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GED Mathematical Reasoning Test practice questions

200 free questions with answers and explanations.

Practice test
  1. 101.A production manager is analyzing the efficiency of a new machine. The machine's output, in units per hour, is modeled by the function E(t) = -0.5t² + 10t + 50, where t is the number of hours the machine has been running since the start of the shift. What is the maximum output the machine achieves?Algebraic Problem Solving with Graphs and Functions
  2. 102.A meteorologist is tracking a weather balloon. The balloon's altitude, h(t), in meters, after t minutes, is given by the function h(t) = 50t + 200. What is the practical range of this function if the balloon is tracked for 10 minutes, starting from t=0?Algebraic Problem Solving with Graphs and Functions
  3. 103.A pilot is planning a flight path. On a coordinate plane, the aircraft's current position is (3, 5) and its destination is (9, 13). What is the slope of the straight-line path between these two points?Algebraic Problem Solving with Graphs and Functions
  4. 104.A client is managing their financial portfolio. The value of their investment, V(t), in thousands of dollars, after t years, is represented by the function V(t) = 50 * (1.07)^t. What does the value '1.07' represent in this function?Algebraic Problem Solving with Graphs and Functions
  5. 105.A production manager is analyzing the efficiency of a new machine. The machine's output, in units per hour, is given by the function E(t) = -t² + 10t + 20, where 't' is the number of hours the machine has been running since the start of a shift. After how many hours will the machine reach its maximum output?Algebraic Problem Solving with Graphs and Functions
  6. 106.A manufacturing company's production cost, C, in thousands of dollars, depends on the number of units, x, produced according to the function C(x) = 0.5x + 10. The company wants to keep its production cost below $25,000. Which inequality represents the number of units the company can produce?Algebraic Problem Solving with Graphs and Functions
  7. 107.A technician is monitoring the voltage of a circuit. The voltage, V, in volts, over time, t, in milliseconds, is modeled by the function V(t) = 120 * sin(0.5t) + 60. What is the maximum voltage observed in the circuit?Algebraic Problem Solving with Graphs and Functions
  8. 108.A technician is monitoring the voltage of a circuit. The voltage, V, in volts, over time, t, in milliseconds, is given by the function V(t) = 5sin(πt/2) + 12. What is the maximum voltage recorded in the circuit?Algebraic Problem Solving with Graphs and Functions
  9. 109.A production line's efficiency (E), in units per hour, is modeled by the function E(t) = -t² + 14t - 24, where t is the number of hours the line has been running since midnight (0 ≤ t ≤ 10). What is the practical domain for this function in the given context?Algebraic Problem Solving with Graphs and Functions
  10. 110.A scientist is observing the decay of a radioactive substance. The amount of the substance remaining, A(t), in grams, after t days, is given by the graph below. According to the graph, what is the half-life of the substance?Algebraic Problem Solving with Graphs and Functions
  11. 111.A technician is calibrating a sensor. The sensor's output, in volts, is represented by the function f(x) = 2x - 3, where x is the input signal. What is the value of the output when the input signal is 5?Algebraic Problem Solving with Graphs and Functions
  12. 112.A scientist is tracking the population of a certain bacteria culture. Initially, there are 200 bacteria. The population doubles every 3 hours. Which function represents the bacteria population P(t) after t hours?Algebraic Problem Solving with Graphs and Functions
  13. 113.A drone is flying in a search pattern. Its path is recorded on a coordinate plane, and at one point, it is at (2, 7). Later, it is at (8, 19). Which of the following is the equation of the line representing the drone's path between these two points?Algebraic Problem Solving with Graphs and Functions
  14. 114.A technician is monitoring the temperature of a chemical reaction. The temperature, T (in °C), at time t (in minutes) is given by the function T(t) = -t² + 10t + 20. What is the maximum temperature reached during the reaction?Algebraic Problem Solving with Graphs and Functions
  15. 115.A scientist is tracking the population of a certain bacteria culture. Initially, there are 200 bacteria. The population triples every hour. Which type of function best represents the growth of this bacteria culture, and why?Algebraic Problem Solving with Graphs and Functions
