2022年广东省东莞市中考数学一模试卷（附答案详解）

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2022
ḕᓭᜧ▬ὃᦪᔁ1.ᑡᔜᦪᨬḄ()A.—3B.—2C.0D.32.ᓅ,-ᝍ/᪗1ឋ3✂5678✂“:;<”>12000?@AḄ:☢CᵨᑖᙽGᑴᢈJ,L᪷NOP⚗RᑖSTஹᑖ᪗Vᑴ:W12000ᵨXYᦪZ⊤\]()A.12x103B.1.2x104C.0.12x105D.1.2x1053.ᑡabcdefgeabḄ()D.4.hi4=34°,ᑣi4Ḅ⊡n]()A.56°B.146°C.156°D.166°5.ᑡᔜpqrḄ()A.2a5-3a2=6a10B.(x3)m+(xm)2=xmC.—(ab2)3=—ah6D.(a—b)(~a—b)=—a2—b26.wᑮᜧḄyᦪNz1,1,2,2,6,8,yᦪNḄᦪ?ᙳᦪᑖ()A.2,4B.2,3C.1,4D.1,37.Wᦪy=Q+l)2-2Ḅaᔣ?2ᓫᔣ?3ᓫᑮḄᦪ᪆p()A.y=(x—1)2-5B.y=(x—l)2+1C.y=(x+3)2+1D.y=(x+3)2—58.hᐵxḄᐗ@/+6x—a=0ᨵᦪ᪷ᑣaḄ¡()A.ci<_9B.a>—9C.a>-9D.cz>99.᝞a©ª⌕¬᪥¯3°±ᩚABḄ³´µ¶᝞¯·z(1)ᙠ¹Cᜐ»¼¬n½,¬±ᩚ⚔Ḅ¿ni4CE=aÁ(2)¬n½Ḅ³C஺=aÁ(3)¬n½ᑮ±ᩚḄÃ?ÄÅ஺B=b.ᑭᵨ┦nÈnᦪÉnÈnbḄÊ˱ᩚḄ³L⊤\]()

1A.Q+btanaB.a+bsinaC.a+-^-D.a4—y—tanasina10.᝞aᙠÌbABC஺AB=4,AD=5,EC£Î°¹Ï4EᢚÑÌbBCḄÒÓB'C'ÕÖ¹஺×ØBB',ÙAE,AOᑖÛ¹GஹH,×Ø8஺ÛAE¹Ý.ᑡÞßzজAB'DHâῪÈnb;ঝ=1z3Áঞ8B'?ᑖ44B஺Áট=•ᐸÞßqrᨵêëA.জটB.ঝটC.জঝঞD.জঝট11.ìízêî-2=12.qïÓbḄ᜜n]30஺ᑣñḄᑁn].13.᝞aóÊôõ8M?ᑖi4BC,¹஺8M°¹÷DE஻BCABE,EDB=28°,øù4ECḄᦪ]14.È⚗pᑖúpûᐸúp]x+1,üᑏþÿᩩḄ⚗15.—l,aஹ2,bஹ3,0ᙠᦪ"=$%0Ḅ&'()ᑣaஹbஹc,-ᑮᜧ᣸ᑡ2.16.ᵨ56-789ᢣ;65<9)=>Ḅ?@&AB@&᝞&ᡠE)ᑣ◤⌕Ḅ-7896ᦪᨬIJ.

2?@&B@&17.᝞&)KᱥMy=—/+%+6NxOPAஹ8Q(4ᙠBḄRS))NyOPC,஺2MVACḄW)X2MVAB(;6Y)ZAPD[஺Pᢚ]^ZAPD,ᑣMV4BḄᨬ-_2.4x—6>2(x+l),জ18.abcde3X-6-

