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North Carolina End-of-Grade Tests Mathematics Grade 8

One hundred eight questions on slope, systems, exponents, and volume.

These questions are original. This is not an official North Carolina End-of-Grade test, and FreeExam is not affiliated with the North Carolina Department of Public Instruction.

  1. 1.Surveyors on the Blue Ridge Parkway marked a service path from (2, 1) to (6, 9), with both axes in miles. What is the slope of the path?

  2. 2.Channel markers in the Cape Fear River near Wilmington sit at (5, 2) and (5, 7) on a harbor grid. What is the slope of the line through those markers?

  3. 3.The grounds crew at a Durham ballfield painted a right triangle with legs of 5 feet and 12 feet. What is the length of the hypotenuse, in feet?

  4. 4.A glaze cylinder at a pottery shop in Seagrove holds 18 cubic units. A cone with the same radius and the same height holds how many cubic units?

  5. 5.A cold-storage room at a lab in Research Triangle Park holds 4000 vials. Which expression shows 4000 in scientific notation?

  6. 6.A square herb bed in Pittsboro covers 64 square yards. Using the principal square root, what is the length of one side, in yards?

  7. 7.A connector path near Grandfather Mountain is marked √3 miles long. Which word describes √3?

  8. 8.On Ocracoke, one ferry fare is y = x + 3 and another is y = 2x, with x in hours and y in dollars. At which point do the two lines meet?

  9. 9.A barometer on Mount Mitchell uses the factor 10⁻² in a pressure formula. What is the value of 10⁻²?

  10. 10.A wind turbine near Elizabeth City logs output with the product 3⁴ × 3². Which single power equals that product?

  11. 11.Thread counters at a mill in Kannapolis simplify 8⁵ ÷ 8². Which expression is equivalent?

  12. 12.A radio tower west of Charlotte uses (2³)² in a signal formula. What is the value of (2³)²?

  13. 13.The scoreboard circuit at the Greensboro Coliseum includes the factor 7⁰. What is 7⁰?

  14. 14.A well-depth sensor in the Sandhills records the factor 5⁻¹. What is the value of 5⁻¹?

  15. 15.Gear ratios for bikes on the American Tobacco Trail include 2³ × 2⁻¹. What is that product?

  16. 16.A bakery scale in Winston-Salem multiplies a batch by (1/2)³. What is the value of (1/2)³?

  17. 17.An overnight temperature model for Boone uses (−3)². What is the value of (−3)²?

  18. 18.A warehouse in Mebane ships (4 × 10²) × (3 × 10¹) cartons over two days. Which product is written in scientific notation?

  19. 19.A report compares 6 × 10⁵ people in one North Carolina metro area with 2 × 10² people in the town of Bath. The metro count is how many times the Bath count?

  20. 20.A microscope slide in Chapel Hill shows a grain 0.00045 meter wide. Which expression is the scientific notation for that width?

  21. 21.The North Carolina State Fair counted 8.1 × 10⁶ visitors on Saturday and 9 × 10³ visitors at one exhibit. The Saturday count is how many times the exhibit count?

  22. 22.A cube cooler at the seafood market in Morehead City holds 27 cubic feet. What is the length of one edge, in feet?

  23. 23.A square sail measured in Beaufort has area 81 square feet, so a side s satisfies s² = 81. What is the principal solution for s?

  24. 24.A storage cube in a Fayetteville warehouse has volume 125 cubic feet, so an edge e satisfies e³ = 125. What is e?

  25. 25.A surveyor in Sampson County needs √50 to estimate a field diagonal. Between which two consecutive integers does √50 lie?

  26. 26.Gardeners at Biltmore use π to find the circumference of a round planter. Which description fits π?

  27. 27.A GoRaleigh display showed the repeating decimal 0.272727… as a route ratio. Which fraction equals that decimal?

  28. 28.Hikers in William B. Umstead State Park finished 0.625 of a loop. Which fraction equals 0.625?

  29. 29.Engineers in New Bern compared a span estimate of √10 meters with a second estimate of 3.2 meters. Which estimate is longer?

  30. 30.On a number line in a Hickory classroom, √20 is plotted for a ramp length. Between which two whole numbers does √20 lie?

  31. 31.A depth reading at Jordan Lake is described by √2 + 5. Which statement about √2 + 5 is true?

  32. 32.A scale model of the 1903 glider at Kill Devil Hills uses the factor √9 × √4. What is that product?

  33. 33.A ranger on the Mountains-to-Sea Trail solves 3x + 5 = 20 to find miles past a shelter. What is x?

  34. 34.A cabinet shop in High Point cuts boards using 2(x − 4) = 10, with x in inches. What is x?

  35. 35.A hatchery in Marion fills a tank so that (1/2)x + 3 = 7, with x in liters. What is x?

