全国卷2022届高三一轮复习联考(五)理科数学试题(含答案解析)

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ᔁ2022ὶὃ()ᳮᦪ⚪᪥:
:ὃஹᓫ⌱⚪1.ᔠM={414x43)N={x}>஺},ᑣMC|N=().A.(0,11B.(0,31C.[-1,3]D.[-3,1]2.,-Z=(1+2i)(1-i),ᑣ1ᦪZᙠ14☢ᑁ78Ḅ:;<()A.=>▲B.=@>▲C.=A>▲D.=B>▲3.,-C⚪஻+x+4<0qNxGR,<3',ᑣGᑡIJC⚪Ḅx)A.p^qB.pv(-i^)C.(-ip)vqD.J")PJq).ᵞST᝭y2=1ḄWᯖ:I(-3,0)ᑣm=().A.^2B.14.Z[T\]2-J—tn48C.272D.85b-cdᙠRfḄ᜻hᦪ/Q)kl/G)=/(2-x),nx/0,l]p/(x)=xᑣ/(11)=()A.-1:O1B.则D.2-厂=)D.6,-sina=2j^vOS-在亚MA.B.-55557,-:wIxᱥ\C)2=4xḄᯖ::AIxᱥ\Cf=>▲ᑁḄ:nz\AFḄ|}~I:ᑣb=()A.B,2C,438+2”Ḅ@⚗ᦪI128,-|3x,ᑣᨵᳮ⚗Ḅ⚗ᦪI()ᔁ=1⚓ᐳ5⚓

1A.0B.2C.3D.59᝱Ღ᪻᤺1600WWᜮᜧ£Ḅ᪵¥¦,-᪵§¨Ḅ©ªᓫ;cm«¬᝱ᑖ¯N
7,G2,n©ᙠ6cmᑮ8cm±²Ḅᓰ᪵§´3ᦪḄᑣ᪵§©µ£<8cmḄ¶ீᲦ᪻ᦪ¸¹Iª)4A.40B.120C.200D.240D,-S,Iᦪᑡº»Ḅ¼஻⚗*=-2஺%+2S,=2"+l,ᑣ%2¾().A.2000B.2010C.2020D.202111᡻À☢ḄÁÂ᪾ÄnÅᐭḄ஺=31og2,b=21og3,ᑣÅÇMIª).32A.1B.3C.5D.72,-ᐵ0ḄËÌᨵ1W᦮ᦪᑣ¨ᦪ஺ḄÎÐѪÒ.A.[—2,In2—1B.
—2,In2—1]C.τIn2-l,ln3-D,ÓIn2-l,ln3-1Ò13jlL@ஹÔÕ⚪13.,-ᔣ×Ø=ª"ÙÒS=
2,4,n01ᔜᑣ¨ᦪÛ=_□.14.,-SIÉÞᦪᑡ4Ḅ¼"⚗a+a=10,ᑣ$=à.nn289-15.,-á஻Iᦪnz\஻â-=0ãᙊ
x-2>+
y+l=3ᑖᡂ☢æçÉḄèéᑖᑣA+@Ḅᨬ£ÎI.mn16.,-AஹBஹCஹ஺IÕ²µᐳ☢ḄBW:ëBC=B஺=2AB=2/■,ᑣìAí┵A-8C஺ïæᨬᜧpᐸ᜜òᳫḄ⊤☢æI_AஹËõ⚪ᔁ=2⚓ᐳ5⚓

217.öẆø£ᡝ᜜úûp²üýþp²ÿᜐḄ⌕᪵Ḅᙢ100ᜩ"#ᡝ᜜&'Ḅ()*+,Ḅ-./012ᜩᡝ᜜&'()341(Ḅ5678ᐸ:5ᡝ᜜8;<=>?ᑮ᝞B2x2ᑡὶ⊤H3ᔠ>67830ᡝ᜜830K>50100পNO2x2ᑡὶ⊤⊡ᐙR᦮TᑨVᔲᨵ95%[\Ḅ]^_5“ᔲ5678aaᔲ“ᨵᐵcফef503Ḅᢥᔲ678hiᑖk᪵Ḅlimnop55Ḅ᪵qef5⌱i3stuhvwf3678xᦪXḄᑖ{ᑡaᦪ|}.ὃᦪHP(K2±k)0.0500.0100.0010kc3.8416.63510.828iz(ad-be(ὃHK2=Q+M+“)Q+C"஺ᐸ(+…+஻.)X18.ᙠᑁA,B,CᡠḄᑖ5a,b,c,COSA=4“sinA+csinC-bs'mB=V^csinA.পwC¢(2)£c=^^,wAA8cḄ☢¥.19.᝞¦ᡠ§¨©A8CO5ª©EA=EB=BC=2,E4_LEB,¯☢ABC£)_L¯☢ABE,#F%CE±.²ᔁ´3⚓ᐳ5⚓

