# SAT / ACT Prep Online Guides and Tips

Understanding how to do your best on the ACT math section means understanding how the math section is structured and where you can get the most points for your time and energy.

We’ll walk you through how each ACT math section is organized and how you can use this information to your benefit, both in your studies and as you take your official ACTs.

## ACT Math Organization

The ACT math section is ordered in two main ways—by difficulty and by content. Let's look at each.

### Math Organization Type 1: Difficulty

Of the two organization categories, the biggest factor that determines the order of questions is difficulty level. "Difficulty" on the ACT math questions is characterized by: the time necessary to solve a problem, the steps required, how many math concepts you must employ, and/or how familiar or unfamiliar you are likely to be with the material. And the difficulty level increases over the course of the math test.

You can generally split the difficulty of ACT math problems into three even zones. There are 60 math questions total and you can arrange them roughly like so:

• Questions 1-20 — "easy"
• Questions 21-40 "medium"
• Questions 41-60 "hard"

The reason we put these terms in quotes is due to the fact that these breakdowns are approximately true, but not everyone will have the same concept of "easy" or "hard" when it comes to math problems. The difficulty of any particular problem will depend on your experience with the topic, how well you understand the phrasing of the question, or even your level of fatigue and concentration at the time. But splitting the ACT math section this way works as a rough guideline for most students.

In general, with each new tier of difficulty, the questions will take longer to solve and often require more steps. For instance, it might take you as little as 10 seconds to solve question number 3, but take as many as a two or three minutes to puzzle over question 55. (Note: we will talk more about how you can balance your time per question later in the guide.)

### Math Organization Type 2: Content

Because “difficulty” is partially determined by how well you’re likely to know the material (based on the typical middle and high school curriculum), this follows that the test is also ordered, in part, by topic. The more years you’ve spent studying a math topic, the more likely that you are to consider a particular question “easy.”

Though the topics mix and mesh with one another, there are still overarching patterns of where you are most likely to find your algebra questions or your trigonometry problems. Because you’re likely to have seen and studied single variable equations for more years than you've studied trigonometry, you’ll see more of your algebra questions early on in the test and more of your coordinate geometry and trig questions later in the test. So most of the algebra questions will be "easy" (though not all) and most of the geometry and trig questions will be "medium" or "hard" (though, again, not all).

The ACT is a standardized test, so each test will look very similar. We have broken down one ACT math test (test code 67C) by math topic to demonstrate this pattern in action.

 1 Algebra 31 Plane and Solid Geometry 2 Algebra 32 Numbers 3 Algebra 33 Coordinate Geometry 4 Numbers 34 Coordinate Geometry 5 Algebra 35 Numbers 6 Algebra 36 Coordinate Geometry 7 Algebra 37 Plane and Solid Geometry 8 Algebra 38 Plane and Solid Geometry 9 Algebra 39 Coordinate Geometry 10 Plane and Solid Geometry 40 Plane and Solid Geometry 11 Plane and Solid Geometry 41 Coordinate Geometry 12 Algebra 42 Trigonometry 13 Numbers 43 Numbers 14 Algebra 44 Coordinate Geometry 15 Numbers 45 Plane and Solid Geometry 16 Numbers 46 Plane and Solid Geometry 17 Plane and Solid Geometry 47 Plane and Solid Geometry 18 Numbers 48 Plane and Solid Geometry 19 Numbers 49 Algebra 20 Plane and Solid Geometry 50 Coordinate Geometry 21 Algebra 51 Coordinate Geometry 22 Trigonometry 52 Coordinate Geometry 23 Numbers 53 Algebra 24 Coordinate Geometry 54 Algebra 25 Algebra 55 Algebra 26 Numbers 56 Plane and Solid Geometry 27 Plane and Solid Geometry 57 Trigonometry 28 Coordinate Geometry 58 Numbers 29 Algebra 59 Algebra 30 Coordinate Geometry 60 Numbers

As you can see, the math topics are mixed in with one another, but there are some distinct patterns.

