Mathematics
Mathematics covers algebra, trigonometry, coordinate geometry, calculus, vectors, matrices, sequences and series, probability, and statistics. The paper rewards formula recall plus the ability to simplify before substituting numbers.
Core rules
- Quadratic formula: x = [−b ± √(b² − 4ac)] / 2a; the discriminant decides the nature of roots.
- Standard limits: lim(x→0) sin x / x = 1, with x in radians.
- Derivative rules: d/dx(xⁿ) = nx^(n−1), product and quotient rules, chain rule.
- Integration is anti-differentiation; include the constant of integration for indefinite integrals.
- Distance, midpoint, and section formulas in coordinate geometry; slope m = (y₂ − y₁)/(x₂ − x₁).
- Probability of an event = favourable outcomes / total equally likely outcomes; P(A∪B) = P(A) + P(B) − P(A∩B).
Worked example. Evaluate lim(x→2) (x² − 4)/(x − 2). Direct substitution gives 0/0, so factorise: x² − 4 = (x − 2)(x + 2). Cancel the common factor (x − 2) for x ≠ 2, leaving x + 2. The limit is 2 + 2 = 4.
Traps. Set the calculator to radians for calculus; check domain restrictions before cancelling; a 0/0 form is indeterminate, not zero; add +C for indefinite integrals; do not confuse permutations with combinations; a matrix inverse exists only when the determinant is non-zero.