北京市西城区2022-2023学年高考数学仿真测试模拟试卷（三模）有答案

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2022ὃᦪ⚪⚪ᑖᑖ⚗1.⚪ᑏḄஹஹὃ!"#2.&'ᫀ)*ᑏᙠ⚪ᓱ-Iᔁ⌱⌱1../0ᔠ/={XWN|XV6},B={xeR\x2-3X>0}ᑣ4n8=3A.9,4,5}B.M5,6}.{x|3;A.-1B.1C.7D.33.ᔣ@,BCDᙠ)EFGHIḄ:J᝞LᡠNT"R,ᑣ2_஻>;A.3B.3C.-3D.34.U!VᦪᑡXYḄ஻⚗Z6S”;A.4B.5C.6D.75../aᱥcd=2pxp>0
ḄecDᙊx-3>+F=16gᑗ<ᑣ2Ḅ_6

1ூ
ὃ௃A.2B.1C.2D.4=logs(logj4)6.U4ᑣ>cx;=3x+bcosx,XWR,ᑣ“b=0”“zᦪᐵ;6᜻zᦪ”ḄA.ᐙᑖ⌕ᩩB.⌕ᐙᑖᩩC.ᐙᑖ⌕ᩩD.ᐙᑖX⌕ᩩ8../ᙊ┵Ḅ⊤☢63w,Ḅ☢Lᙊ<ᑣᙊ┵Ḅ6>;nA.B.3C.3nD.69../ᙊCx2+y2+2x-Ay+\=Q,OᙠᙊCIᙠᨴ8,¡¢45=2ᨵ<¥N8ḄI§஻ᙠ¨c2x+;*Q0-<ᑣ«ᦪ%Ḅ^_®>;A.[-2^,2B]B.[-5,5]C.>-B;A.OÅ4Y>",ᑣᦪᑡÅÈYᔜ⚗ᙳᜧ`ᡈ!`MB,OÅ%Y>”,Å஽AM,ᑣX+4Y>2Mc,O“»M,ᑣ▭Y>лOÅ%Y>”,ᑣÅ2a“+lYt>2M+lÔHᔁ>×⌱⌱;ÙᔁÚᑖ

2ூ
ὃ௃11.ᙠ1ḄÛI<´ᦪ⚗6.12.'zᦪ஻x;=c°s2xḄLÝᔣÞßà᜛>9>0;ᓫ:âã<ᑮzᦪg>x;ḄLÝ.Ozᦪ8>᜜ḄLÝᐵ`槲ç<ᑣ஺Ḅ^_6./(x)=sinx-/M13.Uzᦪ2êḄë§6<஽<*3,O<஽<ìᡂ!îᦪᑡ<ᑣ14.ᙠÚïðñ⚞ó<ôõîö÷øḄù⚪.ᵫôõûᩭḄýãþÿᙠᦋḼᡃḄ.AlphaG஺ᑮᜧ"ὡ$%&Ḅ'(,*+,-./0ᐸᳮ34ẠḄ.ᙠ-.67ᨵ9:;<⌕Ḅ>ᦪ@0>ᦪSigmo>ᦪ°GxIᓽ+-.7ᨬᨵLḄ>ᦪM9ᐸN᪆P0Q""-l+e-.WᑡᐵZSigm஺>ᦪḄ⊤\]Ḅ+Q.জSigmo>ᦪ+ᓫ`⌴b>ᦪcdIঝSigm஺>ᦪḄfg+9hi@fji@012mঞiZopqᦪ“st0GI="ᨵwxᨵ9hNcটSigmo>ᦪḄzᦪ{|Qb'GxI=bGxIGl-bGxII.ᔁmᑖஹ⚪15.Ḅ+ᙶ᪗Ḅ9h⚔0“^2°I,ᩩ,/0ᙊ10Ḅᙊ*ᑗᑣ¡Ḅst+¡Ḅ᪗¢st+ᔁm£ஹN¤⚪bsinZ=஺cos16.ᙠAA8C7,প«8cফ®஺=5,.«a.

