Further Maths is taken alongside A-Level Maths and assumes it throughout. Complex numbers, matrices, further calculus and further pure extend techniques you already meet in the main course, so gaps in core algebra and calculus cause far more trouble here than they do there.
The subject rewards fluency over familiarity. Many questions are long, and a technique you can only just perform will run out of time or accuracy halfway through. The aim is to reach the point where the standard manipulations are automatic and your attention is free for the actual problem.
Proof is a larger part of the course than students expect. Induction in particular is a structured argument with a required form, and marks are awarded for the structure — base case, assumption, inductive step, conclusion — as much as for the algebra inside it.
These notes cover complex numbers, matrices, further calculus and further pure, with worked examples for each method.
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