Creating and manipulating expressions and formulae

Find the missing angle between the two secants to the circle when the two angles at the centre subtended by the arcs created by the intersections of the secants and the circle are 50 and 120 degrees.

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

If a sum invested gains 10% each year how long before it has doubled its value?

Take any two numbers between 0 and 1. Prove that the sum of the numbers is always less than one plus their product?

Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

A, B & C own a half, a third and a sixth of a coin collection. Each grab some coins, return some, then share equally what they had put back, finishing with their own share. How rich are they?

Given any two polynomials in a single variable it is always possible to eliminate the variable and obtain a formula showing the relationship between the two polynomials. Try this one.

Find all the solutions to the this equation.