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 :\( \frac{16}{x^3 }\)
Looking for the best resource to help you succeed on the ALEKS Math test?
The Best Study Guide for the ALEKS Math Test
More from Effortless Math for ALEKS Test …
Do you know What Does ALEKS Stands for?
We answered this question here: What Does ALEKS Stand for?
Everything you need to know about how to prepare for the ALEKS Math Test is here: How to Prepare for the ALEKS Math Test?
If you are looking for free resources, you’ll get help from the sort of following websites to pass the ALEKS math test: Top 10 Free Websites for ALEKS Math Preparation
The Best Books to Ace the ALEKS Math Test
Have any questions about the ALEKS Test?
Write your questions about the ALEKS or any other topics below and we’ll reply!
Related to This Article
More math articles
- Digital Platforms: Revolutionizing Math Education
- 7th Grade NHSAS Math Worksheets: FREE & Printable
- 8th Grade MCAS Math Practice Test Questions
- The Ultimate OAR Math Course (+FREE Worksheets)
- The Ultimate OAE Elementary Education Math (018-019) Course (+FREE Worksheets & Tests)
- 5th Grade RISE Math Worksheets: FREE & Printable
- The Ultimate 6th Grade MCAP Math Course (+FREE Worksheets)
- 5th Grade Common Core Math Worksheets: FREE & Printable
- Tips for Learning Mathematics for the Humanitarians
- Top 10 Tips to Retake GED Math Test
What people say about "FREE ALEKS Math Practice Test - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.