RM TB ESSEN 1e TOCaplustestbank.eu/sample/Test-Bank-for-Precalculus-Essentials-32190… · Ratti &...

CONTENTS

Test Forms A, B, C, and D are Free Response Test Forms E and F are Multiple Choice

Chapter P Tests.............................................................................................................. 1 Chapter 1 Tests............................................................................................................ 15 Chapter 2 Tests............................................................................................................ 43 Chapter 3 Tests............................................................................................................ 59 Chapter 4 Tests............................................................................................................ 75 Chapter 5 Tests............................................................................................................ 95 Chapter 6 Tests.......................................................................................................... 107 Chapter P Test Keys.................................................................................................. 121 Chapter 1 Test Keys .................................................................................................. 124 Chapter 2 Test Keys .................................................................................................. 129 Chapter 3 Test Keys .................................................................................................. 135 Chapter 4 Test Keys .................................................................................................. 140 Chapter 5 Test Keys .................................................................................................. 145 Chapter 6 Test Keys .................................................................................................. 147

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Chapter P Test Form A Name Ratti & McWaters, Precalculus Essentials

1) Evaluate the following expression for the given values of x and y.

2

; 3, 7x y

x yx y

− +=− =−

−

1)

2) Rewrite the following expression without absolute value bars.

7 11−− −− 2)

3) Write [ )2,− ∞ using inequality notation and sketch its graph. 3)

4) Factor 3 26 14 15 35x x x− + − . 4)

5) Factor 2 2 48x x− − . 5)

6) Convert 15 / 4x to radical notation, simplify your answer. Assume all variables represent positive values. 6)

In exercises 7–13, find the exact solution to the equation.

7) ( ) ( )2 3 4 7 5 2 7x x x− − = + 7)

8) 26 7 20x x− = 8)

9) 3 22 3 18 27 0x x x+ − − = 9)

10) 4 213 36 0x x− + = 10)

11) 5 2 3 11 46x− + = 11)

12) 11 1

07 5x x+ =

− +

12)

13) 2 5 3 8x x+ − = − 13)

14) Simplify 2 3 2 63 33 2 7 16y x y x y− . Assume all variables represent

positive values 14)

In exercises 15–20, solve the inequality. Write your answer using interval notation.

15) 8 5 3 11x− < − ≤ 15)

16) 2 3 5 4

12 3 2 3

x x x x++ − >− +

16)

17) 2 3 70 0x x+ − > 17)

1


Chapter P Test Form A Name Ratti & McWaters, Precalculus Essentials

2

18) 2

40

2 15

x

x x

−≥

+ −

18)

19) 3 7 8x+ ≥ 19)

20) 2 5 6 4 22x+ + < 20)

21) Expand ( )( )3 4 5 6 .i i− + Write the result in the standard form a bi+ . 21)

In exercises 22–23, simplify the expressions. Write your final answer using only positive exponents.

22) 44

2

3x y

x

−⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜⎝ ⎠

22)

23) ( )3/ 25 1/3

1/ 2 1/3

9x y

x y

−

− 23)

24) Rationalize the denominator in the following expression.

2 7 3

4 7

−

−

24)


Chapter P Test Form B Name Ratti & McWaters, Precalculus Essentials


( )2; 7, 3

x yx y

y x

+=− =

−

1)


4 7−− − − 2)

3) Write ( ), 4−∞ using inequality notation and sketch its graph. 3)

4) Factor 3 26 15 14 35x x x+ − − . 4)

5) Factor 2 15 50x x− + . 5)

6) Convert 10 / 3y to radical notation, simplify your answer. Assume all

variables represent positive values. 6)


7) ( ) ( ) ( )3 2 4 5 3 4 3 7x x x x+ − + = − + 7)

8) 26 7 20 0x x+ − = 8)

9) 3 23 4 75 100 0x x x− − + = 9)

10) 4 234 225 0x x− + = 10)

11) 4 3 5 7 17x+ − = 11)

12) 12 3

04 6x x+ =

+ −

12)

13) 3 5 5 8x x− − = − 13)

14) Simplify 5 3 37 20 3 45y x y x x y− . Assume all variables represent

positive values. 14)


15) 7 3 5 12x− ≤− − < 15)

16) 5 3 4

26 3 6 6

x x x x++ − ≥− +

16)

17) 2 5 24 0x x− − < 17)

3


Chapter P Test Form B Name Ratti & McWaters, Precalculus Essentials

4

18) 2

60

2 8

x

x x

+≤

+ −

18)

19) 5 4 11x+ > 19)

20) 4 3 2 20 24x+ − ≤ 20)

21) Expand ( )( )7 2 3 4 .i i+ − Write the result in the standard form a bi+ . 21)


22) 31 4

35

x y

x

−−⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜⎝ ⎠

22)

23)

( )1/3 3/ 4

2/34 28

x y

x y

−

−

23)


7 2 5

5 1

−

−

24)


Chapter P Test Form C Name Ratti & McWaters, Precalculus Essentials


2 2

; 5, 35

x yx y

xy

−= =−

−

1)


5 21− −− 2)

3) Write )( 4,− ∞ using inequality notation and sketch its graph. 3)

4) Factor 3 25 6 15 18x x x+ − − . 4)

5) Factor 2 11 28x x+ + . 5)

6) Convert 19 / 4y to radical notation, simplify your answer. Assume all

variables represent positive values. 6)


7) ( ) ( )4 3 5 8 5 2 9x x x− − =− − 7)

8) 28 14 15 0x x− − = 8)

9) 3 25 4 80 64 0x x x+ − − = 9)

10) 4 24 109 225 0y y− + = 10)

11) 2 6 7 3 25x− + = 11)

12) 2 3

2 7x x=

+ −

12)

13) 3 4 8x x+ + = 13)

14) Simplify 7 5 2 4 23 34 3 24x x y x y x y+ . Assume all variables represent



15) 9 7 4 10x− < − ≤ 15)

16) 2 4 2

13 2 2 3

x x x x−− + + < +

16)

17) 2 4 77 0x x− − ≤ 17)

5


Chapter P Test Form C Name Ratti & McWaters, Precalculus Essentials

6

18) 2

70

2 15

x

x x

−≥

− −

18)

19) 5 2 8x+ ≥ 19)

20) 5 3 4 42 23x+ − < 20)

21) Expand ( )( )5 2 6 3 .i i− + Write the result in the standard form a bi+ . 21)


22) 25 4

3

7x y

x

−−

−

⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜⎝ ⎠

22)

23) ( )1/ 23 3/5

3/ 2 1/3

25x y

x y

−

− 23)


3 11 2

3 11

−

−

24)


Chapter P Test Form D Name Ratti & McWaters, Precalculus Essentials


2; 8, 6

x xyx y

y x

+=− =−

−

1)


12 16−− −− 2)

3) Write ( ], 2−∞ using inequality notation and sketch its graph. 3)

4) Factor 3 220 16 15 12x x x− + − . 4)

5) Factor 2 3 40x x+ − . 5)

6) Convert 11/ 2x to radical notation, simplify your answer. Assume all variables represent positive values. 6)


7) ( ) ( ) ( )3 2 7 2 4 8 2 4 5x x x x+ − + = − − 7)

8) 26 15 0x x− − = 8)

9) 3 23 5 12 20 0x x x+ − − = 9)

10) 4 24 61 225 0x x− + = 10)

11) 4 4 5 7 19x− + = 11)

12) 1 2

4 6x x=

+ +

12)

13) 4 1 5x x+ + = 13)

14) Simplify 2 3 448 75xy xy x y+ . Assume all variables represent



15) 11 5 7 23x− <− − ≤ 15)

16) 5 1 5 3 4

6 2 3 6 3

x x x x+− + + ≤ −

16)

17) 2 2 35 0x x− − ≥ 17)

7


Chapter P Test Form D Name Ratti & McWaters, Precalculus Essentials

8

18) 2

20

3 28

x

x x

+≤

− −

18)

19) 3 5 10x+ > 19)

20) 4 7 13x+ ≤ 20)

21) Expand ( )( )4 3 6 5 .i i+ − Write the result in the standard form a bi+ . 21)


22) 37 5

42

x y

y

−⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜⎝ ⎠

22)

23)

( )4/3 3/10

2 /34 2 /5125

x y

x y

−

−

23)


2 13 1

2 13

+

+

24)


Chapter P Test Form E Name Ratti & McWaters, Precalculus Essentials

1) Evaluate 2x y

x y

− +

− when 6 and 8.x y=− =−

a) 29− b) 35− c) 29 d) 5−

1)

2) Rewrite 11 3−−− −− without absolute value bars.

a) 8− b) 8 c) 14− d) 14

2)

3) Use inequality notation to describe ( ]2,3− and sketch the interval.

a) 2 3x− < < ;

b) 2 3x− < ≤ ;

c) 2 3x− ≤ < ;

d) 2 3x− ≤ ≤ ;

3)

4) Factor 3 26 15 14 35x x x− + − .

a) ( )( )23 5 2 7x x− + b) ( )( )22 7 3 5x x− +

c) ( )( )22 5 3 7x x− + d) ( )( )22 5 3 7x x+ −

4)

5) Factor 2 2 24x x− − .

a) ( )( )4 6x x− + b) ( )( )6 4x x− +

c) ( )( )3 8x x− + d) ( )( )8 3x x− +

5)

6) Write 19 / 4x in simplified radical form.

a) 4 19x b) 44 3x x c) 19 4x d) 5 4x x

6)


7) ( ) ( )2 3 4 7 5 3 7x x x− − =− +

a) { },−∞ ∞ b) { }0 c) { }2930

− d) ∅

7)

8) 212 23 10x x=− −

a) { }3 42 5

, b) { }3 42 5

,− − c) { }523 4

, d) { }523 4

,− −

8)

9) 3 25 5 60x x x+ =

a) { }4,0,3− b) { }4,0, 3− c) { }4,5, 3− d) { }4,5,3−

9)

9



10

10) 4 216 63 0x x− + =

a) { }7, 3± ± b) { }7, 3± ± c) { }7, 3± ± d) ∅

10)

11) 3 5 1 7 14x− − + =−

a) { }85

b) { }4 215 3

,− c) { }6 85 5

,− d) ∅

11)

12) 8 3

05 6x x+ =

+ −

a) { }3 b) { }635

c) { }3− d) ∅

12)

13) 2 2 3 8x x− − = +

a) { }7, 17− − b) { }7− c) { }17− d) ∅

13)

14) Simplify 3 35 87 16 4 54x x x+ . Assume all variables represent positive values.

a) 3 326 2x x b) 32 226 2x x c) 2 326 2x x d) 2 326x x

14)


15) 12 6 3 15x− < − ≤

a) ( ]6,3− b) ( ]3,6− c) [ )6,3− d) [ )3,6−

15)

16) 7 5 3 7 3

36 3 3 2

x x x x− +− − + < +

a) ( ),−∞ ∞ b) ∅ c) ( ), 20−∞ d) ( )20,− ∞

16)

17) 2 5 36 0x x+ − <

a) ( ) ( ), 9 4,−∞ − ∪ ∞ b) ( ) ( ), 4 9,−∞ − ∪ ∞

c) ( )9, 4− d) ( )4,9−

17)

18) 2

50

13 36

x

x x

+≥

− +

a) [ ) ( )5,4 9,− ∪ ∞ b) ( ) [ ], 5 4,9−∞ − ∪

c) ( ] [ ], 5 4,9−∞ − ∪ d) [ ] [ )5,4 9,− ∪ ∞

18)



19) 4 9 5x− ≥

a) 72

1,⎡ ⎤⎢ ⎥⎣ ⎦ b) [ )1,− ∞

c) ( ] )72

,1 ,⎡−∞ ∪ ∞⎢⎣ d) ( [ )72

, 1,⎤−∞ − ∪ − ∞⎥⎦

19)

20) 5 7 3 31 49x+ − <

a) ( )233

,3− b) ( ) ( )233

, 3 ,−∞ − ∪ ∞

c) ( )233

3,− d) ( ) ( )233

, 3,−∞ − ∪ ∞

20)

21) Expand ( )( )5 3 6 2 .i i+ − Write the result in the standard form a bi+ .

a) 24 28i+ b) 24 28i− c) 36 8i− d) 36 8i+

21)


22)

23 2

4

3x y

x

−−⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

a) 14

49

x

y b)

4

149

y

x c)

4

14

9y

x d)

14

4

9x

y

22)

23) ( )1/ 34 1/ 2

2 / 3 5 / 3

27x y

x y−

a) 2

11/ 6

3x

y b)

3 / 2

2

9y

x c)

2

3 / 2

3x

y d)

2

3 / 2

9x

y

23)

24) Rationalize the denominator of 3 7 5

5 7

−

−.

a) 5 7 2

9

− b)

10 7 23

9

− c)

7 10

3

− − d)

2 7 11

3

− +

24)

11


Chapter P Test Form F Name Ratti & McWaters, Precalculus Essentials

12

1) Evaluate 2x y

x y

− −

+ when 5 and 10.x y=− =−

a) 23

− b) 73

− c) 23

d) 6−

1)

2) Rewrite 12 5−− −− without absolute value bars.

a) 7 b) 7− c) 17− d) 17

2)

3) Use inequality notation to describe [ )4, 2− and sketch the interval.

a) 4 2x− < < ;

b) 4 2x− ≤ < ;

c) 4 2x− < ≤ ;

d) 4 2x− ≤ ≤ ;

3)

4) Factor 3 210 35 6 21x x x− + − .

a) ( )( )22 7 5 3x x− + b) ( )( )22 7 5 3x x+ −

c) ( )( )25 7 2 3x x− + d) ( )( )22 3 5 7x x− +

4)

5) Factor 2 6 40x x+ − .

a) ( )( )8 5x x− + b) ( )( )5 8x x− +

c) ( )( )10 4x x− + d) ( )( )4 10x x− +

5)

6) Write 19 / 3y in simplified radical form.

a) 319 y b) 193 y c) 6 3y y d) 5 23y y

6)


7) ( ) ( )5 2 3 11 2 2 5x x x− + =− −

a) { },−∞ ∞ b) { }0 c) { }52

d) ∅

7)

8) 28 38 35x x= −

a) { }7 52 4

, b) { }7 52 4

,− − c) { }2 47 5

, d) { }2 47 5

,− −

8)

9) 3 27 14 168x x x+ =

a) { }6,4,7− b) { }4,6,7− c) { }6,0,4− d) { }6,0, 4−

9)



10) 4 210 24 0x x− + =

a) { }6, 2± ± b) { }6, 2± ±

c) { }6, 2± ± d) ∅

10)

11) 2 4 3 11 9x− − + =−

a) { }134

b) { }7 134 4

,− c) { }13 74 4

,− d) ∅

11)

12) 10 3

06 7x x+ =

− +

a) { }887

− b) { }4− c) { }4 d) ∅

12)

13) 1 3 2 11x x− + = +

a) { }5, 16− − b) { }16− c) { }5− d) ∅

13)

14) Simplify 4 49 55 243 3 48x x x− . Assume all variables represent positive values.

a) 2 421x x b) 2 421 3x x c) 2 49 3x x d) 2 49x x

14)


15) 11 9 4 17x− ≤ − <

a) ( ]2,5− b) [ )2,5− c) [ )5,2− d) ( ]5,2−

15)

16) 11 3 7 5 4

36 2 3 2

x x x x−− − > +

a) ( ),−∞ ∞ b) ∅ c) ( ), 33−∞ − d) ( )33,∞

16)

17) 2 11 26 0x x− − >

a) ( ) ( ), 13 2,−∞ − ∪ ∞ b) ( ) ( ), 2 13,−∞ − ∪ ∞

c) ( )13,2− d) ( )2,13−

17)

18) 2

40

9 14

x

x x

−≤

+ +

a) ( ] [ ], 7 2,4−∞ − ∪ − b) [ ] [ )7, 2 4,− − ∪ ∞

c) ( ) ( ], 7 2,4−∞ − ∪ − d) ( ) [ )7, 2 4,− − ∪ ∞

18)

13



14

19) 3 8 13x− ≥

a) ( [ )53

, 7,⎤−∞ − ∪ ∞⎥⎦ b) ( ] )53

, 7 ,⎡−∞ − ∪ ∞⎢⎣

c) 53

,7⎡ ⎤−⎢ ⎥⎣ ⎦ d) )53

,⎡ ∞⎢⎣

19)

20) 3 5 4 7 26x+ − <

a) ( ) ( )32

, 4 ,−∞ − ∪ ∞ b) ( )32

,−∞

c) ( )32

,4− d) ( )32

4,−

20)

21) Expand ( )( )4 5 3 7 .i i+ − Write the result in the standard form a bi+ .

a) 23 43i− + b) 23 43i− − c) 47 13i+ d) 47 13i−

21)


22)

35 3

3

2x y

x

−−⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

a) 9

248

y

x b)

24

98

x

y c)

24

9

8x

y d)

9

24

8y

x

22)

23) ( )1/ 49 2 / 3

3/ 4 1/12

16x y

x y

−

−

a) 3 / 2

1/ 4

2x

y b)

3

1/12

2x

y c)

3

1/ 4

2x

y d)

3

1/ 4

4x

y

23)

24) Rationalize the denominator of 4 5 3

3 5

−

−.

a) 3 5 19

4

− − b)

5 5 21

4

− + c)

9 5 11

4

+ d)

15 5 29

4

−

24)


Chapter 1 Test Form A Name Ratti & McWaters, Precalculus Essentials

1) Give the coordinates of the points on the following graph.

1)

2) Find the distance and midpoint between ( )4,3− and ( )10, 11− . 2)

3) Find the x- and y-intercepts of 2 20y x x= − − . 3)

In exercises 4–6, find the equations of the following lines. Write your answers in slope-intercept form.

