精品解析:【市级联考】2019届南通、徐州、盐城、常州等市四月大联考 高三 英语(解析版)
2019届四市联考语文试卷及答案
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江苏省南通市、宿迁市等2019届高三第一次调研测试26.简答题(10分)(1)阅读下丽的《红楼梦》选段,回答问题。
犹未想完,只听“咯吱”一声,宝钗使故意放重了脚步,笑着叫道:“擎儿,我看你往那里藏!”一面说,一面放意往前赶。
文中“蟹儿”指谁?小说中作者为什么借宝玉之口给她取名“肇儿”?(4分)(到{狂人日记·序》中写狂入“然已早愈,赴某地候补矣”。
请简要分析作者这样写的意图。
(6分)三、材料概括分析题(15分)阅读下面的材料,回答27-29题。
在历史题材剧的创作和拍摄过程中,究竟是忠于史实,还是发挥想象力进行虚构,永远是摆在创作团队面前的一个难趣。
当一部部盲目猎奇、不惜篡改历史来剌激大众感官的电视剧呈现在观众面前的时候,�人物所打上的烙印尺远比真实的史书滴布汇石::王人不倦”的创作态度也反映出当今某些编,JtJ历史精神和文化品格的缺失。
高明的历史剧创作,不应单纯迎合观众,成为金钱的附庸,而应坚守艺术追求和品位。
比如,风靡一时的电视剧《雍正王朝》里,编剧刘和平遵循“大事不虚,小事不拘”的原则,将康熙的八子、十四子有意比真实历史“多活”了十年,但并不影响该剧的严肃格调。
当年的《雍正王朝》完成剧本创作后,面对不少专家针对该刷一些内容与历史不符的质疑,清史专家、中央民族大学历史系教授王锺输说了一句分量很重的话:“人家是艺术创作,不是历史考证。
”给历史A•J 一定的宽容皮,自然是对创作的尊重。
不过,“张飞打岳飞”“汉武帝爱上霍去病”这样魔幻的情节就超出了改编历史题材的底线,沦为不负责任的胡编戏说。
越是历史题材,越是妥避免简孚粗暴的网络“央文”式改编,这也是今人对历史传统应有的尊重和敬畏。
其实,历史人物和事件、、---『-的元杂性,往往超出我们的想象,只要把握』盐韭血草草丘值判断、历史思维和审美追求,完全能拍tll t良好看、很有戏剧性的历史剧来。
(有删改)27.历史剧篡改历史的原因有哪些?请结合材料简要概括。
【精品试题】【市级联考】江苏省七市2019届(南通、泰州、扬州、徐州、淮安、宿迁、连云港)高三第二次调研考
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2019届高三第二次调研测试一、填空题:本大题共14小题,每小题5分,共计70分.1.已知集合,.若,则实数a的值为____.【答案】4【解析】【分析】由确定a值即可【详解】∵,∴a=4故答案为4【点睛】本题考查集合的交集,熟记交集的概念与运算是关键,是基础题2.复数(为虚数单位)的实部为____.【答案】【解析】【分析】由复数运算化简为z=a+bi的形式,则实部可求【详解】故实部为故答案为【点睛】本题考查复数代数形式的除法运算,熟记运算性质,准确计算是关键,是基础题3.某单位普通职工和行政人员共280人.为了解他们在“学习强国”APP平台上的学习情况,现用分层抽样的方法从所有职员中抽取容量为56的样本.已知从普通职工中抽取的人数为49,则该单位行政人员的人数为____.【答案】35【解析】【分析】由题意可得,抽取的行政人员数为7,再求得抽样的比列,再用7除以此比例,即得该学校的行政人员人数.【详解】由题意可得,抽取的行政人员数为56﹣49=7,抽样的比列为,故该学校的行政人员人数是735,故答案为 35.【点睛】本题主要考查分层抽样的定义和方法,利用数据计算抽样比例是关键,属于基础题.4.从甲、乙、丙、丁这4名学生中随机选派2人参加植树活动,则甲、乙两人中恰有1人被选中的概率为____.【答案】【解析】【分析】确定基本事件的个数,即可求出概率.【详解】随机选派2人参加植树活动,有6种,甲、乙两人中恰有1人被选中有4种,∴所求概率为,故答案为.【点睛】本题考查古典概型,考查概率的计算,确定基本事件的个数是关键,是基础题5.执行如图所示的伪代码,则输出的S的值为____.【答案】30【解析】【分析】分析程序中各变量、各语句的作用,再根据流程图所示的顺序,可知:该程序的作用是累加并输出满足条件S的值,模拟程序的运行即可得解.【详解】模拟程序的运行,可得i=1,S=2满足条件i<7,执行循环体,S=2×1=2,i=3满足条件i<7,执行循环体,S=2× 3=6,i=5满足条件i<7,执行循环体,S=6×5=30,i=7此时,不满足条件i<7,退出循环,输出S的值为30.故答案为30【点睛】本题考查流程图,根据流程图写程序的运行结果,是算法这一模块重要的题型,其处理方法是:①分析流程图,②建立数学模型,③解模,确定何时结束流程是关键,是基础题6.函数的定义域为___.【答案】【解析】【分析】由4x﹣16≥0即可求得函数的定义域.【详解】∵4x﹣16≥0,∴4x≥16,∴x≥2,故答案为[2,+∞).【点睛】本题考查函数定义域及其求法,重点考查指数函数的性质的应用,属于基础题.7.将函数的图象向左平移个单位长度得到的图象,则的值为___.【答案】【解析】【分析】先由平移得f(x)的解析式,再将代入解析式求值即可【详解】f(x)=2sin3(x+=2sin(3x+,则故答案为【点睛】本题考查图像平移,考查三角函数值求解,熟记平移原则,准确计算是关键,是基础题8.在平面直角坐标系中,已知双曲线的右顶点到渐近线的距离为,则b的值为___.【答案】2【解析】【分析】右顶点为A( 2,0 ),一条渐近线为bx﹣2y=0,根据点到直线的距离公式,求出b,即可求出结果.【详解】右顶点为A( 2,0 ),一条渐近线为bx﹣2y=0,根据点到直线的距离公式,可得b=2故答案为2【点睛】本题考查双曲线的标准方程,以及双曲线的简单性质的应用,熟记双曲线基本概念,准确计算点线距是关键,是基础题9.在△ABC中,已知C 120°,sinB 2 sinA,且△ABC的面积为,则AB的长为____.【答案】【解析】【分析】由sinB=2sinA,利用正弦定理可得:b=2a.可得S△ABC,解得a,b,再利用余弦定理可得AB【详解】在△ABC中,由sinB=2sinA,利用正弦定理可得:b=2a.∴S△ABC,解得a.∴b=4.∴c2=b2+a2﹣2bacosC=16+4﹣2cos120°=28,解得c,即AB=故答案为【点睛】本题考查了正弦定理余弦定理,考查了推理能力与计算能力,属于中档题.10.设P,A,B,C为球O表面上的四个点,PA,PB,PC两两垂直,且PA 2 m,PB 3 m,PC4 m,则球O的表面积为____m2.【答案】【解析】【分析】由已知中P,A,B,C是球O表面上的四个点,PA,PB,PC两两垂直,构造以PA,PB,PC为棱的长方体,易求出球O的半径,进而求出球O的表面积.【详解】∵P,A,B,C是球O表面上的四个点,PA,PB,PC两两垂直,则球的直径等于以PA,PB,PC长为棱长的长方体的对角线长∵PA 2 m,PB 3 m,PC 4 m,∴2R=则球O的表面积S=4πR2=29π故答案为【点睛】本题考查的知识点是球的表面积,及球的内接多面体,其中根据已知条件构造长方体,计算出球O 的半径,是解答本题的关键,是基础题11.定义在R上的奇函数满足,且在区间上,则函数的零点的个数为___.【答案】5【解析】【分析】由图分析画出与在同一个坐标系的图像,即可求解【详解】由题知函数的周期为4,又函数为奇函数,∴,即故f(x)关于(2,0)中心对称,又g(x)=为偶函数,则画出f(x)与g(x)在同一个坐标系的图像如图所示:故交点有5个故答案为5【点睛】本题考查函数与方程,明确函数f(x)的周期性奇偶性,准确画出图像是关键,是基础题12.已知关于的不等式( a,b,c R ) 的解集为{ x | 3 < x < 4},则的最小值为___.【答案】【解析】【分析】由不等式解集知a<0,由根与系数的关系知,将b,c分别用a 表示代入,利用基本不等式求最小值即可【详解】由不等式解集知a<0,由根与系数的关系知则,当且仅当-24a=即取等故答案为【点睛】本题考查基本不等式的应用,二次不等式解法,根与系数的关系,求得a,b,c的关系是关键,是中档题13.在平面直角坐标系xOy中,已知点A,B在圆上,且,点P(31),,设的中点M的横坐标为x0,则x0的所有值为____.【答案】【解析】【分析】设AB中点为M由弦长公式,求出M的轨迹方程;由得,将向量坐标化得到的方程组,求解即可求出【详解】设AB中点为M由勾股三角形知OM=,即,又则,即∴, ②,将联立得故答案为【点睛】本题考查圆的轨迹方程,向量的坐标运算,圆的弦长公式,确定AB中点的轨迹是突破点,向量坐标化运算是关键,是中档题14.已知集合,从集合中取出个不同元素,其和记为;从集合中取出个不同元素,其和记为.若,则的最大值为____.【答案】44【解析】【分析】欲使m,n更大,则所取元素尽可能小,所以从最小开始取S由得到令2n-1=t,则m+2n=t+m+1,t为奇数,m为整数,则,由基本不等式得取等条件不成立,则检验t=22附近取值,只有t=21,m=22和t=23,m=20,成立,则问题得解.【详解】欲使m,n更大,则所取元素尽可能小,所以从最小开始取,S=即令2n-1=t,则m+2n=t+m+1,t为奇数,m为整数,则,由基本不等式当且仅当m=t=22时取等,∵t为奇数,∴的最大值在t=22附近取到,则t=21,m=23(舍);t=21,m=22,成立;t=23,m=21(舍); t=23,m=20,成立;故m+t的最大值为43,所以的最大值为44故答案为44【点睛】本题考查不等式的应用,数列求和问题,分析转化能力和计算求解能力,是中档题二、解答题:本大题共6小题,共计90分.15.在平面直角坐标系中,设向量 , ,其中.(1)若∥,求的值; (2)若,求的值.【答案】(1);(2)【解析】 【分析】(1)由向量共线的坐标表示可求进而求出,(2)由,求得将展开即可代入求解【详解】(1)因为∥, 所以,所以.因为,所以.于是 解得.(2)因为,所以,又,故.因为,所以,又,解得.因此,.【点睛】本题考查两角和的正弦公式,同角三角函数基本关系式,向量共线坐标运算,熟记三角基本公式,准确计算是关键,是中档题 16.如图所示,在直三棱柱ABC A 1B 1C 1中,侧面BCC 1B 1为正方形,A 1B 1⊥B 1C 1.设A 1C 与AC 1交于点D ,B 1C 与BC 1交于点E .求证:(1)DE∥平面ABB1A1;(2)BC1⊥平面A1B1C.【答案】(1)见解析;(2)见解析【解析】【分析】(1)利用三角形中位线的性质证明DE∥AB,即可证明DE∥平面ABB1A1;(2)因为三棱柱ABC A1B1C1为直三棱柱,所以BB1⊥平面A1B1C1,进而BB1⊥A1B1,证得A1B1⊥平面BCC1B1,进而A1B1⊥BC1,又因为侧面BCC1B1为正方形,所以BC1⊥B1C.进一步证明平面BC1⊥平面A1B1C即可.【详解】(1)因为三棱柱ABC A1B1C1为直三棱柱,所以侧面ACC1 A1为平行四边形.又A1C与AC1交于点D,所以D为AC1的中点,同理,E为BC1的中点.所以DE∥AB.又AB ABB1 A1,DE ABB1 A1,所以DE∥平面ABB1A1.(2)因为三棱柱ABC A1B1C1为直三棱柱,所以BB1⊥平面A1B1C1.又因为A1B1A1B1C1,所以BB1⊥A1B1.又A1B1⊥B1C1,BB1,B1C1BCC1B1,BB1∩B1C1 B1,所以A1B1⊥平面BCC1B1.又因为BC1BCC1B1,所以A1B1⊥BC1.又因为侧面BCC1B1为正方形,所以BC1⊥B1C.又A1B1∩B1C B1,A1B1,B1C A1B1C,所以BC1⊥平面A1B1C.【点睛】本题考查线面平行的证明,线面垂直的判定,熟记判断定理,准确推理是关键,是基础题.17.图①是一栋新农村别墅,它由上部屋顶和下部主体两部分组成.如图②,屋顶由四坡屋面构成,其中前后两坡屋面ABFE和CDEF是全等的等腰梯形,左右两坡屋面EAD和FBC是全等的三角形.点F在平面ABCD 和BC上的射影分别为H,M.已知HM 5 m,BC 10 m,梯形ABFE的面积是△FBC面积的2.2倍.设∠FMH .(1)求屋顶面积S关于的函数关系式;(2)已知上部屋顶造价与屋顶面积成正比,比例系数为k(k为正的常数),下部主体造价与其高度成正比,比例系数为16 k.现欲造一栋上、下总高度为6 m的别墅,试问:当为何值时,总造价最低?【答案】(1);(2)当为时该别墅总造价最低【解析】【分析】(1)由题知FH⊥HM,在Rt△FHM中,所以,得△FBC的面积,从而得到屋顶面积;(2)别墅总造价为=令,求导求最值即可【详解】(1)由题意FH⊥平面ABCD,FM⊥BC,又因为HM ABCD,得FH⊥HM.在Rt△FHM中,HM 5,,所以.因此△FBC的面积为.从而屋顶面积.所以S关于的函数关系式为().(2)在Rt△FHM中,,所以主体高度为.所以别墅总造价为记,,所以,令,得,又,所以.列表:所以当时,有最小值.答:当为时该别墅总造价最低.【点睛】本题考查函数的实际应用问题,将空间问题平面化,准确将S表示为函数是关键,求最值要准确,是中档题18.如图所示,在平面直角坐标系xOy中,已知椭圆C1:,椭圆C2:,C2与C1的长轴长之比为∶1,离心率相同.(1)求椭圆C2的标准方程;(2)设点为椭圆C2上一点.①射线与椭圆C1依次交于点,求证:为定值;②过点作两条斜率分别为的直线,且直线与椭圆C1均有且只有一个公共点,求证:为定值.【答案】(1);(2)①见解析,②见解析.【解析】【分析】(1)由题所求椭圆a=,离心率,由得b即可;(2)①当直线OP斜率不存在时,得当直线OP斜率存在时,设直线OP的方程为,与椭圆联立,同理,推得从而可求;②设,直线的方程为即,记,则的方程为,代入椭圆C1的方程得,由,得,再将代入得,同理,得到关于为根的方程,由韦达定理及点P在椭圆上化简即可求得为定值【详解】(1)设椭圆C2的焦距为2c,由题意,,,,解得,因此椭圆C2的标准方程为。
2019届南通、徐州、盐城、常州等市四月大联考 高三 英语 word版(含听力,详解)
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南通、徐州、盐城、常州等四月大联考点评1.单选答案:21-25 BDCBC 26-30 ACCAD 31-35 BDCAB第21题这题考察的是词义辨析。
句意:—女士,护照的表格这样填写就足够了吧?—你的护照申请表应该贴有两张近照。
Be accomplished by 伴随着,固定搭配,故选B第22题这题考察的是表语从句。
句意:一些商人热衷于开展公共福利,因此这就是当地服务是怎样被资助的。
How引导宾语从句,强调是怎样被资助,故选D第23题这题考察的是固定搭配。
句意:我们提出付我们那一半费用,但是查尔斯坚决不答应。
Have none of it 坚决不允许(做)某事;不接受(做)某事,故选C。
第24题这题考察的是动词时态。
句意:—这周六下午去赏风景怎么样?—对不起,那时候我整个周末都在写我的研究报告。
Will be writing将来进行时,强调未来某事会在做某事,故选B第25题这题考察的是非谓语做补语,句意:年轻的夫妇会很开心的见到他们的孩子在出生时被赐予健康的身体和智力。
Be blessed with 被赐予,固定搭配,故选C。
第26题这题考察的是介词短语。
句意:言语传来,30个消防员为了换取国家财产的安全向国家献出了他们的生命。
in exchange for 换取,选A第27题这题考察的是词义辨析。
句意:与良心斗争于究竟要不要给一个摔倒的老人提供帮助,绝大多数人选择了帮助。
Compromise妥协,contradiction矛盾,不一致,Conscience良心,良知,competence能力。
由题意,battled with conscience,与良心斗争,故选C。
第28题这题考察的是动词时态。
句意:不要中途放弃,你会发现当你到达目的地时的风景比出发时更美。
当你达到目的地时,start off已成了过去的事情,故用过去时,选C,此题模仿2015年的高考真题,总统希望这个国家在他卸任的时候比他过去上任的时候要好,要研读真题啊!第29题这题考察的是独立主格。
江苏省南通、徐州、盐城、常州等市2019届高三四月大联考英语试题
