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

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2022-2023
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3⚓/49⚓

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52022-2023
ḕ☘ὃᦪ⚗ᓣ⚪+ஹ⌱+⌱1.OP2010Q◀᜛TᜩḄVW;8ᓃVW;-2࠷,ᑣTᜩḄVW[VW\]^A.10࠷B.-10࠷C.6࠷D.-6࠷ூ`abᫀ௃Aூᑖ᪆௃ᵨVWhiVWj᪷kᨵᳮᦪḄhmn@mᑣ“hi+,ᦪ34p"T,ᦪḄqrᦪ”ᓽuvbᫀ.ூwx௃8-
-2=8+2=10^.ᓽTᜩḄVW[VW\ior.ᦑ⌱A.2."☢{|}~+{|}ḄqrḄ;]^`}ᳫA.1,B.2,C.3,D.4,ூ`abᫀ௃Bூwx௃⚪ᑖ᪆ஹ;ᑖᱥ}`☢"☢ᡠvᑮḄ.⚪x᪆ᙊஹᑖ;8ஹᙊ/qrᙊ┵ஹᑖ;ஹᨵᙊḄᙊ/qrᳫஹ;ᙊ/qr`}ஹ;`/qr.ᐳ2,~+,{|}Ḅ/qr.ᦑ⌱B.ὃᓫ{|}Ḅ.H6⚓/K49⚓

63.᝞AB//CD,BEᑖNABC,CD4D,ZCDE=150°,ᑣZCḄ¡ᦪ&]).A.150°B.130°C.120°D.100°ூ`abᫀ௃Cூwx௃x•AB஻CD,AZCDB=ZABD,,rZCDB=1800-ZCDE=30°,AZABD=30°,ீBEᑖNABC,AZABD=ZCBD,ZABC=ZCBD4-ZABD=60°,VAB/7CD,ZC=180°-ZABC=180°-60°=120°.ᦑ⌱C.4.r[¥¦ᦪḄ§(-3,2),ᑣT,§+¨()ஹ3/ஹA.(2,-3)B.(-,-1)C.(-1,1)D.(2,-2)ூ`abᫀ௃Bூwx௃x:ªr[¥¦ᦪḄx᪆«&y=kx(k),•,r[¥¦ᦪḄ§(-3,2),2-3k=2,xvk=--,2♦•r[¥¦ᦪḄx᪆«&y=-yX.H7⚓/K49⚓

724Aஹ•.•2x=2(y=--x2=--6-3)...'ᙠ¦ᦪ§"ᦑ¶⌱⚗┯¹533323Bஹ\•2x=—(y=-x—=-1,...'ᙠ¦ᦪ§"ᦑ¶⌱⚗`a23222Cஹ,2x=-l(y=-yx(-1)=§#1,...'ᙠ¦ᦪ§"ᦑ¶⌱⚗┯¹24Dஹ2x=2(y=--x2=--#-2)...'ᙠ¦ᦪ§"ᦑ¶⌱⚗┯¹.33ᦑ⌱B.5.:Ã~ÄÅÆᦪÇὁÉ〈ËÌÍÎᓱÐÑÒ⍝ὁÉḄÌÍᙠ10ᨴÖ×ÑØὁÉÌÍḄᭆ᳛;()1111A.—B.—C.—D.—28293031ூ`abᫀ௃Dூwx௃⚪x᪆..TOᨴ+ᐳ31ᜩÑØὁÉÌÍḄᭆ᳛;-L,31ᦑ⌱D.6.ÞḄᕜ8&8cm,\&1cm,ᑣâÞ<ã¡ᦪ[&()A.31B.41C.51D.61ூ`abᫀ௃Cூwx௃᝞ᡠä•ÞḄᕜ8&8cm,ÞḄ!8&2cm,•ÞḄ\&1cm,..AEI..si=---=-AB2çZB=30°,/.ZC=150°,ᑣâÞ<ã¡ᦪ[&51,H8⚓/K49⚓

8ᦑ⌱C.7.᝞BA(m,n)>B(m-1,n-2)ᙳᙠ¦ᦪïkx+b(k#))Ḅ§"Ö×kḄ)&()A.2B.1C.-1D.-2ூ`abᫀ௃Aூwx௃⚪x᪆♦,A(m,n)>B(m-l,n-2)ᙳᙠ¦ᦪó=1:*+6(k/0)Ḅ§"n=mk+b**n-2=[m-\)k->rhxvk=2.ᦑ⌱A.8.ᙊḄõ&13cm,<ö/5஻CQ,Z5=24cm,C/>10cm,ᑣ<öCQḄøù;()A.7cmB.17cmC.12cmD.7cmᡈ17cmூ`abᫀ௃Dூᑖ᪆௃ᑖZBஹCQᙠᙊḄ~ûüû<ýþÿ᪷ᚖᳮᳮᓽ.ூ௃ᙠᙊḄ!•*.*CD=1Ocm,OE_LCD,/.QE=/CD=/xl0=5(cm),:ᙊḄ9:1᝕m,•:00=13cm,...ᑭᵨᳮ?@9⚓/C49⚓

