2022-2023学年上海市杨浦区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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62022-2023
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17(Ill)#ᨵজঝḄNᙠᦪ⊤ᩭ.(IV)#ᨵḄNL3

18.•.>ᦪ-------=362(3)..•ᙠ40G!HI35ḄᦪKL30%,.•.200x30%=60(P)!ᵫ᪵ᦪ!RS᪥ᔜVWHI35ḄᦪKLX30%,ᑣSᑜ[\200P]^H!_`[\60P35I.a⚪ὃd$ᩩfgS!ᡧfgS!ijᵨ᪵RS=l!mn⚪op⚪Ḅᐵr.21.᝞!ᙠaABC!AB=AC,iAByzḄ00ᑖ|}BC,AC~5D,E,D஺0ḄᑗDF,~AC5F.(I)DF±AC(2)OOḄz4,NCDF=22.5°,▢ᑖḄ☢.ூᫀ௃(1)᪆(2)4—8.ூᑖ᪆௃(1)஺D!᧕"NABC=NODB,ᵫ=᧕"N4BC=NACB,¡¢$ᣚ"NODB=NACB,ᑭᵨ¤¥Ḅᑨ§¨OO///C,ᵫᑗḄឋª¨஺«_L஺஺!¨"®¯(2)OE,ᑭᵨ(1)Ḅ®¯¨48C=NZC8=67.5°,᧕"NB4c=45°,¨"ZAOE=90°,ᑭᵨᡧfḄ☢²³´µ¶fḄ☢²³¨"®¯.ூ௃(1)0஺!:19⚓/=52⚓

19ZABC=NODB,VAB=AC,.NABC=NACB./.ZODB=ZACB,.♦.OD஻AC.DFp00Ḅᑗ!ADFIOD..*.DF±AC.(2)®OE,VDF±AC,ZCDF=22.5°./.ZABC=ZACB=67.5°,AZBAC=45°.VOA=OE,.,.ZAOE=90°.•••0஺Ḅz4,¹Sᡧf40E=4!^>MOE=S!▢=4%-8.⚪º⌕ὃd$ᑗḄឋª!ᡧfḄ☢}µ¶fḄ☢²³!ᙊᕜ¶§ᳮ¡!"〉ÀḄÁÂ!ᑭᵨᑗឋª´ᙊᕜ¶§ᳮ!ᦪfpa⚪Ḅᐵr.22.᝞!¹⁂ÄÅ>5ÆᛞPḄᓅÉÊ66.1஺Ëᔣ!ÍÎÆᛞ120ÄÏḄAᜐ!ÐÑᓭËᔣÓ¥¹ÔÕ6Ö,ᑮ×>5ÆᛞPḄᓭÉÊ45஺ËᔣØḄBᜐ!BP´BAḄÙ(®ÚÛ᦮ᦪ).Ýὃᦪsin66.1°~0.91,cos66.1°~0.41,tan64°~2.26,ÞÛ1.414.ூᫀ௃BPḄÙ154ÄÏ!BAḄÙ158ÄÏ.ூᑖ᪆௃᝞5C.ᙠRtZi/PC!"PCஹ/CḄÙ!ᙠRtZkPCB"«3ḄÙ!+àáâã⚪.:20⚓/=52⚓

20ூ௃᝞PC_LAB5C.ᵫ⚪oNA=66.1°,ZB=45°,PA=120,PCACᙠRtAAPC!sinA=-----,cosA=------,PAPCPC=PAsinA=120*sin66.1°,AC=PA*cosA=120*cos66.1°ᙠRt^PCB!VZB=45°,APC=BC,PC120x0.91/.PB=sin45°y/2=154.AB=AC+BC=120«cos66.1°+l20sin66.1°=120x0.41+120x0.91-158.BPḄÙ154ÄÏ´BAḄÙ158ÄÏ.⚪ὃd$y¶µ¶fḄÞᵨ-Ëᔣ¶ã⚪!ÓÄḄä▭ã⚪!)y¶µ¶fḄæᐵçèᨵ!l#$ᦪÞᵨ5ä▭êḄëì.23.í᪶᪻ðñSᑜðñ,87ðòª᪶᪻ᐳ30ô!õç7ð᪶᪻ḄVö¢ᑖ|800ᓟø/ôஹ1000ᓟø/ô!ᦈ[úûᑖ|p4.2ᐗ/ᓟøஹ4ᐗ/ᓟø.(1)ýᦈþ7ð᪶᪻ḄV=ö¢25800ᓟø!ᑣ4ஹ87ð᪶᪻ᔜðñ$&ÿ
(2)4᪶᪻஺ᐰᦈᦈᐭwᐗwaḄᦪᐵ.⌕ᨴ᪶᪻Ḅ☢#$ᨵ&'8᪶᪻Ḅ()*+4ஹ8-᪶᪻ᔜ/&0Ḅᦈᐭ1/
1/2/&ᐗ
ூ456ᫀ௃(1)4ஹ8-᪶᪻ᔜ:21<9.(2)/ஹ8-᪶᪻ᔜ10ஹ200Ḅᦈᐭ1/1/2113600ᐗ.>21⚓/52⚓

