Test bank for college algebra 12th edition by lial

Exam
Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use set notation, and list all the elements of the set.
1) {19, 20, 21, . . . , 25}
A) {19, 20, 22, 24, 25}
C) {19, 20, 21, 22, 23, 24, 25, 26}

2) 1,

1)
B) {19, 20, 21, 22, 23, 24, 25}
D) {19, 21, 23, 25}

1 1
1
, ,...,
3 9
243

2)

A) 1,

1 1 1 1
1
, ,
,
,
3 9 27 81 243

B) 1,

1 1 1
1
, ,
,
3 9 27 243

C) 1,

1 1 1
1
1
, ,
,
,
3 9 27 729 19,683

D) 1,

1 1 1 1 1
, , , ,
3 5 6 7 8
3)

3) {15, 22, 29, . . ., 64}
A) {15, 22, 29, 36, 43, 50, 57, 64}
C) {15, 22, 29, 36, 43}

B) {15, 22, 29, 37, 44, 51, 58, 65}
D) {15, 22, 28, 35, 42, 49, 56, 63}
4)

4) {82, 77, 72, . . ., 32}
A) {82, 77, 72, 66, 61, 56, 51, 46, 41, 36, 31}
B) {82, 77, 72, 62, 52, 42, 32}
C) {82, 87, 92, 97, 102, 107, 112, 117, 122, 127, 132}
D) {82, 77, 72, 67, 62, 57, 52, 47, 42, 37, 32}
5) The first four natural numbers.
A) {0, 2, 4, 6}
B) {0, 1, 2, 3, 4}

C) {1, 2, 3, 4}

D) {0, 1, 2, 3}

5)

6) The natural numbers between 3 and 5.
A) {3, 5}
B) {0, 1, 2, 3}

C) {3, 4, 5}

D) {4}

6)

Identify the set as finite or infinite.

7) {6, 7, 8, . . ., 11}
A) infinite

7)
B) finite

8) {3, 5, 7, . . .}
A) finite

9) 1,

8)
B) infinite

1 1 1
, ,
, . . .,
3 9 27

9)

A) finite

B) infinite

10) {x|x is a natural number larger than 1}
A) finite

10)
B) infinite

1


11) {x|x is a fraction between 0 and 1}
A) finite

B) infinite

11)

12) {x|x is an even natural number}
A) infinite

B) finite

12)

13) {x|x is a person alive now}
A) infinite

13)
B) finite

Insert ∈ or ∉ in the blank to make the statement is true.
{7, 8, 9, 10}
14) 10

14)

A) ∈
15) 10

B) ∉
{6, 9, 12, 10, 8}

15)

A) ∈
16) -9

B) ∉
{9, 11, 13, 15}

16)

A) ∉
17) 0

B) ∈

{7, 9, 0, 11, 10}

17)

A) ∈
18) 0

B) ∉

{4, 5, 6, 7, 8, 9}

18)

A) ∉
19) {9}

B) ∈
{9, 10, 11, 12, 13, 14}

19)

A) ∉

B) ∈

20) {10}

{8, 10, 12, 14}

20)

A) ∉
21) {0}

B) ∈
{0, 4, 5, 6, 7}

21)

A) ∈
22) 4

B) ∉

∅

22)

A) ∈
23) ∅

B) ∉

∅

23)

A) ∉

B) ∈

Tell whether the statement is true or false.
24) 6 ∈ {4, 54, 6, 7}
A) True

24)
B) False

25) 7 ∈ {-3, 8, 9, 12}

A) True

25)
B) False

2


26) 11 ∉ {0, 9, 10, 12, 14}
A) True

B) False

27) {0, 8, 11, 16} = {11, 8, 16, 0}
A) True

B) False

26)

27)

28) {1, 6, 4, 7} = {4, 1, 6}
A) True

28)
B) False

29) {x | x is a natural number greater than 1} = {1, 2, 3, . . .}
A) True

B) False

29)

30) Let A = {9, 10, 11, 12, 13, 14}, B = {11, 13, 15}, C = {9, 10, 12, 14}, D = {9, 14}, and
U = {9, 10, 11, 12, 13, 14, 15}.

30)

A⊆U
A) True

B) False

31) Let A = {8, 9, 10, 11, 12, 13}, B = {10, 12, 14}, C = {8, 9, 11, 13}, D = {8, 13}, and
U = {8, 9, 10, 11, 12, 13, 14}.
A⊆B
A) True

31)

B) False

32) Let A = {2, 3, 4, 5, 6, 7}, B = {4, 6, 8}, C = {2, 3, 5, 7}, D = {2, 7}, and U = {2, 3, 4, 5, 6, 7, 8}.
C⊆A
A) True

32)

B) False

33) Let A = {6, 7, 8, 9, 10, 11}, B = {8, 10, 12}, C = {6, 7, 9, 11}, D = {6, 11}, and U = {6, 7, 8, 9, 10, 11, 12}.
∅⊆D
A) True

33)

B) False

34) Let A = {6, 7, 8, 9, 10, 11}, B = {8, 10, 12}, C = {6, 7, 9, 11}, D = {6, 11}, and U = {6, 7, 8, 9, 10, 11, 12}.
C ⊆∅
A) True

34)

B) False

35) Let A = {2, 3, 4, 5, 6, 7}, B = {4, 6, 8}, C = {2, 3, 5, 7}, D = {2, 7}, and U = {2, 3, 4, 5, 6, 7, 8}.
{6, 8} ⊆ B
A) True

35)

B) False

36) Let A = {5, 6, 7, 8, 9, 10}, B = {7, 9, 11}, C = {5, 6, 8, 10}, D = {5, 10}, and U = {5, 6, 7, 8, 9, 10, 11}.
{0, 6, 10} ⊆ C
A) True

B) False

3

36)


37) Let A = {7, 8, 9, 10, 11, 12}, B = {9, 11, 13}, C = {7, 8, 10, 12}, D = {7, 12}, and
U = {7, 8, 9, 10, 11, 12, 13}.
B⊈C
A) True

B) False

38) Let A = {5, 6, 7, 8, 9, 10}, B = {7, 9, 11}, C = {5, 6, 8, 10}, D = {5, 10}, and U = {5, 6, 7, 8, 9, 10, 11}.
D⊈C
A) True

