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分类讨论是高中阶段数学解题时经常使用的数学思想之一.解决分类讨论问题的实质是整体问题化成部分问题来解决,化成部分问题后,就增加了题设的条件.这一实质注定了使用分类讨论的方法来解决问题时过程较为繁琐.不少学生由于审题等多方面原因,对部分题目盲目地使用分类讨论的方法来解决,从而增加了解题的繁琐程度和错解的风险.那么,如何简化或者直接避免不必要的分类讨论呢?下面,将一些常见的策略利用例题形式呈现给读者.
Category discussion is one of the mathematical ideas frequently used in high school mathematics problem solving.It is one of the mathematical thinking that is often used in solving mathematical problems in senior middle school.It is the essence of the problem to solve the classification that the whole problem is solved into some problems, The use of classification to discuss the process to solve the problem is more complicated.Many students due to many issues such as exams, some of the topics blindly use the method of classification to solve the problem, thus increasing the complexity of the problem-solving and misdirection of the risk. So, how to simplify or directly avoid unnecessary classification discussion? Here, some common strategies to use the sample form presented to the reader.