Elementary Education Chapter 0 Express the statement as an equation involving the indicated

Ch.0 ChapterR:Review

0.1 RealNumbers

1 WorkwithSets

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

UseU=universalset={0,1,2,3,4,5,6,7,8,9},A={1,2,3,5,8},B={2,3,5,7},andC={1,4,9}tofindtheset.

1) B∪C

A) {1,2,3,4,5,7,9} B) {} C) {0} D) {1,2,3,5,7,9}

2) A∪C

A) {1,2,3,4,5,8,9} B) {4,6,7,9} C) {1} D) {1,2,3,5,7,9}

3) A∩B

A) {2,3,5} B) {1,2,3,5,7,8} C) {2,3,5,7} D) {1,2,3,5,8}

4) A∩C

A) {1} B) {1,2,3,4,5,7,8,9}

C) {4,6,7,9} D) {1,2,3,5,7,9}

5) (A∩B)∪C

A) {1,2,3,4,5,9} B) {1,2,3,5} C) {1,2,3} D) {2,3,5}

6) (B∪C)∩A

A) {1,2,3,5} B) {1,2,3,4,5,7,9} C) {} D) {1,2,3}

7) B

A) {0,1,4,6,8,9} B) {1,4,6,8,9} C) {0,1,4,6,7,8,9} D) {0,1,4,6,9}

8) A∪B

A) {0,4,6,9} B) {4,6,9} C) {1,4,6,8,9} D) {1,2,3,5,7,8}

9) A∩C

A) {0,2,3,4,5,6,7,8,9} B) {1}

C) {1,2,3,4,5,7,8,9} D) {1,2,3,4,5,6,7,8,9}

10) B∩C

A) {0,6,8} B) {6,8} C) {1,2,3,4,5,7,9} D) {}

2 ClassifyNumbers

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

ListalltheelementsofBthatbelongtothegivenset.

1) B=15,6,–14,0,2

9,–9

2,8.6

Integers

A) {15

,

–14

,

0} B) {15

,

0} C) {15

,

–14} D) {15,0,6}

Page1

2) B=2,7,–19,0,2

3,–3

2,1.8

Naturalnumbers

A) {2} B) 2,0,–3

2C) {2,0} D) {–19

,

0,2}

3) B=9,7,–13,0,0

7

Realnumbers

A) 9,7,–13,0,0

7B) {9

,

–13

,

0} C) 9,–13,0,0

7D) 9

,

–13

4) B=8,6,–16,0,0

4,0.87

Rationalnumbers

A) 8,–16,0,0

4,0.87 B) {8

,

0} C) { 6}D)6,0

4,0.87

5) B=19,7,–6,0,0

8,0.46

Irrationalnumbers

A) { 7}B){7,0.46} C) 7,0

8D) 7,0

8,0.46

6) B={2,6,–12,0,2

7,–7

2,7.6,16π,0.166166166…}

Integers

A) {2

,

–12

,

0} B) {2

,

0} C) {2

,

–12} D) {2,0,6}

7) B={15,6,–2,0,7

9,–9

7,2.4,6π,0.625625625…}

Naturalnumbers

A) {15} B) 15,0,–9

7C) {15

,

0} D) {–2

,

0,15}

8) B={20,8,–24,0,0

1,16,0.3,–8π,0.161616…}

Rationalnumbers

A) 20,–24,0,0

1,16,0.3,0.161616… B) 20,–24,0,0

1,0.3

C) 20,–24,0,0

1,0.3,0.161616… D) 20,–24,0,0

1,16,0.3,–8π,0.161616…

Page2

9) B={17,5,–19,0,0

3,,0.23,–5π,0.161616…}

Irrationalnumbers

A) { 5,–5π}B){5

}

C) 5,0

3,–5πD) { 5,–5π,0.161616…}

Approximatethenumberroundedtothreedecimalplaces,andtruncatedtothreedecimalplaces.

10) 5.5469

A) 5.547

5.546

B) 5.548

5.546

C) 5.547

5.547

D) 5.546

5.547

11) 0.61538462

A) 0.615

0.615

B) 0.616

0.615

C) 0.615

0.616

D) 0.614

0.616

12) 11

7

A) 1.571

1.571

B) 1.572

1.571

C) 1.571

1.572

D) 1.572

1.572

3 EvaluateNumericalExpressions

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

Writethestatementusingsymbols.

1) Thesumof14and7is21.

A) 14+7=21 B) 14

7

=2C)14

·7=98 D) 14–7=7

2) Thedifference3less1equals2.

A) 3–1=2B)

3

1

=3C)3

+1=4D)3·1=3

3) Theproductof6and2 equals12.

A) 6·2=12 B) 6

2

=3C)6

+2=8D)6–2=4

4) Thequotient28dividedby14is2.

A) 28

14

=2B)28·14 =392 C) 28 +14 =42 D) 28–14 =14

5) Thesumoffourtimesxand5decreasedby7is8.

A) 4x+5–7=8 B) 4(x+5)–7=8C)7–(4x+5)=8 D) 4(x+5–7)=8

6) Threetimesthedifferenceofxand8is–10.

A) 3(x–8)=–10 B) 3–x–8= –10 C) 3x–8= –10 D) 3+x–8= –10

7) Thequotientofxandthesumof5andx.

A) x

5+xB) x+5+x C) x(5+x) D) x+5

x

Page3

Evaluatetheexpression.

8) –4+9+7

A) 12 B) –2C)

–6D)

–20

9) 3+2

9

A) 29

9B) 27

9C) 29

2D) 27

2

10) 4·[6(8–5)–2]

A) 64 B) 48 C) 10 D) 44

11) 7·[5+7·(2+3)]

A) 280 B) 420 C) 70 D) 416

12) –9–(–6+3·–5+8)

A) 4 B) –22 C) 20 D) –8

13) 20

16

·2

5

A) 1

2B) 2 C) 5

4D) 8

5

14) 3

2

·4

5

+4

15

A) 8

5B) 6

5C) 8

15 D) 16

5

15) 1

4

·8–1

5

+9

A) 219

20 B) 54

5C) 84

5D) 12

5

16) 8+9

5+1

A) 17

6B) –1

6C) 17

4D) –1

4

17) 4–1

1–4

A) –1B)4 C)

–4D)3

18) 5

11

+1

13

A) 76

143 B) 1

4C) 1

143 D) 19

Page4

19) 5

8

–2

9

A) 29

72 B) 1

24 C) 3

8D) 29

8

20)

1

2

7

8

A) 4

7B) 7

4C) 7

16 D) 16

7

21) 1

3

+1

6

·1

4

A) 3

8B) 1

8C) 11

9D) 1

36

4 WorkwithPropertiesofRealNumbers

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

UsetheDistributivePropertytoremovetheparentheses.

1) 4(x+4)

A) 4x+16 B) 4x+4C)x+16 D) 16x

2) 4x(x+8)

A) 4x2+32x B) 4x2+8C)x

2+32x D) 32x2

3) 4(2x+6)

A) 8x+24 B) 6x+10 C) 8x+6 D) 32x

4) 5 2

5x–1

10

A) 2x–1

2B) 2x–1

5C) 2x–1

10 D) 2

5x–1

2

5) (x+1)(x–11)

A) x2–10x–11 B) x2–11x–10 C) x2–11x–11 D) x2–10x–10

6) (x+10)(x+6)

A) x2+16x+60 B) x2+60x+16 C) x2+15x+60 D) x2+16x+16

7) (x+9)(x–9)

A) x2–81 B) x2–18 C) x2–18x–81 D) x2+18x–81

Page5

0.2 AlgebraEssentials

1 GraphInequalities

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

Ontherealnumberline,labelthepointswiththegivencoordinates.

1) –11

,

–9

,

–7

,

–5



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

A)

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

B)

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

C)

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

D)

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

2) –3.75,–1

,

1

,

3.25



–4–3–2–1012345–4–3–2–1012345

A)

–4–3–2–1012345–4–3–2–1012345

B)

–4–3–2–1012345–4–3–2–1012345

C)

–4–3–2–1012345–4–3–2–1012345

D)

–4–3–2–1012345–4–3–2–1012345

3) 11

5,–11

5

-4 -3 -2 -1 0 1 2 3 4-4 -3 -2 -1 0 1 2 3 4

A)

-4 -3 -2 -1 0 1 2 3 4-4 -3 -2 -1 0 1 2 3 4

B)

-4 -3 -2 -1 0 1 2 3 4-4 -3 -2 -1 0 1 2 3 4

C)

-4 -3 -2 -1 0 1 2 3 4-4 -3 -2 -1 0 1 2 3 4

D)

-4 -3 -2 -1 0 1 2 3 4-4 -3 -2 -1 0 1 2 3 4

Insert<,>,or=tomakethestatementtrue.

4) –5 –6

A) >B)

<

C) =

5) –7.8 –7.7

A)

<

B) >C) =

6) –54 –62

A) >B)

<

C) =

Page6

7) 16 –16

A) >B)

<

C) =

8) 1

4

 0.25

A) =B)

<

C) >

9) 1.73  3

A)

<

B) >C) =

10) 3.14 π

A)

<

B) >C) =

Writethestatementasaninequality.

11) yispositive

A) y>0B)y

<

0C)y

≤0D)y≥0

12) yisgreaterthan–43

A) y>–43 B) y

<

–43 C) y≥–43 D) y≤–43

13) yisgreaterthanorequalto50

A) y≥50 B) y>50 C) y

<

50 D) y≤50

14) zislessthanorequalto–2

A) z≤–2B)z

<

–2C)z> –2D)z= –2

15) xislessthan5

A) x

<

5B)x>5C)x≤5D)x≥5

Graphthenumbersontherealnumberline.

16) x>0

–9–8–7–6–5–4–3–2–10123456789–9–8–7–6–5–4–3–2–10123456789

A)

–9–8–7–6–5–4–3–2–10123456789–9–8–7–6–5–4–3–2–10123456789

B)

–9–8–7–6–5–4–3–2–10123456789–9–8–7–6–5–4–3–2–10123456789

C)

–9–8–7–6–5–4–3–2–10123456789–9–8–7–6–5–4–3–2–10123456789

D)

–9–8–7–6–5–4–3–2–10123456789–9–8–7–6–5–4–3–2–10123456789

Page7

17) x

<

6

–9–8–7–6–5–4–3–2–10123456789–9–8–7–6–5–4–3–2–10123456789

A)

–9–8–7–6–5–4–3–2–10123456789–9–8–7–6–5–4–3–2–10123456789

B)

–9–8–7–6–5–4–3–2–10123456789–9–8–7–6–5–4–3–2–10123456789

C)

–9–8–7–6–5–4–3–2–10123456789–9–8–7–6–5–4–3–2–10123456789

D)

–9–8–7–6–5–4–3–2–10123456789–9–8–7–6–5–4–3–2–10123456789

18) x≥–4

–9–8–7–6–5–4–3–2–10123456789–9–8–7–6–5–4–3–2–10123456789

A)

–9–8–7–6–5–4–3–2–10123456789–9–8–7–6–5–4–3–2–10123456789

B)

–9–8–7–6–5–4–3–2–10123456789–9–8–7–6–5–4–3–2–10123456789

C)

–9–8–7–6–5–4–3–2–10123456789–9–8–7–6–5–4–3–2–10123456789

D)

–9–8–7–6–5–4–3–2–10123456789–9–8–7–6–5–4–3–2–10123456789

Page8

19) x≤–7

–9–8–7–6–5–4–3–2–10123456789–9–8–7–6–5–4–3–2–10123456789

A)

–9–8–7–6–5–4–3–2–10123456789–9–8–7–6–5–4–3–2–10123456789

B)

–9–8–7–6–5–4–3–2–10123456789–9–8–7–6–5–4–3–2–10123456789

C)

–9–8–7–6–5–4–3–2–10123456789–9–8–7–6–5–4–3–2–10123456789

D)

–9–8–7–6–5–4–3–2–10123456789–9–8–7–6–5–4–3–2–10123456789

2 FindDistanceontheRealNumberLine

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

Usethegivenrealnumberlinetocomputethedistance.

