MATH 60
REVIEW FOR FINAL
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Evaluate the expression for the given values.
x-6
1)
x+8
1)
(a) x = -7
(b) x = 7
(c) x = 0
A) (a) -
1
13
(b) 15
3
(c) 4
2)
B) (a) - 13
(b) 15
3
(c) 4
C) (a) (b)
1
13
1
15
(c) -
D) (a) - 13
1
(b)
15
(c) -
3
4
3
4
5x - 4
x
(a) x = 0
(b) x = 16
(c) x = -4
A) (a) 0
19
(b)
4
(c) 6
2)
B) (a) undefined
19
(b)
4
C) (a) undefined
19
(b)
4
(c) - 6
D) (a) 0
21
(b)
4
(c) 6
(c) 6
Solve the problem.
3) For a certain computer desk, the manufacturing cost C per desk (in dollars) is C =
where x is the number of desks manufactured.
a. Find the average cost per desk when manufacturing 200 desks.
b. Find the average cost per desk when manufacturing 1000 desks.
A) a. $475
B) a. $525
C) a. $75
b. $495
b. $505
b. $55
500x + 5000
x
D) a. $550
b. $525
Find the value(s) of the variable for which the rational expression is undefined.
x2 - 49
4)
2
x + 14x + 48
A) 0
5)
B) 7, -7
C) 8, -6
4)
D) -8, -6
5y + 2
3
y - 4y2 - 12y
A) 6, 2
3)
5)
C) 6, -2
B) 0, 6, 2
1
D) 0, 6, -2
Simplify the rational expression. Assume that no variable has a value which results in a denominator with a value of
zero.
3-m
6)
6)
m-3
A) -1
7)
D) m
21
3m - 18
A)
8)
C) -m
B) 1
7
m + 18
7)
B)
7
m+6
C)
7
m-6
D)
7
m - 18
x3 + 4x2 + 4x
x2 + 6x + 8
A)
x+2
x+4
8)
B)
x(x + 2)
x+4
C)
x+2
x(x + 4)
D)
x3 + 4x2 + 4x
x2 + 6x + 8
Perform the indicated operation.
r2 - y2
r
9)
·
r+y
r2 - ry
A) -
10)
B) 1
D) -r
C) r
x-3
3
·
15x - 12 x2 - 9
A)
11)
1
r
9)
1
(5x - 4)(x + 3)
10)
B)
1
(5x + 4)(x - 3)
C) (5x - 4)(x + 3)
m2 - 9
m-3
·
2
m + 4m - 21 21 + 4m - m 2
A)
-9
27(x2 - 9)
11)
m-3
(m + 7)(m - 7)
C) -
D)
B)
m-3
m2
m+3
(m + 7)(m - 7)
D) -
2
m-3
(m + 7)(m - 7)
Solve the problem.
12) Write an algebraic expression for the area of the rectangle.
12)
7x
ft
2
x - 81
x+9
ft
10x3
A)
7x2
ft2
10(x - 9)
B)
7
ft2
2
10x (x + 9)
C)
9
ft2
3
10x - 90
D)
7
ft2
2
10x (x - 9)
Perform the indicated operation.
2m 9 n 3 3m 4n 7
13)
÷
9m
4n 2
A)
14)
8m 5
27n 8
C)
8m 4
27n 3
D)
8m 5
27n 3
7(x + 1)
x5 (x - 1)
14)
B)
84(x + 1)
x5 (x - 1)
C)
84x5 (x + 1)
(x - 1)
p2 - 3p + pq - 3q
p-3
÷
2
2
6p
- 6q
9p - 9q
B)
2
3
D)
(x - 1)(x + 1)3
54(p - q)2
6(p2 - 3p + pq - 3q)
9(p + q)(p - 3)
16)
x3 - 9x2
2
x + 7x - 18
C)
84x84
(p - 3)2
x3
x2 - 4
A) -
D)
15)
A) 1
C)
16)
B)
84x7
x12
÷
x2 - 1 (x + 1)2
A)
15)
8m 4
27n 2
13)
x(x + 9)
(x + 2)(x - 9)
B)
x(x + 9)
(x + 2)(x - 9)
D)
3
x5(x - 9)
(x + 2)(x + 9)(x - 2)2
x(x - 9)
(x + 2)(x + 9)
17)
m 2 - 8m
15
+
m-5
m-5
A)
18)
m 2 - 8m + 15
m-5
17)
B) m - 5
C) m + 3
D) m - 3
y2
12y + 36
+
y2 - 36
y2 - 36
A)
y+6
y-6
18)
B) -1
C)
y+ 6
2(y - 6)
D)
y-6
y+6
Solve the problem.
19) Find the perimeter of the square.
19)
7
cm
x+6
A)
28
cm
x+6
B)
7
cm
x + 24
C)
28
cm
x + 12
D)
28
cm
x + 24
Perform the indicated operation.
