Sketch the members of the family of graphs given by y = a^3/(x^2+a^2) for a=1, 2 and 3.

Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.

Can you sketch these difficult curves, which have uses in mathematical modelling?

Can you construct a cubic equation with a certain distance between its turning points?

Consider these analogies for helping to understand key concepts in calculus.

What is the quickest route across a ploughed field when your speed around the edge is greater?

Find the relationship between the locations of points of inflection, maxima and minima of functions.

A point moves on a line segment. A function depends on the position of the point. Where do you expect the point to be for a minimum of this function to occur.

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