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) 

{18, 19, 20, . . . , 24} 

1) 

_______ 
A) 

{18, 19, 20, 21, 22, 23, 24} 

B) 

{18, 19, 20, 21, 22, 23, 24, 25} 
C) 

{18, 20, 22, 24} 

D) 

{18, 19, 21, 23, 24} 

 
2) 

2) 

_______ 
A) 

B) 

C) 

D) 

 
3) 

{17, 25, 33, . . ., 73} 

3) 

_______ 
A) 

{17, 25, 32, 40, 48, 56, 64, 72} 

B) 

{17, 25, 33, 41, 49, 57, 65, 73} 
C) 

{17, 25, 33, 42, 50, 58, 66, 74} 

D) 

{17, 25, 33, 41, 49} 

 
4) 

{91, 89, 87, . . ., 71} 

4) 

_______ 
A) 

{91, 89, 87, 83, 79, 75, 71} 
B) 

{91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111} 
C) 

{91, 89, 87, 85, 83, 81, 79, 77, 75, 73, 71} 
D) 

{91, 89, 87, 84, 82, 80, 78, 76, 74, 72, 70} 

 
5) 

The first three natural numbers. 

5) 

_______ 
A) 

{0, 1, 2, 3} 

B) 

{0, 1, 2} 

C) 

{1, 2, 3} 

D) 

{0, 2, 4} 

 
6) 

The natural numbers between 3 and 5. 

6) 

_______ 
A) 

{3, 4, 5} 

B) 

{3, 5} 

C) 

{4} 

D) 

{0, 1, 2, 3} 

 
Identify the set as finite or infinite. 
7) 

{5, 7, 9, . . ., 15} 

7) 

_______ 
A) 

finite 

B) 

infinite 

 
8) 

{4, 11, 18, . . .} 

8) 

_______ 
A) 

finite 

B) 

infinite 

 
9) 

9) 

_______ 
A) 

infinite 

B) 

finite 

 
10) 

{x|x is a natural number larger than 1} 

10) 

______ 
A) 

finite 

B) 

infinite 

 
11) 

{x|x is a fraction between 0 and 1} 

11) 

______ 
A) 

finite 

B) 

infinite 

 
12) 

{x|x is an even natural number} 

12) 

______ 
A) 

finite 

B) 

infinite 

 
13) 

{x|x is a plant alive now} 

13) 

______ 
A) 

finite 

B) 

infinite 

 
Insert ∈ or ∉ in the blank to make the statement is true. 
14) 

10  {7, 8, 9, 10} 

14) 

______ 
A) 

∉ 

B) 

∈ 

 
15) 

12  {8, 11, 14, 12, 10} 

15) 

______ 
A) 

∉ 

B) 

∈ 

 
16) 

-5  {5, 7, 9, 11} 

16) 

______ 
A) 

∉ 

B) 

∈ 

 
17) 

0  {2, 4, 0, 6, 5} 

17) 

______ 
A) 

∈ 

B) 

∉ 

 
18) 

0  {4, 5, 6, 7, 8, 9} 

18) 

______ 
A) 

∉ 

B) 

∈ 

 
19) 

{8}  {8, 9, 10, 11, 12, 13} 

19) 

______ 
A) 

∈ 

B) 

∉ 

 
20) 

{4}  {2, 4, 6, 8} 

20) 

______ 
A) 

∈ 

B) 

∉ 

 
21) 

{0}  {0, 4, 5, 6, 7} 

21) 

______ 
A) 

∈ 

B) 

∉ 

 
22) 

3  ∅ 

22) 

______ 
A) 

∉ 

B) 

∈ 

 
23) 

∅  ∅ 

23) 

______ 
A) 

∈ 

B) 

∉ 

 
Tell whether the statement is true or false. 
24) 

6 ∈ {4, 5 4, 6, 7} 

24) 

______ 
A) 

True 

B) 

False 

 
25) 

10 ∈ {- 6, 11, 12, 15} 

25) 

______ 
A) 

True 

B) 

False 

 
26) 

11 ∉ {0, 9, 10, 12, 14} 

26) 

______ 
A) 

True 

B) 

False 

 
27) 

