2018届湖南省长沙市长郡中学高三上学期第四次月考理科数学试卷及答案 精品

湖南省长沙市长郡中学2024-2025学年高三上学期9月月考地理试题本试题卷分选择题和非选择题两部分，共8页。

时量75分钟。

满分100分。

注意事项：1. 答卷前，考生务必将自己的姓名、准考证号填写在答题卡上。

2. 回答选择题时，选出每小题答案后，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。

回答非选择题时，将答案写在答题卡上。

写在本试卷上无效。

3. 考试结束后，将本试卷和答题卡一并交回。

第Ⅰ卷一、选择题：本题共16小题，每小题3分，共48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。

康养旅游近年来较为火热，其在增强游客体验，推广地域文化，促进地方经济发展等方面具有重要作用。

黑龙江省大兴安岭地区塔河县十八站鄂伦春民族乡是鄂伦春族主要聚居区之一，景色优美，拥有独特的民族文化旅游资源，如其传统特色民居斜仁柱(见图1) “夏宽冬窄”，具有可拆卸的特点。

该地区发展康养旅游潜力巨大，但一直以来，外界对其知之甚少。

据此完成1~3题。

1. 近年来我国康养旅游发展迅速的主要条件有①医疗发展水平的提高②居民康养需求与理念变化③人口老龄化程度较高④发展休闲旅游的资源丰富A. ①②B. ②③C. ①③D. ②④2. 鄂伦春族传统特色民居斜仁柱“夏宽冬窄”的主要影响因素是A. 气候B. 土壤C. 植被D. 水源3. 挖掘鄂伦春民族乡康养旅游发展潜力的首要措施为A. 完善交通等基础设施建设B. 做好民族文化的保护与传承C. 利用新媒体增强旅游推介D. 引进旅游配套产品生产厂家农业生态效率是综合考虑农业产值等期望产出和非期望产出，如在农业生产评价中通常将化肥、农药、农膜等化学制品的过度使用产生的环境污染视为非期望产出，将农业碳排放作为非期望产出整体指标。

读图2，据此完成4~5题。

4. 2000-2017年长江中游城市群农业生态效率变化特征是A. 整体升高B. 南部全体下降C. 省域间差距缩小D. 两极分化加剧5. 长沙农业生态效率变化的原因可能是A. 生产资料投入增加B. 劳动力投入增加C. 土壤有机质减少D. 农业污染减轻人口迁移同时发生在不同尺度的区域之间和不同层级的聚落之间。

湖南省长沙长郡中学2015届高三上学期第四次月考数学（理）试题（word 版）本试题卷包括选择题、填空题和解答题三部分。

时量120分钟。

满分150分。

一、选择题：本大题共10小题，每小题5分，共50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．若复数iai-+12（a ∈R ）是纯虚数（i 是虚数单位），则a 的值为 A ．-2 B ．-1 C ．1 D ．2 2．若S n ，是等差数列{a n }的前n 项和，有S 8－S 3=10，则S 11的值为 A ．12 B ．18 C ．44 D ．223．一空间几何体的三视图如图所示，则该几何体的体积为A ．322+πB ．324+πC ．3322+π D ．3324+π 4．设f （x ）=⎪⎩⎪⎨⎧≤+⎰ax dt t x x gx 020,30.,1，若f （f （1））=l ，则a 的值是 A ．-1B ．2C ．1D ．-25．已知α，β表示两个不同的平面，m 为平面α内的一条直线，则“α⊥β”是 “m ⊥β”的A ．充分不必要条件B ．必要不充分条件C ．充要条件D ．既不充分也不必要条件 6．△ABC 中，锐角A 满足sin 4A －cos 4A≤sin A －cos A ，则A ．0<A≤6πB ．0<A≤4π C ．6π≤A≤4πD ．4π≤A≤3π7．斜率为22的直线与椭圆)0(12222>>=+b a by a x 交于不同的两点，且这两个交点在x轴上的射影恰好是椭圆的两个焦点，该椭圆的离心率为 A ．22B ．21C ．33D ．31 8．已知等边△ABC 中，点P 在线段AB 上，且AP AP λ=，若Cp ·PA AB =·PB ，则实数λ的值为 A ．2B ．22 C ．1－22 D ．33 9．已知方程kx+3－2k =24x -有两个不同的解，则实数k 的取值范围是A ．⎪⎭⎫⎝⎛43,125 B ．⎥⎦⎤⎝⎛1,125C ．⎥⎦⎤⎝⎛43,125D ．⎥⎦⎤ ⎝⎛43,010．考察正方体6个面的中心，甲从这6个点中任意选两个点连成直线，乙也从这6个点中任意选两个点连成直线，则所得的两条直线相互平行但不重合的概率等于 A ．752B ．754C ．152D ．251 二、填空题：本大题共5小题，每小题5分，共25分．把答案填在答题卡中对应题号后的横线上．11．523⎪⎭⎫ ⎝⎛+x x 的展开式中的常数项为 。

湖南省长沙长郡中学2015届高三上学期第四次月考化学试题时量：90分钟满分：100分可能用到的相对原子质量：H～1C-12 O～16 S～32 Cr～52 Fe～56 Cu～64 Ba～137【试卷综析】本试卷是理科化学单独试卷，知识考查涉及的知识点：化学计量的有关计算、无极推断题、化学反应速率、化学平衡等；以基础知识和基本技能为载体，以能力测试为主导，在注重考查学科核心知识的同时，突出考查考纲要求的基本能力，重视学生科学素养的考查。

试题重点考查：化学与生活、元素周期律、弱电解质的电离、化学平衡的移动、常见的无机物及其应用、有机合成等主干知识。

注重常见化学方法，应用化学思想，体现学科基本要求，难度不大。

第I卷选择题（共48分）一、选择题（本题共16小题，每小题3分，共48分，每小题只有一个选项符合题意）【题文】1．化学与生产生活、环境保护、资源利用、能源开发等密切相关。

下列说法错误的是A．煤炭经气化、液化和干馏等过程，可以转化为清洁能源B．利用二氧化碳制造全降解塑料，可以缓解温室效应C．利用生物方法脱除生活污水中的氮和磷，防止水体富营养化D．高纯硅广泛应用于太阳能电池、计算机芯片和光导纤维【知识点】煤的干馏和综合利用；"三废"处理与环境保护；硅和二氧化硅D1O3【答案解析】【解析】D 解析：A．煤炭经气化、液化和干馏等过程，可以转化为清洁能源，可以节约能源，减少污染物的排放，故A正确；B．利用二氧化碳制造全降解塑料，减少了二氧化碳的排放，可以缓解温室效应，故B正确；C．氮和磷是植物的营养元素，可造成水体富营养化，故C正确；D．光导纤维的成分是二氧化硅，不是硅单质，故D错误；故答案选D【思路点拨】本题考查了化学与社会、环境的关系，把握能源使用及污染物的排放为解答的关键，注重基础知识的考查，题目难度不大.【题文】2．在汽车尾气净化装置中，气体在催化剂表面吸附与解吸作用的过程如图所示。

湖南省长沙市长郡中学2024-2025学年高二上学期10月月考数学试题一、单选题 1．已知复数3i1iz +=+，则z =（ ） AB C ．3 D ．52．无论λ为何值，直线()()()234210x y λλλ++++-=过定点（ ） A ．()2,2-B ．()2,2--C ．()1,1--D ．()1,1-3．在平行四边形ABCD 中，()1,2,3A -，()4,5,6B -，()0,1,2C ，则点D 的坐标为（ ） A ．()5,6,1--B ．()5,8,5-C ．()5,6,1-D ．()5,8,5--4．已知1sin 33πα⎛⎫+= ⎪⎝⎭，则cos(2)3πα-=（ ）A ．79-B ．79C ．29-D ．295．直线2410x y --=关于0x y +=对称的直线方程为（ ） A ．4210x y --= B ．4210x y -+= C ．4210x y ++=D ．4210x y +-=6．已知椭圆C ：()22104x y m m +=>，则m =（ ）A ．B ．C ．8或2D ．87．已知实数,x y 满足()22203y x x x =-+≤≤，则41y x ++的范围是（ ） A ．[]2,6 B ．(][),26,-∞+∞UC ．92,4⎡⎤⎢⎥⎣⎦D ．(]9,2,4⎡⎫-∞+∞⎪⎢⎣⎭U8．已知平面上一点(5,0)M 若直线l 上存在点P 使||4PM =则称该直线为点(5,0)M 的“相关直线”，下列直线中不是点(5,0)M 的“相关直线”的是（ ） A ．3y x =-B ．2y =C ．430x y -=D ．210x y -+=二、多选题9．已知直线l ：20x y λλ+--=，圆C ：221x y +=，O 为坐标原点，下列说法正确的是（ ） A ．若圆C 关于直线l 对称，则2λ=- B ．点O 到直线lC ．存在两个不同的实数λ，使得直线l 与圆C 相切D ．存在两个不同的实数λ，使得圆C 上恰有三个点到直线l 的距离为1210．已知圆1F ：()()222328x y m m ++=≤≤与圆2F ：()()222310x y m -+=-的一个交点为M ，动点M 的轨迹是曲线C ，则下列说法正确的是（ ）A ．曲线C 的方程为22110064x y +=B ．曲线C 的方程为2212516x y +=C ．过点1F 且垂直于x 轴的直线与曲线C 相交所得弦长为325D ．曲线C 上的点到直线4510x ++=11．在边长为2的正方体ABCD A B C D -''''中，M 为BC 边的中点，下列结论正确的有（ ）A ．AM 与DB ''B ．过A ，M ，D ¢三点的正方体ABCD A BCD -''''的截面面积为3 C ．当P 在线段A C '上运动时，PB PM '+的最小值为3D ．若Q 为正方体表面BCC B ''上的一个动点，E ，F 分别为AC '的三等分点，则QE QF +的最小值为三、填空题12．通过科学研究发现：地震时释放的能量E （单位：焦耳）与地震里氏震级M 之间的关系为lg 4.8 1.5E M =+.已知2011年甲地发生里氏9级地震，2019年乙地发生里氏7级地震，若甲、乙两地地震释放能量分别为1E ，2E ，则12EE =13．直线()243410a x ay +-+=的倾斜角的取值范围是.14．如图，设1F ，2F 分别是椭圆()222210x y a b a b+=>>的左、右焦点，点P 是以12F F 为直径的圆与椭圆在第一象限内的一个交点，延长2PF 与椭圆交于点Q ，若222PF F Q =u u u u r u u u u r，则直线1PF的斜率为.四、解答题15．已知两圆222610x y x y +---=和2210120x y x y m +--+=．求： (1)m 取何值时两圆外切？(2)当45m =时，两圆的公共弦所在直线的方程和公共弦的长． 16．在ΔABC 中，内角,,A B C 的对边分别为,,a b c .已知cos 2cos 2cos A C c aB b--=（1） 求sin sin CA的值 （2） 若1cos ,24B b == ，求ΔABC 的面积.17．如图，在四棱锥P ABCD -中，PA ⊥平面ABCD ，2PA AB AD ===，四边形ABCD 满足AB AD ⊥，BC AD ∥，4BC =，点M 为PC 的中点，点E 为棱BC 上的动点.(1)求证：//DM 平面PAB ；(2)是否存在点E ，使得平面PDE 与平面ADE 所成角的余弦值为23？若存在，求出线段BE 的长度；若不存在，说明理由.18．某校高一年级设有羽毛球训练课，期末对学生进行羽毛球五项指标（正手发高远球、定点高远球、吊球、杀球以及半场计时往返跑）考核，满分100分.参加考核的学生有40人，考核得分的频率分布直方图如图所示.(1)由频率分布直方图，求出图中t 的值，并估计考核得分的第60百分位数；(2)为了提升同学们的羽毛球技能，校方准备招聘高水平的教练.现采用分层抽样的方法（样本量按比例分配），从得分在[)70,90内的学生中抽取5人，再从中挑出两人进行试课，求两人得分分别来自[)70,80和[)80,90的概率；(3)若一个总体划分为两层，通过按样本量比例分配分层随机抽样，各层抽取的样本量、样本平均数和样本方差分别为：m ，x ，21s ；n ，y ，22s .记总的样本平均数为w ，样本方差为2s ，证明：()(){}22222121s m s x w n s y w m n ⎡⎤⎡⎤=+-++-⎢⎥⎢⎥⎣⎦⎣⎦+. 19．已知动直线l 与椭圆C:22132x y +=交于()11,P x y ，()22,Q x y 两个不同点，且OPQ ∆的面积OPQ S ∆其中O 为坐标原点. (1)证明2212x x +和2212y y +均为定值;(2)设线段PQ 的中点为M ，求OM PQ ⋅的最大值；(3)椭圆C 上是否存在点D ，E ，G ，使得ODE ODG OEG S S S ===V V V 判断DEG △的形状；若不存在，请说明理由.。