3ூ°ὃ௃³´£c=জ=7,@4hᩩ¹7o⌱9h⊡ᐙᙠ½☢¿⚪7À/¤.ÁQ᝞Ã⌱ÄÅhᩩ¹ᑖÆN¤ᢥhN¤Èᑖ.17.7ÉᓅᧅÌÍzÎÏÐ+7ÉÑẆᑴḄᐰᳫÌÍzÎÏÐ⚜È2020×ᓅᧅᐰᳫÏÐØÙÚᐰ☢Ûᡂ.᝞f+ᙠÝ᜜ßàḄá᛻Wᓅᧅãäåᓅᧅä³ᙽᑖÆḄ50hçḄèஹéᙶ᪗êëḄìᐸ7“■”⊤ïᓅᧅãä³ᙽḄêëḄì,"+”⊤ïᓅᧅä³ᙽḄêëḄì.GᓫçQðIGIIᓅᧅãäḄ50hç7òóôõ9h«öèᙶ᪗êëḄìᜧZ10ðḄᭆ᳛cGIIIf74B,C,஺£hç7òó⌱ùhúX0ᐸ7éᙶ᪗êëḄìüZ-4ḄçḄhᦪ«XḄᑖýᑡåᦪþÿ
IIIᓅᧅᓅᧅᙽᙶ᪗ḄḄᜧ.⌕18.᝞%&ᙠ(┵*TBQ.&P8_L2☢48°,BA=BP=BQ=2஺&஺&8&*fᑖ:;BQ,AP,8*Ḅ.<&*஺=E0@A

4ூJὃ௃M(2)2☢PAB=2☢PCDᡠᡂQḄRST
(3)b>0)P20.pqᙊ/b2'15|=—IFF,!6ஹ&⚔

5

6ூJMᫀ:1.Bூ௃ᵫà{xeN|x46},8=/á/¿3»0}ÓH/={0,1,2,3,4,5,6},8=ᮞã3ä0},ᦑ"C8={4,5,6},ᦑ⌱B2.Cூᑖ᪆௃✌ᐜéêëḄ´&ᯠ8íᦪÞÔḄᐙᑖï⌕ᩩñᓽóÓôᦪ஺ḄT.ூ௃(l+az)/=z+az2=i-a=-a+i=3+iᑭᵨíᦪÞÔḄᐙᑖï⌕ᩩñóÓ.-a=3,,“=-3ᦑ⌱HC.3.Dூᑖ᪆௃ᑭᵨᔣøùÓ“-10'-3),ᑭᵨᔣøḄᙶ᪗úêឋü&ᔣøÞÔᓽóÓÌ.ூ௃ýH᪷ÿᔣ
Ḅa-b=Ae+//e=2(l,O)+//(O,l)=(A,/7)}2.•4=1஻=-3,41———ᑣ஻3ᦑ⌱D.4.Bூᑖ᪆௃

7ூὃ௃᪷⚪!ᦪᑡḄ$!%&ᦪᑡḄ'஻⚗)S”᪷s”Ḅ⊤,-.ூ/௃0$!1",ᑣ4+஺6=2n%=ln9+4d=lnd=-2,S=9n+—xn(«-1)x(-2)=-n2+10??c2,ᡠ67஻=58S,9:ᦑ⌱B5.Cூ/௃P_;ᱥ=y2=2px(p>0)Ḅ>=?@1x=-5,1;ᱥ=y2=2px(p>0)Ḅ>=Aᙊ(x-3)2+y2=16DᑗP_ᡠ63+2=4,p=2Fᦑ⌱C.6.Cூᑖ᪆௃ᵫᢣᦪKᦪḄᓫMឋ)OᦪKᦪḄᓫMឋᡃQR6ᑨTa,b,cA0,1ḄᜧVᐵX%&ᑮZᫀ.ூ/௃a=(1)°5>b=(1)°5c=log,(log,4)40<(-)05<(-)0=1(-)05>(-)°=144,ᓽ0<”1,'3ᓃᓽb>l,c=log,(log4)

