人教版高中数学必修一第一章集合与函数概念教案名师优秀教案(完整版)资料.doc

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1、人教版高中数学必修一第一章集合与函数概念教案名师优秀教案（完整版）资料(可以直接使用，可编辑 优秀版资料，欢迎下载）人教版高中数学必修一第一章集合与函数概念教案第一章 集 合 1 、1、1集合的含义 【探索新知】 在小学、初中我们就接触过“集合”一词。 例子: (1)自然数集合、正整数集合、实数集合等。 2(2)不等式2x,x,7,0解的集合(简称解集)。 2(3)方程解的集合。 x,3x，2,0(4)到角两边距离相等的点的集合。 2(5)二次函数 图像上点的集合。 y,x(6)锐角三角形的集合 (7)二元一次方程解的集合。 2x，y,1(8)某班所有桌子的集合。 现在，我们要进一步明确集合的

2、概念。 问题1、从字面上看，怎样解释“集合”一词, 、如果上面例子中的数、点、图形、数对和物体等称为“研究对象”，那么集合又是什2么呢, 知识点一:1、集合、元素的概念 再看例子 (9)质数的集合。 1y,(10)反比例函数图像上所有点。 x222x(11)、 xy，y,2y(12)所有周长为20厘米的三角形。 问题3、从集合中元素个数看，上面例子(1)(2)(4)(5)(6)(7)(9)(10)(12)与例子(3)(8)(11)有什么不同, 知识点二 2、有限集和无限集 choose water fountains, water-saving products should be purch

3、ased. As compared to open v-Groove type water supply system, sealed nipple water system can save water 81.35% saving bedding consumption 56.3%; sanitation and drinking water, and a variety of harmful gases concentrations decline, increased laying rate 13.79%, economic efficiency improved. Chicken Co

4、op construction should pay attention to several problems, chicken distribution notes: a rational structure of the hen-house layout, can provide a good environment for chicken, making its full productive potential, so other than in understanding the physiological characteristics of the chicken itself

5、, and must be properly planned and constructed sheds. 1. sites to choose away from populated areas, traffic convenient, away from the road 2. Gaozao terrain, a lot of sunshine. Winter sun as possible, summer wind, and not after the rain water. Larger, leaving room for development 3. Abundant water r

6、esources pollution-free, easy to access, sufficient power is guaranteed 4. Building structure, the economy, saving money, and saving energy, it is facing in accordance with local environmental and physiological condition, lighting is good, easy to ventilation, easy to operate, so conducive to coolin

7、g in the summer, to insulation in winter cold 5. Layout of premises should be reasonable, do distinguish between production and non-production areas and non-production areas and water sources are on a chicken farm in the wind, net road and dirt road separating uncrossed, dung farm is located in the

8、指出:集合论是德国数学家Cantor(1845,1918)在十九世纪创立的，集合知识是现代数学的基本语言，为进一步研究数学提供了极大的便利。 知识点三 集合、元素的记法 问题4、(1)集合、元素各用什么样的字母表示, ,(2)、等各表示什么集合, NZRQN(N)，知识点四 元素与集合的关系 阅读教材填空: 如果a是集合A的元素 ， 就记作_，读作“_”; 如果a不是集合A的元素，就记作_ _，读作“_ _”. 用或填空: ,31,1、6_N ， _Q ， _Z ，_Q _Q， 3.14232、设不等式2x,1,0的解集为A，则 5_A , ,3_A 3、,2的解集为B，则_B , _B ,

9、_B 2x,y，1,0(,1,4)(1,3)问题5、元素a与集合A有几种可能的关系, 知识点五 集合的性质 ? 确定性: 例子1、下列整体是集合吗, ?个子高的人的全体。?某本数学资料中难题的全体。?中国境内的海拔高的山峰的全体。 22、集合A中的元素由x=a+b(a?Z,b?Z)组成，判断下列元素与集合A的关系, 11 (1)0 (2) (3) 21,32,?互异性: 2例子、集合M中的元素为1，x，x-x，求x的范围, choose water fountains, water-saving products should be purchased. As compared to open

10、 v-Groove type water supply system, sealed nipple water system can save water 81.35% saving bedding consumption 56.3%; sanitation and drinking water, and a variety of harmful gases concentrations decline, increased laying rate 13.79%, economic efficiency improved. Chicken Coop construction should pa

