Step2Study

GED Mathematical Reasoning Test practice questions

200 free questions with answers and explanations.

Practice test
  1. 51.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
  2. 52.A financial analyst is modeling the quarterly profit (P) of a company, which is described by the equation P(x) = -2x^2 + 24x - 54, where x represents the number of units sold in thousands. What is the maximum profit the company can achieve?Algebraic Problem Solving with Expressions and Equations
  3. 53.A small business sells custom-printed t-shirts. The profit (P) in dollars for selling 'x' shirts can be modeled by the function P(x) = -0.5x² + 50x - 300. How many shirts must be sold to achieve the maximum profit?Algebraic Problem Solving with Expressions and Equations
  4. 54.A civil engineer is calculating the load on a bridge support. The load (L) in tons is given by the expression 5(x - 3) + 2x - 7, where 'x' is a variable representing traffic density. Simplify this expression.Algebraic Problem Solving with Expressions and Equations
  5. 55.A chemist is studying the decay of a certain radioactive isotope. The remaining amount, A, in grams, after 't' hours is given by the formula A = A₀ * (1/2)^(t/h), where A₀ is the initial amount and 'h' is the half-life in hours. If the initial amount is 200 grams and the half-life is 5 hours, how much of the isotope remains after 15 hours?Algebraic Problem Solving with Expressions and Equations
  6. 56.A botanist is studying the growth of a rare plant species. The height of the plant, H, in centimeters, is modeled by the function H(t) = 3(1.15)^t, where 't' is the number of weeks after planting. What is the approximate height of the plant after 5 weeks?Algebraic Problem Solving with Expressions and Equations
  7. 57.Given the equation 5x - 2y = 10 and 3x + y = 7, what is the value of x?Algebraic Problem Solving with Expressions and Equations
  8. 58.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
  9. 59.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
  10. 60.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
  11. 61.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
  12. 62.A technician is monitoring the temperature of a chemical reaction. The temperature, T, in degrees Celsius, is given by the function T(h) = -2h² + 16h + 20, where 'h' is the number of hours since the reaction started. What is the maximum temperature reached during the first 10 hours?Algebraic Problem Solving with Expressions and Equations
  13. 63.A civil engineer is designing a parabolic arch for a pedestrian bridge. The height (y) of the arch in meters, as a function of its horizontal distance (x) from one end in meters, is given by y = -0.1x² + 4x. What is the maximum height of the arch?Algebraic Problem Solving with Expressions and Equations
  14. 64.A researcher is growing a bacterial colony. The number of bacteria, N, after 't' hours, is given by the formula N(t) = 100 * 2^(t/3). How many hours will it take for the colony to reach 800 bacteria?Algebraic Problem Solving with Expressions and Equations
  15. 65.A map has a scale of 1:25,000. If two cities are 8.5 centimeters apart on the map, what is the actual distance between them in kilometers?Quantitative Problem Solving with Rational Numbers
  16. 66.A car travels 324 miles on 12 gallons of gasoline. At this rate, how many miles can the car travel on 7 gallons of gasoline?Quantitative Problem Solving with Rational Numbers
  17. 67.A baker uses a recipe that calls for 3/4 cup of sugar for every 2 cups of flour. If the baker has 5 cups of sugar, how much flour is needed to maintain the same ratio?Quantitative Problem Solving with Rational Numbers
  18. 68.A scientist is observing bacterial growth. The number of bacteria doubles every hour. If there are initially 300 bacteria, how many bacteria will there be after 4 hours?Quantitative Problem Solving with Rational Numbers
  19. 69.A chemist is preparing a solution. She needs 3/5 of a liter of a chemical. She only has a measuring beaker marked in milliliters. How many milliliters of the chemical does she need? (Note: 1 liter = 1000 milliliters)Quantitative Problem Solving with Rational Numbers
  20. 70.A homeowner is building a fence around a square garden. Each side of the garden measures 15.5 feet. If fencing costs $3.50 per foot, what is the total cost of the fencing?Quantitative Problem Solving with Rational Numbers
  21. 71.A carpenter is installing crown molding around a rectangular room that measures 14.5 feet by 18 feet. The molding is sold in 8-foot sections. How many sections of molding will the carpenter need to purchase?Quantitative Problem Solving with Rational Numbers
  22. 72.A city's population increased from 120,000 to 129,600 in one year. What was the percentage increase in the population?Quantitative Problem Solving with Rational Numbers
  23. 73.A painter estimates that he uses 2 1/3 gallons of paint for every 500 square feet of wall space. If a project requires painting 1,750 square feet, how many gallons of paint will he need?Quantitative Problem Solving with Rational Numbers
  24. 74.A recipe calls for 1.5 cups of flour for every 2 cups of sugar. If a baker uses 6 cups of sugar, how many cups of flour are needed?Quantitative Problem Solving with Rational Numbers
  25. 75.A city's water reservoir has a capacity of 5.4 x 10^7 gallons. If the city uses 1.8 x 10^6 gallons of water per day, how many days will it take for the reservoir to be completely empty if it starts full?Quantitative Problem Solving with Rational Numbers
  26. 76.A scientist is tracking the growth of a plant. On Monday, the plant was 18 cm tall. On Tuesday, it grew by 1/6 of its Monday height. On Wednesday, it grew by an additional 0.5 cm. What was the plant's height at the end of Wednesday?Quantitative Problem Solving with Rational Numbers
  27. 77.A biologist is studying a bacterial culture that initially contains 2.5 x 10^3 bacteria. The culture triples in size every hour. How many bacteria will be in the culture after 3 hours?Quantitative Problem Solving with Rational Numbers
