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数学知识点汇集网站：http://gaokao.juren.com/news/201208/316628.html
(凡是字数不是特别多但无法复制的，我都会发网住，自行点击进入即可）
公式汇集：
向量公式：
1.单位向量：单位向量a0=向量a/|向量a|
2.P(x,y) 那么 向量OP=x向量i+y向量j
|向量OP|=根号（x平方+y平方）
3.P1(x1,y1) P2(x2,y2)
那么向量P1P2=｛x2-x1,y2-y1｝
|向量P1P2|=根号[(x2-x1)平方+(y2-y1)平方]
4.向量a=｛x1,x2｝向量b=｛x2,y2｝
向量a*向量b=|向量a|*|向量b|*Cosα=x1x2+y1y2
Cosα=向量a*向量b/|向量a|*|向量b|
(x1x2+y1y2)
= ————————————————————
根号(x1平方+y1平方)*根号（x2平方+y2平方）
5.空间向量：同上推论
（提示：向量a=｛x,y,z｝）
6.充要条件：
如果向量a⊥向量b
那么向量a*向量b=0
如果向量a//向量b
那么向量a*向量b=±|向量a|*|向量b|
或者x1/x2=y1/y2
7.|向量a±向量b|平方
=|向量a|平方+|向量b|平方±2向量a*向量b
=(向量a±向量b)平方
三角函数公式：
1.万能公式
令tan(a/2)=t
sina=2t/(1+t^2)
cosa=(1-t^2)/(1+t^2)
tana=2t/(1-t^2)
2.辅助角公式
asint+bcost=(a^2+b^2)^(1/2)sin(t+r)
cosr=a/[(a^2+b^2)^(1/2)]
sinr=b/[(a^2+b^2)^(1/2)]
tanr=b/a
3.三倍角公式
sin(3a)=3sina-4(sina)^3
cos(3a)=4(cosa)^3-3cosa
tan(3a)=[3tana-(tana)^3]/[1-3(tana^2)]
4.积化和差
sina*cosb=[sin(a+b)+sin(a-b)]/2
cosa*sinb=[sin(a+b)-sin(a-b)]/2
cosa*cosb=[cos(a+b)+cos(a-b)]/2
sina*sinb=-[cos(a+b)-cos(a-b)]/2
5.积化和差
sina+sinb=2sin[(a+b)/2]cos[(a-b)/2]
sina-sinb=2sin[(a-b)/2]cos[(a+b)/2]
cosa+cosb=2cos[(a+b)/2]cos[(a-b)/2]
cosa-cosb=-2sin[(a+b)/2]sin[(a-b)/2]
(凡是字数不是特别多但无法复制的，我都会发网住，自行点击进入即可）
公式汇集：
向量公式：
1.单位向量：单位向量a0=向量a/|向量a|
2.P(x,y) 那么 向量OP=x向量i+y向量j
|向量OP|=根号（x平方+y平方）
3.P1(x1,y1) P2(x2,y2)
那么向量P1P2=｛x2-x1,y2-y1｝
|向量P1P2|=根号[(x2-x1)平方+(y2-y1)平方]
4.向量a=｛x1,x2｝向量b=｛x2,y2｝
向量a*向量b=|向量a|*|向量b|*Cosα=x1x2+y1y2
Cosα=向量a*向量b/|向量a|*|向量b|
(x1x2+y1y2)
= ————————————————————
根号(x1平方+y1平方)*根号（x2平方+y2平方）
5.空间向量：同上推论
（提示：向量a=｛x,y,z｝）
6.充要条件：
如果向量a⊥向量b
那么向量a*向量b=0
如果向量a//向量b
那么向量a*向量b=±|向量a|*|向量b|
或者x1/x2=y1/y2
7.|向量a±向量b|平方
=|向量a|平方+|向量b|平方±2向量a*向量b
=(向量a±向量b)平方
三角函数公式：
1.万能公式
令tan(a/2)=t
sina=2t/(1+t^2)
cosa=(1-t^2)/(1+t^2)
tana=2t/(1-t^2)
2.辅助角公式
asint+bcost=(a^2+b^2)^(1/2)sin(t+r)
cosr=a/[(a^2+b^2)^(1/2)]
sinr=b/[(a^2+b^2)^(1/2)]
tanr=b/a
3.三倍角公式
sin(3a)=3sina-4(sina)^3
cos(3a)=4(cosa)^3-3cosa
tan(3a)=[3tana-(tana)^3]/[1-3(tana^2)]
4.积化和差
sina*cosb=[sin(a+b)+sin(a-b)]/2
cosa*sinb=[sin(a+b)-sin(a-b)]/2
cosa*cosb=[cos(a+b)+cos(a-b)]/2
sina*sinb=-[cos(a+b)-cos(a-b)]/2
5.积化和差
sina+sinb=2sin[(a+b)/2]cos[(a-b)/2]
sina-sinb=2sin[(a-b)/2]cos[(a+b)/2]
cosa+cosb=2cos[(a+b)/2]cos[(a-b)/2]
cosa-cosb=-2sin[(a+b)/2]sin[(a-b)/2]
英语：
一、不定式用法
动词不定式具有名词、形容词和副词的特征。因此在句中可以做主语、表语、宾语、宾语补足语、定语和状语。 一、不定式做主语： 1、不定式做主语一般表示具体的某次动作。===动名词doing 表示习惯的，经常的动作。 e.g: To finish the building in a month is difficult. To do such things is foolish. To see is to believe. (对等) 注: 1). 不定式作主语时,谓语用单数 2). 当主语较长，谓语较短时，常用it做形式主语，而将不定式放到谓语的后面。 it做形式主语，不定式放在谓语动词之后常用于下列结构中： (1)It is/was +adj.+of sb. to do… (2) It is +adj.+for sb.