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【市级联考】江苏省南通、徐州、盐城、常州等市2019届高三四月大联考英语试题学校:___________姓名:___________班级:___________考号:___________一、单项选择1.— Is it enough to finish the form for a passport, Madam?— Your passport application form should be ________ by two recent photos.A.updated B.accompaniedC.established D.identified2.Some business owners are keen on public welfare. This is local services have been funded.A.whether B.what C.where D.how3.We offered to pay our half of the cost that was needed to restore the shared doorway but Charles would have of it.A.nothing B.anythingC.none D.any4.—How about going sightseeing this Saturday afternoon?Sorry, I _______ my research report the whole weekend.A.will have written B.will be writingC.have written D.have been writing5.Young couples will be happy to see their babies _______ with good health and intelligence when they are born.A.to bless B.blessingC.blessed D.being blessed6.Word came that 30 firefighters gave their lives to our country _______ national property security.A.in exchange for B.in response toC.in terms of D.in contrast with7.Having battled with their _______ over whether to offer help to an aged man or woman who has fallen over, most people choose to help.A.compromise B.contradictionC.conscience D.competence8.Don't give up half way, and you will find the scenery is more beautiful when you reach the destination than when you _______.A.start off B.have started offC.started off D.will start off9.We completed one third of the project, and the loan _______ in place, we had to delay the rest till the next month.A.not arranged B.was not arrangedC.not arranging D.had not been arranged10.for years of hard training, she would not be standing on the stage, receiving huge cheers and applause.A.It were not B.It had not beenC.Were it not D.Had it not been.11.Office furniture like chairs and sofas should be attractive as well as comfortable. A.manually B.visuallyC.physically D.securely12._______ many Chinese holidays are directed towards services remembering ancestors, the Ching Ming Festival is beyond doubt the largest.A.Unless B.SinceC.Once D.While13.More and more people prefer to live in the countryside, _______ appeal for them lies in the quiet and slow-paced life.A.who B.WhichC.whose D.what14.The infrastructure project has consumed so much money that we can't find any financial support and have to ______.A.pull out B.pull throughC.catch up D.catch on15.Though our football boys are faced with four goals behind, they are still struggling hard in the field to ______.A.face the music B.save faceC.cost their arm and leg D.land on their feet二、完形填空At 15, I had started a band with three mates I'd met at the local rehearsal (排练)rooms.We played our first performance at a pub in Bolton. We were 16 , but the crowd didn't seem to mind,and after a few more local concerts, we recorded some songs and we started to 17 .We sent out hundreds of demo(样本)tapes in 18 of our favourite band, the Manics. After finishing my high school, we drove to London to play at the Dublin Castle. Only five people 19 .But we persevered(坚持) and slowly things began to 20 . Two years after our first performance, we 21 a record deal. We 22 endlessly for the next two years and built up a small but 23 following. At the end of 2002, the Manics 24 us to play with them. My teenage dreams had come true, the band I looked up to seemed to 25 of us.We 26 performing in New York, and to 5,000 people at the Fuji Rock festival in Japan. There's no greater 27 than the moment you step on stage. The lights darken, the crowd swells (波浪起伏) and they 28 in applause as you finish.Our album was 29 in 2003. Unfortunately, no one bought the thing. 30 , I think that was about right. 31 I' m extremely proud of the music we produced, we were riding a wave of hype(天花乱坠的宣传) we could 32 live up to. Our record company quietly 33 us and, as quickly as it had started, my time in a band was over. We 34 peacefully on the day it was released. We even had a"last supper"to mark our demise(停业).The band had 35 everything. My old school welcomed me back and I worked harder and was finally admitted to Oxford University at the grand old age of 21. 16.A.troublesome B.thrilled C.hopeful D.terrible 17.A.hesitate B.succeed C.dream D.qualify 18.A.imitation B.favour C.charge D.celebration 19.A.dropped out B.turned up C.dived in D.passed by 20.A.catch on B.take off C.pick up D.get round 21.A.declined B.lost C.expected D.signed 22.A.practiced B.studied C.toured D.waited 23.A.separated B.devoted C.concerned D.relieved 24.A.persuaded B.required C.reminded D.invited 25.A.approve B.tire C.hear D.think26.A.gave up B.ended up C.put off D.insisted on 27.A.risk B.pain C.loss D.rush 28.A.erupt B.gather C.squeeze D.withdraw 29.A.preserved B.released C.displayed D.evaluated 30.A.Looking forward B.Looking down C.Looking backD.Looking up31.A.Though B.Since C.Unless D.Before 32.A.actually B.somehow C.always D.never 33.A.betrayed B.dropped C.impressed D.sponsored 34.A.split up B.hung around C.moved away D.broke down 35.A.experienced B.disturbed C.changed D.replaced三、阅读选择Among all the tourist attractions in Sydney. the magnificent Opera House is the shining star. On the edge of Bennelong Point, a tongue of land sticking out into Sydney Harbor, this UNESCO World Heritage Site consists of a complex of roofs shaped like huge shells or billowing sails that mix beautifully with its waterfront location.Today visitors can admire the great beauty of the building. Much more than an opera house, the structure encompasses(包含) theaters, studios, a concert hall, rehearsal, and reception rooms, restaurants, and a spectacular open-air forecourt overlooking the harbor and city. American architect Louis Kahn once said, "The sun did not know how beautiful its light was, until it was reflected off this building.”Tips and TacticsBook seats for productions well in advance. Performances commence promptly so visitors should allow enough time to access the building, collect tickets, and stow cloaks, large bags, and jackets.Consider enjoying a meal in one of the restaurants to enjoy the stunning harbor views. One of the best sites to photograph the Opera House is Mrs. Macquarie's Chair in the Royal Botanic Gardens or from the water aboard a harbor cruise.Getting to the Sydney Opera HouseVisitors can catch a Sydney Bus, travel by City Rail, or hop aboard a Sydney Ferry to Circular Quay, which is a 5 to 7 minute walk from the Sydney Opera House.A free shuttle bus for elderly and mobility-challenged patrons (顾客)runs between Circular Quay near Stand E (under the Cahill Expressway) and the Vehicle Concourse.Bike parking is available under the Sydney Opera House Monumental Steps. Wilson's Sydney Opera House Car Park is located at 2 Macquarie St, with vehicle access next to the Sydney Opera House Forecourt.Admission: Ticket prices vary from attraction to attraction.Location: Bennelong Point, Sydney.36.Which of the characteristics of Sydney Opera House might attract visitors most?A.Its historical context. B.Its unique architectureC.Its waterfront location D.Its superb harbor views37.If you are a visitor to Sydney Opera House, you can ______.A.take a ferry directly to Sydney Opera House,B.ride a free shuttle bus without