- Improve the design of polystyrene cups
- What is the best way of tackling the jumps in a downhill ski race to minimise your time of descent?
- Determine the spacing of road humps so that a vehicle does not exceed the speed limit.
- Determine the distance of a barrier from a building so that a passerby is not hit by objects falling off the building.
- Calculate the length of bungee ropes to give a safe but exciting jump.

This section explains what is meant by “mathematical modelling” and also provides a real-life problem for you to work through to illustrate these ideas.