Achievable ASVAB

2. Math Knowledge

Our ASVAB course is currently in development and is a work-in-progress.

Math strategies

5 min read

Multiple-choice tests like the ASVAB measure not only what you know, but also how efficiently you can reason under time pressure. Even if your math feels rusty, a few reliable strategies can help you work faster and more accurately.

One key rule to keep in mind: the ASVAB doesn’t allow calculators on the math sections. That means you’ll want strategies that keep your work simple, quick, and accurate.

Rounding

Rounding replaces a fraction or decimal with a nearby “easy” number. The goal is to estimate quickly, then use the answer choices to pick the only reasonable option.

You don’t need to round on every problem. It’s most useful when exact arithmetic would take too long, and the answer choices are far apart. Let’s solve this using rounding, then check with the exact answer.

Example:

A factory produces $19.6$ pieces of sheet metal a day. How many pieces of sheet metal does it make in $5$ days?

A. $91$
B. $98$
C. $106$
D. $117$

Start by rounding. Since the answer choices are integers, round $19.6$ to $20$ .

Now compute:

$20 \times 5 = 100$

So the factory makes about $100$ pieces in $5$ days.

Because we rounded $19.6$ up to $20$ , the exact answer must be a little less than $100$ .

Look at the answer choices:

$98$ is just below $100$ ✔

The others are either too small or too large

So B. $98$ is the best estimate.

Now confirm with exact multiplication:

$19.6 \times 5 = 98$

Rounding helped us get the correct answer faster.

Sidenote

Times tables

If you don’t know your times tables, this is the time to learn them. You can’t use a calculator on the ASVAB, and you’ll do a lot of multiplication.

Try printing off a $12$ x $12$ table and crossing off the columns you already know, such as $0, 1, 2$ , and so forth. Then work on one column at a time until you have them memorized.

Process of elimination

On a multiple-choice test, a practical way to improve your odds is to reduce the number of answer choices you’re considering. Even if you end up guessing, eliminating choices first makes that guess much more likely to be correct.

Starting with $4$ choices gives you a $25%$ chance of guessing correctly. Eliminating one choice raises your odds to $33.3%$ . Eliminating two choices raises your odds to $50%$ .

So, how do you eliminate answer choices?

Start by using logical reasoning:

If the answer must be negative, eliminate any positive answers.
If a line must have a slope that’s less than $1$ , eliminate any answer with a slope greater than one.

As you work through the problem, keep removing choices that can’t be true until only the correct one remains.

Example:

What is the difference of $(3 x - 5) - (10 x + 8)$ ?

A. $- 7 x + 3$
B. $- 7 x - 13$
C. $13 x + 3$
D. $13 x - 13$

Use process of elimination by simplifying one part at a time.

Start with the $x$ -terms:

$3 x - 10 x = - 7 x$

This means the final answer must have a $- 7 x$ term, so eliminate choices C and D since they have $+ 13 x$ .

Now handle the constants by distributing the negative:

$3 x - 5 - 10 x - 8$

Combine like terms:

$3 x - 10 x - 5 - 8 = - 7 x = - 13$

So the expression simplifies to:

$- 7 x - 13$

Only choice B matches.

Plugging in numbers and answers

Because the ASVAB is multiple choice, you can sometimes use the answer choices (or simple test numbers) to avoid heavier algebra. The test only scores whether your final choice is correct, so efficient methods matter.

Plugging in answers

With plugging in answers, you work backward: test the given answer choices in the original equation until you find the one that works.

This works best when:

The answers are simple numbers
Checking is faster than solving

Example:

If $x$ is a positive integer and $\frac{( x ^{2} + 9 )}{3 ^{x}} = \frac{2}{3}$ , what is $x$ ?

A. $1$
B. $2$
C. $3$
D. $4$

Test the choices.

Try B: $x = 2$

$\frac{( 2 ^{2} + 9 )}{3 ^{2}} = \frac{13}{9}$

Not $\frac{2}{3}$ → eliminate B.

Try A: $x = 1$

$\frac{( 1 ^{2} + 9 )}{3} = \frac{10}{3}$

Not $\frac{2}{3}$ → eliminate A.

Try C: $x = 3$

$\frac{( 3 ^{2} + 9 )}{3 ^{3}} = \frac{18}{27} = \frac{2}{3}$

So the correct answer is C.

Plugging in numbers

With plugging in numbers, you choose a value for a variable and evaluate the original expression. Then you check which answer choice gives the same result.

This is useful when:

The problem asks for an equivalent expression
The algebra looks messy

Example:

What is equivalent to $\frac{x ^{2} - 4 x - 32}{x + 4}$ , where $x \neq = - 4$ ?

A. $x - 8$
B. $2 x - 4$
C. $x + 6$
D. $x - 4$

Pick a value for $x$ that follows the rule $x \neq = - 4$ . Use $x = 2$ (small and easy to compute).

Evaluate the original expression:

$\frac{4 - 8 - 32}{6} = \frac{- 36}{6} = - 6$

Now test the answers:

A: $2 - 8 = - 6$ ✔

B: $4 - 4 = 0$ ✘

C: $2 + 6 = 8$ ✘

D: $2 - 4 = - 2$ ✘

Only A matches, so the answer is A.

