A-level Further Mathematics for Year 12 - Course 1

This course by Imperial College London is designed to help you develop the skills you need to succeed in your A-level further maths exams.

You will investigate key topic areas to gain a deeper understanding of the skills and techniques that you can apply throughout your A-level study. These skills include:

Fluency – selecting and applying correct methods to answer with speed and efficiency

Confidence – critically assessing mathematical methods and investigating ways to apply them

Problem-solving – analysing the ‘unfamiliar’ and identifying which skills and techniques you require to answer questions

Constructing mathematical argument – using mathematical tools such as diagrams, graphs, logical deduction, mathematical symbols, mathematical language, construct mathematical argument and present precisely to others

Deep reasoning – analysing and critiquing mathematical techniques, arguments, formulae and proofs to comprehend how they can be applied

Over eight modules, you will be introduced to

complex numbers, their modulus and argument and how they can be represented diagrammatically

matrices, their order, determinant and inverse and their application to linear transformation

roots of polynomial equations and their relationship to coefficients

series, partial fractions and the method of differences

vectors, their scalar produce and how they can be used to define straight lines and planes in 2 and 3 dimensions.

Your initial skillset will be extended to give a clear understanding of how background knowledge underpins the A-level further mathematics course. You’ll also be encouraged to consider how what you know fits into the wider mathematical world.

What you'll learn

• How to extend the number system to include and the definition of a complex number.
• How to add, subtract, multiply and divide complex numbers.
• How to represent complex numbers on an Argand diagram and the modulus and argument of a complex number.
• How to write complex numbers in modulus-argument form.
• How to define loci in the complex plane.
• How to define a matrix by its order.
• How to add and subtract conformable matrices.
• How to multiply two conformable matrices.
• How to use matrices to define linear transformations.
• How to find invariant lines and lines of invariant points.
• How to find the determinant and inverse of a 2 x 2 and 3 x 3 matrix.
• How to use matrices to solve systems of linear equations.
• How to use standard series formulae to find the sums of other series.
• How to separate algebraic fractions into partial fractions.
• How to use the method of differences to find the sum of a series.
• How to find the scalar (dot) product of two vectors.
• How to define the equation of a line using vectors.
• How to define a plane using vectors.
• How to use vectors to solve problems involving lines and planes.