三、填空题：本题共3小题，每小题5分，共15分.12.2024 年,杭州某科技公司研发的智能扫地机器人销量持续增长.已知该产品 2024 年前七个月的月销量(单位:万台)与月份t的函数关系为f(t）=2t²+3t,则1 月到3 月月销量的均增长率为万台/月.3an，则a=180α,x^在x=1 处的导数为f'(1）,则使得f'(1)≥14 的正整数n 的最小值为四、解答题：本题共5小题，共77分.解答应写出文字说明、证明过程或演算步骤.15.(13分）记 S,是等差数列α,}的前n项和,已知α,=4,S,=54.（I)求α}的通项公式;（Ⅱ)求数列a,+2"}的前n项和 T.16.(15分)某科技公司2025年计划推出量子加密通信设备,该设备可实时保护数据传输，目标用户为学校、企业和自由开发者.该公司调查了不同用户对该设备的需求情况,得到数据如下(单位：个)：学校企业自由开发者有需求3m1702n无需求m120n已知调查了400个学校和150个自由开发者.（ I)求m和n的值;（Ⅱ)估计目标用户对该设备有需求的概率;（Ⅲ)是否有99%的把握认为学校用户与非学校用户对该设备的需求情况有差异？P(x²≥k)0. 10. 010.001n(ad -bc)²附：x=(a+b)(c+d)(a+c)(b+d)k2. 7066. 63510. 828数学试题 第3页(共4页)O □

26-30CBDDATony:Hey,LiMei!Inoticedchrysanthemums二语言知识运用（菊花）everywhereonmywayto补全对话school.(51))26.Wewill leavefortheairportassoonasDadhome.Li Mei:Yes.It'stheDoubleNinthFestival tomorrow.A.is arrivingB.arrivedC.arrivesD.will arriveTony:(52)Isit because it's the)27.Withthelittleboytheway,wefound theoldman’s house29thtomorrow?without any difficulty.Li Mei:No.It'stheninth dayof theninthlunarmonth tomorrow.That'sA.leadB.leadingC.toleadD.ledwhere the name is from.51-55CBGAD)28.Carspollute theenvironment,？So let'stry to use cars less.Tony:Isee.LiMei:InChinese,nineisregarded（认为）asthenumberof“Yang”andA.will theyB.do theyC.won't theyD.don'tthey"Chong”means double.(53))29.—Ihearyourbirthdayiscoming.IwonderTony:Howdoyou celebrate it?Byeating outwithmyfamily.Li Mei:(54)For example,we eat Chongyang cake,drinkA.where are you going tocelebratechrysanthemum wine（酒）andclimbmountains.B.how areyou goingtocelebrateTony:Wow!(55)C.whereyou aregoing tocelebrateA.There are a lot of activities.D.howyou aregoing tocelebrateB.Why is it called“Double Ninth"?C.Are you celebrating anything special?)30.—Myparents are planning to takeme toDisneyland.!Everydayfeelslikea holiday atDisneyland.D.Chinaisreallyrichin culture and traditionsE.Thefestivalhasalonghistoryof2,000yearsA.Have funB.Good luckC.Well doneD.Nice ideaF.It is a timefor family andfriends to come together.G.Sothefestivalis alsocalled theChongyangFestival.Festival Planner is an appwhere people can get information about完形填空Whenthespringarrived，peopleinMadeira（马德拉群岛）welcomedfestivals from around the world. Let's seewhat Lilyhas discovered.三阅读theFlowerFestival.Visitorsfromallovertheworldcameheretocelebrate10:00thetraditionalfestival together.Amongthehappypeoplewasa31boyFestival PlannerDiwali(Festival of Lights)namedTim.Hecameouttoenjoythebeautifulflowerfloats（游行花车）asusual.Place:Mostly celebrated in IndiaAsTimwas32thestreet,henoticeda strangersittingalone infrontTime:October or Novemberofa coffee shop.He seemed tobe33among thehappy people.TimActivities:People place oil lanterns throughout theirhousesandinthe streets tocelebrate thevictory（胜利）wanted tohelp.Heintroducedhimselftothemanandlearntthattheman'soflight over darkness.They alsogive gifts,eat deliciousnamewasMaxJohnson.TimsharedstoriesaboutthetownwithMrJohnsonsweets,andset offfireworks（烟花）andeveninvited（邀请）themantojoinhimandhis34forlunch.Huazhao Festival)31.A.poorB.localC.strangeD.hungryPlace:Celebrated in ChinaA)32.A.tidying upB.pointing atATime:Early springActivities:People usually wear hanfuto cnjoy flowers,C.walkingdownD.learning aboutwrite articles about them,and make flower cakes.It‘s a)33.A.lonelyB.excitedC.coolD.surprisedtime to enjoy thebeauty ofnature andwelcome thenewD.familyseason.)34.A.classmatesB.friendsC.team3Monkey Bufft（自助餐）FestivalPlace:Celebrated inThailand（泰国）Time:November31-34BCADAetivities:Thai people believe monkeys are a symbolofgoodluck.They prepare fuitvegetables and snacksto treat monkeys.There are also traditional dances andmusic,making the festival more exciting.