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Massachusetts Comprehensive Assessment System Mathematics Grade 8

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

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.A footpath across Boston Common is graphed from (1, 4) to (4, 10), with both axes in grid units. What is the slope of the path?

  2. 2.A line on a Charles River map passes through (7, 2) and (7, 9). What is the slope of that line?

  3. 3.A right triangle marked on a Blue Hills trail has legs of 9 meters and 12 meters. What is the hypotenuse, in meters?

  4. 4.A cylinder in a Gloucester workshop holds 15 cubic units. A cone with the same radius and the same height holds how many cubic units?

  5. 5.A warehouse in Brockton stores 6000 crates. Which expression shows 6000 in scientific notation?

  6. 6.A student in Worcester evaluates the principal square root of 36. What is that value?

  7. 7.A trail marker near Walden Pond shows the number √7. Which statement about √7 is true?

  8. 8.The lines y = x + 4 and y = 3x show two paths that cross near Harvard Square. At which point do the lines meet?

  9. 9.The walkway toward the Bunker Hill Monument rises 6 feet while running 18 feet horizontally. What is the slope of the walkway?

  10. 10.A Boston Harbor channel chart shows a straight line through (3, 12) and (11, 4). What is the slope of that line?

  11. 11.A line for the Charles River Esplanade has slope 3 and crosses the y-axis at 5. Which equation matches the line?

  12. 12.A bike rental shop in Cambridge charges $8 plus $3 for each hour. Which equation gives the cost y, in dollars, after x hours?

  13. 13.A painted line through Lexington Green has slope 4. A second line is parallel to it. What is the slope of the second line?

  14. 14.A footpath in Concord has slope 2. What is the slope of a path perpendicular to it?

  15. 15.A boardwalk in Provincetown passes through the grid points (2, 6) and (9, 6). What is the slope of the boardwalk?

  16. 16.A line with slope -3 passes through (2, 5) on a Plymouth harbor grid. What is the y-coordinate when x = 4?

  17. 17.At a Springfield snack stand, the number of pretzels p and the number of waters w satisfy p + w = 11 and p - w = 3. How many pretzels were sold?

  18. 18.How many solutions does the system y = 2x + 1 and y = 2x + 5 have?

  19. 19.How many solutions does the system 2x + 4y = 10 and x + 2y = 5 have?

  20. 20.The lines y = 4x - 1 and y = x + 8 cross above the Rose Kennedy Greenway. What is the x-coordinate of the crossing?

  21. 21.A counter at the Museum of Science shows the product 10^4 × 10^3. What is that product written as a single power of 10?

  22. 22.Simplify the quotient 10^8 ÷ 10^2 that appears on a Lynn shoreline data sheet.

  23. 23.A model of the Zakim Bridge uses the expression (10^3)^2 for a scale count. What is the simplified value?

  24. 24.A lab card in Waltham asks for 5^(-2) written as a fraction. Which fraction is correct?

  25. 25.On a scoreboard at Gillette Stadium, a formula uses 9^0. What is the value of 9^0?

  26. 26.A crane in New Bedford lifts one load of 4 × 10^3 kilograms and another of 2 × 10^3 kilograms. What is the total mass in scientific notation?

  27. 27.A Salem harbor chart covers 8 × 10^6 square meters, and a smaller inset covers 2 × 10^3 square meters. How many times as large as the inset is the chart?

  28. 28.A shell fragment from Crane Beach is 0.00045 meter across. Which expression is that width in scientific notation?

  29. 29.A cube-shaped crate on the Gloucester dock has volume 64 cubic feet. What is the edge length, in feet?

  30. 30.A planner in Andover estimates √50 without a calculator. Between which two consecutive whole numbers does √50 lie?

  31. 31.Which expression is an irrational number?

  32. 32.Which product is a rational number?

  33. 33.On a coordinate map of Worcester, how far apart are the points (1, 2) and (4, 6)?

  34. 34.A right triangle along the Minuteman Bikeway has a hypotenuse of 13 meters and one leg of 5 meters. What is the other leg, in meters?

  35. 35.A triangle cut for a sign in the Berkshires has sides 6, 8, and 10. Which statement is true?

  36. 36.A cylindrical tank in Quincy has radius 3 feet and height 10 feet. Which expression gives its volume, in cubic feet?

  37. 37.A spherical buoy in Gloucester harbor has radius 3 units. Which expression gives its volume?

  38. 38.A cone of frozen lemonade in Salem has radius 2 inches and height 6 inches. Which expression gives its volume, in cubic inches?

