2021-2022学年山东省济南市市中区中考联考数学试题含解析及点睛

《2021-2022学年山东省济南市市中区中考联考数学试题含解析及点睛》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。

2021-2022ὃᦪᔁ
⚗1.ᔁὃḄஹὃஹὃᑏᙠ⚪ᔁ⚪ᓱ!஺ᵨ2B$%ᔁ&'B(ᙠ⚪ᓱ)*+!஺ᩩ-ṹ/0ᙠ⚪ᓱ1!2஻ᩩ-ṹ/0ᜐ஻o2.7⌱9⚪:⌱;<=⚪ᫀ?ᵨ2B$%@⚪ᓱ!A*⚪B⌱⚗ḄᫀCDE(FG᝞◤ᦋKᵨLMNOP?Q⌱(ᐸSᫀ஺ᫀTUᙠ⚪ᔁ!஺3,V⌱9⚪WᵨF⁐YZḄ[%ᡈ]Y%7ᫀWᑏᙠ⚪ᓱᔜ⚪Bᢣ`abᑁ)*+!G᝞◤ᦋKᐜᑜᣵgᩭḄᫀᯠ?Qᑏ!jᫀGTkᵨ$%(ᦋl஺Tᢥn!⌕p7qᦔ஺4.ὃWs⚪ᓱḄ᦮u஺ὃvw?xyᔁ⚪ᓱz{|}஺zஹ⌱9⚪~yᜧ⚪ᐳ12=⚪<=⚪4ᑖᐳ48ᑖ.ᙠ<=⚪;Ḅ⌱⚗ᨵz⚗ᔠ⚪B⌕pḄ.1.᝞ABCZB=70°,ᑣNBAC=30஺AABCEC:┐EDC.EBḄA*EDាᙠAC!:NCAEḄᦪ~A.30°B.40°C.50°D.60°2.Ex“yD,
xz,y2
,
x,yᦪy=-,¡!ḄE{¢yiீ0

1()BCBDADC.-----D.——ACAfiBCAC6.áâãä4ᨴæᢗᐭ1000éᐗëẆíîïᑜ6ᨴæᢗᐭëẆíî4ᨴð500éᐗ.ñòâãä5ஹ6ᨴᢗóëẆíîḄᨴôᙳÂö᳛Öx,ᑣᡠᑡ¬º§¨ḄÖ~A.1000(l+x)2=l000+500B.1000(1+X)2=500C.500(l+x)2=1000D.1000
1+2x=1000+5007.᝞45஺஺ḄÁùAB=S,úᚖÁôᑖ05,Eü40!ḄKEÙEýEEᙠü40!©A°Kᑮ஺Ḅ¹ºÚÛCf•ÿḄ☢43ᔆ4A.4ᐔ+3B.4n+—y/3C.y/3D.—n+3y/3r42ax+by=3\x=18.ᐵx,yḄᐗ,τḄீᑣa-2bḄ)ax-by=1=TA.-2B.2C.3D.-39.ᑡ!"Ḅ()A.=B.ஹ/(—3)=-3C.a*a2=a2D.(2a3)2=4a610.cos30°ḄA&R]_D.BA.-----o.------232211.ᙠ“ᜧ*+,ᩭ”Ḅ/᩟1᪥3456789᪥10:1;<6ᡂ>?@᝞BᡠD.FG10:1;Ḅ<6ᡂ>,ᑡHI7┯KḄ

2LᦪC,ᙳᦪ90D.᩽1512.᝞ᙠAABCDACN஺5C=NABC=G,AC=3ᑣCDḄ()22ஹ⚪"(#ᜧ⚪ᐳ6&'⚪('⚪4ᑖᐳ24ᑖ.)13.᝞ᙠAABCAB=AC,+Cᙊ-+CB./0ᙊ1,3ACḄ456D,78BD,9NA=32஺,ᑣNCDBḄᜧ'____;.14.9<=>Ḅ&᜜@45஺ᑣA<=>Ḅᦪ.15.ᙠAABCNANBNNC=1N2N3,CD8AB6D,9AB=1(),ᑣBD=16.᝞RtAABCZABC=90°,AB=BC,B5'ஹCᑖDEFAஹBஹCG1\஻஻.96HbḄIJ5,bHKḄIJ7,ᑣR3A8CḄ☢M17.NOᩰQG@(1),RSTUᑡWX(2)N

