AMC 10:
1. AOPS Volume 1
2. AOPS Introduction Series
AMC 12:
1. AOPS Volumes 1 and 2
2. AOPS Introduction Series
3. AOPS Intermediate Series + Pre-Calculus
AIME:
1. Geometry parts of AOPS Volumes 1 and 2
2. AOPS Intermediate Series + Pre-Calculus
3. Challenging Problems in Geometry by Posamentier and Salkind
4. The 100 + k Series by Titu Andreescu and others
5. HMMT problems
USA(J)MO:
1. Problem Solving Strategies by Engel
2. The 100 + k Series by Titu Andreescu and others
3. Geometry Revisited by Coxeter
4. Participate in WOOT at AOPS
5. USAMO and IMO problems for the last 30 years
Remark:
1) Many people like "The Art and Craft of Problem Solving" by Paul Zeitz. My main criticism of the book is that there are basically no solutions to the exercises. Kids need to learn from good solutions to improve.
2) Until 10 years ago, a strong student could work on only AOPS Volumes 1 and 2 and qualified for USAMO. It is almost impossible now!
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