2022-2023学年湖南省娄底市中考数学专项提升仿真模拟试题（一模二模）含解析

《2022-2023学年湖南省娄底市中考数学专项提升仿真模拟试题（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。

2022-2023
ᓭḕὃᦪ⚗ᓣ⚪Iᔁ⌱⌱ᔁᑖஹᓫ⌱⚪1.-2022Ḅ᎔ᦪ------B.------C.-2022D.2022202220222.Ḅ-3a3b6A.B.--a3b5C.--a3b5D.--a3b622883.᝞ABHCD,Eᑖ8,CD
E,F,EGᑖNBEF,/EFG=64°,ᑣNEG஺Ḅᜧ#C.122°D.112°4.$%&'()ᕈᳫ,ᡈ.ᙊ,ᨵᒹ23ᜧ4100m.$%&'()5ᐜ78ᙠ:;<=Ḅ&'()>?@ABᕈḇ&,ᡠEFG&'().IJKLMNḄ&'()ᨵO5$%&'()PQBPḄ&'()PQR5&'().S100nmlnm=109m
ᵨUVWᦪX⊤ZGA.lxlO7mB.lxl08mC.lxl09mD.lxl06mDF5.᝞஺Z8C஺;[E஺Ḅ;[EC\]5஺Q[Eᑣ=_=

1ூ;ὃ௃cd6.AᑡfXghḄA.Gij⌼lmḄnᜓpqḄrstuv⌱wx᪵z{B.ij|}~1
VḄtuv⌱wᐰ☢z{C.;ᝄqD.rᙢᙳᒴḄg☢ᯠq7.᝞ᙠ,48C஺;\]ZC,8஺Q[஺[E,ᑖ4஺Ḅ;[,¡N8=6cm,8c=8cm.ᑣḄ¢A.2.2cmB.2.3cmC.2.4cmD.2.5cm8.£¤ᦪ¥=2*+2¦G§ᦪa¨©ª«¬¤ᦪy=3aG§ᦪa^O
ᙠ☢]Xᙶ᪗°ᑁḄ²ᜧ³G9.᝞´ᜧ᪛¶·¸¹Ὺ»¼᪛᪷4ᑮ»¼[Ḅ¢¿4m,ᢚ¼ÁᑖP8©ᙢ☢ᡂ40஺Ḅᜳ]ÄÅÆᩭ᪛Ḅ¢¿ÈC.(4+4sin40°)ÈD.cos40'

210.᝞Ë45CᑁQᙊO,/8=65஺ZC=70°,BC=2ᚗ,ᑣÖ8cḄ¢GB.eᐔC.2ÙD.2ÛII.᝞S1;ḄÝ,Þᱏà\]áᡂ4â]ã],äᡂ᝞2Ḅåæ,58çÞᱏèéêëìí◣.åæ,ᨴ8C஺Ḅ☢ðG13,;éòóᜐḄåæ,EFG”Ḅ☢ðG1,]ã],Ḅùᩩ]æᑖG஺û6,ᑣ஺+62=A.12B.13C.24D.2512.᝞ᙠ☢]ᙶ᪗°;ᱥy=-N+20xḄ⚔/xḄ5,ᱥᑣOP+/NPḄᨬ$%&(.C.3D.273.IIᔁ&0⌱⌱(2ᔁ34ᑖ6ஹ89⚪

3ூ<ὃ௃?@13.ᙠC☢EFᙶ᪗I<J45L(8&1,-2(ᐵxᑣ0+6=14.᝞QRSTUVWᕜYᜩ[\Ḅᢚ^_Qᑣ`7ᜩḄ[\Ḅ+2147Ḅ᦮ᦪj16.klmnf-2x-8=0Ḅp᪷r3,ᑣ&^+/t17.᝞QᙠfῪEFtFvN8C<w4஺8=90஺,L஺=8஺,஺஺_1/18஺</EOFCO|Rᑣ~Ḅ%AO18.᝞Q&1(,ᙠA/8C<AB=AC,ZBAC=90°,Z2Ḅ஺/ᔣ88cḄEBᔣCD,EpḄᜧ$|f,x=/£>,y=AE+CD,yᐵxḄᦪQ᝞Q&2(,Q&0,2(,ᑣQḄᙶ᪗R

4l'A2ᔁᐭ4ᑖ19._V12-(2021-^)0-2xcos30o+^--J20.ᐜᓄ%(1-11ᓝt6ᐸ

5ூ<ὃ௃?@1(⊤<",b=ß&2
᪵áᡂÓḄᵬ'(?,?ᜩ25$'(?,?ᜩ30.1
@ᵬஹ$%&'(ᔜᨵBC*+,DE

6(2)=IJ0ᡂK9%L>Mᵬ'(NᵨᐜP9ᜓ+,Ḅ+.ᦔ᳛QI20%,$'(UᢝWX.Y$'(Z[\]^*+,(+.ᦔ᳛D_+,`a)ᵬ'(UᢝWX.9Ḅb%L0ᡂḄ\(`a.জ@$'(◤[\Ḅ+,ᦪঝ]ᵬ'(Nᵨ9ᜓḄNf?ᜩ900ᐗNᵨi(j◤Mkឋmnopqrᵨ1500ᐗ$'(◤mn[\Ḅ+,?,?ᜩ200ᐗ.u>vwxyḄrᵨὃ⇋{⌱}~L⁚ḕmEᳮᵫ.24.᝞488Ḅ/C,8஺`O,E“஺ḄGᙠ,EFLAB,OG//EF.(1)@¡>¢£OEFG¥(2)]AD=\0,EF=4,@OE¦BGḄ§.25.᝞ᙠḄ£8C¨M஺©஺=ᙊ«OC=¬®஺஺஺஺D£`ᑗO,AC^AD,°04஺஺E,°CE,±²§³Z8.(1)@¡>4C஺஺Ḅᑗ4ফ]”=10,tanB=-,@஺஺Ḅ¬(3)]F%ABḄ¾¿ÀBD+CEDAFḄᦪÁᐵñᳮᵫ.26.᝞1,Åᱥy=--+bx+cÌ/(-1,0),8(3,0)DyÍC.ᙠxÍᨵMÎE(w,0)(0

7ூὃ௃éê@஺Ḅᙶ᪗(3)᝞2,°8ë±²§yÍN,°ìA1,OM,9Ḅ☢í=S/,4MONḄ☢í=S2,]S/=2S?,@”Ḅî.

8ïᫀ>1.Aூᑖ᪆௃᪷᎔ᦪḄôõ>᝞%&ᦪḄöí=1÷øb%&ᦪù=᎔ᦪᓽQûüïᫀ.ூýÖ௃A-2022Ḅ᎔ᦪ-+Y.2022ᦑ⌱>A.ÿ⚪ὃ᎔ᦪ1Ḅᦪ᎔ᦪ⚪Ḅᐵ.2.Dூ௃⚪ᑖ᪆᪷!"Ḅ#$Ḅ#%&'ᑣ)ᓽ+,-ab2j=J.a3.(b2)3=-1a3b6.ᦑ⌱D.3.Cூᑖ᪆௃ᑭᵨ=>?ḄឋA)NFEB,ᑭᵨF=ᑖ?)/8EG,Jᑭᵨ=>?ḄឋA+KLᫀ.ூ௃&'ABHCD,NEFG+NFEB=180஺,•'ZEFG=64°,.■.ZFE5=180°-64o=116o,•/EGᑖ/BEF,4FEG=/BEG=58°,•••ABIICD

9/BEG+NEGD=180஺,Z.EGD=180°-58°=122°.ᦑ⌱C.U⚪ὃḄ=>?ḄឋAF=ᑖ?ḄឋAVWXY⚪Ḅᐵ.4.Aூᑖ᪆௃Z[\ᦪ'Ḅ⊤^_`10"Ḅ_`ᐸbWcd10,?᦮ᦪ.fg஻Ḅij⌕lmnᦪoᡂajqᦪrstuvw஻Ḅi$qᦪrstḄwᦪxc.ynᦪiᜧ{ᡈ}{10j஻~᦮ᦪ-ynᦪḄiq{1j஻᦮ᦪ.ூ௃100nm(lnm=109m)ᵨZ[\ᦪ'⊤^lxl0"m-ᦑ⌱A.U⚪⌕ὃZ[\ᦪ'Z[\ᦪ'⚪Ḅᐵ.5.Dூᑖ᪆௃᪷!_ABCD=>_KᑮAD஻BC,AD=BC,KDEFS/\BCF,ᵫrE/஺ḄbrKᑮ஺E==ᵫKᑮ==?.22BFBC2ூ௃_ABCD=>_-.AD஻BC,AD=BC,/.DEF^-ABCF,•.•rEḄbr'.DE=-AD=-BC,22.DFDE_\"BF~BC~2'