4) Passing through ( )5, 3− with slope 2− . 4)

5) Passing through ( )3,7− and ( )1,5 . 5)

6) Parallel to 3 2 5x y− + =− passing through ( )3, 2− . 6)

7) Determine the a) domain and b) range of the function graphed below.

7)

8) Write the equation of the circle centered at ( )5,7− with a radius of 9. 8)

9) Determine the equation of the circle in standard form described by 2 24 6 36 0x x y y− + + − = . 9)

15



16

10) Find the domain of ( ) 2 2 15f x x x= + − .

Write your answer using interval notation. 10)

11) Determine which symmetries the graph of 4 23 4x y+ = possesses. 11)

12) Find ( )1f x− for ( ) 4 11f x x= − 12)

13) Given ( )f x and ( )g x , find ( )( )f g x and determine its domain.

( ) ( )22 5, 5f x x g x x= − = − 13)

14) List the transformations to the basic graph and graph the function.

( ) ( )22 3 9f x x=− − +

14)

15) Given the following graph determine: a) where is the graph increasing, b) where is the graph decreasing, c) where is the graph constant.

15)



16) Graph the function given below and determine the given functional values.

( )1 3

5 3

x if xf x

if x

⎧− − ≤⎪⎪=⎨⎪ >⎪⎩; ( ) ( ) ( )3 , 3 , 6f f f−

16)

17) Write the formula for the graph of ( )f x below.

17)

18) A company charges $50 to design a custom coffee mug and $13 each to make them. Find the function, ( )C x , that represents the cost to purchase

x coffee mugs and determine how many could be purchased with $400. 18)

19) Find the average rate of change of ( ) 2 9f x x= + as x changes from

1 to 5.a b=− = 19)

17



18

20) Graph ( ) 31

2f x x= − .

20)


Chapter 1 Test Form B Name Ratti & McWaters, Precalculus Essentials


1)

2) Find the distance and midpoint between ( )5, 7− and ( )1,1 . 2)

3) Find the x- and y-intercepts of 5 100y x= + . 3)


4) Passing through ( )4,3− with slope 5 . 4)

5) Passing through ( )4,1 and ( )1, 3− − . 5)

6) Perpendicular to 2 3 7x y+ = passing through ( )4,7 6)


7)

8) Write the equation of the circle centered at ( )7, 9− with a radius of 6. 8)

9) Determine the equation of the circle in standard form described by 2 210 8 5 0x x y y+ + − + = . 9)

19



20



11) Determine which symmetries the graph of 2 45y x x= − possesses. 11)

12) Find ( )1f x− for ( ) 3 8f x x= − 12)


( ) ( )2

2

1, 7

7

xf x g x x

x

+= = +

+

13)


( ) ( )212

5 4f x x= + −

14)


15)




( )3 2

3 2

x if xf x

if x

⎧− + >−⎪⎪=⎨⎪ − ≤−⎪⎩; ( ) ( ) ( )4 , 2 , 2f f f− −

16)


17)



19) Find the average rate of change of ( ) 33 14f x x=− − as x changes from

1 to 2.a b=− = 19)

21



22

20) Graph ( ) 3 2f x x= − .

20)


Chapter 1 Test Form C Name Ratti & McWaters, Precalculus Essentials


1)

2) Find the distance and midpoint between ( )8,5 and ( )4, 9− . 2)

3) Find the x- and y-intercepts of 5 2 32y x= − . 3)


4) Passing through ( )1, 2− with slope 3− . 4)

5) Passing through ( )2,1− and ( )4, 4− 5)

6) Parallel to 5 3 4x y− = passing through ( )10,3− 6)


7)


9) Determine the equation of the circle in standard form described by 2 26 10 9 0x x y y− + + + = . 9)

23



24



11) Determine which symmetries the graph of 3 2 4 8x y x= − possesses. 11)

12) Find ( )1f x− for ( ) 8 5f x x= − 12)


( ) ( )23 2, 7f x x g x x= + = − 13)


( ) ( )23 2 9f x x= + −

14)


15)




( )3 4

1 4

if xf x

x if x

⎧ >⎪⎪=⎨⎪− + ≤⎪⎩; ( ) ( ) ( )4 , 4 , 8f f f−

16)


17)



19) Find the average rate of change of ( ) 211 5f x x= − as x changes from

3 to 5.a b=− = 19)

25



26

20) Graph ( ) 31

3f x x= − .

20)


Chapter 1 Test Form D Name Ratti & McWaters, Precalculus Essentials


1)

2) Find the distance and midpoint between ( )6,1− and ( )4, 9− . 2)

3) Find the x- and y-intercepts of 3 27y x= + . 3)


4) Passing through ( )2,3− with slope 4 4)

5) Passing through ( )1, 2− − and ( )4,2 5)

6) Perpendicular to 4 3 5x y− − = passing through ( )8,5− 6)


7)


9) Determine the equation of the circle in standard form described by 2 214 8 56 0x x y y− + + + = . 9)

27



28

10) Find the domain of ( ) 2 3 10f x x x= − − .


11) Determine which symmetries the graph of 5 32 7y x x= + possesses. 11)

12) Find ( )1f x− for ( ) 11 5f x x= − 12)


( ) ( )2

2, 2

3

xf x g x x

x= = −

+

13)


( ) ( )22 5 6f x x=− + +

14)


15)




( )3 1

5 1

x if xf x

if x

⎧− + <⎪⎪=⎨⎪ − ≥⎪⎩; ( ) ( ) ( )1 , 1 , 5f f f−

16)


17)



19) Find the average rate of change of ( ) 22 7f x x=− − as x changes from

5 to 4.a b=− = 19)

29



30

20) Graph ( ) 3 3f x x= − .

20)


Chapter 1 Test Form E Name Ratti & McWaters, Precalculus Essentials

In exercises 1–2, refer to the graph to the right.

1) What are the coordinates of point A?

a) ( )3,9− b) ( )3, 9−

c) ( )9, 3− d) ( )9,3−

2) What are the coordinates of point B?

a) ( )4,0− b) ( )4,0

c) ( )0, 4 d) ( )0, 4−

1) 2)

3) Find the average rate of change of ( ) 2 2f x x x= − as x changes from 4 to 3.a b=− =

a) 27

7 b)

5

7− c) 3− d) 21

3)


4) Passing through ( )1,4− with slope 3 .

a) 3 7y x= + b) 3 4y x= + c) 3 1y x= − d) 3 13y x= −

4)

5) Passing through ( )4,3− and ( )2,4 .

a) 6 27y x= + b) 6 21y x=− − c) 1 116 3

y x= + d) 716 3

y x=− +

5)

6) Parallel to 2 5 13x y+ = passing through ( )5, 3− .

a) 5 312 2

y x= − b) 25

5y x= − c) 5 192 2

y x=− + d) 25

1y x=− −

6)

7) Write the equation of the circle centered at ( )7, 1− with a radius of 2.

a) ( ) ( )2 27 1 4x y+ + − = b) ( ) ( )2 2

7 1 4x y− + + =

c) ( ) ( )2 27 1 2x y+ + − = d) ( ) ( )2 2

7 1 2x y− + + =

7)

8) Determine the equation of the circle described by 2 28 10 59 0x x y y− + + − = .

a) ( ) ( )2 28 10 59x y− + + = b) ( ) ( )2 2

4 5 41x y− + + =

c) ( ) ( )2 24 5 100x y− + + = d) ( ) ( )2 2

4 5 59x y− + + =

8)

31



32

9) Determine which symmetries the graph of 2 3 4xy x xy+ = possesses.

a) x-axis b) y-axis c) origin d) all

9)

In exercises 10–12, use ( )2 4

3 4

x if xf x

if x

⎧− − ≤⎪⎪=⎨⎪ >⎪⎩

10) Graph ( )f x .

a) b)

c) d)

10)

11) Determine the value of ( )4f .

a) 3 b) 6− c) 2 d) 1−

11)

12) Determine the value of ( )7f − .

a) 5 b) 9− c) 3 d) 5−

12)



13) Graph ( ) ( )22 3 2f x x=− − +

a)

b)

c) d)

13)

In exercises 14–15 use the points ( )2,3− and ( )6, 5− .

14) Find the distance between the points.

a) 4 5 b) 4 c) 2 13 d) 8 2

14)

15) Find the midpoint between the points.

a) ( )4, 4− b) ( )2, 1− c) ( )4, 4− d) ( )2,1−

15)

16) Given ( ) 27 4f x x= + and ( ) 8 ,g x x= − find ( )( )f g x and determine its domain.

a) 24 7x− ; ( ),−∞ ∞ b) 24 7x− ; ( ],8−∞

c) 60 7x− ; ( ],8−∞ d) 60 7x− ; [ )8,∞

16)

33



34

17) Find the coordinates of the x- and y-intercepts of 2 42y x x= − −

a) ( ) ( ) ( )42,0 , 0, 6 , 0,7− b) ( ) ( ) ( )42,0 , 0, 7 , 0,6−

c) ( ) ( ) ( )0, 42 , 7,0 , 6,0− − d) ( ) ( ) ( )0, 42 , 6,0 , 7,0− −

17)

18) Which of the following is not a transformation of the basic function in

( ) ( )212

3 1g x x= + −

a) vertical shift of 1 down b) vertical reflection

c) vertical stretch of 12

d) horizontal shift of 3 to the left

18)


a) [ ]7,2− b) [ ]2,7−

c) ( ] [ ), 7 2,−∞ − ∪ ∞ d) ( ] [ ), 2 7,−∞ − ∪ ∞

19)

20) Write the formula for the function graphed to

the right

a) ( ) 3 4 5f x x=− + +

b) ( ) 14 5

3f x x= − +

c) ( ) 2 4 5f x x=− − +

d) ( ) 3 4 5f x x=− − +

20)

21) A company charges $35 to design a custom coffee mug and $9 each to make them. Find

the function, ( )C x , that represents the cost to purchase x coffee mugs and determine

how many could be purchased with $250.

a) ( ) 35 9; 13 mugsC x x= + b) ( ) 35 9; 14 mugsC x x= +

c) ( ) 9 35; 23 mugsC x x= + d) ( ) 9 35; 24 mugsC x x= +

21)

22) Given ( ) 3 27f x x= − , find ( )1f x− .

a) ( )1 3 27f x x− = + b) ( )13

1

27f x

x− =

−

c) ( )1 3 27f x x− = + d) ( )1 3 27f x x− =− −

22)




23) Determine the domain of the function.

a) ( )3,− ∞ b) [ )3,− ∞

c) ( ),8−∞ d) ( ],8−∞

24) Determine the range of the function.

a) ( )3,− ∞ b) [ )3,− ∞

c) ( ),8−∞ d) ( ],8−∞

23) 24)


25) When is the graph increasing?

a) ( )2, 2− b) ( )6,9

c) ( ) ( ), 2 2,6−∞ − ∪ d) Never

26) When is the graph decreasing?

a) ( )2, 2− b) ( )6,9

c) ( ) ( ), 2 2,6−∞ − ∪ d) Never

27) When is the graph constant?

a) ( )2, 2− b) ( )6,9

c) ( ) ( ), 2 2,6−∞ − ∪ d) Never

25) 26) 27)

35



36

28) Graph ( ) 3 4f x x= − .

a)

b)

c) d)

28)


Chapter 1 Test Form F Name Ratti & McWaters, Precalculus Essentials


1) What are the coordinates of point A?

a) ( )2, 2− b) ( )2, 2−

c) ( )2, 2− − d) ( )2,2

2) What are the coordinates of point B?

a) ( )4,0− b) ( )4,0

c) ( )0, 4 d) ( )0, 4−

1) 2)

3) Find the average rate of change of ( ) 3 8f x x x= + as x changes from 2 to 1.a b=− =

a) 33− b) 1

3 c) 5− d) 11

3)


4) Passing through ( )5,4− with slope 3− .

a) 3 17y x=− + b) 3 1y x=− − c) 3 4y x=− + d) 3 11y x=− −

4)

5) Passing through ( )3, 2− − and ( )2,5 .

a) 7 395 5

y x=− + b) 7 115 5

y x= + c) 5 457 7

y x=− + d) 5 257 7

y x= −

5)

6) Perpendicular to 4 3 11x y− + = passing through ( )6,5 .

a) 3 194 2

y x=− + b) 3 14 2

y x= + c) 1314 2

y x=− + d) 714 2

y x= +

6)

7) Write the equation of the circle centered at ( )5,2− with a radius of 5.

a) ( ) ( )2 25 2 5x y− + + = b) ( ) ( )2 2

5 2 25x y− + + =

c) ( ) ( )2 25 2 5x y+ + − = d) ( ) ( )2 2

5 2 25x y+ + − =

7)

8) Determine the equation of the circle described by 2 26 8 56 0x x y y+ + − − = .

a) ( ) ( )2 26 8 56x y+ + − = b) ( ) ( )2 2

3 4 81x y+ + − =

c) ( ) ( )2 23 4 25x y+ + − = d) ( ) ( )2 2

3 4 56x y+ + − =

8)

37



38

9) Determine which symmetries the graph of 2 2 4x y y x− = possesses.

a) x-axis b) y-axis c) origin d) all

9)

In exercises 10–12, use ( )1 3

6 3

x if xf x

if x

⎧− − ≥⎪⎪=⎨⎪ <⎪⎩

10) Graph ( )f x .

a) b)

c) d)

10)


a) 6 b) 4− c) 2 d) 2−

11)


a) 9− b) 7 c) 6 d) 2

12)



13) Graph ( ) ( )212

3 5f x x= + −

a)

b)

c) d)

13)

In exercises 14–15, use the points ( )4, 4− and ( )8,10− .

14) Find the distance between the points.

a) 2 85 b) 2 13 c) 26 d) 2 10

14)

15) Find the midpoint between the points.

a) ( )2,3− b) ( )6, 7− c) ( )7,6− d) ( )2, 3−

15)

16) Given ( )2

2

3

2

xf x

x

−=

+and ( ) 3,g x x= + find ( )( )f g x and determine its domain.

a) 2

2

4 3

2

x

x

+

+; ( ),−∞ ∞ b)

2

2

4 3

2

x

x

+

+; [ )3,− ∞

c) 5

x

x+; ( ], 3−∞ − d)

5

x

x+; [ )3,− ∞

16)

39



40

17) Find the coordinates of the x- and y-intercepts of 3 9 216y x= +

a) ( ) ( )24,0 , 0,6 b) ( ) ( )24,0 , 0,6−

c) ( ) ( )0, 24 , 6,0 d) ( ) ( )0, 24 , 6,0−

17)

18) Which of the following is not a transformation of the basic function in

( ) ( )23 2 7g x x=− − +

a) vertical stretch of 13

b) vertical reflection

c) horizontal shift of 2 to the right d) vertical shift of 7 up

18)

19) Find the domain of ( ) 2 5 24f x x x= − − . Write your answer using interval notation.

a) [ ]8,3− b) [ ]3,8−

c) ( ] [ ), 8 3,−∞ − ∪ ∞ d) ( ] [ ), 3 8,−∞ − ∪ ∞

19)

20) Write the formula for the function graphed to

the right

a) ( ) 2 3 2f x x=− + −

b) ( ) 2 3 2f x x= + −

c) ( ) 13 2

2f x x= + −

d) ( ) 2 3 2f x x= − −

20)

21) A company charges $45 to design a custom coffee mug and $14 each to make them.

Find the function, ( )C x , that represents the cost to purchase x coffee mugs and

determine how many could be purchased with $350.

a) ( ) 45 14; 7 mugsC x x= + b) ( ) 45 14; 8 mugsC x x= +

c) ( ) 14 45; 22 mugsC x x= + d) ( ) 14 45; 21 mugsC x x= +

21)

22) Given ( ) 4

5f x

x=

−, find ( )1 .f x−

a) ( )1 5 4xf x

x− +

= b) ( )1 5

4

xf x− −

=

c) ( )1 4

5f x

x− =−

− d) ( )1 4

5f x

x− =

+

22)





a) ( ],6−∞ b) ( ),6−∞

c) [ )8,− ∞ d) ( )8,− ∞


a) ( ],6−∞ b) ( ),6−∞

c) [ )8,− ∞ d) ( )8,− ∞

23) 24)


25) When is the graph increasing?

a) ( ) ( ), 2 5,9−∞ − ∪ b) ( )2,5

c) ( )2, 2− d) Never

26) When is the graph decreasing?

a) ( ) ( ), 2 5,9−∞ − ∪ b) ( )2,5

c) ( )2, 2− d) Never

27) When is the graph constant?

a) ( ) ( ), 2 5,9−∞ − ∪ b) ( )2,5

c) ( )2, 2− d) Never

25) 26) 27)

41



42

28) Graph ( ) 31

4f x x= − .

a)

b)

c) d)

28)



1) For ( ) ( )( ) ( )4 63 27 2 5 16 5f x x x x x= − + + , determine: a) the real roots,

b) their multiplicity, and c) whether the graph crosses or touches the x-axis at each root. 1)

2) For the following polynomial use Descartes’s rule of signs to determine the

possible number of positive and negative rational roots.

5 4 3 23 5 15 4 12x x x x x− − + + − 2)

3) List all the possible rational roots of 3 22 3 29 60x x x− − + and factor the polynomial. 3)

4) Use the given roots to factor 5 4 3 22 9 9 3 7 6x x x x x+ + + + − .

, 2x i= − 4)

5) Find the equation in standard form of the quadratic function that passes through ( )1,27 with vertex at ( )3, 5− − . 5)

6) Sketch the graph of ( ) 3 22 11 12f x x x x= − − + .

State the x- and y-intercepts.

