北师大版必修三各单元知识要点及语法
一．各单元知识点
第七单元：关系副词，介词+which引导的定语从句，形容词的比较级
第八单元：限制性和非限制性定语从句，静态动词和动态动词
第九单元：现在完成进行时态，现在完成时态和现在完成进行时态
3. 全书单词数量为：262个
词组数量为：40个
必修三语法知识
一、Relative Clause with where, when and why, where, when, why 引导的定语从句
关系副词where, when 引导的定语从句可提供时间和地点的信息，在reason后可用why 引导的定语从句。介词+ which /whom 引导的定语从句
关系代词可做介词的宾语，通常在which和whom前加介词即介词+which/whom 结构
This is the book for which he is looking.
可以根据定语从句所修饰的名词或代词来选介词，也可以依据从句的相关动词来选用。但在日常英语中，通常是吧介词放在从句句末，省略关系代词which 和whom
The train(which /that) I’m travelling on is for Shanghai.
二、形容词和副词的比较
More and more 越来越…
Less /the least 不如/最不…
The …the …越…就越… The less I worried, the better I worked.
三、修饰形容词比较级
Much, a lot, slightly, a little, almost, a bit, far, even, still, twice/ three times …more than/twice as much/many as/twice the +n +of …比…多/是…的两倍/三倍。
四、状态或动作动词
英语中动词分为两类：动作动词和状态动词。动作动词描述动作，可用于一般时态和进行时态；状态动词描述状态，一般不用于进行时态。
状态动词
表达思维活动的动词：admit, believe, know, mean, prefer, realize, remember, think, understand, want,
表达情感的动词：adore，care, like, dislike, love, hate, hope
表达拥有和存在的动词：appear, be, belong, contain, have, include, need, seem, possess, own.
感官动词feel, hear, look, see, smell, sound, taste,有些状态动词也可以表示动作，在此意义上，这些动词可用于现在时。How are you feeling?
感官动词后用形容词修饰二不用副词。
The roses look and smell beautiful.
四、定语从句：defining and non-defining 限制性和非限制性定语从句
Ⅰ. 概念：
(1) 定语从句：在主从复合句中用作定语的从句叫定语从句。定语从句一般紧接在先行词(antecedent)后面。
(2) 先行词：被定语从句修饰的成份。先行词可以为一个词，短语，或整个主句。
(3) 引导定语从句的词叫关系词，分为关系代词和关系副词。
关系词的作用：
1) 引导定语从句，连接主句和从句，相当于一个连词；
2) 必在从句中作某个句子成份（可以做主语，宾语，表语，定语，状语）
常用的关系代词: that、which、who、whom、whose、as 、but (文语, 置于否定词之后=that/who…not…,
"没有……不……", 在从句中作主语，宾语)
常用的关系副词（在从句中只作状语）: when、why、where
The student who answered the question was John.
I know the reason why he was so angry.
The boy (whom) you are talking to is my brother.
I'd like a room whose window looks out over the sea.
定语从句三步：
第一找出先行词；
第二看先行词在定语从句中的语法功能（做主语、宾语或状语）；
第三选择合适的关系词。
Ⅱ. 几个关系代词的基本用法：
●that: 可指人或物；在定语从句中作主语，宾语，表语。(指人时，相当于who或whom；指物时，相当于which)(一般不用于非限制性定语从句; 不可置于介词后作宾语) 如：
1. A letter that/which is written in pencil is difficult to read. (主语)
2. Do you know the gentleman that/who spoke just now?
3. You can take anything ( that) you like. （宾语）
4. What is the question (that/which) they are talking about?
5. Here is the man ( who/whom/that ) you want to see.
6. She's no longer the girl ( that) she used to be before.（表语）
7. Our hometown is no longer the one (that) it used to be.
= Our hometown is not the same as it used to be.
= Our hometown is different from what it used to be。
= Our hometown is not what it used to be.
●which: 指物；在定语从句中作主语，宾语，表语，定语。如：
1. The book which/that was on the desk was bought by my father.（主语）
2. The book (which/that) I bought yesterday is very interesting.（宾语）
3. The factory in which his father works is far from here.
4. He was proud, which his brother never was. （表语）
5. Tom spent four years in college, during which time he learned French.（定语）
6. He may be late, in which case we ought to wait for him.
●who, whom, whose:
who: 主格, 在从句中作主语，在口语或非正式用法中作宾语; 只可指人
whom: 宾格，在从句中作宾语; 只可指人
whose: 属格，在从句中作定语，可指人也可指物。
I like the students who/that work hard. （主语）
All who heard the story were amazed. (代词如he, they, any, those, all, one等后多用who.)
Chaplin, for whom life had once been very hard, was a success as an actor. （宾语）
He's a man from whom we should learn.
= He's a man (whom/who/that) we should learn from.
比较：He is the student whom you think to be worthy of your praise.
He is the student who you think is worth praising.
A child whose parents are dead is called an orphan.（指人）
I'd like a room whose window faces south. （指物）
=I'd like a room of which the window faces south.
=I'd like a room the window of which faces south.
There is a teapot shaped like a Chinese duck, out of whose mouth tea is supposed to come
关系代词作介词宾语:
关系代词在定语从句中用作介词宾语时, 介词可放于从句之首, 也可放于从句之末. 但以放于句首较为正式.（介词前置，必须注意不影响动词词组的含义。关系代词who 和that 用作介词宾语时, 介词必须放在句末.）
This is the book for which you asked.
=This is the book (that/which) you asked for.
Do you know the person with whom I shook hands？= Do you know the person (whom/who/that) I shook hands with?
The beginning of agriculture was a big step in human progress with which nothing could compare until our information age.
In the dark street, there wasn't a single person to whom she could turn for help.
