词汇与结构例题精讲
词汇与结构（共5小题；每小题3分，满分15分）
考试要求：
【语法】考生应掌握基本的英语语法知识，并能在听、说、读、写、译中较正确地加以运用。Singing these songs, I could not help the good old days.
A thinking over
B thinking out
C thinking of
D thinking up
试题与难度：等级1 难度1
This train is going the tunnel quickly.
A down
B through
C along
D in
试题与难度：等级1 难度1
Peter worked so fast with the maths problems a lot of mistakes.
A as to make
B that made
C to make
D that he made
this is an event of world historic significance is quite evident.
A What
B That
C Because
D Since
试题与难度：等级2 难度1
—In our English study reading is more important than speaking, I think.
—I don’t agree with you. Speaking is reading.
A as important as
B so important as
C the most important
D the same as
试题与难度：等级2 难度1
一、语法
1. 各种从句：（定语从句、状语从句、名词从句、强调句型）
模拟试题
1. While I was in the university, I learned taking a photo, is very useful now for me. B
A. it
B. which
C. that
D. what
2. It is the best I have seen. A
A. that
B. who
C. whom
D. which
3. Did you notice the guy head looked like a big potato? C
A. who
B. which
C. whose
D. whom
4. The film brought the hours back to me I was taken good care of in that remote village. A
A. when
B. where
C. that
D. until
5. No matter , the little sisters managed to round the sheep up and drive them back home safely. D
A. it was snowing hard
B. hard it was snowing
C. how it was snowing hard
D. how hard it was snowing.
6. Children under fifteen are not permitted to see such kind of movies bad for their mental development. C
A. that is
B. which is
C. as is
D. what are
7. Important his discovery might be, it was regarded as a matter of no account in his time. C
A. when
B. until
C. as
D. although
8. It was on the beach Miss White found the kid lying dead. A
A. that
B. this
C. it
D. which
9. It is not until you have lost your health you know its value. D
A. until
B. when
C. what
D. that
10. People at the party worried about him, because no one was aware he had gone. A
A. of where
B. of the place where
C. where
D. the place
11. I have the complacent feeling I’m highly intelligent. C
A. what
B. which
C. that
D. this
12. With his work completed, the manager stepped back to his seat, feeling pleased he was a
man of action. B
A. which
B. that
C. what
D. whether
13. We all thought pity that you were unable to attend our meeting. D
A. that
B. which
C. this
D. it
14. As the busiest woman there, she made her duty to look after all the other people’s affairs in that
town. D
A. this
B. that
C. one
D. it
15. no need the radio as I’m used to studying with it on. D
A. It’s；to turn down
B. It’s；to turning up
C. There’s；to turn off
D. There’s；turning off
16. is the population of Paris? D
A. How many
B. How much
C. How
D. What
17. —? C
—She’s our history teacher.
A. What’s she
B. Where does the woman work
C. Who is she
D. How is the woman
18. —What’s his mother like?
— . D
A. She’s very happy.
B. She’s at home.
C. She likes watching TV.
D. She’s tall and thin.
历年真题
1. TOEFL is a test for students native language is not English. C
A. that
B. of whom
C. whose
D. which
2. He studied hard in his youth, ____contributed to his great success in later life. D
A. that
B. it
C. what
D. which
3. I’ll never forget the day ______ I became a doctor. B
A. which
B. when
C. of which
D. in that
4. This is the house in ______ Lu Xun once lived in the 20’s. B
A. that
B. which
C. whose
D. whom
5. He's determined to finish the job long it takes. B
A. no matter
B. however
C. wherever
D. whatever
6. Do not make the same mistake _______ I did. D
A. which
B. that
C. like
D. as
7. He is so honest ____ every student in our class loves him. D
A. why
B. which
C. when
D. that
8. It is not that I am unwilling to help you ____I’m very busy. C
A. so
B. or
C. but that
D. that
9. Scientists say it may be five or ten years __ it is possible to test this medicine on human patients. B
A. since
B. before
C. after
D. when
10. is no reason for dismissing him. C
A. Because he was a few minutes late
B. Owing to a few minutes being late
C. The fact that he was a few minutes late
D. Being a few minutes late
11. Five minutes earlier, __ we could have caught the last tram. A
A. and
B. or
C. so
D. but
12. The furniture in his room is quite different __ in yours. B
A. from those
B. from that
C. from that one
D. from those ones
13. The population of many Alaskan cities has doubled in the past three years. C
A. larger than
B. as great as
C. more than
D. as many as
14. There was little hope ____proper medicine could be found. D
A. if
B. if not
C. with
D. unless
15. We’ll go on with the experiment ____he approves ____disapproves. A
A. whether … or
B. neit her … nor
C. not only … but also
D. so …. that
16. Although Mary is satisfied with her success, she wonders will happen to her private life.C
A. how
B. who
C. what
D. that
17. We should give the seat to is old or sick. B
A. whom
B. whoever
C. who
D. whose
18. Mother doesn’t know _______ the hammer after her son had used it. C
A. where did her son put
B. where her son putting
C. where her son put
D. where to put
19. I am very grateful to you for what you've given me and you have done for me. D
A. which
B. that
C. all what
D. all that
20. It was not until she had arrived home remembered her appointment with the doctor.B
A. when she
B. that she
C. and she
D. she
21. It was in 2001_________ this type of car began to be popular with the teenagers. D
A. which
B. then
C. when
D. that
22. I would like to see a suit ____ the one in the window. D
A. than
B. from
C. as D like
23. __ evidence that language acquiring ability must be stimulated. C
A. It being
B. It is
C. There is
D. There being
2. 非谓语动词：（不定式、动名词、分词）
模拟试题
1. I had my meals when I was ill in bed with a bad cold. C
A. to bring
B. bring
C. brought
D. bringing
2. After the Minister of Education had finished speaking at the press conference, he was made__ all sorts of awkward questions. D
A. answer
B. answering
C. answered
D. to answer
3. Would you let to the park with my classmate, Mum? A
A. me go
B. me going
C. I go
D. I going
4. A sudden noise of a fire-engine made him to the door. C
A. hurrying
B. hurried
C. hurry
D. to hurry
5. I have been looking forward to from my parents. D
A. hear
B. being heard
C. be heard
D. hearing
6. A police officer claimed that the young man had attempted to paying his fare.A
A. avoid
B. reject
C. refuse
D. neglect
7. You object ,don’t you ? D
A. that they come
B. that they came
C. to their come
D. to their coming
8. you Xiao Li, do you? D
A. call
B. to call
C. to calling
D. my calling
9. The new order means overtime. D
A. works
B. worked
C. to work
D. working
10. What a bad memory I’ve got! I even forgot the book with me. B
A. took
B. taking
C. take
D. taken
11. Charles regretted the TV set last year. The price has now come down. A
A. buying
B. to buy
C. of
D. from
12. his examination of the patient, the doctor wrote out a prescription. A
A. Having finished
B. Finishing
C. Finished
D. Having been finished
13. tomorrow’s lessons, Frank has no time to go out with his friends. B
A. Not preparing
B. Not having prepared
C. Not to prepare
D. Being not prepared
14. There was so much noise in the classroom that the teacher couldn’t make himself. A
A. heard
B. hearing
C. to hear
D. hear
15. The wild flowers looked like a soft orange blanket the desert. A
A. covering
B. covered
C. cover
D. to cover
16. — Why does he look sad?
