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新目标英语九年级(全册)知识点归纳

新目标英语九年级(全册)知识点归纳
新目标英语九年级(全册)知识点归纳

新目标英语九年级全册知识点归纳

Unit 1

一、知识点

1. by + doing通过……方式如:by studying with a group

by 还可以表示:“在…旁”、“靠近”、“在…期间”、“用”、“经过”、“乘车”等

如:I live by the river.

I have to go back by ten o’clock.

The thief entered the room by the window.

The student went to park by bus.

2.too…to 太…而不能常用的句型too+adj./adv. + to do sth.

如:I’m too tired to say anything. 我太累了,什么都不想说。3.be / get excited about sth.=== be / get excited about doing sth.

= be excited to do sth. 对…感兴奋

如:I am / get excited about going to Beijing.=

I am excited to go to Beijing. 我对去感到兴奋。

4. ①end up doing sth 终止做某事,结束做某事

如:he party ended up singing. 晚会以唱歌而结束。

②end up with sth. 以…结束

如:The party ended up with her singing. 晚会以她的歌唱而告终。5.one of +(the+ 形容词比较级)+名词复数形式…其中之一如:She is one of the most popular teachers. 她是最受欢迎的教师之一。

6. It’s +形容词+(for sb. ) to do sth. (对于某人来说)做某事…

如:It’s difficult (for me ) to study English. 对于我来说学习英语太难了。

句中的it 是形式主语,真正的主语是to study English

7.unless 假如不,除非引导条件状语从句

如:You will fail unless you work hard..假如你不努力你会失败。

I won’t write unless he writes first. 除非他先写要不我不写8.see sb. / sth. doing看见某人正在做某事强调正在发生see sb. / sth. do看见某人在做某事如:

如:She saw him drawing a picture in the classroom.她看见他正在教室里画画。

9. aloud, loud与loudly的用法 : 三个词都与"大声"或"响亮"有关。

①aloud是副词,重点在出声能让人听见,但声音不一定很大,

常用在读书或说话上。通常放在动词之后。aloud没有比较级形式。

如: He read the story aloud to his son.他朗读那篇故事给他儿子听。

②loud可作形容词或副词。用作副词时,常与speak, talk, laugh等动词连

用,多用于比较级,须放在动词之后。如:

She told us to speak a little louder. 她让我们说大声一点。

③loudly是副词,与loud同义,有时两者可替换使用,但往往

含有令人讨厌或打扰别人的意思,可位于动词之前或之后。如:

He does not talk loudly or laugh loudly in public. 他不当众大声谈笑。

10. get + 宾语+宾补(形容词过去分词动词不定式)使某种情况发生

例:Get the shoes clean. 把鞋擦干净

Get Mr. Green to come. 让格林先生进来

I want to get my bike repaired. 我想去修自行车

You can’t get him waiting. 你不能让他老等着.

11. 动词不定式做定语

①与所修饰的名词构成主谓关系

The next train to arrive was from New York. He is always the first to come.

②与所修饰的名词构成动宾关系

I have nothing to say. I need a pen to write with.

I need some paper to write on. I don’t have a room to live in.

12. join加入某团体并成为其中一员 attend 出席参加会议或讲座

join in与take part in指参加到某项活动中去。

13 .instead: adv. 代替,更换。

例:We have no coffee, would you like tea instead?

我们没有咖啡了,改喝茶好吗?

It will take days by car, so let’s fly instead.

开车去要好几天呢,咱们还是坐飞机吧。

Tom was ill, so I went instead.汤姆病了,所以换了我去。

instead of doing sth. 作为某人或某事物的替换

例:Let’s play cards instead of watching TV.

We sometimes eat rice instead of potatoes.

Give me the red one instead of the green one.

14. 提建议的句子:

①What/ how about +doing sth.? 如:What/ How about going shopping?

②Why don’t you + do sth.? 如:Why don’t you go shopping?

③Why not + do sth. ? 如:Why not go shopping?

④Let’s + do sth. 如: Let’s go shopping

⑤Shall we/ I + do sth.? 如:Shall we/ I go shopping?