9OE=y/OD2-DE2=V132-52=12(cm),EᳮF0F=5cm,/.EF=OE-OF=\2cm-5cm=7cm@HIJEF=OE+OF=17cm.ᐸM᪵/OPᑖ᪆STUḄVW:7cmᡈ17cm,ᦑDZ[.\⚪ὃ_ḄJᚖᳮ`ᳮḄaᵨᮣcaᵨᳮஹᶇfᑖ/8ஹC஺ᙠᙊḄEijkJ⚪Ḅᐵm.39.nSopy=kx(k>0)tuvpy=wxyA(xyjB(x,y)yᑣxm+XzyiḄP22x:()A.-6B.-9C.0D.9ூZ[ᫀ௃A3ூ௃:••yA(xi,y)B(X2>v?)JuvpPḄy,xAxryi=X2*y2=3.@10⚓/C49⚓

103•opy=kx(k>0)tuvpy=—wxyA(xiyi),B(X2,y2)yx.*.xi=-X2>yi=-yi***xiy2+x2yi=_xiyi-x?y2=-3-3=-6.ᦑ⌱A.10.nSyA(a-2b,2-4ab)ᙠᱥpy=x2+4x+10PᑣyAᐵxᱥpḄyᙶ᪗:()A.(-3,7)B.(-1,7)C.(-4,10)D.(0,10)ூZ[ᫀ௃Dூᑖ᪆௃ᶍூ௃••yA(a-2b,2-4ab)ᙠᱥpy=x2+4x+10P.(a-2b)2+4X(-2b)+10=2-4ab,aa2-4ab+4b2+4a-8b+10=2-4ab,(a+2)2+4(b-1)2=0,Aa+2=0,b-l=0,?a=-2,b=l,••a-2b=-2-2x1=-4,2-4ab=2-4x(-2)xl=10,••yAḄᙶ᪗:(-4,10),,4,:opx=-——=2,2x1••yAᐵxḄyḄᙶ᪗:(0,10).ᦑ⌱D.ᶍஹ"#⚪11.ᖪ:├ᖪ:3ᐗḄᖪᑡ¢£¤¥¦§¨©ª«5¬ᢥ®¯°/¦ឋ§¨5¬Pª«²ᑖᡭ´ᢚ.¶·¨஻¬¹ᖪᐳ¯27ᐗᑣ"ḄJ@11⚓/C49⚓

11ூZ[ᫀ௃10ூᑖ᪆௃¦§¨5¬ᑣ¼¯°15ᐗ½ᯠ¶·§¨ᦪÀª«5¬ᵨ஻⊤Âꫲᑖ¼¯ḄÄÅÆP15ᐗÇx27ᐗ?ᑮ¢ÉF.ூ௃ᵫ⚪f?3x5+(஻—5)x3x08=27,?“=10.ᦑ10.\⚪ὃ_ᐗ¢ÉḄaᵨᵨ«⊤Âê«5¬²ᑖ¼¯ḄÄJ⚪Ḅᐵm.12.ÎÏж⚪ÑÒ⌱⚪Ó¦Ô⌱ᑣᢥᡠ⌱Ḅ⚪ᑖ.A.ZÖ×ØḄÐ᜜ÚḄÛᦪJ____.B.ÜÝᜧ¶2tan71஺_____(â“>”ஹ"="ᡈ“<”)ூZ[ᫀ௃জ.72஺ঝ.<ூ௃ç⚪᪆:A.360஺+5=72஺.ZÖ×ØḄÐ᜜ÚḄÛᦪJ72஺.B.V2tan71o~5.808,=6.856,.•.2tan71°<747.ᦑᫀ:72஺<.13.ᔜ×íÛîJ᦮ᦪஹ×í:11ḄðÚØᐳᨵÐ.ூZ[ᫀ௃36ூ௃ç⚪᪆òó᜜×í:x,y,ô©õòISxWyWll⌕᪀ᡂðÚØüýx+yN12.ÿy
11.x=l,2,3,…11,ᨵ11y
10x=2,3,…10,ᨵ9y
ᑖ9,8,7,6x
ᦪᑖ7,5,3,1,.••᪷$ᑖ%&ᦪ'ᳮ)ᡠ+Ḅᦪ11+9+7+5+3+1=36.ᦑ/ᫀ136.212⚓/549⚓

1214.᝞8AABC9AB=AC,NBAC=45஺BC=2,D;?@@DᐵBC;ABஹACḄEF@ᑖMஹN,ᑣ;

13ACH=(1--)AB,2VBH2+CH2=BC2,.(1£AB)2+[(1-—)AB]*22.AB2=4+20,•••AD=7^'.MN=“71;ᓝ^----L------•a2+la4-la+1-a4+6a''+6o-3ூLM/ᫀ௃^-1ூPQ௃R⚪ᑖ᪆1᪷$ᑖzḄoᑣᓽ+/ᫀ.214⚓/549⚓

