高三数学知识点总结大全 高三英语省略句常见省略现象

高三数学知识点总结大全 数学公式整理归纳

有些数学题的解题方法，也可以用表格化难为易、驭繁为简。例如，用列表法解乘积或分式不等式，解含绝对值符号的方程或不等式，计算多项式的乘法，求整系数方程的有理根等等，都是很好的方法，这种记忆法在复习中尤其应该提倡。

高三数学公式知识点

三倍角公式

sin3α=4sinα·sin(π/3+α)sin(π/3-α)

cos3α=4cosα·cos(π/3+α)cos(π/3-α)

tan3a=tana·tan(π/3+a)·tan(π/3-a)

三倍角公式推导

sin3a

=sin(2a+a)

=sin2acosa+cos2asina

辅助角公式

Asinα+Bcosα=(A^2+B^2)^(1/2)sin(α+t)，其中

sint=B/(A^2+B^2)^(1/2)

cost=A/(A^2+B^2)^(1/2)

tant=B/A

Asinα+Bcosα=(A^2+B^2)^(1/2)cos(α-t)，tant=A/B

降幂公式

sin^2(α)=(1-cos(2α))/2=versin(2α)/2

cos^2(α)=(1+cos(2α))/2=covers(2α)/2

tan^2(α)=(1-cos(2α))/(1+cos(2α))

推导公式

tanα+cotα=2/sin2α

tanα-cotα=-2cot2α

1+cos2α=2cos^2α

1-cos2α=2sin^2α

1+sinα=(sinα/2+cosα/2)^2

=2sina(1-sin2a)+(1-2sin2a)sina

=3sina-4sin3a

cos3a

=cos(2a+a)

=cos2acosa-sin2asina

=(2cos2a-1)cosa-2(1-sin2a)cosa

=4cos3a-3cosa

sin3a=3sina-4sin3a

=4sina(3/4-sin2a)

=4sina[(√3/2)2-sin2a]

=4sina(sin260°-sin2a)

=4sina(sin60°+sina)(sin60°-sina)

=4sina_2sin[(60+a)/2]cos[(60°-a)/2]_2sin[(60°-a)/2]cos[(60°-a)/2]

=4sinasin(60°+a)sin(60°-a)

cos3a=4cos3a-3cosa

=4cosa(cos2a-3/4)

=4cosa[cos2a-(√3/2)2]

=4cosa(cos2a-cos230°)

=4cosa(cosa+cos30°)(cosa-cos30°)

=4cosa_2cos[(a+30°)/2]cos[(a-30°)/2]_{-2sin[(a+30°)/2]sin[(a-30°)/2]}

=-4cosasin(a+30°)sin(a-30°)

=-4cosasin[90°-(60°-a)]sin[-90°+(60°+a)]

=-4cosacos(60°-a)[-cos(60°+a)]

=4cosacos(60°-a)cos(60°+a)

上述两式相比可得

tan3a=tanatan(60°-a)tan(60°+a)

半角公式

tan(A/2)=(1-cosA)/sinA=sinA/(1+cosA);

cot(A/2)=sinA/(1-cosA)=(1+cosA)/sinA.

sin^2(a/2)=(1-cos(a))/2

cos^2(a/2)=(1+cos(a))/2

tan(a/2)=(1-cos(a))/sin(a)=sin(a)/(1+cos(a))

三角和

sin(α+β+γ)=sinα·cosβ·cosγ+cosα·sinβ·cosγ+cosα·cosβ·sinγ-sinα·sinβ·sinγ

cos(α+β+γ)=cosα·cosβ·cosγ-cosα·sinβ·sinγ-sinα·cosβ·sinγ-sinα·sinβ·cosγ

tan(α+β+γ)=(tanα+tanβ+tanγ-tanα·tanβ·tanγ)/(1-tanα·tanβ-tanβ·tanγ-tanγ·tanα)

两角和差

cos(α+β)=cosα·cosβ-sinα·sinβ

cos(α-β)=cosα·cosβ+sinα·sinβ

sin(α±β)=sinα·cosβ±cosα·sinβ

tan(α+β)=(tanα+tanβ)/(1-tanα·tanβ)

tan(α-β)=(tanα-tanβ)/(1+tanα·tanβ)

和差化积

sinθ+sinφ=2sin[(θ+φ)/2]cos[(θ-φ)/2]

sinθ-sinφ=2cos[(θ+φ)/2]sin[(θ-φ)/2]

cosθ+cosφ=2cos[(θ+φ)/2]cos[(θ-φ)/2]

cosθ-cosφ=-2sin[(θ+φ)/2]sin[(θ-φ)/2]

tanA+tanB=sin(A+B)/cosAcosB=tan(A+B)(1-tanAtanB)

tanA-tanB=sin(A-B)/cosAcosB=tan(A-B)(1+tanAtanB)

积化和差

sinαsinβ=[cos(α-β)-cos(α+β)]/2

cosαcosβ=[cos(α+β)+cos(α-β)]/2

sinαcosβ=[sin(α+β)+sin(α-β)]/2

cosαsinβ=[sin(α+β)-sin(α-β)]/2

诱导公式

sin(-α)=-sinα

cos(-α)=cosα

tan(—a)=-tanα

sin(π/2-α)=cosα

cos(π/2-α)=sinα

sin(π/2+α)=cosα

cos(π/2+α)=-sinα

sin(π-α)=sinα

cos(π-α)=-cosα

sin(π+α)=-sinα

cos(π+α)=-cosα

tanA=sinA/cosA

tan(π/2+α)=-cotα

tan(π/2-α)=cotα

tan(π-α)=-tanα

tan(π+α)=tanα

诱导公式记背诀窍：奇变偶不变，符号看象限

高三数学知识点总结

1. 对于集合，一定要抓住集合的代表元素，及元素的确定性、互异性、无序性。

2. 中元素各表示什么?

