2022-2023学年天津市南开区中考数学专项突破仿真模拟试题（一模二模）含解析

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2022-2023
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6ூ⚗ẚ௃ᔁ2022-2023
ᜩᓭὃᦪ⚗ẚ⚪ஹ⌱⌱r⚪3ᑖᐳ24ᑖ¡1,ᑡ¢£¤Ḅ¥¡A.x-x4=x5B.x6^x3=x2C.3X2-X2=3D.2x2¡3=6/ூ£¤ᫀ௃Aூ®௃ᑖ᪆+Aஹ᪷*{±ᦪ²Ḅ³´´ᑣµ¢.Bஹ᪷*{±ᦪᕆḄ◀´´ᑣµ¢.Cஹ᪷*ᔠ{¹⚗´ᑣµ¢.Dஹ᪷*Ḅ³^´ᑣ»¼µ¢.®+Aஹ£¤Bஹl+d=/,À⌱⚗┯Â+Cஹ3/—Ä2=2Å2,À⌱⚗┯ÂzDஹ2/¡3=8/,À⌱⚗┯Â.ᦑ⌱A.%Ç+ὃÈ{±ᦪÉḄ◀´ᔠ{¹⚗{±ᦪÊḄ³´Ḅ³^ËÌÍÎḄ¢´ᑣ¥⚪ḄᐵÏ.2.K1+Ðᨬ}ÑḄ᦮ᦪ¥¡A.4B.3C.2D.1ூ£¤ᫀ௃Bூᑖ᪆௃ᵫ$4<5<6.25C9,ᵫÀ᪷*¢ÖM^᪷ḄᭆØÙqÚᑮ5}ÑḄÛᐰM^ᦪÝÞ¢K1+⍩ᨬ}ÑḄ᦮ᦪᓽÙ..ூ®௃+4<5<6.25<9,.,.2<75<2.5<3.7

7ூ⚗ẚ௃ᔁ7áᨬ}ÑḄ᦮ᦪ¥2,âK1+J?ᨬ}ÑḄ᦮ᦪ¥3,ᦑ⌱+B.À⚪ä⌕ὃÈ<åᳮᦪḄÞ¢çèÞ¢åᳮᦪḄ\᎛“ᜳë´”¥Þ¢Ḅí^´î¥ïᵨ^´.3.ᙠM☢ðPᙶ᪗k%(4,-3)ᐵ$8%óôḄ%¥()A.(-4,-3)B.(-4,3)C.(4,-3)D.(4,3)ூ£¤ᫀ௃Bூ®௃ᑖ᪆+ᑭᵨᐵ$8%óô%Ḅឋ÷øoᫀᓽÙ.®+%(4,-3)ᐵ$8%Ḅóô%ᙶ᪗+(-4,3).ᦑ⌱B.%Ç+ᐵ$8%óôḄ%ùᙶ᪗úûᙶ᪗üýþÿᦪ.4.⊟200ᐗᢚᑭ20%,ᑣ⊟Ḅ()A.80ᐗB.90ᐗC.100ᐗD.110ᐗூ&'(ᫀ௃Cூ+,௃ᑖ᪆/0⚪Ḅ23ᐵ5/6▭=᪗Ḅᢚ=X(1+ᑭ᳛)=>?ᦪᑡABC,ᓽ.+,/=Xᐗᑣ(1+20%)X=200X0.6,,E/x=100.ᑣG⊟Ḅ100ᐗ.ᦑ⌱C.JK/ὃMᐗABḄNᵨ.PQḄRS/ᑭT=6▭-.5.W?ᐵXxḄABxZ-4x+c+l=0ᨵ]^_2Ḅ6ᦪ᪷ᑣaᦪcḄb()A.-1B.3C.1D.0ூ&'(ᫀ௃Bூᑖ᪆௃᪷dABḄ5ᦪ᪷ḄᑨfSg=(),ᓽEhᐵXcḄᐗAB,iᓽEhjk.8

