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This is “Review Exercises and Sample Exam”, section 1.8 from the book Beginning Algebra (v. 1.0). For details on it (including licensing), click here.
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1.8 Review Exercises and Sample Exam
Review Exercises
Real Numbers and the Number Line
Choose an appropriate scale and graph the following sets of real numbers on a number line.
1. −4, 0, 4
2. −30, 10, 40
3. −12, −3, 9
4. −10, 8, 10
Fill in the blank with <, = , or >.
5. 0 ___−9
6. −75 ___−5
7. −12 ___−(−3)
8. −(−23) ___ 23
9. |−20| ____−|−30|
10. −|6| ____−|−(−8)|
Determine the unknown.
11. | ? |=2
12. | ? |=1
13. | ? |=−7
14. | ? |=0
Translate the following into a mathematical statement.
15. Negative eight is less than or equal to zero.
16. Seventy-
17. Negative nine is greater than negative ten.
18. Zero is equal to zero.
Adding and Subtracting Integers
Simplify.
19. 12+(−7)
20. 20+(−32)
21. −23−(−7)
22. −8−(−8)
23. −3−(−13)+(−1)
24. 9+(−15)−(−8)
25. (7−10)−3
26. (−19+6)−2
Find the distance between the given numbers on a number line.
27. −8 and 14
28. −35 and −6
29. What is 2 less than 17?
30. What is 3 less than −20?
31. Subtract 30 from the sum of 8 and 12.
32. Subtract 7 from the difference of −5 and 7.
33. An airplane flying at 22,000 feet descended 8,500 feet and then ascended 5,000 feet. What is the new altitude of the airplane?
34. The width of a rectangle is 5 inches less than its length. If the length measures 22 inches, then determine the width.
Multiplying and Dividing Integers
Simplify.
35. 10÷5⋅2
36. 36÷6⋅2
37. −6(4)÷2(−3)
38. 120÷(−5)(−3)(−2)
39. −8(−5)÷0
40. −24(0)÷8
41. Find the product of −6 and 9.
42. Find the quotient of −54 and −3.
43. James was able to drive 234 miles on 9 gallons of gasoline. How many miles per gallon did he get?
44. If a bus travels at an average speed of 54 miles per hour for 3 hours, then how far does the bus travel?
Fractions
Reduce each fraction to lowest terms.
45. 180300
46. 252324
47. Convert to a mixed number: 238.
48. Convert to an improper fraction: 359.
Simplify.
49. 35(−27)
50. −58(−13)
51. −34÷67
52. 415÷283
53. 445÷6
54. 5÷813
55. 54÷152⋅6
56. 524÷32÷512
57. 112−14
58. 56−314
59. 34+23−112
60. 310+512−16
61. Subtract 23 from the sum of −12 and 29.
62. Subtract 56 from the difference of 13 and 72.
63. If a bus travels at an average speed of 54 miles per hour for 213 hours, then how far does the bus travel?
64. Determine the length of fencing needed to enclose a rectangular pen with dimensions 1212 feet by 834 feet.
Decimals and Percents
65. Write as a mixed number: 5.32.
66. Write as a decimal: 7325.
Perform the operations.
67. 6.032+2.19
68. 12.106−9.21
69. 4.23×5.13
70. 9.246÷4.02
Convert to a decimal.
71. 7.2%
72. 538%
73. 147%
74. 2712%
Convert to a percent.
75. 0.055
76. 1.75
77. 910
78. 56
79. Mary purchased 3 boxes of t-
80. A retail outlet is offering 12% off the original $39.99 price of tennis shoes. What is the price after the discount?
81. If an item costs $129.99, then what is the total after adding 714% sales tax?
82. It is estimated that 8.3% of the total student population carpools to campus each day. If there are 13,000 students, then estimate the number of students that carpool to campus.
Exponents and Square Roots
Simplify.
83. 82
84. (−5)2
85. −42
86. −(−3)2
87. (29)2
88. (123)2
89. 33
90. (−4)3
91. (25)3
92. (−16)3
93. −(−2)4
94. −(−1)5
95. 49
96. 225
97. 225
98. −121
99. 350
100. −412
101. 49
102. 825
103. Calculate the area of a square with sides measuring 3 centimeters. (A=s2)
104. Calculate the volume of a cube with sides measuring 3 centimeters. (V=s3)
105. Determine the length of the diagonal of a square with sides measuring 3 centimeters.
106. Determine the length of the diagonal of a rectangle with dimensions 2 inches by 4 inches.
Order of Operations
Simplify.
107. −5(2)−72
108. 1−42+2(−3)2
109. 2+3(6−2⋅4)3
110. 5−3(8−3⋅4)2
111. −23+6(32−4)+(−3)2
112. 52−40÷5(−2)2−(−4)
113. 34[29( −3)2−4]2
114. (12)2−34÷916−13
115. 2−3(6− 3 2)24⋅5−52
116. (2⋅8− 6 2)2−10273−(2( −5)3−7)
117. 8−5|3⋅4−(−2)4|
118. |14−|−3−52||
Find the distance between the given numbers on a number line.
119. −14 and 22
120. −42 and −2
121. 78 and −15
122. −512 and −114
Sample Exam
1. List three integers greater than −10.
2. Determine the unknown(s): | ? |=13.
3. Fill in the blank with <, =, or >: −|−100| ___ 92.
4. Convert to a fraction: 3313%.
5. Convert to a percent: 234.
6. Reduce: 75225.
Calculate the following.
7. a. (−7)2; b. −(−7)2; c. −72
8. a. (−3)3; b. −(−3)3; c. −33
9. a. |10|; b. −|−10|; c. −|10|
Simplify.
10. −(−(−1))
11. 23+15−310
12. 10−(−12)+(−8)−20
13. −8(4)(−3)÷2
14. 12⋅(−45)÷1415
15. 35⋅12−23
16. 4⋅5−20÷5⋅2
17. 10−7(3−8)−52
18. 3+2|−22−(−1)|+(−2)2
19. 13[52−(7−|−2|)+15⋅2÷3]
20. 116
21. 372
22. Subtract 2 from the sum of 8 and −10.
23. Subtract 10 from the product of 8 and −10.
24. A student earns 9, 8, 10, 7, and 8 points on the first 5 chemistry quizzes. What is her quiz average?
25. An 834 foot plank is cut into 5 pieces of equal length. What is the length of each piece?
Review Exercises Answers
1:
3:
5: >
7: <
9: >
11: ±2
13: Ø, No Solution
15: −8≤0
17: −9>−10
19: 5
21: −16
23: 9
25: −6
27: 22 units
29: 15
31: −10
33: 18,500 feet
35: 4
37: 36
39: Undefined
41: −54
43: 26 miles per gallon
45: 35
47: 278
49: −635
51: −78
53: 45
55: 1
57: −16
59: 43
61: −1718
63: 126 miles
65: 5825
67: 8.222
69: 21.6999
71: 0.072
73: 1.47
75: 5.5%
77: 90%
79: $1.75
81: $139.41
83: 64
85: −16
87: 4/81
89: 27
91: 8125
93: −16
95: 7
97: 10
99: 152
101: 23
103: 9 square centimeters
105: 32 centimeters
107: −59
109: −22
111: 31
113: 3
115: 5
117: −12
119: 36 units
121: 4340 units
Sample Exam Answers
1: −5, 0, 5 (answers may vary)
3: <
5: 275%
7:a. 49; b. −49; c. −49
9:a. 10; b. −10; c. −10
11: 1730
13: 48
15: −1130
17: 20
19: 10
21: 182
23: −90
25: 134 feet
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