2022-2023学年江苏省南京市中考数学专项提升仿真模拟卷（一模二模）含解析

《2022-2023学年江苏省南京市中考数学专项提升仿真模拟卷（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。

2022-2023
ḕᓭὃᦪ⚗ᓣᔁஹ⌱⌱ᜧ⚪ᐳ6⚪⚪3ᑖᑖ18ᑖᙠ⚪ᡠḄ⌱⚗ាᨵ⚗ᔠ⚪⌕!Ḅ⌱"#$⌱⚗Ḅ%&'()ᙠ*⚪ᓱ,-Ḅ./011.ᙠ4,-6,0,2ᦪᨬḄ4ᦪ)A.-6B.-4C.0D.22.5ᑡᔜ89:9#$Ḅ1A.4a2-2a2=2B.(a2)3=a5C.a3*a6=a9D.(3a)2=6a23.ᙠ5ᑡ<☢>?@ABC>?DBC>?Ḅ)A,ஹ5
4.᝞>ᵫ,G#HIJᡂḄLI>?MḄNO>P(A.2B.3C.4D.6m+n6.Qx=mRnm

17.1-31=_________8.xyz2017|4}ᙢsVP4745ᐗ8.2%,ᐰḕ✌.ᐸḄ4745ᵨᦪ⊤P—.9.a-343,IJ66+24-a1ḄV.10.“ᡭ¢100⚓Ḅ£#¤p30⚓“¥—⌱g“¦§”ᡈ“aᯠ”ᡈ“«ᨵ¬”1.11.᝞>AB஻CD,AF=EF,µ/C=62°,ᑣ/A=_¸.12.ᙊ┵?Ḅ»¼Ḅ&½P5cm,À☢ÁÂP3cm,ᑣ¥ᙊ┵?Ḅ»¼ḄÃ☢ÄPcm2.ᵨ⚓⊤1.13.Å஺ஹbHÈ/+x-2018=0ḄÊ«ᨵWḄ4᪷ᑣÌ+2“+6ḄVP______.14.ÍÎÏḼᚁ¸P1:3ḄÓᚁᔣ0ÕÖ200m,ᑣ×ᓣÙÖÚ.15.᝞>ᙠÛABC,ZABC=90°,BC=5.µDEÛABCḄ.½,ÝDEÞaABCḄ᜜àNACMḄ<ᑖ½ãäF,YDF=9,ᑣCEḄP__.16.᝞>äEஹFᑖZåP2Ḅ#H?ABCDåBCஹCD0ḄæäYBE=CF,çnDEஹAF,ÞãPäéPNJ_CDãNäPMLBCãMäçnMN,ᑣMNḄᨬVPëஹì*⚪ᜧ⚪ᐳ10⚪ᑖ102ᑖjᙠ*⚪ᓱᢣîïᑁé*ì*S-ᑏa⌕Ḅᦻ%òóஹôóõÈᡈö9÷ø1p2⚓/s53⚓

2A2117.(1):9û#+(—5)ü5m45஺+3°x6(2)ìᑖUHÈû——+——=1.x-2x+218.Í᪥PÖìþ|ÿ
(1)
Ḅᡂ᪵ᢥAஹBஹCஹD!"#$%"#&'(ᑴᡂ᝞+Ḅ"#,-.,/ᡠ12345+ᑡ7⚪9(:;9A990ᑖ?100ᑖ@B975ᑖ?89ᑖ@C:60ᑖ?74ᑖ@D960ᑖ+)(1)-FG᪵/DḄ
Hᦪ$JᩩL"#,⊡ᐙO᦮@(2)RS᪥ᨵ500V
-.ᵨX᪵Y#/75?100ᑖḄ
Hᦪ.19.\]^ᨵ_;Ḅ`a/bᨵ2cᳫe1fᳫghᳫ◀j⁐᜜ᐸnopq.(1)ᤅᒴtu/᥎G\ᳫ᥎ᑮcᳫḄᭆ᳛z{|}(2)ᤅᒴtu/᥎G\ᳫ~+j⁐tᤅᒴ᥎G\ᳫ~+j⁐-ᵨ᪛,(ᡈᑡ⊤)FgᳫozcᳫḄᭆ᳛.20.᝞,ᙠAABC/ZABC=90°.(1)ᵨeᙊACḄᚖᑖABDஹACE(^ᨵ⌕Fᑏᶇ,)@(2)R(1)/AB=4,BC=3,FADḄ¡.21.᝞,Z89ᑖ¢£xஹy¦§(6,0)ஹ8¨8Ḅx©3⚓/¬53⚓

3¦Ḅ®¦C,¯஺890C=391.(2)FBCḄ±ᦪᐵ³´@(3)RP(□2)ᙠAABCḄᑁ¸F¹Ḅº»½.22.¾¿ᵯ
ÁÂÃ᪷ÅÆÇᑖ᪆ÉÊË᦮ÁÌ
ÁÍᜓÏᕜ(ᢥ120ÑÒ#Ó)
ÁÔËᘤஹÖᵯஹ×Øᐳ360Ú¯×ØÛ|
Á60ÚÜÝ
Ágh¿ᵯÁÌÏÚᡠ◤ÑÒeÏÚÁ»᝞+⊤9¿ᵯVßÔËÖᵯ×Ø\_j_ÑÒT34Á»(ᓟ432ᐗ)ãÏᕜ
ÁÔËᘤxÚஹÖᵯyÚஹ×ØzÚ.(1)ᵨåzḄæᦪ´ᑖ¢⊤çGx£yḄ»-ᑏGF4¨è@(2)Ïᕜé
ÁÔËᘤஹÖᵯஹ×Øᔜ{|ÚëìíÁ»}Á»z{|}(ᓟᐗᓫï)23.᝞,ðABCᑁñABòDᙠ஺0ó¨D஺஺Ḅᑗ£ACḄõ¡E,¯ED஻BC,÷ñADBCF.(1)Fù9ZBAD=ZDAE@(2)RDF=?,AD=5,F©0Ḅ®ò.©4⚓/¬53⚓

4I)24.ᙠAABC/ZB=45°,ZC=30°.AP_LAB,BCP.(1)᝞,1,RAB=3tFBCḄ¡@(2)DzBCþó\÷ñAD,%ÿADA⌮┐90஺ᑮAE.জ᝞2,EᙠACCE=2BD#CE2ঝ᝞3,AD_LBC()ᑏ+-Ḅ/.AB225.᝞(y=kx456>=-99:AஹB<C=>?@▲ᑁ-.X(1)FAḄᙶ᪗=(a,3),aḄ/#3(2)1<=--KCA=CB,ZACB=90°CḄᙶ᪗#2(3)AABC=N?OPCḄᙶ᪗=(m,n),SmஹnTUḄᐵWX.26.᝞ZᱥTiy=—X2—2x+3>T2y=x2—2x+5,ᐸbZᱥTi4xc9:AஹB<,4yc9:C.Pexc-fghPiKᚖ(:xcḄ(4ZᱥklT2ᑖno9:NஹM<.rPḄsᙶ᪗=t.(1)ᵨvtḄwᦪX⊤zMNḄ{#t=|/MNᨵᨬ/i+ᨬ/#>5⚓/53⚓

5(2)ḼPg1ஹMஹN?Ḅᓄ.t|/ᐸb-e᜜<)Ḅb(3)Zᱥ3AḄ=A(m-3,n),ᐸbgwmwj,KḄZᱥCZᱥ⚔ᡠ¡ᑮḄḄᙶ᪗.>6⚓/53⚓

62022-2023
ḕᓭὃᦪ⚗ᓣᔁஹ⌱⌱ᜧ⚪ᐳ6⚪⚪3ᑖ!ᑖ18ᑖᙠ⚪ᡠ$%Ḅ'(⌱⚗ាᨵ⚗+,ᔠ⚪.⌕0Ḅ⌱123⌱⚗Ḅ45678ᙠ9⚪ᓱ;<Ḅ=>?1.ᙠ-4,-6,0,2£fᦪbᨬḄ¤ᦪe¥A.-6B.-4C.0D.2ூ§¨©ᫀ௃Aூ¬௃ூᑖ᪆௃᪷°¤ᦪḄᜧ²³´ᑣ§ᦪᜧ:0,0ᜧ:¶ᦪoÜÝᦪØᨵᢣᦪoÔᦑC§¨#Dஹ3ḄÈe9,ᦑD┯Ú#ᦑ⌱C.ὃ1ஹßḄÜÈ4àḄÜÈ#2ஹᔠiÑÒ⚗#3ஹÑÝᦪáḄÜ´.3.ᙠÊᑡ☢PbãecäPåeäPḄe¥Ï>7⚓/53⚓