1) Findd(A,B)

–5–4–3–2–1012345

AB

–5–4–3–2–1012345

AB

A) 9 B) –9C)10D)8

3 EvaluateAlgebraicExpressions

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

Evaluatetheexpressionusingthegivenvalues.

1) x+2y x=–2

,

y=–1

A) –4B)

–3C)

–5D)0

2) –9xy+8y–7x=2

,

y=2

A) –27 B) –20 C) –13 D) 45

3) –8x+yx=–4

,

y=3

A) 35 B) –29 C) –1D)

–5

4) 7x–3y

15 x=6,y=2

A) 12

5B) 13

5C) 16

5D) 4

15

5) 8x–12y

x+8x=5,y=2

A) 16

13 B) 44

13 C) 22

5D) 8

5

Page9

6) 5xy+30

xx=5,y=7

A) 41 B) 11 C) 65 D) 6

7) x+yx=–8

,

y=2

A) 6 B) 10 C) –6D)

–10

8) x –y x=–5

,

y=8

A) –3B)13C)3 D)

–13

9) 6x–7y x=5

,

y=7

A) 19 B) 79 C) –19 D) –79

10) |x|

x

+|y|

yx=3andy=–4

A) 0 B) 2 C) 1 D) –1

11) |–4x–9y| x=–4

,

y=3

A) 11 B) 43 C) 24 D) 48

12) 4 x +5y x=2

,

y=–9

A) 53 B) –37 C) –53 D) 37

UsetheformulaC=5

9(F–32)forconvertingdegreesFahrenheitintodegreesCelsiustofindtheCelsiusmeasureof

theFahrenheittemperature.

13) F=158°

A) 70°C B) 75°C C) 65° C D) 80° C

Expressthestatementasanequationinvolvingtheindicatedvariables.

14) TheareaAofarectangleistheproductofitslengthlanditswidthw.

A) A=lw B) A=l+wC)A=2(l+w) D) A=l

w

15) TheperimeterPofarectangleistwicethesumofitslengthlanditswidthw.

A) P=2(l+w) B) P=l+wC)P=lw D) P=2lw

16) ThecircumferenceCofacircleistheproductofπ anditsdiameterd.

A) C=πdB)C=π

dC) C=π+dD)C=2πd

17) TheareaAofatriangleisone–halftheproductofitsbasebanditsheighth.

A) A=1

2bh B) A=2bh C) A=1

2(b+h) D) A=bh

18) ThevolumeVofasphereis4

3

timesπtimesthecubeoftheradiusr.

A) V=4

3

πr3B) V=4

3

πr2C) V=4

3

π3r D) V=4

3

πr

Page10

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

A) S=4πr2B) S=4πrC)S=4π rD) S=πr2

20) ThevolumeVofacubeisthecubeofthelengthxofaside.

A) V=x3B) V=3xC) V=3x D) V=x2

21) ThesurfaceareaSofacubeis6timesthesquareofthelengthxofaside.

A) S=6x2B) S=6x C) S=6+x2D) S=x2

Solvetheproblem.

22) TheweeklyproductioncostCofmanufacturingxcalendarsisgivenbyC(x)=34+6x,wherethevariable

Cisindollars.Whatisthecostofproducing270calendars?

A) $1654.00 B) $9186.00 C) $1620.00 D) $304.00

23) Atthebeginningofthemonth,Christopherhadabalanceof$240 inhischeckingaccount.Duringthenext

month,hewroteacheckfor$37,deposited$67,andwroteanothercheckfor$236.Whatwashisbalanceat

theendofthemonth?

A) $34 B) –$34 C) –$100 D) $100

4 DeterminetheDomainofaVariable

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

Determinewhichvalue(s),ifany,mustbeexcludedfromthedomainofthevariableintheexpression.

1) x2–64

x

A) x=0B)x=8

,

x= –8C)x=8

,

x=0D)x= –8

2) 8x–5

x2–25

A) x=5

,

x=–5B)x=25 C) x=5D)x=5

8

3) x3+8x4

x2+25

A) x=0,x=–1

8B) x=–25 C) x= –5 D) none

4) x2+6x+7

x3–25x

A) x=5

,

x=–5

,

x=0B)x=5

,

x= –5C)x=0D)x=5

,

x=0

5) x

x–8

A) x=8B)x=–8C)x=0 D) none

6) 5

x+7

A) x=–7B)x=7C)x=0 D) none

Page11

7) x–8

x–3

A) x=3B)x=–3C)x=0 D) none

5 UsetheLawsofExponents

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

Simplifytheexpression.

1) 53

A) 125 B) 15 C) –125 D) –15

2) –62

A) –36 B) 12 C) 36 D) –12

3) 4–2

A) 1

16 B) –16 C) 16 D) 1

8

4) (–2)–4

A) 1

16 B) –16 C) 16 D) –1

16

5) –5–4

A) –1

625 B) –625 C) 625 D) 1

20

6) (–5)3

A) –125 B) 125 C) –15 D) 15

7) 5–5·52

A) 1

125 B) 125 C) 25 D) 1

625

8) (2–3)–1

A) 8 B) 1

8C) 1

4D) 4

Simplifytheexpression.Expresstheanswersothatallexponentsarepositive.Wheneveranexponentis0or

negative,weassumethatthebaseisnot0.

9) (5xy)3

A) 125x3y3B) 125xy C) 5x3y3D) 1

125x3y3

10) (6x3)–2

A) 1

36x6B) 36x6C) x6

36 D) 36

x6

Page12

11) (–3x3)–1

A) –1

3x3B) –1

27x3C) 1

3x3D) 1

27x3

12) (x3y–1)9

A) x27

y9B) y9

x27 C) 1

x27y9D) x27y9

13) (x–7y)5

A) y5

x35 B) y5

x7C) 1

x35y5D) x35y5

14) x–2y6

xy8

A) 1

x3y2B) 1

xy2C) y2

x3D) x

y2

15) x–4y4

x6y13

A) 1

x10y9B) x10y9C) y9

x10 D) x10

y9

16) 4x–1

9y–1

–3

A) 729x3

64y3B) 64x3

729y3C) 729y3

64x3D) 64y3

729x3

17) 4x–3

7y–3

–1

A) 7x3

4y3B) 4x31

7y31 C) 7y3

4x3D) 4x3

7y3

18) (x–4y9)–8z6

A) x32z6

y72 B) y72z6

x32 C) x32

y72z6D) y72

x32z6

19) –4x3y–3

5z2

–2

A) 25y6z4

16x6B) 16x6

25y6z4C) 25z4

16x6y6D) 25y6

16x6z4

Page13

Evaluatetheexpressionusingthegivenvalueofthevariables.

20) (x+3y)2forx=4,y=2

A) 100 B) 10 C) 20 D) 49

21) –7x–1y2forx=–2,y=–2

A) 14 B) 2

7C) 7

8D) 56

22) 2x2+4y2forx=–2,y=–2

A) 24 B) 0 C) –8D)12

23) 2x3–3x2–3x–2forx=2

A) –4 B) 8 C) 20 D) 0

Solve.

24) Whatisthevalueof(6666)2

(2222)2?

A) 9 B) (3333)2C) 18 D) (2222)2

6 EvaluateSquareRoots

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

Simplifytheexpression.

1) 9

A) 3 B) 81 C) 1

9D) notarealnumber

2) (–5)2

A) 5 B) 625 C) 1

25 D) notarealnumber

Findthevalueoftheexpressionusingthegivenvalues.

3) x2x=4

A) 4 B) 2 2 C) –4D)

–22

4) ( x)2x=3

A) 3 B) 9 C) 1

9D) 1

3

5) x2+y2x=15,y=20

A) 25 B) 13 C) 18 D) 24

6) x2+y2x=–5,y=3

A) 34 B) 8 C) –2D)15

7) x2+y2x=1,y=5

A) 6 B) –4C)26D)4

Page14

8) yxx=–2,y=4

A) 1

16 B) 16 C) –16 D) –1

16

7 UseaCalculatortoEvaluateExponents

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

Useacalculatortoevaluatetheexpression.Roundtheanswertothreedecimalplaces.

1) (–2.86)–5

A) –0.005 B) 0.005 C) –191.351 D) 191.351

2) –(–3.51)–4

A) –0.007 B) 0.007 C) –151.785 D) 151.785

3) (–5.41)–2

A) 0.034 B) –0.034 C) –29.268 D) 29.268

8 UseScientificNotation

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

Writethenumberinscientificnotation.

1) 1467

A) 1.467×103B) 1.467×104C) 1.467×10–3D) 1.467×101

2) 79.8

A) 7.98×101B) 7.98×10–1C) 7.98×102D) 7.98×10–2

3) 581.29

A) 5.8129×102B) 5.8129×10–2C) 5.8129×101D) 5.8129×10–1

4) 54

,

000

A) 5.4×104B) 5.4×10–4C) 5.4×103D) 5.4×10–3

5) 4,200,000

A) 4.2×106B) 4.2×10–6C) 4.2×107D) 4.2×10–7

6) 0.000134

A) 1.34∘10–4B) 1.34×104C) 1.34×10–5D) 1.34×10–3

7) 0.000084119

A) 8.4119×10–5B) 8.4119×105C) 8.4119±10–4D) 8.4119×104

8) 0.0000042914

A) 4.2914×10–6B) 4.2914×106C) 4.2914×10–5D) 4.2914×10–7

9) 0.000000351016

A) 3.51016×10–7B) 3.51016×107C) 3.51016×10–6D) 3.51016×106

Page15

10) 0.000000015102

A) 1.5102×10–8B) 1.5102×108C) 1.5102×10–7D) 1.5102×10–9

11) Inacertaincity

,

thesubwaysystemcarriedatotalof1,240,000,000 passengers.

A) 1.24×109B) 12.4×109C) 1.24×108D) 1.24×1010

12) Abusinessprojectsnextyearʹsprofitstobe$934,000,000.

A) 9.34×108B) 9.34×107C) 9.34×109D) 9.34×10–9

13) Acomputercompilesaprogramin0.000575 seconds.

A) 5.75×10–4B) 5.75×10–5C) 5.75×10–6D) 5.75×103

Writethenumberasadecimal.

14) 6.98×105

A) 698,000 B) 6,980,000 C) 69,800 D) 349

15) 3.205×105

A) 320,500 B) 3,205,000 C) 32,050 D) 160.25

16) 4.0056×107

A) 40,056,000 B) 400,560,000 C) 4,005,600 D) 280.392

17) 4.47×10–4

A) 0.000447 B) 0.00447 C) 0.0000447 D) –447

,

000

18) 6.378×10–5

A) 0.00006378 B) 0.0006378 C) 0.000006378 D) –637,800

19) 6.141×10–6

A) 0.000006141 B) 0.00006141 C) 0.0000006141 D) –6

,

141

,

000

20) 2.0692×10–7

A) 0.00000020692 B) 0.0000020692 C) 0.000000020692 D) –206920

,

000

21) Thereare2.988×102milesofhighways,roads,andstreetsinacertaincity.

