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What Type of Math Is on the ASVAB? Full Guide With Examples

Tina Tran

Created at June 9, 2025

What type of math is on the ASVAB is one of the most common concerns among future military recruits preparing for the test. Since calculators are not allowed, many test takers worry about whether their math skills are strong enough to succeed. The good news is that the math sections focus on fundamental concepts that can be mastered with the right approach. In this article, we’ll break down exactly what kind of math you can expect on the ASVAB and how to prepare effectively for each part.

What type of math is on the ASVAB?

The ASVAB test includes a range of math topics designed to measure both your practical problem-solving skills and your understanding of fundamental mathematical concepts.

The test features two separate math sections: Arithmetic Reasoning (AR) and Mathematics Knowledge (MK). Each covers different types of questions and math skills. Below is a breakdown of the main math concepts you can expect in each section.

Geometry

Geometry questions on the ASVAB test your ability to work with shapes, spatial reasoning, and the properties of geometric figures. These problems often require mental visualization and basic formula recall, especially since calculators are not allowed. Key knowledge you may encounter includes:

Geometric figures

You will be expected to recognize basic shapes and understand their properties, such as sides, angles, and symmetry. For example:

Right angle = 90°, has a special square symbol.
Supplementary angles = Add up to 180°
Complementary angles = Add up to 90°
Angles in a triangle = Add up to 180°

Geometric concepts

This includes understanding how different parts of shapes relate to each other and applying that knowledge to solve problems.

Parallel lines: Identify and apply the rules for angles formed by parallel lines and transversals (such as corresponding, alternate interior, and same-side interior angles).
Angle relationships: Know how to calculate unknown angles using relationships such as supplementary, complementary, vertical, and adjacent angles.
Side relationships: Understand how the sides of shapes relate, especially in triangles and parallelograms. For example:
- Equilateral: All 3 sides and all 3 angles are equal (each angle is 60°)
- Isosceles: 2 sides are equal → the base angles are also equal
- Scalene: No sides or angles are equal
- Right triangle: Has one 90° angle → the side opposite is called the hypotenuse
- Pythagorean theorem (only for right triangles): $a^2+b^2=c^2$

Measurement skills

You’ll be asked to solve problems involving area, perimeter, and volume on the ASVAB. The table below summarizes the most important ones:

Shape	Area	Perimeter	Volume
Rectangle	$\text{Area} = \text{length} \times \text{width}$	$P = 2 \times (\text{length} + \text{width})$	$V = \text{length} \times \text{width} \times \text{height}$
Square	$\text{Area} = \text{side}^2$	$P = 4 \times \text{side}$	$V = \text{side}^3$
Triangle	$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$	Add all sides	—
Circle	$\text{Area} = \pi \times \text{radius}^2$	$\text{Circumference} = 2\pi r$	—
Rectangular prism	—	—	$V = \text{length} \times \text{width} \times \text{height}$
Cylinder	—	—	$V = \pi r^2 h$

Algebra

Algebra is another kind of math that is on the ASVAB test. It focuses on solving problems that involve variables, expressions, and equations. You’ll need to know how to work with unknowns and manipulate algebraic expressions using basic operations.

Solving equations

These are problems where you solve for the unknown variable (x, y, etc.) by isolating it using addition, subtraction, multiplication, or division.(e.g. Solve $3x + 8 = 21$ )

Working with expressions

You may be asked to simplify algebraic expressions or substitute values for variables. (e.g. Simplify: $5x + 3x - 9$ )

Polynomials

A polynomial is an algebraic expression that includes terms made up of variables raised to whole-number powers.

- Polynomial terms: Each part of a polynomial separated by + or − is a term. In particular:
  - $4x^3$ : cubic term
  - $x$ : linear term
  - $-7$ : constant term
  - The degree of a polynomial is the highest exponent of the variable. (e.g. $5x^2 + 3x + 8$ → Degree is 2 )

Multiplying polynomials: You may be asked to expand expressions like binomials. (e.g. $(x + 2)(x + 3)$ )

Arithmetic

This section tests your ability to solve real-world word problems using basic math concepts.

Fractions

You will be expected to add, subtract, multiply, and divide fractions and mixed numbers. Questions may involve simplifying fractions or converting between improper fractions and mixed numbers.
Example: If you run $\frac{2}{3}$ of a mile each day, how many miles do you run in 5 days?

Probability and statistics

This section tests your ability to interpret data, calculate likelihoods, and understand basic statistical concepts. You’ll often work with averages and simple probability rules.

Basic statistical concepts

Mean (Average): Add all the numbers, then divide by how many numbers there are.
Example: Mean of 4, 6, 8 → (4 + 6 + 8) ÷ 3 = 6
Median: The middle number in an ordered list.
Example: 2, 5, 9 → Median is 5
If there’s an even number of values, take the average of the two middle numbers.
Mode: The number that appears most frequently.
Example: 2, 4, 4, 5, 7 → Mode is 4
Range: Subtract the smallest value from the largest value.
Example: 3, 7, 10 → Range = 10 − 3 = 7

Basic probability concepts

Probability measures the chance that something will happen. It’s always a number between 0 and 1 (or 0% to 100%).

