上海市徐汇区2017-2018自招考题

上海专科层次自主招生考试习题集①（含答案）1、团队领导在团队中一般扮演着三个方面的角色, ( )不属于其中之一.A使用资源 B.完成工作 C.建设团队 D.培养个人2、团队的领导张总认为建立团队成员之间的公开性是很重要的,他通常为团队成员创造一些机会和环境,帮助他们增加团队成员之间的公开性,对公开性的建立不起作用的是( ).A 面对每个员说出自己真实的感觉B.通过社交活动,帮助成员相互认识C.团队成员各自都有自己单独做事的方式D.欣赏团队成员不同形式的贡献3、要想使团队具有合作的气氛,必须具备的条件包括( )A.团队成员自己做自己的事B.互相牵制制约C.明确的团队目标D.互相避免交流4、协商的领导方式是( ).A 在做决定时,领导者与团队成员进行讨论:B.在做决定时,领导者与团队进行协商,并让团队成员提出他们的观点进行讨论C. 领导者在团队采取某种想法或行动之前,首先应该说服团队接受D.领导者提出方案,让团队成员讨论5、根据期望理论,人们得到激励以后,就会出现一级的结果,第一级的结果总是与绩效相联系,其中不属于第一级结果的是( ).A.工作目标B.团队目标C.得到领导的提拔和认可D.一个项目的成功完成6、日本本田汽车及摩托车的创始人本田中一郎,从一个穷学生开始,历尽磨难,数次跌倒,没有放弃,反而不断总结、修正、调整自己,最终创立了自己的汽车王国-本田公司。

这个事例说明,在坚持自己的目标计划实施过程中( ).A 必须要得到额外的资源供给自己支持B.根据情况,要不断地进行修正和调整自己的计划C.必须重新进行外配工作D.必须不时地改变工作运作方式7、华星公司的项目团队是一个有效的团队,这个团队利用各种角色的人来承担各种职责,李某是一个会设定目标,制定计划、组织人力、建立制度,以保证按时完成任务的人,那么李某在团队中的角色为().A.挑战者B.评价者C.探索者D.推动者8、近些年电子邮件的出现对邮政业务带来了很大的冲击,这说明（）A.技术的发展不利于企业的发展B.企业要做好外部环境威胁的准备C.企业必须警惕威胁,捕捉机遇D.替代产品的出现对企业构成了一种威胁9、某公司现在的业务遍及铁路运输、无线电通信、旅游、能源等行业,那么这个公司的经营战略是( )。

