2021-2022学年湖南省长沙市开福区九年级（下）入学限时训练数学试卷（附答案详解）

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2021-2022
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ᐵmnḄᙠZ▲Aᑣ஻Ḅᙠᦪl⊤IRSḄ'1111A-1~1—1~~Bτ11]τ1>Cτ11,1τ»DQ---1o1234-101234--101234,1012348.ᦪy=-2+1Ḅ\()A.▲B.▲C.▲D.Z▲9.᝞\AABCC┐A8Ḅm¡,E,AḄm¡,஺A£Eា¥¦ᙠ§4CA¨©AD,ª4ACB=30஺AᑣḄ«ᦪ'A.60°B.65°C.70°D.75°10.᝞\Aᙠ¬☢®ᙶ᪗°xOy±A²]AO8CḄ[⚔஺ᙠᙶ᪗A§OBᙠxlḄR´lAsinZTlOB='&µ¶ᦪy=?ᙠ▲ᑁḄ\4,BC
ஹF,ᑣa/lOFḄ☢¸¹A.30B.40C.60D.8011.⌕»ᑖ¼ᨵ¾¿AᑣxḄ'____.x-212.ᑖÁ¼Ãa3—a=.13.ᡧ]Ḅ´Å,ᙊÇ®,45஺AᑣÈᡧ]ḄÉ'cm.14.᝞\AZ§]A8CDᑁ©ᙊ஺A4800=108°,ᑣN8C0Ḅ«ᦪ'«.BDC

215.᝞\A£wÊËᚁ«i=lÃ8Ḅᚁ☢ᵫAᑮ8ÐÑ56<,Ô▭ᓣḄ׫BC=<.16.ᐵØx>/3+஺=0ᨵ[᪷,1,ᑣx>ḄÛ[᪷,.17.ÜQÃ2sin60°+(1)-1-(2022)°-|-V3|.18.ᐜᓄåAæçÃ(7-1)+”éᧅ1,ᐸ±x=2022.19.᝞\Aᙠ¬☢®ᙶ᪗°±AA/IBCḄ[⚔Ḅᙶ᪗ᑖ_,4(5,4),8(0,3),C(2,l).(1)íîAABCᐵᡂ±ÇmnḄAAiBiGAðᑏîGḄᙶ᪗ò(2)íîAaBiCiCóᢥ┐xᔣ90஺ᡠöḄ&B2GAðᑏîÇᙶ᪗.20.,5Á±ὃsùEúûüAý᪥þ
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3
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ᔜᦪᡧ1221.᝞7+ᙠ஺ABCD+ஹEஹᑖhᙠBCஹAO+5.BE=DF.(1):AE=CF-,(2)AEqᑖNBA஺+BE=3,COḄ.22.ᙠ2ᨴ21+ᙠ᫥¡Ḅ¢£ᜐ+ᩩ¥¦᪻¨©ª«¬®¯ᱏ᫥¡ᱏḄ±⍝³ᙠ^´µ¶·.e±⍝¸¹᢬»}+ᐸ¼½ᜧ¿À¸¹Ḅ»}Á¼½m¿ÀÂ8Ã}Ä+ᜧ¿À¸120Ã}Äm¿À¸80Ã}ÄÀ½ᦪÅg.(1)ᜧ¿Àm¿À¼½ᔜ¸¹»}ÂÇÃ}ÄÈ(2)Éᐳᨵᜧm¿Àᐳ20½+¼ᜩ◤¸432Ã}ÄÍ»+ᜧm¿Àᔜ◤⌕ÂǽÈ23.᝞7+ÏAABCḄACÐÑÒÓ஺஺+!AB"ஹD,EIACÔ+¬஺E,Õ¢஺஺ÖÔ׬AF,Ø=(1)8cI஺஺Ḅᑗ.(2)·AE=ADr+জNFAC=25஺r+4BḄᜧm"ঝ஺4=5,AD=6,OEḄ.

