A-Level Edexcel Further Maths
Complete revision notes and practice questions for Edexcel A-Level Further Mathematics (9FM0). Core Pure, Further Pure, Further Statistics, Further Mechanics & Decision Maths.
9FM0Spec Code
4Papers
51Topics
Core Pure Mathematics — Papers 1 & 2 (Mandatory)
1. Proof
Core Pure
1a
Proof by Mathematical Induction
NotesPractice
1b
Induction for Series, Divisibility & Matrices
NotesPractice
2. Complex Numbers
Core Pure
2a
Introduction to Complex Numbers
NotesPractice
2b
Solving Equations with Complex Roots
NotesPractice
2c
Argand Diagrams
NotesPractice
2d
Modulus & Argument
NotesPractice
2e
Modulus-Argument & Exponential Form
NotesPractice
2f
Loci in Argand Diagrams
NotesPractice
2g
De Moivre’s Theorem
NotesPractice
2h
Roots of Complex Numbers & nth Roots of Unity
NotesPractice
3. Matrices
Core Pure
3a
Introduction to Matrices
NotesPractice
3b
Matrix Multiplication
NotesPractice
3c
Determinants (2×2 and 3×3)
NotesPractice
3d
Inverse Matrices
NotesPractice
3e
Solving Simultaneous Equations Using Matrices
NotesPractice
3f
Transformations Using Matrices
NotesPractice
3g
Invariant Points & Lines
NotesPractice
4. Further Algebra & Functions
Core Pure
4a
Roots of Polynomials
NotesPractice
4b
Linear Transformations of Roots
NotesPractice
4c
Sums of Integers, Squares & Cubes
NotesPractice
4d
Method of Differences
NotesPractice
4e
Maclaurin Series
NotesPractice
5. Further Calculus
Core Pure
5a
Improper Integrals
NotesPractice
5b
Mean Value of a Function
NotesPractice
5c
Further Integration with Partial Fractions
NotesPractice
5d
Volumes of Revolution
NotesPractice
6. Further Vectors
Core Pure
6a
Vector Equation of a Line
NotesPractice
6b
Dot Product & Cross Product
NotesPractice
6c
Scalar Triple Product
NotesPractice
6d
Equation of a Plane
NotesPractice
6e
Distances Between Points, Lines & Planes
NotesPractice
7. Polar Coordinates
Core Pure
7a
Polar Curves & Sketching
NotesPractice
7b
Area Enclosed by Polar Curves
NotesPractice
7c
Tangents at the Pole & Tangent Lines
NotesPractice
8. Hyperbolic Functions
Core Pure
8a
Definitions of sinh, cosh & tanh
NotesPractice
8b
Inverse Hyperbolic Functions
NotesPractice
8c
Hyperbolic Identities & Equations
NotesPractice
8d
Differentiating & Integrating Hyperbolic Functions
NotesPractice
9. Differential Equations
Core Pure
9a
First-Order Differential Equations
NotesPractice
9b
Second-Order Homogeneous DEs
NotesPractice
9c
Second-Order Non-Homogeneous DEs
NotesPractice
9d
Boundary Conditions & Modelling
NotesPractice
9e
Coupled Differential Equations
NotesPractice
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Further Pure Mathematics 1 — Paper 3A (Option)
FP1.1 Further Trigonometry
Option 1
FP1.1a
t-Formulae (Weierstrass Substitution)
NotesPractice
FP1.1b
Applications of t-Formulae
NotesPractice
FP1.2 Further Calculus
Option 1
FP1.2a
Reduction Formulae
NotesPractice
FP1.2b
Arc Length
NotesPractice
FP1.2c
Surface Area of Revolution
NotesPractice
FP1.3 Further Differential Equations
Option 1
FP1.3a
Taylor Series Method
NotesPractice
FP1.3b
Reducible Differential Equations
NotesPractice
FP1.4 Coordinate Systems
Option 1
FP1.4a
Parabola, Ellipse & Hyperbola
NotesPractice
FP1.4b
Tangents & Normals to Conics
NotesPractice
FP1.4c
