2022年江苏省南京高考数学一模试卷（附答案详解）

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2022
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2,3B.R|4B|·´ᨬᜧ-m=lC.Rë4cBᨬ2-ᐸíîëD.ï•ñḄᨬᜧ24412.᝞ò-Ñïóô4BCD-EFGHḄõ☢)÷l4Ḅ=Òø-CG=m,MCGḄ-Põ☢EFG”Ḅæ-ᑣ?@A.Rm=4-°ᙠPPA+PM=8B.Rm=4-°ᙠùḄPº1PM=ÛC.Rm=4-BPIAMḄḄúûlm2ü2⚓-ᐳ17⚓

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ᐵឋLᑨu.S⚪ὃXvwhᦪḄᕜyឋᓫ{ឋMN|}Ḅ~ឋ.[\Ạ⚪g.ூR`௃R:A2•hᦪ/(%)=sin3%*)3>0)ᙠ[0ಘᨵᨵvp,/(0)=sin(-^)<0,•••/(%)ḄᨬᕜyT<7T,ᙠ(0,71)4],X>"%1)=1/(2)=-1/(%1)-/஺2)=2,ᦑA~;2#8⚓ᐳ17⚓

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10᪷jkឋUmnPḄbcO2ᐔX?-4rs=s%ᦑ஺.ᦑ⌱BCD.ABvwCDᙶ᪗G%xᔠ⌱⚗⌲|}~%ᑭᵨknU[ᑨAeᑭᵨᚖCPU[ᑨBenbcU[ᑨC,D.⚪ὃB⚪ᓄO:☢⚪%xᔠ᪆Ḅᐵm%@᫏⚪.13.ூᫀ௃8ூ᪆௃ூᑖ᪆௃⚪ὃ¢᣸ᑡ¥ᔠḄ¦ᔠ⚪%§Ạ⚪.ᐜªA«¬ᢧ®%¯°Ḅᐰ᣸ᑡᓽU.ூ௃ᓫ´2ᵱ2᝕·¸᣸ᑮAஹ8ஹC»|«¬¼½¾■ÀÁÂ%A«¬⌕¸᣸1ᵱ1᝕%ᦑᨵ©•©=4ÇUÈ%¯°É®ᐰ᣸ᑡᓽU%ᦑÊËḄᫀᦪ4•Í=8Ç%ᦑᫀO8.14.ூᫀ௃2ூ᪆௃ÎSn-1ÐÑÒÓᦪᑡ%•••(S2-I)2=(Si-1)(S-1),3ÖeS2=%+02=1V=0,S3=%++×3=%-&+%=%,"1=(«1-1)(«1-1)%5O=0ᡈ2,ÖaH0,n%=2,ᦑᫀO2.ᵫ⚪ÜUm(S2-I)2=(111)(S-1),ÝxᔠÒÓᦪᑡḄÞ⚗ßàᓽUxá.3⚪â⌕ὃ¢ÒÓᦪᑡḄÞ⚗ßà%§Ạ⚪.15.ூᫀ௃Î11,12,13Ðூ᪆௃äOåæà@f7⚗Ḅè⚗àGᦪᨬᜧ%᝞áëᨵf7⚗Ḅè⚗àGᦪᨬᜧ%ìí=12,᝞áf7⚗îf8⚗Ḅè⚗àGᦪᨬᜧ%ìï=13,᝞áf6⚗Qf7⚗Ḅè⚗àGᦪᨬᜧ%ᑣn=ll,

11ᦑn=11,12ᡈ13,ᦑᫀO:{11,12,13).᪷jè⚗àGᦪḄឋôõmᑖ÷øù%ᓽëᨵf7⚗ᡈf7⚗îf8⚗ᡈf6⚗Qf7⚗Ḅè⚗àGᦪᨬᜧ%ᓽU.⚪ὃ¢è⚗àúᳮḄ`ᵨ%üýᑮᑖ÷øù%§Ạ⚪.16.ூᫀ௃Òூ᪆௃ூᑖ᪆௃⚪ὃᳫḄ⊤☢ÿḄ
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Mᓝ☢#Ḅ᜜/ᳫ⊤☢Oᵨ/⊤6ᓝ☢#Ḅ⊤☢Oᓽ20ST,UV-Ḅ☢OWX
Mᩭᵨ/⊤6KLZᖪ\ᑮ]ᫀ.ூ`]௃`bᵫcdᓝ☢#Ḅ᜜/ᳫᓽ&eI+$┵Ḅ᜜/ᳫᐸ12&R+,-Ḅ᜜/ᙊ12&gᓝ☢#Ḅ$%&/,£ᑣj=sin36°=\r=—,r56ᡠ)+$┵Ḅ⚔9ᑮ;☢Ḅ<=uv="2_y==z,ᡠ)R2=r2+(/?-/i)2,ᓽR2=G)2+(Rᓟ/)2,`\R=.ᡠ)ᓝ☢#Ḅ᜜/ᳫ⊤☢O&Sᡂ=4ᐔ/?2=4x(/=/12,7rLᓝ☢#Ḅ⊤☢OuSᔍ#=20x1x/xZxsin600=5y/3l2,ᡠ)ᓝ☢#Ḅ⊤☢Oᓝ☢#Ḅ᜜/ᳫ⊤☢OWT#=2ஹᳫ367rᦑ]ᫀ&b.17.ூ]ᫀ௃`b()&b(l+cosC)=V5csin¡4BC,ᵫ£Cᳮᨵsin¡4BC(1+cosC)=KsinCsin¡4BC,&¡4BCG(0,TT),ᡠ)sinz/BC40,§12⚓ᐳ17⚓