21ூ@A௃B⚪ᑖ᪆F(1)/HIX8HI(30-X)᪷KLMḄNMᐵOP(ᐗQRA(ᐗQRᓽOA6T(2)/HI஺2HI(30-a)᪷K☢#ḄᐵOP஺*(30Y),AOP஺ḄVWY᪷K⚪ZPᑮw<஺ḄᐵᑭᵨᦪḄឋ_ᓽOA6.AFপ/᪶᪻:xᵫ⚪ZOP800x+1000(30—x)=25800,APx=21,30—x=9.ᓽ4ஹB-᪶᪻ᔜ:21<9.(2)ᵫ⚪ZOPm=800aX4.2+1000(30-a)X4=120000—640஻ᓽ᝞aḄᦪᐵ120000-640&FadF(30-a),Aa^lO,.,.fa=100>=120000—640஺VPWh0m=113600,30-a=20,ᓽ/ஹ8-᪶᪻ᔜ10ஹ200Ḅᦈᐭ1/1/2113600ᐗ.ijFk⚪ὃm:(ᐗQRḄnᵨ<ᦪḄnᵨA6k⚪Ḅᐵo2p5⚪Zqᡠs⚪◤⌕ḄᩩvᑭᵨᦪḄwxឋA6s⚪.24.᝞y1,ᙠ{☢|}ᙶ᪗iO2ᙶ᪗iX8C஺2+ஹ4Ḅᙶ᪗(-3,4),iCᙠxḄ4)|/Cy'i஻y'i3M.y1y2(1)ABCOḄT(2)|ZCḄA᪆T(3)ii/ᢚ/3CQᔣ2ᓫ/Ḅᔣi஺ᒴ-/XPMBḄ☢#5(▭0),iḄ0জf022⚓/52⚓

22315f5——t+—A023⚓/52⚓

23113315S=xBP-HM=zrx-(5-2f)=--Ý(T22224f3Vzs50BP=2t-5/?=-,f22!,τ5ஹ5255=-BP'h=—x—(2z-5)=—t-----222243150—t------24⚓/52⚓

24ôIIöᑖiᦈᙠXḄ4)ஹiᦈᙠXḄ÷)-ÅÆ᪷K·¸¹ᳮᑡòó;ôIIIöᵫôIöOùPA=PM,iMḄᙶ᪗ô0,xö,᪷K·¸¹ᳮᑡQRxḄW.@AFôIöåAN_LPM'N,ᑣAOMN2ýAN=OM=3,MN=OA=2,2AMḄᚖ|{ᑖT.PA=PM,ᙠRtAAPNAN2+PN2=AP2,ᓽ32+y-22=y2,’13••PḄᙶ᪗3,——4ᦑᫀ3,"4II"Mᙠx&Ḅ'()*+ᙠRtAAPNAN2+PN2=AP2,ᓽx2+y-22=y*2,y=-^-x2+l,1ᳮ"Mᙠx)Ḅ3()*+x,y45Ḅᐵ789:=ᔁ/+1,.x,y45Ḅᐵ789$2+1IIIᵫIAB,PA=PM,⌕DAMPAEFGHIJ◤MA=MPᓽA:AḄᙶ᪗0,2,MḄᙶ᪗0,x,,",AM=V22+X2,M-^-X2+1=/2+X2,12X=±2A/3-...NMPAEFGHI+MḄᙶ᪗273-0ᡈQ2R0.S25⚓/V52⚓

