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必修五第二单元知识点

Unit 2:

1. consist of =be made up of 由……组成(没有进行时无被动)

e.g. The UK consists of Great Britain and Northern Ireland.

=Great Britain and Northern Ireland make up the UK.

Consist in 在于基于

The beauty of Venice consists in the style of its ancient buildings

威尼斯之美就在于它具有古代建筑风格

Make up 组成

Be made up of be composed of 由组成

2. 区别:

Ø separate ... from (把联合在一起或靠近的人或物分离出来)

Ø divide...into 把…分开(把整体分为若干部分)

e.g. The teacher divided the class into two groups.

The Taiwan Strait separates Taiwan from Fujian.

3. debate about sth.

e.g. They debate about the proposal for three days.

4.clarify: vt./vi. (cause sth. to )become clear or easier to understand 澄清;阐明;清楚;明了

Clarif one‘s stand 、position阐明自己的立场

e.g. I hope what I say will clarify the situation.

Can you clarify the question?

5. be linked to = be connected to /be joined to 连接

【习惯用语】★ link A to B 将A和B连接起来

Link A and B together

Link up with sb sth 连接,结合

6. refer to

1)提及,指的是……

e.g. When he said “some students”, do you think he was referring to us?

2) 参考;查阅;询问

e.g. If you don't understand a word you may refer to your dictionaries.

Please refer to the last page of the book for answers.

3) 关系到;关乎

e.g. What I have to say refers to all of you.

This rule refers to everyone.

reference: n. 参考 e.g. reference books 参考书

7. to one's surprise (prep)

“to one's + 名词” 表“令某人……”

常见的名词有“delight, disappointment, enjoyment, astonishment 等

e.g. I discovered, to my horror, that the goods were entirely unfit for sale.

To John's great relief they reached the house at last.

8. ... found themselves united peacefully

“find +宾语+宾补( adj; adv; v-ing; pp; 介词短语;不定式)”

e.g. A cook will be immediately fired if he is found smoking in the kitchen.

You'll find him easy to get along with.

They found themselves trapped by the bush fire.

When I woke up, I found myself in hospital.

I called on him yesterday, but I found him out.

9. get sth done =have sth done 使某事被做…….

e.g. I'll just get these dishes washed and then I'll come.

get + n. + to do

get + n. + doing

You'll get her to agree.

I'll get the car going.

get done: 用于意想不到、突然或偶然发生,意为“被…….”

e.g. Be careful when you cross this very busy street.

10. break away (from sb / sth) 脱离;破除…

e.g. It is not easy for him to break away from bad habits.

The man broke away from his guards.

break down (会谈)破裂,失败;(汽车等)出故障;(人的健康状况)变得恶劣;(情感)失控

e.g. His car broke down on the way to work this morning.

His health broke down under the pressure of work.

He broke down and wept when he heard the news.

Talks between the two countries have completely broken down.

Ø break in 闯入;打岔

Ø break off 中断,折断

Ø break into 闯入

Ø break out 爆发;发生

Ø break up 驱散;分散,拆散

11. as well as 不仅…而且;既…又…

e.g. He is a teacher as well as a writer.

The children as well as their father were seen playing football in the street.

12.convenience: n.方便;便利(convenient: adj. )for

For the convenience of 为了方便。。。。

For convenience 为了方便起见

At sb’s convenience 在方便时,在适宜的地点

Be convenient for sb sth 对于。。。方便

It is convenient for sb to do sth某人方便做某事

Eg is this evening convenient for you to go out?

Eg come and see me whenever it is convenient to you

e.g. We bought this house for its convenience.

13. attraction: (attract: v.)attract one’s attention 吸引某人的注意力

1). 吸引;引力(不可数n.) e.g. attraction of gravitation 重力

2). 吸引人的东西;喜闻乐见的东西;精彩节目(可数n.)

He can't resist the attraction of the sea on a hot day.

A big city offers many and varied attractions.

What are the principle attractions this evening?

14. influence

1) v. 对…产生影响 e.g. What influence you to choose a career in teaching?

2)可数n. 产生影响的人或事 e.g. He is one of the good influences in the school.

3) (不可数n.) 影响 e.g. A teacher has great influence over his pupils.

Have an influence on sb 对某人有影响

15 leave out 1 遗漏,缺漏2 不理会,忽视,

Arrange 安排,筹备

Arrange sth for sb 为某人安排某事arrange for sb to do sth 安排某人做某事Arrange sth 整理

Eg we arranged for a car to collect us form the airport我们安排一辆轿车到机场接我们Eg;I have arranged with the neighbors about feeding the cat while we

Are away我们外出时喂猫的事,我已和邻居安排好了

She arranged the flowers in a vase 他把花瓶中的花插好

take the place of = replace 代替

=take sb’s place 代替某人

take place 发生, 举行

in place of =instead of 代替

puzzle over 苦思be in a puzzle about 对……不解

人puzzled

物puzzling

9. be in/ come into conflict with 与…冲突/ 矛盾

10.be unwilling to do sth 不愿意做某事

11. break away from 摆脱,脱离…

break down 坏(抛锚, 出故障, 身体跨了)

break into 闯入,

break out (war/fire/disease) 爆发

break off 中断

break the rules 违反规则

break the records 打破记录

. It is worthwhile to do sth. 值得做某事

It is worthwhile doing sth

be worthy to be done

be worthy of being done

be worth n/pron /doing

eg.The book is worth reading.

