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Pennsylvania System of School Assessment Mathematics Grade 8

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

These questions are original. This is not an official Pennsylvania System of School Assessment test, and FreeExam is not affiliated with the Pennsylvania Department of Education.

  1. 1.A night crew in Harrisburg tests a backup lamp rated 2^5 watts. What is that rating in watts?

  2. 2.A Lancaster bakery card uses 5^0 for the number of extra salt shakes on a plain pretzel order. What is 5^0?

  3. 3.A Pittsburgh workshop tag lists 10^(-3) kilogram of solder paste. Which mass equals 10^(-3) kilogram?

  4. 4.An Erie marina multiplies the signal codes 3^4 and 3^2. What whole number is the product?

  5. 5.A Scranton library printer simplifies the toner ratio 8^6 ÷ 8^4. What is the quotient?

  6. 6.A Reading greenhouse label shows (4^2)^3 for a heater setting. What whole number is that value?

  7. 7.A York bike shop evaluates (2 × 5)^3 while checking a gear pack. What is the value?

  8. 8.A Bethlehem sample tag shows 7^(-2). Which value equals that expression?

  9. 9.An Allentown scoreboard simplifies (9^5 × 9^(-2)) ÷ 9. What whole number is the result?

  10. 10.A classroom model lists the Schuylkill basin as 13,000 square kilometers. How is 13,000 written in scientific notation?

  11. 11.A Hershey lab measures 0.00046 gram of cocoa dust. Which expression is that mass in scientific notation?

  12. 12.A shoreline crew near Presque Isle records 4.2 × 10^5 meters of measuring line. What is that length in ordinary notation?

  13. 13.A Philadelphia dye test uses 6.5 × 10^(-3) liter of coloring. What is that volume as a decimal?

  14. 14.A sketch lists Allegheny County at 1.25 × 10^6 residents and a nearby borough at 8.4 × 10^5 residents. How many more residents are in the county figure?

  15. 15.A Pocono weather balloon report multiplies 3 × 10^4 by 2 × 10^3. What is the product in scientific notation?

  16. 16.A State College notebook divides 8.4 × 10^8 by 2.1 × 10^2. What is the quotient in scientific notation?

  17. 17.A Williamsport park order adds 5.6 × 10^4 seeds and 3.1 × 10^3 seeds. What is the sum in scientific notation?

  18. 18.A Gettysburg field guide prints 9.3 × 10^7 miles for a comparison distance. What is that number in ordinary notation?

  19. 19.A square teaching garden in Gettysburg covers 144 square feet. What is the length of one side?

  20. 20.A cube supply bin in a Johnstown classroom holds 125 cubic inches. What is the edge length?

  21. 21.A square patio in West Chester has an area of 196 square feet. How long is one side?

  22. 22.A Hawk Mountain trail card asks between which two consecutive whole numbers √50 lies. Which pair is correct?

  23. 23.A cube of fudge packed in Lititz has a volume of 216 cubic centimeters. What is the edge length?

  24. 24.A square tile in a Kennett Square packing room has area 81/16 square feet. What is the side length?

  25. 25.A Chadds Ford crate has a square panel of area 16 square feet and a cube compartment of volume 8 cubic feet. What is the panel side length multiplied by the cube edge length?

  26. 26.A square plot near Falling Spring has an area of 20 square meters. Which of these values is closest to the side length?

  27. 27.A temperature offset on an Oil City lab card is the cube root of −27. What is that offset?

  28. 28.A bike path near Harrisburg rises 6 meters across a horizontal run of 15 meters. What is the slope of the path?

  29. 29.A Lancaster farm stand sells apples at a proportional price of $3 for 2 pounds. What is the cost of 8 pounds?

  30. 30.On a map of a Philadelphia trolley route, a straight segment passes through (2, 5) and (6, 13). What is the slope?

  31. 31.Four fare rules are posted at a Harrisburg cab stand, with x in miles and y in dollars. Which equation is a proportional relationship?

  32. 32.A ramp line at the Philadelphia Museum of Art is modeled by y = −3x + 7, with x in meters. What is the slope?

  33. 33.A walkway at Point State Park is graphed through (0, 0) and (20, 3), in feet. What is the slope?

  34. 34.A Strasburg market table is proportional. Cups x and ounces y include the pair (4, 10). What is the constant of proportionality k in y = kx?

  35. 35.A trail line on an Allegheny ridge map goes through (−2, 8) and (3, −2). What is the slope?

  36. 36.A service road beside the Pennsylvania Turnpike is graphed through (1, 4) and (9, 4). What is the slope?