12ᡠ)1+cosC=V3sinC,B|JV3sinC-cosC=1,ᡠ)sin(C-g)=IoL®&0ö=1ḄTîᦪᑡ

13ᡠ)ñ+g+…+ë0=5X4+x1=30;&&0,ë᪀ᡂ✌⚗&8,àî&”>=5ḄTîᦪᑡᡠ)&o+ë1+,ú1+ë5=6x8+6(621)x1=72;&ë5,ë6,…û᪀ᡂ✌⚗&16,:;<=>=^=üTîᦪᑡ,o63ᡠ)ë5+ë6+…+ᓃ21=7x164—3-X—=168,qý721=&+12+30+72+168—(/?3+/++ë5)=-+282-(2+4+8+16)7=-+252=—.2'22ூ`᪆௃×⚪ὃØTîᦪᑡTᦪᑡḄÿᔠ
ᵨᑖᓄ⚪.(1)ᵫS3=7=%++஺3஺4+஺5+஺6=56,ᑭᵨ"#ᦪᑡḄ'⚗)*+*,ᖪ,./ᦪᑡ012Ḅ)#3ᵫ"#ᦪᑡḄ4஻⚗)*6'⚗)*ᓽ./89(2)ᑭᵨᑖᓄ;ᔠ⚪<ᩩ>"?ᦪᑡḄ4஻⚗)*@A/;B.19.ூEᫀ௃(1)HIJ#KᵬMᐜ/(11ᑖ)OPQR>A,ᑣR>AUᒹWR>BR>C,R>8[ᵬ\3ᡭ3^ᳫᵬᐜ/(11ᑖ)OPR>C[ᵬ\3ᡭ4^ᳫᵬᐜ/(11ᑖ)OP.R>B[ᵬ\3ᡭ3^ᳫI`^ᳫᙳQᵬbᑣp(8)=de)3=/R>C[ᵬ\3ᡭ4^ᳫᑣ4`^ᳫᵬb+^ᨬhi^ᳫᵬbᑣp(C)=C^(|)2x128-X—=—;3327ᑣPG4)=P(B)+P(C)=/+^=3(2)XḄ.stuQ1,2,3,4.P(X=1)=-,p(X=2)=iX-=—,p(X=3)=-X1X-=—,p(X=4)=iXiXi=w/4w'4416w,44464w7444164ᡠMXḄᑖzᑡQ[ᐸUE(X)=lx`+2x`+3x`+4x-^=~.')416646464ᓽᦪQ364ூ8᪆௃(1)ᑖ᪆+ᵬ\3ᡭ3^ᳫI`^ᙳQᵬbᵬ\3ᡭ4^ᳫ,ᐸU4`^ᳫᵬb+^ᨬhi^ᳫᵬbᑖᭆ᳛ᓽQ;9(2)xḄ.stuQ1,2,3,4,
Ḅᭆ᳛ᑏᑖzᑡu.⚪ὃᦣḄᑖzᑡ6ὃḄAsU᫏⚪.14⚓ᐳ17⚓