3D(1)·¸HBFA.AC-,ফwOFa¯☢8£>EᡠᡂḄ¼½¾.20.¿ÀÁᙊ஺H:+ᓃ=1(஺>6>0)ḄÆஹÈᯖ±ᑖa2bi122ᙠÁᙊC\Ð'ÑMFFḄᕜÓ54+2..পwÁᙊCḄÔ¢ফÕA,8ᑖÁᙊCḄÆஹÈ⚔±஺5ᙶ᪗±±P5ÚÛx=2\Ḅ'±ÜÝAPÞÁᙊß±Q(àß±A).ᑨVá•4ã+%\ᔲ52¾Õwäå2¾¢ÕᔲNæ¸ᳮᵫ.21.¿Àéᦪ/G)=ax-(.2a+l)lnx=(a>0).xপíîéᦪ/G)Ḅᓫឋ¢(2)Õ£ெ2,31Vx,XG[1,21,3óm+In2>|/G)-/(x)ឤᡂùwúᦪûḄi121121¾ý.2ᙠ¯☢Úᙶ᪗þxOy
/Ḅᦪீ/T(rᦪ)
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x"Ḅ#$"᩽"%&᩽ᙶ᪗(.প*/Ḅ+,-ᙊCḄ᩽ᙶ᪗.7Cফ1OP4e=_7ᙊcḄ9M(;<=)
7/Ḅ9N,*?Ḅ4A.3CDEᦪ/(x)=Bx-n|-k+2|.পK”3M
*NOPfG)42ḄST.UᔁW4⚓
ᐳ5⚓

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ᐳ5⚓

5ὃhᫀ41.BூS᪆௃ூᑖ᪆௃TᔠḄopqr.ூsS௃ᵫ⚪᧕w஻nN=(0,3Lᦑ⌱:B2.AூS᪆௃ூᑖ᪆௃᪷ᦪḄqr
ᓽ*ᦪz,᪷ᦪḄ^
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3f(x)=/(-log(In3))=3-iog3(in3)+log(ln3)=+log(ln3)>0,min33In33ᦑ\VxeR,x<3x,¾q¨¡⚪
..(rp)vg¨¡⚪
UᔁW1⚓
ᐳ14⚓

6ᦑ⌱4c.4.DூS᪆௃ூᑖ᪆௃᪷Ḅᐵ(ÃrS.ூsS௃ÄÅmÇ1ḄÈᯖ(-3,0),mᡠc=3,ᡠm+1=32,SwÊ=8.ᦑ⌱4D.5.BூS᪆௃ூᑖ᪆௃ᵫ⚪D/G)ḄᕜÍ4,ᯠÏᑭᵨᕜÍ-EᦪᙠÐḄS᪆P*SᓽூsS௃/G)᜻Eᦪ
ᡠf(-x)=-/(x),f(x)=/(2-x),ᡠ/(2-x)=-/(-x),§-x=f,ᑣ/(2+஺=/(஺,ᡠ/(4+஺=-/(2+/)=/0)
ᡠ/G)ḄᕜÍ4,ᡠ/(11)=/(11-3x4)=/(-1)=-/(1)=-1.ᦑ⌱4B.6.DூS᪆௃ூᑖ᪆௃ᑭᵨÔ¤ÕPÖ×*S.ூsS௃coqa-Ùsina=2ÛUᔁW2⚓
ᐳ14⚓

7ᦑ⌱4D.7.CூS᪆௃ூᑖ᪆௃¯,Ü=m,᪷ḄÝÞßàFḄᙶ᪗
*AḄᙶ᪗
áᐭãᱥ*Sᓽ.ூsS௃ᵫ⚪^ᯖåæ1,0ç,
AåḄÝÞßZ¯|AF|=஻ê
..º+஻?COS.,n?sin.
ᑣ—+,᪗j
IJIJáᐭãᱥᓄñw3
"2-8஻?-16=0,4Swò=4ᡈÊ=æôõç3ᓽkö=4.ᦑ⌱4c8.CூS᪆௃ூᑖ᪆௃ᐜ᪷øùPú⚗P(ᦪḄ-*஻=7,wᑮ,⚗ÕP
*ᨵᳮ⚗Èᦪ.ூsS௃ᵫ⚪øùPú⚗P(ᦪḄ-2"=128
Sw஻=7,.2Yᡠú⚗P13þ+j,ᑣøùPḄ,⚗7=2,37-ÿr=0,1,2...,7.r+17ᡠr=0,3,6T=237-rCx77ᨵᳮ⚗r+17ᡠᨵᳮ⚗ᐳ3⚗.ᦑ⌱C.ᔁ3⚓ᐳ14⚓