424.᝞7+Ýᱥy=a/-2ax-3a(aßᦪ+a<0)xàᑖh¢ÖA,80Ô(ÔAᙠÔ8Ḅáâ)+yà¢ÖÔC,ØOB=OC.(1)aḄã"(2)Ô஺ITÝᱥḄ⚔Ô+ÔP(m,n)Iåæ▲ᑁÝᱥḄÔ+ᑖh¬B/ᐭBCஹCDஹBP,·4PBA=/CBDr+Ḅã"(3)ÔKᙶ᪗q☢ᑁÔ+DK=2,ÔMíBKḄÔ+¬4M,·AMᨬᜧr+ÔKḄᙶ᪗.ᜓᵨ7

5?ᫀñ>᪆1.ூ?ᫀ௃Aூ>᪆௃>2021Ḅ᎔ᦪ÷ᑣḄÅùᦪI:-/ü9ᦑ⌱A.Ñᑭᵨ᎔ᦪÏ&ÅùᦪḄÿᑖ᪆ᫀ.⚪⌕ὃ᎔ᦪᦪᐵ⚪ᐵ.2.ூᫀ௃Dூ᪆௃:0,000000007=7x10-9+ᦑ⌱.D.ᵫ012ᦪ340.000000007=7x10-9+5⚪ὃ012ᦪ3+67012ᦪ3ax109:a;஻Ḅ>⚪Ḅᐵ.3.ூᫀ௃Cூ᪆௃.Aஹ(a2)3=a6,ᦑ5⌱⚗┯G+Bஹ3a2+a,HIJ⚗HKᔠMᦑ5⌱⚗┯G+Cஹa5-i-a2=a3(a0),+஺ஹa(a+1)=a2+a,ᦑ5⌱⚗┯G.ᦑ⌱.C.᪷PᔠMIJ⚗3ᑣRḄSTḄឋVᓫ⚗X;Y⚗XS33ᑣIZᦪ[Ḅ◀3ḄឋV]ᔜ⌱⚗ᑖ᪆ᑨ`aᑭᵨ᣸◀3e.5⚪ὃᔠMIJ⚗3ᑣfḄSTḄឋVᓫ⚗X;Y⚗XS33ᑣIZᦪ[Ḅ◀3ḄឋV.673ᑣ⚪Ḅᐵ.4.ூᫀ௃Aூ᪆௃.Aஹh]ijᫀᦑ⌱⚗kᔠ⚪>+8ஹHh]ijᫀᦑ⌱⚗Hᔠ⚪>+CஹHh]ijᫀᦑ⌱⚗Hᔠ⚪>+஺ஹHh]ijᫀᦑ⌱⚗Hᔠ⚪>+ᦑ⌱.A.᪷P᝞pqrjstqᩩvwᢚyvwz{Ḅ|ᑖK}~ᔠrjsh]ijsᑖ᪆ᓽ.

6⚪⌕ὃh]ijsᐵh]ijs.5.ூᫀ௃Dூ᪆௃.☢qzrTsrTsᦑ⌱.D.᪷P☢ᑮḄjsjᫀ.5⚪ὃᓫᔠḄj☢ᑮḄjsj.6.ூᫀ௃Dூ᪆௃.4ஹ”>qrsᐸᑁ360஺”HKᦑA┯G+Bஹ4¡¢ᳫ¤¥ᕒᢗ¢ᢗ:Ḅᭆ᳛0.6,ᑣªᢗᓝ¬Kᢗ:6¬ᦑB┯G+Cஹ®᪵°⌱±᪵5²ᡠ⌱᪵5⌕ᐹᨵ¶·ឋஹ¸⊤ឋᦑC┯G+஺ஹº»¡¼½Ḅ¾¿VÀÁᵨ®᪵°3ᦑ஺+ᦑ⌱.D.᪷Pᭆ᳛ÂÃḄKឋᫀ.5⚪ὃᭆ᳛Ḅ>ᭆ᳛᧜ÂÃÅÆḄᜧḄᭆÈÉ⊤ÊÂÃḄÅÆḄᜧ,ÅÆᜧËHqÂÃÅÆËᨵKÂÃ.7.ூᫀ௃Cூ᪆௃ூᑖ᪆௃⚪⌕ὃᐵÌÍÎ]iÎḄឋVÏÐHÑXHÑXḄ3⚪ᐵ.vÒᑭᵨᐵÌÍÎ]iÎḄឋVᐵÌ஺ḄHÑXÓeᫀ.ூ௃.•••ÎP(a-3,2-a)ᐵÌÍÎ]iḄÎᙠ×Ø▲.•.ÎP(a-3,2-a)ᙠØ▲.(ci-3VoAl2-a>0.a<2.ᑣaḄ±Þàᙠᦪh⊤ÊḄ.á^;).-101234ᦑ⌱.C.8.ூᫀ௃Cூ᪆௃.,:q¬äᦪy=-2x+1:k=—2<0,h=1>0,••.äᦪḄjØéêqஹஹ×Ø▲HéêØ▲.

