GRE Math Formulas Cheat Sheet

Before walking into the GRE, it is a good idea to know the following formulas/tidbits. In fact, not knowing the information below can seriously hurt your chances of answering a question correctly.

At the same time, while this is a very useful cheat sheet, do not just memorize formulas without actually applying them to a question. Often students will see a question and will assume that a certain formula is relevant. This is not always the case. So make sure you practice using the formulas so you will know when they pertain to a question.

Interest

Work Rates

{\dfrac{1}{T}}={\dfrac{1}{time_1}}+{\dfrac{1}{time_2}}, where T is the time to completion of a task when two workers are combining effort.

Sets

{A+B}-{({A}\bigcup{B})}

Distance, Rate, and Time

D=rt, Distance=Rate \times Time

Circles

Area=\pi{r}^2

Circumference=2\pi{r}

Arc Length={\dfrac{x}{360}}2{\pi}r

Area of sector={\dfrac{x}{360}}{\pi}r^2

Squares

Perimeter = 4s, where s = side

Area = s^2

Rectangles

Area = l \times w, where l = length and w = width

Perimeter = 2l+2w

Trapezoids

{\dfrac{Base1+Base2}{2}} \times \text{height}

Polygons

Total degrees = 180(n-2), where n = # of sides

Average degrees per side or degree measure of congruent polygon = 180\dfrac{(n-2)}{n}

The Distance Formula

\sqrt{\bigg({x_2}-{x_1}\bigg)^2+\bigg({y_2}-{y_1}\bigg)^2}

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)

Fast Fractions

{\dfrac{1}{x}}+{\dfrac{1}{y}}={\dfrac{x+y}{xy}} i.e. {\dfrac{1}{2}}+{\dfrac{1}{5}}={\dfrac{2+5}{2*5}}={\dfrac{7}{10}}

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=\dfrac{n!}{r!(n-r)!}

nPr=\dfrac{n!}{(n-r)!}

Probability

\text{\it{Probability of event}} = \dfrac{\text{\it{number of ways that fit the requirement}}}{\text{\it{number of total ways}}}