Now that you’ve gathered together all your ACT math study materials, it’s time to put together a plan of attack. Having the right study materials is key, but understanding how to use them to their best effect is just as important. (What good is a tool wielded improperly, after all?)
We’ve put together a comprehensive plan on how to make use of your ACT math study materials and boost your math score. We’ll walk you through how to best use your math practice problems and how to make the best study plan possible to prepare yourself for test day.
Importance of Using Proper ACT Study Materials
Before we talk about how to use your study material, it’s important to make sure you have the best material possible from which to work. Unfortunately, the internet is teeming with “ACT study materials” of questionable quality, and using this material as a resource is more likely to hinder you than help you.
Using poorly designed study material will give you a false sense of how you’ll do on the real ACT (whether better or worse), which is not helpful for your study time and test prep. The most accurate and highest quality study material will come from ACT, Inc. itself. After that, only prep programs that use and truly base their questions off this material are worth your time.
We have gathered together all the best free ACT study material and practice problems, so definitely start there for all your ACT math practice problem needs.
Ready, set, let's go!
How to Begin — Identifying Your Current Strengths and Weaknesses
Before you tailor your study plan to your needs, you must first find your current strengths and weaknesses by running a diagnostic on your current performance.
Step 1: Take a Practice Test
If you haven’t taken one already, start by taking a full practice test. This will give you the best sense of your current projected score and percentile rank. Though you may be more focused on improving your math score right now, you will still need to take a full test so that you can best replicate a real testing environment.
Not only will taking a full test show you your current strengths and weaknesses, but it will also show you how your math scores fit into your larger testtaking picture. The ACT is a marathon, and your scores will fluctuate depending on your energy and concentration levels over the course of the entire test. So you’ll only get a full picture of your current levels per topic if you take the complete test all together.
This is a baseline, so be honest. Only then will you be able to tell where you’re starting and how far you have to go. So take it as you would the real test, adhere to the timing rules and don’t stop and look things up. As you go through, make sure to also mark your test—put a mark any time you feel unsure about a question and cross out any eliminated answer options. This will help you to identify patterns in your overall testtaking later.
Step 2: Examine Your TestTaking Patterns
Once you’ve corrected your practice test, look at your spread of right and wrong answers. Are there any patterns to the distribution?
There are two general ways to categorize your mistakes: by location on the test and by content. If you can organize your errors accordingly, it will help you understand why you're missing questions and make a study plan to address your weaknesses.
The ACT math section is 60 questions, and they are arranged in ascending order of difficulty, which means that locationspecific errors are generally errors due to difficulty.
To spot patterns of locationbased errors, ask yourself whether you are:

Missing questions over the entire math section, seemingly evenly throughout?

Missing several questions in the 120 range? (Though it is normal to miss some or even several questions on the overall ACT math section, try to carefully analyze and improve upon your mistakes in this range. The earlier questions will be the quickest and "simplest" to solve and so will net you a nice cushion of points if you can grab them.)

Missing questions in a cluster around the 3040 marker? (This is where the test transitions from "easy" to "mediumlevel" difficulty and that transition can trip many students up.)

Missing questions mostly in the 4060 range? (This is the transition from "medium" to "mediumhigh" difficulty.)

Missing questions mostly in the 5060 range? (This is the "highest" difficulty range and so is tough for the vast majority of students.)
You may also be getting questions wrong by topic. Though math topics on the ACT tend to cluster in certain locations (for example, more algebra questions appear at the beginning of the test than they do at the end), you will also find each topic scattered throughout the test (more on this in our ACT Math question distribution guide). As such, you must look at each of your errors closely in order to see if there is a topicspecific pattern to your errors.
To spot trends in content errors, ask yourself whether you are:

Getting all or most questions wrong in a particular topic, no matter where the questions are located in the test? (E.g., are you missing all triangle questions, whether they are appear as question 5 or question 50?)

Getting questions wrong by topic only in the medium or high level difficulty? (For instance, can you solve "easy" slope questions, but miss all the "difficult" slope questions?)