Is this the factory to which you paid a visit last week?
Is this factory the one to which you paid a visit last week?
This is the girl whom they are looking after. (介词after与look构成固定词组，不可前置。look at, look for, look after, take care of等)
●as 的用法:(as 引导定语从句, 在定语从句中作主语、宾语、表语)
①如为限制性的，多用于the same …as ; the same as；such …as …; as many/much as；so …as等结构中。如：
※I have the same book as you (have). 我有一本和你的一样的书。
Her attitude to him was quite the same as it had always been. (关系代词as和指示代词same连用, 在从句中用作表语, 先行词是same.)
.---Why didn't you mention that in face of the police just now?
--- I thought it was such a minor detail as was hardly worth mentioning.
We will only discuss such problems as have something to do with our own interests.
Don't do such things as you are not sure about.
There is no such place as you dream of in all this world.
比较：I live in the same house that he used to live in.
I'm wearing the same shirt as you wore yesterday.
比较：Here is so big a stone as no one can lift. （定语从句）
Here is so big a stone that no one can lift it.（结果状语从句）
②如为非限制性的，多单独引导一个定语从句，这种定语从句可置于句首，句中或句尾，译为"正如，这一点"。（动词常为know, see, expect, point out, etc.）
As we all know, smoking is harmful to one's health . (as 作宾语)
=As is known to all, smoking is harmful to one's health . （as 作主语）
=It's known to all that smoking is harmful to one's health .
=Smoking is harmful to one's health , as we all know .（as 作宾语）
=Smoking, as we all know, is harmful to one' health.
He was a foreigner, as I knew from his accent. (宾语, 先行词是前面整个句子)
Ⅲ. 关系副词引导的定语从句:
●When 指时间，在定语从句中作时间状语。其先行词是表时间的名词（如：time, day, week, tear, month, etc.）He came last night when I was out.
We will put off the picnic until next week, when the weather would be better.
注意：先行词为"时间名词"，可用when引导定语从句，when在定语从句中作状语；还可以用which或that 引导，which或that在从句中作主语或宾语。
比较: I still remember the day when /on which my brother joined the army.（作状语）
Next month, when you will be in your hometown, is just around the corner.
I still remember the days which/that we spent together. （作宾语）
Next winter which/that you'll spend in Harbin, I'm sure, will be exciting.
I shall never forget the day when Shen Zhou Ⅴwas launched, which has a great effect on my life.
There are occasions when joking is not permissible.
●Where 指地点，在定语从句中作地点状语。其先行词是表示地点的名词，如：place, school, factory, room, etc.
This is the place where I was born.
I live in the room where /in which he used to live.
注意：先行词是"地点名词"，定语从句可用where引导，还可用which或that引导，which/that 在从句中作主语或宾语。
比较: ※This is the factory where /in which he worked last year. （作状语）
The treatment will continue until the patient reaches the point where he can walk correctly and safely.
I think you have got to the point where a change is needed, or you would fail.
Government reports, legal papers and most business letters are the main situations where English is used. He's got himself into a dangerous situation where he's likely to lose control of the plane.
The small mountain village where we spent our holiday last month lies in what /the place which is now part of Hubei.
This is the park which/that they visited last year. （作宾语）
Not having been there before, he simply had no idea about the place, which everyone says is worth visiting.
●Why 指原因，在定语从句中作原因状语。先行词为reason 时，可用for which指代；当关系词在从句中作主语或宾语时，则用which或that 引导。如：
The reason why / for which / (that) he didn't attend the meeting was that he was ill.
I don't believe the reason (that/which) he gave me. （作宾语）
Have you asked him the reason that may explain his success? （作主语）
Ex.) He was late .That's because he got up late.
.He got up late. That's why he was late.(表语从句)
(the reason) why/for which he was late. (定语从句)
当先行词为way时，定语从句常用that, in which,或how引导，that常可以省略。
way后的定语从句的引导词不用时较多。但如果关系词在句中作主语或宾语
时，则用which或that 引导。如:
This is the way (that) /in which I do such things.
比较: Please do the experiment in the way （that/which）I have shown you.
Ⅳ. 限制性定语从句与非限制性定语从句的区别：
1. 形式上，非限制性定语从句往往用逗号隔开。
2. 语法上，非限制性定语从句一般不用that.
3. 语义上，限制性定语从句与先行词关系紧密，起限定作用，如果去掉了这个定语从句，整个句子就不完整或者会改变意思；而非限制性定语从句与先行词关系不是很紧密，对先行词起补充说明或描述的作用。This is the book I like best. 这就是我最喜欢的那本书。
Beijing, which has been China's capital for more than 800 years , is rich in cultural and historic relics. 北京是中国八百年之久的古都，它有着丰富的文化和历史遗产。
4. 翻译时，限制性定语从句可译为一句（较短的一般译为"的"字结构）；而非限制性定语从句可译为两句。（见上句翻译）
比较: He has a sister, who is a musician.
He has a sister who is a musician.
引导非限制性定语从句的关系代词，指人时用who, whom, whose , 指物时用which , whose; 关系副词when，where, why, etc.
1. He studied hard at school when he was young, which leads to his success in his later life.
2. Tom's father, who arrived just now, is a famous scientist.
3. They set up a separate state of their own, where they would be free to keep Negroes as slaves.
4. He was proud, which his brother never was.
Ⅴ. 几个易混淆的关系代词的比较:
●that & which:
在定语从句中，which 和that 在指代事物时，一般可以互换使用，但并非在任何情况下都是这样，这里介绍宜用that, 而不宜用which 的情况.
①先行词为不定代词,all,much,something,everything,anything,nothing,none,the one等,
1.We should do all that is useful to the people .
2.There's nothing that can be said about it .
3.Do you mean the one that was bought yesterday?