  36. 36.Two toll formulas for the Southport ferry are set equal in 4x + 1 = 4x + 6. How many solutions does the equation have?

  37. 37.Ticket clerks at Durham Bulls Athletic Park compare the expressions in 2(x + 3) = 2x + 6. How many solutions does the equation have?

  38. 38.Longshore workers at the Port of Wilmington solve 5x − 2x + 4 = 19 for the number of crates. What is x?

  39. 39.A dock extension in the town of Washington fits 6x − 4 = 2x + 12, with x in feet. What is x?

  40. 40.A forecast for Asheville uses −3x + 7 = 1, where x is a drop in degrees. What is x?

  41. 41.A road crew in Gastonia models a wait with the inequality −2x > 8. Which inequality describes x?

  42. 42.A library in Salisbury keeps a supply order in the range −5x + 1 ≤ 11. Which inequality describes x?

  43. 43.A gauge on the Neuse River at Kinston moved from the point (1, 8) to the point (4, 2), in feet. What is the slope of that change?

  44. 44.A Carolina Beach boardwalk stays level from (0, 4) to (9, 4) on a planner's grid. What is the slope of the boardwalk?

  45. 45.A rental log in Carrboro lists hours and dollars as the pairs (1, 7), (2, 10), and (3, 13). What is the rate of change in dollars per hour?

  46. 46.A kayak shop in Bryson City uses y = 6x + 15, with x in hours and y in dollars. What does the 15 represent?

  47. 47.A kiln log in Star uses the line y = −4x + 9 for temperature over time. What is the slope?

  48. 48.A corn maze in Archdale compared four rules for path length y after x turns. Which rule is not a linear function?

  49. 49.A rest-area vending machine on I-40 near Morganton pairs each button number with a snack code. Which set of pairs is a function?

  50. 50.Temperatures logged in Waynesville are graphed with time on the horizontal axis. Which graph shows temperature as a function of time?

  51. 51.A snowplow in Boone cleared 12 miles in 3 hours at a steady speed, starting from mile 0. Which equation gives miles y after x hours?

  52. 52.A candle shop in Blowing Rock starts a candle at 18 cm, and it burns 2 cm each hour. Which equation gives the height y after x hours?

  53. 53.On a Mooresville rail-trail map, line A passes through (0, 1) and (2, 7), and line B is y = 2x + 1. Which line has the greater slope?

  54. 54.A balloon company in Statesville lists hours and cost as (0, 40), (1, 55), and (2, 70). What is the initial value of the cost?

  55. 55.A hiker on the Art Loeb Trail climbs steeply, walks a flat ridge, then descends into the valley. Which graph of height versus time matches that trip?

  56. 56.A stand in Elkin sells pecans by the pound with no extra fee. Which equation is a proportional relationship between pounds x and dollars y?

  57. 57.Two concession plans in Concord are y = x − 1 and y = 3x − 9. At which point do the plans cost the same?

  58. 58.At a museum in Winston-Salem, ticket counts satisfy x + y = 10 and x − y = 4. What is the solution (x, y)?

  59. 59.Two Charlotte bus fares are y = 2x + 1 and y = 2x + 5. How many solutions does this system have?

  60. 60.A greenway rule in Cary is written both as y = −x + 4 and as 2y = −2x + 8. How many solutions does the system have?

  61. 61.At a farm stand in Snow Hill, two baskets and one jar cost $11, and one basket and one jar cost $7. What is the price of one basket?

  62. 62.Survey lines in Alamance County follow y = −x + 6 and y = x. At which point do the lines cross?

  63. 63.A wheelchair ramp at a school in Jacksonville forms a right triangle with hypotenuse 10 feet and one leg 6 feet. What is the other leg, in feet?

  64. 64.On the beach at Nags Head, a taut kite string is 15 meters long and the kite is 9 meters above the sand. How far, in meters, is the holder from the point on the sand directly below the kite?

  65. 65.Two trail posts along the Haw River are at (1, 2) and (4, 6) on a kilometer grid. What is the straight-line distance between them?

  66. 66.Two buoys in Pamlico Sound are charted at (−1, 2) and (5, 10). What is the distance between them?

  67. 67.A triangle marked on a field in Tarboro has side lengths 9, 12, and 15. Which statement is true?

  68. 68.A shipping crate in Lenoir measures 2 feet by 3 feet by 6 feet. What is the length of the space diagonal, in feet?

  69. 69.A 17-foot ladder leans against a barn in Yadkinville, with its base 8 feet from the wall. How many feet up the wall does the ladder reach?

  70. 70.A cylindrical silo in Duplin County has radius 3 feet and height 10 feet. What is its volume, in cubic feet?

  71. 71.Road crews in Carteret County shape road salt into a cone of radius 3 meters and height 4 meters. What is the volume of the cone, in cubic meters?

  72. 72.A spherical buoy in Albemarle Sound has radius 3 feet. What is its volume, in cubic feet?

