北京市西城区某中学2022-2023学年九年级上学期开学数学试卷（含答案）

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16ூᑖ᪆௃᪷NO⚗PḄ!ᑖ58=ᨬSḄᡠᨵ5ᡂ#Ḅ8UV"+HCḄH[\ᔠ4>஻>C,4ஹbஹCᙳ0᦮ᦪḄᩩdᑡeVfgḄH[᪷NᔜḄ5ᡂ#᣸◀ijᔠ⚪lḄH.ூmn௃mP6@“BC⁚”O⚗Ḅ!ᑖ58“ᑣ஻2=5Q+6+c(,=ᙠ6@“BC⁚”Ḅ5ᡂ#ᑖF21,6,9,4,m=21+6+9+4=40..,.5a+b+c4=40,.".a+b+c—8.\'a>b>c,aஹbஹcᙳ0᦮ᦪ.,.xc=lzb=2,ᑣa=53xc=lzb=3,ᑣa=4,{z)*ḄO⚗|)*5Uᑖ20<21ᑖijᔠ⚪l~3xc=2zb=3,ᑣa=3,i~3xc=3z஻=4,ᑣa=l,i~.ᡠUa—5,b=2,c=l.ᦑnᫀa+b+c—a=5.ூ௃6⚪ὃᨵᳮᦪḄ᦮Bὃ⇋?@“BC⁚”PḄ!ᑖ58==5ᡂ#Ḅ8|m6⚪Ḅᐵ..mn⚪17ஹ22ஹ25
⚪5ᑖ18ஹ19ஹ23ஹ24
⚪6ᑖ20ஹ21
⚪4ᑖ26ஹ27ஹ28
⚪7ᑖᐳ68ᑖ(17.$5ᑖ(AxV6-|V3-2|W48-ூᑖ᪆௃✌ᐜ-@᪷ஹᓄ-@᪷8HᨬSᔣ¡@¢VḄH|£¤ᓽf.ூmn௃mMxVe+¦-|V3-2|W48=V3X6+J^+V3-2+72X34=31+31+M-2+473=61+5᝞-2.ூ௃{⚪¨⌕ὃ©-@᪷Ḅªᔠ⌕«¬®mn{⚪Ḅᐵ|⌕¯°জ²ᨵᳮᦪḄªᔠ*³´µᐜ¶[◀ᨬS·ᨵ¸¹Ḅᐜ¸¹º

17☢Ḅ.ঝᙠ
᪷f½¾|*“ᓫ⚗”£i¿ÀḄ-@᪷Ḅ8f½¾“£⚗18.(6ᑖ)ᵨ〉xḄ¶m¶Æ(1)=7x3(2)+4x-5=0.ூᑖ᪆௃(1)ᐜÈ⚗[ᑭᵨÊËÌͶÆḄÎÌᑖmÏÐUVÑᐵÒxḄ*ᐗ*@¶Æ[Ô*Õ¢mᓽf3(2)ᑭᵨᓝ×ØͶÆḄÎÌᑖmÏÐUVÑᐵÒxḄ*ᐗ*@¶Æ[Ô*Õ¢mᓽf.ூmn௃mপC2D=7x,-/-7x=0,/.X(X-7)=0,Û!|x=0ᡈx-7=0>mUxi=0,m=73(2)•./+4x-5=0,(x+5)(x-1)=0,Ûi]x+5=0ᡈx-1=0,mUxi=-5,%2=1.ூ௃6⚪¨⌕ὃm*ᐗ-@¶Æm*ᐗ-@¶ÆãᵨḄ¶ᨵäåæç¶ஹÌᑖmஹËèé¶m⚪Ḅᐵ|᪷N¶ÆḄᱯ⌱ìíḄ¶.19.(6ᑖ)îïᐵÒxḄ¶Æ(3m+1)x+3=0.(1)¢ðiñ“òóH¶Æᨵôᦪ᪷3(2)>¶ÆᨵÑ᦮ᦪ᪷¢᦮ᦪ”ḄH.ூᑖ᪆௃(1)ᑖÀõñm=08ö#0Ñøùúû¶Æ᪷Ḅᦪ3(2)ü+(3,஻+1)x+3=0ÌᑖmUᑮᵨ=-þX2=-3,᪷N⚪lfï-þ|᦮mmᦪN{¢V0᦮ᦪÿḄ
.ூ௃(1)=0ᓄx+3=0,ᨵ᪷x=-3!஻2/0wx2+(3஻?+1)x+3=0(ᐵ*xḄ+ᐗ-..A=(3/n+l)2-4஻3X3=9m+6஻?+l-12m=(3m-1)2>0,

