Elementary Education Chapter 1 Center City East Parking Garage has a capacity of 256 cars more

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Ch.1 EquationsandInequalities

1.1 LinearEquations

1 SolveaLinearEquation

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Solvetheequation.

1) 5x=–5

A) {–1} B) {1} C) {5} D) {–5}

2) 3x=10

A) 10

3B) –10

3C) 3

10 D) –3

3) 2x+8=0

A) {–4} B) {4} C) {2} D) {–2}

4) 3x–5=0

A) 5

3B) –5

3C) 3

5D) –3

5) 10x+8=0

A) –4

5B) 4

5C) 5

4D) –5

6) 5

6x=1

A) 3

10 B) 10

3C) –3

10 D) –3

7) 16x=–3+15x

A) {–3} B) {3} C) {–2} D) {12}

8) 7x–12=3x–48

A) {–9} B) {9} C) {–12} D) {12}

9) –7x+72=2x+18

A) {6} B) {–6} C) {8} D) {–8}

10) –4–8x=4–4x

A) {–2} B) {2} C) {–1} D) {1}

11) 7x–(2x–1)=2

A) 1

5B) 1

9C) –1

5D) –1

12) 4(3x–1)=16

A) 5

3B) 1 C) 17

12 D) 5

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13) 14(4x–4)=5x–5

A) 1 B) 61

51 C) –1 D) 51

14) 6(x+5)=7x–(3–x)

A) 51

8B) –15

4C) 15

4D) –51

15) 5(x+5)=6(x–6)

A) {61} B) {–61} C) {–11} D) {6}

16) 3(2x–2)=5(x+2)

A) {16} B) {–4} C) {–16} D) {7}

17) 7(x+5)=(7x+35)

A) allrealnumbers B) {70} C) {0} D) nosolution

18) 3x+7+4(x+1)=4x+5

A) –2B) 11

8C) 4

5D) {4}

19) –9x+6+7x=–2x+11

A) nosolution B) {5} C) {–6} D) allrealnumbers

20) x

–4=1

A) {20} B) {–20} C) {12} D) {–12}

21) x

–1

=–2

A) {–9} B) {9} C) {–11} D) {11}

22) 2x

=4+x

A) {60} B) {–60} C) {120} D) {–120}

23) x

–1=x

+7

A) –48 B) 48 C) –4

3D) 4

24) 1

+x

=11

A) 7

2B) –7

2C) 7

4D) –7

25) –10.4x+1.7=–15.7–1.7x

A) {2} B) {–26} C) {1.7} D) {1.8}

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26) 5x+3

+9

=–7x

A) –36

29 B) 18

29 C) –18

29 D) –36

2 SolveEquationsThatLeadtoLinearEquations

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Solvetheequation.

1) 1–4

=9

A) 40

3B) –40

3C) –5 D) 8

2) 5

+2

=7

A) {5} B) {–5} C) {2} D) {–2}

3) (x+9)(x–1)=(x+1)2

A) 5

3B) 3

2C) 10

9D) {10}

4) x(2x–1)=(2x+1)(x–2)

A) –1B) –2

3C) –2 D) {2}

5) x(1+3x)=(3x–1)(x–3)

A) 3

11 B) –3

11 C) 3

121 D) –3

121

6) x(x2+4)=9+x3

A) 9

4B) {4} C) {9} D) 4

7) 3

x+5

+2

2x+1

=4

x–2

A) –46

47 B) 46

47 C) –47

46 D) 47

8) 2x

x2–4

=3

x2–4

–4

x+2

A) 11

6B) –5

6C) 5

2D) –1

9) 5–x

+3

=7

A) {–8} B) –8

7C) {8} D) {–4}

Page3

10) 1

+1

x+4

=x+5

x+4

A) {1} B) {–4} C) {–1} D) {4}

11) 6

2x–3

=4

2x+5

A) –21

2B) 21

2C) –2

21 D) 2

12) x–2

x–5

=x+6

x–7

A) 22

5B) –15

7C) {–4} D) 8

13) 8x+7

2x–8

=20x+9

5x–2

A) –58

161 B) 58

123 C) –86

161 D) 86

123

14) 6

–1

x+1

=3

x(2x+2)

A) 3

2B) {3} C) 3

10 D) nosolution

15) 2

x+5

–4

x–5

=6

x2–25

A) {–18} B) {18} C) {3 3} D) {36}

16) 4x–9

2x–7

=10x+8

5x–4

A) 92

7B) 4

5C) 20

7D) 4

17) 8

+7

=–4

A) –15

4B) –4

15 C) 15

4D) 4

3 SolveProblemsThatCanBeModeledbyLinearEquations

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Solvetheequation.Thelettersa,b,andcareconstants.

1) ax–b=c,a≠0

A) x=b+c

aB) x=b–c

aC) x=c–b

aD) x=–b+c

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2) x

+x

=c,a≠0,b≠0,a≠–b

A) x=abc

a+bB) x=abc C) x=c

ab D) x=a+b

abc

3) a

+b

=c,c≠0

A) x=a+b

cB) x=c

a+bC) x=ab

cD) x=c

Solvetheformulafortheindicatedvariable.

4) PV=nRTforT

A) T=PV

nR B) T=PV

RC) T=nPV

RD) T=PVR

5) S=2πrh+2πr2forh

A) h=S–2πr2

2πrB) h=S–rC)h=S

2πr

–1D)h=2π(S–r)

6) F=9

5C+32forC

A) C=5

9(F–32) B) C=9

5(F–32) C) C=F–32

9D) C=5

F–32

7) A=P(1+rt)forr

A) r=A–P

tP B) r=A+P

tP C) r=–A+P

tP D) r=P–A

8) P–7Q

=P+3

+1forP

A) P=25+14Q

5B) P=25 –14Q

5C) P=5–14Q

5D) P=5+14Q

Solvetheproblem.

9) MaryandherbrotherJohncollectforeigncoins.Maryhastwice thenumberofcoinsthatJohnhas.

Togethertheyhave120foreigncoins.FindhowmanycoinsMaryhas.

A) 80coins B) 40coins C) 16 coins D) 72coins

10) CenterCityEastParkingGaragehasacapacityof256 carsmorethanCenterCityWestParkingGarage.If

thecombinedcapacityforthetwogaragesis1230cars,findthecapacityforeachgarage.

A) CenterCityEast:743cars

CenterCityWest:487cars

B) CenterCityEast:487cars

CenterCityWest:743cars

C) CenterCityEast:753cars

CenterCityWest:477cars

D) CenterCityEast:477cars

CenterCityWest:753cars

11) Duringanintramuralbasketballgame,TeamAscored16 fewerpointsthanTeamB.Together,bothteams

scoredatotalof144points.HowmanypointsdidTeamAscoreduringthegame?

A) 64points B) 80points C) 65 points D) 72points

Page5

12) Anautorepairshopchargedacustomer$527 torepairacar.Thebilllisted$87forpartsandtheremainder

forlabor.Ifthecostoflaboris$55perhour,howmanyhoursoflabordidittaketorepairthecar?

A) 8hr B) 7hr C) 9 hr D) 8.5hr

13) Goingintothefinalexam,whichwillcountasthreetests,Jeromehastestscoresof61,72,59,75,and77.

WhatscoredoesJeromeneedonthefinalinordertoearnaC,whichrequiresanaverageof70?

A) 72 B) 75 C) 70 D) 79

14) Aftera13%pricereduction,aboatsoldfor$21,750.Whatwastheboatʹspricebeforethereduction?

(Roundtothenearestcent,ifnecessary.)

A) $25,000 B) $2827.50 C) $167,307.69 D) $24,577.50

15) Inclusiveofa6.7%salestax,adiamondringsoldfor$1707.20.Findthepriceoftheringbeforethetaxwas

added.(Roundtothenearestcent,ifnecessary.)

A) $1600 B) $1821.58 C) $1592.82 D) $114.38

16) Itcosts$40perhourplusaflatfeeof$25 foraplumbertomakeahousecall.Afterwritinganequationfor

thissituation,supposethetotalcosttohaveaplumbercometoahouseis$425.Howmanyhoursdidthe

plumberwork?

A) 10hr B) 8hr C) 20 hr D) 18hr

17) Arectangularcarpethasaperimeterof234 inches.Thelengthofthecarpetis83inchesmorethanthe

width.Whatarethedimensionsofthecarpet?

A) 100in.by17in. B) 100in.by117 in. C) 67 in.by84 in. D) 108.5 in.by117 in.

18) Theperimeterofatriangleis65centimeters.Findthelengthsofitssides,ifthelongestsideis7centimeter

longerthantheshorterside,andtheremainingsideis4centimeterslongerthantheshorterside.

A) 18cm,22cm,25cm B) 16cm,20cm,29cm

C) 20cm,22cm,23cm D) 17cm,20cm,28cm

19) xrepresentsthenumberoftextbookspurchasedat$56 perbook,andyrepresentsthetotalamountof

moneyspentontextbooks.Whatisanequationoftheformy=axforthissituation?

A) y=56x B) y=112x C) y=28x D) y=168x

20) Itcosts$38perhourplusaflatfeeof$32 foraplumbertomakeahousecall.Whatisanequationofthe

formy=ax+bforthissituation?

A) y=38x+32 B) y=32x+38 C) y=38x D) y=32x

21) Usingaphonecardtomakealongdistancecallcostsaflatfeeof$0.81 plus$0.21perminutestartingwith

thefirstminute.Whatisanequationoftheformy=ax+bforthissituation?

A) y=0.21x+0.81 B) y=0.81x+0.21 C) y=0.81x D) y=0.21x

22) xrepresentsthenumberoftextbookspurchasedat$54 perbook,andyrepresentsthetotalamountof

moneyspentontextbooks.Afterwritinganequationforthissituation,whatisthecostof3textbooks?

