.;X "K .#B >E3
.;X #J.CBB .;X --#J.CBB @+ #B.HBJ
.;X #J.CBB @+ #C.DFD .;X --#J.CBB @+
#B #E.IFA
,,EXAMPLE #C ,SOLVE A R1L-LIFE
TRIGONOMETRIC EQU,N
.,,OC1NOGRAPHY ,! WAT] DEP? .;D =!
,BAY ( ,FUNDY C 2 MODEL$ 0": .;D IS
M1SUR$ 9 FEET & .;T IS ! "T 9 H\RS4 ,IF
.;T .K #J REPRES5TS MIDNI<T1 AT :AT "T
7;S7 IS ! WAT] DEP? #G FEET8
,,ANO!R ,,WAY
,= ALT]NATIVE ME?ODS = SOLV+ ! PRO#M 9
,EXAMPLE #C1 TURN 6PAGE #ICH =! .,PRO#M
.,SOLV+ .,"W%OP4
,SOLU;N
,SUB/ITUTE #G = .;D 9 ! MODEL & SOLVE
= .T4
,ON ! 9T]VAL #J "K.K .;T "K.K #BD
7REPRES5T+ "O FULL "D71 ! WAT] DEP? IS
#G FEET :5 .;T .K #AB.D7#J7 .K #J 7T IS1
AT MIDNI<T7 & :5 .;T .K #AB.D7#A7 .K
#AB.D 7T IS1 AT #AB3BD ,P4,M474
------------------------------------#ICC
.,GUID$ .,PRACTICE = ,EXAMPLES #A1B1 &
#C
.#A4 ,F9D ! G5]AL SOLU;N (! EQU,N #B
S9 .;X @+ #D .K #E4
.#B4 ,SOLVE ! EQU,N #C CSC #B .;X .K
#D 9 ! 9T]VAL #J "K.K ..;X "K .#B @4
.#C4 .,,OC1NOGRAPHY ,9 ,EXAMPLE #C1 AT
:AT "T7;S7 IS ! WAT] DEP? #FC FEET8
,,EXAMPLE #D ,/&>DIZ$ ,TE/ ,PRACTICE
,:AT IS ! G5]AL SOLU;N ( S9 #C .;X --
#D S9 .;X .K #J8
.,A
.;,B
.;,C .;X .K @+ .#B;N
.;,D .;X .K .#B;N OR .;X .K @+ #B;N
,SOLU;N
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
S9 #C .;X -- #D S9 .;X .K #J @3
.,WRITE .ORIG9AL .EQU,N4
S9 .;X 7S9.' #B .;X -- .#D7 .K #J @3
,FACTOR \ S9.' X4.-
S9 .;X 7.S9 .;X @+ .#B7 7.S9 .;X --
.#B7 .K #J @3 ..,FACTOR DI6];E (
.SQU>ES4
,SET EA* FACTOR EQUAL 6#J & SOLVE =
;X1 IF POSSI#4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
S9 .;X .K #J @3 S9 .;X @+ #B .K #J @3
S9 .;X -- #B .K #J
.;X .K #J OR .;X .K @3 S9 .;X .K --#B
@3 S9 .;X .K #B
,,ELIM9ATE ,,SOLU;NS
,2C S9 .;X IS N"E LESS ?AN --#A OR
GRT] ?AN #A1 "! >E NO SOLU;NS ( S9 .;X
.K --.#B & S9 .;X .K #B4
,! ONLY SOLU;NS 9 ! 9T]VAL #J "K.K .;X
"K #B >E .;X .K #J & .;X .K @4
,! G5]AL SOLU;N IS .;X .K #B;N OR .;X
.K @+ #B;N ": .;N IS ANY 9TEG]4
,! CORRECT ANSW] IS ,D4 ..,A ;,B ;,C
.;,D
,,EXAMPLE #E ,USE ! QUADRATIC =MULA
,SOLVE COS #B .;X -- #E COS .;X @+ .#B
.K #J 9 ! 9T]VAL #J "K.K .;X "K.K @4
,SOLU;N
,2C ! EQU,N IS 9 ! =M .AU #B @+ .BU @+
.;C .K #J ": .;U .K COS .;X @1 Y C USE !
QUADRATIC =MULA 6SOLVE = COS X4
,9 ! 9T]VAL #J "K .;X "K #GG1 ! ONLY
SOLU;N IS .;X #A.AB4
------------------------------------#ICD
.,,EXTRANE\S .,,SOLU;NS ,:5 SOLV+ A
TRIGONOMETRIC EQU,N1 X IS POSSI# 6OBTA9
EXTRANE\S SOLU;NS4 ,S1 Y %D ALW *ECK YR
SOLU;NS 9 ! ORIG9AL EQU,N4
,,EXAMPLE #F ,SOLVE AN EQU,N ) AN
EXTRANE\S SOLU;N
..,SOLVE #A @+ COS ;X .K S9 ;X 9 !
9T]VAL .#J "K .;X "K #B4
,,REVIEW ,,FOIL ,,ME?OD
,= HELP MULTIPLY+ BINOMIALS1 SEE P4
#BDE @4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#A @+ COS .;X .K S9 .;X @3 .,WRITE
.ORIG9AL .EQU,N4
7#A @+ COS .;X @7 #B .K 7S9 .;X @7 #B
@3 .,SQU>E .BO? .SIDES4
#A @+ #B COS .;X @+ COS #B .;X .K S9.'
#B .;X @3 .,MULTIPLY4
#A@+#B COS .;X @+ COS #B .;X .K .#A --
COS.' #B .;X @3 .,PY?AGOR1N .ID5T;Y
#B COS #B .;X @+ #B COS .;X .K #J @3
.,QUADRATIC .=M
#B COS .;X 7COS .;X @+ #A7 .K #J @3
..,FACTOR \ #B COS .X4
#B COS .;X .K #J OR COS .;X @+ .;L .K
#J @3 .,Z]O .PRODUCT .PROP]TY
COS .;X .K #J OR COS .;X .K --#A @3
,SOLVE = COS.' X4.-
,ON ! 9T]VAL #J "K.K .;X "K #B1 COS
.;X .K #J HAS TWO SOLU;NS3
,ON ! 9T]VAL #J "K.K .;X "K #B1 COS
.;X .K --#A HAS "O SOLU;N3 .;X .K @4
,"!=E1 #A @+ COS .;X .K S9 .;X HAS
?REE POSSI# SOLU;NS3 @4
.,,*ECK ,6*ECK ! SOLU;NS1 SUB/ITUTE !M
96! ORIG9AL EQU,N & SIMPLIFY4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#A @+ COS .;X .K S9 .;X @3 #A @+ COS
.;X .K S9 .;X @3 #A @+ COS .;X .K S9 .;X
@3 #A @+ .COS .S9 @3
.#A @+ .#J #A @3 #A @+ 7--.#A7 .#J @3
#A @+ #J --#A
#A .K #A @3 #J .K #J @3 #A @6.K --#A
,! APP>5T SOLU;N IS EXTRANE\S 2C X
DOES N *ECK 9 ! ORIG9AL EQU,N4 ,! ONLY
SOLU;NS 9 ! 9T]VAL #J "K .;X "K .#B >E &
.;X .K @4 ,GRAPHS ( EA* SIDE (! ORIG9AL
EQU,N 3FIRM ! SOLU;NS4
..,GUID$ ,PRACTICE = ,EXAMPLES #D1 #E1
& .#F
,F9D ! G5]AL SOLU;N (! EQU,N4
.#D4 S9 #C .;X - S9 .;X .K .#J
.#E4
,SOLVE ! EQU,N 9 ! 9T]VAL #J "K.K .;X
"K.K @4
.#F4 .#B S9 .;X .K .;C SC .;X
.#G4 TAN #B .;X - S9 .;X TAN #B .;X .K
.#J
------------------------------------#ICE
#AD.D ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
,,WS#BD = ,EXS4 #E1AC1 & #DC
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE ,EXS4
#B1AE1CF1DB1 & #DD
.K .,,MULTIPLE .,,REPRES5T,NS ,EX#.DC
,,SKILL ,,PRACTICE
#A4 ,,VOCABUL>Y ,:AT IS ! DI6];E 2T A
TRIGONOMETRIC EQU,N &A TRIGONOMETRIC
ID5T;Y8
#B4 ,,WRIT+ .,DESCRIBE S"EAL TE*NIQUES
= SOLV+ TRIGONOMETRIC EQU,NS4
,,EXAMPLE #A
ON P4 #ICA = ,EXS4 #C-AE
,,*ECK+ ,,SOLU;NS ,V]IFY T ! GIV5
;X-VALUE IS A SOLU;N (! EQU,N4
#C4 #B @+ #C COS .;X -- #E .K #J1 .;X
.K .#D
#D4 SEC .;X @+ .K #J1 .;X .K
.#E4
.#F4
.#G4
.#H4
,,G5]AL ,,SOLU;NS ,F9D ! G5]AL SOLU;N
(! EQU,N4
#I4 #B S9 .;X -- #A .K #J
.#AJ4
.#AA4
.#AB4
#AC4 #D COS #B .;X -- #C .K #J
.#AD4 #C TAN #B .;X -- #I .K #J
#AE4 ..,,MULTIPLE ,,*OICE ,:AT IS !
G5]AL SOLU;N (! EQU,N #D S9 ;X .K #B S9
;X @+ .#A8
,A
;,B
;,C
;,D
,,EXAMPLE #B
ON P4 #ICB = ,EXS4 #AF-BC
,,SOLV+ ,,EQU,NS ,SOLVE ! EQU,N 9 !
9T]VAL #J "K.K .;X "K #B4
#AF4 #E @+ #B S9 .;X -- #G .K #J
.#AG4
.#AH4 #C COS .;X .K COS .;X -- #A
#AI4 #B S9 #B .;X -- #A .K #J
.#BJ4 #E TAN #B .;X -- #AE .K #J
.#BA4 #D COS #B .;X -- #A .K #J
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 SOLV+ ! EQU,N 9 ! 9T]VAL
.#BB4
.#BC4
,,EXAMPLE #D
ON P4 #ICC = ,EXS4 #BD-BI
,,G5]AL ,,SOLU;NS ,F9D ! G5]AL SOLU;N
(! EQU,N4
.#BD4 S9 .;X COS .;X -- #C COS .;X .K
#J
.#BE4
.#BF4 #B S9 #C .;X .K S9 .;X
.#BG4 #B TAN #D .;X -- TAN #B .;X --
#AE .K #J
.#BH4
.#BI4
------------------------------------#ICF
.,,EXAMPLES #E .& #F
ON PP4 #ICC-ICD = ,EXS4 #CJ-CE
,,SOLV+ ,SOLVE ! EQU,N 9 ! GIV5
9T]VAL4 ,*ECK YR SOLU;NS4
.#CJ4 SEC .;X .;C SC #B .;X .K #B SEC
;X2 #J "K.K .;X "K .#B
.#CA4
.#CB4 #B S9 #B .;X -- COS .;X -- #A .K
#J2 #J "K.K .;X "K #B
.#CC4
.#CD4 TAN #B .;X -- #C TAN .;X @+ #B
.K #J2 #J "K .;X "K
.#CE4 COS .;X @+ S9 .;X TAN .;X .K #B2
"K.K .;X "K .#B
.#CF4 .,,MULTIPLE .,,*OICE ,:AT >E !
PO9TS ( 9T]SEC;N (! GRAPHS ( .;Y .K #D
S9 .;X @+ #A & .;Y .K #B S9 .;X @+ #B ON
! 9T]VAL #J "K.K .;X "K #B8
.,A
.;,B
.;,C
.;,D
,,9T]SEC;N ,,PO9TS ,F9D ! PO9TS (
9T]SEC;N (! GRAPHS (! GIV5 FUNC;NS 9 !
9T]VAL #J "K.K ..;X "K .#B @4
.#CG4 .;Y .K COS #B ;X
;Y .K .#B COS .;X -- .#A
..#CH4 ;Y .K .#I S9 #B .;X
;Y .K S9 #B .;X @+ .#H S9 .;X -- .#B
.#CI4
#DJ4 .,,*ALL5GE ,A NUMB] .;C IS .A
.FIX$ .PO9T (A FUNC;N .;F IF .;F 7;C7 .K
C4 ,= EXAMPLE1 #J IS A FIX$ PO9T (_/7;X7
.K S9 .;X 2C .;F 7#J7 .K S9 #J .K #J4
A4 .,R1SON+ ,USE GRAPHS 6EXPLA9 :Y !
FUNC;N ;G7;X7 .K COS .;X HAS ONLY "O
FIX$ PO9T4
B4 .,GRAPH+ .,CALCULATOR ,F9D ! FIX$
PO9T ( ;G7;X7 .K COS X4
,,EXAMPLE #C
ON P4 #ICB = ,EXS4 #DA-DB
,PRO#M ,SOLV+
#DA4 .,,W9D .,,SPE$ ,! AV]AGE W9D SPE$
.;S 7IN MILES P] H\R7 9 ! ,BO/ON ,H>BOR
C 2 APPROXIMAT$ 0.;S .K #C.CH ": .;T IS
! "T 9 "DS1 ) .;T .K #J REPRES5T+
,JANU>Y #A4 ,ON : "DS (! YE> IS ! AV]AGE
W9D SPE$ #AJ MILES P] H\R8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
#DB4 .,,%ORT .,,RESPONSE ,! NUMB] (
DEGREES NOR? ( DUE EA/ @7 .1 #J7 OR S\?
( DUE EA/ @7 "K #J7 T ! SUN RISES 9
,*EY5NE1 ,WYOM+1 C 2 MODEL$ 0": .;T IS !
"T 9 "DS1 ) .;T .K #A REPRES5T+ ,JANU>Y
#A4 ,USE AN ALGEBRAIC ME?OD 6F9D AT :AT
"D7;S7 ! SUN IS #BJ;DG NOR? ( DUE EA/ AT
SUNRISE4 .,EXPLA9 H[ Y C USE ! GRAPH (
7.;T7 6*ECK YR ANSW]4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.K .,,"W$-.,,\ .,,SOLU;NS ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
.K .,,MULTIPLE .,,REPRES5T,NS
------------------------------------#ICG
#DC4 .,,MULTIPLE .,,REPRES5T,NS ,!
SURFACE >EA .;,S (A H"OYCOMB CELL C 2
E/IMAT$ 0! EQU,N %[N AT ! "R4 ,9 !
EQU,N1 .;H IS ! HEI<T 7IN 9*ES71 .;,S IS
! WID? (A SIDE 7IN 9*ES71 & .#F IS !
ANGLE 7IN DEGREES7 9DICAT$ 9 ! DIAGRAM4
A4 ,US+ .A .,DIAGRAM ,USE ! VALUES (
.;H & .;S 9 ! DIAGRAM 6SIMPLIFY ! EQU,N4
B4 .,MAK+ .A .,TA# ,USE A GRAPH+
CALCULATOR 6MAKE A TA# =! FUNC;N F "P
7A74 ,= :AT VALUE7;S7 ( DOES .;,S .K #I
SQU>E 9*ES8
C4 .,DRAW+ .A .,GRAPH ,USE A GRAPH+
CALCULATOR 6GRAPH ! FUNC;N F "P 7A74
,:AT VALUE ( M9IMIZES ! SURFACE >EA8
#DD4 .,,EXT5D$ .,,RESPONSE ,! P[] .;,P
7IN WATTS7 US$ 0A MICROWAVE OV5 IS !
PRODUCT (! VOLTAGE .;,V 7IN VOLTS7 &!
CURR5T .,I 7IN AMP]ES74 ,SUPPOSE !
VOLTAGE & CURR5T C 2 MODEL$ BY
.;,V .K #AGJ COS #ABJ .;T & .,I .K
#AA.C COS #A .#BJ .;T ": .;T .IS ! "T
7IN SECONDS74
A4 .,MODEL ,WRITE ! FUNC;N .;,P7.;T7
=! P[] US$ 0! MICROWAVE4
B4 .,SOLVE ,AT :AT "TS DOES !
MICROWAVE USE #CGE WATTS ( P[]8
C4 .,GRAPH+ .,CALCULATOR ,GRAPH !
FUNC;N .;,P7.;T74 .,DESCRIBE H[ ! GRAPH
DI6]S F T (A COS9E FUNC;N (! =M .;Y .K
.A COS .BT4
#DE4 .,,*ALL5GE ,MATRIX MULTIPLIC,N C
2 US$ 6ROTATE A PO9T 7;X1 ;Y7
C.T]CLOCKWISE AB ! ORIG9 "? AN ANGLE4 ,!
COORD9ATES (! RESULT+ PO9T @7 .;X @'@1
.Y0'7 >E DET]M9$ 0! MATRIX EQU,N %[N AT
! "R4
A4 ,! PO9T 7#B1 #C7 IS ROTAT$
C.T]CLOCKWISE AB ! ORIG9 "? AN ANGLE (
@4 ,:AT >E ! COORD9ATES (! RESULT+ PO9T8
B4 ,"? :AT ANGLE M/ ! PO9T 7#F1 #B7 2
ROTAT$ 6PRODUCE @7 .;X @'@1 .Y0'7 .K
,,MIX$ ,,REVIEW
,,PREVIEW
,PREP>E = ,LESSON #AD.E 9 ,EXS4
#EJ-EH4
,P]=M ! 9DICAT$ OP],N 7;S74
.#DF4
.#DG4
.#DH4
.#DI4
,GRAPH ! FUNC;N4
.#EJ4 ;Y .K #C S9 ;X @7 P4 #IJH @7
.#EA4
.#EB4 ;Y .K COS #B;X @7 P4 #IJH @7
.#EC4 ;G7;X7 .K #C S9 #D;X @7 P4 #IJH
@7
.#ED4 ;Y .K COS #D;X @+ #C @7 P4 #IAE
@7
.#EE4 _/7;X7 .K COS ;X @+ #I @7 P4
#IAE @7
.#EF4 ;G7;X7 .K --S9 ;X @+ #B @7 P4
#IAE @7
.#EG4 ;Y .K TAN #D7;X--@7 @7 P4 #IAE
@7
.#EH4
.,,EXTRA .,,PRACTICE = ,LESSON #AD.D1
P4 #AJBC
.,,ONL9E .,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#ICH
,PRO#M ,SOLV+ ,"W%OP ,LESSON #AD.D3
,US+ ,ALT]NATIVE ,ME?ODS
,ANO!R ,WAY 6,SOLVE ,EXAMPLE #C1 PAGE
#ICB
.,,MULTIPLE .,,REPRES5T,NS ,9 ,EXAMPLE
#C ON PAGE #ICB @1 Y SOLV$ A
TRIGONOMETRIC EQU,N ALGEBRAIC,Y4 ,Y C AL
SOLVE A TRIGONOMETRIC EQU,N US+ A TA# OR
US+ A GRAPH4
,,PRO#M
.,,OC1NOGRAPHY ,! WAT] DEP? .;D =!
,BAY ( ,FUNDY C 2 MODEL$ 0": .;D IS
M1SUR$ 9 FEET & .;T IS ! "T 9 H\RS4 ,IF
.;T .K #J REPRES5TS MIDNI<T1 AT :AT
"T7;S7 IS ! WAT] DEP? #G FEET8
,,ME?OD #A
.,US+ .A .,TA# ,! PRO#M REQUIRES SOLV+
! EQU,N #CE--#BH @4 ,"O WAY 6SOLVE ?
EQU,N IS 6MAKE A TA# ( VALUES4 ,Y C USE
A GRAPH+ CALCULATOR 6MAKE ! TA#4
.,,/EP .#A .,5T] ! FUNC;N 96A GRAPH+
CALCULATOR4 ,NOTE T "T IS N[ REPRES5T$
0.;X & WAT] DEP? IS N[ REPRES5T$ 0.Y4
.,,/EP#B .,MAKE A TA# ( VALUES =!
FUNC;N4 ,SET ! TA# S T ! .;X -VALUES />T
AT #J & 9CR1SE 9 9CRE;TS ( #J.A4 7,BE
SURE T ! CALCULATOR IS SET 9 RADIAN
MODE47
.,,/EP .#C .,SCROLL "? ! TA# 6F9D ALL
! "TS .;X AT : ! WAT] DEP? .;Y IS #G
FEET4 ,ON ! 9T]VAL #J "K .;X "K #BD 7:
REPRES5TS "O FULL "D71 Y C SEE T !
FUNC;N EQUALS #G :5 .;X IS #J & #AB.D4
,! WAT] DEP? IS #G FEET :5 .;X .K #J
7T IS1 AT MIDNI<T7 & :5 .;X .K .#AB..D
7T IS1 AT #AB3BD P4M474
------------------------------------#ICI
,,ME?OD #B
.,US+ .A .,GRAPH ,ANO!R APPROA* IS
6USE A GRAPH 6SOLVE ! EQU,N @4 ,Y C USE
A GRAPH+ CALCULATOR 6MAKE ! GRAPH4
.,,/EP .#A .,5T] ! FUNC;NS & .;Y .K #G
96A GRAPH+ CALCULATOR4 ,AG1 NOTE T "T IS
N[ REPRES5T$ 0.;X & WAT] DEP? IS N[
REPRES5T$ 0.;Y @4
.,,/EP .#B .,GRAPH ! FUNC;NS4 ,SET YR
CALCULATOR 9 RADIAN MODE4 ,ADJU/ ! VIEW+
W9D[ S T Y C SEE ": ! GRAPHS 9T]SECT ON
! 9T]VAL #J "K.K .;X "K.K #BD4
.,,/EP .#C .,F9D ! 9T]SEC;N PO9TS (!
TWO GRAPHS US+ ! .9T]SECT F1TURE (!
GRAPH+ CALCULATOR4 ,ON ! 9T]VAL #J "K.K
.;X "K.K #BD1 ! GRAPHS 9T]SECT AT 7#J1
#G7 & 7#AB.D1 #G74 ,2C .;X REPRES5TS !
NUMB] ( H\RS S9CE MIDNI<T1 Y "K T ! WAT]
DEP? IS #G FEET AT MIDNI<T & #AB3BD
,P4,M4
,,PRACTICE
,,SOLV+ ,,EQU,NS ,SOLVE ! EQU,N US+ A
TA# & US+ A GRAPH4
.#A4
.#B4
.#C4 --#AJ COS .#B .;X .K #C
.#D4
.#E4
.#F4
.#G4 .,,:AT .,,IF8 ,9 ! PRO#M ON PAGE
#ICH @1 SUPPOSE Y WANT 6F9D ! "T7;S7 :5
! DEP? (! WAT] 9 ! ,BAY ( ,FUNDY IS #AE
FEET4 ,F9D ! "T7;S7 US+ A TA# & US+ A
GRAPH4
.#H4 .,,WRIT+ .,EXPLA9 :Y ! EQU,N #B
S9 .;X @+ #C .K #J HAS NO SOLU;N4 ,H[
DOES A GRAPH %[ ?8
.#I4 .,,BUOY ,AN OC1N BUOY BOBS UP &
D[N Z WAVES TRAVEL PA/ X4 ,! BUOY'S
4PLACE;T .;D 7IN FEET7 ) RESPECT 6SEA
LEVEL C 2 MODEL$ 0.;D .K #C S9 .;T ":
.;T IS ! "T 7IN SECONDS74 ,DUR+ ! "O
SECOND 9T]VAL #J "K.K .;T "K.K #A1 :5 IS
! BUOY #A.E FEET ABV SEA LEVEL8 ,SOLVE !
PRO#M US+ A TA# & US+ A GRAPH4
------------------------------------#IDJ
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,LESSONS #AD.A-AD.D
.#A4 .,,MULTI-.,,/EP .,,PRO#M ,Y PUT A
REFLECTOR ON A SPOKE ( YR BICYCLE :EEL4
,Z Y RIDE YR BICYCLE1 ! REFLECTOR'S
HEI<T .;H 7IN 9*ES7 ABV ! GR.D IS MODEL$
0.;H .K #AC.E @+ #AA.E COS #B ;T ": .;T
IS ! "T 7IN SECONDS74
.A4 ,GRAPH ! GIV5 FUNC;N4
.B4 ,:AT IS ! FREQU5CY (! FUNC;N8 ,:AT
DOES ! FREQU5CY REPRES5T 9 ? SITU,N8
.C4 ,AT :AT "T7;S7 ON ! 9T]VAL W !
REFLECTOR 2 #H 9*ES ABV ! GR.D8
.#B4 .,,MULTI-.,,/EP .,,PRO#M ,Y /&
#HJ FEET F ! LAUN* SITE (A HOT AIR
BALLOON4 ,Y LOOK AT YR FR :O IS TRAVEL+
/RAI<T UP 9 ! BALLOON 6A HEI<T ( #AEJ
FEET4
.A4 ,WRITE & GRAPH AN EQU,N T GIVES YR
FR'S 4T.E .;D 7IN FEET7 ABV ! GR.D Z A
FUNC;N (! ANGLE ( ELEV,N #I F Y 6YR FR4
.B4 ,:AT IS ! ANGLE ( ELEV,N :5 YR FR
IS AT A HEI<T ( #ABJ FEET8
.#C4 .,,GRI4$ .,,ANSW] ,:AT IS !
AMPLITUDE (! GRAPH 2L8
.#D4 .,,EXT5D$ .,,RESPONSE ,AT AN
AMUSE;T P>K Y WAT* YR FR G ON A RIDE T
SIMULATES A FREE-FALL4 ,Y >E /&+ #BJJ
FEET F ! BASE (! RIDE Z X SL[LY 2G9S
6PULL YR FR UP 6! TOP4 ,! RIDE IS #ABJ
FEET TALL4
.A4 ,WRITE AN EQU,N T GIVES ! 4T.E .;D
7IN FEET7 YR FR IS F ! TOP Z A FUNC;N (!
ANGLE ( ELEV,N4
.B4 ,:AT IS ! DOMA9 (! FUNC;N8
.C4 ,GRAPH ! FUNC;N4 ,EXPLA9 H[ !
GRAPH RELATES 6! GIV5 SITU,N4
.#E4 .,,OP5-.,,5D$ ,F9D TWO DI6]5T
COS9E FUNC;NS T H 7#J1 #F7 Z A MAXIMUM &
@7@1 --#D7 Z A M9IMUM4
.#F4 .,,GRI4$ .,,ANSW] ,! NUMB] .;N
7IN MILLIONS7 ( GALLONS ( ICE CR1M
PRODUC$ 9 ! ,UNIT$ ,/ATES C 2
APPROXIMAT$ BY
": .;T IS ! "T 7IN "DS7 ) .;T .K #A
REPRES5T+ ,JANU>Y #A4 ,:AT VALUE ( .;T
CORRESPONDS 6! F/ "D T #ABE MILLION
GALLONS ( ICE CR1M W 2 PRODUC$8 ,R.D YR
ANSW] 6! NE>E/ 9TEG]4
.#G4 .,,%ORT .,,RESPONSE ,9 CALCULUS1
X C 2 %[N T ! RATE ( *ANGE (! FUNC;N
;F7;X7 .K --CSC ;X--S9 ;X IS GIV5 0?
EXPRES.N3
CSC ;X COT ;X--COSX
.A4 ,%[ T ! EXPRES.N =! RATE ( *ANGE C
2 WRITT5 Z COS ;X COT #B X4
.B4 ,LI/ ! ID5TITIES US$ 6SOLVE "P
7A74
------------------------------------#IDA
#AD.E ,WRITE ,TRIGONOMETRIC ,FUNC;NS
& ,MODELS
.,2F ,Y GRAPH$ S9E & COS9E FUNC;NS4
.,N[ ,Y W MODEL DATA US+ S9E & COS9E
FUNC;NS4
.,:Y8 ,S Y C MODEL ! NUMB] (
BICYCLI/S1 Z 9 ,EX4 #BF4
,KEY ,VOCABUL>Y
99 .S9USOID
,GRAPHS ( S9E & COS9E FUNC;NS >E CALL$
.S9USOIDS4 ,"O ME?OD 6WRITE A S9E OR
COS9E FUNC;N T MODELS A S9USOID IS 6F9D
! VALUES (A1 .;B1 .;H @1 & .;K = .;Y .K
.A S9 ..;B7;X--;H7 @+ .;K OR .;Y .K .A
COS .;B7.;X -- .;H7 @+ .;K
": _\A_\ IS ! AMPLITUDE1 IS ! P]IOD @7
.;B .1 #J71 .;H IS ! HORIZONTAL %IFT1 &
.;K IS ! V]TICAL %IFT4
,SIDEB>3
,/&>DS
,MA!MATICAL .,A NALYSIS3 #D.J ,/UD5TS
GRAPH FUNC;NS (! =M ;F7;T7.K,A S9 @7
.,BT @+ .;,C @7 OR ;F7;T7 .K ,A COS 7,BT
@+ ;,C7 & 9T]PRET ,A1 ;,B1 & ;,C 9 T]MS
( AMPLITUDE1 FREQU5CY1 P]IOD1 & PHASE
%IFT4
,,EXAMPLE #A ,SOLVE A MULTI-/EP PRO#M
,WRITE A FUNC;N =! S9USOID %[N 2L4
,SOLU;N
.,,/EP .#A .,F9D ! MAXIMUM VALUE .;,M
& M9IMUM VALUE .M4 ,F ! GRAPH1 .;,M .K
#E & .;M .K --#A4
.,,/EP .#B .,ID5TIFY ! V]TICAL %IFT1
.K4 ,! VALUE ( .;K IS ! M1N (! MAXIMUM &
M9IMUM VALUES4 ,! V]TICAL %IFT IS
,S1 .;K .K #B4
.,,/EP .#C .,DECIDE :E!R ! GRAPH %D 2
MODEL$ 0A S9E OR COS9E FUNC;N4 ,2C !
GRAPH CROSSES ! MIDL9E .;Y .K .#B ON !
;Y-AXIS1 ! GRAPH IS A S9E CURVE ) NO
HORIZONTAL %IFT4 ,S1 .;H .K .#J4
.,,/EP .#D .,F9D ! AMPLITUDE & P]IOD4
,! P]IOD IS @4 ,S1 .;B .K #D4 ,!
AMPLITUDE IS @4 ,! GRAPH IS N A
REFLEC;N1 S .A .1 #J4 ,"!=E1 .A .K #C4
,! FUNC;N IS .;Y .K #C S9 #D;X @+ #B4
,,F9D ,,P]IOD
,2C ! GRAPH REP1TS E UNITS1 ! P]IOD IS
@4
------------------------------------#IDB
,,EXAMPLE #B ,MODEL CIRCUL> MO;N
.,,JUMP .,,ROPE ,AT A ,D\# ,DUT*
-PETI;N1 TWO P SW+ JUMP ROPES Z %[N 9 !
DIAGRAM 2L4 ,! HI<E/ PO9T (! MI4LE ( EA*
ROPE IS #GE 9*ES ABV ! GR.D1 &! L[E/
PO9T IS #C 9*ES4 ,! ROPE MAKES #B
REVOLU;NS P] SECOND4 ,WRITE A MODEL =!
HEI<T .;H 7IN FEET7 (A ROPE Z A FUNC;N
(! "T .;T 7IN SECONDS7 IF ! ROPE IS AT
XS L[E/ PO9T :5 .;T.K.#J4
,SOLU;N
.,,/EP .#A .,F9D ! MAXIMUM & M9IMUM
VALUES (! FUNC;N4 ,A ROPE'S MAXIMUM
HEI<T IS #GE 9*ES1 S .;,M .K #GE4 ,A
ROPE'S M9IMUM HEI<T IS #C 9*ES1 S .;M .K
#C4
.,,/EP .#B .,ID5TIFY ! V]TICAL %IFT4
,! V]TICAL %IFT =! MODEL IS3
.,,/EP .#C .,DECIDE :E!R ! HEI<T %D 2
MODEL$ 0A S9E OR COS9E FUNC;N4 ,:5 .;T
.K #J1 ! HEI<T IS AT XS M9IMUM4 ,S1 USE
A COS9E FUNC;N ^: GRAPH IS A REFLEC;N 9
! .;X -AXIS ) NO HORIZONTAL %IFT @7 .;H
.K #J74
.,,/EP .#D .,F9D ! AMPLITUDE & P]IOD4
,! AMPLITUDE IS @4
,2C ! GRAPH IS A REFLEC;N1 .A "K #J4
,S1 .A .K --#CF4 ,2C A ROPE IS ROTAT+ AT
A RATE ( #B REVOLU;NS P] SECOND1 "O
REVOLU;N IS -PLET$ 9 #J.E SECOND4 ,S1 !
P]IOD IS @1 & .;B .K #D4
,A MODEL =! HEI<T (A ROPE IS .;H .K
--#CF COS .#D .;T @+ #CI4
..,GUID$ ,PRACTICE = ,EXAMPLES #A &
.#B
,WRITE A FUNC;N =! S9USOID4
.#A4
.#B4
.#C4 .,,:AT .,,IF8 .,DESCRIBE H[ !
MODEL 9 ,EXAMPLE #B WD *ANGE IF ! L[E/
PO9T (A ROPE IS #E 9*ES ABV ! GR.D &!
HI<E/ PO9T IS #GJ 9*ES ABV ! GR.D4
------------------------------------#IDC
.,,S9USOIDAL .,,REGRES.N ,ANO!R WAY
6MODEL S9USOIDS IS 6USE A GRAPH+
CALCULATOR T HAS A S9USOIDAL REGRES.N
F1TURE4 ,! ADVANTAGE ( ? ME?OD IS T X
USES ALL (! DATA PO9TS 6F9D ! MODEL4
,,EXAMPLE #C ,USE S9USOIDAL REGRES.N
.,,5]GY ,! TA# 2L %[S ! NUMB] (
KILOWATT H\RS .;,K 7IN ?\S&S7 US$ EA*
MON? =A GIV5 YE> 0A HANG> AT ! ,CAPE
,CANAV]AL ,AIR ,/,N 9 ,FLORIDA4 ,! "T
.;T IS M1SUR$ 9 MON?S1 ) .;T .K #A
REPRES5T+ ,JANU>Y4 ,WRITE A
TRIGONOMETRIC MODEL T GIVES .;,K A
FUNC;N ( .T4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;T @3 #A3 #B3 #C3 #D3 #E3 #F3 #G3 #H3
#I3 #AJ3 --@3 #AB
.;,K @3 #FA.I3 #EI3 #FB3 #GJ.A3 #HA.D3
#IC.A3 #AJB.C3 #AJF.H3 #AJE.D3 #IB.I3
#HA.B3 #FI.I
,SOLU;N
.,,/EP#A .,5T] ! DATA 9 A GRAPH+
CALCULATOR4
.,,/EP .#B .,MAKE A SCATT] PLOT1
.,,/EP .#C .,P]=M A S9USOIDAL
REGRES.N1 2C ! SCATT] PLOT APPE>S
S9USOIDAL4
.,,/EP .#D .,GRAPH ! MODEL &! DATA 9 !
SAME VIEW+ W9D[4
,! MODEL APPE>S 6BE A GD FIT4 ,S1 A
MODEL =! DATA IS .;,K .K #BC.I S9
7#J.ECC .;T -- #B.FI7 @+ #HB.D4
..,GUID$ ,PRACTICE = ,EXAMPLE .#C
.#D4 .,,METEOROLOGY ,USE A GRAPH+
CALCULATOR 6WRITE A S9E MODEL T GIVES !
AV]AGE DAILY TEMP]ATURE .;,T 7IN DEGREES
,FAHR5HEIT7 = ,BO/ON1 ,MASSA*USETTS1 Z A
FUNC;N (! "T .;T 7IN MON?S71 ": .;T .K
#A REPRES5TS ,JANU>Y4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;T @3 #A3 #B3 #C3 #D3 #E3 #F3 #G3 #H3
#I3 #AJ3 #AA3 #AB
.;,T @3 #BI3 #CB3 #CI3 #DH3 #EI3 #FH3
#GD3 #GB3 #FE3 #ED3 #DE3 #CE
------------------------------------#IDD
#AD.E ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
,,WS#BD = ,EXS4 #E1I1 & #BE
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE ,EXS4
#B1 #AH1 #AI1 #BJ1 & #BH
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,:AT IS A S9USOID8
.#B4 .,,WRIT+ .,DESCRIBE TWO ME?ODS Y
C USE 6MODEL A S9USOID4
,,WRIT+ ,,FUNC;NS ,WRITE A FUNC;N =!
S9USOID4
,,EXAMPLE #A
ON P4 #IDA = ,EXS4 #C-AI
.#C4
.#D4
.#E4
.#F4
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 F9D+ ! AMPLITUDE & V]TICAL %IFT
=A S9USOID )A MAXIMUM PO9T AT 7#B1AJ7 &A
M9IMUM PO9T AT 7#D1 --#F74
.#G4
.#H4
,,WRIT+ ,,FUNC;NS ,WRITE A FUNC;N =!
S9USOID ) MAXIMUM AT PO9T .,A & M9IMUM
AT PO9T .,B4
.#I4 .,A7 @1 #F71 .;,B7.#C @1 --#F7
.#AJ4 .,A 7#J1 #D71 .;,B7 @1 --#D7
#AA4
.#AA4
.#AB4
.#AC4
.#AD4 .,A 7#J1 #E71 ;,B7#F1 --#AA7
.#AE4 ,A7#J1 #J71 ;,B7#D1 --#D7 #AF4
.#AF4
.#AG4
#AH4 .,,MULTIPLE .,,*OICE ,DUR+ "O
CYCLE1 A S9USOID HAS A M9IMUM AT 7#AF1
#CH7 &A MAXIMUM AT 7#BD1 #FJ74 ,:AT IS !
AMPLITUDE ( ? S9USOID8
,A #H
;,B #AA
;,C #BB
;,D #DI
------------------------------------#IDE
#AI4 .,,MULTIPLE .,,*OICE ,:AT IS AN
EQU,N (! GRAPH %[N AT ! "R8
,A4
,B4
,C4
,D4
#BJ4 .,,WRIT+ ,ANY S9USOID C 2 MODEL$
0BO? A S9E FUNC;N &A COS9E FUNC;N4
,"!=E1 Y C *OOSE ! TYPE ( FUNC;N T IS M
3V5I5T4 .,EXPLA9 : TYPE ( FUNC;N Y WD
*OOSE 6MODEL A S9USOID ^: .;Y -9T]CEPT
O3URS AT ! M9IMUM VALUE (! FUNC;N4
#BA4 .,,R1SON+ ,MODEL ! S9USOID 9
,EXAMPLE #A ON PAGE #IDA )A COS9E FUNC;N
(! =M .;Y .K .A COS .;B7.;X--.;H7 @+ .K4
,USE ID5TITIES 6%[ T ! MODEL Y F.D IS
EQUIVAL5T 6! S9E MODEL 9 ,EXAMPLE #A4
#BB4 .,,*ALL5GE ,WRITE A S9E FUNC;N =!
S9USOID )A M9IMUM AT &A MAXIMUM AT
,,PRO#M ,,SOLV+
,,EXAMPLE #A
ON P4 #IDA = ,EXS4 #BC-BD
.#BC4 .,,CIRCUITS ,A CIRCUIT HAS AN
ALT]NAT+ VOLTAGE ( #AJJ VOLTS T P1KS E
#J.E SECOND4 ,USE ! GRAPH %[N AT ! "R
6WRITE A S9USOIDAL MODEL =! VOLTAGE .;,V
Z A FUNC;N (! "T .;T 7IN SECONDS74
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#BD4 .,,CLIMATOLOGY ,! GRAPH 2L %[S !
AV]AGE DAILY TEMP]ATURE ( ,H\/ON1
,TEXAS4 ,WRITE A S9USOIDAL MODEL =!
AV]AGE DAILY TEMP]ATURE .;,T 7IN DEGREES
,FAHR5HEIT7 Z A FUNC;N ( "T .;T 7IN
MON?S74
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#BE4 .,,CIRCUL> .,,MO;N ,"O (! L>GE/
SEW+ MA*9ES 9 ! _W HAS A .FLY:EEL 7:
TURNS Z ! MA*9E SEWS7 T IS #E FEET 9
DIAMET]4 ,WRITE A MODEL =! HEI<T .;H 7IN
FEET7 (! H&LE AT ! $GE (! FLY:EEL Z A
FUNC;N (! "T .;T 7IN SECONDS74 ,ASSUME T
! :EEL MAKES A -PLETE TURN E #B SECONDS
&! H&LE IS AT XS M9IMUM HEI<T ( #D FEET
ABV ! GR.D :5 .;T .K #J4
,,EXAMPLE .#B
ON P4 #IDB = ,EX4 #BE
------------------------------------#IDF
,,EXAMPLE #C
ON P4 #IDC = ,EXS4 #BF-BG
.#BF4 .,,BICYCLI/S ,! TA# 2L %[S !
NUMB] ( ADULT RESID5TS .;,R 7IN
MILLIONS7 9 ! ,UNIT$ ,/ATES :O RODE A
BICYCLE DUR+ ! MON?S ( ,OCTOB] #BJJA "?
,SEPTEMB] #BJJB4 ,! "T .;T .IS M1SUR$ 9
MON?S1 ) .;T .K #A REPRES5T+ ,OCTOB]
#BJJA4 ,USE A GRAPH+ CALCULATOR 6WRITE A
S9USOIDAL MODEL T GIVES .;,R Z A FUNC;N
( .T4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;T @3 #A3 #B3 #C3 #D3 #E3 #F3 #G3 #H3
#I3 #AJ3 #AA3 #AB
.;,R @3 #CE3 #CJ3 #BD3 #BD3 #BF3 #BI3
#CE3 #CD3 #CI3 #DC3 #DD3 #CG
#BG4 .,,MULTI-.,,/EP .,,PRO#M ,! TA#
2L %[S ! NUMB] ( EMPLOYEES ;,N 7IN
?\S&S7 AT A SPORT+ GDS -PANY EA* YE> =
ELEV5 YE>S4 ,! "T .;T IS M1SUR$ 9 YE>S1
) .;T .K #A REPRES5T+ ! F/ YE>4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;T @3 #A3 #B3 #C3 #D3 #E3 #F3 #G3 #H3
#I3 #AJ3 #AA
.;,N @3 #BJ.H3 #BB.G3 #BD.F3 #BC.B3
#BJ3 #AG.E3 #AF.G3 #AG.H3 #BA3 #BB3
#BD.A
A4 .,MODEL ,USE A GRAPH+ CALCULATOR
6WRITE A S9USOIDAL MODEL T GIVES .;,N Z
A FUNC;N ( .T4
B4 .,CALCULATE ,PREDICT ! NUMB] (
EMPLOYEES 9 ! TWELF? YE>4
#BH4 .,,EXT5D$ .,,RESPONSE ,! L[ TIDE
AT ,EA/PORT1 ,MA9E1 IS #C.E FEET & O3URS
AT MIDNI<T4 ,AF #F H\RS1 ,EA/PORT IS AT
HI< TIDE1 : IS #AF.E FEET4
A4 .,MODEL ,WRITE A S9USOIDAL MODEL T
GIVES ! TIDE DEP? .;D 7IN FEET7 Z A
FUNC;N (! "T .;T 7IN H\RS74 ,LET .;T .K
#J REPRES5T MIDNI<T4
B4 .,CALCULATE ,F9D ALL ! "TS :5 L[ &
HI< TIDES O3UR 9 A #BD H\R P]IOD4
C4 .,R1SON+ .,EXPLA9 H[ ! GRAPH (!
FUNC;N Y WROTE 9 "P 7A7 IS RELAT$ 6A
GRAPH T %[S ! TIDE DEP? .;D AT ,EA/PORT
.;T H\RS AF #C3JJ ,A4,M4
#BI4 .,,*ALL5GE ,! TA# 2L %[S ! AV]AGE
MON?LY SEA TEMP]ATURES .;,T 7IN DEGREES
,CELSIUS7 = ,SANTA ,B>B>A1 ,CALI=NIA4 ,!
"T .;T IS M1SUR$ 9 MON?S1 ) .;T .K #A
REPRES5T+ ,JANU>Y4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;T @3 #A3 #B3 #C3 #D3 #E3 #F3 #G3 #H3
#I3 #AJ3 #AA3 #AB
.;,T @3 #AD3 #AC.F3 #AC.D3 #AB.E3
#AC.I3 #AE.F3 #AF.H3 #AG.B3 #AG.G3
#AG.A3 #AE.E3 #AD.A
A4 ,USE A GRAPH+ CALCULATOR 6WRITE A
S9E MODEL T GIVES .;,T Z A FUNC;N ( .T4
B4 ,F9D A COS9E MODEL =! DATA4
.K .,,"W$-.,,\ .,,SOLU;NS ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#IDG
,,MIX$ ,,REVIEW
,,PREVIEW
,PREP>E = ,LESSON #AD.F 9 ,EXS4
#CF-DA4
,WRITE ! /&>D =M (! EQU,N (! P>ABOLA
)! GIV5 FOCUS & V]TEX AT 7#J1 #J74 @7 P4
#FBJ @7
.#CJ4 7#F1 #J7
.#CA4 7-#D1 #J7
.#CB4 7#J1 --#C7
.#CC4
.#CD4
.#CE4
,EVALUATE ! FUNC;N )\T US+ A
CALCULATOR4 @7 P4 #HFF @7
.#CF4 COS 7-#BAJ;DG7
.#CG4 TAN #CAE;DG
.#CH4 S9 7-#ABJ;DG7
.#CI4
.#DJ4
.#DA4
,F9D ! >EA ( )! GIV5 SIDE L5G?S &
9CLUD$ ANGLE4 @7 P4 #HHB @7
.#DB4 ,A .K #CF;DG1 ;B .K #H1 ;C .K #E
.#DC4 ,A .K #GI;DG1 ;B .K #AD1 ;C .K
#H
.#DD4 ;,C .K #ADE;DG1 A .K #D1 ;B .K
#AD
.#DE4 ;,B .K #EJ;DG1 A .K #G1 ;C .K #I
.#DF4 ,A .K #ABC;DG1 ;B .K #BF1 ;C .K
#CA
.#DG4 ;,C .K #AJE;DG1 A .K #BB1 ;B .K
#AI
,,QUIZ .= .,LESSON .#AD..C-.AD..E
,SIMPLIFY ! EXPRES.N1 @7 P4 #IBD @7
.#A4 S9 .;X SEC .;X
.#B4 S9 .#J 7.#A @+ COT #B @7
.#C4
.#D4 COS #B @+ S9 #B @+ TAN #B
.#E4
.#F4
,F9D ! G5]AL SOLU;N (! EQU,N1 @7@4 P4
#ICA @7
.#G4 COS .;X @+ COS 7--.;X7 .K #A
.#H4
.#I4 #B S9 #B .;X -- S9 .;X .K .#A
,WRITE A FUNC;N =! S9USOID1 @7 P4 #IDA
@7
.#AJ4
.#AA4
.#AB4 .,,DAILY .,,TEMP]ATURES ,! TA#
2L %[S ! AV]AGE DAILY TEMP]ATURE .;,D
7IN DEGREES ,FAHR5HEIT7 9 ,DETROIT1
,MI*IGAN4 ,! "T .;T IS M1SUR$ 9 MON?S1 )
.;T .K #A REPRES5T+ ,JANU>Y4 ,USE A
GRAPH+ CALCULATOR 6WRITE A S9USOIDAL
MODEL T GIVES .;,D Z A FUNC;N ( .T4 7.P4
.#IDA7
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;T @3 #A3 #B3 #C3 #D3 #E3 #F3 #G3 #H3
#I3 #AJ3 #AA3 #AB
.;,D @3 #BD.E3 #BG.B3 #CF.I3 #DH.A3
#EI.H3 #FI3 #GC.E3 #GA.H3 #FC.I3 #EA.I3
#DJ.G3 #BI.F
,,EXTRA ,,PRACTICE = ,LESSON #AD.E1 P4
#AJBC
..,,ONL9E ,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#IDH
,,CBL ,ACTIV;Y3 #AD.E ,COLLECT &
,MODEL ,TRIGONOMETRIC ,DATA
,USE AF LESSON1 #AD.E
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
,KEY/ROKES
,MAT]IALS
99 MUSICAL 9/RU;T
99 ,CALCULATOR ,BAS$ ,LABORATORY
7,,CBL7
99 ,,CBL MICROPH"O
99 GRAPH+ CALCULATOR
,SIDEB>3
,/&>DS
.,MA!MATICAL .,ANALYSIS3 #AI.J ,/UD5TS
>E ADEPT AT US+ ANALYSIS 9 A V>IETY (
APPLIC,NS & ^W PRO#MS4
,,"Q ,H[ IS MUSIC RELAT$
6TRIGONOMETRY8
,S.D IS A V>I,N 9 PRESSURE TRANSMITT$
"? AIR1 WAT]1 OR O!R MATT]4 ,S.D TRAVELS
Z A WAVE4 ,! S.D (A PURE NOTE C 2
REPRES5T$ US+ A S9E 7OR COS9E7 WAVE4 ,M
-PLICAT$ S.DS C 2 MODEL$ 0! SUM ( S"EAL
S9E WAVES4
,,EXPLORE ,ANALYZE ! S.D (A MUSICAL
9/RU;T
,PLAY A NOTE ON A MUSICAL 9/RU;T4
,WRITE A S9E FUNC;N 6DESCRIBE ! NOTE4
,,/EP #A ,PLAY NOTE
,PLAY A PURE NOTE ON A MUSICAL 9/RU;T4
,USE ! ,,CBL &! ,,CBL MICROPH"O 6COLLECT
! S.D DATA & /ORE X 9 A GRAPH+
CALCULATOR4
,,/EP#B ,GRAPH FUNC;N
,USE ! GRAPH+ CALCULATOR 6GRAPH !
PRESSURE (! S.D Z A FUNC;N ( "T4
,,/EP #C ,F9D "*I/ICS ( GRAPH
,USE ! GRAPH (! S.D DATA 6CALCULATE !
NOTE'S AMPLITUDE & FREQU5CY 7! NUMB] (
CYCLES 9 "O SECOND74
,,/EP#D ,WRITE FUNC;N
,WRITE A S9E FUNC;N =! NOTE4
,,DRAW ,,3CLU.NS ,USE YR OBS]V,NS
6-PLETE ^! EX]CISES
.#A4 ,*OOSE A NOTE 6PLAY & H A
CLASSMATE AL *OOSE A NOTE4 ,F9D TWO S9E
FUNC;NS .;Y .K .;F7.;X7 & .;Y .K ;G7 .;X
@7 T MODEL ! TWO NOTES4 ,!N PLAY ! NOTES
SIMULTANE\SLY & USE ! ,,CBL &A GRAPH+
CALCULATOR 6GRAPH ! RESULT+ S.D WAVE4
.,-P>E ? GRAPH )! GRAPH ( ..;Y .K
;F7.;X7 @+ ;G7;X74 ,:AT D Y NOTICE8
.#B4 ,! PIT* (A S.D WAVE IS DET]M9$ 0!
WAVE'S FREQU5CY4 ,! GRT] ! FREQU5CY1 !
HI<] ! PIT*4 ,: (! NOTES 9 ,EX]CISE #A
_H A HI<] PIT*8
.#C4 ,:5 Y *ANGE ! VOLUME (A NOTE1 :AT
HAPP5S 6! GRAPH (! S.D WAVE8
.#D4 .,-P>E ! S9E WAVES = DI6]5T
9/RU;TS PLAY+ ! SAME NOTE4
------------------------------------#IDI
#AD.F ,APPLY ,SUM & ,DI6];E ,=MULAS
.,2F ,Y F.D TRIGONOMETRIC FUNC;NS (A
GIV5 ANGLE4
.,N[ ,Y W USE TRIGONOMETRIC SUM &
DI6];E =MULAS4
.,:Y8 ,S Y C SIMPLIFY A RATIO US$ =
AERIAL PHOTOGRAPHY1 Z 9 ,EX4 #DC4
,KEY ,VOCABUL>Y
99 .TRIGONOMETRIC .ID5T;Y @1 P4 #IBD
,SIDEB>3
,/&>DS
.,MA!MATICAL .,ANALYSIS3 #AJ.J ,/UD5TS
DEMON/RATE AN "U/&+ (! A4I;N =MULAS =
S9ES & COS9ES & _! PRO(S & C USE ^?
=MULAS 6PROVE &_/OR SIMPLIFY O!R
TRIGONOMETRIC ID5TITIES4
,9 ? LESSON1 Y W /UDY =MULAS T ALL[ Y
6EVALUATE TRIGONOMETRIC FUNC;NS (! SUM
OR DI6];E ( TWO ANGLES4
,,KEY ,,3CEPT .,= .,YR .,NOTEBOOK
,SUM & ,DI6];E ,=MULAS
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,SUM ,=MULAS3 ,DI6];E ,=MULAS
S9 7.A @+ .;B7 .K S9 .A COS .;B @+ COS
.A S9 .;B @3 S9 @7 .A--.;B7 .K S9 .A COS
.;B -- COS .A S9 .;B
COS 7A @+ .;B7 .K COS .A COS .;B - S9
.A S9 .;B @3 COS @7 .A--.;B7 .K COS .A
COS .;B @+ S9 .A S9 .;B
@3
,9 G5]AL1 S9 7A @+ .;B7 @6.K S9 .A @+
S9 .;B @4 ,SIMIL> /ATE;TS C 2 MADE =!
O!R TRIGONOMETRIC FUNC;NS ( SUMS &
DI6];ES4
,,EXAMPLE #A ,EVALUATE A TRIGONOMETRIC
EXPRES.N
,F9D ! EXACT VALUE ( 7A7 S9 #AE;DG &
7;B7
.A4
.B4
,,REVIEW ,,3JUGATES
,= HELP ) US+ 3JUGATES 6R,NALIZE
DENOM9ATORS1 SEE P4 #BFF @4
------------------------------------#IEJ
,,EXAMPLE #B ,USE A DI6];E =MULA
,F9D COS @7 .A -- .;B7 GIV5 T COS ) &
S9 )
,SOLU;N
,US+ A ,PY?AGOR1N ID5T;Y & QUADRANT
SIGNS GIVES S9 & @4
..,GUID$ ,PRACTICE = ,EXAMPLES #A &
.#B
,F9D ! EXACT VALUE (! EXPRES.N4
.#A4 S9 #AJE;DG
.#B4 COS #GE;DG
.#C4
.#D4
.#E4 ,F9D S9 @7 .A -- .;B7 GIV5 T S9 )
& COS )
,,EXAMPLE #C ,SIMPLIFY AN EXPRES.N
..,SIMPLIFY ! EXPRES.N COS @7 .;X @+
@7@4
,,EXAMPLE #D ,SOLVE A TRIGONOMETRIC
EQU,N
,SOLVE
,,ANO!R ,,WAY
,Y C AL SOLVE 0US+ A GRAPH+
CALCULATOR4 ,F/ GRAPH EA* SIDE (!
ORIG9AL EQU,N & !N USE ! .9T]SECT F1TURE
6F9D ! ;X-VALUE7;S7 ": ! EXPRES.NS >E
EQUAL4
,9 ! 9T]VAL #J "K.K .;X "K #B1 ! ONLY
SOLU;N IS @4
------------------------------------#IEA
,,EXAMPLE #E ,SOLVE A MULTI-/EP PRO#M
.,,"DLI<T .,,H\RS ,! NUMB] .;H ( H\RS
( "DLI<T = ,DALLAS1 ,TEXAS1 & ,AN*ORAGE1
,ALASKA1 C 2 APPROXIMAT$ 0! EQU,NS 2L1
": .;T IS ! "T 9 "DS & .;T.K.#J
REPRES5TS ,JANU>Y #A4 ,ON : "DS (! YE> W
! TWO CITIES H ! SAME AM.T ( "DLI<T8
,DALLAS3
,AN*ORAGE3
,SOLU;N
.,,/EP .#A .,SOLVE ! EQU,N .;H #A .K
.;H #B = .T4
.;T --#HD.GF @+ #AHB .;N
.,,/EP .#B .,F9D ! "DS )9 "O YE> 7#CFE
"DS7 = : ,DALLAS & ,AN*ORAGE W H ! SAME
AM.T ( "DLI<T4
.;T --#HD.GF @+ #AHB7#A7 #IG1 OR ON
,APRIL #H
.;T --#HD.GF @+ #AHB7#B7 #BGI1 OR ON
,OCTOB] #G
.,GUID$ .,PRACTICE = ,EXAMPLES #C1D1 &
#E
,SIMPLIFY ! EXPRES.N4
.#F4 S9 @7 .;X @+ #B @7
.#G4 COS 7..;X--.#B @7
.#H4 TAN 7;X -- @7
.#I4 ,SOLVE
------------------------------------#IEB
#AD.F ,EX]CISES
,HOME"W ,KEY
.K .,,"W$-.,,\ .,,SOLU;NS ON P4
,,WS#BE = ,EXS4 #I1 #BC1 & #DC
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE ,EXS4
#B1AA1AH1 #CB1 & #DD
,,SKILL ,,PRACTICE
.#A4 .,,VOCABUL>Y ,GIVE ! SUM & DI6];E
=MULAS = S9E1 COS9E1 & TANG5T4
.#B4 .,,WRIT+ .,EXPLA9 H[ Y C EVALUATE
TAN #GE;DG US+ EI ! SUM OR DI6];E =MULA
= TANG5T4
,,EXAMPLE #A
ON P4 #IDI = ,EXS4 #C-AJ
.,,F9D+ .,,VALUES ,F9D ! EXACT VALUE
(! EXPRES.N4
.#C4 TAN 7--#AE;DG7
.#D4 S9 7--#AFE;DG7
.#E4 TAN #AIE;DG
.#F4 COS #AE;DG
.#G4
.#H4
.#I4
.#AJ4
.#AA4 .,,%ORT .,,RESPONSE ,DERIVE !
C(UNC;N ID5T;Y US+ ! DI6];E =MULA = S9E4
,,EXAMPLE #B
ON P4 #IEJ = ,EXS4 #AB-AH
.,,EVALUAT+ .,,EXPRES.NS ,EVALUATE !
EXPRES.N GIV5 T COS ) & S9
.#AB4 S9 7A @+ .;B7
.#AC4 COS 7.A @+ .;B7
.#AD4 TAN @7 .A @+ .;B7
.#AE4 S9 7A -- .;B7
.#AF4 COS 7.A--.;B7
.#AG4 TAN 7A -- .;B7
.#AH4 .,,MULTIPLE .,,*OICE ,:AT IS !
VALUE ( S9 @7 .A--.;B @7 GIV5 T ) & @4
.,A
.;,B
.;,C
.;,D
,,EXAMPLE #C
ON P4 #IEJ = ,EXS4 #AI-CA
.,,SIMPLIFY+ .,,EXPRES.NS ,SIMPLIFY !
EXPRES.N4
.#AI4 TAN 7;X @+7
.#BJ4 S9 7;X @+7
.#BA4 COS 7;X @+ #B7
.#BB4 TAN 7;X--#B7
.#BC4
.#BD4
.#BE4
.#BF4
.#BG4
.#BH4
.#BI4
.#CJ4
.#CA4 .,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 SIMPLIFY+ ! EXPRES.N4
,,EXAMPLE #D
ON P4 #IEJ = ,EXS4 #CB-CH
.#CB4 .,,MULTIPLE .,,*OICE ,:AT IS A
SOLU;N (! EQU,N S9 7;X--#B7 @+ TAN
7;X--#B7 .K #J ON ! 9T]VAL "K .;X "K #C
#G8
.,A
.;,B
.;,C #B
.;,D #C
------------------------------------#IEC
,,SOLV+ ,,TRIGONOMETRIC ,,EQU,NS
,SOLVE ! EQU,N = #J "K .;X "K #B4
.#CC4
.#CD4
.#CE4
.#CG4
.#CH4 S97 .;X @+ @7 @+ COS7 .;X @+ @7
#CI4 .,,*ALL5GE ,3SID] A -PLEX NUMB]
..;Z .K A @+ .BI 9 ! -PLEX PLANE %[N4
,LET .;R 2 ! L5G? (! L9E SEG;T JO9+ .;Z
&! ORIG91 & LET 2 ! ANGLE T ? SEG;T
MAKES )! POSITIVE R1L AXIS1 Z %[N4
A4 .,EXPLA9 :Y .A .K .;R COS & .;B .K
.;R S91 S T .;Z .K 7RCOS @7 @+ .;I 7RS9
@7@4
B4 ,USE ! RESULT F "P 7A7 6%[ !
FOLL[+3 .;Z #B .K ;R #B ,77COS COS--S9
S9 @7 @+ ;I7S9 COS @+ COS S9 @7@7'
C4 ,USE ! SUM & DI6];E =MULAS 6%[ T !
EQU,N 9 "P 7;B7 C 2 WRITT5 Z .;Z #B .K
;R #B 7COS .#B @+ .;I S9 .#B @7@4
,PRO#M ,SOLV+
,,EXAMPLE #E
ON P4 #IEA = ,EXS4 #DJ-DA
.#DJ4 .,,METEOROLOGY ,! NUMB] .;H (
H\RS ( "DLI<T = ,ROME1 ,ITALY1 & ,MIAMI1
,FLORIDA1 C 2 APPROXIMAT$ 0! EQU,NS 2L1
": .;T IS ! "T 9 "DS & .;T .K #J
REPRES5TS ,JANU>Y #A4
.,ROME3
.,MIAMI3
,ON : "DS (! YE> W ! CITIES H ! SAME
AM.T ( "DLI<T8
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#DA4 .,,CLOCK .,,T[] ,! HEI<TS .;M &
.;H 7IN FEET7 (A CLOCK T[]'S M9UTE H& &
H\R H&1 RESPECTIVELY1 C 2 APPROXIMAT$ 0&
": .;T IS ! "T 9 M9UTES & .;T .K #J
REPRES5TS #C3JJ ,P4,M4 ,USE A GRAPH+
CALCULATOR 6F9D H[ L;G X TAKES =! HEI<T
(! M9UTE H& 6EQUAL ! HEI<T (! H\R H&4
@A.,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#DB4 .,,PHYSICAL .,,SCI;E ,:5 A WAVE
TRAVELS "? A TAUT /R+1 ! 4PLACE;T ;Y (
EA* PO9T ON ! /R+ DEP5DS ON ! "T .;T &!
PO9T'S POSI;N .X4 ,! EQU,N (A ./&+ .WAVE
C 2 OBTA9$ 0A4+ ! 4PLACE;TS ( TWO WAVES
TRAVEL+ 9 OPPOSITE DIREC;NS4 ,SUPPOSE
TWO WAVES C 2 MODEL$ 0^! EQU,NS3
,%[ T
------------------------------------#IED
.#DC4 .,,MULTI-.,,/EP .,,PRO#M ,A
PHOTOGRAPH] IS AT A HEI<T .;H TAK+
AERIAL PHOTOGRAPHS4 ,! RATIO (! IMAGE
L5G? .,,WQ 6! L5G? .,,NA (! ACTUAL
OBJECT IS
": .;F IS ! FOCAL L5G? (! CAM]A1 #J;IS
! ANGLE 2T ! V]TICAL L9E P]P5DICUL> 6!
GR.D &! L9E F ! CAM]A 6PO9T .,A @1 & .;T
IS ! TILT ANGLE (! FILM4
.A4 ,USE ! DI6];E =MULA = TANG5T
6SIMPLIFY ! RATIO4
.B4 ,%[ T @4
#DD4 .,,EXT5D$ .,,RESPONSE ,YR FR
PULLS ON A WEI<T ATTA*$ 6A SPR+ & !N
REL1SES X4 ,A SPLIT SECOND LAT]1 Y 2G9
FILM+ ! SPR+ 6ANALYZE XS MO;N4 ,Y F9D T
! SPR+'S 4T.E .;Y 7IN 9*ES7 F XS
EQUILIBRIUM PO9T C 2 MODEL$ 0.;Y .K #E
S9 7#B .;T @+ ;,C7 ": .;,C .K TAN -#A &
.;T IS ! ELAPS$ "T 7IN SECONDS7 S9CE Y
2GAN FILM+4
A4 ,F9D ! VALUES ( S9 .;,C & COS ,C4
B4 ,USE A SUM =MULA 6%[ T .;Y .K #E S9
7#B .;T @+ ;,C7 C 2 WRITT5 Z .;Y .K #D
S9 #B .;T @+ #C COS .#BT4
C4 ,GRAPH ! FUNC;N F.D 9 "P 7;B7 & F9D
XS MAXIMUM VALUE4 .,EXPLA9 :AT ? VALUE
REPRES5TS4
#DE4 .,,*ALL5GE ,! BUSY SIGNAL ON A
T\*-T"O PH"O IS A -B9,N ( TWO T"OS )
FREQU5CIES ( #DHJ H]TZ & #FBJ H]TZ4 ,!
9DIVIDUAL T"OS C 2 MODEL$ 0! FOLL[+
EQU,NS3
.#DHJ .H]TZ3 .;Y #A .K COS #IFJ .;T
.#FBJ .H]TZ3 .;Y #B .K COS #ABDJ .;T
,! S.D (! BUSY SIGNAL C 2 MODEL$ 0.;Y
#A @+ .;Y #B @4 ,%[ T3 .;Y ;R @+.;Y #B
.K .#B COS #AAJJ .;T #ADJ .;T @2
,MIX$ ,REVIEW
,PREVIEW
,PREP>E = ,LESSON #AD.G 9 ,EXS4
#EF-FA4
,SKET* ! ANGLE4 ,!N F9D REF];E ANGLE4
7.P#..HFF7
.#DF4 #BCJ;DG
.#DG4 --#EAJ;DG
.#DH4 #GCJ;DG
.#DI4 --#CEE;DG
.#EJ4 #DFJ;DG
.#EA4 #HFJ;DG
,SOLVE .,,ABC @4 7.P#..HHB7
.#EB4 .,A .K #AAJ;DG1 .;,C .K #CJ;DG,A
.K #AE
.#EC4 .;,B .K #BJ;DG1 .;B .K #AJ1 .;C
.K #AA
.#ED4 .;,C .K #AJC;DG1 .;,B .K #BH;DG1
.;B .K #BF
.#EE4 .;,C .K #ABB;DG1 .A .K #AB1 .;C
.K #AH
,SOLVE ! EQU,N 9 ! 9T]VAL #J "K.K .;X
"K #B 7.P#..ICA7
.#EF4
.#EG4 --#E @+ #H S9 .;X .K --#A
.#EH4 #D COS .;X .K #B COS .;X -- #A
.#EI4 #E TAN #B .;X -- #AE .K #J
.#FJ4 #D S9 #B .;X -- #C .K #J
.#FA4 #B COS #B .;X -- S9 .;X -- #A .K
#J
..,,EXTRA ,,PRACTICE = .,LESSON #AD.F1
P4 #AJBC
..,,ONL9E ,,QUIZ AT _+CLASSZONE.COM_:
------------------------------------#IEE
#AD.G ,APPLY ,D\#-,ANGLE &
,HALF-,ANGLE ,=MULAS
.,2F ,Y EVALUAT$ EXPRES.NS US+ SUM &
DI6];E =MULAS4
.,N[ ,Y W USE D\#-ANGLE & HALF-ANGLE
=MULAS4
.,:Y ,S Y C F9D ! 4T.E AN OBJECT
TRAVELS1 Z 9 ,EXAMPLE #D4
,KEY ,VOCABUL>Y
99 S9E1 .P4 #HEB
99 COS9E1 .P4 #HEB
99 .TANG5T @1 P4 #HEB
,SIDEB>3
,/&>DS
..,MA!MATICAL ,ANALYSIS3 #AB.J ,/UD5TS
DEMON/RATE AN "U/&+ ( HALF-ANGLE & D\#
ANGLE =MULAS = S9S & COS9ES & C USE ^?
=MULAS .6PROVE &_/OR ..SIMPLIFY O!R
TRIGONOMETRIC .ID5TITIES
,9 ? LESSON1 Y W USE =MULAS = D\#
ANGLES 7ANGLES ( M1SURE .#B;A7 & HALF
ANGLES 7ANGLES ( M1SURE @7@4
KEY ,3CEPT .,= .,YR .,NOTEBOOK
,D\#-,ANGLE & ,HALF-,ANGLE ,=MULAS
,D\#-,ANGLE ,=MULAS
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
S9 .#B;A .K .#B S9 .A COS .A @3 COS
.#B;A .K #A--#B S9 #B .A @3
--@3 COS .#B;A .K .#B COS #B .A -- #A
@3 --
--@3 COS .#B;A .K COS #B A--S9 #B A @3
--
,HALF-,ANGLE ,=MULAS
,! SIGNS ( DEP5D ON ! QUADRANT 9 :
,,EXAMPLE #A ,EVALUATE TRIGONOMETRIC
EXPRES.NS
,,*OOSE ,,SIGNS
,2C #AFE;DG IS 9 @3 ,QUADRANT ,,II &!
VALUE ( COS9E IS NEGATIVE 9 ,QUADRANT
,,II1 ! FOLL[+ =MULA IS US$
,F9D ! EXACT VALUE ( 7A7 COS #AFE;DG &
7;B7 @4
.A4
.B4
------------------------------------#IEF
,,MULTIPLY ,,AN @3 ,,9EQUAL;Y
,9 "P 7;B71 Y C MULTIPLY "? ! 9EQUAL;Y
06GET ,S1 ,S1 IS 9 ,QUADRANT ,,II4
,,EXAMPLE #B ,EVALUATE TRIGONOMETRIC
EXPRES.NS
,GIV5 COS @1 F9D 7A7 S9 .#B;A & 7;B7
@4
,SOLU;N
.A4 ,US+ A ,PY?AGOR1N ID5T;Y GIVES S9
.B4 ,2C IS 9 ,QUADRANT ,,II1 IS
POSITIVE4
,,EXAMPLE #C ,/&>DIZ$ ,TE/ ,PRACTICE
,: EXPRES.N IS EQUIVAL5T TO
.,A S9
.;,B COT
.;,C CSC
.;,D COS
,SOLU;N
,! CORRECT ANSW] IS ,B4 ..,A ;,B ;,C
.;,D
,GUID$ ,PRACTICE = ,EXAMPLES #A1B1 &
#C
,F9D ! EXACT VALUE (! EXPRES.N4
.#A4
.#B4
.#C4 COS #AE;DG
.#D4 ,GIV5 S9 ) @4
.#E4 ,GIV5 COS ) @4
,SIMPLIFY ! EXPRES.N4
.#F4
.#G4
.#H4
------------------------------------#IEG
..,,PA? ,,( ,A .,,PROJECTILE ,! PA?
TRAVEL$ 0AN OBJECT T IS PROJECT$ AT AN
9ITIAL HEI<T ( .;H #J FEET1 AN 9ITIAL
SPE$ ( .;V FEET P] SECOND1 & AN 9ITIAL
ANGLE .#J IS GIV5 BY
": .;X IS ! HORIZONTAL 4T.E 7IN FEET7
& .;Y IS ! V]TICAL 4T.E 7IN FEET74 7,?
MODEL NEGLECTS AIR RESI/.E47
,,EXAMPLE #D ,DERIVE A TRIGONOMETRIC
MODEL
.,,SO3] ,WRITE AN EQU,N =! HORIZONTAL
4T.E TRAVEL$ 0A SO3] BALL KICK$ F GR.D
LEVEL @7 .;H #J .K #J7 AT SPE$ .;V &
ANGLE4
,,USE ,,Z]O ,,PRODUCT @3 ,,PROP]TY
,"O SOLU;N ( ? EQU,N IS .;X .K #J1 :
CORRESPONDS 6! PO9T ": ! BALL L1VES !
GR.D4 ,? SOLU;N IS IGNOR$ 9 LAT] /EPS1
2C ! PRO#M REQUIRES F9D+ ": ! BALL .L&S4
,SOLU;N
.,GUID$ .,PRACTICE = ,EXAMPLE #D
.#I4 .,,:AT .,,IF8 ,SUPPOSE Y KICK A
SO3] BALL F GR.D LEVEL ) AN 9ITIAL SPE$
( #GJ FEET P] SECOND4 ,C Y MAKE ! BALL
TRAVEL #BJJ FEET8
.#AJ4 .,,R1SON+ ,USE ! EQU,N S9 .#BJ
6EXPLA9 :Y ! PROJEC;N ANGLE T MAXIMIZES
! 4T.E A SO3] BALL TRAVELS IS .K #DE;DG4
------------------------------------#IEH
,,EXAMPLE #E ,V]IFY A TRIGONOMETRIC
ID5T;Y
..,V]IFY ! ID5T;Y .COS .#C;X .K .#D
.COS #C .;X -- .#C .COS .X4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
COS #C;X .K COS 7#B;X @+ ;X73 ,REWRITE
COS #C;X Z COS.' 7#B;X @+ ;X74.-
.K COS.' #B;X COS ;X -- S9.' #B;X S9
;X @3 ..,USE A SUM .=MULA4
.K 7#B COS.' #B ;X -- .#A7 COS ;X --
7.#B .S9 .;X .COS ;X7 S9 ;X @3 .,USE
.D\#-.ANGLE .=MULAS4
.K #B COS #C ;X--COS ;X--#B S9.' #B
.;X COS ;X @3 .,MULTIPLY4
.K #B COS #C ;X--COS ;X--#B 7.#A --
COS.' #B ;X7 COS ;X @3 ..,USE A
,PY?AGOR1N .ID5T;Y4
.K #B COS #C ;X--COS ;X--#B COS ;X @+
#B COS #C ;X @3 .,4TRIBUTIVE .PROP]TY
.K #D COS #C ;X--#C COSX @3 .,-B9E .L
.T]MS4
..,,EXAMPLE #F ,SOLVE A TRIGONOMETRIC
.EQU,N
,SOLVE S9 .#B;X @+ #B COS .;X .K #J =
#J "K.K .;X "K #B4
,SOLU;N
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
..S9 #B;X @+ .#B COS .;X .K .#J @3
.,WRITE .ORIG9AL .EQU,N4
#B S9.' ;X .-COS.' ;X @+ #B COS .;X .K
.#J @3 ..,USE A D\#-ANGLE .=MULA4
.#B COS .;X 7S9 ;X @+ ..#A7 .K .#J @3
.,FACTOR4
,SET EA* FACTOR EQUAL 6#J & SOLVE = X4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#B COS .;X .K #J @3 S9 .;X @+ #A .K #J
COS .;X .K #J @3 S9 .;X .K --#A
@3
.,,*ECK ,GRAPH ! FUNC;N .;Y .K S9 #B
.;X @+ #B COS .;X ON A GRAPH+
CALCULATOR4 ,!N USE ! .Z]O F1TURE 6F9D !
.;X -VALUES ON ! 9T]VAL #J "K ;X "K
#B;TT = : .;Y .K #J4 ,! TWO .;X -VALUES
>E3
&
,,SOLVE ,,EQU,NS
,Z SE5 9 ,EXAMPLE #G1 "S EQU,NS T @3
9VOLVE D\# OR HALF ANGLES C 2 SOLV$ )\T
RESORT+ 6D\#- OR HALF-ANGLE =MULAS4
,,EXAMPLE ,F9D A G5]AL SOLU;N
,F9D ! G5]AL SOLU;N ( @4
------------------------------------#IEI
.,GUID$ .,PRACTICE = ,EXAMPLES #E1F1 &
#G
,V]IFY ! ID5T;Y4
.#AA4 S9 #C .;X .K #C S9 .;X -- #D S9
#C .;X
.#AB4 #A @+ COS ;L#J .;X .K #B COS #B
.#E;X
,SOLVE ! EQU,N4
.#AC4 TAN .#B;X @+ TAN .;X .K #J = #J
"K.K .;X "K .#B
.#AD4
#AD.G ,,EX]CISES
,HOME"W KEY
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#BE = ,EXS4 #G1AC1 & #EC
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE ,EXS4
.#B1.AA1.BG1.ED @1 & .#EE
,SKILL ,PRACTICE
.#A4 .,,VOCABUL>Y ,COPY & -PLETE3 S9
.#B;A .K #B S9 "K#B COS A IS CALL$ ! @8
=MULA = S9E4
.#B4 .,,WRIT+ .,EXPLA9 H[ 6DET]M9E !
SIGN (! ANSW] :5 EVALUAT+ A HALF-ANGLE
=MULA = S9E OR COS9E4
,,EXAMPLE#A
ON P4 #IEE @3 = ,EXS4 #C-AA
.,,EVALUAT+ .,,EXPRES.NS ,F9D ! EXACT
VALUE (! EXPRES.N4
.#C4 S9 #AJE;DG
.#D4 TAN #AAB.E;DG
.#E4 TAN 7--#AFE;DG7
.#F4 COS 7--#GE;DG7
.#G4
.#H4
.#I4
.#AJ4
#AA4 .,,MULTIPLE .,,*OICE ,:AT IS !
EXACT VALUE ( TAN #AE;DG8
,A
;,B
;,C
;,D
,,EXAMPLE #B
ON P4 #IEF = ,EXS4 #AB-BJ
.,,HALF-.,,ANGLE .,,=MULAS ,F9D !
EXACT VALUES ( @1 & @4
.#AB4
.#AC4
.#AD4
.#AE4
.#AF4 .,,]ROR .,,ANALYSIS .,DESCRIBE &
CORRECT ! ]ROR 9 F9D+ ! EXACT VALUE (
GIV5 T @4
.,,D\#-.,,ANGLE .,,=MULAS ,F9D ! EXACT
VALUES ( S9 #B;A1 COS #B;A1 & TAN #B;A4
.#AG4
.#AH4
.#AI4
.#BJ4
------------------------------------#IFJ
.,,EXAMPLE .#C ON P4 #IEF = ,EXS4
#BA-BI
,,SIMPLIFY+ ,,EXPRES.NS ,REWRITE !
EXPRES.N )\T D\# ANGLES OR HALF ANGLES1
GIV5 T @4 ,!N SIMPLIFY ! EXPRES.N4
.#BA4
.#BB4
.#BC4 7#A--TAN @7 TAN #B
.#BD4
.#BE4
.#BF4
#BG4 .,,MULTIPLE .,,*OICE ,: EXPRES.N
IS EQUIVAL5T 6COT @+ TAN .#FA
,A CSC #B
;,B #B CSC #B
;,C SEC #B
;,D #B SEC #B
,,]ROR ,,ANALYSIS .,DESCRIBE & CORRECT
! ]ROR 9 SIMPLIFY+ ! EXPRES.N4
.#BH4
.#BI4
,,EXAMPLE #E
ON .P4 #IEH = ,EXS4 #CJ-CE
,,V]IFY+ ,,ID5TITIES ,V]IFY ! ID5T;Y4
.#CJ4 #B COS #B .#F .K #A @+ COS #BJ
.#CA4 S9 #C .K S9 7#D COS #B #J--#A7
.#CB4
.#CC4
.#CD4
.#CE4 COS #DJ .K COS #D #J--#F S9 #B
#J COS #B #J @+ S9 #D #J
.,,EXAMPLE .#F ON P4 #IEH = ,EXS4
#CF-DA
,,SOLV+ ,,EQU,NS ,SOLVE ! EQU,N = #J
"K.K ..;X "K .#B @4
.#CF4
.#CG4
.#CH4 TAN .;X -- TAN .#B;X .K .#J
.#CI4
.#DJ4 COS .#B;X .K --.#B COS #B .;X
.#DA4 .#B S9 .#B;X S9 .;X .K .#C COS
.;X
,,EXAMPLE #G
ON .P4 #IEH = ,EXS4 #DB-DG
,,F9D+ ,,G5]AL ,,SOLU;NS ,F9D ! G5]AL
SOLU;N (! EQU,N4
.#DB4
.#DC4
.#DD4 S9 .#B;X .K S9 .;X
.#DE4 COS .#B;X @+ COS .;X .K .#J
.#DF4
.#DG4
.#DH4 .,,R1SON+ ,%[ T ! ?REE D\#-ANGLE
=MULAS = COS9E >E EQUIVAL5T4
.#DI4 .,,*ALL5GE ,USE ! DIAGRAM %[N AT
! "R 6DERIVE ! =MULAS = @1 & :5 IS AN
ACUTE ANGLE4
.K .,,"W$-.,,\ .,,SOLU;NS
ON P4 ,,WS#A
.K ..,,/&>DIZ$ ,,TE/ .,,PRACTICE
------------------------------------#IFA
,,PRO#M ,,SOLV+
,,EXAMPLE #D
ON P4 #IEG = ,EXS4 #EJ-EA
.#EJ4 .,,GOLF ,USE ! EQU,N S9 #B F
,EXAMPLE #D ON PAGE #IEG 6F9D !
HORIZONTAL 4T.E A GOLF BALL W TRAVEL IF
X IS HIT AT AN 9ITIAL SPE$ ( #EJ FEET P]
SECOND & AT AN 9ITIAL ANGLE ( #DJ;DG4
@A .,HOME,TUTOR = PRO#M SOLV+ HELP AT
_+CLASSZONE.COM_:
.#EA4 .,,SO3] ,SUPPOSE Y >E ATTEMPT+
6KICK A SO3] BALL F GR.D LEVEL4 ,"? :AT
RANGE ( ANGLES C Y KICK ! SO3] BALL ) AN
9ITIAL SPE$ ( #HJ FEET P] SECOND 6MAKE X
TRAVEL AT L1/ #AEJ FEET8
.,ANIMAT$ .,ALGEBRA AT
_+CLASSZONE.COM_:
#EB4 .,,MULTI-.,,/EP .,,PRO#M ,AT
LATITUDE .;,L @1 ! A3EL],N DUE 6GRAV;Y
.;G 7IN C5TIMET]S P] SECOND SQU>$7 AT
SEA LEVEL C 2 APPROXIMAT$ BY3
.;G .K #IGH @+ #E.AG S9 #B .;,L --
#J.JAD S9 .;,L COS .;,L
A4 ,SIMPLIFY ! EQU,N ABV 6%[ T .;G --
#IGH @+ #E.AG S9 #B .;,L -- #J.JJG S9
.#B,L4
B4 ,GRAPH ! FUNC;N F "P 7A74
C4 ,USE ! GRAPH 6APPROXIMATE ! A3EL],N
DUE 6GRAV;Y :5 ! LATITUDE IS #DE;DG1
#CJ;DG1 & #J;DG4
#EC .,,MA* .,,NUMB] ,AN AIRPLANE'S
,MA* NUMB] ;,M IS ! RATIO ( XS SPE$ 6!
SPE$ ( S.D4 ,:5 AN AIRPLANE TRAVELS FA/]
?AN ! SPE$ ( S.D1 ! S.D WAVES =M A C"O
2H ! AIRPLANE4 ,! ,MA* NUMB] IS RELAT$
6! APEX ANGLE .#F (! C"O 0! EQU,N @4
,F9D ! ANGLE T CORRESPONDS 6A ,MA* NUMB]
( #B.E4
#ED4 .,,%ORT .,,RESPONSE ,A .,M]CATOR
.PROJEC;N IS A MAP PROJEC;N (! GLOBE
ONTO A PLANE T PRES]VES ANGLES4 ,ON A
GLOBE ) RADIUS ;R1 3SID] A PO9T .;,P T
HAS LATITUDE .;,L & L;GITUDE .,T4 ,!
COORD9ATES 7JC1 ;Y7 (! CORRESPOND+ PO9T
.,P0' ON ! PLANE C 2 F.D US+ ^! EQU,NS3
A4 ,USE HALF-ANGLE & SUM =MULAS 6%[ T
! EQU,N =! ;Y-COORD9ATE C 2 WRITT5 Z @4
B4 ,:AT IS A R1SONA# DOMA9 =! EQU,N 9
"P 7A78 .,EXPLA94
------------------------------------#IFB
#EE4 .,,EXT5D$ .,,RESPONSE ,AT A
BASKETBALL GAME1 A P]SON HAS A *.E 6W9
#A MILLION DOLL>S 0MAK+ A HALF C\RT %OT4
,! 4T.E F HALF C\RT 6! PO9T 2L !
#AJ-FOOT-HI< BASKETBALL RIM IS #DA.GE
FEET4
A4 ,WRITE AN EQU,N T MODELS ! PA? (!
BASKETBALL IF ! P]SON REL1SES ! BALL #F
FEET HI< ) AN 9ITIAL SPE$ ( #DJ FEET P]
SECOND4
B4 ,SIMPLIFY ! EQU,N4 ,USE A
CALCULATOR 6F9D ! ANGLES AT : ! P]SON C
MAKE ! HALF C\RT %OT4
C4 ,ASSUME ! P]SON REL1SES ! BALL AT
"O (! ANGLES F.D 9 "P 7;B74 ,:AT O!R
ASSUMP;N7;S7 M/ Y MAKE 6SAY T ! %OT IS
MADE8
#EF4 ,,*ALL5GE ,A RECTANGLE IS 9SCRIB$
9 A SEMICIRCLE ) RADIUS #A1 Z %[N4 ,:AT
VALUE ( .#F CR1TES ! RECTANGLE )! L>GE/
>EA8
,,MIX$ ,,REVIEW
,GRAPH ! FUNC;N4
.#EG4 .;Y .K #C_\ .;X -- #B_\ @+ #A
7.P#..ABC7
.#EH4 .;Y .K #B .;X @7 .;X -- #G7
7.P#..BDE7
.#EI4 .;F7.;X7 .K .;X #B @7 .;X @+ #D7
7.P#..CHG7
.#FJ4 .;Y .K LN .;X @+ #C 7.P#..DII7
.#FA4 .;Y .K TAN .;X 7.P#..IJH7
.#FB4 .;Y .K #C;TAN @7 .;X @+ @7
7.P#..IAE7
,SOLVE ! EQU,N4
.#FC4 #AA .;X #B -- #DD .;X .K #J
7.P#..BEI7
.#FD4 .;Z #C @+ #I .;Z #C -- #J
7.P#..CEC7
.#FE4
.#FF4 #D #C .;X -- #AD .K #AF #E .;X
7.P#..EAE7
.#FG4 7.P#..EHI7
.#FG4 7.P#..ICA7
.,,SKI+ ,A SKI SLOP AT A M.TA9 HAS AN
ANGLE ( ELEV,N ( #BG.D;DG4 ,! V]TICAL
HEI<T (! SLOP IS #AIJH FEET4 ,H[ L;G IS
! SKI SLOP8 7.P#..HEB7
,,QUIZ .= .,LESSONS .#AD..F-.AD..G
,F9D ! EXACT VALUE (! EXPRES.N1 TOP4
#IDI1 .#IEE7
.#A4
.#B4 S9 7--#BB.E;DG7
.#C4 TAN 7--#CDE;DG7
.#D4
,SOLVE ! EQU,N = #J "K .;X "K .#B;TT4
.#E4
.#F4 COS #B .;X .K #C S9 ..;X @+ .#B
@7 P4 #IEE @7
,F9D ! EXACT VALUES (& TAN .#B;A4 @7
P4 #IEE @7
.#G4
.#H4
.#I4 ,,FOOTBALL ,USE ! =MULA S9 #BJ
6F9D ! HORIZONTAL 4T.E .;X 7IN FEET7 T A
FOOTBALL TRAVELS IF X IS KICK$ F GR.D
LEVEL ) AN 9ITIAL SPE$ ( #BE FEET P]
SECOND AT AN ANGLE ( #CJ;DG4 @7 P4 #IEE
@7
.,,EXTRA .,,PRACTICE = ,LESSON #AD.G1
P4 #AJBC .,,ONL9E .,,QUIZ AT CLASS
_+ONE.COM_:
------------------------------------#IFC
,MIX$ ,REVIEW ( ,PRO#M ,SOLV+
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,LESSONS #AD.E-AD.G
.#A4 .,,MULTI-.,,/EP .,,PRO#M ,SUPPOSE
TWO MI4LE-,A TUN+ =KS >E /RUCK AT DI6]5T
"TS S T _! VIBR,NS >E SLI<TLY \ ( PHASE4
,! -B9$ PRESSURE *ANGE .;,P 7IN PASCALS7
CAUS$ 0! TUN+ =KS AT "T .;T 7IN SECONDS7
IS GIV5 BY3
.;,P .K #C S9 #HHJ .;T @+ #D COS #HHJ
.;T
.A4 ,GRAPH ! EQU,N ON A GRAPH+
CALCULATOR4 ,USE A VIEW+ W9D[ ( #J "K.K
.;T "K.K #J.JJE & --#F "K.K .;,P "K.K
#F4 ,:AT D Y OBS]VE AB ! GRAPH8
.B4 ,WRITE ! GIV5 MODEL 9 ! =M .;Y .K
.A COS .;B7.;X--.;H7 @4
C4 ,GRAPH ! MODEL F "P 7;B7 63FIRM T !
GRAPHS >E ! SAME4
.#B4 .,,OP5-.,,5D$ ,RECALL T A SPECIAL
ANGLE IS "O T IS A MULTIPLE ( #CJ;DG OR
#DE;DG4 ,F9D AN ANGLE T IS N A SPECIAL
ANGLE B T C 2 WRITT5 Z ! SUM OR DI6];E (
TWO SPECIAL ANGLES4 ,!N USE A SUM OR
DI6];E =MULA 6F9D ! COS9E (! ANGLE4
.#C4 .,,%ORT .,,RESPONSE ,! =MULA =!
9DEX ( REFRAC;N .;N (A TRANSP>5T MAT]IAL
IS ! RATIO (! SPE$ ( LI<T 9 A VACUUM 6!
SPE$ ( LI<T 9 ! MAT]IAL4 ,"S -MON
MAT]IALS & _! 9DICES >E AIR 7#A.JJ71
WAT] 7#A.CC71 & GLASS 7#A.E74 ,TRIANGUL>
PRISMS >E (T5 US$ 6M1SURE ! 9DEX (
REFRAC;N BAS$ ON ! =MULA %[N 2L4
.A4 ,%[ T ! 9DEX ( REFRAC;N C 2
SIMPLIFI$ Z %[N3
.B4 ,USE A GRAPH+ CALCULATOR 6F9D !
VALUE ( :5 .A .K #FJ;DG &! PRISM IS MADE
( GLASS4
.#D4 .,,GRI4$ .,,ANSW] ,9 ! FIGURE %[N
2L1 ! ACUTE ANGLE ( 9T]SEC;N1 #B -- #A
@1 ( TWO L9ES ) SLOPES .;M #A & .;M #B
IS GIV5 0? EQU,N3
,F9D ! ACUTE ANGLE ( 9T]SEC;N (! L9ES
& .;Y .K #B .;X -- #D4 ,R.D YR ANSW] 6!
NE>E/ T5? (A DEGREE4
.#E4 .,,EXT5D$ .,,RESPONSE ,! GRAPH 2L
%[S ! AV]AGE DAILY TEMP]ATURE .;,T 7IN
DEGREES ,FAHR5HEIT7 9 ,D5V]1 ,COLORADO4
,! "T .;T IS M1SUR$ 9 MON?S1 ) .;T .K #J
REPRES5T+ ,JANU>Y #A4
.A4 ,TELL :E!R ! GRAPH %D 2 MODEL$ 0A
S9E OR COS9E FUNC;N4 .,EXPLA9 YR R1SON+4
.B4 ,WRITE A TRIGONOMETRIC MODEL =!
AV]AGE DAILY TEMP]ATURE 9 ,D5V]1
,COLORADO4
.C4 ,ON : "DS (! YE> IS ! AV]AGE DAILY
TEMP]ATURE 9 ,D5V]1 ,COLORADO1
#GJ;DG;,F8
------------------------------------#IFD
#AD ,,*APT] ,,SUMM>Y
.,ANIMAT$ ,ALGEBRA
_+CLASSZONE.COM_:
,ELECTRONIC ,FUNC;N ,LIBR>Y
,,BIG ,,ID1S
,= ,YR ,NOTEBOOK
,BIG ,IDEA #A
,GRAPH+ ,TRIGONOMETRIC ,FUNC;NS
,! GRAPHS ( .;Y .K .A S9 .BX & .;Y .K
.A COS .BX >E %[N 2L = .A .1 #J & .;B .1
#J4
,6GRAPH A FUNC;N (! =M .;Y .K .A S9
..;B7;X--;H7 @+ .;K OR .;Y .K .A COS .;B
@7 ..;X--;H7 @+ .;K @1 %IFT ! GRAPH (
.;Y .K .A S9 .BX OR .;Y .K .A COS .BX @1
RESPECTIVELY1 HORIZONT,Y .;H UNITS &
V]TIC,Y .;K UNITS4 ,!N1 IF .A "K #J1
REFLECT ! GRAPH 9 ! MIDL9E .;Y .K .K4
,BIG ,IDEA #B
,SOLV+ ,TRIGONOMETRIC ,EQU,NS
,! TA# 2L %[S /RATEGIES T MAY HELP Y
SOLVE TRIGONOMETRIC EQU,NS4 ,ONLY ! F/
FEW /EPS >E %[N4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,FACTOR3 ,USE ! QUADRATIC =MULA3 ,USE
AN ID5T;Y
.;X S9 #B .;X -- .;X .K #J @3 COS #B
.;X -- #F COS .;X @+ #A .K #J @3 COS #B
.;X -- #A .K #I S9.' #B .;X
.;X @7 S9.' #B .;X - #A @7 .K #J @3 @3
COS #B .;X -- #A .K #I7 #A--COS.' #B .;X
@7
.;X 7S9.' ;X @+ #A77S9.' ;X -- #A7 .K
#J @3 @3 #AJ COS #B .;X .K #AJ
--@3 --@3 COS #B .;X .K #A
,BIG ,IDEA #C
,APPLY+ ,TRIGONOMETRIC ,=MULAS
,USE ! =MULAS 2L 6EVALUATE
TRIGONOMETRIC FUNC;NS ( C]TA9 ANGLES4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,SUM .=MULAS @3 S9.' 7A @+ ;B7 .K S9
.A COS .;B @+ COS .A S9 .;B
COS @7 .A @+ .;B @7 .K COS .A COS .;B --
S9 .A S9 .;B @3
.,DI6];E .=MULAS @3 S9.' 7A--;B7 .K S9
.A COS .;B -- COS .A S9 .;B COS
7.A--.;B7 .K COS .A COS @+ S9 .A S9 .;B
@3
.,D\#-.ANGLE .=MULAS @3 COS #B .A .K
COS #B .A -- S9 #B .A
COS #B .A .K #B COS #B A--#A
COS #B .A .K #A--#B S9 #B
.S9 .#B;A .K #B S9 A COS .A @3
.,HALF-.ANGLE .=MULAS @3 @3
------------------------------------#IFE
#AD ,*APT] ,SUMM>Y
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
99 ,MULTI-,LANGUAGE ,GLOSS>Y
99 ,VOCABUL>Y PRACTICE
,,REVIEW ,,KEY ,,VOCABUL>Y
99 AMPLITUDE1 P4 #IJH
99 P]IODIC FUNC;N1 P4 #IJH
99 CYCLE1 P4 #IJH
99 P]IOD1 P4 #IJH
99 FREQU5CY1 P4 #IAJ
99 TRIGONOMETRIC ID5T;Y1 P4 #IBD
99 S9USOID1 P4 #IDA
,,VOCABUL>Y ,,EX]CISES
.#A4 ,COPY & -PLETE3 ,FREQU5CY GIVES !
NUMB] ( @8 P] UNIT ( "T4
.#B4 .,,WRIT+ .,EXPLA9 H[ 6F9D ! P]IOD
( .;Y .K .A S9 .;B @7 .;X--.;H @7 @+ .K4
,,REVIEW ,,EXAMPLES ,,& ,,EX]CISES
,DET]M9E :E!R ! GIV5 NUMB] IS !
.AMPLITUDE ;Y .P]IOD @1 OR .FREQU5CY (!
GRAPH ( @4
.#C4 #D
.#D4 #GG
.#E4 #J.BE
,USE ! REVIEW EXAMPLES & EX]CISES 2L
6*ECK YR "U/&+ (! 3CEPTS Y H LE>N$ 9 EA*
LESSON ( ,*APT] #AD4
#DA.A ,GRAPH ,S9E1 ,COS9E1 & ,TANG5T
,FUNC;NS
PP4 #IJH-IAD
,,EXAMPLE
,GRAPH 7A7 & 7;B7
.A4 .,AMPLITUDE3
.,P]IOD3
.,9T]CEPTS3
.,MAXIMUM3
.,M9IMUM3
.B4 .,P]IOD3
,9T]CEPT3 7#J1J7
,ASYMPTOTES3 ..;X .K--.;X .K
.,HALFWAY .PO9TS3
,,EX]CISES
,,EXAMPLES #A1B1 & #D
ON PP4 #IJI-IAB = ,EXS4 .#F-.I
,GRAPH ! FUNC;N4
.#F4 .;Y .K S9 #B .;X
.#G4
.#H4 .;G @7 .;X @7 .K #E S9 .;X .;X
.#I4
------------------------------------#IFF
#AD ,*APT] ,REVIEW
#AD.B ,TRANSLATE & ,REFLECT
,TRIGONOMETRIC ,GRAPHS ,,PP4 #IAE-IBB
,,EXAMPLE
,GRAPH .;Y .K #C COS @7 .;X -- .;W
@7--#A4
,6GRAPH .;Y .K #C COS @7 .;X -- @7 --
#A1 />T )! GRAPH ( .;Y .K #C COS .X4
,!N1 TRANSLATE ! GRAPH "R UNITS & D[N #A
UNIT4
.,AMPLITUDE3 _\#C_\ .K#C
.,P]IOD3 #B
,HORIZONTAL %IFT3
.,V]TICAL .%IFT3 --#A
..,ON ;Y .K .;K @3
.,M9IMUM3 7#B1 --#D7
,MAXIMUMS3 @7 @1 #B72 7#C #B7
,,EX]CISES
,,EXAMPLES #A1B1 & #D
ON PP4 #IAE-IAG = ,EXS4 #AJ-AE
,GRAPH ! FUNC;N4
.#AJ4 .;F7.;X7 .K COS .#B;X @+ #D #AA4
.#AB4
.#AC4
.#AD4 .;G7.;X @7 .K --#A--#C COS #D
.;X
.#AE4
#AD.C ,V]IFY ,TRIGONOMETRIC ,ID5TITIES
PP #IBD-ICJ
,EXAMPLE
,V]IFY ! ID5T;Y
,,EXAMPLES #B1 #C1D1 & #E
ON PP4 #IBE-IBF = ,EXS4 #AF-BJ
,,EX]CISES
,SIMPLIFY ! EXPRES.N4
.#AF4 --COS .;X TAN @7 -.;X @7
.#AG4 SEC .;X TAN #B .;X @+ SEC .;X
.#AH4
,V]IFY ! ID5T;Y4
.#AI4
.#BJ4
------------------------------------#IFG
,SIDEB>3
@A,HOME,TUTOR
_+CLASSZONE.COM_:
#AD.D ,SOLVE ,TRIGONOMETRIC ,EQU,NS
PP4 #ICA-ICG
,,EXAMPLE
.,SOLVE .#B .COS #B ..;X .K #A 9 !
9T]VAL .#J "K .;X "K .#B @4
,9 ! 9T]VAL #J "K .;X "K #B1 ! SOLU;NS
>E
,,EXAMPLES #A & #D
ON PP4 #ICA-ICC = ,EXS4 #BA-BC
,,EX]CISES
,SOLVE ! EQU,N 9 ! 9T]VAL #J "K ..;X
"K .#B @4
.#BA4 --#D S9 #B .;X .K --#C
.#BB4 COS #B .;X .K COS .;X
.#BC4 TAN #B #D .;X .K #C
#AD.E ,WRITE ,TRIGONOMETRIC ,FUNC;NS &
,MODELS
PP4 #IDA-IDG
,,EXAMPLE
,WRITE A FUNC;N =! S9USOID4
.,,/EP .#A .,F9D ! MAXIMUM VALUE ;,M &
M9IMUM VALUE M4 ,F ! GRAPH1 ;,M .K #C &
.;M .K --#A4
.,,/EP .#B .,ID5TIFY ! V]TICAL %IFT1
.K4
.,,/EP .#C .,DECIDE :E!R ! GRAPH %D 2
MODEL$ 0A S9E OR COS9E FUNC;N4 ,2C !
GRAPH CROSSES ! MIDL9E1 .;Y .K #A1 ON !
.;Y -AXIS & !N DECR1SES 6XS M9IMUM
VALUE1 ! GRAPH IS A S9E CURVE )A
REFLEC;N B NO ,HORIZONTAL %IFT4 ,S1 .A
"K #J & .;H .K .#J4
.,,/EP .#D .,F9D ! AMPLITUDE & P]IOD4
,! P]IOD IS @4 ,S1 .;B .K #C4
,! AMPLITUDE IS ,S1 ..A .K--.#B @4
,A FUNC;N =! S9USOID IS ..;Y .K--.#B
S9 .#C;X @+ #A4
,,EXAMPLE #A
ON P4 #IDA = ,EXS4 #BD-BE
,,EX]CISES
.#BD4
.#BE4
------------------------------------#IFH
#AD ,,*APT] ,,REVIEW
#AD.F ,APPLY ,SUM & ,DI6];E ,=MULAS
PP4 #IDI-IED
,,EXAMPLE
,F9D ! EXACT VALUE (! EXPRES.N4
.A4
.B4
,,EX]CISES
,,EXAMPLES #A & #B
ON PP4 #IDI-IEJ = ,EXS4 #BF-CJ
,F9D ! EXACT VALUE (! EXPRES.N4
.#BF4 COS #AIE;DG
.#BG4 TAN #GE;DG
.#BH4
.#BI4
.#CJ4 ,F9D COS @7 .A- .;B @7@1 GIV5 T
)
#AD.G ,APPLY ,D\#-,ANGLE &
,HALF-,ANGLE ,=MULAS .,,PP @4 #IEE-IFB
,EXAMPLE
,F9D ! EXACT VALUE (! EXPRES.N4
.A4
.B4
,,EX]CISES
,F9D ! EXACT VALUE (! EXPRES.N4
,,EXAMPLES #A & #B
ON PP4 #IEE-IEF = ,EXS4 #CA-CE
.#CA4 S9 #GE;DG
.#CB4 TAN 7--#AE;DG7
.#CC4
.#CD4
.#CE4 ,GIV5 ) @1 F9D S9 .#B;A &
------------------------------------#IFI
#AD ,*APT] ,TE/
,GRAPH ! FUNC;N4
.#A4 .;F7.;X7 .K .#D COS .#B;X
.#B4
.#C4
.#D4 .;Y .K S9 @7 .;X -- @7--#B
.#E4
.#F4
,SIMPLIFY ! EXPRES.N4
.#G4
.#H4 COS#B;X @+ S9#B;X--COS#B;X
.#I4
,WRITE A FUNC;N =! S9USOID4
.#AJ4
.#AA4
.#AB4 ,V]IFY ! ID5T;Y COS .#C;X .K #D
COS #C .;X -- #C COS X4 ..,SOLVE ! EQU,N
9 ! 9T]VAL #J "K ;X "K .#B4
,SOLVE ! EQU,N 9 ! 9T]VAL #J "K.K .;X
"K #B
.#AC4 #I S9 #B .;X TAN .;X .K #AF TAN
.#AD4
.#AE4
,F9D ! G5]AL SOLU;N (! EQU,N4
.#AF4 #F TAN #B .;X -- #B .K #J
.#AG4 COS .;X .K S9 #B .;X S9 .;X
.#AH4
,F9D ! EXACT VALUE (! EXPRES.N4
.#AI4 S9 #BEE;DG .#BJ4
.#BA4
.#BB4
.#BC4 .,,BOAT+ ,! PA4LE :EEL (A %IP IS
#AA FEET 9 DIAMET]1 REVOLVES #AE "TS P]
M9UTE :5 MOV+ AT TOP SPE$1 & IS #B FEET
2L ! WAT]'S SURFACE AT XS L[E/ PO9T4
,US+ ? SPE$ & />T+ F A PO9T AT ! V TOP
(! :EEL1 WRITE A MODEL =! HEI<T .;H 7IN
FEET7 (! 5D (! PA4LE RELATIVE 6! WAT]'S
SURFACE Z A FUNC;N ( "T .;T 7IN M9UTES74
.#BD4 .,,PRECIPIT,N ,! TA# 2L %[S !
MON?LY PRECIPIT,N .;,P 7IN 9*ES7 9
,BISM>CK1 ,NOR? ,DAKOTA4 ,! "T .;T IS
M1SUR$ 9 MON?S1 ) .;T .K #A REPRES5T+
,JANU>Y4 ,USE A GRAPH+ CALCULATOR 6WRITE
A S9USOIDAL MODEL T GIVES .;,P Z A
FUNC;N ( .T4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;T @3 #A3 #B3 #C3 #D3 #E3 #F3 #G3 #H3
#I3 #AJ3 #AA3 #AB
.;P @3 #J.E3 #J.E;I3 #J.I3 #A.E3 #B.B3
#B.F3 #B.F3 .#B..B @3 .#A..F @3 .#A..C
@3 .#J..G @3 .#J..D
------------------------------------#IGJ
#AD ,/&>DIZ$ ,TE/ ,PREP>,N
,SCOR+ ,RUBRIC
,FULL ,CR$IT
99 SOLU;N IS -PLETE & CORRECT
,"PIAL ,CR$IT
99 SOLU;N IS -PLETE B HAS ]RORS1 .OR
99 SOLU;N IS )\T ]ROR B 9COMPLETE
,NO ,CR$IT
99 NO SOLU;N IS GIV51 .OR
99 SOLU;N MAKES NO S5SE
,,EXT5D$ ,,RESPONSE ,,"QS
,,PRO#M
,! HORIZONTAL 4T.E .;X 7IN FEET7
TRAVEL$ 0A FOOTBALL KICK$ F GR.D LEVEL
AT SPE$ .;V & ANGLE .#F C 2 MODEL$ 0S9
#BJ4
.A4 ,WRITE AN EXPRES.N = HALF (!
HORIZONTAL 4T.E4 ,H[ IS ? EXPRES.N
RELAT$ 6! FOOTBALL'S MAXIMUM HEI<T8
.B4 ,WRITE A SIMPLIFI$ EXPRES.N =!
FOOTBALL'S MAXIMUM HEI<T4
.C4 ,:AT IS ! MAXIMUM HEI<T (A
FOOTBALL KICK$ F GR.D LEVEL )A SPE$ (
#HJ FEET P] SECOND & AN ANGLE ( #CE;DG8
,2L >E SAMPLE SOLU;NS 6! PRO#M4 ,R1D
EA* SOLU;N &! -;TS 9 BLUE 6SEE :Y !
SAMPLE REPRES5TS FULL CR$IT1 "PIAL
CR$IT1 OR NO CR$IT4
,SAMPLE #A3 ,FULL CR$IT SOLU;N
,! EXPRES.N IS CORRECT1 & XS
SIGNIFIC.E IS FULLY EXPLA9$4
.A4
,2C ! BALL TRAVELS 9 A P>ABOLIC PA?1 !
MAXIMUM HEI<T O3URS AT HALF ! HORIZONTAL
4T.E4
.B4 ,SUB/ITUTE ! EXPRES.N F "P 7A7 =
.;X 9 ! EQU,N =! PA? (A PROJECTILE4
,NOTE T ! 9ITIAL HEI<T .;H #J IS #J4
,! CORRECT =MULA IS US$ =! PA? (A
PROJECTILE4
.C4 ,6F9D ! MAXIMUM HEI<T (! BALL1
SUB/ITUTE #HJ = .;V & #CE;DG =4
,! ANSW] IS CORRECT4
------------------------------------#IGA
,SAMPLE #B3 ,"PIAL CR$IT SOLU;N
,! ANSW] IS CORRECT1 B "W IS N %[N &
NO EXPLAN,N IS GIV54
.A4
.B4
,! EXPRES.N IS N FULLY SIMPLIFI$4
.C4 ,! MAXIMUM HEI<T (! FOOTBALL IS3
,! ANSW] IS CORRECT4
,SAMPLE #C3 ,NO CR$IT SOLU;N
,! EXPRES.NS 9 "PS 7A7 & 7;B7 >E
9CORRECT1 & NO "W IS %[N4
.A4
.B4 ,! MAXIMUM HEI<T IS GIV5 BY
,! VALUES >E SUB/ITUT$ 9CORRECTLY4 ,!
ANSW] IS WR;G4
.C4
,! MAXIMUM HEI<T IS AB #AI FEET4
,SIDEB>3
,/&>DS
.,MA!MATICAL .,ANALYSIS3 #AI.J ,/UD5TS
>E ADEPT AT US+ ANALYSIS 9 A V>IETY (
APPLIC,NS & ^W PRO#MS4
,,PRACTICE ,APPLY ! ,SCOR+ ,RUBRIC
,SCORE ! FOLL[+ SOLU;N 6! PRO#M ON !
PREVI\S PAGE ..Z FULL CR$IT1 "PIAL
.CR$IT @1 OR .NO .CR$IT4 .,EXPLA9 YR
R1SON+4 ,IF Y *OOSE ."PIAL .CR$IT OR .NO
.CR$IT @1 EXPLA9 H[ Y WD *ANGE ! SOLU;N
S T X E>NS A SCORE ( FULL CR$IT4
.A4 ,HALF (! TOTAL HORIZONTAL 4T.E IS
S9 #B4 ,? IS ! HORIZONTAL 4T.E :5 ! BALL
IS AT XS MAXIMUM HEI<T4
.B4 ,A SIMPLIFI$ EXPRES.N =! MAXIMUM
HEI<T (! BALL IS @4
.C4 ,SUB/ITUTE #HJ = ;V & #CE;DG = 9 !
EXPRES.N F "P 7;B7 6F9D ! MAXIMUM HEI<T
(! FOOTBALL4
------------------------------------#IGB
#AD ,/&>DIZ$ ,TE/ ,PRACTICE
,,EXT5D$ ,,RESPONSE
#A4 ,S.D TRAVELS 9 WAVES T C 2
REPRES5T$ US+ S9E FUNC;NS4 ,:5 TWO NOTES
>E PLAY$ AT ! SAME "T ON A MUSICAL
9/RU;T1 ! RESULT+ S.D WAVE C 2 MODEL$ 0!
SUM ( TWO S.D WAVES4
A4 ,PLAY+ ;,C & ;,G TGR CR1TES H>MONY
& PRODUCES A PL1SANT S.D4 ,USE A GRAPH+
CALCULATOR 6GRAPH ! S.D WAVE T RESULTS F
PLAY+ ;,C & ;,G AT ! SAME "T4
B4 ,PLAY+ ;,C & ;,B TGR CR1TES 4SON.E
& PRODUCES AN UNPL1SANT S.D4 ,USE A
GRAPH+ CALCULATOR 6GRAPH ! S.D WAVE T
RESULTS F PLAY+ ;,B & ;,C AT ! SAME "T4
C4 ,MAKE A 3JECTURE AB ! REL,N%IP 2T
H[ ! NOTES S.D :5 PLAY$ TGR &! RESULT+
S.D WAVE4 .,EXPLA9 YR R1SON+4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,NOTE3 ,S.D WAVE
.;C @3 .;Y .K S9 #EBC.BF .;T
.;,G @3 .;Y .K S9 #GHD;T
.;,B @3 ;Y .K S9 #IHG.GF;T
#B4 ,! BLADES (A FAN ROTATE
C.T]CLOCKWISE AT A SPE$ ( #HJJ ROT,NS P]
M9UTE4 ,! L5G? ( EA* BLADE IS #I 9*ES4
,! MAXIMUM HEI<T (! TIP (A FAN BLADE ABV
! GR.D IS #DH 9*ES4
A4 ,:AT IS ! M9IMUM HEI<T (! TIP (A
FAN BLADE ABV ! GR.D8
B4 ,WRITE A FUNC;N T MODELS ! HEI<T (!
TIP (! HI<E/ FAN BLADE Z A FUNC;N ( "T4
,ASSUME T ! BLADE />TS 9 ! POSI;N %[N 9
! DIAGRAM4
C4 ,D YR ANSW]S 6"PS 7A7 & 7;B7 *ANGE
IF ! FAN ROTATES CLOCKWISE8 .,EXPLA9 :Y
OR :Y N4
#C4 ,! *>T %[S ! AV]AGE MON?LY
TEMP]ATURE 7IN DEGREES ,FAHR5HEIT7 &A
H\SEHOLD'S GAS USAGE 7IN CUBIC FEET7 =
#AB MON?S4
A4 ,USE ! *>T 6MAKE A TA# ( VALUES
GIV+ ! MON? .;T 7) ,JANU>Y CORRESPOND+
6.;T .K #J71 ! AV]AGE MON?LY TEMP]ATURE
.;Y #A &! GAS USAGE .;Y #B 7IN ?\S&S (
CUBIC FEET74
B4 ,USE ! TA# F "P 7A7 &A GRAPH+
CALCULATOR 6F9D TRIGONOMETRIC MODELS =!
AV]AGE MON?LY TEMP]ATURE .;Y #A Z A
FUNC;N ( "T &! GAS USAGE .;Y #B Z A
FUNC;N ( "T4
C4 ,GRAPH ! TWO REGRES.N EQU,NS ON YR
GRAPH+ CALCULATOR4 .,DESCRIBE ! REL,N%IP
2T ! TEMP]ATURE & GAS USAGE TR5D4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,JANU>Y3 ,FEBRU>Y3 ,M>*3 ,APRIL
#CB;DG;,F3 #BA;DG;,F3 #AE;DG;,F3
#BB;DG;,F
#BJ1JJJ FT #C @3 #BG1JJJ FT #C @3
#BC1JJJ FT #C @3 #BB1JJJ FT #C
.,MAY @3 .,JUNE @3 .,JULY @3 .,AUGU/
#CE;DG;,F3 #DI;DG;,F3 #FB;DG;,F3
#GH;DG;,F
#BA1JJJ FT #C @3 #AD1JJJ FT.' #C @3
#H1JJJ FT.' #C @3 #I1JJJ FT #C
.,SEPTEMB] @3 .,OCTOB] @3 .,NOVEMB] @3
.,DECEMB]
#GA;DG;,F3 #FC;DG;,F3 #EE;DG;,F3
#DJ;DG;,F
#AC1JJJ FT #C @3 #AE1JJJ FT #C @3
#AI1JJJ FT #C @3 #BC1JJJ FT.' #C
------------------------------------#IGC
.,,/ATE .,,TE/ .,,PRACTICE
_+CLASSZONE.COM_:
,,MULTIPLE ,,*OICE
#D4 ,! GRAPH ( : FUNC;N IS %[N8
,A .;Y .K --#C COS #B .;X
;,B .;Y .K --#B COS #C .;X
;,C
;,D
#E4 ,: EXPRES.N IS .N EQUIVAL5T 6#A8
,A TAN .;X SEC .;X COS .;X
;,B S9 #B .;X @+ COS #B .;X
;,C
;,D
#F4 ,:AT IS ! G5]AL SOLU;N (! EQU,N
COS #C .;X .K #BE COS .;X @8
,A
;,B
;,C
;,D
,,GRI4$ ,,ANSW]
.#G4 ,:AT IS ! .;X -9T]CEPT (! GRAPH (
ON ! 9T]VAL #J "K ;X "K #C8
.#H4 ,F9D ! VALUE ( TAN @7 .A @+ .;B
@7 GIV5 T ! FOLL[+ >E TRUE3
)
COS )
.#I4 ,F9D ! .;Y -COORD9ATE (! PO9T (
9T]SEC;N (! GRAPHS ( .;Y .K #B @+ S9 .;X
& .;Y .K #C--S9 ;X 9 ! 9T]VAL @4
.#AJ4 ,F9D ! AMPLITUDE (! S9USOID %[N
2L4
,,%ORT ,,RESPONSE
.#AA4 ,USE ! FACT T ! FREQU5CY (A
P]IODIC FUNC;N'S GRAPH IS ! RECIPROCAL
(! P]IOD 6%[ T AN OSCILLAT+ MO;N )
MAXIMUM 4PLACE;T .A & FREQU5CY .;F C 2
MODEL$ 0.;Y .K .A S9 #B .FT OR .;Y .K .A
COS #B .FT @4
.#AB4 ,A BASKETBALL IS DROPP$ F A
HEI<T ( #AE FEET4 ,C ! HEI<T (!
BASKETBALL OV] "T 2 MODEL$ 0A
TRIGONOMETRIC FUNC;N8 ,IF S1 WRITE !
FUNC;N4 ,IF N1 EXPLA9 :Y N4
.#AC4 ,3SID] ! FOLL[+ FUNC;N3
.;F7.;X7 .K S9 ;X COS ;X
,)\T GRAPH+ ! FUNC;N1 :AT WD Y EXPECT
! GRAPH 6LOOK L8 .,EXPLA9 YR R1SON+4
,COPY & -PLETE ! TA# 2L & DET]M9E :E!R
YR PREDIC;N 0 CORRECT4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 --@3 @3 @3 @3 #J3 @3 @3 @3 --
.;F7.;X7 @3 @8@3 @8@3 @8@3 @8@3 @8@3
@8@3 @8@3 @8@3 @8
------------------------------------#IGD
,3T5TS ( ,/UD5T ,RES\RCES
,SKILLS ,REVIEW ,H&BOOK
PAGES #IGE-AJJI
,OP],NS ) ,POSITIVE & ,NEGATIVE
,NUMB]S
#IGE
,FRAC;NS1 ,DECIMALS1 & ,P]C5TS
#IGF
,CALCULAT+ ) ,P]C5TS
#IGG
,FACTORS & ,MULTIPLES
#IGH
,RATIOS & ,PROPOR;NS
#IHJ
,3V]T+ ,UNITS ( ,M1SURE;TS
#IHG
,SCI5TIFIC ,NOT,N
#IHB
,SIGNIFICANT ,DIGITS
#IHC
,WRIT+ ,ALGEBRAIC ,EXPRES.NS
#IHD
,BINOMIAL ,PRODUCTS
#IHE
,,LCD,'S ( ,R,NAL ,EXPRES.NS
#IHF
,! ,COORD9ATE ,PLANE
#IHG
,TRANS=M,NS
#IHH
,L9E ,SYMMETRY
#IIJ
,P]IMET] & ,>EA
#IIG
,CIRCUMF];E & ,>EA (A ,CIRCLE
#IIB
,SURFACE ,>EA & ,VOLUME
#IIC
,ANGLE ,REL,N%IPS
#IID
,TRIANGLE ,REL,N%IPS
#IIE
,3GRU5T & ,SIMIL> ,FIGURES
#IIF
,M ,PRO#M ,SOLV+ ,/RATEGIES
#IIH
,LOGICAL ,>GU;T
#AJJJ
,3DI;NAL ,/ATE;TS & ,C.T]EXAMPLES
#AJJB
,V5N ,DIAGRAMS
#AJJD
,M1N1 ,M$IAN1 ,MODE1 & ,RANGE
#AJJE
,GRAPH+ ,/ATI/ICAL ,DATA
#AJJF
,ORGANIZ+ ,/ATI/ICAL ,DATA
#AJJH
,EXTRA ,PRACTICE = ,*APT]S #A-AD
PAGES #AJAJ-AJBC
,TA#S
PAGES #AJBD-AJCD
,SYMBOLS
#AJBD
,M1SURES
#AJBE
,=MULAS
#AJBF
,PROP]TIES
#AJCC
,5GLI%-,SPANI% ,GLOSS>Y
PAGES #AJCE-AJHD
,9DEX
PAGES #AJHE-AAJD
,CR$ITS
PAGES #AAJE-AAJF
,"W$-,\ ,SOLU;NS
PAGE ,,WS#A
,SELECT$ ,ANSW]S
PAGE ,,SA#A
------------------------------------#IGE
,SKILLS ,REVIEW ,H&BOOK
,OP],NS ) ,POSITIVE & ,NEGATIVE
,NUMB]S
,EXAMPLE ,ADD OR SUBTRACT4
A#.A @+ 7--#E7
99 #A @+ 7--#E7 .K --#D
B4--#B --7--#E7 .K--#B@+ #E
,! OPPOSITE ( --#E IS #E4
99 --#B--7--#E7 .K #C
,6MULTIPLY OR DIVIDE POSITIVE &
NEGATIVE NUMB]S1 USE ! FOLL[+ RULES4
99 ,! PRODUCT OR QUOTI5T ( TWO NUMB]S
)! .SAME SIGN IS .POSITIVE4
99 ,! PRODUCT OR QUOTI5T ( TWO NUMB]S
) .DI6]5T SIGNS IS .NEGATIVE4
,EXAMPLE
,MULTIPLY OR DIVIDE4
.A4 #C@*#G .K #BA
.B4 --#C7--#G7 .K #BA
.C4 #AH @/ #B .K #I
.D4 --#AH @/ 7--#B7 .K #I
.E4 --#C7#G7 .K --#BA
.F4 #C 7--#G7 .K --#BA
.G4 --#AH @/ #B .K --#I
.H4 #AH@/ 7--#B7 .K --#I
,PRACTICE
,P]=M ! 9DICAT$ OP],N4
.#A4 #B @+ 7--#H7
.#B4 #E--#AB
.#C4 -- #F7#AJ7
.#D4 --#CJ @/ 7--#B7
.#E4 --#D @+ #F
.#F4 #G7--#E7
.#G4 #AH--#AJ
.#H4 --#G @+ 7--#AB7
.#I4 #AA7#D7
.#AJ4 #HA@/ 7--#I7
.#AA4 --#AB @/ #C
.#AB4 --#I7--#H7
.#AC4 --#A @+ #AC
.#AD4 #DE@/ 7--#I7
.#AE4 --#F7#AB7
.#AF4 #AD--7--#I7
.#AG4 --#CB @/ #AF
.#AH4 --#BC @+ 7--#E7
.#AI4 --#H--7--#E7
.#BJ4 #AG--7--#AH7
.#BA4 --#I7--;L7
.#BB4 --#C--7--#AA7
.#BC4 --#AH @/ 7--#C7
.#BD4 #AD @+ 7--#G7
.#BE4 #E 7--#C7
.#BF4 #BA @+ 7--#H7
.#BG4 --#B--#AJ
.#BH4 --#I @+ #BF
.#BI4 --#BJ @/ 7--#D7
.#CJ4 #BB@/ 7--#B7
.#CA4 --#G7--#F7
.#CB4 #A--#BD
.#CC4 --#AE--#B
.#CD4 #J @+ 7--#D7
.#CE4 #AF@/ #H
------------------------------------#IGF
,FRAC;NS1 ,DECIMALS1 & ,P]C5TS
,,SKILLS ,,REVIEW ,,H&BOOK
.,A .P]C5T IS A RATIO )A DENOM9ATOR (
#AJJ4 ,! ^W .P]C5T M1NS 8P] HUNDR$10 OR
8\ ( "O HUNDR$40 ,! SYMBOL = P]C5T IS
@3P.
,9 ! MODEL AT ! "R1 #GA (! #AJJ SQU>ES
>E %AD$4 ,Y C WRITE ! %AD$ "P (! MODEL Z
A FRAC;N1 A DECIMAL1 OR A P]C5T4
.,FRAC;N3 SEV5TY-"O DIVID$ 0"O HUNDR$1
OR
.,DECIMAL3 SEV5TY-"O HUNDR$?S1 OR
#J.GA
.,P]C5T3 SEV5TY-"O P]C5T1 OR #GA@3P
,EXAMPLE ,WRITE Z A FRAC;N4
.A4
.B4
.C4
,EXAMPLE ,WRITE Z A DECIMAL4
.A4
.B4
.C4
,EXAMPLE ,WRITE Z A P]C5T4
.A4
.B4
.C4
,PRACTICE
,WRITE Z A FRAC;N4
#A4 #J.FE
#B4 #J.JH
#C4 #A.E
#D4 #J.AC
#E4 #J.G
#F4 #EJ@3P
#G4 #BF@3P
#H4 #C@3P
#I4 #IE@3P
#AJ4 #AAJ@3P
,WRITE Z A DECIMAL4
.#AA4
.#AB4
.#AC4
.#AD4
.#AE4
.#AF4 #AF@3P
.#AG4 #ADB@3P
.#AH4 #A@3P
.#AI4 #CJ@3P
.#BJ4 #F.E@3P
,WRITE Z A P]C5T4
.#BA4 #J.F
.#BB4 #J.BD
.#BC4 #A.C
.#BD4 #J.JG
.#BE4 #J.DE
.#BF4
.#BG4
.#BH4
.#BI4
.#CJ4
------------------------------------#IGG
,CALCULAT+ ) ,P]C5TS
,,SKILLS ,,REVIEW ,,H&BOOK
,Y C USE EQU,NS 6CALCULATE ) P]C5TS4
,REPLACE ^WS ) SYMBOLS Z %[N 9 ! TA# AT
! "R4 ,2L >E ?REE TYPES ( "QS Y C ANSW]
) P]C5TS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,^W3 :AT3 (3 IS
.,SYMBOL @3 .;N @3 .;X @3 .K
,EXAMPLE ,ANSW] ! "Q4
.A4 ,:AT IS #AE@3P ( #BJ8
.;N .K #J.AE ;,X #BJ
.;N .K #C
.#C IS #AE@3P ( #BJ4
.B4 ,:AT P]C5T ( #H IS #F8
.;N ;X #H .K #F
;N .K #F @/ #H .K #J.GE .K #GE@3P
#GE@3P ( #H IS #F4
.C4 #HJ@3P ( :AT NUMB] IS #D8
#J.H ;,X .;N .K #D
.;N .K #D @/ #J.H .K #E
#HJ @3P ( #E IS #D
,6F9D A P]C5T ( *ANGE1 CALCULATE
,EXAMPLE ,F9D ! P]C5T ( *ANGE4
.A4 ,A CLASS 9CR1SES F #BA /UD5TS 6#BE
/UD5TS4
9CR1SE
.B4 ,A PRICE DECR1SES F 4#AB TO 4#I4
DECR1SE
,PRACTICE
,ANSW] ! "Q4
.#A4 ,:AT IS #IH@3P ( #BJJ8
.#B4 ,:AT IS #BE@3P ( #H8
.#C4 ,:AT IS #CJ@3P ( #ABH8
.#D4 ,:AT IS #E@3P ( #GJJ8
.#E4 ,:AT IS #AJJ@3P ( #AG8
.#F4 ,:AT IS #AEJ@3P ( #AD8
.#G4 ,:AT IS #J4 #B@3P ( #EJJ8
.#H4 ,:AT IS #F.E@3P ( #CJJJ8
.#I4 ,:AT P]C5T ( #AJJ IS #ED8
.#AJ4 ,:AT P]C5T ( #AH IS #I8
.#AA4 ,:AT P]C5T ( #HJ IS #H8
.#AB4 ,:AT P]C5T ( #AE IS #BJ8
.#AC4 ,:AT P]C5T ( #CJ IS #F8
.#AD4 ,:AT P]C5T ( #E IS #H8
.#AE4 ,:AT P]C5T ( #EJ IS #A8
.#AF4 #EJ@3P ( :AT NUMB] IS #F8
.#AG4 #EE@3P ( :AT NUMB] IS #DD8
.#AH4 #AJ@3P ( :AT NUMB] IS #F8
.#AI4 #GE@3P ( :AT NUMB] IS #DE8
.#BJ4 ,I@3P ( :AT NUMB] IS #B8
.#BA4 #IJ@3P ( :AT NUMB] IS #FC8
.#BB4 #AB@3P ( :AT NUMB] IS #FJ8
.#BC4 #BJJ@3P ( :AT NUMB] IS #AF8
,F9D ! P]C5T ( *ANGE4 ,R.D 6! NE>E/
P]C5T IF NEC4
.#BD4 ,A CLASS 9CR1SES F #BJ 6#BH
/UD5TS4
.#BE4 ,"T DECR1SES F #FJ 6#DE M9UTES4
.#BF4 ,A PRICE IS REDUC$ F 4#BJJ TO
4#AHJ4
.#BG4 ,VOTES 9CR1SE F #BJJ 6#CJJ4
.#BH4 ,A TE/ IS %ORT5$ F #DJ 6#CB
ITEMS4
.#BI4 ,MEMB]%IP 9CR1SES F #HBJ 6#AFJE4
.#CJ4 ,A WAGE RISES F 4#H.GE TO
4#AJ.JJ4
.#CA4 ,! TEMP]ATURE DROPS F #BD;DG;,F
6#E;DG,F4
------------------------------------#IGH
,FACTORS & ,MULTIPLES
,,SKILLS ,,REVIEW ,,H&BOOK
.,FACTORS >E NUMB]S OR EXPRES.NS T >E
MULTIPLI$ TGR4 ,A .PRIME .NUMB] IS A
:OLE NUMB] GRT] ?AN #A T HAS EXACTLY TWO
:OLE NUMB] FACTORS1 #A & XF4 ,! TA# %[S
ALL ! PRIME NUMB]S LESS ?AN #AJJ4 ,A
.-POSITE .NUMB] IS A :OLE NUMB] GRT] ?AN
#A T HAS M ?AN TWO :OLE NUMB] FACTORS4
,:5 Y WRITE A -POSITE NUMB] Z A
PRODUCT ( PRIME NUMB]S1 Y >E WRIT+ XS
.PRIME .FACTORIZ,N4
,! FOLL[+ TA# IS 9 LI/$
=MAT4 ,= EA* CELL ! H1D+ IS %[N
FOLL[$ 0A COLON1 SPACE &! CELL
3T5TS
..,PRIME ,NUMB]S ,LESS ,?AN .#AJJ @3
#B1C1E1G1 #AA1 #AC1AG1AI1BC1 #BI1 #CA1
#CG1 #DA1 #DC1 #DG1 #EC1 #EI1 #FA1 #FG1
#GA1 #GC1 #GI1 #HC1 #HI1 #IG
,EXAMPLE ,WRITE ! PRIME FACTORIZ,N (
#FJ4
,USE .A .FACTOR .TREE4 ,WRITE #FJ AT !
