合个本2(x-y.-的最小二乘法估计公式分别为6=à=y-6x是GAt,-):10)·T918参考数据：2=292.立x2=204,22=730348.xy,=12041,i=15732=328329,√105≈10.25，√7369≈85.84旺出四21.(本题满分12分)中0已知点P0,-2),点A,B分别为椭圆C:+片=e0的左右顶点，直线BP交C于点Q,△ABP是等腰直角三角形，且PD-i,(1)过椭圆C的上顶点M引两条互相垂直的直线L,,记C上任一点N到两直线,的距离分别为d,d2,求d+d的最大值：(2)过点H(4,0)且斜率不为零的直线与椭圆C相交于E,F两点试问：是否存在x轴上的定点G,使得∠EGO=∠FGH若存在，求出定点G的坐标；若不存在，说明理由.水可22.(本题满分12分)已知函数f(x)=lnx-x+l.(1)求f(x)的最大值；(2)设函数g(x)=f(x)+a(x-1)},若对任意实数b∈(2,3)，当x∈(0，b时，函数g(x)的最大值为g(b),求a的取值范围：(3)若数列{an}的各项均为正数，a=1,an1=f(an)+2a。+1(n∈N).求证：an≤2”-1.高三二模数学试卷第6页（共6页）

19.(本小题满分12分)已知数列(a.)满足a1=3,2a+1-aa+1-1.1)记6一。与求数列(6，)的通项公式(2)记c.=(a1·a·…·an)2,S。为数列{cn)的前n项和，求证：S.<23.20.(本小题满分12分)已知圆C:x+(y-1)=},动圆M与圆C相外切，且与直线)一2相切.(1)求动圆圆心M的轨迹E的方程；(2)点P是(1)中曲线E上任意一点，曲线E在点P处的切线为1，过点Q(0,5)且与1行的直线交曲线E于A,B两点，当PALPB时，求点P的纵坐标.【高三数学第5页（共6页）】

学科核心素养·总复·数学（十一数与代数综合题号四(满分120分时间：120分钟)二填空题（本大题共6小题，每小题3分，共18分1得分总分累分人7.已知：代数式-6+√25-a的值为整数，则整数a一造择题本大共6小题，每小题3分，共8分8.若单项式2x2y与单项式-3xy可以合并成一项4+6的1.下列各数是无理数的是值是A.169.已知：1+2x-=0,则22-4x+2021=10.在面直角坐标系中点P(a,b)在第四象限，点P到x轴的距离为5且a2=4,则P点的坐标c.0.5151151(后面每两个5之间多一-个1)111.幻方是一个古老的数学问题，我国古代的（洛书》中记载了最早的三阶幻方—九宫图.如图所示的幻方中，每一横行、每一竖D.0.32若巴：+b:+=0是一元二次方程则口”可以为列以及两条对角线上的数字之和都相等.九官图中。-b+cA.aB.0C._1指D.1al3.202年9月27，日教育部分绍我园数育投入十年塔加3万化元。一半以上用于义务教育。请将3万亿用科学记数法表示为A.30×10”B.3×102(C.3×1013D.3×1044.下列计算结果与4计算结果相等的是12.在面直角坐标中，A1(1,5),A2(2,8),A(3,11),A(4,14)A.6-2B.2÷2×2…按照此规律判断.若Ax(m,n)是这列数中的一点，则m、n的关系」-12c-3D.（-√-2)2三、解答题（本大题共5小题，每小题6分，共30分】5.已知：二次函数y=2x2+4x-6不能通过移使得抛物线经过原13.(10计算：-1-11+-27+(2)-2023：点的是(2)解不等式组：r3x>9A.向左移1个单位B.向右移3个单位4x≤2x+8C.向上移6个单位D.向上移8个单位6函数，(>0)和=(x>0)的图象.及它们庆于)轴时称的函数图象如图所示.由图象可获得的正确信息()Y2=XA.若y1>y2,则-1

信息五：均数中位数众数方差九年级一班82.5m90158.75九年级二班80.575174.75根据以上信息，解决列问题：(1)填空：m,=70(2)你认为哪个班级的成绩更加稳定，请说明理由：（3)在本次测试中：九年级一班甲同学和九年级二班乙同学的成绩均为80分，你认为两人在各自班级中谁的成绩排名更靠前？请说明理由y装以的九年数班崩或结更加绝立因九班的方差地九班的小茎我的乙同浮更指荔风为九年转班的的数比九心班的狗接的防七、（本题满分12分）2,如图，在口ABCD中，AC是一条对角线，且AB=AC=5,BC=6,E,F是AD边上两点，点F在点E的右侧，AE=DF,连接CE并延长，CE的延长线与BA的延长线交于点G.)如图1，M是BC边上一点，连接AM,MF,MF与CE交于点N,AE=多①若M为BC中点，求证：EN=NC;②求AG的长；(2)如图2，连接GF,H是GF上一点，连接EH.若∠HED=∠CED,且HF=2GH,求EF的长.山0记明AC形形和5印31C3AM AAEC94FC·lEAC九地0efW≌4mC0se城EN-IVC图2MAUC2AFDCDFIRC八、（本题满分14分）23.在面直角坐标系xOy中，点(2，m)和点(6，n)在抛物线y=ax2+bx(Q<0)上.(1)若m=4,n=一12，求抛物线的解析式；(2)已知点A(1,y),B(4,y2)在该抛物线上，且mn=0.①比较y,y2,0的大小，并说明理由；②将线段AB沿水方向移得到线段A'B',若线段A'B与抛物线有交点，直接写出点A'的横坐标x的取值范围:作4：九t0孙10(2心6，y4的城上s开的14时2b日牛X1-2-sapbb139o/490年所仿真极品试卷·数学（三）第4页