any restrictions,C.take an equally good photo from any angle,D.drive a car to 2 Macquarie St and park there.Men don't go through pregnancy or childbirth. Their hormone (荷尔蒙) levels don't nosedive. What exactly have they got to be depressed about? Quite a lot, according to research from Sweden showing that, over the past 10 years, a significant number of men have struggled with the transition(过渡) to fatherhood.This latest research tries to quantify just how many men get postnatal(产后)depression. Previous studies have found between 4% and 10% of men. while, in this smallish sample of 447 Swedish fathers who volunteered (and may therefore not represent your average dad), a surprising 28% of men had symptoms that scored above mild levels of depression. Overall, 4% had moderate depression. Fewer than one in five fathers who were depressed sought help, even though a third of those had thought about harming themselves. While women in the UK are often asked a series of questions that screen for postnatal depression (which affects up to 13% of women), the mental health of fathers is rarely assessed.The lead author of the Swedish paper, Elisa Psouni, from the department of psychology at Lund University, says the Edinburgh Postnatal Depression Scale(EPDS) used for both women and men is not so accurate in picking up depression in fathers. Her research showed higher levels of depression in dads because it added in a score more reflective of "male" symptoms ofdepression such as agitation, anger, irritability(易怒), working longer hours and drinking too much.Depression in fathers may be rising not just because researchers are looking for it, but because more new dads are struggling. Psouni believes fathers increasingly face the same dilemmas that mothers do-including trying to combine parenthood with working Fathers who got depressed often had external pressures, such as job issues, and if their partner was depressed, their own risk of depression doubled. Lack of sleep, having twins and conflict in the relationship can all contribute.A depressed dad will play and smile less with his child. Children are deeply affected by paternal postnatal depression with studies showing poorer measures of wellbeing and more behavioral problems at the age of seven.Fathers who sense they may be struggling and partners, relatives or friends who notice an increase in imitability and anxiety in a man in the first year of parenthood (paternal depression is more dispersed throughout the first 12 months) should consider the possibility of paternal postnatal depression.Cognitive behavioral therapy(认知行为疗法) can help, as can antidepressants. If the depression is not recognised, says Psouni, "one of most terrible things is that you catch up with yourself a year later and realise you have been really down and struggling-and the first year of your child's life has gone.”38.What is revealed about men according to a Sweden research?A.They experience a sharp decline in hormone.B.Many of them suffer from postnatal depression.C.They seldom go through pregnancy or childbirthD.Many of them qualify for the transition to fatherhood.39.What do the statistics in Paragraph 2 indicate?A.The researchers should invite more Swedish fathers.B.Over half of Swedish fathers tend to harm themselves.C.The mental health of fathers deserves more attention.D.Postnatal depression affects British women more easily.40.Why did Psouni's research show higher levels of depression in dads? A.Researchers use a new measure for male symptom of depression.B.Researchers adopt EPDS to accurately pick up depression in dads.C.Fathers have trouble in coping with internal and external pressures.D.Fathers are often faced with the doubled risk of partner depression.41.What may happen to a father with paternal depression?A.He may develop terrible behavioral habits.B.He may avoid being recognized with depression.C.He may decline cognitive behavioral therapy.D.He may miss the chance of giving proper childcare.Cane toads, also known as bufo toads, are yet another invasive (入侵) species that has found a hospitable home in warm southern Florida. Deliberately introduced from South and Central America in the 1930s, they were supposed to control beetles damaging the sugarcane crop—that’s how they got the name “cane toads.”Cane toads can pose a particular danger because the adult ones shoot toxin ( 毒素) from their back when attacked. The tiny toads don’t carry enough toxin to be deadly yet, but big adult ones can easily send a dog into a seizure ( 疾病发作) or even kill it. The toxin is “very viscous and would stick inside the dog’s mouth,” says Steve Johnson, a wildlife ecologist at the University of Florida. Owners should try to wi pe out an affected dog’s mouth and immediately take it to the vet.Tilford started Toad Busters in 2017. The woman who lived there had nine cats, which she fed by dumping almost a bag of cat food every night. Cane toads normally eat bugs, but they are happy to eat pet food, too.Cane toads have adapted beautifully to the Florida suburbs, so a lot of Tilford’s work also involves getting people to rethink their suburban backyard. No more cat food, for example. Pet poop (粪便) can also attract insects, which can in turn attract toads. As do lights. And toads love to breed (繁殖) in attractive pools of water, such as the lake in the affected Palm Beach Garden neighborhood. For “these larger communities that want to build these beautiful ponds and want to have house s on ponds,” Tilford said, “this is almost a pest-control service.” The cane toads aren’t going away, but they can be managed like mosquitoes or rats.Dealing with toads amounts to an annoying thing in Florida, but they can also create more dramatic problems. In Australia—where they were also deliberately introduced in the 1930s to protect sugarcane—they are a genuine scourge (灾祸).The issue is that Australia has no native toad species, so none of the predators (食肉动物) knew how to avoid the toxic toads. As the cane toads advanced east to west across the continent, “they left a wake of dead animals in their paths,” says Sean Doody, an ecologist at the University of South Florida at St. Petersburg who has studied cane toads in Australia. Turtles, lizards, and crocodiles just started dying out, which was good news for their prey (受害者). “If you were a small species that was previously being eaten, suddenly you’re on a honeymoon,” says Rick Shine, a biologist at Macquarie University in Sydney, Australia, who has also studied the impact of cane toads on Australian wildlife.42.What can cane toads be described as?A.Invasive species introduced to South America.B.Natural enemies of beetles damaging sugarcane.C.Dangerous species making active attacks on dogs.D.A great threat presented to some wildlife ecologists.43.Which might be the proper way of avoiding cane toads according to Tilford? A.Abandon the suburban backyard.B.Light up the backyard at night.C.Control the number of large houses.D.Keep pet food away from backyard.44.What happened in Australia after cane toads being introduced?A.Cane toads destroyed some food chains.B.Most of the predators