15. enjoy doing sth . 喜欢做…乐意做… 如:

She enjoys playing football. 她喜欢踢足球。

enjoy oneself 过得愉快如:He enjoyed himself. 他过得愉快。

16. too many 许多修饰可数名词如:too many girls

too much 许多修饰不可数名词如:too much milk

much too 太修饰形容词如:much too beautiful

二.短语:

1.by making flashcards 通过做单词抽认卡

2. ask…for help 向某人求助

3.read aloud 朗读

4.that way (=in that way) 通过那种方式

5.improve my speaking skills 提高我的会话技巧

6.for example (=for instance)例如

7.have fun 玩得高兴 8.have conversations with friends 与朋友对话

9.get excited 高兴,激动 10.end up speaking in Chinese 以说汉语结束对话

11.do a survey about…做有关…的调查 12.keep an English notebook 记英语笔记

13.spoken English (= oral English) 英语口语 14.make mistakes 犯错误

15.get the pronunciation right 使发音准确 16.practise speaking English 练习说英语

17.first of all 首先 18.begin with 以…开始

https://www.doczj.com/doc/869869182.html,ter on随后 20.in class在课堂上

https://www.doczj.com/doc/869869182.html,ught at 嘲笑 22.take notes 记笔记

23.enjoy doing 喜欢干… 24.write down 写下,记下25.look up (v + adv) 查找,查询 26.native speakers 说本族话的人

27.make up 编造,虚构,化妆,打扮 28.around the world 全世界29.deal with 对待,处理,解决 30.worry about (be worried about) 担心,担忧

31.be angry with 生某人的气 32.stay angry 生气

33.go by 消逝 34. regard…as…把…当做…

https://www.doczj.com/doc/869869182.html,plain about/of 抱怨 36. change…into…把…变成…(= turn into)

37.with the help of 在…的帮助下 38. compare…to (with)…把…和…作比较

39.think of (think about) 想起,想到 40.physical problems身体上的问题

41.break off 中断,突然终止

42. not…at all 根本不,全然不

Unit 2

1.used to do sth. 过去常常做某事

否定形式:didn’t use to do sth. / used not to do sth.

如:He used to play football after school. 放学后他过去常常踢足球。

Did he use to play football? Yes, I did. No, I didn’t.

He didn’t use to smoke. 他过去不吸烟。

2. 反意疑问句(中考不考,可作了解)

①肯定述句+否定提问如:Lily is a student, isn’t she?

Lily will go to China, won’t she?

②否定述句+肯定提问如:She doesn’t come from China, does she?

You haven’t finished homework, have you?

③提问部分用代词而不用名词 Lily is a student, isn’t she?

④述句中含有否定意义的词

如:little, few, never, nothing, hardly等。其反意疑问句用肯定式。

如:He knows little English, does he? 他一点也不懂英语,不是吗?

They hardly understood it, did they?他们几乎不明白,不是吗?

3.interest ed adj. 感兴趣的,指人对某事物感兴趣,往往主语是人

interest ing adj.有趣的,指某事物/某人具有趣味,主语往往是物

①be interested in sth. 对…感兴趣

②be interested in doing sth. 对做…感兴趣

如:He is interested in math, but he isn’t interested in speaking English.

他对数学感兴趣,但是他对说英语不感兴趣。

4.害怕…be terrified of sth.如:I am terrified of the dog.

be terrified of doing sth.如:I am terrified of speaking。

5.spend 动词,表示“花费金钱、时间”

①spend…on sth. 在某事上花费(金钱、时间)

②spend…doing sth.花费(金钱、时间)去做某事

如:He spends too much time on clothes. 他花费太多的时间在衣着He spend 3 months building the bridge.他花费了三个月去建这座桥。

pay for 花费如:I pay 10 yuan for the book. 我花了10元买这本书。

take 动词有“花费”的意思常用的结构有:

take sb. … to do sth.如:It takes me a day to read the book.

take … to do sth.

6.how to swim 怎样游泳

不定式与疑问词连用:动词不定式可以和what, which, how, where, when 等引导的疑问句连用,构成不定工短语。

如:The question is when to start. 问题是什么时候开始。

I don’t know where to go. 我不知道去哪。

7. make sb./ sth. + 形容词make you happy

make sb./ sth. + 动词原形 make him laugh

8.as + 形容词./副词+as sb. could/can 尽某人的…能力

如: Zhou run as fast as her could/can. 她尽她最快的能力去跑。

9.take pride in sth. 以…而自豪

如:His father always take pride in him. 他的爸爸总是以他而自豪

10. pay attention to sth. 对…注意,留心

如:You must pay attention to your friend. 你应该多注意你的朋友。

11. be able to do sth. 能做某事

如:She is able to do it. 她能够做到。

12. give up doing sth. 放弃做某事

如:My father has given up smoking. 我爸爸已经放弃吸烟了。

13.不再①no more == no longer如:I play tennis no more/ longer.我不再打网球。

②not …any more == not …any longer

如:I don’t play tennis any more/longer. 我不再打网球。

Unit 3

1.allow句型①allow sb to do sth 允许某人做某事

如: We do not allow people to smoke in the hall.

