2022-2023学年山东省青岛市中考数学专项突破仿真模拟试题（一模二模）含解析

《2022-2023学年山东省青岛市中考数学专项突破仿真模拟试题（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。

2022-2023ḕ☘ὃᦪ⚗ẚ⚪ஹ⌱⌱⚪ᑖ24ᑖᐳᨵ8⍝⚪⚪3ᑖ1.ḄA.B.-75C.D.52.!"ᡂ$%Ḅ&'()0.000000001s,-0.000000001sᵨ/01ᦪ34⊤6)A.0.1X108sB.0.1X10"9sC.IX10-8sD.IXlO^s3.AᑡCDEFGHIJKEFLJKEFḄGMMᑖ_ஹNஹஹAB.C.>.D.O,Ww/+3)D.(a+2,b—3)6.4ஹ᜛{ᙢ}~18Okk,Ḅᙠ4ஹ᜛{ᙢḄ⌶]ᙳ50%,4ᙢᑮ6ᙢḄ&'2k.lᩭḄ]ᙳ)3/k,ᑣ᪷⚪4ᑡ)¡1⚓/M53⚓

1180180,180180,x(1+50%)x(l+50%)xx180180,180180,C.=1D.--------------1x(l-50%)x(l-50%)xx7.᝞EᡧF¤ᡧ"ᐰᡭ᜜¨{©ᩩZ8¬ZCḄᜳ®)120஺45)25cm,±¤²ᑖḄ³3஺)15cm,l¤ᡧ{☢±¤ᑣ±¤Ḅ☢µ)A.1757tcm2B.35O7tcm2C.---ncm2D.ISOncm238.᝞E¹º»¼ᦪ,=4xḄE¿À¹º»¼ᦪÁ=ÀḄEÂ}ÃÄ/ஹB,ᐸGd4XḄÅᙶ᪗)2,ÆÇÈ)ÉxḄÊÌA.x<-2ᡈx>2B.x<-2ᡈ02ஹ⚪⚪!ᑖ18ᑖ#ᐳᨵ6⍝'⚪#('⚪3ᑖ,9.:io.“ÓÔÕÖ×”ÙÚÛᑜᑴ⌼%ßàᑖáâãÀὅ)åæç²ᑖãÀὅèéêᑴ⌼ë⁐ஹí⁐ஹî⁐ஹï⁐Cð⁐%ßàḄᦪñ.᪷_ᑮḄæçᦪòᑴᡂ᝞Eᡠ6ḄᡧFôE.lõᐳᨵ12000öãÀὅᑣ÷ᐸG⌱øï⁐%ßàḄ(ᨵö.¡2⚓/M53⚓

211.᝞EAB00ḄùúC,D஺஺kḄ{dlNBCD=28°,ᑣ/ABD=12.-Dஹ³ஹᑖf)3cmஹ2cmஹ1cmḄûüᙽþᡂDᙊ
ᙽᑣᙊ
ᙽḄ☢S(cm2)h(cm)Ḅᦪᐵ.13.᝞ᙠ4C5஺"#$%஺£8c'(%CE=5,FOEḄ%.)CE*Ḅᕜ,18,ᑣOFḄ,.14.᝞./,20cmḄ012Ḅᔜ⚔%5%ᙠᔜ/'ᑖ7894cm,Ḅ:ᩩ<=8>Ḅ:?5%@ᡠᙠ/Ḅᚖ᪀ᡂ0?ᨵF?GḄH/.IJKLMNᣵᵨᒕRḄ12ᢚᡂ(?0ḄTUVWᑣJḄXcn?.15.YZ[

32/7+1(1)ᓄj:nn(2)ᐵ$xḄ(ᐗmno2x2+3x-m=0ᨵF?p"qḄrᦪ᪷]mḄ9tv.17.w⚨ywz{“᥎ᳫ":ᙠ(?pḄWᨵ14ḄH?ᳫ(◀᜜"),᥎(?ᳫRᦪ᥎(?ᳫRᦪ.)Fnᦪyᜧ$5,ᑣw⚨ᔲᑣwz.?ᓫᔩ¡¢▊ᳮᵫ.18.wᙠ¦§ᳫA'¨ᑮª«¬®F¯Ḅᜧ᫑8C,±²>8ஹCF%Ḅ´ᑖ745஺ஹ35°.YZᜧ᫑8cᙢ☢ᙠ¶(o·☢'ᐸ,·100m,]¦§ᳫ¹ᙢ☢Ḅ·.º»¼½ᶇ᦮ᦪÀºÁὃᦪÃ[sin35°=0.57,cos350=0.82,tan35°=0.70᪷Ã.'ÄÅ᦮ᳮᑖ᪆ᦪÃ᝞R:ᙳᡂÌ/ÍÎᦪ/ÍÏᦪ/Í.ᵬa771.2Ñ7b8C(1)ᑏ⊤Éa,b,cḄt;(2)ᑖ7Òᵨ⊤ḄH?ÓcÔj⌕ᑖ᪆FÖ×ᕒḄÙÚÛÜᡂÌ.)⌱Þᐸ(ÖÁß,àáâ⌱ãÖ×ᕒ.20.äᔆᑴ⌼ᵬஹÑFèͽᒹV.YZê᪵ᵨ6mḄᩞᧇᑴᡂᵬVḄ?ᦪîᑴᡂÑVḄ?ᦪe4⚓/h53⚓

4ï2?aᑴᡂ(?ᵬVîᑴ⌼(?ÑV◤]ñᵨ20%Ḅᩞᧇ.(I)]ᑴ⌼ò?ᵬVஹÑVᔜᵨñïᩞᧇ¡(2)᝞¼ᑴ⌼ᵬஹÑFèᒹV3000?aᵬVḄᦪÔpï$ÑVᦪÔḄ2óôõ¢ᑏᡠ◤ᩞᧇh,·/(஻)ᵬVᦪÔ”(?)Ḅᦪᐵ±]ᨬï◤]ñïùᩞᧇ.21.YZ[᝞ᙠ஺ABCDE,Fᑖ7ú/AD,BC'Ḅ%aAE=CF,GEFᑖ7#BAḄûüஹDCḄûü$%G,H,#BD$%O.(1)]ý[AABE^ACDFþ(2)ÿDG,
DG=BG,ᑣBEDF▊ᳮᵫ.22.᝞ᡠ⍝Ḅ☢ᵫᱥ᪀ᡂ!Ḅ12m,"4m.ᢥ᯿%ᡠḄ&'ᙶ᪗*!ᱥ+,ᵨ.-⊤!1ᱥ2Ḅ3CᑮḄ567896173m,ᑮᙢ☢O1Ḅ789;m.2(1)<ᱥḄ=ᦪᐵ*@!ABCDE⚔஺ᑮᙢ☢஺4Ḅ78H(2);JKLMNO;PQRSTU96m,"94m,᝞V⍝ᑁXYᔣN⍝![\JKN]ᔲ_`(3)ᙠᱥbEc2◤

5ᡂz{D|ᵨn᪷lḄᩈ;'ᩈᒕ!]ᡂrsnḄmῪ'ᡂz<|nᎷX]ᡂmnḄmῪ'!9

6n78910mÈnᑖÅᵨ11᪷ஹ12᪷ஹ13᪷ஹ14᪷lḄᩈÉÊËÌ

72022-2023ḕ☘ὃᦪ⚗ẚ⚪;ஹ⌱;⌱ü⚪þᑖ24ᑖ!ᐳᨵ8⍝⚪⚪3ᑖ1.ḄA.B.-75C.D.5ூᫀ௃Cூᑖ᪆௃ᦪ⊤"ᦪaḄ$%&$Ḅ'()*ᦪaḄ.ூ+,௃--ḄI-#1=75ᦑ⌱C3⚪ὃ᪶67$8.,⚪ᐵ:$8ᳮ,Ḅ<=.2.?@ABCDᡂF3GBḄHIJK0.000000001S,O0.000000001sᵨQRSᦪTU⊤"KA.0.1X10^sB.0.1X109sC.IX10-«sD.IX109sூᫀ௃Dூᑖ᪆௃\1Ḅ]ᦪ^U_ᑭᵨQRSᦪT⊤"abcdKaxlT",%iᜧᦪḄQRSᦪTklḄᐸᡠGᵨḄ]ᢣᦪpᢣᦪᵫ&ᦪrstukKvḄᦪwx☢Ḅ0Ḅuᦪᡠz{.ூ+,௃0.000000001sᵨQRSᦪTU⊤"K1x10-95.ᦑ⌱8D.3⚪ὃ|}ᵨQRSᦪT⊤"iḄᦪabcdKaxlT"ᐸ~lW|a|<10,nKᵫ&ᦪrstukKvḄᦪwx☢Ḅ0Ḅuᦪᡠz{.ḄB.D.8⚓/53⚓

