高中数学知识点总结(最全版)

-2-1041.512345412111223212223363132333435364104142434445464748494102-3-104:11.11.1.11.2NNNZQR.3aMaMaM.4..{x|x}x.-4-104.5..().1.1.26BA)ABAB(1)AA(2)A(3)BABCAC(4)BABAABA(B)BAABBABABA1AA(2)ABBCACBAABABBA(1)AB(2)BAA(B)7A(1)nn2n21n21n22n.1.1.38AB{|,xxA}xB1AAA2A3ABAABBBAAB{|,xxA}xB1AAA2AA3ABAABBBAUAe{|,}xxUxA1()UAAe2()UAAUe1||(0)xaa{|}xaxa||(0)xaa|xxa}xa()()()UUUABAB()()()UUUABAB-5-104||,||(0)axbcaxbccaxb||xa||(0)xaa224bac0002(0)yaxbxcaO20(0)axbxca21,242bbacxa12)xx122bxxa20(0)axbxca1{|xxx2}xx{|x}2bxaR20(0)axbxca12{|}xxxx1.21.2.11ABfAxB()fxABABfAB:fAB:2,ababaxbx[,]abaxbx(,)abaxbaxbx[,)ab(,]ab,,,xaxaxbxbx[,),(,),(,aabb{|}xaxb(,)abab-6-104ab3()fx()fx()fx1tanyx()2xkkZ()fx()fx[,]ab[()]fgx()agxb4()yfxyx2()()()0ayxbyxcy()0ay,xy2()4()()0byaycy1.2.256ABfAB-7-104ABABfAB:fABAB,aAbBabbaab1.31.3.11Ix1x2,x1x2f(x1)f(x2)f(x)x1x2y=f(X)xyf(x)1f(x)2o1234Ix1x2x1x2f(x1)f(x2)f(x)y=f(X)yxoxx2f(x)f(x)2111234[()]yfgx()ugx()yfu()ugx[()]yfgx()yfu()ugx[()]yfgx()yfu()ugx[()]yfgx()yfu()ugx[()]yfgx2()(0)afxxax()fx(,]a[,)a[,0)a(0,]a3()yfxIM1xI()fxMyxo-8-10420xI0()fxMM()fxmax()fxM()yfxIm1xI()fxm20xI0()fxmm()fxmax()fxm1.3.24f(x)xf(x)=f(x),f(x)12f(x)xf(x)=f(x),f(x)12y()fx0x(0)0fyy10,0,|()()hhhhyfxyfxh|0,0,|()()kkkkyfxyfxk|01,1,()()yfxyfx01,1,()()AAyfxyAfx-9-104()()xyfxyfx()()yyfxyfx()()yfxyfx1()()yxyfxyfx()(||)yyyyfxyfx()|()|xxyfxyfx23()2.12.1.11,,,1nxaaRxRnnNxannannanannanna0n0annananan0a()nnaannnaan(0)||(0)nnaaaaaa2(0,,,mnmnaaamnN1)n0011()()(0,,,mmmnnnaamnNaa1)n03(0,,)rsrsaaaarsR()(0,,)rsrsaaarsR()(0,0,)rrrabababrR2.1.24(0xyaa1)axayyxayy-10-1041a01aR(0,)(0,1)0x1yRR1(0)1(0)1(0)xxxaxaxax1(0)1(0)1(0)xxxaxaxaxaaa2.22.2.11(0,1)xaNaaxaNlogaxNaNlog(0,1,0)xaxNaNaaN2log10alog1aalogbaab3lgN10logNlnNlogeN2.71828e,40,1,0,0aaMNlogloglog()aaaMNMNlogloglogaaaMMNNloglog()naanMMnRlogaNaN-11-104loglog(0,)bnaanMMbnRbloglog(0,1)logbabNNbba2.2.25log(0ayxa1)a1a01a(0,)R(1,0)1x0y(0,)(0,)log0(1)log0(1)log0(01)aaaxxxxxxlog0(1)log0(1)log0(01)aaaxxxxxxaaa(6)()yfxAC()yfxx()xyyC()xyxA()xyxy()xy()yfx1()xfy1()yfx7()yfx1()xfy1()xfy1()yfx8xyO(1,0)1xlogayxxyO(1,0)1xlogayx-12-104()yfx1()yfxyx()yfx1()yfx(,)Pab()yfx'(,)Pba1()yfx()yfx2.31yxx2-13-1043(y)()(0,)(1,1)0[0,)0(0,)xyqp,pqpqZpqqpyxpqqpyxpqqpyx,(0,)yxx101xyx1xyx101xyx1xyx12()(0)fxaxbxca2()()(0)fxaxhka12()()()(0)fxaxxxxa2x()fx32()(0)fxaxbxca,2bxa24(,)24bacbaa0a(,]2ba[,)2ba2bxa2min4()4acbfxa0a(,]2ba[,)2ba2bxa-14-1042max4()4acbfxa2()(0)fxaxbxca240bacx11221212(,0),(,0),||||||MxMxMMxxa420(0)axbxca20(0)axbxca12,xx12xx2()fxaxbxca2bxakx1x2xy1x2x0aOabx20)(kfkxy1x2xOabx2k0