14a+\஺+13R⚪Q᪆1'z=>;+>a+1(a(2+1(a+l)~a-3a2+1(a-l)(a2+1)a+\'a2-l(a+1)2a-3"(a-l)(a2+l)(a-l)(a2+l)a+\(2a(a+l)‘(a-3)(a-D(/+1)(a-l)(a+l)(a2+1)(tz-l)(a+l)(a2+l)(-a4+6a3+6a-3a4-l'@1ᑖḄᑖzᓄᡂᑖḄᑖz¢£¤ᑖ¤ᑖ¥ᑖᑖzḄ¦§¨©ᓄªᑖᑖzḄ¦§.17.᝞8«)ABC,ZC=90°.¬ᵨ®]>L¯°CL¯Ḅ>⚔ᐸ³⚔@ᑖᙠABஹBCஹACµ=.(¶ᶇ]8¸¹ᑏ])ூLM/ᫀ௃]8»Q᪆ூPQ௃R⚪ᑖ᪆1᪷$⚪¼CL¯Ḅ>⚔½¾NC¨L¯Ḅ>ᑁL¯ḄE;Àᑖ>ÁEᡠÂ]NCḄÀᑖ;ÃABB>@ᐸ³⚔@ᑖᙠABஹBCஹACµ=½¾½@¨L¯ḄÄ>⚔@Å\M]ACஹBCḄᚖ;ᑖÃACஹBCB@EஹD,ᡠÂǵMECDᓽᡠ+ḄL¯.R⚪Q᪆1᝞81ǵMECDᓽᡠ+ḄL¯.215⚓/549⚓

1518.ÈÉ⚪JÁÊÊQÈËÌᵯ?ÎÏÐḄÑÒEÈÓᓬÕÖ×ØËÌAஹBஹCஹDÇÙÚÛḄ£ÊÜ&Ýᑴᡂ᝞ßàáÜ&8ᙳãä1ØÕÖ×åæÙËÌḄᵯ?ÎÏÐᐳèéêë2àáÜ&8⊡ᐙãä3îØÓᓬÕ&ᑜðñæÇòÚÛḄᵯ?ÎÏÐ180ê+CÚᵯ?ÎÏÐóðñèéêëூLM/ᫀ௃1600ê.2⊡8»Q᪆3540ê.ூᑖ᪆௃ô᪷$BËÌ210êᓰ5öḄ35%,ᓽ+5ö2᪷$19+Ḅ5ᦪᡧÜ&89CËÌᡠᓰḄùᑖúᓽ+CËÌḄᦪû{|⊡ᐰᩩÜ&8᪷$ᩩÜ&89AஹDḄᦪû5ᦪᓽ+ᡠᓰḄùᑖúþ|⊡ᐰᡧÜ&83᪷$ᡧÜ&8ᡠᓰḄùᑖúᓽ+Q.ூPQ௃Q11210-35%=600ê./1ØÕÖ×åæÙËÌḄᵯ?ÎÏÐᐳ600ê.2CËÌ1600x30%=180AËÌ1150+600=25%;DËÌ160-600=10%.⊡ᐰÜ&8᝞8.31800x30%=540ê.216⚓/549⚓

16/1CÚᵯ?ÎÏÐóðñ540ê.19.ÿ
48C஺EஹFᑖCDஹDAḄCE=DF,4E&BF'()ஹM.
AE=BFூᫀ௃᪆ூᑖ᪆௃᪷CE=£IAF=DE,Ḅឋ"ᑮ4ABF$Z^DAE(SAS)ᓽ&.ூ(௃)
ᙠABCD:AB=AD=CD,NBAD=ZADC=90°,VCE=DF-.AD-DF=CD-CE,ᓽAF=DE,.17⚓/149⚓

17ᙠAABF24DAEAB=DA

18-2z+3x=20+x
x=10-:.BH=2+*(10-6)=10V3-l~16.3(i).
lmḄosh16.3i.21.Cᔆᦪh10ᔴ50ᔴᔴḄᡂ3yMᐗ/ᔴQ2ᦪxMᔴQḄvᦪᐵḄP᝞Pᡠ¡.M1Qyᐵ¢xḄvᦪ᪆£¤ᑏVxḄ¦§©;M2Q«ᔴḄᡂ3h7ᐗḄᦪ.M10Wx<50Q-M2Qᔴᡂ3h7ᐗḄᦪ40ᔴ.ூ(௃±⚪ᑖ᪆
M1QZ²=1«+5MkµQᯠ·ᑭᵨ¹ºᦪBvᦪ᪆£:M2Q»y=7¼ᐭvᦪᐵ£¾¿ᓽ&.±⚪᪆
M1QZkx+bMk¥0Q,ᵫP&,vᦪPM10,10Q,M50.6Q,ᑣ10Ã+6=1050k+b=6'\__LJio.b=llᦑ²=——x+11M10