7ᦑ⌱.c.5⚪ὃḄq¬äᦪḄឋVᓽq¬äᦪy=kx+bkë0
:ìk<0,b>0²äᦪjØéêqஹஹ×Ø▲.ᐜ᪷Pq¬äᦪî=-2ᑐ+1:ð=-2,b=lᑨ`äᦪjØéêḄØ▲Óñò.9ூᫀ௃Dூ᪆௃ூᑖ᪆௃5⚪⌕ὃóôḄឋV⚪ḄᐵóôḄឋV.জ]öÎᑮóô:÷ḄøùÑ.ঝ]öÎ;óô:÷ᡠûwüḄᜳÑÌóô.ঞóôÿஹ
Ḅᐰ.ᵫឋABC"DEC,41cB=4DCE=30஺ஹAC=DC,ᫀ.ூ௃ᵫ⚪ABCgADEC,ᑣ4cB=4DCE=30஺!AC=DC,“AC==1^=75஺!ᦑ⌱D.10.ூᫀ௃Bூ᪆௃%&4'AM_Lx()&᝞ᡠ,.-஺4=Q,ᙠRt/kCMM/!AAMO=90°,OA=a,sin/AOB=2AM=0A-smz.AOB&a,OM=^JOA2-AM2=1,.•.&AḄᙶ᪗6(|a,ga).•••&Aᙠ789:ᦪy=?Ḅ<=!34122do-a--a=—=48,a—10,ᡈa=-10(?@).•AM=8,OM=6,OB=0A=10.•
,BCQAC5DE!&FᙠC3C=!11•
SMOF=᮱./OBCA=,4M=40.ᦑ⌱B.%&A'FML%()&M,-04=a,H%IJKJLM&AḄᙶ᪗!Nᔠ789:ᦪ<=&Ḅᙶ᪗ᱯQᓽSM஺ḄT!U᪷BC஺ACBDEஹ&FᙠC5c=!ᓽMS00F=0S./OBCA1NᔠEḄ☢XYZᓽMN[•

8\⚪ὃ^_EḄឋஹIJKJ`a789:ᦪ<=&Ḅᙶ᪗ᱯQ!⚪ḄᐵcDLMSAAOF=5s.ᱥ)BCA111.ூᫀ௃xf2ூ᪆௃hᑖjkl2#0,ᓽx#2o!ᑖZlஹᨵq.x—2ᦑᫀ6x*2.ᑖZᨵq!ᑣᑖjs-2F0,ᵫ᧕SxḄvTx.\⚪ὃ^_ᑖZᨵqḄᩩz.{`|K}~☢ᳮᑖZḄᭆ(1)ᑖZqQᑖj6(2)ᑖZᨵq=ᑖj6(3)ᑖZT60ᑖ6ᑖj6.12.ூᫀ௃a(a+l)(a-l)ூ᪆௃ூᑖ᪆௃\⚪ὃ^_YZ!YZᑖZ!vYZ
ᑭᵨ~YZᑖ!⌕ᑖ.ᐜvYZU¡|Ḅ¢⚗Zᑭᵨ~YZ¤ᑖ.ூ௃a3—a=a(a2—1)=a(a+l)(a—1).ᦑᫀ6a(a+l)(a-1).13.ூᫀ௃2nூ᪆௃ᵫ⚪!ᡧḄ§¨680“!ᙊ¬J645஺!ᦑᡧḄ¯°6±ᜐ=2ᐔ!loUᦑᫀ62n.᪷¯°YZ´µᓽ.⚪ὃ^_ᡧ¯°Ḅ´µ!¶)·Ạ⚪!\⚪ḄᐵcD¹º»¼¯°´µYZ!½¾l¿.14.ூᫀ௃126ூ᪆௃:•:5BOD=108°,•••5A=65BOD=54°,

