Name: ________________________ Class: ___________________ Date: __________ ID: A

4

Algebra I CP Midterm Review

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

____ 1. Identify the graph that displays the speed of a baseball being pitched and then hit by the batter.

a. c.

b. d.

Name: ________________________ ID: A

2

____ 2. Identify the graph that displays the height of a ping pong ball after it is dropped.

a. c.

b. d.

Name: ________________________ ID: A

3

____ 3. Which relation is a function?

a. c.

b. d.

____ 4. Which relation is a function?

a.

x y

3 8

5 10

6 6

9 −2

c.

x y

3 8

5 10

6 6

5 −2

b.

x y

3 8

5 10

3 6

9 −2

d.

x y

6 8

5 10

6 6

9 −2

Name: ________________________ ID: A

4

____ 5. Which relation is a function?

a. c.

b. d.

____ 6. Which relation is a function?a. {(5, 3), (2, 8), (–5, –1), (4, 7), (2, 1)}b. {(5, 3), (2, 8), (–5, –1), (4, 7), (5, 7)}c. {(–5, 3), (2, 8), (–5, –1), (4, 7), (2, 2)}d. {(5, 3), (2, 8), (–5, –1), (4, 7), (–2, 1)}

Name: ________________________ ID: A

5

____ 7. Which relation is a function?

a. c.

b. d.

Short Answer

Evaluate the expression.

8. 2 + 2 2( ) 2 5( ) + 8

9. 54 – 3(8 – 4)

10. Evaluate the following expression if a = 12, b = 5, and c = 4.3c + bc – 2a

11. Evaluate the following expression if x = 12, y = 8, and z = 6.x 2 y − 2z

4

Name: ________________________ ID: A

6

12. Solve the equation.

a =6 14 − 8( )2 8( ) + 2 + 10

13. Find the solution of the equation if the replacement set is b = 35, 51, 81, 66, 63{ }.b7 − 2 = 7

Find the solution set for the inequality using the given replacement set.

14. x − 2 < 11; 11, 12, 13, 14, 15{ }

15. 4a − 4 ≥ 24; 7, 8, 9, 10, 11{ }

Evaluate the expression. Show each step.

16. 5 + 5(33 − 52) + 3

17. 11 + 7 16− 42Ê

ËÁÁÁÁ

ˆ

¯˜̃̃˜ + 7

Simplify the expression. If not possible, write simplified.

18. 2 11d − 5( )

19. 4 8n + 10d − 7d( )

Write an algebraic expression for the verbal expression. Then simplify.

20. three times the sum of c and d decreased by d

21. two times the square of x plus the difference of x squared and eight times x

Simplify the expression.

22. 3 1.2x + 2.2yÊËÁÁ

ˆ¯̃̃ + 2 3.2x + yÊ

ËÁÁˆ¯̃̃

23. 9x + 8 6x + 2( )

Translate the sentence into an equation.

24. Four times the number x increased by 15 is 83.

25. Eighty-five minus five times x is equal to ten.

26. The sum of one-fifth p and 38 is as much as twice p.

Name: ________________________ ID: A

7

27. Fourteen minus four times y is equal to y increased by 4.

28. The difference of five times the cube of x and two times the square of x is 18.

29. The product of five and four more than x is 60.

30. Three times the sum of a and b is equal to five times c.

31. The number x divided by the number y is the same as six less than three times the difference of x and y.

Solve the equation. Then check your solution.

32. x − 4 = 2

33. 119 = n − 66

34. a – 12 = 3

5

35. – 25 + a = 1

5

36. h − 5.3 = 2.6

37. −5.4 = −1.5 + h

38. x + 19 = 5

39. −22 = −40 + r

40. 45 + x = 3

7

41. 114 = a + 3

8

42. h + 1.5 = 8.4

43. 8 = 1.88+ a

44. v7 = 3

45. x90 = 7

9

46. 5p = 140

Name: ________________________ ID: A

8

47. −448 = 64q

48. n54 = 4

9

49. 59 d = 9

10

50. −217

ÊËÁÁÁ

ˆ¯˜̃̃ p = −3

51. –8p = −314

52. 1.6a = –9.12

53. –4.2 = –2.1n

54. 2x + 7 = 79

55. a−7 − 7 = 5

Write an equation and solve each problem.

