2021-2022学年广东省佛山市禅城区七年级（下）期末数学试卷（附答案详解）

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2021-2022
ḕἱ
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Ḅ2⚓ᐳ21⚓

2A.ᙠ“ᜮஹᑐஹ”ḄḄ“ᑐ”B.ᙢᙳᒴḄ$%&'()ᙢ*☢,-Ḅ.ᦪ6C.0ᙢᙳᒴḄ1212$☢,-D.ᵨ2,3,44ᦪ5᣸ᡂ48ᦪ᣸ḄᦪᏔᦪ12.᝞;Rt^ACB^,^ACB=90°,<=BCḄ>?ᑖA4DஹBEBCD.P,EPFPFJ.4DCBCḄGHAD.F,C4cD.”ᑣJᑡLMNজP4PB=135°QঝBF=BA3PH=PD;টSTCP,CP?ᑖ/ACBU$VḄ
A.1B.2C.3D.4WஹXY⚪[ᜧ⚪ᐳ6⚪ᐳ24.0ᑖ13.]^3_=5,3y=2,ᑣḄ`.14.4>bḄ4ᩩACD.d.ef4>bḄgh.15.ᙠi>4>bᨵ┦>k┦>Ḅ2lᑣdm┦>ᑖnf.16.]^oῪ4>bḄmqHᑖnf4cmr8cm,ᑣs4>bḄᕜHfcm.17.u☢$%bḄH%&vf6,u☢$%bqHf10.᝞wxḄvyzu☢$%bqH{|a,}~xḄ&{|18.᝞;H%bᱏ4BCD,ḼBEᢚCஹ஺.ᑖn)ᙠ.CZ?iᜐ.qCi%E.4,4C1B4=50°,ᑣP4EB=.4ஹ⚪[ᜧ⚪ᐳ6⚪ᐳ60.0ᑖ19.N(2)ᐜᓄ`N[(%-y)2+(+y)(x-y)]+2xᐸx=1,y=-2021.

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²᥎1⁐ᳫḄᭆ᳛f”21.ᕜ³ᙶµC¶ᑮᦻ¹µº»§¼½U0.8*¾ᑮ¿ÀÁÂᶇÄ*žÆÇᙶµC¶ᑮᦻ¹µºᙠȽÄ*ž᱆᱆ʶB¨ḄËAÌᦻ¹µº᝞;§¤È½ḄËÍs(/cm)ÎȽ*Åt(/i)ḄᐵÐ;Ñ᪷Ó;ÔJᑡÕ⚪N(1);Öz©×z©Q½ᑮᦻ¹µºḄËÍfkm(2)ÀÁÂᶇḄ*Åfؼ½Uᑮ¿ᦻᓄµºḄ?ᙳÙÚf______km/h(3);ḄB.⊤ÜQ(4)᱆᱆ʶE°ÝÞ-ßs*àÈᦻ¹µº°áß22.᝞;ᙠAABCAB=AC.(1)ᑭᵨãäFABqḄᚖi?ᑖACACD.஺C4Bæ.E.(yᑏFéêᶇF;ëì)(2)ᙠ(1)STBD,!DBC=27°,îNAḄÚᦪ.23.ï▅ñᩞᧇô“ᦪbLᔠ”ö÷g⌕Ḅᦪùúû%é.ü᝞Nᙠùý“᦮ÿḄ
”ᡃ᪀⌼ᵨ“”ᙢᐰ!:(a+b)2=a2+2ab+᝞1).%4⚓ᐳ21⚓

4ᑭᵨ“ᦪ*ᔠ”Ḅ,-./01ᦪ23456⚪8./ᵨᐵ:451ᦪ6⚪.12<=ᵨ>᪷@/AᩞᧇDEḄᡂGᑡ6⚪I(1)ᵫ2.O!IIᵫ3.O!IQ(2)ᑭᵨ3OᑮḄ*S456⚪Ia+b+c=15,ab+ac+be=35,ᑣa?+b2+c2=Q(3)᝞4,]ᵨᐸ_`abcdaḄeyabcdbḄezabcᑖjdaஹbḄclᱏnop☢d(2a+b)(a+2b)c(rs◣ஹruvᙢnw))ᑣx+y+z=Q(4)᝞4,]ᨵ3abcdaḄelᱏ4abcᑖjdabḄclᱏ5abcdbḄelᱏ.0_z]{alᱏ|}lᱏ~zoa.zḄlᱏnᡂope(rs◣ஹruvᙢnw)ᑣnᡂḄeḄbcᨬc./d.<>(5)eᦪa,b,cm,m,a+m=b+n=a+=k,᪀⌼bcdkḄeᑭᵨ☢ᩭa/+bm+s

