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Quadratics
y = a(x − h)² + k (vertex form)
y = a(x − r)(x − s) (factored form)
x = (−b ± √(b²−4ac)) / 2a (quadratic formula)
Discriminant: D = b² − 4ac
Trigonometry
sin²θ + cos²θ = 1
sin(A±B) = sinA·cosB ± cosA·sinB
cos(A±B) = cosA·cosB ∓ sinA·sinB
Law of Sines: a/sinA = b/sinB = c/sinC
Law of Cosines: c² = a² + b² − 2ab·cosC
Exponentials & Logarithms
aˣ · aʸ = aˣ⁺ʸ
log_a(xy) = log_a(x) + log_a(y)
log_a(x/y) = log_a(x) − log_a(y)
log_a(xⁿ) = n·log_a(x)
A = P(1 + r/n)^(nt) (compound interest)
Calculus (MCV4U)
f'(x) = lim[h→0] (f(x+h) − f(x)) / h
d/dx [xⁿ] = nxⁿ⁻¹ (power rule)
d/dx [f·g] = f'g + fg' (product rule)
d/dx [f/g] = (f'g − fg') / g² (quotient rule)
d/dx [f(g(x))] = f'(g(x))·g'(x) (chain rule)
Physics (SPH3U / SPH4U)
v = d/t a = Δv/Δt
d = v₁t + ½at²
v₂² = v₁² + 2ad
F = ma W = Fd·cosθ
E_k = ½mv² E_p = mgh