11、y attention to several problems, chicken distribution notes: a rational structure of the hen-house layout, can provide a good environment for chicken, making its full productive potential, so other than in understanding the physiological characteristics of the chicken itself, and must be properly pl

12、anned and constructed sheds. 1. sites to choose away from populated areas, traffic convenient, away from the road 2. Gaozao terrain, a lot of sunshine. Winter sun as possible, summer wind, and not after the rain water. Larger, leaving room for development 3. Abundant water resources pollution-free,

13、easy to access, sufficient power is guaranteed 4. Building structure, the economy, saving money, and saving energy, it is facing in accordance with local environmental and physiological condition, lighting is good, easy to ventilation, easy to operate, so conducive to cooling in the summer, to insul

14、ation in winter cold 5. Layout of premises should be reasonable, do distinguish between production and non-production areas and non-production areas and water sources are on a chicken farm in the wind, net road and dirt road separating uncrossed, dung farm is located in the ?无序性: 反思总结: 【课堂检测】 233新疆王

15、新敞奎屯1、实数x,x,x,是集合P中的元素，则P最多含( ) x,xA 2个元素 B 3个元素 C 4个元素 D 5个元素 abab2、设a、b都是非零实数，y=+可能的取值为( ) |a|b|ab|A.3 B. 3,2,1 C. 3，1，-1 D. 3，-1 反思总结: 【拓展提升】-活动与探究 1数集A满足条件:若a?A，则?A(a?1). 1,a(1)若2?A，试求出A中其他所有元素. (2)设a?A，写出A中所有元素. 【练习】 1、设一边长为1且有一内角为40?的等腰三角形组成集合P，试问P中有多少个元素? 22a，2a，3a，32、已知集合A有三个元素， (a，1)1,A (1)

16、若，则集合A中还有哪些元素, 1,A (2)若，则a应满足什么条件? choose water fountains, water-saving products should be purchased. As compared to open v-Groove type water supply system, sealed nipple water system can save water 81.35% saving bedding consumption 56.3%; sanitation and drinking water, and a variety of harmful gase

17、s concentrations decline, increased laying rate 13.79%, economic efficiency improved. Chicken Coop construction should pay attention to several problems, chicken distribution notes: a rational structure of the hen-house layout, can provide a good environment for chicken, making its full productive p

18、otential, so other than in understanding the physiological characteristics of the chicken itself, and must be properly planned and constructed sheds. 1. sites to choose away from populated areas, traffic convenient, away from the road 2. Gaozao terrain, a lot of sunshine. Winter sun as possible, sum

19、mer wind, and not after the rain water. Larger, leaving room for development 3. Abundant water resources pollution-free, easy to access, sufficient power is guaranteed 4. Building structure, the economy, saving money, and saving energy, it is facing in accordance with local environmental and physiol

20、ogical condition, lighting is good, easy to ventilation, easy to operate, so conducive to cooling in the summer, to insulation in winter cold 5. Layout of premises should be reasonable, do distinguish between production and non-production areas and non-production areas and water sources are on a chi

21、cken farm in the wind, net road and dirt road separating uncrossed, dung farm is located in the 1、1、2集合的表示法 【复习检测】 一、集合、元素的概念;集合如何按元素个数分类, 二、集合、元素的记法 三、元素与集合的关系 四、集合的性质。 ,2问题:1、在初中我们曾用 表示, 但是象抛物线上的点的集合、 Ny,x1,2,3,4 实数集等又怎样表示呢, 1x,2、在初中人们常说不等式,3x，1,0的解集为，但在高中这样的说法就是不恰3当的，究竟应该这样表示这些集合呢, 【探索新知】集合的表示法 知

22、识点一 列举法 例1、用列举法表示下列集合 2(1)方程解的集合。 x,3x，2,0(2)24与18的公约数的集合。 (3)大于5且小于30的质数的集合。 (4)二元一次方程的正整数解的集合。 2x，y,10又如:下列集合也可以用列举法表示 (1)自然数集 (2)正整数的倒数集合 (3)小于50的且被3除余1的正整数的集合。 问题1、下列集合可以用列举法表示吗, (1)直角三角形的集合。 x，1x,2(2)不等式的解集。 23choose water fountains, water-saving products should be purchased. As compared to ope

