Liu Shi-Xiong. Problems And Solutions In Mathematical Olympiad: High School 2

Wspc / Ecnup, 2021. — 607 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.Editorial Board
Preface
Maximum and Minimum Values
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Usual Methods for Proving Inequalities
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Common Techniques for Proving Inequalities
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Arithmetic and Geometric Sequences
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Arithmetic Sequences of Higher Order
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Sequence Summation
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Synthetic Problems for Sequences
Illustrative Examples
Exercises
Coordinates Systems
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Straight Lines
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Circles
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Ellipses
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Hyperbolas
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Parabolas
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Parametric Equations
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Families of Curves
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Derivatives
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Mathematical Induction (I)
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Complex Numbers
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Geometric Meaning of Complex Operations
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Mean Value Inequalities
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Cauchy Inequality
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Rearrangement Inequalities
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Convex Functions and Jensen’s Inequality
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Recursive Sequences
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Periodic Sequences
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Polar Coordinates
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Analytic Method for Plane Geometry
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Synthetic Problems for Complex Numbers
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Mathematical Induction (II)
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Proof by Contradiction
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Construction Method
Key Points of Knowledge and Basic Methods
Illustrative Examples
Exercises
Solutions
Maximum and Minimum Values
Usual Methods for Proving Inequalities
Common Techniques for Proving Inequalities
Arithmetic and Geometric Sequences
Arithmetic Sequences of Higher Order
Sequence Summation
Synthetic Problems for Sequences
Coordinates Systems
Straight Lines
Circles
Ellipses
Hyperbolas
Parabolas
Parametric Equations
Families of Curves
Derivatives
Mathematical Induction (I)
Complex Numbers
Geometric Meaning of Complex Operations
Mean Value Inequalities
The Cauchy Inequality
Rearrangement Inequalities
Convex Functions and Jensen’s Inequality
Recursive Sequences
Periodic Sequences
Polar Coordinates
Analytic Method for Plane Geometry
Synthetic Problems for Complex Numbers
Mathematical Induction (II)
Proof by Contradiction
Construction Method