ASVAB Practice

Mathematics Knowledge

200 Mathematics Knowledge practice questions, each with the correct answer and the method behind it.

Practice tests Practice test 1 Practice test 2 Practice test 3 Practice test 4 Practice test 5 Practice test 6 Practice test 7 Practice test 8
  1. What is the value of |-7| + |3|?10
  2. What is the largest prime factor of 84?7
  3. Evaluate 8 + 3 x (10 - 6) / 214
  4. Written in scientific notation, 0.00042 equals 4.2 x 10 to what power?-4
  5. What is the value of -5 - (-12)?7
  6. Simplify x to the 5th power times x cubed. The result is x to what power?8
  7. What is the value of (2 cubed) squared?64
  8. What is the value of 5 to the power of 0?1
  9. What is the value of 3 to the power of -2?1/9
  10. What is the square root of 196?14
  11. Which of the following is the simplified form of the square root of 72?6 root 2
  12. If x = 4, what is the value of 3x squared minus 2x plus 1?41
  13. Combine like terms: 7a + 3b - 2a + 5b. What is the coefficient of a?5
  14. In the expansion of (x + 3)(x - 5), what is the coefficient of x?-2
  15. The expression x squared minus 49 factors as (x + a)(x - a). What is a?7
  16. Which of the following is a factor of x squared plus 7x plus 12?(x + 4)
  17. Simplify 4(2x - 3) + 5. What is the constant term?-7
  18. Solve for x: 3x + 7 = 225
  19. Solve for x: 5x - 3 = 2x + 125
  20. Solve for x: 2(x - 4) = 109
  21. The area of a triangle is given by A = one half times b times h. If A = 24 and b = 6, what is h?8
  22. If x + y = 12 and x - y = 4, what is the value of x?8
  23. Solve the inequality 3x - 5 < 16x is less than 7
  24. What is the larger solution of x squared minus 5x plus 6 = 0?3
  25. Solve for x: x divided by 4, plus 3, equals 1028
  26. A line passes through the points (2, 3) and (6, 11). What is its slope?2
  27. At what value of y does the line y = 3x - 4 cross the y-axis?-4
  28. What is the x-coordinate of the midpoint of the segment joining (1, 5) and (7, 9)?4
  29. How far apart are the points (0, 0) and (6, 8)?10
  30. In which quadrant does the point (-3, 5) lie?Quadrant II
  31. Two angles are complementary. If one measures 35 degrees, what does the other measure?55 degrees
  32. Two angles are supplementary. If one measures 118 degrees, what does the other measure?62 degrees
  33. Two angles of a triangle measure 43 and 61 degrees. What is the third angle?76 degrees
  34. Two parallel lines are cut by a transversal. If one interior angle measures 65 degrees, what does the interior angle on the same side of the transversal measure?115 degrees
  35. In an isosceles triangle the apex angle measures 40 degrees. What does each base angle measure?70 degrees
  36. A right triangle has legs of 9 and 12. What is the length of the hypotenuse?15
  37. Two triangles are similar. Sides of 6 and 9 in the first correspond to sides of 8 and x in the second. What is x?12
  38. What is the area of a rectangle measuring 14 by 9?126
  39. What is the area of a triangle with a base of 16 and a height of 7?56
  40. A circle has a radius of 5. Using 3.14 for pi, what is its circumference?31.4
  41. A trapezoid has parallel sides of 8 and 12 and a height of 5. What is its area?50
  42. What is the sum of the interior angles of a hexagon?720 degrees
  43. A circle has a radius of 10. Using 3.14 for pi, what is its area?314
  44. A rectangle measuring 12 by 8 has a rectangular piece measuring 4 by 3 cut out of it. What area remains?84
  45. What is the volume of a cube with an edge of 4?64
  46. What is the volume of a rectangular solid measuring 5 by 3 by 8?120
  47. Using 3.14 for pi, what is the volume of a cylinder with a radius of 3 and a height of 10?282.6
  48. What is the surface area of a cube with an edge of 5?150
  49. What is the next term in the sequence 4, 9, 14, 19, ...?24