5m
4m
20)
- 9
9
A) m
21)
4x + 8
x+4
D) 1
21)
B)
4x - 22
x+4
C)
4x - 8
x+4
D)
4x + 22
x+4
7k2 - 4 7k + 7
k-4
4-k
A) -
23)
C) -m
B) 0
8x + 15 4x + 7
x+4
x+4
A)
22)
20)
7k2 + 7k + 3
k- 4
22)
B)
7k2 + 7k + 3
k- 4
C)
7k2 - 7k + 11
k- 4
D)
7k2 + 7k + 3
2k
p2 + 2py
y2
y2 - p2
p2 - y2
A) 1
23)
B) 0
C)
p+y
y- p
D)
p-y
y-p
Find the LCD of the given rational expressions.
5
9
24)
;
10xy 15x2
A) 30x3 y
24)
B) 30xy2
C) 30x2 y
4
D) 30xy3
25)
3
3
;
m 2 + 5m m 2 + 7m + 10
25)
A) m(m + 3)(m + 2)
B) (m + 3)2
C) m(m + 5)(m + 2)
D) m(m + 3)2
Perform the indicated operation.
6
7
26)
2
x
x
A)
27)
9
20a3 b
A)
28)
31)
7x - 6
x
C)
6 - 7x
x2
D)
6 + 7x
x2
8
27)
25ab2
45b + 32a 2
100a 3b2
B)
45b - 32a 2
100a 2 b3
C)
45b - 32a 2
100a 3 b2
D)
45b - 8a 2
100a 3b2
4x + 5
x+3
28)
B)
5x - 5
x+3
C)
4x - 5
x+3
D)
3x - 5
x+3
4
s-7
+
s-7 s+7
A)
30)
-
B)
4x - 8
+1
x+3
A)
29)
6x + 7
x2
26)
s-3
2s
29)
B)
s-3
(s - 7)(s + 7)
C)
s2 - 10s + 77
(s - 7)(s + 7)
D)
s2 + 10s - 77
(s - 7)(s + 7)
3
7
+
2
2
x - 3x + 2 x - 1
30)
A)
11x - 10
(x - 1)(x + 1)(x - 2)
B)
42x - 11
(x - 1)(x + 1)(x - 2)
C)
10x - 11
(x - 1)(x - 2)
D)
10x - 11
(x - 1)(x + 1)(x - 2)
x
5
6
+
2
x
5
x
+
x - 25
A)
6x2 - 25x + 150
x(x + 5)(x - 5)
31)
B)
25(x - 6)
(x + 5)(x - 5)
C)
5
-25(x - 6)
x(x + 5)(x - 5)
D)
25(x + 6)
x(x + 5)(x - 5)
Simplify the complex rational expression using either Method I or Method II.
12
m(m - 5)
32)
6
m-5
A)
33)
72
m(m - 5)
C)
12
m
D)
2
m
33)
2 7
+
m n
5n - 6m
2n + 7m
B)
5m - 6n
2m + 7n
C)
-1(m + n)
9(m - n)
D)
5n + 6m
2n - 7m
7
7
x+3 x-3
34)
5
2
x -9
A)
35)
B)
5
6
m n
A)
34)
m
2
32)
42
( x - 3)
5
B)
2x
5
C) -
42
5
D) 0
5
x+3
35)
5
- 40
x+3
A)
-1
8x - 25
B)
1
8x + 23
C)
Name the quadrant or axis in which the point lies.
36) (0, -4)
A) quadrant II
B) quadrant III
1
8x - 23
D)
-1
8x + 23
36)
C) x-axis
6
D) y-axis
Plot the point.
37) (-1, -4)
37)
y
6
4
2
-6
-4
-2
2
4
x
6
-2
-4
-6
A)
B)
y
-6
-4
y
6
6
4
4
2
2
-2
2
4
6
x
-6
-4
-2
-2
-2
-4
-4
-6
-6
C)
2
4
6
x
2
4
6
x
D)
y
-6
-4
y
6
6
4
4
2
2
-2
2
4
6
x
-6
-4
-2
-2
-2
-4
-4
-6
-6
7
Graph the equation by plotting points.
38) y = -2x2 + 8
38)
y
10
5
-10
-5
5
10
x
-5
-10
A)
B)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C)
5
10
x
5
10
x
D)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
8
List the intercepts of the graph.
39)
39)
y
10
5
-10
-5
5
10
x
-5
-10
A) (0, -5), (5, 0)
C) (0, -5), (0, 5)
B) (-5, 0), (5, 0)
D) (-5, 0), (0, 5)
40)
40)
y
5
-5
5
x
-5
A) (0, 0)
B) (0, 1)
C) (1, 0)
9
D) (1, 1)
Solve the problem.
41) The graph below shows the height, in feet, of a ball thrown straight up with an initial speed of 96
feet per second from an initial height of 112 feet after t seconds.
41)
y
(3, 256)
250
200
150
(0, 112)
100
50
1
2
3
4
5
6
7
x
What is the height of the ball after 2.5 seconds?
A) approximately 260 feet
C) approximately 225 feet
B) approximately 250 feet
D) approximately 200 feet
Provide an appropriate response.