  28. 78.A baker uses 3/4 cup of sugar for one batch of cookies. If the baker wants to make 2 1/2 batches of cookies, how much sugar in cups will be needed?Quantitative Problem Solving with Rational Numbers
  29. 79.A financial analyst is reviewing an investment portfolio. The value of the portfolio increased by 1/5 in the first quarter and then decreased by 1/10 of its new value in the second quarter. If the initial value was $12,000, what is the value of the portfolio at the end of the second quarter?Quantitative Problem Solving with Rational Numbers
  30. 80.A student scored 85% on a math test. If there were 40 questions on the test, how many questions did the student answer correctly?Quantitative Problem Solving with Rational Numbers
  31. 81.A rectangular garden measures 8 1/2 feet by 12 feet. What is the area of the garden in square feet?Quantitative Problem Solving with Rational Numbers
  32. 82.A stock's value decreased by 15% in January and then increased by 20% in February. If the stock started at $120, what was its value at the end of February?Quantitative Problem Solving with Rational Numbers
  33. 83.A truck's fuel tank is 2/3 full. After using 1/4 of the tank's capacity, what fraction of the tank is still full?Quantitative Problem Solving with Rational Numbers
  34. 84.A survey of 500 people found that 60% prefer coffee, 25% prefer tea, and the rest prefer hot chocolate. How many people prefer hot chocolate?Quantitative Problem Solving with Rational Numbers
  35. 85.A survey conducted among 150 employees showed that 40% prefer working from home, 30% prefer working in the office, and the rest have no preference. How many employees have no preference?Quantitative Problem Solving with Rational Numbers
  36. 86.A quality control inspector checks 120 items. She finds that 15% of the items have minor defects and 5% have major defects. What fraction of the inspected items have no defects?Quantitative Problem Solving with Rational Numbers
  37. 87.A construction worker needs to cut a pipe into pieces that are each 1.25 meters long. If the total length of the pipe is 15.5 meters, how many full pieces can be cut from the pipe?Quantitative Problem Solving with Rational Numbers
  38. 88.A store offers a 25% discount on all items. If a shirt originally costs $36, how much will a customer pay after the discount?Quantitative Problem Solving with Rational Numbers
  39. 89.A drone is flying in a search pattern. Its path is recorded on a coordinate plane, and at two specific points, its coordinates are (2, 5) and (8, 17). What is the equation of the line representing the drone's path?Algebraic Problem Solving with Graphs and Functions
  40. 90.A architect is designing a ramp for a building. The ramp must rise 1.5 feet for every 18 feet of horizontal distance. What is the slope of the ramp?Algebraic Problem Solving with Graphs and Functions
  41. 91.A client is managing their financial portfolio. The value of their investment, V(t), in thousands of dollars, over t years, is modeled by the function V(t) = 15(1.06)^t. What does the number 1.06 represent in this function?Algebraic Problem Solving with Graphs and Functions
  42. 92.A nutritionist is tracking a patient's weight loss. The patient's weight, W (in pounds), over d days is represented by the function W(d) = -0.5d + 200. What is the meaning of the y-intercept in this context?Algebraic Problem Solving with Graphs and Functions
  43. 93.A city planner is analyzing population growth. The population, P, in thousands, can be modeled by the function P(t) = 2t + 50, where t is the number of years since 2000. What was the population in 2015?Algebraic Problem Solving with Graphs and Functions
  44. 94.A chef is experimenting with a new recipe. The cost of ingredients, C, in dollars, is given by the function C(x) = 0.5x + 3, where x is the number of servings. The revenue R, in dollars, from selling x servings is R(x) = 2x. At what number of servings will the cost equal the revenue (break-even point)?Algebraic Problem Solving with Graphs and Functions
  45. 95.A satellite's orbit around Earth can be approximated by an elliptical path. On a coordinate plane, with Earth at the origin (0,0), the satellite's position at a certain time can be given by the coordinates (x, y). If the satellite's path is modeled by the equation x^2/a^2 + y^2/b^2 = 1, what does the variable 'a' represent in this context?Algebraic Problem Solving with Graphs and Functions
  46. 96.A meteorologist is tracking the temperature change in a city. At 8 AM, the temperature was 50°F. By 1 PM, the temperature had risen to 65°F. Assuming a constant rate of change, which equation models the temperature, T, in degrees Fahrenheit, as a function of the time, h, in hours, since 8 AM?Algebraic Problem Solving with Graphs and Functions
  47. 97.A nutritionist is tracking a patient's weight loss. The patient's weight, W (in pounds), over time, t (in weeks), is modeled by the function W(t) = -2.5t + 220. What is the practical range of this function for a 20-week program, assuming the patient starts at 220 pounds and cannot weigh less than 100 pounds?Algebraic Problem Solving with Graphs and Functions
  48. 98.A biologist is studying the growth of a plant. She records the plant's height in centimeters (cm) over several weeks. The data points are plotted on a coordinate plane, where the x-axis represents the number of weeks and the y-axis represents the height in centimeters. If the biologist observes that the plant's height increases by 2.5 cm every week, what is the slope of the line representing this growth?Algebraic Problem Solving with Graphs and Functions
  49. 99.A production line's efficiency (E), in units per hour, is modeled by the function E(t) = -0.5t^2 + 6t + 10, where 't' is the number of hours since the start of the shift (0 ≤ t ≤ 8). At what time 't' is the efficiency at its maximum?Algebraic Problem Solving with Graphs and Functions
  50. 100.A meteorologist is tracking a weather balloon. The altitude of the balloon, in meters, is given by the equation A = 20t + 500, where t is the time in minutes. Which of the following statements about the balloon's movement is true?Algebraic Problem Solving with Graphs and Functions