died of toad toxin.C.Cane toads bred at a much slower pace.D.Big species learned to avoid cane toads.Some of the greatest moments in human history were fueled by emotional intelligence. When Martin Luther King. Jr. presented his dream, he chose language that would stir the hearts of his audience. Delivering this electrifying(震撼性的) message required emotional intelligence—the ability to recognize, understand, and manage emotions.Emotional intelligence has been highly recommended by leaders, policymakers, andeducators as the solution to a wide range of social problems. If we can teach our children to manage emotions, the argument goes, we'll have less bullying and more cooperation. If we can cultivate emotional intelligence among leaders and doctors, we'll have more caring workplaces and more compassionate healthcare.Emotional intelligence is important, but the uncontrolled enthusiasm has obscured (掩盖)a dark side. New evidence shows that when people sharpen their emotional skills, they become better at manipulating (把持) others. When you're good at controlling your own emotions, you can hide your true feelings. When you know what others are feeling, you can motivate them to act against their own best interests.Social scientists have begun to document this dark side of emotional intelligence. In a research led by University of professor Jochen Menges, when a leader gave an inspiring speech filled with emotion. the audience was less likely to scrutinize (细察) the message and remembered of the content. Ironically(讽刺的是) audience members were so moved by the speech that they claimed to recall more of it.The authors call this the awestruck effect, but it might just as easily be described as the dumbstruck effect. One observer reflected that Hitler's persuasive impact came from his ability to strategically express emotions—he would "ear open his heart—and these emotions affected his followers to the point that they would"stop thinking critically and just emote.”Leaders who master emotions can rob us of our capacities to reason. If their values are out of step with our own. the results can be destructive. New evidence suggests that when people have self-serving motives (动机), emotional intelligence becomes a weapon for manipulating others. In a study led by the University of Toronto psychologist Stephane Cote, university employees filled out a survey about their Machiavellian(不择手段的) tendencies, and took a test measuring their knowledge about effective strategies for managing emotions. Then, Cote's team assessed how often the employees deliberately undermined (逐渐削弱) their colleagues. The employees involved in the most harmful behaviors were Machiavellians with high emotional intelligence. They used their emotional skills to lower the dignity of their peers for personal gain.Shining a light on this dark side of emotional intelligence is one mission of a research team led University College London professor Martin Kilduff. According to these experts, emotional intelligence helps people disguise (伪装) one set of emotions while expressing another for personal Professor Kiiduit's team writes,""The strategic disguise of one's ownemotions and the manipulation of others' emotions for strategic ends are behaviors evident not only on Shakespeare's stage but also in the offices and corridors where power and influence are traded.”Of course, people aren't always using emotional intelligence for nefarious ends. More often than not, emotional skills are simply instrumental tools for goal accomplishment. A research team discovered that founder Anita Roddick used emotional intelligence to inspire her employees fundraise for charity. As Roddick explained, "Whenever particular project we always tried to break their hearts we wanted to persuade our staff to support a particular project we always tried to break their hearts.”There is growing recognition that emotional intelligence--like any skill--can be used for good or evil. So if we're going to teach emotional intelligence in schools and develop it at work, we need to consider the values that go along with it and where it's actually useful. 45.Why does the author mention Martin Luther King, Jr?A.To honor the great leader for his courage.B.To recommend his speech to other leaders.C.To impress the readers with a major topic.D.To advocate a society with fewer problems.46.Which of the following belongs to a dark side of emotional intelligence? A.Developing the capability to control one's own emotion.B.Inducing people to do what brings disadvantages to them.C.Appealing to the audience to concentrate and remember more.D.Encouraging the moved audience to a more of the speech.47.What is the dumbstruck effect of Hitler's emotional intelligence?A.His followers would tear open their hearts to him.B.His followers would express emotions strategically.C.His followers would lose the ability to reason properly.D.His followers would develop the self-serving motives.48.How do people use their emotional intelligence for personal gain?A.They disguise their emotions to earn others' trust.B.They help their colleagues to build up confidence.C.They present their strategic behaviors on the stage.D.They lower their own dignity to gain popularity.49.Which may mean the same as the underlined word in Paragraph 8?A.Immoral. B.Unimportant.C.Illegal. D.Uncontrollable.50.What would be the best title for the passage?A.The benefits of emotional intelligenceB.The ways of disguising one's emotionsC.The reasons for using emotional skillsD.The dark side of emotional intelligence四、任务型阅读请认真阅读下列短文,并根据所读内容在文章后表格中的空格里填入一个最恰当的单词。
【市级联考】江苏省七市(南通、泰州、扬州、徐州、淮安、宿迁、连云港)2019届高三第二次调研考试(含听力)
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2019届南通市高三第二次调研联考英语试卷注意事项考生在答题前请认真阅读本注意事项及各题答题要求考试时间120分钟。
考试结束后,只要将答题纸交回。
1.本试卷共14页,包含第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分,共120分。
2.答题前,请您务必将自己的姓名、学校、考试号用书写黑色字迹的0.5毫米签字笔填写在答题纸上,并用2B铅笔把答题纸上考试号对应数字框涂黑,如需改动,请用橡皮擦干净后,再正确涂写。
3.请认真核对监考员在答题卡上所粘贴的条形码上的姓名、考试证号与你本人的是否相符。
4.答题时,必须用书写黑色字迹的0.5毫米签字笔写在答题纸上的指定位置,在其它位置作答一律无效。
第I卷 (三部分,共85分)第一部分听力(共两节,满分20分)第一节听下面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。
1.【此处有音频,请去附件查看】What color is the sofa?A. Brown.B. White.C. Blue.【答案】B【解析】【分析】M: We need a new sofa. This one is starting to sink in the middle and it looks shabby.W: Yes. White wasn’t a good choice of color. The next one should be darker. Brown or blue maybe. 【详解】此题为听力题,解析略。
2.【此处有音频,请去附件查看】What meal are the speakers about to eat?A. Breakfast.B. LunchC. Dinner.【答案】C【解析】【分析】M: When will the pizza be ready? I haven’t eaten since this morning. What about you?W: I skipped breakfast, but I had a pretty big lunch, so you can have most of the pizza.【详解】此题为听力题,解析略。
2019届南通、徐州、盐城、常州等市四月大联考 高三 英语(含答案) word版
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2019届南通、徐州、盐城、常州等市四月大联考英语试题注意事项:1.答卷前,考生务必用黑色字迹的钢笔或签字笔在答题卡上填写自己的准考证号、姓名、试室号和座位号。
用2B型铅笔把答题卡上试室号、座位号对应的信息点涂黑。
2.选择题每小题选出答案后,用2B型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的相应位置上;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整洁。
考试结束后,将试卷和答题卡一并交回。
第I卷(三部分,共85分)第一部分听力(共两节,满分20 分)第一节听下面 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。