{0, 7, 10, 15} = {10, 7, 15, 0} 

27) 

______ 
A) 

True 

B) 

False 

 
28) 

{6, 11, 9, 12} = {9, 6, 11} 

28) 

______ 
A) 

True 

B) 

False 

 
29) 

{x | x is a natural number greater than 9} = {9, 10, 11, . . .} 

29) 

______ 
A) 

True 

B) 

False 

 
30) 

Let A = {5, 6, 7, 8, 9, 10}, B = {7, 9, 11}, C = {5, 6, 8, 10}, D = {5, 10}, and 

A ⊆ U 

30) 

______ 
A) 

True 

B) 

False 

 
31) 

Let A = {7, 8, 9, 10, 11, 12}, B = {9, 11, 13}, C = {7, 8, 10, 12}, D = {7, 12}, and 

A ⊆ B 

31) 

______ 
A) 

True 

B) 

False 

 
32) 

Let A = {6, 7, 8, 9, 10, 11}, B = {8, 10, 12}, C = {6, 7, 9, 11}, D = {6, 11}, and 

C ⊆ A 

32) 

______ 
A) 

True 

B) 

False 

 
33) 

Let A = {8, 9, 10, 11, 12, 13}, B = {10, 12, 14}, C = {8, 9, 11, 13}, D = {8, 13}, and 

∅ ⊆ D 

33) 

______ 
A) 

True 

B) 

False 

 
34) 

Let A = {8, 9, 10, 11, 12, 13}, B = {10, 12, 14}, C = {8, 9, 11, 13}, D = {8, 13}, and 

C ⊆ ∅ 

34) 

______ 
A) 

True 

B) 

False 

 
35) 

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

{13, 15} ⊆ B 

35) 

______ 
A) 

True 

B) 

False 

 
36) 

Let A = {2, 3, 4, 5, 6, 7}, B = {4, 6, 8}, C = {2, 3, 5, 7}, D = {2, 7}, and 

{0, 3, 7} ⊆ C 

36) 

______ 
A) 

True 

B) 

False 

 
37) 

Let A = {7, 8, 9, 10, 11, 12}, B = {9, 11, 13}, C = {7, 8, 10, 12}, D = {7, 12}, and 

B ⊈ C 

37) 

______ 
A) 

True 

B) 

False 

 
38) 

Let A = {4, 5, 6, 7, 8, 9}, B = {6, 8, 10}, C = {4, 5, 7, 9}, D = {4, 9}, and 

D ⊈ C 

38) 

______ 
A) 

True 

B) 

False 

 
39) 

Let A = {4, 5, 6, 7, 8, 9}, B = {6, 8, 10}, C = {4, 5, 7, 9}, D = {5, 9}, and 

U ⊆ C 

39) 

______ 
A) 

True 

B) 

False 

 
Insert ⊆ or ⊈ in the blank to make the statement true. 
40) 

{8, 9, 10}  {0, 8, 9, 10, 11, 12} 

40) 

______ 
A) 

⊆ 

B) 

⊈ 

 
41) 

{12, 16}  {9, -10, 14, -12, 16, 11} 

41) 

______ 
A) 

⊈ 

B) 

⊆ 

 
42) 

{6, 8, 11, 13}  {6, 6, 8, 9, 10, 11} 

42) 

______ 
A) 

⊆ 

B) 

⊈ 

 
43) 

{3, 4, 5, 8}  {3, 7, 5, 6, 4, 8} 

43) 

______ 
A) 

⊆ 

B) 

⊈ 

 
44) 

{0, 8, 10, 13}  {8, 10, 13, 14, 15, 16} 

44) 

______ 
A) 

⊆ 

B) 

⊈ 

 
45) 

∅  {1, 4, 8, 0, 5, 9} 

45) 

______ 
A) 

⊆ 

B) 

⊈ 

 
46) 

{-14, 9, -15, 0, 13}  ∅ 

46) 

______ 
A) 

⊆ 

B) 

⊈ 

 
47) 

∅  ∅ 

47) 

______ 
A) 

⊆ 

B) 

⊈ 

 
Tell whether the statement is true or false. 
48) 

{5, 8, 9, 11} ∩ {8, 9, 12, 13} = {8, 9} 

48) 

