A-Level Mathematics
Formula Sheet

Pure maths and mechanics formulas. From algebra to calculus and beyond.

Pure Mathematics

Algebra

(a+b)² = a² + 2ab + b²
(a-b)² = a² - 2ab + b²
a² - b² = (a+b)(a-b)
logₐ(b) = ln(b)/ln(a)

Trigonometry

sin²θ + cos²θ = 1
tanθ = sinθ/cosθ
sin(A±B) = sinAcosB ± cosAsinB
cos(A±B) = cosAcosB ∓ sinAsinB

Calculus

d/dx [xⁿ] = nxⁿ⁻¹
∫ xⁿ dx = xⁿ⁺¹/(n+1) + C
d/dx [eˣ] = eˣ
∫ eˣ dx = eˣ + C

Mechanics

Kinematics

v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t

Forces

F = ma
W = mg
F = kx (Hooke's law)
p = mv (momentum)

Energy

KE = ½mv²
PE = mgh
Work = Fd cos θ
Power = W/t = Fv

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