IB Maths formulas A–Z

A–Z

A

• Arc length l = rθ
• Area of a sector A = ½r²θ
• Area of a triangle (½ab sin C) Area = ½ab sin C
• Arithmetic sequence (nth term) uₙ = u₁ + (n − 1)d

B

• Binomial distribution P(X = r) = nCr pʳ(1 − p)ⁿ⁻ʳ
• Binomial expansion (a + b)ⁿ = Σ nCr aⁿ⁻ʳ bʳ

C

• Chain rule dy/dx = dy/du × du/dx
• Compound interest FV = PV(1 + r/100k)^kn
• Conditional probability P(A | B) = P(A ∩ B) / P(B)
• Cosine rule a² = b² + c² − 2bc cos A

D

• Derivative of sin x d/dx (sin x) = cos x
• Distance formula d = √((x₁ − x₂)² + (y₁ − y₂)²)

G

• Gradient formula m = (y₂ − y₁) / (x₂ − x₁)

I

• Integration by parts ∫ u dv = uv − ∫ v du

L

• Laws of logarithms log xy = log x + log y

M

• Magnitude of a vector |v| = √(v₁² + v₂² + v₃²)
• Midpoint formula M = ((x₁ + x₂)/2, (y₁ + y₂)/2)

N

• nCr formula (combinations) nCr = n! / (r!(n − r)!)
• Normal distribution (z-score) z = (x − μ) / σ

P

• Probability formulas P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
• Product rule d/dx (uv) = u dv/dx + v du/dx
• Pythagoras' theorem a² + b² = c²

Q

• Quadratic formula x = (−b ± √(b² − 4ac)) / 2a
• Quotient rule d/dx (u/v) = (v u′ − u v′) / v²

S

• Scalar (dot) product v · w = |v||w| cos θ
• Sine rule a/sin A = b/sin B
• SOH CAH TOA (right-angled trigonometry) sin = opp/hyp, cos = adj/hyp, tan = opp/adj
• Standard deviation σ = √(Σ(x − μ)² / n)
• Sum of a geometric series Sₙ = u₁(1 − rⁿ)/(1 − r)
• Sum of an arithmetic series Sₙ = n/2 (2u₁ + (n − 1)d)
• Sum to infinity of a geometric series S∞ = u₁ / (1 − r)

T

• Trig identities sin²θ + cos²θ = 1

V

• Volume of a cone V = ⅓πr²h
• Volume of a sphere V = ⁴⁄₃πr³

By topic

Algebra

Binomial expansionLaws of logarithmsnCr formulaQuadratic formula

Number and finance

Compound interest

Sequences and series

Arithmetic sequenceSum of a geometric seriesSum of an arithmetic seriesSum to infinity of a geometric series

Geometry and trigonometry

Arc lengthArea of a sectorArea of a triangleCosine rulePythagoras' theoremSine ruleSOH CAH TOATrig identities

Coordinate geometry

Distance formulaGradient formulaMidpoint formula

Mensuration

Volume of a coneVolume of a sphere

Vectors

Magnitude of a vectorScalar (dot) product

Calculus

Chain ruleDerivative of sin xIntegration by partsProduct ruleQuotient rule

Statistics and probability

Binomial distributionConditional probabilityNormal distributionProbability formulasStandard deviation