10ᦑ⌱D.⚪ὃ=>_ḄឋAxF_ḄᑨgឋA\=>_ḄឋAKDEF^ABCF⚪Ḅᐵ.6.Bூᑖ᪆௃᪷!ஹᯠ+Ḅᭆஹᐰ☢¡¢᪵¡Ḅᭆᑨ¤ᓽ+.ூ௃Aஹ¥⌼§¨Ḅ©ᜓ«ḄA¬®¯⌱°ᐰ☢¡U⌱⚗²'┯´µᔠ⚪·-Bஹ¸¹º»1
¼c[Ḅ½¾®¯⌱°ᐰ☢¡U⌱⚗²'~fµᔠ⚪·-Cஹ¿ÀÁÂÃÄbᝄU⌱⚗²'┯´µᔠ⚪·-DஹÆÇÁÈAᙢᙳᒴḄÌÍÎÏ~☢ÐWU⌱⚗²'┯´µᔠ⚪·-ᦑ⌱B.U⚪ὃḄᯠஹ+ஹḄᭆஹᐰ☢¡¢᪵¡.ᯠᢣᙠÁgᩩÔÁgÕÖḄ.+ᢣᙠÁgᩩÔÁgÕÖḄfgᓽᢣᙠÁgᩩÔ+ÕÖ×+ÕÖḄ.7.Dூᑖ᪆௃᪷!Ø_ឋAKÙN/8C=90஺BD=AC,BO=OD,᪷!ÚÛgᳮ)Ù/C,ÝÞ)Ù8஺ஹOD,᪷!F_bw?)ÙEßḄàᓽ+.ூ௃_48COØ_.,.48C=90°,BD=AC,BO=OD,:48=6cm,8C=8cm,••ᵫÚÛgᳮKAC=^AB2^BC2=A/62+82=10(cm),

11**.B£>=10cm,OO=5cm,♦.•rEஹßᑖá/஺ஹḄbrNO஺Ḅbw?.•.M=go஻=2.5cm,ᦑ⌱D.U⚪ὃÚÛgᳮØ_ឋAF_bw?Ḅ¯ᵨF_Ḅbw?=>{âãä}{âḄÁå.8.Cூ௃ூᑖ᪆௃ᑖæ®ᑖ᪆ya>0jᡈya<0j.ூ௃ya>0jÁçèᦪé=a*+2êëìíஹîஹë▲-ðñòèᦪy=⁐êëᙠஹXë▲-ya<0jÁçèᦪé=2*+2êëìíâîஹஹë▲-ðñòèᦪy=?êëᙠâîஹXë▲.ᡠVõᨵ⌱⚗cµᔠᩩ.ᦑ⌱CU⚪ὃ᪶XYrÁçèᦪðñòèᦪḄêë.⚪ᐵr\ÁçèᦪðñòèᦪḄឋA.9.Bூᑖ᪆௃nᩭ᪛Ḅàú»ß8+ᑓüḄà.ýXVḄi+ᙠþV8b᪷!NP8/Ḅúᦪÿ
8Ḅ.ூ
௃
8ZPBA=40°,%=44..PB=PA^sin4Q°=-----sin40°

12.4'.PA+PB=4+--------.sin40°ᦑ⌱:B.⚪⌕ὃḄ
Ḅ!▭#ᵨ%&'()ᵨ*ᐵ,-.

/01⚪Ḅᐵ2.10.Aூᑖ᪆௃34OB,OC.✌ᐜ78AOBC9ῪOBᓽ<
=>⚪.ூ௃34OB,OC.ZA=180°-ZABC-ZACB=l80஺-65஺-70஺=45஺ZBOC=90°,BC=2#.,.OB=OC=2,-~Bஹi90xrx28cḄD=ᐔ1oUᦑ⌱A.⚪ὃᙊᕜHᳮJKL9ῪḄឋNḄ9OP
⚪Ḅᐵ2'(QRSOP11.Dூᑖ᪆௃᪷UVḄឋN

13hiHᳮW/+஻-_᪷U☢nop☢nKLWg_᪷Uqᐰ]rKLᓽ<W3+6)2.ூ
௃VVḄXYZ[ᚖ]ᑖ••4`ᐰ9:.NADH=NBAE,NDAH+NHAD=9஺,AD=AB=BC=CD,ZDAB=90°,.•t*N8CDurvurḄ☢nD13,•.urḄ*Dw᪷UhiHᳮᑣ/=y᜛=13,•••{|}ᜐḄt*EFG”Ḅ☢nD1,4`Ḅ☢nD13-1=12,.M=12+4=3,22ab=12,v(a+b)2=a2+b2-\-2ab,(a+b)=12+13=25.ᦑ⌱D.⚪ὃurḄឋNᑨHVḄឋNhiHᳮqᐰ]rKLW
⚪Ḅᐵ2.12.Cூᑖ᪆௃3440ஹAB,PB,6PHLO4H,BC_L/OC,᝞
rWᑮ-7+26=0WB(2^/3,0),ᑭᵨrWᑮ/(3),ᑣ஺/=26_<ᑨ/JOBD9*4Ḽᑭᵨ/O/P=30஺WᑮᑭᵨᱥYḄXឋWᑮPO=PB,ᡠOP+^AP=PB+PH,᪷U{YᨬWᑮ"ஹPஹ8ᐳYP8+P//Ḅᨬ¡,ᨬ¡

14D8CḄᯠ¤¥¦8CḄᓽ<.ூ
௃
3440ஹAB,PB,6PHLO8H,BCLAO^C,᝞ᡠ§,y=0-/+2ḕx=0,
Wx/=0,/=20ᑣ8200
,y=-x2+2y/3x=-x->/3
2+3,ᑣZ3
,••OA=+3,=2_AB=AO=2\[3,:AB=AO=OB,408D9*NQ/P=30஺:.PH=^AP,ᚖ]ᑖOB,'.PO=PB,'.0P+gAP=PB+PH,஻ஹPஹ3ᐳY23+஻Ḅᨬ¡ᨬ¡D8cḄ,;BC=®AB==>2?=3,22...OP+g/PḄᨬ¡D3,ᦑCu©.ᦑ⌱C.⚪ὃª«¬ᦪḄឋNhiHᳮḄ#ᵨ9*ḄᑨHឋNpᨬ®¯Ḅ
=r@OP+g4PAᓄCPB+PH,᪷U4ஹPஹ8ᐳY8+P4Ḅᨬ¡ᨬ¡D8cḄ
=⚪Ḅᐵ2.13.3

15ூᑖ᪆௃᪷UᐵX°XḄ±ᙶ᪗´µ¶ᙶ᪗ZD[·ᦪW6Ḅ-_ᓽ<Wa+bḄ.ூ
௃•••4(a,b)8(1,-2)ᐵx°Xa—l,b—2,a+b=3.ᦑ3.⚪ὃ]☢ᙶ᪗,ᐵᙶ᪗°XḄḄᱯ¹QRᐵᙶ᪗°XḄḄᱯ¹
⚪Ḅᐵ2.14.26ூᑖ᪆௃º7ᜩḄ¼½ᢥ¡ᑮᜧ᣸ᑡ¤᪷UÂᦪḄHÃ
ᓽ<.ூ
௃
᪷U7ᜩḄ¼½ᢚYÅ¥ºÆ7ᜩḄ¼½ᢥ¡ᑮᜧ᣸ᑡD20,22,24,26,28,28,30,ᦑÂᦪD26࠷.ᦑ26.⚪⌕ὃÂᦪḄHúÇÈᦪUᢥ᯿¡ᑮᜧ(ᡈᜧᑮ¡)ḄÌÍ᣸ᑡ᝞ÎÆÈᦪUḄ`ᦪ᜻ᦪᑣᜐ{ÂÐḄᦪÑÆÈᦪUḄÂᦪ᝞ÎÆÈᦪUḄ`ᦪᏔᦪᑣ{`ᦪUḄ]ᙳᦪÑÆÈᦪUḄÂᦪ.15.3ூᑖ᪆௃4
ᔜ`´9LḄ
ÕÖ×KᐳØᑖÖÙu᦮ᦪ
ᓽ<.

