The ASVAB Math Survival Guide: What to Study and Why
Integers are numbers without fractions or decimals and include all positive whole numbers, negative whole numbers, and zero. Examples of integers are -5, 0, and 8. On the ASVAB, you may be asked to perform arithmetic operations (addition, subtraction, multiplication, division) using integers or identify which numbers belong in certain categories.
A rational number can be written as a fraction a/b, where a and b are integers and b is not zero. For example, 3/4, -2, and 0.25 are all rational numbers. Even terminating or repeating decimals are rational because they can be written as fractions.
These are numbers that cannot be expressed as simple fractions. Their decimal expansions are non-repeating and non-terminating. Examples include √2 and π (pi). You don’t need to memorize many irrational numbers for the ASVAB, but knowing the distinction helps when answering questions about number sets.
The set of real numbers includes both rational and irrational numbers. Real numbers are any number you can find on the number line. Understanding how different categories of numbers relate can help you eliminate wrong answer choices.
Operations with signed numbers are common on the ASVAB. Here’s how they work:
Mistakes with negative signs are common, especially when multiple steps are involved.
The absolute value of a number is its distance from zero on the number line, regardless of direction. It’s always non-negative.
On the ASVAB, you might see absolute value in equations or simple expression evaluation. Pay attention to whether the question is asking for the value itself or the result after operations.
A factor of a number divides it evenly without a remainder. For example, factors of 12 are 1, 2, 3, 4, 6, and 12. The ASVAB may ask you to find the greatest common factor (GCF) or list all factors.
A multiple is the result of multiplying a number by an integer. Multiples of 4 include 4, 8, 12, 16, and so on. Questions may ask you for the least common multiple (LCM) or the next number in a list of multiples.
A prime number has exactly two distinct positive divisors: 1 and itself. Common primes include 2, 3, 5, 7, 11, 13, 17. You should memorize the first ten or so prime numbers for quick recall.
Prime factorization—the process of breaking a number down into prime factors—might also appear in questions involving GCF and LCM.
Knowing divisibility rules can save time on the ASVAB when you need to test whether one number divides evenly into another.
Remainders are what’s left after division. If 14 ÷ 4 = 3 R2, that means 4 goes into 14 three times with 2 left over. The test may ask you to interpret this or solve problems involving remainders.
Being fluent in converting and simplifying fractions is essential.
Exponents indicate repeated multiplication:
Key exponent rules:
A square root is the number that gives the original number when multiplied by itself:
Cube roots and higher may appear, but square roots are most common on the test.
Used to simplify very large or small numbers:
You’ll need to convert between standard form and scientific notation and perform operations like multiplying or dividing in scientific notation.
A factorial is the product of all positive integers up to a given number:
Factorials appear in counting, arrangement, and probability problems.
PEMDAS is a guideline for evaluating expressions:
Example:
Ignoring the proper order leads to incorrect answers.
Used to expand or simplify expressions:
Changing the order of addition or multiplication doesn’t change the result:
Changing grouping in addition or multiplication doesn’t affect the result:
Recognizing these can help you simplify complex expressions.
A ratio compares two values:
A proportion is an equation of two equal ratios:
A rate is a ratio of two different units:
You’ll solve many proportion and rate problems in ASVAB word problems.
Percentages are tested often, especially in word problems and practical applications.
Average = (Sum of values) / (Number of values)
The middle number in an ordered list. If the list has an even number of elements, average the two middle ones.
The most frequent value. There can be multiple modes or none.
These are often used in word problems involving sets of data.
Probability measures the likelihood of an event occurring:
For two events A and B:
Probability may involve combinations, dice, cards, or spinners, so practicing scenarios helps.
An arithmetic sequence increases or decreases by the same amount each step.
To find the nth term:
Where:
Recognizing and working with sequences may be part of ASVAB pattern and logic questions.
An algebraic expression combines variables, constants, and mathematical operations (addition, subtraction, multiplication, division) without an equal sign.
Examples:
These are not equations because they don’t contain an equality ( = ) symbol.
You’ll often be asked to simplify, expand, or factor these expressions.
Terms with the same variable(s) raised to the same power are like terms.
Examples:
Combine like terms by adding or subtracting the coefficients.
Example:
FOIL stands for First, Outside, Inside, Last.
Example:
Factoring is the reverse of multiplication. It means writing an expression as a product of its factors.