U⊆C
A) True

40)

A) ⊈

B) ⊆
{5, -6, 10, -8, 12, 7}

41)

A) ⊆

B) ⊈
{4, 4, 6, 7, 8, 9}

42)

A) ⊈
43) {7, 8, 9, 12}

B) ⊆
{7, 11, 9, 10, 8, 12}

43)

A) ⊆
44) {0, 2, 4, 7}

B) ⊈
{2, 4, 7, 8, 9, 10}

44)

A) ⊆
45) ∅

B) ⊈

{6, 9, 13, 0, 10, 14}

45)

A) ⊆
46) {-13, 8, -14, 0, 12}

B) ⊈
∅

46)

A) ⊆
47) ∅

39)

B) False

Insert ⊆ or ⊈ in the blank to make the statement true.
40) {9, 10, 11}
{0, 9, 10, 11, 12, 13}

42) {4, 6, 9, 11}

38)

B) False

39) Let A = {1, 2, 3, 4, 5, 6}, B = {3, 5, 7}, C = {1, 2, 4, 6}, D = {2, 6}, and U = {1, 2, 3, 4, 5, 6, 7}.

41) {8, 12}

37)

B) ⊈

∅

47)

A) ⊆

B) ⊈

Tell whether the statement is true or false.
48) {10, 13, 14, 16} ∩ {13, 14, 17, 18} = {13, 14}
A) True

48)
B) False

49) {6, 8, 9, 11} ∪ {0, 10, 8, 13, 6} = {6, 8}
A) True

49)
B) False

4


50) {5, 7, 8, 10} ∩ ∅ = {5, 7, 8, 10}
A) True

B) False

51) {8, 10, 11, 13} ∪ ∅ = {8, 10, 11, 13}
A) True

B) False

50)

51)

Use these sets to find the following. Identify any disjoint sets.
52) Let U = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}, M = {5, 7, 9, 11}, N = {6, 8, 10, 12, 14},
Q = {5, 7, 9, 11, 13, 15}, and R = {5, 6, 7, 8}.
M∩R
A) ∅; M and R are disjoint sets.
C) {5, 7}

52)

B) {5, 6, 7, 8, 9, 11}
D) {5, 6, 7, 8}

53) Let U = {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}, M = {4, 6, 8, 10}, N = {5, 7, 9, 11, 13},
Q = {4, 6, 8, 10, 12, 14}, and R = {4, 5, 6, 7}.
M∪N
A) {4, 5, 6, 7, 8, 9, 10, 11, 13}
C) {5, 6, 7, 8, 9, 10, 11, 12, 13}

53)

B) {4, 5, 6, 7, 8, 9, 13}
D) ∅; M and N are disjoint sets.

54) Let U = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, M = {2, 4, 6, 8}, N = {3, 5, 7, 9, 11}, Q = {2, 4, 6, 8, 10, 12},
and R = {2, 3, 4, 5}.
M∩N
A) {3, 4, 5, 6, 7, 8, 9, 10, 11}
C) {4, 5, 6, 7, 11}

54)

B) ∅; M and N are disjoint sets.
D) {2, 3, 4, 5, 6, 7, 8, 9, 11}

55) Let U = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}, M = {5, 7, 9, 11}, N = {6, 8, 10, 12, 14},
Q = {5, 7, 9, 11, 13, 15}, and R = {5, 6, 7, 8}.

55)

N'
A) M, or {5, 7, 9, 11}
C) Q, or {5, 7, 9, 11, 13, 15}

B) {7, 9, 11, 13, 15}
D) {6, 8, 10, 12, 14}

56) Let U = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, M = {2, 4, 6, 8}, N = {3, 5, 7, 9, 11}, Q = {2, 4, 6, 8, 10, 12},
and R = {2, 3, 4, 5}.

Q ∩R'
A) {4, 6, 8, 10, 12}
C) ∅; Q and R' are disjoint sets.

56)

B) {6, 8, 10, 12}
D) {5, 6, 7, 8, 9, 10, 11, 12}

57) Let U = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, M = {3, 5, 7, 9}, N = {4, 6, 8, 10, 12}, Q = {3, 5, 7, 9, 11, 13},
and R = {3, 4, 5, 6}.
∅∪N
A) {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}
B) N, or {4, 6, 8, 10, 12}; N and ∅ are disjoint sets.
C) {5, 7, 9, 11, 13}
D) ∅; N and ∅ are disjoint sets.

5

57)


58) Let U = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}, M = {5, 7, 9, 11}, N = {6, 8, 10, 12, 14},
Q = {5, 7, 9, 11, 13, 15}, and R = {5, 6, 7, 8}.
(N ∪ R) ∩ Q
A) ∅; N and R are disjoint sets.
C) {7}

58)

B) {5}
D) {5, 7}

59) Let U = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, M = {3, 5, 7, 9}, N = {4, 6, 8, 10, 12}, Q = {3, 5, 7, 9, 11, 13},
and R = {3, 4, 5, 6}.
Q' ∩ (N' ∩ U)
A) {4, 6, 8, 10, 12}
C) {4, 5, 6, 7, 8, 9}

59)

B) ∅; Q' and (N' ∩ U) are disjoint sets.
D) {3, 5, 7, 9, 11, 13}

60) Let U = {9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19}, M = {9, 11, 13, 15}, N = {10, 12, 14, 16, 18},
Q = {9, 11, 13, 15, 17, 19}, and R = {9, 10, 11, 12}.
(R ∪ N) ∩ M'
A) M, or {9, 11, 13, 15}
C) ∅; M' and (R ∪ N) are disjoint sets.

