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
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
1) Evaluate the following expression for the given values of x and y.
( )2; 7, 3
x yx y
y x
+=− =
−
1)
2) Rewrite the following expression without absolute value bars.
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)
In exercises 7–13, find the exact solution to the equation.
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)
In exercises 15–20, solve the inequality. Write your answer using interval notation.
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)
In exercises 22–23, simplify the expressions. Write your final answer using only positive exponents.
22) 31 4
35
x y
x
−−⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜⎝ ⎠
22)
23)
( )1/3 3/ 4
2/34 28
x y
x y
−
−
23)
24) Rationalize the denominator in the following expression.
7 2 5
5 1
−
−
24)
Chapter P Test Form C Name Ratti & McWaters, Precalculus Essentials
1) Evaluate the following expression for the given values of x and y.
2 2
; 5, 35
x yx y
xy
−= =−
−
1)
2) Rewrite the following expression without absolute value bars.
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)
In exercises 7–13, find the exact solution to the equation.
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
positive values. 14)
In exercises 15–20, solve the inequality. Write your answer using interval notation.
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)
In exercises 22–23, simplify the expressions. Write your final answer using only positive exponents.
22) 25 4
3
7x y
x
−−
−
⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜⎝ ⎠
22)
23) ( )1/ 23 3/5
3/ 2 1/3
25x y
x y
−
− 23)
24) Rationalize the denominator in the following expression.
3 11 2
3 11
−
−
24)
Chapter P Test Form D Name Ratti & McWaters, Precalculus Essentials
1) Evaluate the following expression for the given values of x and y.
2; 8, 6
x xyx y
y x
+=− =−
−
1)
2) Rewrite the following expression without absolute value bars.
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)
In exercises 7–13, find the exact solution to the equation.
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
positive values. 14)
In exercises 15–20, solve the inequality. Write your answer using interval notation.
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)
In exercises 22–23, simplify the expressions. Write your final answer using only positive exponents.
22) 37 5
42
x y
y
−⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜⎝ ⎠
22)
23)
( )4/3 3/10
2 /34 2 /5125
x y
x y
−
−
23)
24) Rationalize the denominator in the following expression.
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)
In exercises 7–13, find the exact solution to the equation.
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
Chapter P Test Form E Name Ratti & McWaters, Precalculus Essentials
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)
In exercises 15–20, solve the inequality. Write your answer using interval notation.
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)
Chapter P Test Form E Name Ratti & McWaters, Precalculus Essentials
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)
In exercises 22–23, simplify the expressions. Write your final answer using only positive exponents.
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)
In exercises 7–13, find the exact solution to the equation.
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)
Chapter P Test Form F Name Ratti & McWaters, Precalculus Essentials
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)
In exercises 15–20, solve the inequality. Write your answer using interval notation.
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
Chapter P Test Form F Name Ratti & McWaters, Precalculus Essentials
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)
In exercises 22–23, simplify the expressions. Write your final answer using only positive exponents.
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
Chapter 1 Test Form A Name Ratti & McWaters, Precalculus Essentials
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)
Chapter 1 Test Form A Name Ratti & McWaters, Precalculus Essentials
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
Chapter 1 Test Form A Name Ratti & McWaters, Precalculus Essentials
18
20) Graph ( ) 31
2f x x= − .
20)
Chapter 1 Test Form B Name Ratti & McWaters, Precalculus Essentials
1) Give the coordinates of the points on the following graph.
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)
In exercises 4–6, find the equations of the following lines. Write your answers in slope-intercept form.
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) Determine the a) domain and b) range of the function graphed below.
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
Chapter 1 Test Form B Name Ratti & McWaters, Precalculus Essentials
20
10) Find the domain of ( ) 2 4 12f x x x= + − .
Write your answer using interval notation. 10)
11) Determine which symmetries the graph of 2 45y x x= − possesses. 11)
12) Find ( )1f x− for ( ) 3 8f x x= − 12)
13) Given ( )f x and ( )g x , find ( )( )f g x and determine its domain.
( ) ( )2
2
1, 7
7
xf x g x x
x
+= = +
+
13)
14) List the transformations to the basic graph and graph the function.
( ) ( )212
5 4f 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)
Chapter 1 Test Form B Name Ratti & McWaters, Precalculus Essentials
16) Graph the function given below and determine the given functional values.
( )3 2
3 2
x if xf x
if x
⎧− + >−⎪⎪=⎨⎪ − ≤−⎪⎩; ( ) ( ) ( )4 , 2 , 2f f f− −
16)
17) Write the formula for the graph of ( )f x below.
17)
18) A company charges $40 to design a custom coffee mug and $11 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 $300. 18)
19) Find the average rate of change of ( ) 33 14f x x=− − as x changes from
1 to 2.a b=− = 19)
21
Chapter 1 Test Form B Name Ratti & McWaters, Precalculus Essentials
22
20) Graph ( ) 3 2f x x= − .
20)
Chapter 1 Test Form C Name Ratti & McWaters, Precalculus Essentials
1) Give the coordinates of the points on the following graph.