8ூᫀ௃Bூᑖ᪆௃᪷%Ḅᭆ,.ூ+,௃A⌱⚗8k.ᦑ⌱⚗kᔠ⚪

9(a+2,b—3)ூᫀ௃Aூᑖ᪆௃᪷$Ðஹ8º»ÒÓᙶ᪗ḄµᓄU¼¸¹Ð3ᔣrº»2uᓫ×ᔣº»}3uᓫ×ᯠÙ{஺ஹ6ḄÛÜU¼ᫀ.ூ+,௃ᵫ⚪

10800A.1757tcm2B.350ᐔcm2C.-----item-?I).150ᐔcm23ூQRᫀ௃Bூᑖ᪆௃t^uᑖḄ☢z'ᜧᡧ]Ḅ☢zᡧ]ADEḄ☢zPᵫᓽ*..ூ-.௃VAB=25,BD=15,AAD=10,(120-^rx252120NX1()2)Sẓ*=------------------------x2=175nx2=350cm2,(360360)ᦑ⌱B.C⚪D⌕ὃGᡧ]☢zḄḄᵨP.C⚪ḄᐵWVᡧ]☢z(.8.᝞ZPᦪ,=4xḄZᦪ=ḄZ/ஹB¢Pᐸ¤¢4XḄ¥ᙶ᪗42,¨©>%«PxḄ¬$®V()A.xV-2ᡈx>2B.x<-2ᡈ02ூQRᫀ௃Dூᑖ᪆௃ᐜ᪷;ᦪᦪḄឋ²³&B¢ᙶ᪗P´ᵫᦪZᓽ*%&µ¶.ூ-.௃.0•••ᦪᦪḄZᙳᐵ2¢¸¹P:.AஹB¢ᐵ2¢¸¹P:¢AḄ¥ᙶ᪗42,.♦.¢BḄ¥ᙶ᪗4-2,•••ᵫᦪZ*»P¨-22«ᦪyi=kḄZᙠ¼=%Ḅ½?P1X-x...¨yi>y2«,xḄ¬$®V-22.ᦑ⌱0D.C⚪ὃGḄVᦪᦪḄ¢ᡂLP¾᪷;ᦪ]³&k>¿2«xḄ¬$®V.}11⚓/53⚓

11⚪ḄᐵW.ÀஹÁÂ⚪ÃC⚪Äᑖ18ᑖPᐳᨵ6⍝⚪PÈ⚪3ᑖPÉV32-V89.:ூQRᫀ௃2ூᑖ᪆௃ᐜÊÀD᪷(ᓄ4ᨬÍÀD᪷(PᯠcÊÏÐᑁᔠÓc´ÀD᪷(Ḅ◀Õᓽ*%&ᫀ.ூ-.௃2(=472—½É+&=272-72=2.ᦑᫀ42.C⚪ὃGÀD᪷(ḄÙᔠ.ÊÀD᪷(ᓄ4ᨬÍÀD᪷(P´᪷;ÙᔠÚÛV.⚪ḄᐵW.10.“ÝÞßàá”ãäåᑜᑴ⌼éêᑖëìíὅP4PïGuᑖíὅPðñòᑴ⌼ó⁐ஹõ⁐ஹö⁐ஹ÷⁐øùú⁐éêḄᦪS.᪷;%ᑮḄïGᦪ;Pûᑴᡂ᝞ZᡠýḄᡧ]NZ.xCDᐳᨵ12000þíὅPᑣÿᐸ⌱⁐Ḅᨵ.ூᫀ௃2400ூ௃ᐸ⌱⁐Ḅᨵ12000X20%=2400ᦑᫀ240011.᝞AB!Ḅ"#C,D!$Ḅ%&'NBCD=28°,ᑣNABD=)12⚓/,53⚓

12ூᫀ௃620ூ௃-⚪ᑖ᪆12AD,᪷4AB!"#56ZADB=90஺ᯠ9᪷4:;ᡠ=Ḅᙊᕜ@5ANBAD=/DCB=28஺ᯠ9᪷4"@B@CḄ%┦@E⊡5ANABD=62஺.ᦑ62.&GH⚪I⌕ὃLMᙊᕜ@Nᳮ⚪Pᐜᑭᵨ"#ᡠ=Ḅᙊᕜ@"@Aᑮ"@B@C,ᯠ9᪷4:;ᡠ=Ḅᙊᕜ@VWᓽ5Y.12.Z[\]ஹ_ஹ`ᑖa3cmஹ2cmஹ1cmḄ]bcdᙽfᡂ[\ᙊhcdᙽᑣiᙊhcdᙽḄj☢lS(cm2)m`h(cm)noḄpᦪᐵst.ூᫀ௃1ூ௃-⚪ᑖ᪆᪷4⚪u5AdᙽḄcl=3x2x1=663,ᑣᙊhcḄcl=5|=663,ᑣ16s=[.hὃ&wxypᦪḄᵨ13.᝞ᙠbCABC஺=@{/Cm5஺V|}&஺EBC%,CE=5,~OEḄ&.'FḄᕜ]18,ᑣOFḄ].ூᑖ᪆௃ᵫ"@B@CḄ{YDEḄ]ᑭᵨB@C{NᳮNᳮYBE)13⚓/,53⚓

13Ḅ]ᓽ5Yᫀ.ூ௃•CABCD!bC,ZDCE=90°,OD=OB,VDF=FE,.*.CF=FE=FD,VEC+EF+CF=18,EC=5,EF+FC=13,ADE=13,.\DC=7P£2-EC2=12»/.BC=CD=12,BE=BCEC=7,VOD=OB,DF=FE,7r.OF=vBE=-22⚪ὃLbCḄឋB@CḄ{Nᳮ"@B@C{ḄឋW6⚪Ḅᐵ!6}ὃὃ⚪.14.᝞]20cmḄB@CḄᔜ⚔&&ᙠᔜ$ᑖa4cm]Ḅ¡ᩩ{£¤AḄ¡\&¥ᡠᙠḄᚖ{᪀ᡂB\ᨵ%\"@ḄC.Z¨©ª«{¬ᣵᵨᒕ¯Ḅᢚᡂ[\jB@CḄ±²hC³´ᑣ¨Ḅµlcn?.ூᫀ௃144ூ௃᝞ᵫ⚪uAMBCWB@C&OPQWB@CAD=AK=BE=BF=CG=CH=4cm,AZJ=ZB=ZC=60°,AB=BC=AC,NPOQ=60°,N4DO=NAKO=90஺.1¶AO,¥QMVOP}M.ᙠRthAODZOAD=ZOAK=30°,)14⚓/,53⚓

14OD=—AD=cm.,:PQ=OP=DE=20-2x4=12(cm),:.OA/=(9P«sin60°=12x=673332(CTW),...±²hC³´Ḅµl=1É12ஹ60ÉÊË=144(c"#)ᦑᫀ144.Bஹ⚪(ᐳ1Ñ⚪Òᑖ4ᑖ)15.Ô6{£aÖNACB.Y¥஺0,Ú஺0ᙠNACBḄᑁÜCO=a,Ý஺0mNACBḄ%ᑖaVᑗ.ூᫀ௃¥ß᪆ூ௃-⚪ᑖ᪆᪷4¥¥[\@W}Ô6@ᯠ9¥à\@Ḅ@áᑖ{ᯠ9{£0CḄ]¥ᚖ{âᚖ{£Ḅ]ã#0&¥ᙊᓽ5.-⚪᪆᝞ᡠä00ᓽᡠY.ஹ⚪(⚪Òᑖ74ᑖᐳᨵ9⍝Ñ⚪,)16.æ2஻+1n2-\(1)ᓄè:+஻)+nn(2)ᐵ}xḄ[ᐗìIbí2x2+3x-m=0ᨵ%\ñVWḄòᦪ᪷YmḄóõ.)15⚓/,53⚓

15஻+19ூᫀ௃(1)——;(2)m>--«-18ூ௃-⚪ᑖ᪆1öt÷ø%⚗úᑖûᑭᵨ:ᑖüᑖtḄýþþᑣæ:Pᑭᵨ◀ᑣᑖᓽᑮ;2᪷ᨵḄᦪ᪷,ᑮ᪷Ḅᑨᜧ!0,"#mḄ%ᓽ.'⚪)᪆+)+1,=.+2"+1•—ߟ_(_஻_+__1_)2•------------n-----------=--஻--+---1n஻21n(w+1)(M-1)n-19
2..,2%2+3x-"?=0ᨵḄᦪ᪷.•.4=9+8">0,)+m>---.856+7⚪ὃ9:ᑖḄ;ᔠ=>?@᪷ḄᑨABCD=>ᑣE)F7⚪ḄᐵH.17.I⚨KILM"᥎ᳫ"QR:ᙠ2UVḄWXYZᨵ[\]1^4Ḅ_ᳫ◀[\᜜bcd,eYfg᥎#2ᳫhiᦪjklmneY᥎#2ᳫhiᦪj.opᦪjqKᜧ!5,ᑣI⚨rᔲᑣILr.tQRuᓫwxᔩz{▊Vᳮᵫ.ூFᫀ௃wxᳮᵫ)᪆ூ)௃'⚪ᑖ᪆+᪷⚪#᪛nᑖ"#pᦪjqKᜧ!5KpᦪjqKᜧ!5Ḅᭆ᳛᝞ᭆ᳛ᑣQRwx᝞ᭆ᳛ᑣQRwx'⚪)᪆+᪷⚪᪛᝞i+
1
1234Illi2345APpᦪjqKᜧ!5=—=஺PpᦪjqKᜧ!5=22168168..35.,88QRwx16⚓/53⚓

