四川省宜宾2021-2022学年中考数学最后冲刺浓缩精华卷含解析及点睛

《四川省宜宾2021-2022学年中考数学最后冲刺浓缩精华卷含解析及点睛》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

2021-2022ὃᦪᔁ⚗1.⚪ὃᐜḄஹὃṹᑏ!ᩩ#ṹ$%&ᙠᩩ#ṹ()ᑁ஺2.⚪,-ᢥ⌕0ᵨ2஺3.-ᢥ᯿⚪45ᙠ⚪ᓱᔜ⚪8Ḅ⚪()ᑁ9:;⚪()<ᑏḄᫀ>ᦔ@ᙠ₝BCஹᔁD⚪>ᦔ஺4.9EFᐜGᵨH2I;$JKLMᵨN⁐PQḄRP2SN஺5.Tᢝᓱ☢WX⌕ᢚZஹX⌕[ẚஹ[]XGᵨ^ᦋ`ஹabcஹdCᑐ஺fஹ⌱h⚪iᐳ10k⚪lk⚪3ᑖᐳ30ᑖn1.᝞EpqrsḄtuEᡠ⊤xᦪPyz{|kb}sḄ~ᦪᑣzqrsḄbuEpinᵫ2.ᑡb$Ḅp()A.(a+b)2=a2+b2B.3n+3n+3n=3n+1C.a3+a3=a6D.(ab)2=abz3.ᦪy=ax-2
2+c,x=xi,ᦪyᑘ@x=X2,ᦪy-2|>-2],ᑣᑡ⊤b$ḄpinA.ji+j>2>0B.ji-j2>0C.aji-j2>0D.aji+yz
>04.ᙠ᝞EᡠxḄ5yxḄᦪᐵᡠḄEyin[M----ᓈ|X21~~-{+4jI6.᝞Eky¡¢£AB,ᐜᙠBA¤¥¦D§f¨D,©ᙠª«§f¨C,¬NCAD=60஺ZBCA=30°,AC=15m,®¢AB£yi

1A.15mB.56mC.106mD.12>/3m7.¯ᱥ¦±=ᑗd-8´-8µx¶ᨵ¸¨ᑣ¹Ḅ§»pi)A.m>-2B.tn>-2C.ni>-2¼"#0D.m>-2¼/n^O8.½¾¿À⚙ᝄÃ᝞EᡠxÄḄÅuEpin/*ᡊ•ᔣD.Æ9.᝞EÇABCBC=4,DPAABCḄÈᡈÈḄ¤¥¦Êᑗ.஺PÌÍy2,
ABCḄ☢Îy5,ÏABCA.8B.10C.13D.1410.᝞EÇOABÐO¨⌮,┐ÓÔ60஺¬ᑮÇOCD,OA=4,ZAOB=35°,ᑣᑡÖ×┯ÙḄpinA.ZBDO=60°B.ZBOC=25°C.OC=4D.BD=4ஹÚ⚪iÛᜧ⚪ᐳ6~k⚪lk⚪3ᑖᐳ18ᑖn11.᝞EAABCNACB=90஺NABC=25஺ݨCyÓÔÞ4,┐ÓÔK¬ᑮAABC,¼¨AᙠABDᑣÓÔßy________________12.᝞Eᦪ¶D¨Aᡠ⊤xḄáᦪp

