2022年内蒙古呼和浩特市中考数学真题（含答案解析）

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20>1@᪷ÕãᦪÕäÒᙠ254x<28,284x<31Ḅ⚣ᦪᓽ()᪷Õæᦪ9ÏçᦪḄèᓽ(RGdḄz;>2@᪷ÕÏçᦪḄë().>3@᪷Õᑡ⊤Ä(ᭆ᳛().প)§30\ᦪÕï&ᑮᜧ᣸ᑡ᝞ò,13,14,15,15,15,15,16,16,16,16,16,17,17,17,18,18,19,19,19,22,23,24,26,27,27,27,28,30,32,32,ᙠ25Vx<28ḄᦪÕ126,27,27,27,4\ᦑa=4,ᙠ284x<31ḄᦪÕ128,30,ᐳ2\,ᦑb=2,ᐸÏ16Òö5ᦪᨬøᦑc=16,s15Ás16\ᦪÕ118,ᦑd=18,ᦑqᫀ14,2,16,18.ফ18úᐗᳮᵫ᪷ÕÏçᦪ118úᐗû[üýþḄ⃩ᕒᑮ├᪗ᨴ├18ᐗᔠ〉,ব⃩ᕒA,8!Ḅ⃩ᕒC,£>,ᑡ⊤᝞),ABCDAABACADBBABCBDCCACBCDDDADBDCᐳᨵ12./012⃩ᕒᙠ45ᑁḄ78ᨵ4.0,41ᦑ⃩ᕒᙠ45ᑁḄᭆ᳛==@.Bᫀ14⚓ᐳ24⚓

21ூFG௃I⚪ὃLM⚣ᦪᑖQ⊤RSᦪTᦪᑡ⊤UVᭆ᳛WXᦪYZ[Ḅ\U]^Vᭆ᳛Ḅ\U_`⚪Ḅᐵb.20.(1)cdef`ফh5ூ`᪆௃ூᑖ᪆௃(1)lmA஺ᵫpq0rACBC,s᪷Y/Ὺvw8Ḅvxᔠ5ឋzᓽ0cd1|.(2)ᵫ(1)0rC£>=4,8c=8,᪷YtanC=Jᓽ0VrA£>=2,}~ᑭᵨᳮᓽ0VrAC,ᵫAB஺஺Ḅpqr/BEC=N4£>C=90஺NCᐳw0r^ADC~/\BEC,᪷Yvw8Ḅឋzᓽ0VrCE,}~0V`.(1)cdlmA஺᝞ᡠ஺஺Ḅpq-.ADLBC,TA8=AC,vw8ABC/Ὺvw8.•.AOBCḄᚖpᑖx.\BD=CD.(2)ᵫ(1)0rB£)=C£>=4,ADAD\"tanC=-----=-----=—,BC=2BD=8,CD42AD=29Bᫀ15⚓ᐳ24⚓

22ᙠAC£R/.AC=yiADrCDr=722+42=2+A8஺஺ḄpqNBEC=ZADC=90°,NC=NC,AADC~AB£C,.ᙶ=0,ᓽ/BCCE8CE.CEH5AE=CE-AC^^^--2^=—.55ூFG௃I⚪ὃLMvw8ᙊḄ¡ᔠ¢⚪ὃLM/Ὺvw8Ḅᑨ^ឋzஹᙊᕜwᳮஹvw8Ḅᑨ^ឋzஹ┦wvw§ᦪ^ᳮḄ¨ᵨ©ªWX/Ὺvw8vxᔠ5Ḅឋz^vw8«¨¬ᡂ®¯Ḅឋz_`⚪Ḅᐵb.13221-প³´+µ³“22x(2)xJᡈ0ºxºlூ`᪆௃ூᑖ᪆௃(1)᪷YFCḄᙶ᪗^FAFḄ¼ᙶ᪗0VrC஺Ḅ½FBḄ¾ᙶ᪗}~0VrACḄ½ᑭᵨᳮᓽ0VrAO,}~FAḄᙶ᪗}~0VrÀ®¯§ᦪḄ`᪆Á}~0VrFBḄᙶ᪗sᑭᵨÂÃᦪUᓽ0Vr5ħᦪ`᪆Á.(2)Å8Æ/ÁÇ+ȺÉᓽʺ³᪷Yᦪ81ᔠËÌÀ®¯§ᦪÍᙠ5ħXᦪÍÎ\ḄÏᑖᓽ0V`.(1)`AFḄ¼ᙶ᪗1,CD=X-X%=-Ñ,CAs6AC=CD=—,2ᙠRsADCRBᫀ16⚓ᐳ24⚓