—There are so many problems .C
A. remaining to settle
B. remained settling
C. remaining to be settled
D. remained to be settled
17. —The physics exam is not difficult, is it?
— . Even Harry to the top students failed in it. C
A. Yes；belongs
B. No；belonged
C. Yes；belonging
D. No；belonging
18. Would you like something ? B
A. drink
B. to drink
C. drinking
D. for drinking
历年真题
1. a teacher in a university, it is necessary to have at least a master's degree. A
A. To become
B. Become
C. One becomes
D. On becoming
2. we shall ask for samples _____ and then we can make our decision. A
A. to be sent
B. being sent
C. to send
D. to have been sent
3. I must tell you _____ a letter from you. A
A. I was pleased to receive
B. I was pleased to receiving
C. I pleased to receive
D. I was pleased receiving
4. If you don’t want to get wet, then you had better ____ this umbrella with you. A
A. take
B. to take
C. taken
D. for taking
5. He doesn’t know much about doing the job, yet he can do it keep it going. C
A. good enough to
B. enough well to
C. well enough to
D. well enough for
6. The planets are so for away that it is impossible _____ in miles. C
A. that we measure it
B. to use to measure them
C. for us to measure them
D. measuring them
7. Bob said that it is easy . C
A. for him being on time
B. being on time for him
C. for him to be on time
D. on time for him
8. Jean did not have time to go to the concert last night because she was busy ___ for her examination. C
A. to prepare
B. to be prepared
C.preparing
D. being prepared
9. The government official explained that there's no point__ about the cultural gap in that city. C
A. to worry
B. with them worrying
C. in worrying
D. worry
10. The guest said that they wouldn’t mind ____ a little light mu sic. B
A. to have
B. having
C. have
D. that they have
11. The thief admitted gold rings in the store. D
A. steal
B. to have stolen
C. to steal
D. stealing
12. I don’t know why she avoids _______ her opinion on the subject. C
A. to give
B. to be given
C. giving
D. being given
13. The match was cancelled because most of the members a match without a standard court. A
A. objected to having
B. objected to have
C. were objected to have
D. were objected to having
14. They talked in whispers, but still, I couldn't help but __ their conversation. C
A. overhear
B. to overhear
C. overhearing
D. overheard
15. If I had remembered the window, the thief would not have got in. A
A. to close
B. closing
C. to have closed
D. having closed
16. Many Americans worry about leisure and hurry from one activity to the next, little time to stop and think. B
A. leave
B. leaving
C. left
D. to leave
17. Cambridge has announced plans to establish a business school the master's degree in business administration. B
A. representing
B. offering
C. presenting
D. supplying
18. Having been asked to speak at the convention __ . B
A. some notes were prepared for Dr. Smith
B. Smith prepared some notes
C. The convention members were pleased to hear Dr. Smith
D. Some notes were prepared by Dr. Smith
19. Air pollution , this city is still a good place to live in. A
A. being greatly reduced
B. greatly being reduced
C. to greatly reduce
D. greatly to reduce
20. __ such a good chance, he planned to learn more. C
A. Giving
B. Having given
C. Having been given
D. To be given
21. enough manpower and financial support, we certainly can finish the work. C
A. As if
B. Although
C. Given
D. Because
22. New ideas sometimes have to wait for years before they are . C
A. fully accepting
B. accepting fully
C. fully accepted
D. acceptfully
23. _______ with the size of the whole earth, the highest mountain does not seem high at all. A
A. When compared
B. Compare
C. While comparing
D. Comparing
24. From now on I want to keep myself_______ of how things are going on with you. C
A. to inform
B. informing
C. informed
D. be informed
25. Before he came to Japan, he had never heard a single Japanese word . D
A. speaking
B. speak
C. to speak
D. spoken
26. The concert usually takes place at the People's Square, with the audience on the ground. B
A. seating
B. seated
C. be seating
D. to seat
3. 虚拟语气：（wish, as if, would rather, it’s time that, suggest, require, desire, essential etc. ） 模拟试题
1. Had you come five minutes earlier, you the train to Birmingham. But now you missed it.B
A. would catch
B. would have caught
C. could catch
D. should catch
2. The dean of the Philosophy Department requested that the visiting scholar a lecture on the philosopher Sartre. B
A. gave
B. give
C. would give
D. had given
3. It’s time we the lecture because everybody has arrived. D
A. will start
B. shall start
C. start
D. started
4. I wish everybody the meeting tomorrow. B
A. will attend
B. would attend
C. had attended
D. is going to attend
5. The old lady is quarrelling with others as if she mad. D
A. was
B. is
C. are
D. were
6. I would rather two weeks earlier. D
A. you should come here
B. you come here
C. you came here
D. you had come here
7. Each person at the reunion was required to talk to other relatives to find out if they would buy one of the histories it were printed. B
A. whether
B. if
C. when
D. after
历年真题
1. ______ yesterday, I would have asked him not to do that. A
A. If he had come
B. if he came
C. Provided he came
D. Has he came
2. If the whole program ___beforehand, a great deal of time and money would have been lost. D
A. was not planned
B. were not planned
C. would not be planned
D.had not been planned
3. If he ______ such a good chance, he would have planned to learn more. C
A. was giving
B. had given
C. had been given
D. was to give
4. , he would have been the top student in the class. B
A. If he worked hard
B. If he had worked hard
C. If he was working hard
D. Working hard
5. If only he __ what I tell him, but he won't. B
A. had done
B. would do
C. would have dope
D. has done
6. He told me how he had given me shelter and protection without which I of hunger. C
A. would be died
B. would die
C. would have died
D. will die
7. we desire that the tour leader __ us immediately of any changes in plans. A
A. inform
B. informs
C. informed
D. has informed
8. This is a very difficult operation. It is essential that you __ for emergency. C
A. are to be prepared
B. would prepared
C. be prepared
D. must be prepared
9. It is required that all the teachers in the department on a picnic next Saturday. C
A. to go
B. went
C. go
D. might go
10. Isn't it about the time you to do morning exercises? A
A. began
B. begin
C. should begin
D. have begun
11. Most insurance agents would rather you anything about collecting claims until they investigate the situation. B
A. don't do
B. didn't do
C. would not do
D. do
4. 情态动词（could, should (ought to ), must + have done）
模拟试题
1. My wallet is nowhere to be found. I in the store. B
A. must drop it
B. must have dropped it
C. should have dropped it
D. ought to have dropped it
2. He didn’t pass the final examination. He it. C
A. must have prepared for
B. ought to preparing for
C. ought to have prepared for
D. ought to prepare for
3. You buy some reference books when you go to college. B
A. could
B. will have to
C. must to
D. might
4. The young lady coming over to us our English teacher；the way she walks tells us that! A
A. must be
B. can be
C. would be
D. could be
●历年真题
1. The computer doesn't work well, so something wrong. C
A. can have gone
B. should have gone
C. must have gone
D. ought to have gone
2. Although Jack made a foolish mistake, we __ at him. B
A. ought to have laughed
B. oughtn’t to have laughed
C. ought to laugh
D. should not to laugh
3. I didn’t hear the phone. I _______ asle ep. C
A. must be
B. should be
C. must have been
D. should have been
4. A computer ____ think for itself, it must be told what to do. A
A. can’t
B. couldn’t
C. may not
D. might not
5. I believed his wife ____for him just as I was praying for James. B
A. should be praying
B. must be praying
C. would be praying
D. must pray
5. 倒装句、主谓一致(never, scarcely, little, under no circumstance, hardly…/when etc.)