8ூὃ௃ᑣ/(0)=3x0+6cos0=0=6=0,ᡠ6b=0nKᦪ/ব1᜻KᦪḄᐙᑖq⌕ᩩt.ὃu1.ᐙᑖq⌕ᩩtḄᑨTF2.KᦪḄ᜻Ꮤឋ.8.Cூᑖ᪆௃ᙊ┵Ḅ|☢~)ᙊ┵Ḅ=Aᙊ┵Ḅ.ூ/௃0ᙊ┵Ḅ|☢~1r,ᙊ┵Ḅ=1/,ᵫTT/=2W,/=2r,S=nr3+Ttr-lr=3TT/-2=3n,ᡠ6ᡝ=1,=1ᡠ6ᙊ┵Ḅ1h=du=/=6,V=—nr1h=-7txl2x>/3=^-nᡠ6ᙊ┵Ḅ1333.ᦑ⌱C.9.Dூᑖ᪆௃᪷ᩩtuMḄᑭᵨuMḄA=2x+y+k=Qᨵ$ᐳuᓽRᑡZ.ூ/௃ᙊC/_y+2¡%+1=0Ḅᙊ£C(T2),~¥=2,M1=§Z8ḄuᑣCW/8,\CM\=)2=]8,ªnu”Ḅn6uC1ᙊ£11~Ḅᙊ&u«ᙠ=ᐭ+®¯0°,="ᜧᱏ¯0Au”Ḅᨵ$ᐳu²&³´µ¶4¸4¹,

9ூὃ௃ᡠ6ºᦪ»Ḅ9:½n¾µ¿¿À.ᦑ⌱D10.Dூᑖ᪆௃ÁÂᦪᑡ11,2,1,2,1,2...,7M=L58ᑨTAF7"=-38ᑨTCF7ᦪᑡÆ%Ç11,2,1,2,1,2...,ÈÇ12,1,2,1,2...,”=L68,ᑨTBFÊ᪷ËRᑨTDÌÍ.ூ/௃OªAᙠᦪᑡ1,2,1,2,1,2…M=1,5,ᦪᑡᔜ⚗ᙳᜧªᡈªM´ᡂÓ,ᦑA┯ÕFOªBᦪᑡÆ""Ç11,2,1,2,1,2...,ÈÇ12,1,2,1,2...,M=\,6,&Æ%+"Çᔜ⚗ᙳ13,ᑣÆ""+"Ç>2"´ᡂÓᦑB┯ÕFOªCᙠᦪᑡ1,2,1,2,1,2…஻=-3,8ÖÇ>“´ÌÍᦑC┯ÕFOªDØᑣÆ2%+1Ç2஺“+1A2aᔣ+1ÚÛᨵµÜ´Vª2/+1,ᦑÆ2%+1Ç>2"+1ÌÍ,ᦑ⌱D.11.60ூᑖ᪆௃᪷⚗ÝÞÁ⚗ßᑮàᦪ⚗ᓽR.ூ/௃Ci(-)4(-x2)2=15x4=60᪷⚗ÝÞÁ⚗᧕ãxᦑ60.7112.4

