# 50+ GMAT Math Formulas

#### This article covers most frequently needed math formulas for GMAT exam. These GMAT Math Formulas will be helpful for beginners for getting quickly ready for the exam.

This is an All in one math formulas list for GMAT.

### Formulas for powers or indices

• $a^0 = 1 \mbox{, for all a }$
• $a^m \times a^n = a^{m+n}$
• $a^m / a^n = a^{m-n}$
• $a^{-m} = \frac {1} {a^m}$
• $a^{b^c} = a^{bc}$

### Square Formulas

• $(a + b)^2 = a^2 + 2ab + b^2$
• $(a - b)^2 = a^2 - 2ab + b^2$
• $a^2 - b^2 = (a - b)(a + b)$
• $(a + b)^2 + (a - b)^2 = 2(a^2 + b^2)$
• $(a + b)^2 - (a - b)^2 = 4ab$

### Cube Formulas

• $(a + b)^3 = a^3+ 3a^2b + 3ab^2+ b^3$
• $(a - b)^3 = a^3- 3a^2b + 3ab^2- b^3$

### Special number zero

• 0/a = 0, where a is not equal to 0.
• $a^0 = 1$
• $0^a = 0$
• $a \times 0 = 0$
• a/0 is undefined

### Simple Interest Calculation

The formula to calculate simple interest is: $\mbox{p }\times \mbox{t }\times \mbox{r }$

where,

p = principal
r = interest rate
t = time

### Compound Interest Calculation

Formula to calculate the Final amount for compound interest is : $\mbox{A }= \mbox{p }(1+\frac{\mbox{r}}{\mbox{n}})^{\mbox{nt}}$

where,
A = final amount
p = principal
r = interest rate
t = time in years
n = number of times per year, interest is compounded

### Arithmetic Progression(AP)

Formula for finding nth term in an AP is : $a + (n-1) d$

Formula for finding sum(S) of n terms in an AP is : $S = \frac {n} {2} [\mbox{first term} + \mbox{last term}]$

or, $S = \frac {n} {2} [2a + (n-1)d]$

### Geometric Progression(GP)

Formula for nth term in geometric progression is : $ar^{n-1}$

Formula for sum of terms in geometric progression is :

if r >1, then $S = \frac {a(r^n - 1)} {r - 1}$

if r <1, then $S = \frac {a(1 - r^n)} {1 - r}$

### Logarithms

• $log_a (mn) = log_a m + log_a n$
• $log_a (m/n) = log_a m - log_a n$
• $log_a (m^n) = n log_a m$
• $log_n (m) = log_a m / log_a n$
• $log_n (m) = 1/log_m n$

### Sets $|A \cup B| = |A| + |B| - |A \cap B|$

For disjoint sets, $|A \cup B| = |A| + |B|$

### Permutations and Combinations

• $P(n,r) = \frac {n!} {(n-r)!}$
• $C(n,r) = \frac {n!} {r! (n-r)!}$

### Probability $P(E) = \frac {\mbox{No of outcomes in E}} {\mbox{Total outcomes}}$ $P(not E) = 1 - P(E)$ $P(E \cup F) = P(E) + P(F) - P(E \cap F)$

The standard form of quadratic equation is : $ax^2 + bx + c = 0, a\ne 0$

Its roots can be found as :

• $x = \frac {-b + \sqrt(b^2 - 4ac)} {2a}$
• $x = \frac {-b - \sqrt(b^2 - 4ac)} {2a}$

### Coordinate Geometry Formulas:

• Distance between two points (x1,y1) and (x2,y2) formula $d = \sqrt {(x_2-x_1)^2 + (y_2-y_1)^2}$
•

• Midpoint formula: $(\frac {x_1+x_2} {2} , \frac {y_1+y_2} {2})$

#### Parallels lines intersected by another line If lines are parallel, then :

• Corresponding angles are equal. $\angle {1} = \angle 5, \angle 2= \angle 6, \angle 3 = \angle 7, \angle 4 = \angle 8$

• Alternate Interior angles are equal. $\angle 3 = \angle 6, \angle 4 = \angle 5$

• Alternate Exterior angles are equal. $\angle 1 = \angle 8, \angle 2 = \angle 7$

• Same side interior angles are supp. $\angle 3 + \angle 5 = 180, \angle 4 + \angle 6 = 180$

### Triangles:

By Sides

• Scalene – all sides different
• Isosceles – 2 equal sides
• Equilateral – 3 equal sides

By Angles:

• Acute triangle – all acute angles
• Right triangle– one right angle
• Obtuse triangle – one obtuse angle
• Equiangular – 3 congruent angles(60º)
• Equilateral ↔ Equiangular

Exterior angle of a triangle equals the sum of the 2 non-adjacent interior angles.

Mid-segment of a triangle is parallel to the third(opposite) side and half the length of the third side

#### Pythagorean Theorem:

If in a right triangle with sides a, b, c, where c is the hypotenuse, then $c^2 = a^2 + b^2$

Conversely, If the sides of a triangle satisfy $c^2 = a^2 + b^2$, then the triangle is a right triangle.

#### 30-60-90 triangle: In 30-60-90 triangle, the sides are x, $x\sqrt {3}$ and the hypotenuse is 2x (double the
size of the smallest side)

### Circles

Equation of circle center at origin(0,0): $x^2 + y^2 = r^2$, where r is the radius.

Equation of circle not at origin(0,0): $(x-h)^2 + (y-k)^2 = r^2$, where (h,k) is the center and r is the radius.

### Sum of interior angles of Polygon

The formula for sum of the interior angles of a n-sided polygon is : $(n-2) 180 \textdegree$

For example, the sum of angles in a triangle is (3-2)180° = 180°.

### Area and Perimeter

• #### Square

If length of each side of a square is a, then the area and perimeter can be calculated as : $Area = a^2$ $Perimeter = 4*a$

• #### Rectangle:  $Area = length*width$ $Perimeter = 2(length) + 2(width)$

• #### Parallelogram: $Area = base*height$ $Perimeter = 2(base) + 2(height)$

• #### Circles: $Area = \pi r^2$ $Circumference = 2 \pi r$

### 3D figures

V=Volume, SA = Surface Area, B = Base, h = Height

References