2021-2022学年江苏省南通市海安市高二（下）期末数学试卷（附答案详解）

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2021-2022
ḕᓭᦪᔁஹᓫ⌱⚪ᜧ⚪ᐳ8⚪ᐳ40.0ᑖ1.%ᐸ=./ᑣm=A.6B.5C.4D.32.᪷4᪵640,2.2,82,4.4,஺4,9:ᑴḄᦣ6>?᪵6ᕈABCDEBឋGHIJKg=0.65x+2.5,ᑣn=A.6.6B.5.1C.4.8D.3.83.PQRSᐳᨵ8PᜧUVḄᳫᐸS3PXᳫ5PYᳫZS[\᥎^2Pᳫᑣ_ᑮXᳫḄPᦪḄaKA—B.iC.dD.i4.eᓝghijᝍlm2022
3ᨴ4op3ᨴ13oᙠSrᡂtuv.w?Zx᪥4zᵱ|}ὅ2z᝕|}ὅS⌱^3ᑖjᝍஹjᝍᳫ᫹|}ὅEᨵ1z᝕|}ὅᐭ⌱ᑣVḄ⌱IᫀᐳᨵA.36B.42C.48D.725.ᢗᵬஹἠᦈᓫdᐗᑖ᝞⊤dᵬἠᦈᑖ¡ᑡἠᦈᑖ¡ᑡᦈ-102ᦈ012ᭆ᳛0.10.30.6ᭆ᳛0.20.50.3ᑣᑡ¦§¨©ḄªA.ᢗᵬἠaᦈᜧB.ᢗἠaᦈᜧC.ᢗᵬἠḄ«◅D.ᢗἠḄ«◅6.ᙠ®☢°04BCS±²=dOB=b´=36஺µ¶·=%¹²EK4DḄS6OE=^a+^b+^c,ᑣ;1=()244D|A-I7.¾¿ᓄÁᙠÂêÄ⁐ஹÄÆஹÄÇஹÈḄÉÊË°ᨵÌÍḄÎÏឋᙠᵯᘤÒÓI☢ᐹᨵÕÖᵨ⌶.w?¾¿ᓄÁᑖR᪀Úᕈ¨Û☢°P☢ܪ¨gÝÞ,᝞>ᡠà_¨Û☢°Ḅᩩâᙠeᩩâ_ãm®

1åÞ/BCDḄᩩåḄᩩæç_eᩩâᑣ_^ḄᩩâᡠᙠḄABªè☢ABḄᭆ᳛K()A.IB.1C.-D.-9911118.%(1+2x)3(%—2>=Ḅ+a1é+a2/+……+ᑣ%)+஺2+஺4+஺6=()A.-54B.-43C.-27D.54ஹê⌱⚪(ᜧ⚪ᐳ4⚪ᐳ20.0ᑖ)9.ëm᪵Uᐵíᦪr,ᑡ¦§¨©Ḅª()A.rîᜧᡂë᪵ᦪ4ḄBឋUᐵJïîðB.r=0,ᡂë᪵ᦪ4ñᨵòUᐵᐵíC.róôõ᪵6öSmxᩩABḄJïD.ᡂë᪵ᦪ4UᐵḄ¨÷ឋørḄùú(¨÷)UVio.w?^S/ªûüḄgPᓫᔣþᑡ¦§¨©Ḅª()A.%a஻ᡈb//c,ᑣ"B.a^ᐳ☢ᑣb,ᐳ☢C.ḄᔣPᙠᦪx,y,Z,p=x4+y»+zD.B!Ḅ"#$ᑣa+Bb+c>%+'(!Ḅ"#$11.)*ᐳᨵᒹ-./Ḅ3012320425*67ᙢ9:;<20ᵨ4⊤?“A:<ᑮ12”ᵨB⊤?“AD:<ᑮ12”EF)A.P(A)=P(B)B.P(4B)=P(4)P(B)C.P(A+B)=0.9D.P[.B\A)=0.512.ᙠHIJ☢KABC஺-HiBiGCi*AB=AD=AA,^AB=/.A^AD=^.DAB=r60஺MPᙠNOBQPᑣ()A.AP1B௃CB.PᑮaBi3CDḄST.UC.APV&BiᡠᡂYḄZ[\ᨬ^_`D.4PVH☢4BC0ᡠᡂYḄ1[\ᨬᜧ_:cஹe⚪(gᜧ⚪ᐳ4^⚪ᐳ20.0ᑖ)13.iᑏkMCḄᙶ᪗noVM4(1,1,0)cMᐳN.A2⚓ᐳ17⚓