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)
In exercises 4–6, find the equations of the following lines. Write your answers in slope-intercept form.
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) Determine the a) domain and b) range of the function graphed below.
7)
8) Write the equation of the circle centered at ( )2,9− with a radius of 3. 8)
9) Determine the equation of the circle in standard form described by 2 26 10 9 0x x y y− + + + = . 9)
23
Chapter 1 Test Form C Name Ratti & McWaters, Precalculus Essentials
24
10) Find the domain of ( ) 2 2 24f x x x= + − .
Write your answer using interval notation. 10)
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)
13) Given ( )f x and ( )g x , find ( )( )f g x and determine its domain.
( ) ( )23 2, 7f x x g x x= + = − 13)
14) List the transformations to the basic graph and graph the function.
( ) ( )23 2 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)
Chapter 1 Test Form C Name Ratti & McWaters, Precalculus Essentials
16) Graph the function given below and determine the given functional values.
( )3 4
1 4
if xf x
x if x
⎧ >⎪⎪=⎨⎪− + ≤⎪⎩; ( ) ( ) ( )4 , 4 , 8f f f−
16)
17) Write the formula for the graph of ( )f x below.
17)
18) A company charges $60 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 $450. 18)
19) Find the average rate of change of ( ) 211 5f x x= − as x changes from
3 to 5.a b=− = 19)
25
Chapter 1 Test Form C Name Ratti & McWaters, Precalculus Essentials
26
20) Graph ( ) 31
3f x x= − .
20)
Chapter 1 Test Form D Name Ratti & McWaters, Precalculus Essentials
1) Give the coordinates of the points on the following graph.
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)
In exercises 4–6, find the equations of the following lines. Write your answers in slope-intercept form.
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) Determine the a) domain and b) range of the function graphed below.
7)
8) Write the equation of the circle centered at ( )7,8− with a radius of 11. 8)
9) Determine the equation of the circle in standard form described by 2 214 8 56 0x x y y− + + + = . 9)
27
Chapter 1 Test Form D Name Ratti & McWaters, Precalculus Essentials
28
10) Find the domain of ( ) 2 3 10f x x x= − − .
Write your answer using interval notation. 10)
11) Determine which symmetries the graph of 5 32 7y x x= + possesses. 11)
12) Find ( )1f x− for ( ) 11 5f x x= − 12)
13) Given ( )f x and ( )g x , find ( )( )f g x and determine its domain.
( ) ( )2
2, 2
3
xf x g x x
x= = −
+
13)
14) List the transformations to the basic graph and graph the function.
( ) ( )22 5 6f 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)
Chapter 1 Test Form D Name Ratti & McWaters, Precalculus Essentials
16) Graph the function given below and determine the given functional values.
( )3 1
5 1
x if xf x
if x
⎧− + <⎪⎪=⎨⎪ − ≥⎪⎩; ( ) ( ) ( )1 , 1 , 5f f f−
16)
17) Write the formula for the graph of ( )f x below.
17)
18) A company charges $45 to design a custom coffee mug and $12 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 $500. 18)
19) Find the average rate of change of ( ) 22 7f x x=− − as x changes from
5 to 4.a b=− = 19)
29
Chapter 1 Test Form D Name Ratti & McWaters, Precalculus Essentials
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)
In exercises 4–6, find the equations of the following lines. Write your answers in slope-intercept form.
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
Chapter 1 Test Form E Name Ratti & McWaters, Precalculus Essentials
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)
Chapter 1 Test Form E Name Ratti & McWaters, Precalculus Essentials
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
Chapter 1 Test Form E Name Ratti & McWaters, Precalculus Essentials
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)
19) Find the domain of ( ) 2 5 14f x x x= + − .
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)
Chapter 1 Test Form E Name Ratti & McWaters, Precalculus Essentials
In exercises 23–24, refer to the graph to the right.
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)
In exercises 25–27, refer to the graph to the right.
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
Chapter 1 Test Form E Name Ratti & McWaters, Precalculus Essentials
36
28) Graph ( ) 3 4f x x= − .
a)
b)
c) d)
28)
Chapter 1 Test Form F 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) ( )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)
In exercises 4–6, find the equations of the following lines. Write your answers in slope-intercept form.
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
Chapter 1 Test Form F Name Ratti & McWaters, Precalculus Essentials
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)
11) Determine the value of ( )3f .
a) 6 b) 4− c) 2 d) 2−
11)
12) Determine the value of ( )8f .
a) 9− b) 7 c) 6 d) 2
12)
Chapter 1 Test Form F Name Ratti & McWaters, Precalculus Essentials
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
Chapter 1 Test Form F Name Ratti & McWaters, Precalculus Essentials
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)
Chapter 1 Test Form F Name Ratti & McWaters, Precalculus Essentials
In exercises 23–24, refer to the graph to the right.
