| The automatic math problem solving is an important research direction of artificial intelligence.At present,the existing research mainly focuses on solving math word problems,and there are few related researches on the mathematics problems of the college entrance examination.In this paper,we study the intelligent algorithms for two types of problems of National College Entrance Examination of china,analytic geometryand derivative application.Combining the advantages of human thinking and computer symbolic computing,based on the Python programming language,an intelligent system with high accuracy and interpretability is established.For analytic geometric problems,the solution process is divided into three parts: the establishment of geometric objects,the algebraic representation of geometric relations and problems,and the automatic solution of algebraic problems.Based on human’s problem-solving thinking,weattribute the goal of solving geometric problems to nine types of algebr-aic problems,and establish a fully automatic solution path for each typeof problem,transforming it into a problem of solving equations or get the range of functions.Furthermore,we use the idea of the elimination method introduced by humans to realize the automatic solution of the e-quation system and the automatic conversion of the multivariate functionto the univariate function,and obtain the range of the objective function.Aiming at the problem of derivative application,the goal is attribut-ed to eight essential mathematical problems such as "get the monotonic-ity of the function",and the logic framework of the eight types of problems is established,and the overall solving path is designed.Among them,"get the monotonicity of the function" is the basis for solving problems such as "get the maximum of expression",and the expression forms are complex and diverse,and the problem-solving skills are flexible and changeable.In response to the above problems,we have establishedfour core functional modules to closely combine human intuition thinking and computer symbolic computing to achieve generalized automatic solutions.In addition,this paper proposes a knowledge relationship graph representation method of automatic problem-solving path,which intuitively displays the logical structure of the problem-solving path.Furthermore,a method for establishing the main frame of the knowledge association graph is proposed and applied to the analysis of the logical relationship of "the automatic solution path of derivative application". |
