Edexcel Further Core Maths A-Level
It is advisable to check the official Edexcel Further Core Maths A-Level specification in case of any changes.
Contents
Complex Numbers
Complex Numbers
- Real and imaginary numbers
- Addition, subtraction and multiplying complex numbers and simplifying powers of i
- Complex conjugates
- Division of a complex number by a complex number
- Argand diagrams
- Modulus and argument of a complex number
- Solving problems with complex numbers
- Square roots of a complex number
- Solving quadratic equations with complex roots
- Solving cubic equations
- Solving quartic equations
- Exam Questions - Complex numbers
- Geometrical effects of conjugating a complex number
- Exam Questions - Finding roots
- Modulus-argument form of a complex number
- Exponential Form (Euler's relation)
- Multiplication and division rules for mod and argument of two complex numbers
- Exam Questions - Further complex numbers
De Moivre’s Theorem
Loci in the Complex Plane
Matrix Algebra
Matrices
- Introduction and dimension of a matrix
- Addition and subtraction and multiplying a matrix by a scalar
- Matrix multiplication
- Identity and Inverse of a 2x2 matrix
- Exam Questions - Identity and inverse of a 2x2 matrix
- Transposed and symmetric matrices
- Finding the determinant of a 3x3 matrix
- Finding the inverse of a 3x3 matrix where it exists
Simultaneous Equations by Matrix Methods
Matrix Linear Transformations
- Linear transformations - rotations
- Linear transformations - reflections
- Linear transformations - enlargement
- How well do you know your transformations?
- Combinations of transformations
- Inverse matrices to reverse linear transformations
- Determinant as the area scale factor of a transformation
- Exam Questions - Matrix transformations
Roots of Polynomial Equations
Series
Standard Summations
Method of Differences
Maclaurin’s Series
Proof by Mathematical Induction
Sum of Series
Various Types of Proofs
Further Calculus
Applications of Integration – Volumes of revolution
- Volume of revolution about the x-axis
- Exam Questions - Volume of revolution about the x-axis
- Volume of revolution about the x-axis generated between curves
- Volume of Revolution about the y-axis
- Exam Questions - Volume of Revolution about the y-axis
- Volume of Revolution about the y-axis generated between curves
- Volume of revolution for a curve given in parametric form
- Exam Questions - Volume of revolution: parametric form
Improper Integrals
Mean Value of a Function
Integrals involving Partial fractions
Differentiating Inverse Trigonometric Functions
Standard Integrals Involving Inverse Trigonometric Functions
Vectors
Scalar Product (Dot Product)
Vector Equations of Lines
Exam Questions – Vectors
Planes
Polar Coordinates and Curves
Polar Coordinates
Equations of Curves
Area Bounded by a Polar Curve
Tangents
Hyperbolic Functions
Hyperbolic Functions
- Definitions
- Graphs of sinh(x), cosh(x) and tanh(x)
- Graphs of sech(x), cosech(x) and coth(x)
- Solving equations using inverse and exponential functions
- Hyperbolic identities
- Osborn's rule
- Inverse hyperbolic functions and their graphs
- Expressing inverse hyperbolic functions as natural logarithms
- Solving hyperbolic equations using hyperbolic identities
Differentiation of Hyperbolic Functions
Standard Integrals Involving Hyperbolic Functions
First Order Linear Differential Equations
Exact Equations (Integrating Factors)
Second Order Linear Differential Equations
Equations of the form a d²y/dx² + b dy/dx + cy = 0
Equations of the form a d²y/dx² + b dy/dx + cy = f(x)
- General solutions where f(x) = k (constant types)
- General solutions where f(x) = kx (linear types)
- General solutions where f(x) = kx2 (quadratic types)
- General solutions where f(x) = kepx (exponential types)
- General solutions where f(x) = λ cosωx + µ sinωx (trig types)
- Special types of particular integrals
- Exam Questions - General solutions where f(x) = kx (linear types)
- Particular solutions using boundary conditions to solve differential equations
- Exam Questions - Exponential Type kepx (exponential types)
- Exam Questions - Trig Type
- Exam Questions - Particular solutions using boundary conditions