上海市徐汇区2017-2018 学年高考数学二模试卷（理科）一．填空题（本大题满分56 分）本大题共有14题，考生应在答题纸相应编号的空格内直接填写结果，每个空格填对得 4 分，不然一律得0分．1．（ 4 分）已知会集 A=，会集 B={y|y=x 2， x∈A} ，则 A ∩B= ．2．（ 4 分）若复数 z=1﹣ 2i（ i 为虚数单位），则=．3．（ 4 分）已知直线l 的一个法向量是，则此直线的倾斜角的大小为．4．（ 4 分）某中学采纳系统抽样的方法从该校2014-2015 学年高一年级全体800 名学生中抽取50 名学生进行体能测试．现将800名学生从 1 到 800 进行编号，求得间隔数k==16．若从1～ 16 中随机抽取 1 个数的结果是抽到了 7，则在编号为 33～ 48 的这 16 个学生中抽取的一名学生其编号应当是．5．（ 4 分）在△ ABC 中，角 A ， B ，C 所对的边分别为a， b， c，若 a=，则△ ABC 的面积为．x﹣1（log2 5）的解为．6．（ 4 分）设函数 f （x） =log 2（ 2 +1），则不等式2f（ x）≤f7．（ 4 分）直线 y=x 与曲线 C：（θ为参数，π≤θ≤2）的交点坐标是．8．（ 4 分）甲、乙两人各进行一次射击，假设两人击中目标的概率分别是0.6 和 0.7，且射击结果相互独立，则甲、乙至多一人击中目标的概率为．9．（ 4 分）矩阵中每一行都构成公比为 2 的等比数列，第i 列各元素之和为S i，则=．10．（ 4 分）以以下图：在直三棱柱 ABC ﹣ A 1B 1C1中， AB ⊥BC ，AB=BC=BB 1，则平面 A1B1C 与平面 ABC 所成的二面角的大小为．11．（ 4 分）履行以以下图的程序框图，输出的结果为a，二项式的睁开式中x3项的系数为，则常数m= ．12．（ 4 分）设 f （ x）是定义域为 R 的奇函数， g（ x）是定义域为 R 的偶函数，若函数 f （ x）+g （ x）的值域为 [1， 3），则函数 f（ x）﹣ g（ x）的值域为．13．（ 4 分）△ABC 所在平面上一点P 满足，若△ ABP的面积为 6，则△ ABC 的面积为．14．（ 4 分）关于曲线 C 所在平面上的定点 P0，若存在以点P0为极点的角α，使得α≥∠ AP 0B 关于曲线 C 上的任意两个不一样的点 A ，B 恒建立，则称角α为曲线 C 相关于点 P0的“界角”，并称此中最小的“界角”为曲线C相关于点P0的“确界角”．曲线 C：y=相关于坐标原点O 的“确界角”的大小是．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，不然一律得 0 分．15．（ 5 分）以下不等式中，与不等式≥0 同解的是（）A ． （ x3）（ 2 x ） ≥0 B ． （ x 3）（ 2 x ）＞ 0 C ． ≥0 D ．≥016．（ 5 分） M 、N 两个随机事件，假如 M 、 N 互斥事件，那么（） A ． 是必然事件B ．M ∪ N 是必然事件C ．与 必定 互斥事件D ．与 必定不 互斥事件17．（ 5 分）在极坐 系中，与曲 ρ=cos θ+1 关于直 θ= （ ρ∈R ） 称的曲 的极坐 方程是（） A ． ρ=sin （+θ）+1 B ． ρ=sin （θ）+1 C ． ρ=sin （ +θ） +1 D ． ρ=sin （ θ） +1218．（ 5 分）已知函数f （ x ） =x ?sinx ，各 均不相等的数列{x n } 足 |x i |≤（ i=1 ， 2，3， ⋯，*n ）．令 F （ n ） =（x 1+x 2+⋯+x n ） ?[f （ x 1） +f （ x 2）+⋯f （ x n ） ]（ n ∈N ）． 出以下三个：（ 2）若数列 {x n } 的通 公式， F （ 2k ）＞ 0 k ∈N *恒建立；（ 3）若数列 {x n } 是等差数列， F （n ） ≥0 n ∈N *恒建立．此中真的序号是（）A ． （ 1）（2）B ． （ 1）（ 3）C ． （ 2）（ 3）D ．（ 1）（ 2）（3）三．解答 （本大 分 74 分）本大 共有 5 ，解答以下各 必 在答 相 号的 定地域内写出必需的步 ．19．（ 12 分）如 ，在 Rt △AOB 中，∠ OAB= ，斜 AB=4 ，D 是 AB 的中点． 将 Rt △ AOB以直角AO 旋 一周获得一个 ，点C 底面 周上的一点，且∠BOC=．（ 1）求 的全面 ； （ 2）求异面直AO 与 CD 所成角的大小．（ 果用反三角函数 表示）20．（ 14 分）一个随机 量 ξ的概率分布律以下：ξ x 1 x 2Pcos2Asin （ B+C ）此中 A ， B ， C 角三角形 ABC 的三个内角．（ 1）求 A 的 ；（ 2）若 x 1=cosB ，x 2=sinC ，求数学希望 E ξ的取 范 ．21．（ 14 分）用 管 接而成的花 构件如右 所示， 它的外框是一个等腰梯形 PQRS ，内部是一段抛物 和一根横梁．抛物 的 点与梯形上底中点是 接点 O ，梯形的腰 靠在抛 物 上，两条腰的中点是梯形的腰、抛物 以及横梁的 接点A ，B ，抛物 与梯形下底的两个 接点 C ， D ．已知梯形的高是 40 厘米， C 、 D 两点 的距离 40 厘米．（ 1）求横梁 AB 的 度； （ 2）求梯形外框的用料 度．（注： 管的粗 等要素忽视不 ， 算 果精确到1 厘米．）22．（ 16 分）已知函数f （ x ） =， g （ x ） = ．（ 1）求函数 h （x ） =f （ x ） +2g （ x ）的零点；（ 2）若直 l ：ax+by+c=0 （ a ，b ，c 常数） 与 f （ x ）的 象交于不一样的两点的 象交于不一样的两点 C 、 D ，求 ： |AC|=|BD| ；A 、B ，与g （ x ）（ 3）求函数F （ x ） =[f （ x ） ] 2n [g （ x ） ] 2n （ n ∈N *）的最小 ．23．（ 18 分） 于一 向量（ n ∈N *），令，假如存在（ p ∈{1 ，2，3⋯，n} ），使得 ||，那么称是 向量 的 “h 向量 ”．（ 1）=（n ， x+n ）（n ∈N *），若是向量的 “h 向量 ”，求 数 x 的取 范 ；（ 2）若（ n ∈N *），向量能否存在 “h 向量 ”？ 出你的 并 明原由；（ 3）已知均是向量的 “h 向量 ”，此中 =（ sinx ，cosx ）， =（ 2cosx ，2sinx ）． 在平面直角坐 系中有一点列Q 1，Q 2，Q 3，⋯，Q n 足： Q 1 坐 原点，Q 2 为 的地点向量的终点，且Q 2k+1 与 Q 2k 关于点 Q 1 对称， Q 2k+2 与 Q 2k+1（ k ∈N *）关于点Q 2 对称，求 | |的最小值．上海市徐汇区 2015 届高考数学二模试卷（理科）参照答案与试题分析一．填空题（本大题满分 56 分）本大题共有14 题，考生应在答题纸相应编号的空格内直接 填写结果，每个空格填对得 4 分，不然一律得0 分．1．（ 4 分）已知会集 A=，会集 B={y|y=x2， x ∈A} ，则 A ∩B={1} ．考点 ： 交集及其运算． 专题 ： 会集． 分析： 把 A 中元素代入 B 中求出 y 的值，确立出B ，找出 A 与 B 的交集即可．解答：解：∵ A={1 ， 2， } ， B={y|y=x 2，x ∈A} ，∴ B={ ，1， 4}，则 A ∩B={1} ， 故答案为： {1}评论： 此题观察了交集及其运算，娴熟掌握交集的定义是解此题的要点．2．（ 4 分）若复数 z=1﹣ 2i （ i 为虚数单位） ，则 =6﹣ 2i ．考点 ： 复数的基本看法；复数代数形式的乘除运算． 专题 ： 计算题．分析： 把复数 z=1﹣ 2i 及它的共轭复数代入，将其化简为 a+bi （ a ， b ∈R ）的形式，即可．解答： 解：观察复数基本运算=（ 1﹣ 2i ）（ 1+2i ）+1﹣ 2i=6 ﹣ 2i ．故答案为： 6﹣ 2i ．评论：此题观察复数的基本看法，复数代数形式的乘除运算，是基础题．3．（ 4 分）已知直线 l 的一个法向量是，则此直线的倾斜角的大小为 ．考点 ： 直线的斜率． 专题 ： 直线与圆．分析： 设直线的方向向量为 =（ a ， b ），直线的倾斜角为 α．利用 =0，即可得出．解答：解：设直线的方向向量为 =（ a ， b ），直线的倾斜角为 α．则=a ﹣b=0，∴ =tan α，∴ α= ，故答案为：．评论： 此题观察了直线的方向向量与法向量、向量垂直与数目积的关系，观察了计算能力，属于基础题．4．（ 4 分）某中学采纳系统抽样的方法从该校 2014-2015 学年高一年级全体 800 名学生中抽取 50 名学生进行体能测试． 现将 800 名学生从 1 到 800 进行编号， 求得间隔数 k==16．若从1～ 16 中随机抽取 1 个数的结果是抽到了 7，则在编号为 33～ 48 的这 16 个学生中抽取的一名学生其编号应当是39．考点 ： 系统抽样方法． 专题 ： 概率与统计．分析： 依据系统抽样的定义进行求解．解答：解：∵样本间隔 k=16 ，若从 1～ 16 中随机抽取 1 个数的结果是抽到了7，∴抽取的号码数为 7+16x ，当 x=2 时， 7+16×2=39 ， 即在编号为 33～48 的这 16 个学生中抽取的一名学生其编号应当 39，故答案为： 39评论： 此题主要观察系统抽样的应用，比较基础．5．（ 4 分）在 △ ABC 中，角 A ， B ，C 所对的边分别为 a ， b ， c ，若 a= ，则△ ABC 的面积为．考点 ： 正弦定理． 专题 ： 解三角形． 分析： 利用余弦定理可得 b ，再利用三角形面积计算公式即可得出．解答：解：∵ a=，∴ a 2=b 2+c 2﹣2bccosA ，∴ 3=4+b 2﹣ 4b ×，化为 b 2﹣ 2b+1=0，解得 b=1．∴ S △ABC ===．故答案为：．评论： 此题观察了余弦定理、三角形面积计算公式，观察了推理能力与计算能力，属于中档题．x ﹣1（log 2 5）的解为（﹣ ∞， 0] ．6．（ 4 分）设函数 f （x ） =log 2（ 2 +1），则不等式 2f （ x ） ≤f 考点 ： 指、对数不等式的解法．专题 ： 函数的性质及应用．分析：先依据函数的定义域求出x 的范围，而后代入分析式，解对数不等式，转变为指数不等式进行求解，即可求出 x 的取值范围解答：解： f ﹣ 1x（ x ）=log 2（ 2 ﹣ 1），x ∈（ 0，+∞）．由 2f （ x ） ≤f ﹣1（log 25），2log 2（ 2x+1 ）≤log 2（﹣ 1） =log 24，∴ log 2（ 2x+1）≤1∴ 0＜ 2x +1≤2，∴ 0＜ 2x≤1，? x ≤0； 综上， x ≤0；故答案为：（﹣ ∞， 0]．评论： 此题主要观察了反函数的求解，以及对数函数图象与性质的综合应用，同时观察转变与划归的思想，计算能力，属于中档题7．（ 4 分）直线 y=x 与曲线 C ：（ θ为参数， π≤θ≤2）的交点坐标是．考点 ： 参数方程化成一般方程． 专题 ： 坐标系和参数方程．分析： 此题由曲线 C 的参数方程消去参数后，获得其一般方程，再用双方程联列方程组，获得交点坐标，即此题结论．解题时要注意纵坐标的取值范围．解答：解：由曲线 C ：（θ为参数， π≤θ≤2），获得：（y ≤0）．由，获得，∵ y ≤0，∴，∴．∴直y=x与曲C：（θ 参数，π≤θ≤2）的交点坐是．故答案：．点：本考了将曲的参数方程化一般方程，本度不大，属于基．8．（ 4 分）甲、乙两人各行一次射，假两人中目的概率分是0.6 和 0.7，且射果相互独立，甲、乙至多一人中目的概率0.58．考点：相互独立事件的概率乘法公式．：算；概率与．分析：依据意可得两人能否中目是相互独立的，利用相互独立事件的概率乘法公式可得答案．解答：解：由意可得：两人能否中目是相互独立的，因两人中目的概率分是0.6 和 0.7，所以两人都中目的概率：0.6×0.7=0.42 ，所以甲、乙至多一人中目的概率：1 0.42=0.58 ．故答案： 0.58 ．点：本主要考相互独立事件的定与相互独立事件的概率乘法公式的用，此属于基，只要学生知心的算即可获得全分．9．（ 4 分）矩中每一行都构成公比 2 的等比数列，第i 列各元素之和S i，=．考点：数列的极限；数列的乞降．：算；等差数列与等比数列．分析：i ﹣ 1（1+2+ ⋯+n）=i ﹣1，再求极限即可．先求出 S i =2?2解答：解：∵矩中每一行都构成公比 2 的等比数列，第i 列各元素之和S i，∴ S i=2i﹣1（ 1+2+ ⋯+n） =?2i﹣1，∴==．故答案：．点：本考数列的极限与乞降，考学生的算能力，正确乞降是关．10．（ 4 分）如所示：在直三棱柱ABC A 1B 1C1中， AB ⊥BC ，AB=BC=BB 1，平面 A 1B1C与平面 ABC 所成的二面角的大小．考点：二面角的平面角及求法．：空角．分析：通意易得直三棱柱ABC A1B 1C1即正方体的一半，直接得出答案．解答：解：依据意，易得直三棱柱ABC A 1B1C1即正方体的一半，∴所求即平面 A 1B1C 与平面 A 1B1C1所成的二面角，即∠C1B 1C，又∵△ B 1C1C 等腰直角三角形，∴∠C1B1C= ，故答案：．点：本考二面角的求法，“直三棱柱 ABC A 1 1 1 即正方体的一半”是解决本B C的关，属于中档．11．（ 4 分）行如所示的程序框，出的果 a，二式的睁开式中x 3的系数，常数 m= ．考点 ： 程序框图．专题 ： 算法和程序框图；二项式定理． 分析：依据程序求出 a 的值，而后利用二项式定理的内容即可获得结论．解答：解：当 i=1 ，满足条件t ＜ 2014， a==﹣ 1， i=2 ，当 i=2 ，满足条件t ＜ 2014， a== ， i=3 ，当 i=3 ，满足条件t ＜ 2014， a==2， i=4 ，当 i=4 ，满足条件t ＜ 2014， a==﹣ 1， i=5 ，∴ s 的取值具备周期性，周期数为3，∴当 i=2014 ，不满足条件 i ＜ 2014 ，∴当 i=2013 时， a=2，二项式的睁开式的通项公式为 （2 4 ﹣ k）x ） ?（k?x ，由 8﹣ =3，解得： k=2= m ∴当 k=2 时 x 3项的系数是m=1，可解得： m= ．故答案为： ．评论： 此题主要观察程序框图的应用，以及二项式定理的应用，综合性较强．12．（ 4 分）设 f （ x ）是定义域为 R 的奇函数， g （ x ）是定义域为 R 的偶函数，若函数 f （ x ）+g （ x ）的值域为 [1， 3），则函数 f （ x ）﹣ g （ x ）的值域为（﹣ 3，﹣ 1] ．考点 ： 奇偶性与单调性的综合；函数的定义域及其求法；函数的值域；函数奇偶性的性质． 专题 ： 函数的性质及应用．分析： 依据函数奇偶性和单调性之间的关系，进行判断即可．解答：解：∵ f （ x ）是定义域为 R 的奇函数， g （ x ）是定义域为R 的偶函数，∴﹣ [f （ x ）﹣ g （ x ） ]=﹣ f （ x ）+g （ x ） =f （﹣ x ） +g （﹣ x ），∵函数 f （ x） +g（ x）的值域为 [1， 3），∴1≤f（﹣ x） +g （﹣ x）＜ 3，即 1≤﹣[f （ x）﹣ g（ x） ] ＜ 3，则﹣ 3＜f （x）﹣ g（x）≤﹣ 1，即函数 f （ x）﹣ g（ x）的值域为（﹣3，﹣ 1]，故答案为：（﹣ 3，﹣ 1]评论：此题主要观察函数值域的求解，依据函数奇偶性的性质进行转变是解决此题的要点．