B.Space Tourism Industry Wins Great Popularity.C.Branson's Space Trip Opens Door to Space Tourism.D.Branson's Virgin Galactic Flight is a Great Success.第二节（共5小题，每小题2分，满分10分）根据短文内容，从短文后的选项中选出能填入空白处的最佳选项。选项中有两项为多余选项It's reported that only about 9%of plastic waste in the world is recycled andthat millions and millions of tons of plastic waste ends up in landfills(垃圾填埋场and ocean environments such as rivers and oceans.Can we do anything about allthis?36Make a list of the plastics in your home.Before you can cut back on plastic,it helps to understand how much you'reusing.Do it now.Take out a pen and make a list of various kinds of plastics in yourapartment::chip bags,.condiment bottles(调料瓶)，etc.37 Check out your localrecycling program,and see which of those plastics can actually be recycled.38Look at the items on your plastic list and ask yourself,"What can I replace theplastic with?"You can start with carrying reusable water bottle and chopsticks to theoffice instead of using one-off ones.And Every time you go to the local store,bringyour own containers to avoid using the plastic bags provided.Make some“noise'”.A lot of plastie packaging that's created and used today can't be recycled.If youbring home a produet you like but its package isn't recyclable,39 Use the英语试题（七）第11页（共16页）

561D21:35画1℃的令36%☐5.设Fc,0),A0,-b),则直线AF的方程为-上=1，c b因为B在y轴左侧，所以渐近线方程为y=。x,1/10答案第1页，共10页x=ac,得a--5-06,e,n=5-以e·气。6，e=5-g。a-c:e=￡=万，-c-4-d-1=,六a=b,六双曲线的渐近线方程为y=士x,aa2故双曲线渐近线的夹角为子，选4。6.己知a=(-2,),万=(1,1)，由于a⊥b,所以a.6=(-2)×1+×1=0,解得元=2，所以a=(2,2),万=(11)，得a-i=(-3,),则(a-列6=(-3)x1+1x1=-2,-P+下=2，故a-b在b方向上的投影为得a-6在万方向上的投影向量为-2.万1-.选D.7.由题意可得，e[f"(x)+fx】=2x+3,令g(x)=ef(x),则g'(x)=e[fx)+f(x]=2x+3,故g(x)=x2+3x+c.又80=@=1=c,所以g=+3x+1,故/=+3x+1,所以了=+2-山，ee当x>1或x<-2时，∫(x)<0,函数分别单调递减：当-20,函数单调递增放当x=1时，函数取得极大值0-=8当x=-2时，函数取得极小值/(-2)=-2。x>0时fx)>0,x→+o时fx)→0，故x轴是图象的水渐近线，其图象如图所示。结合函数的图象，要使关于x的方程fx)m=0恰有两个实数根，实数m的取值箱H是（←心.0U得。选8。8.设事件A为：该单元有2户人家月用水量严重超标，事件B为：该单元有3户人家月用水量严重超标，则P(A)=CI-p)p2=31-p)p2,P(B)=Cp3=p3,即f(p)=P4)+P(B)=31-p)p2+p3=3p2-2p'(0

第二节书面表达One Possible Version:Boys and girls,To enrich the after-class activities of senior three students,the school English Club is goingto hold an English inspirational speech activity themed "My Growth Experience"in the schoollecture hall from 3 to 5 this Friday afternoon.The activity is arranged as follows.We have invited Li Hua,a schoolmate who graduated from Peking University,to deliver aspeech,in which he'll introduce his own experience of how he changed from a student who didnot love learning to a super learner.After the speech,there's a question-and-answer session.He'll answer the questions raised by the audience.All senior three students are welcome to attend on time,and we believe you'll certainly getsomething from the activity.(118 words)The English Club(一)评分原则1.本题总分为25分，按5个档次给分。2.评分时，先根据文章的内容和语言初步确定其所属档次，然后以该档次的要求来衡量，确定或调整档次，最后给分。3.词数少于80和多于130的，酌情扣分。4.评分时应注意的主要内容为：内容要点、应用词汇和语法结构的丰富性和准确性及上下文的连贯性。5.拼写与标点符号是语言准确性的一个方面。评分时应视其对交际的影响程度予以考虑。英、美拼写及词汇用法均可接受。(二)内容要点1.时间地点(7分)；2.活动安排(8分)；3.表达希望(6分)。4.适当发挥(4分)。(三)评分标准第五档(21一25分)：完全完成了试题规定的任务，完全达到了预期的写作目的一覆盖所有内容要点。应用了较多的语法结构和词汇。语法结构或词汇方面有些许错误，但为尽力使用较复杂结构或较高级词汇所致；具备较强的语言运用能力。英语试题答案第2页（共3页）

所以5=+2-1（号+2a22x2……11分②当me(-na》即me(-)时，是-2x2+ax=m的小根且<-号：x2是-ax=m的根，即m=-2.所以+m=点+0-，m+2+=-0+a-242X2 2x-dxx a-2x又a-2>2a,所以+m=-,a+a-2xe2a-XjX2 q-2x2o).综上：+me(g+l+o).2….15分第5页共5页

