Identities
- (a + b)² = a² + 2ab + b²
- (a − b)² = a² − 2ab + b²
- a² − b² = (a + b)(a − b)
- (a + b)³ = a³ + 3a²b + 3ab² + b³
- (a − b)³ = a³ − 3a²b + 3ab² − b³
- a³ + b³ = (a + b)(a² − ab + b²)
- a³ − b³ = (a − b)(a² + ab + b²)
Quadratics
- Standard form: ax² + bx + c = 0
- Quadratic formula: x = (−b ± √(b² − 4ac)) / 2a
- Sum of roots: −b/a
- Product of roots: c/a
Exponents
- aᵐ × aⁿ = aᵐ⁺ⁿ
- aᵐ ÷ aⁿ = aᵐ⁻ⁿ
- (aᵐ)ⁿ = aᵐⁿ
- a⁰ = 1 (a ≠ 0)
- a⁻ⁿ = 1/aⁿ
Logarithms
- logₐ(mn) = logₐm + logₐn
- logₐ(m/n) = logₐm − logₐn
- logₐ(mⁿ) = n·logₐm
How to use this sheet
Keep this open alongside practice papers rather than memorizing it in isolation — recognizing when to apply an identity is the harder skill, and comes from working through problems, not from re-reading the list.