16ூ
௃
ᵫ2x+147,
Wx<3,ᵫx>2,ä´9LḄ
Õ22ᦑ´9L2X+147Ḅu᦮ᦪ
D3,ᦑ/ᫀ3.⚪ὃ
ÇᐗÇ«´9LÈḄ
Õg´9LÈḄu᦮ᦪ

⚪Ḅᐵ2QR
´9LÈḄS)¦ᑣ
Õ¤ÙéêᩩfḄu᦮ᦪ
ᓽ<.16.20ூᑖ᪆௃ᵫrV-2x-8=0Ḅ᪷Daஹp,ᑭᵨ᪷,ᦪḄᐵ,Wa+/?=2,4=-8,ºᐸòᐭa?+᜛2=(a+/J)?-2a£<a2+??Ḅ.ூ
௃•rf-2x-8=0Ḅ᪷Daஹ0,aP=-=-8,a'.a2+/32=(a+/3)2-2a/3=22-2X(-8)=20ᦑ20.⚪⌕ὃÇᐗª«r᪷,ᦪ{Ḅᐵ,ᓽ“øùHᳮ”'(QR“᪷g9bc᪷n9
=⚪Ḅᐵ2.aa

17ூᑖ᪆௃ᵫ9ῪḄឋNWᑮ஺Ḅᓽ/2ூᑖ᪆௃$%&ᦪ()᪷+(),-(0,2)ᓽ/01NB2/CḄ3᪀⌼6N8E^Z\C4஺8AஹEஹNᐳ:V;<ᨬ>?ᑭᵨBCD1E:Ḅx?ᓽ/.ூF௃G᪷+HIḄᱯ/•.•()-(0,2),ᓽ8x=ZO=8E=0:஺KAᔠEKBᔠE:y=/E+CD=NB+ZC=2,NῪ

18/.AB=AC=1,-AO4PD
B6NBJ.BC,QR?᝞(ᡠWE::AD=BE=x,AC=BN=1,'.AF=AC-sin450=—f2F,'/BEN=4FEA,/NBE=/AFE:.GNBEs2FE.NBBE•[\]‘1x/2-1...()Ḅ_ᙶ᪗NGV2-1.

19ᦑb-1.⚪ὃIc⚪Ḅ&ᦪ()ᐰḄᑨfKឋBCḄᑨfKឋg-ᑖ᪆Ihijᔠ&ᦪ()01ABஹACḄ3kg-᪀⌼ᐰlᑮᨬ>?n⚪Ḅᐵ.19.o+3ூᑖ᪆௃᪷+ᱯq&ᦪ?ஹrstஹuᢣᦪwxys᪷zḄH{/T|}D.ூF௃G~z=26-l-2x+42+3-⚪⌕ὃᱯq&ᦪ?ஹrsᗩஹuᢣᦪxys᪷zḄH{ᱯq&ᦪ?ஹrsஹuᢣᦪwxys᪷zḄH{⚪Ḅᐵ.20.ᓃ⌳yx+12ூᑖ᪆௃ᐜᑁḄfᨬᑖ|}gᑖ◀:◀H{ᓄNH{]H{:⌕ᐜᑖஹᑖzᑖḄᐜᑖᯠ¡ᑖ¢?|}ys᪷zᓄ£{.ூF௃2-x+x-1(x+1)2_2—xx+1

208X=y[2—1::~z=*!ªy/2,—1+13-3>/2-2221.(1)a=8,6=20(2)2.0,.x<2.4(3)F»᪆(4)240¼ூᑖ᪆௃(1)᪷+⚣ᦪᑖ¾[(/¿D

21⚪ὃ⚣ᦪᑖÎ⊤ஹ⚣ᦪᑖÎ[(ஹhᦪஹᵨ᪵ë£ìíê⚪Ḅᐵî⚪ᑭᵨᦪjᔠïðê.22.131.6஺%ூᑖ᪆௃-AOAF1BCPF,᪷+ῪḄᔠ\ឋ

22(2)জaxyJ@A◤OPzCDE1᪷f“|ᡂHI~ḄPA”ᑡᑖqr;,ᓽuLঝᐜ;<|ᡂHI~ᡠ◤ḄPA1ᑖ;<◤Ḅᵨ1ᓽu,.ூ,௃(1)aᵬ@AᨵxCDEFGHI1J@AᔜᨵyCDEFGHI1ᵫ⚪

23(2)ᐜ;É/E=5,ᵫÊËÌᳮÎÏ<ᑮ/Ð=3,ᵫyº»Ìᳮ<ᑮOE=g/(8=g/O=5,<ÑijFG=5,BG=AB-AF-FG=2.ூ,௃,R(1)¸¹:•.•ÀÁ048CQ$Ó01x஺$8஺Ḅy1■:EADy1I.0EABDḄyº»1'.OE//FG,■'OG//EF,'.ÀÁ0OEFG$ÂÃÀÁ0,'EFVAB,xÂÃÀÁ0OEFG$È0.(2);•E$/஺Ḅy140=10,,,.AE=—AD=52INEE4=9Q°,EF=4,...ᙠRt^AEFy,AF=y/AE2-EF2=ᑁ-=3-•••ÀÁ0/SCO$Ó01'.AB=AD=\0,'.OE=IAB=5,:ÀÁ0OEFG$È01'.FG=OE=5,xBG=AB-AF-FG=10-3-5=2.ᦑOE=5,BG=2.%⚪ὃ*+È0Ḅឋ5hᑨÌ1Ó0Ḅឋ5ஹÊËÌᳮ2¾Ö1,⚪Ḅᐵ78×ØᱯÚÀÁ0Ḅឋ5hᑨÌÛÜyὃÝὃ⚪Þ1◤⌕ß×Ø.25.প·,᪆L8ফ-3(3)AF^CE+BD,ᳮᵫ·,᪆

24ூᑖ᪆௃(1)àá஺£>,ᵫᑗ»Ḅឋ5u,DE,ᵫ“S4ru¾èCOEéè£>(?£,JKNOCE=NOED,ᵫ/.0ᑁ.hÌᳮu

25••x=z2.f:BC=6,,.,4C=ZO=8,45=10,:BD=2,•'OB2=OD2+BD2,'.(6-OC)2=062+4,.8OC=-L3oᦑ஺஺Ḅðñ$§L(3),RAF=CE+BD,ᳮᵫ᝞õ:ᵫ(1)u¾RG4COqAADO,'.ZACO=ZADO=90Q,NAOC=NAOD,F,'CO=DO,OE=OE,'./\COE^/\DOE(SAS),:/OCE=/ODE,•'OC=OE=OD,'.ZOCE=ZOEC=ZOED=/ODE,'.ADEF=\^Q-AOEC-/OED=T80஺-2NOCE,öÐ8y1ZACB=90°,:.CF=BF=AF,:/FCB=/FBC,'.ZDFE=\S00-ZBCF-ZCBF=\S00-2ZOCE,'./DEF=/DFE,

