Book二Unit5 music
Goals : remember important points in this unit
高一英语组 20xx-12-18
1 Have you dreamed of being in front of thousands of people at a concert, with everyone clapping and enjoying singing? 你曾否梦想过在音乐会上面对成千上万的观众,你一边唱歌,观众们一边欣赏你的歌唱为你鼓掌?
(1) dream of
<要点导航> dream of = dream about doing
I have dreamed of being a singer 我一直梦想当歌星
When he was a young man, he dreamed of going to Beijing年轻时他梦想去北京。 我梦想买自己的汽车。(翻译)
_______________________________________
[归纳拓展] dream的过去式和过去分词为:dreamed, dreamed; dreamt, dreamt。 dream of/about sb./sth. 表示“梦见”。
dream of/about sth.和dream of/about doing sth.表示“梦想;想象”。
dream 还可以跟同源宾语,构成dream a dream。
昨夜我做了一个可怕的梦。 _____________________________
We used to_____________________________.我们过去曾想去国外居住。
(2) with everyone clapping and enjoying singing
[要点导航] with everyone clapping and enjoying singing是“with+n./pron.+doing”结构,在句中作伴随状语。例如:
The singer came into the hall with many fans following him.
那位歌星在众多歌迷的簇拥下进了大厅。
She fell asleep with the light burning.亮着灯她就睡着了。
[归纳拓展] “With+宾语+宾语补足语”结构在句子中多数充当状语,表示行为方式,伴随情况、时间、原因或条件;也可以作定语。构成方式如下:
1). with+名词/代词+形容词;
He usually sleeps with the windows open even in winter.
2). with+名词/代词+副词;
One family lived in a house with very tall trees all round.
3). with+名词/代词+介词短语;
English lessons are broadcast every day on the radio with explanations in English。
4). with+名词/代词 +动词不定式;
With so much homework to do,I can't go to the party tonight.
5). with+名词/代词 +分词。
In parts of Asia you must not sit with your feet pointing at another person. He stood for an instant with his hand raised.他举着手站了一会儿。
__________________(由那位小男孩领路),we will find the house easily tomorrow. He lay on the bed _________________________(卧室门关着).
______________________(吃完饭),we all went home.
2.But just how do people get to form a band?
那么,人们又是怎样在一起组成乐队的呢?
[要点导航]form vt. 形成;组成;构成;排成;养成。例如:
I can’t form any idea about it. 这件事我形不成什么意见。
The states united to form a nation. 这些州联合成一个国家。
Form good habits when young.年轻时要养成好习惯。
[归纳拓展] form还可以作名词,表示“.形状,形态,外形,表格,形式”。
in the form of 以……的形式
fill in the form填写表格
in form形式上 in fine form 心情很好
form into形成,使形成
form the habit of养成……的习惯
take the form of采取……的形式
He _______________________(已经养成了拜访我的习惯)on weekends.
They are_____________________________.(形式上不同)
3. They may play to passers-by in the street or subway so that they can earn some extra money.
⑴ passer-by
[要点导航] passer-by [C] 路人,过路的人(复数为passers-by)。例如:
[问题探究] 你知道复合名词怎样变复数吗?
提示:一般说来复合名词的复数形式有三种情况:
① 通常是把最后一个词变成复数形式:
boy-friends男朋友 grown-ups 成年人
go-betweens 中间人 drawbacks 缺陷
② man和 woman位于复合名词的第一部分时,两部分都要变成复数:
men drivers男司机 women drivers女司机
③ 把表示主要含义的词变为复数:
lookers-on旁观者 sisters-in-law嫂子,弟媳
⑵ earn
[要点导航] earn 挣得;获利;赢得。例如:
She earned a living as a part-time secretary.
她靠做半职秘书为生。
earn a/one’s living=_______________ make money_______________
raise money________________
(3)so that
[要点导航] so that conj. 以便,为了(引导的 目的状语从句,从句的谓语常由“can/could/may/might/should”等情态动词构成,=in order that)。例如: She has brought the book in order that she can follow TV lessons
.她带上了书以便跟上电视课。
I hired a boat so that I could go fishing. 我租了条船以便能钓鱼。
Speak clearly_______________________________.
说清楚点 以便每个人都能听懂。
[思维拓展] so that还可引导结果状语从句,意为“结果,以至于”,前面常用逗号同主句分开,从句中通常不用情态动词。例如:
He came late, so that he missed the train.
他来晚了,结果没有赶上过车。
4. However, after a year or so in which they became more serious about their work, “The Monkees” started to play their own instruments and write their own songs like a real band.
