高中數(shù)學(xué)88個(gè)常用公式及結(jié)論總結(jié)

AxCAxCAxAAA1:x,.U2U21n21a,a,,a}2nn12n22有3nfff(x)axbxc(a0);2(x)a(xh)k(a0)(,)hk2(x)a(xx)(xx)(a0)(x,0),(x,0)x1212（f(x)a(xx)(d(a0)ykxd20x045n個(gè)n1nxn個(gè)p或q且pq或xxp且q6互否互互否為逆為逆互否否(1)、pqP是qq是ppqqP是qppqpP是qppqP是q7y隨xx,xD,且xxxD1221f(x)f(x)xDD121y隨xx,xD,且xxxD1221f(x)f(x)xDD21+=+==↓↓↑↑↑↑↑↓↓↓↑↓x,xa,b,xx1212f(x)f(x)(xx)f(x)f(x)0120f(x在a,bxx121212f(x)f(x)(xx)f(x)f(x)010f(x在a,b2xx121212yf(x)f(x)0f(x)f(x)0f(x)8f(x)f(xf(x)f(x)0，則0和0相同R.f(x)f(x)y0和0相反yy9TT是）2=-；2mn；1(3)、f(xm)。f(x)yyyyy=logxk<0k>0oxoxo1x1y=kx+b+bx+coxabf(x)(xRf(xa)fbx)恒成立,則函數(shù)f(x)xy;兩2bayf(xa)yfbx)x與2mana（a0,,1mnNnnm11ma0,m,nNn1（anmanamn(a)a.nna,a0a|nannaaa,a0.nnn(a0,a1,N0)NbaNb.a1apa0a(a)）；(3)、a01(1)、ap；（mnmnmam(4)、araa(a0,r,sQ)；(5)、an；srsn(1)、ya(a1)xya(0a1)）xMNM(1)、logMlogNlog(MN)；Naaaaaa3nbmbmb；(5)、log10(3)、bnmaaaaamloga1b(6)、；(7)、alogaba(1)、ylogx(a1)aylogx(0a1)）alogx0a,x或a,x)(3)、a(4)、logx0a則x)或a則xaN:N010,mN01(a,ammaamN010(aa,NalogNanbb010(aa,NnmmaaMlog(MN)logMlogN;MN;NaaaaaanMnM(nR);NN(,mR)。nnmaaaamppxyy0N(1p).x）aa(nddnaan11naa(nk)dnk）aSS(n2)nnn1n(aa)前n）S）Snaa1n21nnn(nd2nnn1）S）SSa(n2)n1naaa12naaaa；mnpqa是a,a2aaapmnpmnp4ba、bannnn,SS,SSaSnSnm2mm3m2mnq,ap,則a0；apqpqn(n2）a）aaqq(nN)anqn11n*q1n1aaqnknk）aSS(n2)nnn1前n）S）SSa(n2)nnn1naaa12n(q(q1）Sqn)an11qaaaa；mnpqa是a,aaaap2mnpmnpba、bannnnab(1b)n)x元a元,nb(1b)1n（x)sinxxtanx.2)xx.12若x2|sinx||cosx1.sinsincos1tan：22，=，cossin()sincoscossincos()coscossinsin;;5tantan().1tanasinbcossin()=ab22ba(,)ab2sinsincos.121tan2cos2cossin2cos112sin2222.1tan221212.1212122222sin(x)cos()x，x∈R(A,ω,A≠0)的周期y，x∈Ryytan(x)，xTk,kZT.||2||yy11-π/23π/2oπx-2π-3π/2π/2-ππx-π2π-2π-3π/2oπ/2-/2π3π/22π-1-1abc2R為ABC：ABCa2Rsin,b2RsinB,c2RsinC::sin:sin:sinabcCABabcbccosA;bcacacosB;cab2abcosC.222222222111SSS（h、h、h222abcabc111CAB.2221||OB)22.22Sa－cr,r斜邊內(nèi)切圓abc：直角內(nèi)切圓2()ABCCABCABC2(AB).222aa;aaa;6a+b)=λab.a與ba·bab|cos。a=a=(x,y),b=,b=(x,y)a+b=(xx,yy)..11221212(x,y)(x,y)a-b=(xx,yy)11221212(x,y)(x,y)(,)ABOBOAxxyy.A1122a=2121(x,y),R(x,y).a=a=(x,y),b=(x,y)·b=.a(xxyy)11221212abxxyy(,)(,)(a=xy,b=xy1212|a||b|yxy1122x21222221|ABABAB(xx)(yy)(x,y)(x,y)=22dA,B21211122a=(x,y),b=(x,y)b01122baxyxy0ab1221xxyy0a·bab(a0)1212(x,y)P(x,y)(,)，PxyPP,P，11122212xxx12PPPP12y112yy121OPtOP)tOP（t112A(x,y)B(x,y)C(x,y)、、112233xxxyyyG(,).31233123,B,Ca,b,c設(shè)O為ABCO為ABC222.O為ABCO為ABCO為ABC0..0.O為ABCA的.a,bRab2ab22aba,bR2bcabc(a0,b0,c0).a333ababab.72aba2b2ab22x,y2pxxyyxyp；1s2.sxy4a,b,x,yR1axby1111byax(axby)()abab2ab(ab)2。