+to do… It is easy / difficult / hard / foolish / unwise / right / wrong / unnecessary (3) it is +a +名词+ to do... ? It is a pity / a pleasure / a pleasant thing / one’s duty / an honor / a shame / a crime / no easy job… to do It takes (sb.) some time / courage / patience …to do… ? It requires courage / patience / hard work… to do… *注意: probable 和 possible 均可作表语，但possible可以用不定式作真实主语， 而probable不能用不定式作真实主语。 ?It is probable for him to come to the meeting.(错） ?It is possible for him to come to the meeting. ?It is possible / probable that he will come to the meeting. 二、不定式做表语 主语是以aim duty hope idea intention plan job suggestion wish purpose task 等为中心词的名词词组 或以 what 引导的名词性从句表示，后面的不定式说明其内容, 不定式作表语常表示将来或现在的动作或状态。 eg :My idea is to climb the mountain from the north. Your mistake was not to write that letter. What I would suggest is to start work at once. 三 动词不定式作宾语 以不定式结构为宾语的动词有： ask, agree, care, choose, demand, decide, expect, fail, help, hope, learn, manage, offer, plan, prepare, pretend, promise, refuse, want, wish等只能用动词不定式作宾语 口诀（接不定式作宾语的动词） 想要学习 早打算（ want learn plan） 快准备 有希望（ prepare hope wish expect） 同意否 供选择（agree offer choose） 决定了 已答应（decide be determined promise） 尽力去 着手做（manage undertake） 别拒绝 别假装（refuse pretend） 失败不是属于你（fail） e.g.Tom refused to lend me his pen. We hope to get there before dark. The girl decided to do it herself. *注意:某些及物动词可用-ing也可用动词不定式作宾语但意义不同的有 stop go on remember forget regret try mean can’t help be used to
二、不定式
定义：动词不定式是非谓语动词的一种，它没有人称和数的变化，在句子中不能独立作谓语，但它仍保持动词的特点，既可以有自己的宾语和状语。 E.g. He want his students to read the book aloud. A． 1不定式的构成 （以动词do为例） 主动形式 被动形式 一般式 to do to be done 完成式 to have done to have been done 进行式 to be doing 无 完成进行式 to have been doing 无 2?不定式的意义 不定式的一般式(to do ) 一般式表示的动作或状态，发生在谓语动词表示的动作或状态的同时或之后 My wish is to become a doctor He seemed to be tired. She stopped to have a rest. 不定式的被动式 (to be done) 当不定式的逻辑主语是这个不定式所表示的动作的承受者时,不定式一般要用被动式. The building to be finished next month is for our teachers. I am going to Beijing, I have something to take to my parents, do you have something to be taken to your parents? 如果谓语表示的动作(情况)发生时, 不定式表示动作正在进行,这时候不定式就要用进行式.（to be doing） They are said to be building another bridge across the street. They seemed to be talking about something important. When I went to his home, he happened to be traveling around the world. I’m glad to be working with you. 如果不定式所表示的动作或状态发生在谓语动词所表示动作或状态之前，就用完成式 (to have done) ；若是在此基础上的被动含义，就用完成被动式( to have been done). He is said to have written a novel about the Long March. He thought it a pity not to have invited us. The assistant seemed to have been fired. He is said to have been taught French when he was a child. Einstein is said to have built up his theory when he was in his twenties. 如果不定式的动作是在谓语所表示的时间之前一直在进行的动作，就要用完成进行式. They are said to have been collecting folk song in Xinjiang. We’re happy to have been working with the experts all the month.
