GRE Math Formulas

slope intercept formula

y = mx + b

m = slope

b = y-intercept

(a^x)(a^y)=?

a^(x+y)

(a^x)/(a^y)=?

a^(x-y)

two point slope formula

(Δy)/(Δx)

PEMDAS

Parentheses, exponents, multiplication and devision (L to R), addition and subtraction (L to R)

√1

1

√2

1.4

√3

1.7

√4

2

negative × negative = ?

positive

positive × negative = ?

negative

Only even prime number

2

x⁻ⁿ = ?

1/xⁿ

A number is divisible by 3 if...

The sum of its digits is divisible by 3

A number is divisible by 5 if...

It ends in 0 or 5

A number is divisible by 2 if...

Its ones place is divisible by 2

Area of a Δ

½bh

Pythagorean Theorem

(Only applies to right triangles)

c² = a² + b² where a and b are the sides and c is the hypotenuse

Area of a O

πr²

Circumference of a O

2πr or πd

Distance between two points

d = √(x₁-x₂)² + (y₁-y₂)²

Volume of rectangular solid

lwh

Volume of circular cylinder

πr²h

Calculating an Average

(total value, or sum)/(# of numbers being averaged)

Calculating Percent Change

(difference/original) × 100

Quadratic Equations

x²-y² = (x+y)(x-y)

(x+y)² = x² + 2xy + y²

(x-y)² = x² - 2xy - y²

Solving an Inequality

When multiplying or dividing both sides by a negative number, always change the inequality sign (i.e. if it was < then change it to >, if it was > then change it to <)

Calculating Probability

(# favorable outcomes)/(total # possible outcomes)

Finding the Midpoint

When the endpoints are (x₁, y₁) and (x₂, y₂), the midpoint is: ((x₁+x₂)/2), ((y₁+y₂)/2)

Calculating Average Speed

(total distance)/(total time)

Median

The value that falls in the middle of a set of values

Mode

The value that appears most often in a set of values

Standard Deviation

The bigger the standard deviation is, the more dispersed the values are; the smaller the standard deviation is, the more closely the values in a set are to the mean.

Characteristics of an Isosceles Δ

1. Contains one 90° angle;

2. Has 45°, 45°, and 90° angles;

3. The two non-hypotenuse sides are equal length;

4. Where a non-hypotenuse side is equal to a, the hypotenuse is equal to a√2

Characteristics of a 30-60-90 Δ

1. Contains one 90° angle;

2. Has 30°, 60°, and 90° angles;

3. Where the shortest side has a length of a, the longer side has a length of a√3 and the hypotenuse has a length of 2a

a⁰ = ?

1

a¹ = ?

a

The sum of the angles in a Δ

180°

Area of a parallelogram

bh

Volume of a cube

l³

Characteristics of a 3-4-5 Δ

1. Contains one 90° angle;

2. The sides are integers with the ratio 3:4:5

Characteristics of a 5-12-13 Δ

1. Contains one 90° angle;

2. The sides are integers with the ratio 5:12:13

The sum of the angles in a polygon

(n-2) × 180° where n = number of sides

Counting Possibilities

If there are m ways to do one thing and n ways to do another, then there are (m × n) ways for the two events to happen

Average A per B

(total A)/(total B)

(aⁿ)^x = ?

a^(nx)