The book is worthy to be read/ of being read.

It is worthwhile to read the book.

18. leave out 遗漏, 漏掉

leave A for B 离开A去B

leave alone 不管; 撇下…一个人

leave aside 搁置

leave behind 遗忘, 遗留

leave+宾语+宾补(adj/v-ing/v-ed ) 使..

19. sb. be familiar with sth

sth be familar to sb 熟悉某物

20. whisper to sb 悄悄说

21. pick up 捡

22. make a list of 列…清单

23. delight

n. to one’s delight 使某人高兴的是…

vt. delight sb

adj delighted be ~ ed at sth, be delighted to do sth

物delighting

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2.悦亲戚之情话古:知心话今:男女间谈情说爱的话 3.将有事于西畴古:农事今:指有事情 4.既窈窕以寻壑古:幽深曲折的样子今:指女子文静而美好 5.于时风波未静古:指战乱今:常用来比喻乱子 6.景翳翳以将入古:日光今:景色,光景 7.或命巾车古:有时今:或者,或许 8.何不委心任去留古:指生死今:离开留下 9.或植杖而耕耔古:立今:种植 四、一词多义 1.夫问征夫以前路(名词,行人) 乐夫天命复奚疑?(助词,起舒缓语气的作用) 2.归田园将芜胡不归?(动词,归隐) 聊乘化以归尽(动词,到死) 五、虚词积累 1.以既自以心为形役(介词,让) 农人告余以春及(介词,把) 舟遥遥以轻飏,风飘飘而吹衣。(表修饰,而) 眄庭柯以怡颜,倚南窗以寄傲。(表目的,来) 2.而门虽设而常关(表转析) 觉今是而昨非(表并列) 时矫首而遐观(表修饰) 鸟倦飞而知还(表承接) 3.之悦亲戚之情话(结构助词,的) 感吾生之行休(助词,主谓之间无意义) 胡为乎遑遑欲何之(动词,往) 六、特殊句式 1.介宾结构后置 将有事于西畴/农人告余以春及 2.宾语前置 胡为乎惶惶欲何之?/复驾言兮焉求?/ 乐夫天命复奚疑?

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数列知识点总结 二、求数列通项公式的方法 1、通项公式法:等差数列、等比数列 2、涉及前n项和S n 求通项公式,利用a n 与S n 的根本关系式来求。即 例1、在数列{n a }中,n S 表示其前n项和,且2 n n S =,求通项n a . ⎩⎨ ⎧≥-===-) 2()1(111n s s n a s a n n n

例2、在数列{n a }中,n S 表示其前n项和,且n n a 32S -=,求通项n a 3、已知递推公式,求通项公式。 (1)叠加法:递推关系式形如()n f a a n 1n =-+型 例3、已知数列{n a }中,1a 1=,n a a n 1n =-+,求通项n a 练习1、在数列{n a }中,3a 1=,n n 1n 2a a +=+,求通项n a 〔2〕叠乘法:递推关系式形如 型 例4、在数列{n a }中,1a 1=, ,求通项n a 练习2、在数列{n a }中,3a 1=,n n 1n 2a a •=+,求通项n a 〔3〕构造等比数列:递推关系式形如B Aa a n 1n +=+(A,B 均为常数,A ≠1,B ≠0) 例5、已知数列{n a }满足4a 1=,2a 3a 1n n -=-,求通项n a 练习3、已知数列{n a }满足3a 1=,3a 2a n 1n +=+,求通项n a (4)倒数法 例6、在数列{a n }中,已知1a 1=, ,求数列的通项n a 四、求数列的前n 项和的方法 1、利用常用求和公式求和: 等差数列求和公式:d n n na a a n S n n 2 ) 1(2)(11-+=+= 等比数列求和公式:⎪⎩⎪⎨⎧≠--=--==) 1(11)1()1(111q q q a a q q a q na S n n n 2、错位相减法:主要用于求数列{a n ·b n }的前n 项和,其中{}n a 、{}n b 分别是等差数列和等比数列 .[例1] 求数列 ⋅⋅⋅⋅⋅⋅,2 2,,26,24,2232n n 前n 项的和. [例2] 求和:1 32)12(7531--+⋅⋅⋅++++=n n x n x x x S 3、倒序相加法:数列{n a }的第m 项与倒数第m 项的和相等。即: 1m n m 1n 2n 1a a a a a a +--+==+=+ [例3] 求 89sin 88sin 3sin 2sin 1sin 2 2 2 2 2++⋅⋅⋅+++的值 [例4] 函数()x f 对任R x ∈都有()()2 1 x 1f x f = -+,求: ()n f a a n 1n =+n 1 n a 1 n n a +=+2 a a 2a n n 1n +=+

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