# FREE ASTB Math Practice Test

Welcome to our FREE ASTB 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 ASTB Math test. Not only does the test closely match what you will see on the real ASTB, but it also comes with detailed answer explanations.

For this practice test, we’ve selected 20 real questions from past exams for your ASTB Practice test. You will have the chance to try out the most common ASTB 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 ASTB Math practice tests and study resources (updated for 2021) to ace the ASTB 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 ASTB** **Math** Test

## 10 Sample **ASTB** Math Practice Questions

1- Mr. Jones saves $2,500 out of his monthly family income of $55,000. What fractional part of his income does he save?

A. \(\frac{1}{22} \)

B. \(\frac{1}{11} \)

C. \(\frac{3}{25} \)

D. \(\frac{2}{15} \)

2- Four one-foot rulers can be split among how many users to leave each with \(\frac{1}{6} \) of a ruler?

A. 4

B. 6

C. 12

D. 24

3- Simplify the expression.

\((6x^3-8x^2+2x^4 )-(4x^2-2x^4+2x^3 )\)

A. \(4x^3-12x^2\)

B. \(4x^4+4x^3-12x^2\)

C. \(8x^3-12x^2\)

D. \(x^4+4x^3-12x^2\)

4- In two successive years, the population of a town is increased by \(15\%\) and \(20\%\). What percent of the population is increased after two years?

A. \(32\%\)

B. \(35\%\)

C. \(38\%\)

D. \(68\%\)

5- What is the surface area of the cylinder below?

\(\img{https://appmanager.effortlessmath.com/public/images/questions/82.png}\)

A. \(48 {\pi} \space in^2\)

B. \(57 {\pi} \space in^2\)

C. \(66 {\pi} \space in^2\)

D. \(288 {\pi} \space in^2\)

6- A cruise line ship left Port A and traveled 80 miles due west and then 150 miles due north. At this point, what is the shortest distance from the cruise to port A in miles? ____________

7- A shirt costing $200 is discounted \(15\%\). After a month, the shirt is discounted another \(15\%\). Which of the following expressions can be used to find the selling price of the shirt?

A. \((200) (0.70)\)

B. \((200) – 200 (0.30)\)

C. \((200) (0.15) – (200) (0.15)\)

D. \((200) (0.85) (0.85)\)

8- \(5 + 8 \times (- 2) – [4 + 22 \times 5] \div 6 = ? \)

A. \(-30\)

B. \(-20\)

C. \(-10\)

D. 0

9- Which of the following points lies on the line \(x+2y=4\)?

A. \((-2, 3)\)

B. \((1, 2)\)

C. \((-1, 3)\)

D. \((-3, 4)\)

10- 5 less than twice a positive integer is 83. What is the integer?

A. 39

B. 41

C. 42

D. 44

11- 11 yards 6 feet and 4 inches equal to how many inches?

A. 388

B. 468

C. 472

D. 476

12- Mr. Carlos’s family is choosing a menu for their reception. They have 3 choices of appetizers, 5 choices of entrees, 4 choices of cake. How many different menu combinations are possible for them to choose from?

A. 12

B. 32

C. 60

D. 120

13- The average of five consecutive numbers is 38. What is the smallest number?

A. 38

B. 36

C. 34

D. 12

14- What is the difference between the smallest 4–digit number and the biggest 4–digit number?

A. 6666

B. 6789

C. 8888

D. 8999

15- How many tiles of 8 cm\(^2 \) are needed to cover a floor of dimension 6 cm by 24 cm?

A. 6

B. 12

C. 18

D. 24

16- A ladder leans against a wall forming a \(60^ \circ \) angle between the ground and the ladder. If the bottom of the ladder is 30 feet away from the wall, how long is the ladder?

A. 30 feet

B. 40 feet

C. 50 feet

D. 60 feet

17- The average weight of 18 girls in a class is 60 kg and the average weight of 32 boys in the same class is 62 kg. What is the average weight of all the 50 students in that class?

A. 60

B. 61.28

C. 61.68

D. 62.90

18- An angle is equal to one-fifth of its supplement. What is the measure of that angle?

A. 20

B. 30

C. 45

D. 60

19- In a stadium, the ratio of home fans to visiting fans in a crowd is 5:7. Which of the following could be the total number of fans in the stadium?

A. 12,324

B. 42,326

C. 44,566

D. 66,812

20- If \(40\%\) of a class are girls, and \(25\%\) of girls play tennis, what percent of the class play tennis?

A. \(10\%\)

B. \(15\%\)

C. \(20\%\)

D. \(40\%\)

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

## Answers:

1- **A**

2,500 out of 55,000 equals to \(\frac{2500}{55000}= \frac{25}{550}= \frac{1}{22} \)

2- **D**

\(4 \div \frac{1}{6} = 24 \)

3-** ****B**

Simplify and combine like terms.

\((6x^3-8x^2+2x^4 )-(4x^2-2x^4+2x^3 ) {\Rightarrow} (6x^3-8x^2+2x^4 )-4x^2+2x^4-2x^3 {\Rightarrow}

4x^4+4x^3-12x^2\)

4- **C**

the population is increased by \(15\%\) and \(20\%\).

\(15\%\) increase changes the population to \(115\%\) of original population.

