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近两年江西省中考数学卷的第14题都是一道“满足条件的多解”题,这种题型在解答时需要灵活运用分类讨论的数学思想。因此,我们在复习中应加强多向思维的培养,克服思维的片面性,防止漏解、错解。掌握分类的方法关键有两条:一是要有强烈的分类意识,善于从问题情境中抓住分类的对象;二是要根据问题的实际情况,找出科学合理的分类标准,这个标准应当满足互斥、无漏、最简的原则。下面举例说明。一、数与式的分类讨论例1(2013江西样卷)若(a-2)~(5-a)=1,则a=________。分析根据幂的特殊性,以底数作为分类标准,并按底数三种情况(a-2≠0,a-2=1,a-2=-1)综合考虑指数,即可解决问题。解当a-2≠0时,5-a=0。所以a=5。
In the past two years, the 14th grade of Jiangxi province senior high school entrance examination mathematics volume is a “multi-solution to meet the conditions”, this kind of question needs to flexibly apply the mathematical thought of classified discussion. Therefore, we should strengthen the training of multi-directional thinking during the review, overcome the one-sidedness of thinking, and prevent misunderstanding and misunderstanding. There are two key ways to grasp the classification: one is to have a strong sense of classification, good at seizing the classification of the object from the problem context; the second is based on the actual situation of the problem, to find a scientific and reasonable classification criteria, this standard should meet Mutual exclusion, no leakage, the most simple principle. Here’s an example. First, the number and type of classification Discussion Example 1 (2013 Jiangxi sample) If (a-2) ~ (5-a) = 1, then a = ________. According to the power of the particularity of the analysis, the base as the classification criteria, and according to the bottom three cases (a-2 ≠ 0, a-2 = 1, a-2 = -1) considering the index, you can solve the problem. Solution When a-2 ≠ 0, 5-a = 0. So a = 5.