北京市2022-2023学年高三上学期开学考试数学试卷(含答案)

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222021-2022ὃᔁ
ᦪ⚪ᦪᜓ20228ᨴᔁᑖIᔁ⌱⚪nᔁ⌱⚪ᑖᐳ150ᑖ,ὃᵨ120ᑖ!஺ὃ#$%&ᔁ'(⚪)*+,஺-ᔜ/ὃ0ὃ1ᑭ3ஹᓫ⌱⚪67⚪4ᑖᐳ40ᑖ1.89:ᔠA={x|-14x42},8={x|x>0},ᑣAu5=()A.{x|0-l}D.{?>0}2.89@ᦪzBCLDEḄGH1A.-1B.1C.-iD.i3.IᑡKᦪLMN'ONᙳQRḄHA.y=lnxB.y=exC.y=x3D.^=-X4.l-x
4ḄRS/ḄUᦪQA.12B.-12C.6D.-65.V9஺=1X3,%=Qjc=l°g-ᑣ”,஺Ḅᜧ7ᐵUQ
hA.a>b>cB.b>a>c

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2²ஹ³´⚪(67⚪5ᑖᐳ25ᑖ)11.Kᦪ/(1)=µ|ḄLMNQ__________.Vl-x12.¹Kᦪ/(x)=P2R+Iᙠxy¼஻+2]|Ḅᨬ7OQ4,ᑣ¾ᦪ஻Ḅ¿O:ᔠQ13.89Àp(2,3)ᙠaḄÃÄ|ᑣsina=Åcos(4+a)=.14.¹Kᦪ+(a>0f"1).জ¹a=:ᑣf(/(-l))=[log“x,x>22Åঝ¹f(x)ᨵᨬ7Oᑣ¾ᦪ஺Ḅ¿OÍH.15.89ᦪᑡ%ᔜ⚗ᙳQᦪᐸÐ஻⚗S“ÒÓqjS"=9(஻=l,2,…).×ØIᑡÙª#ÚÛজ4Ḅ2⚗7C3ÅঝÜ,QBᦪᑡÅঞ4Q⌴nᦪᑡÅটÜ,ßᙠ7CàḄ⚗.ᐸᡠᨵá#ÚḄâãH.äஹå(⚪(ᐳ85ᑖ)16.(12ᑖ)89/(x)=sinx-6COSX.(1)ç/(X)ḄèÀÅ(2)çf(x)Ḅᓫi⌴kxy.17.(13ᑖ)89ḄᑁéA,8,CᡠêḄêÄᑖëQa,dc,ᕜíQ&+1,fsinA+sin8=V2sinC•পçcḄO;

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sina=cos7v+a=-cosa=——/=----------VF+3713'7VF7713ᦑ%ᫀde-3e.131314.-2l2-ஹ2ᡠf(T)=-(T)+3=4,ᡠ""—1))=/(4)=1%4=-2m2{xW2|7/(x)=-x+3,{x=2|7/(x)=—x+3xᨬY=1,{0<“<1|7}x>2|7/(x)=logx1|7}x>2|7fix'=log„x>log„2,⌕ᦪᨵᨬY=7ᑣlog“2Zl,1<஺42.ᦑ%ᫀ-2mi

1215.জঞটூ᪆௃ூᑖ᪆௃99_.஺஻=-------!./ஹḄ=7ᑨজmᑭᵨᑨঝটmᑭᵨᦪᑡᓫឋḄ
ᑨঞ.ூ௃ᵫ⚪7VneN\0,99{=1|7஻=9,¡=3m{஻22|7ᵫS“=S,“=—,¤¥¦an-l994=-----------!4%999ᡠ7--P§-¡,ᑣ7-஺2=3,᦮ᳮq+31-9=0,>.0,.=3,3¬3,জ/mᎷ®ᦪᑡ¯°,±u²ᦪᑡ7®ᐸ`²4,ᑣA="◍3,ᓽ·=°-7ᡠ7Sm=S23,஺m(1+4)2=¸(1+4+/),g=o,tᔠ»⚪7ᦑᦪᑡ¯4±t¼u²ᦪᑡ7ঝ┯;{஻22|7q=2-2=¿À^0,ீa,,“ᡠ7ᦪᑡ¯%±⌴Åᦪᑡ,a„«„-1ঞ/mᎷ®/ÈḄ஻eN’,%2Ê7ᑣSmooRlOOOOOx+=1000799I_ᡠ74()0000=^---477c¬Ð7ÑᎷ®ÒÓ7Ꮇ®tᡂÕ7ট/.,^10(XXX)1UU