13．（ 4 分）△ABC 所在平面上一点P 满足，若△ ABP的面积为 6，则△ ABC 的面积为12．考点：平面向量的基本定理及其意义．专题：计算题；平面向量及应用．分析：由已知中P 是△ABC 所在平面内一点，且满足，我们依据向量加法的三角形法规可得m =2 ， C 到直线 AB 的距离等于 P 到直线 AB 的距离的 2 倍，故 S△ABC =2S△ABP，联合已知中△ABP 的面积为6，即可获得答案．解答：解：取 AC 的中点 O，则，∵，∴m =2 ，∴C 到直线 AB 的距离等于 P 到直线 AB 的距离的 2 倍，故 S△ABC=2S△ABP=12 ．故答案为： 12．评论：此题观察的知识点是向量的加减法及其几何意义，此中依据m =2，获得S△ABC =2S△ABP，是解答此题的要点．14．（ 4 分）关于曲线 C 所在平面上的定点 P0，若存在以点P0为极点的角α，使得α≥∠ AP 0B 关于曲线 C 上的任意两个不一样的点 A ，B 恒建立，则称角α为曲线 C 相关于点 P0的“界角”，并称此中最小的“界角”为曲线C相关于点P0的“确界角”．曲线 C：y=相关于坐标原点O 的“确界角”的大小是．考点：曲线与方程．专题：综合题；直线与圆；圆锥曲线的定义、性质与方程．分析：画出函数（f x）的图象，过点 O 作出两条直线与曲线无穷凑近，x≥0 时，曲线 y=与直线 y=k 1x 无穷凑近，考虑渐近线，求出22（ x k1=1； x＜ 0 时，曲线可化为 x +（y﹣ 2） =1＜ 0），圆心到直线的距离为=1，故 k2=﹣，再由两直线的夹角公式即可获得所求的“确界角”．解答：解：画出函数 f（ x）的图象，过点 O 作出两条直线与曲线无穷凑近，设它们的方程分别为 y=k 1x， y=k 2x，当 x≥0 时，曲线 y=与直线 y=k 1x 无穷凑近，即为双曲线的渐近线，故k1=1；当 x＜ 0 时，曲线可化为22=1，故 k2= x +（ y﹣ 2） =1（ x＜ 0），圆心到直线的距离为﹣，由两直线的夹角公式得，tanθ=||=2+ ，故曲线 C 相关于点 O 的“确界角”为．故答案为：．评论：此题观察新定义“确界角”及应用，观察直线与圆的地点关系，属于中档题．双曲线的性质：渐近线，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，不然一律得 0 分．15．（ 5 分）以下不等式中，与不等式≥0 同解的是（）A ．（ x﹣ 3）（ 2﹣ x）≥0B ．（x﹣3）（2﹣x）＞0C．≥0 D ．≥0考点：其余不等式的解法．专题：不等式的解法及应用．分析：将不等式进行等价变形进行比较即可．解答：解：不等式≥0等价为，即≥0，应选： D．评论：此题主要观察分式不等式的求解和变形，比较基础．16．（ 5 分）设 M 、N 为两个随机事件，假如M 、 N 为互斥事件，那么（）A ．是必然事件B．M∪ N 是必然事件C．与必定为互斥事件D．与必定不为互斥事件考点：互斥事件与对峙事件；随机事件．专题：概率与统计．分析：有 M 、 N 是互斥事件，作出相应的表示图，即可得．解答：解：由于 M 、 N 为互斥事件，如图：，无论哪一种状况，是必然事件．应选 A．评论：此题观察借助表示图判断事件间的关系，观察互斥事件的定义，属于基础题17．（ 5 分）在极坐标系中，与曲线ρ=cosθ+1关于直线θ=（ρ∈R）对称的曲线的极坐标方程是（）A ．ρ=sin（+θ）+1 B．ρ=sin（﹣θ）+1 C．ρ=sin（+θ） +1 D ．ρ=sin（﹣θ）+1考点：简单曲线的极坐标方程．专题：坐标系和参数方程．分析：第一步：将对称轴方程化为直角坐标方程；第二步：在已知曲线ρ=cosθ+1 上任取一点，并化为直角坐标；第三步：求 点关于 称 称的点，并化 极坐 形式；第四步：将此极坐 逐一代入四个 中 即可达到目的． 解答：解：由 θ=，得tan θ=，即，得 称 方程．在方程 ρ=cos θ+1 中，取 θ=，，由，得点（， 1）的直角坐 （0， 1），点（0， 1）且与直垂直的直 的直角坐 方程，从而此两直 的交点坐 ，由中点公式，得点（0， 1）关于直称的点，其极坐 （ρ0，θ0）， ，取 ，又，得点 ，此点必在曲ρ=cos θ+1 关于直 θ= （ ρ∈R ） 称的曲 上，在四个 中，只有 C 中的方程 足．故 ： C ．点 ： 本 考 了极坐 与直角坐 之 的相互 化，及 称 的 理， 点是点关于直 称的点的求法，求解 擅长运用中点公式及两直 相互垂直的充要条件．18．（ 5 分）已知函数2 ni（ i=1 ， 2，3， ⋯，f （ x ） =x ?sinx ，各 均不相等的数列 {x } 足 |x |≤*n ）．令 F （ n ） =（x 1+x 2+⋯+x n ） ?[f （ x 1） +f （ x 2）+⋯f （ x n ） ]（ n ∈N ）． 出以下三个：（ 2）若数列 {x n } 的通 公式， F （ 2k ）＞ 0 k ∈N *恒建立；（ 3）若数列 {x n } 是等差数列， F （n ） ≥0 n ∈N *恒建立．此中真的序号是（）A ． （ 1）（2）B ． （ 1）（ 3）C ． （ 2）（ 3）D ．（ 1）（ 2）（3）考点 ： 的真假判断与 用．：等差数列与等比数列；不等式的解法及 用．分析：由 意， f （x ）=x 2s inx 是奇函数，只要考 0＜x ≤1 的性 ，此 y=x2，y=sinx 都是增函数，得 f （ x ）=x 2sinx 在[0，1] 上是增函数；即x 1+x 2≠0 ，（ x 1+x 2）（f （x 1） +f （ x 2））＞ 0；于（ 1），取≤x 1= x 3 ， x 2=0，即可判断；于（ 2），运用等比数列的乞降公式和性 ，即可判断；于（ 3），运用等差数列的乞降公式和性 ， 合函数f （x ）的 性，即可判断．2解答： 解：由 意得 f （ x ）=x sinx 是奇函数，当 0＜ x ≤ ， y=x 2， y=sinx 都是增函数， ∴ f （ x ） =x 2sinx 在[0 ， ] 上 增，∴ f （ x ） =x 2sinx 在[， ] 上是增函数；若 x 1+x 2＜ 0， x 1＜ x 2，∴ f （x 1）＜ f （ x 2），即 f （ x 1）＜ f （ x 2），∴ f （ x 1） +f （ x 2）＜ 0；同理若 x 1+x 2＞ 0，可得 f （ x 1）+f （x 2）＞ 0； ∴ x 1+x 2≠0 ，（ x 1+x 2）（ f （ x 1）+f （ x 2））＞ 0．于（ 1），取≤x 1=x 3， x 2=0， F （ 3） =（ x 1+x 2+x 3） ?[f （x 1） +f （ x 2） +f （ x 3） ] =0，所以（ 1）正确；于（ 2），∵ ，∴ x 1+x 2+⋯+x n = ＜ 0，又 f （ 2k 1） +f （ 2k ）= + =＜ 0，∴ F （ 2k ）＞ 0 k ∈N *恒建立，故（ 2）正确；于（ 3），如 x 1+x 2+⋯+x n =0， F （ n ） =0 ，若数列 {x n } 是等差数列，x 1+x 2+⋯+x n ＞ 0， x 1+x n ＞0，f （ x 1）＞ f （ x n ），可得 x 2+x n ﹣ 1＞ 0，⋯，f （ x 2）＞ f （ x n ﹣1），⋯相加即可获得 F （ n ）＞ 0，同理 x 1+x 2+⋯+x n ＜ 0，即有 f （ x 1）+f （ x 2）+⋯f （ x n ）＜ 0，即 F （ n ）＞ 0，（ 3）正确．故D ．点 ： 本 通 真假的判断，考 了新定 的函数的性 以及 用 ，函数的 性与奇偶性 ，等差与等比数列的性 与 用 ，是 合 ．三．解答 （本大 分 74 分）本大 共有 5 ，解答以下各 必 在答 相 号的 定地域内写出必需的步 ．19．（ 12 分）如 ，在 Rt △AOB 中，∠ OAB= ，斜 AB=4 ，D 是 AB 的中点． 将 Rt △ AOB以直角AO 旋 一周获得一个 ，点C 底面 周上的一点，且∠BOC=．（ 1）求 的全面 ；（2）求异面直 AO 与 CD 所成角的大小．（果用反三角函数表示）考点：异面直及其所成的角；棱柱、棱、棱台的面和表面．：空地点关系与距离．分析：（ 1）求出底面半径，的面S 侧，而后求解的全面．（ 2） D 作 DM ∥ AO 交 BO 于 M， CM ，明∠ CDM 异面直 AO 与 CD 所成角，在Rt△ CDM 中，求解异面直 AO 与 CD 所成角的大小．解答：解：（ 1） Rt△ AOB 中， OB=2即底面半径 2的面S 侧=πrl=8 π⋯.4’故的全面S 全 =S 侧 +S 底 =8π+4π=12 π⋯.6’（2） D 作 DM∥AO 交 BO 于 M， CM∠ CDM 异面直AO 与 CD 所成角⋯.8’∵AO ⊥平面 OBC ∴ DM ⊥平面 OBC ∴ DM ⊥ MC在 Rt△ AOB 中，∴，∵D 是 AB 的中点∴ M 是 OB 的中点，∴OM=1 ∴．在 Rt△ CDM中，，⋯.10’∴，即异面直 AO 与 CD 所成角的大小⋯.12’点：本考异面直所成角的求法，几何体的全面的求法，考空想象能力以及算能力．20．（ 14 分）一个随机量ξ的概率分布律以下：ξx1x2P cos2A sin（ B+C ）此中 A ， B， C 角三角形ABC 的三个内角．（1）求 A 的；（2）若 x1=cosB ，x2=sinC ，求数学希望 Eξ的取范．考点：失散型随机量的希望与方差．：概率与．分析：（ 1）通概率和1，利用三角形的内角和化求解即可．（ 2）利用（ 1）的果求出B+C ，表示出的范，而后求解希望的范．解答：解：（ 1）由 cos2A+sin（ B+C ） =1，⋯2’12⋯4’2sin A+sinA=1又 A 角，得⋯6’（ 2）由得，，即⋯8’⋯9’==，⋯11’由△ ABC 角三角形，得，得⋯14’点：本考概率的用，希望的求法，概率与三角函数相合，目新，是好．21．（ 14 分）用管接而成的花构件如右所示，它的外框是一个等腰梯形PQRS，内部是一段抛物和一根横梁．抛物的点与梯形上底中点是接点O，梯形的腰靠在抛物上，两条腰的中点是梯形的腰、抛物以及横梁的接点 A ，B，抛物与梯形下底的两个接点C， D ．已知梯形的高是40 厘米， C、 D 两点的距离40 厘米．（1）求横梁 AB 的度；（2）求梯形外框的用料度．（注：管的粗等要素忽视不，算果精确到1 厘米．）考点：直与曲的关系．：曲的定、性与方程．分析：（ 1）以 O 原点，梯形的上底所在直x ，建立直角坐系，梯形下底与y交于点2（ p＜ 0），利用 D，求出 p，获得抛物方程，即可求M ，抛物的方程： x =2py解横梁 AB 的度．（2）明梯形腰的中点是梯形的腰与抛物独一的公共点，立在与抛物方程，通相切关系，求出直的斜率，而后求解制作梯形外框的用料度．解答：解：（ 1）如，以O 原点，梯形的上底所在直x ，建立直角坐系，2梯形下底与y 交于点M ，抛物的方程：x =2py（ p＜ 0），2由意 D ，得 p= 5，x = 10y⋯3’，取，即，答：横梁AB 的度28cm．⋯6’（ 2）由意，得梯形腰的中点是梯形的腰与抛物独一的公共点⋯7’，，即⋯10’得，梯形周．答：制作梯形外框的用料度141cm⋯14’点：本考抛物方程的用，直与抛物的地点关系的用，考分析解决的能力．22．（ 16 分）已知函数 f （ x） =， g（ x） =．（ 1）求函数h（x） =f （ x） +2g（ x）的零点；（ 2）若直 l ：ax+by+c=0 （ a，b，c 常数）与 f（ x）的象交于不一样的两点A、B，与g（ x）的象交于不一样的两点C、 D，求： |AC|=|BD| ；（ 3）求函数F（ x） =[f （ x） ] 2n[g（ x） ]2n（ n∈N*）的最小．考点 ： 函数与方程的 合运用；函数的最 及其几何意 ． ： 函数的性 及 用；二 式定理． 分析：（ 1）求出 H （ x ）的分析式，令H （x ） =0 ，解方程即可获得零点；（ 2） 出 A ， B ，C ， D 的坐 ， 立直 方程和 f （ x ）、 g （ x ）消去 y ，运用 达定理和中点坐 公式，即可得 ；（ 3）运用二 式定理睁开和合并，再由基本不等式 合二 式系数的性 ，即可求得最小 1．解答：解：（ 1）由 意可得，即有函数 h （ x ）的零点；（ 2） 明：A （ x 1 ，y 1），B （ x 2， y 2），C （ x 3， y 3），D （ x 4，y 4），，同原由， ，AB 中点与 CD 中点重合，即 |AC|=|BD| ；（ 3）由 意可得==[（ x2n ﹣ 2 2﹣ 2n2n ﹣66﹣ 2n（ x6﹣2n2n ﹣ 6（ x2﹣2n 2n+x）+（ x+x）+⋯++x）++x﹣2 ） ]=2n ﹣ 1?2?2=1，当且 当 x= ±1 ，等号建立．所以函数 F （ x ）的最小 1．点 ：本 考 函数的性 和运用，主要考 函数的零点和最 的求法，注意运用函数和方程的思想，以及二 式定理和基本不等式的运用：求最 ，属于中档 和易 ．23．（ 18 分） 于一 向量（ n ∈N *），令，假如存在 （ p ∈{1 ，2，3⋯，n} ），使得 ||，那么称是 向量 的 “h 向量 ”．（ 1）=（n ， x+n ）（n ∈N *），若是向量的 “h 向量 ”，求 数 x 的取 范 ；（ 2）若（ n ∈N *），向量能否存在 “h 向量 ”？出你的 并 明原由；（ 3）已知均是向量的 “h 向量 ”，此中=（ sinx ，cosx ），=（ 2cosx ，2sinx ）． 在平面直角坐 系中有一点列Q 1，Q 2，Q 3，⋯，Q n 足： Q 1 坐 原点，Q 2的地点向量的 点，且Q 2k+1 与 Q 2k 关于点 Q 1 称， Q 2k+2 与 Q 2k+1（ k ∈N *）关于点Q 2 称，求 | |的最小 ．考点 ： 数列与向量的 合． ： 平面向量及 用．分析：（ 1）通 “h 向量 ”的定 直接 算即可；（ 2）通 “h 向量 ”的定 ， n 分奇偶数 即可；（ 3）通 算可得，、 Q n （ x n ， y n ），依 意 算可得 =，利用基本不等式可得≥1 当且 当（ t ∈Z ） 等号建立，故 ．解答：解：（ 1）由 意，得：，，解得： 2≤x ≤0；（ 2） ：是向量 的 “h 向量 ”．原由以下：，，当 n 奇数 ，，∴ ，故= ，即 ；上海市徐汇区20172018学年高考数学二模试卷理科Word版含解析当 n 为偶数时，，故=，即；综合得：是向量组的“h 向量”；（ 3）由题意，得：，，即，即，同理，，三式相加并化简，得：，即，，所以，设，由得：，设 Q（ x，y ），则依题意得：，n n n得（ x2k+2， y2k+2）=2[ （x2， y2）﹣（ x1， y1）]+（ x2k， y2k）故（ x2k+2， y2k+2）=2k[ （ x2， y2）﹣（ x1， y1） ] +（ x2， y2）（ x2k+1， y2k+1）=﹣ 2k[ （ x2，y2）﹣（ x1， y1） ]+（ x2， y2），所以，当且仅当（ t∈Z）时等号建立，故．评论：此题观察新定义，向量模的计算，等比数列的乞降，二倍角公式，基本不等式，注意解题方法的累积，属于中档题．。

