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### Number and algebra

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### Working mathematically

### For younger learners

### Advanced mathematics

# Set Square

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### Five Circuits, Seven Spins

### Mach Attack

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Age 16 to 18

Challenge Level

A triangle PQR, right angled at P, slides on a horizontal floor

with Q and R in contact with perpendicular walls. What is the locus

of P?

A circular plate rolls inside a rectangular tray making five circuits and rotating about its centre seven times. Find the dimensions of the tray.

Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.

Make an accurate diagram of the solar system and explore the concept of a grand conjunction.