$P(\text{Event}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}}$

Two events are independent if the outcome of one does not affect the other. Probability of two independent events A and B both happening is presented by:

$P(A \text{ and } B) = P(A) \times P(B)$

Distance, rate, & time

You’ll solve problems using the formula: Distance = Rate × Time. These problems usually ask you to find one of the three values when the other two are known. For instance:

Find the distance: A fast-food delivery car travels at a speed of 40 miles per hour. It takes 1.25 hours to deliver the food. How far is the delivery address from the restaurant?
Find the rate: A train travels 300 miles in 5 hours. What is its average speed?
Find the time: A car travels 120 miles at a certain speed. If the speed of the car was 40 mph, how long did it take to cover the 120 miles?

Math operations

With ASVAB math operations questions, you need to confidently perform basic arithmetic:

Addition, subtraction, multiplication, and division.
Solving multi-step problems with the correct order of operations (PEMDAS), in particular.
- Do all calculations inside parentheses first, starting with the innermost.
- Calculate exponents like squares or cubes next.
- Multiplication and division from left to right, whichever comes first.
- Do addition and subtraction from left to right last.

Percentage

You will solve problems involving finding percentages, percentage increase/decrease, and converting between decimals and percentages. (e.g., What is 25% of 160?)

Ratio & proportion

Ratios and proportions are math problems that compare quantities and find missing values using equivalent relationships.

Ratios compare two values, written as a fraction or with “:”.

Example: If there are 12 apples and 8 oranges, what is the ratio of apples to oranges?

Proportions: You will solve problems where two ratios are set equal to each other:
$\frac{a}{b} = \frac{c}{d}$

Example: The ratio of boys to girls is 3:2. If there are 15 boys, how many girls are there?

Unit conversion

In the ASVAB, unit conversion problems test your ability to change a measurement from one unit to another, including:

Inches ↔ Feet
Ounces ↔ Pounds
Minutes ↔ Hours
Metric system conversions (cm, m, kg, etc.)

Number properties

Number properties are basic rules about how numbers work. You’ll need to recognize and apply them to solve ASVAB math problems quickly and accurately.

Number Types

Whole numbers: 0, 1, 2, 3… (no fractions, no negatives)
Integers: …-2, -1, 0, 1, 2…
Rational numbers: Numbers that can be written as a fraction (e.g. $\frac{1}{2}$ , 0.75)
Irrational numbers: Cannot be written as a simple fraction (e.g. π, $\sqrt{2}$ )
Prime numbers: Only divisible by 1 and itself (e.g., 2, 3, 5, 7…)

Other properties

Even & odd numbers: Problems may ask you to identify if a number is even (divisible by 2) or odd, or to solve problems involving sums or products of even and odd numbers.
Factors and multiples: You might be asked to find the factors of a number (numbers that divide it exactly) or multiples (numbers you get by multiplying it by whole numbers).
Divisibility rules: These rules help quickly determine if one number is divisible by another without doing full division. For example:
- Divisible by 2 → if the last digit is even
- Divisible by 3 → if the sum of the digits is divisible by 3
- Divisible by 5 → if the number ends in 0 or 5
Factorials: A factorial (written with an exclamation mark, like 5!) means you multiply a whole number by every whole number below it down to 1.
Exponents: Exponents show how many times to multiply a number by itself. (e.g $2^2 = 2 \times 2 = 4$ )
Absolute value: The absolute value of a number is its distance from zero on the number line, always positive. (e.g. |5| = 5)
Square roots: A square root asks what number, when multiplied by itself, gives you the original number. (e.g. $\sqrt{25} = 5$ )
Cube roots: A cube root tells you what number, when multiplied by itself three times, equals the original number. (e.g. $\sqrt[3]{8} = 2$ )

How to practice for the ASVAB math section?

$How to practice for the ASVAB math section?$

How to practice for the ASVAB math section?

If you want to improve your math skills and score higher on the ASVAB, it’s important to focus on three key areas: theory, practice, and reviewing mistakes.

1. Learn theory and memorize important formulas

Understanding the theory behind math problems is essential. In addition, you should master basic formulas. You can find a helpful list of essential formulas here: ASVAB Math Formulas. Make it a habit to learn 3 to 5 formulas daily. Write them down from memory and create simple examples to see how they apply.

2. Practice calculation without a calculator

Since calculators are not allowed during the ASVAB test, practicing manual calculations is crucial. Daily practice helps increase your speed and accuracy in solving math problems by hand.
Use free online resources like ASVAB Mathematics Practice Test or ASVAB Arithmetic Reasoning Practice Test to get real test experience. Track your time and accuracy to monitor improvement.

3. Review mistakes, learn from your errors

Simply checking which answers are right or wrong isn’t enough. After each practice session, identify the problems you missed. Write down the type of problem, why you made a mistake (such as misunderstanding the question, calculation errors, or forgetting steps), and the correct solution process.

FAQs

1. What math level is on the ASVAB?

The ASVAB covers basic high school-level math, primarily pre-algebra, algebra I, and geometry. It doesn’t go into advanced calculus or statistics.

2. Is the math on the ASVAB hard?

It depends on your math background. Some concepts may feel tricky for those out of school for a while. However, with targeted prep, most people can improve significantly in just a few weeks.

Final thoughts

Knowing what type of math is on the ASVAB helps you focus your study effectively. Math is one of the most challenging sections of the ASVAB for many test-takers, and it’s also one of the most influential in determining your ASVAB scores. The Arithmetic Reasoning (AR) and Mathematics Knowledge (MK) subtests directly impact your AFQT score, which determines your military eligibility and job qualifications.

That’s why mastering math is not optional; it’s critical. Remember, consistent practice and understanding key concepts are the best ways to succeed on the ASVAB math sections.