320.᝞&)ᙠc¿ZABCW)P24BCᑁ;)Q2AABC᜜;)ÂÃAPஹBPஹAQஹC஺ஹPQ,ᐸWN4BP=NÅCQ,BP=CQ.ᑨÇAPQḄÈ»ÉÊËÌḄÍÎ.21.|ᙢ᩟ÑÒ?ÓdÔ᩟ÕÖᡲᵯᖪÚÛÜÝpÞßà├âãä)¡ãäå├âᵬ¯QæÞßà)¯æÞßàḄᓫèᵬæÞßàᓫèḄ2éI20ᐗ)ᵨ900ᐗëìᵬæÞßàḄᦪíîᵨ1200ᐗëì¯æÞßàḄᦪí½.(1)¼ᵬஹ¯QæÞßàḄ├âᓫè.(2)§|h¡ãäâïᵬஹ¯QæÞßàᐳ100)ñòᜩâïḄᵬæÞßàᦪíbIP¯æÞßàᦪíḄ3é)ôõ¡ãäòᜩ├âöḄᨬᜧ_.22.᝞&)0஺÷ø4BஹC)ñᙊú஺ᙠ஺ABC஺ḄBC¿()AOḄWEûᙠ஺஺(.(1)¼4BḄüᦪ.(2)ÂÃ8D,¼sin¯48஺Ḅ_.23.ᙠýÈABCDW)4D>CD,஺2ACḄW)P2AO(;)ÂÃPD,øPþPE1PDBCஹE,ÂÃ஺E.(1)᝞&(1),PᙠAO(ÿ
NDEPḄᜧᔲᦋᳮᵫ.(2)᝞(2),PB,PB1AC,஺514஺4(7PB=4,DP=276,Ḅ.

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6\⚪ὃ_`"H⊡"Ḅ4F\⚪Ḅᐵbcd⊡Ḅ1"H<180஺.5.ூFᫀ௃Bூ4᪆௃4KA┯¥¦<6a7DBXsDC┯¥,¦<-a3b6DO┯¥¦<-(a?Ob2).ᦑ⌱KB.᦮6Ḅ´ᔠµ¶&K·ᦪ¸@¹·ᦪEᢣᦪ@»D·ᦪ¼@◀·ᦪEᢣᦪ@¾.᪷¿OÀᑣÂÃĶᓽ.\⚪ὃ_᦮6Ḅ´ᔠµ¶.᪷᦮6Ḅµ¶lᑣĶÅÆÇ⚪Eᜧ.6.ூFᫀ௃Bூ4᪆௃4K¿Èᦪ&2CÉḄÊᦪᨬ|ᦑËᦪ2Dᙳᦪ=ix(-1+1+24-2+6+8)=3.6ᦑ⌱KB.᪷ËᦪᙳᦪḄtᓽ:CFᫀ.\⚪ὃ_`ËᦪᙳᦪḄcdᔜÑḄᭆÓ4⚪ᐵb.7.ூFᫀ௃Aூ4᪆௃4KgÔÊÕᦪy=(x+1×-2ḄØᔣÚ{2Wᓫ~ÜÝÞᔣß{3Wᓫ~ÜÝ:ᑮḄÔÊÕᦪ4᪆6y=(x+1-2y-2-3,ᓽy=(x-1)2-5.ᦑ⌱KA.ᢥ᯿“ã»Ú¾7»ß¾”ḄÀåÂæCᓽ.⚪ὃ_`'ᱥ)Ḅ{+'ᱥ)4᪆6ḄᓄÀåKã»Ú¾7»ß¾.8.ூFᫀ௃Cூ4᪆௃4K᪷⚪:4=62-4xlx(-a)>0,4:a>-9.ᦑ⌱KC.᪷OᐗÔÊì᪷Ḅᑨí6Ḅ:ᑮA=62-4x1x(-a)>0,ᯠïCEV6Ḅðᐳòᑖᓽ.\⚪ὃ_`᪷Ḅᑨí6KOᐗÔÊìa-+bx+c=0(a40)Ḅ᪷,d=b2-4acᨵ᝞ßᐵ%K/>0
ìᨵ1WE@VḄ÷ᦪ᪷D21=0
ìᨵ1W@VḄ÷ᦪ᪷D4<0


