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ACT Math: Algebra and Functions

Number, expressions, equations, inequalities, and functions.

ACT is a registered trademark of ACT, Inc. FreeExam is not affiliated with ACT, Inc., and these questions are original practice, not an official test.

  1. 1.What is 2^5 - 3^2?

  2. 2.Add the square root of 81 and the square root of 16.

  3. 3.Which number equals 5^0 times 4^2?

  4. 4.Subtract the absolute value of 3 from the absolute value of -7.

  5. 5.What is 8^2 divided by 4^2?

  6. 6.What is (2^3)^2?

  7. 7.What is the cube root of 27?

  8. 8.What is 3/4 of 36?

  9. 9.In lowest terms, the ratio of 18 to 24 equals which fraction?

  10. 10.What is the absolute value of the sum of -5 and 12?

  11. 11.What is 4^(-2)?

  12. 12.Divide the square root of 144 by the square root of 9.

  13. 13.Which number equals 3^2 times 3^3?

  14. 14.What is 2^4 times 5^2?

  15. 15.A paint mix uses 45 milliliters of blue for every 60 milliliters of white. In lowest terms, what is the ratio of blue to white?

  16. 16.Add the absolute value of 6 - 15 to the absolute value of -2.

  17. 17.What is 16^(1/2) times 8^(1/3)?

  18. 18.What is 10^3 - 10^2?

  19. 19.What is (-2)^4?

  20. 20.What is 81 divided by 3^2?

  21. 21.What is the solution of 4x - 7 = 21?

  22. 22.Solve 5(x + 2) = 35.

  23. 23.What value of x satisfies (2/3)x = 12?

  24. 24.Solve -2x + 6 = 18.

  25. 25.Which inequality is the complete solution of 2x - 5 > 9?

  26. 26.Which inequality is the complete solution of -4x <= 20?

  27. 27.Which pair solves the system x + y = 11 and x - y = 3?

  28. 28.Which list gives every solution of x^2 - 5x + 6 = 0?

  29. 29.The function f is defined by f(x) = 3x - 4. What is f(5)?

  30. 30.The function g(t) = 40 + 8t gives the pages a reader has finished after t minutes, including 40 pages read earlier. How many pages does the reader finish per minute?

  31. 31.Cookies are packed in boxes of 6, and 4 cookies are left over. There are 58 cookies in all. How many full boxes are there?

  32. 32.Which pair of positive consecutive integers has a product of 42?

  33. 33.Which list gives every solution of the absolute value equation |x - 3| = 8?

  34. 34.A recipe uses flour and sugar in the ratio 5:2. If 15 cups of flour are used, how many cups of sugar are used?

  35. 35.The function f is defined by f(x) = x^2 - 2x. What is f(4)?

  36. 36.A game score is 12 points plus 6 points for each puzzle solved. Which inequality gives every number of puzzles p that makes the score at least 90?

  37. 37.Which pair solves 2x + y = 13 and x + y = 8?

  38. 38.Which expression equals the square root of 50?

  39. 39.Solve x/4 + 3 = 11.

  40. 40.Which list gives every solution of x^2 = 49?

  41. 41.Functions f and g are defined by f(x) = 2x + 1 and g(x) = x - 4. What is f(g(6))?

  42. 42.A tank holds 120 liters. Water drains at 8 liters per minute. After how many minutes are 24 liters left?

  43. 43.Simplify 6^5 divided by 6^2. What number is the result?

  44. 44.Which inequality describes every number x whose absolute value is less than 4?

  45. 45.If 2/5 = x/35, what is x?

  46. 46.Solve 7x - 3x + 5 = 21.

  47. 47.What is the solution of x^2 + 6x + 9 = 0?

  48. 48.A linear function satisfies f(1) = 5 and f(3) = 11. What is f(5)?

  49. 49.Adult tickets cost 12 dollars and student tickets cost 8 dollars. A group buys 10 tickets for 96 dollars. How many student tickets does the group buy?

  50. 50.Which inequality is the complete solution of 3(x - 2) <= 15?

  51. 51.What is 2^(-3) times 2^5?

  52. 52.Add the cube root of 64 and the square root of 25.

  53. 53.Solve x/2 + x/3 = 5.

  54. 54.The function h is defined by h(x) = -2x + 9. For which x is h(x) = 1?

  55. 55.A plumber charges 45 dollars to arrive and 30 dollars for each hour of work. A bill is 165 dollars. For how many hours did the plumber work?

