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Pennsylvania System of School Assessment Mathematics Grade 6

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

These questions are original. This is not an official Pennsylvania System of School Assessment test, and FreeExam is not affiliated with the Pennsylvania Department of Education.

  1. 1.A Reading market stand sells 18 soft pretzels for $9. What is the price of one pretzel?

  2. 2.On the Three Rivers Heritage Trail in Pittsburgh, Nia rides 12 miles in 2 hours and Omar rides 15 miles in 3 hours. Who has the greater speed?

  3. 3.Five matching baskets at a Lancaster orchard stand hold 40 apples altogether. How many apples are in each basket?

  4. 4.For a waterfront mural in Erie, 3 gallons of paint cover 2 panels. How many gallons cover 10 panels at that same rate?

  5. 5.Jonah times a walk beside the Susquehanna in Harrisburg and covers 6 blocks in 18 minutes without stopping. How many minutes does one block take?

  6. 6.A Scranton hiking shop blends 2 cups of nuts with 5 cups of dried fruit. How many cups of dried fruit should be mixed with 8 cups of nuts?

  7. 7.Gift bags at a Bethlehem craft table use 4 yards of ribbon for every 3 bags. Which pairing keeps that same ratio?

  8. 8.A school bus serving York travels 84 miles on 6 gallons of fuel. How many miles does the bus travel per gallon?

  9. 9.An Allentown cafeteria chart shows 2 cups of broth with 7 cups of vegetables, and 4 cups of broth with 14 cups of vegetables. How many cups of broth go with 21 cups of vegetables?

  10. 10.Four student tickets at a Gettysburg museum desk cost $28 altogether. What is the price of one student ticket?

  11. 11.A batch of 24 cocoa squares at a Hershey shop includes 9 dark squares, and the rest are milk squares. What is the ratio of dark squares to milk squares in simplest form?

  12. 12.At a track in State College, a runner finishes 5 laps in 20 minutes and keeps that pace. How many laps does the runner finish in 36 minutes?

  13. 13.A bookstore on Market Street in Philadelphia marks a $40 atlas down by 15%. How many dollars is the discount?

  14. 14.In a Reading school club, 30 of the 120 members walk to school. What percent of the members walk?

  15. 15.A diner in Pittsburgh adds a 20% service charge to a $45 meal. What is the total bill, including the charge?

  16. 16.On a Harrisburg quiz, a student answered 18 of 20 items correctly. What percent of the items were correct?

  17. 17.A Lancaster farm stand adds 6% sales tax to a $50 basket. How many dollars is the tax?

  18. 18.An Erie auditorium has 200 seats, and 150 of them are filled. What percent of the seats are filled?

  19. 19.A Scranton class has raised $80 toward a $200 field-trip goal. What percent of the goal has been raised?

  20. 20.A juice bottle in an Allentown cafeteria is 25% apple juice. How many ounces of apple juice are in a 16-ounce bottle?

  21. 21.A sewing class in Wilkes-Barre has 3/4 yard of fabric and cuts it into pieces that are each 1/8 yard long. How many pieces does that make?

  22. 22.A shop in Chester has 2/3 gallon of paint, and each classroom door needs 1/12 gallon. How many doors can be painted?

  23. 23.A crew near Lebanon is marking 3 1/2 miles of trail in sections of 1/2 mile. How many sections is that?

  24. 24.A cook in Easton has 2/3 cup of stock and uses 1/6 cup for each bowl. How many bowls can be seasoned?

  25. 25.A club in Altoona has 9/4 feet of cord and cuts pieces that are each 3/4 foot long. How many pieces result?

  26. 26.A market in Johnstown splits 5/2 pounds of cheese equally among 4 sandwiches. How much cheese does each sandwich get?

  27. 27.A garden row in Williamsport is 4/5 meter long and is planted in equal parts of 1/10 meter. How many parts fit in the row?

  28. 28.A stand in the Poconos has 8/3 liters of cider and serves cups of 2/3 liter. How many full cups can be served?

  29. 29.A clerk in Philadelphia adds a receipt of $12.45 to a receipt of $7.80. What is the sum?

  30. 30.A bridge-toll fund in Pittsburgh starts at $56.30 and then spends $18.75. How much money remains?

  31. 31.A print shop in Harrisburg charges $3.25 for each poster and prints 14 posters. What is the total cost?

  32. 32.A Reading co-op splits a $93.60 produce bill equally among 8 families. How much does each family pay?

  33. 33.A boathouse in Erie sells 2.4 meters of rope at $6.50 per meter. What is the cost of that rope?

  34. 34.A farmer’s ledger in Lancaster shows $104.08. After a refund of $26.49 is subtracted, what is the new balance?

