PROBLEMS AND SOLUTIONS IN MATHEMATICAL OLYMPIAD (HIGH SCHOOL 2) (Mathematical Olympiad Series)

✍ Scribed by Shi-Xiong Liu

• Publisher: Wspc / Ecnup
• Year: 2021
• Tongue: English
• Leaves: 607
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Contents
Editorial Board
Preface
1. Maximum and Minimum Values
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
2. Usual Methods for Proving Inequalities
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
3. Common Techniques for Proving Inequalities
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
4. Arithmetic and Geometric Sequences
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
5. Arithmetic Sequences of Higher Order
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
6. Sequence Summation
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
7. Synthetic Problems for Sequences
1. Illustrative Examples
2. Exercises
8. Coordinates Systems
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
9. Straight Lines
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
10. Circles
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
11. Ellipses
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
12. Hyperbolas
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
13. Parabolas
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
14. Parametric Equations
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
15. Families of Curves
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
16. Derivatives
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
17. Mathematical Induction (I)
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
18. Complex Numbers
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
19. Geometric Meaning of Complex Operations
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
20. Mean Value Inequalities
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
21. Cauchy Inequality
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
22. Rearrangement Inequalities
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
23. Convex Functions and Jensen’s Inequality
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
24. Recursive Sequences
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
25. Periodic Sequences
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
26. Polar Coordinates
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
27. Analytic Method for Plane Geometry
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
28. Synthetic Problems for Complex Numbers
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
29. Mathematical Induction (II)
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
30. Proof by Contradiction
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
31. Construction Method
1. Key Points of Knowledge and Basic Methods
2. Illustrative Examples
3. Exercises
Solutions
1. Maximum and Minimum Values
2. Usual Methods for Proving Inequalities
3. Common Techniques for Proving Inequalities
4. Arithmetic and Geometric Sequences
5. Arithmetic Sequences of Higher Order
6. Sequence Summation
7. Synthetic Problems for Sequences
8. Coordinates Systems
9. Straight Lines
10. Circles
11. Ellipses
12. Hyperbolas
13. Parabolas
14. Parametric Equations
15. Families of Curves
16. Derivatives
17. Mathematical Induction (I)
18. Complex Numbers
19. Geometric Meaning of Complex Operations
20. Mean Value Inequalities
21. The Cauchy Inequality
22. Rearrangement Inequalities
23. Convex Functions and Jensen’s Inequality
24. Recursive Sequences
25. Periodic Sequences
26. Polar Coordinates
27. Analytic Method for Plane Geometry
28. Synthetic Problems for Complex Numbers
29. Mathematical Induction (II)
30. Proof by Contradiction
31. Construction Method