Bin Xiong, Zhigang Feng. Problems and Solutions of mathematical Olympiad: High School 1

Wspc / Ecnup, 2021. — 580 p.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.Preface
Concepts and Operations of Sets
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Number of Elements in a Finite Set
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Quadratic Functions
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Graphs and Properties of Functions
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Power Functions, Exponential Functions, and Logarithmic Functions
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Functions with Absolute Values
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Maximum and Minimum Values of Functions
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Properties of Inequalities
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Basic Inequalities
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Solutions of Inequalities
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Synthetical Problems of Inequalities
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Concepts and Properties of Trigonometric Functions
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Deformation via Trigonometric Identities
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Trigonometric Inequalities
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Extreme Value Problems of Trigonometric Functions
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Inverse Trigonometric Functions and Trigonometric Equations
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
The Law of Sines and the Law of Cosines
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Concepts and Operations of Vectors
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
“Angles” and “Distances” in Spaces
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Cross Sections, Folding, and Unfolding
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Projections and the Area Projection Theorem
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Partitions of Sets
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Synthetical Problems of Quadratic Functions
Illustrative Examples
Exercises
Maximum and Minimum Values of Discrete Quantities
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Simple Function Itearation and Functional Equations
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Constructing Functions to Solve Problems
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Vectors and Geometry
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Tetrahedrons
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
The Five Centers of a Triangle
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Some Famous Theorems in Plane Geometry
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
The Extreme Principle
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Solutions
Concepts and Operations of Sets
Number of Elements in a Finite Set
Quadratic Functions
Graphs and Properties of Functions
Power Functions, Exponential Functions, and Logarithmic Functions
Functions with Absolute Values
Maximum and Minimum Values of Functions
Properties of Inequalities
Basic Inequalities
Solutions of Inequalities
Synthetical Problems of Inequalities
Concepts and Properties of Trigonometric Functions
Deformation via Trigonometric Identities
Trigonometric Inequalities
Extreme Value Problems of Trigonometric Functions
Inverse Trigonometric Functions and Trigonometric Equations
The Law of Sines and the Law of Cosines
Concepts and Operations of Vectors
“Angles” and “Distances” in Spaces
Cross Section, Folding, and Unfolding
Projections and the Area Projection Theorem
Partitions of Sets
Synthetical Problems of Quadratic Functions
Maximum and Minimum Values of Discrete Quantities
Simple Function Iteration and Functional Equations
Constructing Functions to Solve Problems
Vectors and Geometry
Tetrahedrons
The Five Centers of a Triangle
Some Famous Theorems in Plane Geometry
The Extreme Principle