FreeExam

New York State Testing Program Mathematics Grade 6

Ratios, rates, percents, expressions, equations, and area.

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 Brooklyn bakery sells 20 bagels for $15. What is the price of one bagel?

  2. 2.During four steady hours, the Staten Island Ferry carries 6,000 passengers. How many passengers is that per hour?

  3. 3.A Hudson Valley orchard blends apple cider and pear juice in the ratio 5:3. A pitcher holds 24 cups of the blend. How many cups are apple cider?

  4. 4.A hiker on an Adirondack trail walks 9 miles in 3 hours at a steady pace. How far does the hiker walk in 5 hours at that pace?

  5. 5.A Buffalo pizzeria uses 2 cups of sauce for 6 slices. Which pairing of cups to slices uses the same ratio?

  6. 6.A bakery in Astoria packs 48 cookies into 6 boxes with the same number in each box. How many cookies are in one box?

  7. 7.One Metro-North run covers 120 miles in 2 hours. Another covers 150 miles in 3 hours. Which comparison of their unit rates is correct?

  8. 8.A school bus kept in Yonkers travels 84 miles on 6 gallons of fuel. How many miles does it travel per gallon?

  9. 9.On a scale drawing of a Rochester bridge, 1 inch stands for 7 feet. How many inches show a tower that is 35 feet tall?

  10. 10.At a festival booth in Ithaca, 21 of the 60 cups poured in one hour are hot cider. What percent of the cups are hot cider?

  11. 11.A shop in Saratoga Springs takes 20% off a $45 wool hat. How many dollars are taken off the price?

  12. 12.Of the 80 singers at a concert in Troy, 16 are sixth graders. What percent of the singers are sixth graders?

  13. 13.A science museum in Albany adds a 5% materials fee to a $30 workshop ticket. What is the fee in dollars?

  14. 14.In a Bronx survey, 48 of 160 students ride the bus to school. What percent of the students ride the bus?

  15. 15.A team store in Buffalo discounts a $56 jersey by 25%. What is the sale price?

  16. 16.A robotics club in Schenectady has collected $45 toward a $90 goal. What percent of the goal has been collected?

  17. 17.A weather notebook in Watertown lists 9 snow days out of 25 school days. What percent of those school days are snow days?

  18. 18.In a Harlem art room, a ribbon 3/4 yard long is cut into pieces that are each 1/8 yard long. How many pieces does that make?

  19. 19.Six mural artists in Buffalo split 3/4 gallon of paint equally. How much paint does each artist receive?

  20. 20.A lunchroom pitcher in Queens holds 5/2 liters of juice. Each cup holds 1/4 liter. How many full cups can be poured?

  21. 21.A gardener in the Catskills sets out 9/2 pounds of seed, using 3/4 pound in each row. How many rows receive seed?

  22. 22.A woodshop in Troy cuts pegs that are 1/8 foot long from a board that is 7/8 foot long. How many pegs does the board yield?

  23. 23.An Albany kitchen has 9/4 cups of soup. Each bowl holds 3/8 cup. How many bowls can be filled?

  24. 24.An art class in Yonkers has 5/6 pound of clay, and each small sculpture uses 1/12 pound. How many sculptures can be made?

  25. 25.Four school clubs in Syracuse share 8/3 yards of banner paper equally. How much paper does each club get?

  26. 26.A deli counter in the Bronx totals $18.46. The customer pays with a $20 bill. How much change is due?

  27. 27.A lumber aisle in Rochester prices pine boards at $3.25 each. A builder buys 8 boards. What is the cost before tax?

  28. 28.A cafeteria in White Plains opens 12.6 liters of milk and pours it evenly into 6 pitchers. How many liters go into each pitcher?

  29. 29.At Niagara Falls, three friends spend $4.85, $3.20, and $6.15 on snacks. What is the combined cost?

  30. 30.A runner at the Central Park reservoir covers 5.8 kilometers in the morning and 3.45 kilometers later. How much longer is the morning run?

  31. 31.A fabric shop in Manhattan charges $7.40 per yard. A customer buys 2.5 yards. What is the charge?

  32. 32.Four classmates from Utica share a $23.60 planetarium fee equally. How much does each classmate pay?

  33. 33.Two crates at a market in Syracuse weigh 15.75 pounds and 9.4 pounds. What is their total weight?

  34. 34.A market in Queens has 36 apples and 48 pears. They are packed into the greatest number of identical boxes with none left over. How many boxes is that?

  35. 35.A tower clock in Albany sounds one pattern every 6 minutes and another every 8 minutes. After they sound together, how long until they sound together again?

