SAT / ACT Prep Online Guides and Tips

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.

Recent Posts

Complete List of FREE SAT Math Practice Problems

Posted by Courtney Montgomery | Jun 13, 2020 12:00:00 PM

SAT Math

Need to study for the SAT Math section but don't know where to start? On a budget, too? Not to worry! In this article, we've put together a comprehensive list of all the best (and free!) SAT Math study materials and guides currently available online.

Note: For info on the best SAT study materials you have to pay for, check out our picks for top SAT prep books.

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The Ultimate SAT Math Prep Guide: Tips, Formulas, and Practice

Posted by Courtney Montgomery | Mar 20, 2020 12:00:00 PM

SAT Math

It's entirely possible to train for the SAT Math section. The more you understand how it works, the better you'll perform on test day. Here, we'll give you absolutely everything you'll need to know to master SAT Math.

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The Basic Guide to Integers on ACT Math

Posted by Courtney Montgomery | Feb 28, 2020 3:30:00 PM

ACT Math

"Let $x$ and $y$ be integers such that ..."

"If $y$ is a positive integer, what is ... ?"

If you've taken the ACT or an ACT practice test, these types of math questions might look familiar to you. You've likely come across several questions on the ACT that mention the word "integer." And if you don't know what this term means, these problems will be difficult to solve.

Questions involving integers are common on ACT Math, so it's important to have a solid grasp of them as you prepare for the test. What are integers and how do they fit into the larger ACT Math picture?

This article will be your guide to basic integers for the ACT, going over what they are, how they change, and how you'll see them used on the test. For the more advanced integer concepts, including absolute values, exponents, roots, and more, refer to our advanced guide to ACT integers.

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The 15 Hardest SAT Math Questions Ever

Posted by Courtney Montgomery | Feb 26, 2020 3:00:00 PM

SAT Math

Want to test yourself against the most difficult SAT math questions? Want to know what makes these questions so difficult and how best to solve them? If you're ready to really sink your teeth into the SAT math section and have your sights set on that perfect score, then this is the guide for you.

We've put together what we believe to be the 15 most difficult questions for the current SAT, with strategies and answer explanations for each. These are all hard SAT Math questions from College Board SAT practice tests, which means understanding them is one of the best ways to study for those of you aiming for perfection.

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Complete List of FREE ACT Math Practice Questions

Posted by Courtney Montgomery | Feb 1, 2020 12:00:00 PM

ACT Math

Whether you're on a budget or just want to see what kinds of ACT Math study materials you can access for free, you've come to the right place. Though the internet is chock-full of ACT resources of dubious quality, we've collected and put together only the highest quality free ACT Math study material available.

So let's jump right in!

Note: For guides and reviews of the best for-pay ACT study, check out our list of ACT study links, which includes all official practice tests, and our top picks for ACT prep books.

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The Easy Guide to the 30-60-90 Triangle

Posted by Courtney Montgomery | Jan 23, 2020 6:02:00 PM

General Education

Acute, obtuse, isosceles, equilateral…When it comes to triangles, there are many different varieties, but only a choice few that are "special." These special triangles have sides and angles which are consistent and predictable and can be used to shortcut your way through your geometry or trigonometry problems. And a 30-60-90 triangle—pronounced "thirty sixty ninety"—happens to be a very special type of triangle indeed.

In this guide, we'll walk you through what a 30-60-90 triangle is, why it works, and when (and how) to use your knowledge of it. So let's get to it!

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The 28 Critical SAT Math Formulas You MUST Know

Posted by Courtney Montgomery | Jan 20, 2020 12:00:00 PM

SAT Math

The SAT math test is unlike any math test you've taken before. It's designed to take concepts you're used to and make you apply them in new (and often strange) ways. It's tricky, but with attention to detail and knowledge of the basic formulas and concepts covered by the test, you can improve your score.

So what formulas do you need to have memorized for the SAT math section before the day of the test? In this complete guide, I'll cover every critical formula you MUST know before you sit down for the test. I'll also explain them in case you need to jog your memory about how a formula works. If you understand every formula in this list, you'll save yourself valuable time on the test and probably get a few extra questions correct.

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How to Improve Reading Comprehension: 8 Expert Tips

Posted by Courtney Montgomery | Jan 18, 2020 10:48:00 AM


Reading is a skill many people take for granted, but the act of reading and properly comprehending a text is a complex and interactive process. It requires several different brain functions to work together and most often requires one to puzzle through multiple layers of context and meaning.