23) Determine the domain of the function.
a) ( ],6−∞ b) ( ),6−∞
c) [ )8,− ∞ d) ( )8,− ∞
24) Determine the range of the function.
a) ( ],6−∞ b) ( ),6−∞
c) [ )8,− ∞ d) ( )8,− ∞
23) 24)
In exercises 25–27, refer to the graph to the right.
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
Chapter 1 Test Form F Name Ratti & McWaters, Precalculus Essentials
42
28) Graph ( ) 31
4f x x= − .
a)
b)
c) d)
28)
Chapter 2 Test Form A Name Ratti & McWaters, Precalculus Essentials
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
Chapter 2 Test Form A Name Ratti & McWaters, Precalculus Essentials
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)
Chapter 2 Test Form B Name Ratti & McWaters, Precalculus Essentials
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)
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 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= + − − .
State the x- and y-intercepts.
6)
7) Determine the end behavior for ( ) ( ) ( )6 34 7 .f x x x x= + − 7)
8) Find the equation of the oblique asymptote for
( )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
Chapter 2 Test Form B Name Ratti & McWaters, Precalculus Essentials
46
In exercises 10–11, graph the rational function. List all intercepts and asymptotes.
10) ( )2
2
9 3 2
16
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 100C x x= + and
the revenue for selling x items is given by ( ) 2420 4 .R x x x= − Find the
value of x that maximizes profit and state that maximum profit. 12)
13) The difference of two numbers is 110. 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 27 45 48 47 145 21
.4
x x x x x
x
+ + − + ++
14)
Chapter 2 Test Form C Name Ratti & McWaters, Precalculus Essentials
1) For ( ) ( )( ) ( )2 74 24 4 5 4 3f 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)
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 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= − − + .
State the x- and y-intercepts.
6)
7) Determine the end behavior for ( ) ( ) ( )6 23 4 7 .f x x x x=− − + 7)
8) Find the equation of the oblique asymptote for
( )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
Chapter 2 Test Form C Name Ratti & McWaters, Precalculus Essentials
48
In exercises 10–11, graph the rational function. List all intercepts and asymptotes.
10) ( )2
2
2 7 4
25
x xf x
x
− −=
−
10)
11) ( )2
2
20
xf x
x x
+=
− −
11)
12) The cost, in dollars, to produce x items is given by ( ) 30 210C x x= + and
the revenue for selling x items is given by ( ) 2400 5 .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 70. 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 25 27 67 79 47 57
.3
x x x x x
x
− + − − +−
14)
Chapter 2 Test Form D Name Ratti & McWaters, Precalculus Essentials
1) For ( ) ( ) ( ) ( )34 523 5 2 1 6f 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)
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 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= − − +
State the x- and y-intercepts.
6)
7) Determine the end behavior for ( ) ( ) ( )2 34 3 2 .f x x x x= − + 7)
8) Find the equation of the oblique asymptote for
( )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
Chapter 2 Test Form D Name Ratti & McWaters, Precalculus Essentials
50
In exercises 10–11, graph the rational function. List all intercepts and asymptotes.
10) ( )2
2
5 3 2
9
x xf x
x
+ −=
−
10)
11) ( )2
4
4 12
xf x
x x
+=
+ −
11)
12) The cost, in dollars, to produce x items is given by ( ) 12 96C x x= + and
the revenue for selling x items is given by ( ) 2420 6 .R x x x= − Find the
value of x that maximizes profit and state that maximum profit. 12)
13) The difference of two numbers is 120. 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 26 19 72 70 87 43
.5
x x x x x
x
+ − − + ++
14)
Chapter 2 Test Form E Name Ratti & McWaters, Precalculus Essentials
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
Chapter 2 Test Form E Name Ratti & McWaters, Precalculus Essentials
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)
Chapter 2 Test Form E Name Ratti & McWaters, Precalculus Essentials
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
Chapter 2 Test Form E Name Ratti & McWaters, Precalculus Essentials
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)
Chapter 2 Test Form F Name Ratti & McWaters, Precalculus Essentials
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
Chapter 2 Test Form F Name Ratti & McWaters, Precalculus Essentials
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)
Chapter 2 Test Form F Name Ratti & McWaters, Precalculus Essentials
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
Chapter 2 Test Form F Name Ratti & McWaters, Precalculus Essentials
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)
Chapter 3 Test Form A Name Ratti & McWaters, Precalculus Essentials
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
Chapter 3 Test Form A Name Ratti & McWaters, Precalculus Essentials
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)
Chapter 3 Test Form B Name Ratti & McWaters, Precalculus Essentials
In exercises 1–6, solve the equation. Round your answer to three decimal places when necessary.
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)
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.
( )3( ) log 6 4f x x= + −
9)
10) How old is a fossil that has 5% of the original Carbon-14 remaining? Round to the nearest whole year. 10)
11) Write the expression ( )
4
35
7log
3
x
y x+ in expanded form.
11)
61
Chapter 3 Test Form B Name Ratti & McWaters, Precalculus Essentials
62
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.
2( ) 3 5xf x += −
12)
13) Use the change of base formula to find the value of 3log 7 . 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
2500
1 99 tN t
e−=
+. When will there be 1500 bacteria?
