# FREE ALEKS Math Practice Test

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

For this practice test, we’ve selected 20 real questions from past exams for your ALEKS Mathematics Practice test. You will have the chance to try out the most common ALEKS 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 ALEKS Math practice tests and study resources (updated for 2022) to ace the ALEKS 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 ALEKS Math Test

## 10 Sample ALEKS Math Practice Questions

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

2- 15 is what percent of 75?_______

3- Last Friday Jacob had $32.52. Over the weekend he received some money for cleaning the attic. He now has $44. How much money did he receive?______

4- Simplify. \(\frac{\frac{1}{2}-\frac{x+5}{4}}{\frac{x^2}{2} – \frac{5}{2}} \)?______

5- Solve.\(5 + 8 × (–2) – [4 + 22 ×5] ÷ 6\) = ?______

6- A man owed $4265 on his car. After making \(55\) payments of $77 each, how much did he have left to pay?______

7- Find all values of \(x\) in this equation: \( 4x^2 + 14x + 6 = 0\)?______

8- Solve.\((x^6)^\frac{5}{8}\)?______

9- If a vehicle is driven 32 miles on Monday, 35 miles on Tuesday, and 29 miles on Wednesday, what is the average number of miles driven each day?______

10- In the following triangle what is the value of \(x\)?______

11- Find the factors of \( x^2 + 5x – 6\)?______

12- 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?______

13- What is the distance between the points \((1, 3)\) and \((–2, 7)\)?______

14- Write the \(\frac{4}{140}\) as a decimal?______

15- If \( f(x) = x – \frac{5}{3} \) and \(f ^{–1}\) is the inverse of \(f(x)\), what is the value of

\( f ^{–1}(5)?\)_______

16- Anita’s trick–or–treat bag contains 12 pieces of chocolate, 18 suckers, 18 pieces of gum, 24 pieces of licorice. If she randomly pulls a piece of candy from her bag, what is the probability of her pulling out a piece of sucker?______

17- What is the value of cos \(30^\circ\)?______

18- If \(\ \theta \) is an acute angle and \( sin \theta = \frac{3}{5} \) then \(cos \theta = ? \)______

19- Solve.

\(|9 – (12 ÷ | 2 – 5 |)| = ?\)______

20- What’s the reciprocal of \(\frac{x^3}{16} ?\)______

## Best ALEKS Math Prep Resource for 2022

## Answers:

1- **4**

Underline the tenth place: \(5231.\underline{\\4}8245\) Look to the right if it is 5 or bigger, add 1 to the underlined digit. Then, round up the decimal to 5231.5

2- **20**

\( 75 × \frac{x}{100} = 15 \) ⇒\( 75 × x = 1500 ⇒ x = \frac{1500}{75} = 20\)

3-** 11.48$**

\($44 – $32.52 = $11.48\)

4-** \(\frac{-x-3}{2x^2-10}\)**

\(\frac{\frac{1}{2}-\frac{x+5}{4}}{\frac{x^2}{2}-\frac{5}{2}} =\frac{\frac{1}{2}-\frac{x+5}{4}}{\frac{x^2-5}{2}} = \frac{2(\frac{1}{2}-\frac{x+5}{4})}{x^2-5}\)

⇒Simplify:

\( \frac{1}{2} -\frac{x+5}{4} = \frac{-x-3}{4}\)

\(\frac{2(\frac{-x-3}{4})}{x^2-5} =\frac{\frac{-x-3}{2}}{x^2-5}=\frac{-x-3}{2(x^2-5)}=\frac{-x-3}{2x^2-10}\)

5- **\(–30\)**

Use PEMDAS (order of operation): \( 5 + 8 × (–2) – [4 + 22 ×5] ÷ 6 = 5 + 8 × (–2) – [4 + 110] ÷ 6 = 5 + 8 × (–2) – [114] ÷ 6 = 5 + (–16) – 19 = 5 + (–16) – 19 = –11 – 19 = –30\)

6- **$30**

\(55×$77=$4235\) Payable amount is:\($4265-$4235=$30\)

7- **\( – 3\)**

\(x1,2 = \frac{-b ± \sqrt{(b^2-4ac)} }{2a}\)

\(ax^2 + bx + c = 0\)

\(4x^2 + 14x + 6 = 0\) ⇒then: a = 4, b = 14 and c = 6

\(x = \frac{-14 + \sqrt{14^2 – 4 ,4 ,6} }{2 ,4} = – \frac{1}{2}\)

\(x = \frac{-14 – \sqrt{14^2 – 4 ,4 ,6} }{2 ,4} = – 3\)

8-** \(x^{\frac{ 15}{4}}\)**

\( (x^6)^{\frac{5}{8}} = x^{6 × \frac{5}{8}} = x^{\frac{ 30}{8}} =x^{\frac{ 15}{4}} \)

9- **32**

\(32 + 35 + 29 = 96\)

Average = \( \frac{96}{3} = 32\)

10-** \(45^\circ\)**

\(90^\circ + 45^\circ = 135^\circ\)

\(180^\circ- 135^\circ = 45^\circ\)

11- **\((x – 1)(x + 6)\)**

\( x^2 + 5x – 6 = (x – 1)(x + 6)\)

12-

The relationship among all sides of special right triangle \(30^\circ-60^\circ- 90^\circ\) is provided in this triangle:

13- **5**

\(C = \sqrt{(x_A- x_B)^2 + (y- y_B)^2 ) }\)

\(C = \sqrt{(1-(-2))^2 + (3- 7)^2}\)

\(C = \sqrt{(3)^2 + (- 4)^2 )} \)

\(C = \sqrt{9 + 16}\)

\(C = \sqrt{25} = 5\)

14-** \(0.02857143 \cong 0.0286 \)**

\( \frac{4}{140} = \frac{1}{35} = 0.02857143 \cong 0.0286 \)

15- **\(\frac{20}{3} \)**

\( f(x) = x – \frac{5}{3} ⇒( y = x) (– \frac{5}{3} ) ⇒y+ \frac{5}{3} = x \)

\(f^{-1} = x+ \frac{5}{3} \)

\(f ^{–1}(5) = 5 + \frac{5}{3} = \frac{20}{3} \)

16- **\(\frac{ 1}{4}\)**

Probability \(=\frac{number of desired outcomes}{number of total outcomes} = \frac{18}{12+18+18+24} = \frac{18}{72} =\frac{ 1}{4}\)

17-** \(\frac{\sqrt{3}}{2}\)**

\(cos 30^\circ = \frac{\sqrt{3}}{2}\)

18- **cosθ=\(\frac{4}{5}\)**

sinθ\(=\frac{3}{5}\)⇒ we have following triangle, then \(c=\sqrt{5^2-3^2 }=\sqrt{25-9}=\sqrt{16}=4) \)

cosθ\(=\frac{4}{5}\)

19- **5**

\(|9 – (12 ÷ | 2 – 5 |)| = |(9-(12÷|-3|))|=|9-(12÷3)|=|9-4|=|5|=5\)

20- **\( \frac{16}{x^3 }\)**

\( \frac{x^3}{16 } \) ⇒ reciprocal is :\( \frac{16}{x^3 }\)

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