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Massachusetts Comprehensive Assessment System Mathematics Grade 10

Algebra, quadratic and exponential functions, geometry, and statistics.

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 survey crew on the Charles River Esplanade marked a path from (0, −2) to (4, 6), with both axes in blocks. What is the slope of the path?

  2. 2.Buoys in Boston Harbor sit at (3, 1) and (3, 8) on a chart. What is the slope of the line through those buoys?

  3. 3.A ramp beside the State House drops from (1, 9) to (5, 1) on a grid measured in feet. What is the slope of the ramp?

  4. 4.The top of a seawall in Hull runs from (2, 6) to (9, 6) on a planner grid. What is the slope of that top edge?

  5. 5.A delay model for the Green Line in Brookline is y = −3x + 12. What is the y-intercept?

  6. 6.A footpath near Walden Pond follows y = (1/4)x − 2. What is the slope of the path?

  7. 7.A trail map in Charlemont shows a line through (2, 5) with slope 3. What is the y-coordinate when x = 4?

  8. 8.On a path map in Lincoln, which equation is a different line parallel to y = 4x − 1?

  9. 9.A trail on Mount Greylock is perpendicular to a line of slope 2. What is the slope of the trail?

  10. 10.What is the slope of the line through (1, −3) and (4, 6) on a grid of Lexington Green?

  11. 11.Two triangles have side lengths 5, 7, and 9 centimeters. Which criterion establishes their congruence?

  12. 12.Two triangles each have sides 6 and 10 with an included angle of 40 degrees. Why are the triangles congruent?

  13. 13.Why does angle-angle establish similarity but not necessarily congruence?

  14. 14.Similar triangles have corresponding short sides 4 and 10. A longer side of the smaller triangle is 6. What is the corresponding larger side?

  15. 15.A right triangle has legs 8 and 15 and hypotenuse 17. For the acute angle opposite the side of length 8, what is the sine?

  16. 16.A ladder makes a 60-degree angle with level ground. Its base is 5 feet from a vertical wall. Which expression gives the height it reaches?

  17. 17.A right triangle has a 30-degree angle and hypotenuse 12. Given sin(30°) = 1/2, how long is the side opposite that angle?

  18. 18.A figure is dilated by a scale factor of 3. Its original area is 14 square units. What is the image area?

  19. 19.A circle has a central angle of 100 degrees. An inscribed angle intercepts the same arc. What is the inscribed angle?

  20. 20.A circle has radius 6 units. What is the length of a 90-degree arc?

  21. 21.Which equation describes a circle with center (2, −1) and radius 4?

  22. 22.A transversal cuts parallel lines. One corresponding angle is 72 degrees. Why must the matching corresponding angle also be 72 degrees?

  23. 23.Which transformation maps (−3, 2) to (3, 2) while preserving distances?

  24. 24.A mooring in Marblehead costs 12 dollars plus 3 dollars per foot of boat. What is the cost, in dollars, for a 15-foot boat?

  25. 25.The equation 5x − 8 = 22 models the number of crates x unloaded at a pier in New Bedford. What is x?

  26. 26.A print shop at the Boston Public Library uses 2(x + 4) = 18 to count a stack of maps. What is x?

  27. 27.A bakery in the North End uses (2/3)k = 8, where k is the number of cups of flour in a full batch. What is k?

  28. 28.A print shop in Worcester solves −6 + 4p = 10 for a page adjustment p. What is p?

  29. 29.Harbor staff in Rockport solve 7a − 3 = 4a + 9 for the number of anchors a. What is a?

  30. 30.A cab from Logan Airport charges 4 dollars plus 2.50 dollars per mile. A ride costs 19 dollars. How many miles is the ride?

  31. 31.In Manchester-by-the-Sea, red buoys and green buoys are in the ratio 3:5. There are 15 green buoys. How many red buoys are there?

  32. 32.Two consecutive even dock numbers in Plymouth add to 46. What is the smaller number?

  33. 33.In the Blue Hills, the summit path is 3 miles longer than the pond loop. Together they cover 11 miles. How many miles is the pond loop?

  34. 34.A planner in Worcester compared y = 2x + 1 and y = 2x + 5. How many solutions does the system have?