23AD=DAC?-CD2=JÔÕ_(|)2=|,51-»=5-5=2,FAḄᙶ᪗(1,2),FAᙠÀ®¯§ᦪ%=×ḄÍÎX.*.2=p`r஻7=2,2À®¯§ᦪḄ`᪆Á%=—x112Ú,=_µÛ_7=_`rx=-422xFBḄᙶ᪗(-4,—Ñ),ÜA(l,2)8(-4,-g)Ýᐭ5ħᦪß=Ç+Èr2=k+bk=1i஻`r3——=-4k+b.32bEFi2135ħᦪḄ`᪆Áফᵫ⚪àr772mkx+b-—<0ᓽá+b

24ூFG௃I⚪ὃLM5ħᦪÀ®¯§ᦪḄ¡ᔠ¨ᵨὃLMÂÃᦪUV§ᦪ`᪆Á^᪷YÍ^ឋz`è¢⚪ஹVÆ/ÁḄ`穪WXÂÃᦪUV§ᦪḄ`᪆Áéᝯëìᦪ81ᔠíî`è¢⚪_`⚪Ḅᐵb.22.@1ïðñòᔴôõḄᙳ÷ø_2200ᐗ@2ï¨Ü175ᔴôõùúᡂûᱏᨬᜧᑭÿ202500ᐗூ᪆௃ூᑖ᪆௃1ᔴḄᙳxᐗᑣ!Ḅᙳx+1000ᐗ#!Ḅᙳx-1000ᐗ᪷&#Ḅ!ᦪ(!ᦪ(Ḅ)*&+ᑡ-./02ᐜ/23ᡠ!Ḅ5ᦪ᪷&ᡠᨵ!Ḅ78ᐰ:;<=>ᵨ@ABC60ᜩᐸG;<ᡂIᱏḄᦪ(AKL;<ᡂMNḄᦪ(Ḅ;&+ᑡAPQR/ᯠT/2ᨬᜧᑭX.1ᔴḄᙳxᐗ,300000ஹ500000ᵫ⚪]^,x2=x+200_____x-200^d>=2200,fghdX=2200iᑖQ-.Ḅ>jᔠ⚪],l:ᔴḄᙳ2200ᐗ0ফnᔳ,3=375ᔴ,ᵫ1^3Ḅᦪ:2400rs஻?ᔴ;<ᡂIᱏ,ᑣrs375-wᔴ;<ᡂMN,m>^375—/nᵫ⚪]^wm375-m—+----------<60158^d150VmM175,{ᑭXd700^+400375—;=300஻7+150000,~=175@-ᑭXᨬᜧᨬᜧᑭXd300x175+15X00=202500ᐗ.lᫀ18⚓ᐳ24⚓

25ldrs175ᔴ;<ᡂIᱏᨬᜧᑭX202500ᐗ.ூ௃+⚪ὃᑖQ-.ᐗAPQḄrᵨl⚪Ḅᐵ⚪]2ᦪ2ᔠ〉ḄP(ᐵᑡ-./.23.(1)AG=CE(2)C.᪆(3)0,C.᪆ூ᪆௃ூᑖ᪆௃L(1),᪷&EBCḄG^lᫀ0L(2),AG=EC,EG,BGEPῪ¡¢£¢¤¥G4E¦CEF,^lᫀ0L(3),BC=x,ᑣᑣ§=&kxGEC=(1-k)x,¥ᑭᵨPῪ¡¢£¢¤Ḅឋ©⊤«EPḄ¬ᑭᵨ®¯¤Ḅᑨ±^²⌕EP=FC,ᓽµ¶⚪.(1)dBCḄG-.BE=CE.•••GA8ḄG-.BG=AG,-.AG=CE.ᦑlᫀdAG=CE(2)AG=EC,EG.•••®¯¤ABC஺º-¤,-.AB=BC,ZB=90°.lᫀ19⚓ᐳ24⚓

26VAG=CE,:.BG=BE,BGE
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;<ZBCD=90°.♦CF
;<ABCD᜜Ḅ>ᑖZZCF=45°,ZECF=90°+45o=135°.VAE1EF,ZAEB+ZFEC=90°.*/ZBAE+ZAEB=90°f/BAE=/CEF,.,.GAE^ACEF,.AE=EF
3@A=B9PEC
>C9.᝞.ᵫD2&GAE^^CEF,.CF=EG.E8C=x,ᑣBE=H,GE=JikxEC=X-kx.'JEPLAC,•••PEC
Ὺ78/PEC=45°,-ᫀ/20⚓ᐳ24⚓

