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Massachusetts Comprehensive Assessment System Mathematics Grade 6

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

These questions are original. This is not an official Massachusetts Comprehensive Assessment System test, and FreeExam is not affiliated with the Massachusetts Department of Elementary and Secondary Education.

  1. 1.An art class uses 4 markers in each kit. Which expression gives the number of markers in k kits?

  2. 2.A cyclist leaves Hopkinton and rides 45 miles in 3 hours at a steady speed. What is the speed in miles per hour?

  3. 3.A rental desk records a $21 fee split equally among 3 friends. If 3x = 21, what is x?

  4. 4.Riders from Brockton sit in a pattern of 5 sixth graders for every 3 eighth graders. One bus holds 40 students in that same pattern. How many of them are sixth graders?

  5. 5.On a number line drawn in a Plymouth class, one marker is at −3 and another is at 5. What is the distance between the markers?

  6. 6.A number line has an open circle at 6 with shading to the right. Which inequality does it represent?

  7. 7.A craft table in Lexington has 3/4 yard of ribbon. Each bookmark uses 1/8 yard. How many bookmarks can be cut?

  8. 8.On a January morning in Pittsfield, the temperature is −6 degrees Fahrenheit. What is the absolute value of that temperature?

  9. 9.A commuter train from Worcester to Boston covers 44 miles in 2 hours. What is the average speed in miles per hour?

  10. 10.A regatta pennant in Falmouth is a triangle with base 10 inches and height 6 inches. What is its area in square inches?

  11. 11.A cyclist in Duxbury rides 1/2 mile in 1/4 hour at a steady speed. What is that speed in miles per hour?

  12. 12.Five identical crates in Chicopee weigh 45 pounds altogether. If y is the weight of one crate, then 5y = 45. What is y?

  13. 13.A museum requires visitors aged 12 or older to attend a workshop alone. Which inequality describes permitted ages a?

  14. 14.A woodshop in Athol has a board that is 9/10 meter long and a piece that is 3/5 meter long. How many times as long as the piece is the board?

  15. 15.Which value makes 7x = 42 true?

  16. 16.In a batch of 80 clam shells collected in Ipswich, 20 shells are broken. What percent of the shells are broken?

  17. 17.The ages, in years, of four dogs at a shelter in Holyoke are 3, 11, 7, and 4. What is the range of the ages?

  18. 18.A student in Amherst types 180 words in 6 minutes. How many words per minute is that?

  19. 19.A rectangle has width 6 units and length n units. Its area is 54 square units. Which equation represents its area?

  20. 20.A rental shop on Plymouth harbor keeps kayaks and canoes in the ratio 4 to 7. The shop has 28 kayaks. How many canoes does that ratio call for?

  21. 21.A harbor gauge in Fairhaven reads 4 feet above its zero mark. What is the absolute value of that reading?

  22. 22.Which ordered pair lies in Quadrant III?

  23. 23.A weather note for Nantucket says the chance of rain is 8 percent. How is 8 percent written as a decimal?

  24. 24.A baker in Lowell has 2/5 pound of butter and packs it into portions of 1/10 pound each. How many portions does the butter make?

  25. 25.A crate on a New Bedford wharf is 5 feet long, 4 feet wide, and 3 feet high. What is the volume of the crate in cubic feet?

  26. 26.A market in Essex sells bundles priced by the expression 4(2y + 3). Which expression is equivalent by the distributive property?

  27. 27.On a map of Cape Cod, 1 centimeter stands for 4 miles. A marked bike path is 7 centimeters on the map. How many miles long is the path?

  28. 28.What is |−2| × |−9|?

  29. 29.A point at (2, −5) is reflected across the x-axis. What is its image?

  30. 30.Paint for a wall in Somerville measures 5/6 gallon. It is poured into trays that each hold 1/3 gallon. What is (5/6) ÷ (1/3)?

  31. 31.A shop has a $36 supply bill and has already paid $14. Which equation finds the unpaid amount u?

  32. 32.A board at a lumberyard in Orange is 3.6 meters long. A second board is 2.5 times as long. How many meters long is the second board?

  33. 33.An herb bed in Lincoln is a triangle with base 9 feet and height 8 feet. What is its area in square feet?

  34. 34.A teacher in Leominster has 18 pencils and 24 markers. The teacher makes the greatest possible number of identical kits and uses every pencil and marker. How many kits is that?

  35. 35.Four friends in Beverly split a stack of n postcards so that each friend gets 6. The equation is n/4 = 6. What is n?