●模拟试题
1. Two thousand dollars enough for the car. D
A. being
B. were
C. are
D. is
2. Both the kids and their parents English, I think. I know it from their accent. C
A. is
B. been
C. are
D. was
3. The young interested in pop music. D
A. is
B. have
C. has
D. are
4. I will count three hundred and not one of you move a bit. A
A. is to
B. are to
C. is
D. are
5. She has two best friends. of them is in the country. D
A. All
B. Both
C. No one
D. Neither
6. Never before see such a terrible car accident on the road! D
A.I have
B. have I
C.I did
D. did I
7. Hardly on stage the audience started cheering. C
A. he had come/than
B. he had come/when
C. had he come/when
D. had he come/than
●历年真题
1. How close parents are to their children___ a strong influence on the character of the children. C
A. have
B. having
C. has
D. to have
2. Both China and Japan _______ located in the east of Asia. A
A. are
B. be
C. is
D. was
3. It ____ John and Mary that helped me the other day. C
A. has been
B. are
C. was
D. were
4. Neither bill nor his parents ____ at home. C
A. is
B. has
C. are
D. was
5. A suitcase with shirt, trousers and shoes __ stolen from the car. C
A. have been
B. has
C. was
D. are
6. This article deals with the natural phenomenon which most interesting to everyone. B
A. are
B. is
C. they are
D. it is
7. In no circumstance_________________________. B
A. smoking should be allowed on the campus
B. should smoking be allowed on the campus
C. should smoking allowed on the campus
D. should smoking allow on the campus
8. Hardly ever get a good job these days without a good education. C
A. people might
B. people can
C. do people
D. have people
9. Nowhere else in the world more attractive scenery than in Switzerland. C
A. you can find
B. is found
C. can you find
D. has been found
6. 时态
●模拟试题
1. When the railway is completed, we get to town much easily. D
A. must
B. would
计数原理与排列组合题型解题方法总结 计数原理 一、知识精讲 1、分类计数原理： 2、分步计数原理： 特别注意:两个原理的共同点：把一个原始事件分解成若干个分事件来完成。 不同点：如果完成一件事情共有n类办法，这n类办法彼此之间相互独立的，无论哪一类办法中的哪一种方法都能单独完成这件事情，求完成这件事情的方法种数，就用分类计数原理。分类时应不重不漏（即任一种方法必须属于某一类且只属于这一类） 如果完成一件事情需要分成n个步骤，各个步骤都是不可缺少的，需要依次完成所有的步骤，才能完成这件事，而完成每一个步骤各有若干种不同的方法，求完成这件事情的方法种数就用分步计数原理。各步骤有先后，相互依存，缺一不可。 3、排列 (1)排列定义,排列数 (2)排列数公式: (3)全排列列: 4.组合 (1)组合的定义,排列与组合的区别; (2)组合数公式: (3)组合数的性质 二、.典例解析 题型1:计数原理 例1.完成下列选择题与填空题 (1)有三个不同的信箱,今有四封不同的信欲投其中,则不同的投法有种。 A.81 B.64 C.24 D.4 (2)四名学生争夺三项冠军,获得冠军的可能的种数是( ) A.81 B.64 C.24 D.4 (3)有四位学生参加三项不同的竞赛, ①每位学生必须参加一项竞赛,则有不同的参赛方法有; ②每项竞赛只许有一位学生参加,则有不同的参赛方法有;
③每位学生最多参加一项竞赛,每项竞赛只许有一位学生参加,则不同的参赛方法有 。 例2（1）如图为一电路图，从A 到B 共有 条不同的线路可通电。 例3: 把一个圆分成3块扇形，现在用5种不同的颜色给3块扇形涂色，要求相邻扇形的颜色互不相同，问有多少钟不同的涂法？若分割成4块扇形呢？ 例4、某城在中心广场造一个花圃，花圃分为6个部分(如图).现要栽种4种不同颜色的花，每部分栽种一种且相邻部分不能栽种同样颜色的花，不同的栽种方法有 ________ 种.(以数字作答) 例5、 四面体的顶点和各棱的中点共10个，在其中取4个不共面的点，问共有多少种不同的取法？ 例6、（1）电视台在”欢乐今宵”节目中拿出两个信箱,其中存放着先后两次竞猜中成绩优秀的观众来信,甲信箱中有30封,乙信箱中有20封.现有主持人抽奖确定幸运观众,若先确定一名幸运之星,再从两信箱中各确定一名幸运伙伴,有多少种不同的结果? （2）三边均为整数，且最大边长为11的三角形的个数是 D C B A
例1 用0到9这10 个数字．可组成多少个没有重复数字的四位偶数？ 例2三个女生和五个男生排成一排 （1）如果女生必须全排在一起，可有多少种不同的排法？ （2）如果女生必须全分开，可有多少种不同的排法？ （3）如果两端都不能排女生，可有多少种不同的排法？ （4）如果两端不能都排女生，可有多少种不同的排法？ 例3 排一张有5个歌唱节目和4个舞蹈节目的演出节目单。 （1）任何两个舞蹈节目不相邻的排法有多少种？ （2）歌唱节目与舞蹈节目间隔排列的方法有多少种？ 例4某一天的课程表要排入政治、语文、数学、物理、体育、美术共六节课，如果第一节不排体育，最后一节不排数学，那么共有多少种不同的排课程表的方法． 例5现有3辆公交车、3位司机和3位售票员，每辆车上需配1位司机和1位售票员．问车辆、司机、售票员搭配方案一共有多少种？ 例6下是表是高考第一批录取的一份志愿表．如果有4所重点院校，每所院校有3个专业是你较为满意的选择．若表格填满且规定学校没有重复，同一学校的专业也没有重复的话，你将有多少种不同的填表方法？ 例77名同学排队照相． (1)若分成两排照，前排3人，后排4人，有多少种不同的排法？
(2)若排成两排照，前排3人，后排4人，但其中甲必须在前排，乙必须在后排，有多少种不同的排法？ (3)若排成一排照，甲、乙、丙三人必须相邻，有多少种不同的排法？ (4)若排成一排照，7人中有4名男生，3名女生，女生不能相邻，有多少种不面的排法？ 例8计算下列各题： (1) 215 A ； (2) 66 A ； (3) 1 1 11------?n n m n m n m n A A A ； 例9 f e d c b a ,,,,,六人排一列纵队，限定a 要排在b 的前面（a 与b 可以相邻，也可以不相邻），求共有几种排法． 例10 八个人分两排坐，每排四人，限定甲必须坐在前排，乙、丙必须坐在同一排，共有多少种安排办法？ 例11 计划在某画廊展出10幅不同的画，其中1幅水彩画、4幅油画、5幅国画，排成一行陈列，要求同一品种的画必须连在一起，并且不彩画不放在两端，那么不同陈列方式有 例12 由数字5,4,3,2,1,0组成没有重复数字的六位数，其中个位数字小于十位数的个数共有（ ）． 例13 用5,4,3,2,1，这五个数字，组成没有重复数字的三位数，其中偶数共有（ ）． 例14 用543210、、、、、共六个数字，组成无重复数字的自然数，(1)可以组成多少个无重 复数字的3位偶数？(2)可以组成多少个无重复数字且被3整除的三位数？
指数函数及其基本性质 指数函数的定义 一般地，函数()10≠>=a a a y x 且叫做指数函数，其中x 是自变量，函数的定义域是R . 问题：指数函数定义中，为什么规定“10≠>a a 且”如果不这样规定会出现什么情况？ (1)若a<0会有什么问题？（如2 1 ,2= -=x a 则在实数范围内相应的函数值不存在） (2)若a=0会有什么问题？（对于0≤x ,x a 无意义） (3)若 a=1又会怎么样？（1x 无论x 取何值,它总是1,对它没有研究的必要.） 师：为了避免上述各种情况的发生,所以规定0>a 且 1≠a . 指数函数的图像及性质 函数值的分布情况如下：
指数函数平移问题（引导学生作图理解） 用计算机作出的图像，并在同一坐标系下作出下列函数的图象，并指出它们与指数函数y =x 2的图象的关系（作图略）， ⑴y =1 2+x 与y =2 2+x . ⑵y =12 -x 与y =2 2 -x . f (x )的图象 向左平移a 个单位得到f (x ＋a )的图象; 向右平移a 个单位得到f (x －a )的图象; 向上平移a 个单位得到f (x )＋a 的图象; 向下平移a 个单位得到f (x )－a 的图象.
