A Level Maths formulas A–Z

A–Z

A

• Arc length l = rθ
• Area of a sector A = ½r²θ

B

• Binomial distribution P(X = r) = nCr pʳ(1 − p)ⁿ⁻ʳ
• Binomial expansion (1 + x)ⁿ = 1 + nx + n(n − 1)x²/2! + …

C

• Chain rule dy/dx = dy/du × du/dx
• Cosine rule a² = b² + c² − 2bc cos A

D

• Derivative of sin x d/dx (sin kx) = k cos kx
• Double angle formulas sin 2A = 2 sin A cos A

E

• Equation of a circle (x − a)² + (y − b)² = r²

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

N

• Normal distribution (z-score) z = (x − μ) / σ

P

• Product rule d/dx (uv) = u dv/dx + v du/dx

Q

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

S

• Sine rule a/sin A = b/sin B
• Standard deviation σ = √(Σx²/n − x̄²)
• Sum of a geometric series Sₙ = a(1 − rⁿ)/(1 − r)
• Sum of an arithmetic series Sₙ = n/2 (2a + (n − 1)d)
• Sum to infinity of a geometric series S∞ = a / (1 − r)
• SUVAT equations v = u + at, s = ut + ½at²

T

• Trig identities sin²θ + cos²θ = 1

By topic

Algebra

Binomial expansionLaws of logarithmsQuadratic formula

Sequences and series

Sum of a geometric seriesSum of an arithmetic seriesSum to infinity of a geometric series

Geometry and trigonometry

Arc lengthArea of a sectorCosine ruleDouble angle formulasSine ruleTrig identities

Coordinate geometry

Equation of a circleGradient formula

Calculus

Chain ruleDerivative of sin xIntegration by partsProduct ruleQuotient rule

Mechanics

SUVAT equations

Statistics and probability

Binomial distributionNormal distributionStandard deviation