2021-2022学年南京市联合体中考数学四模试卷含解析及点睛

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ᦪ«1ᑮøùtᨵᨴûøùtüᨵᨵýê;(2)᪷*gÿḄḄᙶ᪗ᦪḄ᪆ᵨᦪᦪḄ᪆ᓽ(3)ᦈᵨḄ᎛!"Ḅ#$%#&'()*ᓽ.:পজ;30(2)y0kix+30,y2=kx,ᵫ⚪3456(500,80),(500,100)ᑖ89ᐭᓽ52500kl+30=80,.,.ki=0.1,500k2=100,.,.k=0.22ᦑᡠḄ᪆&yi=0.1x+30y2=0.2x(3)=>?yi=y2,40.2x=0.1x+30,4x=300x=300y=l.ᦑᵫAB=C?ᙠ300ᑖEᑁ⌱H=CঝJK=C?L300ᑖE⌱H=CজJK=C?ᙠ300ᑖE⌱H=CজஹঝN᪵JK.20ஹ(1)45°(2)26°.ூ
᪆௃(1)᪷QᙊᕜTUᙊVTḄᐵUAX$4NABCUNABDḄᜧZ(2)᪷Q⚪3U[\]Ḅឋ_ஹᑗ]Ḅឋ_$4NOCDḄᜧZ.ூ
௃(1)TABa஺஺ḄcdNBAC=38஺.,.ZACB=90°,eZABC=ZACB-ZBAC=90°-38°=52஺2D&fABḄg,ZAOB=180°,/.ZAOD=90°,eNABD=45°

17(2)|}OD,•••DPᑗ஺OPD,AODIDP,ᓽNODP=90஺VDP//AC,NBAC=38°,ZP=ZBAC=38°,VZAODLODPḄ᜜ZAOD=ZP+ZODP=128°,:.ZACD=64°,VOC=OA,ZBAC=38°,AZOCA=ZBAC=38°,ZOCD=ZACD-ZOCA=64°-38°=26°.ூ௃⚪ὃᑗḄឋஹᙊᕜJᳮ.⚪ḄᐵLI⚪ᡠ:⚪◤⌕ḄᩩᑭᵨᦪEᔠḄ..21ஹ.᪆ூ᪆௃.ᳮᵫ᝞ᑡ⊤:12321,22,23,231,32,33,341,42,43,4ᵫ⊤T¡ᐳᨵ9£¤T¥Ḅ¦ᐸGᦪ§¨©3ḄªᦪḄᨵ3£¦ᦪ§¨©4ḄªᦪḄᨵ2£,312ᑣᵬ®Ḅᭆ᳛=;ஹ²®Ḅᭆ᳛³939...´µ¶·ᵬஹ²¸¹.ூ௃ὃḄLµ¶ឋḄᑨ½.ᑨ½µ¶ឋ¾⌕¿ÀÁÂḄᭆ᳛ᭆ᳛ä¾ᔲᑣ¾.ᵨᑮḄ¡Åᭆ᳛=ᡠÆÇᦪ'ÈÆÇᦪ¨É.22ஹ(1)150Êz(2)⊡%.᪆z(3)144஺z(4)300Ì.ூ᪆௃(1)᪷ÎÏÐAÑᕡḄÓ᝘Ḅ@ÕÊᦪ©ᡠᓰ×ᑖÉᓽT"ÙḄ@Õᦪ.(2)ᵨÙÈÊᦪÚÛAஹBஹDÜ£ÏÐÝÑᕡÓ᝘ḄÊᦪÏÐCÑᕡÓ᝘ḄÊᦪ⊡ᐰß¿%.ᵨ360஺

