【中考数学】2022-2023学年湖北省武汉市专项突破仿真模拟试卷（一模二模）含解析

《【中考数学】2022-2023学年湖北省武汉市专项突破仿真模拟试卷（一模二模）含解析》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。

ூ
ὃᦪ௃2022-2023ᓅḕ⚗ẚᔁஹ⌱⌱1.aஹbஹcᨵᳮᦪ2a-3b+cḄᦪA.3b-2a-cB.-3b-2a+cC.3b-2a+cD.3b+2a-cx+y2.᝞ᑖ—Ḅx᡽ᜧ3,ᑖḄ2xyA.᡽ᜧ3B.c.3D.63.!ᑡᔜ$ᵨ&'()*+Ḅ)A.B.C.(_Q_gb)(q_-6)D.4.!ᑡ.$ḄA./01234ᓣB.ᙠᓭ᩽9:ᑮ<<'ᔣC.>?@A1ὑCᓱEFD.>?@AGᾙIJ5.!ᑡᐵLxḄ'MN(l)ax2+bx+c=O-ঝ3(x-9)2-(x+1)2=1-(3)x+3=—-ট(a2+l)x2-a=0-ঠJx+1=xX-1,ᐸSᐗUV'MḄWᦪA.1B.2C.3D.46.X9Z1,3
ᔣY&Z2Wᓫ3\ᔣ!&Z4Wᓫ3]ᑮ98,ᑣ98Ḅᙶ᪗aA.(-1,0)B.(-1,-1)C.(-2,0)D.(-2,-1)7.᝞b2cḄdebg?AOBdC.DL?8.ᙠ2016fᡃhijkᐺmnop10Wqpᓫ3ᡂst*᝞bᡠvwLx10Wqpᓫ3Ḅᡂs!ᑡyz┯|Ḅ}1⚓/55⚓

1Ḅ5-A.ᦪ90B,&ᙳᦪ90C.3ᦪ90D.᩽(159.᝞bAB=AC=AD,ZCBD=2ZBDC,ZBAC=44",ᑣ/CADḄᦪaA.68°B.88°C.90°D.112°10.᝞b'/BCDCEFGḄᑖaஹ"Ḅ☢ḄA.஻ḄᜧiᨵᐵB.
ntஹ"ḄᜧiᨵᐵC.ḄᜧiᨵᐵD."Ḅᜧiᨵᐵஹ⚪:11.ᙢᜩḄ£¤a-2࠷,£¤a-8࠷,xᜩḄ¤(࠷.12.¦t*ᐰᳫ©ᑖª«ᨵ8500000ᔴ2᣸ᐭ°±²³ᑣ©ᑖªḄ᣸´ᵨµj¶ᦪz⊤v¸ᔴ.13.¹ᦪ-2,-y,0,4º»SWᦪ¶am,\¹¼!Ḅ½Wᦪº»SWᦪ¶an,k=mn,ᑣo¾¿ᦪy=kxḄbÀ}½ஹÀ▲Ḅᭆ᳛.14.᝞b.X'ÄᱏN8C஺ᢚÈÉÊ8ஹC8ᙳËᙠwÌÍ8஺4ᢚBEஹBF,ᑣNEBFḄᜧ.}2⚓/55⚓

215.9P(a,b)ᙠÎÍy=-x-l49Q(-a,2b)ᙠÎÍy=x+l4ᑣÏᦪa?-4b?-1=.16.᝞bÐᙊ0ḄÎÒAB=2,ÓCD஻AB,ZCOD=90°,ᑣbᨩÕÖᑖḄ☢a___.17.Ø'MN(3x+l)2=9X+3.18.᝞b9A,B,C,DᙠSᩩÎÍ4ÚABFgADCE.Û$]ÜÝÞßàá(âᑏܽ19.2026f3ᨴᐰåæçèᑭêëᦪjᐶᕡiîïæçðñÜò⚣᳛ḄôõNAῃ÷øù.B.ú⁐üý.C.þÿ
.D.ᩗ᪵⌱"ᡃᨬᐵ!"Ḅ᝞$%᪷'()*ᑴḄ,-./0Ḅ12$.34᪷'12$56Ḅ789:;ᑡᡂ>?(1)@AᐳDE(2)ᩩG12$m=,n=E(3)ᡧG12$BᡠᙠᡧGḄᙊMNḄOᦪ%E(4)Q᪥ᐜTUVWᨬᐵ!DḄᐜTḄᭆ᳛%Z[\]3⚓/`55⚓

3ᩩ$%&'ᡧ$%&'ni20.᝞$ᙠa☢cNᙶ᪗fxQyghiy=—jciy=-2x+2klm.x(1)nḄoE(2)nQghijciy=-2x+2pkmBḄᙶ᪗.21.qr?᝞$ᙠsXBCBC=AC,t8cucvḄ஺஺jxN8yklm஺DE1.AC,ᚖ{umE.পn}?m஺%ḄmEফᑨDEj஺஺Ḅᙢᐵf}4Ḅ(EবOOḄcvu18,co,nḄ.322.u᪗ᡃ᜜ᐷḄT◤/ஹ8ᑖ〈100ᔴ50ᔴTᱥ¤.qrQᱥ¤ᙠᵬ¦§¨ᨵ80ᔴª¦§¨ᨵ70ᔴᵬஹª,¦§〈ᱥ¤ᑮḄ¬ᵨ(ᐗ/ᔴ)᝞⊤ᡠ±?]4⚓/`55⚓

4+,(ᐗ/))*ᵬ᳛A)1420B)108(1)²ᵬ¦§〈ᑮ/Ḅᱥ¤uxᔴn`¬y(ᐗ)jx(ᔴ)³´Ḅµᦪᐵf¶ᑏ¸xḄWoºE(2)n¸¬ᵨ▊¬ᵨ¼Ḅ½.23.᝞$1,ᙠ4ABCAB=AC,¾iBPBAᡠᙠᙢ¿ÀÁmB¼┐ÄÅÄÅNua(0°”"="“<”),iÐBDஹCDjAD³´ḄᦪÑᐵf%E(2)ÆNBAC=120஺¼ÇBPÄÅᑮ$3ᙢmDᙠ¾iBPNCDP=60஺n}?BD-CD=0ADE(3)Ç$3ḄBPÒÓÄÅÆ3()஺va<180஺¼mD%ciBPm(mP.ᙠiÐBD)NCDP=120஺3cÔᑏ¸iÐBDஹCDjAD³´ḄᦪÑᐵf(.Õ}).24.᝞$1,ÖAµᦪyi=(x-2)(x-4)Ḅ$×jxØklAஹB,m(mAᙠmBḄÙÚ),ᐸÜÝØ1jxØklmC,ÞḄ⚔mumD.(1)ᑏ¸mDḄᙶ᪗.(2)mPᙠÜÝØ1lmCàáCP=2CD,tPu⚔mḄÖAµᦪy=ax2+bx+c(a/O)2Ḅ$×mA.জã▊ÖAµᦪy2=ax2+bx+c(a/0)Ḅ$×mBEঝmRᙠÖAµᦪ=(x-2)(x-4)Ḅ$×ᑮxØḄåæud,ÆmRḄᙶ᪗u¼,yiÖAµᦪyz=ax2+bx+c(a0)Ḅ$×ᨵá⌕èmᑮxØḄåæl2dEঞ᝞$2,qr0

5níᦪmḄo.]6⚓/`55⚓

6ூ
ὃᦪ௃2022-2023ᓅḕ⚗ẚᔁஹ⌱⌱1.aஹbஹcî%ᨵᳮᦪðñ2a-3b+cḄyòᦪ%óôA.3b-2a-cB.-3b-2a+cC.3b-2a+cD.3b+2a-cூö÷:ᫀ௃Aூú9௃᪷'yòᦪḄûüý2a-3b+cḄyòᦪ%-2a-3b+cþ3b-2a-c.ᦑ⌱A.2.᝞ᑖ*Ḅx᡽ᜧ3ᑖḄ2xyA.᡽ᜧ3B.C.3D.6ூᫀ௃Cூᑖ᪆௃᪷"ᑖḄឋ$ᑨ&ᓽ(;ூ*+௃+,-ᑖ.Ḅxy᡽ᜧ32xy3x+3y=3x+Q/'2x3x^y929
32xy'ᑖḄ3.ᦑ⌱,C.2⚪4⌕ὃ78ᑖḄ92ឋ$:ᑖ᪆;<=+⚪Ḅᐵ?.3.@ᑡᔜCᵨEFGH;<Ḅ=A.IJK6
4-K6
B.+C.-a-gb/aJ;b
D.-aJ;6
a+K6
ூᫀ௃cூ*+௃᪷"EFGHa+b
a-b
=a2-b\(L,AஹN⚗PQRᔠEFGHKT7⚓/W55⚓

