2023年新高考地区数学名校地市选填压轴题好题汇编（十三）（解析）

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2023
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+8"஺212-^332zi2zi4cos*-80+:cos80sin4+sin*-90+cos~ὡ)2cos24+§cos4sin%+q2i—cos20+sin20+1oQ21+—27ᡠ2&+ᚪ,?ᡠsin(24+£|e-1,1e0,y33ᡠ஻£^7_o4_ᦑ⌱ABC21.(2022•ᓭᓣ"#$᪥&'▤)*+),-.ᦪ/(x)=sin[cosx]+coskinx],ᐸ12⊤4567"ᦪxḄᨬᜧ᦮ᦪ<ᑡᐵ?.“X)@ABCḄDA./[fj=coslB.஻x)ḄEFᕜHD2IC.஻x)ᙠ(0,I)KᓫM⌴OD.“X)ḄᨬᜧPᜧ?BூRᫀ௃ABDூU᪆௃ᵫ/(x)=sin[cosx]+c(Msinx],X?A,/^^=sinO+cosl=cosl,ᦑABCX?B,f(x+2»)=sin[cos(x+2/r)]+cos[sin(x+2஻)]=sin[cosx]+cos[sin%]=/(%),ᡠ/(x)ḄEFᕜHD2%,ᦑBBC

20X?C,YZ0^-+1>y/2ᦑDBC;2ᦑ⌱ABD(x+2a,x<022.(2022•ᓭᓣ"#$᪥&'▤)*+),-.ᦪ/(x)={,ஹa,bᐵ?xḄcd[ᔆ-ar,x>0f(/(x))=0ᨵ8F5Ḅ"᪷ᑣ”ḄPkl.A.-6B.8C.9D.12ூRᫀ௃CDூU᪆௃Y஺n0Z./(x)=0ox=0-᪷ᦑ/(70))=0ᨵ8F5Ḅ"᪷5klᡂr.Y஺>0Z,tuvwYf(/(x))=0Z,/(x)=-2aj(x)=0,/(x)=ax/(/(x))=0ᨵ8F5Ḅ"᪷ᦑ<(x)=-2aᨵ'᪷zy=/Eg=(xE]jE12ᦑ-2a>-|=>a>8.x~(x)=0ᨵ'᪷fiM=aᨵ᪷za<2a=>a>0.423.(2022•ᓭ•ᕜᓭ1$&'▤)*+)b.ᦪ/")=1g+“-2+1)(4€/?)ᙠF᩽P,ᵯa<஽)ᑣ()A..ᦪ/(x)ᨵEFB.a<0ᡈ஺>2C.0l-21n22ூRᫀ௃ACD[U᪆]X?A,/(x)=lnx+6f(x2-2x+l)=lnx+6f(x-l)2

21f(l)=lnl+a(l—1)2=0,..x=lD/*)ḄEFᦑABCTnஹ]/ccஹ2tZX2-2tZX+lX?B,()=E+஻(2X-2)=------------------xx•••/«ᙠF᩽P,஽(<ᵯ).-.2ax2-2ax+\=0ᨵF5Ḅ"ᦪ᪷ᓽf(x)ᨵF%>0,>0.•.A>0,HP(-2a)2-4x2ax1=4c/2-8iz=4a(a-2)>0,a>2ᡈa<0x,+x=1>02x᳝>0,%>0,1c.U4>012=>°2aKa>2,ᦑB┯^X?C,ᵫB⌱⚗kX1+±=l,/.x=l-x),/.1-Xj,/.0

22a—ln2-}§h(a)=a-Ina-In2-1(஺>2)//ஹi1a—\ah(a)=1—=----->0aaᨵ/?(a)ᙠ(2,+oo)KᓫM⌴¨.-./!(«)>//(2)=2-ln2-ln2-1=l-21n2,ᦑDBCᦑ⌱ACD24.(2022•ᓭ•E1&'▤)*+)©ª«ᙠRKḄ.ᦪ/a)ng(x)Ḅ¬.ᦪᑖ®f(x)¯g'"),bg(x)-/(3-x)=2,r(x)=g[x-1),zg(x+2)᜻.ᦪᑣ<ᑡ±²1EªBCḄD()A..ᦪg(x)Ḅvwᐵ?1=1X³B./(2)+/(4)=420232023C.£g(A)=0D.£/(´=-4046*=1k=lூRᫀ௃ACூU᪆௃f'(x)=g'(x—l),ᑣf(x)+a=g(x-1)+6g(x)-f(3-x)=2,ᡠg(x)=/(3-x)+2,ᵨ3—x¶·x,ᡠᨵ/(x)=g(3-x)—2,ᡠᨵg(3-x)-2+a=g(x-l)+¸¹x=2¤ᐭᑮgপ-2+a=g6+bᑣ-2=b,aᦑg(3-x)=g(x-l),ᵨx+1ᣚx,kg(2-x)=g(x),.ᦪg(x)Ḅvwᐵ?x=lX³ᦑABC

