Chapter 1 Find The Volume The Radius Inches And

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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) 3x=–6

A) {–2} B) {2} C) {3} D) {–3}

2) 8x=11

A) 11

8B) –11

8C) 8

11 D) –8

3) 3x+18=0

A) {–6} B) {6} C) {3} D) {–3}

4) 7x–11=0

A) 11

7B) –11

7C) 7

11 D) –7

5) 8x+1=0

A) –1

8B) 1

8C) 8 D) –8

6) –1

2x=–8

A) 16

9B) 9

16 C) –16

9D) –32

7) 9x=17+8x

A) {17} B) {–17} C) {18} D) {25}

8) 8x+12=2x+48

A) {6} B) {–6} C) {8} D) {–8}

9) –2x+84=5x+21

A) {9} B) {–9} C) {12} D) {–12}

10) –63–4x=18+5x

A) {–9} B) {9} C) {–7} D) {7}

11) 9x–(4x–1)=2

A) 1

5B) 1

13 C) –1

5D) –1

12) 4(3x–1)=16

A) 5

3B) 1 C) 17

12 D) 5

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13) 14(5x–5)=4x–5

A) 65

66 B) 25

22 C) –65

66 D) 65

14) 6(x+5)=7x–(3–x)

A) 51

8B) –15

4C) 15

4D) –51

15) 2(x+3)=3(x–4)

A) {18} B) {–18} C) {–6} D) {3}

16) 2(2x–2)=3(x+5)

A) {19} B) {–11} C) {–19} D) {13}

17) 5(x+4)=(5x+20)

A) allrealnumbers B) {40} C) {0} D) nosolution

18) 2x+7–2(x+1)=7x+5

A) 0 B) 7

8C) 7

5D) {7}

19) –6x+9+4x=–2x+14

A) nosolution B) {5} C) {–9} D) allrealnumbers

20) x

–3=1

A) {24} B) {–24} C) {12} D) {–12}

21) x

–1

=–3

A) {–8} B) {8} C) {–10} D) {10}

22) 2x

=4+x

A) {60} B) {–60} C) {120} D) {–120}

23) x

–3=x

–7

A) 30 B) –30 C) 8

15 D) –8

24) 4

+x

=11

A) 3

5B) –3

5C) 3

2D) –3

25) –6.7x+1.5=–8.5–1.7x

A) {2} B) {–15} C) {1.5} D) {1.7}

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26) –7x+4

+1=–5x

A) –14 B) –2 C) 2 D) 14

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

=2

A) 28

45 B) –28

45 C) –28 D) 1

2) 5

+2

=7

A) {5} B) {–5} C) {2} D) {–2}

3) (x+8)(x–1)=(x+1)2

A) 9

5B) 8

5C) 9

8D) {9}

4) x(5x–2)=(5x+1)(x–2)

A) –2

7B) –1

4C) –2

3D) {3}

5) x(1+3x)=(3x–1)(x–3)

A) 3

11 B) –3

11 C) 3

121 D) –3

121

6) x(x2+6)=2+x3

A) 1

3B) {6} C) {2} D) 3

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

=1

x2–4

–3

x+2

A) 7

5B) –1 C) 5 D) –1

9) 5–x

+3

=7

A) {–8} B) –8

7C) {8} D) {–4}

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10) 1

+1

x–8

=x–7

x–8

A) {1} B) {8} C) {–1} D) {–8}

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) 6x+6

2x–5

=9x+5

3x+2

A) –37

65 B) 37

5C) –1

5D) 13

14) 6

–1

x+1

=2

x(3x+3)

A) –8

3B) {–8} C) –8

15 D) nosolution

15) 4

x+3

–2

x–3

=8

x2–9

A) {13} B) {–13} C) {3} D) {26}

16) 8x–8

2x–3

=20x+6

5x+8

A) 23

36 B) –23

12 C) –41

36 D) 41

17) 6

+1

=–6

A) –7

6B) –6

7C) 7

6D) 6

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–5Q

=P+3

+1forP

A) P=35+10Q

7B) P=35 –10Q

7C) P=7–10Q

7D) P=7+10Q

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259 carsmorethanCenterCityWestParkingGarage.If

thecombinedcapacityforthetwogaragesis1237cars,findthecapacityforeachgarage.

A) CenterCityEast:748cars

CenterCityWest:489cars

B) CenterCityEast:489cars

CenterCityWest:748cars

C) CenterCityEast:758cars

CenterCityWest:479cars

D) CenterCityEast:479cars

CenterCityWest:758cars

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

scoredatotalof146points.HowmanypointsdidTeamAscoreduringthegame?

A) 65points B) 81points C) 66 points D) 73points

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12) Anautorepairshopchargedacustomer$259 torepairacar.Thebilllisted$59forpartsandtheremainder

forlabor.Ifthecostoflaboris$50perhour,howmanyhoursoflabordidittaketorepairthecar?

A) 4hr B) 3hr C) 5 hr D) 4.5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16%pricereduction,aboatsoldfor$21,840.Whatwastheboatʹspricebeforethereduction?