徐汇中学自招题目
摘要：
1.幸福路火锅店金二升金三服务评分概述
2.金二升金三服务评分的评价标准
3.幸福路火锅店金二升金三服务评分的优势和不足
4.结论：幸福路火锅店金二升金三服务评分的价值和意义
正文：
一、幸福路火锅店金二升金三服务评分概述
幸福路火锅店是我国一家知名的火锅连锁店，以其独特的口味和优质的服务赢得了广大消费者的青睐。

其中，金二升金三服务评分是该店的一大特色，也是消费者评价该店服务的重要标准之一。

二、金二升金三服务评分的评价标准
金二升金三服务评分是幸福路火锅店对员工服务的一种评价方式，评分标准主要包括：
1.服务态度：员工对顾客的态度、服务是否热情周到等。

2.服务效率：员工是否能及时满足顾客的需求，处理投诉和问题等。

3.服务质量：员工提供的服务是否能使顾客满意，是否有较高的顾客满意度等。

三、幸福路火锅店金二升金三服务评分的优势和不足
金二升金三服务评分的优势主要体现在：
1.激励员工提高服务质量，提升顾客满意度。

2.有助于幸福路火锅店提升品牌形象，吸引更多的消费者。

然而，该评分方式也存在一些不足，如：
1.主观性强，可能存在评分不公的情况。

2.过于依赖评分，可能会忽视其他影响服务质量的因素。

四、结论：幸福路火锅店金二升金三服务评分的价值和意义
总的来说，幸福路火锅店金二升金三服务评分是一种有效的服务质量评价方式，对于激励员工提高服务质量，提升顾客满意度，提升品牌形象都具有一定的价值和意义。

交大附中自招练习（五）I.Choice（30%）1.Paper produced every year is_______ the world’s production of vehicles.A.the three times of weight ofB.three times the weight ofC.as three times heavy asD.three times as heavier as2.He is a student of______.A.Class FirstB.the Class OneC.Class OneD.First Class3.This morning I had my finger_______.A.cuttingB.to cutC.to be cuttingD.cut4.The house had one of the windows_______in the storm yesterday.A.breakingB.to be breakingC.brokenD.to be broken5.You’d better______some money for special use.A.pick upB.set asideC.put offD.give6.In order to______with the advanced countries,we must keep learning.A.catch upB.get alongC.put upD.go on7.Do you mind______alone at home?A.Jane leavingB.Jane having leftC.Jane’s being leftD.Jane to be left8.The two things______they felt very proud were Jim’s gold watch and Della’s hair.A.about whichB.of whichC.in whichD.for which9.Not only______drive the car,but also________repair it.A.he is able to...he canB.is he able to...can heC.he is able to...can heD.is he able to...he can10.Meet me at the same place______you did yesterday.A.whereB.in whichC.thatD.as11.The world_______is made up of water.A.in that we liveB.on which we liveC.where we live inD.we live in12.The eating habits in the north are very much different_______those in the south.A.thenB.withC.asD.from13.This is a secret.Keep it______the two of us.A.betweenB.inC.amongD.inside14.I don’t like_______you speak to her.A.the wayB.the way in thatC.the way whichD.the way of which15.Was it in 1969______the American astronaut succeeded______landing on the moon.A.when...onB.that...onC.when...inD.that..in16._______he said so really disappointed the people present at the meeting.A.HowB.WhatC.ThatD.Why17.The question was_______we are going to take the children to the theater or to leave them at home.A.howB.whatC.ifD.whether18.Smith_______be a policeman,for he is much too short.A.needn’tB.can’tC.shouldD.may19.Jane's pale face suggested that she______ill,and her parents suggested that she______a medical examination.A.be....should haveB.was...haveC.should be... hadD.was...has20. Take it_________.Everything will be fine in a day or two.A.easyB.quietC.calmD.light21.I bought a shirt because it was good in quality and______in price.A.reasonableB.valuablefortableD.enjoyable22.The pair of shoes_______worn out.A.wasB.wereC.have beenD.had been23.All but one _______ here just now.A.isB.wasC.are 'D.were24.One more week,_______we will accomplish the task.A.orB.so thatC.andD.if25.The suit fitted him well______the color was a little brighter.A.except forB.except thatC.except whenD.besides26.Ps and Qs in the English language______”Pleases”and”Thank you”.A.are short ofB.are lack ofC.are short forD.are lacking in27.It is______that the English,in day-to-day contact with each other,is more_____than French or GermanmonB.believing...ordinaryC.believed...normalD.believed...formal28.There is little or no money for the expansion of classroom.A.areaB.fieldC.placeD.space29.The virus scan on your computer can easily ________this new kind of virus.A.killB.destroyC.damageD.harm30.It is generally_______that the old should_______the young person.A. acceptable...give way toB. accepted...give way toC. acceptable...lead the way toD. accepted...lead the way toII. Cloze ( 40% )(A)A 31 man was reported to_32 _by a pig he was __33_,according to the daily news in a certain newspaper. The report said the _34___ man, surnamed San, lived ____35___in a village not far away from the town.Raising pigs and chicken was his___36___and he bought the man-eating porker four years___37___.One morning last week,San was seen______the pig pen as usual.It was the last time anybody saw him____39___.Afraid that something was wrong,San’s neighbors broke into his home and found the pig______away on the elderly man’s bones.( )31.A.71-years-old B.71-year old C.71-year-old D.71 years old( )32.A.to be eaten B.to have been eaten C.eat D.have eaten( )33.A.raised B.growing C.raising D.grown( )34.A.elder B.older C.junior D.elderly( )35.A.alone B.lonely C.simply D.easily( )36.A.major B.hobby C.life D.course( )37.A.since B.ago C.before ter( )38. A. clearing B. cleaning C. working D. doing( )39.A.dead B.alike . C. lively D. alive( )40.A.running B.staying C.chewing D.tasting(B)“Two out of six, who committed suicide, died," the Labor Daily has reported. What 41 local citizens even more was the fact 42 most pupils at the school have not shown much 43 or sorrow about the tragedy. They seem to feel that death is not 44 frightening. It is quite common that simply____45___poison and going to sleep,_______which they never give up, is the best way to end their lives when they don’t feel happy enough.Surely enough, a group suicide, _47_ children at such a young age are so unhappy_48___end their lives, is extremely rare. Experts believe it may have _49_ to do with excessive pressure being put on children.A Beijing report said that more than l,000 children had written to the State Youth Commission 50 that they had too much homework and were not receiving sufficient care from their4 parents. Child welfare experts have appealed to parents to give their children more free time.( )41.A.pleased B.satisfied C.shocked D.relieved( )42.A.that B.which C.what D.where( )43. A. pleasure B. enjoyment C. regret D. excitement( )44.A.that B.such C.still D.even( )45.A.eating B.taking C.swallowing D.chewing( )46.A.on B.in C.with D.from( )47.A.in which B.in that C.on which D.on that( )48. A. in order to B. as to C. to D. in order that( )49.A.anything B.nothing C..something D.little( )50.A.wishing B.expecting C.quarreling plainingII .Lading Comprehension ( 20% )(A)Dear Editor,My Chinese teacher, who I also consider to be my friend, is very young. My classmates often make fun of him in class. But he hides his unhappiness and has never showed his anger.In fact,he feels hurt by their actions.How can I help him?I am looking forward to your suggestions. Yours sincerely,MikeDear Mike,The letter you wrote reached us yesterday,from which we know you are mature enough to understand your Chinese teacher’s emotion when he is hurt by your classmates.Do what you should do for any classmate who is being picked on(捉弄).Stand up for your teacher.If you are strong enough, you will be able to deal with that.To stand apart from the crowd and to speak your mind is very brave and wonderful thing to do.Many kids don’t realize that teachers have the same feeling just as you do.The simply love to be part of a crowd.If you stand up for your teacher and tell your classmates how unhappy they make him feel, many kids will feel bad about upsetting him.They will stop making fun of him.Perhaps your teacher has chosen to deal with these kids by ignoring them. But, if he is still feeling upset, he might feel better teaching in a different way. Suggest to him that he discipline them. Because he is still so young, he will have to work hard enough to gain his students' respect. But he must at least try.Normally, it is students who turn to teachers for help. But in this case, you can help your teacher. You will grow from the experience. You'll get a lot of respect, and you'll make your teacher friend's life a lot happier. These are our suggestions just for your reference. Hopefully they will work in dealing with the problem you face up to. Best wishes to you, and keep in touch if you have any problem with your study and some other fields related.Yours friendly.Editor( )51.The letter by Mike had covered the problem that .A. the students had some difficulty in learning ChineseB. his Chinese teacher lacked experience in dealing with his tough studentsC. his Chinese teacher was unhappy, but never showed his anger.D. Mike himself was hurt when he was not respected by his classmates( )52.The underlined phrase stand up [or the teacher in the first paragraph most probably means that . .A. to stand up when you are asked to answer a question in class.B. to be more polite, you should stand closer to your teacher when you chat with him.C. to support your teacher when you find what he is doing is right.D, to punish any classmate who makes fun of your Chinese teacher.( )53. One of the reasons why so many kids liked to make fun of the teacher was that___________.A. they just wanted to be on the side of a big crowd without considering the bad feeling that the Chinese teacher had.B. it might be easy for them to stand apart from a big crowd.C. they knew that kidding was just fun, would could keep the smooth running ofclassroom performance.D.they just wanted to make the Chinese teacher angry by doing so( )54.The advice, as good as if not better than, from the editor was that________.A.the Chinese teacher should first of all respect his kids in order to be well respectedB.the students should turn to the teacher for the exchange of their viewpoints on teaching and learningC.the Chinese teacher should make friends with his kidsD.Young as he was, the Chinese teacher should well discipline his students and at the same time he should worked hard to gain the students’ respect( )55.The Chinese teacher who teaches Mike is_________.A.middle-agedB.youngC.oldD.elderly(.B )There are many single parents because there are many divorces in the United States. A young woman who gets married must think carefully about having a child. There is 50 percent chance that she will have to take care of that child alone someday. Here is the story of one single parent who is happy with her life."My name is Sara. I am a secretary for a businessman in a small city. I have two daughters and a son. I was divorced three years ago. My ex-husband, Ron comes to see the children one or two times a month. He usually takes them to a movie or a restaurant."The life of a single parent is hard. I work all of the time. I work at my job all day.Then I gohome to work all evening. I am often tried when I get home at 5:30 in the evening. Tired or not, I make dinner for my children and listen to their problems. After dinner, I clean the house, wash clothes, shop for food, or help the children with their homework. My children are young, but they help me around the house.My biggest problem is money. When Ron and I divorced, he let me have the small house the children and I live in. I'm glad I have it because it is good for the children. Now I have to pay for it every month and pay the bills. That's difficult. I make about $ 18,000 a year at my job. Ron has to pay me$450 a month to help with the children. Everything is very expensive now. There isn't enough money for everything. I have to be very careful.Do I have to marry again? Maybe. I am going to be very careful. If I marry again, want to be sure it will be a good marriage this time. I don't want to marry. I am happier by myself than in a bad marriage”( )56.The word "ex-husband" (line 2 para.2) probably means .A. former husbandB. future husbandC. husbandD. Boyfriend( )57. What work does Sara NOT do in the evening?A. WashingB. ShoppingC. CleaningD. Going to a movie( )58.How much does Sarah Not do in the evening?A.WashingB.ShoppingC.CleaningD.Going to movie( )59.Sara’s biggest problem is that______.A.she is tired all of the timeB.she lacks moneyC.she has to do a lot of houseworkD.she has to look after her children alone( )60.The life of single parents is hard for Sara has to_______.A.get back at 5:30 in the eveningB. make dinner for her childrenC. work hard all dayD. clean the houseIV. Fill in the blanks with the words in their proper forms ( 10% )1. The new suspension bridge ______ ( design ) by the end of last month.2. ---Hi, Mary, you look tired.---I am tired. I_______( paint ) the living room all day.3. Robert is said to _______( study ) abroad, but I don't know what country he studied in.4. The reporter said that the UFO_______( travel) east to west when he saw it.5.The new secretary is supposed to report to the manager as soon as she _____( arrive).6. In some parts of the world, tea _______( serve ) with milk and sugar.7.The pen I thought I - ( lose ) is on my desk, right under my nose.8. As she was reading the newspaper, Granny ______( fall ) asleep.9. You don't have to describe her. I_______( meet ) her several times.10. I don't think Jim saw me; he_______( just stare ) into space.Key:I.BCDCB ACBDD DDAAD CDBBA AADCB CCDABII.CBCDA BBBDC CACAB DABCDIII.略IV.had been designed have been painting to have been studying was traveling arrives is served had lost fellHave met was just staring。

