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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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Doesn't Add Up

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

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From All Corners

Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.

Lap Times

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

If the track length is L then you can write down the speeds and the distance between the cyclists at any given time in terms of L. The cyclists meet when the relative distance covered is a multiple of L. You might like to model this using a cardboard tube and threads. Think of the length of the tube as the time axis and the threads around the tube showing the cyclists path on the track.