214.tu(x-⊤xḄyz{*A3⚗3A4⚗ḄD⚗{~ᦪ./ᑣyz{*D⚗Ḅ~ᦪ_.15.ᙠ%☢⚪*⌱⚪n⚪1nM4!ᱥNGn/=2஺0)VN஺2n/2=1ᙠA▲ḄᐳMMB,Cᑖ!6ḄNVḄᩩNḄMᑣABCḄ☢¢_⚪2ntuᳫḄK¢U3⊤☢¢Sᙳ!ᳫ§¨RḄªᦪᑖ«_V(R),S(R),ᳫ஺Ḅ§¨R®V'(R)=3S'(R),MPᑮᳫ±஺ḄST_1,²MPH☢a,ᑣH☢a´ᳫ஺ᡠ´☢ᙊḄ☢¢Ḅᨬ^\_.¶n᝞¸⌱⍝⚪ᑖºᑣᢥAº¼ᑖ.16.½ᖪ¿ᐳᨵcÀᨬÁÂᑜAÀ_35ÄÅÆᵨ2ÇADÀ_35ÄÈ-ÇAcÀ_30Ä⚶ÊÇ.ËᖪÌᨬÍᔜÀᔜÏÇÐḄᦪ(ᓫÒnÄ)Ó¼᝞%⊤nÅÆᵨ2ÇÈ-Ç⚶ÊÇAÀ2573ADÀ4274AcÀ61235AÀÇÐ*ÕÖ;Äᑣ×ÇÐVᨬÁÂᑜØḄᭆ᳛_:5×ᖪ¿ᡠᨵÇÐ*ÕÖ;Äᑣ×ÇÐVᨬÁÂᑜØḄᭆ᳛_.Ûஹº⚪(gᜧ⚪ᐳ6^⚪ᐳ70.0ᑖ)17.ᙠ%☢⚪*⌱⚪n⚪1ntuS”!UÜᦪᑡÞᓽàḄán⚗3ã%=1,55=25,ån(1)ᦪᑡÞᓽàḄæ⚗{ç(2)ᦪᑡÞ^^^àḄán⚗37ç.anan+l⚪2nᙠA/IBC*êu48=3,AC=2®B=ìM஺ᙠíBCPãBD=1,ån(1)4஺ç71(2)sin(C--)¶n᝞¸⌱⍝⚪ᑖºᑣᢥAº¼ᑖ.

318.½᪥_òºóÅKôõö÷øḄùÕÖ;<ò100ÒóÅúIûüý¸᝞%n7“”Ḅþᦪᓰ
ᦪḄᙠ“”Ḅᵱᦪ᝕ᦪḄ*ᙠ“”Ḅ᝕ᦪᓰ(1)᪷!"#ᑏ%☢2x2ᑡὶ⊤-./ᭆ᳛2a=0.001Ḅ78ឋ:;,ᑨ>?@ABCDEFḄGᔲIឋJᨵᐵM(2)ᔠOᵱ᝕ᔠO▬:a0.10.050.010.0050.001XQ2.7063.8416.6357.87910.828Yὃ[\]ᐸ_2=)=a+b+c+d.ᐸ“(2)defghABCDEFiABjkḄl᪗ᦔo?pi@q100r?stABjkujkᡂwᢚyᡂzᑖᑴ}~60ᑖdl᪗96%Ḅ?l᪗ᑣdl᪗ᦔo℉.q100r?Ḅjkᡂw᝱ᑖN(70,25),kᑨ>᪥ghABCDEFil᪗ᦔoᔲ℉M▬]X,,ᑣP(஻-a/-BAD=90%ACI8஺¯°0.(1)±²]BD1³☢P4C´(2)±µ☢ªP-CD-BḄ¶·2.¸4⚓ᐳ17⚓