Sidenote

Tips:

For percents, using $100$ is very helpful
Avoid using $1$ or $0$
Pick numbers that follow the rules of the problem
Test every answer choice when using this method
Keywords like equivalent or in terms of often signal this strategy

When to use these strategies

Benefits:

Avoids complicated algebra
Helps you check your work automatically

Drawback:

Can take longer if you test too many choices

In practice, switch between these strategies and direct solving depending on what is fastest.

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Math strategies

One key rule to keep in mind: the ASVAB doesn’t allow calculators on the math sections. That means you’ll want strategies that keep your work simple, quick, and accurate.

Rounding

Rounding replaces a fraction or decimal with a nearby “easy” number. The goal is to estimate quickly, then use the answer choices to pick the only reasonable option.

Example:

A factory produces $19.6$ pieces of sheet metal a day. How many pieces of sheet metal does it make in $5$ days?

A. $91$
B. $98$
C. $106$
D. $117$

Start by rounding. Since the answer choices are integers, round $19.6$ to $20$ .

Now compute:

$20 \times 5 = 100$

So the factory makes about $100$ pieces in $5$ days.

Because we rounded $19.6$ up to $20$ , the exact answer must be a little less than $100$ .

Look at the answer choices:

$98$ is just below $100$ ✔

The others are either too small or too large

So B. $98$ is the best estimate.

Now confirm with exact multiplication:

$19.6 \times 5 = 98$

Rounding helped us get the correct answer faster.

Sidenote

Times tables

If you don’t know your times tables, this is the time to learn them. You can’t use a calculator on the ASVAB, and you’ll do a lot of multiplication.

Try printing off a $12$ x $12$ table and crossing off the columns you already know, such as $0, 1, 2$ , and so forth. Then work on one column at a time until you have them memorized.

Process of elimination

Starting with $4$ choices gives you a $25%$ chance of guessing correctly. Eliminating one choice raises your odds to $33.3%$ . Eliminating two choices raises your odds to $50%$ .

So, how do you eliminate answer choices?

Start by using logical reasoning:

If the answer must be negative, eliminate any positive answers.
If a line must have a slope that’s less than $1$ , eliminate any answer with a slope greater than one.

As you work through the problem, keep removing choices that can’t be true until only the correct one remains.

Example:

What is the difference of $(3 x - 5) - (10 x + 8)$ ?

A. $- 7 x + 3$
B. $- 7 x - 13$
C. $13 x + 3$
D. $13 x - 13$

Use process of elimination by simplifying one part at a time.

Start with the $x$ -terms:

$3 x - 10 x = - 7 x$

This means the final answer must have a $- 7 x$ term, so eliminate choices C and D since they have $+ 13 x$ .

Now handle the constants by distributing the negative:

$3 x - 5 - 10 x - 8$

Combine like terms:

$3 x - 10 x - 5 - 8 = - 7 x = - 13$

So the expression simplifies to:

$- 7 x - 13$

Only choice B matches.

Plugging in numbers and answers

Plugging in answers

With plugging in answers, you work backward: test the given answer choices in the original equation until you find the one that works.

This works best when:

The answers are simple numbers
Checking is faster than solving

Example:

If $x$ is a positive integer and $\frac{( x ^{2} + 9 )}{3 ^{x}} = \frac{2}{3}$ , what is $x$ ?

A. $1$
B. $2$
C. $3$
D. $4$

Test the choices.

Try B: $x = 2$

$\frac{( 2 ^{2} + 9 )}{3 ^{2}} = \frac{13}{9}$

Not $\frac{2}{3}$ → eliminate B.

Try A: $x = 1$

$\frac{( 1 ^{2} + 9 )}{3} = \frac{10}{3}$

Not $\frac{2}{3}$ → eliminate A.

Try C: $x = 3$

$\frac{( 3 ^{2} + 9 )}{3 ^{3}} = \frac{18}{27} = \frac{2}{3}$

So the correct answer is C.

Plugging in numbers

With plugging in numbers, you choose a value for a variable and evaluate the original expression. Then you check which answer choice gives the same result.

This is useful when:

The problem asks for an equivalent expression
The algebra looks messy

Example:

What is equivalent to $\frac{x ^{2} - 4 x - 32}{x + 4}$ , where $x \neq = - 4$ ?

A. $x - 8$
B. $2 x - 4$
C. $x + 6$
D. $x - 4$

Pick a value for $x$ that follows the rule $x \neq = - 4$ . Use $x = 2$ (small and easy to compute).

Evaluate the original expression:

$\frac{4 - 8 - 32}{6} = \frac{- 36}{6} = - 6$

Now test the answers:

A: $2 - 8 = - 6$ ✔

B: $4 - 4 = 0$ ✘

C: $2 + 6 = 8$ ✘

D: $2 - 4 = - 2$ ✘

Only A matches, so the answer is A.