7A-B-Dc-FD-ூ§¨©ᫀ௃Bூ¬௃ூᑖ᪆௃᪷°cäP4äPḄᭆç⌲-¹ºᑨêᓽ¼.ூ¬௃AஹecäPØᨵeäPᦑØᨵëᔠ⚪ì#BஹecäPeäPᦑëᔠ⚪ìCஹeäPØᨵecäPᦑØᨵëᔠ⚪ì#DஹecäPØᨵeäPᦑØᨵëᔠ⚪ìᦑ⌱B.ÆÇíäP4cäPḄᭆç.cäPḄᐵÉeîïäcPðäcñ¼òᔠäPe⌕îïäP180஺4ôPòᔠ.4.᝞eᵫoѧÈö÷ᡂḄùöPúḄûü=¥ÏC.ூᑖ᪆௃ïᑮý§☢þᡠᑮḄPᓽ¼.ூ¬௃ý§☢þ¼ᑮᐳᨵ4ᑡᑡḄᦪᑮ3ஹ1ஹ1ஹ2,ᨵD⌱⚗ᔠᦑ⌱D.⚪ὃ!"#Ḅ$%&'()*"#+ᱥ-Ḅ☢/0ᑮḄ#+1⚪Ḅᐵ3.5.5ᦪ61,2,4,x,6,8Ḅ7ᦪ+1,ᑣ95ᦪ6Ḅ:;ᦪ+<=A.2B.3C.4D.6ூ?@ᫀ௃BC8⚓/F53⚓

8ூH1௃ூᑖ᪆௃ᐜ᪷67ᦪḄᭆN?OPXḄQR᪷6:;ᦪḄᭆNST?OᓽV0.ூH1௃•.•5ᦪ61,2,4,X,6,8Ḅ7ᦪ+1,/.X=1,95ᦪ6ᑮᜧ᣸Z[1,1,2,4,6,8,2+4•••:;ᦪ[-~-=3,2ᦑ⌱B.⚪*⌕ὃ7ᦪ]:;ᦪḄ^_:;ᦪ+`5ᦪ6ᑮᜧ(ᡈᜧᑮ)de᣸ᑡfᨬ:hḄiᦪ(ᨬ:hjᦪḄkᙳᦪ)m7ᦪ+5ᦪ6:PnᦪopḄᦪqr〉:.6.tx=mun(my>yC.>%>%D.23%>>ூ?@ᫀ௃DூH1௃ூᑖ᪆௃y=x2—4x+3,ᐜPᦪy=x2-4x+3=(x-2)2Ḅx=2,Rᵫ$?OPm+n=4,R᪷6ᦪḄឋSTᓽV.ூH1௃y=x?-4x+3,ᑣᨵᦪy=x2-4x+3=(x-2)2-1Ḅx=2,\•tx=mun(m2vy£ḼxḄ¥ᜧ¦¥ᜧ,n+l

9•••§§ᦑ⌱D.⚪ὃᦪḄឋ᪷6⚪^᪀⌼ᦪ{ᑭᵨᦪḄឋST1⚪+ᐵ3.HஹIJ⚪(ᜧ⚪ᐳ10⚪⚪3ᑖ!ᑖ30ᑖ.MN9ᫀPQIᑏᙠ9⚪ᓱ;<=>?)7.|-3|=_______ூ?@ᫀ௃3ூH1௃ᑖ᪆[᪷6¬ᦪḄQz9ᦪḄyᦪᓽV0P@ᫀ.1@[1:|-3|=3.ᦑ@ᫀ3.8.¯°±2017²³nᙢµ¶·FQ¸4745¹ᐗ¥»8.2%,¥¼½ᐰḕ✌;ᐸ:Ḅ4745ᵨÂÃÄᦪÅ⊤Ç—.ூ?@ᫀ௃4.745X10,ூH1௃ூᑖ᪆௃ÂÃÄᦪÅḄ⊤ÇxaxionḄxᐸ:lw|a|10,n᦮ᦪᢥËxÌᡠÎḄᦪ⊤ÇPᩭᓽV.ூH1௃?OnḄQv⌕/ÌÐᦪÑᡂavᦪÓÔpÕ;nḄQ]ᦪÓÔḄ;ᦪyÖ.tÐᦪQ1vn+ᦪmtÐᦪḄQ1vn+¬ᦪ4745=4.745x103,ᦑ@ᫀ4.745x103.⚪ὃÂÃÄᦪÅḄ⊤ÇÅ.ÂÃÄᦪÅḄ⊤ÇxaxlOnḄxᐸ:l|a|10,n᦮ᦪ⊤Çvᐵ3⌕??OaḄQ×nḄQ.9.$a-36=3,ᑣ66+2(4-a)ḄQ+.ூ?@ᫀ௃2ூᑖ᪆௃ÌᡠØḄxÙÚÛÜfST᦮ᳮᯠf`a36ß᦮-wᐭSTØQᓽV.ூH1௃a-3b=3,-2(a-3b)=-6,C10⚓/F53⚓

1066+24-஺==66+8-2஺=-2a-3b
+8=-6+8=2,ᦑ2.⚪ὃwᦪxḄØQᑭᵨ“᦮-wᐭÅ”ØwᦪxḄQ.10.”ä^ᡭæ100⚓Ḅçè+C30⚓“9+—<⌱é“£ê”ᡈ“ᯠ”ᡈ“ëᨵVì”=.ூ?@ᫀ௃£êூH1௃ூᑖ᪆௃᪷6ëᨵ?Oᓽ£ê+ᢣᙠ••OᩩðñVìò¶óVìëᨵò¶ḄV0@ᫀ.ூH1௃ä^ᡭæ100⚓Ḅçè+C30⚓9Vìò¶óVìëᨵò¶ôË9+£êᦑ@ᫀ£ê.ὃ£ê1õ⚪◤⌕?ᳮ1ᯠஹëᨵVìஹ£êḄᭆN.ᯠᢣᙠOᩩðñOò¶Ḅ.ëᨵVì+ᢣᙠOᩩðñOëᨵò¶Ḅ.ëᨵ?Oᓽ£ê+ᢣᙠOᩩðñVìò¶óVìëᨵò¶Ḅ.11.᝞#AB஻CD,AF=EF,ùNC=62°,ᑣNA=—r.ூ?@ᫀ௃31ூH1௃ூᑖ᪆௃᪷6AF=EF,V0/A=NE,R᪷6kTḄឋV0NEFB=NC=62஺᪷6!úḄ᜜úzëᨵyüḄjᑁúḄuV0/EFB=NA+NE,¦V0NA=31஺.ூH1௃VAF=EF,.'.ZA=ZE,VAB//CD,.,.ZEFB=ZC=62°,þNEFB+4AEFḄ᜜úZ.ZEFB=ZA+ZE,Cn⚓/F53⚓

11.".ZA=31°,ᦑᫀ31.⚪ὃḄឋஹῪḄឋஹ᜜Ḅឋ!"ᔜឋ$%⚪Ḅᐵ'.12_.*+,-ᙊ┵Ḅ01Ḅ235cm,7☢9:3cm,ᑣ<-ᙊ┵Ḅ01Ḅ=☢>cm2.(ᵨ“⊤C).ூFGᫀ௃15⚓ூJ%௃ூᑖ᪆௃᪷Nᙊ┵Ḅ=☢>OPQR%ᓽTU.ூJ%௃V⚪W+23/5cm,7☢9:r=3cm,ᑣᵫᙊ┵Ḅ=☢>OPU[S=7trl=7tx3x5=157c(cm2),ᦑᫀ157r.⚪ὃᙊ┵Ḅbcdᙊ┵Ḅ=☢>OP$%⚪Ḅᐵ'.13.e“ஹb$gh/+x-2018=0Ḅm-nᨵḄp᪷ᑣ஺2+2“+gḄr.ூFGᫀ௃2017ூᑖ᪆௃᪷N,ᐗtughḄ%v᪷wxᦪḄᐵxTUza2+a=2018ஹa+b=-l,|ᐸ~ᐭa2+2a+b=(a2+a)+(a+b)ᓽTRz.ூJ%௃Va,b$ghx2+x-2018=0Ḅm-pᦪ᪷a2+a=2018,a+b=-1,.\a2+2a+b=(a2+a)+(a+b)=2018-1=2017.ᦑᫀ2017.⚪ὃ᪷wxᦪḄᐵxv,ᐗtughḄ%᪷N,ᐗtughḄ%v᪷wxᦪḄᐵxza2+a=2018ஹa+b=-l$%⚪Ḅᐵ'.14.Ḽᚁ1:3Ḅᚁᔣ200m,ᑣᓣ.ூFGᫀ௃20V10ூJ%௃ூᑖ᪆௃᪷NᚁᚁḄFᑗrvFᑗḄTeᓣxm,ᑣ3xm,᪷NᳮRUᫀ.ூJ%௃eᓣxm,᪷Nᚁ¢1[3,ᑣTU3xm,ᵫᳮUx2+(3x)12002,£12⚓/¤53⚓

