AIME Preparation

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Prepare for AIME.

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Table of Contents

Volume 1

Chapter 1. Solid Geometry – Cube and Prism 1

Chapter 2. Plane Geometry Similar Triangles 22

Chapter 3. Algebraic Manipulations 56

Chapter 4. Solving Equations 82

Chapter 5. Cauchy Inequalities112

Index143

Volume 2

Chapter 6. Eight Cubic Identities 1

Chapter 7. Solid Geometry - Tetrahedron 29

Chapter 8. Geometry - Area and Area Method 56

Chapter 9. Logarithms92

Chapter 10. Gaussian Function118

Index158

Volume 3

Chapter 11. Counting with Solid Geometry 1

Chapter 12. Geometry - Angle Measurement 31

Chapter 13. Radicals and Radical Equations 60

Chapter 14. Geometry Angle Bisector and Median97

Chapter 15. Plane Geometry Menelaus and Ceva134

Index168



ACKNOWLEDGEMENTS

We wish to thank the following reviewers for their invaluable solutions, insightful comments, and suggestions for improvements to this book:

Anthony Cheng (UT), William Sun (VA), Kevin Wang (CO), Stephan Xie (TX), Cindy Ye (AR); Christopher Kang (WA), Dr. L. Lin (WA),  Jessica Chen (NC), Jin Cheng (CA), Felix Cui (NE), Dr. Maria Du (OH), Dr. Changyong Feng (NY), Linda Gong (CA), Deepak Haldiya (FL), Dr. Ziying Han (NY), Yanli Huang (NJ), Tommy Hu (MA), Dr. Li Yong (I L), Latha Philip (Ontario, Canada), Aditya Sharma (IL), Huili Shao (MA), Yiqing Shen (TN), Dr. Yang Wei (TX), Yihan Zhong (CT), and Guihua Zhou (CT).

We would also like to thank the following math contests for their mathematical ideas. Many problems in this book are modified or inspired from these tests. We also cited a few problems directly from these tests for the purpose of comparisons with our own solutions.

The AIME (American Invitational Mathematics Examination)
The ARML (American Regions Mathematics League)
The China High School Math Competition
USAMO
IMO 

Please email ourmathcounts@gmail.com for suggestions, corrections, or clarifications. Thanks.