2017届上海市普陀区高三下学期质量调研(二模)数学试卷(解析版)

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【全国区级联考】上海市普陀区2017届高三下学期质量调研(二模)数学试题(解析版)

2016-2017年上海市普陀区高三下学期质量调研（二模）数学一、填空题：共12题1. 计算：.【答案】【解析】由题意，得；故答案为1.2. 函数的定义域为.【答案】【解析】要使有意义，须，即，解得或，即函数的定义域为；故答案为.3. 若，则.【答案】【解析】因为，所以，即，即，解得或，又因为，所以；故答案为3.4. 若复数表示虚数单位)，则.【答案】【解析】因为，所以；故答案为.5. 曲线为参数)的两个顶点之间的距离为.【答案】【解析】因为，则，即曲线的两个顶点为，即两个顶点之间的距离为2；故答案为2.6. 若从一副张的扑克牌中随机抽取张，则在放回抽取的情形下，两张牌都是的概率为.(结果用最简分数表示).【答案】【解析】由题意，得从一副张的扑克牌中随机抽取张，则在放回抽取的情形下，两张牌都是K的概率为；故答案为.7. 若关于的方程在区间上有解，则实数的取值范围是.【答案】【解析】将化成，即，因为，所以，，即；故答案为.8. 若一个圆锥的母线与底面所成的角为,体积为,则此圆锥的高为.【答案】【解析】设圆锥的高为，底面圆的半径为，因为圆锥的母线与底面所成的角为，体积为，所以，解得；故答案为5.9. 若函数)的反函数为，则= .【答案】【解析】令，即，解得或，即或（舍）；故答案为.10. 若三棱锥的所有的顶点都在球的球面上，平面，，，则球的表面积为.【答案】【解析】由题意，得三棱锥是长方体的一部分（如图所示）球是该长方体的外接球，其中，设球的半径为，则，则球O的表面积为；故答案为.11. 设，若不等式对于任意的恒成立，则的取值范围是.【答案】【解析】因为不等式对于任意的恒成立，所以不等式对于任意的恒成立，令，即对于任意的恒成立，因为，所以，则，即，解得或（舍）；故答案为.【方法点晴】本题主要考查三角函数的有界性以及不等式恒成立问题，属于难题．不等式恒成立问题常见方法：①分离参数恒成立(可)或恒成立（即可）；②数形结合(图象在上方即可)；③讨论最值或恒成立；④讨论参数.本题是利用方法③求得的最大值.12. 在△中，、分别是、的中点，是直线上的动点.若△的面积为，则的最小值为.【答案】【解析】因为、分别是、的中点，且是直线上的动点，所以到直线的距离等于到直线的距离的一半，所以，则，所以，则，由余弦定理，得，显然，都为正数，所以，，，令，则，令，则，当时，，当时，，即当时，取得最小值为；故答案为.二、选择题：共4题13. 动点在抛物线上移动，若与点连线的中点为，则动点的轨迹方程为A. B. C. D.【答案】B【解析】设，因为与点连线的中点为，所以，又因为点在抛物线上移动，所以，即；故选B.14. 若、，则“”是“”成立的A. 充分非必要条件B. 必要非充分条件C. 充要条件D. 既非充分也非必要条件【答案】D【解析】因为，所以“”不是“”成立的充分条件，若，则不存在，所以“若,，则”为真命题，即“”不是“”成立的必要条件，所以“”是“”成立的既非充分也非必要条件；故选D.15. 设、是不同的直线，、是不同的平面，下列命题中的真命题为A. 若，则B. 若，则C. 若，则D. 若，则【答案】C【解析】若，则相交或平行，故A错误，若，则相交或平行，故B错误，若，则由面面垂直的判定定理得，故D错误、C正确；故选C.【方法点晴】本题主要考查线面平行的判定与性质、面面垂直的性质及线面垂直的判定，属于难题.空间直线、平面平行或垂直等位置关系命题的真假判断，常采用画图（尤其是画长方体）、现实实物判断法（如墙角、桌面等）、排除筛选法等；另外，若原命题不太容易判断真假，可以考虑它的逆否命题，判断它的逆否命题真假，原命题与逆否命题等价.16. 关于函数的判断，正确的是A. 最小正周期为，值域为，在区间上是单调减函数B. 最小正周期为，值域为，在区间上是单调减函数C. 最小正周期为，值域为，在区间上是单调增函数D. 最小正周期为，值域为，在区间上是单调增函数【答案】C............三、解答题：共5题17. 在正方体中，、分别是、的中点.(1)求证：四边形是菱形；(2)求异面直线与所成角的大小 (结果用反三角函数值表示) .【答案】(1)证明见解析；（2）.【解析】试题分析：（1）建立空间直角坐标系，如图所示：先证其是平行四边形，再根据空间向量模相等说明邻边相等即可；（2）可得，利用空间向量夹角余弦公式可得结果.试题解析：（1）设正方体的棱长为1，建立空间直角坐标系，如图所示：则,,,,所以,即且,故四边形是平行四边形又因为,所以故平行四边形是菱形(2)因为设异面直线与所成的角的大小为所以, 故异面直线与所成的角的大小为.【方法点晴】本题主要考查异面直线所成的角以及空间向量的应用，属于难题.求异面直线所成的角主要方法有两种：一是向量法，根据几何体的特殊性质建立空间直角坐标系后，分别求出两直线的方向向量，再利用空间向量夹角的余弦公式求解；二是传统法，利用平行四边形、三角形中位线等方法找出两直线成的角，再利用平面几何性质求解.18. 已知函数、为常数且).当时，取得最大值.(1)计算的值；(2)设，判断函数的奇偶性，并说明理由.【答案】(1)；（2）偶函数.【解析】试题分析：首先，根据辅助角公式得到，然后根据最值建立等式，得到，再化简函数.（1）将代入解析式求值；（2）求出解析式，利用奇偶函数定义判断奇偶性.试题解析：(1)，其中根据题设条件可得，即化简得，所以即，故所以(2)由(1)可得，，即故所以)对于任意的)即，所以是偶函数.19. 某人上午7时乘船出发，以匀速海里/小时从港前往相距50海里的港，然后乘汽车以匀速千米/小时()自港前往相距千米的市，计划当天下午4到9时到达市.设乘船和汽车的所要的时间分别为、小时，如果所需要的经费(单位：元)(1)试用含有、的代数式表示；(2)要使得所需经费最少，求和的值，并求出此时的费用.【答案】(1)；（2）.【解析】试题分析：（1）分析题意，先用表示，先用表示，代入，化简即可；（2）求出满足的约束条件，由约束条件画出可行域，要求走得最经济，即求可行域中的最优解，将目标函数看成是一条直线，分析目标函数与直线截距的关系，进而求出最优.试题解析：(1)，得，得所以(其中)(2)其中，令目标函数, 可行域的端点分别为则当时，所以(元),此时答：当时，所需要的费用最少，为元.【方法点晴】本题主要考查线性规划的应用及求目标函数的最值，属简单题.求目标函数最值的一般步骤是“一画、二移、三求”：（1）作出可行域（一定要注意是实线还是虚线）；（2）找到目标函数对应的最优解对应点（在可行域内平移变形后的目标函数，最先通过或最后通过的顶点就是最优解）；（3）将最优解坐标代入目标函数求出最值.20. 已知曲线，直线经过点与相交于、两点.(1)若且，求证：必为的焦点；(2)设，若点在上，且的最大值为，求的值；(3)设为坐标原点，若，直线的一个法向量为，求面积的最大值.【答案】(1)证明见解析；（2）或；（3）.【解析】试题分析：（1）利用两点之间距离公式，即可求得的值，由椭圆的方程，即可求得焦点坐标，即可证必为的焦点；（2）利用两点之间距离公式，根据二次函数的单调性，当时，取最大值，代入即可求得的值；（3）求得直线的方程，代入方程，由韦达定理，弦长公式及点到直线的距离公式，利用基本不等式的性质，即可求得面积的最大值.试题解析：(1)，解得，所以点由于，故的焦点为，所以在的焦点上.(2)设，则(其中)对称轴，所以当时，取到最大值，故，即，解得或因为，所以.(3),,将直线方程与椭圆方程联立，消去得，其中恒成立。

2017年上海市普陀区中考二模试卷（含听力文本和答案）

2016学年第二学期普陀区初三模拟考英语试卷2017.4Part 1 Listening (第一部分听力)I. Listening comprehension (听力理解）（共30 分）A. Listen and choose the right picture (根据你听到的内容，选出相应的图片）（6分)B. Listen to the dialogue and choose the best answer to the question you hear (根据你听到的对话和问题，选出最恰当的答案）（8分）7. A. Sunny.B. Cloudy. C. Snowy. D. Rainy.8. A. By car. B. By underground. C. By taxi. D. By bus.9. A. Yesterday. B. Today. C. Tomorrow. D. Next week.10. A. Watching a basketball game. B. Going to work.C. Shopping in the new mallD. H aving Italian food.11. A. Because she dislikes watching plays.B. Because she needs to see the doctor.C. Because she has watched the playD. Because she'll visit her sick cousin.12. A. A library. B. A kindergarten.C. A shopping centre.D. A restaurant.13. A. Wait for the man B.Drive to the party.C. Call her boss.D. Cancel their dinner.14. A. Discussing an interesting film. B. Complaining about a cinema.C. Sharing their favourite music.D. Talking about their troubles.C. Listen to the passage and tell whether the following statements are true or false (判断下列句子是否符合你听到的内容，符合的用“T”表示，不符合的用“F”表示）（6分）15. By the age of 16, Tony had lived in many countries with his parents.16. Tony and Maureen found a job as tourist guides after they got married.17. It took the couple half a year to travel from London to Australia.18. Tony’s first guidebook was about their trip through some Asian countries.19. The couple stopped travelling after they started a company called Lonely Planet.20. Today Lonely Planet is a big company with 400 members and over 650 guidebooks.D. Listen to the passage and complete the following sentences (听短文，完成下列句子。

上海市普陀区高三数学下学期质量调研考试试题理(普陀二模)苏教版

上海市普陀区2014届高三4月教学质量调研（二模）数学理试题考生注意：1.答卷前，考生务必在答题纸上将姓名、考试号填写清楚，并在规定的区域贴上条形码.2.本试卷共有23道题，满分150分.考试时间120分钟.3.本试卷另附答题纸，每道题的解答必须写在答题纸的相应位置，本卷上任何解答都．．．．．．．．．．．．．．．．．．．．．不作评分依据．．．．．．. 一、填空题（本大题满分56分）本大题共有14小题， 1．若复数ii i z 1=（i 是虚数单位），则=z . 2．若集合}40,tan |{π≤<==x x y y A ，}02|{2<--=x x x B ，则=B A .3．【理科】方程1)4(log )1(log 42=+-+x x 的解=x .4．【理科】若向量),1(x a =，)1,2(=b ，且b a ⊥，则=+||b a . 5．【理科】若0>a ，在极坐标系中，直线2)3cos(=+⋅πθρ与曲线a =ρ相切，则实数=a .6．【理科】若偶函数)(x f y =(R x ∈)满足条件：)1()(x f x f +=-，则函数)(x f 的一个周期为 . 7．【理科】若P 为曲线⎩⎨⎧==ααtan sec y x （α为参数）上的动点，O 为坐标原点，M 为线段OP的中点，则点M 的轨迹方程是 .8．【理科】某质量监测中心在一届学生中随机抽取39人，对本届学生成绩进行抽样分析.统计分析的一部分结果，见下表:根据上述表中的数据，可得本届学生方差的估计值为 (结果精确到1.0).9．【理科】等比数列}{n a 的前n 项和为n S ，若对于任意的正整数k ，均有)(lim k n n k S S a -=∞→成立，则公比=q .10．【理科】在一个质地均匀的小正方体六个面中，三个面标0，两个面标1，一个面标2，将这个小正方体连续掷两次，若向上的数字的乘积为偶数ξ，则=ξE .11．【理科】如图所示，在一个)12()12(-⨯-n n (N n ∈且2≥n )的正方形网格内涂色,要求两条对角线的网格涂黑色，其余网格涂白色.若用)(n f 表示涂白色网格的个数与涂黑色网格的个数的比值，则)(n f 的最小值为 .12．【理科】若三棱锥ABC S -的底面是边长为2的正三角形，且⊥AS 平面SBC ，则三棱锥ABC S -的体积的最大值为 .13．若ij a 表示n n ⨯阶矩阵⎪⎪⎪⎪⎪⎪⎭⎫⎝⎛nn a25191410181396128537421中第i 行、第j 列的元素（i 、n j ,,3,2,1 =），【理科】则=nn a （结果用含有n 的代数式表示）.14．【理科】已知函数⎩⎨⎧>≤+-=0,ln 0,2)(2x x x x x x f ，若不等式1|)(|-≥ax x f 恒成立，则实数a的取值范围是 .二、选择题（本大题满分20分）本大题共有4题，每题有且只有一个结论是正确的，必须把正确结论的代号写在答题纸相应的空格中. 每题选对得5分，不选、选错或选出的代号超过一个（不论是否都写在空格内），或者没有填写在题号对应的空格内，一律得零分. 15. 下列命题中，是假命题．．．的为…………………………………………………………………………（）)(A 平行于同一直线的两个平面平行. )(B 平行于同一平面的两个平面平行. )(C 垂直于同一平面的两条直线平行. )(D 垂直于同一直线的两个平面平行.16.【理科】已知曲线1C :122=+y m x （1>m ）和2C :122=-y nx （0>n）有相同的焦第11题图点，分别为1F 、2F ,点M 是1C 和2C 的一个交点,则△21F MF 的形状是………………………………………（）)(A 锐角三角形. )(B 直角三角形. )(C 钝角三角形. )(D 随m 、n 的值的变化而变化. 【17. 若函数a x x x f -+=2)(，则使得“函数)(x f y =在区间)1,1(-内有零点”成立的一个必要非充分条件是…………………………………………………………………………………………………………（）)(A 241≤≤-a . )(B 241<≤-a . )(C 20<<a . )(D 041<<-a .18. 对于向量i PA （n i ,2,1=），把能够使得||||||21n PA PA PA +++ 取到最小值的点P 称为i A （n i ,2,1=）的“平衡点”. 如图，矩形ABCD 的两条对角线相交于点O ,延长BC 至E ,使得CE BC =，联结AE ,分别交BD 、CD 于F 、G 两点.下列结论中，正确的是……………………………………（）)(A A 、C 的“平衡点”必为O . )(B D 、C 、E 的“平衡点”为D 、E的中点.)(C A 、F 、G 、E 的“平衡点”存在且唯一. )(D A 、B 、E 、D 的“平衡点”必为F .三、解答题（本大题满分74分）本大题共有5题，解答下列各题必须在答题纸规定的方框内写出必要的步骤. 19、 (本题满分12分) 本题共有2个小题，第1小题满分6分，第2小题满分6分．如图，在xoy 平面上，点)0,1(A ，点B 在单位圆上，θ=∠AOB （πθ<<0）（1）【理科】若点)54,53(-B ，求)42tan(πθ+的值；（2）若OC OB OA =+，四边形OACB 的面积用θS 表示，求OC OA S ⋅+θ的取值范围.20、(本题满分14分) 本题共有2个小题，第1小题满分6分，第2小题满分8分．如图，已知AB 是圆柱1OO 底面圆O 的直径，底面半径1=R ，圆柱的表面积为π8；点C 在底面圆O 上，且直线C A 1与下底面所成的角的大小为︒60. （1）【理科】求点A 到平面CB A 1的距离；（2）【理科】求二面角C B A A --1的大小（结果用反三角函数值表示）.21、(本题满分14分) 本题共有2个小题，第1小题满分6分，第2小题满分8分．已知函数12)(-=x x f 的反函数为)(1x f y -=，记)1()(1-=-x f x g .（1）求函数)()(21x g x fy -=-的最小值；（2）【理科】若函数)()(2)(1x g m x f x F -+=-在区间),1[+∞上是单调递增函数，求实数m 的取值范围.22、（本题满分16分）本题共有3个小题，第（1）小题4分，第（2）小题6分，第（3）小题6分．已知曲线Γ:x y 42=，直线l 经过点)2,0(且其一个方向向量为),1(k d =. （1）若曲线Γ的焦点F 在直线l 上，求实数k 的值；（2）当1-=k 时，直线l 与曲线Γ相交于A 、B 两点，求||AB 的值；（3）当k （0>k ）变化且直线l 与曲线Γ有公共点时，是否存在这样的实数a ,使得点第20题图)0,(a P 关于直线l 的对称点),(00y x Q 落在曲线Γ的准线上. 若存在,求出a 的值；若不存在，请说明理由.23、（本题满分18分）本题共有3个小题，第（1）小题4分，第（2）小题6分，第（3）小题8分.用记号∑=ni ia表示n a a a a a +++++ 3210，∑==ni in ab 02，其中N i ∈，*N n ∈.（1）设n n n n nk kx a x a x a x a a x 221212221021)1(+++++=+--=∑ （R x ∈），求2b 的值；（2）若0a ，1a ，2a ，…，n a 成等差数列，求证：()∑==ni iniC a 0102)(-⋅+n n a a；（3）【理科】在条件（1）下，记∑=-+=ni i nii n Cb d 1])1[(1，且不等式n n b d t ≤-⋅)1(恒成立，求实数t 的取值范围.第22题图数学理答案一、填空题（本大题满分56分）本大题共有14小题，要求直接将结果填写在答题纸对应的空格中.每个空格填对得4分，填错或不填在正确的位置一律得零分.1.i +-1；2.]1,0(；3.【理科】5；4. 【理科】10；5. 【理科】2；6. 【理科】1等；7. 【理科】4122=-y x ；；8.【理科】.56； 9. 【理科】21； 10. 【理科】83；； 11. 【理科】 54； 12. 【理科】21； 13. 【理科】1222+-n n ；14、5二、选择题（本大题满分20分）本大题共有4题，每题有且只有一个结论是正确的，必须把正确结论的代号写在答题纸相应的空格中. 每题选对得5分，不选、选错或选出的代号超过一个（不论是否都写在空格内），或者没有填写在题号对应的空格内，一律得零分.三、解答题（本大题满分74分）本大题共有5题，解答下列各题必须写出必要的步骤. 19、 (本题满分12分) 本题共有2个小题，第1小题满分6分，第2小题满分6分．【解】（1）【理科】由于)54,53(-B ，θ=∠AOB ，所以53cos -=θ，54sin =θ 253154cos 1sin 2tan =-=+=θθθ于是)42tan(πθ+321212tan12tan1-=-+=-+=θθ（2）θS θθsin sin 11=⨯⨯=由于)0,1(=,)sin ,(cos θθ=……7分，所以)sin ,cos 1(θθ+=+=OB OA OCθθθcos 1sin 0)cos 1(1+=⨯++⨯=⋅OC OA …………9分OC OA S ⋅+θ1)4sin(21cos sin ++=++=πθθθ（πθ<<0）由于4544ππθπ<+<，所以1)4sin(22≤+<-πθ，所以120+≤⋅+<S θ20、(本题满分14分) 本题共有2个小题，第1小题满分6分，第2小题满分8分．【解】（1）【理科】设圆柱的母线长为l ，则根据已知条件可得，πππ8222=+⋅=Rl R S 全，1=R ，解得3=l因为⊥A A 1底面ACB ，所以AC 是C A 1在底面ACB 上的射影，所以CA A 1∠是直线C A 1与下底面ACB 所成的角，即CA A 1∠=︒60在直角三角形AC A 1中，31=AA ，CA A 1∠=︒60，3=AC .AB 是底面直径，所以6π=∠CAB .以A 为坐标原点，以AB 、1AA 分别为y 、z 轴建立空间直角坐标系如图所示：则)0,0,0(A 、)0,23,23(C 、)3,0,0(1A 、)0,2,0(B ,于是)0,23,23(=,)3,2,0(1=A ,)0,21,23(-=CB 设平面CB A 1的一个法向量为),,(z y x =，则⎪⎩⎪⎨⎧=-=+-⇒⎪⎩⎪⎨⎧=⋅=⋅03202123001z y y x A CB n ，不妨令1=z ，则)1,23,23(=n ，所以A 到平面CB A 1的距离232|4943|||=+==n AC n d 所以点A 到平面CB A 1的距离为23。