56. Five less than one fifth of a number is two. Find the number.

57. Fifty-six is twelve added to four times a number. What is the number?

58. Find three consecutive even integers with a sum of 48.

59. Find three consecutive integers with a sum of 24.

60. Find four consecutive odd integers with a sum of –32.

Solve the equation. Then check your solution.

61. −7m+ 20 = −17m− 10

62. 6 + 17z = 13z + 18

63. 45 k – 5 = –7 + 2

5 k

64. − 45 w + 1

4 = 15 + 1

3 w

65. −58x − 26 = 8x − 230.6

Name: ________________________ ID: A

9

66. −16 − 10.2g = −14.7g + 16.85

67. 6 = −2 10n + 7( )

68. 15(−42x + 40) = 15(−8x + 244)

69. 4 – 35 (3a + 4) = 7

70. 12 (15 + 7d) = − d

4

71. 3.7(−83x − 3) = 3.7(7x − 30)

Solve the proportion. If necessary, round to the nearest hundredth.

72. 67 =

p

42

73. 104b = 13

10

Solve the equation or formula for the variable specified.

74. df + 10h = 3 for d

75. 3qr + 9t = 7u for r

The formula for the perimeter, P, of a rectangle is P = 2™ + 2w, where ™ is the length and w is the width.

76. Solve the formula for the perimeter of a rectangle for w.

77. Find the width of a rectangle which has a perimeter of 54 centimeters and a length of 18 centimeters.

The circumference of a circle is given by the formula C = 2π r, where r is the measure of the radius.

78. Solve the formula for r.

Express each relation as a graph and a mapping. Then determine the domain and range.

79. {(3, 1), (2, –5), (2, 4), (3, 3)}

80. {(1, 1), (–2, 3), (2, 4), (3, 1)}

81. {(1, 0), (–2, –3), (2, 1), (2, 0)}

Express each relation as a graph and a table. Then determine the domain and range.

82. {(4, 0), (3, 2), (3, 0), (–3, –2), (4, –1)}

Name: ________________________ ID: A

10

83. {(5, –2), (4, 4), (2, –3), (0, 5), (1, 5)}

84. {(0, –1), (3, 4), (–4, –3), (0, –3), (–4, –2)}

85. f(x) = 5x + 2, find f(3).

86. If g(x) = x 2 + 4x − 5, find g(−4).

Find the solution set for the equation, given the replacement set.

87. y = 7x + 6; {(5, 41), (6, 44), (4, 39), (7, 42)}

88. –x + 5y = –2; {(7, 1.6), (5, 0.6), (6, 3.6), (4, –1.4)}

Solve the equation for the given domain. Graph the solution set.

89. y = 2x – 1 for x = {–3, –1, 1, 2, 3}

90. 3x – y = –1 for x = {–1, 0, 1, 4}

Determine whether the sequence is an arithmetic sequence. If it is, state the common difference.

91. 5, 0, –5, –10, . . .

92. 2.6, 4.2, 3.1, 2.4, . . .

Find the next three terms of the arithmetic sequence.

93. 55, 47, 39, 31, . . .

94. 149 , 21

9 , 279 , 34

9 , . . .

95. The table below shows the cost of cartons of milk.

Number of cartons 1 2 3 4 5

Cost ($) 1.50 3.00 4.50 6.00 7.50

Graph the data.

96. The table below shows the distance traveled by a person driving at the rate of 60 miles per hour.

Hours 1 2 3 4 5Distance (miles) 60 120 180 240 300

Write an equation to describe the relationship.

Name: ________________________ ID: A

11

Source: U.S. Bureau of Census

97. For which 10-year period was the rate of change of the population of Green Bay the greatest?

98. For which 10-year period was the rate of change of the population of Green Bay the least?

99. Find the rate of change from 1970 to 1980.

Find the slope of the line that passes through the pair of points.

100. (–3, –2), (5, 4)

101. (2, –3), (–5, 1)

Write an equation of the line with the given slope and y-intercept

102. slope: 27 , y-intercept: –3

Write an equation of the line that passes through each point with the given slope.

103. −3, − 4ÊËÁÁ

ˆ¯̃̃ , m = 3

104. 0, 6ÊËÁÁ

ˆ¯̃̃ , m = −3

Write an equation of the line that passes through the pair of points.

