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Golden Thoughts

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

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Ladder and Cube

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

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Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

Largest Product

Stage: 3 and 4 Challenge Level: Challenge Level:1
Thinking about rectangles and cuboids might be useful.
Try some numbers out for yourself.