26'.DE=DF=CE,'.AF=BF=DF+BD=CE+BD.%⚪8ᙊḄøᔠ⚪1ὃ*+ᙊḄᨵᐵ¾Ö1ᑗ»ḄᑨÌhឋ51ᐰ2/.0ḄᑨÌhឋ5,ÊËÌᳮ1┦./.çᦪ2¾Ö1ᮣûüᵨýþឋ5ÎÃÿᳮ
⚪Ḅᐵ.26.(1)=-/+2+3,஺(0,3)(2)(1,1)ᡈ(3)-2ூᑖ᪆௃(1)ᵨ!"ᦪ$ᓽ&'((2))
*+,-Ḅ.Ὺ0-12ᑣ&*ᑖ8=/஺ᡈ5678,ᑖ9'(ᓽ&(3)᪷;S/=g/ExyM,2s2=0NXM,ᓽ&'(.ூB(௃f—1—b+c=0(E(1)FG4ஹ3Ḅᙶ᪗LᐭNᱥP⊤RST°VW2[-9+36+c=0[=2(T22[c=3ᦑNᱥPḄ⊤RS+y=-7+2x+3,^x=0_2y=3,ᦑGC(0,3)(2)^஻?=1_2GE(1,0),cG஺Ḅᙶ᪗+(1,a),ᵫG4ஹCஹ஺Ḅᙶ᪗T2AC=(0+1/+(3-0)2=e,fᳮ&TEg72CD={l+(a-3)2,জ^_2ᓽJa2+4=Jl+(a-3)2,(T஺=1;ঝ^_2fᳮ&T஺=ne(opqr)ᦑG஺Ḅᙶ᪗+(1,1)ᡈ(1,s)t3u,:Etv20u,&cGA/t஻?2-v?+2m+3u,

27-m2+2m+3=sm+£cyPḄ⊤RS+y=sx+f,ᑣ0=3s+E'___1_(TEz.I,t=------tn+\13ᦑyPᵨWḄ⊤RS+y=--\x+—7W+17W+1333^x=0_2y=-ᦑGN(0,--),ᑣON=+m+1m+\m+1Si=^AE^yM=yx(v+1)x(-m2+2m+3\32s2=ONXM=---xm=S]=gx(w+1)x(-m2+2m+3)fm+12(Tᵨ=-2±(opqr)2{|}~=J7-2
Ḅ᪷2ᦑ஻2=J7-2.⚪ὃḄ
ᦪᔠᵨ2ᑮᦪḄឋஹ.Ὺ0-1Ḅឋஹ☢Ḅ.2ᐸ(2),⌕ᑖ'(2⍡.

282022-2023
ᓭḕὃᦪ⚗ᓣ⚪ஹ⌱⌱tᜧ⚪ᐳ10¡⚪2¢¡⚪3ᑖ2ᐳ30ᑖu1.-2018ḄrḄ£¤ᦪ
t)11A.-----B.C.2018D.-2018201820182.§ᑡ©ªḄ
tuA.3x—2=xB.(2x2)3=8x5C.xx4=x5D.(a+b)2=a2+b23.᝞®2yPa஻b,F¯30஺-Ḅy-0-°᝞®±²2y-⚔G´ᙠyPb¶2)/1=4.·᝕᣸º»ὶ½2017—2018½¾2¶¿ÀᜩÂ᝕᣸ÃÄÅᡊ2ᨬÈÉÊḄᜩÂ᝕᣸ËÌÍÎḄÏÐѶÒ⚞ᝄÕ.½ÖᢈØÙ2½¾º»ÚÛÜÝÞᐳTᑮ804ᑖ2ß⌼Ò᝕᣸ὶ½TᑖḄᔊâãä.804åᦪᵨæçãᦪ$⊤è+tuA.8.04X102B.8.04X103C.0.84X103D.84.0X1025.§ᑡêëì2ᐸ0í®î
ᐰ.®1Ḅ
tuA,ᙊñB.ᙊ┵C.0ó┵D.ᳫ6.ᐵõxḄᐗx2-2x+k+2=0ᨵùᦪ᪷2ᑣkḄúrüᙠᦪý¶⊤詪Ḅ
tu7.þ*§ÿ
ᱏᭆ᳛Ḅ

29টA,
B.
C.

D.
ᨵ
8.᝞
AB஺0Ḅ&'(C,D,Eᙠ஺0+,NAED=20°,ᑣ/BCDḄ3ᦪA.100°B.110°C.115°D.120°9.᝞
8Ὺ:;/8CḄ<=8c?4,☢B16,ῪZCḄᚖ&FᑖHEFᑖJKAC,=LE,F
.,(஺BC=Ḅ((MrHOEF+P(ᑣQ8/ᕜ?10.STUᱥHW=ax2+bx+c஺\0Ḅ&Hx=2,]xḄ^K(ᙶ᪗4,0,ᐸbᑖ
c᝞
ᡠefᑡhijজUᱥHlm(ঝa-b+cVOঞsx

30A,জঝঞB,জটঠC.জঝটD.ঞটঠஹ>?⚪@ᜧ⚪ᐳ6CD⚪EFD⚪3ᑖEᐳ18ᑖHIᫀ>ᙠI⚪ᓱḄNOPQR.11.jRL-S=__.12.ᦪy=-xḄ13.ᨵᦪj2,a,4,6,7,ḄFᙳᦪ5,ᑣᦪḄᦪ.14.᝞
ᙠAABCDAB+Ḅ(᝞fjজBᙊBD?'KBCL(FঝᑖJD,FᙊBD?'ា¡LAC+Ḅ(Eᜐঞ£¤DE,FE.,AB=6,BC=4,¥¦AD=.15.᝞
AD&'ḄᙊORt^ABCḄª=ABḄ^«(K&;=ACL(E.BஹEᙊḄ:8ᑖ(,஺A=2,ᑣ
▢®bᑖḄ☢B.16.᝞
¯AD=2,AB=5,PC஺=+ḄP(s]ABCP±v,DP=Ar-BDp

31ஹSI⚪@ᜧ⚪ᐳ9CD⚪Eᐳ72ᑖ.17.ᐜᓄ´µj4-(———ᐸx=G+l.X2-2X+1X-1x18.ᡃº»¼½¾¿ᦋ☩ÂÃÄḄÅÆÄஹᔠKÈÉÊᨵËᜧÌÍὁÏÐÐÑᡠᦟÓÔÃÕÅÃÄஹᔠKÈḄᐹ×ØÙÚÓbᑖÃÕÐÛ^ᨴḄÝÞ,ßàháᑖᡂãäAjᱯJBjCjæDj¡çßàháèᑴᡂfêᨵë᦮Ḅí
îï᪷í
fᑡñ⚪j1ÚóὁÏᐳÐõöÃᐸCä᝕ÕᨵõDäᵱÕᨵõ2à+☢Ḅᩩí
⊡ᐙë᦮3ÐᐳöüὁÏýþÿḄADᑖ⌱“”ᵨᑡ⊤ᡈ᪛!Ḅ"#$ᡠ⌱&ា()ᵱ᝕Ḅᭆ᳛.19.᝞!ᜧ4567ᨵ9:ᱥᙠ9:ᱥḄ=>ᨵ?@4ᙠ@4Ḅ⚔B஺ᜐEF9:ᱥ>GHCḄJKL30஺EFᜧ4⚔B4ḄPKL45஺RH8,C,EᙠVWXYZ[.\]48=80_DE=\0m,#9:ᱥ8,C&H`Ḅab.Rcdeᶇ᪷h[□□□□□□□□

3220.᝞!j@kᙠlm30m,o20,஻ḄqrᙢZtu&vwx⍝vwx⍝Ḅoz{L2|1,ᐸ~ᑖ₝x⍝ᡠᓰ☢)᦮lrᙢ☢Ḅ.75(1)#vஹwx⍝ḄoᔜL(2)tu12⍝◤750ᐗ1@₝◤25஺ᐗtu◤?IIII21.᝞!\]ᵨaAOBḄXK>OAᙠxZ0A=2,AB=1,ᵨAOBH0⌮k¢┐¤¥90஺Fᑮ7J/ACOD,©{ª«ᦪy=HB.x(1)#©{ª«ᦪ®᪆°±(2)²³BD,HP)©{ª«ᦪ!µZḄH¶0PAOBDḄᕜmᑖᡂ¹ºḄ&ᑖ#HPḄᙶ᪗.22.᝞!஺OḄX½AC¾¿BD¹ÀÁHF,HE)DBÃmYZḄHZEAB=ZADB.(1)#Å|EA)ḄᑗY;(2)HB)EFḄHAB=273>CB=2«#AEḄm.23.“ÊËÌÍÎᩈ”ÐÑᵨᓫÓÔᜩᦪÖ×ᓄḄÙ°jdÎᑭᵨ30ᜩ¢`ᡂÛL10ᐗ/ÜḄdÎÝÞßàFᑮdÎᓫÓᙠáxᜩ(xL᦮ᦪ)Ḅ¹ᐵãä᝞å!⊤ᡠæ|ç"(Ü)n——x+50