A) $162 B) $324 C) $81.00 D) $18.00

23) xrepresentsthenumberofcassettetapessoldat$6.50 pertape,andyrepresentsthetotalcostofthe

cassettetapes.Afterwritinganequationforthissituation,whatisthetotalcostof18cassettes?

A) $117 B) $234 C) $58.50 D) $0.36

24) Itcosts$34perhourplusaflatfeeof$31 foraplumbertomakeahousecall.Afterwritinganequationfor

thissituation,whatisthetotalcosttohaveaplumbercometoahousefor4hours?

A) $167 B) $158 C) $136 D) $1058

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1.2 QuadraticEquations

1 SolveaQuadraticEquationbyFactoring

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Solvetheequationbyfactoring.

1) 7x2–9x=0

A) { 9

7,0} B) { 9

7,–9

7} C) {0} D) {–9

7,0}

2) 60x2+44x=0

A) {–11

15,0} B) { 11

15,–11

15} C) {0} D) { 11

15,0}

3) x2–25=0

A) {5

–5} B) {5} C) {–5} D) {25}

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

4) x2–x=72

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

5) x2–11x+30=0

A) {5

6} B) {5

–6} C) {–5

6} D) {–5

–6}

6) x2–2x–24=0

A) {–4

6} B) {–4

–6} C) {4

–6} D) {4

6}

7) 5x2+8x–4=0

A) { 2

5,–2} B) { 2

5,2} C) {–2

5,–2} D) {–2

5,2}

8) 2x2–22=0

A) {–11,11} B) {12} C) {–11

11} D) {11}

9) x(x–3)+2=0

A) {1

2} B) {1

–2} C) {–1

2} D) {–1

–2}

10) 25x2–90x+81=0

A) { 9

5}B){

9}C){

–9

5}D){

–5

11) 12x2–5x–25=0

A) { 5

4,5

3}B){

4,–5

3}C){

–5

4,5

3}D){

–5

4,–5

Page7

12) 9x–17=2

A) {–1

9,2} B) {–1

9,9} C) { 1

17,–1

9}D){

–9

2}

13) 10x+16

=–28

A) {–4

5,–2} B) { 4

5,2} C) {–5

4,2} D) {10,1

14) x–4

=15

x+4

A) {16

–1} B) {16

1} C) {4

–1} D) {4

1}

SolvetheequationbytheSquareRootMethod.

15) x2=196

A) {14

–14} B) {14} C) {15

–15} D) {98}

16) (x–5)2=4

A) {7

3} B) {9} C) {2

–2} D) {3

–7}

17) (2x–1)2=81

A) {5

–4} B) {4

–5} C) {10

–8} D) {8

–10}

18) x2=6

A) { 6,–6}B){6

–6} C) { 6}D)norealsolution

19) (x+5)2=14

A) {–5+14,–5–14}B){5+14,5–14}

C) { 14,–14}D){9}

2 SolveaQuadraticEquationbyCompletingtheSquare

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Solvetheequationbycompletingthesquare.

1) x2–4x+1=0

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

2) x2+4x=3

A) {–2–7,–2+7}B){2+7}

C) {–1–7,–1+7}D){

–2–27,–2+27}

3) x2+6x+8=0

A) {–2

–4} B) {2

4} C) {1

–1} D) {12

–4}

4) x2+12x+21=0

A) {–6–15,–6+15}B){6+15}

C) {6–21,6+21}D){

–12+21}

Page8

5) x2+5x–5=0

A) { –5–35

2,–5+35

2}B){

5+35

C) { –5–35

2}D){

–5–35,–5+35}

6) x2+8x–7=0

A) {–4–23,–4+23}B){4+23}

C) {–1–23,–1+23}D){

–4–223,–4+223}

7) x2–8x–3=0

A) {4–19,4+19}B){4–3,4+3}

C) {–4–19,–4+19}D){8–67,8+67 }

8) 1

3x2+1

12x–1

=0

A) { 33–1

8,–33+1

8}B){

8,–33

C) { 1

8,–1

8}D){

33–1

8,33+1

9) 3x2–2x–4=0

A) { 1–13

3,1+13

3}B){

3–13

9,3+13

C) {–4,14

3}D){

–1–13

3,–1+13

10) 4x2+24x+35=0

A) {–5

2,–7

2}B){

–5

4,–7

4}C){

2,7

2}D){

–7

2,21

11) x2–4

7x–5

=0

A) {–1

7,5

7}B){

7,5

7}C){

–1

7,–5

7}D){

7,–5

3 SolveaQuadraticEquationUsingtheQuadraticFormula

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Findtherealsolutions,ifany,oftheequation.Usethequadraticformula.

1) x2+8x–7=0

A) {–4–23,–4+23}B){4+23}

C) {–1–23,–1+23}D){

–4–223,–4+223}

2) x2–12x–7=0

A) {6+43,6–43}B){6+7,6–7}

C) {–6+43,–6–43}D){12+43,12–43}

Page9

3) 2x2+2x–12=0

A) {2

–3} B) {2

3} C) {–2

–3} D) {–2

3}

4) 8x2–x+1=0

A) { –1–33

16 ,–1+33

16 }B){

–1+33

16 ,1+33

16 }

C) { –1–33

16 ,1+33

16 }D)norealsolution

5) x2+5x+2=0

A) { –5–17

2,–5+17

2}B){

5–17

2,5+17

C) { –5–17

10 ,–5+17

10 }D){

–5–33

2,–5+33

6) 5x2+x–1=0

A) { –1–21

10 ,–1+21

10 }B){

–1–21

2,–1+21

C) { 1–21

10 ,1+21

10 }D)norealsolution

7) 4x2+10x+3=0

A) { –5–13

4,–5+13

4}B){

–5–13

8,–5+13

C) { –10–13

4,–10+13

4}D){

–5–37

4,–5+37

8) 5x=11x2

A) {0,5

11}B){

11,–5

11} C) {0} D) {0,–5

11}

9) 36x2+60x+25=0

A) {–5

6}B){

6}C){

–5

6,30} D) norealsolution

10) 49x2+24=–70x

A) {–4

7,–6

7}B){

–4

49,–6

49}C){

7,6

7}D){

–6

49,30

49}

11) 2x2+10x=–4

A) {–5–17

2,–5+17

2}B){

–5–17

4,–5+17

C) { –10–17

2,–10+17

2}D){

–5–33

2,–5+33

Page10

12) 2x2=–6x–3

A) { –3–3

2,–3+3

2}B){

–3–3

4,–3+3

C) { –6–3

2,–6+3

2}D){

–3–15

2,–3+15

13) 4x=1+–1

A) { 1–17

8,1+17

8}B){

–1+17

8,1–17

C) { 1–17

8}D)norealsolution

Findtherealsolutions,ifany,oftheequation.Usethequadraticformulaandacalculator.Expressanysolutions

roundedtotwodecimalplaces.

14) x2+11x–11=0

A) {–5.37

2.05} B) {–2.05

5.37} C) {–5.37

–2.05} D) {–5.37

5.37}

Findtherealsolutions,ifany,oftheequation.Usethequadraticformulaandacalculator.Expressanysolutions

roundedtotwodecimalplaces.Use3.14toapproximateπ.

15) πx2+πx–5=0

A) {–1.86

0.86} B) {0.86

1.86} C) {–0.86

1.86} D) {–1.86

–0.86}

Usethediscriminanttodeterminewhetherthequadraticequationhastwounequalrealsolutions,arepeatedreal

solution,ornorealsolutionwithoutsolvingtheequation.

16) x2–3x–4=0

A) repeatedrealsolutio

B) twounequalrealsolutions C) norealsolution

17) x2–12x+36=0

A) repeatedrealsolutio

B) twounequalrealsolutions C) norealsolution

18) x2+4x+5=0

A) repeatedrealsolutio

B) twounequalrealsolutions C) norealsolution

Solveusingthequadraticformula.Roundanyanswerstotwodecimalplaces.

19) 1

4x2–23x=3

A) {–0.82,14.67} B) {0.82,–14.67} C) {–0.21,14.67} D) {0.21,–14.67}

4 SolveProblemsThatCanBeModeledbyQuadraticEquations

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Solvetheproblem.

1) Thelengthofavegetablegardenis6 feetlongerthanitswidth.Iftheareaofthegardenis112 squarefeet,

finditsdimensions.

A) 8ftby14ft B) 7ftby15 ft C) 9 ftby15 ft D) 7ftby13 ft

Page11

2) TheareaofacircleisfoundbytheequationA=πr2.IftheareaAofacertaincircleis64πsquare

centimeters,finditsradiusr.

A) 8cm B) 8πcm C) 8 πcm D) {8cm,–8 cm}

3) A33–inch–squareTVisonsaleatthelocalelectronicsstore.If33 inchesisthemeasureofthediagonalof

thescreen,usethePythagoreantheoremtofindthelengthofthesideofthescreen.

A) 33 2

in. B) 33in. C) 33

in. D) 1089

in.

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

4) ThesurfaceareaAofarightcircularcylinderisA=2πr2+2πrh,whereristheradiusandhistheheight.

Findtheradiusofarightcircularcylinderwhosesurfaceareais95.36πsquareinchesandwhoseheightis

11.7inches.

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

5) Anopenboxistobeconstructedfromasquaresheetofplasticbyremovingasquareofside3 inchesfrom

eachcorner,andthenturningupthesides.Iftheboxmusthaveavolumeof675cubicinches,findthe

lengthofonesideoftheopenbox.

A) 15in. B) 18in. C) 21 in. D) 14in.

6) Aballisthrownverticallyupwardfromthetopofabuilding144 feettallwithaninitialvelocityof128 feet

persecond.Thedistances(infeet)oftheballfromthegroundaftertsecondsiss=144+128t–16t2.After

howmanysecondswilltheball passthetopofthebuilding onitswaydown?

