# Elementary Algebra, v. 1.0

by John Redden

## 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.

6.

7.

8.

9.

10.

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.

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-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. $1−42+2(−3)2$ 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

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