18i$jkClᕡḄn᝘pᦪᡠᓰrᑖstugVTvᦪ.(3)ᵨwpᦪi$AஹBlᕡn᝘jxpᦪᡠᓰḄrᑖs4yᫀ.ூ
௃5(1){|}~Ḅᨵ30+20%=150p(2)C8pᦪ&150-(30+45+15)=60p,⊡ᐰᩩXA᝞5(3)ᡧXAgctuḄgVTvᦪa150ᦑyᫀ&144°453(4)60()x(t°)=30()(p)150y5n᝘uᖪ〈᪥Ḅn᝘gA,BlᕡḄn᝘ᐳ300.ூ௃{⚪ὃ~ᩩXAUᡧXAḄᔠᵨA¡ḄAg4¢⌕Ḅ¤¥a⚪Ḅᐵ¦.23ஹ(1)MḄᙶ᪗&(2,-1)(2)B(4,3)(3)m=-5-ᡈ©m45.162ூ
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௃5(1)y=nx2-4nx+4n-1=n^x1-4x^+4n-l=-1,³ᱥ]Ḅ⚔MḄᙶ᪗&(2,—1)

192
ᵫ1B³ᱥ]Ḅ⚔MḄᙶ᪗&2,—1³ᱥ]Ḅtµ¾c]ax=2,••AḄᙶ᪗&0,3
,AB//X¾¿³ᱥ]ÀB,•••AÁBᐵÀc]x=2tµ•.B4,3
3
:³ᱥ]y=nx?-4nx+4n-1Áy¾¿ÀA0,3
,4n—1=3n=1.³ᱥ]Ḅ⊤·&y=x2-4x+3.e³ᱥ]GḄ᪆&5y=x2+4x+319ᵫ/x+m=x+4x+3.ᵫ=,45m=-----16•••³ᱥ]y=X?-4x+3Áx¾Ḅ¿CḄᙶ᪗&1,0
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20⚪ὃ!"#ᦪ%&'()*ᣚàJáᦪB!"#ᦪḄ.᪆0ஹ!"#ᦪḄ%&©ឋâ#ᦪGḄ%&L.⚪Ḅᐵ.24ஹ(1)12ãz(2)(2+86)ãூ᪆௃(1)ä஺E=x,ᐜåAACELæÜEZCAE=60°,NAEC=30஺ᑮAE=16,᪷ÎEF=8xḄKᑮᫀz(2)ç
NMèç
PP,ᐜᑖéPBஹCDᑮPD,ᑭᵨNN஺4=45஺ᑮNP,ᓽTMN.ூ௃(1)᝞%äOE=x,•AB=DF=4,NACB=30஺.••AC=8,"ZECD=60°,.•.ACELæÜE'JAF//BD,.•.NCAf=30°,.ZCAE=60°,ZAEC=30°,.AE=16,.♦.RtAAEFGEF=S,ᓽx-4=8,.x=12,.•.᪛OEḄì12ãz(2)ç
NMè05ç
P4ᑣAM=BP=6,ᵫ(1)¡C0=CE=xeAC=4×BC=4&,.PD=BP+BC+CD=6+48+4×=6+8×,:NNDP=A5஺,íNNP஻=90஺.NP=PD=6+Sy/3,.NM=NP-MP=6+873-4=2+86!îᚪMNḄì(2+873)ã.

21îூ௃%⚪acTÆTXḄJ▭uᵨὃ~cTÆTXḄឋ_30஺TᡠtḄcTÈÉÀÊÈḄNË┦TÆTᦪ6¬BḄ]ÍÎTÏᙠuḄcTÆTXgᑭᵨÆTᦪ⚪ᵫ%ÐuḄÑÒ]a⚪Ḅᐵ¦.25ஹপ⊤ÓgÔ|Õ1(),100.5,25,().25,150.5,1(2)0.25,100(3)1000x(0.3+0.1+0,05)=450(Ö).ூ
᪆௃(1)ᵫ⚣ᦪcABØÙa50,ᑖØᦪᑡgÔ|Õᑏ100.5,150.50.5-50.5Ḅ⚣ᦪ=100x0.1=10,ᵫᔜØḄ⚣᳛ÞUÉÀ1B5100.5-150.5Ḅ⚣᳛=1-0.1-0.2-0.3-0.1-0.05=0.25,ᑣ⚣ᦪ=100x0.25=25,ᵫ%Õ⊤ᓽ(2)ᙠ⚣᳛ᑖàcAgáXABCDḄ☢ã&50x0.25=12.5,ä|}~Ḅ᪵{å"a100(3)ᐜ4*ᙠ150ᐗ$èḄḄ⚣᳛éê4ut᪥1000gëìÖí⚗ïð..ூ
௃5(1)Õ⊤᝞:ᑖØ⚣ᦪ⚣᳛0.5~50.5100.150.5"100,5200.2100.5~150.5250.25150.5200.5300.3200.5~250.5100.1250.5~300.550.05ᔠ100(2)áXABCDḄ☢ã&0.25,᪵{å"a100(3)íä⚗ïðḄpᦪ=1000x(0.3+0.1+0.05)=450p.ூ௃