1.What kind of shoes will the woman probably buy?A. Dress shoes.B. Soccer shoes.C. Tennis boots.2.How does the woman sound?A. Relieved.B. Worried.C. Disappointed.3.What does the woman want to do?A.Attend a party.B.Call the Trumps.C.Get Michael’s number.4.What are the speakers talking about?A. The weather.B. Writing skills.C. Weekend plans.5.What is the woman complaining about?A. The busy line.B. The wrong food.C. The late delivery.第二节听下面 5 段对话或独白。
2019届江苏省南通、徐州、盐城、常州等市高2016级高三四月大联考英语试卷及解析
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2019届南通、徐州、盐城、常州等市高2016级高三四月大联考英语试卷★祝考试顺利★第I 卷(三部分,共 85 分)第一部分听力(共两节,满分 20 分)第一节听下面 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。
1. What kind of shoes will the woman probably buy?A. Dress shoes.B. Soccer shoes.C. Tennis boots.2. How does the woman sound?A. Relieved.B. Worried.C. Disappointed.3. What does the woman want to do?A. Attend a party.B. Call the Trumps.C. Get Michael’s number.4. What are the speakers talking about?A. The weather.B. Writing skills.C. Weekend plans.5. What is the woman complaining about?A. The busy line.B. The wrong food.C. The late delivery.第二节听下面 5 段对话或独白。
每段对话或独白后有几个小题,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。
听每段对话或独白前,你将有时间阅读各个小题,每小题 5 秒钟;听完后,各小题将给出 5 秒钟的作答时间。
每段对话或独白读两遍。
听下面一段对话, 回答第 6 和第 7 两个小题。
6. When does the conversation take place?A. In the morning.B. At noon.C. In the afternoon.7. What does the man expect the woman to do?A. Pass on a message.B. Attend a meeting.C. Call him back.听下面一段对话, 回答第 8 和第 9 两个小题。
精品解析:【市级联考】江苏省苏州、无锡、常州、镇江四市2019届高三教学情况调研考试语文试题(解析版)
![精品解析:【市级联考】江苏省苏州、无锡、常州、镇江四市2019届高三教学情况调研考试语文试题(解析版)](https://img.taocdn.com/s3/m/ea024e5e783e0912a2162a63.png)
阅读下面的文言文,完成各题。
盛溪绿生志
胡胤嘉
吾乡吕水山先生,通博异才,微及艺事, 率尔造极。书法精劲,画无尘埃气。余尝得其所写《双柑图》,枝叶扶映,生气可摘。性好奖成人材,凡有片长,引接不倦。
我家乡的吕水山先生,通达渊博,才能特出,稍一接触艺术之事,就能达到最高境界。书法精妙道劲,绘画没有尘俗之气。我曾经得到他所画的《双柑图》,枝叶交映,栩栩如生,好像可以摘下来一般。他性喜助人成材,凡有微小的长处,推荐提拔不感到厌倦。
3.在下面一段文字横线处填入语句,衔接最恰当的一项是
月光洒满庭院,,,,。,,。她脚下的绿茵和近旁的花草也披了月光,柔软无声地在她脚下延展。
①泛着皎洁的月光 ②承载着银色的光华③在那里荡漾 ④喷水池里的微波
⑤远处枝叶扶疏的桂树 ⑥轻逸而静寂⑦烘出淡灰的影
A.④②⑥⑤⑦①③B.⑤②⑦⑥④①③
C.⑤①⑦④②③⑥D.④①③⑦⑤②⑥
【点睛】对于考查语句连贯性的题目,考生应按照如下步骤操作:1.抓中心。首先要统揽全局,抓中心句,分析句子的性质和作用(如总领句、总结句、过渡句、解说句、观点句、材料句等),然后分析其他句子是如何围绕中心句来组织的。2.抓思路。句子中的思路一般指三个方面:时间顺序、空间顺序和逻辑思维的顺序。空间顺序如从上到下,从左到右,从外到内;逻辑顺序,就是人们认识客观世界的具有规律性的顺序。3.抓标志。语言标志常常表现为:关联词语、暗示性词语、句子之间的对应关系(内容上、形式上)、陈述对象或议论角度、抓句式等等。4.抓语境。文章要表达的情感或喜或悲或褒或贬,或高昂或低沉,是通过一定的情景色彩渲染而完成的。在同一段文字中,这种基调、气氛、色彩要保持一致。此类题目要在快速阅读整段文字,初步感知大体内容的基础上,结合具体语境,根据上下文的句子结构、逻辑顺序等来分析、推理、判断,可以用排除法。
精品解析:【市级联考】江苏省苏锡常镇四市2019届高三教学情况调查(二)数学试题含附加题(解析版)
![精品解析:【市级联考】江苏省苏锡常镇四市2019届高三教学情况调查(二)数学试题含附加题(解析版)](https://img.taocdn.com/s3/m/14d88ee876a20029bd642d96.png)
江苏省苏锡常镇四市2019届高三教学情况调查(二)数学试题一、填空题(本大题共14小题,每小题5分,共70分,请将答案填写在答题卷相应的位置上.)1.已知集合A=,B=,则A B=_______.【答案】【解析】【分析】直接由交集运算得解。
【详解】因为A=,B=,所以【点睛】本题主要考查了交集的运算,属于基础题。
2.已知复数,其中是虚数单位,则=_______.【答案】1【解析】【分析】利用复数的除法及乘法运算求得,再利用复数的模的公式求解。
【详解】因为所以【点睛】本题主要考查了复数的乘法、除法运算,还考查了复数的模的定义,考查计算能力,属于基础题。
3.已知双曲线C的方程为,则其离心率为_______.【答案】【解析】【分析】由双曲线C的方程可求得,,问题得解。
【详解】由双曲线C的方程可得:所以,所以【点睛】本题主要考查了双曲线的简单性质,考查计算能力,属于基础题。
4.根据如图所示的伪代码,最后输出的i的值为_______.【答案】8【解析】【分析】按程序图依次执行即可得解。
【详解】依据程序图依次执行得:成立成立成立不成立,结束循环输出【点睛】本题主要考查了循环结构语句及其执行流程,属于基础题。
5.某校高一、高二、高三年级的学生人数之比为4:4:3,现按年级用分层抽样的方法抽取若干人,若抽取的高三年级的学生数为15,则抽取的样本容量为_______.【答案】55【解析】【分析】设高一、高二分别抽取,个人,按分层抽样方法列出比例关系,解方程即可求得,,问题得解。
【详解】设高一、高二分别抽取,个人,由题可得:,解得:,所以抽取的样本容量为(人)【点睛】本题主要考查了分层抽样方法中的比例关系,考查方程思想,属于基础题。
6.口装中有形状大小完全相同的四个球,球的编号分别为1,2,3,4.若从袋中随机抽取两个球,则取出的两个球的编号之积大于6的概率为_______.【答案】【解析】【分析】从袋中随机抽取两个球共有6个不同的结果,其中取出的两个球的编号之积大于6的有2种不同的结果,利用古典概型概率公式即可得解。
江苏省南通、徐州、盐城、常州等市2019届高三英语四月大联考试题(含解析)
![江苏省南通、徐州、盐城、常州等市2019届高三英语四月大联考试题(含解析)](https://img.taocdn.com/s3/m/c3784c6c7cd184254b3535d4.png)
江苏省南通、徐州、盐城、常州等市2019届高三英语四月大联考试题(含解析)第I 卷(三部分,共 85 分)第一部分听力(共两节,满分 20 分)第一节听下面 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。
1. What kind of shoes will the woman probably buy?A. Dress shoes.B. Soccer shoes.C. Tennis boots.2. How does the woman sound?A. Relieved.B. Worried.C. Disappointed.3. What does the woman want to do?A. Attend a party.B. Call the Trumps.C. Get Michael’s number.4. What are the speakers talking about?A. The weather.B. Writing skills.C. Weekend plans.5. What is the woman complaining about?A. The busy line.B. The wrong food.C. The late delivery.第二节听下面 5 段对话或独白。
每段对话或独白后有几个小题,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。
听每段对话或独白前,你将有时间阅读各个小题,每小题 5 秒钟;听完后,各小题将给出 5 秒钟的作答时间。
每段对话或独白读两遍。
听下面一段对话, 回答第 6 和第 7 两个小题。
6. When does the conversation take place?A. In the morning.B. At noon.C. In the afternoon.7. What does the man expect the woman to do?A. Pass on a message.B. Attend a meeting.C. Call him back.听下面一段对话, 回答第 8 和第 9 两个小题。
【市级联考】江苏省南通市2019届高三模拟练习卷(四模)数学试题(解析版)
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江苏省南通市2019届高三练习卷(四模)数学试题一、填空题(本大题共14小题,每小题5分,共70分,请将答案填写在答题卷相应的位置上.)1. 已知集合{}12A x x =-<≤,{}0B x x =<,则A B =_______. 【答案】{}10x x -<< 【解析】 【分析】由集合交集的定义运算即可.【详解】已知集合{}12A x x =-<≤,{}0B x x =<,则A B ={}10x x -<< 故答案为{}10x x -<<【点睛】本题考查了交集及其运算,熟练掌握交集的定义是解本题的关键,属于基础题.2. 已知复数221z i i=++(i 是虚数单位),则z 的共轭复数为_______. 【答案】1i - 【解析】 【分析】利用复数代数形式的乘除运算化简得z ,再由共轭复数的定义得答案. 【详解】22(1)221211(1)(1)i z i i i i i i i i -∴=+=+=-+=+++- ∴1z i =-. 故答案为1i -【点睛】本题考查复数代数形式的乘除运算,考查共轭复数的基本概念,属于基础题. 3. 执行如图所示的伪代码,则输出的S 的值为_______.【答案】17 【解析】【分析】模拟执行程序代码,依次写出每次循环得到的i ,S 的值,即可得解输出的S 的值. 【详解】模拟执行程序代码,可得S =3 第1步:i =2,S =S +i =5; 第2步:i =3,S =S +i =8; 第3步:i =4,S =S +i =12; 第4步:i =5,S =S +i =17; 此时,退出循环,输出S 的值为17. 故答案为17.【点睛】本题主要考查了循环结构的程序代码,正确依次写出每次循环得到的i ,S 的值是解题的关键,属于基础题.4. 从某小学随机抽取100名学生,将他们的身高(单位:cm )数据绘制成如图所示的频率分布直方图,则身高在[120,130)内的学生人数为__.【答案】30 【解析】 【分析】由题意,可由直方图中各个小矩形的面积和为1求出a 值,再求出此小矩形的面积即此组人数在样本中的频率,再乘以样本容量即可得到此组的人数.【详解】由图知,(0.035+a +0.020+0.010+0.005)×10=1,解得a =0.03; ∴身高在[120,130]内的学生人数为100×0.03×10=30. 故答案为30.【点睛】本题考查频率分布直方图,解题的关键是理解直方图中各个小矩形的面积的意义及各个小矩形的面积和为1,属于基础题.5. 在平面直角坐标系xOy 中,已知双曲线22221x y a b -=(0,0a b >>)的两条渐近线的方程为2y x =±,则该双曲线的离心率为_______.【解析】 【分析】由双曲线的两条渐近线方程是y =±2x,得b =2a,从而c ==,即可求出双曲线的离心率.【详解】∵双曲线22221x y a b-=(0,0a b >>)的两条渐近线方程是y =±2x,∴2b a =,即b =2a ,∴c ,∴c e a==.【点睛】本题考查双曲线的离心率,考查双曲线的性质,考查学生的计算能力,属于基础题.6. 现有3个奇数,2个偶数.若从中随机抽取2个数相加,则和是偶数的概率为__.【答案】25【解析】 【分析】从中随机抽取2个数相加,基本事件总数2510n C ==,和是偶数包含的基本事件的个数2232C C 4m =+=,由此能求出和是偶数的概率.【详解】现有3个奇数,2个偶数.从中随机抽取2个数相加,基本事件总数2510n C ==, 和是偶数包含的基本事件的个数2232C C 4m =+=,则和是偶数的概率为42105m p n === . 故答案为25.【点睛】本题考查概率的求法,考查古典概型计算公式等知识,意在考查学生的转化能力和计算求解能力,属于基础题.7. 已知圆锥的轴截面是直角边长为2的等腰直角三角形,则该圆锥的侧面积为____. 【答案】 【解析】 【分析】设圆锥的底面半径为r ,依题意,222r =,即2r =,所以该圆锥的侧面积为rl π=22π.【详解】依题意,设圆锥的底面半径为r ,已知圆锥的轴截面是直角边长为2的等腰直角三角形,如图所示,所以2222222r =+=,即2r =,又因为圆锥的母线长为2l =, 所以该圆锥的侧面积为rl π=22π. 故答案为22π.【点睛】本题考查了圆锥的结构特点,圆锥的侧面积.属于基础题.8. 给出下列三个函数:①1y x =;②sin y x =;③e x y =,则直线12y x b =+(b R ∈)不能作为函数_______的图象的切线(填写所有符合条件的函数的序号). 【答案】① 【解析】 【分析】分别求得三个函数的导数,由导数的几何意义,解方程可得不满足题意的函数. 【详解】直线12y x b =+的斜率为k =12, 对于①1y x =,求导得:'21y x =-,对于任意x≠0,21x -=12无解,所以,直线12y x b =+不能作为切线;对于②sin y x =,求导得:'1cos 2y x ==有解,可得满足题意; 对于③x y e =,求导得:'12xy e ==有解,可得满足题意; 故答案为①【点睛】本题考查导数的运用:求切线的斜率,考查导数的运算,以及方程思想、运算能力,属于中档题.9. 如图,在平面四边形ABCD 中,90CBA CAD ∠=∠=︒,30ACD ∠=︒,AB BC =,点E 为线段BC 的中点.若AC AD AE λμ=+(,R λμ∈),则λμ的值为_______.43【解析】 【分析】以A 为原点,建立平面直角坐标系,设AB =BC =2后,写出各点坐标,用向量的坐标运算可得.