摘要在中学数学学习中，数形结合思想已经开始大量渗透，因此，将数形结合的思想理解透、掌握牢将是学生打好中学数学基础的必备能力，是老师教授数学知识必须引导的解题方向.另外数形结合作为一种数学思想方法，包括两个方面：第一是“以数解形”，而第二是“以形助数”.高考题是中学数学题目的经典题目，在多年的高考题中可以发现，有大量的数学试题蕴含着数形结合的思想。可见数形结合方法在数学解题和研究中的地位之高。54631

本文就是以数形结合的思想来解决中学数学中遇到的常见问题，主要为最值问题和不等式问题两大类以及数学公式法则验证、数形结合在高考中的体现.在涉及绝对值问题，函数问题和图形求最值的问题等中，数形结合的方法能够帮助我们巧妙地简捷地抓住问题本质而又好又快的解决问题。另外在不等式问题中，我们通常会根据题目代数的形式，建构出相应的坐标系中情况或者几何图形，这样能够高效准确的解决问题，并且可以有利于更好的掌握及日后的运用.

总之，数形结合思想是一种重要的数学思想，利用好数形结合思想将帮助学生在数学解题过程中发挥事半功倍的效果。

 The adoption of symbolic-graphic combination, which is regarded as a must in problems solving, has been closely related with middle school mathematics. Meanwhile, symbolic-graphic combination acts as a mathematical method of thinking, including the following two aspects: First is to use algebra to solve geometry problems .Second is to use geometry to help solve algebra problems. Taking questions of NMET int consideration, there is obvious that the application of symbolic-graphic combination will make some abstract problems solving even easier.  

This article is going to solve the common problems with the adoption of symbolic-graphic combination in middle school mathematics, which will mainly focus on the solution of constrained and unconstrained optimization and inequality problems. As for the problems of absolute value, functions and geometries, the adoption of symbolic-graphic combination makes them easier and more clear. What’s more, when it comes to the problems of inequality, construction of geometry and coordinate system is usually adopted to make the process more efficient and easier and meanwhile offers students a better understanding.

In conclusion, symbolic-graphic combination is quite a significantly important method in problems solving. If you can master this method into real application, it does carry a big weight in your studying.

毕业论文关键词： 数形结合； 解题；绝对值；不等式 

Keyword: Symbolic-graphic combination；Problem solving；Absolute value； Inequality

目    录

1. 引言 2

1.1 研究背景： 2

1.2 研究意义 2

2. 数形结合解决最值问题 4

2.1 绝对值问题的最值 4

2.2 函数问题的最值 5

2.3 图形问题的最值 6

3. 数形结合解决不等式问题 8

3.1 构造坐标系解决不等式 8

3.2