论文部分内容阅读
所谓创新型问题,就是在现有的常规题的基础上,要么给出新的定义,要么让结果隐去由学生去探索,要么将有关信息进行迁移,甚至针对某一问题开展研究性学习等等.由于创新型问题编制角度新颖,突出能力立意,突出对学生数学素质的考查,所以在近几年各地高考模拟试题或高考试题中多次出现.下面选取儿例与集合相关的创新型问题,供参考.1.新定义型集合问题例1 对于集合{a_1,a_2,a_3,…,a_n}和实常数 a_0,定义:S_n~2=1/n[sin~2(a_1-a_0)+sin~2(a_2-a_0)+…+sin~2(a_n-a_0)]为集合{a_1,a_2,a_3,…,a_n}相对于 a_0的“正弦方差”.求集合{π/9,(7π)/9,(13π)/9}相对于实常数 a_0的正弦方
The so-called “innovative” problem is based on the existing conventional questions, either giving new definitions or leaving the results hidden by the students to explore, or relocating the relevant information, or even conducting research-based learning on certain issues. Etc. Since the innovation problem is novel in terms of drafting angles, highlights the ability to develop ideas, and highlights the examination of students’ mathematics qualities, it has appeared many times in the simulated or high-examination subjects in college entrance examinations in recent years. The following sets forth the innovative problems related to children and collections. For reference, 1. New definition type set problem example 1 For the set {a_1, a_2, a_3, ..., a_n} and the real constant a_0, define: S_n~2=1/n[sin~2(a_1-a_0)+ Sin~2(a_2-a_0)+...+sin~2(a_n-a_0)] is the sine variance of the set {a_1,a_2,a_3,...,a_n} with respect to a_0. Find the set {π/9 ,(7π)/9,(13π)/9} Relative to the sine of the real constant a_0