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New York State Testing Program Mathematics Grade 7

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

These questions are original. This is not an official New York State Testing Program test, and FreeExam is not affiliated with the New York State Education Department.

  1. 1.A bakery on Elmwood Avenue in Buffalo uses 12 cups of flour for 8 loaves of rye. How many cups of flour does each loaf use?

  2. 2.Ticket sales at a booth at the New York State Fair in Syracuse stay proportional to the hours the booth is open. The booth sells 45 tickets in 3 hours. What is the constant of proportionality, in tickets per hour?

  3. 3.A cyclist circles the loop in Prospect Park and covers 9 miles in 45 minutes. What is the speed in miles per hour?

  4. 4.A coach leaving Albany goes 84 miles on 6 gallons of fuel. A coach leaving Rochester goes 90 miles on 5 gallons. How many more miles per gallon does the Rochester coach get?

  5. 5.A deli in Astoria charges the same price for every sandwich. Five sandwiches cost $32.50. What is the cost of 8 sandwiches?

  6. 6.Painters of a mural in the Bronx use 2 cans of paint for every 5 square yards of wall. How many cans are needed for 35 square yards?

  7. 7.A graph of a Hudson River current study is a straight line through the origin and the point (4, 10). Which equation matches that proportional relationship?

  8. 8.A breakfast stand in Ithaca pours 3/4 cup of maple syrup over 6 pancakes, using the same amount on each one. How much syrup is on each pancake?

  9. 9.A plow crew in Plattsburgh clears 2.4 miles of street every 20 minutes and keeps that rate. How many miles does the crew clear in 2 hours?

  10. 10.Last summer a boardwalk ride at Coney Island cost $16. This summer the same ride costs $20. What is the percent increase?

  11. 11.A shop in White Plains marks an $80 jacket down by 15%. What is the sale price?

  12. 12.Lunch in Saratoga Springs costs $36 before an 8% sales tax. What is the total after tax?

  13. 13.A student estimates a lighthouse near Montauk to be 90 feet tall. The measured height is 75 feet. What is the percent error of the estimate?

  14. 14.A family in Brooklyn leaves a 20% tip on a dinner bill of $47.50. How much is the tip alone?

  15. 15.After a 25% increase, a Hudson River ferry fare is $15. What was the fare before the increase?

  16. 16.A student in Rochester deposits $400 in an account that pays 3% simple interest each year. How much interest is earned in 2 years?

  17. 17.A wildlife center near the Adirondacks counts 250 animals in June and 200 in September. What is the percent decrease?

  18. 18.A tour guide at Niagara Falls earns a 12% commission on $650 of ticket sales. How much is the commission?

  19. 19.At dawn in Lake Placid the temperature is -8°F. By noon it has risen 15 degrees. What is the noon temperature?

  20. 20.A trail above a creek at Watkins Glen starts 40 feet higher than the creek and then drops 65 feet. Where is the end of that drop, relative to the creek?

  21. 21.A club account in Albany shows a balance of -$12.50. A deposit of $40.75 is recorded next. What is the new balance?

  22. 22.One afternoon it is 6°F in Buffalo and -9°F in a town farther inland. How many degrees warmer is Buffalo?

  23. 23.A cook in Queens changes a soup recipe by -2/3 cup and then by another -1/6 cup. What is the combined change?

  24. 24.A model submarine in a Buffalo museum moves from a depth of -2.4 meters to a depth of -5.1 meters. What is the change in position?

  25. 25.A bridge sensor in Syracuse starts from a reading of -7.8 and then subtracts 4.2. What is the result?

  26. 26.A cider press in the Finger Lakes changes its stock by -3 1/2 gallons and later by +1 1/4 gallons. What is the net change?

  27. 27.Along a delivery route in the Bronx, the elevation changes by -18 feet, then +11 feet, then -5 feet. What is the net change?

