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Ohio's State Tests Mathematics Grade 6

Ratios, rates, percents, expressions, equations, and area.

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.A lockkeeper in Peninsula writes the water-level rule −5m > 15. Which solution describes every value of m that makes the rule true?

  2. 2.A baker in German Village divides a 2/5-pound block of butter into portions of 1/10 pound each. How many portions does the block make?

  3. 3.A lantern at a shop on High Street in Columbus costs 60 dollars. The shop takes 25 percent off that price. How many dollars is the discount?

  4. 4.A delivery van that left Dayton traveled 120 miles in 4 hours at a steady speed. What was that speed in miles per hour?

  5. 5.A triangular garden bed beside a school in Yellow Springs has a base of 12 feet and a height of 4 feet. What is the area of the bed?

  6. 6.The floor of a storage room under a library in Oberlin is marked −6 meters relative to the sidewalk. What is the absolute value of that mark?

  7. 7.A ticket window in Sandusky uses the equation 2x + 7 = 19. What is the value of x?

  8. 8.Five syrup samples from a sugar house near Chardon have readings 3, 8, 1, 8, and 4. What is the median?

  9. 9.The cooling target at a rink in Strongsville is written −3t < 18, where t is a temperature change in degrees. Which inequality gives every value of t that meets the target?

  10. 10.A buoy log off Marblehead uses −2h ≥ 8 for a depth index h. Which solution set matches the log?

  11. 11.A scale card in a Geneva orchard says −6w > −24. Which values of w satisfy the card?

  12. 12.A posted load rule for a covered bridge near Ashtabula is −8p < −40. Which solution matches the rule?

  13. 13.A buyer at Findlay Market keeps a count b that must satisfy −5b ≤ −15. Which inequality shows every allowed value of b?

  14. 14.A depth tag at a quarry in Marble Cliff reads −7k > 21. Which solution is correct for k?

  15. 15.A wind sensor on the Maumee riverfront in Toledo accepts readings v that satisfy −4v ≥ −12. Which solution describes v?

  16. 16.A boarding count n for the ferry to Kelleys Island must satisfy −9n < 27. Which inequality is the solution?

  17. 17.A mill ledger in Millersburg uses −2s > −10 for a sack count s. Which values of s fit the ledger?

  18. 18.At a canal lock in Roscoe Village, the gate mark y satisfies −3y ≤ 12. Which solution set is right?

  19. 19.A survey stake on a bluff in Hocking Hills is labeled −8z ≥ 32. Which inequality solves for z?

  20. 20.A grain sensor on a silo in Findlay shows −6g < −18. Which solution describes g?

  21. 21.A crate count at a warehouse in Dayton must satisfy −2(x + 3) > 8. Which inequality gives every possible x?

  22. 22.A dock tally in Sandusky uses 4 − 3r ≤ 13. Which solution describes r?

  23. 23.A mileage marker along the towpath in Cuyahoga Valley is written m ÷ (−4) < 2. Which inequality solves for m?

  24. 24.A mural crew in Over-the-Rhine mixes 3 cups of blue paint with 5 cups of white paint. What is the ratio of blue paint to the whole mixture?

  25. 25.At the West Side Market in Cleveland, 4 pounds of apples cost 6 dollars. What is the price of one pound?

  26. 26.At North Market in Columbus, jar A holds 12 ounces of honey and costs 6 dollars. Jar B holds 8 ounces and costs 5 dollars. Which jar has the lower price per ounce?

  27. 27.On a trail map of Mohican State Park, 2 centimeters stand for 5 kilometers. How many centimeters stand for 15 kilometers?

  28. 28.A chili recipe from a kitchen in Cincinnati uses 2 cups of beans for 6 servings. How many cups of beans are needed for 15 servings at the same rate?

  29. 29.A bus leaves Bowling Green and travels at a steady 45 miles per hour. How far does that bus go in 2 hours?

  30. 30.A cyclist on the Ohio and Erie Towpath near Boston Mills rides at a steady 12 miles per hour. How long does a 30-mile ride take at that speed?

  31. 31.In a band room in Oberlin, 18 students play string instruments and 12 play wind instruments. What is the ratio of string players to wind players in simplest form?

  32. 32.A bead tray in Athens holds red and gold beads in the ratio 4 to 3. There are 28 red beads. How many gold beads are in the tray?

  33. 33.A carpenter in Lancaster measures a porch that is 8 feet long. How many inches is that length?

  34. 34.Cloth at a shop in Gallipolis costs 4.25 dollars per yard. What is the cost of 3 yards?

  35. 35.In a library in Mansfield, printer A finishes 40 pages in 5 minutes and printer B finishes 27 pages in 3 minutes. Which printer is faster?

  36. 36.A greenhouse in Wooster plants 6 tomato seedlings for every 4 pepper seedlings. If 18 tomato seedlings are planted, how many pepper seedlings go in?

