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New York State Testing Program Mathematics Grade 8

Slope, systems of equations, exponents, the Pythagorean theorem, and volume.

These questions are original. This is not an official New York State Testing Program test, and FreeExam is not affiliated with the New York State Education Department.

  1. 1.A lamp formula for a river beacon north of Newburgh uses 2^5. What is the value of 2^5?

  2. 2.A weather desk in Albany writes 10^(−3) for one thousandth of a meter. What is the value of 10^(−3)?

  3. 3.A scoreboard along the Buffalo waterfront includes the factor 7^0 in a lighting count. What is 7^0?

  4. 4.A print shop in Rochester multiplies 3^4 by 3^2 while counting ink dots. Which single power equals that product?

  5. 5.A science lab in Syracuse divides 5^7 by 5^3. Which single power of 5 equals the quotient?

  6. 6.A greenhouse timer in Ithaca simplifies (2^3)^4. Which single power of 2 matches that value?

  7. 7.A fountain program in Saratoga Springs evaluates (−4)^2. What is that value?

  8. 8.A trail sketch in the Catskills uses the scale factor (1/2)^3. What is that factor as a single fraction?

  9. 9.A warehouse tag in Queens simplifies 2^(−2) × 2^5. What is the value?

  10. 10.A census comparison for Manhattan is written as 1.6 × 10^6. What is that number in standard form?

  11. 11.A water sample from Long Island contains 4.2 × 10^(−4) gram of a mineral. What is that mass in standard form?

  12. 12.A Niagara gorge note lists 51,000 millimeters and rewrites it in scientific notation. Which expression is correct?

  13. 13.A ranger multiplies (3 × 10^4) by (2 × 10^3) to estimate seedlings in an Adirondack plot. What is the product in scientific notation?

  14. 14.A lab on one of the Finger Lakes divides (8 × 10^6) by (2 × 10^2). What is the quotient in scientific notation?

  15. 15.A tally for the Brooklyn Bridge walkway adds 2.5 × 10^3 and 4.1 × 10^3. What is the sum in scientific notation?

  16. 16.Two Bronx school groups are estimated as 7.2 × 10^5 and 8.9 × 10^4. Which estimate is larger?

  17. 17.A Staten Island ferry log records 46,800 passengers in a month. Which expression is 46,800 in scientific notation?

  18. 18.Two Erie Canal markers are 3.5 × 10^4 meters and 1.2 × 10^4 meters from a lock. How much farther is the first marker, in scientific notation?

  19. 19.A square garden bed in Central Park covers 144 square feet. What is the length of one side, in feet?

  20. 20.A storage cube at Prospect Park holds 125 cubic feet. What is the edge length, in feet?

  21. 21.A paving square near Battery Park has area 50 square meters. Between which two consecutive integers does the side length lie?

  22. 22.A workshop cube in Gowanus has a volume of 64 cubic inches. What is the edge length, in inches?

  23. 23.A tile order for a library in Flushing must be a perfect square. Which of these counts is a perfect square?

  24. 24.A square mural in Harlem satisfies x^2 = 81, and the side length x is positive. What is x, in feet?

  25. 25.A packing cube in Yonkers satisfies y^3 = 27. What is the positive edge length y, in centimeters?

  26. 26.A courtyard square in White Plains has area 48 square yards. Which integer is closest to the side length?

  27. 27.A cube crate in Newburgh has volume 8 cubic feet, and a square rug there has area 8 square feet. Which length is greater?

  28. 28.A Metro-North distance graph passes through (0, 0) and (4, 10), with x in hours and y in miles. What is the slope?

  29. 29.A boardwalk stand at Coney Island graphs pretzels against dollars on a line through the origin and (5, 20). What is the slope?

  30. 30.A downhill path near Cold Spring is graphed from (2, 11) to (6, 3). What is the slope?

  31. 31.A bakery in Troy sells loaves proportionally: 2 loaves cost $7, 4 cost $14, and 6 cost $21. What is the constant of proportionality, in dollars per loaf?

  32. 32.A Peekskill ferry chart lists hours and miles. Table A is (1, 8), (2, 16), (3, 24). Table B is (1, 8), (2, 15), (3, 22). Which table is proportional?

  33. 33.A line on a Kingston map passes through (1, 3) and (5, 11). What is the slope?

  34. 34.A level towpath near Poughkeepsie is graphed from (2, 6) to (9, 6). What is the slope?

  35. 35.An elevator shaft in Utica is graphed through (4, 1) and (4, 8). What is the slope?

  36. 36.A delivery route in Binghamton is proportional, has slope 3, and passes through the origin. Which equation matches it, with x in hours and y in miles?

