江西省南昌某学校2022-2023学年数学九年级上册期末经典试题含解析

《江西省南昌某学校2022-2023学年数学九年级上册期末经典试题含解析》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
ᦪᔁ⚗1.⚪ὃᐜḄஹὃ!ᑏ#$ᩩ&ṹ()*ᙠὃ,-ᩩ&ṹ)*.஺2.⌱1⚪234ᵨ2B67!89:⌱1⚪234ᵨ0.5;<=⁐?@ḄA?7Bᑏ?CD᦮ஹ7@#$஺3.Fᢥ᯿⚪IJᙠᔜ⚪LḄ⚪.MᑁOPQ⚪.MBᑏḄᫀSᦔ9ᙠ₝VWஹ⚪ᔁ⚪Sᦔ஺4.Xᢝᓱ☢#\]⌕ᢚ`]⌕aẚஹac]4ᵨ8ᦋeஹfghஹiWᑐ஺kஹ⌱1⚪(m⚪4ᑖᐳ48ᑖ)1.qrᙊᑁtguv&Ḅvwx1,ᑣzᙊḄᑁtg{|&Ḅ☢}~()46373.------B.2GL•---------34AD2AE2.᝞ᙠABCDE//BC,k=kᑣkḄ~()AB5EC3.ᱥy=(x+1)2+2Ḅ⚔()A.(-1,2)B.(2,1)C.(1,2)D.(-1,-2)4.ᑡ&x&x&Ḅx()D.5.C~ABḄᑖᒘAC>BC,ᑡg(Ḅᨵ()জAC=^1AB,ঝAC=3-AB,ঞABAC=ACBC,টACM.618AB22A.1B.2C.3D.46.᝞ᦪy=ax2+hx+c(ax0)Ḅ¡¢Xg£¤¥¦AஹB§¢¤¥¦C,~¨x=2,OA=OC,ᑣᑡ©ª:জabcX)®9a+3b+c<0ঞc>k1টᐵ¦xḄ¯°iz?+ᮞ+³=0஺0)ᨵk᪷~4+c,ᐸg(Ḅ©ªᦪᨵ()

1A.1B.2C.3D.47.᝞ᙠABCBC=S,¶40=6,E,·ᑖ¸ᙠAB,ACG,·ᙠ5c¹ºv&EFG”x»&,E·=2E”½ᑣ»&EFG”Ḅᕜw~¿À8.qrXIஹX2xᐵ¦xḄ¯°*2-^*—1=0Ḅ§Áᦪ᪷ᑡ©ªkÂg(Ḅx¿)11A.X#X2B.xi+x2>0C.x2>0D.—+—>01Xex29.᝞Ã43,஻À¢Bk5
ᐵ¦ÅᑣÆ+஻=
B.2C.-2D.-810.k]ÇÈḄÉÊËÌᨵ5ÍᨵÎ⁐]ÏḄᳫᐸ2Ñᳫ3ÒᳫÓÉÊÔÕ᥎Qkᳫ᥎QÑᳫḄᭆ᳛x¿À411.qrÙÚÛᦪÜ=kᑡ©ªg(Ḅx¿ÀxA.¡ᙠÝஹº¡▲B.¹x<0½ᦪÀ'ÔXḄâᜧäâᜧC.¡ßà-2,-2D.¡¢À,Ḅ¥~0,412.᝞ºv&A3⏚x஺஺Ḅᑁtºv&Eᙠv஺ḄæwNA6C=U0஺ᑣNAOEḄçᦪ~

2EA.55°B.70°C.90°D.110°ஹ⚪(⚪4ᑖᐳ24ᑖ)13.᝞⁂ᛞCḄᓅ60஺ᔣᛞ60Ḅ!"A#$%&ᓭᔣ()*+,-,ᑮ0ᛞCḄᓭ45஺ᔣ1ḄBᜐ,2+B3!"AḄ4,.ᓅ14.᝞D46ABCḄ8AC1Ḅ9:;BD,<=NABD=NC,AB=6,AD=4,>?*CDḄ@.15.᝞<=AABCA,DஹEஹBᑖC48ABஹACஹ8C1Ḅ9S.DE//BC,EF//AB,D4):OB=1:2,Eb=9,FG8ᡝ16.IJᐰ=LMNAOPQᑖᙳS᦮ᦪVᑖ10ᑖ2IMNAᵬஹXYZOP[ᦪ\S6[ᡂ^᝞_`ᵬ:7,9,10,1,5,9X`9,6,1,10,7,1.(1)b⊡ᐙe᦮_☢Ḅᡂ^ghᑖ᪆⊤`kᙳᑖlmᦪAᦪᵬZ19