89.Cூ#᪆௃ூᑖ᪆௃᪷()᝱ᑖ+Ḅ-.ឋᓽ12345.ூ6#௃.•.589:)᝱ᑖ+N(7,o2),.•.ᐸ)᝱<=ᐵ?@=A=7-.3B58ᙠ6cmᑮ8cmEFḄ5Gᓰ᪵JKᦪḄM41(3ᵫ-.ឋ1O᪵J58PQ?8cmḄRᲦ᪻ᓰ᪵JKᦪḄx11-21᪵J58PQ?8cmḄUᲦ᪻Vᨵ11600=200.8ᦑ⌱C.10.Aூ#᪆௃ூᑖ᪆௃᪷(Wn⚗X““ḄᐵZ[3“+«=2,ᓽ12#.nn"+inூ6#௃ᵫ⚪1[஻+2S=2/1+1,«+1n஻N2a+2s=2/7—1,:.nn-1ᵫ[a-a+2(5-S)=2,᦮ᳮ[a+a=2(஻*2),n+lnnn-1ZH-1nBᵫ"=-20,1ᡠS=a+Q+a)+Q+஻)+…+Q+a)=-20+1010x2=2000.ᦑ⌱A.2021123452020202111.cூ#᪆௃ூᑖ᪆௃᪷(`a᪾cḄdefgᑨijᐭlᜧQn⌱o᡻qderstu.ூ6#௃a=31og2=log8e(l,2),Z?=21og3=log9>3,ᓽᨵ3322ᔁ4⚓ᐳ14⚓

9ᡠM=஻x஺-1=31og2x21og3-1=5.32ᦑ⌱c12.Bூ#᪆௃ூᑖ᪆௃[/(1)>0ᵫ⚪1[Py(x)="x+2-xlnx>0ᨵ1᦮ᦪ#,ᑭᵨᦪ4ᔠ1[.ஹ[/(2)<0ᓽ2.ூ6#௃ᵫ⚪1OX€(஺,+8),ᡠPax2+2x-mlnx>0ᓽ+2—xlnx>0ᨵM᦮ᦪ#/(x)=ax+2-xlnx,P,f(x)>0ᨵ1᦮ᦪ#y=or+2,g(x)=xlnx,ᑣᦪg(x)=xlnxcᨵ1ᙶ᪗᦮ᦪḄ¡¢ᙠ@=y=ax+2Ḅ£¤,¥g'(x)=1+Inx,ᵫg'(x)=1+Inx=0,[ᱏ©@=y=ax+2ឤ¯¡(0,2),t3ᦪg(x)=xlnª«@=y=ax+2Ḅᜧ¬c,|/(1)>0ᓽM2<441n2-l.|/(2)<0ᦑ⌱B.ூ¡²௃ᔁ5⚓ᐳ14⚓

10ᐵ³¡¡²J⚪Ḅᐵ³´µ¶⚪·ᓄᦪg¹xº=xlnx«@=y=«x+2ḄḄ¼¡Ḅ½¾¶⚪ᯠÀᑭᵨᦪ4ᔠ#Á.13.-2ூ#᪆௃ூᑖ᪆௃ᑭᵨᔣÃᚖ@Ḅᙶ᪗⊤Æᓽ2.ூ6#௃.•.ᔣÃ஺=¹Ç1º,b-¹2,4º,a±b1~a-6=Cn,lº¹2,4º=2m+4=0,ᡠÈ=M2.ᦑuᫀ-2.14.45ூ#᪆௃ூᑖ᪆௃ᐜ᪷(Ë⚗ḄaÌ23஺5,ÍÎϯWn⚗2XÐ2[uᫀ.ூ6#௃9¹a+aºᵫa+a=10=2஺=10na=5,Ò=---1---J=9a=45.2855925ᦑuᫀ45.15.9ூ#᪆௃ூᑖ᪆௃᪷(`aᩩÔ1[@=஻Õ-=0¯¡¹2,-1º,nᑭᵨ"1”Ḅᝯᵨrstu.ூ6#௃@=᝞-஻y-l=0Ùᙊ
X-2>+G+1>=3ᑖᡂ☢ÝÞḄßàᑖᑣ@=mx-ny-1=0á¯ᙊâ¹2,-1º,ÒIãä+1=¹ä+1
2å+஻º=æ+522çè+5=9,éᓽ2m+n=l,mnmnmnVnᔁ6⚓ᐳ14⚓