60)

B) {9, 10, 12, 14, 16, 18}
D) N, or {10, 12, 14, 16, 18}

61) Let U = {7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17}, M = {7, 9, 11, 13}, N = {8, 10, 12, 14, 16},
Q = {7, 9, 11, 13, 15, 17}, and R = {7, 8, 9, 10}.
(U ∪ ∅) ∩ R'
A) ∅; R' and (U ∪ ∅) are disjoint sets.
C) R, or {7, 8, 9, 10}

61)

B) U, or {7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17}
D) {11, 12, 13, 14, 15, 16, 17}

List all the elements of set B that belong to the indicated set.
0
62) B = 14, 7, -14, 0, , 25
1

62)

Integers
A) 14, -14, 0,

0
,
1

25

B) 14, 0,

C) 14, -14, 0

63) B = 11,

5, -17, 0,

D) 14, 0

0
,
4

16

Whole numbers
0
A) 11, 0, , 16
4

64) B = 14,

8, -14, 0,

25

63)

C) 11, -17, 0

B) 11, 0

0
,
4

D) 11, -17, 0,

4

64)

Natural numbers
A) 14, 0,

4

16

B) 14,

4

C) 14, 0

6

D) 14, 0,

0
4


65) B = 5,

7, -16, 0,

0
,
8

9,

-5
, 0.59
0

65)

Rational numbers
7,

9

B) 5, -16, 0,

C) 5, 0,

9

D)

A)

7,

0

,
8

9, 0.59

0
, 0.59
8

Evaluate the expression.
66) 3 6

66)

A) 18

B) 324

C) 729

D) 72.9

67) -3 6
A) -18

B) 729

C) -729

D) 18

68) (-4)3
A) -12

B) -64

C) 144

D) 64

69) -4 · 5 2
A) 400

B) -100

C) 100

D) -400

67)

68)

69)

70) -5(-2)3
A) -1,000

B) 40

C) 1,000

D) -40

71) 26 + 28 · 2 + 7
A) 89

B) 63

C) 115

D) 486

72) 11 + 62 - (-3) · 7
A) 26

B) 308

C) 68

D) 182

73) 81 - 8 · 3 + 4
A) 223

B) 61

C) 511

D) 80

74) 92 - 22 · 4 + 224 ÷ (-16)
A) -997

B) -10

C) -19

D) 266

75) (-2)3 - (-2)2
A) -12

B) -4

C) 12

D) 4

70)

71)

72)

73)

74)

75)

76) (9 + (-2))[7 + (4 + 8)]
A) 22

B) 26

C) 133

D) 89

77) -8[-1 + 2(-9 + 3)]
A) 44

B) 48

C) 104

D) -4

78) (9 - 82 )(-8 +
A) 73

B) -4895

C) -47

D) -55

76)

77)

81)

78)

7


79) -

3
1
- 8
4
A)

80)

-

3 7
2 8

1
2

79)
C) -

B) 0

5
4

D) -

3
4

-7 · 5 + 3 - (-1 + 6)
-7 · 8 + 2
A)

61
70

80)
B)

37
70

C)

Evaluate the expression for x = -2, y = 3, and a = -4.
81) -3x + 7y + 5a
A) 23
B) 7

59
54

D)

37
54

81)
C) -7

D) -43

82) -4a - 6y - 3x
A) 8

B) 4

C) 23

D) 19

83) (-5x - 3y)(-8a)
A) 32

B) -32

C) 140

D) -288

84) 9x2 - 4y - a
A) 28

B) 22

C) 26

D) 25

85) x3 - 7y + 3a
A) -28

B) -25

C) -41

D) -37

86)

85)

86)
3
19

B) -

1

23

C) 0

D) -

1
19

87)

x 9
+
2 y
4
3

B)

5
2

C) 0

D) 2

-(x + 5)2 - 2y
-2 - a
A) -

89)

84)

6 a
y 2

A)

88)

83)

y + 2x
y - 4a
A) -

87)

82)

3
2

88)
B)

35
2

C)

15
2

D) -

15
2

2x + 2(3 + a)2
y-1
A) 9

89)
C) - 1

B) 19

8

D) 33


Identify the property illustrated by the statement. Assume all variables represent real numbers.
90) 6 · 1 = 6
A) Distributive
B) Identity
C) Closure
D) Inverse

91) (2 + 3) + 6 = (3 + 2) + 6
A) Associative

B) Commutative

C) Distributive

D) Closure

92) 8 + 0 = 8
A) Associative

B) Closure

C) Inverse

D) Identity

93) 3(x + 8) = 3x + 24
A) Commutative

B) Distributive

C) Associative

D) Closure

94) 4 + (-4) = 0
A) Associative

B) Identity

C) Inverse

D) Closure

95) 2 + 9 = 9 + 2
A) Associative

96)

91)

92)

93)

94)

95)
B) Commutative

C) Identity

D) Inverse

1
· (a + 2) = 1, if a + 2 ≠ 0
(a + 2)
A) Identity

97) (8 · 4) · 6 = 8 · (4 · 6)
A) Commutative
98) 6(π) is a real number.
A) Closure

90)

96)

B) Inverse

C) Distributive

D) Closure

B) Associative

C) Distributive

D) Identity

97)

98)
B) Distributive

C) Identity

D) Associative

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
5
99) (-8y)
99)
4
A) -10y

100)

100)
B) 5y

D) -5y

C) 4y

5
(16y - 16x + 20z)
4
A) 20y + 20x + 25z

102)

D) 20y

1
y (-15)
3

A) 3y

101)

C) -9y

B) 10y

101)
B) 20y + 20x - 25z

C) 20y - 20x + 25z

D) 20y - 20x - 25z

1
10
10y +
x - 20
5
3
A) 2y +

2
x-4
3

102)
B) 2y +

2
x+4
3

C) 2y -

9

2
x-4
3

D) 2y -

2
x+4
3


Use the distributive property to rewrite a sum as a product or the product as a sum.
103) -11y + 3y
A) 8y
B) -14y
C) -8y

103)
D) 14y

104) 2 - 10b
A) -8b

B) 2(1 - 6b)

C) 2(1 - 5b)

D) 12b

105) -4(x + k)
A) -4x - 4k

B) -4xk

C) -4x + k

D) -4x + 4k

106) -(-3 - 9b)
A) 3 + 9b

B) -3 - 9b

C) 3 - 9b

D) -3 + 9b

107) -(-5y + 8k)
A) -5y + 8k

B) 5y + 8k

C) 5y - 8k

D) -5y - 8k

104)

105)

106)

107)

Decide whether the statement is true or false. If false, correct the statement so it is true.
108) 5 - 10 = 5 - 10
A) True
B) False; 5 - 10 = 10 - 5
109) 2 - 8 = 8 - 2
A) True

