2021-2022学年湖南省长沙市某校中考押题数学预测卷含解析

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2021-2022
ᓭḕ᪥ὃ⚪ᦪ⚜ᔁ
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10ூ௃«⚪ὃ®Ḅ`/.⚪ᐵ¯°±®Ḅ`/®ᵨᩭ⊝cx´ᦪµ¶ᜧḄc®¸ᜧ⊤gº´ᦪ»¼tᙳᦪ¸ᜧᓽµ¶¸ᜧᦪ¸¿YÀÁ®¸⊤gº´ᦪᑖÂÃÄÅ4ᔜᦪ»¼tᙳᦪ¸ᓽµ¶¸ᦪ¸¿.15ஹ3(a+b)(a-b).ூ᪆௃(2a+b)2-(a+2b)2=4a2+4ab+b2-(a2+4ab+4b2)=4a2+4ab+b2-a2-4ab-4b2=3a2-3b2=3(a2-b2)=3(a+b)(a-b)16ஹ2,----2ூ᪆௃Ç⚪ᑖ᪆᪷ÈÀᦪÉ᎔ᦪḄ/ᑖË,u}-2ḄÈÀᦪ2,-2Ḅ᎔ᦪ-2ὃ8᎔ᦪYÈÀᦪ.IஹÌ⚪(ᐳ8⚪ᐳ72ᑖ)17ஹ(1)120;(2)42ÏY(3)90°;(4)iூ᪆௃(1)ÐÑᑭᵨῪÓᡠᓰÃSÖ×ᩩK24Ïᦪᓽ?ºÙÚaÛḄ᩟ÝÏᦪY(2)ᑭᵨᩩKÞ¨2Ö×᪵«ᦪc?àáâãäḄÏᦪY(3)ᑭᵨ“ᑜæç”Ïᦪᙠ᪵«4ᡠᓰÃS?“ᑜæç”ᡠᙠᡧKḄᙊQJḄéᦪY(4)ᑭᵨ᪛ë2ᑡìᡠᨵḄí,î?ᭆ᳛.ூ௃(1)ºÙÚaÛḄ᩟ÝÏᦪp24+20%=120(Ï)YᦑÌᫀp120(2)àáâãäḄÏᦪp120-24-15-30-9=42(Ï)᝞2ᡠó

11(3)ᡧ“ᑜ”ᡠᙠᡧḄᙊ#$Ḅ%ᦪ'ஹ360஺=90஺(4)᝞ᡠ,鹿最花即炫批加/0个不//个、/、/'划划4\花广花划花广腰广暧腰龙龙场鼓鼓场鼓鼓龙鼓场鼓舞戏戏舟舞舟舞戏舟1ᐳᨵ124567ា9⌱“;<=ஹᑜ”>?@⚗BḄᨵ24567ᦑា9⌱“;<=ஹᑜ”>?@⚗BḄᭆ᳛j.ூFG௃I⚪K⌕ὃNOᡧPQᩩḄSᵨU᪛WXYᭆ᳛7Z[ᑡ]^ᡠᨵ56_⚪ᐵa.18ஹ(1)bcde_᪆(2)S=i(m+1)2+y(mg(2)2ᡈ1.ூ_᪆௃i⚪ᑖ᪆(1)ᑭᵨ?FlḄmnopq^AB=5,r!]AB=OA,rI]5᪷u“HL”bcvABC^^AOD(2)wFBxyzBE,yzy=-m{E,xAF±BE{F,᝞7bcRtAABF^RtABCE,ᑭᵨ|}~5'BC=(m+1),ᙠRtAACB7ᵫᳮ'AC2=AB2+BC2=25+F(m+D2,ᯠbcvAOBs^ACD,ᑭᵨ|}Ḅឋ'1=(SAAOB=£,{5'S=(m+1)2+(mgs102&(2)xBHJLy{H,᝞7ᑖAB஻CD7r!j/ACD=NCAB,ᵫAAOBsaACD'NACD=NAOB,ᡠPNCAB=NAOB,ᑭᵨ$ᦪ'ᑮtanZAOB=2,tanNACB==,ᡠP=2AD/7BC,r!|N5=NACB,

