HiSET Math Practice Test: 12 Original Questions With Worked Solutions

How should you use this 12-question Math set?

This page is a set of 12 original HiSET Math questions with worked solutions, not a full practice test; PSI's free official Mathematics FPT9 form has 25 questions in 45 minutes. The live Math subtest has 55 questions in 90 minutes, according to PSI's Test at a Glance (both checked November 3, 2026).

Passy wrote these problems, and the scenarios are invented. They are not official HiSET questions, this is not a mock exam, and we don't claim they match the live test's difficulty. Each has five choices, A through E, like PSI's sample Math questions (checked November 6, 2026), and all answers sit in their own section after question 12.

PSI's shares are approximate averages across forms (checked November 3, 2026). Our split follows them only roughly.

1. Set a timer for about 20 minutes. That is Passy's arithmetic, not a PSI rule: 90 ÷ 55 is about 1.6 minutes per question, so 12 questions take just under 20 minutes.
2. Keep the official formula sheet beside you. PSI's Test at a Glance says it leaves out distance = rate × time, the Pythagorean theorem, and the quadratic formula. This set uses all three on purpose, which says nothing about their frequency.
3. Work on paper, with a basic calculator if you want one. PSI's FAQ says the test center supplies the calculator and personal calculators are prohibited (checked November 3, 2026).
4. Answer every question. PSI's statistical report says, "There is no penalty for answering incorrectly," so don't leave live questions blank either (checked November 6, 2026).

Math had the lowest first-attempt pass rate of the five subtests in PSI's 2024/2025 report, 70.9% for tests in English (checked November 6, 2026). That describes past test takers, not your odds, and how hard the HiSET is puts it in context.

For a longer test, start with FPT9, which PSI's practice tests page labels half-length. PSI's readiness chart also lists full-length forms such as OPT12 and PPT8, and the HiSET practice test readiness guide explains each type.

Twelve questions only sample these skills. Full HiSET prep planned for launch is organized by the five subtests.

Algebra: can you solve questions 1–5?

Question 1. A moving company charges a $45 booking fee plus $30 per hour. A customer's bill is $195. How many hours did the move take?

• A. 4
• B. 5
• C. 6
• D. 6.5
• E. 8

Question 2. A van has a load limit of 1,900 pounds. The driver weighs 180 pounds, and each box of tile weighs 65 pounds. With the driver on board, what is the greatest number of boxes the van can carry?

• A. 26
• B. 27
• C. 28
• D. 29
• E. 30

Question 3. A garden club sold 90 plants. Plants cost $4 in small pots and $7 in large pots. Total sales were $471. How many plants in small pots did the club sell?

• A. 30
• B. 37
• C. 45
• D. 53
• E. 60

Question 4. A truck leaves a warehouse at 9:00 a.m., traveling 50 miles per hour. At 10:00 a.m., a van follows the same route from the same warehouse at 70 miles per hour. How many hours after leaving does the van catch the truck?

• A. 0.4
• B. 1.5
• C. 2.5
• D. 3
• E. 3.5

Question 5. A ball is thrown upward from a platform. Its height in meters after t seconds is h = −5t² + 14t + 3. After how many seconds does it reach the ground, where h = 0?

• A. 0.2
• B. 1.4
• C. 2.8
• D. 3
• E. 6

Numbers and operations: can you solve questions 6–8?

Question 6. A coat listed at $120 is marked down 25%. Sales tax of 6% is then added to the sale price. What does the customer pay?

• A. $90.00
• B. $95.40
• C. $97.20
• D. $100.70
• E. $127.20

Question 7. A recipe uses 2 1/4 cups of flour for 18 muffins. At the same rate, how many cups are needed for 30 muffins?

• A. 1 7/20
• B. 3
• C. 3 1/3
• D. 3 1/2
• E. 3 3/4

Question 8. Dana pays 1/3 of her monthly pay for rent, then spends 1/4 of what remains on food. She has $900 left. What is her monthly pay?

• A. $1,200
• B. $1,350
• C. $1,800
• D. $2,160
• E. $2,700

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

Question 9. A straight cable runs from a point 15 feet up a vertical pole to a stake in level ground 8 feet from the pole's base. The pole and the ground form a right angle. How long is the cable, in feet?

• A. 11.5
• B. 12.7
• C. 17
• D. 23
• E. 289

Question 10. A rectangular lawn, 30 feet by 20 feet, contains a circular flower bed with a diameter of 10 feet. Using π ≈ 3.14, how many square feet of the lawn are not flower bed?

• A. 286
• B. 521.5
• C. 568.6
• D. 584.3
• E. 678.5

Question 11. A shop's electric bills for six months were $120, $135, $110, $145, $130, and $140, in that order. What is the median monthly bill?

• A. $35
• B. $127.50
• C. $130
• D. $132.50
• E. $135

Question 12. A community center surveyed 200 members. One member who uses the pool is chosen at random. What is the probability that this member is under 30?

• A. 18%
• B. 30%
• C. 40%
• D. 45%
• E. 60%

What are the answers and worked solutions?

Stop the timer and mark all 12 before you read on.

