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Two circles of equal size intersect and the centre of each circle is on the circumference of the other. What is the area of the intersection? Now imagine that the diagram represents two spheres of equal volume with the centre of each sphere on the surface of the other. What is the volume of intersection?

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Power Up

Show without recourse to any calculating aid that 7^{1/2} + 7^{1/3} + 7^{1/4} < 7 and 4^{1/2} + 4^{1/3} + 4^{1/4} > 4 . Sketch the graph of f(x) = x^{1/2} + x^{1/3} + x^{1/4} -x

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Fractional Calculus I

You can differentiate and integrate n times but what if n is not a whole number? This generalisation of calculus was introduced and discussed on askNRICH by some school students.

Interactive Workout - Mathmo

Stage: 5 Short Challenge Level: Challenge Level:1

This workbook generates random questions from the UK core A-level mathematics syllabus.
It is very powerful and contains a huge range of topics, including graph sketching, trigonometry and all aspects of algebra and calculus. It is instant to use and comes equipped with the answers.
There are no time limits, targets or scores: just the opportunity for simple, unpressured practice.
There are many ways in which you can use this resource:
  1. It is ideal for quiet use in the computer room for individual study or revision
  2. You can point students who are having difficulty towards it for targeted practice on a certain question type.
  3. You can suggest that 'high fliers' use the resource to practise their skills, maximise their chances of a good A and improve their own algebraic fluency. They will appreciate this when they arrive at university where a high level of algebraic fluency gives a huge advantage.
  4. You can use the workbook for quick lesson starters. By revising old, previously covered topics the knowledge of students will be kept fresh and will have great benefit on the students' overall mathematical skill.
  5. You can suggest that students about to start university or year 13 use the workbook as a refresher after the holidays.
  6. You can have a go yourself as the teacher if you are teaching new material, feeling a little rusty or simply want to hone your already impressive algebraic skill!
More workbooks are planned. Please do get in touch if you have any comments.