9ABCD=180°-/.A=126°.ᦑᫀD126.ᐜ᪷ᙊᕜJÄᳮᑮ஻=jzSOD=54஺!ᯠ
᪷ᙊᑁÎBCḄឋS/BCDḄ¾ᦪ.\⚪ὃ^_ᙊᑁÎBCḄឋ!ᙊᕜJÄᳮᙠÒᙊᡈᙊ/!Ò¯ᡈ¯ᡠḄᙊᕜJÓ!Ô)Õᩩ¯ᡠḄᙊ¬JḄl§.15.ூᫀ௃3ூ᪆௃ூᑖ᪆௃\⚪ὃ^ḄDIJKJḄÖᵨ-ᚁ¾ᚁJØ⚪!»¼┦JKJ:ᦪḄÄqஹᚁ¾ᚁJḄᭆD⚪Ḅᐵc.᪷ᚁ¾ḄᭆSM᪷IJKJḄឋ.ூ௃1i=1V3,-'■tan/1=V5=T!


4=30°,BC=^AB=3àáâ!ᦑᫀ63.16.ூᫀ௃2ூ᪆௃-~ãḄäl}᪷6஻?!᪷⚪l+m=3,m=2.ᦑᫀ62.-~ãḄäl}᪷6᝞᪷ç᪷èé)ᓽMᐵ)êḄlᐗl~ã!èᓽMN[.\⚪ὃ^_᪷ìíᦪḄᐵí!ᱞïç᪷èé)-D⚪Ḅᐵc.a17.ூᫀ௃ñZ=2x/+3-l-ò=^+3-1-73=2.

10ூ᪆௃ᑭᵨᱯôJḄKJ:ᦪT!õ᦮ᦪᢣᦪøḄq!ᢣᦪùḄqéúTḄqᓄüýµᓽ.\⚪þ⌕ὃ^_ÿᦪḄᑭᵨᱯḄᦪ᦮ᦪᢣᦪḄᢣᦪḄḄ⚪Ḅᐵ.218.ூᫀ௃&'(==*+£./10X+1/0%-1/~X-l'-0x+l/21=x+1'7x=20229'(=:.ூ᪆௃'(<=>?⚗AᑖCDᑖEᑖ(ḄFGGᑣID9ᑭᵨ◀GGᑣKLMᑖNᑮᨬQRSTxḄUᐭIᓽXYZ.[⚪ὃ]^ᑖ(ḄᓄQY`abcGᑣd⚪Ḅᐵ.19.ூᫀ௃&01/᝞gᡠiAA/iCinᡠYoGᙶ᪗n0s2,-1/u02/᝞gᡠiv஽B2clᓽnᡠYoZḄᙶ᪗n0s5,2/.ூ᪆௃01/ᑖ{|Z⚔oᐵ~'oḄoᓽXNu02/ᑖ{|Zoஹ7oQᢥ9┐90஺ᡠNḄoᓽXN.[⚪⌕ὃ]^gLḄKᣚNZo⚪ᐵ.20.ூᫀ௃4054200ூ᪆௃&01/12+30%=400/,ᦑd᪵Ḅᦪ40uᦑᫀn&40u02/”Ḅᦪ360஺X¡=54°,C£ᦪn40-6-12-8=140/,TᩩL¥Ig⊡ᐙ¨᦮᝞gᡠi&