3111(a-by=a-b121(aU=a'—2ab-F133114641(a—3,=a3a*b—3ab--g(a-6)4=j-4/b-6a%N7a*-6(1)ফ᪷[\☢ᔜXḄ^_ᑣ(a+b)618.᝞ᡠaFyb<.bḄcdP,0xbḄe5ᑖDHfghiᦪy=-±jy=2Ḅk36Aj5,9Cxbcd7lACஹBC,ᑣAAZfCḄ☢MGஹmn⚪"(#ᜧ⚪ᐳ9&'⚪ᐳ78ᑖmnoᑏqᦻstuஹvuFwᡈyz{|.19.(6ᑖ)(1)}z"(-2)2-(0+1)2-4COS60°(2)ᓄ"=23+.1)(1X-xX20.(6ᑖ)ᱥ5.=2++3Ḅᔣ⚔P(1)9Pᙶ᪗(4,-1),ᱥ5Ḅm᪆X(2)9ᱥ5F(4,-1),1ᜧ9yḄ(ᵨaḄᦪX⊤a)(3)9a=LOWxWlᱥ5ḄᑮxbIJḄᨬᜧ6,bḄ21.(6ᑖ)ᨵ¤¥¦§Ḅ┝j©¥¦§Ḅªᓇᐸ¤¥ªᓇា®ᑖD¯ᡭ±¤¥┝ᐸ²Ḅªᓇ¦¯ᡭ±¤¥┝.³ᙠcdq¥ªᓇ´cd¥┝.(1)Nᵨᑡ⊤ᡈµ᪛·Ḅ¸⊤aq¹ºᡠᨵ»¯8¼(2)½ᡭ┝Ḅᭆ᳛.22.(8ᑖ)᝞ᱥ5y=ax2+bx+cHxb36A(-1,0),B(4,0),Hyb36C(0,2)(1)ᱥ5Ḅ⊤ÀX(2)ᱥ5ḄÁÂbHxb36M,DHCᐵ6MÁÂÄᙠAᱥ5ḄÁÂbᔲÆᙠP,ÇABMPHÈABDÉÊË9ÆᙠNqᡠᨵÌÍᩩÏḄPḄᙶ᪗9¦ÆᙠNtuᳮᵫ.

42—x42x+4
23.
8ᑖÒm¦WXÓ,A—1,RᑏqA¦WXÓḄᨬᜧ᦮ᦪm.x<-------+1324.
10ᑖÒÕᖪ×├ÙAÚjBÚ¤ÛᵯᾯᐸAÚᵯᾯ(ÞḄᑭà400ᐗBÚᵯᾯ(ÞḄᑭà500ᐗ.Aᖪ×}ᑜã½ឋåæ¤ÛÚçḄᵯᾯᐳ100ÞᐸBÚᵯᾯḄæèé¦êFAÚᵯᾯḄ2ëìåæAÚᵯᾯxÞ±100ÞᵯᾯḄ├Ùíᑭàyᐗ.yᐵ6xḄiᦪᐵîXAᖪ×åæAÚஹBÚᵯᾯᔜ=ïÞð¯Ç├Ùíᑭàᨬᜧᨬᜧᑭà=ïËñ▭æèᔆôÁAÚᵯᾯqᔆõUöa
0VaV200ᐗ▲øᖪ×ᨬ=åæAÚᵯᾯ60Þ9ᖪ×ùᢝ§ÛᵯᾯḄÙõ¦ûNü᪷[+ýþì}qDZ100Þᵯᾯ├ÙíᑭàᨬᜧḄæè¸ᫀ.25.
10ᑖᱥᑖ2—4,zx+a—xABAᙠB,ᱥḄ⚔O.1-:1~O1234^-1--2-
1ᱥMḄ
2AB=2ᱥMḄᦪ⊤;
3ᙠ2Ḅᩩ!"/y#஺0
%&ᱥḄ⚔஺'=஻ᱥ”ᨵ-./ᐳ12Ḅ3ᙶ᪗ᑖ6789y=஻/ḄḄ3ᙶ᪗7;<;>0=-?ᨵ᳝AB>D3-D2>0,EFᔠᦪḄHIJᑏLᦇḄNOQ.26.
12ᑖ᝞HᙠSTABCDUAB=1DA,VAᙊXABYZḄᙊ[DCE,ADḄ\]F,^DA=L_ECḄ]HU▢abᑖḄ☢d.