6)

7) Determine the end behavior for ( ) ( ) ( )3 52 1 3 .f x x x x=− − + 7)

8) Find the equation of the oblique asymptote for

( )3 2

2

2 9 10 29

3 10

x x xf x

x x

− − +=

− −

8)

9) Given ( ) 24 52 21f x x x=− + + , determine: a) if function has a maximum

or minimum value, b) where this value occurs, and c) what that value is. 9)

43



44

In exercises 10–11, graph the rational function. List all intercepts and asymptotes.

10) ( )2

2

2 5 3

25

x xf x

x

+ −=

−

10)

11) ( )2

3

2 15

xf x

x x

−=

− −

11)

12) The cost, in dollars, to produce x items is given by ( ) 20 400C x x= + and

the revenue for selling x items is given by ( ) 2500 10 .R x x x= − Find the

value of x that maximizes profit and state that maximum profit. 12)

13) The sum of two numbers is 90. Determine if the numbers have a maximum or minimum product and find that product.

13)

14) Use synthetic division to determine the quotient and remainder of 5 4 3 23 22 46 65 69 72

.5

x x x x x

x

− + − + −−

14)



1) For ( ) ( ) ( ) ( )532 25 3 2 9 4f x x x x x=− + + − , determine: a) the real roots,

b) their multiplicity, c) whether the graph crosses or touches the x-axis at each root, and d) the end behavior of the graph. 1)



5 4 3 23 5 15 4 12x x x x x+ − − + + 2)

3) List all the possible rational roots of 3 23 5 88 60x x x− − + and factor the polynomial. 3)

4) Use the given roots to factor 5 4 3 23 4 5 10 68 24x x x x x− − − − + .

2 ,3x i= 4)

5) Find the equation in standard form of the quadratic function that passes through ( )4, 5− − with vertex at ( )2,7− . 5)

6) Sketch the graph of ( ) 3 22 29 30f x x x x= + − − .


6)

7) Determine the end behavior for ( ) ( ) ( )6 34 7 .f x x x x= + − 7)


( )3 2

2

4 11 18 37

6

x x xf x

x x

− + + −=

− −

8)

9) Given ( ) 26 38 14f x x x= + − determine: a) if function has a maximum or

minimum value, b) where this value occurs, and c) what that value is. 9)

45



46


10) ( )2

2

9 3 2

16

x xf x

x

− −=

−

10)

11) ( )2

3

2 15

xf x

x x

+=

+ −

11)




13) The difference of two numbers is 110. Determine if the numbers have a maximum or minimum product and find that product.

13)


.4

x x x x x

x

+ + − + ++

14)



1) For ( ) ( )( ) ( )2 74 24 4 5 4 3f x x x x x= − + − , determine: a) the real roots,




5 4 3 27 15 5 16 12x x x x x− + − − + 2)

3) List all the possible rational roots of 3 22 54 72x x x− − − and factor the polynomial. 3)

4) Use the given roots to factor 5 4 3 25 12 6 6 11 6x x x x x− − − − + .

,3x i=− 4)

5) Find the equation in standard form of the quadratic function that passes through ( )4, 6− with vertex at ( )5, 8− . 5)

6) Sketch the graph of ( ) 3 23 22 24f x x x x= − − + .


6)

7) Determine the end behavior for ( ) ( ) ( )6 23 4 7 .f x x x x=− − + 7)


( )3 2

2

3 14 14 47

3 10

x x xf x

x x

− − +=

− −

8)

9) Given ( ) 24 70 91f x x x= + − determine: a) if function has a maximum or

minimum value, b) where this value occurs, and c) what that value is. 9)

47



48


10) ( )2

2

2 7 4

25

x xf x

x

− −=

−

10)

11) ( )2

2

20

xf x

x x

+=

− −

11)




13) The sum of two numbers is 70. Determine if the numbers have a maximum or minimum product and find that product.

13)


.3

x x x x x

x

− + − − +−

14)



1) For ( ) ( ) ( ) ( )34 523 5 2 1 6f x x x x x=− − + − , determine: a) the real roots,




5 4 3 29 20 12x x x x x− − + + + 2)

3) List all the possible rational roots of 3 23 28 52 48x x x− + + and factor the polynomial. 3)

4) Use the given roots to factor 5 4 3 24 21 30 60 56 96x x x x x− + − + + .

2 ,4x i=− 4)

5) Find the equation in standard form of the quadratic function that passes through ( )3,5 with vertex at ( )4,7 . 5)

6) Sketch the graph of ( ) 3 22 19 20f x x x x= − − +


6)

7) Determine the end behavior for ( ) ( ) ( )2 34 3 2 .f x x x x= − + 7)


( )3 2

2

2 81 177

2 35

x x xf x

x x

− + + −=

+ −

8)

9) Given ( ) 28 84 50f x x x=− + − determine: a) if function has a maximum

or minimum value, b) where this value occurs, and c) what that value is. 9)

49



50


10) ( )2

2

5 3 2

9

x xf x

x

+ −=

−

10)

11) ( )2

4

4 12

xf x

x x

+=

+ −

11)




13) The difference of two numbers is 120. Determine if the numbers have a maximum or minimum product and find that product.

13)


.5

x x x x x

x

+ − − + ++

14)



In exercises 1–2, use ( ) 5 4 3 23 5 27 32 12f x x x x x x= + − − − −

1) What are the possible number of negative rational roots?

a) 3,1 b) 4,2,0 c) 1 d) 2,0

1)

2) What are the possible number of positive rational roots?

a) 3,1 b) 4,2,0 c) 1 d) 2,0

2)

3) Determine the end behavior for ( ) ( )( )53 1 6 .f x x x x=− − +

a) as

as

y x

y x

⎧ →−∞ →−∞⎪⎪⎨⎪ →−∞ →∞⎪⎩ b)

as

as

y x

y x

⎧ →−∞ →−∞⎪⎪⎨⎪ →∞ →∞⎪⎩

c) as

as

y x

y x

⎧ →∞ →−∞⎪⎪⎨⎪ →∞ →∞⎪⎩ d)

as

as

y x

y x

⎧ →∞ →−∞⎪⎪⎨⎪ →−∞ →∞⎪⎩

3)

4) Which of the following is not a possible rational root of 3 25 41 54 72?x x x+ + −

a) 85

b) 53

c) 6 d) 35

−

4)

5) Use the given roots to factor 5 4 3 22 5 13 16 84 144;x x x x x− − + − + 2 ,4x i=−

a) ( )( )( )( )( )3 4 2 3 2 2x x x x i x i+ − − − +

b) ( )( )( )( )( )3 4 2 3 2 2x x x x i x i+ + + − +

c) ( )( )( )( )( )3 4 2 3 2 2x x x x x+ − − − +

d) ( )( )( )( )( )3 4 2 3 2 2x x x x x− + − − +

5)

6) For which root does the graph of ( ) ( ) ( ) ( )64 327 4 5 1 2f x x x x x= − + − touch the x-axis?

a) 0 b) 54

c) 2 d) i−

6)

7) Which root of ( )( ) ( )4 63 27 2 5 16 5x x x x− + + has multiplicity 3?

a) 52

b) 5− c) 0 d) none

7)

8) Which of the following is not the coordinate of an intercept of 3 22 43 40x x x− − − ?

a) ( )5,0− b) ( )8,0− c) ( )1,0− d) ( )0, 40−

8)

9) Determine the coordinates of the minimum of ( ) 210 22 40.f x x x= − +

a) ( )684115 5

,− b) ( )115

,40 c) ( )7631110 10

,− d) ( )2791110 10

,

9)

51



52

10) Determine the equation of the horizontal asymptote for ( )2

2

15 2

21 4

x xf x

x x

− −=

− −

a) 57

y = b) 2y =− c) 2y = d) 2y x=

10)

11) Sketch the graph of ( ) 3 22 43 40f x x x x= − − −

a) b)

c) d)

11)

12) Find the equation, in standard form, of the quadratic function that passes through

( )1,4− with the vertex at ( )3, 4 .− −

a) ( ) ( )22 3 4f x x=− + − b) ( ) ( )22 3 4f x x=− − −

c) ( ) ( )22 3 4f x x= − − d) ( ) ( )22 3 4f x x= + −

12)

13) Find the equation of the oblique asymptote for ( )3 2

2

3 17 31 24

5 14

x x xf x

x x

+ − −=

+ −.

a) 3y x= b) 3 17y x= + c) 3 2y x= + d) 3y =

13)



14) Graph ( )2

2

25

6

xf x

x x

−=

+ −.

a) b)

c) d)

14)

15) Use synthetic division to find the quotient and remainder of 4 3 23 4 2 30

.2

x x x

x

− + −+

a) 23 2 6x x+ + ; 18− b) 3 23 2 6 12x x x+ + + ; 6−

c) 23 10 22x x− + ; 74− d) 3 23 10 22 44x x x− + − ; 58

15)

16) The difference of two numbers is 80. Determine if the numbers have a maximum or

minimum product and find the product.

a) Maximum; 1600 b) Minimum; 1600 c) Maximum; 1600− d) Minimum; 1600−

16)

53



54

17) Graph ( )2

1

4 12

xf x

x x

+=

+ −.

a) b)

c) d)

17)

18) The cost, in dollars, to produce x items is given by ( ) 12 120C x x= + and the revenue

for selling x items is given by ( ) 2116 4 .R x x x= − Find the value of x that maximizes

profit and state that maximum profit.

a) 16;x = $1,144 b) 16;x = $904

c) 13;x = $796 d) 13;x = $556

18)



In exercises 1–2, use ( ) 5 4 3 25 3 17 28 12f x x x x x x= − + + − +

1) What are the possible number of negative rational roots?

a) 3,1 b) 4,2,0 c) 1 d) 2,0

1)

2) What are the possible number of positive rational roots?

a) 5,3,1 b) 4,2,0 c) 3,1 d) 2,0

2)

3) Determine the end behavior for ( ) ( ) ( )32 7 6 .f x x x x= − +

a) as

as

y x

y x

⎧ →−∞ →−∞⎪⎪⎨⎪ →−∞ →∞⎪⎩ b)

as

as

y x

y x

⎧ →−∞ →−∞⎪⎪⎨⎪ →∞ →∞⎪⎩

c) as

as

y x

y x

⎧ →∞ →−∞⎪⎪⎨⎪ →∞ →∞⎪⎩ d)

as

as

y x

y x

⎧ →∞ →−∞⎪⎪⎨⎪ →−∞ →∞⎪⎩

3)

4) Which of the following is not a possible rational root of 3 23 13 6 40?x x x+ − −

a) 35

b) 23

− c) 8− d) 53

4)

5) Use the given roots to factor 5 4 3 23 4 14 42 117 54;x x x x x− + − − − 3 , 1x i= −

a) ( )( )( )( )( )3 2 3 1 3 3x x x x i x i− + − − +

b) ( )( )( )( )( )3 2 3 1 3 3x x x x i x i+ − + − +

c) ( )( )( )( )( )3 2 3 1 3 3x x x x x− + − − +

d) ( )( )( )( )( )3 2 3 1 3 3x x x x x+ − + − +

5)

6) For which root does the graph of ( ) ( ) ( ) ( )24 65 23 3 5 4 5f x x x x x= + + + cross the

x-axis?

a) 0 b) 53

− c) 4− d) 2i

6)

7) Which root of ( ) ( )( )5 34 25 4 3 9 4x x x x+ + − has multiplicity 5?

a) 4 b) 34

− c) 0 d) none

7)

8) Which of the following is not the coordinate of an intercept of 3 2 26 24x x x− − − ?

a) ( )4,0 b) ( )1,0− c) ( )6,0 d) ( )0, 24−

8)

9) Determine the coordinates of the minimum of ( ) 26 15 13.f x x x= + +

a) ( )52

,13− b) ( )5 294 8

,− c) ( )52

,88 d) ( )5 3294 8

,

9)

55



56

10) Determine the equation of the horizontal asymptote for ( )2

2

20 7 3

12 4

x xf x

x x

− −=

− −.

a) 3y x= b) 3y = c) 3y =− d) 53

y =

10)

11) Sketch the graph of ( ) 3 23 22 24f x x x x= − − +

a) b)

c) d)

11)

12) Find the equation, in standard form, of the quadratic function that passes through ( )1, 3−

with the vertex at ( )2, 5− .

a) ( ) ( )22 2 5f x x=− + − b) ( ) ( )22 2 5f x x= − −

c) ( ) ( )22 2 5f x x=− − − d) ( ) ( )22 2 5f x x= + −

12)

13) Find the equation of the oblique asymptote for ( )3 2

2

3 4 50 29

2 15

x x xf x

x x

− − + −=

+ −.

a) 3y x=− b) 3 4y x= − c) 3y =− d) 3 2y x=− +

13)



14) Graph ( )2

2

16.

6

xf x

x x

−=

− −

a) b)

c) d)

14)

15) Use synthetic division to find the quotient and remainder of 4 32 5 7 10

.3

x x x

x

+ − −+

a) 3 22 3 16x x x− + − ; 38 b) 3 22 11 33 92x x x+ + + ; 266

c) 22 11 26x x+ + ; 68 d) 22 4x x− − ; 2

15)

16) The sum of two numbers is 60. Determine if the numbers have a maximum or minimum

product and find the product.

a) Maximum; 900 b) Minimum; 900 c) Maximum; 900− d) Minimum; 900−

16)

57



58

17) Graph ( )2

1.

12

xf x

x x

−=

+ −

a) b)

c) d)

17)

18) The cost, in dollars, to produce x items is given by ( ) 16 180C x x= + and the revenue

for selling x items is given by ( ) 2400 8 .R x x x= − Find the value of x that maximizes

profit and state that maximum profit.

a) 24;x = $4,788 b) 24;x = $4,428 c) 26;x = $5,588 d) 26;x = $5,228

18)



In exercises 1–6, solve the equation. Round your answer to three decimal places when necessary.

1) 3log (9 5 ) 4x− = 1)

2) ( )2 19 3 5 12

x− − = 2)

3) 2 3 54 8x x− += 3)

4) ( )log 2 7 3x+ =− 4)

5) ( ) ( )3 3log 2 4 2 log 3x x+ = + − 5)

6) ( ) ( ) ( )27 7 7log 3 5 log 4 log 2 30x x x+ + − = − 6)

7) Write the expression log 9 7 log 4log 5loga a a ax y z− + − in condensed

form. 7)

8) How long would it take money deposited in an account earning 3.2% per year, compounded quarterly, to double? 8)

9) For the given logarithmic function: a) sketch the graph, b) determine the

domain, c) determine the range d) find the equation of the asymptote.

( )2( ) log 4 3f x x=− + +

9)

10) How old is a fossil that has 20% of the original Carbon-14 remaining? Round to the nearest whole year. 10)

11) Write the expression ( )

3

2

3log

1a

y

x x− in expanded form.

11)

59



60

12) For the given exponential function, a) sketch the graph, b) determine the domain, c) determine the range d) find the equation of the asymptote.

( ) 1( ) 2 2

xf x

+=− −

12)

13) Use the change of base formula to find the value of 7log 19 . Round your

answer to three decimal places. 13)

14) The number of bacteria, ( )N t , in an experiment t hours after it begins is

given by ( )0.035

1000

1 49 tN t

e−=

+. When will there be 800 bacteria?

14)

15) Solve the inequality ( )4 3 7 15x + > 15)

16) Determine the domain of ( )5( ) 7 log 16 4 .f x x= − 16)




1) 4log (11 3 ) 2x− = 1)

2) ( )3 28 5 6 17

x− − = 2)

3) 3 2 327 81x x− += 3)

4) ( )ln 3 5 2x− =− 4)

5) ( ) ( )2 2log 2 5 3 log 7x x+ = + − 5)

6) ( ) ( ) ( )2log 2 3 log 4 logx x x x− + + = + 6)

7) Write the expression 6 log log17 8log 3logx z y− − + in condensed form. 7)

8) How long would it take money deposited in an account earning 4.1% per year, compounded monthly, to triple? 8)



( )3( ) log 6 4f x x= + −

9)



4

35

7log

3

x

y x+ in expanded form.

11)

61



62


2( ) 3 5xf x += −

12)




given by ( )0.035

2500

1 99 tN t

e−=


14)

15) Solve the inequality ( )2 6 10 16x + ≤ 15)

16) Determine the domain of ( )5( ) 7 log 2 18 .f x x= + 16)




1) 5log (15 4 ) 3x− = 1)

2) ( )3 54 5 16 5

x+ − =− 2)

3) 5 4 264 16x x− += 3)

4) ( )log 2 7 2x− =− 4)

5) ( ) ( )2 2log 3 4 4 log 7x x+ = + − 5)

6) ( ) ( ) ( )23 3 3log 2 log 2 5 log 32x x x− + + = + 6)

7) Write the expression 5ln 2 ln ln17 7 lnx y z− + + − in condensed form. 7)

8) How long would it take money deposited in an account earning 3.7% per

year, compounded monthly, to double? 8)

9) For the given logarithmic function: a) sketch the graph, b) determine the domain, c) determine the range d) find the equation of the asymptote.

( )2( ) log 5 4f x x=− + −

9)



5

34

ln11 4

xy

x− in expanded form.

11)

63



64


( ) 412

( ) 1x

f x−

= +

12)




given by ( )0.035

1800

1 24 tN t

e−=


14)

15) Solve the inequality ( )6 5 21 3x − ≥− 15)

16) Determine the domain of ( )( ) 10 ln 18 3 .f x x=− − 16)




1) 4log (17 3 ) 3x− = 1)

2) ( )5 29 2 11 5

x− − = 2)

3) 3 5 381 243x x+ −= 3)

4) ( )ln 3 4 2x+ =− 4)

5) ( ) ( )7 7log 3 5 2 log 6x x− = + − 5)

6) ( ) ( ) ( )23 3 3log 2 1 log 3 log 11x x x+ + − = + 6)

7) Write the expression log 13 6log 5log 4loga a a ay z x− + − in condensed

form. 7)

8) How long would it take money deposited in an account earning 4.2% per year, compounded quarterly, to triple? 8)



( )3( ) log 3 1f x x= + −

9)



7

3

5ln

2

x

x z+ in expanded form.

