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GED Mathematical Reasoning Test practice questions

200 free questions with answers and explanations.

Practice test
  1. 1.A painter is hired to paint the walls of a cylindrical water tower. The tower has a radius of 7 feet and a height of 20 feet. If a single can of paint covers 300 square feet, how many cans of paint will the painter need to buy to cover the entire lateral surface of the tower?Quantitative Problem Solving with Measurement
  2. 2.A city planner is designing a new public square in the shape of a trapezoid. The parallel sides of the trapezoid are 60 meters and 90 meters, and the perpendicular distance between them is 40 meters. What is the area of the public square?Quantitative Problem Solving with Measurement
  3. 3.A cylindrical storage silo has a radius of 5 meters and a height of 12 meters. The silo needs to be painted on its top and curved side, but not the bottom. If one liter of paint covers 10 square meters, how many liters of paint are needed to paint the silo, rounded up to the nearest whole liter? (Use π ≈ 3.14)Quantitative Problem Solving with Measurement
  4. 4.A civil engineer is designing a parabolic arch for a bridge. The height of the arch, h, in meters, at a horizontal distance, x, from the left support, is modeled by the function h(x) = -0.1x(x - 40). What is the maximum height of the arch?Algebraic Problem Solving with Expressions and Equations
  5. 5.A manufacturer is designing a new spherical display case with a radius of 3 feet. To calculate the amount of glass needed, they must find the total surface area of the sphere. What is the total surface area of the display case, rounded to the nearest square foot? (Use π ≈ 3.14)Quantitative Problem Solving with Measurement
  6. 6.A pharmaceutical company is developing a new drug. The concentration of the drug in a patient's bloodstream, C, in mg/L, after 't' hours is given by C(t) = 50e^(-0.15t). What is the concentration of the drug after 3 hours? (Round to the nearest hundredth).Algebraic Problem Solving with Expressions and Equations
  7. 7.A farmer is planning to build a rectangular fence around a new pasture. The pasture is 150 feet long and 75 feet wide. If fencing material costs $2.50 per foot, what is the total cost of the fence?Quantitative Problem Solving with Measurement
  8. 8.A metal worker is fabricating a conical funnel with a radius of 6 cm and a slant height of 10 cm. If the worker needs to calculate the lateral surface area of the funnel (excluding the base) to determine the amount of material needed, what is the area, rounded to the nearest square centimeter? (Use π ≈ 3.14)Quantitative Problem Solving with Measurement
  9. 9.A technician is installing a new security camera on a pole. The camera is 24 feet above the ground, and a sensor needs to be placed 7 feet away from the base of the pole on the ground. What is the straight-line distance between the camera and the sensor?Quantitative Problem Solving with Measurement
  10. 10.A packaging company is designing a box in the shape of a rectangular prism. The box needs to hold a product that measures 5 inches long, 3 inches wide, and 2 inches high. What is the volume of the box required to fit this product exactly?Quantitative Problem Solving with Measurement
  11. 11.A contractor is installing a new triangular window. The window has a base of 6 feet and a height of 8 feet. If glass costs $15 per square foot, what is the total cost of the glass for this window?Quantitative Problem Solving with Measurement
  12. 12.A construction worker needs to determine the length of a diagonal brace for a rectangular gate. The gate is 8 feet tall and 6 feet wide. What is the length of the diagonal brace?Quantitative Problem Solving with Measurement
  13. 13.A worker needs to replace a square piece of glass in a window frame. The diagonal measurement of the square window is 30 inches. What is the approximate area of the glass needed, in square inches?Quantitative Problem Solving with Measurement
  14. 14.A manufacturer is designing a new cylindrical can with a radius of 3 cm and a height of 8 cm. What is the total surface area of the can, including the top and bottom? (Use π ≈ 3.14)Quantitative Problem Solving with Measurement
  15. 15.A packaging company is designing a new shipping box in the shape of a rectangular prism. The box needs to be 10 inches long, 6 inches wide, and 4 inches high. What is the total volume of the box?Quantitative Problem Solving with Measurement
  16. 16.A rectangular garden measures 12 feet in length and 8 feet in width. If a fence is to be built around the entire perimeter of the garden, what is the total length of fencing needed?Quantitative Problem Solving with Measurement
