2019.1海淀高三期末试题及答案word版

海淀区高三年级第一学期期末练习反馈题物理 2019.1一、本题共10小题，每小题3分，共30分。

在每小题给出的四个选项中，有的小题只有一个选项是正确的，有的小题有多个选项是正确的。

全部选对的得3分，选不全的得2分，有选错或不答的得0分。

把正确的答案填涂在答题纸上。

1．图1画出了某静电场的一条电场线，线上有A、B两点。

设A、B两点的电场强度大小分别为E A、E B，电势分别为ϕA、ϕB，则下列判断正确的是（）A．E A<E B B．E A>E B C．ϕA <ϕB D．ϕA>ϕB2. 如图2所示，通电细杆ab质量为m,置于倾角为θ的导轨上,导轨和杆间不光滑,有电流时,杆静止在导轨上,图3是四个侧视图,标出了四种匀强磁场的方向,其中摩擦力可能为0的是图2 图33．如图4所示，将带铁芯的线圈A通过滑动变阻器和开关连接到电源上，线圈B的两端连接到灵敏电流计上，把线圈A放进线圈B的里面。

下列说法正确的是A.开关闭合后,线圈A插入或拔出都会引起电计指针偏转B.线圈A插入线圈B中后,开关闭合和断开的瞬间电流计指针均不会偏转C.线圈A插入线圈B中后,开关闭合和断开的瞬间电流计指针向相反的方向偏转D.开关闭合后,只有滑动变阻器的滑片P加速滑动,电流计指针才会偏转4．如图5所示，理想变压器的原线圈接在的交流电源上，副线圈接有R =55的负载电阻，原、副线圈匝数之比为4:1，电流表、电压表均为理想电表。

下列说法正确的是 A.原线圈的输入功率为B.电流表的读数为0.25AC.电压表的读数为D.副线圈输出交流电的周期为50s5．如图6所示，半径为r 的圆形区域内有垂直于纸面向里的匀强磁 场，一个带电粒子以速度v 从A 点沿直径AOB 方向射入磁场，经过Δt 时间从C 点射出磁场，∠AOC 为1200。

现将带电粒子的速度变为v /3，仍从A 沿直径射入磁场，不计重力，则（ ）A.运动半径为rB.运动半径为D.粒子在磁场中运动时间变为2Δt6．如图7所示，电路中R 1、R 2均为可变电阻，电源内阻不能忽略，平行板电容器C 的极板水平放置，闭合电键S ，电路达到稳定时，带电油滴悬浮在两板之间静止不动。

海淀区高三年级第一学期期末练习语文2019.1一、本大题共6小题，共25分。

阅读下面的材料，完成1-6题。

材料一一篇文章的优劣，取决于能否映射现实、有无社会观照。

倘若文风浮夸自大，标题一惊一乍，事实似是而非，这不仅唐突了读者，也丧失了传播价值，污染了舆论生态。

最近在网上，“美国害怕了”“日本吓傻了”“欧洲后悔了”之类的文章，总能赚取不少莫名点击。

然而，纵观这些所谓“爆款”文章，其实却了无新意，一味夸大，文风堪忧。

比如，有的任意拔高、以偏概全，高喊《在这些领域，中国创下多个“世界第一”！无人表示不服》；有的自我安慰、贻人口实，鼓吹《别怕，我国科技实力超越美国，居世界第一》；有的内容一厢情愿、断章取义，将国外的只言片语，放大成“中国在世界舞台上占据中心位置…中国现在是全球第一经济体”等声音。

这些“雄文”的共性，一无事实骨架，二无内容血肉，三无思想含量，徒有浮躁外壳，经不起一点风吹日晒。

要知道，文章不会因为浮夸而增色，国家也不会因为自大而变强。

挑动极端情绪、肆意传播偏见，容易造成公众走进夜郎自大、自吹自擂的狂妄误区，导致社会陷入信息碎片化、思维程序化的认知闭环。

新闻学有一种观点认为，“最好的编辑一定是个营销专家”。

而某些媒体，其浮夸自大的文风，无异于“吸晴涨粉”的气球，一触即破。

这类文章的始作俑者，把标题当作一枚带着诱饵的鱼钩，诸如“全球首款”“世界第一”的标题党，给标题大加“刺激”的猛料，以博人眼球，吊人胃口。

然而，新闻不是爽文。

如果只讲营销不讲营养，只要眼球不讲责任，即使一时流量爆棚，也是在误导大众。

有网友感慨，进入了自媒体时代，新闻越来越多，离真相却越来越远。

的确，浮夸自大的文风套路，看似抄了“10万+”的近路，实则误入新闻生产的歧路。

据统计，去年新媒体运营行业人数超过300万，各类机构对内容创业者的投资金额超过50亿元，可谓既有前途，又有“钱途”。

然而，面对如此大好的形势，自媒体要想创作自如，就更需恪守自律。

海淀区高三年级第一学期期末练习2019.1一、本大题共6小题，共25分。

阅读下面的材料，完成1-6题。

材料一一篇文章的优劣，取决于能否映射现实、有无社会观照。

倘若文风浮夸自大，标题一’晾-乍，事实似是而非，这不仅唐突了读者，也丧失了传播价值，污染了舆论生态。

最近在网上，“美国害怕了”“日本吓傻了”“欧洲后悔了”之类的文章，总能赚取不少莫名点击。

然而，纵观这些所谓“爆款”文章，其实却了无新意，一味夸大，文风堪忧。

比如，有的任意拔高、以偏概全，高喊《在这些领域，中国创下多个“世界第一”！无人表示不服》；有的自我安慰、贻人口实，鼓吹《别怕，我国科技实力超越美国，居世界第一》；有的容一厢情愿、断章取义，将国外的只言片语，放大成“中国在世界舞台上占据中心位置…中国现在是全球第一经济体”等声音。

