<p>Yeah, I agree. The most important thing is that you have just some way that’s not completely “usual” or “standard” of showing your enthusiasm for math/science… and honestly, there are some things that are even better for that than school clubs. For instance, you could solve some really challenging problems out of a reasonably advanced university text related to your courses, or even propose your own questions, and write up short papers describing the answers (some of which you would then send to Caltech.) You could undertake a larger research project over the summer to submit to the research competitions (Intel Science Talent Search and Westinghouse). You could write some innovative software using your scientific knowledge, like a theorem proving engine…</p>
<p>All of these things would catch the attention of an admissions committee, and none of them requires staying after school. I perfectly understand your situation – my transportation wasn’t flexible either. The key is that you find some way to convey your passion for science, and it can often be done even better outside the clubs and such that you mentioned. So, in your place, I would think about what ideas are now sparked in your mind and find a way to produce/do something – ANYTHING – atypical that makes it clear to an outside observer how strong your enthusiasm is and how perfect a fit you are for Caltech. The final picture is what matters, and not the exact details of how you painted it</p>