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ḕḝ2022᪥ὶὃᦪᔁ▅ᔁ-------------------ஹᓫ⌱⚪ᐳ12⚪ᐳ24ᑖᑖ1.2ᑖ-8ḄA.8B.-8C.-D.--88ூᫀAூ᪆ூᦪḄḄᦪᡠ-8Ḅ8.ᦑᫀ"A.ூᑖ᪆᪷$ᦪḄ"ᐸᦪ&'.2.2ᑖ(7760000ᵨ-./ᦪ0⊤2"A.7.76x105B.7.76x106C.77.6x106D.7.76x107ூᫀBூ᪆ூ7760000Ḅ5ᦪ6ᔣ89:6;<ᑮ7.76,ᡠ7760000ᵨ-./ᦪ0⊤2"7.76x106,ᦑᫀ"B.ூᑖ᪆-./ᦪ0Ḅ⊤2?@"ax1?Ḅ?@ᐸCDEF10,n"ᦪ.IJnḄK⌕MNOᦪPᡂaK5ᦪ69:RST;nḄU5ᦪ69:Ḅ;ᦪV.WOᦪX1KnYᦪZWOᦪḄF1Knᦪ.3.2ᑖ\]3a2/3Ḅ_`A.4a5B.4a6C.3a5D.3a6ூᫀCூ᪆ூ3a2-a3=3a5,ᦑᫀ"C.ூᑖ᪆ᑭᵨᓫ⚗@Uᓫ⚗@eḄ0ᑣ\]ᓽh.4.2ᑖiᑡᔜ@YIḄA.2a2+3a2=5a4B.a2-a=a3
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10AC=V3BC=2V3,AB=2BC,MNBC=2,AB=4,ᓽO#ḄP.17.1ᑖF⁂Rᙠ☟U2ḄᨬᜧXY30km",Z[ᨬᜧXY\]^_X`120kmᡠᵨab,d[ᨬᜧXY⌮_X`60/onᡠᵨabfgᑣ]UḄ_Ykm/h.ூ'ᫀ10ூ᪆ூ'(h]UḄ_Y%km/h,᪷8⚪kG:1206030+x=30^G(x=10,l(x=10mḄ᪷'(]UḄ_YlOkm/n.ᦑ'ᫀ(10.ூᑖ᪆h]UḄ_Yxkm/h,ᑣ^_ḄYo30+xkm/h,⌮_ḄYo30-xkm/h,^_120kmᡠ◤Ḅabq⌮_60kmᡠ◤Ḅabrᯠ᪷8abfgᑡOᓽ.18.1ᑖuvwxyz{4|}ᳫ5|ᳫFᐳ466ᐗᐸ2}ᳫḄᓫᳫḄᓫ4ᐗO}ᳫḄᓫᳫḄᓫ.h}ᳫḄᓫ%ᐗᳫḄᓫyᐗ⚪kᑡy.(4x+5y=466ூ'ᫀIx—y=4ூ᪆ூ'h}ᳫḄᓫxᐗᳫḄᓫyᐗᵫ⚪kG:(4x+5y=466Ix-y=4(4x+5y=466ᦑ'ᫀ:I%-y=4ூᑖ᪆᪷8⚪kᑡyᓽ▅ᔁᐭ—%ஹ&'⚪ᐳ8⚪ᐳ73ᑖᑖ19.10ᑖ(15ᑖ%+y*2-y2x+y425ᑖ+ᓃ+va—2'a—2ூ'ᫀপ:m="+2xy+y2—2xy—y2=x2
11(2)(m=(+)+ᝅ_a23—6a4-9a—2a—2a2—9(a-3)2a-2CL-2(a+3)(a—3)CL—3a+3ூ᪆ூᑖ᪆(1)᪷8ÀᐰÂÃஹᓫ⚗d⚗ḄÆÇÇᑣ[>ᔠgÉ⚗ÇᑣᓄÊᓽ4(2)BËÌ2ḄÍÎ`ÏᑖBËÌᑖḄᑖÍᑭᵨÂÑÃÎ`ᑖᯠ◀ÇᓄÆÇÓÎ`ÔᑖᓽBmÎ`ᓄÊ.20.(8ᑖ)u¥²Ö×5ᨴ1§¨8§2ᓤ12aḄ²³(ᓫØ(")ᳮᑖÙÚᑴᡂᡠḄÝÞ.᪷82ßḄàá'âᑡã⚪(A:()20TB:20r~233CC:ῖ)23+□;(2)(1ᑖ)OᡧJ2ᡧJAḄᙊ;Ḅoᦪ(3)(5ᑖ)£M¤¥5ᨴ1§¨5§Ḅ5ᜩ2ª«¬2ᜩOា¯¬ᑮ2ᜩ2ᓤ12aḄ²³ᙳµ20Ḅᭆ᳛.ூ'ᫀ(1)21421.5(2)135°(3)(hº|ᨴ1§¨5§5ᜩ2ᓤ12aḄ²³»¼Ai,A2,A3,A4,A5,ª«¬2ᜩ2ᓤ12aḄ²³,ᐳᨵ((Ai,A),(Ai,A3),(Ai,A),(Ai,A),(A,A3),2452