8ூ⚗ẚ௃ᔁூ+,௃•.•ABx2-4x+c+l=0ᨵ]^_2Ḅ6ᦪ᪷Z.A=(-4)2-4(C+1)=12-4c=0,,E/c=3.ᦑ(ᫀ⌱B.m⚪ὃMn᪷ḄᑨfS,⚪ḄᐵopqḄrs᪷ḄᑨfSḄNᵨ.6.AABCᙠuvwḄxy᝞{ᡠ}(~^&AḄᙳ1),AD±BCXD.ᑡ⌱⚗w┯Ḅ()D.sinp=cospூ&'(ᫀ௃Dூᑖ᪆௃ᑭᵨ┦ᦪᐵ5ᑖfᑨᔜ⌱⚗Eh(ᫀ.ூ+,௃᝞{ᡠ}/AD=BD,ᑣNa=45஺,ᦑsina=cosa=Y^,ᦑ⌱⚗A&'ᨵᔠ⚪;2tanC=-----=2,ᦑ⌱⚗B&'ᨵᔠ⚪DCtana=l,ᦑ⌱⚗C&'ᨵᔠ⚪sinp=,cos0=4^.=£,Jsin#cos£,ᦑ⌱⚗D┯ᔠ⚪;AC5AC59

9ூ⚗ẚ௃ᔁᦑ⌱D.0⚪⌕ὃMn,&'rsᐵ5,⚪ᐵo.7.᝞{Ḅ{ᐸ¡☢£¤¥A.6B.4nC.67tD.12TIூ&'(ᫀ௃Cூ+,௃ᑖ᪆/¦§{?/¨ᙊª«3cm,¬☢2cm,•••¡☢£/ndh=᝞X3=6TT.ᦑ⌱C.8.᝞{ᙠABCw®J8ᙊ¯®84°±²³8cXJ஺´µ஺.¶·8=40஺,ZC=36°,ᑣ·0/஺Ḅ¸ᦪ¤¥A.70°B.44°C.34°D.24°ூ&'(ᫀ௃Cூᑖ᪆௃᧕E4ABD2Ὺ᪷d⚔¼h¬½ᵨ᜜ឋÀChND4cூ+,௃VAB=BD,ZB=40°,/.ZADB=70o,•/ZC=36°,.'.ZDAC=ZADB-ZC=34°.ᦑ⌱C.m⚪ὃMḄ¸Á¼pqrs᜜ឋÀ,⚪Ḅᐵo.10

10ூ⚗ẚ௃ᔁஹ⚪(⚪3ᑖ!ᐳ24ᑖ)9.ᑖ,ÂS/2a2+4a+2=.ூ&'(ᫀ௃2(a+1)2ூᑖ᪆௃ூ+,௃2a2+4a+2=2(a+1)2.ᦑ(ᫀ2(a+1)2ὃJ/ÂSᑖ,10.ÄÅ᪷SwxḄÆbÈூ&'(ᫀ௃x>3ூ+,௃,/᪷dÄÅ᪷SÊËAᦪÌÍÎÏᦪḄᩩ⌕ÑÒᙠ6ᦪÈᑁᨵÔ,ÌÍx-320,Ax>3.ᦑx23.11.6ᦪ“ᙠᦪÖ×Ḅxy᝞{ᑣ|a-G|=.a01ூ&'(ᫀ௃ூᑖ᪆௃᪷dᦪÖ×JḄxyᑨha-ÚḄ&ÏᑭᵨbḄÛᦪÔᓄÝᓽEᑮjß.ூ+,௃•.à<(),஺-Ú<0ᑣâS=ã-஻ᦑ(ᫀã-a12.åæᱥèy=2x2ᔣ×êë2^ᓫx½ᔣíêë3^ᓫxᡠEæᱥèḄ,᪆Sூ&'(ᫀ௃y^2(x-3)2+211

11ூ⚗ẚ௃ᔁூᑖ᪆௃᪷dÄÅᦪ{îêëḄïðñC,ᓽE.ூ+,௃᪷d“×òó”Ḅâᑣ?æᱥèy=2x2ᔣ×êë2^ᓫxᡠEæᱥèḄ,᪆Sy=2x2+2᪷d“öòíó”Ḅâᑣ?æᱥèy=2x2+2ᔣíêë3^ᓫxᡠEæᱥèḄ,᪆Sy=2(x-3)2+2.ᦑ(ᫀy=2(x—3)2+2.m⚪ὃMÄÅᦪ{øḄêëùḄ,᪆SCæᱥèy=ox2+6x+c•(ü0)ýᙶ᪗ÖêëùḄ,᪆S,ÿᐜᐸᡂ⚔a(x-“+/)ᑭᵨᱥᣚḄᨵᐵ%&'(ᣚᓽ.ᱥᣚḄ%&+,-./(ᙠ12ᑁ)4-5/(ᙠ67).13.:ᐵ;xḄ—•ᐗ?@A(m-l)x2+5x+m2—1=0ḄHI᪷K0,ᑣmḄNK.ூPQRᫀ௃-1ூᑖ᪆௃Hᐗ?@AḄ᪷WKHᐗ?@AḄXWKYZ[A,.\]^_Ḅ`aᦪḄN.cx=0dᐭAᓽfᑮHIᐵ;mḄAhijfmḄNk⌕mnHᐗ?@AḄoᦪpᨵY_;0.ூqX௃X+cx=0dᐭ(m—I)x2+5x+m2—1=0sf+m2—1=0Xf+m=lᡈm=-l,Vm-1/0,m#l,/.m=-l,ᦑ-1.x⚪z⌕ὃ|ḄKHᐗ?@AḄ᪷ᓽAḄXḄ}~X⚪As⌕mnHᐗ?@AḄoᦪpᨵY_;0.14.᝞KᵫI]ᑖ34Ḅᐰ_ḄᡂḄ“”ḄᜧPᑁᢗ┐ᑣ┐ᙠ▢ᑖḄᭆ᳛K12