7BஹDN⚗PQRᔠEFGHKCஹḄN⚗=J⚗[ᐰPQ]J⚗^_PQᦪRᔠEFGH.ᦑ⌱C.4.@ᑡ=(CḄ=()A.efghiᓣB.ᙠᓭ᩽noᑮqqFᔣC.stuvgὑxᓱz{D.stuv|ᾙ~ூᫀ௃Bூ*+௃᪷"Ḅ(Cឋᜧ(L,Aஹefghi■,ᓣ=ᯠᦑA┯KBஹᙠᓭ᩽noᑮqqFᔣ=(CᦑBKCஹstuvgὑxᓱz{=ᯠᦑC┯KDஹstuv|ᾙ~=ᦑD┯Kᦑ⌱B.5.@ᑡᐵxḄF,জax?+bx+c=OKঝ3(x-9)2-(x+1)2=1K(3)x+3=—K(4)(a2+l)x2-a=0KঠJx+1=xx-1,ᐸJᐗ¤4FḄ¥ᦪ=()A.1B.2C.3D.4ூᫀ௃Bூ*+௃᪷"Jᐗ¤4FḄ¦§,¨ᨵJ¥ªLᦪªLᦪḄ4ᦪ_2,᦮FজaḄC_0,ᦑ=ঝᓄ®_,2X2-56X+241=0,=Jᐗ¤4Fঞ=ᑖFটa2+lwo,gJᐗ¤4Fঠ=ᙠᳮFᦑ=ᵫµ(L=Jᐗ¤4FḄᨵঝট¶N¥.ᦑ⌱B.6.¸¹nZ(1,3)ᔣ»E¼2¥ᓫi¾ᔣ@E¼4¥ᓫi¿ᑮn8,ᑣn8Ḅᙶ᪗_()A.(-1,0)B.(-1,-1)C.(-2,0)D.(-2,-1)ூᫀ௃Bூ*+௃+,ÄLn4(1,3)ᔣ»E¼2¥ᓫi¾ᔣ@E¼4¥ᓫi¿ᑮn8,᪷"ᔣ»E¼Åᙶ᪗ᔣ@E¼Æᙶ᪗ḄE¼ÇÈ(¿nBḄÅᙶ᪗_1-2=-1,Æᙶ᪗_3-4=-1,T8⚓/W55⚓

8ᡠÊBḄᙶ᪗_-1,-1.ᦑ⌱B.ὃn,ᙶ᪗ËÌÍᓄ-E¼.7.᝞ÌhÏḄÐÑÌ=&A.Q-Iூᫀ௃Aூᑖ᪆௃oᑮÔ☢Öᡠ¿ᑮḄÌÍᓽ(.ூ*+௃᪷"×ØsḄÙÑÌ(LÚ×ØsḄÐÑÌ=J¥ᙊJᩩÝÞ.ᦑ⌱A.8.ᙠ2016ßᡃáâãᐺåæçè10¥éèᓫiᡂëì;᝞Ìᡠíî¶10¥éèᓫiḄᡂë@ᑡïð┯Ḅ=B.Eᙳᦪ=90C.iᦪ=90D.᩽G=1580+85x2+90x5+95x2=89ூ*+௃Eᙳᦪ=10ᦑ⌱B.9.᝞ÌòLAB=AC=AD,ZCBD=2ZBDC,NBAC=44°,ᑣNCADḄõᦪ_()A.68°B.88°C.90°D.112°T9⚓/W55⚓

9ூᫀ௃Bூ*+௃ö⚪ᑖ᪆,2⚪ὃ78÷ῪÙùÍḄឋ$4⌕ᑭᵨ8÷ῪÙùÍNûùP÷üýឋ$=+⚪Ḅᐵ?.᪷"÷ῪÙùÍNûùP÷þÿNABC=NACB,
/CBD,ᯠ᪷NABD=NABC-NCBDᓽ.᝞•AB=AC=AD,BஹCஹDᙠAᙊABḄḄᙊZCBD=2ZBDC,ZCAD=2ZCBD,ZBAC=2ZBDC,AZCAD=2ZBAC,/BAC=44°,.../CAD=88°,cὃ!ᙊᕜ#$ᳮ10.᝞&'(NBC஺*CE+GḄ,ᑖ./ஹ஻12A/EGḄ☢4Ḅ568A.9"?ஹ஻Ḅᜧ=>ᨵᐵB.9"A஻Ḅᜧ=>ᨵᐵC.B9᪷Ḅᜧ=ᨵᐵD.B9஻Ḅᜧ=ᨵᐵூ&DEᫀ௃DூH௃!᪷I#(Ḅ☢4JZiGCEḄ☢4KgcGCEg/.JL,(ABCGKM#N(᪷N(Ḅ☢4OP☢4KgCAB+CGBC=g6Q+஻8QST8EḄ☢4K!yBE*AB=-^6/+஻8QUV5AJEG-=5ACG£+5N(ABCG-SAAB"y«2.ᦑSTEGḄ☢4Ḅ5B9஻Ḅᜧ=ᨵᐵ.X10⚓/[55⚓

10ᦑ⌱!D.V⚪_⌕ὃab&'(Ḅ☢4ᡂd⚪ᐵeKᔠᳮᑭᵨI#(Ḅ☢4ஹN(Ḅ☢4
*ijᯠᑨlmᔲoQஹ஻ᨵᐵ.ஹ⚪11.qᙢqᜩḄtu-2࠷,tu-8࠷,{ᜩḄuiK______°C.ூ&DEᫀ௃6ூᑖ᪆௃᪷⚪ᑡPᓽᑮ.ூH௃ᵨuuᯠ᪷ᨵᳮᦪḄᑣᦪoQ{ᦪḄᦪᓽ!628-6-88=—2+8=6࠷.V⚪ὃabᨵᳮᦪḄᑣK⚪Ḅᐵe.12.ᐰᳫᑖᨵ8500000ᔴ¤¥᣸ᐭ¨©ª«ᑣᑖḄ᣸¤¬ᵨ®¯ᦪ⊤±²Kᔴ.ூ&DEᫀ௃8.5x106ூᑖ᪆௃´ᜧo106ᡈὅ=o18Ḅ᦮ᦪ¯axl0-QWa<108Ḅ'P½¾®¯ᦪ.ூH௃!8500000=8.5xlO5.ᦑ8.5x106⚪ÀoÁẠᵨ⚪B◤ᐜÅ®¯ᦪḄ⊤±'ᓽÆᡂ.13.Èᦪ-2,-y,0,4ËÌÍᦪ¯m,ÈÏÐḄIᦪËÌÍᦪ¯n,Òk=mn,ᑣÔÕÖᦪy=kxḄ×XIஹ×▲Ḅᭆ᳛K.ூ&DEᫀ௃-6ூH௃Èᦪ-2,-0,4ËÌÍ1ᦪ¯m,ÈÏÐ3ᦪËÌÍᦪ¯n.2᪷⚪Û᝞Ð!X11⚓/[55⚓

11ᐳᨵ12ÝÞßᵫ⚪JÔÕÖᦪá=1«Ḅ×XIஹ×▲ᓽᑮ1<=!1»>0.ᵫ᪛ã121Jäᔠmn>0ḄÞßᐳᨵ2ÝUVÔÕÖᦪá=1«Ḅ×XIஹ×▲Ḅᭆ᳛K3=!.126ᦑEᫀ.614.᝞.å'(æᱏN8CDᢚéê,/8ஹCBᙳìᙠí#î80ᢚï88RᑣNEBFḄᜧ=.ூᑖ᪆௃᪷ᢚéḄឋñNEBD=gNABD,/FBD=g/CBD,ᓽ
NEBF.ூH௃!å'(æᱏ/BC஺ᢚéê,/8ஹC8ᙳìᙠí#î3஺ᢚBEஹBFò|JNEBD=NABEóZABD,ZFBD=ZCBF=yZCBDVZABC=90°AZEBF=ZEBD+ZFBD=yZABD+yZCBD=yZABC=45°ᦑEᫀ!45°⚪_⌕ὃabᢚéḄឋñô#ḄᭆõK⚪Ḅᐵe.15.öJP(a,b)ᙠMîy=x-lQ(-a,2b)ᙠMîy=x+lᑣ÷ᦪPa?-4b?-1=______.ூ&DEᫀ௃1.ூH௃ø⚪ᑖ᪆!ᐜ᪷⚪ᐵoaḄ'ùú
a,bḄ5÷ᐭ÷ᦪPᓽ.ø⚪᪆!P(a,b)ᙠMîy=Q(-a,2b)ᙠMîy=x+lX12⚓/[55⚓