42) Use the map to represent the relation as a set of ordered pairs.
x
Alice
Brad
Carl
42)
y
cat
dog
A) {(Alice, cat), (Brad, dog), (Carl, dog)}
C) {(cat, Alice), (dog, Brad), (dog, Carl)}
B) {(Alice, dog), (Brad, cat), (Carl, cat)}
D) {(dog, Alice), (cat, Brad), (cat, Carl)}
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
43) Use the set of ordered pairs to represent the relation as a map.
{(5, 25), (6, 30), (7, 35), (8, 40)}
43)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Identify the domain and range of the relation.
44)
Bob
Ann
Dave
44)
Ms. Lee
Mr. Bar
A) domain: {Bob, Ann, Dave}
range: {Ms. Lee, Mr. Bar}
B) domain: {Ms. Lee, Mr. Bar}
range: {Bob, Ann, Dave}
10
Identify the domain and the range of the relation from the graph.
45)
6
45)
y
6 x
-6
-6
B) Domain: (-∞, ∞)
Range: [0, ∞)
D) Domain: (-∞, ∞)
Range: (-∞, ∞)
A) Domain: (-∞, 0)
Range [-5, ∞)
C) Domain: (-∞, 0);
Range: [0, ∞)
46)
46)
10
5
-10
-5
5
10
-5
-10
A) Domain: [-4, 6]
Range: [-7, 3]
B) Domain: [-7, ∞)
Range: [3, ∞)
C) Domain: (-∞, 3]
Range: (-∞, -4]
D) Domain: [-7, 3]
Range: [-4, 6]
Determine whether the relation represents a function. If it is a function, state the domain and range.
47)
3
4
5
6
→
→
→
→
12
16
20
24
A) function
domain: {3, 4, 5, 6}
range: {12, 16, 20, 24}
B) function
domain:{12, 16, 20, 24}
range: {3, 4, 5, 6}
11
C) not a function
47)
48)
48)
Bob
Ann
Dave
carrots
peas
squash
A) function
domain: {carrots, peas, squash}
range: {Bob, Ann, Dave}
B) function
domain: {Bob, Ann, Dave}
range: {carrots, peas, squash}
C) not a function
49)
49)
Bob
Ann
Dave
Ms. Lee
Mr. Bar
A) function
domain: {Bob, Ann, Dave}
range: {Ms. Lee, Mr. Bar}
B) function
domain: {Ms. Lee, Mr. Bar}
range: {Bob, Ann, Dave}
C) not a function
50) {(-2, -8), (1, 4), (4, -4), (8, -2)}
A) function
domain: {-2, 1, 4, 8}
range: {-8, 4, -4, -2}
50)
B) function
domain: {-8, 4, -4, -2}
range: {-2, 1, 4, 8}
51) {(11, -2), (-5, -1), (-5, 0), (-4, 1), (4, 3)}
A) function
B) function
domain: {-2, -1, 0, 1, 3}
domain: {11, -4, -5, 4}
range: {11, -4, -5, 4}
range: {-2, -1, 0, 1, 3}
52) {(-2, 6), (-1, 3), (0, 2), (1, 3), (3, 11)}
A) function
domain: {-2, -1, 0, 1, 3}
range: {6, 3, 2, 11}
C) not a function
51)
C) not a function
52)
B) function
domain: {6, 3, 2, 11}
range: {-2, -1, 0, 1, 3}
Determine whether the equation is a function.
53) y2 = 6 - x2
C) not a function
53)
A) function
B) not a function
54) x - 7y = 2
A) function
B) not a function
54)
12
Determine whether the graph is that of a function.
55)
55)
y
10
5
-10
-5
5
10
x
-5
-10
A) function
B) not a function
56)
56)
y
5
-5
5
x
-5
A) function
B) not a function
Find the function value.
57) Find f(-12) when f(x) = -4x + 2.
A) 46
B) -46
57)
C) 50
58) Find f(x + h) when f(x) = 2x2 + 3x + 3.
A) 2x2 + 2h 2 + 7x + 7h + 3
58)
B) 2x2 + 2xh + 2h 2 + 3x + 3h + 3
C) 2x2 + 4xh + 2h 2 + 3x + 3h + 3
59) f(x) =
D) 48.2
D) 2x2 + 2h 2 + 3x + 3h + 3
x-9
; f(-7)
2x + 13
A) 1
59)
C) -1
B) 16
D) -16
Solve the problem.
60) If f(x) = 4x3 + 3x2 - x + C and f(-2) = 1, what is the value of C?
A) C = -45
B) C = -1
C) C = 19
13
60)
D) C = -21
61) A projectile is fired from a cliff 300 feet above the water at an inclination of 45° to the horizontal,
with a muzzle velocity of 140 feet per second. The height h of the projectile above the water is
-32x2
given by h(x) =
+ x + 300, where x is the horizontal distance of the projectile from the base of
(140)2
61)
the cliff. How far from the base of the cliff is the height of the projectile a maximum?
A) 153.13 ft
B) 453.13 ft
C) 306.25 ft
D) 759.38 ft
Find the domain of the function.
