# GMAT Math Formulas List

To achieve a good score on the math section, it is essential that you memorize the necessary GMAT math formulas. Below, you will find a free review sheet full of formulas that are used frequently on the quantitative section.

## Algebra Formulas

### Exponential Equations

x

^{n}*x^{m}= x^{n + m}

(x^{n})/(x^{m}) = x^{n - m}

(x/y)^{n}= (x^{n})/(y^{n})

x^{n}*y^{n}= (xy)^{n}

(x^{y})^{z}= x^{yz}

x^{-n}= 1/(x^{n})

1^{n}= 1

x^{0}= 1

0^{n}= 0, except 0^{0}= 1 or undefined

F_{V}= C_{V}(1 + g)^{T}

Examples

### Quadratic Equations

ax^{2}+ bx + c = 0.

Examples

### Interest

Simple Interest = P*r*t

P = starting principle; r = annual interest rate; t = number of years

Annual Compound Interest = P(1+r)^{t}

Compound Interest = P(1 + r/x)^{xt}x = number of times the interest compounds over the year

### Other

Distance = Rate*Time

Wage = Rate*Time

## Arithmetic Formulas

### Combinatorics

Combinations:

_{n}C_{k}= n!/((n-k)k!)!

Permutations:_{n}P_{k}= n!/(n-k)!

Circular: (n-1)!

k = number of objects selected from a pile ofnobjects

n = total number of objects from whichkobjects can be selected

### Fractions

(a/b)/(c/d) = (a/b) * (d/c)

### Percents

Percent Change, as a decimal = (New - Old)/Old

N = (1 + G)O; N = New Value, 0 = Old Value, G = Growth Rate as decimal

### Probability

Probability that event E occurs = P(E) = (Number of outcomes in E) / (Total number of possible outcomes)

P(not E) = 1 - P(E)

P(E or F) = P(E) + P(F) - P(E and F)

P(E and F) = P(E)P(F)

### Number Properties

(Odd)(Even) = Even

(Odd)(Odd) = Odd

(Even)(Even) = Even

(Odd) ± (Even) = Odd

(Odd) ± (Odd) = Even

(Even) ± (Even) = Even

(Positive)(Positive) = Positive

(Positive)(Negative) = Negative

(Negative)(Negative) = Positive

(Positive)/(Negative) = Negative

(Positive)/(Positive) = Positive

(Negative)/(Negative) = Positive

### Statistics

Average (Arithmetic Mean): (sum of all numbers)/(number of numbers)

Median: the middle number (or average of the two middle numbers if there are an even number of figures) when all values are arranged in ascending order

Mode: the mos frequently occuring value in a dataset

## Geometry Formulas

### Angles

Sum of Interior Angles of Polygon = (n-2)(180)

n = number of sides of a polygon

Central Angle = 2(Inscribed Angle)

### Area

Square: A = a

^{2}

Rectangle: A = lw

Parallelogram: A = bh

Trapezoid: A = .5(a+c)h, where a and c are the lengths of the parallel sides

### Circles

π = pi = 3.1415

Area: A = πr^{2}

Circumference: C = 2πr

Central Angle = 2(Inscribed Angle)

Area of Sector = (x/360)πr^{2}

### Perimeter

Square: P = 4l

Rectangle: P = 2w + 2l

Parallelogram: P = 2b + 2a, where a and b are the lengths of the non-parallel sides

Circle: P = 2πr

### Triangles

Area: A = .5bh

Pythagorean Theorem: A^{2}+ B^{2}= C^{2}where A = one leg, B = the other leg, C = hypotenuse

### Volume

Cube: V = a

^{3}whereais the length of a side

Rectangular Solid: V = hwl

Cylinder: V = πr^{2}h