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AIME Preparation (Volumes 1,2, 3) (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.



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 Inequalities                                                                       112

Index                                                                                                               143
Volume 2

Chapter 6 Eight Cubic Identities                                                                    1

Chapter 7 Solid Geometry - Tetrahedron                                                      29

Chapter 8 Geometry - Area and Area Method                                               56

Chapter 9 Logarithms                                                                                    92

Chapter 10 Gaussian Function                                                                       118

Index                                                                                                               158
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 Median                                       97

Chapter 15 Plane Geometry Menelaus and Ceva                                          134

Index                                                                                                               168


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