25WXY⚪ὃ\]^I_ᙶ᪗`aᚖcdᑖ`ḄឋgEFGHIḄᑨijkiᳮḄlᵨ,nopq`᪀⌼cHGHItuvᵨjkiᳮw9Y⚪Ḅᐵx.2022-2023
ᩰὃᦪ⚗ᓣ⚪Qஹ⌱Q⌱Yᜧ⚪ᐳ6⚪}⚪4ᑖ4ᑖ24ᑖ1.~ᑡᔜᦪ9ᳮᦪḄ9A.cos60°B.jjC.(1cmḄᙊᕜD.ᡃ2.~ᑡv'Ḅ9A.m^n-2mB.win
3-mn3C.2/=D.M4-w2=m33.3x>-3y,ᑣ~ᑡᨵE8QiᡂḄ9A.x+y>oB.x-y>0C.x+y<0D.x-y<04.᪥120Qᕜᵨ▅᜜Ḅ+Ḅ⚣᳛ᑖc¡^᝞^ᡠ¤.ᐸ▅+S26⚓/V52⚓

2698-10§+Ḅ⚣ᦪ¨⚣᳛ᑖ©9⚣᳛0.15(10.1250.10U().075().0500.0251012§+ᦈ<¬A.15,0.125B.15,0.25C.30,0.125D.30,0.255.~ᑡ^I9°±^IḄ9ூ6.᝞^(1ḄᙊOµ_(3Ḅᙊ஺2·ᑁᑗ᝞º(2Ḅᙊ_ᙊOµ¨ᙊ02»·ᑗ¼½¾᪵ḄᙊḄ¬ᦪ9ÀஹÁÂ⚪Yᜧ⚪ᐳ12⚪}⚪4ᑖ4ᑖ48ᑖ7.aa+b-ba+b=___.8."a<0,b>0+.ᓄÈXJa^>=.9.ÊᦪËJ-+J775ÍÎÏxḄÐÑÓ9___.10.᝞ºÔÕÖÊᦪ×=&Ḅ^Ù/2,Ú_83,A,¼½FḄÑE___________.X11.GÝᨵÞÝឋ©·1Ḅᭆ᳛9.12.25à110áâãäḄᡂåæV᝞~⊤XÝᦪ1234510S27⚓/V52⚓

27éᦪ15825101720¼½ãäéᦪḄàᦪ9.13.êëì*íÍîï*⌶ñ⍝óôõöï÷î]Qaóᑮ᪥ᐳᵨ+15ᑖâ.᝞ºùíÍîïḄdᙳûü9}ᑖâ250ýöï÷îḄdᙳûü9}ᑖâ80ýùþÿ᪥Ḅ2900ḄxᑖᑡḄ.14.ᔣ+"^=.15.%&'஻Ḅᑁ*140°,ᑣ஻=.16.᝞.ZXABCZA=80°,ZB=40°,BCḄᚖ01ᑖ23AB45D,ὶ7DC.᝞8AD=2,BD=6,AADCḄᕜ:.17.᝞.';49CḄ:2,5Aஹ8ᙠ>?8ḄᙊA5஺ᙠᙊᑁC'AA5cD5A⌮┐┐GHI5஺JKᙠᙊAGH*Ḅ'ᑗM18.Iᐵ4xḄOᐗQJax2+bx+c=0ᨵSᦪ᪷VᐸOX᪷YOX᪷Ḅ2Z[\“Z᪷᝞8ᐵ4xḄOᐗQJx2+(m-2)x-2m=0“Z᪷”mḄM._ஹ`a⚪(dᜧ⚪ᐳ7⚪gᑖ78ᑖ)19.ᐜᓄklmMn±zl^x'-2x_3_L+x—5/2+1•x—1x"+2x+1x—\2x2-y=320.`o.22x-y2=2(x+y)21.%&n᝞.ᙠp45CDDC//AB,AD=BC,BDBC/ABC,ZJ=60°.q28⚓/t52⚓

28mn(1)mNCDBḄuᦪv(2)I/஺=2wxmy*22஺Ḅ:zpZ8C஺Ḅ☢|.22.}&~BஹC_ᙢᙠOᩩA/ᙢᙠ8ᙢḄ'ᓭ3ᓟᜐᵬஹᑖ/ஹBᙢᔣ'ᔣḄḄᙢCᒴ0ᑖzᙢḄs(ᓟ)ᡠᵨḄf(~)Ḅᦪᐵ᝞.ᡠ.(1).Ḅ2h(“ᵬ”ᡈ“”)Ḅᦪ.஺ᙢᙠ8ᙢḄ'ᔣᓟᜐv(2)ᐜᑮCᙢmᵬᑮCᙢḄ¡v(3)᝞8u᠒Ḅᙠ£⍗¥¦§¨V©ᐜᑮὅ«1~ᑮCᙢm¨¥Ḅu.23.%&n᝞.ᙠw4885Gy*2NCḄ5¬5GḄ02EFᑖ3N8ஹCD45EஹF,¬5GḄ02MNᑖ349ஹ8c45MஹN,
NAGE=NCGN.(1)mnENFN1v(2)IENFM®mnBE=BN.1,24.᝞.ᙠ1☢0*ᙶ᪗±ᱥ2V=+6X+Cx³345AB,y³345C,02´x+454ஹC,5P±ᱥ2Aµ4024CAḄOX¶5.(1)m±ᱥ2Ḅ⊤¸vq29⚓/t52⚓