13ᦑ%ᫀজঞট.ூ4I௃ᐵ×44IJ⚪ᙠঝটḄÙÚ|7ᑭᵨÙ☢ᳮÜÝᩖ|7ßᵨᩭáâ_.TT7T57r16.(1)x=kji4—,kRZஹ(2)[2,k/r-----------------],kGZ.366ூ᪆௃ூᑖ᪆௃7T7T(1)ãäåæä[`ᓄè7f(x)=2sin(x-77B=kwZ,xm(2)B2kᐔëᑖìᡂ¤[¦ëᑖ஺TTBf(x)=0,íljsin(x-§)=0,x-$=k%,keZ,3x=k7r+—,keZ,3rr•ᦪf(x)Ḅï4¼x=+keZ.~ᜐZᑖ7é┯7ᑡᦪ=ïëᑖ7ñᓄòìóôiᑖ7i/ᑖ஺(2)^-Ikn

14ᑣ+keZ,/¤ᑖ[2÷øù72%1+2],%€26666••./(x)Ḅᓫýþÿ.17.(1)1(2)C=60ூ᪆௃ூᑖ᪆௃(1)ᑭᵨᳮᓄᓽ(2)ᑭᵨ☢!"#$ᑭᵨ%ᳮᓽ(1)&'()ᕜ+'0+1ᡠ.a+b+c=/+l4ᑖ&'sinA+sinB=J5sinC,ᡠ.ᵫᳮ>n+Z?=&c4ᑖᡠ.Bc+c=^+l>c=l.4ᑖ(2)ᵫAABCḄ☢:MsinC=sinC>G4ᑖ26ᵫ(1)a+b=6,ᵫ%ᳮ>a2+H-c2(a+b)2-lab-c1-31K•M------஺-----=—?—=3Pᑖ2ab2ab423RCe(0°,180°)Kᑖᡠ.C=60Vᑖ23.(1)WXY᪆

15e3>/55ফ[ூᑖ᪆௃(1)᪷]()Ḅ^_`ᳮabcd)Ḅឋfgᔠ`☢bcḄᑨᳮᓽ!j(2)⌱lজ᪷]nopḄqa`☢ᚖnḄឋfᳮsᑨᳮtuvwnᙶ᪗z>"{ᐵ}Ḅᙶ᪗ᑖ~!"b☢ABGḄᔣ$ᑭᵨᔣḄᜳ[.!"`☢Ḅ.⌱lঝ᪷]nopḄqa`☢ᚖnḄឋfᳮsᑨᳮtuvwnᙶ᪗z>"{ᐵ}Ḅᙶ᪗ᑖ~!"b☢A8GḄᔣ$ᑭᵨᔣḄᜳ[.!"`☢Ḅ.⌱lঞ᪷]nopḄqan`ᑮb☢ḄḄq$ᑭᵨ`☢ᚖnḄឋfᳮsᑨᳮtuvwnᙶ᪗z>"{ᐵ}Ḅᙶ᪗ᑖ~!"b☢ABGḄᔣ$ᑭᵨᔣḄᜳ[.!"`☢Ḅ.(1)AGḄ^}'•••E,ᑖ~BCAGḄ^}gaὡ.,஺A3Ḅ^}=,n(opABC-AAG:.EF^AD.d)ADEF'bcd).J.AF//DERb☢ACGAAFub☢ACGAᡠ.DE஻b☢4CGA.fiᑖ(2)⌱lᩩজ«C±ACIj

