2022-2023学年湖南省长沙市中考数学专项提升仿真模拟试题（一模二模）含解析

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2022-2023
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18(2)93000x—=450(¢).60Lá.“᤬º»¼”ᐳᨵ450¢;(3)ã᪛ìSTᵬVWX/N/1\/T\/4\VWXᵬWXᵬVXᵬVW•.•ᐳᨵ12åj9ÆḄÇÈាÊ⌱ÍÎஹÏxÐËÑḄÇÈᦪ2,2I(ាÊ⌱ÍÎஹÏxÐËÑḄᭆ᳛=æ⚪ὃCḄJᩩ´µ.ᡧ´µ.ஹᵨᑡ⊤ᡈÁ᪛Ã7ᭆ᳛.ᑡ⊤ᡈÁ᪛Ã9§ëᨵmìëᨵ⍡îḄᑡᡠᨵ9ÆḄÇÈᑡ⊤〉ᔠðxᡂḄ᪛Ã〉ᔠxᡈx§ᡂḄñÀᭆ᳛=ᡠ7ÒÓᦪ©ÒÓᦪòª.21.(1)7073m(2)^=80^111ூᑖ᪆௃DF(1)QELN8ðE,ᵫ⚪À¬ZADE=30°,AD=\40,ᑭᵨcos4DE=?WX7ADᓽ9;LᫀN11⚓ᐳ47⚓

19DFr-(2)QFL8CðEᵫ⚪À¬tan/OW===J5,ôõ´8öᵨJ÷´/ᑖ-7Ḅøqᓽ9.(1)᝞DE_LABðE,.•ZED=90஺,ᵫ⚪À¬/ù஺£=30஺,/஺=140,DE•/cosZ.ADE------,ADᓽcos30°=^=—,2140¬DE=70*,ᡠ§o஺ᑮḄ{|70Gü;(2)+DFLBC,F,tan/.DCF==-f=-=ᵫ⚪À¬CFýTNDEB=NEBF=NDFB=90°,..ôõ´8EDEJ÷´DF=BE=AB-AE,BF=DE=706LᫀN12⚓ᐳ47⚓

20ᙠRt/XADEÍAE=>JAD2-DE2=70-vAB=\W,:.DF=BE=3Q,CF-.BC=BF+CF=80/,ᡠ§᝛ÿḄ8c80.⚪ὃḄᵨᳮ⚪!"#$%&'ᵨᦪḄ)*+⚪Ḅᐵ-.22.(1)4⛲5Ḅᓫ740ᐗ8⛲5Ḅᓫ715ᐗ.(2)ᨵ;:জ>?A@A⛲523CB@A⛲577C;ঝ>?A@A⛲524CB@A⛲576C;ঞ>?N@A⛲525C8@A⛲575C.ூᑖ᪆௃(1)J/⛲5Ḅᓫ7xᐗᑣ8Ḅᓫ7(x—25)ᐗ᪷P>?Q,8S;@AḄTUU⛲5ḄVWXYZX>?48S;@A⛲5Ḅᦪ[ᵫ>?8;Ḅᦪ[+/;Ḅ3]^_ᩩCabcdeᓽX.(2)J>?/⛲5Ḅᦪ[C>?8⛲5Ḅᦪ[(100-h)Cᵫ⚪abiᨵjklemḄnoqr᪷Pms᦮ᦪu>?48S;@A⛲5Ḅᦪ[ᓽXvw>?.পJ/⛲5Ḅᓫ7xᐗᑣ8Ḅᓫ7(x-25)ᐗᵫ⚪Xw:8001700-800X3=,wx=40xx-25z{|x=40+}cdḄ,ᑣx-25=15~/⛲5Ḅᓫ740ᐗ8⛲5Ḅᓫ715ᐗ.~ᫀ13⚓ᐳ47⚓

