9．已知集合A={y|y²-(a²+a+1)y+a(a²+1)>0},B={y|y=x²/2-x+5/2,0£x£3},若A∩ B=Æ,求实数a的取值范围

8．设全集I=R，A={x|£0},B={x|lg(x²-2)=lgx},求A∩

7．若集合A={3-2x,1,3} ,B={1,x²},且AÈ B=A,求实数x

5．设集合A={x|x²+x-1=0},B={x|ax+1=0},若BA,则实数a的不同取值个数为　　 　

6设全集I=R，集合A={x|x²-x-2= -y²,yÎ R,y≠0},B={y|y=x+1,xÎA},则

=　　　　 　

4．若{1,2}AÍ{1,2,3,4,5}, 则满足这一关系的集合A的个数为　　 　

3．设集合A={x|x²<a} ,B={x|x<2},若A∩ B=A,则实数a的取值范围是( )

(A)a<4　　　　　 (B)a£4　　　　 (C)0<a£4　　　 (D)0<a<4

+(200÷30)＝146

所以，符合条件的数共有200－146＝54(个)

例6 已知全集，A={1,}如果，则这样的实数是否存在？若存在，求出，若不存在，说明理由

分析：此题的关键是理解符号是两层含义：

解：∵　 　∴，即＝0，

　 解得

　 当时，，为A中元素

　 当时，

当时，

∴这样的实数x存在，是或

另法：∵　 　∴，

∴＝0且

∴或

变式思考题：

同时满足条件：①②若，这样的集合M有多少个，举出这些集合来

答案：这样的集合M有8个：

例7　某学校艺术班有100名学生，其中学舞蹈的学生67人，学唱歌的学生45人，而学乐器的学生既不能学舞蹈，又不能学唱歌,人数是21人,那么同时学舞蹈和唱歌的学生有多少人？

解：设学舞蹈的学生有x人，学唱歌的人有y人，

既学舞蹈又学唱歌的人又z人，

由题意可列方程：

　 　　　解得

所以，同时学舞蹈和唱歌的有33人

例8对于集合,是否存在实数？若存在，求出的取值，若不存在，试说明理由

解：　 ∴ , 即二次方程:

，

　 　,解之得

　　 故存在实数

例9已知集合，,

,求的值

解：由可知，

(1)，或(2)

解(1)得，

解(2)得

又因为当时，与题意不符

所以，

例10已知为全集，,

解:由

所以

　 由

例11已知集合，求的值

解：

(1)当含有两个元素时：；

(2)当含有一个元素时：

　　　 若

若

综上可知：

小结：

1正确理解集合中元素的特征：确定性，互异性，无序性；

2用列举法或描述法给出集合，考察元素与集合之间的元素；或不给出集合中的元素，但只给出若干个抽象的集合及某些关系，运用文氏图解决有关问题

3熟练运用集合的并、交、补的运算并进行有关集合的运算

4注意符号的理解，相互之间的转化：例如等等

学生练习

题组一：

1已知集合M={x|x²＜4}，N={x|x²－2x－3＜0}，则集合M∩N等于

A{x|x＜－2}　 B{x|x＞3}　 C{x|－1＜x＜2}　 D{x|2＜x＜3}

解析：M={x|x²＜4}={x|－2＜x＜2}，

N={x|x²－2x－3＜0}={x|－1＜x＜3}，结合数轴，

∴M∩N={x|－1＜x＜2}

答案：C

2已知集合A={x∈R|x＜5－}，B={1，2，3，4}，则(A)∩B等于

A{1，2，3，4}　　 B{2，3，4}　　 C{3，4}　　　　 D{4}

解析：A={x∈R|x≥5－}，而5－∈(3，4)，

∴(A)∩B={4}

答案：D

3设集合P={1，2，3，4，5，6}，Q={x∈R|2≤x≤6}，那么下列结论正确的是

AP∩Q=P　 BP∩QQ　　 CP∪Q=Q 　 DP∩QP

解析：P∩Q={2，3，4，5，6}，∴P∩QP

答案：D

4设U是全集，非空集合P、Q满足PQU，若求含P、Q的一个集合运算表达式，使运算结果为空集，则这个运算表达式可以是______

解析：构造满足条件的集合，实例论证

U={1，2，3}，P={1}，Q={1，2}，

则(Q)={3}，(P)={2，3}，易见(Q)∩P=

答案：(Q)∩P

5已知集合A＝{0，1}，B＝{x｜x∈A，x∈N^*}，C＝{x｜xA}，则A、B、C之间的关系是________

解析：用列举法表示出B＝{1}，C＝{，{1}，{0}，A}，易见其关系这里A、B、C是不同层次的集合，C以A的子集为元素，同一层次的集合可有包含关系，不同层次的集合之间只能是从属关系

答案：BA，A∈C，B∈C

题组二：

1设全集为实数集R，集合M={x|x²-1999x-2000>0},P={x||x-1999|<a}(a为常数),且-1ÎP,则M与P满足　 (　　　 )

(A) 　　　　(B)　

(C)　 　　(D)