1618.IVᙠᳫAᑮ¡Ḅᜧ᫑8C,¤¥8ஹC5Ḅ§¨ᑖ]45஺ஹ35஺.¬ᜧ᫑8c¯ᙢ☢ᙠ²2³☢ᐸµ³]100m,"ᳫ¸ᙢ☢Ḅ¹³.ºᶇ᦮ᦪd½ὃᦪ+sin35°=0.57,cos35°=0.82,tan35°=0.70dூFᫀ௃233mூᑖ᪆௃ÇAD_LBCÌCBḄÍÎÏ!D,ÐAD]x,⊤Ó#DBKDC,᪷ᑗḄᭆÕ"#xḄÖᓽ.ூ)௃)+ÇAD_LBCÌCBḄÍÎÏ!D,ÐAD]X,ᵫ⚪ZABD=45°,ZACD=35",ᙠRtAADBY,NABD=45°>DB=x,ᙠRtZ^ADCYNACD=35°,tanNACD=——CD.x_7"x+ioo-To')x^233.ᡠ?ᳫ¸ᙢ☢Ḅ¹³]233Ý.ᦑ233.7⚪ὃ9ḄE)ߨà¨Ḅ=ᵨᳮ)â¨K§¨ḄᭆÕஹCD┦¨à¨äᦪḄᭆÕE)⚪ḄᐵH)FåᶇÇ#æçÏ᪀⌼ߨà¨.19.ᵬஹìíîᕒ½ðñòóôᡂöᑖ÷ᑴᡂiᑡúû+17⚓/53⚓

17ᵬòóüöìîᕒñòóôᡂö᪷?ýþ᦮ᳮᑖ᪆ᦪ᝞i:xᙳᡂ
/ᦪ/ᦪ/ᵬa771.27b8C(1)ᑏ⊤a,b,cḄ;(2)ᑖ!ᵨ⊤Ḅ#$%&'()⌕ᑖ᪆,-./ᕒḄ1234ᡂ
.5⌱7ᐸ9.:;,<=>?⌱@./ᕒ.ூBCDᫀ௃(1)a=7,b=7.5,c=4.2J(2)7/ᕒ:;(ᳮᵫMN᪆ூᑖ᪆௃(1)᪷PQᩗSᙳᦪḄ&UVW(ᦪḄCXYZḄ&UVWᓽ\]ᑮaஹbஹcḄJ(2)᪷PSᙳᦪஹᦪஹᦪஹ`abcᑖ᪆ᓽ\]ᑮDᫀ.5x1+6x2+7x44-8x2+9x1ூdN௃(1)a==7,1+2+4+2+1e12Ḅᦪfg▰ᑡ>j3ஹ4ஹ6ஹ7ஹ7ஹ8ஹ8ஹ8ஹ9ஹ10,.•.12Ḅᦪ6=——=7.5,2•.•12Ḅaᦪq10a(.•.C=[(3-7)2+(4-7)2+(6-7)2+2X(7-7)2+3X(8-7)2+(9-7)2+(10-7)2]=4.2J(2)xSᙳᡂ
y(ᵬஹḄᡂ
z{(|q7Jxᦪy(ᵬ17}~ḄaᦪJxᦪy(ᵬ17Ḅaᦪᨬ(18ḄaᦪᨬJxy(ᵬḄᡂ
(ᔠ}~ᔜ⌕(579.:Q;Ḅ(\⌱:;(ᵫ]ᑖḄ\ឋᜧ.18⚓/53⚓

18⚪ὃᦪPḄ%&&U(᪷P(¡QᩗSᙳᦪḄ&UVW(ᦪḄ&UVW(Ḅ&UVWqN⚪Ḅᐵ£.20.¤ᔆᑴ⌼ᵬஹ-¨©ᒹ«¬.®¯᪵ᵨ6mḄᩞᧇᑴᡂᵬ¬Ḅ$ᦪᑴᡂ¬Ḅ$ᦪ³2$(´ᑴᡂ9$ᵬ¬ᑴ⌼9$¬◤¶ᵨ20%Ḅᩞᧇ.(1)¶ᑴ⌼·$ᵬ¬ஹ¬ᔜᵨ³ᩞᧇ¸(2)᝞ºᑴ⌼ᵬஹ-¨ᒹ«¬3000$(´ᵬ¬Ḅᦪ'»³¬ᦪ'Ḅ2¼(½¾¿ᑏᡠ◤ᩞᧇÁÂ/(஻?)Åᵬ¬ᦪ'“($)ÇÈḄÉᦪᐵÊW(˶ᨬ³◤¶³Ìᩞᧇ.ூBCDᫀ௃ᵬ¬ᵨ0.6mᩞᧇJᑴ⌼·$¬ᵨ0.5mᩞᧇJ/=0.5+1500,1700.ூᑖ᪆௃✌ᐜÏᑴ⌼·$¬ᵨxmᩞᧇ(ᑣᑴ⌼ᵬ¬ᵨ(1+20%)xmᩞᧇ(᪷PḄᦪ'9ᵬḄᦪ'=2ᑡᑖWbc¶NJ᪷P⚪Ñ]஻ḄÒÔ(ᯠÖ᪷P/Å஻ḄᐵÊᑡÉᦪN᪆W(᪷PÉᦪḄ×Øឋ¶ᨬ.ூdN௃Nj(1)Ïᑴ⌼·$¬ᵨxmᩞᧇ(ᑣᑴ⌼ᵬ¬ᵨ(1+20%)xmᩞᧇᵫ⚪\]jx-(l20%)x=2+N]x=0.5(m)ÙÚÛx=0.5qÜḄN(ᡠ}ᑴ⌼ᵬ¬ᵨ0.6mDjᑴ⌼·$ᵬ¬ᵨ0.6mᩞᧇJᑴ⌼·$¬ᵨ0.5mᩞᧇÝ22(3000—஻)(2)ᵫ⚪<[n<30002000ீ”<3000I=0.6M+0.5(30009஻)=0.1"+1500":k=0A>0,án×ᜧ×ᜧ(âã“=2000ä(/ᨬ=1700å⚪ὃæᑖWḄ!ᵨ(ÉᦪḄឋç(᪷P⚪Ñ]zᐵḄ{'ᐵÊWqN⚪Ḅᐵ£.21.è®j᝞é(ᙠëABCD(E,FᑖqìAD,BC~Ḅí(´AE=CF,îïEFᑖðBAḄñòïஹDCḄñòïíG,H,ðBDíO.19⚓/53⚓

19D
1¶ójAABEôz^CDFJ
2õöDG,5DG=BG,ᑣ#ì÷BEDFqø¾#ì÷¸¿▊úᳮᵫ.ூBCDᫀ௃û1óúMN᪆Jû2#ì÷BEDFqü÷JᳮᵫMN᪆.ூdN௃ý⚪ᑖ᪆jû1þᵫSc#ì÷Ḅឋç]AB=CD,ZBAE=ZDCF,ᵫSASóúÿABEgACDFᓽ
2ᵫḄឋAD஻BC,AD=BC,DE=BF,BEDFOB=OD,ᵫῪḄᔠឋEFLBD,ᓽ
BEDF.⚪᪆!1"!•••ABCD.AB=CD,ZBAE=ZDCF,AB=CDᙠ%ABE'ACDF(?NBAE=ZDCF,AE=CF.".%ABE^ACDF
SAS
2BEDFᳮᵫ᝞+!,ABCD.AD஻BC,AD=BC,VAE=CF,.DE=BF,BEDF.•.OB=OD,!DG=BG,AEFIBD,BEDF.22.᝞-ᡠ/0⍝Ḅ2☢ᵫ4ᱥ'67᪀ᡂ67Ḅ612m,:4m.ᢥ᯿-(ᡠ=20⚓/@53⚓

20/ḄAᙶ᪗D4ᱥ
EᵨG-1/+K+0⊤/N4ᱥOḄPCᑮOBḄSTUVW6173m,ᑮᙢ☢04ḄUVWm.21]^4ᱥḄ_ᦪᐵDbcdef⚔஺ᑮᙢ☢04ḄUV2]jklmno67pqrstuW6m,:W4m,᝞v0⍝ᑁxyᔣn⍝{|}jkn~ᔲ3]ᙠ4ᱥfO◤^r᣸Vᙢ☢ḄuT᝞vVᙢ☢ḄuT8m,{|᣸ḄSTUVᨬூᫀ௃1]4ᱥḄ_ᦪᐵDbW-1X2+2X+4,f⚔஺ᑮᙢ☢ḄUVW10m2]6
Eᳮᵫ᪆3]᣸ḄSTUVᨬ4.ூᑖ᪆௃1]᪷¡P8'PCᙠ_ᦪ-¢Oᑭᵨ¤¥Dᦪ¦^6'cḄ¨©ª_ᦪ᪆b᪷¡᪆b^⚔Pᙶ᪗2]᪷¡⚪«nᨬ᜜®ᙢ☢஺¯Ḅ°PW2,0]ᡈ10,0]],ᯠt^³x=2ᡈx=10¶yḄ¨®6¸¹ºᜧ¹6ᜧ¼
E¹6¼~3]½8¾ᐭ_ᦪxḄ¨ᯠt¸ÀÁᨬ¨.ூÂ௃!1]ᵫ⚪ÃP80,4],C3Dᙠ4ᱥOc=4ᡠEÅ26b=2Åc=4=21⚓/@53⚓

