Taking Further Mathematics HL or not

I am an IB student in India (US citizen). Since 8 grade I have been learning and doing very rigorous and challenging math. When I joined an IB school in 11 grade, I took Mathematics HL. I found out that I have already done the whole core Math HL portion along with the options that are offered at my school.

I wish to go to top universities MIT, Caltech, Princeton and Yale. These universities look for something different in their applicants. Many people take Math HL and get a 7 in it. So I won’t be doing anything outstanding or new as compared to other applicants who are applying.

I find taking Further Math HL as a platform to show my mathematical capabilities to these top universities. If allowed, I will also be the first and only person to take till now in my school. I believe that I will be able to handle Further Math HL and get a 7 (or at least a 6 in it). Should I take it?

If I take it, will this show to top universities how different I might be and how I have pushed myself beyond my limits.

Obviously, my other parameters like ACT, SAT scores and high school grades, extracurricular activities, achievements are up to the mark and great.

So considering I take it, will this increase my chances of getting accepted to MIT, Caltech, Stanford, Yale e.t.c.

Further mathematics in itself probably won’t increase your chances by a significant amount, but note that getting a 5 or below in the subject will probably harm your chances - so take it with caution. However, if you are actively interested in the subject and supplement this by taking part in math competitions or creating math projects, then that’s great.

Do note that everything comes with an opportunity cost. The time that you spend studying for further math could also be spent doing something else, possibly more valuable. I hope you take this into account when deciding whether or not to take further math.

You should study as much math as your interests lead you to. Especially if you are interested in a STEM field, knowing more math will open up many opportunities in college.

The chances of getting into the schools you noted are very small for any unhooked applicant. My suggestion would be to take what interests you.

Further math HL vs Math HL Won’t be the make or break element if your application. If you feel comfortable taking Further Math HL and getting a 6 as well as getting three other 7’s go for it. But your total, no matter what, would need to be 37-38+, so don’t jeopardize that if you’re not confident you can handle such a competitive curriculum.
On the other hand, beside caltech, doing well in FurtherMath HL would also qualify you for HarveyMudd and Williams (superb for math) as well as the special math program at Northwestern.

@MYOS1634 you said that Further Math HL vs Math HL wont be the make or break element, but I had question: out of 5 applicants for Princeton from my school, 2 of them are Further Math HL students while I am not. Does that lower my chances, since my immediate high school colleagues have further math?

What major will you apply for? What major will they apply for?
More important than further math HL v. math HL will be a personable essay and the whole package (IE., what else are you taking? Are you confident you can get a predicted 38? What kind of person are you? What makes you tick? What will you bring to their community and will your being there make their campus life better?)