2021年全国各地中考数学试卷分类汇编：规律探索

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16O஺OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO஺O஺OOOOO஺OOOOO஺O஺$1%&$2%&$3%&$4%&ூᫀB᪆௃46.ூj⚪B௃67³U];<ᡠᨵUV>᜜µ¶ᨵ¬ᙊ)*#Ḅ·>¬ᙊḄᦪUV]⊤h1x2,UV]⊤h2x3,UV]⊤h3x4,UV]⊤h4x5,ᡠᨵnUV>¬ᙊḄᦪ]⊤h4+ncn+lSᦑ6UV>¬ᙊḄᦪ46.ூᢣ௃E⚪ὃ7᪷UVÁ,-.ḄÂÃ)B,-.Ḅ⚪/Ä✌ᐜÁ,ᔜÆᑖḄᐳÈWᯠL,ᔜÆᑖḄÈW)X⚪/ÊkḄᩩÌÍᨵ,ᑮ-.]Î᯿⚪/ᩩÌÐvÑTᑏÓ)Ô3-5fqᡈUVᓽ],ᑮ-..15.2021¦ØÙ)13,3ᑖSÚÂÛᦪ2,4,8,16,32,ᢥ-.)ᑣnᦪ.ூᫀB᪆௃2"ூj⚪B௃ᐜ67ᡠÊḄᦪ)HᑮÓᦪÞ2ḄÓ)ß·Hᑮnᦪ2Ḅn.ூᢣ௃⚪ὃᦪ"Ḅ#ᓄ)4567)ᑖ᪆ஹ'(?;<ᐸ>Ḅ-.)?@ᵨ;<Ḅ-.BCà▭D⚪)B⚪ḄᐵGâãÓᦪä2ḄÓ.16.2021åæåç)22,14ᑖSᡃéÂ⍝)ê5ëWḄìᱥîḄB᪆f]^y—ax2+bxa:^0'c1Sðñ*᪵Ḅìᱥî⚔Wᙶ᪗c1,1SÄ)a—⚔Wᙶ᪗c஻õ)m,mWOÄ)஺ùḄᐵMf

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2
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18(3)Bn•.•⚔A஻ᙠKy=xqDT4Ḅᙶ᪗(&n),{ᡠᙠḄ%ᱥ⚔ᙶ᪗S0ᵫ(1)(2)D?஺“ᡠᙠḄ%ᱥB᪆:=—1^+ᔠt:!_!.•.஺"Ḅᙶ᪗(2n,ri)),--(2/t)2+2X2஻=஻t4"=3f•'ஹ஻_᦮ᦪtW12,▬W12."=3,6ᡈ9.ᩩ/Ḅ!03,6ᡈ9ூᢣ௃⚪ὃ<ᦪḄ⚔ᙶ᪗9:ᦪqḄᙶ᪗ᐸB᪆:Ḅᐵ᜜¢£ᑮ!ḄឋZ.,<ᦪ⚔ᙶ᪗¤D¥ᵨ9:¦D¥ᵨ§ᦪqḄᙶ᪗〉ᔠᐸᦪB᪆:Bk©(3)⚪¤⌕«S஻Ḅfgiᔞ17.(2021¯°±²16,4ᑖ)᝞ᡠOᡠᨵ´µ!Ḅ)¶·¸x)⚔ᙠyq¹ᑁᑮ᜜»¼Ḅ02,4,6,8,....⚔ᵨ¾ஹA2ஹA3ஹ4ஹ…⊤Oᐸ'A4xஹ¿4444ஹ44ஹ…ᙳÁÂ)ᓫÄᑣ⚔Ḅᙶ᪗_,42Ḅᙶ᪗_.

19yூkᫀB᪆௃0,V3-1
,-8,-8
.ூÅ⚪Bk௃ᵫ¸22+3=7Æ1,Ç4Ḅᙶ᪗-1,-1
,Ḅᙶ᪗-2,—2
4Ḅᙶ᪗-3,—3
ÈḄᙶ᪗-8,-8
ூᢣ௃BÉᦪÊËÌᡈ!ËÌÍẚÏ)ᵨ⊤ÐqÑaᦪḄÒÓ!ḄÒÓ⊤OÔᩭÕᙠc☢ᑏÔ»ḄØÙ#᪵Û᧕ÝÔᐸ'ḄËÌ;´.Bk⚪1.2021²ßᓭá27,10ᑖ>â¸ãÁä´µ!åᐭæᕜèᢥâêëÒìíḄᔣ)᪵îïð#ã´µ!ñëÁänåᐭæᕜèᢥâêëÒìíḄᔣÁòîïð#ã´µ!ñ⌮Áä஺ô᝞᝞জZvlBCö÷“£C'æᕜèA8C4/TBC'/TìíḄᔣ)᪵,