35èé113(2)ᵬéëìḄíᦪ¶¦èéᡠïëìḄᡂñò¦èéóèé]ÏᵬéḄô~ëìéḄᡂñ⌕ò¦ᵬéFõöQkᩩ÷ᢝèéøḄᳮᵫ_____________________________.17.᝞,ᙠ»&4BCQEᙠAB,ᙠ»&ABCDḄᑁüOg¯&8EFG.¹AB=6,BC=8½¨AE»&ABCDḄ☢}ᑖᡂ1:3§üᑖᑣBEḄw~.18.FᑏQkýþᔣ
yḄᙶ᪗(0,4)ḄᱥḄ⊤.ஹ⚪(ᐳ78ᑖ)19.(8ᑖ)᝞
Aᙊ஺᜜!
஺ᙊ஺!
ᙊ஺"8,ZACB=-ZBOC.2(1)#$%ACᙊ஺Ḅᑗ'(2)()A8=l,AC=2,#஺ᑮ+AOḄ,-.20.(8ᑖ)“/01
203”ᡃ6789⍗;<=>0?@A⍳CḄDᑣ.FGHᜩJKLM3NOP⌕R7S89
Ꮇ᝞HS89<=>0U/0V20WḄ?XYZ
HS89Ḅ<=>0[\]^/0V20._`aᜩFGJKLNbP᪥OP
R7S89dᜮfᑮ<=>0.(1)gh᪛j
ᑡlFGfᑮ<=>0mnopḄᡠᨵst'(2)#FG⌶RS89v⍗ᑮ/0Ḅᭆ᳛.21.(8ᑖ)y)%᝞জ
ᙠ|Ὺ+~~A8CU
ZACB=90°,BC=m,AB8?┐90஺ᑮ87஺C8Ḅ"E,C£>.(1)#$%AACBABED(2)63஺Ḅ☢(ᵨ
஻Ḅ⊤).%᝞ঝ
ᙠ!ḄR3A5C,ZACB=90°,BC=m,4B8?┐90஺ᑮB஺
Q9,ᵨ
஻Ḅ⊤63Q9Ḅ☢
Gᳮᵫ.

4ᵨ%᝞ঞ
ᙠ|ῪA5CU
A8=AC,8c=8,A8ᔵ?┐90°ᑮ80,CD,ᑣ8C஺Ḅ☢'¡5C=/n,ᑣBCDḄ☢¢ᵨ£Ḅ⊤¤.22.10ᑖ¤()¥¦§¨ᦪª=1ᔣ1#0
¦§¨ᦪ®=¯¢°2±0
Ḅ²"³ஹB´
AḄᙶ᪗2,1
.41
#¥¦§¨ᦪஹ¦§¨ᦪḄ⊤'2
#BḄᙶ᪗.23.10ᑖ¤µ¶·¸¹^º»·¼2⁐o3
¾o^ᐳ¿ᓫNÁÂ.জaÃÄᐳ¿ᓫNÅᙠÆÇᙢ☢OḄÉᱥ
ঝᐸË
ᐸUA3ஹvᙢ☢1Ç3
NÌÍÎ32cm,N5CD=64஺
BC=60an,ᙶÏEBḄBE15cm.জঝ1
#ᙶÏEᑮᙢ☢Ḅ,-'2
᪷ÑRÒ
ÓᙶÏEᑮCOḄ,-Ô᦮³Ö×Ḅ0.8?
ᙶL¦Ø—〉.FGḄ×Û80c/w,pᙶÏEÔ᦮ÜᙶL—〉ÝÞßà#Ḅ.¢áâãäᑮ0.1cm,åὃᦪÑ%sin64°®0.90,cos64°a0.44,tan640®2.05
24.10ᑖ1
᝞1,O|aABCᑁ!
OAஹOBஹOC,OA=3,OB=4,OC=5,BAOB?┐èᑮaBCD,OD.#%জ~ḄÞᦪ;ODḄ.ঝ#NBDCḄÞᦪ'2
᝞2ᡠ
O|Ὺ+~AABCZABC=90°
ᑁ!
OAஹOBஹOC,BAOB?┐èᑮaBCD,OD.ÓOAஹOBஹOCêëì`ᩩî?
NODC=90஺ïgðo$G.