12ூ⚗ẚ௃ᔁூPQRᫀ௃0.04ூqX௃᪷¢£¤}ᳮaPḄ]¦§=2☢©20,▢ᑖḄ☢©=PḄ☢©-4IḄ☢©=204xgX2X4=20-16=4,41ᦑ┐ᙠ▢ᑖḄᭆ᳛H=-,205ᦑRᫀ+.15.᝞ª¦«ABCDḄ]BC¬E,[CE=BD,®AE,᝞¯/ADB=40஺ᑣZE=.ூPQRᫀ௃20஺ூᑖ᪆௃᝞®AC.±⌕²³CE=CA,´µ/E=NCAE,jµNACEᓽX¶·⚪.ூqX௃X+᝞®AC.:]ABCDK«,¹.AC=BD,VEC=BD,¹.AC=CE,/.ZE=ZCAE,᧕²NACB=NADB=40°,VZACB=ZE+ZCAE,/.ZE=ZCAE=20°,ᦑRᫀ20°.»⚪ὃ|¼«Ḅឋ¾ஹ_ῪḄᑨ}ឋ¾Ḅ᜜Ḅឋ¾_aÃX⚪ḄᐵÄ13

13ூ⚗ẚ௃ᔁKÅÆÇ-ÈᵨÉÊ᪀⌼_ῪX¶·⚪.16.᝞Ía«48CDḄ⚔/ஹ஺ᑖÎᙠxÏஹyÏ஺஺=2஺=6,AD48=3+1.ᑣBḄᙶ᪗K.ூᑖ᪆௃3ÒBELxÏ;E,᪷¢«Ḅឋ¾fᑮND43=90஺᪷¢ÓḄឋ¾fᑮZADO=ZBAE,᪷¢^ÔḄឋ¾fᑮ%00=2,DE=-OA=\,;KfᑮÕÖ.33ூqX௃X+8ÒBELtÏ;E,,]×88K«JNZQC=90஺,.ZAD0+ZOAD=ZOAD+ZBAE=90°,...NADO=NBAE,••.OADSAEBA,.ODAE=OABE=ADAB•OD=2OA=6,.OA=3ADxAB=31,11.AE=-0D=2,BE=-0A=l,33OE=3+2=5,.B(5,1)ᦑ(5,1)14

14ூ⚗ẚ௃ᔁ»⚪ὃ|¼«Ḅឋ¾^ÔḄᑨ}ឋ¾ᙶ᪗Øឋ¾PQḄÒµÉÊÙ²³ÚOADs^EBAKX⚪ḄᐵÄ.$ஹ%&⚪(⚪ᐳᨵ6*⚪!ᔜ*⚪6ᑖ!ᐳ36ᑖ3x-(x-l)<617.Xpᨵ_ã+2x+l,------2,3ᦑpᨵ_ãḄXç—2

15ூ⚗ẚ௃ᔁõö+x=2dᐭ(x+2)(x-2)s(x+2)(x-2)=0,x=2KûAḄü᪷?ûAîX.ý+ὃ|XᑖAᐵÄKïᑖðcᑖAñᓄ᦮AXAᓽ.mnᑖAH}⌕õö.19.᝞ᡠ

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20ூ⚗ẚ௃ᔁ(2)¸CD=3,EC=26
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1᪷VNEDC+NEDA=180°,NB+ZEDA=180°.[ᑮZB=NEDC,»I4B=AC,᪷V^4,^¼[ᑮNB=ZC,᪷V^)%ᣚ[ᑮNEDC=ZC,᪷V^¼,^4ᓽGQ.
2DEAE,᪷V^ῪÀ¼ÀÁᔠḄឋW[ᑮBC=2EC=473,(“BCs^EDC,᪷V]ÃÀ¼ḄឋWᓽFÄABḄ¹.ூ`௃1GQ•,(ZEDC+ZEDA=180°,ZB+ZEDA=180°.ZB=ZEDC,)