Because reading comprehension is so complicated, we can often find ourselves understanding the most basic interpretation of a text, but missing the emotional core or the "big picture." Or we might just find our brains spinning with no clue at all as to what a text is attempting to convey.

But luckily for everyone who struggles in English classes, on standardized tests, or in daily life, reading comprehension can be improved upon (and it's never too late to start!). In this guide, I explain step-by-step how to improve reading comprehension over time and offer tips for boosting your understanding as you read.

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Probability Questions on ACT Math: Strategies and Practice

Posted by Courtney Montgomery | Jan 14, 2020 4:00:00 PM

ACT Math

What is the probability that you’ll toss a coin and get heads? What about twice in a row? Three times? Probability questions ask you determine the likelihood that an event or any number of events is to occur, and the more you practice, the better your odds will be at mastering these types of questions on the ACT (see what we did there?).

This will be your complete guide to probability on the ACT—how probability works, the different types of probability questions you’ll see on the test, and the steps you’ll need to take to solve them.

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Triangles on SAT Math: Geometry Strategies and Practice Problems

Posted by Courtney Montgomery | Dec 27, 2019 5:00:00 PM

SAT Math

Triangle questions account for less than 10% of all SAT math questions. That being said, you still want to get those questions right, so you should be prepared to know every kind of triangle: right triangles, isosceles triangles, isosceles right triangles—the SAT could test you on any one of them. Since triangle problems only account for a small percent of the SAT math questions, you shouldn’t spend all of your study time on triangles.

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Algebra Functions on ACT Math: Lesson and Practice Questions

Posted by Courtney Montgomery | Dec 23, 2019 10:30:00 AM

ACT Math

Functions. Just hearing the word is enough to send some students running for the hills. But never fear! Though function problems are considered some of the more challenging questions on the ACT, this is only due to the fact that most of you will be far more used to dealing with other math topics (like fractions, exponents, or circles) than you are functions.

On the ACT, question difficulty is categorized by how familiar you are likely to be with any given question, and the only way to combat this challenge is to practice and get used to dealing with questions that are a little less familiar to you. You will generally see 3-4 function questions on any given ACT, so for those of you who are not yet comfortable with functions (or just want a tune up), this guide is for you.

This will be your complete guide to ACT functions. We'll walk you through exactly what functions mean, how to use, manipulate, and identify them, and exactly what kind of function problems you'll see on the ACT.

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How to Guess Strategically on SAT Math

Posted by Courtney Montgomery | Aug 18, 2019 9:00:00 AM

SAT Strategies, SAT Math

The SAT doesn't give any penalties for incorrect answers, so you should always guess on a section, including the Math section. But guessing requires strategy, especially if you're hoping to get a high (or even perfect!) SAT Math score.

In this guide, we’ll go through how to guess strategically on SAT Math and show you examples of it in action.

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SAT Math vs ACT Math: What's the Difference?

Posted by Courtney Montgomery | Jun 16, 2019 2:00:00 PM

SAT versus ACT, ACT Math, SAT Math

Which is better/easier/faster—the SAT Math section or the ACT Math section? How does each stack up over the course of the entire test? Most importantly, which math section is right for you?

We’ll break down both the similarities and differences in this SAT Math vs ACT Math guide and help you decide which standardized test suits you better.

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Lines and Slopes in SAT Math: Geometry Strategies

Posted by Courtney Montgomery | May 16, 2019 4:00:00 PM

SAT Math

In our SAT guide to lines and angles, we dealt with parallel lines, perpendiculars, and the many different ways to find angle measures with two or more lines. Now, we’ll look at the other aspect of lines, namely their slopes and equations.

This will be your complete guide to lines and slopes—what slopes mean, how to find them, and how to solve the many types of slope and line equation questions you’ll see on the SAT.

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Guide to ACT Calculators: Expert Tips

Posted by Courtney Montgomery | May 12, 2019 11:00:00 PM

ACT Math

Knowing when where and how to best use a calculator on the ACT can be tricky. You are allowed to bring a calculator on test day (none will be provided for you), and it can mean the difference of several points on the ACT to have a calculator versus having none.

But what kind of calculator should you bring and how should you make best use of it during the test? In this guide, we’ll cover everything you need to know about calculators on the ACT, from when you're allowed to use them, to what kinds are allowed, to how to avoid the most common ACT calculator mistakes.

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