Example:
Factoring is essential for solving quadratic equations.
Memorizing these patterns helps in recognizing how to factor quickly.
Solve by performing the inverse operation.
Example:
Undo operations in the reverse order of PEMDAS.
Example:
Distribute and combine like terms if necessary before solving.
Example:
Be cautious with negative signs and fractions during each step.
Example:
Always try to isolate the variable on one side of the equation.
Inequalities are like equations, but use the symbols:
Solve similarly to equations, but reverse the inequality sign if you multiply or divide by a negative number.
Example:
You may be asked to interpret a graph or draw one based on a given inequality.
Systems include two or more equations with two variables. The ASVAB focuses mostly on solving linear systems.
Example:
Example:
Look out for word problems that translate into systems of equations.
The general form is ax² + bx + c = 0. You must solve by factoring, not graphing, on the ASVAB.
Example:
You may also see trinomials that require more advanced factoring, but always check for common factors first.
Formed by two intersecting lines, always equal in measure.
ASVAB questions often involve solving for missing angles based on these relationships.
When a transversal cuts across parallel lines, several angle pairs are formed:
You may be given a diagram and asked to identify or calculate unknown angles using these properties.
The sum of the interior angles in any triangle is always 180°.
Example:
If two angles are 50° and 60°, the third is 70°.
For right triangles: a² + b² = c²
Where c is the hypotenuse.
Example:
If a = 3, b = 4
Then c² = 9 + 16 = 25 → c = 5
You might also be asked to identify whether a triangle is right-angled based on side lengths.
The interior angles of any quadrilateral sum to 360°.
You may need to plug values into these formulas, so familiarity with π (approx. 3.14) is helpful.
Add all the side lengths.
You will often be given shapes with dimensions and asked to compute the area or perimeter.
Solid geometry deals with three-dimensional figures such as cubes, cylinders, cones, spheres, and rectangular prisms. These shapes have volume and surface area, and the ASVAB often asks you to calculate these quantities using formulas.
Example:
If a rectangular box has a length of 10 cm, a width of 4 cm, and a height of 5 cm, its volume is:
V = 10 × 4 × 5 = 200 cm³
These questions often include diagrams and require you to extract the needed values.
Similar shapes have the same shape but not necessarily the same size. Their angles are equal, and their sides are proportional.
If two triangles are similar, the ratio of their corresponding sides is equal. For example, if one triangle has sides 3, 4, 5 and the other has sides 6, 8, 10, their corresponding side ratios are all 1:2.
You may be asked to find a missing side or scale factor.
Congruent shapes are identical in both size and shape. All corresponding sides and angles are equal. If triangles are congruent, all their parts match exactly.
Questions about similarity and congruence typically involve diagrams and proportional reasoning.
The coordinate plane consists of two axes:
Coordinates are written as (x, y). The origin is the point (0, 0).
Knowing which quadrant a point lies in helps when answering questions about movement and direction.
Slope measures the steepness of a line and is calculated as:
slope (m) = (y₂ − y₁) / (x₂ − x₁)
Example:
Find the slope between (2, 3) and (4, 7):
m = (7 − 3)/(4 − 2) = 4/2 = 2
Slopes:
The most common equation format for a line:
y = mx + b
Where:
Example:
In y = 3x + 2, the slope is 3, and the line crosses the y-axis at (0, 2).
You may be asked to graph this equation, identify the slope, or solve for x or y given a value.
Use the distance formula:
Distance = √[(x₂ − x₁)² + (y₂ − y₁)²]
This is derived from the Pythagorean Theorem and is useful for geometry problems involving the coordinate plane.
Example:
The distance between (1, 2) and (4, 6) is:
√[(4 − 1)² + (6 − 2)²] = √[9 + 16] = √25 = 5
This is helpful for questions involving diagonals or lengths of line segments.
Graphs present data visually. You may be asked to interpret values, compare groups, or determine trends.
Pie charts represent parts of a whole. Each slice represents a percentage of the total. You might need to calculate the actual value from a percentage or determine the missing piece.
Example:
If 25% of a pie chart equals 50 people, the total population is:
50 / 0.25 = 200
Tables show organized data. You may need to perform calculations based on rows and columns or compare entries.
This skill is tested through straightforward questions or word problems referencing a data table.