11%=஻=1ë“=”3ᡠÈ="¥/+©ḄᨬQl9.3mnᦑuᫀ916.187tூ#᪆௃ூᑖ᪆௃ᵫ⚪1[BAஹBCஹBOßßᚖ@äí┵ḄïÝᨬᜧÙäí┵⊡Mñòóᑖô2õ2öᡂ1Ḅñ¤ïᓽ÷ூ6#௃BA.BCஹ8஺ßßᚖ@᝞cäí┵A-8C஺Ḅõ☢øBCDḄ☢ÝXóùë[ᨬᜧlᑣäí┵ḄïÝᨬᜧúÙäí┵⊡Mñòóᑖô2û26,üḄñ¤ïñ¤ïḄ᜜þᳫᓽ
┵Ḅ᜜ᳫᳫḄr=1⊤☢
4ᐔᔆ2=18ᐔ.ᦑᫀ
18ᐔ.17.(1)ᑡὶ⊤᪆ᨵ9(2)ᑖᑡ᪆-5ூ᪆௃ூᑖ᪆௃প᪷$ᦪ$&ᡂ2x2ᑡὶ⊤(᪷$)*+,K2Ḅ-ᯠ/012-⊤3᯿ᜧ6ᓽ7+8ফ᪷$ᑖ:;᪵7=;>Ḅ5?@ABCᨵ3?ᡝ᜜Cᨵ2?EFᑭᵨIJKᑖLᔁN7⚓ᐳ14⚓

12ᓽ7+XḄᑖᑡᨬ/᪷$ST)*ᓽ7+ST-.(1)2x2ᑡὶ⊤⊡ᐙ᝞]:_`a`aᔠcABC304070ᡝ᜜C201030hc5050100100x(30x10-20x40>K2=a4.762>3.841,70x30x50x50ᡠkᨵ95%knḄopq
“sᔲ
ABC0`a0ᔲ”ᨵᐵ.Q)ᵫ⚪7y;>Ḅ5?@ABCᨵ3?ᡝ᜜Cᨵ2?z5?@({|;>3}~ABC~?ᦪXḄᡠᨵ7>-
1,2,3.()஺2.C6/\C31PX=1=ߟ3T=—,PX=2.=132*=,PX=3=~~T=—,C310C310஺310555ᑖᑡ
:X123361PW10E(X)=1x2_+2x^3x10WW57C18.(1)38ফ3+ᡃ4ூ᪆௃ூᑖ᪆௃(1)ᐜ᪷$ᳮEᓄ(᪷$ᳮ+,B,ᯠ/᪷$Ḅ)*+LᔁN8⚓ᐳ14⚓

13=ᫀ8(2)ᐜᵫᳮ+,b,EFᵫḄ☢)*+=ᫀ.(1)ᵫ⚪asmA+cs,mC-bs'mB=y/2.csmA<ᵫᳮ=ᡂ+02-=࠷.•*-cosB=a2+<2=F0<8<ᐔ,ᑣ8=-2^~~24cosA,0n²☢ABE=A8,BC1AB,BCc²☢ABCD,.8CL²☢ABE,ABCVAE,•••EA_LEB,EB[\BC^B,.AEI²☢BCE,.AE1BF,AEB=BC,.E3C
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CE@À$.BF_LEC,AEcEC=E.BF1²☢ACE,.BFLAC.LᔁN9⚓ᐳ14⚓

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x,y,zdz´µ¯ᙶ᪗¸.ᑣ?J,4,2)Jo,:;21E§,0,0),FÊË1Ì—~=(J23^21¡(Î)¡*(Ïᔆ)DF=\ÐÐ,¡1|,BD=0,-22,DE=⊟,-2,[22]Õ²☢8DEḄ¹ᔣ»
¢=G,y,z),

15~BD=0\—2j2y+2z=0ᑣØ_Ù஻ÎÛ[n-DE=QIV2x+V2y-2z=0()Þy=1,Ùljx=1,2=.ᓽ¢=1,1á.ᑣcos(«+åæᡠkOF0²☢BDEᡠᡂḄ-
`620.প+Î=14-(2)s4ூ᪆௃LᔁN10⚓ᐳ14⚓

