# FREE ASVAB Math Practice Test

Welcome to our FREE ASVAB Math practice test, with answer key and answer explanations. This practice test’s realistic format and high-quality practice questions can help you succeed on the ASVAB Math test. Not only does the test closely match what you will see on the real ASVAB Mathematics, but it also comes with detailed answer explanations.

For this practice test, we’ve selected 20 real questions from past exams for your ASVAB Mathematics Practice test. You will have the chance to try out the most common ASVAB Math questions. For every question, there is an in-depth explanation of how to solve the question and how to avoid mistakes next time.

Use our free ASVAB Math practice tests and study resources (updated for 2022) to ace the ASVAB Math test! Make sure to follow some of the related links at the bottom of this post to get a better idea of what kind of mathematics questions you need to practice.

## The Absolute Best Book to Ace the ASVAB Math Test

## 10 Sample ASVAB Math Practice Questions

1- A mobile classroom is a rectangular block that is \(90\) feet by \(30\) feet in length and width respectively. If a student walks around the block once, how many yards does the student cover?

A. \(2,700\) yards

B. \(240\)yards

C. \(120\) yards

D. \(60\) yards

2- What is the distance in miles of a trip that takes \(2.1\) hours at an average speed of \(16.2\) miles per hour? (Round your answer to a whole number)

A. \(44\) miles

B. \(34\) miles

C. \(30\) miles

D. \(18\) miles

3- The sum of \(6\) numbers is greater than \(120\) and less than 180. Which of the following could be the average (arithmetic mean) of the numbers?

A. \(20\)

B. \(26\)

C. \(30\)

D. \(34\)

4- There are \(120\) rooms that need to be painted and only \(12\) painters available. If there are still \(12\) rooms unpainted by the end of the day, what is the average number of rooms that each painter has painted?

A. \(9\)

B. \(12\)

C. \(14\)

D. \(16\)

5- Nicole was making $7.50 per hour and got a raise to $7.75 per hour. What percentage increase was Nicole’s raise?

A. \(2\%\)

B. \(1.67\%\)

C. \(3.33\%\)

D. \(6.66\%\)

6- A snack machine accepts only quarters. Candy bars cost 25¢, a package of peanuts costs 75¢, and a can of cola costs 50¢. How many quarters are needed to buy two Candy bars, one package of peanuts, and one can of cola?

A. 8 quarters

B. 7 quarters

C. 6 quarters

D. 5 quarters

7- The hour hand of a watch rotates \(30\) degrees every hour. How many complete rotations does the hour hand make in \(8\) days?

A. \(12\)

B. \(14\)

C. \(16\)

D. \(18\)

8- Camille uses a \(30\%\) off coupon when buying a sweater that costs $50. If she also pays \(5\%\) sales tax on the purchase, how much does she pay?

A. $35

B. $36.75

C. $39.95

D. $47.17

9-Solve:\((x + 7)(x + 5)\) = ?

A. \(x^2 + 12x + 12\)

B. \( 2x + 12x + 12\)

C. \(x^2 + 35x + 12\)

D. \(x^2 + 12x + 35\)

10- Convert \(670,000\) to scientific notation?

A. \(6.70 × 1000\)

B. \(6.70 × 10^{−5}\)

C. \(6.70 × 100\)

D. \(6.7 × 10^5\)

11- What is the perimeter of the triangle in the provided diagram?

\(\img{https://appmanager.effortlessmath.com/public/images/questions/q28.JPG}\)

A. \(15,625\)

B. \(625\)

C. \(75\)

D. \(25\)

12- If \(x\) is a positive integer divisible by \(6\), and \(x < 60\), what is the greatest possible value of \(x\)?

A. \(54\)

B. \(48\)

C. \(36\)

D. \(59\)

13- There are two pizza ovens in a restaurant. Oven 1 burns four times as many pizzas as oven 2. If the restaurant had a total of 15 burnt pizzas on Saturday, how many pizzas did oven 2 burn?

A. 3

B. 6

C. 9

D. 12

14- Which of the following is an obtuse angle?

A. \(56^\circ\)

B. \(72^\circ\)

C. \(123^\circ\)

D. \(211^\circ\)

15- What is \(5231.48245\) rounded to the nearest tenth?

A. \(5231.482\)

B. \(5231.5\)

C. \(5231\)

D. \(5231.48\)

16- A circle has a diameter of 16 inches. What is its approximate area? \((π = 3.14)\)

A. 200.96

B. 100.48

C. 64.00

D. 12.56

17- Which of the following is the correct calculation for 7!?

A. \(7 × 6 × 5 × 4 × 3 × 2 × 1\)

B. \(1 × 2 × 3 × 4 × 5 × 6\)

C. \(0 × 1 × 2 × 3 × 4 × 5 × 6 × 7\)

D. \(1 × 2 × 3 × 4 × 5 × 6 × 7 × 8\)

18- The equation of a line is given as: \(y=5x-3\). Which of the following points does not lie on the line?

