本文首先对数学高考试卷（理科）进行题目变化趋势分析和题型总结，将题型分

本文首先对数学高考试卷（理科）进行题目变化趋势分析和题型总结，将题型分为函数型压轴题、几何型压轴题和概率型压轴题三种，从题目难度与考察知识出发。最终确定以函数型压轴题为方向。再从近五年高考压轴题目出发，阐述了函数型题目的考察知识、典型题目以及研究意义，对高考压轴题进行初步分析之后文章又具体分析了这些高考压轴题所涉及的思想，接下来主要讲述函数与方程思想、数形结合思想、分类讨论思想、化归思想这四种思想方法及它们的内涵、原则或分类，并且以高考题目为例证，在分析解题中对其中所涉及的思想进行深入探究。最后在掌握学生压轴题解题现状后，从不同方面分析产生现状的原因并以所知原因为导向，针对教学中存在的问题对教师教学提出了改进方法。

本文首先对数学高考试卷（理科）进行题目变化趋势分析和题型总结，将题型分为函数型压轴题、几何型压轴题和概率型压轴题三种，从题目难度与考察知识出发。 最终确定以函数型压轴题为方向。 再从近五年高考压轴题目出发，阐述了函数型题目的考察知识、典型题目以及研究意义，对高考压轴题进行初步分析之后文章又具体分析了这些高考压轴题所涉及的思想，接下来主要讲述函数与方程思想、数形结合思想、分类讨论思想、化归思想这四种思想方法及它们的内涵、原则或分类，并且以高考题目为例证，在分析解题中对其中所涉及的思想进行深入探究。 最后在掌握学生压轴题解题现状后，从不同方面分析产生现状的原因并以所知原因为导向，针对教学中存在的问题对教师教学提出了改进方法。

This paper first analyzes the changing trend of the questions in the college entrance examination of Mathematics (Science) and summarizes the types of questions. The types of questions are divided into three types: function type, geometry type and probability type. Starting from the difficulty of the questions and the knowledge of investigation. Finally, it is determined that the direction is the function type. Then, starting from the last five years' college entrance examination final questions, this paper expounds the investigation knowledge, typical questions and research significance of function type questions. After a preliminary analysis of the final questions of college entrance examination, this paper analyzes the ideas involved in these final questions. Next, it mainly talks about the four kinds of ideas and methods of function and equation, combination of number and shape, classified discussion and reduction Their connotation, principle or classification, and take the college entrance examination as an example, in the analysis and solution of the ideas involved in the in-depth study. Finally, after mastering the current situation of students' final questions, this paper analyzes the causes of the current situation from different aspects, and puts forward some improvement methods for teachers' teaching according to the existing problems in teaching.<br>