It depends where you want to start out in physics or engineering. To finish college, you'll need to know calculus and maybe a little bit of linear algebra depending on what you decide to do. But this is all stuff that you can learn while in college.
You could probably go into college with nothing more than algebra, but it'll delay you from taking introductory physics courses. I would try to start up on precalculus stuff, which is basically Trigonometry and what my school calls function analysis. If you go into college knowing all of precalculus you'll be able to jump into beginning physics and engineering classes and by the time you're done with those you can have taken calculus and be able to move to the more challenging stuff.