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Ohio's State Tests Mathematics Grade 8

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

These questions are original. This is not an official Ohio's State Tests exam, and FreeExam is not affiliated with the Ohio Department of Education and Workforce.

  1. 1.On a grid of the Scioto Mile in Columbus, a paved segment runs from (1, 4) to (4, 10). What is the slope of that segment?

  2. 2.Surveyors following the Cuyahoga through Cleveland mark a line through (7, 2) and (7, 9). What is the slope of that line?

  3. 3.A right triangle staked beside the canal at Lock 29 in Peninsula has legs of 9 feet and 12 feet. How long is the hypotenuse, in feet?

  4. 4.A clay cylinder in a studio in Athens holds 15 cubic inches. A cone with the same base and the same height holds how many cubic inches?

  5. 5.A seed library in Wooster shelves 6,000 packets. Which product is 6,000 written in scientific notation?

  6. 6.A class in Findlay is asked for the principal square root of 36. Which value answers that request?

  7. 7.A trail card at Nelson-Kennedy Ledges lists the number √7. Which statement about √7 is true?

  8. 8.Two routes near the Dayton Arcade follow y = x + 4 and y = 3x. At which point do the routes meet?

  9. 9.Lamp counts in a Piqua workshop follow the product 2^3 × 2^4. Which single power of 2 equals that product?

  10. 10.A gear card at Clifton Mill shows the quotient 5^6 ÷ 5^2. Which single power of 5 equals that quotient?

  11. 11.A bell schedule in Marietta is counted by (3^2)^4. Which power of 3 equals that value?

  12. 12.The reset label on a market counter in Toledo reads 9^0. What is the value of 9^0?

  13. 13.A scale drawing in Oberlin uses the factor 4^-2. What is the value of 4^-2?

  14. 14.A dropper in a teaching lab in Oxford releases 10^-3 liters of dye. What is 10^-3 written as a fraction?

  15. 15.A relay timer in Lima multiplies 2^5 × 2^-3. What integer equals that product?

  16. 16.A print shop in Hamilton evaluates 7^3 ÷ 7^5. What is the value of that quotient?

  17. 17.A harbor model on South Bass Island uses (5^-1)^2. What is the value of that expression?

  18. 18.A crate stencil in Fremont shows (2 × 5)^2. What is the value of that expression?

  19. 19.A baker in Millersburg squares one fourth of a cup, written (1/4)^2. How many cups is that?

  20. 20.A scoreboard in Massillon compares the powers 2^6 and 6^2. Which statement is true?

  21. 21.A beacon on Kelleys Island flashes in a pattern counted by 2^x = 32. What is x?

  22. 22.A freezer log in Archbold records a temperature index whose cube is -8. What is the cube root of -8?

  23. 23.A pollen sample in Chillicothe measures 0.00052. Which expression writes 0.00052 in scientific notation?

  24. 24.A classroom model in Toledo uses the distance 4,500,000 kilometers. Which expression is that distance in scientific notation?

  25. 25.A grain shipment from Maumee is modeled by (4 × 10^2) × (3 × 10^5). Which expression is the product in scientific notation?

  26. 26.A maple-tapping model for Geauga County uses (9 × 10^8) ÷ (3 × 10^3). Which expression is the quotient in scientific notation?

  27. 27.Depth notes near Put-in-Bay list 4.1 × 10^5 and 3.9 × 10^6. Which of those two numbers is greater?

  28. 28.A mayfly model on the Maumee compares 6 × 10^7 with 2 × 10^4. How many times as large as 2 × 10^4 is 6 × 10^7?

  29. 29.Two ticket stacks at the fair in Canfield are listed as 4.2 × 10^3 and 3.1 × 10^3. Which expression is their sum in scientific notation?

  30. 30.A bridge tally in Zanesville adds 5 × 10^4 and 3 × 10^3. Which expression is the sum in scientific notation?

  31. 31.A weather display in Wilmington shows 4.05E6. What is that reading in standard form?

  32. 32.A spore count at The Wilds near Cumberland is written 3.6 × 10^-5. What is that number in standard form?

  33. 33.A canoe rental on the Little Miami near Morrow solves 4x - 7 = 21 to find a missing count. What is x?

  34. 34.A trail club in Logan solves 5x + 2 = 2x + 14. What is x?

  35. 35.A banner shop in Delaware, Ohio, uses the equation 2(x - 5) = 18. What is x?

  36. 36.Dock plans in Port Clinton include the equation 4(x + 2) = 2(x + 10). What is x?

