山东省济南市天桥区2021-2022学年八年级上学期期末数学试题

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ḕᓭᜩ᫑2021-2022ᦪ⚪▅ᔁᓫ⌱⚪ᐳ12⚪ᐳ24ᑖᑖ1.2ᑖ
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8ூ᪆௃ூ௃᪷"4ᦪḄ67,952894.ᦑ4ᦪ.95,ᦑᫀ.C.ூᑖ᪆௃ᑭᵨ4ᦪḄ671ᓽ஺9.ூᫀ௃Bூ᪆௃ூ௃ᵫ<=>xV2?,kx+b>0,ᡠAᐵCxḄDEkx+b>0ḄFGxV2,ᦑᫀ.B.ூᑖ᪆௃HIJᦪ<=ᓽ1.10.ூᫀ௃Dூ᪆௃ூ௃ᵫᚖL#ᑖ%ḄឋAE=BE.BE+BC+CE=AE+CE+BC=AC+BC=8+5=13.•.MBECḄᕜO.13ᦑᫀ.D.ூᑖ᪆௃᪷"ᚖL#ᑖ%ḄឋAE=BE,0ᑭᵨPQRḄᕜOS
ET*ᣚᫀ஺1Lூᫀ௃Bூ᪆௃ூ௃,AḄᙶ᪗.(1,2),,BḄXᙶ᪗.2,VAB=5,...BᙠAḄZ[?,\ᙶ᪗.1-5=-4,BᙠAḄ][?,\ᙶ᪗.1+5=6,...BḄᙶ᪗.(-4,2)ᡈ(6,2).ᦑᫀ.B.ூᑖ᪆௃᪷"#$Cx_ḄL%`ḄḄXᙶ᪗aE,12BḄXᙶ᪗,ᑖBᙠAḄZ[?,BᙠAḄ][?,bcdeᓽ஺12.ூᫀ௃Aூ᪆௃ூ௃Vy=kx+k-l=k(x+1)-1,

9:.x=-l?,y=-l,L%lm-1,-1o,⌱⚗Arᔠ⚪.•.u<0?,yxxyᜧ{|},⌱⚗BDrᔠ⚪,>k-l>0?,k>l,L%l,,P=▲,,⌱⚗CDrᔠ⚪,⌱⚗DDrᔠ⚪.ᦑᫀ.A.ூᑖ᪆௃ᵫ=1«+ᓃ1=1k<0?,yxxyᜧ{|},>k-1>0?,k>LL%l,,P=▲,ᓽ஺13.ூᫀ௃2ூ᪆௃ூ௃•••22=4,A4Ḅ#᪷G2.ᦑᫀ.2.ூᑖ᪆1"#᪷Ḅ671ᓽ.14.ூᫀ௃5ூ᪆௃ூ௃—2x>10,DEb[◀A-2%<-5ᦑᫀ.x<-5ூᑖ᪆௃ᑭᵨDEḄឋDEḄ1ᓽ஺15.ூᫀ௃ூ᪆௃ூ௃ᵬ2=0.76,S/=o.71,S2=0.69,ASᵬ2>s/>Sᵨ2,...P¢£ᡂ¥ᨬ§6ḄG.ᦑᫀ..ூᑖ᪆௃᪷"¨Ḅឋ¨©ᜧᦪ"©D§6ᫀ஺16.ூᫀ௃6