  17. 17.A designer is creating a scaled-down model of a building. The actual building is 60 meters tall, and the model is 1.5 meters tall. If a window on the actual building is 4 meters wide, how wide should the corresponding window on the model be?Quantitative Problem Solving with Measurement
  18. 18.A circular swimming pool has a diameter of 20 feet. What is the approximate circumference of the pool? (Use π ≈ 3.14)Quantitative Problem Solving with Measurement
  19. 19.A client wants to purchase a new spherical fish tank with a radius of 1.5 feet. If the tank needs to be filled with water, what is the approximate volume of water required, in cubic feet?Quantitative Problem Solving with Measurement
  20. 20.A worker is painting a rectangular wall that is 15 feet long and 9 feet high. What is the area of the wall that needs to be painted?Quantitative Problem Solving with Measurement
  21. 21.An architect is designing a scale model of a building. The actual building is 120 meters tall and the model is 30 centimeters tall. If a window on the actual building is 4 meters wide, what will be the width of the corresponding window on the scale model, in centimeters?Quantitative Problem Solving with Measurement
  22. 22.A gardener needs to cover a cylindrical planter with decorative paper. The planter has a radius of 0.5 feet and a height of 2 feet. What is the lateral surface area of the planter (the area of the side, not including the top and bottom)? (Use π ≈ 3.14)Quantitative Problem Solving with Measurement
  23. 23.A city engineer is planning a new pedestrian bridge. A support cable will run diagonally from the top of a 15-foot tower to a point on the ground 8 feet away from the base of the tower. What is the minimum length of the support cable needed, in feet?Quantitative Problem Solving with Measurement
  24. 24.A technician is installing a new antenna pole. To stabilize it, three guy wires are attached from the top of the 12-foot pole to points on the ground 5 feet from the base of the pole. What is the total length of the three guy wires needed?Quantitative Problem Solving with Measurement
  25. 25.A gardener is installing a new circular fountain with a diameter of 6 feet. To prevent weed growth, a special landscape fabric needs to be placed under the fountain. What is the approximate area of the landscape fabric needed, in square feet?Quantitative Problem Solving with Measurement
  26. 26.A contractor is installing a new circular window with a radius of 1.5 feet. To ensure proper sealing, a weatherstripping material needs to be applied around the entire edge of the window. If the material is sold in rolls of 10 feet, how many rolls will the contractor need to purchase?Quantitative Problem Solving with Measurement
  27. 27.A surveyor is mapping a plot of land. Point A is at coordinates (2, 3) and Point B is at coordinates (5, 7). What is the straight-line distance between Point A and Point B?Quantitative Problem Solving with Measurement
  28. 28.A farmer is planning to build a new cylindrical grain silo with a height of 15 meters and a diameter of 8 meters. What is the maximum volume of grain, in cubic meters, that the silo can hold?Quantitative Problem Solving with Measurement
  29. 29.A surveyor is measuring a triangular plot of land. The base of the triangle is 80 meters, and its height is 50 meters. If the land is valued at $2.50 per square meter, what is the total value of the plot?Quantitative Problem Solving with Measurement
  30. 30.A carpenter is building a ramp for a wheelchair. The ramp must rise 1 foot for every 12 feet of horizontal distance. If the ramp needs to reach a height of 2 feet, what is the length of the ramp's base (horizontal distance)?Quantitative Problem Solving with Measurement
  31. 31.A landscaper is designing a triangular flower bed with a base of 10 feet and a height of 6 feet. What is the area of the flower bed?Quantitative Problem Solving with Measurement
  32. 32.A shipping company needs to calculate the volume of a cubic container with side lengths of 5 feet. How much space does the container occupy?Quantitative Problem Solving with Measurement
  33. 33.A farmer is building a new barn with a gable roof. The roof has two rectangular sections, each 40 feet long and 25 feet wide. To purchase enough roofing material, the farmer needs to calculate the total surface area of these two sections. What is the total area of the roof?Quantitative Problem Solving with Measurement
