Most Helpful Girl
Just have a 'normal' conversation with her.
By saying 'only talk to other on matters related to studies' this sounds like you're in class and she wants to concentrate so I wouldn't bother her in class as it would clearly irritate her. But when the bell rings perhaps spark up a conversation about your studies so that it's relevant and try to link it to something. For instance if you've just had English and you're talking about a book you can talk about the characters, what you think etc, ask her opinions etc and then move it on to a film or something like 'oh and that part in the book really reminds me of the new Batman film when...' etc 'have you watched it?'.
I think you just have to go about it like she's been your friend for ages, just chat casually, smile and relax!
0THIS IS NOT RELEVANT ANYMORE