The ACT Math Test is a 60-question, 60-minute test that covers topics from basic arithmetic to more evolved topics in trigonometry and statistics which reflect the work advanced students preparing for college would already have familiarity with and would have been recently working on in school.
Counter-intuitively, those students who are already deep in Calculus and Statistics by the time they take the ACT sometimes fumble on elements of the test during their initial practice tests because they’re doing such advanced math work.
No matter what level of math you’re currently exploring in high school, make sure you’re familiar with the math on the ACT before you take the official test.
Here’s an overview of what math is on the ACT:
The ACT strives to be true to its intention to assess your math background in early fundamentals and see if you’re ready for college level math–that means assessing that you’re ready for anything from College Algebra to Calculus I or Statistics, depending on where you’re planning to begin college.
The ACT calls this element of its test “Preparing for Higher Math,” and the topics included in this part of testing your college readiness take up just short of two-thirds of the math test.
Here’s what ACT.org says about Preparing for Higher Math:
“This category captures the more recent mathematics that students are learning, starting when students begin using algebra as a general way of expressing and solving equations.”
In other words, this is a fancy subsection that tests, basically, everything you learn in high school math.
Below, we’re going to break down the Preparing for Higher Math section using the same subtopics the ACT does in its official list, but we’ll reframe them to offer a simpler, more straightforward interpretation of the skills.
Here you’ll need to show that you understand both real and complex numbers and demonstrate an ability to reason using numbers in different forms, such as integers, rational numbers and irrational numbers.
The ACT organization has also added vectors and matrices to the number and quantity section. You’ll see that it doesn’t take up that much of the test (7-10%) but it still appears regularly, nonetheless.
You’ll need to know linear equations (y= mx + b) inside and out to be successful on the ACT. Every linear equation or polynomial expression falls into this category, as do the relationships between radicals and exponential expressions. Systems of equations and inequalities appear here, too.
There are some key additions to this group that I’ll talk about, some of the most recent and notable inclusions at the bottom of this post.
To be successful on the ACT you have to understand functions–what their notation means, how to interpret them, and how to manipulate them. “Questions may include, but are not limited to, linear, radical, piecewise, polynomial, and logarithmic functions,” according to the ACT on the same official skill list.
In other words, you’re going to see every single thing you saw in the Algebra portion, but this time in function notation, too.
Be sure to understand the rules of function when they’re graphed, too, like how to use the vertical line test and how to translate, as well as notate, shifted graphs of functions.
In short, you do not need to calculate standard deviation on the ACT, but you certainly will be better off if you understand it. You’ll also need a good foundation in mean, median, mode, and range, as well as have a firm grasp on “line of best fit.”
According to ACT.org, in the same document about math topics, you’ll also “apply and analyze data collection methods,” which we have yet to see on the ACT to the degree that it currently appears on the SAT, but it’s clearly coming.
Probability has also increased its presence on the ACT, and you’ll need to consider what happens when two events occur, when one event or the other takes place, when an event doesn’t take place, and conditions of replacement.
You’ll need to know how to use and apply formulas of geometry, many of which you’ll see listed in my previous article, What Formulas Are Given on the ACT? You’ll need to know all about triangles, four-sided figures, circles, and their variants as solids (volume, surface area, etc). While there isn’t an enormous amount of geometry on the ACT, it covers a broad gamut.
You’ll also need to know the graphs and formulas for parabola, ellipse, plotting circles, and hyperbola.
Basically, this is your opportunity to show off your comfortable flexibility with all things arithmetic, like working with prices, rounding, percentages, and number lines. The number and quantity section has also developed to encompass advanced topics.
The ACT considers these topics “concepts typically learned before 8th grade,” and, as I mentioned at the top of this post, these concepts are the ones that usually trip up higher level math students because these problems are so infrequently explored as standalone topics in classes like Pre-Calculus.
These aren’t just number crunching questions that use fractions and decimals, though questions like that do appear. Instead, these problems are designed to test students’ fluency in mathematics. Do you understand the relationships between numbers? Do you know advanced multiplication rules?
Most importantly, it’s key to understand that questions relying on these basics work themselves all the way into the very last math questions on the ACT. The questions are made more difficult to solve by including multiple layers and steps. Don’t overlook these topics.
A mathematical model is an expression or equation designed to represent something: the growth of something over time.
These models don’t actually get their own category of question; the idea of modeling and adjusting models is embedded into all the topics we’ve seen above. In testing modeling, the ACT tests students’ understanding that mathematics represents reality, that’s it’s another language we can use and manipulate to describe things we see or wonder about in the real world.
In this way, we can see that we won’t have questions “about modeling,” but that modeling on the ACT matters.
As the ACT evolves, so do the topics it focuses on. Listed above are some of the topics my students, my colleagues, and I have observed on recent tests.
Take note that a few of the topics here are listed in the official list of math topics, but I’m calling them out here because, frankly, the ACT glosses over them in its prep materials (provided by The Princeton Review, Kaplan, ACT Online, and others) and catches students off guard with how much it emphasizes them.
For starters, the official list of topics tends to gloss over the importance of trigonometry on the ACT, as well as the value of a firm understanding of radians and the unit circle.
If you’re taking the ACT in 2019 and beyond, you’ll also want to be particularly clear on permutations and combinations, probability, vectors, matrices, as well as arithmetic and geometric sequences.
You’ll want to be able to work with systems of equations that you develop from matrices, as well as work with proofs and identify asymptotes–even though these topics don’t appear with much frequency on prep materials from even a few years ago.
Again, be sure to check out my list of formulas you should never take the ACT without knowing in my article, “What Formulas Are Given on the ACT?” Good luck!