四校八大历年自招真题答案目录2013年上中自招试卷2014年上中自招试卷2015年上中自招试卷2011年华二自招试卷2012年华二自招试卷2014年华二自招试卷2013年华二冬令营数学试卷2015年年华二自招试卷2017年年华二自招试卷2013年复附自招试题2014年复附自招试题一2014年复附自招试题二2015年复附自招试题一2015年复附自招试题二2012年交附自招试题2013年交附自招试题2014年交附自招试题2015年交附自招试题2016年交附自招试题2014年七宝自招试题2016年七宝自招试题2016年南模自招试题2016年建平自招试题2017年建平自招试题建平数学培训资料试卷2015年控江自招试题2013年华二冬令营数学试卷1、“帽子函数”的图像如图所示：(1)求此函数的解析式；(2)若有抛物线23(),4y x a a =-+<求它与“帽子函数”图像的交点个数； (3)请试写出一个抛物线解析式，使它与“帽子函数”图像有且只有2个交点，横坐标分别为5722，．【解析】：⑴1,211,12x k x k y x k k x k ⎧≤<+⎪⎪=⎨⎪-+++≤<+⎪⎩⑵0a <时，无交点0a =时，一个交点304a <<时，两个交点 ⑶考虑到34a =时，抛物线234y x =-+与帽子函数交于11,22⎛⎫- ⎪⎝⎭、11,22⎛⎫ ⎪⎝⎭两点， 所以可以将234y x =-+向右平移3个单位，即满足条件 该抛物线解析式为()2334y x =--+2、在一个8×8的正方形方格纸中，一个角剪去一个2×2的小正方形，问其余部分可否剪成15块“L ”型(如图)纸片，若能剪，给出剪切方法，若不能剪，请说明理由。

【解析】（一道基础的染色问题）如图进行黑白相间染色，那么L 型放入方格纸中，必定可以盖住1个黑格子和3个白格子，或者3个黑格子和1个白格子。

2018年上海中学自招数学试卷一. 填空题1. 已知111a b a b +=+，则b a a b +=2. 有 个实数x ，可以使得120x -为整数3. 如图，ABC 中，AB AC =，CD BF =，BD CE =，用含A ∠的式子表示EDF ∠，则EDF ∠=4. 在直角坐标系中，抛物线2234y x mx m =+-(0)m >与x 轴交于A 、B 两点，若A 、B 两点到原点的距离分别为OA 、OB ，且满足1123OB OA -=，则m = 5. 定圆A 的半径为72，动圆B 的半径为r ，72r <且r 是一个整数，动圆B 保持内切于圆 A 且沿着圆A 的圆周滚动一圈，若动圆B 开始滚动时的切点与结束时的切点是同一点，则r 共有 个可能的值6. 学生若干人租游船若干只，如果每船坐4人，就余下20人，如果每船坐8人，那么就有 一船不空也不满，则学生共有 人7. 对于各数互不相等的正整数组12(,,,)n a a a ⋅⋅⋅（n 是不小于2的正整数），如果在i j <时有i j a a >，则称i a 与j a 是该数组的一个“逆序”，例如数组(2,4,3,1)中有逆序“2，1”、“4，3”、“4，1”、“3，1”，其逆序数为4，现若各数互不相同的正整数组123(,,,a a a 456,,)a a a 的逆序数为2，则654321(,,,,,)a a a a a a 的逆序数为8. 若n 为正整数，则使得关于x 的不等式11102119n x n <<+有唯一的整数解的n 的最大值为二. 选择题9. 已知212x ax +-能分解成两个整系数的一次因式的积，则符合条件的整数a 的个数为（ ）A. 3B. 4C. 6D. 810. 如图，D 、E 分别为ABC 的底边所在直线上的两点，DB EC =，过A 作直线l ，作DM ∥BA 交l 于M ，作EN ∥CA 交l 于N ，设ABM 面积为1S ，ACN 面积为2S ，则 （ ）A. 12S S >B. 12S S =C. 12S S <D. 无法确定11. 设1p 、2p 、1q 、2q 为实数，则12122()p p q q =+，若方程甲：2110x p x q ++=，乙：2220x p x q ++=，则（ ）A. 甲必有实根，乙也必有实根B. 甲没有实根，乙也没有实根C. 甲、乙至少有一个有实根D. 甲、乙是否总有一个有实根不能确定12. 设222212310071352013a =+++⋅⋅⋅+，222212310073572015b =+++⋅⋅⋅+，则以下四个选项中最 接近a b -的整数为（ ）A. 252B. 504C. 1007D. 2013三. 解答题13. 直角三角形ABC 和直角三角形ADC 有公共斜边AC （B 、D 位于AC 的两侧），M 、N 分别是AC 、BD 中点，且M 、N 不重合.（1）线段MN 与BD 是否垂直？证明你的结论；（2）若30BAC ︒∠=，45CAD ︒∠=，4AC =，求MN 的长.14. 是否存在m 个不全相等的正数1a 、2a 、⋅⋅⋅、m a (7)m ≥，使得它们能全部被摆放在一个圆周上，每个数都等于其相邻两数的乘积？若存在，求出所有这样的m 值；若不存在，说明理由.参考答案一. 填空题1. 1-2. 113. 1902A ︒-∠4. 25. 116. 447. 138. 220二. 填空题9. C 10. B 11. C 12. B二. 解答题13.（1）垂直；（262-. 14. 6m k =，2k ≥，k 为正整数.。

2018年上海市重点高中自招模拟卷一word版(word版可编辑修改) 编辑整理：尊敬的读者朋友们：这里是精品文档编辑中心，本文档内容是由我和我的同事精心编辑整理后发布的，发布之前我们对文中内容进行仔细校对，但是难免会有疏漏的地方，但是任然希望（2018年上海市重点高中自招模拟卷一word版(word版可编辑修改)）的内容能够给您的工作和学习带来便利。

同时也真诚的希望收到您的建议和反馈，这将是我们进步的源泉，前进的动力。

本文可编辑可修改，如果觉得对您有帮助请收藏以便随时查阅，最后祝您生活愉快业绩进步，以下为2018年上海市重点高中自招模拟卷一word版(word版可编辑修改)的全部内容。

上海市模拟卷一第一节单项选择（共25题,总分25分）1.——Excuse me， is this seat taken？——________。

that man got his books and left a few minutes ago.A.I’m afraid so B。

I don't think so C. I don’t know D。

I hope not2.-—________ is the population of your city?-—About two million.A.How B。

What C。

How many D。

How much3.——What about the color of the shirt?-—oh, ________I don't like it.A.That’s beautiful B。

It’s OK C. that’s too bright D。

that’sall right4.Would you mind ______ the door?A.I closingB. to closeC. me closing D。

my close5.——Have all the students know that our class will visit the factory this afternoon。

徐汇2017年事业单位招聘考试真题及答案解析【最新版】-事业单位真题1：人类的大脑细胞具有________的抵抗癌症的能力，不但可以调节人体免疫系统能力，还能________肿瘤细胞的生长，人类实现自主抗癌不再是幻想。

填入划横线处最恰当的一项是（）。

单项选择题显著，减缓潜在，遏制轻微，压迫优异，阻止2：刻板印象是指人们通过直接或间接经验形成起来的，对社会中某一群体或事件较为固定的看法．根据以上定义．下列不属于刻板印象的是（）单项选择题商人是唯利是图的娱乐圈就是乌七八糟的北方人是豪爽的静止是相对的3：某县为壮族自治县，依照宪法该县人大常委会主任或副主任人选应当符合下列哪一规定?()单项选择题由壮族的公民担任主任由壮族的公民担任副主任主任必须由壮族的公民担任，其他民族的公民可担任副主任主任或副主任中有壮族公民即可4：下列没有语病的一句是（）单项选择题建国初期，县委就抓紧进行绿化的工作，不仅在山地植树造林，而且增加经济林木的结果是改善了人民的生活,也为国家积累了资金。

由于地球上有生命，有人类，人类总希望有地球外的文明，总是在进行寻找地外文明的努力，然而至今毫无结果。

中国大力发展股份制的方向不会改变，但是一定要做到严格管理，并且将集到的资金投入生产。

清朝政府宁肯与外国侵略者妥协，谋求议和，结束第二次鸦片战争，因为它不希望人民群众起来抗英。

5：批复是答复下级请示的文件，是单项选择题被动文件主动文件是对报告的批件下级没有请示，用来指导工作的6：支持男孩和女孩分开受教育的理论是，我们在生理或社会经验与社会需要上十分不同。