TOP4 ,!N DRAW TWO BRAN*ES & WRITE #FJ Z
! PRODUCT ( TWO FACTORS4 ,3T9UE 6DRAW
BRAN*ES UNTIL ALL ! FACTORS >E PRIME
NUMB]S4 ,TWO FACTOR TREES = #FJ >E GIV5
AT ! "R4 ,BO? %[ #FJ .K #B 99 #B 99 #C
99 #E4
99 ,! PRIME FACTORIZ,N ( #FJ IS #B #B
99 #C 99 #E4
,A :OLE NUMB] T IS A FACTOR ( TWO OR M
NONZ]O :OLE NUMB]S IS A .-MON .FACTOR (!
NUMB]S4 ,! L>GE/ (! -MON FACTORS IS !
..GRTE/ -MON FACTOR 7.,,GCF74
,EXAMPLE ,F9D ! GRTE/ -MON FACTOR
7,,GCF7 ( #AH & #DE4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,ME?OD #A ,LI/ FACTORS43 ,ME?OD #B
,USE PRIME FACTORIZ,N4
,FACTORS ( #AH3 #A1B1C1F1I1 #AH
,FACTORS ( #DE3 #A1C1E1I1 #AE1DE
,! ,,GCF IS #I1 ! GRTE/ (! -MON FACTORS4
@3 ,PRIME FACTORIZ,N ( #AH3 #B 99 #C 99
#C
,PRIME FACTORIZ,N ( #DE3 #C 99 #C 99 #E
,! ,,GCF IS ! PRODUCT (! -MON PRIME
FACTORS3 #C 99 #C .K #I4
,A .MULTIPLE (A :OLE NUMB] IS !
PRODUCT (! NUMB] & ANY NONZ]O :OLE
NUMB]4 ,A .-MON .MULTIPLE ( TWO OR M
NUMB]S IS A MULTIPLE ( ALL (! NUMB]S4 ,!
..L1/ -MON MULTIPLE 7.,,LCM7 IS !
SMALLE/ (! -MON MULTIPLES4
,EXAMPLE ,F9D ! L1/ -MON MULTIPLE
7,,LCM7 ( #AB & #AE4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,ME?OD #A ,LI/ MULTIPLES43 ,ME?OD #B
,USE PRIME FACTORIZ,N4
,MULTIPLES ( #AB3AB1 #BD1 #CF1 #DH1
#FJ1
,MULTIPLES ( #AE3 #AE1 #CJ1 #DE1 #FJ1'''
,! ,,LCM IS #FJ1 ! L1/ (! -MON
MULTIPLES4 @3 ,PRIME FACTORIZ,N ( #AB3
#B #B 99#C
,PRIME FACTORIZ,N ( #AE3 #C 99 #E
,=M ! ,,LCM (! NUMB]S 0WRIT+ EA* PRIME
FACTOR 6! HI<E/ P[] X O3URS 9 EI NUMB]3
#B #B 99 .#C 99 .#E .K #FJ4
------------------------------------#IGI
,! .L1/ -MON .DENOM9ATOR 7.,,LCD7 (
TWO FRAC;NS IS ! L1/ -MON MULTIPLE (!
DENOM9ATORS4 ,USE ! ,,LCD 6ADD OR
SUBTRACT FRAC;NS ) DI6]5T DENOM9ATORS4
,,SKILLS ,,REVIEW ,,H&BOOK
,EXAMPLE
.,ADD3
,! L1/ -MON MULTIPLE (! DENOM9ATORS1
#AJ & #H1 IS #DJ4 ,S1 ! L1/ -MON
DENOM9ATOR 7,,LCD7 (! FRAC;NS IS #DJ4
,REWRITE ! FRAC;NS US+ ! ,,LCD ( #DJ3
,ADD ! NUM]ATORS & KEEP ! SAME
DENOM9ATOR3
,PRACTICE
,WRITE ! PRIME FACTORIZ,N (! NUMB]4
,IF ! NUMB] IS PRIME1 WRITE .PRIME
.#A4 #DB
.#B4 #AJD
.#C4 #GE
.#D4 #BC
.#E4 #GJ
.#F4 #BG
.#G4 #GB
.#H4 #AHJ
.#I4 #DG
.#AJ4 #AJJ
.#AA4 #HH
.#AB4 #DI
.#AC4 #HC
.#AD4 #ADB
.#AE4 #CB
,F9D ! GRTE/ -MON FACTOR 7,,GCF7 (!
NUMB]S4
.#AF4 #D1F
.#AG4 #BD1DJ
.#AH4 #AJ1BE
.#AI4 #EE1DD
.#BJ4 #BH1CE
.#BA4 #H1 #BJ
.#BB4 #E1 #H
.#BC4 #AE1 #AB
.#BD4 #AF1 #CB
.#BE4 #GJ1 #IJ
.#BF4 #B1 #AH
.#BG4 #I1 #BA
.#BH4 #CF1 #DB1 #ED
.#BI4 #G1 #AB1 #AG
.#CJ4 #DE1 #FC1 #HA
,F9D ! L1/ -MON MULTIPLE 7,,LCM7 (!
NUMB]S4
.#CA4 #D1 #AF
.#CB4 #B1 #AD
.#CC4 #E1 #F
.#CD4 #AF1 #BD
.#CE4 #F1 #H
.#CF4 #AB1 #BJ
.#CG4 #C1 #F
.#CH4 #AH1 #H
.#CI4 #I1 #AB
.#DJ4 #I1 #E
.#DA4 #AJ1 #AE
.#DB4 #G1 #I
.#DC4 #DJ1 #D1 #E
.#DD4 #BE1 #CJ1 #C
.#DE4 #BG1 #HA1 #CC
,P]=M ! 9DICAT$ OP],N 7;S74 ,SIMPLIFY
! RESULT4
.#DF4
.#DG4
.#DH4
.#DI4
.#EJ4
.#EA4
.#EB4
.#EC4
.#ED4
.#EE4
.#EF4
.#EG4
.#EH4
.#EI4
.#FJ4
.#FA4
.#FB4
.#FC4
.#FD4
.#FE4
.#FF4
.#FG4
.#FH4
.#FI4
------------------------------------#IHJ
,RATIOS & ,PROPOR;NS
,,SKILLS ,,REVIEW ,,H&BOOK
.,A .RATIO USES DIVI.N 6-P>E TWO
QUANTITIES4
,Y C WRITE A RATIO ( TWO QUANTITIES .A
& .;B @1 ": .;B IS N EQUAL 6#J1 9 ?REE
WAYS4
,Y %D WRITE RATIOS 9 SIMPLE/ =M4
,! FOLL[+ TA# IS 9 LI/$
=MAT4 ,= EA* CELL ! H1D+ IS %[N
FOLL[$ 0A COLON1 SPACE &! CELL
3T5TS
,?REE ,WAYS 6,WRITE ! ,RATIO (.' A
.-6.;B @3 99 .A .6.;B
,?REE ,WAYS 6,WRITE ! ,RATIO (.' A
.-6.;B @3 .A@3.;B
,?REE ,WAYS 6,WRITE ! ,RATIO (.' A
.-6.;B @3
,EXAMPLE ,WRITE ! RATIO ( #AB BOYS
6#AF GIRLS 9 ?REE WAYS4
,F/ WRITE ! RATIO Z A FRAC;N 9 SIMPLE/
=M3
99 ,?REE WAYS 6WRITE ! RATIO ( BOYS
6GIRLS >E #C 6#D1 #C3D1 &
,A .PROPOR;N IS AN EQU,N /AT+ T TWO
RATIOS >E EQUAL4
,Y C USE CROSS MULTIPLIC,N 6SOLVE A
PROPOR;N4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,US+ ,CROSS ,MULTIPLIC,N 6,SOLVE
,PROPOR;NS
,IF ": .;B @6.K #J & .;D @6.K #J1 !N
.AD .K .BE4
,EXAMPLE ,SOLVE ! PROPOR;N4
.A4
#E 99 #ED .K #I 99 .;N .,CROSS
.MULTIPLY
#BGJ .K .#I;N .,SIMPLIFY4
#CJ .K .;N .,SOLVE .= .;N
.B4
.;X 99 #H .K #DJ 99 #C .,CROSS
.MULTIPLY
.#H;X .K #ABJ .,SIMPLIFY4
.;X .K #AE ,SOLVE = .X4
,PRACTICE
..,WRITE ! RATIO 9 SIMPLE/ =M4
,EXPRESS ! ANSW] 9 .?REE WAYS4
#A4 #C 6#I
#B4 #AF 6#BD
#C4 #AJ 6#H
#D4 #F 6#B
#E4 #BE 6#CJ
#F4 #FJ 6#AJ
#G4 #D 6#D
#H4 #H 6#BJ
#I4 #CB 6#GB
#AJ4 #DB 6#AE
#AA4 #AD 6#B
#AB4 #AB 6#AE
,SOLVE ! PROPOR;N4
.#AC4
.#AD4
.#AE4
.#AF4
.#AG4
.#AH4
.#AI4
.#BJ4
.#BA4
.#BB4
.#BC4
.#BD4
.#BE4
.#BF4
.#BG4
.#BH4
------------------------------------#IHA
,3V]T+ ,UNITS ( ,M1SURE;T
,,SKILLS ,,REVIEW ,,H&BOOK
,! TA# ( M1SURES ON PAGE #AJBE GIVES
_M /ATE;TS ( EQUIVAL5T M1SURES4 ,US+ EA*
/ATE;T1 Y C WRITE TWO DI6]5T 3V].N
FACTORS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,/ATE;T ( ,EQUIVAL5T ,M1SURES3 ,3V].N
,FACTORS
..#AJJ CM .K #A .;M @3
,63V]T F "O UNIT ( M1SURE;T 6ANO!R1
MULTIPLY 0A 3V].N FACTOR4 ,USE ! "O T W
ELIM9ATE ! />T+ UNIT & KEEP ! DESIR$
UNIT4
,EXAMPLE ,COPY & -PLETE4
.A4 #C.E ;M .K @8 CM
,S1 #C.E ;M .K #CEJ CM4
.B4 #FBJ CM .K _?_ ;M
99 ,S1 #FBJ CM .K #F.B M4
,"S"TS Y NE$ 6USE M ?AN "O 3V].N
FACTOR4
,EXAMPLE ,COPY & -PLETE3 #G "DS .K _?_
SEC
,F9D ! APPROPRIATE /ATE;TS ( EQUIVAL5T
M1SURES4 #BD ;H .K #A "D1 #FJ M9 .K #A
;H1 & #FJ SEC .K #A M9
,WRITE 3V].N FACTORS3
,MULTIPLY 03V].N FACTORS 6ELIM9ATE "DS
& KEEP SECONDS4
99 ,S1 #G "DS .K #FJD1HJJ SEC4
,PRACTICE
,COPY & -PLETE4
.#A4 #F ;,L .K @8 M,L
.#B4 #B MI .K @8 FT
.#C4 #HJ;OZ .K _?_ LB
.#D4 #D;"DS .K _?_ ;H
.#E4 #GG;MM .K _? CM
.#F4 #E GAL .K _?_ QT
.#G4 #DH FT .K _?_ YD
.#H4 #AEJJ M,L .K _?_ ;,L
.#I4 #DJ ;M .K _? CM
.#AJ4 #ABE LB .K _?_ OZ
.#AA4 #HJJ ;G .K _?_ KG
.#AB4 #IJJ SEC .K _?_ M9
.#AC4 #GB IN4 .K _?_ FT
.#AD4 #B.E TON .K _?_ LB
.#AE4 #IJ M9 .K _?_ ;H
.#AF4 #FE1JJJ MG .K _?_ ;G
.#AG4 #AJJ;YD .K _?_ IN4
.#AH4 #C.E;KG .K _?_ ;G
.#AI4 #F;PT .K _?_ QT
.#BJ4 #A WEEK .K _?_ M9
.#BA4 #B OZ .K _?_ LB
.#BB4 LKM .K _;,L_MM
.#BC4 ;L MI .K _?_ IN4
.#BD4 #E;GAL .K _?_ ;C
.#BE4 #BHH IN4 #B .K _?_ FT #B
.#BF4 #BD PT .K _?_ GAL
.#BG4 #D KG .K _?_ ;G
.#BH @4 #G HR .K @8 SEC
------------------------------------#IHB
,SCI5TIFIC ,NOT,N
,,SKILLS ,,REVIEW ,,H&BOOK
.,SCI5TIFIC .NOT,N IS A WAY 6WRITE
NUMB]S US+ P[]S ( #AJ4 ,A NUMB] IS
WRITT5 9 .SCI5TIFIC .NOT,N IF X HAS ! =M
;C ;,X #AJ0 ": #A "K.K ;C "K #AJ & .;N
IS AN 9TEG]4 ,! TA# %[S "S P[]S ( T5 9
ORD] F L1/ 6GRTE/4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,P[] ( ,T53 #AJ -#C @3 #AJ -#B @3 #AJ
-#A @3 #AJ;DG3 #AJ #A @3 #AJ #B @3 #AJ
#C
,VALUE3 #J.JJA3 #J.JA3 #J.A3 #A3 #AJ3
#AJJ3 #AJJJ
,EXAMPLE ,WRITE ! NUMB] 9 SCI5TIFIC
NOT,N4
A4 #AB1HJJ1JJJ ,/&>D =M
,MOVE ! DECIMAL PO9T #G PLACES 6!
LEFT4
#A.BH ;,X #AJ #G ,USE #G Z AN EXPON5T
( #AJ4
.B4 #J.JJJJJCI ,/&>D =M
,MOVE ! DECIMAL PO9T #F PLACES 6! "R4
#C.I ;,X #AJ -#F ,USE --#F Z AN
EXPON5T ( #AJ4
,EXAMPLE
,WRITE ! NUMB] 9 /&>D =M4
.A4 #F.A ;,X #AJ #D ,SCI5TIFIC NOT,N
#F.A ;,X #AJ #D ,! EXPON5T ( #AJ IS #D4
,MOVE ! DECIMAL PO9T #D PLACES 6! "R4
#FA1JJJ ,/&>D =M
.B4 #E.GD ;,X #AJ --#E ,SCI5TIFIC
NOT,N
#E.GD ;,X #AJ -#E ,! EXPON5T ( #AJ IS
--#E4
,MOVE ! DECIMAL PO9T #E PLACES 6!
LEFT4
#J.JJJJEGD ,/&>D =M
,PRACTICE
,WRITE ! NUMB] 9 SCI5TIFIC NOT,N4
.#A4 #J.F
.#B4 #BE1JJJ1JJJ
.#C4 #J.JH
.#D #J.JJEDB
.#E4 #DJ.H
.#F4 #G
.#G4 #J.JJJCHE
.#H4 #H1ADE1JJJ
.#I4 #DA1BCF
.#AJ4 #J.JJJJJAF
.#AA4 #DHF1JJJ
.#AB4 #J.JJJJJJJJI
.#AC4 #J.JAJJB
.#AD4 #A1JJJ1JJJ1JJJ
.#AE4 #GJEJ.E
.#AF4 #J.CG
.#AG4 #IHEJ
.#AH4 #J.JJJJBJF
.#AI4 #HJE
.#BJ4 #J.JJJE
,WRITE ! NUMB] 9 /&>D =M4
.#BA4 #E ;,X #AJ #C
.#BB4 #D ;,X #AJ -#B
.#BC4 #H.B ;,X #AJ -#A
.#BD4 #F.IC ;,X #AJ #B
.#BE4 #C.B ;,X #AJ -#C
.#BF4 #I.JA ;,X #AJ -#E
.#BG4 #G.CDE ;,X #AJ #E
.#BH4 #B.CH ;,X #AJ --#B
.#BI4 #A.HAD ;,X #AJ #J
.#CJ4 #B.G ;,X #AJ #H
.#CA4 #A ;,X #AJ #F
.#CB @4 #D.I ;,X #AJ -#D
.#CC4 #H ;,X #AJ -#F
.#CD4 #E.F ;,X #AJ #D
.#CE4 #A.HG ;,X #AJ #I
.#CF4 #G ;,X #AJ -#D
.#CG4 #F.JH ;,X #AJ #F
.#CH4 #I.JJI ;,X #AJ -#C
.#CI4 #C.DJA ;,X #AJ #G
.#DJ4 #E.CB ;,X #AJ #A
------------------------------------#IHC
,SIGNIFICANT ,DIGITS
,,SKILLS ,,REVIEW ,,H&BOOK
.,SIGNIFICANT .DIGITS 9DICATE H[
PRECISELY A NUMB] IS "KN4 ,USE ! FOLL[+
GUIDEL9ES 6DET]M9E ! NUMB] ( SIGNIFICANT
DIGITS4
99 ,ALL NONZ]O DIGITS >E SIGNIFICANT4
99 ,ALL Z]OS T APPE> 2T TWO NONZ]O
DIGITS >E SIGNIFICANT4
99 ,=A DECIMAL1 ALL Z]OS T APPE> AF !
LA/ NONZ]O DIGIT >E SIGNIFICANT4 ,=A
:OLE NUMB]1 Y _C TELL :E!R ANY Z]OS AF !
LA/ NONZ]O DIGIT >E SIGNIFICANT1 S Y %D
ASSUME T !Y >E N SIGNIFICANT4
,"S"TS CALCUL,NS 9VOLVE M1SURE;TS T H
V>I\S NUMB]S ( SIGNIFICANT DIGITS4 ,9 ?
CASE1 A G5]AL RULE IS 6C>RY ALL DIGITS
"? ! CALCUL,N & !N R.D ! RESULT 6! SAME
NUMB] ( SIGNIFICANT DIGITS Z ! M1SURE;T
)! .FEWE/ SIGNIFICANT DIGITS4 ,:5 Y
CALCULATE ) UNITS T _C 2 DIVID$
96FRAC;NAL "PS1 S* Z NUMB] ( P1 3SID]
ONLY ! SIGNIFICANT DIGITS (! O!R
NUMB]7;S74
,EXAMPLE ,P]=M ! CALCUL,N4 ,WRITE YR
ANSW] )! APPROPRIATE NUMB] ( SIGNIFICANT
DIGITS4
A4
B4
.C4 4#FA.BJ RE/AURANT BILL @/ #F P
,! NUMB] ( P IS EXACT1 S 3SID] ONLY !
#D SIGNIFICANT DIGITS (! BILL1 4#FA.BJ4
,! ANSW] %D H #D SIGNIFICANT DIGITS4
4#FA.BJ @/ #F .K 4.#AJ..BJ
99 ,EA* P]SON PAYS 4#AJ.BJ4
,PRACTICE
,P]=M ! CALCUL,N4 ,WRITE YR ANSW] )!
APPROPRIATE NUMB] ( SIGNIFICANT DIGITS4
.#A4 #FJJ @+ #CJ
.#B4 #E--#B.F
.#C4 #AB 99 #F.GE
.#D4 #J.JIH @+ #J.AD @+ #J.CFI
.#E4 #C.FJEC--#A.GBJ
.#F4 #DJ @/ .#C.E
.#G4 #H.J--#C.A
.#H4 #CA.G 99 #F.H 99 #J.DCE
.#I4 #CJ.E 99 #F.DJ
.#AJ4 #C.AH @+ #B.JJJE
.#AA4 #J.JHH--#B.DD
.#AB4 #HFEJ @+ #CHJ--#DI
.#AC4 #DJAF--#CJJG
.#AD4 #A.CE @+ #AD.H
.#AE4 #CBJ @/ #AH
.#AF4 #CH.A 99 #C.JD @/ #J.JBD
.#AG4 4#A.DE P] NOTEBOOK 99 #AB
NOTEBOOKS
.#AH4 #AJ.J LIT]S ( WAT]--#D.E LIT]S (
WAT]
.#AI4 #BFJ P9TS ( MILK @/#AJF /UD5TS
.#BJ4 #J.E Y>D ( FABRIC @+ #J.HG Y>D (
FABRIC
.#BA4 #BG1IGC BOOKS @/ #AA LIBR>IES
.#BB4 #AB.GF GALLONS ( GAS @+ #F.JH
GALLONS ( GAS
.#BC4 4#F.IE P] TICKET 99 #AHJ TICKETS
.#BD4 #AEDJ P.DS--#AFJ P.DS--#HE P.DS
------------------------------------#IHD
,WRIT+ ,ALGEBRAIC ,EXPRES.NS
,,SKILLS ,,REVIEW ,,H&BOOK
,6SOLVE A PRO#M US+ ALGEBRA1 Y (T5 NE$
6WRITE A PHRASE Z AN ALGEBRAIC EXPRES.N4
,EXAMPLE ,WRITE ! PHRASE Z AN
ALGEBRAIC EXPRES.N4
.A4 #F LESS ?AN A NUMB]
,8,LESS ?AN0 9DICATES SUBTRAC;N4
99 .;N -#F
.B4 ,! CUBE (A NUMB]
8,CUBE0 9DICATES RAIS+ 6! ?IRD P[]4
99 .;N #C
.C4 ,D\# A NUMB]
8,D\#0 9DICATES MULTIPLIC,N 0#B4
99#B .;N
,EXAMPLE ,WRITE AN ALGEBRAIC EXPRES.N
6ANSW] ! "Q4
.A4 ,REBE3A WALKS ?REE "TS Z F> 6S*OOL
Z ,ME<AN DOES4 ,IF ,ME<AN WALKS .;M
BLOCKS 6S*OOL1 H[ _M BLOCKS 6S*OOL DOES
,REBE3A WALK8
99 #C;M
.B4 ,KATE IS #H 9*ES TALL] ?AN ,NOAH4
,IF ,NOAH IS .;N 9*ES TALL1 H[ TALL IS
,KATE8
99 ;N @+ #H
,PRACTICE
,WRITE ! PHRASE Z AN ALGEBRAIC
EXPRES.N4
.#A4 #H M ?AN A NUMB]
.#B4 #AJ "TS A NUMB]
.#C4 ,TWICE A NUMB]
.#D4 #F LESS ?AN A NUMB]
.#E4 ,"O FIF? (A NUMB]
.#F4 #D GRT] ?AN A NUMB]
.#G4 #E "TS A NUMB]
.#H4 ,A NUMB] SQU>$
.#I4 #BE@3P (A NUMB]
.#AJ4 ,HALF A NUMB]
.#AA4 #B LESS ?AN A NUMB]
.#AB4 ,! SQU>E ROOT (A NUMB]
,WRITE AN ALGEBRAIC EXPRES.N 6ANSW] !
"Q4
.#AC4 ,ALLISON IS #D YE>S "Y] ?AN H]
SI/] ,CAMILLE4 ,IF ,CAMILLE IS .;C YE>S
OLD1 H[ OLD IS ,ALLISON8
.#AD4 ,RYAN B"\ A MOVIE TICKET = .;X
DOLL>S4 ,HE PD )A 4#BJ BILL4 ,H[ M*
*ANGE %D ,RYAN GET8
.#AE4 ,BRIDGET SP5T 4#E M ?AN ,TOM
SP5T AT ! MALL4 ,IF ,TOM SP5T .;X
DOLL>S1 H[ M* DID ,BRIDGET SP5D8
.#AF4 ,M>C HAS TWICE Z _M BASEBALL
C>DS Z HOCKEY C>DS4 ,IF ,M>C HAS .;H
HOCKEY C>DS1 H[ _M BASEBALL C>DS DOES HE
H8
.#AG4 ,ELIZABE?'S BALLET CLASS IS #DE
M9UTES L;G4 ,IF ,ELIZABE? IS .;M M9UTES
LATE = BALLET CLASS1 H[ _M M9UTES W %E
SP5D 9 CLASS8
.#AH4 ,/EVE DROVE ;X MILES P] H\R = #E
H\RS4 ,H[ _M MILES DID ,/EVE DRIVE8
.#AI4 ,W5DY B"\ #AJ P5S PRIC$ AT .;X
DOLL>S EA*4 ,H[ M* DID %E SP5D8
------------------------------------#IHE
,BINOMIAL ,PRODUCTS
,,SKILLS ,,REVIEW ,,H&BOOK
,A MONOMIAL IS A NUMB]1 A V>IA#1 OR !
PRODUCT (A NUMB] & "O OR M V>IA#S4 ,A
BINOMIAL IS ! SUM ( TWO MONOMIALS4 ,9
O!R ^WS1 A BINOMIAL IS A POLYNOMIAL )
TWO T]MS4 ,Y C USE A GEOMETRIC MODEL
6F9D ! PRODUCT ( TWO BINOMIALS4
,EXAMPLE ,SIMPLIFY 7#B;X@+#A77;X@+
#C74
,DRAW A RECTANGLE ) DIM5.NS .#B;X @+
#A & ;X @+ #C4 ,USE ! DIM5.NS 6DIVIDE !
RECTANGLE 96"PS4 ,!N F9D ! >EA ( EA* "P4
,! BINOMIAL PRODUCT 7#B;X @+ ;L77;X @+
#C7 IS ! SUM (! >1S ( ALL ! "PS4
,"! >E #B BLUE "PS ) >EA ;X #B @1 #G
GRE5 "PS ) >EA ;X1 & #C YELL[ "PS ) >EA
#A4
7#B;X @+ ;L77;X @+ #C7 .K #B;X #B @+
#G;X @+ #C
,ANO!R WAY 6F9D ! PRODUCT ( TWO
BINOMIALS IS 6USE ! 4TRIBUTIVE PROP]TY
SY/EMATIC,Y4 ,MULTIPLY ! .F/ T]MS1 !
.\T] T]MS1 ! .9N] T]MS1 &! .LA/ T]MS (!
BINOMIALS4 ,? IS CALL$ ,,FOIL =! ^WS
,F/1 ,\T]1 ,9N]1 & ,LA/4
,EXAMPLE ,SIMPLIFY 7.;X @+
#B77#D;X--#E74
.K #D;X #B -- #E;X @+ #H;X--#AJ
,MULTIPLY4
.K #D;X #B @+ #C;X--#AJ ,-B9E L T]MS4
,PRACTICE
,SIMPLIFY4
.#A4 7.A @+ #E7 7.A @+ #C7
.#B4 7.;M @+ #D7 7.;M @+ #AA7
.#C4 7.;T @+ #H7 7.;T @+ #G7
.#D4 7.;Z @+ #A7 7.;Z @+ #F7
.#E4 7.;Y @+ #D7 7.;Y @+ #B7
.#F4 7.;X @+ #I7 7.;X @+ #I7
.#G4 7.;Y -- #B7 #B
.#H4 7.;N @+ #F7 #B
.#I4 7#D -- .;Z7 #B
.#AJ4 7.A @+#AJ7 7.A --#AJ7
.#AA4 7;Y @+ #C77;Y--#G7
.#AB4 7.;K @+ ,I7 #B
.#AC4 7#E .;X -- #D77#E .;X @+ #D7
.#AD4 7#C @+ .;N7 #B
.#AE4 7.;C @+#E77#B .;C --#G7
.#AF4 7.A @+ #E7 7.A @+ #E7
.#AG4 7#G -- .;Z7 7#G @+ .;Z7
.#AH4 7#C .;X -- #H7@7 .;X -- #F7
.#AI4 7.#D;A @+ #C7 #B
.#BJ4 7#C -- .;G @77#B .;G @+ #C7
.#BA4 7#D -- .;X @77#H @+ .;X @7
.#BB4 7#C .;N -- ;L7@7 .;N -- #D7
.#BC4 7--.A @+ #I7@7 .A -- #I7
.#BD4 7#H .;X @+ ;L7@7 .;X @+ #A7
.#BE4 7#E .;X @+ #B77#B .;X -- #E7
.#BF4 7.#B;D -- #E7 7.#C;D -- #A7
.#BG4 7--#D .;Z @+ #C77#F .;Z -- #A7
------------------------------------#IHF
,,LCD,'S ( ,R,NAL ,EXPRES.NS
,,SKILLS ,,REVIEW ,,H&BOOK
,A R,NAL EXPRES.N IS A FRAC;N ^:
NUM]ATOR & DENOM9ATOR >E NONZ]O
POLYNOMIALS4 ,! L1/ -MON DENOM9ATOR
7,,LCD7 ( TWO R,NAL EXPRES.NS IS ! L1/
-MON MULTIPLE (! DENOM9ATORS4 ,6F9D !
,,LCD1 FOLL[ ^! ?REE /EPS3
.,,/EP .#A ,WRITE EA* DENOM9ATOR Z !
PRODUCT ( XS FACTORS4
.,,/EP#B ,WRITE ! PRODUCT 3SI/+ (!
HI<E/ P[] ( EA* FACTOR T APPE>S 9 EI
DENOM9ATOR4
.,,/EP#C ,SIMPLIFY ! PRODUCT F ,/EP #B
6WRITE ! ,,LCD4
,EXAMPLE
,F9D ! L1/ -MON DENOM9ATOR (! R,NAL
EXPRES.NS4
.A4
.B4
.C4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,,/EP .#A @3 _+FACTORS::_:
_+FACTORS::_: ,FACTORS3
--@3 .#E;XY .K #E 99 .;X 99 .;Y
;Y.' #C .K;Y.' #C @3 #H;X #B .K #B #C 99
.;X .#B
#AB;X .K #B #B 99 #C 99 .;X @3 #C;X @+
#F .K #C 99 7;X @+ #B7
;X #B -- #C;X--#AJ .K 7;X @+ #B7 99
7;X--#E7
.,,/EP .#B @3 ,PRODUCT3 #E 99 .;X 99
;Y #C @3 ,PRODUCT3 #B #C 99 #C 99 ;X.'
#B @3 ,PRODUCT3 #C 99 7;X @+ #B7 99
7;X--#E7
.,,/EP .#C @3 .,,LCD3 #E;XY #C @3
.,,LCD3 #BD;X #B @3 .,,LCD3 #C7;X @+
#B77;X--#E7
,PRACTICE
,F9D ! L1/ -MON DENOM9ATOR (! R,NAL
EXPRES.NS4
.#A4
.#B4
.#C4
.#D4
.#E4
.#F4
.#G4
.#H4
.#I4
.#AJ4
.#AA4
.#AB4
.#AC4
.#AD4
.#AE4
.#AF4
.#AG4
.#AH4
.#AI4
.#BJ4
.#BA4
.#BB4
.#BC4
.#BD4
.#BE4
.#BF4
.#BG4
------------------------------------#IHG
,! ,COORD9ATE ,PLANE
,,SKILLS ,,REVIEW ,,H&BOOK
.,A .COORD9ATE .PLANE IS =M$ 0!
9T]SEC;N (A HORIZONTAL NUMB] L9E CALL$ !
;X-AXIS &A V]TICAL NUMB] L9E CALL$ !
;Y-AXIS4 ,! AXES MEET AT A PO9T CALL$ !
.ORIG9 & DIVIDE ! COORD9ATE PLANE 96F\R
.QUADRANTS @1 NUMB]$ ,I1 ,,II1 ,,III1 &
,,IV4
,EA* PO9T 9 A COORD9ATE PLANE IS
REPRES5T$ 0AN .ORD]$ .PAIR4 ,! F/ NUMB]
IS ! .;X- .COORD9ATE @1 &! SECOND NUMB]
IS ! .;Y-.COORD9ATE4
,! ORD]$ PAIR 7#C1 #A7 IS GRAPH$ AT !
"R4 ,! ;X-COORD9ATE IS #C1 &!
;Y-COORD9ATE IS #A4 ,S1 ! PO9T IS "R #C
UNITS & UP #A UNIT F ! ORIG94
,EXAMPLE ,GRAPH ! PO9TS .,A7.#B @1
--#A7 & ;,B7--#D1 #J7 9 A COORD9ATE
PLANE4
.,A7.#B @1 --.#A7 ,/>T AT ! ORIG94
,! ;X-COORD9ATE IS #B1 S MOVE "R #B
UNITS4 ,! ;Y-COORD9ATE IS --#A1 S MOVE
D[N #A UNIT4 ,DRAW A PO9T AT 7#B1 --#A7
& LABEL X ,A4
.;,B 7--.#D1.J7 ,/>T AT ! ORIG94
,! ;X-COORD9ATE IS --#D1 S MOVE LEFT
#D UNITS4 ,! ;Y-COORD9ATE IS #J1 S MOVE
UP #J UNITS4 ,DRAW A PO9T AT 7--#D1 #J7
& LABEL X .,B4
,PRACTICE
,GRAPH ! PO9TS 9 A COORD9ATE PLANE4
#A4 ,A7#G1 #B7
#B4 ;,B7#F1 --#G7
#C4 ;,C7#B1 --#C7
#D4 ;,D7--#H1 #J7
#E4 #7--#D1 --#H7
#F4 ;,F7;L1 #C7
#G4 ;,G7#C1 #J7
#H4 ;,H7;L1 --#E7
#I4 #G7#J1 --#B7
#AJ4 7--#F1 #E7
.#AA4 .;,K7.#E @1 .#H7
#AB.A7#H1--#B7
#AC4 ;,M7--#C1--#D7
.#AD4 #G;,V7--#G1 .#H7
#AE4 ;,P7--#E1 #A7
#AF4 ;,Q7--#B1 --#F7
#AG4 ;I87#J1F7
#AH4 ;,S7--#D1 --#A7
#AI4 ;,T7#D1D7
#BJ4 ;,F7--#C1G7
,GIVE ! COORD9ATES &! QUADRANT OR AXIS
(! PO9T4
#BA4 .,A
#BB4 .;,B
#BC4 .;,C
#BD4 .;,D
#BE4 .;,E
#BF4 .;,F
#BG4 .;,G
#BH4 .;,H
#BI4 .,I
#CJ4 .;,K
#CA4 .;,L
#CB4 .;,M
#CC4 .;,N
#CD4 .,O
#CE4 .;,P
#CF4 .;,Q
#CG4 .;,R
#CH4 .;,S
#CI4 .;,T
#DJ4 .;,U
#DA4 .;,V
#DB4 .;,W
#DC4 .;,X
#DD4 .;,Y
------------------------------------#IHH
,TRANS=M,NS
,,SKILLS ,,REVIEW ,,H&BOOK
,A .TRANS=M,N IS A *ANGE MADE 6!
POSI;N OR 6! SIZE (A FIGURE4 ,EA* PO9T
7;X1 ;Y7 (! FIGURE IS MAPP$ 6A NEW PO9T1
&! NEW FIGURE IS CALL$ AN .IMAGE4
,A .TRANSL,N IS A TRANS=M,N 9 : EA*
PO9T (A FIGURE MOVES ! SAME 4T.E 9 !
SAME DIREC;N4 ,A FIGURE & XS TRANSLAT$
IMAGE >E 3GRU5T4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,TRANSL,N.' A .-,UNITS ,HORIZONT,Y &.'
;B .-,UNITS ,V]TIC,Y.'.-
7.;X1 .;Y7 7;X @+ ..A1 ;Y @+ .;B7
,EXAMPLE ,TRANSLATE "R #C UNITS & D[N
#A UNIT4
,6MOVE "R #C UNITS1 USE .A .K #C4
,6MOVE D[N #A UNIT1 USE .;B .K --#A4 ,S1
USE 7;X1 .;Y7 7;X @+ #C1 .;Y @+ 7--#A77
) EA* 5DPO9T4
.;,F7.#B @1 #D7 ;,F7#B @+ #C1 #D @+
7--#A77 .K ,F0'7#E1 #C7 ;,G7;L1 #A7
,G0'7;L @+ #C1A @+ 7--#A7 .K ,G0'7#D1
#J7
,GRAPH ! 5DPO9TS 7#E1 #C7 & 7#D1 #J74
,!N DRAW ! IMAGE4
,A .REFLEC;N IS A TRANS=M,N 9 : A
FIGURE IS REFLECT$1 OR FLIPP$1 9 A L9E1
CALL$ ! .L9E .( .REFLEC;N4 ,A FIGURE &
XS REFLECT$ IMAGE >E 3GRU5T4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,REFLEC;N 9 ;X-AXIS3 ,REFLEC;N 9
;Y-AXIS
7.;X1 .;Y7 7.;X1 --.;Y7 @3 7.;X1 .;Y7
7--.;X1 .;Y7
,EXAMPLE ,REFLECT .,,ABC 9 ! ;Y-AXIS4
,USE 7;X1 ;Y7 7-;X1 ;Y7 ) EA* V]TEX4
.,A7.#D @1 #C7 .,A0' 7--#D1 #C7
.,*ANGE .EA*
.;,B7.#A @1 #B @7 ,B0'7--;L1 #B7
.;X-.COORD9ATE
;,C7#C1 #A7 ,C0' 7--#C1 #A7 .6.XS
.OPPOSITE4
,GRAPH ! NEW V]TICES4 ,!N DRAW !
IMAGE4
,A .ROT,N IS A TRANS=M,N 9 : A FIGURE
IS TURN$ AB A FIX$ PO9T1 CALL$ ! .C5T]
.( .ROT,N4 ,! DIREC;N C 2 CLOCKWISE OR
C.T]CLOCKWISE4 ,A FIGURE & XS ROTAT$
IMAGE >E 3GRU5T4
,! FOLL[+ TA# IS 9 LI/$
=MAT4 ,= EA* CELL ! H1D+ IS %[N
FOLL[$ 0A COLON1 SPACE &! CELL
3T5TS
..,ROT,N ,AB ! .,ORIG9 @3 .#AHJ;DG .EI
.DIREC;N
..,ROT,N ,AB ! .,ORIG9 @3 7.;X1 .;Y7
7--.;X1 --.;Y7
..,ROT,N ,AB ! .,ORIG9 @3 .#IJ;DG
.CLOCKWISE
..,ROT,N ,AB ! .,ORIG9 @3 7.;X1 .;Y7
7.;Y1 --.;X7
..,ROT,N ,AB ! .,ORIG9 @3 .#IJ;DG
.C.T]CLOCKWISE
..,ROT,N ,AB ! .,ORIG9 @3 7.;X1 .;Y7
7--.;Y1 .;X7
,EXAMPLE ,ROTATE ,,R/V #AHJ;DG AB !
ORIG94
,USE 7;X1 ;Y7 7--;X1 --;Y7 ) EA*
V]TEX4
.;,R7.#B @1 #B7 --#D FL0'7--#B1 --#B7
.,*ANGE .E
;,S7#D1 #B7 ,S0'7--#D1 --#B7
.COORD9ATE
;,T7#D1A7 ,T0'7--#D1 --#A7 .6.XS
.OPPOSITE
;,V7#A1 #J7 .;,V7--.;L @1 #J7
,GRAPH ! NEW V]TICES4 ,!N DRAW !
IMAGE4
------------------------------------#IHI
,,SKILLS ,,REVIEW ,,H&BOOK
.,A .DIL,N IS A TRANS=M,N 9 : A FIGURE
/RET*ES OR %R9KS DEP5D+ ON ! DIL,N'S
.SCALE .FACTOR4 ,A FIGURE ./RET*ES IF
.;K .1 #A & .%R9KS IF #J "K ;K "K #A4 ,A
FIGURE & XS DILAT$ IMAGE >E SIMIL>4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,DIL,N ) ,SCALE ,FACTOR.' ;K .-)
,RESPECT 6! ,ORIG9.'.-
7..;X1 ;Y7 7KX1 .KY7
,EXAMPLE ,DILATE .,,JKLM US+ A SCALE
FACTOR ( #J.E4
,! SCALE FACTOR IS .;K .K #J.E1 S
MULTIPLY E COORD9ATE 0#J.E4 ,USE 7;X1
;Y7 7#J.E;X1 #J.E;Y7 ) EA* V]TEX4
.;,J 7#D1D7 .,J0' 7#J.E.D1J.E.D7.K
.;,J @' 7#B1 #B7
.;,K 7#F1 #D7 .;,K ,87#J.E 99 #F1 #J.E
99 #D7 .K .;,K ,87#C1 #B7
.;,L 7#F1 --#A7 .;,L ,87#J.E 99 #F1
#J.E 99 7--#A77 .K .;,L ,87#C1 --#J.E7
;,M7#D1 --#A7 ,M0'7#J.E 99 #D1 #J.E 99
7--#A77 .K ,M0'7#B1 --#J.E7
,GRAPH ! NEW V]TICES4 ,!N DRAW !
IMAGE4
,PRACTICE
,F9D ! COORD9ATES ( ;,N7--#C1H7 AF !
GIV5 TRANS=M,N4 ,= ROT,NS1 ROTATE AB !
ORIG94
.#A4 ,ROTATE #AHJ;DG4
.#B4 ,REFLECT 9 ;X-AXIS4
.#C4 ,TRANSLATE UP #C UNITS4
.#D4 ,REFLECT 9 ;Y-AXIS4
.#E4 ,ROTATE #IJ;DG CLOCKWISE4
.#F4 ,TRANSLATE LEFT #E UNITS4
.#G4 ,ROTATE #IJ;DG C.T]CLOCKWISE4
.#H4 ,TRANSLATE "R #B UNITS & D[N #I
UNITS4
,TRANS=M .,,P/4 ,GRAPH ! RESULT4 ,=
ROT,NS1 ROTATE AB ! ORIG94
.#I4 ,REFLECT 9 ;X-AXIS4
.#AJ4 ,ROTATE #IJ;DG C.T]CLOCKWISE4
.#AA4 ,ROTATE #IJ;DG CLOCKWISE4
.#AB4 ,TRANSLATE D[N #G UNITS4
.#AC4 ,REFLECT 9 ;Y-AXIS4
.#AD4 ,TRANSLATE LEFT #D UNITS4
.#AE4 ,ROTATE #AHJ;DG4
.#AF4 ,TRANSLATE "R #B UNITS4
.#AG4 ,TRANSLATE "R #A UNIT & UP #D
UNITS4
.#AH4 ,TRANSLATE LEFT #F UNITS & UP #B
UNITS4
,! COORD9ATES (! V]TICES (A POLYGON >E
GIV54 ,DRAW ! POLYGON4 ,!N F9D !
COORD9ATES (! V]TICES (! IMAGE AF !
SPECIFI$ DIL,N1 & DRAW ! IMAGE4
.#AI4 7#A1 #C71 7#C1 #B71 7#B1 #E72
DILATE US+ A SCALE FACTOR ( #C
.#BJ4 7#B1 #H71 7#B1 #D71 7#F1 #H71
7#F1 #D72 DILATE US+ A SCALE FACTOR (
.#BA4 7#C1 #C71 7#F1 #C71 7#C1 --#C71
7#F1 --#C72 DILATE US+ A SCALE FACTOR (
.#BB4 7#B1 #B71 7#B1 #G71 7#E1 #G72
DILATE US+ A SCALE FACTOR ( #B
.#BC4 7#B1 --#B71 7#F1 --#B71 7#D1
--#F71 7#J1 --#F72 DILATE US+ A SCALE
FACTOR (
------------------------------------#IIJ
,L9E ,SYMMETRY
,,SKILLS ,,REVIEW ,,H&BOOK
,A FIGURE HAS .L9E .SYMMETRY IF A L9E1
CALL$ A .L9E .( .SYMMETRY @1 DIVIDES !
FIGURE 96TWO "PS T >E MIRROR IMAGES (
EA* O!R4 ,2L >E F\R FIGURES ) _! L9ES (
SYMMETRY %[N 9 R$4
,EXAMPLE ,A L9E ( SYMMETRY =! FIGURE
IS %[N 9 R$4 ,F9D ! COORD9ATES ( PO9T
.,A4
,PO9T ,A IS ! MIRROR IMAGE (! PO9T
7#C1 --#F7 ) RESPECT 6! L9E ( SYMMETRY
;Y .K --#B4 ,! ;X-COORD9ATE .( .,A IS
#C1 ! SAME Z ! ;X-COORD9ATE ( 7#C1
--#F74 ,2C --#F IS ! ;Y-COORD9ATE ( 7#C1
--#F71 & --#B--7--#F7 .K #D1 ! PO9T 7#C1
--#F7 IS .D[N #D UNITS F ! L9E (
SYMMETRY4 ,"!=E1 PO9TS M/ 2 .UP #D UNITS
F ! L9E ( SYMMETRY4 ,S1 ! ;Y-COORD9ATE (
.,A IS --#B @+ #D .K #B4 ,! COORD9ATES (
PO9TS >E 7#C1 #B74
,,PRACTICE
,TELL H[ _M L9ES ( SYMMETRY ! FIGURE
HAS4
#A4
#B4
#C4
#D4
.#E4 ,A P>ALLELOGRAM
.#F4 ,A SQU>E
.#G4 ,A RHOMBUS
.#H4 ,AN EQUILAT]AL TRIANGLE
,A L9E ( SYMMETRY =! FIGURE IS %[N 9
R$4 ,F9D ! COORD9ATES ( PO9T .,A4
#I4
#AJ4
#AA4
------------------------------------#IIA
,P]IMET] & ,>EA
,,SKILLS ,,REVIEW ,,H&BOOK
.,! .P]IMET] .;,P (A FIGURE IS ! 4T.E
>.D X4 ,6F9D ! P]IMET] (A FIGURE1 ADD !
SIDE L5G?S4
,EXAMPLE ,F9D ! P]IMET] (! FIGURE4
A4
,PICTURE3 ..;,P .K #E @+ #AB @+ #AC .K
#CJ .IN4
B4
,PICTURE3 ..;,P .K #B7#D7 @+ #B7#AH7
.K #H @+ #CF .K #DD .;M
.,! .>EA .,A (A FIGURE IS ! NUMB] (
SQU>E UNITS 5CLOS$ 0! FIGURE4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
..,>EA (A .,TRIANGLE
,A.K
@3 ..,>EA (A .,RECTANGLE
,A.K .LW
@3 ..,>EA (A .,P>ALLELOGRAM
,A.K .BH
@3 ..,>EA (A .,TRAPEZOID
,EXAMPLE ,F9D ! >EA (! FIGURE4
A4
,PICTURE3 ..,A.K 7#AE7 7#G7 .K #AJE
.IN4 #B
B4
,PICTURE3 ..,A.K 7#E7 7#E7 .K#BE .FT
#B
C4
,PRACTICE
,F9D ! P]IMET] & >EA (! FIGURE4
.#A4
.#B4
.#C4
.#D4
.#E4
.#F4
.#G4
.#H4
------------------------------------#IIB
,CIRCUMF];E & ,>EA (A ,CIRCLE
,,SKILLS ,,REVIEW ,,H&BOOK
,A .CIRCLE 3SI/S ( ALL PO9TS 9 A PLANE
T >E ! SAME 4T.E F A FIX$ PO9T CALL$ !
.C5T]4
,! 4T.E 2T ! C5T] & ANY PO9T ON !
CIRCLE IS ! .RADIUS4 ,! 4T.E ACR !
CIRCLE "? ! C5T] IS ! .DIAMET]4 ,!
DIAMET] IS TWICE ! RADIUS4
,! .CIRCUMF];E (A CIRCLE IS ! 4T.E >.D
! CIRCLE4 ,= ANY CIRCLE1 ! RATIO (!
CIRCUMF];E 6! DIAMET] IS 7PI71 AN
IRR,NAL NUMB] T IS APPROXIMATELY #C.AD
OR
,6F9D ! CIRCUMF];E ;,C (A CIRCLE )
RADIUS .;R @1 USE ! =MULA ;,C .K #B ;R
,6F9D ! >EA .,A (A CIRCLE ) RADIUS .;R
@1 USE ! =MULA ,A .K ;R #B
,EXAMPLE ,F9D ! CIRCUMF];E & >EA (A
CIRCLE ) RADIUS #F CM4 ,GIVE AN EXACT
ANSW] & AN APPROXIMATE ANSW] = EA*4
,CIRCUMF];E
;,C.K#B ;R
.K #B 7#F7
.K #AB
#AB7#C.AD7
#CG.G
99 ,! CIRCUMF];E IS #AB C5TIMET]S1 OR
AB #CG.G C5TIMET]S4
,>EA
.,A .K .;R #B
.K 7#F7 #B
.K #CF
#CF7#C.AD7
#AAC
99 ,! >EA IS #CF SQU>E C5TIMET]S1 OR
AB #AAC SQU>E C5TIMET]S4
,PRACTICE
,F9D ! CIRCUMF];E & >EA (! CIRCLE4
,GIVE AN EXACT ANSW] & AN APPROXIMATE
ANSW] = EA*4
.#A4
.#B4
.#C4
.#D4
.#E4
.#F4
.#G4
.#H4
.#I4
.#AJ4
.#AA4
.#AB4
------------------------------------#IIC
,SURFACE ,>EA & ,VOLUME
,,SKILLS ,,REVIEW ,,H&BOOK
.,A .SOLID IS A ?REE-DIM5.NAL FIGURE T
5CLOSES "P ( SPACE4
,! .SURFACE .>EA .;,S (A SOLID IS !
>EA (! SOLID'S \T] SURFACE 7;S74
,! .VOLUME .;,V (A SOLID IS ! AM.T (
SPACE T ! SOLID O3UPIES4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,RECTANGUL> .,PRISM
;,S .K .#B;LW @+ .#B;LH @+ ..#B;: ;,V .K
.L:
@3 .,CYL9D]
.;,S .K #B ;R.' #B @+ #B RH.'
;,V .K ;R #B ;H
,EXAMPLE ,F9D ! SURFACE >EA & VOLUME
(! RECTANGUL> PRISM4
,SURFACE >EA
.;,S .K .#B;LW @+ .#B;LH @+ .#B;:
.K .#B 7#E7 7#C7 @+ #B 7#E7 7#G7 @+#B
7#C7 7#G7
.K #CJ @+ #GJ @+ #DB
.K #ADB .FT #B
,VOLUME
;,V.K#:
.K 7#E7 7#C7 7#G7
.K #AJE FT #C
,EXAMPLE
,F9D ! SURFACE >EA & VOLUME (! CYL9D]4
,SURFACE >EA
.;,S .K #B .;R #B @+ .#B .RH
.K #B 7#C7 #B @+ #B 7#C77#AB7
.K #IJ ;M #B .,EXACT .ANSW]
#BHC .;M #B .,APPROXIMATE .ANSW]
,VOLUME
;,V .K #G ;R #B ;H
.K 7#C7 #B 7#AB7
.K #AJH RM #C .,EXACT .ANSW]
#CCI .;M #C .,APPROXIMATE .ANSW]
,PRACTICE
,F9D ! SURFACE >EA & VOLUME (! SOLID4
.#A4
.#B4
.#C4
.#D4
.#E4
.#F4
------------------------------------#IID
,ANGLE ,REL,N%IPS
,,SKILLS ,,REVIEW ,,H&BOOK
,AN .ANGLE .BISECTOR IS A RAY T
DIVIDES AN ANGLE 96TWO 3GRU5T ANGLES4
,TWO ANGLES >E .-PLE;T>Y .ANGLES IF !
SUM ( _! M1SURES IS #IJ;DG4
,TWO ANGLES >E .SUPPLE;T>Y .ANGLES IF
! SUM ( _! M1SURES IS #AHJ;DG4
,EXAMPLE ,F9D ! VALUE ( .X4
.A4 BISECTS .,,ABC & .,,ABC .K #FD;DG4
,2C BISECTS .,,ABC @1 ! VALUE ( .;X IS
HALF .,,ABC4
.B4 .,,GFJ & .,,HFJ >E -PLE;T>Y4
,2C .,,GFJ & .,,HFJ >E -PLE;T>Y
ANGLES1 _! SUM IS #IJ;DG4
7#B;X--#F7 @+ #D;X .K #IJ
#F;X--#F .K #IJ
;X .K #AF
.C4 .,,CBD & .,,ABD >E SUPPLE;T>Y4
,2C ,,CBD & .,,ABD >E SUPPLE;T>Y
ANGLES1 _! SUM IS #AHJ;DG4
7#C;X--#A7 @+ 7;X--#C7 .K #AHJ
#D;X--#D .K #AHJ
;X .K #DF
,PRACTICE ..IS ! ANGLE BISECTOR .(
..,,ABC4 ,F9D ! VALUE ( .X4
.#A4
.#B4
.#C4
,,ABD & ..,,DBC >E -PLE;T>Y4 ,F9D !
VALUE ( .X4
.#D4
.#E4
.#F4
,,ABD & ..,,DBC >E SUPPLE;T>Y4 ,F9D !
VALUE ( .X4
.#G4
.#H4
.#I4
------------------------------------#IIE
,TRIANGLE ,REL,N%IPS
,,SKILLS ,,REVIEW ,,H&BOOK
,! SUM (! ANGLE M1SURES ( ANY TRIANGLE
IS #AHJ;DG4
,EXAMPLE ,F9D ! VALUE ( .X4
#FJ @+ #CE @+ .;X .K #AHJ ..,! SUM (!
ANGLE M1SURES IS .#AHJ;DG
#IE @+ .;X .K #AHJ .,SIMPLIFY4
.;X .K #HE .,SOLVE .= .X4
,9 A "R TRIANGLE1 ! .HYPOT5USE IS !
SIDE OPPOSITE ! "R ANGLE4 ,! .LEGS >E !
SIDES T =M ! "R ANGLE4 ,! .,PY?AGOR1N
.!OREM /ATES T ! SUM (! SQU>ES (! L5G?S
(! LEGS EQUALS ! SQU>E (! L5G? (!
HYPOT5USE4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,PY?AGOR1N ,!OREM
A #B @+ ;B #B -- ;C #B
,EXAMPLE ,F9D ! VALUE ( .X4
A4
#F #B @+ #H #B .K .;X #B .,PY?AGOR1N
.!OREM
#CF @+ #FD .K .;X #B .,SIMPLIFY4
#AJJ .K .;X #B .,SIMPLIFY4
.;X .K #AJ FT .,SOLVE .= .X4
B4
.;X #B @+ #AB #B .K #AC #B .,PY?AGOR1N
.!OREM
.;X #B @+ #ADD .K #AFI .,SIMPLIFY4
.;X #B .K #BE .,SOLVE .= .;X #B @4
.;X .K #E CM .,SOLVE .= .X4
,PRACTICE
,F9D ! VALUE ( .X4
.#A4
.#B4
.#C4
.#D4
.#E4
.#F4
.#G4
.#H4
#I4 ,A TRIANGLE ) ANGLES T M1SURE
.;X;DG1 .;X;DG @1 & #GJ;DG
------------------------------------#IIF
,3GRU5T & ,SIMIL> ,FIGURES
,TWO FIGURES >E .3GRU5T IF !Y H ! SAME
%APE &! SAME SIZE4 ,IF TWO FIGURES >E
3GRU5T1 !N CORRESPOND+ ANGLES >E 3GRU5T
& CORRESPOND+ SIDES >E 3GRU5T4 ,!
TRIANGLES AT ! "R >E 3GRU5T4 ,MAT*+ >CS
%[ 3GRU5T ANGLES1 & MAT*+ TICK M>KS %[
3GRU5T SIDES4
,TWO FIGURES >E .SIMIL> IF !Y H ! SAME
%APE B N NECESS>ILY ! SAME SIZE4 ,IF TWO
FIGURES >E SIMIL>1 !N CORRESPOND+ ANGLES
>E 3GRU5T &! RATIOS (! L5G?S (
CORRESPOND+ SIDES >E EQUAL4
.,EXAMPLE ,TELL :E!R ! FIGURES >E
.3GRU5T1 .SIMIL> @1 OR .NEI4
,SKILLS ,REVIEW ,H&BOOK
A4
,Z %[N1 CORRESPOND+ ANGLES >E 3GRU5T &
CORRESPOND+ SIDES >E 3GRU5T4 ,S1 !
FIGURES >E 3GRU5T4
B4
,Z %[N1 CORRESPOND+ ANGLES >E 3GRU5T1
B CORRESPOND+ SIDES H DI6]5T L5G?S4 ,S1
! FIGURES >E N 3GRU5T1 B !Y MAY 2
SIMIL>4
,! FIGURES >E SIMIL> IF ! RATIOS (!
L5G?S ( CORRESPOND+ SIDES >E EQUAL4
99 ,2C CORRESPOND+ ANGLES >E 3GRU5T &!
RATIOS (! L5G?S ( CORRESPOND+ SIDES >E
EQUAL1 .,,ABCD IS SIMIL> 6.,,EF<4
,EXAMPLE ,! TWO POLYGONS >E SIMIL>4
,F9D ! VALUE ( .X4
A4
,! ANGLE ) M1SURE .;X;DG .CORRESPONDS
6! ANGLE ) M1SURE #FJ;DG1 S .;X .K #FJ4
;B
,! SIDE ) L5G? #AB CORRESPONDS 6! SIDE
) L5G? #H1 &! SIDE ) L5G? #I CORRESPONDS
6! SIDE ) L5G? .X4
,WRITE A PROPOR;N4
#AB;X .K ..#GB ,CROSS .MULTIPLY
.;X .K #F ,SOLVE = .X4
------------------------------------#IIG
,PRACTICE
,,SKILLS ,,REVIEW ,,H&BOOK
,TELL :E!R ! FIGURES >E .3GRU5T1
.SIMIL> @1 OR .NEI4 .,EXPLA94
.#A4
.#B4
.#C4
.#D4
.#E4
.#F4
.#G4
.#H4
.#I4
,! TWO POLYGONS >E SIMIL>4 ,F9D !
VALUE ( .X4
.#AJ4
.#AA4
.#AB4
.#AC4
.#AD4
.#AE4
.#AF4
.#AG4
.#AH4
------------------------------------#IIH
,M ,PRO#M ,SOLV+ ,/RATEGIES
,,SKILLS ,,REVIEW ,,H&BOOK
,PRO#M SOLV+ /RATEGIES C HELP Y SOLVE
MA!MATICAL & R1L-LIFE PRO#MS4 ,LESSON
#A.E %[S H[ 6APPLY ! /RATEGIES ..USE A
=MULA1 LOOK =A PATT]N1 DRAW A .DIAGRAM
@1 & ..USE A V]BAL .MODEL4 ,2L >E F\R M
/RATEGIES4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,/RATEGY3 ,:5 6,USE3 ,H[ 6,USE
,MAKE ..A LI/ OR .TA# @3 ,MAKE A LI/
OR TA# :5 A PRO#M REQUIRES Y 6RECORD1
G5]ATE1 OR ORGANIZE 9=M,N43 ,MAKE A TA#
) COLUMNS1 R[S1 & ANY GIV5 9=M,N4
,G5]ATE A SY/EMATIC LI/ T C HELP Y SOLVE
! PRO#M4
.,"W .BACKW>D @3 ,"W BACKW>D :5 A
PRO#M GIVES Y AN 5D RESULT & Y NE$ 6F9D
2G9N+ 3DI;NS43 ,"W BACKW>D F ! GIV5
9=M,N UNTIL Y SOLVE ! PRO#M4 ,"W =W>D "?
! PRO#M 6*ECK YR ANSW]4
..,GUESS1 *ECK1 & .REVISE @3 ,GUESS1
*ECK1 & REVISE :5 Y NE$ A PLACE 6/>T OR
Y WANT 6SEE H[ ! PRO#M "WS43 ,MAKE A
R1SONA# GUESS4 ,*ECK 6SEE IF YR GUESS
SOLVES ! PRO#M4 ,IF X DOES N1 REVISE YR
GUESS & *ECK AG4
..,SOLVE A SIMPL] .PRO#M @3 ,SOLVE A
SIMPL] PRO#M :5 A PRO#M C 2 MADE EASI]
0US+ SIMPL] NUMB]S43 ,?9K (A WAY 6MAKE !
PRO#M SIMPL]4 ,SOLVE ! SIMPL] PRO#M1 !N
USE :AT Y LE>N$ 6SOLVE ! ORIG9AL PRO#M4
,EXAMPLE ,LEE "WS Z A CA%I]4 ,9 H[ _M
DI6]5T WAYS C ,LEE MAKE @4#.EJ 9 *ANGE
US+ QU>T]S1 DIMES1 & NICKELS8
,USE ! /RATEGY ..MAKE A LI/ OR .TA#4
,!N C.T ! NUMB] ( DI6]5T WAYS4
99 ,LEE C MAKE @4#.EJ 9 QU>T]S1 DIMES1
& NICKELS 9 #AJ DI6]5T WAYS4
.,EXAMPLE ,9 A CAFET]IA1 #C COOKIES
CO/ @4#.EJ LESS ?AN A S&WI*4 ,IF A S&WI*
CO/S 4#D.BE1 H[ M* DOES "O COOKIE CO/8
,USE ! /RATEGY ."W .BACKW>D4
#D.BE - #J.EJ .K #C.GE ..,CO/ ( #C
.COOKIES
#C.GE @/ #C .K #A.BE ..,CO/ ( #A
.COOKIE
.,,*ECK #A.BE .;,X .#C .K #C.GE ..,CO/
( #C .COOKIES
#C.GE @+ #J.EJ .K #D.BE .,CO/ .(
.S&WI*
99 ,"O COOKIE CO/S 4#A.BE4
------------------------------------#III
,,SKILLS ,,REVIEW ,,H&BOOK
,EXAMPLE ,NOLANS CLASS HAS #F M BOYS
?AN GIRLS4,"! >E #BH /UD5TS ALT4 ,H[ _M
GIRLS >E 9 ,NOLANS CLASS8
,USE ! /RATEGY ..GUESS1 *ECK1 &
.REVISE4 ,GUESS A NUMB] ( GIRLS T IS
LESS ?AN HALF ( #BH4
.,F/ .GUESS3 #AB GIRLS1 #AB @+ #F .K
#AH BOYS1 #AB @+ #AH .K #CJ /UD5TS .,TOO
.HI<
.,SECOND .GUESS3 #AJ GIRLS1 #AJ @+ #F
.K #AF BOYS1 #AJ @+ #AF .K #BF /UD5TS
.,TOO .L[
.,?IRD .GUESS3 #AA GIRLS1 #AA @+ #F .K
#AG BOYS1 #AA @+ #AG .K #BH /UD5TS
.,CORRECT
,"! >E #AA GIRLS 9 ,NOLAN'S CLASS4
,EXAMPLE ,H[ _M DIAGONALS DOES A
REGUL> DECAGON H8
,USE ! /RATEGY ..SOLVE A SIMPL] PRO#M4
.,A DECAGON HAS #AJ SIDES1 S F9D ! NUMB]
( DIAGONALS ( POLYGONS ) FEW] SIDES &
LOOK =A PATT]N4
,NOTICE T ! DI6];E (! NUMB]S (
DIAGONALS = 3SECUTIVE FIGURES KEEPS
9CR1S+ 0#A3
#B--#J .K #B
#E--#B .K #C
#I--#E .K #D
#AD--#I .K #E
,S1 AN #H-SID$ POLYGON HAS #AD @+ #F
.K #BJ DIAGONALS1 A #I-SID$ POLYGON HAS
#BJ @+ #G .K #BG DIAGONALS1 &A #AJ-SID$
POLYGON HAS #BG @+ #H .K #CE DIAGONALS4
99 ,A REGUL> DECAGON 7A #AJ-SID$
POLYGON7 HAS #CE DIAGONALS4
,PRACTICE
.#A4 ,B5 HAS A 3C]T AT #G3CJ ,P4,M4
,F/ HE M/ D
.#B H\RS ( HOME"W4 ,!N1 D9N] &A %[] W
TAKE AB #DE M9UTES4 ,B5 WANTS 6ALL[ A
HALF H\R 6GET 6! 3C]T4 ,:AT "T %D ,B5
/>T 8 HOME"W8
.#B4 ,QU9N & ,KYLE COLLECT$ #HG
ALUM9UM CANS 6RECYCLE4 ,QU9N COLLECT$
TWICE Z _M CANS Z ,KYLE4 ,H[ _M CANS DID
EA* P]SON COLLECT8
.#C4 ,9 H[ _M DI6]5T WAYS C ?REE SI/]S
=M A L9E AT A TICKET BOO?8
.#D4 ,! #H ;,X #H GRID AT ! "R HAS "S
#A ;,X #A SQU>ES1 "S #B ;,X #B SQU>ES1
"S #C ;,X #C SQU>ES1 & S ON4 ,H[ _M
TOTAL SQU>ES DOES ! GRID H8
.#E4 ,IF ,KALEI< DRAWS #BJ DI6]5T
DIAMET]S 9 A CIRCLE1 96H[ _M "PS WI !
CIRCLE 2 DIVID$8
.#F4 ,SIX FRS =M A T5NIS L1GUE4 ,EA*
FR W PLAY A MAT* ) E O!R FR4 ,H[ _M
MAT*ES W 2 PLAY$8
.#G4 ,SUSAN HAS #AC CO9S 9 H] POCKET
)A TOTAL VALUE ( 4#A.JE4 ,%E HAS ONLY
DIMES & NICKELS4 ,H[ _M ( EA* TYPE ( CO9
DOES ,SUSAN H8
-----------------------------------#AJJJ
,LOGICAL ,>GU;T
,,SKILLS ,,REVIEW ,,H&BOOK
,A LOGICAL >GU;T HAS TWO GIV5 /ATE;TS1
CALL$ .PREMISES @1 &A /ATE;T1 CALL$ A
.3CLU.N @1 T FOLL[S F ! PREMISES4 ,2L IS
AN EXAMPLE4
.,PREMISE .#A ,IF A TRIANGLE HAS A "R
ANGLE1 !N X IS A "R TRIANGLE4 .,PREMISE
.#B ,9 .,,ABC1 .;,B IS A "R ANGLE4
.,3CLU.N .,,ABC IS A "R TRIANGLE4
,LRS >E (T5 US$ 6REPRES5T ! /ATE;TS (A
LOGICAL >GU;T & 6WRITE A PATT]N =!
>GU;T4 ,! TA# 2L GIVES FIVE TYPES (
LOGICAL >GU;TS4 ,9 ! EXAMPLES1 .;P1 .;Q
@1 & ;R REPRES5T ! FOLL[+ /ATE;TS4
.;P3 A FIGURE IS A SQU>E
.;Q3 A FIGURE IS A RECTANGLE
.;R3 A FIGURE IS A P>ALLELOGRAM
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,TYPE ( ,>GU;T3 ,PATT]N3 ,EXAMPLE
,DIRECT ,>GU;T3 ,IF .;P IS TRUE1 !N
.;Q IS TRUE4 .;P IS TRUE4 ,"!=E1 .;Q IS
TRUE4 @3 ,IF .,,ABCD IS A SQU>E1 !N X IS
A RECTANGLE4 .,,ABCD IS A SQU>E4 ,"!=E1
.,,ABCD IS A RECTANGLE4
,9DIRECT ,>GU;T3 ,IF .;P IS TRUE1 !N
.;Q IS TRUE4 .;Q IS N TRUE4 ,"!=E1 .;P
IS N TRUE4 @3 ,IF .,,ABCD IS A SQU>E1 !N
X IS A RECTANGLE4 .,,ABCD IS N A
RECTANGLE4 ,"!=E1 .,,ABCD IS N A SQU>E4
,*A9 ,RULE3 ,IF .;P IS TRUE1 !N .;Q IS
TRUE4 ,IF .;Q IS TRUE1 !N .;R IS TRUE4
,"!=E1 IF .;P @1 !N R4 @3 ,IF .,,ABCD IS
A SQU>E1 !N X IS A RECTANGLE4 ,IF
.,,ABCD IS A RECTANGLE1 !N X IS A
P>ALLELOGRAM4 ,"!=E1 IF .,,ABCD IS A
SQU>E1 !N X IS A P>ALLELOGRAM4
.,OR ,RULE @3 .;P IS TRUE OR CJ IS
TRUE4 .;P IS N TRUE4 ,"!=E1 .;Q IS TRUE4
@3 .,,ABCD IS A SQU>E OR A RECTANGLE4
.,,ABCD IS N A SQU>E4 ,"!=E1 .,,ABCD IS
A RECTANGLE4
.,& ,RULE @3 .;P & .;Q >E N BO? TRUE4
.;Q IS TRUE4 ,"!=E1 .;P IS N TRUE4 @3
,,ABCD IS N BO? A SQU>E &A RECTANGLE4
.,,ABCD IS A RECTANGLE4 ,"!=E1 .,,ABCD
IS N A SQU>E4
,AN >GU;T T FOLL[S "O ( ^! PATT]NS
CORRECTLY HAS A .VALID .3CLU.N4
,EXAMPLE ,/ATE :E!R ! 3CLU.N IS .VALID
OR .9VALID4 ,IF ! 3CLU.N IS VALID1 "N !
TYPE ( LOGICAL >GU;T US$4
.A4 ,IF X IS RA9+ AT NOON1 ,PET]'S
FAMILY W N H A PICNIC LUN*4 ,PET]'S
FAMILY _H A PICNIC LUN*4 ,"!=E1 X 0 N
RA9+ AT NOON4
99 ,! 3CLU.N IS VALID4 ,? IS AN
EXAMPLE ( 9DIRECT >GU;T4
.B4 ,IF A TRIANGLE IS EQUILAT]AL1 !N X
IS AN ACUTE TRIANGLE4 ,TRIANGLE .,,XYZ
.IS AN ACUTE TRIANGLE4 ,"!=E1 TRIANGLE
.,,XYZ IS EQUILAT]AL4
99 ,! 3CLU.N IS 9VALID4
.C4 ,IF .;X .K #D1 !N .#B;X--.#G .K
#A4 ,IF #B;X--#G .K #A1 !N .#B;X .K #H4
;X .K #D4 ,"!=E1 IF .;X .K #D1 !N #B;X
.K #H4
99 ,! 3CLU.N IS VALID4 ,? IS AN
EXAMPLE (! *A9 RULE4
.D4 ,IF X IS AT L1/ #HJ;DG;,F \TSIDE
TD1 Y W G SWIMM+4 ,X IS #HE;DG;,F \TSIDE
TD4 ,"!=E1 Y W G SWIMM+4
99 ,! 3CLU.N IS VALID4 ,? IS AN
EXAMPLE ( DIRECT >GU;T4
-----------------------------------#AJJA
,,SKILLS ,,REVIEW ,,H&BOOK
,A .-P.D ./ATE;T HAS TWO OR M "PS JO9$
0.OR OR .&4
99 ,= AN .& -P.D /ATE;T 6BE TRUE1 EA*
"P M/ 2 TRUE4
99 ,= AN .OR -P.D /ATE;T 6BE TRUE1 AT
L1/ "O "P M/ 2 TRUE4
,EXAMPLE ,/ATE :E!R ! -P.D /ATE;T IS
.TRUE OR .FALSE4
A4
99 ,TRUE1 2C EA* "P IS TRUE4
B4
99 ,FALSE1 2C "O "P IS FALSE4
C4
99 ,TRUE1 2C AT L1/ "O "P IS TRUE4
;D
99 ,FALSE1 2C E "P IS FALSE4
,PRACTICE
,/ATE :E!R ! 3CLU.N IS .VALID OR
.9VALID4 ,IF ! 3CLU.N IS VALID1 "N !
TYPE ( LOGICAL >GU;T US$4
.#A4 ,IF ,SCOTT GOES 6! /ORE1 !N HE W
BUY SUG>4 ,IF HE BUYS SUG>1 !N HE W BAKE
COOKIES4 ,SCOTT GOES 6! /ORE4 ,"!=E1 HE
W BAKE COOKIES4
.#B4 ,IF A TRIANGLE HAS AT L1/ TWO
3GRU5T SIDES1 !N X IS ISOSCELES4
,TRIANGLE .,,MNP HAS SIDES #E IN41 #F
IN41 & #E IN4 L;G4 ,"!=E1 TRIANGLE
.,,MNP IS ISOSCELES4
.#C4 ,IF A HORSE IS AN ,>ABIAN1 !N X
IS LESS ?AN #AF H&S TALL4 ,&REA'S HORSE
IS #AC H&S TALL4 ,"!=E1 ,&REA'S HORSE IS
AN ,>ABIAN4
.#D4 ,IF A FIGURE IS A RHOMBUS1 !N X
HAS F\R SIDES4 ,FIGURE .,,WXYZ .HAS F\R
SIDES4 ,"!=E1 .,,WXYZ IS A RHOMBUS4
.#E4 LEFF _C BUY BO? A NEW COAT & NEW
BOOTS4 ,JEFF DECIDES 6BUY NEW BOOTS4
,"!=E1 ,JEFF _C BUY A NEW COAT4
.#F4 ,IF .;X .K #J1 !N .;Y .K #D4 ,IF
.;Y .K #D1 !N .;Z .K .#G4 ,"!=E1 IF .;Z
.K #G1 !N .;X .K #J4
.#G4 ,KATE W ORD] EI TACOS OR BURRITOS
= LUN*4 ,KATE DOES N ORD] TACOS = LUN*4
,"!=E1 ,KATE ORD]S BURRITOS = LUN*4
.#H4 ,IF A TRIANGLE IS EQUILAT]AL1 !N
X IS EQUIANGUL>4 ,TRIANGLE .,,ABC IS N
EQUIANGUL>4 ,"!=E1 TRIANGLE .,,ABC IS N
EQUILAT]AL4
.#I4 ,AN ANIMAL _C 2 BO? A FI% &A
BIRD4 ,C\RTNEY'S PET IS N A FI%4 ,"!=E1
,C\RTNEY'S PET M/ 2 A BIRD4
,/ATE :E!R ! -P.D /ATE;T IS .TRUE OR
.FALSE4
..#AJ4 --#G "K --.#E & --.#E "K --.#F
..#AA4 #F .1 .#B OR .#H "K .#D
..#AB4 #J "K --.#A OR .#E .1 .#E
..#AC4 #D "K .#C OR .#AB .1 .#AC
..#AD4 #C "K .#E & --.#C "K --.#E
..#AE4 #A .K --.#A OR .#A .K .#A OR
.#A .K .#J
..#AF4 #G "K .#H & .#H "K .#AB
..#AG4 --#B "K .#B & .#C .1 .#B
..#AH4 #C7--#D7 .K .#AB OR --.#C7.#D7
.K .#AB
..#AI4 --#H .1 .#H OR --.#H .K .#H OR
--.#H .1 .#J
.#BJ4 #ADJ @6.K #ADE OR .#ADJ .1
--#ADE OR --.#ADJ "K --#ADE
..#BA4 --#H7#I7 .K --.#GB & ..#H
7--#I7 .K --.#GB
..#BB4 #BB "K .#BC & --..#BB "K --#BC
& #BC .1 .#BB
-----------------------------------#AJJB
,3DI;NAL ,/ATE;TS & ,C.T]EXAMPLES
,,SKILLS ,,REVIEW ,,H&BOOK
.,A .3DI;NAL ./ATE;T HAS TWO "PS1 A
HYPO!SIS &A 3CLU.N4 ,:5 A 3DI;NAL /ATE;T
IS WRITT5 9 .IF-.!N .=M @1 ! 8IF0 "P
3TA9S ! .HYPO!SIS &! 8!N0 "P 3TA9S !
.3CLU.N4 ,AN EXAMPLE (A 3DI;NAL /ATE;T
IS %[N 2L4
,! .3V]SE (A 3DI;NAL /ATE;T IS =M$
0SWIT*+ ! HYPO!SIS &! 3CLU.N4 ,! 3V]SE
(! /ATE;T ABV IS Z FOLL[S3
,IF ..EA* ANGLE (A TRIANGLE M1SURES
.#FJ;DG @1 !N ..! TRIANGLE IS
.EQUIANGUL>4
,EXAMPLE ,REWRITE ! 3DI;NAL /ATE;T 9
IF-!N =M4 ,!N WRITE XS 3V]SE & TELL :E!R
! 3V]SE IS .TRUE OR .FALSE4
.A4 ,BOB W E>N 4#BJ 0M[+ ! LAWN4
.,IF-.!N .=M3 ,IF ,BOB M[S ! LAWN1 !N
HE W E>N 4#BJ4
.,3V]SE3 ,IF ,BOB E>NS 4#BJ1 !N HE M[$
! LAWN4 ,FALSE
.B4 .;X .K .#H :5 #E;X @+ #A .K #DA4
.,IF-.!N .=M3 ,IF #E;X @+ #A .K #DA1
!N .;X .K #H4
.,3V]SE3 ,IF .;X .K #H1 !N #E;X @+ #A
.K #DA4 ,TRUE
,A .BICONDI;NAL ./ATE;T IS A /ATE;T T
HAS ! ^WS 8IF & ONLY IF40 ,Y C WRITE A
3DI;NAL /ATE;T & XS 3V]SE TGR Z A
BICONDI;NAL /ATE;T4
..,A TRIANGLE IS .EQUIANGUL> IF & ONLY
IF ..EA* ANGLE (! TRIANGLE M1SURES
.#FJ;DG4
,A BICONDI;NAL /ATE;T IS TRUE ONLY :5
! 3DI;NAL /ATE;T & XS 3V]SE >E BO? TRUE4
,EXAMPLE ,TELL :E!R ! BICONDI;NAL
/ATE;T IS .TRUE .OR .FALSE4 ,EXPLA94
.A4 ,AN ANGLE M1SURES #IJ;DG IF & ONLY
IF X IS A "R ANGLE4
.,3DI;NAL3 ,IF AN ANGLE IS A "R ANGLE1
!N X M1SURES #IJ;DG,TRUE
.,3V]SE3 ,IF AN ANGLE M1SURES #IJ;DG1
!N X IS A "R ANGLE4 ,TRUE
99 ,! BICONDI;NAL /ATE;T IS TRUE 2C !
3DI;NAL & XS 3V]SE >E BO? TRUE4
.B4 ,BONNIE HAS 4#EJ IF & ONLY IF %E
HAS TWO QU>T]S4
.,3DI;NAL3 ,IF ,BONNIE HAS TWO QU>T]S1
!N %E HAS @4#.EJ4 ,TRUE
.,3V]SE3 ,IF ,BONNIE HAS @4#.EJ1 !N %E
HAS TWO QU>T]S4 ,FALSE
99 ,! BICONDI;NAL /ATE;T IS FALSE 2C !
3V]SE IS N TRUE4
-----------------------------------#AJJC
,,SKILLS ,,REVIEW ,,H&BOOK
,A .C.T]EXAMPLE IS AN EXAMPLE T %[S T
A /ATE;T IS FALSE4
,EXAMPLE ,TELL :E!R ! /ATE;T IS .TRUE
OR .FALSE4 ,IF FALSE1 GIVE A
C.T]EXAMPLE4
.A4 ,IF A POLYGON HAS F\R SIDES &
OPPOSITE SIDES >E P>ALLEL1 !N X IS A
RECTANGLE4
99 ,FALSE4 ,A C.T]EXAMPLE IS !
P>ALLELOGRAM %[N4
.B4 ,IF ;X #B .K #DI1 !N .;X .K #G4
99 ,FALSE4 ,A C.T]EXAMPLE IS .;X .K
--#G1 2C 7--#G7 .K #DI4
,PRACTICE
,REWRITE ! 3DI;NAL /ATE;T 9 IF-!N =M4
,!N WRITE XS 3V]SE & TELL :E!R ! 3V]SE
IS .TRUE .OR .FALSE4
.#A4 ,! GRAPH (! EQU,N .;Y .K .MX @+
.;B IS A L9E4
.#B4 ,Y W E>N 4#CE = "W+ #E H\RS4
.#C4 ,A2Y C G SWIMM+ IF %E F9I%ES H]
HOME"W4
.#D4 ,9 A "R TRIANGLE1 ! SUM (! SQU>ES
(! L5G?S (! LEGS EQUALS ! SQU>E (! L5G?
(! HYPOT5USE4
.#E4 .;X .K #E :5 .#D;X @+ #H .K #BH4
.#F4 ,! SUM ( TWO EV5 NUMB]S IS AN EV5
NUMB]4
,TELL :E!R ! BICONDI;NAL /ATE;T IS
.TRUE OR .FALSE4 .,EXPLA94
.#G4 ,TWO L9ES >E P]P5DICUL> IF & ONLY
IF !Y 9T]SECT 6=M A "R ANGLE4
.#H4 ;X #C .K #BG IF & ONLY IF .;X .K
#C4
.#I4 ,A VEGETA# IS A C>ROT IF & ONLY
IF X IS ORANGE4
.#AJ4 ,A RHOMBUS IS A SQU>E IF & ONLY
IF X HAS F\R "R ANGLES4
.#AA4 ,! GRAPH (A FUNC;N IS A P>ABOLA
IF & ONLY IF ! FUNC;N IS .;Y .K .;X
.#AB4 ,AN 9TEG] IS ODD IF & ONLY IF X
IS N EV54
,TELL :E!R ! /ATE;T IS .TRUE OR
.FALSE4 ,IF FALSE1 GIVE A C.T]EXAMPLE4
.#AC4 ,IF AN 9TEG] IS N NEGATIVE1 !N X
IS POSITIVE4
.#AD4 ,IF Y 7 BORN 9 ! SUMM]1 !N Y 7
BORN 9 ,JULY4
.#AE4 ,IF A POLYGON HAS EXACTLY #E
3GRU5T SIDES1 !N ! POLYGON IS A P5TAGON4
.#AF4 ,IF ;X .K --#F1 !N ;X #B .K #CF4
.#AG4 ,IF .;,B IS #F 9*ES F .,A & #H
9*ES F ;,C1 !N .,A IS #AD 9*ES F ,C4
.#AH4 ,IF A TRIANGLE IS ISOSCELES1 !N
X IS OBTUSE4
.#AI4 ,IF ,*>LIE HAS 4#A.JJ 9 CO9S1 !N
HE HAS F\R QU>T]S4
.#BJ4 ,IF Y >E 9 ,MONTANA1 !N Y >E 9 !
,UNIT$ ,/ATES4
-----------------------------------#AJJD
,,SKILLS ,,REVIEW ,,H&BOOK
,V5N ,DIAGRAMS
,A .,V5N .DIAGRAM USES %APES 6%[ H[
SETS >E RELAT$4
,EXAMPLE
,DRAW A ,V5N DIAGRAM (! POSITIVE
9TEG]S LESS ?AN #AC ": SET .,A 3SI/S (
FACTORS ( #AB & SET .;,B 3SI/S ( EV5
NUMB]S4
,POSITIVE 9TEG]S LESS ?AN #AC3 #A1 #B1
#C1 #D1 #E1 #F1 #G1 #H1 #I1 #AJ1 #AA1
#AB
,SET4 ,A 7FACTORS ( #AB73 #A1 #B1 #C1
#D1 #F1 #AB ,SET .;,B 7EV5 NUMB]S73 #B1
#D1 #F1 #H1 #AJ1AB ,BO? SET .,A & SET
.;,B3 #B1 #D1 #F1 #AB ,NEI SET ,A NOR
SET .;,B3 #E1 #G1 #I1 #AA
,EXAMPLE
,USE ! ,V5N DIAGRAM ABV 6DECIDE IF !
/ATE;T IS .TRUE OR .FALSE4 ,EXPLA9 YR
R1SON+4
A4 ,IF A POSITIVE 9TEG] LESS ?AN #AC
IS N EV51 !N X IS N A FACTOR ( #AB4
99 ,FALSE4 #A & #C >E N EV51 B !Y >E
FACTORS ( #AB4
B4 ,ALL POSITIVE 9TEG]S LESS ?AN #AC T
>E EV5 >E FACTORS ( #AB4
99 ,FALSE4 #H & #AJ >E EV51 B !Y >E N
FACTORS ( #AB4
,PRACTICE
,DRAW A ,V5N DIAGRAM (! SETS DESCRIB$4
.#A4 ,(! POSITIVE 9TEG]S LESS ?AN #AA1
SET ,A 3SI/S ( FACTORS ( #AJ & SET .;,B
3SI/S ( ODD NUMB]S4
.#B4 ,(! POSITIVE 9TEG]S LESS ?AN #AJ1
SET .,A 3SI/S ( PRIME NUMB]S & SET .;,B
3SI/S ( EV5 NUMB]S4
.#C4 ,(! POSITIVE 9TEG]S LESS ?AN #BE1
SET ,A 3SI/S ( MULTIPLES ( #C & SET .;,B
3SI/S ( MULTIPLES ( #D4
,USE ! ,V5N DIAGRAMS Y DREW 9
,EX]CISES #A-C 6DECIDE IF ! /ATE;T IS
.TRUE OR .FALSE4 .,EXPLA9 YR R1SON+4
.#D4 ,! ONLY FACTORS ( #AJ LESS ?AN
#AA T >E N ODD >E #B & #AJ4
.#E4 ,IF A NUMB] IS NEI A MULTIPLE (
#C NOR A MULTIPLE ( #D1 !N X IS ODD4
.#F4 ,ALL PRIME NUMB]S LESS ?AN #AJ >E
N EV54
.#G4 ,IF A POSITIVE ODD 9TEG] LESS ?AN
#AA IS A FACTOR ( #AJ1 !N X IS #E4
.#H4 ,"! >E #B POSITIVE 9TEG]S LESS
?AN #BE T >E BO? A MULTIPLE ( #C &A
MULTIPLE ( #D4
.#I4 ,IF A POSITIVE EV5 9TEG] LESS ?AN
#AJ IS PRIME1 !N X IS #B4
-----------------------------------#AJJE
,M1N1 ,M$IAN1 ,MODE1 & ,RANGE
,,SKILLS ,,REVIEW ,,H&BOOK
,M1N1 M$IAN1 & MODE >E M1SURES (
C5TRAL T5D5CY2 !Y M1SURE ! C5T] ( DATA4
,RANGE IS A M1SURE ( 4P].N2 X M1SURES !
SPR1D ( DATA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,! .M1N (A DATA SET IS ! SUM (! VALUES
DIVID$ 0! NUMB] ( VALUES4 ,! M1N IS AL
CALL$ ! .AV]AGE4 @3 ,! .M$IAN (A DATA
SET IS ! MI4LE VALUE :5 ! VALUES >E
WRITT5 9 NUM]ICAL ORD]4 ,IF A DATA SET
HAS AN EV5 NUMB] ( VALUES1 ! M$IAN IS !
M1N (! TWO MI4LE VALUES4 @3 ,! .MODE (A
DATA SET IS ! VALUE T O3URS MO/ (T54 ,A
DATA SET C H NO MODE1 "O MODE1 OR M ?AN
"O MODE4 @3 ,! .RANGE (A DATA SET IS !
DI6];E 2T ! GRTE/ VALUE &! L1/ VALUE4
,EXAMPLE
,F9D ! M1N1 M$IAN1 MODE7;S71 & RANGE
(! DATA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,"D @3 ,SUN"D3 ,MON"D3 ,TUES"D3
,W$NES"D3 ,?URS"D3 ,FRI"D3 ,SATUR"D
.,TEMP]ATURE7;DG.;,F7 @3 #GF3 #GD3
#GJ3 #FI3 #GJ3 #GE3 #GH
.,M1N ,ADD ! VALUES4 ,!N DIVIDE 0!
NUMB] ( VALUES4
#GF @+ #GD @+ #GJ @+ #FI @+ #GJ @+ #GE
@+ #GH .K #EAB
M1N .K #EAB @/ #G #GC ,! .M1N (! DATA
IS AB #GC;DG,F4
.,M$IAN ,WRITE ! VALUES 9 ORD] F L1/
6GRTE/4 ,F9D ! MI4LE VALUE 7;S7
#FI1 #GJ1 #GJ1 #GD1 #GE1 #GF1 #GH
M$IAN .K #GD ,! .M$IAN (! DATA IS
#GD;DG;,R
.,MODE ,F9D ! VALUE T O3URS MO/ (T54
MODE .K #GJ ,! .MODE (! DATA IS
#GJ;DG,F4
.,RANGE ,SUBTRACT ! L1/ VALUE F !
GRTE/ VALUE4
RANGE .K #GH--#FI .K #I ,! .RANGE (!
DATA IS #I;DG,F4
,PRACTICE
,F9D ! M1N1 M$IAN1 MODE7;S71 & RANGE
(! DATA4
.#A4 ,A"P;T R5TS3 4#FEJ1 4#HJJ1 4#GJJ1
4#EBE1 4#FGE1 4#GEJ1 4#EJJ1 4#FEJ1 4#GBE
.#B4 ,AGES ( NEW DRIV]S3 #AE1 #AE1
#AE1 #AE1 #AF1 #AF1 #AF1 #AF1 #AF1
#AG1AG1 #AG1 #AH1 #AH
.#C4 ,MON?LY CELL-PH"O M9UTES3 #EHA1
#GAC1 #DBC1 #HEB1 #IDH1 #CCG1 #HAJ1
#FJD1 #HIG
.#D4 ,PRICES (A ;,,CD3 4#AB.IH1
4#AD.II1 4#AC.DI1 4#AB.IH1 4#AC.HI1
4#AF.IH1 4#AA.IH
.#E4 ,COOKIES 9 A BAT*3 #CF1 #FJ1 #EB1
#DD1 #DH1 #DE1 #DH1 #DA1 #FJ1 #DE1 #CH1
#EE1 #FJ1 #DH1 #DJ
.#F4 ,AGES ( FAMILY MEMB]S3 #DA1 #DE1
#H1 #AJ1 #DJ1 #DD1 #C1 #E1 #DB1 #DB1
#AC1 #AD1 #FG1 #GJ
.#G4 ,H\RLY RATES ( PAY3 4#H.HJ1
4#F.EJ1 4#AJ.HE1 4#G.IJ1 4#I.EJ1 4#I1
4#H.GJ1 4#AB.CE
.#H4 ,WEEKLY QUIZ SCORES3 #H1 #I1 #H1
#AJ1 #AJ1 #G1 #I1 #H1 #I1 #I1 #AJ1 #G1
#H1 #F1 #AJ1 #I1 #I1 #H1 #H1 #AJ
.#I4 ,P ON A BUS3 #I1 #AD1 #E1 #BB1
#AH1 #CJ1 #F1 #BE1 #AH1 #AB1 #AE1 #AJ1
#H1 #BB1 #AJ1 #AA1 #BJ
-----------------------------------#AJJF
,GRAPH+ ,/ATI/ICAL ,DATA
,,SKILLS ,,REVIEW ,,H&BOOK
,"! >E _M WAYS 64PLAY DATA4 ,AN
APPROPRIATE GRAPH C HELP Y ANALYZE DATA4
,! TA# AT ! "R SUMM>IZES H[ DATA >E %[N
9 "S /ATI/ICAL GRAPHS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,B> .,GRAPH @3 ,-P>ES DATA 9
CATEGORIES4
.,CIRCLE .,GRAPH @3 ,-P>ES DATA Z "PS
(A :OLE4
.,L9E .,GRAPH @3 ,%[S DATA *ANGE OV]
"T4
,EXAMPLE
,USE ! B> GRAPH 6ANSW] ! "QS4
A4 ,ON : "D (! WEEK 7 ! GRTE/ NUMB] (
C>S P>K$ 9 ! /UD5T LOT8
99 ,! TALLE/ B> ON ! GRAPH IS =
,FRI"D4 ,S1 ! ANSW] IS ,FRI"D4
B4 ,H[ _M C>S 7 P>K$ 9 ! /UD5T LOT ON
,MON"D8
99 ,! B> = ,MON"D %[S T AB #GJ C>S 7
P>K$ 9 ! /UD5T LOT4
,EXAMPLE
,USE ! CIRCLE GRAPH 6ANSW] ! "QS4
A4 ,: TYPE ( TRANSPORT,N IS US$ ALM
HALF ! "T8
99 ,ALM HALF (! TOTAL >EA (! CIRCLE IS
LABEL$ 8,C> #DE@3P40 ,S1 A C> IS US$ ALM
HALF ! "T4
B4 ,: TYPE ( TRANSPORT,N IS US$ ! L1/
(T58
99 ,! SMALLE/ "P (! CIRCLE IS LABEL$
8,BUS #BJ@3P40 ,S1 A BUS IS US$ ! L1/
(T54
,EXAMPLE
,USE ! L9E GRAPH 6ANSW] ! "QS4
A4 ,9 : MON? 7;S7 0 ,JAMIE'S BAL.E
4#BEJ8
99 ,! PO9TS ON ! GRAPH 6! "R ( 4#BEJ
%[ T ,JAMIE'S BAL.E 0 4#BEJ 9 ,MAY &
,DECEMB]4
B4 ,2T : TWO 3SECUTIVE MON?S DID
,JAMIE'S BAL.E 9CR1SE ! MO/8
99 ,(! GRAPH'S L9E SEG;TS T H POSITIVE
SLOPE1 ! GRAPH IS /EEPE/ F ,JUNE 6,JULY4
,S1 ,JAMIE'S BAL.E 9CR1S$ ! MO/ 2T ,JUNE
& ,JULY4
-----------------------------------#AJJG
,,SKILLS ,,REVIEW ,,H&BOOK
,PRACTICE
,USE ! L9E GRAPH 6ANSW] ,EX]CISES
#A-E4
.#A4 ,AT : H\R DID ,F]R>O'S H #BB
D9]S8
.#B4 ,AT : H\R DID ,F]R>O'S H ! MO/
D9]S8
.#C4 ,H[ _M D9]S 7 AT ,F]R>O'S AT #AA
,P4,M48 ,7 !Y G"O 0MIDNI<T8
.#D4 ,2T : TWO 3SECUTIVE H\RS DID !
NUMB] ( D9]S AT ,F]R>O'S *ANGE ! MO/8
.#E4 ,H[ _M FEW] D9]S 7 AT ,F]R>O'S AT
#AJ ,P4,M4 ?AN AT #F ,P4,M48
,USE ! B> GRAPH 6ANSW] ,EX]CISES #F-H4
.#F4 ,9 : S1SON 7 ! FEWE/ /UD5TS BORN8
.#G4 ,9 : S1SON7;S7 7 #G /UD5TS BORN8
.#H4 ,H[ _M M /UD5TS 7 BORN 9 SPR+ ?AN
9 SUMM]8
,USE ! CIRCLE GRAPH 6ANSW] ,EX]CISES
#I-AA4
.#I4 ,:AT IS ! H1T S\RCE ( M ?AN HALF
! HOMES 9 ! ,UNIT$ ,/ATES8
.#AJ4 ,:AT P]C5T ( HOMES 9 ! ,UNIT$
,/ATES >E H1T$ ) ELECTRIC;Y8
.#AA4 ,IF Y R&OMLY SELECT$ #EJJ ,U4,S4
HOMES1 AB H[ _M WD 2 H1T$ ) FUEL OIL8
.#AB4 ,! TA# 2L %[S ! HI< TEMP]ATURES
9 DEGREES ,FAHR5HEIT = "O WEEK4 ,4PLAY !
DATA 9 A L9E GRAPH4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,MON43 ,TUES43 ,W$43 ,?URS43 ,FRI4
,SAT43 ,SUN4
.#HC @3 .#HI @3 .#GI @3 .#GC @3 .#FI
.#FG @3 .#GA
.#AC4 ,A HI< S*OOL 3DUCT$ A SURVEY
6DET]M9E ! NUMB]S ( /UD5TS 9VOLV$ 9
V>I\S S*OOL ACTIVITIES4 ,4PLAY ! SURVEY
RESULTS 9 A B> GRAPH4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,-PUT] .CLUB @3 .,MUSIC .CLUB @3
.,YE>BOOK .CLUB @3 .,DRAMADUB @3 .,/UD5T
.C\NCIL @3 .,*ESS .CLUB
.#CD @3 .#GE @3 .#AF @3 .#EG @3 .#BH
@3 .#AB
.#AD4 ,! TA# 2L %[S ! ITEMS SOLD AT A
CAFE 9 "O "D4 ,4PLAY ! DATA 9 A CIRCLE
GRAPH4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,JUICE3 ,SODA3 ,WAT]3 ,MU693 ,COOKIE
.#IE @3 .#AHJ @3 .#AJJ @3 .#EE @3 .#DJ
-----------------------------------#AJJH
,ORGANIZ+ ,/ATI/ICAL ,DATA
,,SKILLS ,,REVIEW ,,H&BOOK
,2C X IS DI6ICULT 6ANALYZE UNORGANIZ$
DATA1 X IS HELP;L 6ORGANIZE DATA US+ A
L9E PLOT1 /EM-&-L1F PLOT1 HI/OGRAM1 OR
BOX-&-:ISK] PLOT4
,EXAMPLE
,SYDNEY'S MA? TE/ SCORES >E
#IJ1HE1HH1IE1AJJ1GG1HE1AJJ1 #HJ1GG1 &
#IJ4
.A4 ,DRAW A L9E PLOT 64PLAY ! DATA4
,MAKE A NUMB] L9E F #GE 6#AJJ4 ,EA* "T
A VALUE IS LI/$ 9 ! DATA SET1 DRAW AN
;,X ABV ! VALUE ON ! NUMB] L9E4
.B4 ,DRAW A /EM-&-L1F PLOT 64PLAY !
DATA4
,F/ WRITE ! L1VES NEXT 6_! /EMS4 ,!N
ORD] ! L1VES F L1/ 6GRTE/4
.C4 ,DRAW A HI/OGRAM 64PLAY ! DATA4
,F/ MAKE A FREQU5CY TA#4 ,USE EQUAL
9T]VALS4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,SCORE3 ,T,Y3 ,FREQU5CY
#GA-HJ3 @3 #C
#HA--#IJ3 @3 #E
#IA-AJJ3 @3 #C
,!N MAKE A HI/OGRAM4
.D4 ,DRAW A BOX-&-:ISK] PLOT 64PLAY !
DATA4
,WRITE ! DATA 9 ORD] F L1/ 6GRTE/4
,ORD]$ DATA >E DIVID$ 96A L[] HALF & AN
UPP] HALF 0! M$IAN4 ,! M$IAN (! L[] HALF
IS ! .L[] .QU>TILE @1 &! M$IAN (! UPP]
HALF IS ! .UPP] .QU>TILE4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.#GG @3 .#GG @3 .#HJ @3 .#HE @3 .#HE
@3 .#HH @3 .#IJ @3 .#IJ @3 .#IE @3 #AJJ3
.#AJJ
.,L[ @3 --@3 .,L[] @3 --@3 --@3
.,M$IAN @3 --@3 --@3 .,UPP] @3 --@3
.,HI<
.VALUE @3 --@3 .QU>TILE @3 --@3 --@3
--@3 --@3 --@3 .QU>TILE @3 --@3 .VALUE
,PLOT ! M$IAN1 QU>TILES1 & L[ & HI<
VALUES 2L A NUMB] L9E4 ,DRAW A BOX 2T
QU>TILES )A V]TICAL L9E "? ! M$IAN Z
%[N4 ,DRAW :ISK]S 6! L[ & HI< VALUES4
-----------------------------------#AJJI
,,SKILLS ,,REVIEW ,,H&BOOK
,PRACTICE
,USE ! FOLL[+ LI/ ( TICKET PRICES
6ANSW] ,EX]CISES #A-D3 4#EJ1 4#DB1 4#FE1
4#ED1 4#GJ1 4#FE1 4#EI1 4#CJ1 4#FG1
4#DI1 4#ED1 4#CJ1 4#GC1 4#DG1 & 4#ED4
.#A4 ,DRAW A L9E PLOT 64PLAY ! DATA4
.#B4 ,H[ _M TICKET PRICES >E 4#EJ OR
LESS8
.#C4 ,DRAW A /EM-&-L1F PLOT 64PLAY !
DATA4
.#D4 ,:AT IS ! RANGE ( TICKET PRICES
CO/S8
,USE ! FOLL[+ LI/ ( H\RLY WAGES (
EMPLOYEES 6ANSW] ,EX]CISES #E-H3 4#H.EJ1
4#F1 4#AJ1 4#AD.BE1 4#E.GE1 4#G1 4#F.EJ1
4#AD1 4#AJ1 4#I1 4#F.EJ1 4#H.BE1 4#H.EJ1
4#AA.BE1 4#G1 4#AF1 4#AB1 4#F1 4#F.GE4
.#E4 ,DRAW A HI/OGRAM 64PLAY ! DATA4
,2G9 )! 9T]VAL 4#E.JJ TO 4#F.II4
.#F4 ,COPY & -PLETE3 ,! GRTE/ NUMB] (
EMPLOYEES E>N F @8 TO @8 P] H\R4
.#G4 ,DRAW A BOX-&-:ISK] PLOT 64PLAY !
DATA4
.#H4 ,COPY & -PLETE3 ,AB HALF (!
EMPLOYEES H AN H\RLY WAGE ( @8 OR LESS4
,USE ! L9E PLOT1 : %[S ! RESULTS (A
SURVEY ASK+ P ! AV]AGE NUMB] ( ;E-MAILS
!Y RCV DAILY1 6ANSW] ,EX]CISES #I & #AJ4
.#I4 ,COPY & -PLETE3 ,MO/ P SURVEY$
RCV AN AV]AGE ( @8 ;E-MAILS P] "D4
.#AJ4 ,H[ _M P RCV AN AV]AGE ( M ?AN
#AJ ;E-MAILS P] "D8
,USE ! /EM-&-L1F PLOT1 : %[S ! WEI<TS
7IN P.DS7 ( DOGS AT AN ANIMAL %ELT]1
6ANSW] ,EX]CISES #AA-AC4
.#AA4 ,H[ _M DOGS 7 AT ! %ELT]8
.#AB4 ,F9D ! M$IAN (! DATA4
.#AC4 ,F9D ! RANGE (! DATA4
,USE ! HI/OGRAM 6ANSW] ,EX]CISES
#AD-AF4
.#AD4 ,: AGE GR\P _H ! GRTE/ ATT5D.E
AT ! BASEBALL GAME8 ,: _H ! L1/8
.#AE4 ,H[ _M *N UP 6! AGE ( #I YE>S
ATT5D$ ! BASEBALL GAME8
.#AF @4 ,: AGE GR\P _H ! SAME ATT5D.E
Z ! OLDE/ GR\P8
,USE ! BOX-&-:ISK] PLOT 6ANSW]
,EX]CISES #AG-AI4
.#AG4 ,:AT IS ! M$IAN NUMB] ( S;GS ON
,SAM'S ,,CD,'S8
.#AH4 ,:AT IS ! UPP] QU>TILE ( S;GS ON
,SAM'S ,,CD,'S8
.#AI4 ,:AT IS ! L1/ NUMB] ( S;GS ON "O
( ,SAM'S ,,CD,'S8 ,:AT IS ! GRTE/ NUMB]8
-----------------------------------#AJAJ
,EXTRA ,PRACTICE
,*APT] #A
#A.A ,GRAPH ! NUMB]S ON A NUMB] L9E4
.#A4
.#B4
.#C4
#A.A ,P]=M ! 9DICAT$ 3V].N4
.#D4 #AH FEET 69*ES
.#E4 #BJ \NCES 6P.DS
.#F4 #C YE>S 6H\RS
#A.B ,EVALUATE ! EXPRES.N =! GIV5
VALUE (! V>IA#4
.#G4 --.#B;P @+ #E :5 .;P .K --#E
.#H4 #C;X #B -- ;X @+ #G :5 ;X .K --#A
.#I4 #H;Z #C -- #F;Z :5 .;Z .K #B
#A.B ,SIMPLIFY ! EXPRES.N4
.#AJ4 #B;Y #B -- #C;Y @+ #E;Y #B
.#AA4 #D;R #B -- #E;R @+ #B;R #B @+
#AB
.#AB4 --.;W #C @+ .;W #B -- .#G;W #B
-- #H .;W #C
.#AC4 .#B7.;B @+ #E7 @+ #C7#B;FO--#AJ7
.#AD4 --#G7;T #B @+ #B7 @+ #I7;F--#B7
.#AE4 #D7;M--#C7 -- .#E7.;M #B --.;M7
#A.C ,SOLVE ! EQU,N4 ,*ECK YR SOLU;N4
.#AF4 #C;A @+ #B .K #AA
.#AG4 --#I .K .;B -- #AD
.#AH4 #H--#J.E;C .K #A
.#AI4 --#C;N--#G .K --.;N @+ #AG
.#BJ4 #AB;M .K #AE;M--#G.E
#BA4 ..#F;P @+ #A .K #BA--.#D;P
.#BB4 #F7;X @+ #A7 .K #B .;X -- #AJ
.#BC4 #D7;Y--#C7 .K #B7;Y @+ #H7
.#BD4 ;LL7;Z--#E7 .K #B7;Z @+ #F7--#AC
#A.D ,SOLVE ! EQU,N = .Y4 ,!N F9D !
VALUE ( .;Y =! GIV5 VALUE ( .X4
.#BE4 #F;Y--;X .K #AH2 ;X .K #B
.#BF4 #B;X @+ #C;Y .K #AB2 ;X .K --#F
.#BG4 #D;Y--#I;X .K --#CJ2 ;X .K #F
.#BH4 #C;X--XY .K #BJ2 ;X .K #H
.#BI4 #D;Y @+ #F;XY .K #AJ2 ;X .K --#B
.#CJ4 #E;X @+ #H;Y @+ #D;XY .K #J2 ;X
.K --#A
#A.E ,LOOK =A PATT]N 9 ! TA#4 ,!N
WRITE AN EQU,N T REPRES5TS ! TA#4
#CA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X @3 .#J @3 #A3 .#B @3 .#C
.;Y @3 .#BE @3 #BB3 .#AI @3 .#AF
#CB4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
;,X3 #A #J3 #A3 #B3 #C
.;R @3 .#A..E @3 .#D @3 .#F..E @3 .#I
#A.F ,SOLVE ! 9EQUAL;Y4 ,!N GRAPH !
SOLU;N4
.#CC4 ;X @+ #B.1#I
.#CD4 --#AC--#C;X"KLL
.#CE4 #D;X--#I "K #B;X @+ #A
.#CF4 --#C;X--#H .1 --#I;X @+#AJ
.#CG4 --#G "K ;X @+ #C "K #A
.#CH4 --#D "K #C;X--#G "K #D
.#CI4 --#I"K.K#E--#B;X"K.K#G
.#DJ4 ;X @+#C"K--#B;OR .;X --#G.1#J
.#DA4 #B;X @+ #I .1 #C OR--#E;X @+ #A
"K #J
#A.G ,SOLVE ! EQU,N4 ,*ECK = EXTRANE\S
SOLU;NS4
.#DB4 _\;G@+#E_\ .K.#D
#DC4
.#DD4 _\#AJ--#C .;T _\ .K .;T @+ #D
.#DE4 _\#C;Z@+ .;L_\ .K --.#F;Z
#A.G ,SOLVE ! 9EQUAL;Y4 ,!N GRAPH !
SOLU;N4
.#DF4 _\.A_\ "K#B
.#DG4 _\#B;C_\ .1 #AD
.#DH4 _\;G@+LL_\.1.K#B
.#DI4 _\#D;Y--#G_\ "K.K #I
.#EJ4 _\#J.BE;M @+ #C_\.1;L
.#EA4 _\;L#J--#B;P_\.1#I
.#EB4 _\O#.F;R @+ #H_\ "K #AG
.#EC4 _\#E;T--#I_\ @+ #I "K .#AJ
-----------------------------------#AJAA
,*APT] #B
,,EXTRA ,,PRACTICE
#B.A ,TELL :E!R ! REL,N IS A FUNC;N4
.,EXPLA94
#A4
#B4
#C4
#D4
#B.B ,F9D ! SLOPE (! L9E PASS+ "? !
GIV5 PO9TS4 ,!N TELL :E!R ! L9E ..RISES1
FALLS1 IS .HORIZONTAL @1 OR .IS
.V]TICAL4
.#E 7--#C1 #J71 7#E1 --#D7
.#F 7#B1 --#A71 7#H1 --#A7
.#G 7#C1 #E71 7#C1 --#AB7
.#H 7#A1 #H71 7--#A1 --#D7
#B.B ,TELL :E!R ! L9ES >E .P>ALLEL1
.P]P5DICUL> @1 OR .NEI4
.#I4 ,L9E #A3 "? 7#E1 --#D7 & 7--#D1
#B7 ,L9E #B3 "? 7--#E1 --#D7 & 7--#B1
--#B7
.#AJ4 ,L9E #A3 "? 7#J1 --#D7 & 7--#B1
#B7 ,L9E #B3 "? 7#D1 --#C7 & 7#E1 --#F7
#B.C ,GRAPH ! EQU,N US+ ANY ME?OD4
.#AA4 ;Y .K #B;X--#B
.#AB4 ;Y .K --;X @+ #B
.#AC4
.#AD4 .;X @+ #B;Y .K --#F
.#AE4 --#D;X @+ #E;Y .K #AJ
.#AF4 .;Y -- #B .K #J
.#AG4 --#B;X .K #F;Y @+ #E
.#AH4 #B;Y @+ #AJ .K --#B.E;X
#B.D ,WRITE AN EQU,N (! L9E T
SATISFIES ! GIV5 3DI;NS4
.#AI4 .;M .K #G1 .;B .K --#C
.#BJ4 ;B .K #D
.#BA4 ;M .K #J1 PASSES "? 7#G1 --#B7
.#BB4 @1 PASSES "? 7#C1 #F7
.#BC4 PASSES "? 7--#A1 --#C7 & 7#B1
#G7
.#BD4 PASSES "? 7#D1 --#B7 & 7#J1 #D7
#B.E ,! V>IA#S ;X & .;Y V>Y DIRECTLY4
,WRITE AN EQU,N T RELATES .;X & .Y4 ,!N
F9D ;Y :5 .;X.K --.#B4
.#BE4 ;X .K #B1 ;Y .K #D
.#BF4 ;X .K --#A1 ;Y .K #C
.#BG4 ;X .K --#BH1 ;Y .K --#G
.#BH4 ;X .K #F1 ;Y .K --#D
#B.F ,9 ,EX]CISES #BI & #CJ1 7A7 DRAW
A SCATT] PLOT (! DATA1 7;B7 APPROXIMATE
! BE/-FITT+ L9E1 & 7;C7 E/IMATE .;Y :5
.;X .K #AB4
.#BI @1
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X @3 .#A @3 .#B @3 .#C @3 .#D @3
.#E
.;Y @3 .#H @3 .#AA @3 .#AC @3 .#AF @3
.#AH
#CJ4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 .#A @3 .#B @3 .#C @3 .#D @3 .#E
.;Y @3 .#EJ @3 --@3 .#DA @3 .#CG @3
.#BB @3 .#BJ
#B.G ,GRAPH ! FUNC;N4 .,-P>E ! GRAPH
)! GRAPH ( .;Y .K _\.;X_\
.#CA4 ;Y .K _\;X @+ #C_\
.#CB4 ;Y .K --#B_\;X--#E_\
.#CC4 ;Y .K #C_\;X @+ ;L_\--#B
.#CD4
#B.H ,GRAPH ! 9EQUAL;Y 9 A COORD9ATE
PLANE4
.#CE4 ;X "K #D
.#CF ;Y .1.K --#B
.#CG ;Y "K.K --;X--#A
.#CH ;X @+ #B;Y .1 #H
.#CI --;X--#D;Y"K#F
.#DJ #C;X @+ #D;Y.1#AB
.#DA ;Y"K_\;X@+;L_\
.#DB ;Y.1 #C_\;X--#B_\--#A
-----------------------------------#AJAB
,*APT] #C
,,EXTRA ,,PRACTICE
#C.A ,GRAPH ! L9E> SY/EM & E/IMATE !
SOLU;N4 ,!N *ECK ! SOLU;N ALGEBRAIC,Y4
.#A ..;Y .K .#B;X -- #A
;Y .K ;X--#D
.#B .;Y .K --;X @+ #C
;Y .K --#D .;X
.#C ;X @+ #B;Y .K #F
--#E;X @+ #F;Y .K --#B
.#D --..#B;X @+ .LY .K --#G
#D;X--#AD;Y .K #AD
#C.B ,SOLVE ! SY/EM US+ ANY ALGEBRAIC
ME?OD4
.#E4 --#E;X--;Y .K --#C
.;X -- #D;Y .K #I
.#F4 #D;X--#B;Y .K --#F
--#C;X @+ ;Y .K --#C
.#G4 #D;X @+ #C;Y .K --#E
#AB;X @+ #D;Y .K #AJ
.#H4 #C;X @+ #B;Y .K #D
--#G;X--#E;Y .K --#G
#C.C ,GRAPH ! SY/EM ( 9EQUALITIES4
.#I4 ;X.1#D ;Y.1--;L
.#AJ4 ;X @+ ;Y"K--#B
;X--#C;Y.1#F
.#AA4 ;X"K#E
;Y.1#C
;Y .1 .;X
.#AB4 ;X.1--#C
.;X "K #B
.;X .#B;X @+ #C;Y "K #AJ
;Y.1--#D;X
#C.D ,SOLVE ! SY/EM US+ ANY ALGEBRAIC
ME?OD4
.#AC4 #C;X @+ ;Y -- .;Z .K--#F
--;X @+ #B;Y @+ #C;Z .K --#A
#E;X--#B;Y @+ #F;Z .K #ED
.#AD4 ;X @+ ;Y -- .;Z .K #G
#B;X--#C;Y @+ .;Z .K .#B
#D;X @+ #B;Y -- .#B;Z .K #BJ
.#AE4 --;X @+ ;Y--#B;Z .K #A.E
#D;X--;Y @+ #E;Z .K --#F
#B;X--#C;Y -- .;Z .K --#F
#B;X @+ ;Y -- .#B;Z .K #F
.#AF4 --.#F;X @+ ;Y @+ #I;Z .K #D
#B;X--#C;Y--;Z .K --#F
#H;X @+ #E;Y--#D;Z .K #AJ
#C.E ,P]=M ! 9DICAT$ OP],N4
#AG4
#AH4
#AI4
#C.F ,F9D ! PRODUCT4 ,IF ! PRODUCT IS
N DEF9$1 /ATE ! R1SON4
.#BJ4
.#BA4
.#BB4
#C.G ,EVALUATE ! DET]M9ANT (! MATRIX4
.#BC4
.#BD4
.#BE4
.#BF4
#C.G ,USE ,CRAM]'S RULE 6SOLVE ! L9E>
SY/EM4
.#BG4 #B;X @+ ;Y .K --#H
--#E;X--#B;Y .K #AC
.#BH4 #H;X @+ #C;Y .K #A
#G;X @+ #C;Y .K --#A
.#BI4 #B;X--#B;Y--#C;Z .K #I
#C;X @+ .;Z .K #AJ
;X @+ ;Y.K#J
.#CJ4 #B;X @+ ;Y @+ #C .;Z .K #D
--#H;X @+ #D;Y @+ .;Z .K --#G
;X @+ #B;Y @+ #C;Z.K--;L
#C.H ,F9D ! 9V]SE (! MATRIX4
.#CA4
.#CB4
.#CC4
.#CD4
#C.H ,USE AN 9V]SE MATRIX 6SOLVE !
L9E> SY/EM4
.#CE4 ;X @+ #C;Y .K --#D
--#B;X @+ ;Y .K --#CD
.#CF4 #B;X @+ #C;Y .K #F
--;X--#F;Y .K --#I
.#CG4 #C;X--#H;Y .K #J
#B;X @+ ;Y .K --#AI
.#CH4 .;X @+ ;Y .K #G
--#E;X @+ #C;Y .K --#C
-----------------------------------#AJAC
,,EXTRA ,,PRACTICE
,*APT] #D
#D.A ,GRAPH ! FUNC;N4 ,LABEL ! V]TEX &
AXIS ( SYMMETRY4
.#A4 .;Y .K #C;X #B @+ #E
.#B4 .;Y .K --.;X #B -- #D;X--#D
.#C4 .;Y .K --.#B;X #B @+ #D;X @+ #A
.#D4 .;Y .K .#B;X #B @+ .#E .;X @+ #F
#D.B ,GRAPH ! FUNC;N4 ,LABEL ! V]TEX &
AXIS ( SYMMETRY4
.#E4 .;Y .K #D7;X--#B7 #B @+ #A
.#F4 ;Y .K --7;X @+ #C7 #B -- #B
.#G4 ;Y .K #C7;X--;L77;X--#E7
.#H4
#D.B ,WRITE ! QUADRATIC FUNC;N 9 /&>D
=M4
.#I4 ;Y .K #G7;X @+ #B77;X @+ #D7
.#AJ4 ;Y--#B7;X @+ #E77;X--#C7
.#AA4 ;Y .K 7;X--#G7 #B @+ #G
.#AB4 ;Y .K --7;X @+ #A7 #B -- #D
#D.C ,FACTOR ! EXPRES.N4 ,IF !
EXPRES.N _C 2 FACTOR$1 SAY S4
.#AC4 ;X #B -- #D;X @+ #D
.#AD4 .;T #B -- .#AA;T -- #BF
.#AE4 ;X #B @+ #BA;X @+ #AJH
.#AF4 .;B #B -- #DJJ
#D.C ,SOLVE ! EQU,N4
.#AG4 ;X #B @+ #E;X--#AD .K #J
.#AH4 ;X #B -- LLX @+ #BD .K #J
.#AI4 .;C #B @+ #F;C .K #EE
#BJ4 .;N #B .K .#E;N
#D.D ,FACTOR ! EXPRES.N4 ,IF !
EXPRES.N _C 2 FACTOR$1 SAY S4
.#BA4 #B;X #B @+ ;X--#AE
.#BB4 #AJ;A #B -- #AI;A @+ #G
.#BC4 #C;R #B @+ #I;R--#D
.#BD4 #D;R #B @+ #H;F @+ #C
#D.D ,F9D ! Z]OS (! FUNC;N 0REWRIT+ !
FUNC;N 9 9T]CEPT =M4
.#BE4 ;Y .K .#HA;X #B -- #AF
.#BF4 ;Y--#B;X #B -- #I;X--#E
.#BG4 ;Y .K #D;X #B @+ #AH;X @+ #AH
.#BH4 ;Y .K --#C;X #B -- .#CJ;X -- #BG
#D.E ,SIMPLIFY ! EXPRES.N4
.#BI4
.#CJ4
.#CA4
.#CB4
#D.E ,SOLVE ! EQU,N4
.#CC4 .;B #B .K #H
.#CD4 .;P #B @+ #F .K #ABG
.#CE4 7;X--#E7 #B .K #AJ
.#CF4 #C7;X @+ #B7 #B -- #D .K #AA
#D.F ,WRITE ! EXPRES.N Z A -PLEX NUMB]
9 /&>D =M4
.#CG4 7#E @+ .#B;I7 @+ 7#F--#E .;I @7
.#CH4 --#C_/7#G @+ .;I @7
#CI4
#DJ4
#D.G ,SOLVE ! EQU,N 0-PLET+ ! SQU>E4
.#DA4 ;X #B @+ #F;X .K #AJ
.#DB4 ;X #B -- #I;X--#B .K #J
.#DC4 #B;C #B -- #AB;C @+ #F .K #J
.#DD4 .#C;Z #B -- .#C;Z @+ #I .K #J
#D.H ,USE ! QUADRATIC =MULA 6SOLVE !
EQU,N4
.#DE4 ;X #B @+ ;L#J;X--#AJ .K #J
.#DF4 ;X #B -- ;X--#A .K #J
.#DG4 #D;S #B @+ #CE .K #AB
.#DH4 --#B;R #B .K .;R @+ #AG
#D.I ,SOLVE ! 9EQUAL;Y US+ ANY ME?OD4
.#DI4 ;X #B -- ;L#J;X .1.K #J
.#EJ4 ;X #B -- #H;X @+ #AB "K #J
.#EA4 --;X #B @+ #G;X @+ #F .1 #A
.#EB4 #C;X #B @+ #AF;X @+ #B "K #C;X
.#D..AJ ,WRITE A QUADRATIC FUNC;N 9
/&>D =M =! P>ABOLA T PASSES "? ! GIV5
PO9TS4
.#EC4 7--#A1 --#F71 7#J1 --#G71 7#B1
#I7
.#ED4 7--#B1 --#A71 7#A1 #B71 7#C1
--#F7
.#EE4 7--#C1 #CF71 7#J1 #CF71 7#B1
#AF7
-----------------------------------#AJAD
,*APT] #E
,,EXTRA ,,PRACTICE
#E.A ,WRITE ! ANSW] 9 SCI5TIFIC NOT,N4
.#A4 7#C.D ;,X #AJ #C @77#B.H ;,X #AJ
#H @7
.#B4 7#E.H ;,X #AJ #F @7 #D
#C4
#E.A ,SIMPLIFY ! EXPRES.N4 ,TELL :
PROP]TIES ( EXPON5TS Y US$4
.#D4
#E4 7.#D;A #E .;B --#B @7 --#C
.#F4 7#B;R #C ;S #C @77;R #G ;S #E @7
.#G4
#E.B ,GRAPH ! POLYNOMIAL FUNC;N4
.#H4 .FIX7 .K ;X #D
.#I4 _/7;X7 .K ;X #C @+ ;X @+ #D
.#AJ4 .FIX7 .K --;X #C @+ #C;X
.#AA4 .FIX7 .K ;X #E @+ #B;X #C
#E.C ,P]=M ! 9DICAT$ OP],N4
.#AB4 7#D;Z #C @+ #I7 @+ 7#C;Z #B --
#D;Z--#B7
.#AC4 7;X #B @+ #C;X--#A7--7#D;X #B @+
#G7
.#AD4 7#C;X--#D7 #C
#E.D ,FACTOR ! POLYNOMIAL -PLETELY US+
ANY ME?OD4
.#AE4 #C;X #D @+ #AH;X #C @+ #BG;X #B
.#AF4 #CDC;X #C @+ #AJJJ
.#AG4 #B;X #C @+ ;X #B -- #H;X--#D
#E.D ,F9D ! R1L-NUMB] SOLU;NS (!
EQU,N4
.#AH4 #C;X #C @+ #AH;X #B .K #DH;X
.#AI4 ;X #D @+ #CB .K #AD;X #B
.#BJ4 #B;X #C @+ #DH .K #C;X #B @+
#CB;X
#E.E ,DIVIDE US+ POLYNOMIAL L;G DIVI.N
OR SYN!TIC DIVI.N4
.#BA4 7#B;X #C @+ #D;X #B -- #E;X @+
#AF7 @+ 7;,X--#C7
.#BB4 7;X #D @+ #B;X #C -- #G;X #B --
#AD7 @+ 7;X @+ #B7
#E.F ,F9D ALL R1L Z]OS (! FUNC;N4
.#BC4 .;F7.;X7 .K .#B;X #C @+ #C;X #B
-- #H;X @+ #C
.#BD4 .FIX7 .K .#B;X #D @+ ;X #C --
#EC;X #B -- #AD;X @+ #BJ
#E.G ,DET]M9E ! POSSI# NUMB]S (
POSITIVE R1L Z]OS1 NEGATIVE R1L Z]OS1 &
IMAG9>Y Z]OS (! FUNC;N4
.#BE4 .FIX7 .K --;X #C @+ #B;X #B --
LLX--#A
.#BF4 .FIX7 .K #D;X #E @+ #C;X #B --
#H;X--#AJ
.#BG4 .FIX7 .K ;X #D -- #C;X #C --
#G;X--#AC
#E.H ,E/IMATE ! COORD9ATES ( EA* TURN+
PO9T & /ATE :E!R EA* CORRESPONDS 6A
LOCAL MAXIMUM OR A LOCAL M9IMUM4 ,!N
E/IMATE ALL R1L Z]OS & DET]M9E ! L1/
DEGREE ! FUNC;N C H4
.#BH4
.#BI4
.#CJ4
#E.I ,USE F9ITE DI6];ES &A SY/EM (
EQU,NS 6F9D A POLYNOMIAL FUNC;N T FITS !
