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Virginia Standards of Learning Mathematics Grade 7

Proportions, rational numbers, equations, circles, and probability.

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.Mara stopped at an orchard outside Winchester and paid $18 for 6 bushels of apples. At that same price per bushel, what does 1 bushel cost?

  2. 2.A Jamestown ferry log shows that 2 miles take 10 minutes and 5 miles take 25 minutes. Minutes are proportional to miles. What is the constant of proportionality, in minutes per mile?

  3. 3.Kayak rentals on the Rappahannock River follow c = 12h, with c the cost in dollars and h the number of hours. What is the constant of proportionality?

  4. 4.A farm stand in Culpeper uses p = 2.5n, where p is the price in dollars and n is the number of pounds of peaches. What is the price of 8 pounds?

  5. 5.Which equation on a worksheet in Wytheville shows a proportional relationship between x and y?

  6. 6.A snack shop in Staunton mixes almonds and dried cranberries in the ratio 3 cups to 5 cups. How many cups of almonds belong with 20 cups of cranberries?

  7. 7.A ride from a neighborhood in Alexandria covers 15 miles and costs $6. At the same cost per mile, what would a 40-mile ride cost?

  8. 8.Painters in Roanoke use 2 gallons of paint to cover 350 square feet of wall. How many gallons are needed to cover 875 square feet at that rate?

  9. 9.Lena keeps a steady 12 miles per hour on the Virginia Capital Trail. How far does she ride in 2.5 hours?

  10. 10.At a market in Lexington, a 4-pound bag of potatoes costs $3.60 and a 6-pound bag costs $5.10. Which statement gives the better buy?

  11. 11.A bakery in Lynchburg uses 2 cups of flour to make 12 muffins. How many cups of flour are needed to make 42 muffins?

  12. 12.A graph drawn in a Harrisonburg science class shows a proportional relationship through (0, 0) and (4, 18). What is the constant of proportionality?

  13. 13.A hose at a community garden in Petersburg releases water at 3.5 gallons per minute. How many gallons are released in 12 minutes?

  14. 14.Blue tiles and white tiles in a museum mosaic in Newport News stay in the ratio 5 to 8. The mosaic uses 40 blue tiles. How many white tiles does it use?

  15. 15.A book at a shop in Richmond is priced at $24 before tax. The sales tax rate is 5.3%. What is the tax, to the nearest cent?

  16. 16.Dinner for a family in Norfolk comes to $48 before the tip. The family leaves a 15% tip. How much money is the tip?

  17. 17.A jacket on a rack in Charlottesville is marked $80. During a sale the price is reduced by 25%. What is the sale price?

  18. 18.A flock at a farm in Loudoun County grew from 40 sheep to 50 sheep. What was the percent increase?

  19. 19.A depth gauge at Smith Mountain Lake fell from 80 feet to 68 feet. What was the percent decrease?

  20. 20.In a band at a middle school in Harrisonburg, 30% of the students play clarinet, and that section has 18 students. How many students are in the whole band?

  21. 21.A craft booth in Waynesboro buys plain mugs for $8 and marks each one up by 40%. What is the selling price of one mug?

  22. 22.A student in Fairfax puts $200 into an account that pays 3% simple interest per year. How much interest does the account earn in 2 years?

  23. 23.A soccer team in Manassas won 12 of the 16 games it played. What percent of the games were wins?

  24. 24.A tour guide in Williamsburg earns an 8% commission on ticket sales. Tickets worth $250 were sold one afternoon. How much commission did the guide earn?

  25. 25.A poster in a museum shop in Ashland costs $15. The tax rate is 6%. What is the total cost, including tax?

  26. 26.Students in Fredericksburg planted 80 trees, and 45% of those trees were oaks. How many oaks did they plant?

  27. 27.At dawn on a Skyline Drive ridge, the temperature was −6°F. It then rose 11°F by noon. What was the temperature at noon?

  28. 28.A diver near the Chesapeake Bay Bridge-Tunnel is at an elevation of −18 feet, while the pier deck is at 7 feet. How many feet above the diver is the deck?

  29. 29.A notebook at Wallops Island multiplies a tide change of −6 feet by −2. What is the product?

  30. 30.A clerk in Bristol, Virginia, divides a 3/4-pound block of cheese into portions of 1/8 pound. How many portions does the block make?

  31. 31.The low at Big Meadows was −9°C. What is the absolute value of that temperature?

  32. 32.A weather log in Monterey, Virginia, lists −1.5, −3/2, −1.2, and −5/4 degrees Celsius. Which listed value is the greatest?

  33. 33.Four creek elevations near Old Rag, in meters, are −2, −1/2, 0.5, and 1. Which list orders them from least to greatest?

  34. 34.A hiker on the Appalachian Trail in Virginia walked 2.75 miles before lunch and 3.4 miles after lunch. How many miles was the whole walk?

  35. 35.A recipe from a farm in Orange County calls for 5/8 cup of honey. What is 5/8 written as a decimal?

  36. 36.A square garden plot in Danville covers 81 square feet. What is the length of each side?

  37. 37.On a card in a classroom in Martinsville, a student must name the additive inverse of −7/3. Which number is that inverse?

