Edexcel A-Level Maths: Equations & formulae not given

Quadratic Formula

x = -b±(√b²-4ac)/2a

Straight Line Equation

y-y₁ = m(x-x₁)

Line Length Equation

√(x₂-x₁)²+(y₂-y₁)²

Sine Rule (Lengths)

a/sinA = b/sinB = c/sinC

Sine Rule (Angles)

sinA/a = sinB/b = sinC/c

Cosine Rule (Lengths)

a² = b²+c²-2bc(cosA)

Cosine Rule (Angles)

cosA = (b²+c²-a²)/2bc

Midpoint for lines - endpoints (x₁, y₁) & (x₂, y₂)

(x₁+x₂)/2, (y₁+y₂)/2

Circle Equation - centre (a, b), radius (r)

(x-a)²+(y-b)² = r²

Circle Equation - centre (-f, -g), radius (√f²+g²-c)

x²+y²+2fx+2gy+c = 0

Magnitude of a vector

|a| = √x²+y²

Tangent to a curve: y = f(x) - point w/co-ords (a, f(a))

y-f(a) = f'(a)(x-a)

Normal to a curve: y = f(x) - point w/co-ords (a, f(a))

y-f(a) = -1/f'(a)(x-a)

Multiplication Law of Logs

logₐx+logₐy = logₐxy

Division Law of Logs

logₐx-logₐy = logₐ(x/y)

Power Law of Logs

logₐ(x^k) = klogₐx

Power Law of Logs - Special case when k = -1

logₐ(1/x) = logₐ(x⁻¹) = -logₐx