23g(x+2)ᙠRK᜻.ᦪᑣg(x+2)7(0,0),vÂᔣÄÅÆFᓫÇᑮg(x)7(2,0),ᦑg(x)vÂᐵ?(2,0)X³g(2)=()g(x+2)=-g(-x+2),Èg(2—x)=g(x),ᡠᨵg(x+2)=-g(x),ᑣg(x)ḄᕜHT=4;xg(x)vÂᐵ?(2,0)X³g(2)=0.ᦪg(x)Ḅvwᐵ?x=lX³,ᦑg(D=-g(3),g(2)=g(4)=0.2023£g(A)=gপ+g(2)+…+g(2023)=gপ+g(2)+g(3)=0,ᦑcBC.k=l/(x)=g(3-x)-2,Dᵫg(x)ḄvÂÅÆᓄÈᩭᦑAx)ᕜHÒ4,g(D=-g(3),g(2)=g(4)=0,ᡠf(2)=gপ-2,஻4)=g(-l)-2=g(-l+4)-2=g(3)-2,ᡠ/(2)+,(4)=gপ-2+g(3)-2=-4,ᦑB┯^f(x)=g(3-x)-2,F(x)ᕜH4,f(T)=g(2)-2=-2,f(2)=g(l)-2J(3)=g(0)-2=-2,f(4)=g(-1)-2=g(-1+4)-2=8ব-22023ᦑZfÚ=/প+/ফ+…+7(2023)=505X(-8)+/•প+/(2)+/(3)=-4046+g(l),Jt=l->(P3ᵫ?gপḄPâ-gপ5Eª0,ᡠã²ᑨå£/uḄP-4046,*=1ᦑD┯^ᦑ⌱:AC.25.(2022•ᓭè□•&'▤)*+)ᙠêëìí1ABC஺-ABC஺1ZBAD=60,ABAD=AA,=2,PCG1Qð=2ᔊ+஻ò,[€[0,l]஻q0,l]).<ᑡ@ABCḄD()A.bõ+஻=1,ᑣë☢÷A8PQḄ÷øªP.B.b4Q஻ù☢A8P,ᑣ4QḄᨬúPû.C.büAB஺Ḅ᜜þᑣÿ•42.D.WX=Y,ᑣ஺Ḅg".ூᫀ௃ABDூ᪆௃A,ᵫ=/1$+஻'(+஻=1,ᡠ*Q,C,Q-ᐳ/0ᡠ*஺ᙠCR,CA஻AB,cq

24Ḅ=>0AABPḄ☢?0ᡠ*@☢AABP஺ḄA?0ᡠ*ABC0B,DḄEᑖGM,N,HIAM,MN,AN,ᑣAA7஻8P07☢ABP,BPu7☢ABP,ᡠ*AM஻7☢ABP,Z[MN஻CDஹ,AB//CD,,ᡠ*MN஻A1,7☢A8P,tABu7☢ABP,MN஻7☢ABP,MNcA஻=M,MN,AMu7☢AMN,ᡠ*7☢AMN஻7☢AQu7☢40N,ᡠ*AQ7☢48J0ᡠ*KAQLMNL0A஺ᨬN0/BAD=60,AB=AD=AA1=2,ᡠ*AM=O,MN-O,AN=VAD2+DN2-2ADDNcos120°=£+1^2x2xlx^lj=ᶭ0ᡠ*4M?+MN2=AN?,ᡠ*Q,MQᔠ0ᡠ*AQḄᨬNO0ᡠ*BBC0C,S^AB஺Ḅ᜜UM,VMW//,X3+2ஹ=2Z,ᡠ*4[4\=]4/=4,ᡠ*C┯_0D,VAW4஺0GDO,ᑣ`a஺n_L7☢44GA,A஺u7☢AMGD0ᡠ*_L\O,jrG2noR=A0GR,ORu7☢QRGC0ᡠ*A஺07☢OAGC,OD,=A,DCO^=\,,ᙠ஺஺,஺6dD&04,faAA=60A4=I0ᑣA4=A&=J7,O4=O4="H=2,ᡠ*SAQ=S.ᑣ஺ᙠ*஺ᙊU02noḄᙊpq&drs0஺஺=1,AA=6,ᡠ*24஺%=(,ᑣᙊp4q3vw0ᡠ*DBC0