Questions 1-30 are more algebra and numbers heavy (70% of the questions), while questions 31-60 are more geometry and trig heavy (67% of the questions). This pattern will hold true for any given ACT.

The difficulty of questions may increase as you go, but if you take it one step at a time, you'll soon be scaling to the top.

There is no guessing penalty on the ACT, so your goal is to answer as many questions as accurately as possible across the board. Of course you are also on a strict time crunch, so this is not always easy.

Depending on your current scores (and your target scores), this may mean that you focus most of your time and energy on a particular section of the test and then blindlyor, time permitting, strategicallyguess the rest of your questions. (Note: for more on how to guess to your best advantage, check out how to guess on the ACT math section). For others, your score goals may mean that you look at at and attempt every single question.

There will, however, be a general step-by-step guideline to follow for students scoring at all levels. So let's break it down.

### Step 1: Take a Full Practice Test

Taking a practice testa full practice test!is always step one when embarking on any kind of study plan for a standardized test. You won’t truly know where you currently stand or how to specifically improve from there without first taking a practice test. And though you may be concerned specifically with your math score right now, that score fits into the larger test-taking picture. The ACT lasts for several hours at a time, and your levels of concentration and fatigue will fluctuate. So only by taking the full test will you be able to see how your math score fits into your overall ACT score.

Try to emulate the structure of the real test as much as possible, so carve out a few hours on a weekend and take the full practice test in a quiet environment. Here, you can find free full ACT practice tests and answer keys

### Step 2: Set a Target Score Goal

Now that you’ve taken your practice test and scored the results, check out how your scores currently stack up and set yourself a target score goal. This will be the score that you aim to reach by test day, and both your current scores and your progress towards this goal will determine how you go about your studying.

### Step 3: Find the Patterns in Your Right and Wrong Answers

Now take a look at all your wrong answers and see if you can spot any patterns to the errors. Are you mostly getting wrong answers in a particular section, like questions 25 - 35 or 45 - 60? Are you mostly getting questions wrong by topic (do those triangle problems throw you for a loop no matter where they are on the test)?

Let's look at the different types of errors by location and by content and see which apply to your current test scores.

Different types of location errors include:

• Errors spread fairly evenly throughout the math test (so about as many wrong answers in questions in the first 20 questions as the last 20).
• Errors clustered in pockets. Usually, these occur around questions 25-35 and questions 40-50 because this is where the test transitions difficulty levels.
• Errors mostly contained in the "medium-high" and "high" difficulty ranges of questions 45-60.

Now look over your math test and see if you can identify the questions according to topic. How did your right and wrong answers sync up with specific ACT math topics being tested? Tally how many questions on each topic were on the test and how many questions you answered correctly for each topic. (So if questions 15 and 29 were sequence questions and you answered number 15 correctly and 29 incorrectly, give yourself a score of \$1/2\$ in sequences.)

Often, student errors will be a combination of location and topic, so don’t be alarmed if this is the case.

Write down on a separate piece of paper:

1. The location of most of your errors

2. Your personal "score" by math topic (e.g., \$3/6\$ in lines and angles, \$4/4\$ in statistics, and so forth.)

### Step 4: Brush Up on the Most Important Content

The big-picture goal when studying for the ACT is the maximize your score gain for every hour spent studying. This means that the best strategy for success is to focus your time and energy on places you can make the easiest (and, therefore, quickest) improvements and areas where you can make the most improvement. So let's divide and conquer.

Making Quick Improvements

Each and every question on the ACT is worth one point. It doesn't matter if it was the easiest question on the test and took you all of three seconds to solve, or if it was the hardest question on the test and took three minuteseach question is worth the same amount of points as every other question. This means you should maximize your time and energy by picking up any points you're missing in the first half of the test (which, you'll remember, is the "easier" half of the test). This will net you a point increase in the shortest amount of time.

