Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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?

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?

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.