2020年高考文数真题试卷（新课标Ⅲ)

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2020
ὃᦻᦪ⚪ᔁ᪗
ὃ⚪——ᑖᑖ▅ᔁஹ⌱⚪⚪ᐳ12⚪!"⚪5ᑖ!ᐳ60ᑖ஺ᙠ"⚪%&Ḅ(⌱⚗*!+ᨵ⚗-.ᔠ⚪0⌕2Ḅ஺ᐳ3ᑖ12⚪4ᐳ57ᑖ1.5ᑖPᔠA={1,2,3,5,7,11},B={x|3D.?>7.5ᑖAOᙶ᪗E5?>x=2G<ᱥ>Cy2=2pxp>0KLD,E25NOD1OE,ᑣCḄᯖ5ᙶ᪗

1..........OOA.(1,0)B.(J,0)C,(1,0)D.(2,0)4Z....8.(5ᑖ)5(0,-1)ᑮ?>y=fc(x+1)Ḅᨬᜧ()....A.1B.y/2,C.y[3D.2....9.(2ᑖ)¢£~¤¥¦Ḅ§¨£ᑣ©¤¥¦Ḅ⊤☢«1()郑郑............................OO..;.;..^..;..;..^.A.6+4V2B.4+4V2C.6+2y/3D.4+2;;区II£10.(5ᑖ)Aa=log32,b=log53,c=@,ᑣ()-;...;.^...A.a¶=ᐔ´µ.®..;..;..D.f(x)Ḅ£±ᐵL?>¸´µ.........▅ᔁᐭ..6ஹ78⚪⚪ᐳ4⚪!"⚪5ᑖ!ᐳ20ᑖ஺¹O4⚪4ᐳ20ᑖ)O3ᑖ...x+y>0,..13.(5ᑖ)Nx,yº»¼ᩩ¾2x-y>0,ᑣz=3x+2yḄᨬᜧ....x<1,..14.(5ᑖ)A¿À>C4-4=1(a>0,b>0)Ḅ\ᩩÁÂ>y=V2x,ᑣCḄ氐abM.Ã᳛________.........15.(5ᑖ)A¬ᦪ/(%)=Ç.N/(I)=J,ᑣ2=........2/22.OO.:•.•

216.5ᑖᙊ┵ḄÍ☢ÎÏ1,Ð>Ñ3,ᑣ©ᙊ┵ᑁÎÏᨬᜧḄᳫḄ¦«.▅ᔁ----------------->ஹ?@⚪ᐳ5⚪4ᐳ60ᑖ3ᑖ17.12ᑖAÓÔᦪᑡÖanغ»Ḅ+a2=4,cz-a=8.3x16ᑖÚÖa“ḄÜ⚗yÞß26ᑖàSᦪᑡÖlog3anØḄán⚗â.NS+S=S+3,Úm.nmm+xm18.12ᑖ~måᐶç°]èéêë}~ì100ᜩVíᜩḄîïðñÓâᜩᑮ~yòóôḄõö᦮ᳮᦪ`ùᑮ¢⊤ᓫᜩóôõön|p[0,200](200,400](400,600]ÀîïðñÓ1ü216252ý510123þÿ
6784
72014ᑖᑖᜩḄ1,2,3,4Ḅᭆ᳛"24ᑖ#ᜩᑮ%&'(Ḅ)ᙳ+,Ḅ-./Ḅᦪ1ᵨ/34Ḅ5-6⊤"34ᑖ89ᜩḄ1ᡈ2,ᑣ<=ᜩ“?”"89ᜩḄ3ᡈ4,ᑣ<=ᜩ“A?”.᪷1ᡠEᦪ1FGᡂI☢Ḅ2x2ᑡὶ⊤FN᪷1ᑡὶ⊤FᑨPQᔲᨵ95%ḄWXYᜩᑮ%&'(Ḅ+,Z[ᜩḄᨵᐵ]+,“0+,>40()?A?7______n(ad_bc).______(a+b)(c+d)(a+c)(b+d)᝕P(K2>k)0.0500.0100.001k3.8416.63510.828Oo