16•.,n(opABC-AAG..CG1.b☢ABC,3(7¡b☢48஺஺62஺•.♦BC1AC,,:.AC,ACC=G,AG,CGub☢ACC,\,}ᡠ.8C_Lb☢4CC௃A.[HCub☢ACC]ABCVAC;.BஹCJIBC!ACJIAC,:.B.C,±A.C,..C1'¢}ᑖ~.GAG8£GCᡠᙠᔣ'x¥y¥z¥tu᝞§ᡠ¨ḄvwnᑣA(2,0,3),3(0,2,3),C,(0,0,0),0(1,1,3),£(0,1,0),ᡠ.ª=(2,0,3),C=(0,2,3),DE=(-1,0,-3),«3=(x,y,z)'b☢ABGḄK¬ᔣᑣgG4=0[2x+3z=0Pᓽ4,w-C,fi=0[2y+3z=0®x=3,¯I]y=3,z=—2,n=(3,3,-2),«n`DE°b☢ABGᡠᡂḄ'²ᑣ

17sinXᑭᶢP´µ὚·◤ᡠ.n`OE°b☢ABGᡠᡂḄḄ'◤.⌱lᩩঝDE!B©,AAḄ^}'஺K஺•n(opABC-AAG஺0ᑖ~AB,44Ḅ^},••.OR_Lb☢A4C4Gub☢AB|G.■.BiGJ.OR,•/DEJ_4G,DEnDD\=D,DE,DD,ub☢DEDஹ,ᡠ.8G_Lb☢OER.[ED,ub☢DEDi.B,C,±ED,.ᑖ~8,GA∞Ḅ^}.-.£D/M,CII>.C1'¢}ᑖ~.GAGAGCᡠᙠᔣ'x¥y¥z¥tu᝞§ᡠ¨Ḅvwnᙶ᪗zG-xyz,ᑣA(2,0,3),B(0,2,3),G(0,0,0),0(1,1,3),£(0,1,0),ᡠ.C=(2,0,3),C,B=(0,2,3),Å=(K1,0,—3),

18«஻=(Æy,z)'b☢A8GḄK¬ᔣᑣÇGA=O2x+3z=0Ȫ=02y+3z=0®x=3,ᑣy=3,z=—2,஻=(3,3,—2),«n`QE°b☢ABC1ᡠᡂḄ'᜜ᑣ1.ÊP|(T)X3+0X3+(_3)X(_2)|=3-sin0=|cos^n,DE^|=WI//32+32+(-2)2X^(-1)+02+(-3)2110Aᡠ.n`DE°b☢ABGᡠᡂḄḄ'Ë”.⌱lᩩঞDEᑮb☢ACCIAḄ'1.Í}஺Î஺G_LAC,ᚖÏ'G,•••n(opABC-A8©,CG_Lb☢ABC,06<=b☢48஺(^6_106,■.■DGLAC,.•.4஺0஺6=0஺96<=b☢?^஺0ᡠ.Z5Gb☢4CGA.ACJ_b☢ACGA.ᡠ.DGACᵫ(I)ÐZ)E//b☢ACGA&'DEᑮb☢ACCHḄ'1,ᡠ.஺G=1.R3c=2,ᡠ.஺G=ggcR&'஺A8Ḅ^},ᡠ.GACḄ^}.•.QG஻BC.r.8CACR.•.81G//BCAG//AC,B,C,±ACI..q'¢}ᑖ~.GAGAccᡠᙠᔣ'X¥y¥z¥tu᝞§ᡠ¨Ḅvwn

