Vince Kotchian's Complete GRE Math Guide
Complete GRE Math Concept List (updated for 2022)
How To Study For The GRE Even If You're Bad At Math
My name is Vince Kotchian, and I've been helping people raise their GRE scores since 2008 as a full-time tutor and author.
Maybe you haven't done math in years (or decades!) -- or maybe you never felt like you were good at math. Unfortunately, all of the popular GRE prep materials out there brush over math concepts very quickly and, worst of all, don't provide the basic-level practice that you probably need. That's why I've created this guide!
The big picture:
First, learn and practice math concepts at an easy level to make sure you know them (this page will show you how). I also highly recommend Prepswift.
Learn some helpful strategies. My Choose Your Own GRE Math Adventure guide is designed to teach you those.
Drill concepts at a GRE level with the Manhattan 5-lb. book, as described in my study plans.
So, for example - let's say you learn the arithmetic concepts from Khan Academy or Prepswift. Then you can jump into doing the arithmetic chapters in the 5-lb. book. And then you'll be ready to tackle some ETS questions involving arithmetic. All of the above is designed to prepare you to be able to do the ETS stuff in their books and practice tests - which, in turn, will enable you to ADAPT to the random, creative GRE questions that will appear on your screen when you take the real test.
IMPORTANT: You must be willing to adjust if you're not able to do the material in front of you on a particular day. In other words, if you're not getting 80% or more of the questions right, either slow down or move to easier practice material, or both. This is common when people move from Khan Academy to the 5-lb. book / ETS, so don't feel bad if it happens to you. Skip the questions you can't do and come back to them. Try starting with the ETS Big Book (the old one with 27 tests) and then moving into the current ETS books.
A Brief Overview of This Guide
Here's what you'll learn on this page:
- NEW! All about my new GRE math practice app. (Scroll down just a bit for more.)
- How long should you study for the GRE?
- What kind of math is on the GRE?
- Why certain practice materials are way better than others
- The best GRE math books for 2023
- My most important GRE math advice
- Some important tips about using Khan Academy
- All about the GRE calculator
Finally, at the very bottom of this page, you'll find my complete list of GRE math concepts with links to Khan Academy for relevant practice questions and helpful videos.
To skip straight to that complete GRE math concepts list, just click right here, or scroll way down.
A GRE math practice app you'll actually enjoy!
Our kingdom is held hostage by evil monsters whose only weakness is GRE math!
In GRE Math Knight, you'll hone your math skills by practicing the most commonly tested GRE math concepts.
First, build your skills on the training ground, where you can drill the basics like mental math, fractions, percents, and more, then travel to four different biomes to solve arithmetic, algebra, geometry, and data analysis GRE math questions in order to defeat the monsters.
You'll find scrolls with math formulas along the way to aid you in your quest, and fun games to play to break up your studying.
Can you save the kingdom and become a true GRE math knight??
Download Vince's GRE Math Knight for iPhone / iOS here and download for Android here, or use the buttons below.
"I have been studying for the GRE for a long time now - needless to say, it can be frustrating not being having adequate time for hobbies (i.e. play video games). Because of that, this game is AWESOME - not only is it engaging, but it keeps you motivated to keep studying and learn key concepts. Even though studying can seem boring sometimes, this game definitely alleviates some of that pain. The concepts and explanations for problems are spelled-out clearly - so it’s easy to understand where your strengths and weaknesses are."
(This cat aced the GRE.)
How Long Should You Study for the GRE?
In terms of timeframe, I've found that most people need to work hard on GRE math for 2 or ideally more like 3 months. (By "work hard" I mean study for 2 hours a day or so.) However, if you do work hard and work smart, it's predictable that your GRE math score will go up. It's a standardized test, and we can predict most of what it's going to throw at you.
If you're looking for a shortcut to master GRE math, I have bad news. There isn't one. You get better at GRE math by solving questions on your own, and it takes time to do lots of questions.
What Kind of Math is on the GRE?
The GRE has a brief - very brief - review of all the math concepts it tests in the free ETS Math Review. Please take a minute to stop reading and click on it and scroll through it a bit. The Math Review tells us what's on the test. In a nutshell, arithmetic, algebra, geometry, and "data analysis" - which means statistics and probability.
Now, mark which concepts you know and which ones you might not or don't know. Use the Math Review to try to learn ones you don't know. This means read about the concepts and do all the practice exercises both within the chapter and at the end of each section.