5R27.
12ᑖ`ᡂaLbc⍝efghᩭhiᑮklḄᐵm8n□☘qaẆsᡠtuvwxyz71100:1;{Ꮇ7}~}Ḅᦪᦪ᦮ᦪᐗ81;᪛!"Ḅ.᪷vwᦪᑴᡂx⚣ᑖ⚣ᦪ⚣᳛0.5—50.50.1—50.5-_______200.2100.5=150.5——_______200.5300.3200.5=250.5100.1᳛ᑖ⊤⚣᳛ᑖB᝞B.
2ᙠ⚣᳛ᑖB7845஺Ḅ☢GvwḄ᪵y;
3Ẇsᡠ8F150ᐗḄ1;¡¢⁚¤Ḅf¥.¦§@F¨᪥1000:1;7¤©q:1;G⚗f¥.eὃgᫀஹ⌱¬⚪yᜧ⚪ᐳ12¯°⚪8±°⚪4ᑖ8ᐳ48ᑖ.ᙠ±°⚪²Ḅ³¯⌱⚗78´ᨵ⚗¶ᔠ⚪¸⌕ºḄ.1ஹC

6ூ᪆௃ᵫ¿ÀᑁÀÂᳮÄÅNACB=80஺8ᵫÆÇḄឋÉÄÅAC=CE,ZACE=ZACB=80°,ᵫÊῪḄឋÉÄÅZCAE=ZAEC=50°.ூÌ௃VZB=70°,ZBAC=30°/.ZACB=80°,ÍAABCÎÏCÐÑ┐ÆÇÅÓEDC..♦.AC=CE,ZACE=ZACB=80°.,.ZCAE=ZAEC=50°ᦑ⌱C.ூÏÕ௃y⚪ὃwxÆÇḄឋÉ8ÊῪ¿ÀḄឋÉ8×ØᵨÆÇḄឋÉy⚪ḄᐵÚ.2ஹDூ᪆௃ᐜ᪷Ü5ÝÞᦪḄ᪆ßᑨáÞᦪBâᡠᙠḄâ▲äᙠ±â▲ᑁÞᦪḄåæឋ8ç᪷yiV0Vy22••Ï
xi,yiᙠî³â▲8X2,yzஹX3,yaïÏᙳᙠîâ▲8X2

7B᝞BᡠD8ö÷CM,TMABḄ7Ï8•SAACM=SABCM=—SAABC,2øùÑ8SAMPQ=SAACM=_SAABC;ᵫP,QïÏúÑû8üúÑᑮýþÏ,ÿ
PᑮACḄ

QᑮBCḄ
,SAMPQ=^SAABC;SAMPQ=SABCM=-SAABC.MPQḄ☢ᜧᓄᐜᜧ.ᦑ⌱C.4ஹDூ᪆௃⚪ᑖ᪆✌ᐜ⌕ᳮ&'(⚪)*⍝,Ḅ-.ᦪ01,Ḅ2ᦪ3ᯠ5ᵨ᣸◀9:;ᑖ᪆<=ᑮ>?@ᫀ.&᪷C,2ᦪᑡEFG40m+10=43m+l,জ┯Jট>?L᪷C-.ᦪᑡEFGMNO3P^,ঝ┯Jঞ>?L4043ᡠU>?Ḅঞট.ᦑ⌱D.ὃ
ᵫX▭Z⚪[\]^ᐗ^`EF.5ஹDூ᪆௃᪷C┦bcbdᦪḄefghijkljm=@ᫀ.ூ$௃BDBCCDcos«=---=----=----•BCABACᦑ⌱D.ூ
o௃q៉st┦bcbdᦪḄefᐵv.6ஹAூ᪆௃