21³x=——=6¶È=102a1_9•4ᱥ᪆bW^=-+2x+4,f⚔஺ᑮᙢ☢஺¯ḄUVW1062]ᵫ⚪Ãnᨬ᜜®ᙢ☢O4Ḅ°PW2,0]ᡈ10,0]]22³x=2ᡈx=10¶y=—>6,3ᡠE
E3]ÎÏ=8,ᓽ1X2+2X+4=8,
Ð2—12X+24=0,6X]=6+2-\/3>®=6-2-73X,-x=42!᣸ḄSTUVᨬ423.ᡂÕÖ!ᵨn᪷ØḄᩈÚÛÜᩈÚÝᒕß]~ÛᡂàáḄῪᡂÕâ^!ãᎷx~ÛᡂmàáḄῪWâ^m®nåæḄᐵDᡃ
E©ᐭèéêஹìíஹî¹ïðஹñòóô.â^!ᵨ3᪷ØḄᩈÚÛᡂÜ~ÛᡂàáḄõ¶öᯠ~ÛᡂàῪ.ᡠE³n=3¶m=lᵨ4᪷ØḄᩈÚÛᡂÜ~ÛᡂàáḄø
ᑖᡂ1᪷ᩈÚஹ1᪷ᩈÚ'2᪷ᩈÚ}àùú~ÛᡂᡠE³n=4¶m=0ᵨ5᪷ØḄᩈÚÛᡂÜ~ÛᡂàáḄûᑖᡂ1᪷ᩈÚஹ1᪷ᩈÚ'3᪷ᩈÚᑣ~ÛᡂûᑖW2᪷ᩈÚஹ2᪷ᩈÚ'1᪷ᩈÚᑣ~ÛᡂàῪᡠE³n=5¶m=lᵨ6᪷ØḄᩈÚÛᡂÜ~ÛᡂàáḄûᑖᡂ1᪷ᩈÚஹ1᪷ᩈÚ'4᪷ᩈÚᑣ~Ûᡂ=22⚓/@53⚓

22ûᑖW2᪷ᩈÚஹ2᪷ᩈÚ'2᪷ᩈÚᑣ~ÛᡂàῪᡠE³n=6¶m=lýOᡠþ
⊤জn3456m1011
ᵨ7᪷ḄᩈᡂᡂḄῪ᯿
!"ᑏ$%&'()*+,-ᙠ⊤ঝ12ᑖ4ᵨ8᪷ஹ9᪷ஹ10᪷ḄᩈᡂᡂḄῪ6◤*+,-ᙠ⊤ঝ12n7S910m89ᑖ4ᵨ11᪷ஹ12᪷ஹ13᪷ஹ14᪷Ḅᩈ:;<=
……ᜐᳮᡂAᵨn᪷ḄᩈᩈBᒕD2ᡂḄῪEnᑖ4F4k-lஹ4kஹ4k+lஹ4k+2,ᐸ1kH᦮ᦪ*+,-ᙠ⊤ঞ12n4J4k4L+14k+2mᡂAMᵨᵨ2016᪷ḄᩈᩈBᒕD2ᡂḄῪ⌕
ᑏ$%&'(2O23⚓/R53⚓

23ᐸ1☢UḄῪVῪᵨW᪷ᩈ.6-+,2ூZ[&ᫀ௃n=7,m=2d503d672.ூᑖ᪆௃12ஹ᪷kl$Ḅ%⚪!"n$&ᫀd22ஹ᪷k⚪op⊤q-ᑏrsdMᵨ12ஹ᪷k⚪on$kḄuvwn$Ḅᦪ᪷kḄឋyn$&ᫀ.ூz%௃{⚪%᪆
12|ᑖᡂ1᪷ᩈஹ1᪷ᩈ}5᪷ᩈᑣᡂ|ᑖ2᪷ᩈஹ2᪷ᩈ}3᪷ᩈᑣᡂῪ|ᑖ3᪷ᩈஹ3᪷ᩈ}1᪷ᩈᑣᡂῪ22ᡠ>n=7>m=2n78910m2122n4k-l4k4L+14k+2mkk-ikkᡂAMᵨ112016=4X504ᡠk=504,ᑣᡂk-l=503ḄῪdফ672ὃ⚪24.᝞ᙠABCD1AB=6cm,BC=8cm,AC,BDF0.PvA$!ᔣᒴM¡¢lcm/sdQvD$DC!ᔣᒴM¡¢lcm/s1¥M¡¦§1¥M¡.¨©PO)«¬BCFE,'Q®QF஻AC,BDFF.EM¡±²ts20

24B2c(1)t¹uAAOPHῪ(2)Eº»OECQFḄ☢US(cm2),{[½s¾tḄ¿ᦪᐵÁÂd(3)ᙠM¡'(1ᔲÄᙠÅÆt,ÇSº»SḄÈOECQF1SACD=9116?|Äᙠ
A$tḄud|ÄᙠÊ▊Ìᳮᵫd(4)ᙠM¡'(1ᔲÄᙠÅÆ3ÇODÎᑖNCOP?|Äᙠ
$tḄud|Äᙠ,Ê▊Ìᳮᵫ.2513QூZ[&ᫀ௃(1)—ᡈ5d(2)S=--/"H—/+12d(3)—d(4)2.88.8322ூz%௃{⚪ᑖ᪆(1)᪷kḄឋy}ÕÖ½ᳮnᑮ/C=10,জ᝞1,'25Ù®᪷kÚÛḄឋynᑮ4P=/=—ঝ/Ù=/஺=ᱏ5,FHnᑮ+Þd8(2)EHL4cH,0M_LZCF஻DN1ACN,஺ÙFG,᪷kᐰḄឋynᑮCE=4஽f,᪷kÚÛḄឋy⊤ç$᪷kÚÛḄឋy⊤ç$஺FQ,᪷kḄ☢Uᓽnᑮ+Þd(3)᪷k⚪oᑡ!(nᑮḄuFHnᑮ+Þd(4)ᵫÎᑖḄឋynᑮ஺MḄé᪷kÕÖ½ᳮnᑮONḄéᵫḄ☢UêÂ⊤ç$OP,᪷kÕÖ½ᳮᑡ!(ᓽnᑮ+Þ.{⚪%᪆(1):ᙠ/BCD1Ab=6cm,BC=8cm,:.AC=10,জAP=PO=t,᝞1,'ì®PMA0,i5.\AM=-AO=—,229:ZPMA=ZADC=90°/PAM=/CAD,f:.AAPMs/\ADC,APAM---=---->ACADO25⚓/R53⚓

25:AP=t=—,8ঝ4P=4O=ᱏ5,25/ᡈ5íî஺ÙHῪ;8(2)®EH_L/CF஻0A/_LZCF஻DNkACN,஺FFG,ᙠíîÙ஺¾íCE஺1,:ZPAO=ZECOAO=OC,ZAOP=ZCOEff••íZOP§íCOE,JCE=AP=t,:ACEHS/XABC,.EH_CE>~AB~~AC>3♦.EH=+t,5ADCD24:DN=ACy:QM஻DN,•JCQMsRCDN,QM6-tQM_CQ=,ᓽ-6~~DN~~CD524-4z:.QM=52424-4z4••DG=—5-5--5":FQ//AC,:./\DFQ^>/\DOC,.FQ__DG_••fOCDN5:.FQ=-t,.1.3I]24-4/13..2Sº»OECQSAOESñ»OCQ—xDx—Zd—(—Z+5)-----------=——/H—Z+12,2526532O26⚓/R53⚓

261,3.••S¾/Ḅ¿ᦪᐵÁÂ5=-ì+ߟ/+12d32(3)ÄᙠVSA.4=7X6'8=24,CD1399KSKLMOECQF:S^ACD—(—1ö+5+12)24=916»%n/=øZ=0,(ᔠ⚪oúû),•ᱏSº»SZ»QKC0FSAJCD=916d(4)᝞3,'஺®஺ML4cFM,DNLACNN,*/ZPOD=/COD,24:.DM=DN=—>5___________7:.ON=OM=>OD2-DN2=->•:OPDM=3PD,u5:.OP=5——t,8185:.PM=---------1,58VPD-=PM2+DM2io594.••(8-Z)2=(---Z)2+(—)2,%nᓛ15(ᔠ⚪)2.88,585.•.ᱏ2.88ODOᑖNCOP.27⚓/53⚓