A) 8sec B) 144sec C) 7 sec D) 10sec

7) Aspartofaphysicsexperiment,Mingdropsabaseballfromthetopofa330–footbuilding.Tothenearest

tenthofasecond,forhowmanysecondswillthebaseballfall?(Hint:Usetheformulah=16t2,which

givesthedistanceh,infeet,thatafree–fallingobjecttravelsintseconds.)

A) 4.5sec B) 82.5 sec C) 20.6 sec D) 1.1sec

8) Thenetincomey(inmillionsofdollars)ofPetProductsUnlimitedfrom1997to1999isgivenbythe

equationy=9x2+15x+52,wherexrepresentsthenumberofyearsafter1997.Assumethistrend

continuesandpredicttheyearinwhichPetProductsUnlimitedʹsnetincomewillbe$352million.

A) 2002 B) 2004 C) 2001 D) 2003

9) TheformulaA=P(1+r)2isusedtofindtheamountofmoney,A,inanaccountafterPdollarshavebeen

investedintheaccountpayinganannualinterestrate,r,for2years.Findtheinterestraterif$500grows

to$980in2years.

A) 40% B) 96% C) 4% D) 240%

Page12

10) Acircularpoolmeasures16feetacross.Onecubicyardofconcreteistobeusedtocreateacircularborder

ofuniformwidtharoundthepool.Iftheborderistohaveadepthof1inch,howwidewilltheborderbe?

Use3.14toapproximateπ.Expressyoursolutionroundedtotwodecimalplaces.(1cubicyard=27cubic

feet)

A) 4.93ft B) 15.48 ft C) 5.69 ft D) 10.78 ft

11) Ifapolygon,ofnsideshas1

2n(n–3)diagonals,howmanysideswillapolygonwith152diagonalshave?

A) 19sides B) 20sides C) 18 sides D) 21sides

1.3 ComplexNumbers;QuadraticEquationsintheComplexNumberSystem

1 Add,Subtract,Multiply,andDivideComplexNumbers

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Writetheexpressioninthestandardforma+bi.

1) (2–3i)+(6+7i)

A) 8+4i B) 8–4i C) –4+10i D) –8–4i

2) (8+3i)–(–6+i)

A) 14+2i B) 14–2i C) 2 +4i D) –14 –2i

3) 3(3–3i)

A) 9–9i B) 9+9i C) 9i–3i D) 3–9i

4) 8i(9–2i)

A) 16+72i B) 72i–16 C) 72i–16i2D) 72i+16i2

5) –2i(–5+5i)

A) 10+10i B) –10+10i C) 10i–10i2D) 10i+10i2

6) (–9+2i)(3+i)

A) –29–3i B) –25–3i C) –29 –15i D) –25 –15i

7) (3+8i)(8+8i)

A) –40+88i B) –40–88i C) 88 +40i D) 64i2+88i+24

8) (8+7i)(2–6i)

A) 58–34i B) 58+34i C) –26 +62i D) –42i2–34i+16

9) (9+8i)(9–8i)

A) 145 B) 81–64i2C) 17 D) 81–64i

Page13

10) (–6+i)(–6–i)

A) 37 B) –6C)36D)

–35

11) (7+5i)(7–5i)

A) 74 B) 49–25i2C) 24 D) 49–25i

12) 2

5+i

A) 5

–1

13iB)

+1

13iC)

+1

12iD)

–1

12i

13) 9

7–i

A) 63

+9

50iB)

–9

50iC)

+3

16iD)

–3

16i

14) 9

4–5i

A) 36

+45

41iB)

–45

41iC)

–4+5i D) –4–5i

15) 5i

2+i

A) 1+2i B) –1+2i C) 1 +5i D) 1–2i

16) 3+2i

2–3i

A) i B) –iC)1 D)

–1

17) 31–8i

3–4i

A) 5+4i B) 5–4i C) 4 +5i D) 4–5i

18) 7+7i

9–8i

A) 7

145

+119

145 iB)

–7i C) 119

145

–7

145 iD)7–7i

19) (1–6i)2

A) –35–12i B) 37–12i C) –35 D) 1–12i+36i2

20) 2

+2

i2

A) i B) –iC)

2D) –i

21) i8

A) 1 B) –1C)i D)

–i

Page14

22) i15

A) –i B) i C) 1 D) –1

23) i9

A) i B) –iC)1 D)

–1

24) i18

A) –1 B) 1 C) i D) –i

25) 2i15–i7

A) –iB)i C)

–1D)1

26) 5i5(1+i3)

A) 5+5i B) 5–5i C) –5–5i D) –5+5i

27) (1+i)3

A) –2+2i B) 2+2i C) –2–2i D) –2+i

28) i10+i8+i6+1

A) 0 B) 1 C) i D) –1

Performtheindicatedoperationsandexpressyouranswerintheforma+bi.

29) –4

A) 2i B) –i2 C) –2i D) ±2

30) –36

A) 6i B) i 6 C) –6i D) ±6

31) (5+12i)(12i–5)

A) 13i B) –13i C) –13 D) 13

Writetheexpressioninthestandardforma+bi.

32) Ifz=8–2i,evaluatez+z.

A) 16 B) 16–4i C) –4i D) 16+4i

33) Ifw=8+3i,evaluatew–w.

A) 6i B) –16+6i C) 16 D) 0

34) Ifz=3–8i,evaluatezz.

A) 73 B) 9–64i2C) –55 D) 9–64i

35) Ifz=4+5iandw=–7+i,evaluatez–w.

A) 11–4i B) 11+4i C) –3+6i D) –11 –4i

36) Ifz=8–6iandw=5+8i,evaluatez+w.

A) 13+2i B) 13–2i C) 3 +14i D) –13 –2i

Page15

2 SolveQuadraticEquationsintheComplexNumberSystem

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Solvetheequationinthecomplexnumbersystem.

1) x2+36=0

A) {–6i,6i} B) {6i} C) {6} D) {–6

6}

2) x2+8x+41=0

A) {–4–5i,–4+5i} B) {–4–25i,–4+25i} C) {–4+5i} D) {–9

1}

3) x2+x+7=0

A) {–1

–33

2i,–1

+33

2i} B) { 1–33

2,1+33

C) { 1

–33

2i,1

+33

2i} D) { –1–33

2,–1+33

4) 16x2+1=5x

A) { 5

–39

32 i,5

+39

32 i} B) {–5

–39

32 i,5

+39

32 i}

C) { 5

–39

32 i,–5

+39

32 i} D) {–5

–39

32 i,–5

+39

32 i}

5) x3–27=0

A) {3,–3

–33

2i,–3

+33

2i} B) {3,–3

–33

2,–3

+33

C) {3

–3i,3i} D) {3}

6) x4=1

A) {–1

1

–i, i} B) {–1

1} C) {1} D) {–1

1

7) x4–6x2–7=0

A) {–7,7,i,–i} B) { 7i,i} C) {–7i,–i} D) { 7,7}

Withoutsolving,determinethecharacterofthesolutionsoftheequationinthecomplexnumbersystem.

8) x2–4x+3=0

A) twounequalrealsolutions

B) arepeatedrealsolutio

C) twocomplexsolutionsthatareconjugatesofeachother

9) x2–8x+16=0

A) arepeatedrealsolutio

B) twounequalrealsolutions

C) twocomplexsolutionsthatareconjugatesofeachother

10) x2+4x+5=0

A) twocomplexsolutionsthatareconjugatesofeachother

B) twounequalrealsolutions

C) arepeatedrealsolutio

Page16

11) x2+8x+6=0

A) twounequalrealsolutions

B) arepeatedrealsolutio

C) twocomplexsolutionsthatareconjugatesofeachother

Solvetheproblem.

12) 4–iisasolutionofaquadraticequationwithrealcoefficients.Findtheothersolution.

A) 4+iB)4–iC)

–4+iD)

–4–i

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Writetheexpressioninthestandardforma+bi.

13) Ifz=3–6iandw=1+5i,evaluatez+w.

1.4 RadicalEquations;EquationsQuadraticinForm;FactorableEquations

1 SolveRadicalEquations

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Findtherealsolutionsoftheequation.

1) x+5=5

A) {20} B) {25} C) {30} D) {100}

2) 3x–2=2

A) {2} B) {4} C) { 2

3}D){

3) 4x+5=5

A) {5} B) {25} C) { 15

2}D){

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

4) 34x–5+7=8

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

5) 32x+4=5

A) { 121

2}B){

2}C){

125

2}D){

123

6) 51–x=–2

A) {33} B) {–32} C) {–33} D) {32}

7) 31+x=–1

A) {–2} B) {2} C) {–1} D) {1}

8) x=12 x

A) {0,144} B) {0,12} C) {–144

144} D) {–12

12}

Page17

9) 6x+27 =x

A) {9} B) {–3

9} C) {–27

5}D)norealsolution

10) 16x–16=x+3

A) {5} B) {–4} C) {–5} D) {7}

11) x+7+x=3

A) { 1

9} B) {4} C) {1} D) norealsolution

12) x2–3x+16=x+1

A) {3} B) {–3} C) {–3

2}D){4}

13) x2–2x+66=x+4

A) {5} B) {–5} C) {9} D) {1}

14) x2+2–2x+5=0

A) {3,–1} B) {–3,1} C) {3} D) norealsolution

15) 2x+3–x+1=1

A) {3,–1} B) {3} C) {–3,–1} D) norealsolution

16) 2x+5–x–2=3

A) {2,38} B) {3,8} C) {2} D) {–2}

17) 3x+10–x+2=2

A) {–2,2} B) {2} C) {–3} D) {–2}

18) 2–3x=6

A) { 34

3}B){

–34

3}C){

3}D)norealsolution

19) (3x–7)1/2=4

A) { 23

3}B){

3}C){

3}D)norealsolution

20) (3x+2)1/2=3

A) { 7

3} B) {3} C) {–2

3}D){6}

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

21) 34x–5+7=8

Page18

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

22) (4x+5)1/3=–4

A) {–69

4}B){

4}C){

–16} D) {–68

23) (x+3)1/3=–2

A) {–11} B) {1} C) {–9} D) norealsolution

24) (x2+4)1/2=7

A) {3 5,–35}B){45

–45} C) { 3}D){3}

25) x3

2–4x1

2=0

A) {0,4} B) {0,16} C) {2} D) { 2}

26) x5/4–4x1/4=0

A) {0,4} B) {–4,0,4} C) {0,2} D) {0}

2 SolveEquationsQuadraticinForm

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Findtherealsolutionsoftheequation.