A) 298.8 B) 2988 C) 29.88 D) 29,880

0.3 GeometryEssentials

1 UsethePythagoreanTheoremandItsConverse

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

Thelengthsofthelegsofarighttrianglearegiven.Findthehypotenuse.

1) a=12

,

b=5

A) 13 B) 10 C) 4 D) 169

2) a=6

,

b=8

A) 10 B) 5 C) 7 D) 9

Page16

Thelengthsofthesidesofatrianglearegiven.Determineifthetriangleisarighttriangle.Ifitis,identifythe

hypotenuse.

3) 5

,

12

,

13

A) righttriangle;13 B) righttriangle;12 C) righttriangle;5 D) notrighttriangle

4) 6

,

7

,

8

A) righttriangle;8 B) righttriangle;7 C) righttriangle;6 D) notrighttriangle

5) 12

,

16

,

20

A) righttriangle;20 B) righttriangle;16

C) righttriangle;12 D) notarighttriangle

6) 20

,

48

,

52

A) righttriangle;52 B) righttriangle;48

C) righttriangle;20 D) notarighttriangle

7) 28

,

96

,

100

A) righttriangle;100 B) righttriangle;96

C) righttriangle;28 D) notarighttriangle

8) 10

,

20

,

25

A) righttriangle;25 B) righttriangle;20

C) righttriangle;10 D) notarighttriangle

9) 6

,

8

,

12

A) righttriangle;12 B) righttriangle;8

C) righttriangle;6 D) notarighttriangle

Solve.UsethefactthattheradiusoftheEarthis3960milesand1mile=5280feet.

10) Aguardtoweratastateprisonstands108 feettall.Howfarcanaguardseefromthetopofthetower?

Roundtothenearesttenthofamile.

A) 12.7mi B) 5600.3 mi C) 18 mi D) 931.1 mi

11) Apersonwhois6feettallisstandingonthebeachandlooksoutontotheocean.Suddenly,aship

appearsonthehorizon.Howfaristheshipfromtheshore?Roundtothenearesttenthofamile.

A) 3mi B) 5600.3 mi C) 4.2 mi D) 218.1 mi

2 KnowGeometryFormulas

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

Solvetheproblem.

1) FindtheareaAofarectanglewithlength9 in andwidth19 in.

A) A=171in2B) A=342in2C) A=28in2D) A=36in2

2) FindtheareaAofarectanglewithlength4.2 yd andwidth5.9 yd.

A) A=24.78yd2B) A=49.56yd2C) A=10.1yd2D) A=16.8yd2

3) FindtheareaAofatrianglewithheight2 cm andbase6 cm.

A) A=6cm2B) A=6 cm C) A=12cm2D) A=12 cm

Page17

4) FindtheareaAandcircumferenceCofacircleofradius3 ft.Expresstheanswerintermsofπ.

A) A=9πft2;C=6πft B) A=6πft2;C=6πft

C) A=36πft2;C=3πft D) A=12πft2;C=3πft

5) FindtheareaAandcircumferenceCofacircleofdiameter3 cm.Use3.14forπ.Roundtheresulttothe

nearesttenth.

A) A=7.1cm2;C=9.4cm B) A=9.4cm2;C=9.4cm

C) A=28.3cm2;C=4.7cm D) A=18.8cm2;C=4.7cm

6) FindthevolumeVofarectangularboxwithlength3 yd

,

width2 yd

,

andheight6yd.

A) V=36yd3B) V=12yd3C) V=72yd3D) V=54yd3

7) FindthesurfaceareaSofarectangularboxwithlength2 ft,width5 ft,andheight

2ft.

A) 48ft2B) 60ft2C) 24ft2D) 38ft2

8) FindthevolumeVandsurfaceareaSofasphereofradius4 centimeters.Expresstheanswerintermsofπ.

A) V=256

3

πcm3;S=64πcm2B) V=64

3

πcm3;S=256

3

πcm2

C) V=256πcm3;S=4πcm2D) V=64πcm3;S=16πcm2

9) FindthevolumeVofasphereofradius4 yd.Use3.14forπ.Ifnecessary,roundtheresulttothenearest

tenth.

A) V=267.9yd3B) V=67yd3C) V=150.7yd3D) V=2143.6yd3

10) FindthevolumeVofarightcircularcylinderwithradius5 ft andheight19 ft.Expresstheanswerinterms

ofπ.

A) V=475πft3B) V=475

4

πft3C) V=95πft3D) V=95

2

πft3

11) FindthesurfaceareaSofarightcircularcylinderwithradius5 cm,andheight7cm.Use3.14forπ.

Roundyouranswertoonedecimalplace.

A) 376.8cm2B) 188.4cm2C) 549.5cm2D) 266.9cm2

12) FindthevolumeVofasphereofdiameter6m.Use3.14forπ.Ifnecessary,roundtheresulttothenearest

tenth.

A) V=113m3B) V=37.7m3C) V=63.6m3D) V=904.3m3

Page18

13) Findtheareaoftheshadedregion.Expresstheanswerintermsofπ.

7

A) 49–49

4

πsquareunits B) 196 –49πsquareunits

C) 49–49

2

πsquareunits D) 49

4

π+49squareunits

14) Findtheareaoftheshadedregion.Expresstheanswerintermsofπ.

1

A) 1

2

πsquareunits B) 1

4

πsquareunits C) 1

2

squareunits D) 1πsquareunits

15) Findtheareaoftheshadedregion.Expresstheanswerintermsofπ.

4

A) 8π–16squareunits B) 4π–16 squareunits

C) 16squareunits D) 4π–4 squareunits

16) Abicyclewheelmakes5revolutions.Determinehowfarthebicycletravelsininchesifthediameterofthe

wheelis23in.Useπ≈3.14.Roundtothenearesttenth.

A) 361.1in. B) 72.2 in. C) 115 in. D) 722.2 in.

17) Arectangularpatiohasdimensions10feetby15feet.Thepatioissurroundedbyaborderwithauniform

widthof3feet.Findtheareaoftheborder.

A) 186ft2B) 84ft2C) 162ft2D) 114ft2

Page19

18) Acircularswimmingpool,20feetindiameter,isenclosedbyacirculardeckthatis6feetwide.Whatisthe

areaofthedeck?Useπ=3.1416.

A) 490.1ft2B) 772.8ft2C) 1206.4ft2D) 314.2ft2

19) Findtheperimeter.Approximatetheresulttothenearesttenthusing3.14forπ.

8ft

4ft

A) 26.3ft B) 32.6 ft C) 30.3 ft D) 36.6 ft

20) Findtheareaofthewindow.Approximatetheresulttothenearesttenthusing3.14forπ.

9ft

4ft

A) 42.3ft2B) 86.2ft2C) 61.1ft2D) 39.1ft2

Page20

3 UnderstandCongruentTrianglesandSimilarTriangles

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

Thetrianglesaresimilar.FindthemissinglengthxandthemissinganglesA,B,C.

1)

96°

16 28

39° 45°

14

A) x=8units;A=96°;B=39°;C=45° B) x=16 units;A=39°;B=96°;C=45°

C) x=8units;A=45°;B=39°;C=96° D) x=16 units;A=96°;B=39°;C=45°

2)

12°

33°

48

10

30

135°

A) x=16;A=33;B=12;C=135 B) x=48;A=12;B=33;C=135

C) x=16;A=135;B=12;C=33 D) x=48;A=33;B=12;C=135

Solve.Ifnecessary,roundtothenearesttenth.

3) Aflagpolecastsashadowof20feet.Nearby,a10–foottreecastsashadowof2feet.Whatistheheightof

theflagpole?

A) 100ft B) 4ft C) 1 ft D) 400 ft

4) Ifaflagpole15feettallcastsashadowthatis20 feetlong,findthelengthoftheshadowcastbyanantenna

whichis18feettall.

A) 24ft B) 13.5 ft C) 16.7 ft D) 23ft

5) Thezoohashiredalandscapearchitecttodesignthetriangularlobbyofthechildrenʹspettingzoo.Inhis

scaledrawing,thelongestsideofthelobbyis15cm.Theshortestsideofthelobbyis8cm.Thelongest

sideoftheactuallobbywillbe46m.Howlongwilltheshortestsideoftheactuallobbybe?

A) 24.5m B) 0.2m C) 86.3 m D) 0.9m

Page21

6) Ifatree62.5feettallcastsashadowthatis25 feetlong,findtheheightofatreecastingashadowthatis19

feetlong.

A) 47.5ft B) 7.6ft C) 82.2 ft D) 56.5 ft

0.4 Polynomials

1 RecognizeMonomials

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

Tellwhethertheexpressionisamonomial.Ifitis,namethevariable(s)andcoefficient,andgivethedegreeofthe

monomial.

1) 13x

A) Monomial;variablex;coefficient13;degree1

B) Monomial,variablex;coefficient1;degree13

C) Monomial,;variablex;coefficient13;degree0

D) Notamonomial

2) 13x9

A) Monomial;variablex;coefficient13;degree9 B) Monomial;variablex;coefficient9;degree13

C) Monomial;variablex;coefficient9;degree0 D) Notamonomial

3) 7

x

A) Monomial;variablex;coefficient7;degree1 B) Monomial;variablex;coefficient7;degree–1

C) Monomial;variablex;coefficient7;degree0 D) Notamonomial

4) –6x–10

A) Monomial;variablex;coefficient–6;degree–10

B) Monomial;variablex;coefficient10;degree–6

C) Monomial;variablex;coefficient–6;degree10

D) Notamonomial

5) –9xy2

A) Monomial;variablesx,y;coefficient–9;degree3

B) Monomial;variablesx,y;coefficient–9;degree2

C) Monomial;variablesx,y;coefficient–9;degree1

D) Notamonomial

6) –9x3y6

A) Monomial;variablesx,y;coefficient–9;degree9

B) Monomial;variablesx,y;coefficient–9;degree3

C) Monomial;variablesx,y;coefficient–9;degree6

D) Notamonomial

7) 19x

y

A) Monomial;variablesx,y;coefficient19;degree1

B) Monomial;variablesx,y;coefficient19;degree–2

C) Monomial;variablesx,y;coefficient19;degree2

D) Notamonomial

Page22

8) ––2x12

y4

A) Monomial;variablesx,y;coefficient–2;degree12

B) Monomial;variablesx,y;coefficient–2;degree4

C) Monomial;variablesx,y;coefficient–2;degree8

D) Notamonomial

9) 7x3–4

A) Monomial;variablex;coefficient7;degree3 B) Monomial;variablex;coefficient4 ;degree3

C) Monomial;variablex;coefficient7;degree1 D) Notamonomial

2 RecognizePolynomials

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

Tellwhethertheexpressionisapolynomial.Ifitis,giveitsdegree.

1) 5x3–2

A) Polynomial;degree3 B) Polynomial;degree2

C) Polynomial;degree5 D) Notapolynomial

2) 1–4x

A) Polynomial;degree1 B) Polynomial;degree4

C) Polynomial;degree–4 D) Notapolynomial

3) 15

A) Polynomial,degree0 B) Polynomial,degree1

C) Polynomial,degree15 D) Notapolynomial

4) 2π

A) polynomial,degree0 B) polynomial,degree1

C) polynomial,degree2 D) notapolynomial

5) 7x5–3

x

A) Polynomial;degree5 B) Polynomial;degree–1

C) Polynomial;degree1 D) Notapolynomial

6) 3

x

+1

A) Polynomial,degree0 B) Polynomial,degree–1

C) Polynomial,degree3 D) NotaPolynomial

7) –3y5–3

A) Polynomial;degree5 B) Polynomial;degree–3

C) Polynomial;degree3 D) Notapolynomial

8) –5z8+z

A) Polynomial;degree8 B) Polynomial;degree9

C) Polynomial;degree1 D) Notapolynomial

Page23

9) 9x11+24x7

3x3

A) Polynomial;degree7 B) Polynomial;degree11

C) Polynomial;degree0 D) Notapolynomial

3 AddandSubtractPolynomials

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

Addorsubtractasindicated.Expresstheanswerasasinglepolynomialinstandardform.