以绘画来说，女孩喜欢画安静的生活，宠物或花朵，用10多种彩笔，喜欢红色，黄色等暖色调；男孩喜欢画动态的东西，用不超过6种彩笔，喜欢灰色，蓝色和黑色等冷色调。

这种区别是天生的，而老师夸奖女孩们的作品，会让男孩们觉得他们画的不对。

但反对者担心，将男孩和女孩分开，会让人以为性别之间的差异是根本的，这有违教育的根本宗旨。

交大附中自招练习（六）TEST ONE(A)"Dining out" and “eating out" are phrases people use in Britain when they eat in a restaurant. Eating out is more popular in Britain today than it 1 (ever be) In 2006. for the first time ever. British people spent more on eating out in restaurants than on cooking for themselves and eating at home. It seems that many British people 2 (become ) increasingly interested in how good their food tastes and how healthy it is. 3 ,eating out can also be expensive. so British people do not dine out every night. Eating in a restaurant is often seen as 4 special occasion. When 5 (go) on a first date,or if celebrating an anniversary or a birthday, many people like to go to a restaurant, and people often eat in a restaurant 6 going to the cinema or the theater.Naturally, restaurants vary greatly in quality and price. However, almost all British cities have a vast range of cuisines to choose 7 as well as traditional British food. In fact. When asked 8 was their favorite food, more British people said an Indian curry than any other dish!As well as dining in a restaurant, 9 people are too tired l0 (cook)after work they often get a "take-away." This means that they order from a take-away (or take-out) restaurant by phone, and then go to collect it and take it home to eat. Many take-out restaurants also deliver to your house. The most popular take-out foods are pizza (Italian). Indian and Chinese-- and then all you have to do is open the door, pay, and eat!(B)An earthquake rumbles; a building collapses ...Almost before the dust settles. search andrescue (SAR) dogs and handler teams are there searching for victims alive and dead. With a sense of smell far 1 (powerful ) than man's and an ability to probe nooks (角落）and crannies that humans cannot get 2 ,these dogs save lives and bring comfort to those who are anxiously waiting to hear about 3 loved ones. But it's not just about smell-dogs' superior hearing and night vision also come into play.Time is always an issue in search and rescue. In an avalanche situation. for instance, approximately 90 percent of victims 4 alive 15 minutes after burial; 35 minutes after burial, only 30 percent of victims are alive. 5 most avalanche victims don't survive. their chances increase greatly when dogs are in on the search. Even in cases 6 victims are presumed dead, dogs are invaluable assets-they locate the bodies so family members can give their loved one a proper burial.Dogs must be trained in certain ways for them to be qualified as SAR d02s. SAR training ensures that dogs 7 complete their tasks of finding human scent in all conditions regardless of weather or distractions.With the proper trainings, SAR dogs can do a lot of amazing things. including rappeling down（绕绳下降）mountainsides with their handler, locating a human being 8 a 5000-meter radium, finding a dead body 9 in water. climbing ladders and walking across an unstable beam a collapsed building, but it's all toward a single end human scent!TEST TWO(A)Several years ago. I was training at the Olympic Training Center in Colorado Springs, Colorado. During my early moming workout, I noticed a guy _l_ (quart-walk) around the track with a tire full of sand around his neck. It was obviously very heavy.I didn't know 2_ the guy was or wbat he did as an athlete. Finally, one day at lunch I happened to be sitting _3_ the table from him We began talking. His name was Eric."I see you doing the squat-walking every morning. That's incredible What sport do you do?" I said. "I'm a skater. you know, a speed skater." Eric answered. He seemed to be a very unassuming (低调的) person.We met a few more times at lunch and one day I asked him. "How are you going to do at the Winter Olympics?" "I think I'm going to win five gold medals," he said, _4_ a trace of arrogance "Five gold medals! The guy is crazy!" I said to myselfI asked 5 he thought he would win five gold medals. His answer was simple but impressive: "Because I train harder than anyone else in the world."I thought his answer gave _6_ a rational reason for the seemingly irrational belief7 he could win five gold medals. 8 he continued training hard, he'd be giving himself permission 9 ( believe) he could win.He is Eric Heiden. who 10 (participate) in the 1980 Winter Olympics and did win five gold medals.(B)Although Alexander Bell is 9 (often) associated with the invention of the telephone, he also created many other wonderful things.Bell's interests were extremely varied. His work ranged across the scientific landscape and he often went to bed 10_ (read) the Encyclopedia Britannica. searching it for new areas of interest.Bell's inventive genius 11 (honor) only in part (部分地）by the eighteen patents granted in his name alone and the twelve 12 shared with his co-workers. These included fourteen for the telephone and telegraph. four for the photophone. one for the phonograph, five for aerial vehicles, four for hydroairplanes(永上飞机) and two for selenium cells(硒光电管).Bell's inventions covered a wide range of interests, including a metal jacket to assist in breathing, an instrument to detect minor hearing problems. a device to locate icebergs. investigations on how 13 (separate) salt from seawater. and work on 14 (find) new energy to replace fuels.He also invented the metal detector in 1881, _ 15 _ was used in an attempt _16_ (find) the assassin's bullet in the body of U.S. President James Garfield!TEST TRREE(A)He has had countless articles written about him and has even been the subject of a feature on Oprah Winfrey's talk show.A 29-year-old ape, Kanzi is able to understand and communicate with humans and is believed to understand around 450 words-30 to 40 of l he uses daily.Kanzi has been famous 2 the late 1980s when his astonishing ability to communicate _ 3 _ (frrst discover). He lives at the Great Ape Trust in Iowa, U.S.A., where expert Dr. Sue Savage-Rumbaugh has been teaching him to "speak" 4 _ pointing at symbols on a computer.Kanzi speaks by pressing a symbol on the computer which then repeats the word out loud Sue says that he is even able to put together two-word sentences and create new phrases. "When Iowa was hit by storm and 5 _ (flood), he would point out 'big water.' He had a hard time6 (chew) the kale（甘蓝），so he pointed at 'slow lettuce.' For the word 'pizza, ' he pointed at' 'cheese, ' 'tomato' and 'bread. ,,,Sue says she taught Kanzi to communicate 7 same way she taught her son to speak.The Trust also takes care of Teco. Kanzi's 3-month-old son. Teco is also learning to communicate and Sue believes he may one day surpass his father as he . 8 _ (be) around humans since birth.(B)Two people are taken into custody（监禁）for a Crime. The police are aware that evidence is insufficient. so the prisoners are separated and questioned individually. Each prisoner is told that if he speaks and tums the other prisoner in 9 .that prisoner remains silent, he will go free while the silent prisoner will do jail tune. If both prisoners speak up, they will both do some jail time, although the sentence will be shorter than 10 for a prisoner who remains silent while another speaks. If both prisoners remain silent, they will each be given a very short prison sentence.What should the prisoners do? By remaining silent. a prisoner runs the risk of _11_ (hit) with a long sentence while the other prisoner walks. By speaking. a prisoner can hope that the other prisoner stays silent, in which case he goes free. Of course. when both prisoners speak, they both get some jail time, but the risk of remaining silent is far _12_ (great) than the risk of speaking.This is the prisoner's dilemma, a concept in game theory. Game theorists have determined that speaking up is always _13_ answer for both parties in this case. The reason for this is that each party must assume that the other will act with only self-interest in mind.The prisoner's dilemma plays on the idea that people caught in challenging situations usually try to guess what other people will do. Many people use the prisoner's dilemma to show 14 situations can escalate(升级）through a series of seemingly rational options. For example. . people stuck in dense traffic often choose to take selfish actions in the hopes of getting ahead, rather than 15_ (cooperate) with the collective. As a result. gridlock often emerges; witheveryone -1 6_ (lose) in the situation.TEST FOUR(A )For most American teenagers over the age of sixteen, owning a car seems to be a must. Cars have become as much l status symbol for young drivers as they are for many adults.A decade ago, American teenagers would be very excited when their parents gave them a car 2 a high school graduation present. Now, it has become much 3 (easy) for them to get the four-wheel vehicle they want-they can find it 4 (wrap) in ribbon on the street outside their homes on their sixteenth birthday.Young people love to have a car because it will be very convenient to go anywhere in the car. And it seems that owning a car has developed another meaning over time-the person who owns a car 5 (appear) to be independent and cool, and the one 6 doesn't lose face. That's why we always see in American movies and TV series teenagers who don't own a car beg their parents to lend them their car. You know. 7 is a shame arriving at a friend's party by getting dropped off by parents. No wonder Hannah Montana feels embarrassed once she had to be dropped off at a party by her dad 8 she lost her driver's license!(B)Lena. Bridget. Tibby. and Carmen 9 (be) best friends since they were little kids. Now they have just finished their freshman year of high school. Just 10 they are about to spend their frrst summer apart, they discover a pair of jeans that miraculously fits all of them. 11their different physiques (体格) . And not just fit-the pants make each girl look and feel beautiful and confident. In a solemn midnight ceremony. the girls make up a contract about the magical pants, part of 12 is that they'll send them back and forth among themselves throughout the summer. They don't know it yet. but they'll need the confidence that 13 (come) with the pants during a summer that will test them. 14 in different ways.That is the story The Sisterhood of the Traveling Pants tells. The friendship that the four girls share is the kind every teen 15 (long) for: rock solid and dependable, with no rivalries or pettiness (狭隘）to spoil it. filled only with kindness. love and understanding. The author. Ann Brashares, is a great storyteller. She builds a reservoir of affection for each character that makesthe climax of each of their stories effective.16 (publish) in 2001. the book stayed on the New York Times Best Seller list (《组约时报》畅销书榜) for over a year. The movie of the same name, based on the novel. was also a hit.TEST FIVE(A)Rod Allbright is a sixth grader. He goes to school like any other normal kid. Unfortunately, the class bully, a naughty boy called Billy Becker, always picks on him l he is overweight.While Rod's working on his science homework. tiny aliens come 2 (crash) through his bedroom window in a spaceship. They come to the Earth to capture another alien an evil one named BKR. He is known in other galaxies 3 his cruelties. The aliens eat Rod's homework and force him to help them.Rod is 4 honest boy. So when his science teacher asks him 5 his homework is, Rod answers, "Aliens ate my homework." Of course. no one believes him, so they don't bother 6 (ask) him why the aliens are here.Rod helps the tiny aliens to return to their normal size. Later, he finds out that Billy Becker is BKR and he skips school to search his house with the aliens. They get caught when BKR 7 (come) home from school He traps them in a storing device 8 he keeps his alien items. They break free of the device and escape from the house with some difficulty.Finally they defeat BKR through efforts and Rod learns many important lessons about life along the way.(B)A daughter complained to her father about her life and how things were so hard for her. It seemed that when one problem was solved a new one 9 (arise). She did not know how she was going to cope and wanted to give up.Her father, a chef took her to the kitchen. He filled three pots with water and put in them carrots, eggs and coffee beans respectively. He then placed each pot on a high fire and let them sit and boil, 10 saying a word. The daughter waited impatiently, 11 (wonder)what he wasdoing. In about twenty minutes, the pots came to a boil. The father turned off the fire and took out the carrots. the eggs and the coffee beans. He placed them in three bowls and turned to his daughter."Sweetheart, what do you see?" he asked."Carrots. eggs. and coffee," she replied.He asked her to feel the carrots. She did and noted that they were soft. He then asked her to take an egg and break 12 . After pulling off the shell, she observed the hard-boiled egg. Finally, he asked her to sip the coffee. She smiled as she tasted its rich flavor.The daughter was still a bit confused and asked. "What does this mean, dad?""Though the carrots, the eggs and the coffee beans all faced the same adversity---boiling water-they reacted differently," explained the father.The carrots 13 (go) in strong and lard but after being boiled 14 (soften) and became weak. The eggs had been fragile; their thin outer shells had protected their liquid interior. But after boiling. their inside became hardened. The coffee beans were unique, however. 15 put in the boiling water, they changed the water."Which are you." the father asked his daughter. "When adversity knocks on your door, 16 do you respond? Are you a carrot, an egg, or a coffee bean?”KEYS:TEST ONE A) has ever been are becoming However a going before from which because to cookB) more powerful to the are while where can in in FindingTEST TWO A) quart-walking who at for if out that As long as to believe participatedB) often to read honored is to separate finding which to findTEST THREE A) which in was discovered for flood to chew in has beenB) any hit greater the the cooperation lostTEST FOUR A) of to easier wrapped appears who what whenB) are as with it comes but longs PublishedTEST FIVE A) as crashing for an what to ask came whenB) arised for wondered down went softened Before how。