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8•••AB'=AB=4,AD=5,^AB'D=90°,B'D=7AD2-AB'2=3,■■S^=\AD-B'M=\AB'-B'D,ABIDB'M="";=AD5DM=\lDB'2-B'M2=J32-ḋ2=IBN=AM=AD-DM=5--=—,55VB'N=B'M+MN=^+4=y,BB'=yjB'N2+BN2==ᵫᢚ-.AG1BB',B(=BH=W,AG=y/AB'2-B'G2='((?2=@,•:UGH=B'MH=90°,/LAHG=B'HM,:AAGHSAB'MN,475l.GH_MHDGH=V^x,ᑣM”=3%,B'H=^--V5x,"B'M2+MH2=B'H2,...(£)2+(3%)2=(.EF%)2,x=|(IJK᪷)2V5,8Vs2V56>/5••GH=—,DBuH=---------=——,5555•GH$B'H=1%3,ᦑঝ2347EEPLB'D,5B'DḄMNO67P,ᵫᢚ-.EP=EC,••Z.ADC=90°,•Q4DB'+Z,PDE=(PDE+PED=90°,Z.ADB1=PED,•"B'D=Z.P=90°,AB'D^LDEP,ADBID:.-=--9DEPEDEC=EP=x,ᑣ஺E=4—x,

953*'4-X-X"|.DE=4--=-,22VAB//DE,•)ABFSADEF,.AF_BF_AB_4_8••———u—,EFOFEDI5$.DF=—BD=—>/AB2+AD2=—V41DE,131313♦DEFHZ-DFE,vAB//DE,•Z-BAG=DEF,vZ.BFG=DFE,Z.BAGSZ-BFG>•Z.ABG+Z-BAG=Z-FBG+Z-BFG=90°,••Z.ABGHZ.FBG,BB'TUᑖQ4BD,ᦑঞ┯Y4ZZQJL4D7Q,ᑣFQ//DE,•)AED,FQ_AF"ED-AE9..AF_8AF_8V=—/.=—,EF5AE13lc8…8520•FQ=——EO=—X-=E,71313213cIf1-2050AS=-AD•FQ=-x5x—=E,AAFD2721313ᦑট234ᦑ⌱D.জᵫᢚ-N4BB'=N4B'B,\]ᵫ^_ḄឋaNDB'H=஽WB=4DHB',cᑨef!2Y4ঝ7EEP1B'஺5᜛஺ḄMNO67P,᪷Ḅ☢ijklB'MmAG,\]ᵫnoḄឋapqr]ᑨef!Ḅ2Y4ঞ7EEP1B'஺5᜛஺ḄMNO67P,ᵫnoḄឋalOE5஺Z\]3NB4G5N8FGḄᜧtᐵucᑨef!2Y4টFZQAD7஺v|JFQ஻DE,ᵫxAFQs^AE஺lFQ,\]lx4FDḄ☢icᑨef!2Y.

10f⚪yᔠ⚪zὃ|}ḄឋaஹᢚᣚḄឋaஹᳮஹnoḄᑨ5ឋaஹḄ☢i/.4f⚪yᔠឋᨵE᪀⌼Omno⚪Ḅᐵ.11.ூ#ᫀ௃9ூ᪆௃%k===9.ᦑ#ᫀ%9.᪷K᦮ᦪᢣᦪḄᑣ\ᓽ.f⚪ὃ|ḄK᦮ᦪᢣᦪᓽK᦮ᦪᢣᦪ'/ᦪ¡¢Ḅ2᦮ᦪᢣᦪᗩḄ᎔ᦪ.12.ூ#ᫀ௃1800°ூ᪆௃ூᑖ᪆௃f⚪ὃ|}©ᑁ5᜜©ᑁmᳮ52)•180(7123,°஻᦮ᦪ)4©Ḅ᜜m/360ᐜᑭᵨ©Ḅ᜜m/360p©Ḅᦪᯠ¶᪷©Ḅᑁmjk.ூ#௃%·¸2©Ḅᦪ@=12,ᡠº·¸2©Ḅᑁm(122)x1800=1800°.ᦑ#ᫀ1800஺.13.ூ#ᫀ௃56஺ூ᪆௃W%-DE//BC,EDB=28°,•••Z.EDB=CBD=28",^AED=Q4BC,À%Uᑖ஻BC,Z.ABD=Z.CBD=28",4ABe=/.AED=56°.ᦑ#ᫀ%56஺.ÁUOḄឋaNEDB=4CBD=28஺^AED=Z.ABC,Å᪷UᑖOḄᓽᑮQ4BO=ACBD=28°,ᓽpQ4BC=AAED=56".f⚪Ç⌕ὃ|}UOḄឋaÉÊ⚪ḄᐵËÌ%ÍOUÎÏn/4ÍOUᑁ┯n/.