1) (4x2+10x–11)+(20x+11)

A) 4x2+30x B) 4x2+30x–22 C) 4x2+10x+22 D) 34x3

2) (8x2+8x–9)+(2x2+3x+3)

A) 10x2+11x–6B)

–7x2+11x+11 C) 10x2–11x–6 D) 10x2+11x+6

3) (8x2+13x+14)–(2x2–3x–6)

A) 6x2+16x+20 B) 6x2+15x+8C)6x

2+16x+8D)6x

2+16x–20

4) (6x3–2x2)+(8x3–4x2)

A) 14x3–6x2B) 14x6–6x4C) 8x5D) 8x10

5) (12x5–16x4)–(2x5–15x4)

A) 10x5–1x4B) 10x5–31x4C) 9x9D) 14x5–31x4

6) (2x5+5x2)+(8x5+3x2–9)

A) 10x5+8x2–9 B) 10x5+5x2–9x C) –9x+8x5–7x2D) 11x8

7) (7x2–9)–(–x3–10x2+1)

A) x3+17x2–10 B) 8x3–19x2–1C)x

3–3x2–8D)8x

3–10x2–10

8) (3x5+4x3+4)–(5x5+17x3–14)

A) –2x5–13x3+18 B) –2x5+9x3–10 C) –2x5–13x3–10 D) 3x8

9) (6x7–19x4–9)–(12x4+4x7–2)

A) 2x7–31x4–7B)2x

7–15x4–11 C) 2x7–31x4–11 D) –36x11

10) (2x6–8x3–5x)+(9x6–6x3+2x)

A) 11x6–14x3–3x B) 4x6–4x3–6x C) 11x–14x6–3x3D) –6x10

11) –3(x2+9x+1)+(–3x2–x+4)

A) –6x2–28x+1B)0x

2–28x+1C)

–6x2–27x+1D)

–6x2–28x+5

12) 7(2x3+x2–1)–9(9x3–4x+2)

A) –67x3+7x2+36x–25 B) –67x3+7x2–36x–25

C) –67x3+x2+36x–25 D) –67x3+7x2+36x+25

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13) (x2+1)–(9x2+9)+(x2+x–6)

A) –7x2+x–14 B) –9x2+x–14 C) –8x2+x–14 D) –7x2+10x–5

14) 8(1–y3)–5(1+y+y2+y3)

A) –13y3–5y2–5y+3B)

–13y3+5y2–5y–3

C) –13y3–5–ay2–5y+3 D) 13y3–5y2–5y+3

4 MultiplyPolynomials

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

Performtheindicatedoperations.Expresstheanswerasasinglepolynomialinstandardform.

1) –4x(7x–10)

A) –28x2+40x B) 12x2C) –28x2–10x D) 7x2+40x

2) 5x7(–10x–2)

A) –50x8–10x7B) –50x–10 C) –50x8–2D)

–60x7

3) 8x4(–11x5–9)

A) –88x9–72x4B) –88x5–72 C) –88x9–9D)

–160x4

4) 3x2(–9x7–4x6–8)

A) –27x9–12x8–24x2B) –27x9–12x8

C) –27x9–4x6–8D)

–27x7–12x6–24

5) (x–12)(x2+7x–6)

A) x3–5x2–90x+72 B) x3+19x2+78x–72

C) x3–5x2–78x–72 D) x3+19x2+90x+72

6) (2y+11)(10y2–2y–4)

A) 20y3+106y2–30y–44 B) 20y3–4y2–8y+11

C) 130y2–26y–52 D) 20y3+114y2+30y+44

MultiplythepolynomialsusingtheFOILmethod.Expresstheanswerasasinglepolynomialinstandardform.

7) (x–5)(x+2)

A) x2–3x–10 B) x2–10x–3C)x

2–4x–10 D) x2–3x–3

8) (4x–10)(x+10)

A) 4x2+30x–100 B) 4x2–100x+30 C) 4x2+30x+30 D) 4x2+28x–100

9) (3x+8)(3x–6)

A) 9x2+6x–48 B) 6x2+6x–48 C) 9x2+6x+6D)6x

2+6x+6

10) (x+7y)(x–10y)

A) x2–3xy–70y2B) x–3xy–70y C) x2–3xy–3y2D) x2–6xy–70y2

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11) (x+12y)(5x–10y)

A) 5x2+50xy–120y2B) x2+50xy–120y2

C) 5x2+50xy+50y2D) x2+50xy+50y2

12) (–4x+2y)(–3x–2y)

A) 12x2+2xy–4y2B) 12x2–6xy–4y2C) 12x2+8xy–4y2D) 12x2+2xy+2y2

5KnowFormulasforSpecialProducts

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

Multiplythepolynomials.Expresstheanswerasasinglepolynomialinstandardform.

1) (x+13)(x–13)

A) x2–169 B) x2–26 C) x2–26x–169 D) x2+26x–169

2) (2x+11)(2x–11)

A) 4x2–121 B) x2–121 C) 4x2–44x–121 D) 4x2+44x–121

3) (x+3)2

A) x2+6x+9B)x

2+9C)9x

2+6x+9D)x+9

4) (x–10)2

A) x2–20x+100 B) x2+100 C) 100x2–20x+100 D) x+100

5) (8x+3)2

A) 64x2+48x+9 B) 64x2+9C)8x

2+48x+9D)8x

2+9

6) (x+13y)(x–13y)

A) x2–169y2B) x2–26y2C) x2–26xy–169y2D) x2+26xy–169y2

7) (3y+x)(3y–x)

A) 9y2–x2B) 6y2–x2C) 9y2–6xy–x2D) 9y2+6xy–x2

8) (6x–7)2

A) 36x2–84x+49 B) 36x2+49 C) 6x2–84x+49 D) 6x2+49

9) (t–b)2

A) t2–2tb+b2B) t2–tb+b2C) t2–2tb–b2D) t2+2tb+b2

10) (6x+7y)2

A) 36x2+84xy+49y2B) 36x2+49y2

C) 6x2+84xy+49y2D) 6x2+49y2

11) (3x–4y)2

A) 9x2–24xy+16y2B) 9x2+16y2C) 3x2–24xy+16y2D) 3x2+16y2

12) (x–4)3

A) x3–12x2+48x–64 B) x3–4x2+24x–64

C) x3–12x2+24x–64 D) x3–12x2+12x–64

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13) (2x+4)3

A) 8x3+48x2+96x+64 B) 8x3+48x2+48x+64

C) 4x6+8x3+4096 D) 4x2+16x+16

6 DividePolynomialsUsingLongDivision

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

Findthequotientandtheremainder.

1) 9x8–15x4dividedby3x

A) 3x7–5x3;remainder0B)9x

7–15x3;remainder0

C) 3x9–5x5;remainder0D)3x

8–5x4;remainder0

2) 16x2+8x–13dividedby4x

A) 4x+2;remainder–13 B) 4x2+2x–13

4;remainder0

C) 16x+8;remainder–13 D) 4x–11;remainder0

3) x2+11x+18dividedbyx+9

A) x+2;remainder0B)x–9;remainder0

C) x2+2;remainder0D)x

3–9;remainder0

4) 9x2+36x–45dividedbyx+5

A) 9x–9;remainder0B

)9x+9;remainder0

C) x–9;remainder0D)9x–9;remainder7

5) x2+3x–13dividedbyx+6

A) x–3;remainder5B)x–3;remainder0C)x+3;remainder5D)x–5;remainder3

6) x2+8x+7dividedbyx+2

A) x+6;remainder–5B)x+6;remainder5

C) x+6;remainder0D)x+7;remainder0

7) 3x3+18x2–73x+72dividedbyx+9

A) 3x2–9x+8;remainder0B)3x

2+9x+8;remainder0

C) x2+10x+11;remainder0D)x

2+9x+3;remainder0

8) 25x3–25x2–6x+3dividedby–5x+1

A) –5x2+4x+2;remainder1B)

–5x2+4x+2;remainder0

C) –5x2+4x+2;remainder4D)x

2+2;remainder4

9) 5x3–7x2+7x–8dividedby5x–2

A) x2–x+1;remainder–6B)x

2–x+1;remainder6

C) x2–x+1;remainder10 D) x2+x–1;remainder–6

10) x4+81dividedbyx–3

A) x3+3x2+9x+27;remainder162 B) x3+3x2+9x+27;remainder81

C) x3+3x2+9x+27;remainder0D)x

3–3x2+9x–27;remainder162

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11) –25x3–35x2–37x–6dividedby–5x–3

A) 5x2+4x+5;remainder9B)5x

2+4x+5;remainder0

C) 5x2+4x+5;remainder12 D) x2+5;remainder4

12) –15x3–10x2+34x+20dividedby3x+5

A) –5x2+5x+3;remainder5B

)

–5x2+5x+3;remainder0

C) –5x2+5x+3;remainder8D)x

2+3;remainder5

13) x4+7x2+10dividedbyx2+1

A) x2+6;remainder4B)x

2+6x+3

2;remainder0

C) x2+6;remainder0D)x

2+6x+2;remainder4

14) x4+16dividedbyx–2

A) x3+2x2+4x+8;remainder32 B) x3+2x2+4x+8;remainder16

C) x3+2x2+4x+8;remainder0D)x

3–2x2+4x–8;remainder32

15) x2–25a2dividedbyx–5a

A) x+5a B) x–5a C) x2–10xa D) x2+10xa

7 WorkwithPolynomialsinTwoVariables

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

MultiplythepolynomialsusingtheFOILmethod.Expresstheanswerasasinglepolynomialinstandardform.

1) (x+12y)(x+9y)

A) x2+21xy+108y2B) x+21xy+108y C) x2+21xy+21y2D) x2+18xy+108y2

2) (–4x+3y)(2x+10y)

A) –8x2–34xy+30y2B) –8x2+6xy+30y2

C) –8x2–40xy+30y2D) –8x2–34xy–34y2

Multiplythepolynomialsusingthespecialproductformulas.Expresstheanswerasasinglepolynomialin

standardform.

3) (x+8y)(x–8y)

A) x2–64y2B) x2–16y2C) x2–16xy–64y2D) x2+16xy–64y2

4) (4x+y)(4x–y)

A) 16x2–y2B) 8x2–y2C) 16x2–8xy–y2D) 16x2+8xy–y2

5) (4x+9y)(4x–9y)

A) 16x2–81y2B) 16x2–72xy–81y2

C) 8x2–18y2D) 16x2+72xy–81y2

6) (x–y)2

A) x2–2xy+y2B) x2–xy+y2C) x2–y2D) x2–2x2y2+y2

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7) (x–7y)2

A) x2–14xy+49y2B) x2–7xy+49y2C) x2–y2D) x2+14xy+49y2

8) (6x–y)2

A) 36x2–12xy+y2B) 36x2–6xy+y2C) 36x2+y2D) 36x2–12xy–2y2

9) (2x+5y)2

A) 4x2+20xy+25y2B) 4x2+25y2C) 2x2+20xy+25y2D) 2x2+25y2

10) (3x–8y)2

A) 9x2–48xy+64y2B) 9x2+64y2C) 3x2–48xy+64y2D) 3x2+64y2

0.5 FactoringPolynomials

1 FactortheDifferenceofTwoSquaresandtheSumandDifferenceofTwoCubes

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

Factorthepolynomialbyremovingthecommonmonomialfactor.

