FreeExam

ISEE Upper Mathematics Achievement

Arithmetic, algebra, geometry, and data for students applying to grades 9 through 12, without a calculator.

ISEE is a registered trademark of E3n. FreeExam is not affiliated with E3n, and these questions are original practice, not an official test.

  1. 1.A music store marks a $64 drum pad down by 25%. What is the sale price, in dollars?

  2. 2.The ratio of maple trees to oak trees in a park is 4 to 7. There are 28 maple trees. How many oak trees are there?

  3. 3.What is the value of 3^4?

  4. 4.Solve 5x + 8 = 43 for x.

  5. 5.In the system 3x + y = 17 and x + y = 9, what is y?

  6. 6.Which inequality is equivalent to −3x < 12?

  7. 7.Which expression is a factorization of x^2 − 9?

  8. 8.A line passes through (1, 2) and (4, 11). What is the slope of the line?

  9. 9.A right triangle has legs of length 8 and 15. What is the length of the hypotenuse?

  10. 10.Two parallel lines are cut by a transversal. One same-side interior angle measures 118 degrees. What is the measure, in degrees, of the other same-side interior angle?

  11. 11.A round window has a radius of 9 feet. What is its circumference, in terms of pi?

  12. 12.A model of a roof truss is similar to the full-size truss, and each full-size length is 5 times the model length. A beam on the model is 6 centimeters. How long is the matching beam on the full-size truss, in centimeters?

  13. 13.What is the distance between the points (2, 1) and (7, 13)?

  14. 14.Five crates weigh 4, 9, 10, 15, and 22 pounds. What is the mean weight, in pounds?

  15. 15.The scores on five quizzes are 8, 3, 12, 5, and 9. What is the median score?

  16. 16.A bag holds 4 red marbles, 5 green marbles, and 6 yellow marbles. One marble is drawn at random. What is the probability that it is green?

  17. 17.What is 30% of 250?

  18. 18.A weekly train pass rises in price from $40 to $50. What is the percent increase?

  19. 19.A glaze uses 2 liters of blue pigment for every 5 liters of white base. A potter uses 8 liters of blue pigment. How many liters of white base keep the same ratio?

  20. 20.What is the value of 4^3 divided by 4?

  21. 21.If (x/3) − 4 = 5, what is x?

  22. 22.The equations 4x + y = 18 and 4x − y = 6 are both true. What is x + y?

  23. 23.Which inequality describes the solution of 7 − 2x ≥ 1?

  24. 24.Which expression is a factorization of x^2 + 7x + 12?

  25. 25.What is the slope of the line through (−2, 5) and (4, −1)?

  26. 26.A right triangle has legs of 9 meters and 12 meters. What is the hypotenuse, in meters?

  27. 27.Two parallel lines are cut by a transversal. An angle measures 73 degrees. What is the measure, in degrees, of the angle corresponding to it?

  28. 28.A round stage has a radius of 6 meters. What is the area of the stage, in terms of pi?

  29. 29.Two similar stained-glass windows have a scale factor of 2 from the smaller window to the larger window. The smaller window has area 13 square feet. What is the area of the larger window, in square feet?

  30. 30.Each side of a square patio is doubled. The original area is 15 square meters. What is the new area, in square meters?

  31. 31.What is the distance between the points (−1, 2) and (2, 6)?

  32. 32.The mean of four numbers is 18. Three of the numbers are 12, 16, and 21. What is the fourth number?

  33. 33.The ages, in years, of seven cousins are 14, 6, 22, 9, 11, 18, and 7. What is the median age?

  34. 34.A spinner has 8 equal sections, and 3 of the sections are winning sections. The spinner is used once. What is the probability that it stops on a section that is not a winning section?

  35. 35.A student answered 18 of 24 problems correctly. What percent of the problems were answered correctly?

  36. 36.A ticket price of $45 rises by 20%. What is the new price, in dollars?

  37. 37.The ratio of boys to girls in a robotics club is 5 to 3. The club has 24 students. How many of the students are boys?

  38. 38.What is the value of (2^3)^2?

  39. 39.Find x when 3(x − 4) = 21.

  40. 40.Solve the system x + 2y = 16 and x − 2y = 4. What is y?

  41. 41.Which inequality is equivalent to −4x > 20?

  42. 42.Which expression is the complete factorization of 2x^2 + 8x?

  43. 43.A line has slope 4 and passes through (1, 3). What is the y-coordinate of the point on the line where x = 3?

  44. 44.The foot of a ladder is 7 feet from a wall, and the top of the ladder meets the wall 24 feet above the ground. How long is the ladder, in feet?

  45. 45.Two parallel lines are cut by a transversal. One interior angle measures 54 degrees. What is the measure, in degrees, of its alternate interior angle?

  46. 46.A circular track has a diameter of 20 meters. What is the circumference of the track, in terms of pi?

  47. 47.Two similar sails have corresponding sides in the ratio 3 to 1, from the larger sail to the smaller sail. A side of the larger sail is 27 inches. What is the corresponding side of the smaller sail, in inches?

  48. 48.A rectangle is 9 inches long and 14 inches wide. What is its area, in square inches?

  49. 49.What is the distance between the points (−4, −1) and (4, 5)?

  50. 50.The lengths, in minutes, of five study sessions are 5, 8, 8, 10, and 19. What is the mean length?

