2021-2022学年北京市丰台区高二（下）期末数学试卷（附答案详解）

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1A.ᐙᑖæÛç⌕ᩩÆB.ç⌕æÛᐙᑖᩩÆC.ᐙᑖç⌕ᩩÆD.êÛᐙᑖëÛç⌕ᩩÆ9.T⚗ì¦◤⌕îᒹðᵬÎÏᙠᑁḄ6òóôὅö᣸ᑮA,B,Cùú«ûüýþÿ
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ᑣ᣸ᫀḄᦪ()A.24B.36C.48D.7210..ᜧ01Ḅ2᦮ᦪᐸ56GN*.9%++…+270,ᑣ2᦮ᦪznḄᨬ
A()A.23B.24C.25D.26CஹEF⚪(Hᜧ⚪ᐳ5
⚪ᐳ25.0ᑖ)11.KLឋNOP.ᔲRSTUVᡭXᳫḄZ[ឋᨵ]^R_T40UV`aKbᔁdefᑮ᝞⊤Ḅ2x2ᑡὶ⊤:Z[ᡭXᳫZ[ᡭXᳫᔠoᵱVm420᝕V820ᔠon40ᑣm_,n=.12.ᵫv“1”v“2”yᡂḄḄ{|ᦪᨵ.(ᵨᦪ~)13.ᦪ/(x)=?ᙠx=1ᜐḄᓄ᳛.14.ᦪᑡᓽḄ⚗Ḅ1=p/+n(peR),9+i<ᑣpḄA15.Sᑴ⌼ᖪᑴ⌼ᳫḄSᧇ.¢£Ḅ⌼¤ᓃ(ᓫ|§ᐗ)ஹᑁᧇḄªᑭ஺2(ᓫ|§ᐗ)ᑖN£Ḅ®¯r(ᓫ|§cm,r<5)²³Ḅᐵµ᝞¶ᵬஹᡠ¸.¹ᑴ⌼ᖪḄᑭº/Xr)=P-Pf¼½ᑡ{¾¿§2জÁre(0,6)/(r)<0Âঝ/(r)ᙠ³(Ä5)Åᓫd⌴ÇÂঞf(r)ᙠ³(0,q)ÅËᙠ᩽
AÂট/''(r)ᙠ³(O.rJÅËᙠ᩽
A.ᐸ5ᡠᨵ2Ѿ¿ḄÒÓ.Ô2⚓ᐳ14⚓

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⚪ᐳ85.0ᑖ)16.SUᙠÅU⌶5⌕ZÙÚÛᎷ¹ÝÞßÅUᙠ_ÚÛ⍗ᑮáâḄᭆ᳛!._Uᕜᨵ3ᜩÞßÅU.(I)è_Uᙠé3ᜩÅU⌶5ាᨵ1ᜩ⍗ᑮáâḄᭆ᳛Â(II)ë_Uᙠé3ᜩÅU⌶5⍗ᑮáâḄᜩᦪX,èXḄᑖìᑡíᦪUîïE(X).17.ñòᦪᑡ5Ḅón⚗ô52=9,ö÷ᩩùজஹᩩùঝévᩩù5⌱ûLü½☢Ḅb⚪§(I)èᦪᑡaḄ⚗Ân(II)9ᦪᑡ%ÿ
=2aL3,ᦪᑡẑḄn⚗ᩩজa=74ᩩঝ:S4=22.᝞⌱!"#ᩩᑖ%&'(ᢥ*+#&',ᑖ.18./01ᦪ/(*)=A—2Q%2+a€R.(I)9஺=2;(/(x)ᙠ>?@1,3ABḄᨬᜧEᨬFEG(n)/(H)ḄᓫJ>?.19.+ᐶMFNOP&5RAPPḄTᵨVW(ᙠXY>Z[\]P200_`aJb(cᑮTᵨe5R4PpḄ_ᦪghR4PPḄij᳛(Jbᦪl᝞⊤APP*1R*2R*3R*4R*5RTᵨ4PPḄ_ᦪ160901509080ij᳛0.850.750.80.70.75(I)ne200_oZ[\]1_(p_Tᵨ*2RAPPḄᭆ᳛;(u)᪷lJbᦪl(wTᵨ_ᦪxy50%ḄAPP{O“}~4PP”.ᐶMFNne5R4PPoZ[⌱]3R(ᐸo“}~4PP”Ḅ#ᦪOX,XḄᑖᑡgᦪE(X)G(JU)ᎷhR4PPY>OijḄᭆ᳛⊤oRPPḄij᳛(ᵨ“=1”⊤*kRAPPij(“=0”⊤*kRAPPij(k=l,2,3,4,5),ᑏ஺(&),D&)(D&)஺(&)(D(A)ḄᜧFᐵ¤.(¥◤ᑏ§¨)

