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Pennsylvania System of School Assessment Mathematics Grade 7

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

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 bakery on Broad Street in Lititz sells soft pretzels at one steady price. Six pretzels cost $9. At that same price, what do 10 pretzels cost?

  2. 2.Last April a bleacher seat for a baseball game at PNC Park in Pittsburgh cost $28. The club raised that price by 15%. What is the new price?

  3. 3.At dawn the temperature along the bayfront in Erie was -8°F. By noon the temperature had risen 13 degrees. What was the noon temperature?

  4. 4.A student investment club in Harrisburg tracks one share that loses $2.50 each day for 6 straight days. What is the total change in the share price?

  5. 5.A parking garage near Station Square in Pittsburgh charges $4 to enter plus $2.50 for every hour. Nora's receipt totals $16.50. For how many hours did she park?

  6. 6.A backpack for a day hike in Ricketts Glen State Park must weigh less than 18 pounds. It already holds 7.5 pounds of water and a map. Which inequality gives every additional weight w, in pounds, that may still be packed?

  7. 7.On a Lancaster County map, 1 inch represents 5 miles. A road is 4.5 inches on the map. How long is the road?

  8. 8.A circular splash basin near the fountain at Point State Park in Pittsburgh has a radius of 9 feet. Using 3.14 for pi, what is the circumference of the basin?

  9. 9.Two painted lines cross at a plaza near the State Capitol in Harrisburg and form a 38° angle. What is the measure of the angle vertical to that 38° angle?

  10. 10.A rectangular flower bed in Fairmount Park is 15 feet long and 9 feet wide. A walkway 2 feet wide surrounds the bed on every side. What is the area of the walkway alone?

  11. 11.A game booth at the Kutztown Folk Festival keeps 4 red tokens, 5 blue tokens, and 3 green tokens in a bag. One token is drawn at random. What is the probability that it is blue?

  12. 12.A principal in Lancaster wants the favorite lunch of all 840 students. She asks the 28 students in a single seventh-grade homeroom. Which statement best describes that sample?

  13. 13.A cyclist on the Schuylkill River Trail holds a steady pace, covering 18 miles in 1.5 hours. How far does the cyclist travel in 4 hours at that pace?

  14. 14.A winter coat at a shop in King of Prussia is marked $80. During a weekend sale the price decreases by 25%. What is the sale price?

  15. 15.A diver at Presque Isle starts on a dock 6 feet above Lake Erie and then descends 17 feet. What is the diver's elevation relative to the lake surface?

  16. 16.A science class in Williamsport computes -3.6 ÷ 0.9 while calibrating a sensor. What is the quotient?

  17. 17.A garden club in West Chester uses the expression -5y + 8 - 2y - 3 for yards of edging still on the spool. Which expression is equivalent?

  18. 18.Volunteers at a food pantry in Hazleton may stay only while 2x - 5 ≤ 11, where x is the number of hours since opening. Which solution shows the permitted values of x?

  19. 19.On a scale drawing of a classroom in Reading, 1 centimeter represents 2 feet. A desk is drawn 3.5 centimeters long. What is the actual length of the desk?

  20. 20.A circular mulch bed at a community garden in Hershey has a diameter of 18 meters. Which expression is the area of the bed, left in terms of pi?

  21. 21.A triangular pennant sewn for a school in Erie has angles of 48° and 67°. What is the measure of the third angle?

  22. 22.A camping tent sold at a shop in the Poconos is a triangular prism. Each triangular end has a base of 8 feet and a height of 3 feet, and the tent is 10 feet long. What is the volume?

  23. 23.In a classroom in West Chester, a student flips a fair coin two times. What is the probability that both flips land on heads?

  24. 24.A biologist nets a random sample of 40 trout in a lake near Ohiopyle and finds that 8 have a healed fin injury. About 500 trout live in the lake. About how many of those 500 would be expected to have the same injury?

  25. 25.A shoofly pie recipe printed for a Lancaster County fair uses 3 cups of molasses for every 8 cups of flour. How many cups of molasses are needed for 20 cups of flour?

  26. 26.The population of a borough near Altoona grew from 2,400 people to 2,640 people. What was the percent increase?

  27. 27.A carpenter in Strasburg records a leftover length, in feet, as 3/4 - 5/6. What is that difference?

