# GRE Math Formulas Cheat Sheet

Having trouble remembering your GRE math formulas on the fly? This free, downloadable GRE math formulas cheat sheet should help you! We’ll show you how to incorporate this GRE resource into your Quant prep below.

Although memorizing a GRE math formula (or twelve) isn’t the only way to study for GRE Quant, knowing certain frequently-tested formulas by heart will help you improve your speed on test day. Once you learn these formulas, be sure to practice using them! A little timed practice can go a long way.

Download our GRE math formulas cheat sheet PDF and read on to learn a little bit more about what to expect from the math section of the GRE.

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## How to Use the GRE Math Formulas Cheat Sheet

Memorizing this GRE math formula cheat sheet is just the first step to mastering GRE math. Knowing which math formulas to use, then using them quickly and correctly, can really help you do well on GRE quant.

The GRE Quantitative Reasoning section tests concepts that you likely learned during sophomore and/or junior year of high school. These concepts DO NOT INCLUDE higher level math like trigonometry, calculus, or geometry proofs. They DO INCLUDE things you’ve probably long forgotten like properties of shapes, integer properties, exponent rules, and word problems.

The thing that takes these concepts to the GRE level is their complexity. Figuring out what each question is asking you to accomplish can be really tricky, whereas the math involved in solving them tends to be fairly straightforward. And you won’t get partial credit for showing your work, so picking the correct answer choice is very important! So study up the GRE math formulas cheat sheet and then practice using the formulas so you will know when they pertain to a question.

## Important GRE Math Formulas to Know

Here are the most important GRE math formulas to know and practice before exam day!

### Geometry

Squares
$$\text{Perimeter}=\text{4}\times\text{s}$$, where s = side

$$\text{Area} = s^2$$

Rectangles
$$\text{Area} = \text{l}\text{w}$$, where l = length and w = width

$$Perimeter = 2l+2w$$

Trapezoids
$$\text{Area}=\frac{Base1+Base2}{2}\times\text{height}$$

Polygons
$$\text{Total degrees}=180(\text{n}-2)$$, where n = # of sides

Average degrees per side or degree measure of congruent polygon=$$180(n-2)/n$$

Circles
$$\text{Area}=π\text{r}^2$$

$$\text{Circumference}={2}{π}\text{r}$$

$$\text{Arc Length}=\frac{x}{360}\times{2}{π}\text{r}$$

$$\text{Area of sector}=\frac{x}{360}\times{π}{r^2}$$

Triangles
$$\text{Area}=\frac{1}{2}\times\text{bh}$$

$$\text{Pythagorean Theorem}: a^2={b^2+c^2}$$

### Divisibility

• 3 : sum of digits divisible by 3
• 4 : the last two digits of number are divisible by 4
• 5 : the last digit is either a 5 or zero
• 6 : even number and sum of digits is divisible by 3
• 8 : if the last three digits are divisible by 8
• 9: sum of digits is divisible by 9

### Combinations and Permutations

$$nCr={n!}/{r!(n-r)!}$$ n is the total number, r is the number you are choosing

$$nPr={n!}/{(n-r)!}$$

### Prime Numbers and Integers

• 1 is not a prime. 2 is the smallest prime and the only even prime.
• An integer is any counting number including negative numbers (e.g. -3, -1, 2, 7…but not 2.5)

### Average

$$\text{Average}=\frac{\;\text{sum of n numbers}}{n}$$

$$\text{Average speed}=\frac{\;\text{total distance}}{\text{total time}}$$

### Probability

$$\text{Probability of event}=\frac{\;\text{number of ways that fit the requirement}}{\text{number of total ways}}$$

### Percentages

Percent Increase
$$\frac{\;\text{new amount-original amount}}{\text{original amount}}\times{100}$$

Percent Decrease
$$\frac{\;\text{original amount-new amount}}{\text{original amount}}\times{100}$$

### Interest rate

Simple Interest
$$V=P(1+rt/100)$$, where P is principal, r is rate, and t is time

Compound Interest
$$V=P(1+r/{100n})^nt$$, where n is the number of times compounded per year

### Distance, rate, time

$$D=rt$$, $$Distance=Rate*Time$$

The Distance Formula
$$sqrt{({x_2}-{x_1})^2+({y_2}-{y_1})^2}$$

### Slope of a line

$$y=mx+b$$

## GRE Math Formulas Practice Problems

1. Point A in the xy-coordinate system is shown below. Given two other points B (4a, b) and C (2a, 5b), what is the area of triangle ABC in terms of a and b?