18...9:ᨵ;<ᦪ᪷.>?ᡠABC஻7EF
Gᨵᦪ᪷.H2IHJx+1IHx+3I=0,.1஺..xi=-—,X2—-3.m!ᨵ;<᦮ᦪ᪷Om(᦮ᦪ'.m=-1ᡈm=1.ூQR௃S⚪U⌕ὃXY᪷Ḅᑨ[\Ḅ]^S⚪⌕_`+ᐗ-.᪷Ḅabcᑨ[\dḄᐵeH1IdfHIᨵ;

19BOCூᑖ᪆௃H1I᪷s|}⊡ᐰ|uᓽ.H2I᪷ªutuḄᑨ´´ᳮµ¶ᫀ.ூ௃H1I⊡ᐰ|u᝞|.H2IOA=OC,OB=OD,uABCD(ªu.H«¬gᑖḄuªuI"2ACVBD,uA8C஺tu.H«¬gᚖḄªutuIᦑᫀªu!«¬gᑖḄuªu!«¬gᚖḄªutu.ூQR௃S⚪ὃXz{s|ஹªutuḄᑨ´º»_`ªutuḄᑨ´´ᳮ(S⚪Ḅᐵ¼.21.H4ᑖI48cx½*QAH1,0I,cy½*QBH0,-2I.H1I~48Ḅ᪆\!H2I¿AB?+QCᙠÀ+Á▲OBOC=2,~QCᙶ᪗.ூᑖ᪆௃H1IpABḄ᪆\y=H+4ÆQAH1,0ஹBH0,-2Iᑖ[Çᐭ᪆\ᓽÉᡂÉÊ˵ᑮABḄ᪆\!H2IpQCḄÍᙶ᪗x,᪷άu☢ÏÐ\ÑSMOC=2~¶CḄÍᙶ᪗ÒÇᐭᓽ~¶Óᙶ᪗Ḅ
Ê˵ᑮᐸᙶ᪗.

20ூ௃(1)p48Ḅ᪆\(&/0),•.,AB}QA(1,0)ஹB(0,-2),...[k+b=0,1b=-2µÖ=2,Ib=-2ABḄ᪆\y=2x-2.(2)pQ஺ḄÍᙶ᪗×■:SABOC=2,.,.A«2«M=2,2µx=±2,AB?+QCᙠÀ+Á▲.••x=2,y=2X2-2=2,...QCḄᙶ᪗((2,2).ூQR௃S⚪ὃXYØ´eᦪ~+.ÙᦪḄ᪆\9⚪BÚ⌕º៉Ùᦪ|Á?QḄᙶ᪗ᱯÝÞ⌕º៉άuḄ☢ÏÐ\.22.(5ᑖ)ßàÀ6áâã“äå”æçᡃéêëᙢíãîïðqñòóᜧõöøᜧᨵ᩽ïḄẚûî.᝞|âã“äå”üêýþᔣA3ᵫAᔣBC,ᙠAᜐCᙠᓅ45°ᔣᙠBᜐCᙠᓅ60°ᔣAB=(400+40073)ᓟᙊᕜ"600ᓟᑁ$%&'(.(1)C$%&ᔩ+,-+(2)/Ḅ1220ᓟ/4ᑣ%&6ᢝ8Ḅ49ᨵ;<+(=>?ᶇ᦮ᦪCὃᦪEFGH1.41,I41.73,75^2.24)ூᑖ᪆௃(1)ᑭᵨPῪRSTSUVW302ḄRSTSUḄឋYZCDḄ<[\

21ZC^ᔲ$%&`2
ᑭᵨabcᳮZEZ
eEFḄ<[\Z%&6ᢝ8Ḅ49.ூfg௃fhi1
C$%&ᳮᵫhjCkCOl஺AZADC=ZBDC=90°,'2ZCAD=45°,2.ZACD=45°,2.AD^CD,*2NDBC=30°,2.BD=\[3CD,hA3=400+400noᓟ.,.AB=AO+8O=C£>+pC£o=400+400F.♦.CD=400ᓟᙊᕜ"600ᓟᑁ$%&'(.•.C$%&`2
rEC=600h஻FC=600ᑗ?4vw%&CxV£D=^2_2=200V5km
,CECD."z=400{᱐Ḅ1220ᓟ/}4.•.400⍩+20-45i}4o.gh%&6ᢝ8Ḅ49ᜧ45}4.ூ௃⚪ὃḄ^abcᳮᙠ▭Ḅᵨfg⚪Ḅᐵ^᪀⌼ZRSTSUᑭᵨabcᳮfg.23.6ᑖo᝞UABCOḄSACஹBDlO,jBkBE//AC,BE^AOECஹED.