指数函数·经典例题解析 (重在解题方法) 【例1】求下列函数的定义域与值域： (1)y 3 (2)y (3)y 12x ＝＝＝-+---213321x x 解 (1)定义域为x ∈R 且x ≠2．值域y ＞0且y ≠1． (2)由2x+2－1≥0，得定义域{x|x ≥－2}，值域为y ≥0． (3)由3－3x-1≥0，得定义域是{x|x ≤2}，∵0≤3－3x －1＜3， ∴值域是≤＜．0y 3 及时演练求下列函数的定义域与值域 （1）4 12-=x y ； （2）|| 2()3 x y =； （3）1241++=+x x y ； 【例2】指数函数y ＝a x ，y ＝b x ，y ＝c x ，y ＝d x 的图像如图2．6－2所示，则a 、b 、c 、d 、1之间的大小关系是 [ ] A ．a ＜b ＜1＜c ＜d B ．a ＜b ＜1＜d ＜c C ． b ＜a ＜1＜d ＜c D ．c ＜d ＜1＜a ＜b 解 选(c)，在x 轴上任取一点(x ，0)，则得b ＜a ＜1＜d ＜c ． 及时演练
排列组合知识点汇总及典型例题(全)
一．基本原理 1．加法原理：做一件事有n 类办法，则完成这件事的方法数等于各类方法数相加。 2．乘法原理：做一件事分n 步完成，则完成这件事的方法数等于各步方法数相乘。 注：做一件事时，元素或位置允许重复使用，求方法数时常用基本原理求解。 二．排列：从n 个不同元素中，任取m （m ≤n ）个元素，按照一定的顺序排成一 .m n m n A 有排列的个数记为个元素的一个排列，所个不同元素中取出列，叫做从 1.公式：1.()()()()! ! 121m n n m n n n n A m n -= +---=…… 2. 规定：0!1= (1)!(1)!,(1)!(1)!n n n n n n =?-+?=+ (2) ![(1)1]!(1)!!(1)!!n n n n n n n n n ?=+-?=+?-=+-； (3) 111111 (1)!(1)!(1)!(1)!!(1)! n n n n n n n n n +-+==-=- +++++ 三．组合：从n 个不同元素中任取m （m ≤n ）个元素并组成一组，叫做从n 个不同的m 元素中任取 m 个元素的组合数，记作 Cn 。 1. 公式： ()()()C A A n n n m m n m n m n m n m m m ==--+= -11……!!!! 10 =n C 规定： 组合数性质：.2 n n n n n m n m n m n m n n m n C C C C C C C C 21011=+++=+=+--……，， ①；②；③；④ 111 12111212211r r r r r r r r r r r r r r r r r r n n r r r n n r r n n n C C C C C C C C C C C C C C C +++++-+++-++-+++++=+++ +=++ +=注： 若1 2 m m 1212m =m m +m n n n C C ==则或 四．处理排列组合应用题 1.①明确要完成的是一件什么事（审题） ②有序还是无序 ③分步还是分类。 2．解排列、组合题的基本策略 （1）两种思路：①直接法； ②间接法：对有限制条件的问题，先从总体考虑，再把不符合条件的所有情况去掉。这是解决排列组合应用题时一种常用的解题方法。 （2）分类处理：当问题总体不好解决时，常分成若干类，再由分类计数原理得出结论。注意：分类不重复不遗漏。即：每两类的交集为空集， 所有各类的并集为全集。 （3）分步处理：与分类处理类似，某些问题总体不好解决时，常常分成若干步，再由分步计数原理解决。在处理排列组合问题时，常常既要分 类，又要分步。其原则是先分类，后分步。 （43．排列应用题： （1）穷举法（列举法）：将所有满足题设条件的排列与组合逐一列举出来； (2)、特殊元素优先考虑、特殊位置优先考虑； （3）．相邻问题：捆邦法： 对于某些元素要求相邻的排列问题，先将相邻接的元素“捆绑”起来，看作一“大”元素与其余元素排列，然后再对相邻元素内部进行排列。 （4）、全不相邻问题，插空法：某些元素不能相邻或某些元素要在某特殊位置时可采用插空法.即先安排好没有限制条件的元素，然后再将不相 邻接元素在已排好的元素之间及两端的空隙之间插入。 （5）、顺序一定，除法处理。先排后除或先定后插 解法一：对于某几个元素按一定的顺序排列问题，可先把这几个元素与其他元素一同进行全排列，然后用总的排列数除于这几个元素的全排列数。即先全排，再除以定序元素的全排列。 解法二：在总位置中选出定序元素的位置不参加排列，先对其他元素进行排列，剩余的几个位置放定序的元素，若定序元素要求从左到右或从右到左排列，则只有1种排法；若不要求，则有2种排法； （6）“小团体”排列问题——采用先整体后局部策略 对于某些排列问题中的某些元素要求组成“小团体”时，可先将“小团体”看作一个元素与其余元素排列，最后再进行“小团体”内部的排列。 （7）分排问题用“直排法”把元素排成几排的问题，可归纳为一排考虑，再分段处理。 （8）．数字问题（组成无重复数字的整数） ① 能被2整除的数的特征：末位数是偶数；不能被2整除的数的特征：末位数是奇数。②能被3整除的数的特征：各位数字之和是3的倍数； ③能被9整除的数的特征：各位数字之和是9的倍数④能被4整除的数的特征：末两位是4的倍数。 ⑤能被5整除的数的特征：末位数是0或5。 ⑥能被25整除的数的特征：末两位数是25，50，75。 ⑦能被6整除的数的特征：各位数字之和是3的倍数的偶数。 4．组合应用题：（1）.“至少”“至多”问题用间接排除法或分类法: （2）． “含”与“不含” 用间接排除法或分类法: 3．分组问题： 均匀分组：分步取，得组合数相乘，再除以组数的阶乘。即除法处理。 非均匀分组：分步取，得组合数相乘。即组合处理。 混合分组：分步取，得组合数相乘，再除以均匀分组的组数的阶乘。 4．分配问题： 定额分配：（指定到具体位置）即固定位置固定人数，分步取，得组合数相乘。
高中数学排列与组合 （一）典型分类讲解 一.特殊元素和特殊位置优先策略 例1.由0,1,2,3,4,5可以组成多少个没有重复数字五位奇数. 解:由于末位和首位有特殊要求,应该优先安排, 先排末位共有1 3C 然后排首位共有1 4C 最后排其它位置共有 34A 由分步计数原理得1 1 3 434 288C C A = 练习题:7种不同的花种在排成一列的花盆里,若两种葵花不种在中间，也不种在两端的花盆里，问有多少不同的种法？ 二.相邻元素捆绑策略 例2. 7人站成一排 ,其中甲乙相邻且丙丁相邻, 共有多少种不同的排法. 解：可先将甲乙两元素捆绑成整体并看成一个复合元素，同时丙丁也看成一个复合元素，再与其它元素进行排列，同时对相邻元 素内部进行自排。由分步计数原理可得共有 522522480A A A =种不同的排法 练习题:某人射击8枪，命中4枪，4枪命中恰好有3枪连在一起的情形的不同种数为 20 三.不相邻问题插空策略 例3.一个晚会的节目有4个舞蹈,2个相声,3个独唱,舞蹈节目不能连续出场,则节目的出场顺序有多少种？ 解:分两步进行第一步排2个相声和3个独唱共有55A 种， 第二步将4舞蹈插入第一步排好的6个元素中间包含首尾两个空位共有种 46 A 不同的方法,由分步计数原理,节目的不同顺序共有54 56A A 种 练习题：某班新年联欢会原定的5个节目已排成节目单，开演前又增加了两个新节目.如果将这两个新节目插入原节目单中，且两个新节目不相邻，那么不同插法的种数为 30 四.