  36. 36.A ferry leaving Hyannis allows at most 48 passengers. There are already 31 people on board. If p more passengers board, which inequality represents the counts that are allowed?

  37. 37.Fabric for a sail repair in New Bedford is 2/3 yard long. Each patch uses 4/9 yard. What is the quotient (2/3) ÷ (4/9)?

  38. 38.Evaluate 5² − 3 × 4.

  39. 39.A rectangular prism is 7 centimeters long, 4 centimeters wide, and 3 centimeters high. What is its surface area?

  40. 40.A cube net has six square faces with side length 3 centimeters. What total area does the net cover?

  41. 41.Two crews pick cranberries in Carver. Crew A picks 84 pounds in 7 hours. Crew B picks 90 pounds in 6 hours. Which comparison is correct?

  42. 42.A triangular prism has a triangular base area of 12 square units and length 5 units. What is its volume?

  43. 43.A Northampton shop fills family bags with 18 almonds and 24 dried cranberries. What is the ratio of almonds to cranberries in simplest form?

  44. 44.A lesson in Nahant asks for |−12| + |3|. What is that sum?

  45. 45.A histogram has 6 students in the 0–9 minute bin, 9 in the 10–19 minute bin, and 5 in the 20–29 minute bin. How many students were recorded?

  46. 46.Forty-five percent of the seats in a Sandwich town hall are filled. Which fraction in simplest form equals 45 percent?

  47. 47.At a farm stand in Concord, 25 percent of the 60 jars of honey are wildflower honey. How many of the jars are wildflower honey?

  48. 48.Snow falls at a steady rate in Lenox and totals 6 inches in 4 hours. How many inches fall per hour?

  49. 49.Morning temperatures, in degrees Fahrenheit, at a station in Adams are 10, 2, 6, and 18. What is the median?

  50. 50.An Ipswich chowder recipe uses 2 cups of milk to make 3 servings. How many cups of milk make 12 servings?

  51. 51.On a coordinate grid used in a Medford class, a point is plotted at (−3, 4). In which quadrant does that point lie?

  52. 52.A set of wait times has quartiles 5 and 13 minutes. What is its interquartile range?

  53. 53.A gardener in Wellesley divides 7/8 pound of seeds into 2 equal packets. What fraction of a pound is in each packet?

  54. 54.A trail counter in the Blue Hills records these five hourly visitor counts: 3, 8, 1, 8, and 4. What is the median?

  55. 55.A meal in the North End of Boston costs $40 before the tip. How many dollars is a 15 percent tip?

  56. 56.A triangular piece of sailcloth in Marion has area 20 square feet and base 5 feet. What is the height in feet?

  57. 57.A park lawn in Lynn is a parallelogram with base 11 meters and height 4 meters. What is the area of the lawn in square meters?

  58. 58.A class counts the number of pets in each student’s home. Why is this a statistical question?

  59. 59.A book drive in Lexington wants at least 60 books. Volunteers already have 27 books. If b more books arrive, which inequality states the goal?

  60. 60.A pitcher in Oak Bluffs holds 5/2 liters. Each cup holds 5/8 liter. How many cups fill the pitcher exactly?

  61. 61.A dot plot of book counts shows one dot at 1, two at 2, and three at 3. What is the median?

  62. 62.A book in a Cambridge shop costs $30 before a sales tax of 5 percent. How many dollars is the tax?

  63. 63.Which question is statistical?

  64. 64.Apples at a farm stand in Stow sell for $8 for 4 pounds. What is the price for 1 pound?

  65. 65.Half of the photos in an album from Nantucket equals 9. The equation is 0.5p = 9. What is p?

  66. 66.Lemonade sold in Springfield uses 2 lemons for every 5 cups of water. How many lemons are needed for 20 cups of water?

  67. 67.What is |−8| − |5|?

  68. 68.A data set is 4, 4, 6, 6. What is the mean absolute deviation?

  69. 69.At a farm in Hadley, 10 percent of the corn stalks in a sample is 7 stalks. How many stalks are in the whole sample?

  70. 70.A bus covers the 120 miles from Springfield to Boston in 4 hours at a steady speed. What is that speed in miles per hour?

  71. 71.The ferry from Woods Hole to Vineyard Haven travels 12 miles in 40 minutes at a steady speed. What is that speed in miles per hour?

  72. 72.Quiz scores in Andover are 9, 9, 3, 7, and 5. What is the median score?

  73. 73.Marchers in New Bedford carry red flags and blue flags in the ratio 5 to 2. They have packed 14 blue flags. How many red flags match that ratio?

