Understanding the ACT Math Section – Questions, Strategies & More

About the ACT Math Section

In many ways, the ACT Math section is the most straightforward section on the whole test. It’s the one with questions that are most like those you’ve encountered in school. In addition, it’s the only section of the ACT where you can see your score improve simply by being in school and learning more math! Sure, there are strategies and tactics that can help you eke out a few extra points on this section, but it remains the most substantive section on the test. Nevertheless, to score well on the Math section, you first and foremost need to know how to do the math.

General Structure & Content

Officially, ACT Math questions are divided into two categories: Integrating Essential Skills (~40% of the test) and Preparing for Advanced Math (~60% of the test). The first category can be thought of roughly as the pre-algebra skills taught in middle school, and it includes basic arithmetic, percentages, ratios and proportions, averages, and very basic geometry formulas. The Advanced Math section is drawn from Geometry, Algebra 2, and Precalculus classes and includes the following content:

• Algebra — equation solving, word problem modeling, absolute value, inequalities, systems of equations; equation solving, word problem modeling
• Functions — function graphing and shifting; linear, quadratic, logarithmic, and exponential functions and models; rational functions; function graphing and shifting
• Geometry — area and volume relationships; similarity and congruence; Euclidean geometry of circles, triangles and other polygons; trigonometry; conic sections, including ellipses and hyperbolae
• Statistics & Probability — interpretation of data presented in various types of charts and graphs; distributions including standard deviation; probability rules for combined events;
• Numbers & Operations — real, rational, and imaginary numbers; rational exponents; vectors and matrices

In short, the ACT Math exam is more or less like a multiple-choice final exam in math that covers all middle and high school math up to and including precalculus. Its difficulty is not so much due to fts depth but its breadth. No one question is likely to be the most challenging question on the test you took in school on that particular topic, but by test day you’ll need to be prepped and ready for everything, all at the same time.

Here’s one other fact about how the Math section is put together: it’s the only section of the test that’s arranged in difficulty order. That’s super-helpful. On other sections, you don’t know where you’ll find the hard questions. On the Math section, you do. They’re at the end, so plan accordingly.

That planning, however, might look different for different students. All students should, of course, work carefully through the first thirty or so questions, being sure to pick up all the “easy” points they can. Students aiming for moderate scores should spend more time on the first half of the section than the second, since that’s where they will likely earn most of their points. Students aiming for much higher scores, however, will need to finish the first half in much less than half of the allotted time in order to finish all of the harder problems before time is called. That being said, some problems at the end of the test might be easy for you, especially if you’ve completed precalculus. A problem about expanding a logarithm or finding the period of a trig function will likely be at the very end, because it’s an advanced concept. But it might be a really straightforward question about that concept, so the question could still be fairly quickly answered and easy for you if you know what you’re doing.

ACT Math Problem-Solving Strategies

The math section is more about subject matter knowledge than any other section of the test, so preparing for the math section of the ACT will likely involve reviewing — and even relearning — concepts you’ve already seen. There’s no substitute for knowing the math, but there definitely are strategies that will help you to squeeze every point out of the math you already do know.

Strategy 1: Backsolving and Substituting Wisely

If you’ve done any test prep at all — even just looked through a book — you’ve likely come across the ideas of backsolving (testing the answers) and substitution (picking numbers and doing arithmetic instead of algebra). Those methods are nearly universal in the industry. Why? Because they work. Remember that this isn’t like a test in school. Your precalculus teacher isn’t grading your ACT. It’s not that you don’t have to show your work; it’s that you literally can’t show your work, but that doesn’t matter. The only thing that matters is whether you filled in the right little bubble. There are no style points on the ACT; nor is there any partial credit.

So, the best way to solve o problem is to do it the quickest and easiest way. If it’s a really easy problem, it will likely be most efficient to just do the two needed steps of algebra. After all, easy algebra is better than doing sometimes tedious number crunching with your calculator. Even if you’re an ace math student, though, it’s likely that algebra will let you down at some point on the ACT — especially at the very end. So, remember that alternate methods can serve as a super-effective Plan B when needed. After all, admittedly tedious number crunching is way better than blind guessing. So, before you put down a random guess, always ask yourself: “Can I just test the answers?” or “Can I pick any numbers to help me get started and understand what’s happening?”

Strategy 2: Utilizing Your Calculator and Your Pencil

Now, about that calculator of yours. It’s really great for calculations, but it’s really bad at algebra. It’s important to use the right tool for the right job on the ACT. Use your calculator for all the arithmetic on the test but use your pencil for writing out and setting up problems. Mental math is bad and mental algebra is even worse!! It’s not as though your math score comes with an asterisk because you “did all of the math in your head.” Don’t be a hero. Use your pencil and your calculator as often as necessary.

Many students push back on that and say that they are already pressed for time and don’t have any more to write out the steps. They’re wrong. The reason that many students run short on time is that they read problems or start calculating too quickly and make hasty errors. Then they must start over, laden with the mistaken impression that they’re doing a “hard” problem. It’s better to be careful and methodical, to write out all of the steps, and to correctly answer each question the first time. That’s how you finish the test in time. One analogy that works here is the fire drill. You likely have more fire drills in school than you care to remember. Right? What should everyone do when that bell rings? Bolt? No, that would bring chaos. You’d take wrong turns, fall down, then get up and turn around, and basically waste a lot of time and energy. It’s the same thing on the ACT. When it comes to answering questions on the test, slow can be fast.