定序问题倍缩空位插入策略 例4. 7人排队,其中甲乙丙3人顺序一定共有多少不同的排法 解:(倍缩法)对于某几个元素顺序一定的排列问题,可先把这几个元素与其他元素一起进行排列,然后用总排列数除以这几个元素 之间的全排列数,则共有不同排法种数是： 73 73/A A (空位法)设想有7把椅子让除甲乙丙以外的四人就坐共有 47 A 种方法，其余的三个位置甲乙丙共有 1种坐法，则共有4 7A 种方法。 思考:可以先让甲乙丙就坐吗? （插入法)先排甲乙丙三个人,共有1种排法,再把其余4四人依次插入共有 方法 练习题:10人身高各不相等,排成前后排，每排5人,要求从左至右身高逐渐增加，共有多少排法？ 5 10C 五.重排问题求幂策略 例5.把6名实习生分配到7个车间实习,共有多少种不同的分法 解:完成此事共分六步:把第一名实习生分配到车间有 7 种分法.把第二名实习生分配到车间也有7种分依此类推,由分步计数原 理共有6 7种不同的排法 练习题： 1． 某班新年联欢会原定的5个节目已排成节目单，开演前又增加了两个新节目.如果将这两个节目插入原节目单中，那么不同插 法的种数为 42 4 4 3 允许重复的排列问题的特点是以元素为研究对象，元素不受位置的约束，可以逐一安排各个元素的位置，一般地n 不同的元素没有限制地安排在m 个位置上的排列数为n m 种
实用标准 指数函数·例题解析 第一课时 【例1】（基础题）求下列函数的定义域与值域： (1)y 3 (2)y (3)y 1 2x ＝＝＝-+---213321x x 解 (1)定义域为{x|x ∈R 且x ≠2}．值域{y|y ＞0且y ≠1}． (2)由2x+2－1≥0，得定义域{x|x ≥－2}，值域为{|y|y ≥0}． (3)由3－3x-1≥0，得定义域是{x|x ≤2}，∵0≤3－3x －1＜3， ∴值域是≤＜．0y 3 1.指数函数Y=ax （a>0且a ≠1）的定义域是R ，值域是（0，+∞） 2. 求定义域的几个原则：①含根式（被开方数不为负）②含分式，分母不为０③形如a0,(a ≠ 0) 3. 求函数的值域:①利用函数Y=ax 单调性②函数的有界性(x2≥0;ax>0)③换元法.如:y=4x+6×2x-8(1≤x ≤2) 先换元,再利用二次函数图象与性质(注意新元的范围)
【例2】（基础题）指数函数y＝a x，y＝b x，y＝c x，y＝d x的图像如图2．6－2所示，则a、b、c、d、1之间的大小关系是 [ ] A．a＜b＜1＜c＜d B．a＜b＜1＜d＜c C．b＜a＜1＜d＜c D．c＜d＜1＜a＜b 解选(c)，在x轴上任取一点(x，0)，则得b＜a＜1＜d＜c．
【例3】（基础题）比较大小： (1)2(2)0.6 、、、、的大小关系是：． 2481632 35894 5 12--() (3)4.54.1________3.73.6 解(1)y 221()x ∵，，，，，函数＝，＞，该函数在－∞，＋∞上是增函数，又＜＜＜＜，∴＜＜＜＜．22224282162133825491 2 28416212313525838949 3859=====
第一章 走进细胞 走进细胞 从生物圈到细胞 生命活动离不开细胞 生命系统的结构层次 组织：由形态相似，结构、功能相同的细胞联合在一起的细胞群 器官：不同的组织按照一定的次序结合在一起而构成器官 系统：能够共同完成一种或几种生理功能的多个器官按照一定的次序组合在起而构成系统 个体：由各种器官(植物)或系统(动物和人)协调配合共同完成复杂的生命活动的生物。单细胞生物是由一个细胞构成的生物体。 种群：在一定的自然区域内，同种生物的所有个体是一个种群。 群落：在一定的自然区域内，所有的种群(生物)组成一个群落。 生态系统：生物群落与它的无机环境相互作用而形成的统一整体 生物圈：由地球上所有的生物和这些生物生活的无机环境共同组成 细胞的多样性和统一性 观察细胞(显微镜的使用) 原核细 胞与真核细胞 低倍镜的视野大(小)，通过的光多(少)，放大倍数小(大)； 物镜放大倍数小(大)，镜头较短(长) 显微镜放大倍数=目镜放大倍数×物镜放大倍数 先用低倍镜观察清楚，把要放大观察的移到视野中央，再换高倍镜观察 看到物像是倒像，因而物像移动的方向与实际材料(装片)移动方向相反 主要内容：(1)细胞是一个有机体，一切动植物都是由细胞发育而来，并由细胞和细胞产物所构成。(2)细胞是一个相对独立的单位，既有它自己的生命，又对与其他 细胞共同组成的整体的生命起作用。(3)新细胞可以从老细胞中产生 细胞学说 从学说的建立过程可以领悟到科学发现具有以下特点： 1、 科学发现是很多科学家的共同参与，共同努力的结果 2、 科学发现的过程离不开技术的 3、 科学发现需要理性思维和实验的结合 4、 科学学说的建立过程是一个不断开拓、继承、修正和发展的过程 细胞：细胞是生物体结构和功能的基本单位
指数函数 1．指数函数的定义： 函数)1 (≠ > =a a a y x且叫做指数函数，其中x是自变量，函数定义域是R 2.指数函数的图象和性质： 在同一坐标系中分别作出函数y=x2，y= x ? ? ? ? ? 2 1 ，y=x 10，y= x ? ? ? ? ? 10 1 的图象. 我们观察y=x2，y= x ? ? ? ? ? 2 1 ，y=x 10，y= x ? ? ? ? ? 10 1 图象特征，就可以得到)1 (≠ > =a a a y x且的图象和性质。 a>10 ()x f c 的大小关系是_____． 分析：先求b c ，的值再比较大小，要注意x x b c ，的取值是否在同一单调区间内． 解：∵(1)(1)f x f x +=-， ∴函数()f x 的对称轴是1x =． 故2b =，又(0)3f =，∴3c =． ∴函数()f x 在(]1-， ∞上递减，在[)1+，∞上递增． 若0x ≥，则321x x ≥≥，∴(3)(2)x x f f ≥； 若0x <，则321x x <<，∴(3)(2)x x f f >． 综上可得(3)(2)x x f f ≥，即()()x x f c f b ≥． 评注：①比较大小的常用方法有：作差法、作商法、利用函数的单调性或中 间量等．②对于含有参数的大小比较问题，有时需要对参数进行讨论． 2．求解有关指数不等式 例2 已知2321(25)(25)x x a a a a -++>++，则x 的取值范围是___________． 分析：利用指数函数的单调性求解，注意底数的取值范围． 解：∵2225(1)441a a a ++=++>≥， ∴函数2(25)x y a a =++在()-+，∞∞上是增函数， ∴31x x >-，解得1 4x >．∴x 的取值范围是14 ??+ ??? ， ∞． 评注：利用指数函数的单调性解不等式，需将不等式两边都凑成底数相同的指数式，并判断底数与1的大小，对于含有参数的要注意对参数进行讨论． 3．求定义域及值域问题 例3 求函数y = 解：由题意可得2160x --≥，即261x -≤， ∴20x -≤，故2x ≤． ∴函数()f x 的定义域是(]2-， ∞． 令26x t -=，则y =， 又∵2x ≤，∴20x -≤． ∴2061x -<≤，即01t <≤． ∴011t -<≤，即01y <≤． 高考排列组合典型例题 Company number：【WTUT-WT88Y-W8BBGB-BWYTT-19998】 排列组合典型例题 例1 用0到9这10 个数字．