AFOQT math preparation should include both fast arithmetic reasoning and more direct math knowledge. The official Air Force AFOQT information pamphlet describes the test as an aptitude test used for officer commissioning programs, with quantitative scoring connected to arithmetic relationships and mathematical terms, formulas, and relationships. It also shows Arithmetic Reasoning and Math Knowledge as separate subtests with 25 items each.
The 15 original problems below are not official AFOQT questions. They are designed to help you see which math skills need attention before you move into timed practice. For official test structure and sample item style, review the Air Force AFOQT information pamphlet.
How to Use This Practice Set
Work the problems without a calculator unless your official testing instructions say otherwise for your administration. Write enough work that you can find your error later. After checking the answer key, sort misses into arithmetic, algebra, geometry, or word-problem setup.
15 AFOQT Math Practice Questions
1. A vehicle travels 180 miles in 3 hours. At the same rate, how far will it travel in 5 hours?
2. A jacket originally costs $120 and is discounted 15%. What is the sale price?
3. If 4x – 7 = 29, what is x?
4. A rectangular room is 18 feet long and 12 feet wide. What is its area?
5. A mixture uses 2 parts concentrate for every 7 parts water. How many parts concentrate are needed for 35 parts water?
6. Simplify 3(2x – 5) + 4x.
7. The average of 8, 12, 15, and n is 13. What is n?
8. A plane descends 1,500 feet in 6 minutes. What is the average descent rate in feet per minute?
9. What is 3/5 of 250?
10. A right triangle has legs of 9 and 12. What is the length of the hypotenuse?
11. If y = 2x^2 – 3x and x = 4, what is y?
12. A tank is 3/4 full. After 18 gallons are removed, it is 1/2 full. What is the tank’s capacity?
13. Factor x^2 + 7x + 12.
14. A map scale is 1 inch = 25 miles. Two cities are 4.2 inches apart on the map. What is the actual distance?
15. A number is increased by 20% and becomes 72. What was the original number?
Answer Key and Short Explanations
1. 300 miles. The rate is 60 miles per hour. 2. $102. The discount is 0.15 x 120 = 18, so 120 – 18 = 102. 3. x = 9. Add 7, then divide by 4. 4. 216 square feet. 5. 10 parts concentrate. Multiply both parts of 2:7 by 5. 6. 10x – 15. 7. n = 17 because the total must be 52. 8. 250 feet per minute. 9. 150. 10. 15 by the 9-12-15 right triangle or the Pythagorean theorem. 11. 20 because 2(16) – 12 = 20. 12. 72 gallons. The removed 18 gallons is 1/4 of the tank. 13. (x + 3)(x + 4). 14. 105 miles. 15. 60 because 1.2x = 72.
What Your Misses Mean
| If you missed… | Likely gap | Next practice |
|---|---|---|
| 1, 5, 8, 14 | Rates, ratios, and scale | Unit-rate drills and proportion setup |
| 2, 9, 15 | Percents and fractions | Percent increase/decrease and fraction-of-a-number practice |
| 3, 6, 11, 13 | Algebra | Equations, expressions, substitution, and factoring |
| 4, 10 | Geometry formulas | Area, perimeter, volume, and right triangles |
| 7, 12 | Multi-step reasoning | Average problems and reverse fraction problems |
Build a 10-Day Math Review
Days 1-2 should focus on arithmetic: fractions, decimals, percents, rates, and ratios. Days 3-4 should focus on algebra: simplifying expressions, solving equations, substitution, exponents, and factoring basics. Days 5-6 should focus on geometry: area, perimeter, volume, right triangles, and unit conversion. Days 7-8 should use mixed word problems. Days 9-10 should be timed review with corrections.
For every missed problem, write the setup you should have used. On AFOQT-style math, the setup is often the real skill. Once the equation or proportion is correct, the arithmetic is usually manageable.
Timed Practice Strategy
After you can solve these questions untimed, repeat the set with a timer. Do not try to race through all skills at once. Start with five questions in eight minutes, then review every missed or skipped item. A skipped item is useful data: it often means you did not recognize the problem type quickly enough.
Use a two-column error log. In the first column, name the topic: percent change, rate, equation, factoring, geometry, or average. In the second column, name the action: memorize a formula, practice a setup, slow down arithmetic, or learn a shortcut. This keeps AFOQT math review specific and prevents vague notes such as “study more math.”
When to Move Beyond Basic Review
Move into longer mixed sets when you can explain at least 12 of the 15 answers without looking back at the solution. Mixed practice is important because the actual test will not warn you that the next item is a ratio or geometry problem. The goal is flexible recognition under time pressure.
ViewMath AFOQT Math Next Step
If this set exposed several gaps, use a structured resource such as the ViewMath AFOQT Math Workbook or browse the AFOQT Math collection. A workbook is best when you need repetition. A study guide is better when you need lessons before practice.
Do not measure progress only by whether you got one problem right after reading the solution. Measure progress by whether you can solve a similar problem two days later, under time pressure, without being told the topic.