12(A2,A4),(A2,A5),(A3,A4),(A3,As),(A4,As)10åægḄÇ.ᐸ22ᓤ12a²³µ20"ḄAi,Ai,A,4Nា¯ᨵ2ᜩ2ᓤ12a²³ᙳµ201Ḅçèᨵ(A"A),(AHA),(A,A)3åægḄ2424Çêëា¯¬ᑮ2ᜩ2ᓤ12a²³ᙳµ20"Ḅᭆ᳛ì.ூ᪆ூ'í((1)5ᨴ1§¨8§2ᓤ12a²³ḄÂᙳᦪ((19+16+27+17+21+22+25+26)+8=21࠷4ᔜᦪᢥ᯿MxᑮᜧḄ^õᑡ(16,17,19,21,22,22,25,26•••2Øᦪ(21ø=215࠷;ᦑÂᙳᦪ21"2Øᦪ21.54(2)êµ20úḄᜩᦪᨵ3ᜩᡠ[ᡧJ2ᡧJAḄᙊ;Ḅoᦪ(360°x|=135°;O'(ᡧJ2ᡧJAḄᙊ;Ḅoᦪ135.ூᑖ᪆(1)✌ᐜ5ᨴ18ᓤ12ᯠ◀8ᙳᦪᔜᦪᢥ᯿ᑮᜧḄ#$ᑡ'()ᦪ*Ḅᙳᦪ+ᦪ,(2)ᑭᵨ12204Ḅᜩᦪ◀6ᜩᦪᯠ7360ᡠᓰᡧ>ᙊ@AḄBᦪ,(3)CD)ᨴ155ᜩᓤ12ḄEFGAiஹA2ஹA3ஹA4ஹAs,ᑡNᡠᨵPḄQRSាUᨵ2ᜩᓤ12ᙳ12204ḄQRᯠᑭᵨᭆ᳛XYZ[\].21.(10ᑖ)bᙠd2ABCAB=AC,DiBCjkḄlmnAD,BEᑖpABCqAC2lE,rlEsEFCBCqAB2lF.(1)(5ᑖ)uvC=36vBADḄBᦪ:(2)(5ᑖ)xpFB=FE.ூzᫀ(1)}ppAB=AC,.•."=4ABC,
13,..□C=36,.,.□ABC=36°,VBD=CD,AB=AC,/.ADDBC,.•.4ADB=90/.□BAD=90°-36°=54°2xppBEᑖDABC,.,.□ABE=CBE=|DABC,VEFDBC,.•.4FEB="BE,.\[IFBE=FEB,FB=FE.ூ}᪆ூᑖ᪆1᪷*jA□C=CABC360,᪷*ῪA>ḄᔠADIZIBC,ᦑE1ADB=9O᪷*AA>Ḅ(┦A]IBADḄBᦪ,2᪷*AᑖḄDABE=^CBE,᪷*[ᑁ┯A4FEB=dCBE,ᦑCFBE=OFEB,᪷*AjFB=FE.22.10ᑖBᎷᨵᵬ¡¢£15'¤¡¢£20'.ᢥ¥ᨵ¦puᐰ¨ᐭªᜩ⃩¬G8500ᐗ,uᵬஹ¤(¡¢£ᙳᨵ10'ᐭªᜩ⃩¬G5000ᐗ.15ᑖᵬஹ¤(¢£¯'¥ᨵ¦ᑖ°i±²ᐗ³25ᑖBᎷ¤¡¢£G´µ¶QR·Ẇ¹¥pu¯)£'¯ᜩᢥ¥ᨵ¦£'ºᐰ¨ª»,¼¯)£'¯ᜩḄ¦¯½¾20ᐗ¿ºᨵ()£'ÀÁ.¢ê£'BᎷ◤¯)£'¯ᜩÅ80ᐗḄᔜÆᵨ.¼¯'£'¦G±²ᐗ¤¡¢£¯ᜩḄᑭÇmᨬᜧᨬᜧᑭÇi±²ᐗ³ூzᫀ1}pCᵬஹ¤(¢£¯'¥ᨵ¦ᑖ°ixᐗஹyᐗ᪷*⚪Êp[]Ox+10y=5O0o'ft?Îfx=300}y=200zpᵬஹ¤(¢£¯'¥ᨵ¦ᑖ°i300ᐗஹ200ᐗ,2}pC¯ᜩḄ¦½¾Ïa)20ᐗᑣᨵ2a)£'ÀÁ,
