2021-2022学年甘肃省庆阳市宁县高二（下）期末数学试卷（理科）（附答案详解）

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2021-2022
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2k+l2k+2C------D------—•2k+lk+1•2fc+l2k+26._`ᦪzi-lz=1+i,ᐸi/ᦪᓫᑣWḄsA.-1B.1C.0D.27.ḼᓅᝍḄᔡἝᱥ“£¤¤”¦§¨ᑁ᜜«ᨵ3®ᐰ°±Ḅ“£¤¤”ᵬஹ³ஹ´ஹµ4¶·ᕒ⌕lº3“£¤¤”»ᡂ᣸½᯿ᶇÀᑣᨵÁÂᨵ2“£¤¤”°ÃḄ᣸ÄÅ.ᦪsA.240B.480C.1440D.28808.Æ-2y2x-ysḄÈO/y4ḄÉᦪsA.80B.24C.-12D.—48

19._`aᦪf(x)Ḅdᦪ((x)ÍᙠÁ/'(1)=2,ᑣA.t஺ÑÒ)-Ó=()-2AxA.-B.--C.1D.—12210._`ÔÕÖf×ØP᝱ᑖÚN(0,o2),1P(f>2)=0.023,ᑣP(-24fW2)=()A.0.977B.0.954C.0.5D.0.02311.ÜÔ᪀ÞßàḄáâEãᢣ᪗iæçjEãᢣ᪗yèéêëᑖ᪆ìᑮ1=7,y=5.5,ÁíìîឋðuÅ~s;=bx-0.11ÜßàḄáâEãᢣ᪗sI஺ᑣôëõḄçjEãᢣ᪗s()A.7.8B.7.9C.8D.8.112._`aᦪf(x)=52-(1ö÷∑ᨵùúûᑣüᦪaḄýþ
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14.᝞3*4(1,0),*C(3,9),ᦪ/'(x)=x2,7ᙠ894BCDᑁ;<=>*ᑣ?*=@▢BCᑖḄᭆ᳛FG.15.IJKLᵬஹNஹOஹPQRST100UVWA,B,C,஺QYZ[ὅ⚜^VW_`4abᵬcdNcQeBabᵬcOc>eCabNcOcde஺abNcdPc>.VW_fghiQYZ[ὅjR⚜^Ḅklmnᨵpqᨵ>lrstḄVW_`uᨵvᑡxyᑣᵬrcx.16.>{nᨵ᪗ᨵ}ṹ1ஹ2ஹ3ஹ4Ḅᓱᱏᔜ>jyn=>}ṹgQ}ṹḄᓱᱏᐰC=ᓽᑣា=6yᓱᱏḄᭆ᳛
dஹ⚪(ᜧ⚪ᐳ6⚪ᐳ70.()ᑖ)c2⚓ᐳ14⚓

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3(2)LE᪍%᪛ᩈḄ᪷)*+☢HᩞḄ᪵BMᐵOᦪ(PQᑮ0.01)T(3)V&E᪍ᡠᨵ%᪛ᩈḄ᪷)*+☢82ᑮᡠᨵ%᪛ᩈḄ᪷)*+☢1186nl2.]᪛ᩈḄᩞHᐸ᪷)*+☢_`ᡂab.ᑭᵨefᦪ7ghE᪍%᪛ᩈḄᩞḄi.▬0MᐵOᦪ"l᧡nop▭=1377-21.ᵬஹvwxy᪥{|}~bbᐳx⚗'x⚗210ᑖ20ᑖᨵF.x⚗b2ᑖḄy᪥2.]ᵬy᪥ᙠx⚗Ḅᭆ᳛ᑖ0.5,0.4,0.8,ᔜ⚗ḄbM.(1)Lᵬy᪥2Ḅᭆ᳛T(2)ᵨX⊤¡vy᪥Ḅ2ᑖLXḄᑖ¢ᑡH¤¥.22.]¦ᦪ/(%)=%—((2—a)x2—^ax2lnx(e=2.71828…)(1)஺=¯°±¦ᦪ/(%)ᨵwx᩽i³T(2)0VQ41µ¦ᦪg(x)=/(%)-^bx2-bxᙠ(0,+8)fᓫ¹⌴»°±0b>1+4-e3½4⚓ᐳ14⚓