11)

65



66


( ) 213

( ) 1x

f x−

=− −

12)




given by ( )0.035

1700

1 169 tN t

e−=


14)

15) Solve the inequality ( )7 4 5 26x + < 15)

16) Determine the domain of ( )( ) 17 log 24 8 .f x x= − 16)



In exercises 1–6, solve the equation.

1) 2log (5 6 ) 4x− =

a) 116

x = b) 99956

x =− c) 116

x =− d) ∅

1)

2) ( )3 24 5 1 8

x+ + =

a) 4.622x = b) 0.450x =− c) 0.586x =− d) 0.551x =−

2)

3) 3 2 527 81x x− +=

a) 0.875x = b) 12x = c) 5.2x = d) ∅

3)

4) ( )log 3 8 3x− =−

a) 2.667x = b) 2.683x = c) 1.667x = d) 9.362x =

4)

5) ( ) ( )4 4log 3 1 2 log 2x x+ = + −

a) 3.421x = b) 0.5x =− c) 2.538x = d) ∅

5)

6) ( ) ( ) ( )ln 3 ln 2 ln 7 10x x x+ + − = +

a) 9

5x =− b) 2,8x =− c) 8x = d) ∅

6)

7) How many years would it take money deposited in an account earning 2.5% per year,

compounded monthly, to double?

a) 27.81 years b) 28.07 years c) 27.75 years d) 27.90 years

7)

8) The number of bacteria, ( )N t , in an experiment t hours after it begins is given by

( )0.035

500

1 4 tN t

e−=


a) 10.239t = hours b) 102.39t = hours c) 42.974t = hours d) 7.159t = hours

8)

9) Use the change of base formula to find the value of 6log 5 .

a) 0.778 b) 0.898 c) 1.79 d) 1.113

9)

10) Write the expression 2 ln 4ln ln12 5lny z x− − + in condensed form.

a) 5 2

4

12ln

x y

z

⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠ b)

5 2 4

ln12

x y z⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠ c)

5 2

4ln

12

x y

z

⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠ d)

4

5 2

12ln

z

x y

⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

10)

67



68

In exercises 11–14, use ( )2( ) log 1 2f x x= − + .

11) Sketch the graph of the function.

a) b)

c) d)

11)


a) ( ),−∞ ∞ b) ( ),6−∞ c) ( )1,− ∞ d) ( )1,∞

12)


a) ( ),6−∞ b) ( ),−∞ ∞ c) ( )1,∞ d) ( )1,− ∞

13)

14) Find the equation of the asymptote.

a) 6y = b) 1y =− c) 1x = d) 1x =−

14)

15) Solve the inequality ( )5 8 7 42x + >

a) 1.068x > b) 1.068x < c) 0.936x > d) 0.936x <

15)



In exercises 16–19, use ( ) 2( ) 4 1

xf x

+=− + .


a) b)

c) d)

16)


a) ( )2,− ∞ b) ( ),0−∞ c) ( ),−∞ ∞ d) ( )4,− ∞

17)


a) ( ),−∞ ∞ b) ( )4, ,− ∞ c) ( )1, ,∞ d) ( ),1−∞

18)


a) 0y = b) 0x = c) 1y = d) 1x =

19)

69



70


5

37

13log

6a

x

y x+ in expanded form.

a) ( )( )3 log 13 5log log 7 log 6a a a ax y x− + − − +

b) ( )( )13

log 13 5log log 7 log 6a a a ax y x+ − − +

c) ( )log 13 5log log 7 log 6a a a ax y x+ − − +

d) ( )( )13

log 7 log log 13 5log 6a a a ay z x+ − − +

20)

21) How old is a fossil that has 85% of the original Carbon-14 remaining?

a) 580 years old b) 6776 years old c) 1337 years old d) 15601 years old

21)

22) Determine the domain of ( )( ) 17 ln 21 3f x x=− −

a) [ )7,∞ b) ( ],7−∞ c) ( )7,∞ d) ( ),7−∞

22)



In exercises 1–6, solve the equation.

1) 3log (7 5 ) 2x− =

a) 25

x =− b) 25

x = c) 935

X =− d) ∅

1)

2) ( )3 27 3 5 6

x− − =

a) 0.188x = b) 0.804x = c) 929x = d) 0.590x =

2)

3) 4 2 525 125x x− +=

a) 0.2x =− b) 3.8x =− c) 5.75x =− d) 1.75x =−

3)

4) ( )ln 4 7 3x+ =−

a) 1.738x = b) 3.271x = c) 1.738x =− d) 1x =−

4)

5) ( ) ( )5 5log 5 3 3 log 4x x+ = + −

a) 1x =− b) 4.192x = c) 24.4x = d) ∅

5)

6) ( ) ( ) ( )log 4 log 5 log 3 1x x x+ + − = +

a) 2x =− b) 7x = c) 3,7x =− d) ∅

6)

7) How long would it take money deposited in an account earning 2.2% per year,

compounded quarterly, to triple?

a) 50.48 years b) 50.07 years c) 49.98 years d) 50.21 years

7)

8) The number of bacteria, ( )N t , in an experiment t hours after it begins is given by

( )0.035

3000

1 74 tN t

e−=


a) 118.15t = hours b) 16.896t = hours

c) 168.96t = hours d) 54.530t = hours

8)

9) Use the change of base formula to find the value of 6log 18 .

a) 0.4771 b) 0.620 c) 0.977 d) 1.613

9)

10) Write the expression log 21 4log 2log 7 logy x z− − + in condensed form.

a) 2 4 7

log21

x y z⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠ b)

2 4

7log

21

x y

z

⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠ c)

7

2 4

21log

z

x y

⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠ d)

2 4

7

21log

x y

z

⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

10)

71



72

In exercises 11–14, use ( )3( ) log 2 1f x x=− + − .


a) b)

c) d)

11)


a) ( ),−∞ ∞ b) ( )2,∞ c) ( )2,− ∞ d) ( )1,− ∞

12)


a) ( ), 2−∞ b) ( )4,− ∞ c) ( ),−∞ ∞ d) ( )2,− ∞

13)


a) 2x = b) 2x =− c) 2y = d) 4y =−

14)

15) Solve the inequality ( )4 7 7 13x − <

a) 0.827x > b) 0.827x < c) 1.210x > d) 1.210x <

15)



In exercises 16–19, use ( ) 114

( ) 3x

f x−

=− + .


a) b)

c) d)

16)


a) ( ),1−∞ b) ( )1,− ∞ c) ( ),−∞ ∞ d) ( ),3−∞

17)


a) ( ),−∞ ∞ b) ( )1,− ∞ c) ( )3,∞ d) ( ),3−∞

18)


a) 3x = b) 3y = c) 1x =− d) 1y =−

19)

73



74


7

2log

5 4

x y

x− in expanded form.

a) ( )( )2 7 log log log 5 2log 4a a a ax y x− + − − −

b) ( )( )12

7 log log log 5 2log 4a a a ax y x+ − − −

c) ( )7 log log log 5 2log 4a a a ax y x+ − − −

d) ( )( )12

log 5 2log 4 7 log loga a a ax x y+ − − −

20)

21) How old is a fossil that has 73% of the original Carbon-14 remaining?

a) 10768 years old b) 2588 years old c) 5249 years old d) 1124 years old

21)

22) Determine the domain of ( )( ) 15log 3 24f x x= −

a) ( )8,∞ b) [ )8,∞ c) [ )8,− ∞ d) ( )8,− ∞

22)



1) Find the exact value, in radians, of θ if 3

tan3

θ =− and θ lies in

quadrant IV. 1)

2) Convert 630 to radians. Write your answer as an exact expression in terms of .π 2)

3) Convert 3

5

π to degrees.

3)

4) Given 24

sin25

θ =− and sec 0θ > , find tanθ and determine in which

quadrant θ lies. 4)

5) Find the exact value of cot θ if 36

sin85

θ =− and θ lies in quadrant III. 5)

6) Graph one cycle of ( ) 3sin 2 2.3

πf x x

⎛ ⎞⎟⎜=− − −⎟⎜ ⎟⎜⎝ ⎠

6)

7) How far would a wheel with a diameter of 22 inches roll if it rotates

through an angle of 620 ? Round your answer to the nearest hundredth and use 3.14159.π = 7)

8) ( )5,7P − is a point on the terminal side of the angle .θ Find the exact

values of the six trigonometric functions of .θ 8)

9) Find the amplitude, range, period, and phase shift of

( ) 4cos 5 2.4

πf x x

⎛ ⎞⎟⎜= − +⎟⎜ ⎟⎜⎝ ⎠

9)

75



76

10) Find the period and phase shift for ( ) tan .2 8

x πf x

⎛ ⎞⎟⎜= − ⎟⎜ ⎟⎜⎝ ⎠

10)

11) Find the exact value of 1 1tan sin .

4−⎛ ⎞⎛ ⎞⎟⎜ ⎟⎜ ⎟− ⎟⎜ ⎜ ⎟⎟⎜ ⎜ ⎟⎜ ⎝ ⎠⎝ ⎠

11)

12) Find the exact value of 1 11sin sin .

3

π− ⎛ ⎞⎛ ⎞⎟⎜ ⎟⎜ ⎟⎟⎜ ⎜ ⎟⎟⎜ ⎜ ⎟⎜ ⎝ ⎠⎝ ⎠

12)

13) Graph one cycle of ( ) 2sec 1.6

πf x x

⎛ ⎞⎟⎜=− − +⎟⎜ ⎟⎜⎝ ⎠

13)

14) Simplify sec csc

tan cot

x x

x x

++

. 14)

15) Verify the identity 2cot1 sin .

tan cot

θ θθ θ

= −+

15)

16) Determine if the graph of ( )sin tany π x x= − + has symmetry with

respect to the x-axis, y-axis, or origin. 16)

17) Use a sum or difference formula to find the exact value of ( )tan 15 . 17)

18) Let 7

sin25

u =− and 12

cos ,13

v =− with 3

2

ππ u< < and .2

πv π< < Find

the exact value of ( )sin .u v− 18)

19) Given that 41

csc9

θ =− where 270 360θ< < , find the exact value of

( )cos 2 .θ 19)



20) Solve the right triangle ABC , 90 ,C = if 10.3b = and 22 .A= Round your answers to one decimal place. 20)

21) The angle of elevation to the top of a radio tower from a point on the

ground 120 feet from its base is 37 . How tall is the tower? Round your answer to one decimal place. 21)

22) Safety requirements at a painting company require ladders to make at most

a 77 angle of elevation with respect to the ground. What is the highest point you could reach on the side of a building with a 20 foot ladder? 22)

23) Find the values of A and ,B in degrees, in the triangle ABC , 90 ,C = if 8a = and 3.b = Round your answers to one decimal place. 23)

77



78


sin2

θ =− and θ lies in quadrant

IV. 1)


3) Convert 4

3

π to degrees.

3)

4) Given 37

csc12

θ =− and cos 0θ> , find cot θ and determine in which


5) Find the exact value of cosθ if 15

cot112

θ =− and θ lies in quadrant II. 5)

6) Graph one cycle of ( ) 2cos3 2.3

πf x x

⎛ ⎞⎟⎜= + −⎟⎜ ⎟⎜⎝ ⎠

6)



8) ( )5, 6P − is a point on the terminal side of the angle .θ Find the exact



( ) 6sin 7 2.5

πf x x

⎛ ⎞⎟⎜=− − +⎟⎜ ⎟⎜⎝ ⎠

9)



10) Find the period and phase shift for ( ) cot .3 9

x πf x

⎛ ⎞⎟⎜= + ⎟⎜ ⎟⎜⎝ ⎠

10)

11) Find the exact value of 1 3cos tan .

7−⎛ ⎞⎛ ⎞⎟⎜ ⎟⎜ ⎟− ⎟⎜ ⎜ ⎟⎟⎜ ⎜ ⎟⎜ ⎝ ⎠⎝ ⎠

11)

12) Find the exact value of 1 13tan tan .

5

π− ⎛ ⎞⎛ ⎞⎟⎜ ⎟⎜ ⎟− ⎟⎜ ⎜ ⎟⎟⎜ ⎜ ⎟⎜ ⎝ ⎠⎝ ⎠

12)

13) Graph one cycle of ( ) 2csc 2.6

πf x x

⎛ ⎞⎟⎜= + −⎟⎜ ⎟⎜⎝ ⎠

13)


tan cot

x x

x x

−+

. 14)

15) Verify the identity 2tan1 cos .

tan cot

θ θθ θ

= −+

15)

16) Determine if the graph of ( )cos secy π x x= − − has symmetry with


17) Use a sum or difference formula to find the exact value of ( )cos 15 . 17)

18) Let 24

cos25

u =− and 5

sin ,13

v = with 3

2

ππ u< < and .2

πv π< < Find

the exact value of ( )cos .u v− 18)

19) Given that 61

sec11


( )tan 2 .θ 19)

79



80

20) Solve the right triangle ABC , 90 ,C = if 12.2a = and 43 .B = Round your answers to one decimal place. 20)

21) The angle of elevation to the top of a 300 foot radio tower from a point on

the ground is 42 . How far from the tower is the point on the ground? Round your answer to one decimal place. 21)


a 65 angle of elevation with respect to the ground. How close to the side of a building could the bottom of a 30 foot ladder be placed? 22)

23) Find the values of A and ,B in degrees, in the triangle ABC , 90 ,C = if 11a = and 14.c = Round your answers to one decimal place. 23)




cos2

θ =− and θ lies in

quadrant II. 1)


3) Convert 2

5

π to degrees.

3)

4) Given 28

sin53

θ =− and sec 0θ < , find tanθ and determine in which



csc44

θ =− and θ lies in quadrant IV. 5)


πf x x

⎛ ⎞⎟⎜=− + +⎟⎜ ⎟⎜⎝ ⎠

6)



8) ( )3, 7P − − is a point on the terminal side of the angle .θ Find the exact



( ) 3cos 6 2.3

πf x x

⎛ ⎞⎟⎜= − −⎟⎜ ⎟⎜⎝ ⎠

9)

81



82


x πf x

⎛ ⎞⎟⎜= − ⎟⎜ ⎟⎜⎝ ⎠

10)

11) Find the exact value of 1 2sin cos .

5−⎛ ⎞⎛ ⎞⎟⎜ ⎟⎜ ⎟− ⎟⎜ ⎜ ⎟⎟⎜ ⎜ ⎟⎜ ⎝ ⎠⎝ ⎠

11)


6

π− ⎛ ⎞⎛ ⎞⎟⎜ ⎟⎜ ⎟⎟⎜ ⎜ ⎟⎟⎜ ⎜ ⎟⎜ ⎝ ⎠⎝ ⎠

12)


πf x x

⎛ ⎞⎟⎜= + +⎟⎜ ⎟⎜⎝ ⎠

13)


tan cot

x x

x x

+−

. 14)

15) Verify the identity ( )

sec sin.

tan cot cos 2

θ θθ θ θ

=−−

15)

16) Determine if the graph of ( )sin cscy π x x= + + has symmetry with


17) Use a sum or difference formula to find the exact value of ( )sin 75 . 17)

18) Let 8

sin17

u = and 12

cos ,13

v = with 2

πu π< < and

32 .

2

πv π< < Find

the exact value of ( )sin .u v+ 18)

19) Given that 35

cot12


( )sin 2 .θ 19)



20) Solve the right triangle ABC , 90 ,C = if 9.7c = and 51 .A= Round your answers to one decimal place. 20)

21) The angle of elevation to the top of a radio tower from a point on the

ground 200 feet from the base is 43 . How tall is the tower? Round your answer to one decimal place. 21)


a 71 angle of elevation with respect to the ground. What is the highest point you could reach on the side of a building with a 25 foot ladder? 22)

23) Find the values of A and ,B in degrees, in the triangle ABC , 90 ,C = if 7b = and 15.c = Round your answers to one decimal place. 23)

83



84

1) Find the exact value, in radians, of θ if tan 3θ = and θ lies in quadrant III. 1)


3) Convert 7

5

π to degrees.

3)

4) Given 61

csc60

θ =− and cos 0θ> , find cot θ and determine in which


5) Find the exact value of cscθ if 88

tan105

θ =− and θ lies in quadrant II. 5)

6) Graph one cycle of ( ) 3cos 2 1.6

πf x x

⎛ ⎞⎟⎜=− − −⎟⎜ ⎟⎜⎝ ⎠

6)



8) ( )8,3P − is a point on the terminal side of the angle .θ Find the exact



( ) 7sin 4 5.2

πf x x

⎛ ⎞⎟⎜=− + −⎟⎜ ⎟⎜⎝ ⎠

9)




x πf x

⎛ ⎞⎟⎜= + ⎟⎜ ⎟⎜⎝ ⎠

10)

11) Find the exact value of 1 3cos sin .

8−⎛ ⎞⎛ ⎞⎟⎜ ⎟⎜ ⎟− ⎟⎜ ⎜ ⎟⎟⎜ ⎜ ⎟⎜ ⎝ ⎠⎝ ⎠

11)

12) Find the exact value of 1 10cos cos .