完形填空Duringthemeal,Tim’sparentstreatedMrJohnsonlikeanoldfriend.The三阅读foodwasverydelicious,andthey35alotandlaughedloudlyatthetable.Mr56-58AABJohnsonfeltmuch36thanhedidinthemorning.BeforeMrJohnsonleftTimgavehima_37.Itwasapairofprettyflowerbracelets（手环）Monthslater,Timlearned thatMrJohnsonwasgoingthroughahard)56.HowdopeoplecelebrateDiwali?time when they38.But Tim'swarmthandkindness lethimsee theA.Bysettingofffireworks.B.Byenjoying natural beauty.beautyoftheworld39.AndTimlearnedthatthe40_ofthefestivalisC.By writing articles about lanterns.not just about celebration—it's about reaching out to others and makingD.By placing snacks throughout the houses.themfeel welcomeandhappy.)57.WhenistheHuazhaoFestivalcelebrated?)35.A.readB.talkedC.thoughtD.studiedA.In spring.B.In summer.C.In autumn.D.In winter.)36.A.busierB.betterC.calmerD.healthier)58.WhichofthefollowingisTRUEabout thethreefestivals?37.A.signB.flagC.dishD.presentA.They are celebrated inNovember.38.A.metB.joinedC.leftD.movedB.They are celebrated inAsian countries.39.A.tooB.againC.earlyD.aloneC.Theybecomepopularfor deliciousfood.)40.A.historyB.dateC.meaningD.funD.They can help people get close tonature.35-40BBDABCItwasTartanDay.TheMenteithsdecidedtotakepartinthecelebration完形填空Binthepark.Gordonwasexcited about theparade,andhis41Jessicawas三阅读interestedintheactivitiesafterthat.“42did you come toAmerica,Dad?Gordon asked.DoyouknowWorldStationeryDay（世界文具日）？ItfallsontheIwasabout tenyearsold.Itseemslikea longtime ago,butIstilllastWednesdayofAprileachyear.Thedayreminds（提醒）usofthe43Scotlandwell,answered Gordon's father.importanceof handwritingandusingstationeryinourdailylives,especially“Mum,wereyou born inScotland,too?”Jessica questioned.intoday'sdigital（数字的）world.No,Iwasbornhere.Imet44dadatschool.IdoknowmuchaboutHowdopeoplecelebratethisspecialday?ManychoosetowritelettersScotlandnow,"Mumlaughed.orcardstofriendsorfamily.TheybelievethatwritingwithapenfeelsmoreThefamilytalkedallthewaytothe_45_.Afterarriving,theyfoundapersonal thantyping（打字）ona screen.placetosit.Gordonlooked46.Hiseyeswerefull（充满的）ofinterestinWhat'smore,stationerystoresoftenhavesales andofferdiscountssoeverythinggoingon.Therewas tartaneverywhere helooked.Bpeoplecanpaylessfor thingslike colorful pensor cutenotebooks.Some)41.A.sisterB.friendC.auntD.cousinorganizationsevenholdfun activities,such ascalligraphy（书法）classes.)42.A.WhyB.WhenC.HowSchools alsojoinin.Theymaygive students specialwritingexercisesD.WhereB.protectC.leadD.rememberorlessonsaboutthehistoryofstationery.Thishelpsstudentsunderstand)43.A.trust)44.A.hisB.theirC.herD.yourwhyhandwritingskillsarestillimportant.C.parkInaword,WorldStationeryDayencourageseveryonetoslowdown,)45.A.hallB.storeD.houseC.again)46.A.outB.aroundD.inside41-46ABDDCB)59.WhenisWorldStationeryDaythisyear?完形填空三阅读April2025“WhatisTartanDay？Isitadayinhonourof（为纪念）Americans？asked Jessica."No.TartanDayisa47day，”said Mum.“It'saday tohonour themenandwomenfromScotlandwhodidsomethinggreattohelpAmerica."Assoonasshefinishedspeaking,thebandstarted48_,whichmeanttheparadewas about tobegin,49theystopped towatchit.They alsowatchedashowbytheHighlanddancersandaScottishconcert.)60.Why do manypeople choose towriteletters on this day？Everyonehadgreatfun.Itwas thebesttime theyhadspentas afamilyA.To save money.B.To practice handwriting.inyears.They50to do that again thenextyear.C.To show their writing skills.D.To be more personal.)61.What does the underlinedword“discounts”mean?)47.A.specialB.luckyC.busyD.darkA.Lower prices,B.New things.)48.A.getting offB.falling awayC.warmingupD.going backC.More ways.D.Free gifts.49.A.orB.becauseC.soD.but)62.What is the passagemainly about?)50.A.forgotA.Some popular stationery stores in theworld.B.decidedC.refusedD.affordedB.The differences between handwriting and typing.C.Thehistoryanddevelopmentofdigitalwritingtools.D.Ways tocelebrateWorldStationeryDay and its meaning.47-50ACCB59-62CDAD2