420.»ᙊC]½+¾=1,(஺>ᓃ>0)ḄÀᯖ°ᡝ(2,0),Ã⚔°4(3,0).(1)±CḄÅÆ´(2)ÇBdC°(ÈÀஹÃ⚔°)MdÊË4BḄ°஺dᙶ᪗Í°ÎÊOMIÎÊÐx=-!"#$N,±²]AB1NF.21.Ñᦪ/'(X)=%—xbtr—1.(1)²Õ]/(%)<0´(2)Öe*2aØ+1,±a.22.ÙᜧÛÜÝÞßtàáâãÝḄäâ᳛dp.(1)Öp=0.9,æçèé2êÝëèᑮãÝḄêᦪd±fḄᭆ᳛ᑖîᦪ?pï´(2)@ÜÝÞᡠᨵÝstñ⊈ᓄ;péᡠᨵãÝ.Åᫀ᝞%]ᢥ)k(kGN*)êÝõᑖõ-ö÷õḄkêÝḄ⊈ùᔠᙠúᓄ;Öûüᨵý⚪ÿᑖ
k⌲ᓄ.Ḅᓄᦪ24kW8nḄᦪ!"#E5)<1,+pḄ-.0.

51ᫀ34᪆1.ூ1ᫀ௃Dூ4᪆௃48ᵫ4=m/•>./m/=6ᦑm=3.ᦑ⌱8D.᪷D᣸ᑡᦪG▤IJKLMᓽO.P⚪R⌕ὃU᣸ᑡᦪG▤IJKVWXẠ⚪.2.ூ1ᫀ௃Cv஽஻\]1bji10+2+4஺—2.2+4.4+n6.6+nூ4᪆௃48%=—y-=2,y=---=—Oc᪵PeḄfgḄᙶ᪗j2,klmᐭ9=0.65%+2.5,c^^=0.65X2+2.5,4cn=4.8.ᦑ⌱8C.ᵫtu+c᪵PeḄfgḄᙶ᪗mᐭvឋxyz{ᓽO+cn..P⚪ὃUvឋxyz{Ḅ|ᵨ~vឋxyz{ឤ᪵PeḄfgᐵXẠ⚪.3.ூ1ᫀ௃Aூ4᪆௃48fᐳᨵ8ᜧḄᳫᐸf3ᳫ5ᳫf᥎2ᳫᑣᑮᳫḄᦪᑖᦑ-ᑮᳫḄᦪḄ"#2x8=84ᦑ⌱8A.᪷DtuᩩᔠᑖḄ"#JKᓽO+4.P⚪R⌕ὃUᑖḄ"#JKVWXẠ⚪.4.ூ1ᫀ௃Dூ4᪆௃48ᵫ⚪¢ᨵ£᝕¥¦ὅḄ⌱¨ᨵ©©ª=72¬ᦑ⌱8D.ᐜ⌱£᝕¥¦ὅᐳᨵ0¬®⌱2£ᵱ¥¦ὅᐳᨵ©¬ᨬ±²³ᐰ᣸ᑡᓽµ6⚓ᐳ17⚓

