2021年河北省中考数学试卷（附答案详解）

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2021
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17.2021.
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314.2021.
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825.2021•ᓅḕᔊ⚪n᝞!
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18ூR᪆௃RA⌱⚗íc=-2î4=W=-ᦑ⌱⚗£¤ᔠ⚪z;2+248⌱⚗íc=0î/=5ᦑ⌱⚗£¤ᔠ⚪zc⌱⚗ð!:2+2c2+c=2(2+0-2(2+0C-2(2+c)9VC<-2,24-c<0,c<0,•2(2+c)V0,•••A>\,ᦑ⌱⚗¤ᔠ⚪z஺⌱⚗ícvoî•••2(2+c)Ḅ%ñ&•A-Ḅᜧòó&ᦑ⌱⚗£¤ᔠ⚪zᦑ⌱C.ôc=-2}0ᑖpõᐭAÌ*+7÷ᓽGᑨD,A,BḄn┯íc<-2}c<0î*+í-:Ḅ%ñᓽGᑨD,C,஺Ḅn┯.2+C2H⚪ὃKLᑖéḄ7÷ᑖéḄêÜøùúÖûᜧòQR⚪ḄᐵT.16.ூVᫀ௃DூYZ/௃üýù½-!ù½ஹᡧx☢ÿḄ
ஹḄឋஹᚖᑖḄᭆᐸឋஹῪḄឋஹᙊḄᐵூ᪆௃!᝞#$%&EM,EN,MF.NF.•••OM=ON,OE=OF,•••)*MENF+,)*$•••EF=MN,)*MENF+$ᦑ(I)/0$12#345NMOF*AAOB,"Sᡧ=FOMCSᡧ=AOB>ᦑ(n)┯8$ᦑ⌱!D.

19᝞#$%&EM,EN,MF.NF,᪷>Ḅᑨ@AB)*MENF+$CDBNMOFCLAOB,45(D)┯8.J⚪ὃMN#-PᩖN#$ḄᚖᑖḄឋ$Ḅᑨ@$ᡧḄ☢T5U$⚪ḄᐵV+WXYZ[\]JN#$^_`ὃaὃ⚪b.17.ூeᫀ௃a2+b24ூ5U௃hᐰjkஹhᐰjlkḄmnopூ᪆௃!(1)ᵫ#45!rᙽᵬ\uᱏ☢Twa2,rᙽz\uᱏḄ☢Tw᮱$rᙽ|\uᱏ☢Tw•••}ᵬஹzuᱏᔜ1ᙽ$ᐸ☢Tw&2+᮱$ᦑeᫀw!a2+b2-,(2)}|\uᱏxᙽᵨᡂrḄ/j$a2+4b2+xab+rhᐰjk$•••xF4,ᦑeᫀw!4.(1)ᵫ#45!rᙽᵬ\uᱏ☢Twrᙽz\uᱏḄ☢Tw᮱$rᙽ|\uᱏ☢Tw⊈ᓽ4;(2)ᑭᵨhᐰjlk4.J⚪ὃMhᐰjk$YZhᐰjlk+⚪ḄᐵV.18.ூeᫀ௃10ூ5U௃Ḅ᜜ឋஹᑁ@ᳮூ᪆௃!EF,GCDHஹG,᝞#!•K•LACB=180°-50°-60°=70°,•••*ECD=*ACB=70°.11,Z.DGF=*DCE+",•••*DGF=700+30°=100°.•••*EFD=110°,*EFD=*DGF+*D,£20⚓$ᐳ31⚓