  28. 28.Students painting a mural scale in Philadelphia multiply -3/4 by 8/9. What is the product?

  29. 29.A rowing club on the Susquehanna solves x/3 - 4 = 2 to find how many extra oars to borrow. What is the value of x?

  30. 30.A cooling pipe at a chocolate factory in Hershey may run only while -3x ≥ 15. Which inequality gives every permitted value of x?

  31. 31.A model of one section of the State Capitol dome in Harrisburg is built so that 1 inch represents 8 feet. That section of the model is 6.25 inches tall. How tall is the matching section of the actual dome?

  32. 32.A round tomato-pie pan at a bakery in East Passyunk, Philadelphia, has a radius of 6 inches. Using 3.14 for pi, what is the area of the pan?

  33. 33.A timber joint in a Lancaster workshop forms a pair of complementary angles. One of the angles measures 28°. What is the measure of the other angle?

  34. 34.A pool deck in Montgomery County is the L-shaped region left after a 4-meter by 3-meter rectangle is cut from one corner of a 10-meter by 6-meter rectangle. What is the area of the deck?

  35. 35.A number cube labeled 1 through 6 is rolled once in a classroom in Bethlehem. What is the probability of rolling a number greater than 4?

  36. 36.A radio station in Philadelphia invites listeners to call and name a favorite team, then treats the calls as a portrait of every city resident. Of 200 callers, 150 name one particular team. Which statement is best?

  37. 37.A printer in a Harrisburg office produces 84 pages in 6 minutes at a constant rate. How many pages does it produce in 15 minutes?

  38. 38.An orchard near Gettysburg picked 250 bushels of apples one autumn. The next autumn the harvest decreased by 12%. How many bushels were picked the second autumn?

  39. 39.A student account at a credit union in Bethlehem shows a balance of -$35. A paycheck deposit of $52 is posted the same afternoon. What is the new balance?

  40. 40.A recipe card from a market in Lebanon asks for the value of (-5/6) ÷ (2/3). What is that quotient?

  41. 41.The perimeter of a rectangular garden in Chester County is 54 feet, and the length is 15 feet. What is the width?

  42. 42.A ferry on the Delaware River near New Hope can carry at most 40 passengers. There are already 27 people on board. Which inequality describes the number n of additional passengers who may still board?

  43. 43.A floor plan of a house in Media uses the scale 1/4 inch = 1 foot. A living room measures 3 inches on the plan. What is the actual length of that room?

  44. 44.The circular platform of a carousel at a fair in Elysburg has a diameter of 28 feet. Using 3.14 for pi, what is the circumference of the platform?

  45. 45.Two parallel avenues in Philadelphia are cut by one transversal street. A pair of corresponding angles includes an angle of 124°. What is the measure of the other angle in that corresponding pair?

  46. 46.A gift box from a shop in Easton is a rectangular prism 8 inches long, 5 inches wide, and 2 inches high. What is its surface area?

  47. 47.A cooler at a tailgate near Citizens Bank Park holds 6 bottles of water and 4 bottles of juice. One bottle is taken at random and not replaced, then a second bottle is taken. What is the probability that both bottles are juice?

  48. 48.A school district has 600 seventh graders. In a random sample of 50 of them, 18 walk to school. About how many of the 600 seventh graders walk to school?

  49. 49.A kayak rental on Lake Wallenpaupack logs a steady pace: 7 miles in 2 hours, 14 miles in 4 hours, and 21 miles in 6 hours. What is the constant of proportionality in miles per hour?

  50. 50.A bookstore in York charges 6% sales tax. A field guide costs $15 before tax. What is the total cost with tax?

  51. 51.A hiker on the Laurel Highlands Trail gains 180 feet of elevation in the morning and then loses 245 feet in the afternoon. What is the total elevation change for the day?

  52. 52.A weather club in Lock Haven multiplies -2.4 by -1.5 while combining two correction factors. What is the product?

  53. 53.A warehouse in Carlisle labels a stack of bins with the expression 2(4a - 3) - (a + 5). Which expression is equivalent?

  54. 54.A stream gauge near Pine Grove must satisfy -4 < x ≤ -1 before a floodgate drill begins. Which value of x meets that condition?

  55. 55.A model of a covered bridge in Bucks County is built at a scale of 1:40. The model is 9 inches long. How long is the actual bridge?