12%Ux=20jiUᦑᫀ20¨.⚪ὃ%©Ḅªᵨᚁᚁ«⚪!"ᚁ¢ᚁḄFᑗ$%⚪Ḅᐵ'.15.᝞ᙠaABCZABC=90°,BC=5.²DE$µABCḄ¶·3DE¸µABCḄ᜜NACMḄᑖ»F,½DF=9,ᑣCEḄ3__.ூJ%௃ூᑖ᪆௃᪷NDE$µABCḄ¶TUDE//BC,DE=yBC,ᵫCFᑖNACMT¿UEC=EF,᪷NDFvBCḄ3ᓽTRUCEḄ3.ூJ%௃[DE$AABCḄ¶11.,.DE//BC,DE=vBC=-x5=2.5,22VDF=9,Á.EF=DF-DE=9-2.5=6.5,ÁCFᑖNACM,AZECF=ZFCM,VDF//BC,/.ZEFC=ZFCM,r.ZDFC=ZECF,CE=EF=6.5,ᦑᫀ6.5.⚪ὃ¶ᳮஹῪḄᑨwឋ%⚪Ḅᐵ'$ᮣŪᵨ¶ᳮஹ!"ῪḄᑨwឋ.16.᝞»EஹFᑖÆ$Ç32ḄFgABCDÇBCஹCDḄÈ»½BE=CF,ÉÊDEஹAF˸P»ÍPNJ_CDN»PMLBCM»ÉÊMN,ᑣMN3ḄᨬÑr£13⚓/¤53⚓

13ூFGᫀ௃V5-1ூJ%௃ூᑖ᪆௃ÉÊCP,ᵫ⚪W᧕UÓÇPMCN$ÔÕÖᨵPC=MN,ᵫFgḄឋvᩩ1TᑨØAADFÙZ\DCE,ÕÖTUNDAP=NEDC,᪷NNEDC+NADP=NADC=90஺TUNDAP+/ADP=90஺ÕÖᨵNAPD=90஺ÚÖT+»PḄÛ:$,ÜAD©:ḄᙊÝ,eADḄ»O,ÉÊCO¸Ý»P,ÞßCPḄ3ᨬÑRzCOஹPOḄ3ᓽTRzCPḄᨬÑrᓽMNḄᨬÑr.ூJ%௃ÉÊCP,•.•NPNC=/PMC=NC=90஺.,.ÓÇPMCN$ÔÁ.PC=MN,•.•ÓÇABCD$Fg.".ZADC=ZBCD=90°,AD=BC=CD,áÁBE=CF,Á.EC=FD,AADF^ADCE,tNDAP=NEDC,VZEDC+ZADP=ZADC=90°,AZDAP+ZADP=90°,ZAPD=90°,ᙠâÈãhNAPD=90஺äᢝnᨵæt»PḄÛ:$,ÜAD©:ḄᙊÝeADḄ»O,ÉÊCO¸Ý»P,ÞßCPḄ3ᨬÑᓽMN3ḄᨬÑrÁZAPD=90஺0AD»PO=OD=yAD=1,ᙠRtACODC0=7CD2+OD2=V22+l2=V5.,.CP=CO-OP=V5-1-ᓽMN3ḄᨬÑr$ᔲ-1,ᦑᫀ-1£14⚓/¤53⚓

14o⚪ÓÇḄèᔠªᵨêvᑮᐰᳮÔḄᑨwឋFgḄឋ+íGz»PḄâÈÛ:ÕÖUzîïß᎛CPᨵᨬÑr$%ñ⚪Ḅᐵ'⚪ὃ+íòóèᔠឋòôõòᜧ.TஹU9⚪(ᜧ⚪ᐳ10⚪!ᑖ102ᑖMᙠ9⚪ᓱᢣWXYᑁ[9U9\<ᑏ%]⌕Ḅᦻ4_`ஹa`bcᡈefgh)2117.(1)bc[-^+(--)-|xsin450+30X6(2)%ᑖPgh[——+—U=Lx-2x+2ூFGᫀ௃(1)1(2)1ூJ%௃ூᑖ᪆௃(1)ᑖÆQᑖ2ᨵᳮᓄஹøᢣᦪúḄbcஹḄûᦪrஹ0u£Ḅbc,ᯠýᢥÿ
ᓽ(2)(x-2)(x+2),ᓄ᦮᦮
ᓽ.ூ௃(1)=-2ஹᵯ+1=1#2(2)$%(x-2)(x+2),x(x+2)+6(x-2)=(x-2)(x+2),#x=l,#&x=l$,(x-2)(x+2)(ᡠ%x=l*Ḅ᪷ᡠ%Ḅ#x=l.-⚪ὃ012ᦪḄ4ᔠ6ᑖ2ᦪ4ᔠ6Ḅᐵ9*⌕;<=Ḅ>=?ᦪ@AᢣᦪCḄ6Dᑣ0FCḄ6DᑣGᑖ$⌕H
.18.I᪥1KLMNOPQRSTU%KLM(1)VNOḄPQRSᡂX᪵-ᢥAஹBஹCஹD[\GM
]^_]`abᑴᡂ᝞eḄ]fghfiᡠjklmeᑡo⚪#p15⚓/s53⚓

15(uv#AM#90ᑖw100ᑖBM#75ᑖw89ᑖCM#60ᑖw74ᑖDM#60ᑖ%e)(1)gyz᪵-iDMḄNO{ᦪ^|ᩩ~]f⊡ᐙ᦮(2)᪥KLMᨵ500NOghᵨ᪵-PQRSi75w100ᑖḄNO{ᦪ.ூmᫀ௃(1)᪵-iDḄNO{ᦪ5{⊡f᪆(2)ᨵ330{.ூ௃ூᑖ᪆௃(1)᪷AḄ{ᦪ%ᡠᓰḄᑖ%y᪵-{ᦪᯠᵨ᪵-{ᦪAஹBஹCḄ{ᦪᓽᑮDḄ{ᦪᯠ⊡ᐰf~ᓽ(2)᪷⚪ᵨAஹBᡠḄ(%KLMḄNOᦪ500ᓽ.ூ௃(1)1020%=50({)50-10-23-12=5({)ᓽ᪵-iDḄNO{ᦪ5{⊡f᝞fᡠ(2)500x(20%+46%)=500x66%=330({)m#PQRSi75-100ᑖḄNO{ᦪ330{.-⚪ὃ01ᩩ~]fᡧ~]fᵨ᪵-sPᓫf~ᑮ¡ᐵkl*⚪Ḅᐵ9.19.¢£¤ᨵ¥vḄ¦§i¨ᨵ2\©ᳫ(1\«ᳫ¬ᳫ◀¯⁐᜜ᐸ³´¡.(1)ᤅᒴ·i᥎z¢\ᳫ᥎ᑮ©ᳫḄᭆ᳛*»¼½p16⚓/s53⚓

16¾2Àᤅᒴ·i᥎z¢\ᳫHe¯⁐ᙢὡᤅᒴÃF᥎z¢\ᳫHe¯⁐gᵨ᪛Åf¾ᡈᑡ⊤DÀy¬\ᳫ´*©ᳫḄᭆ᳛.24ூmᫀ௃¾1À-¾2À-ூ௃ூᑖ᪆௃¾1À¦i¢ᐳ3\ᳫᐸiᨵ2\©ᳫ᪷ᭆ᳛ḄÌᓽ᥎ᑮ©ᳫᭆ᳛;¾2ÀÎz᪛ÅfᯠyᐰÏTUḄsᦪÐᔠᩩÑḄTUᦪÒÓὅḄ@Õ*ᐸÖOḄᭆ᳛.ூ௃¾1À¦§i¨ᨵ2\©ᳫ1\«ᳫᐳ3\ᳫ2·i᥎z¢\ᳫ᥎ᑮ©ᳫḄᭆ᳛*P¾¢\ᳫ*©ᳫÀ=-3¾2À᪛Åf᝞e:.♦•¢ᐳᨵ9ÛÜḄ`aF᥎zḄ´*©ᳫḄᨵ4Û4•••P¾\ᳫ´*©ᳫÀ=-.9-⚪ὃ0Ḅ*ᵨᑡ⊤DᡈÎ᪛ÅfDyᭆ᳛.ᑡ⊤DᡈÎ᪛ÅfD%¤ᨵÝÞ¤ᨵ⍡àḄᑡzᡠᨵÜḄ`a〉ᔠâãᡂḄ.ᵨᑮḄäåæ#ᭆ᳛=ᡠyTUᦪsTUᦪç.20.᝞fᙠAABCiZABC=90°.¾1Àᵨïð(ᙊòóACḄᚖïõᑖö÷ABâDஹ÷ACâE澤ᨵ⌕yᑏóDûᶇófýþÀ¾2À¾1ÀiAB=4,BC=3,yADḄÿ.
17⚓/53⚓

1725ூᫀ௃(1)᪆(2)—8ூᑖ᪆௃(1)ᑖAஹCᙊᜧ!AC"#$%&ᙠAC()ᨵ(+,-./(-0123AB,-D,3AC,-E4(2)56DC,ᵫDE8ACḄᚖ1;ᑖ2<=DC=AD,ᙠRt^BCD>ᑭᵨABCᳮᓽ<=.ூF௃(1)᝞ᡠIDEᓽᡠJ4(2)56DC,•4DE8ACḄᚖ1;ᑖ2,4.DC=AD,VZB=90°,...ᙠRtABCD>CD2=BD2+BC2,25LAD=x,ᑣx2=32+(4—x)2,=x=q,25ᓽADḄ"N.8O⚪ὃRḄ8SO0TABCᳮḄUᵨVW2Xᚖ1;ᑖ2Ḅ0Y8Z⚪Ḅᐵ\.21.᝞1248!]-x-6ᑖ3xஹy^,_(6,0)^8(-.-BḄ12,x^Ḅ`#^-C,a!0C=3!1.
18⚓/53⚓

