# A-level Further Mathematics for Year 12 - Course 2

### 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?

Proof:

• Methods of proof
• Mathematical induction o Sums of series
• Divisibility
• Matrix results

Polar Coordinates:

• Conversion between polar and Cartesian coordinates
• Sketching polar curves
• Area enclosed by a polar curve

Further Calculus (split into two modules):

• Volumes of revolution
• The mean value of a function
• Improper Integrals
• Extending partial fractions to include a quadratic denominator (that can’t be factorised)
• Integration using partial fractions
• Differentiating inverse trig functions

Complex Numbers (split into two modules):

• DeMoivre’s theorem
• multiple angle formulae
• Sums of series
• nnth roots of a complex number
• Roots of unity and geometrical interpretation

Hyperbolic Functions (split into two modules):

• Definitions of hyperbolic functions and their graphs, domains, ranges
• Differentiation and integration
• Inverse hyperbolic functions and their domains and ranges
• The use of hyperbolic functions in integration

### 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.