C1 is ridiculously easy for (more or less) anyone who can get an A at GCSE.
C2 doesn't seem to hard up too now.
Looking at some C3/4 past papers, there doesn't seem to be anything too tricky that you won't get taught.
Edit: AQA C1 math involved (varies from exam board):
- surds; simplifying equations involving surds
- differentiation; finding the gradient/tangent/normal of a curve at certain points, finding the nature of 'stationary points'
- integration; finding the area under a curve
- co-ordinate geometry; circles, lines, distance between 2 points, working out a linear gradient..
- 'completing the square'; to find the minimum point co-ordinates
- factorising
- polynomials; factor/remainder theorem (not as hard as they sound)