这些“雄文”的共性，一无事实骨架，二无容血肉，三无思想含量，徒有浮躁外壳，经不起一点风吹日晒。

要知道，文章不会因为浮夸而增色，国家也不会因为自大而变强。

挑动极端情绪、肆意传播偏见，容易造成公众走进夜郎自大、自吹自擂的狂妄误区，导致社会陷入信息碎片化、思维程序化的认知闭环。

新闻学有一种观点认为，“最好的编辑一定是个营销专家”。

而某些媒体，其浮夸自大的文风，无异于“吸晴涨粉”的气球，一触即破。

这类文章的始作俑者，把标题当作一枚带着诱饵的鱼钩，诸如“全球首款”“世界第一”的标题党，给标题大加“刺激”的猛料，以博人眼球，吊人胃口。

然而，新闻不是爽文。

如果只讲营销不讲营养，只要眼球不讲责任，即使一时流量爆棚，也是在误导大众。

有网友感慨，进入了自媒体时代，新闻越来越多，离真相却越来越远。

的确，浮夸自大的文风套路，看似抄了“10万+”的近路，实则误入新闻生产的歧路。

据统计，去年新媒体运营行业人数超过300万，各类机构对容创业者的投资金额超过50亿元，可谓既有前途，又有“钱途”。

然而，面对如此大好的形势，自媒体要想创作自如，就更需恪守自律。

海淀区高三年级第一学期期末练习数 学 (文科) 2019.1第Ⅰ卷（选择题 共40分）一、选择题：本大题共8小题,每小题5分,共40分.在每小题列出的四个选项中,选出符合题目要求的一项.1．sin 240o的值为A ．12-B ． 12C． D2. 若等差数列{}n a 的前n 项和为n S ，且236a a +=，则4S 的值为 A. 12 B.11 C.10 D. 93. 设,αβ为两个不同的平面，直线l α⊂，则“l β⊥”是“αβ⊥”成立的 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4. 某部门计划对某路段进行限速，为调查限速60 km/h 是否合理，对通过该路段的300辆汽车的车速进行检测，将所得数据按[40，50)，[50,60)，[60,70)，[70,80]分组，绘制成如图所示的频率分布直方图.则这300辆汽车中车速低于限速的汽车有A.75辆B.120辆C.180辆D.270辆 5.点(2,)P t 在不等式组4030x y x y --≤⎧⎨+-≤⎩表示的平面区域内，则点(2,)P t 到直线34100x y ++=距离的最大值为 A.2 B. 4 C. 6 D.8 6. 一空间几何体的三视图如图所示,则该几何体的体 积为A ．12B ．6C ． 4D ．2 7. 已知函数1()sin ,[0,π]3f x x x x =-∈， 01cos 3x =（0[0,π]x ∈），那么下面结论正确的是A ．()f x 在0[0,]x 上是减函数 B. ()f x 在0[,π]x 上是减函数 C. [0,π]x ∃∈, 0()()f x f x > D. [0,π]x ∀∈, 0()()f x f x ≥车速O40506070800.0100.0350.030a频率组距正视图左视图俯视图8. 已知椭圆E ：1422=+y m x ，对于任意实数k ，下列直线被椭圆E 所截弦长与l ：1+=kx y 被椭圆E 所截得的弦长不可能．．．相等的是 A ．0kx y k ++= B ．01=--y kx C ．0kx y k +-= D ．20kx y +-=二、填空题:本大题共6小题,每小题5分,共30分.把答案填在题中横线上.9. 若直线l 经过点（1，2）且与直线210x y +-=平行,则直线l 的方程为__________. 10.某程序的框图如图所示，执行该程序，若输入4， 则输出的S 为 .11．椭圆2212516x y +=的右焦点F 的坐标为 .F ，则其标准方程为 .12．在一个边长为1000投放一个爆破点，则爆破点距离监测站200点被监测到的概率为_______.13已知向量(1,),(1,)t t ==-a b .若-2a b 与b 垂直, 则||___=a .14．在平面直角坐标系xOy 中，O 为坐标原点.定义()11,P x y 、()22,Q x y 两点之间的“直角距离”为1212(,)d P Q x x y y =-+-为. 若点()1,3A -，则(,)d A O = ； 已知()1,0B ，点M 为直线20x y -+=上动点，则(,)d B M 的最小值为 .三、解答题: 本大题共6小题,共80分.解答应写出文字说明, 演算步骤或证明过程.15．（本小题满分13分）设函数1()sin cos 22f x x x =+，R x ∈. （I ）求函数)(x f 的周期和值域；（II ）记ABC ∆的内角C B A ,,的对边分别为c b a ,,，若3(),2f A = 且2a =， 求角C 的值.16. （本小题满分13分）某学校三个社团的人员分布如下表（每名同学只参加一个社团） 学校要对这三个社团的活动效果进行抽样调查，按分层抽样的方法从社团成员中抽取30人，结果围棋社被抽出12人. (I) 求这三个社团共有多少人？(II) 书法社从3名高中和2名初中成员中，随机选出2人参加书法展示，求这2人中初、高中学生都有的概率. 17. （本小题满分13分）如图，棱柱ABCD —1111A B C D 的底面ABCD 为菱形 ，AC BD O =I ，侧棱1AA ⊥BD,点F 为1DC 的中点．（I ） 证明：//OF 平面11BCC B ； （II ）证明：平面1DBC ⊥平面11ACC A .18. （本小题满分13分）已知函数322()1,af x x x=++其中0a >. （I ）若曲线()y f x =在(1,(1))f 处的切线与直线1y =平行，求a 的值； （II ）求函数()f x 在区间[1,2]上的最小值. 19. （本小题满分14分）已知圆22:4O x y +=,点P 为直线:4l x =上的动点.(I)若从P 到圆O 的切线长为P 点的坐标以及两条切线所夹劣弧长； （II ）若点(2,0),(2,0)A B -，直线,PA PB 与圆O 的另一个交点分别为,M N ,求证:直线MN 经过定点(1,0).20. （本小题满分14分）已知集合{}1,2,3,,2A n =L *()n N ∈.对于A 的一个子集S ，若存在不大于n 的正整数m ，使得对于S 中的任意一对元素12,s s ，都有12s s m -≠，则称S 具有性质P.A BC1B 1C 1A D F1D O（Ⅰ）当10n =时，试判断集合{}9B x A x =∈>和{}*31,C x A x k k N =∈=-∈是否具有性质P ？并说明理由.(II)若集合S 具有性质P ，试判断集合 {}(21)T n x x S =+-∈)是否一定具有性质P ？并说明理由.海淀区高三年级第一学期期末练习数 学（文）答案及评分参考 2019．1第Ⅰ卷（选择题 共40分）一、选择题（本大题共8小题,每小题5分,共40分）第II 卷（非选择题 共110分）二、填空题（本大题共6小题,每小题5分, 共30分.有两空的题目，第一空3分，第二空2分）9.240x y +-= 10. 19 11.(3,0) 212y x = 12.25π13. 2 14. 4 3三、解答题(本大题共6小题,共80分) 15．（共13分） 解：（I ）Θx x x f cos 23sin 21)(+=)3sin(π+=x ， ............................... 3分 )(x f ∴的周期为π2 （或答:0,,2≠∈k Z k k π）. ................................4分 因为x R ∈，所以3x R π+∈,所以)(x f 值域为]1,1[- . ...............................5分（II ）由（I ）可知，)3sin()(π+=A A f , ...............................6分23)3sin(=+∴πA , ...............................7分3433πππ<+<∴A , ..................................8分 2,33A ππ∴+= 得到3A π= . ...............................9分,23b a =Θ且Bb A a sin sin = , ....................................10分sin bB =, ∴1sin =B , ....................................11分 π<<B 0Θ， 2π=∴B . ....................................12分6ππ=--=∴B A C . ....................................13分16. （共13分）解：（I ）围棋社共有60人， ...................................1分 由150301260=⨯可知三个社团一共有150人. ...................................3分 （II ）设初中的两名同学为21,a a ，高中的3名同学为321,,b b b , ...................................5分 随机选出2人参加书法展示所有可能的结果:1211121321{,},{,},{,},{,},{,},a a a b a b a b a b 2223121323{,}, {,},{,},{,},{,}a b a b b b b b b b ，共10个基本事件. ..................................8分 设事件A 表示“书法展示的同学中初、高中学生都有”， ..................................9分 则事件A 共有111213212223{,},{,},{,},{,},{,},{,}a b a b a b a b a b a b 6个基本事件. ...................................11分 故参加书法展示的2人中初、高中学生都有的概率为35. ................................13分 17. （共13分）解：（I ）Θ四边形ABCD 为菱形且AC BD O =I ，O ∴是BD 的中点 . ...................................2分 又点F 为1DC 的中点,∴在1DBC ∆中，1//BC OF , ...................................4分 ⊄OF Θ平面11BCC B ，⊂1BC 平面11BCC B ,∴//OF 平面11BCC B . ...................................6分 （II ）Θ四边形ABCD 为菱形,AC BD ⊥∴, ...................................8分 又⊥BD 1AA ，1,AA AC A =I 且1,AA AC ⊂平面11ACC A ,.................................10分 ⊥∴BD 平面11ACC A , ................................11分 ⊂BD Θ平面1DBC ,∴平面1DBC ⊥平面11ACC A . ................................13分 18. （共13分）解：3332222()()2a x a f x x x x -'=-=，0x ≠. .........................................2分 （I ）由题意可得3(1)2(1)0f a '=-=，解得1a =， ........................................3分此时(1)4f =，在点(1,(1))f 处的切线为4y =，与直线1y =平行.故所求a 值为1. ........................................4分 （II ）由()0f x '=可得x a =，0a >， ........................................ 5分 ①当01a <≤时，()0f x '>在(1,2]上恒成立 ，所以()y f x =在[1,2]上递增， .....................................6分 所以()f x 在[1,2]上的最小值为3(1)22f a =+ . ........................................7分 ②当12a <<时，由上表可得()y f x =在[1,2]上的最小值为2()31f a a =+ . ......................................11分 ③当2a ≥时，()0f x '<在[1,2)上恒成立，所以()y f x =在[1,2]上递减 . ......................................12分 所以()f x 在[1,2]上的最小值为3(2)5f a =+ . .....................................13分....................................10分综上讨论，可知：当01a <≤时， ()y f x =在[1,2]上的最小值为3(1)22f a =+； 当12a <<时，()y f x =在[1,2]上的最小值为2()31f a a =+； 当2a ≥时，()y f x =在[1,2]上的最小值为3(2)5f a =+. 19. （共14分）解：根据题意，设(4,)P t . (I)设两切点为,C D ，则,OC PC OD PD ⊥⊥，由题意可知222||||||,PO OC PC =+即222242t +=+ ， ............................................2分 解得0t =，所以点P 坐标为(4,0). ...........................................3分 在Rt POC ∆中，易得60POC ∠=o ，所以120DOC ∠=o . ............................................4分 所以两切线所夹劣弧长为24233ππ⨯=. ...........................................5分 （II ）设1122(,),(,)M x y N x y ，(1,0)Q ， 依题意，直线PA 经过点(2,0),(4,)A P t -，可以设:(2)6tAP y x =+， ............................................6分和圆224x y +=联立，得到22(2)64t y x x y ⎧=+⎪⎨⎪+=⎩ ， 代入消元得到，2222(36)441440t x t x t +++-= ， ......................................7分 因为直线AP 经过点11(2,0),(,)A M x y -，所以12,x -是方程的两个根，所以有2124144236t x t --=+， 21272236t x t -=+ ， ..................................... 8分代入直线方程(2)6ty x =+得，212272224(2)63636t t t y t t -=+=++. ..................................9分 同理，设:(2)2tBP y x =-，联立方程有 22(2)24ty x x y ⎧=-⎪⎨⎪+=⎩， 代入消元得到2222(4)44160t x t x t +-+-=，因为直线BP 经过点22(2,0),(,)B N x y ，所以22,x 是方程的两个根，代入(2)2ty x =-得到2222288(2)244t t t y t t --=-=++ . .....................11分 若11x =，则212t =，此时2222814t x t -==+显然,,M Q N 三点在直线1x =上，即直线MN 经过定点Q (1,0)............................12分若11x ≠，则212t ≠，21x ≠，所以有212212240836722112136MQt y t t k t x t t -+===----+， 22222280842811214NQt y t t k t x t t ---+===----+................13分 所以MQ NQ k k =， 所以,,M N Q 三点共线，即直线MN 经过定点Q (1,0).综上所述，直线MN 经过定点Q (1,0). .......................................14分 20. （共14分）解：（Ⅰ）当10n =时，集合{}1,2,3,,19,20A =L ，{}{}910,11,12,,19,20B x A x =∈>=L 不具有性质P . ...................................1分因为对任意不大于10的正整数m ，都可以找到集合B 中两个元素110b =与210b m =+，使得12b b m -=成立 . ...................................3分 集合{}*31,C x A x k k N =∈=-∈具有性质P . ....................................4分 因为可取110m =<，对于该集合中任意一对元素112231,31c k c k =-=-，*12,k k N ∈ 都有121231c c k k -=-≠ . ............................................6分 （Ⅱ）若集合S 具有性质P ，那么集合{}(21)T n x x S =+-∈一定具有性质P . ..........7分 首先因为{}(21)T n x x S =+-∈，任取0(21),t n x T =+-∈ 其中0x S ∈， 因为S A ⊆，所以0{1,2,3,...,2}x n ∈，从而01(21)2n x n ≤+-≤，即,t A ∈所以T A ⊆ ...........................8分 由S 具有性质P ，可知存在不大于n 的正整数m ，使得对S 中的任意一对元素12,s s ，都有 12s s m -≠， ..................................9分 对上述取定的不大于n 的正整数m ，从集合{}(21)T n x x S =+-∈中任取元素112221,21t n x t n x =+-=+-， 其中12,x x S ∈， 都有1212t t x x -=- ； 因为12,x x S ∈，所以有12x x m -≠，即 12t t m -≠ 所以集合{}(21)T n x x S =+-∈具有性质P ． .............................14分 说明：其它正确解法按相应步骤给分.。