14)
15) Solve the inequality ( )2 6 10 16x + ≤ 15)
16) Determine the domain of ( )5( ) 7 log 2 18 .f x x= + 16)
Chapter 3 Test Form C Name Ratti & McWaters, Precalculus Essentials
In exercises 1–6, solve the equation. Round your answer to three decimal places when necessary.
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)
10) How old is a fossil that has 95% of the original Carbon-14 remaining? Round to the nearest whole year. 10)
11) Write the expression ( )
5
34
ln11 4
xy
x− in expanded form.
11)
63
Chapter 3 Test Form C Name Ratti & McWaters, Precalculus Essentials
64
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.
( ) 412
( ) 1x
f x−
= +
12)
13) Use the change of base formula to find the value of 4log 31 . 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
1800
1 24 tN t
e−=
+. When will there be 1200 bacteria?
14)
15) Solve the inequality ( )6 5 21 3x − ≥− 15)
16) Determine the domain of ( )( ) 10 ln 18 3 .f x x=− − 16)
Chapter 3 Test Form D Name Ratti & McWaters, Precalculus Essentials
In exercises 1–6, solve the equation. Round your answer to three decimal places when necessary.
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)
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.
( )3( ) log 3 1f x x= + −
9)
10) How old is a fossil that has 18% of the original Carbon-14 remaining? Round to the nearest whole year. 10)
11) Write the expression ( )
7
3
5ln
2
x
x z+ in expanded form.
11)
65
Chapter 3 Test Form D Name Ratti & McWaters, Precalculus Essentials
66
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.
( ) 213
( ) 1x
f x−
=− −
12)
13) Use the change of base formula to find the value of 6log 25 . 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
1700
1 169 tN t
e−=
+. When will there be 1400 bacteria?
14)
15) Solve the inequality ( )7 4 5 26x + < 15)
16) Determine the domain of ( )( ) 17 log 24 8 .f x x= − 16)
Chapter 3 Test Form E Name Ratti & McWaters, Precalculus Essentials
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−=
+. When will there be 450 bacteria?
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
Chapter 3 Test Form E Name Ratti & McWaters, Precalculus Essentials
68
In exercises 11–14, use ( )2( ) log 1 2f x x= − + .
11) Sketch the graph of the function.
a) b)
c) d)
11)
12) Determine the domain of the function.
a) ( ),−∞ ∞ b) ( ),6−∞ c) ( )1,− ∞ d) ( )1,∞
12)
13) Determine the range of the function.
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)
Chapter 3 Test Form E Name Ratti & McWaters, Precalculus Essentials
In exercises 16–19, use ( ) 2( ) 4 1
xf x
+=− + .
16) Sketch the graph of the function.
a) b)
c) d)
16)
17) Determine the domain of the function.
a) ( )2,− ∞ b) ( ),0−∞ c) ( ),−∞ ∞ d) ( )4,− ∞
17)
18) Determine the range of the function.
a) ( ),−∞ ∞ b) ( )4, ,− ∞ c) ( )1, ,∞ d) ( ),1−∞
18)
19) Find the equation of the asymptote.
a) 0y = b) 0x = c) 1y = d) 1x =
19)
69
Chapter 3 Test Form E Name Ratti & McWaters, Precalculus Essentials
70
20) Write the expression ( )
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)
Chapter 3 Test Form F Name Ratti & McWaters, Precalculus Essentials
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−=
+. When will there be 2500 bacteria?
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
Chapter 3 Test Form F Name Ratti & McWaters, Precalculus Essentials
72
In exercises 11–14, use ( )3( ) log 2 1f x x=− + − .
11) Sketch the graph of the function.
a) b)
c) d)
11)
12) Determine the domain of the function.
a) ( ),−∞ ∞ b) ( )2,∞ c) ( )2,− ∞ d) ( )1,− ∞
12)
13) Determine the range of the function.
a) ( ), 2−∞ b) ( )4,− ∞ c) ( ),−∞ ∞ d) ( )2,− ∞
13)
14) Find the equation of the asymptote.
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)
Chapter 3 Test Form F Name Ratti & McWaters, Precalculus Essentials
In exercises 16–19, use ( ) 114
( ) 3x
f x−
=− + .
16) Sketch the graph of the function.
a) b)
c) d)
16)
17) Determine the domain of the function.
a) ( ),1−∞ b) ( )1,− ∞ c) ( ),−∞ ∞ d) ( ),3−∞
17)
18) Determine the range of the function.
a) ( ),−∞ ∞ b) ( )1,− ∞ c) ( )3,∞ d) ( ),3−∞
18)
19) Find the equation of the asymptote.
a) 3x = b) 3y = c) 1x =− d) 1y =−
19)
73
Chapter 3 Test Form F Name Ratti & McWaters, Precalculus Essentials
74
20) Write the expression ( )
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)
Chapter 4 Test Form A Name Ratti & McWaters, Precalculus Essentials
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
Chapter 4 Test Form A Name Ratti & McWaters, Precalculus Essentials
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)
Chapter 4 Test Form A Name Ratti & McWaters, Precalculus Essentials
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
Chapter 4 Test Form B Name Ratti & McWaters, Precalculus Essentials
78
1) Find the exact value, in radians, of θ if 1
sin2
θ =− and θ lies in quadrant
IV. 1)
2) Convert 420 to radians. Write your answer as an exact expression in terms of .π 2)
3) Convert 4
3
π to degrees.