  73. 73.A candle mold in Old Salem is a cylinder of volume 32π cubic inches and radius 2 inches. What is the height, in inches?

  74. 74.A glass float in Beaufort is a sphere of volume 36π cubic centimeters. What is the radius, in centimeters?

  75. 75.A roof model in Edenton is a cone of volume 20π cubic inches and radius 2 inches. What is the height, in inches?

  76. 76.In an Asheville glass studio, a sphere of radius 3 inches is compared with a cylinder of radius 3 inches and height 4 inches. How do their volumes compare?

  77. 77.A triangular sail in Oriental has two angles of 47° and 58°. What is the third angle?

  78. 78.At a park in Hillsborough, a triangle has remote interior angles of 40° and 65°. What is the exterior angle at the third vertex?

  79. 79.Two parallel streets in Raleigh are cut by a side street. One angle formed by the side street is 70°. What is the measure of its alternate interior angle?

  80. 80.A railroad and a parallel access road near Hamlet are cut by a crossing. One interior angle is 118°. What is the consecutive interior angle on the same side of the crossing?

  81. 81.Two triangles on a mural in Greensboro each have angles of 35° and 80°. Which conclusion follows?

  82. 82.A small print of the Cape Hatteras Lighthouse is 4 inches tall, and a larger print is 10 inches tall. What is the scale factor from the small print to the large print?

  83. 83.A bench icon on a Pullen Park map sits at (3, −2). The icon is translated 4 units left and 5 units up. What are the new coordinates?

  84. 84.A buoy in Bogue Sound is plotted at (2, −6) and then reflected across the x-axis. What is the image point?

  85. 85.A trail marker at (−4, 3) on a Pisgah map is reflected across the y-axis. What is the image point?

  86. 86.A garden corner at (1, 0) in Apex is rotated 90° counterclockwise about the origin. What is the image?

  87. 87.A lamp on a Greenville map is at (5, −2). It is rotated 180° about the origin. What is the image?

  88. 88.On a Durham blueprint, a vertex at (2, 6) is dilated by a scale factor of 1/2 centered at the origin. What is the image?

  89. 89.A logo point for a Charlotte team is at (1, −2). A dilation by scale factor 3 about the origin moves it where?

  90. 90.Two postage stamps compared at the Salisbury post office match by a rigid motion. Which sequence shows they are congruent?

  91. 91.Two festival banners in Wilmington have the same shape, and one is larger. Which sequence can carry the smaller banner onto the larger one?

  92. 92.A scatter plot from a Wilson middle school graphs hours studied and quiz scores, and the points rise from left to right in a straight pattern. Which association is that?

  93. 93.On a scatter plot of rainfall and plant height from Robeson County, one point sits far above a tight linear cloud. What is that point called?

  94. 94.For a stand on Emerald Isle, a line of best fit is y = 2x + 5, where x is degrees above 70°F and y is cones sold. What does the slope mean in this setting?

  95. 95.Smoothie sales at Atlantic Beach follow the line of best fit y = 3x + 4. What value of y does the line predict when x = 5?

  96. 96.A scatter plot for a delivery van based in Sanford shows miles driven and gallons left, and the points fall from left to right. Which association is shown?

  97. 97.A Goldsboro school surveyed students. Of the 16 in band, 6 also play soccer, and of the 24 not in band, 9 play soccer. Among the band students, what fraction also play soccer?

  98. 98.In Lumberton, 30 eighth graders were asked how they get to school: 18 ride the bus and 12 walk. What fraction of these eighth graders walk?

  99. 99.Pumpkin weights at a farm in Rolesville mostly fall between 8 and 10 pounds, with one pumpkin at 20 pounds. Which description fits the data?

  100. 100.A scatter plot of a ball's height over time at a game in Chapel Hill rises and then falls in a curve. Which description fits?

  101. 101.A mill in Eden simplifies the gear ratio 6⁴ ÷ 6⁶. What is the value of that quotient?

  102. 102.Jockey's Ridge had 3.2 × 10⁴ visitors, and a nearby sound-side lot had 1.5 × 10³ visitors the same day. What is the sum in scientific notation?

  103. 103.A hall in Rocky Mount sets chairs using 4(x + 2) − 3x = 11. What is x?

  104. 104.A hillside railway plan at Chimney Rock passes through (0, 1) and (6, 4). What is the slope of the railway?

  105. 105.A juice stand in Pinehurst mixes batches so that y = 4x and x + y = 15. What is the solution (x, y)?

  106. 106.A gift box at a shop in Hendersonville is a cube with volume 8 cubic inches. What is the edge length, in inches?

  107. 107.A scale drawing of the State Capitol uses the factor (3²)⁰. What is the value of (3²)⁰?

  108. 108.A property line in Chatham County passes through (1, 4) and (8, 4). Which equation matches the line?