Mathematics - compulsory written examination
What the mathematics paper tests
The Mathematics compulsory written examination tests core syllabus mathematics and your ability to communicate a method. Expect algebra, functions, calculus, geometry, vectors, probability and statistics, depending on your course. The paper rewards justified reasoning, exact values where appropriate, correct notation and interpretation of results in context. A correct answer with no working can lose method marks; a clear method with a slip can still earn partial credit.
Core rules
- State the domain before differentiating, simplifying or solving.
- Show substitution, factorisation and sign analysis; do not jump from derivative to conclusion.
- Distinguish exact and approximate answers; round only at the end and state units.
- For optimisation on a closed interval, test critical points and endpoints.
- Interpret probability and statistics in the context of the question, not just as numbers.
Worked example
Find the absolute extrema of f(x) = x³ − 3x on [−2, 2]. f′(x) = 3x² − 3 = 3(x − 1)(x + 1), so the critical points are x = −1 and x = 1. Evaluate f at critical points and endpoints: f(−2) = −8 + 6 = −2; f(−1) = −1 + 3 = 2; f(1) = 1 − 3 = −2; f(2) = 8 − 6 = 2. Therefore the maximum value is 2, attained at x = −1 and x = 2, and the minimum value is −2, attained at x = −2 and x = 1. The table of values is part of the justification: it shows why endpoints matter and why a critical point is not automatically a maximum.
Traps that cost marks
Forgetting endpoints in a closed-interval optimisation; assuming every critical point is an extremum; losing a negative sign in expansion or substitution; rounding before the final answer; omitting the domain; and writing a numerical answer without units or interpretation. In probability, confusing independent and mutually exclusive events is another frequent error.