北京海淀区2019高三上年末考试试题--数学（理）word版数 学〔理〕2018.01【一】选择题：本大题共8小题，每题5分，共40分.在每题给出的四个选项中，只有一项为哪一项符合题目要求的. 〔1〕复数52i=+ ( ) 〔A 〕2i - 〔B 〕21i 55+ 〔C 〕105i - 〔D 〕105i 33- 〔2〕如图，正方形ABCD 中，点E 是DC 的中点，点F 是BC 的一个三等分点.那么=EF〔A 〕1123AB AD -〔B 〕1142AB AD +〔C 〕1132AB DA +〔D 〕1223AB AD -〔3〕假设数列{}n a 满足：119a =，13(*)n n a a n +=-∈N ，那么数列{}n a 的前n 项和数值最大时，n 的值是〔A 〕6 〔B 〕7 〔C 〕8 〔D 〕9 〔4〕平面α，β，直线l ，假设αβ^，l αβ=，那么〔A 〕垂直于平面β的平面一定平行于平面α 〔B 〕垂直于直线l 的直线一定垂直于平面α 〔C 〕垂直于平面β的平面一定平行于直线l 〔D 〕垂直于直线l 的平面一定与平面α,β都垂直〔5〕函数()sin(2)(,)f x A x A ϕϕ=+?R 的部分图象如下图，那么(0)f = 〔 〕〔A 〕12-〔B〕2- 〔C 〕1- 〔D〕-〔6〕执行如下图的程序框图，输出的i 值为开始i=1,s=0 s=s+2 i -1ii= i +1〔 〕〔A 〕5 〔B 〕6 〔C 〕7 〔D 〕8〔A 〕()f x 既不是奇函数也不是偶函数〔B 〕()f x 在[,0]π-上恰有一个零点〔C 〕()f x 是周期函数〔D 〕()f x 在(,2π5π)6上是增函数〔8〕点P 到图形C 上每一个点的距离的最小值称为点P 到图形C 的距离，那么平面内到定圆C 的距离与到定点A 的距离相等的点的轨迹不可能．．．是〔〕 〔A 〕圆〔B 〕椭圆〔C 〕双曲线的一支〔D 〕直线【二】填空题：本大题共6小题，每题5分，共30分，把答案填在题中横线上.〔9〕51)的展开式中2x 的系数是.〔用数字作答〕〔10〕假设实数,x y 满足40,20,250,x y x y x y ì+-?ïïï--?íïï+-?ïïî那么2z x y =+的最大值为.〔11〕抛物线2x ay =过点1(1,)4A ，那么点A 到此抛物线的焦点的距离为.〔12〕甲和乙两个城市去年上半年每月的平均气温〔单位：C °〕用茎叶图记录如下，根据茎叶图可知，两城市中平均温度较高的城市是____________，气温波动较大的城市是____________.22(1)2x y -+=，过点〔13〕圆C ：(1,0)A -的直线l 将圆C 分成弧长之比为1:3的两段圆弧，那么直线l 的方程为.〔14〕正三棱柱'''ABC A B C -的正〔主〕视图和侧〔左〕视图如下图.设,'''ABC A B C ∆∆的中心分别是,'O O ，现将此三棱柱绕直线'OO 旋转，射线OA 旋转所成的角为x 弧度〔x 可以取到任意一个实数〕，对应的俯视图的面积为()S x ，那么函数()S x 的最大值为；最小正周期为.8,3π说明：“三棱柱绕直线'OO 旋转”包括逆时针方向和顺时针方向，逆时针方向旋转时，OA 旋转所成的角为正角，顺时针方向旋转时，OA 旋转所成的角为负角.【三】解答题：本大题共6小题，共80分.解答应写出文字说明，证明过程或演算步骤. 〔15〕〔本小题总分值13分〕在ABC ∆中，角A ，B ，C 所对的边分别为a ，b ，c ，2A B =，sin B =. 〔Ⅰ〕求cos A 及sin C 的值；甲城市乙城市 9 08 7 7 3 1 2 4 72 2 0 4 7侧（左）视图正（主）视图〔Ⅱ〕假设2b =，求ABC ∆的面积. (16)〔本小题总分值13分〕为加强大学生实践、创新能力和团队精神的培养，促进高等教育教学改革，教育部门主办了全国大学生智能汽车竞赛.该竞赛分为预赛和决赛两个阶段，参加决赛的队伍按照抽签方式决定出场顺序.通过预赛，选拔出甲、乙等五支队伍参加决赛. 〔Ⅰ〕求决赛中甲、乙两支队伍恰好排在前两位的概率；〔Ⅱ〕假设决赛中甲队和乙队之间间隔的队伍数记为X ，求X 的分布列和数学期望. (17)〔本小题总分值14分〕在四棱锥P ABCD -中，底面ABCD 是直角梯形，AB ∥CD ，90ABC ??，2AB PB PC BC CD ====，平面PBC ^平面ABCD .〔Ⅰ〕求证：AB ^平面PBC ；〔Ⅱ〕求平面PAD 和平面BCP 所成二面角〔小于90°〕的大小； 〔Ⅲ〕在棱PB 上是否存在点M 使得CM ∥平面PAD ？假设存在，求PMPB的值；假设不存在，请说明理由. (18)〔本小题总分值13分〕函数2()e ()xf x x ax a =+-，其中a 是常数.(Ⅰ)当1a =时，求曲线()y f x =在点(1,(1))f 处的切线方程；〔Ⅱ〕假设存在实数k ，使得关于x 的方程()f x k =在[0,)+∞上有两个不相等的实数根，求k 的取值范围.(19)〔本小题总分值14分〕焦点在x 轴上的椭圆C 过点(0,1)，且离心率为2,Q 为椭圆C 的左顶点. 〔Ⅰ〕求椭圆C 的标准方程；〔Ⅱ〕过点6(,0)5-的直线l 与椭圆C 交于A ，B 两点.〔ⅰ〕假设直线l 垂直于x 轴，求AQB ∠的大小;〔ⅱ〕假设直线l 与x 轴不垂直，是否存在直线l 使得QAB ∆为等腰三角形？如果存在，求出直线l 的方程；如果不存在，请说明理由. (20)〔本小题总分值14分〕集合{1,2,3,,}(*)M n n =?N ，假设集合12{,,,}(*)m A a a a M m=臀N ，且对任意的b M Î，存在,(1)i j a a A i jm 危＃，使得12i j b a a λλ=+〔其中12,{1,0,1}λλ?〕，那么称集合A 为集合M 的一个m 元基底.〔Ⅰ〕分别判断以下集合A 是否为集合M 的一个二元基底，并说明理由； ①{1,5}A =，{1,2,3,4,5}M =；PABC D②{2,3}A =，{1,2,3,4,5,6}M =.〔Ⅱ〕假设集合A 是集合M 的一个m 元基底，证明：(1)m m n +?； 〔Ⅲ〕假设集合A 为集合{1,2,3,,19}M =的一个m 元基底，求出m 的最小可能值，并写出当m 取最小值时M 的一个基底A .参考答案及评分标准2018、01一. 选择题：本大题共8小题，每题5分，共40分. 题号 〔1〕 〔2〕 〔3〕 〔4〕 〔5〕 〔6〕 〔7〕 〔8〕 答案 A D B D C ABD二.填空题：本大题共6小题，每题5分，共30分. 〔9〕5〔10〕7〔11〕54〔12〕乙，乙〔13〕1)y x =+或1)y x =-+〔14〕8；3π注：〔13〕题正确答出一种情况给3分，全对给5分；〔12〕、〔14〕题第一空3分；第二空2分.三.解答题：本大题共6小题，共80分.解答应写出文字说明，证明过程或演算步骤. 〔15〕〔本小题总分值13分〕解：〔Ⅰ〕因为2A B =，所以2cos cos 212sin A B B ==-.………………………………………2分因为sin B =， 所以11cos 1233A =-?.………………………………………3分 由题意可知，(0,)2B πÎ.所以cos B =.………………………………………5分因为sin sin 22sin cos A B B B ===.………………………………………6分 所以sin sin[()]sin()C A B A B π=-+=+sin cos cos sin A B A B =+=.………………………………………8分〔Ⅱ〕因为sin sin b aB A=，2b =，………………………………………10分3=.所以3a =.………………………………………11分所以1sin 29ABC S ab C ∆==.………………………………………13分 (16)〔本小题总分值13分〕解：〔Ⅰ〕设“甲、乙两支队伍恰好排在前两位”为事件A ，那么()23!15!10P A ⨯==.………………………………………4分 所以甲、乙两支队伍恰好排在前两位的概率为110.………………………………………5分〔Ⅱ〕随机变量X 的可能取值为0, 1, 2, 3.………………………………………6分()24!205!5P X ⨯===， ()323!315!10P X ⨯⨯===，()22!32!125!5P X ⨯⨯⨯===，()23!135!10P X ⨯===.………………………………………10分因为01231510510EX =⨯+⨯+⨯+⨯=，所以随机变量X 的数学期望为1.………………………………………13分 (17)〔本小题总分值14分〕〔Ⅰ〕证明：因为90ABC ??，所以AB BC ⊥.………………………………………1分因为平面PBC ^平面ABCD ，平面PBC 平面ABCD BC =，AB Ì平面ABCD ，所以AB ^平面PBC .………………………………………3分 〔Ⅱ〕解：取BC 的中点O ，连接PO . 因为PB PC =，所以PO BC ⊥.因为平面PBC ^平面ABCD ，平面PBC平面ABCD BC =，PO Ì平面PBC ，所以PO ^平面ABCD .