2022-2023学年山东省济南市中考数学专项突破仿真模拟试题（一模二模）含解析

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2022-2023
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72022-2023
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39A.60°B.45°C.30°D.20°ூ567ᫀ௃Cூᑖ᪆௃ᵫOB=BC,OA=OB,?@ᑣNBOCḄAᦪᯠDᵫᙊᕜ?Fᳮ/BACḄAᦪ.ூHI௃•.,OB=BC=OC,/.?@.".ZBOC=60°...᪷KLMᡠOᙊᕜ?#ᙊP?QḄឋSNBAC=gZBOC=30°ᦑ⌱C.T⚪ὃUVᙊᕜ?FᳮW,=>?@ḄᑨFWឋSYZ[\ឋSWFᳮ#I⚪Ḅᐵ^.5._`aᵯcḄᵯdeFfgᵨaᵯchᵯiIjᓫlAmᵯnRjᓫlQ#opqrᦪᐵstḄ"u᝞"ᡠv.ᑣᵨᵯnR⊤vᵯiIḄrᦪ⊤xyejz{I/A02>3,63TrA./=—B.1------C./=——LRRRூ567ᫀ௃DூHI௃|I᪆ye1=}ᑣᨵk=IRᵫ"`R=2h1=3,ᡠk=6,R040⚓/355⚓

40ᡠI᪆yei=g,Rᦑ⌱D.6.᝞"ᙠ5@48'#⌮h┐?஻ᑮḄভmAOᑣ?஺Ḅᜧ{ejzA.30"B.60°C.90°D.120°ூ567ᫀ௃Cூᑖ᪆௃᝞"'%AABBQAABBḄᚖᑖe஺Oᓽe.'%OA,OBSNAOAᓽe?.ூHI௃I᝞"'%AATBB',AA\BBḄᚖᑖeO,Oᓽe.'%OA,OB'NAOAᓽe?.♦.?e90஺ᦑ⌱C.ὃUVḄឋSI⚪Ḅᐵ^#᪷K⚪6FḄ`Aᜧ.041⚓/355⚓

417.ᑡ4x4Ḅ5@{5@Ḅ=ᙳe1,>?@Ḅ⚔¢ᙠ£ᑣmaABC¤¥Ḅ>?@ᡠᙠḄ"@#jz[567ᫀ௃BூHI௃᪷K§¨FᳮAB=722+22=2V2BC=412+AC=J]2+32=©,ᡠaABCḄ>=«peJ52ஹᔊ710=12Aஹ>?@Ḅ>=ᑖ®e2,-^I232=V10-VS2+32=3V2M>=«pe2A/10!3&=5:+?3,ᦑT⌱⚗┯²Bஹ>?@Ḅ>=ᑖ®e2,4,^22+42=2V5>=«pe2425/5=12³ᦑT⌱⚗56042⚓/355⚓

42Cஹ>?@Ḅ>=ᑖ®e2,3,´©µ2=D>=«pe23V13>ᦑT⌱⚗┯²;Dஹ>?@Ḅ>=ᑖ®e·^¹=³V22+32=V13-4,>=«peᮞ{4,ᦑT⌱⚗┯².ᦑ⌱B.8.ᑴ⌼¾@¿⍝hÁÂ⌕ᐜᢥÆ“ÈA"Êᧇ.Ì"#¾@¿⍝ᐸ/஺=/஺=90஺,ḄÎᩩMḄQТ#1000mm,ÑÒ@¿⍝ḄÈAÓe(ÕK3.14)()C.6140mmD.457mmூ567ᫀ௃C90x3.14x1000ூHI௃ᵫ⚪•ᩩMḄAe:--------------------=1570(mm),180*,•ÎᩩMḄAe3140mm.ÑÒ@¿⍝ḄÈAÓe3140+3000=6140(mm).ᦑ⌱C.9.ᙠLᙶ᪗sÚᱥyi=-x?+4xÜy?=2xḄ"u᝞"ᡠvÝÞ,y-x?+4x>2xḄIà#()B.02D.x<0ᡈx>2ூ567ᫀ௃B043⚓/355⚓

