2023年上海市高考考前模拟数学试题含解析2

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2023
ὃᦪᔁ⚗1.ὃ⌕ᑏὃ஺2.⚪ᡠᨵᫀ!ᡈ#ᑏᙠ⚪ᓱ&'ᙠᔁ&()ᦔ஺+,-ᑖᵨ2B01(2+3-ᑖᵨ4⁐67Ḅ961(஺3.ὃ:;<'ὃ=ᔁ⚪ᓱ>ᙠ?☢&'ABὃᕒᦈE஺,ஹ⌱H⚪IJ⚪ᐳ12L⚪'ML⚪5ᑖ'ᐳ60ᑖ஺ᙠML⚪NOḄPQ⌱⚗R'Sᨵ,⚗TUᔠ⚪W⌕XḄ஺1.YA6CTᓫᙊ஺&\]Ḅ^Y'_`0஺a_`A8bcᙊᑁ,YM,eOC=mOA+nOB,m>0,n>0
,/n+n=2,ᑣNAOBḄᨬLij
2.᝞l'/WCRm4=2N8=60஺'Y஺ᙠBC&'ZS4£>=30°,=no஺pA0qrsᑮ^u┵8—ADC,A.a<3<2aB.2a

15.ᦪz(l+3i)z=(l+i)2,ᑣ|z|=()ARMVioA.----B.——C-------Dn.------45256.ᙠRḄᦪ஻x)=ᙠ(0,+ᦪ/(ᑖ+2)4/(—1)!"xe[l,2]ឤᡂ%ᑣ”Ḅ'(*+3Jτ1ே-g,0D.[0,1]A.——,-1B.-1,——C.227.ᙊV+y2-6.-7=0/0ᱥ2V=2pxp>0
Ḅ324ᑗᑣ஺Ḅ(7
IA.1B.2C.-D.428.20208ῃ:;<=ᡊ=?@8AB7CDEFG᪗FIᵬஹLஹMஹN4OPQR⍧ᑮAஹBஹCUV:WXᢄ:⌕[\V:WX]^ᑖᑮ_`ᑣᵬaR⍧ᑮAXḄᑖbᨵ
A.6dB.12dC.24dD.36d9.0ᱥ2y2=2pxp>0
,e70ᱥ2ḄᯖgMN7hᯖgḄi|஺e|=1,|MN|=8,ᑣAOMNḄ☢l7
A.2^2B.35/2C.4,^2D.-^ߟ

2V-2V210.pᙊ+ᓃ=1Ḅᯖg7ὡsgPᙠpᙊIeg1=2,ᑣ/ὡ஺yḄᜧ{7
92A.150°B.135°C.120°D.90°11.᡻}᝞ᡠḄ᪾Ḅ7
12./x
=Acos«yx+e“A>0,cy>0,|ḄQᑖ᝞ᡠᑣ/x
Ḅ⊤
371A.2cos_1+_B.2cosx+—24I43C.2cos2x----D.2cos—x----I424ஹ⚪⚪ᐳ4{⚪\{⚪5ᑖᐳ20ᑖ஺

