I’ve noticed some major patterns in what trips students up on the ACT math. (I’ve worked with hundreds of private tutoring clients on the ACT and SAT, after all.) And I’m also confident as to why those types of questions tend to be difficult for high schoolers. That’s because: there’s a difference between the math they’ve learned in their most recent academic classes…and the math that the ACT actually asks them about.
As you may know, most American students follow the same general progression through Math topics, beginning in early middle school. Here’s the typical order: Arithmetic/Pre-Algebra, Algebra I, Geometry, Algebra 2. For more advanced learners, the steps after that are Pre-Calculus/Trigonometry and Calculus. So, if you’re in tenth grade at the moment, you might be in Geometry, Algebra 2 or some version of Pre-Calculus. If you’re a Junior, you might already be in Calculus (though you might only be learning Algebra 2, depending on where in the progression you are and how your school runs things).
So what does that mean for you and the ACT? Well, by the time you’re beginning to prep for this standardized test—your sophomore or junior year—you might find that the sub-topics that the ACT is asking you about are NOT the math sub-topics that you learned about in recent years in class!
See, to do well on the ACT, you need to remember way more than whatever you happen to be learning this week in Math class. This test also asks you to think back to almost ALL of what you’ve learned from sixth or seventh grade until now (junior or senior year)! To make matters tougher, several questions might stretch way beyond what you’re currently learning in terms of advanced topics…though of course, not all of the advanced topics you have studied will even show up on a given test. And trickier still, you won’t even have the crutch of a math formula reference sheet to help you!
The result can be confusion and disappointing scores for even the most hard-working ACT-taker. That is, unless and until you figure out which math topics you need to revisit and freshen up on, which ones you’re confident you’ll just recall from a recent class…and which topics aren’t worth spending study time on, for you in particular.
Note: big changes are coming for the ACT beginning in Spring 2025! But don’t worry—the Math content covered in this post accurately applies to both the existing version of the test and the version that will kick in beginning April 2025.
Article Contents
A. Video version of this article
1. Structure of the ACT Math Section
2. What is the format of questions?
3. Can you use a Reference Sheet?
C. What Math Is Tested on the ACT?
2. Algebra
6. Functions
7. Trigonometry
8. Statistics, Probability and Counting
9. Miscellaneous ACT Math Topics
C. Conclusion
Watch this article in video form:
Basics of the ACT Math Section
So, what are these mysterious math subtopics of which I speak? The ones that you’ll coast on like a skateboard to a perfect 36? Don’t worry, we’ll cover all that in this post, listing out every single piece of content that you’ll need to learn/remember to ace the ACT’s Math section. But first, you need to understand the basic structure of the test.
1) Outline of the ACT Mathematics Section
Math is the second section of the ACT. It has a straightforward structure:
If you’re taking the curent/”old” format of the ACT, you get 60 minutes to complete 60 questions (if you are a regular time test taker). That bumps up to 90 minutes if you get extended time.
If you take the new version of the ACT (debuting somewhere from Spring 2025 to Fall 2025, depending on the format in which you take it), you get 45 minutes to complete 45 questions.
Either way, of course, those numbers come out to one minute per question (for regular-time test-takers).
The thing about the Math section is that the difficulty of the questions varies…but they are all worth the same number of points. And there is a trend you should be aware of, too: generally speaking, the questions on the Math section get harder later in the test. Here’s what it looks like for the current version of the test:
The test’s first 30 questions tend to be on the “easy” side of things: easier topics, simpler questions, no tricks.
The next 15 questions (#31-45) ratchet up to the “medium” level of difficulty: more challenging math topics, more steps to figure out the answer, or perhaps a twist that tries to get you to stumble an otherwise “easy” math topic.
Finally, the last 15 questions (#46-60) tend to be “hard” questions: easier math topics but with MANY steps, questions with twists and tricks, or super easy questions that you can answer pretty painlessly...IF you happened to have studied that VERY ADVANCED math topic, that is!