12-a-\-b~2{2{—a+1=26b=—4~91••ýP~4x--1=1.416ὃ!Öᦪ×Ḅᙶ᪗ᱯ
.16.᝞ᙊ0ḄAB=2,CD஻AB,ZCOD=90°,ᑣᨩᑖḄ☢90TCX1~TCTCூ௃•.,CD஻/13,♦*♦5*=5cw=------------=—.ᦑ#ᫀ36044%ஹ#⚪17.())x+12=9x+3.12ூ*+#ᫀ௃Xi=--,X2=5.33ூ௃,⚪ᑖ᪆ᑭᵨ01ᑖ23ᐗ56()ᓽ8.,⚪᪆()᦮ᳮ;<3x+l2-3
3x+l=0,ᑖ01;<3x+1
3x+l-3=0,8;3x+l=0ᡈ3x-2=0,12;Xl=----,X2=—.33>?@⚪6⌕ὃCD3ᐗ56()Ḅ2⚪ᐵFGHIJK3ᐗ56()Ḅᱯ>ᯠMNO3ᐗ56()Ḅ2PQR(2ஹS(2ஹT12ஹ01ᑖ2ᔠᳮ⌱Wᓽ8.18.᝞>A,B,C,Dᙠ3ᩩZ[Z\ABF\ADCE.]^;_`abcd

13B'C-----ூ*+#ᫀ௃o᪆.ூ௃ᑖ᪆p⚪⌕ᮣrsᵨᐰu%vwḄឋy.zg%vwᐰu%vwᑣ{|}~u,{|v~up⚪᪆VAABF^ADCE.".ZBAF=ZCDE,ZAFB=ZDEC,ZABF=ZDCE,AB=DC,BF=CE,AF=DE.*.AF#ED,AC=BD,BF஻CE.19.20163ᨴᐰzᑭQᦪᐶᕡz¡_¢⚣᳛Ḅ¥¦Aῃ¨©ª.B.«⁐®.C.¯°±².D.³´µᩗu¥¦·¸D¹᪵»C¼g½¾¿^O⌱W3g“ᡃᨬᐵÃ"Ḅ¥¦᝞G᪷Å»CbÆÇᑴḄzÉÊËÌḄÍÎ.e]᪷ÅÍÎÏÐḄÑÒ#ÓᑡᡂÖ:(1)p6»C3ᐳ»CDÛ½¾(2)ᩩwÍÎm=%n=(3)ᡧwÍÎ¥¦BᡠᙠᡧwḄᙊàvḄáᦪG(4)Oã᪥ᐜæçè¹é3gᨬᐵÃ¥¦DḄᐜæḄᭆ᳛Gëìdூ*+#ᫀ௃(1)300(2)60,90(3)72°(4)Oã᪥ᐜæçè¹é3gᨬᐵÃ¥¦D3ḄᐜæḄᭆ᳛G[20ூ௃,⚪ᑖ᪆(1)᪷ÅAḄïᦪ105ïᡠᓰḄòᑖó35%,õ_mïᦪᓽ8#(2)Cᡠ{|Ḅïᦪmïᦪx30%,Bᡠ{|Ḅïᦪmïᦪ-Aᡠ{|Ḅïᦪ-Cᡠ{|Ḅïᦪ-Dᡠ{|Ḅïᦪᓽ8#j14⚓/m55⚓

14<3i᪷ÅBᡠᓰḄòᑖóx360஺,ᓽ8#<4i᪷Åᭆ᳛T1ᓽ8#.,⚪᪆<1i105+35%=300<ïi.ᦑ#ᫀ300<2in=300x30%=90<ïim=300-105-90-45=60<ïi.ᦑ#ᫀ60,90<3i—x360°=72°.300ᦑ#ᫀ72஺453<4iOã᪥ᐜæçè¹é3gᨬᐵÃ¥¦DḄᐜæḄᭆ᳛G:ù=±.300203#Oã᪥ᐜæçè¹é3gᨬᐵÃ¥¦DḄᐜæḄᭆ᳛G—.20ὃ>ᩩwÍÎᡧwÍÎᭆ᳛.ni20.᝞ᙠR☢vᙶ᪗ýx஺þÿy=—y=-2x+24-1,஺.x1Ḅ2y=-2x+28Ḅᙶ᪗.ூ$%&ᫀ௃1஺=4,)=-4*22,-2.ூᑖ᪆௃1ᐜ.4-1,/ᐭḄ1᪆234aḄ67839AḄᙶ᪗6;.ᐸ/ᐭ=>?@ᦪḄ1᪆2ᓽ39CḄ*2ὶEF@ᦪḄ1᪆261GHIᓽ39.ூJ1௃11.41,஺/ᐭK=-2x+29a=-2x-l+2=4,M15⚓/Q55⚓

15ᑣAḄᙶ᪗S41,4,ITi./-1,4/ᐭT=9C=—1x4=—4*x4)2ᵫ13V6=>?@ᦪḄ1᪆2SWX,xy=-2x+2ὶE646y=X)X=2)x=-119ீ஺ᡈீᓽSAḄᙶ᪗6[y=-2[]4ᑣsḄᙶ᪗S2,-2._⚪ὃbK=>?@ᦪ@ᦪḄcᔠஹᐗXgGHḄhᵨ6jklmnopᦪqr1⚪ᐵt.21.uV᝞w6ᙠy/8C{6BC=AC,|8CS}Ḅ0஺஺6DE1.AC,ᚖSE.প஺rḄ{*ফᑨ஺E0OḄᙢᐵp6Ḅ*ব஺஺Ḅ}S18,co=—,Ḅ.3ூ$%&ᫀ௃11᪆*2ᑗ61᪆*340ூᑖ᪆௃ூJ1௃18,,:BCS}6.,.ZBDC=90°,ACD±AB,M16⚓/Q55⚓

16.,/AC=BC,:AD=BD,••஺r¡8Ḅ{.(2)QEr஺஺Ḅᑗ.OQ,VOB=OC,AD=BD஺஺ryZBCḄ{6C.DOUAC,VDEIAC,ADE10D,QEr஺஺Ḅᑗ*(3)**AC=BC,:./B=NA,co=cosA=,3BD1AᙠRtZ\BDC{6Vco=——=-,8c=18,BC3/.BD=6,/.AD=6,ᙠRt^ADE{,.,cosZ=-----=—,••AE=2,AD3:071_AE?=4V2•22.SW¢£ᡃ¥¦᜜¨©ª«¬ᐷḄ®¯6°◤²³/´µஹ8´µᑖ¶h〈100ᔴ©50ᔴ®¯ᱥº.uVᱥºᙠᵬ¼½¾ᨵ80ᔴ6À¼½¾ᨵ70ᔴ67ᵬஹÀF¼½h〈ᱥºᑮ´µḄÂᵨᐗ/ᔴ᝞⊤ᡠÅM17⚓/Q55⚓

17+,ᐗ/)*ᵬ᳛A)1420B)1081
Æ7ᵬ¼½h〈ᑮÇ´µḄᱥºSxᔴ6QhÂyᐗxᔴÈÉḄ@ᦪᐵp26ᑏ4xḄËÍ*2
4Âᵨ6▊ÂᵨÏḄÐÑ.ூ$%&ᫀ௃1
y=-8x+256030Sᔢ80
*2
Óᵬ¼½ḄᐰªhÕ4´µ6;7À¼½h20ᔴÕ¡´µ6À¼½ḄÖ×ḄᐰªhÕ8´µ.ூJ1௃Ø⚪ᑖ᪆1
Æ7ᵬ¼½hxᔴÕA´µ6᪷Ú⚪Û97ᵬ¼½hÕB´µḄᨵ80-Xᔴ67À¼½hÕA´µḄᨵᔴ6hÕB´µḄᨵ50-80-x
=X-30
ᔴ6;ᵫÜÝᐵpQhÂ=ᵬ¼½hÕA´µḄÂᵨ+ᵬ¼½hÕB´µḄÂᵨ+À¼½hÕA´µḄÂᵨ+À¼½hÕB´µḄÂᵨᑡ2ᓄà6ᓽ39QhÂyᐗxᔴÈÉḄ@ᦪᐵp2*ᵫ⚪Û39X20,8-X20,x-30>0,100-x>0,ᓽ394xḄË*2
ᵫᡠ9Ḅ@ᦪS@ᦪ6ᵫáâឋ3Vyäxáᜧ8âæ6ᑣçx=80Ï6yᨬé64ᨬé6ᑏ4hê.Ø⚪1᪆1Æ7ᵬ¼½hxᔴÕA´µ6ᑣ7ᵬ¼½hÕB´µḄᨵ80-x
ᔴ67À¼½hÕA´µḄᨵᔴ6hÕB´µḄᨵ50-80-x
=X-30
ᔴ6ᡠ|y=14x+20+1080-x
+8x-30
=-8x+2560,xḄËÍr30