3......oo19.12ᑖ᝞mFᙠopqABCD-F5E,FᑖᙠtDDBB11..uFv2DE=ED],BF=2FBஹ.wx:......郑郑............................oo16ᑖ[AB=BC~FEF1AC"..;26ᑖCiᙠ)☢AEFᑁ..;.^.;.20.12ᑖᦪ/x=x3—kx+k2.;.^.16ᑖ/%Ḅᓫឋ";;区f£26ᑖ8/xᨵ5F#kḄ-.-a;..;..^.21.12ᑖᙊcᔁ+ᙛ=105Ḅ᳛FA,BᑖC..;..;....^Ḅஹ⚔5.;...;.^o16ᑖ#CḄp"o;;.26ᑖ85PᙠCuF5Qᙠx=6±,v\BP\=\BQ\,BP1.出..;BQ,#A4PQḄ☢¡.;..^;.▅ᔁ;^ஹA⌱B4-4ᙶ᪗DEFᦪGHIᐳ1⚪4ᐳ10ᑖ恶摒;3ᑖ;...®...x=2-t-t2,t©ᦪv..;..22.10ᑖᙠ¢ᙶ᪗¥xOyF¨CḄ©ᦪp.;.y=2—3t+¬........t/1,CZᙶ᪗®¯A,B°5.........15ᑖ#|AB|oo..25ᑖ²ᙶ᪗³5᩽5Fxµ᩽¶·᩽ᙶ᪗¥F#ABḄ᩽..ᙶ᪗p.....▅ᔁஹA⌱B4-5JKL⌱MIᐳ1⚪4ᐳ10ᑖ直氐3ᑖ......23.10ᑖ¸a,b,c6R,a+b+c=0,abc=l...........15ᑖwxab+bc+ca<0"............4/22oo:•.•

4外o装o订o线内O装O订O线言•(2)(56)海max(a-b"C)渊川a"b♦c+3熟汁血”i£s“max{a"b"c}w

5..........OO@ᫀ?᪆Yᑖ....1.ூÈᫀ௃B....ூὃ5௃ᐗÍZÎᔠᐵ¥ḄᑨP"®ÎÐᐸÒÓ....ூÔ᪆௃ூÔÈ௃ᵫ⚪ØFAQB=[5,7,11},ᦑ4CBᐗÍḄᦪ3.郑郑ᦑÈᫀB........ூᑖ᪆௃ÛᵨᑡÜÝᑡÜÞAHBᐗÍḄᓽà...........2.ூÈᫀ௃D..........ூὃ5௃âᦪḄãäᭆå"âᦪ6ᦪæçḄè◀ÒÓOO2..ூÔ᪆௃ூÔÈ௃ê2=ë=ì(1*ஹ=ᡈ"Fᡠ²z=i.;14-t(l+t)(l-i)2.;..^.ᦑÈᫀD.;..;.ூᑖ᪆௃ᐜᑭᵨ◀ÝÒÓ#ñZ,óᑭᵨᐳõâᦪḄᭆåñᑮZᓽà..^.;;区3.ூÈᫀ௃CII£-;..;..ூὃ5௃᩽öஹpöZ᪗÷ö^...;...;.ூÔ᪆௃ூÔÈ௃êᦪ1axi+b,(i=1,2,…,n)ḄpöQᦪ1ù,(i=1,2,1••,«)Ḅ...^.;...pöḄa2ûF;.^OO;ᡠ²ᡠ#ᦪ1pöIO?x0.01=1;..出.ᦑÈᫀC.;..;..^.ூᑖ᪆௃᪷1þᦪ1Z³ᦪ1ᐵ¥ÿ
ᐵᓽ.;..;^4.ூᫀ௃C摒;;.ூὃ௃ឋḄᵨ.®..;.ூ᪆௃ூ௃"(t)=i+eX(.53)ᡠ$/(&)=i+e-0**-53)=°-95/+.;...........ᑣ0.23(f-53)_,elg..Oᡠ$0.23(t*-53)=lnl933,t*5ញ+53«66.O...ᦑᫀ;t=&?ᐭAᦪ/(t)=C_0D_531ᔠ/C)=095KHfᓽI..氐.M.5.ூᫀ௃B.......ூὃ௃KLMNḄOPQR..........6/22.OO.:•.•

6・・:・•OOூ᪆௃ூ௃ᵫ⚪ZI:sin04-^sin0+-^cos0=1j....[7|||,3.QLV3q_1yf3.z)I1n_b"ᑣ•2sin0+-2-cos0=19sin0+ঝcos0=......deᨵᡠjḄkLAᦪRlmnoᯠqr⌮ᵨKLMḄOPQRᓽIHkLA......OOᦪRḄt...6.ூᫀ௃A....一ூὃ௃ᦪvwḄᙶ᪗⊤{R|}☢ᔣvᦪvwḄ|
...DI*P.ூ᪆௃ூ௃AB=2a(a>0),$AB;ᙶ᪗᝞ᡠḄ}☢L..IIᙶ᪗-K.....:S.....OO.......一8..教.ᑣ0)¨©C.DKªOD1..........OE,......O.O....

