GRE Math Formulas

Question 1

Pythagorean theorem

Answer 1

a^2 + b^2 = c^2

Question 2

Define Integer, Positive number, negative number, real numbers,

Answer 2

Integers:
Any counting number including negative numbers (e.g. -3, -1, 2, 7…but not 2.5)
Real Numbers:
Numbers that appear on the number line (i.e., one that is not imaginary) including pi, the square
root of 2, etc.
A positive number is greater than 0, a negative number is less than 0.

Question 3

Cummulative Property

Answer 3

a + b = b + a (and same for multiplication)

Question 4

Associative Property

Answer 4

(a + b) + c = (c + a) + b

Question 5

Distributive Property

Answer 5

a * (b + c) = ab + ac

Question 6

What is a prime number?

Answer 6

A prime number is one that is divisible only by itself and 1. In other words, a positive integer with exactly 2
positive divisors. This includes 2, 3, 5, 7, and 11, but not 9, because 9 = 3 x 3.

Question 7

Name all the prime numbers between 1-100

Answer 7

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
61, 67, 71, 73, 79, 83, 89, 97

Question 8

What is factorization?

Answer 8

If X can be multiplied by Y to get Z, assuming all of these are positive integers, then X and Y are
considered factors of Z.

Question 9

What is the prime factorization of 7644?

Answer 9

7644 = 2 x 2 x 3 x 7 x 7 x 13.

Question 10

Define the greatest common factor. What is the easiest way to find it? What is the greatest common factor of 56 and 70?

Answer 10

The greatest common factor (aka greatest common divisor) of two numbers is the biggest factor shared by
ttwo numbers.

The easiest way to find
the GCF is to take the prime factorization and multiply all of the primes that appear in both numbers.

GCF of 56 and 70 is 14

Question 11

Define the Least Common Multiple. What is the easiest way to find it? What is the least common multiple of LCM of 4 and 6?

Answer 11

The least common multiple of two numbers is the smallest positive integer with both numbers as a
factor

To find the LCM of any
two numbers, take the prime factorization of each number, find what prime factors appear in both, and
multiply one of each of the shared primes and then by all the unshared primes.

The LCM of 4 and 6 is 12 – it is the smallest number that has both 4 and 6 in its divisors.

Question 12

x^A * x^B

Answer 12

x^(A+B)

Question 13

x^A / x^B

Answer 13

x^(A - B)

Question 14

(x^A)^B

Answer 14

x^(A*B)

Question 15

x^(1/2)

Answer 15

√x

Question 16

x^(2/3)

Answer 16

3√x^2

Question 17

x^-1

Answer 17

1 / x

Question 18

x^-2

Answer 18

1 / x^2

Question 19

Simplifying roots –> √20

Answer 19

√252 = 2√5

Question 20

Simplifying roots –> √54

Answer 20

√336 = 3√6

Question 21

Simplifying roots –> √72

Answer 21

√98 = √3322*2= 6√2

Question 22

2√7 + 9√7

Answer 22

11√7

Question 23

6x^2+12x-144 / (2x^2 - 32)

Answer 23

3(x + 6) / (x+4)

Question 24

How do you solve equations containing inequalities?

Answer 24

They can be treated like regular equations, with the following exception: multiplying or
dividing an inequality by a negative number reverses the sign of the inequality.

Question 25

How do you calculate the total degrees of a polygon?

Answer 25

Polygon is any shape with more than 3 sides

180(n-2)

Question 26

Average degree per side or degree measure per side of a congruent polygon

Answer 26

180(n-2) / n

Question 27

Area of triangle

Answer 27

1/2bh

Question 28

What is an isosceles triangle?

Answer 28

Right triangle - 45:45-90 degrees - sides ratio x : x : x√2

Question 29

Equilateral triangle

Answer 29

equal on all sides and equal angles 60-60-60

Question 30

Name the Pythagorean triples

Answer 30

3-4-5, 5-12-13, 8-15-17, 7-24-25

Question 31

Name general facts about triangles

Answer 31

The length of the longest side can never be greater than the sum of the two other sides.

The length of the shortest side can never be less than the positive difference of the other two sides.

Question 32

Area of Circle

Answer 32

π r^2

Question 33

Circumference of Circle

Answer 33

2π r

Question 34

Arc length

Answer 34

(x / 360) 2π r

Question 35

Area of sector

Answer 35

(x / 360) π r^2

Question 36

Area and Perimeter of a square

Answer 36

Perimeter = 4s (s=side length) Area = s^2

Question 37

Area and Perimeter of a rectangle

Answer 37

Perimeter = 2l + 2w Area=l*w

Question 38

Area and Perimeter of a trapezoid

Answer 38

Area = ((Base1 + Base2) / 2) * height