103 formulas · every one with a full proof

Math Formula Reference

Every essential formula from arithmetic to graduate analysis. Click Show proof on any card.

Basic

Arithmetic & Numbers

Order of operations

Proof

Absolute value

Proof

Fraction addition

Proof

Percentage

Proof

Laws of exponents

Proof

Radicals

Proof

Logarithm laws

Proof

Change of base

Proof
Basic

Algebra

Linear equation

Proof

slope m, intercept b

Quadratic formula

Proof

Discriminant

Proof

Δ>0 two real roots, Δ=0 one, Δ<0 complex

Difference of squares

Proof

Perfect square

Proof

Sum / difference of cubes

Proof

Binomial theorem

Proof

Arithmetic series

Proof

Geometric series

Proof
Basic

Geometry

Pythagorean theorem

Proof

Circle area

Proof

Circle circumference

Proof

Triangle area

Proof

Rectangle area & perimeter

Proof

Trapezoid area

Proof

Sphere volume

Proof

Sphere surface area

Proof

Cylinder

Proof

Cone

Proof

Distance formula

Proof

Midpoint

Proof

Slope

Proof
Basic

Trigonometry

Definitions (SOH-CAH-TOA)

Proof

Pythagorean identity

Proof

Angle sum (sine)

Proof

Angle sum (cosine)

Proof

Double angle

Proof

Law of cosines

Proof

Law of sines

Proof
Intermediate

Analytic Geometry (Conics)

Circle

Proof

Ellipse

Proof

Parabola

Proof

Hyperbola

Proof

Eccentricity

Proof
Intermediate

Probability & Statistics

Mean

Proof

Variance

Proof

Standard deviation

Proof

Permutations

Proof

Combinations

Proof

Binomial distribution

Proof

Bayes theorem

Proof

Normal distribution

Proof
Intermediate

Complex Numbers

Imaginary unit

Proof

Modulus

Proof

Euler's formula

Proof

De Moivre's theorem

Proof
Advanced

Calculus — Derivatives

Definition of derivative

Proof

Power rule

Proof

Product rule

Proof

Quotient rule

Proof

Chain rule

Proof

Common derivatives

Proof

L'Hôpital's rule

Proof
Advanced

Calculus — Integrals & Series

Power rule (integral)

Proof

Fundamental theorem

Proof

Integration by parts

Proof

Common integrals

Proof

Taylor series

Proof

Maclaurin (eˣ)

Proof

Geometric power series

Proof
Advanced

Linear Algebra

Determinant 2×2

Proof

Inverse 2×2

Proof

Eigenvalue equation

Proof

Dot product

Proof

Cross product magnitude

Proof
Graduate / PhD

Vector Calculus

Gradient

Proof

Divergence

Proof

Curl

Proof

Green's theorem

Proof

Divergence theorem

Proof

Stokes' theorem

Proof
Graduate / PhD

Complex Analysis

Cauchy–Riemann

Proof

Cauchy integral theorem

Proof

Cauchy integral formula

Proof

Residue theorem

Proof
Graduate / PhD

Differential Equations

First-order linear

Proof

Separable

Proof

Second-order homogeneous

Proof

Laplace transform

Proof
Graduate / PhD

Fourier & PDEs

Fourier series

Proof

Fourier transform

Proof

Heat equation

Proof

Wave equation

Proof

Laplace's equation

Proof

Schrödinger equation

Proof
Graduate / PhD

Abstract Algebra & Number Theory

Group axioms

Proof

Lagrange's theorem

Proof

Fermat's little theorem

Proof

Euler's theorem

Proof

Chinese remainder theorem

Proof
Graduate / PhD

Analysis & Geometry

Cauchy–Schwarz

Proof

Triangle inequality

Proof

Lebesgue dominated convergence

Proof

Einstein field equations

Proof

Christoffel symbols

Proof