2017年-上海各区-数学高三二模试卷和答案

宝山2017二模一、填空题（本大题共有12题，满分54分，第16题每题4分，第712题每题5分）考生应在答题纸的相应位置直接填写结果.1.若集合{}|0A x x =>，{}|1B x x =<，则A B ⋂=____________2.已知复数z1z i ⋅=+（i 为虚数单位），则z =____________ 3.函数()sin cos cos sin x x f x x x=的最小正周期是____________4.已知双曲线()2221081x y a a -=>的一条渐近线方程3y x =，则a =____________ 5.若圆柱的侧面展开图是边长为4的正方形，则圆柱的体积为____________6.已知,x y 满足0220x y x y x -≤⎧⎪+≤⎨⎪+≥⎩，则2z x y =+的最大值是____________7.直线12x t y t =-⎧⎨=-⎩（t 为参数）与曲线3cos 2sin x y θθ=⎧⎨=⎩（θ为参数）的交点个数是____________8.已知函数()()()220log 01xx f x x x ⎧≤⎪=⎨<≤⎪⎩的反函数是()1f x -，则12f -1⎛⎫= ⎪⎝⎭____________9.设多项式()()()()23*11110,nx x x x x n N ++++++++≠∈的展开式中x 项的系数为n T ，则2limnn T n →∞=____________10.生产零件需要经过两道工序，在第一、第二道工序中产生的概率分别为0.01和p ，每道工序产生废品相互独立，若经过两道工序得到的零件不是废品的概率是0.9603，则p =____________11.设向量()(),,,m x y n x y ==-，P 为曲线()10m n x ⋅=>上的一个动点，若点P 到直线10x y -+=的距离大于λ恒成立，则实数λ的最大值为____________12.设1210,,,x x x 为1,2,,10的一个排列，则满足对任意正整数,m n ，且110m n ≤<≤，都有m n x m x n +≤+成立的不同排列的个数为____________二、选择题（本大题共有4题，满分20分，每题5分）每题有且只有一个正确选项，考生应在答题纸的相应位置，将代表正确选项的小方格涂黑.13.设,a b R ∈，则“4a b +>”是“1a >且3b >”的（） A. 充分而不必要条件B. 必要而不充分条件C. 充要条件D. 既不充分又不必要条件14.如图，P 为正方体1111ABCD A B C D -中1AC 与1BD 的交点，则PAC 在该正方体各个面上的射影可能是（）A. ①②③④B.①③C. ①④D.②④15.如图，在同一平面内，点P 位于两平行直线12,l l 同侧，且P 到12,l l 的距离分别为1，3.点,M N 分别在12,l l 上，8PM PN +=，则PM PN ⋅的最大值为（）A. 15B. 12C. 10D. 916.若存在t R ∈与正数m ，使()()F t m F t m -=+成立，则称“函数()F x 在x t =处存在距离为2m 的对称点”，设()()20x f x x xλ+=>，若对于任意()2,6t ∈，总存在正数m ，使得“函数()f x 在x t =处存在距离为2m 的对称点”，则实数λ的取值范围是（）A. (]0,2B. (]1,2C. []1,2D. []1,4三、解答题（本大题共有5题，满分76分）解答下列各题必须在答题纸的相应位置写出必要的步骤.17.（本题满分14分，第1小题满分8分，第2小题满分6分）如图，在正方体1111ABCD A B C D -中，E 、F 分别是线段BC 、1CD 的中点. （1）求异面直线EF 与1AA 所成角的大小；（2）求直线EF 与平面11AA B B 所成角的大小.18.（本题满分14分，第1小题6分，第2小题8分）已知抛物线()220y px p =>，其准线方程为10x +=，直线l 过点()(),00T t t >且与抛物线交于A 、B 两点，O 为坐标原点.（1）求抛物线方程，并证明：OA OB ⋅的值与直线l 倾斜角的大小无关；（2）若P 为抛物线上的动点，记PT 的最小值为函数()d t ，求()d t 的解析式.19.（本题满分14分，第1小题6分，第2小题8分）对于定义域为D 的函数()y f x =，如果存在区间[](),m n D m n ⊆<，同时满足：①()f x 在[],m n 内是单调函数；②当定义域是[],m n 时，()f x 的值域也是[],m n 则称函数()f x 是区间[],m n 上的“保值函数”.（1）求证：函数()22g x x x =-不是定义域[]0,1上的“保值函数”；（2）已知()()2112,0f x a R a a a x=+-∈≠是区间[],m n 上的“保值函数”，求a 的取值范围.20.（本题满分16分，第1小题满分4分，第2小题满分6分，第3小题满分6分）数列{}n a 中，已知()12121,,n n n a a a a k a a ++===+对任意*n N ∈都成立，数列{}n a 的前n 项和为n S .（这里,a k 均为实数）（1）若{}n a 是等差数列，求k ；（2）若11,2a k ==-，求n S ; （3）是否存在实数k ，使数列{}n a 是公比不为1的等比数列，且任意相邻三项12,,m m m a a a ++按某顺序排列后成等差数列？若存在，求出所有k 的值；若不存在，请说明理由.21.（本题满分18分，第1小题满分4分，第2小题满分6分，第3小题满分8分）设T,R 若存在常数0M >，使得对任意t T ∈，均有t M ≤，则称T 为有界集合，同时称M 为集合T 的上界.（1）设121|,21x xA y y x R ⎧⎫-==∈⎨⎬+⎩⎭、21|sin 2A x x ⎧⎫=>⎨⎬⎩⎭，试判断1A 、2A 是否为有界集合，并说明理由；（2）已知()2f x x u =+，记()()()()()()11,2,3,n n f x f x f x f f x n -===.若m R ∈，1,4u ⎡⎫∈+∞⎪⎢⎣⎭，且(){}*|n B f m n N =∈为有界集合，求u 的值及m 的取值范围；（3）设a 、b 、c 均为正数，将()2a b -、()2b c -、()2c a -中的最小数记为d ，是否存在正数()0,1λ∈，使得λ为有界集合222{|,dC y y a b c ==++a 、b 、c 均为正数}的上界，若存在，试求λ的最小值；若不存在，请说明理由.宝山区答案1.(0,1)2.13. π4.35. 5.16. 37. 28. 19.1210. 0.03 11.212.512 13. B14. C15.A16.A17. （1）（2）arctan 218.（1）24y x =，证明略（2）2)(t),(0t 2)d t ⎧≥⎪=⎨<<⎪⎩19. （1）证明略（2）12a或32a 20. （1）12k =（2）2(21,),(2,)n n n k k N S n n k k N **⎧-=-∈=⎨=∈⎩ （3）25k =-21.（1）1A 为有界集合，上界为1；2A 不是有界集合（2）14u =，11,22m ⎡⎤∈-⎢⎥⎣⎦ （3）15λ=解析：（2）设()()011,,,1,2,3,...n n a m a f m a f a n -====，则()n n a f m =∵()2114a f m m u ==+≥，则222111111024a a a a u a u ⎛⎫-=-+=-+-≥ ⎪⎝⎭且211111024n n n n n a a a u a a ---⎛⎫-=-+-≥⇒≥ ⎪⎝⎭若(){}*|N n B f m n =∈为有界集合，则设其上界为0M ，既有*0,N n a M n ≤∈∴()()()112211112211......n n n n n n n n n a a a a a a a a a a a a a a a ------=-+-++-+=-+-++-+2222121111111...242424n n a u a u a u m u --⎛⎫⎛⎫⎛⎫=-+-+-+-++-+-++ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭222212111111...22244n n a a a m n u u n u u --⎡⎤⎛⎫⎛⎫⎛⎫⎛⎫⎛⎫=-+-++-++-+≥-+⎢⎥ ⎪ ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭⎝⎭⎝⎭⎢⎥⎣⎦若0n a M ≤恒成立，则014n u u M ⎛⎫-+≤ ⎪⎝⎭恒成立，又11044u u ≥⇒-≥ ∴14u =，∴()214f x x =+ 设12m λ=+（i ）0λ>，则()22101011112422a a f m m a a λλλ⎛⎫⎛⎫-=-=++-+=⇒>> ⎪ ⎪⎝⎭⎝⎭∴111...2n n a a a m ->>>>>记()()212g x f x x x ⎛⎫=-=- ⎪⎝⎭，则当1212x x >>时，()()12g x g x >∴()()()2111110n n n n n g a f a a a a g m a a λ----=-=->=-=∴()211n a a n λ>+-，若0na M ≤恒成立，则0λ=，矛盾。

2017届上海市普陀区高考二模试卷(含答案)

普陀区2016学年高三年级第二次学业质量调研测试英语学科试卷(时间120分钟，满分140分)考生注意：I.本试卷共12页。

满分140分。

考试时间120分钟。

2.答题前，考生务必在答题卡(纸)上用钢笔或水笔清楚填写姓名、准考证号，并用铅笔正确涂写准考证号。

3.答案必须全部涂写在答题卡(纸)上。

第1-20小题，第31-70小题，均由机器阅卷，考生应将代表正确答案的小方格用铅笔涂黑。

注意试题题号和答题纸编号一一对应，不能错位。

答案需要更改时，必须将原选项擦去，重新选择。

答案不能涂写在试卷上，涂写在试卷上一律不给分。

第21-30小题，第IV, V大题(即第72-75小题)和VI大题，其答案用钢笔或水笔写在答题纸上，如用铅笔答题或写在试卷上也一律不给分。

I. Listening Comprehension（略）II. Grammar and VocabularySection ADirections: After reading the passage below, fill in the blanks to make the passage coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.Wildlife in DeclineThe populations of Earth’s wild vertebrates (脊椎动物）have declined by 58% over the past four decades, according to the Living Planet Report 2016 published by the World Wildlife Fund.Climate change and activities such as deforestation and poaching（偷猎）are in large part (21)______(blame) for the decline. If the trend continues, by 2020, the world (22)________(lose) two-thirds of its vertebrate biodiversity. “Sadly, there is no sign yet (23)________ this rate will decrease,” the report says.“Across land, fresh water and the oceans, human activities are forcing wildlife populations to the edge," says Marco Lambertini, director-general of WWF International.The Living Planet Report is published every two years. It aims to provide an assessment of the state of the world’s wildlife. The 2016 study included 3700 different species of birds, fish, mammals, amphibians and reptiles around the world. The team collected data from more than 3000 sources, including government statistics and surveys (24) ______ (carry) out by conservation groups. They then analyzed (25) ______ the population sizes had changed over time.Lambertini said some groups of animals had done worse than others. ''We do see particularly strong declines (26) ______ the freshwater environment. For freshwater species alone, the decline stands at 81% since 1970. This is related to the way that water (27)________(use) and taken out of freshwater systems, and also to the fragmentation（分裂）of freshwater systems through dam building, for example.”The report also highlighted other species, such as African elephants, (28) ________ nave suffered huge declines in recent years, and sharks, which are threatened by overfishing.(29) ________ ________ ________ all the terrifying facts, however, some conservationists say there is still hope. “One of the things that I think is the most important is that these wild animals haven't yet gone extinct,” said Robin Freeman，head of the Zoological Societ y of London. “On the whole, (30) ________ are not dying out, andthat means we still have opportunities to do something about the decline.”Section BDirections: Fill in each blank with a proper word chosen from the box. Each word can be used only once. Note that there is one word more than you need.My job puts me in contact with extraordinary leaders in many fields. So I tend to ____31____ a lot on leadership and how we can inspire successful teamwork, cooperation, and partnerships. In my experience, it is clear that the most successful leaders—both men and women—always demonstrate three ____32____ traits.TrustworthinessLeaders must set an example of honesty and justice and earn the trust of their teams through their everyday actions. When you do so with positive energy and enthusiasm for ____33____ goals and purpose, you can deeply connect with your team and customers. A culture of trust enables you to empower employees and ____34____ the foundation for communication, accountability, and continuous improvement.Compassion (共情)You can't forget that organizational success ____35____ from the hearts and minds of the men and women you lead. Rather than treating your people as you’d like to be treated, treat them as they would like to be treated. Small gestures like choosing face-to-face meetings or sending personal ____36____ can have an enormous impact on the spirits of the teams. In addition to thanks and praise, you must also understand people’s needs, pressures, and individual goals, which will allow you to lead them more effectively and ____37____ to their personal ambitions and professional development.DecisivenessIn times of ____38____ employees long for clarity. As a leader, you won't always have all of the answers—no one expects you to—so you must be open to listening and learning from others. Once you understand a particular challenge and ____39____ the options, you have to be confident in making bold and optimistic decisions.Successful leadership demands a lifelong commitment to sharpening these three basic skills. Wherever you have the opportunity to ____40____, the qualities of trustworthiness, compassion, and decisiveness are the keys to leadership and organizational success.Boxing is a popular sport that many people seem to be fascinated by. Newspapers, magazines and sports programmes on TV frequently ____41____ boxing matches. Professional boxers earn a lot of money, and successful boxers are ____42____ as big heroes.It seems to me that some people, especially men, find it ____43____ because it is an aggressive sport. When they watch a boxing match, they can t ____44____ the winning boxer, and this gives them the feeling of being a t ____45____ themselves. It is a fact that many people have feelings of aggressionIII. Reading ComprehensionSection ADirections: 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.Boxing is a popular sport that many people seem to be fascinated by . Newspapers , magazines and sports programmes on TV frequently _________boxing matches . Professional boxers earn a lot of money , and successful boxers are _______as big heroes.It seems to me that people , especially men ,find it _______because it is an aggressive sport . When they watch a boxing match , they can _______ the winning boxer , and this gives them the feeling of being a ______ themselves . It is a fact that many people have feeling of aggression from time to time , but they cannot show their _______in their everyday lives . Watching a boxing match gives them an outlet for this aggression .However , there is a ______side to boxing . It can be a very dangerous sport . Although boxers wear gloves during the fights , and amateur boxers ______have to wear helmets , there have frequently been accident in both professional and amateur boxing , sometimes with ________consequences . Boxers have suffered from head injuries , and occasionally , fighters have even been killed as a result of being knocked out in the__________. Furthermore , studies have shown that there are often long-term effects of boxing , in the form of serious brain _______,even if a boxer has never been knocked out .I am personally not at all in ______of aggressive sports like boxing . I think it would be better if less time was _______to aggressive sports on TV, and we welcomed more men and women from non-aggressive sports as our heroes and heroines in our society . I believe that the world is aggressive enough already ! Of course , people like _______sports , and so do I , but I think that ______other people in an aggressive way is not something that should be regarded as a sport.41. A. broadcast B. cover C. host D. design42. A. kept B. individual C. thought D. treated43. A. appealing B. subjective C. violent D. challenging44. A. pick up B. believe in C. identify with D. long for45. A. winner B. spectator C. inspector D. trainer46. A. ambition B. aggression C. energy D. strength47. A. positive B. indifferent C. deadly D. negative48. A. otherwise B. somehow C. even D. barely49. A. dramatic B. eye-catching C. emotional D. special50. A. court B. ring C. pitch D. yard51. A. loss B. drain C. damage D. disorder52. A. favour B. process C. charge D. power53. A. shifted B. transformed C. given D. delivered54. A. competitive B. quiet C. cooperative D. regular55. A. invading B. insulting C. teasing D. hittingSection BDirections: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. Choose the one that fits best according to the information given in the passage you have just read.(A)FrankensteinFrankenstein was a book by Mary Shelly ----it’s been adapted for the screen dozens of times. The story of Frankenstein is told through a series of letters written by Captain Robert Walton to his sister , as he leads an expedition （长征）to the North Pole . On the way , he meets Victor Frankenstein , who tells Walton the story of his life. Frankenstein is the sur name of the guy who creates the monster . The monster doesn’t actually have a game . Anyway , Victor is a scientist who’s desperate to discover the secret of life . After years of study , he makes an enormous creature out of human remains and brings it to life . Victor intends it to be beautiful . Unfortunately , the creature turns out really hideous , and Victor runs away in terror . Although the monster is good and kind , humans are scared of it . When they mistreat it , the monster becomes angry and evil . Wanting revenge on its creator , the monster murders Dr. Frankenstein’s brother , his wife , and his best friend . When Victor figures out the monster is behind all the deaths , he swears to track it down and kill it .This book was written in 1816, right after a period called the Enlightenment . The Enlightenment emphasized the pursuit of knowledge and reason , and gave rise to the scientific method . Mary Shelley criticized the Enlightenment through the character of Victor Frankenstein , “ He is a neg ative example of an Enlightenment scientist -------he pursues knowledge at any cost , and his obsession with discovering the secret of life destroys him , as well as his friends and family .” Some Enlightenment thinkers might have seen such a loss as neces sary for the advancement of science , but not Mary Shelley . She and her husband , poet Percy Shelly , were part of the Romanic Movement in art and literature . Romancism was a reacrion against the Enlightenment’s embrace of rationality and reason . The Romantics emphasized emotion over rationality , and thought people should feel awe and terror in regard to nature . Frankenstein incorporates all these ideas. To Shelley , Frankenstein doesn’t fear and respect the world of nature enough ------she says that by tempering with nature , he brings about complete disaster . Frankenstein is not just a great Romantic novel . It’s also considered one of the first major works of science fiction . It influences a whole generation of writers , and the monster has become one of the most recognizable figures in Western culture.56. Which of the following is closest in the meaning to ‘hideous’ in Paragraph 1?A. UnattractiveB. EngagingC. CharmingD. Handsome57. What is Victor Frankenstein’s fatal weakness?A. His love of scienceB. His rejection of his own creationC. His lack of respect for natureD. His inability to form human relationship58. How was the Romantic era different from the Enlightenment ?A. The Romantic era emphasized emotion ; the Enlightenment emphasized reason .B. The Romantic era occurred during the 20th century ; the Enlightenment occurred during the 19th century .C. The Romantic era emphasized poetry ; the Enlightenment emphasized prose .D. The Romantic era saw major scientific discoveries ; the Enlightenment was an era of literary discovery .59. What effect did “ F rankenstein” have on later works of fiction ?A. It inspired books about the EnlightenmentB. It inspired technical writingC. It inspired books of poetryD. It inspired science-fiction writing60. If you are a 22-year-old nurse , you can apply for the railcard without ________.A. the signature of your director B $ 28c. application form D. passport-sized photos61. The 1/3 OFF discount may not apply for the railcard holders who travel at _______.A. 11 pm on Sunday in AugustB. 7. am on Tuesday in FebruaryC. 7 am on Monday in JulyD. 11 pm on Friday in March62. Which of the following is True according to the leaflet ?A. If you railcard doesn’t have your name signed , it will be used by someone else.B. The benefits of a railcard are transferable to your friend of your age .C. If you have no ticket but have boarded a train , you will still be eligible for a discounted ticketD. If railcard holders wish to use the Eurostar network , they must pay the full fare.The ‘ Phone Stack(堆)’GameWhenever Michael Carl , the fashion market director at Vanity Fair , goes out to dinner with friends , he plays something, called the “ phone stack” game : Everyone places their phones in the middle of the table ; whoever looks at their device before the check arrives picks up the bill . As smartphones continue to burrow(钻入) their way into our lives , and wearable devices like Google Glass threaten to eat into our person space even further , overburdened users are carving out their own device-free zones with special tricks and life hacks .“Disconnecting is a luxury that we all need ,” Lesley M. M. Blume , a Ne w York writer keeps her phone away from the dinner table at home .” The expectation that we must always be available to employers ,colleague, family : It creates a real obstacle in trying to set aside private time . But that private time is more important than ever. “ Much of the digital detoxing （戒毒）is centered on the home , where urgent e-mails from co-workers , texts from friends , Instagram photos from acquaintances and updates on Facebook get together to disturb domestic quietness.A popular method is to appoint a kind of cellphone lockbox , like the milk tin that Brandon Holley , the former editor of lucky magazine , uses. “ If my phones is buzzing or lighting up , it’s still a distraction , so it goes in the box . “, said Ms. Holley , who lives in a r ow house in Red Hook , Brooklyn , with her son ,Smith , and husband , John .” It’s not something I want my kid to see.” Sleep is a big factor , which is why some people draw the cellphone-free line at the bedroom.” I don’t want to sleep next to something t hat is a charged ball of information with photos an e-mails ,” said Peter Som , the fashion designer , who keeps his phone plugged in the living room overnight .” “It definitely is a head clearer and describes daytime and sleep time clearly .”Households with young children are especially mindful about being overconnected , with parents sensitive to how children may imitate bad habits . But it’s not just inside the home where users are separating themselves from the habit . Cellphone overusers are making efforts to disconnect in social settings ,whether at the request of the host or in the form of friendly competition . The phone-stack game is a lighthearted way for friends to police against rude behavior when eating out . The game gained popularity after Brian Perez, a dancer in Los Angeles , posted the idea online.63. What might be the reason for Michael Carl to play the “ phone stack” game?A. His friends aren’t willing to pay for the meal voluntarily .B. He wants to do some funny things with those phonesC. He has been fed up with digital devices being present everywhereD. The wearable devices have brought threats to his privacy .64.Why is it difficulty for people to break away from their digital device at home ?A. Because they have to do some work at homeB. Because they are expected to be always available to the outsideC. Because people have been addicted to digital devices.D. Because digital devices can enrich people’s family life.65. What does Peter Som do to ensure his sleeping quality at night ?A. He puts his phone in the living room .B. He ignores any information in the phoneC. He deletes all information in his phoneD. He puts his phones in a lockbox66. Why does the phone-stack game become popular as soon as it is posted online?A. The game helps create a harmonious relationship among friends.B. The game makes the host get along well with the guestC. The game can prevent children from imitating their parents’ behaviorD. The game meets people’s demand for keeping away from phones easilySection CDirections: Read the following passage. Fill in each blank with a proper sentence given in the box. Each sentence can be used only once. Note that there are two more sentences than you need.“Any apple today ?”, Effie asked cheerfully at my window ,. I followed her to her truck and bought a kilo . On credit , of course . Cash was the one thing in the world I lacked just them .All pretense （借口）of payment was drooped when our funds , food and fuel decreased to alarming lows. Effie came often , always bringing some gift: a jar of peaches or some firewood . There were other generosities.___________Effie was not a rich woman . Her income , derived from investment she had made while running an interior decorating shop , had never exceeded $200 a month , which she supplemented by selling her apples .But she always managed to help someone poorer .Years passed before I was able to return the money Effie had given me from time to time . She was ill now and had aged rapidly in the last year .” Here , darling , “ I said , “ is what I owe you ,” _____________” Give it back as I gave it to you -----a little at a time.” “ I think she believed there was magic in the slow discharge of a love debt.The simple fact is that I never repaid the whole amount to Effie , for she died a few weeks later . By now , the few dollars Effie gave me have been multiplied many times . But a curious thing began to happen .___________At that time , it seemed that my debt would forever go unsettled . So the account can never be marked closed , for Effie’s love will go on in hearts that have never known her .IV. Summary WritingDirections:Read the following passage. Summarize the main idea and the main point(s) of the passage in no more than 60 words. Use your own words as far as possible.Chaco Great HouseAs early as the twelfth century A.D., the settlements of Chaco Canyon in New Mexico in the American Southwest were notable for their "great houses," massive stone buildings that contain hundreds of rooms and often stand three or four stories high. Archaeologists have been trying to determine how the buildings were used. Whilethere is still no universally agreed upon explanation, there are three competing theories.One theory holds that the Chaco structures were purely residential, with each housing hundreds of people. Supporters of this theory have interpreted Chaco great houses as earlier versions of the architecture seen in more recent Southwest societies. In particular, the Chaco houses appear strikingly similar to the large, well-known "apartment buildings" at Taos, New Mexico, in which many people have been living for centuries.A second theory contends that the Chaco structures were usedto store food supplies. One of the main crops of the Chaco people was grain maize, which could be stored for long periods of time without spoiling and could serve as a long-lasting supply of food. The supplies of maize had to be stored somewhere, and the size of the great houses would make them very suitable for the purpose.A third theory proposes that houses were used as ceremonial centers. Close to one house, called Pueblo Alto, archaeologists identified an enormous mound formed by a pile of old material. Excavations of the mound revealed deposits containing a surprisingly large number of broken pots. This finding has been interpreted as evidence that people gathered at Pueblo Alto for special ceremonies. At the ceremonies, they ate festive meals and then discarded the pots in which the meals had been prepared or served. Such ceremonies have been documented for other Native American cultures.V. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.72. 想和我一起看电影的人请举手。

