How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?

On the grid provided, we can draw lines with different gradients. How many different gradients can you find? Can you arrange them in order of steepness?

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

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?

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

What fractions can you find between the square roots of 56 and 58?

There is still one unanswered question left, but most of this problem has been solved. Can anyone finish it off?

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.

We asked what was the most interesting fact that you can find out about the number 2009. See the solutions that were submitted.