A-level Further Mathematics for Year 12 - Course 1: Complex Numbers, Matrices, Roots of Polynomial Equations and Vectors
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Brief Introduction
Develop your thinking skills, fluency and confidence in A-level further maths and prepare for undergraduate STEM degrees.
Description
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.
Knowledge
- 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.
Skills for A Level Further Mathematics Course 1: Complex Numbers, Matrices, Roots of Polynomial Equations, Series and Vectors
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Develop your thinking skills, fluency and confidence in A-level further maths and prepare for undergraduate STEM degrees. These skills include: Over eight modules, you will be introduced to...
A-level Further Mathematics for Year 12 - Course 1: Complex Numbers, Matrices, Roots of Polynomial Equations and Vectors
- 0.0
-
![]()
![]()
![]()
![]()
![]()
Develop your thinking skills, fluency and confidence in A-level further maths and prepare for undergraduate STEM degrees. These skills include: Over eight modules, you will be introduced to...