  37. 37.A Reading theater solves 3x + 5 = 20 to find the number of student tickets x. What is x?

  38. 38.An Erie dock crew solves 2(x − 4) = 18 for a length x in feet. What is x?

  39. 39.A York hardware scale is balanced when 5x − 7 = 2x + 8. What is x?

  40. 40.A Scranton club splits a bill with the equation x/4 + 3 = 11, where x is dollars. What is x?

  41. 41.A Lebanon greenhouse solves 8 − 2x = 14 for a temperature change x. What is x?

  42. 42.A Hershey mixing note says 0.5x + 1.5 = 6.5, with x in cups. What is x?

  43. 43.A Bethlehem shop solves 3(x + 4) = 2x + 18 for a beam length x. What is x?

  44. 44.A Wilkes-Barre plumber solves (2x − 1)/3 = 5. What is x?

  45. 45.An Easton stair count fits the equation 7x + 2 − 3x = 18. What is x?

  46. 46.A Philadelphia stand solves x + y = 10 and x − y = 2 for the counts of two snacks. What is the pair (x, y)?

  47. 47.Two fare lines in Harrisburg are y = 2x + 1 and y = −x + 7. What is the solution (x, y)?

  48. 48.A Lancaster market solves 2x + y = 11 and x + y = 7. What is the solution (x, y)?

  49. 49.A Pittsburgh shop solves 3x + 2y = 16 and 3x − 2y = 8. What is the pair (x, y)?

  50. 50.An Erie bait shop uses y = 4x and x + y = 15. What is the solution (x, y)?

  51. 51.The lines y = 2x + 3 and y = 2x − 1 model two tracks near the Horseshoe Curve in Altoona. How many solutions does the system have?

  52. 52.A State College tutor writes the system 2x + 2y = 10 and x + y = 5. How many solutions does it have?

  53. 53.A Chester ferry solves 4x + y = 9 and x − y = 1. What is the solution (x, y)?

  54. 54.A New Hope ticket window solves 2x + 3y = 18 and y = 2. What is x?

  55. 55.A concession rule at a North Shore ballpark is f(x) = 3x − 2, where x is the number of pretzels. What is f(4)?

  56. 56.A Wissahickon trail log lists the pairs (1, 4), (2, 7), (1, 9), and (3, 10). Which statement is true?

  57. 57.A Valley Forge path is the function f(x) = 3x + 1. What is f(5)?

  58. 58.A fountain timer in Rittenhouse Square follows the linear pattern (0, 2), (1, 5), and (2, 8). What is the output when the input is 6?

  59. 59.Two Broad Street fare functions are g(x) = 2x + 5 and h(x) = 2x − 1. For any same input x, how much greater is g(x) than h(x)?

  60. 60.Which rule is a function that is not linear?

  61. 61.A Wilkes-Barre school vending function is c(n) = 1.25n, with n the number of bottles. What is c(3) in dollars?

  62. 62.A stall on Ninth Street in Philadelphia uses f(x) = −2x + 9. What is f(3)?

  63. 63.A bus rule in Allentown is y = 6x + 4, where x is the number of stops after the depot. What is the initial value, the number of riders when x = 0?

  64. 64.A ladder leans on a barn in Adams County. Its base is 9 feet from the wall, and the top rests 12 feet up the wall. How long is the ladder?

  65. 65.A right triangle trail along Pine Creek has legs of 5 meters and 12 meters. What is the hypotenuse?

  66. 66.A kite string at Presque Isle is held tight and is 17 meters long. The kite is directly above a point 8 meters from the holder. How high is the kite?

  67. 67.A surveyor along Octoraro Creek checks a triangle with sides 7 meters, 24 meters, and 25 meters. Which statement is correct?

  68. 68.A right triangle dock at French Creek has a hypotenuse of 10 meters and one leg of 6 meters. What is the other leg?

  69. 69.A rectangular raft on the Youghiogheny River measures 20 meters by 21 meters. What is the length of a diagonal?

  70. 70.A garden triangle in Carlisle has sides 6 feet, 8 feet, and 11 feet. Which statement is correct?

  71. 71.A brace under a Kinzua overlook forms a right triangle with legs of 12 feet and 16 feet. What is the hypotenuse?

  72. 72.A sail triangle at Raystown Lake has a hypotenuse of 26 feet and one leg of 10 feet. What is the other leg?

  73. 73.On a Philadelphia grid, a runner goes from (1, 2) to (4, 6), and each unit is one block. What is the straight-line distance?

  74. 74.Two channel markers on a Susquehanna harbor grid sit at (−1, 2) and (6, 26). What is the distance between them?

