Posted on: October 28, 2020

**ACT Math Overview**

In many ways, the ACT Math section is the most straightforward section on the whole test — it’s the one with questions most like those you’ve encountered in school. In fact, your approach to the Math section is more influenced by what classes you’ve taken in school than is any other section. And it’s the only section of the ACT that improves simply by your being in school and learning more math! Sure, there are strategies and tactics that can help you eke out some extra points on this section, but it remains the most substantive section on the test. 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 pre-algebra skills taught in middle school and include basic arithmetic, percentages, ratios and proportions, averages, and very basic geometry formulas. The advanced math is drawn from Geometry, Algebra 2, and Precalculus classes and includes the following content:

**Algebra**— equations solving, modeling word problems, absolute value, inequalities, systems of equations**Functions**— function graphing and shifting; linear, quadratic, logarithmic, and exponential functions and models; rational functions**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; analyzing 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 math final exam that covers all middle and high school math up to and including precalculus. It’s difficult not so much for its depth but for its breadth. No single question would be the most challenging on the test you took in school on that particular topic, but you need to be prepped and ready for everything, all at the same time, on test day.

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 the hard ones are. On the Math section, you do. They’re at the end, so plan accordingly.

But that planning might look different for different students. All students should, of course, work carefully through the first thirty questions or so, being sure to pick up all the “easy” points they can. Students aiming for more moderate scores, however, should spend more time on the first half of the section than the second, since that’s where they’ll be earning most of their points. Students aiming for much higher scores, however, will need to finish the first half in much less than half the time in order to finish all 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 quick and easy for you if you know what you’re doing.

**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 are definitely strategies to help you squeeze every point out of the math you already do know.

**Backsolve and Substitute 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 near universal in the industry. Why? Because they work. Remember that this isn’t 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. It 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 do a problem is the quickest and easiest way. If it’s a really easy problem, it’s likely most efficient to just do the two 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 the methods can serve as a super-effective Plan B when needed, since 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?”

**Your Calculator and Your Pencil**

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 like your math score comes with an asterisk because you “did all math in your head.” Don’t be a hero. Use your pencil and your calculator as often as you need to.

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

**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? I often hear students employ loaded language like, “I don’t know what I *should* do,” or “What am I *supposed to* do here?” as if it’s some kind of moral dilemma or something. What’s much more helpful is to ask yourself what you *can* do and then go with that. It’s 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 looking for.

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 the test. You likely looked at it and said, “Woah. 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 they’re testing only a few related concepts that you’ve been thinking hard about for the last several weeks. But you’ll need to adopt a more flexible mindset in order to be successful on the Math section of the ACT.

**Answer the Right Question**

While the ACT is undeniably more straightforward than the SAT in terms of the way questions are asked, it’s still important to remember that the wrong answers on this test are full of traps. In fact, the wrong answers are often right answers — just 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 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 you’re keeping your eyes on the prize. The test writers will also fill those wrong answer choices with intermediate answers you might get along the way to the correct answer, so stay the course and make sure you keep writing all those steps right until you get your final answer.

**Strategy for your ACT Math Goals**

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

**Getting to a 23 on the ACT Math**

You’ll need to answer just over half the questions right, 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 get another handful of questions right on the second half of the test through pure guessing, so you don’t need to perfectly run the table on the first thirty, but you should plan to get close. Focus on knowing the geometry formulas and basics of exponents and functions most commonly tested by the ACT.

**Getting to a 28 on the ACT Math**

Now you’ll need almost three quarters of the questions right. You better be answering just about everything correctly from 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 intermediate difficulty problems you’ll need to get right are very wordy, so keep practicing how to efficiently set up and solve those word problems.

**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. 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 you’re prepared for all the precalculus topics covered on the test, even those you haven’t seen yet in school: radians and the unit circle, laws of sines and cosines, logarithms, and conic sections.

**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 perhaps only once in every few tests. Plan on doing lots of practice sections — especially the last 15 questions or so — and make sure 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 see.