  37. 37.A schedule posted in Tiffin is written 2x + 5 = 2x + 9. How many solutions does this equation have?

  38. 38.A quilt rule used in Berlin, in Holmes County, is 3(x + 2) = 3x + 6. How many values of x make it true?

  39. 39.A recipe card in Granville says (2/3)x = 12. What is x?

  40. 40.A depth mark on the Muskingum at McConnelsville satisfies x/4 + 3 = 7. What is x?

  41. 41.A cooling rule for a greenhouse in Medina is written -4x < 20. Which inequality describes the solution?

  42. 42.A gauge on the Hocking River at Athens satisfies -5x + 3 ≥ 18. Which inequality describes every solution?

  43. 43.A toll model for a bridge in Bellaire uses 0.5x + 1.5 = 4. What is x?

  44. 44.A fence plan in Xenia uses 6x - 4 = 2(x + 6). What is x?

  45. 45.Programs stacked at a playhouse in Mansfield follow 7x - 2x - 5 = 15. What is x?

  46. 46.A temperature rule in Ashtabula is -2(x - 3) = 10. What is x?

  47. 47.A path down to the shore at Geneva State Park is graphed from (2, 8) to (6, 0). What is the slope?

  48. 48.A boardwalk at Magee Marsh passes through (3, 5) and (9, 5). What is the slope of the boardwalk?

  49. 49.Miles and hours for a ride on the Olentangy Trail are graphed through (0, 0) and (3, 12). What is the slope, in miles per hour?

  50. 50.A line drawn for a hill at Highbanks Metro Park has slope 3 and crosses the vertical axis at -2. Which equation matches the line?

  51. 51.A trail at John Bryan State Park has slope 2 and passes through (1, 5). Which equation matches the trail?

  52. 52.One rail in a model beside the depot in Galion has slope 4. What is the slope of a rail parallel to it?

  53. 53.A street in Shaker Heights has slope -2/5. What is the slope of a street parallel to it?

  54. 54.A snowfall table in Chardon lists the points (0, 6) and (2, 10). Which equation has a constant rate of change and fits both points?

  55. 55.A farm lane near Utica is graphed from (-2, 1) to (4, 4). What is the slope of the lane?

  56. 56.A descent at Conkle's Hollow, in the Hocking Hills, runs from (1, 5) to (5, 2) on a trail grid. What is the slope?

  57. 57.In Bexley, one driveway has slope 5/2 and the other has slope 2. Which statement is true?

  58. 58.The canal edge at Roscoe Village in Coshocton is horizontal and passes through (4, -3). Which equation is that line?

  59. 59.Two paths in Yellow Springs follow y = 2x - 1 and y = x + 4. At which point do they meet?

  60. 60.A stand in German Village uses the equations 2x + y = 11 and x - y = 1. What is the solution (x, y)?

  61. 61.Two rails in a layout in Bellevue follow y = 2x + 1 and y = 2x - 5. Which statement describes their graphs?

  62. 62.A map of the Little Miami bike trail through Loveland uses y = 4x - 2 and 8x - 2y = 4. Which statement describes the solutions?

  63. 63.At a concert in Troy, adult tickets cost $8 and student tickets cost $5. Ten tickets cost $68 in all. How many of each ticket were sold?

  64. 64.Two notebooks in a shop in Bowling Green have page counts that add to 15 and differ by 3. What are the two counts?

  65. 65.On a coordinate map of bike paths in Akron, two linear equations are solved together. What does one solution of that system represent?

  66. 66.A tally sheet in Marion shows the equations x + y = 8 and x + y = 3. What is the solution of the system?

  67. 67.Corner markers in Oberlin follow y = -x + 7 and 2x + y = 10. At which point do the lines meet?

  68. 68.A farm stand in Circleville uses 3x + 2y = 12 and x + 2y = 8. What is the solution (x, y)?

  69. 69.A librarian in Upper Arlington sorts ordered pairs. Which set is a function?

  70. 70.A street map in Lakewood includes the vertical line x = 3. Is the graph of x = 3 a function of x?

  71. 71.Students in Dublin, Ohio, sort equations. Which equation defines a linear function?

  72. 72.A sycamore seedling at Battelle Darby Creek Metro Park is 6 centimeters tall and grows 2 centimeters each week. Which equation gives the height h, in centimeters, after w weeks?

  73. 73.Depth readings at Paint Creek near Bainbridge are (0, 5), (1, 8), and (2, 11). Which equation fits all three readings?

  74. 74.Function A is y = 3x + 1. Function B contains the points (0, 2) and (2, 10). Which function has the greater rate of change?