3A113.ᙠA4BCR'ᑁA,B,CḄᑖTa,b,c,J3.c1=a1-\-b~-yflab>a=8,sin—=—,ᑣ஺=.23222rv14.ᙠ☢ᙶ᪗¡xOyR'¢£_0,ᓃ=1(>0)Ḅ,ᩩ§¨_©ªj«3¬XᑣQ=_____.a43ry215.ᦪᑡ®,°Ḅᔜ⚗ᙳj³ᦪ'´*°jᦪᑡq¯Ḅ¶஻⚗'e஺,ᵨ=-q=l,ᑣ—a”16.¸¹ºḄ^»l᝞lᡠ¼(ᓫI஺¾)'ᑣÀ¸¹ºḄ⊤☢ÂTcm',ºÂTcmJ□I-----4-----112T³»lûlûl^ஹÄ⚪Iᐳ70ᑖ஺ÄÅᑏOᦻ6ÇÈஹÉÈʪᡈËÌÍÎ஺17.(12ᑖ)᝞l'ᙠAABCR'AB>BC,ZABC=120°,AB=3,NABCḄᑖ_aACbcY஺'BD=1.---------------------B(I)XsinA(D)XMCDḄ☢Â.18.(12ᑖ)ᙠᙶ᪗¡xOyR'Ïᙶ᪗ÐYj᩽Y'xÒḄÓÔÕÒj᩽ÒÖ×᩽ᙶ᪗¡2£_GḄØÙ©ªjx=J3cos0.(X-l)2+y2=l,£_C2ḄÚᦪ©ªjL”jÚᦪ).y=y/2sin஺(I)X£_GCiḄ᩽ᙶ᪗©ªI(II)ÝÞ_ß5஺>°)ᑖa£_Gâbc4,8zY'X|A8|Ḅi.19.(12ᑖ)ᦪF(x)=-L3+x2+2a,G(x)=a

4x,Ý/(x)=F'(x)-G(x).(1)ã஺=,3ä'Xᦪ“X)Ḅᓫåæç;

5(2)Ý©ª_f(x)=c(ᐸRcjêᦪ)Ḅz᪷ᑖj%᜛(஺í4)ÉÈIyHE±£j.0(:r‘(x)T/‘(X)Ḅðᦪ)20.(12ᑖ)ñᙊ஺
+•=10஺ò0)Ḅóô᳛jö'Y÷(—I,ùúᙠñᙊ&.(I)XñᙊḄ᪗û©ª2(II)Ý_y=H+஻?bñᙊCczY'_`ABḄRY”ᙠ_x=l&'XÉI_`ABḄRᚖ_ឤÊÿ.21.(12ᑖ)ZeR,ᦪg(x)=Z(x-e),ᐸeᯠᦪḄᦪ.X(1)ᦪ/()=-------1-lnxজᦇ=-1,ᑨᦪ/(X)g(x)Ḅᙠ(1,6)!ᔲᨵ$%ঝ'()*+ḄkeR,,-y=g(x)./!y=/(x)Ḅᑗ-%(2)ᦪ஻(x)=2x-xlnx+xg(x)-eAx,ᑨᦪ2(x)!ᔲ3ᙠ᩽5673ᙠ7'89Ḅ:6<%/3ᙠ7=>?ᳮᵫ.22.(10ᑖ)ᙠ᝞ᡠDḄEFG7☢BEFIJK7L☢ABC஺NῪPK7ABIICD,AB=2BC,஺AEḄ.(1)'()4஺/L☢஺஺/%(2)NABC=60஺7AC±FB,'8cL☢QᡠᡂSḄIT6.

6VὃXᫀ_ஹ⌱¿⚪⚪ᐳ12{⚪\{⚪5ᑖᐳ60ᑖ஺ᙠ\{⚪ÀḄÁV⌱⚗ÃÄᨵ_⚗Åᔠ⚪G⌕[Ḅ஺1.Dூ
᪆௃ᵫ⚪ÈÉ1=m2+n2+2mncosZAOB%ÊᑭᵨÍᓽÏ[Ð.ூ
௃I0C-mOA+nOBÑÒÉ1=ÓÔ+2+2mncosZAOB,n/.cn1_஻,_஻2l-(m+n)2-\-2mn33.1cosZAOB=----------=-------------------=---------+1<------------------+1=__2mn2mn2mn2x(m+n)21(ÕÖÕm=n=\×Øᡂ%)0

7ᵫ⚪ÏÉhg3åöAO"g£,h8,åC஺Ḅᚖ2ᚖ7஺ᑣ᧕Éc=P=^DO.ùCO=1,ᑣᨵ3O=AJD=2,DE=\,BE=4i,ÏÉA8'=A8=26BD=BD=2.•sina=,sin”úAB'DB'sin=5/3sina>sina,J3>a)•.•஺᜛€|0,ý],sinae[O,^]sin2a=2sinacosa=2sinajl-si"2a>2\Jl-sin2ae[V3,2],sin2a..gsina=sin/2a..(i.ÿ
a?ᑮAᫀ.ூ
௃ᵫ-%4ᡂ7:ᦪᑡE=G•&ᓽ(q+2d)2=q(q+5d),L-d/0,0M=4.ᦑ⌱A.