  56. 56.A circular attic window in a stone house in Doylestown has a radius of 7 feet. Which expression is the circumference, left in terms of pi?

  57. 57.An isosceles triangle on a quilt from a Berks County fair has a vertex angle of 40°. The two base angles are equal. What is the measure of each base angle?

  58. 58.A parade banner in Allentown is a trapezoid with parallel sides of 12 feet and 8 feet and a height of 5 feet. What is the area of the banner?

  59. 59.At a fair in Indiana County, spinner A has 4 equal sections and exactly 1 says win. Spinner B has 5 equal sections and exactly 2 say win. The spins are independent. What is the probability that both spinners land on win?

  60. 60.A bakery in Allentown inspects a random sample of 25 muffins from a batch of 400 and finds 2 underbaked muffins. About how many muffins in the whole batch are underbaked?

  61. 61.A farm stand near Intercourse prices tomatoes at $3.60 for 4 pounds. What is the price for 1 pound?

  62. 62.A museum in Philadelphia welcomed 1,200 visitors on Friday. Saturday's count was 30% greater than Friday's count. How many visitors came on Saturday?

  63. 63.On Monday a pond in French Creek State Park sat 2.5 inches below its normal level, recorded as -2.5 inches. By Friday the water had fallen another 1.75 inches. What was Friday's level relative to normal?

  64. 64.A sewing pattern from a shop in Columbia asks for the value of (7/8) ÷ (-1/4). What is that quotient?

  65. 65.A phone plan in Allentown costs $18 each month plus $0.08 for every text. One bill, before tax, was $26. How many texts were sent that month?

  66. 66.A chess club in Chambersburg keeps playing while 5(x + 2) > 35, where x is the number of extra minutes past noon. Which inequality describes x?

  67. 67.Two towns in the Lehigh Valley are 28 miles apart. On a road map, 1 inch represents 4 miles. How many inches apart are the towns on that map?

  68. 68.A round braided rug in a farmhouse near Bird-in-Hand has a diameter of 16 feet. Using 3.14 for pi, what is the area of the rug?

  69. 69.Two supplementary angles meet at a footbridge railing in Jim Thorpe. The smaller angle is one third of the larger angle. What is the measure of the smaller angle?

  70. 70.A patio in York joins a rectangle 14 feet by 9 feet to a triangle. The triangle uses the 14-foot side as its base and has a height of 6 feet. What is the total area?

  71. 71.A jar in a Pittsburgh classroom holds 2 red pencils and 5 black pencils. A student draws a pencil, puts it back, and draws again. What is the probability that both draws are red?

  72. 72.A candy shop in Hershey wants to estimate what share of its 1,000 Saturday customers buy a souvenir. The manager surveys 40 people already standing in line with souvenirs, and all 40 of them have souvenirs. Which conclusion is reasonable?

  73. 73.An empty water tank at a factory in York fills at a constant 2.5 gallons per minute. How many gallons are in the tank after 36 minutes?

  74. 74.A hardware store in Scranton priced a snow shovel at $24, then raised the price by 12.5%. What is the new price?

  75. 75.The overnight change on a thermometer in Wellsboro is recorded as -7 - (-12) degrees. What is that change?

  76. 76.A lab notebook in State College asks for the value of (-12) ÷ (-0.5). What is the quotient?

  77. 77.A snack bar at a pool in Mechanicsburg uses the equation 0.5n + 3.5 = 10 to find how many fruit cups, n, were sold after the opening tray. What is n?

  78. 78.A rink in Wilkes-Barre keeps the ice bath running only while 6 - 2x ≥ 14. Which inequality gives the permitted values of x?

  79. 79.On a neighborhood map of Pittsburgh, 2 centimeters represent 5 kilometers. Two neighborhoods are 7 centimeters apart on the map. What is the actual distance between them?

  80. 80.A circular warm-up path around a practice field in State College has a radius of 35 meters. Which expression is the circumference of the path, left in terms of pi?

  81. 81.Two parallel rail lines near Altoona are crossed by a station road. One of a pair of alternate interior angles measures 73°. What is the measure of the other alternate interior angle?

  82. 82.A playground mat in Chambersburg is a 20-foot by 12-foot rectangle with a right triangle removed from one corner. The triangle's legs measure 6 feet and 8 feet. What area of matting remains?

