【中考数学】2022-2023学年山东省济南市专项突破仿真模拟卷（一模二模）含解析

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ὃᦪ௃2022-2023ḕᓭ⚗ẚᔁIᔁ⌱⌱ᔁᑖ-----------------ஹᓫ⌱⚪1.ᑡᔜᦪ2Ḅᦪ.A.-3B.-1C.0D.12.᝞#ᡠ%Ḅᱥ'()☢+ᑮḄ-☢#./.16000ᵨ234ᦪ56⊤%8A.0.16xl04B.0.16xl05C.1.6xI04D.1.6xl054.᝞#>ᙽ@45஺BḄCBDBEḄCB⚔GHᙠCJḄKL᝞MNl=33஺PQ/28C.67°D.60°5.ᑡ#.UVWX#.YZWX#.ḄBO஺

1ூὃ௃_`6.a8bbcd᪥fgᕒijklᡠᵨmᦪḄnoW᪥fpijklqrḄ8tᵱfgᕒḄmᦪvwbxy4zḄᦪ{᝞|67ஹ66ஹ67ஹ68ஹ67ஹ69ஹ68ஹ71,ᦪ{Ḅᦪ᩽ᑖ8A.674B.675C.684D.6857.ᑡy)ḄA.3a+a2=3a3B.(a-b)2=a2-b2C.ay=a'2D.a2-^=ah8.᝞#./8CZ,WBNCஹ8஺GO,EAD,.N8CZḄᕜ828,ᑣOEḄA.3.5B.4C.7D.149.ᦪ=h+6yxḄᜧ᝘¢0,ᑣᙠCBᙶ᪗¥ᑁ§Ḅᜧ¨#©10.᝞#-wªK./O8CḄ⚔G஺0,0,A-l,2«G5ᙠxV)¬VLᢥ®

2m¯°#|জ®G஺8ᙊZ〉´µ8¬¶°·ᑖK04,08G஺E-,ঝᑖ®G஺E8ᙊZᜧCEḄ8¬¶°·¹·ᙠᑁGF«ঞ°¼0F,KACGG,ᑣGGḄᙶ᪗8A.75-1,2B.75,2C.3-½,2D.ᨵ-2,211.᝞#8¿À3᪥ÁᩚḄõÄ(Áᩚ)ÅÆ3jᜐḄGCÈÉÊᚁµ8i=l•"ḄÌᚁCDÅv2ijᑮÍGD,ᙠGDᜐHοBÏ¿Áᩚ⚔ÐAḄÑB837஺À¿BÏDEḄÃ81.5j/ஹBஹCஹDஹEᙠÒ-☢ᑁÁᩚ¿BÏÓÔᙢ☢ᚖCᑣÁᩚḄõ8×ᑮ0.1.Øὃᦪ{|sin37°«0.60,A.6.7B.7.7C.8.7D.8.512.ᙠ-☢CBᙶ᪗¥G”I,ÞG83,஻ᐸw஻<0ᙠãᱥäax?+bxa>0L.éGT,®2,"4,"ìᙠíãᱥLᑣ"äZḄᜧᐵ¥A.8>%>ðB.y2>yt>y3c.y}>y}>y2D.yt>y2>y3

3ூὃ௃_`IIᔁ⌱⌱ᔁñஹòó⚪13.ᑖcôõ|1-4/=.14.(1ஹ2ஹ3ö÷øᦪ°8ᓝúLḄᦪûü(ýḄᦪûö÷øᦪ°8øúLḄᦪûPQᡂḄ¹úᦪ4ḄÿᦪḄᭆ᳛15.ஹ*2x?-3x+2=0Ḅ᪷ᑣ+*2-=.16.᝞3Ḅ᪾ABCDEF"#$Aᙊ&AB'(Ḅᡧ*+ᶍḄ-./.ᑣᡠ1ᡧAFB*▢34ᑖ/Ḅ☢7.D,____Pᓃ417.89:;<=>?@

4jᔁl1ᑖfஹgh⚪19.opq(s-3.14)°+cos30°-(g~+|2-6|’3(x-l)22x-5,জ20.gq-x+3ᑏḄᡠᨵ᦮ᦪg.2x<——ঝ221.᝞ᙠ=$£Ḅ=$OEḄbJC8Ḅbc$~.qBC=BF.22.᪥ᵱ¢ஹ᝕¢¤¥᪵§¨.©ªḄ᪵«=ᵱ¢ஹ᝕¢Ḅlᦪ¬,ᑭᵨᡠ1ᦪ°±ᑴ᝞³´o⊤:W·¸/cmAx<155B155Kx<160C160170

