Chapter 1 The table of values was generated by a graphing utility with

Ch.1 EquationsandInequalities

1.1 GraphsandGraphingUtilities

1 PlotPointsintheRectangularCoordinateSystem

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

Plotthegivenpointinarectangularcoordinatesystem.

1) (1

,

3)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page1

2) (–2

,

3)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page2

3) (1

,

–2)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page3

4) (–5

,

–4)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page4

5) (0,1)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page5

6) (5

,

0)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page6

7) –1

2,–3

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page7

8) –5

2,0

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page8

2 GraphEquationsintheRectangularCoordinateSystem

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

Graphtheequation.

1) y=x–1

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page9

2) y=6x+6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page10

3) y=–1

3x+2

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page11

4) y=x2+3

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page12

5) y=x3–3

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page13

6) y=–x+6

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page14

7) y=5|x|

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page15

8) y=–6

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page16

9) y=1

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page17

WritetheEnglishsentenceasanequationintwovariables.Thengraphtheequation.

10) They–valueistwomorethanfivetimesthex–value.

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A) y=5x+2

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B) y= –5x+2

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C) y=–5x–2

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D) y=5x–2

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page18

11) They–valueissixdecreasedbythesquareofthex–value.

x

–8–6–4–2 2468

y

8

6

4

2

-2

-4

-6

-8

x

–8–6–4–2 2468

y

8

6

4

2

-2

-4

-6

-8

A) y=6–x2

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

B) y=6–x

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

C) y=x2–6

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

D) y=x–6

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

Page19

3 InterpretInformationAboutaGraphingUtilityʹsViewingRectangleorTable

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

Matchthecorrectviewingrectangledimensionswiththefigure.

1)

A) [–25

,

25

,

5]by[–25

,

25

,

5] B) [–5

,

5

,

5]by[–5

,

5

,

5]

C) [–50

,

25

,

5]by[–50

,

25

,

5] D) [–25

,

25

,

10]by[–25

,

25

,

10]

2)

A) [–1

,

8

,

1]by[–4

,

5

,

1] B) [–1

,

8

,

1]by[–1

,

8

,

1]

C) [–4

,

5

,

1]by[–1

,

8

,

1] D) [–10

,

5

,

1]by[–10

,

5

,

1]

3)

A) [–4

,

4

,

2]by[–80

,

80

,

8] B) [–16

,

16

,

4]by[–4

,

4

,

2]

C) [–4

,

4

,

2]by[–4

,

4

,

2] D) [–20

,

20

,

2]by[–20

,

20

,

2]

Page20

4)

A) [–10

,

30

,

10]by[–400

,

500

,

100] B) [–1

,

8

,

1]by[–1

,

8

,

1]

C) [–1

,

5

,

1]by[–4

,

8

,

1] D) [–10

,

5

,

1]by[–10

,

5

,

1]

ThetableofvalueswasgeneratedbyagraphingutilitywithaTABLEfeature.Usethefollowingtabletosolve.

5) WhichequationcorrespondstoY2inthetable?

A) y2=2x+3B)y

2=3–2x C) y2=x+3D)y

2=3x–2

6) DoesthegraphofY1passthroughtheorigin?

A) Yes B) No

7) AtwhichpointsdothegraphofY1andY2intersect?

A) (–1,1)and(3,9) B) (2

,

7)and(2

,

4) C) (–1,1)and(2

,

7) D) (2

,

4)and(3,9)

8) ForwhichvaluesofxisY1=Y2?

A) –1and3B)0and3C)

–1and0D)0and–2

Page21

4 UseaGraphtoDetermineIntercepts

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

Usethegraphtodeterminethex–andy–intercepts.

1)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) x–intercept:–2;y–intercept:8B)x

–intercept:2;y–intercept:8

C) x–intercept:–2;y–intercept:–8D)x

–intercept:–8;y–intercept:8

2)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) x–intercepts:–5

,

5;y–intercept:–5B)x

–intercepts:–5

,

5

C) y–intercept:–5D)x

–intercepts:–5

,

5;y–intercept:0

Page22

3)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) x–intercepts:–3

,

1;y–intercept:3B)x

–intercept:–3;y–intercepts:1

,

3

C) x–intercept:3;y–intercepts:–3

,

1D)x

–intercept:1;y–intercept:3

4)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) x–intercept:–3B)y

–intercept:–3C)x

–intercept:3D)y

–intercept:3

5)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) x–intercept:2;y–intercept:–8B)x

–intercept:2;y–intercept:8

C) x–intercept:–2;y–intercept:–8D)x

–intercept:–2;y–intercept:8

Page23

6)

x

-10 -5 5

y

10

5

-5

-10

x

-10 -5 5

y

10

5

-5

-10

A) x–intercepts:–4

,

1,–5;y–intercept:–4B)x

–intercept:–4;y–intercepts:–4

,

1,–5

C) x–intercepts:4

,

1,5;y–intercept:–4D)x

–intercept:–4;y–intercepts:4

,

1,5

7)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) x–intercepts:–2

,

2;y–intercepts:–6

,

6B)x

–intercepts:–2

,

2

C) y–intercepts:–6

,

6D)x

–intercepts:–6

,

6;y–intercepts:–2

,

2

Page24

5 InterpretInformationGivenbyGraphs

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

ThelinegraphshowstherecordedhourlytemperaturesindegreesFahrenheitatanairport.

1) Atwhattimewasthetemperaturethehighest?

A) 1p.m. B) 5p.m. C) 11a.m. D) 2p.m.

2) Atwhattimewasthetemperatureitslowest?

A) 9a.m. B) 6p.m. C) 4p.m. D) 1p.m.

3) Whattemperaturewasrecordedat4p.m.?

A) 76°FB)78°FC)74°FD)77° F

4) Duringwhichhourdidthetemperatureincreasethemost?

A) 10a.m.to11a.m. B) 1p.m.to2p.m. C) 12p.m.to1p.m. D) 9a.m.to10a.m.

5) Atwhattimewasthetemperature79°?

A) 1p.m. B) 4p.m. C) 12p.m. D) 3p.m.

6) Duringwhichtwohourperioddidthetemperatureincreasethemost?

A) 9a.m.to11a.m. B) 10a.m.to11a.m. C) 12p.m.to2p.m. D) 10a.m.to12p.m.

Page25

Matchthestorywiththecorrectfigure.

7) Theamountofrainfallasafunctionoftime,iftherainfellmoreandmoresoftly.

A)

x

y

x

y

B)

x

y

x

y

C)

x

y

x

y

D)

x

y

x

y

Page26

8) Theheightofananimalasafunctionoftime.

A)

x

y

x

y

B)

x

y

x

y

C)

x

y

x

y

D)

x

y

x

y

Page27

9) Markstartedoutbywalkingupahillfor5minutes.Forthenext5minuteshewalkeddownasteephilltoan

elevationlowerthanhisstartingpoint.Forthenext10minuteshewalkedonlevelground.Forthenext10

minuteshewalkeduphill.Determinewhichgraphofelevationabovesealevelversustimeillustratesthestory.

A) B)

C) D)

1.2 LinearEquationsandRationalEquations

1 SolveLinearEquationsinOneVariable

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

Solveandcheckthelinearequation.

1) 5x–5=20

A) {5} B) {20} C) {24} D) {9}

2) 6x–(2x–1)=2

A) 1

4B) 1

8C) –1

4D) –1

8

3) 2x–4=–3+10x

A) –1

8B) –8 C) 8 D) –12

7

4) (7x+1)+9=8(x+6)

A) {–38} B) {38} C) {56} D) {–4}

Page28

5) –4x+5+2(x+1)=–5x+4

A) –1 B) 3

4C) 7

3D) –7

4

6) 6[7x–1+3(x+1)]=2x+4

A) –4

29 B) –8

7C) –10

29 D) –20

7

7) 32–2(8–5)2=63x

A) –1

7B) {7} C) {0} D) 1

8) 0.53(60)+0.70x=0.60(60+x)

A) {40} B) {30} C) {50} D) {20}

9) 0.50x–0.40(50+x)=–0.34(50)

A) {30} B) {20} C) {40} D) {15}

Findallvaluesofxsatisfyingthegivenconditions.

10) y1=8x+4(8+x),y2=3(x–3)+10x,andy1=y2

A) {41} B) {11} C) {–41} D) {–11}

Findallvaluesofxsuchthaty=0.

11) y=2[4x–(5x–2)]–6(x–2)

A) {2} B) {–2} C) 1 D) –1

2 SolveLinearEquationsContainingFractions

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

Solvetheequation.

1) x

2=x

5+8

A) 80

3B) {40} C) {16} D) {10}

2) x

3=x

2+4

3

A) –8 B) –4

3C) 0 D) –1

8

3) 20–x

2=x

3

A) {24} B) 50 C) 50

3D) {4}

4) 2x

5=x

3+5

A) {75} B) {–75} C) {150} D) {–150}

Page29

5) 5x

6–x=x

42 –4

7

A) 3 B) –4 C) 4 D) –3

6) x+5

4=3

2–x–1

5

A) {1} B) 13 C) {0} D) {30}

7) x–18

–9+x+3

3=x+8

A) –45

7B) –81

7C) –9 D) –99

7

Findallvaluesofxsatisfyingthegivenconditions.

8) y1=x+6

5,y2=x+8

7,andy1=y2

A) {–1} B) {1} C) {–2} D) {2}

Findallvaluesofxsuchthaty=0.

9) y=x+9

2+x–2

3–14

3

A) {1} B) 21

2C) {0} D) {28}

3 SolveRationalEquationswithVariablesintheDenominators

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

First,writethevalue(s)thatmakethedenominator(s)zero.Thensolvetheequation.

1) 9

x=3

2x +30

A) x≠0;1

4B) x≠0;{4} C) x≠0,2;21

10 D) Norestrictions;{2}

2) 7

x+2=5

2x +9

4

A) x≠0;18 B) x≠0;1

18

C) x≠0,2,4;18 D) Norestrictions;1

18

3) x–6

3x +5=x+4

x

A) x≠0;18

13 B) x≠0;–13

2

C) x≠0,3;18

13 D) Norestrictions;2

3

4) 45

x–8+5=10

x–8

A) x≠8;{1} B) x≠–8;{1} C) x≠–8;{19} D) x≠8;∅

Page30

5) 18

3x–3+1

3=6

x–1

A) x≠1;∅B) x≠3;{1} C) x≠1;{1} D) x≠–1,3;{1,3}

6) 5

x+1+2

x–1=4

(x+1)(x–1)

A) x≠–1

,

1;∅B) x≠–1

,

1;{2} C) x≠–1;{1} D) Norestrictions;{1}

Solvetheequation.