16ூᑖ᪆௃1
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2,y,⊤ö,¯°"y=&
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+ª=1.4QAû-2,0,2
2,0,ÕÎ
2,yÿ,Q
x,y,0II_
yᑣ0ᡝ=
2,y,OQ=x,y,k=F,0iiAP4ᑣAP6y=£>G+2ᓽ=&+_1442oI+¥=1\y2}ὶτ4.11|1+_iL|x2+y2x+y2-4=0,Iy=yox+yI4)°°fTIo4(y2—4)0______4+y2o4yy=%,i+4o4joL26>^+6M=(2,2y),DO\007()4g_4)8y24(y2+4)...ỏ•2U?+7X4=-_!>____+_Q_=______=4.4+y2y2+4*+4()000ᡠ•24.21.(1)ᫀ!᪆(2)(6ln2-4,+oo)#ᔁ%11⚓ᐳ14⚓

17ூ!᪆௃ூᑖ᪆௃জ,-./ᦪf'
x,ᯠ2ᑖ0I56789:;<ᓽ=/ᦪ222f
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xḄᨬᯠ2JKL⚪Nᓄm+ln2>f
x-f
xPmaxminVae
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21n2-la-l=᪀⌼/ᦪU
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x=ox=2ᡈx=1,a`02,ᵫf'
x>0x<2ᡈc1,ᡠ/ᦪf
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x>0,ᡠ/ᦪi*kḄ⌴efgl0,*0,m⌴hfgB2`a>2•a0<1<2,ᵫf'
x>0x>2ᡈxsLᡠ/ᦪf
xḄ⌴efg
0,
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xḄ⌴efg
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x<0,ᡠ/ᦪf
xᙠ>1,2=pᓫ@⌴hᑣf
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x=f
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x-f
x|ឤᡂ#ᔁ%12⚓ᐳ14⚓

18Am+In2>/G)-/G)=4-2-(2a-l-(2a+l)ln2)=(21n2-Da+In2-1,ᓽmaxminm>(21n2-1)஺-1Pe12,3ឤᡂ,^(PQ)=(21n2-1L-1,ᑣ/ᦪ(pQ)ᙠ2,3pᓫ@⌴eᡠCfn>r(pG)=9(3)=61n2-4.JmaxᡠᦪmḄ(61n2-4,+s).22.(1)%+y£=0,p=^2cos0D2ফL.2ூ!᪆௃ூᑖ᪆௃(I)¦§¨ᦪᓽ,/Ḅ©ª«¬ᑭᵨ¯}=ᙊcḄ᩽ᙶ᪗«¬µ(2)¶M(p,o),N(p,e),3ᵫ⚪=P=1,p=¼12122(1):+r,º/Ḅ¨ᦪ«¬j1j2(¨ᦪ).../Ḅ£¾}«¬x+y-¿=(k;72...ᙊCḄ«¬|X4j+=2,ÃÄx=pcpsg(J7VI1=psine,Èᐭ|x-¥j+y2=,VᓄËBP=Wcos஺,ᙊCḄ᩽ᙶ᪗«¬p=0cos஺.(2)¶M,NÍÎḄ᩽ᙶ᪗BM(p,0),NlP,Gk,127TnJe=_Èᐭp=JTcosOP1="cosஹ==1,414#ᔁ%13⚓ᐳ14⚓

19ᵫ/Ḅ£¾}«¬x+y--j=0,=/Ḅ᩽ᙶ᪗«¬:?2p(sin0+cos0)=,(13JG=np(sin0+cos0)=ÓÔ—2ºÈᐭ4ᡠ|MN|=|P-P|=—•12223.(1)2ফூ!᪆௃ூᑖ᪆௃পᑖÖ;1[3—3x+2+x<2\3—3x—2—x<2[3x-3-2-x42!ºm!,ᡈµ.á4x41,ᡈ.,Jew7,42ᦑ-14X<7,ᡠ{|}Ḅ!än.-I421(2){|}/(x)42n+2|+3|åæ|3_3-3n+2|43,çè-é-|3x+6|4|(3x-a)-(3x+6)|=|a+6|,êPëìXGR,ᙳᨵ/(ï)<2,+2|+3ᡂᑣn+6|43,!-94஺4-3,ᡠᦪ“Ḅñò9,-3].#ᔁ%14⚓ᐳ14⚓