Hi, @ALevelChoices
In theory this is a fine set of A Levels. All of these SoMs will make offers on three A levels and these are the ones most relevant for a Maths degree. They all require FM if the School offers it.
The problem is that so many pupils are now predicted top grades across the board that further selection is needed. For Oxford, Warwick and Imperial, IMO the most important supporting evidence is an excellent mark on a relevant pre-application test. Oxford require this as part of the application and it is a big pre-interview filter for them. Imperial and Warwick offer the option of a pre-application test or STEP, which is taken with A Levels. I will say more about STEP below. Suffice it to say for now that the pre-application test is the easier option!
Would a fourth A level help? If a grade A can be achieved without sacrificing two or three A stars, the mark on the pre-application test, the supra-curriculars Oxbridge like to see (if the opportunity to pursue them has existed) and the applicant’s life and sanity - probably.
Warwick will offer on three A levels anyway, Oxbridge may vary, but Imperial Maths will typically make a dual offer of either three A stars or two A stars in Maths and FM and two As. Where the fourth may help is mostly behind the scenes in deciding who gets offers, because I cannot stress strongly enough how many great applicants won’t.
Cambridge make relatively more offers than the other three and then use STEP to control the size of the incoming cohort. It is brutal. Only about 50% of those with a Cambridge offer make it. IMO to some extent this is because of under preparation. These are the top Maths pupils in their community and many of them are thrown by finding Maths problems difficult for the first time. They don’t have proper study technique (they haven’t needed it), etc. But STEP is inherently difficult and preparation is far from the full story.
Imperial and Warwick (and others) also impose a STEP offer on those who did not take a pre-application test, but Cambridge set the grade boundaries nationwide.
For most students capable of three A stars in Maths, Physics and FM, I think the best advice is to stick with three and do your very best. Cultivate some in depth supra curricular Maths but don’t force it. Decide between C and O if either interests you. Prepare intensively for the pre-application test(s) you take and put some thought into preparing for interviews. Don’t worry about sounding intelligent; you are there because you are intelligent! Think about how to show your best true self and remember that the interview is a two way street.
Everyone, but everyone, needs a good insurance choice. There are many and DS should enjoy researching them. Two he may not have thought of are Glasgow and Lancaster. Both have very high student satisfaction. Glasgow was No 5 in the UK and top in Scotland in the last Research Exercise Framework (REF) and is Russell Group. Lancaster is now considered part of the RG+ and was also top 10 in the last REF (2021). REF matters to top students because in later years they have the chance for independent study. It can be a great experience. Not that UGs will be doing cutting edge Maths research, but the spirit is contagious.
(I also recommend Bath and several others but DS can do his own research. I just thought these two should not be overlooked).
This was a longer answer than you may have anticipated. I hope it helps. Best wishes to DS