29(2)᝞.ICP///OmNA4CḄ'ᑗM;(3)Iº/Pஹ40»Ḅ1qX⚔5ា¾¿ᙠ±ᱥ2AmÀ5PḄᙶ᪗.25.᝞.ᙠp/BCZ)ADUBC,AB=DC=5,AD=\,BC=9,+ஹPFGBCHIJ+ஹ,ÁPH±DC,ᚖÂHᙠ஺CAº5Pᙊô஻>?Äᙊ3Å2´845E.(1)IᙊP¬5/mᙊ´Ḅ>?v(2)ᑖὶ7zE/,LMBEs^CEHN,º5BᙊÕ>?Ḅᙊ8ᙊP£3,Èmᙊ8Ḅ>?ÉḄÊMÌv(3)CÍÎÏÐ02E"Ñᢚ3BC45ÓÈÔ¬ÕÖ×Ø2E4zE´Ḅ©MÙMmÀÙM.q30⚓/t52⚓

302022-2023
ᩰὃᦪ⚗ᓣ⚪Oஹ⌱O⌱Ûdᜧ⚪ᐳ6⚪Ü⚪4ᑖgᑖ24ᑖÝ1.ßᑡᔜᦪáᳮᦪḄÛÝA.cos60°B.jjC.>?1cmḄᙊᕜ:D.ᡃூ'ñaᫀ௃Cூô`௃ᑖ᪆n᪷ö“áᳮᦪ”ḄÙ÷øᑨúᓽ.ô`nA⌱⚗ýcos60°=J,ᡠºA⌱⚗Ḅᦪᨵᳮᦪÿᨵ
⌱A2B⌱⚗I▲ᦪᨵᳮᦪᡠᨵ
⌱BC⌱⚗1cmḄᙊḄᕜ#2%cm,2'(ᳮᦪᡠ)⌱CD⌱⚗ᡃ=2,2ᨵᳮᦪᡠᨵ
⌱D.ᦑ⌱C/0123ᳮ4ᳮᦪḄ561“▲ᨵᦪ89ᳮᦪ”4;<⚪Ḅᐵ?.2.@ᑡBC23ḄDEA.mḛ=2tnB.
ZHM3-mn3C.-m6D.m
,+஻/=m3ூ23;ᫀ௃CK31⚓/O52⚓

31ூQ4௃A.RSᦪTḄUVSᦪᨵWᢣᦪYZᦑAᨵ[ᔠ⚪]B.^ḄU_`U_Ḅ^ᦑBᨵ[ᔠ⚪]C.aḄU_SᦪᨵWᢣᦪYUᦑC[ᔠ⚪]D.RSᦪbḄ◀VSᦪᨵWᢣᦪYdᦑDᨵ[ᔠ⚪]ᦑ⌱1C.<⚪e⌕ὃhijḄU_RSᦪTUVk◀V`lmnopq4;<⚪Ḅᐵ?.3.r3x>-3y,ᑣ@ᑡᨵ`qt5ᡂvḄDEA.x+y>0B.x-y>0C,x+y<0D,x-y<0ூ23;ᫀ௃Aூᑖ᪆௃᪷zᨵ`qḄឋ|)};ᫀ.ூQ4௃41~◀3,}x>_y,~Z}x+y>0,ᦑ⌱1C.<⚪ὃhiᨵ`qḄឋ|4⚪Ḅᐵ?noᨵ`qḄឋ|᪷zᨵ`qḄឋ|4.4.᪥120tᕜᵨ▅᜜ḄḄ⚣᳛ᑖ_᝞ᡠ.ᐸ▅8N10Ḅ⚣ᦪk⚣᳛ᑖDEA.15,0.125B.15,0.25C.30,0.125D.30,0.25ூ23;ᫀ௃DூQ4௃ᑖ᪆1᪷z⚣᳛ᑖ_ḄᦪzkOᦪ120Cᓽ)¡¢ᑨ¤.Q41ᵫ⚣᳛ᑖ_)l1tᕜᑁᵨ▅Ḅᙠ8-10¨©Ḅ1⚣᳛1©ª=0.125,«©K32⚓/O52⚓