10ூὃ௃ூᑖ᪆௃᪷äå¹ḄRKᦪg(x)=c°s(2x+20)᪷⚪æRg(0)=°R-'+/'”9µ:ᓽR.ூ/௃çKᦪ“X)=c°s2xḄèéᔣ¸äåê9>0)ÜᓫëìRg(x)=cos(2x+2°),ᵫKᦪg(x)ḄèéᐵªíuOîRg(0)=cos(2e)=0ᑍk7T2஺=µᓝ°)(p—+——ᡠ62,42,ᐔ(p——7¸=084.7Tᦑ713.2ூᑖ᪆௃/'(x)=sinx-/wxGçKᦪ‘I2”Ḅñuòᓄ1y=sinXJ=MḄôuõᙶ᪗,Kᦪèø,ᑡ?@ñu%&R"?Ḅ:.ூ/௃úsinxµm=0,sinx=msiruµVe0üᑣKᦪûḄñuᓽ1y=sinx,y=ýḄôuõᙶ᪗᝞è:

11ூὃ௃X+X=7Tl2x+x=323xx=xfᵫ131X.=—7T'43=?ᐔ-49X,=—7T34.7ty/2in=sin—=—42V2ᦑᫀ".#14.জঝটூᑖ᪆௃ᵫy=l+e'Ḅᓫ/ឋ஺(3)Ḅᓫ/ឋᑨ6জ7ᑭᵨ°(x)+b(-x)=l,ᑨ6ঝ7ᵫ0(x)Ḅᓫ/ឋᑨ6ঞ7>?஺(x)(l-b(x))@஺'(A)ᑨ6টூB௃1-Xcr(x)=ߟ--F"y=l+e"ᓫ/⌴HIᦪKᡠM1+b"ᓫ/⌴NIᦪKᦑজOPQcr(x)+cr(-x)=——--1—=----1=1F"-l+e-x1+eஹ1+e*1+eஹKᡠMSigm஺IᦪḄWXYZ[\fol]_K[\"I2AᦑঝOP7F"1+b"ᓫ/⌴NIᦪ,cy=l+eஹdl,o(x)e(0,l),ef”e(O,l)iKjk0'GA"ᨵcoᨵYZKᦑঞ┯q7rM-b(x))=Y.J=J1•+e11+v)1+e1+e(1,+e))b'(x)=7~^~o(1+b),ᡠMb'(x)=b(x)(lF(X)),ᦑটOP.ᦑজঝট.

12ூὃ௃ூᑖ᪆௃ᐜᑨ6{|}ḄᯖᙠXKᓽ>?஺=⊈K?{|}ḄjkKᓽᑏ?{|}}ḄjkKᵫᑮ}Ḅᓽ>?bḄᓽ.ூB௃ᨵ{|}YZ⚔"“(&K°),ᯖᙠ*Kᑣ஺=⊈K22-ᓃ=1rᦑ{|}"2b2,ᑣ}±.2y=°,|V26+0|ᦈK஻=2,ᡠM}x±>=°¡=1ᑣ{|}Ḅjk"22.ᦑx¢N=0722.B=-16.(1)3.573+5(2)জa=8Qঝ"-2ூᑖ᪆௃sin8sin/=sin4cosB--\(1)᪷©⚪«ᩩKᵫO®¯ᳮI6±ᓄ³ᓽ>?8.(2)´⌱জKᵫ¶®¯ᳮQa-5«-24=0,ᓽ“Ḅ.´⌱ঝKᑭᵨ¸¹@ḄO®Iᦪ>sin"ḄKᵫO®¯ᳮᓽaḄ.(1)6sinA=acosB--sin5sin=siny4cosB--F"I6±ᵫO®¯ᳮ:V6±F"0