②先行词被only, any, few, little, no, just, very, one of等词修饰时。
1.The only thing that we could do was to wait.
2.That's the very word that is wrongly used.
The last place (that) we visited was the chemical works.
You can take any (=whichever) seat that is free.
I hope the little that I can will be of some help to them.
比较*This is one of the best novels that were published last year.
*This is the only one of the best novels that was published last year.
③先行词是序数词时或被序数词修饰时。
1.When we talk about Wuxi, the first that comes into mind is Tai Lake.
2.This is the third film that has been shown in our school this term.
④先行词是最高级或被最高级修饰时。
1.This is the best that can be done now.
2.The most important thing that should be done right now is how to stop him from going on.
⑤先行词既有人又有物，用which和who都不适合，这时宜用that. 如：
1.The writer and his novel that you have just talked about is really well known .
2.The rider and his bike that had run over an old woman were held up by the police.
⑥被修饰词为数词时.
1.Yesterday I caught two fish and put them in a basin of water .Now you can see the two that are still alive .
⑦如果有两个从句，其中一个关系代词已用which ,另一个关系代词宜用that，以避免语言的单调或重复。Edison built up a factory which produced things that had never been seen before.
⑧疑问词是who或which，关系代词宜用that，以避免重复。
1. Which is the book that you like best?
2. Who is the man that is standing at the gate?
⑨主句是There be 结构，修饰其主句的定语从句宜用that 作关系代词. 如：
1. There is still a seat in the corner that is still free.
⑩被修饰成分为表语时，或者关系代词本身是定语从句的表语时,该关系代词宜用that .
1. That's a good book that will help you a lot.
2. My home village is no longer the place ( that ) it used to be .
定语从句中宜用which而不宜用that 的情况:
①当关系代词的前面有介词时.
1.A zoo is a park in which many kinds of animals are kept for exhibition.
2.Is this the room in which Mr. White lives?
②在非限制性定语从句中.
1.Crusoe's dog, which was are now very old, became ill and died .
2.More and more people are beginning to learn English, which is becoming very popular in our country. (which指代主句)
③在一个句子中有两个定语从句，其中一个定语从句的关系代词用了that, 另一个宜用which .
1. Let me show you the novel，that I borrowed from the library which was newly open to us.
2. At the station I bought some magazines that might help me to pass the time on the train and which I could pass on to others when I finished them.
④当关系代词后面带有插入语时.
1. Here's the English grammar which, as I have told you, will help improve your English.
⑤先行词本身是that, 宜用which .
What's that which she is looking at?
⑥先行词是those+复数名词.
A shop should keep a stock of those goods which sell best.
(B) who & that:
who 和that 指代人时，有些情况宜用who, 而不宜用that
①先行词为anyone, anybody, those, all, one, ones, they, he, people时. 如：
1.The person I want to learn from is the one who studies hard and works well.
2.Anyone who (=Whoever) failed to come to the meeting yesterday must give his reason .
3.Those who are not fit for their work should leave office at once
4.I don't like the ones (= those ) who talk big.
5.Persons who are quarrelsome are despised.
②在There be 结构中，修饰主语的定语从句宜用关系代词who 指代人. 如：
1.There is a gentleman who wants to see you .
2.There are several students in our class who are still not sure about the use of attributive clauses.
③当先行词有较长的后置定语时. 如：
1. I met a foreigner in the park yesterday afternoon who could speak Chinese very well.
④一个句子中带有两个定语从句，其中一个定语从句的关系代词是that ,另一个则宜用who, 以免重复. 如：
1. The student that was praised at yesterday's meeting is the monitor who is very modest and works very hard .
●as & which:
as & which 引导非限制性定语从句的区别：
①位置的不同：
which 引导的定语从句只置于所限制的句子后；as 位置较灵活，也就是说as可置于所限制的句子前面；插在句子中或放在句子后。如：
1. He was late again, which made his teacher very angry.
2. Jack, as you know, is an honest man. 或Jack is an honest man , as you know.
或As you know, Jack is an honest man.
②先行词的不同：
as引导非限制性定语从句时，其先行词多为一个句子；
which引导非限制性定语从句时，其先行词可以是一个词，一个短语或一个句子。
He was proud, which his brother never was. （先行词是一个词）
She was very patient towards the children, which her husband seldom was.
He was proud, which I dislike very much.（先行词是一个句子）
He is an honest man, as is known to all.
He was a foreigner, as I know from his accent.
③as 一般译为"正如""就像"，"这一点"
as we all know；as you know; as is known to all; as you see; as we can see; as has been expected; as we have imagined.
五、现在完成进行时present perfect continuous
用法：1.过去开始的反复或正在进行的尚未完成的动作
I’ve been going everywhere by bike for the last two months.
1.最近的过去开始的对现在又影响的动作。
He ‘s been doing his science project all night.(that’s why he’s so sleepy, now.)
Form:形式
Subject + have /has +been + -ing
You’ve been studying very hard.
六、Present perfect and present perfect continuous
1.我们用现在完成时谈论一个完成的动作，用现在完成进行时谈论未完成的动作。
2.现在完成时关注动作结果，尤其谈到数字或数量时，现在完成进行时关注动作本身，特别是解释动作可见的结果时。
He has run three times
He has been running for an hour.
七、现在完成时和时间状语
现在完成时使用下列时间状语：.