______ 
A) 

True 

B) 

False 

 
49) 

{9, 11, 12, 14} ∪ {0, 13, 11, 16, 9} = {9, 11} 

49) 

______ 
A) 

True 

B) 

False 

 
50) 

{1, 3, 4, 6} ∩ ∅ = {1, 3, 4, 6} 

50) 

______ 
A) 

True 

B) 

False 

 
51) 

{9, 11, 12, 14} ∪ ∅ = {9, 11, 12, 14}  

51) 

______ 
A) 

True 

B) 

False 

 
Use these sets to find the following. Identify any disjoint sets. 
52) 

Let U = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, M = {3, 5, 7, 9},   and 

M ∩ R 

52) 

______ 
A) 

{3, 4, 5, 6} 

B) 

{3, 5} 
C) 

{3, 4, 5, 6, 7, 9} 

D) 

∅; M and R are disjoint sets. 

 
53) 

Let U = {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}, M = {4, 6, 8, 10},   and 

M ∪ N 

53) 

______ 
A) 

{4, 5, 6, 7, 8, 9, 13} 

B) 

{5, 6, 7, 8, 9, 10, 11, 12, 13} 
C) 

{4, 5, 6, 7, 8, 9, 10, 11, 13} 

D) 

∅; M and N are disjoint sets. 

 
54) 

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}, M = {1, 3, 5, 7},   and 

M ∩ N 

54) 

______ 
A) 

{2, 3, 4, 5, 6, 7, 8, 9, 10} 

B) 

{1, 2, 3, 4, 5, 6, 7, 8, 10} 
C) 

∅; M and N are disjoint sets. 

D) 

{3, 4, 5, 6, 10} 

 
55) 

Let U = {9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19}, M = {9, 11, 13, 15},   and 

N' 

55) 

______ 
A) 

{10, 12, 14, 16, 18} 

B) 

{11, 13, 15, 17, 19} 
C) 

M, or {9, 11, 13, 15} 

D) 

Q, or {9, 11, 13, 15, 17, 19} 

 
56) 

Let U = {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}, M = {4, 6, 8, 10},   and 

Q ∩R' 

56) 

______ 
A) 

{6, 8, 10, 12, 14} 

B) 

{8, 10, 12, 14} 
C) 

{7, 8, 9, 10, 11, 12, 13, 14} 

D) 

∅; Q and R' are disjoint sets. 

 
57) 

Let U = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}, M = {5, 7, 9, 11},   and 

∅ ∪ N 

57) 

______ 
A) 

{7, 9, 11, 13, 15} 
B) 

∅; N and ∅ are disjoint sets. 
C) 

N, or {6, 8, 10, 12, 14}; N and ∅ are disjoint sets. 
D) 

{5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} 

 
58) 

Let U = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, M = {2, 4, 6, 8},   and 

(N ∪ R) ∩ Q 

58) 

______ 
A) 

∅; N and R are disjoint sets. 

B) 

{4} 
C) 

{2} 

D) 

{2, 4} 

 
59) 

Let U = {8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18}, M = {8, 10, 12, 14},   and 

Q' ∩ (N' ∩ U) 

59) 

______ 
A) 

{9, 11, 13, 15, 17} 

B) 

{9, 10, 11, 12, 13, 14} 
C) 

∅; Q' and (N' ∩ U) are disjoint sets. 

D) 

{8, 10, 12, 14, 16, 18} 

 
60) 

Let U = {7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17}, M = {7, 9, 11, 13},   and 

(R ∪ N) ∩ M' 

60) 

______ 
A) 

{7, 8, 10, 12, 14, 16} 

B) 

N, or {8, 10, 12, 14, 16} 
C) 

∅; M' and (R ∪ N) are disjoint sets. 