5(3)]஺³ᑮ¯BCA´oា¶ᨵ4B=CD+CE,6I¯CE¢¯48ᨵ·¸¹ºᐵ:»ᳮᵫ.(4)ᙠ஺Ḅ³½_®DEᚖ¿4BCḄ´bÀlkOEC=(ᵨÁaḄ1ᦪ!⊤Ã).%6⚓ᐳ21⚓

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70.12+13>20,ᦑ<=#᪷ᩈ?F᪀ᡂ#$%+Bᔠ⚪D஺ᦑ⌱஺஺4.ூᫀ௃Dூ᪆௃ூᑖ᪆௃⚪ὃ!"HIJK%ḄᭆM.HIJK%ḄᐵNOPQIJH+K%,RᑖᢚTU5Vᔠ.᪷*HIJK%ḄᭆMIᔜ⌱⚗ᑖ᪆ᑨ9ᑭᵨ᣸◀]^.ூ௃:4ஹOHIJK%+ᦑ⌱⚗┯aEbOHIJK%+ᦑ⌱⚗┯aECஹOHIJK%+ᦑ⌱⚗┯aE஺ஹOHIJK%+ᦑ⌱⚗cd.ᦑ⌱:D.5.ூᫀ௃Bூ᪆௃:•••a஻g41=36஺+/43=41=36°,-----------------------------------a•••42+43=180°,/-----------------------bZ2=180-z3=144°./ᦑ⌱:B.⌕^42Ḅiᦪ+j◤᪷*lmnḄឋp^qᐸs⊡$Ḅiᦪᓽ5.⚪ὃ!"lmnḄឋp

8᪷*+©ᯠ+5FḄᱯ®ᑨ9ᓽ5.⚪ὃ!"+v¯°±+©ᯠ+5FḄᱯ®O⚪ḄᐵN.7.ூᫀ௃Cூ᪆௃:᪷*⚪D.K%Ḅ%µ+5¶·Ḅᨬᜧ¸i¹º»¼t-¼Ḅᐵ'ᑖ,¾+ᐜÀU᠒.ᦑ⌱:C.✌ᐜÃK5¶+ÄÅ·ÆḄÇRᑖÈÉRᑖḄÊËg+ᦑ̺tḄᐵ'ÍᐜÀU᠒.ὃ!᪷*ÎÏK%ḄឋpdÐᦪḄKÑ.ÐᦪKÑḄ6KFÒ.⌕F᪷*ÓÏK%.K%ÉḄᦪ*ᑖ᪆q7ᡠIÔḄÐᦪḄÕÖ.ᡠ◤⌕Ḅᩩ+ØᔠÙ▭DÛÜ7cdḄKÑ.8.ூᫀ௃Aூ᪆௃:Þ®B6BD஻Z,:yn஻/?n,Z4=Z1=25°,•••/.ABC=45°,•••Z3=!ABC-Z4=45°-25°=20°,z2=z3=20°.ᦑ⌱:A.✌ᐜÞ®B6ᵫyn5qBD஻஻/m,ᵫ,ynlm+ᑁ┯$|}+ᓽ5^qᫀ44Ḅiᦪ+ñᵫA/IBCOôᨵ45஺$Ḅ#$õ+ᓽ5^q43Ḅiᦪ+ö÷^q42Ḅiᦪ.ø⚪ὃ!"lmnḄឋp.ø⚪ùiᜧ+úDûünḄ6]+úD°±,ynlm+ᑁ┯$|}ᳮḄÔᵨ.9.ூᫀ௃Bூ᪆௃:x+y=3,xy=-2,•••%2-xy+y2=(x+y)2-3xy=32—3X(—2)—15,ᦑ⌱B.ᐜ᪷ᐰ!"#ᐭ%&ᓽ(.

