Math is another potential major to consider. There are fortunately quite a few very good careers that are possible with a degree in mathematics. Quantitative analysis is one of them, but there are lots more as well. A lot of things in this world only work because someone did the math to make sure that they were going to work, and a lot of fields include experts who realize that they need some very strong math smarts to help them get their work done.
In terms of extracurricular activities, I have perhaps three recommendations. First of all, be genuine. Be yourself. Don’t do things just to get them on your resume, instead do what is right for you. If you get into a leadership position, remember that leadership is not about getting your way. Instead leadership is about listening and making the activity better for everyone. A good leader makes their entire team happier and more productive. Also, ECs are definitely NOT about getting the longest list. Instead, you want a moderate length list of activities that you do very well. I think that you will find this advice to be compatible with what you will read in the very good MIT “applying sideways” blog.
The advice of “do what is right for you and do it well” is that my family has done, and it has lead the 4 of us to 8 different very good universities (one each for a bachelor’s and a different one each for a graduate degree), and some of these have been high ranked (one was MIT). This advice is good in general and for any highly ranked school, and not just for MIT. However, what each one of us did was very different. We each just did what was right for us.
Why are you planning on taking the SAT as a sophomore in high school?
At least MIT, Stanford, and some (if not all) of the Ivy League schools do not admit by major. Your chances of getting admitted do not change based on your intended major. At least for MIT if you are admitted, and if you choose to attend, then MIT uses your intended major to help to match you to a freshman year advisor. Then at the end of your freshman year you get to pick any major that you want.
I do understand that this is different for some universities and might for example be different for any specialized business programs. I am not sure about Penn for example (I never considered going there as a math major, but possibly just because I didn’t think of it).
One thing that comes to mind whenever I hear a high school student, particularly a freshman, who is interested in a highly stressful career such as quantitative analysis: Be careful what you wish for because you might get it. Quantitative analysis is a very stressful career that requires long hours.
This makes me think of a friend of mine who graduated with a degree in math from MIT, went to Harvard Law School, graduated and passed the bar. He then went to work for a prestigious New York law firm, and lasted exactly one week. He could not stand the pressure and the competitive atmosphere. He fortunately had graduated with no debt and could afford to go back to university and get a master’s degree in a different but somewhat related field, and ended up with a good career in a different and less stressful field.
The other thing that comes to mind is that you should be careful about jumping ahead in general, and particularly jumping ahead in math classes. In mathematics, what you are learning now is based to a very large degree on what you were learning last year and the year before, and what you are going to be learning next year will depend upon what you are learning now. You want to learn each part very well. You need to understand the concepts very well and specifically do not just memorize formulae. The focus should be on a thorough and complete and solid understanding of the basics and the concepts. If you do this, then it should all fit together very well and high school mathematics, including anything on the SAT, can be relatively straightforward for someone who is strong in math.
When the time comes to apply to universities, then keep an open mind, make sure that you apply to safeties, look for schools that are a good fit for you, and keep your budget in mind. There are a lot of very good universities in the US. As one example…
… if you are from New Jersey then Rutgers is a very good university. I have known a lot of Rutgers graduates and they have all made the university look very good. The first three Rutgers graduates who I met were three graduate students, in a subfield of applied math, at Stanford. They were strong students who did well in the program.