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Illinois Assessment of Readiness Mathematics Grade 7

Proportions, integers, inequalities, circles, and probability.

These questions are original. This is not an official Illinois Assessment of Readiness test, and FreeExam is not affiliated with the Illinois State Board of Education.

  1. 1.The temperature in Rockford was −8 degrees Fahrenheit at dawn. By noon it had risen 13 degrees. What was the noon temperature?

  2. 2.A score sheet at a warehouse in Rock Island asks for the product of −6 and −4. What is that product?

  3. 3.Three club members in Alton share a balance of −15 dollars equally. What integer is one member's share?

  4. 4.On a number line in an Oak Park classroom, one point is at −9 and another is at 4. What is the distance between the points?

  5. 5.A river gauge at Beardstown changes by −3.5 feet and then by 1.2 feet. What is the combined change?

  6. 6.A recipe card in Quincy asks for (−2/3) × (9/4). What is the product in simplest form?

  7. 7.A dive log from Waukegan asks for the value of 5 − (−8). What is that value?

  8. 8.Order these elevation readings, in meters, recorded near Cairo from least to greatest: −2.1, −7/4, −0.5, and 1/5.

  9. 9.A club treasurer in Belleville computes (−18) ÷ (−6). What is the quotient?

  10. 10.A lab calculation in Batavia multiplies −2, −5, and −3. What is the product?

  11. 11.A mixture card in Wheaton asks for (−3/5) ÷ (9/10). What is the quotient in simplest form?

  12. 12.Which decimal equals 5/6, the fraction written on the board in a Normal classroom?

  13. 13.A walking route through the Loop records block changes of 7, −12, and 4. What is the total change?

  14. 14.A gauge in East St. Louis shows −4.5. What is the additive inverse of that reading?

  15. 15.A baker in Arthur computes −1 1/2 + 3/4. What is the sum in simplest form?

  16. 16.A scoreboard test in Pekin uses the product (−8) × 0 × 5. Which statement is true?

  17. 17.On a comparison card in Skokie, which number is greater, −2/5 or −0.5?

  18. 18.An Evanston display uses a 7/8-yard ribbon. How many full 1/4-yard pieces can be cut, and how much ribbon remains?

  19. 19.What is the multiplicative inverse of −4/5, the factor printed on a card in Dixon?

  20. 20.A notebook in Edwardsville asks for the value of (−3)². What is that value?

  21. 21.Solve 4(x − 2) = 20, the equation on a tutoring card in Ottawa.

  22. 22.A parts count in Galesburg satisfies 5x − 8 = 2x + 7. What is x?

  23. 23.The number of crates x in a Jacksonville warehouse satisfies x/3 + 4 = 10. What is x?

  24. 24.Solve 0.5n − 1.5 = 3.5 for a decimal model used in Kankakee.

  25. 25.Solve −6 = 2(y + 1), an equation from a science log in Freeport.

  26. 26.Simplify 4a − 3 + 2a + 9, the expression on a worksheet in Taylorville.

  27. 27.Expand −3(2n − 5), the expression a class in Marion is rewriting.

  28. 28.Which expression is equivalent to 12x + 18, a total from a fundraiser in Effingham?

  29. 29.Six visitors at a historic site near Petersburg each pay $9 for admission and $4 for a tour. What is the total cost?

  30. 30.Evaluate 3x² − x when x = −2, the value in a notebook from Mattoon.

  31. 31.A canoe rental on the Fox River in St. Charles costs $18 plus $7 per hour. A renter pays $53. For how many hours was the canoe rented?

  32. 32.Solve 3(m − 2) = 2m + 4, the equation posted in Elgin.

  33. 33.Which expression is equivalent to 5(2x − 1) − 3x on a card in Lockport?

  34. 34.A rectangular garden in Monticello has length 2w + 3 feet and width w feet. Which expression gives the perimeter in feet?

  35. 35.A pan balance in Geneva holds 4 identical cubes and a 6-gram weight on the left and 26 grams on the right. The pans balance. What is the mass of one cube?

  36. 36.Solve −2x > 10, the inequality on the board in Moline.

  37. 37.A boat count t at a dock in Quincy satisfies t/4 ≤ 3. Solve for t.

  38. 38.A cooling model in a DeKalb lab is −5y ≥ 20. Solve for y.

  39. 39.A club in Naperville uses 2x + 5 < 19 to limit how many raffle books x it will print. Solve for x.

  40. 40.A dispatcher in Aurora uses the inequality 8 − 3x > 2. Solve for x.

  41. 41.Solve −2(x + 4) < 6 for a temperature offset x at a greenhouse in Champaign.

