When is $7^n + 3^n$ a multiple of 10? Can you prove the result by two different methods?

Which is the bigger, 9^10 or 10^9 ? Which is the bigger, 99^100 or 100^99 ?

Take a look at the video showing rhombuses and their diagonals...

In a city with a grid system of roads, how do you get from A to B?

What's special about the area of quadrilaterals drawn in a square?

Can you minimise the amount of wood needed to build the roof of my garden shed?

This comes in two parts, with the first being less fiendish than the second. Itâ€™s great for practising both quadratics and laws of indices, and you can get a lot from making sure that you find all the solutions. For a real challenge (requiring a bit more knowledge), you could consider finding the complex solutions.

This problem is a nice introduction that will give you a feeling for how logs work and what that button on your calculator might be doing.

Here you have an opportunity to explore the proofs of the laws of logarithms.

Can you find cubic functions which satisfy each condition?

Given a sketch of a curve with asymptotes, can you find an appropriate function?

What do we REALLY mean when we talk about a tangent to a curve?

This graph looks like a transformation of a familiar function...