33é1WXW20¢m=ᓫÓMᐗ/Ü[420é21WxW30¢=10+——xm¾x`ᐵî°⊡ᐙñ᦮;ঝàóáôᜩõdÎᓫÓL25ᐗ/ÜR2[#õödÎ30ᜩ÷øᜩᡠùᑭúyRᐗ[ᐵÁxRᜩ[Ḅ«ᦪᐵî°;R3[“ᔛVüᨵý᢬ÿ”✄ᙢ30ᜩᐸᑭḄᜩḄᑭᐰᣎ!“#$ᢄ&”.()*+“#$ᢄ&”ᣎ,-.?24)⚪34:᝞71,AABC>?@ABCADJ_BCGHD,ZABCJHBKL┐NO30°QBA,BC?RSTADᑖVWGHE,F,Z[*4BEF>?@AB.\]^ᵨ*᝞72,ZXABC>?@ABHPbAABC᜜dHZBPC=60°,/BPCJHP⌮L┐UA60஺QPC?ាjHA,klPA,PB,PCmnoᙠḄᦪrᐵtu[vwḄxyz{|}~*᝞73,ᙠBABCDNABC=6O஺,NABCJHBKL┐NOᑮ᝞7ᡠᙠḄᑮNMBN,FbBMdHAF,DF,DFWBNGHE,B,EHាjᐵGTAF.1[v4BEFb>?@ABz2DE=6,BE=2,ZAFḄ.

3425᝞7ᱥTy=-x2+bx+cRxWGA(-1,0),B(5,0)H.(1)ZᱥTḄ᪆z(2)ᙠ▲ᑁ¢dHC,CCDᚖxGHD,¤AC,¥AD=5,CD=8,RSACD¦xᔣ¨©]mªᓫ¬HCᙠᱥTLZmḄ®z(3)ᙠ(2)Ḅᩩ°±¬HC+ᙠᱥT²HE,HPbᱥTdH.(kl*ᙠᱥTbᔲoᙠHQ,´µHBஹEஹPஹQ⚔HḄ¸?Bb©!¸?B¹oᙠºHQḄᙶ᪗z½ᨵoᙠº¿vᳮᵫ.2022-2023
ᓭḕὃᦪ⚗ᓣ⚪()

35dஹ⌱d⌱(ᜧ⚪ᐳ10ªÅ⚪ÆÅ⚪3ᑖᐳ30ᑖ)1.-2018Ḅ®ḄÇᦪb()11A.-------B.----------C.2018D.-201820182018ூÉÊËᫀ௃DூÎ௃ᑖ᪆*ÇᦪḄÏ*ÐᨵÑÒ½ᨵÓḄªᦪÔÇᦪ0ḄÇᦪb0;®ḄឋÖ*dªÉᦪḄ®b×ØzdªᦪḄ®b×ḄÇᦪz0Ḅ®b0.Î:."20181=2018,A2018ḄÇᦪb-2018.ᦑ⌱D.HÚ*⚪ὃÜḄbÇᦪᭆÞß®ḄឋÖ.2.±ᑡáâÉÊḄb()A.3x-2=xB.(2x2)3=8x5C.x-x4=x5D.(a+b)2=a2+b2ூÉÊËᫀ௃CூÎ௃ᑖ᪆*᪷äåᐰ©æçµèéḄᔜëáâìᑣ⌲⚗ᑖ᪆ᓽñ.Î*Aஹ3x-2,½ᨵbÓò⚗½ᨵóᔠuᦑ⌱⚗┯özBஹ(2x2)3=8x6÷x5,ᦑø⌱⚗┯özCஹx-x4=x5,ᦑ⌱⚗ÉÊzD^(a+b)2=a2+b2+2ab/a2+b2,ᦑø⌱⚗┯ö.ᦑ⌱C.HÚ*⚪ὃÜùÓúᦪûḄüìஹýḄüæµèåᐰ©æçḄáᵨþÿ
ឋᑣ⚪Ḅᐵ.3.᝞a஻b,30஺Ḅ᝞⚔ᙠb"#/1=55°,ᑣN2Ḅ$ᦪ&()A.30°B.35°C.45°D.55°

36ூ+,-ᫀ௃Bூ1௃ᑖ᪆4ᐜ᪷789Ḅឋ:;N3Ḅ$ᦪ>ᵫ@ABḄឋ:;/2Ḅ$ᦪᓽF.14•.,a஻b,Zl=55°,.••Z1=Z3=55°,•.•Ḅ⚔ᙠb"AZ3+Z2=90°,Z2=90o-Z3=90°-55°=35°.ᦑ⌱BY4Z⚪ὃ\Ḅ89Ḅឋᓽ@89]^_`.4.bc᝕᣸fgὶi2017—2018im"noᜩq᝕᣸rstᡊᨬwxyḄᜩq᝕᣸z{|}Ḅ~"⚞ᝄ.iᢈbZimfgᐳᑮ804ᑖ⌼᝕᣸ὶiᑖḄᔊ.804ᦪᵨᦪ⊤&()A.8.04XI02B.8.04X103C.0.84X103D.84.0X102ூ+,-ᫀ௃Aூ1௃ᑖ᪆4ᦪḄ⊤£¤&axionḄ£¤ᐸb"]©10,n&᦮ᦪ.,«nḄ¬⌕¯°±ᦪ²ᡂa´ᦪµ¶·¸^nḄ¬o´ᦪµ¶Ḅ^ᦪ_].¹±ᦪ¬º1n+ᦪ»¹±ᦪḄ¬©1n%Xᦪ.1:804ᦪᵨᦪ⊤&8.04X102,ᦑ⌱A.Y4½⚪ὃ\ᦪḄ⊤¾.ᦪḄ⊤£¤&axl()nḄ£¤ᐸbr]

37<10,n&᦮ᦪ⊤ᐵ⌕+,,«aḄ¬¿ÀnḄ¬.5.ÁᑡÃÄÅbᐸÆÇᐰ`£Ḅ(A.ᙊÊB.ᙊ┵C.Ì┵D.ᳫூ+,-ᫀ௃Dூ1௃ᑖ᪆4ÎϾᔣ"ḄÆÇᐰ`£ḄÃÄÅÑᨵᳫᙠÎϾᔣ"ḄÆÇᙊᐸÓḄÃÄÅḄÆÇᨵÔᨵ]Ḅ.1:ᙊÊᙊ┵Ì┵ᳫbÆÇᐰ`£ḄÃÄÅÑᨵᳫᙠÎϾᔣ"ḄÆÇᙊᦑ⌱D.Y4Z⚪ὃ\ÕᓫÃÄÅḄÆZ⚪⚪Ḅᐵ¯;ᔜ£ḄᙠÎϾᔣ"ḄÆ.6,ᐵØxḄÙᐗÛܾÝx2-2x+k+2=0ᨵÞᦪ᪷ᑣkḄ߬áᙠᦪâ"⊤+,Ḅ()ூ+,-ᫀ௃Cூᑖ᪆௃ᵫÙᐗÛܾÝᨵÞᦪ᪷Fãäå()ᓽF;ᐵØ"ḄÙᐗÔᨵ`¤æᓽF;ZḄ߬á.ூ1௃•••ᐵØxḄÙᐗÛܾÝ/_ᐭ+é2=0ᨵÞᦪ᪷.,.ä=(-2)2-4(H2)>0,4k4—l,ᙠᦪâ"⊤&4ᦑ⌱C.Z⚪ὃ\ÙᐗÛܾÝ᪷Ḅᑨë¤.᪷7ÙᐗÛܾÝ᪷Ḅìíᑭᵨ᪷Ḅᑨë¤ᑡ;Ôᨵ`¤⚪Ḅᐵ.

