Find all real solutions of the equation (x^2-7x+11)^(x^2-11x+30) = 1.

Can you explain why a sequence of operations always gives you perfect squares?

Is the mean of the squares of two numbers greater than, or less than, the square of their means?

Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

Clearly if a, b and c are the lengths of the sides of an equilateral triangle then a^2 + b^2 + c^2 = ab + bc + ca. Is the converse true?

Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...

I am exactly n times my daughter's age. In m years I shall be ... How old am I?

Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.

Investigate sequences given by $a_n = \frac{1+a_{n-1}}{a_{n-2}}$ for different choices of the first two terms. Make a conjecture about the behaviour of these sequences. Can you prove your conjecture?

Can you prove our inequality holds for all values of x and y between 0 and 1?

Can you see how to build a harmonic triangle? Can you work out the next two rows?

A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?

To make 11 kilograms of this blend of coffee costs £15 per kilogram. The blend uses more Brazilian, Kenyan and Mocha coffee... How many kilograms of each type of coffee are used?

a) A four digit number (in base 10) aabb is a perfect square. Discuss ways of systematically finding this number. (b) Prove that 11^{10}-1 is divisible by 100.

Give your further pure mathematics skills a workout with this interactive and reusable set of activities.

Mathmo is a revision tool for post-16 mathematics. It's great installed as a smartphone app, but it works well in pads and desktops and notebooks too. Give yourself a mathematical workout!

Can you make a tetrahedron whose faces all have the same perimeter?

How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.

This is the first of a two part series of articles on the history of Algebra from about 2000 BCE to about 1000 CE.

Fancy learning a bit more about rates of reaction, but don't know where to look? Come inside and find out more...

Do each of these scenarios allow you fully to deduce the required facts about the reactants?

Ever wondered what it would be like to vaporise a diamond? Find out inside...