②allow doing允许做某事

③be allowed to do 被允许做某事

④should be allowed to do 应该被允许做某事

2.get their ears pierced 穿耳洞

让/使(别人)做某事 get sth. done(过去分词)

have sth. done

如:I get my car made. == I have my car made. 我让别人修好我的车3.enough 足够

形容词+enough如:beautiful enough 足够漂亮

enough+名词如:enough food 足够食物

enough to 足够…去做…

如:I have enough money to go to Beijing. 我有足够的钱去。

She is old enough to go to school.她够大去读书了。

4. stop doing sth. 停止做某事Please stop speaking.请停止说话。

stop to do sth. 停止下来去做某事Please stop to speak.请停下来说话。

5. 看起来好像… sb. seem to do sth. = it seems that +从句

如:He seems to feel very sad.

It seems that he feels very sad. 他看起来好像很伤心。

6.系动词不能独立作谓语,要和表语一起构成谓语。常用的连系动词有:look, feel, be, become, get, turn, smell, taste, stay(保持), kept等。

连系动词除be 和become 等少数词可接名词作表语外,一般都是接形容词。

如:They are very happy. He became a doctor two years ago. She felt very tired.

7. 倒装句:

由so+助动词(be/do/will/have)/情态动词+主语意为:…也是一样 She is a student. So am I. 她是一个学生,我也是。

She went to school just now. So did I . 她刚才去学校了,我也是 She has finished the work. So have I . 她已经完成了工作,我也完成了。

She will go to school. So will he. 她将去学校,他也是。

8.曾经做某事:

Do you ever get to school late? Yes, I do. No, I don’t.

Have you ever got to school late? Yes, I have. No, I haven’t.

9.be strict with sb. 对某人严厉

如:Mother is strict with her son. 妈妈对她的儿子很严厉。10.keep sb/ sth. +形容词使某人/某物保持…

如:We should keep our city clean.我们应该保持我们的城市干净。11. both…and…+动词复数形式

如: Both Jim and Li Ming play bastketball.

12. learn (sth.) from sb. 向谁学习(什么)

如:Jim learnt English from his English teacher. 吉姆向他的英语老师学习英语

13. have an opportunity to do sth. 有机会做某事

have a chance of doing sth. 有机会做某事

如:I have an opportunity to go to Beijing.

I have a chance of going to Beijing.

14.花费 take ,cost, spend , pay

sth. take (sb.) time to do sth. It took (me) 10days to read the book.

sth.cost (sb.) …… The book cost (me) 100yuan.

sb.spend … on sth. She spent 10days on this book.

sb.spend …doing sth. She spent 10days reading this book.

sb.pay … for sth. She paid 10yuan for this book.

15. have +时间段+off 放假,休息如:have 2 days off

16. reply to 答复某人如:She replayed to MrGreen.

17. agree with sth. 同意某事如:I agree with that idea.

agree to sb. 同意某人的意见如:I agree to LiLei.

18. get in the way of 碍事,妨碍

如: Her social life got in the way of her studies.

她的社会生活妨碍了她的学习。

19.think about 与think of 的区别

①当两者译为:认为、想起、记着时,两者可互用

I often think about/ of that day. 我经常想起那天。

②think about 还有“考虑”之意,think of 想到、想出时两者不

能互用

At last, he thought of a good idea. 最后他想出了一个好主意。

We are thinking about going Qinzhou. 我们正在考虑去。

20. 对… 热衷,对…兴趣

be serious about doing如:She is serious about dancing. 她对跳舞热衷。

be serious about sth.如:She is serious about him. 她对他感兴趣。

21.practice doing练习做某事 She often practice speaking English.

22. care about sb. 关心某人如:Mother often care about her son.

23. also 也用于句中I am also a student. 我也是一个学生

either也用于否定句且用于句末I am not a student either.我也不

是一个学生。too 也用于肯定句且用于句末I am a student too.

我也是一个学生。

Unit 4

1.pretend to do sth.假装做某事 I pretended to sleep just now.

pretend +从句假装… I pretended that I fell asleep.

2. be late for 迟到如:I am late for work/ school/ class/ party.

