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California Assessment of Student Performance and Progress Mathematics Grade 7

One hundred eight questions on proportions, integers, inequalities, and circles.

These questions are original. This is not an official California Assessment of Student Performance and Progress test, and FreeExam is not affiliated with the California Department of Education.

  1. 1.A buoy line at Huntington Beach is modeled by the inequality -2x > 8, where x is the position in meters relative to the lifeguard tower. Which solution describes every x that works?

  2. 2.Divers tracking a shelf off Catalina Island record depths that satisfy -3x < 12. Which inequality shows all possible values of x?

  3. 3.When a wind model for the Altamont Pass is simplified, it becomes -5x ≥ 20. What is the solution?

  4. 4.Crates leaving a Watsonville cooler must satisfy -4x ≤ -16. What is the solution set?

  5. 5.A Fresno robotics club writes -6x < -18 to limit a motor setting. Which values of x are allowed?

  6. 6.At a Petaluma farm stand, the cash difference in dollars obeys -2x + 5 > 17. Solve for x.

  7. 7.Campsite reservations near Yosemite Valley follow 8 - 4x ≤ 20. Which solution is correct?

  8. 8.Harbor staff in Crescent City use -x > 9 for a tide index. What is the solution?

  9. 9.An inequality posted in a Long Beach cargo office reads -8x > -24. Find every x that makes it true.

  10. 10.Cooling hours in an Imperial Valley greenhouse satisfy -7x ≤ 21. What is the solution for x?

  11. 11.A Joshua Tree hike leader says -2x ≥ 10 describes how far, in miles, the group stays from a marker. Which statement matches the solution?

  12. 12.The rose garden at the state capitol in Sacramento is a circle with radius 10 meters. Using 3.14 for pi, what is the area of the garden?

  13. 13.A Ferris wheel sketch for the Santa Cruz boardwalk uses a circle of radius 10 feet. Using 3.14 for pi, what is the circumference?

  14. 14.A circular fountain in Balboa Park has a radius of 5 feet. Using 3.14 for pi, what is the area of the water surface?

  15. 15.A wagon wheel at a historical ranch in Santa Ynez has a diameter of 8 feet. Using 3.14 for pi, what is the circumference?

  16. 16.A circular pond in a Davis courtyard has a diameter of 6 meters. Using 3.14 for pi, what is the area?

  17. 17.Runners loop a circular green in Palo Alto whose radius is 7 meters. Using 3.14 for pi, what is the circumference of the loop?

  18. 18.A student in Anaheim is finding the area of a circular pizza stone with radius 6 inches and will use 3.14 for pi. Which expression equals that area?

  19. 19.An irrigation test plot near Merced is a circle of radius 15 meters. Using 3.14 for pi, what is its area?

  20. 20.A scale model of a lighthouse lens in Point Arena is a circle with radius 9 centimeters. Using 3.14 for pi, what is the circumference of the model?

  21. 21.A shop in Sausalito sells two circular rugs. Rug A has radius 3 feet and rug B has radius 6 feet. Using 3.14 for pi, how much greater is the area of rug B?

  22. 22.A circular irrigation arm near Brawley turns through a circle of radius 20 meters. Using 3.14 for pi, what distance does the outer end travel in one full turn?

  23. 23.A circular patio in Ojai has circumference 31.4 meters when pi is taken as 3.14. What is the radius?

  24. 24.A round mosaic medallion at Mission San Juan Capistrano has radius 12 inches. Using 3.14 for pi, what is the circumference?

  25. 25.Which description gives the area of the circular helipad at a hospital in Torrance?

  26. 26.A shop on Olvera Street marks a $40 woven blanket up by 25 percent. What is the selling price?

  27. 27.A store in Pasadena discounts an $80 windbreaker by 20 percent. What is the sale price?

  28. 28.A diner in Bakersfield adds 8 percent sales tax to a $25 meal. What is the tax amount?

  29. 29.After a harbor cruise out of Santa Barbara, a family adds a 15 percent tip to a $60 bill. How much is the tip?

  30. 30.The number of nesting herons at Bolsa Chica rises from 200 to 250. What is the percent increase?

  31. 31.A used surfboard in Oceanside drops in price from $150 to $120. What is the percent decrease?

  32. 32.Fifteen percent of the seats in a Redding auditorium are reserved, and that reserved group is 45 seats. How many seats does the auditorium have?

  33. 33.A fishmonger at Fisherman's Wharf marks salmon up 40 percent from a $20 wholesale price. What is the retail price?

  34. 34.A realtor in Irvine earns a 3 percent commission on a $200,000 home sale. What is the commission?

  35. 35.A lab in La Jolla reports that 12.5 percent of 80 tide samples contain a certain algae. How many samples is that?

  36. 36.A hiker near Mount Whitney estimates a trail is 8 miles long. The measured length is 10 miles. Using the measured length as the actual value, what is the percent error?

  37. 37.A student in Davis deposits $400 in an account that earns 5 percent simple interest in one year. How much interest is earned?