21(2)J>?/⛲5Ḅᦪ[஻Cᑣ>?8⛲5Ḅᦪ[(100-5)Cᵫ⚪w:j40x0.8xm>720}40x0.8xw+15x0.8x(100-w)<170C'w22.5425,•.•ms᦮ᦪḄo23,24,25,,ᨵ;জ>?A@A⛲523CB@A⛲577Cঝ>?A@A⛲524CB@A⛲576Cঞ>?A@A⛲525CB@A⛲575C.⚪ὃᑭᵨᑖkcdiᨵjkl▭⚪᪷P⚪ᑮᦪ[ᐵᑡᑖkcdiᨵjkl+⚪ᐵ-.23.(1)25°(2)᪆ব10ூᑖ᪆௃(1)ᵫᙊᕜuᳮXw(2)NOCF=90஺ᵫᑗḄᑨuXw(3)JBC=4x,CF=5xᵫ¢£uᳮw(4x*+(5x-6)¤(5xA,e¥3,¦xFBgAFCA,ᵫ§Ḅឋ©w=ªe/F,/EḄ«¦¬/EOsacEB,w®FCCA¯ᑣXw~ᫀ.(1)1C+°ZABC=90%VZA=40°f.ZACB=50°,~ᫀ14⚓ᐳ47⚓

22••$஺+±Ḅ²$••AD=BD.NDCB=ZJCD=-ZJC5=-x50°=25°22(2)•ZC+஺஺Ḅ°N48C=90஺/BEC+NBCE=90஺,■:FC=FE,.NFCE=NFEC,ᵫ(1)X"N8CE=N4CE,•ZFCE+ZACE=90°f.ZOCF=90°,YOC+஺஺Ḅ³°CT+OOḄᑗ(3)4ᙠµ¬¶஺²BE=6,sin//=w.BC_4·JBC=4x,CF=5x,*BC2+BF2=CF2,.(4x)2+(5x-6)2=(5x)2,3x=3ᡈx(¹º)4:.BC=T2,CF=15,BF=9,*NCBF=/ACF=9஺஺,ZF=ZF,:.4FBCsAFCA,.FBBC••FC~CA'.3_12,•»_¼஺=20,~ᫀ15⚓ᐳ47⚓

23OA=—AC=102⚪½⌕ὃᑗḄᑨuஹᙊᕜuᳮஹjῪḄឋ©ஹ¢£uᳮஹ§ḄᑨuÁឋ©j"#!ᑗḄᑨuᙊᕜuᳮ+⚪Ḅᐵ-.24.(1)Âᙠ(0,-1)(2)%=_4ᡈÅ=8(3)a>ÈᡈaW-gூᑖ᪆௃(1)᪷PËÌÍ$ḄuÎXw$/(2,1)ḄËÌÍ$ḄÏᙶ᪗T,Óy=TÕᐭ᜛=x-leᓽX(2)ᵫ⚪w$8ḄÏᙶ᪗-1,J8(m,-1),ᑖS;ÙÚÛk>0ÝÛx<0Ý᪷P¬/OBḄ☢â3,ᑭᵨ☢âḄãe஻ḄoÕᐭä®åᦪ᪆kᓽXe(3)æy=7,ᓽ3a=-1,JSç$Ḅèᙶ᪗ᑖé4ê᪷P᪷ÁᦪḄᐵwë+í2=-*=2,ïð=3᪷P^Sç$ñòḄiᨵóô6,ᑖS;ÙÚaaÛ஺>0ÝÛ”<0ÝᑖéeaḄqᓽX.(1)Âᙠᳮᵫ᝞÷ᵫËÌÍ$ḄuÎXw$/(2,1)ḄËÌÍ$ḄÏᙶ᪗-1,Óy=-lÕᐭy=x-lw-1=x-l,wx=0,$4ḄË$(0,-1);(2)ᵫ⚪w$8ḄÏᙶ᪗-1,J®-1),Ûø>0Ýᑖéô$/ஹ8ù4W_Lxûù8N_LyûAMஹBN5,ஹM,~ᫀ16⚓ᐳ47⚓