8ூ[௃]⚪ὃ_`Naᦪᑡ7NcᦪᑡḄd]eḄfg7+ᙠὃ_hiḄfgj2.4.Aூk᪆௃]⚪mᵨ᣸◀q)ᵫ/ᑶs=᣸◀⌱⚗DR᪷wᱯy6/0᣸◀⌱⚗C;ᵫx>0,zx▲|}~஺7/(2<()᣸◀⌱⚗BRூk௃2*-2-,~⌱⚗Dᵫ⚪+7ᦪ/(x)=y=|x|-cosx557r(5)22~⌱⚗C/s)=>0,ᦑ⌱⚗C᣸◀;T~⌱⚗B>0,zx▲|}~07cosx|}~1<0,2'-2">0,/(x)<0.ᦑ⌱⚗B᣸◀;ᦑ⌱⚗:Aூ[௃]⚪ὃ_ᦪk᪆ᩖḄḄᑨ;ᑭᵨᦪ᜻Ꮤឋஹᱯy6ḄINᨵᐵឋ¢£¤⌲᣸◀!k⚪Ḅᐵ¦;§~᫏⚪.5.Dூk᪆௃31ᐜᓄ«z=1+gi,¬'|z|k.ூk௃

92i2i(l-3i)3j_.z------~10--5+51l+3iᡠ|z|=®.ᦑ⌱)Dூ[௃]⚪®⌕ὃ_ᦪḄ°g±²Ḅfg7+ᙠὃ_hi³´µ¶Ḅᳮk·¸¹L.6.Aூk᪆௃᪷w᜻Ꮤឋº»±ឋ¢ᑨ8ᦪᏔᦪzᙠpF,0r!¼ᦪ7ᵫ½/Nᓄ-1¾+241Rᑭᵨᑖ3131ÀÁeq-4஺4-7'ÂḄᨬᜧ6±—-Ḅᨬ56ᓽᑮÈÉ.XXXxூk௃•••/pXr=/p-%r.,/ËXrº»ᙠRḄᏔᦪ7ᐵ~Ì'ÎÏГXrᙠppr,+er!ÑᦪË2ᙠp-8,0r!¼ᦪ,.,/pax+2r0rḄæ-çᑗ7ᑣᙊép3,0r,êë4,᪷wçᑗµ7ᙊéᑮ,-ḄìÀN~êë7µPḄ62,⌱B.ூk௃=ᙠíᐭkï8.B

10ூ
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Ḅᑖᦪ.ூ
௃᝞ᵬᓫᑮA
ᑣᦪᨵ.᝞ᵬᑮA
ᑣᦪᨵCRxAR=6.ᦑḄᦪᨵ6+6=12.ᦑ⌱Bூ௃⚪⌕ὃ!"᣸ᑡ%ᔠḄ'()*+Ạ⚪.9.Aூ
᪆௃᪷.|OE|=112=434ᑭᵨ7ᱥ9Ḅᯖ;<=>?@ABC☢E=>FGᓽ1.ூ
௃ᵫ⚪J127ᱥ9KLV=4x,MN/P᳝,ySNNp%2,%Sᑣᵫ7ᱥ9TU2,MNHME|+|NF|=jq+W2+2,|X|=8ᑣZ+஽=6.ᵫV=©\yr2=4%r,y}=4Xᑣy+£=24.2]MNL^ᯖNḄ_ᡠ?y%=Yᑣ|%=c+@-2%=40,ᡠ?ττeW=2⊈.ᦑ⌱AூNh௃⚪ὃ7ᱥ9ḄKjᵨklὃmᯖ;<=>n.)*o᫏⚪.10.Cூ
᪆௃᪷.qᙊḄTU1\|P4|=4,s6|=2t4ᑭᵨu_Tᳮᓽ1\ᑮwx.ூ
௃ᵫ⚪Jsᵨ=2஽yᵨ+|z{=6,]||=2,ᑣ|zὡ|=4,……ᔩ᱃/GᦑN-P6=120°.