3)
4) Given 37
csc12
θ =− and cos 0θ> , find cot θ and determine in which
quadrant θ lies. 4)
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)
7) How far would a wheel with a diameter of 40 inches roll if it rotates
through an angle of 540 ? Round your answer to the nearest hundredth and use 3.14159.π = 7)
8) ( )5, 6P − 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
( ) 6sin 7 2.5
πf x x
⎛ ⎞⎟⎜=− − +⎟⎜ ⎟⎜⎝ ⎠
9)
Chapter 4 Test Form B Name Ratti & McWaters, Precalculus Essentials
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)
14) Simplify sec csc
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
respect to the x-axis, y-axis, or origin. 16)
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
θ =− where 180 270θ< < , find the exact value of
( )tan 2 .θ 19)
79
Chapter 4 Test Form B Name Ratti & McWaters, Precalculus Essentials
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)
22) Safety requirements at a painting company require ladders to make at most
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)
Chapter 4 Test Form C Name Ratti & McWaters, Precalculus Essentials
1) Find the exact value, in radians, of θ if 2
cos2
θ =− and θ lies in
quadrant II. 1)
2) Convert 75 to radians. Write your answer as an exact expression in terms of .π 2)
3) Convert 2
5
π to degrees.
3)
4) Given 28
sin53
θ =− and sec 0θ < , find tanθ and determine in which
quadrant θ lies. 4)
5) Find the exact value of cot θ if 125
csc44
θ =− and θ lies in quadrant IV. 5)
6) Graph one cycle of ( ) 2sin 3 3.6
πf x x
⎛ ⎞⎟⎜=− + +⎟⎜ ⎟⎜⎝ ⎠
6)
7) How far would a wheel with a diameter of 38 inches roll if it rotates
through an angle of 650 ? Round your answer to the nearest hundredth and use 3.14159.π = 7)
8) ( )3, 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
( ) 3cos 6 2.3
πf x x
⎛ ⎞⎟⎜= − −⎟⎜ ⎟⎜⎝ ⎠
9)
81
Chapter 4 Test Form C Name Ratti & McWaters, Precalculus Essentials
82
10) Find the period and phase shift for ( ) tan .3 6
x πf x
⎛ ⎞⎟⎜= − ⎟⎜ ⎟⎜⎝ ⎠
10)
11) Find the exact value of 1 2sin cos .
5−⎛ ⎞⎛ ⎞⎟⎜ ⎟⎜ ⎟− ⎟⎜ ⎜ ⎟⎟⎜ ⎜ ⎟⎜ ⎝ ⎠⎝ ⎠
11)
12) Find the exact value of 1 11sin sin .
6
π− ⎛ ⎞⎛ ⎞⎟⎜ ⎟⎜ ⎟⎟⎜ ⎜ ⎟⎟⎜ ⎜ ⎟⎜ ⎝ ⎠⎝ ⎠
12)
13) Graph one cycle of ( ) 2sec 1.3
πf x x
⎛ ⎞⎟⎜= + +⎟⎜ ⎟⎜⎝ ⎠
13)
14) Simplify sec csc
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
respect to the x-axis, y-axis, or origin. 16)
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
θ =− where 90 180θ< < , find the exact value of
( )sin 2 .θ 19)
Chapter 4 Test Form C Name Ratti & McWaters, Precalculus Essentials
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)
22) Safety requirements at a painting company require ladders to make at most
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
Chapter 4 Test Form D Name Ratti & McWaters, Precalculus Essentials
84
1) Find the exact value, in radians, of θ if tan 3θ = and θ lies in quadrant III. 1)
2) Convert 105 to radians. Write your answer as an exact expression in terms of .π 2)
3) Convert 7
5
π to degrees.
3)
4) Given 61
csc60
θ =− and cos 0θ> , find cot θ and determine in which
quadrant θ lies. 4)
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)
7) How far would a wheel with a diameter of 24 inches roll if it rotates
through an angle of 600 ? Round your answer to the nearest hundredth and use 3.14159.π = 7)
8) ( )8,3P − 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
( ) 7sin 4 5.2
πf x x
⎛ ⎞⎟⎜=− + −⎟⎜ ⎟⎜⎝ ⎠
9)
Chapter 4 Test Form D Name Ratti & McWaters, Precalculus Essentials
10) Find the period and phase shift for ( ) cot .2 8
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)
13) Graph one cycle of ( ) 3csc 1.3
πf x x
⎛ ⎞⎟⎜=− − −⎟⎜ ⎟⎜⎝ ⎠
13)
14) Simplify sec csc
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
respect to the x-axis, y-axis, or origin. 16)
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
θ =− where 180 270θ< < , find the exact value of
( )tan 2 .θ 19)
85
Chapter 4 Test Form D Name Ratti & McWaters, Precalculus Essentials
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)
22) Safety requirements at a painting company require ladders to make at most
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)
Chapter 4 Test Form E Name Ratti & McWaters, Precalculus Essentials
1) Find the exact value, in radians, of θ if 3
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)
6) Find the exact value of cot θ if 20
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)
8) Find the exact value of 1 13sin sin .