a0)(kfx1x2kxy1x2x0aOabx2k0)(kfxy1x2xOabx2k0a0)(kfx1kx2af(k)00)(kfxy1x2x0aOkxy1x2xOk0a0)(kfk1x1x2k2-15-104xy1x2x0aO1k2k0)(1kf0)(2kfabx2xy1x2xO0a1k2k0)(1kf0)(2kfabx2x1x2k1x1x2k2f(k1)f(k2)0f(k1)=0f(k2)=0xy1x2x0aO1k2k0)(1kf0)(2kfxy1x2xO0a1k2k0)(1kf0)(2kfk1x1k2p1x2p252()(0)fxaxbxca[,]pq()fx[,]pqMm01()2xpq0a2bpa()mfp2bpqa()2bmfa2bqa()mfq02bxa()Mfq02bxa()MfpxOf(p)f(q)()2bfaxOf(p)f(q)()2bfaxOf(p)f(q)()2bfaxOf(p)f(q)()2bfa0xxOf(p)f(q)()2bfa0x-16-104()0a()2bpa()Mfp2bpqa()2bMfa2bqa()Mfq02bxa()mfq02bxa()mfp1))((Dxxfy0)(xfx))((Dxxfy2)(xfy0)(xf)(xfyx0)(xf)(xfyx)(xfy3)(xfy10)(xf2)(xfy4)0(2acbxaxy02cbxaxx02cbxaxx02cbxaxx21.1xOf(p)f(q)()2bfaxOf(p)f(q)()2bfaxOf(p)f(q)()2bfa0xxOf(p)f(q)()2bfaxOf(p)f(q)()2bfa0x-17-1041'''''EDCBAABCDE'AD2'''''EDCBAP3'''''EDCBAP4,5,671.212341.2.yxz3.512341.31-18-104PLDCBA232rrlS422RRlrrlS524RS1hSV2hSV313hSSSSV)314334RV2.12.1.112145022ACABCD311ALBL=LAB122ABC=ABC233P==LPL32.1.21222rrlSLACBA-19-10424abcabcb4434a'b'abOO(0)ab2.1.32.1.41123aaa=Aa2.2.2.2.11ab=aab2.2.21abab=Pab2=ac2-20-1041232.2.32.2.41aaab=b2=aab=b2.32.3.11LLLLL,PLp2a)b)2.3.21AlB2-l--AB--21-10432.3.32.3.4123.13.11lx,x,xll.,lx,=0.20180.lx,=90.3:(90),k,k=tan?lx,=0,k=tan0=0;?lx,=90,k.,l,k.4:P1(x1,y1),P2(x2,y2),x1x2,P1P2:k=y2-y1/x2-x13.1.21:k1=k2,L1L221234-22-10422122221PPxxyy3.2.11l),(000yxPk)(00xxkyy2lky),0(bbkxy3.2.21),(),,(222211yxPxxP),(2121yyxxy-y1/y-y2=x-x1/x-x22lxA)0,(ayB),0(b0,0ba3.2.31yx,0CByAxAB023.33.3.11L13x+4y-2=0L12x+y+2=034202220xyxyx=-2y=2L1L2M-223.3.23.3.31),(00yxP0:CByAxl2200BACByAxd21l2l1l01CByAx2l2221BACCd2l02CByAx1l4.1.11222()()xaybrA(a,b),r-23-104200(,)Mxy222()()xaybr12200()()xayb2r22200()()xayb=2r32200()()xayb2r4.1.21022FEyDxyx2(1)x2y20xy(2)DEF(3)4.2.11l0cbyaxC022FEyDxyxr)2,2(EDd1rdlC2rdlC3rdlC4.2.2l121rrl1C2C221rrl1C2C3||21rr21rrl1C2C4||21rrl1C2C5||21rrl1C2C4.2.312-24-1044.3.11M),,(zyxxyzPQRxyz2),,(zyx3M),,(zyxMM),,(zyxxMyMzM4.3.21),,(1111zyxP),,(2222zyxP22122122121)()()(zzyyxxPP31.1.11.2.:(1).(2).(3).(4).OyxMM'RPQOyzxMP1P2NM1N2N1M2H-25-104(5).1.1.21YN123451ABABAB-26-1042PABPABABAB31PAAPAAPA2PPAPA121.2.1112APPAINPUTINPUT-27-104345212343123452=XA=BB=A=12211IFTHENELSE2IFTHEN2IFTHENELSEIFTHENELSE1212IFTHENELSE12ENDIFIFTHEN1ELSE23IFTHENIFTHEN34PRINTDispIFTHEN1ELSE2ENDIF12IFTHENENDIF34-28-104ENDIFIFTHEN123WHILEUNTILWHILEUNTIL1WHILE1WHILE2WHILEWHILEWENDWENDWEND2UNTIL1UNTIL2UNTILLOOPUNTIL1WHILEWENDDOLOOPUNTIL-29-104WHILEUNTIL.99...53121PSintPrEndISS2Step99To3FromI1ForForSSintPrhileEndISS2II97Ihile11WWISSintPrhileEnd2IIISS99Ihile11WWISSintPr)99I(001I2IIISSo11UntilLoopDISSint