  75. 75.A trailhead is the origin on a Pocono map, and a cabin is at (8, 15). What is the distance from the trailhead to the cabin?

  76. 76.Two statues in a Center City courtyard are plotted at (−4, −1) and (5, 11). What is the distance between them?

  77. 77.In a Harrisburg parking garage graph, an elevator shaft runs from (2, 5) to (2, −1). What is the distance between those points?

  78. 78.A canal path on a Delaware Canal map runs from (7, −2) to (−1, −2). What is the distance?

  79. 79.On a State College quad, a walker can follow the legs from (−3, 4) to (5, 4) to (5, −2), or take the straight segment from (−3, 4) to (5, −2). How much shorter is the straight segment?

  80. 80.A Delaware River ferry chart marks docks at (4, −2) and (19, 18). What is the distance between the docks?

  81. 81.Two overlooks near Lehigh Gap are plotted at (3, 1) and (15, 17). What is the distance between them?

  82. 82.A map pin near the Liberty Bell starts at (3, −2). It is translated 4 units right and 5 units up. What are the image coordinates?

  83. 83.A kayak symbol at (5, −3) on a Lake Wallenpaupack chart is reflected across the x-axis. What is the image?

  84. 84.A trail marker at (−2, 7) in Cook Forest is reflected across the y-axis. What is the image?

  85. 85.A drone icon at (4, 1) above Harrisburg is rotated 90 degrees counterclockwise about the origin. What is the image?

  86. 86.A booth marker at (3, −2) on a York fair map is rotated 180 degrees about the origin. What is the image?

  87. 87.A mural plan centered at the origin dilates the point (6, 4) by a scale factor of 1/2. What is the image?

  88. 88.A triangle vertex at a Bethlehem mill is at (−1, 4). It is translated by the vector ⟨2, −6⟩. What is the image?

  89. 89.A corner of a Fallingwater floor plan at (4, 0) is reflected across the line y = x. What is the image?

  90. 90.A logo point at (−3, 5) is dilated about the origin by a scale factor of 3. What is the image?

  91. 91.Walnut Street and Chestnut Street in Philadelphia are parallel, and Broad Street cuts across them. A corresponding angle at Walnut measures 74 degrees. What is the matching corresponding angle at Chestnut?

  92. 92.Two parallel rails in Altoona are cut by a transversal. One alternate interior angle measures 65 degrees. What is the other alternate interior angle?

  93. 93.Parallel paths in Fairmount Park are cut by a transversal. One angle in a pair of consecutive interior angles measures 70 degrees. What is the other angle in that pair?

  94. 94.A transversal crosses two parallel lanes near the Pennsylvania Turnpike. One angle measures 42 degrees. What is the measure of the angle vertical to it?

  95. 95.At a crossing of two parallel streets in Lancaster, one angle on a straight line measures 125 degrees. What is the adjacent angle in that linear pair?

  96. 96.Parallel towpaths along the Delaware Canal are cut by a farm road. One alternate exterior angle measures 133 degrees. What does the other alternate exterior angle measure?

  97. 97.A transversal cuts two parallel sidings in Johnstown. An interior angle measures 3x degrees, and its alternate interior angle measures 72 degrees. What is x?

  98. 98.Consecutive interior angles formed by a transversal with parallel streets in Easton measure (2x + 10) degrees and (4x − 10) degrees. What is x?

  99. 99.Corresponding angles at a parallel-rail crossing in Steelton measure (5x − 5) degrees and 80 degrees. What is x?

  100. 100.A grain silo near Lancaster is a cylinder with radius 3 meters and height 10 meters. What is its volume?

  101. 101.A funnel in a Bethlehem shop is a cone with radius 6 centimeters and height 4 centimeters. What is the volume?

  102. 102.A spherical water tank in Erie has a radius of 3 meters. What is its volume?

  103. 103.A cylindrical cistern in Lebanon has a diameter of 8 feet and a height of 5 feet. What is the volume?

  104. 104.A salt pile in a Scranton shed is a cone with radius 3 meters and height 9 meters. What is the volume?

  105. 105.A decorative sphere in a Hershey garden has a radius of 6 inches. What is the volume?

  106. 106.A cylindrical cheese mold in Berks County has radius 5 centimeters and height 2 centimeters. What is the volume?

  107. 107.A cylindrical tank in Harrisburg holds 48π cubic meters, and its radius is 2 meters. What is the height?

  108. 108.A conical gravel pile in Williamsport has volume 100π cubic feet and radius 5 feet. What is the height?