For the second increase, multiply the result by \(120\%\).

\((1.15) \times (1.20) = 1.38 = 138\%\)

38 percent of the population is increased after two years.

5- **C**

Surface Area of a cylinder \(= 2\pi\) r (r + h),

The radius of the cylinder is \(3(6 \div 2)\) inches and its height is 8 inches. Therefore,

Surface Area of a cylinder \(= 2\pi (3) (3 + 8) = 66\pi\)

6- **170**

Use the information provided in the question to draw the shape.

\( \img {https://appmanager.effortlessmath.com/public/images/questions/22222222222222222222222222222.JPG

} \)

Use Pythagorean Theorem: \(a^2 + b^2 = c^2 \)

\(80^2 + 150^2 = c^2 {\Rightarrow} 6400 + 22500 = c^2 {\Rightarrow} 28900 = c^2 {\Rightarrow} c = 170\).

7- **D**

To find the discount, multiply the number by (\(100{\%} – \)rate of discount).

Therefore, for the first discount we get: \((200) (100{\%} – 15{\%}) = (200) (0.85) = 170\)

For the next \(15{\%}\) discount: \((200) (0.85) (0.85)\)

8- **A**

Use PEMDAS (order of operation):

\(5 + 8 \times (-2) – [4 + 22 \times 5] \div 6 = 5 + 8 \times (-2) – [4 + 110] \div 6 = 5 + 8 \times (-2) – [114] \div 6 = 5 + (-16) – 19

5 + (-16) – 19 = -11 – 19 = -30\)

9- **A**

\(x+2y=4\). Plugin the values of \(x\) and \(y\) from the choices provided. Then:

A. \((-2,3) x+2y=4(\rightarrow )-2+2(3)=4(\rightarrow )-2+6=4\) This is true!

B. \((1,2) x+2y=4(\rightarrow )1+2(2)=4(\rightarrow )1+4=4\) (This is NOT true!)

C. \((-1,3) x+2y=4(\rightarrow )-1+2(3)=4(\rightarrow )-1+6=4\) (This is NOT true!)

D. \((-3,4) x+2y=4(\rightarrow )-3+2(4)=4(\rightarrow )-3+8=4\) (This is NOT true!)

10- **D**

Let \(x\) be the integer. Then:

\(2x – 5 = 83\)

Add 5 both sides: \(2x = 88\)

Divide both sides by \(2: x = 44\)

11- **C**

\(11 \times 36 + 6 \times 12 + 4 = 472\)

12- **C**

To find the number of possible outfit combinations, multiply number of options for each factor:

\(3 \times 5 \times 4 = 60\)

13- **B**

Let \(x\) be the smallest number. Then, these are the numbers:

\(x, x+1, x+2, x+3, x+4 \)

average \(= \frac{sum of terms}{number of terms} \Rightarrow 38 = \frac{x+(x+1)+(x+2)+(x+3)+(x+4)}{5} \Rightarrow 38= \frac{5x+10}{5} \Rightarrow 190 = 5x+10 \Rightarrow 180 = 5x \Rightarrow x=36 \)

14- **D**

Smallest 4–digit number is 1000, and biggest 4–digit number is 9999. The difference is: 8999

15- **C**

The area of the floor is: 6 cm \(\times\) 24 cm = 144 cm\(^2 \)

The number of tiles needed \(= 144 \div 8 = 18\)

16- **D**

The relationship among all sides of special right triangle

\(30^ \circ -60^ \circ – 90^ \circ \) is provided in this triangle:

\( \img {https://appmanager.effortlessmath.com/public/images/questions/10-explain-1.png} \)

In this triangle, the opposite side of \(30^ \circ \) angle is half of the hypotenuse.

Draw the shape for this question:

The latter is the hypotenuse. Therefore, the latter is 60 ft.

\( \img {https://appmanager.effortlessmath.com/public/images/questions/10-explain-2.png} \)

17- **B**

average \(= \frac{sum of terms}{number of terms}\)

The sum of the weight of all girls is: \(18 \times 60 = 1080\) kg

The sum of the weight of all boys is:\( 32 \times 62 = 1984\) kg

The sum of the weight of all students is: \(1080 + 1984 = 3064\) kg

average \(= \frac{3064}{50}=61.28 \)

18- **B**

The sum of supplement angles is 180. Let \(x\) be that angle. Therefore,

\(x + 5x = 180\)

\(6x = 180\), divide both sides by 6: \(x = 30\)

19- **A**

In the stadium the ratio of home fans to visiting fans in a crowd is \(5:7\). Therefore, total number of fans must be divisible by \(12: 5 + 7 = 12.\)

Let’s review the choices:

A. \(12,324: 12,324 \div 12 = 1027\)

B. \(42,326: 42,326 \div 12 = 3,527.166\)

C. \(44,566: 44,566 \div 12 = 3,713.833\)

D. \(66,812: 66,812 \div 12 = 5,567.666\)

Only choice A when divided by 12 results a whole number.

20- **A**

The percent of girls playing tennis is:

\(40 \% \times 25\% = 0.40 \times 0.25 = 0.10 = 10\%\)

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### The Best Books** to Ace the ****ASTB** **Math** Test

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