Free, complete A Level Further Mathematics (CAIE 9231) study notes from Mega Lecture — organised by topic so you can revise exactly what you need. Every set is a clean PDF you can download instantly, no sign-up required. Covers pure topics (complex numbers, matrices, series, calculus) plus differential equations and numerical methods.

Topic Notes (9231)

Comprehensive notes for every Further Maths topic — tap to open the PDF.

Complex Numbers

• Complex Numbers I — Notes (PDF)
• Complex Numbers II — Notes (PDF)

Matrices & Vectors

• Matrices — Notes (PDF)
• Vectors I — Notes (PDF)
• Vectors II — Notes (PDF)

Series, Induction & Power Series

• Series I — Notes (PDF)
• Series II — Notes (PDF)
• Power Series — Notes (PDF)
• Proof by Induction — Notes (PDF)

Calculus & Differential Equations

• Differential Equations — Notes (PDF)
• Further Integration — Notes (PDF)
• Solving DEs using Power Series — Notes (PDF)
• Solving DEs by Step-by-Step Methods — Notes (PDF)
• Hyperbolic Functions — Notes (PDF)

Coordinate Geometry & Polar Coordinates

• Conic Sections — Notes (PDF)
• Polar Coordinates — Notes (PDF)

Algebra — Inequalities

• Inequalities I — Notes (PDF)
• Inequalities II — Notes (PDF)

Numerical Methods

• Numerical Methods for Solving Equations — Notes (PDF)

Related resources

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Frequently asked questions

Where can I download free A Level Further Maths notes?

Right here — every topic above links to a free PDF you can open or download instantly, with no sign-up.

Which syllabus do these notes follow?

They are written for the Cambridge International (CAIE) Further Mathematics 9231 syllabus.

Which topics are covered?

Complex numbers, matrices, vectors, series and induction, power series, differential equations, hyperbolic functions, polar coordinates, inequalities and numerical methods.

Are the notes really free?

Yes. All notes are completely free. For live teaching, you can also book a free demo lecture below.