204஺=10°.§#`ND=20°,ND¨10஺.ᦑeᫀw!$10.EF,©C஺_G,ª>Ḅᑁ@ᳮ4z4CB,᪷>«⚔4®NDCE,Cᵫᑁ@ᳮḄ¯°®ᑮNDGFḄ²ᦪ´ᑭᵨNEFC=110஺$Ḅ᜜Ḅឋ4®4஺Ḅ²ᦪ$µ§®¶·°.J⚪¸⌕ὃMḄ᜜Ḅឋ$Ḅᑁ@ᳮ.WXºᵨ»¼@ᳮ+⚪ḄᐵV.19.ூeᫀ௃(4,15)4ூ5U௃r½¾ᦪ¿ÀÁ¾ᦪÂᔠூ᪆௃!পa=15Å$y=15,(60(x=4ly=15,ᦑeᫀw!(4,15)´60ফᵫy=7y=-1.271(-50,-1.2),=—40=r1.5'•B(_40,-1.5),wÇᑮ᪷ᙠ4(-50,-1.2)8(-40,-1.5)ÉÊḄr᦮#3$◤⌕Í#1`ᙶ᪗Ḅᓫ²ÑÒÓwÔᩭḄ;,4Ö᦮ᦪk=4.ᦑeᫀw!4.(_60_(l)a=15Å$y=15,'rᑐ®!:Ö;Ú$ᓽ/஻?Ḅ©ᙶ᪗w(4,15)´(y=15U-_60(_60{7=~®4(-50,-1.2),ᵫஹ=ß®8(-40,-1.5),wÇᑮàᙶ᪗+r50Ḅy=-1.2(y=-1.5$◤⌕Í#1`ᙶ᪗Ḅᓫ²ÑÒÓwÔᩭḄ;$ᓽ4®᦮ᦪk=4.4J⚪ὃM¿ÀÁ¾ᦪ#3Ḅ©ᙶ᪗$á᪷>©ᙶ᪗â᦮ᙶ᪗ᓫ²Ḅã⚪$⚪ḄᐵV+¶ABḄᙶ᪗.20.ூeᫀ௃(1)ᵫ⚪ä4®!Q=4m+10n´

21(2)Ím=5xIO4,n=3x1()3åᐭ(çk®!<2=4x5x104+10x3x103=2.3x105.ூ5U௃ᑡåᦪkஹéêëᦪì-í«îïᜧḄᦪூ᪆௃(1)ᑖ᪆⚪ñ$òó⚪äᓽ4᪷>⚪äᑡ¶åᦪk´(2)᪷>(1)kḄåᦪkÍᦪôåᐭ$Cᵨéêëᦪì⊤ö¶ᓽ4.J⚪ὃMᑡåᦪkᵨéêëᦪì⊤öïᜧḄᦪ$ò÷⚪äᑡ¶åᦪkYZéêëᦪìḄ⊤öjì+⚪ḄᐵV.21.ூeᫀ௃!(1)ᗩᗩᡠᑡjúw101—x=2x,®!x=33|,ûw᦮ᦪ$•••%=331ßᔠ⚪ä$üüḄDìß/0.(2)AýþÿᳫᨵxᑣBᳫᨵ(101-)⚪101-X228,x<36p᦮ᦪxḄᨬᜧ36.Aᳫᨬᨵ36.ூ!௃#ᐗ#%&'(Ḅ)ᵨஹᵫ-▭/⚪012#ᐗ#%34ூ᪆௃(1)ᗩᗩᡠᑡḄ342xḄᵫxḄ&᦮ᦪᓽ2;;Ḅ<=&>?@(2)AAᳫᨵxᑣBᳫᨵ(101-C᪷E8ᳫF4ᳫGH28ᓽ2ᐵJxḄ#ᐗ#%&'(Kᓽ2xḄMNᐸPḄᨬᜧ᦮ᦪᓽ2QR.S⚪ὃUV#ᐗ#%&'(Ḅ)ᵨWXᵫ-▭/⚪012#ᐗ#%34⚪ḄᐵYZ:(1)\]#ᐗ#%34^2xḄ@(2)᪷Eᔜᦪ`KaḄᐵb>?ᑡ2#ᐗ#%&'(.22.ூᫀ௃(1)ᗩ;dᑮᓝg⍝iAᔣᓅdḄᭆ᳛/(2)⊡ᐰ᪛st᝞v:w22⚓ᐳ31⚓