  28. 28.A science class in Troy multiplies the signed factors -6, -4, and -1/2. What is the product?

  29. 29.A boat on Lake George changes position by -3.6 meters during 0.9 hour. What is the average change in meters per hour?

  30. 30.A chef in Manhattan computes (-2/5) ÷ (4/15) while resizing a stock recipe. What is the quotient?

  31. 31.A quiz in Schenectady applies a change of -1.25 points, and that same change happens 8 times. What is the total change?

  32. 32.A tank at a dairy in Utica changes by -18 liters in all. Each pouring changes the tank by -3/4 liter. How many pourings were made?

  33. 33.A wind study on Long Island uses the signed factors -0.4 and -2.5. What is their product?

  34. 34.A land plan in the Catskills multiplies 7/8 acre by -4/7. What is the product?

  35. 35.An elevator in a Manhattan tower changes position by -45 feet in 1.5 minutes. What is the average change in feet per minute?

  36. 36.A fabric shop in Brooklyn multiplies -2 1/2 yards by 1 1/5. What is the product?

  37. 37.The width, in feet, of a concert stage in Albany satisfies 4(x − 3) = 20. What is x?

  38. 38.A contractor in Poughkeepsie simplifies 6x − 4 + 2x + 9, where x is a length in feet. Which expression is equivalent?

  39. 39.The equation (2/3)x = 12 gives the number of crates, x, loaded at a dock in Red Hook. What is x?

  40. 40.A set designer in Harlem expands -3(2y − 5) to find a signed length. Which expression is equivalent?

  41. 41.A balance scale at a market in Flushing is modeled by 5x + 7 = 3x + 19. What is x?

  42. 42.A lab notebook in Ithaca asks for the value of 3(n − 4) + 2n when n = -2. What is that value?

  43. 43.The equation -2x + 9 = 1 gives the setting x on a thermostat in a school in Binghamton. What is x?

  44. 44.The length of a rectangular garden in Saratoga Springs is 4 feet more than twice its width. The perimeter is 44 feet. What is the width?

  45. 45.A workshop in Troy simplifies (1/2)(8x − 6) − 3x. Which expression is equivalent?

  46. 46.A trivia team in Yonkers has a signed score x. After a 7-point bonus, the score must be greater than 2. Which inequality describes every allowed value of x?

  47. 47.A marina on the Hudson posts the wind limit -3x ≤ 18, where x is a signed speed index. Which inequality describes x?

  48. 48.A loading dock in Hempstead allows a pallet count x only when 4x − 1 < 11. Which value of x satisfies the inequality?

  49. 49.A canoe on the Erie Canal can carry at most 180 pounds. Supplies already aboard weigh 45 pounds, and each paddler's gear weighs 15 pounds. What is the greatest whole number of paddlers?

  50. 50.A banner length, in feet, for a parade in Albany must satisfy 2(x − 4) ≥ 10. Which inequality describes x?

  51. 51.A museum in Cooperstown charges $6 to enter and $2 for each exhibit hall. A student can spend at most $20. What is the greatest number of halls the student can visit?

  52. 52.A depth gauge on the Hudson satisfies -x/4 < 3, where x is a signed reading. Which inequality describes x?

  53. 53.A school fundraiser in Queens already has $80. Each raffle ticket adds $15, and the team needs more than $250. What is the smallest whole number of tickets that meets the goal?

  54. 54.A cold-storage room in Buffalo may be used only while 7 − 2x > 15, where x is the control setting. Which inequality describes x?

  55. 55.On a Hudson Valley map, 1 inch represents 8 miles. A trail is 3.5 inches on the map. How long is the trail?

  56. 56.On a scale drawing of a classroom in White Plains, 1 centimeter represents 2.5 meters. A wall is 6 centimeters on the drawing. What is the actual length of the wall?

  57. 57.A floor plan of a library in New Rochelle shows a reading room 4.5 inches long. The room is actually 18 feet long. What is the scale factor from the plan to the room when both lengths are in inches?