18(3).w3{ḄBPúûòó6ç30஺

19/.AD=AE,ZDAC=ZEAB,ZCAB=ZCAE+ZEAB=60°,/.ZDAE=60°,•._ADEC4D,-.ADE=AD.BD=BE+DE,JBD=CD+AD.ᦑ=,BD=CD+AD!(2)᝞O3,kACBD3lXTO,ᙠBPQeRBE=CD,VAE,WA;AF_LBDXF.VZCDP=60°,AZCDB=120°.VZCAB=120°,AZCDB=ZCAB,VZDOC=ZAOB,AADOC^AAOB,AZDCA=ZEBA.AC=ABᙠADCAAEBA/2Z.ACD=/ABE,CD=BEAADCA^AEBA(SAS),AAD=AE,ZDAC=ZEAB.,/ZCAB=ZCAE+ZEAB=120°,ZDAE=120°,180°-120°AZADE=ZAED==30°.2••ᙠRL^ADF/ZADF=30°,.-.DF=—AD,2.*.DE=2DF=V3AD,JBD=DE+BE=6AD+CD,.'BD-CD=&AD!(3)জ᝞O4,BD-CD=JJAD,ᳮᵫC9ᙠBDQRSTE,UBE=CD,VAE,WA;AF1.BDXF,WAABE^AACD,AE=AD,ZBAE=ZCAD,DF=FE,620⚓/h55⚓

20.,ZBAC=ZBAE+ZCAE=120°,.*.ZCAD+ZCAE=120°,ᓽNDAE=120஺ZDAF=60°,,DFsinZDAF=sin60°=-----,ADADF=—AD,2ADE=2DF=V3AD,BD-CD=BD-BE=DE=73AD!ঝ᝞O5,BD+CD=JJAD,ᳮᵫC9\]DBᑮE,UBE=CD,VAE,WA;AFJ_BDXF,VZBAC=120°,AB=AC,.,.ZACB=ZABC=30°,AZEBA=150°-ZDBC,VZCDP=120°,AZBCD=120o-ZDBC,ZACD=ZBCD+30°=150°-ZDBC,AZACD=ZEBA,AAAEB^AADC,AAE=AD,ZEAB=ZCAD,DF=EF,VZBAC=ZDAE=120°,621⚓/h55⚓

21.•.ZDAF=60°,Iᳮ89DF=?±AD,2AED=V3AD,/.DE=BD+BE=BD+CD=^3AD.Qᡠ9BD+CD=GADᡈCD-BD=6AD.⚪ᔠὃ4Ὺ,-.ஹᐰ4,-.Ḅឋ;<=᪀?+,-.ᐰ4C⚪Ḅᐵ!⌕ᐰ4+Dᜳ-Ḅ8ᔜ3CS0T!Iᵨ-Ḅ,-Zᦪ⊤DḄᙠ/Ḅ¡¢CS0T£¤¥9¦§¨©ᓄᑮISᩩQ9জᙠDeR¬Dঝ\]¬D4XD!®“eᡈ”.24.᝞O1,a³Zᦪyµ(x-2)(x-4)ḄO¸x¹lXAஹB+T(TAᙠTBḄº»),ᐸ1®¹1x¹lXTC,½Ḅ⚔T¥TD.(1)ᑏTDḄᙶ᪗.(2)TPᙠ1®¹1QÂXTCQÃÄCP=2CD,ÅP¥⚔TḄa³Zᦪy2=ax2+bx+c(aÉ)ḄO¸WTA.জÊ▊a³Zᦪy2=ax?+bx+c(a0)ḄO¸WTB!ঝTRᙠa³Zᦪyi=(x-2)(x-4)ḄO¸Qᑮx¹ḄÎÏ¥d,ÑTRḄᙶ᪗¥,a³Zᦪy2=ax?+bx+c(a/0)ḄO¸QᨵÄÓ⌕,0Tᑮx¹ḄÎÏ4X2d!ঞ᝞O2,ÕÖ0

22ᦪmḄ¥1.ூ`$௃Ê⚪ᑖ᪆9é1êᑭᵨìè©a³Zᦪ=éx-2êéx-4êí.¥⚔Tîᵫïᓽð8GH!é2êজᵫTµᙠ1®¹/Qð8a³Zᦪ%=©2++஺ḄO¸Ḅ1®¹¥/,BT48ᐵX1®¹/1®a³Zᦪ%=E+ô+Céõ0êḄO¸WT/,ᓽð8a³Zᦪy=aC+hx+cé஺ÉêḄO¸WT8!2ঝᵫa³Zᦪ%=#+ô+஺éᑖ0êḄO¸QᨵÄÓ⌕,0Tᑮx¹ḄÎÏ4X2",ᓽð8d=I,Bøa³Zᦪ%=é%-2êéx-4ê/ᑓ=±1[xᓽð8GH:6HN22ঞkᮞ஻,0),ᑣÅ(஻-2(஻-2)(஻-4)),஺(஻(஻-2)(஻-4)),ᵫïᓽð8ߟߟ=--~7=7HQ2+13HNHG2᪷Ḅឋᓽ==T᪷ឋ9.KG=t)tHQHE3KE2>0,ᑣGḄᙶ᪗3-f,!"EḄᙶ᪗3-2Z,m,ᵫ(ᓽᐵ*","Ḅ-ᐗ/01"2/01ᓽ3"஻5.7⚪2᪆:1:y|=x-2x-4=x2-6x+8=x-32-l,⚔E஺Ḅᙶ᪗3,-1.ᦑHᫀ3,-1.2জKELᙠN/P"Q*ECP/"SCP=2C£>,...EVḄᙶ᪗3,2,...-WXᦪ%=x-2x-4[\+]+஺Ḅ^_ḄNᙳL3,..,E/ஹ8ᐵ*bcx=3""-WXᦪ%de0Ḅ^_fEgঝ•.•-WXᦪ%=&+d+CḄ⚔Eᙶ᪗?3,2,S^_PᨵSm⌕oEᑮxNḄqrs*2d,K.2d=2,2:d=\.uv=x-2x-4=/-6x+8wx=±1"ᓽX?-6x+8=±௃"2:|=3—/"4=3+~"X3=3,...ERḄᙶ᪗3—0"1ஹ3+"1ᡈ3,-1.ᦑHᫀ3-0,1ஹ3+JI"1ᡈ3,-1.ঞfEMxNḄbcN/*EK,bc/-WXᦪ%=++C0Ḅ^_ḄN.23⚓/55⚓

23K-WXᦪv=
2+ᔊ+cfE4ஹB,S⚔Eᙶ᪗P(3,2),.•.-WXᦪ%=-2G-2)(x-4).N(஻"0),ᑣH(«,-2(n-2)Cn-4)),Q(஻"(஻-2)(w-4)),/.HN=2(w-2)(nHNHN22-4),QN=(H-2)(w-4),-----=2>BP------=-------QNHQ2+131HNHG2•/4GHNsுEHQ,=F=7ri\JLILLJ.KGTVG>஻ᐵ*bc/"/.KG=KH=^HG,'~KE~2KG=Z(F>0),ᑣGḄᙶ᪗(3஻?),EḄᙶ᪗-2/,/w),ᵫ⚪:*[-2(3-/-2)(3-Z-4)=n?c,2:2ᡈ"2().(3-2/-2)(3-2/-4)=mnt=1m=1Ḅ51.24⚓/55⚓

