PROBLEMS AND SOLUTIONS IN MATHEMATICAL OLYMPIAD (HIGH SCHOOL 1) (Mathematical Olympiad Series, 18)

✍ Scribed by Bin Xiong, Zhigang Feng

• Publisher: Wspc / Ecnup
• Year: 2021
• Tongue: English
• Leaves: 580
• 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. 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