可组成多少个没有重复数字的四位偶数 分析：这一问题的限制条件是：①没有重复数字；②数字“0”不能排在千位数上；③个位数字只能是0、2、4、6、8、，从限制条件入手，可划分如下： 如果从个位数入手，四位偶数可分为：个位数是“0”的四位偶做，个位数是 2、4、6、8的四位偶数（这是因为零不能放在千位数上）．由此解法一与二． 如果从千位数入手．四位偶数可分为：千位数是1、3、5、7、9和千位数是2、4、6、8两类，由此得解法三． 如果四位数划分为四位奇数和四位偶数两类，先求出四位个数的个数，用排除法，得解法四． 解法1：当个位数上排“0”时，千位，百位，十位上可以从余下的九个数字中任选3个来排列，故有39A 个； 当个位上在“2、4、6、8”中任选一个来排，则千位上从余下的八个非零数字中任选一个，百位，十位上再从余下的八个数字中任选两个来排，按乘法原理有281814A A A ??（个）． ∴ 没有重复数字的四位偶数有 2296179250428181439 =+=??+A A A A 个． 解法2：当个位数上排“0”时，同解一有39A 个；当个位数上排2、4、6、8中之一时，千位，百位，十位上可从余下9个数字中任选3个的排列数中减去千 位数是“0”排列数得：)(283914 A A A -?个 ∴ 没有重复数字的四位偶数有 22961792504)(28391439 =+=-?+A A A A 个． 第 指数函数·例题解析 【例1】求下列函数的定义域与值域： (1)y 3 (2)y (3)y 12x ＝＝＝-+---213321x x 解 (1)定义域为x ∈R 且x ≠2．值域y ＞0且y ≠1． (2)由2x+2－1≥0，得定义域{x|x ≥－2}，值域为y ≥0． (3)由3－3x-1≥0，得定义域是{x|x ≤2}，∵0≤3－3x －1＜3， ∴值域是≤＜．0y 3 【例2】指数函数y ＝a x ，y ＝b x ，y ＝c x ，y ＝d x 的图像如图2．6－2所示，则a 、b 、c 、d 、1之间的大小关系是 [ ] A ．a ＜b ＜1＜c ＜d B ．a ＜b ＜1＜d ＜c C ． b ＜a ＜1＜d ＜c D ．c ＜d ＜1＜a ＜ b 解 选(c)，在x 轴上任取一点(x ，0)，则得b ＜a ＜1＜d ＜c ． 【例3】比较大小： (1)2(2)0.6 、、、、的大小关系是：． 2481632 358945 12--() (3)4.54.1________3.73.6 解(1)y 221()x ∵，，，，，函数＝，＞，该函数在－∞，＋∞上是增函数，又＜＜＜＜，∴＜＜＜＜．22224282162133825491 2 28416212313525838949 3859===== 解 (2)0.6110.6∵＞，＞， ∴＞． --- -45 12 451 232 32 ()() 解 (3)借助数4.53.6打桥，利用指数函数的单调性，4.54.1＞4.53.6，作函数y 1＝4.5x ，y 2＝3.7x 的图像如图2．6－3，取x ＝3.6，得4.53.6＞3.73.6 ∴ 4.54.1＞3.73.6． 说明 如何比较两个幂的大小：若不同底先化为同底的幂，再利用指数函数的单调性进行比较，如例2中的(1)．若是两个不同底且指数也不同的幂比较大小时，有两个技巧，其一借助1作桥梁，如例2中的(2)．其二构造一个新的幂作桥梁，这个新的幂具有与4.54.1同底与3.73.6同指数的特点，即为4.53.6(或3.74.1)，如例2中的(3)． 【例4】解 比较大小与＞且≠，＞． 当＜＜，∵＞，＞， a a a a a n n n n n n n n n n n n -+-+-=-111 1 111 1(a 0a 1n 1)0a 1n 10() () 排列组合典型例题 典型例题一 例1 用0到9这10 个数字．可组成多少个没有重复数字的四位偶数？ 分析：这一问题的限制条件是：①没有重复数字；②数字“0”不能排在千位数上；③个位数字只能是0、2、4、6、8、，从限制条件入手，可划分如下： 如果从个位数入手，四位偶数可分为：个位数是“0”的四位偶做，个位数是 2、4、6、8的四位偶数（这是因为零不能放在千位数上）．由此解法一与二． 如果从千位数入手．四位偶数可分为：千位数是1、3、5、7、9和千位数是2、4、6、8两类，由此得解法三． 如果四位数划分为四位奇数和四位偶数两类，先求出四位个数的个数，用排除法，得解法四． 解法1：当个位数上排“0”时，千位，百位，十位上可以从余下的九个数字中任选3个来排列，故有3 A个； 9 当个位上在“2、4、6、8”中任选一个来排， 则千位上从余下的八个非零数字中任选一个，百位，十位上再从余下的八个数字中任选两个来排，按乘法原理有2 8181 4 A A A ??（个）． ∴ 没有重复数字的四位偶数有 2296 179250428181439=+=??+A A A A 个． 解法2：当个位数上排“0”时，同解一有3 9 A 个；当个位数上排2、4、6、8中之一时，千位，百位，十位上可从余下9个数字中任选3个的排列数中减去千位数是“0”排列数得：) (28391 4 A A A -?个 ∴ 没有重复数字的四位偶数有 2296 1792504)(28391439=+=-?+A A A A 个． 解法3：千位数上从1、3、5、7、9中任选一个，个位数上从0、2、4、6、8中任选一个，百位，十位上从余下的八个数字中任选两个作排列有 2 81 515A A A ??个 干位上从2、4、6、8中任选一个，个位数上从余下的四个偶数中任意选一个（包括0在内），百位，十位从余下的八个数字中任意选两个作排列，有 2 81414A A A ??个 ∴ 没有重复数字的四位偶数有 一．基本原理 1．加法原理：做一件事有n 类办法，则完成这件事的方法数等于各类方法数相加。 2．乘法原理：做一件事分n 步完成，则完成这件事的方法数等于各步方法数相乘。 注：做一件事时，元素或位置允许重复使用，求方法数时常用基本原理求解。 二．排列：从n 个不同元素中，任取m （m ≤n ）个元素，按照一定的顺序排成一 .m n m n A 有排列的个数记为个元素的一个排列，所个不同元素中取出列，叫做从 1.公式：1.()()()()! ! 121m n n m n n n n A m n -= +---=…… 2. 规定：0!1= (1)!(1)!,(1)!(1)!n n n n n n =?-+?=+ (2) ![(1)1]!(1)!!(1)!!n n n n n n n n n ?=+-?=+?-=+-； ' (3)111111 (1)!(1)!(1)!(1)!!(1)! n n n n n n n n n +-+==-=-+++++ 三．组合：从n 个不同元素中任取m （m ≤n ）个元素并组成一组，叫做从n 个不同的m 元素中任取 m 个元素的组合数，记作 Cn 。 1. 公式： ()()()C A A n n n m m n m n m n m n m m m ==--+= -11……!! !! 10=n C 规定： 组合数性质：.2 n n n n n m n m n m n m n n m n C C C C C C C C 21011=+++=+=+--……，， ① ；②；③；④ 11112111212211r r r r r r r r r r r r r r r r r r n n r r r n n r r n n n C C C C C C C C C C C C C C C +++++-+++-++-+++++=+++ +=++ +=注： 若1 2 m m 1212m =m m +m n n n C C ==则或 四．