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

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?

Match the charts of these functions to the charts of their integrals.

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

Investigate why the Lennard-Jones potential gives a good approximate explanation for the behaviour of atoms at close ranges

Several graphs of the sort occurring commonly in biology are given. How many processes can you map to each graph?

Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.