181
J-BḄᙶ᪗42
J12BCḄdᦪᐵfg4h3
Phi2
ᙠAABCḄᑁkJlḄmnp.4ூᫀ௃h1
0,6
42
]3x+643
ூF௃ூᑖ᪆௃h1
16q-Ḅᙶ᪗rᐭ<=4h2
ᵨtCfᦪY<=4h3
u]2ᑖrᐭ12ABv12BCḄ᪆gCᐵ\-Ḅᙶ᪗wxJymḄmnp.ூF௃h1
q-46,0
rᐭ1248Ḅ᪆g<=!0=—6—b,=!6=-6,•1248Ḅ᪆g{-x+6,8-ᙶ᪗h0,6
.2
YOB:஺஺=3!1,.OC=2,••-஺Ḅᙶ᪗h-2,0
,L8cḄ᪆g8{Ax+6,ᑣ0=-24+6,=!k=3f,128cḄ᪆g8!]3/6.,43
u{2rᐭ{-/6=x=44uy=2rᐭ]3x+6>=,4

19“4ᦑ(1)(0,6)4(2)y=3x+6(3)--z260,
20⚓/53⚓

20ÊNËÌ0,ᡠWÏZḄÑᜧxÒÓᡠ¼z=60W1050ᓟᐗ2L13z=60x=—z=30,y=360——z=270.!ᕜU{ᘤ30¤ஹᵯ270¤ஹ¡¢60¤¶·¸{n{n81050ᓟᐗ.O⚪ὃRÚdᦪḄUᵨ=y{n3{½ÛḄᐵfg8⚪Ḅᐵ\.23.᝞AABCᑁ600,AB1$-Dᙠ00à.-D0஺஺Ḅᑗ23ACḄâ"2,-E,aED஻BC,56AD,BC-F.h1æJç!ZBAD=ZDAE4h2æèDF=£,AD=5,J00Ḅ#$.ூᫀ௃h1æçê᪆h2æ3ூF௃ூᑖ᪆௃h1æ56OD,ᵫED00Ḅᑗ2᪷ᑗ2ḄឋÅ=ᑮODLED,ᵫAB஺OḄ1$=¥ljNACB=90஺᪷;ò2ḄᑨCvឋÅ=ᑮôõÛḄᐵföÊOA=OD,=¥!J/BAD=/ADO,ùyúû/BAD=NDAE4h2æ56BD,=ᑮ/ADB=90஺çêDBFS/\DAB,<=ᜐ=",wx=ADBDBD2=DF«AD=yx5=H,ᙠRtZ\ADBᑭᵨᳮAB=6,ᓽḄ3.ூ௃!1#$%OD,(ED஺஺Ḅᑗ,.\OD_LED,(AB஺OḄ/.,.ZACB=90o,(BC஻ED,AZACB=ZE=ZEDO=90°,621⚓/:53⚓

21DAE஻OD,

22ᓽCE=2PE=2BD?ঝ᝞^$%PE,᪷_`ᩩbxZADPEjZAD=m,ᑣᨵBD=PD=EP=m,CP=CD-PD=(6-1)m,ᑭᵨᳮᑖ¢AB2=2m2,CE2=5m2-261£2,ᓽ.ூ௃(1)sAoAH_LBCrH,AZAHB=ZAHC=90°,ᙠRtZ\AHB..AB=3¤ZB=45°,/.BH=ABco=3,AH=ABsi=3,ᙠRtZ\AHCVZC=30°,AAC=2AH=6,CH=ACcosC=3g,BC=BH+CH=3+35!2
জ$%PE,••{,|AD}sA⌮┐90஺ᑮ,|AE,AE=AD,ZDAE=90°,VZBAP=90°,ZB=45°,AZAPB=45°=ZB,AAP=AB,.\ZBAD=ZPAE,AAABD^AAPE,ABD=PE,ZB=ZAPE=45°,.*.ZEPB=ZEPC=90°,VZC=30°,ACE=2PE,/.CE=2BD?ঝ᝞^$%PE,••{,|AD}sA⌮┐90஺ᑮ,|AE,AAE=AD,ZDAE=90°,VZBAP=90°,ZB=45°,AZAPB=45°=ZB,AAP=AB,NBAD=NPAE,AAABD^AAPE,BD=PE,ZB=ZAPE=45°,ZAEP=ZADB=90°,/.ZEPB=ZEPC=90°,623⚓/:53⚓

23xZADPEjZAD=m,ᑣᨵBD=PD=EP=m,"LLஹCD=-------=V3m,CP=CD-PD=(J3-1)m,tan30°AB2=AD2+BD2=2m2,CE2=PE2+CP2=5m2-273m2,.CE25-2A/3.----=-------.AB22N⚪ὃQRḄឋTὃQRᐰ]XYZḄᑨ\ឋTZḄᑨ\ឋT/YXYZḄvᵨ]«fghi,j⚪Ḅᐵl.25.᝞^/,y=kx\®¯,°=-9qrAஹB±ssC6X²▲ᑁzs.X(1)usAḄᙶ᪗(a,3),aḄ·?3(2)d1:=zz¹CA=CB,ZACB=90°CsḄᙶ᪗?2(3)daABC]xXYZsCḄᙶ᪗(m,n),»mஹn¼½Ḅᐵ¾¿.ூᫀ௃(1)-2?(2)(-3,-2)?(3)mn=18ூ௃ூᑖ᪆௃(1)/%ÁAsᙶ᪗ÂᐭÄÅÆÇᦪ᪆¿ᓽ?(2)$%CO,oAD±yÊrDsoCEᚖ/yÊrEsDADOÌD()£((,36ᵫÏzzxÐy=---x=±2,y=±3,Asᙶ᪗(-2,3),ᵫ2xDADO^AOECW,CE=OD=3,EO=DA=2,C(-3,-2)?624⚓/:53⚓

24!3
$%CO,oAD_LyÊrDsoCE_LyÊrEsDADOs^OEC,᪷VWXYZḄឋTÒÓᓽ.(1)Á(a,3)Âᐭy=-9,3=-9,a=-2?ூ௃xa(2)$%CO,oAD±yÊrDsoCEᚖ/yÊrEsᑣNADO=/CEO=90஺,.,.ZDAO+ZAOD=90°,•../,Ôkx\®¯,°=-9qrAஹB±s...OAMOB,xdCA=CB,NACB=90°?.CO=AO,ZBOC=90°,ᓽ/COE+/BOE=90°,ZAOD=ZBOE,ZDAO=ZEOC,.'.DADO^AOEC,336fx.=-2(x-,=2Õk=Öᵫy=-----xÐy=------c(-,ᡠAsᙶ᪗(z2,22x1%=3[%=-33),ᵫDADOgZXOECCE=OD=3,EO=DA=2,ᡠC(-3,-2)?(3)$%CO,oAD_LyÊrDsoCE_LyÊrEsᑣ/ADO=/CEO=90஺.,.ZDAO+ZAOD=90°,;/,Ôkx\®¯,᜛=z£qrAஹB±s...OAMOB,X'.'DABC]xXYZCA=CB,/ACB=60஺ZBOC=90°,ᓽNCOE+NBOE=90஺,VZAOD=ZBOE,AZDAO=ZEOC,.•.DADO^AOEC,.ADOPAO••—CE-OC'625⚓/:53⚓

25Û,VZACO=yZACB=30°,ZAOC=90°,=tan30°OCT'ீCḄᙶ᪗!m,n#,ACE=-m,OE=-n,AD=-OD=—^^m,33A,~n,—^^m#,Âᐭy=—9,33xmn=18.N⚪ὃQRÄÅÆÇᦪ\ÇᦪḄÝᔠßàᑮᐰ]XYZḄᑨ\ឋTஹVWXYZḄᑨ\ឋT]᪷⚪á^ZfgḄhi,j⚪Ḅᐵl.26.᝞^âᱥ,Ti(y=-x2-2x+3,T(y=x2-2x+5,ᐸâᱥ,Ti\xÊqrAஹB±s2\yçqrCs.PsjxÊyzèésPsê¹ᚖ/rxÊḄ/,\âᱥ,TiÐT2ᑖ¢VqrNஹM±s.PsḄìᙶ᪗t.(1)ᵨítḄÂᦪ¿⊤ï,|MNḄw?dtð·,|MNᨵᨬò·êóᨬò·?(2)ôḼPsöéPஹMஹNXsḄ÷øùúûüᓄ.þdtð·ᐸzsjÿ᜜
Ḅ(3)ᱥ3AḄ(m—3,n),ᐸ;WmW?,!"Ḅᱥ22#C%"ᱥ⚔ᡠ()ᑮḄḄᙶ᪗..26⚓/353⚓