  35. 35.Two fare rules from South Station are y = x + 2 and y = 3x − 4, with x in miles and y in dollars. Which point (x, y) is where the fares match?

  36. 36.At Fenway, the club count c and the bleacher count b satisfy c + b = 10 and c − b = 4. Which pair (c, b) is the solution?

  37. 37.A bus schedule in Cambridge can be written as y = 5x − 2 or as 2y = 10x − 4. How many solutions does that system have?

  38. 38.A stand at Faneuil Hall sells muffins for 3 dollars and cider for 2 dollars. A visitor buys 4 items and pays 11 dollars. How many muffins does the visitor buy?

  39. 39.Two crate totals on a wharf in Fall River satisfy 2x + y = 11 and x + y = 7. Which pair (x, y) is the solution?

  40. 40.Two paths in the Arnold Arboretum follow y = −x + 6 and y = 2x on a map grid. Where do they cross?

  41. 41.A Museum of Science display uses 3x + 2y = 16 and y = 2. Which pair (x, y) is the solution?

  42. 42.At a lab in Cambridge, f(x) = 3x − 4 gives a sensor reading. What is f(5)?

  43. 43.A gauge in Holyoke follows g(x) = 2x + 6. Which input makes g(x) = 0?

  44. 44.Hourly visitor counts at the Gardner Museum in Boston include the pairs (1, 4), (2, 7), and (3, 10). Which equation fits all three pairs?

  45. 45.A ticket rule for a field trip to Plimoth Patuxet is t(n) = 8n, and n can be 0, 1, 2, or 3 students. What is the domain used here?

  46. 46.Using t(n) = 8n for a Plimoth Patuxet field trip, with n equal to 0, 1, 2, or 3, what is the range?

  47. 47.From hour 1 to hour 4, a counter on the Cape Cod Canal goes from 10 boats to 22 boats. What is the average rate of change in boats per hour?

  48. 48.A two-step discount in Braintree uses f(x) = x − 2 and g(x) = 3x. What is f(g(4))?

  49. 49.A stall in Northampton uses p(x) = x + 9 for the price after a 9-dollar fee. Which input returns a price of 20 dollars?

  50. 50.Two membership plans in Brookline are f(x) = 2x + 1 and h(x) = 5x − 8. For which x is f(x) = h(x)?

  51. 51.A population model is P(t) = 120(1.05)^t. What does 1.05 represent?

  52. 52.Which situation is modeled by exponential decay?

  53. 53.A culture starts with 50 cells and doubles every hour. Which model gives its count after t hours?

  54. 54.What is 27^(2/3)?

  55. 55.For real values of x, what is the domain of f(x) = √(x − 4)?

  56. 56.Which expression equals x^(3/2) for x ≥ 0?

  57. 57.A linear function adds 6 each step. An exponential function triples each step. Which statement describes their rates of change?

  58. 58.What is the average rate of change of f(x) = x² from x = 1 to x = 4?

  59. 59.The height model h(t) = −(t − 3)² + 16 is in vertex form. What is its maximum height?

  60. 60.Which pair gives all zeros of f(x) = (x + 2)(x − 5)?

  61. 61.Which expression completes the square for x² + 8x + 3?

  62. 62.Why does x² + 4x + 7 = 0 have no real solutions?

  63. 63.A rectangle has sides x + 2 and x + 5. Which polynomial gives its area?

  64. 64.A student factors x² − 9 as (x − 3)². Which correction is valid?

  65. 65.A square garden plot in Concord has area 49 square yards, so x² = 49, where x is the side length in yards. What is the positive solution?

  66. 66.The equation x² − 5x + 6 = 0 models a frame in Framingham. What is the smaller solution?

  67. 67.A ball path at a park in Jamaica Plain is y = −x² + 6x. What is y when x = 2?

  68. 68.A sign placement in Andover uses (x − 3)(x + 5) = 0. What is the negative solution?

  69. 69.A radius sketch in Cohasset uses (x − 1)² = 9. What is the larger solution?

  70. 70.A patio plan in Dedham expands (x + 3)². Which expression is the expansion?

  71. 71.A shop poster in Natick shows x² + 7x + 12. Which expression is the factored form?

  72. 72.A height model in the Berkshires is q(x) = x² − 2x. What is q(5)?