6O.P⚪ὃU·᣸ᑡᔠḄ¸ᔠ¹⚪ᐜ⌱±᣸ᨬXPḄᢣ»¼½VWXẠ⚪.5.ூ1ᫀ௃Cூ4᪆௃48ᵬᦈÀḄ"#E(X)=-1x0.1+0x0.3+2x0.6=1.1,D(X)=(-1-l.l)2x0.1+(-1.1)2x0.3+(2-l.l)2x0.6=1.29,ÁᦈÀḄ"#E(V)=0x0.2+1x0.5+2x0.3=1.1,஺(Ã)=(0-l.l)2x0.2+(1-l.l)2x0.5+(2-l.l)2x0.3=0.49,ᦑE(X)=E(y),D(X)>D(Y),ᦑᢗÅᵬÁÆἠḄ"#ᦈÀÈᢗÅÆἠᵬÉᢗÅÆἠÁḄÊ◅Ì.ᦑ⌱8C.᪷Dtuᩩᑖ
+ᵬஹÁ¬Æἠ"#GzÎÏÉÐᓽO+4.P⚪R⌕ὃUÑᦣÓ"#GzÎḄ+4VWXẠ⚪.6.ூ1ᫀ௃Aூ4᪆௃48ᵫ⚪¢OcÔ="+Ö)+×+Ö)=*Ù+ᓭ+4Û)——[OA+OB+A(OC—OB)]=—OA+—(1—A)OB+—AOC——a+—(1—A)b+—Ac,Üᮞ=%+4+G,244ᡠß==4c/(=àᦑ⌱8A.ᑭᵨᔣḄvឋãMOcä=[k+T(1—#3+[4Á®ᔠtu᪷DᔣḄXPæᳮO+c4Ḅ..P⚪R⌕ὃUᔣḄXPæᳮὃUãM+4èéVWXẠ⚪.7.ூ1ᫀ௃Dூ4᪆௃48᪷D⚪¢OcᎷëìíéBCD-AB,ᑣGéBî☢ḄðvCE,DE,CF,DF,ᳮOcBC,CD,4஺Ḅî☢ðvᡠßµᩩñ-òWëìíABC஺Ḅᩩìµó-ḄñGµ-cñî☢ðvḄz¨ᦪᨵ4x4¬

7ôM“÷-øù☢úḄûᩩñµᩩñ-òWëìí4BCDḄᩩì”
N“ᩩᩩᡂ☢”ᑣ☢Ḅᩩᨵ12x11!"ᐸ$%&'()4BCDḄᩩ(ᨵ4x11!"ᡠ/P1M3=^=%2173=ᯅ=9ᡠ/P1N|M3=^^ᦑ⌱=D.ᑭᵨ☢Ḅ@ABCDEᩩḄᡠᨵFGHᑭᵨᩩᭆ᳛KLBMᓽO.Q⚪ὃTᩩᭆ᳛UVWẠ⚪.8.ூ[ᫀ௃CூM᪆௃M=_x=1%3+Ḅ+a2+…...+a=27,7_x=-1d+—1f+a+a+a3=-81,357Lij21a0+a?++cig3=—54,ᦑa஺+a2+-27.ᦑ⌱=C.ᑖs_x=Lu-1,ᓽOᑮᐵVxyL$᜻ᦪ⚗}ᦪuVᏔᦪ⚗}ᦪuḄ!,MC᜻ᦪ⚗}ᦪuᓽO.Q⚪ὃT"ᙠẆ⚗xyL}ᦪḄᵨUV$᫏⚪.9.ூ[ᫀ௃ABூM᪆௃M=iᐵ}ᦪrᵨᩭ⊝ḄឋiᐵḄiᐵ}ᦪr&VV1ḄḄᜧiᐵᜧᦑ4┯iᐵ}ᦪ0¡¢ᙠiᐵᐵ}£¤¥⊤¡¢ᙠᐸ§¨Ḅᐵ}ᦑB┯ᵫiᐵ}ᦪḄᭆªO«r•®¯᪵Q9±$V²ᩩḄᡂ᪵Qᦪ³iᐵḄ´ឋrḄµ¶1´3i·ᦑC஺¸.ᦑ⌱=AB.᪷³º«ᩩ»ᔠiᐵ}ᦪḄᭆªᓽO½%BM.Q⚪¾⌕ὃTiᐵ}ᦪḄᭆªUVWẠ⚪.8⚓ᐳ17⚓

