ACT Math test

The 60 minute Math section appears second in the four-section sequence of the ACT. You will answer 60 questions; all of the test questions are multiple choice. The correct answer to the math questions is among five possible answer choices. Although many students are intimidated by math, the ACT Math Test is in many ways the easiest of the four sections to prepare for; by memorizing certain common patterns and formulas — many of which students have already learned in high school math — even a low-scoring test-taker can start seeing improvements. In this article, we’ll take you through the basic math skills and test-taking strategies you’ll need to know to raise your ACT Math section score.

Basic algebra

By far the most common math skill tested on the ACT is basic algebra (including pre algebra). This broad topic includes order of operations, simplifying expressions, fractions, decimals, percentages, and exponents. Early in the test these basic algebra skills are tested on their own; as the test gets more difficult, however, basic algebra is often tested in conjunction with other types of questions.


What is the value of x when 3x/2 + 16=10

A. -9
B. -4
C. 4
D. 9
E. 39


Basic geometry

The next most common math skill is basic geometry: finding the measures of angles, finding the area and perimeter of a two-dimensional shape, finding the volume and surface area of a three dimensional shape, or finding the area, radius, or circumference of a circle. The ACT mathematics test also includes coordinate geometry and plane geometry. The ACT provides with you with the necessary formulas for all shapes that appear on the test, but, for the sake of time on test day, it is best if the student has these all of these formulas memorized beforehand.


In the figure below [we’ll need to add photo of right triangle] the measure of ∠XAB is 150°; the measure of ∠YCB is 81°; and X, A, C, and Y are collinear. What is the measure of ∠B?

A. 30°
B. 51°
C. 60°
D. 69°
E. 77°


Functions

Functions also appear with frequency on the ACT: graphs of polynomials, finding roots and factoring, domain and range, reflecting a function across an axis, and assessing a function at a given point. Knowing the shapes of common graphs — lines, parabolas, and square roots, for instance — can save you a lot of time, since these graphs are pretty common on the ACT.


If f(x)=x2 – x + 1, what is f(-3)?

A.  -11
B. -5
C. 7
D. 10
E. 13


Trigonometry

Students will also find trigonometry very well-represented on the ACT Math Test, especially in the later, more difficult questions: sine, cosine, and tangent, graphs of trigonometric functions, converting from radians to degrees, using the unit circle, and simplifying trigonometric expressions using trigonometric identities. Trigonometry is among the highest-level math topics on the ACT – which is to say, it’s often a topic students learn late in their math careers and find tough. Because only a few trigonometric ideas are represented on the ACT, however, it’s easy enough to familiarize yourself with all the possible trig questions you will encounter.


Given that sin A=20/25, which of the following values could tan A equal?

A. 5/20
B. 15/20
C. 20/15
D. 4
E. 5


Smaller topics

Beyond these topics, many smaller topics appear once or twice per test: these include logarithms, combinations and permutations, graphs of inequalities, logic, and number theory, to name a few.


A news anchor made the true statement below.
If it is raining, then the parade is cancelled.
Which of the following statements is logically equivalent to the news anchor’s statement?

A. If it is not raining, then the parade is not cancelled.
B. The parade is cancelled if and only if it is raining.
C. If it is not raining, then the parade is cancelled.
D. If the parade is cancelled, then it is raining.
E. If the parade is not cancelled, then it is not raining.


Some math topics — like sequences and matrices — appear so infrequently that you might need to take two or three full-length math sections just to run into one such question!

What’s next?

Read our Ultimate Guide to ACT Test Prep — it summarizes everything you’ll need to know, whether you are preparing to take the ACT next month or in a few years.

Thinking about getting a tutor for ACT Math prep? Our online ACT test prep will teach you to apply these strategies and many more for success on the ACT. Get in touch to schedule a free lesson or take a free practice test.