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Unlike the SAT, the ACT does not provide you with a list of basic math formulas to rely upon at the beginning of the ACT math test. This means you will need to be able to recall math formulas on the ACT. Below you will find lists of "Must Know" ACT math formulas, "Good to Know" formulas, and "Bonus" formulas to commit to memory for the ACT! Learn them all, then check out our list of ACT math topics to begin applying them!

Must-Know ACT Math Formulas

Though the ACT tests different concepts on each exam, there are popular topics that come up again and again. This list contains the best ACT math formulas to know. For more practice, try Magoosh ACT prep.

Average

S/T (Average = Sum/Number of things)

Lines

1. Slope intercept form:

y = mx + b (where m is the slope and b is the y-intercept)

2. Slope

Triangles

1. Area of a triangle:

1/2bh (1/2 base x height)

2. Pythagorean Theorem

Quadrilaterals

1. Perimeter of a rectangle:

2l + 2w (where l is the length and w is the width)

2. Area of a rectangle:

lw (length x width)

3. Volume of a box:

lwh (length x width x height)

4. Surface area of a rectangular solid:

2lw + 2wh + 2lh

5. Diagonal in a rectangular solid

Apply the Pythagorean theorem twice or

Circles and Spheres

1. Area of a circle:

2. Circumference of a circle:

3. Volume of a sphere:

Cylinders

Trigonometry

1. SOHCAHTOA:

sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent

2. You should also know your quadrants and where sine, cosine, and tangent are positive or negative:

Probability

1. Probability:

Number of desired outcomes / number of total outcomes

2. Factorials (e.g. 8!):

To find the factorial of any integer, multiply it by every positive integer below it, e.g.:
8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

Bonus: the "Must Know" math formulas on the ACT also appear in your high school math classes. So, you're really studying for two things at once. Nice.

Bonus bonus: Check out the video below to watch ACT expert Kristin discuss 6 of the must-know ACT math formulas in greater detail:

ACT Formulas that are Good to Know

Volume and Area

1. Volume of a cone:

2. Volume of a pyramid:

3. Area of a trapezoid:

(Add the bases, divide by two, then multiply by the height.)

Logarithms

1. Definition:

2. Change of base rule:

Triangles

1. 30-60-90 Triangle Ratio:

2. 45-45-90 Triangle Ratio:

Additional Formulas

1. Equation of a circle:

2. Arithmetic sequences:

3. Geometric sequences:

4. Exponential Growth Formula:

Where P = principal (starting value), r = rate of growth, n = number of months, t = time in years, and A = new amount.

Bonus Things to Know

1. Quadratic Equation:

Often, you will be better off applying a strategy such as backsolving to solve a complicated algebra problem, but if you are comfortable with the quadratic equation, keep it in the back of your mind.

2. Permutations:

3. Combinations:

An Important Note About ACT Math Formulas

Occasionally, an ACT math problem may rely upon a more advanced formula, such as the surface area of a sphere. In these cases, the question itself will typically provide you with the formula you need. So no need to think you need to memorize everything. However, being able to recall basic formulas will ensure you can tackle problems that don't provide a formula with confidence! The list below includes formulas for the concepts the ACT tests most frequently.

Important ACT Math Formulas to Know (PDF)

Sometimes it's easier to memorize formulas by studying a little bit every day. To make this easier, we created a printable Magoosh ACT Math Formulas PDF. Here's the link where you can get your copy.

Let us know if you have any questions about these ACT formulas. 🙂

About Kristin Fracchia

Dr. Kristin Fracchia makes sure Magoosh's sites are full of awesome, free resources that can be found by students prepping for standardized tests. With a PhD from UC Irvine and degrees in Education and English, she's been working in education since 2004 and has helped students prepare for standardized tests, as well as college and graduate school admissions, since 2007. She enjoys the agony and bliss of trail running, backpacking, hot yoga, and esoteric knowledge.

Magoosh blog comment policy: To create the best experience for our readers, we will approve and respond to comments that are relevant to the article, general enough to be helpful to other students, concise, and well-written! :) If your comment was not approved, it likely did not adhere to these guidelines. If you are a Premium Magoosh student and would like more personalized service, you can use the Help tab on the Magoosh dashboard. Thanks!
Image Credit: hotmath.com and getmathhelp.jimdo.com

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32 ACT Math Formulas - What to Absolutely Study [PDF]

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The ACT Math Test doesn't give you a list of the math formulas to know on the exam. So, it's up to you to memorize the math formulas on the ACT. Our free PDF can help. Download it, print it out, and study a little bit every day.