810.ூ[ᫀ௃CDூM᪆௃M=V4=Â0Ãb//cজH6)ᑣ0/ÅᦑA┯ÆVB=ÂC2,ᐳ☢ᑣÇb3¡@ᐳ☢ᦑB┯ÆVC=VÈḄÉᔣp,(5,3,Ë¡ᐳ☢)Í¢ᙠÎᦪx,y,z,Ïp=xÐ+yb+zcᦑC¸ÆV஺=ÂC¯1&ÈḄWÑᑣÐ+Eb+cÒ+СᐳÓO/&ÈḄWÑᦑ஺¸.ᦑ⌱=CD.Ôᑭᵨᐳᔣuᐳ☢ᔣᔣḄWÑWẠ«ÕuiᐵḄ@Aᑨ×ØஹBஹCஹDḄ»Ú.Q⚪ὃTḄ«Õ⌕9=ᐳᔣuᐳ☢ᔣᔣḄWѾ⌕ὃTÛÜWẠ«ÕḄᳮMUVWẠ⚪.11.ூ[ᫀ௃ACDூM᪆௃M=4"04)=1P(48)=|x==VP(AB)=lx1=^,"P(B)=P(4B)+P(4B)=Í+Í=|,ᦑA⌱⚗ÆB,•••P(4)P(B)=|x|ᓝPG4B),ᦑB⌱⚗┯=C,P(A+B)=PQ4)+P(B)-PG4B)=0.9,ᦑC⌱⚗¸Æ3D,P(B|4)=ᯠ=à=0.5,ᦑ஺⌱⚗¸.ᦑ⌱=ACD.᪷³⚪ÉᑖsBPQ4),P9,H᪷³ᭆ᳛ḄKL⌲ᑨ×ᓽO.Q⚪ὃTᩩᭆ᳛ὃTÛÜḄâãäØ&WẠ⚪.12.ூ[ᫀ௃BCDூM᪆௃M=V4Â2P1B1C,᧕'()BCCiBiæ)ᑣBiCJ.BGç4PCBG=P,AP,BCiu☢4PB,O«81c1☢4PB,ᑣ81cJL☢ABCiDiéᯠêë,ᦑA┯ÆVB,ᐸ$P9ᙠìBCií,8GîᑖBCìḄᚖîᑖðAB௃/

9/CD,O«BQíᡠᨵ9ᑮCOḄôõiᦑB¸ÆVC,öî÷ø☢4BC0-ùúḄ4Ḅ(ûa,᧕AC=ga,ᐸ$|ýj=|ÿ+
+|||=^\AB\2+\BC\2+\CC^\2+2AB-JC+2AB-CC+2BC-CCl=na1=AiB\HAB,ᑣ4P4Biᡠᡂᓽ/PAB,PᑮCiᜐ!"!COSNPABᨬ$ᓽ4P4%ᡠᡂḄ'()ᨬ$cos=('ᔩ:12ஹ4ᦑC678᧕PᑮGᜐ!"!4P;☢48C஺ᡠᡂᨬᜧᓽ6()ᨬᜧ@A.
=C+Ṙ+CCJ-(AD-AB)=AB-AD-AB2+BC-AD-BC-AB+CC^AD-'CCi-AB=-a2—a2+a2--a2+-a2--a2=0,2222ᑣACiJLBD,=AC1BD,ACClAC=A,AC,ACa^A^ACC1,ᑣBD1☢AiACGtrKGEJ.4C,ᚖNE,OijBD_LGE,=BD,ACu☢ABC஺STUᑣC௃E1☢4BCD,ᑣNGACᓽ4G;☢4BCDᡠᡂᑣᨵcos“i4C=(ஹZ[*.=]ᦑ6()ᨬᜧᓃ஺67.2xV6axV3a33ᦑ⌱dBCD.ᵫAPIBiCgᔠ/C1BC1i%&C_USUBCi4,%mnᓽᑨp4⌱⚗8ᵫBC1rsBiCḄᚖt;ᑖrS4i&஻CD,ᓽᑨpB⌱⚗8ᵫw☢trᜳḄyzᓽᑨpC⌱⚗dᵫr☢Ḅyzᓽᑨp஺⌱⚗.{⚪ὃ~Ḅᔠᵨ᫏⚪.13.ூᫀ௃(-13ூ᪆௃dC(a,b,c),ᵫC4(—1,1,0),8(—1,0,1)ᐳr,ᦑᨵ஻
^AB=AAC.-.•AC=(a+l,b-l,c)>AB=(0,-l,l))(0,—1,1)=A(Q+l,b—1,c),•Q+1=0,A(b—1)=-1,Ac=1,D,a=—1.A=2,b=Ic=p10⚓ᐳ17⚓