B) False; 2 - 8 = 2 - 8

110) -12 = - 12
A) True

B) False; -12 = -(-12) = 12

111) -3 = 3
A) True

B) False; -3 = - 3 = -3

109)

110)

111)

112) (-4)3 = - (4)3

112)
B) False; (-4)3 = 4 3

A) True

113)

-4
-4
=
5
5

113)

A) True

B) False;

114) -5 · 10 = -5 · 10
A) True

Evaluate the expression.
115) -12
A) ±12
116) 23
A) 23

108)

4
-4
=
5
-5
114)

B) False; -5 · 10 = - 5 · 10

115)
B) -12

C) 12

D) 0
116)

C) ±23

B) 0

10

D) -23


117) - 20
A) ±20

B) 0

C) -20

D) 20

118) - -2
A) 0

B) ±2

C) 2

D) -2

119) -

118)

1
7

119)

A) ±

120) - -

1
7

B)

1
7

C) -

1
7

D) 0

8
3

A) -

121) -

117)

120)

8
3

B) ±

8
3

C) 0

D)

8
3

8
7
A) 0

121)
B) -

8
7

C)

8
7

D) ±

8
7

122) Let x = -19, y = -18. Evaluate |21x|.
A) -342
B) 342

C) 399

D) -399

123) Let x = -8, y = 5. Evaluate x + y .
A) -3
B) 3

C) 13

D) -13

124) Let x = -8, y = 4. Evaluate x + y .
A) 4
B) 12

C) -4

D) -12

125) Let x = 18, y = -6. Evaluate |y - x|.

A) 12
B) 24

C) -12

D) -24

126) Let x = 2, y = 5. Evaluate 6x - 7y .
A) 47
B) -23

C) -47

D) 23

122)

123)

124)

125)

126)

127) Let x = -9, y = 13. Evaluate |9y - 2x|.
A) -99
B) 135

C) 99

D) -135

128) Let x = 9, y = -2. Evaluate 4 x + 5 y .
A) -26
B) 46

C) 26

D) -46

127)

128)

129) Let x = -18, y = 12.
Evaluate |4y - 5x| - |4y|.
A) 60
B) 36

129)
C) 84

11

D) 90


130) Let x = 6 and y = -3. Evaluate
A) -1

131) Let x = 5, y = -1. Evaluate
A)

5
22

|x| |y|
.
+
x
y

130)

B) 1

C) 2

D) 0

|x + 2| - |2y|
.
| 3y + 5x|
B)

131)

5
28

C)

9
22

D)

1
2

Determine which property of absolute value justifies the statement.
132) x ≥ 0
A) Property 1: the absolute value of a number is positive or 0.
B) Property 5: the triangle inequality
C) Property 1: the absolute value of a number is positive.
D) Property 1: the absolute value of a number is greater than 0.

132)

133) -x = x
A) Property 5: the triangle inequality
B) Property 1: the opposite of a number is equal to the absolute value of the number .
C) Property 2: the opposite of the absolute value of a number is equal to the absolute value of
the number.
D) Property 2: the absolute value of a number and its opposite are equal.

133)

134) x + y ≤ x + y
A) Property 4: the absolute value of the sum of the numbers is less than or equal to the sum of

the two numbers.
B) Property 5: the sum of the absolute values of two numbers is less than or equal to the
absolute value of their sum (the triangle inequality).
C) Property 5: the absolute value of the sum of two numbers is less than or equal to the sum of
their absolute values (the triangle inequality).
D) Property 4: the sum of two numbers is less than or equal to the absolute value of the sum of
the numbers.

134)

Find the distance between two points given their coordinates.
135) Find the distance between points P and Q on a number line, with coordinates 3 and 10,
respectively.
A) d(P, Q) = -13
B) d(P, Q) = 7
C) d(P, Q) = 13
D) d(P, Q) = -7

135)

136) Find the distance between points R and S on a number line, with coordinates -2 and 4,
respectively.
A) d(R, S) = 2
B) d(R, S) = -2
C) d(R, S) = -6
D) d(R, S) = 6

136)

137) Find the distance between points P and Q on a number line, with coordinates -10 and 3,

respectively.
A) d(P, Q) = 7
B) d(P, Q) = 13
C) d(P, Q) = -7
D) d(P, Q) = -13

137)

138) Find the distance between points R and S on a number line, with coordinates 8 and -7,
respectively.
A) d(R, S) = -15
B) d(R, S) = 1
C) d(R, S) = 15
D) d(R, S) = -1

138)

12


139) Find the distance between points P and Q on a number line, with coordinates 5 and -12,
respectively.
A) d(P, Q) = 17
B) d(P, Q) = -7
C) d(P, Q) = -17
D) d(P, Q) = 7

139)

140) Find the distance between points R and S on a number line, with coordinates -4 and -7,

respectively.
A) d(R, S) = -11
B) d(R, S) = 11
C) d(R, S) = 3
D) d(R, S) = -3

140)

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
141) xy < 0
A) x and y have different signs.
B) x and y must be negative.
C) x and y have the same sign.
D) x and y must be positive.

142)

x
>0
y

142)

A) x and y have the same sign.
C) x and y have different signs.
143) -

B) x and y must be negative.
D) x and y must be positive.

x
>0
y

143)

A) x and y must be positive.
C) x and y have different signs.

B) x and y must be negative.
D) x and y have the same sign.

144) x2 y < 0
A) x and y must be negative.
C) x must be negative.

145)

144)
B) x and y have different signs.
D) y must be negative.

x2
<0
y

145)

A) y must be negative.
C) x and y must be negative.

146)

141)

B) x must be negative.
D) x and y have different signs.

x3
>0
y

146)

A) x and y have different signs.
C) x and y have the same sign.

B) x and y must be positive.
D) x and y must be negative.