2x - 3
62) f(x) =
x+9
A) x|x ≠ -9,
63) f(x) =
62)
3
2
B) x|x ≠
3
2
C) {x|x ≠ 9}
D) {x|x ≠ -9}
1
7x + 4
A) x|x ≠ -
63)
4
,0
7
B) x|x ≠ -
4
7
C) x|x ≠
4
7
D) x|x ≠ 0,
4
7
Graph the function.
64) f(x) = 3x + 4
64)
y
10
8
6
4
2
-10 -8 -6 -4 -2
-2
2
4
6
x
8 10
-4
-6
-8
-10
A)
B)
y
y
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
-2
2
4
6
8
10
x
-10 -8 -6 -4 -2
-2
-4
-4
-6
-6
-8
-8
-10
-10
14
2
4
6
8
10
x
C)
D)
y
y
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
-2
2
4
6
8
10
x
-10 -8 -6 -4 -2
-2
-4
-4
-6
-6
-8
-8
-10
-10
2
4
6
8
10
x
65) g(x) = 2x - 10
65)
y
10
8
6
4
2
-10 -8 -6 -4 -2
-2
2
4
6
x
8 10
-4
-6
-8
-10
A)
B)
y
y
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
-2
2
4
6
8
10
x
-10 -8 -6 -4 -2
-2
-4
-4
-6
-6
-8
-8
-10
-10
15
2
4
6
8
10
x
C)
D)
y
y
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
-2
2
4
6
8
10
x
-10 -8 -6 -4 -2
-2
-4
-4
-6
-6
-8
-8
-10
-10
2
4
6
8
10
x
66) h(x) = x2 - 4
66)
y
10
8
6
4
2
-10 -8 -6 -4 -2
-2
2
4
6
8
x
10
-4
-6
-8
-10
A)
B)
y
y
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
-2
2
4
6
8
10
x
-10 -8 -6 -4 -2
-2
-4
-4
-6
-6
-8
-8
-10
-10
16
2
4
6
8
10
x
C)
D)
y
y
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
-2
2
4
6
8
10
x
-10 -8 -6 -4 -2
-2
-4
-4
-6
-6
-8
-8
-10
-10
2
4
6
8
10
x
67) G(x) = x - 2
67)
y
10
8
6
4
2
-10 -8 -6 -4 -2
-2
2
4
6
8
x
10
-4
-6
-8
-10
A)
B)
y
y
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
-2
2
4
6
8
10
x
-10 -8 -6 -4 -2
-2
-4
-4
-6
-6
-8
-8
-10
-10
17
2
4
6
8
10
x
C)
D)
y
y
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
-2
2
4
6
8
10
x
-10 -8 -6 -4 -2
-2
-4
-4
-6
-6
-8
-8
-10
-10
Match the graph to the function listed whose graph most resembles the one given.
68)
A) square function
C) cube root function
2
4
6
8
10
x
68)
B) cube function
D) square root function
69)
69)
A) cube function
C) cube root function
B) square root function
D) square function
Sketch the graph of the function. Label at least three points.
70) f(x) = x
y
5
-5
5
x
-5
18
70)
A)
B)
y
y
5
5
(4, 2)
(1, 1)
(0, 0)
-5
(1, -1)
5
x
-5
(0, 0)
5
x
5
x
(2, -4)
-5
-5
C)
D)
y
y
5
5
(2, 4)
(1, 1)
(0, 0)
-5
5
x
-5
(0, 0)
(1, -1)
(4, -2)
-5
71) f(x) =
-5
1
x
71)
y
5
-5
5
x
-5
19
A)
B)
y
y
5
5
(1, 1)
(-2, 1/2)
(3, 1/3)
-5
5
(4, -1/4)
x
-5
5
x
5
x
(-1, -1)
(-1/4, -4)
-5
-5
C)
D)
y
y
5
5
(1/3, 3)
(-1/3, 3)
(-1, 1)
(1, 1)
(2, 1/2)
(-2, 1/2)
(3, -1/3)
-5
5
x
-5 (-3, -1/3)
(1/2, -2)
(-1/2, -2)
-5
-5
The graph of a function f is given. Use the graph to answer the question.
72) Use the graph of f given below to find f(100).
72)
100
-100
100
-100
A) 120
B) 100
C) 200
20
D) 0
73) How often does the line y = 2 intersect the graph?
73)
10
-10
10
-10
A) once
C) three times
B) twice
D) does not intersect
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve.
74) Michael decides to walk to the mall to do some errands. He leaves home, walks 2 blocks in
7 minutes at a constant speed, and realizes that he forgot his wallet at home. So Michael
runs back in 6 minutes. At home, it takes him 4 minutes to find his wallet and close the
door. Michael walks 3 blocks in 9 minutes and then decides to jog to the mall. It takes him
10 minutes to get to the mall which is 4 blocks away. Draw a graph of Michael's distance
from home (in blocks) as a function of time.
y
x
21
74)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the compound inequality. Express the solution using interval notation. Graph the solution set.
