江西省2024届九年级第五次阶段适应性评估[PGZX A JX]数学.考卷答案

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江西省2024届九年级第五次阶段适应性评估[PGZX A JX]数学.考卷答案试卷答案

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综合能力提升检测(14)参考答案及部分解析参考答案1-5BBCAC6-10ABCCA11-15BAABB16-20ABCAC21-25ACBCB26-30ABACD31-35CDACB36-40EDBFC41-45ACDBC46-50ADBCA51-55DACBD56.performance57.to58.beautifully59.isreduced60.What61.took62.tolet63.and64.forgiving65.amazing写作第一节Onepossibleversion:DearLucy,I'mwritingtoaskyoutocontributeanEnglishstorytoourschool'sradiostation.Itwillbeairedinourschoolduringtheafternoonbreak.Thetopicofthestorycanbeinspiringteenagersnowadaysorimportantpeopleinhistory.Hopefully,thestorycaninspirestudentsinonewayoranother.Inaddition,thestoryshouldbewrittenusingsimplewordsandshortsentences,sothatallofuscanfollowit.Thestorytobesharedshouldlastabout5minutes.So,canyourecommendastoryofabout300words?Lookingforwardtoyourreply!Yours,LiHua第二节Onepossibleversion:"David!David!"Mr.ManningcalledDavidoutsidehishome.Hearingthat,Davidwentoutside.HesawMr.Manningandatruck.Mr.Manningsmiledathim,"Iheardyoutalkingtoyourfriendatthestore.Iknowwhatyoudid.Iknowhowmuchyouwantedthosesneakers,andIsawyousellinglemonadeanddeliveringnewspapers.Andtoday,Isawyouletallthatwishgo,justtohelpafriendwhowasindeeperneedthanyouwere.Davidloweredhisheadoutofshyness.Mr.Manningcontinued,"AndIthinkthiskindoffriendshipoughttobecelebrated.Socomeon!Getonthebackofthistruckandpickupasmanypairsofshoesasyou'dlike.Don'tworryaboutthemoney;thisisallonme."Davidhesitated,andthenrantowardsthetruckwitheyesshininginexcitement."Hurry,we'llalsogotoyourfriend'shouse.Therearefreeshoesforhim,too!"【补充说明】takesb.aback:使某人震惊,使某人大吃一惊部分解析阅读第一节A篇

分析对于A,可举x=$\frac{π}{3}$∈(0,π),检验不等式即可判断;对于B,构造t=x2(t>0),f(t)=et-1-t,运用导数判断单调性即可得到;对于C,令f(x)=sinx+tanx-2x(0<x<π),求出导数,判断单调性,即可得到结论;对于D,lnx+ex>x$-\frac{1}{x}$+2,即为lnx+$\frac{1}{x}$>x+2-ex,(x>0),设f(x)=lnx+$\frac{1}{x}$,g(x)=x+2-ex,分别求出导数,判断单调性,求得最值,即可判断.

解答解:对于A,可举x=$\frac{π}{3}$∈(0,π),可得(x+1)cosx=(1+$\frac{π}{3}$)×$\frac{1}{2}$>1,即有A不恒成立;
对于B,可令t=x2(t>0),由f(t)=et-1-t的导数为f′(t)=et-1>0,即为f(t)在t>0递增,
即有f(t)>f(0)=0,则原不等式恒成立;
对于C,令f(x)=sinx+tanx-2x(0<x<π),f′(x)=cosx+sec2x-2=cosx+$\frac{1}{co{s}^{2}x}$-2,
设t=cosx(0<t<1),则g(t)=t+t-2-2,g′(t)=1-2t-3<0,g(t)在(0,1)递减,即有g(t)>g(1)=0,
则f(x)>0恒成立;
对于D,lnx+ex>x$-\frac{1}{x}$+2,即为lnx+$\frac{1}{x}$>x+2-ex,(x>0),
设f(x)=lnx+$\frac{1}{x}$,g(x)=x+2-ex,f′(x)=$\frac{1}{x}$-$\frac{1}{{x}^{2}}$,
当x>1时,f(x)递增,0<x<1时,f(x)递减,
即有x=1处f(x)取得最小值1;g(x)的导数为g′(x)=1-ex
当x>0时,g′(x)<0,即有g(x)<1,故原不等式恒成立.
故选:A.

点评本题考查不等式恒成立问题的解法,注意运用构造函数,运用导数判断单调性求得最值,考查运算能力,属于中档题.