Solve the problem.
147) The formula C =

5
(F - 32) expresses the relationship between Fahrenheit temperature, F, and
9

147)

Celsius temperature, C. Use the formula to convert 86°F to its equivalent temperature on the

Celsius scale.
A) 97°C
B) 30°C
C) 6°C
D) 66°C
148) A stone is dropped from a tower that is 730 feet high. The formula h = 730 - 16t2 describes the
stone's height above the ground, h, in feet, t seconds after it was dropped. What is the stone's
height 1 seconds after it is released?
A) 739 ft
B) 714 ft
C) 689 ft
D) 724 ft

13

148)


149) If a rock falls from a height of 70 meters above the ground, the height H (in meters) after x seconds
can be approximated using the formula H = 70 - 4.9x2 . What is the height of the rock after 2
seconds?
A) 50.4 m

B) -26.04 m

C) 260.4 m

149)

D) 60.2 m

150) As the relative humidity increases, the temperature seems higher than it is. The formula T = 0.117x
+ 87.16 approximates the apparent temperature for an actual temperature of 95°F, where x is the
relative humidity. What is the apparent temperature (to the nearest degree) for a relative humidity
of 100%?
A) 187°F
B) 87°F
C) 1020°F
D) 99°F

150)

151) Use the formula

151)

Y
T
I
C
, where A = number of passes
Passing Rating ≈ 85.68
+ 4.31
+ 326.42
- 419.07
A
A
A
A
attempted, C= number of passes completed, Y = total number of yards gained passing, T = number

of touchdown passes, and I = number of interceptions, to approximate the passing rating for C.
Felix. Round to the nearest tenth.
Quarterback
A. Smith
B. Jones
C. Felix
A) 82.3

A
461
473
584

C
227
266
311

Y
3015
3107
4378

T
23
27
24

I
4

13
13

B) 83.6

C) 83

D) 82

152) The Blood Alcohol Concentration (BAC) of a person who has been drinking is given by the
expression
number of oz × % alcohol × .075 ÷ body weight in lb - hours of drinking × .015.
Find the BAC to the nearest thousandth for a 142-lb woman, who, in 3 hours, has drunk 3 10-oz
beers (30 oz), each having a 3.2% alcohol content.
A) -0.028

B) -0.215

C) -199.949

14

D) 0.006

152)


153) The NSC (Not So Consistent) Corporation has just completed its first year of business. The
following chart shows its monthly profit (or loss).
Month

January
February
March
April

Profit (Loss) in Dollars
-14,526
1874
-8977
-14,107

May

14,073

June

14,632

July

-13,834

August

-13,170

September
October

-4860
6630

November

-3338

December

-974

The profit was smallest in
A) June

?

.

B) December

C) January

D) February

154) The NSC Corporation has just completed its first year of business. The following chart shows its
monthly profit (or loss).
Month

Profit (Loss) in Dollars

January

-14,526

February
March
April

1874
-8977
-14,107

May

14,073

June

14,632

July

-13,834

August

-13,170

September
October

-4860
6630

November

-3338

December

-974

The absolute value of the profit or loss was smallest in
A) June

153)

B) December

?

.

C) February

15

D) January

154)

155) During a certain football game, a player gained 38 yards rushing and -54 yards returning fumbles.
Find his total yardage. Is this the same as the sum of the absolute values of the two categories?
Why or why not?
A) -16 yards; Yes, it is the same.
B) -16 yards; No, it is not the same because the sum of the absolute values is 92.
C) 92 yards; No, it is not the same because the sum of the absolute values is -16 .
D) 16; yards; No, it is not the same because the sum of the absolute values is -92.

155)

156) Find the magnitude of the difference between a windchill factor of -50 and a windchill factor of -5.
A) 45
B) -55
C) -45
D) 55

156)

157) Find the magnitude of the difference between a windchill factor of 82 and a windchill factor of -45.
A) -37
B) 37
C) 127
D) -127

157)

158) It is recommended that a woman who is pregnant should exercise such that her heart rate does not
exceed 140 beats per minute. Use absolute value notation to write an expression that describes the

difference between the heart rate achieved by each of the following pregnant women and the
recommended maximum heart rate. Then evaluate that expression.

158)

(i) Abigail: 138 beats per minute
(ii) Mathilda: 147 beats per minute
A) (i) Abigail: 138 - 140 = 2
(ii) Mathilda: 147 - 140 = 7
C) (i) Abigail: 138 + 140 = 278
(ii) Mathilda: 147 + 140 = 287

B) (i) Abigail: 140 - 138 = -2
(ii) Mathilda: 140 - 147 = -7
D) (i) Abigail: 138 - 140 = -2
(i) Mathilda: 147 - 140 = 7

Simplify the expression. Assume all variables represent nonzero real numbers.
159) (3a 3 ) · (5a 8 )
A) 15a 24

159)

B) 8 24

C) 15a 11

D) 8 11

B) 15n 6

C) 8n 5

D) 8n 6

B) 8 13

C) 4 40

D) 1640

B) x6

C) (2x)8

D) x8

B) 1213

C) 6 40

D) 6 13

164) (2a6 b8 )(-4a 7 b4 )
A) 8a 13b13

B) -8a 13b12

C) -8a 42b8

D) 8a 41b8

165) (-4x6 y)(-7x4 y5 )
A) -28x10y5

B) 28x10y6

C) -11x10y5

D) 28x24y5

160) (3n 2 ) · (5n 3 )
A) 15n 5

160)

161) 4 8 · 4 5
A) 4 13

161)

162) x4 · x2
A) (2x)6

162)

163) 6 8 · 6 5
A) 3640

163)

164)

165)

16


166) (-2t5 )(5t2 )(-3t7 )
A) 0t12

166)
B) 0t14

C) 30t15

D) 30t14

2x4 y4 4
z4

167)

A)

168) -

2x16y16
z8

167)
B)

2x16y16
z 16

C)

16x16y16
z 16

D)

5x3 0
y2
A) -1

168)
B)

y2

C) 1

625x12

D)

Decide whether the expression has been simplified correctly.
169) (ab)4 = ab4

A) Not simplified correctly

170)

16x8 y8
z8

625x12
y8

169)
B) Simplified correctly

x 5 x5
=
8
8

170)

A) Not simplified correctly

B) Simplified correctly

171) 6 0 x = 0
A) Simplified correctly

171)
B) Not simplified correctly

172) 6 0 x = 6x
A) Simplified correctly

B) Not simplified correctly

173) 6 0 x = 1
A) Not simplified correctly

B) Simplified correctly

174) 4 0 x = x
A) Not simplified correctly

B) Simplified correctly

175) x4 · x2 = x6
A) Simplified correctly

B) Not simplified correctly

176) (x4 )2 = x6
A) Simplified correctly

B) Not simplified correctly

177) x3 · x2 = x6
A) Not simplified correctly

B) Simplified correctly

178) (x4 )2 = x8
A) Not simplified correctly

B) Simplified correctly

172)