  37. 37.A museum group in Albany uses 4x + 7 = 31, where x is the number of discounted tickets. What is x?

  38. 38.A bus-pass equation in Buffalo is 5(x − 2) = 3x + 4. What is x?

  39. 39.A canal-lock counter in Rochester satisfies x/3 + 5 = 11. What is x?

  40. 40.A balance scale in a Syracuse classroom is modeled by 9x − 4 = 2x + 17. What is x?

  41. 41.A temperature model in Plattsburgh uses −3x + 8 = 20. What is x?

  42. 42.A rental equation in Glens Falls is 2(3x + 1) = 20. What is x?

  43. 43.A price check in Oswego is written as 4x + 1 = 4x + 6. How many solutions does the equation have?

  44. 44.A marina balance in Watertown is 6x − 9 = 3(2x − 3). How many solutions does the equation have?

  45. 45.A trail scale in Massena satisfies 0.5x − 1.5 = 2.5. What is x?

  46. 46.A snack stand in Schenectady uses y = 2x and x + y = 12. What is x?

  47. 47.A farm stand in Rome, New York, uses x + y = 10 and x − y = 4. What is x?

  48. 48.A boathouse in Auburn uses y = x + 5 and 2x + y = 17. What is y?

  49. 49.A market in Cortland graphs y = 3x + 1 and y = 3x − 4. How many solutions does the system have?

  50. 50.A co-op in Oneonta writes 2x + 4y = 10 and x + 2y = 5. How many solutions does the system have?

  51. 51.A library count in Elmira uses y = −x + 7 and y = x + 1. What is the solution pair (x, y)?

  52. 52.At a concert in Geneva, New York, 1 adult ticket and 1 student ticket cost $18, while 2 adult tickets and 1 student ticket cost $28. What is the adult price?

  53. 53.A dock tally in Lockport uses 3x + y = 20 and y = 5. What is x?

  54. 54.A pier measurement in Dunkirk uses 4x + y = 18 and y = 2. What is x?

  55. 55.A bike share in Brooklyn charges a $3 unlock fee plus $2 for each hour. Which equation gives the cost y, in dollars, for x hours?

  56. 56.A garden record in Queens compares list P, the pairs (1, 4), (2, 7), (3, 10), and (4, 13), with list Q, the pairs (1, 4), (2, 5), (2, 9), and (3, 6). Which list is a function?

  57. 57.A building model in Manhattan uses f(x) = 4x − 1 for the number of windows on floor x. What is f(6)?

  58. 58.A ferry table in the Bronx lists x-values 0, 1, 2, and 3 with y-values 5, 8, 11, and 14. What is the rate of change of y with respect to x?

  59. 59.A tide chart on Staten Island includes the pairs (2, 5), (4, 5), and (2, 8). Why is this relation not a function?

  60. 60.A snowfall graph in Buffalo passes the vertical line test. What does that test show?

  61. 61.A planetarium in Rochester compares four rules. Which equation does not define a linear function?

  62. 62.An empty-seat rule for a trolley in Albany is y = −4x + 20, where x is the number of stops already made. What is y when x = 0?

  63. 63.At a fair in Syracuse, f(x) = x + 9. Which input gives f(x) = 15?

  64. 64.A right triangle trail near the Hudson has legs of 9 meters and 12 meters. What is the hypotenuse?

  65. 65.A right triangle on a Bear Mountain trail has legs of 8 meters and 15 meters. What is the hypotenuse, in meters?

  66. 66.A ladder at Watkins Glen is 13 feet long, and its foot sits 5 feet from the wall. How many feet up the wall does the top of the ladder reach?

  67. 67.A sketch at Letchworth Gorge has sides 7 meters, 24 meters, and 25 meters. Does it form a right triangle?

  68. 68.A right triangle on Fire Island has a hypotenuse of 10 meters and one leg of 6 meters. What is the other leg, in meters?

  69. 69.A sail triangle at Montauk has legs of 20 feet and 21 feet. What is the hypotenuse, in feet?

  70. 70.A triangle at Saratoga Spa State Park has sides 6 yards, 8 yards, and 11 yards. Is it a right triangle?

  71. 71.A right triangle on a Lake Placid field has legs of 12 meters and 16 meters. What is the hypotenuse, in meters?

  72. 72.A right triangle on a field in Cooperstown has hypotenuse 26 yards and one leg of 10 yards. What is the other leg, in yards?

  73. 73.Two markers on an Empire State Plaza map are at (1, 2) and (4, 6). What is the distance between them, in grid units?

