Mathematics Written Examination
Domain 3: Mathematics written examination
The mathematics written paper tests reasoning, proof, modelling and fluent technique across the syllabus. Marks are awarded for method and justification, so a correct answer with no working can lose most of the credit, while a clear method with a slip can still earn heavily.
What is assessed
- Analysis: functions, limits, derivatives, integrals, sequences and series, depending on your level.
- Geometry and vectors; probability and statistics; complex numbers or linear algebra where the syllabus includes them.
- Proof: induction, contradiction, counterexample; 'show that' questions require a logical chain, not a guess.
- Modelling: define variables, state assumptions, interpret parameters, validate the answer in context.
Technique that earns marks
- Show every non-trivial step; use exact values (surds, pi, ln) unless a decimal is requested.
- State domain restrictions and continuity/differentiability conditions.
- In 'hence' questions, use the previous result; in 'show' questions, do not assume what you are proving.
- Use the calculator to check, not to replace algebra.
Worked example
Let f(x) = x^2 e^(-x). Find f'(x) and classify the stationary points. Product rule: f'(x) = 2x e^(-x) - x^2 e^(-x) = x(2 - x)e^(-x). Stationary points at x = 0 and x = 2. Sign analysis: for x < 0, x is negative and (2 - x) is positive, so f' < 0; for 0 < x < 2, f' > 0; for x > 2, f' < 0. Hence x = 0 is a local minimum and x = 2 is a local maximum. The sign table is the justification; writing only 'second derivative test' without evaluating it is weaker.
Traps
- Rounding early and carrying the error through.
- Losing a solution when dividing by a variable, for example by x without considering x = 0.
- Ignoring domain restrictions (logarithm arguments, denominators, roots).
- Misreading 'hence' as 'or otherwise'.
- In modelling, giving a pure number without units or context.