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3DஹMᑖ¶ᙠ4ABஹOA6
èAD=2DB,AM=2MO,éᦪy=kx+bḄí>3DM,îïðéᦪy=—Ḅí3D,ÖBCḄB3IN.x(1)FîïðéᦪéᦪḄ⊤óô_(2)¸3Pᙠ³ÁDM6
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22ூ⚗ẚ௃ᔁAD(-3,2),m=Dᙶ᪗>ᐭ@=A%-B=-6,x...DEF᪆Gv=-9,X•ZM=2M0,/.MO=^OA=l,ᓽM(-1,O),—k+h=O=A/஺ᙶ᪗>ᐭy=kx+bH%-36ᒹ2%:k=b=-\,ᑣKLDM᪆Gy=-x-\9ফP(x,y),•OPMḄ☢!2,.-OM-\y\=2,ᓽ6=4,%-N±4ON4Px=-5,ON-4,x=3,ᑣᙶ᪗G(—5,4)ᡈ(3,-4).R⚪ὃUVWXᦪYᦪᐵX/01Ḅឋ\]^_`1☢Ḅabc^de7f7ghijWXᦪYk⚪Ḅᐵl.25.mnopqRᵯᾯtuvwᙠyz{|}~0A0BᡠᙠtuLḄᜳ`G120°P,(᝞1),☢}G2ᵨPGVᦣ᝛ᙠ☢ᐭᦣBCOᵯᾯᑮBOWw(᝞3),☢}G4.dOA=OB=28cm,O'CIOB!7C,0,C=14cm.(ὃᦪ-71=1.4146*1.732V5«2,236)(1)"NCBOḄᦪ.(2)|}~Ḅ⚔A'EᩭᓣVcm?(ᑮ0.1cm)23

23ூ⚗ẚ௃ᔁ(3)᝞4,ᐭᦣ⌕|}~0WtuLḄᜳ`£¤ᢝ120஺ᑣ|}~O7V¨©70'ᢥ¬P┐0ᔣ¯°(±ᨵᑏ´µ¶ᑏ)ூ/·ᫀ௃(1)30°(2)17.8(3)30°ூ+௃ᑖ᪆-(1)º´K`_`1ᓽ%ᑮ;(2)"¼ᙠḄᩭḄ½¾ᓽ.(3)|}~¨©7஺ᢥ¬P┐0ᔣ¯30°.+-¿lÁ0'C_L8C,04=03=28cm,O'CO'C_14_1.sin/C5O'=J~OB~28~2O'B•••NC8O=30°(2)¼ᙠḄ-/'C=4O'+(7C=28+14=42(CMᩭḄ-AO-sin60°=14>/3®24.25cm,42-24.25«17.8CTM..•.|}~Ḅ⚔"EᩭᓣV17.8cm9(3)|}~OW¨©7஺ᢥ¬P┐0ᔣ¯30°ᳮᵫ-•••|}~஺”tuLḄᜳ`£¤ᢝ120°,...|}~OW¨©7஺ᢥ¬P┐0ᔣ¯30°.7Ó-Ô⌕ὃUK`_`1c^V¯Ḅឋ\/ḄÕᵨ_`ᦪk⚪Ḅᐵl.26.ᙠÖ1H43=3,/஺=4,×7Ø78Ù]ÚÛ1ÜᓫḄÞßᔊ1ᔣ7/á×âP7஺Ø7CÙ]ÚÛ2ÜᓫḄÞßCBᔣ78á×äå஺P,QD,PD.çèÜ7âPÕ×ḄPéGxÛ(0VE2),·ᑡì⚪-(1)OxGíPP0LO0(2)AOP஺Ḅ☢GS,ᵨðxḄᦪᐵX⊤}SOxGíPSᨵᨬm°ó"ᨬm.24