  74. 74.Four harbor readings are −0.5, 2, −3, and 1.5. Which reading is closest to zero?

  75. 75.A box plot has minimum 2, lower quartile 5, median 8, upper quartile 10, and maximum 16. What is the range?

  76. 76.A cook in Provincetown has 4 cups of fish stock. Each bowl uses 2/3 cup. How many bowls can be filled?

  77. 77.A class compares two data sets with the same mean. Which additional information helps describe how spread out the values are?

  78. 78.A coat in a shop on Newbury Street costs $80 before a markdown of 20 percent. What is the sale price in dollars?

  79. 79.Seven shell lengths, in centimeters, from Plum Island are 2, 9, 4, 9, 6, 1, and 8. What is the median length?

  80. 80.Jars of cranberry sauce from Carver are packed small to large in the ratio 2 to 3. A crate of 45 jars follows that ratio. How many jars in the crate are large?

  81. 81.A garden plot covers 32 square meters and is 4 meters wide. The equation 4l = 32 gives its length. What is l?

  82. 82.A student in Quincy has $25. A notebook costs $4 and a pen costs d dollars. The student buys one of each and must not spend more than $25. Which inequality fits?

  83. 83.Three friends in Medford share 3/5 of a pie equally. What fraction of the whole pie does each friend get?

  84. 84.Which expression is equivalent to 3(x + 7)?

  85. 85.On a 20-item quiz in Brookline, a student answers 18 items correctly. What percent of the items are correct?

  86. 86.Six commute times, in minutes, for a carpool in Braintree are 1, 3, 5, 7, 9, and 11. What is the interquartile range?

  87. 87.A fountain in the Boston Public Garden uses 18 gallons of water in 9 minutes at a steady flow. How many gallons does it use per minute?

  88. 88.Two points are (−2, 1) and (−2, 8). What is the distance between them?

  89. 89.A Gloucester fish display holds 6 cod for every 9 haddock. Which ratio uses 2 cod and keeps the same relationship?

  90. 90.Which number has the greater absolute value, −11 or 7?

  91. 91.A classroom formula uses d = 4t for distance after t seconds. Which variable is the dependent variable?

  92. 92.Two buses leave a Worcester terminal at the same moment. One returns every 6 minutes, and the other returns every 8 minutes. After how many minutes will they next leave together?

  93. 93.The gable on a barn in Shelburne is a triangle with base 12 feet and height 4 feet. What is the area of that triangle in square feet?

  94. 94.At dawn in Great Barrington the temperature is −2 degrees Fahrenheit. By noon it is 6 degrees Fahrenheit. By how many degrees did the temperature rise?

  95. 95.Five donations, in dollars, at a bake sale in Sudbury are 1, 2, 3, 4, and 20. What is the median donation?

  96. 96.A community garden in Lowell plants 7 tomato seedlings for every 4 pepper seedlings. A bed has 16 pepper seedlings. How many tomato seedlings belong in that bed?

  97. 97.After 9 birds leave a wire in Haverhill, 14 birds remain. If x is the number that were on the wire, then x − 9 = 14. What is x?

  98. 98.A parallelogram has base 9 units and perpendicular height 5 units. A triangle with the same base and height is removed. What area remains?

  99. 99.A fraction card in a Harwich classroom shows (1/2) ÷ (3/4). What is the quotient?

  100. 100.A student rewrites 18 + 30 as 6(3 + 5). Which property supports this equality?

  101. 101.Forty percent of the 50 seats on a Lowell trolley are filled. How many seats are filled?

  102. 102.The masses, in kilograms, of four pumpkins at a fair in Westport are 4, 8, 6, and 14. What is the mean mass?

  103. 103.A walker on the Charles River path covers 6 miles in 2 hours at a steady pace. What is the unit rate in miles per hour?

  104. 104.A tank holds v liters. After 8 liters are removed, 19 remain. Which equation models the situation?

  105. 105.Painters restoring a mural in Worcester mix 3 cups of blue paint with 5 cups of white paint. They use 15 cups of blue. How many cups of white paint should they mix with it?

  106. 106.A light display in the Boston Seaport starts with 1 lamp. The number of lamps doubles at each of the next 5 steps. How many lamps are on after those 5 doublings?

  107. 107.A map point is 5 units left of the origin and 3 units above it. Which ordered pair locates the point?

  108. 108.In a Framingham survey, 30 percent of 200 students walk to school. How many of those students walk?