7) x

2x+2=–2x

4x+4+2x–3

x+1

A) {3} B) 3

2C) {–3} D) –12

5

8) 2

y+5–8

y–5=4

y2–25

A) {–9} B) {9} C) { 37} D) {54}

9) 1

x+5+2

x+3=–2

x2+8x+15

A) ∅B) {–5} C) {3} D) {0}

10) m+7

m2+2m–15

–7

m2+10m+25

=m–7

m2+2m–15

A) { –13 } B) { –91 } C) { 13 } D) { –77 }

Findallvaluesofxsatisfyingthegivenconditions.

11) y1=1

x+6,y2=2

x+3,y3=–3

x2+9x+18 ,andy1+y2=y3

A) {0} B) {–6} C) {3} D) ∅

12) y1=7

x+4,y2= 5

x–4,y3=2

x2–16 ,andy1–y2=y3

A) {25} B) {–25} C) {7} D) {50}

4 RecognizeIdentities,ConditionalEquations,andInconsistentEquations

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

Determinewhethertheequationisanidentity,aconditionalequation,oraninconsistentequation.

1) 5(4x+26)=20x+130

A) Identity B) Conditionalequation C) Inconsistentequation

2) 5x+3x=7x

A) Identity B) Conditionalequation C) Inconsistentequation

3) –5(x+1)–47=2x–7(x+8)

A) Identity B) Conditionalequation C) Inconsistentequation

4) 2x+2(–3x–3)=–7–3x

A) Identity B) Conditionalequation C) Inconsistentequation

Page31

5) 7x+10(x+1)=17(x+1)–7

A) Identity B) Conditionalequation C) Inconsistentequation

6) 9x+1–2x–8=5x+2x–10

A) Identity B) Conditionalequation C) Inconsistentequation

7) 8x

x=8

A) Identity B) Conditionalequation C) Inconsistentequation

8) 3x

x–8=24

x–8+9

A) Identity B) Conditionalequation C) Inconsistentequation

9) 7x+2

7+6

7=–5x

3

A) Identity B) Conditionalequation C) Inconsistentequation

10) 7

y+3–5

y–3=12

y2–9

A) Identity B) Conditionalequation C) Inconsistentequation

11) 1

x+5+2

x+3=–2

x2+8x+15

A) Identity B) Conditionalequation C) Inconsistentequation

5 SolveAppliedProblemsUsingMathematicalModels

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

Solvetheproblem.

1) Thereisarelationshipbetweentheexpectednumberofticketssoldforaraffleandthedollarvalueoftheprize

fortheraffle.TheequationT–6P=100describesthisrelationship,whereTistheexpectednumberoftickets

sold,andPisthedollarvalueoftheraffleprize.Supposetheexpectedticketsalesforacertainraffleare5500.

Substitute5500intotheequationtodeterminethedollarvalueoftheraffleprize.

A) $900 B) $33,100 C) $850 D) $5400

2) TheequationV=–3000t+21,000describesthevalueindollarsofacertainmodelofcarafteritistyearsold.If

acarisworth$9000,substitute9000intotheequationtofindtheageofthecar.

A) 4years B) 3years C) 5 years D) 6years

3) Acertainstorehasafaxmachineavailableforusebyitscustomers.Thestorecharges$1.35tosendthefirst

pageand$0.40foreachsubsequentpage.Thetotalprice,P,forthefaxingxpagescanbemodeledbythe

formulaP=0.40(x–1)+1.35.Determinethenumberofpagesthatcanbefaxedfor$3.75.

A) 7pages B) 33pages C) 3 pages D) 9pages

4) Alocalraceforcharityhastakenplacesince1993.Usingtheactualspeedsofthewinnersfrom1993through

1998,mathematiciansobtainedtheformulay=0.18x+6,inwhichxrepresentsthenumberofyearsafter1993

andyrepresentsthewinningspeedinmilesperhour.Inwhatyearisthewinningspeedpredictedtobe7.98

mph?

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

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5) Acarrentalagencycharges$225perweekplus$0.20 permiletorentacar.Thetotalcost,C,fortherentingthe

carforoneweekanddrivingitxmilescanbemodeledbytheformulaC=0.20x+225.Howmanymilescan

youtravelinoneweekfor$345?

A) 600miles B) 575miles C) 294 miles D) 1725 miles

6) Theformulay=29,000+300x

xmodelstheaveragecostperunit,y,forElectrostufftomanufacturexunitsof

ElectrogadgetIV.Howmanyunitsmustthecompanyproducetohaveanaveragecostperunitof$480?

A) 161units B) 163units C) 167 units D) 97units

7) Supposeacost–benefitmodelisgivenbyy=2749x

100–x,whereyisthecostforremovingxpercentofagiven

pollutant.Whatpercentofpollutantcanberemovedfor$26,000?Roundyouranswertothenearesttenthofa

percent.

A) 90.4% B) 111.8% C) 9.0% D) 486.1%

8) TheU.S.MaritimeAdministrationestimatedthatthecostpertonofbuildinganoiltankercouldberepresented

bythemodely=116,000

x+205 ,whereyisthecostindollarspertonandxisthetons(inthousands).Whatsizeof

oiltanker(inthousandsoftons)canbebuiltfor$350perton?

A) 126thousandtons B) 209thousandtons C) 536 thousandtons D) 13thousandtons

1.3 ModelsandApplications

1 UseLinearEquationstoSolveProblems

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

Usethefive–stepstrategyforsolvingwordproblemstofindthenumberornumbersdescribedinthefollowingexercise.

1) Whenfourtimesthenumberisaddedto9 timesthenumber,theresultis39.Whatisthenumber?

A) 3 B) –4.3 C) 4.3 D) 1

2) When4timesanumberissubtractedfrom7timesthenumber,theresultis24.Whatisthenumber?

A) 8 B) 3 C) –8 D) 0.7

3) Whenanumberisdecreasedby30%ofitself,theresultis280.Whatisthenumber?

A) 400 B) 8 C) 1333 D) 120

4) When30%ofanumberisaddedtothenumber,theresultis156.Whatisthenumber?

A) 120 B) 36 C) 23 D) 130

5) 90%ofwhatnumberis99?

A) 110 B) 1100 C) 11 D) 89.1

6) Onenumberexceedsanotherby7.Thesumofthenumbersis–5.Whatarethenumbers?

A) 1and–6B)0and–5C)

–1 and–5D)Nosolution

Findallvaluesofxsatisfyingthegivenconditions.

7) y1=6x,y2=(5x–1),andy1exceedsy2by2.

A) 1 B) 1

11 C) –1 D) –1

11

8) y1=x,y2=4+x,y3=3(x–6)+10x,andthesumof8timesy1and4timesy2equalsy3.

A) {34} B) {10} C) {–34} D) {–10}

Page33

9) y1=1

x+6,y2=1

x+3,y3=–3

x2+9x+18 ,andthesumofy1and2timesy2isy3.

A) {0} B) {–6} C) {3} D) ∅

10) y1=1

x+3,y2= 1

x–3,y3=1

x2–9,andthedifferencebetween4timesy1and2timesy2istheproductof12

andy3.

A) {15} B) {–15} C) { 5} D) {30}

Solvetheproblem.

11) Acarrentalagencycharges$175perweekplus$0.25 permiletorentacar.Howmanymilescanyoutravelin

oneweekfor$225?

A) 200miles B) 175miles C) 231.25 miles D) 900 miles

12) Atrainticketinacertaincityis$2.00.Peoplewhousethetrainalsohavetheoptionofpurchasingafrequent

riderpassfor$18.00eachmonth.Withthepass,eachticketcostsonly$1.25.Determinethenumberoftimesin

amonththetrainmustbeusedsothatthetotalmonthlycostwithoutthepassisthesameasthetotalmonthly

costwiththepass.

A) 24times B) 25times C) 23 times D) 26times

13) Youinherit$10,000withthestipulationthatforthefirstyearthemoneymustbeinvestedintwostockspaying

6%and11%annualinterest,respectively.Howmuchshouldbeinvestedateachrateifthetotalinterestearned

fortheyearistobe$800?

A) $6000investedat6%;$4000investedat11% B) $4000 investedat6%;$6000investedat11%

C) $5000investedat6%;$5000investedat11% D) $7000 investedat6%;$3000investedat11%

14) Youinherit$56,000fromaverywealthygrandparent,withthestipulationthatforthefirstyear,themoney

mustbeinvestedintwostockspaying4%and10%annualinterest,respectively.Howmuchshouldbe

investedateachrateifthetotalinterestearnedfortheyearistobe$3200?

A) $40,000investedat4%;$16,000investedat10%

B) $16,000investedat4%;$40,000investedat10%

C) $30,000investedat4%;$26,000investedat10%

D) $26,000investedat4%;$30,000investedat10%

15) Abookcaseistobeconstructedasshowninthefigurebelow.Theheightofthebookcaseis4feetlongerthan

thelengthofashelf.If20feetoflumberisavailablefortheentireunit(includingtheshelves,butNOTtheback

ofthebookcase),findthelengthandheightoftheunit.

A) length=2feet;height=6feet B) length=8.0 feet;height=9.0feet

C) length=3feet;height=7feet D) length=2 feet;height=8feet

Page34

16) Anautorepairshopchargedacustomer$354 torepairacar.Thebilllisted$74 forpartsandtheremainderfor

labor.Ifthecostoflaboris$40perhour,howmanyhoursoflabordidittaketorepairthecar?

A) 7hours B) 6hours C) 8 hours D) 7.5 hours

17) Aftera14%pricereduction,aboatsoldfor$27,520.Whatwastheboatʹspricebeforethereduction?(Roundto

thenearestcent,ifnecessary.)

A) $32,000 B) $3852.80 C) $196,571.43 D) $31,372.80

18) Inclusiveofa7.2%salestax,adiamondringsoldfor$2144.00.Findthepriceoftheringbeforethetaxwas

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

A) $2000 B) $2298.37 C) $1989.63 D) $154.37

19) Thelengthofarectangularroomis8feetlongerthantwicethewidth.Iftheroomʹsperimeteris208 feet,what

aretheroomʹsdimensions?

A) Width=32ft;length=72ft B) Width=64 ft;length=144ft

C) Width=48ft;length=56ft D) Width=37 ft;length=82ft

20) Thereare18moresophomoresthanjuniorsinan8AMalgebraclass.Ifthereare94studentsinthisclass,find

thenumberofsophomoresandthenumberofjuniorsintheclass.

A) 56sophomores;38juniors B) 38 sophomores;56juniors

C) 112sophomores;76juniors D) 94 sophomores;76juniors

21) Thepresidentofacertainuniversitymakesthreetimesasmuchmoneyasoneofthedepartmentheads.Ifthe

totaloftheirsalariesis$180,000,findeachworkerʹssalary.