10••C(-1,᧊)ᦑᫀd(—1,).ᵫ⚪¢%CḄᙶ᪗ᑭᵨ¦§ᔣ©ᐳrḄឋ«¦§ᔣ©Ḅ¬z¦§ᔣ©ᙶ᪗®¯Ḅ°zᑣ±°yg².{⚪³⌕ὃ~¦§ᔣ©ᐳrḄឋ«¦§ᔣ©Ḅ¬z¦§ᔣ©ᙶ᪗®¯Ḅ°zᑣµẠ⚪.14.ூᫀWூ᪆௃dᵫ⚪¢¸¹=ºᦑn=2+3=5,ᦑ¼¯(x—⊤¾ᐸÀ⚗d5]=*Â*(ÃÄ)k=(_,5Æ=2,/k=2,ᦑ/ḄÇᦪ(ɾÊ=|.ᦑᫀd|.ᐜ᪷Í⚗¯ÇᦪḄឋ«y%ᯠÉÏᑭᵨÀ⚗y%gÐ.{⚪ὃ~⚗¯ÑᳮÓÔ⚗¯ÇᦪḄឋ«ஹÀ⚗Ḅὃ~µẠ⚪.15.ூᫀ௃d35ᐔூ᪆௃d(1)Ö×ᱥrC1:=2py(p>0)ÚÛr%2—y2=iᙠÃÞ▲àᨵáÃâᐳã%2=2py(p>0)äᐭ%2-y2=1ᑁᨵy2-2py+1=0,4=4p2-4=0,p=1.4(ç,1)ÚÛrḄèérêëy=±x,¸ᑣaABCḄ☢íS=iX(1+1)X(i+1)=^.(2"'(R)=(ᐔ/?3)=4ᐔR2,3S'(R)=3x(4JIR2Y=3x8nR=24JIR,ᐸV'(R)=3S'(R),R=6,ᦑó☢ᙊ[õḄᨬ$)VR2Ãi=ö,ᑣó☢ᙊ☢íḄᨬ$)357r.ᦑᫀd7;357r.4(1)ὶ×ᱥrÚÛrḄêëᨵy2-2py+1=0,᪷Í⚪¢A=4p?Ã4=0,û

11P=I,ϱ°a,B,cḄᙶ᪗y☢íᓽ8(2)᪷ÍV'(R)=3S'(R)R=6,ü᪷ÍᚖtᐵÇy%;☢aóᳫ஺ᡠó☢ᙊḄ☢íḄᨬ$)ᓽ{⚪³⌕ὃ~×ᱥrḄឋ«íᨬ)Ḅyÿ
⚪.16.ூᫀ௃ூ᪆௃:,ᑣ"#ᨬ%&ᑜ(Ḅᭆ᳛,fl="ᖪ1ᡠᨵᑣ"#ᨬ%&ᑜ(Ḅᭆ᳛,4◤6=ᦑᫀ,8᪷:ᩩ<=ᔠ?ᐺᭆAᭆ᳛BCDEFGᓽIJKᫀ.L⚪ὃN?ᐺᭆAᭆ᳛BCOẠ⚪.17.ூᫀ௃⚪188(1)TUᦪᑡ#ḄBU,XᑣS5=5al+\d=5x1+10d=25,ᡠad=2.ᡠaa=14-(n—l)x2=2n—1,B|Ja=2n—1inn(2)ᵫ(1)aa~(2n-l)(2n+l)-2^2n-l-2n+l*nn+1r--1ஹtrf-,1/I1.11,11ஹ1/T1ஹWᡠra஻=-X(-----------F•••4----------)=-X(1-----)=---.n2V13352n-l2n+ly2ஹ2n+ly2n+l⚪288(1)ᙠqABDᵫtuvᳮ4D2=AB2+DB2-2XABXDBXCOSB,J871O2=32+I2-2x3x1xcos^=7,ᡠa஺=᜛i(2)ᙠqABCᵫuvᳮ=#sineSITLDJS஺="ஹ558==8,ᙠᵫAB0,ᦑcosC=V1—sin2C=—,4ᡠasin(C--)=sinC-cos--cosC-sin-=ூ᪆௃⚪1(1)TUᦪᑡa4ḄBU,d,᪷:Ti⚗ḄBCᓽIi(2)᪷:(1)IJ=2n-l,⚗ᓽIi⚪28(1)ᵫtuvᳮK4)Ḅi(2)ᵫuvᳮJ6UsinC,KcosC,ᑭᵨuU£BC¤FG.12⚓ᐳ17⚓

