A-Level OCR MEI (B) Further Maths
Complete revision notes and practice questions for OCR MEI (B) A-Level Further Mathematics (H645). Core Pure, Mechanics, Statistics, Modelling with Algorithms, Numerical Methods & Extra Pure.
H645Spec Code
3-4Papers (Flexible)
37Topics
Core Pure Mathematics — Mandatory Paper (Y420)
1. Proof by Induction
Core Pure
1a
Induction for Sums and Divisibility
NotesPractice
1b
Induction with Matrices and Roots
NotesPractice
2. Complex Numbers
Core Pure
2a
Modulus-Argument Form & Loci
NotesPractice
2b
De Moivre’s Theorem & Trigonometric Identities
NotesPractice
2c
Solving Equations & Complex Roots
NotesPractice
3. Matrices
Core Pure
3a
Determinants and Inverse Matrices
NotesPractice
3b
Linear Transformations in 2D and 3D
NotesPractice
3c
Eigenvalues, Eigenvectors & Diagonalisation
NotesPractice
4. Further Algebra & Series
Core Pure
4a
Roots of Polynomials & Coefficients
NotesPractice
4b
Standard Series & Method of Differences
NotesPractice
4c
Maclaurin Series Expansion
NotesPractice
5. Further Calculus
Core Pure
5a
Integration using Partial Fractions
NotesPractice
5b
Improper Integrals
NotesPractice
5c
Volumes of Revolution & Mean Value
NotesPractice
6. Polar Coordinates
Core Pure
6a
Sketching Polar Curves
NotesPractice
6b
Finding Areas in Polar Coordinates
NotesPractice
7. Vectors
Core Pure
7a
Vector and Scalar Products
NotesPractice
7b
Equations of Lines and Planes
NotesPractice
7c
Intersections and Shortest Distances
NotesPractice
8. Differential Equations
Core Pure
8a
First Order ODEs & Integrating Factor
NotesPractice
8b
Second Order Linear Differential Equations
NotesPractice
8c
Coupled First Order ODEs
NotesPractice
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Mechanics — Major (Y421) / Minor (Y431) Options
M1. Dimensional Analysis
Mechanics
M1a
Finding Dimensions & Checking Consistency
NotesPractice
M2. Work, Energy, Impulse & Momentum
Mechanics
M2a
Work-Energy Principle & Power
NotesPractice
M2b
Conservation of Momentum (1D & 2D)
NotesPractice
M2c
Newton’s Law of Restitution & Impacts
NotesPractice
M3. Centre of Mass & Circular Motion
Mechanics
M3a
Centres of Mass (Rigid Bodies & Calculus)
NotesPractice
M3b
Motion in a Circle (Horizontal & Vertical)
NotesPractice
M3c
Hooke’s Law & Elastic Potential Energy
NotesPractice
Statistics — Major (Y422) / Minor (Y432) Options
S1. Probability Distributions
Statistics
S1a
Discrete Distributions (Poisson, Binomial, Uniform)
NotesPractice
S1b
Continuous Distributions (PDFs & CDFs)
NotesPractice
S1c
Linear Combinations of Random Variables
NotesPractice
S2. Hypothesis Testing & Intervals
Statistics
S2a
Confidence Intervals (Normal & t-distribution)
NotesPractice
S2b
Chi-Squared Tests (Goodness of Fit & Contingency)
NotesPractice
S2c
Non-Parametric Tests (Wilcoxon, Sign Test)
NotesPractice
Modelling with Algorithms — Minor Option (Y433)
A1. Algorithms & Network Routing
Algorithms
A1a
Sorting & Packing Algorithms
NotesPractice
A1b
Network Algorithms (Prim, Kruskal, Dijkstra)
NotesPractice
A1c
Linear Programming & The Simplex Method
NotesPractice
Numerical Methods — Minor Option (Y434)
N1. Numerical Analysis
Numerical
N1a
Numerical Solution of Equations (Newton-Raphson)
NotesPractice
N1b
Numerical Integration (Trapezium, Simpson, Midpoint)
NotesPractice
N1c
Numerical Differentiation & ODEs (Euler method)
NotesPractice
Extra Pure — Minor Option (Y435)
E1. Advanced Pure Topics
Extra Pure
E1a
Recurrence Relations
NotesPractice
E1b
Group Theory (Axioms, Subgroups, Isomorphisms)
NotesPractice
E1c
Surfaces, Partial Differentiation & Vector Calculus
NotesPractice
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