11ᦑ⌱c.ூNh௃⚪ὃqᙊḄTUὃu_Tᳮὃ~()*+Ạ⚪.11.DூG᪆௃ᵫK᪾TK1\wx.ூG௃᡻K1\s=o+J+/+/+/=ᔁ.ᦑ⌱D.ூNh௃⚪ὃK᪾.G⚪1K~Ḅᓄᯠ1\wxl1?ᵫK᪾TKᯠFG.12.DூG᪆௃ᵫFA?@ᦪ)=/(x)ḄᨬᕜTḄᑭᵨᕜ=>1F\জḄᯠN,21Ḅᙶ᪗¢ᐭᦪy=/(x)ḄG᪆>wᔠ஺Ḅ¥§F9Ḅᵫ¨1\ᦪy=/(x)ḄG᪆>.ூG௃ᵫ1\A=2,ᦪy=/(x)ḄᨬᕜLT=—.•.0=2©=ª.N(¬,2¢ᐭᦪy=/(x)ḄG᪆>\/ড=285®2+9¯2,\cos(e+?)=l,7171717137771cᑍ---<᜛<9/.-------<67H<9|᜛~1-0.(P=-------992244444°¨஻x)=2cosg-1].ᦑ⌱D.ூNh௃⚪ὃᑭᵨFABᦪG᪆>ὃᑖ᪆±⚪²G³±⚪Ḅ)*on⚪.

12ஹ⚪⚪ᐳ4⚪⚪5ᑖᐳ20ᑖ஺13.9ூ0᪆௃L-ᵫᳮᓽ
C=ᵫsin4=
cos4=2ᓽ
sinA,ᑭᵨ¢ᳮᓽ
£¤.42323ூ¥0௃A1ᵫᳮ=6+¦-2abcosC#=4+¨2©஺ᓃ
cosC=——sinC=——)-2-322A2V2..c•AA4V2f»®acᵨ¯cos—=----».,.sin=2sin-cos=-----%ᵫ°ᳮ-R--=—~~—•»c=9.23229smAsinCᦑAᫀ³9.ூ௃⚪ὃ¢ᳮᙠ0´µḄ¶ᵨ·¸¹.14.3ூ0᪆௃22º»Ḅᯖᙠx½¾¿³y=±—x,£ᔠ¾¿Âóy=-x
a3ூ¥0௃Ä2V222ųº»'—=1(a>0)Ḅ¾¿³y=±—x,Æᩩ¾¿Âóy=-x,a4a3ᡠÈa=3.ᦑAᫀ³3.ூ௃⚪É⌕ὃº»Ḅ¾¿Ë̺»ḄᯖÍÎᑏк»Ḅ¾¿ÂÃḄ*¶´<Ñ0ḄᐵÒÓÔὃᦪ(Õ?Ḅ᪶×ØÙ.15.63ூ0᪆௃*%=^஻cN*)Ý©ᓄß
à=2,á᪷67:ᦪᑡâ஻⚗#;<Ý©0ᓽ
³+1%ூ¥0௃ᵫ4+1="a”+:=2aj=>a,,J-a)=a)+a-a„tn+i