  35. 35.A workshop in Bethlehem cuts 7.2 meters of trim into pieces that are 0.6 meter long. How many pieces are cut?

  36. 36.Three supply orders for a lab in Wilkes-Barre cost $8.06, $14.70, and $5.25. What is the total cost?

  37. 37.A cafe in Scranton sells 16 muffins at $1.75 each. What is the total price?

  38. 38.A measured stretch of the Schuylkill River Trail is 13.44 miles and is marked in equal segments of 0.32 mile. How many segments is that?

  39. 39.A State College club has 18 markers and 24 posters to pack into identical kits, using every item. What is the greatest number of kits the club can make?

  40. 40.Two tour groups in Gettysburg leave the gate together. One group comes back every 6 minutes, and the other comes back every 8 minutes. What is the soonest time, in minutes, when both groups are at the gate again?

  41. 41.A Hershey pantry has 36 cocoa packets and 48 sugar packets. What is the greatest common factor of 36 and 48?

  42. 42.From a Philadelphia dock, a ferry departs every 9 minutes and a shuttle departs every 12 minutes. They depart together at noon. What is the soonest time, in minutes after noon, when they next depart together?

  43. 43.A band room in Pittsburgh has 28 drumsticks and 42 music folders. What is the greatest common factor of 28 and 42?

  44. 44.In Harrisburg, a bell rings every 10 minutes and a clock chimes every 15 minutes. They sound together at 1:00. How many minutes later do they next sound together?

  45. 45.A Reading library is packing 45 bookmarks and 60 pencils into the greatest possible number of equal bundles, using every item. How many bundles is that?

  46. 46.Harbor staff in Erie inspect one boat every 8 days and another boat every 12 days. Both boats were inspected today. What is the smallest number of days until both are inspected on the same day again?

  47. 47.At dawn in the Poconos the temperature is −7°C. By noon it has risen 12 degrees. What is the noon temperature?

  48. 48.A trail marker near the Allegheny River is at an elevation of 40 meters. A cave entrance is 65 meters lower. What is the elevation of the cave entrance?

  49. 49.A student account in Philadelphia shows a balance of −$14. After a deposit of $30, what is the new balance?

  50. 50.The temperature in Erie is −3°F and then falls another 8 degrees. What is the new temperature?

  51. 51.A mine elevator in Scranton is at −40 feet, using ground level as 0, and then rises 55 feet. What is its height then?

  52. 52.A club ledger in Johnstown shows −$23. The club then spends another $9. What is the new balance?

  53. 53.Which of these temperatures on a Harrisburg weather chart is the highest?

  54. 54.A Lancaster scoreboard shows a point change of −18. What is the opposite of −18?

  55. 55.A Pittsburgh sensor reads −13 degrees from its set point. What is the absolute value of −13?

  56. 56.A subway entrance in Philadelphia is 8 feet below street level, recorded as −8. How many feet is the entrance from street level?

  57. 57.A State College lab compares the values −17 and 12. Which value has the greater absolute value?

  58. 58.A York hiking log records elevation changes of −6 meters and 4 meters. What is the sum of the absolute values of those changes?

  59. 59.The temperature in Bethlehem changes from −4°C to 7°C. What is the absolute value of that change?

  60. 60.Which statement is true about the number line posted in an Allentown classroom?

  61. 61.A map of Harrisburg places a fountain at the point (4, −3). In which quadrant is that point?

  62. 62.A park map in Philadelphia places a statue at (−6, 2). In which quadrant is that point?

  63. 63.A bridge point on a Pittsburgh grid is (5, −2). What is the reflection of that point across the x-axis?

  64. 64.A buoy on an Erie harbor chart is plotted at (0, −7). How many units is the buoy from the origin?

  65. 65.Which point lies in Quadrant III on a town grid used in Reading?

  66. 66.On a Lancaster farm grid, a barn is 3 units left of the origin and 8 units up. Which ordered pair names the barn?

  67. 67.On a Scranton coordinate grid, a library is at (2, 5) and a school is at (2, −3). What is the distance between them?

  68. 68.A marker on a York map is at (−4, 9). Which point is the same distance from the y-axis, on the opposite side, with the same y-coordinate?

  69. 69.A clerk in Philadelphia evaluates 4 × (7 + 3) − 5. What is the value?

  70. 70.The expression 3n + 8 gives the cost, in dollars, of n posters at a Pittsburgh shop, including an $8 setup fee. What is the cost when n = 5?

  71. 71.Students in Harrisburg evaluate 18 − 6 ÷ 2 + 1. What is the value?

  72. 72.A Reading orchard charges $2 for each peck of apples and adds a $5 basket fee. Which expression gives the cost of p pecks?

