FreeExam

California Assessment of Student Performance and Progress Mathematics Grade 8

One hundred eight questions on slope, exponents, roots, and volume.

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.On a Marin Headlands map, a fire road runs from (1, 2) to (4, 8), with both coordinates in miles. What is the slope of the road?

  2. 2.A raisin plant in Fresno multiplies the factors 2^3 and 2^4 when it scales a drying schedule. What is 2^3 × 2^4?

  3. 3.A square patio behind a Santa Barbara cottage covers 81 square feet. How long is each side of the patio?

  4. 4.A cylinder mold at a Santa Cruz sand contest holds 30 cubic feet. A cone mold has the same radius and the same height. What is the volume of the cone?

  5. 5.Harbor planners for the San Francisco Bay graph y = x + 2 and y = 2x. At which point do the two lines meet?

  6. 6.The tram across Yosemite Valley stays level. On a graph it passes through (0, 5) and (9, 5). Which description of its slope is correct?

  7. 7.Tiles in a Pasadena courtyard are cut to a length of √2 feet. Which statement about √2 is true?

  8. 8.Biologists at the Salton Sea recorded a pelican count as 3 × (10 to the fourth power). Which number equals that count?

  9. 9.Painters marked a right triangle on a Long Beach lifeguard tower. The legs are 6 feet and 8 feet. How long is the hypotenuse?

  10. 10.A property edge in Sacramento passes through (3, 1) and (3, 8). What is the slope of that edge?

  11. 11.A tag on a square planter in Davis shows area 49 and asks for the side as a square root. What is √49?

  12. 12.A Berkeley lab records a wafer coating as 10^-3 meters thick. Which decimal equals 10^-3?

  13. 13.A well in the Central Valley has depth function f(x) = 2x - 6, with x in months. What is f(5)?

  14. 14.Highway 1 drops along a straight grade near Big Sur. The grade passes through (2, 9) and (5, 3). Find the slope.

  15. 15.A cubic crate of oranges in Riverside has a volume of 27 cubic feet. What is the edge length, the cube root of 27?

  16. 16.The Port of Long Beach logs 45,000 containers in one week. Which expression writes 45,000 in scientific notation?

  17. 17.A ramp at a Santa Barbara mission forms a right triangle. The hypotenuse is 15 feet and one leg is 9 feet. How long is the other leg?

  18. 18.A print shop in Red Bluff solves 3x + 5 = 20 to find how many booklets fill a carton. What is x?

  19. 19.An Oakland scoreboard shows the reset factor 8^0 before the next inning. What is the value of 8^0?

  20. 20.At a Ventura packing house, avocado crates x and lemon crates y satisfy x + y = 10 and x - y = 4. What is the pair (x, y)?

  21. 21.A conical hopper in the Imperial Valley has the same radius and height as a cylinder that holds 48 cubic feet of grain. What is the hopper's volume?

  22. 22.An Ojai tile shop compares four cut lengths. Which length is an irrational number?

  23. 23.Davis marked a bike path with the endpoints (0, 1) and (6, 4). The slope of that path is which number?

  24. 24.A Monterey Bay water sample has plankton density 0.00072. Which expression is that density in scientific notation?

  25. 25.A Death Valley station lists (hour, temperature) pairs. Which list is a function?

  26. 26.Two buoys off Catalina Island sit at (1, 2) and (4, 6) on a grid in miles. What is the straight-line distance between them?

  27. 27.Power readings at Moss Landing compare 5^6 with 5^2 by division. What is 5^6 ÷ 5^2?

  28. 28.A levee crest in the Sacramento-San Joaquin Delta never changes height. It contains the points (1, 7) and (8, 7). What is the slope of the crest?

  29. 29.A bakery in Solvang sold scones and cookies. Twice the number of scones plus the number of cookies equals 14, and the scones plus the cookies equal 9. How many of each were sold?

  30. 30.A segment of the John Muir Trail is √50 miles long. Between which two consecutive integers does √50 lie?

  31. 31.A conical salt pile in the South Bay has volume 9 cubic meters. A cylinder with the same radius and the same height holds how much?

  32. 32.Kayak rentals at Lake Tahoe satisfy the equation 4(x - 2) = 2x + 6. What is x?

  33. 33.Modesto warehouses compute (2 × 10^3) × (4 × 10^2) almond crates. What is that product in scientific notation?

  34. 34.A snow-depth model for Mammoth Mountain uses the value (-3)^3. What is (-3)^3?

  35. 35.A ramp along the Embarcadero rises 4 feet for every 2 feet of horizontal run. What is the slope of the ramp?

