The best way to prepare for ALEKS isn’t reading about it — it’s doing practice problems until the most common question types feel familiar. ALEKS adapts to what you know, but the topics it draws from are well-documented, and targeted practice across those areas is how you move your placement score.
Below are 15 practice problems covering the core ALEKS topic areas. They’re written in the style of problems that commonly appear on math placement assessments — not exam copies, but representative problems at the right level. Work through them before checking the answers.
ViewMath is not affiliated with or endorsed by McGraw-Hill or the ALEKS program. These are original practice problems, not released test items.
Section 1: Fractions, Decimals, and Percents
1. Simplify the expression: (3/4) ÷ (9/16)
2. A store is offering 35% off all shoes. A pair of shoes originally costs $120. What is the sale price?
3. Order these values from least to greatest: 0.6, 5/8, 0.605, 3/5
4. A recipe calls for 2½ cups of flour. If you want to make 1.5 times the recipe, how many cups of flour do you need?
Section 2: Ratios, Proportions, and Rates
5. A car uses 3 gallons of gas to travel 87 miles. At this rate, how many miles can it travel on a full 12-gallon tank?
6. The ratio of cats to dogs in a shelter is 5:3. If there are 48 animals total, how many are cats?
7. A worker earns $13.50 per hour and works 40 hours per week. If they receive a 12% raise, what will their new hourly rate be?
Section 3: Algebra — Expressions and Equations
8. Solve for x: 4(x − 3) = 2x + 10
9. Simplify: 3x² − 5x + 2x² + 8x − 4
10. If f(x) = 2x² − 3x + 1, find f(−2).
11. Solve the inequality: −3x + 7 ≥ 1. Write the solution and graph it on a number line (describe the graph).
Section 4: Geometry and Measurement
12. A right triangle has legs of length 9 cm and 12 cm. What is the length of the hypotenuse?
13. Find the volume of a cylinder with radius 5 cm and height 10 cm. Use π ≈ 3.14.
14. Two parallel lines are cut by a transversal. One of the co-interior (same-side interior) angles measures 67°. What is the measure of the other co-interior angle?
Section 5: Statistics and Probability
15. The data set is: 12, 15, 11, 18, 14, 11, 20, 13. Find the mean, median, and mode. Then identify whether the mean or the median is a better measure of center and explain why.
Answers and Explanations
Question 1
Answer: 4/3 (or 1⅓)
Dividing by a fraction means multiplying by its reciprocal: (3/4) × (16/9) = 48/36 = 4/3. A common error here is inverting the wrong fraction — remember, invert the divisor (the second fraction).
Question 2
Answer: $78
35% of $120 = 0.35 × 120 = $42 discount. $120 − $42 = $78. You can also calculate directly: 100% − 35% = 65%, so 0.65 × $120 = $78.
Question 3
Answer: 3/5, 0.6, 0.605, 5/8
Convert everything to decimals: 3/5 = 0.600, 5/8 = 0.625, 0.6 = 0.600, 0.605 = 0.605. Ordering: 0.600 = 0.600 < 0.605 < 0.625. So: 3/5 = 0.6 < 0.605 < 5/8. (3/5 and 0.6 are equal, so they both come first.)
Question 4
Answer: 3¾ cups
2½ × 1.5 = 2.5 × 1.5 = 3.75 cups = 3¾ cups.
Question 5
Answer: 348 miles
87 miles ÷ 3 gallons = 29 miles per gallon. 29 × 12 = 348 miles.
Question 6
Answer: 30 cats
Total ratio parts = 5 + 3 = 8. Each part = 48 ÷ 8 = 6 animals. Cats = 5 × 6 = 30.
Question 7
Answer: $15.12 per hour
12% of $13.50 = 0.12 × 13.50 = $1.62 raise. $13.50 + $1.62 = $15.12. Note: the 40 hours per week detail is extra information not needed for this calculation.
Question 8
Answer: x = 11
Distribute: 4x − 12 = 2x + 10. Subtract 2x: 2x − 12 = 10. Add 12: 2x = 22. Divide: x = 11. Check: 4(11 − 3) = 4 × 8 = 32; 2(11) + 10 = 22 + 10 = 32. ✓
Question 9
Answer: 5x² + 3x − 4
Group like terms: (3x² + 2x²) + (−5x + 8x) + (−4) = 5x² + 3x − 4.
Question 10
Answer: 15
f(−2) = 2(−2)² − 3(−2) + 1 = 2(4) + 6 + 1 = 8 + 6 + 1 = 15.
Question 11
Answer: x ≤ 2
−3x + 7 ≥ 1 → −3x ≥ −6 → x ≤ 2. (Inequality flips when dividing by a negative.) Graph: closed circle at 2, shaded to the left (all values ≤ 2).
Question 12
Answer: 15 cm
a² + b² = c². 9² + 12² = 81 + 144 = 225. √225 = 15. This is a 3-4-5 triple scaled by 3: (3×3, 3×4, 3×5) = (9, 12, 15).
Question 13
Answer: 785 cm³
V = πr²h = 3.14 × 5² × 10 = 3.14 × 25 × 10 = 3.14 × 250 = 785 cm³.
Question 14
Answer: 113°
Co-interior (same-side interior) angles are supplementary — they add to 180°. 180° − 67° = 113°.
Question 15
Mean: 14.25. Median: 13.5. Mode: 11.
Sum = 12 + 15 + 11 + 18 + 14 + 11 + 20 + 13 = 114. Mean = 114 ÷ 8 = 14.25.
Ordered set: 11, 11, 12, 13, 14, 15, 18, 20. Median (average of 4th and 5th values) = (13 + 14) ÷ 2 = 13.5.
Mode = 11 (appears twice).
Better measure of center: The median (13.5) is a better measure here because the value 20 is somewhat high relative to the rest of the data. The mean is pulled upward by this outlier. When data has extreme values, the median more accurately represents the “typical” value.
How to Use These Problems for Your ALEKS Prep
If you missed questions in a specific area, that topic deserves focused review before your test. Don’t just re-read the problem — go practice 5–10 more problems in that topic area until the type feels familiar.
For more structured practice, the ViewMath ALEKS Math series offers full-length practice tests and comprehensive study guides covering all the topic areas above and more. The 5 Full-Length Practice Tests for ALEKS Math is the deepest practice resource — five complete tests with detailed explanations for every answer.
Browse the full collection at viewmath.com/books/aleks-math/. All books are instant PDF downloads.