大联考长郡中学2025 届高三月考试卷(一)地理得分本试题卷分选择题和非选择题两部分，共8页。

时量 75 分钟，满分100 分.一、选择题(本大题共16小题，每小题3分，共48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)大源村是广州郊区的一个城中村，邻近服装批发市场。

2018年以来，大源村逐步把旧厂房改造为电商产业园，同时成立了大源电子简务协会，并构建了“政—校一企”三方合作平台。

下图为大源利由传统电商向新型电商转型示意图。

据此完成1~3题。

1.2012年前后，影响广州部分电商企业布局变化的主要因素是A.市场B.基础设施C.土地价格 B.政策2.大源村将旧厂房改造为电商产业园，首先影响到当地电商产业发展的A.产业环境B.产业布局C.产业链条 D 产业结构3.大源村电商产业园区吸引个体电商入驻的原因是A.竞争压力小B.销售方式多C.供货渠道广D.产业规模大J古城由都城、离宫和军事卫城构成。

战国时期，都城是古城中心，离宫的东南角城门可供船只通行。

秦汉时期，离宫成为古城中心。

此后，由于环境变迁，J古城衰落。

19世纪起，S市人口集聚，现已发展为地级市。

下图示意长江流域局部地区。

据此完成4~6题。

4. J古城建设之初，都城未建在离宫处，主要是考虑A.减少水患B.便于取水C.方便耕作D.利于防卫b.古城中心的变迁，反映了战国至秦汉期间该地区气候趋向A.湿润B.干旱C.温暖·I).寒冷6.根据J古城和S市的地理位置，可推知战国时期至现代长江干流图示河段A.整体向北移动B.8市附近河道没有明显摆动C. 整体向南移动D. S市附近河道摆动幅度较大大小交路是指列车在线路上的运行距离有长、短路两种方式，在线路的部分区段共线运行。

石家庄地铁1号线于2021年起在规定时间段内执行该运行模式(如下图)：大交路(西王—福泽)10分钟/次，小交路(西王—汶河大道)5分钟/次。

据此完成7~8题。

7.石家庄地铁1号线采用大小交路运行的目的有①提高运输能力②缓解客流压力③提高运行速度④降低能源消耗A.①②B.②③C.①④D.③④8.下列时间段中；最适合以大小交路运行的是A 工作日·6:00-7:30 B.工作日9:00—19:30C.节假日6:00—7:30D.节假日9:00—19:30温度露点差是温度与露点(露点：在气象学中是指在固定气压之下，空气中所含的气态水达到饱和而凝结成液态水所需要降至的温度)的差值，是相对湿度的一种度量，温度露点差越大，湿度越小，当温度露点差接近0℃时，表示空气中的水汽达到近似饱和状态。

湖南省长沙市长郡中学2015届高三上学期第二次月考数学（理）试题（解析版）得分：____________ 【试卷综析】本试卷是高三月考理科试卷，是一次摸底考试，也是一次模拟考试，命题模式与高考一致，考查了高考考纲上的诸多热点问题，突出考查考纲要求的基本能力，重视学生基本数学素养的考查。

知识考查注重基础、注重常规，也有综合性较强的问题，试题必做部分重点考查：函数、三角函数、数列、立体几何、概率、解析几何等，涉及到的基本数学思想有数形结合、函数与方程、转化与化归、分类讨论等，试题难度适中，兼达到高考关于区分度的要求，适合高三学生模拟考试使用。

本试题卷包括选择题、填空题和解答题三部分，共8页。

时量120分钟。

满分150分。

一、选择题：本大题共10小题，没小题5分，共50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.“0x <”是“()ln 10x +<”的A.充分不必要条件B.必要不充分条件C. 充分必要条件D. 既不充分也不必要条件 【知识点】充分、必要条件的判断 A2【答案解析】B 解析：0x <时，11x +<，则()()ln 1010x x +<-<<时或()ln 1x +不存在()1x ≤-时，所以“0x <”是“()ln 10x +<”的不充分条件；()ln 10x +<时，011x <+<，即10x -<<，则0x <成立，所以“0x <”是“()ln 10x +<”的必要条件。

【思路点拨】根据不等式的性质，利用充分条件和必要条件的定义进行判断即可得到结论。

2.已知函数33y x x c =-+的图像与x 轴恰有两个公共点，则c = A.-2或2 B.-9或3 C.-1或1 D.-3或1 【知识点】导数与极值 B12【答案解析】A 解析：求导函数可得()()2'33311y x x x =-=+-令'0y >，可得11x x <->或；令'0y <，可得11x -<<； ∴函数在()(),1,1,-∞-+∞上单调增，在()1,1-上单调递减 ∴函数在1x =-处取得极大值，在1x =处取得极小值 ∵函数33y x x c =-+的图像与x 轴恰有两个公共点 ∴极大值等于0或极小值等于0∴130130c c -+=-++=或 ∴22c c ==-或 故选A ．【思路点拨】求导函数，确定函数的单调性，确定函数的极值点，利用函数33y x x c =-+的图象与x 轴恰有两个公共点，可得极大值等于0或极小值等于0，由此可求c 的值3.已知函数()sin f x x ω=在，则实数ω的一个值可以是【知识点】函数()()sin f x A x ωϕ=+的性质 C4【答案解析】C 解析：函数()sin f x x ω=在故选：C，从而可求ω的一个值。

长郡中学2023届高三月考试卷数 学本试卷共8页。

时量120分钟，满分150分。

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||1|1,{} ==--∈A y y x x R ，{}3|log 1,=≥B x x ，则A∩=RBA ．{|1}≥-x xB ．{}|3<x xC ．}{|13-≤≤x xD ．{}|13-≤<x x2.若复数z 满足||2,3-=⋅=z z z z ，则2z 的实部为A -2B ．-1C ．1D ． 2★3.函数()()241--=-x x x e e f x x 的部分图象大致是★4.如图，在边长为2的正方形ABCD 中，其对称中心O 平分线段MN ，且2MN BC =，点E 为DC 的中点，则⋅=EM ENA ． 12-B ．32-C ． -2D ．-3★5.随着北京冬奥会的举办，中国冰雪运动的参与人数有了突飞猛进的提升。

某校为提升学生的综合素养、大力推广冰雪运动，号召青少年成为“三亿人参与冰雪运动的主力军”，开设了“陆地冰壶”“陆地冰球”“滑冰”“模拟滑雪”四类冰雪运动体验课程，甲、乙两名同学各自从中任意挑选两门课程学习，设事件A=“甲乙两人所选课程恰有一门相同”事件B=“甲乙两人所选课程完全不同”，事件C=“甲乙两人均未选择陆地冰壶课程”，则 A ． A 与B 为对立事件 B ．A 与C 互斥 C ． B 与C 相互独立D ． A 与C 相互独立★6.已知三棱锥P-ABC 中，PA ⊥平面ABC ，底面△ABC 是以B 为直角顶点的直角三角形，且23，π=∠=BC BCA ，三棱锥P-ABC的体积为3，过点A 作⊥AM PB 于M ，过M 作MN ⊥PC 于N ，则三棱锥P-AMN 外接球的体积为A ．323π B．3C．3D ．43π 7.若sin 2sin ,sin()tan()1αβαβαβ=+⋅-=，则tan tan αβ=A ．2B ．32C ． 1D ．128.已知函数f （x ），g （x ）的定义域为R 。

湖南省长沙市长郡中学2022-2023学年高三上学期月考（四）化学试题一、单选题1. 化学与生活息息相关。

下列叙述错误的是A．抗击新冠肺炎提倡勤用速干消毒液洗手B．衣服挂件上珍珠的主要成分是碳酸钙C．利用活性炭粉还原性除去冰箱异味D．用铝盆装食盐水浸泡变暗的银首饰0.1溶液、、、0.1溶液、、、、、、、、、A．A B．B C．C D．D3. 利用如图装置控制反应且能收集一瓶干燥气体的是A．A B．B C．C D．D4. 北京工商大学苏发兵课题组最近合成CuO/ZnO纳米材料提高有机硅单体合成反应(Rochow—Muller Process)的选择性和产率。

化学反应如下：下列有关叙述正确的是A．甲分子是正四面体形非极性分子B．乙晶体是含非极性键的共价晶体C．催化剂中第一电离能：Cu>Zn>O D．熔点：丙>甲>乙5. 厦门大学周志有教授和王韬副研究员团队阐释了在不同表面电势下，丙烯分子在金属Pd和PdO表面的不同吸附构型以及不同反应路径。

在金属Pd和PdO表面的不同吸附构型和反应路径使得PdO更利于1，2-丙二醇的生成，电化学结果表明PdO生成1，2-丙二醇的量是金属Pd的3倍。

PdO电氧化丙烯的反应路径示意图如图所示：下列叙述错误的是A．相同条件下，PdO催化效率大于Pd B．中双键端基上原子与PdO 结合C．丙烯发生催化氧化生成1，2-丙二醇D．1，2-丙二醇分子间氢键决定其稳定性6. 铼(Re)广泛用于电子制造工业。

工业上，利用粗经高温氢气还原制得粗为阿伏加德罗常数的值。

Fe 1535 2750已知：铼酸的酸性与高氯酸的相当。

下列叙述错误的是A．由0.1mol 制备18.6g纯铼粉转移电子数为0.7B．制铼反应为C．除去粗铼粉中Fe、C杂质的温度为3500℃D．1L 0.5溶液中数目为0.57. 中科院上海药物所杨财广课题组发现新型抗生素，结构如图所示。

下列叙述正确的是A．(R)-ZG197不能发生水解反应B．苯环上一氯代物有4种同分异构体C．1个(R)-ZG197分子含3个手性碳原子D．(R)-ZG197的分子式为8. 某小组设计实验探究是否能与形成络离子。

湖南省长郡中学2018届高三月考试题（二）地理试题第Ⅰ卷一、选择题（本大题共25小题，每小題分，共50分。

在每小題给出的四个选项中，只有一项是符合题目要求的。

）三叉戟纪念塔，在瑞士境内，三个戟分别指向德国、法国和瑞士。

读图完成下列问题。

1、景观图中的河流是A、莱茵河B、罗讷河C、阿勒河D、萨林河2、下列说法正确的是A、瑞士地形平坦，河网纵横B、该地区主要为温带海洋性气候C、莱茵河是德国和法国、瑞士、奥地利之间的界河D、瑞士境内罗讷河的流域面积大于莱茵河图a是某区等高线略图（单位：m），图中公路（虚线）向偏北方向逐渐上升，桥梁下方河流水位为314m。

图b是盘山公路常用的凸面镜，用于视线受阻的情况下观察对向车辆。

读图完成下列问题。

3、图中瀑布的落差不可能是A、20mB、30mC、34mD、36m4、图中阴影区域的坡度大小，由东南向西北A、一直增大B、一直减小C、先增大后减小D、先减小后增大5、图中有必要设置凸面镜的地点是A、①B、②C、③D、④气温垂直递减率是指气温随海拔高度增加的变化程度，空气湿度增加和植被覆盖率升高会使气温垂直递减率降低。

图中甲为秦岭太白山地形图，乙为该南坡、北坡气温垂直递减率年变化图（数据来源于各气象站点）。

据此完成下列问题。

6、若A气象站7月均温为20.5℃，B气象站7月均温可能为A、24℃B、26℃C、28℃D、30℃7、与北坡相比，南坡A、夏季气温较高B、夏季大气湿度较小C、冬季降水较少D、植被覆盖率较低8、太白山北麓传统民居多呈坡屋顶及南北窄东西长的内庭院设计风格，主要原因是A、夏季干热时间长，利于遮荫B、增强夏季风，加快散热C、冬季气候较干燥，改善湿度D、冬季降雨多，利于排水下图为北半球某区域图及沿不同方向的气压变化图。

读图完成下列问题。

9、根据图示信息可推断出A、乙地近地面吹东北风B、丁地以晴朗天气为主C、甲地降水概率小于乙地D、甲地气温低于乙地10、乙地将要经历的天气变化过程最有可能是A、湿度增加，风和日丽B、气温降低，大风阴雨C、气压降低，天气转晴D、连续阴雨，风力加大读“宁波某地等高线地形图”，完成下列问题。

