wpegg: Do not attempt to impress a girl. At age15 any attempts to impress a girl can only end up in varying degress of feeling like a tit (as opposed to getting to feel a tit).
Think about it, even by now you must have witnessed all the stupid ways kids sell out to impress the fairer sex. It will go wrong in some way, you will regret it.
The thing is you don't need to impress her. Teenagers are a boiling pot of hormones, combined with a raging sense of insecurity. This means that simply being around, not attempting to be impressive, will give you a massive advantage of the posturing morons sitting to the left and right of you.
This article helps to accurately represent the teenage state of mind (albeit that of the boys, but I think there's similarish thoughts on the other side).
Remember - massive boiling pot of hormones, massive insecurity. Just talk to her enough to show you're interested, and wait for the right signals.
You have a point.
And I only just managed to send her a friend request on facebook. :)