5ூ=ὃ௃ÂÃᵱ¢·¸⚣ᦪᑖÅÆÇ᝕¢·¸ᡧ´o᪷°⊤ÈÉḄÊËÌh³ᑡÎ⚪q(1)᪵«=᝕¢·¸ᙠEḄᨵ2l᪵§¨AÏ᝕¢Ð(2)⊡ᐰᩩ´oÐ(3)᪵«=ᵱ¢Ḅ·¸=ÓᦪᙠÐ(4)©ª᪥ᐳᨵᵱ¢400-,᝕¢380l,ÕÖo·¸ᙠ160

68Ḅᙶ᪗!1,$%y=')*8.Xm(1)-aḄ/0$%y=1Ḅ2᪆45X(2))*8Ḅ7$%>=9Ḅ:;<=!C,?48cḄ☢B!1.জ-BCḄ2᪆453Iঝ*BHBD//x=^=-5X-5L஺PBCḄ;£tBA=BC,DA=DE,/Eᙠ?Z8CḄᑁu,vfEC,EB2ED,3EC=k5BD(ArWO).(1)6NABC=/ADE=60°z᝞1,{-hA/|}~5(2)6N4BC=N4DE=90°zজ᝞2,(1)Ḅ/ᔲᓄ᝞ᓄ{}~5᝞ᨵᓄ{-h/|ᳮᵫ527.᝞ᱥ”+2x-37x=L4ஹ8^5(1,0).

7ூὃ௃Q2(1)-ᱥḄ2᪆4oḄᙶ᪗5(2)᝞1,ᙠxeḄO1ᑖN/P8z-Ḅᙶ᪗524ব᝞2,¡3ᑖ¢7£ஹy=LCஹ^஺஺¤eḄᱥḄ;

8®ᫀ1.Aூᑖ᪆௃᪷±ᨵᳮᦪḄᜧ´µ¶·ᑣᓽº».ூ¼2௃2ᨵᳮᦪḄᜧ´µ¶·ᑣdᦪᜧL0,½ᦪ´L0,½ᦪ/ᜧḄ¾¿´ᦑ⌱A.Â⚪ὃÄÅᨵᳮᦪḄᜧ´µ¶·ᑣÆÇÈÉᨵᳮᦪḄᜧ´µ¶·ᑣ2⚪ᐵË.2.Aூᑖ᪆௃᪷±Ìd☢Í»ᑮḄ_Ïк»®ᫀ.ூ¼2௃2Ìd☢ͺ»_᝞¤ᦑ⌱A.Â⚪ὃÄÅÑᓫaᔠÔḄ9ÐÌd☢Í»ᑮḄ_ÏÐÌUÍ»ᑮḄ_ÕÐÌUÍ»ᑮḄ_Ð.3.Cூᑖ᪆௃Ö×Øᦪ·Ḅ⊤Ú_4!ax10஻Ḅ_4ᐸ1WÝ10,஻!᦮ᦪ.ßà஻Ḅ/z⌕Íâãᦪᡂ“z´ᦪåOÅæ஻Ḅ/7´ᦪåOḄæᦪçÝ.ூ¼2௃

9ூὃ௃216000ᵨÖ×Øᦪ·º⊤Ú!1.6X103ᦑ⌱C.è⚪ὃÄÖ×Øᦪ·Ḅ⊤Úe·.Ö×Øᦪ·Ḅ⊤Ú_4!axlO஻Ḅ_4ᐸ1WÝ10,"!᦮ᦪ⊤ÚzᐵË⌕dßßàaḄ/S0"Ḅ/.4.Bூ¼2௃2᝞•••â;ᙽ9ìḄ⚔îᙠïḄ;U/3=90஺-/1=90஺-33஺=57஺':a//b,:.Z2=Z3=57°.ᦑ⌱B.ூ¼2௃2A.VW_ðñVW_ᦑÂ⌱⚗óᔠ⚪ô5B.VW_ñVW_ᦑÂ⌱⚗óᔠ⚪ô5C.VW_ñVW_ᦑÂ⌱⚗óᔠ⚪ô5D.õVW_öñVW_ᦑÂ⌱⚗óᔠ⚪ô.ᦑ⌱D.Â⚪ὃÄÅñVW_7VW_Ḅᭆø2⚪ḄᐵËÈÉVW_ḄᐵËùúVW_^uᑖᢚû]ºüᔠñVW_⌕ùúVWñýþ180ÿ
ᔠ.6.Bூᑖ᪆௃᪷ᦪḄ᩽Ḅᑖᓽ.