12ᵫAAOBs/iACD?ᑮN4=N5,õö|NACB=N4,᪷IJ÷ᦪ/?ᑮtan/4=஺tanNACB===rᑣø=4ùùù+1ù+ûᯠ¦ᑖËᐵmḄýᓽ?ᑮmḄþ.Ç⚪᪆(1)^gA(0,5),B(2,1),.,.AB=3+(5-1)=5,AB=OA,VAB±BC,.,.ZABC=90°,ᙠRtAABCÉRtAAOD4(I=I.,.RtAABC^RtAAOD(2)ÿBBEJ_y=-mE,AF^BEF,᝞N1+N2=9O஺Zl+Z2=90°,J.N2=N2,.RtAABFsRtABCE,=2ᓽ=ᙠRtAACBAC2=AB2+BC2=25+^(m+1)2,'.•ABCgAOD,/.ZBAC=ZOAD,ᓽN4+NOAC=NOAC+N5,.,.Z4=Z5,AO=AB,AD=AC,AAAOB^AACD,-(■)'=.£——+/)SAOB=/5X2=A

13/.S=L(m+1)?+=(m>-)(2)xBHJ_y{H,᝞7AB஻CD7r(INACD=NCAB,4AOB^AACD,/.ZACD=ZAOB,AZCAB=ZAOB,tanZAOB=55=2,***zr-=2,_'m=lAD஻BC,r|N5=NACB,ifOAAOB^AACD,:.Z4=Z5,:.NACB=N4,tanN4=55=%tanZACB=5r=—,4+7_'m=2.ᡠ7mḄ2ᡈ1.ὃF|}ᔠ⚪.19ஹ(1)y=-x2+2x+3y=x+l(2)aḄ-3ᡈ4±J7.

14ூ_᪆௃(1)FBUDḄᙶ᪗¢ᐭ¤ᱥzy=-x?+bx+c'^¦§¨7_¦§¨ᓽ5ᵫ¤ᱥz_᪆pY^FAḄᙶ᪗7ªyzADḄ_᪆py=kx+a,AUDḄᙶ᪗¢ᐭ'^¦§¨7_¦§¨ᓽ5(2)ᑖ?4«¬জaV-17DF஻AE®DF=AE,'^F(0,3),ᵫAE=-La=2,Y^aḄঝa>-l7°ᯠFSᙠx±¦7EF஻AD®EF=AD,ªF(a-3,-3),¢ᐭ¤ᱥz_᪆p7ᓽ5'^²³.ூd_௃[-9+3b+c=Q_(1)FBUDḄᙶ᪗¢ᐭ¤ᱥzy=-x2+bx+c'´71ஹ-4+2b+c=3_'b=2,c=3,¤ᱥzḄ_᪆py=-x?+2x+3y=07-x2+2x+3=0,_'x=3,ᡈx=-l,VB(3,0),...A(-1,0)ªyzADḄ_᪆py=kx+a,—k+a=0AUDḄᙶ᪗¢ᐭ'"2¶+஺=3_':k=l,a=l,yzADḄ_᪆py=x+l(2)ᑖ?4«¬জaV-17DF஻AE®DF=AE,ᑣFFᓽ(0,3),VAE=-l-a=2,:.a=-3ঝa>-l7°ᯠFSᙠx±¦7EF஻AD®EF=AD,ªF(a-3,-3),ᵫ-(a-3)2+2(a-3)+3=-3,_'a=4+V7;ᡠ7º»ᩩ¼ḄaḄ-3ᡈ4±¾.ூFG௃¿⚪ὃN¤ᱥzxḄÀFÁᦪḄឋÂÃᦪXYÁᦪ_᪆pQÄÅÆÇḄᑨ7ᔠឋÉÊ.

