Math Formula Reference
Algebra Formulas
Quadratic Formula
x = (-b ± √(b² - 4ac)) / 2a
Used to find the roots of a quadratic equation ax² + bx + c = 0
Distance Formula
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Calculates the distance between two points (x₁, y₁) and (x₂, y₂)
Slope Formula
m = (y₂ - y₁) / (x₂ - x₁)
Finds the slope of a line passing through points (x₁, y₁) and (x₂, y₂)
Arithmetic Sequence
aₙ = a₁ + (n - 1)d
nth term of an arithmetic sequence with first term a₁ and common difference d
Geometry Formulas
Area of Circle
A = πr²
Area of a circle with radius r
Pythagorean Theorem
a² + b² = c²
In a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides
Volume of Sphere
V = (4/3)πr³
Volume of a sphere with radius r
Surface Area of Cylinder
SA = 2πr² + 2πrh
Surface area of a cylinder with radius r and height h
Calculus Formulas
Power Rule
d/dx(xⁿ) = nx^(n-1)
Derivative of x raised to the power n
Chain Rule
d/dx[f(g(x))] = f'(g(x)) · g'(x)
Derivative of a composite function
Integration by Parts
∫u dv = uv - ∫v du
Method for integrating products of functions
Fundamental Theorem of Calculus
∫ₐᵇ f(x)dx = F(b) - F(a)
Relates derivatives and integrals, where F'(x) = f(x)
Statistics Formulas
Mean (Average)
x̄ = Σxᵢ / n
Sum of all values divided by the number of values
Standard Deviation
σ = √(Σ(xᵢ - x̄)² / n)
Measure of spread in a dataset
Combination Formula
C(n,r) = n! / (r!(n-r)!)
Number of ways to choose r items from n items (order doesn't matter)
Normal Distribution
Z = (X - μ) / σ
Z-score formula for standardizing normal distributions
Custom Formulas
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