  36. 36.At a field day in Yonkers, 27 runners and 36 volunteers are each grouped into squads of the greatest equal size with nobody left out. What is that squad size?

  37. 37.Ribbon rolls in Ithaca measure 30 inches and 45 inches. Both are cut into the longest equal pieces with nothing left over. How long is each piece?

  38. 38.Holiday lights in Saratoga Springs blink every 9 seconds on one block and every 12 seconds on the next. How many seconds pass between blinks that happen together?

  39. 39.A Staten Island schedule lists minutes past the hour. Which of these times is a common multiple of 5 and 6?

  40. 40.From a station in Rochester, one bus leaves every 10 minutes and another every 15 minutes. After they leave together, when do they leave together again?

  41. 41.A warehouse in Schenectady has stacks of 16 small cartons and 40 large cartons. What is the greatest number that divides both stack counts?

  42. 42.At dawn in Lake Placid the temperature is −4°F. By noon it has risen 11 degrees. What is the noon temperature?

  43. 43.One January morning, Albany is −2°C and Binghamton is −7°C. Which comparison is correct?

  44. 44.A garage elevator in Manhattan is on floor 2, with street level labeled 0. It goes down 5 floors. Which integer names the floor it reaches?

  45. 45.A student club in Buffalo has a balance of −$12. A $30 deposit arrives. What is the new balance?

  46. 46.On a Catskill trail, a sign is 40 feet above a stream and a cave mouth is 15 feet below it. How many feet apart are the sign and the cave mouth?

  47. 47.A quiz bowl team in Syracuse has 6 points when a 10-point penalty is applied. What is the score after the penalty?

  48. 48.A model submarine in a Brooklyn aquarium tank sits at −18 feet and then rises 7 feet. What is its new position?

  49. 49.Tide readings along the Hudson are 3, −5, −1, and 0. Which list orders them from least to greatest?

  50. 50.A lab in Ithaca records temperature changes of −8 degrees and 5 degrees. Which statement is true?

  51. 51.A trail marker in the Adirondacks shows an elevation change of −42 meters from a zero point. How many meters is the marker from that zero point?

  52. 52.On a number line in a Harlem classroom, which value is 6 units from 0?

  53. 53.A dock log in Nyack records one tide at −2 feet and a later tide at 7 feet. What is the sum of the absolute values of those readings?

  54. 54.The low temperature in Plattsburgh is −9°C and the high is 4°C. How many degrees apart are those temperatures?

  55. 55.A club ledger in Troy shows a balance of −15 dollars. What is the absolute value of that balance?

  56. 56.A science class in Queens compares the distances |−3|, |8|, and |−1|. Which list orders them from least to greatest?

  57. 57.A math club game in Manhattan shows a change of 11 points and a change of −6 points. What is the absolute value of the difference of those changes?

  58. 58.On a coordinate grid of a Syracuse campus, which point lies in Quadrant II?

  59. 59.On a downtown Albany grid, a library is at (−5, 2). How is that point reached from the origin?

  60. 60.From (−1, 2) on a Peekskill schoolyard grid, a student moves 3 units right and 2 units down. Where does the student stop?

  61. 61.A Brooklyn park map places a fountain at the origin. The carousel is plotted at (4, −3). In which quadrant is the carousel?

  62. 62.A trail map near Slide Mountain plots a shelter at (−8, −1). In which quadrant is the shelter?

  63. 63.A coordinate sketch of the Erie Canal includes these points. Which point lies on the x-axis?

  64. 64.At a fair in New Paltz, booth A is at (−2, 5) and booth B is at (7, 5). What is the distance between the booths?

  65. 65.Two buoys on a Long Island Sound chart are at (2, −4) and (2, 6). What is the distance between the buoys?

  66. 66.A stand at Coney Island sells bags of popcorn for $3 and adds a $2 tray fee to the order. Which expression is the cost of n bags?

  67. 67.A puzzle card at the Rochester library asks for the value of 2³ + 4 × 2. What is that value?

  68. 68.A scoreboard drill in a Queens gym asks for the value of 4 + 6 × 3 − 5. What is that value?

  69. 69.An exhibit card at a museum in Manhattan asks for the value of 3(8 − 2) + 4². What is that value?

  70. 70.A bike-club formula in Ithaca is written 7x + 3 + 2x − 1. Which expression is equivalent?

  71. 71.A garden sketch in the Hudson Valley uses the expression 12y + 8. Which expression is equivalent?

  72. 72.A charter boat leaving Staten Island charges $6 for each passenger and then takes $4 off the whole bill. Which expression is the cost for p passengers?

  73. 73.A teacher in Albany writes 5(n + 4) on the board. Which expression is equivalent?