第40期参考答案7.W:Where is Angela?I need her help.hamburgers and eggs.Flora and Eden like rice and55.A test about blue candies./...第1版M:She is at the Lost and Found.She lost hervegetables.Our English teacher is Mrs.King.She56.It is good for our eyes./.主题阅读1-4BCBAbook in the library this morning.is nice to us.Her birthday is coming.Eden and I57.Green food.第2一4版Q:Where is Angela now?want to get her a birthday card.Flora wants to get58.Because people don't think blue is a food期末综合能力评估试题Ⅱ听力材料及参考答案8.W:Dad,I need a pair of sports shoes fora notebook for her.color and they don't think it is safe or听力材料Sports Day.四、听力填空本题你将听到一篇短文。请你根healthy to eat the bluc food./...一、情景反应本题共5个小题，每小题你将听到M:OK!Let's go to the clothes store.I need a据所听内容，完成下面的表格，并将获取的信息59.I eat food in different colors every day./...一组对话。请你从每小题所给的A、B、C三幅图pair of sports socks,too.填到相应的位置上。每空一词。短文读两遍。八，60.Where6l.and62.are63.They64.do片中，选出与你所听到的信息相关联的一项，并Q:Who needs a pair of sports socks?I'm Barry.I'm busy in January.I have a65.An 66.from 67.for 68.to 69.about将其字母标号填入题前括号内。每小题读两遍。9.W:I have a trip with my friends on March 8th.science test and a math test on the 11th.A history70.classmates 71.our 72.really 73.third1.W:Tom,what time do your family haveAre you free to come with us?74.to watch/watching 75.days 76.eatingbreakfast on Saturdays?M:Well...no,I'm not.I have an art test fromtest and a geography test are on the 22nd.On thelast day of January,we have English Day77.but 78.fat 79.buysM:We have breakfast at about nine thirty.the 8th to the 9th.February is a great month for me.I have a big九，One possible version:2.W:David,do you want to go to the store withQ:When does the boy's art test finish?party with my friends on the 13th.On the 20th,IHello,Becky!Welcome to our class.We are like ame?10.W:Alan,it's 10:00 a.m.Let's watch theM:Yes.I need to buy a radio.tennis game on TV.have a family trip for five days.So,what aboutbig family,and there are 45 students in our class.We are busy on school days.We have four lessons3.W:Who is that woman in a white skirt,Paul?M:Oh,I can't.I have a Chinese class on theyour January and February?M:She is our music teacher.computer at 10:15.参考答案in the morning and three in the afternoon.Thisterm,we have cight subjcets-English,Chinesc,4.M:Jenny,how much are these tomatoes?Q:What time does Alan have a Chinese class?-、I-5 CAABC二，6-I0 ACABBmath,music,art,P.E.,history and geography.W:They're twelve yuan.三、语篇理解本题你将听到一篇短文。请你根三II-I5 ABBACSchool activities are fun and relaxing.We have a5.M:Sally,what's your favorite month?据短文内容和所提出的5个问题，从每小题所给四、l6.Busy17.science18.3lst/thirty--firstmusic festival in March,Sports Day in April,aW:Of all the months,July is my favorite.的A、B、C三个选项中，选出一个最佳选项，并将二、对话理解本题共5个小题，每小题你将听到其字母标号填入题前括号内。短文读两遍：19.with 20.five /5book sale in May and an English party in June.五21-25 FDEBGYou're sure to like them!一组对话和一个问题。请你从每小题所给的A、I'm Erin.E-R-I-N,Erin.This is our classroom.B、C三个选项中，选出一个最佳选项，并将其字Our class has twenty girls and eighteen boys.六、26-29BCCA30-33BCBB母标号填入题前括号内。每小题读两遍。Flora and Eden are my good friends.Flora likes七、34-38 BCBAB39-43 CCBBA44-48 ADBFE6.W:Of the numbers on the card,I like six andmusic and her CD player is in her desk.Eden49.clothes 50.always 51.free 52.60/sixtynine.What about you?loves sports.A basketball is under his chair.Art is53.helpsM:Number three is my favoritemy favorite.Some pictures are in my schoolbag.54.我们的父母总是要求我们吃绿色蔬菜，掌上周报小程⊙.：英语周报》官方小程序Q:What is the boy's favorite number?All three of us have lunch at school.I like因为它们健康。

第四部分【写作提示】升入四年级后，作者被老师告知他的阅读理解能力和单词发音能力要低于其他同学。经测试，作者被诊断有诵读困难。虽然医生安慰了作者，也给出了克服诵读困难的建议，但作者在了解了诵读困难的一些相关信息后，并没有信心能克服写作诵读困难，也因此对自己的未来充满了恐惧和担忧。1.根据续写第一段的首句可知，作者的父母第四部给作者带来一本关于克服人生挑战的书。作者从中受到鼓舞了吗？作者按照医生的建议尝试克服诵读困难了吗？成功了吗？本段可围绕这些内容展开叙述。2.根据续写第二段的首句可知，几年后，当写作者在同一家医院做志愿者时，一个有阅读障碍的女孩让作者给她读一本书。作者是怎么做的呢？小女孩有什么反应？作者有何感受？本段可围绕这些内容展开叙述。One possible version:They brought me a book about some peoplebeating off life challenges.They read it together四部分with me every day.Gradually,I was confident anddetermined that I would overcome my own lifechallenge.Based on Dr.Waites'suggestions,I setout to remove my dyslexia.Each day,I kept写作reading aloud,remembering words,doing sports,etc.Besides,I went to hospital for speech therapyregularly and my parents supported me.Finally,I overcame my learning disability.Dr.Waitesconfirmed this when I was tested again.Several years later,when I volunteered at the same四部hospital,a girl who had dyslexia asked me to read abook to her.I read the book very slowly so that shecould understand the story and the words.When itcame time for me to leave,the girl thanked me.Iwalked out of her room with a huge smile on my写face.I had overcome my disability and was helpingothers to overcome theirs.I am determined tosucceed in life,and in the process,help others facegand conquer the challenges that I have overcome.本WRITING TIPS其余参考They went into my room to take away mylaptop.I was upset and angry,but they hadmade up their minds.Finally I gave the laptop to答案them unwillingly.6