3.what if + 从句如果…怎么办,要是… 又怎么样

如:What if she doesn’t come? 要是她不来怎么办?

What if LiLei knows? 如果雷知道了怎么办?

4. add sth.to sth.添加…到… 如:I added some sugar to water. 我把糖添加到水里。

5.ask sb. to do 叫…做某事

ask sb. not to do sth.叫…不要做某事

tell sb. to do 告诉…做某事

tell sb. not to do sth. 告诉…不要做某事

如:Teacher asked me to clean the classroom.

Teacher asked me not to clean the classroom.

6. start doing==start to do.开始做某事

如:He started speaking/ to speak. 他开始说话。

7. borrow sth. from sb. 从某人那里借来某物

如:I borrowed a book from Lily. 我从莉莉那里借来一本书。

8. introduce sb. to sb. 把某人介绍给某人

如:I introduced Lily to Anna. 我把莉莉介绍给安娜。

9. invite sb. to do 邀请某人做某事

如:Lily invited me to go to her home for supper. 莉莉邀请我去她家吃晚饭。

10.get along with sb. 与…相处

如:Do you get along well with your friends? 你和你的朋友相处得好吗?

11. would rather do sth. than do sth.表示愿做某事而不愿做某事

如:I would rather walk than run.

12.let sb. down 让某人失望如:Don’t let your mother down.不要让你的妈妈失望。

13. come up with sth.提出如He:came up with a good idea.他提出了一个好主意。

catch up with sb.追上赶上如:Lily caught up with Anna. 莉莉赶上了安娜。

14. have experience doing在做某事有经验

如:I have experience teaching Chinese. 我在教英语方面有经验。

15.宾语从句宾语从句在复合句中作主句的宾语。

由连接词+ 主语+ 谓语构成

常由下面的一些词引导:

㈠由that 引导表示述意义 that 可省略

He says (that) he is at home. 他说他在家里。

㈡由if , whether 引导表示一般疑问意义(带有是否、已否、对否等)

I don’t know if / whether Wei Hua likes fish. 我不知道韦华是否喜欢鱼。

㈢由连接代词、连接副词(疑问词) 引导表示特殊疑问意义

Do you know what he wants to buy? 你知道他想要买什么吗?

㈣从句时态要与主句一致

当主句是一般现在时,从句根据情况使用任何时态

He says (that ) he is at home. 他说他在家里。

I don’t know (that) she is singing now. 我不知道她正在唱歌。

She wants to know if I have finished my homework.

她想要知道我是否已经完成了我的作业。

Do you know when he will be back? 你知道他将会什么时候回来?

当主句是一般过去时,从句应使用过去某时态(一般过去时,过去进行

时,过去将来时,过去完成时)

He said (that) he was at home. 他说他在家里。

I didn’t know that she was singing now. 我不知道她正在唱歌。

She wanted to know if I had finished m homework.

她想要知道我是否已经完成了我的作业。

Did you know when he would be back? 你知道他将会什么时候回来?

Unit 5—Unit 8

※1.prefer v.更喜爱,更喜欢,相当于like……better,其过去式、过去分词为preferred,常用于以下结构:

(1)prefer+名词、代词I preferred music. Which do you prefer?

(2)prefer+动词不定式“宁愿干……”She prefers to live among the working people.

(3) prefer+v-ing I prefer living abroad.

(4)prefer+动词不定式复合结构:

常见的搭配有:

①prefer……to……喜欢……而不喜欢……(to为介词)She prefers apples to bananas.

② prefer doing to doing(to为介词)He prefers running to walking.

③prefer to do …… rather than do sth.宁愿干……而不愿干……

They prefer to play games rather than watch TV.

※2. not only … but (also) … 不但… 而且… 用来连接两个并列的成分 (1) 引导以not only …but (also)… 开头的句子往往引起部分倒装。也

是说得要把前面的句子中的助动词或者是情态动词放在主语的前面。

如:Not only can I do it but (also) I can do best. 我不仅能做到而且做得最好。

⑵Not only…but (also)… 接两主语时,谓语动词随后面的主语人称和

数的变化也就是就近原则如:Not only Lily but (also) you like

cat. 不仅莉莉而且你也喜欢猫。

常见的就近原则的结构有:

Neither… nor…即不…也不… (两者都不)

Either… or… 不是…就是… (两者中的一个)

Not only …but(also)…

There be

Unit 9

1.被动语态:它是由“was/were+动语“过去分词”构成的。”

2.be used for:意思是“被用来做什么”,强调用途或作用.