10ூ!௃"67%&'3)*%&Ḅ)ᦪᨬ,*ᑣᦪ.67/᩽."71-66=5/ᦑ⌱"B.7⚪ὃ:'᩽ᦪ*᩽;᧜'=>ᦪ?ᓄBḄᜧD*E᩽Ḅ.ᵨ=>ᦪGḄHIJᨬDH/ᦪ.=>ᦪG%&)ᦪᨬ,Ḅᦪ.7.Cூᑖ᪆௃᪷ᔠLMN⚗*PᐰRST*UḄVW*MXᦪUḄV⌲⚗ᑖ᪆ᑨ[ᓽE.ூ!௃"Aஹ3a
a?`.MN⚗*`aᔠL*b⌱⚗`cᔠ⚪d/Bஹ=/-2/+஻┯j*b⌱⚗`cᔠ⚪d/cஹlm*b⌱⚗cᔠ⚪d/Dஹ┯j*b⌱⚗`cᔠ⚪d/ᦑ⌱"C.o⚪ὃ:'ᔠLMN⚗*PᐰRST*pḄVW*MXᦪUḄV*lmḄ.⚪Ḅᐵr.8.Aூᑖ᪆௃✌ᐜ᪷vwḄឋyE%z{L|%05=஺஺*ᯠᑭᵨwGḄឋyᓽE%ᫀ.ூ!௃•.•vwḄᕜ{28,/8=28+4=7,OB=0D,"E஺zG*

11ூGὃ௃.48஺ḄG*OE=-AB=~x7=3.5,22ᦑ⌱"A.o⚪⌕ὃ:vwḄឋywGᳮ*vwḄឋy.⚪Ḅᐵr.9.Aூᑖ᪆௃᪷=)ᦪḄឋyᵫyxḄᜧIDᓽᑨ[Ḅc,ᵫ¡0ᓽᑨ[bḄc*ᓽ|%ᫀ.ூ!௃"*.,=)ᦪ*=J+GyxḄᜧID*
kb,:.b0,*=)ᦪ¢=b+bḄ£¤=ஹஹ¥▲*ᦑ⌱A.o⚪ὃ:'=)ᦪḄឋy*⚪ᐵrᙠ¨©ª=)ᦪ¥«Ḅ¬.10.Aூᑖ᪆௃®¯°ᳮᓽ|ᑮR/MOHG*40=,®²1GO=NZOG,ᓽ|³lj/G=ZO=⌲,|%//6=l-1,|GḄᙶ᪗.ூ!௃"᝞ᡠ¸"

12•••ᑗ஺8cḄ⚔O(0,0),A(-1,2),:.AH=l,HO=2,:.Rt^AOH^,AO=#,ᵫ⚪|*OFRᑖN/O8,ZAOG=ZEOG,1:AGUOE,:.NAGO=NEOG,:.ZAGO=ZAOG,:.AG=AO=y/5,:.G(.V5-L2)/ᦑ⌱"A.o⚪⌕ὃ:'RᑖḄ»*¯°ᳮ¼R¥zwḄឋyḄWᵨ*©ªR¥zwḄឋy¯°ᳮ.⚪Ḅᐵr.11.Bூᑖ᪆௃½{¾¿8C¨"*¤E»¨F.ᑣ¥zw8//EF.Áw*ÂÃE%AF,8ÄᓽÅÆ⚪.ூ!௃"½{ED¾¿BC¨4,¤£»¨Ä.

13ூGὃ௃ᵫ⚪d|DHLBC,ᙠRtACDH,NDHC=90஺,tanZDCH=i=\:?.ZDCH=30°,:.CD=2DH,>CD=26,:.DH=6CH=3,■:EFLAB,ABA.BC,EDIBC,:.NBFE=NB=NBHE=9Q஺,:.¥zwFBHEÁw*:.EF=BH=BC+CH=6,FB=EH=ED+DH=1.5+5ᙠ᝞/£"/G*ZAFE=90°,4F=EPtan/ZE46x0.75%.5,.,.AB=AF+FB=6+6~6+1.73~7.7,ÈᩚZ8ḄÊËÌ7.7Í.ᦑ⌱"B.o⚪⌕ὃ:ÎwḄÏᵨ-ÐÑÆ⚪ᚁËᚁÓÆ⚪*ÐÑᚁËᚁÓḄ*L᪷⚪d᪀Õᔠ〉ḄÎw.⚪Ḅᐵr.12.C

14ூᑖ᪆௃31ᑖN×Ø6ḄlÙ¬*᪷஻7஻<0|ÛÜÝᙠÄ;
Îßà*᪷ᔜᑮÛÜÝḄâãᑨ[yHᜧD.ூ!௃"y=ax2+bx(a>0),•••èᱥêëᔣí*ï6=0ð*èᱥ⚔*x>0ðyxᜧᜧ*஻>ò>0`óô⚪d*ïb>0ð*èᱥÛÜÝᙠyÝö÷*Mᳮ*">/n>0`óô⚪d*.'.b<0,èᱥÛÜÝᙠyÝù÷*ú=1ð”?<0,%=3ð஻>0,ᓽèᱥxÝḄ2ý¾*=ý(0,0),þ᜜
ᙠ1331ᱥᙠ::22ᓽ22a2.(2,v)ᨬ!(4,#)ᨬ$:.y

