# OCR Further Pure Core Maths A-Level

It is advisable to check the official OCR Further Pure 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
- Complex numbers specimen questions (mixed exam boards)

## Loci in the Complex Plane

## De Moivre’s Theorem

## 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
- 3D matrix transformations
- Invariant points

## Vectors

## Scalar Product (Dot Product)

## Vector Equations of Lines

## Exam Questions – Vectors

## Vector Product

## Lines: Vector to Cartesian form

## Planes

## Further Calculus

## Maclaurin’s Series

## Improper Integrals

## 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

## Mean Value of a Function

## Integrals involving Partial fractions

## Differentiating Inverse Trigonometric Functions

## Integrals Involving Inverse Trigonometric Functions

## Differentiation: Hyperbolic Functions

## Integrals Involving Hyperbolic Functions

## First Order Linear Differential Equations

## Separating the Variables

## Exact Equations (Integrating Factors)

## Substitution Types

## 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) = kx
^{2}(quadratic types) - General solutions where f(x) = ke
^{px}(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 ke
^{px}(exponential types) - Exam Questions - Trig Type
- Exam Questions - Particular solutions using boundary conditions

## Using a Substitution

## Simple Harmonic Motion

## Linear Systems

## Past Papers for OCR Further Pure Core Maths A-Level

For further revision and practice I have past papers, some with worked solutions – Check them out.