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A Level Further Mathematics Edexcel
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A Level Further Mathematics Edexcel
free revision notes.
A Level Further Mathematics Edexcel
– Topics
Core Pure Mathematics 1
Scalar product
Equations of planes in 3D
Equations of lines in 3D
Proving statements involving matrices
Proving divisibility results
Proof by mathematical induction
Inverses of linear transformations
Linear transformations in 3D
Successive transformations
Enlargements and stretches
Reflections and rotations
Linear transformations in two dimensions
Solving systems of equations using matrices
Inverting a 3 x 3 metric
Inverting a 2 x 2 matrix
Determinants
Matrix multiplication
Matrices
Modelling with volumes of revolution
Adding and subtracting volumes
Volumes of revolution around the y-axis
Volumes of revolution around the x-axis
Linear transformations of roots
Expressions relating to roots of polynomials
Roots of quartic equations
Roots of cubic equations
Roots of polynomials
Sums of squares and cubes
Sums of natural numbers
Regions in Argand diagrams
Loci in Argand Diagrams
Modulus-argument form of complex numbers
Modulus and Argument
Argand Diagrams
Cubic and quartic equations
Roots of quadratic equations
Complex conjugation
Multiplying Complex Numbers
Imaginary & Complex Numbers
Core Pure Mathematics 2
Coupled first-order simultaneous differential equations
Damped and forced harmonic motion
Simple harmonic motion
Modelling with first-order differential equations
Boundary conditions
Second-order non-homogeneous differential equations
Second-order homogeneous differential equations
First-order differential equations
Differentiating hyperbolic functions
Identities and equations
Inverse hyperbolic functions
Hyperbolic Functions
Tangents to polar curves
Area enclosed by a polar curve
Sketching curves
Polar coordinates and equations
Integrating hyperbolic functions
Modelling with volumes of revolution
Volumes of revolution of parametrically defined curves
Volumes of revolution around the y-axis
Volumes of revolution around the x-axis
Integrating using partial fractions
Integrating with inverse trigonometric functions
Differentiating inverse trigonometric functions
The mean value of a function
Improper integrals
Series expansions of compound functions
Maclaurin series
Higher derivatives
Series: The method of differences
Solving geometric problems
nth roots of complex numbers
Sums of series
Trigonometric identities
De Moivre's theorem
Multiplying and dividing complex numbers
Exponential form of complex numbers
Decision Mathematics 1
Two-Stage Simplex
The Simplex Method
The Vertex Method
The Objective Line Method
Feasible Regions
Linear programs
Scheduling
Resource Histograms
Gantt Charts
Critical Paths
Activity Networks
Travelling Salesman Problems (AS)
Route Inspection Problems (AS)
Floyd's Algorithm
Dijkstra's Algorithm (AS)
Prim's Algorithm (AS)
Spanning Trees and Kruskal's Algorithm (AS)
The Planarity Algorithm
Graphs (AS)
Bin Packing Algorithms (AS)
Sorting Algorithms (AS)
Algorithms (AS)
Decision Mathematics 2
Decision Analysis
Recurrence relations
Game theory
Dynamic programming
Flows in networks
Allocation (assignment) problems
Transportation problems
Further Mechanics 1
Elastic Collisions in Two Dimensions: Oblique Collisions of Spheres
Elastic Collisions in Two Dimensions: Successive Oblique Impacts
Successive Elastic Collisions in One Dimension (AS)
Elastic Collisions in One Dimension (AS)
Elastic Energy
Power
The Work-Energy Principle
Work and Energy
Momentum and Impulse in 2D
Momentum and Impulse Problems (AS)
Momentum and Impulse (AS)
Further Mechanics 2
Elastic Collisions in Two Dimensions: Oblique Impacts
Further Kinematics
Further Dynamics
Further Centres of Mass
Centres of Mass of Plane Figures
Motion in a Circle
Further Pure Mathematics 1
Simpson's Rule
Numerical Solution of Differential Equations
Further Numerical Methods
3D Geometry
Scalar Triple Product (AS)
Vector Cross Product (AS)
Loci Problems (AS)
Tangents and Normals to Curves (AS)
Parabolas, Ellipses and Hyperbolas (AS)
Reducible Differential Equations
Taylor Series and Differential Equations
Leibniz's Theorem
Limits
Taylor Series
The t-formulas (AS)
Further Statistics 1
Algebraic Inequalities (AS)
The Geometric Distribution
Poisson Approximation to B(n, p) (AS)
The Poisson Distribution (AS)
Mean and Variance of Binomial Distribution (AS)
Mean and Variance of Discrete Distributions (AS)
Further Statistics 1*
Probability Generating Functions
Central Limit Theorem
Chi Squared Tests (AS)
Geometric Hypothesis Tests
Poisson Hypothesis Tests
The Negative Binomial Distribution
Chi Squared Tests
Further Statistics 2
Quality of Tests
Other Hypothesis Tests and Confidence Intervals
Linear Regression
Estimation, Confidence intervals and tests using a normal distribution
Continuous Probability Distributions
Confidence intervals and Tests using the t- distribution
Combinations of Random Variables