2017年上海市普陀区高考数学二模试卷含详解

2017年上海市普陀区高考数学二模试卷一、填空题（共12小题，每小题4分，满分54分）1．（4分）计算：（1+）3=．2．（4分）函数f（x）=log2（1﹣）的定义域为．3．（4分）若＜α＜π，sinα=，则tan=．4．（4分）若复数z=（1+i）•i2（i表示虚数单位），则=．5．（4分）曲线C：（θ为参数）的两个顶点之间的距离为．6．（4分）若从一副52张的扑克牌中随机抽取2张，则在放回抽取的情形下，两张牌都是K的概率为（结果用最简分数表示）．7．（5分）若关于x 的方程sinx+cosx﹣m=0在区间[0，]上有解，则实数m 的取值范围是．8．（5分）若一个圆锥的母线与底面所成的角为，体积为125π，则此圆锥的高为．9．（5分）若函数f（x）=log22x﹣log2x+1（x≥2）的反函数为f﹣1（x）．则f﹣1（3）=．10．（5分）若三棱锥S﹣ABC的所有的顶点都在球O的球面上．SA⊥平面ABC．SA=AB=2，AC=4，∠BAC=，则球O的表面积为．11．（5分）设a＜0，若不等式sin2x+（a﹣1）cosx+a2﹣1≥0对于任意的x∈R恒成立，则a的取值范围是．12．（5分）在△ABC中，D、E分别是AB，AC的中点，M是直线DE上的动点，若△ABC的面积为1，则•+2的最小值为．二、选择题（共4小题，每小题5分，满分20分）13．（5分）动点P在抛物线y=2x2+1上移动，若P与点Q（0，﹣1）连线的中点为M，则动点M的轨迹方程为（）A．y=2x2B．y=4x2C．y=6x2D．y=8x2 14．（5分）若α、β∈R，则“α≠β”是“tanα≠tanβ”成立的（）A．充分非必要条件B．必要非充分条件C．充要条件D．既非充分也非必要条件15．（5分）设l、m是不同的直线，α、β是不同的平面，下列命题中的真命题为（）A．若l∥α，m⊥β，l⊥m，则α⊥βB．若l∥α，m⊥β，l⊥m，则α∥βC．若l∥α，m⊥β，l∥m，则α⊥βD．若l∥α，m⊥β，l∥m，则α∥β16．（5分）关于函数y=sin2x的判断，正确的是（）A．最小正周期为2π，值域为[﹣1，1]，在区间[﹣，]上是单调减函数B．最小正周期为π，值域为[﹣1，1]，在区间[0，]上是单调减函数C．最小正周期为π，值域为[0，1]，在区间[0，]上是单调增函数D．最小正周期为2π，值域为[0，1]，在区间[﹣，]上是单调增函数三、解答题（共5小题，满分76分）17．（14分）在正方体ABCD﹣A1B1C1D1中，E、F分别是BC、A1D1的中点．（1）求证：四边形B1EDF是菱形；（2）求异面直线A1C与DE所成的角（结果用反三角函数表示）．18．（14分）已知函数f（x）=asinx+bcosx（a，b为常数且a≠0，x∈R）．当x=时，f（x）取得最大值．（1）计算f（）的值；（2）设g（x）=f（﹣x），判断函数g（x）的奇偶性，并说明理由．19．（14分）某人上午7时乘船出发，以匀速v海里/小时（4≤v≤20）从A港前往相距50海里的B地，然后乘汽车以匀速ω千米/小时（30≤ω≤100）自B港前往相距300千米的C市，计划当天下午4到9时到达C市．设乘船和汽车的所要的时间分别为x、y小时，如果所需要的经费P=100+3（5﹣x）+（8﹣y）（单位：元）（1）试用含有v、ω的代数式表示P；（2）要使得所需经费P最少，求x和y的值，并求出此时的费用．20．（16分）已知椭圆T：+=1，直线l经过点P（m，0）与T相交于A、B 两点．（1）若C（0，﹣）且|PC|=2，求证：P必为Γ的焦点；（2）设m＞0，若点D在Γ上，且|PD|的最大值为3，求m的值；（3）设O为坐标原点，若m=，直线l的一个法向量为=（1，k），求△AOB 面积的最大值．21．（18分）已知数列{a n}（n∈N*），若{a n+a n+1}为等比数列，则称{a n}具有性质P．（1）若数列{a n}具有性质P，且a1=a2=1，a3=3，求a4、a5的值；（2）若b n=2n+（﹣1）n，求证：数列{b n}具有性质P；（3）设c1+c2+…+c n=n2+n，数列{d n}具有性质P，其中d1=1，d3﹣d2=c1，d2+d3=c2，若d n＞102，求正整数n的取值范围．2017年上海市普陀区高考数学二模试卷参考答案与试题解析一、填空题（共12小题，每小题4分，满分54分）1．（4分）计算：（1+）3=1．【考点】6F：极限及其运算．【专题】11：计算题；52：导数的概念及应用．【分析】根据题意，对（1+）3变形可得（1+）3=（+++1），由极限的意义计算可得答案．【解答】解：根据题意，（1+）3==（+++1）=1，即（1+）3=1；故答案为：1．【点评】本题考查极限的计算，需要牢记常见的极限的化简方法．2．（4分）函数f（x）=log2（1﹣）的定义域为（﹣∞，0）∪（1，+∞）．【考点】33：函数的定义域及其求法．【专题】51：函数的性质及应用．【分析】根据对数函数的性质得到关于x的不等式，解出即可．【解答】解：由题意得：1﹣＞0，解得：x＞1或x＜0，故答案为：（﹣∞，0）∪（1，+∞）．【点评】本题考查了函数的定义域问题，考查对数函数的性质，是一道基础题．3．（4分）若＜α＜π，sinα=，则tan=3．【考点】GW：半角的三角函数．【专题】35：转化思想；49：综合法；56：三角函数的求值．【分析】利用同角三角函数的基本关系求得cosx的值，再利用半角公式求得tan的值．【解答】解：若＜α＜π，sinα=，则cosα=﹣=﹣，∴tan==3，故答案为：3．【点评】本题主要考查同角三角函数的基本关系，半角公式的应用，属于基础题．4．（4分）若复数z=（1+i）•i2（i表示虚数单位），则=﹣1+i．【考点】A5：复数的运算．【专题】11：计算题；35：转化思想；4O：定义法；5N：数系的扩充和复数．【分析】先化简，再根据共轭复数的定义即可求出【解答】解：z=（1+i）•i2=﹣1﹣i，∴=﹣1+i，故答案为：﹣1+i．【点评】本题考查复数代数形式的乘除运算以及共轭复数，是基础的计算题．5．（4分）曲线C：（θ为参数）的两个顶点之间的距离为2．【考点】QH：参数方程化成普通方程．【专题】11：计算题；34：方程思想；5S：坐标系和参数方程．【分析】根据题意，将曲线的参数方程变形为普通方程，分析可得曲线C为双曲线，且两个顶点的坐标为（±1，0），由两点间距离公式计算可得答案．【解答】解：曲线C：，其普通方程为x2﹣y2=1，则曲线C为双曲线，且两个顶点的坐标为（±1，0），则则两个顶点之间的距离为2；故答案为：2．【点评】本题考查参数方程与普通方程的互化，涉及双曲线的几何性质，关键是将曲线的参数方程化为普通方程．6．（4分）若从一副52张的扑克牌中随机抽取2张，则在放回抽取的情形下，两张牌都是K的概率为（结果用最简分数表示）．【考点】CB：古典概型及其概率计算公式．【专题】11：计算题；34：方程思想；4O：定义法；5I：概率与统计．【分析】先求出基本事件总数n=52×52，再求出两张牌都是K包含的基本事件个数m=4×4，由此能求出两张牌都是K的概率．【解答】解：从一副52张的扑克牌中随机抽取2张，在放回抽取的情形下，基本事件总数n=52×52，两张牌都是K包含的基本事件个数m=4×4，∴两张牌都是K的概率为p===．故答案为：．【点评】本题考查概率的求法，考查古典概型及应用，考查推理论证能力、运算求解能力，考查函数与方程思想、化归转化思想，是基础题．7．（5分）若关于x 的方程sinx+cosx﹣m=0在区间[0，]上有解，则实数m 的取值范围是[1，] ．【考点】GF：三角函数的恒等变换及化简求值．【专题】33：函数思想；4R：转化法．【分析】由题意，关于x 的方程sinx+cosx﹣m=0在区间[0，]上有解，转化为函数y=sin（x+）与函数y=m的图象有交点问题．【解答】解：由题意，sinx+cosx﹣m=0，转化为：sinx+cosx=m，设函数y=sin （x+）x∈[0，]上，则x+∈[，]∴sin（x+）∈[]∴函数y=sin（x+）的值域为[1，]关于x 的方程sinx+cosx﹣m=0在区间[0，]上有解，则函数y=m的值域为[1，]，即m∈[1，]故答案为：[1，]．【点评】本题考查了方程有解问题转化为两个函数的交点的问题．属于基础题．8．（5分）若一个圆锥的母线与底面所成的角为，体积为125π，则此圆锥的高为5．【考点】L5：旋转体（圆柱、圆锥、圆台）．【专题】15：综合题；34：方程思想；4G：演绎法；5F：空间位置关系与距离．【分析】设圆锥的高为h，则底面圆的半径为h，利用体积为125π，建立方程，即可求出此圆锥的高．【解答】解：设圆锥的高为h，则底面圆的半径为h，∵体积为125π，∴=125π，∴h=5．故答案为：5．【点评】本题考查圆锥体积的计算，考查方程思想，比较基础．9．（5分）若函数f（x）=log22x﹣log2x+1（x≥2）的反函数为f﹣1（x）．则f﹣1（3）=4．【考点】4R：反函数．【专题】15：综合题；35：转化思想；4G：演绎法；51：函数的性质及应用．【分析】由题意，log22x﹣log2x+1=3，根据x≥2，即可得出结论．【解答】解：由题意，log22x﹣log2x+1=3，∵x≥2，∴x=4，故答案为4．【点评】本题考查对数方程，考查反函数的概念，正确转化是关键．10．（5分）若三棱锥S﹣ABC的所有的顶点都在球O的球面上．SA⊥平面ABC．SA=AB=2，AC=4，∠BAC=，则球O的表面积为20π．【考点】LG：球的体积和表面积．【专题】11：计算题；35：转化思想；49：综合法；5F：空间位置关系与距离．【分析】由余弦定理求出BC=2，利用正弦定理得∠ABC=90°．从而△ABC截球O所得的圆O′的半径r=AC=2，进而能求出球O的半径R，由此能求出球O 的表面积．【解答】解：如图，三棱锥S﹣ABC的所有顶点都在球O的球面上，∵SA⊥平面ABC．SA=AB=2，AC=4，∠BAC=，∴BC==2，∴AC2=BC2+AB2，∴∠ABC=90°．∴△ABC截球O所得的圆O′的半径r=AC=2，∴球O的半径R==，∴球O的表面积S=4πR2=20π．故答案为：20π．【点评】本题考查三棱锥、球、勾股定理等基础知识，考查抽象概括能力、数据处理能力、运算求解能力，考查应用意识、创新意识，考查化归与转化思想、分类与整合思想、数形结合思想，是中档题．11．（5分）设a＜0，若不等式sin2x+（a﹣1）cosx+a2﹣1≥0对于任意的x∈R恒成立，则a的取值范围是a≤﹣2．【考点】3R：函数恒成立问题．【专题】35：转化思想；4R：转化法；51：函数的性质及应用．【分析】不等式进行等价转化为关于cosx的一元二次不等式，利用二次函数的性质和图象列不等式组求得答案．【解答】解；不等式等价于1﹣cos2x+acosx+a2﹣1﹣cosx≥0，恒成立，整理得﹣cos2x+（a﹣1）cosx+a2≥0，设cosx=t，则﹣1≤t≤1，g（t）=﹣t2+（a﹣1）t+a2，要使不等式恒成立需：求得a≥1或a≤﹣2，而a＜0故答案为：a ≤﹣2．【点评】本题主要考查了一元二次不等式的解法，二次函数的性质．注重了对数形结合思想的运用和问题的分析．12．（5分）在△ABC 中，D 、E 分别是AB ，AC 的中点，M 是直线DE 上的动点，若△ABC 的面积为1，则•+2的最小值为．【考点】9O ：平面向量数量积的性质及其运算．【专题】35：转化思想；41：向量法；5A ：平面向量及应用．【分析】由三角形的面积公式，S △ABC =2S △MBC ，则S △MBC =，根据三角形的面积公式及向量的数量积，利用余弦定理，即可求得则•+2，利用导数求得函数的单调性，即可求得则•+2的最小值；方法二：利用辅助角公式及正弦函数的性质，即可求得•+2的最小值．【解答】解：∵D 、E 是AB 、AC 的中点，∴A 到BC 的距离=点A 到BC 的距离的一半， ∴S △ABC =2S △MBC ，而△ABC 的面积1，则△MBC 的面积S △MBC =，S △MBC =丨MB 丨×丨MC 丨sin ∠BMC=，∴丨MB 丨×丨MC 丨=． ∴•=丨MB 丨×丨MC 丨cos ∠BMC=．由余弦定理，丨BC 丨2=丨BM 丨2+丨CM 丨2﹣2丨BM 丨×丨CM 丨cos ∠BMC ，显然，BM 、CM 都是正数，∴丨BM 丨2+丨CM 丨2≥2丨BM 丨×丨CM 丨，∴丨BC 丨2=丨BM 丨2+丨CM 丨2﹣2丨BM 丨×丨CM 丨cos ∠BMC=2×﹣2×．．∴•+2≥+2×﹣2×=，方法一：令y=，则y′=，令y′=0，则cos∠BMC=，此时函数在（0，）上单调减，在（，1）上单调增，∴cos∠BMC=时，取得最小值为，•+2的最小值是，方法二：令y=，则ysin∠BMC+cos∠BMC=2，则sin（∠BMC+α）=2，tanα=，则sin（∠BMC+α）=≤1，解得：y≥，•+2的最小值是，故答案为：．【点评】本题考查了向量的线性运算、数量积运算、辅助角公式，余弦定理，考查了推理能力与计算能力，属于中档题．二、选择题（共4小题，每小题5分，满分20分）13．（5分）动点P在抛物线y=2x2+1上移动，若P与点Q（0，﹣1）连线的中点为M，则动点M的轨迹方程为（）A．y=2x2B．y=4x2C．y=6x2D．y=8x2【考点】J3：轨迹方程．【专题】15：综合题；35：转化思想；4G：演绎法；5D：圆锥曲线的定义、性质与方程．【分析】先设PQ中点为（x，y），进而根据中点的定义可求出M点的坐标，然后代入到曲线方程中得到轨迹方程．【解答】解：设PQ中点为M（x，y），则P（2x，2y+1）在抛物线y=2x2+1上，即2（2x）2=（2y+1）﹣1，∴y=4x2．故选：B．【点评】本题主要考查轨迹方程的求法，考查运算求解能力，考查数形结合思想、化归与转化思想．属于基础题．14．（5分）若α、β∈R，则“α≠β”是“tanα≠tanβ”成立的（）A．充分非必要条件B．必要非充分条件C．充要条件D．既非充分也非必要条件【考点】29：充分条件、必要条件、充要条件．【专题】38：对应思想；4R：转化法；5L：简易逻辑．【分析】根据正切函数的性质以及充分必要条件的定义判断即可．【解答】解：若“α≠β”，则“tanα≠tanβ”不成立，不是充分条件，反之也不成立，比如α=，β=，故选：D．【点评】本题考查了充分必要条件，考查正切函数的性质，是一道基础题．15．（5分）设l、m是不同的直线，α、β是不同的平面，下列命题中的真命题为（）A．若l∥α，m⊥β，l⊥m，则α⊥βB．若l∥α，m⊥β，l⊥m，则α∥βC．若l∥α，m⊥β，l∥m，则α⊥βD．若l∥α，m⊥β，l∥m，则α∥β【考点】LP：空间中直线与平面之间的位置关系．【专题】11：计算题；35：转化思想；4R：转化法；5F：空间位置关系与距离．【分析】在A中，α与β相交或平行；在B中，α与β相交或平行；在C中，由面面垂直的判定定理得α⊥β；在D中，由面面垂直的判定定理得α⊥β．【解答】解：由l、m是不同的直线，α、β是不同的平面，知：在A中，若l∥α，m⊥β，l⊥m，则α与β相交或平行，故A错误；在B中，若l∥α，m⊥β，l⊥m，则α与β相交或平行，故B错误；在C中，若l∥α，m⊥β，l∥m，则由面面垂直的判定定理得α⊥β，故C正确；在D中，若l∥α，m⊥β，l∥m，则由面面垂直的判定定理得α⊥β，故D错误．故选：C．【点评】本题考查命题真假的判断，考查空间中线线、线面、面面间的位置关系的应用，考查推理论证能力、运算求解能力、空间思维能力，考查化归转化思想、数形结合思想，是中档题．16．（5分）关于函数y=sin2x的判断，正确的是（）A．最小正周期为2π，值域为[﹣1，1]，在区间[﹣，]上是单调减函数B．最小正周期为π，值域为[﹣1，1]，在区间[0，]上是单调减函数C．最小正周期为π，值域为[0，1]，在区间[0，]上是单调增函数D．最小正周期为2π，值域为[0，1]，在区间[﹣，]上是单调增函数【考点】GS：二倍角的三角函数；H7：余弦函数的图象．【专题】15：综合题；35：转化思想；4O：定义法；57：三角函数的图像与性质．【分析】先化简函数，再利用余弦函数的图象与性质，即可得出结论．【解答】解：y=sin2x=（1﹣os2x）=﹣cos2x+∴函数的最小正周期为π，值域为[0，1]，在区间[0，]上是单调增函数，故选：C．【点评】本题考查三角函数的化简，考查余弦函数的图象与性质，属于中档题．