2．若非空集合A={x|2a+1£x£3a-5},B={x|3£x£22},则能使AÍB

成立的所有a的集合是(　　 )

(A){a|1£a£9}　　 (B){a|6£a£9}　　　 (C){a|a£9}　 (D)Æ

(A)根据要求完成小作文，词数：30词左右。(5分)

　　 假如你叫Rick，你的朋友Edward送给你一件你非常喜欢的礼物，请你写一封短小的

感谢信。

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(B)根据要求完成大作文，词数：60-80词。(15分)

　　 三年的学习生活就要结束了，在这几年的英语(或语文、数学……)学习中，你一定积累

了不少的学习经验。请选择-个学科，写一篇短文，谈谈你对该学科的学习经验和感受。

要求：字迹工整，语言连贯。文中不得出现真实姓名和所在学校的相关信息。

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(A)根据短文内容，从各题的四个选项中选择一个最佳答案，将其于字母标号写在答题纸的

　 相应位置上。

　　 A report card is a card that a western student___36___ once a semester or term from their school. This usually includes grades for each of the school subjects and___37___from their subject teachers and class teacher．The report cards should be given to___38___by the students themselves or sent to them by mail．If a student has bad grades，he must be worried about___39___ the subject teachers will say． Maybe you．have seen an American movie．It tells

___40___a boy called Tommy．He doesn’t like science．He tries hard，but he 6nds science very difficult．After the end-of-year exams，he___41___ home very late．As soon as he comes back home，his parents ___42___ his report card．He tells them he has___43___ it．Tommy is just one of these students who get bad grades．Most of them may be nervous about__44__ their bad grades to their parents．

In western culture，the day that report cards are ___45___ is always an important day for students，especially for the students with bad grades!

36．A．receives　　　　 B．gives　　　　　　 C．takes　　　 　　　D．sends

37．A．the grades　　　 B．the comments　　　 C．the classes　　　 D．the school

38．A．their friends　　 B．their subjects　　　 C．their teachers　　 D．their parents

39．A．when　　　　　 B．why　　　　　　　 C．what　　　　　　 D．where

40．A．about"　　　　 B．to　　　　　　　　 C．with　　　　　　 D．for

41．A．gets　　　　　 B．arrives in　　　　　 C．gets to　　　　　　 D．reaches to

42．A．want to　　　　 B．ask to　　　　　　 C．ask for　　　　　　 D．want for

43．A．lost　　　　　 B．lose　　　　　　　　 C．losing　　　　　 　D．losed

44．A-writing　　　　　 B．showing　　　　　 C．getting　　　　　　 D．having

45．A．given back　　 B．given away?　　　　 C．given up　　　　　　 D．given out

(B)根据短文内容，从方框中选择适当的单词并用其正确形式填空，使短文完整、正确，将

答案写在答题纸的相应位置上。

　 A few months___46___，my mom sent me some old pictures．I___47___a little girl in the

pictures．I was drawing，dancing or singing．There were also___48___ pictures of me with my

sisters in which we enjoyed___49___ together．

I looked at each photograph___50___. Each picture reminded me of special times. In one

picture , I was dancing. I smiled ___51___. I saw that picture. That was fun, I blushed(脸红)

when I looked at another picture．I was singing for my family in that picture．Then I saw that

picture of my sisters and me．We had so much fun together．I enjoyed___52___at these

pictures．My mom sent a short note___53___these pictures．She told me，to ___54___care of these pictures．Each photograph is a good ___55___She is right

59．If you want to learn a skill in two months，you can learn__________

　 A．how to use the new software　　 B．swimming

　 C．how to take pictures　　　　　 D．painting

60．Which of the following statements is true?

　　 A-Prof．G．White gives a talk about English learning for students on Monday morning．

　　 B．You can go to learn how to use office 2000 from Prof．J．Brown．

　　 C．If you want to learn swimming，you should go there 0n Sunday afternoon．

　　 D．Prof．J．Brown teaches children English from 3：00-4：30 on Saturday afternoon．

Passage 2

　　 Once a group of 17-year-old schoolboys decided to break the world basketball marathon

record(马拉松纪录)．They wanted to play for ninety hours and that is to add six hours t0 the

　record．Each team had nine players，with five at a time．The boys decided each person would

play 21．5 hours and then rest for 2 hours．Then they started at 6 o'clock in the evening．

　 The first night was very hard for．the players．When it was their turn to rest．they were too

excited to fall asleep at once．

　 After sleeping for a short time，they had to play again．On the second night，they fell

asleep as soon as they stopped．Some of them had trouble with their feet and hands．but the

only serious problem was a psychological(心理上的)one．Each boy was thinking：Why am I

doing this? How can I play any longer? After the third night，the players knew they could finish

the ninety hours．The basketball on the fourth night was very slow．But in the final hours．，the

players got better. For the last few minutes，the pla3rers looked as fresh as they were when they

started．How happy everyone was !