D) 

M, or {7, 9, 11, 13} 

 
61) 

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

(U ∪ ∅) ∩ R' 

61) 

______ 
A) 

U, or {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} 

B) 

∅; R' and (U ∪ ∅) are disjoint sets. 
C) 

R, or {5, 6, 7, 8} 

D) 

{9, 10, 11, 12, 13, 14, 15} 

 
List all the elements of set B that belong to the indicated set. 
62) 

B = 
Integers 

62) 

______ 
A) 

10, 0 

B) 

10, -4, 0 

C) 

10, -4, 0, ,  

D) 

10, 0,  

 
63) 

B = 
Whole numbers 

63) 

______ 
A) 

6, 0   

B) 

6, 0, ,  

C) 

6, -16, 0   

D) 

6, -16, 0,   

 
64) 

B = 
Natural numbers 

64) 

______ 
A) 

11, 0   

B) 

11, 0,  

C) 

11, 0,      

D) 

11,   

 
65) 

B = 
Rational numbers 

65) 

______ 
A) 

, , 0.99 

B) 

10, 0,   
C) 

,   

D) 

10, -17, 0, , , 0.99 

 
Evaluate the expression. 
66) 

34 

66) 

______ 
A) 

81 

B) 

12 

C) 

144 

D) 

8.1 

 
67) 

- 35 

67) 

______ 
A) 

15 

B) 

- 15 

C) 

- 243 

D) 

243 

 
68) 

(-4)2 

68) 

______ 
A) 

64 

B) 

16 

C) 

-16 

D) 

-8 

 
69) 

-4 ∙  

69) 

______ 
A) 

36 

B) 

- 36 

C) 

- 144 

D) 

144 

 
70) 

-5 

70) 

______ 
A) 

320 

B) 

- 8,000 

C) 

8,000 

D) 

- 320 

 
71) 

23 + 15 ∙ 10 + 27 

71) 

______ 
A) 

407 

B) 

1406 

C) 

75 

D) 

200 

 
72) 

10 + 42 - (-7) ∙ 5 

72) 

______ 
A) 

95 

B) 

-9 

C) 

125 

D) 

61 

 
73) 

78 - 2 ∙ 15 + 6 

73) 

______ 
A) 

54 

B) 

97 

C) 

1146 

D) 

1596 

 
74) 

80 - 14 ∙ 3 + 182 ÷ (-13) 

74) 

______ 
A) 

184 

B) 

24 

C) 

-19 

D) 

-939 

 
75) 

 -  

75) 

______ 
A) 

252 

B) 

180 

C) 

-252 

D) 

-180 

 
76) 

(8 + (-7))[4 + (4 + 7)] 

76) 

______ 
A) 

71 

B) 

16 

C) 

15 

D) 

12 

 
77) 

2[4 + 8(1 + 3)] 

77) 

______ 
A) 

96 

B) 

92 

C) 

40 

D) 

72 

 
78) 

(4 - 82)(-9 + ) 

78) 

______ 
A) 

-60 

B) 

-98 

C) 

-6540 

D) 

-364 

 
79) 

 -  

79) 

______ 
A) 

-  

B) 

0 

C) 

D) 

-  

 
80) 

80) 

______ 
A) 

B) 

C) 

D) 

 
Evaluate the expression for x = -2, y = 3, and a = -4. 
81) 

2x - 9y - 6a 

81) 

______ 
A) 

-7 

B) 

14 

C) 

-23 

D) 

48 

 
82) 

-5a - 2y - 9x 

82) 

______ 
A) 

-9 

B) 

32 

C) 

-3 

D) 

4 

 
83) 

(2x + 3y)(-2a) 

83) 

______ 
A) 

-104 

B) 

-40 

C) 

40 

D) 

0 

 
84) 

7 - 5y - a 

84) 

______ 
A) 

15 

B) 

14 

C) 

17 

D) 

11 

 
85) 

 - 9y + 2a 

85) 

______ 
A) 

-30 

B) 

-39 

C) 

-43 

D) 

-27 

 
86) 

86) 

______ 
A) 

-  

B) 

-  

C) 

-  

D) 

-  

 
87) 

87) 

______ 
A) 

B) 

1 

C) 

D) 

 
88) 

88) 

______ 
A) 

- 1 

B) 

-  

C) 

D) 

 
89) 

89) 

______ 
A) 

19 

B) 

9 

C) 

- 1 

D) 

33 

 
Identify the property illustrated by the statement. Assume all variables represent real numbers. 
90) 

6 ∙ 1 = 6 

90) 

______ 
A) 

Inverse 

B) 

Closure 

C) 

