Further pure math 1(Edexcel AS and A level modular mathematics)

Complex numbers

Real and imaginary numbers

Multiplying complex numbers and simplifying powers of i

The complex conjugate of a complex number

Representing complex numbers on an Argand diagram

Finding the value of r, the modulus of a complex number z, and the value of θ, the argument of z

The modulus–argument form of the complex number z

Solving problems involving complex numbers

Solving polynomial equations with real coefficients

Numerical solutions of equations

Solving equations of the form f(x) = 0 using interval bisection

Solving equations of the form f(x) = 0 using linear interpolation

Solving equations of the form f(x) = 0 using the Newton–Raphson process

Coordinate systems

Introduction to parametric equations

The general equation of a parabola

The equation for a rectangular hyperbola and finding tangents and normals

Review Exercise 1

Matrix algebra

Finding the dimension of a matrix

Adding and subtracting matrices of the same dimension

Multiplying a matrix by a scalar (number)

Multiplying matrices together

Using matrices to describe linear transformations

Using matrices to represent rotations, reflections and enlargements

Using matrix products to represent combinations of transformations

Finding the inverse of a 2 × 2 matrix where it exists

Using inverse matrices to reverse the effect of a linear transformation

Using the determinant of a matrix to determine the area scale factor of the transformation

Using matrices and their inverses to solve linear simultaneous equations

Series

The Σ notation

The formula for the sum of the first n natural numbers, Σr

Formulae for the sum of the squares of the first n natural numbers, Σr², and for the sum of the cubes of the first n natural numbers, Σr³

Using known formulae to sum more complex series

Proof by mathematical induction

Obtaining a proof for the summation of a series, using induction

Using proof by induction to prove that an expression is divisible by a certain integer

Using mathematical induction to produce a proof for the general terms of a recurrence relation

Using proof by induction to prove general statements involving matrix multiplication

Review Exercise 2

Examination style paper