FREE ALEKS Math Practice Test

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For this practice test, we’ve put together 20 ALEKS-style questions 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 2026) 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.

20 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 2027

Answers:

2- 20
\( 75 × \frac{x}{100} = 15 \) ⇒\( 75 × x = 1500 ⇒ x = \frac{1500}{75} = 20\)

3- 11.48$
\($44 – $32.52 = $11.48\)

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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-
Answer: 60 feet. In a \(30^\circ-60^\circ- 90^\circ\) triangle, the hypotenuse is twice the short leg. The 30-foot side is the short leg, so the ladder is 2 × 30 = 60 feet. The side relationships are shown 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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Recommended EffortlessMath Books

For a structured workbook covering every ALEKS topic, the ALEKS Math for Beginners (resource currently unavailable) walks through every concept with worked examples. For complete placement-test prep, the ALEKS Math Test Prep Bundle (resource currently unavailable) bundles the workbook with practice tests.

How Real ALEKS Questions Differ from This Practice Test

This page gives you questions to work on paper. The real ALEKS placement assessment works a little differently, so keep these points in mind.

• No answer choices. You type your answer into an answer box, so you cannot work backward from options.
• It adapts to you. A correct answer leads to harder questions and a wrong one leads to easier ones. Do not worry if questions feel tough; that can mean you are doing well.
• Exact form matters. If a question asks for a simplified fraction or both solutions, give exactly that. For Question 7, for example, the full answer is x = −3 and x = −½.
• Calculator only when shown. ALEKS gives an on-screen calculator on some questions only. Practice the rest by hand.

Worked Solution: The Ladder Problem (Question 12)

The ladder, the wall and the ground form a right triangle. The 60° angle is at the ground, the 30 feet is the side next to that angle, and the ladder is the hypotenuse.

1. Use cosine, since it links the adjacent side and the hypotenuse: cos 60° = 30 ÷ L.
2. cos 60° = ½, so ½ = 30 ÷ L.
3. Solve: L = 30 × 2 = 60 feet.

You can also use the 30-60-90 pattern. The side next to the 60° angle is the short leg, and the hypotenuse is always twice the short leg, so 2 × 30 = 60 feet.

Frequently Asked Questions

Is the ALEKS math test multiple choice?

No. Most ALEKS math placement questions are open response, so you type your answer, such as a number, fraction or expression, using the on-screen tools. That means you cannot work backward from answer choices. When you practice, solve every problem all the way to the end and write your final answer in simplest form.

How many questions are on the ALEKS math placement test?

ALEKS is adaptive, so the exact number varies, but colleges commonly describe the placement assessment as having up to about 30 questions. Many students finish in about 60 to 90 minutes. Each question adjusts to what you showed on earlier ones, so do your honest best on every item instead of guessing quickly.

Is the ALEKS math placement test hard?

The ALEKS placement test feels harder as you go because it adapts, moving to tougher topics like quadratics, exponents and trigonometry when you answer correctly. That is normal and is how it finds your level. Reviewing algebra basics first, such as solving 2x − 5 = 9 (x = 7) and simplifying exponents, helps you place into a higher course.

What topics are on the ALEKS math placement test?

ALEKS math placement covers arithmetic and fractions, percents and proportions, linear equations and inequalities, quadratics, exponents and polynomials, coordinate geometry, and some trigonometry and precalculus. The 20 practice questions sample those same areas, so use your results to see which topics to review before the real test.

Is ALEKS math free?

It depends on your college. Some schools cover the cost of the ALEKS placement assessment, while others charge a fee, so check your college’s placement page for details. You can practice for free before you start, for example with these 20 sample questions and their step-by-step solutions.

What is the ALEKS Prep and Learning module?

The Prep and Learning module is the review course ALEKS opens after your first placement attempt. It builds a study plan from the topics you missed, and many colleges require several hours in it before you can retake the test. Working through it carefully can raise your score and help you place into a higher math course.

Related EffortlessMath Lessons

If a topic on this practice test feels rusty, these short lessons go deeper:

• ALEKS Math Formula Cheat Sheet
• How to use the quadratic formula
• How to find the slope of a line
• Rules of exponents
• Order of operations (PEMDAS)