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Virginia Standards of Learning Mathematics Grade 8

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

These questions are original. This is not an official Virginia Standards of Learning test, and FreeExam is not affiliated with the Virginia Department of Education.

  1. 1.A Richmond floodwall model uses the factor 2^7. What is the value of 2^7?

  2. 2.On a Norfolk harbor chart, a depth mark is written 10^-4 meter. Which number equals 10^-4?

  3. 3.A Charlottesville bakery uses 12^0 as the scale factor for a one-loaf test batch. What is 12^0?

  4. 4.A sign at Maymont in Richmond shows (-6)^2 for a squared length in a garden model. What is (-6)^2?

  5. 5.A James River lock record multiplies 6^3 by 6^2. What is the product?

  6. 6.A notebook at a Staunton observatory divides 5^7 by 5^3. What is the quotient?

  7. 7.A model of the Chesapeake Bay Bridge-Tunnel uses (3^2)^3 panels in one section. What is that number?

  8. 8.At the Virginia Aquarium in Virginia Beach, a tank card shows 7^-2. Which fraction equals 7^-2?

  9. 9.Engineers timing the Roanoke star combine the factors 10^5 and 10^-2. What single number do those factors make?

  10. 10.A Lynchburg library display evaluates (-4)^3. What is the value?

  11. 11.Gardeners at Monticello simplify 11^6 / 11^6. What is the value?

  12. 12.A Hampton Roads ferry worksheet asks for 2^-3 × 2^-1. Which value is equivalent?

  13. 13.Crate labels at a Winchester orchard show the count (10^2)^3. Evaluate that expression.

  14. 14.A Fredericksburg museum card asks for the value of (1/3)^-2. What is it?

  15. 15.On a scale drawing at Mount Vernon, a measurement is written 4^-2 × 4^5. Which number equals that product?

  16. 16.A Blacksburg lab note states that (3 × 4)^2 equals which expression?

  17. 17.A Fairfax County poster lists 2,430,000 residents in a planning example. How is that number written in scientific notation?

  18. 18.A water sample from the York River has mass 0.000307 gram. Which expression is that mass in scientific notation?

  19. 19.A Chesapeake Bay count lists 4.2 × 10^7 oysters on one reef and 4.2 × 10^6 oysters on another. Which statement is true?

  20. 20.A cargo note at the Port of Virginia multiplies (5 × 10^2) by (3 × 10^5). What is the product in scientific notation?

  21. 21.A Shenandoah rainfall table divides 8.1 × 10^9 by 2.7 × 10^3. What is the quotient in scientific notation?

  22. 22.A lab card in Newport News shows 6.04 × 10^-4 gram. What is that mass in standard form?

  23. 23.Two James River gauges read 2.6 × 10^4 cubic feet and 1.3 × 10^4 cubic feet. What is the sum in scientific notation?

  24. 24.A dune study at False Cape records 7.2 × 10^5 sand grains in one sample. What is that number in standard form?

  25. 25.Order these Chincoteague visitor counts from least to greatest: 8.5 × 10^2, 3.2 × 10^3, and 8.5 × 10^1. Which list is correct?

  26. 26.Cartographers scaling a Hampton Roads satellite image multiply 1.5 × 10^-2 by 2 × 10^6. Give the product in scientific notation.

  27. 27.Botanists in the Great Dismal Swamp weighed one pollen grain at 0.00000815 gram. Write that mass in scientific notation.

  28. 28.River keepers in Giles County split a New River flow of 9.6 × 10^7 into equal groups of size 1.2 × 10^4. How many groups is that, in scientific notation?

  29. 29.A leaflet for First Landing State Park says a boardwalk is 4.08 × 10^4 meters long. How many meters is that?

  30. 30.Two samples at Gloucester Point measure 5.5 × 10^-3 liter and 5.5 × 10^-4 liter. Which statement is true?

  31. 31.Surveyors mapping a Richmond canal record a path from grid point (1, -1) to grid point (4, 11). Find the slope of that path.

  32. 32.The railing beside the Virginia Beach boardwalk stays at height -3 from x = 4 through x = 11. Find the slope of that railing.

  33. 33.Climbers near Old Rag follow a route that stays at x = -4 while the height coordinate changes from 1 to 8. What slope does that vertical route have?

  34. 34.Hikers between two Skyline Drive overlooks drop from the point (1, 11) to the point (5, 3). How steep is that drop, written as a slope?

  35. 35.A bike lane in Arlington is modeled by y = -5x + 2. What is the slope of the lane?

  36. 36.A delivery route in Alexandria gains 16 blocks north for every 10 blocks east. What is the slope, as north over east?

  37. 37.A road plan in Loudoun County includes the line y = (3/4)x - 2. Which line is parallel to it?