湖南2024届高三月考试卷（四）数学（答案在最后）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.已知复数12z i =+，其中i 为虚数单位，则复数2z 在复平面内对应的点的坐标为（）A.()4,5- B.()4,3 C.()3,4- D.()5,4【答案】C 【解析】【分析】根据题意得234i z =-+，再分析求解即可.【详解】根据题意得：()22212i 14i 4i 34i z =+=++=-+，所以复数2z 在复平面内对应的点的坐标为：()3,4-.故选：C.2.若随机事件A ，B 满足()13P A =，()12P B =，()34P A B ⋃=，则()P A B =（）A.29B.23C.14D.16【答案】D 【解析】【分析】先由题意计算出()P AB ，再根据条件概率求出()P A B 即可.【详解】由题意知：()3()()()4P A B P A P B P AB ==+- ，可得1131()32412P AB =+-=，故()1()1121()62P AB P A B P B ===.故选：D.3.设{}n a 是公比不为1的无穷等比数列，则“{}n a 为递减数列”是“存在正整数0N ，当0n N >时，1n a <”的（）A.充分而不必要条件B.必要而不充分条件C .充分必要条件D.既不充分也不必要条件【答案】A【解析】【分析】根据充分条件、必要条件的定义判断即可.【详解】解：因为{}n a 是公比不为1的无穷等比数列，若{}n a 为递减数列，当11a >，则01q <<，所以11n n a a q -=，令111n n a a q -=<，则111n qa -<，所以1111log log qq n a a ->=-，所以11log q n a >-时1n a <，当101a <<，则01q <<，所以111n n a a q -=<恒成立，当11a =，则01q <<，所以11n n a a q -=，当2n ≥时1n a <，当10a <，则1q >，此时110n n a a q -=<恒成立，对任意N*n ∈均有1n a <，故充分性成立；若存在正整数0N ，当0n N >时，1n a <，当10a <且01q <<，则110n n a a q -=<恒成立，所以对任意N*n ∈均有1n a <，但是{}n a 为递增数列，故必要性不成立，故“{}n a 为递减数列”是“存在正整数0N ，当0n N >时，1n a <”的充分不必要条件；故选：A4.设π(0,2α∈，π(0,)2β∈，且1tan tan cos αβα+=，则（）A.π22αβ+=B.π22αβ-=C.π22βα-= D.π22βα+=【答案】D 【解析】【分析】根据给定等式，利用同角公式及和角的正弦公式化简变形，再利用正弦函数性质推理即得.【详解】由1tan tan cos αβα+=，得sin sin 1cos cos cos αβαβα+=，于是sin cos cos sin cos αβαββ+=，即πsin()sin()2αββ+=-，由π(0,)2α∈，π(0,2β∈，得20π,0<ππ2αββ<+-<<，则π2αββ+=-或ππ2αββ++-=，即π22βα+=或π2α=（不符合题意，舍去），所以π22βα+=.故选：D5.若52345012345(12)(1)(1)(1)(1)(1)x a a x a x a x a x a x -=+-+-+-+-+-，则下列结论中正确的是（）A.01a = B.480a =C.50123453a a a a a a +++++= D.()()10024135134a a a a a a -++++=【答案】C 【解析】【分析】利用二项式定理，求指定项的系数，各项系数和，奇次项系数和与偶数项系数和.【详解】由()52345012345(12)1(1)(1)(1)(1)x a a x a x a x a x a x -=+-+-+-+-+-，对于A 中，令1x =，可得01a =-，所以A 错误；对于B 中，[]55(12)12(1)x x -=---，由二项展开式的通项得44145C (2)(1)80a =⋅-⋅-=-，所以B 错误；对于C 中，012345a a a a a a +++++与5(12(1))x +-的系数之和相等，令11x -=即50123453a a a a a a +++++=，所以C 正确；对于D 中，令2x =，则50123453a a a a a a +++++=-，令0x =，则0123451a a a a a a -+-+-=，解得5024312a a a -+++=，5135312a a a --++=，可得()()10024135314a a a a a a -++++=，所以D 错误.故选：C.6.函数()()12cos 2023π1f x x x ⎡⎤=++⎣⎦-在区间[3,5]-上所有零点的和等于（）A.2B.4C.6D.8【答案】D【分析】根据()y f x =在[]3,5-的零点，转化为11y x =-的图象和函数2cosπy x =的图象在[]3,5-交点的横坐标，画出函数图象，可得到两图象关于直线1x =对称，且()y f x =在[]3,5-上有8个交点，即可求出.【详解】因为()()112cos 2023π2cosπ11f x x x x x ⎡⎤=++=-⎣⎦--，令()0f x =，则12cosπ1x x =-，则函数的零点就是函数11y x =-的图象和函数2cosπy x =的图象在[]3,5-交点的横坐标，可得11y x =-和2cosπy x =的函数图象都关于直线1x =对称，则交点也关于直线1x =对称，画出两个函数的图象，如图所示.观察图象可知，函数11y x =-的图象和函数2cosπy x =的图象在[]3,5-上有8个交点，即()f x 有8个零点，且关于直线1x =对称，故所有零点的和为428⨯=.故选：D7.点M 是椭圆()222210x y a b a b+=>>上的点，以M 为圆心的圆与x 轴相切于椭圆的焦点F ，圆M 与y 轴相交于P ，Q ，若PQM 是钝角三角形，则椭圆离心率的取值范围是（）A.(0,2B.0,2⎛⎫⎪ ⎪⎝⎭ C.,12⎛⎫⎪ ⎪⎝⎭D.(2-【解析】【分析】依据题目条件可知圆的半径为2b a ，画出图形由PQMc >，即可求得椭圆离心率的取值范围.【详解】依题意，不妨设F 为右焦点，则(),M c y ，由圆Ｍ与x 轴相切于焦点F ，M 在椭圆上，易得2b y a =或2b y a =-，则圆的半径为2b a.过M 作MN y ⊥轴垂足为N ，则PN NQ =，MN c =，如下图所示：PM ，MQ 均为半径，则PQM为等腰三角形，∴PN NQ ==∵PMQ ∠为钝角，∴45PMN QMN ∠=∠> ，即PN NQ MN c =>=c >，即4222b c c a ->，得()222222a a c c ->，得22a c ->，故有210e -<，从而解得6202e <<.故选：B8.已知函数22,0,()414,0,x x f x x x ⎧⎪=⎨-++<⎪⎩ 若存在唯一的整数x ，使得()10f x x a -<-成立，则所有满足条件的整数a 的取值集合为（）A.{2,1,0,1}--B.{2,1,0}--C.{1,0,1}-D.{2,1}-【答案】A 【解析】【分析】作出()f x 的图象，由不等式的几何意义：曲线上一点与(,1)a 连线的直线斜率小于0，结合图象即可求得a 范围.【详解】作出()f x 的函数图象如图所示：()10f x x a-<-表示点()(),x f x 与点(),1a 所在直线的斜率，可得曲线()f x 上只有一个点()(),x f x （x 为整数）和点(),1a 所在直线的斜率小于0，而点(),1a 在动直线1y =上运动，由()20f -=，()14f -=，()00f =，可得当21a -≤≤-时，只有点()0,0满足()10f x x a -<-；当01a ≤≤时，只有点()1,4-满足()10f x x a-<-.又a 为整数，可得a 的取值集合为{}2,1,0,1--.故选：A.二、选择题：本题共4小题，每小题5分，共20分.在每小题给出的选项中，有多项符合题目要求.全部选对的得5分，部分选对的得2分，有选错的得0分、9.已知双曲线C过点(，且渐近线方程为3y x =±，则下列结论正确的是（）A.C 的方程为2213x y -= B.CC.曲线21x y e -=-经过C 的一个焦点D.直线10x --=与C 有两个公共点【答案】AC 【解析】【分析】由双曲线的渐近线为3y x =±，设出双曲线方程，代入已知点的坐标，求出双曲线方程判断A ；再求出双曲线的焦点坐标判断B ，C ；联立方程组判断D ．【详解】解：由双曲线的渐近线方程为33y x =±，可设双曲线方程为223x y λ-=，把点代入，得923λ-=，即1λ=．∴双曲线C 的方程为2213x y -=，故A 正确；由23a =，21b =，得2c ==，∴双曲线C3=，故B 错误；取20x -=，得2x =，0y =，曲线21x y e -=-过定点(2,0)，故C 正确；联立221013x x y ⎧-=⎪⎨-=⎪⎩，化简得220,0y -+-=∆=，所以直线10x -=与C 只有一个公共点，故D 不正确．故选：AC ．10.已知向量a ，b 满足2a b a += ，20a b a ⋅+= 且2= a ，则（）A.2b =B.0a b +=C.26a b -= D.4a b ⋅=【答案】ABC 【解析】【分析】由2a b a += ，得20a b b ⋅+= ，又20a b a ⋅+= 且2= a ，得2b = ，4a b ⋅=- ，可得cos ,1a b a b a b⋅==- ，,πa b = ，有0a b += ，26a b -= ，可判断各选项.【详解】因为2a b a += ，所以222a b a += ，即22244a a b b a +⋅+= ，整理可得20a b b ⋅+= ，再由20a b a ⋅+= ，且2= a ，可得224a b == ，所以2b = ，4a b ⋅=- ，A 选项正确，D 选项错误；cos ,1a b a b a b⋅==- ，即向量a ，b 的夹角,πa b = ，故向量a ，b 共线且方向相反，所以0a b += ，B 选项正确；26a b -=，C 选项正确.故选：ABC11.如图，正方体1111ABCD A B C D -的棱长为2，点M 是其侧面11ADD A 上的一个动点（含边界），点P是线段1CC 上的动点，则下列结论正确的是（）A.存在点,P M ，使得二面角--M DC P 大小为23πB.存在点,P M ，使得平面11B D M 与平面PBD 平行C.当P 为棱1CC 的中点且PM =时，则点M 的轨迹长度为23πD.当M 为1A D 中点时，四棱锥M ABCD-外接球的体积为3【答案】BC 【解析】【分析】由题意，证得1,CD MD CD DD ⊥⊥，得到二面角--M DC P 的平面角1π0,2MDD ⎡∠∈⎤⎢⎥⎣⎦，可得判定A 错误；利用线面平行的判定定理分别证得11//B D 平面BDP ，1//MB 平面BDP ，结合面面平行的判定定理，证得平面//BDP 平面11MB D ，可判定B 正确；取1DD 中点E ，证得PE ME ⊥，得到2ME ==，得到点M 在侧面11ADD A 内运动轨迹是以E 为圆心、半径为2的劣弧，可判定C 正确；当M 为1AD 中点时，连接AC 与BD 交于点O ，求得OM OA OB OC OD ====，得到四棱锥M ABCD -外接球的球心为O ，进而可判定D 错误.【详解】在正方体1111ABCD A B C D -中，可得CD ⊥平面11ADD A，因为MD ⊂平面11ADD A ，1DD ⊂平面11ADD A ，所以1,CD MD CD DD ⊥⊥，所以二面角--M DC P 的平面角为1∠MDD ，其中1π0,2MDD ⎡∠∈⎤⎢⎥⎣⎦，所以A 错误；如图所示，当M 为1AA 中点，P 为1CC 中点时，在正方体1111ABCD A B C D -中，可得11//B D BD ，因为11B D ⊄平面BDP ，且BD ⊂平面BDP ，所以11//B D 平面BDP ，又因为1//MB DP ，且1MB ⊄平面BDP ，且DP ⊂平面BDP ，所以1//MB 平面BDP ，因为1111B D MB B = ，且111,B D MB ⊂平面11MB D ，所以平面//BDP 平面11MB D ，所以B 正确；如图所示，取1DD 中点E ，连接PE ，ME ，PM ，在正方体1111ABCD A B C D -中，CD ⊥平面11ADD A ，且//CD PE ，所以PE ⊥平面11ADD A ，因为ME ⊂平面11ADD A ，可得PE ME ⊥，则2==ME ，则点M 在侧面11ADD A 内运动轨迹是以E 为圆心、半径为2的劣弧，分别交AD ，11A D 于2M ，1M ，如图所示，则121π3D E D M M E ∠=∠=，则21π3M M E ∠=，劣弧12M M 的长为π3π223⨯=，所以C 正确当M 为1A D 中点时，可得AMD 为等腰直角三角形，且平面ABCD ⊥平面11ADD A ，连接AC 与BD 交于点O ，可得OM OA OB OC OD =====，所以四棱锥M ABCD -外接球的球心即为AC 与BD 的交点O ，所以四棱锥M ABCD -，其外接球的体积为348233π⨯=，所以D 错误.故选：BC.12.若存在实常数k 和b ，使得函数()F x 和()G x 对其公共定义域上的任意实数x 都满足：()F x kx b≥+和()G x kx b ≤+恒成立，则称此直线y kx b =+为()F x 和()G x 的“隔离直线”，已知函数()()2f x x R x =∈，()()10g x x x=<，()2ln h x e x =（e 为自然对数的底数），则（）A.()()()m x f x g x =-在x ⎛⎫∈ ⎪⎝⎭内单调递增；B.()f x 和()g x 之间存在“隔离直线”，且b 的最小值为4-；C.()f x 和()g x 之间存在“隔离直线”，且k 的取值范围是[]4,1-；D.()f x 和()h x 之间存在唯一的“隔离直线”y e =-.【答案】ABD 【解析】【分析】令()()()m x f x g x =-，利用导数可确定()m x 单调性，得到A 正确；设()f x ，()g x 的隔离直线为y kx b =+，根据隔离直线定义可得不等式组22010x kx b kx bx ⎧--≥⎨+-≤⎩对任意(),0x ∈-∞恒成立；分别在0k =和0k <两种情况下讨论b 满足的条件，进而求得,k b 的范围，得到B 正确，C 错误；根据隔离直线过()f x 和()h x 的公共点，可假设隔离直线为y kx e =-；分别讨论0k =、0k <和0k >时，是否满足()()e 0f x kx x ≥->恒成立，从而确定k =，再令()()e G x h x =--，利用导数可证得()0G x ≥恒成立，由此可确定隔离直线，则D 正确.【详解】对于A ，()()()21m x f x g x x x=-=-，()212m x x x '∴=+，()3321221m x x x ⎛⎫''=-=- ⎪⎝⎭，当x ⎛⎫∈ ⎪⎝⎭时，()0m x ''>，()m x '∴单调递增，()2233220m x m ⎛'∴>-=--+= ⎝，()m x ∴在x ⎛⎫∈ ⎪⎝⎭内单调递增，A 正确；对于,B C ，设()f x ，()g x 的隔离直线为y kx b =+，则21x kx bkx bx ⎧≥+⎪⎨≤+⎪⎩对任意(),0x ∈-∞恒成立，即22010x kx b kx bx ⎧--≥⎨+-≤⎩对任意(),0x ∈-∞恒成立.由210kx bx +-≤对任意(),0x ∈-∞恒成立得：0k ≤.⑴若0k =，则有0b =符合题意；⑵若0k <则有20x kx b --≥对任意(),0x ∈-∞恒成立，2y x kx b =-- 的对称轴为02kx =<，2140k b ∆+∴=≤，0b ∴≤；又21y kx bx =+-的对称轴为02bx k =-≤，2240b k ∴∆=+≤；即2244k b b k⎧≤-⎨≤-⎩，421664k b k ∴≤≤-，40k ∴-≤<；同理可得：421664b k b ≤≤-，40b ∴-≤<；综上所述：40k -≤≤，40b -≤≤，B 正确，C 错误；对于D ， 函数()f x 和()h x 的图象在x =处有公共点，∴若存在()f x 和()h x 的隔离直线，那么该直线过这个公共点.设隔离直线的斜率为k，则隔离直线方程为(y e k x -=，即y kx e =-+，则()()e 0f x kx x ≥->恒成立，若0k =，则()2e 00x x -≥>不恒成立.若0k <，令()()20u x x kx e x =-+>，对称轴为02k x =<()2u x x kx e ∴=-+在(上单调递增，又0ue e =--=，故0k <时，()()e 0f x kx x ≥->不恒成立.若0k >，()u x 对称轴为02kx =>，若()0u x ≥恒成立，则()(22340k e k ∆=-=-≤，解得：k =.此时直线方程为：y e =-，下面证明()h x e ≤-，令()()2ln G x e h x e e x =--=--，则()x G x x-'=，当x =时，()0G x '=；当0x <<()0G x '<；当x >()0G x '>；∴当x =()G x 取到极小值，也是最小值，即()min 0G x G==，()()0G x e h x ∴=--≥，即()h x e ≤-，∴函数()f x 和()h x 存在唯一的隔离直线y e =-，D 正确.故选：ABD .【点睛】本题考查导数中的新定义问题的求解；解题关键是能够充分理解隔离直线的定义，将问题转化为根据不等式恒成立求解参数范围或参数值、或不等式的证明问题；难点在于能够对直线斜率范围进行准确的分类讨论，属于难题.三、填空题：本题共4小题，每小题5分，共20分.13.已知函数()y f x =的图像在点()()11M f ，处的切线方程是122y x =+，则()()11f f '+＝______．【答案】3【解析】【分析】根据导数的几何意义，可得'(1)f 的值，根据点M 在切线上，可求得(1)f 的值，即可得答案.【详解】由导数的几何意义可得，'1(1)2k f ==，又()()11M f ，在切线上，所以15(1)1222f =⨯+=，则()()11f f '+=3，故答案为：3【点睛】本题考查导数的几何意义的应用，考查分析理解的能力，属基础题.14.如图，由3个全等的钝角三角形与中间一个小等边三角形DEF 拼成的一个较大的等边三角形ABC ，若3AF =，33sin 14ACF ∠=，则DEF 的面积为________．【解析】【分析】利用正弦定理以及余弦定理求得钝角三角形的三边长，根据等边三角形的性质以及面积公式，可得答案.【详解】因为EFD △为等边三角形，所以60EFD ∠= ，则120EFA ∠= ，在AFC △中，由正弦定理，则sin sin AF ACACF AFC=∠∠，解得sin 7sin 23314AF AC AFC ACF =⋅∠==∠，由余弦定理，则2222cos AC AF FC AF FC AFC =+-⋅⋅∠，整理可得：21499232FC FC ⎛⎫=+-⨯⋅⋅- ⎪⎝⎭，则23400FC FC +-=，解得5FC =或8-（舍去），等边EFD △边长为532-=，其面积为122sin 602⨯⨯⋅=o .15.已知数列{}n a 的首项132a =，且满足1323n n n a a a +=+．若123111181n a a a a +++⋅⋅⋅+<，则n 的最大值为______．【答案】15【解析】【分析】应用等差数列定义得出等差数列,根据差数列通项公式及求和公式求解计算即得.【详解】因为12312133n n n n a a a a ++==+，所以1112,3n n a a +=+，即11123n n a a +-=，且1123a =，所以数列1n a ⎧⎫⎨⎬⎩⎭是首项为23，公差为23的等差数列.可求得()12221333n nn a =+-=，所以()()1232211111212222333n n n n n n a a a a ++⨯+⨯++⨯+++⋅⋅⋅+===，即()()181,12433n n n n +<+<且()*1,N n n n +∈单调递增,1516240,1617272⨯=⨯=.则n 的最大值为15.故答案为:15.16.在棱长为3的正方体1111ABCD A B C D -中，点E 满足112A E EB =，点F 在平面1BC D 内，则|1||A F EF +的最小值为___________.【答案】6【解析】【分析】以点D 为原点，建立空间直角坐标系，由线面垂直的判定定理，证得1A C ⊥平面1BC D ，记1AC 与平面1BC D 交于点H ，连接11A C ，1,C O ，AC ，得到12A H HC =，结合点()13,0,3A 关于平面1BC D 对称的点为()1,4,1G --，进而求得1A F EF +的最小值.【详解】以点D 为原点，1,,DA DC DD所在直线分别为,,x y z 轴，建立空间直角坐标系D xyz -，如图所示，则()13,0,3A ，()3,2,3E ，()0,3,0C，因为BD AC ⊥，1BD A A ⊥，且1AC A A A ⋂=，则BD ⊥平面1A AC ，又因为1AC ⊂平面1A AC ，所以1BD A C ⊥，同理得1BC ⊥平面11A B C ，因为1AC ⊂平面11A B C ，所以11BC A C ^，因为1BD BC B = ，且1,BD BC ⊂平面1BC D ，所以1A C ⊥平面1BC D ，记1AC 与平面1BC D 交于点H ，连接11A C ，1C O ，AC ，且AC BD O = ，则11121A H A C HC OC ==，可得12A H HC =，由得点()13,0,3A 关于平面1BC D 对称的点为()1,4,1G --，所以1A F EF +的最小值为6EG ==.故答案为：6.四、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.已知函数()23sin 2cos 2xf x x m ωω=++的最小值为2-.（1）求函数()f x 的最大值；（2）把函数()y f x =的图象向右平移6πω个单位，可得函数()y g x =的图象，且函数()y g x =在0,8π⎡⎤⎢⎥⎣⎦上为增函数，求ω的最大值.【答案】（1）2（2）4【解析】【分析】（1）化简函数为()2sin 16f x x m πω⎛⎫=+++ ⎪⎝⎭，再根据函数()f x 的最小值为2-求解；（2）利用平移变换得到()2sin g x x ω=的图象，再由()y g x =在0,8π⎡⎤⎢⎥⎣⎦上为增函数求解.【小问1详解】解：()23sin 2cos 2xf x x m ωω=++，3sin cos 1x x m ωω=+++，2sin 16x m πω⎛⎫=+++ ⎪⎝⎭，函数()f x 的最小值为2-212m ∴-++=-，解得1m =-，则()2sin 6f x x πω⎛⎫=+⎪⎝⎭，∴函数()f x 的最大值为2.【小问2详解】由（1）可知：把函数()2sin 6f x x πω⎛⎫=+ ⎪⎝⎭向右平移6πω个单位，可得函数()2sin y g x x ω==的图象.()y g x = 在0,8π⎡⎤⎢⎥⎣⎦上为增函数，∴函数()g x 的周期22T ππω=4ω∴ ，即ω的最大值为4.18.为了丰富在校学生的课余生活，某校举办了一次趣味运动会活动，学校设置项目A “毛毛虫旱地龙舟”和项目B “袋鼠接力跳”.甲、乙两班每班分成两组，每组参加一个项目，进行班级对抗赛.第一个比赛项目A 采取五局三胜制（即有一方先胜3局即获胜，比赛结束）；第二个比赛项目B 采取领先3局者获胜。

