A level maths formulas that are not in the booklet

Quadratic formula

ax² + bx + c = 0 has roots x = (−b ± √(b² − 4ac)) / 2a

Laws of indices

aˣ × aʸ = aˣ⁺ʸ, aˣ ÷ aʸ = aˣ⁻ʸ, (aˣ)ʸ = aˣʸ

Definition of a logarithm

x = aⁿ means n = logₐ x (for a > 0 and x > 0)

Laws of logarithms

logₐ x + logₐ y = logₐ(xy), logₐ x − logₐ y = logₐ(x/y), k logₐ x = logₐ(xᵏ)

Equation of a straight line with gradient m through (x₁, y₁)

y − y₁ = m(x − x₁)

Condition for two lines to be perpendicular

m₁m₂ = −1 (the gradients multiply to −1)

nth term of an arithmetic sequence

uₙ = a + (n − 1)d

nth term of a geometric sequence

uₙ = arⁿ⁻¹

Sine rule

a / sin A = b / sin B = c / sin C

Cosine rule

a² = b² + c² − 2bc cos A

Area of a triangle using sine

Area = ½ab sin C

Pythagorean identity

cos²A + sin²A ≡ 1

Identities for sec² and cosec²

sec²A ≡ 1 + tan²A and cosec²A ≡ 1 + cot²A

Double angle formulas

sin 2A ≡ 2 sin A cos A, cos 2A ≡ cos²A − sin²A, tan 2A ≡ 2 tan A / (1 − tan²A)

Arc length and sector area (θ in radians)

s = rθ and A = ½r²θ

Derivative of xⁿ

nxⁿ⁻¹

Derivatives of sin kx and cos kx

sin kx gives k cos kx. cos kx gives −k sin kx.

Derivatives of eᵏˣ and ln x

eᵏˣ gives keᵏˣ. ln x gives 1/x.

Product rule

The derivative of f(x)g(x) is f′(x)g(x) + f(x)g′(x)

Chain rule

The derivative of f(g(x)) is f′(g(x))g′(x)

Integral of xⁿ

xⁿ⁺¹ / (n + 1) + c, for n ≠ −1

Integrals of cos kx and sin kx

cos kx gives (1/k) sin kx + c. sin kx gives −(1/k) cos kx + c.

Integrals of eᵏˣ and 1/x

eᵏˣ gives (1/k)eᵏˣ + c. 1/x gives ln|x| + c.

Area under a curve between x = a and x = b

The integral of y dx from a to b (where y ≥ 0)

Magnitude of the vector xi + yj + zk

√(x² + y² + z²)

Weight, friction and Newton's second law

Weight = mg. Friction F ≤ μR. Resultant force F = ma.

Velocity and acceleration with variable acceleration

v = dr/dt and a = dv/dt = d²r/dt². Going back: r = ∫v dt and v = ∫a dt.

Mean of a set of data

x̄ = Σx / n, or Σfx / Σf for a frequency table

Standard normal variable

Z = (X − μ) / σ, where X ~ N(μ, σ²)

Area of a trapezium

½(a + b)h, where a and b are the parallel sides and h the distance between them