xyxyxyab1xya,b,x,yRabxy(xy)()abab2(ab)xyxy2bxc0(或0)(a0,b4ac0)與axbxcax2a22bxca與ax2xxx(xx)(xx)0(xx)；121212xx,或xx(xx)(xx)0(xx).1021212xaxaaxa.22xaxaxa或xa.22：yyk(x,y)P(x,y)、.（P12xx11122221（yyyk(xx)lP(x,y)k．11l在y111kxbyyxx(yyPxy、Pxy(xxyy(,)(,),11yyxx1211122212122121(xx)(yy)(yy)(xx)0211211xy(1ba、b0)abAxByC0BAxByC0(,)(,)ABlBAlkk||.(lykxb，lykxb,::1)21kk1kk1112221221ABAB||:0:0,AABB0.(lAxByC,lAxByC21221AABB111122212121212lll與l.122128l到l12kk:ykxbl:ykxb.(l，,kk1)12211kk11122221ABAB.(lAx:ByC0l:AxByC0,AABB,01221AABB1111222212121212lll到l.12212|C|(,)lAxByC0點(diǎn)Pxy：：d00AB2002x2(xa)(yb)r.222yDxEyF0DE4F(222xar.ybrxx)(xx)(yyyy)0x,y)x,y)、12121122P(x,y)(xa)(yb)r22200(ax)by)dr點(diǎn)Pdr點(diǎn)P若d2200dr點(diǎn)PAxByC0()()xaybr222AaBbC(dA2B2dr0;dr0;dr0.dOr，OO121212drr;12drr;12rrdrr相交條公切線;內(nèi)含內(nèi)切相交外切相離1212drr內(nèi)切條公切線;do12ddd0drr內(nèi)含無(wú)公切線r+r12.r-r2112xaxy2cba222abe1yb.，a2b2aab22)p。cc2b2.axy22ab0)a2b2Faa22e(x)a，e(x)a；Sc|yb21。21c2c12P9xy2x202y2022ab1PP(x,y)..00a2b2abxy2x2y2022(x,y)1ab0200a2b2abxy2xxyy02ab(,)Pxy01.a2b200ab22xy2xxyy21(,)1.Pxy0a202200b2xy22ab0)AxByC0AaBbc.22222a2b2xy2cba22a2c2a0,b0)e1a2b2ab2c2b2.)paaa22|e(x)|a||e(x)|a|，，1c2cFSb。212F12x2y102xy22byx.a2b2a2b2axyx22y.2byx0abab2ax22y12x22y2ab2ab2（0x0y。bxy2xxyy021(a0,b(,)Pxy01.a2b200ab22xy2xxyy021(,)Pxy01.a2b200a2AaBbc.b2xy221AxByC022222a2b2y22pxpy22px(p0)x.20ppxxxxp.22121210bacb2aybxca(x)(a0)22ab4bb4b122(,)(,)；2a4a2a4a4b12y.4a(xx)(yy)221212kxx)4xx]|xx|1|yy|1t2或22221211212yb(x,yB(x,y)20消去yaxbxcAF(x,y)01122,0k|xx(xx)4xx2.121212:（（（.:（（（（（（設(shè)a＝(a,a,a)，b＝(b,b,b)123123(ab,ab,ab)a＋b＝；；112233(ab,ab,ab)a－b＝112233(a,a,a)a＝123ababa·b＝ab11；2233ababab設(shè)a＝(a,a,a)，b＝(b,b,b)abcos,.112233123123aaabbb212223221232：|CDn|d(ln，,lDl,ldl,l為是|n|121212點(diǎn)B|ABn|d（nA，是.|n|4R2．R3VS311,6aa61663a的a的a34434NNmmm.12nmmm.12nn！(n(nm=nm1.，mn：A=nm*(nm！nnnm2m！n！AnmnAm*NmnC=m==(n，mnmC=C1.C+C=CCm1mnmmmn10nnnnn(ab)CaCabCabCabCbT;n0n1n12n22rnrrnnnnnnn(r2，n).Cabrnrrr1nf(x)(b)aaxaxaxn2n012naaaaf(1)；aaa(af(af(0)；。n012n012n0n12n·AAn12n12n12nnkP(k)CP(1P).kknknnxPxPxP1122nnE(b)aE)b.（2）若～B(,p)np.1(k)g(k,p)qp若P.k1p22DxEpxEpxEp21122nn標(biāo)準(zhǔn)差：=.；baDDa(,)npp)～Bnp.q.(k)g(k,p)qp若Pk1(3)p2