Academic Essay/ Research Project

<p>So, I've heard of people who do some kind of research projects with colleges (while in high school) in order to boost their application. Do they really help? If yes, then of what kind should they be?</p>

<p>I'm highly interested in calc/differential equations/analysis and I REALLY want to make this known to the colleges I will be applying to. How can I do that? Like, do I need to do some kind of research or something? Or is there any international calc-based competition where I can try my luck? Another thing: Regarding the academic essay, does it have to be something that has never been done before(like a post-doc research paper)?</p>

<p>Any help would be appreciated. Please give in your inputs. Thanks :D</p>

<p>Please reply, guys. I need opinions urgently to help myself decide. Please!</p>