大联考长郡中学2025届高三月考试卷（一）物理得分：________本试题卷分选择题和非选择题两部分，共8页。

时量75分钟。

满分100分。

第Ⅰ卷 选择题（共44分）一、选择题（本题共6小题，每小题4分，共24分。

每小题只有一项符合题目要求）1．下列关于行星和万有引力的说法正确的是A ．开普勒发现了行星运动规律，提出行星以太阳为焦点沿椭圆轨道运行的规律，并提出了日心说B ．法国物理学家卡文迪什利用放大法的思想测量了万有引力常量G ，帮助牛顿总结了万有引力定律C ．由万有引力定律可知，当太阳的质量大于行星的质量时，太阳对行星的万有引力大于行星对太阳的万有引力D ．牛顿提出的万有引力定律不只适用于天体间，万有引力是宇宙中具有质量的物体间普遍存在的相互作用力2．如图所示，甲，乙两柱体的截面分别为半径均为R 的圆和半圆，甲的右侧顶着一块竖直的挡板。

若甲和乙的质量相等，柱体的曲面和挡板可视为光滑，开始两圆柱体柱心连线沿竖直方向，将挡板缓慢地向右移动，直到圆柱体甲刚要落至地面为止，整个过程半圆柱乙始终保持静止，那么半圆柱乙与水平面间动摩擦因数的最小值为AB ． CD ．★3．我国首个火星探测器“天问一号”在海南文昌航天发射场由“长征5号”运载火箭发射升空，开启了我国行星探测之旅。