  83. 83.A student in Carbondale rolls a fair number cube numbered 1 through 6 and flips a fair coin. What is the probability of rolling a 3 and getting heads?

  84. 84.A band director in Reading asks a random sample of 30 members from a band of 240 whether they can attend a Saturday rehearsal. Twelve of the 30 can attend. About how many of the 240 members can attend?

  85. 85.A juice stand at Reading Terminal Market mixes 5 cups of apple cider with 2 cups of cranberry juice. How many cups of cranberry juice should be mixed with 15 cups of apple cider to keep the same ratio?

  86. 86.A bike shop in State College lowered the price of a helmet from $45 to $36. What was the percent decrease?

  87. 87.A depth reading on a creek near Bellefonte is recorded as -2/3 + (-1/5) meters relative to a marker. What is that sum?

  88. 88.During a cold front, the temperature in Johnstown falls 1.8 degrees each hour for 5 hours. What is the total change in temperature?

  89. 89.Students at a club fair in Lewisburg simplify 3(2x - 5) + 4x. Which expression is equivalent?

  90. 90.A student chorus hoping to sit at the Mann Center in Philadelphia needs a score of at least 80. Maya already has 62 points and will earn p more points. Which inequality shows the values of p that let her qualify?

  91. 91.A planting plan for a path in Kennett Square uses the scale 1 inch = 6 feet. The real path is 18 feet long. How long should the path be drawn on the plan?

  92. 92.A round banquet table at a fire-company hall in Pittston has a radius of 3.5 feet. Using 3.14 for pi, how long is a ribbon that wraps exactly once around the edge of the table?

  93. 93.A right triangle in a roof truss built in the Poconos has one acute angle of 35°. What is the measure of the other acute angle?

  94. 94.A stage platform in Lebanon is built from two rectangular prisms. One prism measures 6 feet by 4 feet by 1 foot. The other measures 6 feet by 2 feet by 2 feet. What is the total volume of the platform?

  95. 95.A history club in Philadelphia makes 10 cards. Four cards show Independence Hall, and the other six show different sites. One card is drawn at random. What is the probability that it does not show Independence Hall?

  96. 96.A planner in Erie draws a random sample of 25 workers from 2,000 workers in one district. The sample mean commute is 18 minutes. Using that mean as the estimate for every worker, about how many minutes do all 2,000 workers spend commuting in total?

  97. 97.A SEPTA regional rail train travels 42 miles in 48 minutes at a constant speed. How many miles does it travel in 16 minutes at that speed?

  98. 98.A trail association in the Poconos had a budget of $4,000 and spent 35% of it on trail signs. How much money was left?

  99. 99.At Kinzua Bridge State Park the morning temperature was -3.4°C. By afternoon the temperature had changed by +1.8°C. What was the afternoon temperature?

  100. 100.A math team in Doylestown computes (-6) × (-4.5) during a scoring drill. What is the product?

  101. 101.A community theater in Hershey charges $6 for each ticket plus a $3 fee on the whole order. One order totaled $45. How many tickets were in that order?

  102. 102.A service gate at Valley Forge National Historical Park opens when a gauge reading x satisfies x ≥ -2.4. Which reading keeps the gate open?

  103. 103.A blueprint of a barn near Lebanon uses the scale 1 centimeter = 3 meters. The barn is drawn 7.5 centimeters wide. What is the actual width of the barn?

  104. 104.A circular reflection pool in a courtyard in Swarthmore has a radius of 11 yards. Which expression is the area of the pool, left in terms of pi?

  105. 105.Two parallel avenues in Bethlehem are cut by a transversal. One same-side interior angle measures 118°. What is the measure of the other same-side interior angle?

  106. 106.A trophy made in Easton has a rectangular prism base that is 9 centimeters by 6 centimeters by 2 centimeters. A triangular prism sits on top: its triangle has base 6 centimeters and height 4 centimeters, and the prism is 9 centimeters long. What is the total volume?

  107. 107.Letter tiles spell HARRISBURG for a classroom display. One tile is drawn at random. What is the probability of drawing the letter R?

  108. 108.A librarian in Scranton wants to estimate how many of the town's 5,000 library-card holders visited last month. She asks 80 card holders selected at random, and 24 of them visited. About how many of the 5,000 card holders visited?