  38. 38.One buoy on the James River is at −4.5 meters and another is at 2.5 meters. What is the distance between these elevations?

  39. 39.A sailor in Hampton started with a rope 5 1/2 feet long and cut off 2 3/4 feet. How much rope was left?

  40. 40.A land survey of Prince Edward County records a distance as 4.2 × 10^4 meters. What is that distance in standard form?

  41. 41.A tide table in Colonial Heights asks for the quotient (−18) ÷ (−6). What is that quotient?

  42. 42.Before noon, a trail crew in Grayson Highlands finished 2/3 of a 9-mile section. How many miles had the crew finished?

  43. 43.A park cleanup in Front Royal ended with 23 volunteers. That total was 9 more than the number who arrived at the start. How many volunteers were there at the start?

  44. 44.After 7 crab pots were taken off a stack in Reedville, 15 pots were left. How many pots were on the stack before any were removed?

  45. 45.Canoes at a livery on Claytor Lake rent for $15 each. One morning the canoe rentals brought in $90. How many canoes were rented?

  46. 46.A teacher in Salem, Virginia, divides 48 worksheets equally among 6 groups. How many worksheets does each group receive?

  47. 47.A pecan sale in Leesburg uses the equation 3x + 5 = 26, where x is the number of boxes one donor still must buy. What is x?

  48. 48.Minutes after a checkpoint, a balloon over Louisa County satisfies 4x − 6 = 18. What is the value of x?

  49. 49.At a campsite in Douthat State Park, half of the campers plus 3 counselors equals 11 people. How many campers are at the site?

  50. 50.Ribbon for a parade float in Covington, Virginia, costs $2.50 per yard. A decorator spends exactly $10. How many yards of ribbon were bought?

  51. 51.To balance a scale model in a classroom in Wise, a student solves −5x = 35. What is x?

  52. 52.A rectangular pen on a farm in Fauquier County has a perimeter of 18 meters and a width of 4 meters. Its length x satisfies 2(x + 4) = 18. What is the length?

  53. 53.On the beach at First Landing State Park, three times the number of canoes, decreased by 4, equals 14. How many canoes are on the beach?

  54. 54.A student in Strasburg simplifies and solves 5x + 2x = 28. What is x?

  55. 55.Nia has $20 at a shop in Blacksburg. She buys a $4 notebook and spends the rest on markers that cost $2 each. How many markers can she buy?

  56. 56.The elevation, in meters, of a sensor in a cave at Luray is the solution of x + 12 = 5. What is that elevation?

  57. 57.A cooling fan in a library closet in Arlington must stay on while −3t > 15, where t is the thermostat setting. Which inequality describes every allowed value of t?

  58. 58.A field trip from a school in Chesapeake needs at least $180. The class already has $45, and each car-wash ticket earns $5. Which inequality models the number of tickets, n, the class must sell?

  59. 59.A cargo rule for a skiff in Deltaville is 2x + 3 < 17, where x is the number of crates. Which inequality gives the allowed values of x?

  60. 60.Students in Buena Vista test values in the inequality x − 4 ≥ 6. Which value is a solution?

  61. 61.A backpack for a hike on Massanutten can hold at most 12 pounds. It already holds 3.5 pounds of water. Let f be the additional pounds of food that can be packed. Which inequality is correct for f?

  62. 62.A club in Falls Church requires more than 20 hours of volunteering. Let h be the number of hours. Which inequality matches the rule?

  63. 63.On a board in Radford, students solve −2x ≤ 8. Which inequality is the solution?

  64. 64.Tickets to a concert in Portsmouth cost $12 each. Jordan can spend no more than $60. What is the greatest number of tickets Jordan can buy?

  65. 65.A marker project at Natural Bridge uses x/3 ≥ 4 for the number of posts, x. Which inequality shows every possible value of x?

  66. 66.Which of these numbers is not a solution of y < −2 on a number line sketched in Appomattox?

  67. 67.On a Shenandoah map, 1 inch represents 4 miles. A trail is 6.5 inches on the map. How many miles long is the trail?

  68. 68.A model of the Capitol in Richmond uses the scale 1 inch represents 20 feet. The dome on the model is 3.5 inches tall. How tall is the actual dome?

  69. 69.Two similar banners hang in a gym in Vinton. The smaller banner is 4 feet wide and the larger banner is 10 feet wide. What is the scale factor from the smaller banner to the larger banner?

  70. 70.On a scale drawing of a classroom in Virginia Beach, 1 centimeter represents 2 meters. A whiteboard in the room is 12 meters long. How long is the whiteboard on the drawing?

  71. 71.Two similar sails at a marina in Gloucester have corresponding sides. On the larger sail, two sides measure 6 feet and 9 feet. The side corresponding to the 6-foot side is 4 feet on the smaller sail. How long is the smaller side that corresponds to 9 feet?

  72. 72.A photographer in Crozet enlarges a rectangular picture by a scale factor of 3. The original picture is 2 inches by 5 inches. What is the area of the enlargement?

  73. 73.On a map of the Blue Ridge Parkway in Virginia, 1 centimeter represents 8 kilometers. Two overlooks are 5.5 centimeters apart on the map. What is the actual distance between them?

