2021-2022学年内蒙古中考三模数学试题含解析及点睛

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5!ὃ#ᫀ1ஹ⌱⚪(ᜧ⚪ᐳ12+⚪,+⚪4ᑖᐳ48ᑖ.ᙠ,+⚪wḄ⌱⚗Dᨵ1⚗ᔠ⚪⌕Ḅ./1ஹDூL᪆௃⚪ᑖ᪆'ᙊ┵Ḅ☢Tr,ᑣ2r,☢ᕜ2ᙊ┵Ḅ☢7Ḅᙊn஺ᑣ^^=2L'n=180°.ᦑ⌱D.180ὃ;'ᙊ┵Ḅg.2ஹAூL᪆௃ᑖCLi¢£ᑮx<203-2a,ᵫ¦¢£§ᨵ5᦮ᦪLᑣ¢£§ḄL©3-2ax-5®33-2a,•.•¢£§ᨵ5᦮ᦪL"¢£§ḄL©3-2a

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8BE=EF=6,ABEF%Ὺ'()᧕+,GED-%Ὺ'()ট┯01,3456%জঝঞᦑ⌱?௃A⚪CᔠឋFὃGHIᢚKᣚḄឋMN3O)ḄឋMᐰ'()ḄᑨRឋMSTRᳮᨵWRḄX.7ஹAூ
᪆௃21Z⚪ὃGHᭆ᳛]^Ḅ_ᵨ.abᵨᑮḄ+d>e<ᭆ᳛=ᡠhᦪjᦪkl.᪷n⚪bo<-------=q2+3+a3o/.OM±OD,OM_LEF,ZMFO=60°,:.ZMOD=ZOMF=90°,ூ>?௃A⚪ὃGH3{)Nᙊஹ3z{)ḄឋMஹ'(ᦪஹSTRᳮ13z{)ḄឋMᵫ'(ᦪhOM%q⚪Ḅᐵ.9ஹB

9ூ᪆௃345ஹ745ᑖ9:ᱥ<☢ஹ>☢?ᡠ,ᑮḄ5.ூ௃Bᔠ345D745EFᨬHᨵ4JKL"<MNFᨬHᨵ1JKL"<OPQᡂSJTU<ḄK"<ḄJᦪᨬH5J.ᦑ⌱-B.ூYZ௃P⚪ὃ]ᵫ45ᑨTU<⚪ᐵ_ᙠab9510ஹBூ᪆௃ᑖ᪆-᪷deᱥfy=ax2+bx+cghijkᦪy=2Ḅ5lᙠMml▲ᨵmJoᐳY,b>0,᪷dqYrᙶ᪗u1,X,a+b+c=b,,a,cvuwhᦪxP,mykᦪy=bx+acḄ5l.-•••eᱥfy=ax2+bx+cghijkᦪy=PḄ5lᙠMml▲ᨵmJoᐳYXAb>0,•
•qYrᙶ᪗u1,:.a+b+c=b,:.a+c=0,:.ac<0,...mykᦪy=bx+acḄ5lz{Mmஹஹ|l▲.ᦑ⌱B.YZ-ὃ]}mykᦪḄ5lhijkᦪḄឋNykᦪḄឋᐵ_,ᑮb>0,acVO.11,Cூ᪆௃᪷dEᦪḄᑣAᑨ᪷dḄ"Bᑨ᪷d᦮ᦪᢣᦪḄCᑨ᪷dNy᪷ḄDᑨ.ூ௃-Aஹ=a3,ᡠA⌱⚗┯Bஹ=a2b2,ᡠB⌱⚗┯Cஹ=g,ᡠC⌱⚗Dஹ=26,ᡠD⌱⚗┯.