32ª2,.tᕜᑁᵨ▅Ḅᙠ8-10¨©Ḅ⚣᳛=0.125x2=0.25,¯•.•Oᦪ120±tᕜᑁᵨ▅Ḅᙠ8-10¨©Ḅ⚣ᦪ=120x0.25=30.²³ᡠ´⌱⚗Dᦪz23.ᦑ⌱D./01<⚪4⚪Ḅᐵ?ᨵ~/1D1E⌕µ¶·¸³Ḅᦪz“⚣᳛1©ª”Ḅ¹«ᨵ⚣᳛D2E⌕º¶ᔜ¼Ḅ⚣ᦪஹ⚣᳛kOᦪ¾Ḅᐵb.5.@ᑡ¿ÀÁ¿Ḅூ௃ூ23;ᫀ௃Bூᑖ᪆௃᪷zÀÁ¿ḄᭆøÀÁ¿ÄÀÁ¿¿ÅÀÁÆÇ180ÈÉÄÊËᔠ,ᓽ)4⚪.AஹᨵÀÁ¿ᦑ<⌱⚗┯Í1BஹÀÁ¿ᦑ<⌱⚗23CஹᨵÀÁ¿ᦑ<⌱⚗┯ÍDஹᨵÀÁ¿ᦑ<⌱⚗┯Í.ᦑ⌱B.ὃ/1ÀÁ¿.ூQ4௃ÎᙠÏÐᐭQ4Ò6.᝞1ḄᙊOiÄ3Ḅᙊ஺Yᑁᑗ᝞×2ḄᙊÄᙊ஺kᙊ5YᑗØÙ¨᪵ḄᙊḄ(ᦪDEK33⚓/O52⚓

33()J02A.1B.2C.3D.4ூ23;ᫀ௃CூQ4௃ᑖ᪆1Ü0ÝCh¡ß0Q2³t/ᙊá¡t2Ḅᙊâ¨(ᙊãäåÄᙊ0Ýᙊ02R᜜ᑗḄæç(ᓽᙊ03)êëᔣíîïðñ¿ò(ᙊḄᑖ᪆ᓽ)}ᑮ[ᔠ⌕ḄᙊḄ(ᦪ.Q41᝞@(1)ô2ḄᙊRkᙊ0Ýᙊ02᜜ᑗõᙊᙠᙊ03Ḅæç(2)ô2Ḅᙊkᙊ0”ᙊ02ᑁᑗõᙊᙠᙊ04Ḅæç(3)ô2Ḅᙊkᙊ01᜜ᑗ«kᙊ஺2ᑁᑗõᙊᙠᙊ05Ḅæç²³ᡠ´[ᔠ⌕Ḅ2Ḅᙊᐳᨵ3(.ᦑ⌱C./01÷ᢝᙊ6ஹᙊ02ḄæçᨵùßOQ2³t(/ᙊá¡t(2ḄᙊðñᐸãäúíîïÜûÄᙊ஺ஹᙊ02Ḅæçᐵbò(ᙊḄᜧᓽ)}ᑮ<⚪ᡠ;ᫀ.ýஹþÿ⚪(ᜧ⚪ᐳ12⚪⚪4ᑖᑖ48ᑖ)7.a(a+b)-b(a+b)=.ூᫀ௃(a+b)(a-b).ூᑖ᪆௃ᐜ(஺+6),ᯠ#$%#᦮ᳮᓽ).ூ*+௃a(a+b)-b(a+b)=(a+b)(tz-b)..34⚓/352⚓

34⚪ὃ78ᑖ+9:;<⚗ᓄᡂ@;᦮ḄBCḄDEFᑖ+.ᑖ+GᵨḄIJᨵLজ$JLঝJOঞᓝRSBJOটᑖUᑖ+J.ᑖ+VWᑖ+ᑮ;YZᨵ[\ᑖ+].8._Q<0,6>0b.ᓄcLJa2b=ூᫀ௃—ay[bூ*+௃ᑖ᪆Lᢥ᯿fg᪷ḄSᐵjkJᑣmឋopqrkᓽ).*+L*.*a<0,bு0,**•y]a2b=|a|"\/6=-a>[b-ᦑᫀ.-a-JbxyLz{fg᪷Ḅ|}ឋo~+⚪ḄᐵL(1)U=«.▲a>0,b>0)(2)a(a>0)=0(a=0).-a(a<0)9.ᦪy=—'ߟ+Jx+2,xḄ%~_____1-xூᫀ௃x"2xrlூ*+௃ᑖ᪆L᪷ᑖmfg᪷ᨵḄ⌕ᑡᐵXḄZᨵU+ZᨵUᓽ)¡XḄ%.*+LVy-----Jx+2ᨵ1-xfl-x*OS§+¡L¨2-2¨1.x+2>0.35⚓/352⚓

