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Praxis Core Academic Skills for Educators: Mathematics (5733) practice questions

200 free questions with answers and explanations.

Practice test
  1. 1.A landscaper is designing a rectangular garden plot that is 15 feet long and 8 feet wide. If they want to place a fence around the entire perimeter of the garden, how many feet of fencing will they need?Geometry
  2. 2.A cartographer is creating a map. A particular region is a trapezoid with parallel bases measuring 12 km and 18 km, and a height of 10 km. What is the area of this region?Geometry
  3. 3.A manufacturer is designing a new product with a prism-shaped component whose base is a right triangle. The legs of the right triangle are 3 cm and 4 cm, and the height of the prism is 10 cm. What is the volume of this triangular prism?Geometry
  4. 4.A company is designing a new cylindrical water tank. The tank has a diameter of 8 feet and a height of 15 feet. What is the volume of the tank?Geometry
  5. 5.A construction worker is laying a rectangular concrete slab that needs to be 12 feet long and 9 feet wide. To ensure the slab is perfectly rectangular, the worker must verify that the diagonals are equal in length. What is the length of one diagonal?Geometry
  6. 6.A manufacturer is designing a new packaging box for a product. The box needs to be a rectangular prism with dimensions of 6 inches by 4 inches by 3 inches. If the box is to be covered entirely with a decorative paper, what is the total surface area of the box that needs to be covered?Geometry
  7. 7.A surveyor needs to determine the height of a flagpole. From a point on the ground 40 feet away from the base of the flagpole, the angle of elevation to the top of the flagpole is 30 degrees. How tall is the flagpole to the nearest foot?Geometry
  8. 8.A designer is creating a tile pattern using regular octagons. If one interior angle of a regular octagon is 135 degrees, what is the measure of one exterior angle?Geometry
  9. 9.A civil engineer is designing a new road. A section of the road needs to be represented on a coordinate plane as a line segment. If the midpoint of this segment is (3, 4) and one endpoint is (1, 6), what are the coordinates of the other endpoint?Geometry
  10. 10.A technician is installing a new antenna mast. To stabilize the mast, two guy wires are attached from the top of the 24-foot mast to the ground. Each wire makes an angle of 60 degrees with the ground. What is the approximate total length of both guy wires needed?Geometry
  11. 11.A machinist is cutting a metal plate in the shape of a regular hexagon. If one side of the hexagon measures 6 cm, what is the area of the hexagon?Geometry
  12. 12.A carpenter is cutting a triangular piece of wood. If the base of the triangle is 10 inches and its height is 6 inches, what is the area of the triangular piece of wood?Geometry
  13. 13.A designer is creating a logo that involves a regular pentagon. If the sum of the interior angles of a regular polygon is given by the formula (n-2) × 180°, where 'n' is the number of sides, what is the measure of one interior angle of this regular pentagon?Geometry
  14. 14.A packaging engineer is designing a container in the shape of a cylinder. The cylinder has a radius of 4 cm and a height of 10 cm. What is the approximate surface area of the cylinder, including the top and bottom circular bases?Geometry
  15. 15.A surveyor is measuring a plot of land that is shaped like an isosceles trapezoid. The parallel sides measure 20 meters and 30 meters, respectively. The height of the trapezoid is 12 meters. What is the area of this plot of land?Geometry
  16. 16.A painter is using a ladder to reach a window. The ladder is 13 feet long and its base is placed 5 feet away from the wall. Assuming the wall is perfectly vertical, how high up the wall does the ladder reach?Geometry
  17. 17.A designer is creating a custom-shaped swimming pool. The pool's base can be modeled as a composite figure consisting of a rectangle and a semicircle. The rectangle is 10 meters long and 6 meters wide. The semicircle is attached to one of the 6-meter sides. What is the approximate total area of the pool's base?Geometry
  18. 18.A civil engineer is designing a road that will pass through a tunnel. The tunnel opening is a semi-circle with a diameter of 20 feet. If the road needs to be 16 feet wide at the base of the tunnel, what is the maximum height of a vehicle that can pass through the tunnel at the edge of the 16-foot wide road?Geometry
  19. 19.A construction worker is building a ramp. The ramp rises 3 feet vertically for every 4 feet of horizontal distance. What is the angle of elevation of the ramp to the nearest degree?Geometry
  20. 20.A gardener is planning to install a circular flower bed with a diameter of 10 feet. What is the approximate circumference of the flower bed?Geometry
  21. 21.A designer is creating a circular logo with a diameter of 14 centimeters. What is the approximate area of the logo?Geometry
  22. 22.A packaging company is designing a new rectangular box. The box has dimensions of 5 cm by 4 cm by 3 cm. What is the surface area of this box?Geometry
  23. 23.A sculptor is creating a large pyramid structure for an exhibit. The pyramid has a square base with sides of 10 feet and a height of 12 feet. The sculptor needs to calculate the volume of the pyramid to determine the amount of material required. What is the volume of the pyramid?Geometry
  24. 24.A scientist is studying the movement of a particle on a coordinate plane. The particle starts at (3, 2) and undergoes a dilation centered at the origin with a scale factor of 3. What are the new coordinates of the particle after this transformation?Geometry
  25. 25.A surveyor measures the angles of a quadrilateral. Three of the angles are 85°, 110°, and 70°. What is the measure of the fourth angle?Geometry
