ACT Math practice test: a free timed drill and the formulas to know
ACT Math has 45 questions in 50 minutes, about 67 seconds each, with four answer choices and a calculator allowed. Take the free 12-question drill below at that pace, covering algebra, functions, geometry, statistics and number topics, then see every step explained. The formulas below are the ones the ACT keeps coming back to.
- 45
- questions on the real section
- 50 min
- about 67 seconds each
- 4
- answer choices per question
- Free
- no sign-up
Last checked · Section facts from ACT, read 22 October 2026
Free Math drill: 12 original ACT-style questions at the real ACT Math pace, then every answer explained. No sign-up.
12
questions
13:20
time limit
Free
every answer explained
By the LifeScore Editorial Team · Updated · How we check facts · How this is scored
What math is on the ACT?
Pre-algebra through basic trigonometry: numbers and quantity, algebra, functions, geometry, and statistics and probability, plus multi-step questions that combine them.
| Category | What it includes |
|---|---|
| Number and Quantity | Fractions, exponents and roots, complex numbers, sequences |
| Algebra | Linear equations and inequalities, systems, quadratics, expressions |
| Functions | Function notation, graphs, linear and exponential models, logarithms |
| Geometry | Area, volume, triangles, circles, right-triangle trigonometry |
| Statistics and Probability | Mean, median, percentages, rates, tables, probability |
The ACT reaches a little further than the SAT in a few places: arithmetic and geometric sequences, complex numbers, logarithms and trigonometry beyond right triangles appear more often. Our ACT drill includes sequence, complex number and logarithm questions for that reason.
What do ACT Math questions look like?
Mostly short, direct problems, getting harder as the section goes on. Here are two worked step by step.
ACT-style question 1 · Sequences
The first term of an arithmetic sequence is 5 and the fourth term is 20. What is the 10th term?
- A50
- B45
- C55
- D25
Worked answer
A: 50. Three steps take 5 to 20, so the common difference is 5. The 10th term is 5 + 9 × 5 = 50.
- From term 1 to term 4 is 3 steps: d = (20 - 5) ÷ 3 = 5.
- Term n = 5 + (n - 1) × 5.
- Term 10 = 5 + 45 = 50.
The trap: Using 10 steps instead of 9 (55), or dividing by 4 steps instead of 3.
ACT-style question 2 · Complex numbers
What is (3 - 2i)(3 + 2i)? (Note: i² = -1)
- A13
- B5
- C9 - 4i
- D9 + 4i
Worked answer
A: 13. This is a difference of squares: 3² - (2i)² = 9 - 4i² = 9 + 4 = 13.
- (a - b)(a + b) = a² - b².
- 3² - (2i)² = 9 - 4i².
- i² = -1, so 9 + 4 = 13.
The trap: Treating i² as +1, which gives 5.
ACT-style question 3 · Trigonometry
A right triangle has legs of length 9 and 12. What is the sine of the angle opposite the leg of length 9?
- A3/5
- B4/5
- C3/4
- D4/3
Worked answer
A: 3/5. The hypotenuse is √(81 + 144) = √225 = 15. Sine is opposite over hypotenuse: 9/15 = 3/5.
- Hypotenuse: √(9² + 12²) = √225 = 15.
- Sine = opposite ÷ hypotenuse.
- 9 ÷ 15 = 3/5.
The trap: Using the other leg as the hypotenuse (9/12 = 3/4, the tangent), or taking the cosine (12/15 = 4/5).
What formulas should I know for ACT Math?
The ACT gives you no formula sheet, so learn these by heart: slope, the quadratic formula, sequences, Pythagoras and trig ratios, and the area and circle formulas.
| Topic | Formula |
|---|---|
| Slope | (y₂ - y₁) ÷ (x₂ - x₁) |
| Line | y = mx + b |
| Quadratic formula | x = (-b ± √(b² - 4ac)) ÷ 2a |
| Arithmetic sequence | aₙ = a₁ + (n - 1)d |
| Geometric sequence | aₙ = a₁ × rⁿ⁻¹ |
| Pythagoras | a² + b² = c² |
| Trig ratios | sin = opp/hyp, cos = adj/hyp, tan = opp/adj |
| Circle | area πr², circumference 2πr |
| Logarithm | log_b(x) = y means bʸ = x |
Four Math drills and eight mocks
The ACT Pass Pack has four Math drills, eight full mocks and the working for every answer.