1520ஹ1ËÌÍ⍝Ï7ÐÑÒAᙢᑮBᙢᜧÕ⌕Ö136.4ᓟØ2ÐÑÒAᙢᑮBᙢ~ÙᩭÛÖḄܧ27.2ᓟØூ
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1wFCxABḄᚖzCD,ᚖ»D,ᙠy$AACD7_y$$Y^CD,Þ_ᓽ5
2ᙠy$ACBD7_y$$Y^BD,Y^AD,ÞY^ÐÑÒAᙢᑮBᙢ~ÙᩭÛÖßÛܧ.ூ
௃_1wFCxABḄᚖzCD,ᚖ»D,CDVAB±CD,sin30°=—,BC=80ᓟØ,BC.CD=BC*sin30°=80x-=40àᓟØá,22ã=*4஺äᓟØá,2AC+BC=80+4072=40x1.41+80=136.4àᓟØá,ËÌÍ⍝Ï7ÐÑÒAᙢᑮBᙢᜧÕ⌕Ö136.4ᓟØ;BD
2Vcos30°=—.BC=8
àᓟØá,BC*=40æ.BD=BC»cos30°=80xàᓟØá,Vtan45°=——CD=40àᓟØá,ADAD=——=—=40àᓟØá7tan4501AAB=AD+BD=40+4043-40+40x1.73=109.2àᓟØá,:.AᙢᑮBᙢ~ÙᩭÛÖßÛܧAC+BC-AB=136.4-109.2=27.2àᓟØá.ÐÑÒAᙢᑮBᙢ~ÙᩭÛÖḄܧ27.2ᓟØ.ூFG௃¿⚪ὃNOᳮḄçᵨPQ_1è$7Y$ḄÇᡈéḄê⚪1è5Pëᓄ_y$$Ḅê⚪7_íḄ¦Xîxéz.

1621ஹ(1)4x6-5=24-25=-ফᫀ"#.᝞(+2)-(+/)=-2;ব(+2)-(+/)=+21(ð+2ð+/)~1-1n—1-1kX7LnJ—1ô-1_XLJ_17=ூ᪆௃(1)᪷%জঝঞḄ*+,-",Ḅ.ᑖ0123ᑏ15Ḅ*+6(2)7(1)89Ḅ23ᵫᱯ<ᑮ>?1@A6(3)BᡂD.ᑭᵨ᦮+ḄHᔠJ*KLMNOP.22ஹ(l)c>-2(2)xi=-1,X2=l.ூ᪆௃(1)᪷%Qᱥ-xSᨵUVWbJ4ac>0ᑡ"Y+Z[ᓽ\6(2)ᐜZ1QᱥḄ^_S`᪷%QᱥḄ^_ឋZ1Qᱥ-xSḄbVWᙶ᪗ᯠf᪷%ghᦪ-ᐗgKkḄᐵm[.ூ௃(D[•••Qᱥ-xSᨵUVW.".b2-4ac>0,ᓽ16+8c>0,[?c>-2(2)[ᵫy=-2x2+4x+c?QᱥḄ^_Sox=l,•.•Qᱥpq(-1,0),•••Qᱥ-xSḄbVWo(1,0),rKk-2X2+4X+C=0Ḅ᪷oxi=-1,X2=l.ூt௃ὃwxQᱥ-xSḄWy⚪ஹghᦪ-ᐗgKk[⚪ᐵ{|Jᵨx᪷-mᦪḄᐵmN}ghᦪḄ^_ឋ.23ஹ(1)~ᢇTឰḄ|90ᐗ6(2)ᒕḄTឰ⌕80ᐗ.ூ᪆௃(1)~ᢇTឰ|xᐗᑣ~ᢇ|(x+9)ᐗ`᪷%Yᐵm~ᢇḄᦪ=~ᢇ