43ூHI௃ᵫ"`Úᱥyi=-x2+4xḄ"uᙠyz=2xḄ"u£ãᑖᡠOḄxḄÕfå#02xḄIà#0

44>a=3.ᦑ5ᫀ3.ὃ᪷@AᦪḄᐵA.12.D.EஹFஹGᑖHI3cmஹ2cmஹ1cmḄE(JKᙽMᡂ.ᙊOJKᙽᑣPᙊOJKᙽḄQ☢SS(cm2)@Gh(cm)TUḄVᦪᐵAWI.ூ345ᫀ௃-hூ௃7⚪ᑖ᪆᪷Y⚪Z[>KᙽḄJS=3x2x1=60?,ᑣᙊOJḄJS=sh=6a„3,ᑣ6s=.hὃ]^_VᦪḄ`ᵨ13.᝞cGI0.8deᳫᑮcḄ)hijI3d"kᙠᡭcᳫ⌕oᳫាqrᡭsctuាqᙠjc4dḄᙢwxᑣᳫyeᳫḄGhhId.=-41#31i~ூ345ᫀ௃1.4ூᑖ᪆௃᪷Yz{|}~ᡂ^_ᑡWᓽ[>.ூ௃ᵫ⚪Z>,‘=4+3h>h=14ᦑ5ᫀI1.4.⚪ὃz{|}~Ḅ`ᵨឋᳮ⚪Ḅᐵ.14.᝞ᙊ0ḄᚖC஺ᚖE,4=22.5°,0C=4,ḄEI:45⚓/<55⚓

45cTZ7ூ345ᫀ௃4ூᑖ᪆௃᪷Yᙊᕜ}ᳮ>N8OC=2/4=45஺ᵫ஺஺ḄN3ᚖCD᪷Yᚖᳮ>CE=0E,t[ᑨ©ªOCEI«Ὺ}|}~ᡠ®CE=YZOC=20ᯠ²ᑭ2ᵨC0=2CE´µ.ூ௃•••44=22.5°ZBOC=2ZA=45°OOḄᚖCD.CE=DEªOCEI«Ὺ}|}~.CE=—OC=2y[22:.CD=2CE=4Bᦑ5ᫀ4\¹⚪ὃᚖᳮᚖḄºᑖ»ᩩ½tºᑖᡠḄ¾ᩩ¿.Àὃ«Ὺ}|}~ḄឋÁᙊᕜ}ᳮ.15.ÃᦪPq,ᡃÇᵨÈÉmin{p,q}⊤ÑPq¾ᦪÒÓ"Ḅᦪ᝞min{l,2}=l,ÕÖmin×VI,Ú}=ÛÜmin{(x-l)2,x2}=1,ᑣ*=.ூ345ᫀ௃জ.-V3ঝ.2ᡈ:46⚓/<55⚓

46ூ௃7⚪ᑖ᪆ᵫ-᩹<75,ᡠ®min{75_4}=_å.fx2=l>᳝=1ç%^=-1Ûx—l
2è=2,x,=0ç%.ὃéêÃᦪᜧ"Ḅ^Óᐗì().|ஹ5⚪ᐳ64ᑖ%16.x2-2x-15=0.íWî%ூ345ᫀ௃xi=5,X2=-3.ூᑖ᪆௃᪷YíWîḄïðᓽ[ᜐᳮᡂ.ூ௃Vx2-2x-15=0,,b=-2,c=-15..b2-4QC=4+60=64>0..2±V64..x=----.2/.xi=5,x?=-3.⚪ὃíWîᐗì()òᐗì()Ḅó᪷íWᐵ.17.᝞Z^ABCÒDᙠABxôNACD=NABC,ÜAC=GAD=1,óDBḄE.Aூ௃7⚪ᑖ᪆᪷YZACD=NABC,ZAíᐳ}>õªACDs^ABC,öᑭᵨz{Z|}~Ḅឋ>õABḄE÷øóõDBḄE.7⚪᪆:47⚓/<55⚓

47VZACD=ZABC,ùZA=ZA,AAABC^AACD,.ADAC**AC-AB';AC=5AD=1,.1_V3♦♦ὡ=û’Û.AB=3,/.BD=AB-AD=3-1=2ý⚪ì⌕ὃz{|}~Ḅᑨ®þz{|}~Ḅឋᑭᵨz{|}~ḄឋóõABḄE⚪ᐵ.18..ᙊ~ÿḄᑖᱏ᝞ᡠᑭᵨᑮᙊ஺.⌕ᑏᶇ!"#ூ%&'ᫀ௃*+᪆.ூ-+௃.⚪ᑖ᪆✌ᐜᙠᙊᕜ456789AஹBஹC,ᯠ<=>AC?AB,ᑖ@AC?ABḄAᚖCDᩩAᚖCḄF9GHᙊ..⚪+᪆+᝞9஺ᓽJᡠ.K48⚓/N55⚓