19
2y=7——x+11=7,10x=40.
ᔴᡂ3h7ᐗḄᦪ40ᔴ.22.h7ÊËÌᳫÎ3ÏᵬஹRஹÑ@ÒÓÔÊÕÌᳫÖᳫ×ØᳫSÙÚÛÜÝÞÖᑮßÙÚÛÜÒÖᳫÚÖᳫàᐸâcÚḄÞãᙳ?ḄᵫᵬåæÖᳫᐳÖ@è.M1Qkᵨ᪛êPᑡìV@èÖᳫḄᑗ&îïð-
2@èÖᳫ·ᳫñᑮᵬÛÜḄᭆ᳛ᜧôÖᑮRÛÜḄᭆ᳛ᜧõூᫀ௃M1ஹᫀ᪆-M2ஹᳫñᑮRÛÜḄᭆ᳛ᜧூᑖ᪆௃M1ஹ᪷⚪ö÷V᪛êPᓽ&-
2ஹ᪷M1Ḅ᪛Pᑭᵨᭆ᳛ø£ᑡ£ÊÕ¾¿ᓽ&ᑖVᳫñᑮᵬÛÜḄᭆ᳛µÖᑮRÛÜḄᭆ᳛ùúᜧûᓽ&.ூ(௃M1ஹ᪷⚪ö÷V᪛êP᝞Ü:ᵫ᪛P&@èÖᳫᨵ8?&îpq;213
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1&@èÖᳫ·ᳫñᑮᵬÛÜḄᭆ᳛==-ÖᑮRÛÜḄᭆ᳛=?,848ᡠþᳫñᑮRÛÜḄᭆ᳛ᜧ.ὃ
ᑡ⊤
᪛.23.᝞ADᙊOḄᑗᑗA,ABᙊOḄ.BBC//AD,ᙊOC,AC,CCD//AB,ADD.AOBCM,CḄP,/BCP=NACD.20⚓/49⚓

201
ᑨ!PC
ᙊ0Ḅᙢ#ᐵ%▊'ᳮᵫ*2
+AB=9,BC=6,,PCḄ-.27ூ/01ᫀ௃41
PC
ᙊ஺6ᑗ42
PC=—7ூ78௃8*41
PC
ᙊO6ᑗ.ᳮᵫ᝞9*᝞COᙊON,BN,VAB//CD,.,.ZBAC=ZACD,•/ZBAC=ZBNC,/.ZBNC=ZACD,VZBCP=ZACD,:.NBNC=/BCP,VCNᙊOḄ;ZCBN=90°,ZBNC+ZBCN=90°,/.ZBCP+ZBCN=90°,ZPCO=90°,ᓽPC_LOC,=•CᙠᙊO@PC
ᙊ஺6ᑗ(2)*ADᙊOḄᑗAAD1OA,ᓽNOAD=90஺,VBC//AD,AZOMC=1800-ZOAD=90°,ᓽOM_LBC,:.MC=MB,:.AB=AC,21⚓/49⚓

21ᙠRtAAMCBNAMC=90°,AC=AB=9,MC=—BC=3,2ᵫCDEᳮFAM=J/-MC°=g_32=6P,Qᙊ0ḄS;r,ᙠRtAOMCBZOMC=90°,OM=AM-AO=672-r-MC=3,OC=r,ᵫCDEᳮFOM2+MC2=OC2,ᓽ(6P—r)+32=?.8FᙠAOMCWAOCPBVZOMC=ZOCP,ZMOC=ZCOP,AOMC-AOCP,27.OMCM60XYZZ3.pc/="OCPC'27&PC'724.᝞ᙠ\☢^ᙶ᪗%xQyBy=/4
ᙶ᪗dᑖf4ஹ8ijᱥl-x2+bx+c4ஹ8i஺qZ5@Xt஺C0_LxwC,jᱥE.(1),jᱥḄ8᪆|.(2),}A&E☢Ḅ.(3)3E,ᔲᙠ஺F}O8EWAD4c+ᙠ,஺ᙶ᪗:+Yᙠ,▊'ᳮᵫ.ூ/01ᫀ௃(1)y=-x'-3x+4(2)■☢Ḅ8(3)ᙠ஺F}O8EW}D4C஺Ḅᙶ᪗(-3,1)ᡈ(-2,2)ூᑖ᪆௃(1)✌ᐜ,ஹ8Ḅᙶ᪗ᯠPᑭᵨE%ᦪ,jᱥḄ8᪆|;22⚓/49⚓

22(2)QCᙶ᪗(m,0)(<0),ᑣEᙶ᪗(஻?,-"/-3”[+4)FOC=-wஹ0/=---3"?+4ஹBF=-m2-?>m,᪷SMBS(W/OFE-SA/OB-SABEFFS=-23"+2)2+8,¡¢F1ᫀ:(3)ᵫ}/CQ£Ὺ^¥^¦}DBEWAD4cᑣ}Q8E§£Ὺ^¥^¦.ᑖi¨©ª«¬⌕,EḄᙶ᪗ᵫEᙠjᱥ@ᑣ¢®ᵫ¡ᑡ°±,²³ᦪ.ூ´µ178௃ᙠ8᪆|¶x+4B·x=0,F¶4:·¶0,Fx=-4,.A(-4,0),B(0,4).:/(-4,0),B(0,4)ᙠjᱥl-᮱++c@,.J-16-4b+c=0,•]c=48F:b--3,c=4,jᱥḄ8᪆|*y=--3x+4.ூ´µ278௃᝞/EஹEdºQCᙶ᪗(m,0)Cm<0),ᑣEᙶ᪗(-m2-3m+4),»ljOC=-m,OF=-m2-3"?+4,"OA=OB=4,BF=-m2-3m,ᑣSMBE=S«,KAOFE_S^AOB_SZBEF23⚓/49⚓