20øù÷48CñëÁäE᝞ঝZVIBCöZW9C,æᕜèABCA49CAìíḄᔣÁòøù"BC÷A£Cñ⌮Áä஺(1)᪷QIஹIIûin.Ḅᩩ/D?Ñᑡ´âÁä´µ!nজ÷ADE÷ABCEঝ4GH0+/\KFOঞ÷NQP÷NM஺஺ᐸ'ñëÁäḄ_:ñ⌮ÁäḄ_஺(þᑏᡠᨵÿᔠ⌕Ḅ)(2)᝞ঞᙠ┦4BCNA᪆:(1)জঝCঞ(4ᑖ)

212>C᪷-PᙠABCḄ/0ᑖ&EF#G3H஺I!G3HC᝞জPᙠBCJKBஹ஺PLM42ᩩPQiஹPQ1,ᑖNIONCPQi=N4,ZBPQ=ZA,PᓃRPQICஹ^PBQIWZXABC%&2⌮()஺IXG3HC᝞ঝᙠACJKAஹO8ZNC8A/=NA,BM[4c./\PᙠAMJKMRPiLM41ᩩP஺NAPiQ=N4BC,]RAPiQABC%&⌮()C\PᙠCMRPLM42ᩩ^0ஹ^஺2,ᑖ_2NA2Qi=NABC,NCP2Q=NABC,]R4ᓃ஺`WAABC%&⌮()஺I#G3HC᝞ঞPᙠ4BJK4ஹBCZNBCO=NA,ZAC£=ZB,CDஹCEᑖ_[4ca஺ஹEo\PᙠADJK0RPLM41ᩩP஺b4P|Q=NABC,]RAQPiABC%&⌮()c\PᙠDERPLM42ᩩ22஺1ஹ22஺2,ᑖ_2

22ZAPQt=ZACB,2NBP2Q2=NBCA,]RAQ1P2ஹAQ28P2WABC%&⌮();\PᙠBEJKEkRP3LM41ᩩ23஺',NBRQ'NCA,]RQ'BRABC%&⌮()஺J10ᑖk17.J2021•t⃩17,4ᑖk᝞ᡠxyz/:>=~AJ0,1kZyḄᚖ[/aB,BZ/Ḅᚖ[ya4;4ZkḄᚖ[,a8,Z/Ḅᚖ[ya4C……ᢥ]ZFᑣ□Ḅᙶ᪗&.--------------FI17⚪kᫀCJ0,4233kᡈJ0,26kJEᫀ⌱!"Wk>᪆C&y=XḄᔣḄᜳ&30°,ᡠENAOB=60°,3ᙠR/AAOB&0A=l,ᡠE0B=2,ᡠE஺4=4,ᓽA1Ḅᙶ᪗&J0,4k,.ᳮ஺88,ᡠᙠ¦AA?஺஺&=16,ᓽA2Ḅᙶ᪗&

23(0,42)©ª«¬40I3Ḅᙶ᪗&(0,42°ᡈ(0,24°26).17.(2021•®¯17,3ᑖ)᝞ᡠxᙠ°☢ᙶ᪗²!³´µ஺4¶,ᢥᔣᔣ·ᔣFᔣ·Ḅᔣ¸ᙢº³»º³!"ᓫ/ᑮ4(0,1),A2(1,1),A3(1,0),A(2,0),…¾¿4"+1"&Âᯠ4ᦪ)Ḅᙶ᪗&(ᵨn⊤x)ὃᑖ᪆CÈÉÊCḄᙶ᪗.Ë⚪ᑖ᪆CÈÉÊ.ᑖ᪆C᪷-$ᑖ_4஻=1ஹ2ஹ3RÍḄA4஻+IḄᙶ᪗ᯠÎ᪷-ÏᓄÈÉᑏ4ᓽÒ.>C>CᵫÒz”=1R4x14-1=5,A5(2,1),஻=2R4x2+1=9,A9(4,1),”=3R4x3+1=13,43(6,1),ᡠE44"+1(2஻1).ᦑᫀ&C(2஻1).ÙCÚ⚪ὃÛÜḄᙶ᪗ḄÏᓄÈÉÝÞßà$ᑖ_4஻=1ஹ2ஹ3RÍḄA4"+lḄÍḄᙶ᪗á>⚪Ḅᐵã.

2417.J2021•äå17,3ᑖk\æ⁐è$"ᦪ஻éa1,2,3…Rᵫæ⁐è$êêë⁐è$ìᡂḄ$ᑖ_᝞ᡠx.ᑣI஻"$æ⁐è$êë⁐è$Ḅ"ᦪîêéa_____________.Jᵨ஻⊤x஻á᦮ᦪkOᵫns|/i=2ᫀCn2+4nὃᑖ᪆CÚ⚪á!⍝ÈÉ12⚪ὃÛÜóôᑖ᪆12ÈÉḄõö.ÙC>÷]«ø⚪áÍᐜßàᫀḄÏᓄúûᯠδI!"$üýᑖ᪆þᵨ´ᱯᑮḄᑖ᪆ᦪḄᓄᨬᨵ஻Ḅ!ᦪ"#⊤%.1.)2021•⊞.4ᑖ0᝞2ᡠ%ᙠ5ABCD:;<=10,NA=60஺.CDEF5ABCDᔜ;:HIJK;AIBICIDIMCDEFK;ARICIDIᔜ;:HIJK;A2B2c2D2;CDEFK;A2B2C2D2ᔜ;:HIJK;A3B3c3D3MᢥSTUVW....ᑣK;A2B2C2D2Ḅᕜ