525.12ᑖAAᦪOZ=[Pᨬᐹ᜻ஹ⌼Ḅ+4AO+ẆSᡃ᪥¡AP¢₞¤AOP¥¦ᦪ§¨©ª«ᦪOḄᝍ®2¤ª¯4°±S᜻ḄAOP²ᜓḄ.2¤ª´µ¶ᡃ·=L¸¹PºAḄᶧ¼½¾⌕Ḅ4ÀÁᡃ·ÂÃÄÅஹÆÇÈὃஹÊËÌḄÍ.ÎOḄ▅©OÐSÑѸOP▅©ᦔÓᡃ·ஹḄOPAÔÕᔜ⌱20ØÙ«ᦪOḄᝍ®Úª▅©ᦔÓÛMÜÝÚIMÜVᑖ`100ᑖ.ÞÎMÜᡃ·ᦈàᑮ20ØOPQᑖḄᦪá᝞_`9610089956275938686939595889495689280789010098969594929292929286848382787874646092ÞÎ᦮ᳮYZᦪáḄkᙳᦪஹAᦪஹmᦪl᝞⊤:ìíkᙳᦪAᦪmᦪl87.591m96.1586.2n92113.06ãäOåOPQᑖᢥᑖᦪ*6070,70

62
⊡ᐰ⚣ᦪᑖô+º'ᡧö÷U
70Wx<80ᡠøᵨḄᙊù~Þ'3
R7ᑖ᪆PûᑖYøüý¢þ“ÿ”ᡈ“”
4
▅ᦔᳮᵫ.26.!ᜓ#$%&'5000ᐗḄᙳ+,᜜├/ᵫ012▾ᨵᐵ6ᙢ8Ḅ9:;<=>?6ὅᢝBCD.EFGHIᕜK6ᙢ8LMᖪ,+OPQRSTU>VW#$%&'4050ᐗḄᙳ+L├/.1
X%ᙳ$STUḄYᑖ᳛\2
]!ᜓ#Lᙳ+?^ᝅ100%&'Ḅ6`.LMᖪabc#TRdef&ᫀ#h⌱jkজᡭ9.8ᢚ├/\ঝpᡭᢚ〈Rᱥstᳮuᱥstᳮuv$%&'$ᨴ1.5ᐗxd&ᫀefyzὃ|ᫀஹ⌱j⚪$⚪4ᑖᐳ48ᑖ1ஹcூᑖ᪆௃᪷ᙊᑁḄv1<ᙊḄ1,ᑭᵨWᳮX<ᑁḄY3<☢.2ூ௃kᵫ⚪¡<ᙊḄ1,'.,ABCAO=LAD±BC,BD=CD,AO=BO,13:.DO=-AD=—9922:.BD=y/OB2-OD2=—,2•••BC=5•F8c

7ᦑ⌱kc.ூ¤¥௃¦⚪ὃ§Ḅ¨©¤vªḄឋ¬#®᪷ᙊᑁªḄX<ᙊḄv¯⚪Ḅᐵ°.2ஹAூᑖ᪆௃᪷%±²ᑖ²³ᡂµ¶Wᳮᑡ<µ¶¸¹ᐭ»¼ᑮ|ᫀ.AD2ூ௃k♦••¾==AB5.AD2••=fDB3,JDE//BC,*AEAD2"EC~BD~?>'ᦑ⌱kA.ூ¤¥௃¦⚪ὃ§Ḅv%±²ᑖ²³ᡂµ¶WᳮᮣÂÃᵨWᳮஹÄ!,ÅᐵÆv⚪Ḅᐵ°.3ஹAூ᪆௃ᵫÇᱥ²⚔¤ᙶ᪗˸Ìy=a(x-h)2+kÍ⚔¤ᙶ᪗(h,k)αX.ூ௃k••)=(x+l)2+2,•••Çᱥ²⚔¤ᙶ᪗(-1,2),ᦑ⌱kA.ூ¤¥௃ὃ§SÐᦪḄឋ¬ÒÓSÐᦪḄ⚔¤¸v⚪Ḅᐵ°ᓽᙠy=a(x-h)2+kÍ⚔¤ᙶ᪗(h,k),,Ö×®²x=h.4ஹDூᑖ᪆௃᪷ÍØ,ÖÙḄWÚkÛK180ÜÝ>ÞßàáᔠÖÍØ,Ö×,Övᢚã>äåÞßàæᐰáᔠÖ×,Ö᪷WÚè⚪.ூ௃kAஹvÍØ,ÖÙpv×,ÖÙᦑ¦⌱⚗┯ë\BஹpvÍØ,ÖÙv×,ÖÙᦑ¦⌱⚗┯ë\CஹpvÍØ,ÖÙv×,ÖÙᦑ¦⌱⚗┯ë\DஹìvÍØ,ÖÙív×,ÖÙᦑ¦⌱⚗î.ᦑ⌱kD.ூ¤¥௃¦⚪ὃ§ḄvÍØ,ÖÙï×,ÖÙḄWÚ.5ஹC

