2023年新课标全国卷高考冲刺数学模拟试题含解析

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2023
ὃᦪᔁ⚗1.⚪ὃᐜḄஹὃᑏ!ᩩ#ṹ%&'ᙠὃ)*ᩩ#ṹ&'+஺2.⌱.⚪/01ᵨ2B34567⌱.⚪/01ᵨ0.589:⁐<=Ḅ><4?ᑏ<@A᦮ஹ4=!஺3.Cᢥ᯿⚪FGᙠᔜ⚪IḄ⚪+JᑁLMN⚪+J?ᑏḄᫀPᦔ6ᙠ₝STஹ⚪ᔁU⚪Pᦔ஺4.Vᢝᓱ☢Z[⌕ᢚ^[⌕_ẚஹ_a[1ᵨ5ᦋcஹdefஹgTᑐ஺iஹ⌱.⚪j⚪ᐳ12l⚪ml⚪5ᑖᐳ60ᑖ஺ᙠml⚪oNḄpq⌱⚗rsᨵi⚗uvᔠ⚪I⌕xḄ஺1.yzi{|ᦪᓫ~ᦪx+2ii=y-i,ᑣ{B.y/2C.73D.7522.M0,2Ḅ/ᙊC+=1[Ḅp,Q,஺ᙠP஺{ḄᙊḄ᜜,ᑣ/Ḅ᳛kḄ¡{3.{¢£ᦪᑡ¥%§Ḅ஻⚗©,24+%+%+34+஺|2=66,ᑣ«=A.56B.66C.77D.784.yz¬ᦪz=2-,ᑣzḄ|{Z-1A.-1B.-iC.1D.iY2y25.A3{ᙊA+ᓃ=1r¯Ḅ°ὡ{ᙊḄᯖᑣ46A8☢³Ḅᨬᜧ{16925A.20B.30C.50D.606.yz¶ᱥCV=4x©஺2,0,ᑁ=¸-2¶ᱥC[A,B,8஺¶ᱥCºiE.oN»ᑨ½জ¿{Ḅᙊ¶ᱥÀÁ6ঝOBOEḄ᳛ó{-2ঞA,B,EḄᙊḄᙊ¯ᙶ᪗{9,஺¸È{Éᑣ/--=4.ᐸrᡠᨵe%ᑨ½ḄGuA.জঝB.জঞC.ঝঞD.জঝঞ

17,yzA"3uÌᦪ/͸={'"ÑÒU[ḄÓy=/xᙠA"3ᜐḄᑗÖᔠᑣxlnx-tz,x>0ᦪ஺Ḅᨬlu¸1]_A.—1B.--C.D.1228.yz×⚪஻VxeR,x2>o,ᑣØu)A.VxeR,x2<0B.3x0eR,x40.C.ÙeR,xு0D.VxÛR,x2<0.9.Ìᦪ஻x=1fx-ÜÝcosx¸ÞXHOḄÑßàá{xâânV2210.yzãÓ஺É—1=1஺>0,6ு0Ḅæஹçᯖᑖè{éஹK"¶ᱥy=2pxp>0ãÓCᨵÀḄᯖ.஺{¶ᱥãÓCḄiqÞcos/P£E=m"ᑣãÓ஺ḄÁ¯᳛{¸A.⊈ᡈ&B.⊈ᡈ3C.2ᡈîD.2ᡈ311.ïðñuᡃóᓭõö÷Ḅᦪøùúûpüḕþÿ
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2A.7B.8C.9D.1012.6஻/=ln2,஻=lg2,9!!()A.m-n>iru2>m-¥nB.m-n>m^-n>mnC.m+n>mn>m—nD.771+H>m—n>nm<ஹ>?⚪A⚪ᐳ4C⚪"DC⚪5ᑖ"ᐳ20ᑖ஺13.GHIJ┵஺LABC஺"M☢IOPABCORSTP"PA=PB=PC=PD,IJ┵ḄVWRX"ᙠZI3J┵ᑁ\]Lᳫ஺"ᑣᳫ஺VWḄᨬᜧbR.14.cᦪ/x=sin3x+3cos2xxe-e1fḄbgR.15.hḼjkḄlm"noḄpqrstᩭtv"ᡃjḄnᙳyz{|}jᡂᨵᜧz.RpḄVᏉ"ᔠᳮᑴ᪥Vplmᑜ"Lᐰz}ᵱpyz¡¢£¤"ᦪ¥¦§ᐰ30000¨z}ᵱpḄyz<ᓫªḄ«¬S᝱ᑖ®N172Q2,±P172<"180=0.4,³´Zyzzµ180cmḄz}ᵱpnᦪᜧ¶R.16.z}ᐳᨵ1800n"ᐸ}zLஹz<ஹz¸¹ºḄnᦪ»ᡂ¼½ᦪᑡ"ᵨᑖÀÁ᪵ḄTì}ÁÄ60n"³´z<¹ºÅÁÄḄnᦪR.