【详解】以A 为原点,建立如图所示的平面直角坐标系,不妨设AB =BC =2, 则有A (0,0),B (2,0),C (2,2),E (2,1),AC =2, AD =226,过D 作DF⊥x 轴于F ,∠DAF=180°-90°-45°=45°, DF =263sin45°=6223323⨯=,所以D (233-,33), AC =(2,2),AD =(2323),AE =(2,1),因为AC AD AE λμ=+,所以,(2,2)=λ(233-23+μ(2,1),所以,2322232μμ⎧+=⎪⎪+=,解得:3343λμ⎧=⎪⎪⎨⎪=⎪⎩λμ4343【点睛】本题考查了平面向量的基本运算,建系用坐标表示是解题的关键,属于中档题.10. 已知实数,x y 满足(2)(23)0x y x y +--+≥,则22x y +的最小值为_______.【答案】95【解析】 【分析】画出约束条件的可行域,利用目标函数的几何意义求解即可. 【详解】由(2)(23)0x y x y +--+≥,得:20230x y x y +-≥⎧⎨-+≥⎩或20230x y x y +-≤⎧⎨-+≤⎩,不等式组表示的平面区域如图所示;22x y +=()()2200x -+y-,表示平面区域内取一点到原点的距离的平方,即原点到20x y +-=的距离为00222d +-==,原点到230x y +=-的距离为:02033555d -⨯+=== 所以,22x y +的最小值为2355⎛⎫ ⎪ ⎪⎝⎭=95 故答案为95【点睛】本题考查线性规划的简单性质,考查目标函数的几何意义,数形结合以及转化思想的应用,考查计算能力,属于基础题.11. 已知()f x 是定义在R 上且周期为32的周期函数,当30,2x ⎛⎤∈ ⎥⎝⎦时,()121f x x =--.若函数()log a y f x x =-(1a >)在()0,∞+上恰有4个互不相同的零点,则实数a 的值__.【答案】72【解析】 【分析】根据题意得()y f x =与log a y x =有4个交点,画出函数y =f (x )与y =log a x (a >1)在(0,+∞)的图象,根据数形结合可得答案.【详解】当30,2x ⎛⎤∈ ⎥⎝⎦时,得12,02()1211322,22x x f x x x x ⎧<<⎪⎪=--=⎨⎪-≤≤⎪⎩ , 且()f x 是定义在R 上且周期为32的周期函数,函数()log a y f x x =-(a >1)在(0,+∞)上恰有4个互不相同的零点,∴函数()y f x =与log a y x =(a >1)在(0,+∞)上恰有4个不同的交点,分别画出两函数图象如图所示,由图可知,当x =72时,有72log a =1,所以a =72.故答案为72【点睛】本题考查了函数的图象及性质,考查了数形结合思想,属于中档题. 12. 已知正项等比数列{}n a 的前n 项和为n S .若9362S S S =+,则631S S +取得最小值时,9S 的值为_______.【答案】33【解析】 【分析】因为9362S S S =+,所以q≠1,所以936111(1)(1)(1)2111a q a q a q q q q ---=+---,即63(1)(2)0q q --=,得32q =.化简得16311311a q q a S S +-=-+,由基本不等式得其最小值,即可得到9S .【详解】由9362S S S =+,得:q≠1,所以936111(1)(1)(1)2111a q a q a q q q q ---=+---,化简得:936112(1)q q q -=-+-,即963220q q q --+=,即63(1)(2)0q q --=,得32q =,化简得631S S +=6131(1)11(1)a q qq a q --+--=113131a q q a -+≥-, 当11311a q q a -=-,即13a =时,631S S +取得最小值, 所以919(1)1a q S q -==-9(1)13q q --=733故答案【点睛】本题考查了等比数列的前n 项和公式和通项公式的灵活运用,基本不等式求最小值的条件,属于中档题.13. 在平面直角坐标系xOy 中,已知()11,A x y ,()22,B x y 为圆221x y +=上两点,且121212x x y y +=-.若C 为圆上的任意一点,则·CA CB 的最大值为______.【答案】32【解析】 【分析】因为C 为圆221x y +=上一点,设C (sinθ,cosθ),则利用坐标运算即可. 【详解】因为C 为圆x 2+y 2=1上一点,设C (sinθ,cosθ),则()()1122sin ,cos ,sin ,cos CA x y CB x y θθθθ=--=--,∵()11,A x y ,()22,B x y 为圆221x y +=上两点,∴222211221,1x y x y +=+=,又121212x x y y +=-,∴()()2212121212CA CB x x y y x x sin y y cos sin cos θθθθ⋅=+-+-+++1)2θϕ=+1)2θϕ=+ 1sin()2θϕ=-+,其中1212tan y y x x ϕ+=+,∵sin()θϕ+∈[﹣1,1],∴当sin()θϕ+=1时,CA CB ⋅的最大值为32.故答案为32.【点睛】本题考查了平面向量数量积的性质及其运算,利用坐标运算是解题的关键,属于中档题.14. 在ABC ∆中,,,a b c 分别为角,,A B C 所对边的长,S 为ABC ∆的面积.若不等式22233kS b c a ≤+-恒成立,则实数k 的最大值为______.【答案】【解析】 【分析】在ABC ∆中,面积公式1sin 2S bc A =,余弦定理2222cos b c a bc A +-=,代入22233kS b c a≤+-化简得22444cos sin b c bc Ak bc A++≤,由基本不等式得22444cos sin b c bc A bc A++≥84cos sin AA +;令84cos sin A y A +=,得sin 4cos 8y A A -=,由辅助角)8A ϕ-=,进而得sin()A ϕ-=(]0,1∈,求出y 即可得答案.【详解】在ABC ∆中,面积公式1sin 2S bc A =,余弦定理2222cos b c a bc A +-=,代入22233kS b c a ≤+-,有221sin 222cos 2k bc A b c bc A ⨯≤++,即22444cos sin b c bc A k bc A++≤恒成立,求出22444cos sin b c bc A bc A++的最小值即可,而22444cos 8bc 4cos 84cos sin sin sin b c bc A bc A Abc A bc A A++++≥=,当且仅当b c =取等号,令84cos sin Ay A+=,得:sin 84cos y A A =+,即sin 4cos 8y A A -=,)8A A =,令cos ϕϕ=)8A ϕ-=,即sin()A ϕ-=,所以01≤,两边平方,得:26416y ≤+,解得:y ≥=22444cos sin b c bc A bc A++的最小值为k ≤故答案为【点睛】本题考查了三角形的面积公式,余弦定理,以及基本不等式求最小值,辅助角公式的化简,也考查了计算能力,属于中档题.二、解答题(本大题共6小题,共计90分,请在答题纸指定区域内作答,解答时应写出文字说明、证明过程或演算步骤.) 15. 已知函数()sin()f x x ωϕ=+(0>ω,π2<ϕ)的图象关于直线π6x =对称,两个相邻的最高点之间的距离为2π. (1)求()f x 的解析式;(2)在△ABC 中,若3()5f A =-,求sin A 的值.【答案】(1)()πsin 3f x x ⎛⎫=+ ⎪⎝⎭;(2)310.【解析】 【分析】(1)由题意可求正弦函数的周期,利用周期公式可求ω,由图象关于直线π6x =对称,可求62k ππϕπ+=+,结合范围π2<ϕ,可求ϕ,即可求得函数解析式. (2)由已知可求3sin 035A π⎛⎫+=-< ⎪⎝⎭,结合范围A+3π∈(π,43π),利用同角三角函数基本关系式可求cos (A+3π),根据两角差的正弦函数公式可求sinA 的值. 【详解】(1)∵函数()sin()f x x ωϕ=+(ω>0,π2<ϕ)的图象上相邻两个最高点的距离为2π,∴函数的周期T =2π,∴2πω=2π,解得ω=1,∴f(x )=sin (x+φ),又∵函数f (x )的图象关于直线π6x =对称,∴62k ππϕπ+=+,k∈Z , ∵π2<ϕ,∴ϕ=3π,∴f(x )=sin (x+3π). (2)在△ABC 中,∵3()5f A =-,A∈(0,π),∴3sin 035A π⎛⎫+=-< ⎪⎝⎭,∴44,,cos 3335A A ππππ⎛⎫⎛⎫+∈∴+==- ⎪ ⎪⎝⎭⎝⎭, ∴sin sin ()sin cos cos()sin 333333A A A A ππππππ⎡⎤⎛⎫=+-=+-+ ⎪⎢⎥⎣⎦⎝⎭3143433525-⎛⎫⎛⎫=-⨯--⨯= ⎪ ⎪⎝⎭⎝⎭.【点睛】本题主要考查由()Asin y x ωϕ=+的部分图象确定其解析式,考查了三角函数恒等变换的应用,考查了数形结合思想和转化思想,属于中档题. 16. 如图,在直三棱柱111ABC A B C -中,AB AC ⊥,1AC AA =,D 是棱AB的中点.(1)求证:11BC ACD ∥平面; (2)求证:11BC A C .【答案】(1)见详解;(2)见详解. 【解析】 【分析】(1)连接AC 1,设AC 1∩A 1C =O ,连接OD ,可求O 为AC 1的中点,D 是棱AB 的中点,利用中位线的性质可证OD∥BC 1,根据线面平行的判断定理即可证明BC 1∥平面A 1CD .(2)由(1)可证平行四边形ACC 1A 1是菱形,由其性质可得AC 1⊥A 1C ,利用线面垂直的性质可证AB⊥AA 1,根据AB⊥AC,利用线面垂直的判定定理可证AB⊥平面ACC 1A 1,利用线面垂直的性质可证AB⊥A 1C ,又AC 1⊥A 1C ,根据线面垂直的判定定理可证A 1C⊥平面ABC 1,利用线面垂直的性质即可证明BC 1⊥A 1C .【详解】(1)连接AC 1,设AC 1∩A 1C =O ,连接OD ,在直三棱柱ABC ﹣A 1B 1C 1中,侧面ACC 1A 1是平行四边形,所以:O 为AC 1的中点,又因为:D 是棱AB 的中点,所以:OD∥BC 1, 又因为:BC 1⊄平面A 1CD ,OD ⊂平面A 1CD ,所以:BC 1∥平面A 1CD .(2)由(1)可知:侧面ACC 1A 1是平行四边形,因为:AC =AA 1,所以:平行四边形ACC 1A 1是菱形,所以:AC 1⊥A 1C ,在直三棱柱ABC ﹣A 1B 1C 1中,AA 1⊥平面ABC ,因为:AB ⊂平面ABC ,所以:AB⊥AA 1,又因为:AB⊥AC,AC∩AA 1=A ,AC ⊂平面ACC 1A 1,AA 1⊂平面ACC 1A 1,所以:AB⊥平面ACC1A1,因为:A1C⊂平面ACC1A1,所以:AB⊥A1C,又因为:AC1⊥A1C,AB∩AC1=A,AB⊂平面ABC1,AC1⊂平面ABC1,所以:A1C⊥平面ABC1,因为:BC1⊂平面ABC1,所以:BC1⊥A1C.【点睛】本题主要考查了线面平行的判定,线面垂直的性质,线面垂直的判定,考查了空间想象能力和推理论证能力,属于中档题.17. 如图,在宽为14m的路边安装路灯,灯柱OA高为8m,灯杆PA是半径为mr的圆C的一段劣弧.路灯采用锥形灯罩,灯罩顶P到路面的距离为10m,到灯柱所在直线的距离为2m.设Q为灯罩轴线与路面的交点,圆心C在线段PQ上.(1)当r为何值时,点Q恰好在路面中线上?(2)记圆心C在路面上的射影为H,且H在线段OQ上,求HQ的最大值.【答案】(1)当r为25Q在路面中线上;(2)124 5.【解析】【分析】(1)以O为原点,以OA所在直线为y轴建立平面直角坐标系,求出PQ的方程,设C (a,b),根据CA=CP=r列方程组可得出a,b的值,从而求出r的值;(2)用a表示出直线PQ的斜率,得出PQ的方程,求出Q的坐标,从而可得出|HQ|关于a 的函数,根据a 的范围和基本不等式得出|HQ|的最大值.【详解】(1)以O 为原点,以OA 所在直线为y 轴建立平面直角坐标系,则A (0,8),P (2,10),Q (7,0),∴直线PQ 的方程为2x+y ﹣14=0.设C (a ,b ),则222222(2)(10)(8)a b r a b r ⎧-+-=⎨+-=⎩, 两式相减得:a+b ﹣10=0,又2a+b ﹣14=0,解得a =4,b =6, ∴224(68)25r =+-=.∴当25r =时,点Q 恰好在路面中线上. (2)由(1)知a+b ﹣10=0,当a =2时,灯罩轴线所在直线方程为x =2,此时HQ =0. 当a≠2时,灯罩轴线所在方程为:y ﹣10=2aa --(x ﹣2), 令y =0可得x =12﹣20a ,即Q (12﹣20a,0), ∵H 在线段OQ 上,∴12﹣20a≥a,解得2≤a≤10. ∴|HQ|=12﹣20a ﹣a =12﹣(20a+a )≤12﹣220=12﹣45, 当且仅当20a=a 即a =25时取等号.∴|HQ|的最大值为(12﹣45)m .【点睛】本题考查了直线方程,圆的方程,考查基本不等式与函数最值的计算,属于中档题.18. 如图,在平面直角坐标系xOy 中,椭圆C :22221x y a b+=(a >b >0)经过点(0,3),点F 是椭圆的右焦点,点F 到左顶点的距离和到右准线的距离相等.过点F 的直线l 交椭圆于M ,N 两点.(1)求椭圆C的标准方程;(2)当MF=2FN时,求直线l的方程;(3)若直线l上存在点P满足PM·PN=PF2,且点P在椭圆外,证明:点P在定直线上.【答案】(1)22143x y+=;(25250x y±-=;(3)见解析.【解析】【分析】(1)由题意,b3再由点F到左顶点的距离和到右准线的距离相等,得a+c=2acc-,结合隐含条件解得a=2,c=1,则椭圆方程可求;(2)当直线l与x轴重合时,求得MF=3NF,不合题意;当直线l与x轴不重合时,设直线l的方程为x=my+1,M(x1,y1),N(x2,y2),联立直线方程与椭圆方程,化为关于y的一元二次方程,由根与系数的关系及MF=2FN求得m值,则直线方程可求;(3)当直线l的斜率为0时,设P(x0,y),由PM•PN=PF2,求得52x=,当直线l的斜率不为0时,由(2)中的根与系数的关系及PM•PN=PF2,求得3 2ym=,代入直线方程得05 2x=,由此可得点P在定直线52x=上.【详解】(1)设椭圆的截距为2c,由题意,b3,由点F到左顶点的距离和到右准线的距离相等,得a+c=2acc-,又a2=b2+c2,联立解得a=2,c=1.∴椭圆C的标准方程为221 43x y+=;(2)当直线l与x轴重合时,M(﹣2,0),N(2,0),此时MF=3NF,不合题意;当直线l与x轴不重合时,设直线l的方程为x=my+1,M(x1,y1),N(x2,y2),联立22my 1x y 143x =+⎧⎪⎨+=⎪⎩,得(3m 2+4)y 2+6my ﹣9=0.△=36m 2+36(m 2+4)>0.122634m y y m +=-+ ①,1229y y 3m 4=-+②,由MF =2FN ,得y 1=﹣2y 2③, 联立①③得,1222126,3434m my y m m =-=++, 代入②得,()22227293434m m m-=-++,解得m 5=±.20y ±-=; (3)当直线l 的斜率为0时,则M (2,0),N (﹣2,0),设P (x 0,y 0), 则PM •PN =|(x 0﹣2)(x 0+2)|,∵点P 在椭圆外,∴x 0﹣2,x 0+2同号, 又()()()()2220000PF x 1,x 2x 2x 1=-∴-+=-,解得052x =. 当直线l 的斜率不为0时,由(2)知,1212226m 9y y ,y y 3m 43m 4+=-=-++,10200PM y ,PN y ,PF =-=-=. ∵点P 在椭圆外,∴y 1﹣y 0,y 2﹣y 0同号,∴PM •PN =(1+m 2)(y 1﹣y 0)(y 2﹣y 0)=()()221201201m y y y y y y ⎡⎤+-++⎣⎦()()2222002269113434m m y m y m m ⎛⎫=++-=+ ⎪++⎝⎭,整理得032y m =,代入直线方程得052x =.∴点P 在定直线52x =上. 【点睛】本题考查椭圆方程的求法,考查直线与椭圆位置关系的应用,考查计算能力,属于中档题.19. 