2017-2018学年上海市徐汇区南模中学高二（下）期末数学试卷一 •填空题1. （ 3分）若复数z 满足（3 - 4i ） z = 5，则z 的虚部为 ________ .2. （ 3分）正方体 ABCD - A 1B 1C 1D 1中，异面直线 A 1C 和B 1D 1所成角的大小为 ________3. ___________________________________________________________ （ 3分）正四面体S- ABC 的所有棱长都为2，则它的体积为 _________________________________ .4. （ 3分）7个人站成一排，其中甲一定站在最左边，乙和丙必须相邻，一共有 ___________ 种不同的排法.5.（ 3分）某天有10名工人生产同一零部件，生产的件数分别是：15、17、14、10、15、17、17、16、14、12,设其平均数为 a ，中位数为b ,众数为c ,则a 、b 、c 从小到大的 关系依次是 ________ .6. ____________________________________________________________________________ （3分）正三棱锥底面边长为 1,侧面与底面所成二面角为 45°,则它的全面积为 _______________ .7. （3分）正四棱柱ABCD - A 1B 1C 1D 1的底面边长为2，若AC 1与底面ABCD 所成角为60°,则A 1C 1和底面ABCD 的距离是 ________ .& （ 3分）棱长为1的正方体ABCD - A 1B 1C 1D 1的8个顶点都在球 O 的表面上，E , F 分别是棱AA 1, DD 1的中点，则直线 EF 被球O 截得的线段长为 ___________ .9. （ 3分）已知正整数n ,二项式（x 3+——）n 的展开式中含有x 7的项，则n 的最小值是 _x10 . （3分）在复数范围内解方程|z|2+ （z+- ■） i =（i 为虚数单位），z = ________ .11 . （3分）把4个相同的球放进 3个不同的盒子，每个球进盒子都是等可能的，则没有一个空盒子的概率为 ________线y = 0, y = 4围成的封闭图形记为 D ，如图中阴影部分.记 D 绕y 轴旋转一周所得的几 何体为Q .过（0, y ） （0< y < 4）作Q 的水平截面，计算截面面积，利用祖暅原理得出12 . （3分）在xOy 平面上，将双曲线的一支2 X（訂1（X >）及其渐近线y=— x 和直Q的体积为________ .•选择题13. （3分）已知I, m, n是空间三条直线，则下列命题正确的是（A .若I // m, I // n,贝V m // nB .若I丄m, I丄n,贝U m / nC.若点A、B不在直线I上，且到I的距离相等，则直线AB// ID .若三条直线I, m, n两两相交，则直线I, m, n共面14. （3分）一个圆柱形的罐子半径是4米，高是9米，将其水平躺倒，并在其中注入深2米的水，截面如图所示，水的体积是（）立方米.A . 24」•’ .「：B. 36儿I 一；C. 36「——：一「：D. 481…汽.⑴15. （3分）为了研究某药品的疗效，选取若干名志愿者进行临床试验.所有志愿者的舒张压数据（单位：kPa）的分组区间为[12 , 13）, [13, 14） , [14 , 15） , [15 , 16）,[16 ,17],将其按从左到右的顺序分别编号为第一组，第二组，…，第五组.如图是根据试验数据制成的频率分布直方图.已知第一组与第二组共有20人，第三组中没有疗效的有6人,则第三组中有疗效的人数为（）8 cm ,第3页（共22页）A . - 1B . 1C . 2187D . - 218717. （ 3分）从8名女生和4名男生中选出6名学生组成课外活动小组，则按性别分层抽样 组成课外活动小组的概率为（L26 12^12 p" P 2r1218. （3分）已知复数z 满足| - |z+2+i | =3/2（ i 是虚数单位），若在复平面内复数 z 对应的点为Z ,则点Z 的轨迹为（ ）A .双曲线的一支B .双曲线C .一条射线D .两条射线三•解答题19. 求（•：・+丄）8的二项展开式中的第 5项的二项式系数和系数.220. 已知关于x 的方程x +4x+p = 0 （ p€R ）的两个根是 x 1, x 2.（1 ）若X 1为虚数且|x 1|= 5，求实数p 的值； （2）若|X 1- x 2|= 2,求实数p 的值.21. 沙漏是古代的一种计时装置， 它由两个形状完全相同的容器和一个狭窄的连接管道组成, 开始时细沙全部在上部容器中，细沙通过连接管道全部流到下部容器所需要的时间称为 该沙漏的一个沙时.如图，某沙漏由上下两个圆锥组成，圆锥的底面直径和高均为7 2716.（3 分）已知（1- 2x ） = a o +a i x+a 2x + …+ a 7x •贝V |a o |+|a i |+|a 2|+…+|a 7|=细沙全部在上部时，其高度为圆锥高度的一(细管长度忽略不计).(1 )如果该沙漏每秒钟漏下0.02cm3的沙，则该沙漏的一个沙时为多少秒(精确到1秒)？(2)细沙全部漏入下部后，恰好堆成个一盖住沙漏底部的圆锥形沙堆，求此锥形沙堆的高度(精确到0.1cm).22. 在四棱锥P- ABCD中，底面ABCD是矩形，PA丄平面ABCD , PA = AD = 4 , AB = 2.以AC的中点O为球心、AC为直径的球面交PD于点M ,交PC于点N(1)求证：平面ABM丄平面PCD ;(2)求直线CD与平面ACM所成的角的大小；23. 小威初三参加某高中学校的数学自主招生考试，这次考试由十道选择题组成，得分要求是：做对一道题得1分，做错一道题扣去1分，不做得0分，总得分7分就算及格，小威的目标是至少得7分获得及格，在这次考试中，小威确定他做的前六题全对，记6分, 而他做余下的四道题中，每道题做对的概率均为p (0< p V 1),考试中，小威思量：从余下的四道题中再做一题并且及格的概率p1 = p；从余下的四道题中恰做两道并且及格的概2率p2= p，他发现p1> p2,只做一道更容易及格.(1 )设小威从余下的四道题中恰做三道并且及格的概率为P3,从余下的四道题中全做并且及格的概率为P4,求p3及p4;(2)由于p的大小影响，请你帮小威讨论：小威从余下的四道题中恰做几道并且及格的第4页(共22页)概率最大？2017-2018学年上海市徐汇区南模中学高二(下)期末数学试卷参考答案与试题解析一填空题1 . ( 3分)若复数z 满足(3 - 4i ) z = 5，则z 的虚部为_吕【分析】利用复数的运算法则、虚部的定义即可得出. 【解答】解：•••( 3 - 4i ) z = 5, •••( 3+4i ) (3- 4i ) z = 5 (3+4i ), ••• 25z = 5 (3+4i ),故答案为：9 .5【点评】本题考查了复数的运算法则、虚部的定义，属于基础题.2. ( 3分)正方体 ABCD - A 1B 1C 1D 1中，异面直线 A 1C 和B 1D 1所成角的大小为90°【分析】以A 为原点，AB 为x 轴，AD 为y 轴，AA 1为z 轴，建立空间直角坐标系，利用 向量法能求出异面直线 A 1C 和B 1D 1所成角的大小.【解答】解：设正方体 ABCD - A 1B 1C 1D 1中棱长为1,以A 为原点，AB 为x 轴，AD 为y 轴，AA 1为z 轴，建立空间直角坐标系， A 1 (0, 0, 1), C (1, 1, 0), B 1 (1, 0, 1), D 1 (0, 1, 1),A 1C=( 1，1，— 1)，B]D[=(- 1, 1,0),设异面直线 A 1C 和B 1D 1所成角为0,•••异面直线 A 1C 和B 1D 1所成角的大小为 90° 故答案为：90 °第6页(共22页)则 cos0=【点评】考查异面直线所成角的求法，考查空间中线线、线面、面面间的位置等基础知识，考查运算求解能力，考查函数与方程思想，是基础题.3. （3分）正四面体S- ABC的所有棱长都为2，则它的体积为—…'_.~ 3 ~【分析】由正四面体的棱长为1，所以此四面体一定可以放在棱长为.1的正方体中，由此能求出此四面体的体积.【解答】解：•••正四面体的棱长为2,• ••此四面体一定可以放在正方体中，•••我们可以在正方体中寻找此四面体.如图所示，四面体ABCD满足题意，BC = 2,•••正方体的棱长为•此四面体的体积为（占）'-占血X血乂近=罢2. ■3 n—1 3故答案为：上■.3【点评】本题考查四面体的体积问题，考查了空间想象能力，其解答的关键是在正方体中寻找此四面体.4. （3分）7个人站成一排，其中甲一定站在最左边，乙和丙必须相邻，一共有—240一种不同的排法.【分析】本题是一个排列组合及简单计数问题，甲要站在最左边，剩下6个位置，6个人排列，乙和丙必须相邻，把乙和丙看成一个元素，同另外4个人排列，乙和丙之间也有一个排列，相乘得到结果.【解答】解：由题意知本题是一个排列组合及简单计数问题，甲要站在最左边，剩下6个位置，6个人排列，•••乙和丙必须相邻，•••把乙和丙看成一个元素，同另外4个人排列，乙和丙之间也有一个排列，根据乘法原理知共有A55A22= 240种结果，故答案为：240【点评】站队问题是排列组合中的典型问题，解题时要先排限制条件多的元素，把限制条件比较多的元素排列后，再排没有限制条件的元素，最后要用计数原理得到结果，本题的甲不影响排列.5. （3分）某天有10名工人生产同一零部件，生产的件数分别是：15、17、14、10、15、17、17、16、14、12,设其平均数为a，中位数为b,众数为c,则a、b、c从小到大的关系依次是a< b < c .【分析】根据题意求出这组数据的平均数a、中位数b和众数c,再比较大小.【解答】解：计算这组数据的平均数为a= _ 'X（15+17+14+10+15+17+17+16+14+12 ） = 14.7,10求出中位数为b= 15,众数为c= 17,则有a< b< c.故答案为：a< b< c.【点评】本题考查了平均数、中位数和众数的计算问题，是基础题.6. （3分）正三棱锥底面边长为1，侧面与底面所成二面角为45。