Distributive 

D) 

Identity 

 
91) 

(7 + 1) + 9 = (1 + 7) + 9 

91) 

______ 
A) 

Distributive 

B) 

Closure 

C) 

Commutative 

D) 

Associative 

 
92) 

3 + 0 = 3 

92) 

______ 
A) 

Associative 

B) 

Inverse 

C) 

Closure 

D) 

Identity 

 
93) 

6(x + 2) = 6x + 12 

93) 

______ 
A) 

Distributive 

B) 

Closure 

C) 

Commutative 

D) 

Associative 

 
94) 

5 + (-5) = 0 

94) 

______ 
A) 

Associative 

B) 

Identity 

C) 

Inverse 

D) 

Closure 

 
95) 

1 + 7 = 7 + 1 

95) 

______ 
A) 

Identity 

B) 

Inverse 

C) 

Associative 

D) 

Commutative 

 
96) 

 ∙ (a + 9) = 1, if a + 9 ≠ 0 

96) 

______ 
A) 

Distributive 

B) 

Identity 

C) 

Closure 

D) 

Inverse 

 
97) 

(8 ∙ 5) ∙ 6 = 8 ∙ (5 ∙ 6) 

97) 

______ 
A) 

Associative 

B) 

Identity 

C) 

Distributive 

D) 

Commutative 

 
98) 

8(π) is a real number. 

98) 

______ 
A) 

Closure 

B) 

Associative 

C) 

Identity 

D) 

Distributive 

 
Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. 
99) 

(-3y) 

99) 

______ 
A) 

5y 

B) 

6y  

C) 

2y  

D) 

-2y  

 
100) 

(-6) 

100) 

_____ 
A) 

10y  

B) 

15y  

C) 

-10y  

D) 

8y 

 
101) 

- (8y - 8x - 8z) 

101) 

_____ 
A) 

-12y - 12x - 12z 

B) 

-12y + 12x - 12z  
C) 

-12y + 12x + 12z  

D) 

-12y - 12x + 12z  

 
102) 

-  

102) 

_____ 
A) 

3y - x -  

B) 

3y - x +  

C) 

3y + x -  

D) 

3y + x +  

 
Use the distributive property to rewrite a sum as a product or the product as a sum. 
103) 

-9 k + 11 k 

103) 

_____ 
A) 

-2 k  

B) 

-20 k  

C) 

2 k  

D) 

20 k 

 
104) 

3 - 9 k 

104) 

_____ 
A) 

3(1 - 3 k)  

B) 

3(1 - 4 k) 

C) 

12 k  

D) 

-6 k  

 
105) 

-8(k + a) 

105) 

_____ 
A) 

-8 k - 8 a  

B) 

-8 k + 8 a 

C) 

-8 k a  

D) 

-8 k + a  

 
106) 

-(-5 - 3 b) 

106) 

_____ 
A) 

-5 + 3 b  

B) 

-5 - 3 b 

C) 

5 + 3 b  

D) 

5 - 3 b  

 
107) 

-(4 x - 5 r) 

107) 

_____ 
A) 

-4 x - 5 r  

B) 

4 x + 5 r  

C) 

4 x - 5 r 

D) 

-4 x + 5 r  

 
Decide whether the statement is true or false. If false, correct the statement so it is true. 
108) 

 =  -    

108) 

_____ 
A) 

True 

B) 

False;  =  -  

 
109) 

 =  -    

109) 

_____ 
A) 

True 

B) 

False;  =  -    

 
110) 

 = -    

110) 

_____ 
A) 

True 

B) 

False;  = -(- 3) = 3 

 
111) 

 =     

111) 

_____ 
A) 

True 

B) 

False;  = -  = - 6 

 
112) 

 = -   

112) 

_____ 
A) 

True 

B) 

False;  =  

 
113) 

 =  

113) 

_____ 
A) 

True 

B) 

False;  =  

 
114) 

 =  ∙    

114) 

_____ 
A) 

True 

B) 

False;  = - ∙    

 
Evaluate the expression. 
115) 

115) 

_____ 
A) 

±21 

B) 

- 21 

C) 

21 

D) 

0 

 
116) 

116) 

_____ 
A) 

0 

B) 

