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分类讨论是“化整为零,各个击破,再积零为整”的数学策略,有关分类讨论的命题在高考试题中占有重要位置。分类原则主要有:分类对象确定,标准统一,不重复,不遗漏,分层次,不越级讨论。分类方法有:明确讨论对象,确定对象的全体,确定分类标准,正确进行分类;逐类进行讨论,获取阶段性成果;归纳小结。下面通过以下例题来具体分析分类讨论的应用。
Classification discussion is a mathematics strategy of “dividing into zeros, breaking every one, and zeroing into wholes”. The propositions discussed in the classification play an important role in the examination questions. The classification principles mainly include: the classification object is determined, the standard is unified, no repetition, no omission, hierarchy, and no level discussion. The classification methods include: clearly discussing objects, determining the entire object, determining the classification criteria, and correctly classifying; discussing each class, obtaining phased results, and summarizing summary results. The following examples are used to analyze the application of the classification discussion.