2022-2023学年高二上学期9月入学考试数学试题（答案解析）

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/(X)ᨵᨬi-&+1.8(2)ᵫ/õ)=g,Y!ösin(a-?)+l='1,Y!sin(a--)=—44ᡠhcos(2a9=1-2sin?(2-,43ᡠhsin2a=cos(2a--)=—.2420.(⚪ᑖ12ᑖ)ùúûüýþÿḄᐭ▅ᐝ▅⌲ᡂḄ4ᨴ23!.#Ẇ%&᪀()#ᙢ+Ḅ▅,-./0&1᪵34(1008+9:;ᜩḄ▅=>(ᓫ8AᑖC)EFGHIᑮ᪵KḄ⚣᳛ᑖNOPQ᝞QᡠT.(1)U(2)᪷W⚣᳛ᑖNOPQXH:1008+ᜩ▅=>ḄYᙳᦪᐗ(ᓫ8AᑖC);(^_ᦪWᵨa_ᦪWb>Ḅcde⊤T)(3)(Eg()+Ḅ▅PhẆ%&᪀iᵨᑖj1᪵ḄPklᜩ▅=>8mᑖ_n50,60),n60,70)sn80,90)Ḅ+c1v5wlcx⌱2EF34Uᐸc{|ᨵ1ᜩ▅=>8mn8090)Ḅᭆ᳛.

11ூᑖ᪆௃(1)ᵫᡠᨵP☢s=1,ᑡPU)a;(2)᪷W⚣᳛ᑖNOPQcYᙳᦪHhEF(3)ᑡᔠᩩḄKᵨᐺᭆᭆ᳛hEF.ூ)᪆௃)A(1)᪷W⚣᳛ᑖNOPQI:(0.005+0.01+2a+0.045)x10=1,)Ia=0.020,(2)᪷W⚣᳛ᑖNOPQIAYᙳᦪx=(55x0.01+65x0.02+75x0.045+85x0.02+95x0.005)xl0=74,(3)ᵫmn50,60),n60,70)sn80,90)Ḅ⚣᳛A1:2:2,ᦑ1vḄ5cn50,60),n60,70)sn80,90)ᑖ¡A122¢n50,60)Ḅ1a,n60,70)Ḅ26,c,n80,90)Ḅ2A,B,ᦑ0&1v2ᐳᨵ(a,b),(a,c),(a,A),(a,B),(b,c),(h,A),(b,B),(c,A),(A,3)10¦§ᐸc{|ᨵ1ᜩ▅=>8mn80,90)Ḅᒹ©77ᦑᭆ᳛p=—.1021.(K⚪«ᑖ12ᑖ)᝞QPO®¯°┵P—ABCḄµPA=PB,ABLAC,E3PBḄcd.(1)¶·AOE//Y☢R4C(2)»NABO=NCBO=30஺PO=3,PA=5,U¾☢¿ḄÀÁe.ூᑖ᪆௃(1)ÂÃ஺4,OB,ĶI஺4=03,ÅBOÆACmdF,ĶIOE//PF,ᵫÈI¶(2)ÉÊË>O¿ᙶ᪗ÎᑏÐᔜdḄᙶ᪗wUÐY☢ACEÒY☢A3EḄkᔣÔᑭᵨᔣÔḄᜳ¿hI).ூ)᪆௃)A(1)¶·AÂÃ04,OB,×⚪ØOP_LY☢ABC,Û஺4uY☢ABC,08uY☢MC,ᑣOPYOB,