320./01ᦪf(x)=ae2x+(a-2)ex-x(aeR).(I)9(1=0;(®¯y=f(x)±(0/(0))ᜐḄᑗ¯´G(II)µ9a>0;(1ᦪf(x)·ᙠ᩽EG(HI)º1ᦪ/(%)ᙠ>?(-1,+8)Bᨵ¼±(aḄ]E¾.21./0ᦪᑡ஻ÀÁÂᦪᑡ.º%=an+i-an(ᑣ{%OᦪᑡḄ1▤ᦪᑡGºÆ=Ç+1-%(ᑣ{ᦪᑡ0OᦪᑡaḄ2▤ᦪᑡGÈpÉÊ(Ëcᦪᑡn.Ḅp▤ᦪᑡ,ᐸop€N*.(I)ºᦪᑡ;ḄÎ⚗ÏÐOa=n2,ᦪᑡÑÒḄ2▤ᦪᑡḄÎ⚗ÏÐGn(u)ºᦪᑡᓽḄ✌⚗O1,ᐸ+▤ᦪᑡbḄÎ⚗ÏÐOÇ=2n,ᦪᑡÖḄnÎ⚗ÏÐG(×)ºᦪᑡᓽḄÎ⚗ÏÐOᓽ=nm(meN*),ᑏᦪᑡajḄm▤ᦪᑡḄÎ⚗ÏÐ(ÚÛÜᳮᵫ.*4⚓(ᐳ14⚓

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ᓽᑮasḄ⌱⚗.nnn⚪⌕ὃᵫᦪᑡn⚗⚗Ḅ!⚪.ὃ"#ᓄ%ᓄ&'()᦮+'(,-./0ᳮ23ᦪ452367Ạ⚪.4.ூ;ᫀ௃Cூ>᪆௃>@ᵫABC&DE;=o.25x+15,Hy%IJᐵᦑ4┯NOPI=20,;=0.25x20+15=20,QRSTU20cmḄ᪛⚜XᐸZ[U20m,\]^_`ab20m,ᦑ8┯N@᪵d_e᪛ḄSTfg1cm,hᐸZ[fg0.25m,ᦑCOABC&DEឤj᪵kḄdl\᪵dḄk^_`AjABC&DEᦑ஺┯N.ᦑ⌱@C.ᵫnHABC&DE⌲_ᑖ᪆qr⌱⚗;ᫀ.

5⚪ὃABC&DEḄsᵨRᨵᐵvḄwxbᐵyb7Ạ⚪.5.ூ;ᫀ௃Dூ>᪆௃>@ᵫnH{'(t)=-9.8t+4.8,ᑣ'(1)=-9.8+4.8=-5,ᦑ⌱@D.ᦪḄᦪt=lᓽ>.⚪ὃ"ᓄḄ᠒%ᓄ᳛ὃ"4Ḅ52367Ạ⚪.6.ூ;ᫀ௃Bூ>᪆௃>@ᵫ⚪H__ᐳ36¡¢£¤4U“ᔣ§ḄkᦪU1“ᐳ6¡¢£¤B“©Ḅkᦪª«6“ᐳ5¡¢£¤4B¬“ᔣ§ḄkᦪU1©Ḅkᦪª«6“ᐳ1¡¢ᡠ,P(B|A)=◤=[.ᦑ⌱@B.ᑖ´ᑏ£¤aBḄ7£¤᪷¸ᩩ¤ᭆ᳛ᓽ.⚪ὃᩩ¤ᭆ᳛ὃ4Ḅ23`7£¤Ḅrᦪbᐵy.7.ூ;ᫀ௃Aூ>᪆௃>@ᵬ½¾3¿4ÀÁḄ4Â᪥ÄEdÅ⌱_ÂÆgḄ£¤ᦪU43.ᵬ½¾3¿4ÆgḄ᪥ÄEᔜ^JḄ£¤ᦪUᵨ.ᦑᡠᭆ᳛Up=4=--438ᦑ⌱@A.ᑭᵨÊᐺᭆÌḄᭆ᳛ᓽ>.⚪⌕ὃÊᐺᭆÌ67Ạ⚪.8.ூ;ᫀ௃Cூ>᪆௃>@ᵫa=2/(x)=-2),/'(X)=e*(x-2)+e*=-1),ÓÔx6(ߟoo,1)f(x)<0Oxe(1,+8),[(X)>0,•••஻>)ᙠ(_8,1)§ᓫß⌴áᙠ(1,+8)§ᓫß⌴fâ6⚓ᐳ14⚓