三、解答题（共5小题，满分76分）17．（14分）在正方体ABCD﹣A1B1C1D1中，E、F分别是BC、A1D1的中点．（1）求证：四边形B1EDF是菱形；（2）求异面直线A1C与DE所成的角（结果用反三角函数表示）．【考点】LM：异面直线及其所成的角．【专题】15：综合题；35：转化思想；44：数形结合法；5G：空间角．【分析】（1）由题意画出图形，取AD中点G，连接FG，BG，可证四边形B1BGF 为平行四边形，得BG∥B1F，再由ABCD﹣A1B1C1D1为正方体，且E，G分别为BC，AD的中点，可得BEDG为平行四边形，得BG∥DE，BG=DE，从而得到B1F∥DE，且B1F=DE，进一步得到四边形B1EDF为平行四边形，再由△B1BE≌△B1A1F，可得B1E=B1F，得到四边形B1EDF是菱形；（2）以A为原点建立如图所示空间直角坐标系，然后利用空间向量求异面直线A1C与DE所成的角．【解答】（1）证明：取AD中点G，连接FG，BG，可得B1B∥FG，B1B=FG，∴四边形B1BGF为平行四边形，则BG∥B1F，由ABCD﹣A1B1C1D1为正方体，且E，G分别为BC，AD的中点，可得BEDG为平行四边形，∴BG∥DE，BG=DE，则B1F∥DE，且B1F=DE，∴四边形B1EDF为平行四边形，由△B1BE≌△B1A1F，可得B1E=B1F，∴四边形B1EDF是菱形；（2）解：以A为原点建立如图所示空间直角坐标系，设正方体的棱长为1，则A1（0，0，1），C（1，1，0），D（0，1，0），E（1，，0），∴，，∴cos＜＞==．∴异面直线A1C与DE所成的角为arccos．【点评】本题考查空间中直线与直线的位置关系，考查空间想象能力和思维能力，训练了利用空间向量求异面直线所成角，是中档题．18．（14分）已知函数f（x）=asinx+bcosx（a，b为常数且a≠0，x∈R）．当x=时，f（x）取得最大值．（1）计算f（）的值；（2）设g（x）=f（﹣x），判断函数g（x）的奇偶性，并说明理由．【考点】3K：函数奇偶性的性质与判断；GF：三角函数的恒等变换及化简求值．【专题】11：计算题；35：转化思想；49：综合法；56：三角函数的求值．【分析】首先，根据已知得到f（x）=sin（x+θ），然后根据最值建立等式，得到a=b，再化简函数f（x）=asin（x+），（1）将代入解析式求值；（2）求出g（x）解析式，利用奇偶函数定义判断奇偶性．【解答】解：由已知得到f（x）=sin（x+θ），又x=时，f（x）取得最大值．所以a=b，f（x）=asin（x+），所以（1）f（）=asin（3π）=0；（2）g（x）为偶函数．理由：设g（x）=f（﹣x）=asin（﹣x）=acosx，所以函数g（﹣x）=g（x），为偶函数．【点评】本题考查了三角函数的性质以及奇偶性的判定；属于基础题．19．（14分）某人上午7时乘船出发，以匀速v海里/小时（4≤v≤20）从A港前往相距50海里的B地，然后乘汽车以匀速ω千米/小时（30≤ω≤100）自B港前往相距300千米的C市，计划当天下午4到9时到达C市．设乘船和汽车的所要的时间分别为x、y小时，如果所需要的经费P=100+3（5﹣x）+（8﹣y）（单位：元）（1）试用含有v、ω的代数式表示P；（2）要使得所需经费P最少，求x和y的值，并求出此时的费用．【考点】36：函数解析式的求解及常用方法；5C：根据实际问题选择函数类型．【专题】11：计算题；35：转化思想；44：数形结合法；59：不等式的解法及应用．【分析】（1）分析题意，找出相关量之间的不等关系，（2）求出x，y满足的约束条件，由约束条件画出可行域，要求走得最经济，即求可行域中的最优解，将目标函数看成是一条直线，分析目标函数p与直线截距的关系，进而求出最优．【解答】解：（1）由题意得：x=，4≤v≤20，y=，30≤ω≤100，∴P=100+3（5﹣）+（8﹣）=123﹣﹣，其中，4≤v≤20，30≤ω≤100，（2）由（1）可得2.5≤x≤12.5，3≤y≤10，①由于汽车、乘船所需的时间和应在9至14小时之间，∴9≤x+y≤14 ②因此满足①②的点（x，y）的存在范围是图中阴影部分目标函数p=100+3（5﹣x）+（8﹣y）=123﹣3x﹣y，当x=11，y=3时，p 最小，此时，p=123﹣33﹣3=87【点评】本题考查不等式关系的建立，考查线性规划知识，考查学生分析解决问题的能力，属于中档题．20．（16分）已知椭圆T：+=1，直线l经过点P（m，0）与T相交于A、B两点．（1）若C（0，﹣）且|PC|=2，求证：P必为Γ的焦点；（2）设m＞0，若点D在Γ上，且|PD|的最大值为3，求m的值；（3）设O为坐标原点，若m=，直线l的一个法向量为=（1，k），求△AOB 面积的最大值．【考点】K4：椭圆的性质．【专题】35：转化思想；4R：转化法；5D：圆锥曲线的定义、性质与方程．【分析】（1）利用两点之间距离公式，即可求得m的值，由椭圆的方程，即可求得焦点坐标，即可求证P必为Γ的焦点；（2）利用两点之间的距离公式，根据二次函数的单调性，当x0=﹣2时，取最大值，代入即可求得m的值；（3）求得直线AB的方程，代入方程，由韦达定理，弦长公式及点到直线的距离公式，利用基本不等式的性质，即可求得△AOB面积的最大值．【解答】解：（1）证明：由椭圆焦点F（±1，0），由|PC|==2，解得：m=±1，∴P点坐标为（±1，0），∴P必为Γ的焦点；（2）设D（x0，y0），y02=3（1﹣），|PD|2=（x0﹣m）2+y02=﹣2mx0+m2+3，﹣2≤x0≤2，有函数的对称轴x0=4m＞0，则当x0=﹣2时，取最大值，则|PD|2=1+4m+m2+3=9，m2+4m﹣5=0，解得：m=1或m=﹣5（舍去），∴m的值1；（3）直线l的一个法向量为=（1，k），则直线l的斜率﹣，则直线l方程：y﹣0=﹣（x﹣），整理得：ky+x﹣=0，设A（x1，y1），B（x2，y2），，整理得：（3k2+4）y2﹣6ky﹣3=0，则y1+y2=，y1y2=﹣，丨AB丨=•=，则O到直线AB的距离d=，则△AOB面积S=×丨AB丨×d=××==≤=，当且仅当=，即k2=，取等号，∴△AOB面积的最大值．【点评】本题考查椭圆的简单几何性质，直线与椭圆的位置关系，考查韦达定理，弦长公式，基本不等式的性质，考查计算能力，属于中档题．21．（18分）已知数列{a n}（n∈N*），若{a n+a n+1}为等比数列，则称{a n}具有性质P．（1）若数列{a n}具有性质P，且a1=a2=1，a3=3，求a4、a5的值；（2）若b n=2n+（﹣1）n，求证：数列{b n}具有性质P；（3）设c1+c2+…+c n=n2+n，数列{d n}具有性质P，其中d1=1，d3﹣d2=c1，d2+d3=c2，若d n＞102，求正整数n的取值范围．【考点】8B：数列的应用．【专题】15：综合题；35：转化思想；4G：演绎法；54：等差数列与等比数列．【分析】（1）{a n+a n+1}为等比数列，由a1=a2=1，a3=3，可得{a n+a n+1}的公比为2，可得a n+a n+1=2n，进而得出a4、a5的值；（2）证明{b n+b n+1}是以公比为2的等比数列，即可得出结论；（3）求出d n+d n+1=2n，利用d n＞102，求正整数n的取值范围．【解答】解：（1）{a n+a n+1}为等比数列，∵a1=a2=1，a3=3，∴a1+a2=1+1=2，a2+a3=1+3=4，∴{a n+a n+1}的公比为2，∴a n+a n+1=2n，∴a3+a4=23=8，即a4=5，∴a4+a5=24=16，即a5=11；（2）∵b n=2n+（﹣1）n，∴b n+b n+1=2n+（﹣1）n+2n+1+（﹣1）n+1=3•2n，∴{b n+b n+1}是以公比为2的等比数列，∴数列{b n}具有性质P．（3）∵c1+c2+…+c n=n2+n，∴c1+c2+…+c n﹣1=（n﹣1）2+n﹣1，∴c n=2n，∵d1=1，d3﹣d2=c1=2，d2+d3=c2=4，∴d2=1，d3=3，∵数列{d n}具有性质P，由（1）可得，d n+d n+1=2n，∴d4=5，d5=11，d6=21，d7=43，d8=85，d9=171，∵d n＞102，∴正整数n的取值范围是[9，+∞）．【点评】本题考查新定义，考查等比数列的运用，考查学生分析解决问题的能力，属于中档题．。

2024届上海普陀区高考数学二模试卷及答案

普陀区2023 -2024学年第二学期高三数学质量调研2024.4考生注意：1.本试卷共4页，21道试题，满分150分.考试时间120分钟.2.作答必须涂（选择题）或写（非选择题）在答题纸上，在试卷上作答一律不得分.3.务必用钢笔或圆珠笔在答题纸相应位置正面清楚地填写姓名、准考证号，并将核对后的条码贴在指定位置上.一、填空题（本大题共有12题，满分54分）考生应在答题纸相应编号的空格内直接填写结果，每个空格填对前6题得4分、后6题得5分，否则一律得票分.1.已知复数1i z =+，其中i 为虚数单位，则z 在复平面内所对应的点的坐标为______.2.已知R a ∈，设集合{1,,4}A a =，集合{1,2}B a =+，若A B B =，则a =______.3.若3cos 35πθ⎛⎫−=⎪⎝⎭，则sin 6πθ⎛⎫+= ⎪⎝⎭______. 4.已知()2~4,2X N ，若(0)0.02P X <=，则(48)P X <<=______. 5.若实数a ，b 满足20a b −≥，则124ab+的最小值为______.6.设2012(1)(1,N)nn n x a a x a x a x n n +=++++≥∈，若54a a >，且56a a >，则1ni i a ==∑______.7.为了提高学生参加体育锻炼的积极性，某校本学期依据学生特点针对性的组建了五个特色运动社团，学校为了了解学生参与运动的情况，对每个特色运动社团的参与人数进行了统计，其中一个特色运动社团开学第1周至第5周参与运动的人数统计数据如表所示.若表中数据可用回归方程 2.3(118,N)y x b x x =+≤≤∈来预测，则本学期第11周参与该特色运动社团的人数约为______.（精确到整数）8.设等比数列{}n a 的公比为(1,N)q n n ≥∈，则“212a ，4a ，32a 成等差数列”的一个充分非必要条件是______.9.若向量a 在向量b 上的投影为13b ，且|3|||a b a b −=+，则cos ,a b 〈〉=______.10.已知抛物线2y =的焦点F 是双曲线Γ的右焦点，过点F 的直线l 的法向量(1,3)n =−，l 与y 轴以及Γ的左支分别相交A ，B 两点，若2BF BA =，则双曲线Γ的实轴长为______.11.设k ，m ，n 是正整数，n S 是数列{}n a 的前n 项和，12a =，11n n S a +=+，若()11ki ii m t S==−∑，且{0,1}i t ∈，记12()k f m t t t =+++，则(2024)f =______.12.已知R a ∈，若关于x 的不等式(2)e 0xa x x −−−>的解集中有且仅有一个负整数，则a 的取值范围是______.二、选择题（本大题共有4题，满分18分，第13-14题每题4分，第15-16题每题5分）每题有且只有一个正确答案，考生应在答题纸的相应编号上，将代表答案的小方格涂黑，否则一律得零分.13.从放有两个红球、一个白球的袋子中一次任意取出两个球，两个红球分别标记为A 、B ，白球标记为C ，则它的一个样本空间可以是（）A .{,}AB BC B .{,,}AB AC BC C .{,,,}AB BA BC CBD .{,,,,}AB BA AC CA CB14.若一个圆锥的体积为3，用通过该圆锥的轴的平面截此圆锥，得到的截面三角形的顶角为2π，则该圆锥的侧面积为（）AB .2πC .D .15.直线l 经过定点(2,1)P ，且与x 轴正半轴、y 轴正半轴分别相交于A ，B 两点，O 为坐标原点，动圆M 在OAB △的外部，且与直线l 及两坐标轴的正半轴均相切，则OAB △周长的最小值是（）A .3B .5C .10D .1216.设n S 是数列{}n a 的前n 项和(1,N)n n ≥∈，若数列{}n a 满足：对任意的2n ≥，存在大于1的整数m ，使得()()10m n m n S a S a +−−<成立，则称数列{}n a 是“G 数列”.现给出如下两个结论：①存在等差数列{}n a 是“G 数列”；②任意等比数列{}n a 都不是“G 数列”.则（）A .①成立②成立B .①成立②不成立C .①不成立②成立D .①不成立②不成立三、解答题（本大题共有5题，满分78分）解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤S ABCD −ABCD 2SA SB ==E F SC 17.（本题满分14 分）本题共有 2 个小题，第1 小题满分 6 分，第2 小题满分8 分如图，在四棱锥中，底面是边长为1 的正方形，，、分别是、BD 的中点.（1）求证：//EF 平面SAB ；（2）若二面角S AB D −−的大小为2π，求直线SD 与平面ABCD 所成角的大小. 18.（本题满分14分）本题共有2个小题，第1小题满分6分，第2小题满分8分设函数()sin()f x x ωϕ=+，0ω>，0ϕπ<<，它的最小正周期为π.（1）若函数12y f x π⎛⎫=−⎪⎝⎭是偶函数，求ϕ的值；（2）在ABC △中，角A 、B 、C 的对边分别为a 、b 、c ，若2a =，6A π=，2B f ϕ−⎛⎫=⎪⎝⎭，求b 的值.19.（本题满分14分）本题共有2个小题，第1小题满分6分，第2小题满分8分张先生每周有5个工作日，工作日出行采用自驾方式，必经之路上有一个十字路口，直行车道有三条，直行车辆可以随机选择一条车道通行，记事件A 为“张先生驾车从左侧直行车道通行”.（1）某日张先生驾车上班接近路口时，看到自己车前是一辆大货车，遂选择不与大货车从同一车道通行.记事件B 为“大货车从中间直行车道通行”，求()P AB ；（2）用X 表示张先生每周工作日出行事件A 发生的次数，求X 的分布及期望[]E X .20.（本题满分18 分）本题共有 3 个小题，第1 小题满分 4 分，第2 小题满分6 分，第 3 小题满分8 分.设椭圆222:1(1)x y a aΓ+=>，Γ的离心率是短轴长的4倍，直线l 交Γ于A 、B 两点，C 是Γ上异于A 、B 的一点，O 是坐标原点.（1）求椭圆Γ的方程；（2）若直线l 过Γ的右焦点F ，且CO OB =，0CF AB ⋅=，求CBF S ∆的值；（3）设直线l 的方程为(,R)y kx m k m =+∈，且OA OB CO +=，求||AB 的取值范围.21.（本题满分18分）本题共有3个小题，第1小题满分4分，第2小题满分6分，第3小题满分8分. 对于函数()y f x =，1x D ∈和()y g x =，2x D ∈，设12D D D =，若1x ，2x D ∈，且12x x ≠，皆有()()()()1212(0)f x f x t g x g x t −≤−>成立，则称函数()y f x =与()y g x =“具有性质()H t ”.（1）判断函数2()f x x =，[1,2]x ∈与()2g x x =是否“具有性质(2)H ”，并说明理由；（2）若函数2()2f x x =+，(0,1]x ∈与1()g x x=“具有性质()H t ”，求t 的取值范围；（3）若函数21()2ln 3f x x x=+−与()y g x =“具有性质(1)H ”，且函数()y g x =在区间(0,)+∞上存在两个零点1x ，2x ，求证22122x x +>.参考答案一、填空题 1.()1,1− 2. 2 3.354.0.485. 26. 10237. 578. q=39.310.2 11. 7 12.211,23e e ⎡⎫⎪⎢⎣⎭二、选择题13.B 14. C 15. C 16. D 三、解答题 17.（1）证明略（2）3π18.（1）23π（2）19.（1）16（2）分布列：01234532808040101243243243243243243⎛⎫ ⎪ ⎪ ⎪⎝⎭，期望5320.（1）2212x y +=（2）1（3）21.（1）具有，说明略（2）[)2,+∞（3）证明略。