  38. 38.A Lexington sidewalk connects the corner (2, 1) with the corner (4, 11). Calculate its slope.

  39. 39.On a graph of a ferry crossing near Jamestown, the line falls 8 units while it runs 2 units to the right. What is the slope?

  40. 40.Park staff at Byrd Park in Richmond stretch a string from (1, 7) to (5, 9) on a site plan. Which value is the string's slope?

  41. 41.From the low point (-5, -2), an Ashland service road reaches (-1, 6). Use those coordinates to find the slope.

  42. 42.A hill near Roanoke on the Blue Ridge Parkway follows y = (2/3)x + 1. If x increases by 9, by how much does y increase?

  43. 43.Water in a Petersburg ditch flows along the line joining (1, 8) and (7, 5). Determine the slope of that flow.

  44. 44.A level walkway at Natural Bridge is graphed as a horizontal line crossing the y-axis at -6. Which equation matches it?

  45. 45.A ticket booth in Williamsburg solves 4n + 7 = 39 for the number of tickets n. What is n?

  46. 46.A canoe rental on the Rappahannock uses 3(p - 5) = 21. What is p?

  47. 47.A farm stand in Crozet solves 6x - 4 = 2x + 20. What is x?

  48. 48.The equation y = -4x + 11 models a cooling line at a creamery in Broadway. What is the y-intercept?

  49. 49.A bakery in Abingdon uses y = 7x for the cost in dollars of x loaves. What does the 7 represent?

  50. 50.Solve -3(k + 4) = 18 for a depth reading k on a Tangier Island chart. What is k?

  51. 51.A line for a Leesburg bus has slope 5 and crosses the y-axis at -8. Which equation matches the line?

  52. 52.Solve m/4 - 3 = 5 for a mixture amount m at a Harrisonburg lab. What is m?

  53. 53.Printers in Vinton set the job length w so that 8w - 5 equals 3w + 20. What value of w makes that true?

  54. 54.A line on a map of Hopewell has equation y = -2x + 11. Which ordered pair lies on the line?

  55. 55.A trail counter in Douthat State Park solves 3(2x - 1) = 4x + 13. What is x?

  56. 56.A proportional relationship for a Luray Caverns tour passes through the origin and has slope -7. Which equation is correct?

  57. 57.Solve 20 - 3y = 2y for a balance y at a Danville market. What is y?

  58. 58.A cabin heater in Highland County follows y = (1/3)x - 2. What is y when x = 12?

  59. 59.Which equation on a classroom board in Radford is true for every value of x?

  60. 60.A fence company in Warrenton charges by y = 15x + 25, where x is the number of panels. What is the charge, in dollars, for 0 panels?

  61. 61.A right triangle trail in the Blue Ridge has legs of 7 meters and 24 meters. What is the hypotenuse, in meters?

  62. 62.The sail on a boat at Lake Anna is a right triangle. The longest side is 37 feet, and one of the shorter sides is 12 feet. How long is the remaining side, in feet?

  63. 63.A ladder leans against a barn in Orange County. Its base is 9 feet from the wall, and the ladder is 41 feet long. How high up the wall does it reach, in feet?

  64. 64.A picture frame in Farmville has side lengths 16 inches, 63 inches, and 65 inches. Which statement is true?

  65. 65.A rectangular field in Scottsville is 11 meters by 60 meters. What is the length of a diagonal, in meters?

  66. 66.On a Church Hill map in Richmond, a straight path runs from (2, 1) to (30, 46). What is the distance between those points?

  67. 67.A kite string at Sandbridge is 52 meters long, and the kite is 20 meters above the sand. The flyer holds the string at the sand. How far is the flyer from the point directly under the kite, in meters?

  68. 68.A carpentry list in Galax gives four possible sets of board lengths, in centimeters. Which set can be the sides of a right triangle?

  69. 69.The stage crew in Buena Vista is cutting a right triangle from banner cloth. The sides that form the right angle are 15 inches and 36 inches. How long is the remaining side, in inches?

  70. 70.A support wire in Floyd runs from the top of a 16-foot pole to a stake 12 feet from the base. How long is the wire, in feet?

  71. 71.The pool cover in Cape Charles is a 40-foot by 42-foot rectangle. How many feet of cord reach from one corner to the opposite corner?

  72. 72.A Smith Mountain Lake chart pins one dock at (2, 8) and another at (17, 16). How far apart are the docks, in the same grid units?

  73. 73.A table at a Culpeper farm lists the input 4 twice, once with output 7 and once with output 9. Is this relation a function?

  74. 74.For the function f(x) = 4x - 7 used by a Portsmouth shipping clerk, what is f(6)?

  75. 75.At a math night in Purcellville, students compare four graphs. Which graph represents y as a function of x?