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ᨵ2x6=12᣸+ᦑᨵ12+12=24᣸+ᦑ⌱-A../0ᑖ123ᓽ567.9⚪ὃ<=ᭆ᳛@ABᱯDᐗFḄ᣸GHḄᦪGJKLMNOPẠ⚪.10.ூSᫀ௃Bூ6᪆௃6-᪷X⚪Y.Oᦪᑡaj,ZᦪᑡḄ[\⚗ᨬᜧmḄ`ᨬaᵫ@cdᜧOeḄf᦮ᦪZan=1%+=3<70,Z4WnW8g=2,+a+a+—Fa=13<70238Z9

79⚪ὃ<ᦪᑡ@dnoḄឋq,11.ூSᫀ௃1616ூ6᪆௃6-ᵫ⊤ᦪX5mm=20—4=16,ᑣz{ᡭ}ᳫḄᦪh16+8=24,ᦑn=40-24=16.ᦑSᫀh-16+16.᪷Xᩩiᔠᑡὶ⊤ḄᦪXᐵᓽ56.9⚪⌕ὃ<ឋᑡὶ⊤ḄᵨNOPẠ⚪.12.ூSᫀ௃6ூ6᪆௃6-ᵫ(“1”(“2”ᡂḄdḄᦪᨵ=6.ᦑSᫀh-6.ᐜ$(“1”(“2”ᐳ4(ᦪ᣸ᑡhᨵ(“1”(“2”ᐗF◀¡¢.£ᓽ5.9⚪ὃ<=᣸ᑡḄᵨcPẠ⚪.13.ூSᫀ௃1ூ6᪆௃6-ᵫ5m.Q)=3n=n§x=l,ᑣ1(1)=n=1,ᦑSᫀh-1.7«ᦪḄ¬ᦪᯠ®§X=1ᓽ56.9⚪ὃ<=°ᓄḄ²᠒¡´°ᓄ᳛ὃ<=¬ᦪḄµ¶Y·NOPẠ⚪.14.ூSᫀ௃\1(Sᫀd¸\)ூ6᪆௃6-᪷X⚪Yᦪᑡ¹ᓽºḄ»⚗¼ohan=p/+n(peR),Âan+i

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/'(r)ᙠঢ,5)ëᓫÕ⌴íᦑঝ┯ï+᪷XÚá5-ÚáHᐜ²®᠒ðP2Úáᐜ᠒®²ᡠ¡5m/(r)ᙠ(0,6)ëḄ°ᓄcᐜò®íᦑᨵ᩽`ᦑঞfÞ+(஺)=22'-PJ,Zr•õöO1÷2ᙠ÷ᜐḄᑗäå᳛øùᜧOBᙠ÷ᜐḄᑗäå᳛ðZrõöO஺PiᙠrᜐḄᑗäå᳛øùᜧOP2ᙠrᜐḄᑗäå᳛ᡠ¡5m/'(r)ᙠ(0,6)ëḄ°ᓄcᐜò®íᦑᨵ᩽`ᦑটfÞ.ᦑSᫀh-জঞট.᪷X«ᦪᙠúûᜐḄµ¶Y·5⌲\ᑨþ.9⚪ὃ<=«ᦪÚá@¬«ᦪḄµ¶Y·ὃ<«ᦪḄᓫÕឋ@᩽`NO᫏⚪.16.ூᫀ௃(I)“ᙠ3ᜩ⌶ាᨵ1ᜩ⍗ᑮ”!"#4ᑣP(4)=(x|x(l-1-.ᡠ0.ᙠ3ᜩ⌶ាᨵ1ᜩ⍗ᑮḄᭆ᳛!.(U)XḄᡠᨵ6789!0,1,2,3.p(x=°)=0x0)஺x(1,P(X=l)=C^x|x(l-|)2=i,P(X=2)=C^x(|)2x(l-i)1=|)P(X=3)=C^x(|)3x(l-i)°=iXḄᑖDᑡ!X01238421p279927