处理排列组合应用题 1.①明确要完成的是一件什么事（审题） ②有序还是无序 ③分步还是分类。 " 2．解排列、组合题的基本策略 （1）两种思路：①直接法； ②间接法：对有限制条件的问题，先从总体考虑，再把不符合条件的所有情况去掉。这是解决 排列组合应用题时一种常用的解题方法。 （2）分类处理：当问题总体不好解决时，常分成若干类，再由分类计数原理得出结论。注意： 分类不重复不遗漏。即：每两类的交集为空集，所有各类的并集为全集。 （3数原理解决。在处理排列组合问题时，常常既要分类，又要分步。其原则是先分类，后分步。 （4 3．排列应用题： （1）穷举法（列举法）：将所有满足题设条件的排列与组合逐一列举出来； (2)、特殊元 素优先考虑、特殊位置优先考虑； ) （3）．相邻问题：捆邦法： 对于某些元素要求相邻的排列问题，先将相邻接的元素“捆绑”起来，看作一“大”元素与其余元素排列，然后再对相邻元素内部进行排列。 （4）、全不相邻问题，插空法：某些元素不能相邻或某些元素要在某特殊位置时可采用插空 第一章：有理数 ★知识结构图： 正分数 负分数 正整数 负整数 ★正数和负数 概念、定义： 1.大于0的数叫做正数（positive number）。 2.在正数前面加上负号“-”的数叫做负数（negative number）。 3.整数和分数统称为有理数（rational number）。 4.规定了原点、正方向和单位长度的直线叫做数轴（number axis）。 5.在直线上任取一个点表示数0，这个点叫做原点（origin）。 6.一般的，数轴上表示数a的点与原点的距离叫做数a的绝对值（absolute value）。 7.一个正数的绝对值是它本身；一个负数的绝对值是它的相反数；0的绝对值是0。 8.正数大于0，0大于负数，正数大于负数。两个负数，绝对值大的反而小。 ★有理数加法法则： 1.同号两数相加，取相同的符号，并把绝对值相加。 2.绝对值不相等的异号两数相加，取绝对值较大的加数的负号，并用较大的绝对值减去较小的绝对值，互为相反数的两个数相加得0。 3.一个数同0相加，仍得这个数。 4.有理数的加法中，两个数相加，交换交换加数的位置，和不变。 5.有理数的加法中，三个数相加，先把前两个数相加，或者先将后两个数相加，和不变。 6.有理数减法法则：减去一个数，等于加上这个数的相反数。 ★有理数乘法法则 1.两数相乘，同号得正，异号得负，并把绝对值向乘；任何数同0相乘，都得0。 2. 有理数中仍然有：乘积是1的两个数互为倒数。 3. 一般的，有理数乘法中，两个数相乘，交换因数的位置，积相等。 4.三个数相乘，先把前两个数相乘，或者先把后两个数相乘，积相等。 5.一般地，一个数同两个数的和相乘，等于把这个数分别同这两个数相乘，再把积相加。 ★有理数除法法则 1.除以一个不等于0的数，等于乘这个数的倒数。 2.两数相除，同号得正，异号得负，并把绝对值相除。0除以任何一个不等于0的数，都得0。★做有理数混合运算时，应注意以下运算顺序： 指数函数习题 新泰一中闫辉 一、选择题 1．下列函数中指数函数的个数是 ( ). ①②③④ A．0个 B．1个 C．2个 D．3个 2．若，，则函数的图象一定在（） A．第一、二、三象限 B．第一、三、四象限 C．第二、三、四象限 D．第一、二、四象限 3．已知，当其值域为时，的取值范围是（）A． B． C． D． 4．若，，下列不等式成立的是（） A． B． C． D． 5．已知且，，则是（） A．奇函数 B．偶函数 C．非奇非偶函数 D．奇偶性与有关 6．函数（）的图象是（） 7．函数与的图象大致是( ). 8．当时，函数与的图象只可能是（） 9．在下列图象中，二次函数与指数函数的图象只可能是（） 10．计算机成本不断降低,若每隔3年计算机价格降低 ,现在价格为8100元的计算机,则9年后的价格为( ). A．2400元 B．900元 C．300元 D．3600元 二、填空题 1．比较大小： （1）；（2） ______ 1；（3） ______ 2．若，则的取值范围为_________． 3．求函数的单调减区间为__________． 4．的反函数的定义域是__________． 5．函数的值域是__________ ． 6．已知的定义域为 ,则的定义域为__________. 7．当时, ,则的取值范围是__________. 8．时，的图象过定点________ ． 9．若 ,则函数的图象一定不在第_____象限. 10．已知函数的图象过点 ,又其反函数的图象过点(2,0),则函数的解析式为____________. 11．函数的最小值为____________. 12．函数的单调递增区间是____________. 13．已知关于的方程有两个实数解,则实数的取值范围是_________. 14．若函数（且）在区间上的最大值是14，那么等于 _________． 三、解答题 1．按从小到大排列下列各数： ，，，，，，， 2．设有两个函数与，要使（1）；（2），求、的取值范围． 3．已知 ,试比较的大小. 4．若函数是奇函数，求的值． 5．已知，求函数的值域． 6．解方程： 排列组合专题复习及经典例题详解 1. 学习目标 掌握排列、组合问题的解题策略 2.重点 （1）特殊元素优先安排的策略： （2）合理分类与准确分步的策略； （3）排列、组合混合问题先选后排的策略； （4）正难则反、等价转化的策略； （5）相邻问题捆绑处理的策略； （6）不相邻问题插空处理的策略． 3.难点 综合运用解题策略解决问题． 4.学习过程: (1)知识梳理 1．分类计数原理（加法原理）：完成一件事，有几类办法，在第一类办法中有1m 种不同的方法，在第2类办法中有2m 种不同的方法……在第n 类型办法中有n m 种不同的方法，那么完成这件事共有n m m m N +++=...21种不同的方法． 2．分步计数原理（乘法原理）：完成一件事，需要分成n 个步骤，做第1步有1m 种不同的方法，做第2步有2m 种不同的方法……，做第n 步有n m 种不同的方法；那么完成这件事共有n m m m N ???=...21种不同的方法． 特别提醒： 分类计数原理与“分类”有关，要注意“类”与“类”之间所具有的独立性和并列性； 分步计数原理与“分步”有关，要注意“步”与“步”之间具有的相依性和连续性，应用这两个原理进行正确地分类、分步，做到不重复、不遗漏． 3．排列：从n 个不同元素中，任取m(m≤n)个元素，按照一定的顺序排成一列，叫做从n 个不同元素中取出m 个元素的一个排列，n m <时叫做选排列，n m =时叫做全排列. 4．排列数：从n 个不同元素中，取出m(m≤n)个元素的所有排列的个数，叫做从n 个不同元素中取出m 个元素的排列数，用符号m n P 表示. 5．排列数公式：）、（+∈≤-= +---=N m n n m m n n m n n n n P m n ,)! (!)1)...(2)(1( 排列数具有的性质：11-++=m n m n m n mP P P 特别提醒： 规定0!=1 Chapter 1 Invitations to Linguistics 1.1 Why Study Language? 1.Some myths about language 2.Some fundamental views about language 3.Some concrete demonstrations to show Linguistics’importance 1.2 What is Language? 