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

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

19.(12分)已知数列{a.)满足am:十am-2a.+1=2°，a1=1,a2=3.(1)求数列{a.}的通项公式；21+2"-2(2)求数列（一1）1的前n项和T。(n.20.(12分)已知行六面体ABCD-A,B,C,D1,P是线段CD,上-点，且DP=2PC.(1)证明：AC1∥面BDP;(2)已知四边形ABCD是菱形，AB=2AA1,∠BAD=120°，并且∠A:AC为锐角，c0s∠A,AD=cOs∠A,AB=,求二面角P-BD-C的正切值21.2分)已知双曲线C若-1。b>0)的左右顶点分别为AA,双面线C的虚装长与实轴长的比值为，过右焦点F(3,0)的直线交双曲线C于M,N两点(M,N与A,A不重合)()求双曲线C的方程；(2)点M关于原点O的对称点为点P,直线A:P与直线A:N交于点S,直线OS与直线MN交于点T,求T的轨迹方程.2212分)已知函数f(x)=e(tanx一1)一1，f(x)的导函数为f(x),记函数f(x)在区间禁内的零点为，n∈N、,间不支本领个商防自用绿微感置求函数()的单调区铜：的小座「小市他的面，容二品年《2)证明x,1一x,<界有的新真无原宁杀馆华麻x1产色底T为年喜种不的界健示玉的提男子D方外印士位地信忽炉题卷（购）教学礼题第4真（共4贡音

C.1012D、=1012字，的aam10A.1011B.-1011改八2-a)≥(a)+4-4a,则实数a的取值范围为(-0,0]D.(-0,1]二，选择题（本大题共4小题，每小题5分，共20分，在每小题给出的选项中，有多项符合题口要求，A.[0,+∞)B.[1,+∞)全部选对的得5分，部分选对的得2分，有选错的得0分)9.已知两个事件A,B,清足P(0,P(B)>0,则下列结论正确的是A.若A,B为相互独立事件则P(B)=P(B1A)B.若P(B1A)=P(B),则P(AHB)=P(A)C.P(AB)+P(AB)=P(B)D.P(BIA)(BIA)=P(AB)10已知函数/-2n(or+p)(o>0.00,y>0),则A.曲线G关于直线y=x轴对称B.曲线G与直线x+y-6=0有唯一公共点C.曲线G与直线x-y+1=0没有公共点D.曲线G上任意一点到原点的距离的最大值为3V2数学试卷第2页（共4页）

六、（本题满分12分），：21.某学校为了解七年级学生每天的课外活动情况，从七年级学生中随机抽取若干名学生进行调查，按“课程延伸”“文娱活动”“体育训练”和“自主提升”四项绘制成如下统计图（图1、图2），请根据图中的信息解答下列问题：七年级课外活动情况扇形图七年级课外活动情况条形图甲：课程延伸20f人数,定意乙：文娱活动15页8共”舞碳阁丙：体育训练酷两10一举强“武白送步本30%丁：自主提升学0国→成绩暖答“吉回交共第21题图甲乙丙工部春言束点半(1)此次抽查的学生数是多少？并补全条形统计图，众本糖醒孔0！共磁大本)醒致(2)在扇形统计图中，“甲”部分所对的圆心角的度数是多少？四G),A出禁特然{（3)每天的课外活动是“课程延伸”“文娱活动”或“体育训练”中的一项，强强每天的课外活动是“课程延伸”“体育训练”或“自主提升”中的一项，那么某天和强强选择的课外活动项目一样的概率是多少？60七、（本题满分12分）22.如图1，一块钢板截面的一边为线段AB,另一边曲线ACB为抛物线的一部分，现沿线段BC将这块钢板分成①、②两部分，以AB边所在直线为x轴，经过点C且与AB垂直的直线为y轴，建立面直角坐标系xOy,规定一个单位代表1米已知：OA=2米，OB=8米，OC=6米，(1)求曲线ACB所在抛物线的函数关系式不用写出自变量的取值范围；(2)如图2，在该钢板第①部分中截取一个矩形DEFG,其中D为BC的中点，E,F均在线段AB上，G在曲线AC上，求EF的长：(3)如图3，在该钢板第②部分中截取一个△PBC,其中点P在曲线BC上，记△PBC的面积为S)求S的最大值2①AFO E图1图2图3八、（本题满分14分）第22题图23.在四边形ABCD中，对角线AC,BD相交于点O（1)如图1，AC分∠BAD,若AB=AC=BD,AD=AO,求证：AB∥CD;量15i阿(2)如图2，点E在AB边上，EM垂直分AD,垂足为M;EN垂直分BC,垂足为N,若∠BAD=∠ABC,O求证：AC=BD;凌中如图3，E、F分别为4C,BD的中点，EF两端延长分别交BC,AD于H,G,若部05,记△CEH,△ABE的面积分别为S,S,直接写出S的值，SDD图E图1图图3第23题图来安县2023届九年级“二模”试卷·数学试题第4页共4页

12.△ABC中，内角A,B,C的对边分别为a,b,c,a=2,BC边上的中线AD=2,则下列说法正确的有A.AB.AC=3B.b2+c2=9Cg≤cosA是》上的最小值为m,最大值为M,若12√2M十m=0,则实数a的取值范围为】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.：，二17.(10分)代修馆宗越高，代S神恢玉分购，代无怕x如图所示，四棱锥P-ABCD的底面ABCD是行四边形，M、N分别是1：PC、AB的中点.求证：MN∥面PAD.c行m:818.(12分):才}的个【末不，已知面向量a与b满足a·b=一2，向量e是与向量b同向的单位向量，向量a在向量b上的投影向量为一2e.(1)若a+2b与a-b垂直，求|a|的大小；(2)若a与b的夹角为写，求向量a与2a+3b夹角的余弦值，:2(19.(12分)已知函数f(x)=sin2x十√3cos2x.(1)若函数y=f(x十m)是奇函数，求|m的最小值；(2)若fe)=号a∈(0，受），求cos2&的值【高一下学期第二次阶段性考试·数学第3页（共4页）】23096A

