Mathematics and Further Mathematics
What the paper tests
Mathematics Standard 2, Mathematics Advanced, Extension 1 and Extension 2 are separate courses with separate papers. Advanced builds on calculus, functions, trigonometry and probability; Extension 1 adds vectors, proof by mathematical induction and combinatorics; Extension 2 adds complex numbers, mechanics and further integration. Standard 2 is built on financial mathematics, measurement, statistics and networks. Every paper rewards communication in correct notation and logical setting-out, not merely a correct numeral.
Core rules
- Show every step; a correct answer with no working typically earns a single mark.
- Use the reference sheet, but define the variables you substitute.
- Give exact answers unless rounding is specified; round only at the end.
- Check domain restrictions: division by zero, log arguments, square roots, inverse-trig denominators.
- 'Hence' means use the previous part; 'hence or otherwise' permits your own method.
Worked example
Find and classify the stationary points of f(x) = x³ − 3x² + 1. f′(x) = 3x² − 6x = 3x(x − 2), so f′(x) = 0 at x = 0 and x = 2. f(0) = 1 and f(2) = 8 − 12 + 1 = −3. f″(x) = 6x − 6; f″(0) = −6 < 0, so (0, 1) is a local maximum; f″(2) = 6 > 0, so (2, −3) is a local minimum. Both coordinates and the test used must be stated - the classification carries its own mark.
Traps
Differentiating when the question asks for an integral; calculator in the wrong angle mode; rounding intermediate values; discarding the negative root; asserting an induction result without stating the assumption.