35ᦑx2-2xw1.xyL⚪+⚪Ḅᐵ~◤ªL⌕ᦪ«=¬:+ᨵXḄ%◤®b¯°1-X;ᩩ²L1—xwOmX+2N0,fὅ´:Zᨵ).10.᝞¶·¸¹ᦪy=&Ḅº»x4
2,ᑘ½¾8
3,"½¿ÀÁḄ.xÂ3ூᫀ௃:2ூ*+௃ᑖ᪆LᵫÄÅᩩ²᧕¡2yl=k,3y2=k,ᵫÇ)¡2yi=3y2,Dᓽ)¡bḄ.*+L:·¸¹ᦪÉ=Ḅº»xA
2,yi¾B
3,y2½,x/.2yi=k,3y2=k,.•.2yi=3y2.2L=32-3ᦑᫀ2xyLÌÍLÎxAÏabmxBÏÐ஻½ᙠ®:;·¸¹ᦪy="Ḅº»Óᑣ=஻~x+Ô⚪Ḅᐵ.11.ÕÖᨵ°Öឋ×S®Ḅᭆ᳛~.ூᫀ௃1ூ*+௃ᑖ᪆Lᵫ⚪mÚÛÜ▭)ÅL”Õ;Ößàᨵ°;ÖḄឋ×~S®Ḅ”ᓽ)¡ᑮᡠᭆ᳛1.*+L•..ÕÖḄឋ×âᙠ|})[LÏ1ÕÖY~“ᵱឋ”OÏ2ÕÖY~“᝕ឋ”OÏ3ÕÖḄឋ×~“2ᵱ1᝕”OÏ4ÕÖḄឋ×~“2᝕1ᵱ”.36⚓/352⚓

36...ÕÖßàᨵ°;ÖḄឋ×~S®Ḅ■•P<ÕÖᨵfÖtwtm>=1"xyLᑡ⚪ᡠᨵḄ)[æ¶~+⚪Ḅᐵ.12.25ç®è10éêëìḄᡂíî3᝞}⊤LÖᦪ1234510gᦪ15825101720¿ÀëìgᦪḄçᦪ~.ூᫀ௃20ூ*+௃ᑖ᪆L᪷çᦪḄpqrkᓽ)¡ᑮðUᦪḄçᦪ.*+LᵫçᦪḄ)ÅðgëìgᦪḄçᦪ~ñð25ç®èḄëìgᦪᢥòóᑮᜧ᣸ᑡ#Ḅ.12;m13;ᦪḄõᙳᦪ•.•ᵫ⊤÷Ḅᦪᑖ᪆)ÅðUᦪᢥòóᑮᜧ᣸ᑡ#Ḅ.12;m.13;ᦪY~20,ðUëìgᦪḄçᦪ~20.ᦑ20.xyL⚪ὃ7Ḅ~ø᪵:UᦪḄçᦪ+⚪Ḅᐵ~úû''çᦪ"ḄL“9:UᦪᢥòóᑮᜧḄüý᣸ᑡ#ÎᦪUᐳᨵ᜻ᦪ;ᦪᑣᨬ
ᦪᦪḄᦪᦪᦪḄᦪᏔᦪᑣᨬ
ᦪḄᙳᦪᦪḄᦪ”.13.⌶"⍝$%&'()*$ᑮ᪥ᐳᵨ/15ᑖ1.᝞34Ḅᙳ567ᑖ12508'(Ḅᙳ567ᑖ180849:᪥Ḅ$;29008<4'(Ḅ/
xᑖ1=>?ᑡAḄB;.ூDEFᫀ௃80x+250(15-x)=2900ூIJ௃ᑖ᪆L᪷⚪OP(QᔜᡠT$;⊤VAᩭX(QᡠTYZ;29008ᑡAB;ᓽ?.IJL<4'(Ḅ/
xᑖ1᪷⚪O?\L]37⚓/Y52⚓