272022-2023ḕ☘ὃᦪ⚗ẚ⚪ஹ⌱⌱ᜧ⚪ᐳ10!⚪"!⚪3ᑖᐳ30ᑖ஺ᙠ"!⚪&'Ḅ)*⌱⚗,-⌕⚗/ᔠ᪗⚪⌕1241.Ḅ45ᦪ722.᝞9:7ᵨ<ᙽ>ᐰ45Ḅ!@ABCᡂḄEFBG@☢IEFBJᑮḄ:L723.2017M5ᨴ18OᡃQRSᙠᓭUVWUXᡂYZ[\]^ᡂ_`abᙠUXcdefghḄQi.jkᶍmnoᓭUᓅq▮ᚁḄ\]^tuvwᑮ186xᔴz{wᑮᡃQ▮b|ztu{Ḅ50%.ᦪj186xᔴᵨ}~ᦪ\⊤_2A.186x108ᔴB.18.6x109ᔴC.1.86x101஺ᔴD.0.186X1011ᔴ4.ᑡ@Ḅ7228⚓/53⚓

28A.(a+b)2=a2+b2B.(-1+x)(-x-1)=1-x2C.a^a2=a3D.(-2x)3=-6x35.ᦪ~,ᨵ5ᐜḄᡂᑖ786,89,78,93,90.ᑣ5ᐜᡂḄᙳᑖ,¡ᦪᑖ72A.87.2,89B.89,89C.87.2,78D.90,936.᝞:ᑡ¢,@Ḅ72A.N1/37¤¥ᑁ§B.N2N37ᑁ┯§C.N2N47¤¡§D.N3N57À⚔§7.ᨵᑡ¨⚪জªx2=X,ᑣX=lঝªa2=b2,ᑣa=bঞ²³ᚖµᑖ²bḄ¶ᑮ²³·¸Ḅ¹º4»;ট4»Ḅ¾ᡠÀḄᙊᕜ§4»ᐸ,Ĩ⚪Å⌮¨⚪Ç7Ȩ⚪Ḅ*ᦪ72A.1*B.2*C.3*D.4*8.᝞:ᙠËZBC,ZC=90",Z5=30°,϶Ð_ᙊÑÒÓ_ÔÕÖ¾ᑖ×/Cض஻MÛᑖ϶N_ᙊÑÖ¾·¾×ضP,cÝ/PÞßà×BCض஺,ᑣᑡ¢,@Ḅ*ᦪ72জÐ஺7N84CḄᑖ²ঝáWC=60°ঞË48஺7»Ὺä§Lট¶Dᑮµ²ABḄ¹º»ØCDḄÓå.29⚓/53⚓

29A1B.2C.3D.49,ªæ§ä§LḄçèÓ_c,ᑁᑗᙊÔÕ7r,ᑣᑁᑗᙊḄ☢êÅä§L☢êëì727irᑍS7trTtrA--------B.------C.--------D.-z----T-c+2rc+r2c+rc4-r10.᝞:ᡠí᜜Lஹᜧ!>ᐰ45Ḅ²³ᢥ᯿ñòó᤮ᡂᑡ:L1õ:L,Ḅ*ᦪ_ö,2õ:L,Ḅ*ᦪ_Å3õ:L,Ḅ*ᦪ_…1111Ïøùúᑣ+—+—+…Ḅü_)qa2%ý9431D.760ஹ⚪1ᜧ⚪ᐳ5'⚪#('⚪3ᑖ#ᐳ15ᑖ.11.þÿᑖ
2x?-4x+2=____12.᝞AFCEDCEBCFAB=AD,ABCDḄ☢24cm2.ᑣACcm.13.᝞ᵨᡠḄᡧ!ᱏ#ᡂ%ᙊ┵()ᡧḄ*+,5cm,-6ᐔcm,/0#ᡂḄᙊ┵Ḅ12cm.14.3)MஹN5ᐵ7y89:Mᙠ<=^=’-NᙠBy=-x+3C2xD30⚓/G53⚓

30Mᙶ᪗,(a,b),ᑣy=-abx?+(a+b)xḄ⚔ᙶ᪗,.15.XYZজ"ঝVF7Fঞ#+23+3?ট#+2-3+33+ᵬghiXYḄjkᵨilmḄnoBpᑏr☢stḄuJr+23+33+…+283=zஹ
{⚪Z(}ᜧ⚪ᐳ7⚪ᐳ55ᑖ)16.(1)XYZ(/)-3+|-2|-(-2017)(2)ᐜᓄuZ()Z(—L+1)+(x+))ᐸx=4-2sin30°.x—2x—217.᝞᪥ᦟᜧḄ⚔ᨵᙽ“ᦻ¡”Ḅ£¤CD.ᙠ§ᚁḄᚁ©Aᜐ¬£¤®DḄ¯°,60஺²§ᚁᔣ´ᑮBᜐ¬£¤⚔CḄ¯°,45஺.()§ᚁABḄᚁ2i=l:,AB=10¹AE=15¹»ᙽ£¤CDḄ12.(¬°ᘤḄ12½ᶍ¿X,jkᑮ0.1¹.ÀὃᦪÃZ=1.414,=1.732)□□□00018.“ÅÆ”ÇᑮᐰÉÊḄËÌᐵÍÎÏ9ᑖᐜÐÑÅÆ)ÒḄÓ
Ô2ÕᵨÖ×Ø᪵ÚÛḄsÜ᪷ÃÞßᑮḄàáâãäXåᑴÓ☢Ḅ5çè¿éêḄäXëi᪷ÃäXᡠìíḄàá
{îᑡᡂðZ(1)pñòᔁÚÛḄᐜÐᐳᨵôᡧäX“õ}Ó
”ᑖᡠ9öᡧḄᙊ÷°,0;(2)ë⊡ᐰᩩäXû(3)9ÅÆ)Òüᑮ“Ó
”Ô2ḄᐜÐᵱஹ᝕ÐḄÿា2:3,231⚓/53⚓

31ᑣាᑮ1"ᵱ$%1"᝕$Ḅᭆ᳛.19.,ᖪ.⚜ᜓ12ᢇ456789Ḅ⊟;<2=4589?2=8589AB10ᐗEFG1/589⊟;12=8589⊟;8=ᐳ◤1880ᐗJK2=489⊟;LMᑭ20ᐗ2=B89⊟;LMᑭ30ᐗ⌕QᙠSTMᑭ6UV780ᐗX/89⊟;6YV28=.(1)\/ஹ889⊟;1^ᔜ`YUᐗa(2)F<G1/89⊟;`889⊟;Ḅ2bcY4=ᑣᖪdᙠST1eLᨵg5hijGe.20.᝞l`Ḅ᜜nᙊ஺qᙠ5cstN8/CḄwᑖyzVq஺{n8஺ஹCD,|q஺}5cḄw~yḄyzVq.(1)\EPD`஺஺ḄᑗyJ(2)\EAPBDTADCAK(3)45=6,/C=8\yPBḄ.21.ᵬஹ4ᑡ.<◞2hᨵ2ᑡ¡Ḅᑡᵬ¢.᝞l0A`ᑡᑡ¤ᵬḄ¥¦s(km)ª«¬t(h)Ḅ¯ᦪl±,BC`2ᑡ¢ᵬḄ²³´ᵬḄ¥¦s(km)ª«¬t(h)Ḅ¯ᦪl±.µ᪷·lḄ¸¹º»¼ᑡᡂ¾E(1)l±¿²³À¬?ᑡᑡÀ¬lh(Â஻Ä"ᡈ"Ç")qBḄÈᙶ᪗600ḄËÌÍÎ`J(2)µÏnᙠlÐÑÒᑡᑡ¤ᵬḄ¥¦s(km)¬t(h)Ḅ¯ᦪl±J(3)F²³Ḅ100km/h,জ\ÒᑡᑡÑÀY¬Ô²³⍗aঝµÏnᑏÑSᑡ²³ᑁ~Ù⌶Û☢ÝᩭḄß4ᑡᑡ⍗Ḅ¬◞.32⚓/53⚓

3222.᝞làᱥyy=ax2+bx-3xèzVA,B4qyèzVCqXqé2,-3aê,ëìè`Ïyx=l,⚔q`M.é1ê\àᱥyëïḄ¯ᦪ⊤ñòJé2êC,M4q}ÏyxèzVqN,ᙠàᱥytóᔲõᙠS᪵ḄqP,Q÷qP,A,C,N⚔qḄøsùw~øsùaFõᙠµ\ÑqPḄᙶ᪗JF6õᙠµ▊ûᳮᵫJé3êþÏyy=-x+3yèḄzq`D,ᙠyBDtÿ
EB,DᔠA,B,EḄᙊBCF,ᑨ4AEFḄ᜜▊!ᳮᵫ$4%E&y=-x+3-./
031Ḅ234ᔲᡂ789ᑏ;23.2022-2023ḕ☘ὃᦪ⚗ẚ⚪ஹ⌱⌱1ᜧ⚪ᐳ10'⚪#('⚪3ᑖ#ᐳ30ᑖ஺ᙠ('⚪EFḄ+H⌱⚗#I⌕⚗Kᔠ᪗⚪⌕N41.
>Ḅ?@ᦪ&4455A.—B.——C.—D.——5544ூ1⚪Eᫀ௃ூHIEᫀ௃Aூᑖ᪆௃᪷MN⌕PQRḄSTᦪUV?@ᦪWXEᫀ.Y33⚓/\53⚓