A) presidentʹssalary=$135,000;departmentheadʹssalary=$45,000

B) presidentʹssalary=$45,000;departmentheadʹssalary=$135,000

C) presidentʹssalary=$13,500;departmentheadʹssalary=$4500

D) presidentʹssalary=$90,000;departmentheadʹssalary=$45,000

22) Duringaroadtrip,Tonydroveone–thirdthedistancethatLanadrove.Markdrives24moremilesthanLana

drove.Thetotaldistancetheydroveonthetripwas514miles.Howmanymilesdideachpersondrive?

A) Tonydrove70miles,Lanadrove210 miles,andMarkdrove234 miles.

B) Tonydrove210miles,Lanadrove630 miles,andMarkdrove654 miles.

C) Tonydrove62miles,Lanadrove186 miles,andMarkdrove210 miles.

D) Tonydrove630miles,Lanadrove210 miles,andMarkdrove186 miles.

23) Thesumoftheanglesofatriangleis180°.Findthethreeanglesofthetriangleifoneangleistwice thesmallest

angleandthethirdangleis20°greaterthanthesmallestangle.

A) 40°

,

80°

,

60° B) 32°

,

64°

,

84° C) 30°

,

60°

,

90° D) 30°

,

50°

,

100°

24) InarecentInternationalGymnasticscompetition,theU.S.,China,andRomaniawerethebigwinners.Ifthe

totalnumberofmedalswonbyeachteamarethreeconsecutiveintegerswhosesumis54andtheU.S.won

morethanChinawhowonmorethanRomania,howmanymedalsdideachteamwin?

A) U.S.:19medals;China:18medals;Romania:17 medals

B) U.S.:20medals;China:19medals;Romania:18 medals

C) U.S.:56medals;China:55medals;Romania:54 medals

D) U.S.:17medals;China:16medals;Romania:15 medals

25) Meganishavingheryardlandscaped.Sheobtainedanestimatefromtwolandscapingcompanies.CompanyA

gaveanestimateof$240formaterialsandequipmentrentalplus$65perhourforlabor.CompanyBgavean

estimateof$315formaterialsandequipmentrentalplus$50perhourforlabor.Determinehowmanyhoursof

laborwillberequiredforthetwocompaniestocostthesame.

A) 5hours B) 4hours C) 8 hours D) 9hours

Page35

26) Sergioʹsinternetproviderchargesitscustomers$8 permonthplus3¢ perminuteofon–lineusage.Sergio

receivedabillfromtheprovidercoveringa5–monthperiodandwaschargedatotalof$55.90.Howmany

minutesdidhespendon–lineduringthatperiod?(Roundtothenearestwholeminute,ifnecessary.)

A) Thenumberofminutesis530. B) Thenumberofminutesis1120.

C) Thenumberofminutesis1220. D) Thenumberofminutesis53.

2 SolveaFormulaforaVariable

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

Solvetheformulaforthespecifiedvariable.

1) A=1

2bh forb

A) b=2A

hB) b=h

2A C) b=Ah

2D) b=A

2h

2) S=2πrh+2πr2forh

A) h=S–2πr2

2πrB) h=S–rC)h=S

2πr–1D)h=2π(S–r)

3) V=1

3Bh forh

A) h=3V

BB) h=3B

VC) h=V

3B D) h=B

3V

4) 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

5) A=1

2h(a+b) fora

A) a=2A–h

b

hB) a=h

b

–2A

hC) a=2A

b

–h

hD) a=A–h

b

2h

6) d=rt fort

A) t=d

rB) t=dr C) t=r

dD) t=d–r

7) P=2L+2W forW

A) W=P–2L

2B) W=P–LC)W=P–L

2D) W=P–2L

8) A=P(1+nr) forn

A) n=A–P

Pr B) n=P–A

Pr C) n=A

rD) n=Pr

A–P

9) I=Prt fort

A) t=I

Pr B) t=P–I

1+rC) t =P–Ir D) t=P–1

Ir

Page36

10) 1

a+1

b=1

cforc

A) c=ab

a+bB) c=a+b

ab C) c=a+bD)c=ab(a+b)

11) P=A

1+rt forr

A) r=A–P

Pt B) r=P–A

1+tC) r =P–At D) r=P–1

At

12) A=1

2h(B+b) forB

A) B=2A–

b

h

hB) B=2A–

b

hC)B=A–

b

h

hD) B=2A+

b

h

13) P=s1+s2+s3fors1

A) s1=P–s2–s3B) s1=P+s2+s3C) s1=s2+s3–PD)s

1=P+s2–s3

14) I=nE

nr+Rforn

A) n=IR

E–Ir B) n=IR

Ir+EC) n=IR(Ir–E) D) n=–R

Ir–E

1.4 ComplexNumbers

1 AddandSubtractComplexNumbers

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

Addorsubtractasindicatedandwritetheresultinstandardform.

1) (6–4i)+(2+6i)

A) 8+2i B) 8–2i C) 4 +10i D) –8–2i

2) (6+9i)–(–3+i)

A) 9+8i B) 9–8i C) 3 +10i D) –9–8i

3) 7i+(–6–i)

A) –6+6i B) –6+8i C) 6 –6i D) 6–8i

4) 9i–(–9–i)

A) 9+10i B) –9–10i C) 9 –8i D) –9+8i

5) (–9+6i)–6

A) –15+6i B) 15–6i C) –3+6i D) –3–6i

6) –6–(–5–4i)–(–7–7i)

A) 6+11i B) 6–11i C) 12 –11i D) 12+11i

7) (–3–10i)+(1+2i)+(–5+6i)

A) –7–2i B) –9–6i C) 3 –14i D) –2–8i

Page37

2 MultiplyComplexNumbers

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

Findtheproductandwritetheresultinstandardform.

1) –3i(5i–4)

A) 15+12i B) –15+12i C) 12i–15i2D) 12i+15i2

2) 3i(–9i+4)

A) 27+12i B) –27+12i C) 12i–27i2D) 12i+27i2

3) (8+2i)(3–7i)

A) 38–50i B) 38+50i C) 10 +62i D) –14i2–50i+24

4) (–3–5i)(3+i)

A) –4–18i B) –14–18i C) –4+12i D) –14 +12i

5) (9–5i)(–4+2i)

A) –26+38i B) –26–2i C) –46 +38i D) –46 –2i

6) (3+8i)(3–8i)

A) 73 B) 9–64i2C) –55 D) 9–64i

7) (–6+i)(–6–i)

A) 37 B) –6C)36D)

–35

8) (8+9i)2

A) –17+144i B) 145+144i C) –17 D) 64+144i+81i2

Performtheindicatedoperationsandwritetheresultinstandardform.

9) (8+9i)(4–i)–(1–i)(1+i)

A) 39+28i B) 43+28i C) 41 +28i D) 39+44i

10) (6+i)2–(3–i)2

A) 27+18i B) –27+18i C) 9 D) 27–18i

Complexnumbersareusedinelectronicstodescribethecurrentinanelectriccircuit.Ohmʹslawrelatesthecurrentina

circuit,I,inamperes,thevoltageofthecircuit,E,involts,andtheresistanceofthecircuit,R,inohms,bytheformula

E=IR.Solvetheproblemusingthisformula.

11) FindE,thevoltageofacircuit,ifI=(2 +4i)amperesandR=(7 +6i)ohms.

A) (–10+40i)volts B) (–10 –40i)volts C) (40 –10i)volts D) (40 +10i)volts

12) FindE,thevoltageofacircuit,ifI=(18 +i)amperesandR=(3 +2i)ohms.

A) (52+39i)volts B) (52–39i)volts C) (18 +39i)volts D) (18 –39i)volts

3 DivideComplexNumbers

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

Divideandexpresstheresultinstandardform.

1) 5

3–i

A) 3

2+1

2iB)

3

2–1

2iC)

15

8+5

8iD)

15

8–5

8i

Page38

2) 2

3+i

A) 3

5–1

5iB)

3

5+1

5iC)

3

4+1

4iD)

3

4–1

4i

3) 2i

1–i

A) –1+iB)1+iC)

–1+2i D) –1–i

4) 7i

4–i

A) –7

17 +28

17 iB)

7

17 +28

17 iC)

–7

15 +28

15 iD)

–7

17 –28

17 i

5) 5i

7–4i

A) –4

13 +7

13 iB)

7

13 –4

13 iC)

–20

33 –35

33 iD)

35

33 –20

33 i

6) 7+3i

3–7i

A) i B) –iC)1 D)

–1

7) 9–4i

9+2i

A) 73

85 –54

85 iB)

73

77 –54

77 iC)

89

85 +18

85 iD)

89

77 –54

77 i

8) 7+4i

4–6i

A) 1

13 +29

26 iB)

–1

10 –29

20 iC)2

+1i D) –13

5–29

20 i

9) 1+3i

5+8i

A) 29

89 +7

89 iB)

–29

39 –7

39 iC)

–19

89 –23

89 iD)

19

39 –7

39 i

10) 7+4i

5+8i

A) 67

89 –36

89 iB)

–67

39 +12

13 iC)

3

89 –76

89 iD)

–1

13 +12

13 i

11) 8–2i

5–3i

A) 23

17 +7

17 iB)

23

16 +7

16 iC)2

+2i D) 17

8+7

16 i

Page39

4 PerformOperationswithSquareRootsofNegativeNumbers

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

Performtheindicatedoperationsandwritetheresultinstandardform.

1) –25+–81

A) 14i B) –14i C) 45i D) –14

2) –5––121

A) i( 5–11) B) 5i–11 C) 5i–11i D) i( 5+11)

3) 5 –64+4–4

A) 48i B) –48 C) 48 D) –48i

4) 2 –32+5–18

A) 23i 2 B) –23 2 C) 23 2 D) –23i 2

5) (–2––49)2

A) –45+28i B) 53–28i C) 4 +49i D) 4–49i

6) (–3+–64)2

A) –55–48i B) 73+48i C) 9 +64i D) 9–64i

7) ( 3––4)( 3+–4)

A) 7 B) –1C)3

–4i D) 3+2i

8) (6+–2)(2+–3)

A) (12–6)+(6 3+22)i B) (12+6)–18i

C) 6–86

iD)18

+48i

9) –30+–50

5

A) –6+i2 B) –6–i2 C) 6+i2 D) –6+i5

10) –12––72

6

A) –2–i2 B) –2+i2 C) 2+i2 D) –2–i6

11) –64(7––16)

A) 32+56i B) 56i–32 C) 56i–32i2D) 56i+32i2

12) ( –9)( –64)

A) –24 B) 24i2C) 24 D) –24i

Page40

1.5 QuadraticEquations

1 SolveQuadraticEquationsbyFactoring

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

Solvetheequationbyfactoring.