24-S^AQB=S-BM~S6)BN~Sü/MNOBP^x(l+l)x(2-m)-yxlx(-w)-lx(2+l)x2=3,wm=—8,•B(-8,-l),Õᐭä®åᦪy=8k=8,XÛø0Ýᑖéô$4ஹ8ùûý$/ù8N_Lyûý$N,S^AOB=Sþ-S&AOM~^OBNᓽ;x(l+l)x(2+/%)-xlx2-mxl=3,w=4,•3(4,-1),~ᫀ17⚓ᐳ47⚓

25kÕᐭä®åᦪy=£,
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aḄac`“^ᡈe⚪gZhiᦪ-klmiᦪḄᔠo⚪p⌕ὃsZhiᦪḄឋuklmiᦪḄvwxឋuyz{Ḅ☢}᪷-ᦪḄᐵᭆḄᳮR-ᵨVᳮR⚪,ᵨᑖgR⚪Ḅᐵ.ᫀ18⚓ᐳ47⚓

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¡NOBF=ZOAG,᪷tanNOBF=tanZ0/1G=—=/"+1,=-----,AD5]+15m+1□+1ᵨÁ⊤°¡GW=-8G=\
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¡cw==ᵨÈ5/n+l5m+\5/M+I5m+1¡µ¶ᓽ«.(1)RÉজ,88GJ_NC,᝞vᡠ°ÉL•:AB=y[5,ZBC=2AB=2OAC=\lAB2+BC2=J(Ì+(2Í=5ᫀ19⚓ᐳ47⚓

27*/S5BC=34cxBG=ABxBC,:.5BG=&2P,R
ÉBG=2,♦:BE1ED,EDLAD,BGVAC,.ZE=ZEDG=/BGD=90°,¨©{BEDGª{.CE=BG=2PD1ঝ;ᙠRtÏ¿஺C®tanC=—=\CD2.CD=2PD,•PD2+CD2=PC\ᓽ(CQ)+CD2=X2,R
ÉCD=xᡈCD=R^~^~x(ÐÑ)55VZE=ZPDC=90°,ABPE=Z.CPD,•bBPEs'CPD,.BEBP♦PRT'.,BP=2y/5-x,y_2A/5-x••2A/5xf--x5R
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28AG=dAB2-BG?=1:BP=mPC,BP+PC=2U,.mPC+PC=2V,R
ÉPC=^~,m+101tanZC=—,2PD1\=",ᓽCQ=2P஺CD2PD'+CD2=PC2,PD2+Ô2P£
222R
ÉPO='ᡈ¿஺=——JÔÐÑÕ,]+1m+l4ACD=——m+l,ZC=5,45m+1AD=5-CD=5---------=--------,Á+1m+\V^BFO=zlAGO=90°,NBOF=ZAOG,\BOF^\AOG,•/OBF=ZOAG,2PDm+12/.tanZOBF=tanZOJG=-----=AD5஻?+15m+1m+12tanZGSM=—=BG5m+l24AGM=-------BG=5஻?+l5m+145m+5AM=AG+GM=U--------5]+15□+1.CM=AC-AM=5-᝞×20m5m+15/71+15m+5AM_5Á+[]+1MC—20஻?4m5m+1ᫀ21⚓ᐳ47⚓

29e⚪p⌕ὃsÙRÚzyz{ª{Ḅᑨ¤xឋuyz{U²Ḅᑨ¤xឋuyziᦪḄ¤Ü¡ÝÞ!ᑗiᦪḄ¤Ü¡/08¿ḄᑗᵨÁ⊤°¡xCM,gR⚪Ḅᐵ.ᫀ22⚓ᐳ47⚓

302022-2023
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36ᦪd
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378ஹ12Âᦪy=ax24-bx+c(a>0).(1)¹2=Æb=c=-2,gÇÈax?+bx+c=0Ḅ᪷ḄᑨªḄ7+(2)᝞fᡠ$NÂᦪḄfdxA(XIL0),B(X2,0),mXI<0