15ூ]ὃ௃^_ூᑖ᪆௃`a᪛c2daᡠᨵOgឋhdᑮjᡂḄlmᦪ.4ḄnᦪḄopᦪq2,rstᓽO=⚪.ூP=௃`᪛c2q'ᐳᨵ6wxOgḄopᦪᐸ]jᡂḄlmᦪ.4ḄnᦪḄopᦪq2,21ᡠ#jᡂḄlmᦪ.4ḄnᦪḄᭆ᳛=J63ᦑ}ᫀq:.)⚪ὃ,ᑡ⊤Y᪛c2Y'ᑭᵨᑡ⊤Yᡈ᪛c2YᡠᨵxOgḄop஻h]⌱aᔠ/ᡈ8Ḅopᦪm,ᯠᑭᵨᭆ᳛MNNᡈBḄᭆ᳛.15.1ூᑖ᪆௃᪷ᐗ/K᪷ᦪḄᐵMNO᳝+.ூP=௃h᝞pK᝞2+¡+஺=0¤“¦0§Ḅl
¨ᦪ᪷.ᓰஹ஽¬®+஽=-2=rO::■aa-32%1+x=-=3,%,-x=—=2,ᡠ#&+%_ᓰ*2=3-2=[.22)⚪ὃ,ᐗ/K᪷ᦪḄᐵ.16.18ூP=௃='•.•¶·¸¹ABCDEFḄ¸¿q3,AB=BC=CD=DE=EF=FA=3,BAFḄ¿=3x6-3-3=12,...ᡧ¹AFB¤▢ÃÄᑖ§Ḅ☢Æ=912'3=18.

16ᦑ}ᫀq18.)⚪ὃ,¶É¸¹ᙊᡧ¹☢ÆḄ.17.2200ூᑖ᪆௃ÌÍÎḄÏÐq஺Ñ/ÒÍÓḄÏÐqbÑ/Òᵫ[Ö⚪Ḅᦪ×ᐵØÙKjaᐸ=ᓽO'ூP=௃='ÌÍÎḄÏÐq஺Ñ/ÒÍÓḄÏÐq6Ñ/Ò1600+100«=1400+100/?a-2ᵫ⚪Ú,=:1600+300a=1400+200b6=4Ý/ÞßàḄᐰq'1600+300x2=2200Ñ.ᦑ2200Ñ18.3ூᑖ᪆௃✌ᐜäCCO#ᑮCC.NECDḄJᑖᡠBCB5=CD,CABDAB,ᡠ#9.å]AC=2AB,ᡠ#/NC8=30஺ᓽOa}ᫀ.ூP=௃='äCC,•.,æçN8EèAEᢚêëBìᙠAC4ḄB'ᜐ,íæèEFᢚêëCìᙠEBWADḄîCᜐ.:.EC=EC,.•,Z1=Z2,VZ3=Z2,.,.Z1=Z3,ᙠçCC'8'çCC'Z§],

17ூ]ὃ௃^_ZD=NCB'C'=90P

18.ூ<௃>(@-3.14)°+cos30°-(JK+|2-0|=1+N-2+2-62-!G~1--------.2P⚪ὃRS$ᢣᦪ'ஹᱯ*+Ḅ,+-ᦪ.ஹ/᦮ᦪᢣᦪTஹᓄ3.ஹ5ᦪḄ678UVWXᔜZ#8ᑣ⚪ᐵ.20.-2£x<1J-2,-1,0ூᑖ᪆௃ᑖabcজঝfghbciḄj᪷lbciḄjᑏᡠᨵ᦮ᦪᓽ:.ூ<௃'3(x-l)>2x-5,®<-x+342x<----ঝ2bcজ>x>-2bcঝ>x-2£xP⚪ὃRSwᐗwybcihbciḄ᦮ᦪz{Ḅ"#⚪Ḅᐵ.21.|}~᪆.ூ<௃⚪ᑖ᪆>✌ᐜᵫḄឋ:4ᵫᐰ,+ḄᑨᳮAAS:|}HADEABFEᵫ:fg:|}BC=BF.⚪᪆>>•••Z8C஺.AD=BC,•FᙠC8Ḅ:.AD//CF,.\Z1=Z2.,••EḄ:.AE=BE.ᙠ4DE8FE,:NDEA=NFEB,Z1=Z2,AE=BE,:./\ADE^/\BFE(AAS),

19ூὃ௃:.AD=BF,:.BC=BF.>P⚪ὃRSḄឋஹᐰ,+Ḅᑨឋ.ᙠᵨᐰ,+Ḅᑨ⌕¡¢,+£Ḅ¤ᐳஹ¦⚔+¨©¤ᐳ+.22.(1)40(2)~᪆বC(4)332ூᑖ᪆௃(1)hEiᓰḄ¬ᑖᦪu5%,fghJ(2)ᑭᵨᵱ¯°±ᦪ7²ᐸvᔜiḄ±ᦪᓽ:h8iḄ±ᦪ´gµ¶";(3)᪷l¸ᦪḄ¹ºᓽ:J(4){ᵱஹ᝕¼¯½¾ᙠ160st<170¿£Ḅ¬ᑖÀᓽ:h.(1)>EiᓰḄ¬ᑖᦪu1-(17.5%+37.5%+25%+15%)=5%,ÁÂḄ᝕¯±ᦪ>2+5%=40(±)ᦑºᫀ>40J(2)>ᵫ(1)ÁÂḄᵱ¯±ᦪ>40±ᑣ5iḄ±ᦪ:40-4-10-8-6=12(±).⊡ᐰ¶"᝞ᡠÈ>

