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Fifty Lectures for AIME Volume 1 (PDF file)

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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 very 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.



Table of Contents



Chapter 1 Solid Geometry – Cube and Prism                                                             1

Chapter 2 Solid Geometry - Tetrahedron                                                                   19

Chapter 3 Counting with Solid Geometry                                                                  43

Chapter 4 Plane Geometry Similar Triangles                                                              64

Chapter 5 Plane Geometry Area and Area Method                                                   94

Chapter 6 Plane Geometry Menelaus and Ceva                                                         126

Chapter 7 Algebraic Manipulations                                                                            155

Chapter 8 Logarithms                                                                                                 179

Chapter 9 Solving Equations                                                                                      202

Chapter 10 Cauchy Inequalities                                                                                  228

Index                                                                                                                           256

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