DATA 9 ! TA#4
#CA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X @3 #A3 #B3 #C3 #D3 #E3 #F
.;Y @3 #B.E3 #AA3 #BG.E3 #EE3 #IF.E3
#AEE
#CB4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X @3 #A3 #B3 #C3 #D3 #E3 #F
.;Y @3 --#G3 --#F3 #CI3 #AHH3 #EBE3
#AAEH
-----------------------------------#AJAE
,*APT] #F
#F.A ,F9D ! 9DICAT$ R1L .N? ROOT7;S7 (
.A4
.#A4 .;N .K #D1 .A .K #HA
.#B4 .;N .K #C1 .A .K #EAB
.#C4 .;N .K #E1 A .K --#BDC
#F.A ,EVALUATE ! EXPRES.N )\T US+ A
CALCULATOR4
.#D4 #CF --#A/B
.#E4 #FD #E/F
.#F4
.#G4
#F.A ,SOLVE ! EQU,N4 ,R.D ! RESULT
6TWO DECIMAL PLACES :5 APPROPRIATE4
.#H4 ;X #C .K --#H
.#I4 ;X #D @+ #I .K #IJ
.#AJ4 7;X--#C7 #E .K #FJ
.#AA4 --#D;X #F .K --#DJJ
#F.B ,SIMPLIFY ! EXPRES.N4
.#AB4 #D #E/B 99#D --#A/B
#AC4
#AD4
#AE4
#AF4
#AG4
#AH4
#AI4
#F.B ,WRITE ! EXPRES.N 9 SIMPLE/ =M4
,ASSUME ALL V>IA#S >E POSITIVE4
.#BJ4
.#BA4
.#BB4
.#BC4
#FC ,LET .;F 7;X7 .K --.;X @+ #D1
;G7;X7 .K JC #C @1 &4 ,P]=M ! 9DICAT$
OP],N & /ATE ! DOMA94
.#BD4 .;F7.;X7 @+ ;G7;X7
.#BE4 ;G7;X7 -- .;F7.;X7
.#BF4 ;G7;X7 99 .;H7.;X7
.#BG4
.#BH4 .;F 7;G7;X77
#BI4 .;G7.;H7.;X77
#CJ4 .;H7.;F7.;X77
.#CA4 .;F @7 .;F 7;X77
#F.D ,V]IFY T .;F & ;G >E 9V]SE
FUNC;NS4
.#CB4 .;F7.;X7 .K #B;X--#D1
.#CC4
#F.D ,F9D ! 9V]SE (! FUNC;N4
#CD4 .;F7.;X7 .K #E;X--#C
#CE4
#CF4
#CG4
.;F7.;X7 .K --;X #F @+ #B1 "K.K.#J
#CH4
#CI4 .;F7.;X7 .K #CB;X #E @+ #D
#F.E ,GRAPH ! FUNC;N4 ,!N /ATE ! DOMA9
& RANGE4
.#DJ4
.#DA4
.#DB4
.#DC4
.#DD4
.#DE4
.#DF4
.#DG4
#F.F ,SOLVE ! EQU,N4 ,*ECK YR SOLU;N4
.#DH4
.#DI4
.#EJ4
.#EA4
.#EB4 #G .;X #D/C .K #AGE
.#EC4 @7 .;X -- #B7 #C/D .K #A
.#ED4
.#EE4
.#EF4
-----------------------------------#AJAF
,*APT] #G
,,EXTRA ,,PRACTICE
#G.A ,GRAPH ! FUNC;N4 ,/ATE ! DOMA9 &
RANGE4
.#A4
.#B4 ;Y.K--#B 99 #B ;X
.#C4 ;Y.K#C ;X--#C --#B
.#D4
#G.B ,GRAPH ! FUNC;N4 ,/ATE ! DOMA9 &
RANGE4
.#E4
.#F4
.#G4 ;Y .K 7#J.H7 ;X--#C -- #B
.#H4
#G.C ,SIMPLIFY ! EXPRES.N4
.#I4 ;E --#C 99 ;E --#H
.#AJ4 7#B;E #B;X @7 --#E
.#AA4
.#AB4
#G.C ,GRAPH ! FUNC;N4 ,/ATE ! DOMA9 &
RANGE4
#AC4 .;Y.K.#J..E;E #C;X.'.-
.#AD4 ;Y.K#B;E@: ;X --#B
.#AE4 ;Y .K #A.E;E ;X @+ ;,J @+ #C
.#AF4 ;Y.K ;E #C7;X #B @7 @+ #A
#G.D ,EVALUATE ! LOG>I?M )\T US+ A
CALCULATOR4
.#AG4
.#AH4 LOG #F #F
.#AI4 LOG #E #ABE
.#BJ4
#G.D ,SIMPLIFY ! EXPRES.N4
.#BA4 #E LOG #E .;X
.#BB4 #AJ LOG ;,S #I
.#BC4 LOG #D #AF ;X
.#BD4 ;E LN#E
#G.D ,GRAPH ! FUNC;N4 ,/ATE ! DOMA9 &
RANGE4
.#BE4 ;Y .K LOG #G .;X
.#BF4 ;Y .K LOG #A/B 7;X--#D7
.#BG4 ;Y .K LOG #E .;X @+ #C
.#BH4 ;Y .K LOG #C 7;X--#B7 @+ #A
#G.E ,EXP& ! EXPRES.N4
.#BI4
.#CJ4
.#CA4 LN #BJ .;X #C ;Y #B
.#CB4
#G.E ,3D5SE ! EXPRES.N4
.#CC4 LOG4 #BJ @+ #D LOG .;X
.#CD4 LOG#G @+#BA;OGX--#E LOG ;Y
.#CE4 #J.E ,9 #AJJ--#B LNX @+ #H LN ;Y
#G.E ,USE ! *ANGE-(-BASE =MULA
6EVALUATE ! LOG>I?M4
.#CF4 LOG #B #E
.#CG4 LOG #D #HJ
.#CH4 LOG #E #AJJ
.#CI4 LOG @8 #BG
#G.F ,SOLVE ! EQU,N4 ,*ECK = EXTRANE\S
SOLU;NS4
.#DJ4 #B #D 99 @+ #B .K #H ;X @+ #B
.#DA4
.#DB4 #G #I;X .K #AH
.#DC4 ,9 7#C;X @+ #G7 .K ,9 7;X--#A7
.#DD4 LOG #E 7#C;X @+ #B7 .K #C
.#DE4 LOG #F 7;X @+ #I7 @+ LOG #F .;X
.K #B
#G.G ,WRITE AN EXPON5TIAL FUNC;N .;Y
.K .;AB ;X.' .-^: GRAPH PASSES "? ! GIV5
PO9TS4
.#DF4 7#A1 #H71 7#B1 #CB7
.#DG4 7#A1 #C71 7#C1 #AB7
.#DH4 7#B1 --#I71 7#E1 --#BDC7
.#DI4 7#A1 #D71 7#B1 #D7
#G.G ,WRITE A P[] FUNC;N .;Y .K .AX
#AC ^: GRAPH PASSES "? ! GIV5 PO9TS4
.#EJ4 7#B1 #B71 7#E1 #AF7
.#EA4 7#C1 #BG71 7#F1 #DCB7
.#EB4 7#A1 #D71 7#H1 #AG7
.#EC4 7#E1 #CF71 7#AJ1 #BBJ7
-----------------------------------#AJAG
,*APT] #H
,,EXTRA ,,PRACTICE
#H.A ,! V>IA#S .;X & .;Y V>Y 9V]SELY4
,USE ! GIV5 VALUES 6WRITE AN EQU,N
RELAT+ .;X & Y4 ,!N F9D .;Y :5 .;X .K
--#E4
.#A4 ..;X .K #B1 .;Y .K --#AJ
.#B4
.#C4 ;X .K --#C1 ;Y .K --#E
.#D4
#H.A ,DET]M9E :E!R .;X & ;Y %[
..DIRECT V>I,N1 9V]SE .V>I,N @1 OR .NEI4
#E4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
;,X3 .;Y
#B.E3 #CB
#D3 #BJ
#E3 #AF
#F.D3 #AB.E
#H3 #AJ
#F4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X @3 .;Y
#A3 .#B..E
#C.E3 #H.GE
#E3 #AB.E
#H3 #BJ
#I3 #BB #E
#G4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
;X3 .;Y
#AA3 #CJ
#AD3 .#FA
.#AF @3 #HE
#BD3 #IB
#BG3 #AJE
#H4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
;,X3 .;Y
#A3 #AB
#C3 #D
#H3 #A.E
#AB3 #A
#AE3 #J.H
#H.B ,GRAPH ! FUNC;N4 ,/ATE ! DOMA9 &
RANGE4
.#I4
.#AJ4
.#AA4
.#AB4
#H.C ,GRAPH ! FUNC;N4
.#AC4
.#AD4
.#AE4
.#AF4
#H.D ,SIMPLIFY ! R,NAL EXPRES.N1 IF
POSSI#4
.#AG4
.#AH4
.#AI4
.#BJ4
#H.D ,MULTIPLY OR DIVIDE ! EXPRES.NS4
,SIMPLIFY ! RESULT4
.#BA4
.#BB4
.#BC4
.#BD4
.#BE4
.#BF4
#H.E ,ADD OR SUBTRACT ! EXPRES.NS4
,SIMPLIFY ! RESULT4
.#BG4
.#BH4
.#BI4
#H.E ,SIMPLIFY ! -PLEX FRAC;N4
.#CJ4
.#CA4
.#CB4
#H.F ,SOLVE ! EQU,N4 ,*ECK = EXTRANE\S
SOLU;NS4
.#CC4
.#CD4
.#CE4
.#CF4
-----------------------------------#AJAH
,*APT] #I
#I.A ,F9D ! 4T.E 2T ! TWO PO9TS4 ,!N
F9D ! MIDPO9T (! L9E SEG;T JO9+ ! TWO
PO9TS4
.#A4 7--#E1 #J71 7#E1 #D7
.#B4 7#B1 #A71 7#C1 #G7
.#C4 7--#AB1 #AB71 7#AD1 --#D7
.#D4 7#AB1 --#A71 7#AH1 --#I7
#I.B ,GRAPH ! EQU,N4 ,ID5TIFY ! FOCUS1
DIRECTRIX1 & AXIS ( SYMMETRY (! P>ABOLA4
.#E4 ;Y #B .K #B;X
.#F4 .;X #B .K --#D;Y
.#G4 #AD;X #B .K --#BA;Y
.#H4 #AB;Y #B @+ #C;X .K #J
#I.C ,GRAPH ! EQU,N4 ,ID5TIFY ! RADIUS
(! CIRCLE4
.#I4 .;X #B @+ ;Y #B .K #D
.#AJ4 .;X #B @+ .;Y #B .K #AD
.#AA4 .#C;X #B @+ #C;Y #B .K #GE
.#AB4 #AF;X #B @+ #AF_/ .K #D
#I.C ,WRITE ! /&>D =M (! EQU,N (!
CIRCLE T PASSES "? ! GIV5 PO9T & ^: C5T]
IS AT ! ORIG94
.#AC4 7#H1 #J7
.#AD4 7#J1 --#I7
.#AE4 7#G1 --#A7
.#AF4 7--#E1 --#AA7
#I.D ,GRAPH ! EQU,N4 ,ID5TIFY !
V]TICES1 CO-V]TICES1 & FOCI (! ELLIPSE4
.#AG4
.#AH4
.#AI4 #I;X #B @+ #D;Y #B .K #EGF
#I.D ,WRITE AN EQU,N (! ELLIPSE )!
GIV5 "*I/ICS & C5T] AT 7#J1J74
.#BA4 ,V]TEX3 7#D1 #J7
,CO-V]TEX3 7#J1 #B7
.#BB4 ,V]TEX3 7#J1 --#E7
,CO-V]TEX3 7#D1 #J7
.#BC4 ,V]TEX3 7#I1 #J7
,FOCUS3 7--#C1 #J7
.#BD4 ,CO-V]TEX3 7#J1 #AJ7
,FOCUS3 7#H1 #J7
#I.E ,GRAPH ! EQU,N4 ,ID5TIFY !
V]TICES1 FOCI1 & ASYMPTOTES (! HYP]BOLA4
.#BE4
.#BF4 ;X #B -- ;Y #B .K #D
.#BG4 #DI;Y #B -- #HA;X #B .K #CIFI
#I.E ,WRITE AN EQU,N (! HYP]BOLA )!
GIV5 FOCI & V]TICES4
.#BH4 ,FOCI3 7#J1 --#H71 7#J1 #H7
,V]TICES3 7#J1 --#F71 7#J1 #F7
.#BI4 ,FOCI3 7--#B1 #J71 7#B1 #J7
,V]TICES3 7--#A1 #J71 7#A1 #J7
.#CJ4 ,FOCI3 7#J1 --#E71 7#J1 #E7
,V]TICES3 7#J1-- @7@1 7#J1 @7
#I.F ,GRAPH ! EQU,N4 ,ID5TIFY !
IMPORTANT "*I/ICS (! GRAPH4
.#CA4
.#CB4 7;X @+ #B7 #B @+ 7;Y--#A7 #B .K
#D
.#CC4
#I.F ,CLASSIFY ! 3IC SEC;N & WRITE XS
EQU,N 9 /&>D =M4 ,!N GRAPH ! EQU,N4
.#CD4 ;X #B @+ ;Y #B @+ #B;X @+
#B;Y--#G .K #J
.#CE4 #I;X #B @+ #D;Y #B -- #GB;X @+
#AF;Y @+ #AF .K #J
.#CF4 #I;X #B -- #D_/ @+ #AF;Y--#EB .K
#J
.#CG4 ;X #B -- #F;X--#D;Y @+ #AG .K #J
#I.G ,SOLVE ! SY/EM4
.#CH4 ;X #B @+ ;Y #B .K #D
#I;X #B -- #D;Y #B .K #CF
.#CI4 ;Y .K ;X--#B
;X #B @+ ;Y #B -- #F;X--#D;Y--#AB .K
#J
.#DJ4 ;Y #B .K ;X--#E
#I;X #B -- #BE;Y #B .K #BBE
-----------------------------------#AJAI
,*APT] #AJ
,,EXTRA ,,PRACTICE
#AJ.A ,=! GIV5 PASS^W 3FIGUR,N1
DET]M9E H[ _M PASS^WS >E POSSI# IF 7A7
DIGITS & LRS C 2 REP1T$1 & 7;B7 DIGITS &
LRS _C 2 REP1T$4
.#A4 #H DIGITS
.#B4 #H LRS
.#C4 #E LRS FOLL[$ 0#A DIGIT
.#D4 #B DIGITS FOLL[$ 0#B LRS
#AJ.A ,F9D ! NUMB] ( P]MUT,NS4
.#E4 #E ;,P #B
#F4 ;,Q .;,P #A
.#G4 #I ;,P #I
.#H4 #AB ;,P #D
#AJ.A ,F9D ! NUMB] ( 4T+UI%A# P]MUT,NS
(! LRS 9 ! ^W4
.#I4 ,,VANILLA
.#AJ4 ,,*OCOLATE
.#AA4 ,,/RAWB]RY
.#AB4 ,,C(FEE
#AJ.B ,F9D ! NUMB] ( -B9,NS4
.#AC4 #G ;,C #C
.#AD4 #D ;,C ;,X
.#AE4 #AJ ;,C #I
.#AF4 #AE ;,C #F
#AJ.B ,USE ! BINOMIAL !OREM 6WRITE !
BINOMIAL EXPAN.N4
.#AG4 7;X--#C7 #C
.#AH4 7#B;X @+ #C;Y7 #D
.#AI4 7.;P #B @+ #D7 #E
.#BJ4 7;X #C @+ ;Y #B @7 #F
#AJ.C ,Y H AN EQU,Y LIKELY *.E ( *OOS+
ANY 9TEG] F #A "? #BE4 ,F9D ! PROBABIL;Y
(! GIV5 EV5T4
.#BA4 ,AN ODD NUMB] IS *OS54
.#BB4 ,A MULTIPLE ( #C IS *OS54
#AJ.C ,F9D ! PROBABIL;Y T A D>T ?R[N
AT ! GIV5 T>GET W HIT ! %AD$ REGION4
,ASSUME ! D>T IS EQU,Y LIKELY 6HIT ANY
PO9T 9SIDE ! T>GET4
.#BC4
.#BD4
.#BE4
#AJ.D ,EV5TS .,A & .;,B >E 4JO9T4 ,F9D
.;,P7.,A OR .;,B7 @4
..#BF4 ;,P7,A7 .K #J.D1 ;,P7.;,B7 .K
#J.AE
..#BG4 ;,P7,A7 .K #J.C1 ;,P7.;,B7 .K
#J.E
#BH4 .;,P7.,A7 .K #J.G1 .;,P7.;,B7 .K
#J.BA
#AJ.D ,F9D ! 9DICAT$ PROBABIL;Y4 ,/ATE
:E!R .,A & .;,B >E 4JO9T EV5TS4
.#BI4 .;,P7.,A7 .K #J.BE .;,P7.;,B7 .K
#J.EE .;,P7.,AOR,B7 .K @8 ;,P7,AAND,B7
.K #J.B
.#CJ4 .;,P7.,A7 .K #J.EB .;,P7.;,B7 .K
#J.AE .;,P7.,A .OR .;,B7 .K #J.FG
.;,P7.,A & .;,B7 .K @8
.#CA4 ;,P7,A7 .K #J.ED .;,P7.;,B7 .K
#J.BH .;,P7.,A .OR .;,B7 .K #J.FE
;,P7,A& ;,B7 .K @8
.#CB4 ;,P7,A7 .K #J.E .;,P7.;,B7 .K
#J.D ,,PCA OR #E7 .K @8 ;,P7,A& #E7 .K
#J.C
#AJ.E ,F9D ! PROBABIL;Y ( DRAW+ ! GIV5
C>DS F A /&>D DECK ( #EB C>DS 7A7 )
REPLACE;T & 7;B7 )\T REPLACE;T4
.#CC4 ,A JACK1 !N A #C
.#CD4 ,A CLUB1 !N ANO!R CLUB
.#CE4 ,A BLACK ACE1 !N A R$ C>D
#AJ.F ,CALCULATE ! PROBABIL;Y ( TOSS+
A CO9 #AE "TS & GETT+ ! GIV5 NUMB] (
H1DS4
.#CF4 #A
.#CG4 #D
.#CH4 #G
.#CI4 #AE
-----------------------------------#AJBJ
,*APT] #AA
#AA.A ,F9D ! M1N1 M$IAN1 MODE1 RANGE1
& /&>D DEVI,N (! DATA SET4
.#A4 #E1 #E1 #F1 #I1AA1 #AB1 #AD1 #AF1
#AF1 #AF
.#B4 #AF1AH1 #BI1 #CJ1 #CD1 #CE1 #CE1
#CH1 #DF
.#C4 --#D1 --#C1 --#C1 #D1 #A1 #J1 #J1
--#C1 --#B1 #AJ1 #AA
.#D4 #A.G1 #B.B1 #A.H1 #C.J1 #J.D1
#A.B1 #B.H1 #B.I
.#E4 #D.E1 #E.G1 #D.C1 #F.I1 --#B.A1
#E.G1 --#A.B1 #C.H
.#F4 --#G.B1 #C.I1 #B.F1 --#I.A1 #B.E1
--#G.B1 #C.I1 --#G.B
..#AA.B ,F9D ! M1N1 M$IAN1 MODE1
RANGE1 & /&>D DEVI,N (! .GIV5 DATA SET
&(! DATA SET OBTA9$ 0A4+ ! GIV5 3/ANT
6EA* DATA VALUE4
.#G4 #CC1 #CF1 #CF1 #CI1 #DI1 #EF2
3/ANT3 #B
.#H4 #AJ1 #AB1 #AD1 #AF1 #AF1 #AH1AI2
3/ANT3 --#A
#AA.B ,F9D ! M1N1 M$IAN1 MODE1 RANGE1
& /&>D DEVI,N (! GIV5 DATA SET &(! DATA
SET OBTA9$ 0MULTIPLY+ EA* DATA VALUE 0!
GIV5 3/ANT4
.#I4 --#B1 --#B1 #E1 #D1 #B1 --#B1 #H1
#C2 3/ANT3 #A.E
.#AJ4 #EB1 #EB1 #GF1 #EF1 #FG1 #HI1
#GJ2 3/ANT3 #C
#AA.C ,A NORMAL 4TRIBU;N HAS A M1N (
#B.G &A /&>D DEVI,N ( #J.C4 ,F9D !
PROBABIL;Y T A R&OMLY SELECT$ ;R VALUE F
! 4TRIBU;N IS 9 ! GIV5 9T]VAL4
.#AA4 ,2T #B.D & #B.G
.#AB4 ,AT L1/ #C.J
.#AC4 ,AT MO/ #B.A
#AA.D ,ID5TIFY ! TYPE ( SAMPLE
DESCRIB$4 ,!N TELL IF ! SAMPLE IS BIAS$4
.,EXPLA9 YR R1SON+4
.#AD4 ,! [N] (A MOVIE R5TAL /ORE WANTS
6"K H[ (T5 H] CU/OM]S R5T MOVIES4 ,%E
ASKS E T5? CU/OM] H[ _M MOVIES ! CU/OM]
R5TS EA* MON?4
.#AE4 ,A S*OOL WANTS 63SULT P>5TS AB
UPDAT+ XS ATT5D.E POLICY4 ,EA* /UD5T IS
S5T HOME )A SURVEY =A P>5T 6-PLETE4 ,!
S*OOL USES ONLY SURVEYS T >E RETURN$ )9
"O WEEK4
#AA.D ,F9D ! M>G9 ( ]ROR =A SURVEY T
HAS ! GIV5 SAMPLE SIZE4 ,R.D YR ANSW] 6!
NE>E/ T5? (A P]C5T4
.#AF #AJJ
.#AG4 #FJJ
.#AH4 #BIJJ
.#AI4 #EJJJ
#AA.D ,F9D ! SAMPLE SIZE REQUIR$
6A*IEVE ! GIV5 M>G9 ( ]ROR4 ,R.D YR
ANSW] 6! NE>E/ :OLE NUMB]4
.#BJ4 +-#A@3P
.#BA4 +-#B@3P
.#BB4 +-#E.E@3P
.#BC4 +-#F.B@3P
#AA.E ,USE A GRAPH+ CALCULATOR 6F9D A
MODEL =! DATA4 ,!N GRAPH ! MODEL &! DATA
9 ! SAME COORD9ATE PLANE4
#BD4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X @3 #J3 #B3 #D3 #F3 #H3 #AJ3 #AB3
#AD
.;Y @3 --#AJ3 --#C3 #D3 #AJ3 #AD3 #BJ3
#BA3 #CF
#BE4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
;,X3 #A3 #B3 #C3 #D3 #E3 #F3 #G3 #H
;Y3 #J.E3 #JH3 #A.A3 #C3 #I3 #CJ3 #IJ3
#BHJ
-----------------------------------#AJBA
,*APT] #AB
#AB.A ,=! SEQU;E1 DESCRIBE ! PATT]N1
WRITE ! NEXT T]M1 & WRITE A RULE =! N?
T]M4
.#A4 #I1 #AF1BE1CF '
.#B4 '''
.#C4 #AB.E1G1A.E1 --#D1'4
#AB.A ,WRITE ! S]IES US+ SUMM,N NOT,N4
.#D4 #AF @+ #CB @+ #DH @+ #FD @+ 99 99
99 @+ #ADD
.#E
#AB.A ,F9D ! SUM (! S]IES4
.#F4
.#G4
.#H4
.#I4
#AB.B ,WRITE A RULE =! N? T]M (!
>I?METIC SEQU;E4 ,!N GRAPH ! F/ SIX T]MS
(! SEQU;E4
#AJ4 .A #E .K.;L#E;YD .K .#F
.#AA4 .A #AJ .K --#GH1 .;D .K --#AJ
.#AB4
#AB.B ,WRITE A RULE =! N? T]M (!
>I?METIC SEQU;E4 ,!N F9D .A ;L#E @4
.#AC4 #AA1 #BJ1 #BI1 #CH1 '
.#AD4 --#H1 --#AE1 --#BB1 --#BI1'
.#AE4
#AB.B ,WRITE A RULE =! .N? T]M (!
>I?METIC SEQU;E T HAS ! TWO GIV5 T]MS4
.#AF4 .A #B .K #I1 .A #G .K #CG
.#AG4 .A ;,Q .K #AJ.E1 A #AF .K #AH.E
.#AH4
#AB.C ,WRITE A RULE =! N? T]M (!
GEOMETRIC SEQU;E4 ,!N F9D .A L,Q @4
.#AI4
.#BJ4 #E1 #D1 #C1 #B1 #B.EF '
.#BA4
#AB.C ,F9D ! SUM (! GEOMETRIC S]IES4
.#BB4
.#BC4
.#BD4
.#BE4
#AB.D ,F9D ! SUM (! 9F9ITE GEOMETRIC
S]IES1 IF X EXI/S4
.#BF4 #H @+ #D @+ #B @+ #A @+ '
.#BG4 #B--#D @+ #H--#AF @+ '
.#BH4 --#F.GE @+ #D.E--#C @+ #B--'
#AB.D ,WRITE ! REP1T+ DECIMAL Z A
FRAC;N 9 L[E/ T]MS4
.#BI4 #J.CCC'''
.#CJ4 #J.HIHIHI'''
.#CA4 #J.BABABA'''
.#CB4 #A.EJAEJAEJ'''
#AB.E ,WRITE A RECURSIVE RULE =!
SEQU;E4 ,! SEQU;E MAY 2 >I?METIC1
GEOMETRIC1 OR NEI4
.#CC4 #B.E1 #E1 #AJ1 #BJ1'
.#CD4 #B1 --#B1 --#F1 --#AJ1 '
.#CE4 #A1 #B1 #B1 #D1 #H1 #CB1'
#AB.E ,F9D ! F/ ?REE IT]ATES (! FUNC;N
=! GIV5 9ITIAL VALUE4
.#CF4 ..;F7;X7 .K .#B;X -- #E1 ;X #J
.K #C
.#CG4 .;F7.;X7 .K -.#B,.;X #J .K --#AJ
.#CH4 .;F7.;X7 .K .#C;X #B @+ ;X1 .;X
;,Q .K --#A
-----------------------------------#AJBB
,*APT] #AC
,,EXTRA ,,PRACTICE
#AC.A ,LET .#J 2 AN ACUTE ANGLE (A "R
TRIANGLE4 ,F9D ! VALUES (! O!R FIVE
TRIGONOMETRIC FUNC;NS ( .#J4
.#A4 S9 .K
.#B4
.#C4 SEC .K .#B
.#D4
.#AC..A ,SOLVE .,,AABC US+ ! DIAGRAM
&! GIV5 M1SURE;TS4
.#E4 .,A .K #BA;DG1 ;C .K #H
.#F4 #E .K #FF;DG1 A .K #AD
.#G4 .;,B .K #FJ;DG1 ;C .K #BJ
.#H4 .,A .K #BI;DG1 .;B .K #F
.#I4 .,A .K #AH;DG1 .;C .K #AH
.#AJ4 ;,B .K #EF;DG1 ;C .K #G
.#AC..B ,3V]T ! DEGREE M1SURE 6RADIANS
OR ! RADIAN M1SURE 6DEGREES4
.#AA4 #AJJ;DG
.#AB4 --#F;DG
.#AC4
.#AD4
#AC.B ,F9D ! >C L5G? & >EA (A SECTOR
)! GIV5 RADIUS .;R & C5TRAL ANGLE .#J4
.#AE4 ;R .K #E FT1 #J .K #IJ;DG
.#AF4 .;R .K #B IN41 #J .K #CJJ;DG
.#AG4 .;R .K #AB CM1 #J .K
.#AC..C ,SKET* ! ANGLE4 ,!N F9D XS
REF];E ANGLE4
.#AH4 #BEJ;DG
.#AI4 --#CJ;DG
.#BJ4
.#BA4
#AC.C ,EVALUATE ! FUNC;N )\T US+ A
CALCULATOR4
.#BB4 S9 7--#FJ;DG7
.#BC4 CSC #BDJ;DG
.#BD4
.#BE4
.#AC..D ,EVALUATE ! EXPRES.N )\T US+ A
CALCULATOR4 ,GIVE YR ANSW] 9 BO? RADIANS
& DEGREES4
.#BF4 S9 --#A #J
.#BG4 COS --#A
.#BH4 COS --#A #C
.#BI4 TAN --#A #A
#AC.D ,SOLVE ! EQU,N = .#F4
.#CJ4 S9 .K #J.BE2 #IJ;DG "K .#I "K
#AHJ;DG
.#CA4 COS .K #J.I2 #BGJ;DG "K #J "K
#CFJ;DG
.#CB4 TAN .K #B2 #AHJ;DG "K #J "K
#BGJ;DG
#AC.E ,SOLVE .,,AABC4 7.,H9T3 ,"S (!
8TRIANGLES0 MAY H NO SOLU;N & "S MAY H
TWO SOLU;NS47
.#CC4 .,A .K #CD;DG1 .A .K #F1 .;B .K
.#G
.#CD4 .,A .K #EJ;DG1 ;,C .K #FE;DG1
.;B .K #FJ
.#CE4 .;,B .K #HF;DG1 .;B .K #AC1 ;C
.K #AA
.#AC..E ,F9D ! >EA ( ,,ABC )! GIV5
SIDE L5G?S & 9CLUD$ ANGLE4
.#CF4 .,A .K #CE;DG1 .;B .K #EJ1 .;C
.K #ABJ
.#CG4 .;,B .K #CE;DG1 .A .K #G1 ;C .K
#AB
.#CH4 ;,C .K #BJ;DG1 A .K #AJ1 .;B .K
#AF
.#AC..F ,SOLVE .,,AABC4
.#CI4 A .K #AF1 .;B .K #BC1 ;C .K #AG
.#DJ4 ;,C .K #EJ;DG1 ..A .K #AB1
;B.K.;,U
.#DA4 ,A .K #HJ;DG1 .;B .K #G1 ;C .K
#E
.#AC..F ,F9D ! >EA ( .,,ABC )! GIV5
SIDE L5G?S4
.#DB4 .A .K #F1 .;B .K #C1 ;C .K #D
.#DC4 A .K #AD1 ;B .K #CJ1 ;C .K #BG
.#DD4 A .K #AF1 ;B .K #AF1 ;C .K #BJ
-----------------------------------#AJBC
,*APT] #AD
.#AD..A ,GRAPH ! FUNC;N4
.#A4
.#B4 ;Y .K #C S9 ;X
.#C4 ;Y .K S9 #B .;X
.#D4 ;Y .K #B TAN #B;X
.#AD..B ,GRAPH ! S9E OR COS9E FUNC;N4
.#E4
.#F4
.#G4 ;Y .K #B COS ;X @+ #C
.#AD..B ,GRAPH ! TANG5T FUNC;N4
.#H4 ;Y .K #B TAN ;X @+ #B
.#I4
.#AJ4
.#AD..C ,SIMPLIFY ! EXPRES.N4
.#AA4
.#AB4
.#AC4
.#AD..C ,V]IFY ! ID5T;Y4
.#AD4
.#AE4
.#AF4 #B--SEC #B ;X--#A--TAN #B ;X
.#AD..D ,F9D ! G5]AL SOLU;N (! EQU,N4
.#AG4 #AB TAN #B ;X--#D .K #J
.#AH4 #C S9 ;X---#B S9 ;X @+ #C
.#AI4 TAN #B ;X--#B TAN ;X .K --#A
.#AD..D ,SOLVE ! EQU,N 9 ! GIV5
9T]VAL4 ,*ECK YR SOLU;NS4
.#BJ4 COS #B ;X S9 ;X .K #E S9 ;X2 #J
"K ;X "K #B
.#BA4 #B--#B COS #B ;X .K #C @+ #E S9
;X2 #J "K ;X "K #BB
.#BB4 #H COS ;X .K #D SEC .;X2
.#J"K.;X"K
.#BC4 COS #B ;X--#D COS ;X@+#A .K
#J2#J"K;X"K
.#AD..E ,WRITE A FUNC;N =! S9USOID4
.#BD4
.#BE4
#AD.F ,F9D ! EXACT VALUE (! EXPRES.N4
.#BF4 S9 7--#AE;DG7
.#BG4 COS #AFE;DG
.#BH4
.#BI4
.#AD..G ,F9D ! EXACT VALUES ( S9 #B;A1
COS #B;A1 & TAN #B;A4
.#CJ4
.#CA4
.#CB4
.#AD..G ,F9D ! G5]AL SOLU;N (! EQU,N4
.#CC4 COS#B;X--COSX .K #J
.#CD4 .K S9X
.#CE4 S9 #B;X .K--#A
-----------------------------------#AJBD
,TA#S
,SYMBOLS
,,TA#S
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,SYMBOL3 ,M1N+3 ,PAGE
'''@3 & S ON3 #B
--@3 IS APPROXIMATELY EQUAL TO3 #B
99 @3 MULTIPLIC,N1 "TS3 #C
--.A @3 OPPOSITE ( .A @3 #D
;L.' A @3 RECIPROCAL ( .A1 .A @6.K #J
@3 #D
;B.' #A @3 FOSUB #A3 .#BF
--@3 IRR,NAL NUMB] #C.AD3 #BF
"K@3 IS LESS ?AN3 .#DA
.1@3 IS GRT] ?AN3 .#DA
"K@3 IS LESS ?AN OR EQUAL TO3 .#DA
.1@3 IS GRT] ?AN OR EQUAL TO3 .#DA
_\;X_\3 ABSOLUTE VALUE ( .;X @3 #EA
--@3 IS N EQUAL TO3 #EB
7.;X,.;Y7 @3 ORD]$ PAIR3 .#GB
.;F7.;X7 @3 .;F ( .;X @1 OR ! VALUE
(_/AT .;X @3 #GE
.;M @3 SLOPE3 .#HB
--@3 IS P>ALLEL TO3 .#HD
--@3 IS P]P5DICUL> TO3 .#HD
7.;X1 .;Y1 .;Z7 @3 ORD]$ TRIPLE3 .#AGH
@3 MATRIX3 .#AHG
_\,A_\3 DET]M9ANT ( MATRIX .,A @3
.#BJC
,A --#A @3 9V]SE ( MATRIX ,A3 .#BAJ
@3 ! NONNEGATIVE SQU>E ROOT (A3 .#BFF
.;I @3 IMAG9>Y UNIT EQUAL TO @3 .#BGE
_\;Z_\3 ABSOLUTE VALUE ( -PLEX NUMB]
.;Z @3 .#BGI
.;X @+ @3 APPROA*ES POSITIVE 9F9;Y3
.#CCI
@3 RA? ROOT (A3 .#DAD
.;F --#A @3 9V]SE ( FUNC;N .;F @3
.#DCH
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,SYMBOL3 ,M1N+3 ,PAGE
.;E @3 IRR,NAL NUMB] #B.GAH3 .#DIB
LOG ;B ;Y @3 LOG BASE .B(Y @3 .#DII
LOG .;X @3 LOG BASE #AJ (X3 .#EJJ
LNX3 LOG BASE .;E ( .;X @3 .#EJJ
.;N6 @3 .;N FACTORIAL2 NUMB] (
P]MUT,NS ( .;N OBJECTS @3 .#FHD
;N.' ;,P.' ;R.' @3 NUMB] ( P]MUT,NS (
;R OBJECTS F .;N 4T9CT OBJECTS @3 .#FHE
N,C.' ;R.' @3 NUMB] ( -B9,NS ( ;R
OBJECTS F .;N 4T9CT OBJECTS @3 .#FIJ
.;,P7.,A7 @3 PROBABIL;Y ( EV5T .,A @3
.#FIH
.;,P7 @7 @3 PROBABIL;Y (! -PLE;T (
EV5T .,A @3 .#GJI
.;,U @3 UNION ( TWO SETS3 .#GAE
--@3 9T]SEC;N ( TWO SETS3 .#GAE
--@3 EMPTY SET3 .#GAE
--@3 IS A SUBSET (3 .#GAF
.;,P7.;,B_\.,A7 @3 PROBABIL;Y ( EV5T
.;,B GIV5 T EV5T .,A HAS O3URR$ @3 .#GAH
@3 ;X-B>2 ! M1N (A DATA SET3 .#GDD
--@3 SIGMA2 ! /&>D DEVI,N (A DATA SET3
.#GDE
--@3 SUMM,N3 .#GIF
--@3 !TA3 .#HEB
S93 S9E3 .#HEB
COS3 COS9E3 .#HEB
TAN3 TANG5T3 .#HEB
,,CSC3 COSECANT3 .#HEB
SEC3 SECANT3 .#HEB
COT3 COTANG5T3 .#HEB
S90 #A @3 9V]SE S9E3 .#HGE
COS0 #A @3 9V]SE COS9E3 .#HGE
TAN --#A @3 9V]SE TANG5T3 .#HGE
-----------------------------------#AJBE
,M1SURES
,,TA#S
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#FJ SECONDS 7SEC7 .K #A M9UTE 7M97 #FJ
M9UTES .K #A H\R 7;H7 #BD H\RS .K #A "D
#G "DS .K #A WEEK #D WEEKS 7APPROX47 .K
#A MON?3 #CFE "DS #EB WEEKS 7APPROX47
#AB MON?S#AJ Y1S #AJJ YE>S3 .K #A YE> .K
#A DECADE .K #A C5TURY
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,METRIC3 ,UNIT$ ,/ATES ,CU/OM>Y
.,L5G? #AJ MILLIMET]S 7MM7 .K #A
C5TIMET] 7CM7#AJJ CM #AJJJ MM .K .#A
MET] 7;M7#AJJJ ;M .K #A KILOMET] 7KM7 @3
.,L5G? #AB 9*ES 7IN47 .K #A FOOT 7FT7
#CF #C FT IN4 @7' .K #A ,Y>D 7YD7
.#EBHJ .FT @7' .K ..#A MILE 7.MI7 #AGFJ
YD7'
.,>EA #AJJ SQU>E MILLIMET]S .K #A
SQU>E C5TIMET] 7MM #B @7 7CM #B @7
#AJ1JJJ CM #B .K #A SQU>E MET] 7;M #B @7
#AJ1JJJ ;M #B .K #A HECT>E 7HA7 @3 .,>EA
#ADD SQU>E 9*ES 7IN4 #B @7 .K #A SQU>E
FOOT 7FT #B @7 #I FT #B .K #A SQU>E Y>D
7YD #B @7 #DC1EFJ FT#B .K .;L ACRE 7,A7
#DHDJ YD ;,J
.,VOLUME #AJJJ CUBIC MILLIMET]S .K #A
CUBIC C5TIMET] 7MM #C @7 7CM #C @7
#A1JJJ1JJJ CM #C .K #A CUBIC MET] 7;M #C
@7 @3 .,VOLUME #AGBH CUBIC 9*ES 7IN4 #C
@7 .K #A CUBIC FOOT 7FT #C @7 #BG FT #C
.K #A CUBIC Y>D 7YD #C @7
.,LIQUID .,CAPAC;Y #AJJJ MILLILIT]S
7M,L7 #AJJJ CUBIC C5TIMET]S ,ICM
;,J#AJJJ ;,L .K#A KILOLIT] 7K,L7 @3
.,LIQUID .,CAPAC;Y #H FLUID \NCES 7FL
OZ7 .K #A CUP 7;C7 #B ;C .K#A P9T 7PT7
#B PT .K #A QU>T 7QT7 #D QT .K #A GALLON
7GAL7
.,MASS #AJJJ MILLIGRAMS 7MG7 .K #A
GRAM 7;G7 #AJJJ ;G .K #A KILOGRAM 7KG7
#AJJJ KG .K #A METRIC TON 7;T7 @3
.,WEI<T #AF \NCES 7OZ7 .K #A P.D 7LB7
#BJJJ LB .K #A TON
..,TEMP]ATURE ,DEGREES ,CELSIUS
7;DG.;,C7 #J;DG;,C .K FREEZ+ PO9T ( WAT]
#CG;DG;,C .K NORMAL BODY TEMP]ATURE
#AJJ;DG;,C .K BOIL+ PO9T ( WAT] @3
..,TEMP]ATURE ,DEGREES ,FAHR5HEIT
7;DG.;,F7 #CB;DG;,F .K FREEZ+ PO9T (
WAT] #IH.F;DG;,F .K NORMAL BODY
TEMP]ATURE #BAB;DG;,F .K BOIL+ PO9T (
WAT]
-----------------------------------#AJBF
,=MULAS
,,TA#S
,=MULAS F ,COORD9ATE ,GEOMETRY
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,SLOPE (A L9E @7 P4 #HB @7 @3 ": .;M
IS ! SLOPE (! NONV]TICAL L9E "? PO9TS
7;X #A @1 ;Y #A @7 & 7;X #B @1 ;Y #B @7
,P>ALLEL & P]P5DICUL> L9ES @7 P4 #HD
@7 @3 ,IF L9E ;L.' #A HAS SLOPE ;M.'
;X.' & L9E ;L.' #B HAS SLOPE ;M.' #B @1
!N3 ;L.' #A @\@\;L.' #B IF & ONLY IF
;M.' #A .K ;M.' #B ;L.' #A .;L #B IF &
ONLY IF ;M @3 .K @1 OR ;M.' #A ;M.' #B
.K --#A
,4T.E =MULA @7 P4 #FAE @7 @3 ": ;D IS
! 4T.E 2T PO9TS 7;X.' #B ;X.' #A @7 &
7;X #B @1 ;Y #B @7
,MIDPO9T =MULA @7 P4 #FAE @7 @3 IS !
MIDPO9T (! L9E SEG;T JO9+ PO9TS 7;X #A
@1 ;Y.' #A @7 & 7;X #B @1 ;Y #B @7@4
,=MULAS F ,MATRIX ,ALGEBRA
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,DET]M9ANT (A #B;X#B MATRIX @7 P4 #BJC
@7 @3
,DET]M9ANT (A #C;X#C MATRIX @7 P4 #BJC
@7 @3
,>EA (A TRIANGLE @7 P4 #BJD @7 @3 ,!
>EA (A TRIANGLE ) V]TICES 7;X #A ;Y #A3
@7@1 7;X #B @1 ;Y #B @7@1 & 7;X #C @1 ;Y
#C @7 IS GIV5 0,>EA .K ": ! APPROPRIATE
SIGN 7+-7 %D 2 *OS5 6YIELD A POSITIVE
VALUE4
,CRAM]'S RULE @7 P4 #BJE @7 @3 ,LET ,A
.K 2 ! COE6ICI5T MATRIX ( ? L9E> SY/EM3
.AX @+ .BY .K ..;E CX @+ DY .K .;F ,IF
DET .,A @6.K #J1 !N ! SY/EM HAS EXACTLY
"O SOLU;N4 ,! SOLU;N IS
,9V]SE (A #B;,X#B MATRIX @7 P4 #BAJ @7
@3 ,! 9V]SE (! MATRIX IS PROVID$
..AD.1,,TM ;CD @6.K .#J
-----------------------------------#AJBG
,=MULAS & ,!OREMS F ,ALGEBRA
,,TA#S
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,QUADRATIC =MULA @7 P4 #BIB @7 @3 ,!
SOLU;NS ( AX.' #B @+ .BX @+ .;C .K #J >E
": .A1 .;B @1 & .;C >E R1L NUMB]S S* T
.A @6.K #J4
,4CRIM9ANT (A QUADRATIC EQU,N @7 P4
#BID @7 @3 ,! EXPRES.N ;B.' #B --
#D;AC.' IS CALL$ ! 4CRIM9ANT (!
ASSOCIAT$ EQU,N AX.' #B @+ .BX @+ .;C .K
#J4 ,! VALUE (! 4CRIM9ANT C 2 POSITIVE1
Z]O1 OR NEGATIVE1 : CORRESPONDS 6AN
EQU,N HAV+ TWO R1L SOLU;NS1 "O R1L
SOLU;N1 OR TWO IMAG9>Y SOLU;NS1
RESPECTIVELY4
,SPECIAL PRODUCT PATT]NS @7 P4 #CDG @7
@3 .,SUM .& .DI6];E3 7.A @+ ;B77A--;B7
.K A.' #B -- ;B.' #B .,SQU>E .( A
.BINOMIAL3 7A @+ ;B7 #B .K A.' #B @+
.LAB @+ ;B.' #B 7A--;B7 #B .K A.' #B --
#B;AB.' @+ ;B.' #B ,CUBE (A BINOMIAL3
7.A @+ ;B7 #C .K A.' #C @+ #C;A.' #B
;B.' @+ #C;AB.' #B @+ ;B.' #C 7A--;B7 #C
.K A.' #C -- #C;A.' #B ;B.' @+ #C;AB.'
#B -- ;B.' #C
,SPECIAL FACTOR+ PATT]NS @7 P4 #CED @7
@3 .,SUM ( .TWO CUBES3 A.' #C @+ ;B.' #C
.K 7.A @+ ;B77A.' #B -- ;AB.' @+ ;B.' #B
@7 ,DI6];E ( TWO CUBES3 A.' #C -- ;B.'
#C .K 7A.' -- ;B77A.' #B @+ ;AB.' @+
;B.' #B @7
,REMA9D] !OREM @7 P4 #CFC @7 @3 ,IF A
POLYNOMIAL .;F 7;X7 IS DIVID$ 0;X -- .;K
@1 !N ! REMA9D] IS ;R .K .;F7.;K74
,FACTOR !OREM @7 P4 #CFD @7 @3 .,A
POLYNOMIAL_/7;X7 HAS A FACTOR ;X -- .;K
IF & ONLY IF .;F7.;K7 -- #J4
,R,NAL Z]O !OREM @7 P4 #CGJ @7 @3 ,IF
;F 7;X7 .K A.' ;N.' ;X.' ;N.' @+ ''' @+
A.' #A ;X.' @+ A.' #J HAS .9TEG]
COE6ICI5TS1 !N E R,NAL Z]O (_/HAS ? =M3
,FUNDA;TAL !OREM ( ALGEBRA @7 P4 #CGI
@7 @3 .,IF .;F7.;X7 IS A POLYNOMIAL (
DEGREE .;N ": .;N .1 #J1 !N ! EQU,N .;F
7;X7 .K #J HAS AT L1/ "O SOLU;N 9 ! SET
( -PLEX NUMB]S4
,COROLL>Y 6! FUNDA;TAL !OREM ( ALGEBRA
@7 P4 #CGI @7 @3 .,IF .FIX7 IS A
POLYNOMIAL ( DEGREE .;N ": .;N .1 #J1 !N
! EQU,N .FIX7 .K #J HAS EXACTLY .;N
SOLU;NS PROVID$ EA* SOLU;N REP1T$ TWICE
IS C.T$ Z #B SOLU;NS1 EA* SOLU;N REP1T$
?REE "TS IS C.T$ Z #C SOLU;NS1 & S ON4
,-PLEX 3JUGATES !OREM @7 P4 #CHJ @7 @3
,IF_/IS A POLYNOMIAL FUNC;N ) R1L
COE6ICI5TS1 & .A @+ .BI IS AN IMAG9>Y
Z]O ( .;F !N .A--.;B IS AL A Z]O ( .F4
,IRR,NAL 3JUGATES !OREM @7 P4 #CHJ @7
@3 ,SUPPOSE .;F IS A POLYNOMIAL FUNC;N )
R,NAL COE6ICI5TS1 & .A & .;B >E R,NAL
NUMB]S S* T IS IRR,NAL4 ,IF .A @+ IS A
Z]O (1 !N .A -- IS AL A Z]O ( .F4
,DESC>TES' RULE ( SIGNS @7 P4 #CHA @7
@3 ,LET_/7;X7 .K A.' ;N.' ;X.' ;N.' @+
A.' ;N.' _ ;X.' ;X.' ;N.' @: ;L.' @+ '''
@+ A.' #B ;X.' #B @+ A.' ;,Y.' ;X.' @+
A.' #J 2 A POLYNOMIAL FUNC;N ) R1L
COE6ICI5TS499 ,! NUMB] ( .POSITIVE .R1L
.Z]OS ( _/IS EQUAL 6! NUMB] ( *ANGES 9
SIGN (! COE6ICI5TS (_/7;X7 OR IS LESS
?AN ? 0AN EV5 NUMB]499 ,! NUMB] (
.NEGATIVE .R1L .Z]OS (_/IS EQUAL 6!
NUMB] ( *ANGES 9 SIGN (! COE6ICI5TS
(_/7--;X7 OR IS LESS ?AN ? 0AN EV5
NUMB]4
-----------------------------------#AJBH
,=MULAS & ,!OREMS F ,ALGEBRA 7.3T9U$7
,,TA#S
,! FOLL[+ TA# IS 9 LI/$
=MAT4 ,= EA* CELL ! H1D+ IS %[N
FOLL[$ 0A COLON1 SPACE &! CELL
3T5TS
,=MULAS F ,-B9ATORICS
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,FUNDA;TAL C.T+ PR9CIPLE @7 P4 #FHB @7
@3 ,IF "O EV5T C O3UR 9 .;M WAYS & ANO!R
EV5T C O3UR 9 .;N WAYS1 !N ! NUMB] (
WAYS T BO? EV5TS C O3UR IS .;M 99 .N4
,P]MUT,NS (.' ;N .-OBJECTS TAK5 ;R AT
A "T @7 P4 #FHE @7 @3 ,! NUMB] (
P]MUT,NS ( ;R OBJECTS TAK5 F A GR\P (
.;N 4T9CT OBJECTS IS DENOT$ 0;N.' ;,P.'
;R.' & IS GIV5 BY3
,P]MUT,NS ) REPETI;N @7 P4 #FHE @7 @3
,! NUMB] ( 4T+UI%A# P]MUT,NS ( .;N
OBJECTS ": "O OBJECT IS REP1T$ ;S ;X
"TS1 ANO!R IS REP1T$ ;S.' #B "TS1 & S ON
IS3
,-B9,NS (.' ;N .-OBJECTS TAK5 ;R AT A
"T @7 P4 #FIJ @7 @3 ,! NUMB] ( -B9,NS (
;R OBJECTS TAK5 F A GR\P ( .;N 4T9CT
OBJECTS IS DENOT$ 0;N.' ;,C.' ;R.' & IS
GIV5 BY3
,PASCAL'S TRIANGLE @7 P4 #FIB @7 @3
,IF Y >RANGE ! VALUES ( ;N.' ;,C.' ;R.'
9 A TRIANGUL> PATT]N 9 : EA* R[
CORRESPONDS 6A VALUE ( .;N @1 Y GET :AT
IS CALL$ ,PASCAL'S TRIANGLE4 ,! F/ & LA/
NUMB]S 9 EA* R[ >E #A4 ,E NUMB] O!R ?AN
#A IS ! SUM (! CLOSE/ TWO NUMB]S 9 ! R[
DIRECTLY ABV X4
,BINOMIAL !OREM @7 P4 #FIC @7 @3 ,!
BINOMIAL EXPAN.N ( 7A @+ ;B7 ;N.' = ANY
POSITIVE 9TEG] .;N IS3 ,7A @+ ;B7 ;N.'
.K ;N.' ;,C.' ;O.' A.' ;N.' ;B;DG @+
;N.' ;,C.' .-IA.' ;N.' -- ;L.' ;B.' ;L.'
@+ ;N.' ;,C.' #B A.' ;N.' @: #B ;B.' #B
@+ ''' @+ ;N.' ;,C.' ;N.' A;DG;B.' ;N.'
-----------------------------------#AJBI
,=MULAS F ,PROBABIL;Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,!ORETICAL PROBABIL;Y ( AN EV5T @7 P4
#FIH @7 @3 ,:5 ALL \TCOMES >E EQU,Y
LIKELY1 ! !ORETICAL PROBABIL;Y T AN EV5T
,A W O3UR IS3
,O4S 9 FAVOR ( AN EV5T @7 P4 #FII @7
@3 ,:5 ALL \TCOMES >E EQU,Y LIKELY1 !
O4S 9 FAVOR ( AN EV5T ,A >E3
,O4S AG/ AN EV5T @7 P4 #FII @7 @3 ,:5
ALL \TCOMES >E EQU,Y LIKELY1 ! O4S AG/
AN EV5TS >E3
,EXP]I;TAL PROBABIL;Y ( AN EV5T @7 P4
#GJJ @7 @3 ,:5 AN EXP]I;T IS P]=M$ T
3SI/S (A C]TA9 NUMB] ( TRIALS1 !
EXP]I;TAL PROBABIL;Y ( AN EV5T ,A IS
GIV5 BY3
,PROBABIL;Y ( -P.D EV5TS @7 P4 #GJG @7
@3 ,IF ,A& .;,B >E ANY TWO EV5TS1 !N !
PROBABIL;Y ( .,A OR .;,B IS3 .;,P,7.,A
OR .;,B7 .K ;,P7,A7 @+
.;,P7.;,B7--.;,P7.,A & .;,B7.,IF .,A &
.;,B >E 4JO9T EV5TS1 !N ! PROBABIL;Y (4
,A OR .;,B IS3 ..;,P7,A OR ;,B7
.K;,P7,A7 @+;,P7.;,B7
,PROBABIL;Y (! -PLE;T ( AN EV5T @7 P4
#GJI @7 @3 ,! PROBABIL;Y (! -PLE;T (
EV5T ,A1 DENOT$ ,A1 IS3 .;,P7.,A7 .K #A
-- .;,P7.,A7
,PROBABIL;Y ( 9DEP5D5T EV5TS @7 P4
#GAG @7 @3 ,IF ,A& .;,B >E 9DEP5D5T1 !
PROBABIL;Y T BO? ,A& .;,B O3UR IS3
;,P7,AAND,B7 .K .;,P7.,A7 99 .;,P7.;,B7
,PROBABIL;Y ( DEP5D5T EV5TS @7 P4 #GAH
@7 @3 ,IF ,A& .;,B >E DEP5D5T1 !
PROBABIL;Y T BO? ,A& .;,B O3UR IS3
;,P7,AAND#7 .K ;,P7,A7 99
.;,P7.;,B@\.,A7
,BINOMIAL PROBABILITIES @7 P4 #GBE @7
@3 ,=A BINOMIAL EXP]I;T 3SI/+ ( .;N
TRIALS ": ! PROBABIL;Y ( SU3ESS ON EA*
TRIAL IS ;P1 ! PROBABIL;Y ( EXACTLY .;K
SU3ESSES IS3 .;,P7.;K SU3ESSES7 .K ;N.'
;,C.' ;K.' ;P.' ;K.' .-7;L--;P7
;N--;K.'.-
,=MULAS F ,/ATI/ICS
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,M1N (A DATA SET @7 P4 #GDD @7 @3 @4
": ;X 7R1D 8;X-B>07 IS ! M1N (! DATA .;X
@1@1 ;X #I @1'''@1 ;X ;N
,/&>D DEVI,N (A DATA SET @7 P4 #GDE @7
@3 ": A 7R1D 8SIGMA07 IS ! /&>D DEVI,N
(! DATAX ;P ;X.' #B @1'''@1 ;X.' ;N.'.-
,>1S "U A NORMAL CURVE @7 P4 #GEG @7
@3 .,A NORMAL 4TRIBU;N ) M1N ;X & /&>D
DEVI,N A HAS ^! PROP]TIES399 ,! TOTAL
>EA "U ! RELAT$ NORMAL CURVE IS #A4 99
,AB #FH@3P (! >EA LIES )9 #A /&>D DEVI,N
(! M1N4 99 ,AB #IE@3P (! >EA LIES )9 #B
/&>D DEVI,NS (! M1N4 99 ,AB #II.G@3P (!
>EA LIES )9 #C /&>D DEVI,NS (! M1N4
;Z-SCORE @7 P4 #GEH @7 @3 ": ;X IS A
DATA VALUE1 ;X IS ! M1N1 &A IS ! /&>D
DEVI,N
-----------------------------------#AJCJ
,=MULAS = ,SEQU;ES & ,S]IES
,,TA#S
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,=MULAS = SUMS ( SPECIAL S]IES @7 P4
#GIG @7 @3
,EXPLICIT RULE = AN >I?METIC SEQU;E @7
P4 #HJB @7 @3 ,! .N? T]M ( AN >I?METIC
SEQU;E ) F/ T]M A.' ;,Y.' & -MON DI6];E
DIS3 A.' ;N.' .K A.' ;X.' @+
7;N--#A7;D.'.-
,SUM (A F9ITE >I?METIC S]IES @7 P4
#HJD @7 @3 ,! SUM (! F/ .;N T]MS ( AN
>I?METIC S]IES IS3
,EXPLICIT RULE =A GEOMETRIC SEQU;E @7
P4 #HAJ @7 @3 ,! RA? T]M (A GEOMETRIC
SEQU;E ) F/ T]M A.' ;X.' & -MON RATIO ;R
IS3 A ;N .K A #A ;R ;N-#A
,SUM (A F9ITE GEOMETRIC S]IES @7 P4
#HAB @7 @3 ,! SUM (! F/ .;N T]MS (A
GEOMETRIC S]IES ) -MON RATIO .;R @6.K #A
IS3
,SUM ( AN 9F9ITE GEOMETRIC S]IES @7 P4
#HBA @7 @3 ,! SUM ( AN 9F9ITE GEOMETRIC
S]IES ) F/ T]M A.' ;X.' & -MON RATIO ;R
IS PROVID$ _\.;R _\ "K #A4 ,IF _\ .;R _\
.1 #A1 ! S]IES HAS NO SUM4
,RECURSIVE EQU,N = AN >I?METIC SEQU;E
@7 P4 #HBG @7 @3 A.' ;N.' .K A4 ;N -- #A
@+ ;D ": .;D IS ! -MON DI6];E
,RECURSIVE EQU,N =A GEOMETRIC SEQU;E
@7 P4 #HBG @7 @3 A.' ;N.' .K ;R.' 99 A.'
;N--#A ": ;R IS ! -MON RATIO
,=MULAS & ,ID5TITIES F ,TRIGONOMETRY
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,3V].N 2T DEGREES & RADIANS @7 P4 #HFJ
@7 @3 ,6REWRITE A DEGREE M1SURE 9
RADIANS1 MULTIPLY 0,6REWRITE A RADIAN
M1SURE 9 DEGREES1 MULTIPLY BY
,DEF9I;N ( TRIGONOMETRIC FUNC;NS @7 P4
#HFF @7 @3 ,LET .#F 2 AN ANGLE 9 /&>D
POSI;N & 7;X1 .;Y7 2 ANY PO9T 7EXCEPT !
ORIG97 ON ! T]M9AL SIDE ( .#F4 ,LET @4
,LAW ( S9ES @7 P4 #HHB @7 @3 ,IF ,,ABC
HAS SIDES ( L5G? .A1 .;B @1 & .;C @1 !N3
,>EA (A TRIANGLE 7GIV5 TWO SIDES &!
9CLUD$ ANGLE7 @7 P4 #HHE @7 @3 ,IF ,,ABC
HAS SIDES ( L5G? .A1 .;B @1 & .;C @1 !N
XS >EA IS3
-----------------------------------#AJCA
,=MULAS & ,ID5TITIES F ,TRIGONOMETRY
7.3T9U$7
,,TA#S
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,LAW ( COS9ES @7 P4 #HHI @7 @3 ,IF ,A
,,ABC HAS SIDES ( L5G? .A1 .;B @1 & .;C
@1 !N3 A.' #B .K ;B.' #B @+ ;C.' #B --
#B;BC.' COS ,A ;B.' #B .K A.' #B @+ ;C.'
#B -- .LAC COS ;,B ;C.' #B .K A.' #B @+
;B.' #B -- LAB.' COS ;,C
,H]ON'S >EA =MULA @7 P4 #HIA @7 @3 ,!
>EA (! TRIANGLE ) SIDES ( L5G? A1 ;B.'
;F.' & .;C IS ,>EA .K ": ;S .K
,RECIPROCAL ID5TITIES @7 P4 #IBD @7 @3
,TANG5T & COTANG5T ID5TITIES @7 P4
#IBD @7 @3
,PY?AGOR1N ID5TITIES @7 P4 #IBD @7 @3
S9 #B .#F @+ COS #B .K.#A #A @+ TAN #B
.K SEC #B #A @+ COT #B .K ESC #B
,C(UNC;N ID5TITIES @7 P4 #IBD @7 @3
,NEGATIVE ANGLE ID5TITIES @7 P4 #IBD
@7 @3 S9 @7--@7 .K --S9 .#F COS @7--@7
.K COS .#F TAN @7--@7 .K --TAN
,SUM =MULAS @7 P4 #IDI @7 @3 S9 7A @+
;FR7 .K S9 A COS .;B @+ COS A S9 .;B COS
7A @+ .;B7 .K COS A COS ;FR--S9 A S9 .;B
,DI6];E =MULAS @7 P4 #IDI @7 @3 S9 @7
..A--.;B7 .K S9 A COS ;B--COS .A S9 ;FR
COS @7 ..A--.;B7 .K COS A COS .;B @+ S9
A S9 .;B
,D\#-ANGLE =MULAS @7 P4 #IEE @7 @3 COS
.LA -- COS #B A--S9 #B .A S9 #B;A .K #B
S9 .A COS ACOS #B;A--#B COS #B .A -- #A
COS #B;A .K #A--#B S9 #B A
,HALF-ANGLE =MULAS @7 P4 #IEE @7 @3 ,!
SIGNS ( S9 & COS DEP5D ON ! QUADRANT 9 :
LIES4
-----------------------------------#AJCB
,=MULAS F ,GEOMETRY
,,TA#S
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,BASIC .GEOMETRIC .FIGURES @3 ,SEE
PAGES #IIA-IIC = >EA =MULAS = BASIC
TWO-DIM5.NAL GEOMETRIC FIGURES4
..,>EA ( AN EQUILAT]AL .TRIANGLE @3
,>EA ": ;S IS ! L5G? (A SIDE
..,>C L5G? & >EA (A .SECTOR @3 ,>C
L5G? .K .;R ": .;R IS ! RADIUS & .#I IS
! RADIAN M1SURE (! C5TRAL ANGLE T
9T]CEPTS ! >C
..,>EA ( AN .ELLIPSE @3 ,>EA .K -.TRAB
": .A & .;B >E HALF ! L5G?S (! MAJOR &
M9OR AXES (! ELLIPSE
..,VOLUME & SURFACE >EA (A "R
RECTANGUL> .PRISM @3 ,VOLUME .K .I: ":
;I IS ! L5G?1 .;W IS ! WID?1 & .;H IS !
HEI<T ,SURFACE >EA .K #B 7;L ..;W @+ WH
@+ .LH7
..,VOLUME & SURFACE >EA (A "R .CYL9D]
@3 ,VOLUME .K ;R.' #B ;H.' ": .;R IS !
BASE RADIUS & .;H IS ! HEI<T ,LAT]AL
SURFACE >EA .K .#B-.NRH ,SURFACE >EA .K
#B ;R.' #B @+ #B RH.'.-
..,VOLUME & SURFACE >EA (A "R REGUL>
.PYRAMID @3 ": .;,B IS ! >EA (! BASE &
.;H IS ! HEI<T4 ,LAT]AL ": .;N IS !
NUMB] ( SIDES (! BASE1 ;S IS ! L5G? (A
SIDE (! BASE1 & ;I IS ! SLANT HEI<T
..,VOLUME & SURFACE >EA (A "R CIRCUL>
.C"O @3 ;R.' #B ;H.' ": .;R IS ! BASE
RADIUS & .;H IS ! HEI<T ,LAT]AL SURFACE
>EA .K RL ": .;I IS ! SLANT HEI<T
,SURFACE >EA .K ;R#B @+ RL.'.-
..,VOLUME & SURFACE >EA (A .SPH]E @3
": .;R IS ! RADIUS ,SURFACE >EA .K #D #B
-----------------------------------#AJCC
,PROP]TIES
,,TA#S
,PROP]TIES ( ,R1L ,NUMB]S
,LET A1 .;B @72 & .;C 2 R1L NUMB]S4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 .,A4I;N @3 .,MULTIPLIC,N
,CLOSURE ,PROP]TY @7 P4 #C @7 @3 .A @+
.;B IS A R1L NUMB]4 @3 .;AB IS A R1L
NUMB]4
,-MUTATIVE ,PROP]TY @7 P4 #C @7 @3 .A
@+ .;B .K .;B @+ A @3 ;AB .K .BA
,ASSOCIATIVE ,PROP]TY @7 P4 #C @7 @3
@7 .A @+ .;B7 @+ ;C .K .A @+ 7#B8 @+ ;C7
@3 7;AB7;C .K A7BC7
,ID5T;Y ,PROP]TY @7 P4 #C @7 @3 ..A @+
#J .K A1 #J @+ A .K .A @3 A99;L .K
A;,L99A .K A
,9V]SE ,PROP]TY @7 P4 #C @7 @3 .A @+
7-.A7 .K #J @3 A 99 .K #A1 A @6.K #J
,4TRIBUTIVE ,PROP]TY @7 P4 #C @7 @3 ,!
4TRIBUTIVE PROP]TY 9VOLVES BO? A4I;N &
MULTIPLIC,N3 .A7.;B @+ .;C7 .K .;AB @+
.;AC @3 --
,Z]O ,PRODUCT ,PROP]TY @7 P4 #BEC @7
@3 ,LET .,A & .;,B 2 R1L NUMB]S OR
ALGEBRAIC EXPRES.NS4,IF .;,,AB .K #J1
.!N .,A .K #J OR .;,B .K #J4 @3 --
,PROP]TIES ( ,MATRICES
,LET .,A1 .;,B @72 & ,CBE MATRICES1 &
LET ,A3 2 A SCAL>4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,ASSOCIATIVE ,PROP]TY ( ,A4I;N @7 P4
#AHH @7 @3 7.,A @+ .;,B7 @+ ;,C .K .,A
@+ @7 .;,B @+ .;,C7
,-MUTATIVE ,PROP]TY ( ,A4I;N @7 P4
#AHH @7 @3 ..,A @+ ;,B .K .;,B @+ .,A
,4TRIBUTIVE ,PROP]TY ( ,A4I;N @7 P4
#AHH @7 @3 .;K7.,A @+ .;,B7 .K .K,A @+
.K,B
,4TRIBUTIVE ,PROP]TY ( ,SUBTRAC;N @7
P4 #AHH @7 @3 ..;K7,A--;,B7 .K K,A--.K,B
,ASSOCIATIVE ,PROP]TY ( ,MATRIX
,MULTIPLIC,N @7 P4 #AIG @7 @3 @7 .;,,AB7
..;,C .K .,A @7 .,BC7
,LEFT ,4TRIBUTIVE ,PROP]TY ( ,MATRIX
,MULTIPLIC,N @7 P4 #AIG @7 @3 .,A7.;,B
@+ .;,C7 .K .;,,AB @+ .;,,AC
,"R ,4TRIBUTIVE ,PROP]TY ( ,MATRIX
,MULTIPLIC,N @7 P4 #AIG @7 @3 @7 .,A @+
.;,B7.;,C .K .,,AC@+ .,,BC
,ASSOCIATIVE ,PROP]TY ( ,SCAL>
,MULTIPLIC,N @7 P4 #AIG @7 @3
.;K7.;,,AB7 .K 7.K,A7.;,B .K .,A7.K,B7
,MULTIPLICATIVE ,ID5T;Y @7 P4 #BAJ @7
@3 ,AN .;N ;,X .;N MATRIX ) L'S ON ! MA9
DIAGONAL & #J'S ELSE": IS AN ID5T;Y
MATRIX1 DENOT$4 ,= ANY .;N ;X .;N MATRIX
,A1 .,,AI .K .,,IA .K .,A4
,9V]SE ,MATRICES @7 P4 #BAJ @7 @3 ,IF
! DET]M9ANT ( AN .;N ;X .;N MATRIX .,A
IS NONZ]O1 !N .,A HAS AN 9V]SE1 DENOT$
,A -#A @1 S* T ,,AA --#A .K,A.' --;L.'
,A .K ;,L.'.-
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,LET .A & .;B 2 R1L NUMB]S1 & LET .;M
& .;N 2 9TEG]S4 ,PRODUCT ( ,P[]S
,PROP]TY @7 P4 #CCJ @7 A.' ;M.' 99 A.'
;N.' .K A.' ;M @+ ;N.'.-
,P[] (A ,P[] ,PROP]TY @7 P4 #CCJ @7 @3
7A.' ;M.' @7 ;N.' .K A.' .-MN.'.-
,P[] (A ,PRODUCT ,PROP]TY @7 P4 #CCJ
@7 @3 @7 .;AB7 ;M.' .K A.' ;M.' ;B.'
;M.'.-
,NEGATIVE ,EXPON5T ,PROP]TY @7 P4 #CCJ
@7 @3
,Z]O ,EXPON5T ,PROP]TY @7 P4 #CCJ @7
@3 A.' #J .K #A1 .A .;I @6.K #J
,QUOTI5T ( ,P[]S ,PROP]TY @7 P4 #CCJ
@7 @3
,P[] (A ,QUOTI5T ,PROP]TY @7 P4 #CCJ
@7 @3
-----------------------------------#AJCD
,PROP]TIES ( ,RADICALS & ,R,NAL
,EXPON5TS
,,TA#S
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,NUMB] ( ,R1L RA? ,ROOTS.'
@7 P4 #DAD @7 @3 ,LET ;N 2 AN 9TEG] GRT]
?AN #A1 & LET A 2 A R1L NUMB]43 99 ,IF
.;N IS ODD1 !N .A HAS "O R1L N? ROOT3
--@3 99 ,IF FT IS EV5 & .A .1 #J1 !N
.A HAS TWO R1L N? ROOTS3 @3 --
--@3 99 ,IF .;N IS EV5 & .A .K #J1 !N
.A HAS "O N? ROOT3 @3 --
--@3 99 ,IF .;N IS EV5 & .A "K #J1 !N
.A HAS NO R1L N? ROOTS4 @3 --
.,RADICALS .& .,R,NAL @3 ,LET A.'
#A_/;N.' 2 AN N? ROOT ( .A @1 & LET .;M
2 A POSITIVE 9TEG]4 @3 --
,EXPON5TS @7 P4 #DAE @7 @3 99 A.'
.-MLN.' .K 7A.' #A_/;N.' @7 ;M.' .K @3
--
--@3 @3 --
.,PROP]TIES .( .,R,NAL @3 ,ALL (!
PROP]TIES ( EXPON5TS LI/$ ON ! PREVI\S
PAGE APPLY 6R,NAL ,EXPON5TS @7 P4 #DBJ
@7 @3 EXPON5TS Z WELL Z 9TEG] EXPON5TS4
.,PRODUCT .& .,QUOTI5T @3 ,LET ;N 2 AN
9TEG] GRT] ?AN #A1 & LET .A & .;B 2
POSITIVE R1L @3 --
,PROP]TIES ( ,RADICALS @7 P4 #DBA @7
@3 NUMB]S4 ,!N @3 --
,PROP]TIES ( ,LOG>I?MS
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 ,LET ..A1 ;B1 ;C1 ;M1 ;N1 .;X @1
& .;Y 2 POSITIVE R1L NUMB]S S* T .;B
@6.K & .;C @6.K.#A
,LOG>I?MS & ,EXPON5TS @7 P4 #DII @7 @3
LOG ;B .;Y .K .;X IF & ONLY ;I FB.' ;X.'
.K ;Y.'.-
,SPECIAL ,LOG>I?M ,VALUES @7 P4 #DII
@7 @3 LOG FE #A .K #J 2C .;B;DG .K #A &
LOG FE .;B .K #A 2C ;B.' #A .K ;B.'.-
,-MON & ,NATURAL ,LOG>I?MS @7 P4 #EJJ
@7 @3 LOG #AJ .;X .K LOG .;X & LOG ;E ;X
.K LN ;X
,PRODUCT ,PROP]TY ( ,LOG>I?MS @7 P4
#EJG @7 @3 @\OG.' ;B.' .-MN .K LOG FC
.;M @+ LOG #F .;N
,QUOTI5T ,PROP]TY ( ,LOG>I?MS @7 P4
#EJG @7 @3 _<;G.' ;B.' .K LOG.' ;B.'
;M-LOG.' ;B.' ;N.'.-
,P[] ,PROP]TY ( ,LOG>I?MS @7 P4 #EJG
@7 @3 LOG.' ;B.' ;M.' ;N.' .K .;N LOG.'
;B.' .;M
,*ANGE ( ,BASE @7 P4 #EJH @7 @3 LOG.'
;B.' A.'.-
,PROP]TIES ( ,FUNC;NS
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,OP],NS ON ,FUNC;NS @7 PP4 #DBH ,#DCJ7
@3 ,LET_/& .;G 2 ANY TWO FUNC;NS4 ,A NEW
FUNC;N ;N C 2 DEF9$ US+ ANY (! FOLL[+
OP],NS4
--@3 ,A4I;N3 ;N7;X7 .K ..;F7;X7 @+
;G7.;X7
--@3 .,SUBTRAC;N3 ..;H7;X7 .K
;F7;X7--;G7.;X7
--@3 .,MULTIPLIC,N3 ..;H7;X7 .K FIX7
99 ;G7.;X7
--@3 .FIX7 ,DIVI.N3
--@3 .,-POSI;N3 .;H7.;X7 .K ;G7;F7;X77
--@3 ,= A4I;N1 SUBTRAC;N1 MULTIPLIC,N1
& DIVI.N1 ! DOMA9 ( .;H 3SI/S (!
;X-VALUES T >E 9 ! DOMA9S ( BO?_/& .G4
,A4I;N,Y1 ! DOMA9 (! QUOTI5T DOES N
9CLUDE ;X-VALUES = : ;G7;X7 .K #J4
--@3 ,= -POSI;N1 ! DOMA9 ( .;H IS !
SET ( ALL ;X-VALUES S* T ;X IS 9 ! DOMA9
(_/&_/7;X7 IS 9 ! DOMA9 ( G4
,9V]SE ,FUNC;NS @7 P4 #DCH @7 @3
,FUNC;NS .;F & ;G >E 9V]SES ( EA* O!R
PROVID$3 .;F7.;G7.;X77 .K .;X &
.;G7.;F7.;X77 .K .;X
-----------------------------------#AJCE
,5GLI%--,SPANI% ,GLOSS>Y
,5GLI%--,SPANI% ,GLOSS>Y
,A
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
ABSOLUTE VALUE @7 P4 #EA @7 ,!
ABSOLUTE VALUE (A NUMB] .;X @1 REPRES5T$
0! SYMBOL _\ .;X _\, IS ! 4T.E ! NUMB]
IS F #J ON A NUMB] L9E4
..VALOR ABSOLUTO 7P@AG4 .#EA7 ,EL VALOR
ABSOLUTO DE UN N@UM]O .;X @1 REPRES5TADO
POR EL S@IMBOLO _\ .;X _\, ES LA 4TANCIA
A LA QUE E/@A EL N@UM]O DE #J EN UNA
RECTA NUM@ERICA4 @3
ABSOLUTE VALU@E FUNC;N @7 P4 #ABC @7
,A FUNC;N T 3TA9S AN ABSOLUTE VALUE
EXPRES.N4
..FUNCI@ON DE VALOR ABSOLUTO 7P@AG4
.#ABC7 ,FUNCI@ON QUE 3TI5E UNA
EXPRESI@ON DE VALOR ABSOLUTO4 @3 _\ .;Y
_\ .K _\ .;X _\, .;Y .K _\ .;X -- #C_\1
& .;Y .K #D _\ .;X @+ #H_\--#I >E
ABSOLUTE VALUE FUNC;NS4 .;Y .K _\ .;X
_\, .;Y .K _\ .;X -- #C_\;E .;Y .K #D _\
.;X @+ #H_\--#I SON FUNCI"OS DE VALOR
ABSOLUTO4
ABSOLUTE VALUE (A -PLEX NUMB] @7 P4
#BGI @7 ,IF .;Z .K A @+ .BI ,!N !
ABSOLUTE VALUE ( .;Z @1 DENOT$ _\ .;Z
_\, IS A NONNEGATIV]1L NUMB] DEF9$ Z @4
..VALOR ABSOLUTO DE UN N@UM]O -PLEJO
7P@AG4 .#BGI7 ,SI .;Z .K .A @+ .BI @1
5TONCES EL VALOR ABSOLUTO DE .;Z @1
DENOTADO POR _\ .;Z _\, ES UN N@UM]O R1L
NO NEGATIVO DEF9IDO -O @4 @3
ALGEBRAIC EXPRES.N @7 P4 #AA @7 ,AN
EXPRES.N T 3SI/S ( NUMB]S1 V>IA#S1
OP],NS1 & GR\P+ SYMBOLS4 ,AL CALL$ V>IA#
EXPRES.N4
..EXPRESI@ON ALGEBRAICA 7P@AG4 .#AA7
,EXPRESI@ON =MADA POR N@UM]OS1 V>IA#S1
OP]ACI"OS ;Y SIGNOS DE AGRUPACI@ON4 @3
@1 & .;N #B @+ #B .;N >E ALGEBRAIC
EXPRES.NS4
SON EXPRE.NES ALGEBRAICAS4
AMPLITUDE @7 P4 #IJH @7 ,! AMPLITUDE
(! GRAPH (A S9E OR COS9E FUNC;N IS @1 ":
.;,M IS ! MAXIMUM VALUE (! FUNC;N & .;M
IS ! M9IMUM VALUE (! FUNC;N4
.AMPLITUD 7.P@AG4 .#IJH7 ,LA AMPLITUD DE
LA GR@AFICA DE UNA FUNCI@ON S5O ;O COS5O
ES @1 DONDE .;,M ES EL VALOR M@AXIMO DE
LA FUNCI@ON ;Y .;M ES EL VALOR M@INIMO
DE LA FUNCI@ON4 @3
,! GRAPH ( .;Y .K #D S9 .;X HAS AN
AMPLITUDE ( @4
,LA GR@AFICA DE .;Y .K #D S5 .;X TI5E
UNA AMPLITUD DE @4
..ANGLE ( DEPRES.N 7P#..HEE7 ,! ANGLE
0: AN OBS]V]'S L9E ( SI<T M/ 2 DEPRESS$
F ! HORIZONTAL 6! PO9T OBS]V$4
..@ANGULO DE DEPRESI@ON 7P@AG4 .#HEE7
,EL @ANGULO CON EL QUE SE DEBE BAJ> LA
L@INEA DE VISI@ON DE UN OBS]VADOR DESDE
LA HORIZONTAL HA/A EL PUNTO OBS]VADO4 @3
.,SEE ANGLE ( ELEV,N4
.,V] @ANGULO DE ELEVACI@ON4
-----------------------------------#AJCF
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
ANGLE ( ELEV,N @7 P4 #HEE @7 ,! ANGLE
0: AN OBS]V]'S L9E ( SI<T M/ 2 ELEVAT$ F
! HORIZONTAL 6! PO9T OBS]V$4
..@ANGULO DE ELEVACI@ON 7P@AG4 .#HEE7
,EL @ANGULO CON EL QUE SE DEBE ELEV> LA
L@INEA DE VISI@ON DE UN OBS]VADOR DESDE
LA HORIZONTAL HA/A EL PUNTO OBS]VADO4 @3
>I?METIC SEQU;E @7 P4 #HJB @7 ,A
SEQU;E 9 : ! DI6];E ( 3SECUTIVE T]MS IS
3/ANT4
..PROGRESI@ON >ITM@ETICA 7P@AG4 .#HJB7
,PROGRESI@ON EN LA QUE LA DIF]5CIA 5TRE
LOS T@ERM9OS 3SECUTIVOS ES 3/ANTE4 @3
--#D1 #A1 #F1 #AA1 #AF1''' IS AN
>I?METIC SEQU;E ) -MON DI6];E #E4
--#D1 #A1 #F1 #AA1 #AF1''' ES UNA
PROGRESI@ON >ITM@ETICA CON UNA DIF]5CIA
-@UN DE #E4
>I?METIC S]IES @7 P4 #HJD @7 ,!
EXPRES.N =M$ 0A4+ ! T]MS ( AN >I?METIC
SEQU;E4
..S]IE >ITM@ETICA 7P@AG4 .#HJD7 ,LA
EXPRESI@ON =MADA ;AL SUM> LOS T@ERM9OS
DE UNA PROGRESI@ON >ITM@ETICA4 @3
ASYMPTOTE @7 P4 #DGH @7 ,A L9E T A
GRAPH APPROA*ES M & M CLOSELY4
.AS@INTOTA 7.P@AG4 .#DGH7 ,RECTA A LA
QUE SE APROXIMA UNA GR@AFICA CADA VEZ
M@AS4 @3
,! ASYMPTOTE =! GRAPH %[N IS ! L9E .;Y
.K #C
,LA AS@INTOTA P>A LA GR@AFICA QUE SE
MUE/RA ES LA RECTA .;Y .K #C4
AXIS ( SYMMETRY (A P>@ABOLA @7 PP4
#BCF @1 #FBJ @7 ,! L9E P]P5DICUL> 6!
P>ABOLA'S DIRECTRIX & PASS+ "? XS FOCUS
& V]TEX4
..EJE DE SIMETR@IA DE UNA P>@ABOLA
7P@AGS4 #BCF1 .#FBJ7 ,LA RECTA
P]P5DICUL> A LA DIRECTRIZ DE LA P>@ABOLA
;Y QUE PASA POR SU FOCO ;Y SU V@ERTICE4
@3 .,SEE P>ABOLA4
.,V] P>@ABOLA4
;,B
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
BASE (A P[] @7 P4 #AJ @7 ,! NUMB] OR
EXPRES.N T IS US$ Z A FACTOR 9 A REP1T$
MULTIPLIC,N4
..BASE DE UNA POT5CIA 7P@AG4 .#AJ7 ,EL
N@UM]O ;O LA EXPRESI@ON QUE SE USA -O
FACTOR EN LA MULTIPLICACI@ON REPETIDA4
@3 ,9 ! P[] #B #E @1 ! BASE IS #B4
,EN LA POT5CIA #B #E @1 LA BASE ES #B4
-----------------------------------#AJCG
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
BE/-FITT+ L9E @7 P4 #AAD @7 ,! L9E T
LIES Z CLOSE Z POSSI# 6ALL ! DATA PO9TS
9 A SCATT] PLOT4
..MEJOR RECTA DE REGRESI@ON 7P@AG4
.#AAD7 ,LA RECTA QUE SE AJU/A LO M@AS
POSI# A TODOS LOS PUNTOS DE DATOS DE UN
DIAGRAMA DE 4P]SI@ON4 @3
BE/-FITT+ QUADRATIC MODEL @7 P4 #CAA
@7 ,! MODEL GIV5 0US+ QUADRATIC REGRES.N
ON A SET ( PAIR$ DATA4
..MODELO CUADR@ATICO CON MEJOR AJU/E
7P@AG4 .#CAA7 ,EL MODELO DADO ;AL R1LIZ>
UNA REGRESI@ON CUADR@ATICA SOBRE UN
3JUNTO DE P>ES DE DATOS4 @3
BIAS$ "Q @7 P4 #GGB @7 ,A "Q T ELICITS
RESPONSES T D N A3URATELY REFLECT !
OP9IONS OR AC;NS (! P SURVEY$4
..PREGUNTA CAPCIOSA 7P@AG4 .#GGB7
,PREGUNTA QUE 9DUCE A RESPUE/AS QUE NO
REFLEJAN CON EXACTITUD LAS OP9I"OS ;O
A3I"OS DE LOS 5CUE/ADOS4 @3 8,WD Y R SEE
AN EXCIT+ LAS] %[ OR A BOR+ MOVIE80 IS A
BIAS$ "Q4
88,PREF]IR@IAS V] UN EMOCIONANTE
ESPECT@ACULO DE L@AS] ;O UNA PEL@ICULA
ABURRIDA80 ES UNA PREGUNTA CAPCIOSA4
BIAS$ SAMPLE @7 P4 #GFG @7 ,A SAMPLE T
OV]REPRES5TS OR "UREPRES5TS "P (A
POPUL,N4
..MUE/RA SESGADA 7P@AG4 .#GFG7 ,MUE/RA
QUE REPRES5TA DE =MA EXCESIVA ;O
9SUFICI5TE A "PE DE UNA POBLACI@ON4 @3
,! MEMB]S (A S*OOL'S BASKETBALL T1M WD
=M A BIAS$ SAMPLE =A SURVEY AB :E!R
6BUILD A NEW GYM4
,LOS MIEMBROS DEL EQUIPO DE BALONCE/O DE
UNA ESCUELA =M>@IAN UNA MUE/RA SESGADA
SI "PICIP>AN EN UNA 5CUE/A SOBRE SI
QUI]5 QUE SE 3/RUYA UN NUEVO GIMNASIO4
BINOMIAL @7 P4 #BEB @7 ,! SUM ( TWO
MONOMIALS4
.B9OMIO 7.P@AG4 .#BEB7 ,LA SUMA DE DOS
MONOMIOS4 @3 #C .;X -- #A & .;T #C -- #D
.;T >E BINOMIALS4
#C .;X -- #A ;Y .;T #C -- #D .;T SON
B9OMIOS4
BINOMIAL 4TRIBU;N @7 P4 #GBE @7 ,!
PROBABIL;Y 4TRIBU;N ASSOCIAT$ )A
BINOMIAL EXP]I;T4
..4TRIBUCI@ON BINOMIAL 7P@AG4 .#GBE7 ,LA
4TRIBUCI@ON DE PROBABILIDADES ASOCIADA A
UN EXP]I;TO BINOMIAL4 @3
,BINOMIAL 4TRIBU;N = #H TRIALS ) .;P .K
#J.E4
,4TRIBUCI@ON BINOMIAL DE #H PRUEBAS CON
.;P .K #J.E4
-----------------------------------#AJCH
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
BINOMIAL EXP]I;T @7 P4 #GBE @7 ,AN
EXP]I;T T MEETS ! FOLL[+ 3DI;NS4 7#A7
,"! >E .;N 9DEP5D5T TRIALS4 7#B7 ,EA*
TRIAL HAS ONLY TWO POSSI# \TCOMES3
SU3ESS & FAILURE4 7#C7 ,! PROBABIL;Y (
SU3ESS IS ! SAME = EA* TRIAL4
..EXP]I;TO BINOMIAL 7P@AG4 .#GBE7
,EXP]I;TO QUE SATISFACE LAS SIGUI5TES
3DICI"OS4 7#A7 ,HAY .;N PRUEBAS
9DEP5DI5TES4 7#B7 ,CADA PRUEBA TI5E
S@OLO DOS RESULTADOS POSI#S3 @EXITO ;Y
FRACASO4 7#C7 ,LA PROBABILIDAD DE @EXITO
ES IGUAL P>A CADA PRUEBA4 @3 ,A FAIR CO9
IS TOSS$ #AB "TS4 ,! PROBABIL;Y ( GETT+
EXACTLY #D H1DS IS Z FOLL[S3
,UNA MON$A NORMAL SE LANZA #AB VECES4
,LA PROBABILIDAD DE SAC> EXACTA;TE #D
C>AS ES LA SIGUI5TE3
BINOMIAL !OREM @7 P4 #FIC @7 ,!
BINOMIAL EXPAN.N ( @7 .A @+ .;B @7 .;N =
ANY POSITIVE 9TEG] .;N @3
..TEOREMA BINOMIAL 7P@AG4 .#FIC7 ,LA
EXPANSI@ON BINOMIAL DE @7 .A @+ .;B @7
;N P>A CUALQUI] N@UM]O 5T]O POSITIVO .;N
@3
@3
;,C
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
C5T] (A DRDE @7 P4 #FBF @7 ,SEE
CIRCLE4
..C5TRO DE UN C@IRCULO 7P@AG4 .#FBF7 ,V]
C@IRCULO4 @3 ,! CIRCLE ) EQU,N @7 .;X --
#C7 #B @+ @7 .;Y @+ #E7 #B .K #CF HAS XS
C5T] AT 7#C1 --#E74 .,SEE .AL CIRCLE4
,EL C@IRCULO CON LA ECUACI@ON @7 .;X --
#C7 #B @+ @7 .;Y @+ #E7 #B .K #CF TI5E
EL C5TRO EN 7#C1 --#E74 .,V] .TAMBI@EN
C@IRCULO4
C5T] (A HYP]BOLA @7 P4 #FDB @7 ,!
MIDPO9T (! TRANSV]SE AXIS (A HYP]BOLA4
..C5TRO DE UNA HIP@ERBOLA 7P@AG4 .#FDB7
,EL PUNTO M$IO DEL EJE TRANSV]SO DE UNA
HIP@ERBOLA4 @3 .,SEE HYP]BOLA4
.,V] HIP@ERBOLA4
C5T] ( AN ELLIPSE @7 P4 #FCD @7 ,!
MIDPO9T (! MAJOR AXIS ( AN ELLIPSE4
..C5TRO DE UNA ELIPSE 7P@AG4 .#FCD7 ,EL
PUNTO M$IO DEL EJE MAYOR DE UNA ELIPSE4
@3 .,SEE ELLIPSE4
.,V] ELIPSE4
C5TRAL ANGLE @7 P4 #HFA @7 ,AN ANGLE
=M$ 0TWO RADII (A CIRCLE4
..@ANGULO C5TRAL 7P@AG4 .#HFA7 ,@ANGULO
=MADO POR DOS RADIOS DE UN C@IRCULO4 @3
.,SEE SECTOR4
.,V] SECTOR4
-----------------------------------#AJCI
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
CIRCLE @7 P4 #FBF @7 ,! SET ( ALL
PO9TS @7 .;X @1 .;Y @7 9 A PLANE T >E (
4T.E .;R F A FIX$ PO9T1 CALL$ ! C5T] (!
CIRCLE4
.C@IRCULO 7.P@AG4 .#FBF7 ,EL 3JUNTO DE
TODOS LOS PUNTOS @7 .;X @1 .;Y @7 DE UN
PLANO QUE E/@AN A UNA 4TANCIA .;R DE UN
PUNTO FIJO1 LLAMADO C5TRO DEL C@IRCULO4
@3
COE6ICI5T @7 P4 #AB @7 ,:5 A T]M IS !
PRODUCT (A NUMB] &A P[] (A V>IA#1 !
NUMB] IS ! COE6ICI5T (! P[]4
.COEFICI5TE 7.P@AG4 .#AB7 ,CU&O UN
T@ERM9O ES EL PRODUCTO DE UN N@UM]O ;Y
UNA POT5CIA DE UNA V>IA#1 EL N@UM]O ES
EL COEFICI5TE DE LA POT5CIA4 @3 ,9 !
ALGEBRAIC EXPRES.N #B .;X #B @+ 7--#D
.;X @7 @+ 7--#A71 ! COE6ICI5T ( #B .;X
#B IS #B &! COE6ICI5T ( --#D .;X IS
--#D4
,EN LA EXPRESI@ON ALGEBRAICA #B .;X #B
@+ 7--#D .;X @7 @+ 7--#A71 EL COEFICI5TE
DE #B .;X #B ES #B ;Y EL COEFICI5TE DE
--#D .;X ES --#D4
COE6ICI5T MATRIX @7 P4 #BJE @7 ,!
COE6ICI5T MATRIX (! L9E> SY/EM @4
..MATRIZ COEFICI5TE 7P@AG4 .#BJE7 ,LA
MATRIZ COEFICI5TE DELSI/EMA L91L @4 @3
#I .;X @+ #D .;Y .K --#F
#C .;X -- #E .;Y .K --#BA
COE6ICI5T MATRIX3
MATRIZ COEFICI5TE3
MATRIX ( 3/ANTS3
MATRIZ DE 3/ANTES3
MATRIX ( V>IA#S3
MATRIZ DE V>IA#S3
-B9,N @7 P4 #FIJ @7 ,A SELEC;N ( .;R
OBJECTS F A GR\P ( .;N OBJEETS ": ! ORD]
IS N IMPORTANT1 DENOT$ ;N.' ;,C.' ;R.'
": @4
.-B9ACI@ON 7.P@AG4 .#FIJ7 ,SELE3I@ON DE
.;R OBJETOS DE UN GRUPO DE .;N OBJETOS
EN EL QUE EL ORD5 NO IMPORTA1 DENOTADO
;N.' ;,C.' ;R.' ,DONDE @4 @3 ,"! >E #F
-B9,NS (! .;N .K #D LRS,A1 ;,B1 ;,C1 &
;,D SELECT$ .;R .K #B AT A "T3 ;,,AB1
;,,AC1 ,,AD1 ,,BC1 ,,BD1 & ;,,CD4
,HAY #F -B9ACI"OS DE LAS LETRAS .;N .K
#D ,A1 ;,B1 ;,C ;Y ;,D SELE3IONADAS .;R
.K #B CADA VEZ3 ;,,AB1 ;,,AC1 ,,AD1
,,BC1 ,,BD ;Y ;,,CD4
-MON DI6];E @7 P4 #HJB @7 ,! 3/ANT
DI6];E ( 3SECUTIVE T]MS ( AN >I?METIC
SEQU;E4
..DIF]5CIA -@UN 7P@AG4 .#HJB7 ,LA
DIF]5CIA 3/ANTE 5TRE LOS T@ERM9OS
3SECUTIVOS DE UNA PROGRESI@ON
>ITM@ETICA4 @3 .,SEE >I?METIC SEQU;E4
.,V] PROGRESI@ON >ITM@ETICA4
-MON LOG>I?M @7 P4 #EJJ @7 ,A LOG>I?M
) BASE #AJ4 ,X IS DENOT$ 0LOG #AJ OR
SIMPLY 0LOG4
..LOG>ITMO -@UN 7P@AG4 .#EJJ7 ,LOG>ITMO
CON BASE #AJ4 ,SE DENOTA POR LOG #AJ ;@O
SIMPLE;TE POR LOG4 @3 LOG #AJ #AJJ .K
LOG #AJJ .K #B 2C #AJ #B .K #AJJ4
LOG #AJ #AJJ .K LOG #AJJ .K #B YA QUE
#AJ #B .K #AJJ4
-----------------------------------#AJDJ
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
-MON RATIO @7 P4 #HAJ @7 ,! 3/ANT
RATIO ( 3SECUTIVE T]MS (A GEOMETRIC
SEQU;E4
..RAZ@ON -@UN 7P@AG4 .#HAJ7 ,LA RAZ@ON
3/ANTE 5TRE LOS T@ERM9OS 3SECUTIVOS DE
UNA PROGRESI@ON GEOM@ETRICA4 @3 .,SEE
GEOMETRIC SEQU;E4
.,V] PROGRESI@ON GEOM@ETRICA4
..-PLE;T (A SET 7P#..GAE7 ,! -PLE;T (A
SET ,A1 WRITT51 IS ! SET ( ALL ELE;TS 9
! UNIV]SAL SET .;,U T >E .N 9 .,A @4
..-PLE;TO DE UN 3JUNTO 7P@AG4 .#GAE7 ,EL
-PLE;TO DE UN 3JUNTO .,A @1 ESCRITO1 ES
EL 3JUNTO DE TODOS LOS ELE;TOS DEL
3JUNTO UNIV]SAL .;,U QUE .NO E/@AN EN ,A
@3 ,LET .;,U 2 ! SET ( ALL 9TEG]S F #A
6#AJ & LET ,A .K ;7#A1B1D1H724 ,!N .K
;7#C1 #E1 #F1 #G1 #I1 #AJ724
,SEA .;,U EL 3JUNTO DE TODOS LOS N@UM]OS
5T]OS 5TRE #A ;Y #AJ ;Y SEA .,A .K ;7#A1
#B1 #D1 #H724 ,POR LO TANTO1 .K ;7#C1
#E1 #F1 #G1 #I1 #AJ724
-PLET+ ! SQU>E @7 P4 #BHD @7 ,!
PROCESS ( A4+ A T]M 6A QUADRATIC
EXPRES.N (! =M .;X #B @+ .BX 6MAKE X A
P]FECT SQU>E TRINOMIAL4
..-PLET> EL CUADRADO 7P@AG4 .#BHD7 ,EL
PROCESO DE SUM> UN T@ERM9O A UNA
EXPRESI@ON CUADR@ATICA DE LA =MA .;X #B
@+ .BX @1 DE MODO QUE SEA UN TR9OMIO
CUADRADO P]FECTO4 @3 ,6-PLETE ! SQU>E =
.;X #B #;X#JJB;,B2 #AF .;X @1 ADD @4
,P>A -PLET> EL CUADRADO P>A .;X #B @+
#AF .;X @1 SUMA @4
-PLEX 3JUGATES @7 P4 #BGF @7 ,TWO
-PLEX NUMB]S (! =M .A @+ .BI & .A -- .BI
@4
..N@UM]OS -PLEJOS 3JUGADOS 7P@AG4 .#BGF7
,DOS N@UM]OS -PLEJOS DE LA =MA ..A @+ BI
;Y A--.BI4 @3 #B @+ #D .;I @1 #B--#D .;I
-PLEX FRAC;N @7 P4 #EHD @7 ,A FRAC;N T
3TA9S A FRAC;N 9 XS NUM]ATOR OR
DENOM9ATOR4
..FRA3I@ON -PLEJA 7P@AG4 .#EHD7
,FRA3I@ON QUE TI5E UNA FRA3I@ON EN SU
NUM]ADOR ;O EN SU DENOM9ADOR4 @3
-PLEX NUMB] @7 P4 #BGF @7 ,A NUMB] .A
@+ .BI ": .A & .;B >E R1L NUMB]S & .;I
IS ! IMAG9>Y UNIT4
..N@UM]O -PLEJO 7P@AG4 .#BGF7 ,UN N@UM]O
.A @+ .BI @1 DONDE .A ;Y .;B SON N@UM]OS
R1LES ;E .;I ES LA UNIDAD IMAG9>IA4 @3
-PLEX PLANE @7 P4 #BGH @7 ,A COORD9ATE
PLANE 9 : EA* PO9T @7 .A1 .;B @7
REPRES5TS A -PLEX NUMB] .A @+ .BI @4 ,!
HORIZONTAL AXIS IS ! R1L AXIS &! V]TICAL
AXIS IS ! IMAG9>Y AXIS4
..PLANO -PLEJO 7P@AG4 .#BGH7 ,PLANO DE
COORD5ADAS EN EL QUE CADA PUNTO @7 .A1
.;B @7 REPRES5TA UN N@UM]O -PLEJO .A @+
.BI @4 ,EL EJE HORIZONTAL ES EL EJE R1L1
;Y EL EJE V]TICAL ES EL EJE IMAG9>IO4 @3
..-POSI;N ( FUNC;NS 7P#..DCJ7 ,!
-POSI;N ( AFUNC;NG )A FUNC;N .;F IS .;H
@7 .;X @7 .K .;G @7 .;F @7 .;X @7@7@4
..-POSICI@ON DE FUNCI"OS 7P@AG4 .#DCJ7
,LA -POSICI@ON DE UNA FUNCI@ON ;G CON
UNA FUNCI@ON .;F ES .;H7.;X7 .K ;G7 .;F
7;X774 @3
-----------------------------------#AJDA
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.-P.D .EV5T 7.P#..GJG7 ,! UNI@ON OR
9T]SEC;N ( TWO EV5TS4
..SUCESO -PUE/O 7P@AG4 .#GJG7 ,LA UNI@ON
;O LA 9T]SE3I@ON DE DOS SUCESOS4 @3 ,:5
Y ROLL A SIX-SID$ DIE1 ! EV5T 8ROLL A #B
OR AN ODD NUMB]0 IS A -P.D EV5T4
,CU&O LANZAS UN CUBO NUM]ADO DE SEIS
LADOS1 EL SUCESO 8SALIR EL #B ;@O UN
N@UM]O IMP>0 ES UN SUCESO -PUE/O4
-P.D 9EQUAL;Y @7 P4 #DA @7 ,TWO SIMPLE
9EQUALITIES JO9$ BY 8&0 OR 8OR40
..DESIGUALDAD -PUE/A 7P@AG4 .#DA7 ,DOS
DESIGUALDADES SIMPLES UNIDAS POR 8;Y0 ;U
8;O04 @3 #B .;X .1 #J OR .;X @+ #D
"K--;L IS A -P.D 9EQUAL;Y4
#B .;X .1 #J ;@O .;X @+ #D "K --;L ES
UNA DESIGUALDAD -PUE/A4
.3DI;NAL .PROBABIL;Y 7.P#..GAH7 ,!
3DI;NAL PROBABIL;Y ( .;,B GIV5 .,A @1
WRITT5 .;,P @7 .;,B @\ .,A @7@1 IS !
PROBABIL;Y T EV5T .;,B W O3UR GIV5 T
EV5T ,A HAS O3URR$4
..PROBABILIDAD 3DICIONAL 7P@AG4 .#GAH7
,LA PROBABILIDAD 3DICIONAL DE .;,B DADO
.,A @1 ESCRITO .;,P @7 .;,B @\ .,A @7@1
ES LA PROBABILIDAD DE QUE OCURRA EL
SUCESO .;,B DADO QUE HA OCURRIDO EL
SUCESO .,A4 @3 ,TWO C>DS >E R&OMLY
SELECT$ F A /&>D DECK ( #EB C>DS4 ,LET
EV5T .,A 2 8! F/ C>D IS A CLUB0 & LET
EV5T .;,B 2 8! SECOND C>D IS A CLUB40
,!N 2C "! >E #AB 7\ (#AC7 CLUBS LEFT
AM;G ! REMA9+ #EA C>DS4,DOS C>TAS SE
SELE3IONAN ;AL AZ> DE UNA B>AJA NORMAL
DE #EB C>TAS4 ,SEA EL SUCESO .,A 8LA
PRIM]A C>TA ES DE TR@EBOLES0 ;Y SEA EL
SUCESO .;,B 8LA SEGUNDA C>TA ES DE
TR@EBOLES0.,5TONCES YA QUE QU$AN#AB 7DEL
TOTAL DE #AC7 C>TAS DE TR@EBOLES 5TRE
LAS #EA C>TAS RE/ANTES4
3IC @7 P4 #FEJ @7 .,SEE 3IC SEC;N4
.C@ONICA 7.P@AG4 .#FEJ7 ,V] SE3I@ON
C@ONICA4 #A @3 .,SEE 3IC SEC;N4
.,V] SE3I@ON C@ONICA4
3IC SEC;N @7 P4 #FEJ @7 ,A CURVE =M$
0! 9T]SEC;N (A PLANE &A D\#-NAPP$ C"O4
,3IC SEC;NS >E AL CALL$ 3ICS4
..SE3I@ON C@ONICA 7P@AG4 .#FEJ7 ,UNA
CURVA =MADA POR LA 9T]SE3I@ON DE UN
PLANO ;Y UN 3O DO#4 ,LAS SE3I"OS
C@ONICAS TAMBI@EN SE LLAMAN C@ONICAS4 @3
.,SEE CIRCLE1 ELLIPSE1 HYP]BOLA1 .&
P>ABOLA4
.,V] C@IRCULO1 ELIPSE1 HIP@ERBOLA ;Y
P>@ABOLA4
3JUGATES @7 P4 #BFG @7 ,! EXPRES.NS ":
.A & .;B >E R,NAL NUMB]S4
.3JUGADOS 7.P@AG4 .#BFG7 ,LAS EXPRE.NES
CU&O .A ;Y .;B SON N@UM]OS RACIONALES4
@3 ,! 3JUGATE ( @4
,EL 3JUGADO DE @4
3SI/5T SY/EM @7 P4 #AED @7 ,A SY/EM (
EQU,NS T HAS AT L1/ "O SOLU;N4
..SI/EMA -PATI# 7P@AG4 .#AED7 ,SI/EMA DE
ECUACI"OS QUE TI5E ;AL M5OS UNA
SOLUCI@ON4 @3 .;Y .K #B @+ #C .;X
#F .;X @+ #B .;Y .K #D
,! SY/EM ABV IS 3SI/5T1 ) SOLU;N7#J1
#B74
,EL SI/EMA DE >RIBA ES -PATI#1 CON LA
SOLUCI@ON 7#J1 #B74
-----------------------------------#AJDB
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
3/ANT( V>I,N @7 PP4 #AJG @1 #EEA @1
#EEC @7 ,! NONZ]O 3/ANT A 9 A DIRECT
V>I,N EQU,N .;Y .K .AX @1 AN 9V]SEV>I,N
EQU,N @1 OR A JO9T V>I,N EQU,N .;Z .K
.AXY @4
..3/ANTE DE V>IACI@ON 7P@AGS4 #AJG1
#EEA1 .#EEC7 ,LA 3/ANTE 4T9TA DE C]O .A
DE UNA ECUACI@ON DE V>IACI@ON DIRECTA
.;Y .K .AX @1 DE UNA ECUACI@ON DE
V>IACI@ON 9V]SA ;O DE UNA ECUACI@ON DE
V>IACI@ON 3JUNTA .;Z .K .AXY @4 @3 ,9 !
DIRECT V>I,N EQU,N @1 ! 3/ANT ( V>I,N IS
@4
,EN LA ECUACI@ON DE V>IACI@ON DIRECTA
,LA 3/ANTE DE V>IACI@ON ES @4
3/ANT T]M @7 PP4 #AB @1 #CCG @7 ,A T]M
T HAS A NUMB] "P B NO V>IA# "P4
..T@ERM9O 3/ANTE 7P@AGS4 #AB1 .#CCG7
,T@ERM9O QUE TI5E UNA "PE NUM@ERICA P]O
S9 V>IA#4 @3 ,! 3/ANT T]M (! ALGEBRAIC
EXPRES.N #C .;X #B @+ #E .;X @+ 7--#G7
IS --#G4
,EL T@ERM9O 3/ANTE DE LA EXPRESI@ON
ALGEBRAICA #C .;X #B @+ #E .;X @+ 7--#G7
ES --#G4
3/RA9TS @7 P4 #AGD @7 ,9 L9E>
PROGRAMM+1 ! L9E> 9EQUALITIES T =M A
SY/EM4
.RE/RI3I"OS 7.P@AG4 .#AGD7 ,EN LA
PROGRAMACI@ON L91L1 LAS DESIGUALDADES
L91LES QUE =MAN UN SI/EMA4 @3 .,SEE L9E>
PROGRAMM+4
.,V] PROGRAMACI@ON L91L4
3T9U\S FUNC;N @7 P4 #HJ @7 ,A FUNC;N
^: GRAPH IS UNBROK54
..FUNCI@ON 3T9UA 7P@AG4 .#HJ7 ,FUNCI@ON
QUE TI5E UNA GR@AFICA NO 9T]RUMPIDA4 @3
,ANY L9E> FUNC;N1 S* Z .;Y .K #B .;X @+
#D1 IS A 3T9U\S FUNC;N4
,CUALQUI] FUNCI@ON L91L1 -O .;Y .K #B
.;X @+ #D1 ES UNA FUNCI@ON 3T9UA4
3TROL GR\P @7 P4 #GGC @7 ,A GR\P T
DOES N "UGO A PROC$URE OR TR1T;T :5 AN
EXP]I;T IS 3DUCT$4 .,SEE .AL EXP]I;TAL
GR\P4
..GRUPO DE 3TROL 7P@AG4 .#GGC7 ,GRUPO
QUE NO SE "STE A N+@UN PROC$IMI5TO ;O
TRATAMI5TO DURANTE LA R1LIZACI@ON DE UN
EXP]I;TO4 .,V] .TAMBI@EN GRUPO
EXP]I;TAL4 @3 .,SEE EXP]I;TAL GR\P4
.,V] GRUPO EXP]I;TAL4
CORREL,N COE6ICI5T @7 P4 #AAD @7 ,A
M1SURE1 DENOT$ 0.;R ": --#A "K.K .;R
"K.K #A1 ( H[ WELL A L9E FITS A SET (
DATA PAIRS @7 .;X1 .;Y @7@4
..COEFICI5TE DE CORRELACI@ON 7P@AG4
.#AAD7 ,M$IDA DENOTADA POR .;R @1 DONDE
--#A"K.K .;R "K.K #A1 ;Y QUE DESCRIBE EL
AJU/E DE UNA RECTA A UN 3JUNTO DE P>ES
DE DATOS @7 .;X1 .;Y @7@4 @3 ,A DATA SET
T %[S A /R;G POSITIVE CORREL,N HAS A
CORREL,N COE6ICI5T ( .;R L4 .,SEE .AL
POSITIVE CORREL,N .& NEGATIVE CORREL,N4
,UN 3JUNTO DE DATOS QUE MUE/RA UNA
CORRELACI@ON POSITIVA FU]TE TI5E UN
COEFICI5TE DE CORRELACI@ON DE .;R #A4
.,V] .TAMBI@EN CORRELACI@ON POSITIVA ;Y
CORRELACI@ON NEGATIVA4
COSECANT FUNC;N @7 P4 #HEB @7 ,IF IS
AN ACUTE ANGLE (A "R TRIANGLE1 !
COSECANT ( IS ! L5G? (! HYPOT5USE DIVID$
0! L5G? (! SIDE OPPOSITE @4
..FUNCI@ON COSECANTE 7P@AG4 .#HEB7 ,SI
ES UN @ANGULO AGUDO DE UN TRI@ANGULO
RECT@ANGULO1 LA COSECANTE DE ES LA
L;GITUD DE LA HIPOT5USA DIVIDIDA POR LA
L;GITUD DEL LADO OPUE/O A @4 @3 .,SEE
S9E FUNC;N4
.,V] FUNCI@ON S5O4
-----------------------------------#AJDC
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
COS9E FUNC;N @7 P4 #HEB @7 ,IF IS AN
ACUTE ANGLE (A "R TRIANGLE1 ! COS9E ( IS
! L5G? (! SIDE ADJAC5T 6DIVID$ 0! L5G?
(! HYPOT5USE4
..FUND@ON COS5O 7P@AG4 .#HEB7 ,SI ES UN
@ANGULO AGUDO DE UN TRI@ANGULO
RECT@ANGULO1 EL COS5O DE ES LA L;GITUD
DEL LADO ADYAC5TE A DIVIDIDA POR LA
L;GITUD DE LA HIPOT5USA4 @3 .,SEE S9E
FUNC;N4
.,V] FUNCI@ON S5O4
COTANG5T FUNC;N @7 P4 #HEB @7 ,IF IS
AN ACUTE ANGLE (A "R TRIANGLE1 !
COTANG5T ( IS ! L5G? (! SIDE ADJAC5T
6DIVID$ 0! L5G? (! SIDE OPPOSITE @4
..FUNCI@ON COTANG5TE 7P@AG4 .#HEB7 ,SI
ES UN @ANGULO AGUDO DE UN TRI@ANGULO
RECT@ANGULO1 LA COTANG5TE DE ES LA
L;GITUD DEL LADO ADYAC5TE A DIVIDIDA POR
LA L;GITUD DEL LADO OPUE/O A @4 @3 .,SEE
S9E FUNC;N4
.,V] FUNCI@ON S5O4
.COT]M9AL .ANGLES 7.P#..HFJ7 ,ANGLES 9
/&>D POSI;N ) T]M9AL SIDES T CO9CIDE4
..@ANGULOS COT]M9ALES 7P@AG4 .#HFJ7
,@ANGULOS EN POSICI@ON NORMAL CUYOS
LADOS T]M9ALES CO9CID54 @3
,! ANGLES ) M1SURES #EJJ;DG & #ADJ;DG >E
COT]M9AL4
,LOS @ANGULOS QUE MID5 #EJJ;DG ;Y
#ADJ;DG SON COT]M9ALES4
CO-V]TICES ( AN ELLIPSE @7 P4 #FCD @7
,! PO9TS ( 9T]SEC;N ( AN ELLIPSE &! L9E
P]P5DICUL> 6! MAJOR AXIS AT ! C5T]4
..PUNTOS EXTREMOS DEL EJE M5OR DE UNA
ELIPSE 7P@AG4 .#FCD7 ,LOS PUNTOS DE
9T]SE3I@ON DE UNA ELIPSE ;Y LA RECTA
P]P5DICUL> ;AL EJE MAYOR EN EL C5TRO4 @3
.,SEE ELLIPSE4
.,V] ELIPSE4
,CRAM]'S RULE @7 P4 #BJE @7 ,A ME?OD =
SOLV+ A SY/EM ( L9E> EQU,NS US+
DET]M9ANTS3 ,=! L9E> SY/EM .AX @+ .BY .K
.;E1 .CX @+ .DY .K .;F @1 LET .,A 2 !
COE6ICI5T MATRIX4 ,IF DET .,A @6.K #J1 !
SOLU;N (! SY/EM IS Z FOLL[S3
..REGLA DE ,CRAM] 7P@AG4 .#BJE7 ,M@ETODO
P>A RESOLV] UN SI/EMA DE ECUACI"OS
L91LES US&O DET]M9ANTES3 ,P>A EL SI/EMA
L91L .AX @+ ..BY .K ;E1 .CX @+ ..DY .K
;F1 SEA4 .,A LA MATRIZ COEFICI5TE4 ,SI
DET .,A @6.K #J1 LA SOLUCI@ON DEL SI/EMA
ES LA SIGUI5TE3
@3
,APPLY+ ,CRAM]'S RULE GIVES !
FOLL[+@3;,AL APLIC> LA REGLA DE ,CRAM]
SE OBTI5E LO SIGUI5TE3
-----------------------------------#AJDD
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
CROSS MULTIPLY+ @7 P4 #EHI @7 ,A ME?OD
= SOLV+ A SIMPLE R,NAL EQU,N = : EA*
SIDE (! EQU,N IS A S+LE R,NAL EXPRES.N4
..MULTIPLIC> EN CRUZ 7P@AG4 .#EHI7
,M@ETODO P>A RESOLV] UNA ECUACI@ON
RACIONAL SIMPLE EN LA QUE CADA LADO ES
UNA SOLA EXPRESI@ON RACIONAL4 @3 ,6SOLVE
@1 CROSS MULTIPLY4
,P>A RESOLV] @1 MULTIPLICA 5CRUZ#.C7#D
.;X @+ #E7 .K #I7 .;X @+ #A7
#AB .;X @+ #AE .K #I .;X @+ #I
#C .;X .K --#F
.;X .K --#B
CYDE @7 P4 #IJH @7 ,! %ORTE/ REP1T+
POR;N (! GRAPH (A P]IODIC FUNC;N4
.CICLO 7.P@AG4 .#IJH7 ,EN UNA FUNCI@ON
P]I@ODICA1 LA "PE M@AS CORTA DE LA
GR@AFICA QUE SE REPITE4 @3 .,SEE P]IODIC
FUNC;N4
.,V] FUNCI@ON P]I@ODICA4
;,D
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
DECAY FACTOR @7 P4 #DHF @7 ,! QUANT;Y
.;B 9 ! EXPON5TIAL DECAY FUNC;N .;Y .K
;AB.' ;X.' ) .A .1 #J & #J "K .;B "K #A4
..FACTOR DE DECRECIMI5TO 7P@AG4 .#DHF7
,LA CANTIDAD .;B DE LA FUNCI@ON DE
DECRECIMI5TO EXP"ONCIAL .;Y .K ;AB.'
;X.' @1 CON .A .1 #J ;Y #J "K .;B "K L4
@3 ,! DECAY FACTOR =! FUNC;N .;Y .K #C
7#J.E7 .;X IS #J.E4
,EL FACTOR DE DECRECIMI5TO DE LA
FUNCI@ON .;Y .K#C7#J.E7 .;X ES #J.E4
DEGREE (A POLYNOMIAL FUNC;N @7 P4 #CCG
@7 ,! EXPON5T 9 ! T]M (A POLYNOMIAL
FUNC;N ": ! V>IA# IS RAIS$ 6! GRTE/ P[]4
..GRADO DE UNA FUNCI@ON POL9@OMICA
7P@AG4 .#CCG7 ,EN UNAFUNCI@ON
POL9@OMICA1 EL EXPON5TE DEL T@ERM9O
DONDE LA V>IA# SE ELEVA A LA MAYOR
POT5CIA4 @3 .,SEE POLYNOMIAL FUNC;N4
.,V] FUNCI@ON POL9@OMICA4
DEP5D5T EV5TS @7 P4 #GAH @7 ,TWO EV5TS
S* T ! O3URR;E ( "O EV5T A6ECTS !
O3URR;E (! O!R EV5T4
..SUCESOS DEP5DI5TES 7P@AG4 .#GAH7 ,DOS
SUCESOS TALES QUE LA OCURR5CIA DE UNO DE
ELLOS AFECTA A LA OCURR5CIA DEL OTRO4 @3
,TWO C>DS >E DRAWN F A DECK )\T
REPLACE;T4 ,! EV5TS 8! FLR/ IS A #C0 &
8! SECOND IS A #C0 >E DEP5D5T4
,SE SACAN DOS C>TAS DE UNA B>AJA ;Y NO
SE REEMPLAZAN4 ,LOS SUCESOS 8LA PRIM]A
ES UN #C0 ;Y 8LA SEGUNDA ES UN #C0 SON
DEP5DI5TES4
DEP5D5T SY/EM @7 P4 #AED @7 ,A 3SI/5T
SY/EM ( EQU,NS T HAS 9F9ITELY _M
SOLU;NS4
..SI/EMA DEP5DI5TE 7P@AG4 .#AED7 ,SI/EMA
-PATI# DE ECUACI"OS QUE TI5E 9F9ITAS
SOLUCI"OS4 @3 #B .;X -- .;Y .K #C
#D .;X -- #B .;Y .K #F
,ANY ORD]$ PAIR @7 .;X @1 #B .;X -- #C7
IS A SOLU;N (! SY/EM ABV1 S "! >E
9F9ITELY _M SOLU;NS4
,CUALQUI] P> ORD5ADO @7 .;X @1 #B .;X --
#C7 ES UNA SOLUCI@ON DEL SI/EMA QUE
FIGURA >RIBA1 POR LO QUE HAY 9F9ITAS
SOLUCI"OS4
-----------------------------------#AJDE
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
DEP5D5T V>IA# @7 P4 #GD @7 ,! \TPUT
V>IA# 9 AN EQU,N 9 TWO V>IA#S4
.V>IA# .DEP5DI5TE 7.P@AG#..GD7 ,LA V>IA#
DE SALIDA DE UNA ECUACI@ON CON DOS
V>IA#S4 @3 .,SEE 9DEP5D5T V>IA#4
.,V] V>IA# 9DEP5DI5TE4
DET]M9ANT @7 P4 #BJC @7 ,A R1L NUMB] Z
SOCIAT$ ) ANY SQU>E MATRIX ,A1 DENOT$
0DET ,AOR _\ .,A _\.
.DET]M9ANTE 7.P@AG4 .#BJC7 ,N@UM]O R1L
ASOCIADO A TODA MATRIZ CUADRADA .,A @1
DENOTADA POR DET .,A ;O _\ .,A _\. @3
DIM5.NS (A MATRIX @7 P4 #AHG @7 ,!
DIM5.NS (A MATRIX ) .;M R[S & .;N
COLUMNS >E .;M * .;N @4
..DIM5.NES DE UNA MATRIZ 7P@AG4 .#AHG7
,LAS DIM5.NES DE UNA MATRIZ CON .;M
FILAS ;Y .;N COLUMNAS SON .;M * .;N @4
@3 ,A MATRIX ) #B R[S & #C COLUMNS HAS !
DIM5.NS #B * #C 7R1D 8#B 0#C074
,UNA MATRIZ CON #B FILAS ;Y #C COLUMNAS
TI5E POR DIM5.NES #B * #C 7LE@IDO 8#B
POR #C074
DIRECT V>I,N @7 P4 #AJG @7 ,TWO V>IA#S
.;X & ;Y %[ DIRECT V>I,N PROVID$ T .;Y
.K .AX ": .A IS A NONZ]O 3/ANT4
..V>IACI@ON DIRECTA 7P@AG4 .#AJG7 ,DOS
V>IA#S .;X ;E .;Y 9DICAN UNA V>IACI@ON
DIRECTA SIEMPRE QUE ;Y .K .AX @1 DONDE
.A ES UNA 3/ANTE 4T9TA DE C]O4 @3 ,!
EQU,N #E .;X @+ #B .;Y .K #J REPRES5TS
DIRECT V>I,N 2C X IS EQUIVAL5T 6!EQU,N
@4
,LA ECUACI@ON #E .;X @+ #B .;Y .K #J
REPRES5TA UNA V>IACI@ON DIRECTA YA QUE
ES EQUIVAL5TE A LAECUACI@ON @4
..DIRECTRIX (A P>ABOLA 7P#..FBJ7 .,SEE
P>ABOLA4
..DIRECTRIZ DE UNA P>@ABOLA 7P@AG4
.#FBJ7 ,V] P>@ABOLA4 @3 .,SEE P>ABOLA4
.,V] P>@ABOLA4
4CRETE FUNC;N @7 P4 #HJ @7 ,A FUNC;N
^: GRAPH 3SI/S ( SEP>ATE PO9TS4
..FUNCI@ON 4CRETA 7P@AG4 .#HJ7 ,FUNCI@ON
CUYA GR@AFICA 3SI/E EN PUNTOS AISLADOS4
@3
4CRIM9ANT (A G5]AL SECOND-DEGREE
EQU,N7 P4 #FEC @7 ,! EXPRES.N .;,B #B --
#D .;,,AC =! EQU,N .,AX #B @+ .,BXY @+
.,CY #B @+ .,DX @+ .,EY @+ .;,F .K #J4
,US$ 6ID5TIFY : TYPE ( 3IC ! EQU,N
REPRES5TS4
..4CRIM9ANTE DE UNA ECUACI@ON G5]AL DE
SEGUNDO GRADO 7P@AG4 .#FEC7 ,LA
EXPRESI@ON .;,B #B -- #D .;,,AC P>A LA
ECUACI@ON .,AX #B @+ .,BXY @+ .,CY #B @+
.,DX @+ .,EY @+ .;,F .K #J4 ,SE USA P>A
ID5TIFIC> QU@E TIPO DE C@ONICA REPRES5TA
LA ECUACI@ON4 @3 ,=! EQU,N #D .;X #B @+
.;Y #B -- #H .;X -- #H .K #J1 .,A .K #D1
.;,B .K #J1 &.' ;,C .K #A4
.;,B #B -- #D .;,,AC .K #J #B --
#D7#D77;L7 .K --#AF
,2C.' ;,B.' #B -- #D .;,,AC "K #J1 .;,B
.K #J1 &.' ,A @6.K .;,C @1 ! 3IC IS AN
ELLIPSE4
,P>A LA ECUACI@ON #D .;X #B @+ ;Y.' #B
-- #H .;X -- #H .K #J1 .,A .K #D1 .;,B
.K #J ;Y.' ;,C .K #A4
.;,B #B -- #D .;,,AC .K #J #B --
#D7#D77;L7 .K --#AF
,DEBIDO A QUE.' ;,B #B -- #D .;,,AC "K
#J1 .;,B .K #J ;Y.' ,A @6.K .;,C @1 LA
C@ONICA ES UN ELIPSE4
-----------------------------------#AJDF
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
4CRIM9ANT (A QUADRATIC EQU,N @7 P4
#BID @7 ,!EXPRES.N .;B #B -- #D .;AC =!
QUADRATIC EQU,N .AX #B @+ .BX @+ .;C .K
#J2 AL ! EXPRES.N "U ! RADICAL SIGN 9 !
QUADRATIC =MULA4
..4CRIM9ANTE DE UNA ECUACI@ON
CUADR@ATICA 7P@AG4 .#BID7 ,LAEXPRESI@ON
.;B #B -- #D .;AC P>A LA ECUACI@ON
CUADR@ATICA .AX #B @+ .BX @+ .;C .K #J2
ES TAMBI@EN LA EXPRESI@ON SITUADA BAJO
EL SIGNO RADICAL DE LA F@ORMULA
CUADR@ATICA4 @3 ,! VALU@E (! 4CRIM9ANT
(#B .;X #B -- #C .;X -- #G .K #J IS .;B
#B -- #D .;AC .K 7--#C7 #B --
#D7#B77--#G7 .K #FE4
,EL VALOR DEL 4CRIM9ANTE DE #B .;X #B --
#C .;X -- #G .K #J ES .;B #B -- #D .;AC
.K 7--#C7 #B -- #D7#B77--#G7 .K #FE4
4JO9T EV5TS @7 P4 #GJG @7 ,EV5TS .,A &
.;,B >E 4JO9T IF !Y H NO \TCOMES 9 -MON2
AL CALL$ MUTU,Y EXCLUSIVE EV5TS4
..SUCESOS 4JUNTOS 7P@AG4 .#GJG7 ,LOS
SUCESOS .,A ;Y .;,B SON 4JUNTOS SI NO
TI55 CASOS EN -@UN2 TAMBI@EN SE LLAMAN
SUCESOS MUTUA;TE EXCLUY5TES4 @3 ,:5 Y
R&OMLY SELECT A C>D F A /&>D DECK ( #EB
C>DS1 SELECT+ A CLUB & SELECT+ A HE>T >E
4JO9T EV5TS4
;,AL SELE3ION> ;AL AZ> UNA C>TA DE UNA
B>AJA NORMAL DE #EB C>TAS1 SAC> UNA DE
TR@EBOLES ;Y SAC> UNA DE CORAZ"OS SON
SUCESOS 4JUNTOS4
4T.E =MULA @7 P4 #FAD @7 ,! 4T.E .;D
2T ANY TWO PO9TS @7 .;X #A @1 .;Y #A @7
& @7 .;X #B @1 .;Y #B @7 IS @4
..F@ORMULA DE LA 4TANCIA 7P@AG4 .#FAD7
,LA 4TANCIA .;D 5TRE DOS PUNTOS
CUALESQUI]A @7 .;X #A @1 .;Y #A @7 ;Y @7
.;X #B @1 .;Y #B @7 ES @4 @3 ,! 4T.E 2T
7--#C1 #E7 & 7#D1 --#A7 IS @4
,LA 4TANCIA 5TRE 7--#C1 #E7 ;Y 7#D1
--#A7 ES @4
DOMA9 @7 P4 #GB @7 ,! SET ( 9PUT
VALUES (A REL,N4
.DOM9IO 7.P@AG4 .#GB7 ,EL 3JUNTO DE LOS
VALORES DE 5TRADA DE UNA RELACI@ON4 @3
.,SEE REL,N4
.,V] RELACI@ON4
;,E
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
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,LA FUNCI@ON L91L ;Y .K .MX @+ .;B
ESCRITA EN NOTACI@ON DE FUNCI@ON ES .;F
@7 .;X @7 .K .MX @+ .;B @4
;,G
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
G5]AL SECOND-DEGREE EQU,N 9.' ;X .-&.'
;Y @7 P4 #FEC @7 ,! =M .,AX #B @+ .,BXY
@+ .,CY #B @+ .,DX @+ .,EY @+ .;,F .K
#J4
ECUACI@ON G5]AL DE SEGUNDO GRADO EN.' ;X
;E.' ;Y .-7P@AG4 #FEC7 ,LA=MA .,AX #B @+
.,BXY @+ .,CY #B @+ .,DX @+ .,EY @+ .;,F
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@+ .;Y #B -- #H .;X -- #H .K #J >E
SECOND-DEGREE EQU,NS 9 .;X & .;Y @4
#AF .;X #B -- #I .;Y #B -- #IF .;X @+
#CF .;Y -- #CF .K #J .;Y #D .;X #B @+
.;Y #B -- #H .;X -- #H .K #J SON
ECUACI"OS DE SEGUNDO GRADO EN .;X ;E .;Y
@4
-----------------------------------#AJEB
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
GEOMETRIC PROBABIL;Y @7 P4 #GJA @7 ,A
PROBABIL;Y F.D 0CALCULAT+ A RATIO ( TWO
L5G?S1 >1S1 OR VOLUMES4
..PROBABILIDAD GEOM@ETRICA 7P@AG4 .#GJA7
,PROBABILIDAD HALLADA ;AL CALCUL> UNA
RAZ@ON 5TRE DOS L;GITUDES1 @AR1S ;O
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..PROGRESI@ON GEOM@ETRICA 7P@AG4 .#HAJ7
,PROGRESI@ON EN LA QUE LA RAZ@ON 5TRE
CUALQUI] T@ERM9O ;Y EL T@ERM9O PREC$5TE
ES 3/ANTE4 @3 --#AI1 #CH1 --#GF1 #AEB IS
A GEOMETRIC SEQU;E ) -MON RATIO --#B4
--#AI1 #CH1 --#GF1 #AEB ES UNA
PROGRESI@ON #A GEOM@ETRICA CON UNA
RAZ@ON -@UN DE --#B4
.GEOMETRIC .S]IES @7 P4 #HAB @7 ,!