19ᙶ᪗zG-Ñz,ᑣ71(2,0,3),8(0,2,3),Cj(0,0,0),Z)(l,l,3),£(0,1,0),ᡠ.ª=(2,0,3),QB=(0,2,3),DE=(-1,0,-3),«E=(x,y,z)'b☢A8GḄK¬ᔣᑣ=ᓽ|2x+3z=0È.ᓺ=0'12y+3z=0®x=3,ᑣy=3,z=-2,5=(3,3,-2),«n`OE°b☢ABCjᡠᡂḄ'²ᑣDE\|(-1)X3+0X3+(-3)X(-2)|35/55sin^=cos(n,Ö×K^32+32+(-2)2X7(-1)2+02+(-3)2-110ᡠ.n`஺E°b☢ABCjᡠᡂḄḄ'◤.ᓝᑖtz⌕Úᑖ19.(1)6?=3,b=5:Üব஺P8ூ᪆௃

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20Lᳮᡂ)*300ᑖḄ./MN193"#ᡂ)O*300ᑖḄᭆ᳛*,ᡠS
ᐰUᳮᡂ)*300ᑖḄ./MVWN29$%ᨵ&X9"#Ḅᡂ)*300ᑖḄᭆ᳛*Y=||[ᑖA┯\"#ᡂ)*300Ḅᭆ᳛G]ᑖᑡ\ᭆ᳛F^G]ᑖ஺3ᵫ⚪a=8-Z>0

21£>(X)=(100-225+xᔁ+(200-225+59yx(300—225+59|x^-=-2592—2506+6875}*04848,ᡠS~6=8Q(X)ᨬ.ᑖூ௃⚪ḄᐵᳮghᑖᦪIlḄ9ᦪ⊤*9Ḅ⚗Fᯠᙳxy
ᓄ*ᐵbḄᦪḄᨬ⚪.20.(1)(1,e)(2)᪆(3)(0,e)ூ᪆௃ூᑖ᪆௃(1)fY(x0,e"),᪷ᑗḄឋᑡFᓽ;(2)ᑖ᪆ᦪḄᓫ¡ឋᨬᓽ;(3)x¢&£ᦪ¤Bᔠᑨ§᪷eஹ>alnx+lna,ᑖ᪆ᦪ©=e•'Ḅ«¬ᙠᦪ%="Inx+alnaḄ«¬®x¯ᦪ*=a

22x+a

23a«¬ា±ᨵ&•X²ᐳḄ³´µ¶ᓽ·x¢£¸¹ºFᣚ*6'*'+X-114>6\+12£ឤᡂ½᪀⌼ᦪ1g(x)=e*+x,xe(O,y)᪷ᓫ¡ឋᑮlna

24ᵫᑗឋ,:=:!%=1.Hᑖe°=kx஺ᡠSPḄᙶ᪗(l,e).•ᑖ(2)~a=e/(x)=e'-elnr,ᐸMx>0,ᑣ/'(x)=e—£&ᑖÐg(x)=e*-?,ᐸM*>0,JpJg(x)=e+5>0,&ᑖᦑᦪY(x)ᙠ(0,+8)®ᓫ¡⌴×ØÙ1)=0,~xÚᓄxJ'(x)J(x)Úᓄµ¶᝞Ü⊤£HᑖX(0Ý)1(1,+co)àপ—0+/(X)ᓫ¡⌴á᩽ᓫ¡⌴×ᵫ®⊤K,f(x)=஻1)=6.ᡠS/(%)2.&ᑖ11(3)åᦪ”Ḅ(0e).ᳮᵫ᝞Ü£x¢&£(ᦪ¤Bᔠ)ᙠ(0,O)®/(x)=e*-alnx>olnaឤᡂ½ᓽe*>alnx+ln«.}ᦪX=e*Ḅ«¬ᙠᦪ%=alnr+HnaḄ«¬®x.

