US College A-Level Subjects

Hi, I'm in year 12 so will be applying to US colleges pretty soon. I'm going to be applying to the main ones that give generous international financial aid (Harvard, Yale, Princeton etc.) so it's going to be quite competitive to get in. Therefore, I was wondering if it would be worth self-studying A-Level maths over the summer holidays and then get my school to give me a predicted grade as my subjects are primarily essay-based (although econ has a bit of maths in it), so wasn't sure if doing maths independently would make me a more competitive applicant. Right now, I do English lit, RS, history and econ for A-Level and should be predicted A* in all of them apart from history, in which I'll probably get predicted an A. Also, I did the official econ AS exam last month and will hopefully get an A (the maximum grade for AS) on results day. Bearing in mind, my intended major will be Government/Political Science so all my ECs are geared towards that. Therefore, I wasn't sure if as I'm planning on doing an essay-based major anyway, they would look at me any more favourably for doing maths. Also, in year 11 I got an 8 in the 'Level 2 Certificate in Further Mathematics from AQA', so technically my maths qualifications are slightly more advanced than GCSE. Idk if this would make any difference.

Alternatively, I was thinking of self-studying A-Level sociology instead just to get an extra A-Level. It hopefully wouldn't be very hard as the units for GCSE (which I did) and A-Level are the exact same so it would just be a matter of learning a bit extra content. I've heard the essay structure is relatively easy to master, especially as I already do essay subjects for A-Level. However, I wasn't sure if it would give me any extra advantage just by being able to say I've done an extra subject considering it may not be seen as rigorous enough (is that the case?) and it's not going to give me the advantage of being able to say I do a broad mix of subjects.

Thanks in advance

I think it's better to focus on ECs than taking extra exams, but @ry7xsfa might be able to advise for sure.