8xMyz{5ஹ6|ᨴᢗẆḄᨴᙳ᳛Nx,5ᨴᢗẆN1000(1+x),6ᨴᢗẆN1000(1+x)(1+x),ᓽm=@ᫀ.ூ&௃xMyz{5ஹ6|ᨴᢗẆḄᨴᙳ᳛Nx,ᑣ6ᨴᢗẆ1000(1+x)2=1000+500,ᦑ⌱A.ூ
o௃ὃ^ᐗ`EFḄGᵨᙳᓄ᳛ḄE9NxᓄḄ0Na,ᓄḄ0Nb,ᙳᓄ᳛Nx,ᑣ`ᓄḄᦪ0ᐵNa(l±x)2=b.7ஹAூ&᪆௃AC,OC,BC.CFḄ☢=ᡧMAHḄ☢Ḅ☢<NAMH=120஺ᓽm&Z⚪.ூ&௃᝞¡AC,OC,BC,CDABH,ᚖ£ᑖ08,.CO=CB,•OC=OB,.OC=OB=BC,AZABC=6Q°,,AB£¤/.ZACB=90°,AZC4B^30°,VNAR?=ZAHC=90஺...
¥ᙠUACN£¤Ḅ஺M§¨©ªE<4¨©ᑮ஺
ᔆ<4¨©ᑮ//,M//,'MA=MH,J.ZMAH=ZMHAF=30°...ZAMH^\2Q0,

9•••CFi&Ḅ☢d—7TX®2j°2+—X®26°2=4k+3j3604ᦑ⌱oA.ூq௃s⚪u⌕ὃwx▢abᑖ☢dḄyz{|}ᡧTḄ☢d/TḄ☢dys⚪Ḅᐵ.8ஹBூ
᪆௃2ax+by-3{2a-b-3ᐭoax,—by=1[a+b-14a=—3o41ᡠVa-2b=--2x
AA=2.33ᦑ⌱B.9ஹDூ
᪆௃⚪᪆oA.ஹஹ᪷ᔠᦑ⌱⚗┯;B.\—7=3,ᦑ⌱⚗┯C.Z•=$,ᦑ⌱⚗┯D.(25=4'ᦑ⌱⚗£¤.ᦑ⌱D.10ஹDூ
᪆௃᪷¥ᱯ§ᦪO¨gᫀ.ூ
௃ocos30°=——>2ᦑ⌱oD.

10ூ
o௃Ä⚪ὃÅᱯÇbcbdᦪÈqÉᱯÇbcbdᦪÈ&⚪ᐵv.11ஹCூ᪆௃ᵫÊË¡ÌÍḄᦪC᪷CÎᦪஹÏᦪஹᙳᦪஹ᩽ÑḄefᑖÒᑡ]ÓÔ]@ᫀ:ூ$௃&•••90]ÖÅ5`]ÖḄ`ᦪᨬØ.•.Îᦪ90,ᐳᨵ10|ᦪÏᦪ{5ஹ6|ᦪḄᙳᦪ...Ïᦪ90+90+2=90•.•ᙳᦪ
80x1+85x2+90x5+95x2+10=89᩽Ñ95-80=1..•.┯JḄC.ᦑ⌱C.12ஹCூ᪆௃CD᝞âᐭÈᓽm.᪷CNDBC=NA,ZC=ZC,ᑨeÝBCDS2^ACB,᪷CÞßcbàGjḄkÞá=ᑮ3ூ$௃VZDBC=ZA,NC=NC,/.BCD^AACB,.CDBCBCAC.CDV6V63/.CD=2.ᦑ⌱:C.ூ
o௃ä⌕ὃÞßcbḄᑨeåឋçstÞßcbḄᑨeeᳮ&⚪Ḅᐵv.ஹèé⚪®Äᜧ⚪ᐳ6|⚪ê⚪4ᑖᐳ24ᑖ.°13ஹ1ூ᪆௃᪷CáῪcbḄឋçU1cbᑁbíeᳮᙠAABCm=NACB=NABC=74஺᪷CáῪcbḄឋçU1cb᜜bḄឋçᙠABCDm=NCDB=NCBD=ZACB=1°.2