25ᦑ⌱zABD26.(2022•|ᓅ•~-▤)ᦪ/((=(321)28d-a,ᑣ()A.7(x)Ḅ᩽ᜧB.f(x)ḄᨬN-5-aC.KḄᦪᨬL0஺ḄD(,1)D.v/")4ḄḄᨬᜧᨬNN1.2ூᫀ௃ACDூ᪆௃஻x)=(3x2-1)2-“0ᡠ*r(x)=2(3x2-l)?6x-24x2=12r(x-D(3x+l).K-ga<0ᡈx>lL0r(x)>0]Kᡈ(Xr0,aaeº,11,CBC.v/(x)W-a0ᓽ(3/-1)2-8^40,½g(x)=(3x2-l)2-8x3,ᑣg,(%)=2(3x2-l)?6ir-24x2=I2x(x-l)(3x+l).K-]lL0g0(x)>0]Kx<-¿ᡈ0

26ᡠ*g(x)ÁÆᦪÇÈ᝞ÊᡠËz2xg(0.2)=0.882-1.6?0.1,g(L4)>a.882-8?3,ᑣg(x)MOḄḄᨬᜧᨬNN-1.4-0.2=1.2,ᓽvÂ(x)<-aḄḄᨬᜧᨬNN1.4-0.2=12,DBC.ᦑ⌱zACI)27.(2022•|ᓅ•~-▤)Sᵫᦪ᪀⌼ḄᦪᑡÏ%ÐÑÒ4=/(஻)0v,«eN*,0ᧅ+ஹiiiiinτ5(2448888)LÃᓫÓᦈÕᦪ.ᦑf(x)=zX2_22(1_____S஻x)=x+2)2q”(zi+2)2(஻+1)(஻+2)[஻+1n+2J\11111ஹÜ11ஹ10<4+஽2■+•…+a“2(++…+)—2()<1,஻2334H+1஻+22஻+2ᦑ/("=/ᓫÓᦈÕᦪ.\x+2)S஻x)=(

27ᦑ஻X)=[g)+')ᓫÓᦈÕᦪ.S஻x)=lg(l+J)0ᑣ/Tg[l+[=lgV'=lg("+l)-lg">0009L0lg(஻+l)>l,ᦑ/(x)=lg(l+jÃᓫÓᦈÕᦪ.ᦑ⌱zBC.28.(2022•|ᓅ•~-▤)äᦪ/(x)=cosW-2§ᵫç0*ÊèéBCḄÃ()A.ᐔÃᦪ/(x)Ḅᕜì27rB.ᦪ/(x)ᙠ0,7dᓫ«⌴C.ᦪf(x)Ḅí[-î,1]D.ᦪ஻x)ᙠ[-2ᐔ,2ᑁᨵ6ூᫀ௃ABDூ᪆௃Az஻x)=cos|x|-2|sinx|,ᡠ*"0)=cos0-2|sin0|=l,/(7r)=cosJt-2|sin7t|=-1,஻ᐔ)H஻0)0ᡠ*ᐔÃᦪ“X)Ḅᕜì0ᓽ⌱⚗A┯_]BzKOWxK÷L03/(x)=cosx_2sinx=^5(^-cosx-sinx)=Ocos(x+(p),ᐸEcos᜛=4^0sin°=2^,7T7Tûüe┦þ0ᑣr\OKxKyᡠ
9«ᐭ+04^+9,