3.be used as :意思是“被作为什么来用”,强调被当作工具或手段来用.

4.be used by:意思是“被谁使用”,强调使用者.

5.“名词+现在分词/过去分词”构成一个合成形容词,在句中作定语和表语。

6.插入语:当一个词、短语或从句用在句里,而与句子的其他成分没有语法上的关系时,它就是句子的独立成分。插入语就是这种独立成分之一。插入语一般对一句话做一些附加的解释,放在句末时,通常在前面加逗号,放在句中时,

有时在前后加逗号,有时不加任何标点符号。

7.according to+名词意思是按照、依照……所说,随着……的不同而不同

8.according as +从句,意思是根据……而……,按照……而……

※9.prefer to do sth.“更喜欢去做某事”

Prefer 意思是更喜欢,常可与like better ,instead of 进行替换,它所组成的常见句式有:Prefer A to B“比起B来更喜欢A”,prefer doing A to doing B“比起干B这件事来,更喜欢干A这件事”, perfer to do A rather than do B“宁愿做A而不原做B.”

Unit10

1.“take+a+名词”结构来表示一次性动作。

2. happen to sb.某人发生某事, 指偶然地或碰巧发生,强调意外.

3. take place 意思也是发生,指经过安排或计划要发生的事情,强调必然性.

4. by the time 意思是“到……时为止,到……时”,注重时间的截止。

at the time 表示“在……时”,注重时间的开始。

5. give one a ride=hitch a ride with sb.意思是“让某人搭便车”

6. forget to do sth.意思是“忘记做某事”,指“要做的事情忘记做”.

7. forget doing sth.意思是“忘记做了某事”,指“做了某事而把它忘记了”.

8. as...as..“像……一样”,常用来表示比较、倍数或程度,在这个结构中,前一个as是副词,后一个as是连词,它的否定形式是not so...as...或not as...as...

9. have to 是“不得不”的意思,指由于受条件限制或他人制约做某事,有被动的含义,无主观愿望;must是“必须,一定”的意思,有主观愿望和感情色彩.

10.try sb.for a job 试用某人;try one’s best to do sth.竭尽所能做某事;try sb. for sth.因某事而审问某人.

Unit11

1.get some information about the town是“询问有关城镇的信息”的意思.

2.decide to do sth.意思是“决定去做某事”.

3.talk to sb意思是“找某人谈话”

4.“It is +形容词+动词不定式短语”是英语中的一个常用句式,句中的真正主语是动词不定式,it是形式主语。

5.in front of意思是“在……的前面”,指在某个围之外.

6.in the front of 意思是“在……的前部”,指在某个围之.

7.have trouble doing sth.表示“做某事有困难”.

8.in trouble/get into trouble/get sb.into trouble 表示“遇到困难,遇到麻烦”.

【重点语法】

1.※被动语态

Ⅰ.被动语态的构成形式be+Vt.p.p.

(一).语态是英语动词的一种形式,是用于表示主语和谓语之间的关系。英语语态分为主动语态(active voice)和被动语态(passive voice)两种。

主动语态是表示主语是动作的执行者。如:1)Yesterday I parked my car outside the school.

被动语态是表示主语是动作的承受者。2)A sound of piano is heard in the hall.

(二)被动语态的基本时态变化

在被动语态的句子中,谓语部分的结构是be+Vtp.p.(及物动词过去分词)。其中be是变量,随时态的变化而变化;动词的过去分词是常量,永远不发生变化。当然,这只是指谓语部分而言。be动词作为一个独立的谓语动词有自己现在分词(being)和过去分词(been)。那么,下面我们来看看be在各种时态中的变化形式:被动语态通常为八种时态的被动形式。以do为例,各种时态的被动语态形式为:

1)am/is/are+done(过去分词)一般现在时 2)has/have been done 现在完成时

3)am/is/are being done 现在进行时 4)was/were done一般过去时5)had been done 过去完成时 6)was/were being done 过去进行时

7)shall/will be done 一般将来时 8)should/would be done 过去将来时

Ⅱ.一般来说,在我们日常生活中,能用主动语态的时候就尽量不去用被动语态。只有在下列情况中我们才用被动语态:

英语里被动语态的使用似乎比汉语要广泛。英语的被动语态常用在下列的场合:1)当我们不知道动作的执行者的时候,如:1.Look!There’s nothing here.Everything has been taken away.

2.My car has been moved!

2)当我们不必提出动作的执行者的时候,如:I was born in 1960.