………………………………………4分如图，以O 为原点，OB 所在的直线为x 轴，在平面ABCD 内过O 垂直于BC 的直 线为y 轴，OP 所在的直线为z 轴建立空间直角坐标系O xyz -、不妨设2BC =.由 直角梯形ABCD 中2AB PB PC BC CD ====可得P ，(1,1,0)D -，(1,2,0)A .所以(1,DP =-，(2,1,0)DA =. 设平面PAD 的法向量(,,)=x y z m .因为0,0.DP DAìï?ïíï?ïîm m所以(,,)(1,0,(,,)(2,1,0)0,x y z x y z ìï?=ïíï?ïî即0,20.x y x y ìï-+=ïíï+=ïî 令1x =，那么2, y z =-=-所以(1,2,=--m .………………………………………7分取平面BCP 的一个法向量n ()0,1,0=.所以cos ,2⋅==m n m n m n . 所以平面ADP 和平面BCP 所成的二面角〔小于90°〕的大小为4π. ………………………………………9分〔Ⅲ〕解：在棱PB 上存在点M 使得CM ∥平面PAD ，此时12PM PB =.理由如 下：………………………………………10分 取AB 的中点N ，连接CM ，CN ，MN . 那么MN ∥PA ，12AN AB =. 因为2AB CD =， 所以AN CD =. 因为AB ∥CD ，NMPABCD所以四边形ANCD 是平行四边形. 所以CN ∥AD . 因为, MNCN N PA AD A ==，所以平面MNC ∥平面PAD .………………………………………13分 因为CM Ì平面MNC ，所以CM ∥平面PAD .………………………………………14分 (18)〔本小题总分值13分〕解：(Ⅰ)由2()e ()xf x x ax a =+-可得2'()e [(2)]x f x x a x =++.………………………………………2分当1a =时,(1)e f =,'(1)4e f =.………………………………………4分 所以曲线()y f x =在点(1,(1))f 处的切线方程为()e 4e 1y x -=-， 即4e 3e y x =-.………………………………………5分 〔Ⅱ〕令2'()e ((2))0xf x x a x =++=，解得(2)x a =-+或0x =.………………………………………6分当(2)0a -+≤，即2a ≥-时，在区间[0,)+∞上，'()0f x ≥，所以()f x 是[0,)+∞上的增函数.所以方程()f x k =在[0,)+∞上不可能有两个不相等的实数根.………………………………………8分当(2)0a -+>，即2a <-时，()'(),f x f x 随x 的变化情况如下表由上表可知函数()f x 在[0,)+∞上的最小值为2((2))ea f a +-+=. ………………………………………10分因为函数()f x 是(0,(2))a -+上的减函数，是((2),)a -++∞上的增函数， 且当x a ≥-时，有()f x e ()aa a -≥->-.………………………………………11分 所以要使方程()f x k =在[0,)+∞上有两个不相等的实数根，k 的取值范围必须是24(,]e a a a ++-.……………………………………13分 (19)〔本小题总分值13分〕解：〔Ⅰ〕设椭圆C 的标准方程为22221(0)x y a b a b+=>>，且222a b c =+.由题意可知：1b =，2c a =.………………………………………2分 所以24a =.所以，椭圆C 的标准方程为2214x y +=.……………………………………3分 〔Ⅱ〕由〔Ⅰ〕得(2,0)Q -.设1122(,),(,)A x y B x y . 〔ⅰ〕当直线l 垂直于x 轴时，直线l 的方程为65x =-. 由226,514x x y ⎧=-⎪⎪⎨⎪+=⎪⎩解得：6,545x y ⎧=-⎪⎪⎨⎪=⎪⎩或6,54.5x y ⎧=-⎪⎪⎨⎪=-⎪⎩即6464(,), (,)5555A B ---〔不妨设点A 在x 轴上方〕.………………………………………5分那么直线AQ 的斜率1AQ k =，直线BQ 的斜率1BQ k =-. 因为1AQ BQ k k ⋅=-， 所以AQ BQ ^. 所以2AQB π∠=.………………………………………6分 〔ⅱ〕当直线l 与x 轴不垂直时，由题意可设直线AB 的方程为6()(0)5y k x k =+≠.由226(),514y k x x y ⎧=+⎪⎪⎨⎪+=⎪⎩消去y 得：2222(25100)2401441000k x k x k +++-=. 因为点6(,0)5-在椭圆C 的内部，显然0∆>.21222122240,25100144100.25100k x x kk x x k ⎧+=-⎪⎪+⎨-⎪=⎪+⎩………………………………………8分 因为1122(2,), (2,)QA x y QB x y =+=+，116()5y k x =+，226()5y k x =+， 所以1212(2)(2)QA QB x x y y ⋅=+++121266(2)(2)()()55x x k x k x =++++⋅+2221212636(1)(2)()4525k x x k x x k =++++++2222222144100624036(1)(2)()402510052510025k k k k k k k -=+++-++=++.所以QA QB ⊥.所以QAB ∆为直角三角形.………………………………………11分 假设存在直线l 使得QAB ∆为等腰三角形，那么QA QB =取AB 的中点M ，连接QM ，那么QM AB ^.记点6(,0)5-为N .另一方面，点M 的横坐标22122212024225100520M x x k k x k k +==-=-++，所以点M 的纵坐标266()5520M M k y k x k=+=+. 所以222221016666(,)(,)520520520520k k kQM NMk k k k +??++++ 222601320(520)k k +=?+. 所以QM 与NM 不垂直，矛盾.所以当直线l 与x 轴不垂直时，不存在直线l 使得QAB ∆为等腰三角形.………………………………………13分(20)〔本小题总分值14分〕解：〔Ⅰ〕①{1,5}A =不是{1,2,3,4,5}M =的一个二元基底.理由是1212315(,{1,0,1})λλλλ棺+孜-；②{2,3}A =是{1,2,3,4,5,6}M =的一个二元基底. 理由是11213,21203,30213=-??????，41212,51213,61313=??????.………………………………………3分 〔Ⅱ〕不妨设12m a a a <<<，那么形如10i j a a ??(1)ij m ＃?的正整数共有m 个； 形如11i i a a ??(1)i m ＃的正整数共有m 个；形如11ij a a ??(1)ij m ??的正整数至多有2mC 个； 形如(1)1i j a a -??(1)ij m ??的正整数至多有2mC 个. 又集合{1,2,3,,}M n =含n 个不同的正整数，A 为集合M 的一个m 元基底.故22m m m m C C n +++?，即(1)m m n +?.………………………………………8分〔Ⅲ〕由〔Ⅱ〕可知(1)19m m +?，所以4m ³.当4m =时，(1)191m m +-=，即用基底中元素表示出的数最多重复一个.* 假设1234{,,,}A a a a a =为{1,2,3,,19}M =的一个4元基底，不妨设1234a a a a <<<，那么410a ³. 当410a =时，有39a =，这时28a =或7.如果28a =，那么由1109,198,1899,18108=-=-=+=+，与结论*矛盾. 如果27a =，那么16a =或5.易知{6,7,9,10}A =和{5,7,9,10}A =都不是{1,2,3,,19}M =的4元基底，矛盾.当411a =时，有38a =，这时27a =，16a =，易知{6,7,8,11}A =不是{1,2,3,,19M =的4元基底，矛盾.当412a =时，有37a =，这时26a =，15a =，易知{5,6,7,12}A =不是{1,2,3,,19M =的4元基底，矛盾.当413a =时，有36a =，25a =，14a =，易知{4,5,6,1A =不是{1,2,3,,1M =的4元基底，矛盾. 当414a =时，有35a =，24a =，13a =，易知{3,4,5,1A =不是{1,2,3,,M =的4元基底，矛盾.当415a =时，有34a =，23a =，12a =，易知{2,3,4,1A =不是{1,2,3,,1M =的4元基底，矛盾. 当416a =时，有33a =，22a =，11a =，易知{1,2,3,16}A =不是{1,2,3,,M =的4元基底，矛盾.当417a ³时，A 均不可能是M 的4元基底.当5m =时，M 的一个基底{1,3,5,9,16}A =；或{3,7,8,9,10}；或{4,7,8,9,10}等，只要写出一个即可.综上，m 的最小可能值为5.………………………………………14分。