8ூ᪆௃᪷ðIᑖᒘḄᭆóïðIµôα|ᓽ.ூ௃•.•¤Cᦪ²³ABḄðIᑖᒘ¤õAC>BC,.-.AC=2/1Z1AB,ᦑজî\2ᵫAC=@1AB,ᦑঝ┯ë\2BCAC=ACAB,ᓽkABAC=ACBC,ঞî\AC=0.618AB,ᦑটîᦑ⌱C.ூ¤¥௃¦⚪ὃ§EðIᑖᒘᳮðIᑖᒘḄᭆóùúðIᑖᒘḄµû'v⚪Ḅᐵ°.26ஹCூ᪆௃ᵫSÐᦪÙýḄLÌ&ᔣஹ,Ö×Þy×Ḅÿ
ᑖᑨ“ஹcḄ
ᑨজᵫ
x=3j>0,
ᑨঝᵫOA=OC,OAVL
ᑨঞᵫOA=OC,ᑮᨵ!᪷#c,$%X—C᪷#X,ᑣy-=2,'
X=4+Cᓽ
ᑨট
*ᫀ.ூ.'௃ᵫ01ᔣ3
“V0,4y5Ḅ6ᙠX5Ḅ3
CVO,89:5#x=2,ᡠ0,ᡠ<ᑖ>0,...a=>0,ᦑজ?@2aᵫ
x=3y>0,.•.9a+3/>+c>0,ᦑঝ┯BCᵫ
OA<1.,OA=OC,.OC<1,BP-c-1,ᦑঞ?@;•••Q4=OC,•.ᨵ!᪷#c,$%᪷#x.•9:5#EFx=2,...?=2,'Cx=4+c.ᦑট?@GH
?@ḄIJᨵK!.ᦑ⌱C.ூM௃N⚪ὃQRSTUᦪḄWឋY.Z[\]4^ᦪḄᐵ^<`STUᦪ4ஹabcḄᐵ^d'⚪Ḅᐵe.ᱯdᑭᵨi⚪jkḄOA=OC,d'⚪Ḅᐵe.7ஹC2FH6-PHூᑖ᪆௃mnop
•~=------
uE”Ḅvᓽ
u'.86ூ.'௃,EF//BC,

9.♦.AEFs/XABC,.EFAD-EH••=--------9BCADVEF=2EH,BC=8,AD=6,.2EH6-EH••—862412:.õïEFGHḄᕜ@=2x+55ᦑ⌱`C.ூ9ú௃¤⚪ὃüÑýþÿḄᵨ᪷ᡂ⚪Ḅᐵ.ூ᪆௃᪷Ḅᦪᔠ᪷Ḅᑨ"#$%&="+4>0,'($%&©Wxi,)⚪%.ூ*௃a)1-4XIX(-1)=/+4>0,.,.x௃-ax-1=0ᨵ./01Ḅ2ᦪ᪷.,.XiWxi.ᦑ⌱A.ூ56௃7⚪ὃ9:᪷Ḅᑨ"#ᱞ<“>?ᨵ./01Ḅ2ᦪ᪷”⚪Ḅᐵ.ூᑖ᪆௃᪷./5ᐵBC5D?EFGᙶ᪗ḄJKஹMᙶ᪗ḄJKᑖ"N$OP%ᑮm=3,n=-5'(%ᑮRᫀ.ூ*௃T•.,5A(3,n)V5B(-m,5)ᐵBC5DAm=3,n=-5,:.m+n=-2,ᦑ⌱TC.ூ56௃)⚪W⌕ὃ9:ᐵBC5D5Ḅᙶ᪗ᱯ5ᐵZ[5Ḅᙶ᪗Ḅ\ᓄ^_.ூ᪆௃..2/`ᳫஹ3/bᳫcᐳ5/,2...efghij᥎&c/ᳫ᥎&`ᳫḄᭆ᳛n.

