2021年高中数学常用结论集锦.pdf
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1、-.-.word.zl.1.德摩根公式();()UUUUUUCABC AC B CABC AC B.2UUABAABBABC BC AUAC BUC ABR3.假设=123,na aaa,那么的子集有2n个,真子集有(2n1)个,非空真子集有(2n2)个4.二次函数的解析式的三种形式一般式2()(0)f xaxbxc a;顶点式2()()(0)f xa xhk a;零点式12()()()(0)f xa xxxxa.三次函数的解析式的三种形式一般式32()(0)f xaxbxcxd a零点式123()()()()(0)f xa xxxxxxa5.设2121,xxbaxx那么1212()()()0
2、 xxf xf x1212()()0(),f xf xf xa bxx在上是增函数;1212()()()0 xxf xf x1212()()0(),f xf xf xa bxx在上是减函数.设函数)(xfy在某个区间内可导,如果0)(xf,那么)(xf为增函数;如果0)(xf,那么)(xf为减函数.6.函数()yf x的图象的对称性:函数()yf x的图象关于直线xa对称()()f axf ax(2)()faxf x函数()yf x的图象关于直2abx对称()()f axf bx()()f a b xf x.函数()yf x的图象关于点(,0)a对称()(2)f xfa x函数()yf x的图
3、象关于点(,)a b对称()2(2)f xbfa x7.两个函数图象的对称性:函数()yf x与函数()yfx的图象关于直线0 x(即y轴)对称.函数()yf mxa与函数()yf bmx的图象关于直线2abxm对称.特殊地:()yf xa与函数()yf ax的图象关于直线xa对称函数()yf x的图象关于直线xa对称的解析式为(2)yfax函数()yf x的图象关于点(,0)a对称的解析式为(2)yfax函数)(xfy和)(1xfy的图象关于直线y=x 对称.8.分数指数幂mnmnaa0,am nN,且1n.1mnmnaa0,am nN,且1n.9.log(0,1,0)baNbaN aaN.
4、logloglogaaaMNMN(0.1,0,0)aaMN|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 1 页,共 10 页-.-.word.zl.logloglogaaaMMNN(0.1,0,0)aaMN10.对数的换底公式logloglogmamNNa.推论loglogmnaanbbm.对数恒等式logaNaN0,1aa11.11,1,2nnnsnassn(数列na的前 n 项的和为12nnsaaa).12.等差数列na的通项公式*11(1)()naanddnad nN;13.等差数列na的变通项公式dmnaamn)(对于等差数列na,假设
5、qpmn,(m,n,p,q为正整数)那么qpmnaaaa。14.假设数列na是等差数列,nS是其前 n 项的和,*Nk,那么kS,kkSS2,kkSS23成等差数列。如下列图所示:kkkkkSSSkkSSkkkaaaaaaaa3232k31221S321其前 n 项和公式1()2nnn aas1(1)2n nnad211()22dnad n.15.数列na是等差数列naknb,数列na是等差数列nS=2AnBn16设数列na是等差数列,奇S是奇数项的和,偶S是偶数项项的和,nS是前 n 项的和,那么有如下性质:1 前 n 项的和偶奇SSSn2 当 n 为偶数时,d2nS奇偶S,其中 d 为公差
6、;3 当 n 为奇数时,那么中偶奇aSS,中奇a21nS,中偶a21nS,11SSnn偶奇,n偶奇偶奇偶奇SSSSSSSn其中中a是等差数列的中间一项。17假设等差数列na的前12n项的和为12nS,等差数列nb的前12n项的和为12nS,那么1212nnnnSSba。18.等比数列na的通项公式1*11()nnnaaa qqnNq;等比数列na的变通项公式mnmnqaa其前 n 项的和公式11(1),11,1nnaqqsqna q或11,11,1nnaa qqqsna q.|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 2 页,共 10 页文档
7、编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5
8、F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8
9、H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2
10、S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1
11、Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD
12、4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6
13、C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3-.-.word.zl.19.对于等比数列na,假设vumn(n,m,u,v 为正整数),那么vumnaaaa也就是:23121nnnaaaaaa。如下图:nnaanaan
14、naaaaaa112,1232120.数列na是等比数列,nS是其前n 项的和,*Nk,那么kS,kkSS2,kkSS23成等比数列。如下列图所示:kkkkkSSSkkSSkkkaaaaaaaa3232k31221S32121.同角三角函数的根本关系式22sincos1,tan=cossin,tan1cot.2211tancos22.正弦、余弦的诱导公式212(1)sin,sin()2(1)s,nnnncon为偶数为奇数212(1)s,s()2(1)sin,nnconncon为偶数为奇数即:奇变偶不变,符号看象限,如cos()cos,sin()sin22sin()sin,cos()cos23.
15、和角与差角公式sin()sincoscossin;cos()coscossinsin;tantantan()1tantan.22sin()sin()sinsin(平方正弦公式);22cos()cos()cossin.sincosab=22sin()ab(辅助角所在象限由点(,)a b的象限决定,tanba).24.二倍角公式sin 2sincos.2222cos2cossin2cos112sin.升幂公式221cos21cos2cos,sin22降幂公式22 tantan21tan.|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 3 页,共 10
16、 页文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码
17、:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1
18、H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5
19、 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2
20、N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z1
21、0 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O
22、10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3-.-.word.zl.25.万能公式:22tansin 21tan,221tancos21tan26.半角公式:sin1costan21cossin27.三函数的
23、周期公式函数sin()yAx,xR 及函数cos()yAx,xR(A,为常数,且A0,0)的周期2T;假设未说明大于0,那么2|T函数tan()yx,,2xkkZ(A,为常数,且A0,0)的周期T.28.sinyx的单调递增区间为2,222kkkZ单调递减区间为32,222kkkZ,对称轴为()2xkkZ,对称中心为,0k()kZ29.cosyx的单调递增区间为2,2kkkZ单调递减区间为2,2kkkZ,对称轴为()xkkZ,对称中心为,02k()kZ30.tanyx的单调递增区间为,22kkkZ,对称中心为(,0)()2kkZ31.正弦定理2sinsinsinabcRABC32.余弦定理22
24、22cosabcbcA;2222cosbcacaB;2222coscababC.33.面积定理 1111222abcSahbhchabchhh、分别表示a、b、c 边上的高.2111sinsinsin222SabCbcAcaB.(3)221(|)()2OABSOAOBOA OB=1tan2OA OB(为,OA OB的夹角)34.三角形内角和定理在 ABC 中,有()222CABABCCAB222()CAB.35.平面两点间的距离公式,A Bd=|ABAB AB222121()()xxyy(A11(,)x y,B22(,)xy).36.向量的平行与垂直设 a=11(,)x y,b=22(,)xy
25、,且 b0,那么abb=a 12210 x yx y.ab(a0)ab=012120 x xy y.37.线段的定比分公式设111(,)P x y,222(,)P xy,(,)P x y是线段12PP的分点,是实数,且12PPPP,那么|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 4 页,共 10 页文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7H3文档编码:CX5F1H1J8H5 HB2S2N2M1Z10 ZD4O10N6C7
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