Sidenote

Tips:

For percents, using $100$ is very helpful
Avoid using $1$ or $0$
Pick numbers that follow the rules of the problem
Test every answer choice when using this method
Keywords like equivalent or in terms of often signal this strategy

When to use these strategies

Benefits:

Avoids complicated algebra
Helps you check your work automatically

Drawback:

Can take longer if you test too many choices

In practice, switch between these strategies and direct solving depending on what is fastest.

One key rule to keep in mind: the ASVAB doesn’t allow calculators on the math sections. That means you’ll want strategies that keep your work simple, quick, and accurate.

Rounding

Rounding replaces a fraction or decimal with a nearby “easy” number. The goal is to estimate quickly, then use the answer choices to pick the only reasonable option.

Example:

A factory produces $19.6$ pieces of sheet metal a day. How many pieces of sheet metal does it make in $5$ days?

A. $91$
B. $98$
C. $106$
D. $117$

Start by rounding. Since the answer choices are integers, round $19.6$ to $20$ .

Now compute:

$20 \times 5 = 100$

So the factory makes about $100$ pieces in $5$ days.

Because we rounded $19.6$ up to $20$ , the exact answer must be a little less than $100$ .

Look at the answer choices:

$98$ is just below $100$ ✔

The others are either too small or too large

So B. $98$ is the best estimate.

Now confirm with exact multiplication:

$19.6 \times 5 = 98$

Rounding helped us get the correct answer faster.

Sidenote

Times tables

If you don’t know your times tables, this is the time to learn them. You can’t use a calculator on the ASVAB, and you’ll do a lot of multiplication.

Try printing off a $12$ x $12$ table and crossing off the columns you already know, such as $0, 1, 2$ , and so forth. Then work on one column at a time until you have them memorized.

Process of elimination

Starting with $4$ choices gives you a $25%$ chance of guessing correctly. Eliminating one choice raises your odds to $33.3%$ . Eliminating two choices raises your odds to $50%$ .

So, how do you eliminate answer choices?

Start by using logical reasoning:

If the answer must be negative, eliminate any positive answers.
If a line must have a slope that’s less than $1$ , eliminate any answer with a slope greater than one.

As you work through the problem, keep removing choices that can’t be true until only the correct one remains.

Example:

What is the difference of $(3 x - 5) - (10 x + 8)$ ?

A. $- 7 x + 3$
B. $- 7 x - 13$
C. $13 x + 3$
D. $13 x - 13$

Use process of elimination by simplifying one part at a time.

Start with the $x$ -terms:

$3 x - 10 x = - 7 x$

This means the final answer must have a $- 7 x$ term, so eliminate choices C and D since they have $+ 13 x$ .

Now handle the constants by distributing the negative:

$3 x - 5 - 10 x - 8$

Combine like terms:

$3 x - 10 x - 5 - 8 = - 7 x = - 13$

So the expression simplifies to:

$- 7 x - 13$

Only choice B matches.

Plugging in numbers and answers

Plugging in answers

With plugging in answers, you work backward: test the given answer choices in the original equation until you find the one that works.

This works best when:

The answers are simple numbers
Checking is faster than solving

Example:

If $x$ is a positive integer and $\frac{( x ^{2} + 9 )}{3 ^{x}} = \frac{2}{3}$ , what is $x$ ?

A. $1$
B. $2$
C. $3$
D. $4$

Test the choices.

Try B: $x = 2$

$\frac{( 2 ^{2} + 9 )}{3 ^{2}} = \frac{13}{9}$

Not $\frac{2}{3}$ → eliminate B.

Try A: $x = 1$

$\frac{( 1 ^{2} + 9 )}{3} = \frac{10}{3}$

Not $\frac{2}{3}$ → eliminate A.

Try C: $x = 3$

$\frac{( 3 ^{2} + 9 )}{3 ^{3}} = \frac{18}{27} = \frac{2}{3}$

So the correct answer is C.

Plugging in numbers

With plugging in numbers, you choose a value for a variable and evaluate the original expression. Then you check which answer choice gives the same result.

This is useful when:

The problem asks for an equivalent expression
The algebra looks messy

Example:

What is equivalent to $\frac{x ^{2} - 4 x - 32}{x + 4}$ , where $x \neq = - 4$ ?

A. $x - 8$
B. $2 x - 4$
C. $x + 6$
D. $x - 4$

Pick a value for $x$ that follows the rule $x \neq = - 4$ . Use $x = 2$ (small and easy to compute).

Evaluate the original expression:

$\frac{4 - 8 - 32}{6} = \frac{- 36}{6} = - 6$

Now test the answers:

A: $2 - 8 = - 6$ ✔

B: $4 - 4 = 0$ ✘

C: $2 + 6 = 8$ ✘

D: $2 - 4 = - 2$ ✘

Only A matches, so the answer is A.

Sidenote

Tips:

For percents, using $100$ is very helpful
Avoid using $1$ or $0$
Pick numbers that follow the rules of the problem
Test every answer choice when using this method
Keywords like equivalent or in terms of often signal this strategy

When to use these strategies

Benefits:

Avoids complicated algebra
Helps you check your work automatically

Drawback:

Can take longer if you test too many choices

In practice, switch between these strategies and direct solving depending on what is fastest.