105. −5, − 2ÊËÁÁ

ˆ¯̃̃ , 3, − 1Ê

ËÁÁˆ¯̃̃

Name: ________________________ ID: A

12

106. −5, 8ÊËÁÁ

ˆ¯̃̃ , −3, − 8Ê

ËÁÁˆ¯̃̃

Write the equation in slope-intercept form.

107. y + 3 = 3 x − 1( )

108. y – 5 = 34 (x – 5)

Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.

109. Average Cycling Speed

110. Video Rental Fines

Name: ________________________ ID: A

13

111. People Entering Amusement Park

Time (minutes)

112. Cars Passing School

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.

113. y = −x + 5

y = 6x − 2

114. −4x + y = 2

−4x − 5 =y2

Name: ________________________ ID: A

14

Use substitution to solve the system of equations.

115. y = x + 1

8x − 4y = 0

116. −9 = x − 3y

−2x + 6 = 6y

117. The length of a rectangular poster is 10 inches longer than the width. If the perimeter of the poster is 124 inches, what is the width?

118. The sum of two numbers is 90. Their difference is 12. What are the numbers?

119. At a local electronics store, CDs were on sale. Some were priced at $14.00 and some at $12.00. Sabrina bought 9 CDs and spent a total of $114.00. How many $12.00 CDs did she purchase?

120. Jordan is 3 years less than twice the age of his cousin. If their ages total 48, how old is Jordan?

121. Angle A and angle B are complementary, that is their measurements add up to 90°. Angle B measures 32° more than angle A. What are the measurements of the two angles?

122. Joji earns 3 times as much as Masao. If Joji and Masao earn $4500.00 together, how much money does Masao earn?

Use elimination to solve the system of equations.

123. −2x − 10y = 10

−3x + 10y = −10

124. −4x + 2y = −2

4x + 6y = 10

125. −8x + 8y = −8

−8x + 4y = 8

126. 5x − 2y = −3

4x − 2y = −6

127. −3x − 2y = −5

7x + 6y = 1

128. −4x − 6y = −6

7x + 9y = −9

Name: ________________________ ID: A

15

129. The sum of Jack and his father’s ages is 52. Jack’s father’s age is 2 less than 5 times Jack’s age. Find the ages of Jack and his father.

130. Dylan has 15 marbles. Some are red and some are white. The number of red marbles is three more than six times the number of the white marbles. Write a system of equations that can be used to find the number of white marbles, x, and the number of red marbles, y.

131. A gym has 2 kg and 5 kg weights. There are 10 disks in all. The total weight of 2 kg disks and 5 kg disks is equal to 29 kg. Find the number of disks of each kind in the gym.

Solve the inequality. Graph the solution on a number line.

132. k − 3 < 2

133. −2 ≥ w − 6

134. y + 5 > −2

135. 1 ≥ 1 + p

Solve the inequality.

136. −3b8 > −3

137. 9m ≤ −72

138. −2f < 18

139. 3h + 9 > 15

140. 3a + 3− 6a > 15

141. 2x − 10 + 3x4 < −5

142. −1 ≥ −9n − 8+ 4n

143. 5(2g − 3) − 6g ≥ −2(g − 6) + 3

144. −5(3z + 3) < −3(5z − 4)

Solve the compound inequality and graph the solution set.

145. u + 8 ≥ 1 and u − 3 < 3

146. 2k + 5 > 1 and 3k − 9 ≤ 6

Name: ________________________ ID: A

16

147. g − 6 > −1 or g + 2 > 8

148. 0 + v ≤ −4 or −2v ≤ 8

ID: A

1

Algebra I CP Midterm ReviewAnswer Section

MULTIPLE CHOICE

1. A 2. D 3. B 4. A 5. C 6. D 7. A

SHORT ANSWER

8. 50 9. 42 10. 8 11. 285 12. 12 13. 63 14. {11, 12} 15. {7, 8, 9, 10, 11} 16. 5 + 5(33 − 52) + 3

= 5+ 5(33− 25) + 3= 5 + 5(8) + 3= 5 + 40 + 3= 48

17. 11 + 7 16 − 42Ê

ËÁÁÁÁ

ˆ

¯˜̃̃˜ + 7

= 11 + 7 16 − 16( ) + 7= 11 + 7 0( ) + 7= 11 + 0 + 7= 18

18. 22d − 10 19. 32n + 12d 20. 3 c + d( ) − d

3c + 3d − d

3c + d 3 − 1( )