3¸ஹÆÇ⚪ᐳ70ᑖ஺ÆÇÈᑏÊᦻÌÍÎஹÏÎÐÑᡈÓÔÕÖ஺17.(12ᑖ)GHcᦪxe(0,+oo).(1)×Ø/(%)Ḅᓫ£ឋ(2)ÚÛ“X)ᙠÜ(2,/(2))ᜐḄᑗÛß᳛R3(e2-l).(i)á஺(«)ã(x—Z)ra)Z—(x+l)2,á᦮ᦪåḄᨬᜧb.x=1+V2cosco18.(12ᑖ)ᙠæçᙶ᪗ê}"GHÚÛ஺ḄëᦪTÑR(஺Rëᦪ)"ìíÜR᩽Ü"ïḄðñy=l+v2sin^òïR᩽ïó᩽ᙶ᪗ê"ôÛ4Ḅ᩽ᙶ᪗TÑR8=[(-ôÛ/"Ḅ᩽ᙶ᪗TÑR஺=a+£.Vo072(I)ᑏÊÚÛCḄ᩽ᙶ᪗TÑ"õᢣÊ÷øùÚÛ(II)ãôÛ4ÚÛCúµ஺ஹAûÜ"ôÛ4ÚÛ஺úµ஺ஹ8ûÜ"áA4BO☢WḄÄbý.19.(12ᑖ)GHᦪᑡþ%ÿ
q=5,4ᵨ+2=2%.(1)ᦪᑡ
6,Ḅ⚗;(2)=஻(2%4),ᦪᑡḄ஻⚗S“.20.(12ᑖ)ᦪ/()=sin2x+—+cos2x+sinxcosx.6ᐔপব.‘ᦪ/পḄ"#;(2)A,8,C$Ḅ%&ᑁ()/m=|,cos(A+C)=—+)cosCḄ";71-V3cos2xeR21.(12ᑖ),-ᦪ/(x)=cosx-sin.+934(I)/(x)Ḅᨬ12ᕜ4;(II)ᙠ-7Ḅᨬ1"ᨬᜧ".22.(10ᑖ)᝞:);%<=ABC-AqG>)஺,AᑖBCA3,3ᱏḄ>E)AA.=AC=CB=—AB=.2

4(1)>?@8஺|||C☢4஺஺E(2)F☢G஺-AC-EḄHI.JὃLᫀ/ஹ⌱O⚪@Q⚪ᐳ12S⚪TS⚪5ᑖᐳ60ᑖ஺ᙠTS⚪*ḄU0⌱⚗Vᨵ/⚗Xᔠ⚪Z⌕Ḅ஺1.Dூ
᪆௃/ஹX——1+-2+xi=,[y=-2ᑣ,/]=_1+24=6.ᦑ⌱D.2.Dூ
᪆௃abc/@y=kx+2,P(x)y),Q(x,y),ᵫfg஺ᙠhPQ:biḄᙊḄ᜜lmno.o0,ὶqbc22