4¿ᫀ1Á᪆1.ூ¿ᫀ௃BூÁ᪆௃Á0⌱⚗A1஺Ḅ°±ᨬ〉ᔠᵨÉᔠÊ⌱⚗CḄ°±ᨬ〉ᔠᵨÌ°Ê⌱⚗BḄ°±ᨬ〉ᔠᵨᑖ᪆Ê.ᦑ⌱0B.᪷7ÏᳮаḄᱯ³ᓽÓᑨÔ.B⚪ὃ×ÏᳮаḄÊØÙÚẠ⚪.2.ூ¿ᫀ௃CூÁ᪆௃Á0ÜÙ46ÝÞ'=0,A┯á0ÜÙB,(cosx)'=—sinx,8┯áTÜÙC,(nx)'=%CaQTÜÙD,(x+5)'=l,஺┯á.ᦑ⌱0C.᪷7çᦪḄèéᓽÓ2ᑮÐ.B⚪ê⌕ὃ×çᦪḄÚBì9bíÚẠ.3.ூ¿ᫀ௃AூÁ᪆௃Á0f(%)=ᑣ=[/+eᦑ/Xx)Ꮤ¦ᦪ%&(x)=%3>0ᙠ(0,+8)ឤᡂᦑ/(%)ᙠ(0,+8)ឤô,iog23=)1஺9-E(2,i),2^6(2-1,2஺)W2-4e-25e(-3,-2)/(25)>f(log3)>/(2-÷2*•c>a>b,ᦑ⌱0A.✌ᐜ᪷7ç¦ᦪ2ᑮf(x)Á᪆éÓ]f(x)Ꮤ¦ᦪúᑭᵨç¦ᦪᑨÔᓫ¹ឋbíᜧý

5ᓽÓ.B⚪ê⌕ὃ×ᑭᵨç¦ᦪẆÿᦪᓫឋᦪ᜻Ꮤឋ᫏⚪.4.ூᫀ௃C(V=xூ᪆௃᪷⚪ᓃ”3,!"=±1ᡈ஺ᑣf(%)-9(%)Ḅ012(-1,1)(0,0),(1,1),ᑣ56ᡠ8ᡂḄ5:Ḅ☢K£,K~rLZK+Zᦑᵫkᑮk+1epqLfgḄrᓄtuvwxy;{⚗}e~w⚗,ᓽ+31=/ᦑ⌱D.bn=keᑏNfgbn=k+leᑏNfg{ὅ!ᫀ.W⚪ὃYᦪὃYḄᳮx᫏⚪.6.ூᫀ௃Bூ᪆௃ᵫ(i-l)z=l+i,!z=^====7..z=i,ijzḄG21.ᦑ⌱B.qLr:ᑭᵨᦪ¡ᦪ:LḄ¢◀¤Uᓄ¥¦ᵫᐳ¨ᦪḄᭆ!ᫀ.W⚪ὃYᦪ¡ᦪ:LḄ¢◀¤UὃYᦪḄ_Wᭆt_Ạ⚪.7.ூᫀ௃Bª6⚓ᐳ14⚓

6ூ᪆௃¬23“¯°°”±ᐰ³}´ᐸ2“¯°°”ᣊ·¸2ᐗºa,¼᜜1“¯°°”¸2ᐗºb,ᐜ´ᵬஹÂஹÃஹÄ4ŤÆᕒᐰ᣸ᑡᯠË´aஹbᐗºÌᐭ4ŤÆᕒᡠ:ᡂḄÎÏaஹbᐗºp³Ðᑣp}Ḅ᣸Ñᦪ2ᓅ•Ô=480.ᦑ⌱B.´ᐸ2“¯°°”ᣊ·¸2ᐗºa,¼᜜1“¯°°”¸2ᐗºb,´aஹbᐗºÌᐭ4ŤÆᕒᡠ:ᡂḄÎÖᔠÌÎM!ÖØ.W⚪ὃY᣸ᑡÙᔠ¥ᓫTᦪÚᳮ_Ạ⚪ÌÎtᐵÜ.8.ூᫀ௃Aூ᪆௃(^-2y)(2x-y)5=i(2x-y)5-2y(2x-y)5,Ý⚗L(2x-y)5ḄÞ⚗27ß+i=CJ(2x)5-r(_y)r=r.S-r.(1)஺5-ÂC2är=3!T=C^-22-(-l)3x2y3,4.1.(|-2y)(2x-ḄÔåLæ2ç4Ḅèᦪ2--22■(-1)3=80,xᦑ⌱A.ê⚗LÔå!©-2y)(2x-y)5=i(2x-y)5-2y(2x-y)5,¦ᑭᵨÝ⚗L(2x-y)5ḄÞ⚗Mᓽ.W⚪ì⌕ὃYwÝ⚗LRᳮḄ\ᵨ_Ạ⚪.9.ூᫀ௃Dூ᪆௃¬2((1)=2,ᡠ[oSMi)=yï0“1+-প-2AX2Axᦑ⌱D.᪷ðᦪḄRñ᩽▲Ḅ¤UᓽMNᫀ.W⚪ὃYwðᦪḄRñ᩽▲Ḅ¤UὃYwTUx_Ạ⚪.10.ூᫀ௃Bூ᪆௃•ôõröf÷øù᝱ᑖûN(0,ü),P(f>2)=P(f<-2)=0.023,P(-2<<<2)=1->2)-<-2)=1-0.023-0.023=0.954.ᦑ⌱B.