38qᫀஹᓫ⌱⚪s1⚪qᫀ(AÕ(+a±2Ḅ᎔ᦪ2a=l,•*-a=|)ᦑ⌱A.ூὃ௃᎔ᦪs2⚪qᫀ(DÕ(Þ1=2,+=3,x=6+ᦑ⌱D.ூὃ௃ÕᐗÂÇÈ-àᑖÕás3⚪qᫀ(BÕ(+ZDCE=132°,ZDCB=1800-ZDCE=180°-132°=48°ãäåABCD±zæãäåzA=ZDCB=48°,ᦑ⌱B.ூὃ௃ᙊᕜ}êᳮᙊᑁ¦ãäåḄឋqᫀs31⚓ᐳ47⚓

39ᙊQ}ஹíஹîḄᐵs4⚪qᫀ(BÕ(A.ðᢚ^fPᵬḄfóôõᑖᙠ1ö10ö÷ᦪ⌲ᜩúûEü>ýᔠ⚪ÿB.
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½¾ᦑঞ┯.ÇqᡠÈÉÊ.3ḄTজঝᐳ2Ë.ᦑ⌱C.ூὃn௃ÌᱥḄaᵨK_`4ḄÎ▭aᵨLᦪÐÑḄ⌱Aaᵨ^ஹ_`⚪1⚪Iᫀ34⚓ᐳ47⚓

42Iᫀ2a5K2a2•a3=2a2+3=2a5>ᦑ2as.ூὃ௃ÒÓᦪÔḄÕÊÖḄÕG×ḄÕG2⚪Iᫀ2x(3x-2y)K6x2-4x=2x(3x—2y)$ᦑ2x(3x—2y).ூὃ௃ØiᑖK-ᓝÚ0ÕÊØiᑖK-ÛᵨÜiÊØiᑖK-ÝÜØiÊ3⚪Iᫀ7KÞ=104ß1078ÞᵨàáâᦪÊ⊤sT1.078x1071.078x10n=1.078x107:.n=7ᦑ7.ூὃ௃àáâᦪÊ⊤sã¹Ḅᦪ4⚪IᫀJKä⚪ᑖ᪆ᑡç&ᡠᨵèéêᡠ?ḄèéᓰìèéḄíᓽO.ᐳᨵ.î..,î.îî4ïO8ᑣ2ÌðḄBñòz.☢ôqḄᭆ᳛T:4故1-4ூὃ௃ᭆ᳛ÜiIᫀ35⚓ᐳ47⚓

435⚪Iᫀ4K$÷4ADBEḄø`ABDEn0,AB=DE,0E=0D,AB=DE=20D=4,ùBCT1ῪAABCḄÓyAC=AB=4,ᦑ4.ூὃj௃Ò`_`LᦪḄᐵûü<ᳮ1Ὺ_`4Ḅᑨ<ឋ6⚪Iᫀ2.5ÿ⚪ᨚ᪆ᵫ⚪120+80=1.5ᓟ;ᯖᬞḄ120+60=2ᓟḄ360+90=4ᓟᡠ%&ᙳ()*=25ᓟᦑ2.5.ூὃj௃,-./⊤123456789:;Ḅ<;ᩩ:-./>7⚪@ᫀk<0D(Xi>0HIXi+1>0,KLAஹB6P9HQR>Sᡈ>UV▲IXi>0HIᙳᨵyiUV▲Iᡠ%k<0,ᦑk<0.@ᫀ>36⚓Iᐳ47⚓

44ூὃ௃efghᦪ/V]PḄᙶ᪗ᱯm>8⚪@ᫀ21ACBI>AABD,no(pῪrsts:,UuvABCDwxy:I4CDA=9(T,CD=AD,PPzPAᐵRr|DQ}~INADQ=24஺,ZPDQ=zADQ=24°,AD=DP,CD=DP,ZADP=48°,ZCDP=138°,ZDCP=ZDPC==21°.2ᦑ21.ூὃ௃&|Ḅឋdஹef⚪>1⚪@ᫀ;=2+gx-2+|=3.;=2+x—2=2+—2=3.2222ூὃ௃ᱯsḄtshᦪ᦮ᦪᢣᦪ}>2⚪fY6ei2xx—23231@ᫀᫀ=x+2
x-2SS=S=S*x=—2ᐭ;=—■J=—£V2-2+22AT2xx—23231rs;SX+2X-2xx+2-x+2-x+2--x+2,@ᫀ>37⚓Iᐳ47⚓

