高中數(shù)學(xué)會(huì)考知識(shí)點(diǎn)總結(jié)

數(shù)學(xué)復(fù)習(xí)要點(diǎn)1數(shù)學(xué)學(xué)業(yè)水平復(fù)習(xí)提綱第一章集合與簡(jiǎn)易邏輯{。，aA或a；NZ。AA叫BA，ABA,AAB,BCAB,BA則B；ACAA是BBAAB；,AAB,BCAC；AACA{x|xU,且x}；UACA，ACAU，C（CAA；UUUUABAB{x|xA且x}A,AABBBAAAB{x|xA或x}ABA,AAABBABA2000=b2yyy2OxxxOObxc0(a0)ax2121212b{|,}}R2a12ax2bxc0(a0)12ax2bxc0(a0)bb；22ac0|xa的解集是{x|xa,x}|xa的解集是{x|ax}，0|bcbc,bc|bccbc，|x3||2x1|2（p或p且；否互p或p且逆互否為逆互否若q則p若p則q3（p則；q則；p則；q則；（（若若若pqp叫qpqp叫qpqp叫q第二章函數(shù)fABa,bBabb叫aa叫bBA，BBABxaxbxa]axbxa）axbaxb或xaa；100y2|3x|③、偶次根式：被開(kāi)方式0y25x210ylog)xay0.2|x|1ylog(3xx[324yx4x,x)2，y222xxxy2x12sinxy2sinxy3f(x2f(x2x）x12x11f(x)x,求）2xx2f(xx2x）12f(x)f(x)）xDx,xxx1f(x)f(x)f(x)為D12212若xxf(x)f(x)f(x)為D1212Df(x)yf[h(x)]yf(x)yf(x)yf(x)yf(x)和11yf(x)xf(y)、x,yyf(x)yf(x)111yf(x)yf(x)1yxyxyf(x)yf(x)1n（nnN*a的na(a0)aa|annaannnnna(a0)51mmnaaanmnman0001abr,sQaaa,(a)a,(ab)abaarsrsrsrrr，r；raN(a0,alogNbbaN，baaNlog10loga1，aaMlog(MN)logMlogN，loglogMlogN，Naaaaaa1logMnlogMlogMlogMn，n，naaaaylogxa且a1（（）axyyyyxOO1111axOxOx++++性質(zhì)xxaax1圖定點(diǎn)log1a）0）a6xyaylogxyxxa第三章數(shù)列N（{an項(xiàng)a與nna=nnnn1(na=(n1；a2nn（{aaannn11{a：a1a1，{aan1nnn1a1(n（n；nSaaaaa1n123nnSS(n2)nn12d（aa(ndnadn11n(aa)n(n（n．SndSn11n22n（a，AbAa與bAab或2Aab22（aaadann1nna2aaaann1nn2n（anammnnmdaa(nm)dnm7mpqaaaa。annnmpqaa1na,a,a,,aaa,,n123n2n1aaaaaa1n2n13n2a2an1N*SSSSS，a是等差數(shù)列，Sn項(xiàng)的和，k，nnk2kk3k2kS3kaaaaaaaa123kk12k2k1SS3kSkSS2kk3k2kaSSSnn奇偶nnnSSS奇，當(dāng)nSddS偶偶奇2nn1n1當(dāng)n，Sa，Sa中SS奇偶中奇2中偶2中aSbnnS2n1S'n12n12n1S'a。n2n1n2n1b2qq0（aaqq）an11n1na,(q1qn)（n]Saaqa,(q1n1n1q1q1qn)1q○2aaq(q(qSnSn1n1q○3當(dāng)q1Sn10（a與bGa，G，bGa與bGbGabG2aGab（aan1(0)aqqnanna2n1aaanann2n（anammn，nm8qaaqnmnmanmuvaaaannmuvaa1na,a,a,,aaa,,123n2n1aaaaaan1n2n13n2a2an1n，S，Snnkk3kS2kaSkN*S2kSS3kaaaaaaaa123kk12k2k1SS3kSkSS2kk3k2k（nn(n1123n135(2nn123nn(nn，2，222226(235)(235)(235)12n1234(nn1111126(nn1111122334nn112x3x2n1第四章三角函數(shù)|360,kZ}k1180180()5718'y）l||r（r11lr||rrxy022S2220x9yyy_yyr_sinsec+_++++rxxryxxOxxOxcscO___+rysin90costan304560342001006120101233123301331——sincossin1tancot1sincsc1tancot22coscot1cossin122seccsc1cossec1221sin1cos12；2cos1sin22，；22，cossin2cossin2cos22222tancot，cottan2cot②③sincossinsincossin(sincos)12sincos1sin，1sin|sincos|2k360)sink360)cosk360)tan10)sinsin()sinsin(360)sin)costan(360)tan)cos)coscos()cos)tan)tantan()tan)cos222))sin)222)cot)tan()cot)tan(2222：)sin：)sin：cos(a)sinSS()()cos(a)sinC：：C()()tantan：)T())T1tantan1tan()tan)tan)T()AB45B)2cosxabsinxbcosxabsinxa22a2b2a2b2abxxsin)abx)2222bab，(,)tana）sin2sincosS：2C：cos2cossin22221cos211212sin2cos1sin222222tan1tancoscos2：T21tan22221cos2|sin|，1cos2|cos|；11112|sin|2||，222221212；4422；442112121211cossin，，221sin1cosx=T，=-=ykZ）xRT,2k22k2k,222xR(2k,22,(2kytanxk,k{x|xk}222yxyx2222y1220xy21xo2222y1220x212；；yxkxyAx)T；yx,0x；yAx)T212ytanxk,0)yAxT；2Ax)(A0)y1yAx)xRxATfTyAsin(xysinx)當(dāng)A1時(shí)，圖象上各點(diǎn)的縱坐標(biāo)伸長(zhǎng)到原來(lái)的A倍ysinx01yAsinx當(dāng)AA倍1時(shí)，圖象上各點(diǎn)的縱坐標(biāo)縮短到原來(lái)的1當(dāng)倍011sinxysinxy當(dāng)倍當(dāng)0時(shí)，圖象上的各點(diǎn)向左平移個(gè)單位倍當(dāng)0時(shí)，圖象上的各點(diǎn)向右平移||ysinxysin(x)個(gè)單位倍當(dāng)0時(shí)，圖象上的各點(diǎn)向左平移個(gè)單位倍AsinxyAx)y當(dāng)0時(shí)，圖象上的各點(diǎn)向右平移||個(gè)單位倍常：ysinx0時(shí)0時(shí)||到y(tǒng)sin(x)；1yx)101x)y；x)A10A1AyAx)yAx)yy(x)]Ax)Axx當(dāng)x13xarcsina0a1（））x,22xarccosa（1a0）aa0））xxaaR（xa）x（x,22yAxBy2sin(3x)5yxx，12yasinxbcosxabsin(x)22y4sinx3cosxyx2xyxxxx第五章、平面向量001aea；|a|a//b0abbbabaababbaaa的積是一個(gè)向量，記作：a；②：它的長(zhǎng)度：|a|||a|；14000，aa，aa0a；=e,ea12ee；,a121122,e,{eee1212abba,abcabc,a00aaax,y,bx,yabxx,yy11221212.設(shè)xABxx,yy11222121x,yaxyxy,,設(shè)a，babab0,0,00a0.a00，a|a與b在a|b|cosax,y,bx,yabxxyy；11221212xy|a|a|a：|a|aa2x2y222xxyyx,y,bx,ycosabab0a12121122x12y2x2y2122a//bab(R)設(shè)ax,y,bx,ya//bxyxy011221221abab0設(shè)ax,y,bx,yabxxyy011221212Ax,y,Bx,y|AB(xx)(yy)2211221212|PP|PPP，1PP））P）1211122212||215121212yy2122''111SabsinCacsinBbcsinA22)cos2，cos()cot22222abcabcAabc22222222222222232222acb222222222ab,c0acbc若c0acbcabcd0；ynnnn2、（1）2abab2ab(或2xa16,a,a,a(n2)na，123naaanaaan12nn12nnab0ab,ab0abaa1(b0)ab(b0)b1(b0)ab(b0),b,;,;，，，，