Problems And Solutions In Mathematical Olympiad (High School 1)

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: 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 Sections, 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 Extremal Principle Readership: Secondary school students engaged in mathematical competition, coaches in mathematics teaching, and teachers setting up math elective courses.