173)

174)

175)

176)

177)

178)

17


Simplify the expression. Assume all variables represent nonzero real numbers.
179) (x4 )6
A) 6x4

179)

B) 24x

C) x24

D) x10

B) 2512

C) 5 12

D) 257

B) 5t5

C) 5 5 t

D) 5 5 t5

180) (5 4 )3

180)

A) 5 7
181) (5t) 5

181)

A) 25t5
182) (x4 y8 )3
A) x12y24

182)

B) x64y512

C) x7 y11

D) x4 y24

183) (8xy)4

183)

A) 4096x4 y4

B) 32x4 y4

C) 4096xy

B) 6x3

C) -8x3

D) 8x

B) 12x

C) 64x6

D) -64x6

D) 32xy

184) (-2x)3

184)

A) -6x
185) (-2x)6

185)

A) -12x

186)

5 2
x
A)

187)

186)
5
x2

B)

25
x

C)

25
x2

D) 25x2

a4 2
b5
A)

187)
a8
b5

B)

a8
b10

C)

a 10
b8

D)

a5
b10

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.

188) 3 0
188)
A) -1

B) 0

C) 1

D) 3

189) -8 0
A) -8

B) 1

C) 0

D) -1

190) (-2)0
A) 1

189)

190)
B) 2

C) 0

18

D) -1


191) -(-6)0
A) 6

B) -1

C) 0

D) 1

192) 5x0
A) 5

B) 0

C) 1

D) x

193) -9x0
A) 1

B) -1

C) 0

D) -9

194) (5x)0
A) 1
195) (-2x)0
A) -1

191)

192)

193)

194)
B) 0

C) 5

195)
B) 0

C) 1

Identify the expression as a polynomial or not a polynomial.
196) 15x - 3
A) Not a polynomial
197) 2x -

D) 2

196)

B) Polynomial

9
+4
x

197)

A) Polynomial

B) Not a polynomial

198) 7x5 + 4x2 - 14
A) Polynomial

B) Not a polynomial

199)

D) 5x

198)

7
4
+
-9
5
x
x3

199)

A) Polynomial

B) Not a polynomial

200) 0.6x9 - 8.2
A) Polynomial

B) Not a polynomial

200)

201) -9

201)
A) Not a polynomial

B) Polynomial

202) 7x2 y3 - 4x3 y - 3x
A) Not a polynomial

B) Polynomial

202)

Determine the degree of the polynomial.
203) 2x6 - 8x7 + 9x2 - 8

203)

A) 6

B) 7

C) 15

D) 4

204) 4a 2 + 16a 5 - 5a
A) 3

B) 8

C) 7

D) 5

204)

19


205) -3a 4 - 16a 2 + 8a + 4a 6
A) 4

B) 13

C) 12

D) 6

206) -2x2 + 5x3 + 6x4 + 1
A) 4

B) 10

C) 2

D) 9

207) 4t6 + 5t3 + 4 - 3t2
A) 4

B) 11

C) 6

D) 12

208) -a + 7a 3 - 6a 7 + 4a 2
A) 12

B) 7

C) 13

D) 4

209) t - 3t2 + 6t3 + 5
A) 3

B) 1

C) 4

D) 6

210) -x - 3x2 - 6x3 - 2x5
A) 5

B) 11

C) 4

D) 10

205)

206)

207)

208)

209)

210)

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
211) -17x2
A) Monomial
212) -17x
A) Monomial

211)

B) Binomial

C) None of these

D) Trinomial

B) Trinomial

C) Binomial

D) None of these

212)

213) 10y7 + 1
A) Monomial

213)
B) Binomial

C) Trinomial

D) None of these

214) 5z - 4
A) Trinomial

B) Monomial

C) None of these

D) Binomial

215) -16s 7 - 3s - 4
A) Binomial

B) Monomial

C) None of these

D) Trinomial

216) -18y3 + 6y2 + -5
A) Binomial

B) None of these

C) Trinomial

D) Monomial

214)

215)

216)

217) 11c5 - 4c4 - 6c3
A) Trinomial

B) None of these

C) Binomial

D) Monomial

218) -10z 5 + 6z 4 + 9z 3 + 12
A) Binomial

B) Trinomial

C) Monomial

D) None of these

C) Trinomial

D) None of these

217)

218)

219) -19x4 - 4w3 + 8w + 4y5 + 3
A) Monomial
B) Binomial

219)

20


220) 17

220)
A) Monomial

B) None of these

C) Trinomial

D) Binomial

B) 12a 8 - 10a 4

C) 12a 4 - 10a 2

D) 2a 6

Find the sum or difference.
221) (4a 4 - 7a 2 ) + (8a 4 - 3a 2 )

A) 2a 12

221)

222) (7n 6 - 9n + 2n 3 ) + (7n 3 + 6n 6 - 4n)
A) 9n 10

222)
B) -3n 6 + 14n 3 - 2n

C) 13n + 9n 6 - 13n 3

D) 13n 6 + 9n 3 - 13n

223) (-4 - 4x5 + 3x7 + 2x6 ) + (-6x6 - 2x5 - 5 + 4x7 )
A) 7x7 - 4x6 - 6x5 - 9

223)
B) -3x36 - 9
D) 7x14 - 4x12 - 6x10 - 9

C) -10x7 - 10x6 - 2x5 + 6
224) (7x6 + 6x8 - 7 + 4x7 ) - (-1 + 8x7 + 8x8 - 9x6 )
A) -2x8 + 12x7 - 2x6 - 8

224)
B) 14x8 + 12x7 - 2x6 - 6
D) -2x8 - 4x7 + 16x6 - 6

C) 14x8 + 12x7 - 2x6 - 8

225) 2(-2r4 + 9r3 - 3r) - 3(8r4 - 9r3 + 6r2 - 2r)
A) -28r4 + 6r2 - 5r

225)
B) -28r4 - 9r3 + 18r2 - 12r
D) -28r4 + 18r3 - 6r2 - r

C) -28r4 + 45r3 -18r2
226) (3 + 7x2 + 9x4 + 3x3 ) + (-7x3 - 9x2 + 6 + 3x4 )
A) 6x18 + 9

