2020年高考理科数学试卷(全国1卷)(附详细答案)

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1220205231501201.2.2B3.4.2B5.125601z1i,22zz()A0B1CD2z1iz22z=z(z2)=(1i)(i1)=i212=2|z22z|D2A=x|x240B=x|2x+a0A=x|2x1aA-4B-2C2D4A=[-2,2],B=(-2a],AB=[-2,1]2a=1a=2.B3.A.514B.512C.514D.512a,hb,222211154210224bbbabhbaaaa.C.4.AC:y22pxp0AC12y9pA2B3C6D991262pp.C.25.yx20xi,yii12201040yxA.yabxB.yabx2C.yabexDyablnxD6.fxx42x31f1Ay2x1By2x+1C.y2x3Dy2x+1'32'()46,(1)1,(1)2fxxxfkf(1)2(1)yx,21yx.B7.fxcos()6x,fxA.109B.76C.43D.32T-(-)2T,22221242,962kkZ92(2),43kkZ0k3243TC8.25yxxyxx3y3A5B10C15D2022555yyxxyxxyxyxx25yxxyxx3y322234455yxCxyCxyx325yxxyxx3y3245515CC,C90,3cos28cos5sinA.53B.23C.13D.593cos28cos532cos28cos5=03cos+2)(cos2)=0cos=230,2225sin1cos1()33A.10.ABCOO1ABCO14AB=BC=AC=OO1OA64B48C36D32AB=BC=AC=OO1=aO1A=33ar22234123OSraa24rRt?O1OA22216Rar2464SRA.11.M::x2y22x2y20l2xy20PlPMPAPBAB|PM||AB|ABA2xy10B2xy10C2xy10D2xy1022:(1)(1)4MxyM112PAPBMPMAB=CPAAMPMABACAMRtPAMRtACMPAPM1224ACAMPMABAMPAPAPAPM|PM||AB|PAPMlAB//l,22|2112|521PM2AMMCMP225MC45MC41555PCPMMC4AB:2x+y+c=0|2|1155ccAB:2x+y+1=0D12.242log42logababAa2bBa2bCab2Dab22()2logxfxxR+a2b()(2)fafb2222log2log2abab?22422log42log2logabbabb??-?220log2log1bbB452013.xy2201010xyxyyzx7y22010xyxy10xyx+7y=0x+7y=zM10z1+70=1.14.abab|1|ab|22121211,1abaabbabab22221(1)133abaabbab15.F2222:1xyCaba0,b0ACBCBFxAB3C22:33,bbBFxBFaacaBFAFcaAF22332()caccaaeacaa516.P-ABCAC=1AB=AD=3ABACABADCAE30cosFCBRtABC222BCACAB,RtPAB6PBRtPAC222231cos3011PCPAACPC222221261cos22124PCBCPBPCBC7017~212223601712na1a1a2a3(1)an(2)11annan1na1332aaa221112202aaqaqqqq(2)11a1(2)nnbn012211(2)2(2)3(2)(1)(2)(2)nnnSnn?123121(2)2(2)3(2)(1)(2)(2)nnnSnn??-?1211(2)31(2)(2)(2)(2)(2)1(2)nnnnnSnn1[131(2)]9nnSn18(12)DOAEAE=ADABCPDO66PODO(1)PAPBC(2)B-PC-E.(1)1ABC3AD=2,OD=3,OP=22.6AEABCAEBCDOAEOADEBCBCPAPAADERtAOP216122APPB222ABPAPBPAPBDOABCABCDOBCBCPABCPAPBPAPBCPBBCB2,OEODyz.31(,,0)22B31(,,0)22CE(0,1,0)2(0,0,)2PA(0,-1,0)312(,,)222CP,(3,0,0)CB,31(,,0)22CE12(0,1,)2APPBC32APEPC(,,)nabc312302223312022nCPnCPabcabcbnCEnCEabb=13(,1,2)3n103n,APn1125cos531023APnAPnB-PC-E255.191212.123zxy7111111222216245116116181-116-116-18=3418())().1161818116+18+18=516.18+516=7162012ABE2221xyaa1GE8AGGBPx=6PAECPBED1E2CD1(,0),(,0),(0,1)AaBaG8AGGB2(,1)(,1)8183aaaaE2219xy2(6,)Pm:(3),:(3)93mmPAyxPByxm=0CDx0.x0m22(3)919myxxy222327969CCmxmmym22(3)319myxxy2223(1)121DDmxmmym82222222624913273(1)3(3)91CDmmmmmkmmmmm3mCDx32CDxx3(,0)2.2222243(1):[]13(3)1mmmCDyxmmm3m22222433(1)0[]13(3)21mmmmmm22222222433(1)0[]32(1)(1)3313(3)21mmmmmmmmm.CD3(,0)2212()xfxeaxx1a=1fx2x03()12xfx11a2()xfxexx'()2100xfxexx0x'()0fx0x'()0fx()fx002x03()12xfx32112()1xxaxxgxe'12(2)(21)()021,22xxxxagxxaxe12a'()0gx()gx[0max()(0)1gxg12ax[0,2)'()0gx()gx()(0)1gxg1122a9x00,21a)21a(21a,2)2(2,+)'()gx-0+0-()gx12max2747()(2)14aegxgae27142ea12a323111122()()xxxaxxxxgxhxee()1hx()()1gxhxa27,4e10222322[4-4]10xOyC1cossinkkxtyttxC24cos16sin301k=1C12k=4C1C21k=1221:1Cxy12k=42442coscos1sinsinxtxtxyytyt?4cos16sin3041630xy??1xy?2114(1)16302167024yyyyyy14xC1C21144102k=444cossinxtyt4x-16y+3=0444cos16sin30tt2222(2cos4sin)(2cos4sin)30tttt[1cos22(1cos2)][1cos22(1cos2)]30tttt(3cos21)(cos23)30cos2(3cos210)0cos20ttttt24241cos21cos241cos21sin24txttytC1C2114423[4-5]10fx|3x1|2|x1|1yfx2fxfx11fx|3x1|2|x1|13,;31()51,.1;33,1.xxfxxxxx(1)2f1833f(1)4f(2)5fA-1218,33BC14D25BABCCDyfx2yfx1yfx+1375(1)16yxxyxfxfx17|6xxy=f(x+1)

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