387.ï¿ÁðñᱏbóôõßÙñᭆ᳛&'Ḅùú4জঝ<3>টA.âûü£B.ûü£C.ýâûü£þûü£D.âûü£ÿᨵூᫀ௃Cூ௃ᑖ᪆:᪷Ḅᭆ.:জᨵ;ঝ;ঞ;ট"ᨵ;ᦑḄᭆ᳛%3&Ḅᭆ᳛%:&Ḅᭆ᳛%L;"ᨵḄᭆ᳛%;.42ᦑᫀ%C.'()*⚪ὃ-ᭆ᳛Ḅ./ᵨ1234.)᝞627ᨵn89:1;<=>Ḅ9:ឋ@A1ᐸCADEm8F61GHAḄᭆ᳛PA
=—.n8.᝞1AB஺0ḄJK1'C,D,Eᙠ஺0M1NNAED=20°,ᑣNBCDḄPᦪ%RTA.100°B.110°C.115°D.120°ூᫀ௃Bூᑖ᪆௃UVAD,BD,ᵫᙊᕜZ[ᳮ9]/ABD=20஺1ZADB=90°,^;9]/BAD=70°,_ᵫᙊḄᑁVabZc⊡]ᑮNBCD=110஺.

39ூ௃᝞f1UVAD,BD,AgᡠḄᙊᕜZ@i1/ABD=NAED=20஺,)AB%JK1.•.NADB=90஺1/.ZBAD=90°-20°=70°,AZBCD=180°-70°=110°.ᦑ⌱B*⚪ὃ-ᙊCḄZPlm1no/ᵨᙊᕜZ[ᳮpᑁVabḄឋqᐵs.9.᝞1iῪuZ/8CḄvb8Cw%4,☢y16,ῪZCḄᚖJ{ᑖ|EFᑖ}~AC,ABZE,F
.N'஺%8CbḄC'1'M%|EFM2'1ᑣCDMᕜwூᫀ௃Cூᑖ᪆௃UVN஺1ᵫA/BCiῪuZ1'஺8cbḄC'1ᦑ4O_LBC,_᪷uZḄ☢yDḄw1__᪷EE|NCḄᚖJ{ᑖ|91'CᐵJ|EḄ'%'/,ᦑḄw%CM+MZTḄᨬ1ᵫᓽ9]DF.ூ௃)UVFB

40/BCiῪuZ1'஺8cbḄC'1J.ADVBC,ASAJSC=7BC-AD^yx4xz4D=16,]AD=8,•••■|ACḄᚖJ{ᑖ|1&.'CᐵJ|EFḄ'%'A,'.ADḄw%CM+MDḄᨬ1...8MḄᕜwᨬ¡=(CM+MD)+஺=4஺+&8c=8+gx4=8+2=10.ᦑ⌱)C.*⚪ὃ-Ḅ-ᨬ¡§|¨⚪1niῪuZu|ᔠ2Ḅឋq⚪Ḅᐵs.10.ª«ᱥ|y=a/+bx+c(awO)Ḅ%J|X=2,xḄ27~'ᙶ᪗%(4,0),ᐸ¶ᑖ·᝞ᡠ¸1fᑡF)জ«ᱥ|º»'&ঝa-b+c<0&ঞ½x0,/.a-b+c>0,Fঝ┯Ì&ঞÍÎÏᦪ·9)½x

41ঠ)«ᱥ|Ḅ⚔'ᙶ᪗%R2,bT,/.ax2+bx+c=b¿1b2-4ac=0>Fঠ.ÑMᡠÒ1ḄFᨵ)জটঠ.ᦑ⌱B.'()*⚪ὃ-Ó«ᱥ|xḄ~'ஹÕÖÏᦪ·×ᦪḄᐵ×ØÙÕÖÏᦪ·M'Ḅᙶ᪗ᱯÛ1⌲2ᑖ᪆ÝᩩFḄÌ⚪Ḅᐵs.ஹ>?⚪@ᜧ⚪ᐳ6CD⚪EFD⚪3ᑖEᐳ18ᑖHIᫀ>ᙠI⚪ᓱḄNOPQR.11.lm)•2Ö=.ூᫀ௃J5ூᑖ᪆௃ᐜᓄãÕÖ᪷1_ᔠäAåÕÖ᪷ᓽ9.ூ௃718-^=372-272=^.ᦑ0.*⚪è⌕ὃ-ÕÖ᪷ḄᓄãØÙAåÕÖ᪷Ḅᔠä1êëÕÖ᪷ḄᓄãØÙAåÕÖ᪷Ḅᔠä4.⚪ᐵs.12.Ïᦪì=/=C1íîïxḄðò%_______.,y1—Xூᫀ௃x0,9]x

42ூ௃)•••üõᦪḄ{ᙳᦪ%5,2+a+4+6+7.-------------------5L5ý=õᦪᢥ᯿
ᑮᜧḄ᣸ᑡ2,4,6,6,7,ᦪ6,ᦑ6.ὃ1ᦪ2ᙳᦪ14.᝞#$ᙠaABC$D+AB,Ḅ-$./᝞012জ4Bᙊ6$BD7892:;BC<Fঝ?ᑖA4D,Fᙊ6$BD7892:$B:ាDEF

43/xBᩩx$ᡠḄxyᡂ{|.15.᝞#$4AD9Ḅ8ᙊORtaABCḄ_ABḄB$;_AC<E.BஹE+8ᙊ:Ḅᑖ$L0A=2,ᑣ#▢ᑖḄ☢.ூQRSᫀ௃—223ூWX௃JK80,BE,BO,EO,■:B,¡+8ᙊ:Ḅᑖ$/.ZEOA=ZE0B=ZBOD=60°,'.ZBAC=ZEBA=30°,'.BE//AD,/.J^=J£)cos30°=2y/3,:.BC=^AB=45>•,•/,C=VAB2-BC2=3>ahX8CX/C¢Xᶔ¤3=¥$222^BOE¦§¨$¢/XBOEZ8E☢E$#▢ᑖḄ☢SBC-SO^^--60£=ª1--71.MWB236023ᦑSᫀᐔ.23

4416.᝞#$«`/8C஺$AD=2,AB=5,P8_,Ḅ¯$°d/£±²³d■BCPEµ¶,DP=_.ூQRSᫀ௃1ᡈ4ᡈ2.5ூᑖ᪆௃◤⌕ᑖ»¼½AAPDsAPBCbAR4DSAPBC,᪷\¾Eµ`Ḅ_ᡂ{|hDPḄ7¿.ூWX௃n஺P=x,ᑣCP=5-x,ᑖBÀÁÂÁÂ./¼½$ADDPজ°¶$——=——BCCP2x'.-=---,25-xX:x=2.5,AHDP2xঝ°d/PZ)sAP8c¶$——=-$ᓽ----=-$CPBC5-x2Xx=lᡈx=4,È,ᡠÉDP=\ᡈ4ᡈ2.5ூᨒ௃t⚪Ë⌕ὃvḄÌ+`EµḄÍ⚪¯Í⚪$✌ᐜÐᔜxyᵨÒxḄÓᦪÔ./⊤Ö$ᯠc×+ᔲᨵE¦Ḅ$᪷\ḄB_ᡂ{|Ðxyᑏᡂ{|ÔḄ`Ô$ᯠcᑖA./ÛiSᫀ.ᙠXSÜÀÍ⚪Ḅ¶᎛ᓟßᨵiàáXḄàâ$ãÀÁÂä⌕ὃ⇋ᑮ.ஹSI⚪(@ᜧ⚪ᐳ9CD⚪Eᐳ72ᑖ.)17.ᐜᓄç$?hèJ+x+(?——,ᐸx=g+l.X2-2X+1X-1x

456+4ᡭூQRSᫀ௃3ூWX௃ᑖ᪆ïÔðñB⚗óᑖôᑭᵨ¦ᑖöᑖÔḄ÷kkᑣÛ$¦¶ᑭᵨ◀kkᑣù`$úᑖᑮᨬçüý$þxḄèÓᐭ
ᓽ.(x+1)r2xx-1(x—᮱-[x(x-l)x(x-l)_X(X+1)x(x-l)(1)2(X+1)x-1X=JJ+1"#=(0+1)24+20=6+48V3+1-1A/33*+,⚪ὃ/0ᑖḄᓄ4#56789
:ᑣ<=⚪Ḅᐵ?.18.ᡃABCDEFᦋ☩I#JKḄLMNKஹᔠQRSTUᨵWᜧYZ#[ὁ]^00ᡠᦟabJcLMJKஹᔠQRSḄᐹefg#h=aiᑖJcjk0^lmnᨴḄpq#rstuᑖᡂwx#Aᱯ{|}B|}C}D}rstuᑴᡂᨵ᦮Ḅ#᪷ᑡ⚪(1)=#[ὁ]ᐳ0J#ᐸCx᝕cᨵ#Dxᵱcᨵ;(2)s☢Ḅᩩ¡⊡ᐙ᦮;