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

A) $26,000 B) $3494.40 C) $136,500.00 D) $25,334.40

15) Inclusiveofa6.6%salestax,adiamondringsoldfor$2984.80.Findthepriceoftheringbeforethetaxwas

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

A) $2800 B) $3181.80 C) $2787.80 D) $197.00

16) Itcosts$29perhourplusaflatfeeof$30 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$233.Howmanyhoursdidthe

plumberwork?

A) 7hr B) 4hr C) 19 hr D) 16hr

17) Arectangularcarpethasaperimeterof240 inches.Thelengthofthecarpetis68inchesmorethanthe

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

A) 94in.by26in. B) 94in.by120 in. C) 73 in.by99 in. D) 107 in.by120 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$43 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=43x B) y=86x C) y=22x D) y=129x

20) Itcosts$40perhourplusaflatfeeof$34 foraplumbertomakeahousecall.Whatisanequationofthe

formy=ax+bforthissituation?

A) y=40x+34 B) y=34x+40 C) y=40x D) y=34x

21) Usingaphonecardtomakealongdistancecallcostsaflatfeeof$0.77 plus$0.12perminutestartingwith

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

A) y=0.12x+0.77 B) y=0.77x+0.12 C) y=0.77x D) y=0.12x

22) xrepresentsthenumberoftextbookspurchasedat$27 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5textbooks?

A) $135 B) $270 C) $67.50 D) $5.40

23) xrepresentsthenumberofcassettetapessoldat$5.25 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17cassettes?

A) $89.25 B) $178.5 C) $44.63 D) $0.31

24) Itcosts$44perhourplusaflatfeeof$21 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2hours?

A) $109 B) $86 C) $88 D) $926

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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) 15x2–3x=0