3
π− ⎛ ⎞⎛ ⎞⎟⎜ ⎟⎜ ⎟− ⎟⎜ ⎜ ⎟⎟⎜ ⎜ ⎟⎜ ⎝ ⎠⎝ ⎠
a) 3
π b)
2
3
π c)
3
π− d)
7
3
π−
8)
87
Chapter 4 Test Form E Name Ratti & McWaters, Precalculus Essentials
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)
10) Graph one cycle of ( ) 4sin 2 1.4
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)
Chapter 4 Test Form E Name Ratti & McWaters, Precalculus Essentials
12) Graph one cycle of ( ) 2sec 1.6
πf x x
⎛ ⎞⎟⎜=− + +⎟⎜ ⎟⎜⎝ ⎠
a) b)
c) d)
12)
13) Find the period and phase shift for ( ) tan .3 9
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
Chapter 4 Test Form E Name Ratti & McWaters, Precalculus Essentials
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?
a) 14.3 feet b) 12.5 feet c) 7.8 feet d) 4.4 feet
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)
Chapter 4 Test Form F Name Ratti & McWaters, Precalculus Essentials
1) Find the exact value, in radians, of θ if 3
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
θ =− ; quadrant IV
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
Chapter 4 Test Form F Name Ratti & McWaters, Precalculus Essentials
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)
Chapter 4 Test Form F Name Ratti & McWaters, Precalculus Essentials
12) Graph one cycle of ( ) 3csc 1.3
πf x x
⎛ ⎞⎟⎜=− − −⎟⎜ ⎟⎜⎝ ⎠
a) b)
c) d)
12)
13) Find the period and phase shift for ( ) cot .2 4
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
Chapter 4 Test Form F Name Ratti & McWaters, Precalculus Essentials
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?
a) 101.9 feet b) 224.5 feet c) 392.5 feet d) 440.5 feet
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?
a) 10.4 feet b) 17.9 feet c) 23.76 feet d) 38.6 feet
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)
Chapter 5 Test Form A Name Ratti & McWaters, Precalculus Essentials
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
Chapter 5 Test Form A Name Ratti & McWaters, Precalculus Essentials
96
12) Graph 2 3, 5 , 2 6.x t y t t= − = − − < ≤
12)
Chapter 5 Test Form B Name Ratti & McWaters, Precalculus Essentials
1) Solve the triangle ABC if 8.1a = , 11.8b = , and 41 .A= Round your answers to one decimal place. 1)
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)
4) Find the polar coordinates ( ),r θ for the point P with rectangular
coordinates ( )8, 3 ,− with 0r > and 0 360 .θ≤ < Round θ to the
nearest tenth of a degree. 4)
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)
7) Find the rectangular coordinates ( ),x y for the point P with polar
coordinates ( )7, 135 .− 7)
8) Convert the polar equation ( )2 sec 2r θ= to rectangular form. 8)
9) Eliminate the parameter to obtain a Cartesian equation of the curve for
39x t= − , 23
ty = − , 6 12.t− ≤ ≤
9)
10) A triangular flower garden has sides of length 7 feet, 10 feet, and 8 feet. What is the area of the garden? 10)
11) Find the area of a triangle where 9,a = 13,b = and 26 .C = 11)
97
Chapter 5 Test Form B Name Ratti & McWaters, Precalculus Essentials
98
12) Graph 3 2, 7 2 , 1 2.x t y t t= + = − − < ≤
12)
Chapter 5 Test Form C Name Ratti & McWaters, Precalculus Essentials
1) Solve the triangle ABC if 6.3a = , 9.7b = , and 36 .A= Round your answers to one decimal place. 1)
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)
4) Find the polar coordinates ( ),r θ for the point P with rectangular
coordinates ( )7, 4 ,− − with 0r > and 0 360 .θ≤ < Round θ to the
nearest tenth of a degree. 4)
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)
7) Find the rectangular coordinates ( ),x y for the point P with polar
coordinates 5
9, .3
π⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜⎝ ⎠
7)
8) Convert the polar equation 4cos 6sinr θ θ= + to rectangular form. 8)
9) Eliminate the parameter to obtain a Cartesian equation of the curve for
14
tx = + , 22 7y t= + , 4 8.t− ≤ ≤
9)
10) A triangular flower garden has sides of length 12 feet, 7 feet, and 9 feet. What is the area of the garden? 10)
11) Find the area of a triangle where 15,a = 22,b = and 17 .C = 11)
99
Chapter 5 Test Form C Name Ratti & McWaters, Precalculus Essentials
100
12) Graph 3 1, 4 2 , 2 3.x t y t t= + = − − < ≤
12)
Chapter 5 Test Form D Name Ratti & McWaters, Precalculus Essentials
1) Solve the triangle ABC if 7.2a = , 10.7b = , and 39 .A= Round your answers to one decimal place. 1)
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)
4) Find the polar coordinates ( ),r θ for the point P with rectangular
coordinates ( )6,5 ,− with 0r > and 0 360 .θ≤ < Round θ to the
nearest tenth of a degree. 4)
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)
7) Find the rectangular coordinates ( ),x y for the point P with polar
coordinates ( )13,225 . 7)
8) Convert the polar equation 10cos 4sinr θ θ=− − to rectangular form. 8)
9) Eliminate the parameter to obtain a Cartesian equation of the curve for
3 8 40x t= + , 52
ty = + , 13 22.t− ≤ ≤ .
