How do you prepare for AIME?

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Is the best way to prepare for AIME with past problems or with books? If with books, could you recommend some?

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You might already know of the Art of Problem Solving website. That's your best resource. If you are asking for AIME preparation, perhaps you are confident with your AMC skills? If not, you need to focus on this test to make sure you can even get to the AIME. Focus on strengthening your weakest subject. In general, the four "competition subjects" are Algebra, Geometry, Number Theory, and Combinatorics. Learn the basics first. I can't speak for all of the AoPS books, but the self-titled ones "Art of Problem Solving Volume 1&2" are very good. They cover all the topics at a very good level for the AIME.

Experience: AMC 12 DHR, 2-time AIME score of 7 (not that great, but...)