Praxis Core Math Practice Questions: 12 Original Problems With Worked Solutions

How should you use this 12-question Math set?

This page has 12 original Praxis Core Math practice questions with worked solutions, four from each content category ETS lists for test 5733. It is a short set written by Passy, not a full-length test, not ETS questions, and not a score estimate: ETS's Study Companion puts the real test at 56 questions in 90 minutes (checked November 3, 2026). All answers sit in their own section after question 12, so you can finish before you check.

ETS's counts are approximate and include pretest questions. Twelve questions at ETS's shares round to four per category. We do not claim these items match the real test's difficulty.

1. Set a timer for about 19 minutes. That is our arithmetic, not an ETS rule: 90 ÷ 56 is about 1.6 minutes per question, and 12 × 1.6 is about 19.
2. Use paper and a plain four-function calculator. The real test gives you an on-screen four-function calculator, and personal calculators are not permitted.
3. Write the setup and estimate first. ETS's Calculator Use page advises estimating beforehand and not using the calculator just because it's available (both checked November 6, 2026).
4. Mark every answer before you read the solutions. In this set, a one-or-more question counts as right only if you chose every correct choice and no wrong one.

Each question names its format, one of the three ETS uses on this test. For numeric entry, ETS accepts equivalent forms such as 2.5 and 2.50, expects the exact value unless the question asks you to round, and takes a fraction in two boxes (format details checked November 1, 2026).

If you came for a full-length test, ETS says that registering for a test gives you a free interactive practice test for that subject, and it listed the Math practice test at $24.95 on November 6, 2026. ETS also says its Study Companions include sample questions with detailed answers and explanations. The Praxis Core practice tests guide compares those options, and the Praxis Core Math guide explains what each category tests.

Twelve questions only sample these skills. Full Praxis Core prep planned for launch is organized by eight content categories, and the three below are the Math ones.

Number and Quantity: can you solve questions 1–4?

Question 1 (one answer). A teacher mixes paint in a ratio of 3 parts blue to 5 parts white. She needs 24 cups of paint in all. How many cups of blue does she need?

• A. 8
• B. 9
• C. 14.4
• D. 15

Question 2 (numeric entry). A school's enrollment rose from 320 students to 400 students. What was the percent increase? Enter the number only.

Question 3 (numeric entry). A faucet leaks 15 milliliters of water per minute at a steady rate. How many liters leak in 24 hours?

Question 4 (one or more answers). A student claims, "Every odd number greater than 1 is prime." Which numbers are counterexamples to this claim?

• A. 9
• B. 15
• C. 17
• D. 21
• E. 22

Data, Statistics, and Probability: can you solve questions 5–8?

Question 5 (one answer). A teacher asked 10 students how many books they read over a school break. What is the mean number of books per student?

• A. 2.5
• B. 3
• C. 3.2
• D. 3.5

Question 6 (one answer). The owner of a coffee cart fits the line y = −3x + 200 to her sales data, where x is the day's high temperature in degrees Fahrenheit and y is the number of hot drinks sold. How many hot drinks does the model predict for a day with a high of 40 degrees?

• A. 80
• B. 120
• C. 197
• D. 320

Question 7 (one answer). A district finds a strong positive correlation between the number of library books per student at its schools and each school's average reading score. Which statement do these data best support?

• A. Adding library books will raise a school's average reading score.
• B. Higher reading scores cause schools to buy more library books.
• C. Every school with more books per student has a higher score than every school with fewer.
• D. Schools with more books per student tend to have higher average reading scores.

Question 8 (numeric entry, fraction). A jar holds 4 red, 3 blue, and 6 green markers. One marker is picked at random. What is the probability that it is not blue? Give your answer as a fraction.

Algebra and Geometry: can you solve questions 9–12?

Question 9 (one answer). A school rents a bus for a flat fee of $120 plus $9 per student. The total bill is $345. How many students went on the trip?

• A. 13
• B. 25
• C. 38
• D. 52

Question 10 (one or more answers). Which expressions are equivalent to 3(2x − 4) + 2x?

• A. 8x − 4
• B. 8x − 12
• C. 4(2x − 3)
• D. 2(4x − 12)
• E. 6x − 12 + 2x

Question 11 (numeric entry). A rectangular garden is 12 feet long and has a perimeter of 40 feet. What is its area in square feet?

Question 12 (one answer). A 4-inch by 6-inch photo is enlarged so that the new rectangle is similar to the original. The short side of the enlargement is 14 inches. How long is its long side?

• A. 9.3 inches
• B. 16 inches
• C. 20 inches
• D. 21 inches

What are the answers and worked solutions?

Stop the timer and mark all 12 before you read on. Each solution starts with the answer.