海淀区高三年级第一学期期末练习语文 2018.1一、本大题共8小题，共24分。

阅读下面的材料，完成1-8题。

材料一(734字)目前，被誉为“中国天眼”的500米口径球面射电望远镜，还未正式运行就新发现6颗脉冲星。

中国科学家在北京发布了它取得的首批成果。

“中国天眼”是中国“十一五”重大科技基础设施之一，基于选址方法、索网主动反射面、柔性索结合并联机器人的馈源支撑这三项中国自主创新技术，它突破了射电望远镜工程的极限。

在未来可预见的二三十年内，它将是我们这个星球最先进、最灵敏的射电望远镜。

人类迄今已发现2500余颗脉冲星。

但在“中国天眼”问世前，中国望远镜从未捕捉到新的脉冲星。

事实证明，重大的科学突破离不开科研仪器的进步。

世界各国相继认识到大科学装置在国家创新能力建设中的重要地位，中国也在不断兴建重器。

包括“中国天眼”在内，仅中国科学院目前运行和在建的重大科技基础设施就有23个。

2019年国务院印发的《国家重大科技基础设施建设中长期规划（2019 - 2030年）》对能源、生命、天文等7个科学领域进行了系统【甲】bùshǔ。

中国科学院国家天文台台长严俊认为，“中国天眼”调试进展超过预期、打破了大型同类设备调试周期的国际惯例，并有系统的科学产出，这得益于【乙】卓．有成效的早期科学规划和人才储备。

从最初不到5人的研究小组扩大到上百人团队，“中国天眼”凭借国内100多家参建单位的力量，由跟踪模仿发展到集成创新。

发布会当日，人们自发为“中国天眼”之父，项目总工程师兼首席科学家南仁东先生默哀。

2019年9月15日，在“中国天眼”落成近一周年之际，曾为之奔波奋斗的南先生【丙】溘．然长逝。

当年他毅然舍弃高薪，回国就任中国科学院北京天文台副台长。

1993年国际无线电科学联盟大会上，外国科学家们提出要建造新一代射电望远镜，以接受更多来自外太空的讯息。

南先生跟同事们说：“咱们也建一个吧！”从那时起，一干就是二十多年。

2019年海淀区高三年级第一学期期末练习语文一、本大题共6小题，共22分。

阅读下面的诗歌和文言短文，完成1—6题。

甲午元旦①孔尚任萧疏自发不盈颠，守岁围炉竟废眠。

剪烛催乾消夜酒，倾囊分遍买春钱。

听烧爆竹童心在，看抉桃符老兴偏。

鼓角梅花添一部，五更欢笑拜新年。

注释：①元旦，即现在的春节。

1、甲午元旦所写的春节习俗，在下列诗句中没有表现的一项是（3分）A.儿童却立避其锋，当街击地雷霆吼。

B.千家万户瞳瞳日，总把新桃换旧符。

C.一樽岁酒拜庭除，稚子牵衣慰屏屠。

D.明月皎皎千门秀，华灯盏盏万户春。

2、下列诗句与《甲午元旦》一诗尾联表达情感最相近的一项是（3分）A.老去又逢新岁月，春来更有好花枝。

B.故节当歌守，新年把烛迎。

C.奉母犹欣餐有肉，占年更喜梦维鱼。

D.钱岁愁虽剧，迎年喜亦深。

3、下列对联不适合做“春联”的一项是（3分）A.天增岁月人增寿，春满乾坤福满门。

B.家居光天化日下，人在春风和气中。

C.千家笑语漏迟迟，忧患潜从物外知。

D.百福尽随新节至，千祥俱自早春来。

4、这首诗语言朴素平实，言浅意浓，请以“竟”“催”“倾”中的一字为例，对这一特点加以赏析。

（3分）5、请根据诗歌内容，谈谈我们应该怎样过一个和谐文明的春节，100字左右。

（5分）6、用（/）给下面文言短划横线部分断句。

(5分)元旦应酬作苦且阅岁渐深韶光渐短添得一番甲子增得一番感慨庄子曰大块劳我以生此之谓乎吾所取者淑气临门和风拂面；东郊农事，举趾有期。

江梅堤柳，装点春工；晴雪条风，消融腊气。

山居之士，负暄而坐，顿觉化日舒长，为人生一快耳。

（取材于卫泳《闲赏·元旦》）二、本大题共5小题，共18分。

阅读下面的文言文，完成7—11题大定岁丙午冬仲月，予由侍从出守汝南。

既视事之明年，即州之北，得败屋数楹，旁穿上漏，不庇风雨，乃命枝倾补罅，仍．其旧而新之，公余吏退以为燕息之所。

两檐之外，左有笋石，屹然而笔卓；右有仙榆，蔚然而盖偃。

每佳夕胜日，予幅巾杖屦，徜徉乎其间。

英语学习讲义海淀区高三年级第一学期期末练习英语2019.01本试卷共12 页，共150 分。

考试时长120 分钟。

考生务必将答案答在答题纸上，在试卷上作答无效。

考试结束后，将答题纸交回。

第一部分：听力理解（共三节，30 分）第一节（共5 小题；每小题1.5 分，满分7.5 分）听下面五段对话。

每段对话后有一道小题，从每题所给的A、B、C 三个选项中选出最佳选项。

听完每段对话后，你将有10 秒钟的时间来回答有关小题和阅读下一小题。

每段对话你将听一遍。

1. What does the woman want?A. The salt.B. The pepper.C. The spoon.2. What will the weather be like according to the radio?A. Rainy.B. Sunny.C. Windy.3. Who are the paparazzi following?A. Michael.B. Kathy.C. Janice.4. What is the man’s favorite sport?A. Football.B. Baseball.C. Basketball.5. Where will the woman go this weekend?A. To the National Library.B. To the amusement park.C. To the shopping mall.第二节（共10 小题；每小题1.5 分，15 分）听下面四段对话。

每段对话后有几道小题，从每题所给的A、B、C 三个选项中选出最佳选项。

听每段对话前，你将有5 秒钟的时间阅读每小题。

听完后，每小题将给出5 秒钟的作答时间。

每段对话你将听两遍。

6. What is the woman’s research about?A. The movies students like best.B. The things students do after school.C. The sports students are interested in.7. What is the most unexpected finding of the research?A. Students rarely do housework.B. Few students go to the movies.C. Most students play computer games.听第7 段材料，回答第8 至9 题。