A) { 1

5,0} B) { 1

5,–1

5} C) {0} D) {–1

5,0}

2) 6x2+14x=0

A) {–7

3,0} B) { 7

3,–7

3} C) {0} D) { 7

3,0}

3) x2–81=0

A) {9

–9} B) {9} C) {–9} D) {81}

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–6x+8=0

A) {2

4} B) {2

–4} C) {–2

4} D) {–2

–4}

6) x2–5x–36=0

A) {–4

9} B) {–4

–9} C) {4

–9} D) {4

9}

7) 2x2+6x–8=0

A) {1

–4} B) {1

4} C) {–1

–4} D) {–1

4}

8) 2x2–10=0

A) {–5,5} B) {6} C) {–5

5} D) {5}

9) x(x–10)+24=0

A) {4

6} B) {4

–6} C) {–4

6} D) {–4

–6}

10) 64x2–48x+9=0

A) { 3

8}B){

3}C){

–3

8}D){

–8

11) 12x2–5x–25=0

A) { 5

4,5

3}B){

4,–5

3}C){

–5

4,5

3}D){

–5

4,–5

12) 4x–23=6

A) {–1

4,6} B) {–1

4,4} C) { 1

23,–1

4}D){

–4

6}

Page7

13) 10x+25

=–35

A) {–1,–5

2}B){1,5

2}C){

–1,5

2} D) {10,2

14) x–5

=24

x+5

A) {25

–1} B) {25

1} C) {5

–1} D) {5

1}

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

15) x2=100

A) {10

–10} B) {10} C) {11

–11} D) {50}

16) (x–2)2=4

A) {4

0} B) {6} C) {2

–2} D) {0

–4}

17) (2x–5)2=9

A) {4

1} B) {–1

–4} C) {8

2} D) {–2

–8}

18) x2=5

A) { 5,–5}B){5

–5} C) { 5}D)norealsolution

19) (x+2)2=11

A) {–2+11,–2–11}B){2+11,2–11}

C) { 11,–11}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=7

A) {–2–11,–2+11}B){2+11}

C) {–1–11,–1+11}D){

–2–211,–2+211}

3) x2+12x+20=0

A) {–2

–10} B) {2

10} C) {2

–1} D) {30

–10}

4) x2+12x+13=0

A) {–6–23,–6+23}B){6+23}

C) {6–13,6+13}D){

–12+13}

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–5=0

A) {–4–21,–4+21}B){4+21}

C) {–1–21,–1+21}D){

–4–221,–4+221}

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) 7x2–2x–3=0

A) { 1–22

7,1+22

7}B){

7–22

49 ,7+22

49 }

C) {–3,23

7}D){

–1–22

7,–1+22

10) 49x2+98x+48=0

A) {–6

7,–8

7}B){

–6

49,–8

49}C){

7,8

7}D){

–8

7,8

11) x2+1

2x–15

=0

A) {–5

4,3

4}B){

4,3

4}C){

–5

4,–3

4}D){

4,–3

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–5=0

A) {–4–21,–4+21}B){4+21}

C) {–1–21,–1+21}D){

–4–221,–4+221}

2) x2–4x–13=0

A) {2+17,2–17}B){2+13,2–13}

C) {–2+17,–2–17}D){4+17,4–17}

Page9

3) 5x2+13x–6=0

A) { 2

5,–3} B) { 2

5,3} C) {–2

5,–3} D) {–2

5,3}

4) 4x2–x+1=0

A) { –1–17

8,–1+17

8}B){

–1+17

8,1+17

C) { –1–17

8,1+17

8}D)norealsolution

5) x2+5x+1=0

A) { –5–21

2,–5+21

2}B){

5–21

2,5+21

C) { –5–21

10 ,–5+21

10 }D){

–5–29

2,–5+29

6) 3x2+x–1=0

A) { –1–13

6,–1+13

6}B){

–1–13

2,–1+13

C) { 1–13

6,1+13

6}D)norealsolution

7) 2x2+10x+7=0

A) { –5–11

2,–5+11

2}B){

–5–11

4,–5+11

C) { –10–11

2,–10+11

2}D){

–5–39

2,–5+39

8) 6x=4x2

A) {0,3

2}B){

2,–3

2} C) {0} D) {0,–3

9) 25x2–70x+49=0

A) { 7

5}B){

–7

5}C){

5,–35} D) norealsolution

10) 49x2+20=–84x

A) {–2

7,–10

7}B){

–2

49,–10

49}C){

7,10

7}D){

–10

49,30

49}

11) 6x2+12x=–2

A) {–3–6

3,–3+6

3}B){

–3–6

12 ,–3+6

12 }

C) { –12–6

3,–12+6

3}D){

–3–3

3,–3+3

Page10

12) 6x2=–12x–2

A) { –3–6

3,–3+6

3}B){

–3–6

12 ,–3+6

12 }

C) { –12–6

3,–12+6

3}D){

–3–3

3,–3+3

13) 7x=1+–3

A) { 1–85

14 ,1+85

14 }B){

–1+85

14 ,1–85

14 }

C) { 1–85

14 }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+5x–5=0

A) {–3.62

1.38} B) {–1.38

3.62} C) {–3.62

–1.38} D) {–3.62

3.62}

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–4x+3=0

A) repeatedrealsolutio

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

17) x2–8x+16=0

A) repeatedrealsolutio

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

18) x2+4x+6=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8 feetlongerthanitswidth.Iftheareaofthegardenis65 squarefeet,

finditsdimensions.

A) 5ftby13ft B) 4ftby14 ft C) 6 ftby14 ft D) 4ftby12 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81πsquare

centimeters,finditsradiusr.

A) 9cm B) 9πcm C) 9 πcm D) {9cm,–9 cm}

3) A29–inch–squareTVisonsaleatthelocalelectronicsstore.If29 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) 29 2

in. B) 29in. C) 29

in. D) 841

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128 feettallwithaninitialvelocityof112 feet

persecond.Thedistances(infeet)oftheballfromthegroundaftertsecondsiss=128+112t–16t2.After

howmanysecondsdoes theballstrike theground?

A) 8sec B) 129sec C) 7 sec D) 10sec

7) Aspartofaphysicsexperiment,Mingdropsabaseballfromthetopofa310–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) 4.4sec B) 77.5 sec C) 19.4 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$598million.

A) 2004 B) 2006 C) 2003 D) 2005

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$845in2years.

A) 30% B) 69% C) 3% D) 230%

Page12

10) Acircularpoolmeasures10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3inches,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) 2.71ft B) 9.3ft C) 3.53 ft D) 6.72 ft

11) Ifapolygon,ofnsideshas1

2n(n–3)diagonals,howmanysideswillapolygonwith779diagonalshave?

A) 41sides B) 42sides C) 40 sides D) 43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) (6–6i)+(4+9i)

A) 10+3i B) 10–3i C) 2 +15i D) –10 –3i

2) (6+5i)–(–8+i)

A) 14+4i B) 14–4i C) –2+6i D) –14 –4i

3) 6(7–5i)

A) 42–30i B) 42+30i C) 42i–5i D) 7–30i

4) 6i(5–3i)

A) 18+30i B) 30i–18 C) 30i–18i2D) 30i+18i2

5) –6i(–3+9i)

A) 54+18i B) –54+18i C) 18i–54i2D) 18i+54i2

6) (–4–3i)(5+i)

A) –17–19i B) –23–19i C) –17 +11i D) –23 +11i

7) (3+9i)(6+8i)

A) –54+78i B) –54–78i C) 90 +30i D) 72i2+78i+18

8) (6+5i)(4–4i)

A) 44–4i B) 44+4i C) 4 +44i D) –20i2–4i+24

9) (7+6i)(7–6i)

A) 85 B) 49–36i2C) 13 D) 49–36i

Page13

10) (–4+i)(–4–i)

A) 17 B) –4C)16D)

–15

11) (4+6i)(4–6i)

A) 52 B) 16–36i2C) –20 D) 16–36i

12) 5

8+i

A) 8

–1

13iB)

+1

13iC)

+5

63iD)

–5

63i

13) 7

2–i

A) 14

+7

5iB)

–7

5iC)

+7

3iD)

–7

14) 4

2–5i

A) 8

+20

29iB)

–20

29iC)

–8

+20

21iD)

–8

–20

21i

15) 5i

2–i

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

16) 5+2i

2–5i

A) i B) –iC)1 D)

–1

17) –22+32i

2+5i

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

18) 7+3i

7–5i

A) 17

+28

37iB)

–7

6iC)

+14

37iD)

–7

19) (4+6i)2

A) –20+48i B) 52+48i C) –20 D) 16+48i+36i2

20) 2

+2

i2

A) i B) –iC)

2D) –i

21) i16

A) 1 B) –1C)i D)

–i

Page14

22) i3

A) –i B) i C) 1 D) –1

23) i21

A) i B) –iC)1 D)

–1

24) i22

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)5

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

28) i6+i4+i2+1

A) 0 B) 1 C) i D) –1

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

29) –25

A) 5i B) –i5 C) –5i D) ±5

30) –36

A) 6i B) i 6 C) –6i D) ±6

31) (3+4i)(4i–3)

A) 5i B) –5i C) –5D)5

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

32) Ifz=9–3i,evaluatez+z.