3

π− ⎛ ⎞⎛ ⎞⎟⎜ ⎟⎜ ⎟− ⎟⎜ ⎜ ⎟⎟⎜ ⎜ ⎟⎜ ⎝ ⎠⎝ ⎠

12)


πf x x

⎛ ⎞⎟⎜=− − −⎟⎜ ⎟⎜⎝ ⎠

13)


tan cot

x x

x x

−−

. 14)

15) Verify the identity ( )

csc cos.

tan cot cos 2

θ θθ θ θ

=−−

15)

16) Determine if the graph of ( )cos secy π x x= + − has symmetry with


17) Use a sum or difference formula to find the exact value of ( )tan 75 . 17)

18) Let 8

sin17

u =− and 12

cos ,13

v = with 3

2

ππ u< < and 3

2 .2

πv π< <

Find the exact value of ( )cos .u v+ 18)

19) Given that 65

csc16


( )tan 2 .θ 19)

85



86

20) Solve the right triangle ABC , 90 ,C = if 8.3a = and 36 .B = Round your answers to one decimal place. 20)

21) The angle of elevation to the top of a 400 foot radio tower from a point on

the ground is 53 . How far from the tower is the point on the ground? Round your answer to one decimal place. 21)


a 69 angle of elevation with respect to the ground. How close to the side of a building could the bottom of a 35 foot ladder be placed? 22)

23) Find the values of A and ,B in degrees, in the triangle ABC , 90 ,C = if 7a = and 18.b = Round your answers to one decimal place. 23)




cos2

θ =− and θ lies in quadrant III.

a) 4

3

π b)

5

4

π c)

5

6

π d)

7

6

π

1)

2) Convert 48 to radians.

a) 8

15

π b)

4

15

π c)

2

15

π d)

15

π

2)

3) Convert 3

4

π to degrees.

a) 135 b) 180 c) 225 d) 270

3)

4) Given 21

sin29

θ = and sec 0θ < , find tanθ and determine in which quadrant θ lies.

a) 21

tan20

θ =− ; quadrant IV b) 21

tan20

θ =− ; quadrant II

c) 20

tan21

θ =− ; quadrant IV d) 20

tan21

θ =− ; quadrant II

4)

5) Find the exact value of 1 5sec sin .

8−⎛ ⎞⎛ ⎞⎟⎜ ⎟⎜ ⎟⎟⎜ ⎜ ⎟⎟⎜ ⎜ ⎟⎜ ⎝ ⎠⎝ ⎠

a) 39

8 b)

8 39

39 c)

8 89

89 d)

89

8

5)


sin101

θ = and θ lies in quadrant II.

a) 10601

20− b)

20 10601

10601− c)

99

20− d)

20

99−

6)

7) How far would a wheel with a diameter of 28 inches roll if it rotates through an angle of

580 ?

a) 53.756 inches b) 121.475 inches c) 141.721 inches d) 283.441 inches

7)


3

π− ⎛ ⎞⎛ ⎞⎟⎜ ⎟⎜ ⎟− ⎟⎜ ⎜ ⎟⎟⎜ ⎜ ⎟⎜ ⎝ ⎠⎝ ⎠

a) 3

π b)

2

3

π c)

3

π− d)

7

3

π−

8)

87



88

9) ( )6,5P − is a point on the terminal side of the angle .θ Find the exact values of cot θ

and csc .θ

a) 5

cot6

θ =− ; 61

csc5

θ = b) 6

cot5

θ =− ; 61

csc5

θ =

c) 5

cot6

θ =− ; 61

csc6

θ =− d) 6

cot5

θ =− ; 61

csc6

θ =−

9)


πf x x

⎛ ⎞⎟⎜= − +⎟⎜ ⎟⎜⎝ ⎠

a) b)

c) d)

10)

11) Find the period and phase shift of ( ) ( )7cos 6 3 5f x x π=− − + .

a) Period: 6

π; Phase Shift:

2

π b) Period:

6

π; Phase Shift: 3π

c) Period: 3

π; Phase Shift:

2

π d) Period:

3

π; Phase Shift: 3π

11)




πf x x

⎛ ⎞⎟⎜=− + +⎟⎜ ⎟⎜⎝ ⎠

a) b)

c) d)

12)


x πf x

⎛ ⎞⎟⎜= − ⎟⎜ ⎟⎜⎝ ⎠

a) Period: 3

π; Phase Shift:

3

π b) Period: 3π ; Phase Shift:

3

π

c) Period: 3

π; Phase Shift:

9

π d) Period: 3π ; Phase Shift:

9

π

13)

14) Simplify tan cot

.sec csc

x x

x x

++

a) 1

sin cosx x+ b)

1

sin cosx x−

c) sin cosx x+ d) sin cosx x−

14)

89



90

15) Which of the following expressions completes the identity cos

tan cot

θθ θ

=+

?

a) 2cos sinθ θ b) 2sin cosθ θ c) 2

sin

1 sin

θθ+

d) 2

cos

1 cos

θθ+

15)

16) Which symmetry does the graph of ( )2sec csc πy x x= + − have?

a) x-axis b) y-axis c) origin d) none

16)

17) Use a sum or difference formula to find the exact value of ( )cos 75 .

a) 2 6

4

− b)

6 2

4

+− c)

6 2

4

− d)

6 2

4

+

17)

18) Let 8

sin17

u = and 24

cos ,25

v =− with 2

πu π< < and

3.

2

ππ v< < Find the exact

value of ( )cos .u v−

a) 297

425− b)

87

425− c)

304

425 d)

416

425

18)

19) Given that 20

cot21

θ =− and θ lies in quadrant IV, find the exact value of ( )sin 2 .θ

a) 840

841 b)

840

841− c)

41

841 d)

41

841−

19)

20) Find c in the right triangle ,ABC 90 ,C = if 12.3b = and 53 .A=

a) 20.4c = b) 15.4c = c) 9.8c = d) 7.4a =

20)

21) The angle of elevation to the top of a radio tower from a point on the ground 80 feet from

its base is 62 . How tall is the tower?

a) 150.5 feet b) 70.6 feet c) 70.6 feet d) 37.6 feet

21)

22) Safety requirements at a painting company require ladders to make at most a 73 angle of elevation with respect to the ground. What is the highest point you could reach on the side of a building with a 15 foot ladder?


22)

23) Find A in the right triangle ,ABC 90 ,C = if 8a = and 14.c =

a) 29.7A= b) 47.5A= c) 55.2A= d) 34.8A=

23)




sin2

θ =− and θ lies in quadrant IV.

a) 7

6

π b)

11

6

π c)

5

3

π d)

4

3

π

1)

2) Convert 252 to radians.

a) 14

5

π b)

11

5

π c)

9

5

π d)

7

5

π

2)

3) Convert 5

4

π to degrees.

a) 135 b) 180 c) 225 d) 270

3)

4) Given 53

csc45

θ = and cos 0θ < , find cot θ and determine in which quadrant θ lies.

a) 28

cot45

θ =− ; quadrant II b) 28

cot45

θ =− ; quadrant IV

c) 45

cot28

θ =− ; quadrant II d) 45

cot28


4)

5) Find the exact value of 1 11csc cot .

5−⎛ ⎞⎛ ⎞⎟⎜ ⎟⎜ ⎟⎟⎜ ⎜ ⎟⎟⎜ ⎜ ⎟⎜ ⎝ ⎠⎝ ⎠

a) 11 146

146 b)

146

11 c)

5 146

146 d)

146

5

5)

6) Find the exact value of tanθ if 73

sec55

θ =− and θ lies in quadrant III.

a) 5329

55 b)

55 5329

5329 c)

55

48 d)

48

55

6)

7) How far would a wheel with a diameter of 34 inches roll if it rotates through an angle of

510 ?

a) 302.641 inches b) 151.320 inches c) 75.660 inches d) 44.506 inches

7)

8) Find the exact value of 1 14cos cos .

3

π− ⎛ ⎞⎛ ⎞⎟⎜ ⎟⎜ ⎟⎟⎜ ⎜ ⎟⎟⎜ ⎜ ⎟⎜ ⎝ ⎠⎝ ⎠

a) 3

π b)

2

3

π c)

4

3

π d)

8

3

π

8)

91



92

9) ( )7, 4P − is a point on the terminal side of the angle .θ Find the exact values of cot θ

and sec .θ

a) 7

cot4

θ =− ; 65

csc4

θ =− b) 7

cot4

θ =− ; 65

csc7

θ =−

c) 4

cot7

θ =− ; 65

csc4

θ =− d) 4

cot7

θ =− ; 65

csc7

θ =−

9)

10) Graph one cycle of ( ) 3cos 2 2.4

πf x x

⎛ ⎞⎟⎜= + +⎟⎜ ⎟⎜⎝ ⎠

a) b)

c) d)

10)

11) Find the period and phase shift of ( ) ( )8sin 8 5f x x π=− + +

a) Period: 8

π; Phase Shift: π− b) Period:

4

π; Phase Shift:

8

π−

c) Period: 8

π; Phase Shift:

8

π− d) Period:

4

π; Phase Shift: π−

11)




πf x x

⎛ ⎞⎟⎜=− − −⎟⎜ ⎟⎜⎝ ⎠

a) b)

c) d)

12)


x πf x

⎛ ⎞⎟⎜= + ⎟⎜ ⎟⎜⎝ ⎠

a) Period: 2

π; Phase Shift:

4

π− b) Period: 2π ; Phase Shift:

4

π−

c) Period: 2

π; Phase Shift:

2

π− d) Period: 2π ; Phase Shift:

2

π−

13)

14) Simplify tan cot

.sec csc

x x

x x

+−

a) sin cosx x− b) sin cosx x+

c) 1

sin cosx x+ d)

1

sin cosx x−

14)

93



94

15) Which of the following expressions completes the identity sin

tan cot

θθ θ

=+

?

a) 2

sin

1 sin

θθ+

b) 2

cos

1 cos

θθ+

c) 2cos sinθ θ d) 2sin cosθ θ

15)

16) Which symmetry does the graph of ( )sec tany π x x= + + have?

a) x-axis b) y-axis c) origin d) none

16)

17) Use a sum or difference formula to find the exact value of ( )sin 15 .

a) 2 6

4

− b)

6 2

4

+− c)

6 2

4

+ d)

6 2

4

−

17)

18) Let 8

sin17

u =− and 24

cos ,25

v =− with 3

22

πu π< < and

3.

2

ππ v< < Find the exact

value of ( )sin .u v−

a) 416

425− b)

304

425− c)

87

425 d)

297

425

18)

19) Given that 65

csc56

θ = and θ lies in quadrant II, find the exact value of ( )cos 2 .θ

a) 3696

4225− b)

3696

4225 c)

2047

4225− d)

2047

4225

19)

20) Find c in the right triangle ,ABC 90 ,C = if 9.4b = and 62 .B =

a) 8.3c = b) 4.4c = c) 10.6c = d) 20.0c =

20)

21) The angle of elevation to the top of a 200 foot radio tower from a point on the ground is

27 . How far from the tower is the point on the ground?


21)

22) Safety requirements at a painting company require ladders to make at most a 75 angle of elevation with respect to the ground. How close to the side of a building could the bottom of a 40 foot ladder be placed?


22)

23) Find A in the right triangle ,ABC 90 ,C = if 12b = and 23.c =

a) 58.6A= b) 31.4A= c) 27.6A= d) 44.1A=

23)



1) Solve the triangle ABC if 7.7a = , 10.2b = , and 33 .A= Round your answers to one decimal place. 1)

2) Solve the triangle ABC if 47A= , 17b = , and 62 .C = Round your answers to one decimal place. 2)

3) A welder is making a triangular wire frame with sides of length 5 in, 11 in,

and 13 in .What is the angle between the shortest two sides? Round your answers to the nearest tenth of a degree. 3)

4) Find the polar coordinates ( ),r θ for the point P with rectangular

coordinates ( )5,7 ,− with 0r > and 0 360 .θ≤ < Round θ to the

nearest tenth of a degree. 4)

5) Find angle A in triangle ABC if 22a = , 27b = , and 51.c = Round your answers to one decimal place. 5)

6) Two charter boats are sailing towards an island. Initially, both boats are 100

miles apart on an east-west line .The first boat sails at a bearing of S 13 E

and the second sails at a bearing of S 53 W. How far does the boat farthest from the island have to sail? Round your answer to one decimal place. 6)

7) Find the rectangular coordinates ( ),x y for the point P with polar

coordinates 7

7, .6

π⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜⎝ ⎠

7)

8) Convert the polar equation ( )2 csc 2r θ= to rectangular form. 8)

9) Eliminate the parameter to obtain a Cartesian equation of the curve for

2 2x t= − , 28 5y t= − , 7 3.t− ≤ ≤ 9)

10) A triangular flower garden has sides of length 6 feet, 9 feet, and 11 feet. What is the area of the garden? 10)

11) Find the area of a triangle where 11,a = 17,b = and 43 .C = 11)

95



96

12) Graph 2 3, 5 , 2 6.x t y t t= − = − − < ≤

12)




2) Solve the triangle ABC if 16c = , 75B = , and 42 .A= Round your answers to one decimal place. 2)

3) A welder is making a triangular wire frame with sides of length 8 m, 7 m,

and 11 m .What is the angle between the longest two sides? Round your answers to the nearest tenth of a degree. 3)


coordinates ( )8, 3 ,− with 0r > and 0 360 .θ≤ < Round θ to the


5) Find angle B in triangle ABC if 37a = , 63b = , and 24.c = Round your answers to one decimal place. 5)

6) Two charter boats are sailing towards an island. Initially, both boats are 85

miles apart on a north-south line .The first boat sails at a bearing of

S 39 E and the second sails at a bearing of N 69 E. How far does the boat closet to the island have to sail? Round your answer to one decimal place. 6)


coordinates ( )7, 135 .− 7)

8) Convert the polar equation ( )2 sec 2r θ= to rectangular form. 8)


39x t= − , 23

ty = − , 6 12.t− ≤ ≤

9)



97



98

12) Graph 3 2, 7 2 , 1 2.x t y t t= + = − − < ≤

12)




2) Solve the triangle ABC if 10,c = 53 ,A= and 57 .B = Round your answers to one decimal place. 2)

3) A welder is making a triangular wire frame with sides of length 7 ft, 9 ft,

and 12 ft .What is the angle between the shortest two sides? Round your answer to the nearest tenth of a degree 3)


coordinates ( )7, 4 ,− − with 0r > and 0 360 .θ≤ < Round θ to the


5) Find angle C in triangle ABC if 118,a = 76,b = and 40.c = Round your answers to one decimal place. 5)

6) Two charter boats are sailing towards an island .Initially, both boats are 72

miles apart on an east-west line .If the first boat sails at a bearing of

N 43 E and the second sails at a bearing of N 28 W. How far does the boat farthest from the island have to sail? Round your answer to one decimal place. 6)


coordinates 5

9, .3

π⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜⎝ ⎠

7)

8) Convert the polar equation 4cos 6sinr θ θ= + to rectangular form. 8)


14

tx = + , 22 7y t= + , 4 8.t− ≤ ≤

9)



99



100

12) Graph 3 1, 4 2 , 2 3.x t y t t= + = − − < ≤

12)




2) Solve the triangle ABC if 24,b = 28A= , and 78 .C = Round your answers to one decimal place. 2)

3) A welder is making a triangular wire frame with sides of length 5 cm, 13

cm, and 14 cm .What is the angle between the longest two sides? Round your answer to the nearest tenth of a degree. 3)


coordinates ( )6,5 ,− with 0r > and 0 360 .θ≤ < Round θ to the


5) Find angle C in triangle ABC if 78,a = 23,b = and 54.c = Round your answers to one decimal place. 5)

6) Two charter boats are sailing towards an island .Initially, both boats are 100

miles apart on a north-south line .If the first boat sails at a bearing of S

47 W and the second sails at a bearing of N 63 W. How far does the boat closest to the island have to sail? Round your answer to one decimal place. 6)


coordinates ( )13,225 . 7)

8) Convert the polar equation 10cos 4sinr θ θ=− − to rectangular form. 8)


3 8 40x t= + , 52

ty = + , 13 22.t− ≤ ≤ .

9)



101



102

12) Graph 2 1, 2 3 , 2 4.x t y t t= + = − − ≤ <

12)



1) Which of the following is a possible value of triangle ABC if 9.1a = , 11.3b = , and

47 .A=

a) 4.1c = b) 11.5c = c) 64.9B = d) 113.7B =

1)

2) Which of the following is a value from the triangle ABC if 56 ,A= 77 ,B = and 11?c =

a) 14.7a = b) 12.5a = c) 8.3b = d) 9.4a =

2)

3) A welder is making a triangular wire frame with sides of length 7 ft, 4 ft, and 9 ft. What

is the angle between the longest two sides?

a) 25.2 b) 48.2 c) 63.4 d) 106.6

3)

4) Find the polar coordinates ( ),r θ for the point P with rectangular coordinates ( )7,4 ,−

with 0r > and 0 360 .θ≤ <

a) ( )65,150.3 b) ( )65,330.3 c) ( )33,150.3 d) ( )33,330.3

4)

5) Which of the following is a possible angle of triangle ABC if 25,a = 45,b = and

17?c =

a) 28.8A= b) 119.8B = c) 31.4C = d) none of these

5)

6) Two charter boats are sailing towards an island. Initially, both boats are 80 miles apart on

an east-west line. If the first boat sails at a bearing of S 42 E and the second sails at a

bearing of S 57 W, how far does the boat closest to the island have to sail?

a) 67.9 miles b) 54.2 miles c) 44.1 miles d) 60.2 miles

6)

7) Find the rectangular coordinates ( ),x y for the point P with polar coordinates 5, .6

π⎛ ⎞⎟⎜ − ⎟⎜ ⎟⎜⎝ ⎠

a) 5 5 3

,2 2

⎛ ⎞⎟⎜ ⎟⎜− ⎟⎜ ⎟⎟⎜⎝ ⎠ b)

5 5 3,

2 2

⎛ ⎞⎟⎜ ⎟⎜ − ⎟⎜ ⎟⎟⎜⎝ ⎠ c)

5 3 5,

2 2

⎛ ⎞⎟⎜ ⎟⎜− ⎟⎜ ⎟⎟⎜⎝ ⎠ d)

5 3 5,

2 2

⎛ ⎞⎟⎜ ⎟⎜ − ⎟⎜ ⎟⎟⎜⎝ ⎠

7)

8) Convert the polar equation 8sinr θ=− to rectangular form.

a) ( )2 24 16x y+ + = b) ( )2 24 16x y− + =

c) ( )22 4 16x y+ + = d) ( )22 4 16x y+ − =

8)

9) A triangular flower garden has sides of length 5 feet, 8 feet, and 7 feet. What is the area

of the garden?

a) 52.92 ft2 b) 17.32 ft2 c) 74.83 ft2 d) 16.73 ft2

9)

103



104


13

tx = − , 2 2y t t=− + , 3 6.t− ≤ ≤

a) 29 12 3;y x x=− − − 2 1x− ≤ ≤

b) 29 24 15;y x x= + + 2 1x− ≤ ≤

c) 29 12 3;y x x=− − − 15 24x− ≤ ≤−

d) 29 24 15;y x x= + + 15 24x− ≤ ≤−

10)

11) Find the area of a triangle where 16,a = 13,b = and 37 .C =

a) 125.18 b) 166.12 c) 83.06 d) 62.59

11)

12) Graph 2 1, 5 , 3 4.x t y t t= + = − − ≤ <

a) b)

c) d)

12)



1) Which of the following is a possible value of triangle ABC if 8.8a = , 10.7b = , and

53 .A=

a) 4.3c = b) 8.1c = c) 75.2B = d) 104.8B =

1)

2) Which of the following is a value from the triangle ABC if 51 ,A= 82 ,B = and 23?c =

a) 17.0b = b) 24.4b = c) 31.1b = d) 21.6b =

2)

3) A welder is making a triangular wire frame with sides of length 7 m, 11 m, and 5 m.