1.before,ever, never, seldom, sometimes often, usually, just, 这些副词一般放在has /have 之后，有时放在句末。
2. already 用在述句中（一般在have 之后）yet 用在疑问句和否定句中（常放在句末）
3.for, since, all my life
For 说明动作的时间长度，since说明动作的起点。
八、too 加形容词，not + 形容词+ enough
Too + 形容词表示某物超过我们所需。标识语too + 形容词相反的意思用not + 形容词+ enough结构。
九、形容词的顺序
Quality –size/age/shape-color-origin-made of-type/usage-noun
Beautiful long brown hair
Metal half-moon glasses
Old French car
10、Articles 冠词a/an
1，冠词a/an用在单数可数名词前，泛指某人某事，并把该人该事作为一群/一种的例子时。1，第一次谈论某事时用冠词a/an。
The，定冠词
1，当别人知道我们谈论的那个人那件事，并能容易地判定该人，该事时，
The car is dirty.
2,谈论世上独一无二的事物。
3，河流，海洋，山脉和群岛名称前，the Nile.
4,单数名词表达整个种类时，The whale is the biggest mammal.
5,形容词谈论享有同一特征的群体时，
No article
1，在表示泛指的复数名词和不可数名词前
2，在洲，城镇，湖泊，单座山脉，单个岛屿和名称前,,
3，机场，车站，街道的名称前
4，在复数形式的国名和国名中含有一个普通名词的名称前要加the.
智立方教育高一必修一第一章测试卷 1. 选择题： (1) 下列集合中，不是方程（x+1）(x-2)(x-3)=0的解集的集合是（ ） A.{-1,2,3} B.{3，-1,2} C.{x/(x+1)(x-2)(x-3)=0} D.{(-1,2,3)} (2). 下列结论中，不正确的是（ ） A.?=U C U B.U C U =? C.A A C C U U =)( D.}0{=A C U (3).中的元素的个数为则集合已知集合M N m m x N x M },,-8/{∈=∈=（ ） A.7 B.8 C.9 D.10 (4).集合{x 的真子集的个数是且1},41-4/≠<<-∈x x N ( ) A.32 B.31 C.16 D.15 (5)∈=x U {已知全集/+N -2 单元整合训练(一) [语言知识再落实] Ⅰ.单句语法填空 1．I'll make arrangements(arrange) for you to be met at the airport. 2．I was terrified(terrify) out of my mind，giving my first public performance. 3．It didn't take much persuasion(persuade) to get her to tell us the truth. 4．From time to time his sharp cough broke the rather frightening (frighten) stillness. 5．In the light of recent discoveries (discover)，it may be necessary to revise our previous theory. 6．He glanced at the envelope and recognised (recognition) his uncle's handwriting. 7．Of those wounded in the battle，only three survived(survival)，and now they all have passed away. 8．The journey along this route is very attractive (attract) for its picturesque scenery. 9．Yesterday Michael apologised(apologise) to his boss for being late. 10．It is reported that twenty-five thousand deaths per year are caused by air pollution(pollute)． Ⅱ.完成句子 1．Can you arrange for us to visit the Industrial Exhibition tomorrow morning? 你能不能安排我们明天上午参观工业展览会？ 2．I finally managed to persuade her to go out for a drink with me. 我最后终于成功地说服她跟我一起出去喝一杯。 3．People are banned from smoking in many public places in England. 在英国，许多公共场所禁止吸烟。 4．Some strange customs have survived from earlier times. 有些奇怪的风俗从古代沿袭下来。 5．Beautiful flowers in the streets of Beijing attracted many people's attention． 课后训练 基础巩固 ．已知集合M＝{x|－3＜x＜1}，N＝{x|x≤－3}，则M∪N等于()．A．?B．{x|x≥－3} C．{x|x≥1} D．{x|x＜1} 2．设集合U＝{1,2,3,4}，A＝{1,2}，B＝{2,4}，则(A∪B)＝()． A．{2} B．{3} C．{1,2,4} D．{1,4} 3．若A为全体正实数的集合，B＝{－2，－1,1,2}，则下列结论中正确的是()．A．A∩B＝{－2，－1} B．()∪B＝(－∞，0) C．A∪B＝(0，＋∞) D．()∩B＝{－2，－1} 4．集合A＝{0,2，a}，B＝{1，a2}，若A∪B＝{0,1,2,4,16}，则a的值为()． A．0 B．1 C．2 D．4 5．设A，B，I均为非空集合，且满足A?B?I，则下列各式中错误的是()． A．()∪B＝I B．()∪()＝I C．A∩()＝?D．()∩()＝ 6．设全集U＝{1,2,3,4,5}，集合M＝{1,3,5}，N＝{2,5}，则Venn图中阴影部分表示的集合是()． A．{5} B．{1,3} C．{2,4} D．{2,3,4} 能力提升 7．已知集合A＝{3，a2}，集合B＝{0，b,1－a}，且A∩B＝{1}，则A∪B＝()．A．{0,1,3} B．{1,2,4} C．{0,1,2,3} D．{0,1,2,3,4} 8．设U为全集，对集合X，Y，定义运算“⊕”，满足X⊕Y＝(X)∪Y，则对于任意集合X，Y，Z，则X⊕(Y⊕Z)＝()． A．(X∪Y)∪(Z) B．(X∩Y)∪(Z) C．[(X)∪(Y)]∩Z D．(X)∪(Y)∪Z 9．如图，I是全集，M，P，S是I的3个子集，则阴影部分所表示的集合是()． A．(M∩P)∩S B．(M∩P)∪S C．(M∩P)∩(I S) D．(M∩P)∪(I S) 10．设U＝{1,2,3,4,5,6,7,8,9}，()∩B＝{3,7}，()∩A＝{2,8}，()∩()＝{1,5,6}，则集合A＝__________，B＝__________. 11．集合A＝{x|x≤1}，B＝{x|x≥a}，且A∪B＝R，则实数a的取值范围是________．12．