9*⚪ὃ-.ᐰ,/01234⚪Ḅᐵ7,89(x+y)2=x2+2xy+y2.10.ூ;ᫀ௃D300-a_{3>?@°,BᵬDḄEF60^1=60km/h,GDḄEF300+3=100,ᦑA,B,CHI!JKᔠ⚪9@•••60+(100-60)=1.5,GD&M1.5NOPQRᵬD!ᦑ஺┯U!Kᔠ⚪9!ᦑ⌱D.᪷VᦪXY!ᑡ&ᐵ[a,bḄ\!%&a,bḄ]!^_ᓽ(⌲aᑨcᔜe⌱⚗.*⚪ὃ-.agVᦪḄhᵨ!ᳮ3VᦪXYklᑖn%&ᵬஹGpqḄEF23⚪Ḅᐵ7.11.ூ;ᫀ௃Bூ3᪆௃34ᙠ“uᜮஹwᑐஹy”Ḅ{|}!N~&Ḅ2“wᑐ”Ḅᭆ᳛0.33*0.16,ᦑ4⌱⚗JKᔠ⌕%;aeᙢᙳᒴḄH!ᙢO☢RḄᦪ26Ḅᭆ᳛0.16,ᦑ4⌱⚗Kᔠ⌕%@CaᙢᙳᒴḄ!ᙢO2“H☢R”Ḅᭆ᳛==0.5>0.16,ᦑ4⌱⚗JKᔠ⌕%@Dᵨ2,3,4eᦪ᣸ᡂaeᦪ!᣸&Ḅᦪ2ᏔᦪḄᭆ᳛=00667஺0.16,ᦑ4⌱⚗JKᔠ⌕%@ᦑ⌱B.᪷X(!¡¢ᙠ0.16▬¤¥¦!ᓽᐸᭆ᳛P«0.16,¨©e⌱⚗Ḅᭆ᳛!ª0.16ὅᓽHI;ᫀ.*⚪¬⌕ὃ-ᑭᵨ⚣᳛¯ᭆ᳛!ᜧ±²³´¢O!µ¶M·Ḅ⚣᳛ᙠ¸e¹º»¼½᤮¦!¿À᤮¦ḄÁFÂᩭÂN!᪷Äe⚣᳛źឋºᳮ!(kᵨ⚣᳛ḄÇ}ÈÉᩭ¯ᭆ᳛!Äe¹ºḄ¤Ê]Ë2Äeµ¶Ḅᭆ᳛.Ì10⚓!ᐳ21⚓

1012.ூ;ᫀ௃Dூ3᪆௃3ᙠAABC}!•••G4c8=90஺,Z.BAC+ABC=90°,Ï•••A஺ஹBEᑖnᑖ/B4CஹZ.ABC,■■ABAD+G4BE=1(zB4C+/.ABC}=45°,/.APB=135°,ᦑজHI.•••4BPD=45°,XvPF1AD,•••FPB=90°+45°=135°,:.Z-APB=FPB,Ï••Z.ABP=FBP,ᙠÑ48PÒÑF8P}!Z-ABP=FBPBP=BP,Z.APB=FPB•••ÑABPWAFBPG4s4),:,(BAP=஽BFP,AB=FB,PA=PF,ᦑঝHI.••Z.APH=FPD=90°,£.PAH=BAP=BFP,PA=PF,ᙠÒÑFPD}!/.APH=FPD=90°PA=PF,Z-PAH=PFD•ÑAPHÑFPD(ASA),PH=PD,ᦑঞHI.᝞X!ÜÝCP,••Ñ48CḄÞᑖßADஹBEàá[P,••Pᑮ4BஹACḄãäàå!Pᑮ4BஹBCḄãäàå,