Loci Problems
NotesPractice
FP1.5 Further Vectors
Option 1
FP1.5a
Direction Ratios & Direction Cosines
NotesPractice
FP1.5b
Line & Plane Intersections
NotesPractice
FP1.6 Further Numerical Methods
Option 1
FP1.6a
Simpson’s Rule
NotesPractice
FP1.6b
Numerical Solution of Differential Equations
NotesPractice
FP1.7 Inequalities
Option 1
FP1.7a
Algebraic Inequalities
NotesPractice
FP1.7b
Modulus Inequalities
NotesPractice
Further Pure Mathematics 2 — Paper 4A (Option)
FP2.1 Groups
Option 2
FP2.1a
Axioms of a Group
NotesPractice
FP2.1b
Cayley Tables & Cyclic Groups
NotesPractice
FP2.1c
Lagrange’s Theorem
NotesPractice
FP2.1d
Isomorphism
NotesPractice
FP2.2 Further Calculus
Option 2
FP2.2a
Leibnitz’s Theorem
NotesPractice
FP2.2b
L’Hôpital’s Rule
NotesPractice
FP2.3 Further Matrix Algebra
Option 2
FP2.3a
Eigenvalues & Eigenvectors
NotesPractice
FP2.3b
Cayley-Hamilton Theorem
NotesPractice
FP2.3c
Diagonalisation
NotesPractice
FP2.4 Further Complex Numbers
Option 2
FP2.4a
Further Loci & Regions
NotesPractice
FP2.4b
Sums of Series Using de Moivre
NotesPractice
FP2.5 Number Theory
Option 2
FP2.5a
Euclidean Algorithm & Bézout’s Identity
NotesPractice
FP2.5b
Modular Arithmetic & Congruences
NotesPractice
FP2.5c
Fermat’s Little Theorem & Divisibility
NotesPractice
FP2.6 Further Sequences & Series
Option 2
FP2.6a
Further Maclaurin & Taylor Series
NotesPractice
FP2.6b
Limits & Convergence
NotesPractice
Further Statistics 1 — Paper 3B (Option)
FS1.1 Discrete Probability Distributions
Option 3
FS1.1a
Expectation & Variance
NotesPractice
FS1.1b
Mean & Variance of Functions of X
NotesPractice
FS1.2 Poisson & Binomial Distributions
Option 3
FS1.2a
Poisson Distribution
NotesPractice
FS1.2b
Poisson as Approximation to Binomial
NotesPractice
FS1.2c
Additive Property of Poisson
NotesPractice
FS1.3 Geometric & Negative Binomial
Option 3
FS1.3a
Geometric Distribution
NotesPractice
FS1.3b
Negative Binomial Distribution
NotesPractice
FS1.4 Hypothesis Testing
Option 3
FS1.4a
Hypothesis Testing for Poisson & Binomial
NotesPractice
FS1.4b
Critical Regions & Significance Levels
NotesPractice
FS1.5 Central Limit Theorem
Option 3
FS1.5a
Central Limit Theorem & Applications
NotesPractice
FS1.6 Chi-Squared Tests
Option 3
FS1.6a
Goodness of Fit Tests
NotesPractice
FS1.6b
Contingency Tables
NotesPractice
FS1.7 Probability Generating Functions
Option 3
FS1.7a
PGFs and Finding Mean & Variance
NotesPractice
FS1.7b
PGFs for Sums of Random Variables
NotesPractice
FS1.8 Quality of Tests
Option 3
FS1.8a
Type I & Type II Errors
NotesPractice
FS1.8b
Power Function & Size of Test
NotesPractice
Further Statistics 2 — Paper 4B (Option)
FS2.1 Linear Regression
Option 4
FS2.1a
Least Squares Regression
NotesPractice
FS2.1b
Residuals & Analysis
NotesPractice
FS2.2 Continuous Distributions
Option 4
FS2.2a
PDFs, CDFs & Percentiles
NotesPractice
FS2.2b
Rectangular Uniform Distribution
NotesPractice
FS2.3 Correlation
Option 4
FS2.3a
Spearman’s Rank Correlation
NotesPractice
FS2.3b
Hypothesis Testing for Correlation
NotesPractice
FS2.4 Combinations of Random Variables
Option 4
FS2.4a
Linear Combinations of Random Variables
NotesPractice
FS2.5 Confidence Intervals (Normal)
Option 4
FS2.5a
Unbiased Estimators
NotesPractice
FS2.5b