7᪷ᩩᔠ᝱ᑖḄ"#ឋᓽ&'(.)⚪+⌕ὃ.᝱ᑖḄ"#ឋ/01Ạ⚪.1I.ூ5ᫀ௃Bூ(᪆௃(ᵫ1=7,y=5.5,:;ឋ<=>?@;_(Eb=FG=0.8-=bx01ᡠJ<=K;@y=0.8x-O.NᡠJOx=10Py=0,8x10-0.1=7.9-ᦑ⌱:B.ᐜ'T<=>?Ux=10Vᐭᓽ&'E.)⚪ὃ.X;ឋ<=>?ḄYᵨ/01Ạ⚪.12.ூ5ᫀ௃Dூ(᪆௃(ᵫf(%)=ax2—axlnx—e”ᨵbcdeEa7—axlnx—ex=0ᨵbc᪷BPax(x—/nx)=e”ᨵbc᪷ig(x)=x—Inx,g'(x)=1—=l1,Oxe(0,1)P/(%)<0,OmE(1,+8)P/(%)>0,:.g(x)>g(l)=1>0,&Em(%-Inx)>0ᙠ(0,+8)rឤᡂua=evᨵb᪷x^-xlnxiw(X)=ᑣh(x)=={;)(|},''x2-xlnx(x2-xlnx)2(x2-xlnx)2ᵫr&~—Inx>1,A%—1—Inx>0,OX6(0,1)P'(%)<0,(%)ᓫ⌴OmW(l,+8)P,(%)>0,(%)ᓫ⌴•••h(x)Ḅ᩽@(1)==e,Om->0+P(%)T+8,OmT++8P(%)T+8,•.ᦪ/(%)=ax2-axlnx-e”ᨵbcdeᑣᦪaḄ@(e,+8).ᦑ⌱D.⚪ᓄ@a=vNᨵb᪷iw(%)=vᑭᵨᦪ'ᐸ᩽ᓽ&'Eᦪxz-xlnxஹ/x2-xlnxaḄ.)⚪ὃ.ᦪdeḄᑨYᵨὃ.ᓄ=ᓄ¡¢£Xᑭᵨᦪ'᩽ὃ.¤8⚓ᐳ14⚓

