There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?

Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?

Use algebra to reason why 16 and 32 are impossible to create as the sum of consecutive numbers.

The equation a^x + b^x = 1 can be solved algebraically in special cases but in general it can only be solved by numerical methods.

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

Find the equation from which to calculate the resistance of an infinite network of resistances.

Simon from Elizabeth College found solutions to Two Regular Polygons by using a spreadsheet, efficiently combined with some very good reasoning to know when he had all the solutions. We liked the way Simon put the power of the spreadsheet to work under the control of some elegant mathematical thinking.