22⍝$%⍝"#!"#!"#&'(ᔣ*ᓭᓅᓭ*ᓅ*2ᐳᨵ9|'}ḄQ~ᗩ;]ᓝg⍝iᔣḄQ~ᨵ3|ᔣᓭḄQ~ᨵ2|ᔣᓅḄQ~ᨵ2JᔣḄQ~ᨵ2|,••ᔣḄᭆ᳛9ᔣᓭḄᭆ᳛=ᔣᓅḄᭆ᳛=ᔣḄᭆ᳛=I#•ᔣḄᭆ᳛ᜧ.(!௃ᵨᑡ=^ᭆ᳛(ᑡ⊤=᪛st=)ூ᪆௃(1)ᵫᭆ᳛(^ᓽ@(2)⊡ᐰ᪛stᐳᨵ9|'}ḄQ~ᗩ;]ᓝg⍝iᔣḄQ~ᨵ3|ᔣᓭḄQ~ᨵ2|ᔣᓅḄQ~ᨵ2|ᔣḄQ~ᨵ2|ᵫᭆ᳛(^ᓽ.S⚪ὃUḄZᵨᑡ⊤=ᡈ᪛st=^ᭆ᳛.ᑡ⊤=ᡈ᪛st=W&&⍡Ḅᑡ2ᡠᨵ}ḄQ~ᑡ⊤=〉ᔠJᡂḄ¡᪛st=〉ᔠᡈW¢ᡂḄ¡.£ᭆ᳛=ᡠ^¤¥ᦪ¦¤¥ᦪKF.23.ூᫀ௃(1)•@2§¨©ªᓣ¬45஺,±஺4¢Ḅ!Ḅ²³ᙶ᪗¶·.•••4(4,4).A஺4Ḅ᪆(h=ks,1.4k=4.•••k=1.•••0AḄ᪆(h=s.2§»¨©#¼ᢝᙠ1§©Ḅ>v3±¿ÀḄ¨ÁḄÂa¨ÁḄÃÄÅƶ·.•••2§©ḄªᓣᑮAᜐÂÃÄ3ᔣ¢ÈÉV4km,ªᓣÊ4km,1§©Ḅ¨ÁË3/on/min,•••2§©ḄªᓣË4+g=3km/min.

23ফABCḄ᪆(h=ms+n,ᵫ⚪8(7,4),.(7m4-n=4tlOm+Ó=3'm=--193.n=3•••ÔḄ᪆(/1=#Õ+ÖOh=0,ᑣs=19.±⚜Ø2§©Ḽ▮!Ḅᙶ᪗(19,0).ব••PQ&Ü]3km,•5—Ó3.(5-s<3"1—(#Õ+wS32sss13.•••©ÅÆÞ0&Ü]3kmḄÂß(13-2)+3=^min.ூ!௃¬à¬áḄ)ᵨஹ#%âᦪḄ)ᵨூ᪆௃(1)ᵫªᓣ¬45஺OA¢Ḅ!Ḅ²³ᙶ᪗¶·ᵫãᑮ!Aᙶ᪗,ᵨäåbᦪ=OA᪆(^@ᑭᵨ2§»¨©#¼ᢝᙠ1§©Ḅ>v3¿ÀḄ¨ÁḄÂa¨ÁḄÃÄÅƶ·ᵫã^ªᓣË@(2)A8cḄ᪆(Ó=ms+n,ᵫ⚪ç8,Cᙶ᪗èᐭᓽ^@êh=0.^s,ᓽᑮQR@(3)PQ&Ü]3b”ᑮ5-/iS3,ᑭᵨ(1)(2)PḄ᪆(2ᐵJsḄ&'(ë?åsḄM2V©ÅÆÞ஺&Ü]3b"Ḅ¨ÁḄÃÄÅÆN◀W1§¨©Ḅ¨ÁËQR.S⚪í⌕ὃUV¬à¬áḄï¬/⚪äåbᦪ=^âᦪḄ᪆(&'(ë,

