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某些数学问题,因受各种因素的制约,求解时需要分类讨论。通过分类讨论,常能化繁为简,更清楚地暴露事物的本质,并增加解题条件,使问题易于解决。但什么问题需分类,这是学生最感困难的地方。本文通过举例介绍中学数学中九种常见的需分类讨论的问题让学生熟悉,以便适当使用。一、根据数学概念的定义分类有些数学概念是分类定义的(如实数的绝对值、直线和平面所成的角等概念),所以应用这些概念解题时,就需进行讨论。有些数学概念在下定义时已经对所考虑的对象的范围作了限制(如复数的模和辐角
Certain mathematical problems, due to various factors, need to be classified and discussed when solving. Through categorizing and discussing, it is often possible to simplify and simplify, to more clearly expose the essence of things, and to increase the conditions for problem solving so that the problems can be easily solved. However, what kind of problems need to be classified is the most difficult place for students. In this paper, the students are familiarized with the nine common questions that need to be classified and discussed in the middle school mathematics for proper use. First, according to the definition of the mathematical concept of classification Some mathematical concepts are defined by the classification (such as the absolute value of the real number, the angle formed by the straight line and the plane and other concepts), so when applying these concepts to solve problems, we need to discuss. Some mathematical concepts have been limited in the definition of the scope of the object under consideration (such as complex modes and arguments)