3)当我们强调或侧重动作的承受者的时候,如:She is liked by everybody. Ⅲ.特殊的被动结构

1)带情态动词的被动结构:它的固定句式为“情态动词+be+过去分词”。也有个别带to的情态动词例外,如:ought to 和have to,它们的被动结构就只

能在不定式中。例如:The debt must be paid off before next month那笔债务必须在下个月前付清。

2)带有两个宾语的主动语态变成被动语态

将这种主动态的句子完成被动态的句子,可选两个宾语中的任何一个作为被动态句子的主语,而将另一个宾语作为“保留宾语”写入被动态的句中。但有一点要说明,那就是,如果你选直接宾语作“主语”,有时要在被动态句子的“保留宾语”前加上合格的介词。因为这些动词常有两种句式,即:我们可以说give sb.sth.,send sb.sth.,buy sb.sth;我们也可以说give sth to sb,send sth to sb buy sth for sb。请看下面两种情况的对照:

She sent me a novel on my birthday.

I was sent a novel on my birthday.

A novel was sent to me on my birthday.

3)关于带有复合宾语的主动态变成被动态

如果将带有复合宾语(既:宾语+宾语补足语)的主动语态的句子变成被动语态的句子,我们只能选择原来句子的宾语作被动语态句子的主语;而这时,原句里的宾语补足语现在就变成被动语态句子的“主语补足语”了。

The story made us laugh.(宾语补足语)

We were made to laugh by the story.(主语补足语)

4)在使役动词have,make,get以及感官动词see,watch,notice,hear,feel,observe等后面不定式作宾语补语时,在主动结构中不定式to要省略,但变为被动结构时,要加to。

Someone saw a stranger walk into the building.

A stranger was seen to walk into the building.

有些相当于及物动词的动词词组,如“动词+介词”,“动词+副词”等,也可

以用于被动结构,但要把它们看作一个整体,不能分开。其中的介词或副词也不能省略。例The meeting is to be put off till Friday.

6)非谓语动词的被动语态。v+ing形式及不定式to do也有被动语态 (一般时态和完成时态)。例,I don’t like being laughed at in the public.There are two more trees to be planted.

2. 动词不定式

(1)做定语—后置

The best way to learn English is reading aloud.

The fastest way to travel is by plane

(2)与所修饰的名词构成动宾关系

I need a pen to write with.

I don’t have a partner to practice English with.

I need some paper to write on.

I don’t have a room to live in.

3. 动名词

(1)作主语(谓语为第三人称单数)

Memorizing the words of pop songs also helps a little.记流行歌曲的词也起作用。

Swimming is good for our health.

(2)作宾语

在动词(keep\practice\finish \enjoy\hate\be busy\mind) 后只用—ing 作宾语

Eg. We should keep speaking English in class.

He often practices singing in the morning. I have finished

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说明:(1)法则中、可以是单项式,也可以是多项式,要注意它们的取值范围,、都是非负数; (2)(≥0,≥0)可以推广为(≥0,≥0); (≥0,≥0,≥0,≥0)。 (3)等式(≥0,≥0)也可以倒过来使用,即(≥0,≥0)。也称“积的算术平方根”。它与二次根式的乘法结合,可以对一些二次根式进行化简。2. 二次根式的除法 两个二次根式相除,把被开方数相除,根指数不变,即(≥0,>0)。 说明:(1)法则中、可以是单项式,也可以是多项式,要注意它们的取值范围,≥0,在分母中,因此>0; (2)(≥0,>0)可以推广为(≥0,>0,≠0); (3)等式(≥0,>0)也可以倒过来使用,即(≥0,>0)。也称“商的算术平方根”。它与二根式的除法结合,可以对一些二次根式进行化简。? 3. 最简二次根式 (1)被开方数中不含能开方开得尽的因数或因式; (2)被开方数中不含分母。 21.3 二次根式的加减 1. 同类二次根式? 注:判断几个二次根式是否为同类二次根式,关键是先把二次根式准确地化成最简二次根式,再观察它们的被开方数是否相同。? (2)合并同类二次根式:合并同类二次根式的方法与合并同类项的方法类似,系数相加减,二次根号及被开方数不变。? 2. 二次根式的加减? (1)二次根式的加减,先把各个二次根式化成最简二次根式,再将同类二次根式分别合并。? (2)二次根式的加减法与多项式的加减法类似,首先是化简,在化简的基础上去括号再合并同类二次根式,同类二次根式相当于同类项。? 一般地,二次根

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