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《考试说明》中函数(包括集合)部分虽然只有13个知识点,但它在历年高考试题中都占据很重要的地位.因此研究高考试题对该知识块的考查情况,对于指导中学数学教学和提高高考复习效果,都是十分必要的.本文就近年来全国高考数学试题中,关于函数知识考查情况进行分析.一、集合考试题型分析及解法集合知识是历年高考的热点,题型多以选择题形式出现,除1992年外,每年都考.例1 如果I={a,b,c,d,e},M={a,c,d},N={b,d,e},其中I是全集.那么(?)∩(?)等于( ).(’89全国高考题)(A)(?)(B){d}(C){a,c} (D){b,e}.分析:本题主要考查对集合、交集、并集、补集的概念的理解.可先分别求出(?)、(?),再求(?).也可利用摩根定律:(?)=(?)∩(?),(?)∩(?)=(?)∪(?)去求解.容易得出正确答案为(A).例2.设全集I={0,1,2,3,4},集合A={0,1,2,3},集合 B={2,3,4},则(?)∪(?)=( ).(’94全国高考题)(A){0}(B){0,1}(C){0,1,4}(D){0,1,2,3,4}分析:本题与例1形异实同,不难得出答案为(C).例3.集合{1,2,3}的子集共有( ).(’88全国高考题)(A)7个(B)8个(C)6个(D)5个.分析:本题着重考查子集的概念,尤其不可忽视A(?)A与(?)(?)A,所以,一般地,含有n个元素的集合,它的所有子集的个数是2~n,故本题的答案为2~3=8,应选(B).
Although there are only 13 knowledge points in the function (including the collection) part of the “exam description”, it has occupied an important position in the high test questions of the calendar year. Therefore, the examination of the high test questions on the knowledge block is used to guide the mathematics teaching in middle schools and It is very necessary to improve the effect of the college entrance examination review. This article analyzes the function knowledge examination situation in the national college entrance examination mathematics test questions in recent years. First, the analysis of the examination questions and the solution of the collection of knowledge is the hot spot of the college entrance examination over the years. The form of the question appears, except for 1992. Examine every year. Example 1 If I={a,b,c,d,e}, M={a,c,d},N={b,d,e}, Where I is the complete set. Then (?)∩(?) is equal to ().(’89 National Entrance Examination Questions)(A)(?)(B){d}(C){a,c}(D){b, e}. Analysis: This question mainly examines the understanding of the concepts of collection, intersection, union, and complement. It can be found separately (?), (?), and then (?). May also use Morgan’s law: (? )=(?)∩(?),(?)∩(?)=(?)∪(?) to solve. It is easy to get the correct answer as (A). Example 2. Set the full set I={0,1, 2,3,4}, set A={0,1,2,3}, set B={2,3,4}, then (?)∪(?)=( ).(’94 National Entrance Examination Question) (A) {0}(B){0,1}(C){0,1,4}(D){0,1,2,3,4} Analysis: This It is not difficult to find the answer is (C). Example 3. The subset of the set {1,2,3} is common (). (’88 national college entrance examination questions) (A) 7 (B) 8 (C) 6 (D) 5. Analysis: This question focuses on the concept of examining subsets. In particular, A(?)A and (?)(?)A cannot be ignored. Therefore, generally speaking, there are n elements. Set, the number of all its subsets is 2~n, so the answer to this question is 2~3=8, should be selected (B).