3344ூ^_௃_`-aḄ?@ᦪ&ᦑ⌱`A.d⚪ὃfg?@ᦪ._⚪Ḅᐵi&jk?@ᦪḄᭆm.?@ᦪḄᭆm`N⌕PQRḄSTᦪnoUV?@ᦪ.2.᝞qr&ᵨtᙽvᐰ?@ḄxHyz{ᡂḄ|}z~H☢|}zXᑮḄr&ூHIEᫀ௃Bூᑖ᪆௃ᑮ~H☢ᡠXᑮḄrᓽWᶇ/
ᑗ~H☢ᑮḄ⊤᝞r1.ூ^_௃_`~H☢}zᨵ3ᑡHyᑖᨵ`2T2T2T᝞r.ᦑ⌱B.d⚪ὃfgrḄr&~ᱥzḄH☢ᑮḄrẠ⚪.3.20175ᨴ18ᡃᙠᓭ£¤¥£¦ᡂ§¨W©ªᡂV«¬-ᙠ£¦®¯°±²Ḅ³.M´ᶍ¶·¸ᓭ£ᓅº▮ᚁḄW©ª½¾¿Àᑮ186ÁᔴÃ%ÄÀᑮᡃ▮-Åý¾\ÄḄ50%.ᦪM186ÁᔴᵨÆÇÈᦪÉW⊤ÊVY34⚓/\53⚓

34A.186x1()8ᔴB.18.6x109ᔴC.1.86xlO10H'|jD.0.186x10"ᔴூ3⚪Eᫀ௃ூHIEᫀ௃Cூ^_௃⚪_᪆`186Áᔴ=1.86x101஺ᔴ.ᦑ⌱C.4.ÙᑡÚÛHIḄ&()A.(a+b)2=a2+b2B.(-1+x)(-x-1)=1-x2C.a4,a2=axD.(-2x)3=-6x3ூ4⚪Eᫀ௃ூHIEᫀ௃Bூ^_௃_`A.(a+b)2=a2+2ab+b2,ᦑd⌱⚗┯ß$B.(-1+x)(-x-1)=1-x2,ᦑd⌱⚗HI$C.«4-a2=a4+2=«6,ᦑd⌱⚗┯ß$D.(-2x)3=(-2)3x3=-8x3,ᦑd⌱⚗┯ß.ᦑ⌱B.5.ᦪÇâã1ᨵ5äᐜæḄᡂçᑖ&86,89,78,93,90.ᑣê5äᐜæᡂçḄëᙳᑖí1îᦪᑖ&()A.87.2,89B.89,89C.87.2,78D,90,93ூ5⚪Eᫀ௃ூHIEᫀ௃Aூ^_௃ê5äᐜæḄᡂçï▰ᑡV`78ஹ86ஹ89ஹ90ஹ93,ᑣëᙳᦪV`(78+86+89+90+93)-5=87.2,1îᦪV89,Y35⚓/\53⚓

35ᦑ⌱A.6.᝞rÙᑡòÉ1HIḄ&A.N1íN3&RóᑁõB.N2íN3&ᑁ┯õC.N2íN4&RîõD.N3íN5&ö⚔õூ6⚪Eᫀ௃ூHIEᫀ௃Cூ^_௃_`A.N1íN3&RóᑁõHIᔠ⚪/$B./2íN3&ᑁ┯õHIᔠ⚪/$C.N2íN4&Rîõ┯ßPᔠ⚪/$D./3í/5&ö⚔õHIᔠ⚪/$ᦑ⌱`C.7.ᨵÙᑡø⚪`জúx2=X,ᑣX=l$ঝúa2=b?,ᑣa=b$ঞýᚖëᑖ-ḄᑮýSÿḄ
টḄᡠḄᙊᕜᐸ⚪⌮⚪⚪ḄᦪA.IB.2C.3D.4ூ7⚪ᫀ௃ூ!ᫀ௃Bூ"#௃#$%/=()ᑣx=lᡈ,0,ᡠ-জ┯0%஺2=஻)ᑣ7,ᡠ-ঝ┯067ᚖ9:ᑖ6<Ḅ=ᑮ67?@Ḅ
)ᡠ-ঞ!ḄᡠḄᙊᕜ)ᡠ-ট!.C⚪Ḅ⌮⚪⚪.D36⚓/F53⚓

36ᦑ⌱B.=I$J⚪ὃLM⚪Nᳮ$⚪ᑏᡂ“᝞T…)VW…”ḄYZ)[\)“᝞T”]☢_Ḅ`ᑖ⚪a)“VW”]☢#Ḅ`ᑖbc⚪Ḅ“”“Ꮇ”e⚪Ḅᑁghi.jkl⚪mᓽᎷ.⌕▊ql⚪Ḅ!ឋ)st◤vwᳮஹcy)hᑨ{l⚪Ꮇ⚪)|◤}~lᓽ.8.᝞)ᙠ4BC)NC=90°,NB=30°,-=/ᙊ)jᑖ48,4C=MMᑖ-=M,Nᙊ)?=)b48c=஺,ᑣᑡ!Ḅᦪজ/஺NH4CḄ:ᑖ6ঝ/4DC=60°ঞ480Ὺট=Dᑮ96ABḄ
CDḄ.ூ8⚪ᫀ௃ூ!ᫀ௃Dூ"#௃᪷J)ᡠ-জ!)ᵫNC=90°,NB=30°,ᑣNH4c=60°,h/஺:ᑖN84C,ᑣND45=30°,ᡠ-ZADC=ZDAB+ZS=600,ᡠ-ঝ!ᵫ/஺48=/8=30஺)ᡠ-Ὺ)lᑗঞ!ᵫ:ᑖN"C,ᡠ-=஺ᑮ48XCḄ
)h஺CJ_NC,ᑣ=஺ᑮ96N8Ḅ
CDḄ)ᡠ-ট!.ᦑ⌱D.9.%£{Ḅ¤¥c,ᑁᑗᙊr,ᑣᑁᑗᙊḄ☢¦☢¦§¨c+2rc+r2c+rc2+r2ூ9⚪ᫀ௃D37⚓/F53⚓

37ூ!ᫀ௃Bூ"#௃#$a9Ḅ?ᩩ9¥a,b,ᑣᨵ:a+b+c2a+b-cXVr2)a+/?=2+c,,¶ஹஹ-Q+b+cc2+2c/ஹ17º4+6=2)"+0¿ᐭ3=-------¶Â$S=-----------r—+c).22v7ÅÆᑁᑗᙊḄ☢¦a?.,ÇÈḄ¨----.c+rᦑ⌱B.10.᝞ᡠÉ)º᜜ஹᜧÌÍᐰḄ”67ᢥ᯿lNÑÒ᤮ᡂᑡ)D1ÔḄᦪ᜜,D2ÔḄᦪ஺2,D3ÔḄᦪḄ)…)1111-ÕÖw)ᑣl+—+—+…+——ḄØQ]%஺3Û92061589431A.—B.—C.---D.---2184840760[10⚪ᫀ௃ூ!ᫀ௃Cூᑖ᪆௃᪷äNåÔæ=ᦪçḄèᓄê~ᐸḄèᓄÑÒ=஻஻+2"11rl1ஹ1111᦮ᦪ”)íhv~l=--,ºᐸ¿ᐭl+—+—+…+—ᓽvÂbc.a2

38n+2Jqa2a3a\9nூ"#௃#$..•Ô“•"ᨵ%=1x3=3D38⚓/F53⚓

39DñÔ“•”ᨵ4=2x4=8DÔᨵ%=3x5=15.•.D஻Ôᨵ/=஻(஻+2)(஻᦮ᦪ)a2v?n+2)n•ó஻ñ19\111-+-+-T%%%+•191111=-+-+一++旃38151111=---------1-------------1------------FH----------1x32x43x519x211.......+-x211111—ᓝ——1-••*••.ᓝ3243519589"840-ᦑ⌱$CÕ⚪ὃLḄèᓄÑÒ)ê~§ôḄὶö)ê~ÑÒᜐᳮᡂø.ñஹùú⚪$(Jᜧ⚪ᐳ5Ì⚪)üÌ⚪3ᑖ)ᐳ15ᑖ.)11.ýZᑖ#2/—4x+2=ூ11⚪ᫀ௃ூ!ᫀ௃2(x—Ip.ூ௃2X2-4X+2=2(X2-2x+l)=2(x-l)2,ᦑᫀ2(x—1)?.12.᝞AFCEDCE!"BCF$%&!"'AB=AD,*+ABCDḄ☢.24cm2.ᑣAC3cm.439⚓/953⚓

40ூ12⚪ᫀ௃ூ<ᫀ௃4Vூᑖ᪆௃?Rt^AED@RtZXAFB,ABSAAED=SAAFB᪷D+ABCDḄ☢.24cm2EBAFCEḄ☢.24cm2,FBAEஹECḄ3᪷DHIJᳮFBACᓽM.ூ௃+AFCEN.AF=AE,ZE=ZAFC=ZAFB=90°,VAB=AD.*.RtAAED^RtAAFB(HL),•♦SAAED=SAAFB,"/+ABCDḄ☢.24cm2,AFCEḄ☢.24cm2,N.AE=EC=2P᪷DHIJᳮAC=7(2V6)2+(2V6)2=473ᐰRSTḄᑨJVឋXYᦪ[Ḅ\]^᦮`Yᦪ[Ḅ[aὃcdefḄgh"ijklmᜧ◤pqrs.13.᝞tuvᵨᡠyḄᡧ{ᱏ}ᡂ!`ᙊ┵gᡧḄ5cm,36?rcm,}ᡂḄᙊ┵Ḅlcm.[13⚪ᫀ௃ூ<ᫀ௃4ூᑖ᪆௃g3ᓽg}ᡂḄᙊ┵Ḅ☢Ḅ367tcm,᪵FB☢ᙊḄ.ᡧ440⚓/953⚓