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Let's break down exactly what the Math section of the ACT consists of. There are 60 total multiple-choice questions taken from six areas of math: pre-algebra, elementary algebra, intermediate algebra, coordinate geometry, plane geometry, and trigonometry. Thus, the scoring and what math formulas you need to know breaks down like this:

Pre-Algebra / Elementary Algebra: 24 Questions, 24 Points

Intermediate Algebra / Coordinate Geometry: 18 Questions, 24 Points

Plane Geometry / Trigonometry: 18 Questions, 24 Points

Here's the thing about the ACT math section: even with all the ACT math test prep you did, the ACT doesn't give you a cheat sheet with all the math formulas written down on them. Therefore, it's up to you to memorize them. But some critical ACT math formulas are required more frequently than others. These are the must-knows. While it might be tempting to just make a guess and move, it's better if you're prepared from the get-go.

Let's take a look at the most important formulas per section.

Pre-Algebra / Elementary Algebra

These formulas involve basic math and algebra. In other words, it requires the student to solve for an unknown variable.

1. Arithmetic mean (average) = Sum of values / Number of values

Specifically used to calculate the mean value of a given set of numbers.

For example: (10 + 12 + 14 + 16) / 4 = 13

2. Probability = Target outcomes / Total outcomes

Specifically used to calculate the chances of something occurring from a set of possible outcomes.

For example: A jar contains five blue marbles, five red marbles, and ten white marbles. What is the probability of picking a red marble at random?

5 / 20 = .25 or 25%

3. Quadratic Formula: x = −b ± √b²-4ac/2a

Specifically used for determining the x-intercepts of a quadratic (parabolic) equation.

For example: A = 1, B = -4, C = 4

Intermediate Algebra / Coordinate Geometry

These formulas help calculate distances, lengths, and properties of points on a plane, as well as solve for variables in more complex algebraic expressions.

4. Distance Formula: d=√(x₁ - x₂)² + (y₁ - y₂)²

Specifically calculates the distance between two points on a coordinate plane.

For example: Find the distance between points (6, 6) and (2, 3)

5. Slope Formula: Slope = y₂ - y₁ / x₂ - x₁

Specifically calculates the slope (angle) of a line that connects two points on a plane.

For example: Coordinates = (-2, -1) (4, 3)

6. Slope Intercept: y=mx+b

Formula that defines a line on a plane, given a known slope and y-intercept.

For example: Slope = 2, Intercept point (0,3)

7. Midpoint Formula: (x₁+x₂) / 2, (y₁+y₂) / 2

Specifically calculates the midpoint between to points on a plane.

For example: Find the midpoint between (-1, 2) and (3, -6)

Plane Geometry

Formulas for calculations attributes of geometric shapes within a plane and solving for variables based on the angles of a given shape (trigonometric identities).

8. Area of Triangle: area = (1/2) (base) (height)

Specifically calculates the total area within a triangle based on the lengths of the sides.

For example: Base = 5, Height = 8

9. Pythagorean Theorem: a²+b²=c²

Used specifically to calculate the length of an unknown side of a right triangle, given two sides are known.

For example: a = 3, b = 4

10. Area of Rectangle: area = length x width

Calculates specifically the total area within a rectangle shape.

For example: length = 5, width = 2

11. Area of Parallelogram: area = base x height

Specifically calculates the total area within a parallelogram.

For example: base = 6, height = 12

12. Area of Circle: π * r²

Calculates specifically the total area within a circle.

For example: radius = 4

13. Circumference of Circle: circumference = 2π * r

Calculates specifically the length of the outline of a circle.

For example: radius = 7

Trigonometry

Continues with the previous plane geometry section.

14. Sine (SOH): Sine = opposite / hypotenuse

A trigonometric identity that represents the relative sizes of the sides of a triangle and can also be used to calculate unknown sides or angles of the triangle.

For example: opposite = 2.8, hypotenuse = 4.9

15. Cosine (CAH): Cosine = adjacent / hypotenuse

A trigonometric identity that represents the relative sizes of the sides of a triangle and can also be used to calculate unknown sides or angles of the triangle.

For example: adjacent = 11, hypotenuse = 13

16. Tangent (TOA): Tangent = opposite / adjacent

A trigonometric identity that represents the relative sizes of the sides of a triangle and can also be used to calculate unknown sides or angles of the triangle.