  73. 73.The equation x² = 36 has a negative solution used as a coordinate west of a marker in Stockbridge. What is that negative solution?

  74. 74.Two cost formulas in Taunton are added: (3x² + 2x) + (x² − 5x + 1). Which expression is the sum?

  75. 75.A length difference in Hingham is (5x + 4) − (2x − 3). Which expression is the difference?

  76. 76.An area model in a greenhouse in Deerfield uses 4x² × 3x. What is the product?

  77. 77.A volume polynomial in a Chicopee workshop is 6x³ − x + 2. What is its degree?

  78. 78.A diagonal in a barn in Sturbridge has length √72 feet. Which expression is equivalent?

  79. 79.Tile sides in a kitchen in Beverly are √4 inches and √9 inches. What is the product of those square roots?

  80. 80.A viewing distance at Race Point in Provincetown satisfies √x = 5, where x is in meters. What is x?

  81. 81.A guy-wire calculation in Newburyport includes √50. Which expression is equivalent?

  82. 82.Grounds markers at a stadium in Foxborough form a right triangle with legs of 9 yards and 12 yards. What is the hypotenuse, in yards?

  83. 83.A triangle at the Old North Church in Boston has sides of 6, 8, and 10 inches. Which statement is correct?

  84. 84.A right triangle near Minot's Ledge has hypotenuse 13 meters and one leg 5 meters. What is the other leg, in meters?

  85. 85.On a grid of Boston Common, benches sit at (1, 2) and (4, 6). What is the distance between them?

  86. 86.A path through the Public Garden has endpoints (2, 4) and (8, 10). What is the midpoint?

  87. 87.An isosceles right triangle on the Freedom Trail has legs of 7 meters. Which expression is the hypotenuse, in meters?

  88. 88.A triangular sail at a loft in Essex has a base of 10 feet and a height of 6 feet. What is the area, in square feet?

  89. 89.A circular garden in Lenox has radius 3 meters. What is the area, in square meters, in terms of π?

  90. 90.A mill wheel in Lawrence has radius 4 feet. What is the circumference, in feet, in terms of π?

  91. 91.A crate on a wharf in Fairhaven measures 5 feet by 4 feet by 3 feet. What is the volume, in cubic feet?

  92. 92.A tank in Westfield is a cylinder with radius 2 meters and height 5 meters. What is the volume, in cubic meters, in terms of π?

  93. 93.Two angles of a triangle on a plaque in Bedford are 50° and 60°. What is the third angle?

  94. 94.A straight curb in Brockton is cut by a ray that makes a 35° angle with the curb. What is the adjacent angle on that straight line?

  95. 95.A model of the Custom House tower in Boston uses the scale 1:50. A 2-centimeter edge on the model represents how many centimeters on the tower?

  96. 96.In a survey, 30 students bike to school; 18 of those also play an instrument. What is the probability that a randomly selected biking student plays an instrument?

  97. 97.Events A and B have P(A) = 0.4, P(B) = 0.5, and P(A and B) = 0.2. Which conclusion is supported?

  98. 98.A table records 60 students: 20 bike, 25 walk, and 15 ride a bus. What is the relative frequency of walking?

  99. 99.A random sample of 80 students finds that 28 prefer a later lunch. About how many of 600 students would be expected to prefer it?

  100. 100.A scatter plot shows a strong positive association between two variables. What additional conclusion follows from the plot alone?

  101. 101.A model predicts 18 visitors, but 23 are observed. If residual = observed − predicted, what is the residual?

  102. 102.A line fitted to data collected for x from 2 to 8 predicts a value at x = 50. What is the main concern?

  103. 103.Two score distributions have the same mean. Distribution A has a smaller standard deviation. What does this indicate?

  104. 104.A list of incomes has one extremely large value. Which center is generally less affected by that single value?

  105. 105.A researcher randomly assigns volunteers to two teaching methods. Why is random assignment useful?

  106. 106.A bag has 4 red and 6 blue counters. Two are drawn without replacement. What is the probability both are red?

  107. 107.If P(A) = 0.6, P(B) = 0.5, and P(A and B) = 0.3, what is P(A or B)?

  108. 108.A data model y = 2.4x + 8 uses x in hours and y in liters. What are the units of its slope?