Being resourceful

If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?

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

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

How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?

Your school has been left a million pounds in the will of an ex-pupil. What model of investment and spending would you use in order to ensure the best return on the money?

Charlie has moved between countries and the average income of both has increased. How can this be so?

Various solids are lowered into a beaker of water. How does the water level rise in each case?

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?

I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?