213.᝞1
,ᙠABCDᢚBᙠAD!"ᢚ#$AD%BCᑖ'()EஹF.ᯠ,-./012BஹEஹF3⚔Ḅ4BEF63ABCDḄ“ᢚ#89”.᝞2
,ᙠABCDAB=2,BC=4,<“ᢚ#=BEF”☢?ᨬᜧ"EḄᙶ᪗314.᝞DEᱏABCDGH9IBDᢚCḄHJ3C',-ᡠᢚLḄGEFᢚLD%AMᔠ•OAB=3,BC=4,ᑣᢚ#EFḄQ315.RST6+GUTV-6
ḄWXY).x—2<316.ZY[\.cḄ^_`______________.x+3<28ஹ^b⚪Tᐳ8⚪ᐳ72ᑖU17.8ᑖU3e“ᚗgᑖh”ijkl⌕nᚗg⌕ᢥA,B,C8hᑖ'pqᢗsᐸAhᢣvᵯx,z{|}YᨵᚗgBhᢣᒕ}YᚗgChᢣᛛᧇvEYᦈᚗg.ᵬᢗsqᚗgᢗsqᚗg!qᚗgZh.1
ᑏᵬᢗsḄᚗgា`AhḄᭆ᳛ফnᢗsḄᚗgាᨵq$ᵬᢗsḄᚗg`hḄᭆ᳛.X—3OV—31I-18.8ᑖUᓄ-nᓝ2~,x=ᦈ+1x2-1x2+2x+1x-119.8ᑖUᦪ¡ᐶ£¤\3¥¦᝞Tজᡠ¨Ḅ©ª«ᜋḄ®¯Rᵨ1☢±¥¦Ḅ¨²᝞ঝᡠ¨Pᜐsµ1Ḅ1☢±ᐝI·A¸¹z1☢±º,»ºᑮª«ᜋCDḄ⚔½Cᜐ.

3AB_LBDஹCD±BD,¼¬AB=L2m,BP=L8m.PD=12m,0EজEঝzäᜋḄæçiè☢éḄêçëᶍXn-íîf~¡ïðñäᜋæçḄ}ᫀ.⌕0জ☢;xEiX⌕0ᑏIòn@ঝᑏ;}ᫀó;ô⌕Ḅõঞó;Ḅ}ᫀX÷ᵨᑮEঝḄ}ò.20.8ᑖnᙠf~XøḄùúûüᨵýᨵþ⁐XªḄNஹÿ
ᳫᐳ40⚨᥎ᳫ᝛☢Ḅᳫᤅᒴ᥎ᳫ⁐!"#$%&'()*+,⊤.Ḅ/01ᦪ34᥎ᳫḄ5ᦪn10020030050080010003000᥎ᑮ7ᳫḄ5ᦪ8651241783024815991803᥎ᑮ7ᳫḄ⚣᳛)0.650.620.5930.6040.6010.5990.601n1
;<14=஻?ᜧA᥎ᑮ7ᳫḄ⚣᳛BCD;FGHᑮ0.1
Ꮇ᝞K᥎5K᥎ᑮ7ᳫḄᭆ᳛MF7ᳫN=;P

4c.D23.(12ᑖ)᝞[ᙠ¶f1Ḅ·¸¹/ᡂḄ¸»¼)½ABC¾ḼA¿A┐ÁÂ90஺¬ÃACÁÂ+,Ä+Ḅᡧ¹Ḅ☢Æ.24.᝞[ǹABCDAD/7BC,AE_LBC¨E,NADCḄbᑖ¬§AE¨O,£஺fᙊÉOAf´¥ḄᙊÊ+B,§BC¨ËF.(1)±4CDt஺O¦ᑗ(2)³BF=24,OE=5,tan/ABCḄ°.ὃÌᫀஹ⌱Ï⚪(ᐳ10⚪Ò⚪3ᑖᐳ30ᑖ)1ஹBூ
᪆௃᪷3ÔÕ[Òᑡ·¸¹Ḅᦪ×·☢ØÙᑮḄ[¹ᓽÛ.ூ
௃Ü4ÝÕ[᝞[ᡠc4

5ᦑ⌱B.ூÁ௃Ã⚪ὃÅᵫ8ÆᑨÈÉÊËᓫ\ᔠËḄ8Æ.ᵨᑮḄÍÎ3ÏÆ`·ᱥËḄÑ☢ÒLᑮḄÒᑮḄÑÓËḄÔᦪ3ÕÓᔣᨬÖḄÑÓËḄÔᦪ.2ஹBூ᪆௃(1)᪷ØÙᐰ1ÓÛ[ÜÝ^b(2)᪷ØᔠÞh⚗ÜÝ^b(3)᪷ØᔠÞh⚗ÜÝ^b(4)᪷ØàḄáÓÜÝ^b.ூ௃^Aஹ(a+b)2=a2+2ab+b2,ᦑâ⌱⚗┯äBஹ3n+3n+3n=3n+l,ÑCஹa3+a3=2a3,ᦑâ⌱⚗┯äDஹ(ab)2=a2b,ᦑâ⌱⚗┯äᦑ⌱B.ூÁ௃Ã⚪ὃÅ᦮ᦪᢣᦪᗩ%᦮[ḄçS^⚪ᐵé`êëᔜíឋï.3ஹCூ᪆௃ᑖ«>1%«<1ðñò᪷ØóôõᦪḄH6ឋö÷$÷Ḅᜧ¤ᐵøᯠ,Hᔜ⌱⚗ᑖ᪆ᑨÈᓽL^.ூ௃^জ°>1"óôõᦪû/üᔣV|ri-2|>|X2-2|,ýþöᑘ+
Ḅa(ji-J2)>1,ঝaVlᦪᔣ