20.（原创)袋中装有黑球、白球共7个，从中任取2个球都是白球的概率为7(1)现有甲，乙二人从袋中轮流摸取1球，甲先取，乙后取，然后甲再取，取后不放回，直到两人中有一人取到白球为止，每个球在每一次被取出的机会是等可能的求取球次数X的分布列；(2)现从袋中将黑球和白球各取出一个，再让丙从袋中取球，每次取一个，记下颜色后放回再取，直到将同一种颜色的球取出3次为止，记丙取球的次数为Y,求Y的期望21.快递业的迅速发展导致行业内竞争日趋激单件均成本y元烈.某快递网点需了解一天中收发一件快递8的均成本y(单位：元)与当天揽收的快6递件数即揽件量x(单位：千件)之间的关系，对该网点近7天的每日揽件量x,(单位：千件)与当日收发一件快递的均成本y:(单位：元)(i=1,2,3,4,5,6,7)的数据0246810每日揽件量x/千件进行了初步处理，得到散点图及一些统计量的值yW240x-列2%-列(x-)2(w-}i=144.60.37-182.7525.50.55表中W=d(1)根据散点图判断y=ax+b与y=c+二哪一个更适宜作为y关于x的经验回归方程类型？并根据判断结果及表中数据求出y关于x的经验回归方程；(2)已知该网点每天的揽件量x(单位：千件)与单件快递的均价格t（单位：元)之间的关系是x=√59-4t(5.75≤t≤14.5)，收发一件快递的利润等于单件的均价格减去均成本，根据（1)中建立的经验回归方程解决以下问题：①预测该网点某天揽件量为2千件时可获得的总利润；②单件快递的均价格t为何值时，该网点一天内收发快递所获利润的预报值最大？附：对于一组具有线性相关关系的数据(4，：)(i=1,2,…,n),其经验回归直线2(4-列（心-）=u+众的斜率和截距的最小二乘估计分别为=a=v-Bi.∑(4-2.(改编)已知函数f()=xnx二m-x,m∈☑(1)若g(x)=∫(x)(f(x)为f(x)的导函数)，求函数8(x)的单调区间；(2)求函数g(x)在区间L,e]上的最大值：(3)若函数f(x)有两个极值点，x,(化≠)，求证：，1+，1>2.Inx Inx22022-2023学年度第二学期期末七校联考高二数学试题第4页共4页

Myrtle Beachu are looking for coastal views and oceanic adventures.hplace for you!This city is known for its amazing beaches and adventures that offpsthe most forgettabe mmorics.A ide varety ofSan AntonioSan Antonio is a great place to visit for a combination of American history and moderattractions.Favored wetivities inelude the City SSYoutoSant beondVreLake Tahoeake Tahoe is known for its amazing and luxurious(奢华的）ski resorts..For those whthe Get Outdoors in Lae esust This gorgeousgenatural wonders,amazing shows,and lodging to suit your needs.21.What is the purpose of this text?A.To introduce the function of VME.B.To show how to be a good planner.C.To explain how to book a vacation.D.To recommend some popular destinations.22.Which destination attracts people interested in the winter sports?A.Lake Tahoe.B.Nashville TN.C.San Antonio.D.Myrtle Beach.23.What do the four destinations have in common?A.They host wonderful shows.B.They have many amazing wonders.C.They have interesting activities.D.They offer different choices for lodging.乃Nicholas Alston,27,was barely a year into working as a flight attendant(空乘人员)whenthe pandemic influenced the travel industry.By November 2020,due to budget cuts anddecreased service,he had taken a voluntary leave of absence.Alston once worked as a clerk in a food processing factory before becoming a flightattendant in 2019.So when the pandemic slowed his flying schedule,he took it as a sign torevisit his goal of opening a restaurant-a passion project of his since college.In December 2020,he launched his very own restaurant business-Clutch HandheldBreakfastaonperson operation that he ran fromsed ghost kitchenr a cookingfacility that produces food only for delivery and takeout with no dine-in areas.In May 2021,Alston returned to flying full-time and kept a busy schedule:He wouldeproork a the Detoit MetroAirpFrdaysfyound eothohTudayDetotand mmdigo toCoiswhichheOperatedomThursdayadFidaymornings,Alstonintcndedohcreaehsyinghoursi8avemoney and move onto the next period of his business plan:Buying a food trailer.heeedbackne bit ofAlston says of his business plan.Eventually,he hopes to grow Cutchmore employees and expand into new loentions,So far,the best learning experience has beering positive feedback from his customers,which keeps him motivated.He says,my passind of these days,it'sgoing to be a profitable business.24.(易错题)Where did Alston work before20197A.In a restaurant.B.In a travel agency.C.In an airline company.D.In the food industry.新长村版·考商信息卷·第三辑类通国、