1) x2=x+20

A) {–4

,

5} B) {4

,

5} C) {1,20} D) {–4

,

–5}

2) x2+2x–48=0

A) {–8

,

6} B) {8

,

6} C) {–8

,

1} D) {8

,

–6}

3) 6x2+23x+20=0

A) –5

2,–4

3B) 5

2,4

3C) –5

6,–1

5D) 5

2,–4

3

4) 8x2–55x=7

A) –1

8,7 B) –1

8,8 C) 1

55 ,–1

8D) {–8

,

7}

5) 12x2–7x=0

A) 0,7

12 B) 7

12 ,–7

12 C) {0} D) –7

12 ,0

6) 2x(x–1)=7x2–3x

A) 0,1

5B) –1

5,0 C) {0,5} D) {0}

7) 7–7x=(4x+9)(x–1)

A) {–4

,

1} B) 1,–9

4C) {–1,4} D) 1

8) –6x–2=(3x+1)2

A) –1,–1

3B) –1

3C) 1

3,1 D) ∅

2 SolveQuadraticEquationsbytheSquareRootProperty

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

Solvetheequationbythesquarerootproperty.

1) 6x2=150

A) {–5

,

5} B) {–56,56}C){

–6

,

6} D) {0}

2) 4x2=44

A) {–11,11}B){12} C){

–11

,

11} D) {22}

3) 6x2+4=58

A) {–3

,

3} B) {3} C) {–4

,

4} D) {29}

Page41

4) (x–5)2=16

A) {1

,

9} B) {21} C) {–4

,

4} D) {–9

,

1}

5) (2x–1)2=121

A) {–5

,

6} B) {–6

,

5} C) {–10

,

12} D) {–12

,

10}

6) (2x+3)2=25

A) {–4

,

1} B) {1,4} C) {–14

,

14} D) {0,1}

7) 2(x–4)2=12

A) {4±6}B){

–2

,

10} C) {–4±6}D){

–10

,

2}

8) (2x+3)2=6

A) –3–6

2,–3+6

2B) 3–6

2,3+6

2

C) 6–3

2,6+3

2D) –9

2,3

2

9) (5x–6)2=12

A) 6–23

5,6+23

5B) {–25,25}

C) –6–23

5,–6+23

5D) –6

5,18

5

10) (x–5)2=–4

A) {5±2i} B) ±2i

5C) {–5±2i} D) {5i±2}

11) (x–7)2=–2

A) {7±i2

}B){7±2}C){

–7±2i} D) {5

,

9}

3 SolveQuadraticEquationsbyCompletingtheSquare

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

Determinetheconstantthatshouldbeaddedtothebinomialsothatitbecomesaperfectsquaretrinomial.Thenwrite

andfactorthetrinomial.

1) x2+4x

A) 4;x2+4x+4=(x+2)2B) 2;x2+4x+2=(x+4)2

C) 16;x2+4x+16=(x+4)2D) 4;x2+4x+4=(x+16)2

2) x2–12x

A) 36;x2–12x+36=(x–6) 2B) –36;x2–12x–36=(x–6) 2

C) –144;x2–12x–144=(x–12) 2D) 144;x2–12x+144=(x–12) 2

3) x2–11x

A) 121

4;x2–11x+121

4=x–11

2

B) –121

4;x2–11x–121

4=x–11

2

C) 11

2;x2–11x+11

2=x–11

2

D) 121;x2–11x+121=(x–11)2

Page42

4) x2+1

3x

A) 1

36 ;x2+1

3x+1

36 =x+1

6

2

B) 1

9;x2+1

3x+1

9=x+1

3

2

C) 1

6;x2+1

3x+1

6=x+1

3

2

D) 36;x2+1

3x+36=(x+6) 2

5) x2+4

5x

A) 4

25 ;x2+4

5x+4

25 =x+2

5

2

B) 8

25 ;x2+4

5x+8

25 =x+4

5

2

C) 4

5;x2+4

5x+4

5=x+2

5

2

D) 2

25 ;x2+4

5x+2

25 =x+2

5

2

6) x2–2

3x

A) 1

9;x2–2

3x+1

9=x–1

3

2

B) 1

9;x2–2

3x+1

9=x+1

3

2

C) 4

9;x2–2

3x+4

9=x–2

3

2

D) 2

9;x2–2

3x+2

9=x–1

3

2

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

7) x2+4x=9

A) {–2–6.5,–2+6.5}B){2+6.5}

C) {–1–6.5,–1+6.5}D){

–2–1 6.5,–2+1 6.5}

8) x2–14x+13=0

A) {1

,

13} B) {–13

,

–1} C) {–13,13}D){1

,

12}

9) x2+12x+22=0

A) {–6–14,–6+14}B){6+14}

C) {6–22,6+22}D){

–12+22}

10) x2+8x–3=0

A) {–4–19,–4+19}B){4+19}

C) {–1–19,–1+19}D){

–4–119,–4+119}

11) x2–4x–15=0

A) {2–19,2+19}B){2–15,2+15}

C) {–2–19,–2+19}D){4–31,4+31 }

12) x2+3x–9=0

A) –3–35

2,–3+35

2B) 3+35

2

C) –3–35

2D) {–3–35,–3+35}

13) x2+8x+25=0

A) {–4±3i} B) {–4±9i} C) {–4+3i} D) {–7

,

–1}

Page43

14) x2+x+4=0

A) –1±i15

2B) 1±i15

2C) 1±15

2D) –1±15

2

15) 3x2–2x–6=0

A) 1–19

3,1+19

3B) 3–19

9,3+19

9

C) –6,20

3D) –1–19

3,–1+19

3

16) 16x2–7x+1=0

A) 7±i15

32 B) –7±i15

32

C) 7–i15

32 ,–7+i15

32 D) 7±15

32

4 SolveQuadraticEquationsUsingtheQuadraticFormula

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

Solvetheequationusingthequadraticformula.

1) x2+2x–35=0

A) {–7

,

5} B) {7

,

5} C) {–7

,

1} D) {–5

,

7}

2) x2+3x+1=0

A) –3–5

2,–3+5

2B) 3–5

2,3+5

2

C) –3–5

6,–3+5

6D) –3–13

2,–3+13

2

3) 2x2+10x+5=0

A) –5–15

2,–5+15

2B) –5–15

4,–5+15

4

C) –10–15

2,–10+15

2D) –5–35

2,–5+35

2

4) 4x2+x–4=0

A) –1–65

8,–1+65

8B) –1–65

2,–1+65

2

C) 1–65

8,1+65

8D) ∅

5) 2x2=–10x–1

A) –5–23

2,–5+23

2B) –5–23

4,–5+23

4

C) –10–23

2,–10+23

2D) –5–3

2,–5+3

2

Page44

6) x2–10x+50=0

A) {5–5i,5+5i} B) {5–25i,5+25i} C) {5 +5i} D) {0

,

10}

7) 5x2–5x+6=0

A) 5±i95

10 B) 5±95

10 C) –5±i95

10 D) –5±95

10

8) 8x2+1=3x

A) 3±i23

16 B) 3±23

16 C) –3±23

16 D) –3±i23

16

5 UsetheDiscriminanttoDeterminetheNumberandTypeofSolutions

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

Computethediscriminant.Thendeterminethenumberandtypeofsolutionsforthegivenequation.

1) x2+6x–7=0

A) 64;twounequalrealsolutions

B) –8;twocompleximaginarysolutions

C) 0;onerealsolution

2) x2+8x+16=0

A) 0;onerealsolution

B) 64;twounequalrealsolutions

C) –64;twocompleximaginarysolutions

3) 4x2=–5x–3

A) –23;twocompleximaginarysolutions

B) 73;twounequalrealsolutions

C) 0;onerealsolution

6 DeterminetheMostEfficientMethodtoUseWhenSolvingaQuadraticEquation

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

Solvetheequationbythemethodofyourchoice.

1) (4x+5)2=4

A) –7

4,–3

4B) 3

4, 7

4C) –3

4,0 D) 1

4

2) 4x2–31x–8=0

A) –1

4,8 B) –1

4,4 C) –1

4,1

31 D) {–4

,

8}

3) 5x2+10x=–2

A) –5–15

5, –5+15

5B) –5–15

10 , –5+15

10

C) –10–15

5,–10+15

5D) –5–35

5, –5+35

5

Page45

4) 6x2=–12x–3

A) –2–2

2, –2+2

2B) –2–2

12 , –2+2

12

C) –12–2

2, –12+2

2D) –2–6

2, –2+6

2

5) 3x2+12x+5=0

A) –6–21

3, –6+21

3B) –6–21

6, –6+21

6

C) –12–21

3, –12+21

3D) –6–51

3, –6+51

3

6) 5x2=35

A) {–7,7} B) {8} C) {–7

,

7} D) {17.5}

7) 3x2–15=0

A) {–5,5}B){

–15,15}C)

–15

3,15

3D) { 5}

8) x2+18x+67=0

A) {–9–14,–9+14}B){9+14}

C) {9–67,9+67}D){

–18+67}

9) 5x2–20x+200=0

A) {2+6i,2–6i} B) {2–36i,2+36i} C) {2 +6i} D) {8

,

–4}

10) (3x+2)2=6

A) –2±6

3B) 2±6

3C) 6±2

3D) –8

3,4

3

11) (x+10)(x–9)=4

A) –1±377

2B) 1±377

2C) –1±i 377

2D) 1±i 377

2

12) x2

18 +x+35

9=0

A) {–9±11}B){9+11}C){9±70}D){

–18+70}

13) 1

x+1+1

x=1

5

A) 9±101

2B) –11±101

2C) 11±101

2D) –9±101

2

14) 2x

x–7–x

x–4=5

x2–11x+28

A) 1±21

2B) –1±21

2C) 1±i19

2D) –1±i19

2

Page46

15) 7x2–3x–2=0

A) 3±59

14 B) –3±59

14 C) 3±i53

14 D) 3±65

14

Findthex–intercept(s)ofthegraphoftheequation.Graphtheequation.

16) y=x2+5x+4

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) x–intercepts:–1and–4

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B) x–intercepts:1 and4

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C) x–intercepts:1and4

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D) x–intercepts:–1 and–4

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page47

17) y=x2–6x+9

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

A) x–intercept:3

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

B) x–intercept:–3

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

C) x–intercept:18

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

D) x–intercept:none

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

Page48

18) y=x2+4x–7

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) x–intercepts:–2±11

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B) x–intercepts:–4and3

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C) x–intercepts:none

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D) x–intercept:4

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page49

19) y=x2–5x+1

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) x–intercepts:5±21

2

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B) x–intercepts:–1and5

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C) x–intercepts:none

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D) x–intercepts:–5±21

2

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page50

20) y=–x2+2x+3

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) x–intercepts:–1and3

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B) x–intercepts:–3 and1

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C) x–intercepts:–1and3

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D) x–intercepts:–3 and1

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page51

21) y=2x2+12x+22

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) x–intercepts:none

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B) x–intercepts:none

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C) x–intercepts:none

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D) x–intercepts:none

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Findallvaluesofxsatisfyingthegivenconditions.