22(1)hUBECO^U`(2)/AC=2,NABC=60°,஺EḄ<.ூᑖ᪆௃(1)ᵫUḄឋYNBOC=90°,OC=1AC,ZBE=OC,ᓽ¢Z2UBECO^£¤U¥ᵫ/8OC=90°,ᓽ¢Z=¦`(2)ᵫUḄឋYACLB஺OB=XBD,OC=1AC=\,AB=BC,᧕¨ABC^P22TSUZBC=AC=2,ᵫabcᳮZOB=M0ᑣBD=2᝞,ᵫUḄឋYZBE=OC=1,NDBE=90°,ᵫabcᳮᓽ¢Z=>.ூfg௃(1)©h•••UABCQ^U.NBOC=90°,OC=OA=1AC,2"2BE=1AC,2.BE=OC,'JBE//AC,UBECO^£¤UVZBOC=90°,ªUBECO^U`(2)fh•.•UABCD^U.ACVBD,OB=FBD,OC=«AC=1,AB=BC,22VZABC=60°,.♦.¨ABC^PTSU.BC=AC=2,ᙠRt^BOCᵫabcᳮh08rBe2_“2=62-]2=%,.BD=2OB=2-/3,ᵫ(1)hUBECO^U.BE=OC=\,NDBE=90°,

2322=2ᙠRtZiOBEᵫabcᳮh^=VBE+BDV1+(2V3ூ௃⚪ὃ³£¤UḄᑨcஹUḄᑨcµឋYஹPTSUḄᑨcµឋYஹUḄឋYஹabcᳮP¶`·¸¹ºUḄឋYVabcᳮ^f⚪Ḅᐵ.24.i6ᑖo¾¿ᔜ}ÁÂᦟÄÅÆÇᐰ☢ÊËÌÍÎ4ÏÐ.¿ᦟÄѳf6¿ÁÎ4ÏÐÒÓÔÕÖᵬஹØÙᡠÁᔜ100ÝÞ<[¤ßᔁá.Þ<Î4ÏÐḄâᔠᑖäx,æᡠᦪEᑖ5èi“êëì"h90&<100`“ëì”:80WxV90`“õöëì”:70Wx<80`"øùëì"h604V70`“øëì”h஺ú60o,¿ᦟÄÑᦪE[¤³ᑖ᪆.Åᑖûü᝞ýha.ᵬÁÎ4ÏÐᑖÒÓ⚣ᦪᑖb.ᑖᡧc.ᵬஹᡠᑖḄᙳᦪஹᦪஹᦪ᝞⊤:᪥ᙳᦪᦪᦪᵬ85n83817980d.ᵬ“+,-”Ḅᑖᦪ/0ᑮ2᣸ᑡ5᣸ᙠᨬ8Ḅ109ᦪᑖ:;<83,83,83,83,82,81,81,81,80,80.@A᪷CDEFG5HIJᑡK⚪

24ூᑖ᪆௃M1N᪷CᡧḄ,}5ᔜ-⚣᳛SX1ᓽgQḄU5ᑭᵨᦪḄ,}gQᵬᑖḄᦪ5ᓽ஻ḄUVM2N᪷CᙳᦪஹᦪḄᜧᑨᓽgVM3NQᔠsᡠᓰḄᑖᓽg.ூI௃:M1N“+,”ᡠᓰḄᑖX1-40%-7%-18%-10%=25%,ᓽm=25,•••ᵬ“+,-”Ḅᑖᦪ/0ᑮ2᣸ᑡ5᣸ᙠᨬ8Ḅ109ᦪᑖ:;<83,83,83,83,82,81,81,81,80,80..•.ᵬḄ+,ᑖ/0ᑮ2᣸ᑡ85ᜐᙠḄ9ᦪḄᙳᦪX_=281.5,ᦪ;81.5,ᓽ”=81.5,I<5¡=25,n=81.5VM2NᵬḄZ[\]5ᳮᵫ᝞J

