How much independent research/above curriculum knowledge to have a good chance of being admitted?

<p>I am a prospective CalTech applicant, and while I try and do some independent research it is very difficult to get anywhere. Is being highly skilled, interested, and motivated without experience enough for this school? Not many labs want students performing experiments, and it is VERY expensive and impractical to do them independently without an institution backing you. I was able to score some internships at biochem labs and I've tried to write papers based on my thought experiments, but how much is enough to be admitted to CalTech? I am a science oriented person, and I'm not amazing at math, so I have to show the admission committee that I go above and beyond in my field of interest. Is there any other way of doing this besides landing nearly impossible research positions? Also, how far above your school's curriculum do you have to be? I did well in all my AP sciences, and have a cursory knowledge of information above that, but I'm not some sort of genius.</p>