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中学数学课标指出,在数学教学中,发展思维能力是培养能力的核心.要发展学生的思维,培养数学能力,提高文化素质,就应重视数学思想方法的教学.历年的中考试题中,都非常重视对数学思想方法的考查.本文举例浅析分类讨论思想在解题中的应用.一、根据相关数学概念的定义进行分类讨论例1关于x的方程(a-5)x2-4x-1=0有实数根,则a满足().A.a≥1B.a>1且a≠5C.a≥1且a≠5D.a≠5解:当a-5=0,即a=5时,原方程是关于x的一元一次方程,有一个实数根x=-14;当a-5≠0时,原方程是关于x的一元二次方程,当满足△=b2-4ac=(-4)2-4(a-5)·(-1)≥0时,方程有两个实数根,解得a≥1.
Secondary mathematics curriculums pointed out that in mathematics teaching, the development of thinking ability is the core of training ability.In order to develop students’ thinking, develop mathematics ability, improve the quality of culture, we should pay attention to teaching methods of mathematics thought. Attaches great importance to the method of mathematical thinking test.This article gives an example analysis of the classification of the discussion in the application of the problem.First, according to the definition of mathematical concepts related to classification discussionExample 1 on x equation (a-5) x2-4x-1 = 0 has a real root, then a satisfies () .Aa≥1B.a> 1 and a ≠ 5C.a≥1 and a ≠ 5D.a ≠ 5 Solution: When a-5 = 0, that is, a = 5, The original equation is a unary linear equation about x, with a real number root x = -14. When a-5 ≠ 0, the original equation is a quadratic equation about x, and when △ = b2-4ac = (- 4) When 2-4 (a-5) · (-1) ≥0, there are two real roots in the equation, solving for a ≥1.