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Praxis Middle School Mathematics: Geometry and Measurement

Area, volume, angles, coordinates, and measurement for middle school, including what to do when a student's geometry goes wrong.

Teacher certification exams are administered by testing organizations. FreeExam is not affiliated with those organizations, and these questions are original practice, not an official test.

Praxis is a trademark of Educational Testing Service. FreeExam is not affiliated with Educational Testing Service, and these questions are original practice, not an official test.

  1. 1.A rectangle is 4 units by 9 units. What is its perimeter?

  2. 2.A rectangle is 4 units by 9 units. What is its area?

  3. 3.A triangle has base 8 and height 5. What is its area?

  4. 4.Two angles of a triangle measure 50° and 60°. What is the third angle?

  5. 5.An angle measures 35°. What is the measure of its complement?

  6. 6.An angle measures 110°. What is the measure of its supplement?

  7. 7.A square has side length 6. What is its perimeter?

  8. 8.A cube has edge length 3. What is its volume?

  9. 9.A rectangular box is 2 by 5 by 6. What is its volume?

  10. 10.A student finds the area of a 7 by 3 rectangle by adding 7 + 3 = 10. What should the teacher ask the student to compute?

  11. 11.A circle has radius 4. Which expression is its circumference?

  12. 12.A circle has radius 4. Which expression is its area?

  13. 13.A student uses the diameter 10 as if it were the radius and reports the area as 100π. What is the area?

  14. 14.A board is 3 feet long. How many inches is that?

  15. 15.A ribbon is 2 meters long. How many centimeters is that?

  16. 16.Two parallel lines are cut by a transversal. One corresponding angle is 48°. What is the matching corresponding angle?

  17. 17.Two lines cross and form a 33° angle. What is the measure of the vertical angle opposite that one?

  18. 18.An isosceles triangle has a vertex angle of 40°. What is each base angle?

  19. 19.A right triangle has legs 5 and 12. What is the hypotenuse?

  20. 20.What is the distance between (0, 0) and (6, 8)?

  21. 21.What is the midpoint of (1, 2) and (7, 10)?

  22. 22.Point (3, −2) is reflected across the x-axis. Where does it land?

  23. 23.Point (4, 1) is translated 2 units left and 5 units up. What is the image?

  24. 24.A student says a 90° clockwise turn around the origin sends (2, 0) to (0, 2). Where does (2, 0) go?

  25. 25.Two similar rectangles have a scale factor of 3 from the smaller to the larger. A side of the smaller is 4. What is the corresponding side of the larger?

  26. 26.The smaller of two similar figures has area 5. The scale factor to the larger figure is 2. What is the larger area?

  27. 27.A rectangular prism is 3 by 4 by 5. What is its surface area?

  28. 28.A triangular prism has a triangular base of area 10 and a length of 6. What is its volume?

  29. 29.Three angles of a quadrilateral measure 80°, 90°, and 100°. What is the fourth angle?

  30. 30.A student claims every quadrilateral has four right angles. Which counterexample should the teacher draw?

  31. 31.A path is 1.5 kilometers. How many meters is that?

  32. 32.A gallon is 4 quarts. How many quarts are in 3 gallons?

  33. 33.A parallelogram has base 9 and height 4. What is its area?

  34. 34.A trapezoid has bases 6 and 10 and height 4. What is its area?

  35. 35.A net of a cube is folded. How many square faces does the cube have?

  36. 36.A student counts 8 corners on a cube and says the cube has 8 faces. What should the teacher point to?

  37. 37.A right angle is split into a 28° angle and another angle. What is the other angle?

  38. 38.Two adjacent angles form a straight line. One is 115°. What is the other?

  39. 39.A circle has radius 7. Which expression is its area?

  40. 40.A triangle has sides 5, 5, and 6. What is its perimeter?

  41. 41.A rectangle has area 48 and width 6. What is its length?

  42. 42.Point (−4, 5) is in which quadrant?

  43. 43.A scale drawing uses 1 centimeter for 4 meters. A wall is 3 centimeters on the drawing. How long is the wall?

  44. 44.A composite figure is a 6 by 4 rectangle with a triangle of base 6 and height 2 attached along the side of length 6. What is the total area?

  45. 45.How many 1-centimeter cubes fill a 2 by 3 by 4 box?

  46. 46.A cube has edge 2. What is its surface area?

  47. 47.A right triangle has legs 8 and 15. What is the hypotenuse?

  48. 48.A student computes the area of a triangle with base 10 and height 6 as 60. What is the area, and what was omitted?

  49. 49.A segment is 2 feet 6 inches long. How many inches is that?

  50. 50.Which lengths can be the sides of a triangle?

  51. 51.A square has four lines of symmetry. How many lines of symmetry does a non-square rectangle have?

  52. 52.Point (5, −1) is reflected across the y-axis. Where does it land?