61．In the story．there were___________ schoolboys playing basketball marathon

A．9　　 B．14　　　　 C．17　　　 D．18

62．Before this basketball marathon．the world record was__________

A．84 hours　　　 B．86 hours　　　 C．90 hours　　 D．96 hours

63．On the first night it was hard for the players to fall asleep because___________．

　 A．they were too excited　　　　 B．they only slept for a short time　

　 C．no one watched them play　　 D．it was Very long　　

64．“…the players looked as fresh as they were when they started．”Here ”fresh” means

_______________

　 A．新鲜的　　 B．兴奋不已　　　 C．精神饱满的　　 D．伤痕累累的

65．Which of the following sentences is wrong?　

　 A．Some of the boys had pains in their feet and hands．

　 B．It was hard for the players to fall asleep at night．

　 C．The boys started playing at 6 o’clock in the evening．

　 D．In the end．all the boys felt happy．

67．Alice advised Sarah ______________

A．to give her friend a special gift　 B．to apologize(道歉)

C．to find a job　　　　　　　　　 D．to pay for it．

68．Lily’s brother had a terrible argument with

A．his sister　　 B．his girl friend　　 C．his mother　　 D．her friend

69．The beautiful vase was broken by____________

　 A．Lily　　　 B．The mother　 C．Sarah　　　 D．Alice

70．Lily’s brother has stopped--．

　 A．cooking and doing his laundry　　　　 B．speaking to her

　 C．trying hard enough　　　　　　　　 D．dating with her girl friend

Passage 4

　 Anna came to the United States from Poland four years ago．Her life has changed a lot

　since she came here. In her(country she didn’t work． 　She studied and took care of her new

　born son. Her parents helped her a lot．When she came to America，everything changed．

　 At first，she had a problem with English．She couldn’t understand．people around her，so

　Anna had to go to school to learn how to talk in good English. The second problem she had was

the loneliness. in Poland she had parents and friends whom she could ask for help and tell

about her problems. In America，however，she and her husband were alone．They had to and

a place to live in，and her husband had to find。a job to get money for their house and food．

Their parents and all the friends were far away from them and couldn’t help them any more．

　　 Now many things have changed．Anna has got a part-time job working in an office at the

College. Her husband has found a good job that he likes They have made new friends and they

are beginning to feel comfortable．

71．Anna didn’t work

　 A．after　　　 B．since　　　 C．before　　　 D．when

72．What did she do in Poland?

　 A．She helped her parents．　　　　　　　 B．She learned how to speak good English　　

　 C. She worked in an office at the college．　 　D．She studied and looked after her b8by．

73．When she came to the United States，she______________．

　 A．had no problems　　　　 B．had some friends

　 C．asked friends for help　　 D．had a hard life．

74．She and her husband______________ in Poland．

A．were lonely　　　　　　　　　　　 B．couldn’t understand people around them

C．went to school to learn English,　　　 D．could ask her parents and friends for help

75．Which sentence is NOT true?

　 A．One of Anna’s problems was that she was lonely．

　 B．Anna has found a part-time job with the help of her parents and friends．

　 C．In his motherland she didn’t worry about many things．

　 D．Now their life has become better since they found jobs．

(B)根据短文内容，按要求完成任务，将答案写在答题纸相应位置上。(20，每小题2分)

Passage 5

　　 Today 1 went on a bike ride with my friend．Steve． A bike ride is a great way to exercise and enjoy the outdoors．Steve likes to ride his bike because it’s healthy and fun。Riding a bike can be fun for everyone! Before you take a bike ride，test your brakes and bells．It’s good to be safe! We had a problem on the trail today．I got fl flat tire．But Steve is an experienced bike rider，so he had his air pump with

him．He always brings it along just in case he needs it．

　 　Steve and I rode our bikes along one of the rivers in Taipei today．It was fun to explore the City by bike·We went all the way to Bali．That’s where our bike trail ended．I was really tired. I was even too fired to bike back home．Thankfully，we could take t}le MRT home．We had a great day!

flat(adj)(轮胎)泄了气的　　 tire(n)轮胎　　　 air pump(n)打气筒　 trail(n)小径、

根据短文内容，简答下面的问题。

76．why does Steve like to ride his bike7

77．What do people have to do before they take a bike ride?

78．What does Steve take with him when he gets a flat tire?

79．How did they get home

80．They didn’t have a good time，did they?

Passage 6

　 Once upon a time，all the animals came together to see

who Was the most beautiful in the forest．AU the animals were

happy and excited．However，the snake was very sad because

she knew she was not beautiful．The cock was very kind to

her．He lent the snake his crown(鸡冠)．The snake put the

morning the cock got up very early and waited for the snake，but the snake didn’t come．Then

every morning the cock waited and shouted．The snake still didn’t come．To this day．the cock

still gets up early each morning and crows(啼)，“Cock-a doodle-doo!”He is saying．

“Where are you?’’

根据短文内容，完成下列句子。

81．The cock was kind enough to________________ the crown to the snake．

82．The snake felt SO_________________ when she put the crown on her head．

83．The animals said the snake was____________ than the 0thers．

84．The snake did her________________ to look for the missing crown．

85．The snake was______________ to come to see the cock because she lost the crown．

●书面表达

35．______________________________________________________________________