7......oo᪷¬ᱥḄ®ឋI$¯Z.POx=zCOx=I,ᡠ$C(2,2),....?ᐭᱥ
4=4p,Hp=l,ᡠ$ᐸᯖᙶ᪗;8,0),..ᦑᫀ;/2),—..ZZz.....•ÓÔÕÄḄ⊤☢w<3x2+2V3=6+2V3........8/22.oo.:••

8ᦑᫀ;/logs25=1335ᡠ$aa,bᦋᑏ;a=

9..........OOூὃ௃ôᐗCöçÑR÷øùN}☢úê............郑郑............................OO..;.;..^..;..;..^.;;区II£-;..;..^...;.}û”-ý»y=CÑ+*þºA½È¸ᨬᜧÿZᨬᜧ,..;...^..;..ᵫ◤2,1,2,.;.^OO;ᡠZmax=3x14-2x2=7.;..出..;.ᦑᫀ7..;..^.ூᑖ᪆௃%&'()ᑭᵨ,-Ḅ/01234.;..;14^.ூᫀ௃V3摒;;.ூὃ7௃89:Ḅ;ᓫឋ>.®..;..;..ூ3᪆௃ூ3௃ᵫ89:?@£=1'ᐸᯖ7ᙠXEF.........GᐸHᩩJK:y=V2x..Oᡠe=^=Jl=V3-O.......ᦑᫀV3....ூᑖ᪆௃᪷QRS'|=V2,Uᔠ89:Wa,b,cḄᐵYᓽ'[3.氐M15.ூᫀ௃1.......ூὃ7௃]ᦪḄ_`...........10/22.OO.:•.•

10ூ3᪆௃ூ3௃ᵫfᦪḄ3᪆g'/(j)=:\_ex(x+a—1)H/i(x+a)(x+a)Ujil_e]x(l+a-1)_aesNBTt——ae=eᑣ/(ᑐH,2zHzẓyz{,τ|ஹ24(l+a)(a+1)(a+1)᦮ᳮ'a2-2a+1=0,3a=1.ᦑᫀ1.ூᑖ᪆௃ᵫ⚪1✌ᐜ[]fᦪḄ3᪆gᯠᑮᐵᦪaḄ?@3?@ᓽ'ᦪaḄ16.ூᫀ௃ᐔூὃ7௃ᳫḄ⊤☢ூ3᪆௃ூ3௃᧕Sᨬᜧᳫᙊ┵Ḅᑁᑗᳫᳫᙊ┵ᑁᑗḄE,☢᝞¡ᡠ¢,n|pᐸWBC=2,AB=AC=3,£7MBC¦FḄW7_§ᑁᑗᙊḄᙊ¨O,ᵫAM=V32-I2=2V2ᦑS.ABC=1x2x2>^=2V2,§ᑁᑗᙊr,¬111SஹABC=S&AOB+S&BOC+S>AOC=஽'ABxr+2-xBCxr+^xACxr=x(3+3+2)xr=2V23°=¥ᐸ²᝞3=ᐔ.ᦑᫀᐔ.ூᑖ᪆௃³´µ⚪¶ᓄ[3ᙊ┵ᑁᑗᳫḄµ⚪ᯠUᔠ,☢ᐸᓽ'᝕Ḅ.17•ூᫀ௃(1)3§¸¹ᦪᑡឰ¼Ḅ½¹q,