上海市各区高三二模数学试题分类汇编立体几何

20XX 年上海市各区高三数学二模试题分类汇编第7部分:立体几何一、选择题：15．（上海市卢湾区20XX 年4月高考模拟考试文科）如右图，已知底面为正方形的四棱锥，其一条侧棱垂直于底面，那么该四棱锥的三视图是下列各图中的（ B ）．15、（上海市奉贤区20XX 年4月高三质量调研理科）已知一球半径为2，球面上A 、B 两点的球面距离为32π,则线段AB 的长度为（ C ）（A ） 1 （B ）3 （C ） 2 （D ） 2316、（上海市长宁区20XX 年高三第二次模拟理科）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“αβ⊥”是“m β⊥”的 ( B )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 17. (上海市普陀区20XX 年高三第二次模拟考试理科) 四棱A ．俯视主视左视俯视主视左视俯视主视左视B ．C ．D ．第17题图锥P ABCD -底面为正方形,侧面PAD 为等边三角形,且侧面PAD ⊥底面ABCD ,点M在底面正方形ABCD 内运动,且满足MP MC =,则点M 在正方形ABCD内的轨迹一定是（ B ）17. (上海市普陀区20XX 年高三第二次模拟考试文科) 一个正三棱锥的四个顶点都在半径为1的球面上，其中底面的三个顶点在该球的一个大圆上，则该正三棱锥的体积是（ B ）A ．33；B ．3；C ．3；D ．3.17．(上海市松江区20XX 年4月高考模拟文科)三棱锥P —ABC 的侧棱PA 、PB 、PC 两两互相垂直，侧面面积分别是6，4，3，则三棱锥的体积是( A ) A ．4 B ．6 C ．8 D ． 1014．（上海市闸北区20XX 年4月高三第二次模拟理科）将正三棱柱截去三个角（如图1所示A 、B 、C 分别是GHI ∆三边的中点）得到的几何体如图2，则按图2所示方向侧视该几何体所呈现的平面图形为【 A 】[AB CDC.AB CDA.AB CDB.ABCDD.15．（上海市浦东新区20XX 年4月高考预测理科）“直线a 与平面M 没有公共点”是“直线a 与平面M 平行”的（ C ） 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15. （20XX 年4月上海杨浦、静安、青浦、宝山四区联合高考模拟）“直线l 垂直于ABC ∆的边AB ，AC ”是“直线l 垂直于ABC ∆的边BC ”的（B ）.(A)充要条件 (B)充分非必要条件(C)必要非充分条件 (D)即非充分也非必要条件二、填空题：6．（上海市卢湾区20XX 年4月高考模拟考试理科）若体积为8的正方体的各个顶点均在一球面上，则该球的体积为（结果保留π）．10．（上海市卢湾区20XX 年4月高考模拟考试理科）如图，由编号1，2，…，n ，…（*n ∈N 且3n ≥）的圆柱自下而上组成．其中每一个圆柱的高与其底面圆的直径相等，且对于任意两个相邻圆柱，上面圆柱的高是下面圆柱的高的一半．若编号1的圆柱的高为4，则所有圆柱的体积V 为（结果保留π）．128π7[第1010、在正四面体ABCD 中，E 、F 分别是BC 、AD 中点，则异面直线AE 与CF 所成的角是________________。

2017届上海市普陀区高三下学期质量调研(二模)考试理科数学试题及答案

上海市普陀区2017届高三教学质量调研（二模）数学理试题考生注意： 41.答卷前，考生务必在答题纸上将姓名、考试号填写清楚，并在规定的区域贴上条形码.2.本试卷共有23道题，满分150分.考试时间120分钟.3.本试卷另附答题纸，每道题的解答必须写在答题纸的相应位．．．．．．．．．．．置，本卷上任何解答都不作评分依据．．．．．．．．．．．．．．．．. 一、填空题（本大题满分56分）本大题共有14小题， 1．若复数ii i z 1=（i 是虚数单位），则=z . 2．若集合}40,tan |{π≤<==x x y y A ，}02|{2<--=x x x B ，则=B A .3．【理科】方程1)4(log )1(log 42=+-+x x 的解=x . 4．【理科】若向量),1(x a =，)1,2(=b ，且b a ⊥，则=+||b a . 5．【理科】若0>a ，在极坐标系中，直线2)3cos(=+⋅πθρ与曲线a =ρ相切，则实数=a .6．【理科】若偶函数)(x f y =(R x ∈)满足条件：)1()(x f x f +=-，则函数)(x f 的一个周期为 .7．【理科】若P 为曲线⎩⎨⎧==ααtan sec y x （α为参数）上的动点，O 为坐标原点，M 为线段OP 的中点，则点M 的轨迹方程是 .8．【理科】某质量监测中心在一届学生中随机抽取39人，对本届学生成绩进行抽样分析.统计分析的一部分结果，见下表:根据上述表中的数据，可得本届学生方差的估计值为 (结果精确到1.0).9．【理科】等比数列}{n a 的前n 项和为n S ，若对于任意的正整数k ，均有)(lim k n nk S S a -=∞→成立，则公比=q . 10．【理科】在一个质地均匀的小正方体六个面中，三个面标0，两个面标1，一个面标2，将这个小正方体连续掷两次，若向上的数字的乘积为偶数ξ，则=ξE .11．【理科】如图所示，在一个)12()12(-⨯-n n (N n ∈且2≥n )的正方形网格内涂色,要求两条对角线的网格涂黑色，其余网格涂白色.若用)(n f 表示涂白色网格的个数与涂黑色网格的个数的比值，则)(n f 的最小值为 .12．【理科】若三棱锥ABC S -的底面是边长为2的正三角形，且⊥AS 平面SBC ，则三棱锥ABC S -的体积的最大值为 .第11题图13．若ij a 表示n n ⨯阶矩阵⎪⎪⎪⎪⎪⎪⎭⎫⎝⎛nn a25191410181396128537421中第i 行、第j 列的元素（i 、n j ,,3,2,1 =），【理科】则=nn a （结果用含有n 的代数式表示）.14．【理科】已知函数⎩⎨⎧>≤+-=0,ln 0,2)(2x x x x x x f ，若不等式1|)(|-≥ax x f 恒成立，则实数a 的取值范围是 .二、选择题（本大题满分20分）本大题共有4题，每题有且只有一个结论是正确的，必须把正确结论的代号写在答题纸相应的空格中. 每题选对得5分，不选、选错或选出的代号超过一个（不论是否都写在空格内），或者没有填写在题号对应的空格内，一律得零分. 15. 下列命题中，是假命题．．．的为…………………………………………………………………………（）)(A 平行于同一直线的两个平面平行. )(B 平行于同一平面的两个平面平行.)(C 垂直于同一平面的两条直线平行. )(D 垂直于同一直线的两个平面平行.16.【理科】已知曲线1C :122=+y m x （1>m ）和2C :122=-y nx （0>n ）有相同的焦点，分别为1F 、2F ,点M 是1C 和2C 的一个交点,则△21F MF 的形状是………………………………………（）)(A 锐角三角形. )(B 直角三角形. )(C 钝角三角形.)(D 随m 、n 的值的变化而变化.【17. 若函数a x x x f -+=2)(，则使得“函数)(x f y =在区间)1,1(-内有零点”成立的一个必要非充分条件是…………………………………………………………………………………………………………（）)(A 241≤≤-a . )(B 241<≤-a . )(C 20<<a . )(D 041<<-a .18. 对于向量i PA （n i ,2,1=），把能够使得||||||21n PA PA PA +++ 取到最小值的点P 称为i A （n i ,2,1=）的“平衡点”. 如图，矩形ABCD 的两条对角线相交于点O ,延长BC 至E ,使得CE BC =，联结AE ,分别交BD 、CD 于F 、G 两点.下列结论中，正确的是……………………………………（）)(A A 、C 的“平衡点”必为O . )(B D 、C 、E 的“平衡点”为D 、E 的中点.)(C A 、F 、G 、E 的“平衡点”存在且唯一. )(D A 、B 、E 、D 的“平衡点”必为F .三、解答题（本大题满分74分）本大题共有5题，解答下列各题必须在答题纸规定的方框内写出必要的步骤.19、 (本题满分12分) 本题共有2个小题，第1小题满分6分，第2小题满分6分．如图，在xoy 平面上，点)0,1(A ，点B 在单位圆上，θ=∠AOB（πθ<<0）（1）【理科】若点)54,53(-B ，求)42tan(πθ+的值；（2）若OC OB OA =+，四边形OACB 的面积用θS 表示，求OC OA S ⋅+θ的取值范围.20、(本题满分14分) 本题共有2个小题，第1小题满分小题满分8分．如图，已知AB 是圆柱1OO 底面圆O 的直径，底面半径1=R ，圆柱的表面积为π8；点C 在底面圆O 上，且直线C A 1与下底面所成的角的大小为︒60.（1）【理科】求点A 到平面CB A 1的距离；（2）【理科】求二面角C B A A --1的大小（结果用反三角函数值表示）.第20题图21、(本题满分14分) 本题共有2个小题，第1小题满分6分，第2小题满分8分．已知函数12)(-=x x f 的反函数为)(1x f y -=，记)1()(1-=-x f x g . （1）求函数)()(21x g x f y -=-的最小值；（2）【理科】若函数)()(2)(1x g m x f x F -+=-在区间),1[+∞上是单调递增函数，求实数m 的取值范围.22、（本题满分16分）本题共有3个小题，第（1）小题4分，第（2）小题6分，第（3）小题6分．已知曲线Γ:x y 42=，直线l 经过点)2,0(且其一个方向向量为),1(k =.（1）若曲线Γ的焦点F 在直线l 上，求实数k 的值；（2）当1-=k 时，直线l 与曲线Γ相交于A 、B 两点，求||AB 的值；（3）当k （0>k ）变化且直线l 与曲线Γ有公共点时，是否存在这样的实数a ,使得点)0,(a P 关于直线l 的对称点),(00y x Q 落在曲线Γ的准线上. 若存在,求出a的值；若不存在，请说明理由.第22题图23、（本题满分18分）本题共有3个小题，第（1）小题4分，第（2）小题6分，第（3）小题8分.用记号∑=ni i a 0表示n a a a a a +++++ 3210，∑==ni i n a b 02，其中N i ∈，*N n ∈.（1）设n n n n nk k x a x a x a x a a x 221212221021)1(+++++=+--=∑ （R x ∈），求2b 的值；（2）若0a ，1a ，2a ，…，n a 成等差数列，求证：()∑==ni i n i C a 0102)(-⋅+n n a a ；（3）【理科】在条件（1）下，记∑=-+=ni i n i i n C b d 1])1[(1，且不等式n n b d t ≤-⋅)1(恒成立，求实数t 的取值范围.数学理答案一、填空题（本大题满分56分）本大题共有14小题，要求直接将结果填写在答题纸对应的空格中.每个空格填对得4分，填错或不填在正确的位置一律得零分.1.i +-1；2.]1,0(；3.【理科】5；4. 【理科】10；5. 【理科】2；6. 【理科】1等；7. 【理科】4122=-y x ；；8.【理科】.56； 9.【理科】21；10. 【理科】83；； 11. 【理科】 54； 12. 【理科】21； 13. 【理科】1222+-n n ； 14、5二、选择题（本大题满分20分）本大题共有4题，每题有且只有一个结论是正确的，必须把正确结论的代号写在答题纸相应的空格中. 每题选对得5分，不选、选错或选出的代号超过一个（不论是否都写在空格内），或者没有填写在题号对应的空格内，一律得零分.三、解答题（本大题满分74分）本大题共有5题，解答下列各题必须写出必要的步骤.19、 (本题满分12分) 本题共有2个小题，第1小题满分6分，第2小题满分6分．【解】（1）【理科】由于)54,53(-B ，θ=∠AOB ，所以53cos -=θ，54sin =θ253154cos 1sin 2tan =-=+=θθθ 于是)42tan(πθ+321212tan12tan1-=-+=-+=θθ（2）θS θθsin sin 11=⨯⨯=由于)0,1(=,)sin ,(cos θθ=……7分，所以)sin ,cos 1(θθ+=+=OB OA OCθθθcos 1sin 0)cos 1(1+=⨯++⨯=⋅OC OA …………9分OC OA S ⋅+θ1)4sin(21cos sin ++=++=πθθθ（πθ<<0）由于4544ππθπ<+<，所以1)4sin(22≤+<-πθ，所以120+≤⋅+<OC OA S θ20、(本题满分14分) 本题共有2个小题，第1小题满分6分，第2小题满分8分．【解】（1）【理科】设圆柱的母线长为l ，则根据已知条件可得，πππ8222=+⋅=Rl R S 全，1=R ，解得3=l因为⊥A A 1底面ACB ，所以AC 是C A 1在底面ACB 上的射影，所以CA A 1∠是直线C A 1与下底面ACB 所成的角，即CA A 1∠=︒60在直角三角形AC A 1中，31=AA ，CA A 1∠=︒60，3=AC .AB是底面直径，所以6π=∠CAB .以A 为坐标原点，以AB 、1AA 分别为y 、z 轴建立空间直角坐标系如图所示：第20题图y则)0,0,0(A 、)0,23,23(C 、 )3,0,0(1A 、)0,2,0(B ,于是)0,23,23(=,)3,2,0(1=A ,)0,21,23(-= 设平面CB A 1的一个法向量为),,(z y x =，则⎪⎩⎪⎨⎧=-=+-⇒⎪⎩⎪⎨⎧=⋅=⋅03202123001z y y x A CB n ，不妨令1=z ，则)1,23,23(=n ，所以A 到平面CB A 1的距离232|4943|||=+==n d 所以点A 到平面CB A 1的距离为23。

2017届上海市普陀区高三二模数学卷(含答案).

2
3AP CP =.即无人机到甲、丙两船的距离之比为23
.-----------------------7分
(2由:3:1BC AB =得AC =400,且0120APC ∠=, ------------------------------9分由(1,可设AP =2x ,则CP =3x , ---------------------------------------------10分
=⎨+≥⎪⎩,
.若函数( ( g x f x k =-有两个不同的零点,则实数k
的取值范围是____________.
10.某部门有8位员工,其中6位员工的月工资分别为8200, 8300, 8500, 9100, 9500, 9600(单位:元,另两位员工的月工资数据不清楚,但两人的月工资和为17000元,则这8位员工月工资的中位数可能的最大值为____________元.
2017届第二学期徐汇区学习能力诊断卷
高三年级数学学科
2017. 4
一、填空题(本大题共有12题,满分54分,第1~6题每题4分,第7~12题每题5分考生应在答题纸的相应位置直接填写结果.
1.设全集{}1,2,3,4U =,集合{}
2
|540, A x x x x Z =-+<∈,则U C A =____________.
在APC ∆中,由余弦定理,得160000=(2x 2+(3x 2-2(2x (3x cos1200, ------12分解得x
19=
,即无人机到丙船的距离为CP =3x
275≈米. ----14分20、解:(1由条件,得2(1,0 F ,根据220F A F B +=
知, F 2、A、B三点共线,

2017普陀区高三英语二模试卷(完整版)