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。

2022~2023学年度第二学期期末抽测高二年级数学试题注意事项：1,答卷前，考生务必用黑色字迹钢笔或签字笔将自己的姓名、考生号、考场号和座位号填写在答题卡上。用2B铅笔将试卷类型(A)填涂在答题卡相应位置上。将条形码横贴在答题卡右上角“条形码粘贴处”。2.作答选择题时，选出每小题答案后，用2B铅笔把答题卡上对应题目选项的答案信息点涂黑；如需改动，用橡皮擦干净后，再选涂其他答案，答案不能答在试卷上。3.非选择题必须用黑色字迹钢笔或签字笔作答，答案必须写在答题卡各题目指定区域内相应位置上；如需改动，先划掉原来的答案，然后再写上新的答案：不准使用铅笔和涂改液。不按以上要求作答的答案无效。4.考生必须保持答题卡的整洁。考试结束后，将试卷和答题卡一并交回。一、选择题：本题共8小题，每小题5分，共40分。在每小题给出的四个选项中，只有一项是符合题目要求的。1.已知集合A={x-30,b>0,则a+b≥6的一个充分条件是A号=16B.ab=9C.a2+b2=4D.1+1a b高二数学试题第1页（共6页）

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

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

当x∈(0,1)，f'(x)<0,f(x)单调递减当x∈(1，+o),f'(x)>0,f(x)单调递增所以f(x)≥f(1)=e+1-a,若f(x)≥0，则e+1-a≥0，即a≤e+1,所以a的取值范围为(-0，e+1](2)由题知(x)一个零点小于1，一个零点大于1，不妨设x<1化)又圆为)=.成只蓄证/)小》即证g-hx+x-e-n->0,r∈(+o）r片-切0下面证明x>1时.￡->0，axx-<0设g(=g-e,x>1.则g=-e〔=--〔〔g设p()=g(c>D()-日e=e>0所以p(x)>()=e,而e0,所以g(x)>0

准考证号姓名(在此卷上答题无效)绝密★启用前2023年普通高等学校招生萍乡市第三次模拟考试英语(120分钟，总分150分)本试卷分第1卷（选择题）和第Ⅱ卷（非选择题）两部分。共150分。考试时间120分钟。第I卷（三部分，共115分)注意事项：1.答第一卷前，考生务必将自己的姓名、准考证号、考试科目、试卷类型用铅笔涂写在答题卡上。2.每小题选出答案后，用铅笔把答题卡上对应题目的答案标号涂黑。如需改动，用橡皮擦干净后，再选涂其他答案标号。不能答在试卷上。3.考试结束，考生将本试卷和答题卡一并交回。bT第一部分听力（共两节，满分30分）c0做题时，先将答案划在试卷上。录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。第一节（共5小题；每小题1.5分，满分7.5分）01听下面5段对话，每段对话后有一个小题。从题中所给的A,B,C三个选项中选出最佳选项，并标在试卷的相应位置。听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。每段对话仅读一遍。例：How much is the shirt?A.￡19.15.B.￡9.18.C.￡9.15答案是C。1.Where is the woman probably from?APeruB.Britain.C MexicoWhat will the man do tonight?A.Attend a party.B.Reply to an invitation.C.Play football.AWhat does the woman think of her old roommate?A.Selfish.B.ThoughtfulC,CarefulWhat should the city do according to the woman?A.Create more jobs.B.Improve the air quality.C.Close some businesses.英语试卷第1页（共10页)

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

(1)当a=2,b=4时，求)在L,2]上的最大值：(2)若对任意0>0，f()均有两个极值点，(：<名)，(ⅰ)求实数b的取值范围；(i)当a=e时，证明：f(:)+f(x,)>e第6页/共6页

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

第三部分 语法填空（共10小题；每小题3分，满分30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。 The abacus(算盘) was a great invention in ancient China. The counting board 25 (invent)on the basis of small rods (棒).Later,with the26 develop)of productivity,the amount of calculation was much 27 (great).And calculation with counting rods limited the calculation.Thus,people inven ted a more 28 (advance)counter-the abacus. With the application of the abacus,people summarized many abacus rhymes(珠算口诀)，thus 29 (increase)the calculat- ing speed.By the time of the Ming Dynasty,people could use the abacus in addition,subtraction,multiplication and division,

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】 研究发现与陌生人的简短对话能改善情绪，使人们产生认同 感和归属感 。 28.A根据第1段最后两句可知，测试发现，那些和收银员有对话 的顾客在离开星巴克时的心情比那些没有对话的顾客更好。 29.C根据第4段第1句可知，Epley发现人们担心和陌生人说话 会让对方很反感。 30.B根据第4段最后一句可知，和陌生人的眼神交流能让他们 产生归属感。 31.B根据最后一段可知，幸福的生活就像漏气的车胎，需要我们 不断地打“气”，找到并珍惜那些积极的事情。

the importance of time management.The first thing that every person will learn in music school is discipline. 31 They are more likely to have a higher IQ.Parents s are encouraged to let their children take music lessons during their early age because of its effect on IQ.A certain study was able to record the brain development of children who were undergoing musical training and those who were not.32 This is because of the effect of the musical training on how the brain functions. When it comes to language literacy,children who have musi cal training perform better.33 A.They have a better sense of rhythm. B.They have better time management skills. C.This will give you confidence in doing tasks.

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.