16 

C) 

±16 

D) 

- 16 

 
117) 

- 

117) 

_____ 
A) 

- 9 

B) 

9 

C) 

0 

D) 

±9 

 
118) 

- 

118) 

_____ 
A) 

±13 

B) 

13 

C) 

0 

D) 

- 13 

 
119) 

- 

119) 

_____ 
A) 

B) 

-  

C) 

±  

D) 

0 

 
120) 

- 

120) 

_____ 
A) 

B) 

-  

C) 

0 

D) 

±  

 
121) 

121) 

_____ 
A) 

0 

B) 

±  

C) 

D) 

-  

 
122) 

Let x = -13, y = -20.  Evaluate |-6x|. 

122) 

_____ 
A) 

-78 

B) 

-260 

C) 

78 

D) 

260 

 
123) 

Let x = -5, y = 7. Evaluate . 

123) 

_____ 
A) 

2 

B) 

-2 

C) 

12 

D) 

-12 

 
124) 

Let x = -2, y = 8. Evaluate  - . 

124) 

_____ 
A) 

-10 

B) 

10 

C) 

-6 

D) 

6 

 
125) 

Let x = 19, y = -22.  Evaluate |y - x|. 

125) 

_____ 
A) 

-41 

B) 

-3 

C) 

3 

D) 

41 

 
126) 

Let x = 4, y = 4. Evaluate . 

126) 

_____ 
A) 

4 

B) 

-52 

C) 

-4 

D) 

52 

 
127) 

Let x = -21, y = -20.  Evaluate |10y - 2x|. 

127) 

_____ 
A) 

-242 

B) 

158 

C) 

-158 

D) 

242 

 
128) 

Let x = 6, y = -8. Evaluate 4 + 5. 

128) 

_____ 
A) 

64 

B) 

16 

C) 

-16 

D) 

-64 

 
129) 

Let x = -20, y = -7.
Evaluate |-8y + 4x| - |9y|. 

129) 

_____ 
A) 

125 

B) 

195 

C) 

251 

D) 

-39 

 
130) 

Let x = 2 and y = -1. Evaluate  + . 

130) 

_____ 
A) 

-1 

B) 

0 

C) 

1 

D) 

2 

 
131) 

Let x = -5, y = 3.  Evaluate . 

131) 

_____ 
A) 

B) 

C) 

D) 

 
Determine which property of absolute value justifies the statement. 
132) 

 ≥ 0 

132) 

_____ 
A) 

Property 1 the absolute value of a number is positive. 
B) 

Property 5 the triangle inequality 
C) 

Property 1 the absolute value of a number is greater than 0. 
D) 

Property 1 the absolute value of a number is positive or 0. 

 
133) 

 =  

133) 

_____ 
A) 

Property 1 the opposite of a number is equal to the absolute value of the number . 
B) 

Property 5 the triangle inequality 
C) 

Property 2 the absolute value of a number and its opposite are equal. 
D) 

Property 2 the opposite of the absolute value of a number is equal to the absolute value of the number. 

 
134) 

 ≤  +  

134) 

_____ 
A) 

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). 
B) 

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). 
C) 

Property 4 the absolute value of the sum of the numbers is less than or equal to the sum of the two numbers. 
D) 

Property 4 the sum of two numbers is less than or equal to the absolute value of the sum of the numbers. 

 
Find the distance between two points given their coordinates. 
135) 

Find the distance between points P and Q on a number line, with coordinates 2 and 4, respectively. 

135) 

_____ 
A) 

d(P, Q) = - 2 

B) 

d(P, Q) = 2 

C) 

d(P, Q) = 6 

D) 

d(P, Q) = - 6 

 
136) 

Find the distance between points R and S on a number line, with coordinates - 6 and 11, respectively. 

136) 

_____ 
A) 

d(R, S) = - 17 

B) 

d(R, S) = 17 

C) 

d(R, S) = 5 

D) 

d(R, S) = - 5 

 
137) 

Find the distance between points P and Q on a number line, with coordinates - 4 and 2, respectively. 

137) 

_____ 
A) 

d(P, Q) = 2 

B) 

d(P, Q) = - 2 

C) 

d(P, Q) = - 6 

D) 

d(P, Q) = 6 

 
138) 

Find the distance between points R and S on a number line, with coordinates 8 and - 7, respectively. 