  37. 37.A student in Delaware, Ohio, reads 90 pages in 3 hours at a steady pace. What is the reading rate?

  38. 38.On a 40-point quiz in Massillon, a student earns 10 points. What percent of the points did the student earn?

  39. 39.A coat in a store in Hamilton costs 80 dollars before a discount of 15 percent. What is the sale price?

  40. 40.A book in a shop in Oxford, Ohio, costs 20 dollars before tax. The sales tax is 7 percent. How much is the tax?

  41. 41.A bird count at Magee Marsh near Oak Harbor rose from 200 birds to 250 birds. What was the percent increase?

  42. 42.Thirty percent of the tiles planned for a mural in Dayton is 18 tiles. How many tiles are in the whole mural?

  43. 43.In a band in Tiffin, 1/5 of the musicians play percussion. What percent of the band is that?

  44. 44.A meal at a diner in Vermilion costs 30 dollars before the tip. A customer leaves a tip of 20 percent. How many dollars is the tip?

  45. 45.A student in Piqua answers 18 of 24 problems correctly. What percent of the problems are correct?

  46. 46.Two donation jars in Chillicothe are compared. One holds 40 percent of 50 dollars. The other holds 25 percent of 72 dollars. Which amount is larger?

  47. 47.A quilter in Berlin, Ohio, has 3/4 yard of ribbon. Each bow uses 1/8 yard. How many bows can be made?

  48. 48.At a mill in Loudonville, 4 cups of oats are measured with a scoop that holds 1/3 cup. How many level scoops fill those 4 cups?

  49. 49.A 5/6-pound piece of cheese at Findlay Market is shared equally by 2 people. How much cheese does each person get?

  50. 50.A trail crew near Old Man's Cave has 2 1/2 liters of water. Each bottle holds 1/2 liter. How many bottles can be filled?

  51. 51.A seamstress in Marietta has 7/8 yard of cloth, and each pouch needs 1/4 yard. How many pouches does that cloth make, including a partial pouch?

  52. 52.A class in Granville computes (3/4) ÷ (2/5). Which value is that quotient?

  53. 53.A pitcher in a cafe in Yellow Springs holds 9/2 cups. Each glass holds 3/4 cup. How many glasses fill the pitcher exactly?

  54. 54.A woodshop in Xenia cuts a board that is 5/3 feet long into pieces that are each 5/6 foot long. How many pieces does the board make?

  55. 55.A gardener in Circleville has 4/5 kilogram of seed. Each packet holds 2/15 kilogram. How many packets can be filled exactly?

  56. 56.Overnight lows were −2 degrees in Cleveland, 3 degrees in Akron, −7 degrees in Toledo, and 0 degrees in Canton. Which city recorded the lowest temperature?

  57. 57.On a number line in a classroom in Lima, a point is marked at −9. What is the opposite of that number?

  58. 58.A class in Sidney starts at −4 and takes the opposite, then takes the opposite again. What number do the students land on?

  59. 59.A model submersible in a classroom in Toledo starts at −8 meters and then rises 5 meters. What is its position after the rise?

  60. 60.The temperature in Youngstown was 4 degrees Fahrenheit and then fell by 9 degrees. What was the temperature after that drop?

  61. 61.A warehouse tally in Springfield multiplies −6 by −3. What is the product?

  62. 62.A score sheet in Newark divides −42 by 6. What is the quotient?

  63. 63.A number-line card in Elyria shows −8 and 3. Which statement about those two numbers is true?

  64. 64.A receipt at a market in Ironton lists 3.40 dollars for produce and 2.75 dollars for bread. What is the sum of those two amounts?

  65. 65.A map point for a park path in Columbus is plotted at (−3, 5). In which quadrant does that point lie?

  66. 66.On a map grid used by a class in Peebles, a point is 4 units left of the origin and 2 units down. What are its coordinates?

  67. 67.A design class in Kettering reflects the point (2, −5) across the x-axis. What point is the image?

  68. 68.On a coordinate grid in Ada, how far apart are the points (1, 4) and (1, −2)?

  69. 69.A class in Marion orders −1.5, −0.5, 0.2, and −2 from least to greatest. Which list is in that order?

  70. 70.A student-store account in Hudson shows a balance of −12 dollars. A deposit of 20 dollars is recorded. What is the new balance?

  71. 71.A box at Flint Ridge holds some stones. After 9 more stones are added, the box holds 22 stones. How many stones were in the box at the start?

  72. 72.Tickets for a show in Cleveland cost 8 dollars each. A group pays 56 dollars in all. How many tickets did the group buy?

  73. 73.A cistern in Zoar held some liters of water. After 15 liters were used, 27 liters remained. How many liters were there at the start?

  74. 74.A rope in a gym in Parma is 48 feet long and is cut into 6 equal pieces. How long is each piece?