22) y=x2+4xandy=16

A) –2±25 B) –2±210 C) ±25 D) 2 5±2

23) y=9x2–35x–4andy=0

A) –1

9,4B)

–1

9,9C)

1

35 ,–1

9D) –9

,

4

24) y1=(x+2),y2=(x–3),andy1y2=2

A) 1±33

2B) –1±33

2C) 1±i33

2D) –1±i33

2

Page52

25) y1=1

x+13 ,y2=1

x,andy1+y2=1

5

A) –3±269

2B) –23±269

2C) 23±269

2D) 3±269

2

26) y1=7–7x,y2=(4x+9)(x–1),andy1–y2=0

A) –4

,

1B)1,–9

4C) –1,4D)1

7 SolveProblemsModeledbyQuadraticEquations

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

Solvetheproblem.

1) TheformulaN=2x2+4x+1representsthenumberofhouseholdsN,inthousands,inacertaincitythathave

acomputerxyearsafter1990.Accordingtotheformula,inwhatyearwerethere49thousandhouseholdswith

computersinthiscity?

A) 1994 B) 1993 C) 1992 D) 1995

2) TheformulaP=0.67x2–0.046x+2modelstheapproximatepopulationP,inthousands,foraspeciesoffishin

alocalpond,xyearsafter1997.Duringwhatyearwillthepopulationreach55,856fish?

A) 2006 B) 2005 C) 2007 D) 2008

3) Therevenueforasmallcompanyisgivenbythequadraticfunctionr(t)=9t2+13t+520wheretisthenumber

ofyearssince1998andr(t)isinthousandsofdollars.Ifthistrendcontinues,findtheyearafter1998inwhich

thecompanyʹsrevenuewillbe$640thousand.Roundtothenearestwholeyear.

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

4) Asquaresheetofpapermeasures31centimetersoneachside.Whatisthelengthofthediagonalofthispaper?

A) 31 2cm B) 31cm C) 1922 cm D) 62cm

5) Aladderthatis13feetlongis5feetfromthebaseofawall.Howfarupthewalldoestheladderreach?

A) 12ft B) 194ft C) 2 2ft D) 144 ft

6) A12–footpoleissupportedbytwowiresthatextendfromthetopofthepoletopointsthatareeach 16 feet

fromthebaseofthepole.Findthetotallengthofthetwowires.

A) 40ft B) 20ft C) 800 ft D) 56ft

7) Thelengthofarectangularstorageroomis3feetlongerthanitswidth.Iftheareaoftheroomis88 squarefeet,

finditsdimensions.

A) 8feetby11feet B) 7feetby12 feet C) 9 feetby12 feet D) 7feetby10 feet

8) Amachineproducesopenboxesusingsquaresheetsofplastic.Themachinecutsequal–sizedsquares

measuring4inchesonasidefromeachcornerofthesheet,andthenshapestheplasticintoanopenboxby

turningupthesides.Ifeachboxmusthaveavolumeof1600cubicinches,findthelengthofonesideofthe

openbox.

A) 20in. B) 24in. C) 28 in. D) 19in.

Page53

9) Supposethatanopenboxistobemadefromasquaresheetofcardboardbycuttingout4–inch squaresfrom

eachcornerasshownandthenfoldingalongthedottedlines.Iftheboxistohaveavolumeof36cubicinches,

findtheoriginaldimensionsofthesheetofcardboard.

A) 11in.by11in. B) 6in.by6 in. C) 3in.by23in. D) 3in.by3 in.

10) Araingutterismadefromsheetsofaluminumthatare25 incheswide.Theedgesareturneduptoformright

angles.Determinethedepthofthegutterthatwillallowacross–sectionalareaof56squareinches.Thereare

twosolutionstothisproblem.Roundtothenearesttenthofaninch.

A) 2.9in.and9.6in. B) 2.5in.and22.5 in. C) 3.5 in.and11.5 in. D) 2.0 in.and18.0 in.

1.6 OtherTypesofEquations

1 SolvePolynomialEquationsbyFactoring

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

Solvethepolynomialequationbyfactoringandthenusingthezeroproductprinciple.

1) 5x4–245x2=0

A) {–7

,

0,7} B) {–75,0,75}C){

–7

,

7} D) {0}

2) 5x4=135x

A) {0,3} B) {–3

,

0,3} C) {0,5

,

3} D) {0}

3) 3x3+4x2=12x+16

A) –2,–4

3,2 B) –4

3,0 C) –4

3,2 D) {–2

,

2}

4) 3x–5=75x3–125x2

A) –1

5,1

5,5

3B) 0,5

3C) –1

25 ,1

25 ,5

3D) –1

5,1

5,3

5

5) x3+9x2+18x=0

A) {0,–3

,

–6} B) {–3

,

–6} C) {0,3

,

6} D) {3

,

6}

6) x3+6x2–x–6=0

A) {–1,1,–6} B) {1,–6

,

6} C) {–6

,

6} D) {36}

7) 15x3+90x2+120x=0

A) {0,–2

,

–4} B) {–2

,

–4} C) {0,2

,

4} D) {–1

2,–4}

Page54

2 SolveRadicalEquations

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

Solvetheradicalequation,andcheckallproposedsolutions.

1) x+4=7

A) {45} B) {49} C) {53} D) {121}

2) 4x–3=3

A) {3} B) {9} C) 3

2D) ∅

3) 7x+18 =x

A) {9} B) {–2

,

9} C) –3 D) ∅

4) 26x+39=x+8

A) {5} B) {–4} C) {–5} D) {7}

5) x–3x–2=4

A) {9} B) {2,9} C) {–1} D) {1,2}

6) 2x+7=x+3

A) {8} B) {2,8} C) {–4} D) –4,4

3

7) 2x+3–x+1=1

A) {–1,3} B) {3} C) {–3,–1} D) ∅

8) 2x+5–x–2=3

A) {2,38} B) {3,8} C) {2} D) {–2}

9) x+6+2–x=4

A) {–2} B) {2,–2} C) {0} D) { 31,–2}

10) 2 x+3=4x–5

A) 11+69

8B) 11–69

8,11+69

8

C) 11

2D) ∅

11) 1+12 x=1+x

A) {0,100} B) 0,4

11 C) {0,144} D) {0,196}

Findthex–interceptsofthegraphoftheequation.

12) y=2x+3–x+1–1

A) 3,–1B)3 C)

–3,–1D)Nox–intercepts

13) y=2x+5–x–2–3

A) 2,38 B) 3,8C)2 D)

–2

Page55

14) y=3x–2+11+x+1

A) Nox–intercepts B) 0 C) –5

2D) 5

15) y=x+6+2–x–4

A) –2B)2,–2 C) 0 D) 31,–2

Findallvaluesofxsatisfyingthegivenconditions.

16) y=x–3x–2andy=4

A) 9 B) 2,9C)

–1D)1,2

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

Solvetheproblem.

17) Solvetheformular=3V

πhforV.

18) Solvetheformular=2A

θforθ.

3 SolveEquationswithRationalExponents

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

Solveandchecktheequation.

1) x3/2=8

A) {4} B) {2} C) 32D) {16 2}

2) 5x7/2–10=0

A) 74B) 72 C) 4

7D) ∅

3) (x+6)3/2=8

A) {–2} B) {–4} C) 32–6D) {10}

4) (2x+1)1/2=4

A) 15

2B) 8 C) –1

2D) 2

5) (5x+1)1/3=–3

A) –28

5B) 8

5C) –27

5D) –32

6) (6x–3)1/3+3=–2

A) –61

3B) –2 C) 14

3D) ∅

7) (x2+6x+9)3/4–13=14

A) {–12

,

6} B) {6} C) {–12

,

0,6} D) {27}

Page56

Findallvaluesofxsatisfyingthegivenconditions.

8) y=(x+6)3/2andy=125

A) {19} B) {–1} C) 35–6D) {31}

4 SolveEquationsThatAreQuadraticinForm

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

Solvetheequationbymakinganappropriatesubstitution.

1) x4–40x2+144=0

A) {–2

,

2

,

–6

,

6} B) {4

,

36} C) {2

,

6} D) {–2i,2i,–6i,6i}

2) x4–22x2+96=0

A) {–4,4,–6,6}B){

–4,4,–i6,i6}C){16

,

6} D) {4,6}

3) x4–10x2–96=0

A) {–4,4,–i6

,i6}B){

–6,6,–4i,4i} C) {–16

,

6} D) {4,i6}

4) x–4x

–32=0

A) {64} B) {32} C) {128} D) {48}

5) x–12 x+27=0

A) {81

,

9} B) {9

,

3} C) {–9

,

9

,

–3

,

3} D) {–3,3,–3,3}

6) 2x–2x

–40=0

A) {25} B) {5} C) 16

,

25 D) 4

,

5

7) x–2+x–1–110=0

A) –1

11 ,1

10 B) 1

11 ,–1

10 C) {11

,

–10} D) {–11

,

10}

8) x–2+5x–1+4=0

A) –1

4,–1 B) 1

4,1 C) {1

,

4} D) {–1

,

–4}

9) 8x–2–9x–1+1=0

A) {1

,

8} B) –1

8,–1 C) {–1

,

–8} D) 1

8,1

10) x–2+8x–1+13=0

A) –4±3

13 B) –4±23

13 C) 4±3

13 D) –4±3

19

11) x–2x1/2–8=0

A) {16} B) {8} C) {32} D) {12}

12) x2/3+4x1/3–5=0

A) {–125

,

1} B) {–5

,

1} C) {–1

,

5} D) {–1

,

125}

13) x2/5–x1/5–20=0

A) {3125

,

–1024} B) {–3125

,

1024} C) {5

,

–4} D) {–5

,

4}

Page57

14) 2x1/2–13x1/4–24=0

A) {4096} B) 4096,81

16 C) {–8

,

–3} D) 8,–3

2

15) x1/2–6x1/4+5=0

A) {1

,

625} B) {1

,

25} C) {–1

,

–5} D) {1

,

5}

16) (x+1)2–11(x+1)+30=0

A) {4

,

5} B) {6

,

7} C) {–7

,

–6} D) {–5

,

–4}

17) (–6x+3)2–15(–6x+3)+54=0

A) –1

2,–1 B) 1

2,1 C) {6

,

9} D) –11

2,–2

18) (4x–4)2–2(4x–4)–3=0

A) 3

4,7

4B) –3

4,–7

4C) 5

4,–1

4D) –5

4,1

4

19) (x2–4x)2–17(x2–4x)+60=0

A) {–2

,

–1

,

6

,

5} B) {12

,

5}

C) {6

,

5} D) {–2

,

–1

,

12

,

5

,

6

,

5}

20) y–10

y

2

–6y–10

y–27=0

A) {–5

,

–1

,

2

,

10} B) {–3

,

9} C) {–5

,

2} D) nosolution

Matchthegraphwithitsfunctionusingthex–intercepts.

