Problems And Solutions In Mathematical Olympiad (High School 1)

Bin Xiong, Director of Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, Professor at East China Normal University, member of The Chinese Mathematical Olympiad Committee. Zhigang Feng, Principal of Shanghai High School, Mathematics Grand Grade Teacher, Full Professor Title Teacher, Chinese Team Deputy Leader for the 44th, 49th, 51st, 52nd, and 53rd IMOs.

Concepts and Arithmetic of Sets; Number of Elements in aFinite Set; Quadratic Functions; Graphs and Properties of Functions; Powers, Exponentials and Logarithms; Functions with Absolute Values; The Maximum and Minimum of a Function; Properties of Inequalities; Basic Inequalities; Solving Inequalities; Miscellaneous Problems on Inequalities; Concepts and Properties of Trigonometric Functions; Identical Transformation in Trigonometry; Trigonometric Inequalities; Extrema of Trigonometric Expressions; Inverse Trigonometric Functions and Trigonometric Equations; The Sine Law and the Cosine Law; Concepts and Arithmetic of Vectors; Angles and Distances in Space; Cross Section, Folding and Spreading; Projection and the Area Projection Theorem; Partition of Sets; Miscellaneous Problems on Quadratic Functions; Extremum of Discrete Objects; Simple Function Iteration and Functional Equations; Constructing Functions to Solve Problems; Vector and Geometry; Tetrahedrons; The Five Centers of a Triangle; Some Famous Theorems in Plane Geometry; The Extremal Principle;