已知集合A＝{x|－2＜x＜3}，B＝{x|m＜x＜m＋9}． (1)若A∪B＝B，求实数m的取值范围； (北师大版)高一数学必修1全套教案 第一章集合 课题:§0 高中入学第一课（学法指导） 教学目标：了解高中阶段数学学习目标和基本能力要求，了解新课程标准的基本思路，了解高考意向，掌握高中数学学习基本方法，激发学生学习数学兴趣，强调布置有关数学学习要求和安排。 教学过程： 一、欢迎词： 1、祝贺同学们通过自己的努力，进入高一 级学校深造。希望同学们能够以新的行动， 圆满完成高中三年的学习任务，并祝愿同 学们取得优异成绩，实现宏伟目标。 2、同学们军训辛苦了，收获应是：吃苦耐 劳、严肃认真、严格要求 3、我将和同学们共同学习高中数学，暂定 一年，… 4、本节课和同学们谈谈几个问题：为什么 要学数学？如何学数学？高中数学知识结 构？新课程标准的基本思路？本期数学教 学、活动安排？作业要求？ 二、几个问题： 1.为什么要学数学：数学是各科之研究工具，渗透到各个领域；活脑，训练思维；计算机等高科技应用的需要；生活实践应用的需要。 2.如何学数学： 请几个同学发表自己的看法→共同完善归纳为四点：抓好自学和预习；带着问题认真听课；独立完成作业；及时复习。注重自学能力的培养，在学习中有的放矢，形成学习能力。 高中数学由于高考要求，学习时与初中有所不同，精通书本知识外，还要适当加大难度，即能够思考完成一些课后练习册，教材上每章复习参考题一定要题题会做。适当阅读一些课外资料，如订阅一份数学报刊，购买一本同步辅导资料. 3.高中数学知识结构： 书本：高一上期（必修①、②），高一下期（必 修③、④），高二上期（必修⑤、选修系列）， 高二下期（选修系列），高三年级：复习资 料。 知识：密切联系，必修（五个模块）＋选修系列（4个系列，分别有2、3、6、10个模块）能力：运算能力、逻辑思维能力、空间想像能力、分析和解决实际问题的能力、应用能力。 4.新课程标准的基本理念： ①构建共同基础，提供发展平台；②提供多样课程，适应个性选择；③倡导积极主动、勇于探索的学习方式；④注重提高学生的数学思维能力；⑤发展学生的数学应用意识；⑥与时俱进地认识“双基”；⑦强调本质，注意适度形式化；⑧体现数学的文化价值；⑨注重信息技术与数学课程的整合；⑩建立合理、科学的评价体系。 5.本期数学教学、活动安排： 本期学习内容：高一必修①、②，共72课时， 北师大版《函数概念》说课教案 教材分析 一、本课时在教材中的地位及作用 教材采用北师大版（数学）必修1，函数作为初等数学的核心内容，贯穿于整个初等数学体系之中。本章节9个课时，函数这一章在高中数学中，起着承上启下的作用，它是对初中函数概念的承接与深化。在初中，只停留在具体的几个简单类型的函数上，把函数看成变量之间的依赖关系，而高中阶段不仅把函数看成变量之间的依赖关系，更是从“变量说”到“对应说”，这是对函数本质特征的进一步认识，也是学生认识上的一次飞跃。这一章内容渗透了函数的思想，集合的思想以及数学建模的思想等内容，这些内容的学习，无疑对学生今后的学习起着深刻的影响。 本节课《函数概念》是函数这一章的起始课。概念是数学的基础，只有对概念做到深刻理解，才能正确灵活地加以应用。本课从集合间的对应来描绘函数概念，起到了上承集合，下引函数的作用。也为进一步学习函数这一章的其它内容提供了方法和依据 二、教学目标 理解函数的概念，会用函数的定义判断函数，会求一些最基本的函数的定义域、值域。 通过对实际问题分析、抽象与概括，培养学生抽象、概括、归纳知识以及逻辑思维、建模等方面的能力。 通过对函数概念形成的探究过程，培养学生发现问题，探索问题，不断超越的创新品质。 三、重难点分析确定 根据上述对教材的分析及新课程标准的要求，确定函数的概念既是本节课的重点，也应该是本章的难点。 四、教学基本思路及过程 本节课《函数的概念》是函数这一章的起始课。概念是数学的基础，只有对概念做到深刻理解，才能正确灵活地加以应用。本课（借助小黑板）从集合间的对应来描绘函数概念，起到了上承集合，下引函数的作用，也为进一步学习函数 模块3 U7 L1 1 The Spirit of Explorers Viking Voyages to America The Vikings were the first Europeans to reach America. They achieved this long before Columbus ever set sail. The Vikings were a group of people whose ancestors came from Scandinavia. They controlled the seas and coasts of Northern Europe between the 8th and 10th centuries AD. By around 900 AD, there were many places in Northern Europe where the Vikings chose to live. In 982 AD, when a man called Eric the Red decided to set sail further west, there were as many as 10,000 Vikings living in Iceland. According to the old stories of Iceland and Norway, Eric the Red was forced to leave Iceland because he had committed a murder, for which he got into trouble. Eric reached Greenland and discovered that people could live in the place where he landed. He returned to Iceland and told people there about Greenland. He persuaded some people to go back with him to Greenland. Eric set sail once again, this time with 25 ships, of which only 14 made it to Greenland. Not long after Eric the Red had landed in Greenland, a man called Biarni set sail from Iceland in search of Eric's party. Biarni was hoping to join his father who was with Eric, but he was blown off course and found himself in an unknown land, from where he eventually reached Greenland. In the year 1002, when Eric the Red's son Leif was planning a trip further west, Biarni was the man with whom Leif discussed his plans. Leif followed Biarni's directions and sailed to what is believed to be the coast of present-day Canada. He then sailed further south to an island which is now known as Newfoundland. We know about Eric the Red and Leif's deeds through stories which