21)

x

-8 -4 4 8

y

16

12

8

4

-4

-8

-12

-16

x

-8 -4 4 8

y

16

12

8

4

-4

-8

-12

-16

A) y=x4–5x2+4B)y=x4+5x2+4C)y=x4–5x2–4D)y=x4+5x2–4

Page58

22)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

A) y=x4–2x2+1B)y=x4+2x2+1C)y=x4–2x2–1D)y=x4+2x2–1

23)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

A) y=x1/3+3x1/6–4B)y=x1/3–3x1/6–4

C) y=x1/3+3x1/6+4D)y=x1/3–3x1/6+4

Page59

24)

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

A) y=x1/2+15x1/4–16 B) y=x1/2–15x1/4–16

C) y=x1/2+2x1/4+1D)y=x1/2+2x1/4–1

25)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

A) y=x–2–x–1–2B)y=x–2–x–1+2C)y=x–2+x–1–2D)y=x–2+x–1+2

26)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

A) y=x–2+2x–1–3B)y=x–2–2x–1–3C)y=x–2+2x–1+3D)y=x–2–2x–1+3

Page60

27)

x

–10–8-6-4-2 2 4 6 8

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 8

y

10

8

6

4

2

-2

-4

-6

-8

-10

A) y=6x–2–5x–1–1B)y=6x–2+5x–1–1

C) y=6x–2–5x–1+1D)y=6x–2+5x–1+1

28)

x

-10 -5 5

y

10

5

-5

-10

x

-10 -5 5

y

10

5

-5

-10

A) y=(x+2)2+5(x+2)+4B)y=(x+2)2–5(x+2)+4

C) y=(x+2)2+9(x+2)+18 D) y=(x+2)2–9(x+2)+18

Page61

29)

x

-10 -5 5

y

10

5

-5

-10

x

-10 -5 5

y

10

5

-5

-10

A) y=2(x–3)2–3(x–3)–5B)y=2(x–3)2+3(x–3)–5

C) y=2(x+3)2–3(x+3)–5D)y=2(x+3)2+3(x+3)–5

30)

x

–10–8-6-4-2 2 4 6 810

y

120

80

40

-40

-80

–120

x

–10–8-6-4-2 2 4 6 810

y

120

80

40

-40

-80

–120

A) y=x4–25x2+144 B) y=x4+25x2+144

C) y=x4–25x2+12 D) y=x4+25x2–12

Findallvaluesofxsatisfyingthegivenconditions.

31) y=(x2–2x)2–18(x2–2x)andy=–45

A) –1

,

–3

,

3

,

5B)3

,

15 C) 3

,

5D)

–1

,

–3

,

3

,

15

,

3

,

5

32) y=x–12

x

2

–3x–12

xandy=4

A) –4

,

–2

,

3

,

6B)

–1

,

4C)

–4

,

3D)Nosolution

33) y=x2/3–6x1/3andy=–8

A) 8

,

64 B) 2

,

4C)

–4

,

–2D)

–64

,

–8

34) y1=5(2x–1)–1,y2=2(2x–1)–2,andy1exceedsy2by2

A) 3

2,3

4B) –2,–1

2C) –1

2,0D)

–1

2,–1

4

Page62

35) y1=x

x–5+15,y2=8x

x–5,andy1=y2

A) 125

24 ,45

8B) 5

,

3C)

25

4,15

2D) –125

24 ,–45

8

5 SolveEquationsInvolvingAbsoluteValue

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

Solvetheabsolutevalueequationorindicatethattheequationhasnosolution.

1) x =5

A) {–5

,

5} B) {5} C) {–5} D) {25}

2) x+5=8

A) {–13

,

3} B) {13

,

3} C) {–3} D) ∅

3) x–4=9

A) {–5

,

13} B) {–13

,

5} C) {13} D) ∅

4) 7x+5=2

A) –3

7,–1 B) –3

5,–7

5C) 3

7,1 D) ∅

5) 3 x–3=18

A) {9,–3} B) {3,–9} C) {3} D) ∅

6) 4x+2+8=15

A) –9

4,5

4B) {–9

2,5

2}C)

–5

4,9

4D) ∅

7) 8x–5–1=–7

A) –1

8,–11

8B) –1

8C) 11

8,1

8D) ∅

8) 6x–8=x–9

A) –1

5,17

7B) –1

5,–1 C) 1

5,–17

7D) ∅

9) 1

2x+2=3

4x–2

A) {16,0} B) {16,12} C) {10,10} D) ∅

10) 7x+28

4=7

A) {–8

,

0} B) {–8

,

8} C) {8

,

0} D) ∅

11) 3(x+1)+6=18

A) {–9

,

3} B) {–7

,

5} C) {–9

,

0} D) {–7

,

0}

12) x2+2x =0

A) {0,–2} B) {2

,

0,–2} C) {2

,

0} D) ∅

Page63

13) x2–4x–4=8

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

14) 2x2–x–1=3

A) 1–33

4,1+33

4B) –1–33

4,–1+33

4

C) 1–33

4,–1+33

4D) ∅

15) x2–4x+4=2

A) {2–2,2+2}B){2–2}C){2+2}D)

∅

Findallvaluesofxsatisfyingthegivenconditions.

16) y=x–9andy=9

A) 0

,

18 B) –18

,

0C)18 D)Nosolutions

17) y=3x+8andy=9

A) 1

3,–17

3B) 1

8,–17

8C) –1

3,17

3D) Nosolutions

6 SolveProblemsModeledbyEquations

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

Solvetheproblem.

1) Foracultureof40,000bacteriaofacertainstrain,thenumberofbacteriaNthatwillsurvivexhoursismodeled

bytheformulaN=4000 100–x.Afterhowmanyhourswill36,000bacteriasurvive?

A) 19hr B) 91hr C) 64 hr D) 81hr

2) Aformulaforthelengthofadiagonalfromtheuppercornerofaboxtotheoppositelowercorneris

d=L2+W2+H2,whereL,W,andHarethelength,width,andheight,respectively.Findthelengthofthe

diagonaloftheboxifthelengthis22inches,widthis14inches,andheightis9inches.Leaveyouranswerin

simplifiedradicalform.

A) 761in. B) 3 10in. C) 3 5in. D) 1522in.

Page64

3) Aballoonissecuredtoropethatisstakedtotheground.Abreezeblowstheballoonsothattheropeistaut

whiletheballoonisdirectlyaboveaflagpolethatis60feetfromwheretheropeisstakeddown.Findthe

altitudeoftheballooniftheropeis120feetlong.Leaveyouranswerinsimplifiedradicalform.

A) 60 3ft B) 6 30ft C) 60 5ft D) 2 15ft

4) Aformulausedtodeterminethevelocityvinfeetpersecondofanobject(neglectingairresistance)afterit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persecond,findthe

velocityofabowlingballafterithasfallen30feet.(Roundtothenearesttenth.)

A) 43.8ftpersec B) 31.0 ftpersec C) 7.7 ftpersec D) 1920 ftpersec

5) 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9inchesandtheconeis11incheshigh.(Use3.14asan

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

A) 932.6cubicin. B) 103.6 cubicin. C) 8393.2 cubicin. D) 84.8 cubicin.

6) 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25milesperhour.

A) 250ft B) 1563 ft C) 100 ft D) 625 ft

7) 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$45.75billion?

A) 2018 B) 2021 C) 2023 D) 2022

8) 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2seconds.

A) h=4.9t2;19.6mB)h=24.01t;48 mC)h=24.01t2;96mD)h=4.9t;9.8 m

9) 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2wattsandEis10volts.

A) R=E2

P;50ohms B) R=E2

P2;25ohms

C) R=E2P;50ohms D) R=E2P2;25ohms

Page65

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

theformulad=2W

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

constant.SolvethisequationforW.Usetheresulttodeterminetheworkneededtomoveaspring6

centimetersifithasaspringconstantof0.4.

A) W=d2k

2;7.2joules B) W=d2k2

4;1.4joules

C) W=2d2

k;180joules D) W=2d2k;28.8joules

11) Thealgebraicexpression0.07d3/2describesthedurationofastorm,inhours,whosediameterisdmiles.Usea

calculatortodeterminethedurationofastormwithadiameterof5miles.Roundtothenearesthundredth.

A) 0.78hr B) 0.16 hr C) 11.18 hr D) 0.21 hr

12) Twocarsleaveanintersection.Onecartravelsnorth;theothereast.Whenthecartravelingnorthhadgone9

mi,thedistancebetweenthecarswas3mimorethanthedistancetraveledbythecarheadingeast.Howfar

hadtheeastboundcartraveled?

A) 12mi B) 15mi C) 9 mi D) 18mi

13) Aladderisrestingagainstawall.Thetopoftheladdertouchesthewallataheightof15ft.Findthelengthof

theladderifthelengthis5ftmorethanitsdistancefromthewall.

A) 25ft B) 20ft C) 15 ft D) 30ft

1.7 LinearInequalitiesandAbsoluteValueInequalities

1 UseIntervalNotation

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

Expresstheintervalinset–buildernotationandgraphtheintervalonanumberline.

1) (–1

,

4]

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

A) {x

–1<x≤4}

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

B) {x–1<x<4}

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

C) {xx≤4}

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

D) {x–1≤x≤4}

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

2) [–9

,

2)

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

A) {x

–9≤x<2}

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

B) {x–9<x≤2}

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

C) {xx<2}

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

D) {x–9≤x≤2}

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

Page66

3) –∞,7

2

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

A) x x<7

2

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

B) x x>7

2

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

C) x x≤7

2

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

D) {x2≤x≤7}

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

4) [–1

,

3]

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

A) {x

–1≤x≤3}

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

B) {x–1<x≤3}

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

C) {x

–1<x<3}

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

D) {x–1≤x<3}

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

5) (–8

,

∞)

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

A) {xx>–8}

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

B) {xx≥–8}

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

C) {xx>–8}

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

D) {xx≥–8}

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

6) [3

,

∞)

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

A) {xx≥3}

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

B) {xx>3}

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

C) {xx>3}

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

D) {xx≥3}

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

Page67

7) (–∞

,

3.5]

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

A) {x x≤3.5}

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

B) {x x<3.5}

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

C) {x x>3.5}

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

D) {x x≥3.5}

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

2 FindIntersectionsandUnionsofIntervals

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

Usegraphstofindtheset.