20>ᢥ᯿´Ëᑮ¾ḄÍÎᵱ¯Ï20ஹ21бÑᙠCi...¸ᦪᙠCiᦑCJ(4)>400X^^+380X(25%+15%)=180+152=332(±).40º>Ó"Ô᪥½¾ᙠ160Ö×170¿£Ḅ¼¯Ùᨵ332±.ᦑ332.P⚪ὃRÚ⚣ᦪᑖÜÝÞḄßÖàᑭᵨ¶"áÂâãḄßÖJᑭᵨ¶"áÂâã,äåæçèéஹᑖ᪆ஹẆë¶"ìßµz{Ḅᑨíàîï⚪.23.(1)~᪆ூᑖ᪆௃(1)ðñ08,ᑭᵨᑗḄឋN/8O+N/8C=90஺ᵫCO_LCMNN+=90஺øᔠῪ,+Ḅឋ¦⚔+ûᓽ:ü=,´g|øýJ(2)þ஺µ0N_L/8ÿN,C᧕KN4=NECM,ᙠᵨᑭᵨᦪCE,஺EḄᙠZOEᑭᵨᦪNEḄḄᵫᚖ"#ᳮ4N,ᑣ'◤ᙠᵨA/ON)*+ᓽ-"04

21ூὃ௃34Ḅ.(I)6789:08.•8c;஺஺Ḅᑗ=NC80=90஺ZABO+ZABC=90°9••CDLOA,ZJ+NAED=90°,OA=OBtZA=ZABO,./ABC=/AED,••ZAED=NCEB,/.ZCEB=/ABC,.0.CE—CB.(2))8஺CWJ_46N,CCA/_L>8M.EM=BM=-BE=5.2••NADE=ACME=9(F5NAED=/CEM,M18஺஺NNADE—NAED=180஺NNCME—/CEM,

22BPNA=ZECM,?,/sinZ,A--13sinZECM=—=—,^ߟ=—CE13CE13C£=13,DE=CD-CE=\5-\3=2,.DE26/.AE=----=—sinZ.A5AB=AE+BE=—+\0=-f55vOA=OBON1AB,9i38...AN=-AB=—25ᙠRSAON,A0N=5x,OA=13xfaoᑣON?+AN2=OA2,ᓽ(5x>+_=3x>,()2(119)BC247OA=l3x=—30247ᓽ஺஺Ḅ-"Dᘤ.F⚪ὃHIᙊḄᑗ=KῪ+ḄឋNOᑨ#ᚖ"#ᳮᦪḄQᵨRS+ḄឋNOᑨ#TU#ᳮVWXYRᐵឋN#ᳮ;)⚪Ḅᐵ[.24.(1)1\ᜧ^_`1\a^_bcdᑖfg^4ᔴ`1.5ᔴi(2)j᣸8\ᜧ_2\a_ᨬ⁚ḕoᵨᨬḕoᵨ;1240ᐗ.ூᑖ᪆௃(1)A1\ᜧ^_`1\a^_bcdᑖfg^xᔴ`yᔴ᪷t“3\ᜧ^_O4\a^_bcdg^18ᔴஹ2\ᜧ^_O6\a^_bcdg^17ᔴ”ᑡxyz);(2)|g}33ᔴ~ᵨ10\_bcgᦑ10\_ᡠg^10ᔴ~|Dᜧ^_goa^_ᦑᵨᜧ^_oᵨaj᣸ᓽ.(1)

