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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-eight is not equal to twelve.

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. (710)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÷52

36. 36÷62

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÷1526

56. 524÷32÷512

57. 11214

58. 56314

59. 34+23112

60. 310+51216

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. 12.1069.21

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-shirts for a total of $126. If each box contains 24 t-shirts, then what is the cost of each t-shirt?

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. 142+2(3)2

109. 2+3(624)3

110. 53(834)2

111. 23+6(324)+(3)2

112. 5240÷5(2)2(4)

113. 34[29( 3)24]2

114. (12)234÷91613

115. 23(6 3 2)24552

116. (28 6 2)210273(2( 5)37)

117. 85|34(2)4|

118. |14|352||

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+15310

12. 10(12)+(8)20

13. 8(4)(3)÷2

14. 12(45)÷1415

15. 351223

16. 4520÷52

17. 107(38)52

18. 3+2|22(1)|+(2)2

19. 13[52(7|2|)+152÷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: 80

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