Looking for a free ACT math practice test to sharpen your skills before test day? You are in the right place. Below you will find 20 ACT-style math questions covering every major topic on the exam, from pre-algebra to trigonometry, each with a detailed step-by-step explanation so you can learn from every problem you attempt.
The ACT math section tests a wide range of skills, but with focused practice you can identify your weak spots and turn them into strengths. Whether you are just starting your ACT math prep or fine-tuning before the real exam, these questions will help you build confidence and speed.
ACT Math Section: What You Need to Know
Before diving into the practice questions, here is a quick overview of what the ACT math section looks like in 2026.
Topic Breakdown
The ACT math section covers six main content areas. Here is roughly how they break down by question count.
If you want a deep dive into every formula you might need, check out our ACT math formulas cheat sheet. Now, grab a pencil and a calculator, and let us get started.
ACT Math Practice Test: 20 Questions
Try each question on your own before reading the explanation. These questions progress from easier pre-algebra concepts to more challenging trigonometry problems, just like the real ACT.
Pre-Algebra and Elementary Algebra (Questions 1-5)
Question 1
If 3x - 7 = 20, what is the value of x?
A) 7 B) 9 C) 11 D) 13
Show Answer
Answer: B) 9
Add 7 to both sides: 3x = 27. Divide both sides by 3: x = 9.
Question 2
A shirt originally priced at $45 is on sale for 20% off. What is the sale price?
A) $9.00 B) $25.00 C) $36.00 D) $40.00
Show Answer
Answer: C) $36.00
A 20% discount means you pay 80% of the original price. $45 x 0.80 = $36.00. Trap answer: A is just the discount amount ($9), not the sale price.
Question 3
What is the value of |−4| + |3| − |−2|?
A) −3 B) 1 C) 5 D) 9
Show Answer
Answer: C) 5
Absolute value makes every number positive. |−4| = 4, |3| = 3, |−2| = 2. So the expression becomes 4 + 3 − 2 = 5.
Question 4
If the ratio of boys to girls in a class is 3:5 and there are 40 students total, how many girls are in the class?
A) 15 B) 20 C) 24 D) 25
Show Answer
Answer: D) 25
The ratio 3:5 means there are 3 + 5 = 8 parts total. Each part equals 40 / 8 = 5 students. Girls make up 5 parts, so 5 x 5 = 25 girls.
Question 5
Which of the following is equivalent to 2³ × 2&sup4;?
A) 2&sup7; B) 2¹² C) 4&sup7; D) 4¹²
Show Answer
Answer: A) 2&sup7;
When multiplying powers with the same base, add the exponents: 2³ × 2&sup4; = 2³+&sup4; = 2&sup7;. A common mistake is multiplying the exponents (getting 2¹²) or doubling the base.
Intermediate Algebra and Functions (Questions 6-10)
Question 6
If f(x) = 2x² − 3x + 1, what is f(−2)?
A) 3 B) 7 C) 11 D) 15
Show Answer
Answer: D) 15
Substitute −2 for x: f(−2) = 2(−2)² − 3(−2) + 1 = 2(4) + 6 + 1 = 8 + 6 + 1 = 15. Be careful with the signs: (−2)² = 4 (positive), and −3(−2) = +6.
Question 7
What are the solutions to x² − 5x + 6 = 0?
A) x = 1 and x = 6 B) x = 2 and x = 3 C) x = −2 and x = −3 D) x = −1 and x = −6
Show Answer
Answer: B) x = 2 and x = 3
Factor the quadratic: x² − 5x + 6 = (x − 2)(x − 3) = 0. Set each factor to zero: x − 2 = 0 gives x = 2, and x − 3 = 0 gives x = 3. Check: both values multiply to 6 and add to 5.
Question 8
Which of the following represents the solution set for 2x + 5 > 13?
A) x > 4 B) x > 9 C) x < 4 D) x < 9
Show Answer
Answer: A) x > 4
Subtract 5 from both sides: 2x > 8. Divide both sides by 2: x > 4. Since we divided by a positive number, the inequality sign stays the same.
Question 9
The first term of a geometric sequence is 3 and the common ratio is 2. What is the 5th term?
