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Illinois Assessment of Readiness Mathematics Grade 8

Slope, systems of equations, exponents, the Pythagorean theorem, and volume.

These questions are original. This is not an official Illinois Assessment of Readiness test, and FreeExam is not affiliated with the Illinois State Board of Education.

  1. 1.A path on a coordinate map of Grant Park runs from (1, 3) to (5, 11). What is the slope of the path?

  2. 2.A survey line in Galena passes through (4, 1) and (4, 9). What is the slope of the line?

  3. 3.A right triangle on a gym floor in Peoria has legs of 6 feet and 8 feet. What is the length of the hypotenuse?

  4. 4.A cylinder has a volume of 24 cubic units. A cone has the same radius and the same height. What is the volume of the cone?

  5. 5.A mileage log for a truck based in Decatur shows 5000 miles. Which expression writes 5000 in scientific notation?

  6. 6.What is the principal square root of 81?

  7. 7.Which statement about √5 is true?

  8. 8.Where do the lines y = x + 2 and y = 2x meet?

  9. 9.A microscope scale in Urbana is marked 4^-2 meter. Which number equals 4^-2?

  10. 10.Students in Naperville multiply 6^4 by 6^2. Which expression is equivalent?

  11. 11.A tower calculation in Rock Island simplifies 9^7 ÷ 9^4. Which expression is equivalent?

  12. 12.On a blueprint from Vandalia, (2^3)^4 is rewritten as a single power of 2. Which power is it?

  13. 13.A timer in Bloomington shows the power 15^0. What is its value?

  14. 14.Using the order of operations, what is the value of -3^2?

  15. 15.A shipping cube in Elgin has a volume of 125 cubic inches. What is the length of one edge?

  16. 16.A scale drawing in Oak Park uses the fraction 36/49. What is the principal square root of 36/49?

  17. 17.Between which two consecutive integers does √45 lie?

  18. 18.A sample from the Chicago River has a mass of 0.00072 gram. Which expression is that mass in scientific notation?

  19. 19.Which number is greater?

  20. 20.A shipment count uses (4 × 10^3)(2 × 10^5). What is the product in scientific notation?

  21. 21.An area figure for Lake County is (9 × 10^8) ÷ (3 × 10^2). What is the quotient in scientific notation?

  22. 22.Census notes for two Sangamon County tracts list 3.2 × 10^4 people and 1.5 × 10^4 people. What is the combined population in scientific notation?

  23. 23.A route file stores 6.04 × 10^5. What is that number in standard form?

  24. 24.A distance table for a train leaving Chicago's Union Station lists (0 hours, 0 miles), (2 hours, 70 miles), and (4 hours, 140 miles). What is the slope in miles per hour?

  25. 25.The graph of y = 6 on a downtown Chicago grid is a horizontal line. What is its slope?

  26. 26.A bike shop in Evanston uses y = 12x + 8 for the charge in dollars after x hours. What is the y-intercept?

  27. 27.A sample in a Champaign lab cools according to y = -5x + 40, where x is hours and y is degrees Celsius. What does -5 represent?

  28. 28.Which equation has slope 3 and y-intercept -2?

  29. 29.A railing plan along the Illinois River uses 4(x - 3) = 20, with x in meters. What is x?

  30. 30.Solve 7x - 4 = 3x + 16.

  31. 31.Solve (3/4)x = 9.

  32. 32.How many values of x make the equation 5x + 1 = 5x + 9 true?

  33. 33.Which statement about 2(x + 6) = 2x + 12 is true?

  34. 34.What is the solution of 8x - 3 = 5x + 9?

  35. 35.What is the solution of the system x + y = 11 and x - y = 3?

  36. 36.What is the solution of the system y = 4x and x + y = 15?

  37. 37.The lines y = 3x + 2 and y = 3x - 5 are drawn on a Waukegan map. How many intersection points do they have?

  38. 38.Which statement describes the graphs of y = -x + 4 and 2y + 2x = 8?

  39. 39.A table at a Navy Pier counter pairs input 2 with output 5, input 2 with output 9, and input 4 with output 7. Which statement is correct?

  40. 40.Which set of ordered pairs is a function?

  41. 41.Which equation does not represent a linear function?

  42. 42.For y = -2x + 9, what happens to y when x increases by 1?

  43. 43.A club in Carbondale uses the rule f(x) = 3x - 4. What is f(6)?

  44. 44.Point (2, -5) on a Joliet map is translated 4 units right and 3 units up. What is the image?

  45. 45.Point (-3, 7) is reflected across the x-axis. What is the image?

  46. 46.Point (8, -1) is reflected across the y-axis. What is the image?

  47. 47.Point (4, -6) is rotated 180 degrees about the origin. What is the image?

  48. 48.Point (5, 2) is rotated 90 degrees counterclockwise about the origin. What is the image?

  49. 49.Point (3, -4) on a mural grid in Des Plaines is dilated by a scale factor of 2 from the origin. What is the image?

  50. 50.A triangle on a poster has a side of length 7 centimeters and is dilated by a scale factor of 4. What is the corresponding side length?

  51. 51.Two angles of a triangle on a Quincy quilt measure 28 degrees and 73 degrees. What is the third angle?

  52. 52.Two remote interior angles of a triangle measure 35 degrees and 62 degrees. What is the exterior angle at the third vertex?

  53. 53.Parallel streets in Aurora are cut by a transversal. One angle measures 118 degrees. What is the measure of its corresponding angle?

  54. 54.Parallel rails near Galesburg are cut by a transversal. An interior angle measures 54 degrees. What is the alternate interior angle?