1) 6x–12

A) 6(x–2) B) 6(x+2) C) x(x–6) D) x(x+6)

2) 9x2–18x

A) 9x(x–2) B) 9x(x+2) C) 9(x2–2x) D) 9x2(x–2)

Factorthedifferenceoftwosquares.

3) x2–64

A) (x+8)(x–8) B) (x+64)(x–64) C) (x–8)(x–8) D) (x2+8)(x2–8)

4) 64x2–1

A) (8x–1)(8x+1) B) (8x+1)2C) (8x–1)2D) prime

5) 49–x2

A) (7–x)(7+x) B) (7+x)2C) (7–x)2D) prime

6) 49x2–16

A) (7x+4)(7x–4) B) (7x–4)2C) (7x+4)2D) (49x+1)(x–16)

Factorthesumordifferenceoftwocubes.

7) x3–27

A) (x–3)(x2+3x+9) B) (x+3)(x2–3x+9)

C) (x–3)(x2+9) D) (x+27)(x2–1)

8) x3+64

A) (x+4)(x2–4x+16) B) (x–4)(x2+4x+16)

C) (x+4)(x2+16) D) (x–64)(x2–1)

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9) 729y3–1

A) (9y–1)(81y2+9y+1) B) (9y–1)(81y2+1)

C) (729y–1)(y2+9y+1) D) (9y+1)(81y2–9y+1)

10) 343x3+1

A) (7x+1)(49x2–7x+1) B) (7x+1)(49x2+1)

C) (7x+1)(49x2+7x+1) D) (7x+1)(49x2–7x–1)

11) 125–x3

A) (5–x)(25+5x+x2)B)(5+x)(25–5x+x2)

C) (5–x)(25+x2)D)(5+x)(25–x2)

12) 1000x3–729

A) (10x–9)(100x2+90x+81) B) (10x–9)(100x2+81)

C) (1000x–9)(x2+90x+81) D) (10x+9)(100x2–90x+81)

13) 343x3+729

A) (7x+9)(49x2–63x+81) B) (7x+9)(49x2+63x+81)

C) (343x–9)(x2+63x+81) D) (7x–9)(49x2+63x+81)

14) 27–8x3

A) (3–2x)(9+6x+4x2)B

)(3–2x)(9+4x2)

C) (27–2x)(1+6x+4x2)D)(3+2x2)(9–6x+4x2)

Factorcompletely.Ifthepolynomialcannotbefactored,sayitisprime.

15) 3x2–147

A) 3(x+7)(x–7) B) 3(x–7)2C) 3(x+7)2D) prime

16) x4–9

A) (x2+3)(x2–3) B) (x2+3)2C) (x2–3)2D) prime

17) x4–256

A) (x2+16)(x+4)(x–4) B) (x2+16)2

C) (x2–16)2D) prime

18) (x+9)2–49

A) (x+16)(x+2) B) (x+58)(x–40) C) (x–2)(x–16) D) x2+18x+32

19) (x–2)2–16

A) (x+2)(x–6) B) (x+14)(x–18) C) (x–2)(x+6) D) (x–6)2

20) x9+1

A) (x+1)(x2–x+1)(x6–x3+1) B) (x3+1)(x6–x3+1)

C) (x–1)(x2+x+1)(x6+x3+1) D) (x–1)(x+1)(x6–x3+1)

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21) 125x4–x

A) x(5x–1)(25x2+5x+1) B) x(5x–1)(25x2+1)

C) x(125x–1)(x2+5x+1) D) x(5x+1)(25x2–5x+1)

22) (4x+1)3–512

A) (4x–7)(16x2+40x+73) B) (4x+9)(16x2–24x+57)

C) (4x–7)(16x2–24x+57) D) (4x–7)(16x2–24x+73)

23) (3–x)3–x3

A) (3–2x)(x2–3x+9) B) (3–x)(x2–3x+9)

C) (3–2x)(3x2–3x+9) D) (3+2x)(x2–3x+9)

2 FactorPerfectSquares

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

Factortheperfectsquare.

1) x2+30x+225

A) (x+15)2B) (x–15)2C) (x+15)(x–15) D) x2+30x+225

2) x2–12x+36

A) (x–6)2B) (x–6)(x+6) C) (x+6)2D) (x–12)(x+12)

3) 49x2–70x+25

A) (7x–5)2B) (7x+5)2C) (7x+5)(7x–5) D) (7x–6)2

4) 9x2+12x+4

A) (3x+2)2B) (3x–2)2C) (3x+2)(3x–2) D) (3x–3)2

5) x4+8x2+16

A) (x2+4)2B) (x2–4)2C) (x +4)(x–4) D) (x+4)2

Factorcompletely.Ifthepolynomialcannotbefactored,sayitisprime.

6) 98x2+224x+128

A) 2(7x+8)2B) 2(7x–8)2C) 2(7x+8)(7x–8) D) prime

7) x3+24x2+144x

A) x(x+12)2B) x(x–12)2C) x(x+12)(x–12) D) prime

3 FactoraSecond–DegreePolynomial:x^2+Bx+C

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

Factorthepolynomial.

1) x2–x–12

A) (x+3)(x–4) B) (x+4)(x–3) C) (x+1)(x–12) D) prime

2) x2+13x+42

A) (x+7)(x+6) B) (x–7)(x+6) C) (x–7)(x+1) D) prime

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3) x2+7x–44

A) (x+11)(x–4) B) (x–11)(x+4) C) (x–11)(x+1) D) prime

4) x2+16

A) (x+4)(x–4) B) (x+4)2C) (x–4)2D) prime

Factorcompletely.Ifthepolynomialcannotbefactored,sayitisprime.

5) 7x2–7x–42

A) 7(x+2)(x–3) B) (7x+14)(x–3) C) 7(x–2)(x+3) D) prime

6) 2x2–18x+40

A) 2(x–4)(x–5) B) 2(x–20)(x+1) C) (x–4)(2x–10) D) prime

7) 4x3+4x2–80x

A) 4x(x–4)(x+5) B) 4x(x+4)(x–5) C) (4x2+16x)(x–5) D) (x–4)(4x2+20)

8) (x+8)2–11(x+8)+18

A) (x–1)(x+6) B) (x+17)(x+10)

C) (x2+8x–9)(x2+8x–2) D) (x2–8x+9)(x2–8x+2)

9) x4+10x2+24

A) (x2+6)(x2+4) B) (x2–6)(x2+4) C) (x2–6)(x2+1) D) Prime

4 FactorbyGrouping

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

Factorthepolynomialbygrouping.

1) x2+3x+7x+21

A) (x+3)(x+7) B) (x–3)(x–7) C) (x–3)(x+7) D) prime

2) 3x2+2x+6x+4

A) (x+2)(3x+2) B) (3x+2)(3x+2) C) (3x+2)(2x+3) D) prime

3) 8x2–20x+6x–15

A) (4x+3)(2x–5) B) (4x–3)(2x+5) C) (8x+3)(x–5) D) (8x–3)(x+5)

4) 15x2–20x+6x–8

A) (5x+2)(3x–4) B) (5x–2)(3x+4) C) (15x+2)(x–4) D) (15x–2)(x+4)

Factorcompletely.Ifthepolynomialcannotbefactored,sayitisprime.

5) x3–4x+4x2–16

A) (x+2)(x–2)(x+4) B) (x2–4)(x+4)

C) (x–2)2(x+4) D) prime

6) 2x2–14x–8x+56

A) 2(x–7)(x–4) B) (x–7)(x–4) C) (x–7)(2x–8) D) 2(x+7)(x+4)

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7) 2y3+12y2–14y2–84y

A) 2y(y+6)(y–7) B) (y+6)(y–7) C) (y+6)(2y2–14y) D) 2y(y–6)(y+7)

8) 15x4+20x2–12x2–16

A) (5x2–4)(3x2+4) B) (5x2+4)(3x2–4) C) (5x4–4)(3x+4) D) (15x2+4)(x2–4)

9) 20x2–25xy+8xy–10y2

A) (5x+2y)(4x–5y) B) (5x+2)(4x–5) C) (5x–2y)(4x–5y) D) (20x+2y)(x–5y)

10) 20x3–12x2y–25xy2+15y3

A) (4x2–5y2)(5x–3y) B) (4x2–5y)(5x–3y)

C) (4x2+5y2)(5x+3y) D) (20x2–5y2)(x–3y)

Anexpressionthatoccursincalculusisgiven.Factorcompletely.

11) 2(x+6)(x–5)3+(x+6)2·6(x–5)2

A) 2(x+6)(x–5)2(4x+13) B) (x+6)(x–5)2(4x+13)

C) (x+6)(x–5)2(8x+26) D) 2(x+5)(x–6)2(4x+13)

12) (2x+1)2+3(2x+1)–4

A) 2x(2x+5) B) 2x–6 C) 2x(2x+1) D) 2x–1

13) 3(x+5)2(2x–1)2+4(x+5)3(2x–1)

A) (x+5)2(2x–1)(10x+17) B) (x+5)2(2x–1)(x+17)

C) (x+5)2(10x+17) D) (x+5)(2x–1)(10x+17)

5 FactoraSecond–DegreePolynomial:Ax^2+Bx+C,A≠1

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

Factorthepolynomial.

1) 12x2+17x+6

A) (3x+2)(4x+3) B) (3x–2)(4x–3) C) (12x+2)(x+3) D) prime

2) 6y2+13y+6

A) (2y+3)(3y+2) B) (2y–3)(3y–2) C) (6y+3)(y+2) D) prime

3) 15z2+8z–16

A) (3z+4)(5z–4) B) (3z–4)(5z+4) C) (15z+4)(z–4) D) prime

4) 20z2–7z–6

A) (4z–3)(5z+2) B) (4z+3)(5z–2) C) (20z–3)(z+2) D) prime

5) 6x2–5xt–6t2

A) (2x–3t)(3x+2t) B) (2x+3t)(3x–2t) C) (6x–3t)(x+2t) D) prime

6) 12z2–7z–12

A) (3z–4)(4z+3) B) (3z+4)(4z–3) C) (12z–4)(z+3) D) prime

7) x2–x–35

A) (x–35)(x+1) B) (x+5)(x–7) C) (x–5)(x+7) D) prime

Page33

Factorcompletely.Ifthepolynomialcannotbefactored,sayitisprime.

8) 21x2–91x–70

A) 7(3x+2)(x–5) B) 7(3x–2)(x+5) C) (21x+14)(x–5) D) prime

9) 10x2–35x–20

A) 5(2x+1)(x–4) B) 5(2x–1)(x+4) C) (10x–5)(x+4) D) prime

10) 14y2+63y–35

A) 7(2y–1)(y+5) B) 7(2y+1)(y–5) C) (14y–7)(y+5) D) prime

11) 24x2–87x+45

A) 3(8x–5)(x–3) B) 3(8x+5)(x+3) C) (8x–5)(3x–3) D) prime

12) 20x3+37x2+15x

A) x(4x+5)(5x+3) B) x(5x+5)(4x+3) C) (4x2+5)(5x+3) D) x2(4x+5)(5x+3)

13) 27x2+81x+60

A) 3(3x+4)(3x+5) B) 3(3x+1)(3x+20) C) 3(20x+4)(x+5) D) (3x+1)(3x+20)

14) 15(x–7)2–5(x–7)–10

A) (5x–40)(3x–19) B) (5x+12)(3x+9) C) (5x+5)(3x+2) D) (5x+37)(3x+26)

15) 8x4+18x2+9

A) (4x2+3)(2x2+3) B) (2x2–3)(4x2–3) C) (4x2+1)(2x2+9) D) (8x2+3)(x2+3)

16) 15x4–19x2–10

A) (3x2–5)(5x2+2) B) (5x–2)(3x+5) C) (3x2+1)(5x2–10) D) (15x2–5)(x2+2)

17) 15x6+11x3–12

A) (3x3+4)(5x3–3) B) (5x3+3)(3x3–4) C) 15(x3–3)(x3+4) D) (3x3+1)(5x3–12)

18) 7y6–37y3+10

A) (7y3–2)(y3–5) B) y2(7y2–2)(y2–5)

C) y4(7y–2)(y–5) D) (7y3–5y2+y–2)(y3–2y2+y–5)

6 CompletetheSquare

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

Whatnumbershouldbeaddedtocompletethesquareoftheexpression?