0>x>25、絕對(duì)值不等式：|a||b||ab||a||b||a||b||ab||a||b|（|23||25||32||25|3225|8fxxxxxxxf（|x2||x3|x2||3x|x23x5①、范圍：[0)xx0xx90ok，(,)k2當(dāng)k0時(shí),arctank；當(dāng)k當(dāng)k0時(shí),arctank當(dāng)kyyP(x,yP(x,y)k21111222xx21171PP(xx,yy或PP(xx,yy)，k）12211212xx211221k)PP12k)或PP12：yyk(xx)；11xx：；yb：yy11yyxx2121（）：xy1abABC：0CkB），yB//lkk且bbll1AABBCCl時(shí)，；1212121212122kk11ll；AA1BB10ll2122212AxByC0;kAABB（k1121Ax1112ByC0.2222f(x,y)01f(x,y)02k：tankkk11kk0211kk21221kkk1kk0(0,]tank21212121kk21Cd00A2B2CCd21BA22、2C0><（(x,y)、C18C，，C(xa)(yb)rC(a,b)r2224F）DE)2D2E2x2yDxEyF02()2(yx2241E4F0(DED22E24F,)D2222xarxrcos（ybrsinsinyr上(xa)(yb)r，外內(nèi)0222AxByC0和圓xa()()ybr222rdrdr；與ddr20BxCAx，()()xa2yb2r2000Rtx2yr22M(x,y)xxyyr20000xx）019FL）FFL的FL的線L的距離之比為常數(shù)y22px(p0)xy2xy2ab2ab2yyy0xx0xFFFF圓錐曲線的幾何性質(zhì)曲線橢圓雙曲線拋物線yyy圖象0x0x0xFFFFF1212p焦點(diǎn)頂點(diǎn)22222x軸caceea22cb漸近線yxa20x22y21x2y20y2x2yxyxbab2a2b2b2a2baabayxy2xxy0222x2y2yxbab2a2a2b2a2b2ca、b、cc；eeeaae與a、b、ce1b2e1b2）a2a2直線方程聯(lián)立Δ圓錐曲線方程l1kxxkxx)4xx]y）222121212111|yy|yy)4yy]x）2k212k21212y2x2y2px(,)x22py(,)x在y22p2p.lBA21aPPlPl且)、aAααaααl,m,且lml//l//,l,ml//mβlmα22PPP在PADOABEaCabb0ababR）（，（PPaBOPOAtatABttOB或a（At1OPOAOB)1當(dāng)2PO2abpabpxaybx,yR，與，（）xMAyMBxMAyMB或PyOBzOCxyz1且PCOabcp、、23xaybzc，{a，b，ca、b、c使p{p|pxaybzc,,y,z}。a、b、cxb|a||b|a,ba|a：|a|aaa2aeababe|a|a,e，a0(a,a,a),bb,b,b)za123123an0n(,y,z)。0bny、i,j,k}x21212，ij10i）j）ki，j，k0，ik，jk0，、空間向量的坐標(biāo)運(yùn)算：設(shè)a(a,a,a)bb,b,b)，123123）ab(ab,ab,ab)）ab((ab,ab,ab)；112233112233(,,)(,,)R）aaaaaaa（123123aa1bba,,）∥babababa23112233b312a）abab0ababab0．112233babababa·b|ab＜a，b＞112233∴a·b=ababab＝aaa212223·bbb＜a，b＞212223112233ababab＜a，b112233a21a22a23b21b22b23當(dāng)a與b1a與b．A(x,y,z)B(x,y,z)(,,)，，xxyyzz111222212121ABd(xx)(yy)(zz)222AB211212241xxyyzz)(＝,,)2A、BM121212222coscoscos；12OB020201A20C2020a、bO作a∥，∥，與'ab'ba'b'(0,]與a．b2coscoscos12nPPA|OP,)|On2BAO|cosOP,AP||cosn,AP||nPA||n||PA|BOA25ln和n，12An,nn,n則或)1212BnO‘||n,n|12=|n||n|，1212|nn|A則12l|nn|12OPBA‘|nn|12l|nn|12nAOPAP，|nPA||nPA|d|PO||PA|sin|PA|P|n||PA||n