Research On Functions And Equations In Chinese High School Mathematics League

The Chinese High School Mathematics League is one of the high-level mathematics competitions in our country's high school mathematics.It selects excellent mathematics talents for CMO and IMO.Functions and equations are important concepts and core content of high school mathematics learning and teaching,which are reflected in the the Chinese High School Mathematics League Important role.In this paper,the function and equation in the league test in 1981 to2020 is the research object.It mainly adopts the literature analysis method.It is based on How to solve it of Polya as the theoretical basis.The content of this paper is mainly divided into five parts:First,Systemically Introduce the research status of functions and equations in mathematics competition at home and abroad,and define the definitions in the function in the national mathematics league;Second,through the analysis of the question types,scores and test points of the function and equation test questions in the Chinese High School Mathematics League,found the test questions,equation test questions,the priority of filling questions and choices,the function and equation test questions and three test sites that are higher than the frequency of the function and equation test center,and get three rest sists with higher test frequency;Third,introducing some of the nature of function and equation,summarizing the feature and difficulty of 143 league test questions,equation test questions,functions and equation test questions which is concluded that these three types of test questions all attach importance to the examination of questions containing parameters,and the third type of test questions is the most difficult to examine;Fourth,The function and equation test questions study in the league,propose seven problem-solving strategies,and solve the typical problem of function issues,equation issues,functions,functions and equations,and give analysis process and common methods of analysis.In the function problem,elaborated exchange method,construction method,the inequality method,the equation method,the number combination method,the utilization of function properties,mathematics induction,iterative method,similar method,based on these methods,the solution provide five kinds of solving ideas: according to the root characteristics of the equation,using the function nature,use the inequality to take the equal number,use the combination knowledge and method,use the equation equation equivalent to deformation which shows that there are various types of function and equation problems,and specific problems must be specific;Fifth,propose the function of the function and equations in the league applications in other league issues and other mathematical competitions.