# A-level Further Mathematics for Year 12 - Course 1

### What is this course about?

This course has been designed to cover selected topics from the first half of Year 12 in A-level Further Mathematics, both for those learning the material for the first time and those who want to revise it. Further detail about the content covered can be found below

### What topics are covered?

Complex Numbers (split into two modules):

• Imaginary numbers - definition
• Complex numbers – definition
• Complex conjugates and division
• The Argand diagram
• Modulus and Argument
• Loci on the Argand diagram
• Revision/introduction: Radian measure – before modulus and argument

Matrices (split into two modules):

• The order of a matrix
• Multiplication
• Identity matrix
• Transformations in 2D and 3D
• Invariant points and lines
• Determinant
• Inverse matrix
• Simultaneous equations
• Geometrical interpretation of the solution

Further Algebra and Functions (split into two modules):

• Solving polynomial equations with real coefficients
• The relationship between roots and coefficients in a polynomial equation
• Forming a polynomial equation whose roots are a linear transformation of the roots of a given polynomial equation
• Formulae for sums of integers, squares etc.
• Deriving formulae for series using standard formulae
• The method of differences
• [revision/introduction: Partial Fractions]
• PF and method of differences

Vectors (split into two modules):

• Vector and Cartesian forms of an equation of a straight line in 2D and 3D.
• Geometrical problems using vector equations of lines
• Vector and Cartesian forms of the equation of a plane.
• Dot product and angles between lines
• Dot product equation of a plane
• Geometrical problems with lines and planes
• Intersection of a line and a plane.
• Perpendicular dist between two lines, from a point to a line and from a point to a plane.

### Who is this course aimed at?

This module is relevant for all students studying any STEM subject, particularly those looking to consolidate their existing Maths knowledge. If you have not studies Further Maths, this course offers a good opportunity to explore some of the topics covered at A-Level.

### How will this course be delivered?

This is an asynchronous module and will be delivered online, via the EdX platform. The course will be available from Summer 2021 and details about how to access it will be placed in the links to courses tab of your Microsoft Teams space closer to the time.

### How much time will the course take up?

The course is designed to take up roughly 2-4 hours per week of your time.