The ACT Math section is fast, broad and predictable. It covers more topics than the SAT, gives you less time per question, and doesn’t hand you a formula sheet. The upside is that the question types repeat from test to test, so focused practice pays off quickly.
The format
Since the ACT’s 2025 update, the Math section has:
- 45 questions in 50 minutes, about 67 seconds each.
- Four answer choices per question (it used to be five).
- A calculator allowed on every question. Most graphing calculators are fine, including the TI-84. Calculators with a computer algebra system, such as the TI-89 and TI-Nspire CAS, are not allowed.
- No formula sheet. You need to know area, volume and trig formulas yourself.
- A score from 1 to 36. Your composite is the average of English, Math and Reading. Science is now optional and scored separately.
The questions roughly get harder as you go, though not strictly. The first third is mostly algebra and basic geometry, and the last third holds most of the trig, logs and unusual topics.
What it tests
ACT groups its questions into a few areas.
| Area | What shows up |
|---|---|
| Algebra | linear equations and inequalities, systems, quadratics, exponents and radicals, absolute value |
| Functions | notation, domain and range, composition, transformations, exponential and logarithmic functions |
| Geometry | area, volume, triangles, circles, similar figures, coordinate geometry, basic trig |
| Statistics and probability | mean, median, spread, counting, probability, reading data |
| Number and quantity | ratios, percents, number properties, complex numbers, matrices, vectors |
| Modeling and integrating skills | multi-step word problems that combine the above |
Every topic in the table has a matching FreeMathSchool guide, linked below.
What the ACT covers that the SAT doesn’t
If you have studied for the SAT, most of your work carries over. These topics appear on the ACT but rarely or never on the SAT:
- Matrices: adding, multiplying by a number, and occasionally multiplying two matrices or finding a 2×2 determinant (ad − bc).
- Logarithms: evaluating logs and using the log rules. See logarithms explained.
- The unit circle and trig beyond SOH CAH TOA: radians, sine and cosine graphs, period and amplitude. See the unit circle.
- Sequences: arithmetic and geometric nth terms and sums. See sequences.
- Counting: permutations and combinations. See permutations and combinations.
- Complex numbers: i² = −1 and arithmetic with a + bi.
- Ellipses and other conic sections occasionally, beyond the circle. See circles.
The SAT, in turn, has a built-in Desmos calculator, a formula sheet, two adaptive modules and more time per question (44 questions in 70 minutes). The digital SAT math guide covers it.
Formulas to memorize
The ACT gives you none, so know these cold:
- Slope (y₂ − y₁)/(x₂ − x₁), slope-intercept form y = mx + b, midpoint and distance formulas.
- The quadratic formula x = (−b ± √(b² − 4ac))/(2a) and the vertex x = −b/(2a).
- Areas: rectangle, triangle ½bh, trapezoid ½(b₁ + b₂)h, circle πr².
- Circumference 2πr, and arc length and sector area as fractions of the circle.
- Volumes: prism and cylinder (base area × height), cone and pyramid (⅓ × base area × height), sphere (4/3)πr³.
- The Pythagorean theorem and the 30-60-90 (1 : √3 : 2) and 45-45-90 (1 : 1 : √2) triangles.
- SOH CAH TOA, and sin² θ + cos² θ = 1.
- Exponent and log rules.
Make flashcards for these on FMS Study and review them a few minutes a day. The spaced repetition guide explains how to space the reviews.
Pacing
At 67 seconds a question, you can’t afford to get stuck. A plan that works for most students:
- Aim to finish questions 1 to 30 in about 25 minutes. They are usually quicker.
- Spend the remaining 25 minutes on 31 to 45.
- If a question takes more than 90 seconds, mark it, guess, and move on. Come back if you have time.
- Never leave a blank. There is no penalty for wrong answers.
Strategies that save time
- Plug in the answer choices. When the question asks for a value, test the choices in the original equation. Start with a middle value.
- Pick numbers. When the question and answers are full of variables, choose easy numbers for the variables, work out the answer, and see which choice matches.
- Use your calculator for graphs. Graphing both sides of an equation and finding the intersection often beats solving by hand.
- Draw the figure. If a geometry question has no diagram, sketch one and label everything given.
- Read the last line first. In long word problems, knowing what’s being asked tells you which numbers matter.
A four-week plan
| Week | Focus |
|---|---|
| 1 | Take a full timed practice test. Sort every missed question by topic. Review linear equations, inequalities and percentages. |
| 2 | Your two weakest topics from the test, plus quadratics and functions. Do 15 to 20 timed questions a day. |
| 3 | The ACT-only topics above: matrices, logs, the unit circle, sequences, counting. Take a second full practice test at the end of the week. |
| 4 | Redo every question you missed on both tests. Drill formulas daily. Take a final practice test 3 or 4 days before the real one, then rest. |
The how to study for a math test guide has more on building a plan, and FMS Study can make one for your test date.
Practice questions
These are written in the ACT’s style but without answer choices, so you work each one out fully.
What is the determinant of the matrix with rows [3, 5] and [2, 4]?
Show answer
2. For a 2×2 matrix with rows [a, b] and [c, d], the determinant is ad − bc = 12 − 10.
If log₂ x = 5, what is x?
Show answer
32. log₂ x = 5 means 2⁵ = x.
The first term of an arithmetic sequence is 7 and the 10th term is 43. What is the common difference?
Show answer
4. 43 = 7 + 9d, so 9d = 36.
What is (3 + 2i)(1 − i), where i² = −1?
Show answer
5 − i. Multiply out: 3 − 3i + 2i − 2i² = 3 − i + 2.
What is the period of y = 4 sin(2x)?
Show answer
π. The period of sin(bx) is 2π/b, and 2π/2 = π. (The 4 changes the amplitude, not the period.)
A cone has radius 3 and height 8. What is its volume?
Show answer
24π ≈ 75.4. (1/3)π(3²)(8) = 24π.