were written down centuries later in Norway and Iceland. They are the first records we have of Europeans sailing to the Americas. U7 L3 3 The Sea World UNDER WATER WORLD The Best place to See Sea Creatures Polar World We have polar bears and a real iceberg too! You can only see a small part of it above the water. It's three times as big underwater. Watch the acrobatic seals at feeding time. Meet our less energetic but more friendly penguins. You'll love them! Ocean Floor See some of the most beautiful coral and the most unusual fish in the world. Watch some fish “flying” through the water. They are less colourful than some other fish but they move beautifully. Sea Theatre See our intelligent dolphins. There are fantastic shows every two hours. Discovery Pool Especially for younger children. They can touch crabs and other smaller creatures. They can be educated about daily life on the beach in this exciting area. Virtual Reality Voyage Our most up-to-date attraction. Come with us on a “virtual reality” trip to the ocean floor and see some of the strangest fish in the world. 2．选择题 （1）集合{y ∈N/y=-x 2+6,x ∈N}的真子集的个数是（ ） A 9 B 8 C7 D6 (2)下列表示[1]{0}=?,[2]{2}?{2,4,6},[3]{2}∈{x/x 2-3x+2=0},[4]0∈{0}中，错误的是（ ） A[1] [2] B[1][3] C[2][4] D[2][3] 3.用适当的符号填空（=，?，?） （1）已知集合M={1,3,5},集合P={5,1,3},则M_________P (2) 设集合A={x / (x-3)(x+2)=0},B={x / 033 -=+x x },则A_______B 4.图中反映的是“文学作品”“散文”“小说”“叙事散文”这四个文学概念之间的关系，请做适当的选择填入下面的空格： A 为_________ B 为_________ C 为_________ D 为___________ 5.判断下列各式是否正确，并说明理由： （1）}2/{3≤?x x （2）}2/{3≤∈x x （3）{}2/{}3{≤?x x （4）}2/{≤∈?x x (5)}2/{≤??x x (6)}2/{≤??x x (7){a,b,c,d}},,,,{g d b f e ? (8){a,b,c,d}},,,,{g d b f e ? 6.已知集合A,B,C ，且A ,,C A B ??若B={0,1,2,3,4},C={0,2,4,8},集合A 中最多含有几个元素？ 1.用符号“∈”或“? ”填 0_____N 0_____N + -1_____N -1____Z 1_____Q 1/2_____Q 3.14____Q 3.14____Z π__Q π___Z π___R 23___N 23____Z 23___Q 23___R N __0 Z _____1 4.3 Q ______π 若{}x x x A 22==，则A _____2- 若{}0322=--=x x x B ，则B _____3 2.用适当的方法表示下列集合 （1）小于20的素数组成的集合 （2）方程x 2 -4=0的 解的集合 （3）由大于3小于9的实数组成的集合 （4）所有奇数组成的集合 3.下列四个集合中，空集是（ ）A{0} B {x/x>8,且x<5} C{x ∈N/x 2 -1=0} D {x/x>4} 4.选择适当的方法表示下列集合，并指出哪些是无限集，哪些是有限集，哪些是空集？ (1)直角坐标系中纵坐标与横坐标相等的点的集合 （2）方程x 2+x+1=0的实数解集 （3）满足不等式1<1+2x<19的素数组成的集合 5. 填空题 （1）用列举法表示集合{x ∈R/(x-1)2(x+1)=0}为 （2）用列举法表示集合{x ∈N/X -66 ∈N}为 （3）用描述法表示集合{2,4,6,8，}为 (4) 用描述法表示集合（1,1/2,1/3,1/4）为 6.用列举法表示下列集合 （1）B={y ∈N/y=-x 2+6,x ∈N} (2) C={(x,y)/y=-x 2+6,x ∈N,y ∈N} 7．用描述法表示下列集合 （1）直角坐标平面内第四象限内的点集（2）抛物线y=x 2-2x+2上的点组成的集合（3）大于0的偶数。 （4）用描述法可将集合{} ,11,9,7,5,3,1---表示成________________________。 8.一次函数12+=x y 与421 +-=x y 的交点组成的集合。????????? ??517,56? ?????517,56区别是什么？ 9.集合(){}N y x y x y x A ∈=+=,,72,，用列举法表示集合A 。 10.1）{}2__1,2,3 2）{}__,a a b 3）{}{}_____,,a a b c 4）{}__0? 5）{}{}1,4,7____7,1,4 6）{}0,1____N 7）{}2____1x R x ?∈=- 11.已知集合{}2,0,1A =-，那么A 的非空真子集有_________个。 12.求下列四个集合间的关系，并用维恩图表示。 {}{}{}{}A x x B x x C x x D x x ====是平行四边形，是菱形，是矩形，是正方形 13.若集合X 满足{}{}0121012X ??--，，，，，，则X 的个数有几个？ 14.已知集合A={x ∈R/ax 2+2x+1=0,a ∈R}中只有一个元素（A 也可叫做单元素集合），求a 的值，并求出这个元素。 15．当a,b 满足什么条件时，集合A={x/ax+b=0}是有限集，无限集，空集？ 北师大版高中数学必修 知识点总结 内部编号：（YUUT-TBBY-MMUT-URRUY-UOOY-DBUYI-0128） 北师大版高中数学必修3知识与题型归纳 第一章《统计》知识与题型归纳复习 （一）、抽样方法 1、简单随机抽样 （1）、相关概念：总体、个体、样本、样本容量。（2）、基本思想：用样本估计总体。 （3）、简单随机抽查概念。一般的，设一个总体含有N 个个体，从中逐个不放回地抽取n 个个体作为样本)(N n ，如果每次抽取时总体内的各个个体被抽到的机会都相等，就把这种抽样方法叫做简单随机抽样。其特点：①总体个数有限；②逐个抽取；③不放回抽样；④等可能抽样。 （4）、抽样方法：①抽签法；②随机数表。 2、系统抽样 （1）、定义：当总体元素个数很大时，样本容量不宜太小，这时可将总体分为均衡的若干部分，然后按照预先制定的规则，从每一部分抽取一个个体，得到所需要的样本（等距抽样）。 （2）、步骤：①编号；②分段；③不确定起始个体编号；④按规则抽取。 3、分层抽样 （1）、定义：当总体由差异明显的几部分组成时，为了使抽取的样本更好的反应总体情况，我们经常将总体中各个个体按某种特征分成若干个互不重叠的几部分，每一部分叫做层，在各层中按层在总体中所占比例进行简单随机抽样。 适用特征①总体由差异明显的几部分组成；②分成的各层互不重叠；③各层抽取的比例等于样本客样在总体中的比例，即 N n 。 （二）、用样本的频率分布估计总体的分布（统计图表） 1、列频率分布表，画频率分布直方图： （1）计算极差（2）决定组数和组距（3）决定分点（4）列频率分布表（5）画频率分布直方图 2、茎叶图； 3、扇形图； 4、条形图； 5、折线图； 6、散点图。 （三）、用样本的数字特征估计总体的数字特征 1、有关概念 （1）、众数：频率分布最大值所对应的样本数据（或出现最多的那个数据）。 （2）、中位数：累积频率为0.5时，所对应的样本数据。 （3）、平均数：)(121n x x x n x +++= （4）、三个概念的区别：①都是描述一组数据集中趋势的量，平均数较重要。②平均数的大小与每个数相关。③众数考查各个数据出现的频率，大小只与这组数据中的部分数据有关，当一组数据中有不少数据多次重复出现时，众数更能反映问题，中位数仅与排列有关。 2、样本方差与样本标准差 1样本方差：( )()( )[]2 22212 1 x x x x x x n S n -++-+-= 样本方差大说明样本差异和波 动性大。 （2）、样本标准差：方差的算术平方根( )()( )[]2 22211 x x x x x x n S n -++-+-= （3）、要有单位，方差的单位是原数据的单位的平方，标准差的单位与原数据单位同。 （四）、变量的相关性： 综合测试题(二) 本试卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分．满分150分．考试时间120分钟． 第Ⅰ卷(选择题 共60分) 一、选择题(本大题共12个小题，每小题5分，共60分，在每小题给出的四个选项中，只有一项是符合题目要求的) 1．(2016·四川理，1)设集合A ＝{x |－2≤x ≤2}，Z 为整数集，则集合A ∩Z 中元素的个数是（ ) A ．3 B ．4 C ．5 D ．6 2．已知集合A ＝{x |0 A．log34 北师大版高一英语必修3 Unit 7 The sea 单元测试题（一） 一、单选: 每题1分，共15分。 1. The news on ___ air reminded him of ____ old friend who is now in America. A. 不填; an B. 不填; the C. the; an D. the; a 2. Have you seen the film ____ script was written by Catherine? A. which B. its C. of which D. whose 3. What should you say when ___ to a stranger? A. to introduce B. introducing C. introduced D. being introduced 4. The Spring Festival ____, and will you come back home for it with your family? A. is coming B. comes C. has come D. came 5.-How about going out with me for the coming weekend? -_____. My parents may come to see me. A. You’re right B. It depends C. Never mind D. It’s all right 6. The young man ____ his success to many people, his parents in particular. A. gives B. treats C. owes D. devotes 7.-Why do you think he can succeed? -He believes in himself, ____ is the most important, I think. A. that B. what C. which D. who 8. He has made quite a few new friends in the new school, while I have made ____. A. nothing B. any C. some D. none 9. “How did all this ____?” the angry boss asked the scared worker. A. come across B. come about C. come on D. come over 10. He hurried to the station, ____ to catch the last train. A. to hope B. hope C. hoping D. hoped. 11.-It’s already half past 7! -Yes. Tom ____ here at any moment. A. should be B. may be C. should have been D. must have been 12. With so many people ____ the Internet, it is difficult to see online movies at the same time. A. surf B. to surf C. surfing D. surfed 13. You’d better not interrupt me when I am talking, ____ you are. A. who B. whom C. whoever D. whichever 14. The city is in preparation for an important meeting. As a result, the number of cars ____. A. is limited B. limits C. is limiting D. was limited 15.-I want to know whether we shall go rafting today or tomorrow? -Does that make any ____? A. change B. importance C. difference D. value 二、完形填空：每题1.5分，共30分 Nowadays, any traveler might be treated as a terrorist (恐怖分子) by the immigration (入境) officers in the USA. We returned from Iraq and landed safely. My heart 16 when I was asked to the back room by the immigration officer. My 17, with his very American last name, had no trouble at all. In fact, I am 18 American born and raised, 第一单元集合 一、选择题：本大题共12小题,每小题5分,共60分,在每小题给出的四个选项中,只有一项是符合题目要求的. 1.