Interactive Formula Reference — IGCSE 0580 & 0606

x = (−b ± √(b² − 4ac)) ⁄ 2a

a² − b² = (a + b)(a − b)

x² + bx = (x + b⁄2)² − (b⁄2)²

nth term = a + (n − 1)d

nth term = an² + bn + c

A = P(1 + r⁄100)ⁿ

aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ

Eliminate one variable by making coefficients equal

a² + b² = c²

Sum = (n − 2) × 180°

Lengths: k, Areas: k², Volumes: k³

sinθ = O⁄H, cosθ = A⁄H, tanθ = O⁄A

a⁄sin A = b⁄sin B = c⁄sin C

a² = b² + c² − 2bc·cos A

cos A = (b² + c² − a²) ⁄ 2bc

A = ½ × a × b × sin C

sin30=½, cos30=√3/2, tan30=1/√3, sin45=1/√2, cos45=1/√2, tan45=1, sin60=√3/2, cos60=½, tan60=√3

Measure clockwise from North (000° to 360°)

A = πr²

C = 2πr = πd

A = ½(a + b) × h

V = cross-sectional area × length

V = πr²h

V = ⅓πr²h

V = ⁴⁄₃ πr³

SA = 4πr²

CSA = πrl

Arc = (θ⁄360) × 2πr

A = (θ⁄360) × πr²

m = (y₂ − y₁) ⁄ (x₂ − x₁)

y = mx + c

M = ((x₁+x₂)⁄2, (y₁+y₂)⁄2)

d = √((x₂−x₁)² + (y₂−y₁)²)

Mean = Σx ⁄ n

Frequency density = frequency ÷ class width

IQR = Q₃ − Q₁

P(event) = favourable outcomes ⁄ total outcomes

P(A and B) = P(A) × P(B)

P(A or B) = P(A) + P(B)

P(not A) = 1 − P(A)

If y = xⁿ then dy/dx = nxⁿ⁻¹

dy/dx = dy/du × du/dx

dy/dx = u·dv/dx + v·du/dx

dy/dx = (v·du/dx − u·dv/dx) ⁄ v²

∫xⁿ dx = xⁿ⁺¹/(n+1) + C (n ≠ −1)

Set dy/dx = 0 and solve

% Change = (change ÷ original) × 100

Original = final amount ÷ multiplier

Speed = Distance ÷ Time

Density = Mass ÷ Volume

fg(x) = f(g(x))

Replace f(x) with y, swap x and y, solve for y

log(ab) = log a + log b, log(a/b) = log a − log b, log(aⁿ) = n·log a

(a+b)ⁿ = Σ ⁿCᵣ · aⁿ⁻ʳ · bʳ