高中数学公式大全(最新整理版)

高中数学公式大全（最新整理版）f(x)ax2bxc(a0);k(a0);f(x)a(xh)f(x)a(xx)(xx)(a0)2.12§函数a(,0)f(x)f(xa)yf(x)2f(x)f(xa)yf(x)a若yf(x)yf(x)f(ax)f(ax)xaf(2ax)f(x).abxyf(x)f(amx)f(bmx)2f(abmx)f(mx).yf(x)yf(x)0xabxyyf(mxa)yf(bmx)2myf(x)yf1(x)和yf(x)yf(xa)babf(x,y)0f(xa,yb)0abf(a)bf(b)a.11y[f1(x)b]6、若函数yf(kxb)存在反函数,则其反函数为,并不是k1y[f(x)b]y[f(kxb)y[f(kxb)是11k,f(x)cxf(xy)f(x)f(y),f(1)c.f(x)af(xy)f(x)f(y),f(1)a0.x,f(x)logxa,f(xy)f(x)f(y),f(a)a0,a1).(x)xf(xy)f(x)f(y),f(1)f',.f(x)cosx§数列g(x)sinxf(xy)f()f(y)g(x)g(y)，，n,sn1an1ss,n2a}saaan(n12n)nnn1naa(ndad(nN*2、等差数列的通项公式n(aa)n11(n1)d1snnandn(ad)n1n2222211.aaaqq(nN)nn11n*1qn)aqaaqn,q1q,111ns1q1qsnnna,q1,q1或.11aqad,ab(q0)a:n1n1nb(nd,q1abqndbq()d,q1n1nq1nnbn(nd,(q1)1qnsddb)n,(q1)n1qq11q.§三角函数sinsincos1，tan=cos，22tancot1.n(1)sin,2nsin()2n1(1)cos,2n2(s,n)2n1(,2)sincoscossin;)coscossinsin;)1.)sin()sinsin22.)cos()cossin22)asinbab(,)ab2sin((辅助角所在象限由点2=的象限决basin2sincos.coscossin2cos112sin2222.212.3)33.)333.33))1332.ysin(xy))xT；,xkkZ，Tyx)2.abc2RABC.abcbccosA222;bca2cacosB;222cab2abcosC.222111Sh、h、h2122abc（abc.11SCAB222S1||OB)222.xxyycos1212xyxy(x,y)(x,y)21212222(a=1122=|dA,B(xx)(yy)(,)(,)xyxy2222121112(x,y)(x,y)设a=,b=，且b2112xyxy01221.xxyy0a1212.P(x,y)P(x,y)PPPPPP(,)Pxy设111，222，2121xxx121y1yyOPOPOPt1212OPtOPtOP111（21A(x,y)B(x,y)C(x,y)11、22、33xxxyyyG(1,)3231233.O,B,Ca,b,c设为OOA2OB2OC2为为.OOAOBOC0.为OOAOBOBOCOCOA.为OaOAbOBcOC0.O的aOAbOBcOC.A为§直线和圆的方程yyk21(x,y)P(x,y)xx（P111、22221yyk(xx)P(x,y)lk11111ykxbl在yyyxx11yyxxy2yP(x,y)P(x,y)xx(111、222(2121121xy1abb0)ab(AxByC0l:ykxbl:ykxb111，222l||lkk,bb①②121212;llkk11212.l:AxByC0l:AxByC01111,2222ABCl||l1ABC1112①②；222llAABB0；|AxByC|121212d00P(x,y)AxByC02AB2l：00(xa)(yb)r222.xyDxEyF022DE4F22(cosxarybrsin.(xx)(xx)(yy)(yy)0A(x,y)B(x,y)121211、22AxByC0(xa)(yb)r222dr相离0dr相切0dr相交0.;AaBbCdA2B2.(x,y)DxEyF00x2y20D(xx)E(yy)xxyyF0F000(x,y)2200.当圆外时,00D(xx)E(yy)xxyy002200yyk(xx)00ykykxbxyrxxyyr222P(x,y)2000k00ykxr1k2.§圆锥曲线方程cosxaxy222abybsinab2.xy2a2a22abe(x)e(x)a2b21c2c，.xy2xxyy02ab01P(x,y)a2b200ab.22xy22abP(x,y)a2b200xxyy10a20b2.x2y2abAxByC0A2a2B2b2c2.a2b2xy2aa222aba2b2|e(x)||e(x)|1c2c，.x2y12xy22b0yxa2b2a2b2a.xy0abx2y2byxaba22.x2y22x22y221a2bab（0x0yxy2xxyy02a0,b01P(x,y)a2b2ab2200.xy22a0,ba2b2P(x,y)00xxyy10a20b2.xy22a0,ba2b2双曲线与直线AxByC0相切的条件是AaBbc22222.pxy22pxy2pxp2(0)02ppxxxxp221212.bb2yca(x)22(aaab4bb4b122(,2a)(,)4a2a4a标为；（2）焦点的坐标为；（3）准线方程是4b12y4a.y2pxP(x,y)00yyp(xx)00.2y2px(x,y)00yy(xx)00.2P2px(p0)AxByC0pB2AC.y224VR33SR2．1VSh31Sh柱体（V锥体3Sh（nnxxyyxynxyiiiii1i1bnnxxxnx222iii1i1aybxyabx.§极限111limlim0nxxlimlima0，nn（|a1x0，xx.n0x001sinxx1elimx0§导数1xxxC0(x)nx(nQ)'n1.n(sinxcosx.(cosxsinx.x1a1xex；x.a(ee(aalnaxxxx;.(uv)uv'''..(uv)uvuv'''uu'v'()(v'vv2.u(x)xu(x)yf(u)U''xxyfu)uyyu'xyf(x))''''x在点处有导数，且，则复合函数，或写作uxf(x))fux(()'''.x§复数|z||abi|bzabi==.a22(abi)(cdi)(ac)(bd)i;(abi)(cdi)(ac)(bd)i;(abi)(cdi)(acbd)(bcad)i;(abi)(cdi)i(cc2d2c2d2.zzzz1221.(zz)zz(zz)123123.z(zz)zzzz1231213.d|zz(xx)(yy)zxyizxyi22（111，222122121zabizcdi