海淀区高三年级第一学期期末练习参考答案数 学 （理科） 2019.01一、选择题：本大题共8小题，每小题5分，共40分.1. A2. B3. D4. A5. C6. C7.C8. D二、填空题:本大题共6小题，每小题5分，共30分.9. 22(1)4x y -+= 10. 24 11. 2 12. 013.三、解答题15．解： π()2f a = 所以π(2f 因为0a >（Ⅱ）因为f 设sin ,t x = 所以22y t =其对称轴为4t =- 当14at =-<-，即 4a >时，在1t =-时函数取得最小值1a - 当14a t =-≥-，即04a <≤时，在4at =-时函数取得最小值218a -- 16.解：（Ⅰ）设该名学生考核成绩优秀为事件A 由茎叶图中的数据可以知道，30名同学中，有7名同学考核优秀所以所求概率()P A 约为730（Ⅱ）Y 的所有可能取值为0,1,2,3因为成绩[70,80]X ∈的学生共有8人，其中满足|75|10X -≤的学生有5人所以33381(0)56C P Y C ===， 21353815(1)56C C P Y C ===(P ()E Y 所以P17．解：（Ⅰ）在平面PCD 中过点D 作DH DC ⊥，交PC 于H 因为平面ABCD ⊥平面PCD DH ⊂平面PCD平面ABCD I 平面PCD CD = 所以DH ⊥平面ABCD 因为AD ⊂平面ABCD所以 DH AD ⊥ 又AD PC ⊥，且PC DH H =I 所以AD又DH ⊥以D 所以(,D0因为AD ⊥设平面因为DP =u u u r 所以y x ⎧-⎪⎨+⎪⎩2令2z = 所以cos <由题知B PD C --为锐角，所以B PD C -- （Ⅲ） 法一：假设棱BC 上存在点F ，使得MF PC ，显然F 与点C 不同所以,,,P M F C 四点共面于α 所以FC ⊂α，PM ⊂α所以B FC ∈⊂α，A PM ∈⊂α所以α就是点,,A B C 确定的平面，所以P ∈α这与P ABCD -为四棱锥矛盾，所以假设错误，即问题得证 法二：假设棱BC 上存在点F ，使得MF PC连接AC ，取其中点N在PAC ∆中，因为,M N 分别为,PA CA 的中点，所以MNPC因为过直线外一点只有一条直线和已知直线平行，所以MF 与MN 重合 所以点而MC PC ，设BF =33,)22-+因为PC ，所以(0,3,MF PC μμ==所以有120λ-=18因为a 2（Ⅱ）法一： 设1122(,),(,)A x y B x y显然直线l 存在斜率，设直线l 的方程为(2)y k x =+所以()x y y k x ⎧+=⎪⎨⎪=+⎩22122，所以()k x k x k +++-=222221882028160k ∆=->，所以k <212所以k x x k k x x k ⎧-+=⎪⎪+⎨-⎪=⎪+⎩212221228218221 因为22'(,)B x y -所以|'|AB 因为22212121222816()()4(21)k x x x x x x k --=+-=+1y y + 所以 |AB ==因为k ≤20法二：设11(,A x y 当直线l 是当直线l 所以x x t y ⎧+⎪⎨⎪=-⎩22228160t ∆=-> ，所以t >22所以t y y t y y t ⎧+=⎪⎪+⎨⎪=⎪+⎩1221224222因为22'(,)B x y - 所以|'|AB因为 2222222212121212122216()()()[()4](1)(2)t x x ty ty t y y t y y y y t t -=-=-=+-=++所以|'|AB=22)2t ====-+因为t >22，所以|'|AB ∈19所以f 当a =所以f 曲线y因为f 得x 1当a >所以()f x 在[,)+∞0上的最小值为(),()f f x 20中较小的值，而2(0)0ef =>-，所以只需要证明()f x >-e22 因为()x a x a -++=22220，所以()x x a f x ax x x -=-=e e 22222222 设()x a x F x -=e 2，其中x >0，所以()()'()x xa x x a F x ----+==e e2222 令'()F x =0，得a x +=322，当a >0时，x ，'()F x ，()F x 在区间(0,)+∞ 的变化情况如下表:令'()F x =0，得x =31当a >0时，x ，'()h x ，()h x 在区间(0,)+∞ 的变化情况如下表:所以()h x (,)+∞0上的最小值为()h 1，而(1)2e e(2)e 0h a a =+-=> 所以x >0时，'()2e e(2)0x g x a x =+->，所以()g x 在(,)+∞0上单调递增 所以()(0)g x g >而(0)20g =>，所以()0g x >，问题得证 法三：“对任意的x >0，2()e f x >-”等价于“()f x 在(,)+∞0上的最小值大于2e-”因为()'()xx a x af x -++=22，令'()f x =0得当设()xxF x -=e 2，其中x >2 所以()()'()x xx x F x --=-=e e2121 当x >2时，'()F x >0，所以()F x 单调递增，所以()()F x F >=-e242而()--=-->e e e e 2242240 所以()()f x F x >->e222，问题得证法四：因为a >0，所以当x >0时，()x x ax x x f x --=>e e22设()x x F x -=e2，其中x >0所以()'()xx x F x -=e2 所以x ，'()F x ，()F x 的变化情况如下表:,,)n y ，，所以(i i x x ， n x ++ n y ++因为n ααββ*+*=，所以1212n n x x x y y y n +++++++=所以1212,,,,,,,n n x x x y y y 中有n 个量的值为1，n 个量的值为0.显然111122220()()()n n n n x y x y x y x y x y x y αβ≤*=+-++-+++-1122n n x y x y x y n ≤++++++=，当(1,1,,1)α=，(0,0,,0)β=时，αβ，满足n ααββ*+*=，n αβ*=.所以αβ*的最大值为n又11112222()()()n n n n x y x y x y x y x y x y αβ*=+-++-+++-1122()n n n x y x y x y =-+++注意到只有1i i x y ==时，1i i x y =，否则0i i x y = 而1212,,,,,,,n n x x x y y y 中n 个量的值为1，n 个量的值为0所以满足1i i x y =这样的元素i 至多有2n个， 当n 为偶数时，n n n αβ*≥-=. 当22α=所以α*的最小值为2n当n 所以 α* 当22α=1122(1,1,,1,0,0,,0)n n -+时，满足12n β-*=. 所以α*的最小值为12n - 综上：α12n β-*=.（Ⅲ）S 设集合S 记1S ={}21212(,,,)|2,n n S x x x x x x n S αα==+++≤-∈显然1212S S S S S ==∅，集合1S 中元素个数不超过1n +个，下面我们证明集合2S 中元素个数不超过2n C 个212,(,,,)n S x x x αα∀∈=，则122n x x x n +++≤-则12n x x x ，，，中至少存在两个元素 0i j x x ==11 / 11212,(,,,)n S y y y ββ∀∈=，βα≠因为 1n αβ*≥-，所以 ,i j y y 不能同时为0所以对1i j n ≤<≤中的一组数,i j 而言，在集合2S 中至多有一个元素12(,,,)n x x x α=满足i j x x ，同时为0所以集合2S 中元素个数不超过2n C 个所以集合S 中的元素个数为至多为2211n n C n n ++=++ 记1T ={}1212(,,,)|1,n n n x x x x x x n αα=+++≥-∈Ω，则1T 中共1n +个元素， 对于任意的1T α∈，n β∈Ω，1n αβ*≥-.对1i j n ≤<≤，记,12(,,,),i j n x x x β= 其中0i j x x ==，1t x =，,t i t j ≠≠ 记2,{|1}i j T i j n β=≤<≤，显然2,S αβ∀∈，αβ≠，均有1n αβ*≥-.记12S T T =，S 中的元素个数为21n n ++，且满足,S αβ∀∈，αβ≠，均有1n αβ*≥-. 综上所述，S 中的元素个数最大值为21n n ++.。