高三一轮复·数学·高三一轮复周测卷/数学（二十六）一、选择题BC,所以在正方体ABCD-A1B1CD1中，与AB1.C【解析】由题可知①的总体中的个体数较少，宜采成60°角的面对角线共8条，因此所求概率为P=用简单随机抽样，②中高中三个年级学生英语听力水8×122XC2品故选D存在较大差异，层次比较明显，宜采用分层抽样.故选C.2.A【解析】，事件A和事件B不能同时发生，.事件A和事件B是互斥事件；·该同学还有政治和化B学、政治和生物等不同选择，∴.事件A和事件B不是对立事件.综上所述：事件A和事件B是互斥事件，D不是对立事件.故选A.3.C【解析】因为3x1+2023,3x2+2023,3x3+B2023,3x4+2023的均数为3×3+2023=2032，8.B【解析】①举反例：0,0,0,4,11，其均数x=3<方差为32×1=9.故选C.4,但不符合入冬指标；②假设有数据大于或等于10，4.D【解析】观察折线图可知甲同学体温的极差为由极差小于或等于3可知，则此组数据中的最小值为36.8℃一36.4℃=0.4℃，故A选项正确；乙同学体10一3=7，此时数据的均数必然大于7，与x<4矛温按从小到大排成一列：36.5℃，36.5℃，36.6℃，盾，故假设错误，则此组数据全部小于10，符合入冬36.6℃，36.6℃，36.7℃，36.7℃，乙同学体温的众数指标；③举反例：1,1,1,1,11，均数x=3<4,且标1为36.6℃，中位数为36.6℃，均数为五=7×准差s=4,但不符合入冬指标；④在众数等于5且极(36.5×2+36.6×3+36.7×2)=36.6℃，故B选项差小于等于4时，则最大数不超过9.符合入冬指标.正确；乙同学的体温波动比甲同学的体温波动小，极故选B.差为0.2℃，也比甲同学的小，因此乙同学的体温比二、选择题甲同学的体温稳定，故C选项正确；将甲同学的体温9.ABC【解析】概率只是说明事件发生的可能性大从小到大排成一列：36.4℃，36.4℃，36.6℃，36.6℃，小，其发生具有随机性，故A选项，B选项，C选项错36.7℃，36.7℃，36.8℃，因为7×75%=5.25，所以误，D选项正确.故选ABC.甲同学体温的第75百分位数为36.7℃，故D选项错10.ABC【解析】对于A选项，事件“都是红色卡片”是误.故选D,随机事件，故A选项正确；对于B选项，事件“都是5.C【解析】由题意可得360：280：200=9：7：5，所以甲蓝色卡片”是不可能事件，故B选项正确；对于C选付g+9+5×65=27号（钱），乙付g+7+5×65=97项，因为只有2张蓝色卡片，从中任取3张卡片，所以事件“至少有一张红色卡片”是必然事件，故C选21号〔钱)，丙付g++5×65=15品（钱)，所以选项5项正确；对于D选项，事件“有1张红色卡片和2张蓝色卡片”是随机事件，故D选项不正确.故C中的说法错误.故选C选ABC.6.B【解析】依题意，20组随机数中，表示三天中至少11.CD【解析】由图表可知，2021年华为公司在亚太有两天下雨的随机数有：446,072,021,392,325,405，地区营收额比2020年低，故A选项错误；180819631,700,305,311,共10组，所以三天中至少有两天131467=49352百万元，39664-29225=10439下雨的概率约为8-号·故选B百万元，故B选项错误；2021年华为公司在国内的7.D【解析】正方体ABCD-A1BCD,的面对角线营收额占比64.9%，故C选项正确；636807×共12条，易知△ABC,△ABD1均为等边三角形，19.1%-891368×8.1%≈49429百万元，即因为AD∥BC,AC∥A1C,BD∥BD,AD1∥494.29亿元，故D选项正确.故选CD.·131·

第6章数列学生用书第36讲数列的综合应用【课标要求】1.会利用数列的函数性质解与方程、不等式、解析几何相结合的数列综合题.2.掌握相关的数列模型以及建立模型解决实际问题的方法.基础知识夯实教材知识整合【基础检测】A.388B.7721.一百零八塔，位于宁C.1540D.3076夏吴忠青铜峡市，是3.已知数列{an},若a+1=an十a+2(n∈N),始建于西夏时期的喇则称数列{an}为“凸数列”.已知数列{bn}为嘛式实心塔群.该塔“凸数列”，且b1=1,b2=一2，则数列{b}的群随山势凿石分阶而建，依山势自上而下，前2024项和为()第一阶1座，第二阶3座，第三阶3座，第四A.-4B.-5阶5座，第五阶5座，从第五阶开始塔的数C.1D.-1目构成一个首项为5，公差为2的等差数列，4.小李年初向银行贷款M万元用于购房，购房总计108座，故名一百零八塔.则该塔的阶贷款的年利率为p,按复利计算，并从借款后次年年初开始归还，分10次等额还清，每年数是(1次，则每年应还()A.10B.11C.12D.132.1772年德国的天文学家J.E.波得发现了求A洛万元太阳和行星间距离的法则.记地球距离太阳B.Mp(1)0的均距离为10，可以算得当时已知的六大(1+)0二7万元行星距离太阳的均距离如下表：C.M1+p)”万元10星名水星金星地球火星木星土星与太阳的距离47101652100n兴万元除水星外，其余各星与太阳的距离都满足波【知识要点】得定则（某一数列规律）.当时德国数学家高1.数列综合问题中应用的数学思想斯根据此定则推算，火星和木星之间距离太(1)用函数的观点与思想认识数列，将数列阳28应该还有一颗大行星.1801年意大利的通项公式和求和公式视为定义在正整数集或天文学家皮亚齐通过观测，果然找到了火星其有限子集{1,2，…，n}上的函数和木星之间距离太阳28的谷神星以及它所(2)用方程的思想处理数列问题，将问题在的小行星带.请你根据这个定则，估算出转化为数列基本量的方程。从水星开始由近到远算，第10个行星与太(3)用转化化归的思想探究数列问题，将阳的均距离大约是)问题转化为等差、等比数列来研究.175

考点14》导数与函数的单调性、极值、最值1.B解析：由于x>0,对于A选项，f'(x)=2cos2x,f(行）-一1<0，不符合题意；对于B选项，fx)=(x+1)e>0,符合题意；对于C选项，f'(x)=3x2-1,f(兮)=-号<0，不符合题意：对于D选项，f(x)-1+,了(2②)=合<0，不符合题意故述B2.A解析：若函数f(x)=2x2-mx+lnx在(0，+∞)上单调递增，则f)=红-m十士≥0对任意的x∈(@。十∞)恒成立，4x十1≥m对任意的x∈(0，十∞)恒成立即m≤(+)而红+≥2…=4,当且仅当x=之时，等号成立，则m≤4“m<4"是“函数f(x)=2x2-mx十lnx在(0，+o∞)上单调递增”的充分不必要条件.故选A3.C解析：由图可知，函数f(x)在（一∞，一1）上单调递减，在（一1，+∞）上单调递增，则当x∈(-∞，一1)时，f'(x)<0,当x∈(-1，+∞)时，f'(x)>0,且f'(-1)=0.对于函数y=xf'(x),当x∈(-∞，-1)时，xf'(x)>0,当x∈(-1,0)时，xf'(x)<0,当x∈(0，十∞)时，xf'(x)>0,且当x=-1时，xf'(x)=0,当x=0时，xf'(x)=0,显然选项C符合.故选C4.B解折：f(e)=-a,设gx=品别1In x(nc,·函数f(x)在区间(1，+o)上有极值，1数学·参考答案/25