For example: opposite = 15, adjacent = 8

Other Tips

Of course, there are more formulas that might pop up on the ACT, but these ones are the most common. Therefore, they're the most critical to know. Memorize these formulas, study, practice, and you'll be just fine come test day.

Additionally, make sure you get a good night's rest before and prep what you need the night of instead of the morning. There's also no need to cram the night before; instead, relax! Cramming doesn't work, and it's also a better use of your time to take a breather.

Good luck!

Check how your ACT scores affect your acceptance odds with College Raptor!

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16 Critical Math ACT Math Formulas You NEED to Know -- College Raptor

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Let's break down exactly what the Math section of the ACT consists of. There are 60 total multiple-choice questions taken from six areas of math: pre-algebra, elementary algebra, intermediate algebra, coordinate geometry, plane geometry, and trigonometry.

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We have several challenging tests for your ACT Math practice. The Math test on the ACT has 60 questions which must be answered within 60 minutes. It is designed to measure the mathematical skills that students typically acquire by the end of the 11th grade. The questions are multiple choice, and in order to answer them you will need to know basic formulas, computational skills, and reasoning skills. You may use a calculator as long as it doesn't have a built-in computer algebra system. Start your test prep now with our free ACT Math practice!

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We have several challenging tests for your ACT Math practice. The Math test on the ACT has 60 questions which must be answered within 60 minutes. It is designed to measure the mathematical skills that students typically acquire by the end of the 11th grade.

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ACT Test Taking Skills and Tips_CrackACT.com

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Rather than relying solely on heavy ACT prep books to get you ready for your exam, you can lighten your load by moving your ACT prep online. You'll find lots of resources on everything from test content and key strategies to high-quality practice questions. And the best part is that most of these resources are free!

This guide will go over the best test prep websites you should be using if you're aiming to ace the ACT. But first, a word on the perspective I have when it comes to ACT websites.

Disclaimer: How ACT Websites Can Help You

You might be wondering how objective a guide from an online ACT prep company can be about recommending other online ACT resources. To give full disclosure, I personally think PrepScholar has the most insightful and relevant ACT guides available online.

We delve into every aspect of the testing process, such as choosing your test dates, understanding the scoring process, knowing exactly what's on each section, and using time-saving comprehension strategies to maximize your scores. We also take a holistic approach to test prep, keeping in mind that every student has different goals and schedules and can come from any grade in middle school or high school.

That being said, there are several other websites that are important to explore and learn from as you prep for the ACT. Rather than limiting yourself to one source of information, you can best prepare yourself and boost your scores by taking advantage of all free online ACT resources.

This guide is meant to help you find the best ACT websites for the following:

Logistics, such as choosing your test dates and registering for the test

Understanding the content and format of the test

Learning strategies

Locating the highest-quality practice questions that will get you ready for the ACT

First, let's take a look at the official ACT website and the parts of it that are most useful to you.

Official ACT Website

The official ACT website is where you'll register for the ACT. Here, you'll create an account with a username and password, and then upload a photo of yourself.

Besides test dates and registration, the ACT website offers a useful overview of accommodations, what to take with you on test day, and college and financial planning. Since you can find more in-depth information about most of these areas elsewhere, I'd say the most useful part of the ACT website for test prep is its official sample questions for the English, Math, Reading, Science, and Writing sections.

After you create an ACT account, you gain access to additional, helpful study resources. For instance, you can take advantage of the ACT Question of the Day, which can be useful to start early and study a little at a time. The site also offers a useful ACT study guide in both English and Spanish.

If you don't mind spending a bit, you can also purchase the ACT Online Prep Program for $39.95. This program has lessons in English, Reading, Math, and Science; it also has two full practice tests (different from the ones in The Official Guide to ACT Prep 2019-2020) and sample essays. It offers some degree of personalization and keeps track of your progress, so you know what you've studied and what you still need to review.

Practice questions from ACT, Inc., are extremely useful since as they are official questions directly from the test makers and thus the truest representation of what you'll encounter on the ACT. However, they're not updated very often, and the website has a relatively small number of ACT practice questions available for free. I recommend answering these only after having done some other prep first as a way to gauge your level and figure out what you still need to improve.

Another drawback of these ACT practice questions is that your answers are evaluated after each page; this format doesn't simulate the timing or pacing of the actual ACT. And it turns out, getting used to the format of the test is important to earning that perfect score!