“天问一号”离开地球时，所受地球的万有引力与它距离地面高度的关系图像如图甲所示，“天问一号”奔向火星时，所受火星的万有引力与它距离火星表面高度的关系图像如图乙所示，已知地球半径是火星半径的两倍，下列说法正确的是A ．地球与火星的表面重力加速度之比为3∶2B ．地球与火星的质量之比为3∶2C ．地球与火星的密度之比为9∶8121F 1h 2F 2hD4．如图所示，以O 为原点在竖直面内建立平面直角坐标系：第Ⅳ象限挡板形状满足方程（单位：m ），小球从第Ⅱ象限内一个固定光滑圆弧轨道某处静止释放，通过O 点后开始做平抛运动，击中挡板上的P 点时动能最小（P 点未画出），重力加速度大小取，不计一切阻力，下列说法正确的是A ．P 点的坐标为B ．小球释放处的纵坐标为C ．小球击中P 点时的速度大小为5m/sD ．小球从释放到击中挡板的整个过程机械能不守恒5．在如图所示电路中，电源电动势为E ，内阻不可忽略，和为定值电阻，R 为滑动变阻器，P 为滑动变阻器滑片，C 为水平放置的平行板电容器，M 点为电容器两板间一个固定点，电容器下极板接地（电势为零），下列说法正确的是A ．左图中电容器上极板带负电B ．左图中滑片P 向上移动一定距离，电路稳定后电阻上电压减小C ．若将换成如右图的二极管，电容器上极板向上移动一定距离，电路稳定后电容器两极板间电压增大D ．在右图中电容器上极板向上移动一定距离，电路稳定后M 点电势降低6．图甲为用手机和轻弹簧制作的一个振动装置。

湖南省长沙市长郡中学2023-2024学年高三上学期月考卷（四）英语试题学校:___________姓名：___________班级：___________考号：___________一、阅读理解The following are a series of new parks that have opened around the world in the last two years.Katmandu Park, Punta Cana, Dominican RepublicOpened in March 2023 on the east coast of the Dominican Republic, the park is full of mystery. According to legend, explorer Kilgore Goode was on an adventure through Nepal when he came across the “Desirata” jewel, protected by a fierce yeti(雪人).Tickets from $120 for adults; $85 for children.Ghibli Park, JapanLocated outside of Nagoya, Japan, Ghibli Park opened in late 2022. Within the 17.5 forested ground of the Expo 2005, guests will find five areas that recreate several animated(栩栩如生的)famous scenes.Tickets from $15 for adults; $7.50 for children.Peppa Pig Theme Park, FloridaThe world’s first Peppa Pig Theme Park opened in 2022 in Winter Haven, Florida, and has been delighting children ever since. Dedicated to the classic British animated TV show, where little Peppa has everyday adventures with her friends and family, the 4.5-acre park welcomes pint-sized guests with well-designed, multi-sensory activities across six playscapes.Tickets from $34 for adults; $25 for children.Genting SkyWorlds Theme Park, MalaysiaLocated within Resorts World Genting, about an hour’s drive from Malaysia’s capital Kuala Lumpur, Genting SkyWorlds Theme Park opened in February 2022. Across the 26-acre park, which cost $800 million and took nearly 10 years to create, visitors will find 26 attractions across nine areas inspired by movies and explorations.Tickets from $34 for adults; $29 for children.1．How much will the Smiths with their two children pay to visit Ghibli Park?A．$30.B．$37.5.C．$45.D．$118.2．What can we know about Genting SkyWorlds Theme Park?A．It is located in Asia.B．It has been opened for ten years.C．It is the biggest theme park in the world.D．It has nine attractions in all.3．What do the four parks have in common?A．They were all built in the same year.B．They are all involved in adventures.C．They all took a long time to create.D．They are all family-friendly parks.At only 8 years old, Kayzen Hunter has already displayed more character than some people ever manage. It all started about a year ago when the child became a regular diner at the Waffle House in Little Rock, Arkansas. His family goes for breakfast there at least once a week, and they always choose to sit in a certain waiter’s section.Devonte Gardner is a father of two who works hard for his living. He always has a smile on his face, and he quickly formed a friendly relationship with Kayzen and his family. “I come with a positive attitude,” Devonte said. “I treat everybody with smile. I also love to see everybody smile.” His kindness affected Kayzen. “Devonte is just a really nice person,” he explained. “Really good guy. Super nice to everyone he meets.”After a year of contact, the child’s family learned the truth behind Devonte’s bright smile. Devonte, his wife, and their two young daughters have been living in a cheap motel for the past eight months. Their former apartment was filled with bugs and had black mold(黑霉), which made his kids sick. Every cent Devonte makes goes toward keeping his children fed, clothed, and housed, and the struggle was overwhelming. Since he can’t afford a car, he also walks to and from work every day. Even so, he showed up at work every day with a smile on his face, ready to serve and make friends with customers like Kayzen.Kayzen knew right away that he wanted to help his friend. He went home and told his mom, Vittoria Hunter, that he wanted to start a GoFundMe to help Devonte get money for a new car.“Devonte is one of the most joyous and positive people you’ve ever met!” Vittoria and Kayzen wrote on the GoFundMe. “He always greets us with the biggest smile. I hope you will help me spread kindness in the world. ” Their initial goal was $5,000, but word quickly spread in their community. The GoFundMe currently sits at over $100,000!4．Why are Kayzen and his family mentioned in paragraph 1?A．To explain the importance of a smile.B．To show the great popularity of the restaurant.C．To introduce the main character of the text.D．To present the relationship of characters.5．What’s paragraph 3 mainly about?A．The influence of Devonte’s smile on Kayzen.B．The tough situation of Devonte and his family.C．The reason why Devonte always wears a smile.D．The process and result of Kayzen’s investigation.6．What motivated Kayzen to start the GoFundMe?A．Devonte’s positive attitude.B．Devonte’s financial struggle.C．Devonte’s love for seeing smiles.D．Devonte’s relationship with his family. 7．Which of the following can best describe both Devonte and Kayzen?A．Sociable and positive.B．Stressful but optimistic.C．Helpful and kind-hearted.D．Unfortunate but warm-hearted.Inspired by the effortless way humans handle objects without seeing them, a team led by engineers at the University of California San Diego has developed a new approach that enables a robotic hand to rotate (旋转) objects solely through touch, without relying on vision.Using their technique, the researchers built a robotic hand that can smoothly rotate a wide variety of objects, from small toys, cans to even fruits and vegetables, without bruising or damaging them. The robotic hand accomplished these tasks using only information based on touch. The work could aid in the development of robots that can manipulate objects in the dark.To build their system, the researchers attached 16 touch sensors to the palm and fingers of a four-fingered robotic hand. Each sensor costs about $12 and serves a simple function: detect whether an object is touching it or not.What makes this approach unique is that it relies on many low-cost touch sensors that use simple, binary (二进制的) signals—touch or no touch—to perform robotic in-hand rotation. These sensors are spread over a large area of the robotic hand. This contrasts with a variety of other approaches that rely on a few high-cost touch sensors affixed to a small area of the robotic hand, primarily at the fingertips.The researchers then tested their system on the real-life robotic hand with objects that the system has not yet encountered. The robotic hand was able to rotate a variety of objects without stalling or losing its hold. The objects included a tomato, pepper, a can of peanut butter and a toy rubber duck, which was the most challenging object due to its shape.The researchers are now working on extending their approach to more complex manipulation tasks. They are currently developing techniques to enable robotic hands to catch, throw and juggle, for example. “If we can give robots this skill, that will open the door to the kinds of tasks they can perform,” said one of the researchers.8．What does the underlined word “manipulate” probably mean?A．Remove.B．Control.C．Recognize.D．Distribute.9．What can we know about the touch sensors of the robotic hand?A．They are quite expensive.B．They are mainly in its fingertips.C．They perform complex tasks.D．They cover most of its area.10．Why is the toy rubber duck difficult for a robotic hand to rotate?A．It’s never been seen by robots.B．It has an unusual shape.C．It has a unique smell.D．It can damage robots.11．What are researchers probably focusing on at present?A．Upgrading robotic hand skills.B．Diversifying robotic hand shapes.C．Developing more new research tasks.D．Seeking new ways to develop robots.A new museum in Mexico aims to educate the public about the critically endangered salamander (蝾螈). The museum recently opened at Chapultepec Zoo in Mexico City.The salamander is native only to Mexico. The animal is extremely endangered in the wild because its natural environment is increasingly threatened. The salamander has captured wide attention for its ability to heal itself when its body gets harmed. For example, the animal can regrow legs and damaged tissue. It can even repair problems affecting the heart and brain. Scientists have also documented how the salamander can breathe with lungs and gills. It can also take in oxygen through its skin. This can cause problems if the animal comes in contact with polluted water.“They are one of the few animals that can regenerate their skin, muscles, bones, blood vessels, nerves, heart and brain,” said Gual, a conservation official at the zoo. Speaking aboutthe museum, Gual said he sees it as a valuable tool to inform citizens about the unusual creature. “A hugely important part of this space is environmental education,” he said.In the past, salamanders did very well in Xochimilco’s muddy canals. The canals are the only remaining part of a once large waterway system dating back to Aztec times. But studies have shown the spread of cities, polluted water and non-native fish that eat the salamanders have led to their near-total collapse.As the museum opened to its first visitors, the salamander’s popularity with the public was very clear. “The truth is I’m very, very, very, very excited to be able to see how they eat, how they live, just how they are,” said one visitor named Fernando. The man, who did not want to give his last name, showed off a small salamander tattoo he had on his arm. “I’m marked for life,” he said.12．What makes salamanders gain considerable attention?A．Their ability to cure themselves.B．Their being in extreme danger in the wild.C．Their ability to breathe with all organs.D．Their serious habitat loss.13．What can we know about salamanders in paragraph 4?A．Their previous condition.B．Their favorite habitats.C．Reasons for their being endangered.D．Their advantages over other animals. 14．What’s Fernando’s attitude towards visiting the new museum?A．Confused.B．Delighted.C．Worried.D．Curious.15．What can be a suitable title for the text?A．A New Museum in Mexico Is Open to Animal LoversB．More and More Wildlife Is Endangered in MexicoC．Endangered Animals Should Be Protected in the MuseumD．A Museum Aims to Help Save Endangered Salamanders二、七选五you develop your own design style and give you the opportunity to work with other aspiring designers.The fashion industry is one of the most creative and competitive industries in the world.17 To be successful in this industry you need to have a strong creative vision, be able to identify trends and have the ability to translate your ideas into wearable designs.18 They will also give you an insight into the industry, what it is like to work asa fashion designer, and the different career paths that you can take.There are many different courses in fashion design available, so it is important to choose one that is right for you. Look for a course that will teach you about the different aspects of fashion design, from sketching and pattern-making to garment construction and fabric manipulation. 19 This will ensure that you are learning from people who understand the industry and can give you insider tips and advice.Fashion design courses are important not only for those looking to enter the fashion industry but also for those who want to expand their knowledge of fashion. The skills learned in these courses can be applied to other areas of life, such as helping you to dress better for your professional life or improving your sense of style. If you are interested in fashion and want to learn more about it, then taking a course in fashion design is a great way to do this.20A．Fashion design is about making clothes.B．They can teach you about the history and theory of fashion.C．A career in fashion design can be rewarding but also challenging.D．Courses in fashion design can help you develop all of these skills.E．Courses in fashion design can be found at many different colleges and universities.F．It is also important to find a course that is taught by experienced fashion designers.G．It can also be a lot of fun and you might even make some great friends along the way.三、完形填空Zhang Yuan, living in a small mountain village, is a hardworking fellow. He is alwaysanything, simply enjoying the beauty of the moment. Zhang understood that the butterfly’s stillness (宁静) was what26 it to obey the universe. From that moment on, Zhang made it his 27 to develop stillness in his own mind. Every day he spent hours meditating and 28 all his anxieties. Soon, Zhang found the journey towards stillness was a long and 29 one. But he made up his mind to 30 on this path. He believed that with patience and 31 he could also experience the beauty of obeying the universe just like the butterfly did. As he continued to 32 , he came to understand life is too short to worry about things beyond 33 and that everyone should 34 what they already have. With this newfound understanding, he was 35 to find peace and satisfaction in every moment.21．A．release B．explore C．clarify D．define 22．A．dancing B．singing C．kicking D．working 23．A．secretly B．effortlessly C．cautiously D．frequently 24．A．imagined B．confirmed C．predicted D．realized 25．A．struggle B．agree C．refuse D．hesitate 26．A．forced B．allowed C．required D．advised 27．A．hobby B．profession C．mission D．honor 28．A．making up for B．looking down on C．putting up with D．letting go of 29．A．difficult B．different C．magical D．strange 30．A．observe B．think C．learn D．continue 31．A．confidence B．determination C．honesty D．gratitude 32．A．move B．share C．practice D．research 33．A．belief B．description C．control D．recognition 34．A．accept B．keep C．abandon D．treasure 35．A．proud B．willing C．anxious D．able四、用单词的适当形式完成短文阅读下面短文, 在空白处填入1个适当的单词或括号内单词的正确形式。