  74. 74.On a Battery Park grid, one kiosk is at (0, 0) and another is at (8, 6). What is the straight-line distance between them?

  75. 75.Two benches in Prospect Park are at (2, 5) and (11, 5) on a coordinate map. What is the distance between them?

  76. 76.Two gates on a Bronx Zoo map are at (−2, 3) and (2, 3). What is the distance between them?

  77. 77.Two posts on a Coney Island grid are at (1, 1) and (1, 7). What is the distance between them?

  78. 78.Two overlooks near Taughannock Falls are plotted at (−1, 2) and (4, 14). What is the distance between them?

  79. 79.Two viewing spots on a Niagara grid are at (3, −4) and (3, 2). What is the distance between them?

  80. 80.Two lifeguard chairs at Jones Beach are at (−5, 1) and (−1, −2). What is the distance between them?

  81. 81.Two trail posts in Rockefeller State Park are at (0, 1) and (7, 25). What is the distance between them?

  82. 82.A point at (4, −3) on a Central Park grid is reflected across the x-axis. What is the image?

  83. 83.A buoy at (−6, 2) on a Hudson chart is reflected across the y-axis. What is the image?

  84. 84.A statue marker at (1, 5) in Battery Park is translated 3 units right and 2 units down. What is the image?

  85. 85.A point at (5, 1) on an Albany plaza grid is rotated 90 degrees counterclockwise about the origin. What is the image?

  86. 86.A point at (−3, 4) on a Rochester map is rotated 180 degrees about the origin. What is the image?

  87. 87.A mural vertex at (6, 2) in Queens is dilated by a scale factor of 1/2 about the origin. What is the image?

  88. 88.A kiosk at (8, −1) in Times Square is translated 5 units left and 4 units up. What is the image?

  89. 89.A point at (2, −6) on a Syracuse grid is rotated 90 degrees clockwise about the origin. What is the image?

  90. 90.A street corner at (−2, 5) in Brooklyn is dilated by a scale factor of 3 about the origin. What is the image?

  91. 91.Two parallel streets in Manhattan are cut by a transversal. One angle measures 68 degrees. What is the measure of a corresponding angle?

  92. 92.Parallel rail lines near Albany are cut by a transversal. One interior angle measures 115 degrees. What does its alternate interior angle measure?

  93. 93.Parallel avenues in Brooklyn are cut by a transversal. One same-side interior angle measures 70 degrees. What does the other same-side interior angle measure?

  94. 94.Parallel park paths in Buffalo are cut by a transversal. One exterior angle measures 48 degrees. What does its alternate exterior angle measure?

  95. 95.A transversal crosses two parallel roads in Rochester and forms a 127 degree angle. What is the measure of the vertical angle opposite that angle?

  96. 96.A road cuts two parallel canal edges near Lockport. One interior angle measures 35 degrees. What is the measure of a consecutive interior angle?

  97. 97.A triangle between two fences in New Paltz has angles of 54 degrees and 61 degrees. What is the third angle?

  98. 98.A triangle on a farm near Saratoga has remote interior angles of 42 degrees and 67 degrees. What is the exterior angle at the third vertex?

  99. 99.Parallel bike lanes in Queens are cut by a transversal, and one angle measures 124 degrees. What is the measure of the angle that forms a linear pair with it?

  100. 100.Grain near an Erie Canal lock is stored in a cylinder of radius 4 meters and height 12 meters. What is the volume? Use V = πr^2h.

  101. 101.A jumbo ice cream cone at Coney Island has radius 3 inches and height 8 inches. What is the volume of the cone? Use V = (1/3)πr^2h.

  102. 102.A spherical water tank in Rochester has radius 6 feet. What is the volume? Use V = (4/3)πr^3.

  103. 103.A short cookie tin in a Brooklyn bakery is a cylinder with radius 9 centimeters and height 4 centimeters. What is the volume? Use V = πr^2h.

  104. 104.Campers in the Catskills pitch a cone-shaped tent with radius 7 feet and height 6 feet. What is the volume inside the cone? Use V = (1/3)πr^2h.

  105. 105.A globe in an Albany classroom is a sphere with radius 9 centimeters. What is its volume? Use V = (4/3)πr^3.

  106. 106.A storm culvert under a Syracuse street is a cylinder of radius 4 feet and length 15 feet. What volume of water could fill it? Use V = πr^2h.

  107. 107.A mill in Buffalo feeds grain through a cone-shaped hopper of radius 10 meters and height 9 meters. What is the volume? Use V = (1/3)πr^2h.

  108. 108.A spherical display in a Manhattan museum has radius 12 centimeters. What is the volume? Use V = (4/3)πr^3.