FP3: Further Vectors & Multivariable Calculus

3D Vectors, Multivariable Calculus & MEI Extra Pure • Post-2017 Linear Alignment

Modern Specification Alignment (Post-2017 Linear A-Level)

While organized under the legacy module code FP3, these notes cover core topics across modern UK specifications:

Edexcel (9FM0): Core Pure 1 & 2 (Lines, Planes, Vector Cross Products) and Further Pure 1.
AQA (7367): Paper 1 & 2 Pure Core (3D Vectors, Vector Cross Products, Planes).
OCR A (H245): Pure Core 1 & 2 (3D Vectors, Cross Products, Planes) and Additional Pure (Y545).
OCR MEI (H645): Core Pure (Paper Y420 Vectors & Planes) and Extra Pure (Paper Y435 Multivariable Calculus).

View our full Cross-Board Curriculum Mapping Guide →

Practice Examination & Verified Model Solutions

Test your knowledge with our refreshed 75-mark practice examination paper and complete step-by-step model solutions, updated to eliminate historical past paper errors:

Download Practice Paper
75 marks • 1h 30m • Refreshed Edition

Download Model Solutions
Full step-by-step worked proofs • PDF

These study materials are based on the MEI specification for Further Pure Mathematics 3. So far I've written the vectors, multivariable calculus, and Markov chain pages, and the pages for the differential geometry and groups are on the way.

MEI's FP3 syllabus is a gentle introduction to concepts studied in university mathematics courses. I have not included pages for Edexcel FP3 because there is significant overlap with MEI FP2, which I have already put on this website.

Topics

Vectors (MEI) Core Pure Lines, Planes & Cross Products
Multivariable calculus (MEI) Extended Pure OCR MEI Extra Pure (Y435)
Markov chains (MEI) Applied Pure Discrete Transition Matrices