48B19.ᙠRSTUJ4,B,C,஺Ḅᓱᱏ◀TU᜜ᐸ\]ᐰ_`#Ḅ%☢ᑖ@ᑏ4᝞ᡠ%᦮ᦪ0#»45¡ox9¼PJᙊPOJ½¾Ḅᙊ¿xÀF9Aஹ¿yÀF9B,=>AB.K49⚓/N55⚓

491#ÄPJCÅABḄA9;
2AAOBḄ☢Æ.ூ%&'ᫀ௃
1ÄÇ*+᪆¢2SAAOB=24.ூ-+௃.⚪ᑖ᪆1#ᑭᵨᙊᕜ®ÈᳮḄÊËÌ~ABH஺PḄ¾ᓽ|¢
2✌ᐜᎷÎ9Pᙶ᪗Jm,n
m>0,n>0,Ì~OA=2OM=2m,OB=2ON=2n,ÏÐᑭᵨ7®☢ÆÑÒ~ᓽ|..⚪+᪆1ÄÇ•.•/AOB=90஺ÓNAOBH஺PAÔABᡠÕḄᙊᕜ®,AABHGPḄ¾.
2Ö9PPM_LxÀ9M,PN_LyÀ9N,Î9Pᙶ᪗J(m,n)(m>0,n>0),Ø9PH`µ¶·ᦪy=Ùx>0»4o9,x/.mn=12.ᑣOM=m,ON=n.ᵫᚖ¾Èᳮ|9MJ0AA99NJ0BA9,¢.OA=2OM=2m,OB=2ON=2n,•'•SAOB=yBO*OA=Yx2nx2m=2mn=2xl2=24.AK50⚓/N55⚓

50ὃ9`µ¶·ᦪÝᔠ⚪.21.ß4ABCAZACB=9(T,EᙠAB4¼AEJ¾Ḅ஺0¿BC_ᑗD,¿AC_FF,=>AD.(1)ÄAD¬ᑖNBAC¢(2)=>0C,᝞NB=3(T,CF=1,OCḄà.ூ%&'ᫀ௃(1)ÄÇ*+᪆¢(2)'ூᑖ᪆௃(1)=>0D,ᵫOD=OA,|ÌN1=N2,qᵫBCJ஺0ḄᑗC᪷âᑗCḄឋä|Ì/ODB=90஺åNC=90஺ᡠ¼/ODB=/C,ᓽ|ᑨÈOD//AC,᪷â¬çCḄឋä|ÌN3=N2,ᡠ¼N1=N3,ᓽ|ᑨÈADHNBACḄ¬ᑖC¢(2)=>DF,ßNB=30஺|ÌZBAC=60஺qᵫADHNBACḄ¬ᑖC|ÌN3=30஺,ßBCH0OḄᑗC᪷âÔᑗ®Èᳮ|ÌNFDC=N3=30஺ᡠ¼CD=0Cff,èᳮ|ÌAC=VJCD=3,ᡠ¼AF=2,Ö஺OG_LAFG,ᵫᚖ¾Èᳮ|ÌGF=gAF=1,RéODCGHêᡠ¼CG=2,OG=CD=6ᵫÈᳮ|Ì0C=ë.ூ-+௃+(1)ÄÇ=>OD,OD=OA,BCJ஺OḄᑗC.,.ZODB=90°,VZC=90°,.,.ZODB=ZC,.•.OD//AC,.,.Z3=Z2,¢.N1=N3,¢.ADHNBACḄ¬ᑖC¢(2)+=>DF,K51⚓/N55⚓

