In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

The illustration shows the graphs of fifteen functions. Two of them have equations y=x^2 and y=-(x-4)^2. Find the equations of all the other graphs.

Knowing two of the equations find the equations of the 12 graphs of cubic functions making this pattern.

Can you adjust the curve so the bead drops with near constant vertical velocity?

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

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

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

Can you work out the equations of the trig graphs I used to make my pattern?

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

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?

Can you work out which processes are represented by the graphs?

Can you find the gradients of the lines that form a triangle?