First of all, if you're anything like the high schoolers I went to school with, or myself, you are not spending so much time studying that you can't practice piano that much. Just about everyone I knew was involved in sports, held jobs, and did other extracurricular activities. You're also probably not studying for your SAT's until the last two weeks, anyways. Sorry for being rude, but I highly doubt there are any high schoolers out there with a work ethic that has them study for more than an hour a day (unless cramming or they love the subject).
Colleges don't weigh your SAT scores too heavily. Your regular grades matter more. They want consistency, not a really good grade one day of your life. In fact, one would probably see your regular grades reflected in your SAT score, unless you had a horrible day. So they're really nothing to worry about (Though I must admit I got a 2170. Trust me,
nothing suffered because of my SAT study habits, probably because I didn't spend too much time on it
). And you want to know something really annoying about grades? I graduated as the salutatorian of my class, the valedictorian was 0.38 ahead of me. Less than half a point! But now that I'm in college (Music School, an average of 80 would have sufficed, let alone 96.18), not one of my music friends, my honors friends, my honors teachers, or my music teachers care that I was salutatorian. It's not a good conversation topic. (Okay, there's one
slight exception. My piano teacher cares because she thinks my intense studying(hah!)/worrying about grades might be a source of tension for me.) Bottom line, do what you can, but don't push yourself too far. The things you're truly good at in life probably won't be reflected in your grades (though they may), but that doesn't mean your talents don't exist and that there aren't people out there willing to help you with them.
I would recommend the same thing for your study habits and your practice: consistency and efficiency. Don't waste time, and one of the biggest time wasters is not practicing every day. I'm not saying you can't miss a day here and there, but try not to miss two in a row, and if you do miss one practice the next two days at least. Memory decays very, very fast without daily reinforcement. That said, once something (information or music) is firmly in your memory, daily reinforcement is no longer needed. But until then, you must practice every day, whether it be math, french, or Chopin.
Ultimately, your daily practice time will depend on your goals. What pieces do you want to learn? By when? Be realistic, and be concrete. Deadlines work wonders, when timed correctly. Perfection is not a realistic goal, it is an ideal we strive for though we know we can never reach it. We can work towards perfection, dream of perfection, but we cannot achieve it, and at the end of the day, you must achieve
something. You must have a goal for each practice session, even if it be the same one from yesterday, and that goal must be achievable, and it must be achieved. So it seems then that your daily practice time may vary somewhat. It may take you a half-hour to learn 8 bars one day, but only 10 min the next day to relearn them. You will do more on some days and less on others.
One final comment, which seems to be a common theme on my posts: What does your teacher say? If you don't have one, you need one if you want real results. If you do have one, you are paying him/her to teach you. Therefore, he/she should have a specified amount for you to practice on a daily basis. He/she should be able to tell you what is reasonable to achieve between lessons.
Topic: How many hours you should practice to be perfect??