A. \((1, 2)\)

B. \((−2, −13)\)

C. \((3, 18)\)

D. \((2, 7)\)

19- What is the distance between the points \((1, 3)\) and \((−2, 7)\)?

A. 3

B. 4

C. 5

D. 6

20- Solve:\(x^2 – 81 = 0\) , \(x\) could be?

A. 6

B. 9

C. 12

D. 15

## Best ASVAB** **Math Prep Resource for 2022

## Answers:

1- **B**

Perimeter of a rectangle = \(2 × length + 2 × width\) =

\(2 × 90 + 2 × 30 = 180 + 60 = 240\)

2- **B**

\(Speed =\frac{distance}{time }\)

\(16.2=\frac{distance}{2.1}⇒ distance=16.2×2.1=34.02\)

Rounded to a whole number, the answer is \(34\).

3-** B**

Let’s review the choices provided and find their sum.

\(a. 20 × 6 = 120\)

\(b. 26 × 6 = 144\) ⇒ is greater than 120 and less than 180

\(c. 30 × 6 = 180\)

\(d. 34 × 6 = 204\)

Only choice b gives a number that is greater than 120 and less than 180.

4- **A**

\(120 – 12 = 108\)

\(\frac{108}{12} = 9\)

5- **C**

percent of change = \(\frac{change}{original \space number}\)

\(7.75 – 7.50 = 0.25\)

percent of change = \(\frac{0.25}{7.50}\) = 0.0333

\(⇒ 0.0333 × 100 = 3.33\%\)

6- **B**

Two candy bars costs 50¢ and a package of peanuts cost 75¢ and a can of cola costs 50¢. The total cost is: \( 50 + 75 + 50 = 175\)

175 is equal to 7 quarters. \(7 × 25 = 175\)

7- **C**

Every day the hour hand of a watch makes 2 complete rotation. Thus, it makes 16 complete rotations in 8 days.

\(2 × 8 = 16\)

8- **B**

\(30\% × 50 =\frac{30}{100} × 50 = 15 \)

The coupon has $15 value. Then, the selling price of the sweater is $35.

\(50 – 15 = 35\)

Add \(5\%\) tax, then:

\(\frac{5}{100} × 35 = 1.75 \) for tax

then:

\(35 + 1.75 = $36.75\)

9- **D**

Use FOIL (First, Out, In, Last) method.

\((x + 7)(x + 5) = x^2 + 5x + 7x + 35 = x^2 + 12x + 35\)

10- **D**

In scientific notation form, numbers are written with one whole number times 10 to the power of a whole number. Number 670,000 has 6 digits. Write the number and after the first digit put the decimal point. Then, multiply the number by 10 to the power of 5 (number of remaining digits). Then:

\(670,000 = 6.7 × 10^5\)

11- **C**

Perimeter of a triangle = side 1 + side 2 + side 3 \(= 25 + 25 + 25 = 75\)

12- **A**

From the choices provided, 36, 48 and 54 are divisible by 6. From these numbers, 54 is the biggest.

13- **A**

Oven 1 = 4 oven 2

If Oven 2 burns 3 then oven 1 burns 12 pizzas.\( 3 + 12 = 15\)

14- **C**

An obtuse angle is an angle of greater than \(90^\circ\) and less than \(180^\circ\).

15- **B**

5231.48245 rounded to the nearest tenth equals 5231.5

(Because 5231.48 is closer to 5,231.5 than 5,231.4)

16-A

Diameter = 16

then: Radius = 8

Area of a circle =\(πr^2\) ⇒ \(A = 3.14(8)^2 = 200.96\)

17- **A**

\(7! = 7 × 6 × 5 × 4 × 3 × 2 × 1\)

18- **C**

Let’s review the choices provided. Put the values of \(x\) and \(y\) in the equation.

A. \((1, 2) ⇒ x = 1 ⇒ y = 2\) This is true!

B. \((−2, −13) ⇒ x = -2 ⇒ y = -13\) This is true!

C. \((3, 18) ⇒ x = 3 ⇒ y = 12\) This is not true!

D. \((2, 7) ⇒ x = 2 ⇒ y = 7\) This is true!

19- **C**

Use distance formula:

\(d=\sqrt{((x_1-x_2)^2+(y_1-y_2)^2 )} = \sqrt{((1-(-2))^2+(3-7)^2 )}\)

\(\sqrt{(9+16)} = \sqrt{25} = 5\)

20- **B**

\((x^2 \space – \space 81 = 0 ⇒ x^2 = 81 )\) ⇒ \(x\) could be \(9\) or \(–9\).

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