11ூ&௃VAB=AC,NA=32°,NABC=NACB=74஺XVBC=DC,:.ZCDB=ZCBD=-ZACB=1°,2ᦑ@ᫀN1.ூ
o௃Ä⚪ä⌕ὃáῪcbḄឋçcb᜜bḄឋçstájàáb&⚪Ḅᐵvï)cbᑁbíeᳮḄGᵨ.14ஹ1ூ&᪆௃᪷CØj᜜bí360ð>ØjḄᔜ|ᑁbÞáᔜ|᜜bÞá£ᵨ360஺஺45஺m=jᦪ.ூ&௃•Øj᜜bí360ð>ØjḄ^|᜜b45஺.•.360°445°=1ᓽM>ØjḄjᦪLூ
o௃Ä⚪ä⌕ὃÅØj᜜bí360ðí>ØjḄឋç®>ØjḄᔜ|ᑁbÞáᔜ|᜜bÞá°.15ஹ2.1ூ&᪆௃ᐜ]ÝABCNAáò30஺Ḅ£bcbó᪷C30஺bᡠàḄ£bjáòljḄ^ô&.ூ&௃&᪷C⚪)xNAஹNBஹNCNkஹ2kஹ3k,ᑣk+2k+3k=180°,&=k=30஺2k=60°,3k=90°,VAB=10,1.,.BC=-AB=b2VCD±AB,...NBCD=NA=30°,

121.,.BD=-BC=2.1.2ᦑgᫀ2.1.ூq௃s⚪u⌕ὃw©30ªḄTḄឋ¬Tᑁ¯ᳮ|}30஺ᡠḄ±²³±ḄAYஹLABCTs⚪Ḅᐵ.16ஹ17ூ᪆௃&B´EF_LL,hE,hF,᝞HVEF±I,2.•.EF±li±h,:.ZABE+ZEAB=90°,ZAEB=ZBFC=90°,µ,../ABC=90஺/.ZABE+ZFBC=90°,:.ZEAB=ZFBC,ᙠ^ABE·BCFUNAEB=NBFC{NEAB=NFCB,AB=BC.'.ABE^ABCF,.".BE=CF=5,AE=BF=7,ᙠR3ABEUAB2=BE2+AE2,.•.AB2=74,11,/.SAABC=-ABBC=-AB2=17.22ᦑgᫀ17.qos⚪ὃwxᐰ²TḄᑨ¯ឋ¬ஹº»¯ᳮஹ¼½¾Ḅ¿ÀTḄ☢d/⚪ḄᐵÁÂÃ᪀⌼ᐰ²TÆ&ÇÈTᐰ²ɱʲ8ᑭᵨTḄ☢d/ᓽ¨.17ஹa2+2asb+25a4b2+20a-'b3+25a2b4+2abs+b2.