Ultimately, the ACT website is useful for general information and the limited number of practice questions it offers, but you'll want to look elsewhere for test strategy. Since the ACT doesn't want to give away test-taking secrets or strategies for seeing through their tricks, the official site is not going to offer much in the way of this kind of guidance. So what other sites can you use to find strategy as well as additional high-quality ACT practice questions?
These are the best sites for drawing up your ACT game plan.
Best ACT Websites for Strategy

If you've searched for ACT resources online, you've probably noticed that there are a lot more sites devoted to the SAT than the ACT. Even though the ACT is just as popular among students, the test-prep resources don't seem to have quite caught up yet. That's why you'll often search for ACT vocabulary and get referred to lists of obscure SAT vocabulary words, or try to find ACT Questions of the Day only to realize they're not all that specific to the test.

In terms of ACT-specific content and strategy guides, I believe that PrepScholar far outstrips the competition in its level of detail and authenticity. As we'll discuss more below, though, you can also find some helpful strategies for ACT Reading, English, and Writing on Erica Meltzer's blog, The Critical Reader, and learnabout the purpose of the ACT and the approaches you can take through SparkNotes.

PrepScholar offers a wide variety of in-depth guides with specific, realistic ACT examples. We break down exactly what's tested on each section and give you suggested study schedules to help you manage your time as well as strategies for guessing. What's more, we customize our advice to make it relevant to students of all grade levels and with all different target scores and schedules.

Here are some of our especially helpful guides that break down exactly what's tested on each section of the ACT:

While these guides offer some strategy along with explanation of ACT content, you can find others that are specifically oriented toward teaching you strategies and helping you master the test:

In offering you these links, our hope is that all students will have access to the resources they need to succeed in high school and achieve their post-secondary goals. We also welcome comments and emails and try to respond to your questions and input as soon as possible.

If PrepScholar's approach resonates with your ACT goals and learning style, then you should check out our ACT prep 5 day free trial. This gives you access to the full ACT prep program. At the end of the five days, you can call it a day or choose to sign up for the rest of the test prep program.

The best way to make the most of these ACT guides is to try out the strategies they suggest using sample problems and timed practice tests. You can then determine which ones best help you comprehend the material in a deep and efficient way.

Erica Meltzer posts helpful, though sometimes short, blog posts about the Reading, English, and essay sections of the ACT. They are accessible and offer tips and tricks beyond what you would find on the official ACT website.

Some particularly helpful posts include the following:

Reading both this blog and PrepScholar's guides will expose you to different strategies so you can determine which ones work best for you. For instance, Meltzer suggests that students read entire passages before answering questions, which is not necessarily the advice we give for reading ACT passages. By exploring content across various sites, you can learn more than one approach and customize the advice to best fit your learning style and needs.

One quick note about Metzer's site before we move on: you'll quickly realize that The Critical Reader offers tips for more than just the ACT. It can be hard to find the ACT resources, so be prepared to do a little digging to search for what you need!

If the ACT were better served online, then SparkNotes might not have made the list as an especially useful ACT website. Since there aren't many resources for ACT strategy, though, I think SparkNotes is worth looking over for its descriptions of the test and strategies about answering questions and saving time.

Like PrepScholar, SparkNotes encourages students to set target scores and shape their study plans around meeting their individualized score goals. This site is useful for an initial reading about ACT content and strategy. Once you finish reading it, you can then move on to other ACT websites to get more specialized advice with more specific examples from the test.

Since there aren't too many specific examples given on this site, you'll have to seek out practice problems and apply the strategies yourself. That leads us to perhaps the most important part of online test prep: where can you find all the good practice questions?

ACT Websites for Practice Questions

As we discussed above, the official ACT website offers free sample questions for each section, an essay question, and scored sample essays. While official practice questions are the best ones for test prep, there are a lot of high-quality practice questions from well-known test-prep companies. These sites are a good start for finding free online (both official and unofficial) ACT practice questions.

Our convenient guide lets you download and print all official ACT practice tests along with their answer keys. These are real tests administered in past years, so they're exactly like what you'll see on test day!

Once you've printed out a practice test, find a quiet room and time yourself as you take it. After you finish, go back and analyze your strengths and weaknesses.

You can also check out our free five-day trial for our ACT prep program to access tons more practice questions.

This prep website lets you download four free, official ACT practice tests with answer keys (these are the same tests we've compiled above). Once again, try to simulate testing conditions to get a sense of time management and the real test experience. You should also pay close attention to how ACT questions are worded and arranged.