设函数32()f x x ax bx =++(a ,b ∈R)的导函数为()f x ,已知1x ,2x 是()'f x 的两个不同的零点.(1)证明:23a b >;(2)当b =0时,若对任意x >0,不等式()ln f x x x ≥恒成立,求a 的取值范围; (3)求关于x 的方程1211()()()()2x x f x f x x f x -+'+=的实根的个数. 【答案】(1)见解析;(2)[)1,-+∞;(3)1个. 【解析】 【分析】(1)求函数的导数,利用△=4a 2﹣12b >0,得证; (2)分离参数a ,所以a≥ln x x ﹣x 对任意x >0恒成立,令新函数设g (x )=ln xx﹣x 求最值即可,或采用x 3+ax 2﹣xlnx≥0时求左侧最值亦可. (3)转化函数求零点个数可得结论.【详解】(1)函数f (x )=x 3+ax 2+bx (a ,b∈R)的导函数为f′(x )=3x 2+2ax+b . 已知x 1,x 2是f'(x )的两个不同的零点,设x 1<x 2, 所以△=4a 2﹣12b >0,所以:a 2>3b 得证;(2)当b =0时,对任意x >0,f (x )≥xlnx 恒成立,所以x 3+ax 2≥xlnx,即x 3+ax 2﹣xlnx≥0,x 2+ax ﹣lnx≥0对任意x >0恒成立, 所以a≥ln xx﹣x 对任意x >0恒成立, 设g (x )=ln x x ﹣x ,则2221ln 1ln g ()1x x x x x x '---=-= ,令h (x )=1﹣1nx ﹣x 2,则h '(x )=﹣1x﹣2x <0, 所以h (x )在(0,+∞)上单调递减,注意到h (1)=0,当x∈(0,1)时,h (x )>0,g '(x )>0,所以g (x )在(0,1)上单调递增, 当x∈(1,+∞)时,H (x )<0,g '(x )<0,所以g (x )在(1,+∞)上单调递减, 所以,当x =1时,g (x )有最大值g (1)=﹣1, 所以a 的取值范围为[﹣1,+∞);(3)由题意设F (x )=f (x )﹣f (x 1)﹣()'121()2x x f x x +-, 则原问题转化为求函数F (x )的零点的个数,因为导函数为f '(x )=3x 2+2ax+b ,已知x 1,x 2是f'(x )的两个不同的零点,所以:21212,23233x x x x a a a f f b ''++⎛⎫⎛⎫=-=-=-+ ⎪ ⎪⎝⎭⎝⎭,所以: 22212()()323()0233x x a a F x f x f x ax x +⎛⎫=-=++=+ ⎪⎝⎭''', 所以F (x )(0,+∞)上单调递增,注意到F (x 1)=0,所以F (x )在(0,+∞)上存在唯一零点x 1,∴关于x 的方程()()1211()2x x f x f x x f x '+⎛⎫=-+ ⎪⎝⎭有1个实根,【点睛】本题考查函数的极值,最值的综合应用,函数的零点判断,构造新函数求最值的特点,属于难题.20. 已知在数列{a n }中,设a 1为首项,其前n 项和为S n ,若对任意的正整数m ,n 都有不等式S 2m +S 2n <2S m+n (m≠n)恒成立,且2S 6<S 3. (1)设数列{a n }为等差数列,且公差为d ,求1a d的取值范围; (2)设数列{a n }为等比数列,且公比为q (q >0且q≠1),求a 1⋅q 的取值范围. 【答案】(1)1a d<﹣3;(2)a 1⋅q >0 【解析】 【分析】(1)根据已知条件,由于数列是等差数列,运用等差数列的求和公式,建立不等式,进一步求出相应的结果;(2)根据已知条件,由于数列是等比数列,运用等比数列的求和公式,建立不等式,进一步求出相应的结果.【详解】在数列{a n }中,设a 1为首项,其前n 项和为S n ,若对任意的正整数m 、n 都有不等式S 2m +S 2n <2S m+n (m≠n)恒成立, (1)设{a n }为等差数列,且公差为d ,则:2ma 1+2(21)2m m -d+2na 1+2(21)2n n -d <2[(m+n )a 1+()(1)2m n m n ++-d],整理得:(m ﹣n )2d <0,则d <0,由2S 6>S 3,整理得:9a 1+27d >0, 则a 1>﹣3d ,所以d <0,1a d<﹣3; (2)设{a n }为等比数列,且公比为q (q >0且q≠1), 则()()()2m 2n m+n 111a 1q a 1q 2a 1q 1q1q1q---+<---,整理得1a 1q-(2q m+n ﹣q 2m ﹣q 2n )<0, 则:﹣1a 1q -(q m ﹣q n )2<0,所以1a 1q->0,由2S 6>S 3,则:2q 6﹣q 3﹣1<0解得:﹣12<q 3<1,由于q >0,所以:0<q <1,则:a 1>0.即有a 1⋅q >0. 【点睛】本题考查的知识要点:等差数列和等比数列前n 项和公式的应用,也考查了运算能力,属于中档题.21. 已知矩阵 1 2 0A x -⎡⎤=⎢⎥⎣⎦, 5 72 3B ⎡⎤=⎢⎥⎣⎦.B 的逆矩阵1B -满足17 17 7AB y --⎡⎤=⎢⎥-⎣⎦. (1)求实数,x y 的值; (2)求矩阵A 的特征值.【答案】(1)1,3x y ==;(2)2-和1. 【解析】 【分析】(1)利用1()A AB B -=求解即可;(2)矩阵A 的特征多项式12()1f λλλ+-=-求出行列式,然后令f (λ)=0即可.【详解】(1)因为17 17 7AB y --⎡⎤=⎢⎥-⎣⎦, 5 72 3B ⎡⎤=⎢⎥⎣⎦,∴17175712()723514721A AB B y y y ---⎡⎤⎡⎤⎡⎤===⎢⎥⎢⎥⎢⎥---⎣⎦⎣⎦⎣⎦, 即12120514721x y y --⎡⎤⎡⎤=⎢⎥⎢⎥--⎣⎦⎣⎦,∴51417210,3y x x y y ⎧-==⎧⎨⎨-=∴=⎩⎩; (2)矩阵A 的特征多项式12()1f λλλ+-=-=(λ+1)λ﹣2=(λ+2)(λ﹣1),令f (λ)=0,则λ=﹣2或λ=1,∴矩阵A 的特征值﹣2和1. 【点睛】本题考查了逆变换与逆矩阵以及矩阵特征值的求法,属于基础题. 22. 在极坐标系中,圆C 的方程为2cos 0ρθ+=,直线l 的方程为7π2sin 06m ρθ⎛⎫-+= ⎪⎝⎭.(1)若直线l 过圆C 的圆心,求实数m 的值; (2)若2m =,求直线l 被圆C 所截得的弦长.【答案】(1)1m =;【解析】 【分析】(1)将直线与圆的极坐标方程化成直角坐标方程后,利用圆心在直线上列式可得. (2)利用点到直线的距离公式和勾股定理可得.【详解】(1)由ρ+2cosθ=0得ρ2+2ρcosθ=0,得x 2+y 2+2x =0,则圆心为(﹣1,0),半径r =1.由2ρsin(θ﹣76π)+m =0得2ρsinθcos 76π﹣2ρcosθsin 76π+m =0,得直线l 的直角坐标方程为 x +m =0,因为直线l 过圆C 的圆心,则﹣1+m =0,所以m =1. (2)若m =2,则圆心C 到直线的距离1d2==,所以直线l 被圆C 截得的弦长为==. 【点睛】本题考查了极坐标与直角坐标方程的互化,点到直线的距离,属于中档题. 23. 已知实数,,x y z 满足222491212x y z ++=.证明:22222111323x y y z z++≥++. 【答案】见详解. 【解析】 【分析】设a =x 2+2y 2,b =y 2+3z 2,c =z 2,由题意可得4a+b+9c =12,再根据柯西不等式即可证明.【详解】设a =x 2+2y 2,b =y 2+3z 2,c =z 2,∴4(a ﹣2b+6c )+9(b ﹣3c )+12c =12,即4a+b+9c =12,∴222221+1123x y y z z +++11111=(49)12b c a b c a b c a ⎛⎫++=++++ ⎪⎝⎭ 211312a ⎛⋅= ⎝ 故原不等式成立.【点睛】本题考查了不等式的证明,柯西不等式的应用,考查了转化与化归思想,推理论证能力,属于中档题24. 如图,已知F 是抛物线C :24y x =的焦点,过E(﹣l ,0)的直线l 与抛物线分别交于A ,B 两点(点A ,B 在x 轴的上方).(1)设直线AF ,BF 的斜率分別为1k ,2k ,证明:120k k +=; (2)若∆ABF 的面积为4,求直线l 的方程. 【答案】(1)见解析;(2)210x +=. 【解析】 【分析】(1)设直线l 的方程为x =my ﹣1,A (x 1,y 1),B (x 2,y 2),联立抛物线方程利用韦达定理可得121212y yk k 0x 1x 1+=+=--. (2)S △ABF =S △EFB ﹣S △EFA =|y 1﹣y 2|()221212416164y y y y m +-=-=.解得m 即可.【详解】(1)当直线l 的斜率为0时,直线与抛物线只有一个交点,不合题意. 当直线l 的斜率不为0时,设直线l 的方程为x =my ﹣1,A (x 1,y 1),B (x 2,y 2), 联立抛物线方程可得得y 2﹣4my+4=0,可得y 1+y 2=4m ,y 1y 2=4 ∴121212y y k k x 1x 1+=+=--()()()()()1212121222242402222my y y y m mmy my my my -+⨯-⨯==----. (2)S △ABF =S △EFB ﹣S △EFA =|y 1﹣y 2|()221212416164y y y y m +-=-=.解得m =2±(负值舍去).∴直线l 的方程为:210x y -+=.【点睛】本题考查直线与抛物线的位置关系,韦达定理的应用,考查转化思想以及计算能力,属于中档题.25. (1)阅读以下案例,利用此案例的想法化简0112233434343434C C C C C C C C +++.案例:考察恒等式523(1)(1)(1)x x x +=++左右两边2x 的系数.因为右边2301220312232223333(1)(1)()()x x C C x C x C x C x C x C ++=+++++, 所以,右边2x 的系数为011223232323C C C C C C ++,而左边2x 的系数为25C ,所以011223232323C C C C C C ++=25C .(2)求证:22212220(1)()(1)nr n nn n n r r C n C n C --=+-=+∑.【答案】(1)37C ;(2)见解析. 【解析】 【分析】(1)考查恒等式(1+x )7=(1+x )3(x+1)4左右两边x 3的系数可得;(2)根据r11n!(n 1)!C (r 1)!(n r)!(r 1)!(n r)!r n n rC n n ---==⋅=---- ,考查恒等式(1+x )2n =(1+x )n (x+1)n 左右两边x n 的系数.考查恒等式(1+x )2n ﹣1=(1+x )n ﹣1(x+1)n 左右两边x n ﹣1的系数,可得等式成立.【详解】(1)考查恒等式(1+x )7=(1+x )3(x+1)4左右两边x 3的系数, 因为右边(1+x )3(x+1)4=(03C +13C x+23C x 2+33C x 3)(44C x 4+34C x 3+24C x 2+14C x+04C ),所以,右边x 3的系数为0122334343104334C C C C C C C C +++=0112233434343434C C C C C C C C +++ 而左边x 3的系数为:37C ,所以011223343434343347=C C C C C C C C C +++.(2)∵r11n!(n 1)!C (r 1)!(n r)!(r 1)!(n r)!r n n rC n n ---==⋅=----,220(1)()nr nr r C=+=∑22200()2()()nn nr r r nnn r r r rCr C C ===++∑∑∑212121111()2()nn nr r r r n n nn r r r nCn CC C ----====++∑∑∑. 考查恒等式(1+x )2n =(1+x )n (x+1)n 左右两边x n 的系数. 因为右边x n的系数为0011...n n n n n n n nC C C C C C +++=()20nr r nC=∑,而左边的x n 的系数为2nn C .所以220()n r n nnr C C ==∑,同理可求得1211221()nr n n n r C C ----==∑考查恒等式(1+x )2n ﹣1=(1+x )n ﹣1(x+1)n 左右两边x n ﹣1的系数,因为右边(1+x )n ﹣1(x+1)n =(01n C -+11n C -x+…+11n n C --x n ﹣1)(0n C x n +1n C x n ﹣1+…+nn C ), 所以,右边的x n ﹣1的系数为01121111...n n n nn nn nC C C C C C ----+++=11nrn r r n C C =-∑,而左边的xn ﹣1的系数为121n n C--,所以111nrn r r n C C =--∑=121n n C --,220(1)()nr n r r C=+∑﹣2122n n n C --=2122n n n C --+2n 121n n C --+2nn C ﹣2122n n n C --=2n 121n n C --+2n n C =n (121n n C --+121n n C --)+2n n C =n (121n n C --+21n n C -)+2nn C =n 2nn C +2nn C =(n+1)2nn C .【点睛】本题考查了二项式定理展开式指定项的系数,属于难题.。
江苏省南通、徐州、盐城、常州等市2019届高三英语四月大联考试题(含解析)
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江苏省南通、徐州、盐城、常州等市2019届高三英语四月大联考试题(含解析)第I 卷(三部分,共 85 分)第一部分听力(共两节,满分 20 分)第一节听下面 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。
1. What kind of shoes will the woman probably buy?A. Dress shoes.B. Soccer shoes.C. Tennis boots.2. How does the woman sound?A. Relieved.B. Worried.C. Disappointed.3. What does the woman want to do?A. Attend a party.B. Call the Trumps.C. Get Michael’s number.4. What are the speakers talking about?A. The weather.B. Writing skills.C. Weekend plans.5. What is the woman complaining about?A. The busy line.B. The wrong food.C. The late delivery.第二节听下面 5 段对话或独白。
每段对话或独白后有几个小题,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。
听每段对话或独白前,你将有时间阅读各个小题,每小题 5 秒钟;听完后,各小题将给出 5 秒钟的作答时间。
每段对话或独白读两遍。
听下面一段对话, 回答第 6 和第 7 两个小题。
6. When does the conversation take place?A. In the morning.B. At noon.C. In the afternoon.7. What does the man expect the woman to do?A. Pass on a message.B. Attend a meeting.C. Call him back.听下面一段对话, 回答第 8 和第 9 两个小题。
江苏南通市2019届高三下学期4月阶段测试数学试题及精品解析
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12.已知椭圆
x2 a2
y2 b2
1(a
b
0) 上有一个点 A,它关于原点的对称点为 B,点 F
为椭圆的右焦点,且满
足 AF⊥BF,当∠ABF= 12 时,椭圆的离心率为_______.