What is the angle between the shortest two sides?

a) 19.7 b) 28.1 c) 57.4 d) 132.2

3)

4) Find the polar coordinates ( ),r θ for the point P with rectangular coordinates ( )11, 6 ,−

with 0r > and 0 360 .θ≤ <

a) ( )157,151.4 b) ( )157,331.4 c) ( )85,151.4 d) ( )85,331.4

4)

5) Which of the following is a possible value of triangle ABC if 23,a = 19,b = and

47?c =

a) 22.4A= b) 28.7B = c) 128.9C = d) none of these

5)

6) Two charter boats are sailing towards an island. Initially, both boats are 90 miles apart on

an east-west line. If the first boat sails at a bearing of N 61 W and the second sails at a

bearing of N 39 E, how far does the boat farthest from the island have to sail?

a) 44.3 miles b) 57.5 miles c) 71.0 miles d) 79.9 miles

6)

7) Find the rectangular coordinates ( ),x y for the point P with polar coordinates

( )15,120 .

a) 15 3 15

,2 2

⎛ ⎞⎟⎜ ⎟⎜− ⎟⎜ ⎟⎟⎜⎝ ⎠ b)

15 3 15,

2 2

⎛ ⎞⎟⎜ ⎟⎜ − ⎟⎜ ⎟⎟⎜⎝ ⎠ c)

15 15 3,

2 2

⎛ ⎞⎟⎜ ⎟⎜− ⎟⎜ ⎟⎟⎜⎝ ⎠ d)

15 15 3,

2 2

⎛ ⎞⎟⎜ ⎟⎜ − ⎟⎜ ⎟⎟⎜⎝ ⎠

7)

8) Convert the polar equation 10cosr θ=− to rectangular form.

a) ( )2 25 25x y− + = b) ( )2 25 25x y+ + =

c) ( )22 5 25x y+ − = d) ( )22 5 25x y+ + =

8)

9) A triangular flower garden has sides of length 9 feet, 6 feet, and 8 feet. What is the area

of the garden?

a) 20.78 ft2 b) 70.48 ft2 c) 23.53 ft2 d) 99.68 ft2

9)

105



106


2 3x t= + , 24 6y t t= + , 2 3.t− ≤ ≤

a) 2 9 18;y x x= − + 4 54x≤ ≤ b) 2 9 18;y x x= − + 1 9x− ≤ ≤

c) 2 3 ;y x x= − 4 54x≤ ≤ d) 2 3 ;y x x= − 1 9x− ≤ ≤

10)

11) Find the area of a triangle where 23,a = 17,b = and 48 .C =

a) 261.63 b) 130.82 c) 145.28 d) 290.57

11)

12) Graph 3 2, 3 , 4 2.x t y t t= + = − − < ≤

a) b)

c) d)

12)



1) Determine the sum of 16 323 9

18 12 8 ...+ + + + + . 1)

2) Find the sum of ( ) ( )6

1 2

3

1 3 2k

k

k k+

=

− −∑ . 2)

3) Write the first five terms of the sequence ( ) 121

2 3n

nn

an

−−= −

+.

3)

4) For the geometric sequence 400,200,100,50,... , a) find the expression for

na , b) find 20a , c) find 20.S 4)

5) For the arithmetic sequence 110,80,50,... , a) find an expression for na ,

b) find 80a , c) find 80.S 5)

6) A school club is selling tickets for a raffle. The first member sells 6 tickets, the second sells 12 tickets and the third member sells 18 tickets. If this pattern continues and there are 21 members in the club, how much will the club raise if tickets cost $2 each? 6)

7) A radio station is doing a promotion where they hide money in 15 locations

around the city. The first hiding space contains 3 nickels, the second has 6 nickels, and the third has 12 nickels. If this pattern continues, how many nickels are in the last hiding place? How much are all the nickels used in this promotion worth? 7)

In exercises 8–11, solve the following systems of equations.

8)

2 13

2 3 33 49

5 4 20

x y

x y

⎧⎪⎪ − =⎪⎪⎪⎨⎪⎪ − =⎪⎪⎪⎩

8)

9) 10 2 8

4 20 14

x y

y x

⎧ − =⎪⎪⎨⎪ = −⎪⎩

9)

10) 7 14 21

6 3 9

x y

y x

⎧ − =⎪⎪⎨⎪ − = −⎪⎩

10)

11) 2 5 40

7 11 101

x y

x y

⎧ − =⎪⎪⎨⎪− + = −⎪⎩

11)

12) A video store is having a sale. DVDs sell for $9 and game cartridges sell for $12. John buys a total of 11 DVDs and cartridges for $114. How many of each did he buy? 12)

107



108

13) It takes an ice cream store worker 5 minutes to make a double scoop banana split and 8 minutes to make a triple scoop ice cream sundae. If an order takes the worker 47 minutes to complete and uses a total of 18 scoops of ice cream, how many banana splits and sundaes were in the order? 13)

14) 2 2

2 2

2 3 31

5 1

x y

x y

⎧⎪ + =⎪⎪⎨⎪ − =⎪⎪⎩

14)

15) How much money would be in an account after 30 years if $300 is deposited in the account at the end of each month and the account has an annual interest rate of 2%, compounded monthly? Round your answer to the nearest dollar. 15)

In exercises 16–17, find the partial fraction decomposition of the expression.

16) ( )2

5 4

1

x

x

−

−

16)

17) 2

2 37

20

x

x x

+

+ −

17)



1) Determine the sum of 274

16 12 9 ...+ + + + . 1)


2 1 2

2

1 3k

k

k k+

=

− −∑ . 2)

3) Write the first five terms of the sequence ( ) 121

3 2n

nn

an

++= −

+.

3)

4) For the geometric sequence 2,6,18,54,... , a) find the expression for na ,


5) For the arithmetic sequence 20,35,50,65,... , a) find an expression for na ,



7) A coffee house plans to give free coffee to the first patron that correctly

answers a trivia question each day. On the first day, they would award 100 pounds of coffee, on the second 80 pounds, and 64 pounds on the third day. If this pattern continues and someone wins the prize every day, how much coffee would the person win on the 15th day and how much coffee would the coffeehouse give away? Round your answers to the nearest tenth of a pound. 7)


8)

3 5 73

4 3 122 17

6 3 6

x y

x y

⎧⎪⎪ + =⎪⎪⎪⎨⎪⎪ + =⎪⎪⎪⎩

8)

9) 4 10 12

15 15 6

x y

y x

⎧ − − =⎪⎪⎨⎪− = +⎪⎩

9)

10) 6 18 42

6 2 14

x y

y x

⎧ − = −⎪⎪⎨⎪ − =⎪⎩

10)

11) 7 4 65

13 8 127

x y

x y

⎧− + =⎪⎪⎨⎪ − = −⎪⎩

11)

12) A video store is having a sale. DVDs sell for $10 and game cartridges sell for $9. Stephanie buys a total of 12 DVDs and cartridges for $116. How many of each did she buy? 12)

109



110

13) It takes an ice cream store worker 6 minutes to make a triple scoop banana split and 10 minutes to make a quadruple scoop ice cream sundae. If an order takes the worker 70 minutes to complete and uses a total of 31 scoops of ice cream, how many banana splits and sundaes were in the order? 13)

14) 2 2

2 2

3 4 64

5 2 6

x y

x y

⎧⎪ + =⎪⎪⎨⎪ − = −⎪⎪⎩

14)



16) ( )2

5 4

1

x

x

−

−

16)

17) 2

12 18

2 8

x

x x

+

+ −

17)



1) Determine the sum of 272

32 24 18 ...+ + + + . 1)


1 2

3

1 2k

k

k k−

=

− −∑ . 2)

3) Write the first five terms of the sequence ( )2 121

2 3n

nn

an

++= −

+.

3)

4) For the geometric sequence 4,8,16,32,... , a) find the expression for na ,


5) For the arithmetic sequence 10,10,30,...− , a) find an expression for na ,



7) A radio station is doing a promotion where they hide money in 12 locations

around the city. The first hiding space contains 2 pennies, the second has 6 pennies, and the third has 18 pennies. If this pattern continues, how many pennies are in the last hiding place? How much are all the coins used in this promotion worth? 7)


8)

4 1

3 2 63 23

2 5 10

x y

x y

⎧⎪⎪ + =⎪⎪⎪⎨⎪⎪ − = −⎪⎪⎪⎩

8)

9) 12 20 5

10 6 2

x y

y x

⎧ − =⎪⎪⎨⎪ = −⎪⎩

9)

10) 3 21 3

14 2 2

x y

y x

⎧ − =⎪⎪⎨⎪ − = −⎪⎩

10)

11) 11 13 64

9 8 71

x y

x y

⎧ + =⎪⎪⎨⎪ − =⎪⎩

11)

12) A video store is having a sale. DVDs sell for $8 and game cartridges sell for $11. Tina buys a total of 10 DVDs and cartridges for $89. How many of each did she buy? 12)

111



112

13) It takes an ice cream store worker 4 minutes to make a double scoop banana split and 11 minutes to make a triple scoop ice cream sundae. If an order takes the worker 85 minutes to complete and uses a total of 25 scoops of ice cream, how many banana splits and sundaes were in the order? 13)

14) 2 2

2 2

5 2 2

3 14

x y

x y

⎧⎪− + = −⎪⎪⎨⎪ + =⎪⎪⎩

14)



16) ( )22 5

3

x

x

+

+

16)

17) 2

3 13

3 10

x

x x

− −

− −

17)



1) Determine the sum of 843 27

27 6 ...+ + + + . 1)


2 1 2

4

1 2k

k

k k−

=

− −∑ . 2)

3) Write the first five terms of the sequence ( )251

3 2n

nn

an

+= −

−.

3)

4) For the geometric sequence 243,162,108,72,... , a) find the expression for

na , b) find 20a , c) find 20.S 4)

5) For the arithmetic sequence 60,35,10,... , a) find an expression for na ,



7) A coffee house plans to give free coffee to the first patron that correctly

answers a trivia question each day. On the first day, they would award 120 pounds of coffee, on the second 90 pounds, and 67.5 pounds on the third day. If this pattern continues and a someone wins the prize every day, how much coffee would the person win on the 10th day and how much coffee would the coffeehouse give away? Round your answers to the nearest tenth of a pound. 7)


8)

2 5 13

3 6 65 109

4 3 12

x y

x y

⎧⎪⎪ − = −⎪⎪⎪⎨⎪⎪ + =⎪⎪⎪⎩

8)

9) 4 6 10

6 9 13

x y

x y

⎧ − =⎪⎪⎨⎪ = +⎪⎩

9)

10) 15 5 40

3 9 24

y x

x y

⎧ − = −⎪⎪⎨⎪ − =⎪⎩

10)

11) 9 7 84

8 9 29

x y

x y

⎧− + = −⎪⎪⎨⎪ + =⎪⎩

11)

12) A video store is having a sale. DVDs sell for $7 and game cartridges sell for $13. Phillip buys a total of 12 DVDs and cartridges for $96. How many of each did he buy? 12)

113



114

13) It takes an ice cream store worker 7 minutes to make a triple scoop banana split and 5 minutes to make a double scoop ice cream sundae. If an order takes the worker 46 minutes to complete and uses a total of 19 scoops of ice cream, how many banana splits and sundaes were in the order? 13)

14) 2 2

2 2

3 5 6

3 10

x y

x y

⎧⎪ − =⎪⎪⎨⎪− + =⎪⎪⎩

14)



16) ( )2

7 13

2

x

x

+

+

16)

17) 2

23

8 7

x

x x

−

+ +

17)



In exercises 1–3, use the arithmetic sequence 61,57,53,49,...

1) Find the expression for .na

a) 61 4na n= − b) 61 4na n= +

c) 65 4na n= − d) 65 4na n= +

1)

2) Find 80a

a) 255− b) 259− c) 251− d) 261−

2)

3) Find 80S

a) 7760− b) 7505− c) 8019− d) 8282−

3)

4) Write the fifth term of the sequence ( ) 231

5 2 !n

nn

an

−−= −

+

a) 2

245− b)

2

3,628,805− c)

2

245 d)

2

3,628,805

4)


36 30 25 ...− + − + − +

a) 180 b) 180

11− c) 216− d)

216

11−

5)

In exercises 6–8, use the geometric sequence 2500,500,100,20, 4,...


a) ( ) 12500 5

nna

−= b) ( ) 115

2500n

na−

=

c) ( )2500 5n

na = d) ( )15

2500n

na =

6)

7) Find 10a

a) 4

15,625 b)

4

3125 c)

4

625 d)

4

125

7)

8) Find 10S

a) 390,624

125 b)

1,953,124

625 c)

9,765,624

3125 d)

48,828,124

15,625

8)

9) Find the sum ( ) ( )6

2 2

3

1 3k

k

k k+

=

− +∑

a) 66− b) 66 c) 56 d) 56−

9)

115



116

10) A school club is selling tickets for a raffle. The first member sells 5 tickets, the second sells 9 tickets and the third member sells 13 tickets. If this pattern continues and there are 13 members in the club, how much will the club raise if tickets cost $3 each?

a) $1,053 b) $1,131 c) $1,209 d) $1,287

10)

A radio station is doing a promotion where they hide money in 16 locations around the city. The first hiding space contains 5 pennies, the second has 10 pennies, and the third has 20 pennies. Use this information to solve exercises 11–12, assuming the pattern continues.

11) How many pennies are in the last hiding place?

a) 81,920 b) 655,360 c) 327,680 d) 163,840

11)

12) How much are all the coins used in this promotion worth?

a) $1,638.35 b) $3, 276.75 c) $6,553.55 d) $819.15

12)

13) Which of the following is a correct value of a solution to

3 23

2 4 42 13

5 2 10

x y

x y

⎧⎪⎪ − = −⎪⎪⎪⎨⎪⎪ + =⎪⎪⎪⎩

a) 5x =− b) 5y =− c) 5x = d) 5y =

13)

In exercises 14–15, solve the given system of equations.