46(3)^0ᐳj¤#[ὁ]¥¦§ḄAx¨DxJcᑖ{⌱ª«Jjk“”¯°JK#ᵨᑡ⊤:ᡈ´᪛¡Ḅ¶:ᡠ⌱«Jា|<«ᵱJ¨«᝕JḄᭆ᳛.ூ»¼½ᫀ௃(1)20,2,1}(2)Á᪆.(3)g,⊤ÄÁ᪆.ூᑖ᪆௃(1)ᵫᡧ¡Ç#ᱯ{|ḄᓰÉᦪḄ15%,Íᦪᨵᩩ¡Ç3Í#ᡠḄ᪵=ÏÐ<3+15%,ᓽÑCx᝕c¨DxᵱcÍᦪ}(2)᪷(1)ᡠᦪÑᩩ¡ḄZÒᓽ}(3)᪷§ḄAx¨DxJcᵱ᝕cÍᦪᑡ⊤ᓽѽᫀ.ூ௃প3+15%=20,20x25%=5.᝕c5-3=2,1-25%-50%-15%=10%.20x10%=2,ᵱc2-1=1,ᦑ½ᫀ^20,2,1}(2)᝞ᡠÖ(3)᪷[ὁ]¥¦§ḄAx¨DxJcᑖ{⌱ª«Jjk“”¯°JK#sAx×DxJcᑖ^ØÙfg:Aᝯ15^42ᵱDAᵱD᝕A1D᝕A2D᝞᝕DᵱA᝕A1᝕DÝ2Þᑭᵨ⊤Çᡠ⌱«Jា|<«ᵱJ¨«᝕JḄᭆ᳛^:

473_6~2,19.᝞#ᜧâãäåᨵæçᱥ#ᙠæçᱥḄêëᨵìíâOE,ᙠíâḄ⚔ñ஺ᜐôÑæçᱥëõ*CḄö÷^30஺#ôÑᜧâ⚔ñ/Ḅù÷^45஺ú*8,C,£ᙠüýþÿ
.ᨴ8=80DE^iOm,ᱥ8,CḄ.ᶇ᪷
□□□□□□□□ூ!"ᫀ௃70-10(
m.ᑖ᪆+,D-DFLAB.F,,C-CHLDF.H./,01ᑮDFḄ345/,0Rt^CDE1ᑮCEḄ34ᑣ8C=8E-CE.ூ<0௃᝞>,஺-DFVAB.F,,C-CHLDF.H.ᑣDE=BF=CH=lOm,ᙠRtAZ஺/7D’.7F=80"L10/H=70/„,ZADF=45°,'.DF=AF=10m.ᙠRtz^COED:DE=10m,NOCE=30°,DE_10106P
tan30°y/33BC=BE-CE=70-10V3
w."Sᱥ8,CḄT70-106
U.20.᝞>WXYᙠZ[330\20஻?Ḅ_`aᙢcdef/⍝ef/⍝Ḅ\4

48hT2S1,ᐸjkᑖlmn₝p/⍝ᡠᓰ☢tu᦮[aᙢ☢tḄZ.75(1)eஹf/⍝Ḅ\ᔜT{|}(2)pcd1"/⍝◤750ᐗlm1Xn₝◤250ᐗcd◤{|?ூ!"ᫀ௃(1)e/⍝\2m,f/⍝\1□5(2)cd◤⌕226000ᐗ.ூ<0௃ᑖ᪆:(1)f/⍝Ḅ\uxcm,ᑣe/⍝Ḅ\u2xcm,᪷/⍝ᡠᓰ☢tu>19ᫀ☢tḄZᑡ0575(2)᪷⍝Ḅ☢tn₝Ḅ☢tnᓽ.<0S(1)f/⍝Ḅ\Txw,ᑣe/⍝Ḅ\T19ᵫ⚪1(30-2x)(20-4x)=30X20X(l----),75᦮ᳮ1,x2—20x+19—0,01Xl=l,X2=19(¡ᨵᔠ⚪¤¥)••2x=2m."Se/⍝\2஻?f/⍝\1஻?.19,56(2)30X20X——X750+30X20X——X2507575=114000+112000=226000(ᐗ)."Scd◤⌕226000ᐗ.§S¨⚪©⌕ὃ«¬ZᐗḄ®▭°ᵨ²³⚪´Ḅµ᪷⚪´¶Ḅᩩ¸¹ᔠ〉Ḅ»¼ᐵ¾ᑡu0¿À⚪ḄᐵÁ¨⚪Â⍝☢tÃÄḄkᑖ⌕¥ᣵ.21.᝞>RfZXAOBḄÈÉÊOAᙠxË0A=2,AB=1,ÌRfZXAOBÍ0⌮kÏ┐ÑÒ90஺1ᑮ7?/ACOD,ÓhÔÕᦪy=ZB.x(1)ÓhÔÕᦪ0᪆Ø5(2)ÙÚBD,pPuÓhÔÕᦪ>ÜḄZÝ0PÌAOBDḄᕜ3ᑖᡂà»Ḅk

49ᑖPḄᙶ᪗.ூ<0௃ᑖ᪆S1
ᵫ0A=2,AB=11B2,1
,ãᐭ0᪆Øᓽ1"ᫀ52
ᵫÈå0PæABODḄᕜ3ᑖᡂà»ḄkᑖÝOB=OD,DQ=BQ,ᓽQTBDḄDçè1Qᙶ᪗1ÈåBD0᪆ØὶêÓhÔÕᦪ0᪆ØÈåBD0᪆Ø1Pᙶ᪗.<0S(1)VOA=2,AB=1,B(2,1).k2ãB(2,1).ë=ZD1k=2,5.y=ZxX(2)OPìBDí.Q,SOPÌaOBDḄᕜ3ᑖᡂà»ḄkᑖîOB=OD,OQ=OQ,13-,.BQ=DQ,ᓽQTBDḄD5.QZ-
.1331ÈåOPḄ0᪆ØTy=kx,æQI,,5
ãᐭy=kx,15=5^.,.k=3".ÈåBDḄ0᪆ØTy=3xy=3xy[6ᵫ21”ðy=-IXg1=h...Pñ,ò*ô,-V6).§S¨⚪©⌕ὃ«õö¾ᦪÕᦪ0᪆ØÓhÔÕᦪ>ÜḄᙶ᪗ᱯøùúûüõö¾ᦪýÕᦪ0᪆Ø᪷ᕜ3à»1QḄᙶ᪗u0⚪ḄᐵÁ.22.᝞>஺0ḄÈþACìÿBD
F,EDBḄZEAB=ZADB.

50(1)EA஺0Ḅᑗ;(2)BEFḄAB=26CB=2jSAEḄ.ூ%&'ᫀ௃(1)*+᪆-(2)472.ூ0+௃ᑖ᪆(1)23CD,ᵫAC஺0Ḅ789:;/ADC=90°,ᵫ?ḄᐵA9:;NEAC=90°,ᓽ:;EA஺OḄᑗ-(2)23BC,ᵫAC஺0Ḅ789:;NABC=90°,ᵫᙠRTAEAFBEFḄ9:;NBAC=NAFE,ᓽ9:;HEAFs/\CBA,ᑭᵨMNOAEḄ.0+(1):QABMUAB,AZD=ZC.NEAB=ND,-./EAB=NCAC஺OḄ78.•./ABC=90஺/EAB+NCAB=90஺AZDAE=90°,-.AEW஺Oᑗ-ZABC=90°,AB=2A/3,CB=276,-,.AC=7J52+5C2=6>ᵫ(1)XNOAE=90஺ᙠYAEAFBFḄ/.EF=2AB=4A/3

