I have a problem with playing in exams too.
I'm way too nervous in an exam, but here are some ways I'm trying myself to get over it:
Record yourself at home playing. Think to yourself, "This is going to be on tape forever. It had better be good!" Then you'll get nervous and realise the different way you play when nervous. You'll know which bits need to be more secure. Then listen to it. It's never as bad as you thought it was!
Another way is to play on all sorts of different pianos. Last week I went to a piano shop and pretended I had terribly rich parents and they were going to buy me a top-of-the-range grand piano for my birthday. The guy in the shop said, "Go ahead! Play as many pianos as you want!" So I tried my pieces out and felt the way I had to adjust to each giant expensive grand. Also, another thing was, the guy was watching over me so I had an audience! If possible, practice on the piano you will be using for your exam. I will be able to do this for my exam in June, but I know not everyone can.
Yet another way is to play for as many people as you can. Tell your fellow piano student friends, "Examine me!" You could go to their house and make them examine you on their weird piano and get them to write notes down and everything. Do a concert for your grandparents. I found I was really nervous playing for my grandparents, actually. Play a piece at your birthday party. If you know another piano teacher, play for them. That's really scary. Last week, I played a piece in front of a class of piano majors at university. I was so scared, I messed up everything. But it taught me a valuable thing: Even if you totally screw up the piece, it's not the end of the world. I survived it, and wondered why I'd worked myself up into such a state beforehand.
Playing for auditions, however, I'm much less nervous. I don't know why, because in a sense, they're more important. I think, "Well. I don't actually know these people. They don't know who I am, so I'm just going to have fun playing this Steinway." This attitude made me seem quite confident even though inside I was quite shy, and I managed to get accepted into all the places I'd auditioned at.
OK. That's all for now. I'll come back and post again if I make any more discoveries.