  42. 42.A print shop in Crystal Lake charges $12 to set up a job plus $3 per poster. The cost inequality is 12 + 3p ≤ 48. Solve for p.

  43. 43.Solve (x − 1) ÷ (−2) ≥ 5, the inequality posted in a class in Lincoln, Illinois.

  44. 44.A height reading, in meters, near Grafton satisfies x + (−7) > −2. Solve for x.

  45. 45.On a scale drawing of a gym in Peoria, 1 centimeter represents 5 meters. A wall is 2 centimeters long on the drawing. What is the actual length of the wall?

  46. 46.A cyclist rides 18 miles on Chicago's Lakefront Trail in 1.5 hours at a steady speed. What is the unit rate in miles per hour?

  47. 47.At a market stall in Galena, 3/4 pound of cheddar costs $6. What is the price of 1 pound?

  48. 48.A water study in Des Plaines records minutes x and gallons y: when x = 2, y = 7; when x = 4, y = 14; when x = 6, y = 21. What is the constant of proportionality of y to x?

  49. 49.On a map in a Morris library, 1 inch represents 20 miles along the Illinois River. A marked segment is 3.5 inches long. How many miles long is that part of the river?

  50. 50.A bakery in Bloomington uses 2 cups of flour for 12 muffins. How many cups of flour make 30 muffins?

  51. 51.Two similar triangular signs are built in Utica. A 6-centimeter side on the smaller sign matches a 15-centimeter side on the larger sign. Another side of the smaller sign is 8 centimeters. How long is the matching side of the larger sign?

  52. 52.A canoe rental at Starved Rock State Park charges by the hour and has no starting fee. Which equation shows a proportional relationship between hours h and cost c?

  53. 53.A hiker near Giant City walks 2 1/2 miles in 1/4 hour. What is the speed in miles per hour?

  54. 54.A store in Downers Grove sells 5 notebooks for $8.50. What is the price of one notebook?

  55. 55.A market in Berwyn sells 4 pounds of apples for $5. A market in Cicero sells 6 pounds for $8.10. Which choice gives the lower price per pound?

  56. 56.Paint for a mural in Pilsen is mixed as 2 cups of blue for every 5 cups of white. A crew uses 15 cups of white paint. How many cups of blue paint should they mix in?

  57. 57.A commuter train travels 45 miles from Chicago to Aurora in 75 minutes. What is its average speed in miles per hour?

  58. 58.A graph from a study in Urbana shows a proportional relationship passing through (0, 0) and (6, 15). What is the constant of proportionality?

  59. 59.A model of a downtown Chicago tower, shown in Rosemont, uses the scale 1 to 400. The model is 3.4 feet tall. How tall is the tower the model represents?

  60. 60.A chili recipe at the Illinois State Fair serves 8 people and uses 6 cups of beans. How many cups of beans are needed to serve 20 people?

  61. 61.A cab in downtown Chicago charges $3 to start and $2 for each mile. A 4-mile ride costs $11. Why is the fare not proportional to the miles?

  62. 62.A flagpole in Grant Park casts a 12-foot shadow while a 5-foot post casts a 3-foot shadow at the same time. How tall is the flagpole?

  63. 63.During a test, a fountain on the Chicago Riverwalk uses 2.4 gallons of water every 0.3 minute. How many gallons does it use in 1 minute?

  64. 64.An antique shop in Galena marks up an $80 clock by 25 percent. What is the selling price?

  65. 65.Of 250 students at a middle school in Decatur, 30 percent signed up for band. How many students signed up?

  66. 66.A coat at a shop in Oak Brook has a price of $90. The shop reduces that price by 20 percent. What is the sale price?

  67. 67.A family in Highland Park pays $50 for a workshop and then pays 8 percent sales tax on that price. What is the total cost?

  68. 68.After a meal in Greektown, a diner leaves a 15 percent tip on a $24 bill. How much money is the tip?

  69. 69.A class in Charleston plants 18 of its 60 saplings on Friday. What percent of the saplings are planted on Friday?

  70. 70.Attendance at a fair in Du Quoin went from 400 people on Thursday to 500 people on Friday. What was the percent increase?

  71. 71.A bait shop in Havana had 80 jars on Monday and 64 jars on Tuesday. What was the percent decrease?

  72. 72.A guide in Nauvoo earns 6 percent commission on $250 of tour sales. How much is the commission?

  73. 73.A student in Rantoul deposits $200 in an account that pays 5 percent simple interest each year. How much interest is earned in 3 years?

  74. 74.A surveyor near Metropolis estimates that a path is 45 meters long. The measured length is 50 meters. Using the measured length as the actual length, what is the percent error?

