Showing what I can do?

I put this under ‘What are my chances?’ because I could not find a better category to use.

I am a sophomore in High school, and I would like to show what I can do and what I am capable of. I go to a very small school (Graduating class averages around 95 students) and live in a small town. It is because of this that I feel hopeless, the programs and activities at my school seem only in place to exalt it. If you can not throw a football, or anything of the sort, no one will ever know what you can do here. I am writing one paper in mathemarics that does not have a name yet, but an idea of it would be “Objects in 3 and 4 dimensions”. The short paper would have the mathematics of orientation, position, and direction of bodies (e.i. moving and static, particles and rigid bodies). I also have the 3 other papers in mind.

So my question is, how can I show what I can do?