3780x+250(15-x)=2900.ᦑFᫀ80x+250(15-x)=2900.bcLdef⚪ḄghᐵjL'(Ḅ$;+lḄ$;=2900J⚪Ḅᐵm.14.nop43஺ᔣhB+s+জ=.ூDEFᫀ௃ADூIJ௃ᑖ᪆L᪷“ᔣhwx”Ḅyzp{ᑣ|}xᓽ?.IJL᝞~ᡠᵫᔣhwxḄyzp{ᑣ?\LAB+BC+CD=AC+CDUUIX=AD-,,_.uuurᦑFᫀZZ).bcLᳮJᔣhwxḄyzp{ᑣDEJFf⚪Ḅᐵm.15.D஻opḄᑁz140°,ᑣ஻=.ூDEFᫀ௃9ூᑖ᪆௃᪷op7ᑁzᐸḄ᜜z⊡ᑣD஻opḄ7᜜zḄ6ᦪ=180°-140°=40°,ᯠ᪷opḄ᜜zQ360஺ᓽ?\ᑮnḄ.ூIJ௃JL•••D”opḄ7ᑁz140஺.,.DnopḄ7᜜zḄ6ᦪ=180஺-140஺=40஺3604.n=——=9,40ᦑ9.f⚪ὃ)opḄ᜜zQᳮLopḄ᜜zQ360°.]38⚓/Y52⚓

3816.᝞AABCZA=80°,ZB=40°,BCḄᚖᑖABbD,ὶDC.᝞3AD=2,BD=6,=>ADCḄᕜ¢.ூDEFᫀ௃14.ூIJ௃£⚪ᑖ᪆LᵫBCḄᚖᑖABbD,?\CD=BD=6,¤ᵫgo¥gz?¦\NBCDḄ6ᦪ§¨¦\NADCḄ6ᦪᑣ?ᑨ4ACDgῪyzp§¨¦\Fᫀ.£⚪J᪆L•BCḄᚖᑖABbD,CD=BD=6,r.ZDCB=ZB=40o,/.ZADC=ZB+ZBCD=80°,/.ZADC=ZA=80°,/.AC=CD=6,.,.ADCḄᕜ¢LAD+DC+AC=2+6+6=24.ὃbL1.*ᚖᑖḄឋ¬2.gῪyzpḄᑨឋ¬.17.᝞DZ3CḄo¢2,bAஹBᙠ¯°⊈Ḅᙊb஺ᙠᙊᑁ³D´bA⌮/┐┐·¸¹b஺º»ᙠᙊ/·¸zḄDᑗூDEFᫀ௃½3ூᑖ᪆௃¾¿À✌ᐜ¦ANDACḄᜧÄ|¨¦A·¸Ḅz6ᓽ?\AFᫀ.ூIJ௃᝞ᑖÅÆÇOAஹOBஹOD]39⚓/Y52⚓

39VOA=OB=72AB=2,/.OABgῪzyzpAZOAB=45°Èᳮ?ÉLZOAD=45°,NDAB=90஺VZCAB=60°,ZDAC=90°-60°=30°,...·¸zḄDᑗ3,3ᦑFᫀÊ.3Ë⚪ὃgoyzpḄឋ¬·¸Ḅឋ¬bᙊḄÌᐵjJzyzpJ⚪ᐵmᙠ¾¿À.18.¹ᐵxḄᐗκB;ax2+bx+c=0ᨵÐᦪ᪷Ñᐸ᪷Ò᪷Ḅ2Ó/ÔÕ“Ó᪷B;᝞3ᐵxḄᐗκB;x2+(m-2)x-2m=0“Ó᪷B;”=>mḄ.ூDEFᫀ௃-1ᡈ-4ூIJ௃ᑖ᪆L<“Ó᪷B;”—+(□2Ú—2Û=0Ḅ᪷a,ᑣÒ᪷2a,ᵫᐗκB;᪷jᦪḄᐵj?\a+2a=-(஻?-2),2a-a=-2஻?ᵫË?ᑡAᐵmḄB;JB;ᓽ?¦\mḄ.IJLᵫ⚪O<“Ó᪷B;”+(Û2)Þ—2□=0Ḅ᪷a,Ò᪷2a,ᑣᵫᐗκB;᪷jᦪḄᐵj?\L]40⚓/Y52⚓