2017届上海市普陀区高考二模试卷(含答案)II. Grammar and Vocabulary Section A Directions: After reading the passage below, fill inthe blanks to make the passage coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks,use one word that best fits each blank.Wildlife in Decline The populations of Earths wild vertebrates (脊椎动物）have declined by 58% over the past four decades, according to the Living Planet Report 2016 published by the World Wildlife Fund. Climate change and activities such as deforestation and poaching（偷猎）are in large part(21)______(blame) for the decline. If the trend continues, by 2020, the world (22)________(lose) two-thirds of its vertebrate biodiversity. “Sadly, there is no sign yet (23)________ this rate will decrease,” the report says.“Across land, fresh water and the oceans, human activities are forcing wildlife populations to the edge," says Marco Lambertini, director-general of WWF International. The Living Planet Report is published every two years. It aims to provide an assessment of the state of the worlds wildlife. The 2016 study included 3700 different species of birds, fish, mammals, amphibians and reptiles around the world. The team collected data from more than 3000 sources, including government statistics and surveys (24) ______ (carry) out by conservation groups. They then analyzed (25) ______ the population sizes had changed over time. Lambertini said some groups of animals had done worse than others. ''We do see particularly strong declines (26) ______ the freshwater environment. For freshwater species alone, the decline stands at 81% since 1970. This is related to the way that water (27)________(use) and taken out of freshwater systems, and also to the fragmentation（分裂）of freshwater systems through dam building, for example.”The report also highlighted other species, such as African elephants, (28) ________ nave suffered huge declines in recent years, and sharks, which are threatened by overfishing. (29) ________ ________________ all the terrifying facts, however, some conservationists say there is still hope. “One of the things that I think is the most important is that these wild animals haven't yet gone extinct,” said Robin Freeman，head of the Zoological Society of London. “On the whole, (30) ________ are not dying out, andthat means we still have opportunities to do something about the decline.”Section BDirections: Fill in each blank with a proper word chosen from the box. Each word can be used only once. Note that there is one word more than you need.Leadership Traits_（特质）__My job puts me in contact with extraordinary leaders in many fields. So I tend to ____31____ a lot on leadership and how we can inspire successful teamwork, cooperation, and partnerships. In my experience, it is clear that the most successful leadersboth men and womenalways demonstrate three ____32____ traits. Trustworthiness Leaders must set an example of honesty and justice and earn the trust of their teams through their everyday actions. When you do so with positive energy and enthusiasm for ____33____ goals and purpose, you can deeply connect with your team and customers. A culture of trust enables you to empower employees and ____34____ the foundation for communication, accountability, and continuous improvement.Compassion (共情) You can't forget that organizational success ____35____ from the hearts and minds of the men and women you lead. Rather than treating your people as youd like to be treated, treat them as they would like to be treated. Small gestures like choosing face-to-face meetings or sending personal____36____ can have an enormous impact on the spirits of the teams. In addition to thanks and praise, you must also understand peoples needs, pressures, and individual goals, which will allow you to lead them more effectively and ____37____ to their personal ambitions and professional development. Decisiveness In times of ____38____ employees long for clarity. As a leader, you won't always have all of the answersno one expects you toso you must be open to listening and learning from others. Once you understand a particular challenge and ____39____ the options, you have to be confident in making bold and optimistic decisions. Successful leadership demands a lifelong commitment to sharpening these three basic skills. Wherever you have the opportunity to ____40____, the qualities of trustworthiness, compassion, and decisiveness are the keys to leadership and organizational success.III Reading ComprehensionDirections: 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.Boxing is a popular sport that many people seem to be fascinated by . Newspapers , magazines and sports programme on TV frequently _____41____boxing matches . Professional boxers earn a lot of money , and successful boxers are ____42___as big heroes. It seems to me that people , especially men ,find it__43_____because it is an aggressive sport . When they watch a boxing match , they can ___44____ the winning boxer , and this gives them the feeling of being a _ 45_____ themselves . It is a fact that many people have feeling of aggression from time to time , but they cannot show their __46_____in their everyday lives . Watching a boxing match gives them an outlet for this aggression . However , there is a__47____side to boxing . It can be a very dangerous sport . Although boxers wear gloves during the fights , and amateur boxers __48____have to wear helmets , there have frequently been accident in both professional and amateur boxing , sometimes with __49______consequences . Boxers have suffered from head injuries , and occasionally , fighters have even been killed as a result of being knocked out inthe___50_______. Furthermore , studies have shown that there are often long-term effects of boxing , inthe form of serious brain _51______,even if a boxer has never been knocked out . I am personally not at all in __52____of aggressive sports like boxing . I think it would be better if less time was ___53____to aggressive sports on TV, and we welcomed more men and women from non-aggressive sports as our heroes and heroines in our society . I believe that the world is aggressive enough already ! Of course , people like __54_____sports , and so do I , but I think that ___55___other people in an aggressive way is not something that should be regarded as a sport.41. A. broadcast B. cover C. host D. design42.A. kept B.individual C. thought D. treated43.A. appealing B. subjective C. violent D. challenging44.A. pick up B. believe in C. identify with D. long for45. A. winner B. spectator C. inspector D. trainer46. A. ambition B. aggression C. energy D. strength47. A. positive B. indifferent C. deadly D. negative48. A. otherwise B. somehow C. even D. barely49.A. dramatic B. eye-catching C. emotional D. special50. A. court B. ring C. pitch D. yard51.A. Loss B. drain C. damage D. disorder52. A. favour B. process C. charge D. power53.A. shifted B. transformed C. given D. delivered54. A. competitive B. quiet C. cooperative D. regular55. A. invading B. insulting C. teasing D. hittingSection B 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. Choose the one that fits best according to the information given in the passage you have just read.(A)FrankensteinFrankenstein was a book by Mary Shelly ----its been adapted for the screen dozens of times. The story of Frankenstein is told through a series of letters written by Captain Robert Walton to his sister , as he leads an expedition （长征）to the North Pole . On the way , he meets Victor Frankenstein , who tells Walton the story of his life. Frankenstein is the surname of the guy who creates the monster . The monster doesn’t actually have a game . Anyway , Victor is a scientist who’s desperate to discover the secret of life . After years of study , he makes an enormous creature out of human remains and brings it to life . Victor intends it to be beautiful . Unfortunately , the creature turns out really hideous , and Victor runs away in terror . Although the monster is good and kind , humans are scared of it . When they mistreat it , the monster becomes angry and evil . Wanting revenge on its creator , the monster murders Dr. Frankenstein’ brother , his wife , and his best friend . When Victor figures out the monster is behind all the deaths , he swears to track it down and kill it . This book was written in 1816, right after a period called the Enlightenment . The Enlightenment emphasized the pursuit of knowledge and reason , and gave rise to the scientific method . Mary Shelley criticized the Enlightenment through the character of Victor Frankenstein , “ He is a negative example of an Enlightenment scientist -------he pursues knowledge at any cost , and his obsession with discovering the secret of life destroys him , as well as his friends and family .” Some Enlightenment thinkers might have seen such a loss as necessary for the advancement of science , but not Mary Shelley . She and her husband , poet Percy Shelly , were part of the Romantic Movement in art and literature . Romanticism was a reaction against the Enlightenment embrace of rationality and reason . The Romantics emphasized emotion over rationality , and thought people should feel awe and terror in regard to nature . Frankenstein incorporates all these ideas. To Shelley , Frankenstein doesn’t fear and respect the world of nature enough ------she says that by tempering with nature , he brings about complete disaster . Frankenstein is not just a great Romantic novel . Its also considered one of the first major works of science fiction . It influences a whole generation of writers , and the monster has become one of the most recognizable figures in Western culture.56. Which of the following is closest in the meaning to hideous in Paragraph 1?A. UnattractiveB. EngagingC. CharmingD. Handsome57. What is Victor Frankenstein’s fatal weakness?A. His love of scienceB. His rejection of his own creationC. His lack of respect for natureD. His inability to form human relationship58.How was the Romantic era different from the Enlightenment ?A.The Romantic era emphasized emotion ; the Enlightenment emphasized reason .B. The Romantic era occurred during the 20th century ; the Enlightenment occurred during the 19th century .C.The Romantic era emphasized poetry ; the Enlightenment emphasized prose .D.The Romantic era saw major scientific discoveries ; the Enlightenment was an era of literary discovery .59. What effect did “ F rankenstein” have on later works of fiction ?A. It inspired books about the EnlightenmentB. It inspired technical writingC. It inspired books of poetryD. It inspired science-fiction writing60. If you are a 22-year-old nurse , you can apply for the railcard without ________.A. the signature of your director B $ 28 c. application form D. passport-sized photos61. The 1/3 OFF discount may not apply for the railcard holders who travel at _______.A. 11 pm on Sunday in AugustB. 7. am on Tuesday in FebruaryC. 7 am on Monday in JulyD. 11 pm on Friday in March62. Which of the following is True according to the leaflet ?A. If you railcard doesn’t have your name signed , it will be used by someone else.B. The benefits of a railcard are transferable to your friend of your age .C. If you have no ticket but have boarded a train , you will still be eligible for a discounted ticketD. If railcard holders wish to use the Eurostar network , they must pay the full fare. The ‘ PhoneStack(堆)’GameWhenever Michael Carl , the fashion market director at Vanity Fair , goes out to dinner with friends , he plays something, called the “ phone stack” game : Everyone places their phones in the middle of the table ; whoever looks at their device before the check arrives picks up the bill . As smart-phones continue to burrow(钻入) their way into our lives , and wearable devices like Google Glass threaten to eat into our person space even further , overburdened users are carving out their own device-free zones with special tricks and life hacks . “Disconnecting is a luxury that we all need ,” Lesley M. M. Blume , a New York writer keeps her phone away from the dinner table at home .” The expectation that we must always be available to employers ,colleague, family : It creates a real obstacle in trying to set aside private time . But that private time is more important than ever. “ M uch of the digital detoxing （戒毒）is centered on the home , where urgent e-mails from co-workers , texts from friends , Instagram photos from acquaintancesand updates on Facebook get together to disturb domestic quietness. A popular method is to appoint a kind of cellphone lockbox , like the milk tin that Brandon Holley , the former editor of lucky magazine , uses. “ If my phones is buzzing or lighting up , its still a distraction , so it goes in the box . “, said Ms. Holley , who lives in a row house in Red Hook , Brooklyn , with her son ,Smith , and husband , John .” Its not something I want my kid to see.” Sleep is a big factor , which is why some people draw the cellphone-free line at the bedroom.” I don’t want to sleep next to something that is a charged ball of information with photos an e-mails ,” said Peter Som , the fashion designer , who keeps his phone plugged in the living room overnight .” “It definitely is a head clearer and describes daytime and sleep time clearly .”Households with young children are especially mindful about being overconnected , with parents sensitive to how children may imitate bad habits . But its not just inside the home where users are separating themselves from the habit . Cellphone overusers are making efforts to disconnect in social settings ,whether at the request of the host or in the form of friendly competition . The phone-stack game is a lighthearted way for friends to police against rude behavior when eating out . The game gained popularity after Brian Perez, a dancer in Los Angeles , posted the idea online.63.What might be the reason for Michael Carl to play the “ phone stack” game?A.His friends arent willing to pay for the meal voluntarily .B.B. He wants to do some funny things with those phonesC.He has been fed up with digital devices being present everywhereD.The wearable devices have brought threats to his privacy .64.Why is it difficulty for people to break away from their digital device at home ?A. Because they have to do some work at homeB. Because they are expected to be always available to the outsideC. Because people have been addicted to digital devices.D. Because digital devices can enrich peoples family life.65. What does Peter Som do to ensure his sleeping quality at night ?A. He puts his phone in the living room .B. He ignores any information in the phoneC. He deletes all information in his phoneD. He puts his phones in a lockbox66. Why does the phone-stack game become popular as soon as it is posted online?A. The game helps create a harmonious relationship among friends.B. The game makes the host get along well with the guestC. The game can prevent children from imitating their parents behaviorD. The game meets peoples demand for keeping away from phones easily“Any apple today ?”, Effie asked cheerfully at my window ,. I followed her to her truck and bought a kilo . On credit , of course . Cash was the one thing in the world I lacked just them . All pretense （借口）of payment was drooped when our funds , food and fuel decreased to alarming lows. Effie came often , always bringing some gift: a jar of peaches or some firewood . There were other generosities.___________ Effie was not a rich woman . Her income , derived from investment she had made while running an interior decorating shop , had never exceeded $200 a month , which she supplemented by selling her apples .But she always managed to help someone poorer . Years passed before I was able to return the money Effie had given me from time to time . She was ill now and had aged rapidly in the last year .” Here , darling , “ I said , “ is what I owe you ,” _____________” Give it back as I gave it to you -----a little at a time.” “ I think she believed there was magic in the slow discharge of a love debt. The simple fact is that I never repaid the whole amount to Effie , for she died a few weeks later . By now , the few dollars Effie gave me have been multiplied many times . But a curious thing began to happen . ___________At that time , it seemed that my debt would forever go unsettled . So the account can never be marked closed , for Effies love will go on in hearts that have never known her .IV. Summary Writing Directions:Read the following passage. Summarize the main idea and the main point(s) of the passage in no more than 60 words. Use your own words as far as possible.Chaco Great House As early as the twelfth century A.D., the settlements of Chaco Canyon in New Mexico in the American Southwest were notable for their "great houses," massive stone buildings that contain hundreds of rooms and often stand three or four stories high. Archaeologists have been trying to determine how the buildings were used. While there is still no universally agreed upon explanation, there are three competing theories.One theory holds that the Chaco structures were purely residential, with each housing hundreds of people. Supporters of this theory have interpreted Chaco great houses as earlier versions of the architecture seen in more recent Southwest societies. In particular, the Chaco houses appear strikingly similar to the large, well-known "apartment buildings" at Taos, New Mexico, in which many people have been living for centuries.A second theory contends that the Chaco structures were usedto store food supplies. One of the main crops of the Chaco people was grain maize, which could be stored for long periods of time without spoiling and could serve as a long-lasting supply of food. The supplies of maize had to be stored somewhere, and the size of the great houses would make them very suitable for the purpose.A third theory proposes that houses were used as ceremonial centers. Close to one house, called Pueblo Alto, archaeologists identified an enormous mound formed by a pile of old material. Excavations of the mound revealed deposits containing a surprisingly large number of broken pots. This finding has been interpreted as evidence that people gathered at Pueblo Alto for special ceremonies. At the ceremonies, they ate festive meals and then discarded the pots in which the meals had been prepared or served. Such ceremonies have been documented for other Native American cultures.V. Translation Directions: Translate the following sentences into English, using the words given in the brackets.72. 想和我一起看电影的人请举手。