A) 18 B) 18–6i C) –6i D) 18+6i

33) Ifw=8+5i,evaluatew–w.

A) 10i B) –16+10i C) 16 D) 0

34) Ifz=2–8i,evaluatezz.

A) 68 B) 4–64i2C) –60 D) 4–64i

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

A) 13–5i B) 13+5i C) 3 +7i D) –13 –5i

36) Ifz=8–9iandw=9+4i,evaluatez+w.

A) 17–5i B) 17+5i C) –1+13i D) –17 +5i

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+12x+40=0

A) {–6+2i,–6–2i} B) {–6–4i,–6+4i} C) {–6+2i} D) {–4

–8}

3) x2+x+4=0

A) {–1

–15

2i,–1

+15

2i} B) { 1–15

2,1+15

C) { 1

–15

2i,1

+15

2i} D) { –1–15

2,–1+15

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–4x2–5=0

A) {–5,5,i,–i} B) { 5i,i} C) {–5i,–i} D) { 5,5}

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

8) x2+8x+7=0

A) twounequalrealsolutions

B) arepeatedrealsolutio

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

9) x2+12x+36=0

A) arepeatedrealsolutio

B) twounequalrealsolutions

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

10) x2–5x+8=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–7x+3=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+3=5

A) {22} B) {25} C) {28} D) {64}

2) 9x–8=8

A) {8} B) {64} C) { 56

9}D){

3) 3x+4=4

A) {4} B) {16} C) { 20

3}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) 34x+1=–2

A) {–9

4}B){

4}C){

–2} D) {–3}

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=2x

A) {0,4} B) {0,2} C) {–4

4} D) {–2

2}

Page17

9) 8x+33 =x

A) {11} B) {–3

11} C) {–33

7}D)norealsolution

10) 26x–39=x+5

A) {8} B) {–7} C) {–8} D) {6}

11) x+7+x=3

A) { 1

9} B) {4} C) {1} D) norealsolution

12) x2–5x+4=x–3

A) {5} B) {–5} C) {–5

2}D){2}

13) x2–3x+77=x+5

A) {4} B) {–4} 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) (2x+4)1/2=3

A) { 5

2}B){

2}C){

–2} D) {8}

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) (3x+2)1/3=3

A) { 25

3}B){

3} C) {9} D) {12}

23) (x+3)1/3=–2

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

24) (x2+3)1/2=9

A) { 78,–78}B){78

–78} C) { 6}D){6}

25) x3

4–6x1

4=0

A) {0,36} B) {0,1296} C) { 6}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–50x2+49=0

A) {–1,1,–7

7} B) {–7

7} C) {–49

49} D) {–50

50}

2) 5x4+7x2–6=0

A) {–3

5,3

5} B) {–3

5,3

5}C){

–2

5,2

5}D){

–2,2}

3) x6+7x3–8=0

A) {–2

1} B) {8} C) {2} D) {2

–1}

4) 2(x+1)2+11(x+1)+12=0

A) {–5

2,–5} B) {1

3} C) {–3

2,–5} D) {–5

2,–4}

5) (3x–7)2–4(3x–7)–12=0

A) { 5

3,13

3}B){

–5

3,–13

3}C){

3,–1

3}D){

–9

7,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=30

A) {25} B) {5} C) {6} D) {36}

8) x+3x1/2+2=0

A) {1

4} B) {–1

–2} C) { 1

4}D)norealsolution

Page19

9) x1/2–7x1/4+12=0

A) {256

81} B) {16

9} C) {4

3} D) {–4

–3}

10) x2+3x–x2+3x=42

A) { –3+205

2,–3–205

2}B){9

–9}

C) {6} D) {3}

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

2x–1

=–2

(2x–1)2

A) {–1

2,1

4}B){

–2,–1

2}C){

–1

2,0} D) {–1

2,–1

13) 3x–2–10x–1–25=0

A) {–3

5,1

5}B){

5,1

5}C){

–5

3,–5} D) {–5

3,5}

14) x2/3–4x1/3–5=0

A) {–1

125} B) {–1

5} C) {–5

1} D) {–125

1}

15) x2/3–2x1/3–3=0

A) {–1

27} B) {–1

3} C) {–3

1} D) {–27

1}

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–4

andk2–3k=28,findx.

A) { 31

6,13

5}B){

3,13

5}C){

6,1

5}D){

7,13

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4inchesandtheconeis3incheshigh.(Use3.14asan

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

A) 50.2cubicin. B) 12.6 cubicin. C) 452.2 cubicin. D) 16.7 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40milesperhour.

A) 640ft B) 4000 ft C) 256 ft D) 1600 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$39billion?