Since there are no answer explanations here, you'll have to try to analyze your own mistakes and figure out what your errors in reasoning are for any questions you get wrong.

Unlike the official practice tests you'd have to print and score yourself, Varsity Tutors offers free ACT questions you can do online and get automatically scored. These questions are helpful for reviewing concepts and reinforcing content knowledge but less so for gaining familiarity with how actual ACT questions are structured and worded (since they're not official practice questions).

Varsity Tutors also offers free diagnostic tests for the ACT. These are shorter, condensed versions of the ACT designed to help you quickly identify areas where you need to study the most. A diagnostic test can be a great tool to help you study smarter, even if you have to go elsewhere to find more robust study tools.

Even though Khan Academy's test-prep videos are mainly for the SAT, they contain plenty of advice you can apply to the ACT as well. Check out our guide to using Khan Academy for ACT prep to learn exactly how to use this resource.

Khan Academy has numerous videos explaining different math, science, and reading subjects, and many people find that they learn more from watching a video compared to just reading. Try Khan Academy out to see whether it's a good ACT prep resource for you.

Overall, although the ACT is not as well served online as the SAT is, you can still find a number of good resources for test-taking strategy and practice questions in the form of both official tests and practice questions. But what else should you do to make the most of these resources and get prepared for the ACT?

How to Use ACT Websites Effectively

First off, to best use the official ACT website, you'll want to create an account by filling out your personal information and uploading a photo. Make sure to write down your username and password since you'll be creating a lot of online accounts during the college process and don't want to find yourself locked out of your account!

When it comes to PrepScholar's guides, Erica Meltzer's blog, and the other sites discussed above, start by visiting them and checking out the resources. Once you figure out which sites have the materials you need, you can start studying.

Also, don't be afraid to use social media to your advantage! There's an official ACT Student Twitter account, and you can follow PrepScholar on Twitter and Facebook or subscribe to our newsletter for helpful test-prep and college-admissions information.

One site I didn't mention for test prep is College Confidential, since it's not exactly a test prep site. This useful forum lets you discuss test prep and the college process and gain a sense of community among both students and parents. By sharing your questions and stories, you can get valuable insight and support as you work toward achieving your ACT goals.

Above all, I highly recommend searching for and trying out strategies that you think will work best for you. Unfortunately, the official ACT website doesn't publicize many strategies that'll give you an edge on the test.

There are many valuable approaches you can use as you prep for the ACT. Make sure to explore these online resources and figure out what works best for you so that you can achieve your best ACT scores!

What's Next?

The guides on ACT strategy I mentioned above are just a few of the guides PrepScholar offers-and that we're continually adding to every day. Browse more guides on general strategies for taking the test and ones specific to Math, Science, English, Reading, and the essay.

You can also learn more about the exact content and format of each ACT section, such as how much science you actually need to know to master the ACT Science section.

Are you wondering when you should sign up to take the ACT for the first time? This guide describes the most important considerations to help you choose the best test date for you.

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The Best ACT Prep Websites You Should Be Using

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Rather than relying solely on heavy ACT prep books to get you ready for your exam, you can lighten your load by moving your ACT prep online. You'll find lots of resources on everything from test content and key strategies to high-quality practice questions. And the best part is that most of these resources are free!

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Your ACT test score can range between 1 and 36 in each of the four mandatory testing areas. These four scores are averaged together for a composite ACT test score. When people ask you for your ACT test results, they are usually referring to this composite amount and the national average is about 21.

If you choose to take the optional writing test, you will be given an essay prompt with 40 minutes to compose your essay response. This score appears as a writing test subscore of between 2 and 12. The ACT test, like the latest version of the SAT exam, imposes no penalty for guessing.

Your ACT test score report will contain a number of other informative scores. There are figures that tell how many correct answers the student got out of the highest number possible. Also, your subscores on each test will be placed on a number line that contains a bar labeled ACT Readiness Range. This way, you will be able to tell where your subscore falls in terms of scores that show readiness for college-level study.

Also included in the score report is an estimated STEM (Science, Technology, Engineering, and Math) benchmark rating. This is shown to help students plan college and career paths. This benchmark is a result of your combined scores on the Math and Science portions of the ACT test.

Even more career-planning information is given to the student in the report by the way of Career Connector summaries and Interest-Major Fit data. These scores are established through student responses given during registration about interests and experience.

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