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### Triathlon and Fitness

The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?

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### Vector walk

Starting with two basic vector steps, which destinations can you reach on a vector walk?

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### Summing geometric progressions

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?

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### Iff

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

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### Always Perfect

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

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### Perfectly Square

The sums of the squares of three related numbers is also a perfect square - can you explain why?

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### Back fitter

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

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### What's that graph?

Can you work out which processes are represented by the graphs?

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### Bendy Quad

Four rods are hinged at their ends to form a convex quadrilateral.
Investigate the different shapes that the quadrilateral can take.
Be patient this problem may be slow to load.