The ACT Pass Pack gives you 8 full mocks on the real clock, 16 drills of 12 questions for the sections that cost you points, and a predictor that turns your mocks into the odds of reaching your target. One payment, no subscription, and your free score stays free.
Prep courses for these tests usually cost $19 to $129. The ACT Pass Pack is US$39 (£29), once.
- 8
- timed mocks
- 16
- topic drills
- 1
- score predictor
How do I finish ACT Math on time?
Do every question you can in under a minute first, mark the slow ones, and come back. Early questions tend to be easier, so bank time there for the last third.
With 67 seconds a question, a single three-minute question costs you two others. Skip it, mark it, and come back with whatever time is left. Before time runs out, fill in a guess on everything blank: there is no penalty.
Use your calculator for arithmetic you would otherwise do slowly, but not for every step. Many ACT questions are quicker by reasoning: plugging in the answer choices, or estimating to rule out two of them.
Then put it together under the full clock with the free ACT practice test. The other section pages are English, Reading and Science.
How is ACT Math different since 2025?
The enhanced ACT cut Math from 60 questions in 60 minutes to 45 in 50, which gives you about 67 seconds a question instead of 60, and every question now has four answer choices instead of five.
Fewer choices make guessing slightly better and elimination quicker: knock out two wrong options and you have a coin flip, not a one-in-three. Use that on the hardest questions at the end of the section rather than leaving them blank.
The topics did not change much. You still need algebra and functions above all, and geometry and statistics questions still appear throughout. What changed is the pace, which is why older timed practice from a five-choice, 60-minute book can make you rush when there is no need.
Our drill and mocks use the new format: four options, and 30 minutes for 27 questions in a mock, which is the real ACT pace per question.
| Before 2025 | Enhanced ACT | |
|---|---|---|
| Questions | 60 | 45 |
| Minutes | 60 | 50 |
| Time per question | About 60 seconds | About 67 seconds |
| Answer choices | 5 | 4 |
How should I use a calculator on ACT Math?
For arithmetic that would slow you down, and to check an answer by plugging it back in. Set up every problem on paper first, and use the calculator to finish it, not to think for you.
- Bring a calculator you already know well; test day is no time to learn a new one.
- Check that your model is permitted: ACT bans calculators with computer algebra systems and some other features.
- Graph an equation to find intercepts or intersections when algebra would be slow.
- Plug answer choices into the equation when the algebra is messy: with four options, it is quick.
- Do not use it on questions that reason faster: a calculator is slow for comparing fractions you can estimate.
What are the most common ACT Math mistakes?
Answering for x when the question asks for something else, sign errors, and spending too long early in the section.
- Solving for x and stopping, when the question asks for 2x, x + 3 or the area.
- Dropping a negative when distributing or squaring.
- Treating i² as +1 in complex-number questions.
- Counting n steps instead of n - 1 in a sequence.
- Spending three minutes on question 12 and rushing questions 40 to 45.
Frequently asked questions
How many questions are on ACT Math?
Can I use a calculator on ACT Math?
Does the ACT give you formulas?
Does ACT Math still have five answer choices?
What is the hardest math on the ACT?
Is this the real ACT?
Bank more Math points in the same 50 minutes
Eight full ACT-style mocks, four Math drills and 12 more across English, Reading and Science, every step explained, in one payment.
The ACT Pass Pack gives you 8 full mocks on the real clock, 16 drills of 12 questions for the sections that cost you points, and a predictor that turns your mocks into the odds of reaching your target. One payment, no subscription, and your free score stays free.
Prep courses for these tests usually cost $19 to $129. The ACT Pass Pack is US$39 (£29), once.
- 8
- timed mocks
- 16
- topic drills
- 1
- score predictor