ASVAB Mathematics Knowledge practice
Mathematics Knowledge (MK) tests “knowledge of high school mathematics principles” and is the second math subtest in the AFQT. Work the 13 original questions below by hand, then read the explanation.
Last updated · Published by Certloom Learning · Written by Certloom Learning for AptiStep and checked by recomputing every answer. Not real ASVAB questions.
What does ASVAB Mathematics Knowledge cover?
The official description is “Knowledge of high school mathematics principles” (Official ASVAB: What to Expect (checked 2026-11-12)). It is less about stories than Arithmetic Reasoning: fractions, equations, geometry formulas and number rules. Start with fractions and algebra.
How is Mathematics Knowledge tested on the CAT-ASVAB and on paper?
On the computer version the official table lists 15 scored questions and up to 15 unscored tryout questions, with a time limit of 31 minutes without tryout questions or 65 minutes with them. On paper it has 25 questions in 24 minutes. Source: Official ASVAB: What to Expect (checked 2026-11-12).
Free Mathematics Knowledge practice questions
What is 3/4 + 1/8?
- 4/12
- 1/2
- 7/8
- 4/8
Show answer and explanation
Answer: C. 7/8
Use equal-sized parts. Rewrite 3/4 as 6/8. Then 6/8 + 1/8 = 7/8. Adding the denominators would change the size of the parts.
Solve for x: 3x + 5 = 20.
- 5
- 15
- 25/3
- 45
Show answer and explanation
Answer: A. 5
Subtract 5 from both sides to get 3x = 15. Divide both sides by 3: x = 5. Check by substitution: 3(5) + 5 = 20.
What is 2/3 of 18?
- 6
- 9
- 12
- 27
Show answer and explanation
Answer: C. 12
Divide 18 into three equal parts: 18 ÷ 3 = 6. Take two parts: 6 × 2 = 12.
Solve for y: 4y − 7 = 17.
- 6
- 2.5
- 24
- 40
Show answer and explanation
Answer: A. 6
Add 7 to both sides: 4y = 24. Divide by 4: y = 6. Check: 4(6) − 7 = 17.
What is the area of a rectangle 8 feet long and 5 feet wide?
- 13 square feet
- 26 square feet
- 40 square feet
- 80 square feet
Show answer and explanation
Answer: C. 40 square feet
Area is length × width: 8 × 5 = 40 square feet. Adding all four sides gives perimeter, a different quantity measured in feet.
What is 5/6 − 1/4?
Show answer and explanation
Answer: 7/12
Use twelfths: 5/6 = 10/12 and 1/4 = 3/12. Subtract 10 − 3 while keeping the denominator 12. The answer is smaller than 5/6, as subtraction requires.
Find 3/5 of 25.
Show answer and explanation
Answer: 15
One fifth of 25 is 5. Take three of those groups: 3 × 5 = 15. “Of” describes a part of the original quantity here.
A recipe needs 3/4 cup of milk. You make half the recipe. How much milk is needed?
Show answer and explanation
Answer: 3/8 cup
Halve each of the three quarter-cup portions: (3/4) × (1/2) = 3/8. Half a quantity must be smaller than the original quantity.
Which is larger: 7/10 or 2/3?
Show answer and explanation
Answer: 7/10
Compare equal-sized thirtieths: 7/10 = 21/30 and 2/3 = 20/30. The first fraction has one more thirtieth. Comparing numerators alone would not work with the original denominators.
Solve 5x + 4 = 29.
Show answer and explanation
Answer: x = 5
Subtract 4 from both sides: 5x = 25. Divide by 5: x = 5. Check in the original equation: 5(5) + 4 = 29.
Solve 3(y − 2) = 18.
Show answer and explanation
Answer: y = 8
Divide both sides by 3: y − 2 = 6. Add 2 to both sides: y = 8. Check: 3(8 − 2) = 18.
Solve x/4 + 3 = 8.
Show answer and explanation
Answer: x = 20
Subtract 3: x/4 = 5. Multiply both sides by 4: x = 20. Undo the addition before undoing the division.
Solve 2a + 5 = a + 12.
Show answer and explanation
Answer: a = 7
Subtract a from both sides to obtain a + 5 = 12. Subtract 5: a = 7. Both original sides then equal 19.
What is a good way to study Mathematics Knowledge?
Pick one topic a day, do the worked example, then close it and solve a fresh question. Check every equation by substituting your answer back. If a topic keeps failing, go back one step to the rule behind it (equal-sized pieces for fractions, the same operation on both sides for equations).
Frequently asked questions
Is Mathematics Knowledge the same as Arithmetic Reasoning?
No. Arithmetic Reasoning uses word problems; Mathematics Knowledge tests math principles more directly. Both count toward the AFQT.
Do I need to memorize formulas?
Know the common ones, such as area of a rectangle and triangle. The official site does not publish a formula list; check the official sample questions for the style.