  50. What is the next term in the sequence 3, 6, 12, 24, ...?48
  51. What is the value of -8 x (-3)?24
  52. Written as a decimal, 15 percent equals0.15
  53. Which of these values is the largest?0.4
  54. Written out in full, 5.6 x 10 to the 3rd power equals5600
  55. What is the least common multiple of 6 and 8?24
  56. Simplify x to the 9th power divided by x to the 4th power. The result is x to what power?5
  57. When (3x squared) is raised to the 3rd power, what is the resulting coefficient?27
  58. What is the cube root of 27?3
  59. The square root of 50 can be written as a times the square root of 2. What is a?5
  60. What is the value of 2 to the power of -3?1/8
  61. Simplify x cubed times x to the 0 power times x squared. The result is x to what power?5
  62. If a = 5 and b = -2, what is the value of 2a + 3b?4
  63. In the expansion of (x + 4) squared, what is the coefficient of x?8
  64. What is the greatest common factor of 12x and 18?6
  65. Simplify 5(x - 2) - 3(x + 1). What is the coefficient of x?2
  66. The expression x squared minus 3x minus 10 factors as (x + a)(x + b). What is the smaller of a and b?-5
  67. If a = 7 and b = 3, what is the value of (a - b) squared?16
  68. Solve for x: 4x = 369
  69. Solve for x: x - 7 = -34
  70. Solve for x: 3(x + 2) = 5x - 45
  71. If 2x + 3y = 18 and y = 2, what is the value of x?6
  72. The perimeter of a rectangle is P = 2L + 2W. If P = 40 and L = 12, what is W?8
  73. Solve the inequality -2x > 8x is less than -4
  74. If x squared equals 81, what is the positive value of x?9
  75. Solve for x: x divided by 3, minus 2, equals 418
  76. A line passes through the points (2, 5) and (9, 5). What is its slope?0
  77. At what value of y does the line 2x + y = 6 cross the y-axis?6
  78. How far apart are the points (1, 2) and (4, 6)?5
  79. What is the y-coordinate of the midpoint of the segment joining (3, -1) and (3, 7)?3
  80. A line has a slope of -2 and passes through (0, 5). What is y when x = 3?-1
  81. When two straight lines cross, the pair of angles opposite each other areequal in measure
  82. In an equilateral triangle, each angle measures60 degrees
  83. An exterior angle of a triangle equals the sum of the two interior angles not next to it. If those two measure 50 and 60 degrees, what is the exterior angle?110 degrees
  84. A right triangle has a hypotenuse of 13 and one leg of 5. How long is the other leg?12
  85. Two angles of a triangle are equal and the third measures 80 degrees. What does each equal angle measure?50 degrees
  86. When two parallel lines are cut by a transversal, alternate interior angles areequal in measure
  87. A triangle has sides measuring 5, 12, and 13. This triangle isa right triangle
  88. A square has an area of 64. What is the length of one side?8
  89. A parallelogram measures 9 along its base and stands 6 high. What is its area?54
  90. What is the perimeter of a regular octagon with sides of 7?56
  91. What is the measure of each interior angle of a regular hexagon?120 degrees
  92. A circle has a diameter of 16. Using 3.14 for pi, what is its circumference?50.24
  93. A rectangle has a perimeter of 36 and a length of 11. What is its width?7
  94. A triangle has sides of 6, 8, and 10. What is its area?24
  95. Using 3.14 for pi, find the volume of a cylinder that has a radius of 2 and a height of 7.87.92
  96. A cube has a volume of 125. What is the length of one edge?5
  97. Using 3.14 for pi, what is the volume of a sphere with a radius of 3?113.04
  98. What is the surface area of a rectangular box measuring 2 by 3 by 4?52
  99. What is the next term in the sequence 100, 90, 80, ...?70
  100. If f(x) = 2x + 5, what is the value of f(6)?17
  101. What is the value of |-9| + |-4|?13