10ᦑ⌱-c.ூYZ௃⚪ὃ]}Ny᪷Ḅ-Ny᪷wᐜᔜJNy᪷ᓄᡂᨬNy᪷"ᦪwḄNy᪷ᔠᔠ"uᦪw᪷.ὃ]}᦮Ḅ¡¢.12ஹAூ᪆௃ᐜ£eᱥf᪆ᓄu⚔Y¥¦Ḅᑣᓽ.ூ௃N=N;-N+/=¬N-9'+®ᔣ¥°±2Jᓫ³$´ᔣ>°±3Jᓫ³$´,□=
µm¶+2'+
+3=
µ+§’+?=µ3º+/ᦑ⌱A.ூYZ௃⚪ὃ]NykᦪḄ°±»¼°±Ḅᑣ“¥¦”NykᦪḄ°±m*⌕£᪆ᓄu⚔YNஹÀÁ⚪-¬ᜧ⚪ᐳ6JK⚪ÃK⚪4ᑖᐳ24ᑖ.Ä413ஹy=—xூ᪆௃ூᑖ᪆௃᪷dhijkᦪ5l>YḄrஹÅᙶ᪗Æ,ᐵamḄ"Ç"ÇᓽÈ,mḄÉᵫÊ*ᦪᓽÈ,hijkᦪḄ᪆.ூ௃%hijkᦪ᪆uË=ÌXᵫ⚪,-m2=2mx
-l,,-m=2ᡈm=0¬Î⚪ÏÐÄᡠYA
-2,-2,YB
-4,1,ᡠk=4,4ᡠhijkᦪ᪆u-y=—,x4ᦑÑᫀuË=m.xூYZ௃⚪ὃ]}hijkᦪÓhijkᦪ5l>YḄrஹÅᙶ᪗Æ
aijᦪk⚪Ḅᐵ_.

1114ஹ30ூq᪆௃᪷nRᳮoᑮMNḄᨬᜧACᨬᜧACᨬᜧ%hohoᨬᜧ.ூq௃qMஹNᑖ%ABஹBCḄ>ᵫ'()Ḅ+?௃A⚪ὃGH'()ḄRᳮஹῪ('()ḄឋM¡ᙊᕜ(Rᳮq⚪Ḅᐵ%Hq£¤᎛MNḄᨬᜧ,X-ᜧ.15ஹV5-1ூq᪆௃¦AC=x,ᑣBC=2-x,᪷n48=5043ᑡOwhqᓽ.ூq௃q<¦AC=x,ᑣBC=2-x,᪷noB=2(2-x),qo?௃A⚪ὃGH®¯ᑖᒘḄ_ᵨᐵ%±4®¯ᑖᒘᡠ²¡ḄḄl.16ஹ3(m-n)ூq᪆௃

12N3(m2—2mn+n2)=3(m-ri)2ᦑÀ-3¬᪷m஻Ä217ஹ2ூ᪆௃Ú⚪᪆-{YBÛÜfACḄᚖfqÜfACaYÞ᝞5ᡠà.,.,8CEḄ☢A4OEḄ☢Ḅ2áEA8ḄâYSAA஻C=2SABCE9SAABD=2SAADE»SAABC=2SAABD,é4ABCDoABDḄêᙳuBF,.AC=2BD,.OD=2OC.•:CD=k,kQk3ÌYAḄᙶ᪗u¬N3,Y8Ḅᙶ᪗u¬.?•NÄ,3323.AC=3BD=,929.AB=2AC=6AF=AC+BD=-,92CD=k=y/AB2-AF2=J62-¬1Ä2=ð.ூYZ௃⚪ὃ]}hijkᦪ5l>YḄᙶ᪗ᱯòஹḄ☢oó()*ᳮ.᪀⌼Üᑭᵨ()*ᳮøᝯ,úkÉ⚪Ḅᐵ_.18ஹ10%ூ᪆௃⚪%Süý°ᙳÃýḄþ$᳛x,
ᙢ☢44%,ᑣᨵ
1+x,=1+44%,ᓽᫀ.ூ௃

