# Complete GRE Math Concept List (updated for 2021)

# Complete GRE Math Concept List (updated for 2021)

12/30/2020

(Vince's 4 main options to help you with your GRE prep are HERE.)

## How To Study For GRE 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 is really just two steps:

**First, learn and practice math concepts at an easy level to make sure you know them (this guide will show you how).****Next, do as many official GRE math questions as possible to build experience with the GRE's trickiness.**

Those two steps enable you to ADAPT to the random, creative GRE questions that will appear on your screen when you take the real test.

### A Brief Overview of This Guide

Here's what you'll learn on this page:

- 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 2020
- My most important GRE math advice
- Some important tips about using Khan Academy
- All about the GRE calculator

To skip straight to my complete GRE math concepts list itself, just click right here, or scroll to the bottom of this page.

(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.

In my experience, math is definitely the part of the test for which people need a study plan that fits their skill level. This is why I made a verbal course but not a math course - one-size-fits-all math courses don't work for many people.

## 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 2021

**Why buy:** Contains 596 official GRE practice questions, which are worth their weight in gold. Other companies' practice questions and tests, to put it bluntly, suck.

**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

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. This is why I'm always saying "Do as many official company-written math questions (ETS and even GMAT and SAT) as you can". 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.**

### GRE ARITHMETIC

- 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

### GRE ALGEBRA

- 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)
- 2.8 Coordinate Geometry
- Sequences (skip everything below quiz 1)

### GRE 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

- 4.1 Graphical Methods for Describing Data
- 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
- Sets
- Venn Diagrams (skip frequency tables)
- Counting Basics

- Permutations
- Combinations
- 4.4 Probability
- 4.5 Distributions of Data, Random Variables, and Probability Distributions

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