The official ASVAB subtest descriptions distinguish Mathematics Knowledge, which covers high-school mathematical principles, from Arithmetic Reasoning, which focuses on word problems. Both contribute to AFQT calculations along with Word Knowledge and Paragraph Comprehension. The ASVAB does not permit calculators, as the official FAQ explains, so practice exact arithmetic and estimation without depending on a device.
Factors, multiples, primes and composite numbers
A factor divides another integer without remainder. The factors of 18 are 1, 2, 3, 6, 9 and 18. A multiple of 18 is a result of multiplying 18 by an integer, such as 36 or 54. Confusing factors with multiples can reverse the intended search.
A prime number greater than 1 has exactly two positive factors, 1 and itself. A composite number greater than 1 has more than two. The number 1 is neither prime nor composite. This distinction matters when simplifying fractions, finding greatest common factors or interpreting a divisibility question. For example, 18/24 reduces to 3/4 because the greatest common factor is 6.
Ratios, proportions and percentages
A ratio compares quantities, often written as a:b. A proportion states that two ratios are equal. If five identical components cost 35 units of currency, one costs 7 and eight cost 56, assuming the same unit price. You can express the relationship as 5/35 = 8/x and solve for x = 56. Remember that “per” often means a rate such as dollars per hour or miles per gallon.
Percent means per hundred. A 15 percent discount on 80 removes 12, giving a price of 68. A later 15 percent increase on 68 adds 10.2, not 12; sequential percent changes use different bases. State the original quantity clearly before computing any percent change.
Exponents, roots and reciprocals
An exponent tells you how many times a base is multiplied by itself: 3 cubed is 3 × 3 × 3 = 27. A square root reverses squaring for a nonnegative number: the principal square root of 81 is 9. Do not confuse the notation √81, which gives 9, with solving x² = 81, which gives x = 9 or x = −9.
The reciprocal of a nonzero fraction a/b is b/a. The reciprocal of 3/4 is 4/3. Dividing by a fraction is equivalent to multiplying by its reciprocal: 6 ÷ (3/4) = 6 × (4/3) = 8. Check that the divisor is not zero before applying this operation.
Mean, median, mode and range
For the values 2, 4, 4, 7 and 13, the mean is 6, the median is 4, the mode is 4, and the range is 11. The mean uses all values and can be affected by an outlier. The median is the middle value after ordering. A set may have more than one mode or no uniquely most frequent value, depending on how the term is being used.
When a word problem asks for a “typical” value, identify which statistic is actually requested. Do not calculate the mean because it is the first method you remember. For a data set with an extreme value, compare the mean and median to understand why the problem might prefer one measure.
Translate sentences into equations
“The sum of a number and 8 is 23” translates to x + 8 = 23. “Twice the difference between a number and 5” becomes 2(x − 5), not 2x − 5. The words “of,” “difference,” “at least,” and “no more than” can change a mathematical expression or inequality.
Try this original problem: a container holds at most 90 liters and already contains 24 liters. If each addition is 6 liters, how many full additions are possible? The phrase “at most” gives 24 + 6n ≤ 90, so n ≤ 11. Check that the question asks for whole additions, not a fractional quantity.
Practice reading, computing and checking in that order
A short daily routine can focus on five terms, one original example per term and one mixed word problem that uses several together. Explain your answer in ordinary language before checking arithmetic. The ASVAB AFQT score explanation emphasizes that Arithmetic Reasoning and Mathematics Knowledge help determine the AFQT percentile; they are not the entire test or a universal substitute for service-specific qualification rules.
The right objective is reliable interpretation under the applicable time constraints. If a candidate knows what a term means, can translate it into a mathematical relationship and can assess whether the final answer is reasonable, unfamiliar wording becomes much less likely to hide a straightforward problem.