41Ḅ5cmᙊ┵Ḅ&35cm.M᪷DHIJᳮFBᙊ┵Ḅ.ூ௃☢ᙊḄr,ᑣ2ᐔ1*=6ᐔ:.r=3cm,ᙊ┵Ḅ=^52-32=4cm.ᦑᫀ4.14.gMஹN"ᐵ^y'"Mᙠ&¡=’-"Nᙠ£&y=-x+32x"Mᙶ᪗(a,b),ᑣy=-abx2+(a+b)xḄ⚔"ᙶ᪗.ூ14⚪ᫀ௃ூ<ᫀ௃(ª«y)-ூ௃N"ᐵ^gᙶ᪗(a,b),N(-a,b),ᑖ®ᐭ°±Ḅ²ᦪEb=—@,a+3=bঝ2a••ab-y,(஻+S)2=(஻!ᓃ)2+4ᙢ¸¹¹a-t-b=±VTT».ᡭN¿2±«&,⚔"ᙶ᪗(!§¸ÂJTT,4a1"=஻),ᓽÂJU?.2a4a22"ÅÆ⌕ὃÈɸƲᦪḄឋX²ᦪÊ"ḄᱯÌVᐵ^ᙶ᪗Ḅ"Ḅᱯ".ᜐᳮÎ⚪ḄᐵÏrsÐ"Ḅᙶ᪗ÑÒ.15.ÓÔজ"ঝᢓ×ঞJiÚÛÜ"ট᮱T7àáâãäÓÔḄåæᵨäçèḄÑÒ£éᑏB☢ëìḄí+23+33+…+28'=(15⚪ᫀ௃ூ<ᫀ௃406ூ௃7i?=1Nঝ+2^=3=1+2N441⚓/953⚓

42ঞJr+23+33=6=1+2+3Nট-713+23+33+43=10=1+2+3+4,713+23+33+43+•••+283=1+2+3+4+...+28=14x29=406.ᦑᫀ406.Vஹ,-⚪1(ᜧ⚪ᐳ7'⚪#ᐳ55ᑖ)16.পÓÔ(.3+|õ-2|-(-2017)(2)ᐜᓄøÛFíùg(ú!+1)+(x+—!—),ᐸx=4-2sin30°.x—2x—2(16⚪ᫀ௃ூᫀ௃(1)9-6(2)ூ௃⚪ᑖ᪆(1)✌ᐜᯠ!"#ᔣ%&'()*Ḅ,-./ᓽ1(2)✌ᐜᓄ3(45+1)+(x+—!—),ᯠ!9xḄ,:ᐭᓄ3!Ḅ*ᓽ1.x-2x-2⚪᪆(1)<*=8+2-^/^-1=9-A\141(X-l)21(2)<*=----)———>x—2x—2x—I1x=4-2sin30°=4-2x-=3,2<*=---=—.3-1217.᝞NO᪥4QᦟSᜧUḄ⚔WXᨵ4ᙽ஻\]ᦻ_`a(b஻Ḅc\dCD.g_ᙠiᚁḄᚁkAᜐnoc\dpWDḄqrs60°,tiᚁᔣuvᑮBᜐnoc\d⚔WCḄqrs45°.z{iᚁABḄᚁ|i=l:,AB=1OAE=15(ᙽc\dCDḄ|.(nrᘤḄ|ᶍᑮ0.1.ὃᦪ=1.414,=1.732)42⚓/53⚓

43c□□□□□□ூ17⚪ᫀ௃ூᫀ௃2.7ூ௃BFJ_DEF,BG_LAEG□□□□□□GAEᙠRtAADEtanNADE=-------,AE.,.DE="AE"-tanZADE=15£:iᚁABḄᚁ|i=lᨵAB=10BG=5,AG=.EF=BG=5,BF=AG+AE=5^+15NCBF=45°.CF=BF=5^+15/.CD=CF+EF-DE=20-10^=20-10x1.732=2.68=2.7ᙽc\dCDḄ|s2.7.18.“”ᑮᐰḄᐵ¡S¢Wᑖᐜ£¤{¥Ḅ¦§|¨ᵨª«¬᪵®¯Ḅ*°᪷²³ᑮḄ´µ¶·¸¹ᑴ¦u☢Ḅ¼½¾¿ÀḄ¸NÁÂ᪷¸NᡠÄÅḄ´µÆᑡᡂÉ43⚓/53⚓

44ᡧYZ[\ᩩYZ[\(1)ÊËÌᔁ®¯Ḅᐜ£ᐳᨵ_______ÐᡧÒ¸N“ÓÔ¦”Wᑖᡠ¢ÕᡧÒḄᙊ×rs°;(2)Á⊡ᐰᩩÒ¸N(3)Û¢{¥Üᑮ“¦”§|Ḅᐜ£ᵱஹ᝕£Ḅàáាs2:3,ã"ª«¬ä2Ðå{¥æçᑣាé¬ᑮ1êᵱ£ë1ê᝕£Ḅᭆ᳛________.[18⚪ᫀ௃3ூᫀ௃(1)60,90(2)Nï(3)-5ூᑖ᪆௃(1)᪷¦ð/ḄÐᦪëᡠᓰḄòᑖà()¬¯ḄÐᦪóᵨ“ÓÔ¦”ᡠᓰḄòᑖàô360஺ᓽ1()“ÓÔ¦”Wᑖᡠ¢ÕᡧÒḄᙊ×rḄ|ᦪ(2)ᵨ®¯ḄÐᦪö÷“ÓÔ¦”“¦ð/”듦”ḄÐᦪ()¦ḄÐᦪ"ø⊡ᐰ¸N(3)᪷⚪ùᐜú)᪛üNó᪷ᭆ᳛ý*ᓽ1o)ᫀ.ூ௃(1)ÊËÌᔁ®¯Ḅᐜ£ᐳᨵ30-50%=60(Ð)ᡧÒ¸N“ÓÔ¦”Wᑖᡠ¢ÕᡧÒḄᙊ×rs360஺ஹ”=90஺60ᦑ60,90.(2)Ḅᦪᨵ60-15-30-10=5(60-15-30-10=5(A),⊡᝞44⚓/53⚓

45ᓝ(3)"᪛$%:•.•ᐳᨵ20)*+,Ḅ-./ា12ᑮ14ᵱ6714᝕6Ḅᨵ12)9:/123...ា12ᑮ14ᵱ6714᝕6Ḅᭆ᳛=>205?⚪ὃBᩩDEஹᡧDEHIᵨᑡ⊤Mᡈ᪛$MOᭆ᳛/PQ⚪R/᪷T⚪ROUᦪV⚪ḄᐵXYᭆ᳛=ᡠO9:ᦪ[9:ᦪ\].19.^ᖪ`⚜ᜓc>ᢇe)fghiḄ⊟k/lm>n4)hi]>n5)hiop10ᐗYrsc/)hi⊟k12n/8)hi⊟k8n/ᐳ◤1880ᐗYlm>n4hi⊟k+uᑭ20ᐗ/>n8hi⊟k+uᑭ30ᐗ/⌕xᙠz{|uᑭf}~780ᐗ/4hi⊟kf~28n.(1)O/ஹ8hi⊟kcᔜV}ᐗ(2)rlmsc4hi⊟kVBhi⊟kḄ24n/ᑣᖪᙠz{c|+ᨵ)s.[19⚪ᫀ௃ூᫀ௃(1)A)hiḄ⊟kn90ᐗ/B)hiḄ⊟k100ᐗY(2)ᨵ)c(1)Bhi⊟ks10n/Ahi⊟ksc24nY(2)Bhi⊟ks11n/Ahi⊟ksc26n;(3)Bhi⊟ks12n/Ahi⊟ksc28n.[௃⚪ᑖ᪆(1)*ᐵ=A)hi⊟k9nXc+B)hi⊟k10nXc=1810,A)hi⊟k12nXc+B)hi⊟k8nXc=1880Y45⚓/53⚓