51.,.ZBAF=ZBFA.VZABC=ZEAF,.,.7?/AAFE^/?zABAC,.AE_EFAE473"BCAC'2-76-6'AE=4&.bc⚪e⌕ὃhiᑗḄᑨklMm?nḄᑨkWឋp+⚪Ḅᐵqr;stuᵨm?nMvᑗឋp+.23.“xyz{|ᩈ~”ᵨᓫᜩᦪOᓄḄ~|ᑭᵨ30ᜩ~ᡂc10ᐗ/Ḅ|:ᑮ|ᓫᙠxᜩx᦮ᦪḄᐵ᝞¢£⊤ᡠ¦§஻஻=%+50¬lWx<20m=________ᓫmᐗ/420¬21WxW30°=10+——X1জ³´⊤¬lWx<20mWxᐵA⊡ᐙ·᦮-ঝ¹ºᜩ»|ᓫ25ᐗ/¼2»½~|30ᜩ¾¿ᜩᡠÀᑭÁyᐗᐵxᜩḄÃᦪᐵA3“ᔛÅÆᨵÈ᢬ÊË”Ì✄cᙢÏÐÑÒËÓk´½30ᜩᐸÀᑭÕÖḄ×ᜩḄᑭÁᐰÙᣎ;ÛÜ“ÝÞᢄà”.áÑÒ˽â“ÝÞᢄà”ᣎãÖäå¼ூ%&'ᫀ௃1জ,x+20;ঝ10ᜩᡈ28ᜩ»|25ᐗ/è-2y=2

5212----X+15x+500l

53.,.x=21y=--------420=580.21V580<612.5,.•.123ᔣ“67ᢄ9”ᣎ;612.5ᐗ.=>?@⚪ὃCDEFᦪḄHᵨஹKLMFᦪḄឋOP&QR⚪ḄᐵTUVW᪀YFᦪᑭᵨDEFᦪḄឋOR[\⚪]^_ὃ`ὃ⚪a.24.\⚪bc?᝞e1,Z\ABCkPlmnopADJ_BC^=D,sNABCu=Bv┐xy30°{BA,BCl|}~ADᑖ^=E,F,?4BEFkPlmno.Hᵨ?᝞e2,ZkABCkPlmno=PUAABC᜜=NBPC=60°,sNBPCu=P⌮┐xy60°{PClា=A,PA,PB,PCᙠḄᦪᐵḄ?᝞e3,ᙠoABCD_NABC=60஺,sNABCu=Bv┐xyᑮ᝞eᡠᙠḄ¤¥¦ᑮNMBN,FUBM=¨©AF,DF,DFBN^=E,ªB,E«=ាᐵ^¬~AF®.¯1°4BEFUPlmno¯2°ªDE=6,BE=2,AFḄ±.ூ³´µᫀ௃¯1°¸R᪆¯2°PC=PA+PB?(3)3ூºR௃ᑖ᪆?¯1°᪷¼PlmnoḄឋO¦ᑮ/EBF=60஺¾ᵫBDJLAC¦ᑮ/BED=60஺,À+¦Á¯2°ᙠPCÂÃPD=PB,¨©BD,ÄÅÆAPBg^CBG¦PA=GC,ᓽʦÁ;¯3°জ̼B,E«=ᐵ^¬~AF®¦FE=FB,¾ᵫ^NEBF=60°ᓽʦÁঝ¨©AE,Å=ApAHLDE^=H,ʦDH=3,HF=5,NEFA=30°,ᙠR/Z\AHF_ᑭᵨZHFAḄÏÐᓽÊÁAFḄÑ.

54ºR?(1)?:ÆABCkPlmnoAB=AC=BC,/BAC=ZABC=ZACB=60°,ᵫ⚪Ó¦ZABE=30°,ZEBF=60°,DZEBD=ZFBD=30°,VBD±AC,AZBED=60°,AABEFkPlmno(2)PC=PA+PB.?ᙠPCÂÃPD=PB,¨©BD,VZBPC=60°,ABPGkPlmnoBG=BP,ZPBG=60°,PB=BG,DNPBA+NABG=NABG+/GBC=60°.\ZPBA=ZGBC¾AB=BC,AAPB^ACBG,.PA=GC,.PC=PG+CG=PB+PA(3)জ?B,E«=ᐵ^¬~AF®...FE=FB,VZEBF=60°,...ÆBEFUPlmnoঝ¨©AE,Å=ApAH±DE^=H,?B,E«=ᐵ^¬~AF®.AE=AB,•.•ÕloABCDUo...AB=AD,

55.AE=AD,ᡠÖDH=HE=-DE=3,2.♦.HF=HE+EF=3+2=5,ᵫজ&Z\BEFUPlmnoFA1EB,AZEFA=-ZEFB=30°2HFV3.ᙠLZAkAHF_cos/HFA=^——=—,AF2._10_10V3Ar••AF-----p==-------.V33=>:@⚪ὃC;PlmnoḄឋO,ᐰPmnoḄᑨÙ|ឋOÖÚmnFᦪR⚪ḄᐵTU³´pÁÛÜ~ᮣÞßᵨmnoàá.25.᝞eâᱥ~y=-x2+bx+c|xäà^A(-1,0),B(5,0)«=.(1)âᱥ~ḄR᪆å?(2)ᙠæDç▲ᑁÃ=C,pCDᚖ¬xä^=D,ë©AC,ìAD=5,CD=8,sRSACDíxäᔣîïmðᓫ¤=Còᙠâᱥ~mḄÑ(3)ᙠ(2)Ḅᩩôõ=CEòᙠâᱥ~ök=E,=PUâᱥ~®ä=.÷?ᙠâᱥ~Uᔲᙠ=Q,ùÖ=BஹEஹPஹQk⚔=ḄÕloUïûÕloüªூ³´µᫀ௃(1)y=-X2+4X+5(2)mḄÑk7ᡈ9(3)Q=Ḅᙶ᪗(-2,-7)ᡈ(6,-7)ᡈ(4,5)ூᑖ᪆௃(1)ᵫAஹBḄᙶ᪗ᑭᵨᦪᱥḄ᪆(2)ᵫ⚪Cᙶ᪗!"#$ḄCḄ%&CᑣCḄ(ᙶ᪗8,)ᐭ

56ᱥ᪆CḄᙶ᪗ᑣ"#Ḅᓫ.mḄ0(3)ᵫ(2)Eᙶ᪗56BE8%9:;M,>E?EFLx:;F,CBE"DEFGḄFH>Q?%9:ḄᚖᚖKN,ᑣM4PQNPZXEFB,QN,ᓽQᑮ%9:ḄUVᑣQḄWᙶ᪗)ᐭᱥ᪆Qᙶ᪗CBE%XHᵫBஹEḄᙶ᪗YBEḄZᙶ᪗!Q(x,y),ᵫPḄWᙶ᪗ᑣQḄWᙶ᪗)ᐭᱥ᪆QḄᙶ᪗.ூ]௃(1):ᱥy=-x2+bx+cdx:ᑖe8;A(-1,0),B(5,0)i-l-b+c-0ឃ=4ீ-25+5b+c=0[c=5.•.ᱥ᪆y=-x2+4x+5(2)VAD=5,pOA=1,AOD=6,pCD=8,AC(-6,8),!"#$ḄCḄ%&C,ᑣCḄ(ᙶ᪗8,)ᐭᱥ᪆8=-x2+4x+5,x=lᡈx=3,u஺Ḅᙶ᪗(1,8)ᡈ(3,8),VC(-6,8),.•.CCwᙠᱥyHᔣ{"#|7ᡈ9ᓫ.mḄ07ᡈ9(3)'/y=-x2+4x+5=-(x-2)2+9,ᱥ%9:x=2,.,.!P(2,t),ᵫ(2)Eᙶ᪗(1,8),জCBE"DEFGḄFH56BE8%9:;M,>E?EF^x:;F,CBE"DEFGḄFH>Q?%9:ḄᚖᚖKN,᝞

57ᑣNBEF=NBMP=/QPN,ᙠAPQN^EFBZNQPN=NBEFx=-2ᡈx=6,Cx=-2ᡈx=6H)ᐭᱥ᪆y=-7,.Qᙶ᪗(-2,-7)ᡈ(6,-7)ঝCBE%XHVB(5,0),E(1,8),uYBEḄZᙶ᪗(3,4),ᑣYPQḄZᙶ᪗(3,4),!Q(x,y),pP(2,t),...x+2=3x2,x=4,x=4)ᐭᱥ᪆y=5,'.Q(4,5)yQḄᙶ᪗(-2,-7)ᡈ(6,-7)ᡈ(4,5).ὃuᦪᔠ⚪.