  26. 26.A surveyor is measuring angles of a complex intersection. One angle of a transversal intersecting two parallel lines is measured as 4x + 10 degrees. Its corresponding angle is measured as 6x - 20 degrees. What is the value of x?Geometry
  27. 27.A landscaper is designing a flower bed that is a sector of a circle. The radius of the sector is 6 meters, and the central angle is 60 degrees. What is the approximate area of the flower bed?Geometry
  28. 28.A civil engineer is designing a circular traffic roundabout with a radius of 20 meters. A pedestrian walkway is planned along the circumference. If the engineer needs to determine the length of an arc spanning a central angle of 90 degrees for a specific section of the walkway, what is the length of this arc?Geometry
  29. 29.A glassblower is creating spherical ornaments. Each ornament has a radius of 3 cm. What is the approximate volume of one ornament?Geometry
  30. 30.A geometer is analyzing a line segment on a coordinate plane. The segment connects point A (2, 5) and point B (8, 1). What is the length of this line segment?Geometry
  31. 31.A sculptor is creating a cone-shaped artwork. The cone has a radius of 3 feet and a height of 7 feet. What is the approximate volume of the cone?Geometry
  32. 32.A landscape architect is designing a garden bed in the shape of a sector of a circle. The circular garden has a radius of 10 feet, and the central angle of the sector is 144 degrees. What is the area of this garden bed?Geometry
  33. 33.A machinist is programming a robotic arm to cut a triangular piece from a sheet of metal. The vertices of the triangle are at A(1, 2), B(7, 2), and C(4, 8). What is the area of this triangle?Geometry
  34. 34.A city planner is evaluating the area of a proposed park, which is shaped like a regular pentagon. If the length of one side of the pentagon is 80 meters, and its apothem (distance from center to midpoint of a side) is approximately 55.05 meters, what is the approximate area of the park?Geometry
  35. 35.A graphic designer is creating an animation where an object moves from point A(-2, 5) to point B(4, -3). If the object moves along a straight line, what are the coordinates of the midpoint of its path?Geometry
  36. 36.A craftsman is designing a decorative window pane in the shape of a rhombus. One diagonal of the rhombus measures 16 inches, and the other diagonal measures 12 inches. What is the area of the rhombus?Geometry
  37. 37.A carpenter needs to cut a piece of wood in the shape of a right-angled triangle. If one leg measures 6 inches and the hypotenuse measures 10 inches, what is the length of the other leg?Geometry
  38. 38.A high school counselor is analyzing the test scores of 10 students on a recent math exam. The scores are: 78, 85, 92, 78, 95, 88, 78, 90, 85, 82. What is the mode of these test scores?Statistics and Probability
  39. 39.A student is planning a schedule for their final exams. There are 4 different exams to be taken over 4 consecutive days, with only one exam per day. In how many different orders can the student schedule their exams?Statistics and Probability
  40. 40.A card is drawn from a standard deck of 52 cards, then replaced, and a second card is drawn. What is the probability that both cards drawn are aces?Statistics and Probability
  41. 41.A teacher recorded the number of books read by students in a class over a month: 2, 5, 3, 7, 2, 4, 3, 5, 2, 6. What is the median number of books read?Statistics and Probability
  42. 42.A meteorologist is recording the daily high temperatures (in °F) for a week in a particular city: 72, 75, 68, 70, 73, 76, 69. What is the range of these temperatures?Statistics and Probability
  43. 43.A quality control engineer is testing a new production line. Out of 200 items produced, 10 are found to be defective. If this rate continues, what is the probability that the next item produced will NOT be defective?Statistics and Probability
  44. 44.A game involves spinning a fair 4-sided spinner numbered 1, 2, 3, 4, and flipping a fair coin. What is the probability of spinning an odd number AND flipping a tails?Statistics and Probability
  45. 45.A quality control manager is inspecting a batch of 100 manufactured parts. The manager finds that 8 parts are defective. If the manager randomly selects 2 parts from the batch for further testing, without replacement, what is the probability that both selected parts are defective?Statistics and Probability
  46. 46.A librarian is organizing new books on a shelf. There are 7 new novels and 5 new non-fiction books. If the librarian wants to choose 3 novels and 2 non-fiction books to display on a special stand, how many different combinations of books can be chosen?Statistics and Probability
  47. 47.A survey asked 150 people about their favorite type of movie. The results are shown in the pie chart below (percentages are approximate). If 20% prefer action movies and 30% prefer comedy, how many people prefer drama movies if the remaining 50% is split equally between drama and sci-fi?Statistics and Probability
  48. 48.A researcher collects data on the heights of 100 individuals and finds that the mean height is 170 cm with a standard deviation of 5 cm. If the data is normally distributed, approximately what percentage of individuals have a height between 165 cm and 175 cm?Statistics and Probability
  49. 49.A student is randomly selecting 3 books from a shelf containing 8 different books. How many different combinations of 3 books can the student select?Statistics and Probability
  50. 50.A market researcher is analyzing the number of daily visitors to a new website for the first week: 150, 165, 140, 170, 155, 160, 180. What is the median number of daily visitors?Statistics and Probability