  56. 56.Which pair solves x^2 - 4x - 12 = 0?

  57. 57.What is (1/2)^(-3)?

  58. 58.On a trail map, 1 inch stands for 8 miles. A path measures 7 inches on the map. How many miles does that path stand for?

  59. 59.Solve (1/2)x - 3/2 = 5/2.

  60. 60.The function f(x) = 50 - 2x gives the seats left after x rows are reserved. Every reserved row holds the same number of seats. How many seats are in one row?

  61. 61.Solve 9 - 2x = 4x - 3.

  62. 62.Which list gives every solution of |2x - 6| = 10?

  63. 63.Which positive number n satisfies n^2 - 5n = 14?

  64. 64.What is (4^3)^2 divided by 4^4?

  65. 65.Which inequality is the complete solution of (-x)/3 > 4?

  66. 66.The function f is defined by f(x) = x^2 - 4. What is f(-3)?

  67. 67.The ratio of red beads to blue beads is 4:7. There are 28 blue beads. How many red beads are there?

  68. 68.Solve 4(2x - 1) = 3x + 11.

  69. 69.Which pair solves x = y + 2 and 3x + 2y = 16?

  70. 70.What is the absolute value of the quantity 3^2 - 5^2?

  71. 71.The function f is defined by f(x) = (x - 2)^2 + 5. What is the smallest value of f(x)?

  72. 72.A lift may carry under 1800 pounds. It already holds 1260 pounds, and each added rider weighs 90 pounds. Which inequality gives every number of additional riders p who may board?

  73. 73.If 2^x = 32, what is x?

  74. 74.A linear function satisfies f(0) = -3 and f(2) = 7. What is f(1)?

  75. 75.Solve (x + 4)/5 = 3.

  76. 76.Multiply the square root of 12 by the square root of 3.

  77. 77.Which pair solves y = 2x - 1 and 3x + y = 14?

  78. 78.Which inequality is the complete solution of 5 <= 2x + 1 <= 13?

  79. 79.Mei has 80 dollars. She buys a notebook for 8 dollars and spends the rest on markers that cost 6 dollars each. How many markers does she buy?

  80. 80.What is 9^(3/2)?

  81. 81.The function f is defined by f(x) = 4x - x^2. What is f(3)?

  82. 82.Solve (1/4)x = 7.

  83. 83.Which list gives every solution of x^2 + x - 20 = 0?

  84. 84.Multiply the absolute value of -8 by the absolute value of -1/2.

  85. 85.A cafe sells small cups for 3 dollars and large cups for 5 dollars. It sells 20 cups and collects 76 dollars. How many of the cups are large?

  86. 86.Which inequality is the complete solution of 4 - x > 9?

  87. 87.Which equation gives a linear function with f(0) = 6 and slope -1/2?

  88. 88.What is 5^3 - 4^3?

  89. 89.Solve 7x + 2 = 3x - 14.

  90. 90.18 is what percent of 72?

  91. 91.Which list gives every solution of 2x^2 - 8 = 0?

  92. 92.The function f is defined by f(x) = x^2 + 1. What is f(f(2))?

  93. 93.A library shelf has 3 times as many fiction books as science books. Together those two kinds total 84 books. How many of the books are fiction?

  94. 94.What is (2/5)^2?

  95. 95.Which inequality is the complete solution of 6x + 1 < 4x + 9?

  96. 96.The function f is defined by f(x) = 7 - 3x. What is f(0)?

  97. 97.What is the solution of |x + 4| = 0?

  98. 98.What is the square root of 196?

  99. 99.Which pair solves 4x - y = 10 and 4x + y = 22?

  100. 100.A data plan costs 25 dollars a month plus 2 dollars for each extra gigabyte. One bill is 41 dollars. How many extra gigabytes were used?

  101. 101.The function f is defined by f(x) = (x + 1)^2 - 9. What is f(-1)?

  102. 102.If 3/8 = 9/x, what is x?

  103. 103.Which inequality is the complete solution of -5(x - 2) >= 20?

  104. 104.What is 7^2 times 7^0?

  105. 105.For f(x) = 2x + 5, which input gives output 19?

  106. 106.Two numbers add to 30, and the larger is 8 more than the smaller. What is the larger number?

  107. 107.Which expression equals the square root of 72?

  108. 108.A school club sells programs for 4 dollars each and has already collected a 28-dollar donation. The club wants 100 dollars in all. How many programs must it sell?