24ூ⚗ẚ௃ᔁூ/·ᫀ௃প1.25(2)O.1.5P,SᨵᨬmG3.75QBBPூᑖ᪆௃(1)d8P=x,C0=2x,80=4-2x,ᐜᑨ0sAC஺஺!%ᑮ÷=ø,4—2xxᓽ-^=ûXḄᓽ%·ᫀ32x(2)ᵨÖ1Ḅ☢¾ý_ÜK`_`1Ḅ☢ᓽ⊤}S,᪷þÿᦪḄឋᓽ.ூ௃(1)NPQB+NDQC=90஺,•.•ZS=ZC=90°,NPQB+NQPB=90஺,ZQPB=NDQC,.ABPQSACQD,.QB_BP4-2xx----....%BJ-----=--,CDCQ32x%x=L25,()*+ᔠ⚪....x=L25PQ^-DQ9(2)SEF0-12-]X(4-2x)—-x3x2,x—-x4x^3-x)—x2-3x+6=(X-1.5)2+3.75•.•67⚗9ᦪa=l>0,>ᱥ@ABᔣDx=1.5SᨵᨬHIJ3.75.ὃLMNOPQRḄSTUV⚪WX67YḄᨬIZ[\ᳮ^ᐗ67`abcdeḄᑨ\gឋWXhiUjkᔠឋlmno៉ᔜrhiU⚪Ḅᐵt.25

25ூ⚗ẚ௃ᔁ2022-2023
ᜩᓭὃᦪ⚗ẚ⚪⌱^⌱vw⚪3ᑖᐳ36ᑖz1.-2018ḄIḄ᎔ᦪvzA.-2018B.20180ᙠ2.2017~᩟ᙳᦈᐭᑮ10330ᐗrᦪᵨᦪ⊤JvzA.0.1033X105B.1.0330X104C.103.30X102D.10.330X1033.RᑡḄvzA.a!»a:,=2a3B.a^-a=a,C.a+a=2aD.0)%44.Rᑡ¢£¤¥¦¢,§¨ᨵ¥¦¢Ḅv)C.D.5.᝞¢ᙠBABCD£,AD=8,UE,FᑖAB,ACḄ£UᑣEF¯°vA.2B.3C.4D.56.±^r²³´µD☢ḄUᦪUᦪJ᜻ᦪḄᭆ᳛vz.1]_A.yB.-C.D.3457.ᦪy=GTḄ½¾xḄ¿IÁvzA.x>1B.x<1C.xl8.Ãh^r¯ῪdeḄÅÆᑖ2g4,ᑣǯῪdeḄᕜÆJvzA.8ᡈ10B.8C.10D.6ᡈ129.᝞¢ᡠḄNOÌᵫÎrbÏḄH`ÌÐᔠÑᡂḄÓḄÔÕ¢vz26

26ூ⚗ẚ௃ᔁA11.᝞¢U8Öl×ᦪy=&vÎ0ᙠØ▲ᑁ¢ØDḄ^UÛU8Ü1Ý_Lx¤°U4X6C_Ly¤°UC,Ḅ☢ÞJ6,ᑣ%ḄIJvk12.᝞¢ᙠÏ^ᙶ᪗9£vâã`ᔣx¤zᦪ^=^gä=å+3Ḅ¢Øᜧçvz6ஹéê⚪vw⚪3ᑖᐳ18ᑖz27

27ூ⚗ẚ௃ᔁ13.ᑖëìx2y-y^.14.᝞í^rjḄeJ45°,îïrjḄᦪ.15.ᙊ┵Ḅò@Æ8cm,ó☢ᙊḄᕜÆJ12cm,ᑣÇᙊ┵Ḅô☢ÞJ.16.õö÷øḄùúஹûᨴýþÿ
ᵫ1000ᐗᑮ810ᐗ.ᑣᙳᨴḄᑖ᳛.17.᝞DE஻AC,BEEC=21,AC=12,ᑣDE=_____.18.“H”“g”⊤!"#$%&ᦪḄ!"()᝞*:141=0,/
2=1,"3=2,஻4=3,…ᑭᵨ./012":-/(2008)=$ஹ%&⚪ᑏ78⌕Ḅ%⚪;ᐸ@a=-3.a+3a-9a-321.᝞BCᳫEFᘤHIBCᳫ/ᜐL%MN⚔BᜐḄPQ30°,LRMNSCᜐḄTQ60°,BCᳫNḄUVW/஺100YZ;RMNḄ[\BC.型BmBosn目trel岂居tnow鸟nEErrCEmeEmGH!3QEEr?FsEEFBBo3pGn=n-一22.᝞]^ABCDḄ$Q_AC,BD`abc0,cE,FᙠBD/OE=OF.;eAE=CFf28