Strategy 3: Having a Flexible Mindset

Given the amount of material covered on the Math section, even the most prepared students will likely run into a problem that makes them say, “Huh?” So, what do you do then? Students frequently employ loaded language, such as: “I don’t know what I should do,” or “What am I supposed to do here?” as though they were facing some kind of moral dilemma. What’s much more helpful is to ask yourself what you can do and then go with that. It doesn’t matter if you’re not sure where you’re going. That’s ok. Do something. Can you factor an expression? Isolate a variable? Draw or label a diagram? Write down a relevant geometry equation? Getting started helps. Staring at a two-by-three-inch black space typically doesn’t help you get to the “A-ha!” moment you’re hoping to have.

Take any step you can, and you’re likely closer to the right answer than you were before. If you’re like many students, though, you likely don’t feel comfortable doing math this way. Think back to the last math test you took and the hardest question on that test. You likely looked at it and said, “Whoa. That’s hard.” Then you thought about it for a while… and, hopefully, you figured out how to do it. Only then did you pick up your pencil and begin to write something down. Sound familiar? It’s ok; that generally works for most math classes in school, because you’re only being tested on a few related concepts that you’ve been thinking hard about for the last several weeks. You’ll need to adopt a more flexible mindset, however, in order to be successful on the Math section of the ACT.

Strategy 4: Answering the Right Question

Although the ACT is undeniably more straightforward than the SAT in terms of the way questions are asked, it’s still important to remember that wrong answers on this test are full of traps. In fact, the wrong answers are often right answers — but to the wrong question. Oh, shoot, Jim’s age? I answered Bob’s age! The fraction of students not in school? I answered the fraction of those that were in school! What’s x-2? I just answered x! Area? Perimeter. Radius? Diameter. The list goes on and on.

It’s going to be hard to get the right answer if you’re answering the wrong question, no matter how good you are at math. So, it’s worth being a little paranoid about this one. You might want to circle or underline the actual question within the question to make sure that you’re keeping your eyes on the prize. The test writers will also fill those wrong answer choices with intermediate answers that you might get along the way to the correct answer, so stay the course and make sure that you keep writing all of those steps — right until you get the final answer.

Strategy for Reaching your ACT Math Goals

As with other ACT sections, you should look to set reasonable, intermediate goals and be sure to use the appropriate strategies that will bring improvement from your current score. After all, the student who is looking to break 25 will be taking the test very differently from the student who is looking to achieve a perfect score.

Step 1: Getting to a 23 on the ACT Math

To get there, you’ll need to answer just over half of the questions correctly, and a vast majority of those will likely be on the first half of the test, so focus a majority of your efforts — and your time — on the first thirty questions. You’ll likely answer correctly another handful of questions on the second half of the test through pure guesswork, so you don’t need to perfectly run the table on the first thirty, but you should plan to get close to that mark. Focus on knowing the geometry formulas and basics of exponents and functions thar are most commonly tested by the ACT.

Step 2: Getting to a 28 on the ACT Math

To hit this mark, you’ll need to answer correctly almost three quarters of the questions. You had better answer correctly just about everything from questions 1-40. You’ll likely not have much time left at that point, so you’ll need to work strategically and pick your battles wisely, guessing where you must and saving your time for the later problems that you feel prepared to tackle. Many problems of intermediate difficulty that you’ll need to get right are very wordy, so keep practicing how to efficiently set up and solve those word problems.

Step 3: Getting to a 32 on the ACT Math

Your margin for error has now shrunk to between 5 and 10 questions. Since you’ll be answering all the questions, you’ll need more time for the second half of the test than the first half. Plan to rock through the first thirty in something like twenty minutes so that you have enough time to work through those harder problems at the end. Make sure that you’re prepared for all of the precalculus topics that are covered on the test, even those you haven’t seen yet in school — such as radians and the unit circle, laws of sines and cosines, logarithms, and conic sections.

Step 4: Getting to a 36 on the ACT Math

To get a perfect score on the ACT math, you’ll need to combine excellence of execution on the easier problems with a knowledge of the more esoteric math concepts that come up sporadically — perhaps only once in every few tests. Plan on doing lots of practice sections — focusing especially on the last 15 questions or so — and make sure that you clearly understand how to do every problem you’ve seen. The more types of problems you see before test day, the less likely you are to be surprised by anything you face on the test.

ACT Math vs. SAT Math

Between the ACT and SAT, the ACT is generally accepted to be the more straightforward yet speeded test. On the math section, the speeded part is true: students have substantially more time per question on the SAT. The straightforward part, however, will likely depend upon how much math you know since the ACT covers significantly more content than does. Both the SAT and ACT Math sections draw extensively from the standard algebra 1 and 2 curricula. The ACT, however, features a broader range of questions that students would most likely find in either geometry or precalculus. Although precalculus certainly isn’t a prerequisite for taking the ACT, students who expect the highest ACT scores, yet have only completed algebra 2, should expect to do some work and learn some new material before taking the test. Another major difference between the SAT and the ACT is that Desmos, the popular online graphing calculator, is integrated into the digital SAT app but ACT students must bring their trusty TI-84 graphing calculators. So, if you’re already either a Desmos pro or a TI expert, you might want to choose the test that allows you to best use your calculator skills.