AMC 10 Prep

Hi, I am currently a rising sophomore, and will be taking Pre-Calc in the fall. My goal is to go to MIT or Caltech, and just found out that the AMC/AIME was a part of the application. I know I am late to start, but I was wondering if it was a feasible goal to prepare well for the AMC 10 within a month. If so, I would like to do it without spending any money. On that note, can you give me recommendations on how to best spend my time?

Spend lots of time on the ArtofProblemSolving.com website. Work lots of problems, take old tests under the time constraints…good luck!!!