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New Jersey Student Learning Assessments Mathematics Grade 8

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

These questions are original. This is not an official New Jersey Student Learning Assessment, and FreeExam is not affiliated with the New Jersey Department of Education.

  1. 1.A carpenter in Atlantic City cuts a square panel with area 49 square feet. The side length is the principal square root of 49. Which statement is correct?

  2. 2.Rangers at Batsto Village record a straight trail of length equal to the square root of 20 miles. Which description of that length is correct?

  3. 3.A Hoboken ferry log lists a crossing of 0.272727... hours, and the digits 2 and 7 repeat without stopping. What kind of number is that time?

  4. 4.The circular window at the Sandy Hook lighthouse is described using pi. Which statement about pi is true?

  5. 5.A Princeton lab adds the principal square root of 16 to the fraction 1/2. What kind of number is the sum?

  6. 6.Two trail signs at Allaire State Park show the lengths square root of 3 miles and square root of 12 miles. What is the product of those lengths?

  7. 7.A square floor tile in a Morristown hallway has area 4/9 square foot. Using the principal square root, what is the side length?

  8. 8.A notebook in a New Brunswick lab shows 0.101001000100001..., with one extra 0 between the 1 digits each time. Which description fits?

  9. 9.The view platform at High Point State Park is a square of area 50 square meters. Between which consecutive whole numbers does the side length lie?

  10. 10.A clinic in Clifton combines 3.2 times 10 to the fifth power test kits with 4 times 10 to the fourth power kits. What is the sum in scientific notation?

  11. 11.A square herb plot in a Red Bank courtyard covers 10 square feet. Which value is closest to the side length?

  12. 12.A survey crew near the Delaware Water Gap compares the square root of 20 with 4.5. Which comparison is correct?

  13. 13.A Cape May classroom places the square root of 8, the number 3, and pi on a number line, using 3.14 as the estimate for pi. Which list is ordered from least to greatest?

  14. 14.A square community garden in Cherry Hill covers 45 square yards. Between which consecutive whole numbers does one side lie?

  15. 15.A square sail loft in Barnegat Light has area 45 square feet. Which value is closest to the square root of 45?

  16. 16.The scoreboard at a Rutgers-Camden gym uses the factor 9 to the power 0 in a lighting formula. What is that value?

  17. 17.A scale model of the Pulaski Skyway uses the factor 5 to the power negative 2 for a tiny length. Which value equals that factor?

  18. 18.A computer club at Kean University evaluates 3 squared, and then raises that result to the third power. What is the value?

  19. 19.A lab in Piscataway simplifies 10 to the eighth power divided by 10 to the sixth power while counting cells. What is the quotient?

  20. 20.A warehouse in Union Township multiplies 4 cubed by 4 squared while labeling cartons. Which expression equals the product?

  21. 21.Liberty State Park recorded 48000 visitors on a holiday weekend. Which expression writes 48000 in scientific notation?

  22. 22.A water sample from the Raritan River contains 0.00056 gram of a mineral. Which expression is that mass in scientific notation?

  23. 23.A shipping yard in Elizabeth multiplies 3 times 10 to the fourth by 2 times 10 to the third. What is the product in scientific notation?

  24. 24.A weather station in Vernon divides 8.4 times 10 to the sixth by 2 times 10 to the second. What is the quotient in scientific notation?

  25. 25.A club in Montclair solves 4x + 3 = 2x + 15 to split a fundraising total. What is x?

  26. 26.The balance equation for a shop in Jersey City is 7x - 4 = 3x + 20. What is x?

  27. 27.A mural team in Camden solves 2(x + 6) = x + 20. What is x?

  28. 28.A waterfront pass in Weehawken must satisfy 5x + 1 > 2x + 13. Which solution is correct?

  29. 29.A temperature rule at a lab in Edison is 20 - 4x less than or equal to 2x - 4. What is the solution?

  30. 30.A recipe card in Asbury Park uses (1/2)x + 3 = (1/4)x + 9. What is x?

  31. 31.A clerk in Trenton tries to solve 2(x + 4) = 2x + 6. How many solutions does the equation have?

  32. 32.A tutor in Westfield simplifies 3(x - 2) = 3x - 6. Which statement describes the solution?

  33. 33.A footpath in the Watchung Reservation rises 18 meters across a horizontal run of 6 meters. What is the slope, in meters of rise per meter of run?

  34. 34.A curb ramp outside Newark Penn Station rises 2 feet over a horizontal run of 24 feet. What is the slope of the ramp?

  35. 35.On a coordinate map of Paulus Hook, a path goes from (1, 3) to (5, 11), with both axes in blocks. What is the slope?

  36. 36.A road down from Sunrise Mountain in Stokes State Forest is graphed from (0, 30) to (5, 10), with both axes in meters. What is the slope?

  37. 37.A service road across the Meadowlands runs from (2, 9) to (11, 9) on a grid in kilometers. What is the slope?

