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.

A decorator can buy pink paint from two manufacturers. What is the least number he would need of each type in order to produce different shades of pink.

Is it always possible to combine two paints made up in the ratios 1:x and 1:y and turn them into paint made up in the ratio a:b ? Can you find an efficent way of doing this?

If a sum invested gains 10% each year how long before it has doubled its value?

Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?

My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.

Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?

Have you ever wondered what it would be like to race against Usain Bolt?

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?

These Olympic quantities have been jumbled up! Can you put them back together again?

A collection of short problems on ratio, proportion and rates of change.

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?