  75. 75.A bicycle in Schaumburg is priced at $200. The shop takes 10 percent off and then adds 5 percent sales tax on the discounted price. What is the final cost?

  76. 76.A bookstore in La Grange prices an atlas at $64 and then takes 25 percent off that price. Which expression equals the sale price?

  77. 77.A circular rug in a Springfield shop has a radius of 6 units. Using 3.14 for π, what is the area of the rug?

  78. 78.A circular flower bed in Lincoln Park has a radius of 6 meters. Using 3.14 for π, what is the circumference?

  79. 79.A circular window in Elsah has a diameter of 10 feet. Using 3.14 for π, what is the circumference?

  80. 80.A plan for a circular skating rink in Park Ridge uses a radius of 10 meters. Using 3.14 for π, what is the area of the rink?

  81. 81.A circular track in Danville has a circumference of 43.96 meters. Using 3.14 for π, what is the radius?

  82. 82.A semicircular outdoor stage in Highland Park has a radius of 5 feet. Using 3.14 for π, what is the area of the stage?

  83. 83.A round table in a Glen Ellyn library has a radius of 4 feet. Using 3.14 for π, what is the circumference of the table?

  84. 84.A sign in Collinsville is a 10-foot by 6-foot rectangle with a semicircle of radius 3 feet joined along one 6-foot side. Using 3.14 for π, what is the total area of the sign?

  85. 85.On a worksheet in O'Fallon, which expression gives the area of a circle of radius 9 when 3.14 is used for π?

  86. 86.Two adjacent angles form a straight line along a fence in Joliet. One angle measures 40 degrees. What does the other angle measure?

  87. 87.Two complementary angles meet at a window in Matthiessen State Park. One measures 28 degrees. What does the other measure?

  88. 88.Two lines cross at a plaza in Millennium Park and form a 65-degree angle. What is the measure of an angle adjacent to that 65-degree angle?

  89. 89.A triangular sail made for a boat on Carlyle Lake has two angles of 48 degrees and 67 degrees. What is the third angle?

  90. 90.A quadrilateral garden plot in Arcola has three angles of 80 degrees, 100 degrees, and 95 degrees. What is the fourth angle?

  91. 91.A triangular road sign in Vandalia has two equal sides, and the angle between those sides measures 40 degrees. What is each of the other two angles?

  92. 92.A class in Urbana wants one exact triangle from a description. Which description determines a unique triangle?

  93. 93.A rectangular mural in Bronzeville measures 4 feet by 5 feet. A copy is made with every length multiplied by 3. What is the area of the copy?

  94. 94.A storage crate in East Peoria is a rectangular prism 8 feet long, 5 feet wide, and 3 feet high. What is the volume of the crate?

  95. 95.A closed gift box in a Woodstock shop measures 4 inches by 3 inches by 2 inches. What is its surface area?

  96. 96.A cube-shaped planter in a Lisle garden has edges 5 inches long. What is the volume of the planter?

  97. 97.At a market in Andersonville, a plane cuts a rectangular prism of cheese parallel to one face. What shape is the flat cross section?

  98. 98.In a Centralia pantry, a plane cuts through the center of a cylindrical can, perpendicular to the two circular bases. What shape is the cross section?

  99. 99.A trapezoidal garden bed in Mahomet has parallel sides of 12 feet and 8 feet and a height of 5 feet. What is the area of the bed?

  100. 100.A triangular pennant cut in a shop in Tuscola has a base of 14 inches and a height of 9 inches. What is the area of the pennant?

  101. 101.A storage tent at Pere Marquette State Park is a right triangular prism. On each triangular end, the right angle lies between sides of 5 feet and 8 feet. The tent is 9 feet long. What is its volume?

  102. 102.A jar at a math club in Carbondale holds 10 counters, and 3 of them are red. One counter is drawn at random. What is the probability that it is red?

  103. 103.Kayak rentals on five days at a dock in Oregon, Illinois, numbered 4, 7, 7, 9, and 13. What is the mean of those numbers?

  104. 104.A small exhibit in Bishop Hill had 2, 8, 9, 10, and 31 visitors on five different days. What is the median of those counts?

  105. 105.Eagle counts on four mornings along the Mississippi River at Savanna were 2, 4, 6, and 8. What is the mean absolute deviation of those counts?

  106. 106.A random sample of 50 students at a school in Cicero includes 20 who walk to school. The school has 400 students. About how many of the 400 walk to school, based on the sample?

  107. 107.At a picnic in New Lenox, a spinner has two equal sections, red and blue, and a fair coin has heads and tails. Both are used once. What is the probability of red and heads?

  108. 108.In a class experiment in Macomb, a cup is tossed 40 times and lands on its side 30 times. What is the experimental probability that the cup lands on its side?