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.S]IE .GEOM@ETRICA 7.P@AG4 #HAB7 ,LA
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DE UNA PROGRESI@ON GEOM@ETRICA4 @3
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P4 #ACB @7 ,!SET ( ALL PO9TS 9 A
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9EQUAL;Y4
..GR@AFICA DE UNA DESIGUALDAD L91L CON
DOS V>IA#S 7P@AG4 .#ACB7 ,EL 3JUNTO DE
TODOS LOS PUNTOS DE UN PLANO DE
COORD5ADAS QUE REPRES5TAN LAS SOLUCI"OS
DE LA DESIGUALDAD4 @3
GRAPH (A SY/EM ( L9E> 9EQUALITIES @7
P4 #AFH @7 ,! GRAPH ( ALL SOLU;NS (!
SY/EM4
..GR@AFICA DE UN SI/EMA DE DESIGUALDADES
L91LES 7P@AG4 .#AFH7 ,LA GR@AFICA DE
TODAS LAS SOLUCI"OS DEL SI/EMA4 @3
GRAPH ( AN EQU,N 9 TWO V>IA#S @7 P4
#GD @7 ,! SET ( ALLPO9TS @7 .;X1 .;Y @7
T REPRES5T SOLU;NS (! EQU,N4
..GR@AFICA DE UNA ECUACI@ON CON DOS
V>IA#S 7P@AG4 .#GD7 ,ELCONJUNTO DE TODOS
LOS PUNTOS @7 .;X1 .;Y @7 QUE REPRES5TAN
SOLUCI"OS DE LA ECUACI@ON4 @3
-----------------------------------#AJEC
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
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REPRES5T SOLU;NS (! 9EQUAL;Y4
..GR@AFICA DE UNA DESIGUALDAD CON UNA
V>IA# 7P@AG4 .#DA7 ,TODOS LOS PUNTOS DE
UNA RECTA NUM@ERICA QUE REPRES5TAN
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.;X "K #C
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;,H
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,H1D+S & COLUMNS >E SEP>AT$ 0A
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,I
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EQUATES TWO EQUIVAL5T EXPRES.NS4
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ID5T;Y MATRIX @7 P4 #BAJ @7 ,! .;N *
.;N MATRIX T HAS L'S ON ! MA9 DIAGONAL &
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..MATRIZ ID5TIDAD 7P@AG4 .#BAJ7 ,LA
MATRIZ .;N * .;N QUE TI5E LOS #A EN LA
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@4
,LA MATRIZ ID5TIDAD #B * #B ES @4
-----------------------------------#AJED
,5GLI%--,SPANI% ,GLOSS>Y
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,H1D+S & COLUMNS >E SEP>AT$ 0A
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( EQU,NS T HAS NO SOLU;N4
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9DEP5D5T SY/EM @7 P4 #AED @7 ,A 3SI/5T
SY/EM T HAS EXACTLY "O SOLU;N4
..SI/EMA 9DEP5DI5TE 7P@AG4 .#AED7
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SOLUCI@ON4 @3 ,! SY/EM 3SI/+ ( #D .;X @+
.;Y .K #H & #B .;X -- #C .;Y .K #AH HAS
EXACTLY "O SOLU;N1 7#C1 --#D74
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9DEP5D5T V>IA# @7 P4 #GD @7 ,! 9PUT
V>IA# 9 AN EQU,N 9 TWO V>IA#S4
..V>IA# 9DEP5DI5TE 7P@AG4 .#GD7 ,LA
V>IA# DE 5TRADA DE UNA ECUACI@ON CON DOS
V>IA#S4 @3 ,9 .;Y .K #C .;X -- #E1 !
9DEP5D5T V>IA# IS .;X @4 ,! DEP5D5T
V>IA# IS .;Y 2C ! VALUE ( .;Y DEP5DS ON
! VALUE ( .;X @4
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9DEP5DI5TE ES .;X @4 ,LA V>IA# DEP5DI5TE
ES ;Y YA QUE EL VALOR DE .;Y DEP5DE DEL
VALOR DE .;X @4
..9DEX (A RADICAL 7P#..DAD7 ,! 9TEG]
.;N @1 GRT] ?AN #A1 9 ! EXPRES.N @4
..@INDICE DE UN RADICAL 7P@AG4 .#DAD7
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#A ;Y AP>ECE EN LA EXPRESI@ON @4 @3 ,!
9DEX ( IS #C4 ,EL @INDICE DE ES #C4
9ITIAL SIDE ( AN ANGLE @7 P4 #HEI @7
.,SEE T]M9AL SIDE ( AN ANGLE4
..LADO 9ICIAL DE UN @ANGULO 7P@AG4
.#HEI7 ,V] LADO T]M9AL DE UN @ANGULO4 @3
.,SEE /&>D POSI;N ( AN ANGLE4
.,V] POSICI@ON NORMAL DE UN @ANGULO4
-----------------------------------#AJEE
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
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9T]CEPT =M4
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.;X @4
..FUNCI@ON 9V]SA 7P@AG4 .#DCH7
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,LAS FUNCI"OS .;F ;Y ;G SON 9V]SAS
SIEMPRE QUE .;F @7 .;G @7 .;X @7@7 .K
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MATRICES .;N * .;N SON 9V]SAS 5TRE S@I
SI SU PRODUCTO 7DE AMBOS @ORD5ES7 ES LA
MATRIZ ID5TIDAD ..;N * N4 ,V] .TAMBI@EN
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@4
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-----------------------------------#AJEF
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
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QUE @4
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.;F @7 .;F @7 .;X @7@7@1 &( TWO IT],NS
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.IT]ACI@ON 7.P@AG4 .#HCJ7 ,LA -POSICI@ON
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O3URS :5 A QUANT;Y V>IES DIRECTLY )!
PRODUCT ( TWO OR M O!R QUANTITIES4
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,RELACI@ON PRODUCIDA CU&O UNA CANTIDAD
V>@IA DIRECTA;TE CON EL PRODUCTO DE DOS
;O M@AS OTRAS CANTIDADES4 @3 ,! EQU,N
.;Z .K #E .XY REPRES5TS JO9T V>I,N4
,LA ECUACI@ON .;Z .K #E .XY REPRES5TA LA
V>IACI@ON 3JUNTA4
-----------------------------------#AJEG
,5GLI%--,SPANI% ,GLOSS>Y
;,L
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
..LAW ( COS9ES 7P#..HHI7 ,IF ,,ABC HAS
SIDES ( L5G? .A1 .;B @1 & .;C Z %[N1 !N
.A #B .K .;B #B @+ .;C #B -- #B .BC COS
.,A1 .;B #B .K .A #B @+ .;C #B -- #B
.;AC COS .;,B @1 & .;C #B .K .A #B @+
.;B #B -- #B .;AB COS .;,C @4
..LEY DE LOS COS5OS 7P@AG#..HHI7 ,SI
.,,ABC TI5E LADOS DE L;GITUD .A1 .;B ;Y
.;C -O SE 9DICA1 5TONCES .A #B .K .;B #B
@+ .;C #B -- #B .BC COS .A1 .;B #B .K .A
#B @+ .;C #B -- #B .;AC COS .;,B ;Y .;C
#B .K .A #B @+ .;B #B -- #B .;AB COS
.;,C @4 @3
.;B #B .K .A #B @+ .;C #B -- #B .;AC COS
.;,B
.;B #B .K #AA #B @+ #AD #B --
#B7#AA77#AD7 COS #CD;DG
.;B #B #FA.G
.;B #G.HE
.LAW(S9ES 7.P#..HHB7 ,IF .,,ABC HAS
SIDES ( L5G? .A1 .;B @1 & .;C Z %[N1 !N
@4
..LEY DE LOS S5OS 7P@AG#..HHB7 ,SI
.,,ABC TI5E LADOS DE L;GITUD .A1 .;B ;Y
.;C -O SE 9DICA1 5TONCES @3
L1D+ COE6ICI5T @7 P4 #CCG @7 ,!
COE6ICI5T 9 ! T]M (A POLYNOMIAL FUNC;N T
HAS ! GRTE/ EXPON5T4
..COEFICI5TE 9ICIAL 7P@AG4 .#CCG7 ,EN
UNA FUNCI@ON POL9@OMICA1 EL COEFICI5TE
DEL T@ERM9O CON EL MAYOR EXPON5TE4 @3
.,SEE POLYNOMIAL FUNC;N4
.,V] FUNCI@ON POL9@OMICA4
L RADIC@AIS @7 P4 #DBB @7 ,RADICAL
EXPRES.NS )! SAME 9DEX & RADIC&4
..RADICALES SEMEJANTES 7P@AG4 .#DBB7
,EXPRE.NES RADICALES CON EL MISMO
@INDICE ;Y EL MISMO RADIC&O4 @3 >E L
RADICALS4
SON RADICALES SEMEJANTES4
LIKET]MS @7 P4 #AB @7 ,T]MS T H ! SAME
V>IA# "PS4 ,3/ANT T]MS >E AL L T]MS4
..T@ERM9OS SEMEJANTES 7P@AG4 .#AB7
,T@ERM9OS QUE TI55 LAS MISMAS V>IA#S4
,LOS T@ERM9OS 3/ANTES TAMBI@EN SON
T@ERM9OS SEMEJANTES4 @3 ,9 ! ALGEBRAIC
EXPRES.N
#E .;X #B @+ 7--#C .;X @7 @+ #G @+ #D
.;X @+ 7--#B71
--#C .;X & #D .;X >E L T]MS1 & #G & --#B
>E L T]MS4
,EN LA EXPRESI@ON ALGEBRAICA
#E .;X #B @+ 7--#C .;X @7 @+ #G @+ #D
.;X @+ 7--#B71
--#C .;X ;Y #D .;X SON T@ERM9OS
SEMEJANTES1 ;Y #G ;Y --#B TAMBI@EN LO
SON4
L9E> EQU,N 9 "O V>IA# @7 P4 #AH @7 ,AN
EQU,N T C 2 WRITT5 9 ! =M .AX @+ .;,B .K
#J ": .A & .;B >ECON/ANTS & .A @6.K #J4
..ECUACI@ON L91L CON UNA V>IA# 7P@AG4
.#AH7 ,ECUACI@ON QUE PU$E ESCRIBIRSE EN
LA =MA .AX@+ .;B .K #J1 DONDE .A ;Y .;B
SON 3/ANTES ;Y .A @6.K #J4 @3 ,! EQU,N
IS A L9E> EQU,N 9 "O V>IA#4
,LA ECUACI@ON ES UNA ECUACI@ONL91L CON
UNA V>IA#4
-----------------------------------#AJEH
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
L9E> EQU,N 9 ?REE V>IA#S @7 P4 #AGH @7
,AN EQU,N (! =M .AX @+ .BY @+ .CZ .K .;D
": .A1 .;B @1 & .;C >E N ALL Z]O4
..ECUACI@ON L91L CON TRES V>IA#S 7P@AG4
.#AGH7 ,ECUACI@ON DE LA=MA .AX @+ .BY @+
.CZ .K .;D @1 DONDE .A1 .;B ;Y .;C NO
SON TODOS C]O4 @3 #B .;X @+ .;Y -- .;Z
.K #E IS A L9E> EQU,N 9 ?REE V>IA#S4
#B .;X @+ .;Y -- .;Z .K #E ES UNA
ECUACI@ON L91L CON TRES V>IA#S4
L9E> FUNC;N @7 P4 #GE @7 ,A FUNC;N T C
2 WRITT5 9 ! =M .;Y .K .MX @+ .;B ": .;M
& .;B >E 3/ANTS4
..FUNCI@ON L91L 7P@AG4 .#GE7 ,FUNCI@ON
QUE PU$E ESCRIBIRSE EN LA =MA .;Y .K .MX
@+ .;B @1 DONDE .;M ;Y .;B SON 3/ANTES4
@3 ,! FUNC;N .;Y .K --#B .;X -- #A IS A
L9E> FUNC;N ) .;M .K --#B & .;B .K --#A4
,LA FUNCI@ON .;Y .K --#B .;X --#A ES UNA
FUNCI@ON L91L CON .;M .K --#B ;Y .;B .K
-- #A4
..L9E> 9EQUAL;Y 9 "O V>IA# 7P#..DA7
,AN 9EQUAL;Y T C 2 WRITT5 9 "O (! FOLL[+
=MS1 ": .A & .;B >E R1L NUMB]S & .A @6.K
#J3
.AX @+ .;B "K #J1 .AX @+ .;B "K.K #J1
.AX @+ .;B .1 #J1 OR .AX @+ .;B .1.K #J4
..DESIGUALDAD L91L CON UNA V>IA# 7P@AG4
.#DA7 ,DESIGUALDAD QUE PU$E ESCRIBIRSE
DE UNA DE LAS SIGUI5TES =MAS1 DONDE .A
;Y .;B SON N@UM]OS R1LES ;Y .A @6.K #J3
.AX @+ .;B "K #J1 .AX @+ .;B "K.K #J1
.AX @+ .;B .1 #J1 ;@O .AX @+ .;B .1.K
#J4 @3 #E .;X @+ #B .1 #J IS A L9E>
9EQUAL;Y 9 "O V>IA#4
#E .;X @+ #B .1 #J ES UNA DESIGUALDAD
L91L CON UNA V>IA#4
L9E> 9EQUAL;Y 9 TWO V>IA#S @7 P4 #ACB
@7 ,AN 9EQUAL;Y T C 2 WRITT5 9 "O (!
FOLL[+ =MS3
.,AX @+ .,BY "K .;,C1 .,AX @+ .,BY "K.K
.;,C1 .,AX @+ .,BY .1 .;,C @1 OR .,AX @+
.,BY .1.K .;,C @4
..DESIGUALDAD L91L CON DOS V>IA#S 7P@AG4
.#ACB7 ,DESIGUALDAD QUE PU$E ESCRIBIRSE
DE UNA DE LAS SIGUI5TES =MAS3
.,AX @+ .,BY "K .;,C1 .,AX @+ .,BY "K.K
.;,C1 .,AX @+ .,BY .1 .;,C @1 ;O .,AX @+
.,BY .1.K .;,C @4 @3 #E .;X -- #B .;Y .1
--#D IS A L9E> 9EQUAL;Y 9 TWO V>IA#S4
#E .;X -- #B .;Y .1 --#D ES UNA
DESIGUALDAD L91L CON DOS V>IA#S4
L9E> PROGRAMM+ @7 P4 #AGD @7 ,!
PROCESS ( MAXIMIZ+ OR M9IMIZ+ A L9E>
OBJECTIVE FUNC;N SUBJECT 6A SY/EM ( L9E>
9EQUALITIES CALL$ 3/RA9TS4 ,! GRAPH (!
SY/EM ( 3/RA9TS IS CALL$ ! F1SI# REGION4
..PROGRAMACI@ON L91L 7P@AG4 .#AGD7 ,EL
PROCESO DE MAXIMIZ> ;O M9IMIZ> UNA
FUNCI@ON OBJETIVO L91L SUJETA A UN
SI/EMA DE DESIGUALDADES L91LES LLAMADAS
RE/RI3I"OS4 ,LA GR@AFICA DEL SI/EMA DE
RE/RI3I"OS SE LLAMA REGI@ON FACTI#4 @3
,6MAXIMIZE ! OBJECTIVE FUNC;N .;,P .K
#CE .;X @+ #CJ .;Y SUBJECT 6! 3/RA9TS
.;X .1.K #D1 .;Y .1.K #J1 & #E .;X @+ #D
.;Y "K.K #DJ1 EVALUATE .;,P AT EA*
V]TEX4 ,! MAXIMUM VALUE ( #BIJ O3URS AT
7#D1 #E74
,P>A MAXIMIZ> LA FUNCI@ON OBJETIVO .;,P
.K #CE .;X @+ #CJ .;Y SUJETA A LAS
RE/RI3I"OS .;X .1.K #D1 .;Y .1.K #J ;Y
#E .;X @+ #D .;Y "K.K #DJ1 EVAL@UA .;,P
EN CADA V@ERTICE4 ,EL VALOR M@AXIMO DE
#BIJ OCURRE EN 7#D1 #E74
-----------------------------------#AJEI
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
LOCAL MAXIMUM @7 P4 #CHH @7 ,! .;Y
-COORD9ATE (A TURN+ PO9T (A FUNC;N IF !
PO9T IS HI<] ?AN ALL NE>BY PO9TS4
..M@AXIMO LOCAL 7P@AG4 .#CHH7 ,LA
COORD5ADA .;Y DE UN PUNTO CR@ITICO DE
UNA FUNCI@ON SI EL PUNTO E/@A SITUADO
M@AS ALTO QUE TODOS LOS PUNTOS C]CANOS4
@3
,! FUNC;N .;F @7 .;X @7 .K .;X #C -- #C
.;X #B @+ #F HAS A LOCAL MAXIMUM ( .;Y
.K #F :5 .;X .K #J4
,LA FUNCI@ON .;F @7 .;X @7 .K .;X #C --
#C .;X #B @+ #F TI5E UN M@AXIMO LOCAL DE
.;Y .K #F CU&O .;X .K #J4
LOCAL M@INIMUM @7 P4 #CHH @7 ,! .;Y
-COORD9ATE (A TURN+ PO9T (A FUNC;N IF !
PO9T IS L[] ?AN ALL NE>BY PO9TS4
..M@INIMO LOCAL 7P@AG4 .#CHH7 ,LA
COORD5ADA ;Y DE UN PUNTO CR@ITICO DE UNA
FUNCI@ON SI EL PUNTO E/@A SITUADO M@AS
BAJO QUE TODOS LOS PUNTOS C]CANOS4 @3
,! FUNC;N .;F @7 .;X @7 .K .;X #D -- #F
.;X #C @+ #C .;X #B @+ #AJ .;X -- #C HAS
A LOCAL M9IMUM ( .;Y --#F.EA :5 .;X
--#J.EG4
,LA FUNCI@ON .;F @7 .;X @7 .K .;X #D --
#F .;X #C @+ #C .;X #B @+ #AJ .;X -- #C
TI5E UN M@INIMO LOCAL DE .;Y --#F.EA
CU&O .;X --#J.EG4
LOG>I?M ( ;Y ) BASE.' ;B .-7P#.DII7
,LET .;B & .;Y 2 POSITIVE NUMB]S ) .;B
@6.K #A4 ,! LOG>I?M ( .;Y ) BASE .;B @1
DENOT$ LOG ;B.' ;Y.' & R1D 8LOG BASE .;B
( ;Y10 IS DEF9$ Z FOLL[S3
LOG ;B.' ;Y.' .K .;X IF & ONLY IF ;B.'
;X.' .K .;Y @4
LOG>ITMO DE.' ;Y .-CON BASE.' ;B
.-7P@AG4 #DII7 ,S1N .;B ;E .;Y N@UM]OS
POSITIVOS1 CON .;B @6.K #A4 ,EL LOG>ITMO
DE ;Y CON BASE .;B @1 DENOTADO POR LOG
;B.' ;Y.' ;Y LE@IDO 8LOG BASE .;B DE .;Y
@8@1 SE DEF9E DE E/A MAN]A3
LOG ;B.' ;Y.' .K .;X SI ;Y S@OLO SI ;B.'
;X.' .K .;Y @4 @3 LOG #B #H .K #C 2C #B
#C .K #H4
LOG ?1/4# #D .K --#A 2C @4
LOG #B #H .K #C YA QUE #B #C .K #H4
LOG ?1/4# #D .K --#A YA QUE @4
LOG>I?MIC EQU,N @7 P4 #EAG @7 ,AN
EQU,N T 9VOLVES A LOG>I?M (A V>IA#
EXPRES.N4
..ECUACI@ON LOG>@ITMICA 7P@AG4 .#EAG7
,ECUACI@ON EN LA QUE AP>ECE EL LOG>ITMO
DE UNA EXPRESI@ON ALGEBRAICA4 @3 LOG #E
7#D .;X -- #G7 .K LOG #E @7 .;X @+ #E7
IS A LOG>I?MIC EQU,N4
LOG #E 7#D .;X -- #G7 .K LOG #E @7 .;X
@+ #E7 ES UNA ECUACI@ON LOG>@ITMICA4
;,M
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
..MAJOR AXIS ( AN ELLIPSE 7P#..FCD7 ,!
L9E SEG;T JO9+ ! V]TICES ( AN ELLIPSE4
..EJE MAYOR DE UNA ELIPSE 7P@AG4 .#FCD7
,EL SEG;TO DE RECTA QUE UNE LOS
V@ERTICES DE UNA ELIPSE4 @3 .,SEE
ELLIPSE4
.,V] ELIPSE4
-----------------------------------#AJFJ
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
..M>G9 ( ]ROR 7P#..GFH7 ,! M>G9 ( ]ROR
GIVES A LIMIT ON H[ M* ! RESPONSE (A
SAMPLE WD 2 EXPECT$ 6DI6] F ! RESPONSE
(! POPUL,N4
..M>G5 DE ]ROR 7P@AG4 .#GFH7 ,EL M>G5 DE
]ROR 9DICA UN L@IMITE AC]CA DE CU@ANTO
SE PREV@E QUE DIF]IR@IAN LAS RESPUE/AS
OBT5IDAS EN UNA MUE/RA DE LAS OBT5IDAS
EN LA POBLACI@ON4 @3 ,IF #DJ@3P (! P 9 A
POLL PREF] C&IDATE ,A1 &! M>G9 ( ]ROR IS
+-#D@3P1 !N X IS EXPECT$ T 2T #CF@3P &
#DD@3P (! 5TIRE POPUL,N PREF] C&IDATE
,A4
,SI EL #DJ@3P DE LOS 5CUE/ADOS PREFI]E
;AL C&IDATO ,A ;Y EL M>G5 DE ]ROR ES
+-#D@3P1 5TONCES SE PREV@E QUE 5TRE EL
#CF@3P ;Y EL #DD@3P DE LA POBLACI@ON
TOTAL PREFI]E ;AL C&IDATO ,A4
MATRIX1 MATRICES @7 P4 #AHG @7 ,A
RECTANGUL> >RANGE;T ( NUMB]S 9 R[S &
COLUMNS4 ,EA* NUMB] 9 A MATRIX IS AN
ELE;T4
..MATRIZ1 MATRICES 7P@AG4 .#AHG7
,4POSICI@ON RECTANGUL> DE N@UM]OS
COLOCADOS EN FILAS ;Y COLUMNAS4 ,CADA
NUM]O DE LA MATRIZ ES UN ELE;TO4 @3
,MATRIX .,A HAS #B R[S & #C COLUMNS4 ,!
ELE;T 9 ! SECOND R[ & F/ COLUMN IS #J4
,LA MATRIZ .,A TI5E #B FILAS ;Y #C
COLUMNAS4 ,EL ELE;TO EN LA SEGUNDA FILA
;Y EN LA PRIM]A COLUMNA ES #J4
MATRIX ( 3/ANTS @7 P4 #BAB @7 ,!
MATRIX ( 3/ANTS (! L9E> SY/EM .AX @+ .BY
.K .;E1 .CX @+ .DY .K .;F IS @4
..MATRIZ DE 3/ANTES 7P@AG4 .#BAB7 ,LA
MATRIZ DE 3/ANTES DELSI/EMA L91L .AX @+
.BY .K .;E1 .CX @+ .DY .K .;F ES @4 @3
.,SEE COE6ICI5T MATRIX4
.,V] MATRIZ COEFICI5TE4
MATRIX ( V>IA#S @7 P4 #BAB @7 ,!
MATRIX ( V>IA#S (! L9E> SY/EM .AX @+ .BY
.K .;E1 .CX @+ .DY .K .;F IS @4
..MATRIZ DE V>IA#S 7P@AG4 .#BAB7 ,LA
MATRIZ DE V>IA#S DELSI/EMA L91L .AX @+
.BY .K .;E1 .CX @+ .DY .K .;F ES @4 @3
.,SEE COE6ICI5T MATRIX4
.,V] MATRIZ COEFICI5TE4
M@AXIMUM VALU@E (A QUADRATIC FUNC;N @7
P4 #BCH @7 ,! .;Y -COORD9ATE (! V]TEX =
.;Y .K .AX #B @+ .BX @+ .;C :5 .A "K #J4
..VALOR M@AXIMO DE UNA FUNCI@ON
CUADR@ATICA 7P@AG4 .#BCH7 ,LACOORD5ADA
.;Y DEL V@ERTICE P>A .;Y .K .AX #B @+
.BX @+ .;C CU&O .A "K #J4 @3
,! MAXIMUM VALUE ( .;Y .K -- .;X #B @+
#B .;X -- #A IS #J4
,EL VALOR M@AXIMO DE .;Y .K -- .;X #B @+
#B .;X -- #A ES #J4
M1N @7 P4 #GDD @7 ,=! DATA SET .;X #A
@1 .;X #B @1 '''@1 ;X.' ;N.' @1 ! M1N IS
@4 ,AL CALL$ AV]AGE4
.M$IA 7.P@AG4 .#GDD7 ,P>A EL 3JUNTO DE
DATOS .;X #A @1 .;X #B @1 '''@1 ;X.'
;N.' @1 LAM$IA ES @4 ,TAMBI@EN SE LLAMA
PROM$IO4 @3 .,SEE M1SURE ( C5TRAL
T5D5EY4
.,V] M$IDA DE T5D5CIA C5TRAL4
-----------------------------------#AJFA
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
M1SURE ( C5TRAL T5D5CY @7 P4 #GDD @7
,A NUMB] US$ 6REPRES5T ! C5T] OR MI4LE
(A SET ( DATA VALUES4 ,M1N1 M$IAN1 &
MODE >E ?REE M1SURE ( C5TRAL T5D5CY4
..M$IDA DE T5D5CIA C5TRAL 7P@AG4 .#GDD7
,N@UM]O USADO P>A REPRES5T> EL C5TRO ;O
LA POSICI@ON C5TRAL DE UN 3JUNTO DE
VALORES DE DATOS4 ,LA M$IA1 LA M$IANA ;Y
LA MODA SON TRES M$IDAS DE T5D5CIA
C5TRAL4 @3 ..#AD1 #AG1 #AH1 #AI1 #BJ1
#BD1 #BD1 #CJ1 .#CB
,! M1N IS @4
,! M$IAN IS ! MI4LE NUMB]1 #BJ4
,! MODE IS #BD 2C #BD O3URS ! MO/
FREQU5TLY4
,LA M$IA ES @4
,LA M$IANA ES EL N@UM]O C5TRAL1 #BJ4
,LA MODA ES #BD YA QUE #BD OCURRE M@AS
VECES4
M1SURE ( 4P]SI@ON @7 P4 #GDE @7 ,A
/ATI/IC T TELLS Y H[ 4P]S$1 OR SPR1D \1
DATA VALUES >E4 ,RANGE & /&>D DEVI,N >E
M1SURES ( 4P].N4
..M$IDA DE 4P]SI@ON 7P@AG4 .#GDE7
,E/AD@I/ICA QUE TE 9DICA C@OMO SE
4P]SAN1 ;O 4TRIBUY51 LOS VALORES DE
DATOS4 ,EL RANGO ;Y LA DESVIACI@ON
T@IPICA SON M$IDAS DE 4P]SI@ON4 @3 .,SEE
RANGE .& /&>D DEVI,N4
.,V] RANGO .;Y DESVIACI@ON T@IPICA4
M$IAN @7 P4 #GDD @7 ,! M$IAN ( .;N
NUMB]S IS ! MI4LE NUMB] :5 ! NUMB]S >E
WRITT5 9 NUM]ICAL ORD]4 ,IF .;N IS EV51
! M$IAN IS ! M1N (! TWO MI4LE NUMB]S4
.M$IANA 7.P@AG4 .#GDD7 ,LA M$IANA DE .;N
N@UM]OS ES EL N@UM]O C5TRAL CU&O LOS
N@UM]OS SE ESCRIB5 EN ORD5 NUM@ERICO4
,SI .;N ES P>1 LA M$IANA ES LA M$IA DE
LOS DOS N@UM]OS C5TRALES4 @3 .,SEE
M1SURE ( C5TRAL T5D5CY4
.,V] M$IDA DE T5D5CIA C5TRAL4
MIDPO9T =MULA @7 P4 #FAE @7 ,! MIDPO9T
.;,M (! L9ESEG;T JO9+ .,A @7 .;X #A @1
.;Y #A @7 & .;,B @7 .;X #B @1 .;Y #B @7
IS @4
..F@ORMULA DEL PUNTO M$IO 7P@AG4 .#FAE7
,EL PUNTO M$IO .;,M DEL SEG;TO DE RECTA
QUE UNE .,A @7 .;X #A @1 .;Y #A @7 ;Y
.;,B @7 .;X #B @1 .;Y #B @7 ES @3 ,!
MIDPO9T (! L9E SEG;T JO9+7--#B1 #C7 &
7#H1 #F7 IS @4
,EL PUNTO M$IO DEL SEG;TO DE RECTA
QUEUNE 7--#B1 #C7 ;Y 7#H1 #F7 ES @4
M@INIMUM VALUE (A QUADRATIC FUNC;N @7
P4 #BCH @7 ,! .;Y -COORD9ATE (! V]TEX =
.;Y .K .AX #B @+ .BX @+ .;C :5 .A .1 #J4
..VALOR M@INIMO DE UNA FUNCI@ON
CUADR@ATICA 7P@AG4 .#BCH7 ,LA COORD5ADA
.;Y DEL V@ERTICE P>A .;Y .K .AX #B @+
.BX @+ .;C CU&O .A .1 #J4 @3
,! M9IMUM VALUE ( .;Y .K .;X #B -- #F
.;X @+ #E IS --#D4
,EL VALOR M@INIMO DE .;Y .K .;X #B -- #F
.;X @+ #E ES --#D4
M9OR AXIS ( AN ELLIPSE @7 P4 #FCD @7
,! L9E SEG;T JO9+ ! CO-V]TICES ( AN
ELLIPSE4
..EJE M5OR DE UNA ELIPSE 7P@AG4 .#FCD7
,EL SEG;TO DE RECTA QUE UNE LOS PUNTOS
EXTREMOS DE UNA ELIPSE4 @3 .,SEE
ELLIPSE4
.,V] ELIPSE4
-----------------------------------#AJFB
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
MODE @7 P4 #GDD @7 ,! MODE ( .;N
NUMB]S IS ! NUMB] OR NUMB]S T O3UR MO/
FREQU5TLY4
.MODA 7.P@AG4 .#GDD7 ,LA MODA DE .;N
N@UM]OS ES EL N@UM]O ;O N@UM]OS QUE
OCURR5 M@AS VECES4 @3 .,SEE M1SURE (
C5TRAL T5D5CY4
.,V] M$IDA DE T5D5CIA C5TRAL4
MONOMIAL @7 P4 #BEB @7 ,AN EXPRES.N T
IS EI A NUMB]1 A V>IA#1 OR ! PRODUCT (A
NUMB] & "O OR M V>IA#S ) :OLE NUMB]
EXPON5TS4
.MONOMIO 7.P@AG4 .#BEB7 ,EXPRESI@ON QUE
ES UN N@UM]O1 UNA V>IA# ;O EL PRODUCTO
DE UN N@UM]O ;Y UNA ;O M@AS V>IA#S CON
EXPON5TES NATURALES4 @3 >E MONOMIALS4
SON MONOMIO4
MUTU,Y EXCLUSIVE EV5TS @7 P4 #GJG @7
.,SEE 4JO9T EV5TS4
..SUCESOS MUTUA;TE EXDUY5TES 7P@AG4
.#GJG7 .,V] SUCESOS 4JUNTOS4 @3 .,SEE
4JO9T EV5TS4
.,V] SUCESOS 4JUNTOS4
;,N
,! FOLL[+ TA# IS 9 LI/ =MAT4
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COLON & "O BLANK CELL4 ,BLANK CELLS
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NATURAL BASE.' ;E @7 P4 #DIB @7 ,AN
IRR,NAL NUMB] DEF9$ Z FOLL[S3 ,Z .;N
APPROA*ES APPROA*ES .;E #B.GAHBHAHBH4
BASE NATURAL.' ;E .-7P@AG4 #DIB7 ,N@UM]O
IRRACIONAL DEF9IDO DE E/A MAN]A3 ;,AL
APROXIM>SE .;N SE APROXIMA A .;E
#B.GAHBHAHBH4 @3 .,SEE NATURAL LOG>I?M4
.,V] LOG>ITMO NATURAL4
NATURAL LOG>I?M @7 P4 #EJJ @7 ,A
LOG>I?M ) BASE .E4 ,X C 2 DENOT$ LOG ;E
@1 B IS M (T5 DENOT$ 0LN4
..LOG>ITMO NATURAL 7P@AG4 .#EJJ7
,LOG>ITMO CON BASE .E4 ,PU$E DENOT>SE
LOG ;E @1 P]O ES M@AS FRECU5TE QUE SE
DENOTE LN4 @3 LN #J.C --#A.BJD 2C
.;E --#A.BJD 7#B.GAHC7 --#A.BJD #J.C4
LN #J.C --#A.BJD YA QUE
.;E --#A.BJD 7#B.GAHC7 --#A.BJD #J.C4
NEGATIVE CORREL,N @7 P4 #AAC @7 ,!
PAIR$ DATA @7 .;X1 .;Y @7 H A NEGATIVE
CORREL,N IF .;Y T5DS 6DECR1SE Z .;X
9CR1SES4
..CORRELACI@ON NEGATIVA 7P@AG4 .#AAC7
,LOS P>ES DE DATOS @7 .;X1 .;Y @7
PRES5TAN UNA CORRELACI@ON NEGATIVA SI
.;Y TI5DE A 4M9UIR ;AL AU;T> .;X @4 @3
NORMAL CURVE @7 P4 #GEG @7 ,A SMOO?1
SYMMETRICAL1 BELL-%AP$ CURVE T C MODEL
NORMAL 4TRIBU;NS & APPROXIMATE "S
BINOMIAL 4TRIBU;NS4
..CURVA NORMAL 7P@AG4 .#GEG7 ,CURVA
LISA1 SIM@ETRICA ;Y CON =MA DE CAMPANA
QUE PU$E REPRES5T> 4TRIBUCI"OS NORMALES
;Y APROXIM> A ALGUNAS 4TRIBUCI"OS
BINOMIALES4 @3 .,SEE NORMAL 4TRIBU;N4
.,V] 4TRIBUCI@ON NORMAL4
-----------------------------------#AJFC
,5GLI%--,SPANI% ,GLOSS>Y
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,H1D+S & COLUMNS >E SEP>AT$ 0A
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.NORMAL .4TIIBU;N 7.P#..GEG7 ,A
PROBABIL;Y 4TRIBU;N ) M1N .;X & /&>D
DEVI,N MODEL$ 0A BELL-%AP$ CURVE )! >EA
PROP]TIES %[N AT ! "R4
..4TRIBUCI@ON NORMAL 7P@AG4 .#GEG7 ,UNA
4TRIBUCI@ON DE PROBABILIDAD CON M$IA .;X
;Y DESVIACI@ON NORMAL REPRES5TADA POR
UNA CURVA EN =MA DE CAMPANA ;Y QUE TI5E
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.;N TH ROOT (.' A @7 P4 #DAD @7 ,= AN
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.A @1 !N .;B IS AN .;N TH ROOT ( .A @4
,WRITT5 Z @4
..RA@IZ 5@ESIMA DE A 7P@AG4 .#DAD7 ,P>A
UN N@UM]O 5T]O .;N MAYOR QUE #A1 SI ;B.'
;N.' .K .A @1 5TONCES .;B ES UNA RA@IZ
5@ESIMA DE .A4 ,SE ESCRIBE @4 @3 2C
7--#F7 #C .K --#BAF4
YA QUE 7--#F7 #C .K --#BAF4
NUM]ICAL EXPRES.N @7 P4 #AJ @7 ,AN
EXPRES.N T 3SI/S ( NUMB]S1 OP],NS1 &
GR\P+ SYMBOLS4
..EXPRESI@ON NUM@ERICA 7P@AG4 .#AJ7
,EXPRESI@ON =MADA POR N@UM]OS1 OP]ACI"OS
;Y SIGNOS DE AGRUPACI@ON4 @3 --#D7--#C7
#B -- #F7--#C7 @+ #AA IS A NUM]ICAL
EXPRES.N4
--#D7--#C7 #B -- #F7--#C7 @+ #AA ES UNA
EXPRESI@ON NUM@ERICA4
,O
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
OBJECTIVE FUNC;N @7 P4 #AGD @7 ,9 L9E>
PROGRAMM+1 ! L9E> FUNC;N T IS MAXIMIZ$
OR M9IMIZ$4
..FUNCI@ON OBJETIVO 7P@AG4 .#AGD7 ,EN LA
PROGRAMACI@ON L91L1 LA FUNCI@ON L91L QUE
SE MAXIMIZA ;O M9IMIZA4 @3 .,SEE L9E>
PROGRAMM+4
.,V] PROGRAMACI@ON L91L4
O4S AG/ @7 P4 #FII @7 ,:5 ALL \TCOMES
>E EQU,Y LIKELY1
..PROBABILIDAD EN 3TRA 7P@AG4 .#FII7
,CU&O TODOS LOS CASOS SON IGUAL;TE
POSI#S1 @3 ,! O4S AG/ ROLL+ A #D US+ A
/&>D SIX-SID$ DIE >E @1 OR #E3A1
2CAUSE#E \TCOMES CORRESPOND 6N ROLL+ A
#D & ONLY #A \TCOME CORRESPONDS 6ROLL+ A
#D4
,LA PROBABILIDAD EN 3TRA DE SAC> EL #D
;AL LANZ> UN DADO NORMAL DE SEIS C>AS ES
@1 ;@O#E3A1 YA QUE #E CASOS CORRESPOND5
A UN N@UM]O QUE NO SEA EL #D ;Y S@OLO #A
CASO CORRESPONDE ;AL #D4
O4S 9 FAVOR @7 P4 #FII @7 ,:5 ALL
\TCOMES >E EQU,Y LIKELY1
..PROBABILIDAD A FAVOR 7P@AG4 .#FII7
,CU&O TODOS LOS CASOS SON IGUAL;TE
POSI#S1 @3 ,! O4S 9 FAVOR ( ROLL+ A #D
US+ A /&>D SIX-SID$ DIE >E @1 OR #A3E1
2CAUSEONLY #A \TCOME CORRESPONDS 6ROLL+
A #D & #E \TCOMES CORRESPOND 6N ROLL+ A
#D4
,LA PROBABILIDAD A FAVOR DE SAC> EL #D
;AL LANZ> UN DADO NORMAL DE SEIS C>AS ES
@1 ;@O #A3E1 YAQUE S@OLO #A CASO
CORRESPONDE ;AL #D ;Y #E CASOS
CORRESPOND5 A UN N@UM]O QUE NO SEA EL
#D4
-----------------------------------#AJFD
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OPPOSITE @7 P4 #D @7 ,! OPPOSITE1 OR
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9V]SO ADITIVO1 DE CUALQUI] N@UM]O .;B ES
--.B4 @3 #F.B & --#F.B >E OPPOSITES4
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?REE NUMB]S (! =M @7 .;X1 .;Y1 .;Z @7 T
REPRES5TS A PO9T 9 SPACE4
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VALUES 9 A DATA SET4
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ES M*O MAYOR ;O M*O M5OR QUE LA MAYOR@IA
DE LOS OTROS VALORES DE UN 3JUNTO DE
DATOS4 @3 #C IS AN \TLI] 9 ! DATA SET
#C1 #AA1 #AB1 #AC1 #AC1 #AD1 #AE1 #AE1
#AE1 #AE1 #AG4
#C ES UN VALOR EXTREMO DEL 3JUNTO DE
DATOS #C1 #AA1 #AB1 #AC1 #AC1 #AD1 #AE1
#AE1 #AE1 #AE1 #AG4
;,P
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FOCUS &A L9E CALL$ ! DIRECTRIX4 ,! GRAPH
(A QUADRATIC FUNC;N .;Y .K .AX #B @+ .BX
@+ .;C ISA P>ABOLA4
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3JUNTO DE TODOS LOS PUNTOS EQUIDISTANTES
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! SAME PLANE T D N 9T]SECT4
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RECTAS DEL MISMO PLANO QUE NO SE CORTAN4
@3
P>5T FUNC;N @7 P4 #HI @7 ,! MO/ BASIC
FUNC;N 9 A FAMILY ( FUNC;NS4
..FUNCI@ON B@ASICA 7P@AG4 .#HI7 ,LA
FUNCI@ON M@AS FUNDA;TAL DE UNA FAMILIA
DE FUNCI"OS4 @3 ,! P>5T FUNC;N =! FAMILY
( ALLL9E> FUNC;NS IS .;Y .K .;X @4
,LA FUNCI@ON B@ASICA DE LA FAMILIA DE
TODAS LAS FUNCI"OS L91LES ES .;Y .K .X4
"PIALSUM @7 P4 #HBJ @7 ,! SUM ;,S .;N
(! F/ .;N T]MS ( AN 9F9ITE S]IES4
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DE UNA S]IE 9F9ITA4 @3
,! S]IES ABV HAS ! "PIAL SUMS ;,S #A .K
#J.E1 .;,S #B .K #J.GE1 .;,S #C #J.HH1
.;,S #D #J.ID1
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P>CIALES ;,S.' ;L.' .K #J.E1 .;,S #B .K
#J.GE1 ;,S.' #C #J.HH1 .;,S #D #J.ID1
-----------------------------------#AJFE
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@4 @3
P]IOD @7 P4 #IJH @7 ,! HORIZONTAL L5G?
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.,V] FUNCI@ON P]I@ODICA4
P]IODIC FUNC;N @7 P4 #IJH @7 ,A FUNC;N
^: GRAPH HAS A REP1T+ PATT]N4
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OBJECTS4 ,! NUMB] ( P]MUT,NS ( .;R
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.;N .K #C LRS ,A1 ;,B1 & ;,C TAK5 .;R .K
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#C ,A;,,B ;Y ;,C TOMADAS .;R .K #C CADA
VEZ3 ,,ABC1 ,,ACB1 ,,BAC1 ,,BCA1 ,,CAB
;Y ,,CBA4
P]P5DICUL> L9ES @7 P4 #HD @7 ,TWO L9ES
9 ! SAME PLANE T 9T]SECT 6=M A "R ANGLE4
..RECTAS P]P5DICUL>ES 7P@AG4 .#HD7 ,DOS
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FUNC;N DEF9$ 0AT L1/ TWO EQU,NS1 EA* ( :
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DOS ECUACI"OS1 CADA UNA DE LAS CUALES SE
APLICA A UNA "PE DIF]5TE DEL DOM9IO DE
LA FUNCI@ON4 @3
-----------------------------------#AJFF
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BASEBALL COA*ES4 ,! #E@3P ( COA*ES
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,UN P]IODI/A DEPORTIVA SELE3IONA ;AL AZ>
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5TR5ADORES UNIV]SIT>IOS DE B@EISBOL4 ,EL
#E@3P DE LOS 5TR5ADORES QUE RESULT@O
SELE3IONADO ES LA MUE/RA4
-----------------------------------#AJFG
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,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
QUADRANTAL ANGLE @7 P4 #HFG @7 ,AN
ANGLE 9 /&>D POSI;N ^: T]M9AL SIDE LIES
ON AN AXIS4
..@ANGULO CUADRANTAL 7P@AG4 .#HFG7
,@ANGULO EN POSICI@ON NORMAL CUYO LADO
T]M9AL SE 5CU5TRA EN UN EJE4 @3
-----------------------------------#AJFH
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
QUADRATIC EQU,N 9 "O V>IA# @7 P4 #BEC
@7 ,AN EQU,N T C 2 WRITT5 9 ! =M .AX #B
@+ .BX @+ .;C .K #J ": .A @+ #J4
..ECUACI@ON CUADR@ATICA CON UNA V>IA#
7P@AG4 .#BEC7 ,ECUACI@ON QUE PU$E
ESCRIBIRSE EN LA =MA .AX #B @+ .BX @+
.;C .K #J1 DONDE @3 ,! EQU,N .;X #B --
#E .;X .K #CF IS A QUADRATIC EQU,N 9 "O
V>IA# 2C X C 2 WRITT5 9 ! =M .;X #B --
#E .;X -- #CF .K #J4
,LA ECUACI@ON .;X #B -- #E .;X .K #CF ES
UNA ECUACI@ON CUADR@ATICA CON UNA V>IA#
YA QUE PU$E ESCRIBIRSE EN LA =MA .;X #B
-- #E .;X -- #CF .K #J4
QUADRATIC =M @7 P4 #CEE @7 ,! =M .AU
#B @+ .BU @+ .;C @1 ": .;U IS ANY
EXPRES.N 9 .;X @4
..=MA CUADR@ATICA 7P@AG4 .#CEE7 ,LA =MA
.AU #B @+ .BU @+ .;C @1 DONDE .;U ES
CUALQUI] EXPRESI@ON EN .;X @4 @3 ,!
EXPRES.N #AF .;X #D -- #H .;X #B -- #H
IS 9 QUADRATIC =M 2C X C 2 WRITT5 Z .;U
#B -- #B .;U -- #H ": .;U .K #D .;X #B
@4
,LA EXPRESI@ON #AF .;X #D -- #H .;X #B
-- #H E/@A EN LA =MA CUADR@ATICA YA QUE
PU$E ESCRIBIRSE .;U #B -- #B .;U -- #H1
DONDE .;U .K #D .;X #B @4
.QUADRATIC .=MULA 7.P#..BIB7 ,! =MULA
US$ 6F9D ! SOLU;NS (! QUADRATIC EQU,N
.AX #B @+ .BX @+ .;C .K #J :5 .A1 .;B @1
& .;C >E R1L NUMB]S & .A @6.K #J4
..F@ORMULA CUADR@ATICA 7P@AG4 .#BIB7 ,LA
F@ORMULA QUE SE USA P>A HALL> LAS
SOLUCI"OS DELA ECUACI@ON CUADR@ATICA .AX
#B @+ .BX @+ .;C .K #J CU&O .A1 .;B ;Y
.;C SON N@UM]OS R1LES ;Y .A @6.K #J4 @3
,6SOLVE #C .;X #B @+ #F .;X @+ #B .K #J1
SUB/ITUTE #C = .A @1 #F = .;,B @1 & #B =
.;C 9 ! QUADRATIC =MULA4
,P>A RESOLV] #C .;X #B @+ #F .;X @+ #B
.K #J1 SU/ITUYE .A POR #C1 .;B POR #F ;Y
.;C POR #B EN LA F@ORMULA CUADR@ATICA4
QUADRATIC FUNC;N @7 P4 #BCF @7 ,A
FUNC;N T C 2 WRITT5 9 ! =M .;Y .K .AX #B
@+ .BX @+ .;C ": .A @6.K #J4
..FUNCI@ON CUADR@ATICA 7P@AG4 .#BCF7
,FUNCI@ON QUE PU$E ESCRIBIRSE EN LA =MA
.;Y .K .AX #B @+ .BX @+ .;C @1 DONDE .A
@6.K #J4 @3 ,! FUNC;NS .;Y .K #C .;X #B
-- #E & .;Y .K .;X #B -- #D .;X @+ #F >E
QUADRATIC FUNC;NS4
,LAS FUNCI"OS .;Y .K #C .;X #B -- #E ;E
.;Y .K .;X #B -- #D .;X @+ #F SON
FUNCI"OS CUADR@ATICAS4
QUADRATIC 9EQUAL;Y 9 "O V>IA# @7 P4
#CJB @7 ,AN 9EQUAL;Y T C 2 WRITT5 9 ! =M
.,AX #B @+ .BX @+ .;C "K #J1 .AX #B @+
.BX @+ .;C "K #J1 .AX #B @+ .BX @+ .;C
.1 #J1 OR .AX #B @+ .BX @+ .;C .1 #J4
..DESIGUALDAD CUADR@ATICA CON UNA V>IA#
7P@AG4 .#CJB7 ,DESIGUALDAD QUE SE PU$E
ESCRIBIR EN LA =MA .AX #B @+ .BX @+ .;C
"K #J1 .AX #B @+ .BX @+ .;C "K #J1 .AX
#B @+ .BX @+ .;C .1 #J1 ;@O .AX #B @+
.BX @+ .;C .1 #J4 @3 .;X #B @+ .;X "K.K
#J & #B .;X #B @+ .;X -- #D .1 #J >E
QUADRATIC 9EQUALITIES 9 "O V>IA#4
.;X #B @+ .;X "K.K #J ;Y #B .;X #B @+
.;X -- #D .1 #J SON DESIGUALDADES
CUADR@ATICAS CON UNA V>IA#4
QUADRATIC 9EQUAL;Y 9 TWO V>IA#S @7 P4
#CJJ @7 ,AN 9EQUAL;Y T C 2 WRITT5 9 ! =M
.;Y "K .AX #B @+ .BX @+ .;C,.;Y "K.K .AX
#B @+ .BX @+ .;C1 .;Y .1 .AX #B @+ .BX
@+ .;C @1 OR .;Y .1 .AX #B @+ .BX @+ .;C
@4
..DESIGUALDAD CUADR@ATICA CON DOS V>IA#S
7P@AG4 .#CJJ7 ,DESIGUALDAD QUE SE PU$E
ESCRIBIR EN LA =MA .;Y "K .AX #B @+ .BX
@+ .;C1 .;Y "K.K .AX #B @+ .BX @+ .;C1
.;Y .1 .AX #B @+ .BX @+ .;C @1 ;@O .;Y
.1 .AX #B @+ .BX @+ .;C @4 @3 .;Y .1 .;X
#B @+ #C .;X -- #D IS A QUADRATIC
9EQUAL;Y 9 TWO V>IA#S4
.;Y .1 .;X #B @+ #C .;X -- #D ES UNA
DESIGUALDAD CUADR@ATICA CON DOS V>IA#S4
-----------------------------------#AJFI
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
QUADRATIC SY/EM @7 P4 #FEH @7 ,A SY/EM
( EQU,NS T 9CLUDES "O OR M EQU,NS (
3ICS4
..SI/EMA CUADR@ATICO 7P@AG4 .#FEH7
,SI/EMA DE ECUACI"OS QUE 9CLUYE UNA ;O
M@AS ECUACI"OS DE C@ONICAS4 @3 .;Y #B
--#G .;X @+ #C .K #J
#B .;X -- .;Y .K#C
.;X #B @+ #D .;Y #B @+ #H .;Y .K #AF
#B .;X #B -- .;Y #B -- #F .;X -- #D .K
#J
,! SY/EMS ABV >E QUADRATIC SY/EMS4
,LOS SI/EMAS DE >RIBA SON SI/EMAS
CUADR@ATICOS4
;,R
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
RADIAN @7 P4 #HFJ @7 ,9 A CIRCLE )
RADIUS .;R & C5T] AT ! ORIG91 "O RADIAN
IS ! M1SURE ( AN ANGLE 9 /&>D POSI;N ^:
T]M9AL SIDE 9T]CEPTS AN >E ( L5G? .;R @4
.RADI@AN 7.P@AG4 .#HFJ7 ,EN UN C@IRCULO
CON RADIO .;R ;Y CUYO C5TRO E/@A EN EL
ORIG51 UN RADI@AN ES LA M$IDA DE UN
@ANGULO EN POSICI@ON NORMAL CUYO LADO
T]M9AL 9T]CEPTA UN >CO DE L;GITUD .;R @4
@3
RADICAL @7 PP4 #BFF @1 #DAD @7 ,AN
EXPRES.N (! =M ": .;S IS A NUMB] OR AN
EXPRES.N4
..RADICAL 7P@AGS4 #BFF1 .#DAD7
,EXPRESI@ON DE LA =MA @1 DONDE #E ES UN
N@UM]O ;O UNA EXPRESI@ON4 @3
RADICAL EQU,N @7 P4 #DEB @7 ,AN EQU,N
) "O OR M RADICALS T H V>IA#S 9 _!
RADIC&S4
..ECUACI@ON RADICAL 7P@AG4 .#DEB7
,ECUACI@ON CON UNO ;O M@AS RADICALES EN
CUYO RADIC&O AP>EC5 V>IA#S4 @3
RADICAL FUNC;N @7 P4 #DDF @7 ,A FUNC;N
T 3TA9S A RADICAL )A V>IA# 9 XS RADIC&4
..FUNCI@ON RADICAL 7P@AG4 .#DDF7
,FUNCI@ON QUE TI5E UN RADICAL CON UNA
V>IA# EN SU RADIC&O4 @3
RADIC& @7 P4 #BFF @7 ,! NUMB] OR
EXPRES.N 2N A RADICAL SIGN4
.RADIC&O 7.P@AG4 .#BFF7 ,EL N@UM]O ;O LA
EXPRESI@ON QUE AP>ECE BAJO EL SIGNO
RADICAL4 @3 ,! RADIC& ( IS #E1 &! RADIC&
( IS #H .;Y #B @4
,EL RADIC&O DE ES #E1 ;Y EL RADIC&O DE
ES #H ;Y.' #B @4
RADIUS (A CIRCLE @7 P4 #FBF @7 ,! 4T.E
F ! C5T] (A CIRCLE 6A PO9T ON ! CIRCLE4
,AL1 A L9E SEG;T T 3NEETS ! C5T] (A
CIRCLE 6A PO9T ON ! CIRCLE4 .,SEE .AL
CIRCLE4
..RADIO DE UN C@IRCULO 7P@AG4 .#FBF7 ,LA
4TANCIA DESDE EL C5TRO DE UN C@IRCULO
HA/A UN PUNTO DEL C@IRCULO4 ,TAMBI@EN1
ES UN SEG;TO DE RECTA QUE UNE EL C5TRO
DE UN C@IRCULO CON UN PUNTO DEL
C@IRCULO4 .,V] .TAMBI@EN C@IRCULO4 @3 ,!
CIRCLE ) EQU,N @7 .;X -- #C7 #B @+ @7
.;Y @+ #E7 #B .K #CF HAS RADIUS @4 .,SEE
.AL CIRCLE4
,EL C@IRCULO CON LA ECUACI@ON @7 .;X --
#C7 #B @+ @7 .;Y @+ #E7 #B .K #CF TI5E
EL RADIO @4 .,V] .TAMBI@EN C@IRCULO4
-----------------------------------#AJGJ
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
R&OM V>IA# @7 P4 #GBD @7 ,A V>IA# ^:
VALUE IS DET]M9$ 0! \TCOMES (A R&OM
EV5T4
..V>IA# AL1TORIA 7P@AG4 .#GBD7 ,V>IA#
CUYO VALOR VI5E DET]M9ADO POR LOS
RESULTADOS DE UN SUCESO AL1TORIO4 @3 ,!
R&OM V>IA# .;,X REPRES5T+ ! NUMB] %[+ AF
ROLL+ A SIX-SID$ DIE HAS POSSI# VALUES (
#A1 #B1 #C1 #D1 #E1 & #F4
,LA V>IA# AL1TORIA .;,X QUE REPRES5TA EL
N@UM]O QUE SALE ;AL LANZ> UN DADO DE
SEIS C>AS TI5E -O VALORES POSI#S #A1 #B1
#C1 #D1 #E ;Y #F4
RANGE (A REL,N @7 P4 #GB @7 ,! SET (
\TPUT VALUES (A REL,N4
..RANGO DE UNA RELACI@ON 7P@AG4 .#GB7
,EL 3JUNTO DE LOS VALORES DE SALIDA DE
UNA RELACI@ON4 @3 .,SEE REL,N4
.,V] RELACI@ON4
RANGE ( DATA VALUES @7 P4 #GDE @7 ,A
M1SURE ( 4P].N EQUAL 6! DI6];E 2T !
GRTE/ & L1/ DATA VALUES4
..RANGO DE VALORES DE DATOS 7P@AG4
.#GDE7 ,M$IDA DE 4P]SI@ON IGUAL A LA
DIF]5CIA 5TRE EL VALOR M@AXIMO ;Y EL
VALOR M@INIMO DE LOS DATOS4 @3 #AD1 #AG1
#AH1 #AI1 #BJ1 #BD1 #BD1 #CJ1 #CB
,! RANGE (! DATA SET ABV IS #CB --#AD .K
#AH4
,EL RANGO DEL 3JUNTO DE DATOS DE >RIBA
ES #CB--#AD .K #AH4
RATE ( *ANGE @7 P4 #HE @7 ,A -P>ISON (
H[ M* "O QUANT;Y *ANGES1 ON AV]AGE1
RELATIVE 6! *ANGE 9 ANO!R QUANT;Y4
..RELACI@ON DE CAMBIO 7P@AG4 .#HE7
,-P>ACI@ON 5TRE EL CAMBIO PRODUCIDO1 POR
T@ERM9O M$IO1 EN UNA CANTIDAD ;Y EL
CAMBIO PRODUCIDO EN OTRA CANTIDAD4 @3 ,!
TEMP]ATURE RISES F #GE;DG;,F AT #H
,A4,M4 6#IA;DG;,F AT #AB P4M4 ,! AV]AGE
RATE ( *ANGE 9TEMP]ATURE IS @4
,LA TEMP]ATURA SUBE DE #GE;DG;,F A LAS
#H DE LA MA@NANA A #IA;DG;,F A LAS #AB
DEL M$IOD@IA4 ,LA RELACI@ON DE CAMBIO
M$IA EN LA TEMP]ATURA ES @4
R,NAL FUNC;N @7 P4 #EEH @7 ,A FUNC;N
(! =M @1 ": .;P @7 .;X @7 & .;Q @7 .;X
@7 >E POLYNOMIALS & .;Q @7 .;X @7 @6.K
#J4
..FUNCI@ON RACIONAL 7P@AG4 .#EEH7
,FUNCI@ON DE LA =MA @1 DONDE .;P @7 .;X
@7 ;Y .;Q @7 .;X @7 SON POL9OMIOS ;Y .;Q
@7 .;X @7 @6.K #J4 @3 ,! FUNC;NS >],NAL
FUNC;NS4
,LAS FUNCI"OS SONFUNCI"OS RACIONALES4
R,NALIZ+ ! DENOM9ATOR @7 P4 #BFG @7 ,!
PROCESS ( ELIM9AT+ A RADICAL EXPRES.N 9
! DENOM9ATOR (A FRAC;N 0MULTIPLY+ BO? !
NUM]ATOR & DENOM9ATOR 0AN APPROPRIATE
RADICAL EXPRES.N4
..RACIONALIZ> EL DENOM9ADOR 7P@AG4
.#BFG7 ,EL PROCESO DE ELIM9> UNA
EXPRESI@ON RADICAL DEL DENOM9ADOR DE UNA
FRA3I@ON ;AL MULTIPLIC> TANTO EL
NUM]ADOR -O EL DENOM9ADOR POR UNA
EXPRESI@ON RADICAL ADECUADA4 @3
,6R,NALIZE ! DENOM9ATOR ( MULTIPLY !
NUM]ATOR & DENOM9ATOR BY @4
,P>A RACIONALIZ> EL DENOM9ADOR DE @1
MULTIPLICA EL NUM]ADOR ;Y EL DENOM9ADOR
POR @4
RECIPROCAL @7 P4 #D @7 ,! RECIPROCAL1
OR MULTIPLICATIVE 9V]SE1 ( ANY NONZ]O
NUMB] .;B IS @4
.REC@IPROCO 7.P@AG4 .#D7 ,EL REC@IPROCO1
;O 9V]SO MULTIPLICATIVO1 DECUALQUI]
N@UM]O .;B 4T9TO DE C]O ES @4 @3 >E
RECIPROCALS4
SON REC@IPROCOS4
-----------------------------------#AJGA
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
RECURSIVE RULE @7 P4 #HBG @7 ,A RULE
=A SEQU;E T GIVES ! 2G9N+ T]M OR T]MS (!
SEQU;E & !N A RECURSIVE EQU,N T TELLS H[
! .;N TH T]M A.' ;N.' IS RELAT$ 6"O OR M
PREC$+ T]MS4
..REGLA RECURSIVA 7P@AG4 .#HBG7 ,REGLA
DE UNA PROGRESI@ON QUE DA EL PRIM]
T@ERM9O ;O T@ERM9OS DE LA PROGRESI@ON ;Y
LUEGO UNA ECUACI@ON RECURSIVA QUE 9DICA
QU@E RELACI@ON HAY 5TRE EL T@ERM9O
5@ESIMO A.' ;N.' ;Y UNO ;O M@AS DE LOS
T@ERM9OS PREC$5TES4 @3 ,! RECURSIVE RULE
.A #J .K #A1 A.' ;N.' .K .A .;N -- #A @+
#D GIVES ! >I?METIC SEQU;E #A1 #E1 #I1
#AC1
,LA REGLA RECURSIVA .A #J .K #A1 A.'
;N.' .K .A .;N -- #A @+ #D DA LA
PROGRESI@ON >ITM@ETICA #A1 #E1 #I1 #AC1
REF];E ANGLE @7 P4 #HFH @7 ,IF IS AN
ANGLE 9 /&>D POSI;N1 XS REF];E ANGLE IS
! ACUTE ANGLE @' =M$ 0! T]M9AL SIDE ( &!
.;X -AXIS4
..@ANGULO DE REF]5CIA 7P@AG4 .#HFH7 ,SI
ES UN @ANGULO EN POSICI@ON NORMAL1 SU
@ANGULO DE REF]5CIA ES EL @ANGULO AGUDO
@' =MADO POR EL LADO T]M9AL DE ;Y EL EJE
DE .;X @4 @3
,! ACUTE ANGLE @' IS ! REF];E ANGLE =
ANGLE @4
,EL @ANGULO AGUDO @' ES EL @ANGULO DE
REF]5CIA P>A EL @ANGULO @4
REFLEC;N @7 P4 #ABD @7 ,A TRANS=M,N T
FLIPS A GRAPH OR FIGURE 9 A L9E4
.REFLEXI@ON 7.P@AG4 .#ABD7
,TRANS=MACI@ON QUE VUELCA UNA GR@AFICA
;O UNA FIGURA EN UNA RECTA4 @3
,! GRAPH ( .;G @7 .;X @7 IS ! REFLEC;N
(! GRAPH ( .;F @7 .;X @7 9 ! .;X -AXIS4
,LA GR@AFICA DE .;G @7 .;X @7 ES LA
REFLEXI@ON DE LA GR@AFICA DE .;F @7 .;X
@7 EN EL EJE DE .;X @4
REL,N @7 P4 #GB @7 ,A MAPP+1 OR PAIR+1
( 9PUT VALUES ) \TPUT VALUES4
.RELACI@ON 7.P@AG4 .#GB7 ,CORRESPOND5CIA
5TRE LOS VALORES DE 5TRADA ;Y LOS
VALORES DE SALIDA4 @3 ,! ORD]$ PAIRS
7--#B1 --#B71 7--#B1 #B71 7#J1 #A71 &
7#C1A7 REPRES5T ! REL,N ) 9PUTS 7DOMA97
( --#B1 #J1 & #C & \TPUTS 7RANGE7 (
--#B1 #A1 & #B4
,LOS P>ES ORD5ADOS 7--#B1 --#B71 7--#B1
#B71 7#J1 #A7 ;Y 7#C1 #A7 REPRES5TAN LA
RELACI@ON CON 5TRADAS 7DOM9IO7 DE --#B1
#J ;Y #C ;Y SALIDAS 7RANGO7 DE --#B1 #A
;Y #B4
-----------------------------------#AJGB
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
REP1T$ SOLU;N @7 P4 #CGI @7 ,=!
POLYNOMIAL EQU,N .;F @7 .;X @7 .K #J1
.;K IS A REP1T$ SOLU;N IF & ONLY IF !
FACTOR .;X -- .;K HAS AN EXPON5T GRT]
?AN #A :5 .;F @7 .;X @7 IS FACTOR$
-PLETELY4
..SOLUCI@ON REPETIDA 7P@AG4 .#CGI7 ,P>A
LA ECUACI@ON POL9@OMICA .;F @7 .;X @7 .K
#J1 .;K ES UNA SOLUCI@ON REPETIDA SI ;Y
S@OLO SI EL FACTOR .;X -- .;K TI5E UN
EXPON5TE MAYOR QUE #A CU&O .;F @7 .;X @7
E/@A -PLETA;TE FACTORIZADO4 @3 --#A IS A
REP1T$ SOLU;N (! EQU,N7 .;X @+ #A7 #B @7
.;X -- #B7 .K #J4
--#A ES UNA SOLUCI@ON REPETIDA DE LA
ECUACI@ON7 .;X @+ ;L7 #B @7 .;X -- #B7
.K #J4
ROOT ( AN EQU,N @7 P4 #BEC @7 ,!
SOLU;NS (A QUADRATIC EQU,N >E XS ROOTS4
..RA@IZ DE UNA ECUACI@ON 7P@AG4 .#BEC7
,LAS SOLUCI"OS DE UNA ECUACI@ON
CUADR@ATICA SON SUS RA@ICES4 @3 ,! ROOTS
(! QUADRATIC EQU,N .;X #B -- #E .;X --
#CF .K #J >E #I & --#D4
,LAS RA@ICES DE LA ECUACI@ON CUADR@ATICA
.;X #B -- #E .;X -- #CF .K #J SON #I ;Y
--#D4
;,S
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
SAMPLE @7 P4 #GFF @7 ,A SUBSET (A
POPUL,N4
.MUE/RA 7.P@AG4 .#GFF7 ,SUBCONJUNTO DE
UNA POBLACI@ON4 @3 .,SEE POPUL,N4
.,V] POBLACI@ON4
SCAL> @7 P4 #AHH @7 ,A R1L NUMB] 0: Y
MULTIPLY A MATRIX4
.ESCAL> 7.P@AG4 .#AHH7 ,N@UM]O R1L POR
EL QUE SE MULTIPLICA UNA MATRIZ4 @3
.,SEE SCAL> MULTIPLIC,N4
.,V] MULTIPLICACI@ON ESCAL>4
SCAL> MULTIPLIC,N @7 P4 #AHH @7
,MULTIPLIC,N ( EA* ELE;T (A MATRIX 0A
R1L NUMB]1 CALL$ A SCAL>4
..MULTIPLICACI@ON ESCAL> 7P@AG4 .#AHH7
,MULTIPLICACI@ON DE CADA ELE;TO DE UNA
MATRIZ POR UN N@UM]O R1L LLAMADO ESCAL>4
@3
SCATT]PLOT @7 P4 #AAC @7 ,A GRAPH (A
SET ( DATA PAIRS @7 .;X1 .;Y @7 US$
6DET]M9E :E!R "! IS A REL,N%IP 2T !
V>IA#S .;X & .;Y @4
..DIAGRAMA DE 4P]SI@ON 7P@AG4 .#AAC7
,GRANEA DE UN 3JUNTO DE P>ES DE DATOS @7
.;X1 .;Y @7 QUE SIRVE P>A DET]M9> SI HAY
UNA RELACI@ON 5TRE LAS V>IA#S .;X ;E .Y4
@3
SCI5TIFIC NOT,N @7 P4 #CCA @7 ,!
REPRES5T,N (A NUMB] 9 ! =M .;C * #AJ .;N
": #A "K.K ;C "K #AJ & .;N IS AN 9TEG]4
..NOTACI@ON CI5T@IFICA 7P@AG4 .#CCA7 ,LA
REPRES5TACI@ON DE UN N@UM]O DE LA =MA ;C
* #AJ .;N @1 DONDE #A "K.K .;C "K #AJ ;Y
.;N ES UN N@UM]O 5T]O4 @3 #J.FIC IS
WRITT5 9 SCI5TIFIC NOT,N Z #F.IC * #AJ
--#A @4
#J.FIC ESCRITO EN NOTACI@ON CI5T@IFICA
ES #F.IC * #AJ --#A @4
-----------------------------------#AJGC
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
SECANT FUNC;N @7 P4 #HEB @7 ,IF IS AN
ACUTE ANGLE (A "R TRIANGLE1 ! SECANT (
IS ! L5G? (! HYPOT5USE DIVID$ 0! L5G? (!
SIDE ADJAC5T TO @4
..FUND@ON SECANTE 7P@AG4 .#HEB7 ,SI ES
UN @ANGULO AGUDO DE UN TRI@ANGULO
RECT@ANGULO1 LA SECANTE DE ES LA L;GITUD
DE LA HIPOT5USA DIVIDIDA POR LA L;GITUD
DEL LADO ADYAC5TE A @4 @3 .,SEE S9E
FUNC;N4
.,V] FUNCI@ON S5O4
SECTOR @7 P4 #HFA @7 ,A REGION (
ACIRCLE T IS B.D$ 0TWO RADII & AN >E (!
CIRCLE4 ,! C5TRAL ANGLE (A SECTOR IS !
ANGLE =M$ 0! TWO RADII4
.SECTOR 7.P@AG4 .#HFA7 ,REGI@ON DE UN
C@IRCULO DELIMITADA POR DOS RADIOS ;Y UN
>CO DEL C@IRCULO4 ,EL @ANGULO C5TRAL DE
UN SECTOR ES EL @ANGULO =MADO POR DOS
RADIOS4 @3
SEQU;E @7 P4 #GID @7 ,A FUNC;N ^:
DOMA9 IS A SET ( 3SECUTIVE 9TEG]S4 ,!
DOMA9 GIVES ! RELATIVE POSI;N ( EA* T]M
(! SEQU;E4 ,! RANGE GIVES ! T]MS (!
SEQU;E4
.PROGRESI@ON 7.P@AG4 .#GID7 ,FUNCI@ON
CUYO DOM9IO ES UN 3JUNTO DE N@UM]OS
5T]OS 3SECUTIVOS4 ,EL DOM9IO DA LA
POSICI@ON RELATIVA DE CADA T@ERM9O DE LA
SECU5CIA4 ,EL RANGO DA LOS T@ERM9OS DE
LA SECU5CIA4 @3 ,=! DOMA9 .;N .K #A1 #B1
#C1 & #D1 ! SEQU;E DEF9$ 0A.' ;N.' .K #B
.;N HAS ! T]MS #B1 #D1 #F1 & #H4
,P>A EL DOM9IO .;N .K #A1 #B1 #C ;Y #D1
LA SECU5CIA DEF9IDA POR A.' ;N.' .K #B
.;N TI5E LOS T@ERM9OS #B1 #D1 #F ;Y #H4
S]IES @7 P4 #GIF @7 ,! EXPRES.N =M$
0A4+ ! T]MS (A SEQU;E4 ,A S]IES C 2
F9ITE OR 9F9ITE4
.S]IE 7.P@AG4 .#GIF7 ,LA EXPRESI@ON
=MADA ;AL SUM> LOS T@ERM9OS DE UNA
PROGRESI@ON4 ,LA S]IE PU$E S] F9ITA ;O
9F9ITA4 @3 ,F9ITE S]IES3 #B @+ #D @+ #F
@+ #H
,9F9ITE S]IES3 #B @+ #D @+ #F @+ #H @+
'''
,S]IE F9ITA3 #B @+ #D @+ #F @+ #H
,S]IE 9F9ITA3 #B @+ #D @+ #F @+ #H @+
'''
SET @7 P4 #GAE @7 ,A COLLEC;N ( 4T9CT
OBJECTS4
.3JUNTO 7.P@AG4 .#GAE7 ,COLE3I@ON DE
OBJETOS DIF]5CIADOS4 @3 ,IF .,A IS ! SET
( POSITIVE 9TEG]S LESS ?AN #E1 !N .,A .K
;7#A1 #B1 #C1 #D724
,SI .,A ES EL 3JUNTO DE N@UM]OS 5T]OS
POSITIVOS M5ORES QUE #E1 5TONCES .,A .K
;7#A1 #B1 #C1 #D724
.SIGMA .NOT,N 7.P#..GIF7 .,SEE SUMM,N
NOT,N4
..NOTACI@ON SIGMA 7P@AG4 .#GIF7 ,V]
NOTACI@ON DE SUMATORIA4 @3 .,SEE SUMM,N
NOT,N4
.,V] NOTACI@ON DE SUMATORIA4
SIMPLE/ =M (A RADICAL @7 P4 #DBB @7 ,A
RADICAL ) 9DEX .;N IS 9 SIMPLE/ =M IF !
RADIC& HAS NO P]FECT .;N TH P[]S Z
FACTORS & ANY DENOM9ATOR HAS BE5
R,NALIZ$4
..=MA M@AS SIMPLE DE UN RADICAL 7P@AG4
.#DBB7 ,UN RADICAL CON @INDICE .;N E/@A
ESCRITO EN LA =MA M@AS SIMPLE SI EL
RADIC&O NO TI5E -O FACTOR N+UNA POT5CIA
5@ESIMA P]FECTA ;Y EL DENOM9ADOR HA SIDO
RACIONALIZADO4 @3 9 SIMPLE/ =M IS @4
9 SIMPLE/ =M IS @4
EN LA =MA M@AS SIMPLE ES @4
EN LA =MA MAS SIMPLE ES @4
-----------------------------------#AJGD
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
SIMPLIFI$ =M (A R,NAL EXPRES.N @7 P4
#EGC @7 ,A R,NAL EXPRES.N 9 : ! NUM]ATOR
& DENOM9ATOR H NO -MON FACTORS O!R ?AN
+-#A4
..=MA SIMPLIFICADA DE UNA EXPRESI@ON
RACIONAL 7P@AG4 .#EGC7 ,EXPRESI@ON
RACIONAL EN LA QUE EL NUM]ADOR ;Y EL
DENOM9ADOR NO TI55 FACTORES -UNES
ADEM@AS DE +-#A4 @3
S9EFUNC;N @7 P4 #HEB @7 ,IF IS AN
ACUTE ANGLE (A "R TRIANGLE1 ! S9E ( IS !
L5G? (! SIDE OPPOSITE DIVID$ 0! L5G? (!
HYPOT5USE4
..FUNCI@ON S5O 7P@AG4 .#HEB7 ,SI ES UN
@ANGULO AGUDO DE UN TRI@ANGULO
RECT@ANGULO1 EL S5O DE ES LA L;GITUD DEL
LADO OPUE/O A DIVIDIDA POR LA L;GITUD DE
LA HIPOT5USA4 @3
S9USOIDS @7 P4 #IDA @7 ,GRAPHS ( S9E &
COS9E FUNC;NS4
.S9USOIDES 7.P@AG4 .#IDA7 ,GR@AFICAS DE
FUNCI"OS S5O ;Y COS5O4 @3
SKEW$ 4TRIBU;N @7 P4 #GBG @7 ,A
PROBABIL;Y 4TRIBU;N T IS N SYMMETRIC4
.,SEE .AL SYMMETRIC 4TRIBU;N4
..4TRIBUCI@ON ASIM@ETRICA 7P@AG4 .#GBG7
,4TRIBUCI@ON DE PROBABILIDADES QUE NO ES
SIM@ETRICA4 .,V] .TAMBI@EN 4TRIBUCI@ON
SIM@ETRICA4 @3
-----------------------------------#AJGE
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
SLOPE @7 P4 #HB @7 ,! RATIO ( V]TICAL
*ANGE 7! RISE7 6HORIZONTAL *ANGE 7! RUN7
=A NONV]TICAL L9E4 ,=A NONV]TICAL L9E
PASS+ "? ! PO9TS @7 .;X #A .;Y #A @7 &7
.;X #B @1 .;Y #B @7@1 ! SLOPE IS @4
.P5DI5TE 7.P@AG4 .#HB7 ,P>A UNA RECTA NO
V]TICAL1 LA RAZ@ON 5TRE EL CAMBIO
V]TICAL 74TANCIA V]TICAL7 ;Y EL CAMBIO
HORIZONTAL 74TANCIA HORIZONTAL74 ,P>A
UNA RECTA NO V]TICAL QUE PASA POR LOS
PUNTOS @7 .;X #A @1 .;Y #A @7 ;Y @7 .;X
#B @1 .;Y #B @7@1 LA P5DI5TE ES @3 ,!
SLOPE (! L9E T PASSES "? ! PO9TS 7--#C1
#J7 & 7#C1 #D7 IS3
,LA P5DI5TE DE LA RECTA QUE PASA POR LOS
PUNTOS 7--#C1 #J7 ;Y 7#C1 #D7 ES3
.SLOPE-.9T]CEPT .=M 7.P#..IJ7 ,A L9E>
EQU,N WRITT5 9 ! =M .;Y .K .MX @+ .;B ":
.;M IS ! SLOPE & .;B IS ! .;Y -9T]CEPT
(! EQU,N'S GRAPH4
..=MA P5DI5TE-9T]CEPTO 7P@AG4 .#IJ7
,ECUACI@ON L91L ESCRITA EN LA =MA .;Y .K
.MX @+ .;,B @1 DONDE .;M ES LA P5DI5TE
;Y .;B ES EL 9T]CEPTO EN ;Y DE LA
GR@AFICA DE LA ECUACI@ON4 @3 ,! EQU,N IS
9 SLOPE-9T]CEPT =M4
,LA ECUACI@ON E/@A EN LA
=MAP5DI5TE-9T]CEPTO4
SOLU;N (A L9E> 9EQUAL;Y 9 TWO V>IA#S
@7 P4 #ACB @7 ,ANORD]$ PAIR @7 .;X1 .;Y
@7 T PRODUCES A TRUE /ATE;T :5 ! VALUES
( .;X & .;Y >E SUB/ITUT$ 96! 9EQUAL;Y4
..SOLUCI@ON DE UNA DESIGUALDAD L91L CON
DOS V>IA#S7P@AG4 .#ACB7 ,P> ORD5ADO @7
.;X1 .;Y @7 QUE PRODUCE UN ENUNCIADO
V]DAD]O CU&O .;X ;E .;Y SE SU/ITUY5 POR
SUS VALORES EN LA DESIGUALDAD4 @3 ,!
ORD]$ PAIR 7#A1 #B7 IS A SOLU;N ( #C .;X
@+ #D .;Y .1 #H 2C #C7;L7 @+ #D7#B7 .K
#AA1 & #AA .1 #H4
,EL P> ORD5ADO 7#A1 #B7 ES UNA SOLUCI@ON
DE #C .;X @+ #D .;Y .1 #H YA QUE #C7#A7
@+ #D7#B7 .K #AA1 ;Y #AA .1 #H4
SOLU;N (A SY/EM ( L9E> EQU,NS 9 ?REE
V>IA#S @7 P4 #AGH @7 ,AN ORD]$ TRIPLE @7
.;X1 .;Y @1 ;Z @7 ^: COORD9ATES MAKE EA*
EQU,N 9 ! SY/EM TRUE4
..SOLUCI@ON DE UN SI/EMA DE ECUACI"OS
L91LES EN TRES V>IA#S 7P@AG4 .#AGH7
,T]NA ORD5ADA @7 .;X1 .;Y @1 ;Z7 CUYAS
COORD5ADAS HAC5 QUE CADA ECUACI@ON DEL
SI/EMA SEA V]DAD]A4 @3 #D .;X @+ #B .;Y
@+ #C .;Z .K #A
#B .;X -- #C .;Y @+ #E .;Z .K --#AD
#F .;X -- .;Y @+ #D .;Z .K --#A
7#B1 #A1 --#C7 IS ! SOLU;N (! SY/EM ABV4
7#B1 #A1 --#C7 ES LA SOLUCI@ON DEL
SI/EMA DE >RIBA4
SOLU;N (A SY/EM ( L9E> EQU,NS 9 TWO
V>IA#S @7 P4 #AEC @7 ,AN ORD]$ PAIR @7
.;X1 .;Y @7 T SATISFIES EA* EQU,N (!
SY/EM4
..SOLUCI@ON DE UN SI/EMA DE ECUACI"OS
L91LES EN DOS V>IA#S 7P@AG4 .#AEC7 ,P>
ORD5ADO @7 .;X1 .;Y @7 QUE SATISFACE
CADA ECUACI@ON DEL SI/EMA4 @3 #D .;X @+
.;Y .K #H
#B .;X -- #C .;Y .K #AH
7#C1 --#D7 IS ! SOLU;N (! SY/EM ABV4
7#C1 --#D7 ES LA SOLUCI@ON DEL SI/EMA DE
>RIBA4
SOLU;N (A SY/EM ( L9E> 9EQUALITIES 9
TWO V>IA#S @7 P4 #AFH @7 ,AN ORD]$ PAIR
7;X1 ;Y7 T IS A SOLU;N ( EA* 9EQUAL;Y 9
! SY/EM4
..SOLUCI@ON DE UN SI/EMA DE
DESIGUALDADES L91LES EN DOSV>IA#S 7P@AG4
.#AFH7 ,P> ORD5ADO 7;X1 ;Y7 QUE ES UNA
SOLUCI@ON DE CADA DESIGUALDAD DEL
SI/EMA4 @3 ;Y .1--#B .;X -- #E
.;Y "K .;X @+ #C
7--#A1 #A7 IS A SOLU;N (! SY/EM ABV4
7--#A1 #A7 ES UNA SOLUCI@ON DEL SI/EMA
DE >RIBA4
-----------------------------------#AJGF
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
SOLU;N ( AN EQU,N 9 "O V>IA# @7 P4 #AH
@7 ,A NUMB] T PRODUCES A TRUE /ATE;T :5
SUB/ITUT$ =! V>IA# 9 ! EQU,N4
..SOLUCI@ON DE UNA ECUACI@ON CON UNA
V>IA# 7P@AG4 .#AH7 ,N@UM]O QUE PRODUCE
UN ENUNCIADO V]DAD]O ;AL SU/ITUIR LA
V>IA# POR @EL EN LA ECUACI@ON4 @3 ,!
SOLU;N (! EQU,N IS #AE4
,LA SOLUCI@ON DE LA ECUACI@ON ES #AE4
SOLU;N ( AN EQU,N 9 TWO V>IA#S @7 P4
#GD @7 ,ANORD]$ PAIR @7 .;X1 .;Y @7 T
PRODUCES A TRUE /ATE;T :5 ! VAL@UES (
.;X & .;Y >E SUB/ITUT$ 9 ! EQU,N4
..SOLUCI@ON DE UNA ECUACI@ON CON DOS
V>IA#S 7P@AG4 .#GD7 ,P>ORD5ADO @7 .;X1
.;Y @7 QUE PRODUCE UN ENUNCIADO V]DAD]O
;AL SU/ITUIR .;X ;E .;Y POR SUS VALORES
EN LA ECUACI@ON4 @3 7--#B1 #C7 IS A
SOLU;N ( .;Y .K --#B .;X -- #A4
7--#B1 #C7 ES UNA SOLUCI@ON .DE .;Y .K
--#B .;X -- #A4
SOLU;N ( AN 9EQUAL;Y 9 "O V>IA# @7 P4
#DA @7 ,A NUMB] T PRODUCES A TRUE /ATE;T
:5 SUB/ITUT$ =! V>IA# 9 ! 9EQUAL;Y4
..SOLUCI@ON DE UNA DESIGUALDAD CON UNA
V>IA# 7P@AG4 .#DA7 ,N@UM]O QUE PRODUCE
UN ENUNCIADO V]DAD]O ;AL SU/ITUIR LA
V>IA# POR @EL EN LA DESIGUALDAD4 @3 --#A
IS A SOLU;N (! 9EQUAL;Y #E .;X @+ #B .1
#G .;X -- #D4
--#A ES UNA SOLUCI@ON DE LA DESIGUALDAD
#E .;X @+ #B .1 #G .;X -- #D4
SOLVE =A V>IA# @7 P4 #BF @7 ,REWRITE
AN EQU,N Z AN EQUIVAL5T EQU,N 9 : !
V>IA# IS ON "O SIDE & DOES N APPE> ON !
O!R SIDE4
..RESOLV] P>A UNA V>IA# 7P@AG4 .#BF7
,ESCRIBIR UNA ECUACI@ON -O ECUACI@ON
EQUIVAL5TE QUE T5GA LA V>IA# EN UNO DE
SUS LADOS P]O NO EN EL OTRO4 @3 ,:5 Y
SOLVE ! CIRCUMF];E =MULA .;,C.K #B .;R =
.;R @1 ! RESULT IS @4
;,AL RESOLV] P>A .;R LA F@ORMULA DE
CIRCUNF]5CIA .;,C .K #B .;R @1 EL
RESULTADO ES
SQU>E ROOT @7 P4 #BFF @7 ,IF ;B.' #B
.K A.' @1 !N .;B IS A SQU>E ROOT ( .A4
,! RADICAL SYMBOL REPRES5TS A
NONNEGATIVE SQU>E ROOT4
..RA@IZ CUADRADA 7P@AG4 .#BFF7 ,SI ;B.'
#B .K A.' @1 5TONCES .;B ES UNA RA@IZ
CUADRADA DE .A4 ,EL SIGNO RADICAL
REPRES5TA UNA RA@IZ CUADRADA NO
NEGATIVA4 @3 ,! SQU>E ROOTS ( #I >E #C &
--#C 2C #C #B .K #I & 7--#C7 #B .K #I4
,S1 & @4
,LAS RA@ICES CUADRADAS DE #I SON #C ;Y
--#C YA QUE #C #B .K #I .;Y 7--#C7#B .K
#I.,AS@IPUES1 ;Y
/&>D DEVI,N @7 P4 #GDE @7 ,! TYPICAL
DI6];E 7OR DEVI,N7 2T A DATA VALUE &!
M1N4 ,! /&>D DEVI,N (A NUM]ICAL DATA SET
.;X #A @1 .;X #B @1'''@1 ;X.' ;N.' IS
GIV5 0! FOLL[+ =MULA3
..DESVIACI@ON T@IPICA 7P@AG4 .#GDE7 ,LA
DIF]5CIA 7;O DESVIACI@ON7 M@AS -@UN 5TRE
UN VALOR DE LOS DATOS ;Y LA M$IA4 ,LA
DESVIACI@ON T@IPICA DE UN 3JUNTO DE
DATOS NUM@ERICOS .;X #A @1 .;X #B
@1'''@1 ;X.' ;N.' VI5E DADA POR LA
SIGUI5TE F@ORMULA3
@3 #AD1 #AG1 #AH1 #AI1 #BJ1 #BD1 #BD1
#CJ1 #CB
,2C ! M1N (! DATA SET IS #BB1 ! /&>D
DEVI,N IS3
,-O LA M$IA DEL 3JUNTO DE DATOS ES #BB1
LA DESVIACI@ON T@IPICA ES3
-----------------------------------#AJGG
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
/&>D =M (A -PLEX NUMB] @7 P4 #BGF @7
,! =M .A @+ .BI ": .A & .;B >E R1L
NUMB]S & .;F IS ! IMAG9>Y UNIT4
..=MA G5]AL DE UN N@UM]O -PLEJO 7P@AG4
.#BGF7 ,LA=MA .A @+ .BI @1 DONDE .A ;Y
.;B SON N@UM]OS R1LES ;E .;I ES LA
UNIDAD IMAG9>IA4 @3 ,! /&>D =M (! -PLEX
NUMB] .;I 7#A @+ .;I @7 IS --#A @+ .;I
@4
,LA =MA G5]AL DEL N@UM]O -PLEJO .;I 7#A
@+ .;I @7 ES --#A @+ .;I
../&>D =M (A L9E> EQU,N 7P#..IA7 ,A
L9E> EQU,N WRITT5 9 ! =M ..,AX @+ ,BY .K
.;,C ": .,A & .;,B >E N BO? Z]O4
..=MA G5]AL DE UNA ECUACI@ON L91L 7P@AG4
.#IA7 ,ECUACI@ON L91L ESCRITA EN LA =MA
.,AX @+ .,BY .K .;,C @1 DONDE .,A ;Y
.;,B NO SON AMBOS C]O4 @3 ,! L9E> EQU,N
.;Y .K --#C .;X @+ #D C 2 WRITT5 9 /&>D
=M Z #C .;X @+ .;Y .K #D4
,LA ECUACI@ON L91L .;Y .K --#C .;X @+ #D
ESCRITA EN LA =MA G5]AL ES #C .;X @+ .;Y
.K #D4
/&>D =M (A POLYNOMIAL FUNC;N @7 P4
#CCG @7 ,! =M (A POLYNOMIAL FUNC;N T HAS
T]MS WRITT5 9 DESC5D+ ORD] ( EXPON5TS F
LEFT 6"R4
..=MA G5]AL DE UNA FUNCI@ON POL9@OMICA
7P@AG4 .#CCG7 ,LA=MA DE UNA FUNCI@ON
POL9@OMICA EN LA QUE LOS T@ERM9OS SE
ORD5AN DE TAL MODO QUE LOS EXPON5TES
4M9UY5 DE IZQUI]DA A D]E*A4 @3 ,! FUNC;N
C 2 WRITT5 9 /&>D =M Z @4
,LA FUNCI@ON ESCRITA EN LA =MA G5]AL ES
@4
/&>D =M (A QUADRATIC EQU,N 9 "O V>IA#7
P4 #BEC @7 ,! =M .AX #B @+ .BX @+ .;C .K
#J ": .A @6.K #J4
..=MA G5]AL DE UNA ECUACI@ON CUADR@ATICA
CON UNA V>IA# 7P@AG4 .#BEC7 ,LA =MA .,AX
#B @+ .BX @+ .;C .K #J1 DONDE .A @6.K
#J4 @3 ,! QUADRATIC EQU,N .;X #B -- #E
.;X .K #CF C 2 @7 WRITT5 9 /&>D =M Z .;X
#B -- #E .;X -- #CF .K #J4
,LA ECUACI@ON CUADR@ATICA .;X #B -- #E
.;X .K #CF ESCRITA EN LA =MA G5]AL ES
.;X #B -- #E .;X -- #CF .K #J4
/&>D =M (A QUADRATIC FUNC;N @7 P4 #BCF
@7 ,! =M .;Y .K .AX #B @+ .BX @+ .;C ":
.A @6.K #J4
..=MA G5]AL DE UNA FUNCI@ON CUADR@ATICA
7P@AG4 .#BCF7 ,LA=MA .;Y .K .AX #B @+
..BX @+ .;C @1 DONDE .A @6.K #J4 @3 ,!
QUADRATIC FUNC;N .;Y .K #B7 .;X @+ #C7@7
.;X -- #A7 C 2 WRITT5 9 /&>D =M Z .;Y .K
#B .;X #B @+ #D .;X -- #F4
,LA FUNCI@ON CUADR@ATICA .;Y .K #B7 .;X
@+ #C7@7 .;X -- #A7 ESCRITA EN LA =MA
G5]AL ES .;Y .K #B .;X #B @+ #D .;X --
#F4
/&>D NORMAL 4TRIBU;N @7 P4 #GEH @7 ,!
NORMAL 4TRIBU;N ) M1N #J & /&>D DEVI,N
#A4 .,SEE .AL .;Z -SCORE4
..4TRIBUCI@ON NORMAL T@IPICA 7P@AG4
.#GEH7 ,LA 4TRIBUCI@ON NORMAL CON M$IA
#J ;Y DESVIACI@ON T@IPICA #A4 .,V]
.TAMBI@EN PUNTUACI@ON Z4 @3
-----------------------------------#AJGH
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
/&>D POSI;N ( AN ANGLE @7 P4 #HEI @7
,9 A COORD9ATE PLANE1 ! POSI;N ( AN
ANGLE ^: V]TEX IS AT ! ORIG9 & ^: 9ITIAL
SIDE LIES ON ! POSITIVE .;X -AXIS4
..POSICI@ON NORMAL DE UN @ANGULO 7P@AG4
.#HEI7 ,EN UN PLANO DE COORD5ADAS1 LA
POSICI@ON DE UN @ANGULO CUYO V@ERTICE
E/@A EN EL ORIG5 ;Y CUYO LADO 9ICIAL SE
SIT@UA EN EL EJE DE .;X POSITIVO4 @3
/ATI/ICS @7 P4 #GDD @7 ,NUM]ICAL
VALUES US$ 6SUMM>IZE & -P>E SETS ( DATA4
.E/AD@I/ICA 7.P@AG4 .#GDD7 ,VALORES
NUM@ERICOS UTILIZADOS P>A RESUMIR ;Y
-P>> 3JUNTOS DE DATOS4 @3 .,SEE M1N1
M$IAN1 MODE1 RANGE1 .& /&>D DEVI,N4
.,V] M$IA1 M$IANA1 MODA1 RANGO .;Y
DESVIACI@ON T@IPICA4
/EP FUNC;N @7 P4 #ACA @7 ,A PIECEWISE
FUNC;N DEF9$ 0A 3/ANT VALUE OV] EA* "P (
XS DOMA94 ,XS GRAPH RESEM#S A S]IES (
/AIR /EPS4
..FUNCI@ON ESCALONADA 7P@AG4 .#ACA7
,FUNCI@ON DEF9IDA A TROZOS ;Y POR UN
VALOR 3/ANTE EN CADA "PE DE SU DOM9IO4
,SU GR@AFICA P>ECE UN GRUPO DE ESCAL"OS4
@3
SUBSET @7 P4 #GAF @7 ,IF E ELE;T (A
SET .,A IS AL AN ELE;T (A SET .;,B @1 !N
,A IS A SUBSET ( .;B @4 ,? IS WRITT5 .,A
.;,B @4 ,= ANYSET ,A1 & ,A ,A4
.SUBCONJUNTO 7.P@AG4 .#GAF7 ,SI CADA
ELE;TO DE UN 3JUNTO .,A ES TAMBI@EN UN
ELE;TO DE UN 3JUNTO .;,B @1 5TONCES .,A
ES UN SUBCONJUNTO DE .;,B @1 ,E/O SE
ESCRIBE .,A .;B @4 ,P>A CUALQUI] 3JUNTO
,A1 .,A ;Y .,A .,A @3 ,IF .,A .K ;7#A1
#B1 #D1 #H72 & .;,B IS ! SET ( ALL
POSITIVE 9TEG]S1 !N .,A IS A SUBSET (
.;,B1 .,A .;,B @4
,SI .,A .K ;7#A1 #B1 #D1 #H72 ;Y .;,B ES
EL 3JUNTO DE TODOS LOS N@UM]OS 5T]OS
POSITIVOS1 5TONCES .,A ES UN SUBCONJUNTO
DE .;,B @1 #J .,A .;B @4
.SUB/ITU;N .ME?OD 7.P4 #A .#FJ7 ,A
ME?OD ( SOLV+ A SY/EM ( EQU,NS 0SOLV+ "O
(! EQU,NS = "O (! V>IA#S & !N SUB/ITUT+
! RESULT+ EXPRES.N 9 ! O!R EQU,N7;S74
..M@ETODO DE SU/ITUCI@ON 7P@AG4 .#AFJ7
,M@ETODO P>A RESOLV] UN SI/EMA DE
ECUACI"OS M$IANTE LA RESOLUCI@ON DE UNA
DE LAS ECUACI"OS P>A UNA DE LAS V>IA#S
SEGUIDA DE LA SU/ITUCI@ON DE LA
EXPRESI@ON RESULTANTE EN LA7;S7 OTRA7;S7
ECUACI@ON 7ECUACI"OS74 @3 #B .;X @+ #E
.;Y .K --#E
.;X @+ #C .;Y .K #C
,SOLVE EQU,N #B = .;X3 .;X .K --#C .;Y
@+ #C4
,SUB/ITUTE ! EXPRES.N = .;X 9 EQU,N #A &
SOLVE = ;Y3 .;Y .K #AA4 ,USE ! VALUE (
;Y 6FLND ! VALUE ( .;X3 .;X .K --#CJ4
,RESUELVE LA ECUACI@ON #B P>A .;X3 .;X
.K --#C .;Y @+ #C4 ,SU/ITUYE LA
EXPRESI@ON P>A .;X EN LA ECUACI@ON #A ;Y
RESUELVE P>A .;Y3 .;Y .K #AA4 ,USA EL
VALOR DE .;Y P>A HALL> EL VALOR DE .;X3
.;X .K --#CJ4
SUMM,N NOT,N @7 P4 #GIF @7 ,NOT,N =A
S]IES T USES ! UPP]CASE ,GREEK LR SIGMA1
@4 ,AL CALL$ SIGMA NOT,N4
..NOTACI@ON DE SUMATORIA 7P@AG4 .#GIF7
,NOTACI@ON DE UNA S]IE QUE USA LA LETRA
GRIEGA MAY@USCULA SIGMA1 #B4 ,TAMBI@EN
SE LLAMA NOTACI@ON SIGMA4 @3
-----------------------------------#AJGI
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.SYMMETRIC .4TRIBU;N 7.P#..GBG7 ,A
PROBABIL;Y 4TRIBU;N1 REPRES5T$ 0A
HI/OGRAM1 9 : Y C DRAW A V]TICAL L9E T
DIVIDES ! HI/OGRAM 96TWO "PS T >E MIRROR
IMAGES4
..4TRIBUCI@ON SIM@ETRICA 7P@AG4 .#GBG7
,4TRIBUCI@ON DE PROBABILIDAD REPRES5TADA
POR UN HI/OGRAMA EN LA QUE SE PU$E TRAZ>
UNA RECTA V]TICAL QUE DIVIDA ;AL
HI/OGRAMA EN DOS "PES2 @E/AS SON
IM@AG5ES ESPECUL>ES 5TRE S@I4 @3
SYN!TIC DIVI.N @7 P4 #CFC @7 ,A ME?OD
US$ 6DIVIDE A POLYNOMIAL 0A DIVISOR (!
=M .;X -- .;K @4
..DIVISI@ON S9T@ETICA 7P@AG4 .#CFC7
,M@ETODO UTILIZADO P>A DIVIDIR UN
POL9OMIO POR UN DIVISOR EN LA =MA
.;X--.K4 @3
SYN!TIC SUB/ITU;N @7 P4 #CCH @7 ,A
ME?OD US$ 6EVALUATE A POLYNOMIAL FUNC;N4
..SU/ITUCI@ON S9T@ETICA 7P@AG4 .#CCH7
,M@ETODO UTILIZADO P>A EVALU> UNA
FUNCI@ON POL9@OMICA4 @3
,! SYN!TIC SUB/ITU;N ABV 9DICATES T =
.;F @7 .;X @7 .K #B .;X #D -- #E .;X #C
-- #D .;X @+ #H1 .;F 7#C7 .K #BC4
,LA SU/ITUCI@ON S9T@ETICA DE >RIBA 9DICA
QUE P>A .;F @7 .;X @7 .K #B .;X #D -- #E
.;X #C -- #D .;X @+ #H1 .;F 7#C7 .K #BC4
SY/EM ( L9E> 9EQUALITIES 9 TWO V>IA#S
@7 P4 #AFH @7 ,ASY/EM 3SI/+ ( TWO OR M
L9E> 9EQUALITIES 9 TWO V>IA#S4
.,SEE .AL L9E> 9EQUAL;Y 9 TWO V>IA#S4
..SI/EMA DE DESIGUALDADES L91LES CON DOS
V>IA#S7P@AG4 .#AFH7 ,SI/EMA QUE 3SI/E DE
DOS ;O M@AS DESIGUALDADES L91LES CON DOS
V>IA#S4 .,V] .TAMBI@EN DESIGUALDAD L91L
CON DOS V>IA#S4 @3 .;X @+ .;Y "K #H
#D .;X -- .;Y .1 #F
SY/EM ( ?REE L9E> EQU,NS 9 ?REE
V>IA#S7 P4 #AGH @7 ,A SY/EM 3SI/+ ( ?REE
L9E> EQU,NS 9 ?REE V>IA#S4 .,SEE .AL
L9E> EQU,N 9 ?REE V>IA#S4
..SI/EMA DE TRES ECUACI"OS L91LES EN
TRES V>IA#S7P@AG4 .#AGH7 ,SI/EMA =MADO
POR TRES ECUACI"OS L91LES CON TRES
V>IA#S4 .,V] .TAMBI@EN ECUACI@ON L91L
CON TRES V>IA#S4 @3 #B .;X @+ .;Y -- .;Z
.K #E
#C .;X -- #B .;Y @+ .;Z .K #AF
#D .;X @+ #C .;Y -- #E .;Z .K #C
-----------------------------------#AJHJ
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
SY/EM ( TWO L9E> EQU,NS 9 TWO V>IA#S7
P4 #AEC @7 ,A SY/EM 3SI/+ ( TWO EQU,NS T
C 2 WRITT5 9 ! =M .,AX @+ .,BY .K .;,C &
.,DX @+ .,EY .K .;,F ": .;X & .;Y >E
V>IA#S1 .,A & .;,B >E N BO? Z]O1 & .;,D
& .;,E >E N BO? Z]O4
..SI/EMA DE DOS ECUACI"OS L91LES CON DOS
V>IA#S7P@AG4 .#AEC7 ,UN SI/EMA QUE 3SI/E
EN DOS ECUACI"OS QUE SE PU$5 ESCRIBIR DE
LA =MA .,AX @+ .,BY .K .;,C ;Y .,DX @+
.,EY .K .;,F @1 DONDE .;X ;E .;Y SON
V>IA#S1 .,A ;Y .;,B NO SON AMBOS C]O1 ;Y
.;,D ;Y .;,E TAMPOCO SON AMBOS C]O4 @3
#D .;X @+ .;Y .K #H
#B .;X -- #C .;Y .K #AH
;,T
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
TANG5T FUNC;N @7 P4 #HEB @7 ,IF IS AN
ACUTE ANGLE (A "R TRIANGLE1 ! TANG5T (
IS ! L5G? (! SIDE OPPOSITE DIVID$ 0!
L5G? (! SIDE ADJAC5T TO
@4 ..FUNCI@ON TANG5TE 7P@AG4 .#HEB7 ,SI
ES UN @ANGULO AGUDO DE UN TRI@ANGULO
RECT@ANGULO1 LA TANG5TE DE ES LA L;GITUD
DEL LADO OPUE/O A DIVIDIDA POR LA
L;GITUD DEL LADO ADYAC5TE A @4 @3 .,SEE
S9E FUNC;N4
.,V] FUNCI@ON S5O4
T]M9AL SIDE ( AN ANGLE @7 P4 #HEI @7
,9 A COORD9ATE PLANE1 AN ANGLE C 2 =M$
0FIX+ "O RAY1 CALL$ ! 9ITIAL SIDE1 &
ROTAT+ ! O!R RAY1 CALL$ ! T]M9AL SIDE1
AB ! V]TEX4
..LADO T]M9AL DE UN @ANGULO 7P@AG4
.#HEI7 ,EN UN PLANO DE COORD5ADAS1 UN
@ANGULO PU$E =M>SE ;AL FIJ> UN RAYO1
LLAMADO LADO 9ICIAL1 ;Y ;AL GIR> EL OTRO
RAYO1 LLAMADO LADO T]M9AL1 EN TORNO ;AL
V@ERTICE4 @3 .,SEE /&>D POSI;N ( AN
ANGLE4
.,V] POSICI@ON NORMAL DE UN @ANGULO4
T]MS (A SEQU;E @7 P4 #GID @7 ,! VALUES
9 ! RANGE (A SEQU;E4
..T@ERM9OS DE UNA PROGRESI@ON 7P@AG4
.#GID7 ,LOS VALORES DEL RANGO DE UNA
PROGRESI@ON4 @3 ,! F/ #D T]MS (! SEQU;E
#A1 --#C1 #I1 --#BG1 #HA1 --#BDC1''' >E
#A1 --#C1 #I1 & --#BG4
,LOS #D PRIM]OS T@ERM9OS DE LA
PROGRESI@ON #A1 --#C1 #I1 --#BG1 #HA1
--#BDC1''' SON #A1 --#C1 #I ;Y --#BG4
T]MS ( AN EXPRES.N @7 P4 #AB @7 ,! "PS
( AN EXPRES.N T >E A4$ TGR4
..T@ERM9OS DE UNA EXPRESI@ON 7P@AG4
.#AB7 ,LAS "PES DE UNA EXPRESI@ON QUE SE
SUMAN4 @3 ,! T]MS (! ALGEBRAIC
EXPRESSION#C .;X #B @+ #E .;X @+ 7--#G7
>E #C .;X #B @1 #E .;X @1 & --#G4
,LOS T@ERM9OS DE LA EXPRESI@ON
ALGEBRAICA#C .;X #B @+ #E .;X@+ 7--#G7
SON #C .;X #B @1 #E .XY --#G4
-----------------------------------#AJHA
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
!ORETICAL PROBABIL;Y @7 P4 #FIH @7 ,:5
ALL \TCOMES >E EQU,Y LIKELY1 ! !ORETICAL
PROBABIL;Y T AN EV5T .,A W
..PROBABILIDAD TE@ORICA 7P@AG4 .#FIH7
,CU&O TODOS LOS CASOS SON IGUAL;TE
POSI#S1 LA PROBABILIDAD TE@ORICA DE QUE
OCURRA @3 ,! !ORETICAL PROBABIL;Y (
ROLL+ AN EV5 NUMB] US+ A /&>D SIX-SID$
DIEIS 2C #C \TCOMES CORRESPONDTO ROLL+
AN EV5 NUMB] \ ( #F TOTAL \TCOMES4
,LA PROBABILIDAD TE@ORICA DE SAC> UN
N@UM]O P> ;AL LANZ> UN DADO NORMAL DE
SEIS C>ASES YA QUE #C CASOS CORRESPOND5
A UNN@UM]O P> DEL TOTAL DE #F CASOS4
TRANS=M,N @7 P4 #ABC @7 ,A TRANS=M,N
*ANGES A GRAPH'S SIZE1 %APE1 POSI;N1 OR
ORI5T,N4
.TRANS=MACI@ON 7.P@AG4 .#ABC7 ,UNA
TRANS=MACI@ON CAMBIA EL TAMA@NO1 LA =MA1
LA POSICI@ON ;O LA ORI5TACI@ON DE UNA
GR@AFICA4 @3 ,TRANSL,NS1 V]TICAL /RET*ES
& %R9KS1 REFLEC;NS1 & ROT,NS >E
TRANS=M,NS4
,LAS TRASLACI"OS1 LAS EXPAN.NES ;Y
3TRA3I"OS V]TICALES1 LAS REFLEXI"OS ;Y
LAS ROTACI"OS SON TRANS=MACI"OS4
TRANSL,N @7 P4 #ABC @7 ,A TRANS=M,N T
%IFTS A GRAPH HORIZONT,Y &_/OR V]TIC,Y1
B DOES N *ANGE XS SIZE1 %APE1 OR
ORI5T,N4
.TRASLACI@ON 7.P@AG4 .#ABC7
,TRANS=MACI@ON QUE DESPLAZA UNA GR@AFICA
HORIZONTAL ;O V]TICAL;TE1 ;O DE AMBAS
MAN]AS1 P]O QUE NO CAMBIA SU TAMA@NO1
=MA ;U ORI5TACI@ON4 @3
,! GRAPH ( .;Y .K _\ .;X @+ #D_\ --#B IS
! GRAPH ( .;Y .K _\ .;X_\ TRANSLAT$ D[N
#B UNITS & LEFT #D UNITS4
,LA GR@AFICA DE .;Y .K _\.;X@+ #D_\ --#B
ES LA GR@AFICA DE .;Y .K _\.;X_\ ;AL
TRASLAD> @E/A #B UNIDADES HACIA ABAJO ;Y
#D UNIDADES HACIA LA IZQUI]DA4
TRANSV]SE AXIS (A HYP]BOLA @7 P4 #FDB
@7 ,! L9E SEG;T JO9+ ! V]TICES (A
HYP]BOLA4
..EJE TRANSV]SO DE UNA HIP@ERBOLA 7P@AG4
.#FDB7 ,EL SEG;TO DE RECTA QUE UNE LOS
V@ERTICES DE UNA HIP@ERBOLA4 @3 .,SEE
HYP]BOLA4
.,V] HIP@ERBOLA4
TRIGONOMETRIC ID5T;Y @7 P4 #IBD @7 ,A
TRIGONOMETRIC EQU,N T IS TRUE = ALL
DOMA9 VALUES4
..ID5TIDAD TRIGONOM@ETRICA 7P@AG4 .#IBD7
,ECUACI@ON TRIGONOM@ETRICA QUE ES
V]DAD]A P>A TODOS LOS VALORES DEL
DOM9IO4 @3 S9 @7 -- @7 .K --S9
S9 #B @+ COS #B .K #A
S57 -- @7 .K --S5
S5 #B @+ COS #B .K #A
TRINOMIAL @7 P4 #BEB @7 ,! SUM ( ?REE
MONOMIALS4
.TR9OMIO 7.P@AG4 .#BEB7 ,LA SUMA DE TRES
MONOMIOS4 @3 #D .;X #B @+ #C .;X -- #A
IS A TRINOMIAL4
#D .;X #B @+ #C .;X -- #A ES UN TR9OMIO4
-----------------------------------#AJHB
,5GLI%--,SPANI% ,GLOSS>Y
;,U
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
UNBIAS$ SAMPLE @7 P4 #GFG @7 ,A SAMPLE
T IS REPRES5TATIVE (! POPUL,N Y WANT
9=M,N AB4
..MUE/RA NO SESGADA 7P@AG4 .#GFG7
,MUE/RA QUE ES REPRES5TATIVA DE LA
POBLACI@ON AC]CA DE LA CUAL DES1S
9=M>TE4 @3 ,Y WANT 6POLL MEMB]S (! S5IOR
CLASS AB ": 6HOLD ! PROM4 ,IF E S5IOR
HAS AN EQUAL *.E ( 2+ POLL$1 !N ! SAMPLE
IS UNBIAS$4
,QUI]ES 5CUE/> A ALGUNOS E/UDIANTES DE
@ULTIMO CURSO SOBRE EL LUG> DONDE
ORGANIZ> EL BAILE DE F9 DE A@NO4 ,SI
CADA E/UDIANTE DE @ULTIMO CURSO TI5E
IGUALES POSIBILIDADES DE S] 5CUE/ADO1
5TONCES ES UNA MUE/RA NO SESGADA4
..UNION ( SETS 7P#..GAE7 ,! UNION (
TWO SETS .,A & .;,B @1 WRITT5 .,A .;,B
@1 IS ! SET ( ALL ELE;TS 9 .EI .,A OR
.;B @4
..UNI@ON DE 3JUNTOS 7P@AG4 .#GAE7 ,LA
UNI@ON DE DOS 3JUNTOS .,AY,B @1
ESCRITAAU,B1 ES EL 3JUNTO DE TODOS LOS
ELE;TOS QUE E/@AN .5,AO,B4 @3 ,IF .,A .K
;7#A1 #B1 #D1 #H72 & .;,B .K ;7#B1 #D1
#F1 #H1 #AJ721 !N .,A .;,B .K ;7#A1 #B1
#D1 #F1 #H1AJ724
,SI .,A .K ;7#A1 #B1 #D1 #H72 ;Y .;,B .K
;7#B1 #D1 #F1 #H1 #AJ721 5TONCES .,A
.;,B .K ;7#A1 #B1 #D1 #F1 #H1 #AJ724
UNIT CIRCLE @7 P4 #HFG @7 ,! CIRCLE
.;X #B @+ .;Y #B .K #A1 : HAS C5T] 7#J1
#J7 & RADIUS #A4 ,= AN ANGLE 9 /&>D
POSI;N1 ! T]M9AL SIDE ( 9T]SECTS ! UNIT
CIRCLE AT ! PO9T 7COS @1 S9 @7@4
..C@IRCULO UNIDAD 7P@AG4 .#HFG7 ,EL
C@IRCULO .;X #B @+ .;Y #B .K #A1 QUE
TI5E C5TRO 7#J1 #J7 ;Y RADIO #A4 ,P>A UN
@ANGULO EN POSICI@ON NORMAL1 EL LADO
T]M9AL DE CORTA ;AL C@IRCULO UNIDAD EN
EL PUNTO 7COS @1 S5 @7@4 @3
.UNIV]SAL .SET 7.P#..GAE7 ,! SET ( ALL
ELE;TS "U 3SID],N2 DENOT$ .;,U @4
..3JUNTO UNIV]SAL 7P@AG4 .#GAE7 ,EL
3JUNTO DE TODOS LOS ELE;TOS T5IDOS EN
CU5TA2 SE 9DICA .;,U @4 @3 .,SEE -PLE;T
(A SET4
.,V] -PLE;TO DE UN 3JUNTO4
;,V
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
V>IA# @7 P4 #AA @7 ,A LR T IS US$
6REPRES5T "O OR M NUMB]S4
.V>IA# 7.P@AG4 .#AA7 ,LETRA UTILIZADA
P>A REPRES5T> UNO ;O M@AS N@UM]OS4 @3 ,9
! EXPRES.NS #F .;X @1 #C .;X #B @+ #A1 &
#AB--#E .;X @1 ! LR .;X IS ! V>IA#4
,EN LAS EXPRE.NES #F .;X @1 #C .;X #B @+
#A ;Y #AB--#E .;X @1 LA LETRA .;X ES LA
V>IA#4
V>IA# T]M @7 P4 #AB @7 ,A T]M T HAS A
V>IA# "P4
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,T@ERM9O QUE TI5E V>IA#4 @3 ,! V>IA#
T]MS (! ALGEBRAIC EXPRES.N #C .;X #B @+
#E .;X@+ 7--#G7 >E #C .;X #B & #E .;X @4
,LOS T@ERM9OS ALGEBRAICOS DE LA
EXPRESI@ON ALGEBRAICA #C .;X #B @+ #E
.;X@+ 7--#G7 SON #C .;X #B .;Y #E .;X @4
V]BAL MODEL @7 P4 #CD @7 ,A ^W EQU,N T
REPRES5TS A R1L-LIFE PRO#M4
..MODELO V]BAL 7P@AG4 .#CD7 ,ECUACI@ON
EXPRESADA M$IANTE PALABRAS QUE REPRES5TA
UN PRO#MA DE LA VIDA R1L4 @3 ..,4T.E
7MILES7 .K ,RATE 7MILES_/H\R7 @* ,"T
7.H\RS7
..,4TANCIA 7MILLAS7 .K ,VELOCIDAD
7MILLAS_/HORA7 @* ,TIEMPO 7.HORAS7
-----------------------------------#AJHC
,5GLI%--,SPANI% ,GLOSS>Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
V]TEX =M (A QUADRATIC FUNC;N @7 P4
#BDE @7 ,! =M .;Y .K .A @7 .;X -- .;H @7
#B @+ .;K @1 ": ! V]TEX (! GRAPH IS @7
.;H1 .;K @7 &! AXIS ( SYMMETRY IS .;X .K
.;H @4
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EL V@ERTICE DE LA GR@AFICA ES @7 .;H1
.;K @7 ;Y EL EJE DE SIMETR@IA ES .;X .K
.H4 @3 ,! QUADRATIC FUNC;N IS 9 V]TEX
=M4
,LA FUNCI@ON CUADR@ATICA E/@A EN LA =MA
DE V@ERTICE4
V]TEX (A P>ABOLA @7 PP4 #BCF @1 #FBJ
@7 ,! PO9T ON A P>ABOLA T LIES ON ! AXIS
( SYMMETRY4
..V@ERTICE DE UNA P>@ABOLA 7P@AGS4 #BCF1
.#FBJ7 ,EL PUNTO DE UNA P>@ABOLA QUE SE
5CU5TRA EN EL EJE DE SIMETR@IA4 @3 .,SEE
P>ABOLA4
.,V] P>@ABOLA4
V]TEX ( AN ABSOLUTE VALUE GRAPH @7 P4
#ABC @7 ,! HI<E/ OR L[E/ PO9T ON ! GRAPH
( AN ABSOLUTE VALUE FUNC;N4
..V@ERTICE DE UNA GR@AFICA DE VALOR
ABSOLUTO 7P@AG4 .#ABC7 ,ELPUNTO M@AS
ALTO ;O M@AS BAJO DE LA GR@AFICA DE UNA
FUNCI@ON DE VALOR ABSOLUTO4 @3
,! V]TEX (! GRAPH ( .;Y .K _\ .;X --
#D_\ @+ #C IS ! PO9T 7#D1 #C74
,EL V@ERTICE DE LA GR@AFICA DE .;Y .K _\
.;X -- #D_\ @+ #C ES EL PUNTO 7#D1 #C74
V]TICES (A HYP]BOLA @7 P4 #FDB @7 ,!
PO9TS ( 9T]SEC;N (A HYP]BOLA &! L9E "? !
FOCI (! HYP]BOLA4
..V@ERTICES DE UNA HIP@ERBOLA 7P@AG4
.#FDB7 ,LOS PUNTOS DE 9T]SE3I@ON DE UNA
HIP@ERBOLA ;Y LA RECTA QUE PASA POR LOS
FOCOS DE LA HIP@ERBOLA4 @3 .,SEE
HYP]BOLA4
.,V] HIP@ERBOLA4
V]TICES ( AN ELLIPSE @7 P4 #FCD @7 ,!
PO9TS ( 9T]SEC;N ( AN ELLIPSE &! L9E "?
! FOCI (! ELLIPSE4
..V@ERTICES DE UNA ELIPSE 7P@AG4 .#FCD7
,LOS PUNTOS DE 9T]SE3I@ON DE UNA ELIPSE
;Y LA RECTA QUE PASA POR LOS FOCOS DE LA
ELIPSE4 @3 .,SEE ELLIPSE4
.,V] ELIPSE4
;,X
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X -9T]CEPT @7 P4 #IA @7 ,! .;X
-COORD9ATE (A PO9T ": A GRAPH 9T]SECTS !
.;X -AXIS4
9T]CEPTO EN.' ;X .-7P@AG4 #IA7 ,LA
COORD5ADA .;X DE UN PUNTO DONDE UNA
GR@AFICA CORTA ;AL EJE DE .;X @4 @3
,! .;X -9T]CEPT IS #F4
,EL 9T]CEPTO EN .;X ES #F4
-----------------------------------#AJHD
;,Y
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;Y -9T]CEPT @7 P4 #HI @7 ,!
;Y-COORD9ATE (A PO9T ": A GRAPH 9T]SECTS
! .;Y -AXIS4
.9T]CEPTO .EN .;Y 7P@AG#.HI7 ,LA
COORD5ADA ;Y DE UN PUNTO DONDE UNA
GR@AFICA CORTA ;AL EJE DE Y4 @3
,! .;Y -9T]CEPT IS #C4
,EL 9T]CEPTO EN .;Y ES #C4
;,Z
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
Z]O (A FUNC;N @7 P4 #BED @7 ,A NUMB]
.;K IS A Z]O (A FUNC;N .;F IF .;F @7 .;K
@7 .K #J4
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SI .;F @7 .;K @7 .K #J4 @3 ,! Z]OS (!
