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

200 free questions with answers and explanations.

Practice test
  1. 151.A production manager is tracking the output of two different machines. Machine A produces 15 units per hour and has already produced 50 units. Machine B produces 20 units per hour and has already produced 20 units. After how many additional hours will both machines have produced the same total number of units?Algebra and Functions
  2. 152.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 the function h(x) = -0.05x(x - 60). What is the maximum height of the arch?Algebra and Functions
  3. 153.A technician is calibrating a sensor that measures temperature. The sensor's reading 'R' (in ohms) is related to the actual temperature 'T' (in degrees Celsius) by the equation R = 0.5T + 20. If the technician observes a reading of 45 ohms, what is the actual temperature in degrees Celsius?Algebra and Functions
  4. 154.A chemist is mixing a solution. She needs to combine two solutions, one that is 10% acid and another that is 30% acid, to create 5 liters of a 22% acid solution. How many liters of the 10% acid solution should she use?Algebra and Functions
  5. 155.A meteorologist is tracking the temperature in a city. The temperature T (in degrees Fahrenheit) over a 24-hour period can be modeled by the function T(h) = -0.02(h - 14)^2 + 80, where h is the hour of the day (0 ≤ h ≤ 24). What is the maximum temperature recorded during this period?Algebra and Functions
  6. 156.A financial analyst is modeling the quarterly profit of a company. The profit P (in thousands of dollars) from selling x units of a product is given by the function P(x) = -0.5x^2 + 20x - 150. What is the maximum profit the company can achieve?Algebra and Functions
  7. 157.A biologist is studying a population of fruit flies. The population P(t) after t days is modeled by the function P(t) = 50 * (1.15)^t. What was the initial population of fruit flies?Algebra and Functions
  8. 158.A software engineer is optimizing an algorithm. The runtime T (in milliseconds) of the algorithm for an input of size n is given by the function T(n) = 3n^2 + 5n - 2. What is the difference in runtime between an input of size n=5 and an input of size n=3?Algebra and Functions
  9. 159.A company's production cost C (in thousands of dollars) is related to the number of units u (in hundreds) produced by the polynomial function C(u) = 2u^3 - 5u^2 + 10u + 50. If the company produces 300 units, what is the production cost?Algebra and Functions
  10. 160.A biologist is studying a population of insects. The population, P(t), after t days is modeled by the function P(t) = 500 * (1.05)^t. What does the value 1.05 represent in this context?Algebra and Functions
  11. 161.A biologist is tracking the number of cells in a petri dish. The number of cells doubles every 20 minutes. If the initial number of cells was 100, how many cells will there be after 1 hour?Algebra and Functions
  12. 162.A project manager is analyzing task completion times. The time T (in hours) to complete a certain task is modeled by the function T(x) = 2x^2 - 12x + 25, where x is the number of workers assigned to the task. What is the minimum time required to complete the task?Algebra and Functions
  13. 163.A nutritionist is analyzing the calorie counts of 10 different energy bars: 180, 200, 190, 210, 185, 205, 195, 215, 190, 200. What is the standard deviation of these calorie counts, rounded to two decimal places?Statistics and Probability
  14. 164.A scientist is observing a chemical reaction where the temperature decreases by 2.5°C every 15 minutes. If the initial temperature is 20°C, what will the temperature be after 1 hour and 15 minutes?Number and Quantity
  15. 165.A financial analyst is evaluating an investment. The value of the investment is 2.5 × 10³ dollars. If a client wants to invest 0.5 times this amount, what is the client's investment in standard notation?Number and Quantity
  16. 166.A financial analyst is comparing two investment options. Investment A offers an annual interest rate of 4.5% compounded quarterly. Investment B offers an annual interest rate of 4.4% compounded monthly. Which investment has a higher effective annual rate (EAR)?Number and Quantity
  17. 167.A cartographer is marking locations on a grid. Point A is at (3, 7) and Point B is at (9, 15). What is the distance between Point A and Point B?Geometry
  18. 168.A chef is preparing a large batch of soup. The recipe calls for 3/4 cup of broth for every 2 servings. If the chef wants to make 10 servings, how many cups of broth are needed?Number and Quantity
  19. 169.A civil engineer is analyzing the stress on a beam. The stress, S(L), in pascals, is a function of the length of the beam, L, in meters, given by S(L) = 3L^3 - 2L^2 + 5L - 10. What is the stress on a beam that is 2 meters long?Algebra and Functions
  20. 170.A nutritionist is calculating the caloric content of a meal. A serving of rice contains 200 calories. If 3/5 of these calories come from carbohydrates, how many calories from carbohydrates are in one serving of rice?Number and Quantity
  21. 171.A production manager is analyzing machine output. Machine A produces 120 units in 3 hours. Machine B produces 180 units in 4.5 hours. Machine C produces 150 units in 3.5 hours. Which machine has the highest production rate?Number and Quantity
  22. 172.A carpenter is building a custom bookshelf. He has a piece of wood that is 10 1/2 feet long. If each shelf requires 2 3/4 feet of wood, how many full shelves can he cut from the piece of wood?Number and Quantity
  23. 173.A financial analyst is modeling the quarterly profit of a company. The profit P(x) (in thousands of dollars) from selling 'x' hundreds of units is modeled by the function P(x) = -2x^2 + 20x - 18. What is the maximum profit the company can achieve?Algebra and Functions
  24. 174.A quality control specialist is inspecting a batch of microchips. Out of 200 chips, 3% are found to be defective. How many microchips are defective?Number and Quantity
  25. 175.A robotics engineer is programming a robot to navigate a series of platforms. The robot's vertical position, P(t), in meters, at time 't' seconds, is described by the function P(t) = (t - 2)(t - 8). If the robot needs to be at ground level (P(t) = 0) to transition between platforms, at what times does this occur?Algebra and Functions