  55. 55.Parallel lines are cut by a transversal, and one consecutive interior angle measures 67 degrees. What is the other consecutive interior angle?

  56. 56.A right triangle drawn in Lincoln Park has legs of 5 meters and 12 meters. What is the hypotenuse?

  57. 57.A right triangle has a hypotenuse of 25 inches and one leg of 7 inches. What is the other leg?

  58. 58.A triangle has side lengths 4, 5, and 6. Which statement is correct?

  59. 59.On a coordinate map of Springfield, what is the distance between (-1, 2) and (2, 6)?

  60. 60.A cylindrical grain bin in Moline has radius 4 feet and height 10 feet. What is its volume?

  61. 61.A conical pile of sand in Cairo, Illinois, has radius 6 feet and height 5 feet. What is its volume?

  62. 62.A spherical buoy on Lake Michigan has radius 3 feet. What is its volume?

  63. 63.A can from a Danville packing line is a cylinder. The height stays the same while the radius doubles. How does the volume change?

  64. 64.Two spheres in a Kankakee classroom model have radii 1 inch and 2 inches. The larger volume is how many times the smaller volume?

  65. 65.A cone keeps the same radius while its height is tripled. How does the volume change?

  66. 66.Which situation is best modeled by a positive association?

  67. 67.A scatter plot of miles driven and fuel remaining slopes downward from left to right. What does that pattern mean?

  68. 68.On a scatter plot of sapling age and height at Allerton Park, one point sits far above a rising pattern. What is that point called?

  69. 69.A line fitted to hours a fair booth is open and bags of popcorn sold is y = 2.5x + 10. What does 2.5 mean in this model?

  70. 70.A two-way table records 40 students in Cicero: 12 bike and play an instrument, 8 bike but do not play, 6 do not bike but play, and 14 do neither. How many students bike?

  71. 71.Of 50 visitors at a museum shop in Chicago, 20 bought a book. What is the relative frequency of buying a book?

  72. 72.On a scatter plot of January temperatures for towns along the Illinois River, most points form a tight group and one point sits far away. What is the tight group called?

  73. 73.A trend line for a Rockford fundraiser is y = 8x + 5, where x is the number of callers. Using the line, what value of y is predicted when x = 4?

  74. 74.Which of these values is a rational number?

  75. 75.Which of these square roots is a rational number?

  76. 76.Which statement about π is true?

  77. 77.Which comparison is true?

  78. 78.What is the cube root of -64?

  79. 79.A metric label in a Skokie lab uses 10^-3. What is the value of 10^-3?

  80. 80.Which expression is equivalent to 5^6 × 5^-4?

  81. 81.A trail ramp near Starved Rock rises 4 feet over a horizontal run of 12 feet. What is the slope of the ramp?

  82. 82.Line m has slope 2/5. Line n is parallel to line m. What is the slope of line n?

  83. 83.A line with slope 4 and a line with slope 1/4 are drawn on the same axes. Which line is steeper?

  84. 84.A drainage line in La Salle passes through (-2, 5) and (2, -3). What is its slope?

  85. 85.A line passes through (0, 1) and (2, 7). Which equation matches the line?

  86. 86.Solve 2(3x - 1) = 4x + 10.

  87. 87.Solve -3(x + 2) = 15.

  88. 88.Which set of ordered pairs shows a proportional relationship?

  89. 89.A ride in Chicago costs 3 dollars plus 2 dollars for each mile. Why is the cost not proportional to the number of miles?

  90. 90.Two similar triangles have corresponding sides. The smaller has sides 5, 6, and 8, and the shortest side of the larger is 15. What is the longest side of the larger triangle?

  91. 91.A triangle has angles of 40 degrees, 60 degrees, and 80 degrees. Which angles could belong to a similar triangle?

  92. 92.Which transformation always produces a figure congruent to the original?

  93. 93.A cylinder and a cone have the same radius, 4, and the same height, 6. How much greater is the cylinder's volume than the cone's volume?

  94. 94.A silo near Dixon is a cylinder with volume 32π cubic meters and radius 2 meters. What is the height?

  95. 95.A funnel in a workshop in Ottawa has volume 25π cubic inches and height 3 inches. It is a cone. What is the radius?

  96. 96.A spherical tank model in Alton has radius 6 centimeters. What is its volume?

  97. 97.A planning model uses 4.8 × 10^4 for the number of residents in a Fox Valley neighborhood. What is that number in standard form?

  98. 98.What is the value of (1/2)^-3?

  99. 99.Which number is closest to √50?

  100. 100.Which number is closest to √2 on a number line?

  101. 101.A straight line on a graph of a cooling pond passes through (0, 4) and (2, 0). Which equation matches the line?

  102. 102.Function A is y = 5x + 1. Function B is linear and includes (0, 1), (1, 4), and (2, 7). Which function has the greater rate of change?

  103. 103.Function C is y = 2x + 9. Function D is linear and includes the point (0, 6). Which function has the greater value when x = 0?

  104. 104.At a concession stand in Schaumburg, one pretzel and one juice cost 5 dollars. Two pretzels and one juice cost 8 dollars. What is the price of one pretzel?

  105. 105.Which ordered pair is a solution of both y = x - 4 and 2x + y = 5?

  106. 106.A garden plot in Monticello has side lengths 9, 12, and 15. Which statement is correct?

  107. 107.What is (6 × 10^4)(5 × 10^3) written in scientific notation?

  108. 108.A scatter plot of shoe size and spelling-quiz score for students in Belleville is spread with no upward or downward pattern. Which description fits?