A) 11 B) 24 C) 48 D) 96
Show Answer
Answer: C) 48
The nth term of a geometric sequence is a&sub1; × r&sup(n−1). So the 5th term = 3 × 2&sup4; = 3 × 16 = 48. You can also list the terms: 3, 6, 12, 24, 48.
Question 10
If log&sub2;(x) = 5, what is the value of x?
A) 10 B) 16 C) 25 D) 32
Show Answer
Answer: D) 32
A logarithm answers the question: "What power do I raise the base to?" log&sub2;(x) = 5 means 2&sup5; = x. Since 2&sup5; = 32, x = 32.
Geometry (Questions 11-15)
Question 11
A right triangle has legs of length 6 and 8. What is the length of the hypotenuse?
A) 7 B) 10 C) 12 D) 14
Show Answer
Answer: B) 10
Use the Pythagorean theorem: a² + b² = c². So 6² + 8² = 36 + 64 = 100. The hypotenuse c = √100 = 10. This is the classic 3-4-5 right triangle scaled by 2.
Question 12
What is the area of a circle with a diameter of 10?
A) 10π B) 20π C) 25π D) 100π
Show Answer
Answer: C) 25π
Area = πr². The diameter is 10, so the radius is 5. Area = π(5)² = 25π. Common trap: using the diameter instead of the radius, which gives 100π.
Question 13
In the coordinate plane, what is the distance between the points (1, 3) and (4, 7)?
A) 3 B) 4 C) 5 D) 7
Show Answer
Answer: C) 5
Use the distance formula: d = √[(x&sub2; − x&sub1;)² + (y&sub2; − y&sub1;)²]. d = √[(4 − 1)² + (7 − 3)²] = √[9 + 16] = √25 = 5. This is another 3-4-5 right triangle.
Question 14
A rectangle has a perimeter of 36 and a length of 12. What is the area of the rectangle?
A) 36 B) 60 C) 72 D) 144
Show Answer
Answer: C) 72
Perimeter = 2(length + width). So 36 = 2(12 + w), which gives 18 = 12 + w, and w = 6. Area = length × width = 12 × 6 = 72.
Question 15
Two parallel lines are cut by a transversal. If one of the alternate interior angles measures 65°, what is the measure of the corresponding angle on the same side?
A) 25° B) 65° C) 115° D) 125°
Show Answer
Answer: C) 115°
When parallel lines are cut by a transversal, alternate interior angles are equal (both 65°). The co-interior (same-side interior) angles are supplementary, meaning they add up to 180°. So the angle on the same side = 180° − 65° = 115°.
Trigonometry and Advanced Topics (Questions 16-20)
Question 16
In a right triangle, the side opposite angle θ is 5 and the hypotenuse is 13. What is sin(θ)?
A) 5/12 B) 5/13 C) 12/13 D) 13/5
Show Answer
Answer: B) 5/13
Remember SOH-CAH-TOA. Sine = Opposite / Hypotenuse. sin(θ) = 5/13. The adjacent side would be 12 (from the 5-12-13 Pythagorean triple), but you do not need it for sine.
Question 17
What is the value of cos(60°)?
A) 0 B) 1/2 C) √2/2 D) √3/2
Show Answer
Answer: B) 1/2
This is a value you should memorize from the unit circle. In a 30-60-90 triangle, cos(60°) = adjacent/hypotenuse = 1/2. Note: √3/2 is sin(60°), and √2/2 is cos(45°).
Question 18
If tan(θ) = 3/4 and θ is in the first quadrant, what is cos(θ)?
A) 3/5 B) 4/5 C) 3/4 D) 5/4
Show Answer
Answer: B) 4/5
If tan(θ) = opposite/adjacent = 3/4, then opposite = 3 and adjacent = 4. The hypotenuse = √(3² + 4²) = √25 = 5. So cos(θ) = adjacent/hypotenuse = 4/5.
Question 19
Which of the following is equivalent to sin²(θ) + cos²(θ)?
A) 0 B) 1 C) tan²(θ) D) 2sin(θ)cos(θ)
Show Answer
Answer: B) 1
This is the fundamental Pythagorean identity: sin²(θ) + cos²(θ) = 1 for any angle θ. This identity appears frequently on the ACT and is worth memorizing. Note: 2sin(θ)cos(θ) is actually the double angle formula for sin(2θ).
Question 20
A 20-foot ladder leans against a wall, making a 60° angle with the ground. How high up the wall does the ladder reach?