  74. 74.A triangular pennant in Blackstone has sides of 8 cm, 10 cm, and 14 cm. A similar larger pennant has a longest side of 21 cm. What is the length of the side that corresponds to the 10 cm side?

  75. 75.A statue in a park in Norfolk is 15 feet tall. A scale drawing uses 1 inch to represent 5 feet. How tall is the statue in the drawing?

  76. 76.A floor plan of a house in Purcellville is drawn at a scale of 1 to 50. A hallway is 8 centimeters on the plan. What is the actual length of the hallway in meters?

  77. 77.Visitors walking the rim of the fountain at Maymont in Richmond follow a circle of radius 5 feet. How long is one lap around that rim if π is taken to be 3.14?

  78. 78.A church in Middleburg is fitting molding around a round window that measures 8 feet from one side to the opposite side. How many feet of molding are needed for the full rim if π is 3.14?

  79. 79.Gardeners in Rocky Mount will mulch a flower bed that is a circle of radius 10 feet. How many square feet of mulch cover the bed when π is 3.14?

  80. 80.In a cabin near Hungry Mother State Park, a round rug reaches 6 feet from one edge through the center to the far edge. How many square feet of floor does the rug cover if π is 3.14?

  81. 81.A circular track marker in Bedford has a circumference of 31.4 meters. Using 3.14 for π, what is the diameter?

  82. 82.Students measure a circular patio in Altavista. The circumference is 18.84 feet and the diameter is 6 feet. What is the circumference divided by the diameter?

  83. 83.A semicircular garden edge at Monticello has a radius of 4 meters. Using 3.14 for π, what is the length of the curved edge only, not including the straight side?

  84. 84.A pond in Prince William Forest Park is a circle with radius 9 meters. Which expression gives the area of the water?

  85. 85.Marchers in Yorktown circle a flagpole along a path that is 14 yards across. Which expression gives the length of one lap around that path?

  86. 86.A circular stage at a fair in Spotsylvania has an area of 78.5 square feet. Using 3.14 for π, what is the radius?

  87. 87.At a math night in Marion, a student tosses two fair coins. What is the probability of getting two heads?

  88. 88.A fair number cube is rolled at a carnival booth in Elkton. What is the probability of rolling a number greater than 4?

  89. 89.In a class in Grundy, 12 students were born in Virginia and 8 were born in other places. One student is chosen at random. What is the probability that the chosen student was born in Virginia?

  90. 90.A spinner at a festival in Chincoteague has 5 equal sections numbered 1 through 5. What is the probability of spinning an even number?

  91. 91.Playground staff in Suffolk need the area of a round sand pit whose radius is 4 meters. What is that area when π is 3.14?

  92. 92.A bicycle wheel in a race through Farmville has a diameter of 28 inches. Using 22/7 for π, how far does the bicycle travel in one full turn of that wheel?

  93. 93.In a Verona workshop, two cuts for a window frame must be complementary, and one cut is already 28°. How many degrees is the other cut?

  94. 94.Along a straight railing at a lighthouse in Cape Charles, one angle measures 115°. How many degrees are in the adjacent angle that finishes the straight line?

  95. 95.Two lines cross on a site plan in Haymarket and form vertical angles. One of those angles measures 47°. What is the measure of the angle vertically opposite it?

  96. 96.A triangular garden in Berryville has two angles of 48° and 67°. What is the measure of the third angle?

  97. 97.A quadrilateral patio in Pulaski has angles of 80°, 95°, and 110°. What is the measure of the fourth angle?

  98. 98.An isosceles triangle on a banner in Glasgow has a vertex angle of 40°. What is the measure of each base angle?

  99. 99.Two adjacent angles lie on a straight beam in a barn in Madison County, Virginia. One measures 58°. What is the other angle, in degrees?

  100. 100.A right triangle in a roof sketch in Gordonsville has one acute angle of 35°. What is the other acute angle?

  101. 101.Angles around a point on a compass rose in a museum in Kilmarnock measure 90°, 80°, 70°, and x°. A full turn measures 360°. What is x?

  102. 102.A parallelogram sketched for a quilt in Floyd County has one angle of 72°. What is the measure of a consecutive angle?

  103. 103.A bag at a fair in Chesterfield holds 3 red tokens, 5 blue tokens, and 2 green tokens. One token is drawn at random. What is the probability that it is blue?

  104. 104.A forecast for Tappahannock gives a probability of 0.35 that rain will fall. What is the probability that rain will not fall?

  105. 105.A student in Hopewell flips a fair coin and rolls a fair six-sided number cube. What is the probability of heads and a 4 on the same trial?

  106. 106.A spinner at a booth in Galax was spun 40 times and landed on red 10 times. What is the experimental probability of red?

  107. 107.A jar in a classroom in South Boston, Virginia, holds 4 apple stickers and 6 pear stickers. Two stickers are drawn at random without putting the first one back. What is the probability that both are apple stickers?

  108. 108.A cafe in Onancock offers 3 muffin flavors and 4 drink sizes. How many different muffin-and-drink pairs can a customer choose?