1420.ூEᫀ௃8[¢1£H¤¥A8Ḅ¦§Q¨=kt+2,6«ᱥ¥Ḅ¦§ὶ®./%2i2pkx-4p=0,H8(%2¨2)(%1>°%2<°)./=-4²%i+x=2pfc,2(xx')2=12AwViwy?4P2=4,ᵫ஺4-OB=-4./+y2=—4p+4=—4,8/p=2,ᑣ«ᱥ¥Ḅ¦§Q/=4yC(2)ᵫ4c=2cB./=2x?,¸¹i%2=-8,8/%]=4,x=-2,ᓽA(4,4),8(—2,1),2ABḄU»ᙶ᪗Qk=3,ᑣABḄUᚖ¥Ḅ¦§Qy-|=-2(x-1),ᓽQy=g2%,HᙊḄᙊÁQM¢a,b£,./b=g-2a,জᵫ¤¥MAḄÆ᳛QF./AᜐḄᑗ¥ḄÆ᳛Q-Ê4-a4-bᵫ/=4yᓽy=9x2,./y=[x,./4ᜐḄᑗ¥ḄÆ᳛Q2,ᑣiÊ=2,ঝ4-bᵫজঝ8/a=-1,6=—,14Ml=ÍᡠMᙊḄ¦§Q¢x+1Î+¢y—y£2=".ூ8᪆௃¢1£H¤¥ABḄ¦§6«ᱥ¥Ḅ¦§ὶ®ᵨÏÐÑᳮᔣḄᦪÔḄᙶ᪗⊤Ö8¦§./p,×Ø/ᑮ«ᱥ¥Ḅ¦§[¢2£ᵫᔣᐳ¥Ḅᙶ᪗⊤Ö;ᔠÏÐÑᳮ8¦§./4ஹBḄᙶ᪗HᙊÁᙶ᪗ᵫᙊḄᑗ¥ḄឋÜÝᦪḄÞßàá/a,b,3ᙊḄâã./ᡠᙊḄ¦§.⚪ὃ«ᱥ¥ᙊḄ¦§ḄᵨM¤¥«ᱥ¥ஹ¤¥ᙊḄäåᐵç,ὃ¦§èéAsU᫏⚪.21.ூEᫀ௃¢1£êë[tACḄU»ìíMMMB,᝞ï,ðQñò4CG4iஹNQ41clḄU».ᑣ4c1MN,¸ðQABCQ"ô`õòᑣAC1MB,MNCMB=M,MN,MBu÷☢8MN,ᑣᨵ4CJ■÷☢8MM¸BNu÷☢BMN,ᡠMAC_LBN,ñòACCMiUAAஹHCC],÷þÿ
ABBMiAA//BB,l1BB//CC,11

15ᡠ8,C,GBlᐳ☢(2)ᵫ(1)MN1AC,BM14C,ᑣNNMB☢AC-BḄ☢8=UJMB,ᙠ☢2MNᑁMMz1MB,ᨵAC1Mz,Mᙶ᪗#$%᝞'ᡠ(Ḅ)*+ᙶ᪗,>4(1,0,0),B(0,V3,0),C(—1,0,0),W(0,cos0,sin0),C1(1,cosasin஺)CB=(1,V3,0),CCC=(0,cos஺,sin஺),0☢BCGBiḄ12ᔣ4ᐗ=(x.y,z),ᑣ7.9=0,ᓽ;fy=0z=U(n-CC]=0lycosO+zs

160=0tan6☢BCG/Ḅ12ᔣ4ᐗ=(@,1,A)ᵫtan஺=-g,,•ᐗ=(8,-1,—2),AB=(-1,>/3,0),0+CABD☢BCG/ᡠᡂḄa,+•sina=|1cos1|=I|•M:XIINI1|=2,VK2X2=ߟ4,+CA8D☢BCGBᡠᡂḄOPQR.ூT᪆௃(1)WACḄM,XY4CJ■☢8MN[BB//CCI,ᓽ\]ᳮ_`a;(2)ᙠ☢BMNᑁMzlMB,$%)*+ᙶ᪗,cd)*ᔣ4efg.h⚪ὃkᐳ☢ḄXY[C☢ḄOPQḄl2m᫏⚪.22.ூgᫀ௃Tp(1)((%)=2/27nx+62,•g(x)=|%3—mx2+m2x—2x2—2mx+M=|x3—(m+2)x2+(m2+2m)x—m2,•••“(%)=2x2—2(m+2)x+m24-2m,q?n<—2ᡈm>0tu=4(m+2)2—8(m2+2m)<0,•g'(x)>0ឤᡂ%ᓽwᦪg(x)ᙠRyᓫ{⌴}ᦑwᦪg(x)᩽Qq20,0g'Q)=o1᪷i/vq%6gr(x)>0,g(x)ᓫ{⌴}q%G(%%2)“(%)<0,g(X)ᓫ{⌴,q€(%2+8),/(%)>0,g(%)ᓫ{⌴}ᦑwᦪᙠ=W_᩽ᜧQᦑwᦪᙠW_᩽Q16⚓ᐳ17⚓

17yᡠḄWQ(2,2).(2)v/i(x)=(2e2x—2mex+m2)+(21n2x—2m

18x+m2),nt6R,(2e2x—2mex+m2)+(21n2x—2m

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