  36. 36.A square lettuce field in Salinas has area 64 square meters, so each side is √64 meters. Which statement is true?

  37. 37.Two ski trails near Mammoth are modeled by y = 2x + 1 and y = 2x + 6. How many solutions does this system have?

  38. 38.A cylindrical tank in Palm Springs has radius 3 meters and height 5 meters. Which expression is its volume?

  39. 39.A beacon at Point Reyes flashes in a pattern coded by (3^2)^3. What is the value of (3^2)^3?

  40. 40.A piling at Morro Bay is graphed as the line through (5, -2) and (5, 6). What is the slope of that graph?

  41. 41.Researchers in La Jolla model kelp length with one of these equations. Which equation is a linear function?

  42. 42.A garden triangle in Carmel has sides 4 meters, 5 meters, and 6 meters. Could it be a right triangle?

  43. 43.Hetch Hetchy records divide a large reading by a smaller one: (6 × 10^8) ÷ (2 × 10^3). What is the quotient in scientific notation?

  44. 44.A rideshare receipt in San Diego follows y = 3x + 4, where x is miles and y is dollars. What is the y-intercept?

  45. 45.A winter index recorded in Bodie is the cube root of -8. What is that cube root?

  46. 46.A cooling chart in a Sonoma winery uses the line y = -5x + 1. What is the slope of that line?

  47. 47.A cone of beach sand at Pismo Beach has volume 20 cubic feet. How much would a cylinder with the same radius and height hold?

  48. 48.A workshop in Santa Monica sorts four numbers. Which number is irrational?

  49. 49.A fare poster in Oakland states 2x + 3 = 2x + 5. How many values of x make the poster true?

  50. 50.A clerk in Stockton wrote 12 × 10^3 on a crate tag. Which rewrite is the same number in scientific notation?

  51. 51.On a Half Moon Bay beach, a pole, a kite string, and the ground form a triangle with sides 7, 24, and 25 feet. Is it a right triangle?

  52. 52.Shasta Lake staff record gauge pairs (1, 4), (2, 7), (3, 10), and (4, 13), with x in days and y in feet. What is the rate of change of y?

  53. 53.A research buoy in the Santa Barbara Channel stores the reading (-5)^2. What is (-5)^2?

  54. 54.A stall at the Ferry Building posts 4x + 2 = 2(2x + 1). How many solutions does the equation have?

  55. 55.A plaza tile in San Jose is a square of area 121 square meters. What is the side length?

  56. 56.A street in San Francisco has slope 2. A cross street is perpendicular to it. What is the slope of the cross street?

  57. 57.In a San Francisco classroom, a cone and a cylinder have the same radius and the same height. Which solid has the greater volume?

  58. 58.A dilution prepared in Palo Alto is labeled 5^-2. Which value equals 5^-2?

  59. 59.A funicular model in the Los Angeles hills passes through (0, 0) and (4, 12). What is the slope of the model?

  60. 60.Two Central Valley towns have populations 3.2 × 10^4 and 1.5 × 10^4. What is the combined population in scientific notation?

  61. 61.Two ranger stations in Lassen Volcanic National Park are plotted at (0, 0) and (8, 15) on a kilometer grid. What is the distance between them?

  62. 62.A shadow study at Griffith Observatory records (1, 1), (2, 4), (3, 9), and (4, 16) for width and area. What kind of relationship is shown?

  63. 63.A tide gauge in Eureka satisfies x/2 + 3 = 7. What is x?

  64. 64.A vineyard block in Paso Robles is a square covering 100 square meters. What is the length of one side?

  65. 65.Grapes in Lodi are piled in a cone of radius 3 feet and height 4 feet. Which expression is the volume of the pile?

  66. 66.A map of the California Aqueduct shows both y = 4x - 3 and 2y = 8x - 6. How many points lie on both equations?

  67. 67.When a counter at the Bay Bridge toll plaza is cleared, the display shows 10^0. What number is 10^0?

  68. 68.At a Watsonville strawberry stand, four numbers come up in a price discussion. Which number is rational?

  69. 69.From an overlook near Mount Wilson, a fire road is graphed from (1, 5) down to (3, 1). Calculate the slope.

  70. 70.A Sacramento River survey adds 2.5 × 10^5 fish to a later count of 3 × 10^4 fish. What is the sum in scientific notation?

  71. 71.A vertical turbine near the Altamont Pass has a guy wire attached 20 meters up the tower. The wire meets the ground 21 meters from the base. How long is the wire?

  72. 72.A tank in Coachella drains according to y = -2x + 20, with x in minutes and y in gallons. How many gallons are in the tank when x = 0?