A) 10 feet B) 10√2 feet C) 10√3 feet D) 20 feet
Show Answer
Answer: C) 10√3 feet
The ladder is the hypotenuse (20 feet), and the wall height is the side opposite the 60° angle. sin(60°) = opposite/hypotenuse = h/20. Since sin(60°) = √3/2, we get h = 20 × √3/2 = 10√3 ≈ 17.3 feet.
Quick Answer Key
How to Use Your Practice Test Results
Now that you have completed all 20 questions, count up your correct answers and see where you stand.
No matter your score, the key is to understand why you got each question wrong. Review every missed question, identify the concept behind it, and practice more problems of that type. You can take a free ACT math quiz on Larry Learns to get more targeted practice based on your weak areas.
5 Tips for ACT Math Success
- Answer every question. There is no penalty for guessing on the ACT. If you are running out of time, fill in your best guess for every remaining question. Even random guesses give you a 25% chance of being correct.
- Memorize key formulas. Unlike the SAT, the ACT does not give you a formula reference sheet. You need to know area and perimeter formulas, the Pythagorean theorem, slope formula, trig ratios, and common angle values. See our ACT math formulas cheat sheet for the complete list.
- Use your calculator wisely. A calculator is allowed on the entire ACT math section, but not every question needs one. Use it for arithmetic-heavy problems and skip it for concept questions where plugging in numbers is faster by hand.
- Work front to back. The ACT math section is ordered by difficulty. The first 20 questions are the easiest and fastest points. Do not spend five minutes on question 38 when you could be collecting easy points at the beginning.
- Plug in answer choices. When algebra feels overwhelming, try substituting each answer choice back into the problem. This backsolving strategy works especially well for questions with simple numeric answers.
For a complete study plan, check out our guide on how to create an ACT study plan. And if you want to see how other sections work, read up on ACT science and ACT English strategies next.
Why Practice Tests Work
Research from ACT, Inc. consistently shows that students who complete practice tests before the real exam score higher than those who only review content passively. Practice testing forces your brain to actively retrieve information, which strengthens the neural pathways you need on test day.
The best approach combines timed practice (to build speed and stamina) with untimed review (to deeply understand each concept). Start untimed with questions like the ones above, then move to full-length timed practice tests as your exam date approaches. If you are looking for additional resources, our list of the best ACT prep books includes options with multiple full-length practice tests.
Ready to keep practicing? Start a free ACT math quiz on Larry Learns and get instant scoring with personalized feedback on your strengths and weaknesses.
Frequently Asked Questions About ACT Math Practice Tests
How many questions are on the ACT math section?
The enhanced ACT math section (2025 and beyond) has 45 questions to be completed in 50 minutes. Of those, 41 are scored and 4 are unscored field-test questions that ACT uses to evaluate new items. You will not know which questions are unscored, so treat every question as if it counts.
What math topics are covered on the ACT?
The ACT math section covers pre-algebra, elementary algebra, intermediate algebra, coordinate geometry, plane geometry, and trigonometry. Algebra and geometry make up the bulk of the test, with trigonometry appearing in roughly 3 to 5 questions.
Is a calculator allowed on the ACT math test?
Yes, you can use a calculator on the entire ACT math section. Most graphing and scientific calculators are permitted, but calculators with computer algebra systems (like the TI-89 or TI-Nspire CAS) are not allowed. Check the official ACT calculator policy before test day.
What is a good ACT math score?
The national average ACT math score is around 20. A score of 25 or above puts you in roughly the 75th percentile, while a 30 or above places you in the top 10% of test takers. Competitive colleges typically look for math scores of 28 or higher. Use our score calculator to see what your target score should be.
How long should I study for ACT math?
Most students benefit from 4 to 8 weeks of focused preparation, studying 30 to 60 minutes per day. If math is your weakest section, lean toward the longer end. The key is consistent daily practice rather than marathon cramming sessions. Start with a diagnostic to identify weak areas, then target those topics specifically.
Should I take the ACT or SAT?
Both tests are accepted by virtually all U.S. colleges. The ACT math section covers more geometry and trigonometry, while the SAT focuses more on algebra and data analysis. Try a practice test for each and see which format feels more natural. You can take a free practice quiz for both exams right here on Larry Learns to compare your performance.