6V|xi-2|>|X2-2|,ßàHáḄ·âãäa(ji-j2)>1,å)ᡠ*⊤æç·HḄ.aQ.-J2)>1.ᦑ⌱4C.ூ௃é⚪Ý⌕ὃêë5ìᦪḄឋíᑭᵨgë5ìᦪḄðñឋᐵó⌕ôõ᪷3ë5⚗÷ᦪaḄ·âᑖãäøù.4ஹDூ
᪆௃ᐜ5ìᦪḄᐵ÷ç᪷3ìᦪ[ûtᙶ᪗þḄ§ÿᦪḄឋᓽ.ூ
௃ᵫ⚪ᦪᐵᦪy=-lx+4,ᵫk=-lVOyxḄᜧx=0y=4,y=0,x=l.ᦑ⌱D.ூ$%௃'⚪ὃ)*+,-./01ᦪឋḄᳮ.᪷4-./05-./0ᡠ7᧜Ḅᦪᐵᦪy=-lx+4,ᯠ:᪷4ᦪḄḄឋ;.5ஹBூ
᪆௃ᑖ᪆?᪷4@,AḄឋBCᦪḄ@,ADEᐸG7ᦪᨵG7ᦪḄI;.J?K-’ḄG7ᦪ144ᡠN-■Ḅ@,A44ᦑ⌱?B$%?5⚪P⌕ὃ)R;BᦪḄ@,AᐵSTUV@,AḄឋBWᦪḄ@,ADE'X0Ḅ@,AT0,BCᦪḄ@,AᐸG7ᦪ.6ஹAூ
᪆௃YCZCE_LAB,RtAACE[

7VZCAD=60°,AC=15m,11\]5\AZACE=30°,AE=-AC=-xl5=7.5m,CE=ACecos30°=15x22~2~VZBAC=30°,ZACE=30°,ZBCE=60°,:.BE=CE»tan60°=l^^x73=22.5m,2^AB=BE-AE=22.5-7.5=15m,ᦑ⌱A.ூ$%௃'⚪ὃ)Ḅ_$T`abacḄdᵨᐵST᪀g`abac`abac;hᫀ.7ஹCூ
᪆௃᪷4^ᦪḄjI1kᱥmnxoᨵp$ᓽqhᐵEmḄᐗsDtuvᓽqhmḄwAy.ூ
௃?•.•kᱥmy=g2—8x—8zXoᨵp$,"2(-8)2-4/77-(-8)..0q?mN-2m஺0.ᦑ⌱C.ூ$%௃'⚪ὃ)RkᱥmnxoḄp$ஹ^ᦪḄjIN1ᐗsDtuᱞ}“=஻4:0kᱥmnxoᨵp$T⚪ḄᐵS.8ஹCூ
᪆௃W☢ᑮḄc᝞ᡠ:ᦑ⌱C.