  102. What is the value of -14 + 9 - (-6)?1
  103. Evaluate 5 + 2 x (9 - 5) / 47
  104. Evaluate (6 + 4) x 3 - 2 squared26
  105. What is the largest prime factor of 90?5
  106. What is the greatest common factor of 36 and 48?12
  107. What is the value of 47 x 1?47
  108. What is the value of 0 divided by 15?0
  109. Written in scientific notation, 0.0058 equals 5.8 x 10 to what power?-3
  110. Written out in full, 2.3 x 10 to the 4th power equals23000
  111. Simplify y to the 4th power times y to the 6th power. The result is y to what power?10
  112. Simplify z to the 11th power divided by z to the 3rd power. The result is z to what power?8
  113. What is the value of (3 squared) cubed?729
  114. When (2x cubed) is raised to the 4th power, what is the resulting coefficient?16
  115. What is the value of 9 to the power of 0?1
  116. What is the value of 4 to the power of -3?1/64
  117. Simplify a squared times a to the power of -5. The result is a to what power?-3
  118. What is the square root of 225?15
  119. What is the cube root of 125?5
  120. Between which two whole numbers does the square root of 55 fall?7 and 8
  121. Which of the following is the simplified form of the square root of 108?6 root 3
  122. The square root of 80 can be written as a times the square root of 5. What is a?4
  123. If x = 3, what is the value of 5x - 7?8
  124. If x = -2, what is the value of 4x squared - 3x?22
  125. Combine like terms: 9m - 4n - 3m + 6n. What is the coefficient of n?2
  126. Simplify 6p + 5 - 2p - 9. What is the constant term?-4
  127. Simplify 3(2x + 5) - 4. What is the constant term?11
  128. Simplify -2(4x - 7) + 3x. What is the coefficient of x?-5
  129. In the expansion of (x + 4)(x + 6), what is the coefficient of x?10
  130. In the expansion of (2x - 3)(x + 5), what is the coefficient of x?7
  131. Factor out the greatest common factor from 12x + 18. What remains inside the parentheses after factoring out 6?2x + 3
  132. What is the greatest common factor that can be pulled out of 15x squared + 25x?5
  133. Which of the following is a factor of x squared - 2x - 15?(x - 5)
  134. The expression x squared minus 81 factors as (x + a)(x - a). What is a?9
  135. Solve for x: x - 9 = 1625
  136. Solve for x: 4x - 5 = 278
  137. Solve for x: x divided by 6, minus 2, equals 330
  138. Solve for x: 6x + 4 = 3x + 226
  139. Solve for x: 8x - 3 = 5x + 156
  140. The formula for perimeter of a rectangle is P = 2L + 2W. If P = 30 and W = 4, what is L?11
  141. The formula for simple interest is I = Prt. If I = 240, P = 2000, and t = 2, what is r?0.06
  142. Solve the formula d = rt for t, then find t when d = 150 and r = 25.6
  143. If x + y = 15 and x - y = 5, what is the value of y?5
  144. If 2x + y = 11 and x - y = 1, what is the value of x?4
  145. Solve the inequality 2x + 6 > 18x is greater than 6
  146. Solve the inequality -3x + 4 <= 19x is greater than or equal to -5
  147. What is the smaller solution of x squared - 7x + 10 = 0?2
  148. What is the positive solution of x squared - 4x - 21 = 0?7
  149. Solve for x: 5x = 459
  150. Solve for x: 3(x - 2) = x + 87
  151. The point (4, -6) is located in which quadrant?Quadrant IV
  152. In which quadrant does the point (-7, -2) lie?Quadrant III
  153. A line passes through the points (1, 2) and (5, 14). What is its slope?3
  154. A line passes through the points (-2, 5) and (3, -5)? What is its slope?-2
  155. What is the slope of the line y = -4x + 9?-4
  156. At what value of y does the line y = 2x + 7 cross the y-axis?7
  157. What is the y-coordinate of the midpoint of the segment joining (3, 2) and (9, 14)?8
  158. How far apart are the points (1, 1) and (4, 5)?5
  159. What is the x-intercept of the line 2x + 3y = 12?6
  160. For the line 5x - 2y = -10, what is the y-intercept?5
