Review Questions
Use these review questions to practice what you’ve learned in this book. After you work through the review questions, you’re well on your way to understanding the basic concepts of Algebra I.
Chapter 1
1. Which of the following are rational numbers? 
2. Which of the following are prime numbers? 2, 6, 9, 11, 15, 17
3. The multiplicative inverse of 
is _______ .
4. 32 =
5. 2–3 =
6. 72 × 75 = (with exponent)
7. 86 ÷ 84 = (with exponent)
8. (34)5 = (with exponent)
9. 
10. 
11. 
to the nearest tenth.
12. Simplify: 2[(32 + 4) + 2(1 + 2)].
13. The number 12,120 is divisible by which numbers between 1 and 10?
Chapter 2
14. –7 + 6 =
15. (–4)(–2)(–3) =
16. 
17. 
18. 
19. 
20. Change to a decimal: 
21. Change to a fraction: 
22. 20 is what % of 400?
For problems 23 and 24, express each answer in scientific notation.
23. (4 × 103)(3 × 102) =
24. (8 × 10–2) ÷ (2 × 104) =
Chapter 3
25. {1, 2, 3} 
{3, 4, 5} =
26. {1, 3, 5} 
{3, 4, 5} =
27. True or false: {Tom, Bob, Sam} ~ {1, 2, 3}
28. Express algebraically: five less than four times a number n.
29. Evaluate: 2x + 4y2 if x = 3 and y = –2.
Chapter 4
30. Solve for x: 4x + 8 = 32
31. Solve for y: 
32. Solve for r: 5r + 7 = 3r – 15
33. Solve for x: xy + z = w
34. Solve for c: 
35. Solve for x: 
Chapter 5
36. Solve for x and y:
37. Solve for m and n:
Chapter 6
38. 2xy2 + xy2 – 6xy2 =
39. (3x4y2z)(–5x2y2z2) =
40. (5a2b)4 =
41. 
42. Express the answer with positive exponents: x–5yz–2
43. (8a – 4b) – (6a – 3b) =
44. 4x2y – 3xy2 + 2x2y – 2xy2 =
45. (5x + 2y)(2x + 3y) =
46. 
47. (x2 + 4x + 4) ÷ (x + 2) =
48. Factor: 2y2 – 8y =
49. Factor: 9x2 – 16 =
50. Factor: x2 – 10x + 24 =
51. Factor: 4a3 + 6a2 + 2a =
52. Factor: m2 + 5mn + 4n2 =
53. Factor: a + 6 + ab + 6b =
Chapter 7
54. 
55. 
56. 
57. 
58. 
59. 
60. 
61. 
62. 
63. 
64. 
Chapter 8
65. Solve for x: 2x + 5 < 15
66. Solve for x: 3x + 4 ≥ 5x – 8
67. Graph: {x: –2 ≤ x < 2}
68. Graph: {x: x < 6}
69. |–6 – 3| =
70. Solve for x: 2|x – 2| + 5 = 13
71. Solve and graph: 3|x + 1| + 2 > 8
Chapter 9
72. Is 
linear or nonlinear?
73. Graph: y = x – 4
74. Find the slope of 2x + y = 6.
75. Find the equation of the line, in slope-intercept form, passing through the point (5, 3) with a slope of 2.
76. Find the equation of the line, in standard form, passing through the points (2, 3) and (–1, –3).
77. Graph: y ≥ x + 1
Chapter 10
78. Which of the following are graphs of functions?
79. If f(x) = 3x2 – 2x – 1, what is f(3)?
80. If the domain of x2 + 5x + 1 is {2, 3, 4}, then what is the range?
81. If y varies directly as x, find the constant of variation when y is 3 and x is 9.
82. If y varies indirectly as x and the constant of variation is 2, find y when x is 8.
Chapter 11
83. Simplify: 
84. 
85. 
86. 
For problems 87–89, express answers in simplified form with rational denominators.
87. 
88. 
89. 
Chapter 12
90. Solve for x: x2 – 2x = 63
91. Solve: x2 – 81 = 0
92. Solve: x2 + 8x = 0
93. Solve: 3x2 + 3x + 2 = 2x2 + x + 1
94. Solve for x using the quadratic formula: x2 + 3x + 1 = 0
95. Solve for x by completing the square: x2 + 7x + 4 = 0
Chapter 13
96. If Tim invests $200 at a 10% annual rate for three years compounded annually, how much money will he have at the end of three years from this investment?
97. If one number is twice as large as another number and the smaller number is increased by 12, the result is 8 less than the larger number. What is the larger number?
98. Nuts costing $1.40 per pound are mixed with nuts costing $1.00 per pound to produce forty pounds of mixture worth $1.10 per pound. How much of each type is used?
99. Tom is trying to fill his bathtub to take a bath. If Tom turns on only the hot water, the tub will fill in 20 minutes. If Tom turns on only the cold water, the tub will fill in 10 minutes. How long will it take to fill the tub if Tom turns on the hot and cold water faucets at the same time?
Answers: 1. 0, 2, 
2. 2, 11, 17 3. 
4. 9 5. 
6. 77 7. 82 8. 320
9. 8 10. 5 11. approx. 4.2 12. 38 13. 2, 3, 4, 5, 6, 8 14. –1 15. –24
16. 
17. 
18. 
19. 
20. .0625 21. 
22. 5%
23. 12 × 105 = 1.2 × 106 24. 4 × 10–6 25. {3} 26. {1, 3, 4, 5} 27. True
28. 4n – 5 29. 22 30. 6 31. 96 32. –11 33. 
34. 
35. 
36. x = –1, y = 2 37. m = 5, n = 2 38. –3xy2 39. –15x6y4z3 40. 625a8b4
41. 3xyz 42. 
43. 2a – b 44. 6x2y – 5xy2 45. 10x2 + 19xy + 6y2
46. 6mn + 7n 47. x + 2 48. 2y(y – 4) 49. (3x – 4)(3x + 4) 50. (x – 6)(x – 4)
51. 2a(2a + 1)(a + 1) 52. (m + n)(m + 4n) 53. (1 + b)(a + 6) 54. 
55. 
56. 
57. 2(x + 1) 58. 
59. 3 60. 
61. 
62. 
63. 
64. 
65. x < 5 66. 6 ≥ x or x ≤ 6
67.
68.
69. 9 70. 6, – 2 71. x > 1 or x < –3
72. Nonlinear
73.
74. –2 75. y = 2x – 7 76. 2x – y = 1
77.
78. (a) 79. 20 80. {15, 25, 37} 81. 
82. 
83. 
84. 
85. 
86. 
87. 
88. 
89. 
90. 9, –7
91. 9, –9 92. 0, –8 93. –1 94. 
95. 
96. $266.20 97. 40 98. 10 lbs. of
$1.40 nuts and 30 lbs. of $1.00 nuts 99. 