13=(%+i+4)(%+´µ)=a.(a„+«„)=>=«„=>—=2+1°nᦪᑡè4éL✌⚗Lq=1,=¸q=2Ḅn¸ᦪᑡ§6="J4)=-(I)=63\-q1-2ᡠ?$6=63ூNh௃⚪ὃn¸ᦪᑡ+ḄFeᜐᳮºᩖ°>k¼ᵨ+L°>ᑖG½ᑖ஺¾G⚪¿ÀÁ§Ânòn¸Ḅ+ឋ¿16.20+44,8ூ
᪆௃S=2X-X4X2+2-+4X2+2x24=20+4+Å⚪ᑖ᪆ᵫ⚪J\ÆÇÈLAÉÊᦑᐸ⊤☢E2P=-X4X2X2=8cÈE2,ᦑÍ20+4,,8ὃN1.AΪ2.ÏÐÆÇÈḄ⊤☢EÈE.AஹG"⚪ᐳ70ᑖ஺G"jᑏᦻÕÖ|ஹ×|^KᡈÙ(ÚÛ஺17.(I)ܪ(II)-.148ூ
᪆௃Å⚪ᑖ᪆(I)ᙠAA5஺oᵫu_Tᳮ\AO=J7,ᵫ_Tᳮ\Þ=.,1\G;sinAsinZABD(II)ᵫ(I)12cosA,àá\sinC,ᙠMCDoᵫ_Tᳮ\5C,ᡠ?ABC஺Ḅ☢ES=-xBDxfiCxsinZCBDᓽ1\G.2Å⚪G᪆(I)ᙠoᵫu_Tᳮ\AD2=AB2+BD2-2ABxBDxcosZABD=9+l-2x3x\x-=l,2ᡠ?Aâ"ᵫ_Tᳮ\ä=åBDxsinZABDG.,ᡠ?sinA=AD/~IT5(II)ᵫ(I)12cosA=Jl-sin2A20'

14ᙠA48CµsinC=sin(120°+A)=Æ—=.'7227722x/77,,ABBC“ABxsinA3ᙠABCD2,ᵫ¢ᳮ----=-----,ᡠÈ3C=---------=—.sinCsinAsinC2ᡠÈASCDḄ☢óS=ôxBOx6CxsinNCBO=Lxlx3x^=^.2222818.(I)஺2cos6=0,2p2cos26»+3p2sin2^-6=0;(II)|AB|=^-^3ூ0᪆௃(I)᪷6᜛2=õ2+),2,õ=᜛È^ö÷=᜛5m6,
»GḄ᩽ᙶ᪗ÂÃᯠýᐜ>?»C2Ḅÿ
ᨬ᪷᩽ᙶ᪗ᙶ᪗Ḅᓄ.(II)ᑖ©"᩽ᙶ᪗
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G᜛—2cos஺=0,C?ḄO
G2:+3/-6=0ᑣ஺2Ḅ᩽ᙶ᪗
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16x,ᦪ/(x)ḄoG(0,+“)(x)=r+2=+2….XX(1)q=_3/'(X)=+2x+3=_r2X3=_(x3)(x+1),XXXᵫ/'(x)>003,ᦑᦪ/(x)ᙠ(0,3)vᓫw⌴yᙠ(3,+8)vᓫw⌴z.(2)¡¢ᵫᩩ¤(x)=—x+2—3x>0,.■.'(=-1+=XX••
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17(I)ᵫæ2qᙊ^Npj—l,\,13,A/j12)TË/="]eaY2ᡠ?/=44=],ᓽqᙊKLL+y2=i•4X22(II)~4+y=,\Ï1+4è2Ðé2+8g+4m24=0,×|ᵫீy=kx+mᵫê=64Z2M-4Ï1+4è2ë4>-4Ð=-16nz2+64=+16>0,\ì<1+4᝕2,ᵫîïTᳮ1\ᵫ+஽=--^7-1+4%2MA3ḄoN”L(ñ%)\/=ò^3=1ᓽ1+4᮱=-4&õ1τ^TK.m1y=kx?@+m=----r=---%n°01+4&24k.•Ḅoᚖ9KLy+=1(x7'ᓽkx-|ᦑA3\oᚖ9ឤ^NN(,0ூNh௃⚪ὃqᙊḄ᪗øK@ᐸÆÇឋ¿ஹù9qᙊḄúûᐵý@qᙊoḄT±⚪ªὃ~(FG²2þḄÿᔠ
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