May 2003, Stage 4&5

Problems

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Excel Technique: LCM & HCF (or GCD)

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Learn how to use the Excel functions LCM and GCD.

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Excel Interactive Resource: Fraction Addition & Fraction Subtraction

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Use Excel to practise adding and subtracting fractions.

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Excel Investigation: Fraction Combinations

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Choose four numbers and make two fractions. Use an Excel spreadsheet to investigate their properties. Can you generalise?

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Knight Defeated

Stage: 4 Challenge Level: Challenge Level:1

The knight's move on a chess board is 2 steps in one direction and one step in the other direction. Prove that a knight cannot visit every square on the board once and only (a tour) on a 2 by n board. . . .

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Magic W

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

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LOGO Challenge - Following On

Stage: 3, 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?

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Witch of Agnesi

Stage: 5 Challenge Level: Challenge Level:1

Sketch the members of the family of graphs given by y = a^3/(x^2+a^2) for a=1, 2 and 3.

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Teams

Stage: 5 Challenge Level: Challenge Level:1

Two brothers belong to a club with 10 members. Four are selected for a match. Find the probability that both brothers are selected.