28ூ⚗ẚ௃ᔁ23.g@hᦪhᐶjklmn᪥hp$ᵯr⁚tḄu᰿wxyzᑖhpᨬu᰿|%}⁚t3~Ḅhp⌱%}ᨵᨵ⌱Ḅ()ᑴᡂ᝞*Ḅ23ᨵ᦮.᪷@ᡠḄᡂ*ᑡ⚪31;n
Ḅhpᦪf322⊡ᐙ᦮;⁚tᙠᡧ^2@ᡠᓰᙊ£QḄ\ᦪf33¤¥@hᨵ3000¦hp§2¥᪥u᰿ᵯrᒓ⁚tḄᦪ.24.᝞cD©NAOBḄᑖ_OC/ª«%c¬DDE_LOBbE,.DE®¯©D,;eOA©஺DḄᑗ_.25.᝞±²³_y=3x-3ᑖ´axµஹyµbAஹBc·ᱥ_y=x'+bx+cAஹBccC©·ᱥ_xµḄ¹%ac3Acᨵºᔠ.29

29ூ⚗ẚ௃ᔁ(1)?@ᱥBḄ%᪆DE(2)?AABCḄ☢GE(3)ᙠ@ᱥBḄHIJK!LᔲNᙠOP4ABMQRῪ$TUVWXᨵNᙠ!YZ[ᳮᵫEWNᙠ!?7OMḄᙶ᪗.2022-2023
ᜩᓭὃᦪ⚗ẚ⚪()⌱%⌱(⚪3ᑖᐳ36ᑖ)1.-2018ḄaḄ᎔ᦪL()A.-2018B.2018C.c20182018ூde&ᫀ௃Cூg%௃⚪%᪆4-2018ḄaL2018,2018Ḅ᎔ᦪL!.2018ᦑ⌱C.2.2017
klm᩟opqᙳstuᦈᐭxᑮ10330ᐗ!{|}ᦪᵨᦪ⊤Q()A.0.1033X10sB.1.0330X1()4C.103.30X102D.10.330X103ூde&ᫀ௃Bூg%௃⚪%᪆10330{|}ᦪᵨᦪ⊤Q1.0330xl0tᦑ⌱B.3.ᑡdeḄL()30

30ூ⚗ẚ௃ᔁA.a3ea3=2a3B.a3-^a=a3C.a+a=2aD.(a3)2=a5ூÒÓÔᫀ௃Cூ×m௃Z⚪ᑖ᪆ᔜ⌱⚗ᑖ´ÛÜÝSᦪᘤḄÞß◀ßᔠÝ}⚗áḄÞâ!"ᯠä⌱ÒÓ⌱⚗ᓽæ.Z⚪m᪆Aஹa3.a3=a6,ç=2"┯éᦑn⌱⚗┯éfBஹa%a=a"=aç=2"┯éᦑn⌱⚗┯éfCஹa+a="2a",ç=2"ÒÓᦑn⌱⚗ÒÓfD.a3
2=a6,ç=2"┯éᦑn⌱⚗┯é.ᦑ⌱C.ὃc1,ÝSᦪᗩḄ◀ßf2.ᔠÝ}⚗f3.ÝSᦪíḄ◀ßf4.îḄÞâïḄÞâ.4,*ᑡ^@©µ$ð^ñᨵ©$ð^Ḅ©3ூÒÓÔᫀ௃Bூᑖ᪆௃᪷µ$ð^$ð^Ḅᭆó;m.ூ×m௃Aஹ©$ð^ᨵ©µ$ð^ᨵᔠ⚪«fBஹ©µ$ð^ᨵ©$ð^ᔠ⚪«fCஹ©µ$ð^ô©$ð^ᨵᔠ⚪«fDஹ©µ$ð^ô©$ð^ᨵᔠ⚪«.ᦑ⌱B.n⚪õ⌕ὃ÷Ḅ©$ð^µ$ð^Ḅᭆó.µ$ð^Ḅᐵù©úû$ðµᑖᢚýäæºᔠf$ð^©⌕úû$ðþÿ180
ᔠ.5.᝞ᙠABCDAD=8,E,FᑖAB,ACḄᑣEFA.2B.3C.4D.5ூᫀ௃C31