湖南省长沙市长郡中学2025届高三上学期月考（一）数学试题一、单选题1．设集合[),A a =+∞，()1,2B =-，若A B =∅I ，则（ ） A ．1>-aB ．2a >C ．1a ≥-D ．2a ≥2．已知复数z 满足22z -=，z 的取值范围为（ ） A ．[]0,2B ．()0,2C ．[]0,4D ．()0,43．在ABC V 中，若2AB BC BC CA CA AB ⋅=⋅=⋅u u u v u u u v u u u v u u u v u u u v u u u v，则AB BC=u u u v u u u vA ．1BCD 4．若函数()2211x x f x x ++=+的最大值为M ，最小值为N ，则M N +=（ ）A ．1B ．2C ．3D ．45．如图，点N 为正方形ABCD 的中心，ECD ∆为正三角形，平面ECD ⊥平面ABCD ,M 是线段ED 的中点，则A ．BM EN =，且直线,BM EN 是相交直线B ．BM EN ≠，且直线,BM EN 是相交直线C ．BM EN =，且直线,BM EN 是异面直线D ．BM EN ≠，且直线,BM EN 是异面直线6．tan10tan50tan50︒+︒︒︒的值为（ ）A ．B C ．3D 7．一枚质地均匀的正方体骰子，其六个面分别刻有1，2，3，4，5，6六个数字，投掷这枚骰子两次，设事件M =“第一次朝上面的数字是奇数”，则下列事件中与M 相互独立的是（ ） A ．第一次朝上面的数字是偶数 B ．第一次朝上面的数字是1 C ．两次朝上面的数字之和是8D ．两次朝上面的数字之和是78．一只蜜蜂从蜂房A 出发向右爬，每次只能爬向右侧相邻的两个蜂房（如图），例如：从蜂房A 只能爬到1号或2号蜂房，从1号蜂房只能爬到2号或3号蜂房，…，以此类推，用n a 表示蜜蜂爬到n 号蜂房的方法数，则10a =（ ）A ．10B ．55C ．89D ．99二、多选题9．已知一组样本数据1x ，2x ，…，()201220x x x x ≤≤≤L ，下列说法正确的是（ ） A ．该样本数据的第60百分位数为12xB ．若样本数据的频率分布直方图为单峰不对称，且在右边“拖尾”，则其平均数大于中位数C ．剔除某个数据i x （1i =，2，…，20）后得到新样本数据的极差不大于原样本数据的极差D ．若1x ，2x ，…，10x 的均值为2，方差为1，11x ，12x ，…，20x 的均值为6，方差为2，则1x ，2x ，…，20x 的方差为510．在平面直角坐标系中，O 为坐标原点，抛物线()220y px p =>的焦点为F ，点()1,2M ，()11,A x y ，()22,B x y 都在抛物线上，且0FA FB FM ++=ruu r uu r uuu r ，则下列结论正确的是（ ）A ．抛物线方程为22y x =B ．F 是ABM V 的重心C ．6FA FM FB ++=u u u r u u u u r u u u rD ．2223AFO BFO MFO S S S ++=△△△11．已知函数()()()322,,R ,f x x ax bx c a b c f x =-++'∈是()f x 的导函数，则（ ）A ．“0a c ==”是“()f x 为奇函数”的充要条件B ．“0a b ==”是“()f x 为增函数”的充要条件C ．若不等式()0f x <的解集为{1xx <∣且1}x ?，则()f x 的极小值为3227-D ．若12,x x 是方程()0f x '=的两个不同的根，且12111x x +=，则0a <或3a >三、填空题12．点M 在椭圆221259x y +=上，F 是椭圆的一个焦点，N 为MF 的中点，3ON =，则MF =. 13．如图，将一个各面都涂了油漆的正方体切割为125个同样大小的小正方体.经过搅拌后，从中随机取一个小正方体，记它的涂漆面数为X ，则X 的均值()=E X .14．若函数()()52cos sin 2f x a x x x =-+在R 上单调递增，则a 的取值范围是.四、解答题15．△ABC 的内角A ，B ，C 的对边分别为a ，b ，c ，已知向量(),sin m b a C =--u r，(),sin sin n c b A B =++r ，满足//m n u r r ． (1)求A ；(2)若角A 的平分线交边BC 于点D ，AD 长为2，求△ABC 的面积的最小值．16．如图，已知点P 在圆柱1OO 的底面圆O 上，120AOP ∠=o ，圆O 的直径4AB =，圆柱的高13OO =.（1）求点A 到平面1A PO 的距离； （2）求二面角1A PB O --的余弦值大小.17．双曲线()2222:10,0x y C a b a b-=>>的左顶点为A ，焦距为4，过右焦点F 作垂直于实轴的直线交C 于B 、D 两点，且ABD △是直角三角形． (1)求双曲线C 的方程；(2)M 、N 是C 右支上的两动点，设直线AM 、AN 的斜率分别为1k 、2k ，若122k k =-，求点A 到直线MN 的距离d 的取值范围．18．已知函数()()e xf x x a =-，a ∈R .(1)当1a =时，求()f x 的极值；(2)若函数()()ln g x f x a x =-有2个不同的零点1x ，2x . （i ）求a 的取值范围； （ii ）证明：12112e x x a x x +->. 19．已知集合{}()1,2,3,,,3A n n n =∈≥L N ，W A ⊆，若W 中元素的个数为()2m m ≥，且存在u ，()v W u v ∈≠，使得()2ku v k +=∈N ，则称W 是A 的()P m 子集.(1)若4n =，写出A 的所有()3P 子集；(2)若W 为A 的()P m 子集，且对任意的s ，()t W s t ∈≠，存在k ∈N ，使得2k s t +=，求m 的值；(3)若20n =，且A 的任意一个元素个数为m 的子集都是A 的()P m 子集，求m 的最小值.。

长郡中学2023届高三月考试卷（四）地理本试题卷分选择题和非选择题两部分，共8页。

时量75分钟，满分100分。

第I卷选择题（共48分）一、选择题（本大题共16小题，每小题3分，共48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）中山站（°S，°E）位于南极东部的普里兹湾拉斯曼丘陵沿岸，海拔约为15m。

下图示意中山站2018年1月1日3月31日太阳高度角逐日变化。

据此完成1～2题。

1.中山站极昼日数约为日日日日2.图示期间，北京①昼渐长夜渐短②太阳日出方位为东偏南③正午太阳高度角逐日变大④太阳日落方位为西偏北A.①②B.③④C.①③D.②④1961—2020年，三江源地区平均气温和降水量均呈现明显增加趋势。

下图示意1961一2020年三江源地区季节性冻土冻结初始日分布。

据此完成3～4题。

3.影响三江源季节性冻土冻结初始日空间差异的主导因素是A.海拔B.纬度位置C.植被覆盖度D.土层厚度4.有利于冻结初始日推迟的气象条件是封冻前A.增暖、增湿B.降温、减湿C.增暖、减湿D.降温、增湿乌拉斯沟发源于阿尔泰山脉南坡，洪水多发。

下图示意某年5月13～24日乌拉斯沟的一次洪水过程。

据此完成5-6题。

5.此次洪水A.洪峰量巨大B.日变化明显C.持续时间短D.流量与气温无关6.此次洪水的水源来自A.高山冰雪融水B.季节性积雪融水C.大气降水D.地下水云南热带一亚热带地区具有复杂的地质历史，地处东亚与东南亚、喜马拉雅与中国一日本生物区系的节点位置。

下图示意云南省西双版纳、滇东南、铜壁关、独龙江植物区系位置，下表示意四个自然植物区系科、属、种相似性的比较。

据此完成7～8题。

7.从科水平角度看，云南省4个植物区系A.系统进化的起源相同B.无近代的自然地理联系C.地理联系无任何变化D.无历史的自然地理联系8.从种水平角度看，4个植物区系相似性系数较低，主要是因为①彼此相距较远②地形起伏和缓③自然环境差异小④地质历史复杂A.①②B.③④C.②③D.①④传统村落，又称古村落，指村落形成年代较为久远，保留有完整形态与格局，具有一定科学研究意义的文化遗产。

长郡中学2025届高三月考试卷（二）数学得分__________．本试卷共8页．时量120分钟．满分150分．一､选择题（本大题共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{}(){}2,128t A x x B t t ==∈Z ∣∣ ，则A B = （ ） A. []1,3− B. {}0,1 C. []0,2 D. {}0,1,22. 已知复数z 满足i 1z −=，则z 的取值范围是（ ） A. []0,1 B. [)0,1 C. [)0,2 D. []0,23. 已知()2:ln (11)1p f x a x x =+−<< − 是奇函数，:1q a =−，则p 是q 成立（ ） A. 充要条件B. 充分不必要条件C. 必要不充分条件D. 既不充分也不必要条件4. 若锐角α满足sin cos αα−sin 22πα +=（ ） A. 35 B. 35 C. 35 或35 D. 45−或455. 某大学在校学生中，理科生多于文科生，女生多于男生，则下述关于该大学在校学生结论中，一定成立的是（ ）A. 理科男生多于文科女生B. 文科女生多于文科男生C. 理科女生多于文科男生D. 理科女生多于理科男生6. 如图，某车间生产一种圆台形零件，其下底面的直径为4cm ，上底面的直径为8cm ，高为4cm ，已知点P 是上底面圆周上不与直径AB 端点重合的一点，且,AP BP O =为上底面圆的圆心，则OP 与平面ABC 所成的角的正切值为（ ）的的A. 2B. 12 C. D. 7. 在平面直角坐标系xOy 中，已知直线1:2l y kx =+与圆22:1C x y +=交于,A B 两点，则AOB 的面积的最大值为（ ）A. 1B. 12C.D. 8. 设函数()()2ln f x x ax b x =++，若()0f x ≥，则a 的最小值为（ ） A. 2− B. 1− C. 2 D. 1 二､多选题（本大题共3小题，每小题6分，共18分．在每小题给出的选项中，有多项符合题目要求．全部选对的得6分，部分选对的得部分分，有选错的得0分．） 9. 已知2n >，且*n ∈N ，下列关于二项分布与超几何分布的说法中，错误的有（ ）A. 若1(,)3X B n ，则(22113E X n ++ B. 若1(,)3X B n ，则()4219D X n +=C. 若1(,)3X B n ，则()()11P X P X n ===−D. 当样本总数远大于抽取数目时，可以用二项分布近似估计超几何分布10. 已知函数()sin cos (,0)f x x a x x ωωω=+∈>R 的最大值为2，其部分图象如图所示，则（ ）A. 0a >B. 函数π6f x−为偶函数 C. 满足条件的正实数ω存在且唯一D. ()f x 是周期函数，且最小正周期为π11. 已知抛物线2:2(0)C y px p =>的焦点为F ，准线交x 轴于点D ，直线l 经过F 且与C 交于,A B 两点，其中点A 在第一象限，线段AF 的中点M 在y 轴上的射影为点N .若MN NF =，则（ ）A. lB. ABD △是锐角三角形C. 四边形MNDF2 D. 2||BF FA FD ⋅> 三､填空题（本大题共3小题，每小题5分，共15分．）12. 在ABC 中，AD 是边BC 上的高，若()()1,3,6,3AB BC== ，则AD = ______． 13. 已知定义在RR 上的函数()f x 满足()()23e x f x f x =−+，则曲线yy =ff (xx )在点()()0,0f 处的切线方程为_____________.14. 小澄玩一个游戏：一开始她在2个盒子,A B 中分别放入3颗糖，然后在游戏的每一轮她投掷一个质地均匀的骰子，如果结果小于3她就将B 中的1颗糖放入A 中，否则将A 中的1颗糖放入B 中，直到无法继续游戏．那么游戏结束时B 中没有糖的概率是__________． 四､解答题（本大题共5小题，共77分，解签应写出文字说明､证明过程或演算步骤．） 15. 已知数列{}n a 中，11a =，且0,n n a S ≠为数列{}n a 的前nn a =． （1）求数列{}n a 的通项公式；（2）若1(1)n n n n n c a a +−=，求数列{}n c 的前n 项和． 16. 如图，在以,,,,,A B C D E F 为顶点五面体中，四边形ABCD 与四边形CDEF 均为等腰梯形，AB∥,CD EF ∥,224CD CD AB EF ===，AD DE AE ===.的的（1）证明：平面ABCD ⊥平面CDEF ； （2）若M 为线段CD 上一点，且1CM =，求二面角A EM B −−的余弦值. 17. 已知函数2()e 2,R x f x ax a =−∈． （1）求函数()f x 的单调区间；（2）若对于任意的0x >，都有()1f x ≥恒成立，求a 的取值范围．18. 已知双曲线()2222:10,0x y E a b a b−=>>的左､右焦点分别为12,,F F E的一条渐近线方程为y =，过1F 且与x 轴垂直的直线与E 交于P ，Q 两点，且2PQF 的周长为16. （1）求E 的方程；（2）,A B 为双曲线E 右支上两个不同的点，线段AB 的中垂线过点()0,4C ，求ACB ∠的取值范围. 19. 对于集合,A B ，定义运算符“Δ”:Δ{,A B x x A x B =∈∈∣两式恰有一式成立}，A 表示集合A 中元素的个数．（1）设][1,1,0,2A B =−=，求ΔA B ； （2）对于有限集,,A B C ，证明ΔΔΔA B B C A C +≥，并求出固定,A C 后使该式取等号B 的数量；（用含,A C 的式子表示）（3）若有限集,,A B C 满足ΔΔΔA B B C A C +=，则称有序三元组(),,A B C 为“联合对”，定义{}*1,2,,,I n n ∈N ，(){},,,,u A B C A B C I ⊆∣． ①设m I ∈，求满足ΔA C m =的“联合对”(),,A B C u ⊆的数量；（用含m 的式子表示） ②根据（2）及（3）①的结果，求u 中“联合对”的数量．的。