12L⚪§⌕ὃN©UᦪᑡḄª⚗BCஹ⚗ḄFGஹuvᳮḄ«ᵨa¬£UḄuBC᫏⚪.18.ூᫀ௃8(1)¯“±²”Ḅ´ᦪᓰ¶·N´ᦪḄ¸ᑣ¯“±²”Ḅ´ᦪ,100x[=50,¯“±²”ᵱº´ᦪ»᝕º´ᦪḄ?ᑣᵱº´ᦪ,15´᝕º´ᦪ,35´ᙠ¯“¾±²”Ḅ´᝕º´ᦪᓰ¿¯“¾±²”Ḅ´᝕ºᓰ50xg=10´,ᦑ2x2ᑡὶ⊤᝞Ã8±²¾±²ᔠFᵱº154055᝕º351045ᔠF50503)Ä)◤Å+d)=ᯠÄÇ:ÈX25.25>10.828,.•Xᭆ᳛Éa=0.001ḄÊËឋÍÎᑨÐѺÒÓÔÕÖ×Ḅ±²Ø#ឋÙᨵᐵ.(2)Û100ÜѺḄÝÞᡂàá᝱ᑖäN(70,25),ᑣ஻=70,60)=1-P(X<60)=1-"6=æ=1-=0.97725>0.96,ᦑ"᪥èéÕÖ×êë᪗ᦔîï℉.ூ᪆௃(1)᪷:ñᩩ<=ᔠ⚣᳛#⚣ᦪḄᐵóa¬ÊËឋÍÎBCᓽI.(2)᪷:ñᩩ<=ᔠ᝱ᑖäḄÒôឋᓽI.L⚪§⌕ὃNÊËឋÍÎBCὃNõᓄ÷᫏⚪.19.ூᫀ௃(1)øù8ú,APABqPADᙳ,ü£ýᡠa28=4஺.þBC=CD,ᡠaAC,BOḄᚖ.ᡠ஺BDḄ.=PB=PD,ᡠP஺1BD.4CDP0=0,AC,POu☢PAC,ᡠ☢PAC.(2)484஺=90஺஺BOḄᡠ4஺=஺8=0஺.P4=PB=PD,ᡠAPA஺APBO,APD஺ᐰ.ᡠ4P04=APOB=4POD=90°,ᡠP஺1AC.

13ᔠ(1)஺ᙶ᪗OB,OC,0Pᑖ!y!z!"#$%&ᙶ᪗'0-xyz,ᑣB4,0,0)D(*+,0,0),Cᗔ,0)P(0,0,-)ᡠ/=(0,20)3=J,045=(0,067☢PCDḄ*89ᔣ;<=(xyz),__»(V6V2_0ᑣE.££=(),-J2X2y,=x=i,ᑣy=-bz=-1,A"DP=0>?+^Z=0ᡠᐗ=(1,*6*1).7C☢P-CD-BḄᜧE0,Fij|cos0|=\cos(n-OP)\=|^J^|=IᯅI=᜼C☢P-CD-B┦C☢ᡠC☢P-CD-BḄJKLᓛ.5ூ᪆௃(1)ᑭᵨ☢ᚖ&ḄᑨUUᳮᓽXYZ(2)஺ᙶ᪗OB,OC,OPᑖx!y!z!"#$%&ᙶ᪗'஺*xyz,[☢PCDḄ*89ᔣ;ᑭᵨ$%ᔣ;[C☢ᓽX.\⚪^⌕ὃa☢ᚖ&ḄYZC☢bᐸde$%ᔣ;bᐸfᵨ$%ghijḄklmno⚪.20.ூpᫀ௃(1)7rᙊCḄtᯖvc,(c>0),rᙊCw+x=l(a>b>0)Ḅyᯖ?(*2,0),{⚔4(3,0),ᡠQ=3,c=2,Z?2=a2—c2=5,}14⚓ᐳ17⚓