17ÞḄ¼ᦪ5'¦§(2)ªᒕ÷ḄTឰùú¼ûyᐗ7ᵫᑭý=û-Þ7᪷uþᢇḄ├ᑭ650ᐗᑡ.ூ
௃(1)ᢇTឰxᐗᵫ⚪45004950xx+9'x=90!"x=90ᑖ$%Ḅ&ᔠ⚪.:ᢇTឰḄ90ᐗ.(2)ᒕ)ḄTឰyᐗ.4950ᵫ(1)*+ᢇ,$/=50.41ᵫ⚪120'50*++015082-49502650,y>80.45ᒕ)ḄTឰ67⌕80ᐗ.24ஹ(1)জ2ঝ3(2)AD=BC(3):;<᪆>BC=4ூ
᪆௃(1)জ᪷ABCDEḄឋGHAB=AC=1ஹZBAC=60,Iᔠ“K⊡CDE”ḄNOHAB=AC=1ஹNBAC=120஺ᑭᵨῪCDEḄCSᔠHNADC=90஺TUVDCDEHADḄWX>ঝᵫ“K⊡CDE”ḄNOHNBAU=90O=NBACஹAB=AB\AC=ACSZHAABCg/kABC(SAS),᪷AᐰCDEḄឋGHBC=BC=6,\ᑭᵨVDCDE]B^Ḅ_S]BḄ`ᓽHADḄWX>(2)AD=BC,UbB:BE஻AU,cBE=AC,deCEஹDE,ᑣgBEACCBhijgBE᪷AijgBEḄឋGIᔠ“K⊡CDE”ḄNOHNBAC=NABEஹBA=AB\CA=EBSZkHlBACg^AB'E(SAS),᪷AᐰCDEḄឋGHBC=AE,ᵫijgBEḄmDSnoiᑖᓽkHAD=.BC(3):ABஹCDḄᚖViᑖSqbP,ᑣbPhgBEABCDḄ᜜DᙊᙊtUbP:PFJ_BCbF,ᵫ(2)ḄIuHPFḄWXᙠR3BPF_ᑭᵨwxNᳮHBFḄWXZHBCḄWX.ூ
௃(1)জ'.•ABCBCDEBC=1,.,.AB=AC=1,ZBAC=60,

18.•.AB'=AC'=1,NB'AC'=120°.VADoYῪABCḄ.,.AD±B,C\NC=30஺:.ZADCr=90°.ᙠRtAADC'NADC'=90஺AC'=LNU=30°,.*.AD=AC'=2.(g)VZBAC=90°,6ZBrACr=90°.ᙠAABC
ABC_____‘=.-.AABC^AABrCr(SAS),BC=BC=6,AAD=B'C'=3.ᦑᫀoজ2ঝ3.(2)AD=BC.OPᙠ1qBE஻AC,BE=AC஺CEஹDE,ᑣACCBo.,:ZBAC+ZBFACr=140°,NB'AC'+NAB'E=140஺NBAC=NABEᙠBACABE/_____AABAC^AABE(SAS),ABC=AE.VAD=.AE,i•AAD=BC.(3)ᙠ1ABஹCDḄᚖᑖWP,ᑣPoABCDḄ᜜ᙊᙊqPPFLBC

19bF.VPB=PC,PF±BC,.1PFhAPBCḄ_zS.,.PF=AD=3.7ᙠRtABPF_ZBFP=90°,PB=5,PF=3,BF==1..BC=2BF=4.ூb|௃~⚪ὃBCDEḄឋGஹῪCDEḄᑨNឋGஹijgBEḄឋGஹVDCDEஹwxNᳮᐰCDEḄᑨNឋG⚪Ḅᐵ51জᑭᵨ30஺DḄVDCDEHAD=.ACঝᱞVDCDE]B^Ḅ1_S]BḄ`>2᪀⌼ijgBEᑭᵨijgBEmDSnoiᑖHAD=AE=BC
3ᑭᵨ2ḄIuIᔠwxNᳮHBFḄWX.