湖南省长沙长郡中学2015届高三上学期第四次月考英语试题（word版）本试卷分为四个部分，包括听力、语言知识运用、阅读和书面表达。

时量1 20分钟。

满分1 50Part I Listening Comprehension （30 marks）Section A （22．5 marks）Directions In this section ，you will hear six conversations between two speakers．For each conversation , there are．several questions and each question is followed by three choices markedA ,B and C．Listen carefully and then choose the best answer for each question．You will hear each conversation TWICE．Conversation 11．Who used the car this morning?A．The son．B．The aunt．C．The mother．2．Where are the keys found?A．In the purse．B．In the pocket． C．In the drawer．Conversation 23．Which of the following is TRUE about the man?A．He borrowed some money．B．He is caught in the traffic．C．He will meet his teacher．4．How is the man going home?A．By train．B．By bus．C．By taxi．Conversation 35．When was the party held?A．In the morning．B．In the afternoon． C．In the evening．6．Why didn't the woman go to the party?A．She didn't feel well．B．She didn't have the time．C．She didn't get an invitation．Conversation 47．What does the man want to buy?A．A camera．B．A mobile phone．C．A music player．8．Which of the following does the man choose?A．The PE310．B．The RT230．C．The FG160．9．How much does the man pay?A．$300．B．$270．C．$100．Conversation 510．What is the woman?A．A dress designer．B．A basketball player． C．A headmaster．11．What do we know about the man s travel plan?A．He's going by air．B．He's leaving for Paris．C．He's arriving this afternoon．12．Who is going to pick up the man?A．The woman's son．B．The woman's brother．C．The woman herself．Conversation 613．What is the man doing now?A．Looking for a job．B．Studying in a university．C．Teaching at a high school．14．What kind of movie does the man like best?A．Adventure．B．Comedy．C．Drama．15．Where are the speakers going first?A．The supermarket．B．The cinema． C．The cafe．Section B （7．5 marks）Directions In this section @ you will hear a short passage．Listen carefully and then fill in thenumbered blanks with the information you've got．Fill in each blank with NO MORE TH．AN THREE WORDS．You will hear the short passage．TWICE．Essav competition introductionPart ⅡLanguage Knowledge （45 marks）Section A （15 marks）Directions Beneath each of the following sentences there, are four choices marked A，B，C and．D．Choose the one that best completes the sentence．21．It was never clear _____ the man hadn't reported the accident sooner．A．that B．what C．when D．why 22．After the fierce competition, the students were taken to their camp, _____ they would rest for next round．A．where B．who C．which D．what23．To learn English well, we should find opportunities to hear English as much as we can．A．speak B．speaking C．spoken D．to speak24．—Why．Jack, you look so tired!—Well．I the house and I must finish the work tomorrow．A．was painting B．will be paintingC．have painted D．have been painting25．So sudden_____ that the enemy had no time to escape．A．did the attack B．the attack didC．was the attack D．the attack was26．It's not the score you've got, but the attitude you choose ______ determines our evaluation of your work．A．which B．that C．what D．who27．All we are required to do ______ record a "weike" where we explain what we think students are puzzled about．A．are B．is C．was D．were 28．Our school called on us to donate our pocket money to the school damaged by the flood, _____ the students to return to their classrooms．A．enabling B．having enabled C．enable D．to have enabled 29．—I prefer shutting myself in and listening to music all day on Sundays．—That's_____I don't agree．You should have a more active life．A．where B．how C．when D．what 30．John thinks it won't be long _____ he is ready for his new job．A．when B．after C．before D．since31．_____ an important decision more on emotion than on reason, you will regret it sooner or later．A．Based B．Basing C．Base D．To base 32．The manager is said to have arrived back from Paris where he ______ some European partners．A．would meet B．is meeting C．meets D．had met 33．_____ something to drink, as the movie will last three hours．A．Grab B．To grab C．Grabbing D．Grabbed 34．The president hopes that the people will be better off when he quits than when he _____．A．has started B．starts C．started D．will start 35．—I left my handbag on the train, but luckily someone gave it to a railway official．—How unbelievable to get it back! I mean．someone _____ it．A．will have stolen B．might have stolenC．should have stolen D．must have stolenSection B （18 marks）Directions For each blank in the following passage there, are．four words or phrases marked A, B, C and D．Fill in each blank with the word or phrase that best fits the context．Michael Greenberg is a very popular New Yorker．He is not famous in sports or the arts．But people in the streets know about him, especially those who are 36For those people, he is "Gloves" Greenberg．How did he get that name? He looks like anyother businessman, wearing a suit and carrying a briefcase （公文箱）．But he's 37 His briefcase always has some gloves．In winter, Mr．Greenberg does not 38 like other New Yorkers．who look at the sidewalk and 39 the street．He looks around at people．He stops when he sees someone with no gloves．He gives them a pair and then he 40 , looking for more people with cold hands．On winter days．Mr．Greenberg gives away gloves．During the rest of the year, he 41 gloves．People who have heard about him 42 him gloves, and he has many in his apartment．Mr．Greenberg began doing this 21 years ago．Now．many poor New Yorkers know him and 43 his behavior．But people who don't know him are sometimes 44 him．They don't realize that he just wants to make them 45 ．It runs in the 46 Michael's father always helped the poor as he believed it made everyone happier．Michael Greenberg feels the same．A pair of gloves may be a 47 thing．but it can make a big difference in winter．36．A．old B．busy C．kind D．poor 37．A．calm B．different C．crazy D．curious 38．A．act B．Sound C．feel D．dress 39．A．cross over B．drive along C．hurry down D．keep off 40．A．holds up B．hangs out C．moves on D．turns around 41．A．borrows B．sells C．returns D．buys 42．A．call B．send C．lend D．show 43．A．understand B．dislike C．study D．excuse 44．A．sorry for B．satisfied with C．proud of D．surprised by 45．A．smart B．rich C．special D．happy 46．A．city B．family C．neighborhood D．company 47．A．small B．useful C．delightful D．comforting Section C （12 marks）Directions Complete the following passage by filling in each blank with one word．that best fits the context．One day the employees of a large company returned from their lunch and were greeted with a sign on the front door．48 sign said "Yesterday the person who has been limiting your growth in this company passed 49 ．We invite you to join the funeral in the room that has been prepared in the gym．"At first everyone was sad to hear 50 one of their colleagues had died．but after a while they started getting curious 51 who this person might be．The excitement grew 52 the employees arrived at the gym to pay their last respect．Everyone wondered "Who is this person that was limiting my progress? Well．at least he is no longer here．"One by one the employees got closer to the coffin（棺材）53 when they look inside it they suddenly became speechless．There was a mirror inside the coffin everyone 54 looked inside it could see himself．There was also a sign next to the mirror that said "There is only one person who is capable to set limits to your growth it is 55 "Part m Reading Comprehension （30 marks）Directions Read the following three passages．Each passage is followed by several questions or unfinished statements．For each of them there, are four choices marked A，B，C and D．Choosethe．one that fits best according to the information given in the．passage．AJerry was a unique manager because he had several waiters who had followed him around from restaurant to restaurant．The reason the waiters followed Jerry was because of his attitude．He was a natural motivator．It an employee was having a bad day．Jerry was there telling the employee how to look on the positive side of the situation．Seeing this style really made me curious, so one day I went up to Jerry and asked him, "I don't get it! You can't be a positive person all of the time．How do you do it?" Jerry replied, "Each morning I wake up and say to myself, "Jerry, you have two choices today．You can choose to be in a good mood or you can choose to be in a bad mood．' I choose to be in a good mood．Each time something bad happens, I can choose to be a victim or I can choose to learn from it．I choose to learn from it．Every time someone comes to me complaining．I can choose to accept their complaining or I can point out the positive side of life．I choose the positive side of life．The bottom line It's your choice how you live life．" I reflected on what Jerry said．Later．I left the restaurant industry to start my own business．We lost touch, but I often thought about him when I made a choice about life．Several years later．I heard that Jerry did something you are never supposed to do in a restaurant business he left the back door open one morning and was held up at gun point by three armed robbers．While trying to open the safe, he forgot the password, nervous．The robbers panicked and shot him．Luckily, Jerry was found relatively quickly and rushed to the local hospital．After 18 hours of surgery and weeks of intensive care．Jerry was released from the hospital with fragments（碎片）of the bullets still in his body．I saw Jerry about six months after the accident．When I asked him how he was．he replied．"The first thing that went through my mind was that I should have locked the back door," Jerry replied．"Then, as I lay on the floor．I remembered that I had two choices I could choose to live．or I could choose to die．I chose to live．" " Weren ' t you scared? Did you lose consciousness?" I asked．Jerry continued, "The doctors and nurses were great．They kept telling me I was going to be fine．But when they wheeled me into the emergency room and I saw the expressions on the faces of the doctors and nurses, I got really scared．I knew I needed to take action．""What did you do?" I asked．"Well, there was a big．strong nurse shouting questions at me．" said Jerry．"She asked if I was allergic （过敏的）to anything．"Yes．' I replied．The doctors and nurses stopped working as they waited for my reply．I took a deep breath and yelled, "Bullets!' Over their laughter, I told them．"I am choosing to live．Operate on me as if I am alive, not dead．'"Jerry lived thanks to the skill of his doctors, but also because of his amazing attitude．I learned from him that every day we have the choice to live fully．56．The author left Jerry's restaurant because he_____．A．wanted to start business on his ownB．was afraid of another robbery laterC．was not equal to the job any longerD．didn't get along well with others57．Why was Jerry shot?A．Because he left the back door open．B．Because he opened the safe too slowly．C．Because he pretended to forget the password．D．Because he didn't open the safe in time．58．What was Jerry really afraid in the emergency room?A．The doctors and nurses refused to save him．B．He decided to take action to live again．C．The doctors and nurses came with expressions of regret at his being shotD．He might not be saved by doctors and nurses．59．From the passage we can learn that Jerry _____．A．was no longer positive to his life after the operationB．was optimistic even when things were at their worstC．influenced all his colleagues in many waysD．was badly injured and stayed in hospital for six months60．Which of the following is conveyed in this article?A．Where there is life．there is hope．B．Everything comes to him who waits．C．Humor is the best medicine that creates miracle．D．Attitude determines everything．BAn old problem is getting new attention in the United State s—bullying．Recent cases included the tragic case of a fifteen-year-old girl whose family moved from Ireland．She hanged herself in Massachusetts in January following months of bullying．Her parents criticized her school for failing to protect her．Officials have brought criminal charges against several teenagers．Judy Kaczynski is president of an anti-bullying group called Bully Police USA．Her daughter Tina was the victim of severe bullying starting in middle school in the state of Minnesota．She said, "Our daughter was a very outgoing child．She was a bubbly personality, very involved in all kinds of things, had lots of friends．And over a period of time her grades fell completely．She started having health issues．She couldn't sleep．She wasn't eating．She had terrible stomach pains．She started clenching（紧握，紧咬）her jaw and grinding her teeth at night．She didn't want to go to school．"Bullying is defined as negative behavior repeated over time against the same person．It can involve physical violence．Or it can be verba l—for example, insults or threats．Spreading lies about someone or excluding a person from a group is known as social or relational bullying．And now there is cyberbullying, which uses the Internet, e-mail or text messages．It has easy appeal for the bully because it does not involve face-to-face contact and it can be done at any time．The first serious research studies into bullying were done in Norway in the late 1970s．The latest government study in the United States was released last year．It found that about one-third of students aged twelve to eighteen were bullied at school．Susan Sweater is a psychologist at the University of Nebraska-Lincoln and co-director of the Bullying Research Network．She says schools should treat bullying as a mental health problem to get bullies and victims the help they need．She says bullying is connected to depression, anxiety and anti-social behavior, and bullies are often victims themselves．61．From the case of Tina, we can know that _____．A．bullying is rare B．victims suffered a lotC．schools are to blame D．personalities are related 62．Which of the following is NOT bullying?A．To beat someone repeatedly．B．To call someone names．C．To isolate someone from friends．D．To refuse to help someone in need．63．Why is cyberbullying appealing to the bully?A．Because it can involve more people．B．Because it can create worse effects．C．Because it is more convenient．D．Because it can avoid cheating．64．According to Susan Sweater．_____．A．bullies are anti-socialB．bullies should give victims helpC．students are not equally treatedD．bullies themselves also need help65．Which of the following can be the best title of the text?A．Bullyin g—An Irish Girl Committed SuicideB．15-year-old Irish Girl Committed SuicideC．Cyberbullyin g—Taking Off in SchoolsD．How to Find Bullying among TeensC"The days when the management in Western companies presented gold watches to long-serving employees to thank them for loyal service is now just a memory．" says the Educational and Training Support Agency．This new development in the shape and movement of the workforce throughout Western businesses is partly a result of the way that layers of middle management are being removed, leaving more workers responsible for their own development．"Having workers take responsibility for their own development might be dramatic, but it is now the rule," says the Educational and Training Support Agency．"Today, not only are workers more mobile, they have to run to keep up with changes．" says the Government-founded agency．"It is no longer enough for a worker to gain a set of skills．Workers need the ability to react and get used to changes．" This new system is also being pushed along by the way that industry is looking to its workers to renew their own skills．In the United States, some companies have contracts （合同）which repair their employees to show regularly how they have their skills up to date．Contrary to this traditions of the past, employers in the West are now looking for autonomous learners as recruits, people who can develop their own continuing education beyond the school and university system．At the same time．businesses are developing the capacity for workers to take up autonomous learning on site in workplace, so that the skills and abilities of all workers in a business continue to improve and increase．"This．of course," says business theory．"will also improve the productivity （生产率）of the workers and therefore the profits of the company．"66．The management in western companies no longer presents gold watches to their employees because _____．A．they are not loyal to companiesB．other rewards replace gold watchesC．the way prove to be a failureD．serving a company for life is rare now67．The western workforce frequently changes their jobs partly because _____．A．hopping from job to job has become a new trendB．employees are expecting to have more experiences in their lifeC．workers have to take more responsibility for themselvesD．it is easy to complete themselves by doing so68．The passage seems to suggest that the present situation in society requires that workers shouldA．show more loyalty to their companiesB．try to develop their skills to fit in with changesC．go to college to have their skills up to dateD．be quick in changing their careers if there is the possibility69．The phrase "autonomous learner" in the last paragraph means _____．A．people who have received higher educationB．people who study hard themselvesC．people who learn things very quicklyD．people who continue their study beyond regular education70．Companies require their employee's development mainly because _____．A．it will finally help to bring more profits to the companyB．it can attract more workers who pay special attention to self-developmentC．it is good for the employees to develop their skillsD．it will make workers more responsible and loyal to the companyPart Iv Writing （45 marks）Section A （10 marks）Directions Read．the following passage．Fill．in the numbered, blanks by using the information from the passage．Write NO MORE THAN THREE WORDS for each answer．Learning to improve your focus throughout the day can be a little difficult, only because we are talking about 18 to 24 hours, depending on the number of hours you sleep．However, if we break down your day into manageable time frames, it would make it much easier to learn to improve your focus．Focus, or concentration, is a skill that can be taught, so there are some exercises you can do to improve your focus．Start with easy exercises like staring at a picture on the wall for a few minutes without moving or talking to anyone．Once you learn how to block out your surroundings, your focus will improve．Other mind exercises you can do are internalizing．This is when you picture yourself in a desired situation, and then you work around your picture．Actors do this a lot to block out laughter, noise, or other distractions．An example of this would be to imagine you in a potentially stressful situation, like a singer in a concert．Try to play out the scene in your mind what you would do if different scenarios were to happen．This can actually be a lot of fun．and you learn how to improve your focus by concentrating on one thing only．If this sounds a little strange to you, you could try another strategy．Why not make lists? Make a list for the things you need to accomplish for the morning, another for the afternoon．and finally, another list for the evening．Study your lists carefully and see where you can move thingsaround．For instance, if you have a dinner to arrange that evening, don't bunch up everything in the afternoon, right before the guests arrive．Divide your chores and errands between morning and afternoon, and give yourself an hour or two to relax before the guests arrive．Planning helps you focus．It will also not stress you out．Another way to improve your focus is to take breaks．If children have rest and lunch as their breaks, adults should also allow themselves the privilege of stopping for a drink or a 30 minute sitcom on TV．Of course, if you are working in an office, you are allowed coffee breaks．Use this time wisely．Don't spend it with your co-workers beside the coffee machine talking about problems in the office．Doing this would actually stress you and get you to lose focus on the things that need to be done．Your breaks should be as quiet as possible．Read a book．take a walk．or visit a daycare．Go and do anything that will give your brain a rest．The reason why we lose focus so easily is because we have too much on our minds．Of course, it could also be because you are bored with nothing to do all day．A good balance between a too relaxed brain and an overly active brain is a desirable situation to be in．Find your capacity to work, and try not to veer away too far from it on a daily basis．Improving your focus also means knowing what you can do and being confident about doing it well．Focus is important but difficult to improve1．71 to improve your focusI ．Staring at picture．◆Staring at a wall picture 72 to learn to block out surroundingsⅡ．73 ．◆Concentrating on imagining a potentially stressful work place to block out 74Ⅲ．75 ．◆Dividing a day into 76 for chores and errands to be done．as well as arranging time for relaxationIV．Taking breaks．◆Wisely using time to have a drink, watch TV quietly instead of 77 ; just resting your brain2．78 for easily losing focus◆Having too much on minds◆79 all dayConclusion Keeping 80 between extremely relaxed brain and too active brain．Section B （10 marks）Directions Read．the following passage．Answer the questions according to the information given in the passage and the required words limit．Write your answers on your answer sheet．When I was 10 years old, my friend Sydney was diagnosed with a brain tumor．Sydney fought against it, but the tumor did not respond to treatment, and could not be surgically removed．The mass wrapped around her brain stem, the area of the brain that controls the vital functions of life such as breathing and blood pressure．Sydney died at the age of 11．After her death, I felt immense sadness and frustration about pediatric cancer．I decided to turn these negative emotions into positive actions．When I was 11 years old．I founded the Pink Polka Dots Guild（PPD）with two friends．The guild is named after Sydney s favorite color and pattern, which represents both the memory of my friend and the guild's positive approach．Mygoal has been to raise enough money to find a cure for brain cancer, which is the second most common cancer in children．Over the years, PPD has held fundraisers from lemonade stands to art expositions to golf tournaments．I have played a leading role in planning and organizing each PPD event．The very first Pink Polka Dots event, a garage sale．raised $ 9．000, and our most recent fundraiser, the fifth annual golf tournament, brought in over $ 73．000．The guild progressed faster than I ever anticipated．In five years, we have become 40 members strong, and raised almost half of a million dollars．I've been shocked by the public recognition that the guild has earned．PPD received an award from a U．S．Senator, spoke at a TED Conference, was featured in Teen Vogue, and appeared on The Note Berkus Show．Each of these honors has raised awareness and money for our cause．The initiative that I have taken has truly impacted the world of cancer research．PPD has provided start-up funding for scientific discoveries, such as "Tumor Paint", which illuminates cancerous cells so that surgeons can remove them with unprecedented accuracy．The discovery appeared in Time Magazine．, and will be reviewed by the Food & Drug Administration starting in early 2012．1 am extremely proud to have helped fund the research of this life-saving technology．Pink Polka Dots has inspired me to be an activist．My experience has taught me that with passion and dedication, it is possible to make a difference to the world．The determination that Pink Polka Dots sparked in me has carried over to all aspects of my life, making me a driven academic, a competitive debater and a dedicated volunteer．81．Why did the author feel sad and frustrated? （No more than 8 words）82．What was the author s purpose of founding PPD? （No more than 15 words）83．What achievement has PPD made in helping cancer research? （No more than 13 words）84．What did the author learn trom his own experience of founding PPD? （No more than 15 words）Section C （25 marks）Directions Write, an English composition according to the instructions given below．现今，中学生由于学业繁重几乎都没有在家承担任何家务责任。