/
/
/

2. If the circle with center O has area 9π, what is the area of equilateral triangle ABC?

9√3
18
12√3
24
16√3

3. The average (arithmetic mean) of 4 different integers is 75. If the largest integer is 90, what is the least possible value of the smallest integer?

1
19
29
30
33

4. Ten students wrote a test, and the distribution of scores is shown on the frequency table. If the average (arithmetic mean) score is 62, what is the value of x?

ScoreNumber of Students
401
552
703
x4

62
65
71
76
83

5. In 2004, Cindy had $4000 in a mutual fund account. In 2005, the amount in the same account was$5000. If the percent increase from 2004 to 2005 was the same as the percent increase from 2005 to 2006, how much did Cindy have in this account in 2006?

$5800$6000
$6200$7500
$9000 Show answer and video explanation Answer is C. Click here to view the video explanation. 6. Tuk weighs 60 percent more than Kim, Lee weighs 50 percent less than Tuk, and Pat weighs 25 percent more than Lee. If Pat weighs 126 pounds, what is Kim’s weight? Show answer and video explanation Answer is 126. Click here to view the video explanation. 7. In the xy-coordinate system, line k has y-intercept 12 and an x-intercept greater than zero. If the area of the triangular region enclosed by line k and the two axes is 30, what is the slope of line k? Show answer and video explanation Answer is A. Click here to view the video explanation. 8. In the xy-coordinate system, line k has slope and passes through point (0, 5). Which of the following points cannot lie on line k? (-10,0) (8,9) (3, 6.5) (-2, 2) (-8, 1) Show answer and video explanation Answer is D. Click here to view the video explanation. ## Conclusion: Is This All You Need for GRE Math? Like we mentioned before, simply memorizing these GRE math formulas is not enough. You’ll also need to practice so that you know when it’s appropriate to use each formula. Magoosh GRE prep offers lesson videos and practice questions to help you learn to put these formulas to use. And our Android/iPhone Prep App allows you to access that content on the go. And even better than a cheat sheet—check out our free, downloadable GRE Math Formula eBook! P.S. Ready to improve your GRE score? Get started today. ### Most Popular Resources ### 40 Responses to GRE Math Formulas Cheat Sheet 1. Ali Haider May 2, 2017 at 9:17 am # In the book and here there aren’t formulas related to the Normal Distribution, STD, Variance etc. • Magoosh Test Prep Expert May 2, 2017 at 9:23 am # Hi Ali 🙂 You can find the formulas for standard deviation and variance (which is the standard deviation squared) on page 27 of our Math Formula eBook. On the other hand, it looks like normal distribution is not mentioned in either the cheat sheet or eBook :/ With that in mind, we do have a couple of blog posts that go into more detail on normal (or standard) distribution: more on normal distribution 🙂 I hope you find these resources useful! 😀 2. Sa January 15, 2017 at 11:36 pm # How common are questions pertaining to simple interest interest and common interest in the GRE? • Magoosh Test Prep Expert January 16, 2017 at 6:56 am # Hi there 🙂 While problems on simple and compound interest aren’t too common, they are topics that can definitely show up in a question or two on the exam. Hope this helps! 3. Kayla July 12, 2016 at 12:23 pm # Hello what about conversions? Just took a practice test and needed to know how many ounces in a pound. • Magoosh Test Prep Expert July 12, 2016 at 4:01 pm # Measurement conversions are definitely important too— so much so that Mike did an additional blog post on those entitled “What Unit Conversions Should You Know for the GRE?” • N VIJAY BHARGAV October 19, 2016 at 1:32 am # 1 pound is equal to 16 ounces 4. Robert June 12, 2016 at 6:10 pm # Hi – How about adding exponent formulas, pls? • Magoosh Test Prep Expert June 14, 2016 at 7:00 am # Hi Robert 🙂 Thanks for your suggestion! You can find the formulas for exponential expressions in our Math Formula eBook. The eBook is a more complete guide to the fundamental concepts that you’ll be tested on during the GRE, so I definitely recommend checking it out 🙂 5. evan October 14, 2015 at 10:20 am # Hi Chris, are there questions related to interior and exterior angles, circle segments? • N VIJAY BHARGAV October 19, 2016 at 1:33 am # 1 exterior angle is quality to sum of two interior angles • Magoosh Test Prep Expert October 19, 2016 at 8:36 pm # I think you may have been autocorrected! The exterior angle theorem says that an exterior angle is equal to the sum of the two opposing interior angles 🙂 6. Babak July 7, 2015 at 4:10 pm # I have a master degree. Like to pursue with my Phd. How hard is really GRE math. Sometimes I think I am not smart enough for that. I am 40 now and I feel my brain is not quick as before to caluclate something quicky. Please guide a bit. 7. proloy November 3, 2014 at 4:44 am # how come we all have the similar problem and well addressed by Chris. discussion is really helpful. plz keep posting 8. Kaitlyn May 29, 2014 at 5:37 pm # How am I supposed to calculate interest rates without a calculator that has an exponents key? For example, one of the question asks me to calculate how much does a person have in their account after 2 years if she deposit$10,000 in an account that has 3.95% annual rate, compounding semi-annually.