10ூ᪆௃ூ௃YRSABC£,ZC=90°,AC=3,ZB=30°.,AB=2AC=6.ᦑᫀ.6.ூᑖ᪆௃ᑭᵨ®30஺QḄLQPQRḄឋAB=2AC=6o17.ூᫀ௃20ூ᪆௃ூ௃¯°ᙽ²³´ḄµT.x³,°ᙽ¶·ḄµT.y³.ᵫ⚪ᑡ¹º¹ºg)30-°ᙽ²³´ḄTG20³.ᦑᫀ.20.ூᑖ᪆௃¯°ᙽ²³´ḄµT.X³,°ᙽ¶·ḄµT.y³,᪷"⚪ᑡ2¹ºL??ᓅ01ᓽ஺18.ூᫀ௃জঞটூ᪆௃ூ௃•••ᙠMABC£,LA=60°,A/.ABC+^ACB=120°,vBD,CEᑖÅG&4BC,NACBḄQ#ᑖ%,11CBD=Z.ABD=^ABC,BCE=AACE="ACB,11CBD+Z.BCE=/ABC+/4cB=60°,
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MCOM£,OC=OC,ZOCD=OCM/.COD=COM^ASA^OD=OM,CD=CM,.BC=BM+CM=BE+CDBF+CD,ÈÉঝDrᔠ⚪;᝞<,OONJ.ACCN,ÎÏ஺4,ᵫ`ØÙOE=OM,OD=OM,OE=OD,.CZ-OEF=+Z-OCD=60°+Z-OCD*tzOD/V=COD+Z.OCD=60°+LOCD'OEF=ODN,(Z-OFE=OND=90°ᙠAOEF
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/?ÚMAON£,,Û=ᘤI஺Ý=ON•RtAOF=/?t*AON(HL),+++4F=AN,:.AE+AD=AF-EF+AN+DN=AF-EF+AF+EF=2AF,ÈÉঞrᔠ⚪;ᵫ`ØÙ2BOEABOM,ACOD=ACOM,S^BOE=S&BOMS&COD=S&COM'SBEDC=S&BOE+S&BOM+^ACOD+LCOM+^AEDO,=2S&BOM+2sAeOM+S&EDO,=2(S2BOM+SACOM)+SுEDO'

12=2s4B0C+S&EDO'SBEDC=2SKBOC+SKEDO,ÈÉটrᔠ⚪)Þ`,ßàḄÈÉGজঞট,ᦑᫀ.জঞট.ூᑖ᪆௃ᵫᙠM´BC£,&4=60஺,ᵫBD,CEᑖáIâG&48C,&4cBḄQ#ᑖ%,ᑣZCBD+/.BCE=^ABC+^z.ACB=60°,ÈÉজrᔠ⚪)ᙠBC`ËM,BM=BE,ÎÏOM,ijE^ABOEBOMIAS),/.COD=/.COM,!hBC=BM+CM=BE+CD஺BF+C,ÈÉঝDrᔠ⚪)Ù2aOEFPM0DN(44S),2EF=DN,OF=ON,ᙠÙ2RtMAOFPRtMAON(HL),2/E+40=/F—EF+4N+DN=4F—EF+4F+EF=2ZF,ÈÉঞrᔠ⚪)ᵫ`ØÙBOE=BOM,COD=COM,Ù2S^BOE=S^BOM,SACOD=S&COM'0Ù2SãäåBEDCSABOE+S&B0M+SACOD+S^COM+SAED஺,('SBEDC=2S"BOC+SAEDO,ÈÉটrᔠ⚪)ᓽ஺19.ூᫀ௃(1)V12+V27=2V3+3V3=5V3(2)æç2v3=V5xV5-2=5-2=3.ூ᪆௃ூᑖ᪆௃(1)ᐜᑭᵨ᪷Ḅឋᓄê,0ëᓽ)(2)ᐜᑭᵨᑖìᨵᳮᓄᓄê,0ëᓽ஺2஺.ூᫀ௃পÝஹ=3ñজ+ঝ,2x=4,x=2,'x=2*ᐭজ,2+y=3,