  38. 38.A cliff profile along the Palisades is drawn through (6, 1) and (6, 14). What is the slope of that profile?

  39. 39.A River Line graph uses hours as x and miles as y. The graph passes through (0, 0) and (3, 84). What speed, in miles per hour, does the slope give?

  40. 40.A bike lane in New Brunswick follows a line through (2, 5) with slope 3. Which equation matches that line?

  41. 41.A footbridge graph in Lambertville crosses the y-axis at 4 and has slope negative 2. Which equation is the line?

  42. 42.A survey line in Plainsboro passes through (1, 2) and has slope 4. Which ordered pair also lies on that line?

  43. 43.A drainage line in Freehold passes through (4, 6) with slope 1/2. Which equation is correct?

  44. 44.A descending path at Washington Crossing State Park goes through (0, 8) with slope negative 1. Which ordered pair is on the path?

  45. 45.A path along the D&R Canal in Kingston stays at height 5 and passes through (7, 5), so its slope is 0. Which equation describes the path?

  46. 46.A trail grid in Ringwood State Park has a line through (-2, 1) with slope 3. Which ordered pair is also on the line?

  47. 47.Tickets at a theater in Madison follow y = 6x, where x is the number of tickets and y is the cost in dollars. What is the cost of 8 tickets?

  48. 48.A delivery table in Cranford shows the pairs (2, 10), (5, 25), and (7, 35). Which equation fits every pair?

  49. 49.A grocer in Perth Amboy compares pricing rules. Which equation is a proportional relationship between x and y?

  50. 50.A lifeguard pay graph in Ocean Grove passes through the origin and through (4, 52), with x in hours and y in dollars. Which equation matches the graph?

  51. 51.A stand in Ocean City charges one price per cup, and 5 cups of juice cost 15 dollars. If y is the cost in dollars and x is the number of cups, which equation is correct?

  52. 52.A bike rental in Beach Haven tests four pricing tables. Which table is a proportional relationship?

  53. 53.The graph of a proportional relationship at a print shop in Rahway passes through (8, 24). What is y when x = 5?

  54. 54.A savings record in Maplewood lists weeks 1, 2, 3, and 4 with balances 11, 17, 23, and 29 dollars. What kind of relationship is this?

  55. 55.A hospital lab in Hackensack records hours 1, 2, 3, and 4 with counts 5, 10, 20, and 40. Is the relationship linear?

  56. 56.A class in Lawrenceville pairs side lengths 1, 2, 3, and 4 with areas 1, 4, 9, and 16. Which statement is correct?

  57. 57.A science class in Summit compares four tables. Which table shows a linear relationship?

  58. 58.A pond log in Cheesequake State Park lists days 2, 4, 6, and 8 with depths 5, 9, 13, and 17 inches. Which description fits?

  59. 59.A car service in Fort Lee charges by the mile. For miles 1, 2, 3, and 4, the costs are 6, 10, 14, and 18 dollars. Which statement is true?

  60. 60.Two lines on a Teaneck planning map are y = 2x + 1 and y = x + 6. What is their intersection?

  61. 61.A shop in Metuchen sells x muffins and y scones under the equations x + y = 14 and x - y = 4. What is the pair (x, y)?

  62. 62.A cafe in Highland Park solves 2x + y = 13 and x + y = 8. What is the pair (x, y)?

  63. 63.Two campus paths in Ewing follow y = -x + 9 and y = 2x. Where do the paths meet?

  64. 64.A ferry count in Hoboken uses the system x = 4 and 3x + y = 19. What is y?

  65. 65.A designer graphs y = 3x + 2 and y = 3x + 8 for two roads in Paramus. How many solutions does the system have?

  66. 66.A designer in Glen Rock compares y = 2x - 5 and 4x - 2y = 10. Which statement is true?

  67. 67.A stand in Wildwood sold 10 snacks. Pretzels cost 4 dollars each and lemonade costs 2 dollars each. The stand took in 28 dollars. How many pretzels were sold?

  68. 68.A class in Chatham sorts ordered pairs. Which set is a function?

  69. 69.A vending machine at Journal Square has one button code for each snack. Button A always drops one granola bar, and button B always drops one juice. Which statement is correct?

  70. 70.A table at a Millburn school lists inputs 3, 5, 3, and 8 with outputs 1, 2, 6, and 2. Why is this relation not a function?

  71. 71.A coach in Wayne describes graphs without drawing them. Which graph represents y as a function of x?

  72. 72.A teacher in Livingston asks whether y = x squared assigns exactly one output to each input. What is the right response?

  73. 73.A worksheet in West Orange asks which equation does not define y as a function of x. Which choice is it?

  74. 74.A right triangle path in a Morris County park has legs of 8 meters and 15 meters. What is the length of the hypotenuse?

