Year 9–10 Maths — Number, Algebra and Equations

Key Concepts & Formulas

• Index laws: aᵐ × aⁿ = aᵐ⁺ⁿ; aᵐ ÷ aⁿ = aᵐ⁻ⁿ; (aᵐ)ⁿ = aᵐⁿ; a⁰ = 1; a⁻ⁿ = 1/aⁿ; a^(1/n) = ⁿ√a

• Expanding: (a + b)² = a² + 2ab + b²; (a − b)² = a² − 2ab + b²; (a + b)(a − b) = a² − b²

• Factoring: look for common factors first; then difference of squares; then factoring quadratic ax² + bx + c

• Quadratic formula: x = (−b ± √(b² − 4ac)) / 2a — use when factoring is difficult

• Completing the square: convert x² + bx + c to (x + b/2)² + (c − b²/4)

• Surds: √a × √b = √(ab); √a / √b = √(a/b); rationalising the denominator: multiply by √a/√a

• Like surds: 3√2 + 5√2 = 8√2; unlike surds (e.g. √2 and √3) cannot be combined

• Simultaneous equations: substitution or elimination to find values satisfying both equations

• Linear-quadratic simultaneous equations: substitute the linear into the quadratic → solve the resulting quadratic