FUNC;N .;F @7 .;X @7 .K #B7 .;X @+ #C7@7
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@1 #EHD @1 #EII @1 #FDD @1 #FED ,#FEH1
#FHC ,#FIA1 #FIC @1 #GJJ @1 #GJH @1
#GAI @1 #GBF @1 #GDD @1 #GIE @1 #GIG
@1 #HJC @1 #HAA @1 #HBA @1 #HBH @1
#HFB @1 #HGG @1 #HIJ
.,AXIS 7.,AXES7
COORD9ATE1 #IHG
( AN ELLIPSE1 #FCD
( SYMMETRY =A 3IC SEC;N1 #FEB @1 #FEE
( SYMMETRY =A P>ABOLA1 #BCF @1 #FBJ
;,B
.,B> .GRAPH @1 #AJJF-AJJG
.,BASE
(A LOG>I?M1 #DII
(A P[]1 #AJ
.,BE/-.FITT+ .L9E @1 #AAB-ABJ ,#ADC
CORREL,N COE6ICI5T1 #AAD
L9E> REGRES.N &1 #AAF
.,BE/-.FITT+ .QUADRATIC .MODEL @1 #CAA
.,BIAS .9 .SAMPL+ @1 #GFG @1 #GFI @1
#GGJ-GGC
.,BIAS$ ."Q @1 #GGB-GGC
.,BIAS$ .SAMPLE @1 #GFG
.,BICONDI;NAL ./ATE;T @1 #AJJB-AJJC
.,BIG .,ID1S @1 #A @1 #FJ @1 #GA @1 #ADJ
@1 #AEA @1 #BBA @1 #BCE @1 #CAG @1
#CBI @1 #DJA @1 #DAC @1 #DFE @1 #DGG
@1 #ECH @1 #EDI @1 #FJB @1 #FAC @1
#FFH @1 #FHA @1 #GCC @1 #GDC @1 #GHC
@1 #GIC @1 #HCI @1 #HEA @1 #IFD
.,BINOMIAL7.;S7 @1 .,SEE .AL ,POLYNOMIAL
7;S71 #BEB
CUBE (1 #CDG
MULTIPLY+1 #CDG-CEA @1 #IHE
SQU>E (1 #CDG
.,BINOMIAL .4TRIBU;N @1 #GBE-GCA @1 #GCC
@1 #GCF
APPROXIMAT+1 #GFC-GFE
CALCULAT+1 #GCA
SKEW$1 #GBG @1 #GBH
SYMMETRIC1 #GBG @1 #GBH
.,BINOMIAL .EXPAN.N @1 #FIC-FIF
,PASCAL'S TRIANGLE &1 #FIC @1 #FIE
.,BINOMIAL .EXP]I;T @1 #GBE
.,BINOMIAL .!OREM @1 #FIC
US+1 #FIC-FIF @1 #GCE
.,BISECTOR
ANGLE1 #IID
P]P5DICUL>1 #FAE-FAG
.,B.D$ .REGION @1 #AGD
.,B.D>Y .L9E @1 = AN 9EQUAL;Y1 #ACB
.,BOX-.&-.:ISK] .PLOT @1 #AJJH-AJJI
.,BRAN*ES @1 (A HYP]BOLA1 #EEH
.,BREW/]'S .ANGLE @1 #ICJ
;,C
.,CALCULATOR @1 .,SEE .AL ,GRAPH+
CALCULATOR
APPROXIMAT+ ROOTS1 #DAE @1 #DAG
CALCULAT+ -P.D 9T]E/1 #DHA
5T]+ NEGATIVE NUMB]S1 #AG
EVALUAT+ EXPRES.NS1 #AG
EVALUAT+ 9V]SE TRIGONOMETRIC FUNC;NS1
#HGF
EVALUAT+ LOG>I?MS1 #EJJ-EJA
EVALUAT+ P]MUT,NS1 #FHE
EVALUAT+ TRIGONOMETRIC FUNC;NS1 #HED
SIMPLIFY+ NATURAL BASE EXPRES.NS1 #DIB
..,CALCULATOR ,BAS$ ,LABORATORY 7.,,CBL7
@1 #IDH
.,CAUS,N .VS4 .CORREL,N @1 ,A#BE
.,C5T]
(A CIRCLE1 #FBF @1 #IIB
(A 3IC SEC;N1 #FEJ-FEB
(A HYP]BOLA1 #FDB
( ROT,N1 #IHH
.,C5TRAL .ANGLE @1 (A SECTOR1 #HFA
.,C5TRAL .T5D5CY @1 M1SURES (1 #GDD-GEJ
@1 #GHC @1 #GHD @1 #AJJE
.,*A9 .RULE @1 #AJJJ-AJJA
.,*ALL5GE @1 EX]CISES1 ..,"?\T4 ,SEE =
EXAMPLE .#G @1 #I @1 #AE @1 #AF @1 #BC
@1 #BD @1 #CA @1 #CB @1 #CH @1 #CI @1
#DE @1 #DG @1 #EF @1 #EH @1 #GH @1 #GI
@1 #HG @1 #HH @1 #ID @1 #IF
.,*ANGE-.(-.BASE .=MULA @1 #EJH-EJI @1
#ABA
.,*APT] .,REVIEW @1 #FA-FD @1 #ADA-ADD
@1 #BBB-BBF @1 #CAH-CBB @1 #DJB-DJF @1
#DFF-DFH @1 #ECI-EDB @1 #FJC-FJF @1
#FFI-FGB @1 #GCD-GCF @1 #GHD-GHF @1
#HDJ-HDB @1 #HIH-IJJ @1 #IFE-IFH
-----------------------------------#AJHH
.,*APT] .,SUMM>Y @1 #FJ @1 #ADJ @1 #BBA
@1 #CAG @1 #DJA @1 #DFE @1 #ECH @1
#FJB @1 #FFH @1 #GCC @1 #GHC @1 #HCI
@1 #HIG @1 #IFD
.,*APT] .,TE/ @1 .,SEE ,ASSESS;T
.,*ECK+ .SOLU;NS
US+ A CALCULATOR1 #HGF
US+ 5D 2HAVIOR1 #CIC
0GRAPH+1 #BEE @1 #CAA @1 #DDJ @1 #EAH @1
#ICA
US+ A GRAPH+ CALCULATOR1 #AFA @1 #BHE @1
#BIB @1 #BIC @1 #DFB @1 #EAH @1 #EIA
@1 #FEI @1 #IEH
US+ 9V]SE OP],NS1 #CFB
US+ LOGICAL R1SON+1 #CGC @1 #GFC
US+ SLOPE-9T]CEPT =M1 #AED
US+ SUB/ITU;N1 #AH @1 #AI @1 #BJ @1 #CF
@1 #EB @1 #IA @1 #ACC @1 #AEC @1 #AFJ
@1 #AGI @1 #BJE @1 #BFG @1 #BHE @1
#CHA @1 #DEB @1 #DED @1 #DEE @1 #DFH
@1 #EAG @1 #EAH @1 #EIA ,#ICD
US+ UNIT ANALYSIS1 #E @1 #G @1 #CD
.,*OOS+ .A .ME?OD
EX]CISES1 #ID @1 #AFD @1 #AHC @1 #CJE @1
#CEG @1 #ABA @1 #HIC
= SOLV+ L9E> SY/EMS1 #AFC
.,*OOS+ .A .MODEL @1 = DATA1 #GGD-GHA @1
#ABA
.,CIRCLE @1 #FBF @1 #IIB
>EA (1 #IIB
C5T] (1 #FBF @1 #IIB
C5TRAL ANGLE (1 #HFA
CIRCUMF];E (1 #IIB
DEGREE M1SURE (1 #HFJ
DIAMET] (1 #IIB
E35TRIC;Y (1 #FFE-FFF
EQU,N (1 #FBF
GRAPH+1 #FBF-FCC @1 #FFH @1 #FGJ
TRANSLAT$1 #FEJ @1 #FEB-FEG
WRIT+1 #FBG-FCB @1 #FFH @1 #FGJ
F9D+ ! C5T] GIV5 ?REE PO9TS1 #FAF @1
#FAI
9EQUALITIES &1 #FBH @1 #FCJ-FCB
RADIAN M1SURE (1 #HFJ
RADIUS (1 #FBF @1 #IIB
SECTOR (1 #HFA
TRANSLAT$1 #FEJ
UNIT1 #HFG
.,CIRCLE .GRAPH @1 #AJJF-AJJG
.,CIRCUL> .FUNC;N @1 #HFF
.,CIRCUL> .MODEL @1 #FBH @1 #FCJ-FCB
.,CIRCUL> .MO;N @1 MODEL+1 #IAF @1 #IBA
@1 #ABA
.,CIRCUL> .P]MUT,N @1 #FHI
.,CIRCUMF];E @1 (A CIRCLE1 #IIB
.,CLASSIFY+
3ICS1 #FEC @1 #FED @1 #FEF
FUNC;NS1 #GE @1 #HJ-HA @1 #CCG @1 #DGI
@1 #DHG @1 #ABA
9V]SE & DIRECT V>I,N1 #EEA
L9E> SY/EMS1 #AED-AEG
L9ES 0SLOPE1 #HC
NUMB]S1 #B
P>ALLEL & P]P5DICUL> L9ES1 #ABA @1 #HF
PROBABIL;Y 4TRIBU;NS1 #GBG @1 #GBH
SAMPLES1 #GFF @1 #GFI
S]IES1 #HJE
TRIANGLES US+ ! 4T.E =MULA1 #FAD-FAE @1
#FAG
Z]OS (A POLYNOMIAL FUNC;N1 #ABA-CHB @1
#CHD @1 #CHE
,CLOSURE PROP]TY1 #C
.,COE6ICI5T
L1D+1 #CCG
(A P[]1 #AB
.,COE6ICI5T .MATRIX @1 #BJE-BJF
.,C(UNC;N .ID5TITIES @1 #IBD
.,-B9,N7.;S7 @1 #FIJ-FIG @1 #GCC @1 #GCE
=MULA1 #FIJ
,PASCAL'S TRIANGLE &1 #FIB @1 #FIE
PROBABIL;Y &1 #FII @1 #GJB
.,-B9ATORICS @1 =MULAS F1 #AJBH
.,-MON .DI6];E @1 #HJB
.,-MON .FACTORS @1 #IGH
.,-MON .LOG>I?M @1 #EJJ
*ANGE-(-BASE =MULA &1 #ABA-EJI ,#EAA
.,-MON .MISCONCEP;NS @1 .,SEE ,]ROR
,ANALYSIS
.,-MON .MULTIPLE @1 #IGH
.,-MON .RATIO @1 #HAJ
.,-MUNIC,N
DESCRIB+ 9 ^WS1 #G @1 #AC @1 #AG @1 #BB
@1 #CJ @1 #CH @1 #DE @1 #EJ @1 #EF @1
#GG @1 #HF @1 #IC @1 #ID @1 #AJB @1
#AAG @1 #AAH @1 #AAI @1 #ABB @1 #ABG
@1 #ABH @1 #ACF @1 #AEF @1 #AFD @1
#AGA @1 #AHJ @1 #AIJ @1 #AII @1 #BJG
@1 #BJI @1 #BAD @1 #BAF @1 #BDJ @1
#BEF @1 #BFC @1 #BGJ @1 #BHJ @1 #BHA
@1 #BHI @1 #BIF @1 #BIG @1 #CJD @1
#CJH @1 #CAC @1 #CCD @1 #CDD @1 #CDI
@1 #CEG @1 #CFF @1 #CGE @1 #CIJ @1
#CIG @1 #DAH @1 #DBD @1 #DDB @1 #DEJ
@1 #DEF @1 #DHC @1 #DHI @1 #DIF @1
#EJC @1 #EJE @1 #EAJ @1 #EAA @1 #EBJ
@1 #ECD @1 #EEE @1 #EEG @1 #EFB @1
#EFH @1 #EGJ @1 #EGH @1 #EHF @1 #FBC
@1 #FBD @1 #FBI @1 #FCG @1 #FDE @1
#FDF @1 #FEE @1 #FID @1 #GJB @1 #GAJ
@1 #GBB @1 #GDG @1 #GDH @1 #GEC @1
#GED @1 #GFI @1 #GGJ @1 #GGH @1 #ABA
@1 #HAD @1 #HBC @1 #HBI @1 #HCA @1
#HCE @1 #HEF @1 #HFC @1 #HGH @1 #HHF
@1 #HIC @1 #HIH @1 #IAC @1 #IAI @1
#IBJ @1 #IBH @1 #ICE @1 #IDB @1 #ABA
@1 #IEB @1 #IEI @1 #IFJ
R1D+ MA?1 #ED @1 #HC @1 #AGD @1 #BGG @1
#CCI @1 #HCJ @1 #HED @1 #HFA @1 #HFH
WRIT+ 9 MA?1 #F @1 #AC @1 #BA @1 #BE @1
#CG @1 #DD @1 #DI @1 #EE @1 #FA @1 #GF
@1 #HF @1 #IC @1 #AJA @1 #AJI @1 #AAG
@1 #ABG @1 #ABH @1 #ACE @1 #ACF @1
#AEF @1 #AFD @1 #AGA @1 #AHB @1 #AIJ
@1 #AII @1 #BJG @1 #BAD @1 #BDJ @1
#BDI @1 #BEE @1 #BFC @1 #BFI @1 #BGI
@1 #BHH @1 #BIF @1 #CJD @1 #CAB @1
#CAH @1 #CCC @1 #CDA @1 #CDI @1 #CEF
@1 #CGD @1 #CHC @1 #CIJ @1 #CIB @1
#CIG @1 #DJB @1 #DAG @1 #DBD @1 #DCB
@1 #DDB @1 #DDI @1 #DEF @1 #DFF @1
#DHB @1 #DHI @1 #EAJ @1 #EAI @1 #EBE
@1 #ECC @1 #ECI @1 #EEE @1 #EFA @1
#EFH @1 #EGG @1 #EHF @1 #EIB @1 #FAG
@1 #FBD @1 #FBI @1 #FED @1 #FFA @1
#FHF @1 #FID @1 #GAJ @1 #GAD @1 #GBA
@1 #GCD @1 #GDG @1 #GEC @1 #GFJ @1
#GFI @1 #GGH @1 #GIH @1 #ABA @1 #HJG
@1 #HAD @1 #HBC @1 #HDJ @1 #HEF @1
#HFB @1 #HGJ @1 #HGH @1 #HHF @1 #HIB
@1 #HIH @1 #IAB @1 #IAI @1 #IBG @1
#ICE @1 #ICI @1 #IDD @1 #ABA @1 #IEB
@1 #IEI
.,-MUTATIVE .PROP]TY @1 #C
= MATRIX OP],NS1 #AHH ,#AIF
.,-P>E @1 EX]CISES1 #H @1 #CI @1 #FA @1
#ACE @1 #ACG @1 #BJH @1 #BDC @1 #BEA
@1 #BGA @1 #BHI @1 #DEH @1 #EBH @1
#EHJ @1 #FAI @1 #FBC @1 #FDE @1 #ABA
@1 #GJB @1 #GAD @1 #GDI @1 #GHG @1
#HJJ @1 #ABA @1 #HGB @1 #IAB @1 #IDH
.,-P>+
GRAPHS ( ABSOLUTE VALUE FUNC;NS1
#ABA-ABE
GRAPHS ( QUADRATIC FUNC;NS1 #ABA-BCG @1
#BDJ
9DEP5D5T & DEP5D5T EV5TS1 #GAI
/&>D & TRANSLAT$ EQU,NS1 #ABA @1 #FEA
TYPES ( V>I,N1 #EED
.,-PLE;T
( AN EV5T1 #GJI-GAC @1 #GAH
(A SET1 #GAE-GAF
.,-PLE;T>Y .ANGLES @1 #IID
.,-PLET+ .! .SQU>E @1 #BHC-BIA @1 #CAG
@1 #CBA @1 #FEC
US+ ALGEBRA TILES1 #BHC
.,-PLEX .3JUGATES @1 #BGH @1 #CHJ
.,-PLEX .3JUGATES .!OREM @1 #CHJ
.,-PLEX .FRAC;N @1 #EHD
SIMPLIFY+1 #EHD-EHH
.,-PLEX .NUMB] 7.;S7 @1 #BGF
ABSOLUTE VALUE (1 #BGI @1 #BHJ
A4ITIVE 9V]SE (1 #BHJ
,JULIA SET &1 #BHB
,M&ELBROT SET &1 #BHA
MULTIPLICATIVE 9V]SE (1 #BHJ
OP],NS )1 #BGF-BHB @1 #CAG @1 #CBJ-CBA
PLOTT+1 #BGH
/&>D =M (1 #BGF
.,-PLEX .PLANE @1 #BGH
,JULIA SET ON1 #BHB
,M&ELBROT SET ON1 #BHA
.,-POSITE .NUMB] @1 #IGH
.,-POSI;N @1 (A FUNC;N1 #DCJ-DCE @1 #ABA
@1 #DFG
.,-P.D .EV5T @1 #GJG
PROBABIL;Y (1 #GJG-GAC
.,-P.D .9EQUAL;Y @1 #DA-DG
ABSOLUTE VALUE =M (1 #EC
.,-P.D .9T]E/ @1 #DHA @1 #DHC-DHE
-----------------------------------#AJHI
.,-P.D ./ATE;T @1 #AJJA
.,3CEPT .,SUMM>Y @1 #AHH @1 #AIG @1 #CHG
,#HFA
.,3CEPTS @1 .,SEE ,BIG ,ID1S2 ,3CEPT
,SUMM>Y2 ,KEY ,3CEPT
..,3D5S+ A LOG>I?MIC .EXPRES.N @1 #EJH
@1 #EAJ @1 #EDA
.,3DI;NAL .PROBABIL;Y @1 #GAH-GBC
.,C"O @1 9T]SECT$ 0A PLANE1 .,SEE ,3ICS
.,3GRU5T .FIGURES @1 #IIF-IIG
.,3ICS @1 .,SEE .AL ,CIRCLE2 ,ELLIPSE2
,HYP]BOLA2 ,P>ABOLA1 #FDI-FEG
CLASSIFY+1 #FEC @1 #FEF
DEG5]ATE1 #FEG
4CRIM9ANT (1 #FEC @1 #FEF
E35TRIC;Y (1 #FFE-FFF
L9ES ( SYMMETRY (1 #FEB @1 #FEE
TRANSLAT$1 EQU,NS (1 #FEJ-FEG @1 #ABA
.,3JUGATES @1 #BFG
-PLEX1 #BGH
.,3NEC;NS @1 ,SEE ,APPLIC,NS
.,3SI/5T .L9E> .SY/EM @1 #AED-AEG
.,3/ANT
A4+ 6DATA VALUES1 #GEA-GEE
-MON DI6];E1 #HJB
.,3/ANT .RATIO @1 #HAJ
.,3/ANT .T]M @1 #AB
.,3/ANT .( .V>I,N @1 #AJG @1 #EEA
.,3/RA9TS @1 #AGD
.,3T9U\S .FUNC;N @1 #HJ-HA
.,3T9U\SLY .-P.D$ .9T]E/ @1 #DID-DIE @1
#DIG
.,3TROL .GR\P @1 #GGC
.,3V5I;E .SAMPLE @1 #GFF
.,3V]SE @1 (A 3DI;NAL /ATE;T1 #ABA-AJJC
.,COORD9ATE .GEOMETRY @1 =MULAS F1 #ABA
.,COORD9ATE .PLANE @1 #IHG
.,COORD9ATE .SY/EMS
NAVIG,NAL1 ,A#F
POL>1 ,A#D-,A#F
SPH]ICAL1 ,A#E-,A#F
..,COROLL>Y 6! FUNDA;TAL !OREM (
.ALGEBRA @1 #CGI
.,CORREL,N
DESCRIB+1 #AAC-AAD
VS4 CAUS,N1 ,A#BD
.,CORREL,N .COE6ICI5T @1 #AAD
.,COSECANT .FUNC;N @1 .,SEE .AL
,TRIGONOMETRIC FUNC;N 7;S7
EVALUAT+ = ANY ANGLE1 #HFF-HGB
EVALUAT+ = "R TRIANGLES1 #ABA-HEH
.,COS9E .FUNC;N @1 .,SEE .AL
,TRIGONOMETRIC EQU,N7;S72
,TRIGONOMETRIC FUNC;N 7;S7
DI6];E =MULA =1 #IDI
US+1 #IDI-IED
D\#-ANGLE =MULA =1 #IEE
US+1 #IEE-IFB
EVALUAT+ = ANY ANGLE1 #HFF-HGB
EVALUAT+ = "R TRIANGLES1 #ABA-HEH
GRAPH+1 #HGD @1 #IJH-IAD @1 #IFD @1 #IFE
REFLEC;NS1 #IAG @1 #IBJ
TRANSL,NS1 #IAE-IAG @1 #IAI-IBB @1 #ABA
HALF-ANGLE =MULA =1 #IEE
US+1 #IEE-IFB
9V]SE (1 #HGD-HGI @1 #HIG
S9USOIDS1 &1 #IDA-IDH
SUM =MULA =1 #IDI
US+1 #IDI-IED
.,COS9ES @1 LAW (1 #HHI-HIE @1 #HIG @1
#IJJ
.,COTANG5T .FUNC;N @1 .,SEE .AL
,TRIGONOMETRIC FUNC;N 7;S7
EVALUAT+ = ANY ANGLE1 #HFF-HGB
EVALUAT+ = "R TRIANGLES1 #ABA-HEH
.,COTANG5T .ID5TITIES @1 #IBD @1 #IFF
.,COT]M9AL .ANGLE @1 #HFJ @1 #HFC
.,C.T]EXAMPLE @1 #AJJC
.,CO-.V]TICES @1 ( AN ELLIPSE1 #FCD
.,CRAM]'S .RULE @1 #BJE-BJI @1 #BBA @1
#BBF
.,CRITICAL .;X- .VALUES1 #CJC @1 #EII
.,CROSS .MULTIPLIC,N @1 6SOLVE R,NAL
EQU,NS1 #EHI-EIJ
.,CUBE .ROOT .FUNC;N @1 #DDG-DEA @1 #DFE
@1 #DFH
P>5T1 #DDF @1 #DFE
.,CUBES
DI6];E (1 #CED
SUM (1 #CED
.,CUBIC .FUNC;N @1 .,SEE .AL ,POLYNOMIAL
FUNC;N7;S71#CCG
9V]SE (1 #DDA
WRIT+1 #CIC-CII
.,CUBIC .REGRES.N @1 #CIF
.,CUMULATIVE .,REVIEW @1 #BCB-BCC @1
#ABA-DGE @1 #FGH-FGI @1 #HDH-HDI
.,CU/OM>Y .UNITS @1 ,A#B-,A#C
.,CYCLE @1 (A FUNC;N1 #IJH
.,CYL9D]
SURFACE >EA (1 #FC @1 #EFG @1 #EHJ @1
#IIC
VOLUME (1 #CCD @1 #CEJ @1 #EFG @1 #EHJ
@1 #IIC
;,D
.,DATA @1 .,SEE .AL ,GRAPHS2 ,MODEL+2
,/ATI/ICS
ANALYZ+
US+ BE/-FITT+ L9E1 #AAB-ABJ
CAUS,N1 ,A#BE
*OOS+ A MODEL =1 #GGD-GHA @1 #ABA
CORREL,N1 ,A#BD
F9ITE DI6];ES1 #CIC-CII
FITT+ A MODEL TO1 #GGD-GHA
GEOMETRIC M1N1 #GDI
HYPO!SIS TE/+1 #GFD-GFE
M>G9 ( ]ROR1 #GFH-GGA
M1SURES ( C5TRAL T5D5CY1 #ABA-GEJ @1
#GHC @1 #GHD @1 #AJJE
M1SURES ( 4P].N1 #ABA-GEJ @1 #GHC @1
#GHD @1 #AJJE
NEGATIVE CORREL,N1 #AAC @1 #AAD ,#AAG
NORMAL 4TRIBU;N1 #GEG-GFB @1 #ABA @1
#GHE
\TLI]1 #GDF @1 #GDG
POSITIVE CORREL,N1 #AAC @1 #AAD @1 #ABA
QU>TILES1 #AJJH-AJJI
RANGE1 #GDE-GEJ
/&>D DEVI,N1 #GDE-GEJ
VALID;Y1 ,A#AJ
APPLY+ TRANS=M,NS TO1 #ABA-GEE
COLLECT+1 #AAB ,#EEJ
BIAS$ "Q1 #GGB-GGC
BIAS$ SAMPLE1 #GFG
3TROL GR\P1 #GGC
3V5I;E SAMPLE1 #GFF
F AN EXP]I;T1 #CJH @1 #EBH @1 #ABA-GGC
@1 #GGD
POPUL,N1 #GFF
R&OM SAMPLE1 #GFF
SAMPL+1 #GFF-GGA @1 #GHC @1 #GHF
SELF-SELECT$ SAMPLE1 #GFF
US+ SIMUL,N1 #GAD
F A SURVEY1 #GFC @1 #GFD @1 #GFF-GGA @1
#ABA-GGC @1 #GHF
SY/EMATIC SAMPLE1 #GFF
UNBIAS$ SAMPLE1 #GFG
4PLAY+
9 A B> GRAPH1 #AJJF-AJJG
)A CAL5D>1 ,A#AI
9 A CIRCLE GRAPH1 #AJJF-AJJG
9 A L9E GRAPH1 #AJJF-AJJG
9 A SCATT] PLOT1 #AAC-ABJ
9 A SPR1D%EET1 ,A#AH
EVALUAT+ REPORTS1 ,A#I
MISL1D+ 4PLAYS1 ,A#AB-,A#AC
ORGANIZ+
9 A BOX-&-:ISK] PLOT1 #ABA-AJJI
)A CLCULATOR1 ,A#AI
9 A HI/OGRAM1 #GBD @1 #GBF-GCA @1
#ABA-AJJI
9 A L9E PLOT1 #AJJH-AJJI
US+ MATRICES1 #AHI ,#AIB
9 A SPR1D%EET1 ,A#AH
9 A /EM-&-L1F PLOT1 #ABA-AJJI
9 A TA#1 #AAB ,#EBH
9 A ,V5N DIAGRAM1 #GJF
PUBLI%$1 9 M$IA1 ,A#I
.,DECAY .FACTOR @1 #DHF
.,DECAY .FUNC;N
EXPON5TIAL1 #DHF-DIA @1 #ECH @1 #EDJ
9VOLV+ .;E @1 #DIC-DIH
.,DECIMAL .EXPON5TS @1 #DBE
.,DECIMALS @1 FRAC;NS1 P]C5TS1 &1 #ABA
.,DEGREE
3V]T+ 2T RADIANS &1 #ABA-HFD @1 #HII
M1SURE (A CIRCLE1 #HFJ
(A POLYNOMIAL FUNC;N1 #CCG @1 #CCI
.,DEP5D5T .EV5TS @1 #GAH-GBC
.,DEP5D5T .L9E> .SY/EM @1 #AED-AEG
.,DEP5D5T .V>IA# @1 #GD
.,DEPRES.N @1 ANGLE (1 #HEE
-----------------------------------#AJIJ
.,DERIV,N
( ,SNELL'S LAW1 #ICJ
(A TRIGONOMETRIC MODEL1 #IEG
.,DESC>TES @1 ,R5E1 #CHA
..,DESC>TES' ,RULE ( .,SIGNS @1 #CHA
US+1 #CHA-CHB @1 #CHD @1 #CHE
.,DET]M9ANT @1 (A MATRIX1 #BJC-BJI ,#BBF
.,DIAGRAM
DRAW+1 PRO#M SOLV+ /RATEGY1 #ABA @1 #CG
@1 #CI
9T]PRET+1 #CBD @1 #CBF @1 #FJH @1 #FJI
@1 #ABA @1 #HDD @1 #HDF @1 #HDG @1
#ICG
MAPP+1 #GB @1 #GC @1 #GG
,PASCAL'S TRIANGLE1 #FIB @1 #FIE
TREE1 #FHB @1 #FHF @1 #GBJ @1 #IGH
,V5N1 #B @1 #DCJ @1 #GJF-GJH @1 #GAE-GAF
@1 #ABA
.,DIAMET] @1 (A CIRCLE1 #IIB
.,DI6];E
( TWO CUBES1 #CED
( TWO SQU>ES1 #BEC
.,DI6];E .=MULAS @1 #IDI @1 #IFD
US+1 #IDI-IED @1 #IFH
.,DIL,N @1 ON ! COORD9ATE PLANE1 #IHI
.,DIM5.NS @1 (A MATRIX1 #AHG ,#AIE
.,DIRECT .>GU;T @1 #AJJJ-AJJA
.,DIRECT .SUB/ITU;N @1 = EVALUAT+
POLYNOMIAL FUNC;NS1 #CCH
.,DIRECT .V>I,N @1 #AJG-AAA @1 #ADJ
,#ADC
.,DIRECTRIX @1 (A P>ABOLA1 #FBJ
.,4CRETE .FUNC;N @1 #HJ-HA
.,4CRETE .MA!MATICS
C.T+ ME?ODS1 #FHB-FHI
4CRETE FUNC;NS1 #HJ-HA
F9ITE DI6];ES1 #CIC-CII
GRTE/ -MON FACTOR 7,,GCF71 #IGH-IGI
L1/ -MON DENOM9ATOR 7,,LCD71 #IGI
L1/ -MON MULTIPLE 7,,LCM71 #IGH-IGI
MATRICES1 #AHG-BAI
MUTU,Y EXCLUSIVE EV5TS1 #GJG
,PASCAL'S TRIANGLE1 #FIB @1 #FIE
SCATT] PLOTS1 #AAC-ABJ ,#ADC
SEQU;ES1 #GID-HAF
SET !ORY1 #GAE-GAF
TREE DIAGRAM1 #FHB @1 #FHF @1 #GBJ @1
#IGH
TRIANGUL> NUMB]S1 #CID
TRIANGUL> PYRAMIDAL NUMB]S1 #CIE
.,4CRIM9ANT @1 #BID @1 #BIF
(A 3IC EQU,N1 #FEC @1 #FEF
.,4JO9T .EV5T @1 #GJG @1 #GCF
.,4P].N @1 M1SURES (1 #GDD-GEJ @1 #ABA
@1 #GHD @1 #AJJE
.,4T.E .=MULA @1 #FAD @1 #FAI @1 #FFI
.,4TRIBU;N
BINOMIAL1 #GFC-GFE
NORMAL1 #GEG-GFB @1 #GHC @1 #GHE
/&>D NORMAL1 #GEH-GFB
.,4TRIBUTIVE .PROP]TY @1 #C
6ADD & SUBTRACT L RADICALS1 #DBB
= MATRIX OP],NS1 #AHH ,#AIG
= SOLV+ L9E> EQU,NS1 #BJ @1 #ABA-BD
.,DIVI.N
( -PLEX NUMB]S1 #BGH @1 #BHJ
( FUNC;NS1 #DBI-DCE
9EQUALITIES &1 #DB-DG
9TEG]1 #IGE
Z OPPOSITE ( MULTIPLIC,N1 #D
POLYNOMIAL1 #CFB-CFH
PROP]TIES1 #AH
) R,NAL EXPRES.NS1 #EGF-EHJ @1 #FJB @1
#FJE
SYN!TIC1 #CFC-CFH
..,DIVI.N PROP]TY ( .EQUAL;Y @1 #AH
.,DOMA9
(A FUNC;N1 #GC @1 #GF @1 #CIA @1
#DBH-DCJ @1 #DDF-DDG @1 #DFC @1 #DGI
@1 #DHB @1 #DHE @1 #DHG @1 #DHI @1
#DIA
(A REL,N1 #GB
(A SEQU;E1 #GID
.,DOPPL] .E6ECT @1 #EFC
.,D\#-.ANGLE .=MULAS @1 #IEE @1 #IFH
US+1 #IEE-IFB @1 #IFH
..,DRAW ANGLES 9 /&>D .POSI;N @1 #HEI @1
#HFJ @1 #HFC
.,DRAW .3CLU.NS
EXAMPLES1 #ACB
EX]CISES1 #EJ @1 #AAB @1 #ABB @1 #AEB @1
#AGG @1 #BHC @1 #CJH @1 #CCF @1 #DCG
@1 #EBH @1 #EEJ @1 #FDI @1 #FHH @1
#GJF @1 #GGD @1 #HAI @1 #HBF @1 #HGD
@1 #HHA @1 #IBC @1 #IDH
F SAMPLES1 #GFF-GGA
.,DRAW .A .DIAGRAM
EX]CISES1 #HHG @1 #HIE
PRO#M SOLV+ /RATEGY1 #CE @1 #CG @1 #CI
.,DRAW .A .GRAPH
EX]CISES1 #EG @1 #IE @1 #AJD @1 #AAI @1
#ABI @1 #BDB @1 #BIJ @1 #CJF @1 #CAD
@1 #CDC @1 #CDD @1 #DEA @1 #FCA @1
#GBI @1 #HAF @1 #IAD @1 #IBI @1 #ICG
PRO#M SOLV+ /RATEGY1 #DI ,#BGC
;,E
..,E35TRIC;Y ( 3IC .SEC;NS @1 #FFE-FFF
.,E6ICI5CY @1 #EGD @1 #EHJ
.,ELE;T
(A MATRIX1 #AHG
(A SET1 #GAE-GAF
.,ELEV,N @1 ANGLE (1 #HEE
.,ELIM9ATE .*OICES @1 TE/-TAK+ /RATEGY1
#C @1 #BHF @1 #EIJ @1 #FBG @1 #ICC
.,ELIM9,N .ME?OD
= SOLV+ L9E> SY/EMS1 #AFA-AFG @1
#ABA-AHE @1 #BBA @1 #BBC
= SOLV+ QUADRATIC SY/EMS1 #ABA-FFD @1
#FFH
.,ELLIPSE @1 #FCD
>EA (1 #FCF @1 #FCH @1 #FDJ
CO-V]TICES (1 #FCD
E35TRIC;Y (1 #FFE-FFF
EQU,N (1 #FCD
GRAPH+1 #FCD-FCI @1 #FFH @1 #FGA
TRANSLAT$1 #FEJ @1 #FEB-FEG
WRIT+1 #FCE-FCI @1 #FFH @1 #FGA
FOCI (1 #FCD
MAJOR AXIS (1 #FCD
M9OR AXIS (1 #FCD
V]TICES (1 #FCD
.,ELLIPTICAL .GEOMETRY @1 .,SEE SPH]ICAL
GEOMETRY
.,EMPTY .SET @1 #GAE
.,5D .2HAVIOR @1 =A POLYNOMIAL FUNC;N1
#CCF @1 #CCI-CDD
.,EQU,N7.;S7 @1 .,SEE .AL ,=MULAS2
,FUNC;N 7;S72 ,9EQUALITIES2 ,L9E>
EQU,N7;S72 ,POLYNOMIAL7;S72 ,QUADRATIC
EQU,N 7;S71 #AH
ABSOLUTE VALUE1 #EJ-EH @1 #FJ @1 #FD
( CIRCLES1 #FBF-FCC
( 3IC SEC;NS1 #FEJ-FEG @1 #FFH @1
#ABA-FGB
DIRECT V>I,N1 #AJG-AAA
( ELLIPSES1 #FCD-FCI
EQUIVAL5T1 #AH
EXPON5TIAL1 #EAE-EAF @1 #EAI-EBE @1 #ABA
G5]AL SECOND-DEGREE1 #FEC
( HYP]BOLAS1 #FDB-FDH @1 #FEJ-FEG @1
#ABA @1 #FGA @1 #FGB
9V]SE V>I,N1 #EEA-EEG
JO9T V>I,N1 #EEC-EEG
LOG>I?MIC1 #DII-EJA @1 #EJC-EJE
MATRIX1 #AIJ-AIB
( P>ABOLAS1 #FBJ-FBE
RADICAL1 #DEB-DFA @1 #DFE @1 #DFH
R,NAL1 #EHI-EIG @1 #FJB @1 #FJF
) R,NAL EXPON5TS1 #DEC @1 #DEF @1
#DEH-DEI
RECURSIVE1 #HBF-HCC
REWRIT+1 #BF-CB @1 #FC
= SEQU;ES1 #GID-GIE @1 #GIH-HJA
= TRANSLAT$ 3ICS1 #FEJ-FEG
TRIGONOMETRIC1 #HGF-HHJ @1 #ICA-ICI @1
#IFD @1 #IFG
9 TWO V>IA#S1 #GD-GI
.,EQUIVAL5T .EQU,NS @1 #AH
.,EQUIVAL5T .EXPRES.NS @1 #AB
.,EQUIVAL5T .9EQUALITIES @1 #DB
.,]ROR .ANALYSIS
,AVOID ,]RORS1 #AB @1 #BJ @1 #BH @1 #DC
@1 #EB @1 #GC @1 #HB @1 #AJH @1 #AAE
@1 #ABF @1 #ACC @1 #AEC @1 #AFC @1
#AHG @1 #BCH @1 #BDG @1 #BEB @1 #BFJ
@1 #BFG @1 #BGG @1 #BHG @1 #BIB @1
#CCJ @1 #CCH @1 #CDG @1 #CED @1 #CEE
@1 #CFB @1 #CGJ @1 #CGA @1 #DAE @1
#DAF @1 #DBC @1 #DCJ @1 #DDA @1 #DHJ
@1 #DHH @1 #EJG @1 #EEC @1 #EGC @1
#EHD @1 #EII @1 #FDD @1 #FED @1 #FEH
@1 #FHC @1 #FIA @1 #FIC @1 #GJJ @1
#GJH @1 #GAI @1 #GBF @1 #GDD @1 #GIE
@1 #GIG @1 #HJC @1 #HAA @1 #HBA @1
#HBH @1 #HFB @1 #HGG @1 #HIJ
-----------------------------------#AJIA
EX]CISES1 ..,"?\T4 ,SEE = .EXAMPLE #G1
#AC @1 #AG @1 #BB @1 #CJ @1 #CH @1 #DE
@1 #EF @1 #GG @1 #HF @1 #IC @1 #AJB @1
#AAJ @1 #AAH @1 #ABH ,#ACF
.,E/IM,N @1 .,SEE .AL ,APPROXIM,N2
,PREDIC;N
( BE/-FITT+ L9E1 #AAC-ABJ ,#ADC
( COORD9ATES ( TURN+ PO9TS1 #CIJ
( CORREL,N COE6ICI5TS1 #AAD-ABJ
US+ EXPON5TIAL DECAY MODELS1 #DHH-DIA
US+ EXPON5TIAL GR[? MODELS1 #DHJ @1
#DHC-DHE
US+ L9E> GRAPHS1 #IA ,#AEC
US+ NATURAL BASE FUNC;NS1 #DID @1
#DIG-DIH
US+ .N? ROOTS1 #DAF
( SOLU;NS ( L9E> SY/EMS1 #AEC-AEH
US+ TRANS=M$ DATA1 #GHA
.,EUL] @1 ,LEONH>D1 #DIB
.,EUL] .NUMB] .;E @1 #DIB
.,EV5 .FUNC;N @1 #IBH
.,EV5T7.;S7
-PLE;T (1 #GJI
-P.D1 #GJG @1 #GCC @1 #GCF
DEP5D5T1 #GAH-GBC @1 #GCC @1 #GCF
4JO9T1 #GJG @1 #GCF
9DEP5D5T1 #GAG-GAI @1 #GBA-GBC @1 #GCC
@1 #GCF
MUTU,Y EXCLUSIVE1 #GJG
OV]LAPP+1 #GJG @1 #GCC @1 #GCF
PROBABIL;Y1 #FIH
..,EXP&+ A LOG>I?MIC .EXPRES.N @1 #EJH
@1 #EAJ ,#EDA
.,EXPECT$ .VALUE @1 ,A#BJ-,A#BA
.,EXP]I;T @1 #CJH @1 #EBH
BINOMIAL1 #GBE @1 #GBH @1 #GBI
3TROL GR\PS &1 #GGC
DESIGN+1 #GGB-GGC
.,EXP]I;TAL .GR\P @1 #GGC
.,EXP]I;TAL .PROBABIL;Y @1 #GJJ @1 #GJB
.,EXPLICIT .RULE @1 #HBG @1 #HCI
.,EXPON5T 7;S7 DECIMAL1 #DBE
EVALUAT+1 #AJ-AG
IRR,NAL1 #DBE
PROP]TIES (1 #CCJ @1 #DJB @1 #DBJ @1
#DFE @1 #ABA
US+1 #CCJ-CCE @1 #DJB @1 #DBJ-DBG @1
#ABA
R,NAL1 #DAE-DAI @1 #DBJ-DBG @1 #DFE @1
#ABA
.,EXPON5TIAL .EQU,N 7;S71 #EAE
MODEL+ )1 #EAF @1 #EBA-EBB
PROP]TY ( EQUAL;Y =1 #EAE
SOLV+1 #EAE-EAF @1 #EAI-EBE @1 #ECH @1
#EDB
.,EXPON5TIAL .FUNC;N7.;S7 @1 #DGH
DECAY1 #DHF-DIA @1 #ECH @1 #EDJ @1 #GGF
GRAPH+1 #DGH-DHE @1 #DHF-DIA @1 #ECH @1
#ABA @1 #GGF
GR[?1 #DGH-DHE @1 #ECH @1 #ECI
Z 9V]SE ( LOG>I?MIC FUNC;NS1 #ABA
9VOLV+ .;E @1 #DIC-DIH @1 #EDJ
MODEL+ )1 #DHJ-DHA @1 #DHC-DHE @1
#ABA-DIA @1 #EBH @1 #ECJ @1 #ECD-ECF
NATURAL BASE1 #DIC-DIH
WRIT+1 #EBI-ECA @1 #ECC-ECF @1 #EDB
.,EXPON5TIAL .9EQUALITIES @1 #EBF @1
#EBG
.,EXPON5TIAL .REGRES.N @1 #EBH @1 #ECJ
.,EXPON5TIAT+ .AN .EQU,N @1 #EAG
.,EXPRES.N 7;S7
-B9+ L T]MS IN1 #AB-AG
EQUIVAL5T1 #AB
EVALUAT+1 #AJ-AG @1 #FJ @1 #FB @1
#CCJ-CCE
EXPON5TIAL1 #CCJ-CCE
FACTORIAL1 #FHD
LOG>I?MIC1 #DII-EJA @1 #EJC-EJE @1
#ABA-EAB @1 #EDA
NATURAL BASE1 #DIB-DIC @1 #DIE-DIF
NUM]ICAL1 #AJ-AG @1 #CCJ-CCA @1 #CCC
9 QUADRATIC =M1 #CEE
R,NAL1 #EGC-EHH @1 #FJB @1 #FJE
) R,NAL EXPON5TS1 #DAE-DAI @1 #ABA-DBG
@1 #DFG
SIMPLIFY+1 #AJ-AG @1 #FJ @1 #FB @1
#CCJ-CCE @1 #ABA-DBG
T]MS (1 #AB
TRIGONOMETRIC1 #IBE-IBF @1 #IBH @1
#ABA-IEF @1 #IEI @1 #IFJ
WRIT+1 #IHD
.,EXT5D$ .RESPONSE .PRACTICE @1 ..,"?\T4
,SEE = .EXAMPLE #H1 #CB @1 #DG @1 #HH
@1 #IE @1 #AAI @1 #AEH @1 #AFF @1 #ABA
@1 #AHE
.,EXT5.NS
APPROXIMATE BINOMIAL 4TRIBU;NS1 #GFC-GFE
DESIGN SURVEYS & EXP]I;TS1 #ABA-GGC
DET]M9E E35TRIC;Y ( 3IC SEC;NS1 #FFE-FFF
4CRETE & 3T9U\S FUNC;NS1 #ABA-HA
L9E> PROGRAMM+1 #AGD-AGF
PIECEWISE FUNC;NS1 #ACJ-ACA
PROVE /ATE;TS US+ MA!MATICAL 9DUC;N1
#ABA-HCG
SET !ORY1 #GAE-GAF
SOLVE EXPON5TIAL 9EQUALITIES1 #EBF @1
#ABA
SOLVE LOG>I?MIC 9EQUALITIES1 #EBG
SOLVE RADICAL 9EQUALITIES1 #DFB-DFC
SOLVE R,NAL 9EQUALITIES1 #EIH-FJJ
.,EXTRA .,PRACTICE @1 #AJAJ-AJBC
.,EXTRANE\S .SOLU;NS
= ABSOLUTE VALUE EQU,NS1 #EB
= LOG>I?MIC EQU,NS1 #EAH
= RADICAL EQU,NS1 #DED
= R,NAL EQU,NS1 #EIA
= TRIGONOMETRIC EQU,NS1 #ICD
;,F
.,FACTOR 7;S71 #IGH
-MON1 #IGH
3V].N1 #IHA
DECAY1 #DHF
GR[?1 #DGH
SCALE1 #IHI
.,FACTOR .!OREM @1 #CFD @1 #DJD
.,FACTOR .TREE @1 #IGH
.,FACTORIAL @1 .,SEE .AL ,-B9,N 7;S72
,P]MUT,N 7;S71 #FHD
.,FACTOR+
-PLETELY1 #CEC
DI6];E ( TWO SQU>ES1 #BEC
PATT]NS1 #CED
P]FECT SQU>E TRINOMIALS1 #BEC
POLYNOMIALS1 #CEC-CEI @1 #CFD-CFH @1
#ABA
0GR\P+1 #CED @1 #CEG
QUADRATIC EQU,NS1 #BEB-BFE @1 #CAG @1
#ABA-CBJ
QUADRATIC EXPRES.NS1 #BEB-BEC @1
#ABA-BEF @1 #BEI-BFJ @1 #BFC
) SPECIAL PATT]NS1 #BEC @1 #BEF @1 #BFJ
@1 #ABA
! SUM OR DI6];E ( CUBES1 #CED
TRINOMIALS1 #BEB-BFE
Z]OS &1 #BFB-BFE
.,FACTORIZ,N @1 PRIME1 #IGH-IGI
.,F1SI# .REGION @1 #AGD
.,FIBONA3I .SEQU;E @1 #HBH @1 #HCB
RECURSIVE RULE =1 #HBH
.,F9D .! .]ROR @1 .,SEE ,]ROR ANALYSIS
.,F9ITE .DI6];ES @1 #CIC-CII
F/-ORD] DI6];ES1 #CIC
PROP]TIES (1 #CID
SECOND-ORD] DI6];ES1 #CID
?IRD-ORD] DI6];ES1 #CIE
.,F9ITE .SEQU;E @1 #GID
.,F/-.ORD] .DI6];ES @1 #CIC
.,FOCAL .L5G? @1 #EHE @1 #FBD
.,FOCUS 7.,FOCI7
( AN ELLIPSE1 #FCD
(A HYP]BOLA1 #FDB
(A P>ABOLA1 #FBJ
-----------------------------------#AJIB
.,,FOIL .ME?OD @1 #BDH @1 #IHE
.,=MULAS @1 #BF
>EA
(A CIRCLE1 #BF @1 #IIB
(A P>ALLELOGRAM1 #IIA
(A RECTANGLE1 #BF @1 #IIA
(A TRAPEZOID1 #BF @1 #IIA
(A TRIANGLE1 #BF @1 #HHE @1 #HIA @1 #IIA
,B1U=T NUMB]1 #DEH
*ANGE-(-BASE1 #EJH
CIRCUMF];E1 #BF @1 #IIB
-B9,NS1 #FIJ
DEGREES_/RADIANS1 #HFJ
4T.E1 #BF @1 #CD
6! HORIZON1 #DEJ
2T PO9TS1 #FAD @1 #FFI
D\# ANGLE1 #IEE
,FAHR5HEIT_/,CELSIUS1 #BF @1 #DD
HALF ANGLE1 #IEE
9T]E/
-P.D1 #DHA
3T9U\SLY -P.D$1 #DID
9T]IOR ANGLE (A REGUL> POLYGON1 #ABA
,KELV9_/,CELSIUS1 #DEJ
M>G9 ( ]ROR1 #GFH
MIDPO9T1 #FAE
,NEWTON'S LAW ( COOL+1 #EAF
.N? P5TAGONAL NUMB]1 #CID
.N? TRIANGUL> NUMB]1 #CID
P]IMET]1 (A RECTANGLE1 #BF @1 #BG @1
#ABA
P]MUT,N1 #FHE
PROBABIL;Y1 #FIH @1 #GJJ
(! -PLE;T ( AN EV5T1 #ABA
( -P.D EV5TS1 #GJG
( DEP5D5T EV5TS1 #GAH
( 4JO9T EV5TS1 #GJG
( 9DEP5D5T EV5TS1 #GAG
REWRIT+1 #BF-CB @1 #FC
SLANT HEI<T1 (A TRUNCAT$ PYRAMID1 #DEI
SLOPE1 #HB
/&>D DEVI,N1 #GDH
/&>D NORMAL 4TRIBU;N1 #GEH
SUM ( F/ .;N POSITIVE 9TEG]S1 #ABA
SUM ( SQU>ES ( F/ .;N POSITIVE 9TEG]S1
#GIG
SURFACE >EA
(A C"O1 #DEA
(A CYL9D]1 #FC @1 #EFG @1 #EHJ @1 #IIC
(A RECTANGUL> PRISM1 #IIC
(A SPH]E1 #DBG
TA# (1 #AJBF-AJCB
TRIGONOMETRIC DI6];E1 #IDI
TRIGONOMETRIC SUM1 #IDI
VOLUME
(A C"O1 #FE
(A CUBE1 #CEJ
(A CYL9D]1 #CCD @1 #CEJ @1 #EFG @1 #EHJ
@1 #ABA
(A DODECAH$RON1 #DAI
( AN ICOSAH$RON1 #DAI
( AN OCTAH$RON1 #DAI
(A PYRAMID1 #CEJ @1 #CGC
(A RECTANGUL> PRISM1 #CCD @1 #CEJ @1
#ABA
(A SPH]E1 #CCB @1 #DBG @1 #DGE
(A TETRAH$RON1 #DAI
.,=TY-.FIVE .DEGREE .ANGLE @1
TRIGONOMETRIC VALUES =1 #HEC
.,FRACTAL .GEOMETRY
FRACTAL TREE1 #HCH
,JULIA SET1 #BHB
,M&ELBROT SET1 #BHA
,SI]P9SKI C>PET1 #HAF
,SI]P9SKI TRIANGLE1 #HBE
.,FRAC;N 7.;S7
A4+1 #IGI
-PLEX1 #EHD
DECIMALS1 P]C5TS1 &1 #IGF
SUBTRACT+1 #IGI
WRIT+ REP1T+ DECIMALS Z1 #HBB
.,FRAC;N .B>S
Z GR\P+ SYMBOLS1 #AD
.,FREQU5CY
(A P]IODIC FUNC;N1 #IAJ
( POSSI# \TCOMES1 ,A#BJ
.,FUNC;N7.;S7 @1 .,SEE .AL ,GRAPHS2
,L9E> FUNC;N7;S72 ,P>5T FUNC;N2
,QUADRATIC FUNC;N7;S71 #GC @1 #ADJ @1
#ADA
ABSOLUTE VALUE1 #ABA-ABI
CLASSIFY+1 #GE @1 #HJ-HA @1 #DGI @1 #DHG
@1 #DHI
-POSI;N (1 #DCJ-DCE @1 #DFE ,#DFG
3T9U\S1 #HJ-HA
COS9E1 #HEB-HEH @1 #HFF-HGB @1 #IDI-IFB
CUBE ROOT1 #DDF-DEA @1 #DFE @1 #DFH
4CRETE1 #HJ-HA
DOMA9 (1 #GC @1 #GF @1 #DBH-DCJ
EV51 #IBH
EXPON5TIAL GR[? & DECAY1 #DGH-DIA @1
#EBH-ECA @1 #ECC-ECF
FAMILY1 #HI
GRTE/ 9TEG]1 #ACA
9V]SE1 #DCH-DDE @1 #DFE @1 #DFG @1 #EJA
HORIZONTAL L9E TE/ =1 #DDJ
IT]AT+1 #HCJ @1 #HCA @1 #HCC
L9E>1 #GE-GI ,#HI-IG1DCH-DCI1 #ABA-DDD
LOG>I?MIC1 #EJB-EJE
LOGI/IC1 #EBB
NATURAL BASE1 #DIC-DIH
OBJECTIVE1 #AGD
ODD1 #IBH
OP],NS ON1 #DBH-DCE @1 #DFE @1 #DFG
PIECEWISE1 #ACJ-ACA
P[]1 #DBH-DCE @1 #ECA-ECE
PROP]TIES (1 #AJCD
QUADRATIC1 #BCF-BDC @1 #BDE-BEA @1
#ABA-CAE @1 #CBB
RADICAL1 #DDF-DEA @1 #DFE @1 #DFH
RANGE (1 #GC
R,NAL1 #EDH-FJG @1 #FJB @1 #FJD
RECURSIVE RULES &1 #HBG-HCE
REPRES5T+1 #GC-GI
R.D+1 #ACA
S9E1 #HEB-HEH @1 #HFF-HGB @1 #IDI-IFB
SQU>E ROOT1 #DDF-DEA @1 #DFE @1 #DFH
/EP1 #ACA
TANG5T1 #HEB-HEH @1 #HFF-HGB @1 #ABA-IAD
,#IDI-IFB
V]TICAL L9E TE/ =1 #GC-GD @1 #GG
.,FUNC;N .NOT,N @1 #GE
.,FUNDA;TAL .C.T+ .PR9CIPLE @1 #FHB
& P]MUT,NS1 #FHD-FHI @1 #ABA-GCE
) REPETI;N1 #FHC @1 #FHG-FHI
US+1 #FHB-FHC @1 #FHF-FHI @1 #GBJ
..,FUNDA;TAL !OREM ( .ALGEBRA @1 #CGI
APPLY+1 #CGI-CHF @1 #DJE
COROLL>Y TO1 #CGI
;,G
.,GAUSS @1 ,K>L ,FRI$RI*1 #CGI
.,G5]AL .R,NAL .FUNC;NS @1 #EFE-EGA @1
#ABA @1 #FJD
.,G5]AL .SECOND-.DEGREE .EQU,N @1 #FEC
.,G5]ALIZE @1 EX]CISES1 #GJC @1 #GAB
.,GEOMETRIC .M1N @1 #GDI
.,GEOMETRIC .PROBABIL;Y @1 #GJA @1 #GJC
@1 #GJD
.,GEOMETRIC .SEQU;E @1 #HAJ-HAF @1 #HCI
@1 #ABA
RECURSIVE RULES &1 #HBG-HCE @1 #HCI @1
#ABA
.,GEOMETRIC .S]IES @1 #HAB-HAF @1 #HCI
@1 #HDA
9F9ITE1 #HAI-HBE @1 #HCI @1 #HDB
.,GEOMETRY @1 .,SEE .AL ,ANGLE 7;S72
,CIRCLE2 ,=MULAS2 ,TRIANGLE7;S72
,TRIGONOMETRIC FUNC;N7;S7
3GRU5T FIGURES1 #IIF-IIG
3IES1 #FDI-FEG @1 #FFE-FFF
=MULAS F1 #AJCB
GOLD5 RECTANGLE1 #EID
L9E SYMMETRY1 #IIJ
P>ALLEL L9ES1 #HD-HF @1 #II ,#AJB
P]P5DICUL> BISECTOR1 #FAE-FAI
,PY?AGOR1N !OREM1 #IIE
REFLEC;N1 #IHH-IHI
SIMIL> FIGURES1 #IIF-IIG
TRANS=M,N1 #IHH-IHI
TRIANGLE REL,N%IPS1 #IIE
-----------------------------------#AJIC
.,GEOMETRY .S(TW>E .ACTIV;Y @1 EXPLORE !
LAW ( S9ES1 #HHA
.,GOLD5 .RATIO @1 #EID
.,GOLD5 .RECTANGLE @1 #EID
.,GRAPH+ .CALCULATOR
ACTIVITIES
CALCULATE A BINOMIAL 4TRIBU;N1 #GCA
CALCULATE "O-V>IA# /ATI/ICS1 #ABA
5D 2HAVIOR ( FUNC;NS1 #CCF
EVALUATE EXPRES.NS1 #AG
F9D MAXIMUM & M9IMUM VALUES1 #BDD
FUNC;N OP],NS1 #DCE
GRAPH EQU,NS ( CIRCLES1 #FCC
GRAPH L9E> EQU,NS1 #IG
GRAPH LOG>I?MIC FUNC;NS1 #EAD
GRAPH R,NAL FUNC;NS1 #EFD
GRAPH SY/EMS ( EQU,NS1 #AEI
USE MATRIX OP],NS1 #AID
MODEL+ DATA )A QUADRATIC FUNC;N1 #CJH
OP],NS ) FUNC;NS1 #DCE
OP],NS ) SEQU;ES1 #HJA
SET A GD VIEW+ W9D[1 #CDE
SOLV+ L9E> SY/EMS US+ TA#S1 #AEB
USE TA#S 6SOLVE EQU,NS1 #BE
TRANS=M,NS1 #ABA-ABB
TRIGONOMETRIC ID5TITIES1 #IBC
V]IFY OP],NS ) R,NAL EXPRES.NS1 #EHA
BINOMIAL PROBABIL;Y F1TURE1 #GCA
*ECK+ SOLU;NS )1 #AFA @1 #BHE @1 #BIB @1
#BIC @1 #DFB @1 #EAH @1 #EIA @1 #FEI
@1 #IEH
3NECT$ MODE1 #EFD @1 #EHA
CUBIC REGRES.N F1TURE1 #CIF
DOT MODE1 #EFD
5T]+ EQU,NS1 #BE @1 #DH @1 #DI @1 #IG @1
#ABA @1 #ABB @1 #AEB @1 #AEI @1 #CDE
@1 #CIF @1 #DEE @1 #DFJ @1 #DFA @1
#DFB @1 #DFC @1 #DID @1 #EAD @1 #EBC
@1 #EBD @1 #EBE @1 #EFD @1 #EHA @1
#EIF @1 #EIG @1 #FCC @1 #HCD @1 #IBC
@1 #ICI
EXAMPLES
APPROXIMAT+ R1L Z]OS (A POLYNOMIAL
FUNC;N1 #CHB-CHC
-PUT+ 9V]SE MATRICES1 #BAA-BAC
DRAW+ A HI/OGRAM1 #GCA
F9D+ A BE/-FITT+ L9E1 #AAF
F9D+ AN EXPON5TIAL MODEL1 #ABA
F9D+ A POLYNOMIAL MODEL1 #CIF
F9D+ A P[] MODEL1 #ECB
F9D+ TURN+ PO9TS (A POLYNOMIAL FUNC;N1
#CHH
MAXIMIZ+ A POLYNOMIAL MODEL1 #EHI
MODEL+ NATURAL BASE FUNC;NS1 #DID
MODEL+ ! P]IOD (A P5DULUM1 #DDG
S9USOIDAL REGRES.N1 #IDC
SOLV+ AN EQU,N ) TWO RADICALS1 #DEE
SOLV+ AN EXPON5TIAL 9EQUAL;Y1 #EBF
SOLV+ A L9E> QUADRATIC SY/EM1 #FEH
SOLV+ A LOG>I?MIC 9EQUAL;Y1 #ABA
SOLV+ RADICAL 9EQUALITIES1 #ABA-DFC
SOLV+ R,NAL EQU,NS1 #ABA-EIG
SOLV+ R,NAL 9EQUALITIES1 #EIH
SOLV+ TRIGONOMETRIC EQU,NS1 #ABA-ICI
EX]CISES1 #AAH @1 #BDC @1 #BEA @1 #CJE
@1 #DCD @1 #DDD @1 #DHC @1 #DHI @1
#DIA @1 #DIF @1 #DIG @1 #EBA @1
#ECD-ECF @1 #EFI-EGA @1 #FCH @1 #FFB
@1 #GAB @1 #GFA @1 #HAF @1 #HHH @1
#IAD @1 #IBJ @1 #ICG
EXPON5TIAL REGRES.N F1TURE1 #ABA @1 #ECJ
@1 #GGF @1 #GHA
GRAPH+ F1TURE1 #DI @1 #IG @1 #ABA @1
#ABB @1 #CCF @1 #CFA @1 #DEE @1 #DFA
@1 #EAD @1 #EBC @1 #EBE @1 #EBF @1
#EBG @1 #EFG @1 #EIG @1 #EIH @1 #FCC
@1 #FEH @1 #GGE @1 #GGF @1 #GGG @1
#HJA @1 #HCD @1 #IBC @1 #ICI @1 #IDC
9T]SECT F1TURE1 #AEI @1 #CJE @1 #CFA @1
#DEE @1 #DFA @1 #DFC @1 #EBC @1 #EBE
@1 #EBF @1 #EBG @1 #EIG @1 #EIH @1
#FEH @1 #ICI @1 #IEJ
L9E> REGRES.N F1TURE1 #AAF @1 #GGE
LI/ F1TURE1 #AAF @1 #CJH @1 #CAA @1 #GCA
@1 #GHA @1 #ABA
,,LN F1TURE1 #EAD
,,LOG F1TURE1 #EAD
MATRIX F1TURE1 #AID @1 #BAA @1 #BAC
MAXIMUM F1TURE1 #BDD
M9IMUM F1TURE1 #BDD @1 #EFG
P[] REGRES.N F1TURE1 #ECC @1 #ECE
QUADRATIC REGRES.N F1TURE1 #CJH @1 #ABA
@1 #GGG ,#GHF
R&OM NUMB] F1TURE1 #GAD
ROOT F1TURE1 #CHB
SEQU;E MODE1 #HJA @1 #HCD
S9USOIDAL REGRES.N F1TURE1 #IDC
SORT F1TURE1 #GAD
/ATI/ICS F1TURE1 #GEJ
,,/ATPLOT F1TURE1 #AAF @1 #CJH @1 #CAA
@1 #ABA @1 #EBH @1 #ECJ @1 #GGD @1
#GGE @1 #GHA @1 #ABA @1 #IDC
SUMM,N F1TURE1 #HJA
TA# F1TURE1 #BE @1 #DH @1 #DI @1 #AEB @1
#CFJ @1 #ABA @1 #DFB @1 #DIF @1 #EBC
@1 #EBD @1 #EBF @1 #ABA @1 #ECJ @1
#EHA @1 #EIF @1 #EIH @1 #HJA @1 #ABA
TA# SETUP F1TURE1 #BE @1 #DFJ @1 #DFB @1
#EIF
TE/ F1TURE1 #DI
TRACE F1TURE1 #DI @1 #BDD @1 #BIB @1
#BIC @1 #DDG @1 #ABA
W9D[ SETT+S1 #IG @1 #AEI @1 #CDE @1 #CFA
@1 #ABA @1 #IBC
Z]O F1TURE1 #BDC @1 #CHB
ZOOM F1TURE1 #ABA @1 #ABB @1 #FCC
.,GRAPHS
( ABSOLUTE VALUE1 #EJ @1 #EA
( ABSOLUTE VALUE FUNC;NS1 #ABA-ABI
( ABSOLUTE VALUE 9EQUALITIES1 #ABA @1
#EC @1 #ED @1 #EF @1 #ACE @1 #ACF @1
#AFI ,#AGB
B>1 #AJJF-AJJG
( BE/-FITT+ L9ES1 #AAE-ABJ
CIRCLE1 #AJJF-AJJG
( 3T9U\S FUNC;NS1 #HJ-HA
( COS9E FUNC;NS1 #HGD @1 #IJH-IAD @1
#ABA @1 #IFE
TRANSL,NS1 #IAE-IAG @1 #IAI-IBB @1 #ABA
( CUBE ROOT FUNC;NS1 #DDF-DEA @1 #ABA @1
#DFH
( 4CRETE FUNC;NS1 #HJ-HA
( EQU,NS ( CIRCLES1 #FBF-FCC @1 #ABA @1
#FGJ
TRANSLAT$1 #FEJ
( EQU,NS ( ELLIPSES1 #FCD-FCI @1 #ABA @1
#FGA
TRANSLAT$1 #FEB
( EQU,NS ( HYP]BOLAS1 #ABA-FDH @1 #FFH
@1 #FGA
TRANSLAT$1 #FEA
( EQU,NS ( P>ABOLAS1 #FBJ-FBE @1 #ABA @1
#FGJ
TRANSLAT$1 #FEA
( EQU,NS 9 TWO V>IA#S1 #ABA-GI
( EXPON5TIAL DECAY FUNC;NS1 #ABA-DIA @1
#ECH @1 #ECI
( EXPON5TIAL GR[? FUNC;NS1 #ABA-DHE @1
#ECH @1 #ECI
HI/OGRAM1 #GBD @1 #GBF-GCA
( HORIZONTAL & V]TICAL L9ES1 #ABA ,#ID
( HORIZONTAL & V]TICAL TRANSL,N1 #IAF
( 9F9ITE GEOMETRIC S]IES1 #HBJ
9T]PRET+1 #CBE-CBF
( 9V]SE FUNC;NS1 #DCG @1 #DCH @1 #DDJ @1
#ABA @1 #DDE
L9E1 #AJJF-AJJG
( L9E> EQU,NS1 #HI-IG ,#ADB
9 ?REE V>IA#S1 #AGG
( L9E> 9EQUALITIES
9 "O V>IA#1 #DA-DI @1 #FD ,#ACC
9 TWO V>IA#S1 #ACB-ACH @1 #ADD
-----------------------------------#AJID
( L9E>-QUADRATIC SY/EMS1 #FEH @1 #ABA
,#FFB-FFD
( L9E> SY/EMS1 #AEC-AEI @1 #BBA @1 #ABA
( LOG>I?MIC FUNC;NS1 #EJB-EJE @1 #ABA @1
#EDA
( NATURAL BASE FUNC;NS1 #DIC-DID @1
#ABA-DIH
( P>ALLEL & P]P5DICUL> L9ES1 #ABA-HF
( PIECEWISE FUNC;NS1 #ACJ-ACA
( POLYNOMIAL FUNC;NS1 #CCF @1 #ABA-CDD
@1 #CHG-CIB @1 #DJA @1 #DJC @1 #ABA
( QUADRATIC FUNC;NS
9 9T]CEPT =M1 #BDF-BEA @1 #CAG @1 #ABA
9 /&>D =M1 #BCF-BDC @1 #CAG @1 #ABA
9 V]TEX =M1 #BDE-BDF @1 #ABA-BEA @1 #CAG
,#CAI
( QUADRATIC 9EQUALITIES1 #CJJ-CJG
( QUADRATIC SY/EMS1 #FEH-FFD @1 #FFH
( RADICAL FUNC;NS1 #DDF-DEA @1 #DFE @1
#ABA
( R,NAL FUNC;NS1 #EEH-EGA @1 #FJB @1
#ABA
( R1L NUMB]S1 #B
( REL,NS1 #GB @1 #GF
SCATT] PLOTS1 #AAB-ABJ ,#ADC
( SEQU;ES1 #GIE @1 #GIH @1 #HJJ @1 #HJA
( S9E FUNC;NS1 #HGD @1 #IJH-IAD @1 #ABA
@1 #IFE
TRANSL,NS1 #IAE-IAG @1 #IAI-IBB @1 #ABA
( SQU>E ROOT FUNC;NS1 #DDF-DEA @1 #ABA
@1 #DFH
( SY/EMS ( 3/RA9TS1 #AGD-AGF
( SY/EMS ( L9E> 9EQUALITIES1 #ABA-AGC @1
#BBA ,#BBC
( SY/EMS ( QUADRATIC 9EQUALITIES1 #CJA
@1 #CJD @1 #CJE
( TANG5T FUNC;NS1 #IAA-IAD @1 #IFD @1
#ABA
TRANSL,NS1 #IAH @1 #IBJ @1 #IBA
( TRIGONOMETRIC FUNC;NS1 #HGD @1
#ABA-IBB @1 #IFD @1 #IFE
V]TICAL %R9K+ (1 #DGI
V]TICAL /RET*+ (1 #DGI
..,GRTE/ -MON FACTOR 7.,,GCF7 @1
#IGH-IGI
.,GRTE/ .9TEG] .FUNC;N @1 #ACA
.,GR\P+ .SYMBOLS
FRAC;N B>S1 #AD
P>5!SES1 #AE
.,GR[? .FACTOR @1 = AN EXPON5TIAL GR[?
FUNC;N1 #DGH
.,GR[? .FUNC;N
EXPON5TIAL1 #DGH-DHE @1 #ECH @1 #ECI
9VOLV+ ;E1 #DIC-DIH @1 #EDJ
..,GUESS1 *ECK1 & .REVISE @1 PRO#M SOLV+
/RATEGY1 #IIH-III
;,H
.,HALF-.ANGLE .=MULAS @1 #IEE @1 #IFD
US+1 #IEE-IFB @1 #IFH
.,HALF .PLANE @1 #ACB
.,H]ON'S .>EA .=MULA @1 #HIA
.,HEXAGONAL .NUMB] @1 #HCG
.,HI/OGRAM @1 #AJJH-AJJI
ON A GRAPH+ CALCULATOR1 #GCA
PROBABIL;Y 4TRIBU;N1 #GBD @1 #ABA-GCA @1
#GCC
.,HOOKE'S .LAW @1 #DDD
.,HORIZONTAL .ASYMPTOTE @1 #EEH
.,HORIZONTAL .L9E @1 GRAPH (1 #IB
.,HORIZONTAL .L9E .TE/ @1 #DDJ @1 #DDC
.,HORIZONTAL .TRANSL,N @1 GRAPH+1 #IAF
.,HYP]BOLA @1 #EEH @1 #FDB
ASYMPTOTES (1 #FDB
BRAN*ES (1 #FDB
C5T] (1 #FDB
E35TRIC;Y (1 #FFE-FFF
EQU,N (
GRAPH+1 #FDB-FDH @1 #FFH @1 #FGA
TRANSLAT$1 #FEJ @1 #FEA @1 #FEB-FEG @1
#FGB
WRIT+1 #FDC-FDH @1 #FFH @1 #FGA
FOCI (1 #FDB
TRANSV]SE AXIS (1 #FDB
V]TICES (1 #FDB
.,HYPOT5USE @1 #IIE
.,HYPO!SIS @1 #AJJB-AJJC
.,HYPO!SIS .TE/+ @1 #GFD-GFE
,I
.,ID5T;Y @1 #AB
.,ID5T;Y .MATRIX @1 #BAJ
.,ID5T;Y .PROP]TY @1 #C
.,IF-.!N .=M @1 (A 3DI;NAL /ATE;T1
#AJJB-AJJC
.,IMAG9>Y .NUMB] @1 #BGF
.,IMAG9>Y .UNIT .;I @1 #BGE
.,9CONSI/5T .L9E> .SY/EM @1 #AED-AEG
.,9DEP5D5T .EV5TS @1 #GAG-GAI @1
#ABA-GBC
.,9DEP5D5T .L9E> .SY/EM @1 #AED-AEG
.,9DEP5D5T .V>IA# @1 #GD
..,9DEX (A .RADICAL @1 #DAD
.,9DEX .( .REFRAC;N @1 #HGI @1 #ICJ
.,9DEX .( .SUMM,N @1 #GIF @1 #GIG
.,9DIRECT .>GU;T @1 #AJJJ-AJJA
.,9DIRECT .M1SURE;T @1 #HEE @1 #HEG-HEH
.,9DUC;N @1 MA!MATICAL1 #HCF-HCG
.,9EQUALITIES @1 .,SEE .AL ,L9E>
9EQUALITIES
ABSOLUTE VALUE1 #EJ-EH @1 #ACE @1 #ACF
@1 #ABA ,#AGB
-P.D1 #DA-DG
EQUIVAL5T1 #DB
EXPON5TIAL1 #EBF @1 #EBG
L9E>1 #DA-DI ,#ACB-ACH
SY/EMS (1 #AFH-AGF @1 #BBA @1 #BBC
LOG>I?MIC1 #EBG
QUADRATIC1 #CJJ-CJG @1 #CBB
SY/EMS (1 #CJA @1 #CJD @1 #CJE
RADICAL1 #DFB-DFC
R,NAL1 #EIH-FJJ
.,9F9ITE .GEOMETRIC .S]IES @1 #HAI-HBE
@1 #ABA @1 #HDB
.,9F9ITE .SEQU;E @1 #GID
.,9F9ITE .S]IES @1 #GIF
.,9F9;Y @1 POSITIVE & NEGATIVE1 #CCF @1
#ABA
.,9ITIAL .SIDE @1 ( AN ANGLE1 #HEI
.,9TEG]S @1 #B
OP],NS )1 #IGE
.,9T]CEPT .=M @1 (A QUADRATIC FUNC;N1
#BDF-BEA @1 #CAG @1 #CAI
.,9T]E/
-P.D1 #DHA @1 #DHC @1 #DHD @1 #DHE
3T9U\SLY -P.D$1 #ABA-DIE @1 #DIG
.,9T]PRET
EXAMPLES1 #IA @1 #ABD @1 #ACB @1 #DBI @1
#DID @1 #ABA @1 #HFI
EX]CISES1 #HH @1 #CJF @1 #CJG @1 #CCE @1
#DEH @1 #ECE @1 #EEE @1 #GFB @1 #HJI
@1 #HGB @1 #HHH @1 #ICJ
PROBABIL;Y 4TRIBU;NS1 #GBE @1 #GBF
.,9T]SEC;N
( GRAPHS ( L9E>-QUADRATIC SY/EMS1 #FEH
( GRAPHS ( QUADRATIC SY/EMS1 #FEI
( SETS1 #GJG-GAC @1 #GAE-GAF
.,9V]SE .COS9E @1 #HGD-HGI
.,9V]SE .FUNC;N7.;S7 @1 #DCG-DDE @1 #DFE
@1 #DFG
LOG>I?MIC & EXPON5TIAL1 #EJA
TRIGONOMETRIC1 #HGD-HHJ @1 #HIG @1 #HII
.,9V]SE .MATRICES1 #BAJ-BAG @1 #BBA @1
#BBF
.,9V]SE .PROP]TY1 #C ,#EJA
.,9V]SE .REL,N7.;S7 @1 #DCH @1 #DDB
.,9V]SE .S9E @1 #HGD-HGI
.,9V]SE .TANG5T @1 #HGD-HGI
.,9V]SE .V>I,N @1 #EEJ-EEG @1 #FJC
EQU,NS1 #EEA-EEG
MODEL+ )1 #EEJ @1 #EEB @1 #EEF-EEG
.,9VE/IGAT+ .,ALGEBRA @1 .,SEE
,ACTIVITIES
.,IRR,NAL .3JUGATES .!OREM @1 #CHJ
.,IRR,NAL .EXPON5T @1 #DBE
.,IRR,NAL .NUMB] @1 #B
.,IT],N @1 #HCJ @1 #HCA @1 #HCC
-----------------------------------#AJIE
;,J
.,JO9T .V>I,N @1 #EEC-EEG @1 #FJC
.,JULIA .SET @1 #BHB
.,JU/IFY .RESULTS @1 ..,"?\T4 ,SEE =
EXAMPLE .#D @1 #F @1 #G @1 #BGA @1
#BHA @1 #CIA @1 #CIH @1 #DAH @1 #DIJ
@1 #EAB @1 #EEJ @1 #EEF @1 #GDH @1
#HAI @1 #HCB
;,K
.,KEPL]'S .SECOND .LAW @1 #IJD
.,KEY .,3CEPT @1 #B @1 #C @1 #AJ @1 #AB
@1 #AH @1 #DB @1 #EA @1 #ABA @1 #EC @1
#GB @1 #GC @1 #GD @1 #HJ @1 #HB @1 #HC
@1 #HD @1 #HI @1 #IJ @1 #IA @1 #IB @1
#IH @1 #AJG @1 #AAE @1 #ABC @1 #ABF @1
#ACC @1 #AED @1 #AFJ @1 #AFA @1 #AFH
@1 #AGD @1 #AGI @1 #AHG @1 #AIE @1
#BJC @1 #BJD @1 #BJE @1 #BJF @1 #BAJ
@1 #BAB @1 #BAH @1 #BCF @1 #BCG @1
#BDE @1 #BDF @1 #BDH @1 #BEC @1 #BFF
@1 #BGE @1 #BGF @1 #BGI @1 #BHD @1
#BIB @1 #BID @1 #CCJ @1 #CCI @1 #CEC
@1 #CED @1 #CFC @1 #CFD @1 #CGJ @1
#CGI @1 #CHJ @1 #CHA @1 #CHH @1 #CID
@1 #DAD @1 #DAE @1 #DBJ @1 #DBA @1
#DBH @1 #DCH @1 #DDJ @1 #DDF @1 #DEB
@1 #DGH @1 #DHA @1 #DHF @1 #DIB @1
#DIC @1 #DID @1 #DII @1 #EJB @1 #EJG
@1 #EJH @1 #EAE @1 #EAG @1 #EEA @1
#EEC @1 #EEH @1 #EEI @1 #EFE @1 #EGC
@1 #EGE @1 #EGF @1 #EHB @1 #EHC @1
#EHD @1 #FAD @1 #FAE @1 #FBA @1 #FBF
@1 #FCD @1 #FDB @1 #FEJ @1 #FEC @1
#FEE @1 #FHB @1 #FHE @1 #FIJ @1 #FIB
@1 #FIC @1 #FIH @1 #FII @1 #GJJ @1
#GJG @1 #GAG @1 #GAH @1 #GBD @1 #GBE
@1 #GDD @1 #GDE @1 #GEA @1 #GEB @1
#GEG @1 #GFC @1 #GFD @1 #GFH @1 #GID
@1 #GIF @1 #GIG @1 #HJB @1 #HJD @1
#HAJ @1 #HAB @1 #HBA @1 #HBG @1 #HEB
@1 #HEC @1 #HEI @1 #HFJ @1 #HFA @1
#HFF @1 #HFG @1 #HFH @1 #HGE @1 #HHB
@1 #HHC @1 #HHE @1 #HHI @1 #HIA @1
#IJH @1 #IJI @1 #IAA @1 #IAE @1 #IBD
@1 #IDI @1 #IEE
;,L
.,LAW .( .COS9ES @1 #HHI-HIE @1 #HIG @1
#IJJ
..,LAW ( L>GE .NUMB]S @1 ,A#AF-,A#AG
.,LAW .( .S9ES @1 #HHA-HHH @1 #HIG @1
#IJJ
..,LAW ( UNIV]SAL .GRAVIT,N @1 #EEG
.,L1D+ .COE6ICI5T @1 (A POLYNOMIAL
FUNC;N1 #CCG
..,L1/ -MON DENOM9ATOR 7.,,LCD7 @1 #IGI
(A R,NAL EXPRES.N1 #EHC @1 #IHF
= SOLV+ A R,NAL EQU,N1 #EIJ
..,L1/ -MON MULTIPLE 7.,,LCM7 @1
#IGH-IGI
=A R,NAL EXPRES.N1 #EHC
.,LEFT .4TRIBUTIVE .PROP]TY @1 #AIG
.,LEGS @1 (A TRIANGLE1 #IIE
.,L .RADICALS @1 #DBB
A4+ & SUBTRACT+1 #DBB-DBG
.,L .T]MS @1 #AB
-B9+1 #AB
.,LIKELIHOOD @1 ( AN EV5T1 #FIH
.,L9E .GRAPH @1 #AJJF-AJJG
.,L9E .PLOT @1 #AJJH-AJJI
.,L9E .( .REFLEC;N @1 #IHH-IHI
.,L9E .SYMMETRY @1 #IIJ
.,L9E .( .SYMMETRY
=A 3IC SEC;N1 #FEB @1 #FEE
=A PLANE FIGURE1 #IIJ
.,L9E> .EQU,N7.;S7 @1 .,SEE .AL ,L9E>
SY/EMS1 #AH
= BE/-FITT+ L9E1 #AAB-ABJ ,#ADC
DIRECT V>I,N1 #AJG-AAA
=MS (1 #ADJ
GRAPH+1 #HI-IG @1 #AGG
US+ SLOPE-9T]CEPT =M1 #ABA-IG @1 #ADJ @1
#ADB
US+ /&>D =M1 #IA-IF
9 ?REE V>IA#S1 #AGG
) NO SOLU;NS1 #BC
PO9T-SLOPE =M (1 #IH-II @1 #AJA @1 #ABA
REWRIT+1 #BH @1 #CJ-CB
SLOPE-9T]CEPT =M (1 #IJ-IG @1 #IH @1
#ABA @1 #ADJ @1 #ADB
SOLV+1 #AH-BE @1 #FJ @1 #FB
US+ ! 4TRIBUTIVE PROP]TY1 #ABA-BD
/&>D =M (1 #IA-IF
9 ?REE V>IA#S1 #AGG-AHE
WRIT+1 #AI @1 #BJ @1 #BC-BD @1 #IH-AJD
@1 #ADB
.,L9E> .FUNC;N7.;S7 @1 #GE-GI
GRAPH+1 #HI-IG
9V]SE1 #DCH-DCI @1 #DDB-DDD
L9E> PROGRAMM+ &1 #AGD-AGF
.,L9E> .9EQUALITIES
3/RA9TS1 #AGD-AGF
=MS (1 #DA
GRAPH+
9 "O V>IA#1 #DA-DI @1 #FD ,#ACC
SY/EMS ( 3/RA9TS1 #AGD-AGF @1 #ABA @1
#BBC
9 TWO V>IA#S1 #ACB-ACH @1 #ADD
R1D+1 #DA
SOLU;N (1 #DA
SOLV+1 #DA-DI @1 #FD
SY/EMS (1 #AFH-AGC
?REE OR M1 #AGJ-AGC
9 TWO V>IA#S1 #ACB-ACH ,#ADD
.,L9E> .PROGRAMM+ @1 #AGD-AGF
3/RA9TS1 #AGD
F1SI# REGION1 #AGD
OBJECTIVE FUNC;N1 #AGD
.,L9E>-.QUADRATIC .SY/EMS @1 #FEH-FFD
.,L9E> .REGRES.N @1 #AAF
.,L9E> .SY/EMS @1 #AEB ,#AEC
CLASSIFY+1 #AED-AEG
COE6ICI5T MATRIX (1 #BJE-BJF
) 9F9ITELY _M SOLU;NS1 #AED @1 #ABA @1
#AGH ,#AHJ
) NO SOLU;NS1 #AED @1 #AFC @1 #AGH ,#AHJ
NUMB] ( SOLU;NS (1 #AED-AEG
SOLU;N (1 #AEB @1 #AEC @1 #AGH
SOLV+
ALGEBRAIC,Y1 #AFJ-AFF @1 #BBC
US+ AUG;T$ MATRICES1 #ABA-BAI
US+ ,CRAM]'S RULE1 #BJE-BJF @1 #ABA-BJI
@1 #BBA ,#BBF
US+ ! ELIM9,N ME?OD1 #ABA-AFG @1
#AGI-AHE @1 #BBA @1 #BBC
0GRAPH+1 #AEC-AEI @1 #BBA @1 #BBB
US+ 9V]SE MATRICES1 #BAJ-BAG @1 #ABA @1
#BBF
US+ ! SUB/ITU;N ME?OD1 #ABA-AFG
,#AHA-AHE1BBA
US+ TA#S1 #AEB
9 ?REE V>IA#S1 #AGH-AHE @1 #BBD
.,L9ES
CLASSIFY+ 0SLOPE1 #HC
HORIZONTAL L9E TE/1 #DDJ @1 #DDC
P>ALLEL
EQU,NS =1 #II ,#AJB
SLOPE (1 #HD-HF
P]P5DICUL>
EQU,NS =1 #II ,#AJB
SLOPE (1 #HD-HF
( REFLEC;N1 #IHH-IHI
SLOPE (1 #HC ,#AJJ
( SYMMETRY1 #FEB @1 #FEE @1 #IIJ
V]TICAL1 SLOPE (1 #GC-GD @1 #GG
.,LI/ @1 MAK+ 6SOLVE PRO#MS1 #ABA-III
.,LOCAL .MAXIMUM @1 (A POLYNOMIAL
FUNC;N1 #CHH
.,LOCAL .M9IMUM @1 (A POLYNOMIAL FUNC;N1
#CHH
.,LOC,N .,PR9CIPLE @1 #CGH
.,LOG>I?M7.;S7 @1 #DII
*ANGE-(-BASE =MULA &1 #ABA-EJI ,#EAA
-MON1 #EJJ
NATURAL1 #EJJ
PROP]TIES (1 #EJG ,#AJCD
US+1 #EJG-EAC @1 #EDA
.,LOG>I?MIC .EQU,N 7;S71 #EAG
EVALUAT+1 #DII-EJA @1 #EJC-EJE @1 #EDA
MODEL+ )1 #EAI ,#EBA-EBB1EBD-EBE
PROP]TY ( EQUAL;Y =1 #EAG
SOLV+1 #EAG-EBE @1 #ECH @1 #EDB
.,LOG>I?MIC .EXPRES.N7.;S7
3D5S+1 #EJH @1 #EAJ @1 #EDA
EVALUAT+1 #DII-EJA @1 #EJC-EJE @1
#ABA-EAB
EXP&+1 #EJH @1 #EAJ @1 #EDA
.,LOG>I?MIC .FUNC;N 7;S7
GRAPH+1 #EJB-EJE @1 #EAD @1 #EDA
Z 9V]SE ( EXPON5TIAL FUNC;NS1 #ABA
MODEL+ )1 #EJJ @1 #EJD-EJE
-----------------------------------#AJIF
.,LOG>I?MIC .9EQUALITIES @1 #EBG
.,LOGICAL .R1SON+ @1 .,SEE ,R1SON+
.,LOGI/IC .FUNC;N @1 #EBB
..,L[] LIMIT ( .SUMM,N @1 #GIF
.,L[] .QU>TILE @1 #AJJH-AJJI
;,M
.,MAJOR .AXIS @1 ( AN ELLIPSE1 #FCD
.,MAKE .A .LI/ @1 PRO#M SOLV+ /RATEGY1
#ABA-III
.,MAKE .A .TA# @1 PRO#M SOLV+ /RATEGY1
#DH-DI @1 #BGB-BGC @1 #IIH-III
.,M&ELBROT .SET @1 #BHA
.,MANIPULATIVES @1 .,SEE .AL
,CALCULATOR2 ,GRAPH+ CALCULATOR
ALGEBRA TILES1 #BHC
,CALCULATOR ,BAS$ ,LABORATORY1 #IDH
CO9S1 #CJH @1 #EBH
-PASS1 #CJH
FLA%LI<T1 #FDI
9DEX C>DS1 #GGD
M1SUR+ TOOLS1 #AAB @1 #DCG @1 #EEJ
MUSICAL 9/RU;TS1 #IDH
.,MAPP+ .DIAGRAM @1 #GB @1 #GC @1 #GG @1
#ADJ ,#ADA
.,M>G9 .( .]ROR @1 #GFH-GGA
=MULA1 #GFH
.,MA!MATICAL .9DUC;N @1 #HCF-HCG
.,MA!MATICAL .MODEL+ @1 =MULAS F1 #AJCA
.,MATRIX 7.,MATRICES7 @1 #AHG
A4+ & SUBTRACT+1 #AHG @1 #AHI-AIC ,#AID
AUG;T$1 #BAH-BAI
COE6ICI5T1 #BJE-BJF
,CRAM]'S RULE &1 #BJE-BJI
DESCRIB+ PRODUCTS1 #AIE
DET]M9ANT (1 #BJC-BJI
DIM5.NS (1 #AHG ,#AIE
ELE;TS (1 #AHG
EQUAL1 #AHG
EQU,NS1 #AIJ-AIB
ID5T;Y1 #BAJ
9V]SE1 #BAJ-BAG
MULTIPLY+1 #AIE-BJB @1 #ICG
ORD] ( OP],NS1 #AHH
PROP]TIES1 #AHH @1 #AIG ,#AJCC
R[ OP],NS1 #BAH-BAI
SCAL> MULTIPLIC,N1 #AHH-AIB
= SOLV+ L9E> SY/EMS1 #BJE-BJI @1
#BAJ-BAI
TOTAL CO/1 #AIH
TRANSI;N1 #BJA
TRIANGUL> =M1 #BAH-BAI
.,MATRIX .ALGEBRA @1 =MULAS F1 #AJBF
.,MAXIMUM .VALUE
(A POLYNOMIAL FUNC;N1 #CHH-CIB
(A QUADRATIC FUNC;N1 #BCH-BCI @1 #BDA @1
#BDD @1 #BHG
( S9E & COS9E FUNC;NS1 #IJI
.,M1N @1 #GDD @1 #GDF-GEJ @1 #GHC @1
#GHD @1 #AJJE
GEOMETRIC1 #GDI
TRANS=M,N &1 #GEA-GEE
.,M1SURE;T
*OOS+ APPROPRIATE UNITS1 ,A#B-,A#C
3V]T+ M1SURE;TS1 #E @1 #G
3V]T+ UNITS (1 #IHA @1 ,A#B-,A#C
.,M1SURES @1 TA# (1 #AJBE
.,M$IAN @1 #GDD @1 #GDF-GEJ @1 #GHC @1
#GHD @1 #AJJE
TRANS=M,N &1 #GEA-GEE
(A TRIANGLE1 #FAH
.,METRIC .SY/EM @1 ,A#B-,A#C
.,MIDL9E @1 (A TRIGONOMETRIC GRAPH1 #ABA
.,MIDPO9T
=MULA1 #FAE @1 #FFI
( AL9E SEG;T1 #FAE @1 #FAG-FAI
.,M9IMUM .VALUE
(A POLYNOMIAL FUNC;N1 #CHH-CIB
(A QUADRATIC FUNC;N1 #BCH-BCI @1 #ABA
,#BDD
( S9E & COS9E FUNC;NS1 #IJI
.,M9OR .AXIS @1 ( AN ELLIPSE1 #FCD
.,MIX$ .,REVIEW @1 #CC @1 #EI @1 #AJF @1
#ACI @1 #AHF @1 #ABA @1 #BGD @1 #CAF
@1 #CFI @1 #DJJ @1 #DCF @1 #ABA @1
#EJF @1 #ECG @1 #EGB @1 #FJA @1 #FDA
@1 #ABA @1 #GJE @1 #GCB @1 #GEF @1
#GHB @1 #HAH @1 #ABA @1 #HGC @1 #HIF
@1 #IDJ @1 #IFC
..,MIX$ ,REVIEW 0.LESSON @1 ..,"?\T4
,SEE = .EXAMPLE #I1 #AF @1 #BD @1 #CB
@1 #ABA @1 #DG @1 #EH @1 #GI @1 #HH @1
#IF @1 #AJD @1 #AAA @1 #ABA @1 #ABI @1
#ACH ,#AEH
.,MODE @1 #GDD @1 #GDF-GDI @1 #GHC @1
#GHD ,#AJJE
TRANS=M,N &1 #GEA-GEE
.,MODEL+ @1 .,SEE .AL ,EXPRES.N7;S72
,=MULAS2 ,GRAPH+ CALCULATOR2 ,GRAPHS2
,L9E> EQU,N7;S72 ,POLYNOMIAL7;S72
,POLYNOMIAL FUNC;N7;S7;,QUADRATIC
FUNC;N7;S7
ABSOLUTE VALUE1 #EA
US+ ALGEBRAIC EXPRES.NS1 #AC @1 #ABA-AF
US+ >EA MODELS1 #BED @1 #BEG @1 #BEH @1
#ABA @1 #BHC
US+ BE/-FITT+ QUADRATIC MODELS1 #CAA
*OOS+ A MODEL1 #GGD-GHA @1 #GHF
US+ CIRCUL> MODELS1 #FBH @1 #FCJ-FCB
CIRCUL> MO;N1 #IAF @1 #IBA @1 #IBB
-PLET+ ! SQU>E1 #BHC
US+ 3IC SEC;NS1 #FED @1 #FEF-FEG
DIRECT V>I,N1 #AJG-AAA ,#ADC
DROPP$ OBJECTS1 #BFH-BGJ @1 #BGB-BGC
US+ E35TRIC;Y1 #FFF
US+ EQU,NS ( CIRCLES1 #FBH @1 #ABA-FCB
US+ EQU,NS ( ELLIPSES1 #FCF @1 #ABA-FCI
@1 #FDJ
US+ EQU,NS ( HYP]BOLAS1 #FDD @1 #ABA-FDH
US+ EQU,NS ( P>ABOLAS1 #FBB @1 #ABA-FBE
EX]CISES1 #AE @1 #CI @1 #BGA @1 #EEG @1
#EHJ @1 #FCI @1 #ABA @1 #HHH @1 #IDF
EXPON5TIAL DECAY1 #DHH-DIA @1 #GGF
) EXPON5TIAL EQU,NS1 #EAF @1 #ABA-EBC
US+ EXPON5TIAL FUNC;NS1 #ABA-DHA @1
#DHC-DHE @1 #DHH-DIA @1 #ABA @1 #ECJ
@1 #ECD-ECF
EXPON5TIAL GR[?1 #DHJ-DHA @1 #ABA-DHE
FACTORS US+ A TREE1 #IGH
F9ITE DI6];ES1 #CIE ,#CIH
FITT+ A MODEL 6DATA1 #GGD-GHA
US+ HUNDR$S SQU>ES1 #IGF
9F9ITE GEOMETRIC S]IES1 #HAI @1 #HBB @1
#ABA-HBE
US+ 9V]SE (A P[] FUNC;NS1 #ABA-DDB @1
#DDD-DDE
US+ 9V]SE V>I,N1 #EEJ @1 #EEB @1
#ABA-EEG
LAUN*$ OBJECTS1 #BIE @1 #BIH
US+ L9E> EQU,NS1 #AI @1 #BJ @1 #ABA-BD
@1 #BI @1 #CA-CB @1 #IH-AJE @1 #GGE
US+ L9E> 9EQUALITIES1 #DD @1 #DF-DG
US+ LOG>I?MIC EQU,NS1 #EAI @1 #ABA-EBB
@1 #EBD-EBE
US+ LOG>I?MIC FUNC;NS1 #EJJ @1 #ABA-EJE
US+ MAPP+ DIAGRAMS1 #GB @1 #GC @1 #GG
US+ NATURAL BASE FUNC;NS1 #DID @1 #ABA
@1 #DIG-DIH
NORMAL 4TRIBU;N1 #GEG-GFB
US+ A NUMB] L9E1 #B @1 #DA-EA @1 #EC @1
#ABA @1 #EF @1 #CJC @1 #EII @1 #IGE
OP],NS ON SETS1 #GAE-GAF
US+ P>AMETRIC EQU,NS1 ,A#BC
P5DULUM P]IODS1 #DDG
) P[] FUNC;NS1 #ECB-ECC @1 #ABA @1 #EDB
US+ QUADRATIC EQU,NS1 #BED @1 #ABA-BEH
@1 #BFA @1 #BFB @1 #BFD-BFE
US+ QUADRATIC FUNC;NS1 #CJH @1 #ABA
,#CAD
US+ QUADRATIC 9EQUALITIES1 #CJC @1
#ABA-CJG
US+ QUADRATIC REGRES.N1 #CJH ,#CAA
US+ QUADRATIC SY/EMS1 #FFJ @1 #ABA-FFD
US+ R,NAL EQU,NS1 #EHI @1 #ABA-EIG
US+ R,NAL EXPRES.NS1 #EGD @1 #ABA-EHJ
R1L NUMB]S1 #B
REL,NS1 #GB
US+ SCATT] PLOTS1 #AAB-ABJ
) S9E FUNC;NS1 #IAJ @1 #IAC-IAD
-----------------------------------#AJIG
SOLU;NS
6ABSOLUTE VALUE EQU,NS1 #EJ
6ABSOLUTE VALUE 9EQUALITIES1 #ABA @1 #EC
@1 #ED @1 #EF
6L9E> 9EQUALITIES1 #DA @1 #DC @1 #DE
,#DI
) TANG5T FUNC;NS1 #IAH @1 #IBA
US+ TREE DIAGRAMS1 #FHB @1 #FHF @1 #GBJ
@1 #ABA
) TRIGONOMETRIC FUNC;NS1 #HGJ @1
#ABA-HGB @1 #IDA-IDH @1 #IFG
US+ ,V5N DIAGRAMS1 #B @1 #DCJ @1 #FIH @1
#GJF-GJH @1 #GAE-GAF @1 #AJJD
US+ A V]BAL MODEL1 #AC @1 #AI @1 #BJ @1
#BI @1 #CD @1 #CE @1 #CF @1 #DB @1 #ED
@1 #FC @1 #AJJ @1 #AJA @1 #ACD @1 #AEE
@1 #AFB @1 #AHA @1 #BCI @1 #BED @1
#BFA @1 #BFB @1 #CEF @1 #CGC @1 #CHI
@1 #EFJ @1 #ABA @1 #HBI
V]TICAL MO;N1 #BIE @1 #BIH
.,MONOMIAL @1 .,SEE .AL ,POLYNOMIAL7;S71
#ABA @1 #IHE
.,MOORE'S .LAW @1 #EDG
.,MULTIPLES @1 #IGH
.,MULTIPLE .*OICE ."QS
EXAMPLES1 #C @1 #AI @1 #CF @1 #HB @1
#ACB @1 #AEE @1 #AFB @1 #BFH @1 #BHF
@1 #CCB @1 #CCI @1 #CEE @1 #CFE @1
#DCJ @1 #DEC @1 #EJH @1 #EAH @1 #EGE
@1 #ABA @1 #FAD @1 #FBG @1 #GJH @1
#GAG @1 #GDE @1 #GFI @1 #HJE @1 #HBA
@1 #HEC @1 #HGG @1 #ICC @1 #IEF
PRACTICE1 ..,"?\T4 ,SEE = .EXAMPLE #F1
#AD @1 #BD @1 #CJ @1 #CG @1 #CH @1 #DE
@1 #DF @1 #EF @1 #GG @1 #HF @1 #HG @1
#IC @1 .#AJA ,#AJI
.,MULTIPLE .REPRES5T,NS @1 .,SEE .AL
,MANIPULATIVES2 ,MODEL+
EXAMPLES1 #CE @1 #DH @1 #EC @1 #AJE @1
#AJG @1 #AAE @1 #ACD @1 #AEC @1 #AFA
@1 #BAH @1 #BCI @1 #BGB @1 #BHE @1
#BIB @1 #BIC @1 #CDJ @1 #CFJ @1 #CIF
@1 #DDJ @1 #DEE @1 #DFJ @1 #DHJ @1
#DHH @1 #EBC @1 #ECJ @1 #EEB @1 #EFJ
@1 #EFG @1 #EIA @1 #EIF @1 #FCE @1
#FCF @1 #FDJ @1 #FEA @1 #FEB @1 #FEI
@1 #GAD @1 #GBJ @1 #GBD @1 #GHA @1
#GIE @1 #HCD @1 #HEE @1 #HHD @1 #HIE
@1 #IAJ @1 #ICA @1 #ICD @1 #ICH @1
#IEH
EX]CISES1 #AE @1 #BD @1 #CI @1 #EG @1
#IE @1 #AJD @1 #AAI @1 #ABI @1 #AEG @1
#AGC @1 #BAF @1 #BDB @1 #BEH @1 #BIJ
@1 #CJF @1 #CAD @1 #CDC @1 #CFG @1
#CIB @1 #DCD @1 #DEA @1 #DHE @1 #EBA
@1 #EFB @1 #EGJ @1 #FCA @1 #FDG @1
#GJC @1 #GBI @1 #GED @1 #GGI @1 #HJH
@1 #HAF @1 #HEG @1 #HHG @1 #IAD @1
#IBI @1 #ICG
.,MULTIPLIC,N
( -PLEX NUMB]S1 #BGG-BGH @1 #BHJ
CROSS MULTIPLY+1 #EHI-EIJ
( DATA 0A 3/ANT1 #GEB-GEE @1 #GHC @1
#GHE
( FUNC;NS1 #DBI-DCE
9EQUALITIES &1 #DB-DG
9TEG]1 #IGE
MATRIX1 #AIE-BJB
Z OPPOSITE ( DIVI.N1 #D
( POLYNOMIALS1 #CDG-CEB @1 #DJC
PROP]TIES1 #C ,#AH
= MATRICES1 #AIG
( R,NAL EXPRES.NS1 #EGE-EHJ @1 #FJB @1
#FJE
SCAL>1 #AHH-AIB
..,MULTIPLIC,N PROP]TY ( .EQUAL;Y @1 #AH
.,MULTIPLICATIVE .9V]SE @1 #D
(A -PLEX NUMB]1 #BHJ
.,MULTI-./EP .PRO#MS
EXAMPLES1 #BI @1 #HE @1 #IA @1 #ACD @1
#AGJ @1 #AHI @1 #BJF @1 #BAC @1 #BCI
@1 #BFB @1 #CAA @1 #CDJ @1 #CGC @1
#CIF @1 #DBI @1 #DCA @1 #DCI @1 #DDG
@1 #DHJ @1 #DHH @1 #DID @1 #EFJ @1
#EFG @1 #EGD @1 #FAF @1 #FCF @1 #FDD
@1 #FED @1 #FIA @1 #GBJ @1 #GIE @1
#HBI @1 #HFB @1 #HIA ,#IEA
EX]CISES1 #H @1 #BC @1 #CB @1 #CI @1 #DG
@1 #EG @1 #GH @1 #HH @1 #IE @1 #AJC @1
#ACG @1 #AHD @1 #BJJ @1 #BJI @1 #BAF
@1 #BEJ @1 #BEG @1 #BIH @1 #CJG @1
#CAD @1 #CCE @1 #CDD @1 #CEA @1 #CEH
@1 #CGF @1 #DAH @1 #DCC @1 #DDD @1
#DEH @1 #DHD @1 #DIA @1 #DIG @1 #EJE
@1 #ECE @1 #EEF @1 #EGJ @1 #EHJ @1
#FAI @1 #FBE @1 #FCA @1 #FDG @1 #FFC
@1 #FHH @1 #FIF @1 #GAB @1 #GDH @1
#GFA @1 #HJJ @1 #HFD @1 #HGB @1 #HHH
@1 #HIC @1 #IBA @1 #IED @1 #IFA
.,MUTU,Y .EXCLUSIVE .EV5TS @1 #GJG
;,N
.,NATURAL .BASE .;E @1 #DIB
.,NATURAL .BASE .EXPRES.N @1 #DIB-DIC @1
#ABA-DIF
.,NATURAL .BASE .FUNC;N @1 #DIC-DIH
.,NATURAL .LOG>I?M @1 #EJJ
*ANGE-(-BASE =MULA &1 #ABA-EJI ,#EAA
.,NEGATIVE .ANGLE .ID5TITIES @1 #IBD
.,NEGATIVE .CORREL,N @1 #AAC @1 #AAD
,#AAG
.,NEGATIVE .EXPON5T .PROP]TY @1 #CCJ
.,NEGATIVE .NUMB] @1 SQU>E ROOT (1 #ABA
..,NEWTON'S LAW ( .COOL+ @1 #EAF
.,NORMAL .CURVE @1 #GEG
.,NORMAL .4TRIBU;N @1 #GEG-GFB @1 #GHC
@1 #ABA
.N? .ROOT @1 #DAD
EVALUAT+1 #DAD-DAI @1 #DFF
.,NUMB] .L9E @1 #B
6ADD 9TEG]S1 #IGE
= GRAPH+ ABSOLUTE VALUE1 #EJ @1 #EA
= GRAPH+ ABSOLUTE VALUE EQU,NS1 #EJ
= GRAPH+ ABSOLUTE VALUE 9EQUALITIES1 #EJ
@1 #EC @1 #ED @1 #EF
= GRAPH+ L9E> 9EQUALITIES1 #DA-DI
= GRAPH+ QUADRATIC 9EQUALITIES1 #CJC
R1L NUMB]S ON1 #B
6%[ CRITICAL .;X- VALUES1 #EII
6SUBTRACT 9TEG]S1 #IGE
.,NUMB]S
ABSOLUTE VALUE (1 #EJ @1 #EA
CLASSIFY+1 #B
-PLEX1 #BGF
-POSITE1 #IGH
IMAG9>Y1 #BGF
9TEG]S1 #B @1 #IGE
IRR,NAL1 #B
P5TAGONAL1 #CID
PRIME1 #IGH-IGI
PURE IMAG9>Y1 #BGF
R,NAL1 #B
R1L1 #B
TRIANGUL>1 #CID
TRIANGUL> PYRAMIDAL1 #CIE
:OLE1 #B
.,NUM]ICAL .EXPRES.N @1 #AJ-AG @1 #FJ
,O
.,OBJECTIVE .FUNC;N @1 #AGD
.,ODD .FUNC;N @1 #IBH
.,O4S @1 =& AG/ AN EV5T1 #FII-GJJ @1
#GJB-GJC
.,OHM'S .LAW @1 #GDI
.,ONL9E .,QUIZ @1 ..,"?\T4 ,SEE =
.EXAMPLE #I1 #AF @1 #BD @1 #CB @1 #DJ
@1 #DG @1 #EH @1 #GI @1 #HH @1 #IF @1
#AJD @1 #AAA @1 #ABJ @1 #ABI @1 #ACH
.,OP5-.5D$ .PRO#MS @1 #F @1 #AD @1 #CB
@1 #DE @1 #HG @1 #ID @1 #AJC @1 #AAJ
@1 #AAH @1 #ABG @1 #ACF @1 #AEG @1
#AFE @1 #AHC @1 #AIA @1 #BJJ @1 #BJH
@1 #BAE @1 #BEJ @1 #BEG @1 #BGJ @1
#BHJ @1 #BHI @1 #BIG @1 #CJE @1 #CAC
@1 #CCD @1 #CDB @1 #CGE @1 #CHD @1
#CIA @1 #CIH @1 #DAG @1 #DBE @1 #DCC
@1 #DDC @1 #DEF @1 #DHC @1 #DIJ @1
#DIF @1 #EAA @1 #EBJ @1 #EEF @1 #EFB
@1 #EFI @1 #EIC @1 #FAG @1 #FCJ @1
#FCH @1 #GAA @1 #GBB @1 #GBH @1 #GDH
@1 #HAE @1 #HBD @1 #HCA @1 #HGH @1
#IAC
.,OR .RULE @1 #AJJJ-AJJA
.,ORD] .( .OP],NS @1 #AJ-AG
= MATRICES1 #AHH
.,ORD]$ .PAIR @1 #IHG
.,ORD]$ .TRIPLE @1 #AGG ,#AGH
-----------------------------------#AJIH
.,ORD]+ @1 R1L NUMB]S1 #C @1 #F
.,ORIG9 @1 9 A COORD9ATE PLANE1 #IHG
.,\TCOME @1 #FIH
.,\TLI] @1 #GDF @1 #GDG
.,OV]LAPP+ .EV5TS @1 #GJG @1 #GCC @1
#GCF
;,P
.,P>ABOLA @1 #BCF
AXIS ( SYMMETRY (1 #BCF @1 #FBJ
DIRECTRIX (1 #FBJ
E35TRIC;Y (1 #FFE-FFF
EQU,N (1 #FBA-FBE @1 #FFH @1 #FGJ
TRANSLAT$1 #FEJ-FEG
FOCAL L5G? (1 #FBD
FOCUS (1 #FBJ
GRAPH (1 #FBJ-FBE @1 #FFH @1 #FGJ
Z GRAPH (A QUADRATIC FUNC;N1 #BCF-BDC
LATUS RECTUM (1 #FBE
V]TEX (1 #BCF @1 #FBJ
.,P>ALLEL .L9ES
EQU,NS =1 #II ,#AJB
SLOPE (1 #HD-HF
.,P>AMET]S @1 ,A#G-,A#H1 ,A#BB
.,P>AMETRIC .EQU,NS @1 ,A#BB-,A#BC
.,P>5T .FUNC;N
= ABSOLUTE VALUE FUNC;NS1 #ABA ,#ABC
= COS9E FUNC;NS1 #IJH
= CUBE ROOT FUNC;NS1 #DDF ,#DFE
= EXPON5TIAL DECAY FUNC;NS1 #DHF
= EXPON5TIAL GR[? FUNC;NS1 #DGH
= L9E> FUNC;NS1 #HI
= LOG>I?MIC FUNC;NS1 #EJB
= QUADRATIC FUNC;NS1 #BCF
= SIMPLE R,NAL FUNC;NS1 #EEH
= S9E FUNC;NS1 #IJH
= SQU>E ROOT FUNC;NS1 #DDF ,#DFE
.,"PIAL .SUM @1 #HBJ
.,PASCAL @1 ,BLAISE1 #FIB
.,PASCAL'S .TRIANGLE @1 #FIB @1 #FIE
BINOMIAL EXPAN.N &1 #FIC @1 #FIE
.,PATT]N7.;S7
EX]CISES1 #H @1 #CEJ @1 #EAB @1 #FIE
EXPON5TIAL FUNC;N MODELS &1 #EBI-ECA
FACTOR+1 #CED
6MAKE A G5]ALIZ,N1 #BHC
,PASCAL'S TRIANGLE1 #FIB @1 #FIE
P[] FUNC;N MODELS &1 #ECA-ECC
PRODUCT PATT]NS = BINOMIALS1 #CDG
.,P5TAGONAL .NUMB]S @1 #CID
.,P]C5T
CALCULAT+ )1 #IGG
DECR1SE1 #DHH-DHI
FRAC;NS1 DECIMALS1 &1 #IGF
9CR1SE1 #DHJ-DHA @1 #DHC-DHE
.,P]FECT .SQU>E @1 #BHD
.,P]FECT .SQU>E .TRINOMIAL @1 #BEC
.,P]IMET] @1 #IIA
.,P]IOD @1 (A FUNC;N1 #IJH @1 #IJI
.,P]IODIC .FUNC;N @1 .,SEE .AL ,COS9E
FUNC;N2 ,S9E FUNC;N1 #IJH
FREQU5CY (1 #IAJ
.,P]MUT,N7.;S7 @1 #FHD-FHI @1 #GCC @1
#GCD-GCE
CIRCUL>1 #FHI
=MULA1 #FHE
PROBABIL;Y &1 #FII @1 #GJB
) REPETI;N1 #FHE-FHI
.,P]P5DICUL> .BISECTOR @1 #FAE-FAI
.,P]P5DICUL> .L9ES
EQU,NS =1 #II ,#AJB
SLOPE (1 #HD-HF
.,PIECEWISE .FUNC;N @1 #ACJ-ACA
.,PO9T .4CONT9U;Y @1 #EGI
.,PO9T-.SLOPE .=M @1 #IH-II @1 #AJA @1
#ADJ @1 #ABA @1 #ECB
.,POL>
AXIS1 ,A#D
COORD9ATES1 ,A#D-,A#F
.,POLYNOMIAL7.;S7 @1 #CCG
A4+1 #CDF-CEB @1 #DJC
DIVID+1 #CFB-CFH
R,NAL EXPRES.NS1 #EGF-EGG
FACTOR+1 #CEC-CEI @1 #CFD-CFH @1 #DJD
0GR\P+1 #CED @1 #CEG
MULTIPLY+1 #CDG-CEB ,#DJC
R,NAL EXPRES.NS1 #EGE-EGF
9 QUADRATIC =M1 #CEE @1 #CEG
SUBTRACT+1 #CDF-CEB @1 #DJC
!OREMS 9VOLV+1 #CFC @1 #CFD @1 #CGI
.,POLYNOMIAL .EQU,N7.;S7
FACTOR+1 #CEC-CEI @1 #CFD-CFH @1 #DJD
SOLV+1 #CEE-CEI @1 #DJD
.,POLYNOMIAL .FUNC;N7.;S7 @1 #CCG
CLASSIFY+ Z]OS (1 #CHA-CHB @1 #CHD @1
#ABA
DEGREE (1 #CCG ,#CCI
,DESC>TES' ,RULE ( ,SIGNS &1 #ABA-CHB @1
#CHD @1 #CHE
5D 2HAVIOR (1 #CCF @1 #CCI-CDD
EVALUAT+1 #CCH-CDD @1 #DJB @1 #DJC
0SYN!TIC SUB/ITU;N1 #CCH
F9D+ Z]OS (1 #CGJ-CGH @1 #CGI-CHF @1
#ABA @1 #DJE
FUNDA;TAL !OREM ( ALGEBRA &1 #CGI-CHF @1
#DJE
GRAPH+1 #CCF @1 #CDJ @1 #CDB-CDD @1
#CHG-CIB @1 #DJA @1 #DJC @1 #DJF
L1D+ COE6ICI5T (1 #CCG
MAXIMUM (1 #CHH-CIB
M9IMUM (1 #CHH-CIB
/&>D =M (1 #CCG
TURN+ PO9TS (1 #CHH @1 #CIJ
TYPES (1 #CCG
WRIT+1 #CHA @1 #CHD @1 #CHF @1 #CIC-CII
@1 #DJF
.,POLYNOMIAL .L;G .DIVI.N @1 #CFB-CFH
.,POPUL,N @1 #GFF
.,POSITIVE .CORREL,N @1 #AAC @1 #AAD
,#AAG
.,P[] .FUNC;N7.;S7 @1 #DBH-DCE
9V]SE1 #DDJ-DDE
MODEL+ )1 #ECB-ECC @1 #ECE @1 #ECH @1
#ABA
WRIT+1 #ECA-ECE
..,P[] (A P[] .PROP]TY @1 #CCJ @1 #DAD
@1 #ABA
..,P[] (A PRODUCT .PROP]TY @1 #CCJ @1
#DB ;,C
..,P[] PROP]TY ( .LOG>I?MS @1 #EJG
..,P[] ( QUOTI5TS .PROP]TY @1 #CCJ @1
#DB ;,C
.,P[] .REGRES.N @1 #ECC @1 #ECE
.,P[]S @1 .,SEE .AL2 ,EXPON5T7;S72
,EXPON5TIAL FUNC;N7;S7
(A BINOMIAL DI6];E1 #FIC @1 #FIE
(A BINOMIAL SUM1 #FIC-FIE
COE6ICI5T (1 #AB
EVALUAT+1 #AJ-AG
.,PRACTICE @1 ,SEE ,REVIEWS
.,PRECI.N @1 SIGNIFICANT DIGITS &1 #IHC
.,PREDIC;N
US+ DIRECT V>I,N1 #AJH ,#AAJ
EX]CISES1 #AE @1 #AJD @1 #AAJ @1 #AAB @1
#AEH @1 #CJH @1 #CDD @1 #DCG @1 #ECE
@1 #EEJ @1 #FCA @1 #GGD
US+ EXPON5TIAL DECAY MODELS1 #ABA-DIA
US+ EXPON5TIAL GR[? MODELS1 #ABA @1
#DHC-DHE
US+ EXPON5TIAL REGRES.N1 #ECJ
US+ AN 9V]SE FUNC;N1 #DDB
US+ L9E ( FIT1 #AAF-ABJ
US+ RATE ( *ANGE1 #HE
US+ REGRES.N1 #CIF
.,PREMISE @1 #AJJJ-AJJA
.,PREREQUISITE .,SKILLS @1 XXIV1 #GJ @1
#AEJ @1 #BCD @1 #ABA @1 #DAB @1 #DGF
@1 #EDH @1 #FAB @1 #FHJ @1 #ABA @1
#GIB @1 #HEJ @1 #IJF
.,PRIME .FACTORIZ,N @1 #IGH-IGI
.,PRIME .NUMB] @1 #IGH-IGI
.,PROBABIL;Y
BINOMIAL1 #GFC-GFE
BINOMIAL 4TRIBU;N &1 #ABA-GCA @1 #GCC @1
#GCF
-B9,NS &1 #FII @1 #GJB @1 #GCC ,#GCE
(! -PLE;T ( AN EV5T1 #ABA-GAC
( -P.D EV5TS1 #GJG-GAC
3DI;NAL1 #GAH-GBC
( DEP5D5T EV5TS1 #GAH-GBC @1 #GCC @1
#ABA
4CRETE R&OM V>IA#1 ,A#BJ
( 4JO9T EV5TS1 #GJG
EV5T1 #FIH
EXPECT$ VALUE1 ,A#BJ-,A#BA
EXP]I;TAL1 #GJJ @1 #GJB @1 ,A#AF
=MULAS1 #FIH ,#AJBH-AJBI
FREQU5CY1 ,A#BJ-,A#BA
FUNDA;TAL C.T+ PR9CIPLE1 #ABA ,#FHD-FHI1
#GCD-GCE
GEOMETRIC1 #GJA @1 #GJC @1 #GJD
( 9DEP5D5T EV5TS1 #GAG-GAI @1 #ABA-GBC
@1 #GCC @1 #GCF
-----------------------------------#AJII
( MUTU,Y EXCLUSIVE EV5TS1 #GJG
NORMAL 4TRIBU;N &1 #GEG-GFB
O4S &1 #FII-GJJ @1 #GJB-GJC
\TCOME1 #FIH
( OV]LAPP+ EV5TS1 #GJG @1 #GCC @1 #GCF
P]MUT,N &1 #FII @1 #GJB @1 #GCC @1
#ABA-GCE
R&OM V>IA#1 ,A#BJ-,A#BA
SAMPLE SPACE1 ,A#BJ
/&>D NORMAL TA# &1 #ABA-GFB
!ORETICAL1 #FIH @1 ,A#AF
TRIALS1 ,A#AG
,V5N DIAGRAMS &1 #FIH @1 #GJF-GJH
.,PROBABIL;Y .4TRIBU;N @1 #GBD
BINOMIAL1 #GBE-GCA
SKEW$1 #GBG @1 #GBH
SYMMETRIC1 #GBG @1 #GBH
.,PRO#M .SOLV+ ./RATEGIES @1 .,SEE .AL
,ELIM9ATE *OICES2 ,PRO#M ,SOLV+ ,"W%OP
DRAW A DIAGRAM1 #CE @1 #CG-CI
DRAW A GRAPH1 #DI @1 #BGC
USE A =MULA1 #CD @1 #CG-CI
GUESS1 *ECK1 & REVISE1 #IIH-III
9T]PRET A DIAGRAM1 #FJH @1 #FJI @1 #FAJ
LOOK =A PATT]N1 #CE ,#CG-CI
MAKE A LI/1 #IIH-III
MAKE A TA#1 #DH-DI @1 #BGB-BGC @1
#IIH-III
SOLVE A SIMPL] PRO#M1 #IIH-III
USE A V]BAL MODEL1 #CF-CI
WRITE AN EQU,N1 #CF-CI
.,PRO#M .,SOLV+ .,"W%OP @1 #DH-DI @1
#AJE @1 #BAH-BAI @1 #BGB-BGC @1
#CFJ-CFA @1 #DFJ-DFA @1 #EBC-EBE @1
#EIF-EIG @1 #FDJ @1 #GAD @1 #GHA @1
#HCD-HCE @1 #HIE @1 #ICH-ICI
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( SQU>E ROOTS1 #BFF
.,PRO( @1 ,SEE .AL ,R1SON+
US+ MA!MATICAL 9DUC;N1 #HCF-HCG
( PROP]TIES ( LOG>I?MS1 #EAA
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( A4I;N1 #C @1 #AH ,#AHH
( DIVI.N1 #AH
= EXPON5TIAL EQU,NS1 #EAE
( EXPON5TS1 #CCJ @1 #DBJ @1 #AJCC @1
#AJCD
( F9ITE DI6];ES1 #CID
( FUNC;NS1 #AJCD
9V]SE1 #C @1 #EJA
= LOG>I?MIC EQU,NS1 #EAG
( LOG>I?MS1 #EJG ,#AJCD
PRO(S (1 #EAA
( MATRIX OP],NS1 #AHH @1 #AIG ,#AJCC
( MULTIPLIC,N1 #C @1 #AH ,#AIG
( RADICALS1 #AJCD
( R,NAL EXPON5TS1 #DBJ @1 #DFE @1 #AJCD
( R1L NUMB]S1 #B-I ,#AJCC
( SQU>E ROOTS1 #BFF
( SUBTRAC;N1 #AH ,#AHH
Z]O PRODUCT1 #BEC
.,PROPOR;N @1 #IHJ
.,PURE .IMAG9>Y .NUMB] @1 #BGF
.,PY?AGOR1N .ID5TITIES @1 #IBD
.,PY?AGOR1N .!OREM @1 #IIE
US+1 #HEB-HEH @1 #HFF @1 #HIE @1 #HIH
;,Q
.,QUADRANT7.;S7 @1 (A COORD9ATE PLANE1
#ABA
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.,QUADRATIC .EQU,N7.;S7 @1 ,SEE .AL
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) -PLEX SOLU;NS1 #BGF-BHB
4CRIM9ANT IN1 #BID
6MODEL DROPP$ OBJECTS1 #BFH-BGJ @1
#BGB-BGC
6MODEL LAUN*$ OBJECTS1 #BIE ,#BIH
6MODEL V]TICAL MO;N1 #BIE @1 #BIH
ROOTS (1 #BEC
SOLV+
0-PLET+ ! SQU>E1 #ABA-BIA @1 #CAG ,#CBA
0FACTOR+1 #BEB-BFE @1 #CAG @1 #CAI @1
#ABA
0F9D+ SQU>E ROOTS1 #BFF-BGA #BHD1 #CAG
,#CBJ
US+ ! QUADRATIC =MULA1 #ABA-BII @1 #CAG
,#CBA
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SY/EMS (1 #FEH-FFD
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FACTOR+1 #BEB-BEC @1 #BEE-BEF @1
#ABA-BFJ @1 #BFC
.,QUADRATIC .=M @1 (A POLYNOMIAL1 #CEE
#CEG
.,QUADRATIC .=MULA @1 #BIB-BII @1 #CAG
@1 #ABA @1 #ICC
.,QUADRATIC .FUNC;N 7;S7
BE/-FITT+ QUADRATIC MODEL &1 #ABA
GRAPH+
9 9T]CEPT =M1 #BDF-BEA @1 #CAG @1 #ABA
9 /&>D =M1 #BCF-BDC @1 #CAG @1 #ABA
9 V]TEX =M1 #BDE-BDF @1 #BDH-BEA @1 #BHG
@1 #CAG ,#CAI
MAXIMUM VALUE1 #BCH-BCI @1 #BDA @1 #BDD
#BHG
M9IMUM VALUE1 #BCH-BCI @1 #BDA @1 #BDD
P>5T FUNC;N1 #BCF
WRIT+
9 9T]CEPT =M1 #CJI @1 #CAB-CAE @1 #ABA
9 /&>D =M1 #CAJ @1 #CAB-CAE @1 #ABA
9 V]TEX =M1 #CJI @1 #CAB-CAE @1 #CBB
Z]OS (1 #BED-BEF
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CRITICAL .;X- VALUES (1 #CJC
GRAPH+1 #CJJ-CJG @1 #CBB
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.,QUADRATIC .REGRES.N @1 #CJH @1 #CAA
.,QUADRATIC .SY/EM @1 #FEH-FFD @1 #FFH
@1 #FGB
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.,QU>TILE @1 #AJJH-AJJI
..,QUOTI5T ( P[]S .PROP]TY @1 #CCJ ,#DBJ
.,QUOTI5T .PROP]TY
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( SQU>E ROOTS1 #BFF
..,QUOTI5T ( P[]S .PROP]TY @1 #DIE-EJJ
@1 #EDB
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#GBJ-GBF @1 #GEC @1 #GEE
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;,R
.,RADIAN @1 #HFJ
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9DEX (1 #DAD
L1 #DBB
.N? ROOT1 #DAD-DAI
PROP]TIES (1 #DBA-DBG @1 #EJG @1 #AJCD
SIMPLE/ =M1 #DBB
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SOLV+1 #DEB-DFA @1 #DFE @1 #DFH
) TWO RADICALS1 #DEE @1 #DEG
.,RADICAL .FUNC;N @1 GRAPH+1 #DDF-DEA @1
#ABA @1 #DFH
.,RADICAL .9EQUALITIES @1 #DFB-DFC
.,RADICAL .SIGN @1 #BFF
.,RADIC& @1 #BFF
.,RADIUS @1 (A CIRCLE1 #FBF @1 #IIB
.,R&OM .SAMPLE @1 #GFF
.,R&OM .V>IA# @1 #GBD @1 ,A#BJ
.,RANGE
Z AN ABSOLUTE VALUE 9EQUAL;Y1 #ED
DATA1 #GDE-GEJ @1 #GHC @1 #GHD @1 #AJJE
(A FUNC;N1 #GC @1 #DDF-DDG @1 #DGI @1
#DHG
(A REL,N1 #GB
(A SEQU;E1 #GID
TRANS=M,N &1 #GEA-GEE
.,RATE @1 #HE
.,RATE .( .*ANGE
AV]AGE1 #HE @1 #HF
SLOPE &1 #HB-HH @1 #ADB
-----------------------------------#AAJJ
.,RATIO 7;S7
GOLD51 #EID
6ID5TIFY DIRECT V>I,N1 #AJH ,#AJI
P]C5T Z1 #IGF
PROPOR;NS &1 #IHJ
SIMPLE/ =M1 #IHJ
TRIGONOMETRIC1 #HEB-HEH
.,R,NAL .EQU,N @1 #EHI-EIG @1 #FJB @1
#FJF
.,R,NAL .EXPON5T7.;S7 @1 #DAC-DAI @1
#DFE @1 #DFF
EQU,NS )1 #DEC @1 #DEF @1 #DEH-DEI @1
#DFH
PROP]TIES (1 #DBJ-DBG @1 #DFE @1 #DFG @1
#ABA
.,R,NAL .EXPRES.N 7;S71 #IHF
A4+1 #EHB-EHH @1 #FJB @1 #FJE
DIVID+1 #EGF-EHJ @1 #FJB @1 #FJE
L1/ -MON DENOM9ATOR (1 #EHC @1 #IHF
MULTIPLY+1 #EGE-EHJ @1 #FJB @1 #FJE
PO9T 4CONT9U;Y &1 #EGI
SIMPLIFI$ =M (1 #EGC
SIMPLIFY+1 #EGC-EGD @1 #EGG-EHJ @1 #FJB
SUBTRACT+1 #EHB-EHH @1 #FJB @1 #FJE
V]IFY+ OP],NS )1 #EHA
.,R,NAL .FUNC;N 7;S7
GRAPH+
G5]AL1 #EFE-EGA @1 #FJB @1 #FJD
SIMPLE1 #EEH-EFD @1 #FJD
9V]SE V>I,N1 #EEJ-EEG
JO9T V>I,N1 #EEC-EEG
P>5T FUNC;N =1 #EEH
.,R,NAL .9EQUALITIES @1 #EIH-FJJ
.,R,NAL .NUMB]S @1 #B
.,R,NAL .Z]O .!OREM @1 #CGJ
.,R,NALIZ+ .! .DENOM9ATOR @1 #BFG
.,R1DI;S
,PREREQUISITE ,SKILLS1 XXIV1 #GJ @1 #AEJ
@1 #BCD @1 #CBH @1 #DAB @1 #DGF @1
#EDH @1 #FAB @1 #FHJ @1 #GDB @1 #GIB
@1 #HEJ @1 #IJF
,SKILLS ,REVIEW ,H&BOOK1 #IGE-AJJI
.,R1D+
FUNC;N NOT,N1 #GE @1 #DCJ @1 #DCH
GRAPHS1 #GD
L9E> 9EQUALITIES1 #DA
SUBSCRIPTS1 #BF
SUMM,N NOT,N1 #GIF
.,R1D+ .MA? @1 #ED @1 #HC @1 #AGD @1
#BGG @1 #CCI @1 #ABA @1 #HED @1 #HFA
@1 #HFH
.,R1L .NUMB]S
ORD]+1 #C @1 #F
PROP]TIES (1 #B-I @1 #FA ,#AJCC
SUBSETS (1 #B
.,R1SON+
& RULE1 #AJJJ-AJJA
BICONDI;NAL /ATE;T1 #ABA-AJJC
*A9 RULE1 #AJJJ-AJJA
-P.D /ATE;T1 #AJJA
3CLU.N1 #AJJJ-AJJC
VALID1 #AJJJ-AJJA
3DI;NAL /ATE;T1 #AJJB-AJJC
3V]SE1 #AJJB-AJJC
IF-!N =M1 #AJJB-AJJC
C.T]EXAMPLE1 #AJJC
DERIV,NS1 #ICJ @1 #IEG
DIRECT >GU;T1 #AJJJ-AJJA
EX]CISES1 #G @1 #BE @1 #CA @1 #DI @1 #EF
@1 #HG @1 #HH @1 #ID @1 #AJC @1 #AJE
@1 #AAJ @1 #AAG @1 #AAH @1 #ABH @1
#AHC @1 #BAI @1 #BEF @1 #BGC @1 #BHI
@1 #BIG @1 #CCD @1 #CDE @1 #CHD @1
#CHF @1 #CIA @1 #DDC @1 #DEJ @1 #DHE
@1 #DIA @1 #DIG @1 #EJE @1 #EBB @1
#ECA @1 #EEG @1 #EGG @1 #FAH @1 #FCJ
@1 #FCI @1 #FDJ @1 #FDF @1 #FDG @1
#FEF @1 #FFB @1 #FFF @1 #FIE @1 #GJB
@1 #GAD @1 #GAF @1 #GBB @1 #GBC @1
#GDH @1 #GEI @1 #GFA @1 #GGJ @1 #GGA
@1 #HJG @1 #HBC @1 #HCA @1 #HCE @1
#HCG @1 #IBJ @1 #IBC @1 #ICF @1 #IDE
@1 #IDF @1 #IEG @1 #IFJ
HYPO!SIS1 #AJJB-AJJC
HYPO!SIS TE/+1 #GFD-GFE
9DIRECT >GU;T1 #AJJJ-AJJA
9DUCTIVE R1SON+1 #HCF-HCG
OR RULE1 #AJJJ-AJJA
US+ A PATT]N 6MAKE A G5]ALIZ,N1 #BHC
PREMISES1 #AJJJ-AJJA
PRO(
US+ MA!MATICAL 9DUC;N1 #ABA-HCG
= PROP]TIES ( LOG>I?MS1 #EAA
,V5N DIAGRAMS1 #AJJD
.,RECIPROCAL @1 MULTIPLY+ BY1 #D
.,RECIPROCAL .ID5TITIES @1 #IBD
.,RECTANGLE @1 >EA & P]IMET] (1 #IIA
.,RECTANGUL> .PRISM
SURFACE >EA (1 #IIC
VOLUME (1 #CCD @1 #CEJ @1 #IIC
.,RECURSIVE .RULE @1 #HBF @1 #HBG
=A SEQU;E1 #HBF-HCE @1 #HCI @1 #HDB
.,REF];E .ANGLE @1 #HFH @1 #HGA
.,REFLEC;N
ON ! COORD9ATE PLANE1 #IHH-IHI
(! GRAPH (A P>5T FUNC;N
ABSOLUTE VALUE FUNC;N1 #ABD-ABI
COS9E FUNC;N1 #IAG @1 #IBJ
LOG>I?MIC FUNC;N1 #EJB
S9E FUNC;N1 #IAG @1 #IBJ
L9E (1 #IHH-IHI
.,REFRAC;N @1 9DEX (1 #HGI @1 #ICJ
.,REGRES.N
CUBIC1 #CIF
EXPON5TIAL1 #EBH @1 #ECJ
L9E>1 #AAF
P[]1 #ECC @1 #ECE
QUADRATIC1 #CJH @1 #CAA
.,REL,N @1 #GB @1 #ADJ ,#ADA
9V]SE1 #DCH @1 #DDB
.,REMA9D] .!OREM @1 #CFC @1 #DJD
.,REP1T$ .SOLU;N @1 #CGI
.,REP1T+ .DECIMAL @1 #HBB
.,REVIEWS @1 ,SEE ,BIG ,ID1S2 ,*APT]
,REVIEW2 ,*APT] ,SUMM>Y2 ,CUMULATIVE
,REVIEW2 ,MIX$ ,REVIEW2 ,MIX$ ,REVIEW
0LESSON2 ,PREREQUISITE ,SKILLS2
,SKILLS ,REVIEW ,H&BOOK
.,"R .4TRIBUTIVE .PROP]TY @1 #AIG
.,"R .TRIANGLE .TRIGONOMETRY @1 #HEB-HEH
@1 #HIG @1 #HIH
.,ROOT7.;S7 @1 ,SEE .AL ,RADICAL7;S7
EVALUAT+ N? ROOTS1 #DAD-DAI
(A QUADRATIC EQU,N1 #BEC
SQU>E1 #BFF @1 #BGE
.,ROT,N
C5T] (1 #IHH
ON ! COORD9ATE PLANE1 #IHH-IHI
.,R.D+ .FUNC;N @1 #ACA
.,R[ .EQUIVAL5T .MATRICES @1 #BAH
.,R[ .OP],NS @1 #BAH-BAI
;,S
.,SAMPLE 7;S7
BIAS$1 #GFG
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SELECT+1 #GFF
SIZE (1 #GFH
SPACE1 ,A#BJ
.,SAMPL+ @1 #GFF-GGA @1 #GHC @1 #GHF
,,SAT1 ,SEE ,/&>DIZ$ ,TE/ ,PRACTICE
.,SCAL> @1 #AHH
.,SCAL> .MULTIPLIC,N @1 #AHH-AIB
.,SCALE .FACTOR @1 #IHI
.,SCATT] .PLOT @1 #AAC-ABJ ,#ADC
.,SCI;E @1 ,SEE ,APPLIC,NS ,SCI5TIFIC
NOT,N1 #CCA @1 #IHB
PROP]TIES ( EXPON5TS &1 #CCA @1 #ABA
,#CCD
.,SECANT .FUNC;N @1 ,SEE .AL
,TRIGONOMETRIC FUNC;N7;S7
EVALUAT+ = ANY ANGLE1 #HFF-HGB
EVALUAT+ = "R TRIANGLES1 #ABA-HEH
.,SECOND-.ORD] .DI6];ES @1 #CID
.,SECTOR @1 #HFA
>C L5G?1 #HFA-HFE
>EA1 #HFA-HFE
C5TRAL ANGLE (1 #HFA
.,SELF-.SELECT$ .SAMPLE @1 #GFF
.,SEQU;E7.;S7 @1 #GID @1 #HCI
>I?METIC1 #HJB-HJI @1 #HCI @1 #HDA
F9ITE1 #GID
=MULAS F1 #AJBI-AJCJ
GEOMETRIC1 #HAJ-HAF @1 #HCI @1 #HDA
GRAPH+1 #GIE @1 #GIH @1 #HJJ @1 #HJA
-----------------------------------#AAJA
9F9ITE1 #GID
PATT]NS &1 #GID-GIE @1 #GIG-HJA
RECURSIVE RULES &1 #HBF-HCE @1 #HCI @1
#HDB
T]MS (1 #GID
WRIT+ RULES =1 #GIE @1 #GIH @1 #GII-HJJ
.,S]IES
>I?METIC1 #HJD-HJI @1 #HCI @1 #HDA
F9ITE1 #GIF
=MULAS F1 #GIG ,#AJBI-AJCJ
GEOMETRIC1 #HAB-HAG @1 #HCI @1 #HDA
9F9ITE1 #GIF
9F9ITE GEOMETRIC1 #HAI-HBE @1 #HCI ,#HDB
SUMM,N NOT,N &1 #GIF-HJJ
.,SET .!ORY @1 #GAE-GAF
.,%ORT .RESPONSE .PRACTICE @1 ..,"?\T4
,SEE = .EXAMPLE #I1 #AE @1 #BC @1 #CA
@1 #CG @1 #CH @1 #EE @1 #GG @1 #GH @1
#HG @1 #ID @1 #IE @1 #AJC
.,%R9K @1 (! GRAPH (! P>5T ABSOLUTE
VALUE FUNC;N1 #ABD-ABI
.,SI]P9SKI .C>PET @1 #HAF
.,SI]P9SKI .TRIANGLE @1 #HBE
.,SIGMA .NOT,N @1 #GIF
.,SIGNIFICANT .DIGITS @1 #CDH @1 #IHC
.,SIMIL> .FIGURES @1 #IIF-IIG
.,SIMPLE/ .=M .RADICAL @1 #DBB
.,SIMUL,N @1 #GAD
US+ R&OM NUMB]S1 #GAD
.,S9E .FUNC;N @1 ,SEE .AL ,TRIGONOMETRIC
EQU,N 7;S72 ,TRIGONOMETRIC FUNC;N7;S7
DI6];E =MULA =1 #IDI
US+1 #IDI-IED
D\#-ANGLE =MULA =1 #IEE
US+1 #IEE-IFB
EVALUAT+ = ANY ANGLE1 #HFF-HGB
EVALUAT+ = "R TRIANGLES1 #ABA-HEH
GRAPH+1 #HGD @1 #IJH-IAD @1 #IFD @1 #IFE
REFLEC;NS1 #IAG @1 #IBJ
TRANSL,NS1 #IAE-IAG @1 #IAI-IBB @1 #ABA
HALF-ANGLE =MULA =1 #IEE
US+1 #IEE-IFB
9V]SE (1 #HGD-HGI @1 #HIG @1 #HII
S9USOIDS1 &1 #IDA-IDH
SUM =MULA =1 #IDI
.,S9ES @1 LAW (1 #HHA-HHH @1 #HIG @1
#IJJ
.,S9USOIDAL .REGRES.N @1 #IDC
.,S9USOIDS @1 #IDA-IDH @1 #IFG
.,SIXTY-.DEGREE .ANGLE @1 TRIGONOMETRIC
VALUES =1 #HEC
.,SKEW$ .4TRIBU;N @1 #GBG @1 #GBH
.,SKILLS .,REVIEW .,H&BOOK @1 #IGE-AJJI
ALGEBRA REVIEW
BINOMIAL PRODUCTS1 #IHE
EXPRES.NS1 #IHD
GEOMETRY
ANGLE REL,N%IPS1 #IID
3GRU5T FIGURES1 #IIF-IIG
COORD9ATE PLANE1 #IHG
L9E SYMMETRY1 #IIJ
SIMIL> FIGURES1 #IIF-IIG
TRANS=M,NS1 #IHH-IHI
TRIANGLE REL,N%IPS1 #IIE
LOGICAL R1SON+
3DI;NAL /ATE;TS1 #ABA-AJJC
C.T]EXAMPLES1 #AJJC
LOGICAL >GU;T1 #AJJJ-AJJA
,V5N DIAGRAMS1 #AJJD
M1SURE;T
>EA1 #IIA
>EA (A CIRCLE1 #IIB
CIRCUMF];E (A CIRCLE1 #IIB
3V]T+ UNITS (1 #IHA
P]IMET]1 #IIA
SURFACE >EA1 #IIC
VOLUME1 #IIC
NUMB] S5SE
FACTORS & MULTIPLES1 #IGH-IGI
FRAC;NS1 DECIMALS1 & P]C5TS1 #IGF
9TEG]S1 OP],NS )1 #IGE
L1/ -MON DENOM9ATORS1 #IHF
P]C5T1 CALCULAT+ )1 #IGG
RATIOS & PROPOR;NS1 #IHJ
SCI5TIFIC NOT,N1 #IHB
SIGNIFICANT DIGITS1 #IHC
PRO#M SOLV+ /RATEGIES1 #ABA-III
/ATI/ICAL DATA
GRAPH+1 #AJJF-AJJG
M1N1 M$IAN1 MODE1 & RANGE1 #AJJE
ORGANIZ+1 #AJJH-AJJI
.,SLOPE @1 #HB
( BE/-FITT+ L9ES1 #AAD-ABJ
CLASSIFY+ L9ES BY1 #HC
RATE ( *ANGE &1 #HB-HH @1 #ADB
.,SLOPE-.9T]CEPT .=M @1 #IJ-IG @1 #IH @1
#AJJ @1 #ABA @1 #ADB
.,SNELL'S .LAW @1 #ICJ
.,SOLU;N7.;S7
( AN ABSOLUTE VALUE EQU,N1 #EJ
( AN ABSOLUTE VALUE 9EQUAL;Y1 #EJ
( AN EQU,N1 #AH
EXTRANE\S1 #EB @1 #DED @1 #EAH @1 #EIA
@1 #ICD
(A L9E> 9EQUAL;Y 9 TWO V>IA#S1 #ACB
(A POLYNOMIAL FUNC;N1 #CGI @1 #CHG
(A QUADRATIC EQU,N1 #BEC @1 #BID
(A SY/EM ( L9E> EQU,NS1 #ABA ,#AEC
9 ?REE V>IA#S1 #AGH
(A SY/EM ( L9E> 9EQUALITIES1 #ABA
..,SOLVE A SIMPL] .PRO#M @1 PRO#M SOLV+
/RATEGY1 #IIH-III
.,SPECIAL .PATT]NS @1 FACTOR+ )1 #BEC @1
#ABA @1 #BFJ
.,SPR1D%EET
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USE ! ,LOC,N ,PR9CIPLE1 #CGH
.,SQU>E 7;S7
(A BINOMIAL1 #CDG
DI6];E ( TWO1 #CEC
.,SQU>E .ROOT7.;S7 @1 #BFF
IMAG9>Y UNIT .;I &1 #BGE @1 #CAG
(A NEGATIVE NUMB]1 #BGE
PROP]TIES (1 #BFF
Z SOLU;NS 6QUADRATIC EQU,NS1 #BFG-BGA @1
#CAG @1 #CBJ
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GRAPH+1 #DDF-DEA @1 #DFE @1 #DFH
P>5T1 #DDF @1 #DFE
.,/&>D .DEVI,N @1 #GDE-GEJ @1 #GHC @1
#GHD
TRANS=M,N &1 #GEA-GEE
.,/&>D .=M
(A -PLEX NUMB]1 #BGF
(A L9E> EQU,N1 #IA-IF ,#ADJ
(A NUMB]1 #IHB
(A POLYNOMIAL FUNC;N1 #CCG
(A QUADRATIC EQU,N1 #BEC
(A QUADRATIC FUNC;N1 #BCF-BDC @1 #ABA
,#CAH
.,/&>D .NORMAL .4TRIBU;N @1 #GEH-GFB
=MULA1 #GEH
.,/&>D .NORMAL .TA# @1 #GEI
.,/&>D .POSI;N @1 = AN ANGLE1 #HEI
.,/&>DIZ$ .,TE/ .,PRACTICE @1 #FH-FI @1
#ADH-ADI @1 #BCJ-BCA @1 #CBF-CBG @1
#DAJ-DAA @1 #DGB-DGC @1 #EDF-EDG @1
#FAJ-FAA @1 #FGF-FGG @1 #GDJ-GDA @1
#GIJ-GIA @1 #HDF-HDG @1 #IJD-IJE @1
#IGB-IGC
----------------------------------#AAJB
EXAMPLES1 #C @1 #AI @1 #CF @1 #HB @1
#ACB @1 #AEE @1 #AFB @1 #BED @1 #BFH
@1 #BHF @1 #CCB @1 #CCI @1 #CEE @1
#CFE @1 #DEC @1 #EJH @1 #EGE @1 #EIJ
@1 #FAD @1 #FBG @1 #GJH @1 #GAG @1
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EX]CISES1 ..,"?\T4 ,SEE = .EXAMPLE #F1
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#FI @1 #ACI @1 #ADI @1 #AHF @1 #BBJ @1
#BCA @1 #BGD @1 #CAF @1 #CBG @1 #CFI
@1 #DJJ @1 #DAA @1 #DCF @1 #DFD @1
#DGC @1 #EJF @1 #ECG @1 #EDG @1 #EGB
@1 #FJA @1 #FDA @1 #FFG @1 #FGG @1
#GCB @1 #GDA @1 #GHB @1 #HAH @1 #HCH
@1 #HDG @1 #HGC @1 #HIF @1 #IDJ @1
#IFC @1 #IGC
.,/ATI/ICS @1 .,SEE .AL ,DATA2 ,GRAPHS2
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BINOMIAL 4TRIBU;N1 #GFC-GFE
3TROL GR\P1 #GGC
3V5I;E SAMPLE1 #GFF
DIRECT V>I,N1 #AJG-AAA @1 #ADJ ,#ADC
EXP]I;TAL GR\P1 #GGC
EXP]I;TS1 DESIGN+1 #GGB-GGC
=MULAS F1 #AJBI
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M>G9 ( ]ROR1 #GFH-GGA
M1SURES ( C5TRAL T5D5CY1 #GDD-GE ,O1
#GHC @1 #GHD @1 #AJJE
M1SURES ( 4P].N1 #GDD-GEJ @1 #GHC @1
#GHD @1 #AJJE
NEGATIVE CORREL,N1 #AAC @1 #AAD ,#AAG
NORMAL 4TRIBU;N1 #GEG-GFB @1 #GHC @1
#GHE
\TLI]1 #GDF @1 #GDG
P>AMET]1 4T+UI% 2T1 ,A#G-,A#H
POPUL,N1 #GFF
POSITIVE CORREL,N1 #AAC @1 #AAD ,#AAG
R&OM SAMPLE1 #GFF
SAMPL+1 #GFF-GGA @1 #GHC @1 #GHF @1
,A#G-,A#H
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SELF-SELECT$ SAMPLE1 #GFF
SIMUL,NS1 ,A#AD-,A#AE
/&>D DEVI,N1 #GDE-GEJ @1 #GHC @1 #GHD
SURVEYS DESIGN+1 #GGB-GGC
SAMPL+1 #GFF-GGA
SY/EMATIC SAMPLE1 #GFF
TOL].E1 #ED
UNBIAS$ SAMPLE1 #GFG
.,/EM-.&-.L1F .PLOT @1 #AJJH-AJJI
.,/EP .FUNC;N @1 #ACA
.,/RET* @1 (! GRAPH (! P>5T ABSOLUTE
VALUE FUNC;N1 #ABD-ABI
.,SUBSCRIPTS @1 R1D+1 #BF
.,SUBSET @1 #GAF
.,SUB/ITU;N @1 = *ECK+ SOLU;NS1 #AH @1
#AI @1 #BJ @1 #CF @1 #EB @1 #IA @1
#ACC @1 #AEC @1 #AFJ @1 #AGI @1 #BJE
@1 #BFG @1 #BHE @1 #CHA @1 #DEB @1
#DED @1 #DEE @1 #DFH @1 #EAG @1 #EAH
@1 #EIA @1 #ICD
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= EVALUAT+ POLYNOMIAL FUNC;NS1 #CCH
= SOLV+ L9E>-QUADRATIC SY/EMS1 #FEI @1
#FFA @1 #FFB-FFD
= SOLV+ L9E> SY/EMS1 #AFJ-AFG @1
#AHA-AHE @1 #BBA
= SOLV+ QUADRATIC SY/EMS1 #ABA-FFD @1
#FFH @1 #FGB
.,SUBTRAC;N
( -PLEX NUMB]S1 #BGF @1 #BGI
C.T+ PRO#MS &1 #FIA
) FRAC;NS1 #IGI
( FUNC;NS1 #DBH-DCE
9EQUALITIES &1 #DB-DG
9TEG]1 #IGE
MATRIX1 #AHG ,#AHI-AIB1AID
Z OPPOSITE ( A4I;N1 #D
( POLYNOMIALS1 #CDF-CEB @1 #DJC
PROP]TIES1 #AH
= MATRICES1 #AHH
) R,NAL EXPRES.NS1 #EHB-EHH @1 #ABA @1
#FJE
..,SUBTRAC;N PROP]TY ( .EQUAL;Y @1 #AH
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= SPECIAL S]IES1 #GIG
US+1 #IDI-IED @1 #IFH
..,SUM ( TWO .CUBES @1 #CED
.,SUMM,N .NOT,N @1 #GIF-HJJ
.,SUMM+ .RECTANGLES @1 #FDJ
.,SUPPLE;T>Y .ANGLES @1 #IID
.,SURFACE .>EA @1 #IIC
.,SURVEY
DESIGN+1 #GGB-GGC @1 #GHF
PROBABIL;Y &1 #GBF @1 #GBI @1 #GCA
SAMPL+ &1 #GFF-GGA @1 #GHF
.,SYMBOLS
APPROXIMATELY EQUAL TO1 #B
EMPTY SET1 #GAE
FACTORIAL1 #FHD
IMAG9>Y UNIT1 #BGE
9EQUAL;Y1 #EJ @1 #EA
9F9;Y1 #CCF @1 #CCI
M1N1 #GDD
P]C5T1 #IGF
RADICAL SIGN1 #BFF
/&>D DEVI,N1 #GDE
SUBSET1 #GAF
SUMM,N1 #GIF
TA# (1 #AJBD
!TA1 #HEB
!TA PRIME1 #HFH
UNIV]SAL SET1 #GAE
.,SYMMETRIC .4TRIBU;N @1 #GBG @1 #GBH
.,SYMMETRY L9E
(=A 3IC SEC;N1 #FEB @1 #FEE
=A PLANE FIGURE1 #IIJ
.,SYN!TIC .DIVI.N @1 #CFC-CFH
.,SYN!TIC .SUB/ITU;N @1 #CFC
= EVALUAT+ POLYNOMIAL FUNC;NS1 #CCH
..,SY/EM ( L9E> .EQU,NS @1 .,SEE ,L9E>
SY/EMS
..,SY/EM ( L9E> .9EQUALITIES @1 #AFH-AGC
) NO SOLU;N1 #AFI
?REE OR M 9EQUALITIES1 #AGJ-AGC
..,SY/EM ( QUADRATIC .9EQUALITIES1 #CJA
@1 #CJD @1 #CJE
.,SY/EMATIC .SAMPLE @1 #GFF
;,T
.,TA#7.;S7
64PLAY DATA1 #H @1 #I @1 #DG @1 #EG @1
#AJH @1 #AAJ @1 #AAA @1 #AAB @1 #AAE
@1 #AAG @1 #AAH @1 #AAI @1 #ABJ @1
#BJF @1 #DBA @1 #DBF @1 #EEB @1 #EEC
@1 #EGJ @1 #EHJ @1 #GGG @1 #GGI @1
#GHJ @1 #GHA @1 #GHG @1 #HBD @1 #IDF
@1 #IFI @1 #AJJG
6GRAPH CUBE ROOT FUNC;NS1 #DDG
6GRAPH EQU,NS ( P>ABOLAS1 #ABA
6GRAPH EXPON5TIAL DECAY FUNC;NS1 #DHF
6GRAPH EXPON5TIAL GR[? FUNC;NS1 #DGH
6GRAPH L9E> FUNC;NS1 #GE @1 #HJ
6GRAPH POLYNOMIAL FUNC;NS1 #ABA @1
#CDB-CDD
6GRAPH QUADRATIC FUNC;NS1 #BCF @1 #ABA
@1 #BDJ
6GRAPH SQU>E ROOT FUNC;NS1 #DDF
9T]PRET+1 #FJI @1 #FAJ
= NATURAL BASE .;E @1 #DIB
= RECORD+ EXP]I;TAL DATA1 #ABA @1 #HAI
6REPRES5T REL,NS1 #GB
6SOLVE L9E> EQU,NS1 #BE
6SOLVE L9E> SY/EMS1 #AEB
6SOLVE PRO#MS1 EX]CISES1 #AE @1 #BD @1
#CI @1 #IE @1 #AJD @1 #ABI @1 #BIJ @1
#CJF @1 #CAD @1 #CDC @1 #DEA @1 #EGJ
@1 #FDG @1 #GBI @1 #HJH @1 #IAD @1
#IBI @1 #ICG
6SOLVE QUADRATIC 9EQUALITIES1 #CJB
6SOLVE RADICAL 9EQUALITIES1 #DFB
6SOLVE R,NAL 9EQUALITIES1 #EIH
SPR1D%EET1 #HBF
/&>D NORMAL1 #GEI
.,TA#S .( .REF];E
,=MULAS
F ALGEBRA1 #AJBG-AJBH
-----------------------------------#AAJC
F -B9ATORICS1 #AJBH
F COORD9ATE GEOMETRY1 #AJBF
F GEOMETRY1 #AJCB
F MA!MATICAL MODEL+1 #ABA
F MATRIX ALGEBRA1 #AJBF
F PROBABIL;Y1 #AJBH-AJBI
F SEQU;ES & S]IES1 #ABA-AJCJ
F /ATI/ICS1 #AJBI
F TRIGONOMETRY1 #AJCJ-AJCA
,ID5TITIES1 F TRIGONOMETRY1 #ABA-AJCA
,M1SURES1 #AJBE
,PROP]TIES
( EXPON5TS1 #AJCC
( FUNC;NS1 #AJCD
( LOG>I?MS1 #AJCD
( MATRICES1 #AJCC
( RADICALS1 #AJCD
( R,NAL EXPON5TS1 #AJCD
( R1L NUMB]S1 #AJCC
,SYMBOLS1 #AJBD
,!OREMS1 F ALGEBRA1 #ABA-AJBH
.,TANG5T .FUNC;N @1 .,SEE .AL
,TRIGONOMETRIC EQU,N7;S72
,TRIGONOMETRIC FUNC;N7;S7
DI6];E =MULA =1 #IDI
US+1 #IDI-IED
D\#-ANGLE =MULA =1 #IEE
US+1 #IEE-IFB
EVALUAT+ = ANY ANGLE1 #HFF-HGB
EVALUAT+ = "R TRIANGLES1 #ABA-HEH
GRAPH+1 #IAA-IAD @1 #IFE
TRANSL,NS1 #IAH @1 #IBJ @1 #IBA
HALF-ANGLE =MULA =1 #IEE
US+1 #IEE-IFB
9V]SE1 #HGE-HGI @1 #HIG @1 #HII
SUM =MULA =1 #IDI
US+1 #IDI-IED
.,TANG5T .ID5TITIES @1 #IBD
.,TE*NOLOGY @1 .,SEE ,CALCULATOR2
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#ICC
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BINOMIAL !OREM1 #FIC
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FACTOR !OREM1 #CFD
FUNDA;TAL !OREM ( ALGEBRA1 #ABA-CHF @1
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REMA9D] !OREM1 #CFC
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.,?IRD-.ORD] .DI6];ES @1 #CIE
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VALUES =1 #HEC
.,TOL].E @1 #ED
.,TOTAL .CO/ .MATRIX @1 #AIH
.,T[] .( .,HANOI @1 #HJJ
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DATA &1 #GEA-GEE
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MULTIPLE1 #ABE-ABI
( P[] DATA1 #ECB
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(! GRAPH (A P>5T FUNC;N ABSOLUTE VALUE1
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COS9E1 #IAE-IAG @1 #IAI-IBB @1 #IFF
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LOG>I?MIC1 #EJC
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HORIZONTAL1 #IAF
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= FACTOR+ NUMB]S1 #IGH
= F9D+ PROBABIL;Y1 #GBJ
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,,AAS1 #HHB
AMBIGU\S CASE1 #HHC-HHD
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,,ASA1 #HHB
CLASSIFY+1 US+ ! 4T.E =MULA1 #FAD-FAE @1
#FAG
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M$IAN (1 #FAH
P]IMET] (1 #IIA
"R1 TRIGONOMETRY &1 #HEB-HEH @1 #ABA
,,SAS1 #HHI
,,SSA1 #HHC-HHD
,,SSS1 #HIJ-HIA
SUM ( ANGLE M1SURES (1 #IIE
.,TRIANGUL> .NUMB]S @1 #CID
.,TRIANGUL> .PYRAMIDAL .NUMB]S @1 #CIE
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@1 #IFJ-IFB
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US+ SUM & DI6];E =MULAS1 #IDI-IED
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@1 #ABA @1 #IEE-IEF @1 #IEI @1 #IFJ
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@1 #IFH
SUM & DI6];E1 #IDI-IED @1 #IFD @1 #ABA
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( ANY ANGLE1 #HFF-HGB @1 #HII
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@1 #IFG
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SUM =MULAS =1 #IDI
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@1 #ABA
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@1 #AJJ @1 #AJA @1 #ACD @1 #AEE @1
#AFB @1 #AHA @1 #BCI @1 #BED @1 #BFA
@1 #BFB @1 #CEF @1 #CGC @1 #CHI @1
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( AN ANGLE1 #HEI
( AN ELLIPSE1 #FCD @1 #FEJ
(A F1SI# REGION1 #AGD
(A HYP]BOLA1 #FDB @1 #FEJ
(A P>ABOLA1 #BCF @1 #FBJ @1 #FEJ
.,V]TEX .=M @1 ( QUADRATIC A FUNC;N1
#BDE-BDF ,#BDH-BEA1 #BHG @1 #CAG @1
#CAI
.,V]TICAL .ASYMPTOTE @1 #EEH
.,V]TICAL .L9E @1 GRAPH (1 #IB
.,V]TICAL .L9E .TE/ @1 #GC-GD @1 #GG
.,V]TICAL .MO;N .PRO#M @1 #BIE @1 #BIH
.,V]TICAL .%R9K+ @1 (A GRAPH1 #DGI @1
#ABA
.,V]TICAL ./RET*+ @1 (A GRAPH1 #DGI @1
#ABA
.,V]TICAL .TRANSL,N @1 GRAPH+1 #IAF
.,VISUAL .?9K+ @1 .,SEE .AL ,GRAPHS2
,MANIPULATIVES2 ,MODEL+2 ,MULTIPLE
REPRES5T,NS2 ,TRANS=M,N
EX]CISES1 #AE @1 #AJB @1 #AHE @1 #BHA @1
#BIG @1 #ABA @1 #FBD @1 #HFB
.,VOCABUL>Y
OV]VIEW1 #A @1 #GA @1 #AEA @1 #BCE @1
#CBI @1 #DAC @1 #ABA @1 #EDI @1 #FAC
@1 #FHA @1 #GDC @1 #GIC @1 #ABA @1
#IJG
PREREQUISITE1 XXIV1 #GJ @1 #AEJ @1 #BCD
@1 #CBH @1 #ABA @1 #DGF @1 #EDH @1
#FAB @1 #FHJ @1 #GDB @1 #ABA @1 #HEJ
@1 #IJF
REVIEW1 #FA @1 #ADA @1 #BBB @1 #CAH @1
#DJB @1 #DFF @1 #ABA @1 #FJC @1 #FFI
@1 #GCD @1 #GHD @1 #HDJ @1 #ABA @1
#IFE
.,VOLUME @1 .,SEE ,=MULAS
;,W
.,:AT .,IF8 ."QS1 #AA @1 #AC @1 #BA @1
#BI @1 #CF @1 #ABA @1 #GD @1 #HC @1
#HE @1 #IA @1 #AJA @1 #AJI @1 #ABF @1
#ACE @1 #AEE @1 #AFC @1 #AGJ @1 #AHA
@1 #AIH @1 #BAI @1 #BCI @1 #BDF @1
#BDG @1 #BED @1 #BFB @1 #BFI @1 #BGH
@1 #BHG @1 #BIE @1 #CDA @1 #CEF @1
#CFA @1 #CFE @1 #CGC @1 #CHC @1 #CHI
@1 #DAF @1 #DCA @1 #DDG @1 #DEC @1
#DFA @1 #DHJ @1 #DHH @1 #DID @1 #EJA
@1 #EJI @1 #EAI @1 #EBE @1 #ECA @1
#EEB @1 #EFA @1 #EFG @1 #EGD @1 #EIB
@1 #EIG @1 #FBH @1 #FCF @1 #FDD @1
#FFA @1 #FHC @1 #FHD @1 #FIA @1 #FIB
@1 #FII @1 #GJJ @1 #GJA @1 #GJH @1
#GJI @1 #GAG @1 #GAH @1 #GAI @1 #GBA
@1 #GDF @1 #GEB @1 #GEI @1 #GFG @1
#GIE @1 #GIG @1 #HJE @1 #HBB @1 #HBI
@1 #HCE @1 #HEE @1 #HGJ @1 #HGG @1
#HIA @1 #IAA @1 #ICI @1 #IDB ,#IEG
.,:OLE .NUMB]S @1 #B
.,"W .RATE .PRO#MS @1 #BJ @1 #BD
.,WRIT+ @1 .,SEE .AL ,-MUNIC,N2 ,V]BAL
MODEL
ABSOLUTE VALUE FUNC;NS1 #ABE
ALGEBRAIC EXPRES.NS1 #IHD
DIRECT V>I,N EQU,NS1 #AJG-AAA
EQU,NS ( CIRCLES1 #FBG-FCB
EQU,NS ( ELLIPSES1 #FCE-FCI
EQU,NS ( HYP]BOLAS1 #FDC-FDH
EQU,NS ( P>ABOLAS1 #FBA-FBE
EXPON5TIAL FUNC;NS1 #EBI-ECA @1 #ABA-ECF
@1 #EDB
L9E> EQU,NS1 #AI @1 #BJ @1 #BC-BD @1
#ABA-AJD ,#ADB
L9E> SY/EMS Z MATRIX EQU,NS1 #ABA-BAC @1
#BAE-BAG
PIECEWISE FUNC;NS1 #ACA
POLYNOMIAL FUNC;NS1 #CHA @1 #CHD @1 #ABA
@1 #CIB-CII
P[] FUNC;NS1 #ECA-ECE
QUADRATIC FUNC;NS1 #CJI-CAE ,#CBB
R,NAL EQU,NS1 #EHI ,#EID-EIE
RULES = RA? T]M (A SEQU;E1 #ABA-HJI @1
#HAJ-HAF
RULES = SEQU;ES1 #GIE @1 #GIH @1
#ABA-HJJ
SY/EMS ( EQU,NS1 #AEE ,#AEG-AEH1 #ABA
,#AFE-AFF1 #AHA ,#AHD-AHE
SY/EMS ( L9E> 9EQUALITIES1 #AGJ @1
#ABA-AGC
TRIGONOMETRIC EQU,NS1 #HGG @1 #ABA-HHJ
TRIGONOMETRIC FUNC;NS1 #IDA-IDH
;,X
.;X-.AXIS @1 #IHG
.;X-.COORD9ATE @1 #IHG
.;X- .9T]CEPT @1 #IA
(! GRAPH (A POLYNOMIAL FUNC;N1 #CHG
.;X-.VALUES @1 CRITICAL1 #CJC @1 #EII
;,Y
.;Y-.AXIS @1 #IHG
.;Y-.COORD9ATE @1 #IHG
Z LOCAL MAXIMUM (A FUNC;N1 #ABA
Z LOCAL M9IMUM (A FUNC;N1 #ABA
.;Y-.9T]CEPT @1 #HI
;,Z
.;Z-.9T]CEPT @1 #AGG
.;Z-.SCORE @1 #GEH
/&>D NORMAL TA# &1 #ABA-GFB
.,Z]O .EXPON5T .PROP]TY @1 #CCJ
.,Z]O .PRODUCT .PROP]TY @1 #BEC
.,Z]O .SLOPE @1 #HC
.,Z]OS
(A POLYNOMIAL FUNC;N1 #CFD @1 #CFE @1
#ABA @1 #CFG @1 #CGJ-CGH @1 #CHG @1
#DJE
APPROXIMAT+ R1L1 #CHB-CHC ,#CHD
,DESC>TES' ,RULE ( ,SIGNS &1 #ABA-CHB @1
#CHD @1 #CHE
FUNDA;TAL !OREM ( ALGEBRA &1 #CGI-CHF @1
#DJE
(A QUADRATIC FUNC;N1 #BED-BEF
AV]AGE (1 #BFB
(A R,NAL FUNC;N1 #EFF
-----------------------------------#AAJE
,CR$ITS
,PHOTOGRAPHS
.,COV] ,MI*AEL ,WONG_/,CORBIS2
.,AU?ORS3 .TOP ,M]IDIAN ,CR1TIVE ,GR\P1
.TOP .C5T] .,ROB]T ,C4 ,J5KS1 ,J5KS
,/UDIO1 .BOTTOM .C5T] ,MC,D\GAL
,LITTELL1 .BOTTOM ,J]RY ,H1D ,JR42
..,TA# ( ,3T5TS3 ,*APT] .#A
,PHOTO,DISC_/,GETTY ,IMAGES2 .,*APT] .#B
,ALEX ,ROS5FELD_/ ,SCI;E ,PHOTO ,LIBR>Y2
.,*APT] .#C ,JONA?AN ,N\ROK_/,PHOTO,$IT2
.,*APT] .#D ,M&Y ,COLL9S _/,ALAMY2
.,*APT] .#E ,DAVE ,BJORN_/,PHOTO
,RES\RCE ,HAWAII2 .,*APT] .#F ,JOE
,MC,BRIDE_/,GETTY ,IMAGES2 .,*APT] .#G
,RON ,SAN=D_/,CORBIS2 .,*APT] .#H ,RALPH
,WETMORE_/,GETTY ,IMAGES2 .,*APT] .#I
,,NASA2 .,*APT] .#AJ ,J]RY ,WA*T]_/
,SPORTS*ROME1 ,9C42 .,*APT] .#AA
,,AP_/,WIDE ,_W ,PHOTOS2 .,*APT] .#AB
,T$ ,K9SMAN_/,PHOTO ,RESE>*]S1 ,9C42
.,*APT] .#AC ,DAVID ,MADISON_/,GETTY
,IMAGES2 .,*APT] #AD ,?ORNEY
,LIEB]MAN_/,GETTY ,IMAGES2 .,9T]IOR3 .#A
,J5NIF] ,GRAYLOCK_/,,AP_/,WIDE ,_W
,PHOTOS2 #B ,SYLVA9 ,GR&ADAM_/,GETTY
,IMAGES2 #F ,JASON ,HAWKES_/,GETTY
,IMAGES2 #H .ALL ,C\RTESY
,,NASA_/,,JPL-,CALTE*2 #I ,JOEL
,S>TORE_/,GETTY ,IMAGES2 .#AJ ,RU2]BALL
,PRODUC;NS_/,GETTY ,IMAGES2 .#AC ,BR&
;,X ,PICTURES_/ ,GETTY ,IMAGES2 .#AH
,PHOTO,DISC_/,GETTY ,IMAGES2 .#BJ
,CR1TAS_/ ,PUN*,/OCK2 .#BC ,WALT]
,HODGES_/,GETTY ,IMAGES2 #BD .BO?