  75. 75.The grounds crew at a Hamilton soccer field marks a right triangle with legs of 9 yards and 12 yards. What is the hypotenuse?

  76. 76.A right triangle banner across a street in Belmar has legs of 7 feet and 24 feet. How long is the hypotenuse?

  77. 77.A ramp in Bayonne forms a right triangle. The hypotenuse is 13 feet and one leg is 5 feet. What is the other leg?

  78. 78.A garden bed in Moorestown has sides of 6 meters, 8 meters, and 10 meters. Does it have a right angle?

  79. 79.A triangular sail pattern in Toms River uses sides of 5 feet, 6 feet, and 8 feet. Is the triangle right-angled?

  80. 80.A ladder leans against a library in Somerville. The ladder is 10 feet long, and its base is 6 feet from the wall. How high on the wall does the ladder reach?

  81. 81.A rectangular poster at Metropark station in Iselin is 20 inches by 21 inches. What is the length of a diagonal?

  82. 82.A cylindrical water tank in Linden has radius 2 meters and height 5 meters. Use 3.14 for pi. What is the volume?

  83. 83.A grain cylinder in Salem County has radius 5 feet and height 4 feet. Use 3.14 for pi. What is the volume?

  84. 84.A cone-shaped sand pile in Stone Harbor has radius 3 feet and height 4 feet. Use 3.14 for pi. What is the volume?

  85. 85.A paper cone at a fair in Jackson has radius 6 centimeters and height 5 centimeters. Use 3.14 for pi. What is the volume?

  86. 86.A globe in a classroom in East Orange has radius 3 inches. Use 3.14 for pi. What is the volume of the sphere?

  87. 87.A spherical tank at a plant in Paulsboro has radius 6 feet. Use 3.14 for pi. What is the volume?

  88. 88.A cylinder and a cone in a Glassboro workshop have the same radius and the same height. The cylinder holds 75.36 cubic inches. What is the cone's volume?

  89. 89.A party hat in Long Branch is a cone with radius 2 inches and height 9 inches. Use 3.14 for pi. What is the volume?

  90. 90.On a street grid in Union City, a plaza marker is slid 5 blocks east and 2 blocks north without turning. What is that move called?

  91. 91.A logo for a boathouse in Riverton is flipped across a vertical line so that left and right trade places. Each point stays the same distance from that line. Which transformation is this?

  92. 92.A weather vane in Atlantic Highlands turns 90 degrees around its center bolt. The shape does not flip. What transformation is that turn?

  93. 93.A student in Bloomfield slides a paper stamp 6 centimeters to the right. The stamp is not turned, and the image faces the same way. Which statement is correct?

  94. 94.A design on a bridge tower in Phillipsburg is flipped across a horizontal line. Points above the line move below it, and each point stays the same distance from the line. What is the transformation?

  95. 95.A sign at the Lincoln Tunnel entrance is given a half turn around its center. It is upside down, and it is not a mirror image. Which description fits?

  96. 96.Which transformation produces a mirror image of a figure drawn on a poster in Montclair?

  97. 97.Two triangles on a worksheet in South Orange each have angles of 35 degrees, 65 degrees, and 80 degrees. The side lengths are not given. Which conclusion is justified?

  98. 98.A mural in Jersey City is a scaled copy of a small sketch. The scale factor from the sketch to the mural is 3. A side of the sketch is 5 inches. How long is the corresponding side of the mural?

  99. 99.A map of Cape May County uses a scale factor of 1/2 from a larger drawing. A road that is 18 centimeters on the drawing is how long on the map?

  100. 100.A figure on a flag in Fort Lee is rotated 90 degrees about a point. Which statement about the image is correct?

  101. 101.On a worksheet in Collingswood, triangle A has angles of 42 degrees and 58 degrees. Triangle B has angles of 42 degrees and 80 degrees. Are the triangles similar?

  102. 102.A triangle in a Haddonfield park has sides of 5 meters, 7 meters, and 9 meters. A similar triangle uses scale factor 4. What is the perimeter of the larger triangle?

  103. 103.Two parallel streets in Ridgewood are cut by a transversal avenue. One corresponding angle measures 72 degrees. What is the other corresponding angle?

  104. 104.Parallel rails in a Kearny yard are crossed by a diagonal brace. An interior angle on one side of the brace is 118 degrees. What is the alternate interior angle?

  105. 105.Two parallel paths in Branch Brook Park are cut by a transversal. A same-side interior angle measures 65 degrees. What is the other same-side interior angle?

  106. 106.At a crossing in Bound Brook, a transversal meets another line and one angle is 47 degrees. What is the vertical angle across from it?

  107. 107.A transversal crosses a street line in Englewood and forms a 38-degree angle with that line. What is the adjacent angle along the straight street?

  108. 108.Parallel boardwalk rails in Seaside Heights are cut by a transversal. One exterior angle is 123 degrees. What is the same-side exterior angle?