23=Cx4-¼+4
4-7w2-3m+4
--x4x4--x4-஻7
x4-஻½-3m.222=-2m2-8m=-24¾+2
2+8,.•-490஺KJBE=DE,♦BE=OC=-m,:DE=BE=-m,.CE=^m-m=4,:.Em,4
.•Eᙠjᱥl-/_3/4@,.*.4=-nr-3m+4,8F¾=04Yᔠ⚪ÆÇÈÉᡈ=-3,.D-3,1
:ii2NEBD=9Q°,KOBE=BD=-⊈ᙠ£Ὺ^¥^¦£8஺BDE=63BD=-2m,/.CE=4+¾-2m=4-nt,:E4,4-É.•Eᙠjᱥl-%2-3x+4@.*.4-tn=-m2-3m+4,8F஻?=04Yᔠ⚪Æ,ÇÈÉᡈ=-2,.D-2,2
.24⚓/49⚓

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A,BÞᔠ.¿AF£ßàÀAMEFḄᕜ-ᨬ´43É+G,QAB×@ḄiÜtY
A,BÞᔠGQ=2.¿äצMEQGḄᕜ-ᨬ´À,ᨬ´ᕜ-.4åæçèéᶇ᪷ëÉூ/01ᫀ௃41É5:42Ép:43É7+5-V5.ூᑖ᪆௃পᵫᢚÕḄឋñWϦឋñ®FPD=PH=3,CD=MH=4,ZH=ZD=90°,ᑭᵨCDEᳮ¢åæMPḄ-:42É᝞1,MᐵABḄôõM',M'EABF,ᑭᵨi÷øqᨬù¢FFᓽᡠ,EEN±AD,ᚖýN,ᑣAM=AD-MP-PD=4,ᡠ®AM=AM=4,þÿME=MP=5,ᑭᵨᳮMN=3,NM=11,AFMs2\NEMᑭᵨzᓽ!AF"#3$᝞&2,ᵫ#2$()M*)Mᐵ,ABḄ/0)ᙠEN234ER=2,67MR8AB,)G,:;)E

25".PD=PH=3,CD=MH=4,ZH=ZD=90°,-,.MP=732+42=5\(2)᝞&1,<)Mᐵ,ABḄ/0)M',67ME8AB,)F,ᑣ)Fᓽ_ᡠq;)E

26LMNMEQGḄᨬKᕜPV*7+575.ὃ)\1.|}~ᣚᔠ⚪"2.)"3.ᨬVᡂ"4.ᢚ~ᣚ#ᢚfᡂ$"5.ᔠ⚪;6.⚪.k27⚓/n49⚓

272022-2023
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281B᜛EC^-----------------------DA.110°B.115°C.120°D.125°5.
3ᑖ$᝞&ᙠÔN/BCDS/ÕENC,8஺×8,)஺4c=8,BD=6,ᑣNB4DḄØÙV_#$6.#3ᑖ$ᙠy☢ÒÕᙶ᪗ÝS¸ÒEy=kx+3Þyᔣßyà2áᓫãP¾äÃx8,#-2,0,ᑣåḄV_#$5511A,-B.w2C.-4D.-22227.
3ᑖ$᝞&ᙠSZC=90°,/480=60°,BD<ᑖN4BC.æ8=3,ᑣ40Ó,#$A.3B.4C.5D.68.
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299.#3ᑖ$óô⚗ö442-16ᑖZøöḄùú*.10.#3ᑖ$(ØNḄûü*4,êëýáØNḄMÇþ*.11.#3ᑖ$᝞&Ḅÿ஺4ᙠyZAOB=30°,OA=2RtZXHQB12.3ᑖ᝞▲ᑁḄ4ᙠ!"#$ᦪ&'▲ḄBᙠ!"#$ᦪy=5,083,….0Z_L08,—=BCஹ4஺ᚖ34x4CஹD,ᑣ9Ḅ:;.OA413.3ᑖ᝞48=4,ZACB=75°,ZABC=45°,஺?@A8cḄCDEF4஺;3GHOOᑖJKZ6,AC(E,F,MNERᑣPḄᨬR:;.S.TU⚪ᐳ13R⚪Xᑖ81ᑖ14.5ᑖYZ[V18+VS-I-1-|1-V2|.5%—3>2%/15.5ᑖTdefg[2%-1-&30⚓/i49⚓