25-3x+2020=x2-x+2021,ëè5=ì+1éᐭ5ᓽgQIᫀV(2)᪷Cᣚᐗ®ᓽg.ூI௃<(1)V?-x-1=0,.♦./=x+l,Ax4-3x+2020=(x+1)2-3x+2020=7-x+2021=x+l-x+2021=2022.ᦑIᫀX<2022V(2)Ö/+x=y,ØÙ(/+x)2=/5¸;Ú½gÁX᜛-2y-8=0(1),yi=-2,j2=4.Ýy=-25/+x+2=0,-4X1X2=-7<0,1.½ñVÝy=45/+x-4=0,.•x=#1±XLV2Ú½ᨵ9᪷0,ᓽ9>-1᪷;ᦪḄឋ=>ᑮx=3y=9,ᯠA+(3,9).ᐭyi=(Z+l)x-2k+31B>ᑮCᦪD᪆9+1<0,ᓽE<-1ᑭᵨᦪḄឋ=>ᑮx=-2y=9,ᯠA+(-2,9).ᐭ=(K1)x-2k+31I>ᑮCᦪD᪆(3)ᐜ᦮ᳮ>ᑮ-/+6,Mᑗᦪx,yi<”ᡂ!ᑣOPyiQ)2RST>2ᙠyiḄEVᡠXk+l=஻T-2k+3<-Y+6,Z[ᓽ0>\Ḅ"
$.

26ூD]௃D5(1)•••_(-1,2)ᙠyiḄ`aE,-(Z+1)-24+3=2,D>&=0;ᦑ]ᫀf50(2)&+1>0,ᓽ&>-1ᑣx=3.)=9,+(3,9).ᐭ)”=()1+1)x-2k+3>3(h+1)-24+3=9,D>&=3,CᦪD᪆fyi=4x-3ᡃ+1<0,ᓽ/<-1jUx=-2y=9,+(-2,9)yi=(6+1)x-2A+3>-2(A+1)-2%+3=9,D>᝕=-2,CᦪD᪆fyi=-x+7lEyiḄᦪ⊤fyi=4x-3ᡈyi=-x+7(3)y?.=m(x-1)+f)=mx-m+6,•••ᑗᦪx,ᡂ!.♦.Z+l=mT-2k+3<-m+6,-2k+3<~k~1+6,D>k>-2.ூ_n௃o⚪ὃrsᦪQᐗuv5wᦪḄxyz{|}ᦪḄ
ᜧ(ᡈ~)0ḄxḄ"
$wᦪ`aḄxyz{OP>=+ᓃᙠxE(ᡈ)VᑖᡠᨵḄ_Ḅᙶ᪗ᡠ᪀ᡂḄᔠ.ὃrsᦪḄឋ=.27.(7ᑖ)ᙠVABC஺_PPC8PE_4P,PX_P┐90°,>ᑮPPE,CE._EEFLBCF.(1)ᙠ`1⊡ᐰ`(2)জ¤5EF=CF.ঝ¦§CE,CP,C£>¨ᩩPḄᦪᐵ«¬¤(3)P1_P⌮┐90°,ᐸ¯ᩩ°uOᑏ1CE,CP,CD
ᩩPḄᦪᐵ«fCE=6(CD-CP)ᡈCE='³(CD+CP).

27A,_______PADPBCBC`1ᜓᵨ`ூᑖ᪆௃(1);⚪¶⊡ᐰ`ᓽ0(2)জ¤¸APB¼(AAS),¾1¿8=EF,AB=PF,0>Ã4ঝÃ45CP-CD=Iᑭᵨᐰv¨xḄឋ=vῪOx¨xḄឋ=¤ᓽ02(3)জ_PᙠPBCEᙠBAEÇ"ᑣ¸P8MvῪOx¨x¤¸PCEZZVU/P(SAS),>1CE=PM,ᓽ0>1Ã4ঝ_PᙠP5cḄPEᙠBAEÇ"BM=BP.ᑣ¸PBMvῪOx¨xPM=®BP.¤¸PCEgAAMP(SAS),>1CE=PM,ᓽ0>1Ã4.ூD]௃(1)D5⊡ᐰ`᝞`1ᡠÑ5(2)জ¤5᝞`1ᡠÑ•••PPA_P┐90°>ᑮPPE,2.PA=PE,ZAPE=90°,•••ÕÖABCOV.•.NABP=/ABC=90°,AB=8C,¿_LBC¿/.ZPFE=90°=NABP,2.ZEPF+ZPEF=90°,ZAPB+ZEPF=90Q,2./APB=/PEF,ᓽᙠAAPBÛ,