5/GHᙊCKL)MᔠOPQᳮ)ᓽTUVᫀ.ூYZ௃\ᯠ;^x=0a
ᩩc)ᦑT;^/ey^kx+2,f+2—]Pj%,ym,Qx,y',ᵫ<2)Uj1+2᮱r+8᱐+6=0,22y=kx+2v=64/-24j1+2%2m>0,kᡈk<,228Z6"+LF)>2=KTT•••00,&.OPOQ=%%2+%%=%~+j@+2mjAx+2m26jl+£m_16^10-2^+4==j1+&2mX[%2+2ZjX]+9m+41+221+2/1+2•••ZU-<&<6,([2\([7;^/Ḅ᳛kḄ"$ZeUg,ᦑ⌱eD.ூE௃⚪Z⚪ᐵCHᙊḄẠ-ᙊ┵^G;^¡E¢⚪£)¤ᵨ;^ᙊ┵^ὶ¦KL§)¨OPQᳮ©¦ª«᪗Ḅᐵ)ὃ¯°ᑖ᪆²³´µ²³)¶·>᫏⚪.3.CூZ᪆௃᪷»+¼ᦪᑡḄឋ¾TU2(%+%+%)+3(q+«)=6a$+=66,ᓽ%+4஺=11,12ᡠÄS4=14(4E4)=7(4+q஺)=77,ᦑ⌱C.44.AூZ᪆௃

6ᑖvᑖwxyᑖwḄᐳᱥ{ᦪᓽm.ூ~௃2i(i+l)-2+2il-i,ᦑzḄl:/1.i-1(i-l)(i+l)-2ᦑ⌱@A.ூg௃Q⚪ὃ{ᦪḄ◀ὃ/⍝᧕⚪.5.Dூ᪆௃ᐜaAgḄᙶ᪗:(x,y),᪷ឋmn8(-x,-y),ᙠ⊤&ὡAB☢ᵫ%ᑴgAᙠᙊḄ⚔g,ὡA8☢ᨬᜧ£¤ᔠᙊḄ᪗¥¦'ᓽm.ூ~௃ᵫ⚪§aAgḄᙶ᪗:(x)y),᪷ឋmn8(-x,-y),ᑣᱏABḄ☢:S=Ëx|0F|x|2,y|=c|y|,3ᨬᜧᱏ43Ḅ☢ᨬᜧᵫ%mªgAᙠᙊḄ«¬⚔g®48Ḅ☢ᨬᜧ,22¯ᵫ°+ᓃ=1,mnᙊḄ«¬⚔gᙶ᪗:(0,-5),(0,5),16925ᡠhAF,ABḄ☢Ḅᨬᜧ:S=cb=V169-25x5=60.ᦑ⌱@D.ூg௃

7⚪Ï⌕ὃ¯°HᙊḄ᪗ÑKLÒÓᓫḄÕÖឋ¾)ÄÒ%(×☢ÙḄÚᵨ)ḼÜὃ¯°ᦪ×MᔠÝÞ)ÄÒᓄàGáᓄÝÞḄÚᵨ.6.Dூ
᪆௃ã·জ)ᑭᵨæᱥ^ḄQè)ᑭᵨ4=᦮&="ᵬ§ëì=/?TᑨïË222ã·ঝ);^ḄKL$ñ=my+2,Gæᱥ^ὶ¦)ᵨᙶ᪗⊤õ;^08G;^0EḄ᳛÷Ù)ᓽTᑨïËã·ঞ)ùx=jy-2úᐭæᱥ^CḄKLTU)³ü=8,ýþ)%=%)ᑭᵨOPQᳮTU|8ÿ2=16/+48+32,ᵫ/,ᵨm⊤r2,ḄᚖxḄᓽᙊ!I2N%&ᙶ᪗)2m2+4,*a,ᓽᑨ-.ூ
௃᝞0123)4ᱥ஺Ḅᯖ183E):;Ḅᙊ)<1ᑣᙊ!M)8EḄ.23,Eᑮ@ḄABᑖD)41d,O”ḄG;)R,Mᑮ@ḄAB)",2Jᯠ3,E,3LMᐳ1ᑣ஻=4±&=RSTUVᓛ!=Y.ᡠ8জ\].222ᵫ⚪_2:DEḄ`a)x=b+2,cᐭ4ᱥ஺Ḅ`a1ᨵV—4/2-8=0.23,£Ḅᙶ᪗ᑖD)k,y%,mn%1ᑣ,+%=4᪷1q%=r8.ᡠ8᳝=b1+2%tk+2%=.qn+2mX+%%+4=4.