26ூ678ᫀ௃(1)<80?MNᨵᨬDE2(2)

27ᡠ{"Ḅᱥy=—(x+1—m)2+4+n,C(0,3)mᐭ]:3=—(1—m)2+4+n,ᡠ{4+n=3+(m—I)2,|'Wmg*,22521321

282022-2023
ḕᓭὃᦪ⚗ᓣᔁHMஹ⌱M⌱£ᐳ12D⚪¥D⚪3ᑖᐳ36ᑖ.¦1.6ḄEN£¦1A.-6B.6C.MD.062.¨ᑡªᦪ«¬ᳮᦪḄN£¦A.2B.0.5C.ᐔD.-53.᝞°±AB஻CD,ZC=75°,ZE=30°,ᑣNAḄ¸ᦪ()A.30°B.32.5°C.45°D.37.5°D.5.¨ᑡ¹º67ḄN£¦A.a+2a2=3a3B.(a)=a5C.a3^a2=a2D.a9a2-o'6.“ᐳ½ᓫ¿”NᢣÂÃÄÅÆᔠÇᙠ᪥ÊஹᙢÌÍஹÎÏÍஹÐÑÒஹᖪÃÒஹÎᐳÔÕÒÖ×Øe¿ᐳ½ḄMÙÔÕNᐳ½ÚÛḄMÙÜÝ᝱.ßà⚜¹ᢗᐭ31600ãᐳ½ᓫ¿ÔÕ¬äå31600ᵨæçᦪè⊤X£¦A.3.16xl04B.3.16x10sC.3.16xl06D.31.6xl057.Lê᜜ëìíḄᓱᱏᑖV᪗ᨵᦪð1,2,3,ZñòឋôY
êᑣú
êᓱᱏûḄᦪðាö÷D¬3Ḅᭆ᳛N£¦1112A-B.-C.—D,3.963.29⚓/353⚓

298.ᱥý=-þ2"]ᑮÿ=-x2+2x-2,ᑣᱥᑮḄA.ᐜᔣ1ᓫ!"#ᔣ$1ᓫ!B.ᐜᔣ1ᓫ!"#ᔣ&1ᓫ!C.ᐜᔣ(1ᓫ!"#ᔣ$1ᓫ!D.ᐜᔣ(1ᓫ!"#ᔣ&1ᓫ!9.᝞,-./01Ḅ2-᜜4536஺"9:;/01Ḅ0ᦪA.10B.11C.12D.1310.>Ꮙ@ABC᰿EὅᵨHIJKLMN>ᨴ30ᜩ2ᜩᏉ@AḄ@ᦪᓫQR@,SLMT,UᑴᡂN᝞XᡠZḄ[\X.ᙠ2ᜩᡠAḄ@ᦪ;^ᦪ_`"aᦪb`ᦪᑖd@ᦪR@A1.2,1.3B.1.3,1.3C.1.4,1.35D.1.4,1.311.᝞X"gO0i4Ḅj04ABCḄᑁl"SAOBCmgO⌮o┐qr30஺sᑮAOBiG,BiCivBCwgD,BiCivACwgE,yUCE=()A.2B.473-4C.2^3-2D.4-2612.᝞X"ᙠjῪRtAABC`"/C=BC=4&"gPᙠ0ABiḄᙊ&"Mi30⚓/53⚓

30PCḄ`g.gPᙊgABCgBo"gMBCḄ)A.2&+4B.2Rc.4V2+2D.4ஹ⚪ᜧ⚪ᐳ6⍝⚪"2⚪3ᑖ"ᐳ18ᑖ,13.ᑖ¡¢£Qa3-a2=.14.16Ḅ¤¥᪷.15.§¨-^ᦪ_Q1,2,2,3,ᑣ;^ᦪ_Ḅ©.16.᝞X-ª«¬⍝Ḅ®¯☢"±²Ḅ1³0iᙊlḄᙊḄ-´ᑖ"☢AB=8¶,·ªCD=8¶,ᑣ¸ᙊḄ0Ai.17.᝞X"ᙠ☢4ᙶ᪗»xQy`"¾01O0EFb¾0143஺5.1"gFᙠxÀkḄ.À&"gCᙠ0஺E&"ÁÂÃÄᦪV=—Æ0,x>0ḄXÈÉg8,E,±/3=2,xᑣkḄÊi.18.᝞X"/iy=6x,Ég41,0Ë஻3i_LxÀ"Ï/vwgS"Æg஺iᙊl"஺ᵪiÒᙊÓvxÀwg42Ô#ËZÖ2"XÀ"v/wgÆg஺iᙊl"஺ØiÒᙊÓvxÀwgᙠÔ……"ᢥ¸ËÛÜ$Ý"ᑣg/஻Ḅᙶ᪗i.31⚓/53⚓

31Þஹ¡ß⚪(ᜧ⚪ᐳ8⍝⚪"ᐳ66ᑖ")19.\¤QV12-(l+V7)°+sin300-12>^-2|20.¡åQx2-x-2=021.᝞X"gEiæ1ABCD᜜-g"AE=DE,çèEBஹECᑖdÏADévwgFஹG.ê(1)AEAB^AEDCÔ(2)ZEFG=ZEGF.22.>᪥\ᑜíîN“ᜧðñ”óô.iõwöᳮÏøᙢú᣸"ü᪥ýᡠᙠþÿ
ᔜ⚗(⌱⚗)Ḅ.Ḅ!"#ᑴ᝞&'ᡠ)Ḅ*ᨵ,ᐰ'./᪷1&ᑡ34567⚪9(1)ᙠ<=>?@ᡠᙠḄABCᳫ⚗ḄEᨵ_HᡧJ'>KLᳫ⚗ᡠᙠḄᡧJḄᙊNOP___QH(2)⊡ᐰᩩJ'.(3)᝞"᪥ᨵ1000X.Yᐰ᪥>ᨵZ[Cᳫ⚗.\32⚓/_53⚓

3223.᪥ᑜ⌱bᵬஹefg'hi“᪥klh⁚”Ḅ.opᵬ'hḄᓫrPe'hᓫrḄ1.5sHᵨ600ᐗᓫwbxᵬg'hyᓫwbxeg'h⌕[10{.(1)ᵬஹefg'hḄᓫrᑖ}Z[ᐗ~(2)᪥ᑜbxZABC=90°,AB=CB,ÇABÈḄ0OACªD,ªEPABÌͪ(ªE*ᨵΪAஹBÏᔠ)DEḄÑÒÓ஺OªG,DF1DG,BCªF.(1)±×9AE=BFH(2)ØÙEF,±×9ZFEB=ZGDAH(3)ØÙGF,AE=2,EB=4,±AGFDḄ☢Û.26.᝞'ÜᱥÓÞ=0?+⊵+4஺*0)ÎãäஹBfªÎyäªC(0,3),¤\33⚓/_53⚓

33ÜᱥÓḄ⚔ªᙶ᪗M(-1,4).(I)±¤ÜᱥÓḄé᪆ëH(2)§ªDopÜᱥÓìäÍḄíîªïAACD☢Ûð6±ªDḄᙶ᪗H(3)ªPᙠÓAMÍïPCÎyäᚖªPixäḄᚖÓᚖòE,óAPCEôÓCBõᢚªPḄ÷ªPÎPஹEஹCᜐᙠEù☢ᑁ.±úPᙶ᪗ᑨ¼ªPPᔲᙠÜᱥÓÍ.\34⚓/_53⚓

342022-2023
ḕᓭὃᦪ⚗ᓣᔁHஹ⌱⌱ûᐳ12?⚪?⚪3ᑖᐳ36ᑖ.ü1.6ḄýPûü1A.-6B.6C.-D.06ூÿ
ᫀ௃Bூ௃ᑖ᪆᪷Ḅឋ
ᓽ.᪷Ḅឋ|6=6.ᦑ⌱B.⚪ὃ!Ḅឋ"#$ᦪḄ&'()"#*ᦪḄ&'Ḅ+,ᦪ)0Ḅ&0,/0〉2.2.4ᑡ6ᦪ2)789ᳮᦪḄ&;

35ூ௃v⚪ᑖ᪆wxyḄឋGz{|+g)}|h᜜|ḄឋG/஺=4+/,ᦑ⌱C..ὃ1ஹ}|h᜜|Ḅឋ2ஹwxyḄឋ.4,4ᑡ2)L[hḄ&;<ூ$
ᫀ௃Bூ௃AஹL[gῪ}|h)[ᙊᙊ)ᦑA⌱⚗┯BஹL[h)[h)ᦑB⌱⚗$CஹL&h)ᙳ[ᙊ)ᦑC⌱⚗┯DஹL[h)[h)ᦑD⌱⚗┯.ᦑ⌱B.5.4ᑡ$Ḅ&;