1) x4–10x2+9=0

A) {–1,1,–3

3} B) {–3

3} C) {–9

9} D) {–10

10}

2) 5x4+13x2–6=0

A) {–2

5,2

5} B) {–2

5,2

5}C){

–3

5,3

5}D){

–3,3}

3) x6–26x3–27=0

A) {3

–1} B) {27} C) {3} D) {–3

1}

4) 2(x+1)2+9(x+1)+9=0

A) {–5

2,–4} B) {1

2} C) {–3

2,–4} D) {–5

2,–3}

5) (3x–3)2–6(3x–3)+8=0

A) { 7

3,5

3}B){

–7

3,–5

3}C){

3,–1

3}D){

–1

3,1

6) (x–4)2+3(x–4)–18=0

A) {–2,7} B) {–7,2} C) {–6,1} D) {–1,6}

7) x+x=90

A) {81} B) {9} C) {10} D) {100}

8) x+8x1/2+7=0

A) {196

484} B) {14

–22} C) {324} D) norealsolution

Page19

9) x1/2–7x1/4+12=0

A) {81

256} B) {9

16} C) {3

4} D) {–3

–4}

10) x2+5x–x2+5x=6

A) { –5+61

2,–5–61

2}B){25

–25}

C) {2} D) {5}

11) 1

(x–2)2

–2

x–2

=3

A) {1,7

3}B){

–1,1

3} C) {1,1

3}D){

–1,7

12) 2+5

7x–1

=–2

(7x–1)2

A) {–1

7,1

14}B){

–2,–1

2}C){

–1

7,0} D) {–1

7,–1

14}

13) 5x–2–14x–1–3=0

A) {–5,1

3}B){5,1

3}C){

–1

5,–3} D) {–1

5,3}

14) x2/3–5x1/3+6=0

A) {8

27} B) {2

3} C) {–3

–2} D) {–27

–8}

15) x2/3–7x1/3+12=0

A) {27

64} B) {3

4} C) {–4

–3} D) {–64

–27}

Findtherealsolutionsoftheequation.Useacalculatortoexpressthesolutionsroundedtotwodecimalplaces.

16) π(1+x)2–5=2(1+x)

A) {0.62,–1.98} B) {–0.62,0.82} C) {–1.62,–0.62} D) {–0.62,–0.18}

17) x2/5–3x1/5–4=0

A) {–1,1024} B) {–1,4} C) {–1,1.32} D) {–1}

Solvetheproblem.

18) Ifk=x+3

x–3

andk2–4k=21,findx.

A) {4,3

2}B){

4,3

2}C){4,1

4}D){

7,3

19) Foracone,theformular=3V

πh

describestherelationshipbetweentheradiusrofthebase,thevolumeV,

andtheheighth.Findthevolumeiftheradiusis3inchesandtheconeis9incheshigh.(Use3.14asan

approximationforπ,androundtothenearesttenth.)

A) 84.8cubicin. B) 28.3 cubicin. C) 763.0 cubicin. D) 9.4cubicin.

Page20

20) Theformulav=2.5rcanbeusedtoestimatethemaximumsafevelocityv,inmilesperhour,atwhicha

carcantravelalongacurvedroadwitharadiusofcurvaturer,infeet.Tothenearestwholenumber,find

theradiusofcurvatureifthemaximumsafevelocityis15milesperhour.

A) 90ft B) 563ft C) 36 ft D) 225 ft

21) Thefunctionf(x)=6.75 x+12modelstheamount,f(x),inbillionsofdollarsofnewstudentloansxyears

after1993.Accordingtothemodel,inwhatyearistheamountloanedexpectedtoreach$32.25billion?

A) 2002 B) 2005 C) 2007 D) 2006

22) Whenanobjectisdroppedtothegroundfromaheightofhmeters,thetimeittakesfortheobjecttoreach

thegroundisgivenbytheequationt=h

4.9,wheretismeasuredinseconds.Solvetheequationforh.

Usetheresulttodeterminetheheightfromwhichanobjectwasdroppedifithitsthegroundafterfalling

for4seconds.

A) h=4.9t2;78.4meters B) h=24.01t;96 meters

C) h=24.01t2;384.2meters D) h=4.9t;19.6 meters

23) Themaximumnumberofvolts,E,thatcanbeplacedacrossaresistorisgivenbytheformulaE=PR,

wherePisthenumberofwattsofpowerthattheresistorcanabsorbandRistheresistanceoftheresistor

inohms.SolvethisequationforR.UsetheresulttodeterminetheresistanceofaresistorifPis1

watts

andEis20volts.

A) R=E2

P;3200ohms B) R=E2

P2;25,600ohms

C) R=E2P;3200ohms D) R=E2P2;25,600ohms

24) Thenumberofcentimeters,d,thataspringiscompressedfromitsnatural,uncompressedpositionisgiven

bytheformulad=2W

k,whereWisthenumberofjoulesofworkdonetomovethespringandkisthe

springconstant.SolvethisequationforW.Usetheresulttodeterminetheworkneededtomoveaspring

6centimetersifithasaspringconstantof0.6.

A) W=d2k

2;10.8joules B) W=d2k2

4;3.2joules

C) W=2d2

k;120joules D) W=2d2k;43.2joules

3 SolveEquationsbyFactoring

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Findtherealsolutionsoftheequationbyfactoring.

1) x3–49x=0

A) {0,7

–7} B) {0,7} C) {0,–7} D) {0,49}

2) 5x5=45x3

A) {–3

0,3} B) {–35,0,35}C){

–3

3} D) {0}

Page21

3) x3+5x2–4x–20=0

A) {–2

2

–5} B) {4

–5} C) {2

–5} D) {–2

2

5}

4) x3+4x2+4x+16=0

A) {–4} B) {4} C) {–2

2

–4} D) norealsolution

5) 5x4–320x2=0

A) {–8

0,8} B) {–85,0,85}C){

–8

8} D) {0}

6) 3x4=24x

A) {0,2} B) {–2

0,2} C) {0,3

2} D) {0}

7) x3+4x2–12x=0

A) {0,2

–6} B) {2

–6} C) {0,–2

6} D) {–2

6}

8) x3+6x2–x–6=0

A) {–1,1,–6} B) {1,–6

6} C) {–6

6} D) {36}

9) 10x3+70x2+120x=0

A) {0,–4

–3} B) {–4

–3} C) {0,4

3} D) {–1

4,–3}

1.5 SolvingInequalities

1 UseIntervalNotation

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Expressthegraphshownusingintervalnotation.Alsoexpressitasaninequalityinvolvingx.

–7–6–5–4–3–2–1012345678910–7–6–5–4–3–2–1012345678910

A) [–2

5)

–2≤x<5

B) (–2

5)

–2<x<5

C) [–2

5]

–2≤x≤5

D) (–2

5]

–2<x≤5

456789101112456789101112

A) (–∞

8]

x≤8

B) (–∞

8)

x<8

C) [8

∞)

x≥8

D) (8

∞)

x>8

–2–10123456–2–10123456

A) (2

∞)

x>2

B) (–∞

2]

x≤2

C) [2

∞)

x≥2

D) (–∞

2)

x<2

Page22

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

A) (–3

2)

–3<x<2

B) [–3

2]

–3≤x≤2

C) (–3

2]

–3<x≤2

D) [–3

2)

–3≤x<2

–1012345678–1012345678

A) [3

4]

3≤x≤4

B) (3

4)

3<x<4

C) [3

4)

3≤x<4

D) (3

4]

3<x≤4

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

A) [–5

3)

–5≤x<3

B) (–5

3]

–5<x≤3

C) (–∞

3)

x<3

D) [–5

3]

–5≤x≤3

Writetheinequalityusingintervalnotation,andillustratetheinequalityusingtherealnumberline.

7) 6

x

9

A) (6

9)

01234567891011121314150123456789101112131415

B) [6

9]

01234567891011121314150123456789101112131415

C) (6

9)

01234567891011121314150123456789101112131415

D) [6

9)

01234567891011121314150123456789101112131415

8) –10≤x≤–6

A) [–10

–6]

–12–11–10–9-8-7-6-5-4–12–11–10–9-8-7-6-5-4

B) (–10

–6)

–12–11–10–9-8-7-6-5-4–12–11–10–9-8-7-6-5-4

C) [–10

–6]

–12–11–10–9-8-7-6-5-4–12–11–10–9-8-7-6-5-4

D) (–10

–6]

–12–11–10–9-8-7-6-5-4–12–11–10–9-8-7-6-5-4

Page23

9) –4≤x

2

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

A) [–4

2)

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

B) (–4

2]

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

C) (–∞

2)

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

D) [–4

2)

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

10) t≥–6

A) [–6

∞)

–10–9-8-7-6-5-4-3-2–10–9-8-7-6-5-4-3-2

B) [–6

∞]

–10–9-8-7-6-5-4-3-2–10–9-8-7-6-5-4-3-2

C) (–6

∞)

–10–9-8-7-6-5-4-3-2–10–9-8-7-6-5-4-3-2

D) (–6

∞]

–10–9-8-7-6-5-4-3-2–10–9-8-7-6-5-4-3-2

11) y

1

A) (–∞

1)

–3–2–1012345–3–2–1012345

B) (–∞

1]

–3–2–1012345–3–2–1012345

C) [–∞

1]

–3–2–1012345–3–2–1012345

D) [–∞

1)

–3–2–1012345–3–2–1012345

Writetheintervalasaninequalityinvolvingx,andillustratetheinequalityusingtherealnumberline.

