GMAT Math Formula Sheet
1. Algebra
- 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
- (xy)^z = x^z * y^z
- x^-n = 1/x^n
- 1^n = 1
- x^0 = 1
- 0^n = 0 (Note: 0^0 is considered an indeterminate form)
- Quadratic equations:
- General form: ax^2 + bx + c = 0
- Quadratic formula: x = [-b ± sqrt(b² - 4ac)] / 2a
- Other formulas:
- Future Value = Current Value * (1 + growth rate)^Time
- Distance = Speed * Time
- Wage = Rate * Time
- Combinatorics:
- Combinations: nCk = n! / [(n-k)! * k!]
- Permutations: nPk = n! / (n-k)!
- Circular permutations: (n-1)!
- Fractions:
- (a/b) / (c/d) = (a/b) * (d/c)
- Percents:
- Percent change = (New - Old) / Old
- New Value = (1 + Growth Rate) * Old Value
- Probability:
- Probability of Event E = P(E) = Number of favorable outcomes / Total number of 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) (If E and F are independent events)
- 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
- Mean (average) = 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 values) when all values are arranged in ascending order
- Mode: the most frequently occurring value in a data set
- Angles:
- Sum of Interior Angles of a Polygon = (n-2) * 180 (where n = number of sides)
- Central Angle = 2 * Inscribed Angle
- Area:
- Square: A = side^2
- Rectangle: A = length * width
- Parallelogram: A = base * height
- Trapezoid: A = 0.5 * (base1 + base2) * height
- Circle: A = πr^2
- Sector of a Circle = (central angle/360) * πr^2
- Perimeter:
- Square: P = 4 * side
- Rectangle: P = 2 * (length + width)
- Circle: C = 2πr
- Triangles:
- Area: A = 0.5 * base * height
- Pythagorean theorem: a^2 + b^2 = c^2
- Volume:
- Cube: V = side^3
- Rectangular solid (Box): V = length * width * height
- Cylinder: V = πr^2h
- Simple Interest: Interest = Principal * rate * time
- Compound Interest (annually): Interest = Principal * (1 + rate)^time
- Compound Interest (compounded n times per year): Interest = Principal * (1 + rate/n)^(n*time)
This list should cover the majority of the formulas you would need for the GMAT's Quantitative section, but understanding how to apply them is equally important. Practice solving a variety of GMAT problems to become more comfortable with these concepts.
Click below to download a list of GMAT math formulas.
| GMAT Formulas List PDF |