  16. 116.A gardener is designing a rectangular flower bed. The length of the flower bed is 5 feet more than its width. If the area of the flower bed is 84 square feet, what is the width of the flower bed?Algebraic Problem Solving with Graphs and Functions
  17. 117.A scientist is observing the decay of a radioactive isotope. The amount of the isotope remaining, A(t), in grams, after t days is given by the function A(t) = 100 * (0.5)^(t/3). What does the value '0.5' represent in this function?Algebraic Problem Solving with Graphs and Functions
  18. 118.A scientist is observing the decay of a radioactive isotope. The graph shows the amount of the isotope remaining (in grams) over time (in days). Which type of function best models this decay process?Algebraic Problem Solving with Graphs and Functions
  19. 119.A nutritionist is monitoring a patient's weight during a diet program. The patient's weight, W (in pounds), after d days is modeled by the function W(d) = 200 - 0.5d. What does the y-intercept of this function represent in the context of the patient's weight?Algebraic Problem Solving with Graphs and Functions
  20. 120.A scientist is observing the decay of a radioactive substance. The graph shows the amount of substance remaining over time. The graph passes through the points (0, 100) and (2, 25). Which of the following functions best models the amount of substance, A, remaining after t hours?Algebraic Problem Solving with Graphs and Functions
  21. 121.A drone is flying in a search pattern. Its path can be described by the linear equation 3x + 2y = 12. A second drone is flying parallel to the first drone. Which of the following equations could represent the path of the second drone?Algebraic Problem Solving with Graphs and Functions
  22. 122.A biologist is studying the growth of a plant. She records the plant's height in centimeters over several weeks. If the plant grows from 10 cm to 25 cm in 5 weeks, what is the average rate of change of the plant's height per week?Algebraic Problem Solving with Graphs and Functions
  23. 123.A financial analyst is comparing two investment options. Investment A offers a fixed annual return, while Investment B's return depends on market volatility. The growth of Investment A is represented by a straight line on a graph, and Investment B's growth is represented by a curve that initially rises slowly and then more rapidly. What type of function would best describe Investment B's growth?Algebraic Problem Solving with Graphs and Functions
  24. 124.A city planner is analyzing population growth. The population, P, in thousands, can be modeled by the function P(t) = 100 * (1.02)^t, where t is the number of years since the year 2000. In what year will the population first exceed 150 thousand?Algebraic Problem Solving with Graphs and Functions
  25. 125.A client is tracking their savings account balance. The balance (B) in dollars over time (t) in months is represented by the equation B = 150t + 500. What does the number 500 represent in this context?Algebraic Problem Solving with Graphs and Functions
  26. 126.A meteorologist is tracking a weather balloon. The balloon's altitude, h(t), in meters, after t minutes is given by the function h(t) = -t^2 + 10t + 50. What is the practical domain of this function if the balloon's flight ends when it returns to the ground (h(t) = 0)?Algebraic Problem Solving with Graphs and Functions
  27. 127.A company's quarterly profits (in thousands of dollars) are represented by the function P(x) = -x² + 8x - 7, where x is the quarter number (1 for Q1, 2 for Q2, etc.). During which quarter did the company achieve its maximum profit?Algebraic Problem Solving with Graphs and Functions
  28. 128.A scientist is tracking the growth of a bacterial colony. The graph shows the number of bacteria, N, over time, t, in hours. If the graph is a straight line passing through (0, 100) and (4, 700), what is the slope of the line, representing the average growth rate of the colony?Algebraic Problem Solving with Graphs and Functions
  29. 129.A client is tracking their savings account balance. The balance (B) in dollars over time (t) in years is represented by the function B(t) = 1500(1.03)^t. What does the value 1500 represent in this context?Algebraic Problem Solving with Graphs and Functions
  30. 130.A scientist is observing the growth of a bacterial colony. The population, P, in thousands, after t hours, is modeled by the function P(t) = 50 * (1.15)^t. What does the value '1.15' represent in this context?Algebraic Problem Solving with Graphs and Functions
  31. 131.A drone is flying in a search pattern. Its path is recorded on a coordinate plane, and at one point, it is at (2, 5) and later at (8, 17). Which of the following equations represents the line of the drone's path between these two points?Algebraic Problem Solving with Graphs and Functions
