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In Particular

Write 100 as the sum of two positive integers, one divisible by 7 and the other divisible by 11. Then find formulas giving all the solutions to 7x + 11y = 100 where x and y are integers.

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Garfield's Proof

Rotate a copy of the trapezium about the centre of the longest side of the blue triangle to make a square. Find the area of the square and then derive a formula for the area of the trapezium.

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For What?

Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.

Training Schedule

Stage: 4 Challenge Level: Challenge Level:1

Why not use a spreadsheet to calculate quickly the score for each event given the athlete's times or distances?
Then try tweaking her times and distances to see how her scores can be affected by different training schedules.