23ூὃ௃34)8A1\ᜧ^_`1\a^_bcdᑖfg^Xᔴ`ᔴ᪷t⚪:3x+418x=4,):2x+6y=17y=1.581\ᜧ^_`1\a^_bcdᑖfg^4ᔴ`1.5ᔴi(2))8A^g4j᣸ᜧ^_஻\ᑣj᣸a^_(10-)\᪷t⚪:4/M+1.5(10-/M)>33,):7.2,mD᦮ᦪᑣmḄᨬa;8,10\ᜧ_1300ᐗᔠ¤1300ᐗ9\ᜧ_1170ᐗ1\a_100ᐗᔠ¤1270ᐗ8\ᜧ_1040ᐗ2\a_200ᐗᔠ¤1240ᐗᡠdj᣸8\ᜧ_2\a_ᨬ⁚ḕoᵨᨬḕoᵨ;1240ᐗ.F⚪ὃHI¦ᐗbcxyz`bᐗbcK§ḄQᵨ)F⚪Ḅᐵ[;¨©⚪Aªᦪ«ᔠ〉ḄKᐵ®`Kᐵ®ᑡxyz`K§).25.(1)y=-(2)জy=x-lঝ(-1,-2)ᡈ(1,¦)X22ூ³)௃731´⚪ᑖ᪆8(1)᪷tbcᦪ¶·¸Ḅᙶ᪗ᱯ¼ᑮ-:)a=2,ᑣA(2,222--)),ÀÁ#¸BḄᙶ᪗D(2,1),ᯠÄÅB¸ᙶ᪗Æᐭy=%mḄᓽᑮ2xÉÊËᦪḄ)᪆§i(2)জ¸CCE_LAB¸E,᝞¶5.,᪷t+☢ЧᑮSMBC=iÑC£=[1_(fxCE=Õ)CE=3,¸CḄÖᙶ᪗D-L•.•¸CᙠØÙ=᜛=4ᑣ¸CḄᙶ᪗D(-1,-2),ÀᑭᵨÛ#®ᦪÜ*=BCḄ)᪆x§iঝᐜÁ#D(-l,1),᪷t*=BC)᪆§Ḅᱯ¼*=BCOxßḄᜳD45஺BD஻xß;ᑮ/DBC=45஺᪷táx+Ḅᑨ#xÜ'ᨵAPIBDDKῪ*

24+ådæḄbçDèéßêᢚêᢚìÄḄíî+ᡠzᡂḄðç+Dáx+ᑖñòó8ô/BPD=90஺ᑣ¸PᙠBDḄᚖ*õᑖ=᧕÷åP(B-B)iô/BDP=90஺,22ᑭᵨPD஻yß᧕÷åP(-1,-2).731´⚪)᪆8(1),¸A.ᙠ*==-iB-5'.731.—=—a—.222/.a=2.........................................1ᑖAB஻yß~¸BḄùᙶ᪗D1,••¸BḄᙶ᪗D(2,1).'•ØÙ=y=úû¸B(2,1),x/.1=—,ᓽ஻ü=2.22••ÉÊËᦪḄ)᪆§Dýx(2)জ¸CCEJ_AB¸E,᝞¶.CE=”3.”••¸CḄÖᙶ᪗D2•¸CᙠØÙ=ஹ=bx¸CḄᙶ᪗D(-1,-2).A*=BCḄ)᪆§Dþ=ÿ+6,1=2"+b,=Lᑣ—2==k+h.h=-\..••BCḄ᪆N=x-1

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1/=1,ᳮᵫ2᪆32জA5678ᓄ%4=0,ᳮᵫ2᪆ঝtanNE4C=.ூᑖ᪆௃31᪷<⚪=ᑮAABC+AADE?@ABCD.%EFGDABW4EAC,᪷<ᐰACD.ḄឋJK32জ᪷

26EC4Ei—=----=J2,BPEC=5/2BD,~BDAD•**k=y/2;ঝREFLACSF,TAD=OE=a,ᑣ•.•E஺C,:.CD=2a,ᵫVW'ᳮ%AC=-JAD2+CD2=y/5a)ZCFE=ZCDA=90஺%NFCE=ZDCA,:.HCFEs^CAD,.EFCEEF_a=——%ᓽ~r=~5ADCAayJ5a%EF=஺,5:.AF=ylAE2-EF2=—a,5EF1ᑣtan/£/C=—=-.AF3h⚪ὃiḄ@ABCD.ḄឋJஹAῪDCD.ḄឋJஹNOCD.Ḅᑨ'+ឋJ%jkNOCD.Ḅᑨ''ᳮ+ឋJ'ᳮ@⚪Ḅᐵm.27.(1)nᱥ᪆p(42q-3,4ᙶ᪗(-3,0)33(2)Pᙶ᪗H54(3)u஺஺ῪḄAῪCD.Ḅ☢w5C.ூᑖ᪆௃(1)y8ᙶ᪗zᐭnᱥ᪆[*஺Ḅ5%[*nᱥ᪆%|}p0,[

27ூὃ௃N~-Ḅ᪷%[*Zᙶ᪗(2)pᙠx-%P"yS"%[EGO8PG(?᜛p%[*8,ᙶ᪗%ᑭᵨ&'(ᦪ)[*NPḄ᪆%ὶ1%[*pᙶ᪗(3)஺RQHLDESH,ᵫCFḄ᪆[*CஹFḄᙶ᪗%ᔠᩩ[*tan/஺஺”%[ᑖ¥ᵨDQ⊤§UQH+DHḄ¨%ᑖDQ=DE+DQ=QE©ª«¬%ᑖ¥ᵨDQḄ¨⊤§UG0DEḄ☢w%|TUQḄᙶ᪗,ᑭᵨ°!ᦪḄឋJ[*G0DEḄ☢wḄ5.(1)y8(1,0)zᐭ±஺/+2%-3,[“+2-3=0,a=1,°nᱥ᪆p2+´_3,}±0,[/+2q-3=0,x=lᡈ·=-3,ᙶ᪗(-3,0)ফ¸p¹ᑖº4P2,ᑣ/᝞_1,¸Pᙠx-%R1y"S",ᙠG8PO+G᜛PONPOB=2P0B'OP=OPZBPO=ZB'PO:./\BPO^/\B'PO(ASA),:.BO=B'O=l,