12:.ZPOA=ZPOB=90°,OPA=PB,OP=OP,ᑣß஺à¯"03,:.OA=OB,Å80ÆACmdF,ÛAB_LAC,ᑣᙠRtAABFcOMcdÂÃPF,ᙠAPBâcO,Eᑖ23BF,8PḄcdᑣOE//PE,•rOEctY☢PAC,PFuY☢P4C,.•.OE//Y☢R4C(2)/dAãAM//OP,äA3,AC,AMᑖ¡xå)åzåÉÊ᝞QᡠTḄË>O¿ᙶ᪗ÎᵫmPO=3,PA=5,ᵫ(1)æ04=03=4,ÛZA8O=NC8O=30஺ᑣ48=4çP(26,2,3),8(4G,0,0),A(0,0,0),E(3G,1,|),ÛAC=ABlan600=12,ᓽC(0,12,0),éY☢AEBḄêkᔣÔri=(x,y,z)Ûbᨴ=(46,0,0),Aç=(3^,1,1),n-AB=4>/3x=0ᑣ•ì3ᑣÄv”=(0,3,-2),h-AE=3\j3x+y+—z=0éY☢AECḄêkᔣÔᵨ=(஺îc),XAC=(0,12,0),AE=(373,1,-),2m-AC=12b=0ᑣÄvv=(-G,O,6),m•AE=3\Z3tz+/?+—c=02é┦¾☢¿C—AE—BḄY☢¿஺ᑣcos஺Hcos\=\q-1=—,|ᑴᑭ13sin0^yl\-cos20=—,ᓽ¾☢¿C—AE—8ÀÁeU.131322.(K⚪«ᑖ12ᑖ)òæóôᙠRõḄᏔ÷ᦪ/(x)s᜻÷ᦪg(x),ùf(x)+g(x)=e'.(1)U÷ᦪf(x),g(x)Ḅ)᪆h

13g(x—)(2)é÷ᦪâ(x)=-------3+1
¢”(஻)=â(1)+â(2)+â(û)+....+F(•ü3(neN*,Ax-)஻""஻«..2).ý%®ᔲÿᙠ
᦮ᦪḄxe(O,1],g(2x)>H)g(x)ឤᡂᙠᡠᨵᩩḄ
᦮ᦪ"Ḅᙠ!"#ᳮᵫ.ூᑖ᪆௃(1)᪷,-./01ᙠR2ḄᏔ4ᦪ/(X)5᜻4ᦪg(x)f(x)+g(x)=e',᪷,᜻4ᦪ5Ꮤ4ᦪḄឋ8ᡃ:᧕ᑮᐵ>“X)ஹg(x)Ḅ@ABCDEf(-x)+g(-x)=eT,FCDGᓽIᑮf(x),g(x)ḄF᪆.,1ஹg(x))1(2)ᐜᑨL4ᦪM(x)=-------++1ḄNOᐵ>P0
1)ᡂ/QRᓽxeR,F(l-x)+F(x)=2ᡂᓽI,ᑣḄxe(O,1],g(2x)>
(”).g(x)ឤᡂUᓄW/+e-*+1>"ឤᡂ᪷,4ᦪᓫ[ឋᓽInḄ\^_ᔠ஻..2,ᓽIbḄ.ூF᪆௃FE(1)••/.(X)W01ᙠR2ḄᏔ4ᦪ/(-X)=/(X)cீga)W01ᙠR2Ḅ᜻4ᦪg(_x)=_g(x)ᵫ/(x)+g(x)=e*
f(~x)+g(-x)=/(x)-g(x)=ex,g(x)=(e*-ex),/(x)=(e"+e~x),(2)᧕.e■W᜻4ᦪᐸ4ᦪNOᐵ>(0,0)ᡂ/QR,JM/1ஹpix—)4ᦪF(x)=--------J+1ḄNOᐵ>P(1,1)ᡂ/QRY)2ᓽxeR,M(l-x)+M(x)=2ᡂ"(஻)=F(-)+F(-)+F(-)+......+,nnnn."(")=M(ᓃ)+M(■^)+M(■^)+...+F(-),nnnnmnoI

14HA|2n—2ti—1I2஻(஻)=lF(-)+b(——)]+lF(-)+F(——)J+……+FL(——)+F(-)]=2(/7-1)nnnnnnH(n)=/?-1,g(2x)>H(*g(>ᓽe2x-e-2x>(n-Y)(ex-e'x)(e*-e-*)[(e*+e-x)-(M-l)]>0,,/XG(0,1],.\ex-e-x>Q,ex+e~x+\>nឤᡂ=",/G(1,e],ᑣy=!++lᙠ(1,e]2ᓫ[⌴,y>l+l+l=3,:.Q,3,c-..2,.

15=2,3.

16