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

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?

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

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

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

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.

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?

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

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

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...

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

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

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}.

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

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!

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

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

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

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