**Return to A Level Further Mathematics Menu**

Included in the detailed content statements on the material which must be included in A level specifications in further mathematics which makes up approximately 50% of the total content of A level further mathematics, we see the section on Further calculus.

Given that this is a compulsory topic, teachers of Further Maths can usefully look at **specimen and practice materials for all the examination boards**. We can also use technology to demonstrate and check answers. Additionally there are many useful resources offering notes and examples which are freely available.

**WolframAlpha** can very easily be used to check any volumes of revolution and also gives a clear visualisation of the solid formed; note the option to show the surface or solid formed.

From OCR for syllabus A, the **Check In Tests** include Further Calculus (scroll down).

The **A Level notes from CIMT** include some useful notes, activities and exercises for Further Mathematics, if we look at **Chapter 8, Further Calculus** in the Further Pure Mathematics section the we see that the chapter includes Volumes of revolution. We also have reduction formulae which is included in the optinal content for AQA, Edexcel and OCR Specification A.

For more notes, examples and exercises, not just for Calculus but many parts of the Further Maths specification, as well as CIMT, try AJ Hobson’s ‘Just the Maths’ or the Helm Project.

Many useful notes and examples can be found in **AJ Hobson’s Just the Maths** (individual pdfs hosted by UEA) or a complete pdf from the Math Centre: **AJ Hobson’s ‘Just the Maths.**

If you have not come across the HELM Project before, the project was designed to support the mathematical education of engineering students and includes an extensive collection of notes which include very clear worked examples. For easy access to these resources, the ** HELM Project Workbooks **are hosted by

**Alternatively, the**

**Loughborough University’s Mathematics Learning Support Centre**.**complete set is hosted by the Open University**. To access the Open University resources you will need to

**create an account**(easy and free), this will also give you access to the numerous free online courses.

For easy reference. a **Notes and Examples** page has been added to the **Further Maths Series**.

Looking for resources on Improper Integrals, I came across **this** from the University of Pennsylvania, a clear presentation with worked examples.

Such integrals could be shown using WolframAlpha or Desmos. In Desmos, simply type b=infinity for the upper limit. For more on Integration with Desmos, see **Learn Desmos: Integrals.**

Edexcel have a Solution Bank and GeoGebra interactives for their various texts for Maths and Further Maths freely available online. If we look at **Core Pure Mathematics Book 2** for example, you can see the various chapter links. These take you to the interactives for each chapter and to full worked solutions for each exercise. Looking at Chapter 4 for example on Volumes of Revolution, we can see two GeoGebra Interactives allowing exploration of volumes of revolution around the x and y axes.