1) (–8

,

0)∩[–3

,

8]

A) [–3

,

0) B) (–8

,

8] C) (0,8] D) (–8

,

–3]

2) (–6

,

0)∪[–1

,

9]

A) (–6

,

9] B) [–1

,

0) C) (0,9] D) (–6

,

–1]

3) (–∞

,

8)∩[–3

,

19)

A) [–3

,

8) B) (–∞

,

19) C) (8

,

19) D) (–∞

,

–3]

4) (–∞

,

3)∪[–2

,

19)

A) (–∞

,

19) B) [–2

,

3) C) (3

,

19) D) (–∞

,

–2]

5) (3

,

∞)∩[14

,

∞)

A) [14

,

∞)B)(3

,

∞)C)(3

,

14] D) (–∞

,

∞)

6) (1

,

∞)∪[16

,

∞)

A) (1

,

∞)B)[16

,

∞)C)(1

,

16] D) (–∞

,

∞)

3 SolveLinearInequalities

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

Solvethelinearinequality.Otherthan∅,useintervalnotationtoexpressthesolutionsetandgraphthesolutionsetona

numberline.

1) 3x+8<29

–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

Page68

2) –3x≥24

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

A) (–∞

,

–8]

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

B) [–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) (–∞

,

8]

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

3) 7x–2>6x–8

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) (–10

,

∞)

-17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3-17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3

D) [–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

4) –2x+6≥–3x+8

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) (14

,

∞)

7 8 9 10 11 12 13 14 15 16 17 18 19 20 217 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Page69

5) 18x+18>6(2x+5)

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) (8

,

∞)

123456789101112131415123456789101112131415

6) –4(6x–3)<–28x–4

A) (–∞

,

–4)

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

B) (–4

,

∞)

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

C) (–∞

,

–4]

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

D) (–∞

,

–2]

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

Page70

7) –20x–4≤–4(4x+2)

A) [1

,

∞)

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

B) (–∞

,

1]

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

C) (1

,

∞)

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

D) (–∞

,

1)

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

8) 9x+3≤3(2x–3)

A) (–∞

,

–4]

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

B) [–4

,

∞)

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

C) (–∞

,

–4)

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

D) [–∞

,

–2)

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

9) x

6–1

4≤x

3+2

–40 –32 –24 –16 –8 0 8 16 24 32 40–40 –32 –24 –16 –8 0 8 16 24 32 40

A) –27

2,∞

–40 –32 –24 –16 –8 0 8 16 24 32 40–40 –32 –24 –16 –8 0 8 16 24 32 40

B) –∞,–27

2

–40 –32 –24 –16 –8 0 8 16 24 32 40–40 –32 –24 –16 –8 0 8 16 24 32 40

C) –27

2,∞

–40 –32 –24 –16 –8 0 8 16 24 32 40–40 –32 –24 –16 –8 0 8 16 24 32 40

D) –∞,–27

2

–40 –32 –24 –16 –8 0 8 16 24 32 40–40 –32 –24 –16 –8 0 8 16 24 32 40

Page71

10) x–1

24 ≥x–4

30 +1

120

–20 –16 –12 -8 –4 0 4 8 12 16 20 24 28–20 –16 –12 -8 –4 0 4 8 12 16 20 24 28

A) [–10

,

∞)

–20 –16 –12 -8 –4 0 4 8 12 16 20 24 28–20 –16 –12 -8 –4 0 4 8 12 16 20 24 28

B) (–∞

,

–10]

–20 –16 –12 -8 –4 0 4 8 12 16 20 24 28–20 –16 –12 -8 –4 0 4 8 12 16 20 24 28

C) (–10

,

∞)

–20 –16 –12 -8 –4 0 4 8 12 16 20 24 28–20 –16 –12 -8 –4 0 4 8 12 16 20 24 28

D) (–∞

,

–10)

–20 –16 –12 -8 –4 0 4 8 12 16 20 24 28–20 –16 –12 -8 –4 0 4 8 12 16 20 24 28

Useintervalnotationtorepresentallvaluesofxsatisfyingthegivenconditions.

11) y1=8x–2

,

y2=7x+4

,

andy1>y2.

A) (6

,

∞)B)(

–∞

,

6] C) (2

,

∞)D)[6

,

∞)

12) y1=–5x–1

,

y2=–6x–3

,

andy1≤y2.

A) (–∞

,

–2] B) (–∞

,

–2) C) [–2

,

∞)D)[

–4

,

∞)

13) y1=x

2,y2=4+x

10 ,andy1≥y2.

A) [10

,

∞)B)[

–10

,

∞)C)(

–∞

,

10] D) (10

,

∞)

14) y=8–2(3–x)andyisatmost8.

A) (–∞

,

3] B) [3

,

∞)C)(

–∞

,

4] D) (–∞

,

3)

15) y=x–2

20 –x–2

24 –1

120 andyisatleast0.

A) [3

,

∞)B)(

–∞

,

3] C) (3

,

∞)D)(

–∞

,

3)

Solvetheproblem.

16) Whenmakingalongdistancecallfromacertainpayphone,thefirstthreeminutesofacallcost$2.75.After

that,eachadditionalminuteorportionofaminuteofthatcallcosts$0.50.Useaninequalitytofindthenumber

ofminutesonecancalllongdistancefor$3.75.

A) 5minutesorfewer B) 2minutesorfewer C) 1 minutesorfewer D) 8minutesorfewer

17) Ittakes19minutestosetupacandymakingmachine.Oncethemachineissetup,itproduces60 candiesper

minute.Useaninequalitytofindthenumberofcandiesthatcanbeproducedin8hoursifthemachinehasnot

yetbeensetup.

A) 27,660candiesorfewer B) 480 candiesorfewer

C) 7980candiesorfewer D) 9120 candiesorfewer

18) Acertainstorehasafaxmachineavailableforusebyitscustomers.Thestorecharges$2.25tosendthefirst

pageand$0.60foreachsubsequentpage.Useaninequalitytofindthenumberofpagesthatcanbefaxedfor

$10.05.

A) 14pagesorfewer B) 58pagesorfewer C) 4 pagesorfewer D) 17pagesorfewer

19) Clairehasreceivedscoresof85,88,87,and80 onheralgebratests.Whatscoremustshereceiveonthefifthtest

tohaveanoveralltestscoreaverageofatleast82?

A) 70orgreater B) 71orgreater C) 69 orgreater D) 68orgreater

Page72

20) Usingdatafrom1996–1998,theannualnumberofcarssoldatacertaindealershipcanbemodeledbythe

formula

y=2x+1,

whereyisthenumberofcars,inthousands,soldxyearsafter1996.Accordingtothisformula,inwhichyears

willthenumberofcarssoldexceed15thousand?

A) Yearsafter2003 B) Yearsafter2001 C) Yearsafter2005 D) Yearsafter2007

21) ABCphonecompanycharges$21permonthplus5¢ perminute ofphonecalls.XYZphonecompanycharges

$9permonthplus8¢perminuteofphonecalls.HowmanyminutesofphonecallsinamonthmakeXYZ

phonecompanythebetterdeal?

A) Lessthan400minutes B) Morethan400 minutes

C) Morethan40minutes D) Lessthan40 minutes

22) Gregisopeningacarwash.HeestimateshiscostequationasC=5000 +0.05x andhisrevenueequationas

R=1.8x,wherexisthenumberofcarswashedinasix–monthperiod.Findthenumberofcarsthatmustbe

washedinasix–monthperiodforGregtomakeaprofit.

A) Atleast2858cars B) Atleast286 cars C) Atleast28,572 cars D) Atleast1858 cars

23) Astandardtrainticketinacertaincitycosts$1.50 perride.Peoplewhousethetrainalsohavetheoptionof

purchasingafrequent–riderpassfor$18.75eachmonth.Withthepass,aticketcostsonly$0.75perride.How

manytrainridesinamonthmakethefrequent–riderpassabetterdealthanstandardtraintickets?

A) 26ormorerides B) 25ormorerides C) 24 ormorerides D) 27ormorerides

24) EverySunday,Jarodbuysaloafoffreshbreadforhisfamilyfromthecornerbakeryfor$2.00.Thelocal

departmentstorehasasaleonbreadmakersfor$67.Ifthebread–makingsuppliescost$0.93perweek,forhow

manyweekswouldJarodhavetobakealoafofbreadathomebeforethebreadmakerstartssavinghim

money?

A) Atleast63weeks B) Atleast62 weeks C) Atleast65 weeks D) Atleast64 weeks

4 RecognizeInequalitieswithNoSolutionorAllRealNumbersasSolutions

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

Solvethelinearinequality.Otherthan∅,useintervalnotationtoexpressthesolutionsetandgraphthesolutionsetona

numberline.

1) 5(4x+5)–4x<4(6+4x)–6

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

A) ∅

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

B) (–∞

,

∞)

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

C) (–∞

,

5)

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

D) (5

,

∞)

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

Page73

2) 4(x+5)≥3(x–4)+x

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

A) (–∞

,

∞)

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

B) ∅

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

C) (–∞

,

3]

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

D) [3

,

∞)

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

3) –2x≤–2(x–3)

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

A) (–∞

,

∞)

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

B) ∅

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

C) (–∞

,

–3]

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

D) [–3

,

∞)

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

5 SolveCompoundInequalities

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

Solvethecompoundinequality.Otherthan∅,useintervalnotationtoexpressthesolutionsetandgraphthesolutionset

onanumberline.

1) 20<5x≤30

–2–10123456789101112–2–10123456789101112

A) (4

,

6]

–2–10123456789101112–2–10123456789101112

B) [4

,

6)

–2–10123456789101112–2–10123456789101112

C) (–∞

,

4)∪[6

,

∞)

–2–10123456789101112–2–10123456789101112

D) (–∞

,

4]∪(6

,

∞)

–2–10123456789101112–2–10123456789101112

Page74

2) –5<x+3≤6

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

A) (–8

,

3]

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

B) (–2

,

9]

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

C) [–8

,

3)

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

D) [–2

,

9)

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

3) 7≤3x–2≤13

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) –26≤–5x–1<–21

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75

5) –27≤–4x+1≤–7

A) [2

,

7]

–2–101234567891011–2–101234567891011

B) (2

,

7)

–2–101234567891011–2–101234567891011

C) [–7

,

–2]

-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) (–7

,

–2)

-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

6) –4≤–4x–12<4

-10 -5 0 5 10-10 -5 0 5 10

A) (–4,–2]

-10 -5 0 5 10-10 -5 0 5 10

B) (–∞

,

–4]

-10 -5 0 5 10-10 -5 0 5 10

C) (–∞

,

–4)or[–2,∞)

-10 -5 0 5 10-10 -5 0 5 10

D) [–4,–2)

-10 -5 0 5 10-10 -5 0 5 10

7) 9≤7

3x+2<23

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

A) [3

,

9)

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

B) (3

,

9]

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

C) [3

,

4)

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

D) (3

,

4]

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

Solvetheproblem.