W: Derek, how did you get into horseback riding?M: I grew up in a small village where horseback riding was the main way to get around. Next tothe local market where my parents sold vegetables was a wide, empty street. While they weredoing business, I'd ride down it over and over again.W: Do you train for horseback riding?M: I've never had any formal training or dreamed of becoming a professional rider. It's just for fun.I can go to places I could never reach in a club. I just like to see the problems I come up againstbeing solved.W: Can you share what's next?M: I just released my first video, and I have more ideas coming up. The first thing, though, is to goto Canada. I'm going to star in the film An Amateur Rider in Montreal. The landscape there isamazing.(m1x))W: Fred, do you think it's a good idea to go to university straight after high school?company I'd contacted just got in touch with me. I'm good at game design, and Id like to do thatfor a living.So I'm still hesitating.My sister Emma took a gap year before going to university andvisited about 10 countries,but she said she wished she'd done something more useful with hertime, like volunteering for a charity.W: Interesting point! Do you know that some people are putting off going to university because ofthe cost?M: Yes, and many students work while they're studying to support themselves financially. Actually.a lot of employers prefer students who are familiar with what it's really like to work. From astudent's point of view,it can give you a good idea of what you do and don't like about a job.W: Have you ever considered going to a university open day?M: Actually, I just went last weekend. I met some students majoring in Spanish, and they showedme around ...(Text 10)Good morning, boys and girls. In today's class, were going to talk about an important topic: howto recognize risks and help others in times of need. Let me start by sharing a real-life story withyou.Last Friday, there was a baseball game between two schools in the city. A young man namedSam was struck in the chest by a fly ball. He fell to the ground immediately after being hit. Hisparents, who were in the stands, rushed over to check on him, and his coach called for anambulance. Fortunately,a nurse named Maria was stationed nearby at the medical tent. Sheperformed CPR on Sam, connected him to an oxygen tank, and closely monitored his vital signs.She also ensured the area was cleared, giving Sam enough space to breathe. Thanks to Maria'squickresponse,Sam survived the incident.He was taken to thehospital for treatment around 3pmand didn't wake up until about five hours later. His parents were greatly relieved. They were alsoextremely grateful toMaria for being there and saving their son's life.参考答案1-5 BCCAC6-10 BAACB11-15 BCABA16-20 CABAC21-25DDCBC26-30ACDCA31-35BBAAB36-40 FADGC

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A.原子半径：Z>Y>XALNaOHAGHNSHHCIKALB金属单质M，△下列叙述错误的是C.B为FeSD.E→F属于化合反应NHCI湿润红色石蕊试纸a消石灰湿润红色石蕊试纸b浓硫酸甲基橙溶液IIIIIV下列叙述正确的是A.装置I中，反应的化学方程式为2NH4CI+Ca（OH）CaCl+2H20+2NH↑B.装置Ⅱ中，试纸b先变色，试纸a后变色C.装置Ⅲ中，因产生了铵盐而产生“白烟”D.装置IV中，甲基橙溶液变为红色13.DissectolA（乙）是从几种开花植物中分离出来的重排烯苷。一种制备乙的过程如图所示（部分物质未标出）。下列叙述正确的是Pd(PPh)HO~DBUHOCTHFHOOHOHHOOHOH0-0-2甲0页第4页（共8页）化学试题

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