8§¨'(©ª/«⚪.13.ூ5ᫀ௃2x-y-l=0ூ(᪆௃(ᵫ/'¬x=/+2xe-1,E/¬®=2x+2e*+2xe”,•••/¬0=2,/¬0=-1,ᦪf¬°ᙠe¬0,f¬0ᜐḄᑗ;>?@y=2x-l,ᓽ2%-y-1=0.ᦑ5ᫀ@2x-y-l=0.'T³ᦪḄᦪEᑮᦪᙠx=0PḄᦪµ'T/¬0,ᑭᵨK;>?Ḅ¶·¸E5ᫀ.)⚪ὃ.ᑭᵨᦪẆº»¼;r½eᜐḄᑗ;>?ᐵ¿ÀÁÂ1)ÃÄᦪḄᦪ,À1Ạ⚪.14.ூ5ᫀ௃Åூ(᪆௃(▢ÇÈᑖ☢Ê@J¬9-—dx=¬9%_[/Î=¬x3-ix33-¬9x9114281vh1=ÐÑÒABCDḄ☢Ê@¬3-1x9=18,28ᡠJᙠÑÒ4BCDᑁ×ØveÙeÚ▢ÇÈᑖḄᭆ᳛Ä0Ý=11.1827ᦑ5ᫀ@Þ.ᵨÊᑖߨ▢ÇÈᑖ☢Ê◀JÑÒABCDḄ☢ÊᓽE5ᫀ.)⚪ὃ.ÊᑖYᵨᦪ§¨ὃ.ᦪ᧨©ª/01Ạ⚪.15.ூ5ᫀ௃âூ(᪆௃(ãäåæὅèé⚜ëḄbìíîᨵ:ïᨵvìÀðḄᡠJᎷò4óᵬ¤ðõ¤ã┯÷øᑣBóᵬ¤â┯÷ù¤vðøᑣCóõ¤â¬ðù¤¬┯÷øᑣ஺óõ¤¬┯÷|¤v¬ðù¤vûü.ᡠJᎷò4óᵬ¤┯÷õ¤ãðøᑣCóõ¤â¬┯÷ù¤¬ðøᑣBóᵬ¤âðù¤v┯÷øᑣ஺óõ¤¬┯÷|¤v¬ðýᔠ⚪þ.ᦑ5ᫀ@â.

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10⚪⌕ὃGᦪḄ[ᑣᦪḄᦪ£¤l¥ḄᵨẠ⚪.18.ூᫀ௃(1)2x2ᑡὶ⊤᝞.⊤ᡠ®:ᨵ°±L²°±L³"30¶T.18123030¶T·24630³"421860(2)ᵫ⚪lº=»ᯠ½T2.857<6.635,ᡠTÁᨵ99%ḄÄÅÆL±uÇÈÉᨵᐵ.ூ᪆௃(1)᪷y%ᩩÌᔠᑡὶ⊤ÍÎḄᦪyᐵÏᓽ}.(2)᪷y%ᩩÌᔠÐÑឋÓÔᓽ}.⚪⌕ὃÐÑឋÓÔὃÕᓄ×ØẠ⚪.19.ூᫀ௃:(/)Ún=l@Si=a1=|,Ú7122@an=^n~Sn-i=S+2,nãSn=S22),N-3-1n.c_]_3s—1_4<_1_5,,S2+ã;+RS3+9+9S4-(஻)ᵫ(/)ëìSn=^(n€N*),ðDজÚn=l@$1=|=óëìᡂÑঝᎷ
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3Fa᪷N☢RbcX,bᩞRUSᓃᑣ9ᦑf=g*186=1209
63h.Yy0.06ூ᪆௃᪷W⚪iᔠjឋl2mn(Kᙳᦪஹ᪵5qᐵsᦪtuvw᪍yGz᪛ᩈḄbᩞRUḄᓽ%.5⚪ὃ:jឋl2mn>?@᫏⚪.21.ூBᫀ௃DE1@1᪥ᙠ}~⚗@Ḅᭆ᳛ᑖS0.5,0.4,0.8,%Xᑮ~1᪥Ḅᭆ᳛᝞⊤DL}ᵬ1᪥ᭆ᳛0.50.40.81᪥ᭆ᳛0.50.60.2ᵬ1᪥⌕X◤⌕ᙠ3@2জᵬ1᪥3ᐰᭆ᳛SD?!=0.5x0.4x0.8=0.16,ঝᵬ1᪥321ᭆ᳛SDP=0.5x0,4x0.2+0.5x0,6x0.8+0.5x20.4x0.8=0.44,ᡠᵬ1᪥XḄᭆ᳛SDP=Pi+22=0.6Y(2)1᪥ḄbXᑖXḄ%SD0,10,20,30,ᐸᭆ᳛ᑖSDp(x=0)=0.5x0.4x0.8=0.16,P(X=10)=0.5x0.4x0.2+0.5x0.6x0.8+0.5x0.4x0.8=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,ᑣxḄᑖ¢ᑡSDX0102030P0.160.440.340.06XḄ£¤EX=0x0.16+10x0.44+20x0.34+30x0.06=13.ூ᪆௃᪷Wq¥¦§¨Ḅᭆ᳛©4ª«%(¬@1᪥2ᡈὅ3Ḅᭆ᳛,%Xᑮᵬ1᪥XḄᭆ᳛Y1᪥ḄbXᑖXḄ%0,10,20,30,ᑖ(12⚓ᐳ14⚓

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