89ஹCூ᪆௃᪷4bacḄ☢tN1ᑗmjᳮᓽ;hᫀ.ூJ௃PEஹPFஹPG,AP,ᵫ⚪?ZPEC=ZPFA=PGA=90°,11..SAPBC=—BC»PE=—x4x2=4,22ᵫᑗmjᳮ?SAPFC+SAPBG=SAPBC=4,•'•SAFPG=SAABC+SAPFC+SAPBG+SAPBC=5+4+4=13>_1_13ᵫᑗmjᳮSAAPG=-SAFPG=1,22131:.—=-xAGPG,22,13••AG=—2ᵫᑗmjᳮ?CE=CF,BE=BG,/.
ABCḄᕜAC+AB+CE+BE=AC+AB+CF+BG=AF+AG=2AG=13,ூ$%௃'⚪ὃ)ᑗmjᳮ⚪ḄᐵSThmᵨᑗmjᳮ'⚪E[D⚪.10ஹDூ᪆௃ᵫAOABO$⌮┐6()஺qᑮOCDNAOC=NBOD=60஺AO=CO=4ஹBO=DO,45ᑨ¢Cᵫ4AOC,
BODTDbacᑨ¢A⌱⚗¤ᵫNAOB=35஺NAOC=60஺ᑨ¢B⌱⚗45qᫀ.ூJ௃

9•••AOABO⌮┐60஺ᑮOCD,.,.ZAOC=ZBOD=60°,AO=CO=4ஹBO=DO,ᦑC⌱⚗$%&!UAOCஹABOD()*+,-.,.ZBDO=60°,ᦑA⌱⚗$%VZAOB=35°,ZAOC=60°,/.ZBOC=ZAOC-ZAOB=60o-35°=25o,ᦑB⌱⚗$.ᦑ⌱D.ூ0௃2⚪ὃ5Ḅឋ7⚪Ḅᐵ9(:;Ḅឋ7জ=>ᑮ?@ḄABC).ঝ=>E?@ᡠGHIḄᜳ,)K,.ঞMஹNḄ-ᐰ)P)*+,-ḄᑨRSឋ7.ஹTU⚪V2ᜧ⚪ᐳ6YZ⚪[Z⚪3ᑖᐳ18ᑖ]11ஹ50^ூ᪆௃ᵫaACBCb┐ᑮAArBCSᓽdAACB^AA^TSᑣdNAf/BAC,AAA'C()Ὺ+,-iᵫACB?ZACB=90°,ZABC=25°,ᓽdjNA\NBABḄ^ᦪᓽdjNACBḄ^ᦪkljZBCBḄ^ᦪ.ூm௃•.•aACBCb┐ᑮAA'B'C,...
ACB@AA'B'C',AZA^ZBAC,AC=CASZBAC=ZCAAS'.•
ACB?,NACB=90°,NABC=25°,:.ZBAC=90o-ZABC=65°,...NBAC=NCAA=65஺:.ZBrAB=l80o-65°-65o=50°,:.NACB'=I80°-25°-50°-65°=40°,:.ZB,CB=90°-40°=50°.ᦑpᫀr50.ூ0௃s⚪ὃ5tḄឋ7ஹu,+,-Ḅឋ7vP)Ὺ+,-Ḅឋ7.s⚪w^xᜧyz:;MN-Ḅ=>ᐵ{yzᦪ-|ᔠ~Ḅ>ᵨ.12ஹV5-1

10ூ᪆௃Aᑮ-1ḄAB)Ku,+,-*Ḅ^>ᵨRᳮju,+,-*^ᓽd.ூ௃u,+,-*^r+22=5ᑣAᑮ-1ḄAB)KN,ᑣAᡠ⊤Ḅᦪr-1+⌲ூ௃2⚪ὃ5tᑭᵨRᳮjᦪᡠ⊤Ḅᦪ.313ஹV2].2ூ᪆௃᝞BEDᔠABEF☢ᨬᜧ,BE=DE=x,&!]AE=4-x,ᙠRTAABE?VEA2+AB2=BE2,(4-x)2+22=x2,:.BE=ED=-,AE=AD-ED=-,223.•.Eᙶ᪗-,2
.23ᦑpᫀr2
.2ூ0௃2⚪ὃ5ᢚᣚVᢚ¡⚪]ᑭᵨᦪ-|ᔠ~⚪(ᐵ9.2514ஹ—12ூ᪆௃✌ᐜᵫᢚḄឋ7E¦-Ḅឋ7§ABND()Ὺ+,-ᑣᙠRSABN?ᑭᵨRᳮ¨©Kª«ᓽdjANḄiᵫANBGAC'ND,᧕/FDM=/ABN,ᵫ+,ᦪḄឋ7ᓽdjMFḄiᵫ?H