13ூὃ௃--cosS+—sinB=Or-B=—22,ᓽtann8=V3,0<8(KᡠM3.ফ´⌱জKÃUᙠA/8CÅKᵫ¶®¯ᳮQb2=a2+c2-2accosB,Qa-54-24=0,Q஺=8,ᡈa=-3(Ç)K஺=8.C=-sin=sin(5+C)=sin—cos—+cos—sin—=^+y^-´⌱ঝK4,ᑣ34344,a5a_cV6+V2A/2_5G+5ᵫO®¯ᳮQsin/f-sinC,Q42,.“Y217.(I)0.067(II)ᑖÊᑡÌ᪆K17(III)ᓅᧅ3ÏᙽÑᙶ᪗qÔḄjÔᜧÖᓅᧅ×Ï.ூᑖ᪆௃(I)ØÙWÚÛKᙠᓅᧅ3ÏḄ50ZÅKÜᙶ᪗qÔḄᜧÖ10Ýᨵ3ZKᵫÞᐺᭆ᳛Ḅâãᡠ>7(II)ØÙWKA,B,C,஺äZåÅÑᙶ᪗qÔæÖ-4Ḅᨵ¸ZQC,D,ᑣXḄᡠᨵçè"0,1,2,ᑖé>êëḄᭆ᳛Kì?ᑖÊᑡKâãíîᓽ7(III)ØÙÚÛêëḄ᩽ÔKᓽᑨ6êëḄjÔḄᜧæ.ூB௃(I)ᵫKᙠᓅᧅ3ÏḄ50ZÅKÜᙶ᪗qÔḄᜧÖ10Ýᨵ3ZK3—=0.06ᡠMðÅñò⌱?YKóÜᙶ᪗qÔḄᜧÖ10ÝḄᭆ᳛"5஺7(II)ᵫKA,B,C,஺äZåÅÑᙶ᪗qÔæÖTḄᨵ¸ZQC,D,ᡠMXḄᡠᨵçè"0,1,2,b(x=o)=3=3c46,P(X=I)=õ=2P(^=2)=|=lC04

14ூὃ௃ᡠMXḄᑖÊᑡ"X012P121636121F(%)=0x-+lx-+2x-=lᡠMXḄíî"636.(in)ᓅᧅ3ÏᙽÑᙶ᪗qÔḄjÔᜧÖᓅᧅ×Ï.ø⚪ὃùÞᐺᭆ᳛Ḅ>úKMûñòüýḄᑖÊᑡ@íîḄ>úKjÔḄᜧæḄᑨ6Kὃùᦪ_þÿ
ஹᳮ᫏⚪.18.(1)᪆2ফ2-ব.ூᑖ᪆௃(1)ᵫ$%&ᳮ'E/஻஺C,ᯠ/ᵫ%☢12ᑨ&&ᳮឋ5&ᳮ'6%%1278'9:ᡂ<(2)=>B@ᙶ᪗C>ᑖD=A4,BQ,5PᡠᙠK%@xMஹyMஹzMP<᝞RᡠSḄUVKWᙶ᪗X.ᵨUVᔣ[\]^☢WḄ_`a.(3)᪷dᔣ[\]>ᑮ1☢Ḅfg.(1)h@஺C,E,iᑖDj/஺BQ,AP,8PḄ>ᡠ=EF஻/8,DC//AB,ᡠ=lh@1☢PCQ,DCu1☢iCD,ᡠ=EF஻1☢PCDlh@EFu1☢1☢pq“1☢ic஻=G//,ᡠFEF஻GH,lh@Ei஻ᡠ=/8஻G”.

15ூwὃ௃yzফh@i1☢48஺ᡠ=A4,BQ,8i{{ᚖK.=>8@ᙶ᪗C>ᑖD=41,BQ,8PᡠᙠK%@xMஹyMஹzMP<᝞RᡠSḄUVKWᙶ᪗X.ᵫA4=8P=80=2,ᑣ4(2,0,0),£>(1,1,0),C(0,l,0),P(0,0,2)ᡠ=᪗=(-1,1,0),8=(-1,7,2),CP=(0,-1,2)1☢P48Ḅ\ᔣ[@7,ᑣ=(°1°)1☢PACḄ\ᔣ[@"=(x,y,z),ᵫnDP=0,n-CP=0,[-x-y+2z=0'[-y+2z=0,z=i,'7=(o,2,1).mn_0+2+0_2^538Wx-rri.)ᡠ=cos)=IIII,2-ᡠ=1☢PAB1☢PCDᡠᡂWḄ_`a@.(3)._\AD-^i\|0+2+0|26——-5ᵫ>ᑮ1☢Ḅfg'2ᓽ>Aᑮ1☢PCDḄf@.19.(I)஺=2(প᪆