10ᦑ⌱c.11ஹcூᑖ᪆௃᪷NpᦪḄឋr⌲ᩩᑨuᓽ$%&Rᫀ.ூ*௃TA┯xyzᙠ|cஹ}▲B┯x>X

11*CwxᡠᙠḄBᜐ4{|AḄ}~d(30+30).ᦑ*ᫀ#C(30+3073).ூM௃w⚪⌕ὃQR'EKḄᵨ-ᔣ⚪uKḄᡈḄ⚪
<ᓄ#'EKḄ⚪'ḄdF.14ஹ1.ூᑖ᪆௃ᵫb=HᐳᑮKABD4KACBᵫAB4ADvᐭᓽ
uCDḄv.ூ.'௃ᙠABDWACBkZABD=ZC,NA=NA,/.ABD^AACB,.ABAD••=9ACABVAB=6,AD=4,!JCD=AC-AD=9-4=1.ூM௃ὃCKḄᑨ4ឋY.915ஹ-2ூᑖ᪆௃᪷¡¢£FᑖF¤ᡂᳮᑡcᑮAEEC=ADDB=12,BFFC=AEEC=12,¨£ᑖ᪆©ªᓽ
.ூ.'௃'CDE஻BC,AAEEC=ADDB=12,VEF/7AB,ABFFC=AEEC=12,

12VCF=9,9BF=c.29ᦑ*ᫀ#C—.2ூM௃N⚪ὃQḄd¢£FᑖF¤ᡂᳮZ[\]¬ᮣ®¯ᵨᳮ¬°±9ᐵ^d'⚪Ḅᐵe.16ஹ(1)1.5,1(2)²³Ḅ¢ᙳᑖµ¶·¸Ḅ¹{ºᵬ¸¹ᡠ<·¸ᡂ¼½¾.ூᑖ᪆௃(1)᪷¡¹ஹ¢ᙳᦪḄ©ªcuᵬ¸¹W·¸¢ᙳᦪ᪷¡k¿ᦪḄÀÁᵬ¸k¿ᦪ(2)᪷¡(1)k⊤Ãᦪ¡ᑖÄᦪ¡ÅkÆḄk¿ᦪW¢ᙳᑖ`Äᦪ¡ÇÈÆḄ¹Éᵬஹ·²¸,ᵫw°·¸Ëºᵬ¸Ḅᩩᳮᵫ.ூ.'௃(1)ᵬ¸¹C\[(7—8)2+(9—8)2+([0—8)2+(8—8)2+(5—+(9—8ÍS|ᵬ¸ᦪ¡ᵫ{ᑮᜧ᣸ᑡ#C5,7,1,9,9,10ᦑᵬ¸k¿ᦪC(1+9)4-2=1.5·¸¢ᙳᑖC(9+6+1+10+7+1)4-6=1Ñ⊤᝞3C¢ᙳᑖ¹Óᦪk¿ᦪ8ᵬ¸191.535·¸1113(2)²³Ḅ¢ᙳᑖµ¶·¸Ḅ¹{ºᵬ¸ᡠ<·¸ᡂ¼½¾.ᦑ*ᫀ#C1.5,1²³Ḅ¢ᙳᑖµ¶·¸Ḅ¹{ºᵬ¸¹ᡠ<·¸ᡂ¼½¾.ூM௃N⚪ὃQᦪ¡ᑖ᪆Z[\]Äᦪ¡ÅkÔÕḄk¿ᦪஹÓᦪW¢ᙳᦪ<`Äᦪ¡ÇÈÆḄ¹Ḅ©ªcWÀd'⚪ᐵe.12-4817ஹᡈ——511ூᑖ᪆௃ᑖSÖ×ᑖu'Cজ᝞1kØvAÙ68cºa0=CM=4EFA/7ÚABCOḄ☢Üᑖᡂ1:3²Ýᑖ.ঝ᝞2kØvAE6COºM68CḄØvFºK,஺0=£>M=3EFAH