A) 2009 B) 2012 C) 2014 D) 2013

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5seconds.

A) h=4.9t2;122.5meters B) h=24.01t;120.1 meters

C) h=24.01t2;600.3meters D) h=4.9t;24.5 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30volts.

A) R=E2

P;1800ohms B) R=E2

P2;3600ohms

C) R=E2P;1800ohms D) R=E2P2;3600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

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

A) W=d2k

2;2.7joules B) W=d2k2

4;0.8joules

C) W=2d2

k;30joules D) W=2d2k;10.8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–64x=0

A) {0,8

–8} B) {0,8} C) {0,–8} D) {0,64}

2) 3x5=243x3

A) {–9

0,9} B) {–93,0,93}C){

–9

9} D) {0}

Page21

3) x3+3x2–36x–108=0

A) {–6

6

–3} B) {36

–3} C) {6

–3} D) {–6

6

3}

4) x3+2x2+9x+18=0

A) {–2} B) {2} C) {–3

3

–2} D) norealsolution

5) 2x4–32x2=0

A) {–4

0,4} B) {–42,0,42}C){

–4

4} D) {0}

6) 4x4=108x

A) {0,3} B) {–3

0,3} C) {0,4

3} D) {0}

7) x3+3x2–10x=0

A) {0,2

–5} B) {2

–5} C) {0,–2

5} D) {–2

5}

8) x3+8x2–x–8=0

A) {–1,1,–8} B) {1,–8

8} C) {–8

8} D) {64}

9) 15x3+90x2+120x=0

A) {0,–2

–4} B) {–2

–4} C) {0,2

4} D) {–1

2,–4}

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.

–10–9–8–7–6–5–4–3–2–101234567–10–9–8–7–6–5–4–3–2–101234567

A) [–6

3)

–6≤x<3

B) (–6

3)

–6<x<3

C) [–6

3]

–6≤x≤3

D) (–6

3]

–6<x≤3

56789101112135678910111213

A) (–∞

9]

x≤9

B) (–∞

9)

x<9

C) [9

∞)

x≥9

D) (9

∞)

x>9

–5–4–3–2–10123–5–4–3–2–10123

A) (–1

∞)

x>–1

B) (–∞

–1]

x≤–1

C) [–1

∞)

x≥–1

D) (–∞

–1)

x<–1

Page22

-4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 1011-4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 1011

A) (2

5)

2<x<5

B) [2

5]

2≤x≤5

C) (2

5]

2<x≤5

D) [2

5)

2≤x<5

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

A) [–6

–1]

–6≤x≤–1

B) (–6

–1)

–6<x<–1

C) [–6

–1)

–6≤x<–1

D) (–6

–1]

–6<x≤–1

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

A) [–8

8)

–8≤x<8

B) (–8

8]

–8<x≤8

C) (–∞

8)

x<8

D) [–8

8]

–8≤x≤8

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

7) –7

x

–2

A) (–7

–2)

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

B) [–7

–2]

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

C) (–7

–2)

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

D) [–7

–2)

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

8) 1≤x≤6

A) [1

6]

–1012345678–1012345678

B) (1

6)

–1012345678–1012345678

C) [1

6]

–1012345678–1012345678

D) (1

6]

–1012345678–1012345678

Page23

9) –1≤x

8

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

A) [–1

8)

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

B) (–1

8]

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

C) (–∞

8)

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

D) [–1

8)

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

10) t≥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

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) [–8

4)

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

A) –8≤x

4

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

B) –8

x≤4

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

C) x

4

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

D) –8≤x

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

Page24

13) [–1

3]

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

A) –1≤x≤3

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

B) –1

x≤3

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

C) –1

x

3

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

D) –1≤x

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

14) (–5

∞)

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

A) x>–5

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

B) x≥–5

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

C) x>–5

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

D) x≥–5

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

15) [1

∞)

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

A) x≥1

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

B) x>1

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

C) x>1

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

D) x≥1

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

16) (–∞

10)

A) x

10

6789101112131467891011121314

B) x≤10

6789101112131467891011121314

C) x

10

6789101112131467891011121314

D) x≤10

6789101112131467891011121314

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5fromeachsideoftheinequality3+2x>3.

A) –2+2x>–2B)

–2+2x

–2C)

–2–3x> –2D)

–2–3x

–2

2) Multiplyeachsideoftheinequality2+3x

–5by–5.

A) –10–15x>25 B) –10–15x

25 C) –10 +3x>25 D) –10 +3x

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

3) Ifx

2

thenx–2 0.

B) >C) ≤D) ≥

4) Ifx

–9

thenx+9 0.

B) >C) ≤D) ≥

5) Ifx>–3

then5x –15.

A) >B)

C) ≥D) ≤

6) Ifx

4

then–6x –24.

A) >B)

C) ≥D) ≤

7) Ifx>–3

then–4x 12.

B) >C) ≥D) ≤

8) If–1

3x<–2

3,thenx_____2.