13q<¦³´µᙳ´Ḅ·ᙢ¹᳛eX,᪷n⚪bo(1+x)1=1+44%,qo(ª«)xi=0.1.#<³´µᙳ´·ᙢ☢»Ḅ¹᳛e10%.ᦑ#ᫀe10%ூ>?௃Z⚪ὃG¹᳛Ḅ⚪W¼]^e100,qo5,3ó'8,.5WxW8ðe᦮ᦪVy=100x+Lk=100>0,yõxḄ¹ᜧ¹ᜧx=5yᨬÍᨬÍey=100x5+l=9900(ᐗ).#<jÜèᨬÄḄíîOᫀ%<5Ùᜧ×Øஹ5ÙÍ×ØâãA᩟13Ùᜧ×Øஹ2ÙÍ×ØâãB᩟.ᨬÄÜèe9900ᐗ.20ஹ(2)65°(2)2.ூq᪆௃÷⚪ᑖ᪆<(2)xOT,᪷n(µᑖḄឋM¡('()Ḅ³Ì┦(ùúÐoCT_LOT,CTe஺஺Ḅᑗ1(2)б{)OTCEeü)hoOEḄᙠ(AOAEᑭᵨSTRᳮᓽhq.÷⚪q᪆<ফxOT,•.,OA=OT,'NOATuNOTA,TATµᑖ/BAD,...NDAT=NOAT,...NDATuNOTA,

14OT஻AC,XVCT±AC,.\CT±OT,CT஺OḄᑗ$%(2)O&OE_LAD'E,ᑣEAD()XVCT1AC,/.OE^CT,*+,-OTCE.-,CT=/,.♦.OE=12OA=2,...ᙠRtAOAE(AE=/o4I-OE2=1»-AD=2AE=2.5ὃ)52.ᑗ$Ḅᑨ78ឋ:%2.;<7ᳮ%3.ᙊᕜ@7ᳮ.21ஹ(1)7cm(2)BC$CABDEFG)HIJAC+CB=a(cm),ᐸLᩩNOPᑣMN=a(cm);ᳮᵫRS2᪆(3)—b(cm)2ூ᪆௃(1)W“)MஹNᑖZ[ACஹBCḄ()”ᐜMC,CNḄ^_`ᑭᵨMN=CM+CNᓽMNḄ^_ᓽ.(2)W⚪Fde-ᓽfᫀ.(3)W⚪Fde-ᓽfᫀ.ூR௃(1)᝞eAMC-N~~BVAC=8cm,CB=6cm,AB=AC+CB=8+6=14cm,2•)MஹNᑖZ[ACஹBCḄ()11.•.MC=-AC,CN=-BC,221,111/.MN=-AC+-BC=-(AC+BC)=-AB=7cm.22225MNḄ^7cm.(2)BC$CABDEG)IJAC+CB=acm,ᐸiᩩNOPᑣMN=jacm,2AMC-NBᳮᵫ[5•.•)MஹNᑖZ[ACஹBCḄ(),

1511,*.MC=-AC,CN=-BC,22VAC+CB=acm,I,111*MN=-AC+-BC=-(AC+BC)=cm.2222(3):᝞eAMBHC•)MஹNᑖZ[ACஹBCḄ()11/.MC=-AC,CN=-BC,22VAC—CB=bcm,111I:.MN=-AC—-BC=-(AC-BC)=-bcm.2222ὃ)5)Ḅkl.22ஹ(1)RS᪆%(2)BD=9.6.ூ᪆௃m⚪ᑖ᪆5(1)no0B,ᵫᚖq7ᳮfBE=DE,OELBD,BF=DF=BD,`ᵫᙊᕜ@7ᳮfNBOE=ZA,2rsfᑮNO5E+NQBC=90஺ᓽNOBC=90°,u⚪fv.(2)ᵫ;<7ᳮOC,`ᵫwḄ☢஻E,ᓽfy5஺Ḅ^.m⚪᪆5(1)vz5᝞{eᡠ}no0ᕒVE[y80Ḅ():.BE=DE,OEA,BD,BF=DF=ஹBD,2*ZBOE=ZA,ZOBE+NBOE=90°.VZDBC=NA,AZBOE=NDBC,:.ZOBE+ZDBC=9Q°,.Z05c=90஺ᓽBCVOB,:.BC[஺OḄᑗ$.(2)5%஺5=6,BC=8,BCOB,.OC=dOB+BC=10■:sCM=LOCBE=LOBBC,.BE=OB~BC6x8=4.8,QBC22OC10


BD=2BE=9.6.

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