  51. 51.A player's last five scores are 3, 7, 7, 11, and 12. What is the median score?

  52. 52.A jar contains 2 blue tiles, 3 red tiles, and 5 white tiles. One tile is drawn at random. What is the probability that the tile is white or blue?

  53. 53.What percent of 80 is 20?

  54. 54.A price drops from $90 to $72. What is the percent decrease?

  55. 55.A breakfast mix uses oats and milk in the ratio 3 to 8. A cook uses 12 cups of oats. How many cups of milk are needed?

  56. 56.What is the value of 2^6 − 4^2?

  57. 57.The equation 8x − 15 = 3x + 10 is true. What is x?

  58. 58.The graphs of y = 2x + 1 and y = −x + 10 intersect at a point. What is the x-coordinate of that point?

  59. 59.Which inequality is equivalent to −6x ≤ 18?

  60. 60.Which expression is a factorization of x^2 − 5x + 6?

  61. 61.What is the slope of the line through (3, 8) and (9, 8)?

  62. 62.A right triangle has a hypotenuse of 25 and one leg of 15. What is the length of the other leg?

  63. 63.What is the slope of a line parallel to the line through (0, 1) and (2, 7)?

  64. 64.A circular rug has a radius of 11 feet. What is the area of the rug, in terms of pi?

  65. 65.A small triangle is similar to a larger triangle with scale factor 3. The smaller triangle has perimeter 14 centimeters. What is the perimeter of the larger triangle, in centimeters?

  66. 66.What is the value of 2^8?

  67. 67.What is the distance between (0, 0) and (9, 12)?

  68. 68.The mean of four test scores is 85. Three of the scores are 70, 80, and 90. What is the fourth score?

  69. 69.The numbers 20, 15, 31, 8, and 27 are listed. What is the median?

  70. 70.Two fair coins are flipped. What is the probability that both land heads?

  71. 71.A shop adds 8% sales tax to a $250 purchase. What is the tax, in dollars?

  72. 72.40 is what percent of 160?

  73. 73.The width and the length of a poster are in the ratio 2 to 5. The length is 45 centimeters. What is the width, in centimeters?

  74. 74.What is the value of 10^3 × 10^2?

  75. 75.Two-fifths of a number is 16. What is the number?

  76. 76.If 2x + 3y = 12 and x = 3, what is y?

  77. 77.Which inequality describes the solution of −2(x + 4) > 10?

  78. 78.Which expression is a factorization of x^2 + x − 12?

  79. 79.What is the slope of the line through (5, −2) and (8, 7)?

  80. 80.A right triangle has legs of 20 and 21. What is the length of the hypotenuse?

  81. 81.A line has slope −2/5. What is the slope of a line parallel to it?

  82. 82.A circle has circumference 16 pi. What is the radius?

  83. 83.Two similar polygons have corresponding sides of 6 centimeters and 9 centimeters. The smaller polygon has area 20 square centimeters. What is the area of the larger polygon, in square centimeters?

  84. 84.A rectangle is 12 feet long and 3 yards wide. What is its area, in square feet?

  85. 85.A backdrop panel is 4 yards wide. How many inches wide is the panel?

  86. 86.The side length of a square is doubled. By what number is the area multiplied?

  87. 87.What is the distance between the points (1, 2) and (8, 26)?

  88. 88.The values 9, 10, 14, and 23 are recorded. What is the mean?

  89. 89.The values 4, 16, 9, 21, and 11 are recorded. What is the median?

  90. 90.A fair number cube with faces numbered 1 through 6 is rolled once. What is the probability of rolling a number greater than 4?

  91. 91.A club has 35 members, and 60% of them are returning members. How many members are returning?

  92. 92.After a 15% discount, a bicycle costs $170. What was the original price, in dollars?

  93. 93.On a field trip, the ratio of teachers to students is 1 to 12. There are 5 teachers. How many students are on the trip?

  94. 94.What is the value of 3^5 divided by 3^2?

  95. 95.What value of x satisfies 4(2x − 3) = 5x + 9?

  96. 96.For the system 3x + 2y = 16 and x + 2y = 8, what is x − y?

  97. 97.Which inequality describes the solution of 5 − x ≥ 9?

  98. 98.Which expression is a factorization of x^2 − 4x − 21?

  99. 99.What is the slope of the line through (−6, 1) and (−2, −7)?

  100. 100.A right triangle has legs of 12 and 16. What is the length of the hypotenuse?

  101. 101.The equation of a line is y = 7x − 4. What is the slope of a line parallel to it?

  102. 102.A circular pond has a radius of 4 yards. What is its area, in terms of pi?

  103. 103.Two similar triangles have a scale factor of 6 from the smaller to the larger. An angle of the smaller triangle measures 40 degrees. What is the measure, in degrees, of the corresponding angle of the larger triangle?

  104. 104.A photograph is 4 inches wide and 6 inches tall. A similar enlargement is 10 inches wide. What is the height of the enlargement, in inches?

  105. 105.A garden plot is 5 yards long and 8 feet wide. What is its area, in square feet?

  106. 106.A ribbon is 2 feet 6 inches long. What is that length in inches?

  107. 107.A square has a side length of 5 meters. A second square has a side length twice as long. What is the area of the second square, in square meters?

  108. 108.The numbers of books read by five students are 2, 5, 5, 6, and 12. What is the mean number of books?