  38. 38.Attendance at a county fair in Paso Robles falls by 15 percent from 2,000 visitors. How many visitors remain?

  39. 39.A meal in Napa costs $48 before a 25 percent tip. What is the total paid, including the tip?

  40. 40.What does it mean to find 40 percent of a $90 kayak rental in Morro Bay?

  41. 41.On a site plan for a trail in Muir Woods, 1 centimeter represents 5 meters. A segment drawn 4 centimeters long represents what actual length?

  42. 42.On a map of the California coast, 1 inch represents 25 miles. The map distance from Monterey to a marked point near San Simeon is 3 inches. What is the actual distance?

  43. 43.An architect in Oakland draws a room at a scale of 1 centimeter to 2 meters. One wall is 7 centimeters on the drawing. How long is the actual wall?

  44. 44.A footbridge in Chico is 36 meters long. On a drawing where 1 centimeter represents 4 meters, how long should the bridge be drawn?

  45. 45.A model of a schooner in a San Pedro museum uses the scale 1:40. A mast that is 15 centimeters on the model represents what actual length?

  46. 46.A courtyard plan in Santa Monica shows a rectangle that is 3 centimeters by 4 centimeters. The scale is 1 centimeter to 2 meters. What is the actual area of the courtyard?

  47. 47.A trail map in Kings Canyon uses the scale 1 centimeter to 0.5 kilometer. A dotted route measures 12 centimeters. What actual distance is that?

  48. 48.A blueprint for a library in Sacramento uses 2 centimeters to represent 5 meters. A window is drawn 6 centimeters wide. What is the actual width?

  49. 49.A scale drawing of a redwood in Humboldt County shows the tree as 8 centimeters tall. The scale is 1 centimeter to 9 meters. How tall is the tree?

  50. 50.A science kit in a Berkeley classroom holds 10 counters, and 3 of them are red. What is the probability of drawing a red counter at random?

  51. 51.A spinner at a school carnival in Visalia has 8 equal sections, and 2 of them are marked with a star. What is the probability of landing on a star?

  52. 52.A bag of tiles for a mosaic in Solvang has 5 blue tiles and 3 yellow tiles. A tile is drawn at random. What is the probability it is not blue?

  53. 53.Every card in a stack of 12 trail cards at a visitor center in Lee Vining shows a bird. What is the probability of drawing a bird card?

  54. 54.A jar in a classroom in El Centro contains 9 green beads and no red beads. What is the probability of drawing a red bead?

  55. 55.A number cube labeled 1 through 6 is rolled at a picnic in Griffith Park. What is the probability of rolling a number greater than 4?

  56. 56.A bowl at a festival in San Luis Obispo holds 4 red marbles, 5 white marbles, and 1 blue marble. What is the probability of drawing the blue marble?

  57. 57.At a math night in Arcata, a coin is flipped and a fair number cube numbered 1 through 6 is rolled. How many outcomes are in the sample space?

  58. 58.Of 20 surfboards at a rental shop in Ventura, 7 are longboards. If a board is chosen at random, what is the probability it is a longboard?

  59. 59.Two angles along a railing at the Ferry Building form a straight line. One angle measures 55 degrees. What is the measure of the other angle?

  60. 60.Two angles form a right angle at a picture frame in a gallery in Laguna Beach. One measures 28 degrees. What is the other?

  61. 61.A student in Sacramento is sorting angle pairs from a bridge sketch. Which pair of angle measures is supplementary?

  62. 62.On a worksheet from a woodshop in Fort Bragg, which pair of angle measures is complementary?

  63. 63.Two lines cross at a plaza in San Jose and form vertical angles. One of the angles measures 73 degrees. What is the measure of the angle opposite it?

  64. 64.A gate hinge in Sonoma forms a straight angle with the fence. One side of the hinge makes a 120-degree angle with the fence line. What is the adjacent angle on that straight line?

  65. 65.A carpenter in Mendocino cuts two boards so that the angles are complementary. One angle is 47 degrees. What is the other angle?

  66. 66.Adjacent angles along a curb in Glendale are supplementary. One measures 98 degrees. What does the other measure?

  67. 67.The equation x + 36 = 90 describes a complementary pair on a sundial in Santa Cruz. What is x?

  68. 68.A ramp in San Bernardino meets flat ground at 32 degrees. The wall at the top is perpendicular to the ground, so the angle between the ramp and the wall is complementary to 32 degrees. What is that angle?

  69. 69.Two adjacent angles on a pier in Avalon form a straight line. The larger angle is twice the smaller angle. What is the measure of the smaller angle?

  70. 70.A crate of Valencia oranges is packed so that 4(x - 2) = 20, where x is the number of oranges in one row. What is x?

  71. 71.A ranger in Lassen Volcanic National Park solves 3x + 6 = 24 for the number of trail markers x. What is x?

  72. 72.Posters for a concert in Oakland are stacked so that 5(x + 3) = 40. What is x?