11
ᔜᦪᩩ2ᦑᫀn:54.(3)1000x^=200().ᦑ«¬ḄᦪMᨵ200,ᦑᫀn&200u(4)᪷°⚪±᪛Lg᝞³:HEᐳᨵ12µ¶·⌱>¹ºḄᨵ6µ,ᑣP(⌱>¹º)=4=¼(1)᪷°B£Ḅᦪ12,ᡠᓰḄ¾ᑖ¿30%,°[ᓽXYNÀᦪu(2)ᑭᵨ360஺ÁÂḄ¾ᑖ¿ᓽXYNaḄᯠÄᑭᵨ¾ᑖ¿ḄYNC£ḄᦪÅÆ⊡ᐰÈÉgu(3)ᑭᵨ᪵dÊIÀËḄÉGÌᐰ᪥ÀᦪÁÂ஺£ᡠᓰḄ¿ÎXNᫀ(4)ᑭᵨ᪛ÏgGᑡÑZᡠᨵXÒḄRSᯠÄᑭᵨᭆ᳛Õ(ᓽXY.[⚪ὃ]Ḅᵨᑡ⊤Gᡈ᪛ÏgGYᭆ᳛¬ᩩL¥IgஹᡧL¥IgḄᵨ.᪛ÏgGÙᑡ⊤GX«ÚÛ«⍡ÝḄᑡZᡠᨵXÒḄRSᑡ⊤G〉ᔠ~?à¨ᡂḄâãu᪛ÏgG〉ᔠ?àᡈ?àÂä¨ᡂḄâãuåᭆ᳛=ᡠY¶·ᦪÙÀ¶·ᦪæ¿.

1221.ூᫀ௃পèº&•.•êëLABC஺nìíêëL,6.AD=BC,AD//BC,,■BE=DF,>•AD-AF=BC—BF,ᓽ4F=EC,ÆAF஻EC,


êëLAEC”nìíêëL•AE=CF6(2)&MEìᑖ48ï•Z-BAE=Z.DAE1

,êëLA8C஺ìíêëL••Z-DAE=Z-AEB,•Z-BAE=Z.AEB,:.BA=BE=3,CD=BA=3.ூ᪆௃(1)ᐜ᪷°ìíêëLḄឋòN4஺=BC,AD/IBC,ᑣᑭᵨBE=DFNᑮZF=EC,ᑣXᑨôêëLAECõnìíêëLöÆᑭᵨìíêëLḄឋòNᑮR÷u(2)ᵫᙠcABCQ>AEìᑖ4BAD,᧕NvABEûῪLᓽXNCD=AB=BE=3.d⚪ὃ]^ìíêëLḄឋò&ìíêëLḄëýûuìíêëLḄýûuìíêëLḄþÿ
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Ḅᑨ.22.ூᫀ௃(1)xᑣᜧ(x+8)!⚪#$ᛞ='x+8x$x=16,()*x=16+,Ḅ.ᑣᜧ-16+8=24()./16ᜧ/240(2)ᨵ஺ᑣᜧᨵ(20-a).!⚪#$:16a+24(20-a)=432,$a—6,ᑣᜧ-20-6=14().ᜧ◤⌕14◤⌕6.ூ᪆௃(1)xᑣᜧ஺+8)᪷:ᜧ120;<=80;<ᦪ?ᑡA,BCᓽEF0(2)ᨵ஻ᑣᜧᨵ(20-a)᪷:ᜩ◤A432;

13EF.ὃᑖK,ḄLᵨNOᐗOQ,ḄLᵨRSᦪTUVWXὃTYᵨ,Z▭\⚪Ḅ]^⚪Ḅᐵ`+᪷:⚪#U;,.23.ூᫀ௃(1)abcdC£>,᝞f1ᡠh••,4C+஺஺Ḅij•••Z.ADC=90°,Z.CAD+/.ACD=90°,Z.AFD=Z.ACD,Z.AFD=5B,•••Z.ACD=ZB,•••Z.CAD+4B=90°,•••4ACB=90°,BC1AC,•••8c+஺஺Ḅᑗl.(2)@vZ.FDC=Z.FAC=25°,Z.ADE=O5FDC=90°-25°=65°,vAE=AD,:./-ADE=Z.AED=65°,•Z.CAD=180°-2x65°=50°,m•
•/.CAD+=90°,•Z.B=90°-50°=40°0ঝpqErEH1CDsH,᝞f2ᡠhᑣEH஻tvOA=5,AD=6,••.AC=10,AE=6,•EC=AC-AE=4,CD=y/AC2-AD2=V102-62=8,f2vEH//AD,CEHs>CADfEHECCH:.—=—=—,ADACCDwnE"4CHᓽE=ᐗ==,$FW=y,CW=y,DH=CD-CH=8-y=y,

