Over the course of my thirteen years as an SAT and ACT expert, I’ve found that many of my private tutoring clients hit the same stumbling blocks when they’re studying for the math section of the ACT. And I know exactly why that is. Turns out there’s a disconnect between the math they’ve learned in their most recent high school courses…and the math that the ACT actually TESTS you on.
As you may know, U.S. schools tend to lay out the same Math path for most students, beginning in sixth or seventh grade. Here’s the typical order: Arithmetic/Pre-Algebra, Algebra I, Geometry, Algebra 2. For more advanced kids, 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? Well, by the time you’re starting to prep for the ACT—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 most recently learned about in school! See, the ACT doesn’t just expect you to remember what you’re working on this week in Math class…the test asks you to reach back to almost ALL of what you’ve learned from middle school until now! Furthermore, several questions might be way beyond what you’re currently learning…and of course, not all of the advanced topics you have studied will even show up on a given test. And to make matters worse, you won’t even have the fallback of a reference sheet of useful mathematical formulae to help you!
The result can be MASSIVE frustration for even the most earnest ACT-taker—and possibly a low score, too. That is, unless and until you figure out which math topics you need to bump the dust off of and update, which ones you need to simply remember from class…and which topics aren’t worth spending study time on, for you in particular.
Article Contents
1. Structure of the ACT Math Section
2. What is the format of questions?
3. Can you use a Reference Sheet?
B. 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
ACT Math Fundamentals
So, what are the magical math topics in question? The ones that you’ll ride like a surfboard to a perfect 36 out of 36 possible ACT Math points? 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 outline of the test.
1) Structure of the ACT Math Section
Math is the second section of the ACT. It has a straightforward structure: 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.
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 pattern, too: generally speaking, the questions on the Math section get harder as the test goes on:
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 slip up on 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 in a jiffy...IF you happened to have studied that VERY ADVANCED math topic, that is!
2) What type of questions does the ACT Math have?
This one’s easy to answer: 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. Odd, but we can work with that!
3) Can you use a Reference Sheet for the ACT Math?
Unfortunately, no. All those formulas about tangents and how to find the midpoint between two points….need to be written in your brain by test day.
4) Is it Good to Guess on the Math part of the ACT?
If you find yourself struggling to finish all 60 questions within the hour you’re allotted (for regular-time), yes, you’ll need a guessing strategy. Luckily, I’ve developed the best guessing strategy ever, and it’s free to you on my blog.
What Math Is Tested on the ACT?
The ACT powers-that-be say the test distributes its Math questions among sub-topics like so:
Pre-Algebra: 20-25% (14 questions)
Elementary Algebra: 15-20% (10 questions)
Intermediate Algebra: 15-20% (9 questions)
Coordinate Geometry: 15-20% (9 questions)
Plane Geometry: 20-25% (14 questions)
Trigonometry: 5-10% (4 questions)
However, this list is only part of the…equation (see what I did there?!). Because most parents and students *I* know are, understandably, not sure exactly what subject matter falls under the umbrellas of broad terms like “Pre-Algebra,” “Elementary Algebra” and “Intermediate Algebra.” Even I—a Math Olympian, math competition queen, and test prep expert for more than a decade!—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 >a dozen years of getting my private students to master these same topics and make incredible score improvements, 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 do well on 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. Knowing these will help you immensely 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 be well-acquainted with Percentage problems, like 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 mastered 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 moment you talk about “Volume” or “Surface Area” of a shape that’s in three dimensions, you’re talking about 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, determining if a relation IS a Function in the first place, Composite Functions, Inverse Functions, and Transformation of Functions. If you’re gunning for a perfect score, you’ll also need to know about Finding Asymptotes.
7) Trigonometry
For a top ACT Math score, you need to be familiar with the following Trig concepts so that you can nail 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 perfection, you should also be familiar with Polar Coordinates, on the off-chance there’s a question on it.
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
Deep breath…that was a LOT.
But before you get stressed about how much there is to learn, I’ve got good news: after over a decade of teaching this stuff and getting hundreds of fantastic scores (and college acceptances!) for my students, I finally wrote it all down in one concise, easy-to-read place. My ebook connects all the dots FOR you so that you can ace the ACT’s Math Section! If you want to conquer ALL of the ACT Math topics I just mentioned—as well as use my proprietary ACT Math Cheat Sheets—you can purchase my ACT Math Cram Plan here.
Or, if you want to get ACT math tips and tricks directly from me (and tailored for YOU!), you can find out how private tutoring with me works—and if I have availability—by contacting me here.