14᪷*⚪Ñpm=(20-2a)(200+20a-80)=-40a2+160a+2400=-40(a-2)2+2560,V-40<0,...¼a=2mÒᨬᜧÓᨬᜧÓG2560,Ô£'Ḅ¦G200+2x20=240ᐗ.zp¼¯'£'¦G240ᐗ¤¡¢£¯ᜩḄᑭÇmᨬᜧᨬᜧᑭÇi2560ᐗ.ூ}᪆ூᑖ᪆(1)Cᵬஹ¤(¢£¯'¥ᨵ¦ᑖ°ixᐗஹyᐗ᪷*ᐰ¨ᐭªᜩ⃩¬G8500ᐗ15x+20y=8500,᪷*ᵬஹ¤(¡¢£ᙳᨵ10'ᐭªᜩ⃩¬G5000ᐗ10x+10y=5000,ὶÖ}ᓽ,(2)C¯ᜩḄ¦½¾Ïa)20ᐗᑣᨵ2a)£'ÀÁ¤¡¢£ᦪG(20-2a),¯'ḄᑭÇG(200+20a-80),᪷*£'ᦪx¯'ḄᑭÇ=6ᑭÇmØaḄᐵÚYᯠnᔠFÛᦪḄឋÝZ[}z.23.(5ᑖ)bÞß>ABCDḄAACஹBDq2lO,EiOCklmàEB.rlAs/MJLBE,ᚖâGM,AMØBDq2lF.xpOE=OF.ூzᫀxp•••ãj>ABCDiÞß>.Z.BOE=^AOF=90°,OB=OA.ävAM1BE,/.MEA+4MAE=90°=F+^MAE,.Z-MEA=Z.AFO..ABOE=AAOFCAAS).OE=OF.ூ}᪆ூᑖ᪆᪷*Þß>ḄឋÝ□BOEnDAOFngOB=OA,ᑭᵨçAḄA□MEA=DAFO,᪷*“AAS”xEIBOEDெAOF,ᑭᵨᐰA>ḄéjOE=OF.24.(10ᑖ)bᙠ[ãj>ABCDlEᙠjBCkmnAE,EMDAE,ᚖâGE,qCD2lM,AFOBC,ᚖâGF,BHIIAE,ᚖâGH,qAF2lN,lPêADklmà
15CP.(1)(5ᑖ)uDP=2AP=4,CP=V17,CD=5,DACDḄ☢ì.(2)(5ᑖ)uAE=BN,AN=CE,xpAD=V2CM+2CE.ூzᫀ1}psCG4AD2G,b1ᡠí:CPG=x,ᑣDG=4-x,ᙠRtvPGCGC2=CP2-PG2=17-x2,ᙠRtvDGCGC2=CD2-GD2=52-(4-x)2=9+8x-x2,.*.17-x2=9+8x-x2,}px=l,ᓽPG=1,r.GC=4,pDP=2AP=4,AD=6,.,.SDACD=1XADXCG=AX6X4=12,(2)xpmàNE,b2ᡠípVAHAE,AFIBC,AEEM,□AEB+vNBF=□AEB+vEAF=LAEB+□MEC=90°,
16/.[INBF=□EAF=□MEC,ZNBF=^EAFᙠL1NBFEJEAFzSF/V=^EFA,.AE=BN/.□NBFDDEAF(AAS),.\BF=AF,NF=EF,.,.□ABC=45°,□ENF=45°,FC=AF=BF,••.□ANE=DBCD=135°,AD=BC=2AF,(^HEC=/.EAFᙠEZANEvECMAN=EC,ZANE=+ECM.".[IANEOIpECM(ASA),/.CM=NE,ä•.•NF=pNE=¥MC,.•.AF=0MC+EC,2/.AD=V2MC+2EC.ூ}᪆ூᑖ᪆(1)sCGvAD2G,CPG=x,ᑣDG=4-x,ᙠREPGCஹRtDDGCᑭᵨñòᳮxḄÓ᪷*DP=2AP=4ADḄÓᯠ᪷*A>Ḅ☢ìXYZ[\],(2)màNE,᪷*çAḄA□NBF=EZEAF=C]MEC,xINBFDDEAF,ᑮBF=AF,NF=EF,UE^DANEDDECM,ᑮCM=NE,nᔠῪAA>ḄឋÝNF=ôNE=2^MC,ᯠ᪷*AF=AN+NFZ[x.25.(10ᑖ)bABi40ḄõlCG9ḄlCFGvOḄö÷CFtAB,ᚖâGE,màBDqCF2lG,màCD,AD,BF.15ᑖxp4BFG"CDG0(2)(5ᑖ)uAD=BE=2,BFḄø.ூzᫀ1xpimḄl,ACS=CB,
