<p>As for the OP’s question, there are a number of scholastic competitions for high school students. Science Olympiad, Intel/Siements (for research), math team (ASHME/AIME/USAMO/IMO, USAMTS, Mandelbrot,) other olympiad competitions for the sciences, robotics competitions, JETS. Scholastic Bowl and Academic Decathlon are two non-techy competitions I have heard of.<br>
It’s a little late to be thinking about most of these things. However, you could still do research for some prof and submit an intel project. It might not be too late to try to sign up for ASME (I forget the acronym; help me out guys,), the first level of the US math olympiad tryouts. It is in early February. You would have to get moving on that obviously–if interested, I would look up the organization on-line and ask them how you can take the test if your school doesn’t offer it. Someone who is good at math and who has had high school geometry, tryg, and algebra through algebra II could expect to qualify for the next round.</p>