11PᑮBCஹACḄãäàå!.•.Pᙠ/4cBḄᑖßR!/.CP1ᑖ4ACB,ᦑটHI.ᐸ}HIḄ2জঝঞট!ᐳ4e.ᦑ⌱D.᪷ÞᑁÞÒºᳮklÞᑖߺéᑨcজ@᪷ᐰåÞḄᑨºÒឋᑨcঝঞ@᪷ÞᑖßḄᑨºêឋᑨcট.*⚪ὃ-.ÞᑖßḄᑨºêឋ!ÞᐰåḄᑨºë!ÞᑁÞÒºᳮ.ìíàᐵឋ23⚪Ḅᐵ7.13.ூ;ᫀ௃10ூ3᪆௃3@3X=5,3ு=2,Bï=3x-3y=10,ᦑ;ᫀ10ï⌮ᵨñòᦪóḄôëëᑣ!ö÷å#ᐭ¨ᓽ(%&].4⚪ὃ-.ñòᦪµḄôë!0øìíù¨ëᑣ23*⚪Ḅᐵ7.14.ூ;ᫀ௃}ூ3᪆௃3ÞḄᩩ}ßá[a!ÄûÞḄ²ü!ᦑ;ᫀ}.᪷ÞḄ²üḄºé!ᓽ(3;.*⚪ὃ-.ÞḄ²ü!0øìíÞḄ²üḄºé23⚪Ḅᐵ7.15.ூ;ᫀ௃30஺Ò60஺ூ3᪆௃3ýae┦Þ2x,ᑣÿ
┦x,•••2x+x=90°,x=30°,ᑣ2x=60°,ᡠ
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15(2)᪷O"ᦪOVW^_ᓽ
ᑮஹ12(3)᪷Oஹ⊤8ḄQ`abB4ᙶ᪗ᓽ
ᑮB4ᙶ᪗⊤8ḄQ`(4)᪷OcdḄ◀aᓽ
+fg12h᪷OFij⚪ᐵlmᓽR.o⚪ὃqrsᦪḄabWj⚪ḄᦪᐵlḄtᵨR⚪ᐵvwxᳮRz{sᦪḄQ`.22.ூᫀ௃R(1)᝞ᡠ8DEᡠḄ;(2)K4=X,■/0Eᚖ/ᑖ4B,:.AD=BD,J4—Z.ABD=x,!ABC=Z.ABD+Z.DBC=x+27°,AB=4C,:.!ABC=Z.ACB=x+27°,•••ᙠABC"4+/.ABC+4cB=180°,ᓽx+x+27°+x+27°=180°,R
=42°,•••AA=42°.ூR᪆௃(1)᪷O⌕+ᓽ(2)K44=Mᑭᵨᑁᳮ᪀H
.o⚪ὃq-ᩖῪḄឋᑁᳮ¡R⚪Ḅᐵv¢£¤Ḅᚖ/ᑖḄឋ¥¦ᑭᵨ§ᦪ᪀HR¨j⚪.23.ூᫀ௃(2a+b)(a+b)=2a2+b2+3ab(

162a2+±+3ab,(2a+b)(a+b)=2a2+b2+3abᵫ3•••ᜧwHḄ☢¬=(a+b+c)2,ᜧwHḄ☢¬=3wHḄ☢¬+2ªHḄ☢¬+2ªHḄ☢¬+2ªHḄ☢¬=a2+b2+c2+2ab+2ac+2bc,(a+b+c)2=a2+b2+c2+2ab+2ac+2bcᦑᫀ(2a+b)(a+b)=2a2+b2+3ab,(a+b+c)2=a2+b2+c2+2ab+2ac+2bc.(2)••♦ᵫ3
(a+b+c)2=a2+b2+c2+2ab+2ac+2bc,■■a2+b2+c2=(a+b+c)2—(2ab+2ac+26c),=(a+b+c)2—2(ab+ac+be),²a+b+c=15,ab+ac+be=35³ᐭa2+b2+c2=(15)2-2x35=225-75=150.ᦑᫀ150.(3)(2a+b)(a+2b)=2a2+4ab+ab+b2=2a2+5ab+b2,2a2+5ab+᮱a¶ᡂ2¸¹ªaḄwH1¸¹ª6ḄwH5¸¹ªᑖºaஹbḄªH»ᱏ½ᡂḄᜧªHḄ☢¬•••x=1,y=1,z=5,■■x+y+z=7.ᦑᫀ7.(4)3¸¹ªaḄwH»ᱏḄ☢¬3a2,4¸¹ªᑖºabḄªH»ᱏḄ☢¬4ab,5¸¹ªbḄwH»ᱏḄ☢¬5b2,⌕¾*"¿+ÀÁ¸»ᱏ½ᡂÂwH(MÃ◣ஹMÅÆᙢ½È)ᑣ⌱¿Ḅ»ᱏḄ☢¬ËÌ᪀ᡂÍᐰ/Hm•••a⌱¿1¸¹ªaḄwH»ᱏஹ2¸¹ªᑖºabḄªH»ᱏஹ1¸¹ªbḄwH»ᱏTÏᡂḄwH☢¬a?+2ab+ᙽ=(a+b)2,TwHḄ¹ª=a+b,Ña⌱¿1¸¹ªaḄwH»ᱏஹ4¸¹ªᑖºabḄªH»ᱏஹ4¸¹ªbḄwH»ᱏTÏᡂḄwH☢¬஺2+4Ë+4᮱=((2+26)2,TwHḄ¹ª=a+2b,•••½ᡂḄwHḄ¹ªᨬªa4-2b.ᦑᫀa+2b.ম