1. B, 9 cups. Setup: 3 + 5 = 8 parts, and blue is 3 of the 8. Arithmetic: 24 ÷ 8 = 3 cups per part, and 3 × 3 = 9. Trap: 14.4 is 3/5 of 24, which treats a part-to-part ratio as a share of the whole. 15 is the white paint.

2. 25. Setup: percent change = change ÷ original value. Arithmetic: 400 − 320 = 80, and 80 ÷ 320 = 0.25, or 25%. Trap: dividing by the new value gives 80 ÷ 400 = 20%.

3. 21.6. Setup: multiply the rate by the minutes in a day, then convert, using 1,000 milliliters = 1 liter. Arithmetic: 24 × 60 = 1,440 minutes, 1,440 × 15 = 21,600 milliliters, and 21,600 ÷ 1,000 = 21.6 liters. Trap: stopping at 21,600 answers in the wrong unit.

4. A, B, and D. Setup: a counterexample must be odd, greater than 1, and not prime. Arithmetic: 9 = 3 × 3, 15 = 3 × 5, and 21 = 3 × 7. Trap: 22 is not prime, but it is even, so the claim says nothing about it. 17 is prime, so it fits the claim.

5. C, 3.2. Setup: multiply each value by its number of students, add, and divide by the 10 students. Arithmetic: 1 + 2 + 9 + 20 = 32, and 32 ÷ 10 = 3.2. Trap: 2.5 averages the four table values as if each belonged to one student, and 3.5 is the median.

6. A, 80. Setup: substitute x = 40 and keep the negative sign. Arithmetic: −3(40) + 200 = −120 + 200 = 80. Trap: 320 drops the negative sign, and 120 stops after the multiplication.

7. D. Setup: ask what the data show, which is that two measures tend to rise together. No calculation is needed. Trap: A and B claim a cause, which a correlation alone does not show, since something else could affect both measures. C turns a tendency into a rule with no exceptions.

8. 10/13. Setup: probability = favorable outcomes ÷ all outcomes. Arithmetic: 4 + 3 + 6 = 13 markers, and 4 + 6 = 10 are not blue. Trap: 3/13 is the probability of blue. Use 10 and 13 in the fraction boxes rather than dividing, since ETS warns against introducing decimals when you are asked for a fraction.

9. B, 25. Setup: 120 + 9n = 345, where n is the number of students. Arithmetic: 345 − 120 = 225, and 225 ÷ 9 = 25. Trap: 345 ÷ 9 is about 38, which ignores the flat fee.

10. B, C, and E. Setup: distribute, then combine like terms. Arithmetic: 3(2x − 4) + 2x = 6x − 12 + 2x = 8x − 12, and 4(2x − 3) = 8x − 12. Trap: A multiplies only the 2x by 3, and D expands to 8x − 24. Quick check: at x = 1 the original equals −4, which rules out A and D.

11. 96. Setup: perimeter = 2 × (length + width), then area = length × width. Arithmetic: 40 ÷ 2 = 20, 20 − 12 = 8 feet wide, and 12 × 8 = 96. Trap: 40 − 24 = 16 is both widths together, so 12 × 16 = 192 is double the area.

12. D, 21 inches. Setup: similar rectangles keep the same ratio, so 6/4 = x/14. Arithmetic: 6 ÷ 4 = 1.5, and 1.5 × 14 = 21. Trap: 16 adds the same 10 inches to the long side instead of scaling it. 9.3 flips the ratio, and a long side cannot be shorter than the 14-inch short side.

When one category needs more than four items, full Praxis Core prep planned for launch includes 1,200 questions across eight content categories.

What should each miss change in your study?

Use your misses to choose what to study, not to estimate a score. A count out of 12 does not convert to a Praxis score and cannot tell you whether you would pass. Count a lucky guess as a miss. The next steps below are Passy's editorial advice, not ETS rules.

Then look across your misses:

• Misses cluster in one category. Start there, using the skills in the table.
• Misses are spread out. Start with Number and Quantity, the largest category, because its skills can appear inside data and algebra problems.
• You ran out of time. Treat it as a pacing problem and do short timed sets at about 1.6 minutes per question.
• You got all 12. That result covers these 12 items only, so move on to a longer set.

Next, try the 20 free Praxis Core practice questions and note the skill behind each Math miss. Then put your weak skills on a calendar with the free Praxis Core study plan or the eight-week Praxis Core study schedule.

For rules you want to recall quickly, full Praxis Core prep planned for launch includes 450 flashcards.

If you are also taking Reading or Writing, the Praxis Core study guide covers all three tests. Before your appointment, the Praxis Core test day guide covers the calculator rule and what else to expect at a test center.