So if you’re missing five or more questions in the 1-30 range, take a close look at each of your wrong answers. This is about 17% or more of the "easy" half of your test, so see if you can look at your errors and identify whether or not you’re missing these questions based on a lack of knowledge of the content. If so, it’s time to brush up on some of your algebra and numbers topics.

If, however, you’ve taken a look at your errors list and seen that you're mostly missing questions in the later half of the test based on both difficulty and content, it’s time to more specifically hone your focus.

Making the Most Improvement

Let’s say you can organize your current mathematical knowledge into four categories: perfect understanding, good understanding, okay understanding, and no understanding.

Because we're looking to now gain the most improvement from your time, the first step is to focus on improving your "okay" areas. These are areas you have some familiarity with, but aren't the strongest in, and just a quick refresher on the topic can gain you tremendous point value for your time. Our individual math topic guides will take you through the know-how on each and every ACT math topic you need to brush up on. In each, you'll gain a greater understanding of the topic in question as well as how you'll see it presented on the ACT, as well as get a chance to practice on real ACT math problems.

After you've brought these "okay" topics up to speed, the next step is to look at improving your "no understanding" topics. These are areas where you have a current weak foundation and so will represent the greatest potential leap and improvement in your score. (Again, our math topic guides will help you improve your knowledge of each and every ACT math topic you'll see on the test.)

Because this might be difficult to visualize right now, let's take a sample score breakdown of the test by topic.

Let’s say that there were six questions each on four different topics—exponents, circles, lines and slopes, and trigonometry—and your score breakdown of correct answers looked like this:

Exponent questions: 5 out of 6

Circle questions: 2 out of 6

Lines and slope questions: 4 out of 6

Trigonometry questions: 0 out of 6

If we classify each of these topics by your understanding, we would say that you had a “perfect” (or nearly perfect) understanding of exponents, “good” understanding of lines and slopes, an “okay” understanding of circles, and “no understanding” of trigonometry.  Now that you've cataloged your scores, you know which topics to target your study focus on and in which order.

To start with, the next step would be to focus and brush up on your “okay understanding” areas (in this case circles). Although rehashing your near-perfect knowledge might make you feel productive, it won’t actually help you all that much at this moment. Until you start getting “perfects” or nearly perfects in all topics across the board, it’s better to spend your study time on areas where you can make the greatest improvement. In this case, honing your knowledge of exponents would only gain you one more point out of 60. Your time can be better spent elsewhere.

You may also be tempted to perfect those “good” understanding areas (in this case lines and slopes). But the difference between “good” understanding and “perfect” is likely to only be a question or two out of 60. In this case, you would get a maximum return of 2 points, which is not nothing, but you can spend the same amount of time studying circles and probably get a higher point return for that time. Again, only focus on getting your good scores up to perfect once you’ve brought up your scores on all your topics and you’re aiming for that perfect ACT math score.

Now if you bring your “okay” areas up to almost perfect, you will likely be able to gain a significant point increase. In this case, if you spend your study time learning your circle material, you could potentially increase your score by 3 or 4 points.

Once you’ve brushed up on your “okay” understanding areas, set your sights on those “no understanding” math topics. The reason these topics are in “no understanding” purgatory is likely because it is a topic that you dislike or that you haven’t studied much in school. But, despite this, even a little more understanding of the topic than you have now will likely gain you a few more points than you had before.

In addition, bringing up your “okay” understanding and “no understanding” areas will allow you to use your imperfectbut still significantknowledge of the ACT math topics in question to strategically eliminate answer choices. Even if you don’t actually know how to solve the problem, knowing a little more about the topic than you do now will give you a much better foundation to strategically eliminate answer options and guess for your right answer.

Your study time is precious and limited, so distribute it wisely and use it to gain the most point return for your energy. An hour spent brushing up on unfamiliar topics will gain you a much more significant point increase than an hour spent brushing up on topics you already understand almost perfectly.