28Tp᪆±¿+b,yZஹ᜛©ᙶ᪗zᐭ[,±(-3k+b=0[b=lb=\•••/P᪆p;x+1,3y=xx=—2ὶ1,,%V=-X+13333ᙶ᪗55(3)᝞_2,R0H_LCRSCFTH,Tnᱥ"ySM.24":CF^y=-x--,24••[*஺(},0),F(Of--39OC3/.tanZOFC=----=,OF2OQ஻y%JZQDH=ZMFD=ZOFC,3/.tanZHDQ=—,23ÃÄT00=3DH=—j==tHQ=—f=t,1vl3-v13*/G0QE@uDQῪḄAῪCD.%:.UDQ=DE,ᑣSOE/gxÅᑖp2^1Æ

29ூὃ௃¸DQ=QE,ᑣSDEQ=yDE9HQ=yᱏÈÆA•.•ÉÊ9Ì2613.,.DQ=QEGOEQḄ☢wDQ=DEᜧ.24T0ᙶ᪗(x,x2+2x-3),ᑣ஺(x,jx--),•.•஺ᙠCFḄ^-%244232:.DQ=t=-x---(X2+2A--3)=-x2-yx+y=-(x+j)2+3,2x=-§%·Ó=3,654(SADEQ)max=~^=—»54ᓽuQDῪḄAῪCD.Ḅ☢w5.h⚪Ù⌕ὃi°!ᦪḄÛᔠ~ᵨ%ÜÝÞßᨵ&'(ᦪ)ஹD¹ᑖḄ'YஹᐰACD.Ḅᑨ'+ឋJஹCD.Ḅ☢wஹAῪCD.ḄឋJஹ°!ᦪḄឋJÝᑖáâãA.ᙠ32äå'UæpḄ᪆@⚪Ḅᐵm%ᙠ33äᑭᵨ஺஺⊤§UGQDEḄ☢w@⚪Ḅᐵm.h⚪ὃiÞßçè%Ûᔠឋçé%PQêᜧ%ëìçᜧ.

30ூ
ὃᦪ௃2022-2023ḕᓭ⚗ẚᔁíIᔁ3⌱⌱äðᔁñᑖ1.-9ḄNᦪ@3ä11A.——B.-C.9D.-9992.᝞_@óᵫ6óNôḄ,-õöᡂḄõ_.%øḄÙù_@3ä3.ú~“ûüᡭþᐵm᪶ᢈᡊ”ḄẆᨬ7nmḄᐝ⚪ᐸlnm=0.000000001m,ᑣ7nmᵨ'(ᦪ*⊤,-./A.0.7xl0smB.7xl0-8m1C.o.7xio_8mD.7xio-9m4.789:;ᙽ=>?᝞ABCD4=47,ᑣN2Ḅ[ᦪ-()A.43°B.47°,C.133°D.137°5.HᑡJKLMḄN./A.a3^a3=a6B.a3,a3=za6C../Q=R]D.(a஻)2=ah6

31ூὃ௃cd6.HᑡAeᙳ⊤,ᡈᦗiḄ᪗kᐸlNmnoAepNnoAeḄN./A.qᱥstuv᪀D.x▭ញᦗ7.-{|“~ஹṑḨஹஹᱥஹ”⚗ᳮ⌕'tḄṑḨ;50'tᜩḄṑḨ,ᡂṑḨ⚣ᦪᑖ8A᝞Aᡠ,ᑣᡠ'tṑḨḄ¡ᦪ¢ᦪᑖ£-./8.ᓄ¥ᡈ;§Ḅ¨©N.a-ba-ba+bA-F10.᝞Aᙠ«¬®e/8COAC,8஺°±²³O,³EN஺/Ḅ³´µ8E¶