12) [–5

8)

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

A) –5≤x

8

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

B) –5

x≤8

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

C) x

8

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

D) –5≤x

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

Page24

13) [–7

2]

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

A) –7≤x≤2

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

B) –7

x≤2

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

C) –7

x

2

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

D) –7≤x

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

14) (8

∞)

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

A) x>8

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

B) x≥8

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

C) x>8

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

D) x≥8

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

15) [7

∞)

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

A) x≥7

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

B) x>7

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

C) x>7

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

D) x≥7

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

16) (–∞

–2)

A) x

–2

-6 -5 -4 -3 -2 -1 0 1 2-6 -5 -4 -3 -2 -1 0 1 2

B) x≤–2

-6 -5 -4 -3 -2 -1 0 1 2-6 -5 -4 -3 -2 -1 0 1 2

C) x

–2

-6 -5 -4 -3 -2 -1 0 1 2-6 -5 -4 -3 -2 -1 0 1 2

D) x≤–2

-6 -5 -4 -3 -2 -1 0 1 2-6 -5 -4 -3 -2 -1 0 1 2

Page25

2 UsePropertiesofInequalities

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Writetheinequalityobtainedbyperformingtheindicatedoperationonthegiveninequality.

1) Subtract4fromeachsideoftheinequality5–3x≥1.

A) 1–3x≥–3B)1–3x≤–3C)1

–7x≥–3D)1–7x≤–3

2) Multiplyeachsideoftheinequality4+5x> –3by3.

A) 12+15x>–9B)12+15x

–9C)12

+5x> –9D)12+5x

–9

Fillintheblankwiththecorrectinequalitysymbol.

3) Ifx

14

thenx–14 0.

B) >C) ≤D) ≥

4) Ifx

–3

thenx+3 0.

B) >C) ≤D) ≥

5) Ifx>–3

then4x –12.

A) >B)

C) ≥D) ≤

6) Ifx

5

then–3x –15.

A) >B)

C) ≥D) ≤

7) Ifx>–3

then–6x 18.

B) >C) ≥D) ≤

8) If–4x

–20

thenx_____5.

A) >B)

C) ≥D) ≤

3 SolveInequalities

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Solvetheinequality.Expressyouranswerusingintervalnotation.

1) x+3

6

A) (–∞

3)

–4–3–2–1012345678910–4–3–2–1012345678910

B) (3

∞)

–4–3–2–1012345678910–4–3–2–1012345678910

C) (–∞

9)

2 3 4 5 6 7 8 9 10 11 12 13 14 15 162 3 4 5 6 7 8 9 10 11 12 13 14 15 16

D) (–∞

9]

2 3 4 5 6 7 8 9 10 11 12 13 14 15 162 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Page26

2) x+2

–5

A) (–∞

–7)

–14–13–12–11–10–9-8-7-6-5-4-3-2-1 0–14–13–12–11–10–9-8-7-6-5-4-3-2-1 0

B) (–7

∞)

–14–13–12–11–10–9-8-7-6-5-4-3-2-1 0–14–13–12–11–10–9-8-7-6-5-4-3-2-1 0

C) (–∞

–3)

–10–9-8-7-6-5-4-3-2-1 0 1 2 3 4–10–9-8-7-6-5-4-3-2-1 0 1 2 3 4

D) (–∞

–7]

–14–13–12–11–10–9-8-7-6-5-4-3-2-1 0–14–13–12–11–10–9-8-7-6-5-4-3-2-1 0

3) 2x+4

16

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

A) (–∞

6)

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

B) (6

∞)

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

C) [6

∞)

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

D) (–∞

6]

–10–9–8–7–6–5–4–3–2–1012345678910–10–9–8–7–6–5–4–3–2–1012345678910

4) 6x+1>5x–3

A) (–4

∞)

-11 -10 -9 -8 -7 -6 -5 -4 -3 –2 -1 0 1 2 3-11 -10 -9 -8 -7 -6 -5 -4 -3 –2 -1 0 1 2 3

B) (–∞

–4]

-11 -10 -9 -8 -7 -6 -5 -4 -3 –2 -1 0 1 2 3-11 -10 -9 -8 -7 -6 -5 -4 -3 –2 -1 0 1 2 3

C) (–2

∞)

–9–8–7–6–5–4–3–2–1012345–9–8–7–6–5–4–3–2–1012345

D) [–4

∞)

-11 -10 -9 -8 -7 -6 -5 -4 -3 –2 -1 0 1 2 3-11 -10 -9 -8 -7 -6 -5 -4 -3 –2 -1 0 1 2 3

Page27

5) –2x+3≤–3x+2

A) (–∞

–1]

–8–7–6–5–4–3–2–10123456–8–7–6–5–4–3–2–10123456

B) (–∞

–1)

–8–7–6–5–4–3–2–10123456–8–7–6–5–4–3–2–10123456

C) [–1

∞)

–8–7–6–5–4–3–2–10123456–8–7–6–5–4–3–2–10123456

D) [5

∞)

–2–10123456789101112–2–10123456789101112

6) –5x+5≥–6x+11

A) [6

∞)

–1012345678910111213–1012345678910111213

B) (–∞

6)

–1012345678910111213–1012345678910111213

C) (–∞

6]

–1012345678910111213–1012345678910111213

D) (16

∞)

9 10111213141516171819202122239 1011121314151617181920212223

Page28

7) 3x+7>2x+8

A) (1

∞)

–6–5–4–3–2–1012345678–6–5–4–3–2–1012345678

B) (–∞

1]

–6–5–4–3–2–1012345678–6–5–4–3–2–1012345678

C) (15

∞)

8 9 10 11 12 13 14 15 16 17 18 19 20 21 228 9 10 11 12 13 14 15 16 17 18 19 20 21 22

D) [1

∞)

–6–5–4–3–2–1012345678–6–5–4–3–2–1012345678

8) 5–3(1–x)≤–19

–10–8-6-4-2 0 2 4 6 810–10–8-6-4-2 0 2 4 6 810

A) (–∞

–7]

–10–8–6–4–20246810–10–8–6–4–20246810

B) [–7

∞)

–10–8–6–4–20246810–10–8–6–4–20246810

C) (–∞

–6]

–10–8–6–4–20246810–10–8–6–4–20246810

D) (–∞

–7)

–10–8–6–4–20246810–10–8–6–4–20246810

9) –36x–30≤–6(5x+6)

A) [1

∞)

–6–5–4–3–2–1012345678–6–5–4–3–2–1012345678

B) (–∞

1]

–6–5–4–3–2–1012345678–6–5–4–3–2–1012345678

C) [1

∞)

–6–5–4–3–2–1012345678–6–5–4–3–2–1012345678

D) (–∞

1)

–6–5–4–3–2–1012345678–6–5–4–3–2–1012345678

Page29

10) –4(6x+1)

–28x–20

A) (–∞

–4)

-11 -10 -9 -8 -7 -6 -5 -4 -3 –2 -1 0 1 2 3-11 -10 -9 -8 -7 -6 -5 -4 -3 –2 -1 0 1 2 3

B) (–4

∞)

-11 -10 -9 –8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3-11 -10 -9 -8 -7 -6 -5 -4 -3 –2 -1 0 1 2 3

C) (–∞

–4]

-11 -10 -9 –8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3-11 -10 -9 -8 -7 -6 -5 -4 -3 –2 -1 0 1 2 3

D) (–∞

6]

–1012345678910111213–1012345678910111213

11) x

≥5+x

–20 -16 –12 –8 –4 0 4 8 12 16 20–20 -16 –12 –8 –4 0 4 8 12 16 20

A) [12

∞)

–20 –16 –12 –8 –4 0 4 8 12 16 20–20 –16 –12 –8 –4 0 4 8 12 16 20

B) [–12

∞)

–20 –16 –12 –8 –4 0 4 8 12 16 20–20 –16 –12 –8 –4 0 4 8 12 16 20

C) (–∞

12]

–20 –16 –12 –8 –4 0 4 8 12 16 20–20 –16 –12 –8 –4 0 4 8 12 16 20

D) (12

∞)

–20 –16 –12 –8 –4 0 4 8 12 16 20–20 –16 –12 –8 –4 0 4 8 12 16 20

12) (3x+5)–1<0

–5–4–3–2–1012345–5–4–3–2–1012345

A) (–∞,–5

–5–4–3–2–1012345–5–4–3–2–1012345

B) (–5

3,∞)

–5–4–3–2–1012345–5–4–3–2–1012345

C) (–∞,–5

–5–4–3–2–1012345–5–4–3–2–1012345

D) [–5

3,∞)

–5–4–3–2–1012345–5–4–3–2–1012345

Page30

13) 4–1

–1/2>0

–10–8-6-4-2 0 2 4 6 810–10–8-6-4-2 0 2 4 6 810

A) (–∞

8)

–10–8–6–4–20246810–10–8–6–4–20246810

B) (–∞

8]

–10–8–6–4–20246810–10–8–6–4–20246810

C) (8,∞)

–10–8–6–4–20246810–10–8–6–4–20246810

D) [8,∞)

–10–8–6–4–20246810–10–8–6–4–20246810

14) x(4x–1)≤(2x+4)2

–5–4–3–2–1012345–5–4–3–2–1012345

A) [–16

17,∞)

–5–4–3–2–1012345–5–4–3–2–1012345

B) (–∞,–16

17]

–5–4–3–2–1012345–5–4–3–2–1012345

C) [ 16

17,∞)

–5–4–3–2–1012345–5–4–3–2–1012345

D) (–∞,–16

17]

–5–4–3–2–1012345–5–4–3–2–1012345

Page31

4 SolveCombinedInequalities

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Solvetheinequality.Expressyouranswerusingintervalnotation.