25ὃ⇋ᦪë=e*«¬ᙠᦪ©=H>M+Hna«¬ា±ᨵ&X²ᐳḄ³´µ¤᝞«ᡠìíîᙠïᜐᨵ&ᩩ²ᑗÄòfïḄóᙶ᪗*M.eA,><=-,ᵫᑗឋKXa.1ᡠS&=(71nx+ᓽ&=lnx+Ina,00ᵫe'°=&xe^=a,ᡠS&=1ô)+In(xe'f,)ᓽ21nx°+x----=0oo0“0“0%)171õ஻(x)=21nx+x--,xe(0,+a)),ᑣ“(x)=-+l+~y>0,ᡠS஻(x)ᙠ(0,+ᔣ®×ᦪ.>}*஻(1)=0,ᡠSx÷21ô+/-'=஺Ḅ᳝=1.)xo}ì~Hᦪា±ᨵ&Xïïᙶ᪗l,e
,ìᜐ²ᑗÄx÷V=ᡠS~ᦪX=e'Ḅ«¬ᙠᦪy=a

26x+a

27aḄ«¬®xåᦪ஺Ḅ0,e
.2x¢£ù᪀Ú¤úᯠ஺>
,ᙠ0,y
®஻û=᮱&஽111^>&1þឤᡂ½ᓽYô-lnx>lnaឤᡂ½ᓽei—lna>lnxឤᡂ½,

28ᡠSel"+x-ln“>x+Inx=*+Inxឤᡂᑖ᪀⌼ᦪg(x)=e*+x,xe(0,+8),᧕g(x)ᙠ(0,+s)!"ᦪᡠ$x-lna>lnxឤᡂHPIna<(x-lnx),min+==--(x>0),,xe(O,l).,/0<0,ᡠ$஻(x)ᙠ(0,1)ᓫ4⌴6,xe(l,+oo)./?,(x)>0,ᡠ$/z(x)ᙠ(1,+8)ᓫ4⌴"ᡠ$/(;<=MD=1?ᑖᡠ$Ina<1,@A()

29(3)/45.᪷_Ḅᦪ᧕Aᯠg=6.ᵫ4+/+…+4<20|¢☢¤ᯠᨵ¦ᦪ§¦ᦪ¨©!-1ᯠªᑖ«egᓽ|.(1)%=1,q=2,4+%=3,4=4,a+“3=5,ᡠ$஺!5-|⊤ᦪᑡ᧕g®2ᙠi!j¯A4++…+°T=6,ᡠ$஺g!6-|⊤ᦪᑡ.ফ³ª43,´µ஺¶ᑣ¸¹a+%,%+c,a+b+c,a,b,c,6ᦪ¼½ᨵ8¾¿¶,À=4.ᦪᑡQ¶l,4,1,2,ÂÃq=l,a=2,a+a=3,a=4,a+a=5,4342t24+%+4=6,a+a+a=7,a,+a+a,+a=8,:.k=4.23424nm=1{a,b,c,d,e,f}={-1,2,3,4,5,6),ὃ⇋᣸é,᣸éÓg©ᨵàjᔲᑣgÃ20,ë.-1=-1+2(ÛJÅìi)J1b2àí,

30³-1gᙠ?îᑣ2,-1,2,____ð“oi,³x=6,ᑣ5=6+ñTòñᨵ2Åpóàjìi¾¿ò.,.xw6,jᳮ"5,4,3,ᦑ-1ᙠJîg÷µ"=12,AøCø"oi³A=3,ᑣ5=2+3ñᨵ2Åpóàj¾¿òA=4jᳮgA=5,ᑣ6=-1+2+5ñᨵ2Åpóàj¾¿òÍl.ூLM௃ᐵ
ᐜᳮ⚪ᔲ"L⊤ᦪᑡ᪶ᔲᙠḄ⚗⚗!"⊤#$1ᑮ'()Ḅ*+,..⚪/01443456!,"+ᦪᔲ7k<3,/81ᐜ56!,Ḅ"+ᦪᔲ7A45,<=>?=64ᦪᑡ(Ḅ⚗᝞DEᔠGᯠI-1,2,3,4,5,6LḄ+᣸N=>OPᦪQᔠ⚪.