23、n v-Groove type water supply system, sealed nipple water system can save water 81.35% saving bedding consumption 56.3%; sanitation and drinking water, and a variety of harmful gases concentrations decline, increased laying rate 13.79%, economic efficiency improved. Chicken Coop construction should p

24、ay attention to several problems, chicken distribution notes: a rational structure of the hen-house layout, can provide a good environment for chicken, making its full productive potential, so other than in understanding the physiological characteristics of the chicken itself, and must be properly p

25、lanned and constructed sheds. 1. sites to choose away from populated areas, traffic convenient, away from the road 2. Gaozao terrain, a lot of sunshine. Winter sun as possible, summer wind, and not after the rain water. Larger, leaving room for development 3. Abundant water resources pollution-free,

26、 easy to access, sufficient power is guaranteed 4. Building structure, the economy, saving money, and saving energy, it is facing in accordance with local environmental and physiological condition, lighting is good, easy to ventilation, easy to operate, so conducive to cooling in the summer, to insu

27、lation in winter cold 5. Layout of premises should be reasonable, do distinguish between production and non-production areas and non-production areas and water sources are on a chicken farm in the wind, net road and dirt road separating uncrossed, dung farm is located in the (3)某农场的拖拉机的集合。 知识点二 描述法

28、例2、用描述法表示下列集合 (1)直角三角形的集合。 x，1x(2)不等式的解集。 ,223x，4x2(3)不等式的解集。 ,，1,x232x,3x，2,0(4)方程解的集合。 2方程解的集合。 x，1,02问题2、设方程x，1,0解的集合为，中有元素吗? ,你能再举一些这方面的例子吗, (5)二元一次方程的解的集合。 2x,y,12x，y,2,(6)二元一次方程组的解集。 x,y,4,choose water fountains, water-saving products should be purchased. As compared to open v-Groove type wate

29、r supply system, sealed nipple water system can save water 81.35% saving bedding consumption 56.3%; sanitation and drinking water, and a variety of harmful gases concentrations decline, increased laying rate 13.79%, economic efficiency improved. Chicken Coop construction should pay attention to seve

30、ral problems, chicken distribution notes: a rational structure of the hen-house layout, can provide a good environment for chicken, making its full productive potential, so other than in understanding the physiological characteristics of the chicken itself, and must be properly planned and construct

31、ed sheds. 1. sites to choose away from populated areas, traffic convenient, away from the road 2. Gaozao terrain, a lot of sunshine. Winter sun as possible, summer wind, and not after the rain water. Larger, leaving room for development 3. Abundant water resources pollution-free, easy to access, suf

32、ficient power is guaranteed 4. Building structure, the economy, saving money, and saving energy, it is facing in accordance with local environmental and physiological condition, lighting is good, easy to ventilation, easy to operate, so conducive to cooling in the summer, to insulation in winter col

33、d 5. Layout of premises should be reasonable, do distinguish between production and non-production areas and non-production areas and water sources are on a chicken farm in the wind, net road and dirt road separating uncrossed, dung farm is located in the 2(7)抛物线上点的集合。 y,x，12y二次函数的函数值的集合。 y,x，12x二次函

34、数的自变量的取值范围。 y,x，1(8)被3除余1的整数的集合。 指出:有些集合还可以用Venn图表示。 例如、下列集合可以用Venn图表示 ? ? ,1,4,7,91,4,7,9？反思总结: 【课堂检测】 1、下列集合中哪些具有相同的元素, 222 ,A,x|y,x,1B,(x,y)|y,x,1C,y|y,x,122,E,x|x,1, ,， D,y,x,1F,y|y,t,1,t,R2,; G,x|x,y,1,y,Rchoose water fountains, water-saving products should be purchased. As compared to open v-G

35、roove type water supply system, sealed nipple water system can save water 81.35% saving bedding consumption 56.3%; sanitation and drinking water, and a variety of harmful gases concentrations decline, increased laying rate 13.79%, economic efficiency improved. Chicken Coop construction should pay at

36、tention to several problems, chicken distribution notes: a rational structure of the hen-house layout, can provide a good environment for chicken, making its full productive potential, so other than in understanding the physiological characteristics of the chicken itself, and must be properly planne

37、d and constructed sheds. 1. sites to choose away from populated areas, traffic convenient, away from the road 2. Gaozao terrain, a lot of sunshine. Winter sun as possible, summer wind, and not after the rain water. Larger, leaving room for development 3. Abundant water resources pollution-free, easy