Normally, I would take 10,000(1.0198)^4 but I’m unable to punch 1.0198^4 into the calculator nor am I capable of manually calculating that in a quick manner.

• Chris Lele May 30, 2014 at 4:03 pm #

Hi Kaitlyn,

A good strategy is to enter the number, say 1.0198 and then press (X) and (=). That will give you that number squared. Pressing (X) and (=) again, will give you that number to the 4th power. You can play around with that function to give you other derivations, e.g. 1.0198^6, 1.0198^16, etc.

Hope that helps!

• pruthviraj k s August 31, 2015 at 5:16 pm #

will this strategy work on gre exam too?

9. Shrikar March 20, 2014 at 2:47 am #

Super ! Reassuring. Seeing that I’ve covered all of these, gave me quite a confidence boost. 😀

10. stark January 18, 2014 at 2:59 am #

11. nikhil June 24, 2013 at 5:50 am #

thanks a lot on final day of my exam i heleped me a lot .I have scored 164 in quant

• Chris Lele June 24, 2013 at 1:25 pm #

Great! Such a score is always a ringing endorsement :)!

12. Manel May 25, 2013 at 11:39 am #

Thanks a lot…a very good way to see if we got it all hitting the GRE next this ebooks is just what I needed ..You rock guys

13. Supriya May 23, 2013 at 10:00 am #

I was confused from where to start and here you are made things a lot easier. Thank you very much.

• Chris Lele May 23, 2013 at 12:12 pm #

You are welcome — I’m glad I made things easier for you :).

14. Kayla M. August 19, 2012 at 10:26 am #

You have made my life much easier. I cannot remember the last time that I used these equations so when I looked at the practice questions I thought “well this is interesting.”

• Chris August 21, 2012 at 2:42 pm #

15. sai July 3, 2012 at 1:54 am #

this sai from hyd . it is good.
could pls send me formula according news gre topics to the mai id;sdnsh950@gmail.com
pls.pls.pls.pls…………..

16. Alex July 2, 2012 at 7:11 pm #

Chris,

I was going over some of the practice problems in the Princeton review and found that the 3D shape problems have specific equations for them, do we need to know those for the GRE?

• Chris July 3, 2012 at 4:56 pm #

It would help to know the cube, the sphere, and the cylinder. (Though sometimes a question may even supply the formula for a sphere). There are other shapes such as a cone and a pyramid, which I wouldn’t worry about.

Hope that helps 🙂

17. Hamid June 29, 2012 at 11:59 am #

Hi I’m taking the gre revised tomorrow. Do we need to know the quadratic formula?

• Chris June 29, 2012 at 3:08 pm #

Hi Hamid,

No, you should be fine without knowing the quadratic formula. Granted there may be a question in which the quadratic formula could be used, there are often alternative ways of solving the problem, working backwards from answer choices, etc.

Good luck!

18. Glory May 7, 2012 at 4:31 am #

I was searching for GRE maths formula. Chris, Is the list complete and is it that actual GRE maths question will walk around these formulas?

• Chris May 7, 2012 at 11:14 am #

Hi Glory,

Interesting that you ask :). We are coming out with a Math formula e-book in a few weeks! There the formula list will be far more comprehensive than the one above. Stay tuned!

• Glory May 8, 2012 at 4:25 am #

Chris,
Thank you for replying . I would really appreciate if you could post me the compiled eBook at : glorybasumata@hotmail.com

Thank You.

• Chris May 8, 2012 at 11:49 am #

Hi Glory,

Actually, we will have the download link up on the blog in a few short weeks (you can just check back in then :). Also, if you are a Premium Magoosh user the link will automatically show up on your resource page. (You can always check out the free trial version of our product to see how Magoosh can help).

19. Zahid February 15, 2012 at 12:21 am #

20. Zahid February 14, 2012 at 1:24 am #

Hi Chris,

Is there any intrigation and differentiation match problems in revised GRE exam?

• Chris February 14, 2012 at 11:45 am #

No calculus – nor for that matter trig., logarithms, etc.

21. Jhinuk February 2, 2012 at 9:52 am #

Good Job…

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