Subjects A-Level
A-Level Further Maths
The subject I scored 92% in. Core Pure plus whichever optional modules your school teaches.
Who this is for
Anyone taking Further Maths as a full A-Level or AS, on any board. This is the subject I did best in — 92% — and the one I most enjoy teaching, because the ideas are genuinely beautiful once they click.
What we cover
Core Pure — complex numbers (including de Moivre and roots of unity), matrices and transformations, determinants and inverses, series and the method of differences, proof by induction, roots of polynomials, volumes of revolution, polar coordinates, hyperbolic functions, differential equations (first and second order), Maclaurin series.
Optional modules — Further Mechanics, Further Statistics, Further Pure, and Decision / Modelling with Algorithms. Tell me which your school does and we’ll work on those.
Decision and algorithms
I’ve spent a lot of time with the algorithms content — insertion sort, bin packing, Dijkstra, Prim and Kruskal, route inspection, the simplex method, critical path analysis.
These are the modules where marks are most winnable, because the method is mechanical. The trick is total discipline in setting out your working: examiners want to see each pass of the algorithm laid out clearly, and students who scribble lose marks they’d earned.
Mechanics Minor
The difficulty of this module can vary between people, but what I found best which improved my skills drastically is to just practice lots of questions, and analyse what worked and if there are quicker ways of doing it. My advice here is to do questions as soon as you learn a new concept.
Stats Minor
Probably one of the easier modules, as it requires just the recycling of knowledge and understanding how the processes click e.g carrying out hypothesis tests. Make sure to know the content well, and add a little practice alongside just to reinforce.
On complex numbers and matrices: these two topics carry the whole subject. If they feel shaky, everything downstream feels shaky. It’s usually worth spending two full sessions rebuilding them properly rather than patching topic by topic.
Thinking about STEP?
Further Maths is the foundation for both papers — STEP 2 assumes the AS content, and STEP 3 assumes the full A-Level. If your offer is likely to include STEP, have a look at STEP preparation, and start earlier than you think you need to.
Free A-Level Further Maths resources
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