### Step 5: Develop Your Own Personal Timing Plan for the ACT Math Section

One of the hardest aspects of the ACT math section is the fact that you must keep track of your pacing yourself. You are given 60 minutes and 60 questions to do with what you will, so taking too long on some questions will leave you with no time at all to solve others. And yet going too quickly through the test can lead you to make careless errors.

Everyone's pacing and ability to solve questions on a time crunch will be different, and yours may even change from test to test as you get used to ACT questions and the pacing involved. So take the time as you study to develop your own personal timing structure and adapt it as you need to.

A good plan to start with is to break the test into thirds and give yourself varying time limits for each section. So begin by giving yourself:

• 15 minutes for questions 1-20
• 20 minutes for questions 21-40
• 25 minutes for questions 41-60

Now this may not be the perfect timing structure for you, but it's a place to start. See how you need to adapt it to your own personal preferences by experimenting. And if you find that you're simply running short on time no matter what you try, check out our more specific advice on how to stop running out of time of the ACT math section

As you go through your studies, we recommend that you take at least two to three practice tests, evenly distributed across your study time. So, if you have three months to prep, take a practice test about once a month. This will give you not only the chance to practice the best simulation of the real ACT possible, but will also show you how well and in which areas you’re improving. Your study plan will adapt based on your current scores, your score goals, and your rate of improvement.

Current Score is 25 or Under

If you’re currently scoring in the 25 or under range, your goal is to turn yourself into a “jack of all trades, master of none” type of mathematical warrior. If you already have a “perfect” understanding of any given math topic, great! If not, don’t worry about it right this second. Try your best to get yourself up to “okay” or even “good” understanding of each topic before you start mastering any particular one.

As you go through your list of "okay" and "no understanding" topics to improve your knowledge of each, focus first on the topics that come earlier in the test, since most of the questions will be "easy" or "medium" difficulty. So if you have an "okay" understanding on both an algebra topic and a coordinate geometry topic, start by bringing up your knowledge of the algebra topic first. If your knowledge base in each topic is relatively similar, then always start by improving your algebra and numbers topics first, then turn to plane and coordinate geometry, and finally trigonometry.

We have compiled all of our math guides by topic as well all the free ACT math practice you can find online. No matter where you're struggling, we'll help get you up to speed on where you need to be before test day.

Current Score is 26 and Above

Only once you start getting into the 26 and above range should you work on perfecting all of your math topic knowledge as much as possible. At this scoring level, you’ve probably already achieved at least a passing understanding of all the math topics on the test, so now is the time to master them to the best of your ability.

Look to the types of questions and math topics you missed the most questions in and start by focusing your attention there. Again, areas in which you can make the greatest improvement will be the best focus of your time and energy.

And just as you would in the 25 and under range, check out our math topic guides for definitions of each topic, ACT math strategies to solve the questions on each topic based on how you’ll see them on the ACT, and practice questions with answer explanations. Practice and more practice is the way to go when attempting to master an ACT math topic.

Be sure to also test yourself against the most difficult math problems on the test to see where you currently stand against the toughest of the tough and where you can improve.

Deep breaths, clear head. Though it may all seem overwhelming right now, you are entirely capable of mastering the ACT. (John Henderson/Flickr)

## The Take-Aways

Understanding how the ACT math test is structured and how to use that knowledge to your best advantage while studying is a good chunk of the battle won already. The key to mastering the ACT math section is a combination of understanding and practice, and you’re well on your way already.

Your study plan should always be a reflection of your current standing and your target goals, and should adapt as you make progress. Study smart and work with the structure of the test instead, and you’ll see improvements in your scores in no time.

## What’s Next?

Stuck on your ACT math problems? Check out our guide to learn how to spot when you're going down the wrong path and how to correct the course

Stuck procrastinating? Learn how to turn your studying around and overcome your desire to procrastinate

Looking to get a perfect score on the ACT math section? Our guide (written by a perfect-scorer) will help you get those high scores you've been aiming for

Want to improve your ACT score by 4 points?

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Courtney Montgomery

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.

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