28,+9>ᐔᡠ
ᦪ/Xᙠ0,7ᓫឋᓽ⌱⚗B┯C2ᐔ!ᦪ/XḄ#$ᕜ&'(#$ᕜ&[-ᐔᐔ],Ẇ./01xe[0,'f{x}~cosx-2sin%=^cos
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xe[-V5,Uᦑᦪ஻xᙠR,Ḅ/0[-⌲,1],ᦑ⌱⚗CFGD1xe[0,7t],H/
x=0,Icosx=2sinx,Bptanx=—,Jᨵ1$L21xe[n,2jt],Hf
x=0,Icosx=-2sinx,ᓽtanx=-•-,Jᨵ1$L2ᡠ
/*ᙠ[0,2ᐔ],ᨵ2$OP@ᦪ/*Ꮤᦪᡠ
ᙠQRS2ᐔ,2Tᑁᨵ4$OPᓽ⌱⚗D┯.ᦑ⌱ABD.29.
2022•Xᓅ•Z[▤]^_ᦪ/
x=*-lnx
k`ᦪḄab'c!

29

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d)=g|)=_(_£!=?ᦑ⌱⚗AFG⌱⚗B“x-l)᜻ᦪᡠ
/(x)ᐵ(-1,0)v@/஺+1)Ꮤᦪ,ᑣ/(X)ᐵx=lvᡠ
Ax)ᕜ&4x2=8,ᦑ/(x+7)=/(x-l),ᡠ
f(T+7)"(f_l)=_஻xT)=-/(x_l+8)=_஻x+7),/*+7)᜻ᦪᦑ⌱⚗BFG⌱⚗C/*)=-/+1ᙠ6(-1,0),ᓫ⌴@஻x)ᐵ(-1,0)vᡠ
Ax)ᙠ(-2,0),ᓫ⌴,f(x)ᕜ&8,ᦑ/*)ᙠ(6,8),ᓫ⌴ᦑ⌱⚗C┯⌱⚗D᪷⚪ᩩ/(x)y=-lgxḄᦪab᝞aᡠᐸ3y=-lgxᓫ⌴-lgl20/(%)=/(9)=/()=/(%)<஽<*3<ᓃᑣ()A.%!+x=-1B.XX=1234C.---4Xஹ<1<45/2D.00Bg((x)=2'In2-2-'In2=(2J-2'')In2>0,ᡠ
g(x)ᙠ(0,+8),ᓫ⌴@g(x)!Ꮤᦪᡠ
g(x)ᙠ(7,0),ᓫ⌴.´g(x)=2+2-*-2Ḅabᔣ¶·¸$ᓫ¹º»

31Iᑮᦪy=2'+x+2-'-x-2Ḅabᦑᦪy=2"+2-'-x-2Ḅabᐵ½¾x=—lv,ᦑ'Iᑮᦪᙠߟᑘ,Ḅab.Áᦪ“XḄᜧÃab᝞aᡠ.Á·ÄÅÆḄ½¾y=஺10/2Bx\+x+x+x=-2+X+—,2344ᦪy=-2+x+ᙠ1,áâ,ᓫ⌴,xᡠ
0<%+A?+4+4V31-2,ᦑDFG.ᦑ⌱BCD32.2022•Xᓅ•Z[▤]^_äÌå¾y=aey=lnx-InaḄᩩæᑗ¾è4Ḅéê9ᑖìa

32᜛4஺P2,44Ḅᜳ9ᑣîᑡðñFGḄ!()A.sina=cos/7B.tana+tan/?>232C.tand=,ᑣD.P஺'cᙠõ[b▲4eூ©ᫀ௃ABCூL᪆௃᝞ay=ae*y=lnx-lna÷øᦪᦑᦪḄabᐵ½¾>vᑣ44ᐵ>vWa+B=%,sina=sin[]-/7)=cos[,ᦑAFGᵫ⚪Òa,4ᙳ┦9tanc>0,tan£>0,tana+tan/?=tana+tan||=tana+—!—>2,12)tana7T11tana=l,ᓽa=/?=#B(úûᦑBFG464$ᦪabᑖìᑗMNPZOQN=-,ᑣtand==,242tan—3aiᓽ-----)=,LItang=ᡈ#3(þÿ)
1-tan2-4232ᦑ%MN=tan+45஺)=—:=2,
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=e*=2,x=ln2,ᡠᑗ"#(ln2,2),ᡠ%&)
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33

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37

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