2) What format are the answer choices on the ACT Math?
This one’s straightforward: all questions in the ACT Math Section are multiple choice! However, to help prevent you from accidentally filling in the wrong bubble on your answer sheet, the answer choices alternate between A/B/C/D/E and F/G/H/J/K. Huh. A little weird, but shouldn’t affect you negatively!
3) Can you use a Cheat Sheet for the ACT Math?
Unfortunately, no. All those formulas about tangents and how to find the midpoint between two points….you need to know them like the back of your hand by the time you’re sitting in the test seat.
4) Should You Guess on the Math part of the ACT?
If you frequently struggle to complete all 45 or 60 questions within the 45 or 60 minutes you’re allotted (for regular-time test sitters), yes, you can and should guess on the questions you don’t have time to solve properly. But fear not! I’ve developed the only guessing strategy you need, and you can quickly learn it right here.
What Math Is Tested on the ACT?
The ACT powers-that-be say the test divvies up its Math questions among sub-topics like so:
Pre-Algebra: 20-25% (~14 Q’s on the current test; ~10 Q’s on the new version)
Elementary Algebra: 15-20% (~10 Q’s on the current test; ~8 Q’s on the new test)
Intermediate Algebra: 15-20% (~9 Q’s on the current ACT; ~7 Q’s on the new ACT)
Coordinate Geometry: 15-20% (~9 Q’s on the current ACT; ~7 Q’s on the new ACT)
Plane Geometry: 20-25% (~14 Q’s on the current test; ~10 Q’s on the future ACT)
Trigonometry: 5-10% (~4 Q’s on the current ACT; ~3 Q’s on the future test)
However, these topics are only part of the…equation (wink wink). Because most parents and students *I* know are, understandably, not sure exactly what subject matter falls under broader categories like “Pre-Algebra,” “Elementary Algebra” and “Intermediate Algebra.” Even I—a Math Olympian, math competition master, and test prep expert for thirteen years!—find it tricky to know exactly which one of the “Algebras” a math question or math topic might fall under. This is all the more true because so many of these topics refer to each other and overlap.
But don’t despair. After over a dozen years of getting my private students to master these same topics, I’ve rewritten the subject matter breakdown as follows:
Fundamentals / Arithmetic
Algebra
Plane (2-D) Geometry
Solid (3-D) Geometry
Coordinate Geometry
Functions
Trigonometry
Statistics, Probability and Counting
Miscellaneous ACT Math Topics
Because this is the framework that my students have found the most success with, I am going to divide the ACT Math topics into these categories for you, too. I'm confident that once you read through them, my category divisions will make the most sense to you as well!
1) Fundamentals/Arithmetic
To succeed at these questions, you’ll need to understand: the Number System (words like “rational,” “integer,” and “whole number,” etc.), Number Properties (odd/even, positive/negative, primes, etc.), Factors and Multiples (Greatest Common Factors and Least Common Multiples), as well as Divisibility Rules to see if a number can be reduced. Mastering these items will help you greatly when you manipulate Fractions and solve Ratios and Proportions. (And don’t forget about Advanced Fraction Tricks like I wrote about here.) In addition, you should know your Order of Operations, Scientific Notation, and how to translate English words in word problems into math (“English-to-Math Translation”). Finally, you’ll need to know your way around percentage problems, such as percent “of”, percent increase, percent decrease and percent change!
2) Algebra
On the ACT, you also need to understand how to simplify Expressions and solve basic Algebraic Equations, Inequalities, and Absolute Values. Next, you’ll need to find solutions to Algebra Word Problems (Distance, Work, Average, and Rate Conversion questions) with ease. You’ll also need to have conquered topics that might tend to fall into “Algebra 2” territory: Exponents/Powers/Roots, Logarithms, Direct and Inverse Variation, and Factoring Quadratic Polynomials!