3c + 2d

21. 2x 2 + x 2 − 8xÊËÁÁÁ

ˆ¯˜̃̃

2x 2 + x 2ÊËÁÁÁ

ˆ¯˜̃̃ − 8x

3x 2 − 8x

ID: A

2

22. 10x + 8.6y 23. 57x + 16 24. 4x + 15 = 83 25. 85 − 5x = 10 26. 1

5 p + 38 = 2p 27. 14 − 4y = y + 4 28. 5x 3 − 2x 2 = 18 29. 5(x + 4) = 60 30. 3(a + b) = 5c 31. x ÷ y = 3(x − y) − 6 32. 6 33. 185 34. 1 1

10

35. 35

36. 7.9 37. –3.9 38. –14 39. 18 40. − 13

35

41. 78

42. 6.9 43. 6.12 44. 21 45. 70 46. 28 47. –7 48. 24 49. 131

50

50. 125

51. 1332

52. –5.7 53. 2 54. 36 55. –84

56. 15 x − 5 = 2; 35

57. 56 = 12 + 4n; 11 58. x + x + 2( ) + x + 4( ) = 48; 14, 16, 18 59. x + x + 1( ) + x + 2( ) = 24; 7, 8, 9 60. x + x + 2( ) + x + 4( ) + x + 6( ) = −32; –11, –9, –7, –5 61. –3

ID: A

3

62. 3 63. −5 64. 3

68

65. 3.1 66. 7.3 67. –1 68. –6 69. –3 70. –2 71. 0.3 72. 36 73. 80

74. d = 3 − 10hf

75. r = 7u − 9t3q

76. w = P − 2™2

77. 9 centimeters

78. r = C2π

79.

D = {2, 3}; R = {–5, 1, 3, 4}

ID: A

4

80.

D = {–2, 1, 2, 3}; R = {1, 3, 4}

81.

D = {–2, 1, 2}; R = {–3, 0, 1}

ID: A

5

82.

x y

4 0

3 2

3 0

−3 −2

4 −1

D = {–3, 3, 4}; R = {–2, –1, 0, 2}

83.

x y

5 −2

4 4

2 −3

0 5

1 5

D = {0, 1, 2, 4, 5}; R = {–3, –2, 4, 5}

ID: A

6

84.

x y

0 −1

3 4

−4 −3

0 −3

−4 −2

D = {–4, 0, 3}; R = {–3, –2, –1, 4} 85. 17 86. –5 87. {(5, 41)} 88. {(5, 0.6)} 89. {(–3, –7), (–1, –3), (1, 1), (2, 3), (3, 5)}

ID: A

7

90. {(–1, –2), (0, 1), (1, 4), (4, 13)}

91. yes, –5 92. no 93. 23, 15, 7 94. 41

9 , 479 , 54

9

95.

96. d = 60t 97. 1990 - 2000 98. 1970 - 1980 99. 1.7 thousand/yr 100. 3

4

101. − 47

102. y = 27 x – 3

103. y = 3x + 5 104. y = −3x + 6

105. y = 18 x – 11

8

106. y = –8x – 32

ID: A

8

107. y = 3x − 6

108. y = 34 x + 5

4

109. negative; as time passes, speed decreases 110. no correlation 111. positive; as time passes, the number of people entering increases. 112. no correlation 113. one solution; (1, 4)

114. one solution; (–1, –2)

115. (1, 2) 116. (–3, 2) 117. 26 inches 118. 39 and 51 119. 6 120. 31 121. 29° and 61° 122. $1125.00 123. (0, –1) 124. (1, 1) 125. (–3, –4)

ID: A

9

126. (3, 9) 127. (7, –8) 128. (–18, 13) 129. 9, 43 130. x + y = 15

y = 6x + 3 131. 5 kg disk: 3; 2 kg disk: 7 132. k < 5

133. 4 ≥ w

134. y > −7

135. p ≤ 0

136. b < 8 137. m ≤ −8 138. f > −9 139. h > 2 140. a < −4 141. x < −2 142. −12

5 ≤ n 143. g ≥ 5 144. ò (all real numbers) 145. −7 ≤ u < 6

146. −2 < k ≤ 5

147. g > 5

148. ò (all real numbers)