9ᦪGHE(X)=0x?+lx+2xL+3x/=lin99N7ூ᪆௃(I)ᑭᵨT⚗ᑖDḄᭆ᳛VWᓽ6YZ(U)✌ᐜ]ᑮ^_`aXḄ89.bᑖcᑏeᭆ᳛.bᑭᵨGHVWᓽ6Y.f⚪g⌕ὃjklᦣn^_`aḄᑖDᑡoGH.pqrẠ⚪.17.ூᫀ௃(I)⌱ᩩ#জa=7w✌⚗!ᵫ,Vy!d,4ᡠ0{=%}+d=9,]e1=4.ia=%+3d=7(d=14ᦑ=n4-3Z⌱ᩩ#ঝ54=22.ᡠ02=+2+d=9,]N=4Zম=4al+6d=22(d=1ᦑ=n+3Z(II)ᵫ(I)]ᦪᑡ%ᓃ=2-3=2%ᡠ07Z=21+22+…+2n=%:=2n+1-2.ூ᪆௃(I)⌱ᩩ#জঝᑭᵨyᦪᑡḄឋYeᦪᑡḄ✌⚗Vy.YeᦪᑡḄ⚗VWZ(H)ᑭᵨ(I)Ḅ.ᑭᵨᦪᑡḄ⚗VWYeᦪᑡḄ.f⚪ὃjḄ⌕¡ᦪᑡḄ⚗VWḄY¢£ᵨ.ᦪᑡḄY.ᦪᑡḄY,g⌕ὃj¤Ḅ¥¦7§ᦪ¨©7§.pq᫏⚪.18.ூᫀ௃(I)¬஺=2./(%)=%3—4%2+4%,/'(%)=3%2—8%+4=(3%—2)(%-2),¯((%)>0,]x>2ᡈὅx<|,´µ!¶6L1,3·,ᦑf(%)ᙠL1,2)ᓫº⌴¼,ᙠ(1,2·ᓫº⌴½.´µ!=f(2)=0,/(3)=3,ᦑf(x)ᙠL1,3·Ḅᨬᜧ9!3,ᨬÀ9!0Z(II)//(x)=3x2-4ax+a2=(3x—a)(x—a),¬Q=0.f(x)=3x2>0,Á/(%)ᙠRᓫº⌴½.ᦑ/(%)Ḅᓫº½ÃÄ!R,żÃÄZ¬Q>0.¯/'(%)>0,]%>Qᡈὅx

10¬a<0.¯/'(x)>0,]x>Ëᡈὅx0.Ḅᓫº½ÃÄ!(□?.(a,+00),ᓫº¼ÃÄ!G.a)Za<0,f(x)Ḅᓫº½ÃÄ!(—8,a),(p+oo),ᓫº¼ÃÄ!(a)ூ᪆௃(I)¬a=2.ÓÔᦪYÕ.Ẇ×ᐸᙠL1,3·Ḅᓫºឋ.ÙÚÛ¦ᨬ9ᓽ6.(Ü)ÓÔᦪYÕ.ÝÞᦪaḄàᑨâÔᦪᓫºឋᓽ6.f⚪g⌕ὃjᑭᵨÕÔᦪẆ×ÔᦪᓫºឋãYÔᦪᨬ9.pq᫏⚪.19.ூᫀ௃(I)“Ù200ä^_å81ä.Áä⌱æÈ2çAPP”!"#4,ᵫ⊤ᦪê6]200äᨵ90ä⌱æëᵨkÈ2ç4PP,ᡠ0P(A)=ìᦑÙ200ä^_å81ä.Áä⌱æÈ2ç4PpḄᭆ᳛!í(Ü)᪵fᦪêᨵ5ç4PP,ᐸ“ïð4PP”ᨵ2ç.XḄᡠᨵ6789!0,1,2,P(X=0)=ñ=2.P(X=1)=ñ=|,2(*=2)=ó=ᔁ,VeJ.vUeOl>sXUᦑXḄᑖDᑡ!:X012133P10510ᦑXᦪGHE(X)=0xi+lx|+2x^=|Z(ú)᧕஺(fi)=0.85(1-0.85)=0.1275,஺(ᨔ)=0.8(1-0.8)=0.16,O&2)=0.75(1-0.75)=0.1875,D(f)=0.75(1-0.75)=0.1875,5=0.7(1-0.7)=0.21,ᦑ£)(&)