1) x2+12x

A) 36 B) 6 C) 72 D) 18

2) x2–6x

A) 9 B) –3C)18D)5

Page34

3) x2+4

5x

A) 4

25 B) 8

25 C) 16

25 D) 1

5

4) x2–1

2x

A) 1

16 B) –1

8C) 1

4D) –1

4

5) x2–x

A) 1

4B) 1

2C) 1 D) 4

0.6 SyntheticDivisio

n

1 DividePolynomialsUsingSyntheticDivision

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

Usesyntheticdivisiontofindthequotientandtheremainder.

1) x2+11x+16isdividedbyx+8

A) x+3;remainder–8B)x+3;remainder8

C) x+3;remainder0D

)x+4;remainder0

2) x3–x2+6isdividedbyx+2

A) x2–3x+6;remainder–6B)x

2–3x+6;remainder2

C) x2+x+2;remainder–6D)3x

2–4x+2;remainder0

3) x5+x2–2isdividedbyx–2

A) x4+2x3+4x2+9x+18;remainder34 B) x4+2x3+5x2+10x+20;remainder38

C) x4+3x2;remainder4D)x

4+3;remainder4

4) 2x3+6x2–4x+16isdividedbyx+4

A) 2x2–2x+4;remainder0B)

–2x2–4x+4;remainder0

C) 1

2x2+3

2x–1;remainder0D)2x

2x+3

2

+4;remainder0

5) x5–2x4–13x3–8x2–7x–14isdividedbyx–5

A) x4+3x3+2x2+2x+3;remainder1B)x

3+3x2+2x+2;remainder1

C) x4+3x3+2x2+2x–3;remainder3D)x

4+3x3+2x2+2x+1;remainder0

6) x4–4isdividedbyx–2

A) x3+2x2+4x+8;remainder12 B) x3+2x2+4x+8;remainder254

C) x3+6x2+4x+2;remainder12 D) x3+4x2+16x+64;remainder254

Page35

7) x4+1296isdividedbyx–6

A) x3+6x2+36x+216;remainder2592 B) x3+6x2+36x+216;remainder1296

C) x3+6x2+36x+216;remainder0D)x

3–6x2+36x–216;remainder2592

8) 6x5–5x4+x–4isdividedbyx+1

2

A) 6x4–8x3+4x2–2x+2;remainder–5B)6x

4–2x3–x2+1

2x+5

4;remainder–27

8

C) 6x4–8x3+5;remainder–13

2D) 6x4–2x3+x2–1

2x+5

4;remainder–37

8

Usesyntheticdivisiontodeterminewhetherx–cisafactorofthegivenpolynomial.

9) x3–8x2+20x–16;x–4

A) Yes B) No

10) x3+13x2+31x–45;x–3

A) Yes B) No

11) x3–5x2–22x+56;x+4

A) Yes B) No

12) x3–12x2+20x+100;x+6

A) Yes B) No

13) 3x3–22x2+47x–28;x–6

A) Yes B) No

14) 2x3–14x2–28x+96;x+2

A) Yes B) No

15) 4x3–27x2+8x+60;x–6

A) Yes B) No

16) 4x3–27x2+20x+75;x–5

A) Yes B) No

17) 6x5–5x4+x–4;x+1

2

A) Yes B) No

Page36

0.7 RationalExpressions

1 ReduceaRationalExpressiontoLowestTerms

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

Reducetherationalexpressiontolowestterms.

1) x2–36

x–6

A) x+6B)x–6C)

1

x–6D) 1

x+6

2) 4x+2

12x2+22x+8

A) 1

3x+4B) 4x+2

12x2+22x+8

C) 4x+3

3x+22 D) 4x

3x+4

3) y2+5y+6

y2+10y+16

A) y+3

y+8B) 5y+6

10y+16 C) 5y+3

10y+8D) –y2+5y+6

y2+10y+16

4) 3x2–18x+24

x–4

A) 3x–6B)

3x2–18x+24

x–4C) 3x2–24 D) 1

x–4

5) x2+9x+20

x2+11x+28

A) x+5

x+7B) 9x+20

11x+28 C) 9x+5

11x+7D) –x2+9x+20

x2+11x+28

6) 2x2+13x+6

2x2+7x–30

A) 2x+1

2x–5B) x–1

x+5C) 2x+6

2x–6D) x+2

x–4

7) 7x2+21x3

11x+33x2

A) 7x

11 B) 7x2+21x3

11x+33x2C) 7+21x3

11x+33 D) 7

11

8) y3–343

y–7

A) y2+7y+49 B) y3–343

y–7C) y2–49 D) 1

y–7

Page37

Anexpressionthatoccursincalculusisgiven.Reducetheexpressiontolowestterms.

9) (x2+3)·8–(8x+9)·4x

(x2+3)3

A) –24x2–36x+24

(x2+3)3B) –32x2–36x+8

(x2+3)2C) 24x2+36x–24

(x2+3)3D) –40x2–36x+24

(x2+3)3

10) (2x+5)4x–2x2(2)

(2x+5)2

A) 4x(x+5)

(2x+5)2B) 2x

(x+5)2C) 4x

(2x+5)2D) 4(x+5)

(2x+5)2

2 MultiplyandDivideRationalExpressions

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

Performtheindicatedoperationsandsimplifytheresult.Leavetheanswerinfactoredform.

1) 6x

12x+6

·14x+7

3

A) 7x

3B) 7

3C) 7x

18 D) x

3

2) 2x–2

x

·8x2

6x–6

A) 8x

3B) 3

8x C) 16x3–16x2

6x2–6x D) 12x2+24x+12

8x3

3) x3+1

x3–x2+x

·6x

–18x–18

A) –1

3B) x+1

3(–x–1) C) –x3+1

3(x+1) D) –x2+1

3

4) x2+6x+8

x2+4x+4

·x2+4x+4

x2+6x+8

A) 1 B) 1

x+2C) x+2

x+2D) x+4

x+2

5) x2–8x+15

x2–18x+72

·x2–16x+48

x2–11x+24

A) (x–5)(x–4)

(x–6)(x–8) B) (x+5)(x+4)

(x+6)(x+8)

C) (x2–8x+15)(x2–16x+48)

(x2–18x+72)(x2–11x+24)

D) (x–5)

(x–8)

Page38

6) x2+10x+24

x2+12x+32

·x2+8x

x2+3x–18

A) x

x–3B) 1

x–3C) x(x+8)

x–3D) x

x2+12x+32

7) 9x4–72x

3x2–12

·x2+x–2

4x3+8x2+16x

A) 3(x–1)

4B) 3x(x–1)

4C) 3x(x–1)(x–2)2

4(x+2)2D) 3x(x+1)

4

8) x2+13x+40

x2+15x+56

·x2+7x

x2+13x+40

A) x

x+8B) 1

x+8C) x2+7x

x+8D) x

x2+15x+56

9) 10x2–3x–4

5x2–x–4

·15x2+12x

1–4x2

A) 3x(5x–4)

(1–2x)(x–1) B) 3x

(1–2x)(x–1) C) (5x+4)(5x–4)

(1–2x)(x–1) D) 3x(5x+4)

(1–2x)(x–1)

10)

9x–9

5

3x–3

40

A) 24 B) 27(x–1)2

200 C) 1

24 D) 8(9x–9)

3x–3

11)

 2x–2

x

6x–6

5x2

A) 5x

3B) 3

5x C) 10x2(x–1)

6x(x–1) D) 12(x+1)2

5x3

12)

 x2+4x+4

x2+6x+8

x2+2x

x2+10x+24

A) x+6

xB) x+6C)

x+6

x(x+4) D) x

(x+4)(x+2)

Page39

13)

 x2–16x+64

7x–56

6x–48

42

A) 1 B) (x–8)2

49 C) x2–16x+64

(x–8)2D) 42

14)

 1

x+6

3

x2–36

A) x–6

3B) x+6

3C) x–6D)

3

x–6

15)

x2–81

x

x+9

x–10

A) (x–9)(x–10)

xB) (x–9)(x–10) C) (x+9)(x2+9)

x(x–10) D) x

(x–9)(x–10)

16)

16x2–49

x2–16

4x–7

x+4

A) 4x+7

x–4B) 4x–7

x+4

C) (4x–7)(16x2–49)

(x2+4)(x+4)

D) x–4

4x+7

3 AddandSubtractRationalExpressions

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

Performtheindicatedoperationsandsimplifytheresult.Leavetheanswerinfactoredform.

1) x

8

–15

7

A) 7x–120

56 B) x–15

15 C) x–15

56 D) 7x+120

120

2) 5x+7

2

–5x–7

2

A) 7 B) 5x C) 0 D) 49

Page40

3) 8x2

x–1

–8x

x–1

A) 8x B) 8x(x+1)

x–1C) 0 D) 8x

x–1

4) 7

12x

–1

6x

A) 5

12x B) 12

5x C) 1 D) 5

24x

5) 3

11x

+5

11x

A) 8

11x B) 11

8x C) 1 D) 8

22x

6) 5x+6

x

+7x–3

9x

A) 52x+51

9x B) 52x–57

9x C) 38x+51

9x D) 52x+51

9x2

7) 6

x2

–8

x

A) 2(3–4x)

x2B) 2(3+4x)

x2C) 2(4x–3)

xD) 2(3x+4)

x2

8) 4

x

+5

x–9

A) 9x–36

x(x–9) B) 36x–9

x(x–9) C) 9x–36

x(9–x) D) 36x–9

x(9–x)

9) 2

x+6

–5

x–6

A) –3x–42

(x+6)(x–6) B) –3x+18

(x+6)(x–6) C) –3

(x+6)(x–6) D) –3x+42

(x+6)(x–6)

10) 20

x–4

+4

x–4

A) 24

x–4B) 16

x–4C) 16

xD) 20(x–4)

4(x–4)

11) 6x2

x–1

–6x

x–1

A) 6x B) 6x(x+1)

x–1C) 0 D) 6x

x–1

Page41

12) 6–x

x–4

–2x+1

4–x

A) x+7

x–4B) x+5

x–4C) –x+7

x–4D) –x+5

x–4

13) x+9

x+3

–x+9

x–7

A) –10(x+9)

(x+3)(x–7) B) –4(x+9)

(x+3)(x–7) C) 0 D) 10(x+9)

(x+3)(x–7)

14) 7x

x–2

+2

2–x

A) 7x–2

x–2B) 7x+2

x–2C) 7x–2

2–xD) 5x

x–2

15) x2–9x

x–6

+18

x–6

A) x–3B)x+6C)x+3D)x–6

4 UsetheLeastCommonMultipleMethod

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

FindtheLCMofthegivenpolynomials.