17JHcGCbDnE᝞᪀⌼r—¹ªkḄwHAC-CE-EG=AG=k,ᙠwHḄ4¹GᑖºÖ¿4B=a,CD=b,EF=©H6=c,,■•a+m=b+n=c+l=k,•••BC—m,DE=n,FG-I,AH-l,᝞᪀⌼ªH3ªHḄ☢¬a/+bm+cn,ᜧwHḄ☢¬:)al+bm+cn

18ᦑᫀ45°(2)ñ:᝞,vZ-DAE=!BAC,Z.DAE-Z.CAD=Z.BAC-Z.CADf•!BAD=Z.CAE,ᙠôBADôCAE"AB=AC!BAD=/.CAE,AD=AE/.?BAD=^CAE(^SAS)(3)R:CE//AB,ᳮᵫ᝞õᵫ(2)4BAD=LCAE,:.BD=CE,Z-ACE=Z-ABC,vAB=CD+CE,:.AB=CD-^-CE=CD+BD=BC,-AB=AC,:.AB=AC=BC,•.ôABC¹•Z.ABC=Z-BAC=60°,•Z.ACE=Z.ABC=60°,Z,ACE=/LBAC=60°,ACE//ABx(4)R᝞ö஺ELAC,

19ABDCvAD=AE,DE±AC,••Z-DAC=Z.CAE,•••?ABD=^CAE,•••BAD=Z.CAE,Z.ADB=Z.AEC?."BAD="AD=MAEW)AD1BC,•••ADB=Z.AEC=90°,••DELAC,**•Z.CAE+Z,AED=DEC4-Z.AED=90°,."EC=®E/᝞öDE_LBC,•Z.ADE+Z.ADB=90°,180°-aᵫ÷144DE=44BC,Z.ABC=/.ACB=9஺஺ø,2448஺+4/08=90஺•BAD=90°,ABDுCAEi•BAD=Z.CAE=90°,/-ABD=/.ACE=90°-•••Z-DCE=180°—ACB—AACE=a,®20⚓ᐳ21⚓

20vDE1BC,•.DEC=90°-DCE=90°-a.ùGᡠúö஺EᚖÚA/IBCḄû¹ᑣDEC=üᡈ90஺—a.ᦑᫀᡈ90஺-a.(1)᪷OῪḄឋabḄᑁᳮᓽR(2)ᵫ4ZME=ABAC^DAB=/.EAC,ᑭᵨSASᓽ
+(3)ᵫ(2)^BAD4CAE,᪷OᐰḄឋ
BD=CE,^ACE=4BC,ᑣ=CD+CE=CD+BD=BC,
ô4BC¹ᑣ4BC=NB4C=60஺
/.ACE=/.ABC=60°,
+NACE=4B4C=60஺᪷O/WḄᑨ
CE஻/IB(4)ᑖfÛåö஺ElACö஺E1BCᑭᵨᑁᳮabῪḄឋRᓽ.o⚪ùᔠ⚪ὃqrῪḄឋஹᐰḄᑨឋஹ¹Ḅᑨឋ¡R⚪Ḅᐵvÿ
ᐰ⚪ᵨᑖḄ✌ᐜὃ⚪ὃ⚪.