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

200 free questions with answers and explanations.

Practice test
  1. 101.A surveyor measures the length of a plot of land as 150 meters. If 1 inch is approximately 2.54 centimeters, and 1 meter equals 100 centimeters, what is the length of the plot in feet? (Round to the nearest whole number).Number and Quantity
  2. 102.A project manager is analyzing task durations. Task X takes 2 1/2 hours, Task Y takes 1 3/4 hours, and Task Z takes 3/5 of an hour. What is the total time required to complete all three tasks?Number and Quantity
  3. 103.A carpenter needs to cut boards that are each 2 feet 8 inches long. If he has a supply of wood totaling 40 feet, how many full boards can he cut?Number and Quantity
  4. 104.A financial analyst is tracking the value of an investment. The investment initially grew by 20%, then decreased by 10% from its new value, and finally increased by 5% from that subsequent value. What is the overall percentage change of the investment from its original value?Number and Quantity
  5. 105.A technician is weighing chemical samples. Sample A weighs 0.00000000000035 grams. Sample B weighs 8.2 x 10^-14 grams. What is the difference in weight between Sample A and Sample B?Number and Quantity
  6. 106.A store offers a 20% discount on all items. If a customer uses a coupon for an additional 10% off the discounted price, what is the total percentage discount the customer receives?Number and Quantity
  7. 107.Which of the following numbers is an irrational number?Number and Quantity
  8. 108.A student is calculating the value of an expression: 3^2 + (15 - 3) ÷ 4. What is the correct value?Number and Quantity
  9. 109.A software engineer is designing an algorithm where the processing time T (in milliseconds) for n data points is given by T(n) = 2n^2 - 5n + 3. What is the difference in processing time between 5 data points and 3 data points?Algebra and Functions
  10. 110.A nutritionist is analyzing the nutritional content of a meal. The amount of protein P (in grams) in the meal is related to the amount of carbohydrates C (in grams) by the equation 3P + 2C = 120. If a meal contains 24 grams of carbohydrates, how many grams of protein does it contain?Algebra and Functions
  11. 111.A financial analyst is modeling the growth of an investment. The value of the investment, V(t), after t years is given by the function V(t) = 5000(1.04)^t. What is the annual percentage growth rate of this investment?Algebra and Functions
  12. 112.A gardener is designing a rectangular flower bed with a perimeter of 40 feet. If the length of the flower bed is 4 feet longer than its width, what are the dimensions of the flower bed?Algebra and Functions
  13. 113.A chef is creating a new recipe. The amount of sugar (S) in grams needed for a cake is a function of the amount of flour (F) in grams, given by S(F) = 0.6F - 20. If the chef uses 300 grams of flour, how much sugar is needed?Algebra and Functions
  14. 114.A company's profit P (in thousands of dollars) from selling x hundreds of units is modeled by the function P(x) = -2x^2 + 20x - 30. What is the maximum profit the company can achieve?Algebra and Functions
  15. 115.A robotics engineer is programming a robot's movement. The robot's height h (in cm) above the ground at time t (in seconds) is given by the function h(t) = -t^2 + 6t + 7. At what time does the robot reach its maximum height?Algebra and Functions
  16. 116.A landscaper is planning a circular garden. The cost C (in dollars) to plant the garden is a function of its radius r (in meters), given by C(r) = 5πr^2 + 10πr. What is the cost to plant a garden with a radius of 3 meters?Algebra and Functions
  17. 117.A plumber charges a service fee of $75 plus $60 per hour for labor. If a customer's total bill was $255, how many hours did the plumber work?Algebra and Functions
  18. 118.A financial analyst is modeling the value of an investment. The value V(t) in dollars after t years is given by V(t) = 1000(1.05)^t. What is the annual percentage increase of this investment?Algebra and Functions
  19. 119.A botanist observes that the number of leaves on a particular plant follows a pattern. The first leaf appears on day 5, the second on day 8, and the third on day 11. If this pattern continues, on what day will the 8th leaf appear?Algebra and Functions
  20. 120.A civil engineer is designing a suspension bridge. The main cable's height h (in meters) above the road at a horizontal distance x (in meters) from the left tower is modeled by the function h(x) = 0.005x^2 - 0.6x + 20. What is the minimum height of the cable?Algebra and Functions
  21. 121.A park ranger is tracking the population of a certain species of bird. The population P(t) after t years is modeled by the function P(t) = 5000 / (1 + 4e^(-0.5t)). What is the limiting value (carrying capacity) of the bird population according to this model?Algebra and Functions
  22. 122.An environmental scientist is modeling the concentration of a pollutant in a lake. The concentration C(t) in parts per million (ppm) after 't' weeks is given by C(t) = 50e^(-0.1t). What is the initial concentration of the pollutant (at t=0)?Algebra and Functions
  23. 123.A pattern of tiles starts with 3 tiles in the first row, and each subsequent row has 2 more tiles than the previous row. If there are 10 rows of tiles, how many tiles are in the 10th row?Algebra and Functions
  24. 124.A chemist is observing a reaction where the concentration of a certain substance decreases over time. The concentration C(t) in milligrams per liter after t hours is modeled by C(t) = 150 * (0.8)^t. What is the initial concentration of the substance?Algebra and Functions
  25. 125.A meteorologist is tracking the temperature in a region. The temperature T (in degrees Fahrenheit) on a particular day can be modeled by the function T(h) = -|h - 14| + 70, where h is the hour of the day (from 0 to 24). What is the maximum temperature for the day according to this model?Algebra and Functions
  26. 126.A civil engineer is designing a parabolic arch for a bridge. The height of the arch (in meters) above the ground at a horizontal distance 'x' (in meters) from the left support is given by H(x) = -0.1x^2 + 2x. What is the maximum height of the arch?Algebra and Functions
