云南省2023-2024学年高二年级期末考试(604B)试题(数学)

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云南省2023-2024学年高二年级期末考试(604B)试题(数学)试卷答案

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54.A然而这没有阻止我，我继续锻炼基本曲棍球技能，因而A正确

55.B根据前文可知这些因素共同作用，使我成为一个更好的曲棍球手，因而B正确

56.D从后文可知在我大三开始前，我发誓要超越自己，D.better这里做动词，超越，改善，符合语境

57.C我开始认真对待时间，即开始认真学习，C.seriously符合语境

58.A获得了第一个4.0学分，因而A正确

59.B从前文看，不但学习好，而且做好一些小事，因而B正确

60.D做好自己的一些小事包括把自己的书包整理好，因而D正确

【听力录音原文】Text1W:Mr.Brown,Ineedtochecktheapartmentbeforeyoumoveout.M:Noproblem.Comein,please.ButImusttellyouabouttheworncarpet.ItwaslikethatwhenImovedin.W:Don'tworry.Iknowthat.Text2M:Whathaveyoubeendoingallmorning?Writingyourpaper?W:ActuallyIhandeditinyesterday.Iwantedtodosomereadingthismorning,butitwassosunnythatIdecidedtogoforaruninstead.M:Good.Text3M:Whatdoyouthinkofthevolleyballmatchlastnight?W:Oh.Ialmostfellasleepduringthematch.Whataboutyouropinion?M:Generally,itwasanaveragegame,butitwasexcitingatthebeginningText4M:Cindy,youlookdifferenttoday.W:Yes.IhadmyhairdoneyesterdayM:Ireallyloveit.Itmakesyoulookmuchyounger.ItreallysuitstheshapeofyourfaceText5W:Mark,Iheardyou'replayingbadmintonthesedays.Doyouloveit?M:Yes,Ido.Butthere'saproblem.Idon'thaveagoodpartner,soI'mnotimprovingfast.W:Youcanfindatrainer.Itcanhelpyoumore.Text6M:Thisisareallybigbookstore.Howmanyfloorsarethere?W:Therearesevenfloorsinthebuilding.AllofthembutthetoptwobelongtothebookstoreM:Whatkindsofbooksdoyouwanttobuy?W:First,IwanttogotothethirdfloortobuysomefantasybooksformyfriendJason.ThenI'llgoupandchoosesomeautobiographiesformyyoungerbrother.Helovesreadingstoriesofinspiringpeople.M:Won'tyoubuyanybooksforyourself?W:Yes,Iwill.Iwanttomakemygardenabetterplace.SoIwantabookthatcanhelpme.Text7M:Iknow,itwasyourweddinganniversarylastSaturday.HowdidyouandStevenscelebrateit?W:Well...Whenwegoonwalks,myhusbandoftentalksaboutthelitteronthesidewalk.So,onthatday,wedecidedtodosomeclean-up.M:Justthetwoofyou?W:Yes.Itookapickerandheheldabigtrashbag.Togetherwedidlitterpickupnearthehighschool.Iwassurprisedthatthebagfilledupsoquicklyandwedumpeditintheroadsidetrashbin.M:Wow,that'skindofmeaningfulonananniversary.W:Yeah.Itgaveasenseofsatisfaction.Wethoughtofdoingthisonaregularbasis,maybeonceamonthAfterward,wehadanicecupofteaandenjoyedsomecake高三英语参考答案第3页（共4页)

分析观察已知式子，移项变形为a_n+1+2=q（a_n+2），从而得到a_n+2与a_n+1+2的关系，分a_n=-2和a_n≠-2讨论，当a_n≠-2时构造公比为q的等比数列{a_n+2}，进而计算可得结论．

解答解：∵a_n+1=qa_n+2q-2（q为常数，），
∴a_n+1+2=q（a_n+2），n=1，2，…，
下面对a_n是否为2进行讨论：
①当a_n=-2时，显然有a₃，a₄，a₅∈{-5，-2，-1，7}，此时a₁=-2；
②当a_n≠-2时，{a_n+2}为等比数列，
又因为a₃，a₄，a₅∈{-5，-2，-1，7}，
所以a₃+2，a₄+2，a₅+2∈{-3，0，1，9}，
因为a_n≠-2，所以a_n+2≠0，
从而a₃+2=1，a₄+2=-3，a₅+2=9，q=-3或a₃+2=9，a₄+2=-3，a₅+2=1，q=-$\frac{1}{3}$
代入a_n+1=qa_n+2q-2，可得到a₁=-$\frac{17}{9}$，或a₁=79；
综上所述，a₁=-2或-$\frac{17}{9}$或79，
故答案为：-2或-$\frac{17}{9}$或79．

点评本题考查数列的递推式，对数列递推式能否成功变形是解答本题的关键所在，要分类讨论思想在本体重的应用，否则容易漏解，注意解题方法的积累，属于难题．