,DIGITAL ,/OCK_/,CORBIS2 .#BF ,PET]
,ADAMS_/,9DEX ,/OCK ,IMAGERY2 .#BI
,RU2]BALL ,PRODUC;NS2 .#CC ,G>Y ,I4
,RO?/E9_/,,AP_/,WIDE ,_W ,PHOTOS2 #CD
,PHOTO,DISC_/,GETTY ,IMAGES2 .#CE ,JASON
,RE$_/,REUT]S2 .#CH ,EUG5E
,HO%IKO_/,,AP_/,WIDE ,_W ,PHOTOS2 #DA
,ROYALTY-,FREE_/,CORBIS2 #DB ,B>B>A
,LESLIE_/,GETTY ,IMAGES2 #DD ,DAVID ,A4
,NOR?COTT_/,CORBIS2 .#EJ .ALL ,JAY ,P5NI
,PHOTOGRAPHY_/,MC,D\GAL ,LITTELL2 #EA
,DIGITAL ,VI.N ,LTD4_/,SUP],/OCK2 #ED
,JIM ,CUMM9S_/,GETTY ,IMAGES2 .#EI ,D1N
,H(FMEY]_/,,AP_/,WIDE ,_W ,PHOTOS2
.#GJ-.GA ,GEORGE ,D4 ,LEPP_/ ,CORBIS2
#GB ,TOM ,/OCK_/,GETTY ,IMAGES2 #GD
,PAUL ,BATTAGLIA_/,,AP_/,WIDE ,_W
,PHOTOS2 .#GF ,/EPH5 ,FR9K_/,CORBIS2
.#GI ,D4,C4 ,L[E_/ ,SUP],/OCK2 .#HB
,]NE/ ,MANEWAL_/,9DEX ,/OCK ,IMAGERY2
.#HE .BO? ,SUSAN ,RAGAN_/,,AP_/,WIDE ,_W
,PHOTOS2 .#HI ,ANGELA ,WYANT_/,GETTY
,IMAGES2 #IA ,PAUL ,NICKL5_/,N,NAL
,GEOGRAPHIC_/,GETTY ,IMAGES2 .#IH ,NANCY
,RI*MOND_/,! ,IMAGE ,"WS2 .#AJJ ,/EVE
,SKJOLD_/,PHOTO,$IT2 .#AJC ,DAVID
,"Y-,WOLFF_/,PHOTO,$IT2 .#AJG ,DAVE ,G4
,H\SER_/,CORBIS2 .#AJH ,AMOS
,NA*\M_/,CORBIS2 .#AAB ALL ,MC,D\GAL
,LITTELL2 .#AAC ,D\GLAS ,C4
,PIZAC_/,,AP_/,WIDE ,_W ,PHOTOS2 .#AAE
,S&Y ,HU6AK]_/ ,GETTY ,IMAGES2 .#ABC
.TOP ."R ,JOHN ,COLETTI_/,9DEX ,/OCK
,IMAGERY2 .#ACB ,DIGITAL ,VISION_/,GETTY
,IMAGES2 .#ACD .ALL ,/OCKBYTE_/,GETTY
,IMAGES2 .#AEJ-.AEA ,MYRLE5 ,F]GUSON
,CATE_/,PHOTO,$IT2 .#AEC ,DUOMO_/
,CORBIS2 .#AEE ,DAVID ,FRAZI]_/,! ,IMAGE
,"WS2 .#AFJ ,RU2]BALL_/ ,PICTURE,QUE/2
.#AFF ,PETROS ,GIANNAK\RIS_/,,AP_/,WIDE
,_W ,PHOTOS2 .#AFH ,DUNCAN ,SMI?_/,GETTY
,IMAGES2 .#AGJ ,VIVIANE ,MOOS_/,CORBIS2
.#AGC ,JIM ,CUMM9S _/,GETTY ,IMAGES2
.#AGD ,BR& ;,X_/,SUP],/OCK2 .#AGF
,KELLY-,MOONEY ,PHOTOGRAPHY_/,CORBIS2
.#AGH ,*RIS ,DONAHUE_/,,AP_/,WIDE ,_W
,PHOTOS2 .#AHE ,MAN*AN_/,GETTY ,IMAGES2
.#AHF ,-/OCK ,IMAGES_/,ALAMY2 .#AHG
,/EPH5 ,J4 ,C>R]A_/,,AP_/,WIDE ,WO RID
,PHOTOS2 .#AIB ,BR& ;,X
,PICTURES_/,ALAMY2 .#AIE ,MIKE
,P[ELL_/,GETTY ,IMAGES2 .#BJC ,TIM
,WAKEFIELD_/,SUP],/OCK2 .#BAJ ,LEE
,/RICKL&_/,GETTY ,IMAGES2 .#BAE ,WALT]
,M1Y]S ,$W>DS_/,GETTY ,IMAGES2 .#BAF
,GIANNI ,CIGOL9I_/ ,GETTY ,IMAGES2 .#BBJ
,TOM ,B1N_/,CORBIS2 .#BCD-.BCE ,GETTY
,IMAGES2 .#BCF ,C4 ,B4 ,KNI<T_/,GETTY
,IMAGES2 .#BCI ,RICK ,FRI$MAN_/,CORBIS2
.#BDE ,M$=D ,TAYLOR_/,GETTY ,IMAGES2
.#BEA ,DAVID ,HALL_/,NATURE ,PICTURE
,LIBR>Y2 .#BEB ,KAYTE ,M4
,DEIOMA_/,PHOTO,$IT2 .#BEG ,IMAGE ,S\RCE
,LIMIT$_/,9DEX ,/OCK ,IMAGERY2 .#BEI
,GREG ,HUGL9_/,SUP],/OCK2 .#BFA
,JOHN,W>D5_/,SUP],/OCK2 .#BFB
,PHOTO,DISC_/,GETTY ,IMAGES2 .#BFD
.BOTTOM ."R .,SE? ,?OMPSON_/,GETTY
,IMAGES2 .#BFF ,HUB# ,H]ITAGE
,T1M_/,,NASA_/,,AP_/,WIDE ,_W ,PHOTOS2
.#BFI ,MIKE ,M]G5_/ ,,AP_/,WIDE ,_W
,PHOTOS2 .#BGJ ,/EVE ,ALL5_/,BR& ;,X
,PICTURES_/ ,PICTURE,QUE/2 .#BGA
,DUOMO_/,CORBIS2 .#BGD ,*]YL
,HAT*_/,,AP_/,WIDE ,_W ,PHOTOS2 .#BGE
,DR4 ,FR$ ,ESP5AK_/,,SPL_/,PHOTO
,RESE>*]S1 ,9C42 .#BHA
,IMAGEBROK]_/,ALAMY2 .#BHB ,ALFR$
,PASIEKA_/,,SPL_/,PHOTO ,RESE>*]S1 ,9C42
.#BHC .ALL ,MC,D\GAL ,LITTELL2 .#BHD
,JIM ,CUMM9S_/ ,GETTY ,IMAGES2 .#BHG
,DAVID ,MADISON_/,GETTY ,IMAGES2 .#BHI
,RON ,WATTS_/,CORBIS2 .#BIA ,TOM
,/EW>T_/,CORBIS2 .#BIB ,MIKE
,YAMA%ITA_/,CORBIS2 .#BIE .LEFT ,DAVID
,MADISON_/,GETTY ,IMAGES2 .#BIE .C5T]
,ROY ,MORS*_/ ,CORBIS2 .#BIE ."R
,AMWE,WELL _/ ,GETTY ,IMAGES2 .#BII ,B5
,MANGOR_/ ,SUP],/OCK2 .#CJJ
,PHOTO,DISC_/,GETTY ,IMAGES2 .#CJC
,M>CIO ,JOSE ,SAN*EZ_/,,AP_/,WIDE ,_W
,PHOTOS2 .#CJF ,/EPH5 ,FRIS*_/,/OCK
,BO/ON2 .#CJI _+PHOTOLIBRARY.COM/INDEX_:
,/OCK ,IMAGERY2 #CAA ,KEV9
,FLEM9G_/,CORBIS2 .#CAD ,MI*AEL
,WONG_/,CORBIS2 .#CAF ,/OCKBYTE2
.#CBH-.CBI ,REUT]S_/,CORBIS2 .#CCJ
,,NASA_/,CORBIS2 .#CCA ."R ,REUT]S_/
,CORBIS2 .#CCA .LEFT .,DEX ,IMAGE
_/,GETTY ,IMAGES2 .#CCB ,-/OCK ,IMAGES2
.#CCG ,DAVID ,"Y-,WOLFF_/,PHOTO,$IT2
.#CDC .BOTTOM ,?9K,/OCK ,,LLC_/ ,9DEX
,/OCK ,IMAGERY2 .#CDD ,M4 ,PHILIP
,KAHL_/,BRUCE ,COLEMAN1 ,9C42 .#CDF ,TIM
,L>S5_/,,AP_/,WIDE ,_W ,PHOTOS2 .#CDH
,DAVID ,FRAZI]_/,GETTY ,IMAGES2 .#CEC
,RI*>D ,T4 ,N[ITZ_/,CORBIS2 .#CFB ,ORL9
,WAGN]_/ .,,AP_/ ,WIDE ,_W ,PHOTOS2
.#CFE ,ROYALTY-,FREE_/,CORBIS2 .#CFG
,JOE ,CAV>OTTA_/ ,,AP_/,WIDE ,_W
,PHOTOS2 .#CFH ,NEIL ,RAB9[ITZ_/,CORBIS2
.#CGJ .TOP ."R .,VOLK]
,/EG]_/,SIEM5S_/,,SPL_/,PHOTO ,RESE>*]S1
,9C42 .#CGF AGE FOTO/OCK_/,SUP],/OCK2
.#CGI ,PET] ,CORREZ_/,GETTY ,IMAGES2
.#CHC ,PHOTO,DISC_/,GETTY ,IMAGES2 .#CHE
,PET],YATES_/,,SPL_/,PHOTO ,RESE>*]S1
,9C42 .#CHG .TOP ."R ,TURN] @&
DE,VRIES_/,GETTY ,IMAGES2 .#CIC ,T]RY
,R5NA_/,,AP_/,WIDE ,_W ,PHOTOS2 .#CIH
,TOM ,/EW>T_/ ,CORBIS2 .#DJJ ,JOE
,MC,DONALD_/,CORBIS2 .#DAB-.DAC ,DAVID
,B]GMAN_/ ,CORBIS2 .#DAD ,JAVI]
,SORIANO_/,,AFP_/,GETTY ,IMAGES2 .#DAF
,AZURE ,-PUT] @& ,PHOTO
,S]VICES_/,ANIMALS ,ANIMALS2 .#DAI
,MC,D\GAL ,LITTELL_/,H"\ON ,MI6L9 ,CO42
.#DBJ ,CAM]ON ,H]YET_/,GETTY ,IMAGES2
.#DBF ,LE/] ,LEFK[ITZ_/,CORBIS2 .#DBH
,D>RELL ,GUL9_/,CORBIS2 .#DCA
,/REET,/OCK ,IMAGES_/,BR& ;,X
,PICTURES_/,PICTUR1RTS2 .#DCD ,C\RTESY (
,PROFESSOR ,TIM ,P5N+S1 ,HOPE ,COLLEGE2
.#DCF ,ROYALTY-,FREE_/ ,CORBIS2 .#DCG
.BO? ,,RMIP_/,RI*>D ,HAYNES_/,MC,D\GAL
,LITTELL2 .#DCH ,PAUL ,A4
,S\D]S_/,CORBIS2 .#DDA ,GAIL
,BURTON_/,,AP_/,WIDE ,_W ,PHOTOS2 .#DDD
,ROD ,TAYLOR_/,,AP_/,WIDE ,_W ,PHOTOS2
.#DDF ,DUOMO_/,CORBIS2 .#DDG
,NAVASWAN_/,GETTY ,IMAGES2 .#DEA ,BRIAN
,]L]_/,GETTY ,IMAGES2 .#DEB-.DEC ,CA?R9E
,WESSEL_/,CORBIS2 .#DEC ,PHILIPPE
,GIRAUD_/,CORBIS ,SYGMA2 .#DEG ,CASEY
,RI6E_/,M>%FIELD
,NEWS-,H]ALD_/,,AP_/,WIDE ,_W ,PHOTOS2
.#DEH ,,OSF_/,COLBECK1 ,M4_/,ANIMALS
,ANIMALS2 .#DGF .BACKGR.D ,B4,A4,E4
,9C4_/ ,ALAMY2 .#DGH ,GRE] @&
,ASSOCIATES1 ,9C4_/,SUP],/OCK2 .#DHD
,BOB ,DAEMMRI*_/,CORBIS ,SYGMA2 .#DHE
,LYNDA ,RI*>DSON_/,CORBIS2 .#DHF AGE
FOTO/OCK_/,SUP],/OCK2 .#DHH
,PHOTO,DISC_/,GETTY ,IMAGES2 .#DIA
,RI*>D ,A4 ,COOKE_/,CORBIS2 .#DIB ,C\/1U
,SOCIETY
.#DIH ,TIM ,HURSLEY_/,SUP],/OCK2 .#DII
,*UCK ,C>LTON_/,9DEX ,/OCK ,IMAGERY2
.#EJF ,JIM ,MC,NEE_/,9DEX ,/OCK
,IMAGERY2 .#EJG AGE
FOTO/OCK_/,SUP],/OCK2 .#EJI ,ROYALTY-
,FREE _/,CORBIS2 .#EAA .C5T] .LEFT
IMAGE#AJJ_/,ALAMY2 .#EAA .C5T] ,PAT
,LA,CROIX_/,GETTY ,IMAGES2 .#EAA .C5T]
."R ,TONY ,>RUZA_/ ,CORBIS2 .#EAB .C5T]
."R ,RU2]BALL ,PRODUC;NS2 .#EAB .C5T]
.LEFT ,CA?Y ,MELLOAN_/,PHOTO,$IT2 .#EAB
.BOTTOM ,RU2]BALL ,PRODUC;NS2 .#EAE
,ROG] ,RESSMEY]_/,CORBIS2 .#EAF ,JEFF
,%]MAN_/,GETTY ,IMAGES2 .#EBB .BO? ,,AM
,CORPORATION_/ ,ALAMY2 .#EBH .BO? ,JAY
,P5NI ,PHOTOGRAPHY_/,MC,D\GAL ,LITTELL2
.#EBI ,M>K ,*APPELL_/,ANIMALS ,ANIMALS2
.#ECJ ,NICK ,DOLD9G_/,GETTY ,IMAGES2
.#ECB ,G]>D ,LACZ_/,ANIMALS ,ANIMALS2
.#ECD ,BRYN ,COLTON_/ ,ASSIGN;TS
,PHOTOGRAPH]S_/,CORBIS2 .#ECF
,BETTMANN_/,CORBIS2 .#EDH-.EDI ,JEFF
,HUNT]_/,GETTY ,IMAGES2 .#EEJ .BO?
,,RMIP_/,RI*>D ,HAYNES_/ ,MC,D\GAL
,LITTELL2 .#EEA ,LAWR;E
,MANN9G_/,CORBIS2 .#EEB AGE
FOTO/OCK_/,SUP],/OCK2 .#EEC ,RICK
,B[M]_/,,AP_/,WIDE ,_W ,PHOTOS2 .#EEH
,K5 ,REID_/,GETTY ,IMAGES2 .#EFJ .BO?
,C\RTESY ( ;,Z ,CORPOR,N2 .#EFE ,BO2Y
,MODEL_/,N,NAL ,GEOGRAPHIC _/,GETTY
,IMAGES2 .#EFG ,DONALD ,C4
,JOHNSON_/,CORBIS2 .#EFI ,! ,PHOTOLIBR>Y
,WALES_/,ALAMY2 .#EGJ ,SCAL$
,-POSITES_/,,SPL_/,PHOTO ,RESE>*]S1
,9C42 .#EGB ,MI*AEL ,NEWMAN_/,PHOTO,$IT2
.#EGC ,M>Y ,ANN ,*A/A9_/,,AP_/,WIDE ,_W
,PHOTOS2 .#EGI ,TONY
,MC,CONNELL_/,,SPL_/,PHOTO ,RESE>*]S1
,9C42 .#EHB ,LUCA ,DI,CE3O_/,ALAMY2
.#EHI ,D5IS ,BOISSAVY_/,GETTY ,IMAGES2
.#EIB DONJON R$_/,ALAMY2 .#EID ,F$],N
,9T]N,NALE DE ,VOLLEYBALL_/,,AP_/,WIDE
,_W ,PHOTOS2 .#FJA ,PHOTO,DISC_/,GETTY
,IMAGES2 .#FAB-.FAC ,PHOTOTAKE_/,GETTY
,IMAGES2 .#FAD ,NICK,V$ROS @& ,ASSOC4_/
,GETTY ,IMAGES2 .#FAH ,REUT]S_/,CORBIS2
.#FBJ ,/EPH5 ,FR9K_/,GETTY
-----------------------------------#AAJF
,IMAGES2 .#FBD ,HANK ,MORGAN_/,"T
,LIFE ,PICTURES_/,GETTY ,IMAGES2 .#FBE
,ROG] ,RESSMEY]_/,CORBIS2 .#FBF
,ROYALTY-,FREE_/,CORBIS2 .#FCD ,RALPH
,WETMORE_/,GETTY ,IMAGES2 .#FCH .BOTTOM
.LEFT ,,NASA_/,,>C2 .#FCH .BOTTOM ."R
,DETLEV,VAN ,RAV5SWAAY_/,,SPL_/,PHOTO
,RESE>*]S1 ,9C42 .#FDA ,TOM
,UHLMAN_/,VISUALS ,UNLIMIT$2 .#FDB ,PAUL
,A4 ,S\D]S_/ ,CORBIS2 .#FDH ,MIKE
,C>TW"R_/,,AP_/,WIDE ,_W ,PHOTOS2 .#FDI
,,RMIP_/ ,RI*>D ,HAYNES_/,MC,D\GAL
,LITTELL2 .#FEJ ,C\RTESY (
,SUP]DAIRYBOY2 .#FEF ,]IK ,S4
,LESS]_/,,AP_/,WIDE ,_W ,PHOTOS2 .#FEH
,YELL[ ,DOG ,PRODUC;NS_/,GETTY ,IMAGES2
.#FGF ,F]MILAB ,PHOTO2 .#FHJ-.FHA
,ALEX&] ,WALT]_/,GETTY ,IMAGES2 .#FHB
,D\GLAS ,C4 ,PIZAC_/ ,,AP_/,WIDE ,_W
,PHOTOS2 .#FHD ,OLIV]
,MOR9_/,,AFP_/,GETTY ,IMAGES2 .#FIJ
,RO2IE ,JACK_/,CORBIS2 .#FIF ,M>C
,LE/]_/,,AP_/,WIDE ,_W ,PHOTOS2 .#FIH
,PHOTO,DISC_/,GETTY ,IMAGES2 .#FII ,ELL5
,S5ISI_/,! ,IMAGE ,"WS2 .#GJE .BOTTOM
.LEFT ,BIG ,*EESE ,PHOTO_/,FOTO,SE>*2
.#GJG ,JEFF ,GRE5B]G_/,! ,IMAGE ,"WS2
.#GAG ,D5NIS ,MAC,DONALD_/,PHOTO,$IT2
.#GAI ,,NOAA_/,,AP_/,WIDE ,_W ,PHOTOS2
.#GBD ,JOHN ,RUSSELL_/,,AP_/,WIDE ,_W
,PHOTOS2 .#GDB-.GDC ,M>K ,E4
,GIBSON_/,GETTY ,IMAGES2 .#GDD ,OM>
,TORRES_/,,AFP_/,GETTY ,IMAGES2 .#GDF
,BANANA ,/OCK_/,ALAMY2 .#GDH ,ALAN
,DIAZ_/,,AP_/,WIDE ,_W ,PHOTOS2 .#GDI
,&Y ,LYONS_/,GETTY ,IMAGES2 .#GEA
,,NASA-,,HQ-,,GR92 .#GED .BOTTOM ,RIC
,FRANCIS_/,,AP_/,WIDE ,_W ,PHOTOS2 .#GED
.TOP ,PHIL ,CANTOR_/,9DEX ,/OCK
,IMAGERY2 .#GEF .TOP AGE
FOTO/OCK_/,SUP],/OCK2 .#GEF .BOTTOM ,DON
,HEUPEL_/,,AP_/,WIDE ,_W ,PHOTOS2 .#GEF
.BOTTOM C5T] ,?9K,/OCK_/,SUP],/OCK2
.#GEG ,PHOTO,DISC_/,GETTY ,IMAGES2 .#GEI
,K5NAN ,W>D_/,CORBIS2 .#GFB ,B>B>A
,NOVOVIT*_/,REUT]S2 .#GFE
,ROYALTY-,FREE_/,CORBIS2 .#GFF
,DAVID,"Y-,WOLFF_/,PHOTO,$IT2 .#GGB
,SP;ER ,GRANT_/,PHOTO,$IT2 .#GGD ,JAY
,P5NI ,PHOTOGRAPHY_/,MC,D\GAL ,LITTELL2
.#GGE ,B5 ,M>GOT_/,,AP_/,WIDE ,_W
,PHOTOS2 .#GHJ ,JAY ,P5NI
,PHOTOGRAPHY_/,MC,D\GAL ,LITTELL2 .#GHB
,DYNAMIC ,GRAPHICS_/,PICTURE,QUE/2
.#GIB-.GIC ,/EVE ,GS*MEISSN]_/
,,SPL_/,PHOTO ,RESE>*]S1 ,9C42 .#GID
,ROG],WOOD_/,CORBIS2 .#GII ,FRANK
,*MURA_/,PICTURE,QUE/2 .#HJB ,RI*>D
,CUMM9S_/,CORBIS2 .#HJE
,/OCKBYTE_/,PICTURE,QUE/2 .#HJH ^C #BJJG
,SOL ,LE,WITT_/,>TI/ ,"RS ,SOCIETY
7,,>S71 ,NEW ,YORK4 ,PHOTO ,CR$IT3 ,M>Y
,ANN ,SULLIVAN1 ,BLU6TON ,UNIV]S;Y2
.#HAJ ,PHOTO,/OCK,FILE_/,ALAMY2 .#HAC
,,GDT_/,GETTY ,IMAGES2 .#HAE ,AG;E
,V&Y/ADT_/,PHOTO ,RESE>*]S1 ,9C42 .#HAI
.ALL ,JAY ,P5NI ,PHOTOGRAPHY_/,MC,D\GAL
,LITTELL2 .#HBJ ,C\RTESY ( ,GAYLA ,*&L]2
.#HBG ,POPP]FOTO_/,ALAMY2 .#HCH ,G>Y ,S4
,SETTLES_/,PHOTO ,RESE>*]S1 ,9C42
.#HEJ-.HEA ,JOAO ,PAULO_/,GETTY ,IMAGES2
.#HEB ,HU< ,SITTON_/,GETTY ,IMAGES2
.#HEI ,M4 ,SP;ER ,GRE5_/,,AP_/,WIDE ,_W
,PHOTOS2 .#HFD .TOP
,ROYALTY-,FREE_/,CORBIS2 .#HFD .C5T]
,C\RTESY ,,NASA1 ,LIFE ,SCI;ES ,DIVI.N2
.#HFE .BO? ,ROYALTY-,FREE_/,CORBIS2
.#HFF AGE FOTO/OCK_/,SUP],/OCK2 .#HFI
,C\RTESY ,,NASA_/,,JPL-,CALTE*2 .#HGC
.BOTTOM ."R ,BR& ;,X ,PICTURES_/,GETTY
,IMAGES2 .#HGC ."R ,RI*>D
,CUMM9S_/,SUP],/OCK2 .#HGC .BOTTOM ."R
.,YO%IO ,TOMII_/ ,SUP],/OCK2 .#HGE ,GREG
,EB]SOLE_/,,AP_/,WIDE ,_W ,PHOTOS2 .#HGI
,PAOLO ,CURTO_/,! ,IMAGE ,BANK2 .#HHB
,RI*>D ,2RENHOLTZ_/,CORBIS2 .#HHE ,/EVE
,BEIN_/,CORBIS2 .#HHI ,DAVID
,MADISON_/,GETTY ,IMAGES2 .#IJF-.IJG
,ROYALTY-,FREE_/,CORBIS2 .#IJH ,RI*>D
,OLSEIUS_/,N,NAL ,GEOGRAPHIC_/,GETTY
,IMAGES2 .#IAJ ,ANNABELLA
,BLUESKY_/,,SPL_/,PHOTO ,RESE>*]S1 ,9C42
.#IAC ,PET] ,>NOLD1 ,9C4 _/,ALAMY2 .#IAE
.BO? ,CRAIG ,T4 ,LOR5Z_/,PHOTO
,RESE>*]S1 ,9C42 .#IBA ,IMAGE
,S\RCE_/,PUN*,/OCK2 .#IBD ,L[ELL
,OBS]VATORY_/,,NOAO_/,,AURA_/,,NSF2
.#ICA ,SCOTT ,CAMAZ9E_/,PHOTO ,RESE>*]S1
,9C42 .#ICB .BO? ,*RI/OPH]
,MACKAY_/,TANTRAM> ,9T]ACTIVE2 .#IDJ
,PHOTO,DISC_/,GETTY ,IMAGES2 .#IDA ,LEE
,COH5_/,CORBIS2 .#IDE ,/EVE
,*5N_/,CORBIS2 .#IDH ,,RMIP_/ ,RI*>D
,HAYNES_/,MC,D\GAL ,LITTELL2 .#IDI ,H[>D
,K+SNOR?_/,GETTY ,IMAGES2 .#IEA .LEFT
,L>RY ,DUNMIRE_/,SUP],/OCK2 .#IEA ."R
,K5 ,GRAHAM_/,GETTY ,IMAGES2 .#IEE
,PASCAL ,ROND1U_/,GETTY ,IMAGES2 #IFC
,BILL,ROSS_/,CORBIS4
,ILLU/R,NS & ,MAPS
,>GOSY #A1 ..#EA1 #GJ1 #AEA1 #BCE1
#CBI1 #DAC1 #DGG1 #EDI1 .#EEG .TOP @1
.#FAC1 .#FBB .TOP @1 .#FDF1 .#FED1
.#FFB1.FFG .TOP .LEFT @1 .#FHA1 .#GDC1
.#GIC1.HAH .BOTTOM .LEFT2 ..#HEA1 #IJG1
#IBA1 #IDB1 #IED1 .#IEG2 ,K5NE?
,BATELMAN ..#EJD1 #FCF1 #GEB1 #GFF1
#HGA1 #HGI1 #ICJ1 .#IDF2 ,/EVE ,C[D5
..#AE1 #CB1 #CI1 #IE1 #BDA1 .#BDC .TOP
.C5T] @1 .#BDG1 .#BFH1.BIH .C5T] @1
..#DCD1 #DCI1 #DEG1 #DFD1 .#ECE2 ,/EPH5
,DURKE .#BIJ .BOTTOM @1 .#EEB1 .#EGJ1
.#FBB .C5T] @1 .#FFJ1 .#FHI .TOP @1
.#HJJ1 .#HJH .TOP @1 .#HCB1 .#HEH1.HGB
.C5T] ."R @1 .#HIF1 .#IAH1 .#IBI .C5T]
@1 .#IBI .TOP ."R @1 .#IDJ2 ,JOHN
,FRANCIS .#EHJ1 .#GFA @2 ,PATRICK
,GNAN_/,DEBORAH ,WOLFE1 ,LTD4 ..#E1
#ABI1 #BED1 .#CDC .TOP @1 ..#CEA1 #CEF1
#CFJ1 #CGG1 #CIB1 #EHE1 #FDA1 #FDD1
#FEG1 #FGF1 .#HAH .TOP ."R2 ..#HBB1
#HCH1 #HHJ1 #HIJ1 #IJB1 #IJE1 #IBG1
#IEC1 .#IGB2 ,*RIS ,LYONS .#ACI1 .#AEH1
.#FDG .C5T]2 ,/EVE ,MC,5TEE .#DHJ1
.#EFC1 .#HGJ1.HGC .BOTTOM .LEFT @1
.#HGG1 .#HHG1 .#HIC .BOTTOM @1 .#HIC
.C5T] @1 .#IJD1 .#IAD1 .#IAF @2 ,PAUL
,MIRO*A .#DIG1 .#EGD2 ,LAURIE ,O',KEEFE
.#HH1 .#DID1 .#GBI2 ,/EVE ,/ANKIEWICZ
.#BEH1 .#EJE2 ,D\G ,/EV5S .#ABE2 ,DAN
,/UCK5S*NEID] .#AF1 .#DF1.HG ,#A ..#JH1
#AAI1 #ACG1 #AHE1 #AHI1 #BEJ1 #BEG1
.#BFE .TOP ."R @1 ..#CFI1 #CGC1 #DBF1
#DEJ1 #EAI1 #EBD1 #EEF1 .#EEG .C5T] @1
..#FHH1 #GIE1 #HBD1 .#ICF2 ,MATT
,ZANG_/,AM]ICAN ,>TI/S .#EJJ2
,C>OL,ZUB]-,MALLISON ..#AAA1 #BJD1 #BJH1
#BJI1 #CEH1 #EBA1 #EHG1 #FAF1 #FAH1
#FAI1 #FFC1 #GJD1 #HEE1 #HHE1 .#IFA .TOP
."R @1 .#IFA .BOTTOM4 ,ALL O!R ILLU/R,NS
^C ,MC,D\GAL ,LITTELL_/,H"\ON ,MI6L9
,-PANY4
---------------------------------;,,WS#A
,"W$-,\ ,SOLU;NS
,? SEC;N (! BOOK PROVIDES /EP-BY-/EP
SOLU;NS 6EX]CISES ) CIRCL$ EX]CISE
NUMB]S4 ,^! SOLU;NS PROVIDE MODELS T C
HELP GUIDE YR "W )! HOME"W EX]CISES4
,! SEP>ATE .,SELECT$ .,ANSW]S SEC;N
FOLL[S ? SEC;N4 ,X PROVIDES NUM]\S
ANSW]S T Y C USE 6*ECK YR [N ANSW]S4
,*APT] #A
,LESSON #A.A @7 PP4 #F-I @7
.#BA4 #G .A @+ 7#D @+ #E .A @7
.K #G .A @+ 7#E .A @+ #D7 ,-MUTATIVE
PROP]TY ( A4I;N
.K 7#G .A @+ #E .A @7 @+ #D
,ASSOCIATIVE PROP]TY ( A4I;N
.K 7#G @+ #E7 .A @+ #D ,4TRIBUTIVE
PROP]TY
.K #AB .A @+ #D ,SIMPLIFY
#CA4
#EI4
A4 ,PLUTO1 ,NEPTUNE1 ,URANUS1 ,SATURN1
,JUPIT]1 ,M>S1 ,E>?1 ,M]CURY1 ,V5US
B4 ,M]CURY1 ,V5US1 ,E>?1 ,M>S1
,JUPIT]1 ,SATURN1 ,URANUS1 ,NEPTUNE1
,PLUTO
C4 ,! GRT] ! 4T.E F ! SUN1 ! COLD] !
SURFACE TEMP]ATURE4
D4 ,V5US
,LESSON #A.B @7 PP4 #AC-AF @7
.#BA4 ,:5 ;M .K #F3
#H .;M @+ 7#B .;M -- #I7 #C .K #H7#F7
@+ 7#B7#F7--#I7 #C
.K #H7#F7 @+ 7#C7 #C
.K #DH @+ #BG .K #GE
.#BI4 #G7 .;M -- #C7 @+ #D7 .;M @+ #E7
.K #G .;M -- #BA @+ #D .;M @+ #BJ
.K 7#G .;M @+ #D .;M @7 @+ 7-#BA @+
#BJ7 .K ;LL .;M -- #A
.#EI4 #BGJ--#D.E 7.;X7 @4 ,! EXPRES.N
MAKES S5SE = ALL POSITIVE 9TEG] VALUES (
.;X LESS ?AN OR EQUAL 6#FJ4 ,:5 .;X .1
#FJ1 ! BAL.E IS NEGATIVE4
,LESSON #A.C @7 PP4 #BA-BD @7
.#BC4 #E .;B -- #D .K #B .;B @+ #H
#C .;B -- #D .K #H
#C .;B .K #AB
.;B .K #D
,*ECK3
#E .;B -- #D .K #B .;B @+ #H
#E7#D7--#D #B7#D7 @+ #H
#BJ--#D #H @+ #H
#AF .K #AF
#DC4
#C .;T @+ #B .;T .K #FJ
#E .;T .K #FJ
.;T .K #AB
,*ECK3
#F @+ #D #AJ
#AJ .K #AJ
.#GA4 #G.GE7#BE7 @+ #F.BE .;X .K #BEJ
#AIC.GE @+ #F.BE .;X .K #BEJ
.;X .K #I
,Y M/ "W #I H\RS_/WEEK AT ! SECOND
JOB4
,LESSON #A.D @7 PP4 #CJ-CB @7
.#C4
,:5 .;W .K #EJ & ,A .K #BEJ3
,! L5G? (! RECTANGLE IS #E MILLIMET]S4
.#I4
,:5 .;X .K --#D3
---------------------------------;,,WS#B
,,"W$-,,\ ,,SOLU;NS
.#CE4
,:5
7#AH7 .K .;,C
#AJ .K ;,C
,! TEMP]ATURE ( #AJ;DG;,C CORRESPONDS
6#EJ;DG,F4
.,LESSON .#A..E @7 PP4 #CG-DJ @7
.#C4
.#AA4 ,AN EQU,N IS .;Y .K #AA @+ #D
.;X @4
.#BG4
,AN EQU,N IS .;Y .K #AE @+ #A.E .;X @4
,X IS N R1SONA# 6ASSUME ! PATT]N 9 ! TA#
3T9UES 9DEF9ITELY4 ,IF X DID1 ! PLANT WD
2COME 9DEF9ITELY TALL4
.,LESSON .#A..F @7 PP4 #DD-DG @7
.#AC4 .;X "K --.#B OR .;X .1 #D
#BE4 #AE -- .#C;X .1 #C
.;X "K #D
#EE4
A4 ,L[L&3 #J "K.K .;E "K #EJJ
B4 ,ALP9E3 #BJJJ "K.K .;E "K #BDBI
,SUBALP9E3 #ADJJ "K.K .;E"K #BJJJ
,ALP9E & SUBALP9E3 #ADJJ "K.K .;E"K
#BDBI
C4 ,N 9 MONTANE Z"O3 .;E "K #EJJ OR
.;E .1.K#ADJJ
.,LESSON .#A..G @7 PP4 #EE-EH @7
.#BA4 _\#B .A -- #E_\ .K #AC
#B .;D -- #E .K --#AC OR #B .;D -- #E
.K #AC
#B .;D .K --#H OR .#B;D .K #AH
.;D .K-#D OR .;D .K #I
.#DG4 _\ .;D @+ #D_\.1#C
.;D @+ #D "K.K --#C OR ;D @+ #D .1.K#C
.;D "K.K --#G OR .;D .1.K --#A
.#GG4 ,A3EPT3 _\ .;B -- #BA_\ "K.K #A2
,REJECT3 _\ .;B -- #BA_\ "K.K #A
,*APT] #B
.,LESSON .#B..A @7 PP4 #GF-GI @7
.#G4 7#E1 #BJ71 7#AJ1 #BJ71 7#AE1
#CJ71 7#BJ1 #CJ7
,DOMA93 #E1 #AJ1 #AE1 & #BJ2 ,RANGE3
#BJ & #CJ
.#AG4 ,! REL,N IS N A FUNC;N 2C ! 9PUT
--#B IS MAPP$ 6BO? #J & #E4
.#DE4
;,V7#F7 REPRES5TS ! VOLUME (A SPH]E )A
RADIUS ( #F UNITS4
.,LESSON .#B..B @7 PP4 #HF-HH @7
.#I4 @2 ! L9E RISES4
.#AI4 ,L9E #A3 "? 7#A1 #E7 & 7#C1
--#B7
,L9E #B3 "? 7-#C1 #B7 & 7#D1 #J7
,2C & ;M #A @6.K ;M #B @1 ! L9ES >E
NEI P]P5DICUL> NOR P>ALLEL4
.#DE4 ,A2
---------------------------------;,,WS#C
,,"W$-,,\ ,,SOLU;NS
,LESSON #BC @7 PP4 #IC-IF @7
.#AE4
.#CG4 --#E .;X @+ ;L#J .;Y .K #BJ
.;X -9T]CEPT3
-#E .;X @+ #AJ7#J7 .K #BJ
.;X .K --#D
.;Y -9T]CEPT3
-#E7#J7 @+ ;L#J .;Y .K #BJ
.;Y .K #B
#FA4
,! ;Y-9T]CEPT1 #A.E1 REPRES5TS ! CO/
6R5T %OES1 4#A.EJ4 ,! SLOPE1 #C1
REPRES5TS ! CO/ P] GAME1 4#C4
,LESSON #B.D @7 PP4 #AJA-AJD @7
.#AE4 ,LET @7 .;X #A @1 .;Y #A @7 .K
7#G1 --#C7 & .;Y -- .;Y ;L .K ;M7 .;X --
.;X #A @7
.#CE ,LET 7.;X #A @1 .;Y #A @7 .K
7-#E1 --#B7 & 7.;X #B ,.;Y #B @7 .K
7-#C1 #H74
;Y--;Y #A .K ;M7;X--;X #A @7
.;Y- 7-#B7 .K #E7 .;X - 7-#E77
.;Y .K #E .;X @+ #BC
.#EC4 ,AN EQU,N IS #AE;X @+ #I;Y .K
#DEJJ4
,F ! GRAPH1 Y C SEE T IF #BJJ G5]AL
ADMIS.NS TICKETS 7 SOLD1 AB #AFG /UD5T
TICKETS 7 SOLD4
,LESSON #B.E @7 PP4 #AJI-AAA @7
.#E4 .;Y .K .AX
-#BA .K .A 7#F7
,SUB/ITUTE =A 9 .;Y .K .AX4
.#AE4 .;Y .K .AX
-#A.F .K .A 7-#D.H7
,S1
,:5 .;X .K #AB3
.#DA4
,2C ! RATIOS >E APPROXIMATELY EQUAL1 !
DATA %[ DIRECT V>I,N4 ,AN EQU,N RELAT+
.;S & ..;T IS ;T .K #E..AS4
,LESSON #B.F @7 PP4 #AAG-ABJ @7
#I4 ,! CORREL,N COE6ICI5T IS CLOSE/ TO
--#A 2C ! SCATT] PLOT %[S A /R;G
NEGATIVE CORREL,N4
#AA4
A4
B4 ,! L9E %[N APPE>S 6PASS "? 7.;X #A
.;Y #A @7 .K 7#A1ABJ7 & 7.;X #B ,.;Y #B
@7 .K 7#E1 #DB74
;Y--;Y #A .K ;M7;X--;X #A @7
.;Y - #ABJ.K --#AI.E7 .;X - #A7
.;Y .K --#AI.E .;X @+ #ACI.E
C4 ,:5 .;X .K #BJ3
.;Y .K --#AI.E7#BJ7 @+ #ACI.E .K
--#BEJ.E
---------------------------------;,,WS#D
,,"W$-,,\ ,,SOLU;NS
.#BE4 ,A SCATT] PLOT & POSSI# L9E (
BE/ FIT >E %[N4 ,! L9E APPE>S 6PASS "?
@7 .;X #A @1 .;Y #A 7.K 7#J1 #BBDJ7 &
7.;X #B ,.;Y #B @7 .K 7#F1 #BHEJ74
;Y-;Y ;L .K ;M7;X- .;X #A @7
.;Y -- #BBDJ .K #AJA.G7 .;X -- #J7
.;Y .K #AJA.G .;X @+ #BBDJ
,AN APPROXIM,N (! BE/-FITT+ L9E IS .;Y
.K ;L#JL#.G .;X @+ #BBDJ4
.,LESSON .#B..G @7 PP4 #ABG-ABI @7
.#AC4 ,! GRAPH ( IS ! GRAPH ( .;F7.;X7
.K _\;X_\ REFLECT$ 9 ! ;X-AXIS1 V]TIC,Y
%RUNK 0A FACTOR ( @1 & TRANSLAT$ "R #A
UNIT & UP #E UNITS4
.#AI4 ,V]TEX IS 7-#B1 --;L72 .;Y .K
.A_\.;X @+ #B_\--#A ,US+ PO9T 7#J1 #J73
#J .K .A _\#J @+ #B_\--#A
,AN EQU,N IS
.#CI4 ,V]TEX IS 7#FI1 #ADJ72 .;Y .K
.A_\.;X -- #FI_\ @+#ADJ
,US+ PO9T 7#J1 #J73 #J .K .A
_\#J--#FI_\ @+ #ADJ
,AN EQU,N IS
,LESSON #B.H @7 PP4 #ACE-ACH @7
.#AE4
.#BE4
.#DE4 .;X .K Y>DS ( COTTON LACE2 .;Y
.K Y>DS ( L95 LACE #A.E .;X @+ #B.E .;Y
"K#GE
,LET .;X .K #BD3
#A.E7#BD7 @+ #B.E .;Y "K#GE
.;Y "K#AE.F
,Y C BUY #AE.F OR LESS Y>DS ( L95
LACE4
,*APT] #C
.,LESSON .#C..A @7 PP4 #AEF-AEH @7
.#I4 .;Y .K --#C .;X -- #B
#D --#C7-#B7--#B
#D #F--#B
#D.K#D
#E .;X @+ #B .;Y .K --#B
#E 7-#B7 @+ #B7#D7 --#B
-#AJ @+ #H --#B
-#B .K --#B
,! SOLU;N IS 7-#B1D74
#BA4
,! GRAPHS (! EQU,NS >E ! SAME L9E4 ,!
SY/EM HAS 9F9ITELY _M SOLU;NS4 ,! SY/EM
IS 3SI/5T & DEP5D5T4
#CG4
,LET .;Y .K TOTAL CO/4
,LET .;X .K NUMB] ( "DS4
,OP;N .,A3 .;Y.K #ABA @+ .;X
,OP;N ;,B3 .;Y .K #AB .;X
,! PLANS >E EQUAL AF #AA "DS4 ,IF !
DAILY CO/ ( OP;N ;,B 9CR1SES1 ! PLANS W
2 EQUAL 9 FEW] "DS4
---------------------------------;,,WS#E
,,"W$-,,\ ,,SOLU;NS
,LESSON #C.B @7 PP4 #AFD-AFG @7
.#E4 #F .;X -- #B .;Y .K #E
-#C .;X @+ .;Y .K #G .;Y .K#C .;X @+
#G
,:5 .;Y .K #C .;X @+ #G3
#F .;X -- #B7#C .;X @+ #G7 .K #E
#F .;X -- #F .;X -- #AD .K #E
-#AD @6.K #E ,"! IS NO SOLU;N4
.#BI4
,:5 .;Y .K --#F3
#B .;X - #C7-#F7 .K #H
.;X .K --#E ,! SOLU;N IS 7-#E1 --#F74
.#EI4 .;X .K D\#
.;Y .K S+LES
.;X @+ .;Y .K #BF .;Y .K #BF- .;X
#D .;X @+ #B .;Y .K #GF
#D .;X @+ #B7#BF -- .;X @7 .K #GF
#D .;X @+ #EB--#B .;X .K #GF
.;X .K #AB
.;Y .K #BF -- .;X
.;Y .K #BF--#AB
.;Y .K #AD
,"! 7 #AB D\#S GAMES & #AD S+LES GAMES
9 PROGRESS4
.,LESSON .#CC @7 PP4 #AGA-AGC @7
.#I4 #D .;X -- #D .;Y .1.K --#AF
-.;X @+ #B .;Y .1.K --#D
#AI4 #C .;X @+ #B .;Y .1 --#F
-#E @+ #B .;Y .1-#B
.;Y "K #E
#CG4
A4 .;X #A .1.K #B
.;Y .1.K #B
.;X @+ .;Y "K.K #H
.;X @+ .;Y .1.K #E
B4
C4 .,SAMPLE .ANSW]3 #C JUNIORS1 #D
S5IORS2 #D JUNIORS1 #D S5IORS4
.,LESSON .#C..D @7 PP4 #AHB-AHE @7
.#AA4
,NO SOLU;N
.#BE4
,9F9ITELY _M SOLU;NS
#DE
.A4 .;F .K #A/ PLACE2 ;S .K #BND
PLACE2 .;T .K #CRD PLACE
.;F @+ #E @+ .;T .K #BJ ,EQU,N #A
#E .;F @+ #C .;S @+ .;T .K #FH ,EQU,N
#B
..;S .K ;F@+ .;T ,EQU,N #C
.;F @+ @7 .;F @+ .;T @7 @+ .;T .K #BJ
#B .;F @+ #B .;T .K #BJ;,NEW,EQ4 #A
#E .;F @+ #C7 .;F @+ .;T @7 @+ .;T.K
#FH #H .;F @+ #D .;T .K #FH ,NEW,EQ4 #B
-#H .;F -- #H .;T .K --#HJ ,ADD --#D
"TS NEW
;T.K#C
,SUB/ITUTE .;T .K .#C 96NEW ,EQU,N #A4
#B .;F @+ #B7#C7 .K #BJ .;F .K #G
,SUB/ITUTE .;F .K #G & .;T .K #C 9TO
,EQU,N #C4
;S.K;F@+ ;T ;S .K #G @+ #C .K #AJ
#G A?LETES PLAC$ F/1 #AJ A?LETES PLAC$
SECOND1 & #C A?LETES PLAC$ ?IRD4
---------------------------------;,,WS#F
,,"W$-,,\ ,,SOLU;NS
.B4 .;F @+ .;S @+ .;T .K #BJ ,EQU,N #A
#E .;F @+ #C .;S @+ .;T .K #GJ ,EQU,N
#B
..;S .K ;F@+ .;T ,EQU,N #C
..;F@+ 7;F @+ ;T7 @+ .;T .K #BJ #B .;F
@+ #B .;T .K #BJ ,NEW ,EQ4 #A
#E .;F @+ #C7 .;F @+ ..;T7 @+ ;T.K #GJ
#H;F@+.#D;T.K #GJ ,NEW,EQ#.B
.;T _C 2 A FRAC;N2 Y _C H "P (A P]SON4
,? CLAIM M/ 2 FALSE4
.,LESSON .#C..E @7 PP4 #AIA-AIC @7
.#E4
#BA4
#CC4
A4
B4
,! D[NT[N /ORE SOLD #EF ( ,MODEL ,A1
#GH ( ,MODEL ;,B1 & #CJ ( ,MODEL ,C4 ,!
MALL /ORE SOLD #FJ ( ,MODEL ,A1 #EG (
,MODEL ;,B1 & #BF ( ,MODEL ,C4
C4
.,LESSON .#C..F @7 PP4 #AII-BJB @7
.#AC4
.#BC4
.#DA4
,S1 MATRIX .,,PS IS DEF9$4
.K ,7#FEJ7#BA7 @+ #HBE7#DJ7 @+
#AJEJ7#AE7 #FEJ7#AF7 @+ #HBE7#CC7 @+
#AJEJ7#AI77'
.K ,7#FB1DJJ #EG1EGE7'
,! PR(IT = D1L] ,A IS 4#FB1DJJ &!
PR(IT = D1L] ;,B IS 4#EG1EGE4
.,LESSON .#C..G @7 PP4 #BJG-BJI @7
.#AA4
.K 7-#B--#AHJ @+ #J7--7#BD @+ #J @+
#J7 .K --#BJF
.#BC4
,! >EA (! TRIANGLE IS #AB SQU>E UNITS4
---------------------------------;,,WS#G
,,"W$-,,\ ,,SOLU;NS
#DC4
A4 .;X .K S+LE2 .;Y .K D\#2 .;Z .K
TRIPLE
.;X @+ ;Y @+ .;Z .K #ABJ
#J.IJ .;X @+ #A.B .;Y @+ #A.F .;Z .K
#ACD
.;X .K .;Y @+ .;Z .;X -- .;Y - .;Z .K
#J
.K 7-#A.B @+
#A.F--#J.I7--7#A.B--#A.F--#J.I7 .K #J.H
,"! >E #FJ S+LE-SCOOP1 #DJ D\#-SCOOP1
& #BJ TRIPLE-SCOOP C"OS SOLD4
B4 ,NEW PRICE .K #A.A ;,X OLD PRICE
L4L7@4#.IJ7 .K @4#.II2 L4L74#A.BJ7 .K
4#A.CB2 L4L74#A.FJ7 .K 4#A.GF
,NEW SALES .K #J.IE ;,X OLD SALES
#J.IE7#FJ7 .K #EG2 #J.IE7#DJ7 .K #CH2
#J.IE7#BJ7--#AI ,NEW REV5UE .K
@4#.II7#EG7 @+ 4#A.CB7#CH7 @+
4#A.GF7#AI7 .K 4#ADJ.JC
,LESSON #C.H @7 PP4 #BAD-BAG @7
.#C4
.#BE4
,! SOLU;N (! SY/EM IS 7#C1 #B74
.#DG4
#B.C OZ ,BRAN ,CRUN*IES2 #J.H OZ
,TOA/$ ,OATS2 & #A.B OZ ,:OLE ,:1T
,FLAKES
,*APT] #D
,LESSON #D.A @7 PP4 #BDJ-BDC @7
.#AE4
,BO? GRAPHS H ! SAME AXIS ( SYMMETRY4
,! GRAPH (_/7;X7 .K -.;X #B @+ #B OP5S
D[N1 & XS V]TEX IS #B UNITS HI<] ?AN T (
.;Y .K .;X #B @4
.#CG4
.A .1 #J2 ! FUNC;N HAS A M9IMUM VALUE4
,M9IMUM3
.#EG4
,! CA# IS #AJ FEET ABV ! ROAD4
---------------------------------;,,WS#H
.,LESSON .#D..B @7 PP4 #BDI-BEA @7
.#AI4
.A .K #A1 .;P .K --#A1 & .;Q .K --.#B
.;X -9T3 .;X .K --#B & .;X .K --#A
,AXIS ( SYM43
,V]TEX3 7-#A.E1 --#J.BE7
#BI4 .;Y .K 7;X--#C7 #B @+ #F .K
7;X--#C77;X--#C7 @+ #F
.K 7;X #B -- #C;X--#C;X @+ #I7 @+ #F
.K .;X #B -- #F .;X @+ #AE
#EC4
.A4 .;Y .K --#J.JJJBCD;X7;X--#AFJ7
.K --#J.JJJBCD7;X--#J7@7 .;X -- #AFJ7
.;P .K #J1 .;Q .K #AFJ2 ! FIELD IS
#AFJ FEET WIDE4
B4
.;Y .K --#J.JJJBCD7#HJ77#HJ--#AFJ7 .K
#A.E
,! MAXIMUM HEI<T IS AB #A.E FEET4
.,LESSON .#D..C @7 PP4 #BEE-BEH @7
.#CC4 .;Z #B -- .#C;Z -- #ED .K #J
7.;Z--.#I77.;Z @+ #F7 .K #J
.;Z -#I .K #J ;Z .K #I OR ;Z @+ #F .K
#J ;Z.K-#F
#DG4 .;Y .K .;X #B @+ .#G;X -- #CJ .K
@7 .;X @+ #AJ7 @7 .;X -- #C7
,! Z]OS >E --#AJ & #C4
#FG4
A4 .,A.K 7#CJ7 7#BJ7 .K #FJJ FT #B
B4
#AJFD .K 7;X @+ #CJ77;X @+ #BJ7
C4 ;X #B @+ #EJ;X @+ #FJJ .K #AJFD
@7 .;X - #EH7@7 .;X - #H7 .K #J .;X .K
--#EH OR .;X .K #H
,EXP& ! L5G? & WID? 0#H FEET4
.,LESSON .#D..D @7 PP4 #BFC-BFE @7
.#BG4 #BJ .;X #B @+ #ABD;X @+ #BD .K
#D7#E;X #B @+ #CA;X @+ #F7
.K #D7#E .;X @+ ;L7@7 .;X @+ #F7
.#CI4 #F .;R #B -- #G .;R -- #E .K #J
7#C;R--#E77#B;R @+ #A7 .K #J
OR
.#FC4 #IF .K 7#B .;X @+ #H77#B .;X @+
#AB7--#IF
#J .K #D .;X #B @+ #DJ .;X -- #IF
#J .K 7#D .;X - #H7@7 .;X @+ #AB7
.;X .K #B OR .;X .K --#AB
,! BORD]'S WID? %D 2 #B FEET4
.,LESSON .#D..E @7 PP4 #BFI-BGA @7
.#AG4
#BG4
#DA4
A4 ;R #B .K #AJ #B .K #AJJ
B4
C4
.,LESSON .#D..F @7 PP4 #BGI-BHB @7
.#AA4 --#E7;N--#C7 #B .K #AJ 7;N--#C7
#B .K --#B
.#BI4
.#FG4 ,IMP$.E3 #AB @+ #H .;I -- #F .;I
-- #AJ .;I .K #AB--#H .;I OHMS
.,LESSON .#D..G @7 PP4 #BHH-BIA @7
.#BG4 .;X #B -- #B .;X .K --#BE
.;X #B -- #B .;X @+ #A .K --#BE @+ #A
@7 .;X -- #A7 #B .K --#BD
.#DE4
,! V]TEX IS
---------------------------------;,,WS#I
,,"W$-,,\ ,,SOLU;NS
.#FE4 .;Y .K 7#BJJ @+ #AJ .;X @77#DJ
-- .;X @7
.;Y .K #HJJJ @+ #BJJ;X--#AJ .;X #B
.;Y- #HJJJ .K --#AJ @7 .;X #B -- #BJ
.;X @7
.;Y -- #HJJJ @+ 7-#AJ77#AJJ7 .K --#AJ7
.;X #B -- #BJ .;X @+ ;L#JJ7
.;Y- #IJJJ .K --#AJ @7 .;X - #AJ7 #B
.;Y .K --#AJ @7 .;X - #AJ7 #B @+ #IJJJ
,! REV5UE IS MAXIMIZ$ :5 ! PRICE IS
9CR1S$ #AJ "TS2 #AJ74#AJ7 .K 4#AJJ4
.,LESSON .#D..H @7 PP4 #BIF-BII @7
.#AI4 #D .;X #B @+ #C .K .;X #B -- #G
.;X #C .;X #B @+ #G .;X @+ #C .K #J
.#CI4 #G .;R #B -- ..;S .K .#B;R @+
#I;R #B --#B;R #B -- #B;R--#E .K #J
.;B #B -- .#D;AC .K 7-#B7 #B --
#D7-#B77-#E7 .K --#CF "K #J
,TWO IMAG9>Y3
.#GA4 .;,S .K --#J.JJJJAC;,E #B @+
#J.JDB .;,E -- #BA
#AJ .K --#J.JJJJAC .;,E #B @+ #J.JDB
.;,E -- #BA
#J .K --#J.JJJJAC .;,E #B @+ #J.JDB
.;,E -- #CA
.;,E #AADA MET]S OR .;,E #BJIJ MET]S
.,LESSON .#D..I @7 PP4 #CJD-CJG @7
.#AG4
.#CI4 #C .;X #B @+ #B .;X -- #H "K #J
7#C .;X - #D7@7 .;X @+ #B7 .K #J
OR .;X .K --#B
,! SOLU;N IS
.#GC4 #J.JJAG .;X #B @+ #J.ADE;X @+
#B.CE .1 #AJ
#J.JJAG .;X #B @+ #J.ADE;X--#G.FE .1
#J
,TE/ VALUES ;X .K #J & ;X .K #CG
6DET]M9E T ;X .1 #CF.HD4 ,! DOMA9 IS #J
"K ;X "K #DJ4 ,S1 ! L>VAE'S L5G? T5DS
6BE GRT] ?AN #AJ MM 2T >.D #CG 6#DJ "DS4
.,LESSON .#D..AJ @7 PP4 #CAB-CAE @7
.#AI4 ..;Y .K A7;X--;P77.;X -- .;Q7
.;Y .K .A7.;X @+ #C77;X--#C7
,A QUADRATIC FUNC;N IS
#CE4 .;Y--.AX #B @+ .BX @+ .;C
#I .K .A7-.;L7 #B @+ .;B 7-;L7 @+ .;C
.A- .;B @+ .;C .K .#I
#A .K .A7.;L7 #B @+ .;B7.#A7 @+ ..;C A
@+ ;B @+ .;C .K;L
#AG .K .A 7#C7 #B @+ .;B 7#C7 @+ .;C
.#I;A @+ .#C;B @+ .;C .K #AG
,US+ SUB/ITU;N & .;C .K #I -- .A @+
.;B @3 ..A @+ ;B @+ 7#I-A @+ ;B7 .K ;L
;B.K-.#D
#I .A @+ #C7-#D7 @+ 7#I- .A -#D7 .K
#AG .A .K #C
#C--7-#D7 @+ .;C .K #I .;C .K #B
,A QUADRATIC FUNC;N IS .;Y .K #C;X #B
-- #D;X @+ #B4
#DI4
A4
.;Y .K #J.JAAIJ .;X #B -- #J.CJI .;X
-- #J.JJJDH
B4 ,:5 .;X .K #AJ1 .;Y --#A.IJ SECONDS
,*APT] #E
.,LESSON .#E..A @7 PP4 #CCC-CCE @7
.#AG4 7#F.C * #AJ #E @77#H.I * #AJ
-#AB @7 .K #EF.JG * #AJ -#G
.K #E.FJG * #AJ #A * #AJ -#G .K #E.FJG
* #AJ -#F
--------------------------------;,,WS#AJ
,,"W$-,,\ ,,SOLU;NS
.#CA4
,QUOTI5T ( P[]S PROP]TY
.#EA4 ,B1D3 .;D .K #F MM1 .;R .K #C MM
,AB #C.D "TS GRT]
.,LESSON .#E..B @7 PP4 #CDA-CDD @7
.#BA4
.;F 7#C7 .K --#GH
.#BG4 ,! DEGREE IS EV5 &! L1D+
COE6ICI5T IS NEGATIVE4
#EG4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;T @3 #J3 #B3 #D3 #F3 #H3 #AJ3 #AB
.;S @3 #A.B3 #A.DF3 #A.FH3 #A.EI3
#A.DD3 #A.IG3 #D.DA
,! NUMB] ( SN[BO>D]S 0 GRT] ?AN #B
MILLION 9 #BJJB 7:5 ;T #AJ74
.,LESSON .#E..C @7 PP4 #CDI-CEB @7
.#AA4 7#E .;B -- #F .;B #C @+ .#B;B #D
@7--7.#I;B #C @+ .#D;B #D -- #G7
.K .#B;B #D -- .#D;B #D -- .#F;B #C
--.#I;B #C @+ .#E;B@+ .#G
.K --#B;B #D -- #AE;B #C @+ #E;B @+ #G
.#BA4 7.#B;A -- #C77A #B -- #AJ;A --
.#B7
.K 7#B .A -- #C7 @7 .A #B @7--7#B .A
-- #C7 7#AJ .A @7--7#B .A -- #C7 7#B7
.K #B .A #C -- #BC .A #B @+ #BF .A @+
#F
.#FA4 .;,P .K #J.JJBFG;S,F .K
#J.JJBFG;S7#J.JAAF;S #B @+ #J.GHI7
.K #J.JJJJCJIGB .;S #C @+ #J.JJBAJFFC
.;S
,:5 .;S .K #AJ1 .;,P 7#AJ7 .K
#J.JEBJCHC4
,AB #J.JEB HORSEP[] IS NE$$4
.,LESSON .#E..D @7 PP4 #CEF-CEI @7
.#G4 #C .;Y #E -- #DH .;Y #C .K #C .;Y
#C @7 .;Y #B -- #AF7 .K #C .;Y #C 7.;Y
@+ #D7@7 .;Y -- #D7
.#BC4 #D .;C #C @+ #H .;C #B -- #I .;C
-- #AH .K #D;C #B @7 .;C @+ #B7--#I7 .;C
@+ #B7
.K @7 .;C @+ #B77#B .;C @+ #C77#B .;C
- #C7
.#FA4 .;L .K .;X2 .;H .K .;X -- #E2
..;W .K .;X -- #E
.;V .K .L: #BEJ .K 7.;X77.;X --
#E77;X--#E7
#BEJ .K .;X,7.;X #B -- ;L#J;X @+ #BE7
#J .K ;X #C -- #AJ;X #B @+ #BE;X--#BEJ
#J .K ;X #B 7;X--#AJ7 @+ #BE7;X--#AJ7
#J .K 7;X #B @+ #BE77;X--#AJ7 .;X .K
#AJ
.;L .K #AJ IN41 .;H .K #E IN41 .;W .K
#E IN4
.,LESSON .#E..E @7 PP4 #CFF-CFH @7
.#AG4
.#BE4 --#I #A #B --#EA #AJH
.;F7.;X7 .K @7 .;X @+ #I7@7 .;X #B --
#G .;X @+ #AB7
.K @7 .;X @+ #I7@7 .;X -- #D7@7 .;X --
#C7
.#DC4
--------------------------------;,,WS#AA
,,"W$-,,\ ,,SOLU;NS
,LESSON #E.F @7 PP4 #CGD-CGG @7
.#G4 .;G7.;X7 .K #D .;X #E @+ #C .;X
#C -- #B .;X -- #AD
,FACTORS (! 3/ANT T]M3 +-#A1 +-#B1
+-#G1 +-#AD
,FACTORS (! L1D+ COE6ICI5T3 +-#A1
+-#B1 +-#D
,POSSI# R,NAL Z]OS3
.#BA4 ,POSSI# R,NAL Z]OS3
,R1SONA# Z]OS3
,TE/ .;X .K --#C3
.;F7.;X7 .K 7.;X @+ #C77#F;X #B @+
.#G;X -- #E7
.K @7 .;X @+ #C77#B;X- #A77#C;X @+ #E7
,R1L Z]OS >E
.#DG4 .;,V .K .;X7.;X -- #A7@7 .;X --
#B7 #BD .K .;X7.;X #B -- #C .;X @+ #B7
#J .K .;X #C -- #C .;X #B @+ #B .;X --
#BD
,POSSI# R,NAL Z]OS3 +-#A1 +-#B1 +-#C1
+-#D1 +-#F1 +-#H1 +-#AB1 +-#BD
,LESSON #E.G @7 PP4 #CHC-CHF @7
.#AE4 ,POSSI# R,NAL Z]OS3 +-#A1 +-#B1
+-#D1 +-#H
.;F7.;X7 .K .;X #D @+ ;X #C @+ .#B;X
#B @+ #D;X - #H
.K @7 .;X @+ #B7@7 .;X #C -- .;X #B @+
#D .;X -- #D7
.K @7 .;X @+ #B7@7 .;X - ;L7@7 .;X #B
@+ #D7
.K @7 .;X @+ #B7@7 .;X -- ;L7@7 .;X --
#B .;I @7@7 .;X @+ #B .;I @7
,! Z]OS >E --#B1 #A1 .#B;I @1 &
--.#BI4
.#CG4 .;H7.;X7 .K .;X #E -- #B .;X #C
-- .;X #B @+ #F .;X @+ #E
#B SIGN *ANGES2 #B OR #J POSITIVE R1L
Z]OS
;H7 -;X7 .K 7-;X7 #E -- #B7-;X7 #C --
7-;X7 #B @+ #F7-;X7 @+ #E
.K -.;X #E @+ .#B;X #C -- .;X #B --
..#F;X @+ .#E
#C SIGN *ANGES2 #C OR #A POSITIVE R1L
Z]OS4
,POSSI# NUMB]S ( Z]OS3
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,POSITIVE3 ,NEGATIVE3 ,IMAG9>Y3 ,TOTAL
.#B @3 .#C @3 .#J @3 .#E
.#J @3 .#C @3 .#B @3 .#E
.#B @3 .#A @3 .#B @3 .#E
.#J @3 .#A @3 .#D @3 .#E
.#FA4 .;,S .K --#J.JAE .;X #C @+ #J.F
.;X #B -- #B.D .;X @+ #AI
#J .K --#J.JAE .;X #C @+ #J.F .;X #B
-- #B.D .;X -- #EF
,"! >E TWO POSITIVE Z]OS ( ? FUNC;N1
;X #AF.D & ;X #CJ.I1 B ;X #AF.D IS ! MO/
LIKELY AM.T4
,LESSON #E.H @7 PP4 #CIJ-CIB @7
.#C4
.#AI4 ,TURN+ PTS3 7-#B.B1 --#CH71
LOCAL M9IMUM2 7-#A.A1 #J.H71 LOCAL
MAXIMUM2 7#J.C1 --#DJ71 LOCAL M9IMUM2
7#A.I1 #H71 LOCAL MAXIMUM2 7#B.GE1
--#AJ.E71 LOCAL M9IMUM
,Z]OS3 .;X -- #B.F1 .;X --#A.D1 .;X
--#A1 .;X #A.E1 .;X #B.B1 .;X #C
,X M/ 2 AT L1/ A DEGREE #F FUNC;N4
.#DA4
,AT AB #J.IE SECONDS 96! /ROKE !
SWIMM] IS GO+ ! FA/E/4
,LESSON #E.I @7 PP4 #CIG-CII @7
.#I4 .;F7.;X7 .K .A7.;X @+ #E7@7 .;X
@7@7 .;X -- #F7
.#AE4 .;F 7#A7 .;F 7#B7 .;F 7#C7 .;F
7#D7 .;F 7#E7 .;F 7#F7
--------------------------------;,,WS#AB
,,"W$-,,\ ,,SOLU;NS
#BG4
.A4 ;M .K #J.JJJHAGDB;T #C -#J.JBAED;T
#B @+ #J.BDI;T@+#C.AG
.B4
.C4
,*APT] #F
.,LESSON .#F..A @7 PP4 #DAG-DAI @7
.#I4
#BE4 #BG #B/C .K 7#BG #A/C @7 #B .K
7#C7 #B .K #I
.#FC4
#F1ADA1BEJ1JJJ .K .;S #C ;S #AHCA
,AB #AHJJ REVOLU;NS P] M9UTE
.,LESSON .#F..B @7 PP4 #DBD-DBG @7
.#E4 #C #A/D @* #BG #A/D .K #C #A/D @*
#C #A/D @* #C #A/D
.K #C 7#A/D@+#A/D@+#A/D@+#A/D7 .K #C
#A .K #C
.#BG4
.#HE4 .;D .K #A.I,77#E.E * #AJ -#D @7
.;L @7' #A/B
.;L .K #AJ CM .K #AJJ MM
.;D .K #A.I,77#E.E * #AJ -#D
@77;L#JJ77' #A/B #J.DDEF
,! OPTIMUM DIAMET] IS AB #J.DE MM4
.,LESSON .#F..C @7 PP4 #DCB-DCD @7
.#C4 .;F7.;X7 .K .;G7.;X7 .K --#C .;X
#A/C .K #D .;X #A/B @+ #E .;X #A/C @+ #D
.;X #A/B
.K #B .;X #A/C @+ ;E .;X #A/B
,DOMA9 ( ;F3 ALL NONNEGATIVE R1LS
,DOMA9 ( ;G3 ALL NONNEGATIVE R1LS
,DOMA9 ( @+ ;G3 ALL NONNEGATIVE R1LS
.#AC4 ..;G7;X7 @* ;F7.;X7 .K 7#E .;X
#A/B @77#D .;X #B/C @7 .K #BJ .;X #G/F
,DOMA9 ( ;F3 ALL R1LS
,DOMA9 ( ;G3 ALL NONNEGATIVE R1LS
,DOMA9 ( ;G 99 ;F3 ALL NONNEGATIVE
R1LS
#DE4 ,= 4#AE 4C.T3 .;F7.;X7 .K .;X --
#AE
,= #AJ@3P 4C.T3 .;G7.;X7 .K .;X --
#J.L .;X .K #J.I .;X
A4 .;G7.;F7.;X77 .K .;G @7 .;X -- #AE7
.K #J.I @7 .;X -- #AE7
.;X .K #HE3 #J.I7#HE--#AE7 .K
#J.I7#GJ7 .K 4#FC.JJ
B4 .;F7.;G7.;X77 .K .;F 7#J.I .;X @7
.K #J.I .;X -- #AE
.;X .K #HE3 #J.I7#HE7--#AE .K
#GF.E--#AE .K 4#FA.EJ
C4 ,! #AJ@3P 4C.T 2F ! 4#AE 4C.T4
.,LESSON .#F..D @7 PP4 #DDB-DDE @7
.#G4
.#AE4 .;F7.;G7.;X77 .K .;F7.;X -- #D7
.K 7;X--#D7 @+ #D .K .;X
.;G7.;F7.;X77 .K .;G7.;X @+ #D7 .K @7
.;X @+ #D7--#D .K .;X
.#DI4 ,! WAT]L5G? %D 2
.,LESSON .#F..E @7 PP4 #DDI-DEA @7
.#AA4 ,! DOMA9 & RANGE >E ALL R1L
NUMB]S4
#AG4 ,DOMA93 ;X.1 --#A ,RANGE3 ;Y .1
#H
#CG4
A4
B4 ,DOMA93 ;,C .1 --#BGC.AE2 RANGE3
.;V .1 #J
.,LESSON .#F..F @7 PP4 #DEF-DEI @7
.#E4
.#AC4
--------------------------------;,,WS#AC
,,"W$-,,\ ,,SOLU;NS
.#EI4 .;H .K #AEJ3
#A.G .;T
.;H .K #BEJ3
#BA.G .;T
,! ELEPHANT )A %\LD] HEI<T ( #BEJ CM
IS AB #BJ YE>S OLD] ?AN ! ELEPHANT )!
%\LD] HEI<T ( #AEJ CM4
,*APT] #G
.,LE,,SSO,'N .#G..A @7 PP4 #DHB-DHE @7
.#AG @4 ,! DOMA9 IS ALL R1L ,,JU
NUMB]S &! RANGE IS ;Y .1 #C4
#BI4
#CG4
A4 .;,P .K #BBJJ2 .;R .K #J.JC2 .;N .K
#D2 .;T .K #D
,! BAL.E IS 4#BDGI.CH4
B4 .;,P .K #BBJJ2 .;R .K #J.JBBE2 .;N
.K #AB2 .;T .K #D
,! BAL.E IS 4#BDJF.IH4
C4 .;,P .K #BBJJ2 .;R .K #J.JB2 ;W .K
#CFE2 .;T .K #D
,! BAL.E IS 4#BCHC.BC4
.,LESSON .#G..B @7 PP4 #DHI-DIA @7
.#I4
#AI4
,DOMA93 ALL R1L NUMB]S ,RANGE3 .;Y.1
--#A
#CC4
A4
,AB #E YE>S AF X 0 PUR*AS$
B4 .;Y .K #BD1JJJ7#J.HDE7 #EJ --
4#E.BI2 TOO L[
.,LESSON .#G..C @7 PP4 #DIE--#DIH @7
.#E4 7#B .;E #C;X @7 #C .K .#B #C 7.;E
#C;X @7 #C .K .#H;E #I;X.'.-
.#CE4 EXPON5TIAL DECAY
.#EG4 .;,P .K #BJJJ2 .;R .K #J.JD2 .;T
.K #E
.,A .K .,PE RT.' .K #BJJJ;E
7#J.JD77#E7 4#BDDB.HA
.,LESSON .#G..D @7 PP4 #EJC-EJE @7
.#AC4 S LOG #A/B #H.K --#C4
#CC4 LOG #C #HA ;X .K LOG #C 7#C #D @7
;X .K LOG #C #C #D .;X .K .#D;X
#FA4
A4 .;,E .K #B.E ;,X #AJ #BD
.;,M .K #J.BI7LN7#B.E ;,X #AJ #BD
@7@7--#I.I #F.CI
B4 .;,M .K #J.BI7,IN .;,E7 -- #I.I
,? REPRES5TS ! AM.T ( 5]GY REL1S$ Z A
FUNC;N (! 5]GY MAGNITUDE4
.,LESSON .#G..E @7 PP4 #EAJ-EAC @7
.#AA4 LOG #ADD .K LOG #AB #B .K #B LOG
#AB .K #B.AEH
.#AG4 LOG #C .;X #D .K LOG #C @+ LOG
.;X #D .K LOG #C @+ #D LOG .;X
.#GA4
--------------------------------;,,WS#AD
,,"W$-,,\ ,,SOLU;NS
.,LESSON .#G..F @7 PP4 #EAI-EBB @7
.#AE4 ;LL #E .;X .K #CC
LOG #AA ;LL #E .;X .K LOG #AA #CC
.#CE4 #E.B LOG #D #B .;X .K #AF
LOG #D #B .;X #C.JGFI
#D 7LOG #D #B;X7 #D #C.JGFI
#B .;X #GA.BJBJ
.;X #CE.FJAJ
,*ECK3
.#EG4 .;,R .K #AJJ .;E --#JJJJDC .;T
#E .K ;I#JJ .;E --#JJJDC .;T
#J.JE .K .;E --#J.JJJDC .;T
,9 #J.JE .K ,9 .;E --#J.JJJDC .;T
-#B.IIEG --#J.JJJDC .;T
.;T #FIFG YE>S
.,LESSON .#G..G @7 PP4 #ECC-ECF @7
#AA4
,9 .;Y -- #B.HI .K #J.FI7 .;X -- #A7
,9 .;Y .K #J.FI .;X @+ #B.B
.;Y.K.;E #J.FI .;X @+ #B.B
.;Y.K.;E #B.B 7;E #J.FI @7 ;X #I7#B7
;X
#BC4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,9.' ;X @3 #J3 #J.FIC3 #A.JII3 #A.CHF3
#A.FJI
,9.' ;Y @3 -#J.EAA3 #A.DAA3 #B.EAH3
#C.BIF3 #C.IJB
,9 .;Y -- 7-#J.EAA7 .K #B.GDC7,IN .;X
-- #J7
,9 .;Y .K ,9 .;X #B.GDC -- #J.EAA
.;Y .K .;E ,9 .;X #B.GDC -- #J.EAA
.;Y .K .;E -#J.EAA @* .;E ,9 .;X
#B.GDC #J.F .;X #B.GDC
#CC4
A4 ,A MODEL IS ;Y .K #J.DH7#B.JH7 ;X
@4
B4 ,L9E> IF A GRAPH ( 7;X1 ;Y7 APPE>S
L9E>2 EXPON5TIAL IF A GRAPH ( 7;X1 ,9
;Y7 APPE>S L9E>2 P[] IF A GRAPH ( 7,IN
;X1 ,9 ;Y7 APPE>S L9E>4 ,! GRAPH ( 7;X1
;Y7 APPE>S L9E>1 S A MODEL IS ;Y .K
#CC.H .;X @+ #BH4
,*APT] #H
.,LESSON .#H..A @7 PP4 #EED-EEG @7
.#AE4
.#BA4 .;X @* ;Y3 #AB7#ACB7 .K #AEHD
#AH7#AIH7 .K #CEFD
#BC7#BEC7 .K #EHAI
#BI7#CAI7 .K #IBEA
#CD7#CGD7 .K #AB1GAF
;Y_/;X3 #ACB/AB .K #AA
#AIH/AH .K #AA
#BEC/BC .K #AA
#CAI/BI .K #AA
#CGD/CD .K #AA
.;X & .;Y %[ DIRECT V>I,N 2C ! RATIOS
;Y_/;X >E EQUAL4
.#CI4 ,SN[ %OES3
,AN EQU,N IS
,BOOTS3
.,LESSON .#H..B @7 PP4 #EFA-EFC @7
.#E4
,! GRAPH ( LIES F>!R F ! AXES ?AN !
GRAPH ( @1 & X LIES 9 ,QU>DRANTS ,,II &
,,IV 9/1D ( ,QUADRANTS ,I & ,,III4
.#BA4
,! DOMA9 IS ALL R1L NUMBAERS EXCEPT
#D1 &! RANGE IS ALL REL NUMB]S EXCEPT
--#A4
.#CI4 .A4
#B.HI SECONDS 6TRAVEL #A KILOMET]2
#B.HI7#E7 .K #AD.DE SECONDS 6TRAVEL #E
KILOMET]S
--------------------------------;,,WS#AE
,,"W$-,,\ ,,SOLU;NS
.#CI4 .B4
,F ! GRAPH1 Y C E/IMATE ! TEMP]ATURE
6BE #C.I'\X00BA',C4
,LESSON #HC @7 PP4 #EFH-EGA @7
.#G4
,NO .;X -9T]CEPT2 .;X .K --#A & .;X .K
#A >E V]TICAL ASYMPTOTES4
#AE4
#CC4
A4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,DEP?3 ,TEMP4
#AJJJ3 #D.GFCD
#AJEJ3 #D.EGIF
#AAJJ3 #D.DJID
#AAEJ3 #D.BEAE
#ABJJ3 #D.AJDD
#ABEJ3 #C.IFGB
#ACJJ3 #C.HCHI
B4
,! M1N TEMP]ATURE IS #D'\X00BA';,C AT
AB #AC.K#BCH MET]S4
,LESSON #H.D @7 PP4 #EGG-EHJ @7
.#G4 ,_C 2 SIMPLIFI$
.#BE4
.#DI4
,LESSON #H.E @7 PP4 #EHF-EHH @7
.#E
#AG4
#DC4
A4
B4 .;P .K #AE1EJJ2 .;I .K #J.JJE2 .;T
.K #D
,LESSON #H.F @7 PP4 #EIC-EIE @7
.#E4
#D7#C .;X @7 .K #I7 .;X @+ #B7
.;X .K #F
,*ECK3
.#AE4
#B7#B7 @+ #A7 .;X @7 .K #D7#B7 .;X .K
#D
,*ECK3
.#CE4
#GBJ .;T #B -- #HBHJ .;T @+ #BH1CFH .K
#FCE .;T #B -- #GCEJ .;T @+ #BG1BJJ
#HE .;T #B -- #ICJ @+ #AAFH .K #J
,2C #I.DE IS N 9 ! DOMA9 7#J "K.K .;T
"K.K #I71 .;T #A.DE #AIIE4
,*APT] #I
.,LESSON .#I..A @7 PP4 #FAG-FAI @7
.#G4
--------------------------------;,,WS#AF
,,"W$-,,\ ,,SOLU;NS
#BG4 .,A7-.#D @1 #A71 .;,B7-.#B @1
#F71 ;,C7#J1 --#A7
.;,,AB @6.K .,,BC @6.K .;,,AC @1 S
.,,ABC IS SCAL5E4
#EC4
A4
B4
C4
.,LESSON .#I..B 7PP#.FBC-FBE7
.#AE4 #E .;X #B .K --#AE .;Y .;X #B .K
--#C .;Y
,FOCUS3
,DIRECTRIX3 ,AXIS ( SYMMETRY3 .;X .K
#J
#BG4 ,FOCUS3 7-#E1 #J7 .;P .K --#E ;Y
#B .K --#BJ .;X
#EG4
A4
B4 .;X #B .K #D7#DH7 .;Y .;X #B .K
#AIB .;Y
.;Y #B .K #D7-#DH7 .;X .;Y #B .K
--#AIB .;X
C4 ,US+ .;X #B .K #AIB .;Y & .;X .K
#GC1 .;Y --#BG.H
,US+Y .;Y #B .K --#AIB .;X & .;Y .K
#GC1 .;X --#BG.H4
,! DI% IS AB #BG.H 9*ES DEEP4
.,LESSON .#I..C @7 PP4 #FBI-FCB @7
.#AG4 #AE .;X #B @+ #AE .;Y #B .K #FJ
.;X #B @+ .;Y #B .K #D
.#CI4
.#FE4
.,A@3.;X #B @+ 7-#D7 #B .K #BBE .;X .K
+-#AD.E 7-#AD.E1 --#D7
.;,B3 .;X #B @+ 7-#D7 #B .K #AJJ .;X
.K +-#I.B 7-#I.B1 --#D7
.;,C3 .;X #B @+ 7-#D7 #B .K #BE .;X .K
+-#C 7-#C1 --#D7
.;,D3 .;X #B @+ 7-#D7 #B .K #BE .;X .K
+-#C 7#C1 --#D7
.;,E3 .;X #B @+ 7-#D7 #B .K #AJJ .;X
.K +-#I.B 7#I.B1 --#D7
.;,F3 .;X #B @+ 7-#D7 #B .K #BBE .;X
.K +-_\#AD.E _\.K 7#AD.E1 --#D7
.A4 .;,,AF #AAD.E--7-#AD.E7_\ .K #BI
MI
.B4 .,,2 _\#I.B- 7-#I.B7_\ .K #AH.D MI
.C4 .;,,CD _\#C--7-#C7_\ .K #F MI
.,LESSON .#I..D @7 PP4 #FCG-FCI @7
.#AA4 #AF .;X #B @+ #I .;Y #B .K #ADD
@2 .A .K #D1 .;B .K #C
,V]TICES3 7#J1 +-#D72
,CO-V]TICES3 7+-#C1J72
,FOCI3 7#J1 +- @7
.#BI4 .;B .K @7@2 .;C .K #C2 A #B .K
.;B #B @+ .;C #B .A .K #D
.#DI4 ,L>GE/ FIELD3
#B .A .K #AHE .A .K #IB.E2 #B;FO .K
#AEE .;B .K #GG.E
,A .K 7#IB.E77#GG.E7 #BB1EBA SQU>E
MET]S
--------------------------------;,,WS#AG
,,"W$-,,\ ,,SOLU;NS
,SMALLE/ FIELD3
.#B;A .K #ACE .A .K #FG.E2 .#B;B .K
#AAJ .;B .K #EE
.,A .K 7#FG.E77#EE7 #AA1FFC SQU>E
MET]S
#AA1FFC "K.K,A"K.K#BB1EBA
.,LESSON .#I1.E @7 PP4 #FDE-FDH @7
.#AC4 #HA .;X #B -- #AF .;Y #B .K
#ABIF
.A .K @+ #D2 .;B .K #I2
,V]TICES37+-#D1J7
,FOCI3
,ASYMPTOTES3
#BC4 .;C .K #D @2 A .K #D2 .;B #B .K
.;C #B -- .A #B -- .A .;B .K #H
#DA4
A4 ,A7#CJ.E1 #J72#E7#HE1 --#DJ7
B4 ,V]TICES3 7+-#CJ.E1 #J72 HORIZONTAL
TRANS1 AXIS
,S1 AN EQU,N IS
C4
.;H .K #DJ @+ #AD.F .K #ED.F FEET
.,LESSON .#I..F @7 PP4 #FEE-FEG @7
.#C4 @7 .;X @+ #D7 #B .K --#H7 .;Y
#A--#B7
,P>ABOLA2 V]TICAL AXIS2 V]TEX AT 7.;H1
.;K7 .K 7-#D1 #B74
#D .;,P .K --#H .;,P .K --#B
,FOCUS3 @7 .;H1 .;K @+ .;P @7 .K 7-#D1
#J7
,DIRECTRIX3 ..;Y .K ;K--;P .;Y .K #D
.#AI4 ,V]TICES3 7#F1 --#C71 7#F1 #A72
,FOCUS3 7#F1 --#F71 7#F1 #D7
,V]TICAL TRANSV]SE AXIS2
,C5T]3
,4T.E 2T V]TEX 7#F1 --#C7 & 7.;H1 .;K7
@3
.A .K _\-#C -- .;K _\ .K _\-#C--7-#A7
_\ .K #B
,4T.E 2T FOCUS 7#F1 --#F7 & @7 .;H1
.;K @7@3
.;C .K _\-#F -- .;K _\ .K
_\-#F--7-#A7_\ .K #E
.;B #B .K .;C #B -- .A #B .K #BE--#D
.K #BA
,AN EQU,N IS
.#DI4 .;X #B -- ;L#J .;X @+ #D .;Y .K
#J2 .,A .K #A1 .;,B .K #J1 .;,C .K #J
.;,B #B -- .#D,;,AC .K #J--#D7#A77#J7
.K #J--,P>ABOLA
.;X #B -- ;L#J .;X @+ #D .;Y .K #J
@7 .;X #B -- ;L#J .;X @+ #BE7 .K --#D
.;Y @+ #BE
,:5 .;Y .K #J1 ! ;X-9T]CEPTS >E #J &
#AJ1 S ! 4T.E (! JUMP IS #AJ FEET4
.,LESSON .#I..G @7 PP4 #FFA-FFD @7
.#E4
,! SOLU;NS >E APPROXIMATELY 7#J.E1
--#B.F7 & 7#C.E1 #F.F74
.#AE4 #D .;X #B -- #E .;Y #B .K --#GF
#B .;X @+ .;Y .K--#F .;Y .K --#B .;X -
#F
,SUB/ITUTE --.#B .;X -- #F = .;Y 9
,EQU,N #A4
#D .;X #B -- #E7-#B;X- #F7 #B .K --#GF
#D .;X #B -- #BJ .;X #B -- #ABJ .;X --
#AHJ .K --#GF
-#AF .;X #B -- #ABJ .;X -- #AJD .K #J
#B .;X #B @+ #AE .;X @+ #AC .K #J
,:5 .;X .K --#A3 .;Y .K --#B7-;L7--#F
.K --#D
,:5
,! SOLU;NS >E 7-#A1 --#D7 &
--------------------------------;,,WS#AH
,,"W$-,,\ ,,SOLU;NS
#DA4
.A4
,CIRCLE3 .;X #B @+ .;Y #B .K #A
.B4
.C4
,*APT] #AJ
.,LESSON .#AJ..A @7 PP4 #FHF-FHI @7
#AC4
A4 #BF 99 #BF 99 #BF 99 #BF 99 #AJ 99
#AJ .K #DE1FIG1FJJ
B4 #BF 99 #BE 99 #BD 99 #BC 99 #AJ 99
#I .K #CB1BIB1JJJ
#CE4
#FE4 ,P]MUT,NS ( #I OBJECTS TAK5 #C AT
A "T3
.,LESSON .#AJ..B @7 PP4 #FID-FIG @7
.#AG4 .,EXACTLY ."O .QUE53 ,*OOSE #A
(! #D QUE5S & #D (! #DH T >E N QUE5S4
.,NO .QUE53 ,*OOSE #E C>DS F ! #DH 9
DECK T >E N QUE5S4
,! TOTAL NUMB] ( POSSI# H&S IS
#GGH1CBJ @+ #A1GAB1CJD .K #B1DIJ1FBD4
.#BI4 7#B .;S #D @+ #E7 #E .K #E ;,C
#J 7#B .;S #D @7 #E #E #J @+ #E ;,C #A
7#B .;S #D @7 #D #E #A
@+ #E ;,C #B 7#B .;S #D @7 #C #E #B @+
#E ;,C #C 7#B .;S #D @7 #B #E #C @+ #E
;,C #D 7#B .;S #D @7 #A #E #D
@+ #E ;,C #E 7#B .;S #D @7 #J #E #E .K
;L7#CBE #BJ @7 @+ #E7;L#F .;S #AF @77#E7
@+ #AJ 7#H .;S #AB @7 7#BE7 @+ #AJ 7#D
.;S #H @7 7#ABE7 @+ #E 7#B .;S #D @7
7#FBE7
@+ #A7#A7 7#CABE7 .K #CB .;S #BJ @+
#DJJ .;S #AF @+ #BJJJ .;S #AB
@+ #EJJJ .;S #H @+ #FBEJ .;S #D @+
#CABE
.#DI4 ,Y C *OOSE #C (! #AH TYPES (
FL[]S4
.,LESSON .#AJC @7 PP4 #GJB-GJD @7
.#G4 ,FACTORS ( #AEJ F #A 6#EJ3 #A1
#B1 #C1 #E1 #F1 #AJ1 #AE1 #BE1 #CJ1 #EJ
.#AG4 ,"! >E #DH ;,C #F DI6]5T -B9,NS
( #F NUMB]S4 ,ONLY #A IS ! CORRECT
-B9,N4
.#CI4
.,LESSON .#AJ..D @7 PP4 #GAJ-GAC @7
#AA4 ..;,P7,A OR ;,B7 .K ;,P7,A7 @+
;,P7;,B7--;,P7,A& .;,B7
#J.GA .K #J.BH @+ #J.FD -- .;,P7.,A &
.;,B7
-#J.BA .K -..;,P7,A& ;,B7 ;,P7,A&
.;,B7 .K #J.BA #BA4
#BA4
.#DE4 ,! NUMB] ( -B9,NS ( #F FOOD
ITEMS IS #AJ #F @4 ,! NUMB] ( -B9,NS (
#F DI6]5T FOOD ITEMS IS #AJ 99 #I 99 #H
99 #G 99 #F 99 #E4 ,S1 ! PROBABIL;Y T AT
L1/ #B BR+ ! SAME ITEM IS .;,P .K
#A--;,P7N"O >E ! SAME7 .K
.,LESSON .#AJ..E @7 PP4 #GBA-GBC @7
.#AC4 .;,P .K .;,P 7BLUE7 99 .;,P
7GRE57 99 .;,P 7R$7
--------------------------------;,,WS#AI
,,"W$-,,\ ,,SOLU;NS
.#BE4 ,PRIMES F #A 6#BJ3 #B1 #C1 #E1
#G1 #AA1 #AC1 #AG1 #AI4
.#CI4
;,P7;,C7 .K .;,P7.,A & ;,C7 @+
.;,P7.;,B & ;,C7
.K ;,P7,A7 99 .;,P7.;,C@\.,A7 @+
;,P7;,B7 99 .;,P7.;,C@\.;,B7
.K 7#J.EJ7 99 7#J1 #EE7 @+ 7#J1 #EJ7
7#J.DG7 .K #J.EA
.,LESSON .#AJ..F @7 PP4 #GBG-GCJ @7
.#E4
#BA4 ,EA* "Q HAS #D POSSI# ANSW]S1 S !
PROBABIL;Y ( GUESS+ A CORRECT ANSW] IS
.;P .K #J.BE4 ,"! >E #CJ "QS1 S .;N .K
#CJ4 ,! PROBABIL;Y ( R&OMLY GUESS+ #AA
CORRECT ANSW]S IS .;,P7.;K .K #AA7 .K
#CJ ;,C #AA 7#J.BE7 #AA 7;L--#J.BE7 #CJ
--#AA #J.JEE4
#DE4
A4 .;P .K #J.CD2
.;P @7 .;K .K #E7 .K #AJ ;,C #E
7#J.CD7 #E 7#A-J.CD7 #AJ-E #J.AD
B4 .;P .K .;,P 7,RH - @7 .K .;,P 7,O -
@7 @+ .;,P 7,A - @7 @+ .;,P 7;,B - @7 @+
.;,P 7;,,AB - @7
.K#J.AE
.;P @7 .;K .K #B7 .K #AJ ;,C #B
7#J.AE7 #B 7#A-J.AE7 #AJ-B #J.BH
C4
D4 .;P .K .;,P 7,RH @+ @7 .K .;,P 7,O
@+ @7 @+ .;,P 7,A @+ @7 @+ .;,P 7;,B @+
@7 @+ .;,P 7;,,AB @+ @7
,*APT] #AA
,LESSON #AA.A @7 PP4 #GDG-GDI @7
.#E4 ,M1N3
.K #GD.E
,MODE3 #GC & #GH
#AE4 ,RANGE3 #AEH--#ACE .K #BC
.K #ADE.FBE
.K
#BI4
A4 ,! \TLI] IS #E4
B4 .,) .\TLI]3
,M1N3
,M$IAN3 #BB ,MODE3 #BC ,RANGE3 #BE--#E
.K #BJ
,/D4 ,DEV43
#E.D
--------------------------------;,,WS#BJ
,,"W$-,,\ ,,SOLU;NS
,)\T \TLI]4
,M1N3
,M$IAN3 #BC ,MODE3 #BC ,RANGE3
#BE--#AI .K #F
,/D4 ,DEV43
#B.A
.C4 ,! \TLI] CAUSES ! M1N & M$IAN
6DECR1SE1 &! RANGE & /&>D DEVI,N
69CR1SE4 ,! MODE /AYS ! SAME4
.,LESSON .#AA..B @7 PP4 #GEC-GEE @7
#E4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 .,ORIG9AL .DATA @3 ..,A4+ #AG
6DATA .VALUES
,M1N3 #GH3 #GH @+ #AG .K #IE
,M$IAN3 #GG3 #GG @+ #AG .K #ID
,MODE3 #GG3 #GG @+ #AG .K #ID
,RANGE3 #I3 #I
,/&>D DEVI,N3 #B.H3 #B.H
#AA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 .,ORIG9AL .DATA .SET @3
..,MULTIPLY+ DATA VALUES 0.#D
,M1N3 #FA.I3 #FA.I7#D7 .K #BDG.F
,M$IAN3 #FB3 #FB7#D7 .K #BDH
,MODE3 #EH3 #EH7#D7 .K #BCB
,RANGE3 #I3 #I7#D7 .K #CF
,/&>D DEVI,N3 #C.D3 #C.D7#D7 .K #AC.F
#AI4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 .,HEI<TS .)\T ./ILTS @3 .,HEI<TS
.) ./ILTS
,M1N3 .#GJ..H @3 #GJ.H @+ .#BH .K
#IH.H
,M$IAN3 .#GB @3 ..#GB @+ #BH .K .#AJJ
,MODE3 .#GB @3 ..#GB @+ .#BH .K #AJJ
,RANGE3 .#H @3 .#H
,/&>D DEVI,N3 .#B..D @3 .#B..D
.,LESSON .#AA..C @7 PP4 #GFJ-GFB @7
#C4
.#C4 .;,P @7 .;X "K.K -- @7 .K #J.JJAE
@+ #J.JBCE @+ #J.ACE .K #J.AF
#AA4 #BI & #CG >E "O /&>D DEVI,N ON EI
SIDE (! M1N1 : A3.TS = #FH@3P (! DATA4
,S1 ! PROBABIL;Y IS #J.FH4
#CC4
A4
B4 ,! TA# %[S T .;,P7.;X "K --#B.D7 .K
#J.JJHB4 ,S1 ! PROBABIL;Y IS #J.JJHB4
C4 .;,P7.;X "K #BJ.D7 .K #J.IDEB2
.;,P7.;X "K #AI.D7 .K #J.JJHB
.;,P7.;X "K #BJ.D7 -- .;,P7.;X "K
#AI.D7 .K #J.ICG
,LESSON #AA.D @7 PP4 #GFI-GGA @7
.#G4 ,M>G9 ( ]ROR
,! M>G9 ( ]ROR IS AB +-#C.B
.#AI4 ,M>G9 ( ]ROR
.#BI4 .,SAMPLE .ANSW]3 ,X IS N R1SONA#
6ASSUME T ,KO/A IS GO+ 6W9 ! ELEC;N1 2C
! M>G9 ( ]ROR IS +-#E@3P4 ,IF ! M>G9 (
]ROR "WS 9 FAVOR ( ,MURDOCK1 ,KO/A W H
#DI@3P 7#ED@3P--#E@3P7 & ,MURDOCK W H
#EA@3P 7#DF@3P @+ #E@3P74
.,LESSON .#AA..E @7 PP4 #GGH-GHJ @7
.#C4 ,MODEL3 .;Y .K --#J.CH .;X #B @+
L4LX @+ #AF
.#AA4 ,A MODEL =! DATA IS .;Y .K
#J.JJBAA .;X #C --#J.JGFF .;X #B @+
#A.BF .;X -- #J.JFFD4
,*APT] #AB
.,LESSON .#AB..A @7 PP4 #GIH-HJJ @7
.#AI4
.#BJ4
.K #J @+ #A @+ #H @+ #BG @+ #FD .K
#AJJ
--------------------------------;,,WS#BA
,,"W$-,,\ ,,SOLU;NS
#FE4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;N @3 .#A @3 .#B @3 .#C @3 .#D @3 .#E
A.' ;N.' @3 .#A @3 .#C @3 .#G @3 .#AE
@3 .#CA
,A =MULA =! SEQU;E IS .A ;N .K #B ;N
-- #A4
.A #F .K #B #F -- #A .K #FC MOVES = #F
R+S
.A #G .K #B #G -- #A .K #ABG MOVES =
#G R+S
.A #H .K #B #H -- #A .K #BEE MOVES =
#H R+S
.,LESSON .#AB..B @7 PP4 #HJF-HJI @7
.#AE4 ,>I?METIC SEQU;E
.A #A .K --#C2 .;D .K --#A--7--#C7 .K
#B
,A RULE =! .;N TH T]M IS .A ;N.' .K .A
#A @+ @7 .;N -- ;L7 .;D .K --#C @+ @7
.;N -- #A7#B .K #B .;N -- #E
A #BJ .K #B7#BJ7--#E .K #CE
.#DA4
.#FE4 .A4 .A #A .K #D2 .;D .K #H
.A ;N.' .K .A #A @+ @7 .;N -- #A7;D .K
#D @+ @7 .;N -- #A7#H .K --#D @+ #H .;N
.B4 .A ;L#B @+ .A #AA @+ ' @+ .A #B @+
.A #A .K #EGF BLOCKS
.,LESSON .#AB..C @7 PP4 #HAD-HAG @7
.#AI4 ,GEOMETRIC SEQU;E2
.#DI4
.#EI4 .A @4
.;B @4 .;N .K #AJ2 AF #AJ PASSES1 !