11Ḅឋ;qEMḄᑣ¦⚪qூJ௃᝞§BC'nADpEN,EFnADpEM,᪷4ᢚ©Ḅឋq?NNBD=/CBD,AM=DM=-AD,/FMD=/EMD=90°2•••cABCDTªc,..AD//BC,AD=BC=4,/BAD=90°,../ADB=/CBD,.•./NBD=/ADB,.•.BN=DN,§AN=x,ᑣBN=DN=4—x,••ᙠRt^ABN[AB?+AN?=BN?,32+x2=(4-x)2,7x=,87ᓽAN",8•.C'D=CD=AB=3,/BAD=/C=90஺/ANB=/C'ND,.-.ANB¬AC'ND(AAS),.•.^FDM=/ABN,tan/FDM=tan/ABN,ANMF*_______32_______,.ABMD'71MF>="32MF=—,12ᵫᢚ©Ḅឋq?EF_LAD,

12.2.EF//AB,AM=DM13--ME223725EF=ME+MF=-+—,2121225ᦑᫀ.12ூ$%௃'⚪ὃ)Rᢚ©ḄឋᐰDbacḄᑨjnឋbaᦪḄឋN1¯°jᳮD_±ᔠឋ³´ᨵjḄµ¶⚪⌕·ᦪc¸ᔠ¹ºn»/¹ºḄdᵨ.15ஹ2ூ
᪆௃ᑭᵨ½»¾t¿À-.ᓽq.ூ
௃Át=(-(=5-3=2,ᦑᫀ?2.ூ$%௃'⚪ὃ)R^᪷tḄÃᔠ.ÄŽ»¾t¸᪀ᱯÇT'⚪ḄᐵS.16ஹx<-lூ
᪆௃x-2<3জ'x+3<2ঝsDtজq:x<5,sDtঝq:x<-lᡠNsDtuḄÊTx<-LᦑᫀT:x<-l.bஹ⚪(ᐳ8⚪ᐳ72ᑖ)17ஹ(1)-(2)33ூ
᪆௃(1)᪷4ÍᐳbÎAÏᨵÎ`;ᭆ᳛¤

13(2)ᑡhᐸ᪛Ôᯠ:;hÕhÖḄᡠᨵÕ1×ᔠᩩÙḄÕ᪷4ᭆ᳛t;ᓽ.ூ
௃?(1)ᵬᢗÜḄᚗÞាàTAáḄᭆ᳛Tg.ফᑡh᪛Ô᝞ᡠ?ãäᵫᐳᨵ18ÎDÕ¸åᐸ[æᢗÜḄᚗÞាᨵçnᵬᢗÜḄᚗÞTèáḄ¸åᨵ12Î.192ᡠNP(æᢗÜḄᚗÞាᨵçnᵬᢗÜḄᚗÞTèá)===é.1832ᓽæᢗÜḄᚗÞាᨵçnᵬᢗÜḄᚗÞTèáḄᭆ᳛T18ஹV2ூ
᪆௃ê⚪ᑖ᪆?ëᑖtᓄíᯠ:ëxḄAîᐭᓄí:Ḅtð;AñNR.x—3(ᐗ+1)“1ê⚪᪆?Át=------------------X---------------------------+(x+l)(x-l)(x+l)(x-3)x-127^1L2x=3+i'Átὃ$?1.^᪷tḄᓄí;A¤2.ᑖtḄᓄí;A.19ஹ(1)8m(2)ᫀsóூ
᪆௃(1)᪷4ᐭôaDE7ôaqNAPB=NCPD,ᵫAB_LBDஹCD±BDqᑮZABP=ZCDP=90°,õqbacGö᪷4GöbacḄឋᑡh÷øtᓽ;hCDḄ.(2)§-ᡂúa¦⚪;ûüᜋḄþ¶.ூ
௃(1)?ᵫ⚪qNAPB=NCPD,ZABP=ZCDP=90°,