75) x ≤ 5 and x ≤ 3
75)
A) [3, 5]
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
-3
-2
-1
0
1
2
3
4
5
6
7
B) [3, ∞)
-5
-4
C) (-∞, 3] ∪ [5, ∞)
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
-3
-2
-1
0
1
2
3
4
5
6
7
D) (-∞, 3]
-5
-4
76) -6x < 12 and x + 6 > 3
76)
A) (-∞, -3) ∪ (-2, ∞)
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
B) (-2, ∞)
-4
-2
0
2
4
6
C) (-3, -2)
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
D) ∅
-6
22
77) 0 ≤
3x + 2
<3
4
A) -
2 10
,
3 3
-6
B) -
77)
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
-4
-3
-2
-1
0
1
2
3
4
5
6
-4
-3
-2
-1
0
1
2
3
4
5
6
-4
-3
-2
-1
0
1
2
3
4
5
6
2 10
,
3 3
-6
-5
2 10
C) - ,
3 3
-6
D) -
-5
2 10
,
3 3
-6
-5
78) x ≤ 4 or x ≥ 7
78)
A) [-7, -4]
-6
-4
-2
0
2
4
6
B) (-4, 7)
-4
-2
0
2
4
6
8
6
8
10
12
14
16
6
8
10
12
14
16
C) (-∞, 4] ∪ [7, ∞)
4
D) (4, 7)
4
23
79) x > 2 or x < 2
79)
A) (2, ∞)
-2
0
2
4
6
8
10
12
0
2
4
6
8
10
12
0
2
4
6
8
10
12
2
4
6
8
10
12
B) (2, 2)
-2
C) (-∞, 2)
-2
D) (-∞, 2) ∪ (2, ∞)
-2
0
80) -4x + 1 ≥ 9 or 5x + 3 ≥ -17
80)
A) [-2, ∞)
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
-4
-3
-2
-1
0
1
2
3
4
5
6
-4
-3
-2
-1
0
1
2
3
4
5
6
-4
-3
-2
-1
0
1
2
3
4
5
6
B) [-4, ∞)
-6
-5
C) [-4, -2]
-6
-5
D) (-∞, ∞)
-6
-5
Solve the problem.
81) The daily number of visitors v to an amusement park was always at least 808 but never more than
1359. Express this as an inequality.
A) v ≤ 808 or v ≥ 1359
B) 808 ≤ v ≤ 1359
C) 808 < v < 1359
D) v < 808 or v > 1359
Solve the absolute value equation.
82) |18x| = 63
A) {-3.5}
83) |x + 4| = |7 - x|
2
A) 3
81)
82)
B) {0, 3.5, -3.5}
C) {3.5, -3.5}
B) {3}
3
C)
2
D) {3.5}
83)
24
D) ∅
84) |2x + 7| = 9
84)
A) 1, - 8
2
16
C)
,7
7
B) - 1, 8
D) ∅
Solve the inequality. Graph the solution set, and state the solution set in interval notation.
85) |x| - 5 ≤ -2
85)
A) (-∞, -7]
-20
-15
-10
-5
0
5
B) (-∞, 3]
-10
-5
0
5
10
-10
-5
0
5
10
-5
0
5
10
C) [-3, 3]
D) (-∞, -3] ∪ [3, ∞)
-10
86)
8y + 24
<8
3
86)
A) (-6, 6)
-10
-5
0
5
10
-5
0
5
10
-5
0
5
10
0
5
10
B) (0, 6)
-10
C) (-6, 0)
-10
D) (-∞, -6) ∪ (0, ∞)
-10
-5
25
87)
3y + 12
>3
4
87)
A) (0, ∞)
-10
-5
0
5
10
-5
0
5
10
-5
0
5
10
-5
0
5
10
B) (-∞, -8) ∪ (0, ∞)
-10
C) (-8, 0)
-10
D) (-8, 8)
-10
88) |x - 5| + 9 ≥ 11
88)
A) [3, 7]
5
10
15
20
25
30
5
10
15
20
25
30
B) (3, 7)
C) (-∞, 3] ∪ [7, ∞)
5
10
15
20
25
30
5
10
15
20
25
30
D) [7, ∞)
Solve the problem.
89) The length ℓ of a metal rod used in manufacturing cars must not differ from the standard s by more
than 0.3 inches. The manufacturing engineers express this as |ℓ - s| ≤ 0.3. Find the limits of ℓ if the
standard s is 14.4.
A) 14.7 ≤ ℓ ≤ 15
B) ℓ ≤ 14.7 or ℓ ≥ 15
C) ℓ ≤ 14.1 or ℓ ≥ 14.7
D) 14.1 ≤ ℓ ≤ 14.7
26
89)
Evaluate.
90) 100 -1/2
90)
A) 10
B) 20
C)
1
10
D)
1
20
Simplify using rational exponents.
3
91) 27x1/2y3 · 4xy1/2
A) 6x2
92)
5
5
91)
B) 6x2 y
y4
C) 6x2 y
D) 6
4
4
x3 y y
(2a 3b4 )6
A) 2a3 b4
92)
5
2a3 b4
B) 2a 3b5
5
4a 3b4
C) 2a 4 b4
5
2a 3 b4
D) 2a 3 b4
5
a3 b4
Perform the indicated operation and simplify. Assume all variables in the radicand are greater than
or equal to zero.
