How our free revision notes, worked proofs, and practice papers align with the modern post-2017 linear A-level specifications across Pearson Edexcel, AQA, OCR A, and OCR MEI.
In 2017, the UK Department for Education (DfE) and Ofqual reformed A-level Further Mathematics from modular units into a linear assessment sitting at the end of Year 13.
Crucially, at least 50% of the entire A-level qualification is now a nationally standardized, compulsory Core Pure syllabus. The mathematical topics on this site (complex numbers, matrices, induction, differential equations, polar coordinates, vectors) are 100% compulsory across all exam boards!
Assessment: 4 papers (1h 30m each, 75 marks, 300 total).
Compulsory Core Pure (50%): Papers 1 & 2 cover all Core Pure topics.
Options (50%): Papers 3 & 4 chosen from 8 modules: Further Pure (FP1/FP2), Further Mechanics (FM1/FM2), Further Statistics (FS1/FS2), and Decision (D1/D2).
Assessment: 3 papers (2h 00m each, 100 marks, 300 total).
Compulsory Core (66⅔%): Papers 1 & 2 assess pure mathematics, calculus, and numerical methods.
Options (33⅓%): Paper 3 consists of two 50-mark sections chosen from Mechanics, Statistics, and Discrete Mathematics.
Assessment: 4 papers (1h 30m each, 75 marks, 300 total).
Compulsory Core (50%): Pure Core 1 (Y540) & Pure Core 2 (Y541).
Options (50%): Two papers chosen from Statistics (Y542), Mechanics (Y543), Discrete (Y544), and Additional Pure (Y545).
Assessment: 3 or 4 papers (360 scaled marks total).
Compulsory Core (50%): Mandatory Paper Y420 Core Pure (2h 40m, 144 raw marks).
Options (50%): Major/Minor pathways in Mechanics, Statistics, Modelling with Algorithms, Numerical Methods, and Extra Pure.
Use this reference table to find the study notes and practice papers corresponding to your syllabus:
| Mathematical Topic | Site Section | Modern Exam Alignment | Practice Paper |
|---|---|---|---|
| Proof by Induction | FP1 Notes | Mandatory Core Pure across Edexcel (CP1), AQA (P1), OCR A (Y540), OCR MEI (Y420). | FP1 Paper (Q1) |
| Complex Numbers Cartesian, polar, de Moivre, roots of unity, loci |
FP1 Notes FP2 Notes |
Mandatory Core Pure across all boards. Fundamental building block for all linear exams. | FP1 Paper (Q2, 4) FP2 Paper (Q6) |
| Roots of Polynomials Relations between roots & coefficients, complex conjugate pairs, quartic equations |
FP1 Notes | Mandatory Core Pure across Edexcel (CP1), AQA (P1), OCR A, and OCR MEI. | FP1 Paper (Q5) |
| Coordinate Systems & Conics Parabolas, rectangular hyperbolas, tangents, normals, intersection loci |
FP1 Notes | Mandatory Core Pure in Edexcel (Core Pure 1) and Further Pure options across boards. | FP1 Paper (Q9) |
| Numerical Methods Linear interpolation, interval bisection, Newton-Raphson process |
FP1 Notes | Core Pure / Option across AQA, Edexcel FP1, and OCR MEI Numerical Methods. | FP1 Paper (Q8) |
| Matrices & Linear Transformations Determinants, inverses, 2D composite transformations, invariant lines, diagonalisation |
FP1 Notes FP2 Notes |
Mandatory Core Pure across all boards (inverses, transformations). Diagonalisation & invariant lines in Further Pure / MEI. | FP1 Paper (Q1, 6, 7) FP3 Paper (Q5, 6) |
| 1st & 2nd Order Differential Equations Integrating factors, auxiliary equations, SHM, damped oscillations, trial PIs |
FP2 1st Order FP2 2nd Order |
Mandatory Core Pure across all boards (Edexcel CP2, AQA Paper 2, OCR Pure Core 2). | FP2 Paper (Q1, 2) |
| Algebraic Inequalities Non-linear rational inequalities, multiplying by squared denominators, critical values |
FP2 Notes | Mandatory Core Pure in OCR A (Y540), OCR MEI (Y420), and Further Pure options. | FP2 Paper (Q3) |
| Hyperbolic Functions & Integration Definitions, identities, Osborn's rule, hyperbolic calculus, inverse functions |
FP2 Notes | Mandatory Core Pure across Edexcel, AQA, OCR A, and OCR MEI. | FP2 Paper (Q5) |
| Polar Coordinates Cardioids, spirals, horizontal/vertical tangents, area of sectors |
FP2 Notes | Mandatory Core Pure across all boards. | FP2 Paper (Q7) |
| Taylor & Maclaurin Series Series expansions, limits, non-linear ODE approximations |
FP2 Notes | Mandatory Core Pure across all boards. | FP2 Paper (Q4) |
| Summation of Series & Differences Standard summation formulae, telescoping partial fractions |
FP1 Notes FP2 Notes |
Mandatory Core Pure across all boards. | FP1 Paper (Q3) FP2 Paper (Q8) |
| 3D Vectors, Lines & Planes Vector product, scalar triple product, plane equations, skew line distance |
FP3 Notes | Mandatory Core Pure across all boards. | FP3 Paper (Q1, 2) |
| Multivariable Calculus Partial derivatives, 3D stationary points, Hessian classification, tangent planes |
FP3 Calculus | Extended Pure in OCR MEI Extra Pure (Paper Y435) and university mathematics preparation. | FP3 Paper (Q3, 4) |
| Markov Chains & Discrete Models Transition matrices, state diagrams, two-step probabilities, steady-state distribution |
FP3 Markov | Optional Application in OCR MEI Modelling with Algorithms and applied discrete mathematics. | FP3 Paper (Q7) |
| Further Mechanics Variable acceleration, connected particles, friction, statics, moments, 2D vectors, collisions |
M1 Notes | Optional Application across Edexcel (FM1/FM2), AQA (Mechanics), OCR A (Y543), and OCR MEI (Y421/Y431). | M1 Paper (Q1–7) Q1 Kinematics, Q2 Pulleys, Q3 Friction, Q4 Statics, Q5 Moments, Q6 Vectors, Q7 Collisions |
All practice papers have been refreshed in LaTeX with full, rigorous step-by-step model solutions:
| Module | Question Paper | Full Model Solutions |
|---|---|---|
| FP1 (Core Pure Foundations) | FP1 Practice Paper (PDF) | FP1 Model Solutions (PDF) ✓ |
| FP2 (Advanced Core Pure) | FP2 Practice Paper (PDF) | FP2 Model Solutions (PDF) ✓ |
| FP3 (MEI / Advanced Vectors) | FP3 Practice Paper (PDF) | FP3 Model Solutions (PDF) ✓ |
| M1 (Mechanics Applications) | M1 Practice Paper (PDF) | M1 Model Solutions (PDF) ✓ |
Return to Homepage • Notes corrections or feedback: jon@jonbaldie.com