WhatFurther Maths Unit 4 Professional Learning (Further Pure)
WhoKS5 teachers
WhenOctober 2024- July 2025
HowHybrid- Primarily online, with live sessions held to cover the more complicated topics in South and North Wales
To bookfmspwales@swansea.ac.uk

More information

This course will give a comprehensive coverage of FMU4 and is aimed at teachers who currently deliver AS-level Further Maths and would like to deliver A-level Further Maths, or teachers who currently teach FMU4 and would like a refresher.

Course Structure: 6 Sessions. This course will be spread over the whole academic year.

Session 1
Power Series and Trigonometry


Oct 2024
Maclaurin Series
General solution of trigonometric equations
Factor formulae
Use of t=tanĀ½x substitution
Inverse Trigonometric Functions
Session 2
Complex Numbers

Nov-Dec 2024
De Moivre’s Theorem
Applications to powers and roots of complex numbers
Applications to Trigonometry
Geometry of Complex Numbers
Session 3
Hyperbolic Functions

Jan – Feb 2025
Introducing the hyperbolic functions
The inverse hyperbolic functions
The calculus of hyperbolic and inverse hyperbolic functions
The catenary curve
Session 4
Integration

Mar-Apr 2025
Partial Fractions
improper Integrals
Further Integration Methods
Applications of Integration
Session 5
Matrices and Simultaneous Equations

Polar Co-ordinates

May-June 2025
Determinant and Inverse of a 3×3 Matrix
Solution of three simultaneous equations in three unknowns.

Polar co=ordinates and Polar curves
Use of calculus to investigate polar curves
Session 6
Differential Equations

June-July 2025
Exact differential equations and use of Integrating factor.
Solution of Second order linear differential equations
Applications of differential equations

Each module will consist of two online, weekday early evening, zoom sessions, separated by 7-14 days. In these sessions, the tutor will consider the major concepts of the topic. Video recordings of these sessions will be made available so that participants who are not able to attend can view the session that was missed.

Sessions 2 and 6 will include the possibility of you attending a face-to-face session with a tutor. These sessions will be on a weekday and held in both South Wales (Swansea) and North Wales (Wrexham or Bangor). These sessions will take place before the two zoom sessions. They will not only cover the material of the two on-line zoom sessions but also give you the opportunity to meet a member of the tutor team and exchange ideas and experiences with some of your fellow participants.

A full resource pack of learning materials, including the materials used in the zoom and face-to-face sessions, will be made available and it is hoped that you will work through the resources and attempt some exercised provided. During this period of self-study, you will have email access to your tutor.

Participants are expected to attend as many online sessions as possible.

Course Dates:

A face-to-face or online session will be held in each of the weeks indicated. Dates will be set as soon as possible.

Face-to-FaceOnline
Session 1Autumn Term Week 4
Autumn Term Week 6
Session 2Autumn Term Week 3Autumn Term Week 10
Autumn Term Week 12
Session 3Spring Term Week 4
Spring Term Week 6
Session 4Spring Term Week 9
Spring Term Week 10
Session 5Summer Term Week 5
Summer Term Week 6
Session 6Summer Term Week 8Summer Term Week 9
Summer Term Week 10

Sessions will be presented in English; materials will be available bilingually

This course will be certificated.

Each session has a short assessment task which participants will be encouraged to complete and send to their tutor. Each task will contain two or three exam style questions for participants to answer. In addition, participants will be asked to reflect upon the knowledge students will need to tackle such questions and possible teaching approaches that might be used in the classroom. It is hoped that each task should require less than 90 minutes to complete.

Certification will be based on satisfactory completion of these tasks and evidence of attendance at the sessions or independent work through the resource material.

The deadline for certification will be August 2025.