【26题详解】推理判断题。根据最后一段中Li has devoted himself to building the country's first additivemanufacturing technique and application center at the institute to satisfy the thirst for the country'shuman resources in3 D printing.(为了满足我国对3D打印领域人力资源的需求，李在该研究所致力于建设我国首个增材制造技术与应用中心)”可推知，李在研究所的工作是有创造性的。故选D。【27题详解】主旨大意题。根据第一段Li Jianguo,.a49-year-old teacher at the Tianjin Vocational Institute,.is set to be named as one of the "2022 most beautiful teachers"-an annual public awardsponsored by the Publicity Department of the Communist Party of China Central Committee andthe Ministry of Education.(49岁的天津职业学院教师李建国将被评为2022年最美丽教师'之这是由中共中央宣传部和教育部主办的年度公开奖项)”结合文章主要介绍了被评为2022年最美丽教师”之一的天津职业学院教师李建国，介绍了他为培养学生职业技能和国家技术专家所做出的贡献和成就。可知，C选项“职业教师荣获‘最美教师”最符合文章标题。故选C。C篇【答案】28.B29.B30.D31.C【导语】这是一篇说明文。文章主要讲述了中华民族爱惜粮食、节约粮食的传统，同时陈述了人们聚餐造成食物浪费的现象以及背后的原因，从而呼吁我们应该珍惜粮食，养成节俭的好惯。【28题详解】推理判断题。根据第一段的'It is an ancient Chinese tradition to cherish grain..In ancient China,.farming promoted the development of civilization so people regarded grain as a God.(爱惜粮食是中国古老的传统。在中国古代，农耕推动了文明的发展，人们视粮食为神)”和The earthGod "She"and the grain God"Ji"were the earliest gods worshipped by our ancestors and thecountry was called "Sheji'”.(土神社”和谷神“稷”是我们祖先最早崇拜的神，国家被称为“社稷)可知，中国有爱惜粮食的传统，古人把粮食视为神，“社稷”是我们最早崇拜的神。由此推知，提到社稷”是为了说明中华民族爱惜粮食的传统。故选B。【29题详解】推理判断题。根据第二段的Chinese believe in food conservation.(中国人崇尚节约粮食)”可知，本段的主旨是中国人节约粮食。由此推知，提到家禽或家畜中不适合做成主菜的部分总是被烹饪得很美味，是为了说明中国人不浪费食物，即使一点点都舍不得扔掉。故选B。【30题详解】主旨大意题。根据第四段But these ordinarily frugal(节俭的)people often end up wasting food

而抛物线焦点坐标为故A错误；对B,由切于A的切线方程%=3(x+)切于B的切线方程少=3(x+),片=6x,2=6,解得气6,2M+飞，h+当而22)，则yp=yM,故B正确；1+-6+6+M+,+对C,2212,故12,2y+y+当242故PM的中点为6-代入抛物线方程有24故PM的中点在抛物线上，故C正确：对D,取P(-2,0),此时切点弦AB所在直线方程为：0=3(x-2),即x=2,此时AB中点即圆心的坐标为(2,0)，当x=2时，广=12，y=23,37、>2W3故圆的半径为25，而圆心(20)到准线=一2的距离为2>，故此时直线与圆相离，故D错误。故选：BC【点睛】方法点晴：(1)抛物线广=2r上一点M(x。,o)的切线的方程为：y=p(c+)】xy+Y%=12》过椭园+方-1上一点M(,)防切线的方程为云+。1：x2 y2xxo_yyo=1(3)过风双曲线。示1上一点M,人)的切线的方程为产京13.[3,6]【分析】题目等价于f)3x-在区间xoxo+2上M-V的取值范围，分米七之3,专专≤子种情况，分别计经得到答菊【详解】g()=fx+m)+n表示（向左移m个单位，向上移n个单位.不影响M-V的取值范围，等价于f)3x-1在区间x,+2)]上M-N的取值范围.画出函数图像：答案第13页，共24页