注重借助于数轴和文氏图解集合问题。

空集是一切集合的子集，是一切非空集合的真子集。

3. 注意下列性质：

(3)德摩根定律：

4. 你会用补集思想解决问题吗?(排除法、间接法)

的取值范围。

5. 命题的四种形式及其相互关系是什么?

(互为逆否关系的命题是等价命题。)

原命题与逆否命题同真、同假;逆命题与否命题同真同假。

6. 对映射的概念了解吗?映射f：AB，是否注意到A中元素的任意性和B中与之对应元素的唯一性，哪几种对应能构成映射?

(一对一，多对一，允许B中有元素无原象。)

7. 函数的三要素是什么?如何比较两个函数是否相同?

(定义域、对应法则、值域)

8. 求函数的定义域有哪些常见类型?

9. 如何求复合函数的定义域?

10. 求一个函数的解析式或一个函数的反函数时，注明函数的定义域了吗?

11. 反函数存在的条件是什么?

(一一对应函数)

求反函数的步骤掌握了吗?

(①反解x;②互换x、y;③注明定义域)

12. 反函数的性质有哪些?

①互为反函数的图象关于直线y=x对称;

②保存了原来函数的单调性、奇函数性;

13. 如何用定义证明函数的单调性?

(取值、作差、判正负)

如何判断复合函数的单调性?)

高三英语省略句常见省略现象

省略和替代一样，也是一种避免重复、突出关键词并使上下文紧密连接的手段。为了避免重复,常常省略句子中的一个或几个成分,这样的句子叫省略句。高三英语省略句的几种形式有从句中It is 的省略；从句主语和主句主语一致时的省略；表语的承前省略；动词的省略[英语语法]，下面请看常见的省略现象：

并列结构中的省略现象

第一，并列句中的省略现象

(一)省略主语。如，

She went to the hospital and (she) saw a doctor.七七网

【例】— I was wondering if we could go skiing on the weekend.

—________ good.

A. Sound B. Sounded

C. Sounding D. Sounds

【析】 答案是D。省略了主语It。

(二)省略整个谓语或谓语的主要部分。如，

Either Tom must be responsible for the matter or we will be (responsible for the matter).

【例】 ________ and I'll get the work finished.

A. Have one more hour B. One more hour

C. Given one more hour D. If I have one more hour

【析】答案是B。整个句子相当于If you give me one more hour, I'll get the work finished。

(三)省略谓语中的助动词。如，

Was Jack playing the guitar and (was) Alice preparing the supper?

(四)省略谓语中主要动词。如，

Albert needn't stay, but George must (stay).

(五)省略宾语。如，

John likes smoking, but Mary hates (smoking).

(六)省略主语补足语。如，

George was (interested in the performance), but Jim pretended to be, interested in the performance.

(七)省略状语。如，

Mr Brown teaches (in Cambridge), and his son studies in Cambridge.

第二，名词词组中的省略。如，

This is his latest book; I hope it is not his last(book).

What is the difference between a direct question and an indirect (question)?

Tom's work at school is excellent, Harry's(work) is poor.

第三，介词词组中的省略。如，

Bob is bored with (music), but Peter is interested in it.

主从结构中的省略现象

第一，主句中的省略现象。如，

(I) Hope you will like it.

(It is) No / Small / Little wonder they all loved the boy dearly.

【例】—Brad was Jane's brother.

—________ he reminded me so much of Jane!

A. No doubt B. Above all

C. No wonder D. Of course

【析】 答案是C。前面省略了It is。

第二，状语分句中的省略现象。如，

You must be a member of the club since your brother is (a member of the club).

I am prepared to meet them when (they like) and where they like.

They will be arriving either before (the show begins) or after the show begins.

While (I was) waiting, I was reading some old magazines.

If(it is) carefully done, the experiment will be successful.

The old lady was looking well although(she was) living alone.

【例】 Unless ________ to speak, you should remain silent at the conference.

A. invited B. inviting

C. being invited D. having invited

【析】 答案是A。前面省略了you are。

第三，名词性that-分句中的省略现象。如，

Mary will sing at the party, but I know John won't(sing at the party ).

A: —Will it rain today?

B: —I hope (that it will ) not (rain)

【例】—You haven't lost the ticket, have you?

—________. I know it's not easy to get an other one at the moment.

A. I hope not B. Yes, I have

C. I hope so D. Yes, I'm afraid so

【析】答案是A。相当于I hope I haven't lost my ticket。

第四，名词性wh-分句中的省略现象。如，

Someone has used my bike, but I don't know who(has used it).

The cup was broken by someone, but I wonder by whom (the cup was broken)

I don't know when (to meet him) and where to meet him.

黑边网小编推荐你继续浏览：高三英语倒装句常见结构及用法
高三英语阅读理解解题思路及技巧
福利来了：英语必修1-5全部黑体单词汇总
2016年高考英语寒假复习计划