38、 to access, sufficient power is guaranteed 4. Building structure, the economy, saving money, and saving energy, it is facing in accordance with local environmental and physiological condition, lighting is good, easy to ventilation, easy to operate, so conducive to cooling in the summer, to insulatio

39、n in winter cold 5. Layout of premises should be reasonable, do distinguish between production and non-production areas and non-production areas and water sources are on a chicken farm in the wind, net road and dirt road separating uncrossed, dung farm is located in the x，y,1,2.关于方程组的解集,下面表达正确的是_. ,

40、x,y,3,x=2, ?(x,y)| ; ?(2,-1) ; ?(x,y)| (2,-1); ?2,1 ,y=-1【拓展提升】:试用列举法表示下列集合 1212xN,xN,(1)A= | (2)已知B=, ,N,N6,x6,x【练习】 1(用列举法表示下列集合 (1) A=x|x=2n n?Z; B=x|x=2n-4 n?Z; ZZ C=x|x=4n n?N; D=x|x=4n+2 n?N; (2) A=x|x=2n-1 n?Z; B=x|x=2n+1 n?Z; C=x|x=4n?1 n?Z; D=x|x=2n+1 n?N; 2(用列举法表示下列集合 |ab，,(,)abR(1)由所确定的实数

41、集合. ab(2) (x,y)|3x+2y=16，x?N，y?N . 23(设A=x?R|ax+2x+1=0,a?R ?若A=,求a的值; ?若A中只有一个元素,求a的值; ?若A中至多有一个元素,求a的取值集合. choose water fountains, water-saving products should be purchased. As compared to open v-Groove type water supply system, sealed nipple water system can save water 81.35% saving bedding consum

42、ption 56.3%; sanitation and drinking water, and a variety of harmful gases concentrations decline, increased laying rate 13.79%, economic efficiency improved. Chicken Coop construction should pay attention to several problems, chicken distribution notes: a rational structure of the hen-house layout,

43、 can provide a good environment for chicken, making its full productive potential, so other than in understanding the physiological characteristics of the chicken itself, and must be properly planned and constructed sheds. 1. sites to choose away from populated areas, traffic convenient, away from t

44、he road 2. Gaozao terrain, a lot of sunshine. Winter sun as possible, summer wind, and not after the rain water. Larger, leaving room for development 3. Abundant water resources pollution-free, easy to access, sufficient power is guaranteed 4. Building structure, the economy, saving money, and savin

45、g energy, it is facing in accordance with local environmental and physiological condition, lighting is good, easy to ventilation, easy to operate, so conducive to cooling in the summer, to insulation in winter cold 5. Layout of premises should be reasonable, do distinguish between production and non

46、-production areas and non-production areas and water sources are on a chicken farm in the wind, net road and dirt road separating uncrossed, dung farm is located in the 1、2集合之间的关系 1、2、1 子集与真子集 【复习检测】 集合、元素的概念,集合、元素的记法,1、 集合的含义,元素与集合的关系,集合的性质,列举法,2、 集合的表示法描述法,Venn图法,问题:1、实数之间存在着相等或不等关系，那么集合间又有怎样的相等或不

47、等关系呢, 2、元素与集合间是“属于”或“不属于”的关系，那么集合间还是这样的关系吗, 【探索新知】 知识点一 子集的定义 阅读下列一段话: 已知， ,A,1,2,3B,1,2,3,4,5A,BA中任意一个元素都在B中，就说A包含于B，记作(或B 包含A); 也说A是B的子集。 在下列个题中指出哪个集合是哪个集合的子集: ,NZRNQ1、,(或), N，2、?， ,A,x|x,1B,x|x,2?， ,A,x|x,3B,x|,1,x,2?,，, A,x|,3,x,5B,x|,1,x,2,?， A,x|x,1或x,3B,x|x,1或x,2,3、U,x|x是三角形，A,x|x是锐角三角形，B,x|x

48、是钝角三角形 ,C,x|x是直角三角形，D,x|x是斜三角形 问题:集合A是集合A的子集吗, n,N0,n,A,指出:对任意的,，类比可以规定:是任何集合A的子集，即。 知识点二 集合相等的定义 choose water fountains, water-saving products should be purchased. As compared to open v-Groove type water supply system, sealed nipple water system can save water 81.35% saving bedding consumption 56.3%; sanitation and drinking water, and a variety of harmful gases con