Having a seemingly even spread of right and wrong answers by topic throughout the test? (If you answered questions 12 and 48 on functions correctly, but missed question 20, it may have less to do with your understanding of functions as a topic and more to do with the phrasing of the question or the speed at which you were taking the test. Take a careful look at each problem to see if you can spot the pattern.)
The less familiar you are with a particular math topic, the harder it will be to answer the variety of problems on it that you’ll see on the ACT. Take a look at our individual math guides for topicspecific help and practice questions for any of your ACT math topic problem areas.
Most people will start out their ACT practice by missing a combination of locationspecific and topicspecific questions, so don’t worry if your pattern starts out this way too. As you get more and more used to both the material and the way the ACT tests this material, you’ll narrow your range of wrong answers and increase your accuracy in both fields.
Step 3: Make a List of Your ACT Math Strengths and Weaknesses
Now that you’ve looked at your testtaking patterns, make a list on a separate piece of paper of all the math topics in which you missed questions. (For reference, we have put together a complete list of ACT math topics.)
In addition to the topics missed, make a list of the types of errors you made. Why do this? There is a big difference between types of errors on the ACT math test—not knowing how to approach a question at all is very different than misreading a question. You’ll need to examine exactly what kinds of errors you’ve made so that you can learn to avoid them in the future.
 Finding the wrong variable or final value

This is one of the most common errors, especially on problems where you must find an "unusual" final answer. For instance, the problem may ask you to find the value of x + y for your final solution, when your natural instinct is to find the value of x or y alone.

 Misreading the question

This can include misreading any value or variable in the overall question or simply misreading what the question is asking you to do. For example, in a word problem, did you mix up "Andy" and "Amelia"? Did you read "subtract" as "square"? It is easy to make assumptions or to mix up similar words if you're going too quickly through your problems.

 Stopping your solve too early or too late

In a problem that requires multiple steps, you may accidentally find yourself stopping a step or two too early or going a step or two too far. For instance, if you need to find the 10th number in a sequence and you're counting by hand, you might accidentally find the 9th or 11th number in the sequence instead. Many answer choices are generated by this type of error, so be extra cautious in only taking the exact number of steps necessary.

 Running out of time

If you run out of time in the math section, you will likely start making several errors either because you didn't have time enough to solve the question properly or you didn't even have time to look at the question.

 Not knowing how to approach the question at all

Whether it's the wording of the question or the math topic involved, sometimes you'll find yourself completely flummoxed. You may not know how to set up the solve to the problem in the slightest, or you may try and fail to set up the solve. Either way, this is a problem that you simply don't know how to approach.

