<p>At the risk of being pompous, I’m going to say that even if you had raised to 2400, it really wouldn’t make a difference compared to your original score (for Caltech). You already had a high math score, and would make first cut. Using SAT scores to decide between applicants in later cuts is just silly, because SAT reading and writing have little relevance here, and you have to have upper 700’s on math anyway just to show you have a chance of surviving core math.</p>
<p>Let me restate; your AIME score and research are awesome, you were already competitive to begin with. </p>
<p>For the record, my SAT score was lower than both of yours.</p>