1) 8

4x≤24

A) (2

6]

–3–2–101234567891011–3–2–101234567891011

B) [2

6)

–3–2–101234567891011–3–2–101234567891011

C) (–6

–2]

-11 -10 -9 –8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3-11 -10 -9 -8 -7 -6 -5 -4 -3 –2 -1 0 1 2 3

D) [–6

–2)

-11 -10 -9 –8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3-11 -10 -9 -8 -7 -6 -5 -4 -3 –2 -1 0 1 2 3

2) 18≤5x–2≤28

A) [4

6]

–2–10123456789101112–2–10123456789101112

B) (4

6)

–2–10123456789101112–2–10123456789101112

C) [–6

–4]

–12–11–10–9-8-7-6-5-4-3-2-1 0 1 2–12–11–10–9-8-7-6-5-4-3-2-1 0 1 2

D) (–6

–4)

–12–11–10–9-8-7-6-5-4-3-2-1 0 1 2–12–11–10–9-8-7-6-5-4-3-2-1 0 1 2

Page32

3) –36≤–5x–1

–16

A) (3

7]

–2–10123456789101112–2–10123456789101112

B) [3

7)

–2–10123456789101112–2–10123456789101112

C) [–7

–3)

–12–11–10–9-8-7-6-5-4-3-2-1 0 1 2–12–11–10–9-8-7-6-5-4-3-2-1 0 1 2

D) (–7

–3]

–12–11–10–9-8-7-6-5-4-3-2-1 0 1 2–12–11–10–9-8-7-6-5-4-3-2-1 0 1 2

4) –12≤–3x+3≤–6

A) [3

5]

–3–2–101234567891011–3–2–101234567891011

B) (3

5)

–3–2–101234567891011–3–2–101234567891011

C) [–5

–3]

-11 -10 -9 –8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3-11 -10 -9 -8 -7 -6 -5 -4 -3 –2 -1 0 1 2 3

D) (–5

–3)

-11 -10 -9 –8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3-11 -10 -9 -8 -7 -6 -5 -4 -3 –2 -1 0 1 2 3

5) 0≤2x+5

<3

–5–4–3–2–1012345–5–4–3–2–1012345

A) [–5

2,1

–5–4–3–2–1012345–5–4–3–2–1012345

B) [–5

2,1

–5–4–3–2–1012345–5–4–3–2–1012345

C) (–5

2,1

–5–4–3–2–1012345–5–4–3–2–1012345

D) (–5

2,1

–5–4–3–2–1012345–5–4–3–2–1012345

Page33

6) 17≤9

2x+8<44

–5–4–3–2–10123456789101112131415–5–4–3–2–10123456789101112131415

A) [2

8)

–5–4–3–2–10123456789101112131415–5–4–3–2–10123456789101112131415

B) (2

8]

–5–4–3–2–10123456789101112131415–5–4–3–2–10123456789101112131415

C) [2

3)

–5–4–3–2–10123456789101112131415–5–4–3–2–10123456789101112131415

D) (2

3]

–5–4–3–2–10123456789101112131415–5–4–3–2–10123456789101112131415

7) 0<1

<2

A) ( 5

2,∞)

–2–101234567–2–101234567

B) (–∞,5

–2–101234567–2–101234567

C) ( 2

5,∞)

–4–3–2–1012345–4–3–2–1012345

D) (–∞,2

–4–3–2–1012345–4–3–2–1012345

8) 0<(8x–36)–1<1

–6–5–4–3–2–10123456–6–5–4–3–2–10123456

A) (5

∞)

–101234567891011–101234567891011

B) (–∞

5)

–101234567891011–101234567891011

C) [5

∞)

–101234567891011–101234567891011

D) (–∞

5]

–101234567891011–101234567891011

Findaandb.

9) If–4<x<–1,thena<2

3x<b.

A) a=–8

3,b=–2

3B) a=8

3,b=2

3C) a=–8

3,b=2

3D) a=8

3,b=–2

Page34

10) If0<2x<6,thena<x2<b.

A) a=0,b=9B)a=0,b=36 C) a=0,b=16 D) a=0,b=3

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Solvetheproblem.

11) Whatisthedomainofthevariableintheexpression4x–12?

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

12) Inonecity,thelocalcableTVcompanycharges$3.99 foreachpay–per–viewmoviewatched.Inaddition,

eachmonthlybillcontainsabasiccustomerchargeof$28.50.Iflastmonthʹsbillsrangedfromalowof

$48.45toahighof$80.37,overwhatrangedidcustomerswatchpay–per–viewmovies?

A) movieswatchedvariedfrom5to13 inclusive B) movieswatchedvariedfrom4to12 inclusive

C) movieswatchedvariedfrom6to14 inclusive D) movieswatchedvariedfrom4to14 inclusive

13) Duringthefirstfivemonthsoftheyear,Lenearnedcommissionsof$2170

$3680

$3090

$3840

and$3090.

IfLenmusthaveaveragemonthlyearningsofatleast$3140inordertoqualifyforretirementbenefits,

whatmustheearninthesixthmonthinordertoqualifyforbenefits?

A) atleast$2970 B) atleast$3168 C) atleast$3140 D) atleast$3174

14) Arealestateagentagreestosellanofficebuildingaccordingtothefollowingcommissionschedule:

$33,000plus25%ofthesellingpriceinexcessof$700,000.Assumingthattheofficebuildingwillsellat

somepricebetween$700,000and$1,100,000,inclusive,overwhatrangedoestheagentʹscommissionvary?

A) Thecommissionwillvarybetween$33,000 and$133,000

inclusive.

B) Thecommissionwillvarybetween$34,000 and$133,000

inclusive.

C) Thecommissionwillvarybetween$33,000 and$298,000

inclusive.

D) Thecommissionwillvarybetween$208,000 and$308,000

inclusive.

15)

imhasgottenscoresof66and75onhisfirsttwotests.Whatscoremusthegetonhisthirdtesttokeepan

averageof75orbetter?

A) atleast84 B) atleast70.5 C) atleast72 D) atleast82

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

16) Inhisalgebraclass,Robhasscoresof79,85,81,and65onhisfirstfourtests.TogetagradeofC,the

averageofthefirstfivetestsmustbegreaterthanorequalto70andlessthan80.Solveaninequalityto

findtherangeofscoresthatRobcanearnonthefifthtesttogetaC.

17) Marianneisplanningashoppingtriptobuybirthdaygiftsforherson.Sheestimatesthatthetotalpriceof

theitemssheplanstopurchasewillbebetween$350and$400inclusive.Ifsalesaretaxedatarateof

8.375%inherarea,whatistherangeoftheamountofsalestaxsheshouldexpecttopayonherpurchases?

IfMarianneʹsbudgetfortheshoppingtripis$425,willshenecessarilybeabletobuyallthegiftsthatshe

hasplanned?

18) AtBargainCarRental,thecostofrentinganeconomycarforonedayis$19.95plus20centspermile.At

BestDealCarRental,thecostofrentingasimilarcarforonedayis$24.95plus15centspermile.Solvethe

inequality24.95+0.15x<19.95+0.20xtofindtherangeofmilesdrivensuchthatBestDealisabetterdeal

thanBargain.

Page35

1.6 EquationsandInequalitiesInvolvingAbsoluteValue

1 SolveEquationsInvolvingAbsoluteValue

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Solvetheequation.

1) |x|=3

A) {–3

3} B) {3} C) {–3} D) {9}

2) |x|=–10

A) {10} B) {10

–10} C) {–10} D) nosolution

3) |x|+10=5

A) {5} B) {5

–5} C) {–5} D) nosolution

4) |x+9|=6

A) {–15

–3} B) {15

–3} C) {3} D) nosolution

5) |4x+7|=2

A) {–5

4,–9

4}B){

–5

7,–9

7}C){

4,9

4}D)nosolution

6) |x+9|=0

A) {–9} B) {9

–9} C) {9} D) nosolution

7) 3|x–3|=18

A) {9,–3} B) {3,–9} C) {3} D) nosolution

8) |2x+3|+3=7

A) { 1

2,–7

2}B){

3,–7

3}C){

–1

2,7

2}D)nosolution

9) 4x+12

=4

A) {–6

0} B) {–6

6} C) {6

0} D) nosolution

10) 3(x+1)+6=15

A) {–8

2} B) {–6

4} C) {–8

0} D) {–6

0}

11) |x2+2x|=0

A) {0,–2} B) {2

0,–2} C) {2

0} D) nosolution

12) |x2–4x–4|=8

A) {–2,2,6} B) {2,6} C) {–2,2} D) {–2,2,–6}

13) |2x2–x–1|=3

A) { 1–33

4,1+33

4}B){

–1–33

4,–1+33

C) { 1–33

4,–1+33

4}D)nosolution

Page36

14) |x2–4x+4|=2

A) {2–2,2+2}B){2–2}C){2+2}D)nosolution

15) 7x–4=x–3

A) 1

6,7

8B) 1

6,–5

8C) –1

6,–7

8D) ∅

16) 11x+44

=11

A) {–8

0} B) {–8

8} C) {8

0} D) ∅

2 SolveInequalitiesInvolvingAbsoluteValue

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Solvetheinequality.Expressyouranswerusingintervalnotation.