36A.3.16xl04B.3.16xlO5C.3.16xl06D.31.6xl05ூ$
ᫀ௃Aூ௃ᑖ᪆ßàáᦪḄ⊤ãhi[aX10"Ḅhi)ᐸ2lW|a|<10,஻[᦮ᦪ.E"Ḅæ)⌕çèªᦪéᡂ஺æ)Zᦪëì!eí{)஻Ḅ§ZᦪëìḄ{ᦪ+z.îªᦪ21æ)஻&$ᦪîªᦪḄ<1æ)஻&*ᦪ.ï31600ᵨßàáᦪ⊤ã[3.16X10,ᦑ⌱A.⚪ὃ!ßàáᦪḄ⊤ãU.ßàáᦪḄ⊤ãhi[“X10”Ḅhi)ᐸ21Wa|<10,“[᦮ᦪ)⊤ãæᐵ´⌕$E஺Ḅ"Ḅ.7.}ð᜜ñ+zḄᓱᱏᑖB᪗ᨵᦪõ1,2,3,ö2÷øឋùG`ð)ᑣú`ðᓱᱏûḄᦪõាýZ83Ḅᭆ᳛
1„11n2A.-B.-C.-D.-9633ூᫀ௃Cூᑖ᪆௃᪛ᓽ.ூ௃᪛::ᐳᨵ6!Ḅ#$%&'(ᓱᱏ+Ḅᦪ-ា/0123ᨵ234,...'(ᓱᱏ+Ḅᦪ-ា/0123ᭆ᳛=9:3ᦑ⌱C.=⚪ὃ@Ḅᭆ᳛%ABCD᪛⚪ḄᐵF.8.GHᱥJK=-MNOPᑮ%=-x?+2x-2,ᑣTHᱥJKNOᑮ᜜ḄVW
A.ᐜᔣZNO1[ᓫ]^_,aᔣbNO1[ᓫ]^_B.ᐜᔣZNO1[ᓫ]^_,aᔣ+NO1[ᓫ]^_C.ᐜᔣ`NO1[ᓫ]^_,aᔣbNO1[ᓫ]^_D.ᐜᔣ`NO1[ᓫ]^_,aᔣ+NO1[ᓫ]^_ூᫀ௃Cc37⚓/f53⚓

37ூ௃ᑖ᪆✌ᐜG”iVᑏᡂ⚔mnḄon%p&ᑭᵨstuᦪNOvwᫀ.•.'z=-x?+2x-2=-
x2-2x-2="
X72-1,..•THᱥJzNOᑮgḄVWᐜᔣ`NO1[ᓫ]%aᔣbNO1[ᓫ].ᦑ⌱C.m=⚪⌕ὃ@stuᦪḄᣚ%ᑭᵨiVWstuᦪ⚔mnḄon⚪ḄᐵF.9.᝞$[oḄ[᜜036஺%[oḄᦪ
A.10B.11C.12D.13ூᫀ௃Aூᑖ᪆௃oḄ᜜¡¢Ḅ360஺%£¤zoḄᦪ.ூ௃[oḄ[᜜0236஺%.•.oḄᦪ¥360°+36°=10.ᦑ⌱A.=⚪⌕ὃ@oḄ᜜¢ᳮoḄ᜜360°.10.¨Ꮙª«¬᰿/ὅᵨ°±²³´µ¨[ᨴ
30ᜩᜩᏉª«Ḅªᦪ
ᓫ]¸ª,G´µ#$¹ᑴᡂ᝞ᡠ¼Ḅ½¾.ᙠᜩᡠ«ḄªᦪÀᦪÁÂ%ÃᦪÂ]ᦪᑖÄ
ªᦪ¸ªA.1.2,1.3B.1.3,1.3C.1.4,1.35D.1.4,1.3ூᫀ௃Dc38⚓/f53⚓

38ூᑖ᪆௃Â]ᦪGÀᦪÁÈ1ᑮᜧ
ᡈÈᜧᑮ1ËÌ᣸ᑡP%ᨬÂÐḄ[ᦪ
ᨬÂÐ'[ᦪḄNᙳᦪ%ÃᦪÀᦪÁÂÒtᦪÓḄᦪÁ%Á¤ᑨÕᓽ.ூ௃•.•ÀᦪÁÂ1.4ÒḄtᦪÓ%sᙠᜩᡠ«ḄªᦪÀᦪÁÂ%Ãᦪ1.4:ᜩᡠ«ḄªᦪḄÂ]ᦪ1.3+1.3
+2=1.3,sᙠᜩᡠ«ḄªᦪÀᦪÁÂ%ÃᦪÂ]ᦪᑖÄ1.4ஹ1.3.ᦑ⌱D.=⚪⌕ὃ@ÃᦪஹÂ]ᦪḄ×ØW%ÙABCD%¤⚪ḄᐵF⌕ÚGÀᦪÁÈ1ᑮᜧ
ᡈÈᜧᑮ1ËÌ᣸ᑡP%ᨬÂÐḄ[ᦪ
ᨬÂÐ'[ᦪḄNᙳᦪ%ÛÜÀᦪÁḄÂ]ᦪ%ÃᦪÀᦪÁÂÒtᦪÓḄᦪÁ.11.᝞%m0^¥4ÝḄAABCḄᑁß,GAOBCàm0⌮â┐äå30஺ᑮAOBiG,BICIæBC2mD,BiCiæAC2mE,çUCE=
A.2B.473-4C.2^-2D.4-273ூᫀ௃Cூ௃ᑖ᪆èOBBCḄæm¥é%81GNCḄæm¥êméëFNJ_082mN,᪷ÁíoḄឋïzðᑁßḄឋïñòé஺8¥Ὺío%8éḄ^%᪷Áíoᑁ¢ᳮòé8Qô¥30°ḄῪío%ᑮÈ&ᑮ8஺ஹCQḄ^,a᪷Áíoᑁ¢ᳮ/OEC=90஺%ᓽCEḄ^_.è8cḄæm¥õBCi/CḄæm¥ö%êméëéN_LO82mM᝞ᡠ¼.,GòO8Càm஺⌮â┐äå30஺ᑮòO8C”.•.480é=30஺.:m஺^¥4Ḅò/8CḄᑁß%/OBF=3Q°,OB=®AB=4,.AFOBc39⚓/f53⚓

39¥Ὺío%BN=-0B=2,.BF=———=ø⁐=0é.2cosNOBF3•NOBF=NOBiD=NBOBi=30஺,ZBF0=ZB\FD.ZFDBi=30°,:FBFD,f:.BD=OB[=OB=4,.DC=BC-BD=4y/j-4.VZF£>Bi=30°,AZEDC=30°.'ZBCA=60°,:"DEC=9Q0,£C=yZ)C=273-2.Bᦑ⌱C.m=⚪ὃ@íoḄឋïஹíoᑁßḄឋïஹúíoḄឋïzðúío%⚪ḄᐵFJû8஺ஹCQḄ^_.12.᝞%ᙠῪRtAABCÂ%AC=BC=4,mPᙠzüAB¥úýḄþᙊ
MPCḄ.PᙊAB
MḄA.2+4B.2C.472+2D.4%ூᫀ௃Bூ!"௃ᑖ᪆%&Ḅ0ஹZCḄEஹ8cḄ()*0CஹOPஹ0Mஹ0Eஹ0FஹEF,᝞,
ᑭᵨ/Ὺ12324Ḅឋ67ᑮ/8=08C=8,ᑣOC=:/8=4,஺1;/8=4,<᪷>/Ὺ324Ḅឋ67OMLPC,ᑣNCMO90஺
?᪷>ᙊᕜ2Aᳮ7ᑮMᙠDOC1Ḅᙊ
ᵫ?Pᙠ4
MᙠE:PᙠB
ᡭᙠE
ᑣᑭᵨGH4CE஺IJ7ᑮEF=0C=4,ᡠDLḄDEI1Ḅᙊ
ᯠN᪷>ᙊḄᕜO40⚓/R53⚓

40STUV஻Ḅ.!"%&48Ḅ0ஹ/CḄEஹ8cḄF,)*஺CஹOPஹOMஹ0EஹOFஹEF,᝞,
%ᙠ/ῪRtZ\NBC
AC=BC=4g,:.Z8=&8C=8,.0C=^AB=4,1OP=-4B=4.2:ᔊPCḄ
...0A/1.PC,:.NCAf0=90஺
.♦.oᙠD0c1Ḅᙊ
Pᙠ4
஻ᙠE%Iᙠ8
MᙠI
᧕7GH4CE0FJ4
EF=OC=4,r஻ḄDEI1Ḅᙊ
.•.MḄ=-,471=271.ᦑ⌱B.2y%z⚪ὃ}~%ᢥAᡠ4ᡂḄ,4Ḅ."⚪Ḅᐵᑭᵨ/Ὺ324Ḅឋ6ᙊᕜ2AᳮA஻ḄD£I1Ḅᙊ.rஹ⚪(zᜧ⚪ᐳ6⍝⚪
⚪3ᑖ
ᐳ18ᑖ,)13.ᑖ"T%a3-a2=____.ூᫀ௃/(a—1)ூ!"௃ᑖ᪆%AST᪗,ᯠN&STᓽ.!":a3—a2=a2(«—1).ᦑᫀ஺2(a—1).y%z⚪ὃ}~STᑖ"T
zSTḄ⚗&STN¡ᒕ£T1ᡈ-1,¥ᨵ⌕¨⚗.14.16ḄVª«J᪷.ூᫀ௃4ூ!"௃"%•.•(±4)2=16O41⚓/R53⚓