24ூ
ὃᦪ௃2022-2023ᓅḕ⚗ẚᔁஹ⌱⌱ᜧ⚪ᐳ10o¡⚪"¢¡⚪3ᑖ"ᐳ30ᑖ஺¢¡⚪¤Ḅ¥o⌱⚗w"m⌕o⌱⚗§¨Ḅ1.3ᑖ2021•©□ᙠᨵᳮᦪ2,-3,0w"ᨬ¡ḄᦪA.2B.-3C.-D.032.3ᑖ2021•©□᝞^ᡠ²Ḅ³´µᵫ6oᜧ¡¶gḄ¡·/ᙽ¹ᡂḄ"»Ḅ¼½^A.&C.Ä---LJD.S3.(3ᑖ)(2021•©□)¾ᑡÀÁ§¨Ḅ()A.+tz3=a6B.a2-a3=a6C.(ah)2=ab2D.(a2)4=tz84.3ᑖ2021•©□È᪥ÊËÌx“᰿ᡃÐÑ”Ó⚪ḄÔÕ"Ö×ØÙ5oÚÛÜᑮḄÔÕÝÞᦪßᓫQ:áᑖâ48,50,47,44,50,ᑣã1ᦪḄwQᦪA.44B.47C.48D.505.3ᑖ2021•©□oäåæḄçèwᨵ4oéᳫ"6oëᳫ"ãìᳫ◀î⁐᜜ñᐸóôâ"ÖUèwö!᥎1oᳫ"ᑣ᥎ᑮëᳫḄᭆ᳛6.3ᑖ2021•©□úûüᢥ᝞^ᡠ²ḄᙢQ᤮ᙠᑣN1ḄᦪA.45°B.65°C.75°D.85°7.3ᑖ2021•□"#$-4x-l…-2x+lḄ*+ᙠᦪ,⊤./0Ḅ1)325⚓/655⚓

25A.-2101B.-2-101iJττ.C.-2-101D.-2-1018.3ᑖ2021•□᝞8஺1ᙶ᪗<==5ᙠx,ᙠAO4g@/஺=48=5,஺8=6,=4ᙠCDEFᦪy="஻஺08JᑣKḄL9.3ᑖ2021•□᝞8ᙠNO/BCD@CஹE,PᑖQᙠZ8,CDMBE=2AE,DF=2CF,CஹG,஻ᑖQ14CḄU#ᑖ=ᑣVWXḄLS᰿EABCD10.3ᑖ2021•□᝞8ᙠ/YO//8CD@48=4,Z=M[=4\]^_`1aᓫcdḄefghiZjkZ=N[=4\]^_`2aᓫcdḄefᢚh->DC->C8iZn=NiZᑮ=8k=A/,Njk@piZ.qA4AWḄ☢t᜛iZvwxs,ᑣyᑡ8J{ᜧ}C᧜yxFᦪᐵḄ1326⚓/655⚓

26ஹ⚪ᜧ⚪ᐳ6a⚪_⚪3ᑖᐳ18ᑖ11.3ᑖ2021•□20209ᨴ1^ᩭᦟᙢஹஹᓫcஹ“᪥¡”£¤¥¦§¨c3420000a©§ª«¬®¯.ᦪ°3420000ᵨ²³´ᦪµ⊤.____-12.3ᑖ2021•□·$ᑖ*¸—3am2+12an2=___.13.3ᑖ2021•□᝞8¹ᙽ»╔½¾¿ᵫᜧÁ#Ḅ#ÂUÃO᪀ᡂᔣ½¾¿ÇÈᢗʹ˻╔»╔_XÌÍᙠ½¾¿ᑣÎ@ÏÐḄᭆ᳛1¹.14.3ᑖ2021•□ÓÔ஺஺ḄÕÖ17,451஺஺Ḅ×ØN8Ḅd7Ùᑣ×N8ᡠ®ḄᙊᕜÃḄᦪ¹.15.3ᑖ2021•□᝞8ᙠÝ☢Ãᙶ᪗@=/Ḅᙶ᪗5,0,=MḄᙶ᪗0,4,Þ=஻ßA/N//X,=PᙠghàAM4P#ῪUÃOᑣ=âḄᙶ᪗327⚓/655⚓

2716.3ᑖ2021•□᝞8ᙠãO@AB=\,8c=2,å¯4C,Þ=஺ß஺G_LZCè=G^G4GDéÂßãOAADC,å¯4G,êADè=O,Þ=DßDJ14G}t]è=Gê4cè=M1^G4G஺éÂßãO44஺஺2å¯4c2ê4஺è=ᑭÞ=DßDC14Gè=cᔆê4Gè=/2í^C3A2C3DéÂßãO&A3DC3,å¯4c33ê4஺è=O3Þ=஺ßDC,_L4c3è=C4,ê4c2è=…àîÂOḄ☢ts,,îÂO4஺24஻2Ḅ☢t52,îÂO4agM3Ḅ☢t⎃…îÂO4IO”CL“”Ḅ☢ts"ᑣs,=—.òóᵨô/᦮ᦪ஻Ḅ$ö⊤.Uஹ*÷⚪ᜧ⚪ᐳ9⚪ᐳ72ᑖ.*÷øᑏ\ú⌕Ḅüýஹᦻÿ▊
ᡈ
17.5ᑖ2021•□ᐜᓄ+1/2x,ᐸ!x=tan60஺.x-2x-418.6ᑖ2021•□,-./012᪥4ᦻ67᪥⚜ᜓ:./ᢇ<ᳫ>?ᳫ@ABC<ᳫḄ.EFBC?ᳫḄ.EG25ᐗᵨ2000ᐗ:.<ᳫḄᦪKLᵨ750ᐗ:.?ᳫᦪKḄ2MBC<ᳫ>?ᳫḄ.EᔜGOᐗP19.7ᑖ2021•□“S!TUVWᦻ
XYZᦻ7[\”^᪥_ᐰ6ᐜa.b-cUVAdefgᡂiᑖ,jkஹmnஹoCpqr!stuvwᑖᐜaḄefᡂi᪷yz{|}~ᑴᡂḄ᪷y!ᑡᡂi1u᪵z{Ḅᦪ28⚓/55⚓

282ᙠᡧ!ᨩwᑖḄᡧᙊḄᦪL—3gᩩ⊡ᐙ4¦᪥ᐳᨵ1500©ᐜa᪷yu᪵z{Ḅ|}ª«¬efᡂiᑮḄᐜaᦪ.BᡂDᔜFGHᦪᩩ$%&'BᡂDᔜFGHᦪᡧ$%&'Hᦪ65o4o3o般-2o优秀1oOIJKLMFG20.7ᑖ2021•□,-¯°±²100ᕜ´7᪥µ¶-“·²឵•¹²º”»⚪½¾¿⚨ÁÂḄ½¾ᨵᑏĽ¾ஹÅƽ¾ஹÇȽ¾ஹÉʽ¾ᑖËᵨÌÍ4,B,C,஺Î⊤ÐÑÒC½¾ÓÔÑÒCÌÍᑖËᑏᙠÒÕÖᐰ×ØḄÙ
Ḅᓱᱏ_☢ᯠÞgÑÒÕᓱᱏß☢àᒴÞâᙠã☢.1¿⚨r!stuv/ÕᓱᱏLÉʽ¾஺Ḅᭆ᳛L/2¿⚨ᐜr!stuv/ÕᓱᱏæçᓱᱏḄÌÍâèrᒕḄᓱᱏ!stuv/ÕᓱᱏæçᓱᱏḄÌͪᵨᑡ⊤êᡈÆ᪛ìêí¿⚨uvḄÕᓱᱏ!ᨵ/ÕLÇȽ¾CḄᭆ᳛.21.7ᑖ2021•□/ᦪ7ᐶᕡ¿ñòeK/óᕜôᨵôõö÷Ḅc᪛ḄøᙠGᜐâû/C¿ü☢ýþ/ÿ
ᙠាᙠ☢ᑁᑮ᪛Ḅ⚔ZḄG=3/„,$
ᔣ᪛&ᔣ'()9+,ᑮ-஺ᙠ஺ᜐ0123456?Ḅ89CD,᪛⚔4Ḅ;8530஺=>$
Ḅ?@Aᙢ☢ḄCDEF=1.5m,8,D,G,Fᙠ2L4MNOPCD,EᙳᚖMSBF,U᪛Ḅ3.V☢ḄᜧXY4Zᶍ\]^_`ᶇ᪷cd22.V8ᑖdV2021•h□d᝞k48lOOḄMn஺ᙠ஺஺OP4஺஺=90஺Cl஺஺᜜2ᑖqrsCZ,CBஹCD,C4t0஺SMODNCஹN,CBḄuvNt0஺SE,rsAD,ME,PNACD=NE.y29⚓/{55⚓