分46.A.skippedB.runC.wanderedD.slipped47.A.surveyedmell ouch,te vund.Chinmantdrove earrching for their o peta.When they thanked uking careB.lookedC.decidedD.described48.A.suitbranch from the Chinese rentherhile the purpose i和D)中，B.walkC.breakD.fit67(preserve)health.of the dog,I felt very happy.49.A.permissionB.hesitationC.doubtD.question50.A.disgustingisa perfect combination of colr,hapeappear )andB.confusingC.brightD.dryvor.Deliciousdiouoodbeetforny第二节书面表达（满分25分）.Ohio,in51.A.obviouslyB.hardlyC.lightlyD.severelylife厂假定你是李华，来自澳大利亚的交换生Tom在周末逸街时，发现Williams,52.A.noticeB.searchC.feelD.strikeChinese cuisine honrdide6)很多商铺门上有过年时贴的春联。他对光非常多兴惫，8进一步了解化粪池)，53.A.attemptsB.studiesC.ideasD.invitationsrichnd deligeerneisnd贴春联(spring couplets)这一中国春节俗。请根据提示给他写一封r 13-year-54.A.leftB.strongC.goodD.injuredeating custom in ec egion h prdced dihendkith电子邮件，内容包括：55.A.pickedB.liftedC.pushedD.puttheir own 70 (characteristic)1.介绍贴春联的俗（时间、地点、内容、意义等）2.其他found the56.A.breathB.troubleC.sorrowD.control注意：1.词数100左右；opening.57.A.placedB.lainC.sentD.carried616263.2.可以造当增加细节，以使行文连贯；46 in58.A.headB.chestC.backD.foot64.65.66.3.开头和结尾已给出，不计入总词数。59.A.drownB.coughC.cureD.recover>6869Dear Tom,who could60.A.attractiveB.impressive70s,“LowerC.modestD.considerateI'm glad that you are greatly interested in the Chinese spring cou-题号1234567891011121314得分评卷人第四部分：写作（共两节，满分35分）pletsthat答案题号1516171819202122232425262728ce of the答案第一节短文改错（共10小题；每小题1分，满分10分）his little题号2930313233343536373839404142下边一篇短文中共有10处错误。请你进行修改，每句中最多有两53答案题号4344454647484950515253545556处。错误涉及一个单词的增加、删除或修改。d.“Pull答增加：在缺词处加一个漏词符号（八），并在此符号下面写出该加ison had题号57585960的词。答案删除：把多余的词用斜线()划掉。ay from修改：在错的词下画一横线，在空处写出改正后的词。is side,得分评卷人第三部分：英语知识运用（共两节，满分45分】注意：1.每处错误及其修改均仅限一词；after the第二节（共10小题；每小题1.5分，满分15分）2.只允许修改10处，多者（从第11处起）不计分。heard阅读下面材料，在空白处填入适当的内容(1个单词)或括号内单On my way home from school last Friday,I saw a little dog on the词的正确形式。iencedFor those who travel to China,the scenic spots and ancient civilizationmadeare 61(attract)things,and so is Chinese food and drink.Like music,sidewalk looking hopelessly.I was held it firmly up in my arms,took itdance and painting,eating is also an art in China and Chinese cuisine62 (list)as one of the top in the field of world cuisines.home and feed some milk to it.However,my mom was unwilling to keepNobody could tell exactly how many restaurants a specific city has,letalone the roadside eateries (63 (distribute)in streets andthem,saying there was enough pets for us,two cats and a dog.I begged myYours,back lanes.Wherever you would like to eat,in the restaurants 64 theLi Huaroadside eateries,make sure that the restaurant is clean and the food hasmom not to let it go.Finally,we agreed that it would be deciding by mybeen 65(fresh)prepared and is hot.Chinese regard eating as an art,66 is a comprehensive combination ofdad,whom didn'tretu home from work.Just then the girl and her father【群力压轴卷·2023届高三第三次·有听力英语试题·第4页（共4页）】

22.(1)由题意，f)的定义域为(0，+o),f(x)=4--x=--4r+a,2因为fy)=4x-alnr-x2-2有两个极值点，k,2所以方程f'(x)=0即x2-4x+a=0在(0，+0)上有两不等实根，.4即函数g(x)=x2-4x+a在(0，+∞)上有两不同零点，因此只需g(0)=a>08(2)=4-8+a<0'解得00,则h(a)单调递增：当a∈(a,4)时，h'(a)<0,则h(a)单调递减：所以h(a)≤h(a)=(1-a)lna+a-2=lna-alna+a-2=lha+a-3,.10又y=lna+a-3在a。∈(1,2)上显然单调递增，所以lna。+a-3

因为C∈(0，π)sinC≠0，所以sin 4-cosA=12,12sinA0s4色今2 sin Acos-1(sin A-cos A)2=所以4,得4in24=3即4【小问2详解】由(1)知sin A-cos A2sin Acos=4,A∈(0π)】πA∈0，所以（2)，可得sinA>0,cosA>0,与sin2A+cos2A=1联立，sinA=1+V万sin 4-cos4=14有sin4+cosA=1,解得cos 4=7-1411+beS.ABc=bcsin A=x得224osH谷+d-d.万-1分+d=4+万-lc由余弦定理得，2bc4，所以22+c2=4+7-bc≥2c得2，当且仅当b=C时等号成立，bcs-8 4即5-V万g5+vsx+5x46+7)=2+52+V73,得最大值为320.如图，几何体由四棱锥B-AEFC和三棱台EFG-ACD组合而成，四边形ABCD为梯形，AD//BC且AD=2BC,AD⊥CD,CD=2FG,DG⊥面ABCD,DA=DC=2,面EBC与面ABCD的夹角为45°.第17页/共23页

选择性必修一UNITS4-5阶段检测参考答案及部分解析参考答案1-5 BCACA6-10 CBABA11-15 CACAB16-20 BCBAC21-25 CDCDA 226-30 ABCDA31-35DBAB036-40 FBGCE41-45 ADCBB46-50 DACDA51-55 BDCAB56.covered57.was given58.a59.results60.which61.falling62.to survive63.there64.lower65.possibility写作第一节One possible version:

标|loga(x-1)1,14x4,且x<,<<,则(+)(x,十)=四、解答题：本题共6小题，共70分。解答应写出文字说明、证明过程或演算步骤。17.(本题满分10分)已知复数z满足2+2i=(z一1)(1一i)(i是虚数单位).(1)求|z:(2)若复数2一5乏十a2一2az在复面内对应的点在第三象限，求实数a的取值范围.18.(本题满分12分)》已知角α的顶点与原点O重合，始边与x轴的非负半轴重合，它的终边过点P(3,一4).(1)求cos(a-x)-sin(a+受)的值：(2)若锐角B满足cosa十)=号求sing的值，说619.(本题满分12分)在△ABC中，角A、B、C的对边分别为a、b、c,若a=2,且a2cosC=ab-c.(1)求角A的大小；(2)若△ABC是锐角三角形，求bc的取值范围，高三数学第3页共4页