[要点导航] or so 大约(与about, around, some同义)。例如:
He can translate three hundred words or so an hour. 他每小时能译300字左右。 Every day we marched a hundred miles or so. 每天我们要行军一百里左右。
[问题探究] or so与about有什么区别?
about与汉语的“大约”相同,总放在数量词之前(大约五十个人=about fifty people)。 I live about 10 miles away. 我住的地方大约10英里远。
or so的用法同汉语的“左右”相同,总跟在数量词之后(五十人左右=fifty people or so)。 They had to wait an hour or so for the police to arrive.
到警察赶来,他们得等上一小时左右。
5. However, the band broke up in about 1970, but reunited in the mid-1980s. 然而,“门基乐队”在19xx年左右解散了,到xx年代中期才又重组起来。
[要点导航]break up vi.&vt. 解散;驱散;分裂;拆散;结束;使精神垮掉。例如: Their marriage__________________________. 他们的婚姻一年后破裂了。
After midnight, the party__________________. 半夜之后,聚会散了。
Their quarrel_________________________. (拆散了他们的家庭)
[归纳拓展]
break down 机器出故障;崩溃; 瓦解 break in 破门而入;插嘴
break into the house破门而入 break one’s promise/word 食言
break out 战争、火灾等爆发 break through 突破;穿过 The car is always breaking down. 这辆车老是出毛病。
Children shouldn't break in on adults' conversation.小孩子不要打断大人们的谈话。
His house was _____________last night.昨天晚上有人闯入他家。
6. Above all, just have fun. 首先,要玩的开心。
[要点导航] above all 首先,尤其,最重要的是。例如:
Never waste anything, and above all, never waste time.
不要浪费东西,尤其不要浪费时间。
She loves country music, above all she loves John Denver. 她喜欢乡村音乐,尤其喜欢John Denver的。
Above all, they knew how to use their brain.
最重要的是他们知道如何去独立思考。
[思维拓展] 与all构成的其它短语有:
1)above all是从事物的重要性上说的“首先,最终要的是”;
first of all是从事物的排列顺序上说的“第一”;
in all表示“总共;总而言之”;
after all表示“毕竟”。
2)have fun=have a good time 玩的开心;
make fun of 取笑。
常考点记忆
1. To be honest(放句首)说实话 =To tell you the truth
= To be frank; 坦白说;老实说 be honest with sb. 对某人诚实
2. as if+虚拟/真实语气
He looks as if he were ten years older.(现在的虚拟)
He talked as if he had been there(过去的虚拟)
It looks as if it is going to rain.(真实语气,却有可能下雨)
3. pretend to do sth./be doing sth./have done sth.假装要做/正在做/已做过某事 4 .perform v. ;表演;表现;执行(做,履行) perform tasks(任务)/experiments 执行/做 perform one’s promise 履行 He performed well in the game.表现 performance n.表演;表现;执行
5. break up (关系的)破裂; 打碎,拆开; 学校放假,(会议的)结束;分裂,解体,解散 break down (机器等)故障;(人的精神,健康) ;垮了;(计划,谈判等)失败 break off 中断 break into 突然闯入;强行进入Vt break in 闯入;打断;插嘴 vi break through 突破;
break away from 脱离 break out(战争,灾难等)突然爆发
6.play tricks on sb. =make fun of sb. =play a trick on sb 和……开玩笑;捉弄某人
7. attach importance to:重视 be attached to:附属于;喜欢;依恋
8. build up confidence :树立信心 become self-confident : 变得自信
9. take sth. seriously; 严肃,认真对待某事 10.The song was a hit. 这首歌红极一时。 hit: 红极一时的人或物
11. long for/to do 渴望某物/渴望做某事 12. by chance 偶然,意外地=by accident=accidentally
13 rely on =depend on 依赖 依靠
14 be familiar with 对……熟悉 15 in addition 另外 也,除此之外 16 sort out 分类
第二篇:必修5 数列知识点归纳总结
第二章 数列
一、数列的概念:
1、数列、数列的项及其符号表示:
按一定次序排列的一列数叫做数列。数列中的每一个数都叫做这个数列的项。
数列a1,a2,a3,??,an记为{an}
2、数列的通项公式:如果数列{an}的第n项与n之间的关系可以用一个公式来表示,这个公式就叫做这个数列的通项公式。
3、有穷数列与无穷数列:若数列{an}的项数是有限的,则称数列{an}为有穷数列。若数列{an}的项数是无限的,则称数列{an}为无穷数列。
4、递增数列:在数列{an}中,若an?1≥an对任意正整数n都成立,则称数列{an}为递增数列;
5、递减数列:在数列{an}中,?n?N,an?1?an则称{an}为递减数列;
6、常数列:在数列{an}中,?n?N,an?1?an则称{an}为常数列;
7、摆动数列:在数列{an}中,自第二项起,有些项大于它的前一项,有些小于它们的前一项,则称{an}为摆动数列。
8、数列的递推关系:如果已知数列{an}的第一项(或前几项),且任一项an与它的前一项an?1(或前几项)之间的关系可以用一个式子来表示,那么这个式子就叫做这个数列的递推公式。
9、数列{an}的前n项和Sn与第n项an之间的关系是: ??