29V1dU|}cr•lo஺ḄᑗN;V2drs00Ḅn56,tanE=-,UḄ.323.V10ᑖdV2021•h□dᖪ20ᐗḄ(2ᖪᖪ\S(\3S38ᐗ¡}¢ᖪᜩḄ¤yVdAXVᐗd§¨©ᔠ«ᦪᐵ®᝞kᡠ°.V1dUdAx§¨Ḅ«ᦪᐵ®²}V2d¢ᖪᖪ⌕´ᜩµ600ᐗḄᑭ·ᖪḄ¸5¹ºᐗ»V3d¼ᖪᖪᜩµᑭ½Vᐗd¾ᖪḄ5¹ºᐗᜩᑭ·»ᑭ·l24.V10ᑖdV2021•h□d᝞kᙠRtAABCÁAC=BC,NACB=90°,஺ᙠNÂOV஺\AN,BÃᔠdPOB=Ä?/,ᔊl4CuvNOḄ2ÆÇNÈÇN0MÉ஺⌮┐ÌÍ90஺tÇNC8SN.V1d᝞k1,¾4=1ᑨÏNÂAONḄᦪ¤ᐵ®Ð▊ÒᳮᵫÕV2d᝞k2,¾k>lᑨÏNÂAONḄᦪ¤ᐵ®VᵨÚ஻Ḅ²Ü⊤°dÐ|ÒÕV3dᙠÇN8cO
NBON=15஺,PN=kAM)kᱏ1,Pᒹ<àáâMsᑏäå4C2PCḄæVᵨÚçḄ²Ü⊤°d.y30⚓/{55⚓

30'1'2ᜓᵨ'25.(12ᑖ)(2021•h□)᝞kᙠ☢M8ᙶ᪗®ÁìᱥNy=-r+6x+cAxïᑖqtSX8,AyïtSC(0,3).(1)UìᱥNḄð᪆²òóôïÕ(2)᝞k1,஺ACᐵSóôïóôPᙠóôïONB஺=90஺UḄᙶ᪗;(3)/lìᱥNO$Sóôïö÷ḄNᙠìᱥNḄóôïO¾A8MN5øùú8ûâMsᑏäMḄüᙶ᪗.'1ᜓᵨ'y31⚓/{55⚓

31ூ
ὃᦪ௃2022-2023ᓅḕ⚗ẚᔁ2ஹ⌱2⌱Vÿᜧ⚪ᐳ10⚪⚪3ᑖᐳ30ᑖ஺⚪Ḅ⌱⚗⌕⌱⚗Ḅ1.3ᑖ2021•□ᙠᨵᳮᦪ2,-3,0ᨬḄᦪA.2B.-3C.-D.03,--.--3<0<-<2,3.,.ᙠᨵᳮᦪ2,-3,10ᨬḄᦪ-3.3ᦑ⌱-B.2.3ᑖ2021•□᝞1ᡠ3Ḅ456ᵫ6ᜧ9:Ḅ;<ᙽ>ᡂḄ@ḄAB1C4^rFknDBABc,-DAEFGHI

32A.44B.47C.48D.50,-}ᦪDᑮᜧ▰ᑡᜐᙠ3xḄᦪ48,xᦪ48Zᦑ⌱-C.5.3ᑖ2021•□VḄᨵ4ᳫ6ᳫ}ᳫ◀⁐᜜ᐸzD᥎1ᳫᑣ᥎ᑮᳫḄᭆ᳛A.—B.-C.-D.-10255,-•.•ᨵ4ᳫ6ᳫᐳᨵ10ᳫ,.•᥎ᑮᳫḄᭆ᳛h--=105ᦑ⌱-D.6.3ᑖ2021•□¡¢£¤ᢥ᝞1ᡠ3Ḅᙢx᤮¨ᙠ©¤KᑣN1Ḅ«ᦪhB.65°C.75°D.85°,-VZ2+60°+45°=180°,N2=75°.•.•©¤ḄKLIE°±,Nl=N2=75°.7.3ᑖ2021•□V³´-4x-l…-2x+lḄ,rᙠᦪ·K⊤3Ḅ)A.-2-101B.-2-101IJII.D.-2-10133⚓/55⚓

33,-V³´-4x-l…2x+l,¹⚗º--4x+2x..l+l,ᔠ»º-—2x..2,,º-¼1,ᦪ·⊤3᝞1ᡠ3--2-101ᦑ⌱-D.8.3ᑖ2021•□᝞1஺ᙶ᪗¿ÀÀ8ᙠx·KᙠAOISA0AB=5%OB=6%ÀAᙠ:ÄÅÆᦪy=-k஺01ÈKᑣkḄÉ)B.-15C.-20D.08=6,0C=BC=3,ᙠRtAAOC04=5,••AC=Sᮞ-AC?=V52-32=4,4(—3,4),ÌJ(-3,4)Îᐭy=X,кA=12,xᦑ⌱-A.9.(3ᑖ)(2021•□)᝞1ᙠÒJ48coÀÕᑖzᙠZB,CDKÖ=34⚓/55⚓

34DF=2CF,CஹG,“ᑖzZCḄ¢³ᑖÀᑣ×ØÙḄÉh,-:BE=2AE,DF=2FC,AE1CF1----=A=—BE2DF2Gஹ஻ᑖz4CḄ¢³ᑖÀAG1CH1Ü.---=—f---=,GC2AH2AEAG---=---BEGCEGIIBCEGAE1----------——%BCAB3HF1ÝᳮкÞ//4D,—=-,AD3.SEJßGÜ1¼1Ü1SÒJ48஺339ᦑ⌱-A.10.3ᑖ2021•□᝞1ᙠZ
C->C8NàëÀNNàᑮÀ8éÀNÝéìNà•íḄ☢ïhy,Nà¼ðhxs
,ᑣLᑡ1Èñᜧò:᧜yôxõöÆᦪᐵøḄ35⚓/55⚓

35,-ëÀNᙠ/£>KéBP0

36y=—x4x=2x9-2.•.ᑖ!,y=5NI2-2x'=-x2+6x,v-l<0,ᑖ,ᦪ./ᔣ1
ᦑ⌱4B.5ஹ78⚪:;ᜧ⚪ᐳ6>?⚪
@?⚪3ᑖ
ᐳ18ᑖ'11.:3ᑖ':2021•C□'2020E9ᨴ1HIᩭ
ᦟLMN.OᙢQஹRSஹᓫUஹVW“᪥Z[\”^_
`abScU3420000>
ebSfghijk.ᦪl3420000ᵨnopᦪq⊤s—3.42x106—.v4ᦪl3420000ᵨnopᦪq⊤s3.42x106.ᦑ3.42x106.12.:3ᑖ':2021•C□'wxᑖv4—3am2+12an2=_—3a)m+2n)m—In_.v4yx=-3a:»?-4஻?'=-3a:ni+2n)m-2n'.ᦑ-3a:m+2”':?n-2"'.13.:3ᑖ':2021•C□'᝞
ᙽ╔ᵫᜧ?Ḅ?᪀ᡂ
ᔣᢗ╔:╔@ᙠ'
ᑣḄᭆ᳛£337⚓/55⚓

37v4•.•☢¥9>?Ḅ☢¥
ᐸ⁐ᑖ☢¥3>?Ḅ☢¥
╔ᙠ⁐ᑖḄᭆ᳛£-=93ᦑL314.:3ᑖ':2021•C□'©ª஺஺Ḅ«¬£7,£஺஺Ḅ®
¯ZBḄ²76
ᑣ®Z8ᡠjḄᙊᕜḄ·ᦪ_60஺ᡈ120஺_.v4Z4cB»N/OB®49ᡠjḄᙊᕜ
½k஺4ஹOB,᝞
¾஺¿0Hlz8Â"
ᑣ4H=BHZAB=[,2276ᙠRtAOAH
•••cos^OAH=—=,0472NOAH=30°,OA=OB,/.NOBH=ZOAH=30°,N4OB=120°,ZACB=-ZAOB=60°,2ZADB+ZACB=\SO0,=180஺-60஺=120஺
ᓽ®ᡠjḄᙊᕜḄ·ᦪ60஺ᡈ120஺.ᦑÉᫀ60஺ᡈ120஺.D15.:3ᑖ':2021•C□'᝞
ᙠË☢ᙶ᪗Î
ÏḄᙶ᪗:5,0',MḄᙶ᪗:0,4',38⚓/55⚓

