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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...

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Stage: 4 Challenge Level: Challenge Level:1


The distance between centres of two adjacent faces of a cube is $8$cm. What is the side length of the cube?

I can make an equilateral triangle by cutting off the corner of a cube. If the area of the largest equilateral triangle I can create in this way is $140$cm$^2$, what is the side length of this cube?

A third cube has an edge length of $12$cm. At each vertex, a tetrahedron with three mutually perpendicular edges of length $4$cm is cut away. Can you find the volume and the surface area of the remaining solid?