  73. 73.An artichoke shed in Castroville packs boxes so that 5(x + 2) = 3x + 16. What is x?

  74. 74.Near the General Sherman tree, a guide claims that √49 is irrational. Which response is mathematically right?

  75. 75.A cone and a cylinder in a Redding science class have the same radius and hold the same volume. The cylinder is 4 centimeters tall. How tall is the cone?

  76. 76.An avocado grove in Fallbrook is planted as 10 rows of 10 trees. How many trees is 10^2?

  77. 77.Ten people attend a play in Sacramento. Adult tickets cost 8 dollars, child tickets cost 5 dollars, and the group pays 71 dollars. How many adults and children are there?

  78. 78.Driving east across a Sacramento River bridge, elevation stays at 12 meters while horizontal position goes from 0 to 40. What is the slope of that drive?

  79. 79.A fog researcher in San Francisco writes one droplet count four ways. Which writing is scientific notation?

  80. 80.An isosceles right triangle marks a corner of a plaza in Irvine. Each leg is 5 meters. What is the hypotenuse?

  81. 81.A boardwalk counter in Santa Cruz uses y = 4x + 1. What is y when x = 6?

  82. 82.A map of the Sacramento-San Joaquin Delta uses the scale factor 7^-1. Which number equals 7^-1?

  83. 83.Two vineyard rows in Napa are parallel, and one row has slope 3/4. What is the slope of the other row?

  84. 84.A cubic juice cooler at the Big Fresno Fair holds 64 cubic inches. What is the interior edge length?

  85. 85.A checkpoint in Kings Canyon is claimed to lie on the line y = 3x + 1. The checkpoint is (2, 7). Which statement is correct?

  86. 86.Three years of harbor-seal counts at Año Nuevo were 2 × 10^3, 9 × 10^2, and 1.5 × 10^3. Which list orders them from least to greatest?

  87. 87.Road salt in Truckee is piled in a cone of radius 5 feet and height 6 feet. Which expression is the volume?

  88. 88.Two bus routes in Fresno are graphed as a pair of lines. What does an intersection point of the lines represent?

  89. 89.A switchback near Mount Tamalpais is √10 miles long. Between which consecutive integers does √10 lie?

  90. 90.Light meters in a Monterey kelp forest compare intensities by computing 2^5 ÷ 2^8. What is the quotient?

  91. 91.A visitor at El Capitan says the cliff graph has slope 0 because the rock face does not lean. The graph is a vertical line. Which correction is right?

  92. 92.On a pier in San Diego, each button on a snack machine leads to exactly one snack, though two buttons may sell the same almonds. Why is that rule a function?

  93. 93.Grain diameters in the Mojave are compared by (8 × 10^6) ÷ (2 × 10^-2). What is the quotient in scientific notation?

  94. 94.A sail on a boat in San Diego Bay is a right triangle with legs 5 feet and 12 feet. How long is the hypotenuse?

  95. 95.A hanging mobile in San Luis Obispo balances when -3x + 12 = 0. What is x?

  96. 96.A marked path in Joshua Tree is (3 + √2) meters long. What kind of number is that length?

  97. 97.A bike rental in West Hollywood charges 5 dollars to unlock a bike and 2 dollars for each mile. Which equation gives the cost y after x miles?

  98. 98.A conical sand form in Crescent City has volume 7 cubic feet. A cylinder with the same radius and the same height holds how much?

  99. 99.A pipette in a Bodega Bay lab is marked 10^-2 liters. Which decimal equals 10^-2?

  100. 100.Currents near the Carquinez Strait are modeled by y = x - 1 and x + y = 7. Where do the lines meet?

  101. 101.Two garden edges in Napa measure √4 meters and √9 meters. What is the product of those lengths?

  102. 102.A San Joaquin Valley count multiplies (5 × 10^4) by (3 × 10^3). Which product is written in scientific notation?

  103. 103.A tram line in San Francisco has slope 0 and crosses the y-axis at 6. Which equation matches the tram?

  104. 104.A ferry schedule in Sausalito lists the pairs (0, 5), (1, 8), and (2, 11). Which equation matches every pair?

  105. 105.At dawn in Palm Desert, a temperature model passes through (0, 3) and (2, 7), with x in hours. Which equation fits both points?

  106. 106.A square corral in Petaluma has area 36 square meters. The side is √36 meters. Which description fits that side?

  107. 107.A school garden bed in Berkeley is a square of area 1 square meter. What is the side length?

  108. 108.A coast redwood sapling in Humboldt County grows 3 inches every 2 weeks. If height is graphed against time in weeks, what is the slope?