14) 9 6 15

12 8 20

x y

x y

⎧ − =⎪⎪⎨⎪ − =⎪⎩

a) 5 2

,3

yy

⎛ ⎞− ⎟⎜ ⎟⎜ ⎟⎜⎝ ⎠ b)

2 5,

3

yy

⎛ ⎞+ ⎟⎜ ⎟⎜ ⎟⎜⎝ ⎠ c) ( )3, 2 d) ∅

14)

15) 3 15 9

20 4 8

x y

y x

⎧ − =⎪⎪⎨⎪ = −⎪⎩

a) ( )312 10

,− − b) ( )5 3,y y+ c) ( )5 2,y y+ d) ∅

15)

16) Which of the following is a correct value of a solution to 7 6 21

5 9 46

x y

x y

⎧ − = −⎪⎪⎨⎪ + = −⎪⎩?

a) 7

3y = b)

7

3y =−

c) 3

7y = d)

3

7y =−

16)

17) A video store is having a sale. DVDs sell for $8 and game cartridges sell for $9. Angelo

buys a total of 21 DVDs and game cartridges for $179. How many DVDs did he buy?

a) 12 b) 11 c) 10 d) 9

17)



18) It takes an ice cream store worker 5 minutes to make a double scoop banana split and 4 minutes to make a triple scoop ice cream sundae. If an order takes the worker 44 minutes to complete and uses a total of 26 scoops of ice cream, what is the total number of banana splits and sundaes in the order?

a) 10 b) 8 c) 6 d) 4

18)

19) Which of the following is a correct value of a solution to 2 2

2 2

3 5 38

2

x y

x y

⎧⎪ + =⎪⎪⎨⎪ − =⎪⎪⎩?

a) 2x = b) 2y =− c) 6y =− d) 6x =−

19)

20) How much money would be in an account after 30 years if $500 is deposited in the

account at the end of each month and the account has an annual interest rate of 5%, compounded monthly? Round your answer to the nearest dollar.

a) $33,219 b) $77,641 c) $137,609 d) $416,129

20)


21) 2

3 26

12

x

x x

+

+ −

a) 5 2

3 4x x+

− + b)

2 5

3 4x x−

− +

c) 5 2

3 4x x−

− + d)

2 5

3 4x x+

− +

21)

22) ( )23 7

5

x

x

+

+

a) ( )2

2 3

5 5

x

x x

−+

+ + b)

( )

2

2

2 3

5 5

x

x x

−+

+ +

c) ( )

2

2

2 3

5 5

x x

x x

−+

+ + d)

( )22 3

5 5

x x

x x

−+

+ +

22)

117



118

In exercises 1–3, use the arithmetic sequence 86,77,68,59,50,...


a) 95 9na n= + b) 95 9na n= −

c) 86 9na n= + d) 86 9na n= −

1)

2) Find 80.a

a) 616− b) 625− c) 634− d) 643−

2)

3) Find 80.S

a) 20,935− b) 20,319− c) 21,560− d) 22,194−

3)

4) Write the fourth term of the sequence ( ) 341

7 2 !n

nn

an

++= −

−

a) 8

41− b)

8

40,313− c)

8

40,313 d)

8

41

4)


150 60 24 ...− + − + −

a) 100− b) 250 c) 750

7 d)

300

7

5)

In exercises 6–8, use the geometric sequence 21,63,189,567,...


a) ( ) 121 3

nna

−= b) ( )21 3n

na =

c) ( ) 113

21n

na−

= d) ( )13

21n

na =

6)

7) Find 10a

a) 1,240,029 b) 413,343 c) 137,781 d) 45,927

7)

8) Find 10S

a) 68,880 b) 206,661 c) 620,004 d) 1,860,033

8)

9) Find the sum ( ) ( )5

3 2

2

1 2 5k

k

k k−

=

− −∑

a) 15− b) 15 c) 18− d) 18

9)



10) A school club is selling tickets for a raffle. The first member sells 7 tickets, the second sells 11 tickets and the third member sells 15 tickets. If this pattern continues and there are 21 members in the club, how much will the club raise if tickets cost $2 each?

a) $1,890 b) $1,974 c) $2,058 d) $2,142

10)

A coffee house plans to give free coffee to the first patron that correctly answers a trivia question each day for 12 days. On the first day, they would award 90 pounds of coffee, on the second 60 pounds, and 40 pounds on the third day. Use this information to solve exercises 11–12, assuming the pattern continues.

11) How much coffee would the person win on the last day?

a) 1.04 pounds b) 0.69 pounds c) 0.46 pounds d) 1.56 pounds

11)

12) How much coffee would the coffeehouse give away in total?

a) 266.9 pounds b) 267.9 pounds c) 268.6 pounds d) 265.3 pounds

12)

13) Which of the following is a correct value of a solution to

3 23

4 5 203 2 61

2 3 6

x y

x y

⎧⎪⎪ + =⎪⎪⎪⎨⎪⎪ − = −⎪⎪⎪⎩

a) 5x =− b) 5x = c) 5y =− d) 5y =

13)

In exercises 14–15, solve the given system of equations.

14) 6 15 9

8 20 12

x y

x y

⎧ − =⎪⎪⎨⎪ − =⎪⎩

a) ( )1, 1− − b) 5 3

,2

yy

⎛ ⎞+ ⎟⎜ ⎟⎜ ⎟⎜⎝ ⎠ c)

3 5,

2

yy

⎛ ⎞+ ⎟⎜ ⎟⎜ ⎟⎜⎝ ⎠ d) ∅

14)

15) 3 12 9

8 2 12

y x

x y

⎧ = −⎪⎪⎨⎪ − =⎪⎩

a) 3 9

,8 2

⎛ ⎞⎟⎜ − ⎟⎜ ⎟⎜⎝ ⎠ b)

3,

4

yy

⎛ ⎞+ ⎟⎜ ⎟⎜ ⎟⎜⎝ ⎠ c)

6,

4

yy

⎛ ⎞+ ⎟⎜ ⎟⎜ ⎟⎜⎝ ⎠ d) ∅

15)

16) Which of the following is a correct value of a solution to 4 5 29

6 7 58

x y

x y

⎧ + =⎪⎪⎨⎪ − = −⎪⎩?

a) 3

2x =− b)

3

2x =

c) 2

3x =− d)

2

3x =

16)

17) A video store is having a sale. DVDs sell for $7 and game cartridges sell for $8. Clare

buys a total of 20 DVDs and game cartridges for $147. How many game cartridges did she buy?

a) 5 b) 7 c) 9 d) 13

17)

119



120

18) It takes an ice cream store worker 6 minutes to make a double scoop banana split and 4 minutes to make a triple scoop ice cream sundae. If an order takes the worker 62 minutes to complete and uses a total of 29 scoops of ice cream, what is the total number of banana splits and sundaes in the order?

a) 5 b) 7 c) 9 d) 12

18)

19) Which of the following is a correct value of a solution to 2 2

2 2

3 6

2 5 55

x y

x y

⎧⎪ − =⎪⎪⎨⎪ + =⎪⎪⎩?

a) 3y =− b) 3x = c) 3x = d) 3y =−

19)

20) How much money would be in an account after 40 years if $400 is deposited in the

account at the end of each month and the account has an annual interest rate of 6%, compounded monthly? Round your answer to the nearest dollar.

a) $262,092 b) $796,596 c) $800,579 d) $266,024

20)


21) 2

6 23

6

x

x x

+

+ −

a) 7 1

2 3x x−

− + b)

1 7

2 3x x−

− +

c) 7 1

2 3x x+

− + d)

1 7

2 3x x+

− +

21)

22) ( )25 8

3

x

x

−

−

a) ( )

2

2

2 3 2

3 3

x

x x

−+

− − b)

( )22 3 2

3 3

x

x x

−+

− −

c) ( )

2

2

2 3 2

3 3

x x

x x

−+

− − d)

( )22 3 2

3 3

x x

x x

−+

− −

22)


Ratti & McWaters, Precalculus Essentials Answers Chapter P Tests

Form A

1) 8

5 2) 18

3) 2x ≥− ;

4) ( )( )22 5 3 7x x+ − 5) ( )( )8 6x x− +

6) 43 3x x 7) 29

25

⎧ ⎫⎪ ⎪⎪ ⎪−⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭

8) 4 5

,3 2

⎧ ⎫⎪ ⎪⎪ ⎪−⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭ 9)

33, ,3

2

⎧ ⎫⎪ ⎪⎪ ⎪− −⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭

10) { }3, 2,2,3− − 11) { }2,5−

12) { }4− 13) { }10

14) 32 2 11 2y x− 15)

132,

3

⎡ ⎞⎟⎢− ⎟⎟⎢ ⎠⎣

16) ∅ 17) ( ) ( ), 10 7,−∞ − ∪ ∞

18) ( ) [ )5,3 4,− ∪ ∞ 19) ( ] )1, 5 ,

3

⎡⎢−∞ − ∪ ∞⎢⎣

20) 3

3,5

⎛ ⎞⎟⎜− ⎟⎜ ⎟⎜⎝ ⎠ 21) 39 2i−

22) 4

24

81y

x 23)

8

5 / 6

27x

y

24) 5 7 2

9

+

Form B

1) 8

5 2) 11

3) 4x < ;

4) ( )( )23 7 2 5x x− + 5) ( )( )5 10x x− −

6) 3 3y y 7) ∅

8) 5 4

,2 3

⎧ ⎫⎪ ⎪⎪ ⎪−⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭ 9)

45, ,5

3

⎧ ⎫⎪ ⎪⎪ ⎪−⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭

10) { }5, 3,3,5− − 11) 11 1

,3 3

⎧ ⎫⎪ ⎪⎪ ⎪−⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭

12) { }4 13) { }7

121



122

14) 25 5x y xy 15) 4

3,5

⎛ ⎤⎜ ⎥−⎜⎜ ⎥⎝ ⎦

16) ( ),−∞ ∞ 17) ( )3,8−

18) ( ] ( ), 6 4, 2−∞ − ∪ − ` 19) ( ) 7, 3 ,

5

⎛ ⎞⎟⎜−∞ − ∪ ∞⎟⎜ ⎟⎜⎝ ⎠

20) 13

,33

⎡ ⎤⎢ ⎥−⎢ ⎥⎣ ⎦

21) 29 22i−

22) 12

12

125x

y 23)

3

25 /124

x

y

24) 5 5 3

4

−

Form C

1) 4

5− 2) 16

3) 4x >− ;

4) ( )( )2 3 5 6x x− + 5) ( )( )7 4x x+ +

6) 4 34y y 7) 65

14

⎧ ⎫⎪ ⎪⎪ ⎪⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭

8) 3 5

,4 2

⎧ ⎫⎪ ⎪⎪ ⎪−⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭ 9)

44, , 4

5

⎧ ⎫⎪ ⎪⎪ ⎪− −⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭

10) 3 3

5, , ,52 2

⎧ ⎫⎪ ⎪⎪ ⎪− −⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭ 11)

2,3

3

⎧ ⎫⎪ ⎪⎪ ⎪−⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭

12) { }20− 13) { }4

14) 3 23 6 3x y xy 15)

3,4

4

⎡ ⎞⎟⎢− ⎟⎟⎢ ⎠⎣

16) ( ),−∞ ∞ 17) [ ]7,11−

18) ( ) [ )3,5 7,− ∪ ∞ 19) ( ] )6, 2 ,

5

⎡⎢−∞ − ∪ ∞⎢⎣

20) 17

,33

⎛ ⎞⎟⎜− ⎟⎜ ⎟⎜⎝ ⎠ 21) 36 3i+

22) 8

1649

y

x 23)

19 / 30

3

5y

x

24) 7 11 27

2

− −



Form D

1) 4

5− 2) 28

3) 2x ≤ ;

4) ( )( )24 3 5 4x x+ − 5) ( )( )5 8x x− +

6) 5x x 7) ( ),−∞ ∞

8) 3 5

,2 3

⎧ ⎫⎪ ⎪⎪ ⎪−⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭ 9)

52, , 2

3

⎧ ⎫⎪ ⎪⎪ ⎪− −⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭

10) 5 5

3, , ,32 2

⎧ ⎫⎪ ⎪⎪ ⎪− −⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭ 11)

1,2

2

⎧ ⎫⎪ ⎪⎪ ⎪⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭

12) { }2− 13) { }2

14) 29 3xy x 15) 6

4,7

⎡ ⎞⎟⎢− ⎟⎟⎢ ⎠⎣

16) ∅ 17) ( ] [ ), 5 7 ,−∞ − ∪ ∞

18) ( ) [ ), 4 2,7−∞ − ∪ − 19) ( ) 5, 5 ,

3

⎛ ⎞⎟⎜−∞ − ∪ ∞⎟⎜ ⎟⎜⎝ ⎠

20) 3

5,2

⎡ ⎤⎢ ⎥−⎢ ⎥⎣ ⎦

21) 39 2i−

22) 21

278

x

y 23)

4

17 / 3025

x

y

24) 8 13

3

−

Form E 1) C 2) C 3) B 4) C 5) B 6) B

7) D 8) D 9) A 10) B 11) C 12) A

13) B 14) B 15) D 16) A 17) C 18) A

19) C 20) D 21) D 22) A 23) C 24) A

Form F 1) B 2) D 3) B 4) A 5) D 6) C

7) A 8) A 9) C 10) B 11) B 12) B

13) C 14) C 15) A 16) B 17) B 18) C

19) A 20) D 21) D 22) B 23) C 24) C

123


Ratti & McWaters, Precalculus Essentials Answers Chapter 1 Tests

124

Form A

1) A) ( )4,6− ; B) ( )4,8 ; C) ( )6, 3− − ; D) ( )0, 8− 2) Distance: 14 2 ; Midpoint: ( )3, 4−

3) ( ) ( ) ( )4,0 , 5,0 , 0, 20− −

4) 2 7y x=− +

5) 1 112 2

y x=− +

6) 3 132 2

y x= −

7) a) [ )7,− ∞ ; b) ( ],8−∞

8) ( ) ( )2 25 7 81x y+ + − =

9) ( ) ( )2 22 3 49x y− + + =

10) ( ] [ ), 5 3,−∞ − ∪ ∞

11) x-axis, y-axis, origin

12) ( )1 11

4

xf x− +

=

13) ( )( ) 2 15f g x x= − ; [ )5,∞

14)

Horizontal Shift: Right 3 Vertical Shift: Up 9 Vertical Stretch: 2 Vertical Reflection: Yes

15) a) ( )6, 2− − ; b) ( )2,3− ; c) ( ) ( ), 6 3,9−∞ − ∪

16)

( ) ( ) ( )3 2, 3 4, 6 5f f f− = =− =

20)

17) ( ) 2 2 4f x x= + −

18) ( ) 13 50; 26 mugsC x x= +

19) 4



Form B

1) A) ( )6,3− ; B) ( )3,3− ; C) ( )7,9 ; D) ( )0,7 2) Distance: 4 5 ; Midpoint: ( )3, 3−

3) ( ) ( )20,0 , 0,10−

4) 5 23y x= +

5) 4 115 5

y x= −

6) 32

1y x= +

7) a) ( ],7−∞ ; b) [ )7,− ∞

8) ( ) ( )2 27 9 36x y− + + =

9) ( ) ( )2 25 4 36x y+ + − =

10) ( ] [ ), 6 2,−∞ − ∪ ∞

11) y-axis

12) ( )1 8

3

xf x− +

=

13) ( )( ) 8

14

xf g x

x

+=

+; [ )7,− ∞

14)

Horizontal Shift: Left 5 Vertical Shift: Down 4

Vertical Stretch: 12

Vertical Reflection: No

15) a) ( ) ( )9, 6 2,3− − ∪ − ; b) ( )3,∞ ; c) ( )6, 2− −

16)

( ) ( ) ( )4 3, 2 3, 2 1f f f− =− − =− =

20)

17) ( ) 15

1 4f x x= − +

18) ( ) 11 40; 23 mugsC x x= +

19) 9−

125



126

Form C

1) A) ( )9, 2− ; B) ( )8, 2− − ; C) ( )0, 6− ; D) ( )8, 5− 2) Distance: 2 53 ; Midpoint: ( )6, 2−

3) ( ) ( )16,0 , 0, 2−

4) 3 1y x=− +

5) 5 26 3

y x=− −

6) 5 593 3

y x= +

7) a) ( )2,− ∞ ; b) ( ],3−∞

8) ( ) ( )2 22 9 9x y+ + − =

9) ( ) ( )2 23 5 25x y− + + =

10) ( ] [ ), 6 4,−∞ − ∪ ∞

11) x-axis

12) ( )1 5

8

xf x− +

=

13) ( )( ) 23 3f g x x= − ; ( ],7−∞

14)

Horizontal Shift: Left 2 Vertical Shift: Down 9 Vertical Stretch: 3 Vertical Reflection: No

15) a) ( )2,6 ; b) ( ) ( ), 4 6,8−∞ − ∪ ; c) ( )4, 2−

16)

( ) ( ) ( )4 5, 4 3, 8 3f f f− = =− =

20)

17) ( ) 2 5 1f x x=− − −

18) ( ) 14 60; 27 mugsC x x= +

19) 10−



Form D

1) A) ( )7,6− ; B) ( )4, 7− − ; C) ( )0, 8− ; D) ( )5, 1− 2) Distance: 10 2 ; Midpoint: ( )1, 4− −

3) ( ) ( )3,0 , 0,27−

4) 4 11y x= +

5) 645 5

y x= −

6) 34

11y x= +

7) a) ( ), 2−∞ − ; b) [ )4,− ∞

8) ( ) ( )2 27 8 121x y+ + − =

9) ( ) ( )2 27 4 9x y− + + =

10) ( ] [ ), 2 5,−∞ − ∪ ∞

11) origin

12) ( )1 11

5

xf x− −

=

13) ( )( ) 2

1

xf g x

x

−=

+; [ )2,∞

14)

Horizontal Shift: Left 5 Vertical Shift: Up 6 Vertical Stretch: 2 Vertical Reflection: Yes

15) a) ( ) ( )6, 2 6,− − ∪ ∞ ; b) ( )4,6 ; c) ( )2, 4−

16)

( ) ( ) ( )1 4, 1 5, 5 5f f f− = =− =−

20)

17) ( ) 12

4 3f x x=− − −

18) ( ) 12 45; 37 mugsC x x= +

19) 2

127



128

Form E 1) A 2) B 3) C 4) A 5) C 6) D

7) B 8) C 9) D 10) D 11) B 12) A

13) B 14) D 15) B 16) C 17) D 18) B

19) C 20) D 21) C 22) C 23) B 24) D

25) A 26) B 27) C 28) C

Form F 1) A 2) A 3) D 4) D 5) B 6) A

7) D 8) B 9) A 10) B 11) B 12) A

13) C 14) A 15) A 16) D 17) B 18) A

19) D 20) B 21) D 22) A 23) A 24) C

25) B 26) C 27) A 28) A



Form A 1) Root Multiplicity Touch or Cross

0 3 Cross

5

2 1 Cross

5− 6 Touch

2) Number of possible positive rational roots: 3, 1

Number of possible negative rational roots: 2, 0

3) 1 3 5 15

, 1, , 2, , 3, 4, 5, 6, , 10, 12, 15, 20, 30, 602 2 2 2

⎧ ⎫⎪ ⎪⎪ ⎪± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭;

( )( )( )3 4 2 5x x x− + −

4) ( )( )( )( )( )3 2 1 2x x x x i x i+ − + − + 5) ( ) ( )22 3 5f x x= + −

6)

