Hi, just a few things that I want to point out.
Firstly, I think the more respected universities, the very best, are going to be seriously doubtful about an applicant for Maths with an A at GCSE. Is there some reason that you failed to achieve an A* grade at GCSE? I don't mean to sound arrogant, but GCSE is really not that hard, and just to get an A at A-Level, I would say that you ought to possess such proficiency at GCSE level that you should get an A*. Also, what universities are looking for, and this is key, is the fundamental understanding of the theory. This is what STEP questions search for in candidates, and this is the skill you need to succeed at a good university in mathematics. Such an understanding is partly natural, but can be developed, but it can take a long time to develop it, and you have to be extremely dedicated, and reasonably able to begin with. This sort of understand would mean an A* would be no big burden at GCSE, I just think if you apply to Cambridge, they may assume you don't have this understanding and of course, you will have to be out to demonstrate that you can proof their assumptions wrong, with is no easy task, since most interviewers have a vague idea of their decision before you enter the door. With that said, if you are determined, then you stand just as good a chance as everyone, but you must work hard to show them that your mathematics is of a suitable level. The best idea is to do STEP questions and similar styled logic problems, to really get you thinking.
Secondly, in remark to someone who said that maths challenges don't really matter, I beg to differ. Although they are hardly a prerequisite for entry, many people applying to Cambridge, and Oxford as well, will have taken the BMO1 in their Lower 6th year, and this is impressive, regardless what mark you get. It demonstrates ability to think at Olympiad level, enthusiasm, dedication, and hopefully the questions inspire a bit of enjoyment in maths, I know I certainly enjoy olympiad questions far more than any other sort. Of course, qualification for BMO2 is great, but hard to come by, and such an achievement is a huge plus, it demonstrates exactly the sort of ability admissions tutors are looking for. But don't be put off if you don't do it, from my knowledge, perhaps 20-30 pupils who take BMO2 each year are year 12. However, i mentioned it in my interview, said how I enjoyed it, and the interviewers certainly seemed impressed by my participation in both years of 6th form. Taking part is thoroughly recommended, and is something that makes you stand out from the huge crowd of applicants, and helps you to get in.
Chris