Hot Forbidden Mothers -- Secret Wives Series Full Set

The series is edited by the head coaches of China's IMO National Team. Each volume, catering to different grades, is contributed by the senior coaches of the IMO National Team. The Chinese edition has won the award of Top 50 Most Influential Educational Brands in China. The series is created in line with the mathematics cognition and intellectual development levels of the students in the corresponding grades. All hot mathematics topics of the competition are included in the volumes and are organized into chapters where concepts and methods are gradually introduced to equip the students with necessary knowledge until they can finally reach the competition level. In each chapter, well-designed problems including those collected from real competitions are provided so that the students can apply the skills and strategies they have learned to solve these problems. Detailed solutions are provided selectively. As a feature of the series, we also include some solutions generously offered by the members of Chinese national team and national training team. Contents Editorial Board Preface 1. Concepts and Operations of Sets 1.1 Key Points of Knowledge and Basic Methods 1.2 Illustrative Examples 1.3 Exercises 2. Number of Elements in a Finite Set 2.1 Key Points of Knowledge and Basic Methods 2.2 Illustrative Examples 2.3 Exercises 3. Quadratic Functions 3.1 Key Points of Knowledge and Basic Methods 3.2 Illustrative Examples 3.3 Exercises 4. Graphs and Properties of Functions 4.1 Key Points of Knowledge and Basic Methods 4.2 Illustrative Examples 4.3 Exercises 5. Power Functions, Exponential Functions, and Logarithmic Functions 5.1 Key Points of Knowledge and Basic Methods 5.2 Illustrative Examples 5.3 Exercises 6. Functions with Absolute Values 6.1 Key Points of Knowledge and Basic Methods 6.2 Illustrative Examples 6.3 Exercises 7. Maximum and Minimum Values of Functions 7.1 Key Points of Knowledge and Basic Methods 7.2 Illustrative Examples 7.3 Exercises 8. Properties of Inequalities 8.1 Key Points of Knowledge and Basic Methods 8.2 Illustrative Examples 8.3 Exercises 9. Basic Inequalities 9.1 Key Points of Knowledge and Basic Methods 9.2 Illustrative Examples 9.3 Exercises 10. Solutions of Inequalities 10.1 Key Points of Knowledge and Basic Methods 10.2 Illustrative Examples 10.3 Exercises 11. Synthetical Problems of Inequalities 11.1 Key Points of Knowledge and Basic Methods 11.2 Illustrative Examples 11.3 Exercises 12. Concepts and Properties of Trigonometric Functions 12.1 Key Points of Knowledge and Basic Methods 12.2 Illustrative Examples 12.3 Exercises 13. Deformation via Trigonometric Identities 13.1 Key Points of Knowledge and Basic Methods 13.2 Illustrative Examples 13.3 Exercises 14. Trigonometric Inequalities 14.1 Key Points of Knowledge and Basic Methods 14.2 Illustrative Examples 14.3 Exercises 15. Extreme Value Problems of Trigonometric Functions 15.1 Key Points of Knowledge and Basic Methods 15.2 Illustrative Examples 15.3 Exercises 16. Inverse Trigonometric Functions and Trigonometric Equations 16.1 Key Points of Knowledge and Basic Methods 16.2 Illustrative Examples 16.3 Exercises 17. The Law of Sines and the Law of Cosines 17.1 Key Points of Knowledge and Basic Methods 17.2 Illustrative Examples 17.3 Exercises 18. Concepts and Operations of Vectors 18.1 Key Points of Knowledge and Basic Methods 18.2 Illustrative Examples 18.3 Exercises 19. “Angles” and “Distances” in Spaces 19.1 Key Points of Knowledge and Basic Methods 19.2 Illustrative Examples 19.3 Exercises 20. Cross Sections, Folding, and Unfolding 20.1 Key Points of Knowledge and Basic Methods 20.2 Illustrative Examples 20.3 Exercises 21. Projections and the Area Projection Theorem 21.1 Key Points of Knowledge and Basic Methods 21.2 Illustrative Examples 21.3 Exercises 22. Partitions of Sets 22.1 Key Points of Knowledge and Basic Methods 22.2 Illustrative Examples 22.3 Exercises 23. Synthetical Problems of Quadratic Functions 23.1 Illustrative Examples 23.2 Exercises 24. Maximum and Minimum Values of Discrete Quantities 24.1 Key Points of Knowledge and Basic Methods 24.2 Illustrative Examples 24.3 Exercises 25. Simple Function Itearation and Functional Equations 25.1 Key Points of Knowledge and Basic Methods 25.2 Illustrative Examples 25.3 Exercises 26. Constructing Functions to Solve Problems 26.1 Key Points of Knowledge and Basic Methods 26.2 Illustrative Examples 26.3 Exercises 27. Vectors and Geometry 27.1 Key Points of Knowledge and Basic Methods 27.2 Illustrative Examples 27.3 Exercises 28. Tetrahedrons 28.1 Key Points of Knowledge and Basic Methods 28.2 Illustrative Examples 28.3 Exercises 29. The Five Centers of a Triangle 29.1 Key Points of Knowledge and Basic Methods 29.2 Illustrative Examples 29.3 Exercises 30. Some Famous Theorems in Plane Geometry 30.1 Key Points of Knowledge and Basic Methods 30.2 Illustrative Examples 30.3 Exercises 31. The Extreme Principle 31.1 Key Points of Knowledge and Basic Methods 31.2 Illustrative Examples 31.3 Exercises Solutions 1. Concepts and Operations of Sets 2. Number of Elements in a Finite Set 3. Quadratic Functions 4. Graphs and Properties of Functions 5. Power Functions, Exponential Functions, and Logarithmic Functions 6. Functions with Absolute Values 7. Maximum and Minimum Values of Functions 8. Properties of Inequalities 9. Basic Inequalities 10. Solutions of Inequalities 11. Synthetical Problems of Inequalities 12. Concepts and Properties of Trigonometric Functions 13. Deformation via Trigonometric Identities 14. Trigonometric Inequalities 15. Extreme Value Problems of Trigonometric Functions 16. Inverse Trigonometric Functions and Trigonometric Equations 17. The Law of Sines and the Law of Cosines 18. Concepts and Operations of Vectors 19. “Angles” and “Distances” in Spaces 20. Cross Section, Folding, and Unfolding 21. Projections and the Area Projection Theorem 22. Partitions of Sets 23. Synthetical Problems of Quadratic Functions 24. Maximum and Minimum Values of Discrete Quantities 25. Simple Function Iteration and Functional Equations 26. Constructing Functions to Solve Problems 27. Vectors and Geometry 28. Tetrahedrons 29. The Five Centers of a Triangle 30. Some Famous Theorems in Plane Geometry 31. The Extreme Principle The series is edited by the head coaches of China's IMO National Team. Each volume, catering to different grades, is contributed by the senior coaches of the IMO National Team. The Chinese edition has won the award of Top 50 most influential educational brand in China. The series is in line with the mathematics cognition and intellectual development level of the students in the corresponding grade. The volume lines up the topics in each chapter and introduces a variety of concepts and methods to provide with the knowledge, then gradually transitions to the competition level. The content covers all the hot topics of the competition. In each chapter, there are packed with many problems including some real competition questions which students can use to verify their abilities. Selected detailed answers are provided. Some of the solutions are from national training team and national team members, their wonderful solutions being the feature of this series.