226)
B) -4x4 - 4x3 + 15x2 + 6

C) 12x4 - 4x3 - 2x2 + 9

D) 12x8 - 4x6 - 2x4 + 9

227) (2x7 + 6x9 - 7 - 7x8 ) - (2 - 2x8 + 3x9 - 7x7 )
A) 9x9 - 9x8 - 5x7 - 9

227)
B) 3x9 - 9x8 - 5x7 - 5

C) 9x9 - 9x8 - 5x7 - 5

D) 3x9 - 5x8 + 9x7 - 9

228) (3x9 + 11x7 - 4x3 + 8) - (11x9 - 8x5 + 8x3 - 9)
A) 8x9 + 11x7 + 8x5 - 12x3 + 17

228)
B) -8x9 + 11x7 - 8x5 - 12x3 + 17
D) -8x9 + 11x7 + 8x5 - 12x3 + 17

C) 8x9 + 11x7 - 8x5 - 12x3 + 17
229) (5x4 - 9x2 + x) - (2x3 + 8x2 + 3x) + (4x2 - x)
A) 5x4 - 2x3 - 11x2 + 3x

229)
B) 11x5 + 7x4 - 3x
D) 5x4 - 2x3 - 13x2 - 3x

C) 5x4 + 2x3 - 21x2 - 3x
230) -(2x3 + x - 8) + (4x3 + 2x2 ) - (9x2 - 3x -1)
A) 2x3 - 7x2 + 2x + 9

230)
B) 6x3 - 11x2 + 2x - 9
D) 1x3 - 5x2 - 2x + 9

C) 2x3 + 7x2 + 4x - 9

21


Find the product.
231) (3m 4 )(2m 4 )
A) 6m 8

231)
B) -6m 8

C) -6m

B) -8m 5

C) 8m 6

D) 6m

232) (-2m 2 )(4m 3 )
A) -8m

232)
D) 8m

233) (-2x2 y4 )(-2x2 y2 )
A) 4xy6

B) 4x6 y4

C) 4x4 y6

D) 4xy4

234) 3x5 (-8x - 10)
A) 24x6 + 30x5

B) -24x5 - 30

C) -54x6

D) -24x6 - 30x5

235) 2x2 (6x6 + 4x4 )
A) 12x8 + 4x4

B) 12x12 + 8x8

C) 12x8 - 8x6

D) 12x8 + 8x6

233)

234)

235)

236) 7ax7 (2ax3 - 2x2 - 3)
A) -14a 2 x21 + 14ax14 + 21ax7

236)
B) -14a 2 x10 + 14ax9 + 21ax7
D) 14ax21 - 14ax14 - 21ax7

C) 14a 2 x10 - 14ax9 - 21ax7
237) 11ax6 (-4ax7 - 2x5 - 12a)
A) -44a 2 x42 - 22ax30 - 132a 2 x6

237)
B) -44a 2 x13 + 22ax11 + 132a 2 x6

C) -44ax13 - 22ax11 - 132ax6

D) -44a 2 x13 - 22ax11 - 132a 2 x6

238) 12a 2 x8 (-4a 7 x9 - 3x5 - 8a)
A) -48a 14x72 + 36a 2 x40 + 96a 2 x8

238)
B) -48a 9 x17 - 36a 2 x13 - 96a 3 x8

C) -48a 9 x17 - 3x5 - 8a

D) 48a 9 x17 + 36a 2 x13 + 96a 3 x8

239) -3x5 (11x4 + 8x3 )
A) -57x9 - 57x8

B) -33x9 + 8x3

C) -33x9 - 24x8

D) -57x5

240) (5m 2 z 4 )(3m 3 z 2 )
A) 15m 5 z

B) 15mz 5

C) 15mz 6

D) 15m 5 z 6

241) (2x - 6)(x + 5)
A) x2 + 4x + 3

B) 2x2 + 4x - 30

C) 2x2 + 3x - 30

D) x2 - 30x + 4

239)

240)

241)

242) (x + 1)(3x + 6)
A) 3x2 + 8x + 6

B) 3x2 + 9x + 6

C) 3x2 + 6x + 9

D) x2 + 9x + 9

243) (x + 4)(-3x - 2)
A) -3x2 - 14x - 8

B) -3x2 - 8x - 14

C) -3x2 - 16x - 8

D) -3x2 - 14x - 14

242)

243)

22


244) (x + 11y)(x - 4y)
A) x + 7xy - 44y

244)
B) x2 + 7xy + 7y2

C) x2 + 4xy - 44y2

245) (-9a + 5b)(-8a + 3b)
A) 72a 2 + 13ab + 15b2

D) x2 + 7xy - 44y2
245)

B) 72a 2 + 67ab + 15b2
D) 72a 2 - 67ab + 15b2

C) 72a 2 + 15b2
246) (-2 + x)(3x + 1)
A) 3x2 - 2x - 5

B) 3x2 - 6x - 2

C) x2 - 5x - 5

D) 3x2 - 5x - 2

247) (x + 4)(5x - 5)
A) 5x2 - 20x + 15

B) 5x2 + 15x + 15

C) 5x2 + 13x - 20

D) 5x2 + 15x - 20

248) 3x +

246)

247)

1
1

8x 8
4

A) 24x2 +

1
1
x+
4
32

248)
B) 24x2 -

1
1
x+
4
32

C) 24x2 -

249) (7p - 1)(49p2 + 7p + 1)
A) 49p3 - 1

7
1
x4
32

D) 24x2 +

1
1
x4
32
249)

B) 343p3 + 56p2 - 1

C) 343p3 + 1

D) 343p3 - 1

250) (6y - 5)(36y2 + 30y + 25)

250)

A) 216y3 + 150y2 - 125

B) 216y3 - 125

C) 216y3 + 125

D) 36y3 + 125

251) (4x2 + 3x - 1)(x2 - 3x - 3)
A) 4x4 - 12x3 - 21x2 - 6x + 3

B) 4x4 - 9x3 - 21x2 - 6x + 3

C) 4x4 - 12x3 - 22x2 - 6x + 3

D) 4x4 - 9x3 - 22x2 - 6x + 3

251)