1120.ூOᫀ௃Q(I)R஺+,/(%)=-2ex-x,f(x)=-2ex-l,f(0)=-3,YZf(0)=-2,ᡠJ\]y=f(x)_(0J(0))ᜐḄᑗ]cZy-(-2)=-3(x-0),ᓽ3x+y+2=0.(II)//(x)=2ae2x+(a-2)ex—1=(aex—l)(2ex+1),Ra>0+,ᵫ/'(X)=0l,x=In'.ḼxḄ"ᓄ,f'(x)ஹ/'(x)Ḅ"ᓄqr᝞t⊤111X(ߟoojn—)In—(In-,4-oo)aaa/'(X)—0+1f(x)ᓫ{⌴}Ina---Flᓫ{⌴aᡠJf(x)ᙠ᩽C,᩽CZ"஺!+1.(IH)f'(x)=2ae2x+(a-2)ex-1=(aex-l)(2ex+1),Ra<0+,f'(x)<0,/'(x)ᙠ(—1,+8)ᓫ{⌴},/X0)=2a—2<0,YZf(x)ᙠ(-1,+8)ᨵ_,ᡠJ/(_1)=?+I+]=ea+a2+>0,l஺>,7v7e2ee2e+1ᡠJQ0+,/(-I)=4+1=ea+a-2+e2>o,+YZf(x)ᙠ(-1,+8)ᨵ_,ᵫ(H)3/'(x)mm=Ina—^+1<0,YZᦪ9஺),71nQ+1ᦪ,g(l)=0,ᡠJ00,Ra>0+,³◤f(x)m¸="஺3+1W0,±²lae”ee,aḄ¤¦.D⚪ὃGºᑗ]c»⚪,ὃGᦪḄᓫ{ឋ,ᨬ»⚪,ὃGªᦪḄ½ᵨJK¾%¿À12⚓,ᐳ14⚓

12ḄÃÄ,ὃGᑖÅÆÇÈÉ,ÊᓄÈÉ,L&Ë⚪.21.ூOᫀ௃Q(1)YZÌ,=Í,ᡠJÎ=Ï+1—a”=(«+1)2-Ð2=2/1+1,c-b“+i—b=2(n+1)+1—(2n+1)=2nn(II)YZÎ=Cln+l—1=2n,ᡠJCln+l—=2zi,ᡠJ&2_%=2,a-a=4,a-a=6,a-a_!=2(n-1),3243nnÑ☢n-1Ó%¿ÔÕÖ×ᑖØÙÚÛ,lᑮᓽ%=2+4+6+…+2(஺-1),&a”—a=n2—n,xÝYZa1=1,ᡠJÞ=ß-n+1.(HI)ᦪᑡàᓽáḄm▤:ᦪᑡḄã⚗å¿ZæÞ=ç.Jᳮᵫ᝞tQRzn=1+,a=n,nᐸ1▤:ᦪᑡḄãê⚗å¿%=n+l-n=1,t(t>1)▤:ᦪᑡᔜ⚗ᙳZ0.R?n=2+,a=n2,nᐸ1▤:ᦪᑡḄãê⚗å¿í=(7i+I)2—n2=2n+1,2▤:ᦪᑡḄã⚗å¿Zd=2,t(t>2)▤:ᦪᑡᔜ⚗ᙳZ0.Ꮇïzni)▤:ᦪᑡᔜ⚗ᙳnZ0.Rm=k+l+,a஺="+iḄ1▤:ᦪᑡZb=(n+l)fc+1—nk+1=CjJnk+C^nk-1+••+C^n+1n+1+1+1YZa=C+1Ḅk+1▤:ᦪᑡòb=C^nk+C^n^1+…+C^n+1Ḅóô:n+1ᦪᑡ,ᵫᎷï%Ḅk▤:ᦪᑡᔜ⚗ᙳZðᦪõ+ö÷=(k+1)!.YZ4a“+஻b“Ḅ1▤:ᦪᑡZ(40+/)-(Aa_+\-i)=A(a-0-Q+n(b-ᓃ_ù,nnxnnnᡠJᓽ+æḄ1▤:ᦪᑡZᓽḄ1▤:ᦪᑡúûḄ1▤:ᦪᑡḄ=,ü²ᨵᓽ+%Ḅk▤:ᦪᑡZa“Ḅk▤:ᦪᑡúýḄk▤:ᦪᑡḄ=.ᡠJ,ᦪᑡa
Ḅm▤:ᦪᑡḄã⚗å¿Z/ma=m/.nnூ᪆௃(I)᪷9:ᦪᑡḄþ®ÿ
⚗()ᵨ⚗(HI)ᐜ=1=2Ḅm▤ᦪᑡᯠᵨᦪ!"#.%⚪'⌕ὃ*ᦪᑡ⚗Ḅᦪᑡ+Ḅ,-./⚪ᦪ!"Ḅ0ᵨ123,

1367+1⚪.814⚓ᐳ14⚓