13y=l,ᡠA¹ºḄGMl)ফ:[%1<2®•[2x+1>X-1(2)DEজ,xV3,DEঝ,xN-2,ᡠADEºḄFG-23<3.ூ᪆௃ூᑖ᪆௃(1)ᑭᵨõ|öᐗ1ᐗ¹ºᓽ)(2)ᑭᵨDEḄឋDEºḄ1ᓽ஺21.ூᫀ௃•.,AB//CD,.,.ZABD=ZD=50°,NABC+NC=180°.BD#ᑖNABC,.,.ZABC=2ZABD=100°..,.ZC=180°-ZABC=180°-100°=80°.ூ᪆௃ூᑖ᪆௃ᐜᵫ#$%Ḅឋ2/ABD=ND=50஺,ZABC+ZC=180°.0ÈᔠQ#ᑖ%Ḅឋ,ᓽ2ÈÉ஺22.ூᫀ௃Ùø=CE,BF+FC=BC,CE+CF=EF.BC=EFᙠRtMABC
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14:{;%Acᝄû16ᐗ/ü,Bcᝄû4ᐗ/ü.m2oᵫ⚪16x8+4x15=188mᐗo,ÿᵨ188ᐗ.ூ᪆௃ூᑖ᪆௃1Aᝄxᐗ/Bᝄyᐗ/᪷⚪1?᱄!"ᓽ$2᪷⚪ᑡ'()"ᓽ஺24.ூ-ᫀ௃1282/ᦪ1.8$12ᦪ1.535,•ᙠᡠ:;Ḅ᪵>1?@2.0kgḄᦪ@ᓰ8%,,ᵫ᪵>ᦪGHI2500JK1?@2.0kgḄᦪ@Lᓰ8%,ᨵ2500x8%=200,/.I2500JK1,?@2.0kgḄLᨵ200J.ூ᪆௃ூ-O5lm%=l-22%-10%-8%-32%=28%,Sজ1mḄU282,•ᙠIVᦪ11.8'WX16Z'WḄZᦪᨬ\IVᦪḄ/ᦪ1.8$IVᦪḄ]ᦪ5+11+14+16+4=50,•.•_IVᦪᢥabᑮᜧḄef᣸ᑡᐸ1ᜐj1kḄlmᦪno1.5,ᨵpq=1.5,IVᦪḄ12ᦪ1.5$ூᑖ᪆௃1ᵫᔜ?@Ḅsᑖtuv1'mḄUᓽ$2᪷/ᦪஹ12ᦪḄxyH(ᓽ$3_᪵>1?@2.0kgḄᦪ@ᓰ8%,_᪵>1?@2.0ᓟ{ᦪ@|}~]ᦪ@2500ᓽ஺25.ூ-ᫀ௃12$525ᵬᙠ0WxW6yxukḄᦪᐵ)oy=kx,•.•6,60ᙠᦪS/.6k=60,k=10,ᓽᵬᙠ0

15ᙠ0gxS6yxukḄᦪᐵ)oyax+b,++,(2,30),(6,50)ᙠᦪS.2஺+b—30(6a+b=50=5,(b=20ᓽᙠ0

16+++BE_Lx¾jE,/.ZBEC=90°,VAABCo¿Ὺ«Á¶ÁÂAAC=BC,ZACB=90°.VZAOC=ZACB=90°,AZOAC+ZACO=90°,ZACO+ZBCE=90°,AZOAC=ZBCE.ᙠRtAAOCvRtACEB1,Z-AOC=CEBZ-OAC=BCE,.AC=CB/.RtAAOCRtACEB(AAS),.\BE=OC=2,CE=OA=4,AOE=OC+CE=6,+••BḄᙶ᪗(6,2)(2)5জ_Bᙶ᪗(6,2)Åᐭy=x+b,6+b=2,b=4,«¹BDḄ᪆)y=x-4,x=0y=-4,ᓽD(0,-4).AAD=8,/.SAABD=1X8X6=24ঝMḄÈᙶ᪗ÉÊᡈËᡈÌூ᪆௃ூ-௃5ফঝ5M«¹AC«¹ACḄ⊤)y=-2x+4,

17.•.M(x,-2x+4),aஹAM=AE᝞S~AᙊÒAEÓÔÕÖ׫¹ACjMiஹM2,ÕMINI^X¾jNi,ÕM?N2X¾jN2,VA(0,4),B(6,2)C(2,0),$.OA=4,OE=6,OC=2,.1.AE=762+42=2V13ÜAC=V42+22=2V5-CM1=AC+AMi=2V13+2V5,VM(x,-2x+4),MiNi=-2x+4,CNi=2-x,ᙠRSCM1N11MINI2+CNI2=CMI2,.,*(-2x+4)2+(2-x)2=(2>/13+2-\/5)5Xl=_âX2=^+4(ãä).•.MiḄÈᙶ᪗—å$æᳮ5CM=AM-AC=2V13-2V5,22VM(x,-2x+4),.\M2N2=2X-4,CN2=X-2,ᙠRtACM2N21M2N22+CN2=CM2,22(2x-4)2+(x-2)2=(2V13-2V5)2,5xqῶX2=_^+4(ãä)55...M?ḄÈᙶ᪗ê5

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