1) x,x–9

A) x(x–9) B) x–9 C) x D) x2(x–9)

2) 5x+35,x2+7x

A) 5x(x+7) B) 5x+7C)5x

2+7D)5x

2+35

3) x2+8x+16,x2+4x

A) x(x+4)2B) x(x+1)(x+4) C) (x+4)2D) x(x+4)

4) x2+2x–8,3x–6

A) 3(x+4)(x–2) B) 3(x–4)(x+2) C) 3(x+4)(x+2) D) 3(x–4)(x–2)

5) x2+4x–5,x2+11x+30

A) (x–1)(x+5)(x+6) B) (x–1)(x+5)

C) (x+5)(x+6) D) (x+1)(x–5)(x+6)

6) x–10

,

10–x

A) (x–10)or(10–x) B) (x–10)(10 –x) C) –1D)x+10

7) 3x–4

,

3x+4

A) (3x–4)(3x+4) B) (3x–4)or(3x+4) C) (3x–4) D) (3x+4)

8) x2–9x,(x–9)2

A) x(x–9)2B) x(x–9) C) (x+9)(x–9)2D) x(x+9)2

Page42

9) x2–6x–27,x2–9,x2–12x+27

A) (x–9)(x+3)(x–3) B) (x+9)(x+3)(x–3)

C) (x–9)(x+3) D) (x+9)(x–3)2

Performtheindicatedoperationsandsimplifytheresult.Leavetheanswerinfactoredform.

10) 4

x

+7

x–9

A) 11x–36

x(x–9) B) 36x–11

x(x–9) C) 11x–36

x(9–x) D) 36x–11

x(9–x)

11) –1

6

–6

5x

A) –5x–36

30x B) –11

30–5x C) 5x–36

30x D) –5x+36

30x

12) 1

(x+2)(x+5)

–3

(x+5)(x+4)

A) –2(x+1)

(x+2)(x+5)(x+4) B) 2(2x+5)

(x+2)(x+5)(x+4)

C) –2(x+3)

(x+2)(x+5)(x+4) D) 2(x+1)

(x+2)(x+5)(x+4)

13) x–4

x2–8x+15

+2x+3

x2+5x–24

A) 3x2–3x–47

(x–3)(x–5)(x+8) B) 3x2–3x–47

(x+3)(x+5)(x–8)

C) 3x–1

2x2–3x–9D) 3x–1

14) 2

x2–3x+2

+5

x2–1

A) 7x–8

(x–1)(x+1)(x–2) B) 7x–8

(x–1)(x–2)

C) 8x–7

(x–1)(x+1)(x–2) D) 20x–8

(x–1)(x+1)(x–2)

15) x

x2–16

–8

x2+5x+4

A) x2–7x+32

(x–4)(x+4)(x+1) B) x2+7x+32

(x–4)(x+4)(x+1)

C) x2–7x+32

(x–4)(x+4) D) x2–7

(x–4)(x+4)(x+1)

Page43

16) 8

x2+2x

+7

x

+4

x+2

A) 11

xB) 4

xC) 7

xD) 28

x

17) 3x

x+1

+4

x–1

–6

x2–1

A) 3x–2

x–1B) 3x–2

x+1C) x+1

x–1D) 3x

x–1

18) 3x

x2–5x–36

–x–1

x2–16

+1

x2–13x+36

A) 2x2–x–5

(x–9)(x+4)(x–4) B) 2x2–21x+13

(x–9)(x+4)(x–4)

C) 2x–1

(x–9)(x+4) D) 2x–1

(x–9)(x–4)

5 SimplifyComplexRationalExpressions

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

Performtheindicatedoperationsandsimplifytheresult.Leavetheanswerinfactoredform.

1)

2

x

+2

2

x

–2

A) 1+x

1–xB) 2(1+x)

1–xC) 2–x2D) x2

2–x2

2)

1–10

x

1+10

x

A) x–10

x+10 B) x+10

x–10 C) x–10 D) x+10

3)

3

x

+1

3

x

–1

A) 3+x

3–xB) 3 C) x2+3D)

x2

x2+3

Page44

4)

1–1

x

5+1

x

A) x–1

5x+1B) x–1

5x C) x+1

5x–1D) 5x+1

x–1

5)

1–4

x

x–16

x

A) 1

x+4B) 1

x–4C) x+4D)x–4

6)

x

4

–1

x

1+2

x

A) x–2

4B) x+2

4C) 4

x–2D) 4

x+2

7)

9+3

x

4

+1

12

A) 36

xB) x

36 C) 1 D) 36

8)

3

x

+4

x2

9

x2

–16

x

A) 3x+4

9–16x B) 1

3x–4C) 1

3–4x D) 3x2+4

9–16x

9)

5

x

+2

25

x2

–4

A) x

5–2x B) x

5x–2C) 1

5–2x D) 1

5x–2

Page45

10)

x–x

x–5

x–6

A) x

x–5B) x

x–6C) x2

x–5D) x

x+5

11)

7

7x–1

–7

7

7x–1

+7

A) 2–7x

7x B) 2+7x

7x C) 2–x

xD) 7x

2–7x

12)

13

14–x

+14

x–14

5

x

+9

x–14

A) x

14x–70 B) 27x

14x–70 C) –x

14x–70 D) –27x

14x–70

13)

x

x–2

+1

3

x2–4

+1

A) 2x+4

x+1B) x+2

x+1C) 2x+4

x–1D) 2x–4

x–1

14)

2

x+7

+4

x+3

3x+17

x2+10x+21

A) 2 B) 1

2C) 3x+17 D) 6

15)

x+7

x–7

+x–7

x+7

x–7

–x–7

x+7

A) x2+49

14x B) 1 C) (x+7)3

28x(x+8) D) (x+7)2

14x

Page46

16)

1

x+5

+1

x–5

1

x2–25

A) 2x B) x2C) 10 D) –10

17)

2

x2–3x–10

–1

x–5

1

x+2

+1

A) –x

x2–2x–15

B) x

x2–4x–15

C) –x

x2–3x–10

D) –1

Solvetheproblem.

18) Thefocallengthfofalenswithindexofrefractionnis1

f

=(n–1)

1

R1

+1

R2whereR1andR2aretheradii

ofcurvatureofthefrontandbacksurfacesofthelens.Expressfasarationalexpression.

A) f=R1R2

(n–1)(R1+R2)B) f=(n–1)(R1+R2)

R1R2

C) f=R1R2

(n+1)(R1–R2)D) f=n(R1–R2)

R1R2

19) Anelectricalcircuitcontainstworesistorsconnectedinparallel.IftheresistanceofeachisR1andR2

ohms,respectively,thentheircombinedresistanceRisgiventheformula

R=1

1

R1

+1

R2

IftheircombinedresistanceRis2ohmsandR2is3ohms,findR1.

A) 6ohms B) 1

6

ohm C) 2 ohms D) 1ohms

0.8 nthRoots;RationalExponents

1 WorkwithnthRoots

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

Simplifytheexpression.Assumethatallvariablesarepositivewhentheyappear.

1) 327

A) 3 B) 9 C) ±3D)5

2) 3–512

A) –8B)

±8C)64D)23

Page47

3) 4625

A) 5 B) –5 C) 625 D) notarealnumber

2 SimplifyRadicals

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

Simplifytheexpression.Assumethatallvariablesarepositivewhentheyappear.

1) 16y28

A) 4y14 B) 4y28 C) 16y14 D) 4y26

2) 343x2

A) 7x 7 B) 7 7x C) 343x D) 7x27

3) 3–27x30y24

A) –3x10y8B) –3x15y12 C) 3x10y8D) 9x10y8

4) –3–27x18y36

A) 3x6y12 B) 3x6y18 C) –3x18y12 D) 9x6y12

5) 245x7y8

A) 7x3y45x B) 7x7y85x C) 7x3y45 D) 7y45x7

6) 3343x4y5

A) 7xy3xy2B) 5xy 3xy2C) 7xy3xy D) 7xy xy2

7) 48x2y

25

A) 4x 3y

5B) 43x

2y

5C) x48y

5D) 16x 3y

8) y11

A) y5y B) y11 C) y10 y D) y y9

9) 3–64x21

A) –4x7B) 4x7C) –4x21 D) –4x18

10) 3x23

A) x73x2B) x 3x20 C) x9D) 3x23

Page48

11) 313

y18

A)

313

y6B)

313

y15 C) 13

y6D) 313

y18

12) 3375

x15

A) 533

x5B)

3375

x5C) 533

x12 D) 3375

x15

13) ( 11+3)( 11–3)

A) 2 B) 20 C) 11–23 D) 8

14) (7 6)(12 60)

A) 504 10 B) 84 360 C) 3024 10 D) 504 60

15) 321·39

A) 3 37 B) 3189 C) 3 321 D) 6189

16) 9 33·732

A) 6336 B) 16 36 C) 6333·32 D) 6335

17) 8 3+875

A) 48 3 B) 32 3 C) 16 3 D) –48 3

18) 2 98+550

A) 39 2 B) –39 2 C) –11 2 D) 11 2

19) –580–3 245+520

A) –31 5 B) –55 C) 3 5 D) –35

20) 5x2+2 45x2+4 45x2

A) 19x 5 B) 19x 69 C) 6x 69 D) 6x 5

21) 1732–3354

A) 8 32 B) 14 32 C) –832 D) 1732–3354

22) 38y–3128y

A) 2 3y–432y B) 2–432 C) 6 3y D) 4 32y–23y

23) (7 2+4)2

A) 114+56 2 B) 114–56 2 C) 82+56 2 D) 102+56 2

Page49

24) 3 327x+33125x

A) 243x B) 24x C) 3 3152x D) 8 3x

25) 4 316x–23128x

A) 0 B) 8 3x C) 8 3x–23128x D) cannotsimplify

26) 3125+4–312

A) 9–312 B) 3125+4–312 C) 9–236 D) 9 312

27) 2x2–3375+72x2

A) 7x 2–533 B) 6x 2–533 C) 7x 2–515 D) 7 2x2–3375

28) ( 12+z)( 12–z)

A) 12–z B) 12z C) 12–2z D) 12–2 12z

29) 56x5y6

2y4

A) 2x2y7x B) 4x2y7x C) 2x4y27xy D) 28xy x

Solve.

30) 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.Ifanobjectfalls44.1meters

beforeithitstheground,findthetimeittookfortheobjecttofall.

A) 3seconds B) 4seconds C) 9 seconds D) 6seconds

31) Ifthethreelengthsofthesidesofatriangleareknown,Heronʹsformulacanbeusedtofinditsarea.Ifa,b,

andcarethethreelengthsofthesides,Heronʹsformulaforareais:

A=s(s–a)(s–b)(s–c)

wheresishalftheperimeterofthetriangle,ors=1

2(a+b+c).

Usethisformulatofindtheareaofthetriangleifa=5cm,b=11cmandc=12cm.

A) 6 21sq.cm B) 6 42sq.cm C) 8 2737sq.cm D) 3 6sq.cm

Solvetheproblem.

32) Aformulausedtodeterminethevelocityvinfeetpersecondofanobject(neglectingairresistance)afteri

t

hasfallenacertainheightisv=2gh,wheregistheaccelerationduetogravityandhistheheightthe

objecthasfallen.IftheaccelerationgduetogravityonEarthisapproximately32feetpersecond,findthe

velocityofabowlingballafterithasfallen60feet.(Roundtothenearesttenth.)

A) 62.0ftpersec B) 43.8 ftpersec C) 11.0 ftpersec D) 3840 ftpersec

Page50

33) Policeusetheformulas=30fdtoestimatethespeedsofacarinmilesperhour,wheredisthedistance

infeetthatthecarskiddedandfisthecoefficientoffriction.Ifthecoefficientoffrictiononacertaingravel

roadis0.26andacarskidded320feet,findthespeedofthecar,tothenearestmileperhour.