1114.ூ#ᫀ௃/+4x+3(#ᫀTÐEÑÒ⚪Óᓽ)ூ᪆௃%(%+l)(x+3)=x2+4%+3,4.E¸ÔÕ⚗kᑖ×k¶ᐸÙE¸×kÚ+1,ᑏpE¸ÑÒᩩÞḄÔÕ⚗kt+4x+3(#ᫀTÐEÑÒ⚪Óᓽ).ᦑ#ᫀ%x2+4x+3(#ᫀTÐEÑÒ⚪Óᓽ).᪷×kᑖḄq3pÔÕ⚗kᓽ.ß⚪ὃ|}×kᑖᓝánâ/ºã©⚗kâ©⚗käåËÌ×kᑖḄæf⚪Ḅᐵ.15.ூ#ᫀ௃a0,•.a?@ABC4DEFG=>☢Ḅὃ1.᝞J56KL“ᡭᙢPQRSTUVW”YZ[᧕ᑮᫀ.17.ூᫀ௃5-V10ூa᪆௃acy=0,ᑣ=/+%+6=0,a——2,x=3,22,0),B(3,0),:.OA=2,OB—3,ci=0,ᑣy=6,

12C(6,0),$•OC=6,AC=V22+62=2V10,•••஺ACl•••DA=DC=A/10,•••m4?஺ᵫ44PDnOPᢚpᡠ•••DA=DA',••.A'ᙠ!஺ᙊtPAuvḄᙊwx;y,•.AE=0E=1,DE=3,BE=4,•BD=V32+42=5,.“DA=DA'=V10,BA'=5-V10,ᦑᫀ5—V10.ᐜ᪷}~ᱥa᪆#l4B,Cᙶ᪗-#஺4=2,஺8=3,0C=6,᪷}ᳮ#ACḄ8ᯠ᪷}ᢚḄឋ#4ᙠ!஺ᙊtPAuvḄᙊwx;y0D,A',Bᙠ?x@B4'ᨬ&l>CE14B,ᚖE,ᵫᳮ#஺E,0EḄᯠᵫᳮ#BD,-#.⚪ὃ1C~ᱥxḄlᢚᣚஹᳮ!)¡ᨬ&¢£¤¥ᐵ§¨᪷}~ᱥḄឋ#A,B,CḄᙶ᪗.

1318.ூᫀ௃aᵫজx>4,ᵫঝx<6,ᡠ!«¬£Ḅa®4

14(AB=AC\^ABP=ACQ,(8P=CQ••mABPìmACQ(SAS).•AP—AQZ1=z2,fvzl4-z3=60°,:.z2+z3=60°.íIJ4PAQ=60°.••.m4PQ¨£çè*.ூa᪆௃ᵫ4ABC¨£çè*4B=AC,ABAC=60°,ᑭᵨSAS,ᓽ#^ABPdACQ,ᓽ4P=AQ,N1=N2,ᔠ£çè*ḄឋNP4Q=60஺ᓽ#mAPQ¨£çè*.⚪⌕ὃ1Cᐰ£è*Ḅᑨឋ£Ὺè*Ḅឋ)£çè*Ḅᑨ)ឋa⚪Ḅᐵ§¨#mABP^^ACQ.21.ூᫀ௃a(1)óᵬÐôõöḄ├øᓫúxᐗᑣÈÐôõöḄ├øᓫú(2x-20)ᐗa%=30,ûüýx=30¨¹7Ḅaþßᔠ⚪æᑣ2x-20=2x30-20=40,ᵬÐôõöḄ├øᓫú30ᐗᑣÈÐôõöḄ├øᓫú40ᐗ(2)óÿ
ᵬᐳᑣᐳ(100—6)├yᐗᵫ⚪y=30m+40x(100—m)=-10m+4000,m>3(100—m),m>75,ymḄᜧ.,.#7Wᨬ%yᨬᜧ.•.#m=75%yḄᨬᜧ'=-10x75+4000=3250(ᐗ)*
#ᜩ├Ḅᨬᜧ'3250ᐗ.ூ᪆௃(1)0ᵬḄ├ᓫ2xᐗᑣḄ├ᓫ2(2x-20)ᐗᵫ⚪ᵨ900ᐗ45ᵬḄᦪ78ᵨ1200ᐗ45Ḅᦪ79:.ᑡᑖ=>?>?ᓽAB(2)0C
ᵬᐳDᑣᐳ(100-6)├yᐗᵫ⚪y=30m+40x(100-m)=-10m+4000,m>3(100—m),ᑣTH275,EᵫFGHᦪḄឋJ*ᓽA.

