SAT / ACT Prep Online Guides and Tips

If you thought the ACT was a big fan of circles, then brace yourself for its absolutely shameless love of triangles. In one breath, you may be expected to find the various dimensions of an obtuse triangle, and the next, an isosceles right triangle. ACT triangle problems will be as numerous as they are varied, so make sure you familiarize yourself with all the different types before test day.

This will be your complete guide to ACT triangles--the types of triangles that will show up on the ACT, the formulas you’ll need to know to solve them, and the strategies you’ll need to apply when approaching a triangle question. We’ll also break down real ACT math problems and give you the walk-throughs on how to most efficiently and effectively tackle any and all triangle problems you come up against.

If it's always been a dream of yours to shift around graphs and points on the $x$ and $y$ axes (and why not?), then you are in luck! Points, graphs, and shapes can be manipulated in the coordinate plane to your heart's content. Want to scoot that triangle a little to the left? Flip it? Spin it? With reflections, rotations, and translations, a lot is possible.

This will be your complete guide to rotations, reflections, and translations of points, shapes, and graphs on the SAT—what these terms mean, the types of questions you'll see on the test, and the tips and formulas you'll need to solve these questions in no time.

If you’ve already tackled your single variable equations, then get ready for systems of equations. Multiple variables! Multiple equations! (Whoo!) Even better, systems of equations questions will always have multiple methods with which to solve them, depending on how you like to work best.

So let us look not only at how systems of equations work, but all the various options you have available to solve them.

This will be your complete guide to systems of equations questions—what they are, the many different ways for solving them, and how you’ll see them on the ACT.

Reflections, rotations, translations, oh my! Whether you’re dealing with points or complete shapes on the coordinate plane, you can spin 'em, flip 'em, or move 'em around to your heart’s content. And, often enough, you’ll be asked to do so on the ACT.

This will be your complete guide to rotations, reflections, and translations of points, shapes, and graphs on the ACT—what these terms mean, the types of questions you’ll see on the test, and the tips and formulas you’ll need to solve these questions in no time.

A series of numbers that follows a particular pattern is called a sequence. Sometimes, each new term is found by adding or subtracting a certain constant, sometimes by multiplying or dividing. So long as the pattern is the same for every new term, the numbers are said to lie in a sequence.

Sequence questions will have multiple moving parts and pieces, and you will always have several different options to choose from in order to solve the problem. We’ll walk through all the methods for solving sequence questions, as well as the pros and cons for each. You will likely see two sequence questions on any given SAT, so keep this in mind as you find your perfect balance between time strategies and memorization.

This will be your complete guide to SAT sequence problems--the types of sequences you’ll see, the typical sequence questions that appear on the SAT, and the best ways to solve these types of problems for your particular SAT test taking strategies.

Statistics questions on the ACT are often simpler than the statistics questions you have seen in class. Most all of the statistics questions on the ACT boil down to finding or manipulating means, medians, and modes of a set of numbers.

If you are already familiar with these terms, you will have a good head-start on these types of problems. But even if you aren't familiar with these terms, most of ACT stats questions require that you understand and apply just a few key concepts (all of which we will go through in this guide).

This will be your complete guide to ACT means, medians, and modes—what they mean, how you'll see them on the test, and how to solve even the most complicated of ACT statistics questions.

25 to 30% of the SAT math section will involve geometry, and the majority of those questions will deal with polygons in some form or another. Polygons come in many shapes and sizes and you will have to know your way around them with confidence in order to ace those SAT questions on test day.

Luckily, despite their variety, polygons are often less complex than they look, and a few simple rules and strategies will have you breezing through those geometry questions in no time.

This will be your complete guide to SAT polygons—the rules and formulas for various polygons, the kinds of questions you’ll be asked about them, and the best approach for solving these types of questions.

One of the ACT’s absolute favorite shapes is the circle (or at least we assume so, given how often circles show up on the test). You will not be given any formulas on the ACT, so you’ll have to know and memorize the ins and outs of how circles work before test day. And, considering how often circles show up, mastering circle problems is definitely in your best interest.

This will be your complete guide to ACT circles, including areas, circumferences, degrees, arcs, and points on a circle. We’ll take you through what these terms mean, how to manipulate and solve for various aspects of a circle, and how to tackle the most difficult ACT circle questions you may see on test day.

Knowing your lines and angles is crucial for mastering SAT and is one of the foundational steps of geometry. Before you can tackle some of the more complex multi-shape problems that often appear towards the end of the test, you'll need to know just how to solve for all your missing angle measures. 