Word problems can be some of the most challenging parts of the ASVAB. They combine reading comprehension with math reasoning.
Identify:
Translate words into variables. For example:
Example:
“Five more than twice a number is 17” becomes:
2x + 5 = 17
Many word problems can be turned into equations, including:
If stuck, plug in answer choices to see which fits the problem conditions. This is especially effective with multiple-choice questions.
Example:
If x = 4 solves the equation, test it:
2x + 5 = 17 → 2(4) + 5 = 13 — not correct
Try x = 6:
2(6) + 5 = 17 — correct
After solving, verify that your answer makes sense in the context of the problem. Avoid answers that are negative when quantities must be positive or fractions when a whole number is required.
The ASVAB math questions are often rooted in real-world or military contexts, such as:
Example:
If a vehicle travels at 40 mph and needs to go 160 miles, how long will it take?
Time = Distance / Rate = 160 / 40 = 4 hours
Math is used in supply chain logistics, ammunition counts, and budgeting.
Example:
If 500 rounds of ammo are divided among 20 soldiers, how many does each get?
500 ÷ 20 = 25
Many geometry word problems require you to:
Example:
A rectangular field is 3 times as long as it is wide. If the perimeter is 64 meters, what are the dimensions?
Let width = w
Then length = 3w
Perimeter = 2(w + 3w) = 2(4w) = 8w = 64
Solve: w = 8 → length = 24, width = 8
You may see these problems as multiple-choice or diagram-based.
The ASVAB contains two math subtests:
You’ll need both speed and accuracy to perform well. These sections are especially important for calculating your AFQT score, which determines your eligibility for enlistment.
Not all math topics are equally important or equally likely to appear. Here’s how to prioritize:
These appear frequently and are heavily weighted in the Arithmetic Reasoning and Mathematics Knowledge sections.
These are tested, but often with fewer questions. Know the concepts and practice the common types.
While these may appear, they are less common and shouldn’t dominate your study plan unless you’re aiming for a very high score.
Each math section gives you less than two minutes per question. That doesn’t mean you should spend a full two minutes on every item. Some questions should take under 30 seconds. Save time here to invest more in the tough ones.
When you don’t immediately know the answer, eliminate wrong options:
The ASVAB does not penalize for wrong answers. If time is running out, don’t leave any questions blank—make your best guess.
For some problems, especially those involving large numbers or percentages, estimating gives you a faster path to the correct answer.
Example:
If you’re asked what 49% of 200 is, estimating 50% = 100 gets you close enough to find the right answer among the choices.
If a question is taking too long:
Time is your most valuable resource on test day.
Take full-length practice exams under timed conditions to simulate the real test. Focus on both accuracy and speed. Review every incorrect answer.
Memorize these core formulas:
Flashcards work well for memorization. Keep them short and focused.
Don’t study all topics in one sitting. Break sessions into categories:
This focused approach leads to better long-term retention.
Practice using math in everyday life:
Doing math this way builds confidence and familiarity.
Teaching someone else is one of the most effective ways to learn. Explaining how to solve problems will reinforce your understanding. If you don’t have a group, pretend you’re teaching a concept aloud to yourself.
Use short quizzes to identify which topic areas you’re weakest in. Spend more time reviewing those, even if they’re not your least favorite.
Every wrong answer is a chance to learn:
Keep a notebook of your errors and review it before every new study session.
Knowing why the answer is right is more important than just getting it right. Try to explain each step in your reasoning to yourself as you solve problems.
A tired mind struggles to process information. Sleep well the night before, and eat a balanced breakfast that won’t make you sluggish.
You won’t need a calculator—the ASVAB math sections are designed to be solved with mental math, paper, and pencil.
Being calm helps you think more clearly and reduce careless mistakes.
If your test is within the next 2–4 weeks, here’s a sample prep schedule:
Week 1
Week 2
Week 3
Week 4
Make adjustments to this schedule based on your strengths and time availability.
The ASVAB tests math that is mostly from middle school and early high school, but it requires solid problem-solving skills and familiarity with many different types of questions. The key is not just what you know, but how well you can apply it under time pressure.
Here’s what to focus on as your test day approaches:
With consistent practice and smart strategies, you can greatly improve your performance on the math portions of the ASVAB and open up more opportunities in your military career.
Let me know if you want a printable study checklist, practice questions, or personalized help with a specific topic.
Popular posts
Recent Posts