Confidence Intervals Using Normal
NotesPractice
FS2.6 Other Hypothesis Tests
Option 4
FS2.6a
F-Test for Variance
NotesPractice
FS2.6b
Paired & Two-Sample t-Tests
NotesPractice
FS2.7 Confidence Intervals (t-Distribution)
Option 4
FS2.7a
Confidence Intervals Using t-Distribution
NotesPractice
Further Mechanics 1 — Paper 3C (Option)
FM1.1 Momentum & Impulse
Option 5
FM1.1a
Impulse & Momentum
NotesPractice
FM1.1b
Conservation of Momentum
NotesPractice
FM1.1c
Newton’s Experimental Law (Restitution)
NotesPractice
FM1.2 Work, Energy & Power
Option 5
FM1.2a
Work-Energy Principle
NotesPractice
FM1.2b
Power & Variable Forces
NotesPractice
FM1.3 Elastic Strings & Springs
Option 5
FM1.3a
Hooke’s Law
NotesPractice
FM1.3b
Elastic Potential Energy
NotesPractice
FM1.4 Elastic Collisions in 1D
Option 5
FM1.4a
Direct Impact Collisions
NotesPractice
FM1.4b
Successive Impacts & Wall Collisions
NotesPractice
FM1.5 Elastic Collisions in 2D
Option 5
FM1.5a
Oblique Impact Collisions
NotesPractice
Further Mechanics 2 — Paper 4C (Option)
FM2.1 Motion in a Circle
Option 6
FM2.1a
Circular Motion & Angular Speed
NotesPractice
FM2.1b
Vertical Circles & Conical Pendulums
NotesPractice
FM2.2 Centres of Mass (Plane Figures)
Option 6
FM2.2a
Centres of Mass of Standard Shapes
NotesPractice
FM2.2b
Composite Shapes & Frameworks
NotesPractice
FM2.3 Further Centres of Mass
Option 6
FM2.3a
Solids of Revolution
NotesPractice
FM2.3b
Toppling & Sliding
NotesPractice
FM2.4 Further Dynamics
Option 6
FM2.4a
Simple Harmonic Motion
NotesPractice
FM2.4b
Damped & Forced Oscillations
NotesPractice
FM2.5 Further Kinematics
Option 6
FM2.5a
Variable Acceleration (Calculus Methods)
NotesPractice
Decision Mathematics 1 — Paper 3D / 4D (Option)
D1.1 Algorithms & Graph Theory
Option 7
D1.1a
Sorting & Bin-Packing Algorithms
NotesPractice
D1.1b
Graph Theory Fundamentals
NotesPractice
D1.1c
Planarity & Eulerian Trails
NotesPractice
D1.2 Algorithms on Graphs I
Option 7
D1.2a
Minimum Spanning Trees (Kruskal & Prim)
NotesPractice
D1.2b
Dijkstra’s Shortest Path
NotesPractice
D1.3 Algorithms on Graphs II
Option 7
D1.3a
Route Inspection (Chinese Postman)
NotesPractice
D1.3b
Travelling Salesman Problem
NotesPractice
D1.4 Critical Path Analysis
Option 7
D1.4a
Activity Networks & Critical Path
NotesPractice
D1.4b
Gantt Charts & Resource Levelling
NotesPractice
D1.5 Linear Programming
Option 7
D1.5a
Graphical Linear Programming
NotesPractice
D1.5b
Simplex Algorithm
NotesPractice
Decision Mathematics 2 — Paper 4D (Option)
D2.1 Transportation Problems
Option 8
D2.1a
North-West Corner & Least Cost
NotesPractice
D2.1b
Stepping-Stone Method
NotesPractice
D2.2 Allocation (Assignment) Problems
Option 8
D2.2a
Hungarian Algorithm
NotesPractice
D2.3 Flows in Networks
Option 8
D2.3a
Maximum Flow & Min-Cut Max-Flow
NotesPractice
D2.3b
Multiple Sources & Sinks
NotesPractice
D2.4 Dynamic Programming
Option 8
D2.4a
Multi-Stage Decision Problems
NotesPractice
D2.5 Game Theory
Option 8
D2.5a
Play-Safe & Dominance
NotesPractice
D2.5b
Mixed Strategies & LP Formulation
NotesPractice
D2.6 Recurrence Relations
Option 8
D2.6a
Solving Recurrence Relations
NotesPractice
D2.7 Decision Analysis
Option 8
D2.7a
Decision Trees & EMV
NotesPractice
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