24(2)QRPAilAyAn#ᳮᵫ:ñ4⍗7.Z஺஺Ḅô,447Ali4=90°,**P-L.(3)TP4Z஺஺Ḅᑗù,*,•PAy-LA]/7,•Z-PAA=90°,71vZ-PA-^Ay=60°,AA=12,r7■1•PA=AA-tan60°=12V3.7X7ூ!௃ÿḄஹᙊḄᐵஹᑗḄឋூ᪆௃(1)ᑭᵨᓽ.(2)ᑭᵨᙊᕜ#$ᳮ&'ᓽ.(3))#*#+P-ᓽ..⚪ὃ1ᙊ2ᑗḄឋ2ᙊᕜ#$ᳮ22)#*#345,⚪Ḅᐵ789:;<ᙊḄᐵ2=>?ὃ@ὃ⚪A.25.ூCᫀ௃E(1)F᝞FᡠI2ᵫ⚪KLMNOḄPQᙶ᪗(4.5,7),NḄPQ(6,7),W>Xᱥy=-x2+4x+12,_y=0,%2-4x-12=0,cx=-2ᡈ6,•••A(-2,0),•••Q4Ḅgᙶ᪗h-2,ix=4.5j2y=9.75>7,ix=6j2y=0<7,iy=7j27=—/+4x+12,co=-1ᡈ5,•••XᱥLMᓅᨵrQ2srQhR(5,7),uQPvwᙠyzL▤7|}.

25(2)ᵫ⚪KXᱥCEy=-x2+bx+c,~R(5,7),ᨬQḄᙶ᪗hII,r4-^Z£=n•j—4#l—25+5b+c=7c28ᡈ()2.••XᱥCḄ᪆hy=-M+14%-38,Wo=7,••L▤75ḄOḄPQ(6,6),NḄPQh(7.5,6),••XᱥCḄWL▤75ᨵrQ.(3)W>XᱥC1y=-x2+14%-38,_y=0,cᑮ/14%+38=0,cx=7±VT12•••XᱥcrxḄ>(7+VT1,0),iy=2j22=-/+14X-38,cx=4ᡈ40,••.Xᱥ~(10,2),RMBDE?2Z.DEB=90°,DE=1,BE=2,•iQ஺(7+Vn,o)ᔠj2Q8Ḅgᙶ᪗Ḅᨬᜧ2ᨬᜧh8+VTT,iQB(10,2)ᔠj2QBḄgᙶ᪗ᨬ2ᨬh10,••QBgᙶ᪗ḄᨬᜧᨬᜧVTT-1.ூ45Q௃uᦪᔠூ᪆௃(1)ᵫ⚪KL▤ḄOPQ(4.5,7),NPQḄᙶ᪗(6,7),+x=4.5,6jḄyḄ2ᓽᑨ.(2)ᵫ⚪KXᱥCEy=—/+bx+c,~R(5,7),ᨬQḄᙶ᪗h11,᪀+b,c,c¡.(3)+XᱥXḄrQ2¢£y=2j2QḄᙶ᪗2ᑨ+¤¥ᱯ§¨©QBḄgᙶ᪗Ḅ2c¡..⚪=>uᦪᔠ⚪2ὃ1ªuᦪḄឋ2«$ᦪ¬3452⚪Ḅᐵ78v®¯ᱯ§Q°±⚪2=>?ὃ²⚪.26.ூCᫀ௃¡&E&'E•••³/BC,•••Z.A—*B,Z.C—/.D,ᙠAAOD´ABOC?2µ26⚓2ᐳ31⚓

26¸4=*BAD=BC,Z-D=zC•AOOw/kBOCG4sA),•AO—BO9vAO+BO=AB=20,•AO=10|¹ºEsABḄ?QhO,᝞F:iAO¼½¾¨©AO¿AÀj┐ÂÃ60஺j,8Cļ½¾¨©BC'¿QBÀj┐ÂÃ60஺,ÅBO=BC'=10,BC'஺83*#2•••8cÂÃᑮBOḄ¨©2ᓽC¢஺ᔠ2•••AO=AD=CD=10,•/DC83*#2^ADC=60°EÆÇEÈÉCOḄ?QM,iQMQBÊËᨬᜧj2OஹCஹ8ᐳ2஺ÌDQ148>Q,MÌMN_L4B>N,᝞FEᵫÍ4c4஺=10,BD=BC+CD=20,BM=CM+BC=15,s4Q=x,ᑣBQ=20-x,■1AD2-AQ2=DQ2=BD2-BQ2,■■100-x2=400-(20-x)2,co=I2•-AQ=l>