41.♦.16Ḅ«J᪷4-4r16ḄVª«J᪷415.®¯°ᦪ>%1,2,2,3,ᑣ²°ᦪ>ḄJ³.ூᫀ௃yூ!"௃ᑖ᪆%ᐜᵫ«ᙳᦪḄSTUV¶²°ᦪ>Ḅ«ᙳᦪ
<᪷>J³ḄST·UVᓽ.!"%²°ᦪ>Ḅ«ᙳᦪ%(1+2+2+3)+4=2,ᑣ²°ᦪ>ḄJ³%-[(1-2)2+(2-2)2+(2-2)2+(3-2)2]=y.42ᦑᫀy.y%z⚪ὃ}~«ᙳᦪ¸J³
¹ᙢ»஻¼ᦪ>
XIX2,…&Ḅ«ᙳᦪ3
ᑣJ³(X!-X)2+(X2-¾)2+…+(X.-¾)2],¿À᧜~°ᦪ>ḄÂᜧ
nJ³Ãᜧ
ÂឋÃᜧ
ÀÄoᡂÅ.16.᝞,¼ÆÇSÈ⍝ḄÉÊ☢
Ì¿Ḅ4ÍDOᙊÎḄᙊḄÏᑖ
☢AB=8Ð
ÑÆCD=8Ð,ᑣᙊḄOA______.ூᑖ᪆௃ᐜ᪷>ᚖAᳮÔ¶Õ஺Ḅ
<»஺஺Ḅr,ᑣ8fᙠRtZ\/O஺,᪷>Ö×AᳮᓽÔ¶
•ḄØ.ூ!"௃":'CD1AB,AB=im,.'.AD=^-AB=4m,»஺஺Ḅr,ᑣ஺஺=8-r.ᙠRtZ\NO£>
'OA2=OD2+AD2,ᓽ/=(8-ᶭ+42,O42⚓/R53⚓

42"7%r=5.ᦑᫀ5.z⚪ὃ}ḄᚖAᳮḄÚᵨ
ᐜ᪷>ᚖAᳮ7¶Õ஺Ḅ
<᪷>Ö×AᳮÔ""⚪Ḅᐵ.17.᝞,
ᙠ«☢12ᙶ᪗ÜkJ
GH4ODEFGH448஺àJ4
IᙠxâkḄâ
CᙠH஺E
Àãäåᦪæ=(ᱏ0,x>0)Ḅ,éê8,E,Ì48=2,ூ!"௃"%»ÀXX),r8(2/+2),k•.•Àãäåᦪy=-(N0K>0)Ḅ,éê8ஹEX.*.x2=2(x+2),x=1+V5,x=1-V5(ðñ)(2../=ò2=(1+32=6+2ᨵᦑᫀ6+2ó18.᝞,
1ô/y=Gx,ê4(1.0)ö஻8|J_Xâ
¸1ô/ù?3,Dú஺ᙊÎ
஺ûüᙊýùXâ?:<ö/2B2_LXâ
ù1ô/?᧎
஺ᙊ஺ᙊx43……ᢥᑣ஻Ḅᙶ᪗.%43⚓/(53⚓

43ூ,-.ᫀ௃(2"',0)ூᑖ᪆௃3456/y=Gx,7(1,0),/9:x;<ᙠ(2,0),>ᳮ;<A3(4,0),4(8,0),34@A;<஻Ḅᙶ᪗(2஻-1,0).ூBC௃♦.•56/y=0x,4(1,0),,...Fx=1Gy==,,ᓽBi(1,>),•♦tan//1081=-*^3,AZ^]OBi=60°,/48|஺=30°,.OB\=2OA\=2,V
0ᙊ஺ᵨᙊxA,2.A(2,0),2>ᳮ;<As(4,0),A4(8,0),K/஻Ḅᙶ᪗(2”|,0),ᦑ0).M⚪ὃPQ@A⚪RSᦪUVWḄᙶ᪗ᱯYᐜ᪷4ᡠ]Sᦪᑨ_`SᦪaxᜳcdCeM⚪Ḅfẚ᪷4h30°Ḅ5cicjḄᱯ3k<ᑮ4ஹnஹn…ḄḄᙶ᪗dCeM⚪Ḅᐵp.iஹC.⚪(Mᜧ⚪ᐳ8⍝⚪ᐳ66ᑖ)19.uvwV12-(l+5/7)°+sin3Oo-|2^-2|3ூ,-.ᫀ௃x2ூBC௃ᑖ᪆w5yᑭᵨKk᪷{Ḅឋ}~ᢣᦪᕆḄឋ}
Ḅឋ}ᑖᓄ<`.ᫀ.%44⚓/(53⚓

44BCw{=20-1+y-273+23="2,wM⚪⌕ὃPQᦪv,-ᓄᔜᦪdC⚪Ḅᐵp.20.CwX2-X-2=0ூ,-.ᫀ௃x,=2,x=-12ூᑖ᪆௃ᑭᵨᓝ{Ḅ{ᑖCᯠC.ூBC௃Cwᵫ

45AB=DC,KÀEABÃÀEDC(SAS)(2)VAEAB^AEDC,.".ZAEF=ZDEG,VZEFG=ZEAF+ZAEF,ZEGF=ZEDG+ZDEG,/.ZEFG=ZEGF.ὃw1.ᐰicjḄᑨÅaឋ}2.·jḄឋ}.22.Æ᪥uᑜÉÊQ“ᜧÌÍ”ÏÐ.ÑÒᳮaÓᙢÕ᣸²᪥
7»ᡠᙠ×ØÙ²nÚÛᔜ¥ÏÐ⚗Ý(Þßà⌱âÚÛx⚗)ḄãäQåu.æḄçèéᑴQ᝞UᡠëḄìᨵíᐰåuUîï᪷4ᑡñòó.±⚪w(1)ᙠ©kÂ7»ᡠᙠḄ×ØÚÛôᳫ⚗ÝḄ>²ᨵ—ßᡧjåuUÂøùᳫ⚗ÝᡠᙠḄᡧjḄᙊcdxú(2)⊡ᐰᩩjåuU.(3)᝞è²᪥ᨵ1000ý²nîþuᐰ᪥²nÂᨵÿ
ᳫ⚗.
ᦪூᫀ௃(1)5
72°(2)᪆(3)ᐰ᪥ᨵ100
ᳫ⚗.ூ௃ᑖ᪆!(1)᪷#$%
ᦪ◀'$%
ᦪᡠᓰḄ+ᑖ,-./01
ᦪ᪷#ᨵᳮᦪḄ34-.ᳫ⚗Ḅ
ᦪᵨ67ᳫḄ
ᦪ◀'1
ᦪ89'360஺ᓽ-.ᑮᡧ>?@67ᳫ⚗ᡠᙠḄᡧ>ḄᙊCDḄEᦪ(2)᪷#ᳫ⚗Ḅ
ᦪ⊡ᐰ@>ᓽ-(3)᪷#ᐰ᪥
ᦪ9'ᳫ⚗ᡠᓰḄ+ᑖ,-.ᫀ.!(1)2040%=50(
),50-20-10-15=5(
)IJᡠᙠḄKLᳫ⚗ḄMᨵ5
.ᡧ>?@67ᳫ⚗ᡠᙠḄᡧ>ḄᙊCDḄEᦪ=360஺X—=72°.50(2)⊡ᐰ@>᝞O!P46⚓/153⚓

46(3)1000XX=100(
)ᐰ᪥ᨵ100
ᳫ⚗.50Z[!\⚪ὃ_Ḅ`ᩩ>?@bᡧ>?@Ḅcᔠeᵨfg?@hiᨵMḄ?@.ᑮj⌕Ḅlm`no⚪Ḅᐵq.ᩩ>?@rstᙢ⊤wxyz⚗Ḅᦪ#;ᡧ>?@|}~᧜ᑖᓰ1Ḅ+ᑖ,ᜧI.23.᪥ᑜ⌱ᵬஹ@“᪥f⁚”Ḅ.ᵬ@Ḅᓫ`@ᓫḄ1.5ᵨ600ᐗᓫᵬ@,ᓫ@⌕10\.(1)ᵬஹ@Ḅᓫᑖᐗ(2)᪥ᑜ¡@ᐳ40\¤ᢗᐭḄiᨵ§¨1050ᐗ⌕©Ḅᵬ@ᦪªiᨵ«@Ḅᦪªᑣᐳᨵூᫀ௃(1)ᵬ@Ḅᓫ30ᐗ@Ḅᓫ20ᐗ(2)6.ூᑖ᪆௃(1)ᵨ1®ᵨ◀'ᓫᓽᦪª¯@Ḅᓫxᐗᑣᵬ@Ḅᓫ1.5xᐗ᪷#@ᦪª±²Ḅᐵ³ᑡµ¶(2)¯·ᵬ@a\ᑣ·@(40-a)\᪷#“ᢗᐭḄiᨵ§¨1050ᐗᵬ@ᦪªiᨵ«@Ḅᦪª”ᑡxiᨵº»¼no⚪.ூ௃(1)¯@Ḅᓫxᐗᑣᵬ@Ḅᓫ1.5xᐗ600600Àᵫ⚪¾.:--------------=10,x1.5%.!x=20ᑣ1.5x=30,fÁÂÃ.x!x=20`ĵ¶Ḅ᪷.!ᵬ@Ḅᓫ30ᐗ@Ḅᓫ20ᐗ.(2)¯·ᵬ@஺\ᑣ·@(40-a)\,,30஺+2040-஺Æ<1050᪷#⚪¾.:Xa>40-aP47⚓/153⚓