  39. 39.A cylindrical tank in Lowell has volume 75π cubic feet and height 3 feet. What is the radius, in feet?

  40. 40.A decorative sphere at the Massachusetts State House has volume 36π cubic units. What is its radius?

  41. 41.On a model of the Massachusetts State House, 1 centimeter represents 50 centimeters on the building. A door on the model is 4 centimeters tall. How tall is the real door, in centimeters?

  42. 42.A figure centered at the origin is dilated by a scale factor of 3 for a mural in the North End. What is the image of the point (2, -1)?

  43. 43.On a Beacon Hill map, the point (4, 7) is translated 3 units left and 2 units up. What are the new coordinates?

  44. 44.The point (-5, 3) on a Public Garden plan is reflected across the x-axis. What is the image?

  45. 45.The point (8, -2) on a map of the Freedom Trail is reflected across the y-axis. What is the image?

  46. 46.The point (1, 4) is rotated 90 degrees counterclockwise about the origin on a Fenway seating chart. What is the image?

  47. 47.The point (6, -3) is rotated 180 degrees about the origin on a plan of Boston Common. What is the image?

  48. 48.A triangle in a Plymouth classroom has angles of 48 degrees and 67 degrees. What is the third angle, in degrees?

  49. 49.An exterior angle of a triangle built for a float in Newburyport measures 120 degrees. One remote interior angle measures 45 degrees. What is the other remote interior angle, in degrees?

  50. 50.Parallel streets in Back Bay are cut by a transversal. One interior angle measures 118 degrees. What is the same-side interior angle, in degrees?

  51. 51.Two lines cross near Harvard Square and form a 35-degree angle. What is the measure, in degrees, of the vertical angle opposite it?

  52. 52.A straight curb along Commonwealth Avenue forms a straight angle. One of the adjacent angles measures 73 degrees. What is the other angle, in degrees?

  53. 53.Which set of ordered pairs is a function of x?

  54. 54.Which equation does not define y as a function of x?

  55. 55.A kayak on the Merrimack River has already traveled 2 miles when a timer starts, then continues at 6 miles per hour. How many miles has it traveled 5 hours after the timer starts?

  56. 56.Line A has equation y = 5x + 1. Line B passes through (0, 1) and (2, 7) on a graph made in Marblehead. Which line is steeper?

  57. 57.The equation c = 12n + 20 models the cost, in dollars, of a Hyannis trolley charter for n riders. What does the 20 represent?

  58. 58.The equation d = 40t + 15 gives the miles from Boston t hours after noon. What does 40 represent?

  59. 59.A carpenter in Haverhill solves 3(x - 4) = 18 to find a length x. What is x?

  60. 60.Solve 5x + 7 = 2x + 22 for the balance used by a shop in Peabody. What is x?

  61. 61.A recipe scaled for a clambake in Rockport uses the equation (2/3)x = 12. What is x?

  62. 62.How many solutions does the equation 4(n + 2) = 4n + 8 have?

  63. 63.How many solutions does the equation 2(x + 3) = 2x + 5 have?

  64. 64.A sign painter in Taunton evaluates (-3)^2. What is the value?

  65. 65.A calculator entry in Framingham shows -3^2. What is the value of that expression?

  66. 66.Add 3.2 × 10^4 and 4 × 10^3, the two counts on a Chatham ferry log, and write the sum in scientific notation.

  67. 67.Two water samples at Deer Island measure 6.1 × 10^5 cells and 9.8 × 10^4 cells. Which measure is larger?

  68. 68.A baker in the North End makes 45 cannoli in 3 hours at a steady rate. How many cannoli does the baker make in 7 hours?

  69. 69.On a map of Cape Cod, 2 centimeters represent 15 miles. How many miles do 6 centimeters represent?

  70. 70.A delivery route leaving Worcester is graphed as a line with slope 2 and y-intercept -4. Which equation matches the route?

  71. 71.A graph of morning temperatures in Fitchburg passes through (0, 6) and (4, -2). What is the y-intercept of the line?

  72. 72.A line on a plan of the Emerald Necklace passes through (0, 1) and (3, 7). Which equation matches the line?

  73. 73.A scatter plot from a class in Amherst shows hours studied and quiz scores, and the points slope upward overall. Which statement fits the plot?

  74. 74.Most points on a plot of Nantucket wind speed and kite height follow an upward line, but one point sits far above the others. What is that point called?

