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When we watch sports coverage of the multi-discipline events such as the heptathlon, the scoring mechanism is not usually made explicit. This problem explores some of the maths behind the scoring system and invites students to optimise an athlete's performance by choosing a suitable training schedule. Along the way, students can practise substituting into formulas, make sense of functions, and use spreadsheets to repeat routine calculations quickly.
Set the scene by introducing the seven heptathlon events (perhaps asking students if they can name the events). Then display the two equations:
Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...
The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = nÂ² Use the diagram to show that any odd number is the difference of two squares.
Can you make sense of information about trees in order to maximise the profits of a forestry company?