3) PLANE (2-D) GEOMETRY
When I say “Plane Geometry,” think two-dimensional shapes and geometric concepts, such as these: Lines and Angles, Triangles (equilateral, isosceles, right triangles, “special” right triangles), Polygons (quadrilaterals—like parallelograms, rectangles, squares, rhombuses and trapezoids—as well as other shapes), and Circles. You’ll be asked to find Perimeters, Areas, Interior and Exterior Angles, and lengths in Similar Triangles.
4) SOLID (3-D) GEOMETRY
The minute you see a question asking about “Volume” or “Surface Area” of a shape that’s in three dimensions, you’re in the realm of Solid Geometry. All of the solids that the ACT can test you on can be broken down into these three categories: Prisms, Pyramids, and Spheres.
5) COORDINATE GEOMETRY
Whenever any of the equations we’ve talked about (lines, inequalities, quadratics, polynomials, etc) find their way onto the Cartesian or Coordinate Plane, you’re technically doing “Coordinate Geometry”: think of it as graphing equations! Specifically, you’ll need to know about Graphing Lines, the Distance Formula, the Midpoint Formula, and graphing Parabolas. If you’re super advanced, you’ll ALSO need to know about graphing Circles, Ellipses and Hyperbolas in order to get a top ACT Math score.
6) Functions
The moment you see “F(x),” you know you’re dealing with a Function. Most of the time, they’re simply the equations you’ve already been using, but just with “F(x)” instead of the “y.” If you’ve never worked with Functions before, you’ll need to understand Function Vocabulary and basics, in order to nab a few extra points. If you already know what Functions are, you’ll need to brush up on Finding the Domain, Finding the Range, figuring out if a relation IS a Function in the first place, Composite Functions, Inverse Functions, and Transformation of Functions. If you’re targeting a perfect score, you’ll also need to know about Finding Asymptotes.
7) Trigonometry
For a very strong ACT Math score, you need to be familiar with the following Trig concepts so that you can correctly answer the four questions that’ll show up on the test: SOHCAHTOA (Sine, Cosine and Tangent ratios), Reciprocal Trig Ratios (Secant, Cosecant and Cotangent ratios), Graphing Trig Functions, The Law of Sines, and The Law of Cosines. If you’re aiming for a 36, you should also be familiar with Polar Coordinates. It’s not super likely you’ll be asked about it, but you might be.
8) STATISTICS, PROBABILITY and COUNTING
By Statistics, I’m referring to the concepts of Mean, Median, Mode, and Range. You’ll also need to know how to find the basic Probability of a given situation, as well as how to use Counting Principles, Permutations, Combinations, and Sets (think: Venn diagrams) to solve word problems!
9) MISCELLANEOUS ACT MATH TOPICS
There are MANY topics on the ACT Math Section that might not show up on every single test. Lots of these are very advanced math topics that you might not know yet. That said, on each test, a few WILL show up—you just won’t know in advance which topics they are. And if you want a perfect score, you’ll need to be prepared by familiarizing yourself with these: Imaginary Numbers, Complex Numbers, Compound Interest, Logic, Sequences and Series, Vectors, Matrices, and the Binomial Theorem!
Conclusion
Phew! Still with me?
But before you start feeling defeated about how much there is to learn, I’ve got good news: after over a decade of teaching this stuff and getting hundreds of exceptional scores (and “congratulations” letters from thir top college picks!) for my students, I finally wrote it all down in one punchy, digestible place. My ebook takes the guesswork out of things so that you can slam-dunk the ACT’s Math Section!
So, if you want to conquer ALL of the ACT Math topics I just mentioned—as well as use my expert ACT Math Cheat Sheets—you can purchase my ACT Math Cram Plan here.
Or, if you want to consult directly with an expert on the best ACT math tips and tricks for YOU, you can find out more about one-on-one sessions with me —and if I have availability—by contacting me here.