2017届上海市普陀区高三下学期质量调研(二模)考试英语试题及答案

2017学年第二学期普陀区高三英语质量调研试卷（考试时间 120分钟满分 150分）第I卷（共103分）I. Listening ComprehensionSection A Short ConversationsDirections: In Section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the questions you have heard.1. A. At the office. B. Home in bed.C. On his way to work.D. Away on vacation.2. A. His wife. B. A travel agent staff. C. A waiter. D. A hotel clerk.3. A. 11:20. B. 10:30. C.10:50. D. 11:30.4. A. She can’t finish her assignment, either.B. She can’t afford a computer right now.C. The man can use her computer.D. The man should buy a computer right away.5. A. The famous professor has given several lectures.B. The guest lecturer’s opinion is different from Dr. Johnson’s.C. Dr. Johnson and the guest speaker were schoolmates.D. Dr. Johnson invited the economist to visit their college.6. A. The woman does her own housework.B. The woman needs a housekeeper.C. The woman's house is in a mess.D. The woman works as a housekeeper.7. A. The woman didn't expect it to be so warm at noon.B. The woman is sensitive to weather changes.C. The weather forecast was unreliable.D. The weather turned cold all of a sudden.8. A. She wants to take the most direct way.B. She may be late for the football game.C. She is worried about missing her flight.D. She is currently caught in a traffic jam.9. A. The man regrets being absent-minded.B. The woman saved the man some trouble.C. The man placed the reading list on a desk.D. The woman emptied the waste paper basket.10. A. Take the test again in 8 weeks.B. Call to check his scores.C. Be patient and wait.D. Inquire when the test scores are released.Section BDirections: In Section B, you will hear two short passages, and you will be asked three questions on each of the passages. The passages will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. In about 20 years. B. Within a week.C. In a couple of weeks.D. As soon as possible.12. A. Yes, of course. B. Possibly not.C. Not mentioned.D. Definitely not.13. A. Her complaint was ignored. B. The store sent her the correct order.C. The store apologized for their mistake.D. The store picked up the wrong items.Questions 14 through 16 are based on the following passage.14. A. To withdraw his deposit. B. To cash a check.C. To rob the bank.D. To get his prize.15. A. They let him do what he wanted to.B. They helped him find large bills.C. They pressed the alarm.D. They called the police.16. A. He was afraid that he would be caught on the spot.B. Large bills were not within his reach.C. The maximum sum allowed was 55,000.D. He was limited by time and the size of his pockets. Section CDirections: In Section C, you will hear two longer conversations. The conversations will be read twice. After you hear each conversation, you are required to fill in the numbered blanks with the information you have heard. Write your answers on your answer sheet.Blanks 17 through 20 are based on the following conversation. Complete the form. Write NO MORE THAN ONE WORD for each answer.Blanks 21 through 24 are based on the following conversation. Complete the form. Write NO MORE THAN THREE WORDS for each answer.II. Grammar and VocabularySection ADirections: After reading the passages below, fill in the blanks to make the passages coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.(A)Madonna：Singer/actress, born Michigan, USA, 1959Originally a dancer, she had her first popular record ‘Holiday’ in 1983. In 1985 she began her film career and also married actor Sean Penn, but (25)____ marriage lasted less than four years. Her ‘Blond Ambition Tour’ in 1990 with special clothes(26)____(design) by Jean Paul Gaultier caused much conflict. Her career took a more respectable direction, however, with the birth of her first child, Lourdes, in 1997, and her performance in the title role of Evita.Pelé：footballer, born Edson Arantes do Nascimento, Tres Coracoes, Brazil, 1940(27)____(consider) by many to be the greatest footballer of all time, he became a world star at the age of only seventeen, when Brazil first won the World Cup in Sweden. Perhaps his (28)____(great) success in his life was to win the third World Cup in Mexico in 1970. He played in four World Cup competitions, and scored over 1,200 goals in his career before finally (29)____(retire) in 1977. He (30)____(appoint) Brazilian Special Minister for Sport in 1994.Steffi Graf：tennis player, born Neckerau, Germany, 1969(31)____ Graf turned professional at the age of thirteen, she won her first major tournament in 1986 and became the world’s number one a year later. In 1988 she became the first woman since 1970 to win ‘The Grand Slam’(Wimbledon, the US, Australian and French Open tournaments). She (32)____(win) over 100 titles in her career and earned up to $20 million.(B)One in three American children now live with only one parent. (33)____ ____ the traditional family of Japan is strong, divorce still went up quickly between 1980 and 1995.(34)____ is more important is that the nature of the familyis changing. In Sweden and Denmark, around half of all babies are now born to unmarried parents, and in the United Kingdom and France more than a third.Families are getting smaller. The average Turkish family had seven members in 1970; today it has only five. And in Spain and Italy, (35)____ families were always traditionally large, the birthrate was the lowest in the developed world in 1995. This fall in the birthrate is due to the fact that, as more women have careers, they are waiting longer and longer (36)____(start) a family. The age (37)____ ____ the average woman has her first baby is now 28 in Western Europe, and it is getting later.So the nuclear family is clearly changing, but is it in danger of (38)____(disappear) completely?The truth is (39)____ it is still too early to tell. In some countries these patterns are actually reversing. In the United States, Scandinavia and the United Kingdom, the birthrate is rising once more; and in Denmark, for example, marriage is becoming more popular again. In the United States, the divorce rate in fact fell (40)____ 10 per cent between 1980 and 1990, and it is continuing to fall.Section BDirections: Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.A. achievedB. authorityC. availableD. codeE. dominatedF. educationalG. opinionsH. mattersI. relatedJ. representativesK. symbolizationIt is important that students’ feelings, opinions and suggestions are listened to, taken into account, and that the right action is taken. There are a number of ways that this can be __41__, i.e. school councils, year councils and peer mentoring.School councilsMost schools have a school council which exists to let the teachers and head teacher know what students’ __42__ are on a range of school issues. The school council usually consists of two or three elected __43__ from each year group.A school council might meet once or twice a month to discuss issues such as the dress __44__, the use of social areas, charity fundraising and bullying.Year councilsBecause school councils are sometimes __45__ by olderstudents, some schools have introduced year councils. The aim of a year council is to give students the opportunity to express opinions on __46__ of importance to that particular year group. The following is an example of the rules relating to a school’s council for year 8 (pupils aged 12-13).The head of year will attend all council meetings as an observer and both they and the other year staff will be __47__ as required to offer support and advice to council members and to assist in the settlement of arguments.Peer mentoringThere are other ways in which students’ voices can be heard. One of the most popular schemes involves peer mentoring. Those who express an interest receive training to become mentors(导师) so that they are better equipped to help others. This starts from primary school age, when the mentors may get involved in issues __48__ to conflict resolution. At secondary school and at university, mentors are likely to deal with a larger variety of issues, such as __49__ and health-related matters.The belief in schemes like these is that being heard by your peers can be more effective and helpful as fellow students may have more time and understanding than teachers or others in __50__.III. Reading ComprehensionSection ADirections: 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.Many people complain that their memory is bad, particularly as they get older. Life would be so much easier if we could remember things __51__. So how can we improve our memory?Many people think that repeating things is the best way to remember. While this undoubtedly helps short-term memory (remembering a telephone number for a few seconds, __52__), psychologists doubt whether it can help you to remember things for long. The British psychologist E.C. Stanford seemed to __53__ this point when he tested himself on five prayers that he had read aloud every morning for over 25 years. He found that he could remember no more than three words of them! __54__, especially for remembering numbers, is ‘chunking’ (分块), or grouping the information. The following numbers would be __55__ for most of us to remember. 1492178919931848. But look at them in ‘chunks’, and it becomes much easier. 1492 1789 1993 1848.So what about ‘memory training’? We’ve all __56__ people who can memorise packs of card by heart --- how is this done and can anyone learn how to do it? __57__ experts, there are various ways of training your memory. Many of them __58__ forming a mental picture of the items to be memorised. Onemethod, which may be useful in learning foreign languages, is to create a picture in your mind __59__ a word you want to remember. Another method is to invent a story that includes all the things you want to remember. People were asked to remember up to 120 words using this technique; when tested afterwards, on average, they were able to __60__ 90 per cent of them! Surprisingly, however, there is nothing __61__ about these methods --- they were around even in ancient times. Apparently the Roman general Publius Scipio could __62__ his entire army --- 35,000 men in total!__63__, not all of us are interested in learning long lists of names and numbers just for fun. For those studying large quantities of information, psychologists suggest that the best way to ‘form __64__ connections’ is to ask yourself lots of questions as you go along. So, for example, if you were reading about a particular disease, you would ask yourself questions like: ‘Do people get it from water?’, ‘What parts of the body does it affect?’ and so on. This is said to be far more effective than time spent ‘__65__’ reading and re-reading notes.51. A. effortlessly B. purposefully C. exactlyD. carelessly52. A. by contrast B. in that case C. in no wayD. for example53. A. raise B. prove C. discuss D. stress54. A. More helpful B. Much worse C. More difficultD. Much shorter55. A. convenient B. impossible C. meaningfulD. technical56. A. agreed with B. learned from C. heard aboutD. apologized for57. A. Due to B. In case of C. According toD. In spite of58. A. exclude B. mean C. suggest D. involve59. A. isolated from B. sensitive to C. responsible for D. associated with60. A. recall B. recite C. reviseD. restore61. A. effective B. awful C. valuable D. new62. A. train B. recognize C. lead D.command63. A. Furthermore B. However C. SummarilyD. Therefore64. A. unknown B. loose C. meaningful D. personal65. A. passively B. silently C. amusingly D. extensivelySection BDirections: 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. Choose the one that fits best according to the information given in the passage you have just read.(A)A night out in Tokyo is much the same as a night out in Milan these days, according to a survey about socialising, conducted amongst 16 to 34-year-olds around the world. Wherever you live, a typical night out is spent eating burgers, seeing American films or listening to English-language music in clubs and bars. Individual differences do survive but American culture is everywhere.Differences in the social behavior of the two sexes arealso disappearing. Most people surveyed felt that it was ‘perfectly normal’ for groups of young women to go out alone, that it was ‘equally acceptable’ for young women to smoke and drink, and that a couple should split the bill when they go out together. For most young people these were the biggest differences between their own generation and their parents’.Interestingly, however, most young people interviewed said that parents are still stricter with daughters than sons about where they go and who they go with. Overall, only 10 per cent thought that parents treat their sons and daughters equally, and almost no one thought parents were stricter with their sons!Important national differences appear, however, when it comes to time-keeping. In the Far East and Eastern Europe a night out starts --- and finishes --- much earlier: there seven o’clock was the average time for meeting up with friends. For many Southern European and South Americans, on the other hand, an evening out doesn’t even start until ten or eleven o’clock, by which time many of their South Korean or Japanese counterparts are safely home in bed!Parents’ rules reflect this. Most Japanese parents expect their teenagers home by ten o’clock or even earlier, whereasin Europe it is more likely to be eleven or twelve o’clock. The most surprising findings came from Argentina, however, where it is apparently quite normal for 15 and 16-year-olds to stay out all night. But then perhaps this is because their parents have less to worry about --- 80 percent of Argentine youngsters claimed that they rarely or never drink alcohol!66. Night out in Tokyo is similar to it in Milan because ________.A. English-language activities are highly welcomedB. they are experiencing the different globalized-cultureC. American culture is very popular all around the worldD. all the young people have the same habits and hobbies67. One of the biggest differences between young people and their parents lies in ______.A. the music style and stars they lovedB. their attitude towards paying money for dinnerC. the decreasing number of young women smokingD. the time they meet up with people and have evening out68. In the last paragraph, ‚this‛ refers to ______.A. evening outB. drinking alcoholC.time-keeping D. staying up late69. What is the passage mainly talking about?A. The same night-out life in all the modern cities.B. The similarities and differences in social behaviors.C. Comparing night life between the east and the west.D. Parents’different rules between their sons and daughters.(B)Your Write Source book is loaded withinformation to help you learn about writing.One section that will be especially helpfulis the ‚Proofreader’s Guide‛ at the backof the book. This section covers all of the rules for language and grammar.The book also includes four units covering the types of writing that you may have to complete on district or state writing tests. At the end of each unit, there are samples and tips for writing in science, social studies, and math.Write Source will help you with other learning skills, too: study-reading, test taking, note taking, and speaking. This makes the Write Source a valuable writing and learning guide in all of your classes.Your Write Source guide…With practice, you will be able to find information in the book quickly using the guides explained below.The TABLE OF CONTENTS (starting on the next page) lists the six major sections in the book and the chapters found in each section.The INDEX (starting on page 751) lists the topics covered in the book in alphabetical order. Use the index when you are interested in a specific topic.The COLOR CODING used for ‚Basic Grammar and Writing‛(blue), ‚A Writer’s Resource‛ (green), and the ‚Proofreader’s Guide‛ (yellow) make these important sections easy to find.The SPECIAL PAGE REFERENCES in the book tell you where to turn for additional information about a special topic.70. If you want to learn about ‚Tenses of verbs‛ in writing, you should refer to ______.A. Proofreader’s GuideB. Special page referencesC. Table of contentsD. Different Color Coding71. Besides writing skills, which of the following skills can be found in Write Source?A. Classifying contents.B. Taking notes.C. Making science experiments.D. Matching colors.72. The purpose of the passage is to _____.A. persuade readers to buy the boo kB. offer the book’s review to readersC. introduce the useful skills in writingD. helpreaders to use the book skillfully(C)It is well-known that twins are closer to each other than most brothers and sisters ---- after all, they probably spend more time with each other. Parents of twins often notice that they develop special ways of communicating: they invent their own words and one can often finish the other's sentence. In exceptional circumstances, this closeness becomes more extreme: they invent a whole language of their own, as in the case of Grace and Virginia Kennedy from Georgia in the USA, who communicated so successfully in their own special language that they did not speak any English at all until after they started school.However, these special relationships are the result of lives spent almost entirely in each other's company. What happens when twins do not grow up together, when they are separated at birth for some reason? Are they just like any other strangers, or are there still special similarities between them? Professor Tom Bouchard, of the University of Minnesota, set out to find the answer to this question. He traced sixteen pairs of twins, who were adopted by different families whenthey were babies, and often brought up in very different circumstances. Each twin was then interviewed about every small detail of their life.The results of this research make a surprising reading. Many of the twins were found to have the same hobbies, many have suffered the same illnesses, and some have even had the same type of accident at the same point in their lives. One pair of middle-aged women arrived for their first meeting in similar dresses, another pair were wearing similar jewellery. The most incredible similarities are to be found in the case of Jim Springer and Jim Lewis from Ohio in the USA. The story of the 'Jim Twins' made headline news across USA. Born to an immigrant woman in 1939, and adopted by different families at birth, both babies were named Jim by their new parents.But what can be the explanation for these remarkable similarities? Is it all pure coincidence, or is the explanation in some way genetic? Research into the lives of twins is forcing some experts to admit that our personalities may be at least partly due to 'nature'. On the other hand, analysts are also anxious to emphasise that incredible coincidences do happen all the time, not just in the lives of twins.73. The case of Grace and Virginia Kennedy (Para. 1) is to show that ______.A. twins communicate with each other in an unusual wayB. twins are more likely to suffer from speaking problemsC. most twins have exceptional abilities to invent a new languageD. twins won’t have an effective communication until they go to school74. The purpose of Tom Bouchard’s study is to find ______.A. what will happen if twins spend lives entirely in the same companyB. why the 16 pairs of twins have been adopted by different familiesC. whether separated growing up has effect on twins’special similaritiesD. when the special similarities come into being during their growing up75. What does the word ‚reading‛ in Paragraph 3 most probably mean?A. Book.B. Interpretation.C. Literature.D. Measurement.76. According to Tom Bouchard’s research, the special similarities between twins ______.A. depend on what the twins enjoy and suffer fromB. can not be proved or accepted by all the expertsC. result from the twins’ growing up and developmentD. are not closely linked with where the twins are raised77. What can be learned from the last paragraph?A. Incredible coincidences happen to twins all the time.B. Nature is the only way to explain the similarities between twins.C. The differences between twins are to some extent the results of genes.D. Similarities shows the close relationship between two strange persons.Section CDirections: Read the passage carefully. Then answer the questions or complete the statements in the fewest possible words.All of us exist in ‘bodies’ of different shapes, heights, colors and physical abilities. The main reasons for the differences are genetic, and the fact that people’s bodies change as they age. However, a huge range of research indicates that there are social factors too.Poorer people are more likely to eat ‘unhealthy’ foods, to smoke cigarettes and to be employed in physically difficult work or the opposite: boring, inactive employment. Moreover, their housing conditions and neighbourhoods tend to be worse. All of these factors impact upon the condition of a person’s health: the physical shapes of bodies are strongly influenced by social factors.These social factors are also closely linked to emotional wellbeing. People with low or no incomes are more likely to have mental health problems. It is not clear, however, whether poverty causes mental illness, or whether it is the other way around. For example, certain people with mental health issues may be at risk of becoming homeless, just as a person who ishomeless may have an increased risk of illnesses such as depression.There are other types of social factors too. Bodies are young or old, short or tall, big or small, weak or strong. Whether these judgments matter and whether they are positive or negative depends on the cultural and historical context. In fact, the culture of different societies promote very different valuations of body shapes. What is considered as attractive or ugly, normal or abnormal varies enormously. Currently, for example, in rich societies the idea of slimness is highly valued, but historically this was different. In most societies the ideal body shape for a woman was a ‘full figure’, while in middle-aged man, a large stomach indicated that they were financially successful in life.Sociologists are suggesting that we should not just view bodies and minds in biological terms, but also in social terms. The physical body and what we seek to do with it change over time and society. This has important implications for medicine and ideas of health. Thus, the idea of people being ‘overweight’is physically related to large amounts of processed food, together with lack of exercise, and is therefore a medical issue. However, it has also become a mentalhealth issue and social problem as a result of people coming to define this particular body shape as ‘wrong’ and unhealthy. (Note: Answer the questions or complete the statements in NOMORE THAN TEN WORDS.)78. Besides social factors, what are the other two reasons for differences in bodies?79. The social factors are likely to have a great effect on people’s ______ and ______.80. Valuations of body shapes change with ______.81. The ‚This‛ in the last paragraph refers to ______.第II卷（共47分）I. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.1.考官将会问你几个关于科技发展的问题。

2024年上海普陀区高三二模数学试卷和答案

上海普陀区2023-2024学年第二学期高三数学质量调研2024.4考生注意:1.本试卷共4页，21道试题，满分150分.考试时间120分钟.2.作答必须涂（选择题）或写（非选择题）在答题纸上，在试卷上作答一律不得分.3.务必用钢笔或圆珠笔在答题纸相应位置正面清楚地填写姓名、准考证号，并将核对后的条码贴在指定位置上.一、填空题（本大题共有12题，满分54分）考生应在答题纸相应编号的空格内直接填写结果，每个空格填对前6题得4分、后6题得5分，否则一律得零分.1．已知复数1i z =+，其中i 为虚数单位，则z 在复平面内所对应的点的坐标为.2.已知R a ∈，设集合{}1,,4A a =，集合{}1,2B a =+，若A B B = ，则a =.3.若π3cos()35θ-=，则πsin()6θ+=________.4.已知()24,2X N ，若()00.02P X <=，则()48P X <<=.5.若实数a ，b 满足20a b -≥，则124ab+的最小值为_______.6.设()20121nnn x a a x a x a x +=++++ （1,N n n ≥∈），若54a a >，且56a a >，则1nii a==∑_.7.为了提高学生参加体育锻炼的积极性，某校本学期依据学生特点针对性的组建了五个特色运动社团，学校为了了解学生参与运动的情况，对每个特色运动社团的参与人数进行了统计，其中一个特色运动社团开学第1周至第5周参与运动的人数统计数据如表所示.周次x 12345参与运动的人数y3536403945若表中数据可用回归方程 2.3y x b =+（118x ≤≤，N x ∈）来预测，则本学期第11周参与该特色运动社团的人数约为_______.（精确到整数）8.设等比数列{}n a 的公比为q （1,N n n ≥∈），则“212a ，4a ，32a 成等差数列”的一个充分非必要条件是________.9.若向量a 在向量b 上的投影为13b，且3a b a b -=+ ，则cos ,a b = ________.10.已知抛物线2y =的焦点F 是双曲线Γ的右焦点，过点F 的直线l 的法向量(1,n = ，l 与y 轴以及Γ的左支分别相交A ，B 两点，若2BF BA =，则双曲线Γ的实轴长为_______.11.设k ，m ，n 是正整数，n S 是数列{}n a 的前n 项和，12a =，11n n S a +=+，若1(1)ki i i m t S ==-∑，且{}0,1i t ∈，记12()k f m t t t =+++ ，则(2024)f =________.12.已知R a ∈，若关于x 的不等式(2)e 0xa x x --->的解集中有且仅有一个负整数，则a 的取值范围是.二、选择题（本大题共有4题，满分18分，第13-14题每题4分，第15-16题每题5分）每题有且只有一个正确答案，考生应在答题纸的相应编号上，将代表答案的小方格涂黑，否则一律得零分.13.从放有两个红球、一个白球的袋子中一次任意取出两个球，两个红球分别标记为A 、B ，白球标记为C ，则它的一个样本空间可以是…………………………………………（）)A ({},AB BC ()B {},,AB AC BC ()C {},,,AB BA BC CB ()D {},,,,AB BA AC CA CB14.若一个圆锥的体积为3，用通过该圆锥的轴的平面截此圆锥，得到的截面三角形的顶角为π2，则该圆锥的侧面积为…………………………………………（）)A (()B 2π()C ()D 15.直线l 经过定点()2,1P ，且与x 轴正半轴、y 轴正半轴分别相交于A ，B 两点，O 为坐标原点，动圆M 在△OAB 的外部，且与直线l 及两坐标轴的正半轴均相切，则△OAB 周长的最小值是…（）)A (3()B 5()C 10()D 1216.设n S 是数列{}n a 的前n 项和（1,N n n ≥∈），若数列{}n a 满足：对任意的2n ≥，存在大于1的整数m ，使得1()()0m n m n S a S a +--<成立，则称数列{}n a 是“G 数列”.现给出如下两个结论：①存在等差数列{}n a 是“G 数列”；②任意等比数列{}n a 都不是“G 数列”.则…………（）)A (①成立②成立()B ①成立②不成立()C ①不成立②成立()D ①不成立②不成立三、解答题（本大题共有5题，满分78分）解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤17.（本题满分14分）本题共有2个小题，第1小题满分6分，第2小题满分8分如图，在四棱锥S ABCD -中，底面ABCD 是边长为1的正方形，2SA SB ==，E 、F 分别是SC 、BD 的中点.（1）求证：EF ∥平面SAB ；（2）若二面角S AB D --的大小为π2，求直线SD 与平面ABCD 所成角的大小.18.（本题满分14分）本题共有2个小题，第1小题满分6分，第2小题满分8分设函数()()sin f x x ωϕ=+，0ω>，0πϕ<<，它的最小正周期为π.（1）若函数π()12y f x =-是偶函数，求ϕ的值；（2）在ABC ∆中，角A 、B 、C 的对边分别为a 、b 、c ，若2a =，π6A =，(24B f c ϕ-=，求b 的值.19.（本题满分14分）本题共有2个小题，第1小题满分6分，第2小题满分8分张先生每周有5个工作日，工作日出行采用自驾方式，必经之路上有一个十字路口，直行车道有三条，直行车辆可以随机选择一条车道通行，记事件A 为“张先生驾车从左侧直行车道通行”.（1）某日张先生驾车上班接近路口时，看到自己车前是一辆大货车，遂选择不与大货车从同一车道通行.记事件B 为“大货车从中间直行车道通行”，求()P A B ；（2）用X 表示张先生每周工作日出行事件A 发生的次数，求X 的分布及期望[]E X.第17题20.（本题满分18分）本题共有3个小题，第1小题满分4分，第2小题满分6分，第3小题满分8分.设椭圆222:1x y a Γ+=（1a >），Γ的离心率是短轴长的4倍，直线l 交Γ于A 、B 两点，C 是Γ上异于A 、B 的一点，O 是坐标原点.（1）求椭圆Γ的方程；（2）若直线l 过Γ的右焦点F ，且CO OB = ，0CF AB ⋅=，求CBF S ∆的值；（3）设直线l 的方程为y kx m =+（,R k m ∈），且OA OB CO +=，求AB 的取值范围.21.（本题满分18分）本题共有3个小题，第1小题满分4分，第2小题满分6分，第3小题满分8分.对于函数()y f x =，1x D ∈和()y g x =，2x D ∈，设12D D D = ，若12,x x D ∈，且12x x ≠，皆有1212()()()()f x f x t g x g x -≤-（0t >）成立，则称函数()y f x =与()y g x =“具有性质()H t ”.（1）判断函数[]2(),1,2f x x x =∈与()2g x x =是否“具有性质(2)H ”，并说明理由；（2）若函数()(]22,0,1f x x x =+∈与()1g x x=“具有性质()H t ”，求t 的取值范围；（3）若函数()212ln 3f x x x=+-与()y g x =“具有性质(1)H ”，且函数()y g x =在区间()0,+∞上存在两个零点1x ，2x ，求证22122x x +>.评分标准（参考答案）二、选择题13141516BC C D三、解答题17.（1）证明：取线段SB 、AB 的中点分别为H 、G ，连接EH 、HG 、FG ，则1//2EH BC =，1//2FG AD =，………2分又底面ABCD 是正方形，即//BC AD =，则//EH FG =，即四边形EFGH 为平行四边形，则//EF HG ，………4分又EF 在平面SAB 外，HG ⊂平面SAB ，则//EF 平面SAB .………6分备注：连接AC ，利用SAC ∆的中位线性质，证明结论，仿以上步骤，相应评分.（2）取线段AB 的中点为O 点，连接SO 、DO ，又2SA SB ==，底面ABCD 是边长为1的正方形，则SO AB ⊥，且152SO =，52DO =，………4分又二面角S AB D --的大小为π2，即平面SAB ⊥平面ABCD ，又SO ⊂平面SAB ，平面SAB 平面ABCD AB =，则SO ⊥平面ABCD ，则SDO ∠是直线SD 与平面ABCD 所成角，………6分在Rt SDO ∆中，tan SOSDO DO∠==即π3SDO ∠=，则直线SD 与平面ABCD 所成角的大小为π3.………8分备注：用空间向量求解，仿以上步骤相应评分.18.（1）因为函数()()sin f x x ωϕ=+的最小正周期为π，且0ω>，所以2ππω=，即2ω=，………2分则ππ(sin(2)126y f x x ϕ=-=+-，又函数π()12y f x =-是偶函数，则πππ62k ϕ-=+，Z k ∈，………4分即2ππ3k ϕ=+，又0πϕ<<，则2π3ϕ=.………6分（2）由(24B f c ϕ-=得，sin 4B c =，又2a =，π6A =，则sin sin 44b A b B a ===，即b =，………4分由余弦定理得，2222232cos 32a b c bc A c c c =+-=+-⋅⋅，………6分即2c =，则b =………8分19.（1）方法一：依题意得，两辆车从直行车道通行这个样本空间中的基本事件共有23P 个，事件A B 只有1个基本事件，………4分则()23116P A B P == .………6分方法二：依题意得，事件B 的概率为1()3P B =，事件A 基于条件B 的概率为1()2P A B =，…4分则()()()111|236P A B P A B P B ==⨯= .………6分（2）依题意得，事件A 发生的次数X 可取：0,1,2,3,4,5，则X 的分布为：542332450123455555550123452121212121C C C C C C 3333333333⎛⎫⎪ ⎪⎛⎫⎛⎫⎛⎫⎛⎫⎛⎫⎛⎫⎛⎫⎛⎫⎛⎫⎛⎫ ⎪⎪ ⎪⎪⎪⎪ ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭⎝⎭⎝⎭⎝⎭⎝⎭⎝⎭⎝⎭⎝⎭⎝⎭即01234532808040101243243243243243243⎛⎫ ⎪ ⎪ ⎪⎝⎭，………4分则[]80804010112345243243243243243E X =⨯+⨯+⨯+⨯+⨯，………6分则所求的X 的期望[]53E X =.………8分20.（1）由Γ的离心率是短轴的长的4倍，得2a =a =，………2分又1a >，则a =故椭圆Γ的方程为2212x y +=.………4分（2）设Γ的左焦点为1F ，连接1CF ，因为CO OB =，所以点B 、C 关于点O 对称，又0CF AB ⋅=，则CF AB ⊥，由椭圆Γ的对称性可得，1CF CF ⊥，且三角形1OCF 与三角形OBF 全等，………2分则1112CBF CF F S S CF CF ==⋅ ，………4分又1222114CF CF CF CF F F ⎧+=⎪⎨+==⎪⎩，化简整理得，12CF CF ⋅=，则1CBF S = .………6分（3）设11(,)A x y ，11(,)B x y ，00(,)C x y ，又OA OB CO +=，则012()x x x =-+，012()y y y =-+，由2212x y y kx m ⎧+=⎪⎨⎪=+⎩得，222(12)4220k x mkx m +++-=，222222168(12)(1)8(21)m k k m k m ∆=-+-=-+，由韦达定理得，122412mkx x k-+=+，21222212m x x k -=+，………2分又121222()212my y k x x m k+=++=+，则02412mk x k =+，02212my k -=+，因为点C 在椭圆Γ上，所以222242()2()21212mk m k k -+=++，化简整理得，22412m k =+，………4分此时，22222218(21)8(21)6(21)04k k m k k +∆=-+=+-=+>，则AB =====，………6分令212t k =+，即1t ≥，则(]2266333=33,612k t k t t ++=+∈+，则AB的取值范围是.………8分21.解：（1）（1）由[]12,1,2x x ∈，且12x x ≠，得1224x x <+<，即124x x +<，………2分则1212124x x x x x x +⋅-<-，即221212222x x x x -<-，即()()()()12122f x f x g x g x -≤-，则函数[]2(),1,2f x x x =∈与()2g x x =“具有性质(2)H ”.………4分（2）由函数()(]22,0,1f x x x =+∈与()1g x x=“具有性质()H t ”，得()()()()1212f x f x t g x g x -≤-，(]12,0,1x x ∈，且12x x ≠，即2212121122x x tx x +--≤-，整理得21121212()()x x x x x x tx x -+-≤，则1212()t x x x x ≥+对(]12,0,1x x ∈恒成立，………2分又(]12,0,1x x ∈，12x x ≠，则1202x x <+<，1201x x <<，即12120()2x x x x <+<，………4分则2t ≥，即所求的t 的取值范围为[)2,+∞.………6分（3）由函数()y g x =在()0,+∞有两个零点12,x x ，得()()120g x g x ==，又函数()212ln 3f x x x=+-与()y g x =“具有性质(1)H ”，则()()()()12120f x f x g x g x -≤-=，即()()12f x f x =，即122212112ln 32ln 3x x x x +-=+-，………2分令221122,x t x t ==，即121211ln 3ln 3t t t t +-=+-，记()1ln 3h x x x=+-，即()()12h t h t =，因为()22111x h x x x x-'=-+=，当1x <时，()0h x '<；当1x >时，()0h x '>，所以函数()y h x =在区间()0,1是减函数，在()1,+∞上是增函数.………4分要证22122x x +>，即证122t t +>，不妨设1201t t <<<，即证2121t t >->，只需证()()212h t h t >-，即证()()112h t h t >-，设()()()2H x h x h x =--，即()()11ln ln 22H x x x x x=+----，………6分因为()()()()222224111110222x H x x x x x x x -'=-+-+=-≤---，所以函数()y H x =在()0,+∞是减函数，且(1)0H =，又101t <<，则()()110H t H >=，即()()1120h t h t -->，则()()112h t h t >-得证，故22122x x +>.………8分。