9)
10) A triangular flower garden has sides of length 13 feet, 8 feet, and 11 feet. What is the area of the garden? 10)
11) Find the area of a triangle where 12,a = 18,b = and 53 .C = 11)
101
Chapter 5 Test Form D Name Ratti & McWaters, Precalculus Essentials
102
12) Graph 2 1, 2 3 , 2 4.x t y t t= + = − − ≤ <
12)
Chapter 5 Test Form E Name Ratti & McWaters, Precalculus Essentials
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
Chapter 5 Test Form E Name Ratti & McWaters, Precalculus Essentials
104
10) Eliminate the parameter to obtain a Cartesian equation of the curve for
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)
Chapter 5 Test Form F Name Ratti & McWaters, Precalculus Essentials
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
Chapter 5 Test Form F Name Ratti & McWaters, Precalculus Essentials
106
10) Eliminate the parameter to obtain a Cartesian equation of the curve for
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)
Chapter 6 Test Form A Name Ratti & McWaters, Precalculus Essentials
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
Chapter 6 Test Form A Name Ratti & McWaters, Precalculus Essentials
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)
Chapter 6 Test Form B Name Ratti & McWaters, Precalculus Essentials
1) Determine the sum of 274
16 12 9 ...+ + + + . 1)
2) Find the sum of ( ) ( )5
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 ,
b) find 20a , c) find 20.S 4)
5) For the arithmetic sequence 20,35,50,65,... , 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 8 tickets, the second sells 15 tickets and the third member sells 22 tickets. If this pattern continues and there are 19 members in the club, how much will the club raise if tickets cost $3 each? 6)
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)
In exercises 8–11, solve the following systems of equations.
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
Chapter 6 Test Form B Name Ratti & McWaters, Precalculus Essentials
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)
15) How much money would be in an account after 25 years if $400 is deposited in the account at the end of each month and the account has an annual interest rate of 3%, 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
12 18
2 8
x
x x
+
+ −
17)
Chapter 6 Test Form C Name Ratti & McWaters, Precalculus Essentials
1) Determine the sum of 272
32 24 18 ...+ + + + . 1)
2) Find the sum of ( ) ( )6
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 ,
b) find 20a , c) find 20.S 4)
5) For the arithmetic sequence 10,10,30,...− , 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 10 tickets, the second sells 14 tickets and the third member sells 18 tickets. If this pattern continues and there are 15 members in the club, how much will the club raise if tickets cost $3 each? 6)
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)
In exercises 8–11, solve the following systems of equations.
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
Chapter 6 Test Form C Name Ratti & McWaters, Precalculus Essentials
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)
15) How much money would be in an account after 40 years if $200 is deposited in the account at the end of each month and the account has an annual interest rate of 4%, compounded monthly? Round your answer to the nearest dollar. 15)
In exercises 16–17, find the partial fraction decomposition of the expression.
16) ( )22 5
3
x
x
+
+
16)
17) 2
3 13
3 10
x
x x
− −
− −
17)
Chapter 6 Test Form D Name Ratti & McWaters, Precalculus Essentials
1) Determine the sum of 843 27
27 6 ...+ + + + . 1)
2) Find the sum of ( ) ( )7
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 ,
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 11 tickets and the third member sells 16 tickets. If this pattern continues and there are 23 members in the club, how much will the club raise if tickets cost $2 each? 6)
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)
In exercises 8–11, solve the following systems of equations.
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
Chapter 6 Test Form D Name Ratti & McWaters, Precalculus Essentials
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)
15) How much money would be in an account after 35 years if $250 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. 15)
In exercises 16–17, find the partial fraction decomposition of the expression.
16) ( )2
7 13
2
x
x
+
+
16)
17) 2
23
8 7
x
x x
−
+ +
17)
Chapter 6 Test Form E Name Ratti & McWaters, Precalculus Essentials
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)
5) Determine the sum of 125 6256 36
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,...