93) 15m · 17n
A) 255mn
B) 15m + 17n
C) 255mn
D) 32mn
94)
95)
180x7 y8
A) 6x3 y4 5
C) 6x7 y8 5x
D) 6x3 y4 5x
95)
10 a 5
b5
96) 2 20x3 + 5x
A) (4x + 1) 5x
97) 5
94)
B) 6y4 5x7
700a 5 b-5
7ab5
A)
3
a 10b2 + 3
10a 2
b5
B) 10a 4
C) 10a2 b5 7
D)
B) 4x 10x
C) (2x + 1) 5x
D) 5 x
96)
3
ab2
3
A) (5a3 + 3) ab2
97)
3
B) (8a 3) ab2
C) 5a 3 + 3
98) ( 19 + 3x)( 17 - 3x)
A) 323 + 51x + 57x + 3
C) 323 + 51x + 57x - 3
3
ab2
3
D) (5a + 3) ab2
98)
B)
D)
323 +
323 +
51x 51x -
57x + 3x
57x - 3x
Rationalize the denominator.
-5
99)
2 2
A) -
5 2
2
93)
99)
B) -5 2
C) -
27
5 2
4
D) -8
100)
2
3+5
A)
100)
3 6+3 2
15
B)
6-5 2
8
C)
Evaluate the function.
101) For f(x) = -2x + 3, find f(-3).
A) 3
B) 3
6-5 2
-22
6+5 2
-22
D)
101)
C) - 3
D) -3
3
C) -∞,
2
2
D) -∞,
3
Find the domain of the given function.
102) f(x) = -2x + 3
102)
3
B) , ∞
2
A) (-∞, ∞)
Determine the domain and range of the function and graph it.
103) f(x) = x - 5
10
103)
y
8
6
4
2
-10 -8 -6 -4 -2-2
2
4 6
8 10 x
-4
-6
-8
-10
A) domain: [0, ∞), range: [-5, ∞)
10
8
B) domain: [-5, ∞), range: [0, ∞)
y
10
8
6
6
4
2
4
2
-10 -8 -6 -4 -2-2
2
4
6 8 10 x
-10 -8 -6 -4 -2-2
-4
-6
-8
-8
-10
C) domain: [0, ∞), range: [-5, ∞)
6
8 10 x
D) domain: [5, ∞), range: [0, ∞)
y
10
8
6
8
6
4
4
2
2
-10 -8 -6 -4 -2-2
2 4
-4
-6
-10
10
y
2
4
6 8 10 x
-10 -8 -6 -4 -2-2
-4
-4
-6
-8
-6
-8
-10
-10
28
y
2 4
6
8 10 x
Solve the equation.
104) x + 3 = 3
A) {6}
105)
104)
B) {36}
D) {9}
2x + 10 = x + 6
A) {2, 8}
106)
C) {12}
x+6+
A) {0}
105)
4
B) -4,
3
C) {8}
D) {-4}
B) {2, -2}
C) { 31, -2}
D) {-2}
2-x=4
106)
Perform the indicated operation. Write the result in the form a + bi.
107) (3 - 3i) + (7 + 7i)
A) -4 + 10i
B) 10 - 4i
C) 10 + 4i
108) (6 - 8i)(9 + 5i)
A) -40i2 - 42i + 54
109)
107)
D) -10 - 4i
108)
B) 94 - 42i
C) 14 - 102i
D) 94 + 42i
7 - 5i
6 + 8i
A)
109)
1
43
i
50 50
B) -
1
43
i
+
28 28
C) -
41 43
i
+
14 28
D)
41 13
i
25 25
Complete the square in the given expression. Then factor the perfect square trinomial.
110) x2 - 18x
A) x2 - 18x - 324 = (x - 18)2
C) x2 - 18x + 324 = (x - 18)2
111) m 2 +
110)
B) x2 - 18x - 81 = (x - 9)2
D) x2 - 18x + 81 = (x - 9)2
1
m
5
111)
1
1
1 2
m+
= m+
5
25
5
1
1
1 2
C) m 2 + m +
= m+
5
10
5
A) m 2 +
B) m 2 +
1
1
1 2
m+
= m+
5
100
10
D) m 2 +
1
m + 100 = (m +10)2
5
Solve the equation.
5 2
112) 4 x = 49
2
A) {1, -6}
112)
B) {6, -1}
C) {2, -12}
113) m 2 + 18m + 59 = 0
A) {-18 + 59, -18 - 59}
C) {-9 + 22, -9 - 22}
D) {12, -2}
113)
B) {9 +
D) {9 +
29
59, 9 22, 9 -
59}
22}
114) 8w2 - 3w + 1 = 0
3
23 3
23
A) i,
i
+
16
16
16
16
C)
115) -
114)
B) -
3
23 3
23
i,
i
+
16
16
16
16
D)
3
23
3
23
i, i
+
16
16
16
16
3
23
3
23
i, i
+
16
16
16
16
1 2 1
3
z - z=4
7
28
A) -1,
115)
3
7
B) -
3
,1
7
C)
3
7
D) -
3
, -1
7
Determine the discriminant of the quadratic equation. Use the value of the discriminant to determine whether the
quadratic equation has two rational solutions, two irrational solutions, one repeated real solution, or two complex
solutions that are not real.