一、不定式用法
动词不定式具有名词、形容词和副词的特征。因此在句中可以做主语、表语、宾语、宾语补足语、定语和状语。 一、不定式做主语： 1、不定式做主语一般表示具体的某次动作。===动名词doing 表示习惯的，经常的动作。 e.g: To finish the building in a month is difficult. To do such things is foolish. To see is to believe. (对等) 注: 1). 不定式作主语时,谓语用单数 2). 当主语较长，谓语较短时，常用it做形式主语，而将不定式放到谓语的后面。 it做形式主语，不定式放在谓语动词之后常用于下列结构中： (1)It is/was +adj.+of sb. to do… (2) It is +adj.+for sb.+to do… It is easy / difficult / hard / foolish / unwise / right / wrong / unnecessary (3) it is +a +名词+ to do... ? It is a pity / a pleasure / a pleasant thing / one’s duty / an honor / a shame / a crime / no easy job… to do It takes (sb.) some time / courage / patience …to do… ? It requires courage / patience / hard work… to do… *注意: probable 和 possible 均可作表语，但possible可以用不定式作真实主语， 而probable不能用不定式作真实主语。 ?It is probable for him to come to the meeting.(错） ?It is possible for him to come to the meeting. ?It is possible / probable that he will come to the meeting. 二、不定式做表语 主语是以aim duty hope idea intention plan job suggestion wish purpose task 等为中心词的名词词组 或以 what 引导的名词性从句表示，后面的不定式说明其内容, 不定式作表语常表示将来或现在的动作或状态。 eg :My idea is to climb the mountain from the north. Your mistake was not to write that letter. What I would suggest is to start work at once. 三 动词不定式作宾语 以不定式结构为宾语的动词有： ask, agree, care, choose, demand, decide, expect, fail, help, hope, learn, manage, offer, plan, prepare, pretend, promise, refuse, want, wish等只能用动词不定式作宾语 口诀（接不定式作宾语的动词） 想要学习 早打算（ want learn plan） 快准备 有希望（ prepare hope wish expect） 同意否 供选择（agree offer choose） 决定了 已答应（decide be determined promise） 尽力去 着手做（manage undertake） 别拒绝 别假装（refuse pretend） 失败不是属于你（fail） e.g.Tom refused to lend me his pen. We hope to get there before dark. The girl decided to do it herself. *注意:某些及物动词可用-ing也可用动词不定式作宾语但意义不同的有 stop go on remember forget regret try mean can’t help be used to
二、不定式
定义：动词不定式是非谓语动词的一种，它没有人称和数的变化，在句子中不能独立作谓语，但它仍保持动词的特点，既可以有自己的宾语和状语。 E.g. He want his students to read the book aloud. A． 1不定式的构成 （以动词do为例） 主动形式 被动形式 一般式 to do to be done 完成式 to have done to have been done 进行式 to be doing 无 完成进行式 to have been doing 无 2?不定式的意义 不定式的一般式(to do ) 一般式表示的动作或状态，发生在谓语动词表示的动作或状态的同时或之后 My wish is to become a doctor He seemed to be tired. She stopped to have a rest. 不定式的被动式 (to be done) 当不定式的逻辑主语是这个不定式所表示的动作的承受者时,不定式一般要用被动式. The building to be finished next month is for our teachers. I am going to Beijing, I have something to take to my parents, do you have something to be taken to your parents? 如果谓语表示的动作(情况)发生时, 不定式表示动作正在进行,这时候不定式就要用进行式.（to be doing） They are said to be building another bridge across the street. They seemed to be talking about something important. When I went to his home, he happened to be traveling around the world. I’m glad to be working with you. 如果不定式所表示的动作或状态发生在谓语动词所表示动作或状态之前，就用完成式 (to have done) ；若是在此基础上的被动含义，就用完成被动式( to have been done). He is said to have written a novel about the Long March. He thought it a pity not to have invited us. The assistant seemed to have been fired. He is said to have been taught French when he was a child. Einstein is said to have built up his theory when he was in his twenties. 如果不定式的动作是在谓语所表示的时间之前一直在进行的动作，就要用完成进行式. They are said to have been collecting folk song in Xinjiang. We’re happy to have been working with the experts all the month.