  58. 58.On a scale drawing, a rectangular community garden in Harlem is 2 inches by 3 inches. The scale is 1 inch = 4 feet. What is the actual area of the garden?

  59. 59.On a trail map of the Adirondacks, 1 inch represents 12 miles. A hike is 30 miles long. How long is the hike on the map?

  60. 60.Two towns on a Long Island map are 5.25 inches apart. The scale is 1 inch = 6 miles. What is the actual distance between the towns?

  61. 61.A museum in Syracuse displays a model car built at a scale of 1:16. The model is 9.5 inches long. What is the actual length the model represents?

  62. 62.A drawing of a barn in the Finger Lakes is 7 centimeters long, and the barn is 28 meters long. How many meters does 1 centimeter on the drawing represent?

  63. 63.A scale drawing of a sailboat sail in Nyack has an area of 6 square inches. On the drawing, 1 inch represents 3 feet. What is the actual area of the sail?

  64. 64.A circular fountain in Washington Square Park has a radius of 5 feet. Using 3.14 for π, what is the circumference?

  65. 65.A circular stage at Cadman Plaza in Brooklyn has a radius of 4 meters. Using 3.14 for π, what is the area of the stage?

  66. 66.A round pizza at a shop in the Bronx has a diameter of 18 inches. Leave the circumference in terms of π. What is it?

  67. 67.A circular window in a chapel in Albany has a radius of 7 centimeters. Leave the area in terms of π. What is it?

  68. 68.A running loop around a pond in Central Park has a circumference of 62.8 meters. Using 3.14 for π, what is the radius of the loop?

  69. 69.A garden bed in Buffalo is a semicircle with radius 10 feet. Using 3.14 for π, what is the length of the curved edge only?

  70. 70.A circular rug in a Rochester apartment has a diameter of 10 feet. Using 3.14 for π, what is the area of the rug?

  71. 71.One circular plaza at Battery Park has radius 9 feet, and a smaller circle beside it has radius 6 feet. Leave the answer in terms of π. How much longer is the larger circumference?

  72. 72.A circular flower bed at the Brooklyn Botanic Garden has radius 8 feet, and a circular fountain in the center has radius 3 feet. Using 3.14 for π, what is the area of the soil around the fountain?

  73. 73.A window brace in a school in Troy forms a right angle. One of the two angles in that corner measures 28°. What is the other angle?

  74. 74.A straight railing along the Erie Canal makes a straight angle. One of the adjacent angles measures 117°. What is the other adjacent angle?

  75. 75.Two walking paths cross in Union Square and form a 48° angle. What is the measure of the vertical angle opposite that angle?

  76. 76.A triangular garden in Ithaca has two angles of 47° and 68°. What is the third angle?

  77. 77.Two complementary angles appear in a picture frame made in Woodstock. The larger angle is 3 times the smaller angle. What is the smaller angle?

  78. 78.An isosceles triangular flag in Staten Island has a vertex angle of 36°. What is the measure of each base angle?

  79. 79.Two paths cross in Van Cortlandt Park. One of the angles formed measures 125°. What is the measure of an angle adjacent to it?

  80. 80.A right triangular banner in a Syracuse parade has one acute angle of 33°. What is the other acute angle?

  81. 81.A quadrilateral window in a brownstone in Harlem has angles of 80°, 95°, and 110°. What is the fourth angle?

  82. 82.An L-shaped lobby in a museum in Albany is made of a 12-foot by 8-foot rectangle joined, without overlap, to a 5-foot by 4-foot rectangle. What is the total floor area?

  83. 83.A bandshell floor in Forest Park, Queens, is a 15-meter by 6-meter rectangle with a right triangular ramp attached along the 6-meter side. The triangle has height 4 meters. What is the total area?

  84. 84.A team cooler in Buffalo is a rectangular prism 8 inches by 5 inches by 6 inches. What is its volume?

