Core Concept
Quiz

Surds cannot be simplified to rational numbers. √a × √b = √(ab), √a / √b = √(a/b). To rationalise a denominator with (a + √b), multiply by the conjugate (a − √b).

Quadratic formula: x = [−b ± √(b²−4ac)] / 2a. Discriminant Δ = b²−4ac: Δ>0 two real roots, Δ=0 one repeated root, Δ<0 no real roots.

Vertex form: y = a(x−h)² + k, vertex at (h, k). Sum of roots = −b/a, product of roots = c/a.

Substitution: express one variable and substitute. Elimination: add/subtract equations to cancel a variable. Always check solution satisfies BOTH equations.

Domain = set of valid x-values. Range = set of resulting y-values. For y = f(x) + k: shift up/down k. For y = f(x − h): shift right h. For y = −f(x): reflect in x-axis. For y = f(−x): reflect in y-axis.

SOH CAH TOA: sin θ = opp/hyp, cos θ = adj/hyp, tan θ = opp/adj. Sine rule: a/sin A = b/sin B = c/sin C. Cosine rule: a² = b² + c² − 2bc·cos A.

Arithmetic: aₙ = a₁ + (n−1)d, Sₙ = n/2·(2a₁ + (n−1)d). Geometric: aₙ = a₁·rⁿ⁻¹, Sₙ = a₁(rⁿ−1)/(r−1) for r ≠ 1.

Mean = Σx / n. Median = middle value when sorted. Mode = most frequent. P(A) = favourable outcomes / total outcomes. P(A or B) = P(A) + P(B) − P(A and B).