38¾M¿ᵨN஻xÑ
ÒᙠÓA/N
ÔAM4ÒῪ
ᑣÒḄᙶ᪗_4)ᡈ(d—4)ᡈ(10,4).v4ØPḄᙶ᪗(x,4)>ᑖÚÛÜ4জPM=PA,•.•4Ḅᙶ᪗(5,0),MḄᙶ᪗(0,4),._.PM=x,PA=y]42+(5-x)2,PM=PA,x=^/42+(5-x)2,vÞ4x=,.,.PḄᙶ᪗(à
4)á®MP=MA,MP=x,MA=yl42+52=y/41,:MP=MA,/.x=,39⚓/55⚓

39.•.PḄᙶ᪗:᝞
4'áঞ4W=NP,V4O\Ax••AḄᙶ᪗:5,0',MḄᙶ᪗:0,4',AP=y/42+)x-52,MA=y/42+52=741,*/AM=AP,ᔆ.b42+:%-5>="T,vÞ4x:=10,x=0:çè'
2ÒḄᙶ᪗:10,4'áé
ÒḄᙶ᪗:ê
4'ᡈ:4T,4'ᡈ:10,4'.ᦑ:2
4'ᡈ:᝞
4'ᡈ:10,4'.16.:3ᑖ':2021•C□'᝞
ᙠë48C஺
AB=1,8c=2,½k/C,¾஺¿஺Cá_L4CÂC,IG4,C,Dî¿ëAA.DC,,½k4G,ï/஺«,¾஺¿஺G_L4GÂG
ïÏ஺”|
IG4
G஺î¿ëAADC,½kA2cz,ïÂo,,222¾D¿DC,1ACÂC3,ï4GÂáICA,C,Dî¿ëAADC,,½k4G
22}22}ï4஺Â஺3
¾஺¿QC.14c3Âï4Gª3…Ôô2MḄ☢¥H,ô402GM2Ḅ☢¥⎃
ô4஺3c4M3Ḅ☢¥S,…ôḄ☢¥0X4'1S,,ᑣ⎃=_ù:úûᵨüý᦮ᦪ஻Ḅxÿ⊤
40⚓/55⚓

404•/BC஺=90°,ADI/BC,AD=BC=2,CD=AB=\f:.AC=4AB1+BC2=Vl2+22=V5,•••DCAC=ABBC,cVABBC1x22y/sDC௃=----------=—f=~=-------,ACy[55ᳮ2DCஹ=.eSf=2,CC,=gDC1=W%vtanZC^=^=^=l4^5,AD=AC௃=2DC1=-ioaRAM=AC.-CM=2DCh-DC,=-xDC,=}41⚓/55⚓

413ᳮA,M=-XDC.223A2M3=]XDG....34“-M,=QXDC“%•.•/.OA=OD=OA=OC=1,llllᳮ:DC2AC௃=A௃DDC],>x?/-54G251-DC"AB&|DG,ᙠRtADOC#QCᳮOC=^DC2333◍&'30J=*.௃EFS3=1xGXDC,-IXO£xDC=—G2=LG2=*,2S1=Spq/QC2Ml=S,<9…9ஹ,2i9x4ᳮ⎃=5978MDC,-2—20(5)_53202ᕒ69X42S,=—DC2=—x(3203205-542y/59x4-)5„=—DC„2=—x(2n5J-5"+l“202042⚓/55⚓

42TUஹW⚪YZᜧ⚪ᐳ9]⚪ᐳ72ᑖ.W`ᑏbc⌕Ḅfgஹᦻi▊kᡈmkno17.Y5ᑖY2021•p□ᐜᓄtuvwYx+1+,,ᐸ#x=tan60஺.x-2x--4}~8:2(1)(x+2)(x-2)x-22x(1)x+2-----.xx=tan60஺=6,ᐭ}~=3^=1+.6318.Y6ᑖY2021•p□8f᪥ᦻ᪥⚜ᜓ8ᢇᳫᳫᳫḄᳫḄ25ᐗᵨ2000ᐗᳫḄᦪ¢ᵨ750ᐗᳫᦪ¢Ḅ2£vᳫᳫḄᔜ¥ᐗ¦§ᳫḄxᐗᑣᳫḄYx+25ᐗ©⚪ª«=2x¬x+25xx=75,®¯x=75}°oḄ±²ᔠ⚪ª;.x+25=75+25=100.WᳫḄ75ᐗᳫḄ100ᐗ.19.Y7ᑖY2021•p□”¶#·¸¹ºᦻk»¼½ᦻ¾¿”À᪥ÁᐰᐜÃÄŸ¹ÆÇÈÉᡂËᑖÌÍஹÎÏஹUÐÑÒ#ÓÔÕÖ×ᑖᐜÃḄÇÈᡂË᪷ÙÚÛÜÝÞᑴᡂàáâãäḄåæç᪷Ùç#èéWêᑡᡂË43⚓/55⚓

43Y1vZìÕ᪵ÚÛḄîᦪIY2ᙠᡧåæç#ᨩñ×ᑖò`ḄᡧᙊTôḄõᦪ_90஺_IY3Éᩩåæç⊡ᐙãäIY4ù᪥ᐳᨵ1500ûᐜÃ᪷ÙÕ᪵ÚÛḄÜÝüýþæÇÈᡂËÿᑮḄᐜᦪ.BᡂDᔜFGHᦪᩩ$%&'BᡂDᔜFGHᦪᡧ$%&'Hᦪ般-优秀RJKLMFG1ᦪ=50+=1203602ᨩᑖᡧḄᙊ=360஺ஹ^$^-=90°,120ᦑ90஺3Ḅᦪ*120-30-50=40,ᩩ./0᝞0ᡠ34Hᦪ6050403020100RJKLMFG445ᡂ78ᑮḄᐜᦪᨵ1500x,=500,120;<᪥1500>ᐜ?45ᡂ78ᑮḄᐜᨵ500.20.7ᑖ2021•B□*DEFGH100ᕜJ,K᪥LMD“OH឵•QHR”T⚪VW,X⚨Z[ḄVWᨵᑏ]VWஹ^_VWஹ`aVWஹbcVWᑖdᵨfg4,B,C,஺hi⊤3klmVW,noklmfgᑖdᑏᙠlqrᐰtuḄvwxḄᓱᱏ{☢,ᯠ~klqᓱᱏ☢Bᒴ~ᙠ☢.44⚓/55⚓

44iX⚨?$qᓱᱏbcVW஺Ḅᭆ᳛_•5■_42X⚨ᐜ?$qᓱᱏ,ᓱᱏḄfgv,ᒕḄᓱᱏ?$qᓱᱏ,ᓱᱏḄfg,ᵨᑡ⊤ᡈ_᪛0X⚨Ḅ¡qᓱᱏ?ᨵ$q`aVWCḄᭆ᳛.1•.•ᐳᨵ4¤¥¦§Ḅ¨©,ᐸ?bcVW஺Ḅᨵ1¤,,X⚨?$qᓱᱏbcVWDḄᭆ᳛1,4..1ᦑ$42ᵨᑡ⊤⊤3$ᑗ¥¦§Ḅ¨©᝞ᐳᨵ12¤¥¦§Ḅ¨©,¬¤¨©§Ḅ¥¦ឋtu,ᐸ?ᨵ$q`aVWCḄᨵ6¤,X⚨Ḅ¡qᓱᱏ?ᨵ$q`aVWCḄᭆ᳛®=1.21.7ᑖ2021•B□$ᦪKᐶᕡX±²4³$´ᕜµᨵµ¶·¸Ḅ¹᪛Ḅº,ᙠGᜐ½$mX¾☢¿,À$ÁÂÃÄᙠÅÆÇ,ាÉᙠX¾☢¿ᑁËᑮk´¹᪛Ḅ⚔Í/ḄÎ,ÏÇ4ÐFG=3m,kÁÂÃᔣ¹᪛ÔᔣÕÖD9~ᑮ8Æ஺,ᙠ஺ᜐ×½$ºØ*bnḄ4ÛCD,ÏÇ4Ð᪛⚔4ḄÜ*30஺,ÝÞkÁÂÃḄßàáᙢ☢ḄãäEF=15஻,CஹB,D,G,FᙠÂ$çØèé,êCD,EFᙳᚖèí8Å,k´¹᪛Ḅº.X¾☢¿ḄᜧXðñØòᶍv/,¨©·ᶇ᪷ö᝞0,÷ÆC]íÆᑣ=BH=CD=lm,45⚓/55⚓