6
【答案】
3
【解析】 【分析】
根据对称性可知四边形 AFBF1 为矩形,利用直角三角形表示出 AF , AF1 ,根据椭圆定义得到 a, c 满足的方
C=_______.
1
【答案】
10
【解析】 【分析】
由正弦定理求得 tan A tan B tan C ,再利用 tan A tan B tan C tan A tan B tan C 求得
2
3
6
tan A, tan B, tan C ,进而得到 cos A, cos B, cos C ,从而求得结果.
4
【答案】
25
【解析】 【分析】
求解出100 之内是 6 的倍数的数有16 个,根据古典概型求出结果. 【详解】100 之内是 6 的倍数的数有: 6,12,18,,96
可知共有 96 6 1 16 个 6
P 16 4 100 25 4
本题正确结果:
25
【点睛】本题考查古典概型的概率问题的求解,属于基础题. 7.已知一个正四棱锥的侧棱长为 2,侧棱与底面所成的角为 60°,则该棱锥的体积为_______.
4
(1)若
BA
BC
3
,求
a
c
的值;
2
(2)求 cos A cos C 的值. sin A sin C
江苏省南通、徐州、盐城、常州等市2019届高三四月大联考英语试题 Word版含解析
![江苏省南通、徐州、盐城、常州等市2019届高三四月大联考英语试题 Word版含解析](https://img.taocdn.com/s3/m/e8de5808312b3169a451a45a.png)
2019届南通、徐州、盐城、常州等市四月大联考英语试题第I 卷(三部分,共 85 分)第一部分听力(共两节,满分 20 分)第一节听下面 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。
1. What kind of shoes will the woman probably buy?A. Dress shoes.B. Soccer shoes.C. Tennis boots.2. How does the woman sound?A. Relieved.B. Worried.C. Disappointed.3. What does the woman want to do?A. Attend a party.B. Call the Trumps.C. Get Michael’s number.4. What are the speakers talking about?A. The weather.B. Writing skills.C. Weekend plans.5. What is the woman complaining about?A. The busy line.B. The wrong food.C. The late delivery.第二节听下面 5 段对话或独白。
每段对话或独白后有几个小题,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。
听每段对话或独白前,你将有时间阅读各个小题,每小题 5 秒钟;听完后,各小题将给出 5 秒钟的作答时间。
每段对话或独白读两遍。
听下面一段对话, 回答第 6 和第 7 两个小题。
6. When does the conversation take place?A. In the morning.B. At noon.C. In the afternoon.7. What does the man expect the woman to do?A. Pass on a message.B. Attend a meeting.C. Call him back.听下面一段对话, 回答第 8 和第 9 两个小题。
江苏省南通徐州盐城常州等市2019届高三四月大联考英语试题 含解析
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2019届南通、徐州、盐城、常州等市四月大联考英语试题第I 卷(三部分,共 85 分)第一部分听力(共两节,满分 20 分)第一节听下面 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。
1. What kind of shoes will the woman probably buy?A. Dress shoes.B. Soccer shoes.C. Tennis boots.2. How does the woman sound?A. Relieved.B. Worried.C. Disappointed.3. What does the woman want to do?A. Attend a party.B. Call the Trumps.C. Get Michael’s number.4. What are the speakers talking about?A. The weather.B. Writing skills.C. Weekend plans.5. What is the woman complaining about?A. The busy line.B. The wrong food.C. The late delivery.第二节听下面 5 段对话或独白。
每段对话或独白后有几个小题,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。
听每段对话或独白前,你将有时间阅读各个小题,每小题 5 秒钟;听完后,各小题将给出 5 秒钟的作答时间。
每段对话或独白读两遍。
听下面一段对话, 回答第 6 和第 7 两个小题。
6. When does the conversation take place?A. In the morning.B. At noon.C. In the afternoon.7. What does the man expect the woman to do?A. Pass on a message.B. Attend a meeting.C. Call him back.听下面一段对话, 回答第 8 和第 9 两个小题。
江苏南通市2019届高三下学期4月阶段测试数学试题及答案解析
![江苏南通市2019届高三下学期4月阶段测试数学试题及答案解析](https://img.taocdn.com/s3/m/e76bc28669dc5022aaea00c2.png)
【答案】
3
【解析】 【分析】 根据侧棱长和侧棱与底面夹角求得高和底面边长,利用体积公式求得结果.
【详解】
由题意可知: PAO 60 , PA 2
PO PAsin 60 3 , AO PAcos 60 1
AB
AO cos 45
2
V
1 3
S ABCD
程,从而求得离心率.
【详解】
设 F1 为椭圆左焦点,连接 AF1 , BF1
由椭圆对称性和 AF BF 可知:四边形 AFBF1 为矩形
AB FF1 2c
又 ABF 12
AF
AB sin
12
2c sin
12
,
AF1
BF
AB cos
12
2c cos
1„
x„
y
且三数能构成三角形的三边长,若 t
max
1 x
,
x y
,
y
min
1 x
,
x y
,
y ,则 t
的取值范围是 .
【答案】[1,1 5 ) 2
【解析】
试题分析:显然
,又
,
①当
时,
,作出可行区域
限内的交点分别是(1,1)和
,因抛物线
与直线
及
,从而
在第一象
【答案】8 【解析】
【分析】 根据伪代码逆向运算求得结果.
【详解】输入 y 13 ,若 y 6x ,则 x 13 2 ,不合题意 6
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2019届南通、徐州、盐城、常州等市四月大联考英语试题注意事项:1.答卷前,考生务必用黑色字迹的钢笔或签字笔在答题卡上填写自己的准考证号、姓名、试室号和座位号。
用2B型铅笔把答题卡上试室号、座位号对应的信息点涂黑。
2.选择题每小题选出答案后,用2B型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的相应位置上;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整洁。
考试结束后,将试卷和答题卡一并交回。
第I 卷(三部分,共85 分)第一部分听力(共两节,满分20 分)第一节听下面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。
1. What kind of shoes will the woman probably buy?A. Dress shoes.B. Soccer shoes.C. Tennis boots.2. How does the woman sound?A. Relieved.B. Worried.C. Disappointed.3. What does the woman want to do?A. Attend a party.B. Call the Trumps.C. Get Michael’s number.4. What are the speakers talking about?A. The weather.B. Writing skills.C. Weekend plans.5. What is the woman complaining about?A. The busy line.B. The wrong food.C. The late delivery.第二节听下面5 段对话或独白。
每段对话或独白后有几个小题,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。
听每段对话或独白前,你将有时间阅读各个小题,每小题5 秒钟;听完后,各小题将给出5 秒钟的作答时间。
每段对话或独白读两遍。
听下面一段对话, 回答第6 和第7 两个小题。
6. When does the conversation take place?A. In the morning.B. At noon.C. In the afternoon.7. What does the man expect the woman to do?A. Pass on a message.B. Attend a meeting.C. Call him back.听下面一段对话, 回答第8 和第9 两个小题。
8. What are grocery bags like compared with plastic ones?A. Lighter.B. Cheaper.C. Stronger.9. How much can shoppers save by using every reusable bag?A. 3 cents.B. 10 cents.C. 15 cents.听下面一段对话, 回答第10 至第12 三个小题。
10. Where are the speakers?A. In America.B. In France.C. In China.11. Why is the woman here?A. To pick up her son.B. To buy a piano.C. To give a class.12. How far does the man live from here?A. Two blocks east.B. Five blocks west.C. Seven blocks north. 听下面一段对话, 回答第13 至第16 四个小题。
13. What is the woman doing right now?A. Doing a survey.B. Going over the notes.C. Taking part in a quiz show.14. Who are the speakers?A. Students.B. Teachers.C. Reporters.15. When did Iceland announce its ban against foreign fishermen?A. In 1973.B. In 1975.C. In 1980.16. What did Iceland do in 2006?A. It started its first whale hunt.B. It elected a woman president.C. It allowed commercial whaling.听下面一段独白, 回答第17 至第20 四个小题。
17. What made the speaker decide to study psychology?A. Her family background.B. Her observation of adults.C. Her education at university.18. Which group did the speaker study first?A. University students.B. Creative people.C. Ordinary people.19. What can we learn from the “experience examining method”?A. People are happier when concentrating hard.B. Creative people are happier than other people.C. People’s happiness depends on who they are with.20. What does the speaker think of her study?A. Disappointing.B. Confusing.C. Exciting.第二部分英语知识运用(共两节,满分35 分)第一节单项填空(共15 小题;每小题1 分,满分15 分)从每小题所给的四个选项中,选出可以填入空白处的最佳选项。
1.—Is it enough to finish the form for a passport, Madam? —Your passport application form should be by two recent photos.A. updated B. accompanied C. established D. identified 【答案】B 【解析】【详解】考查动词词义辨析。
A. updated更新;B. accompanied伴随、附属;C. established建立;D. identified识别。
句意:——夫人,填好护照申请表就行了么?——您的护照申请表应附两张近照。
根据“by two recent photos”判断此处表示“伴随、附上”,故B项正确。
2.Some business owners are keen on public welfare. This is local services have been funded.A. whetherB. whatC. whereD. how【答案】D【解析】【详解】考查表语从句。
句意:一些企业主热衷于公益事业,这就是地方服务的资金来源。
分析句子结构并结合句意可知,此处为表语从句,从句中缺少方式状语,故D项正确。
3.We offered to pay our half of the cost that was needed to restore the shared doorway but Charles would have of it.A. nothingB. anythingC. noneD. any【答案】C【解析】【详解】考查固定搭配。
句意:我们提出付一半的费用来修复共用的门道,但查尔斯不同意。
have none of 是固定搭配,表示“不同意、不允许”,故C项正确。
4.—How about going sightseeing this Saturday afternoon?Sorry, I _______ my research report the whole weekend.A. will have writtenB. will be writingC. have writtenD. have been writing【答案】B【解析】【详解】考查时态。
句意:——这周六下午去观光怎么样?——不好意思,整个周末我都会在写研究报告。
表示将来的某一时间正在做的事情用将来进行时,故B项正确。
5.Young couples will be happy to see their babies _______ with good health and intelligence when they are born.A. to blessB. blessingC. blessedD. being blessed【答案】C【解析】【详解】考查非谓语动词。
句意:年轻夫妇会很高兴看到他们的孩子出生时拥有良好的健康和智力。
分析句子结构可知此处是非谓语,babies与bless之间是逻辑上的动宾关系,表示被动,用过去分词作宾补,故C项正确。
6.Word came that 30 firefighters gave their lives to our country _______ national property security.A. in exchange forB. in response toC. in terms ofD. in contrast with【答案】A【解析】【详解】考查介词短语。
A. in exchange for作为……的交换、换取;B. in response to响应;C. in terms of依据;D. in contrast with与……对比。
句意:消息传来,30名消防员为国家财产安全献出了生命。