40a+2a=(Û2),2a•a=-2m,ᓄà᦮ᳮ\L஻?2+5஻2+4=0J\â=-4,m=—1.2ᦑ-1ᡈ-4.bcLf⚪J⚪Ḅᐵmã៉ᐗκB;᪷jᦪḄᐵjLᐗκB;bc+bx+c=0(஻w0)Ḅ᪷ᑖÅaஹ஺ᑣ஺+᜛=——,«/?=—.aayஹJF⚪(fᜧ⚪ᐳ7⚪çᑖ78ᑖ)19.ᐜᓄàX¦L±zl^x'_2x-3J,,x=6+l.+x-1x+2x+1x—I2ூDEFᫀ௃——D.X—1ூIJ௃ᑖ᪆LᐜᢥᑖéḄᐵwx{ᑣ³êéᓄàXëìᢥκ᪷éḄᐵwx{ᑣ|}xᓽ?.x-3(x+1)21(x+l)(x-l)(x-3)(x+1)x-\11--------1--------x—\X-12¹x=J5+i/;êé=75=”-bcLf⚪ὃḄᑖéḄᓄà¦î⚪ã៉ᑖéQκ᪷éḄᐵwx{ᑣDEJ⚪Ḅᐵm.21ï=320.JB;.x2-y2=2(x+y)]41⚓/Y52⚓

4131Y1'2=ôX3=-Tx=ூDEFᫀ௃\,.ீ/.%=—135[%=5Ú=-üூIJ௃ᑖ᪆LPêB;Ḅ]ÎB;ýþᑖJ"éÿ
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hij8஺Ḅk5WX48COḄ☢n.'BE42⚓/p52⚓

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៉ῪWXḄឋ5iiXD30஺ḄE43⚓/p52⚓

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46C,tx+4ZஹC,nᱥyz"4Cy{ḄW|}.(I)%nᱥḄ⊤+(2)᝞,CP///O.%NRiCḄ0ᑗ+(3),ஹNOḄ)*'(L'|⚔ាᙠnᱥy.%E.Ḅᙶ᪗.ூ012ᫀ௃(1)nᱥḄ⊤y=-+/-x+4(2)tanZPAC=y(3)Ḅᙶ᪗J5-39.ூᑖ᪆௃ᑖ᪆(1)ᵫ⚪᧕?AஹCḄᙶ᪗ᑖ(Y,0),(0,4),ᙶ᪗ᐭnᱥy=-+/+6x+cᑡ{¤¥8?bஹCḄᓽ@%?nᱥḄ8᪆+(2)᝞K§PH_LAC"H,«¬OP,ᵫᩩ=ᐜ%?PC=2,AC=4&S“PC@%?PH=J5,³ᵫOA=OC?ᑮN=45°,CP஻OA@?/PCA=45°,ᓽ@?ᑮCH=PH=¶ᵫE@?AH=3g᪵ᙠRtZ\APHᵫtanZPAC=——ᓽ@%?ᡠ%2ᫀ¿+AH(3)᝞,'(AOPQÁᔠ⌕%Ḅ)*'(.ᑣE.PQ=AO=4,RPஹQᐵ"nᱥḄÄqx=-lÄᵫE@?PḄÆᙶ᪗-3,ᐭnᱥ8᪆ᓽ@%?E.ḄPḄᙶ᪗.:8(1):y=x+4AஹC,AᙠxqyCᙠyqy...Aᙶ᪗J(-4,0),Cᙶ᪗J(0,4),SnᱥA,CL47⚓/O52⚓

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51(3)ᙠᙊP'9%FᐵEH<=Ḅ%G,ὶ?EG,@PQ_LEGG,HNJ_BCN,ᑣEG=EF,Z1=Z3,EQ=QG,EF=EG=2EQ.AZGEP=2Z1,VPE=PH,N1=N2,AZ4=Z1+Z2=2Z1,AZGEP=Z4,AAEPQ^APHN,EQ=PN,ᵫ(1)!"#PH=3k,ᑣHC=4k,PC=5k,34sinC=—cosC=—55,416k,312sA.NC=4'•)=——NH=4b•)=——5555,,16k9.PN=5b-----=-k5518/1o4.EF=EG=2EQ=2PN=—k,EH=yjHN2+EN2=tuk55%v-w⚪6)⍝z{ᙊஹᐰ}~`ஹᳮஹ7~`1┦~`ᦪḄᔠឋ⚪⚪ᜧ⚪Ḅᐵ6@᝞ᡠḄ៉7ᐵ`Ḅឋ1ᑨ.e52⚓/h52⚓