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

200 free questions with answers and explanations.

Practice test
  1. 51.A researcher collects data on the heights of 100 individuals and finds that the mean height is 170 cm with a standard deviation of 5 cm. If the data is normally distributed, approximately what percentage of individuals have a height between 165 cm and 175 cm?Statistics and Probability
  2. 52.A survey asked 150 people about their favorite type of movie. The results are shown in the pie chart below (percentages are approximate). If 20% prefer action movies and 30% prefer comedy, how many people prefer drama movies if the remaining 50% is split equally between drama and sci-fi?Statistics and Probability
  3. 53.A quality control manager is inspecting a batch of 100 manufactured parts. The manager finds that 8 parts are defective. If the manager randomly selects 2 parts from the batch for further testing, without replacement, what is the probability that both selected parts are defective?Statistics and Probability
  4. 54.A game involves spinning a fair 4-sided spinner numbered 1, 2, 3, 4, and flipping a fair coin. What is the probability of spinning an odd number AND flipping a tails?Statistics and Probability
  5. 55.A quality control engineer is testing a new production line. Out of 200 items produced, 10 are found to be defective. If this rate continues, what is the probability that the next item produced will NOT be defective?Statistics and Probability
  6. 56.A meteorologist is recording the daily high temperatures (in °F) for a week in a particular city: 72, 75, 68, 70, 73, 76, 69. What is the range of these temperatures?Statistics and Probability
  7. 57.A teacher recorded the number of books read by students in a class over a month: 2, 5, 3, 7, 2, 4, 3, 5, 2, 6. What is the median number of books read?Statistics and Probability
  8. 58.A librarian is organizing new books on a shelf. There are 7 new novels and 5 new non-fiction books. If the librarian wants to choose 3 novels and 2 non-fiction books to display on a special stand, how many different combinations of books can be chosen?Statistics and Probability
  9. 59.A card is drawn from a standard deck of 52 cards, then replaced, and a second card is drawn. What is the probability that both cards drawn are aces?Statistics and Probability
  10. 60.A student is planning a schedule for their final exams. There are 4 different exams to be taken over 4 consecutive days, with only one exam per day. In how many different orders can the student schedule their exams?Statistics and Probability
  11. 61.A civil engineer is calculating the strength of a beam. The formula involves (5^2 + 12^2)^1/2. What is the result of this calculation?Number and Quantity
  12. 62.A cartographer is scaling a map. A distance of 1.5 inches on the map represents an actual distance of 30 miles. If two cities are 4.2 inches apart on the map, what is the actual distance between them?Number and Quantity
  13. 63.A civil engineer is planning a road construction project. The total length of the road is 25.5 miles. If the crew completes 1/3 of the road in the first month and 2/5 of the remaining road in the second month, how many miles of road are still left to be constructed?Number and Quantity
  14. 64.A technician is calibrating a sensor that measures temperature. The sensor's reading is 2.5 degrees Celsius, but it needs to be converted to Fahrenheit. The formula for conversion is F = (9/5)C + 32. What is the temperature in Fahrenheit?Number and Quantity
  15. 65.A project manager is estimating task durations. Task X is estimated to take between 3.5 and 4.5 hours. Task Y is estimated to take between 2.75 and 3.25 hours. What is the maximum possible combined time, in hours, for both tasks?Number and Quantity
  16. 66.A biologist is studying a bacterial culture that triples in size every 2 hours. If the culture starts with 500 bacteria, how many bacteria will there be after 6 hours?Number and Quantity
  17. 67.A technician is performing measurements with very small numbers. They need to subtract 3.5 x 10^-5 from 7.2 x 10^-4. What is the result in scientific notation?Number and Quantity
  18. 68.A gardener 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 72 cubic feet of soil mix, how many cubic feet of compost does he need?Number and Quantity
  19. 69.A chef is preparing a dish that requires 3.5 cups of broth. If the chef only has a measuring cup that measures in 1/4 cup increments, how many 1/4 cup servings of broth will be needed?Number and Quantity
  20. 70.A quality control specialist is checking the weight of packages. The ideal weight is 16 ounces. Any package that deviates by more than 0.75 ounces from the ideal weight is rejected. Which of the following package weights would be rejected?Number and Quantity
  21. 71.A caterer is preparing punch for an event. The recipe calls for 3 parts juice A, 2 parts juice B, and 1 part sparkling water. If the caterer needs to make a total of 90 liters of punch, how many liters of juice A are needed?Number and Quantity
  22. 72.An environmental scientist is measuring the concentration of a pollutant in a water sample. The initial concentration is 0.0000000045 grams per liter. How is this concentration expressed in scientific notation?Number and Quantity
  23. 73.A production manager is monitoring machine efficiency. Machine A produces 120 units in 45 minutes. Machine B produces 160 units in 1 hour. Which machine has a higher production rate, and by how many units per hour?Number and Quantity
  24. 74.A baker is making a large batch of cookies. The recipe calls for 1.75 cups of sugar, but the baker only has a measuring cup that measures in eighths of a cup. How many eighths of a cup of sugar are needed?Number and Quantity