31ூ⚗ẚ௃ᔁூᑖ᪆௃ᑭᵨ!"#ឋ%&ᑮBC*ᯠ
,ᑭᵨ-./ᳮ&ᑮEFூ34௃ᙠABCDAD=8,&:lE,FᑖAB,ACḄᡠ@EF>AABCḄ-.EF=-5C=4,ᦑ⌱C2F⚪H⌕ὃK!"#ឋ%LMN#-./ᳮOPᓫ⚪6.STUVWXYZ[☢Ḅᦪᦪ>᜻ᦪḄᭆ᳛.1111A.~B.-C.-D.T2345ூᫀ௃Aூ34௃e⚪4᪆fSTUVWYZᔣ[Ḅ☢Ḅᦪᨵ6ijkᑣᦪ>᜻ᦪᨵ3ijk31ᦑᦪ>᜻ᦪḄᭆ᳛>l=T62ᦑ⌱A.7.nᦪy=ḄpqrxḄtuwA.x>1B.x<1C.x<1D.x>1ூᫀ௃Dூᑖ᪆௃᪷{|}᪷~Ḅᦪᦪ.ூ34௃᪷{⚪&X-1N0,4&Xil.ᦑ⌱D.F⚪ὃKnᦪpqrḄtuwḄ/ᑖ~Ḅ.nᦪpqrḄwTMU☢ὃ⇋f1nᦪ⊤~᦮~Xpqrtᐰᦪ2nᦪ⊤~ᑖ~Xὃ⇋ᑖ~Ḅᑖᨵ>03nᦪ⊤~|}᪷~Xᦪᦪ.8.TUῪMN#Ḅ"*ᑖ24,ᑣῪMN#Ḅᕜ*>32

32ூ⚗ẚ௃ᔁA.8ᡈ10D.6ᡈ12ூde&ᫀ௃Cூg%௃⚪ᑖ᪆4জ2LῪ!$TUḄ$ᑖQ2ஹ2ஹ4,•.2+2=4,.Xᨵᡂ$TU!ঝ2L!$TUḄ$ᑖQ2ஹ4ஹ4,ᡂ$TU!ᕜ=2+4+4=10,Kᡠ!ḄᕜL10.ᦑ⌱C.ὃO41.RῪ$TUḄឋ2.$TU$ᐵE3.ᑖ.9.᝞ᡠḄ¡¢Lᵫ£}¤¥Ḅ*d¦¢ᔠ¨ᡂḄ!Ḅ©ªLூde&ᫀ௃Bூᑖ᪆௃᪷¬©ªḄ®ᓽs°7ᑨ².ூg%௃%4᪷¬⚪³!´¡¢Ḅ©ª᝞:ᦑ⌱4B.(⚪⚪ὃ¶·¸ᓫᔠ¢Ḅ$ª!deº»¼½T¾L%⚪ᐵ¿.10.᝞!¡ABCQ஺OḄᑁÁ$TU!ZBOC=80°,ᑣNARÃA.80°B.60°C.50°D.40°ூde&ᫀ௃D33

33ூ⚗ẚ௃ᔁூ34௃e⚪4᪆fᵫᙊᕜN/ᳮ&,NZ=N8OC=4y,2ᦑ⌱D¤fᙠ¥ᙊᡈᙊ¥§ᡈ§ᡠ¨ḄᙊᕜNᙊ©NḄTª.11.᝞8«¬nᦪy=±@0ᙠ®▲ᑁ®[ḄT±8²ᕒ4_Lx´4x8aLy´C,µ#4OC8Ḅ☢¶>6,ᑣAḄu>ூᫀ௃Bூ34௃4f=>µ#ᨴ0C2Ḅ☢¶>6,ᡠ@OA•AB=6,•.•8«¬nᦪy=&¹0ᙠ®▲ᑁ®[ḄTx|ᱏḄu>6.ᦑ⌱B.12.᝞ᙠ¥Tᙶ᪗½¾ᔣx´nᦪy=&À=Á+3Ḅ®ᜧÄ34

34ூ⚗ẚ௃ᔁூᫀ௃Aூᑖ᪆௃᪷{nᦪÅ«¬nᦪḄ®L½ᦪḄᐵ½².ூ34௃4fAஹᵫnᦪÈ"Ḅ®a>0LÈAx+3Ḅ®”>()TÄxBஹᵫnᦪÈ&Ḅ®%>0L=Á+3Ḅ®4>0,L3>0ÎÏ┯ÑxkCஹᵫnᦪᱏTḄ®Ò<0L᜛=Á+3Ḅ®Ô<0ÎÏ┯ÑxDஹᵫnᦪÕ"Ḅ®Ò>0LÖÁ+3Ḅ®%<0ÎÏ┯Ñ.xᦑ⌱fA.F⚪H⌕ὃK«¬nᦪḄ®ឋ%nᦪḄ®ឋ%⌕×ØÙÚḄឋ%ÛᮣÝ4⚪.ஹ⚪(⚪3ᑖ!ᐳ18ᑖ)13.ᑖ4=~fx2y-^=.ூᫀ௃y(x+1)(x-I)ூᑖ᪆௃ᑭᵨÞß=~Åàß~á=~ᑖ4.ூ34௃4fx2y-y=y(x2-1)=y(x+1)(x-1),ᦑᫀ>y(x+1)(x-1).F⚪ὃK=~ᑖ44⚪Ḅᐵâ×ØÞß=~ãLß~ãḄäᔠåᵨ.14.᝞æTUç"#ḄN>45°,èéêUç"#Ḅ"ᦪ.ூᫀ௃8ூ34௃e⚪4᪆fêUç"#Ḅ"ᦪ360°+45°=8,ᦑᫀ>8.35