28ZABP=ZPFE5PE=PA,NAPE=90°,2.ZAPM+ZCPE=\SO°-90°-45°=45°,ä,/ZMAP+ZAPM=NBMP=45°,2.4MAP=/CPE,ᙠÛ¸4WP

29PC=AM5PE=PA,ZAPE=90°,2.ZPAM=ZEPC,ᙠÛ¸AMP>C=AM

30D`3ூ_n௃o⚪ÕÖlᔠ⚪éὃrsᣚஹVḄឋ=ஹᐰv¨xḄᑨíÛឋ=ஹvῪOx¨xḄᑨQឋ=vîïD⚪ḄᐵðᮣòóᵨᡠôîïDõö⚪ô÷øYùᵨúûP᪀⌼ᐰv¨xDõö⚪ýὃùὃ⚪þ.28.ÿ7ᑖᙠ☢ᙶ᪗Py\4,᝞஺”!஺"PḄ%&.()*1,4.1ᙠ஺12,1,஺2-4,-1,஺38,2PḄ%&"஺2஺3.2஺"PḄ%&Cᙠx456O,P,Q,C⚔Ḅ9:;"<9:;=CḄᙶ᪗.3()B1,>M4,஻?N"6MC:D2Eᔜ:Gᙶ᪗4<ḄHI;75ḄJKLMNBN5ḄPL4,ᙠMNP85QRᙠLSRTUAPRḄ%&VᑏmḄXY[.ூᑖ᪆௃1᪷`abcde)1X2W4X1,IX-4=4X-1,1X8=4X2,ᡠ6஺2஺3"PḄ%&k2l஺x,j,ᑣx=4y,ᓽy=qe)஺ᙠM>=q5EQx,q444஺ᙠx45Iᑣq=4k஺ᙠx4Iᑣ-1=4,ᑖt=xḄY44u=CḄᙶ᪗ᓽe;

31(3)lHI;TḄ9S⚔ᑖtEஹ*ஹGஹH,ᑣE(3,x+1),G(5,m-1),uyBḄ%&ᙠMy=2x5ᑣRḄ%&4ᙠM>=qGMy=2xz4L{▲}ᡂḄ┦Ḅᑁᡈ:5{e)G(5,1)ᙠMy=q5,4ᑣxḄYᨬkE(3,m+\)ᙠMy=2r5ᑣmḄYᨬᜧ=ḄmḄYᓽUᑮxḄXY[.ூ௃(1)71X2^4X1,2.Q\(2,1)"*(1,4)Ḅ%&kV1X(-4)=4X(-1),஺2(-4,-1)"*(1,4)Ḅ%&k71X8=4X2,஺3(8,2)"*(1,4)Ḅ%&ᦑᫀQ2,Q3.(2)᝞LlQ()••஺(x,y)"*(1,4)Ḅ%&y=-ix,4:.Q(x,-kx),44O,4Rᑣ0*=4,PF=1,9:;OCQP"<9:;2.PQ//OC,CQ//OP,CQ=OP,ZQDC=ZOFP=90°,/QCD=/OPF=/COP,2./\QDC^/\OFP(AAS),QO=O*=4,CD=PF=T,஺ᙠx45Iᑣu=4,4•"»x=16,/.xc=16-1=15k஺ᙠx4Iᑣ-L=4,4•»x~~-16,

32*.xc=-16+1=-15,5ᡠ஺Ḅᙶ᪗(15,0)ᡈ(-15,0).(3)lHI;TḄ9S⚔ᑖtEஹFஹGஹH,ᑣE(3,+1),G(5,1),ᵫ(2)e)PḄ%&ᙠMy=L54lB(1,1)Ḅ%&Ḅᙶ᪗(x,y),ᑣ=ᓃ22.•.y=2x,e)BḄ%&ᙠMy=2x±.,.•.RḄ%&AᙠMy=LGMy=2xzL{▲}ᡂḄ┦Ḅᑁᡈ:5,4᝞2,G(5,-1)ᙠM>=q5ᑣ"ḄYᨬ4•2tn-1=^X5,4k4᝞3,E(3,m+1)ᙠMy=2x5ᑣxḄYᨬᜧ♦.•஻?+l=2X3,x=5,஻?ḄX["2w஻W5.3

33ூ௃⚪¢ὃ¤;Gᙶ᪗ஹL¥¦ᦪḄ{Gឋ©ஹ<9:;Ḅᑨஹᐰ%¬;ḄᑨGឋ©ஹHI;Ḅឋ©ஹ®⚪Ḅ=ஹᦪ;¯ᔠGᑖ±²³ᦪ´µ¶Ḅ·ᵨ%)¹GIº⚪»¼½ᜧ¾ὃ¿À4⚪.