At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

Areas and Ratios

What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.

Contact

A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?

Antifreeze

Stage: 3 and 4 Short Challenge Level:

1

Let the extra volume of antifreeze required be $x$ litres. Initially, there are 3.5 litres of antifreeze in the solution. So $3.5+x=0.3(14+x)$, that is, $35+10x=42+3x$, so $x=1$.

This problem is taken from the UKMT Mathematical Challenges.

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