13ÚABCDḄ☢Üᑖᡂ1:3²Ýᑖ.ூ.'௃'C᝞1k$EFAH6ºM,3M=C0=4EFA”ÚA8CDḄ☢Üᑖᡂ1:3²Ýᑖ..AEEH.6-tt••----=—,6412'=M•᝞2k$EFvAÙ68º”68஺ḄØvFºK,CM=OM=3EFA/7ÚA3CQḄ☢Üᑖᡂ1:3²Ýᑖ᧕o²AMDS²KMC•AZ)=CK=8,Ky2\EH//BK9.AEEH~AB~~BK96-tt••=~f61648t=—♦111248GHᡠâãäᩩåḄ/Ḅç#Sᡈè.12-48ᦑ*ᫀ#CSᡈé.ூM௃N⚪êºëGᔠ⚪ὃQRÚḄឋYᐰbKḄᑨWឋY¢£FᑖF¤ᡂᳮbî'⚪ḄᐵedïðᵨᑖñòJḄóôóὃ⚪êºkὃõ5⚪.

1418>y=-x2+4.ூ'᪆௃ö⚪'᪆C01ᔣ3ᑣ஺<0.y5Ḅ6ᙶ᪗#(O,4),c=4.ú!ûᱥF
=R?+22,15/?=-,:.A0=—,2VS^oc=gA஺*CM=ÈACxOC,

15CM=-5ூ
C௃D⚪F⌕ὃIᙊḄᑗ8ḄᑨKឋMᳮNOᳮPQRS8᪀⌼V'&'(61⚪ḄᐵW.20ஹ1
0Y1᪆ᐳᨵ8]^_Ḅ`2
1Oூᑖ᪆௃b⚪ᑖ&cdᡂfghij◤⌕⌱mgnᡠNpfhijqrgcᵨ᪛tu⊤wᡠᨵxy%ᑭᵨᭆ᳛}~#1.ூ01௃1
ᑡ᪛tu᝞:Ë|c/ÉÊ|n/ÉÊᜮÍ|/ÉÊ`Ë`Ë`Ë`Ëᵫ᪛tuNqᐳᨵ8]^_Ḅ`ᓽ5ஹஹஹஹஹஹஹஹ2
ᵫ1
P&n=-.8ூ
C௃b⚪ὃIḄ6ᵨ᪛tu+#ᭆ᳛.᪛tu+〉ᵨcᡈcNdᡂḄ1⚪⌕66.ᵨᑮḄ
5ᭆ᳛=ᡠ#xyᦪxyᦪ.21ஹ51
0Y1᪆1
-m1;5-ml,ᳮᵫ0Y1᪆¡ᵨ16,-m\224ூ1᪆௃51
ᵫ⚪CA=CB,NA=NABC=25஺ᵫ¢£ḄឋMBA=BD,NABD=90஺ZDBE=ZABC,ᓽ¤AACBgZkBED1
ᵫAACBgaBED,BC=DE=m,᪷&'(☢*#+#ABCDḄ☢*5DG_LCB¥CBḄ¦§8G,¤AACBgZ\¨BGD,BC=DG=m,᪷&'(☢*#+#ABCD

16Ḅ☢*;¡ᵨ5ª
AAN_LBCN,ª
DDMJ_BCḄ¦§8
M,ᵫ^Ὺ&'(ḄឋMNBN=BC,ᵫ2ᩩNAAFB04BEDNBN=DM,ᵫ&'(Ḅ☢*}~N.ூ01௃5¤®5(1)'.•ABC6^ῪV'&'(.CA=CB=m,ZA=ZABC=25°,ᵫ¢£ḄឋMBA=BD,ZABD=90°,:.Z£)BE=25°,ᙠ/5KAOEB=ZACB=ZDEB,ZABC=ZDBE»BA=DB:.AACB%ABED(AAS)(1),:AACB/ABED••DE=ZBC=:m**•S^BCD=~~BC^EE)=--m^922ᦑ,ᫀ*",5OG_LCB¥CBḄ¦§8G,u2VZABD=90°,/.ZABC+ZDBG=9Q°,±N45C+NA=90°,:.NA=NDBG,ᙠAAC8KZJSGO='/A²NDBG■NACB=/BGDAB=BD:.ACBmABGD(AAS),BC=DG=ni