1) |x|

1

A) (–1

1) B) (–∞

–1)or(1

∞)

C) [0,1] D) (–∞

–1)and(1

∞)

2) |x|

–11

A) (–11

11) B) {–11} C) (–∞

∞)D)nosolution

3) |x|>–5

A) (–5

5) B) {5} C) (–∞

∞)D)nosolution

4) |5x–4|+7>–1

A) (–∞,–4

5)or(12

5,∞)B)(

–4

5,12

C) (–∞

∞)D)nosolution

5) |x–2|+3≤8

A) [–3

7] B) (–∞

–3)or(7

∞)C)[3

8] D) nosolution

6) |3x+2|+8

11

A) (–5

3,1

3)B)(

–∞,–5

3)or(1

3,∞)C)(

–∞,–5

3)D)nosolution

7) |5x–1|≥5

A) (–∞,–4

5]or[6

5,∞)B)(

–∞,–4

5)or(6

5,∞)C)(

–4

5,6

5)D)[

–4

5,6

8) |5x+2|>3

A) (–∞,–1)or(1

5,∞)B)(

–∞,–1]or[1

5,∞)C)[

–1,1

5]D)(

–1,1

9) 5–7x >9

A) (–∞,–4

7)or(2,∞)B)(

–∞,–4

7)or(4

7,∞)C)(

–4

7,2) D) (–4

7,∞)or(2,∞)

Page37

10) |4x+5|+|–7|≤11

A) [–9

4,–1

4]B)(

–∞,–9

4]or[–1

4,∞)

C) [ 1

4,9

4]D)(

–∞,1

4]or[9

4,∞)

11) |x–7|

0

A) (–7

7) B) (–∞

7) C) (–7

∞)D)nosolution

12) |x+1|≤0

A) {–1} B) {1} C) (–∞

–1) D) nosolution

Solvetheinequality.Expressyouranswerinsetnotation.

13) x2<81

A) {x|9

x

9} B) {x|x

C) {x|–9≤x≤9} D) {x|x

–9orx>9}

14) x2≥4

A) {x|x≤–2orx≥2} B) {x|x

–2orx>2}

C) {x|–2≤x≤2} D) {x|x

–2orx≥2}

15) x2>36

A) {x|x

–6orx>6} B) {x|x≤–6 orx≥6}

C) {x|–6≤x≤6} D) {x|x

–6orx≥6}

16) x2≤9

A) {x|–3≤x≤3} B) {x|x≤3}

C) {x|–3

x

3} D) {x|x≤–3orx≥3}

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Solvetheproblem.

17) Expressthatxdiffersfrom–7bymorethan3asaninequalityinvolvingabsolutevalue.Solveforx.

18) Alandscapingcompanysells40–poundbagsoftopsoil.Theactualweightxofabag,however,maydiffer

fromtheadvertisedweightbyasmuchas0.75pound.Writeaninequalityinvolvingabsolutevaluethat

expressestherelationshipbetweentheactualweightxofabagand40pounds.Overwhatrangemaythe

weightofa40–poundbagoftosoilvary?

19) Chiisassignedtoconstructatrianglewiththemeasurebofthebaseandthemeasurehoftheheight

differingbynomorethan0.2centimeters.Expresstherelationshipbetweenbandhasaninequality

involvingabsolutevalue.

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Findaandb.

20) Ifx+1

3

thena

x+3

b.

A) a=–1

b=5B)a=0

b=6C)a= –4

b=2D)a= –6

b=0

Page38

21) If|x+1|≤2,thena≤1

x+5

≤b.

A) a=1

6,b=1

2B) a=1

2,b=1

6C) a=1

6,b=1

8D) a=1

8,b=1

1.7 ProblemSolving:Interest,Mixture,UniformMotion,ConstantRateJobApplications

1 TranslateVerbalDescriptionsintoMathematicalExpressions

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Translatethesentenceintoamathematicalequation.Besuretoidentifythemeaningofallsymbols.

1) Thesurfaceareaofasphereis4πtimesthesquareoftheradius.

A) IfSrepresentsthesurfaceareaandrtheradius,thenS=4πr2.

B) IfSrepresentsthesurfaceareaandrtheradius,thenS=4πr.

C) IfSrepresentsthesurfaceareaandrtheradius,thenS=πr2.

D) IfSrepresentsthesurfaceareaandrtheradius,then4πS=r2.

2) Thevolumeofarightprismistheareaofthebasetimestheheightoftheprism.

A) IfVrepresentsthevolume,Btheareaofthebase,andhtheheight,thenV=Bh.

B) IfVrepresentsthevolume,Btheareaofthebase,andhtheheight,thenV=B+h.

C) IfVrepresentsthevolume,Btheareaofthebase,andhtheheight,thenV=B

D) IfVrepresentsthevolume,Btheareaofthebase,andhtheheight,thenV=1

2Bh.

3) Speedismeasuredbydistancedividedbytime.

A) IfSrepresentsspeed,ddistance,andttime,thenS=d

B) IfSrepresentsspeed,ddistance,andttime,thenS=t

C) IfSrepresentsspeed,ddistance,andttime,thend=S

D) IfSrepresentsspeed,ddistance,andttime,thent=S

4) Momentumistheproductofthemassofanobjectanditsvelocity.

A) IfMrepresentsmomentum,mmass,andvvelocity,thenM=mv.

B) IfMrepresentsmomentum,mmass,andvvelocity,thenM=1

2mv.

C) IfMrepresentsmomentum,mmass,andvvelocity,thenM=m

D) IfMrepresentsmomentum,mmass,andvvelocity,thenM=m+v.

Page39

5) Theforceofgravitybetweentwoobjectsisthegravitationalconstanttimestheproductoftheirmasses

dividedbythesquareofthedistancebetweenthem.

A) IfFistheforceofgravity,Gthegravitationalconstant,m1themassofoneobject,m2themassofthe

second,anddthedistancebetweenthem,thenF=Gm1m2

d2.

B) IfFistheforceofgravity,Gthegravitationalconstant,m1themassofoneobject,m2themassofthe

second,anddthedistancebetweenthem,thenFG=m1m2

d2.

C) IfFistheforceofgravity,Gthegravitationalconstant,m1themassofoneobject,m2themassofthe

second,anddthedistancebetweenthem,thenF=Gm1m2

D) IfFistheforceofgravity,Gthegravitationalconstant,m1themassofoneobject,m2themassofthe

second,anddthedistancebetweenthem,thenF=Gm1+m2

d2.

6) Thetotalcostofproducingrefrigeratorsinoneproductionlineis$4100 plus$200perunitproduced.

A) IfCisthetotalcostandxisthenumberofunitsproduced,thenC=4100+200x.

B) IfCisthetotalcostandxisthenumberofunitsproduced,thenC=4100x+200.

C) IfCisthetotalcostandxisthenumberofunitsproduced,thenC=(4100+200)x.

D) IfCisthetotalcostandxisthenumberofunitsproduced,thenC=4100

200x .

7) Theprofitderivedfromthesaleofxvideocamerasis$450 perunitlessthesumof$2200costsplus$200

perunit.

A) IfPisprofitandxtheunitssold,thenP=450x–(2200 +200x)orP=250x–2200.

B) IfPisprofitandxtheunitssold,thenP=450x–(2200 –200x)orP=650x–2200.

C) IfPisprofitandxtheunitssold,thenP=450

–(2200+200

x)orP=250

–2200.

D) IfPisprofitandxtheunitssold,thenP=450x+2200 –200xorP=250x+2200.

2 SolveInterestProblems

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Solvetheproblem.

1) DonJameswantstoinvest$67,000toearn$5200 peryear.HecaninvestinB–ratedbondspaying13% per

yearorinaCertificateofDeposit(CD)paying4%peryear.Howmuchmoneyshouldbeinvestedineach

torealizeexactly$5200ininterestperyear?

A) $28,000inB–ratedbondsand$39,000 inaCD B) $39,000 inB–ratedbondsand$28,000 inaCD

C) $29,000inB–ratedbondsand$38,000 inaCD D) $38,000 inB–ratedbondsand$29,000 inaCD

2) Abankloanedout$51,000

partofitattherateof11% peryearandtherestatarateof5%peryear.Ifthe

interestreceivedwas$4650,howmuchwasloanedat11%?

A) $35,000 B) $16,000 C) $36,000 D) $15,000

3) Aloanofficeratabankhas$92,000tolendandisrequiredtoobtainanaveragereturnof16% peryear.If

hecanlendattherateof17%ortherateof11%,howmuchcanhelendatthe11%rateandstillmeethis

requiredreturn?

A) $15,333.33 B) $3285.71 C) $506,000.00 D) $5411.76

Page40

4) Acollegestudentearned$8800duringsummervacationworkingasawaiterinapopularrestaurant.The

studentinvestedpartofthemoneyat10%andtherestat9%.Ifthestudentreceivedatotalof$825in

interestattheendoftheyear,howmuchwasinvestedat10%?

A) $3300 B) $5500 C) $4400 D) $977

5) Susanpurchasedsomemunicipalbondsyielding7%annuallyandsomecertificatesofdeposityielding9%

annually.IfSusanʹsinvestmentamountsto$19,000andtheannualincomeis$1590,howmuchmoneyis

investedinbondsandhowmuchisinvestedincertificatesofdeposit?

A) $5500inbonds;$13,500incertificatesofdeposit

B) $13,000inbonds;$6000incertificatesofdeposit

C) $13,500inbonds;$5500incertificatesofdeposit

D) $6000inbonds;$13,000incertificatesofdeposit

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

6) Martinpurchasedsomemunicipalbondsyielding8%annuallyandsomecertificatesofdeposityielding

11%annually.IfMartinʹsinvestmentamountsto$23,000andtheannualincomeis$2230,howmuch

moneyisinvestedinbondsandhowmuchisinvestedincertificatesofdeposit?