138) 

_____ 
A) 

d(R, S) = 1 

B) 

d(R, S) = - 15 

C) 

d(R, S) = - 1 

D) 

d(R, S) = 15 

 
139) 

Find the distance between points P and Q on a number line, with coordinates 4 and - 7, respectively. 

139) 

_____ 
A) 

d(P, Q) = 3 

B) 

d(P, Q) = - 11 

C) 

d(P, Q) = 11 

D) 

d(P, Q) = - 3 

 
140) 

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

140) 

_____ 
A) 

d(R, S) = - 11 

B) 

d(R, S) = 11 

C) 

d(R, S) = 3 

D) 

d(R, S) = - 3 

 
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 

141) 

_____ 
A) 

x and y have different signs.  

B) 

x and y must be positive. 
C) 

x and y have the same sign.  

D) 

x and y must be negative. 

 
142) 

 > 0 

142) 

_____ 
A) 

x and y must be negative. 

B) 

x and y have the same sign.  
C) 

x and y must be positive. 

D) 

x and y have different signs.  

 
143) 

-  > 0 

143) 

_____ 
A) 

x and y must be positive. 

B) 

x and y have different signs.  
C) 

x and y must be negative. 

D) 

x and y have the same sign.  

 
144) 

y < 0 

144) 

_____ 
A) 

x and y have different signs.  

B) 

x and y must be negative.  
C) 

x must be negative. 

D) 

y must be negative. 

 
145) 

 < 0 

145) 

_____ 
A) 

y must be negative. 

B) 

x and y have different signs.  
C) 

x and y must be negative.  

D) 

x must be negative. 

 
146) 

 > 0 

146) 

_____ 
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.  

 
Solve the problem. 
147) 

The formula  C = (F - 32)  expresses the relationship between Fahrenheit temperature, F, and Celsius temperature, C. Use the formula to convert 50°F to its equivalent temperature on the Celsius scale.  

147) 

_____ 
A) 

10°C 

B) 

32°C 

C) 

46°C 

D) 

2°C 

 
148) 

A stone is dropped from a tower that is 740 feet high. The formula    describes the stone's height above the ground, h, in feet, t seconds after it was dropped. What is the stone's height 5 seconds after it is released? 

148) 

_____ 
A) 

340 ft 

B) 

365 ft 

C) 

315 ft 

D) 

350 ft 

 
149) 

If a rock falls from a height of 90 meters above the ground, the height H (in meters) after x seconds can be approximated using the formula . What is the height of the rock after 4 seconds? 

149) 

_____ 
A) 

-294.16 m 

B) 

11.6 m 

C) 

1361.6 m 

D) 

70.4 m 

 
150) 

As the relative humidity increases, the temperature seems higher than it is. The formula T = 0.110x + 55.05 approximates the apparent temperature for an actual temperature of  where x is the relative humidity. What is the apparent temperature (to the nearest degree) for a relative humidity of 90%? 

150) 

_____ 
A) 

545°F 

B) 

65°F 

C) 

145°F 

D) 

55°F 

 
151) 

Use the formula
	Passing Rating ≈ 85.68 + 4.31  + 326.42  - 419.07 , where A = number of passes 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.

 

151) 

_____ 
A) 

87 

B) 

87.3 

C) 

84.8 

D) 

84.6  

 
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 205-lb woman, who, in 5 hours, has drunk 5 16-oz beers (80 oz), each having a 3.2% alcohol content.

152) 

_____ 
A) 

-0.056 

B) 

-0.356 

C) 

0.019 

D) 

-333.24 

 
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	Profit (Loss) in Dollars
January	-14,526
February	1874
March	-8977
April	-14,107
May	14,073
June	14,632
July	-13,834
August	-13,170
September	-4860
October	6630
November	-3338
December	-974

The profit was smallest in  . 

153) 

_____ 
A) 

December 

B) 

June 

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	1874
March	-8977
April	-14,107
May	14,073
June	14,632
July	-13,834
August	-13,170
September	-4860
October	6630
November	-3338
December	-974

The absolute value of the profit or loss was smallest in  . 