  34. 34.A packaging company is designing a new gift box in the shape of a square pyramid. The base of the pyramid is a square with side lengths of 6 inches, and the slant height of each triangular face is 5 inches. What is the total surface area of the pyramid, including the base?Quantitative Problem Solving with Measurement
  35. 35.A city planner is designing a new public park that includes a circular plaza. The plaza will have a radius of 15 meters. If the city wants to install decorative lighting around the entire edge of the plaza, what is the total length of lighting needed, rounded to the nearest meter?Quantitative Problem Solving with Measurement
  36. 36.A client wants to install new baseboards around a circular room. If the room has a radius of 4 meters, what is the approximate length of baseboard needed? (Use π ≈ 3.14)Quantitative Problem Solving with Measurement
  37. 37.A landscaper is designing a circular flower bed with a radius of 4 feet. If a protective mesh needs to cover the entire top surface of the flower bed, what is the minimum area of mesh required, rounded to the nearest square foot?Quantitative Problem Solving with Measurement
  38. 38.A cylindrical water tank has a radius of 3 meters and a height of 10 meters. What is the maximum volume of water the tank can hold? (Use π ≈ 3.14)Quantitative Problem Solving with Measurement
  39. 39.A homeowner is planning to build a rectangular deck with an area of 180 square feet. If the length of the deck is 15 feet, what is its width?Quantitative Problem Solving with Measurement
  40. 40.A landscape architect is designing a path through a park. The path will be 3 feet wide and will follow the perimeter of a rectangular grassy area that measures 50 feet by 100 feet. If the path is to be paved with stones that cover 1.5 square feet each, approximately how many stones are needed for the path?Quantitative Problem Solving with Measurement
  41. 41.A production manager is tracking the output of two machines. Machine A produces 50 units per hour plus an initial setup batch of 20 units. Machine B produces 60 units per hour with no initial setup batch. After how many hours will Machine B have produced the same number of units as Machine A?Algebraic Problem Solving with Expressions and Equations
  42. 42.A plumber needs to run a pipe diagonally across a rectangular room. The room is 12 feet long and 5 feet wide. What is the shortest possible length of the pipe?Quantitative Problem Solving with Measurement
  43. 43.A scientist is tracking the movement of a drone. The drone starts at point A (1, 2) and flies to point B (7, 10). What is the straight-line distance, in units, the drone traveled?Quantitative Problem Solving with Measurement
  44. 44.A financial analyst is modeling the quarterly profit (P) of a company, which is described by the function P(q) = -2q² + 16q - 24, where 'q' is the number of quarters since the company started. What is the maximum profit the company achieves?Algebraic Problem Solving with Expressions and Equations
  45. 45.A biologist is tracking the population of a certain type of algae in a pond. The population, P(t), in thousands, after 't' days, is modeled by the function P(t) = 50e^(0.08t). Approximately how many days will it take for the algae population to reach 150 thousand?Algebraic Problem Solving with Expressions and Equations
  46. 46.A production manager is analyzing the cost of manufacturing a new product. The fixed costs for setting up the production line are $5,000, and the variable cost per unit produced is $15. If 'C' represents the total cost and 'x' represents the number of units produced, which equation models the total cost?Algebraic Problem Solving with Expressions and Equations
  47. 47.A botanist is studying the growth of a plant. The height of the plant, h, in centimeters, over time, t, in weeks, is modeled by the function h(t) = 3t + 15. What is the initial height of the plant?Algebraic Problem Solving with Expressions and Equations
  48. 48.A technician is calibrating a sensor. The sensor's reading (R) in volts is modeled by the equation R = 3x² - 12x + 15, where 'x' is the input signal strength. What is the minimum possible reading of the sensor?Algebraic Problem Solving with Expressions and Equations
  49. 49.An architect is designing a rectangular room. The length (L) of the room is 3 feet more than twice its width (W). If the perimeter of the room is 66 feet, what is the width of the room?Algebraic Problem Solving with Expressions and Equations
  50. 50.A chemist is observing a reaction where the concentration of a reactant, C, in moles per liter, changes over time, t, in minutes. The change is modeled by the function C(t) = 0.5t² - 3t + 8. At what time, in minutes, is the concentration at its minimum value?Algebraic Problem Solving with Expressions and Equations