3016.5ᑖTᑖfkl[2+4=ᓰ17.5ᑖ᝞op@Aa,b,ᵨᙊtu3vw@A48,xyḄze4a+Ab18.5ᑖ᝞ᙠ|}Z8C஺>AB=CD,NBAC=NDCA.~[AE=CE.B19.5ᑖᡂC⚗lᵬᓫ◤~60ᜩᓫ◤~90ᜩᵫᵬᐜ20ᜩᒕḄᔠwᑣᡂ⚗lᔠw◤~ᜩ20.5ᑖR>ᨵ4!Ḅᡫ[᪻4ஹ᪻2ஹ¡᪻4ஹ¡᪻2.ᐜ4☢£¤ᒴ¦§R¨©.1R¨ª>«¬©Cᡫ©ᑮ᪻Ḅᭆ᳛;.2R¨ª>«¬©ᡫ.±²tᑣt³[R¨©ᑮḄ?CஹC¡ᑣR¨´ᔲᑣR´¶·±²¸ᓫk¹ᔲº».ᑭᵨ᪛¾ᡈᑡ⊤▊21.6ᑖ2022Ã3ᨴ5Å14Æ01ᑖᡃÈᙠÉÊËÌÍÎÏᵨzÐ'ÑÒÏÓÔÕᡂÖ×ØÙᜩ02ᢇËÌ6⚩ÜᐸÞÓḄI⚩ᖪà⍩âËÌÍÎᓣä.åzÐ'Ѫᙢ☢ᑮç/ᜐÆᙠPᜐêë/ḄìíF;30°./ïPḄðñ;6ᓟóyôõᚖ@ᓣ7.5ö÷ᑮç8ᜐøÆᙠùᜐêë8Ḅìí/DP8;45°,~zÐ'Ѫ4ᜐᑮ8ᜐḄ»ᙳüýþÿᑮ1"6=1.732,ᡈ=1.41431⚓/49⚓

31BD22.(7ᑖ)ᦻᦻ!☢#$%&'ஹ#)*+,'ஹ#-./'ஹ#012'3ᡃ*56789Ḅᐺ<6⊤>?@“Bᜧ5ᐺD℉”G@HIᐜKLBᜧD℉Ḅ▅NOPQ“Bᜧ5ᐺD℉RNSHTU”ḄᡂWᙠᐰ᪥ᐜK[\H]᪵_`᪷b_`cdeᑴᡂ᝞hijklḄmnh.A14---------------------------------------12.......................................................10.....................................................s.........................1oᔆ.......6..............1-•4S..)__ττ__°஺U1U2s3U4Uot⌾v᪷bwxyzᜐᳮtᑡᡂW~(1)_`ᡠᦪbḄᦪ3Uᦪ3U~(2)ᡧmnh“4U”ᡠᙠᡧḄᙊ@(3)vᩩmnh⊡ᐙkl(4)᪥ᐳᨵ1560DᐜK.n᪥ᨵNBᜧD℉ḄᐜKᨵ23.(7ᑖ)8ᨌsᑮ᪥ᐜxᚁ¢tᚁ£s¤£᜛(ᓟ¨)©ª«¬x(ᑖ)®¯Ḅ°ᦪᐵ²᝞hᡠ³.(1)´ª8tᚁµy©x®¯Ḅ°ᦪ⊤¶·(2)¸820ᑖ¹µº£s32⚓/49⚓

3224.(8ᑖ)᝞h¼Z8CᑁÀÁOO,4530OḄÅÆE@/BxoÉBE=BC,ÊËCE'4D()ஹD,AD=AC.(1)´Ì~403O஺ḄᑗÎ(2)Ïtan//CE=$0E=3,´8cḄ.25.(8ᑖ)᝞h~ÕᱥÎH=°/+Ø+3ḄhÙÚxÜÁ/(-1,0),B(3,0)ÞÉÚyÜÁÉC.(1)´ÕᱥÎḄI᪆·(2)Éá@ÕᱥÎÙ▲xḄoãÉäÀ8C,A)PCPHLBC()H,´á஻ḄæçèµÉáḄᙶ᪗(3)ᙠ(2)ḄᩩëtÕᱥÎH=ᯠ2+í+3îïÎC8ðñ3BòᓫᑮôḄÕᱥΔÉM@ÉáLöÉÉN@ôÕᱥΔL?ÜxøùoÉᙠôÕᱥÎúxûüoÉG,þwÉ8,M,N,G@⚔ḄᑏᑗᔠᩩḄGḄᙶ᪗.33⚓/49⚓

3326.(10ᑖ)᝞(1,*ZBC.8c1Ḅ.24W=4C,567*Z8CḄ᜜ᙊ:D,<஺>஺E஻8C7ᙊ:E,56ᓽ743Ḅ562:BCCE.(1)DNRC8=60°,BC=4,HMZ)J஺BḄKL(2)জHNOBC=2CEFBঝQtan//CB=x,—=y,H᜛ᐵ:xḄYᦪ⊤\]L(3)᝞(2,>NC_L4C72`4஺:MCEW,a*/BCḄ☢c*CEN☢cḄ6deHtanN/C8Ḅf.34⚓/49⚓