17S^BCD~~~BC^DG=—m^»22ᵨTANJ_8cBN,OMLBCCBḄÕÖBM,.ZNAB+ZABN=90°.''ZABD=9d°,'.NABN+NDBM=90஺,./NAB=ZMBD.•••Ö×8஺ᵫÖ×ABØÙ%ᑮḄ.AB=BD.ᙠAARBÚA8EOhrZNAB=ZDBM■NANB=/DMBAB=BD:AANB)ATiMD(AAS),.BN=DM=—BC=2.2.,•SABCD=—BC«DA/=—x8x2=16,22ÜBC—nitÝ!]BN—D1\1=—BC=—m>22S^BCD=—BC*DM=—x/nx—m=—m12224ᦑRᫀà16,~inl-4ூ56௃7⚪ὃ9:1ῪḄឋrᐰ1ḄᑨãAAS
,ᐰ1ḄឋrOḄឋr☢åæçèéZ[êëì57⚪⚪Ḅᐵ.1222ஹ1
pᦪஹNpᦪḄ⊤î#àT-x,y=cÈ(2)B5ᙶ᪗(-2,-1)2xூ᪆௃ï⚪ᑖ᪆:1
ñ5AஹBḄᙶ᪗ᑖ"òᐭpᦪy=kixk#0
Vpᦪy=HO
h&k|Úk2Ḅᓽ$%ᑮ./pᦪḄ

18᪆#È(2)ñ(1)hᡠ%./pᦪḄ᪆#ôᡂôôᓽ$%ᑮ5BḄᙶ᪗.ï⚪᪆Tk1T(1)ñ5A(2,1)ᑖ"òᐭõkixVø=ù$%TK=—,k=2,2x212ûpᦪஹNpᦪḄ⊤î#ᑖ"àTy=y=—È2x1y=%x(crc7x=—2=2y(2)ᵫ⚪¡%ôT:,%Tτcτஹ2>1%=1X•••5BḄᙶ᪗(-2,-1).23ஹ(1)99.5(2)3.9ூᑖ᪆௃(1)B5ᵫþÿ=£஺311஽஺/=7531146஺ᫀE'H(2)"J_cr>”ᐜ᪷"E'C=/²&£CḄ(),+᪷"ᙠ=CE—CEᫀsinNECDூ23௃(1)᝞61,7EEMJ_CD61ᵫ⚪<=ZBCM=64°ஹEC=BC+BE=60+\5=15cm,AEM=ECsinZBCM=75sin46°«67.5(cm),ᑣᓫFFGᑮᙢ☢ḄK)L67.5+32«99.5(cm)E(2)᝞62ᡠP7H,ᵫ⚪<=E'”=80x0.8=64,

19E'H64ᑣE'CsinZECHsin64°AEE'=CE-CE'=75-7LI=3.9,cm.ூU௃V⚪ὃX3YZ[Z\Ḅ]ᵨ3⚪Ḅᐵ`abc⚪<ᑭᵨ┦Z[Zfᦪhi3.24ஹ(1)জ60°,4ঝ150°(2)OA2+2OB2=OC2,jbk3᪆.ூᑖ᪆௃(1)জ᪷"op[Z\ḄឋrBA=BC,ZABC=60°,+᪷"stḄឋrNOBD=NABC=60°,acustZḄ)ᦪL60°ᵫstḄឋrBO=BD,vwNOBD=60°,ᑣᑨyAOBDLop[Z\ᡠzOD=OB=4ঝᵫ|!«)~Lop[Z\ᑮNBDO=60°,+ᑭᵨstḄឋrCD=AO=3,ᯠ᪷"uᳮḄ⌮uᳮjbOCDLYZ[Z\ZODC=90",ᡠzNBDC=NBDO+NODC=150°(2)᪷"stḄឋrNOBD=NABC=9()஺BO=BD,CD=AO,ᑣᑨyOBDLoῪYZ[Z\ᑣOD=V2OB,ᯠ᪷"uᳮḄ⌮uᳮCD2+OD2=OC2AOCDLYZ[Z\ZODC=90°.ூ23௃3(1)জ•••ABCLop[Z\.,.BA=BC,ZABC=60°,VABAOB┐stᑮaBCD,.,.ZOBD=ZABC=60",.••stZḄ)ᦪL60°•••Aa4OstABCD,:.BO=BD=4,NOBD=ZABC=60°,CD^AO=3,MOD-./0123BDO=60OD=OB=4,ᦑᫀL60஺4ঝᙠAOCOCD=3,OD=4,OC=5,V32+42=52AC£>2+OD2=OC2...AOCDLYZ[Z\ZODC=90,ZBDC=ZBDO+ZODC=60+90=150'