13ூ᪆௃õö÷mUø](a+b)2ḄùúÔN2`7⚗ÔaḄ`ᦪᢥýþ᣸ᑡbḄ`ᦪᢥᓣ᣸ᑡᔜ⚗ᦪᑖ2ஹ2ஹ25ஹ20ஹ25ஹ2ஹ2.ூ$௃(a+b)2Ḅ27⚗aḄᦪᢥ᣸ᑡbḄᦪᢥᓣ᣸ᑡᔜ⚗ᦪᑖ2ஹ2ஹ25ஹ20ஹ25ஹ2ஹ2.ᡠ(a+b)2=a2+2a5b+25a4b2+20a3b3+25a2b4+2ab5+b2.18ஹ1.ூ᪆௃P(0,b),•,"#APB஻x$:A,B%&Ḅ'ᙶ᪗*b,4+&Aᙠ-./0ᦪy=—-Ḅ123x4445b,x=--,ᓽA&ᙶ᪗b),bb27•&Bᙠ-./0ᦪy=—Ḅ123x22••4y=b,x=7,ᓽB&ᙶ᪗(3b),bb/.AB=--(--)=-,bbb116SAABC=-*AB*OP=—b=l.22b9ஹ:;⚪=(?ᜧ⚪ᐳ9BC⚪ᐳ78ᑖ:;DᑏᦻGHIஹJIKᡈMNOP.19ஹ(1)5(2)—ூ᪆௃(1)᪷STᦪḄUNVᑣXYZN⌕\]ᱯ_┦a9a0ᦪbc(2)᪷SᑖḄdᔠUNVᑣXYZN.ூ$௃:=পg=4-2h2+2h1-4x/=7-2(xT)2:x-1(2)g=_X(x+1)(x-1)X

14x-l,Xx(x+l)x-lk1"ri7'ூ&m௃?⚪ὃ᪶qr&=TᦪUNᑖdᔠUN.:⚪ᐵt&=uvwᐵUNVᑣ.1,20ஹ(1)y^-x-2x+3
(2)l-4a2,ᔣ3ᡠy2a2axḄᜧ+C~x=-Lx=2zᐭᓽ|}.(3)12}4x$lᱥ#3Ḅ&ᑮx$Ḅᨬᜧb6,&x=0,x=L%=92b~᪷S$x=—-ᙠXY¡ᓽ.2ூ¢:௃:=(1)ᵫ¤ᱥ#⚔&P(4,-1),ᡠy=a(x-4)2-1=ax2—8ax+16a—1,ᓽ16a—1=3,:}a=—,b=-8a=-24ᡠᱥ#:᪆=y=9/—2x+34(2)ᵫ¤ᱥ#¦&C(4,-1),ᡠkl=16a+4b+3,ᓽb=-4a-l.§ᱥ#y=k(4஺+1)%+3Ḅᔣ3ᑣᨵa>0ᐸ$"#¬=+="f=2+1>2ᡠ4k1WXW2yḼxḄᜧ+C4x=-1y=a+(4a+l)+3=4+5a4x=2,y=4a-2(4a+l)+3=1-4aᡠ4k10xg21—4agy*+5a(3)4a=lᱥ#Ḅ:᪆y=x2+bx+3ᱥ#Ḅ$"#X=-Mᵫᱥ#12q°4x=0,x=lᡈx=-Vᱥ#3Ḅ&x$ᨬ±2ᑖzᐭ}4x=0y=3

15x=ly=b+4hb~x=-y0t,y="-+3জAgVO,ᓽb>031,ᓽbV-2b+4

16᝞³kB´µᨵn+´µḄឋwᐸ´µA·m¸³¹º´µAḄᭆ᳛P(A)=%.n1335353322ஹ(l)y=--x2+±x+2(2)½¾ᩩµḄ&PḄᙶ᪗(Àc)ᡈ(Â-=)ᡈ(Ã5)ᡈ(Ã-5).22242422ூ:᪆௃(1)ᑭᵨÆÇᦪV|ᱥ#Ḅ⊤Éc(2)Ê4BMP4ABDwËḄᨵ9ᑖ|9B&Ḅᙶ᪗.ூ¢:௃(1)ᱥ#Ìx$ÍÎ&A(-1,0),B(4,0),•••ᱥ#Ḅ:᪆y=a(x+1)(x-4),•ᱥ#Ìy$ÍÎ&C(0,2),•\axlx(-4)=2,.11•*3=------22113ᱥ#Ḅ:᪆y=(x+1)(x-4)=-----x2+—x+222213(2)᝞11,ÏÐCD,•.•ᱥ#Ḅ:᪆y=-5X2+5X+2,3...ᱥ#Ḅ$"#x=23AM(-,0),\,&DÌ&CᐵÎ&MC(0,2),2AD(3,-2),VMA=MB,MC=MD,ÒÓÔACBDÕÖYÒÓÔVA(-1,0),B(4,0),C(3,-22),AAB2=25,BD2=(4-1)2+22=5,AD2=(3+1)2+22=20,/.AD2+BD2=AB2,/.ABDÕ"a9aÔ:.ZADB=90°,3&P(—,m),2MP=|m|,3VM(-,0),B(4,0),252,.,BMP4ABDwË

