摘要均值不等式作为高中数学的必修内容,不但形式简单,而且应用十分广泛,是高考考查的重点内容之一,常被用于比较大小、求最值、证明不等式,解决不等式恒成立等问题.首先,本文给出了均值不等式的基本形式以及其变形与推广;然后,论述均值不等式在高中数学中所体现的教育价值;接着,对近几年高考及模拟考中涉及均值不等式的题目进行总结分类,给出解题指导.最后,结合其应用,给出了均值不等式的教学策略.46668
As a compulsory content in senior high school mathematics, Mean Inequality is not only in a simple form, but also widely used. It is one of the important contents of the entrance test, and is often used to compare the size, for most value, prove inequalities, solve inequality permanent establishment problems, and so on. Firstly, this paper giving the basic form of the mean inequality and its deformation and promotion. secondly, it discusses the value as reflected in senior high mathematics. Thirdly, it summarizes and classifieds the college entrance exams and simulation topics related to Mean Inequality, then gives guidance of problem-solving. Finally, it gives the teaching strategies of Mean Inequality with its’ application.
毕业论文关键词:均值不等式;应用;教学
Keyword: Mean Inequality; application; teaching
目 录
摘 要 2
1 绪 论 4
2 均值不等式 4
2.1 表现形式 4
2.2 变形与推广 4
2.2.1 常见变形 4
2.2.2 推广 4
3 均值不等式在高中数学中所体现的教育价值 5
3.1 知识地位 5
3.2 教育地位 5
3.2.1 激发学生学习数学的兴趣 5
3.2.2 培养学生的数学思维 5
3.2.3 为教师进行教学设计提供依据 5
4 均值不等式的应用 6
4.1 不同题型的应用 6
4.1.1 比较大小 6
4.1.2 求最值 6
4.1.3 证明不等式 7
4.1.4 解决不等式恒成立 8
4.2 不同知识背景下的应用 9
4.2.1 函数 9
4.2.2 方程 10
4.2.3 线性规划 10
4.2.4 三角函数