45**=S2ᐭ;=St=S;=¡¢*x=V2—2ᐭ;=—/—=---V2-2+2202xx-23_23_1;=
x+2
x-2SSn=¥S¦=S¦*x=V2—2ᐭ;=—"—=——.V2-2+22ூὃP௃ᑖ;Ḅᓄ®>3⚪@ᫀ1¯L°᪆2J31¯D(Uu:ABCDw´:ABCD,CD//AB,µDE=BF=2,Uu:BFEDw&Uu:ফᵫপºUu:BFEDw&Uu:IBD//EF,ZF=ZABD,2/.tanZF=tanzABD=BG2--=-BF34BG=-3I|ÀBGḄÂÃ(Ä1¯D(Uu:ABCDw´:ABCD,CD//AB,µDE=BF=2/Uu:BFEDw&Uu:ফᵫ1ºUu:BFEDw&Uu:IBD//EF,ZF=ZABD,2tanz.F=tanz.ABD=@ᫀ>38⚓Iᐳ47⚓

46BG_2BF-3,BG=pI|ÀBGḄÂÃ(g.ூὃ௃Å:ḄᑨÇzឋ|Àᚖr&ᑖ|Ḅឋs&ᑖ|Ḅឋ>4⚪@ᫀᶍÊ⚪ᨚ᪆পMG//PQ,NFGM=NFBP=30஺,ᙠRtZXFGH1I2
ËÌA]A2,ᑣÎÏPDiInUu:A1BGA2w´:.AJA=BG=BF=GF=4-|=yÐ2Uu:ABCDÑUu:A1BC1D1owxy:IAB=AjB/A]BCi=ZABC=90°,INABAi=180°-ZAJBCJ=zFBP=180°-90°-30°=60°Ð4|41H0ᙠ᦮ÒÓÔÏÕ1IPAÓÔÖA2Ḅ×Õ(:210IVI•IÐ.•1,*3J1
MG//PQ,,.zFGM=Z.FBP=30°,ᙠRtZ\FGH1IFG=2FH=2X-=-Ð33@ᫀ>39⚓Iᐳ47⚓

47.wQফËÌAÙ2EᑣÎÏPDiInUu:A1BGA2w´:.AJA=BG=BF=GF=4-|=y(Ð)2Uu:ABCDÑUu:AiBgDiowxy:IAB=AiB/AiBCi=4ABC=90°,zABAi=180°-஽AiBCi=zFBP=180°-90°-30°=60°00xtrx2Ð1H0ᙠ᦮ÒÓÔÏÕ1IPAÓÔÖA2Ḅ×Õ(:210IL,I.IÐ.i.»i33ூὃP௃SæhᦪḄçᔠ⚪>5⚪@ᫀ(1)20(2)20(3)5ᡈ1D᪷ê/⊤ëIᵱឋíîïឋ(“xñ”Ḅóᦪw11óI᝕ឋíîïឋ(“xñ”Ḅóᦪw9óIõÒ᪵÷1íîïឋ(“xñ”Ḅóᦪw11+9=20ó2V᝕ឋḄîø(51.2ᓟIíù(1.6ÐI[᝕ឋḄBMIᦪ=ᑶ=ü=2஺3᪷ê/⊤ëᵱឋḄóᦪ(2+2+11+9+m=24+m,᝕ឋḄóᦪ(•᪵÷ÿ
55,.*•24+m+25+n=55,:.m+n=6,m33n2m=3ឋ“Ꮙ”Ḅᵱឋ"ᦪᨵ3+2=5"ឋ“Ꮙ”Ḅ᝕ឋ"ᦪᨵ3+4=7ZE.'(
)*ᫀ,40⚓ᐳ47⚓

