Topics from Year 13 Compulsory Further Pure, session 2 - Further Calculus and Hyperbolic Functions



Do you need to improve your familiarity with the content of the Further Maths Pure curriculum?

Do you feel rusty? Maybe you haven't taught Further Maths recently.

Or maybe you are reasonably confident with the content but would like to develop your pedagogy.

Do you want to help your students with those topics where they struggle, and you are thinking 'How do I teach this?'? 

This course, where we will be covering topics from the Year 13 Further Maths Compulsory Common Pure specifications, is over three sessions, and you can attend all three or just the one or two which cover those topics you are interested in. You will need to sign up separately for each session.

In this session Yvonne Scott and Lesley Swarbrick focus on Further Calculus and Hyperbolic Functions

Session 1 (Wednesday 30th June): Alexandra Hewitt will be looking at SeriesComplex Numbers, and Polar Coordinates

Session 3 (Wednesday 14th July) will cover Differential Equations, techniques, motivation and modelling (Yvonne Scott and Lesley Swarbrick

This course will not be covering content in detail. If you feel that you need more than 6 hours of support to prepare to teach this course, including more detailed coverage of content, you may prefer to join one of our longer courses: On Demand Professional Development (ODPD) AS and A level Further Maths: compulsory Pure Top-ups or our Sustained Course: Teaching Further Maths 1 and 2



  • To develop approaches to teaching that engage all students in A level Further Mathematics learning
  • To develop the confidence of teachers when delivering Further Mathematics Pure topics

Who will benefit from attending?

Current and prospective teachers of Further Pure Mathematics, irrespective of which exam board you use.


  • Evaluate improper integrals where either the integrand is undefined in the range of integration or the range extends to ∞
  • Derive formulae for and calculate volumes of revolution
  • Understand and evaluate the mean value of a function
  • Integrate using partial fractions
  • Differentiate inverse trig functions
  • Integrate functions of the form (a2-x2) and (a2+x2)-1 and be able to choose trig substitutions to integrate associated functions
  • Definitions and graphs of sinh x, cosh x, and tanh x
  • Differentiate and integrate hyperbolic functions
  • Inverse hyperbolic functions
  • Derive and use the logarithmic forms of the inverse hyperbolic functions
  • Integrate functions of the form (x2+a2) and (x2-a2) and choose substitutions to integrate associated functions

Materials and Equipment

The meeting will be on the Zoom platform. 

The link to the meeting will be emailed in the week before the session.

You are advised to use a headset or headphones with a microphone to provide the best sound quality and to prevent audio issues for other users. A laptop with a built-in webcam and microphone may be sufficient if you’re in a quiet area but please take the time to check this before the session.

In order to fully participate in the meeting please be willing to use your camera and microphone, although if this is impossible the chat option will be available.

We will be using Desmos and Geogebra activities so you will need to be using a device which can support this. 

As part of our safeguarding procedures please note the following:
(i) It is important that you log in with the names you used when you registered for the meeting otherwise you may not be allowed into the room. If you prefer to use a shortened/alternative name, then do let us know via email in advance of the session.
(ii) You must not pass on any of the registration or Zoom meeting details to anyone else.

Other Information

We would appreciate that you arrive from 4.15pm for a prompt start at 4.30pm. There will be a break of 10 minutes halfway through.

Key Facts

Event ref:




Curriculum focus:

A level Further Mathematics

Mathematical focus:


Event format:

Face-to-face Professional Development

Event length:

2 hours






Wed 7th Jul 2021

Course times:

16:30 - 18:30



State-sector subsidy:


Priority Area subsidy:



Printable Version


If you have any queries about this event, please do not hesitate to contact:

Lesley Swarbrick
[email protected]
07590 075010

The AMSP, through MEI, holds the NCETM CPD Standard

National Centre for Excellence in the teaching of Mathematics

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