116) 2x2 + 5x = 4
116)
A) One repeated real solution
C) Two irrational solutions
B) Two rational solutions
D) Two complex solutions that are not real
Solve.
117) Find the missing length in the right triangle shown below.
117)
14
11
A) 11
B)
3
C)
317
D) 5 3
Solve the equation.
118) x4 - 2x2 - 63 = 0
118)
A) {-3, 3, -i 7, i 7}
C) {-9, 7}
119) y1/2 - 19y1/4 + 90 = 0
A) {10, 9}
B) {3, i 7}
D) {- 7, 7, -3i, 3i}
119)
B) {10,000, 6561}
C) {100, 81}
Graph the quadratic function. Determine the vertex and axis of symmetry.
30
D) {-10, -9}
120) f(x) = (x - 1)2 - 6
120)
y
10
5
-10
-5
5
10
x
-5
-10
A) vertex: (1, -6)
axis of symmetry: x = 1
B) vertex: (-6, 1)
axis of symmetry: x = -6
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C) vertex: (-1, -6)
axis of symmetry: x = -1
x
5
10
x
y
10
10
5
5
-5
10
D) vertex: (6, -1 )
axis of symmetry: x = 6
y
-10
5
5
10
x
-10
-5
-5
-5
-10
-10
31
121) f(x) = x2 - 2x - 8
121)
y
10
5
-10
-5
5
10
x
-5
-10
A) vertex: (1, - 9)
axis of symmetry: x = 1
B) vertex: (- 1, - 9)
axis of symmetry: x = - 1
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C) vertex: (- 1, - 9)
axis of symmetry: x = - 1
x
5
10
x
y
10
10
5
5
-5
10
D) vertex: (1, - 9)
axis of symmetry: x = 1
y
-10
5
5
10
x
-10
-5
-5
-5
-10
-10
32
Determine the quadratic function whose graph is given.
122)
122)
y
10
5
-10
-5
5
10
x
-5
-10
(1, -9)
A) f(x) = x2 + 2x - 8
C) f(x) = x2 - 2x + 8
B) f(x) = x2 - 2x - 8
D) f(x) = -x2 - 2x - 8
Determine whether the given quadratic function has a maximum or minimum value. Then find the maximum or
minimum value.
123) h(x) = 3x2 - 2x - 3
123)
A) minimum; -
10
3
B) minimum;
1
3
C) maximum; -
10
3
D) maximum;
1
3
Solve.
124) April shoots an arrow upward into the air at a speed of 64 feet per second from a platform that is 28
feet high. The height of the arrow is given by the function h(t) = -16t2 + 64t + 28, where t is the time
is seconds. What is the maximum height of the arrow?
A) 24 ft
B) 28 ft
C) 64 ft
124)
D) 92 ft
125) Shelly can cut a lawn with a riding mower in 3 hours less time than it takes William to cut the lawn
with a push mower. If they can cut the lawn in 5 hours working together find how long to the
nearest tenth of an hour it takes for William to cut the lawn alone.
A) 11.8 hr
B) 8.8 hr
C) 11.7 hr
D) 8.7 hr
125)
126) The profit that the vendor makes per day by selling x pretzels is given by the function
P(x) = -0.004x2 + 2.4x - 150. Find the number of pretzels that must be sold to maximize profit.
126)
A) 600 pretzels
B) 300 pretzels
C) 210 pretzels
D) 1.2 pretzels
127) A box with a rectangular base is to be constructed such that the perimeter of the base of the box is
to be 280 inches. The height of the box must be 10 inches. What is the maximum volume possible?
A) 4900 cu. in.
B) 49,000 cu. in.
C) 700 cu. in.
D) 122,500 cu. in.
33
127)
Find the distance between the two points.
128)
128)
y
10
8
6
4
2
-10 -8 -6 -4 -2
-2
2
4
6
8 10
x
-4
-6
-8
-10
A) 2
B) 6
C) 2 5
D) 20
Find the distance d(P1 , P2 ) between the points P1 and P2 .
129) P1 = (-1, -6); P2 = (-7, -2)
A) 20
129)
B) 2 13
C) 10
D) 20 5
Find the midpoint of the line segment formed by joining the points P1 and P2 .
130) P1 = (5 7, 2 6); P2 = (10 7, 7 6)
5 7 5 6
-5 7 -5 6
A)
,
B)
,
2
2
2
2
131) P1 = - 1,
A)
130)
C) (15 7, 9 6)
D)
15 7 9 6
,
2
2
1
8
; P2 = , - 2
2
5
3
3
,5
2
131)
B) -
13 5
,
10 4
C)
34
13
5
,10
4
D)
3
3
,10
4
Find the center and radius of the circle whose graph is shown. Write the standard form of the equation of the circle.