A) 50mph B) 98mph C) 274 mph D) 2496 mph

34) 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maximumsafespeedforacurveinaroadwitharadiusofcurvatureof350feet.

A) 30mph B) 47mph C) 19 mph D) 12mph

35) Themaximumdistancedinkilometersthatyoucanseefromaheighthinmetersisgivenbytheformula

d=3.5 h.Howfarcanyouseefromthetopofa347–meterbuilding?(Roundtothenearesttenthofa

kilometer.)

A) 65.2km B) 34.8 km C) 18.6 km D) 649.2 km

3 RationalizeDenominators

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

Simplifytheexpression.Assumethatallvariablesarepositivewhentheyappear.

1) 1

22

A) 22

22 B) 22 22 C) 22 D) 22

2) 9

2

A) 92

2B) 9 2 C) 81 2

2D) 13

3) 3

17

A) 317

17 B) 3 17 C) 917

17 D) 292

4) 25

11

A) 511

11 B) 5 11 C) 25 11

11 D) 126

5) –7

40

A) –710

20 B) –710 C) –710

10 D) –40

6) 3

6–5

A) 18+35

31 B) 18–35

31 C) 18+35

–1D) 3

6

–3

5

Page51

7) 6

7+4

A) 42–46

–9B) 42+46

–9C) 42–46

11 D) 342

+76

28

8) 5

53–5

A) 15+1

14 B) 15–1

14 C) 15+1

16 D) 3+1

14

9) 7–2

7+2

A) 51–14 2

47 B) 51+14 2

47 C) 1 D) 47–14 2

51

10) 411

+22

22+11

A) 3 2–2B)52+6C)42–6D)42–2

11) 13

32

A) 1334

2B) 1332

2C) 1334 D) 1332

12) –7

39

A) –733

3B) –739

3C) –739 D) –733

13) x–y

7x+3y

A) x7

–3xy–7xy+y3

7x–3y B) x7

–3xy–7xy+y3

7x+3y

C) 7x–10xy+3y

7x–3y D) 7x–10xy+3y

7x+3y

14) 4

x+h–x

A) 4( x+h+x)

hB) 4x+h+x

hC) 4h

hD) 4( x+h–x)

h

Page52

4 SimplifyExpressionswithRationalExponents

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

Simplifytheexpression.

1) –321/5

A) –2B)16C)32D)

–8

2) 1

32

1

/

5

A) 1

2B) –2C)

–1

2D) 2

3) 274/3

A) 81 B) 729 C) 243 D) 2187

4) 165/4

A) 32 B) 256 C) 128 D) 512

5) 2434/5

A) 81 B) 6561 C) 2187 D) 19,683

6) 8

64

2/3

A) 1

4B) –1

4C) 1

6D) 1

2

7) (–27)4/3

A) 81 B) 729 C) –81 D) notarealnumber

8) 49–3/2

A) 1

343 B) –1

343 C) 343 D) –343

9) 64–4/3

A) 1

256 B) –1

256 C) 256 D) notarealnumber

10) 16–5/4

A) 1

32 B) –1

32 C) 32 D) notarealnumber

11) 32–4/5

A) 1

16 B) –1

16 C) 16 D) notarealnumber

12) –27–4/3

A) –1

81 B) 1

81 C) 81 D) notarealnumber

Page53

13) –243–4/5

A) –1

81 B) 1

81 C) 81 D) notarealnumber

14) 6251/2

A) 25 B) 50 C) 12.5 D) 100

15) 641/3

A) 4 B) 12 C) 256 D) 768

16) 161/4

A) 2 B) 8 C) 16 D) 32

17) 165/4

A) 32 B) 1024 C) 58D) 35

18) 2164/3

A) 1296 B) 46,656 C) 7776 D) 279,936

19) 815/4

A) 243 B) 6561 C) 2187 D) 19,683

20) 16–1/2

A) 1

4B) 4 C) –4D)

–1

4

21) 512–1/3

A) 1

8B) 1

24 C) –8D)8

22) 64–4/3

A) 1

256 B) –1

256 C) –256 D) 256

23) 16–5/4

A) 1

32 B) –1024 C) –1

32 D) –32

24) 4

9

3/2

A) 8

27 B) 27

8C) –27

8D) –8

27

25) 49

64

–1/2

A) 8

7B) 49

128 C) 7

8D) notarealnumber

Page54

26) –125

27

–2/3

A) 9

25 B) 25

9C) –25

9D) notarealnumber

Simplifytheexpression.Expresstheanswersothatonlypositiveexponentsoccur.Assumethatallvariablesare

positive.

27) x5/8·x3/8

A) x B) x15/8 C) x15

/

64 D) 1

x

28) x–2

/

5·x3

/

5

A) x1

/

5B) x–1

/

5C) x6

/

5D) x5/6

29) (x14y7)1

/

7

A) x2yB)x

2|y| C) x14yD)x

2

30) (16x8y4)1

/

2

A) 4x4y2B) 4x4yC)x

4y2D) 4x8y2

31) (5x2

/

3)(9x1

/

4)

A) 45x11

/

12 B) 45x1

/

4C) 45x11

/

7D) 45x2

/

3

32) (x5y3)7

/

4

A) x35

/

4y21

/

4B) x27

/

4y19

/

4C) x21

/

4y35

/

4D) x20

/

7y12

/

7

33) (9x4y–14)3/2

A) 27x6

y21 B) 9x6

y21 C) 27x6y21 D) 27

x6y21

34) (9x1/5·y1/5)2

A) 81x2

/

5y2

/

5B) 81x1

/

25y1

/

25 C) 81x1

/

10y1

/

10 D) 81x2y2

35) x4

/

3·x1

/

2

x–6/5

A) x91

/

30 B) x19

/

30 C) 1

x91/30 D) 1

x19/30

36) (5x1/5)2

x1/6

A) 25x7

/

30 B) 25x17

/

30 C) 5x7

/

30 D) 5x17

/

30

Page55

Anexpressionthatoccursincalculusisgiven.Writetheexpressionasasinglequotientinwhichonlypositive

exponentsand/orradicalsappear.

37) (49–x2)1/2+3x2(49–x2)–1/2

49–x2

A) 49+2x2

(49–x2)3/2 B) 49–4x2

(49–x2)3/2 C) 3x2

(49–x2)3/2 D) 3x2

49–x2

38) 4x3/2(x3+x2)–6x5/2–6x3/2

A) 2x3/2(x+1)(2x2–3) B) 4x3/2(x3–1)+4x3–2x3/2(x–1)

C) x3/2(x–1)[4(x2–1)–2]+4x3D) 4x3/2(x+1)(2x2–3)

39) (x2–1)1/2·3

2(2x+5)1/2·2+(2x+5)3/2·1

2(x2–1)–1/2·2x

A) (2x+5)1/2(5x2+5x–3)

(x2–1)1/2 B) (2x+5)1/2(5x2+5x–3)

(x2–1)–1/2

C) (x2–1)1/2(2x+5)1/2(5x2+5x–3) D) (x2–1)1/2(2x+5)–1/2(5x2+5x–3)

40)

(x2+2)1/2·3

2(2x+1)1/2·2–(2x+1)3/2·1

2(x2+2)–1/2·2x

x2+2

A) (2x+1)1/2(x2–x+6)

(x2+2)3/2 B) (2x+1)1/2(x2–x+6)

(x2+2)–3/2

C) (x2+2)3/2(2x+1)1/2(x2–x+6) D) (x2+2)3/2(2x+1)–1/2(x2–x+6)

Factortheexpression.Expressyouranswersothatonlypositiveexponentsoccur.

41) x3

/

7+3x2

/

7

A) x2/7(x1

/

7+3) B) x2/7(x–1

/

7+3) C) x1/7(x3

/

7+3) D) x1/7(x1

/

7+3)

42) 13x1

/

7–7x–3

/

7

A) x–3

/

7(13x4

/

7–7) B) x1/3(13–7x4

/

7)

C) x–3

/

7(13x4

/

7–7x) D) x1

/

7(13x4

/

7–7x4

/

7)

43) x3

/

5+x2

/

5

A) x2

/

5(x1

/

5+1) B) x2

/

5(x1

/

5)C)x

2

/

5(x1

/

5–1) D) x2

/

5(x1

/

5+x)

44) x–2

/

7–x–3

/

7

A) x–3

/

7(x1

/

7–1) B) x–3

/

7(x1

/

7)C)x

–3

/

7(x1

/

7+1) D) x–3

/

7(x1

/

7–x)

45) (x+5)–3

/

5+(x+5)–1

/

5+(x+5)1/5

A) (x+5)–3

/

5[1+(x+5)2/5+(x+5)4

/

5]B)(x+5)–3

/

5[1+(x+5)–2

/

5+(x+5) –4

/

5]

C) (x+5)–3

/

5[1+(x+5)4

/

5+(x+5)6

/

5]D)(x+5)–3

/

5[1+(x+5)1

/

5+(x+5)3

/

5]

Page56

46) (2m+3)–2/5+(2m+3)1/5+(2m+3) 7/5

A) (2m+3)–2/5[1+(2m+3)3/5+(2m+3) 9

/

5]B)(2m+3)–2

/

5[1+(2m+3)4/5+(2m+3) 7

/

5]

C) (2m+3)–2/5[1+(2m+3)–3/5+(2m+3) –9

/

5]D)(2m+3)–2

/

5[1+(2m+3)3/5–(2m+3) 9

/

5]

Page57

Ch.0 ChapterR:Review

AnswerKey

0.1 RealNumbers

1 WorkwithSets

2 ClassifyNumbers

3 EvaluateNumericalExpressions

4 WorkwithPropertiesofRealNumbers

0.2 AlgebraEssentials

1 GraphInequalities

2 FindDistanceontheRealNumberLine

3 EvaluateAlgebraicExpressions

4 DeterminetheDomainofaVariable

5 UsetheLawsofExponents

6 EvaluateSquareRoots

7 UseaCalculatortoEvaluateExponents

8 UseScientificNotation

0.3 GeometryEssentials

1 UsethePythagoreanTheoremandItsConverse

2 KnowGeometryFormulas

3 UnderstandCongruentTrianglesandSimilarTriangles

0.4 Polynomials

1 RecognizeMonomials

2 RecognizePolynomials

3 AddandSubtractPolynomials

4 MultiplyPolynomials

5 KnowFormulasforSpecialProducts

6 DividePolynomialsUsingLongDivision

7 WorkwithPolynomialsinTwoVariables

0.5 FactoringPolynomials

1 FactortheDifferenceofTwoSquaresandtheSumandDifferenceofTwoCubes

2 FactorPerfectSquares

3 FactoraSecond–DegreePolynomial:x^2+Bx+C

4 FactorbyGrouping

5 FactoraSecond–DegreePolynomial:Ax^2+Bx+C,A≠1

6 CompletetheSquare

0.6 SyntheticDivisio

n

1 DividePolynomialsUsingSyntheticDivision

0.7 RationalExpressions

1 ReduceaRationalExpressiontoLowestTerms

2 MultiplyandDivideRationalExpressions

3 AddandSubtractRationalExpressions

4 UsetheLeastCommonMultipleMethod

5 SimplifyComplexRationalExpressions

0.8 nthRoots;RationalExponents

1 WorkwithnthRoots

2 SimplifyRadicals

3 RationalizeDenominators

4 SimplifyExpressionswithRationalExponents

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