32Api·¸±²³¹º»S5M=3,ᑣHᑡ¨¼½জ¿=:Àঝ&8CE=27À®SAABE=Dr212À®/\AEF^/\ACD.ᐸ;ÂLMḄN./II.᝞A1N;ḄÃÄᵫÆÇஹ´ᩚÉᡲÄËᡂ.´ᩚÌÍᙠÎ;«☢ᑁ/ᚖ8²ÆÇÒ¸[-9cm,5cḄ¸[-10cm,CCḄ¸[ÓÔÕÖ᦮.᝞A2,N8CZ=143஺ØᢝÚÛWXBC,ÜÝÞ180=150஺Ꮇ᝞àá஻8c-âã᝱ᑣåCDḄ¸[-(æὃᦪç½sin53°«0.80,cos53°«0.60)()A.8cmB.7.7cmC.7.5cmD.5.6cm12.èéêëᦪy=x2-5x-6ᙠxmìḄAíîxmïᢚᑮxmHAíḄᐸòóᑖÚÛÝᑮ;ôAíD8ãy=2x+b:õôAíᨵ3÷ᐳ³ᑣbḄù-./A.-úᡈ-12B.-ûᡈ2C.-12ᡈ2D.-üᡈ-12444ýIIᔁ.ÿ⌱
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34BDE22.<᪥#¡¢ᦋḄ¤¥¦§᪥¨Ḅ©ª«¢᜜Ḅ¤¥<᪵®ᐸª«“ᳫ²”“´µ²”“¶·²”“¸¹²”"»²”Ḅ¤¥¼½¾¿À´ᑴ᝞ᡠÂḄÀ.Ã1ª«¸¹²Ḅ©Äᦪ<ª«ᳫ²ḄᦪḄÅᑖÆ<;Ã2ÈÉᩩÀ⊡ᐙÍ᦮ÎÃ3ϧ᪥©Äᐳ1600ÑÒª»²ḄᜧÔᨵ4ÕÖÃ4§¨ª«¶·²4ש,ᨵ1×ᵱÄÃᵨE⊤Â83×᝕ÄÃᑖsrG,H⊤¦ÜᜓÞ,⌱ßàá©ᡂ¶âÈᵨᑡ⊤ᡈµ᪛æḄKçាé⌱,
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ý§øùúḄᑭÿ70ᐗᢇḄᑭ40ᐔ.(1)ᨴᓬ100ᐳ!ᑭ4600ᐗ#$%ᨴ&'ஹᢇḄᦪᑖ+,-.(2)0⃩ឋ345&'Ḅᦪ678,9:ᦪ6Ḅ30%.=⌕0⃩1000#$?᝞A&'BᢇḄᦪ6C8D:ᑭ.:ᑭ,-.ni25.᝞GHPJKᦪy=Nx+lRKᦪy=-(x>0)GUḄVHHᡝḄXᙶ᪗J4,PBVx2x\ᚖ^JH8.(1)`aḄbN(2)HMKᦪy='(x>0)GUefHgHMhi஺_LBn9H஺otanNPAf£)=!,x2`HMḄᙶ᪗.26.ᙠAABC,CA=CB,ZACB=a.HPx☢ᑁ7RHA,C|ᔠḄ~H.AP,APHP⌮┐aᑮDP,AD,BD,CP.(1)᝞G1,%a=60°ḄbBDRCPVᡠᡂḄḄᦪ.(2)Dr\᝞G2,%a=90¡ᑏᘤḄb¤BDRCPVᡠᡂḄḄᦪ¥¦G2Ḅ§¨©ªᳮᵫ.(3)®#⚪

36%a=90oHE,Fᑖ+CA,CBḄ²HHPᙠEFe¡ᑏHC,P,27.᝞Gᙠx☢ᙶ᪗´xQy²nx+4Rᙶ᪗\ᑖ+V94ஹ8¶H·ᱥ-/+bx+cg8¶HH஺JefHgH஺hCDLr\9HC,V·ᱥ9HE.(1)`·ᱥḄ᪆¾.(2)`¿/BE☢ÀḄb.(3)BE,ᔲÂᙠH஺D¿O8EB¿஺/CÄ.oÂᙠ`H஺ᙶ᪗No7Âᙠ©ªᳮᵫ.

37

38Åᫀ:1.cூᑖ᪆௃᪷ËÌᦪḄᭆÎ$ÏᨵÑÒ7ÓḄ¶ÔᦪÕÖ×JÌᦪØÅᫀ.ூÙ௃$-9ḄÌᦪ9,ᦑ⌱$C.Ü⚪Ý⌕ὃßàÌᦪ⚪ḄᐵâãäÌᦪåÏᨵÑÒ7ÓḄ¶ÔᦪÕÖ×JÌᦪæḄᭆÎ.2.Dூᑖ᪆௃᪷ËçèG²ḄÝèG5éêëìíîᑮḄx☢G¨ᓽJÝèG.ூÙ௃$êð☢îᑮḄx☢G¨3ᑡðò¨êóôõö1ᑡᨵ1Ôö2ᑡᨵ2Ôö3ᑡᨵ2Ôᦑ⌱$D.Ü⚪Ý⌕ὃßà÷ᔠøḄçèG⚪Ḅᐵâ᪷ËÝèGḄᭆÎᵫùøG¨ᑮ?Ḅx☢G¨.3.Dூᑖ᪆௃ᵫ⚪᧕7nm=0.000000007m,ᯠí᪷Ëüýþᦪÿ
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