To accompany these problems, this Plus article discusses how the cubic graph $y=x^3$ lies behind the hidden dome of St Paul's Cathedral. You might also like to watch this video from Plus about a very special curve.
You can watch a recording of the webinar in which we discussed the mathematical thinking which can be prompted by these problems.
Exploring cubic functions
Quadratic graphs are very familiar, but what patterns can you explore with cubics?
Curve fitter
This problem challenges you to find cubic equations which satisfy different conditions.
Curvy Equation
This problem asks you to use your curve sketching knowledge to find all the solutions to an equation.