an???S1
?Sn?Sn?1(n≥2) (n-1)
二、等差数列:
1、等差数列的定义:
如果一个数列{an}自第2项起,每一项与它前一项的差等于同一个常数,即an?1?an?d(n?2,d是一个与n无关的常数),则数列{an}叫做等差数列。
2、等差数列的通项公式:an?a1?(n?1)d
3、等差数列的单调性:设等差数列{an}的公差d,当d>0,等差数列{an}为递增数列;当d<0时,等差数列{an}为递减速;d=0时{an}为常数列。
4、等差中项:a、b、c 成等差数列,则称b为a、c的等差中项。
a?c? a、b、c成等差数列。 b为a、c的等差中项?b-a=c-b?2b=a+c?或b?2
5、等差数列的常用性质:设等差数列{an}的公差为d ,k、l、m、n?N*.
1)若k+l=m+n则ak?al?am?an 2)若m+n=2k则am?an?2ak
3)an?am?(n?m)d(n?m) 4)d?
5)a1?an?a2?an?1?a3?an?2?.....
6、等差数列{an}前n项和:
11SN?n(a1?an)?na1?n(n?1)d?an2?bn为常数,(a、b为常数,公22
an?a1am?ak? n?1m?k
差为d
7、项数(下标)的“等和”性质:
n(a1?an)n(a2?an?1)n(am?an?m?1)sn??? 222
8、设等差数列{an}、?bn?的前n项和分别为Sn、Tn,则anS2n?1 ?bnT2n?1
9、“片段和”性质:等差数列{an}的公差为d,前n项和为Sn,则SK,S2K?SK,
2S3K?S2K,??(K?N?)成等差数列,其公差为kd。
10、若等差数列{an}的项数为2n(n?N*),则S2n?n(an?an?1)(其中为中间两项),且
S偶?S奇?nd,S奇S偶?an。 an?1
11、若等差数列{an}的项数为2n-1,则S2n?1?(2n?1)an,(an为中间项)且
S奇?S偶?an,
三、等比数列
1、等比数列的定义: S奇S偶?n n?1
如果一个数列{an}从第二项起,每一项与它的的比等于同一个常数,即an?1?q(n?1, an
n?N?,q 是与n无关的常数),这个数列就叫做等比数列。
2、等比数列{an}的通项公式:an?a1qn?1.
注意:在等比数列{an}中,an?0 ,q?0。
3、等比中项:a、G、b成等比数列,则G叫做a与b的等比中项。a、G、b成等比数列?G2?ab,a2n?1?anan?2
4、等比数列的常用性质:若{an}是等比数列,m、n、k、l?N?
①k+l=m+n?akal?aman
2②m+n=2k?aman?ak
③an?amqn?m
④a1an?a2an?1?a3an?2?akan?k?1(n为正奇数)
5、单调性:设等比数列{an}的公比为q
①当q>1,a1?0或0<q<1,a1?0时,{an}递增;
②当a1?0,0?a?1或a1?0,q?1时{an}递减;
③当q=1时,{an}为常数列; ④当q=-1时,{an}为摆动数列;
na1(q?1)??n6、等比数列{an}的前n项和Sn??a1(1?q)a1?anq ??A?Aqn(q?1)?1?q?1?q
7、设等比数列{an}的前m项和为Sm则Sm,S2m?Sm,S3m?S2m,??仍构
2成公比为qm的等比数列,且有?S2m?Sm??Sm?(S3m?S2m)
8、若数列{an}的前项和Sn?an?1(a?0,a?1),则{an}是等比数列。
9、若等比数列{an}的公比为q,前项和为Sn,则Sn?m?Sn?qnSm
10、若等比数列{an}的项数为2n(n?N*),则S偶
S奇?q
a1?a2n?2 (q?1且q??1),1?q11、若等比数列{an}的项数为2n?1(n?N*),则S奇-S偶?