  75. 75.A lab counter in Athens uses the equation 4n − 3 = 17. Which value of n makes that equation true?

  76. 76.A hall in Steubenville sets out 4 equal rows and uses 28 chairs in all. If s is the number of chairs in one row, which equation matches the hall?

  77. 77.A bead formula in a shop in Medina is 3a + 4. What is the value of that expression when a = 5?

  78. 78.A science display in Bowling Green labels a count as 2 to the fifth power. The count starts at 1 and doubles five times. What is the value?

  79. 79.A score sheet in Canton asks for the value of 8 + 12 ÷ 4 × 2. What is that value?

  80. 80.A packing note in Fairborn says each of 6 crates holds n jars plus 4 extra jars. Which expression equals the total 6(n + 4)?

  81. 81.A class in Mount Gilead factors 18 + 12. Which expression uses the greatest common factor of 18 and 12?

  82. 82.A savings tally in Marysville is written 5k + 3 + 2k. Which expression is equivalent?

  83. 83.A kayak rental on the Maumee River in Napoleon charges 4 dollars for each hour. Which equation gives the cost c, in dollars, for h hours?

  84. 84.A rectangular plot in a community garden in German Village measures 9 feet by 7 feet. What is its area?

  85. 85.A parallelogram banner in a gym in Euclid has a base of 11 inches and a height of 6 inches. What is the area of the banner?

  86. 86.A garden bed in Loveland has two parallel sides of 10 feet and 6 feet, and the height between them is 4 feet. What is the area of that trapezoid?

  87. 87.A triangular sail pattern in Port Clinton has an area of 36 square inches and a base of 9 inches. What is the height of the triangle?

  88. 88.A deck plan in Perrysburg joins two rectangles that do not overlap. One is 10 feet by 4 feet, and the other is 3 feet by 4 feet. What is the total area?

  89. 89.A shipping box in Lockbourne is 8 inches long, 5 inches wide, and 3 inches high. What is its volume?

  90. 90.A baking pan in Worthington measures 1/2 foot by 1/2 foot by 1/4 foot. What is the volume of the pan?

  91. 91.A gift box in Lebanon is a rectangular prism 5 centimeters by 3 centimeters by 2 centimeters. What is its surface area?

  92. 92.On a grid for a field in London, Ohio, a rectangle has vertices (0, 1), (9, 1), (9, 5), and (0, 5). What is the length of each horizontal side?

  93. 93.A box in a shop in Troy has a volume of 96 cubic centimeters. Its base is 8 centimeters by 4 centimeters. What is the height?

  94. 94.A fundraiser in Portsmouth collected 1,176 dollars to split equally among 14 clubs. How many dollars does each club receive?

  95. 95.A shop in Coshocton has one ribbon of 24 inches and another of 36 inches. Both are cut into the longest equal pieces that use each ribbon completely. How long is each piece?

  96. 96.Two buses leave a station in Dayton at the same time. One returns every 8 minutes, and the other returns every 12 minutes. After how many minutes will they next leave together?

  97. 97.A hardware shop in Urbana has 7.5 meters of wire to cut into pieces that are each 1.5 meters long. How many pieces can be cut?

  98. 98.Five pumpkins at a patch in Barnesville weigh 6, 8, 10, 7, and 14 pounds. What is the mean weight?

  99. 99.Shoe sizes recorded in a gym class in Ashland are 7, 8, 7, 9, 7, and 6. What is the mode?

  100. 100.Afternoon highs in Wapakoneta, in degrees Fahrenheit, were 61, 70, 64, 68, and 59. What is the range of those highs?

  101. 101.Trail lengths, in miles, near Logan are 2, 3, 5, 7, 8, and 10. What is the interquartile range?

  102. 102.Three quiz scores in Galion are 4, 6, and 8. What is the mean absolute deviation of those scores?

  103. 103.Which question is statistical for a class in Mount Vernon?

  104. 104.A dot plot of pets per home in Celina shows 2 homes with 0 pets, 5 homes with 1 pet, 3 homes with 2 pets, and 1 home with 3 pets. How many homes are in the plot?

  105. 105.A histogram for workers in Beavercreek counts commutes in four bins, and the right end of each bin is not included: 4 workers from 0 up to 10 minutes, 9 from 10 up to 20, 6 from 20 up to 30, and 2 from 30 up to 40. How many of these workers commute at least 20 minutes?

  106. 106.Quiz scores in Greenville are 70, 72, 74, 71, and 100. The score of 100 is then replaced by 74. Which statement describes the median and the mean?

  107. 107.A box plot of ages at a story hour in Norwalk has least value 4, first quartile 6, median 8, third quartile 11, and greatest value 14. What is the interquartile range?

  108. 108.A reading log in Wilmington lists 12, 14, 13, 15, and 40 pages. Which measure better describes a typical day in that log?