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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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Broad Topics > Calculations and Numerical Methods > Inverses

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Journeys in Numberland

Stage: 2 Challenge Level: Challenge Level:1

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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The Add and Take-away Path

Stage: 1 Challenge Level: Challenge Level:1

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

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Which Symbol?

Stage: 2 Challenge Level: Challenge Level:1

Choose a symbol to put into the number sentence.

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Alphabetti Sudoku

Stage: 3 and 4 Challenge Level: Challenge Level:1

This Sudoku requires you to do some working backwards before working forwards.

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Groups of Sets

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

The binary operation * for combining sets is defined as the union of two sets minus their intersection. Prove the set of all subsets of a set S together with the binary operation * forms a group.

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What's a Group?

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Explore the properties of some groups such as: The set of all real numbers excluding -1 together with the operation x*y = xy + x + y. Find the identity and the inverse of the element x.