1. B, 5 hours. Setup: 45 + 30h = 195. Calculation: 195 − 45 = 150, and 150 ÷ 30 = 5. Check: 45 + 30(5) = 195. Trap: 6.5 ignores the fee.

2. A, 26 boxes. Setup: 180 + 65b ≤ 1,900. Calculation: 1,900 − 180 = 1,720, and 1,720 ÷ 65 is about 26.5. Check: 26 boxes make 1,870 pounds, and 27 make 1,935. Trap: 27 rounds up, but a limit means you round down.

3. D, 53. Setup: with s small pots and 90 − s large pots, 4s + 7(90 − s) = 471. Calculation: 630 − 3s = 471, so 3s = 159 and s = 53. Check: 53 + 37 = 90, and $212 + $259 = $471. Trap: 37 is the large pots.

4. C, 2.5 hours. Setup: use distance = rate × time, which the sheet leaves out. The truck drives one hour longer than the van, so 70t = 50(t + 1). Calculation: 20t = 50, so t = 2.5. Check: 70 × 2.5 = 175 miles, and 50 × 3.5 = 175 miles. Trap: 3.5 is the truck's time.

5. D, 3 seconds. Setup: apply the quadratic formula, which the sheet leaves out, to −5t² + 14t + 3 = 0: t = (−b ± √(b² − 4ac)) ÷ (2a), with a = −5, b = 14, and c = 3. Calculation: 14² − 4(−5)(3) = 196 + 60 = 256, and √256 = 16, so t = (−14 ± 16) ÷ (−10). That gives −0.2 or 3, and time cannot be negative. Check: −5(9) + 14(3) + 3 = −45 + 42 + 3 = 0. Trap: 6 divides by a instead of 2a.

6. B, $95.40. Setup: take the discount first, then tax the sale price. Calculation: 120 × 0.75 = 90, and 90 × 1.06 = 95.40. Check: $120 − $30 + $5.40 = $95.40. Trap: $97.20 charges tax on the full $120.

7. E, 3 3/4 cups. Setup: 30 muffins is 30/18 = 5/3 of the recipe, and 2 1/4 = 9/4. Calculation: 9/4 × 5/3 = 45/12 = 3 3/4. Check: 18 muffins use 2.25 cups, so 6 use 0.75 cup, and 5 × 0.75 = 3.75. Trap: 3 1/3 drops the 1/4.

8. C, $1,800. Setup: rent leaves 2/3 of her pay, and food leaves 3/4 of that. Calculation: 3/4 × 2/3 = 1/2, so her pay is 2 × $900 = $1,800. Check: $1,800 − $600 = $1,200, and $1,200 − $300 = $900. Trap: $2,160 takes both fractions from the full pay.

9. C, 17 feet. Setup: the cable is the hypotenuse of a stated right triangle, so use a² + b² = c², which the sheet leaves out. Calculation: 15² + 8² = 225 + 64 = 289, and √289 = 17. Check: a hypotenuse is longer than either leg and shorter than both together, and 17 fits. Trap: 23 adds the legs.

10. B, 521.5. Setup: subtract the circle from the rectangle, and halve the diameter to get a radius of 5 feet. Calculation: 30 × 20 = 600, 3.14 × 5² = 78.5, and 600 − 78.5 = 521.5. Check: the bed fits inside a 10-by-10 square, so the answer must exceed 500. Trap: 286 uses 10 as the radius.

11. D, $132.50. Setup: sort first: 110, 120, 130, 135, 140, 145. With six values, the median is halfway between the middle two. Calculation: (130 + 135) ÷ 2 = 132.50. Check: three bills fall below it and three above. Trap: $127.50 averages the third and fourth bills without sorting, and $130 is the mean.

12. E, 60%. Setup: the chosen member uses the pool, so the denominator is the 60 pool users. Calculation: 36 ÷ 60 = 0.60. Check: the other 24 pool users are 40%, and 60% + 40% = 100%. Trap: 40% is 36 ÷ 90, the share of under-30 members who use the pool.

When a category needs more than a few items, full HiSET prep planned for launch includes 1,150 questions across the five subtests. That is the overall planned volume, not a Math-only count.

What should each miss change in your study?

Use your misses to choose what to study. This set gives no score: a count out of 12 doesn't convert to a HiSET scaled score, and PSI's FPT9 readiness bands apply only to that form. Count a lucky guess as a miss. The tasks below are Passy's editorial advice, not PSI rules, and they point to sections of the HiSET Math study guide.

Then look across your misses:

• Misses cluster in one category. Start there.
• Misses are spread out. Start with algebra, the largest category, unless arithmetic is blocking your equations.
• You ran out of time. FPT9's directions advise moving past difficult items and returning if time permits.
• You got all 12. That covers these 12 items only, so move on to a longer form.

Next, take FPT9 under its own 45-minute limit and review its rationales. Try the 20 free HiSET practice questions, then put your weak skills on a calendar with the free HiSET study plan or the eight-week HiSET study schedule.

For recall practice alongside problem solving, full HiSET prep planned for launch includes 500 flashcards across the exam.

For the other subtests, read what is on the HiSET test. If you haven't settled on a test, HiSET vs GED compares them.