  75. 75.A quiz-bowl rule in Kent is f(x) = -2x + 9. What is f(4)?

  76. 76.Locker numbers in Perrysburg follow y = 2x + 3, and one output is y = 11. What is the input x?

  77. 77.During a morning at Salt Fork State Park, a temperature graph rises steadily from left to right in a straight line. Which description fits the graph?

  78. 78.At a festival in Lancaster, a graph of the area of a square versus its side length bends upward as the side length grows. Which description fits that graph?

  79. 79.A paper-fold record in Kenton lists inputs 1, 2, 3, 4 and outputs 2, 4, 8, 16. Is this table a linear function?

  80. 80.At a camp in Mohican State Park, tent 4 is assigned to both cabin A and cabin B. Why is that rule not a function from tent number to cabin?

  81. 81.A kite triangle at a park in Sandusky has a hypotenuse of 13 meters and one leg of 5 meters. What is the other leg, in meters?

  82. 82.A rectangular crate in a warehouse in Fairborn measures 2 feet by 3 feet by 6 feet. What is the length of the space diagonal, in feet?

  83. 83.Two overlooks in Cuyahoga Valley sit at (1, 2) and (4, 6) on a map grid. What is the straight-line distance between them, in grid units?

  84. 84.A garden bed in Oakwood, near Dayton, has side lengths 6 feet, 8 feet, and 10 feet. Does it form a right triangle?

  85. 85.Paths at Glen Helen in Yellow Springs form a triangle with sides 4 meters, 5 meters, and 6 meters. Is that triangle a right triangle?

  86. 86.A ladder leans against a barn near Millersburg. The ladder is 10 feet long, and its base is 8 feet from the wall. How many feet up the wall does the ladder reach?

  87. 87.A sail sketch at a club in Huron uses a right triangle with legs of 8 feet and 15 feet. What is the hypotenuse, in feet?

  88. 88.Survey stakes near the Newark Earthworks sit at (-2, 4) and (3, 16). What is the distance between the stakes, in grid units?

  89. 89.A square plaza in Dayton measures 5 meters on each side. What is the length of a diagonal of the plaza?

  90. 90.A poster in a classroom in Springfield says that a^2 + b^2 = c^2, where c is the longest side. For which triangles is that equation true?

  91. 91.A cylindrical grain-bin model in Greenville has radius 3 units and height 5 units. What is its volume, in cubic units?

  92. 92.A funnel at a maple camp near Chardon has radius 3 inches and height 4 inches. What is the volume of that cone, in cubic inches?

  93. 93.A spherical tank model in Marietta has radius 3 feet. What is the volume of the sphere, in cubic feet?

  94. 94.A cylindrical mold in a pottery studio in Sebring has radius 2 inches and volume 20π cubic inches. What is the height, in inches?

  95. 95.A cone of frozen custard on Middle Bass Island has volume 18 cubic inches. A cylinder with the same radius and the same height has what volume, in cubic inches?

  96. 96.A spherical buoy near Kelleys Island has radius 6 units, and a smaller buoy has radius 3 units. The larger volume is how many times the smaller volume?

  97. 97.A cylindrical cistern near Loudonville keeps the same height while its radius is doubled. The new volume is how many times the old volume?

  98. 98.A cone-shaped hat made in Lebanon has radius 3 inches and volume 12π cubic inches. What is the height, in inches?

  99. 99.A class in Steubenville computes the volume of a cylinder. The radius and the height are measured in centimeters. Which unit matches the volume?

  100. 100.A solid hemispherical dome model at Cincinnati Museum Center has radius 3 meters. What is the volume of the dome, in cubic meters?

  101. 101.A meter in Ironton shows the repeating decimal 0.333.... Which statement is true?

  102. 102.A ranger board at Shawnee State Forest shows √20. Between which two consecutive integers does √20 lie?

  103. 103.A fire-tower distance in Wayne National Forest is compared using √50. Which comparison is true?

  104. 104.A cube of sandstone in Amherst has volume 125 cubic units. What is the edge length of the cube, in units?

  105. 105.A sign at Marblehead Lighthouse includes the length √50. Which expression is √50 in simplest radical form?

  106. 106.A worksheet in Ashland lists √12, 0.25, √16, and 7/3. Which of those numbers is irrational?

  107. 107.A distance board at Headlands Beach State Park shows √10. Which integer is closest to √10?

  108. 108.A gauge on the Tuscarawas River at New Philadelphia reads the repeating decimal 0.666.... Which fraction equals that decimal?