2022年全国高考甲卷数学（理）试题

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5

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⚗ᑭᵨḄᭆ᳛Ḅᓽ(2)#⚪%XḄ'()*0,10,20,30,/ᑖ12345Ḅᭆ᳛ᑡᑖ7ᑡᓽ89.(1);ᵬᙠ>⚗?
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IJKḄᭆ᳛*P=P[ABC)+P(ABC)+P[ABC)+P[ABC]=0.5x0.4x0.8+0.5x0.4x0.8+0.5x0.6x0.8+0.5x0.4x0.2=0.16+0.16+0.24+0.04=0.6.(2)#⚪%XḄ'()*0,10,20,30,ᡠp(%=0)=0.5x0.4x0.8=0.16,=10)=0.5x0.4x0.8+0.5x0.6x0.84-0.5x0,4x0.2=0.44,P(X=20)=0.5x0.6x0.8+0.5x0,4x0.2+0.5x0.6x0,2=0.34,P(X=30)=0.5x0,6x0.2=0.06.ᓽXḄᑖ7ᑡ*X01()2030P0.160.440.340.0689E(X)=0x0.16+10x0.44+20x0.34+30x0.06=13.20.(1)/=4x(2)AB:x=y/2y+4.ூ᪆௃WᫀY12⚓ᐳ17⚓

19ூᑖ᪆௃(1)ᵫ^ᱥ`ḄabI|d+§,ᓽIf(2);gḄᙶ᪗j`MN:x=஻o+1,ᵫpqaᳮs᳛I“u=v%,w/ᵫxyḄzᑗ|}~I,=*;j`8:=஺+஻ᔠpqaᳮf.(1)^ᱥ`Ḅ`*x=-5,xᚖjgMḄᙶ᪗*p,=p+§=3,ᡠp=2,ᡠ^ᱥ`CḄ*V=4x(2)/2\/2\/2\/2\;A/,%,᜜?]8?|j`AW:x=wy+l,14744J/\4J/x=my+\ᵫீ2:I/4஻“4=஺¡>0,*=-4[y=4xk=-*4J%=4ᵫs᳛I¥'§_+%©-ᐸ_]i%+4444SVÓj`MD:x=1-y+2,¬ᐭ^ᱥ`I¡>0,®=-8,ᡠ¯2*°ᳮI”=244kᡠ²³=1=´w=µ+¶2(+%)2·¸*j`MNஹḄºsyᑖ1*»,£,ᡠK=tanÁ=Â=Ã⌕Åa-£ᨬᜧᑣ?/*tana-tan᜛k1Ó1O;ÊL23L2Q0,ᑣtan(a^-1+tanatan"2-lf2ஹÖ74+2kVÎÏ=2²ᓽ²=Ðᡂk2WᫀY13⚓ᐳ17⚓

20ᡠa-£ᨬᜧ;j`48:ஹ=0+஻¬ᐭ^ᱥ`IV-40×-4஻=0,¡>0,᜜%=_4஻=4yly2=T6,ᡠ஻=4,ᡠj`AB:x=6y+4.ூgÚ௃ᐵÝggÚfÞ}⚪ḄᐵÝßᑭᵨ^ᱥ`4s᳛àáᓄãᑭᵨpqaᳮIᙶ᪗äḄᐵå.21.(l)(-a),e+l](2)çèéḄf᪆ூf᪆௃ூᑖ᪆௃(1)ᵫëᦪíaîᦪᓫðឋᨬ)ᓽIf(2)ᑭᵨᑖ᪆³ᓄ⌕çèᩩ*Inx-6,/ᑭᵨëᦪᓽIç.(1)/*)Ḅabô*(0,”),õ/(x)=0,Ix=lxe(0,1)J'(x)<0,/(x)ᓫð⌴øxe(1,+8),((x)>0,/(x)ᓫð⌴ù/(x)>/প=e+1-a,Ã/(x)20,ᑣe+1-aû0,ᓽaWe+1ᡠ஺Ḅ()ý*(-8,e+1]ফᵫ⚪%J(x)þgÿ1,ᜧ112ᫀ14⚓ᐳ17⚓

211⌕<1ᓽ<,}e(0,1),ᓽ/&)>/[})/()=/+),ᓽ/(%)>/-\X2Jx-1ᓽ-e--lnx+x-xex-lnx--->0,XG(1,-HX))XXᓽ---xex-2Inx——x>0x2xexi1(5☢7X>19,---xcx>0,lnx--Ix<0XஹFLC'—g(x)=---xev,x>1Kxᑣg'(x)=er+xev-e-ex-1exa(x)=?(x>l)d(x)eX=-X—z-1ex>0exxᡠI9(x)>Q(l)=e,L1-ᡠIᡠIg'(x)>oXᡠIg(x)ᙠ(1,O)ᓫQ⌴SQX1ᓽg(x)>gপ=0,ᡠIJ->0x1V஻(x)=,x>1X)2.x—%2—1—(x—1)1+-<0x272x2ᡠI஻(x)ᙠ஺,ᱥ)ᓫQ⌴Zᓽ/?(x)஺প=0,ᡠIInx-[<0[xe[-2Inx-Ux\]->0ᡠI_2<1.XXூb௃ᫀ15⚓ᐳ17⚓

22ᐵfbgh⚪j᩽lmno⚪ᐵfjpqᑖ᪆t᪀⌼wᦪ7yz஻(x)=lnx-[(x-£|}wᦪ~◤⌕22.পV=6X-2(J20)[ফGGḄᙶ᪗((1,2),GCḄᙶ᪗(-L-2).ூ᪆௃ூᑖ᪆௃(1)ᓽᑮGḄp[(2)GgḄᓄᡂpὶᓽ.(1)x=Uy=4i,ᡠIx=?I,ᓽGḄp/=6x-2(yZ0).66ফX=-¢/=ᡠI6x=-2—VᓽGḄpV=-6x-2(y40),ᵫ2cos6—sine=0n2pcose—psin6=0,ᓽGḄp2x-y=0.ὶ)=6X-2(;20),gᡈf=1ᓽᙶ᪗ª1),(1,2).I2x-y=0b=1[y=212)ὶ¬=g6X-2(g40),g=>ᡈ=gᓽᙶ᪗(-1,-2).I2x-y=0[y=-ll-F=-2<2>23.প¯᪆(2)¯᪆ூ᪆௃ூᑖ᪆௃(1)᪷±/+/+4஺2=/+஻+(2஺)2,ᑭᵨ´µyzᓽg(2)ᵫ(1)¶ᔠ¸¹0

23ᡠI“+b+2cW3,ÃÄÅÃa=b=2c=l9ÆyÇᡠI஻+b+2c43[ফ7gb=2c,a>0,b>0,c>0,ᵫÈ1Éa+b+2c■=a+4c43,ᓽ0-,a+4c3ᵫᩗ¼yz¹_+1=]+”3acaAca+4ca4-4c171ÃÄÅÃ]=9,ᓽ஻=1,஺=:9ÆyÇa4c2ᡠI—F—N3.acᫀ17⚓ᐳ17⚓