8ᑣbcOB®bc0EḄ³᳛y:"=-2.ᡠhঝ·¸.£஽ºx=7-2»ᐭ¼ᱥcCḄ¦'mn%y=8,½¾%=-%•᪷¼ᱥcḄឋmªA,EÁgᐵÃxÄᡠhÅgA,B,EḄᙊḄᙊÆNᙠxÄ«.ᵫ«ᨵÇÈ+h=4᪷+x=4/TI2+4,2ᑣ|BE|2=6+x)?—4XjX+(É+y)2-4>Ê=16m4+48m2+32.222ᡠhcËÌḄᚖc®xÄḄÎg(ᓽᙊÆN)Ïᙶ᪗:2/7/+4,ᡠhQ=2஻Z2+4.Ãr2=\MN|2=2/2+4—+(21^21)+4m4+12.2+8,»ᐭX+%2=4"ᔆ+4,X+%=4Ñ>nÓ=4m4+16M+12ᡠh//Ó=Qᶭ+4Õ/(4Ö4+164+12)=4.ᡠhঞ·¸.ᦑ⌱@Dூg௃Q⚪ὃ+¼ᱥcḄឋØÙᔠὃ+Ùᔠᑖ᪆ÚᓄᑜÝᦪÞ¤ᔠᦪḄßÃà⚪.7.Bூ᪆௃ᐜ᪷áᦪḄâã§äᑏ/(x)ᙠA8ÁgᜐḄᑗc¦'£ᑭᵨÁbc³᳛èéêëìíèéᑡᐵï᪛,½¾n4=3(H/02ñ)òóᦪg(x)=(J—e2x)(%«0),¤ᔠáᦪᨬSᓽm⌱·¸Lᫀ.ூ~௃@x40f(x)=x2+x+a,ᑣô(x)=2x+lx>()f(x)=xlnx-aᑣõ(x)=lnx+LaA(XJ(XJ),8(X21/(X2)):óᦪ%ö«ḄÁgᧅ<஽<0ᡈ0<%|<%2/'(%|)஺/'(û2)1üXᔠ⚪§ᦑ°ý<0<%2.ᑣ/(X)ᙠAᜐḄᑗc¦':y-(x+X1+a)=(2X|+l)(x-xj/(x)ᙠ8ᜐḄᑗc¦':.Õ/°2௃11°2+0=(111*2+1)(%-%2)ᵫÁᑗcþᔠmª

9Inx2+1=2%j+1/᦮ᳮ*a=1(%,2-e2M)(<0).M2g(x)=i(x2-e2x)(x<0)%,2-X-Q="᳝2ᑣg'(x)=x-e2',g"(x)=l-2e2*,ᵫg"(x)=஺*x=glngᑣx=ln1g'x%Ḅᨬᜧ)g'^InM=MrM<0.!%8*%=3/—021%ᙠ-<»,0Sᓫ¡⌴£1ᑣ“2g0%=r.ᦑ⌱:B.ூ©௃«⚪ὃ®¯ᦪḄ±²_³1ὃ®´ᳮµ¶·¸1ὃ®¹ᦪ`aஹᑖ»᦮ᔠஹ½ᓄᓄ¿ÀÁÂ`Ã.«⚪ḄÄÅÆÇ஺ÈkḄ¹ᦪᐵÊË.«⚪Ḅ᧕┯ÅÎÏ.8.BூÐ᪆௃᪷ÒᐰÔÕ⚪Ḅᔲ×)ᱯÔÕ⚪1*ᑮÙÚ.ூÛÐ௃᪷ÒᐰÔÕ⚪Ḅᔲ×)ᱯÔÕ⚪1*ÜpT/eR,ᱏ40«⚪\]⌱⚗Bூ©௃«⚪ὃàáâḄÕ⚪Ḅᔲ×1ãäåẠ⚪.9.DூÐ᪆௃è)/-x%=-x+T%cosx=-x-L%cosx=-/x%,ᦑ¹ᦪÅ᜻¹ᦪ1ᡠ8᣸◀A,Bï*=ð1IJXXf7T=^--%COS71=-571--%<0,ᦑ⌱D.71ᐔὃ1.¹ᦪḄå«ឋó2.¹ᦪḄ0ô.10.DூÐ᪆௃2¿ᑴ=t1|᪻|=஻1᪷Òcos/3ὡgÈ4ᱥឋó*Ç|Üᵨ=*஻1᪷Òøùឋó*Çt=7a,஻=5a,ᨬû᪷Òüý×ᳮᑡ`a*Ç஺ஹcÿḄᐵ᳛.ூ௃