11..........1OO::;-:::‘3=1᪷Q⚪1ᨵq=3....ᡠ=3n-1....(2)3Âb=log3az=log3n-1=n-1,..ni3..Æ(0+n—1)_7i(n-1)郑郑ᡠSn=22....m(m—1)m(m+l)_(m+2)(m+3)....᪷QSm+Sm+1=Sm+3>'-2~ᓝ2H2..........᦮ᳮm2-5m-6=0,Gm>0,ᡠm=6..........ூὃ7௃¸ÊᦪᑡḄË⚗½g¸ÊᦪᑡḄÍn⚗¸¹ᦪᑡḄË⚗½gOOூ3᪆௃ூᑖ᪆௃Î1§¸¹ᦪᑡḄ½¹q,᪷Q⚪1ᑡ&?@Ï[✌.;..;..^.⚗½¹ÐÑ[Ë⚗½gÎ2ᵫÎ1[&log3%¼ḄË⚗½gᑭᵨ¸Êᦪᑡ.;..;.[½g[Sn,᪷QRSᑡ&ᐵmḄ¸ÓᐵYg[UÔ..^.;18•ூᫀ௃Î13ᵫ⚣ᦪᑖ×⊤'SØÙHᜩḄÛÜ>Ó¸Ý1Ḅᭆ᳛;区II£-;.2+-¶25=043,¸Ý2Ḅᭆ᳛5+à12=027,¸Ý3Ḅᭆ᳛.;..^...;...á◤=0.21,¸Ý4Ḅᭆ᳛â2=o,O9.;..^..;...Î23ᵫ⚣ᦪᑖ×⊤'SHᜩWᑮؽäåæḄ²çḄèᙳᦪ;.^OO;100x20+300x35+500x45;.100=350.出..;.Î332x2ᑡὶ⊤᝞ë:.;..^..;²ç<400²ç>400;.^摒;ÛÜ>Óíî3337;..®..ÛÜ>Óî228;..;.......K2=.1஺ᗸñᕡ1óx5.820>3.841'.../UXoU..Gyᨵ95%Ḅõö÷HᜩWᑮؽäåæḄ²çØÙøᜩḄÛÜ>Óᨵᐵ.OO.ூὃ7௃⚣᳛ᑖ×⊤ùúឋûüḄýᵨ....ூ3᪆௃ூᑖ᪆௃Î1᪷Q⚣ᦪᑖ×⊤'þ`&ØÙHᜩḄÛÜ>Ó¸Ýᑖÿ1ஹ2ஹ....3ஹ4Ḅᭆ᳛2ᑭᵨḄ⚣ᦪ◀1003᪷"⊤..氐$Ḅᦪ"%ᗐ2x2ᑡὶ⊤*+,K2Ḅ-./ᔠ12⊤3.M....19.ூ7ᫀ௃1:;<=>?4BCD-48E஺1,ᡠBBi1J☢ABCD3.AC1......BBi,........12/22.OO.:•.•

12<=>?ABCD-A^C^,AB=BCᡠQRSABCDT>SAC1BDO<BBiCBD=B,BBiஹBDcJ☢BBDDSឋjACLBD,᪷"=>?ឋjAClBBi,wxyAC1J☢BBMDᓽ(2){◤y}ECJ/AFᓽᙠCQ[\M]CM=2MG,/JdQRSឋjwdy}ᓽ.20.ூ7ᫀ௃(1):;ᵫ⚪f(x)=3x2—kkW0/(x)>0ឤᡂᡠ/(%)ᙠ(8,+8)[ᓫ⌴O/'(X)>o<—4ᡈ%>ᡠ/(%)ᙠ(—,)[ᓫ⌴ᙠ(-00,-J)'E8)[ᓫ⌴./(-J)>0(2):;ᵫ(1)f(x)ᨵ¡¢£ᑣk>0,¥¦15ஹ/(4)<0O

