A-Level OCR A Further Maths
Complete revision notes and practice questions for OCR A A-Level Further Mathematics (H245). Core Pure, and optional Statistics, Mechanics, Discrete & Additional Pure papers.
H245Spec Code
4Papers (Choose 2 Options)
34Topics
Core Pure Mathematics — Papers 1 & 2 (Y540 & Y541)
1. Proof by Induction
Core Pure
1a
Induction for Series & Divisibility
NotesPractice
1b
Induction for Matrices
NotesPractice
2. Complex Numbers
Core Pure
2a
Arithmetic, Argand Diagrams & Mod-Arg Form
NotesPractice
2b
Loci & Regions in the Complex Plane
NotesPractice
2c
De Moivre’s Theorem & Multiple Angles
NotesPractice
2d
nth Roots of Complex Numbers
NotesPractice
3. Matrices
Core Pure
3a
Operations, Determinants & Inverses
NotesPractice
3b
Solving Simultaneous Linear Equations
NotesPractice
3c
Linear Transformations in 2D and 3D
NotesPractice
3d
Invariant Points and Lines
NotesPractice
4. Further Algebra & Functions
Core Pure
4a
Roots of Polynomials
NotesPractice
4b
Summation of Series & Method of Differences
NotesPractice
4c
Maclaurin Series
NotesPractice
5. Further Calculus
Core Pure
5a
Volumes of Revolution
NotesPractice
5b
Improper Integrals & Mean Value of a Function
NotesPractice
5c
Integration with Partial Fractions
NotesPractice
5d
Inverse Trigonometric Calculus
NotesPractice
6. Polar Coordinates
Core Pure
6a
Sketching Polar Curves & Equivalencies
NotesPractice
6b
Areas Enclosed by Polar Curves
NotesPractice
7. Hyperbolic Functions
Core Pure
7a
Definitions, Graphs & Identities
NotesPractice
7b
Calculus of Hyperbolic Functions
NotesPractice
8. Differential Equations
Core Pure
8a
First Order DEs & Integrating Factor
NotesPractice
8b
Second Order Homogeneous & Non-Homogeneous DEs
NotesPractice
8c
Modelling Oscillations (SHM & Damping)
NotesPractice
9. Further Vectors
Core Pure
9a
Vector and Scalar Products
NotesPractice
9b
Equations of Lines and Planes
NotesPractice
9c
Distances and Intersections
NotesPractice
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Statistics — Paper 3 (Y542)
S1. Combinatorics & Discrete Distributions
Statistics
S1a
Combinatorics & Probability
NotesPractice
S1b
Discrete Random Variables (Poisson, Binomial, Geometric)
NotesPractice
S1c
Probability Generating Functions
NotesPractice
S2. Continuous Random Variables
Statistics
S2a
PDFs, CDFs and Continuous Uniform Distribution
NotesPractice
S2b
Linear Combinations of Random Variables
NotesPractice
S2c
Central Limit Theorem
NotesPractice
S3. Hypothesis Testing & Non-Parametrics
Statistics
S3a
Chi-Squared Tests (Goodness of Fit & Contingency)
NotesPractice
S3b
Non-Parametric Tests (Wilcoxon Rank-Sum & Signed-Rank)
NotesPractice
S3c
Correlation (Pearson & Spearman) and Regression
NotesPractice
Mechanics — Paper 4 (Y543)
M1. Dimensional Analysis
Mechanics
M1a
Dimensions of Physical Quantities
NotesPractice
M1b
Checking and Deriving Formulae
NotesPractice
M2. Work, Energy & Power
Mechanics
M3. Impulse & Momentum
Mechanics
M3a
Direct Impact and Restitution
NotesPractice
M3b
Oblique Impacts (2D Collisions)
NotesPractice
M4. Centre of Mass & Circular Motion
Mechanics
M4a
Centres of Mass (Shapes, Composite & Calculus)
NotesPractice
M4b
Equilibrium, Sliding and Toppling
NotesPractice
M4c
Motion in a Circle
NotesPractice
Discrete Mathematics — Paper 5 (Y544)
D1. Networks & Network Algorithms
Discrete
D1a
Graph Modelling & Properties
NotesPractice
D1b
Minimum Spanning Trees (Prim, Kruskal)
NotesPractice
D1c
Shortest Paths (Dijkstra, Floyd)
NotesPractice
D2. Optimisation & Decision Making
Discrete
D2a
Route Inspection & TSP
NotesPractice
D2b
Linear Programming & Simplex Algorithm
NotesPractice
D2c
Critical Path Analysis
NotesPractice
D2d
Game Theory & Network Flows
NotesPractice
Additional Pure Mathematics — Paper 6 (Y545)
AP1. Recurrence Relations
Add. Pure
AP1a
First and Second Order Recurrence Relations
NotesPractice
AP1b
Solving Non-Homogeneous Linear Relations
NotesPractice
AP2. Number Theory
Add. Pure
AP2a
Modular Arithmetic and Congruences
NotesPractice
AP2b
Fermat’s Little Theorem & Euclidean Algorithm
NotesPractice
AP3. Group Theory
Add. Pure
AP3a
Group Axioms, Cyclic Groups & Cayley Tables
NotesPractice
AP3b
Subgroups, Lagrange’s Theorem & Isomorphisms
NotesPractice
AP4. Further Calculus & Vector Geometry
Add. Pure
AP4a
Partial Differentiation & Surfaces
NotesPractice
AP4b
Vector Product Applications & Calculus of Vectors
NotesPractice
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