Important: If a topic in the math review is explained in a particularly wordy or confusing way, don't get bogged down with it. Add it to your list of things to practice and move on. The math review is mostly a TOOL to show you what you need to practice, NOT a complete learning guide.
Of course, you may very well need much more practice than the ETS Math Review can give you. For example, for certain concepts, you might just need a reminder - like for a certain exponent rule. For other concepts - perhaps probability - you may feel like you need much more depth.
That's where Khan Academy comes in. If you haven't used it before, it's amazing - and 100% free!
Here's a pic from the Khan Academy website to show you where the video lesson, written lesson, and practice questions are for each concept - and where you can take a quiz or test to gauge your skills.
FYI, understanding the video does NOT mean you can do the problem from scratch. So, make sure you take advantage of the practice exercises as well. Doing enough questions to convince yourself you know what you're doing for a given concept is the goal here.
Pro tip: Go straight to the the unit test for each concept which is located at the lower left corner of the screen. This saves time, and the website will prompt you with appropriate videos if you get something wrong.
If you can't do very many of the test's questions, then try starting with the quizzes or even the practice links on the right side of the screen. Don't be afraid to watch the videos, if you need more foundation for something - I'd just watch them at 2x speed.
Note: This process is highly variable depending on the person and how much time they have to prepare. Some of you might need minimal Khan practice, and some of you might need much, much more. If your test date is coming up soon, you may have to skip topics that are either really hard for you or that you've never seen before.
Being halfway good at something won't cut it; if you're going to learn a concept, make sure you learn it well.
GRE Math Practice Questions
Once you've mastered a concept, check it off on the ETS Math Review and move onto the next one. Your job is to get this whole project done ASAP, so you can start practicing with real ETS GRE questions. The more real ETS math questions you successfully solve on your own - i.e., without following someone else's solution - the better you get.
It's a numbers game, pun intended. :)
The reason this works is that, unlike a math test you'd study for in school, the GRE gets really creative with the ways it disguises math concepts. To adapt to unfamiliar problems, you need lots of experience solving real GRE math questions.
Important: Having a plan and schedule is crucial. Make sure you check out my free 1, 2, 3, and 4-month GRE study plans.
And be sure to check out GRE Math Knight - my GRE math practice app!
Download Vince's GRE Math Knight for iPhone here and download for Android here, or use the buttons below.
Video: Why GRE math is like Goldilocks and the Three Bears
Why GRE math is like Goldilocks and the Three Bears.
The Best GRE Math Books for 2023
Why buy: Contains 596 official GRE practice questions, which are worth their weight in gold.
Note: The above is an Amazon affiliate link and I earn a commission if you purchase things through it. However, any commission I earn comes at no additional cost to you, and you pay nothing extra.
You'll find the rest of my recommended resources in my free GRE study plans, which are designed around official ETS GRE books and practice tests. This is the big reason my plans are more effective than plans from companies like Magoosh and Kaplan, whose plans will have you wading through hundreds of unrealistic questions that those companies wrote themselves.
Fun fact: It's incredibly expensive to license ETS GRE questions ($450 per question!) so prep companies write their own. Unfortunately, it's difficult and laborious to duplicate the nuances, logical reasoning shortcuts, intricacies, and wordiness of real ETS questions, so prep companies' questions aren't very realistic and aren't usually good practice. Empty calories. And of course, prep companies' free study plans are designed to steer you into buying their courses.
A common myth is that practicing with "harder" questions than you'll see on the GRE will make the real GRE seem easier. This isn't true, because those "hard" questions - if they're written by test-prep companies like Magoosh, Kaplan, or the like - will be hard for the wrong reasons - unrealistically computation-heavy, obscure, or written with no possibility of a shortcut.
This is why I preach "use ETS" ad nauseam.
Above: Your town celebrating your perfect GRE math score with a fireworks display.
My Most Important GRE Math Tip
Although I do recommend the Manhattan 5-lb. book for repetition of quant concepts, it's important to remember that being able to solve math questions on the real GRE is a skill that comes from practice with real GRE questions. Shocking, right?
Real GRE questions are hard until they're easy. By that, I mean that they're often wordy and complicated but often can be solved by cutting through the words to figure out what the question's asking, or by using a logical shortcut. They're testing your ability to think with math skills - which is why the section is called "Quantitative Reasoning".
