ACT, College admissions

Math

Math is 45 questions in 50 minutes, about 67 seconds per question, and on the enhanced format each question offers four answer choices instead of five. Questions tend to run from easier to harder, so time banked early is time available for the end of the section. A calculator is permitted for the whole section, subject to ACT's published list of prohibited models. ACT reports results in three categories, one of which, Modeling, cuts across the others.

Position: 2 of 5 sections
Questions: 45 questions
Time: 50 minutes
Topics covered: 7 topics in this guide

What is covered

Topics inside this section.

These topics describe the scope students most often review for this part of ACT. Treat them as a study checklist rather than an exhaustive list of what a single exam form can sample.

Preparing for Higher Math: Number and Quantity: Real and complex number systems, integer and rational exponents, vectors, and matrices, along with the numerical reasoning that underlies later algebra work.
Preparing for Higher Math: Algebra: Solving, graphing, and modeling with linear, polynomial, radical, and exponential relationships, including systems of equations and expressions with more than one variable.
Preparing for Higher Math: Functions: Function definition, notation, representation, and application across linear, radical, piecewise, polynomial, and logarithmic functions, plus graphing and transformations.
Preparing for Higher Math: Geometry: Shapes and solids, congruence and similarity, surface area and volume, right triangle trigonometry, and the equations of conic sections.
Preparing for Higher Math: Statistics and Probability: Center, spread, and distribution of data, relationships in bivariate data, probability and counting, and the difference between what a sample supports and what it does not.
Integrating Essential Skills: The pre-high-school foundations applied in harder settings: rates and percentages, proportional relationships, area, surface area and volume, average and median, and expressing numbers in different ways.
Modeling: A cross-cutting category rather than a separate block of questions, scoring how well you produce, interpret, evaluate, and improve models; the same questions also count toward the categories above.

Study tips

How to practice Math.

Section-specific guidance that follows from how this material is usually tested.

Four answer choices instead of five makes a blind guess more valuable, but it is not a strategy; answer every question and guess only after you have spent your time budget.
Do not neglect Integrating Essential Skills, since rates, percentages, proportions, averages, and area are quick points that reward accuracy more than advanced technique.
Bank time on the earlier, easier questions so the harder ones later in the section get more than the 67-second average.
Check your calculator against ACT's prohibited-model list well before test day, and practice with the exact device you will bring.

Where this fits

Math is 2 of 5 sections in the ACT guide. Use the full guide to balance it against everything else you have to review.

Back to the ACT guide Official exam information

Sample Math questions

Practice questions, not yet expert-reviewed

Original practice questions written to the published framework for this section. No expert has reviewed them, and they are not taken from any official exam. Try each one before you open the answer.

Question 1Foundational
What is the arithmetic mean of the five numbers 3, 7, 9, 14, and 17?
1. A9
2. B10
3. C14
4. D50
Show answer
Answer: B. 10
The five values total 50, and 50 divided by 5 is 10. The distractor 9 is the median, the middle value once the list is ordered, which is a different measure of center.
Key insight: The mean divides the total by the count; the median is the middle value.
Question 2Foundational
A bag contains 3 red marbles, 5 blue marbles, and 4 green marbles. If one marble is drawn at random, what is the probability that it is blue?
1. A5/12
2. B1/3
3. C5/7
4. D7/12
Show answer
Answer: A. 5/12
There are 12 marbles in all and 5 of them are blue, so the probability is 5 out of 12. The fraction 5/7 compares blue marbles with non-blue marbles instead of with the whole bag, and 7/12 is the probability of not drawing blue.
Key insight: Probability compares favorable outcomes with the total, never with the leftovers.
Question 3Intermediate
If $f(x) = 2x^2 - 3x + 1$ , what is the value of $f(-2)$ ?If f(x) = 2x^2 - 3x + 1, what is the value of f(-2)?
1. A-1
2. B3
3. C11
4. D15
Show answer
Answer: D. 15
Substituting gives $2(-2)^2 - 3(-2) + 1 = 8 + 6 + 1 = 15$ . The trap answer 3 comes from subtracting 6 instead of adding it after multiplying $-3$ by $-2$ .Substituting gives 2(-2)^2 - 3(-2) + 1 = 8 + 6 + 1 = 15. The trap answer 3 comes from subtracting 6 instead of adding it after multiplying -3 by -2.
Key insight: Square the negative before multiplying, and track the sign of every substituted value.
Question 4Intermediate
What is the area of a circle whose radius is 5 units, expressed in terms of $\pi$ ?What is the area of a circle whose radius is 5 units, expressed in terms of \pi?
1. A10 pi square units
2. B25 pi square units
3. C50 pi square units
4. D100 pi square units
Show answer
Answer: B. 25 pi square units
Area is $A = \pi r^2$ , so the area is $\pi \cdot 5^2 = 25\pi$ square units. The distractor $10\pi$ is the circumference, $2\pi r$ , which uses the radius to the first power.Area is A = \pi r^2, so the area is \pi \cdot 5^2 = 25\pi square units. The distractor 10\pi is the circumference, 2\pi r, which uses the radius to the first power.
Key insight: Area uses the radius squared; circumference uses the radius once.
Question 5Advanced
What is the slope of any line perpendicular to the line 4x + 2y = 10?
1. A-2
2. B-1/2
3. C1/2
4. D2
Show answer
Answer: C. 1/2
Solving for y gives y = -2x + 5, so the line's slope is -2 and a perpendicular line has the negative reciprocal, 1/2. The distractor -1/2 takes the reciprocal without changing the sign, and -2 simply repeats the original slope.
Key insight: Perpendicular slopes are negative reciprocals: their product is -1.

Continue through ACT

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