2017-2018学年第一学期徐汇区学习能力诊断卷初三英语学科 1 （满分150分，考试时间100分钟）Part 1 Listening (第一部分听力)Part 2 Phonetics, Vocabulary and Grammar(第二部分语音、词汇和语法)II. Choose the best answer (选择最恰当的答案): (共20分)26. Which of the following word matches the sound/stɔ:ri/?A) store B) story C) study D) slowly27. Which of the following underlined parts is different in pronunciation with others?A) Tom refused to go shopping with his mum..B) A good detective never jumps to a conclusion.C) Excuse me, can you tell me where the hospital is?D) We had a good time in that amusement park.28. All the visitors are asked to to line up quietly and go into the exhibition hall one at ____ time.A) the B) / C) a D) an29. You can always see people exercise in that park, even _____ cold winter mornings.A) on B) in C) at D) from30. Quite a few people like to take photos of _____ andshare them through WeChat.A) they B) theirs C) themselvesD) them31. After the earthquake, some decided to leave and _____ chose to stay to rebuild their hometown.A) other B) the other C) others D) the others32. Malala Yousafzai, a seventeen-year-old teenager, is _____ Nobel Prize winner in history.A) young B) younger C) youngestD) the youngest33.A: _____ does this pair of new Nike shoes belong to?B: It must be Jeff’s. It’s his birthday present from his dad.A) What B) Who C) WhichD) Whose34. After the accident, the careless driver has to pay﹩9500 _____ the damage of the car.A) on B) to C) forD) with35. The famous writer promised that she _____ all themoney for her new book to charity.A) gave B) would give C) has givenD) is giving36. It’s pro ved that we _____ improve our memory byusing various memorizing methods.A) can B) must C) shouldD) need37. Hello Kitty _____ popular around the world sinceit was created in 1974 by a Japanese company.A) is B) was C) will beD) has been38. _____ helpless the poor little girl is after shelost both her parents in the car accident!A) How B) What C) What a D)What an39. Every year the artist ______ two months living inthe mountain and painting.A) has spent B) will spend C) spendsD) spent40. The organizer decided to cancel the concert _____ the tickets didn’t sell very well.A) if B) until C) althoughD) because41. The young had better _____ to be responsible fortheir own decisions.A) to learn B) learning C) learnD) learnt42. The two girls seem to become _____ to each otherthan before after the competition.A) close B) closer C) closestD) the closest43. If you travel around the world, you will be surprised at ________.A) how different the foreign customs areB) how the foreign customs are differentC) how different are the foreign customsD) how are the foreign customs different44. A: Sorry I’m late, but the bus broke down.B: _______A) Don’t say that.B) Of course.C) That’s all rightD) Congratulations.45. A: Would you like to join us in the picnic?B: _______A) Not at all.B) I don’t think so.C) I’d like to, but I can’t.D) It’s very kind of you.plete the following passage with the words or phrases in the box. Each can only be usedOnce.(讲下列单词或者词组填入空格，每空格限填一词，每个单词或词组只能填一词）（8分）Dogs are not the only animals that can be trained to help people. Helping Hands, an oraganization in the USA, trains capuchin monkeys to be helpers for people inwheelchairs who cannot move their arms or legs. More than 20 years ago, Dr.M.J Willard thought that a monkey might be able to help with some 46 homework. She was right. Monkeys can 47 be trained to help people, they are also wonderful partners.Capuchin monkeys are found in the wild in South Central America. They are about the48 of a friendly and good with their hands. They can use their hands 49 humans.Everyday tasks, like turning on a light, putting something in the fridge, or pressing “play”on a CD player, can be difficult for someone who can not use his orher arms and legs. Capuchin monkeys can easily perform these tasks. This allows their owners more50 .They can do things on their own and can live51 .Helping hands matches p eople with disabilities to monkeys who can help them. But the close 52 between the monkeys and theirowners happen all on their own. The monkeys and their owners become friends and learn to depend on each other. Some owners say the monkeys are almost like childrento them. The monkeys can be naughty(调皮的）and sometimes like to play tricks on their owners. This is especially ture of young monkeys.Mostly, they like to 53 their owners. They like the sweets they recieve when they do a good job, and they like to be praised. eplete the sentences with the given words in their proper forms(用括号中所给单词的适当形式完成下列句子）54.Children should get into a good habit of brushing their at least twice a day.(tooth)55.Emily left her parents and came to teach in Chinain her late .(twenty)56.The school is planning to some parents to share their success stories with the students.(invitation)57.It’s dangerous to tell your personal information to a stranger online.(extreme）58.Some runners quit(退出）the marathon because they thought it was to run in the haze.(harm）59.Dan’s neighbor is from and the family has 3 lovely children.(German)60.It is no teaching the 3-year-old child that much. He can’t understand at all.(useful)61.To add , some comic strips appear in different frame sizes.(various)V. Complete the following sentences as required. 62.There are many unusual inventions on show in that exhibition.（改为反意疑问句）There are many unusual inventions on show in that exhibition,________ _________?63.A Dutch artist Florentijin Hofman designed the famous big yellow rubber duck.(改为被动语态)The famous big yellow rubber duck_________ __________ by a Dutch artist Florentijin Hofman.64.ken said to them, “You should ask the teacher for help.（合并两句为简单句）Ken advised them __________ __________ the teacher for help.65.The restaurant around the corner used to be Tom’s favorite.(对划线部分提问)_________ restaurant ________ Tom’s favorite?66.I won’t start the car unless you put on your seat belt.(保持句意基本不变)I won’t start the car________ you__________ put on your seat belt.67.Jeff took the vase out of the safe very carefully in order not to break it.(保持句意基本不变)Jeff took the vase out of the safe with _______ __________ in order not to break it.68.left, the lights, he, in a hurry,and, the office, turned off(连词成句)___________________________________________________ ________________Part 3 Reading and Writing(第三部分读写)VI Reading comprehensionA .Choose the best answerThe popular Disneyland has some deep, dark, and sometimes amusing secrets that you probably don't know.Read on to learn them.the popular Disneyland has some deep,dark,and sometimes amusingGeneral Main StreetBy using a special method of construction(建筑),Disneyland created an effect that you don't notice until your tired family leaves the park. The next time you enter Disneyland, make note of the distance that it appears you have to travel to get to the “Partners” statue. Then look at the exit of the park from the statue. That's correct. The distance appears to be shorter entering the park than going out. The purpose was to keep guests from wanting to take the long walk out. Birthday funIf you visit Disneyland on your birthday, be sure to tell the person at the gate that it's your big day. You'll be sent to City Hall where you'll be presented with a special sticker by cast members, letting everyone know it's your birthday. You may also be able to score special items from other cast members throughout the park, so it's certainly worth a try! The music never stops.visitors like the music and sounds in the park.Did you know the music never stops at the park? Even when the park was closed,the music and sounds are kept on going.Some believe it cost too much for Disney to keep turning off the music and then restarting it eachday.But the truth is that it helps some workers clean up after 2 a.m!Club 33“Club 33” is the only place in Disneyland that provides guests with alcoholic beverages(酒精饮料). Club 33 members and their guests get free entrance to Disneyland so long as they have a meal at Club 33 on the day of their visit.69.There are ________amusing secrets about Disneyland mentioned in this passage.A.twoB. threeC.fourD.five70.________makes the distance going out of the park seem to be longer.A.The “partner’’ statueB.The gate of the parkC. The construction along the streetD.the music in the park71.If you tell the staff it’s your birthday,youwill___________.A.get free entrance to DisneylandB.be given a special gift at the City HallC.be taken to Club 33 and have a mealD.let everyone in the park know your name72.The music never stops at the park because__________.A.visitors like the music and the sounds very muchB.it’s difficult to shut off the music and the soundsC.Disneyland has to pay a lot to restart the music every dayD.it may keep some late night workers awake and full of energy.73.According to the passage,which of the following statements is NOT true?A.you won’t have fun on your birthday unless you tell the person at the gate.B. Club 33 members may go into the park for free the same day they have a meal there.C.The Disneyland Park is open to the visitors all day and night.D.The effect that Disneyland creates in Main Street is to keep visitors from leaving.74.The purpose of this passage is to__________.A.let the readers know the dark side of Disneyland Park.B.help the readers better enjoy their visits in Disneyland ParkC.encourage the readers to go to visit Disneyland ParkD.make the readers be aware of the importance of Disneyland ParkB Choose the words or expressions and complete the passgae（选择最恰当的单词或词语完成短文）If you are reading this article, you are probably trying to read it quickly. You have been taught to skim and scan, to look for key words so as to understand the main idea of the article and the important points in the article.Skimming and scanning is a good method when you don’t have enough____, such as when you are taking an exam, but, today many people skim and scan everythong and they have lost the ability to enjoy reading.In response to this, something called the “slo w reading movement” has become popular. The idea is that people should ______ their computers and mobile phones for half an hour or forty-five minutes each day and enjoy the pleasures of reading a good book—slowly and quietly!Researchers have found that reading slowly, especiallybooks of fiction, helps people relax and think about what they are reading. It also helps people get to understand the characters’emotions and to see the world ______ the characters’ eyes.Reading, of course, isn’t easy. You have to sit still for one thing. And it can seem____when compared to the excitement of playing video games. But, for me, reading has always been a pleasure in my life. From the age of ten, when I got my first library card, I’ve enjoyed the company (陪伴) of heroes, of evil criminals and clever detectives, of thousands of interesting people I would have never met________.Reading provided me with escape, but it also enabled me to understand the world around me. It was an education in a classroom that had no walls.In your classroom, you have learned to read “fast.” _______, outside of the classroom, you should try to learn to read “slow.” You may be surprised at how much you enjoy it.75. A confidence B time C memoryD support76. A care for B deal with C turn offD take out77. A through B with C into D around78. A strange B interesting C boringD attractive79. A in the book B on the Internet C at school D in real life80. A For example B Finally C HoweverD What’s m oreC Read the passage and fill in the blanks with proper words.（在短文的空格内填入适当的词，使其内容通顺，每空格限填一词，首字母已给）：In March of 1999, Edie and Sarah began hiking（徒步旅行）the Appalachian Trail in Georgia. Sarah was a teacher, she and Edie thought their hike would be an intereting learning experience for students. Before they set off, they visited classrooms f or two weeks. Students had the chance to try on a bag to see how much w_____Sarah and Edie would be carrying during the trip.Students were also able to ask Sarah and Edie questions about the trail. Sarah and Edie planned to post photos and diaries on the Internett during the trip so that the students would be able to check on their p_____. Before they left, Sarah and Edie packed 18 boxes with things they need like biscuits, noodles, peanut butteer , and dried fruits and vegetables. Their parents would mail the boxes to samll towns a______the trail so Sarah and Edie could pick them up wherever they go. That way, Sarah and Edie did not have to carry all their supplies（补给）with them from the beginning of the trip. Sarah and Edie met plenty of friendly hikers during their trip. People who are hiking the Appalachian Trail often creat “trail names” for t______and their friends. That explains why Sarah and Edie met hikers wit h names like”Cold Feet” and “Baked Beans”!There are many shelters. Hiker can stay there overnight, especially in times of bad weather. There are also books called Registers（签到本）at many of the shelters. Hikers can sign the books and leave n_____for friends they have made, giving them some information or justsaying “Hi”.Sarah and Edie met with all kinds of weather on their hike. They had days of beautiful clear weather, but they also hiked through rainstorms. S_______the weather was so hot that they had to drink a lot of water.When Sarah and Edie were in Virginia, there was a forest fire. They had to wait until it was c_____safe to go on. Because of a fire in Shenandoah National Forest, they missed a 45-mile of the hike. Later in their trip, Sarah and Edie had to ask someone to drive them back there so they would not miss a single mile of the AT! Four and a half months after they began the hike in Georiga, Sarah and Edie finally succeeded at Mount Katahdin in Maine.D Answer the questions（根据短文内容回答下列问题）I’d always dreamed of visiting Africa, ever since I read my first Tarzan（人猿泰山）comic as a child. Finally, in 2004, to celebrate my 60th birthday, I wentto Tanzania to experience a safari（东非游猎） and climb Mount Kilimanjaro, the highest mountain in Africa. Seat ed next to me on the flight was Tanzania’s Minister of Water and Wildlife Development. We talked for thousands of miles, and he arranged me to visit a school. When I arrived at the school, I was shocked. The dirt floors turned into mud during the rainy season, and the walls couldn’t keep out the heat, cold or bugs(小昆虫). The school was in need of all material goods.It broke my heart that these children had to try hard to survive, so I asked the headmaster what it would cost to feed them. As little as 20 cents per child per day, he told me. Immediately I got him, I founded（成立）Kids of Kilimanjaro. Since then we’ve grown to provide hot lunches for nearly 13,000 school children in Tanzania every day. The free lunch program has solved an essential problem the children face.I know a good education could really make a difference in these children’s lives. My parentsalways told me the importance of education. I paid my own way through college in Tokyo by teaching English to students and business people. After attending university I moved to San Francisco, when I was 25 years old. In 1978 I realized my American dream when I founde d my own company. My success all started with a good education.It’s amazing that something as simple as a hot lunch can change so many lives. Giving young people a better, healthier life can encourage them to go all the way through college and lead a change in thier country.88. How old was the writer when he went to Tanzania f or the first time?89. What made the writer shocked, the poor condition of the school or the poor children?90. How much would it cost to feed one child a day?91. How does kids of Kilimanjaro help the school children in Tanzania?92. Why did the eriter found kids of Kilimanjaro to help the children in Tanzania?93. What may probably the writer’s purpose of writing this passage?He_________________________________________________ ______Ⅶ writing94. Suppose you are on an educational visit in a foreign country and are asked to make a brief introduction. Write a passage in at least 60 words to introduce yourself and probably your school (ABC school) or your country, so you can leave people a deep impression.假设你正在国外参加教育交流访问活动，你需要做一个简短的，让人印象深刻的自我介绍，请写一篇至少60词的发言稿介绍一下你自己（Danny）或者你的国家和学校（ABC school）。

上海中考自主招生试卷精选 [复旦附中]考智慧、测文理知识综合运用能力自主招生题：■说游戏每个人都玩过游戏，从纵向的角度来看，游戏有时代特征，有年龄特点；从横向的角度来看，游戏有益智类、竞技类、休闲类等等。

当然，在游戏中，也有一些趣味低下、恶作剧的内容。

请谈谈你对“游戏”的思考。

题目背后：初三学生特别喜欢这道题目，他们谈杀人游戏、弄堂游戏、CS等电脑游戏、魔兽世界等网络游戏，甚至有人说出“传承网络游戏”等另类观点。

复旦附中副校长吴坚说，出这道贴近生活的题目，就是让学生有话可说，充分发挥出学生各自的个性。

■说外语随着全球化时代的到来，作为最古老而又最基本的交流工具，语言的重要性显得日益突出。

“英语热”在当前上海中学生中持续升温。

你是如何看待“母语”学习与“外语”学习之间的关系的可不可以借用数学名词或符号来回答这一题目？题目背后：题目出得有点刁难学生，可学生们的回答却充满了智慧。

有学生用“正比例函数”指出母语、外语学习的相辅相成，有同学用“2条平行线”表达母语、外语学习同样重要，还有同学用“母语学习在底层、外语学习在上层，共同构成圆柱体”，来强调学好母语是学好外语的基础。

吴坚说，该题主要考查学生文理知识综合运用的能力。

--推优题：■学生、家长对于学校的选择热情高涨。

小学生要进名气大的中学往往是几十个人争一个位子；在今年的自主招生和推优生招生工作中也可以看到人们对名校趋之若鹜。

针对这种现状，请你谈谈进“名校”的利弊。

题目背后：该题主要通过学生对进“名校”利弊的辨析，了解学生对于“名校”的定义以及对于自己未来的设计。

■总是觉得别人自私的人，通常对待他人也不免有些自私之嫌；总是觉得别人对不起自己的人，自己对别人也未必厚道；总是觉得别人没有趣味的人，自己也通常是令人烦闷的。

读了这段话，你有什么感想与启发？题目背后：现代学生大多是独生子女，遇到问题往往只考虑自己的利益，极少考虑他人的感受。

该题主要检测学生的自省态度，让学生懂得“你对别人的观感和态度其实很大程度上取决于别人对你的观感和态度”。