Almost without fail, there will be exactly two problems on any given SAT on lines and angles (note: these problems are distinct from questions on lines and slopes). Though this is a small percentage of the test in and of itself, line and angle knowledge provides the backbone for other geometry problems and so should be ranked high on your studying priorities. 

This will be your complete guide to lines and angles on the SAT—what they are, how you'll see them on the test, and how to solve these types of questions to maximize your points on test day.

You’ve dealt with the basics of coordinate geometry and points (and if you haven’t already, you may want to take a minute to refresh yourself) and now it’s time to look at the ins and outs of lines and slopes on the coordinate plane.

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 ACT.

Single variable equations are some of the most common types of problems on the ACT math section. You must know how to set up, use, and manipulate these kinds of equations, as they are a foundational element of mathematics upon which more complicated expressions (multiple variable, quadratics, etc.) are based.

So make sure you are prepared to tackle the ins and outs of single variable equations (no matter how they are presented on the ACT), before you take on some of the more complicated elements of ACT math.

This guide will be your complete walk-through of single variable equations for the ACT--what they are, how you’ll see them on the test, and how to set up and solve them.

Fractions and ratios (and by extension rational numbers) are all around us and, knowingly or not, we use them every day. If you wanted to brag over the fact that you ate half a pizza by yourself (and why not?) or you needed to know how many parts water to rice you need when making rice on the stove (two parts water to one part rice), then you need to communicate this using fractions and ratios.

In essence, fractions and ratios represent pieces of a whole by comparing those pieces either to each other or to the whole itself. Don’t worry if that sentence makes no sense right now. We’ll break down all the rules and workings of these concepts throughout this guide--both how these mathematical concepts work in general and how they will be presented to you on the ACT.

Whether you are an old hat at dealing with fractions, ratios, and rationals, or a novice, this guide is for you. This guide will break down what these terms mean, how to manipulate these kinds of problems, and how to answer the most difficult fraction, ratio, and rational number questions on the ACT.

As we mentioned in our math strategy article on plugging in answers, neither the SAT nor the ACT measures how you arrived at your answer. On standardized tests, all that matters is whether your answer is correct or not. There is no such thing as partial credit on a standardized test and no one is looking over your shoulder to see if you solved the question the “proper” way.

This means that finding the right answer—no matter the process—is the only thing that matters. And there are plenty of short-cut techniques you can use to find that correct answer without the need to create and solve complex equations. This guide will take you through the strategy of plugging in your own numbers, one of simplest processes for working out the answers to several different kinds of standardized math questions.

In this guide, we’ll give you a complete walk through on the strategy of plugging your own numbers (PIN) for math questions. We’ll go through the whys, hows, and, most importantly,  whens of using PIN your standardized test(s), as well as take you through several real SAT and ACT practice problems. The other best strategy for working around problems—plugging in the answers—is covered in a separate guide.  

The benefits to standardized testing are two-fold: almost all of the questions are multiple choice, and you do not have to show your work. Why are these benefits to you? Unlike in your math classes, where it is crucial to show your work in order to prove that you know how to solve problems, neither the SAT nor the ACT cares about how you got to your solution. All standardized tests measure is whether or not you have the correct answer.

This means that finding the right answer—no matter the process—is your only goal. There is no such thing as partial credit on standardized testing, but there are plenty of workarounds that can help you to find the correct answer without making you do overly complicated math. This guide will take you through one of simplest processes for working out the answers to several different kinds of standardized math questions—plugging in the answer choices.

In this guide, we'll give you a complete walk through on the strategy of plugging in the answers (PIA)—why use it, how to use it, and when to use it on your standardized test(s). The other best strategy for working around problems—plugging in your own numbers—is covered in a separate guide.

Integer questions are some of the most common on the SAT, so understanding what integers are and how they operate will be crucial for solving many SAT math questions. Knowing your integers can make the difference between a score you’re proud of and one that needs improvement.

In our basic guide to integers on the SAT (which you should review before you continue with this one), we covered what integers are and how they are manipulated to get even or odd, positive or negative results. In this guide, we will cover the more advanced integer concepts you’ll need to know for the SAT.

This will be your complete guide to advanced SAT integers, including consecutive numbers, primes, absolute values, remainders, exponents, and roots—what they mean, as well as how to handle the more difficult integer questions the SAT can throw at you.