17...জ44BMPsADB.BMMP••-----9ADBD5:.5á,275ä.5••m=±+—,4..Pçkkèᡈçk——è2424ঝ4êBMP^ABDABM_MP+k+’5•••2=íV52ᨵ:.m=±5,33APç—95èᡈçk-5è,22353533ᓽ=½¾ᩩµḄ&PḄᙶ᪗Pç-,-èᡈç--èᡈç5èᡈçÀ-5è.242422?⚪ὃðñ0ᦪḄDᵨ:⚪ḄᐵtÕòóḄuv0ᦪḄDᵨ.23ஹ-2,-1,0ூ:᪆௃ᑖ᪆=ᐜ:÷জøùúû⚗ᦪᓄ1,~:÷ঝýᑖþû⚗ᯠ
Ḅ.⚪᪆2-x<2(x+4)জx<+1(2)3জxh2,ঝx

18...Ḅ!-2ᜧ<1.Ḅᨬᜧ᦮ᦪ!x=0,24ஹ(1)=-100X+50000(2)'ᖪ)*+A,34-ஹB,ᵯᾯ66-012├45ᑭ7ᨬᜧᨬᜧᑭ7846600ᐗ;(3);᪆.ூ᪆௃ூᑖ᪆௃(1)᪷@“5ᑭ7=4,ᵯᾯB-ᑭ7xAᵯᾯᦪC+B,ᵯᾯB-ᑭ7xBᵯᾯᦪC”EFᦪ᪆G(2)᪷@“B,ᵯᾯḄ+HCIJA,ᵯᾯḄ2KLᵯᾯᦪC!᦮ᦪ”MxḄOPQᔠ(1)ᡠMFᦪ᪆TUVFᦪḄឋXMEG(3)@⚪YZ=(400+a)x+500(100-x),ᓽy=(a-100)x+50000,ᑖ]^_`abজc00,yexḄfᜧgfᜧ,ᑖk+lM.ூm௃(1)᪷@⚪Yy=400x+500(100-x)=-100x+50000(2)V100-x<2x,.100••x>-----93Vy=-100x4-50000nk=-100<0,exḄfᜧghi•x!oᦪ.♦.x=34dypᨬᜧqᨬᜧq!4660(),r'ᖪ)*+A,34-ஹB,ᵯᾯ66-012├45ᑭ7ᨬᜧᨬᜧᑭ7846600ᐗG(3)@⚪Yy=(400+a)x+500(100-x),ᓽy=(a-100)x+50000,133-0,yexḄfᜧgfᜧ.•.cx=60dypᨬᜧq.ᓽᖪ)*+60-A,ᵯᾯs40-B,ᵯᾯḄ├4ᑭ7ᨬᜧ.ூyz௃⚪ὃ|}UVFᦪḄ~ᵨTUᐗUVḄ~ᵨ⚪Y
⚪nḄᦪCᐵᑡFᦪᐵ