1. Language “is not to be confused with human speech, of which it is only a definite part, though certainly an essential one. It is both a social product of the faculty of speech and a collection of necessary conventions that have been adopted by a social body to permit individuals to exercise that faculty”. --Ferdinand de Saussure (1857-1913): Course in General Linguistics (1916) 2. “Language is a purely human and non-instinctive method of communicating ideas, emotions and desires by means of voluntarily produced symbols.” --Edward Sapir (1884-1939): Language: An Introduction to the Study of Speech (1921) 3. “A language is a system of arbitrary vocal symbols by means of which a social group co-operates.” --Bernard Bloch (1907-1965) & George Trager (1906-1992): Outline of Linguistic Analysis (1942) 4. “A language is a system of arbitrary vocal symbols by means of which the members of a society interact in terms of their total culture.” --George Trager: The Field of Linguistics (1949) 5. “From now on I will consider language to be a set (finite or infinite) of sentences, each finite in length and constructed out of a finite set of elements.” --Noam Chomsky (1928- ): Syntactic Structures (1957) 6. Language is “the institution whereby humans communicate and interact with each other by means of habitually used oral-auditory arbitrary symbols.” --Robert A. Hall (1911-1997): Introductory Linguistics (1964) 7.“Language is a system of arbitrary vocal symbols used for human communication.” --Ronald Wardhaugh: Introduction to Linguistics (1977) 8. “Language is a means of verbal communication.” —It is instrumental in that communicating by speaking or writing is a purposeful act. —It is social and conventional in that language is a social semiotic and communication can only take place effectively if all the users share a broad understanding of human interaction including such associated factors as nonverbal cues, motivation, and socio-cultural roles. -- Our textbook (2006) 9. Language is a system of arbitrary vocal symbols used for human communication.高考排列组合典型例题
《幼儿教育学》第一章知识框架图
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教育的 起源
教育的 概念
教育学 的概念
幼儿教育 的概念
神话起源说
生物起源说
心理起源说
劳动起源说
教育是新生一代成长和人类社会延续、发展的必要手段，是人类社会特有的社 会现象。 广义：有目的、有意识地对人身心施加影响并促进人向社会要求的方向发展的 一种社会实践活动。包括家庭教育、社会教育和学校教育。 狭义：指学校教育，如幼儿园教育，小学、中学和大学教育以及其他人们为了 某种目的而特别组织的教育。
注意三点： 1、教育活动是人类社会特有的社会实践活动 2、教育活动是培养人的社会实践活动 3、学校教育活动是一种专门的培养人的社会实践活动
教育学是研究教育这一社会现象并揭示其规律的一门科学。
幼儿教育主要指的是对 3 到 6 岁年龄阶段的幼儿所实施的教育，是一个人教育与发 展的重要而特殊的阶段。 广义：凡是能够影响幼儿身体成长和认知、情感、性格等方面发展的活动，如幼儿 的家庭生活的形态，父母养育他的态度和方式，幼儿周围的人和事，他所读的书， 接触他的人，看电影、电视等等，都可说是幼儿教育。 狭义的幼儿教育则特指幼儿园和其他专门开设的幼教机构的教育。
幼儿教育 学的概念
幼儿教育 的意义
幼儿教育学是一门研究 3-6 岁幼儿教育规律和幼儿教育机构的教育工作规律的 科学，它是人们从教育幼儿的实践中总结提炼出来的教育理论
（1）促进幼儿在体、智、德、美诸方面全面和谐的发展。 （2）帮助幼儿适应学校生活，为入小学学习做好准备。 （3）减轻父母教养幼儿的负担并改善处境不利幼儿的状况。
幼儿教育对个体发展的意义 （一） 促进生长发育，提高身体素质，使幼儿健康、安全、愉快地成长 （二） 发展儿童的智力潜力和特点，识别和培养他们区别于他人的智能和兴趣， 帮助他们实现富有个性的发展 （三） 培养良好的品行和性格，促进个性、人格的完善和健康发展 （四） 激发幼儿感受美、表现美、创造美的情趣，丰富他们的审美经验，使之 体验到自由表达和创造的快乐
幼儿教育对社会发展的意义 （一） 幼儿教育对巩固提高“普九”水平，发展各类教育，构筑终身教育体系， 具有基础性、全局性和先导性的作用 （二） 幼儿教育的发展使人民群众日益增长的教育需求得到满足 （三） 幼儿教育的发展有力于国民素质的提高，有利于经济社会的持续、健康、 和谐的发展高一数学下指数函数典型例题解析
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