已知集合*{|010,},{1,2,3,4}U x x x N A =≤<∈=,则U A e为 A.{5,6,7,8,9,10} B.{5,6,7,8,9} C.{0,5,6,7,8,9} D.{0,1,2,3,4,10} 2.下列给出的三组对象:①与3相差不大于2的实数;②中国的大城市; ③在平面直角坐标系中非常接近原点的点.其组成的整体能构成集合的个数是 A.0B.1C.2D.3 3.已知集合S 的三个元素,,a b c 是ABC ?的三边长,那么ABC ?一定不是 A.锐角三角形 B.直角三角形 C.钝角三角形 D.等腰三角形 4.下列集合是空集的是 A.2{|0}y y ≤ B.2{|30}x x x ++= C.{|20152015}x x += D.2{(,)|||0,,}x y x y x y R +=∈ 5.已知全集{|09},{3,4,5},{1,3,7}U x N x A B =∈<<==,那么{2,6,8}是 A.A B I B.A B U C.()()U U A B U 痧 D.()()U U A B I 痧 6.设集合12{|,},{|,}24 k k M x x k Z N x x k Z ++==∈==∈,则集合,M N 的关系是 A.N M ≠? B.M N ≠? C.M N = D.4{|,}8 k M N x x k Z +==∈I 7.若集合{1,2},{0,1}A B =--=,则集合{|,,}C z z y x x A y B ==-∈∈的所有真子集的个数为 A.1B.3C.7D.15 8.已知集合1 {,3},{|1}2 M N x mx =-==,若N M ?,则适合条件的实数m 构成的集合P 是 A.1{2,}3- B.11{,}23- C.1 {0,2,}3 - D.{0} 9.已知集合{1,{1,}A B a ==,若A B B =I ,则实数a 等于 A.0 B.0或2 C.1 D.1或2 10.已知A 为非空集合,若任意x A ∈,都有1A x ∈,就称A 是“和谐”集合,则集合 11(1,0,,,1,2,3,4}32 M =-的所有子集中,是“和谐”集合的个数为 A.7B.8C.15D.16 11.设U 为全集,,若存在集合C 使得集合,A B 满足,U A C B C ??e,则下列集合中必为空集的是 高中数学必修1知识点 第一章集合与函数概念 【1.1.1】集合的含义与表示 （1）集合的概念 把某些特定的对象集在一起就叫做集合. （2）常用数集及其记法 N 表示自然数集，N *或N +表示正整数集，Z 表示整数集， Q 表示有理数集，R 表示实数集. （3）集合与元素间的关系 对象a 与集合M 的关系是a M ∈，或者a M ?，两者必居其一. （4）集合的表示法 ①自然语言法：用文字叙述的形式来描述集合. ②列举法：把集合中的元素一一列举出来，写在大括号内表示集合. ③描述法：{x |x 具有的性质}，其中x 为集合的代表元素. ④图示法：用数轴或韦恩图来表示集合. （5）集合的分类 ①含有有限个元素的集合叫做有限集.②含有无限个元素的集合叫做无限集.③不含有任何元素的集合叫做空集(?). 【1.1.2】集合间的基本关系 （6）子集、真子集、集合相等 （7）已知集合A 有(1)n n ≥个元素，则它有2n 个子集，它有21n -个真子集，它有 21n -个非空子集，它有22n -非空真子集. 【1.1.3】集合的基本运算 （8）交集、并集、补集 B {|x x x ∈A A = ?=? B A ? A B B ? B {|x x x ∈A A = A ?= B A ? B B ? ⑷ ⑼ 集合的运算律： 交换律： 结合律: 分配律: 0-1律： 等幂律： 求补律：A ∩ A ∪ =U 反演律： (A ∩B)=( A)∪( B) (A ∪B)=( A)∩( B) 第二章函数 §1函数的概念及其表示一、映射1．映射：设A 、B 是两个集合，如果按照某种对应关系f ，对于集合A 中的 元 素，在集合B 中都有 元素和它对应，这样的对应叫做 到 的映射，记作 .2．象与原象：如果f :A →B 是一个A 到B 的映射，那么和A 中的元素a 对应的 叫做象， 叫做原象。二、函数1．定义：设A 、B 是 ，f :A →B 是从A 到B 的一个映射，则映射f :A →B 叫做A 到B 的 ，记作 .2．函数的三要素为 、 、 ，两个函数当且仅当 分别相同 .;A B B A A B B A ==)()();()(C B A C B A C B A C B A ==)()()();()()(C A B A C B A C A B A C B A ==,,,A A A U A A U A U Φ =ΦΦ ===.,A A A A A A == 必修1全册综合测试题(一) 本试卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分． 满分150分．考试时间120分钟． 第Ⅰ一、选择题(本大题共10个小题，每小题5分，共50分，在每小题给出的四个选项中，只有一项是符合题目要求的) 1．(2011·新课标文)已知集合M＝{0,1,2,3,4}，N＝{1,3,5}，P＝M∩N，则P的子集共有( ) A．2个B．4个 C．6个D．8个 2．(2012·银川高一检测)设函数f(x)＝log a x(a>0，且a≠1)在(0，＋∞)上单调递增，则f(a＋1)与f(2)的大小关系是( ) A．f(a＋1)＝f(2) B．f(a＋1)>f(2) C．f(a＋1) －x )，则x 的取值范围是( ) A ．x >1 B ．x <1 C ．0 【推荐】2020年北师大版英语必修三（全套） 课后练习汇总 课后演练提能 [夯实·基础知识] Ⅰ. 单词拼写 1. On its v________ to New York, the ship was turned over by a storm on the sea. 答案：voyage 2. You should a________ to him for what you said, though you didn't mean to. 答案：apologise 3. An e________usually travels to unknown places to find out more about them. 答案：explorer 4. D________are better than words when people are in need of help. 答案：Deeds 5. As is known to us all, monkeys and humans share a common a________. 答案：ancestor 6. I still remember the day when I attended my first ________ (演讲) in college. 答案：lecture 7. After a long journey, the travelers ________ (最终) reached the destination. 答案：eventually 8. Those who apply for the position need to have good teamwork ________(精神)． 答案：spirit 9. He ________ (说服) his son to give up smoking. 答案：persuaded 10. Could you help me to find out the reason why the ________ (刹车) doesn't work? 答案：brake Ⅱ. 选词填空2019-2020学年北师大版高中英语必修三 单元整合训练(一)【含答案】
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