10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

What fractions can you find between the square roots of 65 and 67?

Four vehicles travel along a road one afternoon. Can you make sense of the graphs showing their motion?

Can you hit the target functions using a set of input functions and a little calculus and algebra?

By tossing a coin one of three princes is chosen to be the next King of Randomia. Does each prince have an equal chance of taking the throne?

Can you work out the equations of the trig graphs I used to make my pattern?

Which line graph, equations and physical processes go together?

By sketching a graph of a continuous increasing function, can you prove a useful result about integrals?

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

2009 was clearly an interesting year! Find out which mathematical fact about 2009 we found most interesting.

In this article, Jennifer Piggott talks about just a few of the problems with problems that make them such a rich source of mathematics and approaches to learning mathematics.