132)
132)
y
10
8
6
4
-10 -8
2
(-2, 1)
(-7, 1)
-6
-4
-2
2
4
6
8
10
x
-2
-4
-6
-8
-10
5; (h, k) = (-2, 1); (x + 2)2 + (y - 1)2 = 5
B) r = 5; (h, k) = (-2, 1); (x - 2)2 + (y + 1)2 = 25
A) r =
C) r = 5; (h, k) = (-2, 1); (x + 2)2 + (y - 1)2 = 25
D) r = 5; (h, k) = (-2, 1); (x - 2)2 + (y + 1)2 = 5
Write the standard form of the equation of the circle whose radius is r and whose center is (h, k).
133) r = 4; (h, k) = (0, 0)
A) x2 + y2 = 8
B) x2 + y2 = 4
C) x2 - y2 = 4
D) x2 + y2 = 16
134) r =5; (h, k) = (0, 10)
A) (x - 10)2 + y2 = 25
133)
134)
B) x2 + (y + 10)2 = 5
C) x2 + (y - 10)2 = 25
D) (x + 10)2 + y2 = 25
Find the center (h, k) and radius r of the circle. Graph the circle.
135) (x - 1)2 + (y + 5)2 = 4
y
x
35
135)
A) (h, k) = (- 1, 5); r = 4
B) (h, k) = (- 1, 5); r = 2
y
-20
y
20
10
10
5
-10
10
20
x
-10
-5
-10
-5
-20
-10
C) (h, k) = (1, -5); r = 2
x
10
20
x
y
10
20
5
10
-5
10
D) (h, k) = (1, -5); r = 4
y
-10
5
5
10
x
-20
-10
-5
-10
-10
-20
Graph the circle whose radius is r and whose center is (h, k).
136) r = 4; (h, k) = (4, 4)
y
x
36
136)
A)
B)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C)
5
10
x
10
20
x
D)
y
y
-20
20
20
10
10
-10
10
20
x
-20
-10
-10
-10
-20
-20
Find the center (h, k) and the radius r of the circle.
137) x2 + y2 + 18x + 14y + 130 = 36
137)
A) (h, k) = (-7, -9), r = 6
C) (h, k) = (-9, -7), r = 6
B) (h, k) = (9, 7), r = 36
D) (h, k) = (7, 9), r = 36
138) x2 + 4x + y2 - 8y + 11 = 0
A) (h, k) = (-2, 4); r = 3
C) (h, k) = (2, -4); r = 9
138)
B) (h, k) = (2, -4); r = 3
D) (h, k) = (-2, 4); r = 9
37
Solve the inequality. Graph the solution set and write the solution set in set-builder notation.
139) x2 + 3x - 10 > 0
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
1
2
3
4
5
6
7
8
9
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
139)
A) {x -5 < x < 2}
B) {x x < -5}
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
C) {x x > 2}
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
D) {x x < -5 or x > 2}
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
140) x2 - 6x - 7 ≤ 0
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
140)
1
2
3
4
5
6
7
8
9
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
A) {x x ≤ -1}
B) {x x ≤ -1 or x ≥ 7}
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
C) {x x ≥ 7}
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
D) {x -1 ≤ x ≤ 7}
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
38
Answer Key
Testname: M60REVIEW2
1) D
2) C
3) B
4) D
5) D
6) A
7) C
8) B
9) B
10) A
11) D
12) D
13) A
14) B
15) C
16) C
17) D
18) A
19) A
20) A
21) A
22) B
23) C
24) C
25) C
26) C
27) C
28) B
29) C
30) D
31) C
32) D
33) A
34) C
35) D
36) D
37) A
38) A
39) A
40) B
41) B
42) A
43)
5
6
7
8
→
→
→
→
25
30
35
40
44) A
39
Answer Key
Testname: M60REVIEW2
45) B
46) D
47) A
48) C
49) A
50) A
51) C
52) A
53) B
54) A
55) B
56) A
57) C
58) C
59) B
60) C
61) C
62) D
63) B
64) C
65) D
66) C
67) B
68) D
69) C
70) B
71) D
72) D
73) C
74)
Distance (in blocks)
y
10
9
8
7
6
5
4
3
2
1
5
10 15 20 25 30 35 40 45 50 55 60 65 x
Time (in minutes)
75) D
76) B
77) C
78) C
79) D
40
Answer Key
Testname: M60REVIEW2
80) D
81) B
82) C
83) C
84) A
85) C
86) C
87) B
88) C
89) D
90) C
91) D
92) A
93) C
94) D
95) D
96) A
97) A
98) D
99) C
100) C
101) B
102) C
103) A
104) A
105) C
106) D
107) C
108) B
109) A
110) D
111) B
112) B
113) C
114) C
115) A
116) C
117) D
118) A
119) B
120) A
121) D
122) B
123) A
124) D
125) C
126) B
127) B
128) C
129) B
41
Answer Key
Testname: M60REVIEW2
130)
131)
132)
133)
134)
135)
136)
137)
138)
139)
140)
D
D
C
D
C
C
B
C
A
D
D
42