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

3

A) (–∞

6)

–1012345678910111213–1012345678910111213

B) (6

∞)

–1012345678910111213–1012345678910111213

C) (–∞

0)

–7–6–5–4–3–2–101234567–7–6–5–4–3–2–101234567

D) (–∞

0]

–7–6–5–4–3–2–101234567–7–6–5–4–3–2–101234567

Page26

2) x+5

8

A) (–∞

3)

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

B) (3

∞)

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

C) (–∞

13)

6 7 8 9 10111213141516171819206 7 8 9 1011121314151617181920

D) (–∞

3]

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

3) 4x+8

36

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

A) (–∞

7)

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

B) (7

∞)

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

C) [7

∞)

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

D) (–∞

7]

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

4) 4x–1>3x+3

A) (4

∞)

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

B) (–∞

4]

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

C) (2

∞)

–5–4–3–2–10123456789–5–4–3–2–10123456789

D) [4

∞)

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

Page27

5) –4x–2≤–5x+4

A) (–∞

6]

–1012345678910111213–1012345678910111213

B) (–∞

6)

–1012345678910111213–1012345678910111213

C) [6

∞)

–1012345678910111213–1012345678910111213

D) [2

∞)

–5–4–3–2–10123456789–5–4–3–2–10123456789

6) –3x–5≥–4x–11

A) [–6

∞)

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

B) (–∞

–6)

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

C) (–∞

–6]

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

D) (–16

∞)

–23-22-21-20-19-18-17-16-15-14-13-12-11-10 –9–23-22-21-20-19-18-17-16-15-14-13-12-11-10 –9

Page28

7) 4x–2>3x–1

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) (–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) [1

∞)

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

8) 11–3(3–x)≤–4

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

A) (–∞

–2]

–10–8–6–4–20246810–10–8–6–4–20246810

B) [–2

∞)

–10–8–6–4–20246810–10–8–6–4–20246810

C) (–∞

–1]

–10–8–6–4–20246810–10–8–6–4–20246810

D) (–∞

–2)

–10–8–6–4–20246810–10–8–6–4–20246810

9) –16x+28≤–4(3x–12)

A) [–5

∞)

–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

B) (–∞

–5]

–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

C) [–5

∞)

–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) (–∞

–5)

–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29

10) –4(6x+1)

–28x+4

A) (–∞

2)

–5–4–3–2–10123456789–5–4–3–2–10123456789

B) (2

∞)

–5–4–3–2–10123456789–5–4–3–2–10123456789

C) (–∞

2]

–5–4–3–2–10123456789–5–4–3–2–10123456789

D) (–∞

–0]

–7–6–5–4–3–2–101234567–7–6–5–4–3–2–101234567

11) x

≥4+x

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

A) [10

∞)

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

B) [–10

∞)

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

C) (–∞

10]

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

D) (10

∞)

–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(9x–4)≤(3x+5)2

–5–4–3–2–1012345–5–4–3–2–1012345

A) [–25

34,∞)

–5–4–3–2–1012345–5–4–3–2–1012345

B) (–∞,–25

34]

–5–4–3–2–1012345–5–4–3–2–1012345

C) [ 25

34,∞)

–5–4–3–2–1012345–5–4–3–2–1012345

D) (–∞,–25

34]

–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) 4

2x≤12

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) 15≤3x+3≤18

A) [4

5]

–2–101234567891011–2–101234567891011

B) (4

5)

–2–101234567891011–2–101234567891011

C) [–5

–4]

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

D) (–5

–4)

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

Page32

3) –16≤–3x–1

–10

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

4) –34≤–5x–4≤–19

A) [3

6]

–2–101234567891011–2–101234567891011

B) (3

6)

–2–101234567891011–2–101234567891011

C) [–6

–3]

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

D) (–6

–3)

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

5) 0≤2x+3

<3

–5–4–3–2–1012345–5–4–3–2–1012345

A) [–3

2,3)

–5–4–3–2–1012345–5–4–3–2–1012345

B) [–3

2,3]

–5–4–3–2–1012345–5–4–3–2–1012345

C) (–3

2,3)

–5–4–3–2–1012345–5–4–3–2–1012345

D) (–3

2,3]

–5–4–3–2–1012345–5–4–3–2–1012345

Page33

6) 9≤5

2x+4<29

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

A) [2

10)

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

B) (2

10]

–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

<1

A) (2

∞)

–3–2–101234567–3–2–101234567

B) (–∞

2)

–3–2–101234567–3–2–101234567

C) ( 1

2,∞)

–4–3–2–1012345–4–3–2–1012345

D) (–∞,1

–4–3–2–1012345–4–3–2–1012345

8) 0<(8x–20)–1<1

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

A) (3

∞)

–3–2–10123456789–3–2–10123456789

B) (–∞

3)

–3–2–10123456789–3–2–10123456789

C) [3

∞)

–3–2–10123456789–3–2–10123456789

D) (–∞

3]

–3–2–10123456789–3–2–10123456789

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$1.99 foreachpay–per–viewmoviewatched.Inaddition,

eachmonthlybillcontainsabasiccustomerchargeof$21.50.Iflastmonthʹsbillsrangedfromalowof

$29.46toahighof$61.30,overwhatrangedidcustomerswatchpay–per–viewmovies?