48m=4ឋ“Ꮙ”Ḅᵱឋ"ᦪᨵ4+2=6"ឋ“Ꮙ”Ḅ᝕ឋ"ᦪᨵ2+4=6"'(
O12ᡠ4᪵67ឋ“Ꮙ”Ḅᵱឋ"ᦪ8ឋ“Ꮙ”Ḅ᝕ឋ"ᦪḄ'(
5ᡈ1.;<(1)᪷@A⊤CDᵱឋឋ“EF”Ḅ"ᦪ
<11"᝕ឋឋ“EF”Ḅ"ᦪ
<9",HI᪵67ឋ“EF”Ḅ"ᦪ
<11+9=20"J(2)V᝕ឋḄL51.2ᓟNO1.6PQ᝕ឋḄBMIᦪ(=U=V=20J(3)᪷@A⊤CD<ᵱឋḄ"ᦪ<2+2+1l+9+m=24+m,᝕ឋḄ"ᦪ

492X1=2,A(l,2).A^~ᙠ'zᦪA}2k=2Xl=2,/.'zᦪ;᪆j

5012CD42ஹ2214...t=iUᨬᜧ...uḄᨬᜧ(஺.4ூὃ^௃^ᐳᙊ,7⚪*ᫀ<প:0C=3CE,K9(EF2-CF2)=0C2,EF2-CF2=—='=CE299OC±CFCF
DOḄᑗJফজJZC0D=2ZB0C,¡JZC0D=2ZDAC,vZCAD=ZBOC,VZOBE=ZACD,AACD^AOBE,ঝJAACD^AOBE,.OE'.-OB•-—EADAC¤ᙊḄ¥¦r,VOC=3CE,AD=4,2_r♦-r=—,3AC*ᫀ,43⚓ᐳ47⚓

51AC=6,^M§ACḄ7^,CM=3,-EG//AB,CGCE1—=x,ACOC3CG=2,MG=CM-CG=3-2=1§MGḄ©ª1.(1)<OC=3CE,9(EF2—CF2)=OC2,EF2-CF2=—,9EF2-CF2=—==CE299.OC±CF.CF
஺0Ḅᑗ<ফজZC0D=2ZB0C,L•:ZC0D=2ZDAC,:.ZCAD=ZB0C,*Z0BE=ZACD,JAACD^AOBE,ঝ

52³´ᳮ,8⚪*ᫀ<(1)A=b2-4ac=(-2)2-4x1x(-2)=8.ফজ¹;᪆º=2ᡈ=-1(»).;<(1)a=g,b=c=-2½¾<^x2-2x-2=0,A=b2-4ac=(-2)2-4x1x(-2)=8.(2)জᙠRt^DEC7zOCB=45°,DC=V2DE=V2CE.L•:ÄAOOADOB,OD=OA=—Xi¡,.OC=OD+DC,:.DC=-c+x,DE=CE=yDC=y(-c+xj,x••EB=BC-CE=-V2c-Ñ(-c+x1)=xÒ(c+x1),AOOF•—EDEEB.-xi_(xmX2)••y/2,ஹ41,ஹ—(-C+X1)--f(c+xi)*ᫀ,45⚓ᐳ47⚓

53ᓽ:Ô)2-"2=0,,ᡈ=—1(»).;<পa=b=c=-2,½¾<Õ-2x-2=0,A=b2-4ac=(-2)2-4x1x2)=8.(2)জ<:Xi+X2=-g,x£+c=Xix=Ec,20C=0B=|c|ᙠÄAOC8ADOB7,£ACO=£ABD«£ACOBZ/1OC=ZDOO=90×ÄAOC=ADOB(ASA),ঝ;

54vyzᦪ1ᔠ⚪*ᫀ,47⚓ᐳ47⚓