普陀区2017学年第一学期高三数学质量调研含参考答案

普陀区2017学年第一学期高三数学质量调研2017.12考生注意:1. 本试卷共4页，21道试题，满分150分. 考试时间120分钟.2. 本考试分试卷和答题纸. 试卷包括试题与答题要求. 作答必须涂（选择题）或写（非选择题）在答题纸上，在试卷上作答一律不得分.3. 答卷前，务必用钢笔或圆珠笔在答题纸正面清楚地填写姓名、准考证号，并将核对后的条码贴在指定位置上，在答题纸反面清楚地填写姓名.一、填空题（本大题共有12题，满分54分）考生应在答题纸相应编号的空格内直接填写结果，每个空格填对前6题得4分、后6题得5分，否则一律得零分.1．设全集{}=1,2,3,4,5U ，若集合{}3,4,5A =，则U A =ð . 2. 若1sin 4θ=，则3cos()2πθ+= . 3. 方程222log (2)log (3)log 12x x -+-=的解=x .4. 91)x的二项展开式中的常数项的值为 . 5. 不等式111x ≥-的解集为_______.6. 函数()22cos 2xf x x =+的值域为 _ . 7. 已知i 是虚数单位，z 是复数z 的共轭复数，若1i012iz +=，则z 在复平面内所对应的点所在的象限为第________象限.8. 若数列{}n a 的前n 项和2321n S n n =-++*(N )n ∈，则lim3nn a n→∞= _ .9. 若直线:5l x y +=与曲线22:16C x y +=交于两点11(,)A x y ，22(,)B x y ，则1221x y x y +的值为 .10. 设1234,,,a a a a 是1,2,3,4的一个排列，若至少有一个()1,2,3,4i i =使得i a i =成立，则满足此条件的不同排列的个数为 .11. 已知正三角形ABCM 是ABC ∆所在平面内的任一动点，若1MA =，则MA MB MC ++的取值范围为________.12. 双曲线2213x y -=绕坐标原点O 旋转适当角度可以成为函数()f x 的图像.关于此函数()f x 有如下四个命题： ①()f x 是奇函数；②()f x的图像过点32⎫⎪⎝⎭或32⎫-⎪⎝⎭； ③()f x 的值域是33,,22⎛⎤⎡⎫-∞-⋃+∞ ⎪⎥⎢⎝⎦⎣⎭；④函数()y f x x =-有两个零点. 则其中所有真命题的序号为 .二、选择题（本大题共有4题，满分20分）每题有且只有一个正确答案，考生应在答题纸的相应编号上，将代表答案的小方格涂黑，选对得5分，否则一律得零分.13. 若数列{}n a *N n ∈（）是等比数列，则矩阵124568a a a a a a ⎛⎫⎪⎝⎭所表示方程组的解的个数是（） )A (0个 ()B 1个 ()C 无数个 ()D 不确定14. “0m >”是“函数()(2)f x x mx =+在区间(0,)+∞上为增函数”的 ………………（）)A (充分非必要条件 ()B 必要非充分条件()C 充要条件 ()D 既非充分也非必要条件15. 用长度分别为2、3、5、6、9（单位：cm ）的五根木棒连接（只允许连接，不允许折断），组成共顶点的长方体的三条棱，则能够得到的长方体的最大表面积为 ……………………（） )A ( 2258cm ()B 2414cm ()C 2416cm ()D 2418cm16. 定义在R 上的函数()f x 满足22,01,()42,10.xxx f x x -⎧+≤<⎪=⎨--≤<⎪⎩，且(1)(1)f x f x -=+，则函数35()()2x g x f x x -=--在区间[1,5]-上的所有零点之和为 ……………………………（） )A (4 ()B 5 ()C 7 ()D 8三、解答题（本大题共有5题，满分76分）解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤17.（本题满分14分）本题共有2个小题，第1小题满分6分，第2小题满分8分如图1所示的圆锥的体积为3，底面直径2AB =,点C 是弧AB 的中点，点D 是母线PA 的中点.（1）求该圆锥的侧面积；（2）求异面直线PB 与CD 所成角的大小.18.（本题满分14分）本题共有2个小题，第1小题满分6分，第2小题满分8分某快递公司在某市的货物转运中心，拟引进智能机器人分拣系统，以提高分拣效率和降低物流成本. 已知购买x 台机器人的总成本为()21150600p x x x =++万元. （1）若使每台机器人的平均成本最低，问应买多少台？19.（本题满分14分）本题共有2个小题，第1小题满分6分，第2小题满分8分设函数()sin()(0,)2f x x πωϕωϕ=+><，已知角ϕ的终边经过点(1,，点11(,)M x y ，22(,)N x y 是函数()f x 图像上的任意两点，当12()()2f x f x -=时，12x x -的最小值是2π. （1）求函数()y f x =的解析式；（2）已知△ABC 的面积为C 所对的边c =cos 4C f π⎛⎫=⎪⎝⎭，求△ABC 的周长.20.（本题满分16分）本题共有3个小题，第1小题满分4分，第2小题满分6分，第3小题满分6分.设点1F ，2F 分别是椭圆C :222212x y t t+=(0)t >的左、右焦点，且椭圆C 上的点到点2F 的距离的最小值为2. 点M ，N 是椭圆C 上位于x 轴上方的两点，且向量1F M 与向量2F N平行.（1）求椭圆C 的方程；（2）当120F N F N ⋅=时，求1FMN ∆的面积；（3）当21F N F M -=2F N 的方程.21.（本题满分18分）本题共有3个小题，第1小题满分4分，第2小题满分6分，第3小题满分8分.设d 为等差数列{}n a 的公差，数列{}n b 的前n 项和n T ，满足1(1)2n n n n T b +=-*(N )n ∈，且52d a b ==. 若实数{}23|k k k m P x a x a -+∈=<<（*N ,3k k ∈≥），则称m 具有性质k P . （1）请判断12,b b 是否具有性质6P ，并说明理由；（2）设n S 为数列{}n a 的前n 项和，若{}2n n S a λ-是单调递增数列，求证：对任意的k （*N ,3k k ∈≥），实数λ都不具有性质k P ；（3）设n H 是数列{}n T 的前n 项和，若对任意的*N n ∈，21n H -都具有性质k P ，求所有满足条件的k 的值.普陀区2017学年第一学期高三数学质量调研评分标准（参考）一、填空题二、选择题三、解答题17.（1）由圆锥的体积21()32ABV OPπ=⋅⋅⋅=，……………………………2分得OP=2PB==, ……………………………………………4分则该圆锥的侧面积为112212222S OB PBπππ=⨯⋅⋅=⨯⨯⨯=. ……………………6分与（2）联结,O D，由条件得//OD PB，即CDO∠是异面直线PBCD所成角或其补角，……………………………………2分点C是弧AB的中点，则CO AB⊥,又PO为该圆锥的高，则PO CO⊥,即CO⊥平面PAB，……………………………4分OD在平面PAB内，则CO OD⊥，即CDO∆为直角三角形，又112DO PB CO===，则4CDOπ∠=，……………………7分即异面直线PB与CD所成角的大小为4π.………………………8分18.（1）由题意得每台机器人的平均成本为()11501600p xxx x=++…………………2分12≥=……………………4分当且仅当150600x x=*(N )x ∈，即300x =时取等号，则要使每台机器人的平均成本最低，应买300台. ………………………………………6分（2）当130m ≤≤时，每台机器人日平均分拣量8()(60)15q m m m =- 28(30)48015m =--+，当30m =时，每台机器人的日平均分拣量最大值为480……2分当30m >时，每台机器人的日平均分拣量仍为480，则引进300台机器人后，日平均分拣量的最大值为19.（1）由角ϕ的终边经过点(1,得tan ϕ= 又2πϕ<，则3πϕ=-，………………………………………………………………3分当12()()2f x f x -=时，12x x -的最小值是2π，则(0)2ππωω=>，即2ω=， ………………………………………………………………………………5分则所求函数的解析式为()sin(2)3f x x π=-. ………………………………………6分（2）由（1）得1cos sin(2)sin 44362C f ππππ⎛⎫==⨯-==⎪⎝⎭，又△ABC 的面积为1sin 2ab C =20ab =， ……………………4分由余弦定理得22212202a b =+-⨯⨯，即2()80a b +=,即a b +=7分则所求的△ABC 的周长为 …………………………………………………………8分20．（1）由0t >得点2(,0)F t ，又椭圆C 上的点到点1F 的距离的最小值为2，2t -=， ………………………………………………3分即2t =，故椭圆C 的方程为22184x y +=.………………………………4分（2）设11(,)N x y ，22M(,)x y ，则2211184x y +=，2222184x y +=且12y 0,0y >>，由（1）得1(2,0)F -，2(2,0)F ，即111(2,y )F N x =+ ，211(2,y )F N x =-，又212111(2)(2)0F N F N x x y ⋅=-++= ，即22114x y +=，联立221122111844x y x y ⎧+=⎪⎨⎪+=⎩，解得1102x y =⎧⎨=⎩，即(0,2)N . ………………………………………………………………2分又1//F M 2F N 且12F N F N ⊥ ，则1(2,2)F N = 是直线1FM 的一个法向量，即直线1F M 的点法向式方程为2(2)20x y ++=，即2220x y ++=.联立22222218420x y x y ⎧+=⎪⎨⎪++=⎩消去2x 整理化简得2223440y y +-=，即223y =或22y =-（舍），得228323x y ⎧=-⎪⎪⎨⎪=⎪⎩，即82(,)33M -. ………………………………………………………………4分则1201140212382133F MN S ∆-==-，即1F MN ∆的面积为43.………………………………6分说明：三角形面积的求法不唯一，可以图形分割，用面积求差来解；也可以用点到直线的距离求出高，再用两点之间的距离公式求出底，用底与高乘积的一半来求等；也可等面积转换求解，请相应给分.（3）延长线段2NF 交椭圆C 于点G ，向量1F M 与向量2F N平行，根据椭圆的中心对称性得21F G FM =且21F N FM >，即2122F N F M F N F G -=-=……………2分又21F N FM >，则直线2F N 的斜率一定存在且值为负，可设直线2F N 的方程为：(2)y k x =-，点1,1N()x y ，2,2G()x y ，且122x x <<，联立方程22184(2)x y y k x ⎧+=⎪⎨⎪=-⎩，整理化简得2222(12)8880k x k x k +-+-=，则2122812k x x k +=+.则221222F N F G -=--124)x x =+-2228(4)1212k k k=-=++，=4212450k k +-=，即22(65)(21)0k k +-=……………5分又0k <，则2k =-，故直线2F N的方程为20x -=. ……………………6分 21.（1）由1111122T b b +=+=-得114b =-， ………………………………1分又312334123441188111616T b b b b T b b b b b⎧+=+++=-⎪⎪⎨⎪+=++++=⎪⎩，得214b =………………………………3分可得5114(5)(5)444n n a a n d n -=+-=+-= 从而65|04P x x ⎧⎫=<<⎨⎬⎩⎭故1b 不具有性质6P ，2b 具有性质6P . …………………………………………4分说明：求2b 是难点，第（1）问不必这样求解，可以直接用等差数列单调性判断下结论，可相应的评分，求2b 以及数列的通项公式的评分可在第（2）问解答过程中体现.（2）()()2174163142242448n n n n n n n S a n λλλλ--++-⎛⎫-=-+⋅-=⎪⎝⎭， ………………………………………2分因为数列{}2n n S a λ-单调递增，所以74322λ+<，即1λ<-，…………………4分又数列{}n a 单调递增，则数列{}n a 的最小项为1314a =->-，则对任意()*,3k k N k ∈≥，都有2314k a λ-<-<-≤，故实数λ都不具有性质k P . ……………………………………………………6分（3）因为1(1)2n n n n T b +=-，所以1*1111(1)(2,N )2n n n n T b n n ----+=-≥∈，两式相减得 111111(1)(1)22n n n n n n n n T T b b -----+-=---*(2,N )n n ≥∈，即 11(1)(1)2n nn n n n b b b --=-+-*(2,N )n n ≥∈，当n 为偶数时，112n n n nb b b --=+，即112n n b -=-，此时1n -为奇数；当n 为奇数时，112n n n n b b b --=--，即1122n n n b b --=-，则1112n n b --=，此时1n -为偶数；则 11(21(2n n nn b n +⎧-⎪⎪=⎨⎪⎪⎩为奇数）为偶数），*N n ∈. ……………………………………3分则 11(20(n n n T n +⎧-⎪=⎨⎪⎩为奇数）为偶数）故 2112342221n n n H T T T T T T ---=+++++246822211(1)1111111124(1)12222223414n n n--=-------=-=--- ……………5分因为114n -对于一切*N n ∈递增，所以311144n ≤-<，所以 211134n H --<≤-.若对任意的*N n ∈，21n H -都具有性质k P ，则11(,]34--⊆6144k k x x ⎧--⎫<<⎨⎬⎩⎭，即61431144k k -⎧≤-⎪⎪⎨-⎪>-⎪⎩，解得1403k <≤，又*2,N k k >∈，则3k =或4，即所有满足条件的正整数k 的值为3和4.………………………………………8分说明：此处可不求n T ，直接用求和定义得2112342221n n n H T T T T T T ---=+++++1234232221=(21)(22)(23)(24)32n n n n b n b n b n b b b b ----+-+-+-++++ 1234232221=[(21)(22)][(23)(24)][32]n n n n b n b n b n b b b b ----+-+-+-++++请相应评分.。