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) {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.


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)


{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) 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


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


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)

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

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}.

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}

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,

0
,
8

9,

-5
, 0.59
0

65)

Rational numbers
7,

9

B) 5, -16, 0,

C) 5, 0,

9

D)

A)

7,

0


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



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)

77)

81)

78)

7


79) -

3
1
- 8
4
A)

80)

-

3 7
2 8

1
2

79)
C) -


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

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) -


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

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


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

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

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

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


A) ±

120) - -

1
7

B)

1
7

C) -

1
7

D) 0

8
3

A) -

121) -

117)

120)

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|.


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

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

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,

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

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

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

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


January

-14,526

February
March
April

1874
-8977
-14,107

May

14,073

June

14,632

July

-13,834

August

-13,170

September
October



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


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



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


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


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


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


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.


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

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


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



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)


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


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 )

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

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


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


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)


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



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)


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


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



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) 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