45ᵫ⚪úÐDF=9m,,DG=DF-FG=6(m),ᙠRtAACH?,/4C஻=30஺,•••tanZ.ACH=-=tan30°=—,CH3:.BD=CH=kAH,•••EF1FB,AB1.FB,NEFG=NABG=90°.ᵫuûüíᐭûÐZEGF=NAGB,\EFG^\ABG,EFFG1.53ᓽAH+\~AH+6Ð=
8+4ÿ*AB=AH+BH=(9+4ᡃ
ᓽ᪛ḄZ8
9+45
.22.
8ᑖ2021•□᝞480஺Ḅ஺ᙠ0஺4஺஺=90஺C0஺᜜ᑖ!"#C/,CBஹCD,஺$஺஺%$0஺%N,C8Ḅ&'($0஺%E,"#NO,ME,Z.ACD=Z£.
1)*+CD஺஺Ḅᑗ(-
2"#஺.0஺Ḅ/6,tan£=-,)஺MḄ0.3146⚓/455⚓

46E5+(1)vZACD=,NE=NBAC,/.NBAC=NACD,AB//CD,AODC=N40D=90°,ᓽOD1CD,.•.8OOḄᑗ(-(2)8஺9஺E1ZC%:,/஺0Ḅ/6,tanE=—=tanZ.ACD=tanZ.OAN%3,ON=—OA=—x6=2,33:.DN=OD-ON=6-2=4,:.CD=3DN=\2,ᙠRtACDN<CN=->jDN2+CD2=V42+122=4V10,ᵫ>?@Ḅ☢BCDEFCNDF=DNCD,ᓽ4ViODF=4xl2,6᝞DF=------,5GH/AMD=-AAOD=-x90°=45°%22ᙠRtADFM<DM=6DF3X^=m.147⚓/455⚓

4723.10ᑖ2021•□IᖪKLMN20ᐗḄPQRSTᖪUVWTᖪUMNXPYZ%SPGY%38ᐗ[\K]^_`+aᖪUMᜩḄcyNdMNXPxᐗefgᔠiᦪᐵl᝞ᡠn.1
)᜛dxefḄiᦪᐵlD-2
aᖪKTᖪU⌕qMᜩrF600ᐗḄᑭtMNᖪUḄXPuWvwᐗx3
yᖪKTᖪUMᜩrᑭwᐗzMNᖪUḄXPWvwᐗ{Mᜩᑭtxᑭt5+1
yydxefḄiᦪᐵlDy=|+~0
,ᵫᡠiᦪE+ᨌ:LᦑydxḄiᦪᐵlD᜛=-2x+120-2
᪷⚪F+x-20
-2x+120
=600,᦮ᳮF+x2-80x+1500=0,5F+x=30ᡈx=50Yᔠ⚪+MNᖪUḄPuW30ᐗ-3
•.•y=-2x+120,148⚓/455⚓

48vv=(x-20)y=(x-20)(-2x+120)=-2X2+160X-2400=-2(x-40)2+800,38.,.zx=38{wᨬᜧ=792,.,.XPW38ᐗ/N{Mᜩᑭtw=792ᐗ.24.(10ᑖ)(2021•□)᝞ᙠRtAABC<AC=BC,NZCB=90஺஺ᙠ(¦N8(஺Yd§8¨ᔠ)nOB=kOA,©4c&'(Ḅ9«(OW,®«(¯஺⌮{┐²³90஺$«(CB%N.(1)᝞1,z4=1{ᑨµ(¦஺஻dONḄᦪcᐵl·▊¹ᳮᵫ+(2)᝞2,z4>1{ᑨµ(¦OMdONḄᦪcᐵl(ᵨ½ḄD¾⊤n)·*¹-(3):ᙠ«(BCoNBON=15°,PN=kAM(k*l),À<3Â!■,Å#ᑏÇ.AC2PCḄÈ(ᵨ½”ḄD¾⊤n).'1'2ᜓᵨ'5+পOM=ON,'19஺%஺஺£t1஺8%£+,NADO=NMDO=4CEO=ZOEN=90°,149⚓/455⚓

49Z.DOE=90°,•;AC=BC,ZACB=90°,/./A=/ABC=45°,ᙠRtAAOD<OD=OA.sinZA=OA.sin45஺=$04,2Îᳮ+0E=J()B,2OA=OB,OD=OE,••NDOE=90°,ZDOM+/MOE=90°,•/2M0N=90°,/./EON+ZMOE=90°,NDOM=NEON,ᙠRtADOMÏRtAEON<Z.MD0=NNEO

50ᵫ1+ZDOM=4EON,4MD0=/NEO=90°,\DOM^\EON,.OMOP_{"~ON~~OE~~k'...ON=kOM.AB=\[2ai•/OB=kOA,lkt—1OB=y/2------a%OA=v2--------a%k+\k+\Â.OE=———OB=-----a%2+1N//N=/ABC-/BON=45°-15°=30°,:.EN=-°E—=6OE=5-^-a,tanNNk+1•CE=OD=—OA=a,2k+11f-k:,NC=CE+EN=——Q+6-----a,+1k+\ᵫ2+-=—=M
OMsNEON,ONOBkNM=NN../Ml•~PN~~k%OMAM~ON~~PNfÂ.\PON^\AOM,151⚓/455⚓

51NP=NA=45°,ZAMO=NN=30°,PE=OE=-a,4+1:.PN=PE+EN=a+V3-a%A+lk+\y=0஺=x,/.DM=px,ᵫZO+OM=ZC+C/F(0+l)x=/C+CM,—1,6A.ஹqr\(%Cy/3—11:.x----(AC+CM)<---(AC+--——AC)=—AC,/.k>\.NC1+▲'■PN“+ÚÛav+w'k+\+1.NC_1+xkPCk-\25.(12ᑖ)(2021•□)᝞ᙠÜ☢?ᙶ᪗l<ßᱥ(y=-d+6x+cdxãᑖ!$%/(-1,0)Ï8,dyã$%C(0,3).(1))ßᱥ(Ḅ5᪆Dåæçã-(2)᝞1,஺dCᐵ%æçãæçPᙠæçãoNBPD=90°,):Ḅᙶ᪗;(3)Wßᱥ(é%æçãêëḄNᙠßᱥ(ḄæçãzA8MNìí>?@{Å#ᑏÇ"Ḅïᙶ᪗.152⚓/455⚓

525Fðßᱥ(Ḅ5᪆Dy=+2~+3,æçãx=~=l.(2)᝞1<"#8஺y8஺Ḅ<T,"#:7,y2(1,ó).•.•஺dCᐵ%æçãæçC(0,3),0(2,3),•••8(3,0)Âᔩ|),BD=y/(3~2)2+32=710,Z.NPD=90°,DT=TB,PT=-BD=—,22..(1-ᡷ+(,”|)2=(÷5Fm=1ᡈ2,..P(l,l)ᡈ(1,2).(3)zMᙠ▲{ABMNìí>?@8598T18N$Ḅ&'(%7,yN(l,),yßᱥ(Ḅæçã$xã%E.153⚓/455⚓

5331••A5MNìí>?@•.NNMB=4NBM=60°,•/2NBT=90°,ZMBT=30°,BT=6BN,HZNMB=4MBT+Z.BTM=60°,...NMBT=NBTM=30஺,MB=MT=MN,g/NBE+/TBJ=90஺%/TBJ+NBTJ=90஺%NNBE=NBTJ,••ZBEN=ZTJB=900%NBENsbTJB,.TJ_BJBT•ùߟùù‘BJ=®,TJ=2y/3,.•.r3+ü20•/NM=MT,A“4+ý26+þ,/Mᙠ:-x2+2x+3,2A/3+/4+^/4+^£=2+2X+3222᦮ᳮF3*+
4+2-12+4ÿ=0,
f=ᡈ2-2,54⚓/55⚓

54“9-6W3-133'᝞3—2,"ᙠ▲NI,஻887_LBNMWḄ!"#$T.%&'73-6஻-2,Mᓃ)Iஹ,22,-.=_ᓃ%+2*ᓃ■+3,222᦮ᳮ3/+Q—46஻412—46=0,
“J'2ᡈ63,/,9+0-473-L3378ᡠ:;<ᩩ>Ḅ஻Ḅ?ᙶ᪗B8)ᡈC).3355⚓/55⚓