What topics are on the ACT Math test?
ACT Math covers algebra, functions, geometry, number and quantity, and statistics and probability, plus a category called Integrating Essential Skills: percentages, rates, proportions, area and volume, and averages, usually inside a word problem. ACT puts Integrating Essential Skills at 20% of the section, each of algebra, functions and geometry at 17–20%, statistics and probability at 12–15%, and number and quantity at 10–12%. ACT also says all problems can be solved without a calculator and that complex formulas and long computations aren't required. Calculus isn't on the test.
Where it shows up on the ACT
| Enhanced ACT | |
|---|---|
| Section | Math |
| Length | 45 questions (41 scored) in 50 minutes, about 67 seconds each |
| Reporting category | Preparing for Higher Math (five topic groups) and Integrating Essential Skills |
| Share of the section | Integrating Essential Skills 20%; Algebra, Functions and Geometry 17–20% each; Statistics and Probability 12–15%; Number and Quantity 10–12% |
| In the Composite | Yes. The Composite averages English, Math and Reading. |
ACT's percentages are approximate shares of the whole Math section; the five topic groups together are Preparing for Higher Math, about 80%. A third label, Modeling, is added on top of the others for questions that use a real-world model, so its questions also count in another category. Source: ACT, Preparing for the ACT 2025–2026, pp. 6–10: what each section covers and its reporting categories.
What the questions ask you to do
- Number and Quantity: real and complex numbers, exponents and roots, vectors and matrices.
- Algebra: linear equations and inequalities, systems, quadratics, polynomials and expressions.
- Functions: function notation, reading graphs, transforming and composing functions; linear, radical, piecewise, polynomial, exponential and logarithmic functions.
- Geometry: shapes and solids, triangles, circles, coordinate geometry, trigonometry, area and volume.
- Statistics and Probability: center and spread of data, reading data displays, probability.
- Integrating Essential Skills: percentages, rates, proportions, area and volume, averages and medians, numbers written in different forms.
The 6 categories at a glance
ACT's reporting categories, with the share ACT gives for each.
| Category | Share of Math | What it covers |
|---|---|---|
| Number and Quantity | 10–12% | Real and complex numbers, integer and rational exponents, vectors and matrices |
| Algebra | 17–20% | Solving, graphing and modeling with linear, polynomial, radical and exponential equations, and systems of equations |
| Functions | 17–20% | Definition, notation and use of functions, including linear, radical, piecewise, polynomial, exponential and logarithmic ones, and features of their graphs |
| Geometry | 17–20% | Shapes and solids, congruence and similarity, surface area and volume, missing values in triangles and circles, trigonometric ratios, equations of conic sections |
| Statistics and Probability | 12–15% | Center and spread of distributions, data collection methods, relationships in two-variable data, probabilities |
| Integrating Essential Skills | 20% | Rates and percentages, proportional relationships, area, surface area and volume, average and median, numbers in different forms, often in several steps |
The first five make up Preparing for Higher Math (about 80%). Modeling is a separate label that overlaps the others.
How many questions each category got
Our count from the scoring keys of ACT's last two published practice tests.
| Category | 2025–26 test (41 scored) | Older test (60) |
|---|---|---|
| Number and Quantity | 3 | 5 |
| Algebra | 6 | 8 |
| Functions | 5 | 8 |
| Geometry | 5 | 8 |
| Statistics and Probability | 6 | 6 |
| Integrating Essential Skills | 16 | 25 |
The older test is the 60-question form in Preparing for the ACT 2024–25. One test per version, so small differences don't mean much.
Topics that rarely came up
Across those two practice tests (101 scored questions), we counted no questions on logarithms, inverse functions, ellipses or hyperbolas, or matrix inverses, and one on the law of sines. They are in ACT's content description, so they can appear, but they are a poor place to start.
Statistics and probability showed up more than its 12–15% share suggests once you count the Integrating Essential Skills questions built on data: by topic, we counted 10 of the 41 scored questions in the 2025–26 test, about 24%.
Common mistakes
Wrong answer choices are often built around these.
- Studying advanced topics first. Logarithms and ellipses are listed, but in ACT's last two practice tests they didn't appear. Percentages, rates and averages did, many times.
- Skipping Integrating Essential Skills because it sounds basic. In ACT's 2025–26 practice test it was 16 of the 41 scored questions, more than any other category.
- Stopping at an intermediate result. Integrating Essential Skills questions often take several steps, and ACT notes that a wrong choice is often the number you get partway through.
- Confusing mean and median. The mean adds and divides; the median is the middle value after sorting.
- Treating i² as 1 in complex number questions. i² = −1.
- Assuming figures are drawn to scale. ACT's directions say they aren't necessarily.
3 example questions with answers
Written by Ashore in the style of the enhanced ACT. They aren't official ACT questions. Try each one before you open the answer.
Question 1 · Easy
For the data set 4, 7, 7, 9, 13, what is the mean minus the median?
- A0
- B1
- C2
- D9
Show the answer
B. The sum is 40, so the mean is 40 ÷ 5 = 8. The values are already in order, so the median is the middle one, 7. The difference is 8 − 7 = 1. 9 is the range, and 0 assumes the mean and median are equal.
Question 2 · Medium
If f(x) = 2x − 3 and g(x) = x² + 1, what is f(g(2))?
- F2
- G5
- H7
- J10
Show the answer
H. Work from the inside out. g(2) = 2² + 1 = 5, then f(5) = 2(5) − 3 = 7. 5 is g(2) alone, and 2 is g(f(2)), with the functions applied in the wrong order.
Question 3 · Hard
Which of the following is equal to (3 + 2i)(1 − i), where i = √(−1)?
- A1 − i
- B3 − 2i
- C5 + i
- D5 − i
Show the answer
D. Multiply out: 3 − 3i + 2i − 2i² = 3 − i − 2i². Since i² = −1, −2i² = +2, giving 5 − i. 1 − i comes from treating i² as 1, 3 − 2i multiplies only the first terms and the last terms, and 5 + i gets the sign of the i term wrong.
More ACT Math guides
- Math formulas to know
- Integrating Essential Skills
- Desmos and calculators
- ACT score calculator: questions right in each section to a 1–36 score and Composite.
- SAT vs ACT: which test fits you better.
- All ACT guides and free tools
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Practice test 1
Example
27
Composite
(28 + 26 + 27) ÷ 3
- English28
- Math26
- Reading27
- ScienceOptional, not in the Composite25