  32. 132.A financial analyst is comparing two investment options. Investment A grows according to the function A(t) = 100(1.05)^t, and Investment B grows according to B(t) = 100 + 10t, where t is the number of years. Which statement accurately describes the growth of these investments?Algebraic Problem Solving with Graphs and Functions
  33. 133.A financial analyst is comparing two investment options. Investment A grows linearly, starting at $1000 and increasing by $50 each year. Investment B grows exponentially, starting at $800 and increasing by 5% each year. Which function correctly models Investment B's value, V(t), after t years?Algebraic Problem Solving with Graphs and Functions
  34. 134.A chemist is observing a chemical reaction where the concentration of a certain substance, C(t), in moles per liter, after t minutes, is given by the function C(t) = 0.5t² - 4t + 10. During which time interval is the concentration of the substance decreasing?Algebraic Problem Solving with Graphs and Functions
  35. 135.A meteorologist is tracking a weather balloon. The balloon's altitude, h(t), in meters, after t minutes, is given by the graph below. Based on the graph, what is the approximate altitude of the balloon after 30 minutes?Algebraic Problem Solving with Graphs and Functions
  36. 136.A gardener is planting rows of flowers. The number of flowers he plants each day follows a pattern: 5, 8, 11, 14, ... . If this pattern continues, what is the total number of flowers he will have planted after 6 days?Algebraic Problem Solving with Graphs and Functions
  37. 137.A company's quarterly profits (in thousands of dollars) are represented by the function P(q) = -2q² + 16q - 10, where q is the quarter number (q=1 for Q1, q=2 for Q2, etc.). What is the maximum profit the company achieves?Algebraic Problem Solving with Graphs and Functions
  38. 138.A client invests $5,000 in an account that earns simple interest at an annual rate of 3.5%. How much interest will the client earn in 4 years?Quantitative Problem Solving with Rational Numbers
  39. 139.A biologist is observing a bacterial culture. The population started with 400 bacteria and increased by 30% every hour for 3 hours. What was the approximate bacterial population after 3 hours?Quantitative Problem Solving with Rational Numbers
  40. 140.A tailor needs 1.75 meters of fabric for each shirt. If a bolt of fabric contains 28 meters, how many full shirts can the tailor make?Quantitative Problem Solving with Rational Numbers
  41. 141.A rectangular swimming pool is 25 meters long and 10 meters wide. A safety rope needs to be placed around the perimeter of the pool. If the rope costs $1.50 per meter, what is the total cost of the rope?Quantitative Problem Solving with Rational Numbers
  42. 142.A painter estimates that he can cover 320 square feet with 1 gallon of paint. If he needs to paint a wall that is 14 feet high and 24 feet long, how many gallons of paint will he need to purchase? Round your answer to the nearest whole gallon.Quantitative Problem Solving with Rational Numbers
  43. 143.A student's scores on five math quizzes were 78, 85, 92, 70, and 85. What is the median score?Quantitative Problem Solving with Rational Numbers
  44. 144.A nutritionist is preparing a meal plan. She wants to divide 5 1/4 cups of quinoa equally among 3 servings. How much quinoa will be in each serving?Quantitative Problem Solving with Rational Numbers
  45. 145.A car's fuel tank is 5/6 full. After a trip, it is now 1/3 full. What fraction of the tank's capacity was used during the trip?Quantitative Problem Solving with Rational Numbers
  46. 146.A recipe requires 3/4 cup of milk for every 2 cups of flour. If a baker uses 6 cups of flour, how many cups of milk are needed?Quantitative Problem Solving with Rational Numbers
  47. 147.A quality control inspector found 12 defective items in a batch of 300 items. What percentage of the items were defective?Quantitative Problem Solving with Rational Numbers
  48. 148.A farmer harvested 5/8 of his cornfield on Monday. On Tuesday, he harvested an additional 1/4 of the cornfield. What fraction of the cornfield is still unharvested?Quantitative Problem Solving with Rational Numbers
  49. 149.A store offers a promotion where customers receive an additional 1/5 off the discounted price of an item. If an item originally cost $100 and was first discounted by 20%, what is the final price after the additional promotion?Quantitative Problem Solving with Rational Numbers
  50. 150.A city's annual budget is $2.5 x 10^8. If 15% of the budget is allocated to public safety, how much money, in dollars, is allocated to public safety?Quantitative Problem Solving with Rational Numbers