This means that memorizing GRE math formulas, reviewing notes, using GRE math cheat sheets, and watching videos are WAY less important than getting your hands dirty by doing a ton of ETS math questions by yourself from a blank page (i.e., you're solving them, not just following a solution that has been taught to you) then keeping a detailed mistake journal (as described in my free GRE study plans).
Studying for GRE math is not like studying for a math test in school. GRE math performance demands fluency with concepts and experience with official questions, which are written in varied and creative ways. A giant database of experience from questions you've done makes it more likely the questions on the real GRE will remind you of ones you've done before.
The good news is that when you study for GRE math, the experience you accumulate doesn't go away easily since you're not memorizing; you're doing. It builds over time as long as you're still studying. Every ETS question you solve is a step in the right direction toward a higher score.
(Above: You studying?)
A Few More Things About Khan Academy
Important note: If you see a concept in the ETS Math Review that you don't know but can't easily find on the Khan page I've linked to, just type it into the Khan Academy search bar. (BTW, the only topic in the ETS math review that I'm confident will NOT be tested is how to calculate standard deviation. You should still understand standard deviation - just don't worry about calculating it with the formula.)
BUT if you find a concept in Khan that is NOT in the ETS Math Review, don't worry about it*. I'll list anything you don't need in Khan next to each Khan link.
*With that said, ETS does sometimes test a very small number of topics that aren't explicitly covered in the math review. For example, sequences. But don't worry - I got you, bro. Sequences are in the list of topics linked to Khan below.
If you do have a topic for which you're not sure whether it might be tested, please ask about it on Reddit (r/GRE). I'm on there a lot, and I don't want you losing sleep over a random topic if you don't need to.
Can You Use a Calculator on the GRE?
Yes! It's an on-screen calculator that you can use at any time during a GRE quantitative section.
Your GRE calculator can add, subtract, multiply, divide, and square root. But that's pretty much it. And the display only fits 8 digits. That's why I created a GRE calculator app to help you get used to those limitations!
Download the version for your phone with the below buttons and make your practice more realistic.
The test center at which you take the GRE will also provide you with scrap paper and a pencil. So practice using a pencil, not a pen. Update: The GRE is now online due to COVID-19. You can take it at home!
So actually, practice with a whiteboard and marker, since if you take the At Home GRE, you won't be allowed to use scrap paper.
All GRE Math Concepts Linked To Khan Academy
You can either use this mindmap or scroll down to see the same topics in a bullet-point list. In the map, more important topics are in a bigger font.
P.S. Once you're better with math concepts, you need to learn math strategies to help you solve certain types of GRE questions. To do that, try my Choose Your Own GRE Math Adventure strategy guide!
P.P.S. If you can afford $7 a month, I now recommend Prepswift over Khan Academy for learning math concepts.
- 1.1 Basic Math Operations
- 1.2 Fractions
- 1.3 Exponents and Roots
- 1.4 Decimals
- 1.5 Real Numbers and their properties
- 1.6 Ratio (includes rates, proportions, and percents)
- 1.7 Percent change or try Vince's percent change video
- 2.1 Operations with Algebraic Expressions (skip independent / dependent variables)
- 2.3 Solving Linear Equations
- 2.4 Solving Quadratic Equations
- 2.5 Solving Linear Inequalities
- 2.6 Functions (skip recognizing fxns, max and min points, and intervals)
- and New Operator Definitions
- Vince's function video
- 2.8 Coordinate Geometry
- (skip any proofs)
- 3.1 Lines and Angles
- 3.2 Polygons
- Area and Perimeter of Shapes (skip anything about nets)
- 3.3 Triangles (skip theorems, bisectors, medians, and centroids)
- 3.4 Quadrilaterals
- 3.5 Circles (skip radians)
- 3.6 Three-Dimensional Figures (skip cones, pyramids, and spheres)
GRE DATA ANALYSIS
- 4.2 Numerical Methods for Describing Data
- Central Tendency (mean, median, mode)
- Measures of Dispersion (range, standard deviation) skip variance; skip calculating standard deviation
- 4.3 Counting Methods
- Venn Diagrams (skip frequency tables)
- Counting Basics
- Vince explains how to tell the difference between permutations and combinations
- 4.4 Probability
- 4.5 Distributions of Data, Random Variables, and Probability Distributions
Good luck, and happy GRE studying! If you enjoyed this free guide, check out Vince's other free GRE resources.
Reminder that we help people prepare for the GRE who are applying to graduate school, business school, and law school. We also specialize in GRE prep for LD / ADHD students as well as older and non-traditional students.