16ூwὃ௃yz/f(x)=—+2X-(6Z+2)/,(2)=tan^=lপ]¤'ᑮ'¨ᫀ./,(஺1)ª«0ᦑ஺=2x°,/(x)ᙠ(1,/)ᓫ¯⌴±ᙠGo,e)ᓫ¯⌴(II)³^g(x)=2x

17x-x2-2x´ᦪᓫ¯⌴±ᦑgO/gkAi,'ᑮ.ூ¹௃প/(x)=alnx+/-«+2)xᦑ/(x)=1+2x_(a+2)‘MA"""½=1,ᦑy/'(x)=:+2x_g+2)=஺O,…)=0,ᓽ஺=2xe(2,e),ÀᙠÁ>,(II)/'(%)=⁐+2%-("+2)=0_Á>@Ä,ᦑᓽa=2x°,/(x)ᙠ(1%)ᓫ¯⌴±ᙠ(ÅÆ)ᓫ¯⌴³ᦑf(x)min=/(X஺)=஺ln/+/2-(a+2)x0=2x(,Inx+x2-(2x+2)x0000=2xInx-x2-2x0000g(x)=2xlnx-%2_2x,ᑣgg(e)=-eÎᦑÏx«le)Ð/(x)>-eÑÒ⚪ὃÓ´ᦪḄᑗ%Õ⚪ᑭᵨ¤ᦪ×Øᓄ@´ᦪḄᨬaj⚪ḄᐵÜ.Ý27V3---1~y=1e=—20.(1)ßᙊCḄáâ@4-,gã᳛2.(2)j&aᳮᵫ᪆.ூᑖ᪆௃(1)å⚪æᑡ6pcèVḄᐵXáâᓽ'9é;

18ூwyzë2
K%áâὶ<áâ'ஹ7{>ᙶ᪗èVḄᐵXíî8•ðᓽ'9é.ூ¹௃•yja2+b2—x2ca=26a2=b2+c2,b=l'ெc=GÑë1
᪷d⚪æ''X2A/3----Fy2=]eᡠ=ßᙊCḄáâ@4-gã᳛2.ë2
h@K%yMᚖKᡠ=K%Ḅò᳛@0,__6K%Ḅáâ@/ëíóôஹNëÌ2,õô,6—+y2=162+4)^2--ty--=Qὶ<áâ4-ᓄö''75-252To÷ᯠ>ᙠßᙊCḄᑁùᡠ=A>0.12Zᑣilh@Në-2°
,ᡠ=8=ëí+2,%ôú=ë஽+2,%
AM-AN=(x+2)3+2)+ýÄ=ü+M+ó1*ᡠ=Z,X4//\16-64(?+1)+48/+16(?+4)2=«(ó+þ+=ᶧ+4)=°ᡠ=8ÿᓽNM4N=90°.⚪ὃᙊḄ᪗᳛ᙊḄᔠᵨ!᫏⚪.

19ூ%ὃ௃'(,_n21.প0)))*1,1,2,ব2,2,4"প஻,Ꮤᦪ/-2,஻,᜻ᦪ/ஹ=஻T24III5678᪆஻=2,n=4প᪷<⚪=>ᑏ@Aᫀ.Ck=-HDEF஻,Ꮤᦪ/k+2,F஻,᜻ᦪ/k+2,HᑮAᫀ.IIIDEF",᜻ᦪ/<=°,MNOᙠQRᐰ,1ḄTᑖᦑ<

20ூ%ὃ௃'(jᡠkf=g”ᡂḄ஻,f஻=2ᡈ஻=4.ὃᦪᑡḄ⚪=ᙠὃḄ[\iᔠᵨi.