 Mixing up or forgetting your formulas
 You will NOT be given any formulas, so it can be easy to misremember or mix up your formulas in your head if you aren't vigilant. If you need to find the area of a circle, make sure you're using the area formula and not the circumference formula.
Note: don’t take “careless errors” like misreading the question lightly! It is easy to think that you wouldn’t make such an obvious mistake next time, but don’t underestimate the effects of adrenaline and exhaustion on your thinking patterns. With practice and diligence, you can avoid making these kinds of mistakes, but you must dedicate yourself to being very careful. Always double check to make sure your answer matches exactly what the test is asking you to find.
Got all your ducks in a row? Excellent!
How to Proceed — Using ACT Math Practice Questions to Raise Your Score
Now that you’ve got your baseline, how do you use your practice material to raise your score? Let’s take a look.
#1: Take a look at your list of strengths and weaknesses and brush up on those math topics that lie in your weak zone.
If you’re simply unfamiliar with a particular math topic, then practicing problem after problem isn’t going to help all that much. You would never walk into French 4 without taking French 1, and math is exactly the same. So don’t dive off the deep end of polygon problems if you’re unfamiliar with their basic principles.
For every topic on the ACT, you must first understand both the ins and outs of the particular math topic as well as how you’ll see it tested on the ACT. Our ACT math guides are tailored to reflect and demonstrate how each topic is presented on the ACT, so you won’t have to waste time reading and memorizing more strategies and facts than you absolutely need to.
By studying the topic first (before diving right into all your practice problems), you’ll also keep your practice problems “fresh.” It’s no use throwing yourself against a wall of function problems if you’ve never studied functions in school—it will only leave you with no new material to study from once you’ve brushed up on how to actually solve function problems.
Once you’ve refreshed your understanding of a math topic and learned what you need to learn, you can use your practice problems solidify the knowledge in your head and get you to where you need to be by test day.
#2: When you do find practice questions, always try to solve them yourself first without looking to the answer.
If you look at a problem and then look straight to the answer, you are not really solving the problem. The answer explanation might make sense to you and even make you feel as though you would have been able to solve the problem on your own, but this feeling can be deceiving.
Solving a puzzle yourself and understanding how a puzzle was solved require two entirely different parts of your brain. Always (always!) try to solve a problem yourself first and commit to an answer choice, before you look up the final answer.
Remember—you can only improve if you have an accurate picture of your current skill level.
#3: Once you’ve brushed up on the topic, take practice problems in multiples at a time, as if you were truly working on the test.
As you go through your practice questions, don’t solve questions one at a time and stop to look up the answer after each one (e.g., solve, stop to look up answer, solve, stop to look up answer, solve, stop, etc.). This kind of pacing does NOT give you an accurate picture of how you’ll do on test day and can hamper your progress. (Remember: you won’t be able to verify whether your answers are correct or not on testday—you simply have to do your best and move forward on multiple questions at a time.)
Even if you don’t always sit down to take a full test or a full math section at once, it is still better to answer two or three questions at a time and look up your answers at the very end than it is to simply answer one.
#4: If you can use multiple solving methods on a problem, try all the different ways so that you can find the one most comfortable for you.
Many ACT math questions can be solved in a variety of ways. Plugging in answers and plugging in numbers are strategies that work for many different types of math questions, but there are others as well. For instance, systems of equations questions can be solved by graphing, subtraction, or substitution, while sequence, polygon, and distance questions can be solved via formulas or by working them out by hand.
These are just a few examples and each of our guides will go into further detail. The point remains that most every ACT question is purposefully designed to be solved in multiple ways and different methods work best for different people.
Once you’ve finished solving your set of problems, go back and solve them again using a different strategy. Compare this to the first time—which method did you like better? Which was faster? Which made you feel the most confident in your answer?
#5: Pace yourself (and your practice questions)
Though it may be tempting to get your studying out of the way, do NOT cram all your studying in one go! Improvement happens over time, and you must pace yourself to get the most out of your prep time.
In addition, if you blow through all your practice problems at once, you will not have anything else to work with fresh. Again, solving a puzzle yourself and understanding how a puzzle was solved are two very different concepts, so try to pace out your fresh material and your review material so that you can use both parts of your brain in your study prep.
#6: Sign up for a testprep program if you feel you need more material than the free practice questions available.
If you feel you’ve exhausted your free study material, then definitely sign up for a testprep program or buy one of the official study guides available, like the Real ACT Red Book. Not only can a prep program provide you with additional material, but can also help you make the most out of your study time.
Our ACT study program at PrepScholar automatically targets your areas of strength and weakness and tailors your studying to you and your needs. No need to assess your patterns yourself—we’ll do all the work for you!
And don't underestimate the power of a good nap after you're done studying.
The TakeAways
The ACT is unlike most tests you’ll ever come across—it is long, comprehensive, and very specifically designed. Going into it blind (or poorly prepared) is difficult and rarely goes well. The more you can prepare, and the higher quality that preparation is, the better you’ll do.
So make sure your study material always comes from the best sources and that you use this material to its absolute best effect while studying. Your goal is to train your brain to look at and solve puzzles in the way that the ACT wants you to, and most people can only do so with focused effort and practice.
But always keep in mind too that the ACT is designed to be an achievable and trainable test. With the right practice, it is absolutely possible to succeed and get the scores you want. Once you know how to hone your focus and target specific areas to study, you’ll be mastering ACT math questions in no time.
What’s Next?
Now that you've looked at your ACT testtaking patterns, check out our individual ACT math guides to help you brush up on any topic that was less familiar to you.
Running out of time on the ACT math section? If you found that you didn't have enough time to finish your ACT math section, check out our guide for how to beat the clock and maximize your ACT math score.
Unsure about your ACT math formulas? Make sure you've memorized your most important formulas and then check out how to use that knowledge to its best effect.
Looking to get a perfect score? Our guide to getting a perfect 36 on ACT math will help get you to where you need to be.
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Courtney scored in the 99th percentile on the SAT in high school and went on to graduate from Stanford University with a degree in Cultural and Social Anthropology. She is passionate about bringing education and the tools to succeed to students from all backgrounds and walks of life, as she believes open education is one of the great societal equalizers. She has years of tutoring experience and writes creative works in her free time.