三、倒装句之部分倒装
高二英语语法倒装句之部分倒装 部分倒装是指将谓语的一部分如助动词或情态倒装至主语之前。如果句中的谓语没有助动词或情态动词，则需添加助动词do,does或did，并将其置于主语之前。 1)句首为否定或半否定的词语，如no,not,never,seldom,little,hardly,atnotime,innoway,notuntil…等。 NeverhaveIseensuchaperformance. Notuntilthechildfellasleepdidthemotherleavetheroom. 当Notuntil引出主从复合句，主句倒装，从句不倒装。 注意如否定词不在句首不倒装。 Ihaveneverseensuchaperformance. 典型例题 1)WhycantIsmokehere? Atnotime___inthemeeting-room A.issmokingpermittedB.smokingispermitted C.smokingisitpermittedD.doessmokingpermit 答案A.这是一个倒装问题。当否定词语置于句首以表示强调时，其句中的主谓须用倒装结构。这些否定词包括no,little,hardly,seldom,never,notonly,notuntil等。本题的正常语序是Smokingispermittedinthemeeting-roomatnotime. 2）Notuntiltheearlyyearsofthe19thcentury___whatheatis. A.mandidknowB.manknowC.didntmanknowD.didmanknow 答案D.看到Notuntil…的句型，我们知道为一倒装句，答案在C，D中选一个。 改写为正常语序为，Mandidnotknowwhatheatisuntiltheearlyyearsofthe19th.现在将not提前，后面就不能再用否定了,否则意思就变了。 以否定词开头作部分倒装 如Notonly…butalso,Hardly/Scarcely…when,Nosooner…than Not only did here fuse thegi ft,healsoseverelycriticizedthesender. Hardly had she gone out when a student came tovisither.
高二英语语法倒装句之部分倒装 部分倒装是指将谓语的一部分如助动词或情态倒装至主语之前。如果句中的谓语没有助动词或情态动词，则需添加助动词do,does或did，并将其置于主语之前。 1)句首为否定或半否定的词语，如no,not,never,seldom,little,hardly,atnotime,innoway,notuntil…等。 NeverhaveIseensuchaperformance. Notuntilthechildfellasleepdidthemotherleavetheroom. 当Notuntil引出主从复合句，主句倒装，从句不倒装。 注意如否定词不在句首不倒装。 Ihaveneverseensuchaperformance. 典型例题 1)WhycantIsmokehere? Atnotime___inthemeeting-room A.issmokingpermittedB.smokingispermitted C.smokingisitpermittedD.doessmokingpermit 答案A.这是一个倒装问题。当否定词语置于句首以表示强调时，其句中的主谓须用倒装结构。这些否定词包括no,little,hardly,seldom,never,notonly,notuntil等。本题的正常语序是Smokingispermittedinthemeeting-roomatnotime. 2）Notuntiltheearlyyearsofthe19thcentury___whatheatis. A.mandidknowB.manknowC.didntmanknowD.didmanknow 答案D.看到Notuntil…的句型，我们知道为一倒装句，答案在C，D中选一个。 改写为正常语序为，Mandidnotknowwhatheatisuntiltheearlyyearsofthe19th.现在将not提前，后面就不能再用否定了,否则意思就变了。 以否定词开头作部分倒装 如Notonly…butalso,Hardly/Scarcely…when,Nosooner…than Not only did here fuse thegi ft,healsoseverelycriticizedthesender. Hardly had she gone out when a student came tovisither.