NUMB] ( ITEMS REMA9+ IS
.,LESSON .#AB..D @7 PP4 #HBC-HBE @7
.#AC4
.#BG4 #FBE7#J.JJA7 @+ #FBE7#J.JJA7 #B
@+ #FBE7#J.JJA7 #C @+ '
.#CI4 ;,D2 .;N .K #CDE @+ #CDE7#J.GHC7
@+ #CDE7#J.GHC7 #B @+ #CDE7#J.GHC7 #C @+
'
.,LESSON .#AB..E @7 PP4 #HCJ-HCC @7
.#AE4 ,GEO;TRIC SEQU;E2 .A #A .K #D2
.;R .K-#C
.A ;N.' .K .;R @* .A .;N -- #A .K
--#C;A .;N -- #A @4
,A RECURSIVE RULE IS .A #A .K#D1 .A ;N
.K --#C .A .;N -- #A
.#BG4
.#DE4 ,RECURSIVE RULE3
.A #A .K #BJJJ1 .A ;N.' .K L#.JAD .A
.;N -- #A -- #AJJ4
,2C .A #BD .K #FB.AD1 ! BAL.E AT !
2G9N+ (! #BD? MON? IS 4#FB.AD4 ,S1 %E W
2 A# 6PAY (F ! BAL.E AT ! 5D (! #BD?
MON?4
,*APT] #AC
.,LESSON .#AC..A @7 PP4 #HEF-HEH @7
.#E
,US+ ! ,PY?AGOR1N !OREM3
--------------------------------;,,WS#BB
,,"W$-,,\ ,,SOLU;NS
.#AA4
.#CC4
.;D #DJB
,! TOTAL DEP? IS #DJB @+ #BEJ .K #FEB
FEET4
,Z ! ANGLE (! DIVE 9CR1SES1 ! DEP?
9CR1SES4
,LESSON #AC.B @7 PP4 #HFB-HFE @7
.#AA4
.#BC4
.#EA4 .A4
.B4 ,>C L5G?3
,LESSON #AC.C @7 PP4 #HGJ-HGB @7
.#E4
.#AG4 @' .K #AHJ;DG- #AEJ;DG .K #CJ;DG
.#CG4
@' .K #BGJ;DG--#BEE;DG .K #AE;DG
#AI.D .;H
,:5 ! RIDE /OPS1 Y >E AB #AJ @+ #GE @+
#AI.D .K #AJD.D FEET ABV ! GR.D4 ,IF !
RADIUS IS D\#D1 YR HEI<T ABV ! GR.D IS
D\#D ONLY IF YR />T+ HEI<T ABV ! GR.D IS
AL D\#D4
,LESSON #AC.D @7 PP4 #HGH-HHJ @7
.#G4 ,:5 @1 ( --#IJ;DG "K.K "K.K
#IJ;DG1 ! ANGLE ^: S9E IS @1 OR @4
.#BC4
TAN .K #C.B2 #AHJ;DG "K "K #BGJ;DG
TAN --#A 7#C.B7 #GB.F;DG1 : IS 9
,QUADRANT ,I4 ,6F9D ! ANGLE 9 ,QUADRANT
,,III 7#AHJ;DG "K "K #BGJ;DG73 #AHJ @+
#GB.F .K #BEB.F;DG
.#CG4
,2C ! ANGLE ( REPOSE REMA9S ! SAME1 Y
C USE .K #CE;DG 6F9D ! RADIUS (! #AE
FOOT HI< PILE3
,! DIAMET] IS AB .;D .K #B .;R .K
#B7#BC7 .K #DF;FT4
--------------------------------;,,WS#BC
,,"W$-,,\ ,,SOLU;NS
.,LESSON .#AC..E @7 PP4 #HHF-HHH @7
.#AC4
.#CA4
.#DE4 .A4
.B4
.C4
.K #AFAB
#AFAB FT #B @/ #BJJ FT #B _/BAG #H.A
BAGS
,Y W NE$ #I BAGS ( F]TILIZ]4
.,LESSON .#AC..F @7 PP4 #HIB-HID @7
.#AG4 .A #B .K .;B #B @+ ;C #B -- #B
.BC COS .,A
#AJ #B .K #C #B @+ #AB #B --
#B7#C77#AB7COS .,A
.#BE4
.#DE4
,IF Y F/ F.D ! L5G? ( @1 Y CD REP1T !
SAME PROCESS US+ .,,ABC & .,,ADC @4
,*APT] #AD
.,LESSON .#AD..A @7 PP4 #IAB-IAD @7
.#E4 ,AMPLITUDE3 #A2 P]IOD3 #B
.#AG4 .;F @7 .;X @7 .K #D TAN .;X
,P]IOD3 @2 9T]CEPT3 7#J1 #J7
,ASYMPTOTOES3
,HALFWAY PO9TS3
.#CA4 .A4 ,EQU,N HAS ! =M .;Y .K .A
COS .BT @4
,P]IOD IS #F1 S @4
,EQU,N IS @4
.B4 ,*OOSE .;Y .K .A COS .BT 2C AT .;T
.K #J1 ! BUOY IS AT XS HI<E/ PO9T4
,LESSON #AD.B 7.PP .#IAI-.IBB7
.#AA4 .;Y .K #B COS .;X @+ #A
,AMPLITUDE3 .A .K #B
,P]IOD3
,HORIZONTAL %IFT3 .;H .K #J2 ,V]TICAL
%IFT3 .;K .K #A
--------------------------------;,,WS#BD
,,"W$-,,\ ,,SOLU;NS
.#BC4
,AMPLITUDE3 _\ .A _\ .K #A
,P]IOD3
.;H .K #J2 .;K .K #C2 .A "K #J1 S
GRAPH IS REFLECT$4
.#EC4 .A4
.;D .K --#CJJ TAN @+ #BJJ
.B4
.C4 #AJJ .K --#CJJ TAN @+ #BJJ
#AH.D;DG
.,LESSON .#AD..C @7 PP4 #IBG-ICJ @7
.#E4 @1 #C "K "K #B
S9 #B @+ COS #B .K #A
.#AA4
.#DA4 .A4
.B4
;C
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 #J3 @3 @3 @3 --
.;R @3 #CE.F3 #C.D3 #A.A3 #J.F3 #J.E
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 @3 @3 @3 #B
.;R @3 #J.F3 #A.A3 #C.D3 #CE.F
,CLOSE/ 4T.E3
,F>!/ 4T.E3
.,LESSON .#AD..D @7 PP4 #ICE-ICG @7
.#E4
.#AC4
.#DC4 .A4
.B4
,:5 #ABB;DG1
.;,S .K #I 9 #B @4
.C4
,A VALUE ( #ED.G;DG M9IMIZES ! SURFACE
>EA4
.,LESSON .#AD..E @7 PP4 #IDD-IDG @7
.#E4 .;,M .K #F1 .;M .K #B
,V]TICAL %IFT3
,! GRAPH IS A COS9E CURVE ) .;H .K #J4
,! GRAPH IS A REFLEC;N1 S .A .K --#B4
,! FUNC;N IS @4
--------------------------------;,,WS#BE
,,"W$-,,\ ,,SOLU;NS
.#I4 .;,M .K #F1 .;M .K --#F
,V]TICAL %IFT3
,! GRAPH IS A S9E CURVE ) .;H .K #J4
,! GRAPH IS N A REFLEC;N1 S .A .K #F4
,! FUNC;N IS @4
.#BE4 ,:5 .;T .K #J1 .;M .K #D2 :5 .;T
.K #A1 .;,M .K #I4
,! GRAPH IS A COS9E CURVE ) .;H .K #J4
,! GRAPH IS A REFLEC;N1 S
,A4 MODEL IS @4
,LESSON #AD.F @7 PP4 #IEB-IED @7
.#I4
.#BC4
.K7S9 .;X @77#J7--7COS .;X @77--#A7 .K
COS .;X
.#DC4 .A4
.B4 ,:5 .;T .K #J3
,LESSON #AD.G @7 PP4 #IEI-IFB @7
.#G4
.#AC4
.#EC4 ,:5
,US+ ! ,PY?AGOR1N ,!OREM3
---------------------------------;,,SA#A
,SELECT$ ,ANSW]S
,*APT] #A
..#A.A ,SKILL .,PRACTICE @7 PP4 #F--#G
@7 .#A4 RECIPROCAL .#C4 .#E4 .#AA4
,ASSOCIATIVE PROP]TY ( A4I;N .#AC4
,-MUTATIVE PROP]TY ( MULTIPLIC,N .#AE4
,4TRIBUTIVE PROP]TY
.#AG4
#AI4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
@7 .;C -- #C7 @+ #C @3 .K @7 .;C @+
7--#C77 @+ #C @3 ,DEF9I;N ( SUBTRAC;N
--@3 .K .;C @+ 77--#C7 @+ #C7 @3
,ASSOCIATIVE PROP]TY ( A4I;N
--@3 .K .;C @+ #J @3 ,9V]SE PROP]TY (
A4I;N
--@3 .K .;C @3 ,ID5T;Y PROP]TY ( A4I;N
#BA4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
#G .A @+ 7#D @+ #E .A @7 @3 .K #G .A
@+ 7#E .A @+ #D7 @3 ,-MUTATIVE PROP]TY (
A4I;N
--@3 .K 7#G .A @+ #E .A @7 @+ #D @3
,ASSOCIATIVE PROP]TY ( A4I;N
--@3 .K #AB .A @+ #D @3 ,-B9E L T]MS4
.#BC4 .,SAMPLE .ANSW]3 .A .K --#B1
.#BE4 4#H.EJ P] ;H .#BG4 4#CF.BE .#BI4
#AIE MI .#CA4 .#CC4 #BBJJ ;G .#CE4 #A.GE
GAL .#CG4 #J.JJAGE TON .#CI4 ,! UNIT
MULTIPLI] %D 2 @2 @4 .#DA4 #BI.C FT_/SEC
.#DC4 #CA.A MI_/;H .#DE4 #J.JD OZ_/SEC
.#DG4 #AHJJ MI_/;H .#DI4 ,ALW2 ?
REPRES5TS ! ASSOCIATIVE PROP]TY ( A4I;N1
: IS TRUE = ALL R1L NUMB]S4 .#EA4
,"S"TS2 X IS TRUE :5 .;C .K .#J4 .#EC4
,ALW2 ? REPRES5TS ! 4TRIBUTIVE PROP]TY1
: IS TRUE = ALL R1L NUMB]S4 .#EE4
..#A.A ,PRO#M .,SOLV+ @7 PP4 #H-I @7
.#EG4 .A4 ,L.E3 #F1 ,D>CY3 #B1 ,JAVI]3
#C1 ,S&RA3 --#B .B4 ,S&RA1 ,D>CY1
,JAVI]1 ,L.E .#EI4 .A4 ,PLUTO1 ,NEPTUNE1
,URANUS1 ,SATURN1 ,JUPIT]1 ,M>S1 ,E>?1
,M]CURY1 ,V5US .B4 ,M]CURY1 ,V5US1 ,E>?1
,M>S1 ,JUPIT]1 ,SATURN1 ,URANUS1
,NEPTUNE1 ,PLUTO .C4 .,SAMPLE .ANSW]3 ,!
PLANETS >E 9 OPPOSITE ORD]S 9 "PS 7A7 &
7;B7 )! EXCEP;N ( ,M]CURY & ,V5US4 .D4
,M]CURY OR ,V5US .#FA4 .A4 *EETAH3
#AJB.FG2 ?REE-TO$ SLO?3 #J.AE2 SQUIRREL3
#AG.F2 GRIZZLY BE>3 #CJ .B4 .,SAMPLE
.ANSW]3 ,! *EETAH IS AB #DFG "TS FA/]
?AN ! ?REE-TO$ SLO?4
..#A.B ,SKILL .,PRACTICE @7 PP4 #AC-AE
@7 .#A4 BASE3 #AB1 EXPON5T3 #G .#C4 ,!
NEGATIVE SIGN %D 2 APPLI$ AF EVALUAT+ !
P[]1 --#C #D .K --#HA4 .#E4 #HA .#G4 #DI
.#I4 --#CB .#AA4 --#AJ1JJJ .#AC4 --#FD
.#AE4 #FD #A .#G4 --#E .#AI4 --#AJJ
.#BA4 #GE .#BC4 #F .#BE4 #E .;X @+ #E
.#BG4 #AC .;Z #B -- #B .;Z @+ #AJ .#BI4
#AA .;M -- #A .#CA4 --#E .;P #B @+ #BA
.#CE4 #AJ .;N @+ #BD2 #DD .#CG4 #BF
.#CI4 #DI .#DA4 .#DC4 --#G .;D @+ #AA
.;C .#DE4 #B .;M #B @+ .;N #B -- #H .;M
.#DG4 #AC .;M #B -- #E .#DI4 --#H .;S @+
#H .;T .#EA4 .,SAMPLE .ANSW]3 #C .;K @+
#D .;K @+ 7--#H7--#B .;J @2 #G .;K --
#H--#B .;J .#EC4 7#D @+ #C7 99 7#E--#B7
.K #BA .#EE4 7#C 99 #D7 #B -- 7#B #C @+
#C7 #B .K #BC
..#A.B ,PRO#M .,SOLV+ @7 PP4 #AE-AF @7
.#EG4 #J1 #AJ1 #BJ1 #CJ2 4#A.HI1 4#C.BJ1
4#D.EA1 4#E.HB .#EI4 #BGJ--#D.E .;X @2
NO2 :5 .;X .1 #FJ "! W 2 A NEGATIVE
BAL.E ON ! C>D1 : M1NS Y W H SP5T M ?AN
:AT Y _H ON ! C>D4 .#FC4 --#F.E .;X --
#F .;Y @+ #BJJ2 4#HH
..#A.C ,SKILL .,PRACTICE @7 PP4 #BA-BC
@7 .#A4 SOLU;N .#C4 #C .#E4 #AB .#G4 #F
.#I4 .#AA4 #D .#AC4 --#A .#AE4 #AH .#AG4
--#I .#BA4 #A .#BC4 #D .#BE4 --#G .#BG4
.#BI4 #D .#CA4 .#CC4 #D .#CE4 --#G .#CG4
--#B .#CI4 #BH .#DA4 ,BO? SIDES (!
EQU,NS %D 2 DIVID$ 09/1D ( SUBTRACT+ F
EA* SIDE2 .#DC4 #AB .#DE4 #FJ .#DG4
--#BC
---------------------------------;,,SA#B
,,SELECT$ ,,ANSW]S
.#DI4 .#EA4 #F2 #AE1 #H1 #AE1 #H .#EC4
#B2 #F1 #F1 #C .#EE4 #D .#EG4 #B .#EI4
#D .#FA4 #B.I .#FC4 NO SOLU;N .#FE4 ALL
R1L NUMB]S .#FG4 @2 .A .K .;C & .;B @6.K
.;D2 .A .K .;C & .;B .K .;D
..#A.C ,PRO#M .,SOLV+ @7 PP4 #BC-BD @7
.#FI4 #C ;H .#GA4 #I ;H .#GC4 .A4 #C .;C
@+ #B .;G .K #H .B4 .#GE4 #AH M9
..#A.D ,SKILL .,PRACTICE @7 PP4 #CJ-CA
@7 .#A4 =MULA .#C4 @2 #E MM .#E4 @2 #F
CM .#G4 .;Y .K #BF--#C .;X @2 #E .#I4 @2
#AA .#AA4 @2 --#C .#AC4 @2 #F .#AG4 ,!
V>IA# .;Y %D ONLY APPE> ON "O SIDE (!
EQU,N1 N BO?2 #D .;Y -- .XY .K #I1 .;Y
7#D -- .;X @7 .K #I1 @4 .#AI4 @2 AB
#D.IF CM .#BA4 @2 #AA .#BC4 @2 .#BE4 @2
#E .#BG4 ,ME?OD #A3 @1 @2 ,ME?OD #B3 #AE
99 #B--#I .;Y .K #BG1 #CJ--#I .;Y .K
#BG1 --#I .;Y .K --#C1 @2 .,SAMPLE
.ANSW]3 ,ME?OD #A IS M E6ICI5T 2C X IS
ALR SOLV$ = .;Y @4 .#BI4 .#CA4
..#A.D ,PRO#M .,SOLV+ @7 PP4 #CA-CB @7
.#CC4 @2 AB #CF IN4 .#CE4 @2 #AJ;DG;,C
.#CG4 .;,R .K #HJ .;C @+ #AEJ .;D @2 @2
#HJ DESIGN] TUX$OS2 #AFJ DESIGN] TUX$OS2
#BDJ DESIGN] TUX$OS .#CI4
..#A.E ,SKILL .,PRACTICE @7 PP4 #CG-CH
@7 .#A4 V]BAL MODEL .#C4 #J.E ;H .#E4
#IJ MI .#G4 #ED FT .#I4 #BJ ;M .#AA4 .;Y
.K #D .;X @+ #AA .#AC4 .;Y .K #DF--#AJ
.;X .#AG4 #D .;X @+ #I .K #AB1 #J.GE FT
.#AI4 ,! PATT]N %[S ! \TPUT IS DECR1S$
0#AJ EA* "T2 AN EQU,N T REPRES5TS ! TA#
IS .;Y .K #GE--#AJ .;X @4 .#BC4 .;Y .K
#G .;X -- #AF
..#A.E ,PRO#M .,SOLV+ @7 PP4 #CH-CI @7
.#BE4 #C.GE KM_/M9 .#BG4 .;Y .K #A.E .;X
@+ #AE2 NO2 ! BAMBOO %OOT W EV5TU,Y SL[
XS GR[? RATE & /OP GR[+4 .#BI4 #C .;X @+
#AH .K #GB1 #AH IN41 #BD IN41 #CJ 9
.#CA4 #DJ .;X @+ #G7#BJ -- .;X 7.K #DJD2
#H BOXES ( BOOKS1 #AB BOXES ( CLO!S
.#CC4 AB #D.JG IN4
..#A.F ,SKILL .,PRACTICE @7 PP4 #DD-DE
@7 .#A4 GRAPH
.#C4
.#E4
.#AA4 --#C "K.K .;X "K.K #A .#AC4 .;X
"K --#B OR .;X .1 #D
.#AG4
.#AI4
.#BC4 .;X "K.K--#B
.#BE4 .;X "K #D
.#CE4 ,! 9EQUAL;Y SYMBOL %D N 2 REV]S$
:5 SUBTRACT+2 #AJ .1 #B .;X @1 #E .1 .;X
@4
.#CG4 --#F "K .;X "K #C
.#CI4 #A "K.K .;X "K #G
.#DC4 .;X "K --#D OR .;X .1 #B
.#DE4 OR .;X .1.K #A
.#DI4 NO SOLU;N .#EA4 NO SOLU;N
..#A.F ,PRO#M .,SOLV+ @7 PP4 #DF-DG @7
.#EC4 #DE .;X @+ #CE "K.K #BEJ1 @2 #D OR
FEW] "DS .#EE4 .A4 #J "K.K .;E "K #EJJ
.B4 #ADJJ "K .;E "K #BDBI .C4 #J "K.K
.;E "K #EJJ OR #ADJJ "K.K .;E "K #BDBI
.#EG4 #EJ "K.K .;,F "K.K #IE2 #AJ "K.K
.;,C "K.K #CE .#EI4 .A4 ,AMY3 #J.FE7#HD7
@+ #J.AE7#HJ7 @+ #J.B .;W .1.K #HE1
,BRIAN3 #J.FE7#HJ7 @+ #J.AE7#AJJ7 @+
#J.B .;X .1.K #HE1 ,CL>A3 #J.FE7#GE7 @+
#J.AE7#IE7 @+ #J.B .;Y .1 #HE1 ,DAN3
#J.FE7#HJ7 @+ #J.AE7#IJ7 @+ #J.B .;Z
.1.K #HE .B4 .;W .1 #IB2 .;X .1 #IJ2 .;Y
.1.K #AAJ2 .;Z .1.K #IG.E .C4 ,AMY1
,BRIAN1 & ,DAN4 .,SAMPLE .ANSW]3 ,X IS
IMPOSSI# 6SCORE OV] #AJJ PO9TS ON A TE/1
S ,CL>A W N 2 A# 6A*IEVE A GRADE ( #HE
OR BETT]4
#A.F ,PRO#M ,SOLV+ ,"W%OP @7 P4 #DI @7
.#A4 .;Y .K --#CE .;X @+ #BJJ2 ;X .1
#BJ .#C4 .;X .1 .1.K#GJJJ
..#A.G ,SKILL .,PRACTICE @7 PP4 #EE-EF
@7 .#A4 ,AN APP>5T SOLU;N T M/ 2 REJECT$
2C X DOES N SATISFY ! ORIG9AL EQU,N4
.#C4 SOLU;N .#E4 N A SOLU;N .#G4 SOLU;N
---------------------------------;,,SA#C
,,SELECT$ ,,ANSW]S
.#I4 --#I1 #I
.#AA4 #J
.#BA4 --#D1 #I .#BC4 @1 #B .#BE4 --#G1
#D .#BG4 --#G1 #B .#BI4 @2 #C .#CA4
--#BJ1 #D .#CC4 ,NO2 ! EQU,N HAS NO
SOLU;NS 2C AN ABSOLUTE VALUE W N"E 2
NEGATIVE4 .#CE4 --#C .#CG4 @1 .#CI4
.#DA4 ,:5 WRIT+ ! SECOND EQU,N1 ! "R
SIDE (! EQU,N %D 2 -- .;X -- #C2 #E .;X
-- #I .K -- .;X -- #C1 #F .;X -- #I
.K--#C1 #F .;X .K #F1 .;X .K #A1 !
SOLU;NS >E #C & #A4
.#DC4 --#E "K.K .;J "K.K #E
.#DE4 --#E "K .;M "K #I
.#FE4 .;C .1 #J1 .;C .K #J1 .;C "K #J
.#FG4 NO SOLU;N .#FI4 .;X "K #I OR .;X
.1 #I
.#GA4 OR .#GC4 OR .#GE4 _\ .;P --
#F.E_\ "K.K #A .#GG4 _\ .;B -- #BA_\ .1
#A .#GI4 _\ .;X -- #DE _\ "K.K #AE .#HA4
_\ .;E -- #FJJH _\ "K.K #EIIB1 _\ .;M --
#DF1JJJ_\ "K.K #DE1JJJ
.,*APT] .,REVIEW @7 PP4 #FA-FD @7 .#A4
EXPON5T1 BASE .#C4 EXTRANE\S SOLU;N .#E4
.,SAMPLE .ANSW]3 #C7 .;X -- #D7 & #C .;X
-- #AB .#G4 ,9V]SE PROP]TY ( MULTIPLIC,N
.#I4 ,4TRIBUTIVE PROP]TY .#AA4 #C .;X --
#F .;Y .#AC4 #AH .;B -- #CC .#AE4 --#B
.;T #D @+ #E .;T #B .#AG4 .#AI4 #I .#BA4
--#A .#BC4 4#GD.II .#BE4 .;Y .K --#AJ
.;X @+ #G2 --#BC .#BG4 ;#AE .#BI4 @2
--#BJ .#CA4 @2 AB #G.GC CM .#CC4 #FJB MI
.#CE4 .;X "K.K #F
.#CG4
.#CI4 --#C "K.K .;X "K.K #C
.#DA4 --#C1
.#DC4 NO SOLU;N
.#DE4 .;Y "K --#A OR .;Y .1 #F
.#DG4 _\ .;V -- #BF_\ "K.K #J.E1 #BE.E
IN4 "K.K .;V "K.K #BF.E IN4
,*APT] #B
..#B.A ,SKILL .,PRACTICE @7 PP4 #GF-GH
@7 .#A4 9DEP5D5T1 DEP5D5T .#C4 DOMA93
--#D1 --#B1 #A1 #C1 RANGE3 --#C1 --#A1
#B1 #C .#E4 DOMA93 --#B1 #A1 #F1 RANGE3
--#C1 --#A1 #E1 #H
.#AA4 ,YES2 EA* 9PUT HAS EXACTLY "O
\TPUT4 .#AC4 ,YES2 EA* 9PUT HAS EXACTLY
"O \TPUT4 .#AE4 .;X IS ! 9PUT & .;Y IS !
\TPUT1 S "! %D 2 "O VALUE ( .;Y = EA*
VALUE ( .;X @2 ! REL,N GIV5 0! TA# IS N
A FUNC;N 2C ! 9PUTS #A & #J EA* H M ?AN
"O \TPUT4 .#AG4 ,NO2 ! 9PUT --#B HAS M
?AN "O \TPUT4 .#AI4 ,NO2 ! 9PUT --#A HAS
M ?AN "O \TPUT4 .#BA4 FUNC;N .#BC4 N A
FUNC;N
.#BE4
.#BG4
.#CE4 N L9E>2 #AJ .#CG4 L9E>2 #F .#CI4
L9E>2 --#C
..#B.A ,PRO#M .,SOLV+ @7 PP4 #GH-GI @7
.#DC4 ,YES2 EA* 9PUT HAS EXACTLY "O
\TPUT4 .#DE4 ,AB #IJE2 ;,V7#F7 REPRES5TS
! VOLUME (A SPH]E ) RADIUS #F4
.#DG4 .A4
DOMA93 #AE "K.K "K.K #BD1 RANGE3
#EG.IE "K.K .;H @7 @7 "K.K #GE.E
.B4 #EI IN4 OR #D FT #AA IN4 .C4 .#BA4
#G IN4 .#DI4 .A4 DOMA93 #AA1CEJ1JJJ1
#AB1BHJ1JJJ1 #AB1DBJ1JJJ1 #AE1IHJ1JJJ1
#AH1IHJ1JJJ1 #BJ1HEJ1JJJ1 #CC1HGJ1JJJ1
RANGE3 #BJ1 #BA1 #BG1 #CA1 #CD1 #EE .B4
,YES2 EA* 9PUT .;P HAS EXACTLY "O \TPUT4
.C4 ,NO2 ! 9PUT #BA HAS M ?AN "O \TPUT4
,EXT5.N @7 P4 #HA @7
.#A4 4CRETE2 --#A1 #A1 #C1 #E1 #G
---------------------------------;,,SA#D
,,SELECT$ ,,ANSW]S
.#C4 3T9U\S2 .;Y .1--#F
.#E4 .;D @7 .;X @7 .K #C.E .;X DOMA93
.;X .1 #J1 RANGE3 .;D @7 .;X @7 .1.K #J2
3T9U\S
.#G4 .;M @7 .;X @7 .K #C .;X DOMA93
:OLE NUMB]S1 RANGE3 MULTIPLES ( #C2
4CRETE
..#B.B ,SKILL .,PRACTICE @7 PP4 #HF-HG
@7 .#A4 SLOPE .#C4 @2 RISES .#E4 @2
FALLS .#G4 --#D2 FALLS .#I4 @2 RISES
.#AA4 UNDEF9$2 IS V]TICAL .#AC4 #J2 IS
HORIZONTAL .#AE4 ,! .;X & .;Y COORD9ATES
7 N SUBTRACT$ 9 ! CORRECT ORD]2 @4 .#AI4
NEI .#BA4 P]P5DICUL> .#BC4 P>ALLEL .#BE4
#AC MI_/GAL .#BG4 #B ;M_/SEC .#BI4 #B
.#CA4 .#CC4 .#CE4 ,NO2 NO4 .,SAMPLE
.ANSW]3 ,! SLOPE ( @4 ,! SLOPE ( @4 ,!
SLOPE ( @4
..#B.B ,PRO#M .,SOLV+ @7 PP4 #HG-HH @7
.#DA4 .#DC4 #F.E@3P .#DG4 .A4 .B4 YES
.C4
..#B.C ,SKILL .,PRACTICE @7 PP4 #IC-ID
@7 .#A4 SLOPE-9T]CEPT
.#C4 ,BO? GRAPHS H A .;Y -9T]CEPT (
#J1 B ! GRAPH ( .;Y .K #C .;X HAS A
SLOPE ( #C 9/1D ( #A4
.#E4 ,BO? GRAPHS H A SLOPE ( #A1 B !
GRAPH ( .;Y .K .;X @+ #E HAS A .;Y
-9T]CEPT ( #E 9/1D ( #J4
.#I4
.#AA4
.#BA4 ,! SLOPE & .;Y -9T]CEPT 7 SWIT*$
>.D4
.#BE4 .;X -9T]CEPT3--#AE1 .;Y
-9T]CEPT3 --#C .#BG4 .;X -9T]CEPT3 #E1
.;Y -9T]CEPT3 --#AJ .#BI4 .;X -9T]CEPT3
#F1 .;Y -9T]CEPT3 --#D.E
.#CA4
.#CC4
.#DC4
.#DE4
.#EE4 .,SAMPLE .ANSW]3 .;X .K #C1 .;Y
.K --#B .#EG4 SLOPE3 @1 .;Y -9T]CEPT3
---------------------------------;,,SA#E
,,SELECT$ ,,ANSW]S
#BC ,PRO#M ,SOLV+ @7 PP4 #ID-IF @7
.#EI4 4#DHJ
.#FA4 4#A.EJ2 4#C
.#FC4 #CJ2 FALL2 ! VALUE (! C>D W
DECR1SE AF Y BUY EA* SMOO?IE1 S ! L9E W
FALL F LEFT 6"R4
.#FE4
.,SAMPLE .ANSW]3 .;R .K #J & .;W .K
#D1 .;R .K #A.GE & .;W .K #A1 .;R .K
#J.HGE & .;W .K #B.E
#FG4 A4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;T 7M9UTES7 @3 .;H 7FEET7
.#J @3 .#BJJ
.#A @3 .#CEJ
.#B @3 .#EJJ
.#C @3 .#FEJ
.#D @3 .#HJJ
.#E @3 .#IEJ
.B4
.C4 .;H @7 .;T @7 .K #AEJ .;T @+ #BJJ
..#B.D ,SKILL .,PRACTICE @7 PP4
#AJA-AJC @7 .#A4 /&>D .#C4 .;Y .K #B
.#E4 .;Y .K #F .;X .#G4 .#I4 .;Y .K #D
.;X -- #B .#AA4 .;Y .K #B .;X @+ #AA
.#AC4 .;Y .K --#I .;X @+ #HE .#AE4 .#AG4
.#AI4 ,! .;X -- & .;Y -COORD9ATES 7
TRANSPOS$2 .;Y -- #A .K --#B7 .;X --
#E71 .;Y -- #A .K --#B .;X @+ #AJ1 .;Y
.K --#B .;X @+ #AA4 .#BA4 .;Y .K -- .;X
@+ #H .#BC4 .;Y .K --#C .;X @+ #AC .#BE4
.#BG4 .;Y .K --#B .;X @+ #F .#BI4
.#CA4 .;Y .K --#C .;X @+ #AA .#CC4 .#CE4
.;Y .K #E .;X @+ #BC .#CG4 .;Y .K --#C
.;X @+ #AG.E .#DA4 --#D .;X @+ .;Y .K
--#C .#DC4 #D .;X -- #E .;Y .K --#G
.#DE4 #D .;X @+ #C .;Y .K #CB .#DG4
.,SAMPLE .ANSW]3
..#B.D ,PRO#M .,SOLV+ @7 PP4 #AJC-AJD
@7 .#EA4 .;N .K #AE .;T @+ #EJ .#EC4 #AE
.;X @+ #I .;Y .K #DEJJ ,F9D ! PO9T ON !
L9E ": .;X IS #BJJ !N ! CORRESPOND+ .;Y
-COORD9ATE IS H[ _M /UD5T TICKETS 7
SOLD4 .#EE4 .;Y .K #A.FF .;X @+ #BA.FB2
4#DH.AH .#EG..A4 #B @+ #B .;W .K #BD .B4
.C4 .,SAMPLE .ANSW]3
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 .;W
.#F @3 .#F
.#G @3 .#E
.#H @3 .#D
.#I @3 .#C
.#AJ @3 .#B
.#B..D ..,PRO#M ,SOLV+ .,"W%OP @7 P4
#AJE @7 .#A4 .;Y .K #D .;X @+ #G .#C4
.#E4 .;Y .K #CB.AD .;X @+ #AGFD.CF
..#B.E ,SKILL .,PRACTICE @7 PP4
#AJI-AAJ @7 .#A4 .,SAMPLE .ANSW]3 ,IF
.;Y .K .AX @1 !N .A IS ! 3/ANT ( V>I,N4
.A IS A 3/ANT RATIO ( .;Y 6.;X = ALL
ORD]$ PAIRS @7 .;X1 .;Y @7@4 .#C4 .;Y .K
#C .;X
---------------------------------;,,SA#F
,,SELECT$ ,,ANSW]S
.#E4 .;Y .K --#C.E .;X
.#AA4 .;Y .K #B .;X @2 #BD .#AC4 .;Y
.K --#J.B .;X @2 --#B.D .#AE4 @2 #D
.#AI4 N DIRECT V>I,N .#BA4 DIRECT V>I,N2
#B.E .#BC4 DIRECT V>I,N2 .#BE4 @2 #C
.#BG4 .;Y .K --#G .;X @2 .#BI4 .;Y .K
--#G.B .;X @2 .#CA4 DIRECT V>I,N2 .#CC4
DIRECT V>I,N2 .;Y .K --#D .;X .#CE4 ,!
QUOTI5TS NE$ 6BE -P>$ 6EA* O!R1 N !
PRODUCTS2 @1 2C ! RATIOS >E N EQUAL1 !
DATA D N %[ DIRECT V>I,N4
..#B.E ,PRO#M .,SOLV+ @7 PP4 #AAJ-AAA
@7 .#CI4 .;W .K #CFJJ .;D @2 #FCJJ LB
.#DA4 DIRECT V>I,N2 .;T .K #E.A .;S
.#DC4 .A4 DIRECT V>I,N2 .;,P .K #D .;S
.B4 ,N A DIRECT V>I,N2 ! RATIOS ( .,A
6.;S >E N EQUAL4 .C4 ,N A DIRECT V>I,N2
! RATIOS ( .,A 6.;,P >E N EQUAL4
..#B.F ,SKILL .,PRACTICE @7 PP4
#AAG-AAH @7 .#A4 BE/-FITT+ L9E .#C4
NEGATIVE CORREL,N .#E4 APPROXIMATELY NO
CORREL,N .#G4 #J .#I4 --#A
.#AA4 .A4 .B4 .,SAMPLE .ANSW]3 .;Y .K
--#BJ .;X @+ #ADA .C4 AB --#BEI
.#AC4 .A4 .B4 .,SAMPLE .ANSW]3 .;Y .K
#F.G .;X @+ #A .C4 AB #ACE
.#AG4 ,! L9E %D G "? ! MI4LE (! DATA
PO9TS4 .,SAMPLE .ANSW]3
.#AI4 .;Y .K #J.JE .;X @+ #A.AD
.#BA4 .A4 .,SAMPLE .ANSW]3 ,M1SUR+ !
DEP? ( WAT] AT DI6]5T "TS :ILE FILL+ A
SWIMM+ POOL4 ,! NUMB] ( GALLONS ( MILK Y
BUY &! TOTAL CO/4 .B4 .,SAMPLE .ANSW]3
,! AGE (A C> & XS CURR5T VALUE4 ,! NUMB]
( MILES Y H DRIV5 S9CE Y LA/ PUT GAS 9 !
TANK &! AM.T ( GAS LEFT 9 ! TANK4 .C4
.,SAMPLE .ANSW]3 ,! HEI<T (A P]SON &!
MON? !Y 7 BORN4 ,! AGE (A P]SON &! NUMB]
( VEHICLES !Y [N4
..#B.F ,PRO#M .,SOLV+ @7 PP4 #AAI-ABJ
@7 .#BE4 .,SAMPLE .ANSW]3 .;Y .K #AJA.C
.;X @+ #BBCF.F .#BG4 .A4 7#J1 #CG71 7#D1
#DI71 7#H1 #EG71 7#AB1 #FD71 7#AD1 #FG71
7#AH1 #GB71 7#BB1 #GG7
.B4 .C4 .,SAMPLE .ANSW]3 .;Y .K #A.H
.;X @+ #DJ.G2 #AJB C.TRIES
..#B.G ,SKILL .,PRACTICE @7 PP4
#ABG-ABH @7 .#A4 V]TEX
.#C4 TRANSLAT$ D[N #G UNITS
.#E4 TRANSLAT$ LEFT #D UNITS & D[N #B
UNITS
.#AE4 .;Y .K --#C_\ .;X _\ .#AG4 .#AI4
.#BA4 .#BC4
.#BI4 ,! GRAPH %D 2 TRANSLAT$ LEFT #C
UNITS4
.#CC4 ,NO4 .,SAMPLE .ANSW]3 ,X DOES N
PASS ! V]TICAL L9E TE/4
---------------------------------;,,SA#G
,,SELECT$ ,,ANSW]S
#B.G ,PRO#M ,SOLV+ @7 PP4 #ABH-ABI @7
.#CG4 #EJ1JJJ PAIRS ( %OES
.#CI4
#DA4 A4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;T @3 .#J @3 .#J..E @3 .#A @3 .#A..E
@3 .#B @3 .#B..E @3 .#C
.;D @3 .#IJ @3 .#FJ @3 .#CJ @3 .#J @3
.#CJ @3 .#FJ @3 .#IJ
.B4 .C4 .;D .K #FJ_\ .;T -- #A.E_\2
.,EXT5.N @7 P4 #ACA @7 .#A4 --#A .#C4
.#E4 .#G4
.#I4
..#B.H ,SKILL .,PRACTICE @7 PP4
#ACE-ACF @7 .#A4 HALF-PLANE .#C4 SOLU;N1
N A SOLU;N .#E4 SOLU;N1 SOLU;N
.#G4 .#I4
.#AI4 ,! B.D>Y L9E %D 2 A DA%$ L9E4
.#BC4 .#BE4
.#BI4 SOLU;N1 N A SOLU;N .#CA4 SOLU;N1
N A SOLU;N
.#CC4 .#CE4
.#CI4 .,SAMPLE .ANSW]3 .;Y .1 .;X @+
#C .#DA4 @2 PICK TWO PO9TS ON ! B.D>Y
L9E 6F9D ! SLOPE & !N USE ! PO9T-SLOPE
=M ( AN EQU,N 6F9D ! EQU,N4 ,! B.D>Y L9E
IS DOTT$1 S ! 9EQUAL;Y DOS N 9CLUDE
PO9TS ON ! B.D>Y4 ,!N *OOSE A PO9T
6DET]M9E : 9EQUAL;Y SIGN 6USE4 .,SAMPLE
.ANSW]3 ,Y & YR SI/] WANT 6SP5D AT L1/
4#AE ON YR LL BRO!R'S BIR?"D4 ,Y WANT
6BUY HM "S RACEC>S T CO/ 4#C EA* & "S
BUILD+ BLOCK SETS T CO/ 4#E EA*4
..#B.H ,PRO#M .,SOLV+ @7 PP4 #ACG-ACH
@7 .#DC4 #J.JC .;X @+ #J.JF .;Y "K.K #BJ
.#DE4 #A.E .;X @+ #B.E .;Y "K.K #GE
.;Y "K.K #AE.F YD
.#DG4 .A4 #AA .;X @+ #BF .;Y "K.K #ABJ
.B4 .,SAMPLE .ANSW]3 #B "DS CANOE+ &
#E "DS BIK+1 #C "DS CANOE+ & #B "DS
BIK+1 #B "DS CANOE+ & #B "DS BIK+
.C4 #AA .;X @+ #BF .;Y "K.K #IF
.,SAMPLE .ANSW]3 #A "D CANOE+ & #C "DS
BIK+1 #D "DS CANOE+ & #B "DS BIK+1 #B
"DS CANOE+ & #B "DS BIK+
---------------------------------;,,SA#H
,,SELECT$ ,,ANSW]S
.,*APT] .,REVIEW @7 PP4 #ADA-ADD @7
.#A4 /&>D .#C4 DIRECT V>I,N .#E4 DOMA93
--#B1 --#A1 #B1 #C1 RANGE3 --#B1 #J1 #F1
#H2 FUNC;N .#G4 L9E> FUNC;N2 #EA .#I4
UNDEF9$ .#AA4 #J
.#AC4 .#AE4
.#AG4 .#AI4 .;Y .K --#H .;X @2 --#BD
.#BA4 .;Y .K --#J.H .;X @2 --#B.D .#BC4
..,SAMPLE ANSW]3 ;Y .K --.;X @+ #B.C
.#BE4 %RUNK V]TIC,Y 0A FACTOR (
.#BG4 4#A.GE1 4#A.BE
.#BI4 SOLU;N
.#CA4 .#CC4
,*APT] #C
..#C.A ,SKILL .,PRACTICE @7 PP4
#AEF-AEG @7 .#A4 9DEP5D5T .#C4 7#A1
--#A7 .#E4 7#D1 --#A7 .#G4 7#E1 #J7 .#I4
7--#B1 #D7 .#AA4 9F9ITELY _M SOLU;NS
.#AC4 7#C1 #C7 .#AG4 7#B1 --#A72 3SI/5T
& 9DEP5D5T .#AI4 NO SOLU;N2 9CONSI/5T
.#BA4 9F9ITELY _M SOLU;NS2 3SI/5T &
DEP5D5T .#BC4 7#B1 #J72 3SI/5T &
9DEP5D5T .#BE4 7#C1 --#A72 3SI/5T &
9DEP5D5T .#BG4 9F9ITELY _M SOLU;NS2
3SI/5T & DEP5D5T .#CA4 NO SOLU;N .#CC4
7--#D1 #B7 & 7--#D1 #B7
..#C.A ,PRO#M .,SOLV+ @7 PP4 #AEG-AEH
@7 .#CE4 LIFEGU>D3 #F ;H1 CA%I]3 #H ;H
.#CG4 #AA "DS2 ! NUMB] ( "DS W DECR1SE2
! NUMB] ( "DS W 2 DIVID$ 0A L>G] NUMB]1
: W DECR1SE ! QUOTI5T1 : IS ! NUMB] (
"DS4 .#CI4 .A4 .;M .K --#J.JIEH .;X @+
#EJ.H .B4 .;W .K --#J.ABD .;X @+ #EG.A
.C4 9 ! YE> #BAIE .D4 ,NO4 .,SAMPLE
.ANSW]3 ,X IS N LIKELY T ! SAME L9E>
MODELS W APPLY 9DEF9ITELY4
..#C.B ,SKILL .,PRACTICE @7 PP4
#AFD-AFE @7 .#A4 SUB/ITU;N .#C4 7#F1
--#A7 .#E4 NO SOLU;N .#G4 .#I4 7#J1 #C7
.#AA4 7--#C1 #H7 .#AC4 7#DD1 --#AG7
.#AE4 .#AG4 7--#F1 --#B7 .#AI4 .#BA4
7--#H1 #F7 .#BC4 NO SOLU;N .#BE4 7#G1
#C7 .#BG4 ,FAIL$ 6MULTIPLY ! 3/ANT BY
--#B4
.#BI4 7--#E1 --#F7 .#CA4 9F9ITELY _M
SOLU;NS .#CC4 7--#H1 #J7
.#CE4 7#G1 --#F7 .#CG4 .#CI4 .#DA4
7#B1 #C7 .#DC4 7#C1 #B7 .#DE4 AB 7#B.IJ1
--#B.AF7 .#DG4 7--#A1 #B7 .#DI4 7#G1 #A7
.#EA4 .#EC4 7#E1 #D7
..#C.B ,PRO#M .,SOLV+ @7 PP4 #AFE-AFF
@7 .#EE4 #E AC\/IC1 #D ELECTRIC .#EG4 ,!
-PANY C FILL XS ORD]S 0OP]AT+ ,FACTORY
,A= #E WEEKS & ,FACTORY ;,B = #C WEEKS4
.#EI4 #AB D\#S GAMES1 #AD S+LES GAMES
.#FA4 #HJ P.DS ( P1NUTS1 #BJ P.DS (
CA%EWS
..#C.C ,SKILL .,PRACTICE @7 PP4
#AGA-AGB @7 .#A4 ,! ORD]$ PAIR M/
SATISFY EA* 9EQUAL;Y (! SY/EM4
.#E4 .#G4 NO SOLU;N
.#I4 .#AG4
.#AI4
.#BG4 .,SAMPLE .ANSW]3 .;Y "K .;X --
;L1 .#BI4
---------------------------------;,,SA#I
,,SELECT$ ,,ANSW]S
..#CC ,PRO#M .,SOLV+ @7 PP4 #AGB-AGC
@7 .#CE4 .;X .1.K #BJ1 .;X "K.K #EJ1 .;Y
.1.K #J.C .;X1 .;Y "K.K #J.G .;X @1 ":
.;X REPRES5TS ! REGUL> PRICE & .;Y
REPRES5TS ! SALE PRICE2 #F "K.K .;Y "K.K
#AD .#CG4 .A4 .;X .1.K #B1 .;Y .1.K #B1
.;X @+ .;Y "K.K #H1 .;X @+ .;Y .1.K #E
.B4 .C4 .,SAMPLE .ANSW]3 #C JUNIORS1
#D S5IORS2 #D JUNIORS1 #D S5IORS
.#CI4 .A4 .;X .1.K #BJ1 .;X "K.K #FE1
.;Y .1.K #J.E7#BBJ -- .;X @7@1 .;Y "K.K
#J.GE7#BBJ -- .;X @7
.B4 .C4 ,NO2 ! P]SON'S HE>T RATE IS
ABV ! T>GET Z"O4 ,A #DJ-YE> OLD P]SON'S
HE>T RATE %D 2 2T #IJ & #ACE HE>TB1TS P]
M9UTE4
.,EXT5.N @7 P4 #AGF @7 .#A4 #A2 #AD
.#C4 #AGJ2 #EHJ .#E4 #E2 #EE .#G4 #F M9I
PI@NATAS1 #F REGUL>-SIZ$ PI@NATAS .#I4
#AB J>S ( TOMATO SAUCE1 #D J>S ( SALSA
..#C.D ,SKILL .,PRACTICE @7 PP4
#AHB-AHC @7 .#A4 .,SAMPLE .ANSW]3 #B .;X
-- #C .;Y @+ .;Z .K #F2 A PLANE .#C4 NO
.#E4 YES .#G4 NO .#I4 7#A1 #E1 #F7 .#AA4
NO SOLU;N .#AC4 7#J1 #D1 --#B7 .#AE4
7#C1 #B1 #A7 .#AG4 7--#F1 #D1 --#D7
.#AI4 7#J1 #J1 --#B7 .#BA4 ,9 ! #BND
EQU,N1 ! COE6ICI5T ( .;Y 0 N MULTIPLI$
0#B2 .#BE4 9F9ITELY _M SOLU;NS .#BG4
7--#A1 #D1 #J7 .#BI4 7--#D1 #E1 --#D7
.#CA4 7#J1 --#B1 #F7 .#CC4 7#B1 #F1
--#E7 .#CE4 7#B1 #A1 #J7 .#CG4 .A .K
#AB1 .;B .K --#D1 .;C .K #AJ2 :5 Y
SUB/ITUTE --#A = .;X @1 #B = .;Y @1 &
--#C = .;Z 96EA* (! EQU,NS1 Y GET !
RESULTS = .A1 .;B @1 & .;C @4
..#C.D ,PRO#M .,SOLV+ @7 PP4 #AHD-AHE
@7 .#DC4 #A/ DELIV]Y3 #CJJ GAL2 #BND
DELIV]Y3 #GEJ GAL2 #CRD DELIV]Y3 #BJEJ
GAL .#DE4 .A4 .;F @+ .;S @+ .;T .K #BJ1
#E .;F @+ #C .;S @+ .;T .K #FH1 .;S .K
.;F @+ .;T @1 ": .;F REPRES5TS ! NUMB] (
F/-PLACE F9I%ES1 .;S REPRES5TS ! NUMB] (
SECOND-PLACE F9I%ES1 & .;T REPRES5TS !
NUMB] ( ?IRD-PLACE F9I%ES2 #G F/-PLACE
F9I%ES1 #AJ SECOND-PLACE F9I%ES1 #C
?IRD-PLACE F9I%ES .B4 ,:5 Y SOLVE = .;F
& ;F1 Y GET A FRAC;NAL ANSW] & Y _C H
FRAC;NS (A P]SON4 .#DG4 .A4 #B.E .;R @+
#D @+ .#B;I .K #CB1 .;R @+ @+ .;I .K
#AB1 .;R .K #B7 @+ .;I @7 ": .;R
REPRES5TS ! NUMB] ( ROSES1 REPRES5TS !
NUMB] ( LILIES1 & .;I REPRES5TS ! NUMB]
( IRISES .B4 #H ROSES1 #B LILIES1 #B
IRISES .C4 YES2 #H ROSES1 #B LILIES1 #B
IRISES
..#C.E ,SKILL .,PRACTICE @7 PP4
#AIJ-AIC @7 .#A4 DIM5.NS .#C4 ,!
CORRESPOND+ 5TRIES 7 N A4$ TGR 6CR1TE A
#B * #A MATRIX1 .#E4
.#G4 .#I4 .#AA4 .#AC4 .#AE4 .#AG4
.#AI4 .#BA4 .#BC4 .#BE4 @1 .;Y .K #D
.#BG4 .;X .K --#B1 .;Y .K --#AF .#BI4
.,SAMPLE .ANSW]2 @1
#C.E ,PRO#M ,SOLV+ @7 PP4 #AIB-AIC @7
.#CA4 .#CC4 .A4 @1 .B4 @2 ! SUM
REPRES5TS ! TOTAL SALES = ,MAY & ,JUNE
.C4
..#C.F ,SKILL .,PRACTICE @7 PP4
#AII-BJJ @7 .#A4 COLUMNS2 R[S .#C4
DEF9$2 #B * #B .#E4 N DEF9$ .#G4 N DEF9$
.#AA4 .#AC4 .#AE4 .#AG4 .#AI4 ,!
MULTIPLIC,N %D 2 R[ #A ( LEFT MATRIX
0COLUMN #A (! "R MATRIX2 #C7#G7 @+
7--#A77#A7 .K #BJ4 .#BC4 .#BE4 .#BG4
.#BI4 .#CA4 .;X .K #C1 .;Y .K #CE .#CC4
.#CE4 .,SAMPLE .ANSW]3
--------------------------------;,,SA#AJ
,,SELECT$ ,,ANSW]S
#C.F ,PRO#M ,SOLV+ @7 PP4 #BJJ-BJB @7
.#CG4
.#CI4 ,FRI"D3 4#AAEJ1 ,SATUR"D3 4#AFGE
.#DA4 ,,PS2 ,7#FB1DJJ #EG1EGE7'1 X %[S
! PR(IT = ALL (! C>S SOLD 0EA* D1L]4
.#DC4 .A4 .B4 @2 ! NUMB] ( -MUT]S AF #A
YE>
.C4 @2 ! NUMB] ( -MUT]S AF #B1 #C1 &
#D YE>S
..#C.G ,SKILL .,PRACTICE @7 PP4
#BJG-BJH @7 .#A4 DET]M9ANT .#C4 --#F
.#E4 #BE .#G4 #H .#I4 #CI .#AA4 --#BJF
.#AC4 --#CD .#AE4 #AAFJ .#AG4 --#DHJ
.#AI4 ,! SUM (! PRODUCTS =! DIAGONALS T
G UP %D 2 SUBTRACT$ F ! SUM (! PRODUCTS
=! DIAGONALS T G D[N2 #AJ @+ #J @+
7--#H7--7#C @+ #BD @+ #J7 .K --#BE .#BC4
#AB .#BE4 #BA .#BG4 #BE .#BI4 7--#D1 #C7
.#CA4 7--#G1 --#E7 .#CC4 7#F1 --#C1
--#G7 .#CE4 7#J1 #D1 #A7 .#CG4 7#H1 #F1
#G7
..#C.G ,PRO#M .,SOLV+ @7 PP4 #BJH-BJI
@7 .#DA4 #AB FT #B .#DC4 .A4 #FJ S+LE
SCOOP1 #DJ D\# SCOOP1 #BJ TRIPLE SCOOP
.B4 4#ADJ.JC .#DE4 .A4 #DGHF MI #B .B4
#CBJA MI #B .C4 #GIHG MI #B .D4 ,3NECT
,V]NAL1 ,,UT1 6,MOAB1 ,,UT4
#C.H ,SKILL ,PRACTICE @7 PP4 #BAD-BAE
@7
.#A4 MATRIX ( V>IA#S @1 MATRIX (
3/ANTS
.#C4 .#E4 .#G4 .#I4 .#AA4 ,! SCAL> %D
2 @2 @4 .#AC4 .#AE4 .#AG4 .#AI4 .#BA4
.#BC4 .#BE4 7#C1 #B7 .#BG4 7--#A1 --#D7
.#BI4 7#AJ1 --#B7 .#CA4 7#A1 --#H7 .#CC4
7--#C1 #E7 .#CE4 7--#I1 #AI1 --#AJ7
.#CG4 7--#A1 --#B1 #C7 .#CI4 7--#B1 #AJ1
#J7 .#DA4 .,SAMPLE .ANSW]3
..#C.H ,PRO#M .,SOLV+ @7 PP4 #BAE-BAG
@7 .#DC4 S+LE-5G9E3 #AEJ ;H1 TW9-5G9E3
#EJ ;H .#DE4 .A4 #B .;X @+ .;Y .K #H1 #C
.;X @+ .;Y .K #AA ": .;X REPRES5TS ROLLS
& .;Y REPRES5TS MU69S .B4 .C4 #C BAT*ES
( ROLLS1 #B BAT*ES ( MU69S .#DG4 ,BRAN
,CRUN*IES3 #B.C OZ1 ,TOA/$ ,OATS3 #J.H
OZ1 ,:OLE ,:1T ,FLAKES3 #A.B OZ .#DI4
.A4 @2 #IJ;DG CLOCKWISE ROT,N .B4
MULTIPLY .,,AAT 0.,A & !N AG 0.,A
..#C.H ,PRO#M ,SOLV+ .,"W%OP @7 P4
#BAI @7 .#A4 ,,DVD3 4#AE1 POPCORN3
4#A.GE1 MOVIE PASS3 4#H .#C4 #AA LBS (
SUNFL[] SE$1 #I LBS ( ?I/LE SE$
.,*APT] .,REVIEW @7 PP4 #BBB-BBF @7
.#A4 3SI/5T1 9CONSI/5T .#C4 ,! NUMB] (
COLUMNS 9 ! LEFT H& MATRIX IS ! SAME Z !
NUMB] ( R[S 9 ! "R H& MATRIX4
.#E4 7--#D1 --#B7
.#G4 7--#C1 #G7 .#I4 7--#F1 #G7
.#AA4 .#AC4
.#AE4 7--#C1 --#H1 #D7 .#AG4 #AJ W9D
9/RU;TS1 #C /R+ 9/RU;TS1 #B P]CUS.N
9/RU;TS .#AI .#BA4 .#BC4 .#BE4 .#BG4
.#BI4 --#DB .#CA4 #AH .#CC4 7#G1 #A7
.#CE4 7--#A1 --#D7
.,CUMULATIVE .,REVIEW @7 PP4 #BCB-BCC
@7 .#A4 --#B .;X #B @+ #G .;X .#C4 --#D
.;X #B @+ #F .;X @+ #AE .#E4 .#G4 #H1 #B
.#I4 --#AF1 #BE
--------------------------------;,,SA#AA
,,SELECT$ ,,ANSW]S
.#AA4 #E "K.K .;X "K.K #AJ
.#AC4 --#A "K .;X "K #I
.#AE4
.#AG4 @2 FALLS .#AI4 #J2 IS HORIZONTAL
.#BA4
.#BC4
.#BE4
.#BG4
.#BI4 FUNC;N
.#CA4 7#E1 --#D7 .#CC4 7--#B1 #D1 #A7
.#CE4
.#CG4 .#CI4 .#DA4
.#DC4 .A4 .B4 ,AB #IH GAMES2 X'S !
SAME4
.#DE4 @2 4#FBEJ .#DG4 .;S .1 #BAC1 .;J
"K #BFC1 .;S @+ .;J .1 #DGB.E
,*APT] #D
..#D.A ,SKILL .,PRACTICE @7 PP4
#BDJ-BDA @7 .#A4 P>ABOLA .#C4 #AF1 #D1
#J1 #D1 #AF .#E4 #H1 #B1 #J1 #B1 #H
.#G4 SAME AXIS ( SYMMETRY & V]TEX1
OP5S UP1 & IS N>R[]
.#I4 SAME AXIS ( SYMMETRY & V]TEX1
OP5S D[N1 & IS N>R[]
.#AI4 ,! =MULA =! .;X -COORD9ATE (!
V]TEX IS @2 @4
.#BA4 .#BC4
.#CC4 MAXIMUM VALUE2 --#A .#CE4 M9IMUM
VALUE2 --#A .#CG4 M9IMUM VALUE2 --#B
.#DA4 .A .K --#J.JB1 .;B .K #A1 .;C .K
#F .#DC4 .,SAMPLE .ANSW]3 .;Y .K -- .;X
#B @+ #H .;X @+ #C1 .;Y .K #B .;X #B --
#AF .;X -- #A1 .;Y .K .;X #B -- #H .;X
-- #F
.#DG4 .#DI4
.#EC4 ,! AXIS ( SYMMETRY HAS 6LIE
HALFWAY 2T ! TWO .;X -COORD9ATES2 .;X .K
--#A4
..#D.A ,PRO#M .,SOLV+ @7 PP4 #BDB-BDC
@7 .#EE4 ,RAISE ! PRICE BY 4#J.GE
69CR1SE REV5UE TO 4#DIJJ P] "D4
.#EG4 AB #AJ FT .#EI4 .A4 PR(IT .K
PRICE 99 SALES--EXP5SES2 .;,P @7 .;X @7
.K 7#BJ -- .;X @77#AEJ @+ #AJ .;X
@7--#AEJJ
B4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X @3 .;,P @7 .;X @7
#J3 #AEJJ
#A3 #AEDJ
#B3 #AEFJ
#C3 #AEFJ
#D3 #AEDJ
#E3 #AEJJ
.C4 ,REDUCE ! PRICE BY 4#B.EJ 69CR1SE
PR(ITS TO 4#AEFB.EJ P] WEEK4
..#D.B ,SKILL .,PRACTICE @7 PP4
#BDI-BEJ @7 .#A4 V]TEX
.#C4 .#E4
--------------------------------;,,SA#AB
,,SELECT$ ,,ANSW]S
.#AC4 .#AE4
.#BC4 .;P .K #B & .;Q .K --#C2 ! .;X
-9T]CEPTS >E #B & --#C4 .#BE4 .;Y .K .;X
#B --#B .;X -- #AE .#BG4 .;Y .K --#C .;X
#B @+ #AH .;X -- #BD .#BI4 .;Y .K .;X #B
-- #F .;X @+ #AE .#CA4 .;Y .K #E .;X #B
@+ #CJ .;X @+ #DA .#CC4 M9IMUM3 --#D
.#CE4 M9IMUM3 #ACJ .#CG4 MAXIMUM3 #GBI
.#CI4 M9IMUM3 --#DEJ .#DA4 MAXIMUM3
#BAA.BE
.#DC4 .#DE4
.#DI4 .,SAMPLE .ANSW]3 .;Y .K @7 .;X
-- #H7@7 .;X @+ #B71 .;Y .K @7 .;X --
#D7@7 .;X -- #B71 .;Y .K @7 .;X @+ #C7@7
.;X -- #I7
..#D.B ,PRO#M .,SOLV+ @7 PP4 #BEJ-BEA
@7 .#EA4 #F FT2 AB #BH FT .#EC4 .A4 #AFJ
FT .B4 AB #A.E FT .#EE4 .A4 AB #AD@3P2
AB #EE.E CM #C .B4 AB #AC.F@3P2 AB #DD.A
CM #C .C4 HOT-AIR3 DOMA93 #E.EB "K .;X
"K #BB.F1 RANGE3 #J "K .;Y "K #EE.E2 HOT
OIL3 DOMA93 #E.CE "K .;X "K #BA.H1
RANGE3 #J "K .;Y "K #DD.A2 S9CE MOI/URE
3T5T & POPP+ VOLUME _C 2 NEGATIVE1 !
DOMA9 & RANGE M/ EA* 2 POSITIVE NUMB]S4
,A POSITIVE DOMA9 O3URS 2T ! ;X-9T]CEPTS
&! GRTE/ NUMB] 9 ! RANGE O3URS AT !
MAXIMUM PO9T1 : IS ! V]TEX4
..#D.C ,SKILL .,PRACTICE @7 PP4
#BEE-BEG @7 .#A4 AN .;X VALUE T MAKES !
FUNC;N EQUAL 6Z]O .#C4 @7 .;X @+ #A7 @7
.;X @+ #E7 .#E4 @7 .A -- #AA7 @7 .A --
#B7 .#G4 _C 2 FACTOR$ .#I4 @7 .;B @+
#H7@7 .;B -- #E7 .#AA4 @7 .;X -- #I7@7
.;X @+ #B7 .#AC4 @7 .;X @+ #AB7@7 .;X --
#C7 .#AE4 @7 .;X @+ #F7@7 .;X -- #F7
.#AG4 @7 .;X -- #AB7 #B .#AI4 @7 .;X @+
#D7 #B .#BA4 @7 .;N @+ #G7 #B .#BC4 @7
.;Z -- #AA7@7 .;Z @+ #AA7 .#BE4 #E1 #F
.#BG4 --#G1 #G .#BI4 --#D1 --#A .#CA4
--#E .#CC4 --#F1 #I .#CE4 #J1 --#I .#CG4
#G .#CI4 ,! EQU,N 0 N FACTOR$ CORRECTLY2
.;X #B -- .;X -- #F .K #J1 @7 .;X --
#C7@7 .;X @+ #B7 .K #J1 .;X .K #C OR .;X
.K --#B4 .#DC4 #C7#AJ77#AB7 .K 7#AJ @+
.;X @77#AB @+ .;X @7 .#DE4 #D .#DG4
--#AJ1 #C .#DI4 #J1 #H .#EA4 --#E1 #E
.#EC4 --#AB1 --#G .#EE4 --#A .#EG4 .;X
#B -- #AI .;X @+ #HH .K #J .#EI4 #D
.#FA4 #C .#FC4 .,SAMPLE .ANSW]3 .;X #B
-- #BJ .;X @+ #IA .K #J
..#D.C ,PRO#M .,SOLV+ @7 PP4 #BEG-BEH
@7 .#FE4 #C7#EJ77#AJJ7 .K 7#EJ @+ .;X
@77#AJJ @+ .;X @7@1 --#BJJ1 #EJ2 #AJJ FT
0#AEJ FT .#FG4 .A4 #FJJ FT #B .B4 >EA (
NEW PATIO .K >EA ( EXI/+ PATIO @+ >EA (
EXPAN.N1 7#CJ @+ .;X @77#BJ @+ .;X @7 .K
#FJJ @+ #DFD .C4 --#EH1 #H2 #H FT .#FI4
#C7#AH77#AE7 .K 7#AH @+ .;X @77#AE @+
.;X @7@1 --#DE1 #AB2 #AAD;FT .#GA4
#B7#AJJ7 .K 7#AJ @+ .;X @77#AJ @+ .;X
@7@2 NO2 "! >E NO R1L NUMB]S .A & .;B S*
T .;AB .K --#AJJ & .A @+ .;B .K #BJ4
..#D.D ,SKILL .,PRACTICE @7 PP4
#BFC-BFD @7 .#A4 #D .#C4 7#B .;X @+
#C7@7 .;X @+ #A7 .#E4 7#D .;R @+ #A7 @7
.;R @+ #A7 .#G4 7#AA .;Z -- #I7 @7 .;Z
@+ #A7 .#I4 _C 2 FACTOR$ .#AA4 7#I .;D
@+ #E7 @7 .;D -- #B7 .#AC4 7#C .;X @+
#A77#C .;X -- #A7 .#AE4 7#G .;N --
#D77#G .;N @+ #D7 .#AG4 7#G .;X @+ #E7
#B .#AI4 7#C .;P -- #B7 #B .#BA4 7#F .;X
-- #G7 #B .#BC4 #B7#C .;Z @+ #D77#C .;Z
@+ #B7 .#BE4 #F .;U @7 .;U -- #D7 .#BG4
#D7#E .;X @+ #A7@7 .;X @+ #F7 .#BI4
--#C7#F .;N -- #E77#B .;N -- #A7 .#CA4
#D %D 2 FACTOR$ \ ( EA* T]M 9 !
BINOMIAL2 #D .;X #B -- #CF .K #D7 .;X #B
-- #I7 .K #D7 .;X @+ #C7@7 .;X -- #C74
.#CC4 --#B1 #B .#CE4 #J1 .#CG4 .#CI4
.#DA4 @1 #E .#DC4 @1 #F .#DE4 @1 #B
.#DG4 --#A1 .#DI4 --#A1 .#EA4 #C .#EC4
--#A1 .#EE4 @1 #B .#EG4 #J1 #D
..#D.D ,PRO#M .,SOLV+ @7 PP4 #BFD-BFE
@7 .#FC4 #B FT .#FE4 4#E.GE2 LETT+ .;X
REPRES5T ! NUMB] ( @4#.BE DECR1SES 9 !
S&WI* PRICE1 ! REV5UE .;,R IS GIV5 0!
FUNC;N .;,R .K 7#CCJ @+ #AE .;X
@77#F--#J.BE .;X @7@4 ,! Z]OS ( ? FUNC;N
>E --#BB & #BD1 & _! AV]AGE IS #A4 ,S1
6MAXIMIZE ! DAILY REV5UE1 EA* S&WI* %D 2
SOLD = #F--#J.BE7#A71 OR 4#E.GE4 ,!
MAXIMUM DAILY REV5UE IS !N 7#CCJ @+
#AE7#A77 7#E.GE7 .K 7#CDE7 7#E.GE7 .K
4#AIHC.GE4 .#FG4 .A4 #GB IN4 .B4 .;W .K
#CB -- .;H2 .;,V .K #CF7#CF -- .;H @7@7
.;H @7 .C4 #AH IN41 #AH IN41 #AA1 #FFD
IN4 #C @2 F9D ! ROOTS (! EQU,N 9 "P 7;B7
6BE #J & #CF1 S ! L9E ( SYMMETRY IS AT
@4 ,6F9D ! MAXIMUM VOLUME1 SUB/ITUTE #AH
= .;H 96! EQU,N F "P 7;B74
..#D.E ,SKILL .,PRACTICE @7 PP4
#BFI-BGJ @7 .#A4 RADIC& .#C4 .#E4 .#G4
#BD .#I4 .#AA4 .#AC4 .#AE4 .#AG4 .#BA4
,! EQU,N HAS TWO SOLU;NS2 .;X #B .K #HA1
.;X .K +-#I4 .#BC4 .#BE4 +-#E .#BG4
.#BI4 +-#AJ .#CA4 .#CC4 .#CE4 ,FACTOR3
.;X #B -- #D .K #J1 @7 .;X @+ #B7@7 .;X
-- #B7 .K #J1 .;X .K --#B OR .;X .K #B2
,SOLVE ! EQU,N .;X #B -- #D .K #J1 .;X
#B .K #D1 .;X .K +-#B4
..#D.E ,PRO#M .,SOLV+ @7 PP4 #BGJ-BGA
@7 .#CI4 ,E>?3 AB #C.A SEC1 ,M>S3 #E
SEC1 ,JUPIT]3 AB #B.J SEC1 ,SATURN3 AB
#C.B SEC1 ,PLUTO3 AB #AB.B SEC .#DA4 .A4
.;R #B .K #AJJ .B4 AB #E.F FT .C4 @2 .;S
#B .K .;R #B @1
..#D.E ,PRO#M ,SOLV+ .,"W%OP @7 P4
#BGC @7 .#A4 #A1 #E .#C4 .#E4 AB --#D.D1
AB #A.D .#G4 AB #AJH MPH .#I4 #A.BE SEC
..#D.F ,SKILL .,PRACTICE @7 PP4
#BGI-BHJ @7 .#A4 .A @+ .BI .#C4 .#E4
+-#B .;I .#G4 .#I4 +- .;I .#AA4 .#AC4
#AG -- .;I .#AE4 --#H @+ #F .;I .#AG4
#AI--#I .;I .#AI4 #BA @+ #I .;I .#BC4
--#H--#D .;I .#BE4 --#AH--#AC .;I .#BG4
#GC .#BI4 .#CA4
--------------------------------;,,SA#AC
,,SELECT$ ,,ANSW]S
.#CC4 .#DC4 .#DE4 .#DG4 #D .#DI4 .#EA4
--#BJ @+ #B .;I .#EC4 --#ABE @+ #IJ .;I
.#EE4 .#EG4 .;I #B .K --#A1 S --#B .;I
#B .K #B2 #D -- .;I @+ #H .;I -- #B .;I
#B .K #F @+ #G .;I @4 .#EI4 .A4 A4ITIVE3
--#B -- .;I @1 MULTIPLICATIVE3 .B4
A4ITIVE3 --#E @+ .;I @1 MULTIPLICATIVE3
.C4 A4ITIVE3 #A--#C .;I @1
MULTIPLICATIVE3
..#D.F ,PRO#M .,SOLV+ @7 PP4 #BHA-BHB
@7 .#FE4 #D--#C .;I OHMS .#FG4 #AB--#H
.;I OHMS
#FI4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,P[]S (.' ;I @3 .;I @3 .;I #B @3 .;I
#C @3 .;I #D @3 .;I #E @3 .;I #F @3 .;I
#G @3 .;I #H
.,SIMPLIFI$ @3 .;I @3 --#A3 -- .;I @3
#A3 .;I @3 --#A3 -- .;I @3 #A
,! PATT]N REP1TS E F\R P[]S ( .;I2 .;I
#I .K .;I1 .;I #AJ .K --#A1 .;I #AA .K
-- .;I1 .;I #AB .K #A4
.#GA4 DOES N 2L;G 6! ,M&ELBROT SET
.#GC4 2L;GS 6! ,M&ELBROT SET .#GE4 .A4
.B4 .C4
..#D.G ,SKILL .,PRACTICE @7 PP4
#BHH-BHI @7 .#A4 ,A BINOMIAL IS ! SUM (
TWO MONOMIALS &A TRINOMIAL IS ! SUM (
?REE MONOMIALS4 .#C4 --#E1 #A .#E4
--#AD1 --#B .#G4 .#I4 .#AA4 .#AC4 #I2@7
.;X @+ #C7 #B .#AE4 #ADD2 @7 .;X -- #AB7
#B .#AG4 #A2 @7 .;X -- #A7 #B .#AI4
.#BA4 .#BC4 .#BE4 .#BG4 .#BI4 .#CA4
.#CC4 .#CE4 .#CG4 .#CI4 7#B.H1 #ABE.DD72
AT #B.H SECONDS ! WAT] W R1* A MAXIMUM
HEI<T ( #ABE.DD FEET4 .#DA4 .;Y .K @7
.;X -- #D7 #B @+ #C2 7#D1 #C7 .#DC4 .;Y
-- @7 .;X @+ #F7 #B @+ #A2 7--#F1 #A7
.#DE4 @2 .#DG4 .;Y .K #B7 .;X @+ #F7 #B
-- #DG2 7--#F1 --#DG7 .#DI4 .;Y .K #B7
.;X -- #G7 #B @+ #A2 7#G1 #A7 .#EA4 #CF
%D 2 A4$ 6EA* SIDE 9/1D ( #I2 #D7 .;X #B
@+ #F .;X @+ #I7 .K #AA @+ #CF2 #D7 .;X
@+ #C7 #B .K #DG2 @2 @2 @4 .#EC4 .#EE4
.#EG4
..#D.G ,PRO#M .,SOLV+ @7 PP4 #BIJ-BIA
@7 .#FC4 #DJ FT .#FE4 ,SELL+ SY/EMS =
4#CJJ WD MAXIMIZE MON?LY REV5UE AT
4#IJJJ4 .#FG4 .A4 #AEJJ .K 7#ABJ--#B .;X
@7@7 .;X @7 .B4 AB #AG.GE1 AB #DB.BE2
#AG.BE M/ 2 REJECT$ 2C X GIVES A L5G? =!
G>D5 T IS GRT] ?AN ! L5G? (! SIDE (!
S*OOL1 .C4 AB #DB.BE FT 0#CE.E FT
..#D.H ,SKILL .,PRACTICE @7 PP4
#BIF-BIG @7 .#A4 4CRIM9ANT .#C4 --#A1 #E
.#E4 .#G4 .#I4 .#AA4 .#AC4 #B .#AE4
.#AG4 .#AI4 .#BA4 .#BC4 #B1 #C .#BE4
--#A1 #C .#BG4 --#B1 #D .#BI4 --#E1 --#C
.#CA4 #J2 "O R1L SOLU;N .#CC4 --#CB2 TWO
IMAG9>Y SOLU;NS .#CE4 --#BJ2 TWO IMAG9>Y
SOLU;NS .#CG4 --#CCE2 TWO IMAG9>Y
SOLU;NS .#CI4 --#CF2 TWO IMAG9>Y SOLU;NS
.#DA4 .#DC4 .#DE4 .#DG4 #J.HGE +- #J.GEB
.;I .#DI4 @2 @2 @2 .;X .K --#A +- #B .;I
@2 .#EA4 @1 : IS ! =MULA =! AXIS (
SYMMETRY4 .#EC4 NEGATIVE .#EG4 .A4 .;C
"K #AF .B4 .;C .K #AF .C4 .;C .1 #AF
.#EI4 .A4 .;C "K #DH .B4 .;C .K #DH .C4
.;C .1 #DH .#FA4 .A4 .;C "K #J.BE .B4
.;C .K #J.BE .C4 .;C .1 #J.BE .#FC4
.#FE4 #B .;X #B @+ #D .;X @+ #D .K #J
..#D.H ,PRO#M .,SOLV+ @7 PP4 #BIH-BII
@7 .#GA4 #AADA ;M1 #BJIJ ;M
#GC4 A4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;T @3 #J3 #J.BE3 #.JE3 #J.GE3 #A
@7 .;X1 .;Y @7 @3 7#J1 #F73 7#E1
#AJ.BE73 7#AJ1 #AB.E73 7#AE1 #AB.GE73
7#BJ1 #AA7
.B4
.C4 ,NO2 ! HEI<T (! BALL :5 .;X .K #AE
IS #AB.GE FEET1 : IS ABV ! BACKBO>D1 S !
FREE ?R[ WD N 2 MADE4
#D.I ,SKILL ,PRACTICE @7 PP4 #CJD-CJE
@7
.#A4 .,SAMPLE .ANSW]3 #C .;X #B -- #B
.;X @+ #E .1 #J1 .;Y .1.K .;X #B @+ #D
.;X -- #H
.#G4 .#I4
.#AI4 ,! 9SIDE (! P>ABOLA %D 2 %AD$4
--------------------------------;,,SA#AD
,,SELECT$ ,,ANSW]S
.#BA4 .#BC4
.#BG4 .;X "K --#C OR .;X .1 #A .#BI4
.;X "K.K --#B OR .;X .1.K #D .#CA4 #B "K
.;X "K #H .#CC4 --#A "K.K .;X "K.K #C
.#CE4 #J "K .;X "K #F .#CG4 .;X "K #J.EI
OR .;X .1 #C.D .#CI4 --#B "K.K .;X "K.K
#A.C .#DA4 #J.FG "K.K .;X "K.K #B.E
.#DC4 --#A.B "K .;X "K #C.G .#DG4 --#I
"K .;X "K --#A .#DI4 OR .;X .1 #E .#EA4
.;X "K.K --#C.E OR .;X .1 #A.E .#EC4
--#J.BG "K.K .;X "K.K #A.E .#EE4 --#B.H
"K.K .;X "K.K --#J.GB .#EG4 .;X "K
--#J.DF OR .;X .1 #A.H .#EI4 --#J.HI "K
.;X "K #A.C .#FA4 NO SOLU;N .#FC4 .;X "K
#J.EB OR .;X .1 #AA.E .#FE4 #J "K.K .;X
"K.K #J.E .#FG4 NO SOLU;N
#D.I ,PRO#M ,SOLV+ @7 PP4 #CJF-CJG @7
.#GA4
.#GC4 #CG "K.K .;X "K.K #DJ2 ! DOMA9
RE/RICTS ! NUMB] ( "DS 6LESS ?AN OR
EQUAL 6#DJ4 .#GE4 .A4 --#J.JED .;X #B @+
#A.DC .;X -- #H "K #J2 .;X "K.K #H.J OR
.;X .1.K #AH.E .B4 ,NO2 ! BALL W G OV] !
GOAL 0.#A4 #C FEET4
..#D.AJ ,SKILL .,PRACTICE @7 PP4
#CAB--#CAC @7 .#A4 BE/-FITT+ QUADRATIC
MODEL .#C4 .;Y .K @7 .;X -- #C7 #B @+ #B
.#E4 .#G4 .;Y .K --@7 .;X -- #A7 #B @+
#F .#I4 .#AA4 .;Y .K #B7 .;X @+ #D7 #B
-- #B .#AC4 .#AG4 .;Y .K --@7 .;X --
#C7@7 .;X @+ #B7 .#AI4 .#BA4 .;Y .K .;X
@7 .;X @+ #C7 .#BC4 .;Y .K #C7 .;X --
#C7@7 .;X -- #G7 .#BE4 .#BG4 ,! V]TEX =M
(! EQU,N %D 2 US$ 9/1D (! 9T]CEPT =M2
.;Y .K .A @7 .;X -- #B7 #B @+ #C2 #E .K
.A 7#A--#B7 #B @+ #C2 #E .K .A @+ #C2 .A
.K #B1 S .;Y .K #B7 .;X -- #B7 #B @+ #C4
.#BI4 .;Y .K #B .;X #B @+ #BJ .;X @+ #DF
.#CA4 .#CC4 .#CE4 .;Y .K #C .;X #B -- #D
.;X @+ #B .#CG4 .#CI4 .#DA4 .;Y .K #H
.;X #B @+ #FD .;X -- #BFD .#DC4 .,SAMPLE
.ANSW]3
#D.AJ ,PRO#M ,SOLV+ @7 PP4 #CAD-CAE @7
.#DG4 .#DI4 .A4 .;Y .K #J.JAB .;X #B
-- #J.CJI .;X -- #J.JJJDH .B4 AB --#A.IJ
SEC
.,*APT] .,REVIEW @7 PP4 #CAH-CBB @7
.#A4 ,IF .A "K #J1 ! FUNC;N HAS A
MAXIMUM VALUE & IF .A .1 #J1 !N ! FUNC;N
HAS A M9IMUM VALUE4 .#C4 V]TEX =M
.#E4 .#G4
.#I4 .#AA4
.#AC4
.#AE4 --#E1 #J .#AG4 --#C1 #I .#AI4
--#I .#BA4 7#GB @+ .;X @77#DH @+ .;X @7
.K #B7#GB77#DH72 #BD FT .#BC4 .#BE4 +-#F
.#BG4 .#BI4 --#I--#AH .;I .#CA4 #BI
.#CC4 --#D @+ #B .;I .#CE4 .#CG4 .#CI4
.#DA4 AB #J.B SEC .#DC4 --#J.FE "K.K .;X
"K.K #D.F .#DE4 .;Y .K #B @7 .;X @+
#C7@7 .;X -- #B7 .#DG4
,*APT] #E
..#E.A ,SKILL .,PRACTICE @7 PP4
#CCC-CCD @7 .#A4 .A4 ,PRODUCT ( P[]S
PROP]TY .B4 ,NEGATIVE EXPON5T PROP]TY
.C4 ,P[] (A PRODUCT PROP]TY .#C4 #BDC2
PRODUCT ( P[]S PROP]TY .#E4 --#CABE2
PRODUCT ( P[]S PROP]TY .#G4 @2 QUOTI5T (
P[]S PROP]TY .#I4 @2 P[] (A QUOTI5T
PROP]TY1 NEGATIVE EXPON5T PROP]TY .#AA4
#GBI2 QUOTI5T ( P[]S PROP]TY .#AC4 @2
PRODUCT ( P[]S PROP]TY1 NEGATIVE EXPON5T
PROP]TY .#AE4 #F.C * #AJ #I .#AG4 #E.FJG
* #AJ --#F .#AI4 #I.BFA * #AJ --#AB
.#BA4 #A.E * #AJ #C .#BC4 #B.BE * #AJ
--#B
--------------------------------;,,SA#AE
,,SELECT$ ,,ANSW]S
.#BE4 #AJBD .;Y #AE @2 P[] (A PRODUCT
PROP]TY1 P[] (A P[] PROP]TY .#BG4 @2
PRODUCT ( P[]S PROP]TY1 NEGATIVE EXPON5T
PROP]TY .#BI4 @2 P[] (A PRODUCT PROP]TY1
P[] (A P[] PROP]TY1 NEGATIVE EXPON5T
PROP]TY .#CA4 @2 QUOTI5T ( P[]S PROP]TY
.#CC4 @2 QUOTI5T ( P[]S PROP]TY1
NEGATIVE EXPON5T PROP]TY .#CE4 @2
PRODUCT ( P[]S PROP]TY1 QUOTI5T ( P[]S
PROP]TY1 NEGATIVE EXPON5T PROP]TY .#CG4
,! EXPON5TS %D 2 SUBTRACT$1 N DIVID$2
.;X #H @4 .#CI4 ,! BASE %D N *ANGE2
7--#C7 #F @4 .#DA4 .#DC4 .;X #AA .;Y #E
.;Z --#C .#DE4 .A --#D .;B #I
..#E.A ,PRO#M .,SOLV+ @7 PP4 #CCD-CCE
@7 .#DI4 ,PACIFIC3 #F.BHFH * #AJ #AG ;M
#C @1 ,ATLANTIC3 #C.JAHBD * #AJ #AG ;M
#C @1 ,9DIAN3 #B.GAFEF * #AJ #AG ;M #C
@1 ,>CTIC3 #A.GJFA * #AJ #AF ;M #C .#EA4
.,SAMPLE .ANSW]3 ,! VOLUME (! PE>L IS
"TS Z L>GE Z ! VOLUME (! B1D4 .#EC4 .A4
AB #D.DBBE * #AJ --#G ;M #C
..#E.B ,SKILL .,PRACTICE @7 PP4
#CDA-CDC @7 .#A4 DEGREE3 #D1 TYPE3
QU>TIC1 L1D+ COE6ICI5T3 --#E1 3/ANT T]M3
#F .#C4 POLYNOMIAL FUNC;N2 .;F @7 .;X @7
.K -- .;X #B @+ #H1 DEGREE3 #B1 TYPE3
QUADRATIC1 L1D+ COE6ICI5T3 --#A .#E4
POLYNOMIAL FUNC;N2 @1 DEGREE3 #D1 TYPE3
QU>TIC1 L1D+ COE6ICI5T3 .#G4 POLYNOMIAL
FUNC;N2 @1 DEGREE3 #C1 TYPE3 CUBIC1 L1D+
COE6ICI5T3 .#I4 --#CB .#AA4 #CGH .#AC4
#AHB .#AE4 #AJI .#AG4 #ADI .#AI4 --#AA
.#BA4 --#GH .#BC4 ,! COE6ICI5T ( .;X #C
0 LEFT \4
.#BE4 DEGREE3 EV51 L1D+ COE6ICI5T3
POSITIVE .#BG4 DEGREE3 EV51 L1D+
COE6ICI5T3 NEGATIVE .#BI4 -- @1 -- .#CA4
-- @1 @+ .#CC4 @+ @1 -- .#CE4 @+ @1 @+
.#CG4 .,SAMPLE .ANSW]3 .;F @7 .;X @7 .K
-- .;X #E -- #B .;X #D @+ #A
.#CI4 .#DA4
.#EA4 .;G @7 .;X @7--Z .;X -- & .;G @7
.;X @7 @+ Z .;X @+
#E.B ,PRO#M ,SOLV+ @7 PP4 #CDC-CDD @7
.#EE4 #AIIH
.#EG4 #BJJB
.#EI4 .A4 #CE.FBE ;G
.B4
.C4 ,S>US4 .,SAMPLE .ANSW]3 ,SUB/ITUT+
#C 96EA* EQU,N GIVES ! ,S>US *ICK WEI<+
AB #ABJ GRAMS &! ,HOOD$ *ICK WEI<+ AB
#IB GRAMS4 ,! WEI<T (! ,S>US IS CLOS]
6#ACJ ?AN ! WEI<T (! ,HOOD$ *ICK IS4
..#E.C ,SKILL .,PRACTICE @7 PP4
#CDI-CEJ @7 .#A4 L T]MS .#C4 #AJ .;X #B
-- #H .#E4 #AD .;Y -- #H .#G4 #G .;S #C
-- #B .;S #B @+ #H .;S @+ #AJ .#I4 #B
.;C #C @+ #E .;C #B @+ .;C @+ #I .#AA4
--#B .;B #D --#AE .;B #C @+ #E .;B @+ #G
.#AC4 #B .;X #D -- .;X #C .#AG4 #CJ .;X
#C @+ #AJ .;X #B .#AI4 #C .;Z #B -- #H
.;Z -- #C .#BA4 #B .A #C -- #BC .A #B @+
#BF .A @+ #F .#BC4 -- .;X #D @+ #AB .;X
#C -- #CD .;X #B @+ #D .;X @+ #C .#BE4
#AB .;Y #D -- #I .;Y #C -- #HE .;Y #B --
#AI .;Y @+ #E .#BG4 ,! CUBE (A BINOMIAL
@7 .A -- .;B @7 #C IS F.D 0.A #C -- #C
.A #B .;B @+ #C .;AB #B -- .;B #C @2 7#B
.;X -- #G7 #C .K 7#B .;X @7 #C -- #C7#B
.;X @7 #B 7#G7 @+ #C7#B .;X @77#G7 #B --
7#G7 #C .K #H .;X #C -- #HD .;X #B @+
#BID .;X -- #CDC4 .#BI4 .;X #C -- #C .;X
#B -- #BE .;X -- #BA .#CA4 #B .A #C --
#E .A #B -- #CG .A -- #CJ .#CC4 --#B .;B
#C @+ #G .;B #B -- #G .;B @+ #B .#CE4
--#AB .;W #C @+ #IE .;W #B -- #ADC .;W
@+ #CJ .#CG4 --#BG .;Q #C @+ #ACB .;Q #B
-- #AGB .;Q @+ #CB .#CI4 .;W #B -- #AH
.;W @2 @+ #HA .#DA4 #D .;C #B @+ #BJ .;C
@+ #BE .#DC4 #BE .;P #B -- #I .#DE4 #D
.A #B -- #HA .;B #B .#DI4 #B .;X #C --
#AC .;X #B @+ #H .;X @+ #DH .#EA4 .#EC4
@7 .A @+ .;B @7 #B .K @7 .A @+ .;B @7@7
.A @+ .;B @7 .K .A #B @+ .;AB @+ .;AB @+
.;B #B .K .A #B @+ #B .;AB @+ .;B #B
.#EE4 @7 .A -- .;B @7 #C .K @7 .A -- .;B
@7@7 .A -- .;B @7@7 .A -- .;B @7 .K @7
.A -- .;B @7@7 .A #B -- #B .;AB @+ .;B
#B @7 .K .A #C -- #B .A #B .;B @+ .;AB
#B -- .A #B .;B @+ #B .;AB #B -- .;B #C
.K .A #C -- #C .A #B .;B @+ #C .;AB #B
-- .;B #C
--------------------------------;,,SA#AF
,,SELECT$ ,,ANSW]S
.#EG4 .A4 @7 .;X -- #A7@7 .;X #D @+
.;X #C @+ .;X #B @+ .;X @+ #A72 @7 .;X
-- #A7@7 .;X #E @+ .;X #D @+ .;X #C @+
.;X #B @+ .;X @+ #A7 .B4 @7 .;X -- #A7@7
.;X .;N -- #A @+ .;X .;N -- #B @+ .;X
.;N -- #C @+ ' @+ #A7
..#E.C ,PRO#M .,SOLV+ @7 PP4 #CEA-CEB
@7 .#EI4 #J.BHA .;T #C -- #AF.H .;T #B
@+ #DFJ .;T @+ #HFJJ .#FA4 .;,F .K
#J.JJJJCA .;S #C @+ #J.JJBAJG .;S @2 AB
#J.JE HORSEP[] .#FC4 .;,N .K --#A.EAEJC
.;T #D -- #BE.ECAJF .;T #C @+ #BAE.IBBF
.;T #B @+ #ABG.GE .;T @+ #IHEH.E2
CALCULATE .;,L ;M @* .;,S ;M @+ .;,L ;W
@* .;,S ;W @4
..#E.D ,SKILL .,PRACTICE @7 PP4
#CEF-CEG @7 .#A4 QUADRATIC .#C4 #G .;X
7#B .;X -- #C7 .#E4 .;C @7 .;C @+ #C7 @7
.;C @+ #F7 .#G4 #C .;Y #C @7 .;Y --
#D7@7 .;Y @+ #D7 .#AA4 @7 .;Y -- #D7@7
.;Y #B @+ #D .;Y @+ #AF7 .#AC4 7#E .;N
@+ #F77#BE .;N #B -- #CJ .;N @+ #CF7
.#AE4 7#B .;C @+ #G7 7#D .;C #B @+ #AD
.;C @+ #DI7 .#AG4 --#E7 .;Z -- #D7@7 .;Z
#B @+ #D .;Z @+ #AF7 .#AI4 @7 .;Y --
#G7@7 .;Y #B @+ #D7 .#BA4 7#C .;M --
#A7@7 .;M #B @+ #C7 .#BC4 @7 .;C @+
#B77#B .;C -- #C77#B .;C @+ #C7 .#BE4 @7
.A #B @+ #A7@7 .A #B @+ #F7 .#BG4 #B .;Z
7#B .;Z -- #A77#B .;Z @+ #A77#D .;Z #B
@+ #A7 .#BI4 #C .;X @7 .;X #B -- #F7 7#E
.;X #B @+ #F7 .#CA4 ,! FACTOR #C .;X %D
AL 2 SET EQUAL 6#J2 .;X .K #J OR .;X .K
--#D OR .;X .K #D4 .#CC4 .#CE4 #B1 --#B1
--#F .#CG4 .#CI4 .#DC4 @7 .;N #B --
#AJ7@7 .;N #B @+ #F7 .#DE4 7#AB .A --
#E77#C .A #B @+ #G7 .#DG4 @7 .;D @+
#C7@7 .;D -- #C77#B .;D #B @+ #E7 .#DI4
#B .;Y #B @7 .;Y #B -- #E77#D .;Y #B @+
#A7 .#EA4 #B .#EC4 #E .#EE4 @7 .;C @+
.;D @7@7 .;C -- .;D @77#G .A @+ .;B @7
..#E.D ,PRO#M .,SOLV+ @7 PP4 #CEH-CEI
@7 .#EI4 #C CM 0#I CM 0#AH CM .#FA4
L5G?3 #AJ IN41 WID?3 #E IN41 HEI<T3 #E
IN4 .#FC4 ,! VOLUME _C 2 2C ! ONLY .;X
VALUE T CORRESPONDS 6T VOLUME IS AB
--#A.CG1 : WD YIELD A NEGATIVE SIDE
L5G?4
..#E.D ,PRO#M ,SOLV+ .,"W%OP @7 P4
#CFA @7 .#A4 #D .#C4 #F .#E4 AB #A.D1 #D
.#G4 #B.E .#I4 HEI<T3 #AB IN41 WID?3 #H
IN41 L5G?3 #AH IN4
..#E.E ,SKILL .,PRACTICE @7 PP4
#CFF-CFG @7 .#A4 ,IF A POLYNOMIAL .;F @7
.;X @7 IS DIVID$ 0.;X -- .;K @1 !N !
REMA9D] IS .;R .K .;F @7 .;K @7@4 .#C4
.#E4 .#G4 .#I4 .#AA4 .#AC4 .#AE4 .#AG4
.#AI4 ,! DEGREE (! ANSW] %D 2 REDUC$
0#A2 @4 .#BA4 @7 .;X -- #F7@7 .;X --
#E7@7 .;X @+ #A7 .#BC4 @7 .;X -- #H7@7
.;X @+ #B7@7 .;X @+ #D7 .#BE4 @7 .;X --
#D7@7 .;X -- #C7@7 .;X @+ #I7 .#BG4 7#B
.;X -- #G7@7 .;X -- #C7@7 .;X -- #A7
.#BI4 --#A1 #F .#CA4 --#J.D1 #A.E .#CC4
.#CG4 .;X @+ #H
..#E.E ,PRO#M .,SOLV+ @7 PP4 #CFG-CFH
@7 .#DA4 #A MILLION ;,T-%IRTS .#DC4
.#DE4 --#J.JJBCC .;X #C @+ #J.BDI .;X #B
-- #BA.J .;X @+ #AGDJ -- @2 DIVID$ !
OV]NI<T /AYS FUNC;N 0! TOTAL VISITS
FUNC;N
..#E.F ,SKILL .,PRACTICE @7 PP4
#CGD-CGE @7 .#A4 3/ANT1 L1D+ COE6ICI5T
.#C4 +-#A1 +-#B1 +-#D1 +-#G1 +-#AD1
+-#BH .#E4 +-#A1 +-#C1 .#G4 +-#A1+-#B1
+-#G1 +-#AD1 @1 .#I4 +-#A1 +-#C1 +-#E1
+-#AE1 @1 .#AA4 #A1 #C1 #H .#AC4 --#E1
--#A1 #F .#AE4 --#B1 --#A .#AG4 --#D1
--#A1 #A1 #B .#AI4 .#BA4 .#BE4 --#A1 @1
#C .#BG4 .#BI4 --#C.E1 --#A1 #B .#CA4
--#B1 #B .#CC4 --#B1 #A1 @1 #C .#CE4
--#C1 @1 #A .#CG4 .;P %D 2 FACTORS ( #E
& .;Q %D 2 FACTORS ( #F2 POSSI# @4 .#DA4
--#A1 #A1 #B2 ;,B .#DC4 --#B2 ,A
..#E.F ,PRO#M .,SOLV+ @7 PP4 #CGF-CGG
@7 .#DE4 L5G?3 #C IN41 WID?3 #C IN41
HEI<T3 #G IN4 .#DG4 .;X #C -- #C .;X #B
@+ #B .;X -- #BD .K #J2 +-#A1 +-#B1
+-#C1 +-#D1 +-#F1 +-#H1 +-#AB1 +-#BD
.#DI4 .A4 --#AJ .;T #C @+ #ADJ .;T #B --
#BJ .;T -- #BAEJ .K #J .B4 #A1 #B1 #E
.C4 #E2 #AIII
..#E.G ,SKILL .,PRACTICE @7 PP4
#CHC-CHE @7 .#A4 REP1T$ .#C4 #D .#E4 #F
.#G4 #G .#AA4 --#E1 --#C1 #A1 #B .#AC4
--#E1 --#B1 #B .#AE4 --#B1 #A1 #B .;I @1
--#B .;I .#AG4 .;I @1 -- .;I @1 .#AI4
.#BA4 .;F @7 .;X @7 .K .;X #C -- #B .;X
#B -- #E .;X @+ #F .#BC4 .;F @7 .;X @7
.K .;X #C -- #D .;X #B --#AE .;X @+ #AH
.#BE4 .;F @7 .;X @7 .K .;X #D -- #D .;X
#C @+ #AD .;X #B -- #CF .;X @+ #DE .#BG4
.;F @7 .;X @7 .K .;X #D -- #AH .;X #C @+
#ABB .;X #B -- #CGJ .;X @+ #DBE .#BI4
.;F @7 .;X @7 .K .;X #D -- .;X #C -- #AH
.;X #B @+ #AJ .;X @+ #H .#CA4 .;F @7 .;X
@7 .K .;X #E -- #AC .;X #D @+ #FJ .;X #C
-- #HB .;X #B -- #ADD .;X @+ #CFJ .#CC4
.,SAMPLE .ANSW]3 .;F @7 .;X @7 .K .;X #E
-- #D .;X #D @+ #F .;X #C -- #F .;X #B
@+ #E .;X -- #B .#CE4 POSITIVE3 #A1
NEGATIVE3 #J1 IMAG9>Y3 #B .#CG4
POSITIVE3 #B OR #J1 NEGATIVE3 #C OR #A1
IMAG9>Y3 #D1 #B1 OR #J .#CI4 POSITIVE3
#C OR #A1 NEGATIVE3 #B OR #J1 IMAG9>Y3
#D1 #B1 OR #J .#DA4 POSITIVE3 #B OR #J1
NEGATIVE3 #A1 IMAG9>Y3 #F OR #D .#DC4
.;X --#A.A1 .;X #A.C .#DE4 .;X --#J.EH1
.;X #A.I .#DG4 .;X --#J.DB1 .;X #B.J
.#DI4 .;X --#C.E1 .;X --#A.A1 .;X .K
--#A1 .;X #B.A1 .;X #C.F .#EA4 ,"! CD 2
#C1 #B1 #A1 OR #J POSITIVE Z]OS1 #C1 #B1
#A1 OR #J NEGATIVE Z]OS1 & #B OR #J
IMAG9>Y Z]OS4 .#EC4 ,POSITIVE R1L Z]OS3
#A1 NEGATIVE R1L Z]OS3 #B1 IMAG9>Y Z]OS3
#J2 ! GRAPH CROSSES ! POSITIVE .;X -AXIS
ONCE &! NEGATIVE .;X -AXIS TWICE4 .#EE4
,POSITIVE R1L Z]OS3 #J1 NEGATIVE R1L
Z]OS3 #A1 IMAG9>Y Z]OS3 #D2 ! GRAPH DOES
N CROSS ! POSITIVE .;X -AXIS & X CROSSES
! NEGATIVE .;X -AXIS ONCE4 ,S9CE !
FUNC;N HAS DEGREE #E1 ! REMA9+ #D Z]OS
M/ 2 IMAG9>Y4
--------------------------------;,,SA#AG
,,SELECT$ ,,ANSW]S
..#E.G ,PRO#M .,SOLV+ @7 PP4 #CHE-CHF
@7 .#EI4 YE> #C & YE> #I .#FA4 AB #AF.D
;G P] M,L .#FC4 #J IN41 AB #EI IN42 !
BOOK%ELF WD H NE>LY #J 9*ES ( DEFLEC;N
NE> EA* 5D 2C (! SUPPORTS HOLD+ !
BOOK%ELF1 S ! ANSW]S MAKE S5SE 2C !Y
REPRES5T EA* 5D (A #FJ 9* BOOK%ELF4
..#E.H ,SKILL .,PRACTICE @7 PP4
#CIJ-CIA @7 .#A4 TURN+
.#C4
.#E4
.#AC4 ,! .;X -9T]CEPTS %D B1T --#B &
#A4
.#AE-.AI4 ,SAMPLE ANSW]S >E GIV54
.#AE4 LOCAL MAXIMUM3 7--#J.C1 #J.C71
LOCAL M9IMUM3 7#J.I1 --#A.C72 Z]OS3
--#J.GE1 #J1 #A.D1 L1/ DEGREE3 #C .#AG4
LOCAL MAXIMUMS3 7#A1 #J71 7#C1 #J71
LOCAL M9IMUM3 7#B1 --#B72 Z]OS3 #A1 #C1
L1/ DEGREE3 #D .#AI4 LOCAL MAXIMUMS3
7--#A.A1 #J.H71 7#A.I1 #H71 LOCAL
M9IMUMS3 7--#B.B1 --#CH71 7#J.C1 --#DA71
7#B.H1 --#AC72 Z]OS3 --#B.F1 --#A.B1
--#A1 #A.E1 #B.B1 #C1 L1/ DEGREE3 #F
.#BC4 .;X -9T]CEPT3 --#B.E2 LOCAL
MAXIMUM3 7--#A.B1 #D.J72 LOCAL M9IMUM3
7#A.B1 #J.IF7 .#BE4 .;X -9T]CEPTS3
--#B.B1 #A1 #A.G2 LOCAL MAXIMUMS3
7--#A.F1 #AJ.E71 7#J.AG1 #B.J72 LOCAL
M9IMUMS3 7#J1 #B71 7#A.E1 --#A.G7 .#BG4
.;X -9T]CEPTS3 --#J.GG1 #D.E2 LOCAL
MAXIMUM3 7#J.DG1 --#B.F72 LOCAL M9IMUMS3
7--#J.AF1 --#C.A71 7#C.D1 --#CI.D7 .#BI4
.;X -9T]CEPTS3 --#J.GG1 #J1 #J.HB2 LOCAL
MAXIMUM3 7#J.DG1A.F72 LOCAL M9IMUM3
7--#J.DF1 --#A.E7 .#CA4 .,SAMPLE .ANSW]3
,QUADRATIC FUNC;NS ONLY H "O TURN+ PO9T1
"!=E "O MAXIMUM OR M9IMUM VALUE4 ,CUBIC
FUNC;NS C H TWO TURN+ PO9TS1 "!=E "O
MAXIMUM & "O M9IMUM1 &! 5D 2HAVIOR IS
69F9;Y1 S "! IS NO R1L MAXIMUM OR M9IMUM
VALUE4 .#CC4 .,SAMPLE .ANSW]3 .;Y .K .;X
@7 .;X @+ #B7@7 .;X -- #D71 .;Y .K .;X
@7 .;X @+ #B7@7 .;X -- #D7 #B @1 .;Y .K
.;X #C @7 .;X @+ #B7@7 .;X -- #D7
.#CE4 DOMA93 ALL R1L NUMB]S1 RANGE3
ALL R1L NUMB]S
.#CG4 DOMA93 ALL R1L NUMB]S1 RANGE3
.;Y .1.K --#BA.C
..#E.H ,PRO#M .,SOLV+ @7 PP4 #CIA-CIB
@7 .#CI4 MAXIMUM3 AB #E.H IN4 0#AC.H IN4
0#B.A IN42 AB #AFH IN4 #C
.#DA4 AF AB #J.IE SEC
.#DC4 .A4
.B4 ,MAXIMUM3 7#AA.G1 #DD1IGA71
M9IMUM3 7#BI.H1 #DJ1JGH74 .,SAMPLE
.ANSW]3 ,! MAXIMUM 9DICATES T 9 #AIGB !
NUMB] ( /UD5TS 5ROLL$ 0 AB #DD1IGA1JJJ4
,! M9IMUM 9DICATES T 9 #AIIJ "! 7 AB
#DJ1JGH1JJJ /UD5TS 5ROLL$4 .C4 #CF1CJJ
"K.K .;Y "K.K #DG1IGH
..#E.I ,SKILL .,PRACTICE @7 PP4
#CIG-CIH @7 .#A4 F9ITE DI6];ES .#C4 .;Y
.K #J.E .;X #C -- #B .;X #B @+ #J.E .;X
@+ #C .#E4 .#G4 .;Y .K #B .;X #C @+ #B
.;X #B -- #H .;X -- #H .#I4 .#AA4 #A %D
H BE5 SUB/ITUT$ = .;X & #C = .;Y @2 #C
.K .A 7#A @+ #A77#A --#B77#A--#E71 #C .K
#H .A @1 @4
.#AC4
--------------------------------;,,SA#AH
,,SELECT$ ,,ANSW]S
.#AE4
.#AI4 .;F @7 .;X @7 .K --#D .;X #B @+
#AE .;X .#BA4 .;F @7 .;X @7 .K --#J.E
.;X #C @+ #E .;X #B -- #B.E .;X @+ #C
.#BC4 #E2 #F2 "! M/ 2 "O M DATA PO9T ?AN
! DEGREE (! EQU,N4
..#E.I ,PRO#M .,SOLV+ @7 PP4 #CIH-CII
@7 .#BE4 .;D .K #J.E .;N #B -- #A.E .;N
.#BG4 .A4 .;M .K #J.JJJHAG .;T #C --
#J.JBAE .;T #B @+ #J.BDI .;T @+ #C.AG
.B4 AB 4#AJ.CJ .C4 #AIIE
.#BI4
.,*APT] .,REVIEW @7 PP4 #DJB-DJF @7
.#A4 LOCAL MAXIMUM1 LOCAL M9IMUM .#C4
,IF X IS 9 ! =M .;C * #AJ ;N ": #A "K.K
.;C "K #AJ & .;N IS AN 9TEG]4 .#E4 #ABH2
PRODUCT ( P[]S PROP]TY .#G4 @2 P[] (A
P[] PROP]TY1 NEGATIVE EXPON5T PROP]TY
.#I4 @2 QUOTI5T ( P[]S PROP]TY1 NEGATIVE
EXPON5T PROP]TY .#AA4 @2 P[] (A QUOTI5T
PROP]TY1 NEGATIVE EXPON5T PROP]TY
.#AC4
.#AE4
.#AG4 #F .;X #C -- #I .;X #B @+ #C .;X
@+ #C .#AI4 #E .;X #C -- #BI .;X #B --
#AD .;X @+ #DH .#BA4 #H7#B .;X -- #A77#D
.;X #B @+ #B .;X @+ #A7 .#BC4 @7 .;X --
#B7@7 .;X @+ #B77#B .;X -- #G7 .#BE4
.#BG4 .#BI4 @7 .;X @+ #B7@7 .;X -- #C7@7
.;X -- #D7 .#CA4 @7 .;X -- #A77#C .;X --
#B77#C .;X @+ #B7 .#CC4 --#C1 #B1 #E
.#CE4 .;X #C -- #B .;X #B -- #AI .;X @+
#BJ .#CG4 .;X #D -- #AE .;X #C @+ #GB
.;X #B -- #ABJ .;X @+ #EF .#CI4 .;X
-9T]CEPT3 --#A.G2 LOCAL MAXIMUM3 7#J1
--#A72 LOCAL M9IMUM3 7--#A1 --#B7 .#DA4
.;Y .K .;X #C -- #H .;X #B @+ #B .;X --
#A
,*APT] #F
..#F.A ,SKILL .,PRACTICE @7 PP4
#DAG-DAH @7 .#A4 9DEX .#G4 #AB #A/C .#I4
#AJ #G/C .#AA4 .#AC4 .#AE4 +-#H .#AG4 #J
.#AI4 NO R1L ROOTS .#BA4 #B .#BC4 #FD
.#BE4 #I .#BG4 #AD .#BI4 .#CA4 .#CE4
#B.HI .#CG4 #B.AJ .#CI4 #AB .#DA4 #J.JA
.#DC4 #J.JB .#DE4 --#J.AH .#DG4 .,SAMPLE
.ANSW]3 #BG #A/C @1 #HA #A/D .#DI4 ,"!
>E TWO R1L SOLU;NS2 .;X .K +-#C4 .#EA4
#F .#EC4 #A1 #I .#EE4 +-#A.FH .#EG4
--#G.FF
..#F.A ,PRO#M .,SOLV+ @7 PP4 #DAH-DAI
@7 .#FA4 AB #D.CJ IN4 .#FC4 @2 AB #AHJJ
,,RPM .#FE4 .A4 #DJIF MM #C .B4
TETRAH$RON3 AB #CB.F MM1 OCTAH$RON3 AB
#BJ.F MM1 DODECAH$RON3 AB #H.AB MM1
ICOSAH$RON3 AB #AB.C MM .C4 ,NO4
.,SAMPLE .ANSW]3 ,! ICOSAH$RON HAS !
GRTE/ NUMB] ( FACES1 #BJ1 & AN $GE L5G?
( #AB.C MILLIMET]S : IS GRT] ?AN ! $GE
L5G? (! DODECAH$RON1 : HAS #AB FACES4
..#F.B ,SKILL .,PRACTICE @7 PP4
#DBD-DBE @7 .#A4 ,NO2 !Y D N H ! SAME
9DEX4 .#C4 #BE .#E4 #C .#G4 #B @* #E
#A/B .#I4 .#AA4 #G #C/D .#AC4 .#AE4 #AJ
.#AG4 .#AI4 #B .#BA4 #C .#BE4 .#BG4
.#BI4 .#CA4 .#CC4 .#CE4 .#CG4 .#CI4
.#DA4 ,! RADIC&S >E N ! SAME1 S !Y _C 2
-B9$2 @4 .#DC4 .;X #G/AB .#DE4 #C .;X
.#DG4 .#DI4 .#EA4 .,SAMPLE .ANSW]3 .;X
#E/D & .;X #A/B .#EC4 .#EE4 .#EG4 .#EI4
.#FA4 .#FC4 #B .;X #B .;Y #A/B .#FE4
.#FG4 P]IMET]3 #BD .;X #A/D @1 >EA3#CE
.;X #A/B .#GA4 .#GC4 .#GE4 .#GG4 #G .;Z
#J.C .#GI4 .#HA4
..#F.B ,PRO#M .,SOLV+ @7 PP4 #DBF-DBG
@7 .#HC4 .A4 AB #EHJ CM #B .B4 AB
#AF1FGA CM #B .#HE4 AB #J.DE MM .#HG4
.A4 AB #B "TS FA9T] .B4 AB #A.F "TS
FA9T] .C4 AB #C "TS FA9T] .#HI4 .A4 .B4
.C4 ,! BALLOON ) TWICE Z M* WAT] W H @1
OR AB #A.EI1 "TS ! SURFACE >EA (!
BALLOON ) LESS WAT]4
..#F.C ,SKILL .,PRACTICE @7 PP4
#DCB-DCC @7 .#A4 -POSI;N .#C4 #B .;X
#A/C @+ #H .;X #A/B @1 ALL NONNEGATIVE
R1L NUMB]S .#E4 --#F .;X #A/C @+ #H .;X
#A/B @1 ALL NONNEGATIVE R1L NUMB]S
--------------------------------;,,SA#AI
,,SELECT$ ,,ANSW]S
.#G4 --#H .;X #A/C @1 ALL NONNEGATIVE
R1L NUMB]S .#I4 #J1 ALL NONNEGATIVE R1L
NUMB]S .#AC4 #BJ .;X #G/F @1 NONNEGATIVE
R1L NUMB]S .#AE4 #BE .;X @1 ALL
NONNEGATIVE R1L NUMB]S .#AG4 @1 POSITIVE
R1L NUMB]S .#AI4 #A1 POSITIVE R1L NUMB]S
.#BA4 --#FD .#BC4 .#BE4 #GA .#BG4 --#FBE
.#BI4 @1 ALL R1L NUMB]S EXCEPT .;X .K #J
.#CA4 @1 ALL R1L NUMB]S .#CC4 .;X @1 ALL
R1L NUMB]S EXCEPT .;X .K #J .#CE4 #D .;X
-- #BA1 ALL R1L NUMB]S .#CG4 #D %D 2
4TRIBUT$ 6EA* T]M1 N J ! F/ T]M2 #D .;X
#B -- #AB4 .#CI4 .,SAMPLE .ANSW]3 .;F @7
.;X @7 .K #C .;X1 .;G @7 .;X @7 .K #B
.;X
..#F.C ,PRO#M .,SOLV+ @7 PP4 #DCC-DCD
@7 .#DC4 .;R @7 .;W @7 .K #BBJ .;W
--#J.BFF @2 AB #ACD BR1?S P] M9UTE1 AB
#DH.C BR1?S P] M9UTE1 AB #AA.C BR1?S P]
M9UTE .#DE4 .A4 4#FC .B4 4#FA.EJ .C4
,APPLY ! #AJ@3P 4C.T 2F ! 4#AE 4C.T2 Y
PAY 4#FA.EJ US+ ? ME?OD & 4#FC US+ ! O!R
ME?OD4
..#F.D ,SKILL .,PRACTICE @7 PP4
#DDB-DDC @7 .#A4 ,AN 9V]SE REL,N
9T]*ANGES ! 9PUT & \TPUT VALUES (!
ORIG9AL REL,N4 .#C4 .#E4 .#G4 .#I4 .#AA4
.#AC4 ,SWIT*+ ! ROLES ( .;X & .;Y DOES N
9CLUDE SWIT*+ ! SIGN (! V>IA#S2 .;X .K
-- .;Y @+ #C1 .;X -- #C .K -- .;Y @1 #C
-- .;X .K .;Y @4 .#AE4 .;F @7 .;G @7 .;X
@7@7 .K .;X -- #D @+ #D .K .;X1 .;G @7
.;F @7 .;X @7@7 .K .;X @+ #D--#D .K .;X
.#AG4 @1 .;G @7 .;F @7 .;X @7@7 .K .#AI4
#I .K .;X -- #I @+ #I .K .;X @1 .#BC4
.#BE4 .#BG4 .#BI4 FUNC;N .#CA4 N A
FUNC;N .#CC4 FUNC;N .#CE4 N A FUNC;N
.#CG4 N A FUNC;N .#CI4 .#DA4 .#DC4
..#F.D ,PRO#M .,SOLV+ @7 PP4 #DDD-DDE
@7 .#DG4 .A4 .;W .K #B--#F .B4 #G LB
.#DI4 @2 AB #CA.C FT
..#F.E ,SKILL .,PRACTICE @7 PP4
#DDI-DEJ @7 .#A4 RADICAL
.#C4 DOMA93 .;X .1.K #J1 RANGE3 .;Y
"K.K #J
.#E4 DOMA93 .;X .1.K #J1 RANGE3 .;Y
"K.K #J
.#AA4 DOMA93 ALL R1L NUMB]S1 RANGE3
ALL R1L NUMB]S
.#AC4 DOMA93 ALL R1L NUMB]S1 RANGE3
ALL R1L NUMB]S
.#AG4 DOMA93 .;X .1.K --#A1 RANGE3 .;Y
.1.K #H
.#AI4 DOMA93 ALL R1L NUMB]S1 RANGE3
ALL R1L NUMB]S
.#BE4 ,! DOMA9 IS LIMIT$ 2C ! SQU>E
ROOT (A NEGATIVE NUMB] IS N A R1L NUMB]4
,S9CE ! DOMA9 IS RE/RICT$1 ! RANGE IS AL
A6ECT$4 .#BI4 ,DOMA93 .;X .1.K #AB1
RANGE3 .;Y .1.K #J2 ! EXPRES.N "U !
RADICAL SIGN M/ 2 GRT] ?AN OR EQUAL 6#J1
S SUB/ITUTE ! L1/ VALUE ( .;X 96! EQU,N
& F9D .;Y @4 .#CA4 ,DOMA93 ALL R1L
NUMB]S1 RANGE3 ALL R1L NUMB]S2 "! >E NO
RE/RIC;NS ON F9D+ ! CUBE ROOT (A NUMB] &
"!=E NO RE/RIC;NS ON ! RANGE4 .#CC4
,DOMA93 .;X .1.K #C1 RANGE3 .;Y .1.K #F2
! EXPRES.N "U ! RADICAL SIGN M/ 2 GRT]
?AN OR EQUAL 6#J1 S SUB/ITUTE ! L1/
VALUE ( .;X 96! EQU,N & F9D .;Y @4
..#F.E ,PRO#M .,SOLV+ @7 PP4 #DEJ-DEA
@7 .#CE4 AB #DC FT ABV SEA LEVEL .#CG4
.A4 .B4 DOMA93 .;,C .1.K --#BGC.AE1
RANGE3 .;V .1.K #J .#CI4 .A4
--------------------------------;,,SA#BJ
,,SELECT$ ,,ANSW]S
B4 .,SAMPLE .ANSW]3
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,A @3 #B3 #D3 #F3 #H3 #AJ
.;V .;T @3 #CJF.A3 #BAF.DD3 #AGF.GB3
#AEC.JE3 #ACF.HI
.C4
..#F.F ,SKILL .,PRACTICE @7 PP4
#DEF-DEG @7 .#A4 EXTRANE\S .#C4 #G .#E4
#A .#G4 #F .#I4 #BI .#AA4 .#AC4 #CDC
.#AE4 #AH .#AG4 #H .#AI4 #AA .#BA4 --#CG
.#BC4 #D .#BE4 #CB .#BG4 #DJ .#BI4 #AJH
.#CA4 #A .#CC4 ,BO? SIDES M/ 2 RAIS$ 6!
P[]2 @7@7 .;X @+ #G7 #A/B @7 #B .K #E #B
@1 .;X @+ #G .K #BE1 .;X .K #AH4 .#CE4
#BE .#CG4 #C1 #H .#CI4 .#DA4 .#DE4 #C
.#DG4 #D .#DI4 .#EA4 --#B1 #B .#EC4 7#D1
#BE7
..#F.F ,PRO#M .,SOLV+ @7 PP4 #DEG-DEI
@7 .#EG4 AB #CIA M9 .#EI4 .,SAMPLE
.ANSW]3 ,! ELEPHANT )A %\LD] HEI<T (
#BEJ C5TIMET]S IS AB #BJ YE>S OLD] ?AN !
ELEPHANT )A %\LD] HEI<T ( #AEJ
C5TIMET]S4 .#FA4 .A4 AB #J.AFB MI_/;H
.B4 AB #HJ.D MI_/;H .C4 #J.AFB "K.K .;S
"K.K #HJ.D
..#F.F ,PRO#M ,SOLV+ .,"W%OP @7 P4
#DFA @7 .#A4 --#CI .#C4 AB #EE.G .#E4 AB
#IG FT .#G4 AB #CG.E CM
.#F..F .,EXT5.N @7 P4 #DFC @7 .#A4 .;X
.1.K #AF .#C4 #J "K.K .;X "K.K #D .#E4
.;X .1.K #A .#G4 #J "K.K .;X "K.K #F.BE
.#I4 #J "K.K .;X "K #A.C .#AA4 #J "K.K
.;X "K #D .#AC4 AB #DAC ;M #B
.,*APT] .,REVIEW @7 PP4 #DFF-DFH @7
.#A4 #D .#C4 P[] .#E4 ,IF A HORIZONTAL
L9E CROSSES ! GRAPH (! FUNC;N M ?AN
ONCE1 ! 9V]SE IS N A FUNC;N4 .#G4 ,TAKE
! SQU>E ROOT ( EA* SIDE2 RAISE EA* SIDE
6! P[]4 .#I4 #J .#AA4 #E .#AC4 .#AE4
--#H .#AG4 .#AI4 .#BA4 #C .;X -- #AD
.#BC4 #D .;X @+ #BF .#BE4
.#BG4 DOMA93 .;X .1.K --#C1 RANGE3 .;Y
.1.K #E
.#BI4 DOMA93 ALL R1L NUMB]S1 RANGE3
ALL R1L NUMB]S
.#CA4 #AF
.,CUMULATIVE .,REVIEW @7 PP4 #DGD-DGE
@7 .#A4 .;Y .K #D .;X -- #AA .#C4 .;Y .K
--#H .;X -- #BB .#E4 .#G4 --#D .#I4 #B1
#G .#AA4 #B1 #J1 --#E
.#AC4
.#AE4
.#AG4
.#AI4
.#BA4
.#BC4 7--#A1 #F7 .#BE4 #I -- .;I .#BG4
#CD @+ #H .;I .#BI4 .;Y .K --@7 .;X --
#F7 #B -- #AJ .#CA4 #H .;X #I .;Y #F
.#CC4 .;X #G .;Y .#CE4 #E .;X #B @+ #F
.;X -- #AF .#CG4 #B .;X #C @+ #C .;X #B
-- #CD .;X @+ #CE .#CI4 @7 .;X #B --
#H7@7 .;X #B @+ #E7 .#DA4 @7 .;X --
#F7@7 .;X -- #C7@7 .;X @+ #C7 .#DC4 #AJ
.;X #B -- #BH .;X -- #F1 ALL R1L NUMB]S
.#DE4 #AJ .;X -- #BI1 ALL R1L NUMB]S
.#DG4 .#DI4 .#EA4 .#EC4 .;Y .K #J.DII
.;X @+ #A.BE2 AB 4#E1BDJ1JJJ .#EE4
4#DFDB .#EG4 .#EI4 .;Y .K .;X #C -- #E
.;X @+ #F2 4#FIJ
--------------------------------;,,SA#BA
,,SELECT$ ,,ANSW]S
,*APT] #G
..#G.A ,SKILL .,PRACTICE @7 PP4
#DHB-DHC @7 .#A4 #B.D1 #A.E1 #EJ@3P
.#G4
.#I4
.#AE4 DOMA93 ALL R1L NUMB]S1 RANGE3
.;Y "K #J
.#AG4 DOMA93 ALL R1L NUMB]S1 RANGE3
.;Y .1 #C
.#BG4 ,! P[] ( @7 .;X -- #C7
TRANSLATES ! P>5T GRAPH #C UNITS 6! "R1
N 6! LEFT4
.#BI4 @1 ": .,A PRES5TS ! AM.T 9 !
A3.T AF .;T YE>S4 .#CA4 .A4 4#AHDD.HA
.B4 #AH ;YR .#CC4 .A4 ,! GRAPH NO L;G]
HAS A V]TICAL /RET* ( #B4 .B4 ,! GRAPH W
9CR1SE SL[]4 .C4 ,! GRAPH W 2 TRANSLAT$
#C UNITS 6! "R 9/1D ( #D UNITS 6! LEFT4
.D4 ,! GRAPH W 2 TRANSLAT$ #A UNIT D[N
9/1D ( #C UNITS UP4
..#G.A ,PRO#M .,SOLV+ @7 PP4 #DHD-DHE
@7 .#CE4 .A4 #J.DB MILLION1 #B.DG1
#ADG@3P
.B4 AB #AF MILLION ,,DVD PLAY]S
.#CG4 .A4 4#BDGI.CH .B4 4#BDJF.IH .C4
4#BCHC.BC .#CI4 .A4 .;,P .K
#DID.BI7#A.JC7 ;T @2 #FFD1BHD P
.B4 DOMA93 .;T .1.K #J1 RANGE3 .;,P
.1.K #DID.BI
.C4 #AIIF .#DA..A4 .;P .K
#DH.BH7#A.JF7 ;T
.B4 #BJJC
.C4 .,SAMPLE .ANSW]3 ,S9CE ! FUNC;N IS
ONLY DEF9$ :5 .;T IS 2T #J & #D1 Y C
LOOK AT ! GRAPH 2T ^! VALUES 6DET]M9E !
M9IMUM OR MAXIMUM T GIVES M1N+;L
RESULTS4 .#DC4 ,NO4 .,SAMPLE .ANSW]3 ,!
AM.TS >E N EQUAL EXCEPT 9ITI,Y & "O YE>
AF ! 9VE/;TS >E MADE4
..#G.B ,SKILL .,PRACTICE @7 PP4
#DHI-DIJ @7 .#A4 #ABEJ1 #J.HE1 #AE@3P
.#C4 EXPON5TIAL DECAY .#E4 EXPON5TIAL
GR[?
.#G4
.#I4
.#AG4 DOMA93 ALL R1L NUMB]S1 RANGE3
.;Y "K #J
.#AI4 DOMA93 ALL R1L NUMB]S1 RANGE3
.;Y .1 --#A
.#BE4 .A4 ,! GRAPH IS A V]TICAL /RET*
0A FACTOR ( @4 .B4 ,! GRAPH W 2 /EEP] 2C
! DECAY FACTOR IS SMALL]4 .C4 ,! GRAPH
MOVES #E UNITS 6! "R 9/1D ( #B UNITS 6!
"R4 .D4 ,! HORIZONTAL ASYMPTOTE MOVES
6.;X .K #C4
--------------------------------;,,SA#BB
,,SELECT$ ,,ANSW]S
..#G.B ,PRO#M .,SOLV+ @7 PP4 #DIJ-DIA
@7 .#CA4 .A4 .;Y .K #BJJ7#J.GE7 ;T @2 AB
4#HD.CH
.B4
.C4 AF AB #B.E ;YR
.#CC4 .A4 AF #E ;YR .B4 4#E.BI2 NO4
.,SAMPLE .ANSW]3 ,A C> DOES N NORM,Y LA/
#EJ YE>S4
.#CE4 .A4 #J.HI1 #AA@3P
.B4
.C4 AB #ACD E7S P] ;YR
.D4 ,*ANGE ! EXPON5T 6J .W4
..#G.C ,SKILL .,PRACTICE @7 PP4
#DIE-DIF @7 .#A4 .;E .#C4 .;E #G .#E4 #H
.;E #I .;X .#G4 .#I4 #C .;E #C .#AA4 #C
.;E #A -- .;X .#AC4 #B .;E #C .;X .#AG4
,! #C %D 2 RAIS$ 6! SECOND P[] AL2 7#C
.;E #E .;X @7 #B .K #C #B .;E 7#E .;X
@77#B7 .K #I .;E #AJ .;X @4 .#AI4 AB
#BJ.JHF .#BA4 AB #I.JBE .#BC4 AB #J.FGJ
.#BE4 AB #AJIF.FCC .#BG4 AB #A.DHB .#BI4
AB --#FF.ACI .#CA4 EXPON5TIAL DECAY
.#CC4 EXPON5TIAL DECAY .#CE4 EXPON5TIAL
DECAY .#CG4 EXPON5TIAL GR[?
.#DC4 DOMA93 ALL R1L NUMB]S1 RANGE3
.;Y .1 #J
.#DE4 DOMA93 ALL R1L NUMB]S1 RANGE3
.;Y .1 --#A
.#EA4 #AJ1JJJ1JJJ1JJJ4 .,SAMPLE
.ANSW]3 ,S9CE SMALL VALUES ( .;N 7
9CR1S+ ! FUNC;N V SL[LY1 ,I *ECK$ L>G]
9T]VALS4 ,I NOTIC$ T E P[] ( #AJ GAVE AN
ANSW] "O DIGIT CLOS] 6! ACTUAL VALUE (
.E4 .#EC4 .,SAMPLE .ANSW]3
..#G.C ,PRO#M .,SOLV+ @7 PP4 #DIG-DIH
@7 .#EE4 AB #HIE MILLION CAM]A PH"OS
.#EG4 4#BDDB.HA .#EI4 .A4 .;,L @7 .;X @7
.K #AJJ .;E --#J.JB .;X
.B4 AB #DE@3P .C4 AB #CE ;M .#FA4 AB
#A.IHF CM #B
..#G.D ,SKILL .,PRACTICE @7 PP4
#EJC-EJD @7 .#A4 -MON .#C4 #D #B .K #AF
.#E4 .#G4 .,SAMPLE .ANSW]3 ,! --#C & >E
SWIT*$ >.D2 @4 .#I4 #B .#AA4 #F .#AC4
--#C .#AE4 .#AG4 #C .#AI4 #B .#BA4 AB
#A.GIB .#BC4 AB #J.GIC .#BE4 AB #A.FHC
.#BG4 AB #D.GJJ .#BI4 .;X .#CA4 #H .#CC4
#D .;X .#CE4 #E .;X .#CG4 .;Y .K #H ;X
.#CI4 .;Y .K LOG #J.D .;X .#DA4 .;Y .K
,9 .;X -- #B .#DC4 .;Y .K .;E ;X -- #A
.#DE4 DOMA93 .;X .1 #J1 RANGE3 ALL R1L
NUMB]S
.#DG4 DOMA93 .;X .1 #J1 RANGE3 ALL R1L
NUMB]S
..#G.D ,PRO#M .,SOLV+ @7 PP4 #EJD-EJE
@7 .#EI4 #B.C .#FA4 .A4 AB #F.D .B4 .;,E
.K .;E @7 .;,M @+ #I.I7_/#J.BI @2 !