  85. 85.A display pedestal in Cooperstown has a 6-foot by 6-foot by 2-foot base and a 4-foot by 4-foot by 3-foot block on top. What is the total volume?

  86. 86.The side of a shed in the Catskills is a rectangle 10 feet wide and 7 feet tall, topped by a triangle with base 10 feet and height 3 feet. What is the area of that side?

  87. 87.A cheese wedge in a shop in Little Italy is a triangular prism. The triangle has base 8 centimeters and height 5 centimeters, and the prism is 12 centimeters long. What is the volume?

  88. 88.A school courtyard in New Rochelle is a 20-yard by 14-yard rectangle. A garden in the middle is a 12-yard by 8-yard rectangle. What is the area of the paved part around the garden?

  89. 89.A warehouse in Jamaica, Queens, stores a 9-foot by 2-foot by 2-foot box beside a cube that measures 2 feet on each edge. What is the combined volume?

  90. 90.A sign near Niagara Falls is a 10-inch by 6-inch rectangle with a semicircle of radius 5 inches attached along the 10-inch side. Using 3.14 for π, what is the total area of the sign?

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

  92. 92.The forecast probability of rain in Rochester on a given afternoon is 0.35. What is the probability that it does not rain that afternoon?

  93. 93.A student in Queens flips a fair coin and rolls a fair number cube numbered 1 through 6. What is the probability of heads and a 4?

  94. 94.A bag in a classroom in the Bronx holds 4 history cards and 6 science cards. Two cards are drawn at random without replacement. What is the probability that both are history cards?

  95. 95.At a booth in Coney Island, one spinner has 4 equal sections and exactly 1 is marked with a star. A second spinner has 5 equal sections and exactly 2 are marked with a star. The spins are independent. What is the probability that both spinners show a star?

  96. 96.A bike rack at a school in White Plains holds 8 silver bikes, 7 black bikes, and 5 red bikes. A student takes one bike at random. What is the probability that it is not red?

  97. 97.A fair number cube numbered 1 through 6 is rolled once at a game in Albany. What is the probability of rolling a 2 or a 5?

  98. 98.A diner in Manhattan offers 3 soups and 4 sandwiches, and every soup-and-sandwich pair is equally likely to be ordered. What is the probability that the order is tomato soup with the rye sandwich?

  99. 99.A box used in a Bronx classroom holds 5 yellow transit cards and 3 blue transit cards. One yellow card is drawn and not replaced. What is the probability that the next card drawn is blue?

  100. 100.Walkers made up 10 of the 40 students drawn at random from an 800-student high school in Yonkers. About how many students in the school walk?

  101. 101.A net pulled at random from a pond near Lake George held 25 fish, and 8 were trout. About 500 fish live in the pond. About how many of them are trout?

  102. 102.Five Staten Island ferry rides, timed from a random sample, took 18, 22, 20, 16, and 24 minutes. What sample mean estimates a typical ride?

  103. 103.Fifteen of 50 trees selected at random in a 400-tree grove in the Catskills showed a fungus. About how many trees in the grove have the fungus?

  104. 104.A cafe owner in Flushing asks only the 24 customers sitting on the patio, and 18 of them want more outdoor seats. The cafe serves 600 customers that week. Which conclusion is supported?

  105. 105.Four used books in a random handful at a library sale in Ithaca are priced at $6, $9, $7, and $10. What is the mean price of this sample?

  106. 106.Eighteen of 60 visitors chosen at random in Prospect Park had arrived by subway. What percent of visitors does that sample rate suggest?

  107. 107.Herons were 12 of the 40 birds in a random count at Jamaica Bay. Extend that rate to a group of 900 birds. About how many are herons?

  108. 108.Snowfall, in inches, at five randomly chosen upstate New York towns was 7, 11, 8, 10, and 9. What is the mean of this sample?