8) TheformulaforconvertingFahrenheittemperature,F,toCelsiustemperature,C,is

C=5

9(F–32).

IfCelsiustemperaturerangesfrom–30°to20°,inclusive,whatistherangefortheFahrenheittemperature?

A) [–22°F,68°F] B) (–22°F,68°F) C) [–21°F,–16°F] D) (–21°F,–16°F)

Page76

9) TheformulaforconvertingCelsiustemperature,C,toFahrenheittemperature,F,is

F=9

5C+32.

IfFahrenheittemperaturerangesfrom95°to185°,inclusive,whatistherangefortheCelsiustemperature?

A) [35°C,85°C] B) (35°C,85°C)

C) [203°C,365°C] D) (203°C,365°C)

10) Onthefirstfourexams,yourgradesare76

,

78

,

73

,

and77.YouarehopingtoearnaCinthecourse.Thiswill

occuriftheaverageofyourfiveexamgradesisgreaterthanorequalto70andlessthan80.Whatrangeof

gradesonthefifthexamwillresultinearningaC?

A) [46

,

96) B) (46

,

96] C) [36

,

86) D) (36

,

86]

11) Onthefirstfourexams,yourgradesare76

,

91

,

60

,

and77.Thereisstillafinalexam,anditcountsastwo

grades.YouarehopingtoearnaCinthecourse.Thiswilloccuriftheaverageofyoursixexamgradesis

greaterthanorequalto70andlessthan80.WhatrangeofgradesonthefinalexamwillresultinearningaC?

A) [58

,

88) B) [58

,

88] C) [46

,

96) D) [46

,

96]

12) Partsforanautomobilerepaircost$551.Themechaniccharges$29 perhour.Ifyoureceiveanestimateforat

least$696andatmost$812forfixingthecar,whatisthetimeinterval,inhours,thatthemechanicwillbe

workingonthejob?

A) [5

,

9] B) [24

,

28] C) [1,9] D) [1,5]

13) TheformulaC=1.5x+19representstheestimatedfuturecostofyearlyattendanceatStateUniversity,whereC

isthecostinthousandsofdollarsxyearsafter2002.Useacompoundinequalitytodeterminewhenthe

attendancecostswillrangefrom31to37thousanddollars.

A) From2010to2014 B) From2009 to2013 C) From2011 to2015 D) From2011 to2013

6 SolveAbsoluteValueInequalities

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

Solvetheabsolutevalueinequality.Otherthan∅

,

useintervalnotationtoexpressthesolutionsetandgraphthe

solutionsetonanumberline.

1) x <2

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

A) (–2

,

2)

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

B) (–∞

,

–2)∪(2

,

∞)

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

C) [–2

,

2]

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

D) (–∞

,

–2]∪[2

,

∞)

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

Page77

2) x >2

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

A) (–∞

,

–2)∪(2

,

∞)

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

B) (–2

,

2)

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

C) [–2

,

2]

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

D) (–∞

,

–2]∪[2

,

∞)

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

3) |x–1|<0

–12–10–8–6–4–2024681012–12–10–8–6–4–2024681012

A) (–1

,

1)

–12–10–8–6–4–2024681012–12–10–8–6–4–2024681012

B) (–∞

,

1)

–12–10–8–6–4–2024681012–12–10–8–6–4–2024681012

C) (–1

,

∞)

–12–10–8–6–4–2024681012–12–10–8–6–4–2024681012

D) ∅

–12–10–8–6–4–2024681012–12–10–8–6–4–2024681012

4) |x–5|>0

–12–10–8–6–4–2024681012–12–10–8–6–4–2024681012

A) (–∞

,

5)∪(5

,

∞)

–12–10–8–6–4–2024681012–12–10–8–6–4–2024681012

B) (–5

,

5)

–12–10–8–6–4–2024681012–12–10–8–6–4–2024681012

C) (5

,

∞)

–12–10–8–6–4–2024681012–12–10–8–6–4–2024681012

D) ∅

–12–10–8–6–4–2024681012–12–10–8–6–4–2024681012

Page78

5) |x–3|≤0

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

A) {3}

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

B) {–3}

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

C) (–∞

,

3)

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

D) ∅

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

6) |x+8|≥0

–12–10–8–6–4–2024681012–12–10–8–6–4–2024681012

A) (–∞

,

∞)

–12–10–8–6–4–2024681012–12–10–8–6–4–2024681012

B) {–8}

–12–10–8–6–4–2024681012–12–10–8–6–4–2024681012

C) (–8

,

8)

–12–10–8–6–4–2024681012–12–10–8–6–4–2024681012

D) (–8

,

∞)

–12–10–8–6–4–2024681012–12–10–8–6–4–2024681012

Page79

7) |x+3|<7

–10–8–6–4–202468101214–10–8–6–4–202468101214

A) (–10

,

4)

–10–8–6–4–202468101214–10–8–6–4–202468101214

B) [–10

,

4]

–10–8–6–4–202468101214–10–8–6–4–202468101214

C) (–∞

,

–10)∪(4

,

∞)

–10–8–6–4–202468101214–10–8–6–4–202468101214

D) ∅

–10–8–6–4–202468101214–10–8–6–4–202468101214

8) |x+6|–5≤1

A) [–12

,

0]

-16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6-16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6

B) (–12

,

0)

-16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6-16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6

C) [–12

,

1]

-16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6-16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6

D) (–∞

,

–12]∪[0

,

∞)

-16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6-16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6

9) 3(x+1)+9≤15

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

A) [–9

,

1]

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

B) (–9

,

1)

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

C) [–7

,

3]

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

D) (–7

,

3)

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

Page80

10) 7y+21

3<7

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

A) (–6

,

0)

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

B) (–∞

,

–6)∪(0,∞)

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

C) (–6

,

6)

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

D) (–∞

,

–6)∪(6

,

∞)

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

11) 2+1–x

2≥5

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

A) (–∞

,

–4]∪[8

,

∞)

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

B) [–4

,

8]

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

C) (–∞

,

–8]∪[4

,

∞)

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

D) [–8

,

4]

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

12) |4x–8|+6<–3

01234567890123456789

A) –∞,17

4

01234567890123456789

B) –1

4,17

4

01234567890123456789

C) –∞,–1

4

01234567890123456789

D) ∅

01234567890123456789

Page81

13) |7x–6|–5>–12

0 2 4 6 8 1012140 2 4 6 8 101214

A) (–∞

,

∞)

0246810121402468101214

B) –1

7,∞

0246810121402468101214

C) –1

7,13

7

0246810121402468101214

D) ∅

0246810121402468101214

Solvetheproblem.

14) Aspinnerhasfiveregionsnumbered1through5.Ifthespinnerisspun100times,wewouldexpectabout20

oftheoutcomestobeRegion1.Itcanbedeterminedthatthespinnerisunbalancedifx,thenumberof

outcomesthatresultinRegion1,satisfiesx–20

4≥1.645.Describethenumberofoutcomesthatdeterminean

unbalancedspinnerthatisspun100times.

A) Fewerthan14ormorethan26outcomes B) Between14 and26outcomes

C) Fewerthan17ormorethan29outcomes D) Between17 and29outcomes

15) Whenanumberissubtractedfrom–7,theabsolutevalueofthedifferenceismorethan3.Useintervalnotation

toexpressthesetofallnumbersthatsatisfythiscondition.

A) (–∞

,

–10)∪(–4,∞)B)(

–∞

,

–4)∪(10,∞)C)(

–∞

,

–10]∪[–4,∞)D)(

–10,–4)

16) 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.Solvetheinequality,and

expresstheanswerinintervalform.

A) |40–x|≤0.75;[39.25,40.75] B) |40+x|≤0.75;[39.25,40.75]

C) |x+0.75|≤40;[39.25,∞) D) |x|–40≤0.75;(–∞

,

40.75]

Page82

Ch.1 EquationsandInequalities

AnswerKey

1.1 GraphsandGraphingUtilities

1 PlotPointsintheRectangularCoordinateSystem

2 GraphEquationsintheRectangularCoordinateSystem

3 InterpretInformationAboutaGraphingUtilityʹsViewingRectangleorTable

4 UseaGraphtoDetermineIntercepts

5 InterpretInformationGivenbyGraphs

Page83

1.2 LinearEquationsandRationalEquations

2 SolveLinearEquationsContainingFractions

3 SolveRationalEquationswithVariablesintheDenominators

4 RecognizeIdentities,ConditionalEquations,andInconsistentEquations

5 SolveAppliedProblemsUsingMathematicalModels

Page84

1.3 ModelsandApplications

1 UseLinearEquationstoSolveProblems

2 SolveaFormulaforaVariable

1.4 ComplexNumbers

1 AddandSubtractComplexNumbers

Page85

2 MultiplyComplexNumbers

3 DivideComplexNumbers

4 PerformOperationswithSquareRootsofNegativeNumbers

1.5 QuadraticEquations

1 SolveQuadraticEquationsbyFactoring

2 SolveQuadraticEquationsbytheSquareRootProperty

Page86

3 SolveQuadraticEquationsbyCompletingtheSquare

4 SolveQuadraticEquationsUsingtheQuadraticFormula

5 UsetheDiscriminanttoDeterminetheNumberandTypeofSolutions

6 DeterminetheMostEfficientMethodtoUseWhenSolvingaQuadraticEquation

Page87

7 SolveProblemsModeledbyQuadraticEquations

1.6 OtherTypesofEquations

1 SolvePolynomialEquationsbyFactoring

2 SolveRadicalEquations

3 SolveEquationswithRationalExponents

Page88

4 SolveEquationsThatAreQuadraticinForm

5 SolveEquationsInvolvingAbsoluteValue

Page89

6 SolveProblemsModeledbyEquations

1.7 LinearInequalitiesandAbsoluteValueInequalities

1 UseIntervalNotation

2 FindIntersectionsandUnionsofIntervals

3 SolveLinearInequalities

Page90

4 RecognizeInequalitieswithNoSolutionorAllRealNumbersasSolutions

5 SolveCompoundInequalities

6 SolveAbsoluteValueInequalities

Page91