  76. 76.The function g(t) = -3t + 10 gives the water depth, in inches, of a Berryville rain barrel after t hours of draining. What is g(0)?

  77. 77.A vending machine in Manassas pairs button A with pretzels, button B with crackers, and button C with pretzels. Is this pairing a function from buttons to snacks?

  78. 78.A survey card from Emporia shows the ordered pairs (-2, 5), (1, 5), and (4, 0). What is the range of this function?

  79. 79.A linear function for a bike share in Bristol, Virginia, is f(x) = 8x - 2. Which statement describes f as x increases by 1?

  80. 80.Which list of ordered pairs (x, y) from a Suffolk classroom shows y as a function of x?

  81. 81.A model in Waynesboro uses h(x) = x^2 - 6. What is h(-4)?

  82. 82.A school in Salem, Virginia, gives each student ID one locker. Some locker numbers go unused, and two students may share a number. Why is this a function from IDs to locker numbers?

  83. 83.A wildlife count in Onancock uses the domain {0, 1, 4} and the rule f(x) = 3x. What is the range?

  84. 84.On a worksheet in Covington, which equation does not define y as a function of x?

  85. 85.A point on a VMFA courtyard map is translated 6 units right and 1 unit down from (-2, 3). What is the image?

  86. 86.Point P(7, -4) is reflected across the y-axis on a coordinate grid of Colonial Williamsburg. What is the image?

  87. 87.Point Q(-3, 6) on a garden grid at Lewis Ginter Botanical Garden is reflected across the x-axis. What is the image?

  88. 88.A logo for a festival in Warm Springs is rotated 180 degrees about the origin. The image of (-4, 5) is which point?

  89. 89.Point R(-2, 4) on a mural grid in the Fan District of Richmond is dilated by a scale factor of 5 with center at the origin. What is the image?

  90. 90.In a design class in Martinsville, which transformation of a triangle makes a similar copy that is not congruent to the original?

  91. 91.On a map at a library in Bedford, the rule (x, y) → (x + 3, y - 5) moves the point (2, 9). What is the image?

  92. 92.A rotation of 90 degrees counterclockwise about the origin sends (x, y) to (-y, x). On a stencil in Front Royal, what is the image of (5, -2)?

  93. 93.Triangle ABC in a Roanoke County class at Hollins has C at (6, -3). After a dilation centered at the origin with scale factor 1/3, what is the image of C?

  94. 94.Point S(4, -2) on a map of Appomattox is reflected across the x-axis and then translated 3 units left. What is the final image?

  95. 95.A translation on a Grayson Highlands trail map sends (0, 0) to (-4, 3). The same translation sends (2, 5) to which point?

  96. 96.Under a dilation centered at the origin, a photo grid in Clarksville sends (10, 4) to (5, 2). What is the scale factor?

  97. 97.A cylindrical grain bin in Rockingham County has radius 4 feet and height 7 feet. What is its volume, in cubic feet?

  98. 98.After a storm, sand at Buckroe Beach in Hampton forms a cone 4 meters tall with a 6-meter radius across the base. How many cubic meters of sand are in the pile?

  99. 99.A navigation buoy floating in the Chesapeake Bay is a sphere of radius 6 inches. Calculate its volume in cubic inches.

  100. 100.A cylinder and a cone in an Altavista shop have the same radius and the same height. The cylinder's volume is 72π cubic centimeters. What is the cone's volume?

  101. 101.A round livestock tank in Louisa County has a base radius of 7 feet and stands 3 feet tall. How many cubic feet of water fill it to the brim?

  102. 102.Students in Verona pour plaster into a cone whose circular opening has radius 5 centimeters and whose tip is 6 centimeters below that opening. What volume of plaster, in cubic centimeters, fills the cone?

  103. 103.For a solar-system display, a Pulaski library builds a sphere of radius 2 centimeters. Find that sphere's volume in cubic centimeters.

  104. 104.On a scale model of the Virginia State Capitol, one column is a cylinder 12 inches across and 4 inches tall. What is the column's volume, in cubic inches?

  105. 105.Two molds in a Gordonsville kiln use radius 4 centimeters. The cone has height 9 centimeters and the cylinder has height 3 centimeters. How do the volumes compare?

  106. 106.A spherical tank in Amelia County has volume 256π/3 cubic feet. What is the radius, in feet?

  107. 107.An ice cream serving in Alexandria is a cone of radius 3 centimeters and height 4 centimeters, topped by a hemisphere of radius 3 centimeters. What is the total volume, in cubic centimeters?

  108. 108.A cylindrical silo in Page County has radius 5 meters and height 8 meters, with a cone roof of the same radius and height 3 meters. What is the total volume, in cubic meters?