17,ABiᙊ0Ḅõ÷CF!AB,.CB=FB,.CD=FB,ACD=BF,VDFØDCDGᡠḄùúiû•••4F=CDG,ᙠDBFGDCDGZF=Z.CDG+FGB=Z.DGCBF=CD.,.□BFGnnCDG,(2)}pmàOF,CᙊOḄüõGr,ᙠADADBBD2=AB2-AD2=(2r)2-2,2çᳮpEF2=OF2-OE2=r2-(r-2)•CD=CB=▭.BD=CF,BD=CF,2-'-BD2=CF2=(2EF)=4Fᓽ(2r)2—2?=4[M&-2ÿr=l()ᡈr=3,2^BF2=FE2+BE2=32-(3-2)+2?=12BF—2\/3.ூ᪆ூᑖ᪆1᪷Ḅᭆe=᪷ᚖᳮCB=ᑣCS=FB,᪷
18ஹḄᐵCD=BF,ᵫᙊᕜ$ᳮ11F=DCDG,ᯠ&᪷ᐰ()$*Ḅᑨᳮ,-./0212OF,3ᙊ0Ḅ45r,ᙠRttADBஹRPOEF᪷78ᳮ⊤:;BD?ஹEF2,᪷CS=6=ᓽᑗD=6,ᑣBD=CF,BD2=CF2=4EF2,?@;rḄAᯠ&ᑭᵨ78ᳮ,-DEᓽ.26.10ᑖHᙠI☢ᙠ$ᙶ᪗MᱥOy=x2-2x-3PxQRSA,BAᙠBḄTURyQSC,D5MᱥOḄ⚔WXQPxQRSE.15ᑖ1YBD,MZO[BD\]^M_P`B,DaᔠcMdMN1BDRMᱥOSNNᙠWXQḄeUcNdNHHxQᚖf5H,RBDSF,PZO[OC\]^gMNhᨬᜧAk@HF+FP+lCḄᨬmA0ফ5ᑖᙠপgMNhᨬᜧAHF+FP+1/3PChmAkpPᔣ\IrstᓫvᑮQ,1YAQ,pxAOQy{k┐}~]Ḅ$a0°
19.MᱥOy=x2-2x-3PxQRSA,B(AᙠBḄTU)RyQSC..y=0xi=-1,X2=3,X=0,y=-3,?.A(-1,0),B(3,0),C(0,-3)2.D5MᱥOḄ⚔¥__L=_W=1,4aci4x1x(—3)—4-42a24a4x1..DḄᙶ᪗5D(1,-4)OBDḄ᪆5y=2x-6,ᵫ⚪°3N(m,m2-2m-3),ᑣF(m,2m-6)|NF|=(2m-6)-(m2-2m-3)=-m2+4m-3..gm=-¶=2kNFhᑮᨬᜧA?kMNhᑮᨬᜧA?kHF=2,?kN(2,-3),F(2,-2),H(2,0)ᙠxQ\¹]K(]»0),12CK,cFdCKḄᚖORCKSJRyQSP,.,.sinDOCK=1,OKCḄ᪆5y=—2Á]3,¥F(2,-2),...PJ=gPC,OFJḄ᪆5y=¥Ä—ÅI..J(2-Æ,-19-472)AFP+IPCḄᨬmAᓽ5FJḄÊ=ËᢤJ33■\HF+FP+lpC\=^^^min
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21
