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:
Over eight modules, you will be introduced to
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.
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.
Module 1: Complex Numbers 1: An Introduction to Complex Numbers
Module 2: Matrices 1: An Introduction to Matrices
Module 3: Further Algebra and Functions 1: Roots of Polynomial Equations
Module 4: Complex Numbers 2: Modulus-Argument form and Loci
The modulus and argument of a complex number
Writing complex numbers in modulus argument form
The geometrical effect of multiplying by a complex number.
Loci on the Argand diagram
Module 5: Matrices 2: Determinants and Inverse Matrices
Module 6: Further Algebra and Functions 2: Series, Partial Fractions and the Method of Differences
Module 7: Vectors 1: The Scalar (dot) Product and Vector Equations of Lines
Module 8: Vectors 2: The Vector Equations of a Plane and Geometrical Problems with Lines and Planes
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