For many years extra-mural classes have been held on Wednesday afternoons at the University of Birmingham for the benefit primarily of teachers of mathematics. Part of one of these courses for sixth form teachers involved taking A level questions and using them as starting points for further enquiries. The intention was to illustrate how almost any A level question can yield something fruitful, beyond its straightforward solution, if one perseveres with asking ancillary questions and exploring alternatives. The approach was presented as a possible means of encouraging students to adopt more divergent thinking than the solution of A level questions generally produces.