I take a fair amount of honors classes and go to a somewhat competitive school. My friend is in all of my classes. Every test we get back, every homework assignment, every exam, she wants to know what I got, what I thought about it, etc. Now I don't mean to seem paranoid or anything; these are standard things that one discusses with their friends. It's how she reacts to my responses that irritate me. If I do better than her or find something she didn't, she's critical of me for the rest of the day and puts me down for everything. She also starts pointing out all of her faults and making excuses for why she didn't do better. If I do worse than her, she says things like, "you're just not as good at this as I am", or, "maybe you didn't work hard enough".

That might just be her way of comforting me because she thinks I hold the same value to grades as she does, but honestly, it makes me very uncomfortable that she views our friendship as a competition. I don't like going to school to earn certain grades or to beat somebody, I like learning new things. Having a friend who is overly enthusiastic about "being better" than me just sucks the joy out of things.
What could I say to her without being offensive to calm her down about earning certain grades?

I know exactly how you feel. I have a friend who does the very same thing. I started to feel like crap every time I talked to her, especially about grades and school. It doesn't help that she's extremely self centered and only wants to talk about herself. The worst part is that everyone, including the teachers, practically worship her.
Since I started to feel so put down everything I was around her, I slowly started to pull away from her. Whenever she asked my grades I refused to tell her, since after all it's technically personal information. I don't know if this is something you would want to do in your situation, but that's what I did. I stopped telling her my grades and I eventually stopped hanging around with her because she made me feel so bad. That's just my personal experience, do what you think is right.

I think you shouldn't be with her because friends should make you feel good about yourself. I think i am dyslexic becuase my mom and dad is so it is a strong possibility that i am too. I have F in math and my friends tell me i'm good at other things and i think that is what friends should do so i think she's not really a friend. But that's my opinion and do what you think is right

Competing is a way for a person to improve themselves. If a person wants to compete with you, it means he/she thinks highly of you. Its like on video games, you want beat someone who's much better than you or something. But not everyone has that kind of mindset. To the person who doesn't have much competitive drive, it causes them stress that worsens their performances.

The fact is she doesn't think of your friendship as just a competition, its more or less her way of showing your friendship. She probably doesn't know any other way to converse with you. She feels that its the only thing that is keeping your friendship. If you followed what >>2 said, you would have stopped hanging out with her. Just tell her the truth that you feel uncomfortable competing with her.

If you really don't want to hang out with her then just stop being friends. It's really annoying if a person acts like he/she enjoys your company but doesn't.