46(2)ᐵXVuᑭf}~699ᐗ/Ahi⊟kf~28n.ᐵ¡=18XAhnᦪ+30XBhnᦪ2699,Ahi⊟knᦪ¥28.⚪᪆(1)¦A)hiḄ⊟knxᐗ/B)hiḄ⊟kyᐗ,©+10ᡝ«஺12x+81880x=90\%"ooA)hiḄ⊟kn90ᐗ/B)hiḄ⊟k100ᐗ;(2)¦Bhi⊟kscmn,ᑣAhi⊟ksc⊟m+4)n,18±2□+4³+30´...699+%µ2^+4.,28\%192WmW12,•.¸=᦮ᦪ/Y.m=10ஹ11ஹ12,2m+4=24ஹ26ஹ28.ᨵ)c(DBhi⊟ks10n/Ahi⊟ksc24nY(2)Bhi⊟ks11n/Ahi⊟ksc26nY(3)Bhi⊟ks12n/Ahi⊟ksc28n.»¼»¼½⚪{⌕ὃB¾ᐗ¿ÀÁ7>ᐗf*¡ÁḄÂÃᡂÅḄÆᵨ/⚪ḄᐵXVPQ᪗⚪ḄRÈ/᪷T᪗⚪ÉUḄᩩn/¦UÊmᦪ/ᑖËÌUᵬÁ7ÎÁÏÐḄÑÒÑÓ/ÌUᔠ〉Ḅ*ᐵ/ᑡU¿ÀÁ/ÖO.20.᝞/VḄ᜜Øᙊ/஺»ᙠ8CÛÜ/NR4CḄßᑖàá஺஺~»஺/âØ8஺ஹCD,ã»஺Ò8CḄßäà/[N8Ḅåæàçá~»P.(1)OéV0஺ḄᑗàY(2)OéAPBDADCA(3)WAB=6,/C=8ë/OàìPBḄí.46⚓/53⚓

47[20⚪ᫀ௃25ூᫀ௃±1î᪆Y±2î᪆Y±3—4ூᑖ᪆௃±1³âØOD/᪷TVNA4cḄïßᑖà/cð+%>=X>᪷TᚖòóᳮḄõö+%஺018C,ᵫPDHBC,ᓽ+éøOD_LP஺/ᓽ+éøPDV0஺ḄᑗàY±2ᵫPD//BCZ[,ZABC=/P,᪷TgùᡠÏḄᙊᕜïç*+%N/8C=NZZC,cð+%Î4Z>C=NP,᪷TᙊᑁØüÛDḄÏïý⊡/+%NABD+ZDCA=180°=ZABD+ZPBD,+%NPBD=NDCA,ᓽ+éøAPBD~ADCA
3âØOD,᪷TþòᡠÏḄᙊᕜï*~90஺/cðÿ
ᳮ5C,ᵫ஺8=DC,Z8,OC,᪷2Ḅᑡᐭᦪᓽ8Ḅ.ூ#$௃1&'()*00,᝞,-஺.N8/1CḄ/0ᑖ,NB4D=NC4D••DB=DC:.DO1BCvPDHBC:.OD1PD.P஺.஺஺Ḅᑗ;(2)VPDHBC:,ZABC=NP:.AC=AC547⚓/853⚓

48ZABC=ZADC:.ZADC=ZPZABD+NDCA=180°=ZABD+ZPBD,NPBD=NDCA:.APBDT/\DCA(3)᝞,)*஺஺•••8c.஺஺Ḅ:;:.ABAC^90°,NBDC=9஺஺ᙠ஺=AB—6,AC-8BC=YIAB2+AC2=10'+■DB=DC:.BD=DCᙠRsBDC=OC=-BC=52•.DC=DB=—BC=5y/22•••^PBDTADCAPB_BD~DC~~CAᓽ>?@5V28'PB_A⚪ὃDEᑗḄ&'F
ᳮᚖ;
ᳮḄHIJK/LḄឋN>ᑨ
:;ᡠQḄᙊᕜ/TU90஺TVᡠQḄᙊᕜ/WTVஹYஹᙊᕜ/Z[Ḅᐵ]^_`abc.$⚪548⚓/853⚓

49Ḅᐵd.21.ᵬஹhijkZ[lmEnopqrᑡo.sbt◞2hᨵxᑡryWzḄnopᑡo{ᵬjl|hj.᝞,0A.ᑡnopᑡolᵬjḄs(km)>-t(h)Ḅᦪ,,BC.xᑡ{hjl|ᵬjḄmoᵬjḄs(km)>-t(h)Ḅᦪ,.᪷,=Ḅ$ᑡᡂ((1){,moo-ᑡnopᑡoo-lh(""ᡈ"")¡BḄ¢ᙶ᪗600Ḅ¦§¨©.((2):*ᙠ,=ª5?ᑡnopᑡolᵬjḄs(km)>-t(h)Ḅᦪ,«(3)moḄry®100km/h,জ5?ᑡnopᑡo°-±>moW⍗³ঝ:*ᑏ¶ᑡmoᑁ¸¹⌶=>»☢ᩭḄW¾iᑡnopᑡoW⍗Ḅ-[◞.ூ¿Àᫀ௃(1)«ᵬஹhijkZ[Ḅ®600ᓟë(2)Ä,Å$᪆«(3)জ5?ᑡnopᑡo2Çȱ>moW⍗«ঝ[◞®1.2ÇÈ.ூᑖ᪆௃(1)ஹ᪷,=¡BḄ¦§¨©ᓽb«(2)ஹ᪷ryWzbi:0¸ᵫ[◞-®2ÇÈb:É(2,0),ª,MNᓽ«(3)ஹজ:BC>:MNḄ$᪆ᵫ$᪆ᑡÌ$ÌᓽW⍗-Íᫀ«ঝ:BC>:OAÏ¡ᓽmo>ÐnoW⍗-ᵫজbW⍗-[◞.ூ#$௃(1)ᵫ,bmoo-ᑡnopᑡoo-lh«¡BḄ¢ᙶ᪗600Ḅ¦§¨©.(ᵬஹhijkZ[Ḅ®600ᓟë(2)᝞,ᡠÑ(549⚓/853⚓

50(3)ஹজÕ:MNḄ$᪆®(S=kit+biVM(2,0),N(6,600),.%+4=0•6,+4=600it=150$(.*.8=1501-300«•.•:BCḄ$᪆®(S=-100t+700,a=-3oo...(150t-300=-100t+700,$(t=4,4-2=2.ঝ᪷⚪¨ᑡnopᑡo$᪆®(y=150t,¶ᑡmoᑁ¸¹⌶=>»☢ᩭḄW¾iᑡnopᑡoW⍗Ḅ-[◞®:150t=-100t+700,$(t=2.8,4-2.8=1.2ÇÈã.22.᝞,äᱥy=ax?+bx-3>xéÏUA,Bi¡>yéÏUC¡ê¡2,-3aã,Qëé.:x=l,⚔¡.M.1ãäᱥQíḄᦪ⊤ï(2ãC,Mi¡Ä:>xéÏU¡N,ᙠäᱥaðᔲòᙠ¶᪵Ḅ¡P,õ`¡P,A,C,N®⚔¡Ḅö÷L®0¸ö÷L³òᙠ¡PḄᙶ᪗«øòᙠ▊'ᳮᵫ«3ãÕ:y=-x+3>yéḄÏ¡.D,ᙠBDaûüx¡Eø>B,Dþᔠ
A,B,EḄᙊBCF,ᑨ4AEFḄ᜜
▊ᳮᵫ4Ey=-x+3&'()*
3+Ḅ,-.ᔲᡂ123ᑏ5,-.750⚓/<53⚓

51ூ>?@ᫀ௃1
y=x2-2x-32
Cᙠ
P2,-3
3
ZXAEFEῪGG.ᳮᵫHI᪆4
4AEFEῪGG.ூᑖ᪆௃1
L⚪(ὶ1OPQR5a,bḄSTUR5Vᦪ⊤YZ2
ᑖ[\x=0,y=0R5AஹBஹCḄᙶ᪗
ᯠT᧕RCMḄI᪆Z.bcdANCPefgcdUR5PḄᙶ᪗3
R5y=-x+3hᙶ᪗iḄD,BḄᙶ᪗.ᯠTbNAFE=NABE=45஺
AE=AF,UbkGAEFEῪGG4
᪷m3
+ᡠR
ᓽUk5Ey=-x+3&'()*
3
+Ḅ,-pᡂ1.—3஻-4tz+2b—3ூrI௃Is1
᪷m⚪(
kJb,
------=1.2aa=\Iktc
'b=-2.•.wᱥyzḄVᦪ⊤YZey=x2-2x-3ফCᙠ.|3AP,CP,᝞~ᡠs751⚓/<53⚓

52\y=0,kX2-2X-3=0,AXI=-1,X2=3.AA(-1,0),B(3,0),C(0,-3).y=(x-l)2-4,,⚔M(L-4),᧕RkCMḄ⊤YZy=-x-3.ᙠy=-x-3+
\y=0,kx=-3.AN(-3,0),AN=2,ᙠy=x2—2x—3+
\y=-3,kxi=0,x=2.2CP=2,AN=CP.AN஻CP,
cdANCPefgcd
*P(2,-3)(3)AAEFEῪGG.752⚓/<53⚓

53
y=-x+3hᙶ᪗iḄD(0,3),B(3,0)..♦.OD=OB,.".ZOBD=45°,•.•C(0,-3),AOB=OC./.ZOBC=45°,ᵫNAEF=/ABF=45஺
ZAFE=ZABE=45°,.".ZEAF=90°,AE=AF./.AEFEῪGG(4)Ey=-x+3&'()*
(3)+Ḅ,-s4AEFEῪGG᪀ᡂ1.⚪ᔠὃEῪGGḄᑨVᦪḄᵨ
ᜧ.753⚓/<53⚓