27AZP£C+ZECF=180°,PE="(1—k)x.2•.PE//CF,~PE#b@®¯¤PECF®¯¤2/1(i-©x=kx2^Æ=ூ௃Ç⍝ᐵL®¯¤ḄÉᔠ¶⚪Ê⌕ὃº-¤Ḅឋ©ᐰP£¢¤Ḅឋ©ᑨ±®¯¤Ḅᑨ±PË.I324.(1)^=——x2+—x+2A(-1,0)0(2)ÎᙠE(0,3)ᡈ(0,-1),Ñ^8஺ÒÓ5஺Ô¯Ḅ¡¢£¢¤0ব2ᡈ,ூ᪆௃ூᑖ᪆௃(1)ᑭᵨÖ±ᦪ×lᓽ/0(2)ᐜ᪷&Gᙶ᪗ÚQ^஺E(0,,஻)¥᪷&)ᙶ᪗ÚQ^DE2+(1-)2=2-2m+dBD2=[4+1j+m2=m2+^-,B£2=/n2+16,¥ᵫßà±ᳮᓽ/0OC1(3)ᐜ/2tan/O8C=ᑶ=d,¥/2¡æ8஺Ḅ᪆QᯠTç(a,-0/+ga+2),ᑣM(a,-g“+2,CF=a,^PM=-g஻2+2a,¥ᑖ£êëìíîdNPCM=2NOBC,CCïCP஻xðñPMLEò/PMC=2/O8C0òNCPM=2NOBC,CPïPGᑖNCPM,ᑣNMPG=/OBC,ᓽ/.(1)dõõ4,0)Ó0,2)öᐭ,^d——xl6+4஻+c=04,2,^d2,c=2c=2lᫀ21⚓ᐳ24⚓

281Q#úᱥæḄ᪆Q"ý/+þ+2,13ÿ0,ᑣ=——x2+—X+2,22=-1,2=4,.,.A(-1,0)(2)ᙠᳮᵫ᝞•.•A(-1,0),C(0,2),஺!"#ACḄ%,&E(0,(),/.£>E2=[-g-0)+(1_m)2=._2m+,B£)2=(4+g)+m2=m2+^-,)=*+16,•••ABDE!-BO01Ḅ23435.,,,,05,81.•(-+16+஻ᔆ:2(+—=+—,44᦮ᳮ<2-2஻?-3=0,(=3ᡈ-1,•EḄᙶ᪗(0,3)ᡈ(0,-1)(3):,1B(4,0),C(0,2),A0B=4OC=2,f-.tanZOBC=—=~,OB2&2"BCḄ᪆Gy=I#0),KB(4,0),C(0,2)Lᐭ4k+b.=0k=-L&=22,=2OᫀQ22⚓ᐳ24⚓

29.•.2"BCḄ᪆Gy=-gx+2,&T(஺-Uᱏ+54+2),ᑣM(a,-/a+2),CF=a,.PM=(-ᕆ+|a+2)_(_ga+2)=-ga2+2a,NPCM=2N0BC,XCYCT஻xZ[PM\F,᝞]ᵬᡠ`ZFCM=ZOBC,BPtanNFCM=tanZOBC=g,NPCF=NFCM,•"Q஻yZ.CF±PQ,.PM=2FM,1,FM=——a2+a,4_J_2.-4a+a_l,a=2ᡈ0(ab)a2••PḄcᙶ᪗2/PMC=2/0BC,/PMC=/BMN,-./BMN=2/0BC,-/OBC+/BMN=9b஺,OC1NO8C=30஺dtanNO8C=e=2fghiᔠ⚪labNCPM=2N0BC,᝞]mᡠ`XPYPGnᑖNCPM,ᑣNMPG=N03C,■:NPMG=NBMN,APMGsMBMN,-./PGM=/BNM=90஺,-.NPGO90஺••PGnᑖNCPM,ᓽNMPG=NCPG,/PCM=/PMC,:.PC=PM,OᫀQ23⚓ᐳ24⚓

3034=5ᡈ0qabr3PḄcᙶ᪗s3tuᡠvTḄcᙶ᪗2ᡈூx௃z⚪{⌕ὃ~ᦪḄtᔠ⚪23435f435ḄᑨឋᦪḄtᔠ⚪23435Ḅឋf435Ḅᑨឋᑭᵨᦪ5ᔠᑖO!⚪Ḅᐵ.OᫀQ24⚓ᐳ24⚓