  27. 127.A scientist is tracking the population of a certain bacteria. The population doubles every hour. If the initial population is 50 bacteria, which function best models the population P(t) after t hours?Algebra and Functions
  28. 128.A technician charges a flat fee of $50 for a service call plus $35 per hour for labor. If the total cost of a service call was $190, how many hours did the technician work?Algebra and Functions
  29. 129.A production manager is tracking the output of two different machines. Machine A produces 50 units per hour, and Machine B produces 70 units per hour. If Machine A runs for 'x' hours and Machine B runs for 'y' hours, and their combined output is 460 units, which equation represents this situation?Algebra and Functions
  30. 130.A project manager is analyzing the budget for a new initiative. The cost C (in thousands of dollars) is related to the number of resources R by the function C(R) = R^2 - 10R + 30. For what number of resources will the cost be 15 thousand dollars?Algebra and Functions
  31. 131.A factory produces widgets at a rate of 200 per hour. The production line starts with 50 widgets already made. Which function represents the total number of widgets (W) produced after 't' hours of operation?Algebra and Functions
  32. 132.A baker uses a recipe that calls for 2.5 cups of flour for every 1.5 cups of sugar. If the baker wants to make a larger batch using 7.5 cups of flour, how many cups of sugar will be needed?Algebra and Functions
  33. 133.The cost C (in dollars) of producing x units of a product is given by the function C(x) = 0.5x^2 - 20x + 500. What is the minimum cost to produce units of this product?Algebra and Functions
  34. 134.A biologist is studying a population of bacteria that doubles every 30 minutes. If the initial population is 100 bacteria, which equation models the population P(t) after 't' hours?Algebra and Functions
  35. 135.A manufacturer's profit P (in thousands of dollars) from selling 'x' units of a certain item is given by P(x) = -x^2 + 10x - 16. For what range of units sold will the manufacturer make a profit (P(x) > 0)?Algebra and Functions
  36. 136.A scientist is tracking the growth of a plant. The height of the plant in cm after 'd' days is given by the function H(d) = 0.5d + 10. What is the meaning of the number 10 in this function?Algebra and Functions
  37. 137.A company's monthly profit P(x) (in thousands of dollars) from selling 'x' units of a product is given by the function P(x) = -0.5x^2 + 10x - 12. At what number of units sold will the company achieve its maximum profit?Algebra and Functions
  38. 138.A rectangular garden has a length that is 5 feet more than twice its width. If the area of the garden is 150 square feet, which equation can be used to find the width (w) of the garden?Algebra and Functions
  39. 139.A software engineer is optimizing an algorithm. The runtime T (in milliseconds) of the algorithm for processing n data points is given by T(n) = 3n^2 + 5n. What is the difference in runtime between processing 10 data points and 5 data points?Algebra and Functions
  40. 140.A chemist is mixing a solution. She needs to combine two solutions, one that is 10% acid and another that is 30% acid. If she wants to make 5 liters of a 22% acid solution, how many liters of the 10% acid solution should she use?Algebra and Functions
  41. 141.A biologist is tracking the number of cells in a petri dish. The number of cells doubles every 4 hours. If the initial number of cells is 200, which equation models the number of cells N after t hours?Algebra and Functions
  42. 142.A project manager is analyzing task completion times. The time T (in hours) to complete a certain task is modeled by the function T(n) = n^2 - 6n + 10, where n is the number of resources assigned to the task. What is the minimum time required to complete the task?Algebra and Functions
  43. 143.A technician is calibrating a sensor. The sensor's reading 'R' (in ohms) is a function of the temperature 'T' (in degrees Celsius). The relationship is given by R(T) = 0.5T + 20. What is the temperature when the sensor reading is 45 ohms?Algebra and Functions
  44. 144.A financial analyst is modeling the quarterly profit of a company. The profit P (in thousands of dollars) is given by the function P(x) = -2x^2 + 20x - 30, where x is the number of units sold (in hundreds). What is the maximum profit the company can achieve?Algebra and Functions
  45. 145.A civil engineer is designing a parabolic arch for a bridge. The height h (in meters) of the arch above the ground at a horizontal distance x (in meters) from the left support is given by h(x) = -0.01x(x - 100). What is the maximum height of the arch?Algebra and Functions
  46. 146.A biologist is studying a population of fruit flies. The population P(t) after t days is modeled by the function P(t) = 50 * (1.05)^t. What is the initial population of fruit flies?Algebra and Functions
  47. 147.A company's production cost C (in thousands of dollars) is related to the number of units produced x by the equation C(x) = x^3 - 10x^2 + 31x - 30. If the cost is $0, which of the following could be the number of units produced?Algebra and Functions
  48. 148.A botanist is studying the growth of a rare plant. The height of the plant 'H' (in cm) after 'd' days is given by the function H(d) = 2.5d + 15. What is the average rate of change of the plant's height between day 5 and day 15?Algebra and Functions
  49. 149.A student collected data on the number of hours they spent studying for an exam and their corresponding score. The data is as follows: (2 hours, 70 score), (3 hours, 75 score), (4 hours, 80 score), (5 hours, 85 score). If the student studies for 6 hours, based on this linear trend, what would be the predicted score?Statistics and Probability
  50. 150.A civil engineer is designing a road that passes over a hill. The height of the road, h(x), in meters above sea level, can be modeled by the polynomial function h(x) = -0.01x³ + 0.5x² - 3x + 100, where x is the horizontal distance in kilometers from a reference point. What is the height of the road at the reference point (x = 0)?Algebra and Functions