  53. 53.A 180° turn around the origin sends (3, 4) to which point?

  54. 54.An equilateral triangle has a perimeter of 21. What is each side, and what is each angle?

  55. 55.Two parallel lines are cut by a transversal. An interior angle on one side of the transversal is 72°. What is the alternate interior angle?

  56. 56.A map distance of 5 centimeters represents 15 kilometers. How many kilometers does 1 centimeter represent?

  57. 57.A bottle holds 3 liters. How many milliliters is that?

  58. 58.A student says every square is a rectangle. Is that true, and why?

  59. 59.A circle has diameter 10. Using 3.14 for π, what is the circumference to the nearest tenth?

  60. 60.A teacher asks which cross section a plane can make through a cube if the plane is parallel to a face. What is that cross section?

  61. 61.The area of a square is 64 square units. What is the side length?

  62. 62.A rectangular garden is 8 yards long and 3 yards wide. How many feet of fence are needed to go around it once?

  63. 63.Two similar triangles have a scale factor of 2. A side of the larger triangle is 14. What is the corresponding side of the smaller triangle?

  64. 64.A student adds 2 feet and 6 inches and writes 8. What should the teacher have the student do first?

  65. 65.One square foot is how many square inches?

  66. 66.The coordinates of a rectangle are (1, 1), (1, 5), (6, 5), and (6, 1). What is its area?

  67. 67.A regular pentagon has how many sides, and what is the sum of its interior angles?

  68. 68.Which figure has exactly one pair of parallel sides?

  69. 69.A wheel has radius 3. About how far does a point on the rim travel in one full turn, in terms of π?

  70. 70.A student reflects (2, 5) across the x-axis and writes (−2, 5). What is the image, and which coordinate was changed by mistake?

  71. 71.The volume of a rectangular prism is 120. The base is 5 by 4. What is the height?

  72. 72.Which transformation moves every point the same distance in the same direction?

  73. 73.A rectangle is 11 by 2. What is its perimeter?

  74. 74.A triangle has angles 90°, 45°, and an unknown angle. What is the unknown angle?

  75. 75.How many edges does a rectangular prism have?

  76. 76.A student says a dilation with scale factor 2 about the origin sends (1, 3) to (2, 5). Where does the point go?

  77. 77.A room is 4 meters by 5 meters. What is its area in square meters?

  78. 78.Two angles are vertical angles. One measures 81°. What does the other measure?

  79. 79.A parallelogram has base 12 and height 3. What is its area?

  80. 80.Which point is 5 units from (0, 0) on the positive x-axis?

  81. 81.A circle has radius 1. Which expression is its area?

  82. 82.A student finds the perimeter of a 9 by 2 rectangle as 11. What is the perimeter?

  83. 83.A trapezoid has bases 5 and 9 and height 2. What is its area?

  84. 84.A figure is translated 4 units right. The image of (−1, 2) is which point?

  85. 85.How many square inches are in 2 square feet?

  86. 86.A right triangle has a hypotenuse of 10 and one leg of 6. What is the other leg?

  87. 87.Which pair of shapes must be similar?

  88. 88.A tank is a rectangular prism 10 centimeters by 2 centimeters by 2 centimeters. What is its volume?

  89. 89.An angle measures 15°. What is its complement?

  90. 90.A student uses the slanted side of a parallelogram, 5, as the height when the base is 8 and the perpendicular height is 3. The student gets area 40. What is the area?

  91. 91.What is the midpoint of (−2, 4) and (6, 4)?

  92. 92.A dilation has scale factor 1/2 about the origin. The image of (8, 2) is which point?

  93. 93.A quadrilateral has angles 70°, 80°, 110°, and an unknown angle. What is the unknown angle?

  94. 94.Which of these is the area of a circle with diameter 6?

  95. 95.A class measures a desk as 120 centimeters. How many meters is that?

  96. 96.A student claims the distance from (0, 0) to (5, 12) is 17, the sum of 5 and 12. What is the distance?

  97. 97.How many lines of symmetry does an equilateral triangle have?

  98. 98.A prism has a pentagonal base. How many faces does the prism have?

  99. 99.The perimeter of a square is 20. What is its area?

  100. 100.Which move shows that two figures are congruent, not merely similar?

  101. 101.A triangle has base 7 and height 4. What is its area?

  102. 102.A teacher wants a counterexample to the claim that every rhombus is a square. Which figure works?

  103. 103.Two yards are how many inches?

  104. 104.Point (0, −3) is rotated 90° counterclockwise about the origin. Where does it land?

  105. 105.A rectangular prism is 1 by 1 by 10. What is its volume?

  106. 106.Which description is a reflection of the point (4, 7) across the horizontal line y = 0?

  107. 107.A similar copy of a figure uses scale factor 4. The original area is 3 square units. What is the copy's area?

  108. 108.A student computes the circumference of a circle with radius 5 as 5π. What should the teacher ask next?