Your friend is always trying to outdo you, so she probably is jealous and is most likely insecure.
The best thing to do is to make her feel good about herself. Compliment her on her hair/eyes/figure and if she ever comes up with things, tell her what a great idea it is. In lessons, tell her if you think she's done good work, and congratulate her if she gets a high mark or gets a really good score in a test. She will feel more secure and self-confident, so won't feel the need to prove how good she is to other people.
As for her bitching behind your back and then sucking up, she oviously wants to appear in a good light so is nice to your face. This is another sign that she's insecure so carry on making her feel good. You can't just ignore the bitching though, talk to her in private and tell her that it upsets you when she says mean things about you (say "It upsets me when you say mean things about me", not "I don't like it when you're mean"). If she sucks up to you then tell her that she doesn't need to, you'll still be her friend, but that you don't want her to keep saying mean things about you behind your back. Tell her that if you ever upset her or make her annoyed then she should come and talk to you about it, instead of moaning to other people.
Hope I Helped,
*+*TropicalBabe*+*

thanks xxxxx

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