  25. 75.A chef is preparing a dish that requires 2.5 cups of broth. If the chef only has a measuring cup that measures in 1/8 cup increments, how many 1/8 cup increments of broth are needed?Number and Quantity
  26. 76.A carpenter is estimating the amount of wood needed. Each piece of wood is 1.75 meters long. If the carpenter needs 12 pieces, and each piece costs $3.50, what is the total length of wood needed in centimeters?Number and Quantity
  27. 77.A civil engineer is surveying a new building site. The elevation at the highest point is +32.5 meters relative to sea level, and the lowest point is -8.75 meters relative to sea level. What is the total vertical distance between these two points?Number and Quantity
  28. 78.A chef is preparing a recipe that calls for 3/8 cup of olive oil. If the chef only wants to make 2/3 of the recipe, how much olive oil, in cups, will be needed?Number and Quantity
  29. 79.A carpenter is building a custom bookshelf. He has a piece of wood that is 10 1/2 feet long. If each shelf requires 1 3/4 feet of wood, how many full shelves can he cut from the piece of wood?Number and Quantity
  30. 80.A financial advisor is explaining compound interest. An initial investment of $5,000 earns 4% interest compounded annually. What will be the value of the investment after 3 years?Number and Quantity
  31. 81.A landscaper needs to estimate the quantity of topsoil. The area to be covered is 120 square feet, and the topsoil needs to be 6 inches deep. If topsoil is sold by the cubic yard, how many cubic yards of topsoil are needed? (1 foot = 12 inches; 1 yard = 3 feet)Number and Quantity
  32. 82.A production line worker is checking product dimensions. The required length of a component is 15.2 cm. Due to manufacturing variations, the actual length can deviate by at most 0.15 cm. Which inequality represents the acceptable range of lengths (L) for the component?Number and Quantity
  33. 83.A quality control technician inspects a batch of 480 electronic components. If 1/16 of the components are found to be defective, how many components are NOT defective?Number and Quantity
  34. 84.A historian is analyzing population data. The population of a city was 250,000 in the year 2000. If the population grew at an average rate of 3% per year, approximately what would be the population in the year 2005?Number and Quantity
  35. 85.A chemist is preparing a solution by mixing two chemicals in a ratio of 3:5. If the total volume of the solution is 240 mL, how much of the second chemical is needed?Number and Quantity
  36. 86.A scientist is observing the growth of a crystal. The crystal's length is currently 3.2 x 10^-4 meters. If it grows by 2.5 x 10^-5 meters each day, what will its length be after 2 days?Number and Quantity
  37. 87.A financial analyst observes that a company's stock value decreased by 15% in January and then increased by 20% in February. If the stock started at $80 per share, what was its final value per share at the end of February?Number and Quantity
  38. 88.A nutritionist is preparing a special dietary supplement. The recipe requires 2 parts protein powder, 3 parts fiber supplement, and 5 parts vitamin mix. If the total weight of the supplement needs to be 300 grams, how many grams of vitamin mix are required?Number and Quantity
  39. 89.An architect is designing a staircase. Each step needs to be 7 3/4 inches high. If the total rise of the staircase is 93 inches, how many steps are needed?Number and Quantity
  40. 90.A project manager is analyzing task durations. Task A takes 3 1/2 hours, Task B takes 2 3/4 hours, and Task C takes 1 1/3 hours. What is the total time required to complete all three tasks?Number and Quantity
  41. 91.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 yields a higher effective annual rate?Number and Quantity
  42. 92.A financial planner is reviewing an investment portfolio. The portfolio initially had a value of $24,000. It then increased by 1/8 of its value, and later decreased by 1/6 of its *new* value. What is the final value of the portfolio?Number and Quantity
  43. 93.A recipe requires 3/4 cup of milk. If a chef wants to make 2/3 of the recipe, how much milk is needed?Number and Quantity
  44. 94.A nutritionist is calculating the caloric content of a meal. A serving of rice contains 200 calories, and a serving of chicken contains 350 calories. If a meal consists of 1/2 serving of rice and 2/3 serving of chicken, what is the total caloric content of the meal?Number and Quantity
  45. 95.A financial advisor is explaining compound interest. An initial investment of $8,000 earns an annual interest rate of 4%, compounded quarterly. If no additional deposits or withdrawals are made, what will be the value of the investment after 2 years?Number and Quantity
  46. 96.A recipe for a large batch of cookies requires 2/3 cup of brown sugar. If a baker decides to make only 3/4 of the recipe, how much brown sugar will be needed?Number and Quantity
  47. 97.A botanist is tracking the growth of a plant. On Monday, the plant was 18.5 cm tall. By Friday, it had grown by 15%. What was the plant's height on Friday?Number and Quantity
  48. 98.A baker uses 1/3 of a bag of sugar for one cake and 1/4 of the same bag for another cake. What fraction of the bag of sugar is left if the bag originally contained 5/6 of its full capacity?Number and Quantity
  49. 99.A recipe calls for 2 3/4 cups of flour. If a baker wants to make 1.5 times the recipe, how much flour, in cups, will be needed?Number and Quantity
  50. 100.A team of researchers is monitoring the growth of a bacterial colony. The colony initially contains 1,200 bacteria and doubles every 30 minutes. How many bacteria will be in the colony after 2 hours?Number and Quantity