27•••DQ=1AD2-AQ2=Ð-DQLAB,MN1AB,•MN//DQ,MNBM.IM——ÑÅ=QᓽÒ-20,15ÓMN8uQMᑮ"ḄÊËh3:ÕÖ:জs)CPr08>"2GÌDG1AB>G,ØÙ஺P2᝞F:vBC=DC=10,CPÚᑖ4BCD,111UBHC=3HC=90஺,BH=-BD=-d,s8G=7n,ᑣ4G=20-m,-AD2-AG2=BD2-BG2f:.100—(20—m)2=d2—m2,d2+300m=--------402DUd+300•BG=--------40•*BHP=*BGD=90°,*PBH=*DBG,BHPsுBGD,BP_BHBD~BGcnBHBD20d2.BP=-------=-----------|BGd2+300ঝ8ÌBG1CD>G,᝞F:sAN=t,Ý=20-t,DN=y/AN2-AD2Vt2-loo.µ28⚓2ᐳ31⚓

28•D=Z.BGN=90°,AND=BNG,•••XADN~XBGN,NG_BN_BGDN-AN-AD'onNG20-tBGᓽ.=--=—,Vt2-iootioÞ(20-ß஻2Too_200-10t1N(J=------------------------
Dkl-",t£RMBCG?2BC=10,20V10t-100CG=VBC2-BG2=••CD=10,DN+NG+CG=10,ᓽ-uÅ+á)ஹ^^+ãäᳮ=I஺2tt•tVt2-100+(20-t)Vt2-100+205/10t-100=IOC,20Vt2-100+20V10t-100=lOt2B|J2Vt2-100=t-2V10C-100,¤Ú2᦮ᳮcE3æ40£=—4£“0£—100,••t஺0,**•3t—40——4V10t—100»ct=çè(ᜧ>20,é)ᡈê=23஺",•.AN=9AD105+V7:.cosct——=--------=-----/N200-40ஹ278,9¬uECÌCKJ.4B>K,FÌFH,4c>H,᝞F:•1AD=CD=10,AD1DC,AC2=200,•••AC2-AK2=BC2-BK2,200-AK2=100-(20-/IK)2,c4K=y,

29CK=yjAC2-AK2=2RtAACK[,tan^KAC=—=^,AK5RtXAFH?2tanz.KAC=—=—,AH5sFH=V7n,ᑣC”=FH=V7n,AH=5n,vAC=AH+CH=10V2,•5n+V7n=10A/2,c"òAF=y/AH2+FH2=V32n=V32-ó=ᨔ,RtADF?2AD105+V7cosa=û=—8,ூ45Q௃ýþãᣚᔠூ᪆௃ᵫ4AOD_4BOC,4஺=BO,4B=20,4஺=10A8ḄO,!4஺"#$%&AO'A()┐+,60஺).BC`abc%&BC''B()┐+,60஺,8c+,ᑮBOḄ%&,ᓽC4஺5ᔠ,"-WC=60°9:!M<3>?ᨬᜧ).OஹCஹBᐳD.E஺FOQ14BH஺.EMFMN14BHMᵫJKAD=10,4Q=x,ᑣBQ=20-x,100-x2=400-(20-x)2,AQ=|.OQ=R.SᵫMN஻OQ,U=V.MN=3W.ᓽ஻ᑮA3Ḅ>?XY8Z[জ]DCPGDBHH,dGFDG14BHG,_`DP,BG=m,ᑣ4G=20-m,ᵫAD2-AG2=BD2-BG2,m=BG=^-^,bBHP-ZiBGD,ᨵh=4040BDߟ,ᓽBP=jᓃBGd2+300ঝEBFBG1CCHG,AN=t,ᑣBN=20-t,DN=y/AN2-AD2=Vt2-100.ᵫXADN7BGN,h=h=h.⊤stNG=(20-t)",-loo,200-10^^&BCGBG=.CG=yz-{U2,᪷~DN+NG+CG=10,ᑡ“2-+(2o-t).2io°+30⚓.ᐳ31⚓

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