试题1(湖南卷,理科第8题)设函数 f(x)=x-a/x-1,集合 M={x|f(x)<0},P={x|f’(x)>0},若 MP,则实数 a 的取值范围是().A.(-∞,1) B.(0,1)C.(1,+∞) D.[1,+∞)试题特点:本题是一道考查不等式、导数及集合运算的综合性题目,以选择题呈现探求参数的取值范围,拓宽了解决问题的思路,也体现了对学生理性思维能力的考查.思路分析:思路1:易求得 f’(x)=a-1/(x-1)~2,A、B、C、D 四个 Test 1 (Hunan Volume, Science Question 8) Let the function f (x) = xa / x-1, the set M = {x | f (x) <0}, P = {x | f ’ }, If MP, the real value of the range of a is () .A. (- ∞, 1) B. (0,1) C. (1, + ∞) D. [1, + ∞) Test Questions Features: The problem is a comprehensive test of inequality, derivative and set of operations to multiple choice of questions to explore the range of values, broaden the way to solve the problem, but also reflects the students ability to think of rational thinking.Line Analysis: Idea 1: Easy to get f ’(x) = a-1 / (x-1) ~ 2, A, B, C, D four