19ஹ
ᐵᑡ8⚪Ḅᐵ.13525ஹ(1)x=2G(2)y——x~+2.x—G(3)k>U-224ூ᪆௃(D᪷@ᱥḄFᦪ⊤ᑭᵨVFᦪḄឋXᓽE
ᱥMḄG(2)᪷@ᱥḄT48=2ᓽEyAஹ8Ḅᙶ᪗᪷@yAḄᙶ᪗ᑭᵨᦪᓽEMᱥMḄFᦪ⊤G(3)ᑭᵨMᱥ⚔y஺Ḅᙶ᪗᯿⚪Y¡¢£¤¥¢£EA<-2,PᑭᵨUVFᦪ¢¦§yḄᙶ᪗ᱯ©E2k+b=-,QᔠᓃḄpqOᓽE«ḄpqO.2ூm௃(1)ᱥMḄ⊤!y=cix~—4QX+a—1,ᱥMḄ!®x=--=2.2aᦑrᫀ!x=2.(2)ᱥ)=2U4᝞+஺U1Ḅ!®²=2,AB=2,.•.yAḄᙶ᪗!(1,0),y8Ḅᙶ᪗!(3,0).´A(l,0)µᐭy=-4ar+a-l,a-4a+a-l=0,a=——,2i3ᱥMḄFᦪ⊤!y=--x2+2x--.(3)Vy=--x2+2x--=-—(x-2)2+—,-222ஹ’2.•.yOḄᙶ᪗!(2,G).;•®y=n½®/Ḅ¿yḄÀᙶ᪗Á!Â3(᳝>0)LcUd5ᨵ%-£>ÇU஽>0/*X20,3®I½Ḅ¿yᙠ(0,-2)Ê.b<-2.•..®/y="+஻(Í஺0)ÎJᱥḄ⚔y஺,

20ூyz௃⚪ὃ|}VFᦪḄឋXஹᦪMVFᦪ᪆ÏTUVFᦪ¢¦§yḄᙶ᪗ᱯ©⚪Ḅᐵ8DᑭᵨVFᦪḄឋX
ᱥḄG2᪷@yḄᙶ᪗ᑭᵨᦪMVFᦪ⊤G3᯿⚪Y¡¢£ᑭᵨᦪ£Qᔠ
.826ஹ
14U21G
1UÐU2G.3ூ᪆௃
1᪷@Ñ£ḄឋXAB=AE=4,+gᑭᵨÒÓᳮDEḄÕᓽErᫀG1ᑭᵨ┦×]×FᦪᐵNDAE=60஺+gM¢n▢ÙÚᑖḄ☢Ü!Sᡧ£FAE-S^DAEMᓽE.ூm௃G1:ᙠÑ£ABCDnAB=1DA,DA=1,AB=AE=4,•••DE=y/AE2-AD2=25/3.,.EC=CD-DE=4-1V3;AD1
1VsinZDEA=-----=—,AE2:.ZDEA=30°,ZEAB=30°,J.¢n▢ÙÚᑖḄ☢Ü!904x41/T30^x48ᐔA5öTFAB-bADAE-5ᡧTEAB=——-------•—XZXZVJ=-"336023603

21Rூq௃÷⚪u⌕ὃwxᡧTḄ☢døùVº»¯ᳮ┦ᦪᐵÙ²ïû᪷¥üïLDEḄ]⚪ᐵ.27ஹপ⊤þUÿ
10,100.5,25,0.25,150.5,1(2)0.25,100(3)1000x(0.3+0.1+0.05)=450().ூ
᪆௃(1)ᵫ⚣ᦪ50,ᑖᦪᑡ
ᑏ100.5,150.50.5-50.5Ḅ⚣ᦪ=100x0.1=10,ᵫᔜḄ⚣᳛1100.5-150.5Ḅ⚣᳛=1-0.1-0.2-0.3-0.1-0.05=0.25,ᑣ⚣ᦪ=100x0.25=25,ᵫ
⊤ᓽ#(2)ᙠ⚣᳛ᑖ%&'(ABCDḄ☢*+50x0.25=12.5,,-.Ḅ᪵012100(3)ᐜ4567ᙠ150ᐗ9:Ḅ;<Ḅ⚣᳛&=>45?@A᪥1000;<CDE;