22á\ᡠâᡠᨵfᩩḄQ'Ḅᙶ᪗5(255,-455),(455,255),(-255,455),(455,-255).ூᑖ᪆(1)᧕A(-1,0),B(3,0),C(0,-3),D(1,-4),ᑭᵨäᦪæ@;OBDḄ᪆3N(m,m2-2m-3),ᑣF(m,2m-6),⊤:;NF,᪷ÛçèᦪḄឋêNFḄᨬᜧAëìWíḄNஹFஹHḄᙶ᪗ᙠxQ\¹]K(-324,0),12CK,cFdCKḄᚖORCKSJRyQSP,᪷)$èᦪḄᭆsin!JOCK=13,@;OKCஹKJḄ᪆ᑮJḄᙶ᪗᧕ÏFP+13PCḄᨬmAᓽ5FJḄÊ?@0(2)ᵫ(1)ÏP(0,]4+22),ᑣQ(0,-2),hAQḄG,12OG,ᑣOG=GQ=12AQ=52,?k□AQO=DGOQ,জG×ᙠyQḄØ4QᑣG(0,-52),cQdQTDxQRxQSI,¥HGOQ=UQᑣ□IOQ'MCJOAQ'MDOAQ,᪷)$èᦪḄᭆIQ,ᑭᵨ78ᳮ@;01,?QḄᙶ᪗0ঝgG×ᙠxQḄï4Q\kðᳮQḄᙶ᪗0ঞgG×ᙠyQḄï4Q\kðᳮQḄᙶ᪗0টgG×ᙠxQḄØ4Q\kðᳮQ'Ḅᙶ᪗.
23⚪ᑖ᪆-ᑖ1ஹᔁ./ᑖ0ᑖ᪆óᑖ103ᑖõö⚪ᓰø25.0(24.3%)ᑖAᑖôùö⚪ᓰø78.0(75.7%)õö⚪ᓰø13(50.0%)⚪úᑖôùö⚪ᓰø13(50.0%)2ஹᔁ⚪1ᑖ0ᑖ᪆ᜧ⚪⚪û⚪üúᓰøᑖAᓰøýþ⚪6(23.1%)6.0(5.8%)⚪8(30.8%)73.0(70.9%)ᓫ⌱⚪12(46.2%)24.0(23.3%)3ஹᔁ234᪀ᑖ᪆᧕ᓰ1(65.4%)2᧕(30.8%)3(3.8%)4ஹᔁ678ᑖ᪆ᑖᓰ⚪1ᙳᦪᐸ8.0(7.8%)20
242!ᐰ#Ḅᑨ&10.0(9.7%)243'30°Ḅ(!2.0(1.9%)124)*+ᦪ,-./ᦪḄᐵ/2.0(1.9%)9)ᐗ2*345Ḅᵨ-89:ᑖ510.0(9.7%)22;⚪6ᐰ#!Ḅᑨ&.ឋ=5.0(4.9%)237ᙊ?ஹAஹBḄᐵ/10.0(9.7%)258ᓫ⚗EFᓫ⚗E2.0(1.9%)39)*+ᦪḄᨬ12.0(11.7%)11,26102ᐗ2*H#E5Ḅᵨ2.0(1.9%)811#Ὺ!Ḅឋ=10.0(9.7%)2112(!Ḅឋ=1.0(1.0%)1613JKLᦪM2⊤OPQᜧḄᦪ2.0(1.9%)214#Ὺ(!10.0(9.7%)2415SᑖE341.0(1.0%)1516EḄUᔠW10.0(9.7%)1917ᚖY&ᳮ11.0(10.7%)16,2518ᭆ᳛]E8.0(7.8%)20
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2636PᨵᳮᦪḄP2.0(1.9%)137!ᐰ#Ḅᑨ&AAS10.0(9.7%)2538ᑖEḄUᔠW10.0(9.7%)1939)*+ᦪḄx▭ᵨ-├{;⚪10.0(9.7%)22403!Ḅឋ=5.0(4.9%)2341ᦪ2.0(1.9%)642ᡧ!,8.0(7.8%)2043!Ḅ☢12.0(11.7%)12,2444]EM.]EMḄᔠWᵨ1.0(1.0%)1445ḄF34.0(3.9%)4.746ᢚ,8.0(7.8%)2047┦+ᦪḄ&10.0(9.7%)26S(!Ḅᵨ-;482.0(1.9%)10⚪
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