  73. 73.A debate club in Sacramento sets up chairs with the equation 6x - 4 = 2x + 20. What is x?

  74. 74.A recipe card in Carmel says (2/3)x = 10, where x is cups of stock. What is x?

  75. 75.A printer in San Luis Obispo solves 0.4x - 1.2 = 2. What is x?

  76. 76.The equation -4x + 9 = -7 describes a temperature offset in Truckee. What is x?

  77. 77.A warehouse in Riverside uses the equation -2(x - 5) = 12. What is x?

  78. 78.Tickets for a planetarium show in San Diego satisfy 2x + 3x - 4 = 21. What is x?

  79. 79.A docent at a mission in Santa Barbara has 3 more than twice as many postcards as a colleague. Together they have 33 postcards. If the colleague has x postcards, then x + (2x + 3) = 33. What is x?

  80. 80.The sum of three consecutive integers used to label cabins at Lake Tahoe is 72. What is the smallest integer?

  81. 81.A rectangular planter in Palm Springs has a length that is 4 feet more than its width. The perimeter is 36 feet. What is the width?

  82. 82.A chemist in La Jolla solves x/5 + 3 = 7. What is x?

  83. 83.A growers' co-op in Modesto sells almonds at a constant rate of $6 per pound. What is the cost of 4.5 pounds?

  84. 84.During a training run, a Sausalito ferry travels 18 miles in 1 hour at a steady speed. How far does it travel in 2.5 hours at that same speed?

  85. 85.A Sonoma cider press yields juice in proportion to the apples pressed. Two bushels produce 8 liters. What is the constant of proportionality in liters per bushel?

  86. 86.Which statement describes a proportional relationship between hours worked and pay for a lifeguard in Malibu?

  87. 87.Bakers in East Los Angeles keep a proportional masa recipe: 3 cups make 24 tortillas. How many cups of masa make 40 tortillas?

  88. 88.Surveyors working along Highway 1 near Big Sur record 186 miles of notes over 6 days at a constant daily rate. How many miles do they record per day?

  89. 89.A cafe in Santa Barbara charges $2 per scone and adds a $1 bag fee. One scone costs $3, two cost $5, and three cost $7. Why is the cost not proportional to the number of scones?

  90. 90.A Sacramento garden uses water in proportion to its planted area. A 20-square-meter bed needs 50 liters. How many liters does a 32-square-meter bed need at the same rate?

  91. 91.A kelp survey off Monterey records 15 sea otters for every 3 acres, and the counts stay proportional. How many otters are expected on 7 acres?

  92. 92.Paint for a mural in San Jose is mixed so that blue and white stay in the ratio 2:5. If the crew uses 8 gallons of blue, how many gallons of white do they use?

  93. 93.A cable car on a San Francisco hill climbs at a steady rate, passing 12 blocks in 15 minutes. How many blocks does it pass in 40 minutes?

  94. 94.A Half Moon Bay chowder recipe that serves 8 people uses 6 cups of clams. How many cups are needed to serve 12 people at the same ratio?

  95. 95.At dawn in Death Valley the temperature is -3.6 degrees Celsius, then it rises 11.4 degrees by noon. What is the noon temperature?

  96. 96.A club treasurer in Stockton records a balance of -$24, then records another $15 expense as a subtraction. What is the new balance?

  97. 97.The elevation change from a trench reading of -18 feet to a dock reading of -7 feet in the Sacramento-San Joaquin Delta is found by -7 - (-18). What is that change?

  98. 98.A cold-storage warehouse in Salinas changes its temperature by -2 degrees each hour for 6 hours. What is the total change?

  99. 99.A research team splits a total change of -48 sample points evenly across 6 tide stations at Point Reyes. What is the change at each station?

  100. 100.A baker in Santa Rosa combines 3/4 cup of honey with 2/3 cup of olive oil for a glaze. How many cups is that altogether?

  101. 101.A trail crew in Sequoia National Park has 5/6 of a mile of brush left and clears 1/2 mile before lunch. How much remains?

  102. 102.A gardener in Fresno uses 3/5 of a 2/3-acre plot for tomatoes. What fraction of an acre is planted in tomatoes?

  103. 103.A winery in Healdsburg divides 3/4 liter of yeast starter into portions of 1/8 liter. How many portions does that make?

  104. 104.The tide at Eureka drops by 1/2 foot each hour, and the drop is recorded as a negative number. What is the change after 5 hours?

  105. 105.Fuel for a boat in Avalon costs $4.25 per gallon, and the tank takes 6 gallons. What is the cost?

  106. 106.A spool of cable in the Port of Oakland is 13.5 meters long and is cut into pieces of 2.25 meters. How many pieces are there?

  107. 107.A hiker near Bishop starts 2 1/4 miles below a trailhead sign, recorded as -2 1/4, and climbs 3 1/2 miles. What is the position relative to the sign?

  108. 108.Dividing -2.4 by 0.6 gives the change per trial in a materials lab in Claremont. What is the quotient?