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

7) Kevininvestedpartofhis$10,000bonusinacertificateofdepositthatpaid6%annualsimpleinterest,and

theremainderinamutualfundthatpaid11%annualsimpleinterest.Ifhistotalinterestforthatyearwas

$700,howmuchdidKevininvestinthemutualfund?

A) $2000 B) $8000 C) $3000 D) $1000

3 SolveMixtureProblems

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Solvetheproblem.

1) Themanagerofacoffeeshophasonetypeofcoffeethatsellsfor$9 perpoundandanothertypethatsells

for$12perpound.Themanagerwishestomix100poundsofthe$12coffeetogetamixturethatwillsell

for$10perpound.Howmanypoundsofthe$9coffeeshouldbeused?

A) 200lb B) 100lb C) 300 lb D) 150 lb

2) Theownersofacandystorewanttosell,for$6perpound,amixtureofchocolate–coveredraisins,which

usuallysellsfor$3perpound,andchocolate–coveredmacadamianuts,whichusuallysellsfor$8per

pound.Theyhavea50–poundbarreloftheraisins.Howmanypoundsofthenutsshouldtheymixwith

thebarrelofraisinssothattheyhittheirtargetvalueof$6perpoundforthemixture?

A) 75lb B) 70lb C) 65 lb D) 80lb

3) Themanagerofacandyshopsellschocolatecoveredpeanutsfor$6 perpoundandchocolatecovered

cashewsfor$9perpound.Themanagerwishestomix70poundsofthecashewstogetacashew–peanut

mixturethatwillsellfor$7perpound.Howmanypoundsofpeanutsshouldbeused?

A) 140lb B) 70lb C) 210 lb D) 105 lb

4) Achemistneeds180millilitersofa52%solutionbuthasonly44%and62%solutionsavailable.Findhow

manymillilitersofeachthatshouldbemixedtogetthedesiredsolution.

A) 100mLof44%;80mLof62% B) 110 mLof44%;70mLof62%

C) 80mLof44%;100mLof62% D) 70 mLof44%;110mLof62%

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5) Howmuchpureacidshouldbemixedwith4 gallonsofa50%acidsolutioninordertogetan80%acid

solution?

A) 6gal B) 2gal C) 16 gal D) 10gal

6) Theradiatorinacertainmakeofcarneedstocontain50 liters of40%antifreeze.Theradiatornowcontains

50litersof20%antifreeze.Howmanylitersofthissolutionmustbedrainedandreplacedwith100%

antifreezetogetthedesiredstrength?

A) 12.5LB)20LC)25L D) 16.7 L

7) Howmanygallonsofa30%alcoholsolutionmustbemixedwith60gallonsofa14%solutiontoobtaina

solutionthatis20%alcohol?

A) 36gal B) 27gal C) 7gal D) 12gal

8) Howmanylitersof80%hydrochloricacidmustbemixedwith40%hydrochloricacidtoget15litersof

65%hydrochloricacid?Writeyouranswerroundedtothreedecimals.

A) 9.375L B) 3.125L C) 4.688LD)8L

4 SolveUniformMotionProblems

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Solvetheproblem.

1) Anairplaneflies460mileswiththewindand310 againstthewindinthesamelengthoftime.Ifthespeed

ofthewindis30,whatisthespeedoftheairplaneinstillair?

A) 154mph B) 144mph C) 159 mph D) 62mph

2) Aboatheadsupstreamadistanceof30milesontheMississippiriver,whosecurrentisrunningat5miles

perhour.Ifthetripbacktakesanhourless,whatwasthespeedoftheboatinstillwater?Givetheanswer

roundedtotwodecimalplaces,ifnecessary.

A) 18.03mph B) 16.58mph C) 6mph D) 15mph

3) TwofriendsdecidetomeetinChicagotoattendaCubʹsbaseballgame.Robtravels172miles inthesame

timethatCarltravels156miles.Robʹstripusesmoreinterstatehighwaysandhecanaverage4mphmore

thanCarl.WhatisRobʹsaveragespeed?

A) 43mph B) 39mph C) 46 mph D) 40mph

4) Garycanhikeonlevelground3milesanhourfasterthanhecanonuphillterrain.Yesterday,hehiked36

miles,spending2hoursonlevelgroundand5hoursonuphillterrain.Findhisaveragespeedonlevel

ground.

A) 72

mph B) 4 2

mph C) 5 1

mph D) 7 5

mph

5) Twocarsstartfromthesamepointandtravelinthesamedirection.Ifonecaristraveling63 milesper

hourandtheothercaristravelingat57milesperhour,howfarapartwilltheybeafter8hours?

A) 48mi B) 960mi C) 504 mi D) 456 mi

6) Twotrainsleaveatrainstationatthesametime.Onetravelseastat11 milesperhour.Theothertrain

travelswestat10milesperhour.Inhowmanyhourswillthetwotrainsbe73.5milesapart?

A) 3.5hr B) 7hr C) 1.8 hr D) 4hr

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7) KenandKaraare25milesapartonacalmlakepaddlingtowardeachother.Kenpaddlesat3 milesper

hour,whileKarapaddlesat6milesperhour.Howlongwillittakethemtomeet?

A) 2 7

hr B) 2 2

hr C) 16 hr D) 8 1

hr

8) Afreighttrainleavesastationtravelingat32km/h.Twohourslater,apassengertrainleavesthesame

stationtravelinginthesamedirectionat52km/h.Howlongdoesittakesthepassengertraintocatchupto

thefreighttrain?

A) 3.2hr B) 4.2hr C) 5.2hr D) 2.2hr

9) Fivefriendsdroveatanaveragerateof60 milesperhourtoaweekendretreat.Onthewayhome,they

tookthesameroutebutaveraged65milesperhour.Whatwasthedistancebetweenhomeandtheretreat

iftheroundtriptook10hours?

A) 312mi B) 51

mi C) 7800 mi D) 624 mi

10) DuringahurricaneevacuationfromtheeastcoastofGeorgia,afamilytraveled290mileswest.Forpartof

thetrip,theyaveraged60mph,butasthecongestiongotbad,theyhadtoslowto30mph.Ifthetotaltime

oftravelwas8hours,howmanymilesdidtheydriveatthereducedspeed?

A) 190mi B) 195mi C) 200 mi D) 185 mi

5 SolveConstantRateJobProblems

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Solvetheproblem.

1) Anexperiencedbankauditorcancheckabankʹsdepositstwiceasfastasanewauditor.Workingtogether

ittakestheauditors4hourstodothejob.Howlongwouldittaketheexperiencedauditorworkingalone?

A) 6hr B) 12hr C) 4 hr D) 8hr

2) BJcanoverhaulaboatʹsdieselinboardenginein15 hours.Hisapprenticetakes30hourstodothesame

job.Howlongwouldittakethemworkingtogetherassumingnogainorlossinefficiency?

A) 10hr B) 4hr C) 45 hr D) 6hr

3) Tracycanwallpaper3roomsinanewhousein12 hours.Togetherwithhertraineetheycanwallpaperthe

3roomsin8hours.Howlongwouldittakethetraineeworkingbyherselftodothejob?

A) 27hr B) 12hr C) 39 hr D) 54hr

4) Brandoncanpaintafencein12hoursandElainecanpaintthesamefencein11hours.Howlongwillthey

taketopaintthefenceiftheyworktogether?

A) 5 13

hr B) 5 3

hr C) 5 17

hr D) 11 1

hr

5) Suecansewaprecutdressin3hours.Helencansewthesamedressin2hours.Iftheyworktogether,how

longwillittakethemtocompletesewingthatdress?Giveyouranswerroundedtoonedecimalplace,if

necessary.

A) 1.2hr B) 5hr C) 1.8hr D) 2.5hr

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

6) Twopumpscanfillawatertankin45minuteswhenworkingtogether.Alone,thesecondpumptakes3

timeslongerthanthefirsttofillthetank.Howlongdoesittakethefirstpumpalonetofillthetank?

Page43

Ch.1 EquationsandInequalities

AnswerKey

1.1 LinearEquations

1 SolveaLinearEquation

2 SolveEquationsThatLeadtoLinearEquations

3 SolveProblemsThatCanBeModeledbyLinearEquations

1.2 QuadraticEquations

1 SolveaQuadraticEquationbyFactoring

2 SolveaQuadraticEquationbyCompletingtheSquare

3 SolveaQuadraticEquationUsingtheQuadraticFormula

4 SolveProblemsThatCanBeModeledbyQuadraticEquations

1.3 ComplexNumbers;QuadraticEquationsintheComplexNumberSystem

1 Add,Subtract,Multiply,andDivideComplexNumbers

2 SolveQuadraticEquationsintheComplexNumberSystem

1.4 RadicalEquations;EquationsQuadraticinForm;FactorableEquations

1 SolveRadicalEquations

2 SolveEquationsQuadraticinForm

3 SolveEquationsbyFactoring

1.5 SolvingInequalities

1 UseIntervalNotation

2 UsePropertiesofInequalities

3 SolveInequalities

4 SolveCombinedInequalities

1.6 EquationsandInequalitiesInvolvingAbsoluteValue

1 SolveEquationsInvolvingAbsoluteValue

2 SolveInequalitiesInvolvingAbsoluteValue

1.7 ProblemSolving:Interest,Mixture,UniformMotion,ConstantRateJobApplications

1 TranslateVerbalDescriptionsintoMathematicalExpressions

2 SolveInterestProblems

3 SolveMixtureProblems

4 SolveUniformMotionProblems

5 SolveConstantRateJobProblems