Math Cheat Sheets

Quick reference guides for algebra, calculus, trigonometry, and more

📐

Algebra Formulas

12 formulas

▾

Quadratic

Quadratic Formulax = (−b ± √(b²−4ac)) / 2a

DiscriminantΔ = b² − 4ac

Vertex Formy = a(x−h)² + k

Factoring

Difference of Squaresa²−b² = (a−b)(a+b)

Perfect Square(a+b)² = a²+2ab+b²

Sum of Cubesa³+b³ = (a+b)(a²−ab+b²)

Diff of Cubesa³−b³ = (a−b)(a²+ab+b²)

Exponents & Logs

Product Ruleaᵐ · aⁿ = aᵐ⁺ⁿ

Power Rule(aᵐ)ⁿ = aᵐⁿ

Log Productlog(ab) = log a + log b

Change of Baselogₐb = log b / log a

∂

Derivatives Cheat Sheet

14 formulas

▾

Basic Rules

Power Ruled/dx[xⁿ] = n·xⁿ⁻¹

Constant Ruled/dx[c] = 0

Product Rule(fg)′ = f′g + fg′

Quotient Rule(f/g)′ = (f′g − fg′) / g²

Chain Ruled/dx[f(g(x))] = f′(g(x))·g′(x)

Trig Derivatives

sin(x)d/dx[sin x] = cos x

cos(x)d/dx[cos x] = −sin x

tan(x)d/dx[tan x] = sec²x

sec(x)d/dx[sec x] = sec x·tan x

Exponential & Log

eˣd/dx[eˣ] = eˣ

aˣd/dx[aˣ] = aˣ·ln a

ln(x)d/dx[ln x] = 1/x

logₐ(x)d/dx[logₐ x] = 1/(x·ln a)

∫

Integration Formulas

12 formulas

▾

Basic Integrals

Power Rule∫xⁿ dx = xⁿ⁺¹/(n+1) + C

Constant∫a dx = ax + C

1/x∫(1/x) dx = ln|x| + C

eˣ∫eˣ dx = eˣ + C

aˣ∫aˣ dx = aˣ/ln(a) + C

Trig Integrals

sin(x)∫sin x dx = −cos x + C

cos(x)∫cos x dx = sin x + C

sec²(x)∫sec²x dx = tan x + C

sec(x)tan(x)∫sec x·tan x dx = sec x + C

Integration Techniques

By Parts∫u dv = uv − ∫v du

Substitution∫f(g(x))g′(x)dx = ∫f(u)du

∿

Trigonometry Identities

16 formulas

▾

Pythagorean Identities

Basicsin²θ + cos²θ = 1

Tangent form1 + tan²θ = sec²θ

Cotangent form1 + cot²θ = csc²θ

Double Angle

sin(2θ)sin 2θ = 2 sin θ cos θ

cos(2θ)cos 2θ = cos²θ − sin²θ

tan(2θ)tan 2θ = 2tan θ / (1−tan²θ)

Sum & Difference

sin(A±B)sin A·cos B ± cos A·sin B

cos(A±B)cos A·cos B ∓ sin A·sin B

tan(A±B)(tan A ± tan B)/(1 ∓ tan A·tan B)

Unit Circle Values

sin 0°0

sin 30°1/2

sin 45°√2/2

sin 60°√3/2

sin 90°1

△

Geometry Formulas

18 formulas

▾

2D Shapes

Circle AreaA = πr²

Circle Circumf.C = 2πr

Rectangle AreaA = l × w

Triangle AreaA = ½ × b × h

Trapezoid AreaA = ½(a+b) × h

Ellipse AreaA = π × a × b

3D Shapes

Sphere VolumeV = (4/3)πr³

Sphere SurfaceSA = 4πr²

Cylinder VolumeV = πr²h

Cylinder SurfaceSA = 2πr(r+h)

Cone VolumeV = (1/3)πr²h

Cube VolumeV = s³

Theorems

Pythagoreana² + b² = c²

Distance Formulad = √((x₂−x₁)²+(y₂−y₁)²)

MidpointM = ((x₁+x₂)/2, (y₁+y₂)/2)

Slopem = (y₂−y₁)/(x₂−x₁)

📊

Statistics & Probability

14 formulas

▾

Descriptive Statistics

Meanx̄ = (Σx) / n

Varianceσ² = Σ(xᵢ − x̄)² / n

Std Deviationσ = √(Σ(xᵢ−x̄)²/n)

Z-Scorez = (x − μ) / σ

Probability

Basic Prob.P(A) = favorable / total

ComplementP(A′) = 1 − P(A)

Addition RuleP(A∪B) = P(A)+P(B)−P(A∩B)

MultiplicationP(A∩B) = P(A)·P(B|A)

Bayes' TheoremP(A|B) = P(B|A)P(A)/P(B)

Combinatorics

PermutationP(n,r) = n! / (n−r)!

CombinationC(n,r) = n! / (r!(n−r)!)

⊞

Linear Algebra

10 formulas

▾

Matrix Operations

Determinant 2×2|A| = ad − bc

Inverse 2×2A⁻¹ = (1/|A|)[[d,−b],[−c,a]]

Transpose(Aᵀ)ᵢⱼ = Aⱼᵢ

Dot Producta·b = |a||b|cos θ

Cross Product|a×b| = |a||b|sin θ

Eigenvalues

DefinitionAv = λv

Char. Equationdet(A − λI) = 0

lim

Limits & L'Hôpital

8 formulas

▾

Limit Laws

Sumlim[f±g] = lim f ± lim g

Productlim[f·g] = lim f · lim g

Quotientlim[f/g] = lim f / lim g

L'Hôpitallim f/g = lim f′/g′ (if 0/0)

Special Limits

sin(x)/xlim(x→0) sin(x)/x = 1

(1+1/n)ⁿlim(n→∞)(1+1/n)ⁿ = e

eˣ−1/xlim(x→0)(eˣ−1)/x = 1