22{⚪ὃ~⚣ᦪᑖà⊤᪵{ñwòஹ᪵{å"ÉBó.ô3⚣ᦪᑖà⊤gwḄ⚣᳛ÞUa1.26ஹ(1)õö8ᑮ÷]/ḄÙù&3km(2)ú÷\Ḅüv&40.6km/hூ᪆௃ý⚪ᑖ᪆5(1)ABÁ1¿ÀO,ᑭᵨNDAO=60஺ᑭᵨNDAOḄþÿ
OAOB,BEᓽ(2)ᐜ
DE=EF+DF=
DE=5J3,ᵫᵫtanNCBE=——
EC,ᓽ
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BE.⚪᪆(1)AB1!O,ᙠRtAAOD$VZOAD=60°,AD=2(km),AnAOA=---------=4(km),cos60°VAB=10(km),.♦.OB=AB-OA=6(km),ᙠRtABOE$NOBE=NOAD=60஺BE=OB»cos60°=3(km),&'(!Bᑮ*1Ḅ+,-3km(2)VZOAD=60°,AD=2(km),.,.OD=ADtan60°=273,VZBEO=90°,BO=6,BE=3,:.OE=JOB?-BE?=3.
DE=OD+OE=5y/3(km)CE=BE»tanZCBE=3tan760,.\CD=CE-DE=3tan76஺-573=3.38(km),1sCDV5(min)=——(h),/.v=—=——=12CD=12x3.38F0.6(km/h),12t1&/0Ḅ2-40.6km/h.ூ!4௃6⚪7⌕ὃ:;<ᔣ>?⚪@Aᑭᵨ┦>E>FᦪᐵI
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2327ஹ(1)A,Bò£óôᵯöᡧḄ├ùᓫúᑖé250ᐗ/ýஹ210ᐗ/ýz(2)A£óôḄᵯöᡧᨬÿ
10(3)ᙠফḄᩩᑭ1400ᐗḄ᪗.ூ᪆௃(1)AஹBᵯ"ᡧḄ├%ᓫ'ᑖ)xᐗஹyᐗ*᪷,3A5BḄᵯᡧᦈᐭ1800ᐗ*4A10BḄᵯᡧᦈᐭ3100ᐗ*ᑡ0123(2)
Aᵯ"ᡧa*ᑣ
Bᵯ"ᡧ(30-a)*᪷,56785400ᐗ*ᑡ9:3(3)ᑭ1400ᐗ*ᑡ013;aḄ<20,=ᔠ(2)Ḅᩩ*?@᪗.ூA௃(1)A,Bᵯ"ᡧḄ├%ᓫ'ᑖ)xᐗ/ஹyᐗ/.3x+5y=1800x=250ð⚪<•JgU+10y=3100y=210CDA,Bᵯ"ᡧḄ├%ᓫ'ᑖ)250ᐗ/ஹ210ᐗ/.(2)
AḄᵯ"ᡧa*ᑣ
BḄᵯ"ᡧ(30—஺).G⚪I*J200a+170(30-a)W5400,Ja<10.:AḄᵯ"ᡧᨬ7
10.(3)G⚪I*ᨵQ50-200)a+(210-170)(30-஺)=1400,Ja=2O.".'a<10,OᙠফḄᩩᑭ1400ᐗḄ᪗.ூPQ௃R⚪ὃTUOᐗVW012XVᐗVW9:ḄYᵨ*CR⚪Ḅᐵ\]^_⚪I*;`@ᦪ*b;ᔠ〉Ḅ9dᐵeX9ᐵe*ᑡ012X9:3.