A) movieswatchedvariedfrom4to20 inclusive B) movieswatchedvariedfrom3to19 inclusive

C) movieswatchedvariedfrom5to21 inclusive D) movieswatchedvariedfrom3to21 inclusive

13) Duringthefirstfivemonthsoftheyear,Lenearnedcommissionsof$3020

$3480

$3190

$2980

and$2620.

IfLenmusthaveaveragemonthlyearningsofatleast$2960inordertoqualifyforretirementbenefits,

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

A) atleast$2470 B) atleast$3041 C) atleast$2960 D) atleast$3058

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

$28,000plus20%ofthesellingpriceinexcessof$900,000.Assumingthattheofficebuildingwillsellat

somepricebetween$900,000and$1,000,000,inclusive,overwhatrangedoestheagentʹscommissionvary?

A) Thecommissionwillvarybetween$28,000 and$48,000

inclusive.

B) Thecommissionwillvarybetween$29,000 and$48,000

inclusive.

C) Thecommissionwillvarybetween$28,000 and$218,000

inclusive.

D) Thecommissionwillvarybetween$208,000 and$228,000

inclusive.

15)

imhasgottenscoresof82and60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83 B) atleast71 C) atleast72 D) atleast81

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|=9

A) {–9

9} B) {9} C) {–9} D) {81}

2) |x|=–1

A) {1} B) {1

–1} C) {–1} D) nosolution

3) |x|+8=–2

A) {10} B) {10

–10} C) {–10} D) nosolution

4) |x+4|=2

A) {–6

–2} B) {6

–2} C) {2} D) nosolution

5) |3x+8|=4

A) {–4

3,–4} B) {–1

2,–3

2}C){

3,4} D) nosolution

6) |x–3|=0

A) {3} B) {–3

3} C) {–3} D) nosolution

7) 3|x–3|=18

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

8) |8x+5|+6=10

A) {–1

8,–9

8}B){

–1

5,–9

5}C){

8,9

8}D)nosolution

9) 3x+6

=3

A) {–4

0} B) {–4

4} C) {4

0} D) nosolution

10) 3(x+1)+6=18

A) {–9

3} B) {–7

5} C) {–9

0} D) {–7

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) 3x+8=x–7

A) –15

2,–1

4B) –15

2,23

4C) 15

2,1

4D) ∅

16) 4x+12

=4

A) {–6

0} B) {–6

6} C) {6

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|

–12

A) (–12

12) B) {–12} C) (–∞

∞)D)nosolution

3) |x|>–7

A) (–7

7) B) {7} C) (–∞

∞)D)nosolution

4) |2x–4|–6>–9

A) (–∞,1

2)or(7

2,∞)B)(

2,7

2)C)(

–∞

∞)D)nosolution

5) |x+7|+9≤15

A) [–13

–1] B) (–∞

–13)or(–1

∞)

C) [13

15] D) nosolution

6) |7x–2|+4

12

A) (–6

7,10

7)B)(

–∞,–6

7)or(10

7,∞)

C) (–∞,–6

7)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) |5x+3|+|–4|≤6

A) [–1,–1

5]B)(

–∞,–1]or[–1

5,∞)

C) [ 1

5,1] D) (–∞,1

5]or[1,∞)

11) |x+1|

0

A) (1

–1) B) (–∞

–1) C) (1

∞)D)nosolution

12) |x+6|≤0

A) {–6} B) {6} C) (–∞

–6) D) nosolution

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

13) x2<4

A) {x|2

x

2} B) {x|x

C) {x|–2≤x≤2} D) {x|x

–2orx>2}

14) x2≥16

A) {x|x≤–4orx≥4} B) {x|x

–4orx>4}

C) {x|–4≤x≤4} D) {x|x

–4orx≥4}

15) x2>16

A) {x|x

–4orx>4} B) {x|x≤–4 orx≥4}

C) {x|–4≤x≤4} D) {x|x

–4orx≥4}

16) x2≤16

A) {x|–4≤x≤4} B) {x|x≤4}

C) {x|–4

x

4} D) {x|x≤–4orx≥4}

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–2

7

thena

x–4

b.

A) a=–9

b=5B)a=–11

b=3C)a= –5

b=9D)a= –3

b=11

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$5000 plus$120perunitproduced.

A) IfCisthetotalcostandxisthenumberofunitsproduced,thenC=5000+120x.

B) IfCisthetotalcostandxisthenumberofunitsproduced,thenC=5000x+120.

C) IfCisthetotalcostandxisthenumberofunitsproduced,thenC=(5000+120)x.

D) IfCisthetotalcostandxisthenumberofunitsproduced,thenC=5000

120x .

7) Theprofitderivedfromthesaleofxvideocamerasis$300 perunitlessthesumof$2100costsplus$200

perunit.

A) IfPisprofitandxtheunitssold,thenP=300x–(2100 +200x)orP=100x–2100.

B) IfPisprofitandxtheunitssold,thenP=300x–(2100 –200x)orP=500x–2100.

C) IfPisprofitandxtheunitssold,thenP=300

–(2100+200

x)orP=100

–2100.

D) IfPisprofitandxtheunitssold,thenP=300x+2100 –200xorP=100x+2100.