  74. 74.A Brooklyn bakery prices an order with 2a + 5b, where a is the number of apple turnovers and b is the number of berry muffins. What is the cost when a = 3 and b = 4?

  75. 75.A shop in New Rochelle uses x + 9 = 24 to find how many stickers were in a box before 9 more made 24. What is x?

  76. 76.A theater in Poughkeepsie solves 4n = 28 to find how many $4 tickets bring in $28. What is n?

  77. 77.Campers near Lake George write m ÷ 6 = 5 for a stack of trail maps. What is m?

  78. 78.A weather club in Buffalo writes t − 8 = −3 for a morning temperature. What is t?

  79. 79.A craft table in Kingston uses 7w = 56 to find how many weeks a ribbon supply lasts. What is w?

  80. 80.A student in the Bronx solves s + 15 = 42 to find a starting savings amount. What is s?

  81. 81.A science class in Oswego writes d + 6 = −2 for a depth model. What is d?

  82. 82.A bakery in Elmira uses n ÷ 3 = 8 to find how many rolls were baked when they were packed 3 to a bag into 8 bags. What is n?

  83. 83.The triangular sail on a model boat at a Hudson marina has a base of 10 inches and a height of 6 inches. What is the area of the sail?

  84. 84.A gym pennant in Syracuse is a triangle with base 14 centimeters and height 9 centimeters. What is its area?

  85. 85.Gardeners in Prospect Park outline a triangular flower bed with base 8 meters and height 5 meters. What is the area of the bed?

  86. 86.A community garden plot in the Bronx is a parallelogram with base 12 feet and height 7 feet. What is its area?

  87. 87.A small outdoor stage in Hudson is a trapezoid with parallel sides of 10 feet and 6 feet and a height of 4 feet. What is its area?

  88. 88.A playground sign in Rochester joins a rectangle 8 inches by 5 inches to a triangle with base 8 inches and height 4 inches. What is the total area?

  89. 89.A trail arrow in the Catskills is a 6-centimeter by 4-centimeter rectangle joined to a triangle with base 4 centimeters and height 3 centimeters. What is the area of the arrow?

  90. 90.A model road sign in a White Plains classroom is a triangle with base 12 centimeters and height 8 centimeters. What is the area of the model?

  91. 91.A corner lot in Newburgh is a rectangle 15 yards by 10 yards. Inside it, a right triangular garden has base 6 yards and height 5 yards. What is the area of the lot outside the garden?

  92. 92.A shipping crate in Red Hook, Brooklyn, is a right rectangular prism 5 feet long, 3 feet wide, and 2 feet high. What is its volume?

  93. 93.A gym locker in Albany is a right rectangular prism 1.5 feet wide, 2 feet deep, and 4 feet tall. What is its volume?

  94. 94.A gift box in a Manhattan shop is a right rectangular prism 10 centimeters long, 4 centimeters wide, and 3 centimeters high. What is its surface area?

  95. 95.A sandbox in a Queens schoolyard is a right rectangular prism 8 feet long, 4 feet wide, and 1 foot deep. How many cubic feet of sand fill it to the top?

  96. 96.A cooler used on a Staten Island beach is a right rectangular prism 6 inches by 4 inches by 5 inches. What is its surface area?

  97. 97.A carton of books in a Rochester library is a right rectangular prism 12 inches long, 9 inches wide, and 8 inches high. What is its volume?

  98. 98.A window planter in Ithaca is a right rectangular prism 5 inches long, 5 inches wide, and 2 inches high, closed on all six faces. What is its surface area?

  99. 99.An aquarium tank in Buffalo is a right rectangular prism 20 inches long, 10 inches wide, and 12 inches high. What is its volume?

  100. 100.Which of these is a statistical question about people at a subway stop in Brooklyn?

  101. 101.Five students in Albany read 12, 15, 9, 18, and 11 pages. What is the mean number of pages?

  102. 102.A class in Syracuse records morning temperatures of 2°C, 7°C, 4°C, 9°C, and 5°C. What is the median?

  103. 103.A soccer team in Rochester scores 1, 3, 2, 3, 0, and 3 goals in six games. What is the mode?

  104. 104.Four bike rides on Long Island measure 8, 11, 6, and 15 miles. What is the mean distance?

  105. 105.Six pretzel sales at a stand in Manhattan are 4, 9, 6, 2, 7, and 10 pretzels. What is the median?

  106. 106.Which of these is not a statistical question about a school in Yonkers?

  107. 107.A club in Utica records weekly balances of $4, $10, $7, and $3. What is the mean balance?

  108. 108.The ages of volunteers at a library in New Rochelle are 12, 14, 12, 15, and 17. Which measure of center equals 12?