Mathematical Olympiad For High School (Solutions and Exercises)

This book is written according to the curriculum of grades 10 to 12 in China. Usually, students in China study mathematics earlier and deeper than American students of the same grade, Therefore, some topics in this book have not yet been taught in American high schools. This book contains eclectic exercises and systematic solutions for mathematics in high school. It consists of 16 topics. Questions in this book are derived from four levels - (1) National College Entrance Examination in China, (2) Mathematical contests in some provinces and cities in China, (3) Mathematical contests in other countries, and (4) International Mathematical Olympiad.It contains approximately 500 questions, each followed by an in-depth and clear explanation. Contents: 1. Set and Mapping 2. Power, Exponential, Logarithmic, Inverse Functions 3. Trigonometry 4. Inequalities 5. Complex Numbers 6. Sequences and Mathematical Induction 7. Permutations, Combinations and Binomial Theorem 8. Important Geometric Theorems 9. Incenters, Circumcenters, Centroids, Orthocenters, Excenters Incenter of a Triangle Circumcenter of a Triangle Centroid of a Triangle Orthocenter of a Triangle Excenters of a Triangle10. Polygons11. Concyclic, Collinear, Concurrent Concyclic Collinear Concurrent12. Circles Radical Axis Properties of Two Intersecting Circles Miscellaneous13. Geometric Inequalities14. Geometric Transformations Isometrical Transformation Homothetic Transformation Affine Transformation and Inverse Transformation15. Solid Geometry Angles in Space Distances in Space Miscellaneous16. Plane Analytic Geometry