154) 

_____ 
A) 

January 

B) 

December 

C) 

June 

D) 

February 

 
155) 

During a certain football game, a player gained 37 yards rushing and -84 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? 

155) 

_____ 
A) 

47; yards; No, it is not the same because the sum of the absolute values is -121. 
B) 

121 yards; No, it is not the same because the sum of the absolute values is -47 . 
C) 

-47 yards; Yes, it is the same. 
D) 

-47 yards; No, it is not the same because the sum of the absolute values is 121. 

 
156) 

Find the magnitude of the difference between a windchill factor of -88 and a windchill factor of -76. 

156) 

_____ 
A) 

12 

B) 

164 

C) 

-164 

D) 

-12 

 
157) 

Find the magnitude of the difference between a windchill factor of 42 and a windchill factor of -37. 

157) 

_____ 
A) 

-5 

B) 

5 

C) 

-79 

D) 

79 

 
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.

(i) Abigail 139 beats per minute
(ii) Mathilda  148 beats per minute 

158) 

_____ 
A) 

(i) Abigail  = -1
(ii) Mathilda  = -8 

B) 

(i) Abigail  = 1
(ii) Mathilda  = 8 
C) 

(i) Abigail 139 - 140 = -1
(i) Mathilda 148 - 140 = 8 

D) 

(i) Abigail  = 279
(ii) Mathilda  = 288 

 
1) 

A 

2) 

C 

3) 

B 

4) 

C 

5) 

C 

6) 

C 

7) 

A 

8) 

B 

9) 

A 

10) 

B 

11) 

B 

12) 

B 

13) 

A 

14) 

B 

15) 

B 

16) 

A 

17) 

A 

18) 

A 

19) 

B 

20) 

B 

21) 

B 

22) 

A 

23) 

B 

24) 

A 

25) 

B 

26) 

A 

27) 

A 

28) 

B 

29) 

B 

30) 

A 

31) 

B 

32) 

A 

33) 

A 

34) 

B 

35) 

A 

36) 

B 

37) 

A 

38) 

B 

39) 

B 

40) 

A 

41) 

A 

42) 

B 

43) 

A 

44) 

B 

45) 

A 

46) 

B 

47) 

A 

48) 

A 

49) 

B 

50) 

B 

51) 

A 

52) 

B 

53) 

C 

54) 

C 

55) 

D 

56) 

B 

57) 

C 

58) 

D 

59) 

C 

60) 

B 

61) 

D 

62) 

C 

63) 

B 

64) 

D 

65) 

D 

66) 

A 

67) 

C 

68) 

B 

69) 

B 

70) 

A 

71) 

D 

72) 

D 

73) 

A 

74) 

B 

75) 

C 

76) 

C 

77) 

D 

78) 

A 

79) 

A 

80) 

A 

81) 

A 

82) 

B 

83) 

C 

84) 

C 

85) 

C 

86) 

C 

87) 

C 

88) 

B 

89) 

C 

90) 

D 

91) 

C 

92) 

D 

93) 

A 

94) 

C 

95) 

D 

96) 

D 

97) 

A 

98) 

A 

99) 

D 

100) 

C 

101) 

C 

102) 

B 

103) 

C 

104) 

A 

105) 

A 

106) 

C 

107) 

D 

108) 

B 

109) 

A 

110) 

B 

111) 

A 

112) 

B 

113) 

A 

114) 

A 

115) 

C 

116) 

B 

117) 

A 

118) 

D 

119) 

B 

120) 

B 

121) 

C 

122) 

C 

123) 

A 

124) 

C 

125) 

D 

126) 

A 

127) 

B 

128) 

A 

129) 

D 

130) 

B 

131) 

A 

132) 

D 

133) 

C 

134) 

B 

135) 

B 

136) 

B 

137) 

D 

138) 

D 

139) 

C 

140) 

C 

141) 

A 

142) 

B 

143) 

B 

144) 

D 

145) 

A 

146) 

C 

147) 

A 

148) 

A 

149) 

B 

150) 

B 

151) 

D 

152) 

C 

153) 

D 

154) 

B 

155) 

D 

156) 

A 

157) 

D 

158) 

B