47.!202?@AᨵC.ᳮᵫ᝞FVfi£=fiC»cos60°=100K.,:NCAN=45°,.".AE=CE=l00y/3m,L/8=100<-100=73&;73—=14.6m/s.5V60ᓟK/RS=^m/s.3T48⚓/V53⚓

48W•••14.6ீY?@AᨵC.35Z[⚪]⌕ὃ`abcdᳮef┦hihjᦪᐵmḄnᵨ>pqrsthihu,45Ḅvwxy⚪2
Ḅᐵz.25.᝞ᙠRtAABC|ZABC=90°,AB=CB,eAB;t}Ḅ0O~AC5D,5EwAB55EAᨵ5AஹBᔠDEḄv~஺05G,DF1DG,~BC5F.1
AE=BF>2
EF,ZFEB=ZGDA3
GF,AE=2,EB=4,AGFDḄ☢.ூᫀ௃1
᪆>2
᪆>3
9ூ௃ᑖ᪆1
8஺ᵫihu/8C;ῪthihuN4NCḄᦪ᪷;ᙊḄt}ᑭᵨᙊᕜhdᳮᑮ;thᓽ8஺ᚖt47,ᑭᵨthihu¡Ḅ|¡Ḅ¢^\AD=DC=BD=-AC,£¤d¥ᑭᵨ¦hḄ2§h¨ᑮ©h¨ᑭᵨASAᑮihuªᓽihu8஺ᐰᑭᵨᐰihu©T49⚓/V53⚓

49n¨ᓽ;(2)EF,BG,ᵫihu/EDihu8EDᐰᑮED=fD,£¤ᑮihuOE¬;ῪthihuᑭᵨᙊᕜhdᳮfῪthihuឋ®ᑮ©¦¯h¨ᑭᵨ¦¯h¨°t±²¥᪷±²Ḅឋ®³¦´ᡠ©Ḅᙊᕜh¨ᓽµ¶>(3)ᵫᐰihu©n¨ᑮ/E=8¬=1,ᙠthihu8EF|ᑭᵨbcdᳮE¬Ḅvᑭᵨ┦hihujᦪd·஺EḄvᑭᵨ°©h¨Ḅihu¨¸ᑮihuªEDihuGEB¨¸ᵫ¨¸¹ºGEḄvᵫGE+EDG஺Ḅv᪷ihuḄ☢7»¼½ᓽ.(1)BO.ᙠ|ZABC=90°,AB=BC,.Z/1=ZC=45O.,AB;ᙊOḄt}^ADB=90°,ᓽBDLAC,.AD=DC=BD=~AC,2ZCBD=ZC=45°,.ZA=ZFBD."DFLDG,.ZFDG=90°,.ZFDB+NBDG=9Q஺.ZA=NFBDZEDA+ZBDG=90°,.ZEDA=ZFDB.ᙠMED³¬஺|AD=BD,[AEDA=NFDB./\AED^/\BFD(ASA),:.AE=BF(2)EF,BG.■:XAEDQlXBFD,.DE=DF.:NEDF=90஺,.♦.¿EZ)¬wῪthihu.ZDEF=45°.VZG=ZJ=45°,:.NG=NDEF,.GB//EF,.NFEB=NGBA.•NGBA=NGDA,:.NFEB=/GDA(3);AE=BF,AE=2,.BF=2.ᙠ|ZEBF=90°,᪷bcdᳮᓺ=■+8Â.•EB=4,BF=2,.EF=y/4222=2-45■+DEÿOEF;ῪthihuNEDF=90°,.cosZDEF=——.EF,:EF=2#>,:.DE=2^X^£=710.2GEEB•/G=N/,/GEB=/AED,AGEBs/\AED,,=,ᓽGEED=AEEB,AEEDT50⚓/V53⚓

50>•V10*GE=8,ᓽGE=ÆÇᑣGD=GE+ED=.55S=GDxDFx-=GDxDEx-=^^-xy/i0x-=9-22525Z[⚪ÉᙊÊᔠ⚪ËfḄÌÍᨵᐰihuḄᑨdឋ®¨¸ihuḄᑨdឋ®bcdᳮᙊᕜhdᳮef±²Ḅᑨdឋ®pqrsᑨdឋ®w[⚪Ḅᐵz.26.᝞Ïᱥy=ax2+bx+c(a*0)xØ~AஹB°5yØ~5C(0,3),ÛÏᱥḄ⚔5ᙶ᪗;M(-1,4).(1)ÛÏᱥḄ᪆»>(2)ß5D;áÌÏᱥ©âØḄãä5åAACD☢6S5DḄᙶ᪗>(3)5PᙠçAMåPCyØᚖtS5PxØḄᚖᚖè;E,éAPCEêtCBëᢚí5PḄ©n5PPஹEஹCᜐᙠ¦±☢ᑁðPᙶ᪗ñᑨò5PwᔲᙠÏᱥ.ூᫀ௃(1)J^=-X2-2X+3>M(-1,4)>(2)5DḄᙶ᪗;(-1,-2)ᡈ(-1,6).;(3)5PAᨵᙠ?Ïᱥ.ூ௃ᑖ᪆(1)ᵫÏᱥḄC5ᙶ᪗ef⚔5MḄᙶ᪗ᑭᵨödmᦪ÷ᓽÏᱥT51⚓/V53⚓

51᪆»>(2)ß5஺ᙶ᪗;(-1,»)),᪷¿48Ḅ☢=6,ᓽᐵឋøùúûḄᐗýþýþᓽµ¶>(3)5¬ᐵtCEḄ©â5P,5PPHLy“PEyN.᪷ḄឋᓽEONCPN,CN=NE,ᵫ4ஹMḄᙶ᪗ᑭᵨ()*ᦪ,-./Ḅ0᪆23PḄᙶ᪗.ᙠRt/kPWC:ᵫ;<)ᳮ-CNḄ>?ᵫ@ABCDḄឋEF/GHḄᐵ*ᓽJPḄᙶ᪗KᐸMᐭOᱥ/0᪆2:QR2SᔲᡂVᵫWᓽXY.c-3bZ0[(1):Oᱥ/`d+fcv+cC(0,3),⚔j3(-1,4),.\--=-1,2aa-b+c=4a=-10[(6=-2,.♦.ᡠ-Oᱥ/Ḅ0᪆2j`-f-2r+3.c=3(2)p᯿⚪stuD᝞u1ᡠw.x`-X2-2X+3=0,0[x=-3ᡈx=l,ᦑX(-3,0),B(1,0),.OA=OC,/OCjRῪ.CBCD./Cx=-1`(-1,᝞■),ᵫ4(-3,0)ஹC(0,3)./ZCḄ0᪆2jr+3,1+3=2,ᓽ`(-1,2).Dᙶ᪗j(-1,y),ᑣ1%-21X3=6.D0[yo=-2ᡈF6,...஺Ḅᙶ᪗j(-1,-2)ᡈ(-1,6).(3)᝞u2,Pj`ᐵ./CEḄP`_LyH,PEyN."NCNP'=NENOᙠEONCPN:,NCP'N=NEON=90°,.EONCP'N5AS).P'C=PC=OENC=m,ᑣNE="3'A(-3,0)ஹM(-1,4).//MḄ0᪆2j2x+6,.♦.y=3x=--,52⚓/53⚓

52333ᓽ`-3,.P,C=PC=-,P'N=3-m.ᙠR3PWC:ᵫ;<)ᳮ[+2223-m2=m20:m=—.f8119CN*P'H=PWP'C,.P,H=P.2210CHCPCP12669ᵫ[——=——.CH=--=.OH=3-.P'CPCNCN55599Ḅᙶ᪗j5.105ooooiooK`',MᐭOᱥ/0᪆2[`-ߟ2-2X—+3=—/.10510101005Pᨵᙠ¡Oᱥ/¢.£[¤⚪ὃ¦§()*ᦪ,-¨ᦪ0᪆2ஹBCDḄ☢ª«2ஹᐰRBCDḄᑨ)FឋEF@ABCDḄឋ0⚪Ḅᐵ®S[Iᑭᵨ()*ᦪ,-¨ᦪ0᪆2°2Jᐵ±²>³´Ḅᐗ¶·°3-Pᙶ᪗.¤⚪¸:᫏⚪º»ᨵ¼3:-PḄᙶ᪗S¤⚪Ḅº½ᵨᚖ.¿ᑖ/ḄឋJḄᙶ᪗Á.53⚓/53⚓