又a()=0可得x=,则x→0时，h(x)→-o;x→+o时，y=aeh(x)→0，则函数h(x)的大致图象如右：●所以00四.解答题：本题共6小题，共70分.解答应写出文字说明、证明过程或演算步骤.·17.解：(1)由已知：sinB+sinC=2 sinAcosB,1分sinB 2sinAcosB-sin(A+B)=sin(A-B),..2分所以B=A-B,或B+A-B=π（舍去），..3分即A=2B.4分=行则4=若若B=..5分(2)由题意得b+c)°-a2_b+c-(b2+c2-2 bccosA)acac2b(1+cosA)2sinB(1+cosA)2sinB(1+cos2B)0=2cosB,.7分sinAsin2B而A+B=3B<元，所以B∈0，(3.8分放2cosB∈(，2，即b+c+ab+c-@eL,2)...10分ac18,解：(1)血题意可得A=f()=5,设函数y=(x)的最小正周期为T,则子=冬，得T=,:0-2红=2，此时，f(x)=V5sin(2x+).2分T内为函数)=f(四的因象天十直我x=号对称，则2x个-写引+9-子+x快e乙)。πe7后+(ke7列.g<号&=-，9-名则r-5s2x+君4分6令-T+2kπ≤2x+2≤+2kπ，得-T+kπ≤x≤2+kπ26-236第3页共8页

第1期B1版Keys:课本链接1-5 FFTTT主题漫步1-3BCD第1期B2B3版Keys:(One possible version客观题除外)SectionAI.1.textbook 2.conversation3.aloud4.sentence5.pronunciationII.1.singing2.patient3.memorizing4.discovered5.expressionⅡ.l.is afraid to tell2.as well3.have a better understanding of4.fallen in love with5.was so easy thatSection BI.1.speed2.create3.knowledge4.lifelong5.activeIⅡ.1.was playing2.wisely3.reviews4.increased5.partnersIΠ.1.depends on2.pay attention to3.are connecting;with4.are born with the ability5.have a lot in common阅读理解1-5 BCABD6-10 BBABB11-15 DFEAB完形填空1-5 DDAAB6-10 CBACC11-15 DDCBA语法填空1.understanding2.to increase3.have learned4.fo15.will memorize6.the7.students'8.ability9.although10.expressions第1期B4版Keys:(One possible version)知识“串联”For Section AI.1.read aloud2.spoken English3.word by word4.word group5.body language6.look up7.repeat out loud8.take notes9.和…交谈10.记日记11.爱上12.关键词13.对…有更好的理解Ⅱ.l.spoken English2.have conversations with3.word by word4.look up5.take notesFor Section BI.1.make mistakes2.get the pronunciation right3.be born with4.learn from mistakes5.pay attention to6.be afraid of...7.取决于8.把…和…连接或联系起来Ⅱ.l.makes mistakes2.pay attention to3.are born with4.connect;with5.depends on语法点击1.by memorizing 2.by subway3.in French4.with glue写作一招鲜Being a good language learner helps us learn any language better and more easily.So,let'slearn about what makes a good language learner!First of all,good language learners enjoy learning.They like learning very much.Andinterest makes their learning less boring.Secondly,good language learners can find ways duringtheir study.For example,they look up new words in dictionaries,take notes and have

to do it again so we can all go to camp (Text 9) M:What's your plan for the summer holiday,Amanda? W:I want to spend a month on my uncle's farm in New York. But my mother wishes me to go to Beijing,China. M:Why does she want you to go to Beijing?Does she want to travel round the city with you? W:No.My mother is from China.She wants to send me to Bei- jing to live with my grandmother,hoping the holiday will teach me a lot about Chinese culture. M:Well,do you want to go there? W:No.It's usually very hot in summer there.I guess I'll tell my mother that I'll go to Beijing in the fall.It's usually very com-

B.It has 16,000 gas stations around the world. C.It has stopped offering oil refueling service. D.It promotes the resolution of Climate Action Summit. 26.What does Christina Bu think of the conversion? A.It is the beginning of a trend. B.It will make travelling easier. C.It was a fun topic in the Summit. D.It means the end of fossil fuel era. 27.Tesla is mentioned to show that A.electric stations are popular worldwide B.the range of electric cars has decreased C.electric charging technology is improving D.electric cars perform better than fuel-powered ones

第二节（共10小题；每小题1.5分，满分15分） 阅读下面短文，在空白处填入1个适当的单词或括号内单词的 正确形式。 Every year,butterfly lovers in California go out in Novem- ber to count monarch butterflies.They get 56 worrying re- sult-the number of monarch butterflies s 57 (drop)by more than 80%since 2017. The orange and black monarch butterflies are famous 58 their long migrations-they fly thousands of miles every year.In the spring and summer they fly north;in the fall they fly south again.Like most butterflies,monarch butterflies are 59 (ex- treme)important for plants.They help create more plants by spreading pollen ()In turn,monarch butterflies depend on plants for food.And they depend completely on a plant 60

【答案与解析】 作者主要介绍了自己的英语老师Ars Roos,以及她的教学态 度。 41.A 我遇到了一些将学生看作个体的老师，他们关心学生的需 要。 42.B我最初对她的教学印象很深刻，她的教学并不是千篇一律、 枯燥乏味的。 43.D 44.C她不希望进行粗放地教学，不把我们当成是为了达到某种 标准而批量生产的产品一样。 45.D 46.B 她认为我们每一位都处在为将来塑造自我的过程中。 47.C 她花时间单独了解我们。

of disseminating disaster prevention knowledge and raising public awareness. Japan in the 1960s thus began actively taking measures to support both the physical and institutional safeguards against disasters,with particular attention being placed on disaster pre vention.These efforts have greatly reduced the number of people who die or become missing as a result of natural disasters.The declining trend is still continuing,and the number has fallen to between 100 and 200 per year in recent years. 28.What causes relatively more natural disasters in Japan? A.Japan's masses of islands. B.Japan's location. C.Japan's large population.

D.Bees have inspired scientists to make environmental mate- rials, 11.What is the main idea of the text? A.Bees may ease plastic problems. B.Bees can help keep nature balanced. C.Plastic will be recycled in many ways. D.The end of plastic waste is on the way.