10PᑖᔣXᱥḄᚖᚖᑖMஹN,!"#|Pὡ|=᪻|%|=஻,ᑣᕜ=|PN|=|-.=/ᵨcos/Pg=ᓧ,•.•P234Ḅ5ᑣ6ᕜ7|-8=2a,ᓽ:--f=2஺஻z=7஺,஻=5a,=>ᵨ=2c,ᙠ@-;BCᵫEFGᳮ2=49ஹ+4ᔆ725K72x7ax2c᦮ᳮ-5ac+6cJ=0,ᓽ/-56+6=0,Qe>l,e=2ᡈe=3.ᦑ⌱PD.ூ5Q௃R⚪ὃUV23᳛ḄWXY23ᱥḄZᓫឋ]ὃU^_W`abcC᫏⚪.11.Bூ᪆௃ᑡghḄi7jᵫklḄvm.ூ௃ᵫ⚪nPlᐭ஻=3,x=l,v=2,m-3tp7qghv=2xl+3=5>஻?=3-1=2,஻=3—1=2,rsghtpuqghu=5xl+2=7,v=2-1=1,஻=2-1=1,rsghtpwqghu=7xl+l=8,஻?=1—1=0,n=\—\=0,xghtlu=8.ᦑ⌱PB.ூ5Q௃R⚪ὃU᪷z_{᪾}~_lm7⌕ᑡ_{Ḅi7jὃU~_`abcẠ⚪.12.D

11ூ
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௃Pv=In2,஻=lg2,ᑣv,஻«0,1),ᡠm+n>mnm-\-n>m—n9911111sl1101cl=------=T"77=log21°Tog2e=log2—>log22=l,nmlg2m2em-n<ᓽ----->1,ᑣm-n>mn,mnᓽm+n>m—n>mn9ᦑ⌱PD.ூ௃R⚪ὃUV!Ḅឋ]Yᣚ@bẠ⚪.uஹ⚪PR⚪ᐳ4⚪i⚪5ᑖᐳ20ᑖ஺13.9ᐔ12ூ
᪆௃ᵫ⚪┵┵P—ABCD,┵ḄP”PE,HE,ᑣᳫ஺ᙠᵨ£Ḅ-”¢4:NOEH=®,ᵫᳫ£┵Ḅᑁᑗᐵ=26,#A8=2a,ᵨ஺஺⊤§┵Ḅ¨©஺஺Ḅᐵª⊤§ᑁᑗᳫḄ«¬W«¬ḄᨬᜧmªWᳫḄ¨©Ḅᨬᜧm.ூ
௃:NOEH=e,AB=2a,ᵫᳫOᑁᑗc┵APEH=2e,EH=a,ᑣP஻=atan2஺ᳫOḄ«¬R=atan9,.1.->__2^6TVP-ABCD=]x4trxatan2஺=-y-l-tan2^