14ARtAABP^RtACDP,.ABCD••=9BPBP?ÿ
ᜋḄ8m(2)ᫀ᝞᝞,3?......cE..........Bᙠ
ᜋamḄEᜐᵨh(m)ḄDE
ᜋ⚔AḄa.ᓽ"#
ᜋABḄAC$%D'DCJ.AB(%C.ᙠRtAACD)ZACD=90°,tana=——CD:.AC=atana,:.AB=AC+BC=atana+hூ%+௃-⚪ὃ01234ឋ6Ḅ7ᵨ.⚪9ᐵ;<=>12Ḅ34ᯠ@᪷BC7DᡂFGᑡ>IJKL〉NḄᦪPQRᩭTU⚪.20ஹপ0.6(2)0.6(3)Xᳫᨵ24[\ᳫᨵ16[.ூ
᪆௃]⚪ᑖ᪆`$⚪ab⊤d"e᥎ᑮXᳫḄᭆ᳛jklm0.6,no᥎ᑮXᳫḄᭆ᳛pqr0.6.21ஹ(1)5.6(2)sᱥMNQP7uvᳮᵫy᪆.ூ
᪆௃(1)᝞'AD_LBC(%DRtAABD),

15AD=ABsin45°=4x—=2722ᙠRtAACD)VZACD=30°.*.AC=2AD=4V2«5.6ᓽz{〈}ACḄ~5.6.(2)sᱥMNQP7uv.ᙠRtAABD)BD=ABcos450=4x—=2>/22ᙠRtAACD)CD=ACcos30°=4>/2x—=2762ACB=CD—BD=22=2(«-02.1VPC=PB—CB=4—2.1=1.9<2sᱥMNQP7uv.1Q22ஹ(1)-(2)y᪆(3)23ூ
᪆௃(1)AB<஺OḄAB=AC,"NADB=90஺NADF=NB,"tanNADFḄr;(2)kOD,ᵫeᩩAC஻,OD,DEJ_AC,"DE<஺OḄᑗ(3)ᵫAF/7OD,"AFE^AODE,"@EFḄ~.ODEDூ
௃(1)AB<஺OḄ.,.ZADB=90°,VAB=AC,.*.ZBAD=ZCAD,VDE±AC,ZAFD=90°,.♦.NADF=NB,tanZADF=tanZB=-^-=—BD2

16cফkOD,VOD=OA,:.ZODA=ZOAD,VZOAD=ZCAD,.•.ZCAD=ZODA,.,.AC஻-OD,VDE±AC,.♦.ODJLDE,...DE••AD=2^5ᳮAF=2,DF=4,VAF//OD,/.
AFE^AODE,.AFEF••----9ODED.2=EF•¶4+EF'.8/.EF=-.3ூ%+௃-⚪ὃ0ᑗḄᙊm3412Ḅ¡ᔠ)ὃ£ὃ⚪R◤¥¦§¨.23ஹ.(1)y᪆(2)©ூ᪆௃(1)᪷Bªd᪀=>%BஹC¬@ḄC7%BஹUḄ¯°ᯠ@±²kᓽ".(2)ᐜ>ACḄ~´᪷Bᡧ4Ḅ☢·¸¹ᑡ¹º»q¼ᓽ".ூ½௃

17:(1)AABX7᝞ᡠÀ:(2)ᵫ"eAC=2,an.w-.?2...AC¬$J)Á$Ḅᡧ4Ḅ☢·=ᐔ/=71.360324ஹ(1)y᪆(2)-2ூ
᪆௃]⚪ᑖ᪆(1)$%O'OG_LDC,ᚖÄG.ᐜNOAD=90஺ÅÆÇljNOAD=NOGD=90஺ᯠ@ᑭᵨAAS"ADOg
GDO,ᑣOA=OG=r,ᑣDC

18DC<஺OḄᑗ.(2)᝞ᡠÀkOF.VOA±BC,.\BE=EF=-BF=1.2ᙠRtAOEF)OE=5,EF=1,.*.OF=7OE2+£F2=13,/.AE=OA+OE=13+5=2.AE3.,.tan/ABC=-----=—.BE2ூ%+௃-⚪Ó⌕ὃ0Ḅ<ᑗḄᑨËஹᚖËᳮஹÌÍËᳮḄ7ᵨஹ┦3ÐᦪḄËÑÖ×-⚪ḄØÙḄ'Ú<⚪Ḅᐵ;.