( ) ( ) ( ) ( )3,0 , 1,0 , 4,0 , 0,12−

7) as and

as

y x

y x

→−∞ →−∞→−∞ →∞

8) 2 3y x= −

9) a) maximum

b) 13

2x =

c) 13

1902

f⎛ ⎞⎟⎜ =⎟⎜ ⎟⎜⎝ ⎠

10)

x-intercept: 12

3,x =−

y-intercept: 325

y =

vertical asymptotes: 5, 5x x=− = horizontal asymptote: 2y =

129



130

11)

x-intercept: 3x =

y-intercept: 15

y =


12) ( )24 $5,360P = 13) Maximum of 2025

14) Quotient: 4 3 23 7 11 10 19x x x x− + − + ; Remainder: 23

Form B 1) Root Multiplicity Touch or Cross

0 2 Touch

2

3− 3 Cross

4 1 Cross

2) Number of possible negative rational roots: 3,1

Number of possible positive rational roots: 2, 0

3) 1 2 4 5 10 20

, 1, , , 2, 3, , 4, 5, 6, , 10, 12, 15, 20, 30, 603 3 3 3 3 3

⎧ ⎫⎪ ⎪⎪ ⎪± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭;

( )( )( )5 3 2 6x x x+ − −

4) ( )( )( )( )( )3 3 1 2 2 2x x x x i x i− − + − + 5) ( )2( ) 3 2 7f x x=− + +

6)

( ) ( ) ( ) ( )6,0 , 1,0 , 5,0 , 0, 30− − −

7) as and

as

y x

y x

→∞ →−∞→∞ →∞

8) 4 7y x=− +

9) a) minimum

b) 19

6x =−

c) 19 445

6 6f⎛ ⎞⎟⎜− =−⎟⎜ ⎟⎜⎝ ⎠



10)

x-intercepts: 32

3,x =−

y-intercept: 916

y =−

vertical asymptotes: 4, 4x x=− = horizontal asymptote: 2y =−

11)

x-intercept: 3x =−

y-intercept: 15

y =−


12) ( )50 $9,900P = 13) Minimum of 3025−

14) Quotient: 4 3 27 17 20 33 13x x x x+ − + + ; Remainder: 31−

Form C 1) Root Multiplicity Touch or Cross

0 4 Touch

5

4 1 Cross

3 7 Cross

2) Number of possible negative rational roots: 1

Number of possible positive rational roots: 4, 2, 0

3) 1 3 9

, 1, , 2, 3, 4, , 6, 8, 9, 12, 18, 24, 36, 722 2 2

⎧ ⎫⎪ ⎪⎪ ⎪± ± ± ± ± ± ± ± ± ± ± ± ± ± ±⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭;

( )( )( )6 2 3 4x x x− + +

131



132

4) ( )( )( )( )( )3 1 5 2x x x x i x i− + − − + 5) ( )2( ) 2 5 8f x x= − −

6)

( ) ( ) ( ) ( )4,0 , 1,0 , 6,0 , 0, 24−

7) as and

as

y x

y x

→∞ →−∞→−∞ →∞

8) 3 5y x= −

9) a) minimum

b) 35

4x =−

c) 35 1589

4 4f⎛ ⎞⎟⎜− =−⎟⎜ ⎟⎜⎝ ⎠

10)

x-intercepts: 12

, 4x =−

y-intercept: 425

y =


11)


y-intercept: 110

y =−




12) ( )37 $6,635P = 13) Maximum of 1225

14) Quotient: 4 3 25 12 31 14 5x x x x− + + − ; Remainder: 42

Form D 1) Root Multiplicity Touch or Cross

0 1 Cross

2

5 4 Touch

6 5 Cross

2) Number of possible negative rational roots: 3,1

Number of possible positive rational roots: 2, 0

3) 1 2 4 8 16

, , 1, , 2, , 3, 4, , 6, 8, 12, 16, 24, 483 3 3 3 3

⎧ ⎫⎪ ⎪⎪ ⎪± ± ± ± ± ± ± ± ± ± ± ± ± ± ±⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭;

( )( )( )6 3 2 4x x x− + −

4) ( )( )( )( )( )4 4 3 2 2 2x x x x i x i− + − − + 5) ( ) ( )22 4 7f x x=− − +

6)

( ) ( ) ( ) ( )4,0 , 1,0 , 5,0 , 0,20−

7) as and

as

y x

y x

→−∞ →−∞→∞ →∞

8) 2 5y x=− +

9) a) maximum

b) 21

4x =

c) 21 341

4 2f⎛ ⎞⎟⎜ =⎟⎜ ⎟⎜⎝ ⎠

10)

x-intercepts: 52

1,x =−

y-intercept: 59

y =−

vertical asymptotes: 3, 3x x=− = horizontal asymptote: 2y =−

133



134

11)


y-intercept: 13

y =−


12) ( )34 $6,840P = 13) Minimum of 3600−

14) Quotient: 4 3 26 11 17 15 12x x x x− − + + ; Remainder: 17−

Form E 1) B 2) C 3) D 4) B 5) A 6) B

7) C 8) B 9) D 10) C 11) C 12) D

13) C 14) C 15) D 16) D 17) D 18) D

Form F 1) C 2) B 3) C 4) A 5) B 6) A

7) B 8) A 9) B 10) B 11) A 12) B

13) D 14) B 15) A 16) A 17) B 18) B



Form A

1) 725

x =− 2) 0.789x =

3) 21x = 4) 3.500x =−

5) 4.429x = 6) 5x =

7) 4

7 5

9loga

y

x z

⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠ 8) 21.747 yearst =

9) a)

b) ( )4,− ∞

c) ( ),−∞ ∞

d) 4x =−

10) 13236 years oldt = 11) ( )( )12

log 3 3log log 2log 1a a a ay x x+ − − −

12) a)

b) ( ),−∞ ∞

c) ( ), 2−∞ −

d) 2y =−

13) 1.513

14) 150.8 hourst =

15) 0.631x > 16) ( ), 4−∞

135



136

Form B

1) 53

x =− 2) 1.172x =

3) 4. 2x =− 4) 1.712x =

5) 10.167x = 6) 2x =

7) 6 3

8log

17

x y

z

⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠ 8) 26.841 yearst =

9) a)

b) ( )6,− ∞

c) ( ),−∞ ∞

d) 6x =−

10) 15601 years oldt = 11) ( )( )13

log 7 4log log 5log 3a a a ax y x+ − − +

12) a)

b) ( ),−∞ ∞

c) ( )5,− ∞

d) 5y =−

13) 1.771

14) 142.87 hourst =

15) 0.613x ≤ 16) ( )9,− ∞



Form C 1) 27.5x =− 2) 1.457x =−

3) 3.8x =− 4) 3.505x =

5) 8.923x = 6) 6x =

7) 2

5 7

17ln

y

x z

⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠ 8) 18.76 yearst =

9) a)

b) ( )5,− ∞

c) ( ),−∞ ∞

d) 5x =−

10) 24636 years oldt = 11) ( )( )13

ln 5ln ln11 4ln 4x y x+ − − −

12) a)

b) ( ),−∞ ∞

c) ( )1,∞

d) 1y =

13) 2.477

14) 110.61 hourst =

15) 0.682x ≥ 16) ( ),6−∞

137



138

Form D

1) 473

x =− 2) 0.566x =

3) 5x =− 4) 1.288x =−

5) 6.283x = 6) 7x =

7) 5

4 6

13loga

z

x y

⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠ 8) 26.295 yearst =

9) a)

b) ( )3,− ∞

c) ( ),−∞ ∞

d) 3x =−

10) 14102 years oldt = 11) ( )( )12

ln 5 7 ln 3ln 2 lnx x z+ − + −

12) a)

b) ( ),−∞ ∞

c) ( ), 1−∞ −

d) 1y =−

13) 1.796

14) c) 190.58 hourst =

15) 0.792x < 16) ( ),3−∞



Form E 1) C 2) D 3) C 4) A 5) C 6) C

7) C 8) B 9) B 10) C 11) C 12) D

13) B 14) C 15) C 16) D 17) C 18) D

19) C 20) B 21) C 22) D

Form F 1) A 2) B 3) C 4) C 5) B 6) B

7) B 8) C 9) D 10) C 11) D 12) C

13) C 14) B 15) B 16) C 17) C 18) D

19) B 20) B 21) B 22) A

139



140

Form A

1) 11

6

π

2) 7

2

π

3) 108

4) 24

tan7


5) 77

36

6)

7) 119.03 inches

8) 7 74

sin74

θ = ; 5 74

cos74

θ =− ; 7

tan5

θ =− ; 74

csc7

θ = ; 74

sec5

θ =− ; 5

cot7

θ =−

9) Amplitude: 4 ; Range: [ ]2,6− ;

Period: 2

5

π; Phase Shift:

20

π

10) Period: 2π ; Phase Shift: 4

π

11) 15

15−

12) 3

π−

13)

14) sin cosx x+ 15) Solutions may vary

16) origin 17) 2 3−

18) 204

325 19)

1519

1681

20) 68B = ; 4.16a = ; 11.1c = 21) 90.427 feet

22) 19.5 feet 23) 69.4A= ; 20.6B =



Form B

1) 11

6

π

2) 7

3

π

3) 240

4) 35

cot12


5) 15

113−

6)

7) 188.50 inches

8) 6 61

sin61

θ =− ; 5 61

cos61

θ = ; 6

tan5

θ =− ; 61

csc6

θ =− ; 61

sec5

θ = ; 5

cot6

θ =−


Period: 2

7

π; Phase Shift:

35

π


π−

11) 7 58

58

12) 2

5

π

13)

14) sin cosx x− 15) Solutions may vary

16) y-axis 17) 2 6

4

+

18) 253

325 19)

1320

3479−

20) 47A= ; 11.4b = ; 16.7c = 21) 333.184 feet

22) 12.7 feet 23) 51.8A= ; 38.2B =

141



142

Form C

1) 3

4

π

2) 5

12

π

3) 72

4) 28

tan45

θ = ; quadrant III

5) 117

44−

6)

7) 215.55 inches

8) 7 58

sin58

θ =− ; 3 58

cos58

θ =− ; 7

tan3

θ = ; 58

csc7

θ =− ; 58

sec3

θ =− ; 3

cot7

θ =


Period: 3

π; Phase Shift:

18

π


π

11) 21

5

12) 6

π−

13)

14) 1

sin cosx x− 15) Solutions may vary

16) origin 17) 2 6

4

+

18) 171

221 19)

840

1369−

20) 39B = ; 7.5a = ; 6.1b = 21) 186.503 feet

22) 23.6 feet 23) 62.2A= ; 27.8B =



Form D

1) 4

3

π

2) 7

12

π

3) 252

4) 11

cot60


5) 137

88

6)

7) 125.66 inches

8) 3 73

sin73

θ = ; 8 73

cos73

θ =− ; 3

tan8

θ =− ; 73

csc3

θ = ; 73

sec8

θ =− ; 8

cot3

θ =−


Period: 2

π; Phase Shift:

8

π−


π−

11) 55

8

12) 2

3

π

13)

14) 1

sin cosx x+ 15) Solutions may vary

16) y-axis 17) 3 2+

18) 220

221− 19)

2016

3713

20) 54A= ; 6.0b = ; 10.3c = 21) 301.422 feet

22) 12.54 feet 23) 21.3A= ; 68.7B =

143



144

Form E 1) D 2) B 3) A 4) B 5) B 6) C

7) C 8) C 9) B 10) C 11) C 12) C

13) B 14) A 15) B 16) B 17) C 18) C

19) B 20) A 21) A 22) A 23) D

Form F 1) C 2) D 3) C 4) A 5) D 6) D

7) B 8) B 9) A 10) B 11) B 12) C

13) D 14) D 15) C 16) D 17) D 18) D

19) C 20) C 21) C 22) A 23) A



Form A

1) 1 46.2B = , 1 100.8C = , 1 13.9c = ; or 2 133.8B = , 2 13.2C = , 2 3.2c =

2) 13.1, 15.9, 71a c B= = = 3) 102.1

4) ( )74,125.5

5) ∅

6) 106.7 miles

7) 7 3 7

,2 2

⎛ ⎞⎟⎜ ⎟⎜− − ⎟⎜ ⎟⎟⎜⎝ ⎠

8) 1

2xy =

9) 22 8 3,y x x= + + 16 4x− ≤ ≤

10) 26.98 ft2

11) 63.77

12)

Form B

1) 1 72.9B = , 1 66.1C = , 1 11.3c = ; or 2 107.1B = , 2 31.9C = , 2 6.5c =

2) 12.0, 17.3, 63a b C= = = 3) 39.4

4) ( )73,339.4

5) ∅

6) 56.2 miles

7) 7 2 7 2

,2 2

⎛ ⎞⎟⎜ ⎟⎜− − ⎟⎜ ⎟⎟⎜⎝ ⎠

8) 2 2 1x y− =

9) 3 9

2,3

xy

−= − 27 135x− ≤ ≤−

10) 27.81 ft2

11) 25.64

12)

145



146

Form C

1) 1 64.8B = , 1 79.2C = , 1 10.5c = ; or 2 115.2B = , 2 28.8C = , 2 5.2c =

2) 8.5, 8.9, 70a b C= = = 3) 96.4

4) ( )65,209.7

5) ∅

6) 67.2 miles

7) 9 9 3

,2 2

⎛ ⎞⎟⎜ ⎟⎜ − ⎟⎜ ⎟⎟⎜⎝ ⎠

8) ( ) ( )2 22 3 13x y− + − =

9) 232 64 39,y x x= − + 0 3x≤ ≤

10) 31.30 ft2

11) 48.24

12)

Form D

1) 1 69.3B = , 1 71.7C = , 1 10.9c = ; or 2 110.7B = , 2 30.3C = , 2 5.8c =

2) 11.7, 24.4, 74a c B= = = 3) 20.9

4) ( )61,140.2

5) ∅

6) 77.8 miles

7) 13 2 13 2

,2 2

⎛ ⎞⎟⎜ ⎟⎜− − ⎟⎜ ⎟⎟⎜⎝ ⎠

8) ( ) ( )2 25 2 29x y+ + + =

9) 3 40

,16

xy

+= 4 6x− ≤ ≤

10) 43.82 ft2

11) 86.25

12)

Form E 1) B 2) B 3) A 4) A 5) D 6) C

7) D 8) C 9) B 10) A 11) D 12) C

Form F 1) A 2) C 3) D 4) B 5) D 6) C

7) C 8) B 9) C 10) D 11) C 12) A



Form A

1) 54 2) 50− 3) 1

5− ; 0 ;

1

9;

2

11− ;

3

13

4) 11

4002

n

na−⎛ ⎞⎟⎜= ⎟⎜ ⎟⎜⎝ ⎠

; 2025

32768a = ; 20

26214375

32768S =

5) 140 30na n= − ; 80 2260a =− ; 80 86,000S =−

6) $2,772

7) 15 49,152a = nickels; 15 $4,915.05S =

8) ( )2, 5− 9) ∅

10) ( )2 3,y y+ 11) ( )5, 6−

12) 6 DVDs and 5 game cartridges 13) 3 banana splits and 4 ice cream sundaes

14) ( ) ( ) ( ) ( ){ }2, 3 , 2,3 , 2, 3 , 2,3− − − −

15) $147,818 16) ( )2

3 2 1

1 1

x

x x

−+

− − 17)

5 3

4 5x x−

− +

Form B

1) 64 2) 148 3) 3

5;

1

2− ;

5

11;

3

7− ;

7

17

4) ( ) 12 3

nna

−= ; 20 2,324,522,934a = ; 20 3,486,784,400S =

5) 15 5na n= + ; 80 1205a = ; 80 49,000S =

6) $4,047

7) 15 4.4a = lb; 15 482.4S = lb

8) ( )3,5− 9) ∅

10) ( )3 7,y y− 11) ( )3,11−


14) ( ) ( ) ( ) ( ){ }2, 13 , 2, 13 , 2, 13 , 2, 13− − − −

15) $178,403 16) ( )2

3 2 1

1 1

x

x x

−+

− − 17)

7 5

2 4x x+

− +

Form C

1) 128 2) 34− 3) 3

5− ;

4

7− ;

5

9− ;

6

11− ;

7

13−

4) ( ) 14 2

nna

−= ; 20 2,097,152a = ; 20 4,194,300S =

5) 20 30na n= − ; 80 1570a = ; 80 62,400S =

147



148

6) $1,710 7) 12 354, 294a = pennies; 15 $5,314.40S =

8) ( )1,3− 9) ∅

10) ( )7 1,y y+ 11) ( )7, 1−


14) ( ) ( ) ( ) ( ){ }2, 2 , 2,2 , 2, 2 , 2,2− − − −

15) $236,392 16) ( )2

1 2

3 3

x

x x

++

+ + 17)

1 4

2 5x x−

+ −

Form D

1) 243

7 2) 82 3) 6 ;

7

4;

8

7;

9

10;

10

13

4) 12

2433

n

na−⎛ ⎞⎟⎜= ⎟⎜ ⎟⎜⎝ ⎠

; 20524,288

4,782,969a = ; 20

3, 485,735,825

4,782,969S =

5) 85 25na n= − ; 80 1915a =− ; 80 74,200S =−

6) $2,806 7) 10 9.0a = lb; 10 453.0S = lb

8) ( )3,5 9) ∅

10) ( )3 8,y y+ 11) ( )7, 3−


14) ( ) ( ) ( ) ( ){ }17, 3 , 17,3 , 17, 3 , 17,3− − − −

15) $356,178 16) ( )2

5 2 3

2 2

x

x x

++

+ + 17)

5 4

7 1x x−

+ +

Form E 1) C 2) A 3) A 4) A 5) D 6) B

7) B 8) C 9) C 10) B 11) D 12) B

13) D 14) B 15) D 16) B 17) C 18) A

19) D 20) D 21) C 22) A

Form F 1) B 2) B 3) C 4) D 5) C 6) A

7) B 8) C 9) D 10) B 11) A 12) B

13) A 14) B 15) D 16) A 17) B 18) D

19) A 20) B 21) A 22) B


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