6) Find the expression for .na
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
Chapter 6 Test Form E Name Ratti & McWaters, Precalculus Essentials
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)
Chapter 6 Test Form E Name Ratti & McWaters, Precalculus Essentials
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)
In exercises 21–22, find the partial fraction decomposition of the expression.
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
Chapter 6 Test Form F Name Ratti & McWaters, Precalculus Essentials
118
In exercises 1–3, use the arithmetic sequence 86,77,68,59,50,...
1) Find the expression for .na
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)
5) Determine the sum of 48 965 25
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,...
6) Find the expression for .na
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)
Chapter 6 Test Form F Name Ratti & McWaters, Precalculus Essentials
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
Chapter 6 Test Form F Name Ratti & McWaters, Precalculus Essentials
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)
In exercises 21–22, find the partial fraction decomposition of the expression.
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
Ratti & McWaters, Precalculus Essentials Answers Chapter P Tests
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
− −
Ratti & McWaters, Precalculus Essentials Answers Chapter P Tests
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
Ratti & McWaters, Precalculus Essentials Answers Chapter 1 Tests
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
Ratti & McWaters, Precalculus Essentials Answers Chapter 1 Tests
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−
Ratti & McWaters, Precalculus Essentials Answers Chapter 1 Tests
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
Ratti & McWaters, Precalculus Essentials Answers Chapter 1 Tests
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
Ratti & McWaters, Precalculus Essentials Answers Chapter 2 Tests
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
Ratti & McWaters, Precalculus Essentials Answers Chapter 2 Tests
130
11)
x-intercept: 3x =
y-intercept: 15
y =
vertical asymptotes: 3, 5x x=− = horizontal asymptote: 0y =
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⎛ ⎞⎟⎜− =−⎟⎜ ⎟⎜⎝ ⎠
Ratti & McWaters, Precalculus Essentials Answers Chapter 2 Tests
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 =−
vertical asymptotes: 5, 3x x=− = horizontal asymptote: 0y =
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
Ratti & McWaters, Precalculus Essentials Answers Chapter 2 Tests
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 =
vertical asymptotes: 5, 5x x=− = horizontal asymptote: 2y =
11)
x-intercept: 2x =−
y-intercept: 110
y =−
vertical asymptotes: 4, 5x x=− = horizontal asymptote: 0y =
Ratti & McWaters, Precalculus Essentials Answers Chapter 2 Tests
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
Ratti & McWaters, Precalculus Essentials Answers Chapter 2 Tests
134
11)
x-intercept: 4x =−
y-intercept: 13
y =−
vertical asymptotes: 6, 2x x=− = horizontal asymptote: 0y =
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
Ratti & McWaters, Precalculus Essentials Answers Chapter 3 Tests
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
Ratti & McWaters, Precalculus Essentials Answers Chapter 3 Tests
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,− ∞
Ratti & McWaters, Precalculus Essentials Answers Chapter 3 Tests
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
Ratti & McWaters, Precalculus Essentials Answers Chapter 3 Tests
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−∞
Ratti & McWaters, Precalculus Essentials Answers Chapter 3 Tests
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
Ratti & McWaters, Precalculus Essentials Answers Chapter 4 Tests
140
Form A
1) 11
6
π
2) 7
2
π
3) 108
4) 24
tan7
θ =− ; quadrant IV
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 =
Ratti & McWaters, Precalculus Essentials Answers Chapter 4 Tests
Form B
1) 11
6
π
2) 7
3
π
3) 240
4) 35
cot12
θ =− ; quadrant IV
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 =−
9) Amplitude: 6 ; Range: [ ]4,8− ;
Period: 2
7
π; Phase Shift:
35
π
10) Period: 3π ; Phase Shift: 3
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
Ratti & McWaters, Precalculus Essentials Answers Chapter 4 Tests
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 =
9) Amplitude: 3 ; Range: [ ]5,1− ;
Period: 3
π; Phase Shift:
18
π
10) Period: 3π ; Phase Shift: 2
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 =
Ratti & McWaters, Precalculus Essentials Answers Chapter 4 Tests
Form D
1) 4
3
π
2) 7
12
π
3) 252
4) 11
cot60
θ =− ; quadrant IV
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 =−
9) Amplitude: 7 ; Range: [ ]12,2− ;
Period: 2
π; Phase Shift:
8
π−
10) Period: 2π ; Phase Shift: 4
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
Ratti & McWaters, Precalculus Essentials Answers Chapter 4 Tests
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
Ratti & McWaters, Precalculus Essentials Answers Chapter 5 Tests
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
Ratti & McWaters, Precalculus Essentials Answers Chapter 5 Tests
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
Ratti & McWaters, Precalculus Essentials Answers Chapter 6 Tests
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−
12) 8 DVDs and 4 game cartridges 13) 5 banana splits and 4 ice cream sundaes
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
Ratti & McWaters, Precalculus Essentials Answers Chapter 6 Tests
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−
12) 7 DVDs and 3 game cartridges 13) 2 banana splits and 7 ice cream sundaes
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−
12) 10 DVDs and 2 game cartridges 13) 3 banana splits and 5 ice cream sundaes
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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