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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
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
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
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)Please email [email protected] for suggestions, corrections, or clarifications. Thanks.