近十年高考不等式理科试题分类解析

发布时间：2019-01-17 08:46

【摘要】：不等式在高中数学中占有重要地位,它是数学基础理论的重要组成部分,是衡量事物间数量关系的重要数学模型,是继续学习数学内容及各学科内容的基础,是高中数学中各知识间联系的纽带.由于以往对高考不等式试题的研究更多地侧重于评析具体年份与省份的高考不等式试题中的考点,内容较零散且不全面,所以本研究以2007年——2016年全国各地的高考不等式理科数学试题为研究对象,对试题进行分类、概括和总结,剖析每一类题型的考点、出题形式和解题方法,试图为高考不等式内容复习提出一些建议.本文共分为五个部分:第一部分,阐述不等式在高中数学中的作用、地位及研究现状,据此提出研究的问题、目的、意义、内容以及方法.第二部分,介绍不等式的9条基本性质和5个重要不等式:基本不等式、柯西不等式、绝对值三角不等式、排序不等式和贝努利不等式.第三部分,根据普通高中数学课程标准(实验),分析高中不等式内容的考点,并统计分析试题中各不等式考点的题型比例和各考点分别占不等式总试题的比例.第四部分,在对大量高考试题的解题思路、考点进行分类分析的基础上,将高考不等式内容分为:性质判断及应用、求解不等式、证明不等式和应用不等式等四个方面.其中,应用不等式包括线性规划问题、恒成立问题、最值问题和取值范围问题.并对每一类型题归纳出考查目的和解题方法.这也是本文的核心内容.第五部分,根据前面研究的不等式内容的出题形式和各类型题的解题方法,提出一些高考复习建议,包括:注意数学思想的应用和注意解题方法的掌握。
[Abstract]:Inequality plays an important role in senior high school mathematics. It is an important part of the basic theory of mathematics, an important mathematical model to measure the quantitative relationship between things, and the basis of continuing to study mathematics content and the contents of various subjects. High school mathematics is the link between the knowledge. Because of the previous research on the college entrance examination inequality test more focused on the evaluation of the specific years and provinces of the examination points in the university entrance examination inequality test, the content is scattered and not comprehensive. So this research takes the mathematics test of college entrance examination inequality from 2007 to 2016 as the research object, classifies, generalizes and summarizes the test questions, analyzes the test points of each type of questions, the form of the questions and the methods of solving the problems. This paper tries to put forward some suggestions for reviewing the inequality of college entrance examination. This paper is divided into five parts: the first part describes the role, status and research status of inequality in senior high school mathematics, and puts forward the research issues, purposes, significance, content and methods. In the second part, we introduce nine basic properties of inequalities and five important inequalities: basic inequality, Cauchy inequality, absolute value triangle inequality, order inequality and Bernoulli inequality. The third part, according to the ordinary senior high school mathematics curriculum standard (experiment), analyzes the senior high school inequality content examination place, and the statistical analysis each inequality examination place question type proportion and each examination place respectively occupies the inequality general question proportion. In the fourth part, on the basis of the classification analysis of a large number of questions in the college entrance examination, the contents of the inequality are divided into four aspects: nature judgment and application, solving inequality, proving inequality and applying inequality. Among them, the applied inequalities include linear programming problem, constant set problem, maximum value problem and value range problem. At the same time, the purpose of examination and the method of solving problems are summed up for each type of problem. This is also the core of this article. In the fifth part, according to the form of inequality and the methods of solving various kinds of problems, the author puts forward some suggestions for the review of college entrance examination, including the application of attention to mathematics and the mastery of methods of solving problems.
【学位授予单位】：深圳大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

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