13..........OOk?+^kG>0...ᓽ¦¨:0V஽V«"|஺27........00,..郑郑ᡠf(x)ᙠ(J1,4)[ᨵ±¢£..........²ᳮ_1<,f(-k-1)=-k3-(/c+l)2<0,............ᡠ/(x)ᙠ[ᨵ±¢£......OO´/(%)ᙠ[ᨵ±¢£ᡠ/(x)ᨵ¡¢£,..;.;..^.µ[kḄ\·(0,¸..;..;..^.ூὃ௃ᑭᵨ¹ᦪẆ»¼ᦪḄᓫឋ¼ᦪ£Ḅᑨrrᳮ;;区ூ:᪆௃ூᑖ᪆௃(1)/(%)=3x2-k½kᑖkWO¾k>0¿ÀÁÂÃ3ᓽ;II£-;..;../(-J)>0.^..;.(2)/(%)ᨵ¡¢£ᵫ(1)k>0,¥Å¥,:ÇÈÉᑮk...;..^.Ëᔜ<஺.;...;.^OḄ·/ᑭᵨ£ÍᙠឋrᳮÎ}ᓽ.O;22;.21.ூ7ᫀ௃প:;...0ᨬ+¾=1(0ீm<5).出..;..;..^..;;.^摒;;.:m=ᡈm=—(Ò).®..;..;../y2......•.CḄ>Ó;Ô+Õ=1,......OᓽÖ+”V1O25+25-1...2:;•.•PᙠC[Qᙠmnx=6[¥|BP|=|BQ|,BP1BQ,....PØxÙᚖnÚM,Ûx=6oxÙÚN....᪷"⚪ÜÝ,ÞS᝞Þ氐M..................14/22.OO.:•.•

14・・・Oo.....筑........•••|BP|=|BQ|,BP1BQ,/PMB=LQNB=90°,....I•••/PBM+/QBN=90°,/BQN4-"BN=90°,O.4PBM=/BQN,..᪷"¡àSᐰÈᩩã“A4S”.一.DI*P;JPMB=JBNQ,.II,25+-25--1'-.•••B(5,0),..:S|PM|=\BN\=6-5=1,..ÛP(Xp,j>)OPåᙶ᪗yp=l,èᐸ¯ᐭëì=1,o..;◤+í=i,..一8:;Xp=3ᡈîï3,.教P(3,1)ᡈ(-3,1),堞.জP(3,1).....ᦑ|MB|=5-3=2,...一..穿•••JPMB=JBNQ,.科O|MB|=\NQ\=2,.o.:Q(6,2),..Ý,Þò᝞Þ.氐............O...

15..........OO............郑郑......................•••A(—5,0),(2(6,2),......OOômnAQḄmn>Ó;2%lly+10=0..;,|2x3-llxl+10||5|.;.᪷"ᑮmnö÷øÉPᑮmnAQḄö÷;d=—J22-=712.^.2+n.;..;.ᙠ.^.;~5;区II£᪷"¿úö÷øÉ;|AQ|=J(6+5û+(2-0)2=5V5,-;..;..^...•••JAPQ☢ü:1x5V5X^=|;...;...^..;..ঝP(-3,1).;.^Oᦑ=5+3=8,O;;..出.••JPMB=JBNQ,.;..;.A\MB\=\NQ\=8,.^..;;.;Q(6,8),^摒;Ý,Þò᝞Þ;..®..;..;.............OO.........•••ÿ5,0),Q(6,8),..氐AQḄ8x-lly+40=0M....,|8x(-3)-llxl+40|.᪷ᑮ!"#$PᑮAQḄ!"d=-----122----------..J8Z+UZ...........16/22.OO.:•.•

16|5|_571857185'᪷,-!"#$\AQ\=7(64-5)2+(8-0)2=V185,APQ☢/V185X,01ᡠ34AAPQ☢/:ூὃ௃,-Ḅ!"#$9ᑮḄ!"#$9:ᙊḄ᪗=9:ᙊḄ>ᓫឋAூB᪆௃ூᑖ᪆௃E1FGC:H+4=1
0<6<54a=5,b=m,᪷"I᳛#$4KᔠMN4ᓽPᫀ9E2PᙠC14Qᙠx=614S\BP\=\BQ\,BP1BQ,TPUxVᚖ4XM,Yx=6ZxVXN,&PMB&BNQ,Pᙶ᪗4\AQḄ4᪷ᑮQ|P5!"#$],!"#$4ᓽ^APQḄ☢/.22.ூPᫀ௃(1)B_`=0,ᑣt2+t-2=0,Bt=-2ᡈt=1(c)4ᑣy=2+6+4=12,ᓽ4(0,12)._y=0,deJt2—3t+2=0,Bt=2ᡈt=l(c)4ᑣ`=2—2—4=-4,ᓽ8(4,0).A\AB\=4(0+4)2+(12—0)2=4A/10
2BᵫE1NI^AB=0_E_g=34ᑣABḄy=3
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