51VZB=30°,ZBAC=60°,VADHNBACḄ¬ᑖCN3=30஺¢BCH00ḄᑗC.".ZFDC=Z3=30°,:.CD=GCF=5¢.AC=6CD=3,¢.AF=2,ÖOOG_LAFG,¢.GF=AF=1,RéODCGHê.CG=2,0G=CD=5¢•OC=^OG2+CG2=D■22.íîᱥCLy=ax2+bx+c
a,b,cHðᦪabc/O¿CIyÀ4Ḅèo9ÓîᱥCLḄ⚔9ᙠCI4ᑣòzîᱥCL¿CIᐹᨵ"”ᐵ±÷ÓøCIùúîᱥCLḄ“ûC”,îᱥCLùúCIḄ“üC
1í"ûCTḄ⊤þÒJy=2x-4,ÿḄ""LḄ⚔Ḅᙶ᪗-1,"”LḄ⊤;
2᝞ᱥy=mx2-2mx+m-1y=nx+lᐹᨵ“"ᐵm,nḄ32Ḅ""L!Ḅ""Tᙠy%&Ḅ'A.()P""L&Ḅ*+Pᙊ-Ḅᙊ“"T.ᑗ0A12PḄᙶ᪗.452⚓/755⚓

523-2-1--J-----1-----------------1--------1--------L»x-2-1O123-1-917ூ:;<ᫀ௃(1)""LḄ⊤y=2x?+4x-4(2)m=2,n=-2(3)PḄᙶ᪗----.48ூ@A௃B⚪ᑖ᪆F(1)ᵫ“"/”Ḅ⊤Fy=2x-4IJ“"/”y%'0(0,-4)Kx=-lLᐭy=2x-4IJy=-6,ᵫNIJ“L”Ḅ⚔ᙶ᪗(-1,-6),“L”O(0,-4)ᓽIJ“L”ḄA᪆(2)ᵫy=mx?-2mx+m-IJ"L”Ḅ⚔ᙶ᪗(1,-1),y%'0(0,m-1),KQRSḄᙶ᪗LᐭTnx+1ᓽIJmஹnḄ(3)᝞Vᵫ(2)I)W“L”Ḅ⚔B,ᑣBᙶ᪗(1,-1),OBYBC_Ly%0C,Z[PA\]^'x%0D,ᵫ஺P“"”/.ᑗ0AIJPD_L/0A,ᵫN`RtAAOD^RtABCAᓽIJDḄᙶ᪗AḄᙶ᪗ᓽIJADḄA᪆y=yx+l,ᵫADḄA᪆a“L”ḄA᪆bᡂdebAdebᓽIJPḄᙶ᪗.B⚪A᪆F((1)•.•“”LḄ⚔ᙶ᪗g-1,h!Ḅ“"”/Ḅ⊤y=2x-4.*.y=2x(-1)-4=-6,i“”LḄ⚔ᙶ᪗(-1,-6).LḄ⊤y=a(x+1)2-6,•.•“"”y=2x-4y%Ḅ'ᙶ᪗(0,-4).)”Lk(0,-4),l(0,-4)LᐭLḄ⊤AJa=2”LḄ⊤y=2(x+1)2-6=2x2+4x-4(2)•.•y=nx+ly%Ḅ'ᙶ᪗(0,1),453⚓/755⚓

53ᱥy=mx2-2mx+m-1y%Ḅ'ᙶ᪗k0,1
,AJm=2,•ᱥ⊤y=2x?-4x+l,ᐸ⚔ᙶ᪗1,-1
\y=nx+l1,-1
,AJn=-23
᝞V“L”Ḅ⚔B,ᑣBᙶ᪗1,-1
,OBYBCy%0C,AZBCA=90°,o••Aᙶ᪗0,1
,AAO=1,BC=1,AC=2.••“"”/gAஹBḄh஺P“"”/.ᑗ0A,Z[PA'x%0D,APA1AB,NDAB=NAOD=90஺.ZADO+ZDAO=90°,XVZDAO+ZBAC=90°,.,.ZADO=ZBAC,••RtAAOD=RtABCA,OD=AC=2,.Dᙶ᪗-2,0
.•.DஹAḄ⊤y=yx+l,:Py=yx+1ᱥLFy=2x2-4x+lḄ',9y=2x2-4x+1x.=0Adeb:1,JFீτ1ᓽAtuv,y=—x+1wx=l172y2~~o917...pḄᙶ᪗y1
.454⚓/755⚓

54zFA{⚪43|⚪Ḅᐵ}gFY2᝞VᡠḄ᪀⌼ᐰJDḄᙶ᪗,IJDAḄA᪆Q᪵ᵫPgDAa“L”Ḅ'ᓽIJPḄᙶ᪗y.455⚓/755⚓