Being resilient

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

Explore the relationships between different paper sizes.

Use the differences to find the solution to this Sudoku.

What do you get when you raise a quadratic to the power of a quadratic?

Starting with two basic vector steps, which destinations can you reach on a vector walk?

Quadratic graphs are very familiar, but what patterns can you explore with cubics?

Find the sum of this series of surds.

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 make sense of the three methods to work out what fraction of the total area is shaded?