12V6tan2-tan?04~16êÿtan6=
ᡂ,2ᓃ=+ᐔ^~=^~ᐔ.°31612ᦑᫀ&ᐔ.12ூ௃⚪ὃ┵Ḅ⚪ᑁᑗᳫ⚪ὃ"#$%&'()*+Ḅ,"-.⚪.-6-3G;14.--^-,3Oூ0᪆௃ᑭᵨᣚᐗ67ᑮg(t)=t3-3t2+3,te-y,l,ᑭᵨ9ᦪ;7<ᦪg(t)Ḅᓫ>ឋ@ᨬBᓽD7ᑮ<ᦪḄBE,7ᑮᫀ.ூF0௃ᵫ⚪HD7f(x)=sinஹ+3cos2x=sin3x-3sin2x+3,x£Lᐰᱏ'4,t=sinx,te--^-,1,ᓽg(t)=F-3t?+3,tG--^-,1ᑣgÌt)=3t2_6t=3t(t-2),—#o,0o,ᓽy=g(t)ᙠ-S,0T<ᦪᙠÌ0,1ÓU<ᦪ

13=g17¥)=6g(O)=3,g(l)=l,ᦑÕᦪḄm×P⁐Ù,3.ூ5Q௃R⚪Ú⌕ὃUVwÛÕᦪḄᨬmYᑭᵨÝᦪẆßÕᦪḄᓫàឋ£ᨬmᐸCâCᔠᳮᑭᵨᣚᐗ{ᑮÕᦪg(f),æᑭᵨÝᦪWÕᦪḄᓫàឋ£ᨬmçâḄᐵèḼêὃUVëᳮ£⚜_`abcẠ⚪.15.3000ூ
᪆௃᪷z᝱3ḄîïឋWPðñ180),ªWòc180cmḄCᵱôõᦪ.ூ
௃Pᐰ÷30000øCᵱôḄòJ(ᓫùP஺v)ú᝱ᑖûN(172,஺(172஺ü180)=0.4,1—04x2ᑣ-
180)=V=0.1,÷òc180cvnḄCᵱôõᦪᜧý30000x0.1=3000.ᦑâᫀP3000.ூ5Q௃R⚪ὃU᝱3ḄîïឋḄÿᵨ
Ạ⚪.16.20ூ
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௃"#ஹஹᦪᑖ&'ᑣ2Z?=a+c)a+Z?+c=1800,*+8=600,ᵨᑖ,᪵Ḅ./060
1230Ḅᦪ'60x4=20.1800ᦑ7ᫀ'+20.ூ:;௃=⚪ὃ?ᑖ,᪵@⚪Ḅ*
ABᑮᦪᑡḄDᐵFG
HIẠ⚪.ஹ*7⚪+ᐳ70ᑖ஺*7KᑏMᦻOPQஹRQSTᡈVWXY஺

1417.(1)ᙠ(Ina,+oo)WTVᙠ(0,Ina)WUV(2)(i)1\(a)2ூ
᪆௃(1);9;X/(%),]஺ᑖ`ab;X/'(x)>0,/'(x)<0Ḅ0ᓽD7XcbV(2)(0ᵫ/(2)=3(e2—l),;X஺ḄBV(H)ᵫ37ᡠ;⚪fᓄ(h-i/-1)+%+12(),XG(0,”)ឤᡂkg(x)=(x—Q(e=1)+X+1,XG(0,+a)),l◤g(x)min20,᪷og(x)Ḅᓫ>ឋᓽD;0.ூ
௃(1);(x)=(x+l)k*-a)aWlr(x)>0,ᓽ“X)ᙠ(0,+pWTVa>lx>

15a,f'(x)<0,0-(x+1)2,ᓽ(x-6(e*-l)+x+120,ᓽg(x)=(x-£>(e*-l)+x+l
l◤gWming'(x)=(x-r+l)e*h<1g'(x)>0,g(x)ᙠ(0,+஺)ᓫ>⌴T,ᡠtg(x)ுg(0)=lு0vw⚪HVx>1g'(x)>0,x>k-l,g'(x)>0,0⌴Uᡠt//(/:)<0ᡠt//~)ᙠ(1,f)Wᓫ>⌴UA(l)=1>0,஻(2)=3-eு0,஻ব=4-/<0

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