202
01+2082="2NQoc=9y,ᳮᵫ᝞VNBAOB┐stᑮAfiCD,ZOBD=AABC=90BO=BD,CD=AO,AOBDLoῪYZ[Z\•OD=0OB•.,C02+O£>2=஺஺2AOCZ
LYZ[Z\NODC=90°:.0A2+08
2=2,ᓽQ4?+2=2OC2OBOCOA,OB,OCQfic+2OB2=OC2ZODC=90".ூU௃V⚪ὃXstḄឋr]ᑮstḄo]stᡠḄᜳZostZst¢ஹḄ6\ᐰo.¤ὃXop[Z\Ḅᑨyឋr¥uᳮḄ⌮uᳮ.25ஹ(1)95ᑖ92ᑖ(2)54(3)¦§(4)¦§k3᪆ூᑖ᪆௃(1)᪷"¨ᦪ¥©ᦪ=ª«¬ᓽ(2)᪷"®ᦪL20®¬¯80Wx<90Ḅ®ᦪ⊡ᐰ⚣ᦪᑖ²Y³6+᪷"⊤µ¯70Wx<80Ḅ®ᦪ&¯ᡠᓰḄ·ᑖ¸¬¯ᙊZ)ᦪᓽ(3)᪷"¦§¦º»ᑖḄ³¼ᑨyᓽ(4)᪷"½ᙳᦪ¥³¼¸¿¯ÀÁᓽ.ூ23௃3(1)¦§º»ᑖḄ¨ᦪv=95(ᑖ)¦ÂÃᑖ᣸ᑡL60,64,74,78,78,82,83,84,86,92,92,92,92,92,92,94,95,96,98,100,

213ᡧ\Ç«670Wx<80®ᦪL3®ᑣᡠᵨḄᙊZL360x—=54,20ᦑᫀL543¦§ᑖḄ³¼È¦ᑖḄ³¼•••¦§º»ᑖÉuᦑᫀL¦§4¦§▅ËᦔÍÎÏ•••¦§▅ËᡂÑḄ½ᙳᦪᜧ¦▅ËᡂÑḄ½ᙳᦪ¦§ᑖḄ³¼È¦ᑖḄ³¼¦§▅ËᦔÍÎÏᫀÓÔ§ÕÖᨵᳮᓽØ.ூU௃V⚪aÇ«=ªḄÙᔠὃXÛÜÝÞ⚣ᦪᑖ²Y³6ᡧ\Ç«6ß³¼=ªa3àV⚪Ḅᐵ`.26ஹ1ஹ10%2ஹ³ᫀ§áâூ3᪆௃ã⚪ᑖ᪆1ஹ䯽ᙳåæçḄ·ᑖ᳛Lx,ᑭᵨ⚜êå½³ë├íîµx1-åæçḄ·ᑖ᳛Ø2=ïðå½³ë├íîµᑡ³ñ3ᓽ2ஹ³ᫀḄcuzò7¸¿óô³ᫀ¯Ḅõᵨজ³ᫀçḄᙳîxl00x0.98ঝ³ᫀçḄᙳîxlOO-óÂḄᱥ÷øᳮõ¸¿cu¯ÎáâḄ³ᫀ.ã⚪3᪆1ஹä½ᙳåæùîḄ·ᑖ᳛ax,᪷"⚪<ᑡ³ñ50001-x2=4050,3xi=10%,X2=1.9Óᔠ⚪<úûؽᙳåæùîḄ·ᑖ᳛L10%.2ஹ³ᫀ§Ḅüýa4050x100x0.98=396900ᐗسᫀḄüýa4050x100-1.5x100x12x2=401400ᐗØV396900ᐗ<401400ᐗ.ὃ§ᐗæ³ñḄ]ᵨ.