长郡中学２０１６届高三月考试卷（一）数学（理科）本试题卷包括选择题、填空题和解答题三部分，共８页。

时量１２０分钟。

满分１５０分。

一、选择题：本大题共１０小题，每小题５分，共５０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ｉ是虚数单位，若＝１－ｉ，则z的共轭复数为Ａ．１－２ｉＢ．２－４ｉＣ．2－２2ｉＤ．１＋２ｉ２．已知狆：１，q：｜x－a｜＜１，若p是q的充分不必要条件，则实数a的取值范围为Ａ．（－∞，３］Ｂ．［２，３］Ｃ．（２，３］Ｄ．（２，３）３．已知，点C在∠AOB内，且∠AOC＝４５°，设等于Ａ．１Ｂ．２22４．已知O是坐标原点，点A（－１，１），若点M（狓，狔）为平面区域上的一个动点，则的取值范围是Ａ．［－１，０］Ｂ．［０，１］Ｃ．［０，２］Ｄ．［－１，２］５．有三个房间需要粉刷，粉刷方案要求：每个房间只用一种颜色，且三个房间颜色各不相同．已知三个房间的粉刷面积（单位：ｍ２）分别为，且x＜y＜z，三种颜色涂料的粉刷费用（单位：元／ｍ２）分别为a，b，c，且a＜b＜c．在不同的方案中，最低的总费用（单位：元）是６．使奇函数上为减函数的θ的值为７．设若函数f（x）为单调递增函数，且对任意实数x，都有（ｅ是自然对数的底数），则f（ｌｎ２）＝Ａ．１Ｂ．ｅ＋１Ｃ．３Ｄ．ｅ＋３８．若θ为两个非零向量的夹角，已知对任意实数的最小值为１．Ａ．若θ确定，则唯一确定Ｂ．若θ确定，则唯一确定Ｃ．若｜a｜确定，则θ唯一确定Ｄ．若｜b｜确定，则θ唯一确定９．已知函数f（x）＝ｓｉｎπx 的图象的一部分如左图，则右图的函数图象所对应的函数解析式为１０．如图所示的空间直角坐标系O－xyz中，一个四面体的顶点坐标分别为（０，０，２），（２，２，０），（１，２，１），（２，２，２），给出的编号为①，②，③，④的四个图，则该四面体的正视图和俯视图分别为Ａ．①和② Ｂ．③和① Ｃ．④和③ Ｄ．④和②二、填空题：本大题共５小题，每小题５分，共２５分．把答案填在答题卡中对应题号后的横线上．１１．计算１２．如图在平行四边形ABCD中，已知AB＝８，AD＝５，的值是．１３．过椭圆的左焦点F1作x轴的垂线交椭圆于点P，F2 为椭圆右焦点，若∠F1PF2＝６０°，则椭圆的离心率为．１４．已知数列满足．定义：使乘积为正整数叫做“易整数”．则在［１，２０１５］内所有“易整数”的和为１５．已知函数f∈（０，２π））有两个不同的零点，且方程f（x）＝m有两个不同的实根，若把这四个数按从小到大排列构成等差数列，则实数m的值为．三、解答题：本大题共６小题，共７５分．解答应写出文字说明、证明过程或演算步骤．本小题设有（ⅰ）（ⅱ）（ⅲ）三个选做题，请考生任选二题作答，如果全做，则按所做前二题计分．（ⅰ）如图：⊙O的直径AB的延长线与弦CD的延长线相交于点P，E 为⊙O上一点，交AB于点F。