Mathematics
HS Mathematics tests procedural fluency and reasoned solutions across algebra, trigonometry, coordinate geometry, calculus, vectors, probability and linear programming. Marks are usually method-based, so a correct final answer with no working can lose most of the credit.
Core rules and concepts
- Algebra: show substitutions; state domain restrictions for rational, logarithmic and inverse trigonometric expressions.
- Trigonometry: use identities to simplify before solving; check the general solution and the given interval.
- Coordinate geometry: write the standard form first, then substitute; keep distance, slope and section formulas distinct.
- Calculus: differentiate using product, quotient and chain rules; for definite integrals, find the antiderivative and then apply limits.
- Vectors and matrices: check conformability; a matrix inverse requires a non-zero determinant.
- Probability: use conditional probability and independence conditions explicitly.
Worked example: definite integral
Evaluate ∫₀¹ (3x² + 2x) dx. Antiderivative: x³ + x². Apply limits: (1³ + 1²) − (0³ + 0²) = 2. Reasoning: integrate term by term, then subtract the lower-limit value from the upper-limit value; no constant of integration is needed for a definite integral.
Traps that cost marks
- Omitting '+ C' in an indefinite integral.
- Losing signs when subtracting limits or expanding brackets.
- Using degrees in calculus; calculus requires radians.
- Ignoring the phrase 'hence' and starting a fresh method.
- Giving a diagram or answer without the required proof or condition.