34gᫀij⚪l᪆.⌱⌱oᐳ8q⚪rᑖ24ᑖsq⚪3ᑖt1.l:—v᎔ᦪ-2.ᦑ⌱OD.2.lOz1☢{|ᐳᨵ~Ḅq1q.ᦑ⌱OC.3.lO200000=2X105.ᦑ⌱OD.4.lO£B஻/8,,JAB//CD,J.AB//CD//EF,NC=ZFEC,NB4E=NFE4,VZC=35°,N4ECFGH,.ZFEC=35°,NBAE=NAEF=9Q°-35°=55°,.-.Zl=1800-ZBAE=180°-55°=125°,ᦑ⌱OD.5.lO᝞(:E,,4BC£XC=8,BD=6,11:AB=AD,OA=^C=4,஺8=᷄=3,ACLBD,J400=90°,.AB=AD=y/OA2+OD2=V42+32=5,uBELAD,11S஺5஺=/x8X6=2435⚓/49⚓

3524:,BE='DFc?4ᙠRtZXZBE.sinN64£>===,ᦑ⌱OC.6.lO2y=Ax+3ᔣ2ᓫKᑮy=Ax+3-2,ᓽ^=+1,••Ḅ2ix7:o-2,0,0=-2H1,lk=i,ᦑ⌱OD.7.lOVZC=90°,N/8c=60°,.ZA=30°,,.•5஺ᑖNZ8C,:.NCBD=NABD=NA=30°,.BD=AD,VZC=90",/DBC=3Q°,:.BD=2CD=6,.AD=BD=6.ᦑ⌱OD.8.lO,¡¢Yᦪy=ax2+&v+cḄa>0,b>0,c>0,...£Yᦪ(¤¥¦ᔣ1⚔ᙠy¨y©,•••£¡¢YᦪḄ(¤ª<ஹ¡¤▲ᦑ⌱OC.¡.®⚪oᐳ5q⚪rᑖ15ᑖsq⚪3ᑖt36⚓/49⚓

369.lO¯]=4(«2-4)=4(a+2)(a-2),ᦑ4(a+2)(a-2).10.lO᝞(᪷±Ḅឋ³´O*BOCµῪ··,<஺>OELBC:E,•••Ḅ©¸4,.BO=4,.OE=BE=IBO=2&,ᦑ2&.11.lO᝞(<H>/'4_Lx:VZAOA'=60°,OA=OA'=2,.ZA'04=30°,,A'H=%A3=1,OH=y[3A'H=V3,.\A'(V3,1),ᦑ(V3,1).12.l:᝞(•••¤▲ᑁḄ4ᙠ»¼½Yᦪy=[1BCஹX஺ᚖ:x:CஹD,.1,*S^AOD=qx4—2,37⚓/49⚓

37'JOALOB,.ZAOD+ZBOC=90°3.ZAOD+ZOAD=90°,J4B0C=40AD,VZBCO=ZODA=90°,JRt*40Z)sRtZ\08C,..OB_3•Ã-Z'.S&OBC_/Äஹ2_9S&AODOA16.999,,S/^OBC=YgS^/0Q=x2=g,19•.”I=SÉ1VO,.,9,k_—Ëᦑgᫀ-13.lOC஺£\OF,<஺>᝞(ᑣÍ'ZACB=75°,ZABC=45°,.ZBAC=60°,/.ZEOF=2ZEAF=120°,'OE=OF,.ZOEF=ZOFE=30°,38⚓/49⚓

38J.OM^^OE,.EM=V3OA/=ÏOE,.EF=ypiOE,aOEḄfᨬqeEFḄfᨬq2`BC1ḄÑ4஺¸,...aᚖBCeḄfᨬqAHLBC:H,VZABH=45°,.AH=&AB=Òx4=2V2,ᓽADḄᨬqf2ÓL.0EḄᨬqfVL.EFḄᨬqfÔxV2=V6.ᦑÕ..lg⚪(ᐳ13q⚪rᑖ81ᑖ)14.lO¯]=3&+2-3-×+1=2Ø.15.lOl˵]5x-3>2x,Ox>\,2%—1xl˵]ᔆOx<2,ᑣ˵]ÞḄlßl

3917.lO᝞(ëCᡠ>.Q18.NíO•NBAC=NDCA,:AB஻CD,./ABE=NCDE,ᙠ*48EJ.(NAEB=NCED5OABE=OCDE(4B=CD.AABE^/\CDE(44S),.AE=CE.19.lOQîᡂð⚗òê~óᔠ>◤Hxᜩ111᪷±⚪öO—X20+(ߟ+—)x=l,606090lOx=24.gOîᡂð⚗òê~óᔠ>◤H24ᜩ.20.lO(1)J•qí÷.ᨵ4øù»ḄᡫûüOý᪻4ஹý᪻2ஹÿ᪻4ஹ᪻2,21•••ᡫᑮ᪻Ḅᭆ᳛-=ᦑ(2)᪷⚪ᑡ⊤᝞%:᪻'᪻2᪻”᪻2᪻/᪻A᪻2᪻A᪻A᪻/᪻2᪻2᪻2᪻4᪻2᪻A᪻2᪻2᪻/᪻A᪻A᪻A᪻2᪻A᪻2᪻2᪻2᪻A᪻2᪻2᪻2᪻/ᐳᨵ12,-./ᦪᐸᑮḄ23ஹᨵ8,,540⚓/749⚓