海淀区高三年级第一学期期末练习英语试题2019.121. My normal monthly emails to and ____ pen pals have disappeared with my tight schedule.A. inB. forC. fromD. through22. - Have you heard about the shark attack accident at the SeaWorld show?- Yea, how horrible! A trainer _____ in front of the audience.A. had been killedB. has been killedC. was killedD. is killed23. The Subway Line 16 ____ in Beijing is planned to open this year.A. being builtB. buildingC. builtD. to build24. This room isn ' t actually ________ I wanted when I made my reservation.A. whatB. whereC. whichD. whether25. My boss is very generous, and he is ____ generous when we get a big order.A. veryB. mostC. onlyD. rather26. The spread of the Ebola virus in Nigeria is believed ____ by August, 2019.A. to be controlledB. to have been controlledC. to controlD. to have controlled27. We have an adviser on hand in this activity ___ you have any worries or problems.A. whenB. now thatC. thoughD. in case28. - Do I have to bring my camera tomorrow afternoon?- I think so. We _____ the Botanical Garden then.A. will be visitingB. are visitingC. have visitedD. visit29. - The zookeeper was really annoyed with me.- How could he have been if you _____ stones at the animals?A. didn ' t throwB. don ' t thCr.ohwadn ' t thrown D. haven ' t thrown30. Every Monday, my English teacher would cheerfully ask me _____ my weekend had been.A. thatB. ifC. whatD. how31. With doubts ____ through my mind, I felt it necessary to carry out a research.A. to runB. runC. runningD. having run32. - You seem busy these days.- Yes. I ' m writing a story. You know, it ' s really not easy to write _a_tt_ra_c_t_ivwe ipthlots.A. thisB. oneC. itD. that33. According to the latest BBC news, a five-year-old boy from England _________ the youngest computer specialist in the world.A. becameB. becomesC. had becomeD. has become34. The glorious moment would live in my mind ____ our football team won the championship.A. whenB. whereC. thatD. which35. - Tom, why don ' t we help our son work on his papers?- We' ve already done more than we ___ . He is on his own this time.A. wouldB. shouldC. couldD. might完型填空He Had a GoIt was a cool spring evening in Melbourne, Australia. I drove to my boxing gym for a Friday night trainingsession. After ___________ (36) up, I started training. Then I noticed a tall and slim young man walking• 1 •through the doors. There was something about him that caught my _____ (37).Before long, I realized that he might have a mental illness. Having volunteered for mental illness support groups, I really ___________ (38) his problems when I looked at him.He paid for the session, put on a pair of gloves and then started hitting the punching bags. I watched him from a ______ (39) and wanted to help him to punch straighter and better. Then I felt it was best to leave that up to the trainer who was _____ (40) watching him.After a few seconds of punching the bag, he stopped and started staring at the _____________ (41). The trainer went up to him and _______ (42) to help him. It was almost like he woke up from a dream. He_____ (43) eye contact with the ceiling at once.Then the bell rang and it was the end of the round. _________ (44) rounds we are required to do five pushups (俯卧撑), _____ (45) all the boys that were training that night did five pushups. He _____ (46)to complete his five pushups. The bell sounded again and the next round began. He punched the bags for a few seconds and then he ___________ (47). This time he was staring at the walls which were decorated with boxing posters.It was clear to me that he could not _____ (48) for long.When I finished training, I decided to go up to him and offer him my help. I held the bag for him and asked him to punch. He _____________ (49) the bag a few times and then stopped again.I smiled at him and asked, “ Do you like boxing? ”He replied with a very shy _____ (50) on his face, “ Yes, boxing is alright. ”What else could I do than _____ (51) this man and his willingness to give it a go? Most people putself-imposed ( 自我强加的) ______ (52) on their lives and stop themselves from having a go. I kept thinking about this man while admiring him for even turning up to a boxing gym, let alone training at what appeared to be his ____ (53).There are many lessons to learn from this man. What I _____ (54) admired about this man was that he had a go! That is what _____ (55) ordinariness from greatness.So what will you have a go at?36. A. lifting B. running C. warming D. going37. A. heart B. attention C. breath D. imagination38. A. experienced B. mentioned C. overcame D. understood39. A. distance B. box C. poster D. screen40. A. still B. even C. also D. ever41. A. bags B. walls C. ceiling D. trainer42. A. offered B. promised C. seemed D. planned43. A. made B. broke C. kept D. avoided44. A. Before B. Through C. During D. Between45. A. for B. but C. or D. so46. A. struggled B. preferred C. refused D. decided47. A. slowed B. stopped C. continued D. hesitated48. A. stand B. stay C. concentrate D. remember49. A. hit B. felt C. grasped D. watched50. A. view B. look C. sight D. scene51. A. accept B. appreciate C. motivate D. notice-2 •52. A. targets B. burdens C. limitations D. minds53. A. worst B. fullest C. greatest D. hardest54. A. really B. hardly C. merely D. nearly55. A. prevents B. protects C. transforms D. separates阅读理解ASummer is slipping away from me. Some days, it makes me want to cry. Other days, I feel a sense of expectation within me just thinking about fall that makes me want to burst. Tonight, all five of us were in the family room doing our own things.At this moment, my littlest kid is my number one trouble and my number one joy. He has a tooth on the way and although it 's such a tiny thing, it 's causing so much gmrieaf.loI t and I ' m'nmothgooldiningg hito lie. I live for his afternoon nap （小睡） so I' m able to actually get dressed and use the restroom.The big E is starting school soon. The other day, I found myself a bit depressed about the end of summer and the beginning of another school year. I looked out of our front window with eyes that were heavy and a bit teary. Then, I suddenly realized just how silly this end of summer depression of mine is. I can ' thcange time. But, I can change my emotions and my thoughts. I decided not to spend my final days of summer vacation walking around with a sad face. I decided to hug the last few days of summer and remind myself that before I know it, we will be back in our school routine and all will go well.This week we plan on meeting teachers. I 'y gmirlttaokihnagvme her nails done before her first day of kindergarten. We want to bake a few dozen cookies. We 'll takeevoeunr ing walks as usual and stay up late.And last but not least , I ' ll get school cloth readIy', ll pack lunches and write lunch notes, we 'll read “The Kissing Hand, ” like we normally do, and I ' ll tuck （掖好被子） my third grader and kindergartener in their little beds before the big first day.Thank you summer, you ' ve been warm and wonderful, you 've been sweet and sticky, you' ve been refreshing and exactly what we need. And your sunsets have been amazing, so thank you.56. According to Paragraph 1, the author ________ .A. feels excitedB. has mixed feelingsC. feels worriedD. has bad feelings57. How will the author spend the final days of the summer vacation?A. Live a simple life.B. Stay at home and relax herself.C. Treasure the vacation.D. Walk around with a depressed face.58. From the passage, we can learn that the author ________ .A. is fond of reading novelsB. has two annoying childrenC. often takes evening walksD. has no time to get dressed B Ever walked to the shops only to find, once there, you ' ve completely forgotten what you went for? Or struggled to remember the name of an old friend? For years we 've accepted that a forgetful brain is as much a part of ageing as wrinkles and grey hair. But now a new book suggests that we ' ve got it all wrong. According to The Secret Life of the Grown-up Brain, by science writer Barbara Strauch, when it comes to the important things, our brains actually get better with age. In fact, she argues that some studies have found that our brain hits its peak betwee n our 40s and 60s -much later tha n previously thought.Furthermore, rather than losing many brain cells as we age, we retain them, and even produce new ones well into middle age. For years it 's been assumed that braminu,ch like the body, declines with age. But the longest, largest study into what happens to people as they age suggests otherwise.This continuing research has followed 6,000 people since 1956, testing them every seven years. It has• 3 •found that on average, participants performed better on cognitive ( 认知的) tests in their 40s and 50s than they had done in their 20s. Specifically, order people did better on tests of vocabulary, verbal memory (how many words you can remember) and problem solving.Where they performed less well was nu mber ability and perceptual speed -how fast you can push a butt on when ordered. However, with more complex tasks such as problem-solving and language, we are at our best at middle age and beyond. In short, researchers are now coming up with scientific proof that we do get wiser with age.Neuroscientists are also finding that we are happier with ageing. A recent US study found older people were much better at controlling and balancing their emotions. It is thought that when we' reyounger we need to focus more on the negative aspects of life in order to learn about the possible dangers in the world, but as we get older we 'rnevde oleuar lessons and are sub-consciously aware that we have less time left in life: therefore, it becomes more important for us to be happy.59. Barbara Strauch probably agrees that ________ .A. the young are better at handling important thingsB. people 's brains work best between their 40s and 60sC. ageing leads to the decline of the function of the brainD. wrinkles and grey hair are the only symbols of ageing60. The continuing research has found older people perform better on ________ .A. vocabulary testsB. number abilityC. perceptual speedD. body balance61. People are happier with age because ________ .A. they learn to value the time leftB. they know how to share feelingsC. they cannot focus on negative aspectsD. they do not realize the possible dangers62. What is the main idea of the passage?A. People get wiser with age.B. People get more forgetful with age.C. People get happier with age.D. People get more self-aware with age.CEveryone procrastinates. We put things off because we don 't want to do them, or because we have too many other things on our plates. Putting things off - big or small - is part of being human. But procrastination does have consequences. When your procrastination leaves you feeling discouraged, it is time to take action, and one of the best ways to get rid of it is to make an un-scheduled.An un-schedule is a weekly calendar of all the ways in which your time is already accounted for. You consider not only your timed commitments such as classes and meetings, but also your untimed activities such as meals, exercise, time with friends, and the like. Once you have made your un-schedule, you may be able to see your time is often filled with more activities than you realize, for instanc e, that you really don ' t have five hours to spend writing on the night before your paper i s due. Procrastinators o'ftivmi e wtesnd tobe unrealistic, and the un-schedule can help you outline a realistic plan. By planning accordingly, youwill not only get a better ni ght's sleep, you may also enudp with a better paper.The un-schedule might also be a good way to get started on a larger project, such as a term paper or an honors paper. You may think that you h ave “all semester ” to wgrei t inthgedone, but if you really map out how much time you have available to write on a daily and weekly basis, you will see that you need to get started sooner, rather than later. In addition, the un-schedule may reveal especially busy weeks or months, which will help you budget time for long-term projects.• 4 •Perhaps most importantly, the un-schedule can help you examine how you spend your time. You may be surprised at how much time you spend watching television, and decide to make a change. It 'e s pecially important that you build time for fun activities into your un-schedule. Otherwise, you will procrastinate in order to steal time for relaxation.You can also use the un-schedule to record your progress towards your goal. Reward yourself for your small successes.Seeing what you 've acllhhieevlpedyowui reinforce （强化） the productive behavior, andyou will feel more motivated in the following process.As you explore ways to conquer procrastination, don 't expect overnight transformation. You developed the habit over a lon g time; you aren 't goingmsatogpically. But you can change the behavior, bit by bit. Ifyou start to make an un-schedule now, you will eventually develop new habits.63. From Paragraph 2, we can know that procrastinators ________ .A. usually have sleeping problemsB. tend to be unrealistic in daily lifeC. spend more time in doing exerciseD. often fail to notice untimed activities64. Which of the following statements best reflects an un-schedule?A. “Now I have more time for fun.B. “”I can start mbyig project later. ”C. “I 'trellat myself to a movie for my progress. ”D. “I 'gmoing to have more time to finish my paper. ”65. According to the writer, people need to make an un-schedule because of their ___________ .A. interests in doing things differentlyB. determination to try out new thingsC. inability to manage time properlyD. lack of concentration on a project66. The author writes the passage to _______ .A. show concernsB. offer suggestionsC. express dissatisfactionD. make commentsDI wish documentaries, not movies. I read history books, not fiction. I use every free moment to accomplish one of the tasks on my never-ending checklist, and I am completely filled with thoughts of productivity. An hour sleeping is an hour wasted. And like the rest of 21st century America, I like it. Butthis fixation on productivity is increasingly destroying character and transforming men into robots.New York Times columnist David Brooks warned American University students of this cultural decline in a speech. “We cut off all things spiritual and emotional incaompetitive urge to stand out ”, he said, “The pressure to succeed professionally, to acquire skills, to do the things you need to do to succeed in an information age economy really became the overwhelming （难以应付的） pressure, and it sort of eclipses the thinking about character and morality.Many students happily go to college, viewing it as a next step on their rise to professional achievement. Forcing as many success-building activities into their schedules as they can, they enjoy keeping busy with little sleep. “ Today ' s outstkainddsinagre likely to spend their afternoons an d weekends shuttling fromone skill- improving activity to the next, ” Brooks wrote in an article, e more“thaWnewf e adrefsaiirleur success. ”A century ago, college was about character building. Today, our characters are in decline. We are experts on economics, material things and professional skills. We fail to discuss and understand relationships, emotions and all things spiritual. Philosophers Karl Popper divided the world into two categories: Clocks and Clouds. Clock problems are those that can be taken apart, examined and solved through deductive reasoning （演绎推理）. Clouds cannot be taken apart. Cloud problems represent whole systems that need to• 5 •be understood in a different way.“ Whenwe have a Cloud problem, we try to turn into a Clock problem, ”Brooks said. And in a reason-centered culture, adding titles to one 's resume becomes a trend. AAt merican University, 85 percent of seniors (and 89 percent of business majors) graduate with at least one practical experience which is often helpful to a student ' s future career, but can sometimes draw focus away from academics.To prevent the death of man a'ctesr,cBharoroks urges rediscovering our human natures through fallingin love. And by love he means love for a task, job, or another person. “ Synchronicity is key to happiness, he said. Rather than crazily increasing our long lists of accomplishments, we need to lose ourselves in what we do, and success will come on its own.67. From Paragraph 1, we can learn that people ________ .A. are controlled by timeB. are keen on reading booksC. are changing their charactersD. are eager to achieve more68. In Paragraph 2, the underlined word “ eclipses ” means _____________________ .A. deletesB. weakensC. worsensD. emphasizes69. The last paragraph mainly tells us that ________ .A. love is more important than focusB. the focus on human natures countsC. more work contributes to happinessD. success comes from devotion to work.70. The purpose of this passage is to ________ .A. bring awareness to character buildingB. stress the importance of productivityC. warn about the pressure to seek successD. criticize students ' desire for achievements 七选五Weighing the OptionsMaking decisions when shopping is often a tough call. Even if you 're satisfied wthiteh first dress you try on, would you go on looking for alternatives, comparing styles and prices, until literally dropped dead?Psychology researchers have studied how people make decisions and concluded there are two basic styles.“ Maximizes ” like to take the i mte and weigh a wide range of options, -sometimes every possible one —before choosing. “Satisficers ” would ratfhaesrt bthean thorough._________ (71) So even if they see what would seem to meet their requirements, they can'mt ake a decision until after they _______ 'veeveexraymoinpetiodn to make sure that they 're making the best possible choice.Researchers followed 548 job-seeking college seniors at 11 schools from October through their graduation in June. They found that the maximizers landed better jobs. _______________________ (72)“The maximizers is kicking himself because he can t examine ever'yoption and at some point had to just pick something, ”they say. “Maximizers make best decisions and end up feeling bad about them.Satisficers also have high standards, but they are happier than maximizers. Maximizers tend to be more depressed and to report a lower satisfaction with life, his research found.Faced with so many choices in our lives, we need to learn how not to waste time and energy on our decision-making._________ (74) For instance, if you 're pickrinagntaforreslutanuch meeting, first deciding on a certain part of town or type of cuisine can narrow your options.Once you've arrived at a decision, stick with it. __________ (75) To limit the number of options you canset a time for decision-making. Say you are buying a new bag, you could spend an amount of time studying features, price and value -but if you give yourself only five minutes to make a decision, and there are only• 6 •bags you can consider, you' II save time. You ' II be happier with your decision, too.A. Maximizers are people who want the best.B. First of all, decrease your range of opti ons.C. Comparing is often a must when you make a decision.D. Just accept that no decisi on is ever completely perfect.E. Satisficers make good decisions and end up feeling good.F. The other is to make decisi ons more accurately at the beg inning.G. Their start ing salaries were 20 perce nt higher but they felt worse about their jobs.WRITING 1 你的英国朋友Tom将来你家共度除夕，你打算当天下午去地铁站接他。