14m;EH1CD,DE=VEH2+DH2=z{n}2+{ᵪ=.ூ᪆௃{1}cdCD,ᵫᙊᕜᳮ$N/10C=90°,^AFD=4CD,aA4a4஺+NB=90°,ᑣ4cB=90°,ᓽE$A0{2}জᵫᙊᕜᳮ$NFDC=AFAC=25஺U4OE=65",ᵫῪḄឋ¢FAN4DE=^AED=65°,£¤$Aᫀ0ঝpqErEH1CD"H,ᑣE஻4D,FAEC=AC-AE=4,CD=8,a§CEHs^CAD,$᦮=^=FA£“=¬CH=^,ᓽE\⚪.ziU2*C/LzJ>²⚪ὃᑗlḄᑨ=ឋ¢ஹᙊᕜᳮஹῪḄឋ¢ஹ´µᳮஹ¶Ḅᑨ=ឋ¢·¸0¹º»¼ᑗlḄᑨ=ឋ¢Nᙊᕜᳮ+⚪Ḅᐵ`.

1524.ூᫀ௃(l)y=a(x2-2x-3)=a(x-3)(x+1),½y=0,$¾=3ᡈ%=—1,


4ᙠ8ḄÂÃ


A(T0),8(3,0),.OB=OC=3,


C(0,3),ÄC(0,3)Åᐭy=ax2—2ax—3a,:.a=—1(2)va=-1,••
Çᱥl-y=-x2+2x+3,vDC=V2,BC=3V2,DB=2>/5,DC2+BC2=(V2)2+(3É¥=(2V5)2=DB2•BCD=90°,
•.%DCB-itnnZ.CBD=>DCJ


P(m,n)+ÇᱥlËḄq•n=—m24-2m+3,••P(m,-m24-2m+3),᝞f1,rPQ1ᑍÍs஺q,vPBA=CBD,1:.tanPB4=tanz.CBD=.PQ__O(-m2+2m+3)_1••ÎߟO$m=3(ÐÑ)ᡈm=O4•m=(3)᝞f2,rq8ᐵsAqÒÓḄEq,•
•8(3,0),ÔO1,0),
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£(-5,0),•DK=2,


KᙠÕ஺-ᙊÖ2-×jḄᙊË᧕·4M-ABEKÙÚlÛEKᨬᜧÝAMᨬᜧ,cdLÞßàá=âsKqãÝEKᨬᜧ,

16rDF1%Íᚖå-FqDF=4,FE=6,ED=2^13,pKqryÍḄ
l=pDFxÍḄ
lâsGq,•KG1DG,•5KGD=5DFE,v0G஻æÍ•.Z,KDG=5DEF,KDGsுDEF,KG_DG_DKwçKG_DG_2¤=Î=⁰'ᓽê=T=-ë4V136713:.KG=ìDG13“í6V13.,wnஹ,-./C(l+—,4+—).ூ᪆௃(1)FAC(0,3),ÄC(0,3)Åᐭy=a'-2ax-3a,ᓽEF;ফᵫপE$y=-/+2x+3,ᯠñᑨòADCB-iE$tan/CBD=g,ᵫPqᙠÇᱥlËᑣP(m,-zn22m+3),rPQ1xÍs஺q,ᑣᨵó=J:=1,ᓽEFm=-õ+(3)rqBᐵsAqÒÓḄEqFAE(-5,0),KᙠÕ஺-ᙊÖ,2-×jḄᙊË᧕·ö÷-^BEKÙÚlÛEKᨬᜧÝ,AMᨬᜧcdEZ)ßàá=஺஺âsKqãÝEKᨬᜧ,rDF1xÍᚖå-FqᑣEFDF=4,FE=6,ED=2V13,pKqr)ÍḄ
l=p஺qrxÍḄ
lâsGq,ᵫDG//XÍOKDG="EF,øùᗗEFKG=ûDG=üᓽEFK(1+ᘊ,4+).²⚪+þQÿᦪḄᔠ⚪ᦪḄឋᮣᵨḄឋᦪᦪᔠ⚪ᐵ!.