25AAA1D1Zy;ijK;A2B2C2D2Z45,AiDi=5,CiDi=AC=5,\/3A2B2-C202=02B2=A2D2=5,K;A2B2c2D2Ḅᕜ

26ὃH¹~ᦪ¬Ḅᓄº.ᑖ᪆~»⚪¹.ᑖ᪆~ᑖ᪆~᪷dᓫ⚗In=¼ᦪ½aḄ¾☢⌕¿ÀÁÂaḄÃᦪ=2nl),aḄᢣᦪ=n.uv~u~¢Ä⚗=-27a8=-128a8.HÆ~Ç⚪Z⍝Ḅ⚪Éʺ⚪¹ᙠ:ὃ:Ë̸.ÍÎḄ⚪É✌ᐜÑÒÓÔᑖ·ÕᓄZᢥ᯿×ØᓄḄ.3.(2021K®ᑁÚ24,6ᑖ)᝞2ᡠ%Ûll:y=g,ÞHM(2,0)àxáḄᚖlãÛl1ÎHN,ÞHNàÛl1ḄᚖlãxáÎHMiMÞHMiàxáḄᚖlãÛl1ÎNi,ÞHNiàÛl1ḄᚖlãxáÎHM2,…MᢥSàTUVWᑣHMioḄᙶ᪗=(884736,0).ὃHDæᦪçᔠ⚪.ᑖ᪆~ᑖ᪆~Ç⚪◤ᐜqOAiOA2Ḅ<ë᪷d⚪ìJᑮOAn=4n,qOA4Ḅ

27uv~u:Ûl1Ḅu᪆Zy=«x,ZNOM=60°.•♦HMḄᙶ᪗Z(2,0),NMIIxáHNᙠÛly=«x¿NM=2⌲ON=2OM=4.ñNM1JJ,ᓽNONM1=90"OMi=2ON=4'OM=8.}ᳮOM2=4OMi=42OM,OM3=4OM2=4X42OM=43OM,OMIO=4IOOM=884736....HMioḄᙶ᪗Z(884736,0)ᦑvᫀZ~(884736,0).HÆ~Ç⚪⌕ὃ᝞õ᪷dDæᦪḄu᪆HḄᙶ᪗qlöḄ<÷gh᝞õ᪷dlöḄ<÷qHḄᙶ᪗u⚪½⌕øìùᐵḄçᔠÑᵨ.4.2021K®⍒ü15,4ᑖ0=ýþ"ÿ"⁚ᵨ᤮"”.᝞ᡠᢥ᯿☢Ḅ!᤮"#n%◤ᵨḄ᪷ᦪ)6n+2.

28.ு.%(3)ὃ1!23Ḅ4ᓄ6.ᑖ᪆9⚪!2.ᑖ᪆ᑖ᪆;<=>?@AB3CB3D6᪷ᯠA᪷FG!ᑏI"nB3ḄḄ᪷ᦪᓽK.LML"1B3ᨵ8᪷"2B3ᨵ14᪷"3B3ᨵ20᪷"nB3ᨵ6n+2᪷.ᦑMᫀ):6n+2.1QR⚪ST34ᓄ!ḄὃUUICVB3ḄḄ᪷ᦪW;

29AlBlḄeᔣᔣgab5Bᓫijᑮ^3A2B2c2D2...,"n`abc^3An-lBn-lCn-lDn-1dAn-lBn-1Ḅeᔣab5Bᓫi,jᑮ^3AnBnCnDn(n>2).(2)yABnḄz)56,{n.ூ}~ᑖ᪆௃(1)᪷FabḄឋjᑮAAi=5,AIA2=5,A2BI=AIBI-AIA2=6-5=1,{IABiAB2Ḅz(2)᪷F(1)_ᡠ{jᑮᦪ4ᓄ!jᑮABn=(n+1)x5+l{InᓽK.ூ⚪LM௃1)VAB=6,"1`abc^3ABCDdABḄeᔣᔣgab5Bᓫijᑮ^3A1B1C1D1,"2`abc^3AIBICIDIdAiBiḄeᔣᔣgab5Bᓫijᑮ^3A2B2C2D2...,AA1=5,A1A2=5,A2BI=AIBI-AiAz=6-5=1,AB1=AA1+A1A2+A2B1=5+5+1=11,AB2Ḅz):5+5+6=16(2)ABi=2x5+l=ll,AB2=3X5+1=16,ABn=(n+1)X5+1=56,Lj:n=10.ூeᢣ௃G⚪⌕ὃUabḄឋᐗ`eḄᵨ᪷FabḄឋjᑮAAi=5,AIA2=5SL⚪ᐵY.

30