  73. 73.Which expression is equivalent to 4(y + 6) for a supply order in Erie?

  74. 74.A Lancaster seed count is given by 5(12 − 4) + 7. What is the value?

  75. 75.An Allentown tutoring group simplifies 9k + 4 + 2k. Which expression is equivalent?

  76. 76.The expression 20 − 3m gives the tickets left after selling m bundles of 3 at a Bethlehem booth. How many tickets are left when m = 4?

  77. 77.Which expression is equivalent to 12x + 18 on a Scranton inventory list?

  78. 78.A York puzzle score is 2[15 − (3 × 4)] + 1. What is the value?

  79. 79.Solve n + 14 = 31 for the number of extra seats needed in a Philadelphia hall.

  80. 80.Solve w − 9 = 22 for the width, in feet, of a Pittsburgh stage panel.

  81. 81.Solve 6t = 54 for the number of tables in a Harrisburg cafeteria plan.

  82. 82.Solve p ÷ 5 = 7 for the number of pencils in a Reading supply box.

  83. 83.Solve x + (−8) = 5 for a temperature change recorded in Erie.

  84. 84.Solve (3/4)y = 12 for the yards of fabric in a Lancaster sewing project.

  85. 85.Solve m + 2.5 = 9.0 for the mass, in kilograms, added in a State College lab.

  86. 86.Solve 48 = 8k for the number of visitors in each equal group on a Gettysburg tour.

  87. 87.Gardeners in Hershey rope off a triangle of lawn with a 10-meter base and a height of 6 meters. What is the area inside the rope?

  88. 88.A parallelogram banner in Philadelphia has a base of 9 feet and a corresponding height of 4 feet. What is its area?

  89. 89.A model sail made in Pittsburgh is a triangle with a 14-inch base and a height of 5 inches. What is the area of the sail?

  90. 90.A trapezoidal path sign in Harrisburg has parallel sides of 8 centimeters and 12 centimeters and a height of 5 centimeters. What is its area?

  91. 91.A Reading courtyard is made of a 6 meter by 4 meter rectangle joined to a 3 meter by 2 meter rectangle, with no overlap. What is the total area?

  92. 92.A right-triangle pennant in Erie has legs of 8 feet and 9 feet. What is its area?

  93. 93.A Lancaster plot is a rectangle 11 yards by 4 yards with a right triangle of base 4 yards and height 3 yards attached along one 4-yard side, without overlap. What is the total area?

  94. 94.A Scranton kite is made of two matching triangles. Each triangle has a base of 12 centimeters and a height of 5 centimeters. What is the total area of the kite?

  95. 95.Packers in Allentown fill a crate 5 feet long, 3 feet wide, and 4 feet high. The crate is a right rectangular prism. What is its volume?

  96. 96.A net for a right rectangular prism box in Bethlehem has two faces that are 6 cm by 2 cm, two faces that are 6 cm by 3 cm, and two faces that are 2 cm by 3 cm. What is the surface area?

  97. 97.A York classroom built a soil planter 4 inches long, 2.5 inches wide, and 3 inches tall, shaped as a right rectangular prism. How many cubic inches of soil fill it to the top?

  98. 98.A narrow case on Market Street in Philadelphia is 10 inches long, 1 inch deep, and 4 inches tall. What is the surface area of this right rectangular prism?

  99. 99.Warehouse staff in Pittsburgh store equipment in a bin 8 meters long, 2 meters from front to back, and 6 meters high. What is the volume of this right rectangular prism?

  100. 100.A hallway locker in Harrisburg stands 5 feet tall, is 2 feet wide, and is 1 foot deep. What is the surface area of the locker if it is a right rectangular prism?

  101. 101.A Reading park sandbox is 9 feet long and 4 feet deep, but only 1/2 foot from front to back. What is the volume of this right rectangular prism?

  102. 102.Before a festival, an Erie shop wraps a box 7 cm long, 7 cm wide, and 2 cm high. What is the surface area of this right rectangular prism?

  103. 103.Which of these is a statistical question about a sixth-grade class in Lancaster?

  104. 104.The numbers of whoopie pies sold at a Hershey stand on five days were 4, 6, 8, 5, and 7. What is the mean?

  105. 105.The heights, in inches, of six seedlings in Scranton are 3, 9, 4, 7, 5, and 8. What is the median?

  106. 106.The numbers of library visits by a York club were 2, 5, 2, 4, 2, and 6. What is the mode?

  107. 107.A Pittsburgh relay team records lap times, in minutes, of 11, 13, 10, and 14. What is the mean time?

  108. 108.The daily high temperatures, in degrees Fahrenheit, recorded in Philadelphia for five days were 61, 70, 64, 68, and 63. What is the median?