14ᦑCḄ—+—=195(2)YZ7,)(&>040>0),+=1,95MABḄᡠM(,)ᡠ&஺MḄ=ᓰ=x=4,'=*ᡠN(W-%),¢£¤=(|,ᾓ/¨=3,-3᝕)ᡠ«.¬=|(ᦇ0-3)+^^=|(q—3)+|^=|(ᑍߟ3)+|(3_3=0,NZ[^XQ+S)Z£[^XQ+S)NLᡠ«J.¤ᡠAB1NF.ூ᪆௃(1)ᵫ⚪µXa=3,c=2,ᑣb2=a2-c2=5,ᓽX[rᙊ(2)7Bᙶ᪗[Mᙶ᪗[&0MḄ==-£[Nᙶ᪗᪷¼ᔣ;Ḅᙶ᪗½eX¤.¾=0ᓽXYZA8J.NF.\⚪ὃarᙊḄ᪗Áᙶ᪗ÂÃᔣ;Ḅᙶ᪗½eὃaÄᓄÆgdeijno᫏⚪.21.ூpᫀ௃(1)YZf(x)=l-x-i-/nx=-/nx,000,/(X)ᓫÏ⌴Ñ0%>1£/'(%)<0,/(%)ᓫÏ⌴Òᡠf(x)max=/(I)=1-1X/nl-1=0,ᡠ/Q)40,Y.(2)e*>ax+1,ᡠe*—ax—1>0,=஺()=ex—ax—1,g'(x)=ex-a,0Q40£g'(%)>0,g(x)ᓫÏ⌴Ñ0Q>0£=g'(%)=0,=Ina,ᡠᙠ(0,Úa)Ûg'(x)v0,g(%)ᓫÏ⌴Ò,ᙠ(Úa,+8)Û,g'(x)>0,g(x)ᓫÏ⌴Ñᡠg(x)min=0(ma)=elna-a"Q-1=a—alna—1,

15ᵫ(1)g(.x)=a-alna-1<0,ᔠ⚪µminÞÛᡠßaḄàLâ(-8,0].ூ᪆௃(1)[ã((x)=Tnx,ᑖ᪆/(x)ḄᓫÏឋᓽXåpᫀ.(2)ᵫe^Nax+l,I3ijex-ax-1>0,=g(x)=e*-ax-1,æ◤g(x)mm2஺ᓽXåpᫀ.\⚪ὃaãᦪḄÞᔠfᵨ⚪éµᑖêëìÆgḄfᵨ◤⌕ᳮíÆîno᫏⚪.22.ூpᫀ௃(1)ᵫ⚪µXfᡠᨵXiàL0,1,2,P(f=0)=(1-0.9)2=0.01,P&=1)=6x0.9x0.1=0.18,%=2)=0.92=0.81,ᦑfḄᭆ᳛ᑖò⊤012P0.010.180.81ᦑEয=0x0.01+1x0.18+2x0.81=1.8.(2)7q=1-p,õö*÷Ḅkæøùúûᑣ஻=%ᔲᑣᡠP(஻=þ=x“P(r]=^4-1)=1-qk,E(஻)=/q"+*+1)(1-q,="+1-ᓃ2WkW8nḄᦪES)<1,G0,/(I)<0,/(8)>0,/(9)<0,——FInq>0,Inq40,——FInq>0,——FInq<0,ln8j,ln9ii••,=<1nq»ᓽHn8-6

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