252) (3k2 + 4k - 3)(k2 - 5k + 1)
A) 3k4 - 15k3 - 20k2 + 19k - 3

B) 3k4 - 15k3 - 17k2 + 19k - 3

C) 3k4 - 11k3 - 20k2 + 19k - 3

D) 3k4 - 11k3 - 17k2 + 19k - 3

252)

253) (2s + 3)(2s 3 - 4s 2 + 3s + 2)
A) 4s 4 - 2s 3 + 15s 2 + 13s + 6

253)
B) 4s 4 - 2s 3 - 6s 2 + 13s + 6
D) 4s 4 - 20s 3 - 6s 2 + 13s + 6

C) 4s 4 - 2s 3 - 6s 2 + 4s + 6
254) ( 2x3 - x2 + 3x - 1) (2x + 2)
A) 3x4 + 6x3 + 6x2 + 6x - 4

254)

B) 4x4 + 2x3 + 4x2 + 4x - 2
D) 5x4 - 2x3 + 3x2 - 4x + 2

C) 4x3 + 2x2 + 4x + 4

23


255) 3x(3x - 1)(4x + 9)
A) 34x2 + 70x - 27

255)
B) 12x3 + 23x2 - 9x
D) 36x3 + 69x2 - 27x

C) 32x3 + 71x2 - 25x
256) (3x - 6y)(5x + 9y + 1)
A) 15x2 - 3xy + 3x - 54y2 - 6y

256)
B) 15x2 - 3xy - 3y2
D) 15x2 + 27xy + 3x - 54y2

C) 15x2 - 30xy + 3x - 54y2 - 6y
257) (2x2 - 11y)(-4x2 + 3y + z)
A) -8x2 + 50xy + 2x2 z - 33y2 - 11z

257)
B) -8x4 + 50x2 y2 - 33y2
D) -8x4 + 50x2 y + 2x2 z - 33y2 - 11yz

C) -8x4 + 50x2 y - 33y4 + 2x2 yz
258) (4x - 2y + 7)(4x - 2y - 7)
A) 8x2 - 4y2 - 98

258)
B) -16xy - 28x + -14y - 49
D) 16x2 - 16xy + 4y2 - 49

C) 16x2 + 16xy - 4y2 - 98
259) n 2 3n -

1
1
11n +
4
2

259)

A) 33n 4 -

17 3 1 2
n - n
4
8

B) 33n 4 -

5 3 1 2

n - n
4
8

C) 33n 4 -

5 3 1 2
n + n
8
4

D) 33n 4 +

5 3 1 2
n - n
4
8

260) (x - 8)(x + 8)(x2 + 64)
A) x4 - 64

260)
B) x4 - 16x2 - 64
D) x4 - 4096

C) x4 - 256x2 + 4096
261) (n - 2)(n - 2)(n + 2)(n + 2)
A) n 4 + 8n - 16

B) n 4 - 8n + 16

C) n 4 - 8n 2 + 16

D) n 4 + 8n 2 - 16

262) (a - 11)(a + 11)
A) a 2 - 22

B) a 2 + 22a - 121

C) a 2 - 121

D) a 2 - 22a - 121

263) (m + 3)(m - 3)
A) m 2 - 6

B) m 2 - 6m - 9

C) m 2 - 6m + 9

D) m 2 - 9

264) (n - 1)(n + 1)
A) n 2 - 1

B) n 2 - 2n - 1

C) n 2 - 2

D) n 2 - 2n + 1

261)

262)

263)

264)

265) (12p + 13)(12p - 13)
A) 144p2 - 312p - 169

265)
B) p2 - 169

C) 144p2 - 169
266) (6r - 5)(6r + 5)
A) 36r2 - 25

D) 144p2 + 312p - 169
266)
B) 6r2 - 25

C) 36 + 60r - 25r2

24

D) 36r2 - 60r - 25

267) (p + 3q)(p - 3q)
A) p2 - 6q2

267)
B) p2 - 6pq - 9q2

C) p2 - 9q2

268) (12y + x)(12y - x)
A) 144y2 - 24xy - x2

D) p2 + 6pq - 9q2
268)

B) 144y2 - x2
D) 24y2 - x2

C) 144y2 + 24xy - x2
269) (8a + 11c)(8a - 11c)
A) 64a 2 - 121c2

269)
B) 8a 2 - 11c2

C) 64a 2 + 176ac - 121c2

D) 64a 2 - 176ac - 121c2

270) (9m - 11w)(9m + 11w)

A) 81m 2 - 198mw - 121w2

270)
B) 81m 2 - 121w2

C) 81m 2 + 198mw - 121w2

D) 9m 2 - 11w2

271) [(5x - y) + 3z][(5x - y) - 3z]
A) 25x2 - 10xy + y2 + 30xz + 6yz - 9z 2

271)
B) 25x2 - 10xy + y2 - 9z 2
D) 25x2 + y2 - 9z 2

C) 25x2 + y2 + 30xz + 6yz - 9z 2
272) (n + 7)2
A) 49n 2 + 14n + 49

272)
B) n + 49

C) n 2 + 49

D) n 2 + 14n + 49

273) (p + 10)2

273)

A) p + 100
C) p2 + 100
274) (w - 4)2
A) w2 + 16

B) p2 + 20p + 100
D) 100p2 + 20p + 100
274)
B) w2 - 8w + 16

C) 16w2 - 8w + 16

275) (r - 15)2
A) r2 - 30r + 225

D) w + 16
275)

B) r + 225
D) 225r2 - 30r + 225

C) r2 + 225
276) (8m + 11)2
A) 8m 2 + 121

276)
B) 8m 2 + 176m + 121

C) 64m 2 + 121

D) 64m 2 + 176m + 121

277) (4a - 7)2
A) 16a 2 - 56a + 49
278) (-2x - 9)2
A) -2x2 + 81

277)
B) 4a 2 + 49

C) 16a 2 + 49

D) 4a 2 - 56a + 49

B) -2x2 + 36x + 81

C) 4x2 + 81

D) 4x2 + 36x + 81

278)

25