  161. Two angles are complementary. If one measures 62 degrees, what does the other measure?28
  162. Two angles are supplementary. If one measures 73 degrees, what does the other measure?107
  163. Two parallel lines are cut by a transversal. If one angle measures 48 degrees, what does its corresponding angle measure?48
  164. Two parallel lines are cut by a transversal. If one interior angle measures 72 degrees, what does the interior angle on the same side of the transversal measure?108
  165. Two angles of a triangle measure 55 and 72 degrees. What is the third angle?53
  166. In a triangle, one angle measures 90 degrees and another measures 34 degrees. What is the third angle?56
  167. A triangle has angles of 60, 60, and 60 degrees. What type of triangle is it?Equilateral
  168. In an isosceles triangle the apex angle measures 100 degrees. What does each base angle measure?40
  169. A right triangle has legs of 5 and 12. What is the length of the hypotenuse?13
  170. A right triangle has a hypotenuse of 17 and one leg of 8. What is the length of the other leg?15
  171. Two triangles are similar. Sides of 4 and 10 in the first correspond to sides of 6 and x in the second. What is x?15
  172. Two triangles have all three pairs of corresponding sides equal in length. What relationship do the triangles have?They are congruent
  173. Two angles are complementary. One measures twice the other. What does the smaller angle measure?30
  174. In a triangle, the three angles are in the ratio 2:3:4. What is the largest angle?80
  175. What is the perimeter of a rectangle measuring 11 by 6?34
  176. A square has a side length of 13. What is its area?169
  177. What is the area of a triangle with a base of 18 and a height of 5?45
  178. A parallelogram has a base of 14 and a height of 9. What is its area?126
  179. A trapezoid has parallel sides of 10 and 16 and a height of 6. What is its area?78
  180. A trapezoid has parallel sides of 7 and 13 and a height of 4. What is its area?40
  181. A circle has a radius of 7. Using 3.14 for pi, what is its circumference?43.96
  182. A circle has a diameter of 12. Using 3.14 for pi, what is its area?113.04
  183. What is the sum of the interior angles of a pentagon?540
  184. What is the measure of each interior angle of a regular octagon?135
  185. A rectangle measuring 10 by 6 has a right triangle with legs 4 and 3 cut from one corner. What area remains?54
  186. A figure is made of a rectangle 8 by 5 with a semicircle of radius 4 attached to one short side. Using 3.14 for pi, what is the total area, rounded to the nearest whole number?65
  187. A square has a perimeter of 52. What is its area?169
  188. A circle has a circumference of 62.8. Using 3.14 for pi, what is its radius?10
  189. What is the volume of a cube with an edge of 6?216
  190. What is the volume of a rectangular solid measuring 7 by 4 by 5?140
  191. Using 3.14 for pi, what is the volume of a cylinder with a radius of 4 and a height of 9?452.16
  192. Using 3.14 for pi, what is the volume of a cylinder with a radius of 2 and a height of 15?188.4
  193. Using 3.14 for pi, what is the volume of a cone with a radius of 3 and a height of 8, rounded to the nearest tenth?75.4
  194. Using 3.14 for pi, what is the volume of a sphere with a radius of 3, rounded to the nearest tenth?113.0
  195. What is the surface area of a rectangular solid measuring 4 by 3 by 5?94
  196. What is the surface area of a cube with an edge of 7?294
  197. What is the next term in the sequence 6, 11, 16, 21, ...?26
  198. In the arithmetic sequence 8, 5, 2, -1, ..., what is the 6th term?-7
  199. What is the next term in the sequence 2, 6, 18, 54, ...?162
  200. If f(x) = 3x squared - 2, what is the value of f(4)?46

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