35ூ⚗ẚ௃ᔁ15.ᙊ┵Ḅ.*8cm,î☢ᙊḄᕜ*>12cm,ᑣᙊ┵Ḅï☢¶>ூᫀ௃48cm2ூ34௃e⚪4᪆f᪷{⚪&ᙊ┵Ḅï☢¶=,x8xl2=48cm2.2ᦑᫀ>48cm2.16.ðiñòḄóô!ஹõᨴö÷ø}ùúûüýúᵫ1000ᐗùᑮ810ᐗ.ᑣᙳᨴḄᑖ᳛.ூᫀ௃10%ூᑖ᪆௃᪷⚪ᑮᐵx(1-%᳛)2=%)Ḅ*+,ᑡ./012ᓽ4.ூ52௃67ᙳᨴḄᑖ᳛X,+⚪;1000(1-X)2=810,ᓄ>;:(1-x)2=0.81,2;xi=0.1,X2=-1.9(BC).ᡠE7ᙳᨴḄᑖ᳛10%,ᦑ10%.G⚪ὃIJKᐗMN/0ḄOᵨKKQR᳛*17ᙳSᓄ᳛Ḅ/T.U6SᓄVḄa,Sᓄ)Ḅb,7ᙳSᓄ᳛x,ᑣZNSᓄ)Ḅᦪᐵa(l±x)2=b(^QR_`aḄ“c”e⌱“+”*^%_`aḄ“c”e⌱).17.᝞j*DE஻AC,BEEC=21,AC=12,ᑣDE=______.ூᑖ᪆௃᪷DE஻AC,r;BEDS/\BCA,sᵫuvwxyzO{|ᡂ~4;.ᫀ.DEBE2ூ52௃2ᵫDE஻AC4;BEDs^BCA,——=--------=-,ACBE+EC3AC=12,4;DE=8.36

36ூ⚗ẚ௃ᔁᦑ8.G⚪ὃI7{Ḅ*uvwxyzO{|ᡂ~Ḅឋ.18.e“g”⊤Z*zKᦪḄ᝞:(1)/(1)=0,/(2)=1,/(3)=2,/(4)=3,…ᑭᵨE¡:K/(2008)=ூᫀ௃1ூ52௃¢⚪ᑖ᪆£¤(1)`Ḅᔜᦪ*ᡃ§4E;.f(2008)=2007,£¤(2)`Ḅᔜᦪ,ᡃ§4E;.f(©K)=2008.ªIJf(ߟ!—)-f(2008)=2008-2007=1.ᦑᫀ1.20082008ὃ¯1.ᨵᳮᦪḄ²T³2.´µ¶.$ஹ%&⚪(ᑏ78⌕Ḅ%⚪;/---s1ÆᦪÃḄÇ*ᐸ`a=JJ—3.஺+393ூᫀ௃—;ᙠ஺+33ூᑖ᪆௃᪷ᑖÃḄ◀TͲT4Eᓄ>⚪Î`ḄÃÏ*ᯠ)Ñ஺ḄÇÆᐭᓄ>)ḄÃÏᓽ4.46a-3ூ52௃2Ã=ÓK/'Æ/~TV--a+3(a+3)(a-3)243Q+3Q+337

37ூÕ⚗×ẚ௃ÙÚ¢ᔁ1a+3^a=^3—3_,Ã=-r-------=-4==.-3+3V33G⚪Ü⌕ὃIJᑖÃḄᓄ>¡*ÞßàáᑖÃâᔠTᑣ*ᓄ>.*ä2⚪Ḅᐵå.21.᝞j*æçᳫéêᘤì*íæçᳫ/ᜐïKðñ⚔ó5ᜐḄôx30°,ïõðñöóCᜐḄ÷x60°,æçᳫñḄø7ùú/஺100û*¢1õðñḄüý8c.5BeBBBBgrMGmoaeGR£B区nunHB©cg©g昌HgBw«ELu已a中raBt?enrwSBf?EmOM目cffsl0口raH科Hnc3ூᫀ௃õðñḄüýBCäÿ
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