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$62,000toearn$6320 peryear.HecaninvestinB–ratedbondspaying13% per

yearorinaCertificateofDeposit(CD)paying7%peryear.Howmuchmoneyshouldbeinvestedineach

torealizeexactly$6320ininterestperyear?

A) $33,000inB–ratedbondsand$29,000 inaCD B) $29,000 inB–ratedbondsand$33,000 inaCD

C) $34,000inB–ratedbondsand$28,000 inaCD D) $28,000 inB–ratedbondsand$34,000 inaCD

2) Abankloanedout$65,000

partofitattherateof12% peryearandtherestatarateof8%peryear.Ifthe

interestreceivedwas$6520,howmuchwasloanedat12%?

A) $33,000 B) $32,000 C) $34,000 D) $31,000

3) Aloanofficeratabankhas$100,000tolendandisrequiredtoobtainanaveragereturnof14% peryear.If

hecanlendattherateof15%ortherateof12%,howmuchcanhelendatthe12%rateandstillmeethis

requiredreturn?

A) $33,333.33 B) $3703.70 C) $966,666.67 D) $6666.67

Page40

4) Acollegestudentearned$5100duringsummervacationworkingasawaiterinapopularrestaurant.The

studentinvestedpartofthemoneyat10%andtherestat8%.Ifthestudentreceivedatotalof$478in

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

A) $3500 B) $1600 C) $2550 D) $637

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$13perpound.Themanagerwishestomix50poundsofthe$13coffeetogetamixturethatwillsell

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

A) 150lb B) 75lb C) 200 lb D) 100 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70–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) 105lb B) 98lb C) 91 lb D) 112 lb

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

cashewsfor$13perpound.Themanagerwishestomix40poundsofthecashewstogetacashew–peanut

mixturethatwillsellfor$8perpound.Howmanypoundsofpeanutsshouldbeused?

A) 100lb B) 50lb C) 140 lb D) 70lb

4) Achemistneeds150millilitersofa27%solutionbuthasonly12%and57%solutionsavailable.Findhow

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

A) 100mLof12%;50mLof57% B) 110 mLof12%;40mLof57%

C) 50mLof12%;100mLof57% D) 40 mLof12%;110mLof57%

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5) Howmuchpureacidshouldbemixedwith9 gallonsofa50%acidsolutioninordertogetan80%acid

solution?

A) 13.5gal B) 4.5gal C) 36 gal D) 22.5 gal

6) Theradiatorinacertainmakeofcarneedstocontain70 liters of40%antifreeze.Theradiatornowcontains

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

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

A) 17.5LB)28LC)35L D) 23.3 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490mileswiththewindand330 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) 153.75mph B) 143.75 mph C) 158.75 mph D) 61.875 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236miles inthesame

timethatCarltravels204miles.Robʹstripusesmoreinterstatehighwaysandhecanaverage8mphmore

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

A) 59mph B) 51mph C) 63 mph D) 55mph

4) Garycanhikeonlevelground3milesanhourfasterthanhecanonuphillterrain.Yesterday,hehiked31

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

ground.

A) 6 4

mph B) 3 4

mph C) 4 3

mph D) 7mph

5) Twocarsstartfromthesamepointandtravelinthesamedirection.Ifonecaristraveling64 milesper

hourandtheothercaristravelingat46milesperhour,howfarapartwilltheybeafter3.4hours?

A) 61.2mi B) 374mi C) 217.6 mi D) 156.4 mi

6) Twotrainsleaveatrainstationatthesametime.Onetravelseastat12 milesperhour.Theothertrain

travelswestat9milesperhour.Inhowmanyhourswillthetwotrainsbe128.1milesapart?

A) 6.1hr B) 12.2 hr C) 3.1 hr D) 6.6hr

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7) KenandKaraare34milesapartonacalmlakepaddlingtowardeachother.Kenpaddlesat5 milesper

hour,whileKarapaddlesat8milesperhour.Howlongwillittakethemtomeet?

A) 2 8

hr B) 1 9

hr C) 21 hr D) 11 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55 milesperhourtoaweekendretreat.Onthewayhome,they

tookthesameroutebutaveraged70milesperhour.Whatwasthedistancebetweenhomeandtheretreat

iftheroundtriptook10hours?

A) 308mi B) 5 3

mi C) 25662

mi D) 616 mi

10) DuringahurricaneevacuationfromtheeastcoastofGeorgia,afamilytraveled280mileswest.Forpartof

thetrip,theyaveraged50mph,butasthecongestiongotbad,theyhadtoslowto10mph.Ifthetotaltime

oftravelwas6hours,howmanymilesdidtheydriveatthereducedspeed?

A) 5mi B) 10mi C) 15 mi D) 0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6hourstodothejob.Howlongwouldittaketheexperiencedauditorworkingalone?

A) 9hr B) 18hr C) 6 hr D) 12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15 hours.Togetherwithhertraineetheycanwallpaperthe

3roomsin10hours.Howlongwouldittakethetraineeworkingbyherselftodothejob?

A) 30hr B) 15hr C) 45 hr D) 60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) 111

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?

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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

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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

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

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

1 SolveRadicalEquations

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2 SolveEquationsQuadraticinForm

3 SolveEquationsbyFactoring

1.5 SolvingInequalities

1 UseIntervalNotation

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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

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