海淀区高三年级第一学期期末练习英语2019.01 本试卷共12 页，共150 分。

考试时长120 分钟。

考生务必将答案答在答题纸上，在试卷上作答无效。

考试结束后，将答题纸交回。

第一部分：听力理解（共三节，30 分）第一节（共 5 小题；每小题 1.5 分，满分7.5 分）听下面五段对话。

每段对话后有一道小题，从每题所给的A、B、C 三个选项中选出最佳选项。

听完每段对话后，你将有10 秒钟的时间来回答有关小题和阅读下一小题。

每段对话你将听一遍。

1.What does the womanwant?A.Thesalt.B.Thepepper.C. Thespoon.2.What will the weather be like according to theradio?A.Rainy.B.Sunny.C. Windy.3.Who are the paparazzifollowing?A.Michael.B.Kathy.C.Janice.4.What is the man’s favoritesport?A.Football.B.Baseball.C.Basketball.5.Where will the woman go thisweekend?A. To theNational Library.B. To theamusement park.C. To the shoppingmall.第二节（共10 小题；每小题 1.5 分，15 分）听下面四段对话。

每段对话后有几道小题，从每题所给的A、B、C 三个选项中选出最佳选项。

听每段对话前，你将有5 秒钟的时间阅读每小题。

听完后，每小题将给出5 秒钟的作答时间。

每段对话你将听两遍。

6.What is the woman’s researchabout?A.The movies students like best.B.The things students do afterschool.C.The sports students are interestedin.7.What is the most unexpected finding of theresearch?A.Students rarely dohousework.B.Few students go to themovies.C.Most students play computergames.听第7 段材料，回答第8 至9 题。

海淀区高三年级第一学期期末练习语文答案2019.1一、本大题共6小题，共25分。

1.（3分）D2.（3分）C3.（2分）黏合剂（聚合剂、连接器、联合器等），符合语境意思的喻体即可。

4.( 2分）夸大其词（哗众取宠、耸人听闻、故弄玄虚）（1分）唯利是图（1分）5.( 2分）C6.(13分)①( 4分）内容真实饱满；形式质朴清新，言之有文；讲求经世致用，持中守正；体现实事求是、真诚的创作态度。

（意思对即可）②（4分）评分要点：结合内容2分，分析文风特点2分。

③（5分）评分要点：指出问题1分，反思问题2分，改进2分。

二、本大题共6小题，共23分。

7.（3分）B8.（2分）D9.（3分）然而糊涂的人说：“满足（自己的）利益、欲望，以此来厚待自己。

”10.（4分）精气是指人不为利益、欲望等外物所改变的品格（人格、操守等）（2分），自强不息的奋斗精神及利国利民的担当精神（2分）。

（意思对即可）11.（5分）作者从“日月天星”各自一刻不停的运转（1分），担负平衡四季、生长万物的重任（1分），悟得人之君子应学而不止（自强不息、死而后已）（1分），以担当使万世太平、为众生谋福利的重任（2分）。

（意思对即可）12.（6分）评分要点：结合恰当的名言警句或链接材料（1分），解说君子所担重任的内容（2分），谈自己对“君子之任”的意义、价值等的理解、思考（3分）。

三、本大题共4小题，共20分。

13.（2分）壮观清静（清幽、幽静、静谧、清雅）山青水绿（山清水秀）鸟语花香……（写出整体特点或局部特点均可，答对3点得2分，答对2点得1分，答对1点不得分）14.（6分）评分要点：结合诗句(2分)，分析词人形象（2分），概括词人形象特点（2分）。

（至少分析两个特点）15.（4分）评分要点：诗句理解（2分），解说寓意（2分）。

16. ①（至若）春和景明②波澜不惊③惊涛拍岸④卷起千堆雪⑤到中流击水⑥浪遏飞舟⑦青山遮不住⑧毕竟东流去（8分，每句1分，有错别字、多字、少字，该句不得分）四、本大题共5小题，共22分。