  75. 75.A line of best fit for a Brookline data set is y = 2x + 5. Using that line, what y-value is predicted when x = 6?

  76. 76.A survey in Lawrence recorded 18 students who bike and prefer mornings, 12 who bike and prefer afternoons, 7 who walk and prefer mornings, and 13 who walk and prefer afternoons. How many students were surveyed?

  77. 77.Of 40 visitors at the New England Aquarium, 24 saw the penguins, and 16 of those penguin visitors also went to the gift shop. What fraction of the penguin visitors also went to the gift shop?

  78. 78.A class in Revere recorded 30 students. Nine play both an instrument and a sport, 6 play an instrument only, 8 play a sport only, and 7 play neither. How many students play an instrument?

  79. 79.A cylindrical column mold in Braintree has radius 2 and height 5, so its volume is 20π. If the radius doubles and the height stays 5, what is the new volume?

  80. 80.A cone mold in Weymouth has volume 6π. The height is tripled and the radius stays the same. What is the new volume?

  81. 81.A model globe in Arlington has radius 1 and volume (4/3)π. If the radius becomes 2, by what number is the volume multiplied?

  82. 82.A ladder leans against a warehouse in Fall River. Its base is 8 feet from the wall, and it reaches 15 feet up the wall. How long is the ladder, in feet?

  83. 83.A clambake on Plum Island uses 3 cups of butter for every 6 ears of corn. Ears of corn are on the x-axis and cups of butter are on the y-axis. What is the slope of that graph?

  84. 84.Overnight in Pittsfield, the temperature fell at a constant rate from 5 degrees Celsius to -3 degrees Celsius in 4 hours. With time on the x-axis, what is the slope in degrees per hour?

  85. 85.At a Lenox concert, two adult tickets cost $24 altogether and each student ticket costs $7. The equation 24 + 7s = 45 models the purchase. How many student tickets were bought?

  86. 86.A Newton farm stand sells apples for $2 each and pears for $3 each. A customer bought 8 pieces of fruit and paid $19. How many apples did the customer buy?

  87. 87.A display at MIT asks for the value of 4^3 × 4^(-3). What is that value?

  88. 88.A problem on a board in Everett asks for the value of 2^6 ÷ 2^4. What is that value?

  89. 89.A town near the Quabbin Reservoir has population 2.5 × 10^4. What is that population in standard form?

  90. 90.A lab in Woods Hole multiplies a count of 3 × 10^2 samples by a factor of 2 × 10^4. Which product is written in scientific notation?

  91. 91.In a set of measurements from Mount Greylock, which number is irrational?

  92. 92.A stack of programs at Symphony Hall is described by 3^4. What is the value of 3^4?

  93. 93.A temperature model for North Adams uses the cube root of -27. What is that cube root?

  94. 94.On a number line drawn in Great Barrington, which value is closest to √20?

  95. 95.Two triangles in a Somerville art class are congruent. One triangle has a side of 11 centimeters. What is the matching side of the other triangle?

  96. 96.Two similar triangles are cut for a quilt in Deerfield. One triangle has angles of 40 degrees and 80 degrees. What is the third angle of the other triangle, in degrees?

  97. 97.A dilation used for a poster of the Old North Church has scale factor 1/4. A segment of length 20 inches maps to a segment of what length?

  98. 98.Which transformation preserves both side lengths and angle measures of a figure on a Charlestown map?

  99. 99.A plan of the USS Constitution is turned by a rotation of 90 degrees about a point. Which description fits that rotation?

  100. 100.A bike counter along the Charles River records x-values 1, 2, and 3 with matching y-values 5, 8, and 11. What is the slope of the line through these points?

  101. 101.A table for a walk across Boston Common shows x-values 0, 1, and 2 with matching y-values 4, 7, and 10. Which equation fits the table?

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

  103. 103.A temperature model used in Northampton is f(x) = 2x - 9. What is f(6)?

  104. 104.The function g(x) = 4x + 1 models a fare from South Station. For which x is g(x) = 21?

  105. 105.A cone at a pottery studio in Sandwich holds 20 cubic centimeters. A cylinder with the same radius and the same height holds how many cubic centimeters?

  106. 106.A cylinder holds 18 cubic units. A cone has the same radius and the same height as that cylinder. Which statement is true?

  107. 107.A triangle drawn in the sand at Marblehead has sides 4, 5, and 6. Which statement is true?

  108. 108.A runner on the Boston Marathon course covers 6 miles in 48 minutes at a steady pace. How many minutes will that pace take to cover 26 miles?