  26. 176.A biologist is tracking the population of a certain species of fish in a lake. The population, P(t), after t years, is modeled by the function P(t) = 1500 / (1 + 4e^(-0.5t)). What is the limiting value of the fish population as time approaches infinity?Algebra and Functions
  27. 177.A landscaper is mixing soil for a new plant bed. He uses 3 parts topsoil, 2 parts compost, and 1 part sand. If he needs a total of 18 cubic feet of soil mix, how many cubic feet of compost will he need?Number and Quantity
  28. 178.A quality control technician is inspecting a batch of 50 newly manufactured circuit boards. Historical data indicates that the probability of a single circuit board being defective is 0.04. Assuming each board's defect status is independent, what is the expected number of defective circuit boards in this batch?Statistics and Probability
  29. 179.A furniture maker is designing a new table. The tabletop will be a rectangle with a length of 6 feet and a width of 4 feet. What is the area of the tabletop?Geometry
  30. 180.A botanist is cultivating a new hybrid plant. The height of the plant, H(d), in centimeters, after 'd' days is modeled by the function H(d) = 0.5d + 10. What is the predicted height of the plant after 14 days?Algebra and Functions
  31. 181.A student is planning their course schedule and needs to select 2 elective courses from a list of 7 available courses. If the order in which the courses are chosen does not matter, how many different combinations of 2 elective courses are possible?Statistics and Probability
  32. 182.A financial analyst is comparing two investment options. Option A's value, A(t), after t years is given by A(t) = 1000(1.05)^t. Option B's value, B(t), after t years is given by B(t) = 1000 + 60t. Which statement about the investments is true?Algebra and Functions
  33. 183.A scientist is observing the growth of a plant. The height of the plant, H(d), in centimeters, after 'd' days is modeled by the function H(d) = 0.5d + 12. What is the predicted height of the plant after 10 days?Algebra and Functions
  34. 184.A student is tracking their daily study time (in minutes) for a week: 90, 120, 80, 100, 150, 110, 95. What is the mean study time for the week?Statistics and Probability
  35. 185.A production line's daily output, Q, is related to the number of hours, h, it operates by the equation Q = 50h - h^2. For what range of hours operated will the daily output be at least 400 units?Algebra and Functions
  36. 186.A land surveyor is marking property lines. She has a total of 150 feet of measuring tape. If she needs to mark segments that are each 12.5 feet long, how many full segments can she mark?Number and Quantity
  37. 187.A chef is baking a cake that requires a pan in the shape of a cube. If the side length of the pan is 8 inches, what is the volume of the cake pan?Geometry
  38. 188.A veterinarian is calculating medication dosages. A dog weighs 45 pounds. If the recommended dosage is 25 milligrams of medication per 5 pounds of body weight, how many milligrams of medication should the dog receive?Number and Quantity
  39. 189.A chef is adjusting a recipe for a large catering event. The original recipe calls for 1 1/4 teaspoons of salt. If the chef needs to make 3 1/2 times the original recipe, how much salt, in teaspoons, is needed?Number and Quantity
  40. 190.A financial analyst is evaluating an investment. The value of the investment is 2.5 × 10³ dollars. What is this value in standard notation?Number and Quantity
  41. 191.A meteorologist is tracking the daily high temperatures in a desert region. The temperature T (in degrees Celsius) for a particular day is given by the expression 5x - 8, where x represents the number of hours past sunrise. If the temperature on this day ranged from 12°C to 27°C, which inequality represents the possible values for x?Algebra and Functions
  42. 192.A city planner is calculating the population density of a new development. The development covers an area of 4 square miles and has a population of 25,000 residents. What is the population density in residents per square mile?Number and Quantity
  43. 193.A scientist is conducting an experiment where the temperature, T(h), in degrees Celsius, of a substance changes according to the function T(h) = (h - 4)^2 + 10, where h is the number of hours since the experiment began. What is the minimum temperature reached during the experiment?Algebra and Functions
  44. 194.A civil engineer is designing a road over a hill. The height of the road, h(x), in meters, relative to the ground, can be modeled by the quadratic function h(x) = -0.02x^2 + 1.2x + 5, where x is the horizontal distance in meters from a reference point. What is the maximum height of the road above the ground?Algebra and Functions
  45. 195.A population of insects grows according to the recursive formula P_n = 2 * P_(n-1) - 50, where P_n is the population in week n, and P_0 is the initial population. If P_0 = 100, what is the population in week 2 (P_2)?Algebra and Functions
  46. 196.A biologist is culturing microorganisms in a petri dish. The initial population is 250 cells. If the population quadruples every 30 minutes, what will the population be after 2 hours?Number and Quantity
  47. 197.A construction crew is pouring concrete for a foundation. They have 3 1/2 cubic yards of concrete remaining. If each section of the foundation requires 1/4 cubic yard of concrete, how many full sections can they pour?Number and Quantity
  48. 198.A biologist is studying the growth of a bacterial colony. The number of bacteria, N(t), after t hours is given by the function N(t) = N_0 * (1.2)^t, where N_0 is the initial number of bacteria. If the biologist observes 500 bacteria after 3 hours, what was the initial number of bacteria (N_0)?Algebra and Functions
  49. 199.A production manager is analyzing machine output. Machine A produces 120 units in 3 hours. Machine B produces 150 units in 4 hours. Which machine has a higher production rate, and by how many units per hour?Number and Quantity
  50. 200.A scientist is observing the growth of a bacterial colony. The colony initially contains 1,200 bacteria and triples in size every 30 minutes. How many bacteria will be in the colony after 2 hours?Number and Quantity