15K⚪ὃMNᑖ=>?ḄOᵨஹFᐗFGQR=ḄOᵨSTFGHᦪḄOᵨB⚪ḄᐵVWX1YZR7ᐵ[\]ᑡᑖ=>?BX2Yᦪ7ᐵ[\]ᑡFᐗFGQR=.•••^_`ABCCab^_`$.AD//BC,AD=BC,•••EḄcd$.AE=-AD,21••OB=±BC,2AE=OB,••^_`ABOEWab^_`•AB=OE,•,OA=OB=OE,••OA=OB-AB,•f/OBR_gh`:./.ABC=60°B(2)id஺kDM1B4lm4ḄnopqdM,•:AD//BC,Z.MAD=Z.ABC=60°,0AM=a,

16ᙠRtAWcAD=-^-=^=2a,8s60஺1MD=AM-tan60°=s•AD=CB=2a,$•AB=OB=-BC=a,2•.BM=4B+AM=2a,$.BD=>JBM2+DM2=J(2a)2+(V3a)2=a,•/(DCDMV3aV21•s

17Z-ABD=—=-p--——,BDy[7a7sin/ABDḄ't.ூ᪆௃(1)uvOA,OE,᪷xab^_`ḄឋJAZD஻BC,AD=BC,E᪷xpzcdḄ{|STR7}ᣚA4E=0B,A^_`ABOEWab^_`ᯠᑭᵨab^_`ḄឋJAtM=0B=AB,AAaOBR_gh`ᓽA*B(2)idZ)kDM_LB4lBAḄnopqdM,᪷xabpḄឋJA4M4D=60஺,ᯠ0AM=a,ᙠRtAAMDcᑭᵨ┦hghHᦪḄ{|A4஺=2a,DM=V3a,ACB=2a,AAB=a,BM=2a,ᨬᙠcᑭᵨ{ᳮBOḄoᑭᵨ┦hghHᦪḄ{|bᓽA*.K⚪ὃMNgh`Ḅ᜜vᙊ8᜜ab^_`ḄឋJhgh`᪷x⚪Ḅᩩᔠ`D〉#ḄpW⚪ḄᐵV.23.ூ*ᫀ௃(1)Qᳮᵫ᝞:,,^_`ABCDW`Z-DCE=90°,•,PEPD,•NDPE=90°,AC,D,P,E^dᐳᙊ••Z.DEP=ACD,4OEPḄᜧQᦋB(2)vDE1AC,•Z.PHE=PHD=90°,$LDEP+EPH=90°,4DPH+4EPH=90஺(DEP=DPH,vZ.DEP=Z-ACD,

18;DPH=cACD,ACD=DP=2V6,-BPLAC,48PC=90°=4WC,¢F
BCP=ACB,•)BPCsுABC,PB_BC•*,—,BAAC0AD=BC=x,ᑣ4c=y/AB2+BC2,AB=CD=DP=2V6,AC=7x2+24,.4_X"2V6F+24'x=4V3,¤¥¦x=4§W>?Ḅ᪷ூ᪆௃X1᪷xNDCE=NDPE=90஺AC,D,P,E^dᐳᙊANDEP=44CDB
2᪷x:hḄ¨h9RANDPH=41C஺ᑣCD=DP=2©Eᑭᵨª«h9R¬4BPCS&ABC,®=¯04D=BC=x,ᑣAC=^°O±Z}ᐭ>?ᓽA.K⚪W^_`³ᔠ⚪´⌕ὃMN`ḄឋJ9¶gh`Ḅᑨ{8ឋJRῪgh`Ḅᑨ{,¬C,D,P,E^dᐳᙊW⚪ḄᐵV.24.ூ*ᫀ௃X1p'=3X%+1=1º+»8x¼lqdO,8y¼lqdE,•••d஺
-1,0,S0½¾••¿ᱥpy=2x2+bx+c8y¼lqdC,•C
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