# Edexcel Further Core Maths AS Tutorials

Outlined below are the topics covered for Edexcel Further Core Maths AS course

It is advisable to check the official Edexcel Further Core Maths AS 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
- Multiplication and division rules for mod and argument of two complex numbers
- Exam Questions - Further complex numbers

## 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

View the Playlist of Tutorials below :

- Relationship between the roots and coefficients of a quadratic equation
- Relationship between the roots and coefficients of a cubic equation

## Series

## Standard Summations

## 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