9V]SE REPRES5TS ! AM.T ( 5]GY REL1S$1 9
]GS1 Z A FUNC;N (! 5]GY MAGNITUDE4
..#G.E ,SKILL .,PRACTICE @7 PP4
#EAJ-EAA @7 .#A4 PRODUCT .#G4 #J.DGG
.#I4 #A.BJD .#AA4 #B.AEH .#AC4 --#J.FJB
.#AE4 LOG #C #D @+ LOG #C .;X .#AG4 LOG
#C @+ #D;LOG .;X .#AI4 LOG #B #B--LOG #B
#E .#BA4 LOG #D .;X -- LOG #D #C--LOG #D
.;Y .#BC4 LOG #G #E @+ #C LOG #G .;X @+
LOG #G .;Y @+ #B LOG #G .;Z .#BE4 .#BG4
.#BI4 .#CA4 ,! TWO "PS %D 2 A4$1 N
MULTIPLI$2 LOG #B #E @+ LOG #B .;X @4
--------------------------------;,,SA#BC
,,SELECT$ ,,ANSW]S
.#CC4 .#CE4 LOG #AA .;X #B .#CG4 .#CI4
,9 #AJ .;X .#DA4 .#DE4 AB #A.DJD .#DG4
AB #B.DFE .#DI4 AB #A.FCA .#EA4 AB
#A.EHA .#EC4 AB #A.EAC .#EE4 #A.E .#EG4
AB #J.HGE .#EI4 AB --#A.CEH .#FA4 ,:5
US+ ! *ANGE ( BASE =MULA1 ! BASE GOES 9
! DENOM9ATOR2 @4 .#FC4 #AEJ DECIBELS
..#G.E ,PRO#M .,SOLV+ @7 PP4 #EAB-EAC
@7 .#FI4 AB #GF DECIBELS .#GA4 #AJ2 #AJ
LOG #AJ .K #AJ7#A7 .K #AJ .#GC4 .A4 .;S
.K #B LOG #B .;F
B4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;F @3 .#A..DAD @3 .#B..JJJ @3
.#B..HBH @3 .#D..JJJ
.;S @3 .AB .#A @3 .#B @3 .AB .#C @3
.#D
.;F @3 .#E..FEG @3 .#H..JJJ @3
.#AA..CAD @3 .#AF..JJJ
.;S @3 .AB .#E @3 .#F @3 .AB .#G @3
.#H
.,SAMPLE .ANSW]3 ,! AM.T ( LI<T
9CR1SES 0AB #A EA* "T4 .C4 ,AB #BB.FBG2
IF Y SET UP ! EQU,N #I .K LOG #B .;F &
SOLVE = .;F ! RESULT IS #B #I/B @4
..#G.F ,SKILL .,PRACTICE @7 PP4
#EAI-EBJ @7 .#A4 EXPON5TIAL .#C4 #H .#E4
.#G4 .#I4 .#AA4 --#B .#AC4 AB --#A.FJI
.#AE4 AB #J.BIB .#AG4 AB --#J.GBC .#AI4
AB #J.FEJ .#BA4 AB --#J.CGH .#BC4 AB
--#J.BJC .#BE4 #F .#BG4 NO SOLU;N .#BI4
.#CA4 .#CC4 .;E #G OR AB #AJIF.FCC .#CE4
AB #CE.FJA .#CG4 #D .#CI4 AB #J.GBI
.#DA4 AB #B.GBJ .#DC4 AB #AJ.BDC .#DE4
,! LOG>I?M 0 N SIMPLIFI$ CORRECTLY1 .;X
LOG #C #F @6.K #B .;X @2 LOG #C #F
#A.FCA1 .;X .K #A.EHE4 .#DG4 .,SAMPLE
.ANSW] @3 #C ;X .K #HA1 LOG #E @7 .;X @+
#D7 .K #J
#G.F ,PRO#M ,SOLV+ @7 PP4 #EBA-EBB @7
.#EE4 AB #BD;DG;,F .#EG4 AB #FIFG ;YR
.#EI4 .A4 ,JAPAN3 AB #ABG1JJJ1JJJ
KILOWATT-H\RS1 ,GREECE3 AB #AA1EJJ1JJJ
KILOWATT-H\RS1 ,,USA3 AB #BC1EJJ
KILOWATT-H\RS .B4 ,JAPAN3 #F.F .K #J.FG
LOG 7#J.CG .;,E @7 @+ #A.DF1ABF1HIC1GJB
KILOWATT-H\RS2 ,GREECE3 #E.I .K #J.FG
LOG 7#J.CG .;,E @7 @+ #A.DF1 #AA1DDF1BFI
KILOWATT-H\RS2 ,,USA2 #D.A .K #J.FG LOG
7#J.CG .;,E @7 @+ #A.DF1 #BC1EEF
KILOWATT-H\RS
..#G.F ,PRO#M ,SOLV+ .,"W%OP @7 P4
#EBE @7 .#A4 AB #J.GII .#C4 AB .#B4 #AJ
.#E4 #J.H .#G4 AB #D.DH .#I4 #BJJA .#AA4
AB #BEA.AI MM .#AC4 AB #J.JCBBE;DG;,C
.,EXT5.N @7 P4 #EBG @7 .#A4 .;X "K.K
#B.GBG .#C4 .;X "K.K #A.EA .#E4 .;X "K.K
#F.JC .#G4 .;X .1.K #BG .#I4 #J "K .;X
"K #CF .#AA4 #J "K .;X "K #CB .#AC4 AF
#E.BE ;YR
..#G.G ,SKILL .,PRACTICE @7 PP4
#ECC-ECD @7 .#A4 EXPON5TIAL .#C4 .#E4
.#G4 .#I4 .;Y .K #D.II 99 #J.DII ;X
.#AA4 .;Y .K #I7#B7 ;X
.#AC4 .;Y .K #G.HC7#A.BE7 .;X
.#AE4 .;Y .K #J.AB .;X #B.CB .#AG4 .;Y
.K #A.BE .;X #A.BF .#AI4 .;Y .K #J.EFI
.;X #A.IA .#BA4 .;Y .K #J.BDA .;X #B.CD
.#BC4 .;Y .K #J.FJF .;X #B.GD
.#BE4 .;Y .K #B.EJ .;X #J.EFG
.#BI4 ,! .;X %D 2 RAIS$ 6! #C1 N
MULTIPLI$ 0X2 LN .;Y .K LN .;X #C -- #B1
.;Y .K .;E LN .;X #C -- #B @1 .;Y .K .;E
LN .;X #C 99 .;E --#B @1 .;Y .K .;E LN
.;X #C 99 .;E --#B @1 .;Y .K #J.ACE .;X
#C
--------------------------------;,,SA#BD
,,SELECT$ ,,ANSW]S
#G.G ,PRO#M ,SOLV+ @7 PP4 #ECD-ECF @7
.#CA4 .A4 .B4 .;Y .K #J.JJJDFF .;X
#B.HJ .C4 AB #FD.H KG
.#CC4 .A4 .;Y .K #J.DGE7#B.JH7 ;X .B4
,GRAPH ! PO9TS @7 .;X1 .;Y @7@2 IF !Y
APPE> L9E>1 !N A L9E IS ! BE/ FIT4 ,IF
N1 GRAPH ! PO9TS @7 .;X @1 LN .;Y @7@2
IF ^! PO9TS APPE> L9E>1 !N AN EXPON5TIAL
MODEL IS ! BE/ FIT =! DATA4 ,IF N1 GRAPH
! PO9TS 7LN .;X @1 LN .;Y @7@2 IF ^!
PO9TS APPE> L9E>1 !N A P[] MODEL IS !
BE/ FIT =! DATA2 .;Y .K #CC.H .;X @+
#B.H4
.#CE4 .A4 .B4
.C4 ,EXPON5TIAL FUNC;N2 ! PO9TS = @7
.;X @1 LN .;Y @7 APPE> M L9E> ?AN !
PO9TS 7LN .;X @1 LN .;Y @7@1 S AN
EXPON5TIAL MODEL APPE>S 6BE ! BE/ FIT =!
DATA4 .D4 .;Y .K #D.IH7#A.JE7 ;X @2 AB
#BDG CM
.,*APT] .,REVIEW @7 PP4 #ECH-EDB @7
.#A4 .;Y .K #E .#C4 .,SAMPLE .ANSW]3 LOG
;B .;Y .K .;X IF & ONLY IF .;B ;X .K .;Y
@4 .#E4 ,EXPON5TIAL FUNC;N4 .,SAMPLE
.ANSW]3 ,! V>IA# IS 9 ! EXPON5T4
.#G4 DOMA93 ALL R1L NUMB]S1 RANGE3 .;Y
.1 #J
.#I4 4#AGBE.CI
.#AA4 DOMA93 ALL R1L NUMB]S1 RANGE3
.;Y .1 --#D
.#AC4 DOMA93 ALL R1L NUMB]S1 RANGE3
.;Y .1 #J
.#AE4 DOMA93 ALL R1L NUMB]S1 RANGE3
.;Y .1 #F
.#AG4 #E .#AI4 --#C
.#BA4 DOMA93 .;X .1 #J1 RANGE3 ALL R1L
NUMB]S
.#BC4 DOMA93 .;X .1 #J1 RANGE3 ALL R1L
NUMB]S
.#BE4 LOG #H #C @+ LOG #H .;X @+ LOG
#H .;Y .#BG4 LOG #H--#D LOG .;Y .#BI4
LOG #G #CHD .#CA4 LN #CF .#CC4 #G .#CE4
.#CG4
,*APT] #H
..#H.A ,SKILL .,PRACTICE @7 PP4
#EEE-EEF @7 .#A4 JO9TLY .#C4 9V]SE V>I,N
.#E4 DIRECT V>I,N .#G4 9V]SE V>I,N .#I4
DIRECT V>I,N .#AC4 @2 #C .#AE4 .#AG4
.#AI4 .#BA4 DIRECT V>I,N .#BC4 9V]SE
V>I,N .#BE4 @2 --#E .#BG4 @2 .#BI4 .;Z
.K --#E .XY @2 #AJJ .#CA4 .#CC4 .#CE4
.,SAMPLE .ANSW]3 .;F @7 .;X @7 .K #B .;X
@1
..#H.A ,PRO#M .,SOLV+ @7 PP4 #EEF-EEG
@7 .#CG4 @2 #BF PHOTOS .#CI4 @2 AB #B.HG
LB_/94 #B .#DA4 .A4 .B4 #F.G * #AJ --#AA
.C4 ,X DECR1SES2 X 9CR1SES4
--------------------------------;,,SA#BE
,,SELECT$ ,,ANSW]S
..#H.B ,SKILL .,PRACTICE @7 PP4
#EFA-EFB @7 .#A4 RANGE2 DOMA9
.#C4 ,! GRAPH LIES F>!R F ! AXES ?AN !
GRAPH ( @4 ,BO? GRAPHS LIE 9 ! #A/ &
#CRD QUADRANTS & H ! SAME ASYMPTOTES1
DOMA91 & RANGE4
.#E4 ,! GRAPH LIES F>!R F ! AXES ?AN !
GRAPH ( & IS LOCAT$ 9 QUADRANTS #B & #D4
,BO? GRAPHS H ! SAME ASYMPTOTES1 DOMA91
& RANGE4
.#AA4 DOMA93 ALL R1L NUMB]S EXCEPT #J1
RANGE3 ALL R1L NUMB]S EXCEPT #C
.#AC4 DOMA93 ALL R1L NUMB]S EXCEPT #A1
RANGE3 ALL R1L NUMB]S EXCEPT #J
.#BE4 ,! GRAPH %D 2 N @4
.#BG4 DOMA93 ALL R1L NUMB]S EXCEPT #C1
RANGE3 ALL R1L NUMB]S EXCEPT #A
.#BI4 DOMA93 ALL R1L NUMB]S EXCEPT #B1
RANGE3 ALL R1L NUMB]S EXCEPT
.#CE4 .,SAMPLE .ANSW]3
#H.B ,PRO#M ,SOLV+ @7 PP4 #EFB-EFC @7
.#CG4 @2
.#CI4 .A4 ,AB #AD.E SEC4 .,SAMPLE
.ANSW]3 ,SUB/ITUTE #BE = .;,T 6F9D .;T
#B.HI4 ,S9CE Y >E #E KILOMET]S AWAY1
MULTIPLY .;T 0#E 6GET #E7#B.HI7 #AD.E
SECONDS4
.B4 AB #C.I;DG;,C
.#DA4 .A4 APPROA*+3 @1 MOV+ AWAY3
.B4 .C4 ,! FREQU5CY (A S.D T IS
APPROA*+ IS GRT] ?AN T (A S.D MOV+ AWAY4
..#H.C ,SKILL .,PRACTICE @7 PP4
#EFH-EFI @7 .#A4 HORIZONTAL ASYMPTOTE
.#C4 ;,C .#E4 ;,B .#G4 N"O2 .;X .K --#A
& .;X .K --#A .#I4 N"O2 .;X .K #E & .;X
.K --#C .#AA4 --#C2 .;X .K #J & .#AC4 ,!
V]TICAL ASYMPTOTE O3URS AT ! Z]OS (!
DENOM9ATOR N ! NUM]ATOR2 ! V]TICAL
ASYMPTOTES O3UR AT ! Z]OS (! DENOM9ATOR
.;X #B -- #H .;X @+ #G4 ,S1 ! V]TICAL
ASYMPTOTES >E AT .;X .K #G & .;X .K #A4
.#AE4
--------------------------------;,,SA#BF
,,SELECT$ ,,ANSW]S
.#AG4 .#BE4 #J "K .;Y "K.K #G.E
.#BG4 ALL R1L NUMB]S EXCEPT --#J.BJI
"K .;Y "K --#D.GIA
..#H.C ,PRO#M .,SOLV+ @7 PP4 #EFI-EGA
@7 .#CA4 .A4 .B4 .C4 .;R #B.EAE FT1 ;I
#E.JCB FT
#CC4 A4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
,DEP? 7;M73 ,M1N ,TEMP]ATURE 7;DG;,C7
#AJJJ3 #D.GFC
#AJEJ3 #D.EHJ
#AAJJ3 #D.DJI
#AAEJ3 #D.BEA
#ABJJ3 #D.AJD
#ABEJ3 #C.IFG
#ACJJ3 #C.HCI
.B4 AB #ABCH ;M
.#CE4 .A4
.B4 AB #I.GH ;M_/SEC #B .C4 AB #I.DG
;M_/SEC #B
.D4 .,SAMPLE .ANSW]3 .;G DECR1SES1 B
AT A V SMALL RATE4
..#H.D ,SKILL .,PRACTICE @7 PP4
#EGG-EGI @7 .#A4 RECIPROCAL .#C4 ;,B
.#E4 ;,C .#G4 SIMPLIFI$ =M .#I4 .#AA4
.#AC4 .#AE4 .#AG4 .#AI4 ,Y C ONLY DIVIDE
\ -MON FACTORS4 ,S9CE ! FACTORS T >E
DIVID$ \ >E N -MON FACTORS (! 5TIRE
NUM]ATOR & DENOM9ATOR1 Y _C DIVIDE !M \2
.#BA4 .#BC4 ,EX]CISE .#BA4 .,SAMPLE
.ANSW]3 ,! P]IMET] ( ,EX]CISE #BA IS
SMALL] &! >1S >E ! SAME4
.#BE4 .#BG4 .#BI4 .#CA4 @7 .;X @+
#B7@7 .;X @+ #G7 .#CC4 .#CE4 .#CG4 .#CI4
.#DA4 .#DC4
.#DE4
#H.D ,PRO#M ,SOLV+ @7 PP4 #EGI-EHJ @7
.#DI4 @2 4#EJ.BA .#EA4 .A4 @1 .;,V
SPH]E .K .;R #B .;H @1 S9CE ! VOLUMES >E
! SAME1 SET ! EQU,NS EQUAL 6EA* O!R
RESULT+ 9 @4 .B4 ;,S SPH]E .K #D .;R #B
@1 .C4 @4 .,SAMPLE .ANSW]3 ,! SPH]ICAL
TANK USES LESS MAT]IAL4
..#H.E ,SKILL .,PRACTICE @7 PP4
#EHF-EHG @7 .#A4 -PLEX FRAC;N .#C4 .#E4
.#G4 #E .#I4 #C .;X @7 .;X -- #B7 .#AA4
#B .;X @7 .;X -- #E7 .#AC4 .;X @7 .;X --
#E7 @7 .;X @+ #E7 .#AG4 .#AI4 .#BA4
.#BC4 .#BE4 ,Y M/ H A -MON DENOM9ATOR 2F
Y C ADD VALUES 9 ! NUM]ATOR2 @4 .#BG4
.#BI4 .#CA4 .#CC4 .#CE4
.#CG4 .,SAMPLE .ANSW]3 @1
..#H.E ,PRO#M .,SOLV+ @7 PP4 #EHG-EHH
@7 .#DA4 @2 AB #AJ.B ;H .#DC4 .A4 .B4
4#CFD.JB
--------------------------------;,,SA#BG
,,SELECT$ ,,ANSW]S
..#H.F ,SKILL .,PRACTICE @7 PP4
#EIB-EIC @7 .#A4 CROSS MULTIPLY+ .#C4
,GRAPH BO? SIDES (! EQU,N4 ,IF ! GRAPHS
9T]SECT AT A POSSI# SOLU;N1 !N X IS A
SOLU;N4 ,IF ! GRAPHS D N 9T]SECT AT A
POSSI# SOLU;N1 !N X IS AN EXTRANE\S
SOLU;N4 .#E4 #F .#G4 #B .#I4 --#A .#AA4
NO SOLU;N .#AE4 #D .#AG4 .#AI4 .#BA4 #A
.#BC4 @1 #H .#BE4 #J1 #G .#BG4 ,! /UD5T
SIMPLY A4$ NUM]ATORS & DENOM9ATORS ON !
LEFT SIDE (! EQU,N4 ,BO? SIDES (! EQU,N
%D H BE5 MULTIPLI$ 0! ,,LCD1 #F .;X @2
@1 #CJ @+ #BC .;X .K #BGJ4 .#BI4
.,SAMPLE .ANSW]3 @2
..#H.F ,PRO#M .,SOLV+ @7 PP4 #EID-EIE
@7 .#CC4 #BF S]VES .#CE4 #AIIE .#CG4
..#H.F ,PRO#M ,SOLV+ .,"W%OP @7 P4
#EIG @7 .#A4 AB +-#E.F .#C4 #I .#E4 AB
+-#C.B .#G4 .A4 #II FT .B4 #CC FT
.,EXT5.N @7 P4 #FJJ @7 .#A4 .;X "K #B
.#C4 .;X "K #C .#E4 --#A.E "K .;X "K #D
.#G4 .;X .1 --#E .#I4 --#A "K.K .;X "K.K
#A .#AA4 #J "K .;X "K #A .#AC4 .;X .1
--#B .#AE4 --#D "K .;X "K --#C OR .;X .1
--#B .#AG4 --#C "K .;X "K --#B OR .;X
.1.K #B .#AI4 #AIII 6#BJJB .#BA4 AT L1/
#AC MO
.,*APT] .,REVIEW @7 PP4 #FJC-FJF @7
.#A4 9V]SE V>I,N .#C4 R,NAL FUNC;N .#E4
CROSS MULTIPLY+ .#G4 .#I4 @2
.#AA4 DOMA93 ALL R1L NUMB]S EXCEPT .;X
.K --#E1 RANGE3 ALL R1L NUMB]S EXCEPT
.;Y .K #B
.#AC4
.#AE4
.#AG4
.#AI4 .#BA4 .#BC4 .#BE4 .#BG4 #E .#BI4
--#A .#CA4 @1 #J .#CC4 #J .#CE4 NO
SOLU;N
,*APT] #I
#I.A ,SKILL ,PRACTICE @7 PP4 #FAG-FAH
@7
.#A4 ,! 4T.E .;D 2T @7 .;X #A @1 .;Y
#A @7 & @7 .;X #B @1 .;Y #B @7 IS @2 !
MIDPO9T (! L9E SEG;T JO9+ .,A @7 .;X #A
@1 .;Y #A @7 & .;,B @7 .;X #B @1 .;Y #B
@7 IS @4 .#C4 #AG2 .#E4 @2 .#G4 @2 7#D1
--#C7 .#I4 @2 7#B1 #B7 .#AA4 @2 .#AC4 @2
.#AE4 @2 7#A.B1 #B7 .#AG4 OR AB #E.FH2
7#J.CE1 --#F7 .#BA4 ,! DI6];E (! SQU>ES
%D 2 A4$ N SUBTRACT$2 @4 .#BC4 ISOSCELES
.#BE4 SCAL5E .#BG4 SCAL5E .#BI4 SCAL5E
.#CA4 .#CC4 .#CE4 .#CG4 .,SAMPLE .ANSW]3
7#F1 #D71 7#B1 #J7 .#CI4 .#DA4 +-#F
.#DC4 --#AJ1 #B .#DE4 @2 @1 7#C1 #F7
..#I.A ,PRO#M .,SOLV+ @7 PP4 #FAH-FAI
@7 .#DG4 #AG ;M .#DI4 AB #F.JB MI .#EA4
AB #D.EE MI .#EC4 .A4 7--#A.E1 #H7 .B4
AB #A.CB MI .C4 AB #A.FH MI .#EE4 AB
#EEJ FT
..#I.B ,SKILL .,PRACTICE @7 PP4
#FBC-FBD @7 .#A4 FOCUS1 DIRECTRIX
.#C4 7#D1 #J71 .;X .K --#D1 .;Y .K #J
.#E4 7#J1 #E71 .;Y .K --#E1 .;X .K #J
.#BC4 ,! P>ABOLA %D OP5 6! "R R ?AN
UP2
--------------------------------;,,SA#BH
,,SELECT$ ,,ANSW]S
.#BG4 .;Y #B .K --#BJ .;X .#BI4 .;X #B
.K --#AF .;Y .#CA4 .;X #B .K --#DJ .;Y
.#CC4 .;Y #B .K --#CF .;X .#CE4 .#CG4
.#CI4 .;Y #B .K --#AB .;X .#DA4 .;Y #B
.K #BJ .;X .#DC4 .;X #B .K #AF .;Y .#DE4
.;X #B .K --#BD .;Y .#DG4 .;Y #B .K #F
.;X .#DI4
.#EA4 .A4 ,! NEW FOCUS W 2 LOCAT$ AT
7#J1 #A7 R ?AN @4 ,! NEW DIRECTRIX W 2
.;Y .K --#A R ?AN @4 ,! P>ABOLA W 2
WID]4
.B4 ,! NEW FOCUS W 2 LOCAT$ AT R ?AN
@4 ,! NEW DIRECTRIX W 2 AT R ?AN @4 ,!
P>ABOLA W OP5 LEFT R ?AN "R & 2 N>R[]4
.#EC4 ,! GRAPH GETS WID]4 .,SAMPLE
.ANSW]3 ,Z ! VALUE ( _\ .;P _\ 9CR1SES1
!N ! FOCUS & DIRECTRIX 7EA* ( : LIE _\
.;P _\ UNITS F ! V]TEX7 GET FUR!R &
FUR!R AWAY F ! V]TEX & F EA* O!R4 ,S9CE
EA* PO9T ON A P>ABOLA IS EQUIDISTANT F !
FOCUS &! DIRECTRIX1 ? HAS ! E6ECT ( MAK+
! P>ABOLA WID] & WID] Z _\ .;P _\
9CR1SES4
#I.B ,PRO#M ,SOLV+ @7 PP4 #FBD-FBE @7
.#EE4 .;X #B .K #BD .;Y @2 AB #C FT
.#EG4 .A4
.B4 .;X #B .K #AIB .;Y1 .;Y #B .K
--#AIB .;X .C4 ,AB #BG.H IN42 NO4
.,SAMPLE .ANSW]3 ,EXCEPT =! DIREC;N !Y
OP51 !Y >E ID5TICAL4 .#EI4 .A4 AB #BJ
IN4 .B4 .,SAMPLE .ANSW]3 .;X #B .K #EJ
.;Y @2 *OOSE A VALUE = .;P S* T #D .;P
.1 #AJ.E2 AB #DC.F IN4 .C4 .,SAMPLE
.ANSW]3 .;X #B .K #H .;Y @2 *OOSE A
VALUE = .;P S* T #D .;P "K #AJ.E2 AB
#AG.D IN4
..#I.C ,SKILL .,PRACTICE @7 PP4
#FBI-FCJ @7 .#A4 C5T] .#C4 ;,C .#E4 ,A
.#G4 ;,F
.#I4 #A
.#AA4 #E
.#BC4 .;X #B @+ .;Y #B .K #FD .#BE4
.;X #B @+ .;Y #B .K #BEF .#BG4 .;X #B @+
.;Y #B .K #AE .#BI4 .;X #B @+ .;Y #B .K
#IF .#CA4 .;X #B @+ .;Y #B .K #CF .#CC4
.;X #B @+ .;Y #B .K #BE .#CE4 .;X #B @+
.;Y #B .K #AJJ .#CG4 .;X #B @+ .;Y #B .K
#AAF .#CI4 .;X #B @+ .;Y #B .K #BFJ
.#DA4 .;X #B @+ .;Y #B .K #BDB
.#DE4
.#DG4
.#EC4 .#EE4 .#EG4 .#EI4 .,SAMPLE
.ANSW]3 .;X #B @+ .;Y #B .K #CE1 .;X #B
@+ .;Y #B .K #CF1 .;X #B @+ .;Y #B .K
#CH
..#I.C ,PRO#M .,SOLV+ @7 PP4 #FCJ-FCB
@7 .#FC4 YES .#FE4 .A4 AB #BH.I MI .B4
AB #AH.C MI .C4 #F MI .#FG4 AB #G.ID FT
..#I.D ,SKILL .,PRACTICE @7 PP4
#FCG-FCH @7 .#A4 FOCI
.#C4 7+-#D1 #J71 7#J1 +-#B71
.#E4 7#J1 +-#G71 7+-#C1 #J71
.#AE4 ,! MAJOR AXIS %D 2 ! .;Y -AXIS1
N ! .;X -AXIS4
--------------------------------;,,SA#BI
,,SELECT$ ,,ANSW]S
.#AG4 .#AI4 .#BA4 .#BC4 .#BE4 .#BG4
.#BI4 .#CA4 .#CC4
.#CG4 .#CI4
.#DE4 ,! 3IC *ANGES F AN ELLIPSE
EL;GAT$ AL;G ! .;Y -AXIS 6A CIRCLE 6AN
ELLIPSE EL;GAT$ AL;G ! .;X -AXIS4
#I.D ,PRO#M ,SOLV+ @7 PP4 #FCH-FCI @7
.#DI4 @1 @2 AB #AA1GJJ "K.K .,A "K.K
#BB1EJJ
.#EA4 .,SAMPLE .ANSW]3
..#I.D ,PRO#M ,SOLV+ .,"W%OP @7 P4
#FDJ @7 .#A4 ,AB #FF1AJJ ;M #B @2 BETT]4
.,SAMPLE .ANSW]3 ,M RECTANGLES M1NS "!
IS LESS >EA (! ELLIPSE N 9CLUD$4
.#C4 .A4 .B4 AB #CI1JJJ ;M #B
#I.E ,SKILL ,PRACTICE @7 PP4 #FDE-FDF
@7
.#A4 V]TICES1 TRANSV]SE AXIS
.#C4 7+-#E1 #J71 @1
.#E4 7#J1 +-#I71 @1
.#AG4 ,! EQU,N (A HYP]BOLA M/ EQUAL
"O1 S ! HYP]BOLA'S V]TICES %D 2 LOCAT$
AT 7+-#D1 #J74
.#AI4 .#BA4 .#BC4 .#BE4
.#BG4 .#BI4
.#CC4 .A4 ,! HYP]BOLA W 2 N>R[]1 !
V]TICES >E ! SAME1 B ! FOCI MOVE TO @4
.B4 ,! HYP]BOLA W 2 WID]1 ! V]TICES >E !
SAME1 B ! FOCI MOVE TO @4 .#CE4 .,SAMPLE
.ANSW]3 @1 @2 Z ! VALUE ( .A GETS L>G] !
HYP]BOLA IS /RET*$ V]TIC,Y4
..#I.E ,PRO#M .,SOLV+ @7 PP4 #FDF-FDG
@7 .#CI4 .#DA4 .A4 7#CJ.E1 #J71 7#HE1
--#DJ7 .B4 .C4 AB #ED.F FT .#DC4 .A4 .B4
.,SAMPLE .ANSW]3 ,*OOSE ANY PO9T ON !
GRAPH & OBS]VE T ! DI6];E (! 4T.ES F T
PO9T &! FOCI REMA9 3/ANT4
..#I.F ,SKILL .,PRACTICE @7 PP4
#FEE-FEF @7 .#A4 ,! 9T]SEC;N (A PLANE &A
D\#-NAPP$ C"O =M !M4
.#C4 P>ABOLA ) V]TEX 7--#D1 #B71 FOCUS
7--#D1 #J71 & DIRECTRIX .;Y .K #D
.#E4 HYP]BOLA ) C5T] 7#F1 --#A71
V]TICES 7#AA1 --#A7 & 7#A1 --#A71
ASYMPTOTES &
.#AC4 @7 .;X @+ #E7 #B @+ @7 .;Y --
#A7 #B .K #CF .#AE4 @7 .;Y @+ #C7 #B .K
#BJ7 .;X @+ #D7 .#AG4 .#AI4
--------------------------------;,,SA#CJ
,,SELECT$ ,,ANSW]S
.#BA4 ,! C5T] IS AT 7--#B1 #C71 N 7#B1
--#C72 @4 .#BC4 .;Y .K #D .#BE4 .;X .K
#C1 .;Y .K #E .#BG4 ANY L9E PASS+ "? !
PO9T 7--#B1 --#A7 .#BI4 CIRCLE .#CA4
ELLIPSE .#CC4 P>ABOLA .#CE4 HYP]BOLA
.#CG4 CIRCLE1 @7 .;X -- #G7 #B @+ @7 .;Y
@+ #B7 #B .K #FD
.#CI4 P>ABOLA1 @7 .;X -- #H7 #B .K #H7
.;Y -- #B7
.#DE4 ,IF ! NON-Z]O COE6ICI5TS ( .;X
#B & .;Y #B >E ! SAME X'S A CIRCLE4 ,IF
! NON-Z]O COE6ICI5TS ( .;X #B & .;Y #B
>E BO? POSITIVE & DI6]5T X'S AN ELLIPSE4
,IF "O (! NON-Z]O COE6ICI5TS ( .;X #B OR
.;Y #B IS NEGATIVE &! O!R "O IS POSITIVE
X'S A HYP]BOLA4 ,IF "O (! COE6ICI5TS (
.;X #B OR .;Y #B IS Z]O X'S A P>ABOLA4
#I.F ,PRO#M ,SOLV+ @7 PP4 #FEF-FEG @7
.#DI4 @2 #F @1 #AJ FT .#EA4 .A4 @7 .;X
-- #AJJ7 #B @+ @7 .;Y @+ #FJ7 #B "K.K
#AEJ #B @1 @7 .;X @+ #HJ7 #B @+ @7 .;Y
@+ #GJ7 #B "K.K #AJJ #B
.B4 ,"O2 ! 4T.E F YR POSI;N 6! HOTEL
IS LESS ?AN ! RADIUS (! HOTEL'S
TRANSMITT]1 B Y >E AB #AJF FEET F !
CAF@E'S TRANSMITT] : IS \ ( RANGE4 .C4
.,SAMPLE .ANSW]3 ,F9D ! 4T.E F ! HOTEL
6! CAFE4 ,IF X'S GRT] ?AN #BEJ Y>DS !Y D
N OV]LAP4 ,X X'S LESS ?AN OR EQUAL 6#BEJ
Y>DS !Y OV]LAP4
#I.G ,SKILL ,PRACTICE @7 PP4 #FFA-FFB
@7
.#A4 QUADRATIC .#C4 7--#D1 --#D71 7#D1
#D7 .#E4 7#J.DGB1 --#B.EH71 7#C.EC1
#F.EH7 .#G4 7--#B.AH1 --#C.CF71
7#A.CH1C.GF7 .#I4 7#C1 --#C71 7--#B1 #B7
.#AA4 .#AC4 7#J1 #B71 .#AE4 7--#A1
--#D71 .#AG4 NO SOLU;N .#AI4 .#BC4 @1
7--#E1 #J7 .#BE4 .#BG4 NO SOLU;N .#BI4
NO SOLU;N .#CA4 7#D1 #J7 .#CC4 7--#A1
--#B71 7#B1 #A7 .#CE4 ,:5 7#A -- .;Y #B
@7 #B 0 EXP&$1 ! LA/ T]M %D H BE5 .;Y #D
@2 #A--#B .;Y #B @+ .;Y #D @+ .;Y #B --
#B @+ #B .;Y #B -- #B .;Y .K --#A1 .;Y
#D @+ .;Y #B -- #B .;Y .K #J4 .#CG4 AB
7--#B.CB1 --#B.JB71 7--#J.BIF1 --#B.HB7
..#I.G ,PRO#M .,SOLV+ @7 PP4 #FFB-FFD
@7 .#CI4 .;D .K #J.H .;T1 .;D .K #B.E
.;T #B @1 #J.CB M9 .#DA4 .A4 .;X #B @+
.;Y #B .K #A1 .B4 @1 .C4 AB #A.DA MI
.#DC4 .A4 7#A1 #A7 .B4 AB 7--#H.ID1
--#B.FH7
.#I..G .,EXT5.N @7 P4 #FFF @7 .#A4 #J
.#C4 .#E4 #A .#G4 .#I4 .#AA4 .#AC4
.,SAMPLE .ANSW]3 .#AE4 ,9 ! ELLIPSE #J
"K .;C "K .A @1 "!=E @4 ,9 ! HYP]BOLA #J
"K .A "K .;C @1 "!=E @4
.,*APT] .,REVIEW @7 PP4 #FFI-FGB @7
.#A4 P>ABOLA .#C4 TRANSV]SE AXIS .#E4 @2
7--#B1 --#D7 .#G4 @2
.#I4 7#J1 #D71 .;Y .K --#D1 .;X .K #J
.#AA4 7#J1 --#A71 .;Y .K #A1 .;X .K #J
.#AC4 .;X #B .K #AB .;Y
.#AE4 #I
.#AG4 #G
.#AI4 .;X #B @+ .;Y #B .K #FH
--------------------------------;,,SA#CA
,,SELECT$ ,,ANSW]S
.#BA4 7+-#E1 #J71 7#J1 +-#D71 7+-#C1
#J7
.#BC4 7#J1 +-#H71 7+-#F1 #J71
.#BE4 .#BG4 7+-#D1 #J71 @1
.#BI4 .#CA4 ELLIPSE1 .#CC4 HYP]BOLA1
.#CE4 7#AF1 #H71 7#A1 #B7 .#CG4 7#B1 #J7
.,CUMULATIVE .,REVIEW @7 PP4 #FGH-FGI
@7 .#A4 .#C4 #E1 #G .#E4 --#B1 --#E1 #D
.#G4 .#I4 #G .#AA4 .#AC4 .#AE4 .#AG4 7#C
.;X -- #D77#B .;X @+ #E7 .#AI4 .#BA4
.#BC4 DECAY .#BE4 .#BG4 .#BI4 .#CA4
.#CC4 .#CE4 @2 .#CG4 CIRCLE1 @7 .;X @+
#F7 #B @+ @7 .;Y -- #B7 #B .K #BE2
.#CI4 P>ABOLA1 @7 .;Y @+ #B7 #B .K
--#F7 .;X @+ #B72
.#DA4 #AAE FT1 #GE FT .#DC4 #DJJ
ADULTS1 #BEJ /UD5TS .#DE4 AB #G MI #B
.#DG4 #J.HE7 .;T -- #EJ71 4#CFE.EJ .#DI4
.;S .K #CDH7#A.JB7 ;T
,*APT] #AJ
..#AJ.A ,SKILL .,PRACTICE @7 PP4
#FHF-FHG @7 .#A4 ,! NUMB] ( WAYS .;N
OBJECTS C 2 ORD]$4
.#C4
.#E4
.#G4 #H WAYS .#I4 #FJ WAYS .#AA4 .A4
#DEF1IGF1JJJ LIC5SE PLATES .B4
#BEH1CCF1JJJ LIC5SE PLATES .#AC4 .A4
#DE1FIG1FJJ LIC5SE PLATES .B4
#CB1BIB1JJJ LIC5SE PLATES .#AE4 .A4
#AAH1HAC1GFJ LIC5SE PLATES .B4
#GH1ICF1JJJ LIC5SE PLATES .#AI4
#CI1IAF1HJJ .#BA4 #DJ1CBJ .#BC4 #A .#BE4
#GBJ .#BG4 #GB .#BI4 #FCJ .#CA4 #CJ
.#CC4 #DJ1CBJ
--------------------------------;,,SA#CB
,,SELECT$ ,,ANSW]S
.#CE4 #GB .#CG4 #EJDJ .#CI4 #CJBD
.#DA4 #A .#DC4 #C .#DE4 #FJ .#DG4 #GBJ
.#DI4 #CCFJ .#EA4 #DJ1CBJ .#EC4 #IJ1GBJ
.#EI4 #AJ
#AJ.A ,PRO#M ,SOLV+ @7 PP4 #FHH-FHI @7
.#FC4 #BBE1FGH1IFJ SETS .#FE4 #EJD
WAYS .#FG4 .A4 #BDJ SELEC;NS .B4 #BEB
SELEC;NS .C4 #FJ1DHJ SELEC;NS .#FI4
#GJ1EFJ 4PLAYS
..#AJ.B ,SKILL .,PRACTICE @7 PP4
#FID-FIE @7 .#A4 .;N TH R[ ( ,PASCAL'S
TRIANGLE .#C4 #AJ .#E4 #HD .#G4 #A .#I4
#BA .#AA4 ,! DENOM9ATOR %D H BE5
MULTIPLI$ 0#B62 @4 .#AC4 #GIB H&S .#AE4
#GGH1CBJ H&S .#AG4 #B1DIJ1FBD H&S .#AI4
.#BA4 .;Y #AJ -- #CJ .;Y #I .;Z @+ #DJE
.;Y #H .;Z #B -- #CBDJ .;Y #G .;Z #C @+
#AG1JAJ .;Y #F .;Z #D -- #FA1BCF .;Y #E
.;Z #E @+ #AEC1JIJ .;Y #D .;Z #F --
#BFB1DDJ .;Y #C .;Z #G @+ #BIE1BDE .;Y
#B .;Z #H -- #AIF1HCJ .YZ #I @+ #EI1JDI
.;Z #AJ .#BC4 #ABH .;S #G -- #DDH .;S #F
.;T #D @+ #FGB .;S #E .;T #H -- #EFJ .;S
#D .;T #AB @+ #BHJ .;S #C .;T #AF -- #HD
.;S #B .;T #BJ @+ #AD .ST #BD -- .;T #BH
.#BE4 .;C #E -- #BJ .;C #D @+ #AFJ .;C
#C -- #FDJ .;C #B @+ #ABHJ .;C -- #AJBD
.#BG4 #DJIF .;P #F -- #FADD .;P #E .;Q
@+ #CHDJ .;P #D .;Q #B -- #ABHJ .;P #C
.;Q #C @+ #BDJ .;P #B .;Q #D -- #BD .PQ
#E @+ .;Q #F .#BI4 #CB .;S #BJ @+ #DJJ
.;S #AF @+ #BJJJ .;S #AB @+ #EJJJ .;S #H
@+ #FBEJ .;S #D @+ #CABE .#CA4 .;X #AB
-- #D .;X #I .;Y #B @+ #F .;X #F .;Y #D
-- #D .;X #C .;Y #F @+ .;Y #H .#CC4
#AJHJ .#CG4 ,! SUM AL;G EA* DIAGONAL
SEG;T IS EQUAL 6! SUM (! TWO PREVI\S
DIAGONAL SEG;T SUMS4 .#CI4 -B9,NS2
#AC1HCF1ACJ1JEF WAYS .#DA4 S #J6 M/
EQUAL #A4
#AJ.B ,PRO#M ,SOLV+ @7 PP4 #FIF-FIG @7
.#DI4 #HAF -B9,NS .#EA4 .A4 #AE1EJD
-B9,NS .B4 #C1JJC -B9,NS .C4 #BEB
-B9,NS2 #AJ -B9,NS2 #C -B9,NS .D4
#CEA1IHB1CEJ1GBJ WAYS
..#AJ.C ,SKILL .,PRACTICE @7 PP4
#GJA-GJC @7 .#A4 GEOMETRIC .#C4 .#E4
.#G4 .#I4 .#AA4 .#AC4 .#AE4 .#AG4 .#BA4
.#BC4 .#BE4 ,! FRAC;N %D 2 \TCOMES N 9 !
EV5T1 #D1 6\TCOMES 9 ! EV5T1 #B2 @4
.#BG4 @4 .,SAMPLE .ANSW]3 ,S9CE !
PROBABIL;Y IS #J.C1 "! >E #C \ ( #AJ
*.ES (! EV5T O3URR+4 ,! NUMB] ( \TCOMES
AG/ EV5T ,A IS #AJ--#C .K #G4 ,S ! O4S 9
FAVOR ( EV5T ,A IS ! RATIO (! NUMB] (
FAVORA# \TCOMES1 #C1 6! NUMB] (
UNFAVORA# \TCOMES1 #G4 .#BI4 @2 !
EXP]I;TAL PROBABIL;Y IS SLI<TLY GRT] ?AN
! !ORETICAL PROBABIL;Y ( @4 .#CA4 @2 !
EXP]I;TAL PROBABIL;Y IS SLI<TLY GRT] ?AN
! !ORETICAL PROBABIL;Y ( @4 .#CC4
..#AJ.C ,PRO#M .,SOLV+ @7 PP4 #GJC-GJD
@7 .#CE4 .#CG4 OR AB #J.BAE .#CI4 .#DA4
.A4 .B4 .C4
..#AJ.D ,SKILL .,PRACTICE @7 PP4
#GAJ-GAA @7 .#A4 -P.D EV5T .#C4 #J.D
.#E4 #J.FE .#G4 .#I4 #J.FE .#AA4 #J.BA
.#AC4 .#AG4 #A .#AI4 .#BA4 .#BC4 .#BE4
.#BG4 ,! PROBABIL;Y (A CLUB & #I M/ 2
SUBTRACT$ 9/1D ( A4$2 @4 .#BI4 #J.FG2 N
4JO9T .#CA4 @2 N 4JO9T .#CC4 #BD@3P2 N
4JO9T .#CE4 .#CG4
..#AJ.D ,PRO#M .,SOLV+ @7 PP4 #GAA-GAC
@7 .#DC4 #J.G .#DE4 AB #J.HDHH .#DG4 .A4
#EH@3P .B4 #EC@3P .C4 ,NO2 :AT P]C5T (!
TOMATOES H BITE M>KS4 .#DI4
.,EXT5.N @7 P4 #GAF @7 .#A4 ;7#A1 #B1
#C1 #D1 #E1 #G1 #I1 #AA1 #AC1 #AF1 #AG72
.#C4 ;7#A1 #D1 #F1 #H1 #I1 #AJ1 #AB1
#AD1 #AE1 #AF1 #AH1 #AI1 #BJ72 .#E4
;7#A1 #B1 #C1 #D1 #E1 #G1 #H1 #I1 #AA1
#AC1 #AD1 #AF1 #AG1 #BJ72 .#G4 ;7#C1 #F1
#G1 #AJ1 #AB1 #AC1 #AE1 #AH1 #AI72 .#I4
NO .#AA4 YES .#AC4 ,APRIL1 ,JUNE1
,SEPTEMB]1 ,OCTOB]1 ,NOVEMB]1 ,DECEMB]
.#AE4 ,JANU>Y1 ,FEBRU>Y1 ,M>*1 ,APRIL1
,MAY1 ,JUNE1 ,JULY1 ,AUGU/ .#AG4 ,YES2
NO2 AN IRR,NAL IS A R1L NUMB] B IS N AN
9TEG]4
..#AJ.E ,SKILL .,PRACTICE @7 PP4
#GBA-GBB @7 .#A4 3DI;NAL PROBABIL;Y .#C4
#J.BD .#E4 #J.H .#G4 #J.GE .#I4 AB
#J.JDG .#AA4 AB #J.JEI .#AC4 AB #J.JAE
.#AG4 #J.CE .#AI4 #J.GE .#BA4 #J.I .#BC4
.#BE4 .#BG4 .A4 .B4 .#BI4 .A4 .B4 .#CA4
.A4 .B4 .#CC4 ,! PROBABILITIES %D 2
MULTIPLI$ 9/1D ( A4$2 .;,P @7 .,A & .;,B
@7 .K #J.D 99 #J.E .K #J.B4 .#CE4 ,S9CE
.,A & .;,B >E 9DEP5D5T EV5TS1 .;,P @7
.,A @7 HAS NO A6ECT ON .;,P @7 .;,B _\
.,A @7 S .;,P @7 .;,B _\ .,A @7 .K .;,P
@7 .;,B @7@4
..#AJ.E ,PRO#M .,SOLV+ @7 PP4 #GBB-GBC
@7 .#CG4 AB #HA@3P .#CI4 #EA@3P .#DA4
.A4 #J@3P2 AB #B@3P2 AB #IH@3P .B4 AB
#BJ@3P1 AB #CJ@3P1 AB #EJ@3P .C4 ,YES2 G
= #B PO9TS AF ! F/ T\*D[N4 ,IF ! #B
PO9TS >E SCOR$1 G = #A PO9T AF ! SECOND
T\*D[N4 ,IF ! TWO PO9TS >E N SCOR$1 G =
#B PO9TS AF ! SECOND T\*D[N2 W93 AB
#DE@3P1 LOSE3 AB #CJ@3P4
--------------------------------;,,SA#CC
,,SELECT$ ,,ANSW]S
..#AJ.F ,SKILL .,PRACTICE @7 PP4
#GBG-GBI @7 .#A4 SYMMETRIC
#C4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X 7VALUE7 @3 #A3 #B3 #C
.;,P7.;X7 @3 @3 @3
#E4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;X 7VALUE7 @3 #A3 #B3 #C
.;,P7.;X7 @3 @3 @3
.#G4 #C .#AA4 AB #J.JJJAH .#AC4 AB
#J.JCG .#AE4 AB #J.ABJ .#AG4 AB #J.JJJAH
.#AI4 AB #J.JJHF .#BA4 AB #J.JEE .#BC4
AB #J.JJJJJJBD .#BE4 AB
#J.JJJJJJJJJJJJJJJJJJHG .#BG4 ,! #E ;,C
#C 0 LEFT \ (! EQU,N2 @4 .#BI4 AB #J.EID
.#CA4 AB #J.HEB .#CC4 SKEW$2 #A SU3ESS
.#CE4 SKEW$2 #J SU3ESSES .#DA4 ;N ;,C ;K
@2 S9CE ORD] DOES N MATT]1 F9D ! -B9,N (
.;N ?+S TAK5 .;K AT A "T4
..#AJ.F ,PRO#M .,SOLV+ @7 PP4 #GBI-GCJ
@7 .#DC4 AB #J.AIF .#DE4 .A4 AB #J.ADC
.B4 AB #J.BGF .C4 AB #J.ABD .D4 AB
#J.III .#DG4 .A4 .;,P 7#J7 .K AB #J.JII1
.;,P 7#A7 .K AB #J.BGA1 .;,P 7#B7 .K AB
#J.CAI1 .;,P 7#C7 .K #J.BJH1 .;,P 7#D7
.K AB #J.JHA1 .;,P 7#E7 .K AB #J.JAI1
.;,P 7#F7 .K AB #J.JJBE1 .;,P 7#G7 .K AB
#J.JJJAD
B4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.;,X @3 .;,P7.;X7
#J3 #J.JII
#A3 #J.BGA
#B3 #J.CAI
#C3 #J.BJH
#D3 #J.JHA
#E3 #J.JAI
#F3 #J.JJBE
#G3 #J.JJJAD
.,*APT] .,REVIEW @7 PP4 #GCD-GCF @7
.#A4 -B9,N .#C4 ,NO2 "! >E M ?AN TWO
\TCOMES = EA* C>D SELEC;N4 .#E4
#DGI1JJA1FJJ WAYS2 #AA1HHJ WAYS .#G4
#ABJ .#I4 #IJ .#AA4 #AF .A #D @+ #CB .A
#C .;B #B @+ #BD .A #B .;B #D @+ #H .;AB
#F @+ .;B #H .#AC4 .;R #AE -- #BJ .;R
#AB .;S @+ #AFJ .;R #I .;S #B -- #FDJ
.;R #F .;S #C @+ #ABHJ .;R #C .;S #D --
#AJBD .;S #E .#AE4 .#AG4 .#AI4 #J.HFH
.#BA4 #J.FH .#BC4 .A4 .B4 .#BE4 .A4 .B4
.#BG4 AB #J.BGC .#BI4 AB #J.JJCI
,*APT] #AA
..#AA.A ,SKILL .,PRACTICE @7 PP4
#GDG-GDH @7 .#A4 C5TRAL T5D5CY2 4P].N
.#C4 AB #E.C2 #E2 #D1 #E & #F .#E4
#GD.E1 #GC.E1 #GC & #GH .#I4 ,! NUMB]S
NE$ 6BE WRITT5 9 9CR1S+ ORD] PRIOR
6*OOS+ ! M$IAN2 #I4 .#AA4 #E1 AB #A.F
.#AC4 #D.G1 AB #A.G .#AE4 #BC1 AB #H.A
.#AG4 #FH2 AB #AJ.G1 #D1 #D1 #FF1 AB
#BJ.C2 #C.E1 #C.E1 #D1 #D1 AB #A.B .#AI4
#J.G2 #AJ1 #AA.F1 #AA.F1 #AB.A1 AB #D.B2
AB #AA.I1 #AA.F1 #AA.F1 #A.I1 AB #J.FG
.#BA4 #AEB2 #GH.H1 #GA.E1 #FF1 #IB1 AB
#BE.A2 AB #GJ.G1 #GA1 #FF1 #BJ1 AB #F.J
.#BC4 .,SAMPLE .ANSW]3 #H1 #H1 #H1 #H1
#AA1 #AA1 #AB1 #AB1 #AB
..#AA.A ,PRO#M .,SOLV+ @7 PP4 #GDH-GDI
@7 .#BG4 AB #AG.H1 #BJ1 #F & #BJ .#BI4
.A4 #E .B4 #BJ.B1 #BB1 #BC1 #BJ1 AB
#E.D2 AB #BA.I1 #BC1 #BC1 #F1 AB #B.A
.C4 .,SAMPLE .ANSW]3 ,! M1N &! M$IAN
9CR1SE :5 ! \TLI] IS REMOV$ &! RANGE &
/&>D DEVI,N DECR1SE4
..#AA.B ,SKILL .,PRACTICE @7 P4 #GEC
@7 .#A4 TRANS=M,N .#C4 #AH1 #AG1 #AG1
#I1 AB #C.J2 #BD1 #BC1 #BC1 #I1 AB #C.J
.#E4 #GH1 #GG1 #GG1 #I1 AB #B.H2 #IE1
#ID1 #ID1 #I1 AB #B.H .#G4 #EF1 #EC1
#EC1 #BA1 AB #G.J2 #CE1 #CB1 #CB1 #BA1
AB #G.J .#I4 ,! /&>D DEVI,N DOES N *ANGE
:5 A4+ A 3/ANT2 #AJ4 .#AA4 AB #FA.I1
#FB1 #EH1 #I1 AB #C.CF2 AB #BDH1 #BDH1
#BCB1 #CF1 AB #AC.D .#AC4 AB #IH.B1
#AJJ.E1 #AJB1 #AI1 AB #F.FB2 AB #BDE.E1
AB #BEA.C1 #BEE1 #DG.E1 AB #AF.F
--------------------------------;,,SA#CD
,,SELECT$ ,,ANSW]S
.#AE4 AB #BBI1 #BBF.E1 #BBB1 #CH1 AB
#AB.J2 AB #BJF.A1 AB #BJC.I1 #AII.H1
#CD.B1 AB #AJ.H
..#AA.B ,PRO#M .,SOLV+ @7 PP4 #GEC-GEE
@7 .#AI4 .A4 AB #GJ.H1 #GB1 #GB1 #H1 AB
#B.D .B4 AB #IH.H1 #AJJ1 #AJJ1 #H1 AB
#B.D .#BA4 .A4 AB #F.HD1 #F.HI1 NO MODE1
#A.AF1 AB #J.CBD .B4 AB #BB.D1 AB #BB.F1
NO MODE1 AB #C.HJ1 AB #A.JF .#BC4 .A4
#GE.H1 AB #GE.D1 #GD.E1 #I.I1 AB #C.J
.B4 AB #BC.F1 AB #BG.G1 #BB.E1 #BC.J1 AB
#BE.H1 AB #BB.F1 AB #BD.I1 AB #BC.F1 AB
#BE.C1 AB #BB.B1 AB #BF.B1 AB #BD.F .C4
AB #BD.C1 #BD.A1 #BC.F1 #E.E1 AB #A.F
.D4 ,! E6ECT IS A MULTIPLIC,N TRANS=M,N
)A FACTOR ( @1 AL;G ) AN A4I;N TRANS=M,N
( AB --#AG.H =! M1N1 M$IAN1 & MODE4
..#AA.C ,SKILL .,PRACTICE @7 PP4
#GFJ-GFA @7 .#A4 NORMAL CURVE .#C4 #J.AF
.#E4 #J.HD .#G4 #J.FH .#I4 #AF@3P .#AA4
#J.FH .#AC4 #J.IGCE .#AE4 #J.HD .#AI4
#J.GBEG .#BA4 #J.JJCE .#BC4 #J.E .#BE4
#J.JEDH .#BG4 #J.ECFC .#BI4 ,! TA# 0
9T]PRET$ 9CORRECTLY2 .;,P @7 .;Z .1.K
--#J.H7 .K #A--#J.BAAI .K #J.GHHA4
..#AA.C ,PRO#M .,SOLV+ @7 PP4 #GFA-GFB
@7 .#CA4 #J.AF .#CC4 .A4 --#B.D1 #A.F
.B4 #J.JJHB .C4 #J.ICG2 .;,P @7 .;Z "K.K
#A.F7 -- .;,P @7 .;Z "K.K --#B.D7 .#CE4
.A4 #B.D .B4 #A.B .C4 ,LISA2 9 A /&>D
NORMAL 4TRIBU;N ,LISA'S SCORE IS HI<]4
.,EXT5.N @7 P4 #GFE @7 .#A4 #I.F1 #B.D
.#C4 #AC.H1 AB #C.A .#E4 #BE.B1 AB #B.G
.#G4 #H.H1 AB #B.H .#I4 #AJE1 AB #E.A
.#AA4 AB #J.IC .#AC4 AB #J.JJAC .#AE4 AB
#J.IH .#AG4 AB #J.IIHG .#AI4 ,YES2 .;,P
@7 .;X "K.K #EF7 #J.JA1 : IS LESS ?AN
#J.JE4 .#BA4 ,YES2 .;,P @7 .;X .1.K #AB7
#A -- .;,P @7 .;Z "K.K #B.E7 #A--#J.IICH
.K #J.JJFB1 : IS LESS ?AN #J.JE4
..#AA.D ,SKILL .,PRACTICE @7 PP4
#GFI-GGJ @7 .#A4 R&OM .#C4 ,SY/EMATIC2
UNBIAS$2 ! SAMPLE IS REPRES5TATIVE (!
CU/OM]S4 .#E4 ,R&OM2 UNBIAS$2 EA* /UD5T
HAS AN EQUAL *ANGE ( 2+ SELECT$4 .#G4
+-#C.B@3P .#I4 +-#A.C@3P .#AA4 +-#D.D@3P
.#AC4 +-#A.J@3P .#AE4 #AAAA P .#AG4 #AJJ
P .#AI4 #CAI P .#BA4 #BCG P .#BE4 AB
#DEC P
..#AA.D ,PRO#M .,SOLV+ @7 PP4 #GGJ-GGA
@7 .#BG4 .A4 AB +-#D.H@3P .B4 2T #I.B@3P
& #AH.H@3P .#BI4 ,NO4 .,SAMPLE .ANSW]3
,S9CE ! M>G9 ( ]ROR IS +-#E@3P1 ,KO/A CD
H #DI@3P (! VOTES & ,MURDOCK CD H #EA@3P
(! VOTES4 .#CA4 .A4 #DG@3P1 #EC@3P .B4
AB +-#D.E@3P .C4 2T #DB.E@3P & #EA.E@3P1
2T #DH.E@3P & #EG.E@3P .D4 NO2 #BGC P
.,EXT5.N @7 P4 #GGC @7 .#A4 .,SAMPLE
.ANSW]3 ,? IS A L1D+ "Q4 ,RESPOND5TS MAY
?9K A 8NO0 RESPONSE M1NS !Y >E N
SUPPORT]S ( C;Y GR[?4 .#C4 .,SAMPLE
.ANSW]3 ,_M PATI5TS MAY ANSW] UNTRU?;LLY
2C _! D5TI/ IS ASK+ ! "Q4 ,! 9=M,N %D 2
COLLECT$ ANONYM\SLY4 .#E4 .,SAMPLE
.ANSW]3 ,! "Q ASSUMES T ! RESPOND5T IS
FAMILI> )! FACTS (! CASE4 ,ANY PRES5T,N
(! FACTS 7Z 9T]PRET$ 0! POLL/]7 MAY 2
BIAS$ Z WELL4 ,X MI<T 2 BE/ !N 6ASK ! "Q
Z GIV5 ONLY 6^? :O REPLY A6IRMATIVELY 6!
"Q1 8,>E Y FAMILI> )! FACTS (! ,C>T]
CASE80 .#G4 .,SAMPLE .ANSW]3 ,! FLAW IS
T ,ALGEBRA #B /UD5TS >E ! EXP]I;TAL GR\P
& ,ALGEBRA #A /UD5TS >E ! 3TROL GR\P2 !
EXP]I;TAL & 3TROL GR\PS %D BO? 2
,ALGEBRA #B /UD5TS4
..#AA.E ,SKILL .,PRACTICE @7 P4 #GGH
@7 .#A4 EXPON5TIAL .#C4 .;F @7 .;X @7 .K
--#J.CHA .;X #B @+ #A.AB .;X @+ #AE.G2
.#G4 ,! .;X &! VALUE ( .;B H BE5
9T]*ANG$2 .;Y .K #I.GA7#A.EE7 ;X @4
..#AA.E ,PRO#M .,SOLV+ @7 P4 #GGI @7
.#AA4 .,SAMPLE .ANSW]3 .;Y .K #J.JJBAA
.;X #C -- #J.JGFF .;X #B @+ #A.BF .;X --
#J.JFFD .#AC4 .A4 QUADRATIC .B4 .;Y .K
--#B.IG .;X #B @+ #DJ.D .;X -- #HE.I
.C4
.D4 ,NO2 AT #A3JJ ,P4,M41 ! FUNC;N
PREDICTS A NEGATIVE NUMB] ( CU/OM]S4
#AA.E ,PRO#M ,SOLV+ ,"W%OP @7 P4 #GHA
@7
.#A4 AB #GD;DG;,F2 .;Y .K
#FA.C7#J.IFB7 ;X @+ #GD
.,*APT] .,REVIEW @7 PP4 #GHD-GHF @7
.#A4 ,/&>D DEVI,N .#C4 .;Z -SCORE .#E4
AB #HD.A1 #HF.E1 #HH1 #AG1 AB #F.B .#G4
AB #ACJ1 #ACJ1 #ADJ1 #EB1 AB #AF.A .#I4
AB #CI.H1 #CH1 #CG1 #AD1 AB #D.F2 AB
#CB.H1 #CA1 #CJ1 #AD1 AB #D.F .#AA4 AB
#CH.J1 AB #CE.D1 #EI.H1 #FB.F1 AB #BJ.H2
AB #A.EJ1 AB #A.CI1 AB #B.CE1 AB #B.DF1
AB #J.H .#AC4 AB #J.JEDH .#AE4 AB #J
.#AG4 AB #J.JAGI .#AI4 +-#B@3P .#BA4
+-#A.D@3P
--------------------------------;,,SA#CE
,,SELECT$ ,,ANSW]S
.#BC4 .;Y .K --#C.GI .;X @+ #BH.C2
,*APT] #AB
..#AB.A ,SKILL .,PRACTICE @7 PP4
#GIH-GII @7 .#A4 SIGMA NOT,N .#C4 #C1
#D1 #E1 #F1 #G1 #H #E.A1 #D1 #I1 #AF1
#BE1 #CF .#G4 #A1 #D1 #AF1 #FD1 #BEF1
#AJBD .#I4 --#D1 --#A1 #D1 #AA1 #BJ1 #CA
.#AA4 --#D1 --#B1 @1 --#A1 @1 .#AC4 @1
#A1 .#AE4 ,Y C WRITE ! T]MS Z 7#E 99
#A--#D71 7#E 99 #B--#D71 7#E 99 #C--#D71
7#E 99 #D--#D71 .A #E .K #BA1 .A ;N .K
#E .;N -- #D4 .#AG4 ,Y C WRITE ! T]MS Z
7--#A7 #A 7#D 99 #A71 7--#A7 #B 7#D 99
#B71 7--#A7 #C 7#D 99 #C71 7--#A7 #D 7#D
99 #D71 .A #E .K --#BJ1 .A ;N .K 7--#A7
;N 7#D 99 .;N @7@4 .#AI4 ,Y C WRITE !
T]MS Z @1 @1 @4 .#BA4 ,Y C WRITE ! T]MS
Z @1 @1 @4 .#BC4 ,Y C WRITE ! T]MS Z
#J.G7#A7 @+ #B.D1 #J.G7#B7 @+ #B.D1
#J.G7#C7 @+ #B.D1 #J.G7#D7 @+ #B.D1 .A
#E .K #E.I1 .A ;N .K #J.G .;N @+ #B.D4
.#BE4 ,Y C WRITE ! T]MS Z #A #B @+ #J.B1
#B #B @+ #J.B1 #C #B @+ #J.B1 #D #B @+
#J.B1 .A #E .K #BE.B1 .A ;N .K .;N #B @+
#J.B4
.#BI4 .#CA4
.#CG4 .#CI4 .#DA4 .#DC4 .#DE4 #DB
.#DG4 #AJJ .#DI4 #HB .#EA4 .#EC4 #CE
.#EE4 #CBE .#EG4 ,! L[] LIMIT IS Z]O1 S
! F/ T]M %D 2 #C2 #C @+ #E @+ #G @+ #I
@+ #AA @+ #AC .K #DH4
..#AB.A ,PRO#M .,SOLV+ @7 PP4 #GII-HJJ
@7 .#FC4 #FJ;DG1 #IJ;DG1 #AJH;DG1
#ABJ;DG1 AB #ABH.EG;DG2 .;,T ;N .K #AHJ7
.;N -- #B72 #AHJJ;DG .#FE4 .A ;N .K #B
;N -- #A2 #FC MOVES1 #ABG MOVES1 #BEE
MOVES .#FG4 .A4 #AE BALLS .B4 #CE BALLS
.C4 ,EXCEPT = LAY] #A1 "! >E ALW M BALLS
9 ! SAME LAY] (! SQU>E PYRAMID4 ,!
DI6];E 9 ! NUMB] ( BALLS IS @4
..#AB.B ,SKILL .,PRACTICE @7 PP4
#HJF-HJG @7 .#A4 -MON DI6];E .#C4
,>I?METIC2 "! IS A -MON DI6];E ( #C 2T
3SECUTIVE T]MS4 .#E4 ,>I?METIC2 "! IS A
-MON DI6];E ( #I 2T 3SECUTIVE T]MS4 .#G4
,>I?METIC2 "! IS A -MON DI6];E ( #J.E 2T
3SECUTIVE T]MS4 .#I4 ,N >I?METIC2 "! IS
N A -MON DI6];E 2T 3SECUTIVE T]MS4 .#AA4
,>I?METIC2 "! IS A -MON DI6];E ( #A.E 2T
3SECUTIVE T]MS4 .#AC4 .A ;N .K --#A @+
#F .;N @2 #AAI .#AE4 .A ;N .K --#E @+ #B
.;N @2 #CE .#AG4 .A ;N .K #CF--#AA .;N
@2 --#AHD .#AI4 @2 .#BA4 ,! EQU,N = AN
>I?METIC SEQU;E IS N CORRECT2 .A ;N .K
.A #A @+ @7 .;N -- #A7 .;D1 .A ;N .K #CG
@+ @7 .;N -- #A7 7--#AC71 .A ;N .K
#EJ--#AC .;N @4 .#BC4 .A ;N .K --#BH @+
#E .;N @2 .#BE4 .A ;N .K #AEB--#AD .;N
@2
.#CA4 .A ;N .K #I @+ #E .;N .#CC4 .A
;N .K #BB--#D .;N .#CE4 .A ;N .K #AC @+
#B .;N .#CG4 .#DA4 --#IF .#DC4 #BEHE
.#DE4 #CAE .#DG4 #ACB .#DI4 .A ;N .K
--#C @+ #E .;N .#EA4 .A ;N .K --#A--#B
.;N .#EC4 ,FALSE4 .,SAMPLE .ANSW]3
,D\BL+ ! -MON DI6];E AL"O DOES N D\# !
SUM4 .#EE4 #AB .#EG4 #BE .#EI4 #AE .#FA4
#BB1EJJ
..#AB.B ,PRO#M .,SOLV+ @7 PP4 #HJH-HJI
@7 .#FC4 .A4 .A ;N .K #F .;N .B4 #BGA
CELLS .#FE4 .A4 .A ;N .K --#D @+ #H .;N
.B4 #EGF BLOCKS .#FG4 4#AJJ
..#AB.C ,SKILL .,PRACTICE @7 PP4
#HAD-HAE @7 .#A4 -MON RATIO .#C4 ,N
GEOMETRIC2 "! IS NO -MON RATIO4 .#E4
,GEOMETRIC2 "! IS A -MON RATIO ( @4 .#G4
,N GEOMETRIC2 "! IS NO -MON RATIO4 .#I4
,GEOMETRIC2 "! IS A -MON RATIO ( .#AA4
,GEOMETRIC2 "! IS A -MON RATIO ( --#C4
.#AC4 ,N GEOMETRIC2 "! IS NO -MON RATIO4
.#AE4 .A ;N .K 7--#D7 .;N -- #A2 #DJIF
--------------------------------;,,SA#CF
,,SELECT$ ,,ANSW]S
.#AG4 .A ;N .K #D7#F7 .;N -- #A
#AHF1FBD .#AI4 @2 .#BA4 @2 .#BC4 .A ;N
.K --#B7#J.D7 .;N -- #A @2 --#J.JJHAIB
.#BE4 .A ;N .K #E7--#B.H7 .;N -- #A @2
#BDJI.DEAEB
.#BI4 .A ;N .K --#B7#F7 .;N -- #A @2
.#CA4 @2
.#CG4 ,! EXPON5T %D 2 .;N -- #A 9/1D (
.;N2 .A ;N .K #C7#B7 .;N -- #A @4 .#CI4
.A ;N .K #C7#B7 .;N -- #A OR .A ;N .K
#C7--#B7 .;N -- #A .#DA4 .#DC4 OR .#DE4
.A ;N .K #F7#C7 .;N -- #A .#DG4 .#DI4
#ACA1JGJ .#EA4 .#EC4 #HCH1HFA .#EE4
.,SAMPLE .ANSW]3
..#AB.C ,PRO#M .,SOLV+ @7 PP4 #HAE-HAG
@7 .#EG4 .A4 .A ;N .K #E7#B7 .;N -- #A
.B4 #GE SKYDIV]S .#EI4 .A4 .B4 #AJ4
.,SAMPLE .ANSW]3 ,ON ! #AA? PASS1 "! IS
ONLY #A T]M 6*OOSE F S X M/ 2 ! ANSW]
.#FA4 .A4 .A ;N .K #AI1JJJ @+ #AJJJ .;N
@1 >I?METIC2 .;B ;N .K #BJ1JJJ7#A.JD7
.;N -- #A @1 GEOMETRIC
.B4
.C4 ,-PANY ,A3 4#EIJ1JJJ2 ,-PANY ;,B3
AB 4#EIE1EFB .D4 #AI ;YR
..#AB.D ,SKILL .,PRACTICE @7 PP4
#HBC-HBD @7 .#A4 "PIAL SUM .#C4 .;,S #A
.K #J.E1 .;,S #B #J.FG1 .;,S #C #J.GB1
.;,S #D #J.GD1 .;,S #E #J.GE2 .;,S ;N
APPE>S 6BE APPROA*+ #J.GE4
.#E4 .;,S #A .K #D1 .;,S #B .K #F.D1
.;,S #C .K #G.HD1 .;,S #D #H.GA1 .;,S #E
#I.BB2 .;,S ;N APPE>S 6BE APPROA*+ #AJ4
.#G4 #AJ .#I4 NO SUM .#AA4 .#AC4 .#AE4
NO SUM .#AG4 .#AI4 ,S9CE .;R .1 #A1 !
9F9ITE GEOMETRIC S]IES HAS NO SUM4 .#BA
.#BC4 #AH .#BE4 .#BG4 .#BI4 .#CA4 .#CC4
..#AB.D ,PRO#M .,SOLV+ @7 PP4 #HBD-HBE
@7 .#CG4 #GJ FT .#DA4 .A4 #AB FT2 #I FT
.B4 .C4 #EF FT .D4
..#AB.E ,SKILL .,PRACTICE @7 PP4
#HCJ-HCA @7 .#A4 IT],N .#C4 #A1 #D1 #G1
#AJ1 #AC .#E4 --#A1 --#F1 --#AA1 --#AF1
--#BA .#G4 #B2 #E2 #BF2 #FGG2 #DEH1 #CCJ
.#I4 #B1 #H1 #AJ1 #AH1 #BB .#AA4 #B1 #C1
#F1 #AH1 #AJH .#AC4 .A #A .K #BA1 .A ;N
.K .A .;N -- #A -- #G .#AE4 .A #A .K #D1
.A ;N .K --#C .A .;N -- #A .#AG4 .A #A
.K #DD1 .#AI4 .A #A .K #ED1 .A ;N .K .A
.;N -- #A -- #AA .#BA4 .A #A .K #AF1 .A
#B .K #I1 .A ;N .K .A .;N -- #B -- .A
.;N -- #A .#BC4 ,! RULE DOES N "W = ALL
(! T]MS (! SEQU;E2 .A #A .K #E1 .A #B .K
#B1 .A ;N .K .A .;N -- #B -- .A .;N --
#A @4 .#BE4 --#D1 --#AD1 --#FD .#BG4
--#B1 --#D1 --#E .#BI4 #E1 #BA1 #DCG
.#CA4 #B1 #D1 #AD .#CE4 .A #A .K #A1 .A
#B .K #B1 .A ;N .K #D7 .A .;N -- #B @+
.A .;N -- #A @7 .#CG4 .A #A .K #B1 .A #B
.K #E1 .A ;N .K #C .A .;N -- #B @+ .A
.;N -- #A .#CI4 .A #A .K --#C1 .A #B .K
--#B1 .A ;N .K --#A7 .A .;N -- #B @+ .A
.;N -- #A @7 .#DA4 .,SAMPLE .ANSW]3 ,IF
! F/ TWO IT]ATES >E #B1 ! GIV5 RULE M/ N
2 A FUNC;N4
..#AB.E ,PRO#M .,SOLV+ @7 PP4 #HCB-HCC
@7 .#DC4 .A4 .A #A .K #EJJJ1 .A ;N .K
#J.H .A .;N -- #A @+ #EJJ2 #CEBD FI% .B4
,! POPUL,N (! LAKE APPROA*ES #BEJJ FI%4
--------------------------------;,,SA#CG
,,SELECT$ ,,ANSW]S
.#DE4 .A ;X .K #BJJJ1 .A ;N.' .K
#A.JAD .A .;N -- #A -- #AJJ2 #BD MO4
.,SAMPLE .ANSW]3 ,Z L;G ,GLADYS DOES N
ADD ANY?+ 6H] CR$IT C>D & 3T9UES H]
PAY;TS1 H] #BD? PAY;T W ONLY 2 4#FB.AD4
.#DG4 .A4 .A ;X.' .K #BJ1 .A ;N.' .K
#J.G .A .;N -- #A @+ #BJ .B4 MG .C4 ,!
MA9T5.E LEVEL (! DRUG D\#S Z WELL2 .A #A
.K #BJ1 .A ;N .K #J.G7#B .A .;N -- #A @7
@+ #B7#BJ74
#AB.E ,PRO#M ,SOLV+ ,"W%OP @7 P4 #HCE
@7
.#A4 ,! SEQU;E APPROA*ES #DJJ4 .#C4 ,!
NUMB] ( MEMB]S APPROA*ES #AE1JJJ4 .#E4
.,SAMPLE .ANSW]3 .#B@3P (! BOOKS >E LO/
( 4C>D$ S #IH@3P >E RETA9$2 .A ;N .K
#J.IH .A .;N -- #A @+ #AAEJ4
,EXT5.N @7 P4 #HCG @7
.#A4 .,BASIS .,/EP3 ,*ECK T ! =MULA
"WS = .;N .K #A4 #B7#A7--#A .K #A #B #A
.K #A
,9DUCTIVE ,/EP3
,ASSUME T #A @+ #C @+ #E @+ ' @+ 7#B
.;K -- #A7 .K .;K #B @4
,%[ T #A @+ #C @+ #E @+ ' @+ 7#B .;K
-- #A7 @+ 7#B7 .;K @+ #A7--#A7
.K @7 .;K @+ #A7 #B @4
#A @+ #C @+ #E @+ ' @+ 7#B .;K -- #A7
@+ 7#B7 .;K @+ #A7--#A7
.K .;K #B @+ 7#B7 .;K @+ #A7--#A7
.K .;K #B @+ #B .;K @+ #B--#A
.K .;K #B @+ #B .;K @+ #A
.K @7 .;K @+ #A7 #B
#C4 ,BASIS ,/EP3
,*ECK T ! =MULA "WS = .;N .K #A4
#B #A--#A .K #B #A -- #A .K #B #J .K
#B--#A #A .K #A
,9DUCTIVE ,/EP3
,ASSUME T #A @+ #B @+ #B #B @+ #B #C
@+ ' @+ #B .;K -- #A .K #B ;K -- #A4
,%[ T #A @+ #B @+ #B #B @+ #B #C @+ '
@+ #B .;K -- #A @+ #B @7 .;K -- #A7 --
#A
.K #B .;K @+ #A -- #A4
#A @+ #B @+ #B #B @+ #B #C @+ ' @+ #B
.;K -- #A @+ #B @7 .;K -- #A7 -- #A
.K 7#B ;K -- #A7 @+ #B @7 .;K @+ #A7
-- #A
.K #B ;K -- #A @+ #B ;K
.K #B7#B ;K @7--#A
.K #B .;K @+ #A -- #A
,*APT] ,REVIEW @7 PP4 #HDJ-HDB @7
.#A4 T]MS .#C4 EXPLICIT .#E4 #ACC .#G4
#AEC .#I4 .A ;N .K #AA--#C .;N .#AA4 .A
;N .K #C @+ #F .;N .#AC4 --#DJC .#AE4
#ABJJ .#AG4 .#AI4 OR .#BA4 #DJHH .#BC4
.#BE4 #D .#BG4 --#J.D .#BI4 .#CA4 .#CC4
#H1 #DJ1 #BJJ1 #AJJJ1 #EJJJ .#CE4 .A ;N
.K #F1 .A ;N .K #C .A .;N -- #A .#CG4 .A
#A .K #G1 .A ;N .K .A .;N -- #A @+ #F
,CUMULATIVE ,REVIEW @7 PP4 #HDH-HDI @7
.#A4 .#C4
.#E4 .#G4
.#I4 .#AA4
.#AC4 #AC .#AE4 #CFJ .#AG4 .#AI4
.#BA4 .#BC4
.#BE4 #EBD1AFJ .#BG4 #A #BI.J.AE .#CA4
AB #AB.HEG1AA1AA1AA1 AB #C.FJC .#CC4 AB
#BAE.EGA1 #BAF1 #BAF1 #BE1 AB #H.JHF
.#CE4 AB #HH.HEG1 #IB1 NO MODE1 #BH1 AB
#H.IFG .#CG4 #BGC .#CI4 AB #B.IGG .#DA4
.A ;N .K --#AA @+ #D .;N1 .A #A .K --#G1
.A ;N .K .A .;N -- #A @+ #D .#DC4 .A ;N
.K #C7#D7 .;N -- #A @1 .A #A .K #C1 .A
;N .K #D .A .;N -- #A .#DE4 #E IN4 .#DG4
9 #E ;YR .#DI4 AB #J.GBG .#EA4 .A ;N .K
#BI1DJJ @+ #AFJJ .;N @2 4#DC1HJJ
,*APT] #AC
.#AC..A .,SKILL .,PRACTICE @7 PP4
#HEF-HEG @7 .#A4 ,! ANGLE =M$ 0! L9E (
SI<T 6AN OBJECT &A L9E P>ALLEL 6! GR.D4
.#C4 @1 .#E4 @1
--------------------------------;,,SA#CH
,,SELECT$ ,,ANSW]S
.#G4 @1 .#I4 @1 @1 @1 @1 .#AG4 .#AI4
@1 .#BA4 .;,B .K #EE;DG1 .A #I.AH1 .;B
#AC.AA .#BC4 .,A .K #GB;DG1 .A --
#BB.HC1 .;B #G.DB .#BE4 .,A .K #AE;DG1
.;B #EE.IH1 .;C #EG.IF .#BG4 .;,B .K
#BF;DG1 .A #FE.FA1 .;C #GC.J
..#AC.A ,PRO#M .,SOLV+ @7 PP4 #HEG-HEH
@7 .#CA4 AB #FC.D CM .#CC4 ,AB #FEB FT4
.,SAMPLE .ANSW]3 ,! L>G] ! ANGLE ! DEEP]
! F9AL DEP?4 .#CE4 .A4 AB #BB1HAH MI .B4
AB #GBFC MI
#AC.B ,SKILL ,PRACTICE @7 PP4 #HFB-HFC
@7
.#A4 ORIG91 9ITIAL SIDE .#C4 ;,B .#E4
,A
.#G4 .#I4
.#AE-.BA4 ,SAMPLE ANSW]S >E GIV54
.#AE4 #DCJ;DG1 --#BIJ;DG .#AG4 #BCE;DG1
--#DHE;DG .#AI4 .#BA4 .#BC4 .#BE4 .#BG4
#BJ;DG .#BI4 #IJJ;DG .#CC4 AB #C.IC ;M1
AB #E.HI ;M #B .#CE4 AB #CA.D FT1 AB
#AHH FT #B .#CG4 AB #AAH IN41 AB #ADGJ
IN4 #B .#CI4 .#DA4 .#DC4 AB #B.DA .#DE4
AB #J.IGE
..#AC.B ,PRO#M .,SOLV+ @7 PP4 #HFD-HFE
@7 .#DI4 #GB1JJJ;DG1 #DJJ .#EA4 .A4 .B4
AB #DE.F FT .#EC4 .A4 AB #AF.E IN4 .B4
#CFJ;DG4 .,SAMPLE .ANSW]3 ,S9CE EA* /EP
HAS A C5TRAL ANGLE ( & "! >E #AF /EPS1 !
/AIRCASE W COV] OR #B1 : IS EQUIVAL5T
6#CFJ;DG4 .C4 AB #EAIE.D IN4 #B
..#AC.C ,SKILL .,PRACTICE @7 PP4
#HGJ-HGA @7 .#A4 QUADRANTAL ANGLE .#C4
@1 @1 .#G4 @1 @1 @1 .#AC4 S9 .K #A1 COS
.K #J1 TAN .K UNDEF9$1 ESC .K #A1 SEC .K
UNDEF9$1 COT .K #J .#AE4 S9 .K --#A1 COS
.K #J1 TAN .K UNDEF9$1 CSC .K --#A1 SEC
.K UNDEF9$1 COT .K #J .#AG4 #CJ;DG .#AI4
#AJ;DG .#BE4 .#BG4 #BI4 #CA4 .#CC4 @2 S9
#IJ;DG .K #A & COS #IJ;DG .K #J S TAN
#IJ;DG IS UNDEF9$ 2C Y _C DIVIDE 0Z]O B
COT @4
..#AC.C ,PRO#M .,SOLV+ @7 PP4 #HGA-HGB
@7 .#CE4 AB #AJ FT .#CG4 ,AB #AJD FT2
NO4 .,SAMPLE .ANSW]3 ,! 9ITIAL HEI<T T !
,F]RIS :EEL IS ABV ! GR.D IS N D\#D S !
5TIRE HEI<T IS N D\#D4
#CI4 A4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,ANGLE .( .SPR9KL]1 @3 #BE;DG3
#CJ;DG3 #CE;DG3 #DJ;DG3 #DE;DG
,HORIZONTAL 4T.E WAT] TRAVELS1 .;D @3
#AE.J3 #AF.I3 #AH.D3 #AI.B3 #AI.E
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
.,ANGLE .( .SPR9KL]1 @3 #EJ;DG3
#EE;DG3 #FJ;DG3 #FE;DG
,HORIZONTAL 4T.E WAT] TRAVELS1 .;D @3
#AI.B3 #AH.D3 #AF.I3 #AE.J
.B4 #DE;DG2 S9CE IS 3/ANT1 ! MAXIMUM
4T.E TRAVEL$ W O3UR :5 S9 #B IS Z L>GE Z
POSSI#4 ,! MAXIMUM VALUE ( S9 #B O3URS
:5 #B .K #IJ;DG1 T IS1 :5 #J .K #DE;DG4
.C4 ,! 4T.ES >E ! SAME4
..#AC.D ,SKILL .,PRACTICE @7 P4 #HGH
@7 .#A4 9V]SE .#C4 .#E4 .#G4 .#I4 .#AC4
AB #A.BJ1 AB #FI.J;DG .#AE4 AB #A.IH1 AB
#AAC.F;DG .#AG4 AB --#J.BJ1 AB
--#AA.E;DG .#AI4 AB #J.AD1 AB #H.A;DG
.#BA4 AB #BJF.G;DG .#BC4 AB #BEB.F;DG
.#BE4 AB #BHD.E;DG .#BG4 AB #CH.G;DG
#BI.ABJ;DG .#CA4 .,SAMPLE .ANSW]3
#FJJ;DG
#AC.D ,PRO#M ,SOLV+ @7 PP4 #HGI-HHJ @7
.#CE4 AB #EC;DG
--------------------------------;,,SA#CI
,,SELECT$ ,,ANSW]S
.#CG4 ,AB #CB.I;DG2 AB #DF.D FT4
.,SAMPLE .ANSW]3 ,! PILE IS #AE FEET HI<
&! ANGLE ( REPOSE IS AB #CB.I;DG1 ! BASE
(! "R TRIANGLE =M$ IS AB #BC.B FEET4
,S9CE ? REPRES5TS ! RADIUS (! PILE1 Y
NE$ 6MULTIPLY 0#B 6GET ! DIAMET]4
.#CI4
..#AC.E ,SKILL .,PRACTICE @7 PP4
#HHF-HHG @7 .#A4 TWO ANGLE M1SURES &!
L5G? (A SIDE1 OR ! L5G?S ( TWO SIDES &!
M1SURE ( AN ANGLE OPPOSITE "O (! TWO
SIDES .#C4 ,,SSA2 "O TRIANGLE .#E4
,,SSA2 NO TRIANGLE .#G4 ,,ASA2 "O
TRIANGLE .#I4 ,,SSA2 NO TRIANGLE .#AA4
,,SSA2 "O TRIANGLE .#AC4 ,A #CG.F;DG1
.;,B #CH.D;DG1 .A #AE.G .#AE4 .;,B .K
#FE;DG1 .A #BC.H1 .;B #CB.B .#AG4 .;,C
.K #IE;DG1 .A #AG.F1 .;B #CG.H .#AI4
.;,B .K #AAI;DG1 .A #F.E1 .;C #H.E .#BA4
.;,B #ED.A;DG1 .;,C #HG.I;DG1 .;C #CJ.H1
OR .;,B #ABE.I;DG1 .;,C #AF.A;DG1 .;C
#H.F .#BC4 .;,B #CG.E;DG1 .;,C #BH.E;DG1
.;C #G.H .#BE4 .;,C .K #II;DG1 .A #FB.G1
.;C #HB.J .#BG4 ,! SIDES 7 N PAIR$ ) _!
OPPOSITE ANGLES2 @1 .;,C #DC.J;DG4 .#BI4
AB #DA.J .#CA4 AB #BIA.I .#CC4 AB #AH.I
.#CE4 AB #AGF.B .#CG4 AB #BHE.F .#CI4 AB
#BJE.C
#AC.E ,PRO#M ,SOLV+ @7 PP4 #HHG-HHH @7
.#DC4 AB #AIC.F FT1 AB #BAB.I FT .#DE4
.A4 .B4 ?IRD SIDE3 AB #GJ.D FT2 O!R
ANGLES3 AB #DG.F;DG1 AB #GD.D;DG C4 #I
BAGS .#DG4 .A4 AB #AEB.I ;M
..#AC.F ,SKILL .,PRACTICE @7 PP4
#HIB-HIC @7 .#A4 SEMIP]IMET] .#C4 LAW (
COS9ES .#E4 LAW ( S9ES .#G4 LAW ( S9ES
.#I4 .;,B #CJ.G;DG1 .;,C #CE.C;DG1 .A
#DA.A .#AA4 .,A #AAJ.D;DG1 .;,C
#DD.F;DG1 .;B #C.FJ .#AC4 .,A #CJ.C;DG1
#E #ABH.D;DG1 .;,C #BA.C;DG .#AE4 .,A
#EE.G;DG1 #E #GF.C;DG1 .;C #AE.C .#AG4
.,A #DB.F;DG1 .;,B #AA.G;DG1 .;,C
#ABE.G;DG .#AI4 .,A #CF.G;DG1 .;,B
#DG.C;DG1 .;C #EH.B .#BA4 AB #AJD .#BC4
AB #AAJH.F .#BE4 AB #BE .#BG4 AB #ACA.I
.#BI4 AB #BBEI.G .#CA4 AB #IID.C .#CE4
,S9CE Y >E LOOK+ = .,A ! EQU,N %D 2 .A
#B .K .;B #B @+ .;C #B -- #B .BC COS .,A
@2 #AH #B .K #AE #B @+ #AJ #B --#B7#AE7
7#AJ7 COS .,A1 .,A COS --#A #J.JJCC
#HI.H;DG4 .#CG4 .,A .K #DE;DG1 .;B
#BE.B1 .;C #AE.C .#CI4 .,A #FH.B;DG1
.;,C #BA.H;DG1 .;B -- #AF.B .#DA4 .,A --
#IC.G;DG1 .;,B -- #CC.I;DG1 .;,C --
#EB.D;DG
..#AC.F ,PRO#M .,SOLV+ @7 PP4 #HIC-HID
@7 .#DC4 AB #AAI.F;DG .#DE4 ,AB #AI.H
ACRES4 .,SAMPLE .ANSW]3 ,F9D !N F9D !
>EA ( .,,ACD & .,,ABC US+ ,H]ON'S =MULA4
.#DG4 .A4 AB #B.F MI .B4 AB #C ;H #DE M9
.C4 ,AB #A ;H #DF M92 #GI.B;DG ;,W ( ,N4
.,SAMPLE .ANSW]3 ,! ANGLE AT HIK] #A IS
#GI.B;DG & Y H P>ALLEL L9ES AT EA* HIK]
PO9T+ 9 ! ,NOR? DIREC;N4 ,! ANGLE AT
HIK] #B IS !N AN ALT]NATE 9T]IOR ANGLE1
& IS 3GRU5T4
#AC.F ,PRO#M ,SOLV+ ,"W%OP @7 P4 #HIE
@7
.#A4 AB #HA.I .#C4 AB #DFAI.E .#E4 AB
#GIB.F FT #B
.,*APT] .,REVIEW @7 PP4 #HIH-IJJ @7
.#A4 ,AN ANGLE 9 /&>D POSI;N HAS XS
V]TEX AT ! ORIG91 & XS 9ITIAL SIDE LIES
ON ! POSITIVE .;X -AXIS4 .#C4 UNIT
CIRCLE .#E4 .,SAMPLE .ANSW]3 ,! LAW (
S9ES IS A RATIO RELAT+ ! S9E ( AN ANGLE
& XS CORRESPOND+ SIDE 6! O!R ANGLES &
CORRESPOND+ SIDES4 .#G4 AB #BF.F ;M .#I4
.#AA4 #CCJ;DG .#AC4 .#AE4 #B .#AG4 AB
#AI.E;DG .#AI4 .,A #CA.G;DG1 .;,C
#DD.C;DG1 .A #AC.E .#BA4 .,A .K #DG;DG1
.A #AF.I1 .;C -- #BB.A .#BC4 .,A
#EH.G;DG1 .;,C #DF.C;DG1 .;B -- #BB.F
,*APT] #AD
#AD.A ,SKILL ,PRACTICE @7 PP4 #IAB-IAC
@7
.#A4 P]IOD .#C4 .#E4 #A1 #B
.#G4 .#I4
.#AG4 .#AI4
.#BE4 .,SAMPLE .ANSW]3 ,! RISE & FALL
(! TIDES V]SUS "T4
#AD.A ,PRO#M ,SOLV+ @7 PP4 #IAC-IAD @7
.#BI4 #H IN4
.#CA..A4 .B4 ,S9CE ! HI< PO9T O3URS AT
.;T .K #J1 ! COS9E FUNC;N BE/ REPRES5TS
SITU,N4
--------------------------------;,,SA#DJ
,,SELECT$ ,,ANSW]S
..#AD.B ,SKILL .,PRACTICE @7 PP4
#IAI-IBA @7 .#A4 #C .#C4 ;,E .#E4 ;,D
.#G4 ,A
.#I4 .#AA4
.#BC4 .#BE4
.#CG4 .#CI4
.#DC4 .;Y .K #C S9 @7 .;X -- @7 @+ #B
.#DE4 .#DG4 ,! GRAPH ( .;Y .K COS .;X C
2 OBTA9$ 0TRANSLAT+ ! GRAPH ( .;Y .K S9
.;X EI 6! LEFT 0OR 6! "R @4
#AD.B ,PRO#M ,SOLV+ @7 PP4 #IBA-IBB @7
.#EA4 .;H .K #C.GE COS 7#BJJ .;T @7
.#EC4 .A4 .;D .K --#CJJ TAN @+ #BJJ
.B4 .C4 AB #AH.D;DG
..#AD.C ,SKILL .,PRACTICE @7 PP4
#IBG-IBH @7 .#A4 ,A TRIGONOMETRIC EQU,N
T IS TRUE = ALL VALUES ( 9 XS DOMA9 .#C4
@1 @1 .#G4 @1 .#AA4 --TAN .#AC4 SEC
.#AE4 S9 #B .;X .#AG4 #A .#AI4 S9 .;X
.#BA4 --#A .#BC4 TAN @7-- .;X @7 .K--TAN
@7 .;X @7@1 S ,/EP #A US$ AN 9CORRECT
SUB/ITU;N2 @4 .#BE4 .#BG4 .#BI4 .#CA4
.#CC4 .#CE4 S9 .;X @1 ESC .;X @1 TAN .;X
@1 COT .;X @2 COS .;X @1 SEC .;X .#CG4
#AD.C ,PRO#M ,SOLV+ @7 PP4 #IBI-ICJ @7
.#CI4
.#DA..A4
.B4
B4
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 #J3 @3 @3 @3 --@3 @3
.;R @3 #CE.F3 #C.DJ3 #A.JG3 #J.FCD3
#J.EDC3 #J.FCD3 #A.JG
AB #EJ1EJJ1JJJ MI1 AB #C1CAJ1HJJ1JJJ
MI .#DC4 ,! VALUE ( TAN 9CR1SES Z !
VALUE ( S9 9CR1SES &! VALUE ( COS
DECR1SES2 @1 & S ON4
..#AD.D ,SKILL .,PRACTICE @7 PP4
#ICE-ICF @7 .#A4 ,A TRIGONOMETRIC ID5T;Y
IS TRUE = ALL R1L VALUES ( .;X ": A
TRIGONOMETRIC EQU,N IS ONLY TRUE = "S
SPECIFIC VALUE7;S7 ( .;X @4 #C.B @+ #C
COS 7#D7 .K #E .K #B @+ #C7#A7--#E .K #J
.#E4 .#G4 .#I4 .#AA4
--------------------------------;,,SA#DA
,,SELECT$ ,,ANSW]S
.#AC4 .#AG4 .#AI4 .#BA4 .#BC4 ,:5 TWO
NEGATIVE VALUES >E DIVID$1 ! QUOTI5T IS
POSITIVE2 @4 .#BE4 .#BG4 OR .#BI4 OR @+
#B .;N .#CA4 .#CC4 AB #J.EGB .#CE4 .#CG4
7#J1 #A7 .#CI4
..#AD.D ,PRO#M .,SOLV+ @7 PP4 #ICF-ICG
@7 .#DA4 ,JULY #BF & ,NOVEMB] #BF
.#DC..A4 .B4 .,SAMPLE3
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 #AF3 #AG3 #AH3 #AI
.;,S @3 #I.AJIE3 #H.IHHG3 #H.HHBE3
#H.GHHD
,! FOLL[+ TA# IS 9 LI/ =MAT4
,H1D+S & COLUMNS >E SEP>AT$ 0A
COLON & "O BLANK CELL4 ,BLANK CELLS
3TA9 TWO DA%ES4
--@3 #ABJ3 #ABA3 #ABB3 #ABC
.;,S @3 #H.IBDF3 #H.IFAI3 #I.JJJE3
#I.JDJE
.C4 AB #AG;DG & AB #ABB;DG AB #ED.G;DG
..#AD.D ,PRO#M ,SOLV+ .,"W%OP @7 P4
#ICI @7 .#A4 AB #J.IHG1 AB #C.JA .#C4 AB
#J.BIH1 AB #J.GJB .#E4 AB #BB.F1 AB
#CG.D .#G4 #A3CB ,,AM1 #AJ3EB ,,AM1
#A3EF ,,PM1 #AA3AF ,,PM .#I4 AB #J.AG
SEC & AB #J.HC SEC
..#AD.E ,SKILL .,PRACTICE @7 PP4
#IDD-IDE @7 .#A4 ,! GRAPH ( S9E OR COS9E
FUNC;NS4 .#C4 .,SAMPLE .ANSW]3 .;Y .K #C
S9 #B .;X .#E4 .,SAMPLE .ANSW]3 .#G4
,6DET]M9E ! AMPLITUDE1 Y M/ TAKE HALF (!
DI6];E 2T ! MAXIMUM &! M9IMUM2 @4
.#I-.AG4 ,SAMPLE ANSW]S >E GIV54 .#I4
.#AA4 .;Y .K --COS #C .;X @+ #D .#AC4
.#AE4 .#AG4 .#BA4 @2 7,4T4 PROP]TY72
7,NEG4 ANGLE ID5T;Y72 .;Y .K #C S9 #D
.;X @+ #B 7,C(UNC;N ID5T;Y7
#AD.E ,PRO#M ,SOLV+ @7 PP4 #IDE-IDF @7
.#BC4 .;,V .K #AJJ S9 #D .;T .#BE4 .;H
.K #B.E S9 .;T @+ #F.E .#BG4 .A4 .;,N .K
#C.FH S9 7#J.GGF .;T -- #J.GJC7 @+ #BJ.D
.B4 AB #BC1AJJ EMPLOYEES
..#AD.F ,SKILL .,PRACTICE @7 PP4
#IEB-IEC @7 .#A4 S9 @7 .A @+ .;B @7 .K
S9 .A COS .;B @+ COS .A S9 .;B @1 S9 @7
.A -- ;B7 .K S9 .A COS .;B -- COS .A S9
.;B @1 COS @7 .A @+ .;B @7 .K COS .A COS
.;B -- S9 .A S9 .;B @1 COS @7 .A -- .;B
@7 .K COS .A COS .;B @+ S9 .A S9 .;B @1
TAN @7 .A @+ .;B @7 .K .#C4 .#E4 .#G4
.#I4 .#AA4 #J7S9 @7 .K COS .#AC4 .#AE4
.#AG4 .#AI4 TAN .;X .#BA4 COS .;X .#BC4
COS .;X #BE4--COS .;X .#BG4 --COT .;X
.#BI4 --COT .;X .#CA4 ,! SIGN 9 !
DENOM9ATOR %D 2 NEGATIVE :5 US+ ! SUM
=MULA2 @4 .#CC4 .#CE4 AB #E.FFH .#CG4
..#AD.F ,PRO#M .,SOLV+ @7 PP4 #IEC-IED
@7 .#DA4 AB #AE M9 #DH SEC .#DC..A4 .B4
..#AD.G ,SKILL .,PRACTICE @7 PP4
#IEI-IFJ @7 .#A4 D\# ANGLE .#C4 .#E4
.#G4 .#I4 .#AC4 .#AE4 .#AG4 .#AI4 .#BA4
#A .#BC4 .#BE4 COS--#A .#BI4 ,! CORRECT
HALF ANGLE =MULA IS .#CA4 S9 #C .K S9
7#B @+7 .K S9 #B COS @+ COS #B S9 .K #B
S9 COS COS @+ 7#B COS #B -- #A7 S9 .K #B
S9 COS #B @+ 7#B COS #B -- #A7S9 .K S9
7#B COS #B @+ #B COS #B -- #A7 .K S9 7#D
COS #B #A7 .#CC4 #B S9 .;X 7#A--COS .;X
@7 .K #B S9 .;X -- #B S9 .;X COS .;X .K
#B S9 .;X -- S9 #B .;X .#CE4 COS #D .K
COS 7#B @+ #B7 .K COS #B COS #B--S9 #B
S9 #B--7COS #B -- S9 #B @7 #B -- 7#B S9
COS @7 #B .K COS #D -- #B COS #B S9 #B
@+ S9 #D --#D S9 #B COS #B .K COS #D #F
S9 #B COS #B #J @+ S9 #D .#CG4 .#CI4
.#DA4 .#DC4 ,! VALUE ( TAN 9CR1SES Z !
VALUE ( S9 9CR1SES &! VALUE ( COS
DECR1SES2 @1 @1 & S ON4
--------------------------------;,,SA#DB
,,SELECT$ ,,ANSW]S
#AD.G ,PRO#M ,SOLV+ @7 PP4 #IFA-IFB @7
.#EA4 #BD.C;DG "K.K "K.K #FE4 #G;DG
.#EC4 AB #DG.B;DG
.#EE..A4
.B4 @2 AB #CF.G;DG OR AB #EH.H;DG .C4
.,SAMPLE .ANSW]3 ,! P]SON AIMS T[>D !
BASKET &! BALL DOES N B\NCE (F ! RIM4
.,*APT] .,REVIEW @7 PP4 #IFE-IFH @7
.#A4 CYCLES .#C4 P]IOD .#E4 FREQU5CY
.#G4
.#I4
.#AA4
.#AC4
.#AE4
.#AG4 SEC #C .;X .#AI4 --S9 #B .#BA4
.#BC4 @1 .#BE4 .,SAMPLE .ANSW]3 .;Y .K
COS .;X -- #B .#BG4 .#BI4 .#CA4 .#CC4
.#CE4
,SKILLS ,REVIEW ,H&BOOK
..,OP],NS ) ,POSITIVE & ,NEGATIVE
.,NUMB]S @7 P4 #IGE @7 .#A4 --#F .#C4
--#FJ .#E4 #B .#G4 #H .#I4 #DD .#AA4
--#D .#AC4 #AB .#AE4 --#GB .#AG4 --#B
.#AI4 --#C .#BA4 #I .#BC4 #F .#BE4 --#AE
.#BG4 --#AB .#BI4 #E .#CA4 #DB .#CC4
--#AG .#CE4 #B
..,FRAC;NS1 ,DECIMALS,& .,P]C5TS @7 P4
#IGF @7 .#A4 .#C4 .#E4 .#G4 .#I4 .#AA4
#J.BE .#AC4 #A.B .#AE4 #J.CGE .#AG4
#A.DB .#AI4 #J.C .#BA4 #FJ@3P .#BC4
#ACJ@3P .#BE4 #DE@3P .#BG4 #HJ@3P .#BI4
#BEJ@3P
..,CALCULAT+ ) .,P]C5TS @7 P4 #IGG @7
.#A4 #AIF .#C4 #CH.D .#E4 #AG .#G4 #A
.#I4 #ED@3P .#AA4 #AJ@3P .#AC4 #BJ@3P
.#AE4 #B@3P .#AG4 #HJ .#AI4 #FJ .#BA4
#GJ .#BC4 #H .#BE4 #BE@3P DECR1SE .#BG4
#EJ@3P 9CR1SE .#BI4 #IF@3P 9CR1SE .#CA4
#GI@3P DECR1SE
..,FACTORS & .,MULTIPLES @7 P4 #IGI @7
.#A4 #B 99 #C 99 #G .#C4 #C 99 #E #B
.#E4 #B 99 #E 99 #G .#G4 #B #C 99 #C #B
.#I4 PRIME .#AA4 #B #C 99 #AA .#AC4
PRIME .#AE4 #B #E .#AG4 #H .#AI4 #AA
.#BA4 #D .#BC4 #C .#BE4 #AJ .#BG4 #C
.#BI4 #A .#CA4 #AF .#CC4 #CJ .#CE4 #BD
.#CG4 #F .#CI4 #CF .#DA4 #CJ .#DC4 #DJ
.#DE4 #HIA .#DG4 .#DI4 .#EA4 .#EC4 .#EE4
.#EG4 .#EI4 .#FA4 .#FC4 .#FE4 .#FG4
.#FI4
..,RATIOS & .,PROPOR;NS @7 P4 #IHJ @7
.#A4 #A 6#C1 #A3C1 .#C4 #E 6#D1 #E3D1
.#E4 #E 6#F1 #E3F1 .#G4 #A 6#A1 #A3A1
.#I4 #D 6#I1 #D3I1 .#AA4 #G 6#A1 #G3A1
.#AC4 #G .#AE4 #BJ .#AG4 #B .#AI4 #E
.#BA4 #DJ .#BC4 #F.GE .#BE4 #II .#BG4
#GB
..,3V]T+ ,UNITS ( .,M1SURE;T @7 P4
#IHA @7 #A.FJJJ .#C4 #E .#E4 #G.G .#G4
#AF .#I4 #DJJJ .#AA4 #J.H .#AC4 #F .#AE4
#A.E .#AG4 #CFJJ .#AI4 #C .#BA4 .#BC4
#FC1CFJ .#BE4 #B .#BG4 #DJJJ
.,SCI5TIFIC .,NOT,N @7 P4 #IHB @7 .#A4
#F * #AJ --#A .#C4 #H * #AJ --#B .#E4
#D.JH * #AJ #A .#G4 #C.HE * #AJ --#D
.#I4 #D.ABCF * #AJ #D .#AA4 #D.HF * #AJ
#E .#AC4 #A.JJB * #AJ --#B .#AE4 #G.JEJE
* #AJ #C .#AG4 #I.HE * #AJ #C .#AI4
#H.JE * #AJ #B .#BA4 #EJJJ .#BC4 #J.HB
.#BE4 #J.JJCB .#BG4 #GCD1EJJ .#BI4
#A.HAD .#CA4 #A1JJJ1JJJ .#CC4 #J.JJJJJH
.#CE4 #A1HGJ1JJJ1JJJ .#CG4 #F1JHJ1JJJ
.#CI4 #CD1JAJ1JJJ
.,SIGNIFICANT .,DIGITS @7 P4 #IHC @7
.#A4 #FJJ .#C4 #HA .#E4 #A.HHE .#G4 #D.I
.#I4 #AIE .#AA4 #J.JCF .#AC4 #AJJI .#AE4
#AH .#AG4 4#AG.DJ .#AI4 #B.E P9TS P]
/UD5T .#BA4 #BEDC BOOKS P] LIBR>Y .#BC4
4#ABEJ
..,WRIT+ ,ALGEBRAIC .,EXPRES.NS @7 P4
#IHD @7 .#A4 .;N @+ #H .#C4 #B .;N .#E4
.;N .#G4 #E .;N .#I4 #J.BE .;N .#AA4 .;N
-- #B .#AC4 .;C -- #D;YR .#AE4 .;X @+ #E
DOLL>S .#AG4 #DE -- .;M M9 .#AI4 #AJ .;X
DOLL>S
.,BINOMIAL .,PRODUCTS @7 P4 #IHE @7
.#A4 .A #B @+ #H .A @+ #AE .#C4 .;T #B
@+ #AE .;T @+ #EF .#E4 .;Y #B @+ #F .;Y
@+ #H .#G4 .;Y #B -- #D .;Y @+ #D .#I4
.;Z #B -- #H .;Z @+ #AF .#AA4 .;Y #B
--#D .;Y -- #BA .#AC4 #BE .;X #B -- #AF
.#AE4 #B .;C #B @+ #C .;C -- #CE .#AG4
-- .;Z #B @+ #DI .#AI4 #AF .A #B @+ #BD
.A @+ #I .#BA4 -- .;X #B --#D .;X @+ #CB
.#BC4 -- .A #B @+ #AH .A -- #HA .#BE4
#AJ .;X #B -- #BA .;X -- #AJ .#BG4 --#BD
.;Z #B @+ #BB .;Z -- #C
..,,LCD,'S ( ,R,NAL .,EXPRES.NS @7 P4
#IHF @7 .#A4 #B .A #B .;B .#C4 .;Z #C
.#E4 #ABF .;M .#G4 #C .;Y #B .#I4 @7 .;N
@+ #B7@7 .;N -- #B7 .#AA4 #E7 .;N @+ #A7
.#AC4 #F7 .;M -- #C7 .#AE4 @7 .;X -- #D7
#B .#AG4 #B .;N #C 7#E .;N @+ #D7 .#AI4
@7 .;K @+ #C7 #D .#BA4 #GJ7 .;N @+ #B7
.#BC4 @7 .A @+ #B7 #B .#BE4 @7 .;K --
#C7@7 .;K -- #B7 .#BG4 @7 .;M -- #G7@7
.;M -- #D7@7 .;M #B @+ #E .;M -- #DE7
--------------------------------;,,SA#DC
,,SELECT$ ,,ANSW]S
,! ,COORD9ATE ,PLANE @7 P4 #IHG @7
.#A-.BJ4
.#BA4 7#B1 #E7 .#BC4 7#E1 --#E7
.#BE4 7#D1 #J7 .#BG4 7#E1 #D7
.#BI4 7#D1 --#B7 .#CA4 7--#B1 #J7
.#CC4 7--#B1 #B7 .#CE4 7#B1 --#D7
.#CG4 7#B1 --#A7 .#CI4 7--#A1 #E7 .#DA4
7--#D1 --#C7 .#DC4 7#A1 --#C7
,TRANS=M,NS @7 P4 #IHI @7
.#A4 7#C1 --#H7 .#C4 7--#C1 #AA7 .#E4
7#H1 #C7 .#G4 7--#H1 --#C7
.#I4
.#AA4
.#AI4
.#BA4
.,L9E .,SYMMETRY @7 P4 #IIJ @7 .#A4
N"O .#C4 #A .#E4 N"O .#G4 #B .#I4 7--#D1
--#A7 .#AA4 7--#B1 #B7
..,P]IMET] & .,>EA @7 P4 #IIA @7 .#A4
#AJ CM1 #F CM #B .#C4 #BF IN41 #BD IN4
#B .#E4 #DH YD1 #HD YD #B .#G4 #AD ;M1
#AJ.H ;M #B
..,CIRCUMF];E & ,>EA (A .,CIRCLE @7 P4
#IIB @7 .#A4 .;,C .K #AJ IN4 OR AB #CA
IN41 .,A .K #BE IN4 #B OR AB #GI IN4 #B
.#C4 .;,C .K #H IN4 FT OR AB #BE IN41
.,A .K #AF IN4 #B OR AB #EJ IN4 #B .#E4
.;,C .K #BD FT OR AB #GE FT1 .,A .K #ADD
FT #B OR AB #DEB FT #B .#G4 .;,C .K #F
FT OR AB #AI FT1 .,A .K #I FT #B OR AB
#BH FT #B .#I4 .;,C .K #B CM OR AB #F
CM1 .,A .K CM #B OR AB #C CM #B .#AA4
.;,C .K #BB IN4 OR AB #FI IN41 .,A .K
#ABA IN4 #B OR AB #CHJ IN4 #B
..,SURFACE ,>EA & .,VOLUME @7 P4 #IIC
@7 .#A4 #AEH IN4 #B @1 #ABJ IN4 #C .#C4
#ED CM #B @1 #BG CM #C .#E4 #AED YD #B
OR AB #DHD YD #B @1 #AIF YD #C OR AB
#FAF YD #C
.,ANGLE .,REL,N%IPS @7 P4 #IID @7 .#A4
#CI .#C4 #H .#E4 #AF .#G4 #BC .#I4 #BI
.,TRIANGLE .,REL,N%IPS @7 P4 #IIE @7
.#A4 #DJ .#C4 #FJ .#E4 #EJ CM .#G4 #AB
FT .#I4 #EE;DG
..,3GRU5T & ,SIMIL> .,FIGURES @7 P4
#IIG @7 .#A4 SIMIL> .#C4 3GRU5T .#E4
3GRU5T .#G4 NEI .#I4 3GRU5T .#AA4 #AA.E
.#AC4 #AD .#AE4 #DJ .#AG4 #G
..,M ,PRO#M ,SOLV+ .,/RATEGIES @7 P4
#III @7 .#A4 #D3AE ,P4,M4 .#C4 #F WAYS
.#E4 #DJ "PS .#G4 #H DIMES1 #E NICKELS
.,LOGICAL .,>GU;T @7 P4 #AJJA @7 .#A4
VALID2 ,*A9 ,RULE .#C4 9VALID .#E4
VALID2 .,& ,RULE .#G4 VALID2 .,OR ,RULE
.#I4 9VALID .#AA4 TRUE .#AC4 FALSE .#AE4
TRUE .#AG4 TRUE .#AI4 FALSE .#BA4 TRUE
..,3DI;NAL ,/ATE;TS & .,C.T]EXAMPLES
@7 P4 #AJJC @7 .#A4 ,IF Y H ! EQU,N .;Y
.K .MX @+ .;B @1 !N Y H ! GRAPH (A L9E2
IF Y H ! GRAPH (A L9E1 !N Y H ! EQU,N
.;Y .K .MX @+ .;B @1 FALSE4 .#C4 ,IF
,A2Y F9I%ES H] HOME"W1 !N %E C G SWIMM+2
IF ,A2Y GOES SWIMM+1 !N %E F9I%$ H]
HOME"W1 FALSE4 .#E4 ,IF #D .;X @+ #H .K
#BH1 !N .;X .K #E2 IF .;X .K #E1 !N #D
.;X @+ #H .K #BH1 TRUE4 .#G4 ,TRUE2 IF
TWO L9ES >E P]P5DICUL>1 !N !Y 9T]SECT
6=M A "R ANGLE & IF TWO L9ES 9T]SECT 6=M
A "R ANGLE1 !N !Y >E P]P5DICUL>4 .#I4
,FALSE2 N ALL ORANGE VEGETA#S >E C>ROTS4
.#AA4 ,FALSE2 ! 3V]SE IS N TRUE4 .#AC4
,FALSE2 Z]O IS NEI POSITIVE NOR
NEGATIVE4 .#AE4 ,FALSE4 .,SAMPLE .ANSW]3
,AN OCTAGON CD H EXACTLY #E 3GRU5T
SIDES4 .#AG4 ,FALSE2 .,A CD 2 9 2T .;,B
& ;,C & "!=E WD ONLY 2 #B 9*ES F ,C4
.#AI4 ,FALSE4 .,SAMPLE .ANSW]3 ,*>LIE CD
H #AJ DIMES4
,V5N ,DIAGRAMS @7 P4 #AJJD @7
.#A4
.#C4
.#E4 ,FALSE4 .,SAMPLE .ANSW]3 #AJ IS
EV51 B X IS N A MULTIPLE ( #C OR .#D4
.#G4 ,FALSE2 #A IS A POSITIVE ODD 9TEG]
&A FACTOR ( #AJ4 .#I4 ,TRUE2 #B IS !
ONLY EV5 PRIME NUMB]4
,M1N1 ,M$IAN1 ,MODE1 & ,RANGE @7 P4
#AJJE @7
.#A4 AB 4#FFD1 4#FGE1 4#FEJ1 4#CJJ
.#C4 #FHE M91 #GAC M91 N"O1 #FAA M9 .#E4
#DH COOKIES1 #DH COOKIES1 #DH COOKIES1
#BD COOKIES .#G4 4#I.BJ1 4#H.IJ1 N"O1
4#E.HE .#I4 #AE P1 #AD P1 #AJ P & #AH P
& #BB P1 #BE P
--------------------------------;,,SA#DD
,,SELECT$ ,,ANSW]S
..,GRAPH+ ,/ATI/ICAL .,DATA @7 P4
#AJJF @7 .#A4 #F ,P4,M4 #C.E D9]S2 YES
#E.AD D9]S .#G4 W9T] & SUMM] .#I4
NATURAL GAS #AA.EJ HOMES
.#AC4
,ORGANIZ+ ,/ATI/ICAL ,DATA @7 P4 #AJJI
@7
.#A4
#C4
,! FOLL[+ TA# IS 9 LI/$
=MAT4 ,= EA* CELL ! H1D+ IS %[N
FOLL[$ 0A COLON1 SPACE &! CELL
3T5TS
,/EM3 #C
,L1VES3 #J
,L1VES3 #J
,L1VES3 --
,L1VES3 --
,L1VES3 --
,/EM3 #D
,L1VES3 #B
,L1VES3 #G
,L1VES3 #I
,L1VES3 --
,L1VES3 --
,/EM3 #E
,L1VES3 #J
,L1VES3 #D
,L1VES3 #D
,L1VES3 #D
,L1VES3 #I
,/EM3 #F
,L1VES3 #E
,L1VES3 #E
,L1VES3 #G
,L1VES3 --
,L1VES3 --
,/EM3 #G
,L1VES3 #J
,L1VES3 #C
,L1VES3 --
,L1VES3 --
,L1VES3 --
,KEY3 #C_\#J .K #CJ
.#E4
.#G4
.#I4 #E .#AA4 #BC DOGS .#AC4 #DC LB
.#AE4 #BE *N .#AG4 #AB S;GS .#AI4 #AJ
S;GS2 #AH S;GS
,EXTRA ,PRACTICE
,*APT] #A @7 P4 #AJAJ @7
.#A4
.#C4
.#E4 #A.BE LB .#G4 #AE .#I4 #EB .#AA4
#F .;R #B -- #E .;R @+ #AB .#AC4 #H .;B
-- #BJ .#AE4 --#E .;M #B @+ #I .;M --
#AB .#AG4 #E .#AI4 --#AB .#BA4 #B
.#BC4 #AD .#BE4 .#BG4 .#BI4 .#CA4 .;Y
.K --#C .;X @+ #BE
.#CC4 .;X .1 #G
.#CE4 .;X "K.K#E
.#DC4 --#A1E .#DE4
.#DG4 .;C "K --#G OR .;C .1#G
.#DI4
.,*APT] .#B @7 P4 #AJAA @7 .#A4
,FUNC;N2 = EA* 9PUT "! IS EXACTLY "O
\TPUT4 .#C4 ,N A FUNC;N2 "! IS M ?AN "O
\TPUT =! 9PUT --#B4 .#E4 @2 FALLS .#G4
UNDEF9$2 IS V]TICAL .#I4 NEI .#AA4
.#AC4 .#AI4 .;Y .K #G .;X -- #C .#BA4
.;Y .K --#B .#BC4 .#BE4 .;Y .K #B .;X @2
--#D .#BG4
.#BI4 .A1 .B4 .C4 AB #CF
.#CA4 %IFT$ LEFT #C
.#CC4 %IFT$ D[N #B1 LEFT #A1 & V]TIC,Y
/RET*$
.#CE4
.#CG4
--------------------------------;,,SA#DE
,*APT] #C @7 P4 #AJAB @7
.#A4 7--#C1 --#G7
.#C4 7#B.E1A.GE7
.#E4 7#A1 --#B7 .#G4
.#I4
.#AA4
.#AC4 7#B1 --#G1E7 .#AE4 .#AG4 .#AI4
.#BA4 N DEF9$2 ! NUMB] ( COLUMNS 9 !
LEFT MATRIX DOES N EQUAL ! NUMB] ( R[S 9
! "R MATRIX4 .#BC4 #FF .#BE4 --#I .#BG4
7#C1 --#AD7
.#BI4 7#C1 --#C1 #A7 .#CA4 .#CC4
.#CE4 7#AD1 --#F7 .#CG4 7--#H1 --#C7
,*APT] #D @7 P4 #AJAC @7
.#A4
.#C4
.#E4
.#G4
.#I4 .;Y .K #G .;X #B @+ #DB .;X @+
#EF .#AA4 .;Y .K .;X #B -- #AD .;X @+
#EF
.#AC4 @7 .;X -- #B7 #B .#AE4 @7 .;X @+
#I7@7 .;X @+ #AB7 .#AG4 --#G1 #B .#AI4
--#AA1 #E .#BA4 7#B .;X -- #E7@7 .;X @+
#C7 .#BC4 N FACTORA# .#BE4 .#BG4 .#BI4
.#CA4 .#CC4 .#CE4 .#CG4 #AA --#C .;I
.#CI4 .#DA4 .#DC4 .#DE4 .#DG4 .#DI4 .;X
"K.K #J OR .;X .1.K #AJ .#EA4 --#J.FEC
"K .;X "K #G.FE .#EC4 .;Y .K #C .;X #B
@+ #B .;X -- #G .#EE4 .;Y .K --#B .;X #B
-- #F .;X @+ #CF
.,*APT] .#E @7 P4 #AJAD @7 .#A4 #I.EB
* #AJ #AA #C.E * #AJ #A .#E4 @2 P[] (A
PRODUCT PROP]TY1 NEGATIVE EXPON5T
PROP]TY .#G4 #G .;X #B .;Y #B @2 PRODUCT
( P[]S PROP]TY1 QUOTI5T ( P[]S PROP]TY1
NEGATIVE EXPON5T PROP]TY .#I4
.#AA4
.#AC4 --#C .;X #B @+ #C .;X -- #H
.#AE4 #C .;X #B @7 .;X @+ #C7 #B .#AG4
@7 .;X -- #B7@7 .;X @+ #B77#B .;X @+ #A7
.#AI4 +- #D .#BA4 .#BC4 .#BE4 POSITIVE3
#B OR #J1 NEGATIVE3 #A1 IMAG9>Y3 #B OR
#J .#BG4 POSITIVE3 #A1 NEGATIVE3 #A1
IMAG9>Y3 #B .#BI4 7--#A.E1 --#D7 LOCAL
M9IMUM1 7#J1 #J7 LOCAL MAXIMUM1 7#A.E1
--#D7 LOCAL M9IMUM2 7--#B1 #J71 7#J1
#J71 7#J1 #J71 7#B1 #J71 DEGREE #D .#CA4
.;Y .K #J.E .;X #C @+ .;X #B @+ #B .;X
-- #A
.,*APT] .#F @7 P4 #AJAE @7 .#A4 +-#C
.#C4 --#C .#E4 #CB .#G4 #AF .#I4 +-#C
.#AA4 +-#B.AE .#AC4 .#AE4 #C .#AG4 .#AI4
.#BA4 .#BC4 .#BE4 .;X #C @+ .;X -- #D1
ALL R1L NUMB]S .#BG4 @1 ALL R1L NUMB]S
EXCEPT .;X .K #J .#BI4 @1 ALL R1L NUMB]S
.#CA4 .;X @1 ALL R1L NUMB]S .#CC4 @1
.#CE4 .#CG4 .#CI4 .#DA4 DOMA93 ALL R1L
NUMB]S1 RANGE3 ALL R1L NUMB]S
--------------------------------;,,SA#DF
,,SELECT$ ,,ANSW]S
.#DC4 DOMA93 .;X .1.K --#B1 RANGE3 .;Y
.1.K --#C .#DI4 #C .#EA4 --#A .#EC4 #C
.#EE4 #A1 #C
.,*APT] .#G @7 P4 #AJAF @7 .#A4 DOMA93
ALL R1L NUMB]S1 RANGE3 .;Y .1 #J .#C4
DOMA93 ALL R1L NUMB]S1 RANGE3 .;Y .1
--#B .#E4 DOMA93 ALL R1L NUMB]S1 RANGE3
.;Y .1 #J .#G4 DOMA93 ALL R1L NUMB]S1
RANGE3 .;Y .1 --#B .#I4 .#AA4 #I .;E #D
.;X .#AC4 DOMA93 ALL R1L NUMB]S1 RANGE3
.;Y .1 #J .#AE4 DOMA93 ALL R1L NUMB]S1
RANGE3 .;Y .1 #C .#AG4 --#B .#AI4 #C
.#BA4 .;X .#BC4 #B .;X .#BE4 DOMA93 .;X
.1 #J1 RANGE3 ALL R1L NUMB]S .#BG4
DOMA93 .;X .1 #J1 RANGE3 ALL R1L NUMB]S
.#BI4 LOG #E #B @+ LOG #E .;X -- #A
.#CA4 LN #BJ @+ #C;LN .;X @+ #B LN .;Y
.#CC4 LOG #D #BJ .;X #D .#CE4 .#CG4 AB
#C.AFA .#CI4 AB #A.FID .#DA4 #A .#DC4 NO
SOLU;N .#DE4 #C .#DG4 .#DI4 .;Y .K #D @*
#A ;X .#EA4 .#EC4 .;Y .K #J.ECH @* .;X
#B.FAA
.,*APT] .#H @7 P4 #AJAG @7 .#A4 .#C4
.#E4 9V]SE V>I,N .#G4 NEI V>I,N .#I4
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.,*APT] .#I @7 P4 #AJAH @7 .#A4 @2
7#J1 #B7 .#C4 @2 7#A1 #D7 .#E4 .#G4 .#I4
#B .#AA4 #E .#AC4 .;X #B @+ .;Y #B .K
#FD .#AE4 .;X #B @+ .;Y #B .K #EJ .#AG4
7+-#I1 #J71 7#J1+-#D71 .#AI4 7#J1
+-#AB71 7+-#H1 #J71 .#BA4 .#BC4 .#BE4
7+-#F1J71 @1 .#BG4 7#J1 +-#I71 @1 .#BI4
.#CA4 C5T]3 7#C1 #J71 V]TICES3 7--#B1
#J7 7#H1 #J71 CO-V]TICES3 7#C1 #C7 7#C1
--#C71 FOCI3 7--#A1 #J7 7#G1J7 .#CC4
C5T]3 7--#A1 #D71 V]TICES3 7--#A1 #E7
7--#A1 #C71 FOCI3 @1 ASYMPTOTES3 .#CE4
ELLIPSE1 .#CG4 P>ABOLA1 @7 .;X -- #C7 #B
.K #D7 .;Y -- #B7 .#CI4 7#J1 --#B7 7#G1
#E7
.,*APT] .#AJ @7 P4 #AJAI @7 .#A4 .A4
#AJJ1JJJ1JJJ PASS^WS .B4 #A1HAD1DJJ
PASS^WS .#C4 .A4 #AAH1HAC1GFJ PASS^WS
.B4 #GH1ICF1JJJ PASS^WS .#E4 #BJ .#G4
#CFB1HHJ .#I4 #ABFJ .#AA4 #FJD1HJJ .#AC4
#CE .#AE4 #AJ .#AG4 .;X #C -- #I .;X #B
@+ #BG .;X -- #BG .#AI4 .;P #AJ @+ #BJ
.;P #H @+ #AFJ .;P #F @+ #FDJ .;P #D @+
#ABHJ .;P #B @+ #AJBD .#BA4 .#BC4 .#BE4
.#BG4 .#J4 #H .#BI4 .#J4 #F2 N 4JO9T
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.#CA4 .#J4 #AG2 N 4JO9T .#CC4 .A4 .B4
.#CE4 .A4 .B4 .#CG4 AB #J.JDAG .#CI4 AB
#J.JJJJCJE
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--#C1 #AE1 #D.IIA .#E4 #C.DE1 #D.D1
#E.G1 #I1 #C.JI .#G4 #DA.E1 #CG.E1 #CF1
#BC1 #H.BBA2 #DC.E1 #CI.E1 #CH1 #BC1
#H.BBA .#I4 #B1 #B.E1 --#B1 #AJ1 #C.E2
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.,*APT] .#AB @7 P4 #AJBA @7 .#A4
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#EC.C .#BC4 #BGC4 #E .#BE4 AB .#BE4 #H
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#B.E1 .A ;N .K #B7 .A .;N -- #A @7 .#CE4
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--#AJ
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#AJ1 .#I4 .;,B .K #GB;DG1 .A #E.EFB1 .;B
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#AB CM1 #GB CM #B .#AI4 #CJ;DG .#BA4
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AB #AHI
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.#AG4 .#AI4 .#BA4
.#BC4 AB .#A4 #BIIE .#BE4 .#BG4 .#BI4
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,VISIT _+CLASSZONE.COM_: & GET 3NECT$
,ONL9E RES\RCES = /UD5TS & P>5TS
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,*APT]-,BAS$ ,SUPPORT
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SUPPORT1 ACTIVITIES1 & EXAMPLES HELP
/UD5TS SU3E$4
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_+CLASSZONE.COM_:
,ANIMAT$ ,,ALGEBRA AT
_+CLASSZONE.COM_:
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,! FOLL[+ TA# IS 9 LI/ =MAT4
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.,*#..A @3 ,EQU,NS & ,9EQUALITIES
.#B @3 ,L9E> ,EQU,NS & ,FUNC;NS
.#C @3 ,L9E> ,SY/EMS & ,MATRICES
.#D @3 ,QUADRATIC ,FUNC;NS & ,FACTOR+
.#E @3 ,POLYNOMIALS & ,POLYNOMIAL
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.#F @3 ,R,NAL ,EXPON5TS & ,RADICAL
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.#G @3 ,EXPON5TIAL & ,LOG>I?MIC
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.#H @3 ,R,NAL ,FUNC;NS
.#I @3 ,QUADRATIC ,REL,NS & ,3IC
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.#AA @3 ,DATA ,ANALYSIS & ,/ATI/ICS
.#AB @3 ,SEQU;ES & ,S]IES
.#AC @3 ,TRIGONOMETRIC ,RATIOS &
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.#AD @3 ,TRIGONOMETRIC ,GRAPHS1
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,,ISBN-#AC3 #IGH-J-FAH-HAAHA-F
,,ISBN-#AJ3 #J-FAH-HAAHA-H
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