40g71ᑣ9:Ḅᭆ᳛3ᔲ=<=9:Ḅᭆ᳛3>ᡠ@ABC.21.Eᵫ⚪GHZAPD=30°,NBPD=45°,4P=6ᓟJNBDP=9Q°,DFᙠRtZ\ZP£V^APD=30°,/L=6ᓟJ/NOP=90°,cosZAPD=cos30°=M,N/஺=PP=3ᓟJPQ=P4cos30°=6XQ=3RSᓟJT,ᙠRtABPD■:NBPD=45",PD=3>/IᓟJZBDP=90°,tanZ5PD=tan450=᯿.BD=PDtan450=3VSᓟJTᦑ/8=5஺-/஺=3W-3^5.196-3=2.196SᓟJT=2196JᑣᜩYNZ4ᜐᑮ8ᜐḄCᙳ]^_2196+7.54293SJ/`TaᜩYNZAᜐᑮBᜐḄCᙳ]^_293J/`.22.ES1bcdeḄfᦪ10+25%=40SfTg1hḄᐜjᨵ40-2-10-8-6=14SfTᦑbcdeᡠHᦪḄkᦪ31hlᦪ3
2+2+2=2ShTᦑ1,2mS2ᡧopqr“4h”ᡠᙠᡧoḄᙊtu360°Xv=54°,ᦑ54m541⚓/749⚓

412(4)1560X^=78(f)aq᪥ᨵgVᜧ℉Ḅᐜjᨵ78f.23.Eপ%ᚁyxḄᦪ⊤x+஻ᑣ:EHᓽ%ᚁyxḄᦪ⊤y=0.5x-5.4(18VxW30).(2)¢x=20£ᐭy=0.5x-5.4,Hy=0.5X20-5.4=4.6.a¥¦§¨©20ᑖ«Ḅᑖ¬¨©4.6ᓟJ.24.E(1)3஺஺Ḅ®N4CB=90°,ᓽNNCE+NBCE=90°,"AD=AC,BE=BC,:.NACE=ND,NBCE=4BEC,
,NBEC=NAED,.ZAED+ZD=90°,/.ZDAE=90Q,ᓽAD1AE,,OA3µ®.AD3OOḄᑗ¸m(2)ᵫtanNZCE=*=tanNOGᑣAD=3஻=ZC,•OE=3,/•OA=a+3AB=2a+6,fBE=a+3+3=a+6=BC,ᙠRtZ\48CᵫÂÃÄᳮHAB2=BC2+AC2,ᓽ(2a+6)2=(஺+6)2+(3a)2,542⚓/749⚓

42EHai=O(ÇÈ)(12=2,***BC=a+6=8.25.E(1)É/(-1,0),B(3,0)£ᐭy=ax2+6x+3H:1nEH:N1Êᱥ¸ḄE᪆y=-f+2x+3m(2)ᙠy=-f+2x+3¥x=0,y=3,.C(0,3),¸8cÏ=Ð+3,¢8(3,0)£ᐭH3%+3=0,EHk--1,¸BCḄE᪆y=-x+3,ÒLÓPE_Lx×ØG,ÚBCØÒE,᝞rP(f,-P+2f+3),ÛljE(f,-f+3),PE—(-P+2f+3)-(-f+3)—~P+3/,VC(0,3),B(3,0),ZOSC=45°,543⚓/749⚓

43PE_Lx×,.-.ZBEG=45°-Z.PEH,.♦.ß“PE-Ὺuáuo,.PH=^PE=^-(-?+3z)=â(z-|)2+ᢤ:ὃVO,a9V2315••¥t=5•?//ᨵæN,çP('—)m8249ᡈ315aP”Ḅæ3éçÒLḄᙶ᪗(í—);824(3)ᵫ(2)ïNO8C=45°,ß80஺3-Ὺuáuo,¢Êᱥ¸ð=-f+2x+3ñò¸CBCó3Víᓫlõ¥Ø¢Êᱥ¸ᔣ÷Có3íᓫløᔣ%Có3íᓫlc.315•ùÊᱥ¸ð=-(x-3)2+2(x-3)+3-3=-X2+8X-15,ÒP(5,1)úûÒM93(-,-),24JùÊᱥ¸ð=-+8%-15úü×3¸x=4,93G(ý-m2+Sm-15),N(4,஻)

44
m+=4+3r3=,I-m2+8m-154-7=n+055••G-m7311s5s!"ᡠ$GḄᙶ᪗'-
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