2017-2018上海复旦附中高一上期中考试
2017-2018年上海市复旦附中高一上学期数学期中试卷带答案
2017-2018年上海市复旦附中⾼⼀上学期数学期中试卷带答案2017-2018学年上海市复旦附中⾼⼀（上）期中数学试卷⼀.填空题1．（3分）已知全集U=Z，A={﹣1，0，1，2}，B={x|x2=x}0则A∩（C U B）=．2．（3分）命题“如果a+b＞0，那么a＞0且b ＞0”的否命题是命题（填“真”或“假”）3．（3分）已知集合A={y|y=x2﹣2x﹣3}，集合B={y|y=﹣x2+2x+13}，则A∩B=．4．（3分）已知α：，β：1﹣2a＜x＜3a+2，若α是β的充分不必要条件，则实数a的取值范围是．5．（3分）设M={a，b}，则满⾜M∪N?{a，b，c}的集合N的个数为．6．（3分）函数f（x）=的定义域为[﹣2，1]，则a的值为．7．（3分）已知函数f（x）=（m﹣1）x+2m﹣3，⽆论m取什么实数，函数f（x）的图象始终过⼀个定点，该定点的坐标为．8．（3分）已知关于x的⽅程x2+kx+k2+k﹣4=0有两个实数根，且⼀根⼤于1，⼀根⼩于1，则实数k的取值范围为．9．（3分）给出下列四个命题：（1）若a＞b，c＞d，则a﹣d＞b﹣c；（2）若a2x＞a2y，则x＞y；（3）a＞b，则；（4）若，则ab＜b2．其中正确命题是．（填所有正确命题的序号）10．（3分）若x∈（﹣∞，2），则的最⼩值为．11．（3分）设函数f（x）=x﹣2，若不等式|f（x+3）|＞|f（x）|+m对任意实数x恒成⽴，则m的取值范围是．12．（3分）对于实数A和正数B，称满⾜不等式|x﹣A|＜B（A∈R，B＞0）的实数x的集合叫做A的B领域，已知t为给定的正数，a、b为正数，若a+b﹣t的a+b领域是⼀个关于原点对称的区间，则a2+b2的最⼩值为．⼆.选择题13．（3分）设实数a1，a2，b1，b2均不为0，则“成⽴”是“关于x的不等式a1x+b1＞0与a2x+b2＞0的解集相同”的（）A．充分⾮必要条件 B．必要⾮充分条件C．充要条件D．⾮充分⾮必要条件14．（3分）解析式为y=2x2+1，值域为{5，19}的函数有（）个．A．4 B．6 C．8 D．915．（3分）设f（x）是定义在正整数集上的函数，且f（x）满⾜：“当f（x）＞x2成⽴时，总可以推出f（x+1）＞（x+1）2成⽴”．先给出以下四个命题：（1）若f（3）≥9，则f（4）≥16；（2）若f（3）=10，则f（5）＞25；（3）若f（5）=25，则f（4）≤16；（4）若f（x）≥（x+1）2，则f（x+1）≥x2．其中真命题的个数为（）A．1个 B．2个 C．3个 D．4个16．（3分）设a，b，c为实数，f（x）=（x+a）（x2+bx+c），g（x）=（ax+1）（cx2+bx+1）记集合S={x|f（x）=0，x∈R}，T={x|g（x）=0，x∈R}．若|S|，|T|分别为集合S，T的元素个数，则下列结论不可能的是（）A．|S|=1且|T|=0 B．|S|=1且|T|=1 C．|S|=2且|T|=2 D．|S|=2且|T|=3三.解答题17．已知集合A={x|（m﹣1）x2+3x﹣2=0}，是否存在这样的实数m，使得集合A 有且仅有两个⼦集？若存在，求出所有的m 的值组成的集合M；若不存在，请说明理由．18．我校第⼆教学楼在建造过程中，需建⼀座长⽅体形的净⽔处理池，该长⽅体的底⾯积为200平⽅⽶，池的深度为5⽶，如图，该处理池由左右两部分组成，。
2017-2018学年上海复旦大学附属中学高一上学期期中考试数学试卷含详解
2017学年复旦附中高一上期中一.填空题1.已知全集U =R ，{1,0,1,2}A =-，2{|}B x x x ==，则U A C B = __________2.命题“如果0a b +>，那么0a >且0b >”的否命题是__________命题（填“真”或“假”）3.已知集合2{|23}A y y x x ==--，2{|213}B y y x x ==-++，则A B = __________4.已知“12a x a ≤≤+”是“1232a x a -<<+”的充分不必要条件，则实数a 的取值范围是__________5.设M={a,b}，则满足M ∪N ⊆{a,b,c}的非空集合N 的个数为______________．6.函数()f x =的定义域为[2,1]-，则a 的值为__________7.已知函数()(1)23f x m x m =-+-，无论m 取什么实数，函数()f x 的图像始终过一个定点，该定点的坐标为__________8.已知关于x 的方程2240x kx k k +++-=有两个实数根，且一根大于1，一根小于1，则实数k 的取值范围为__________9.给出下列四个命题：（1）若a b >，c d >，则a d b c ->-；（2）若22a x a y >，则x y >；（3）若a b >，则11a b a >-；（4）110a b <<，则2ab b <.其中正确命题是________.（填所有正确命题的序号）10.若(,2)x ∈-∞，则2542-+-x x x 的最小值为__________11.设函数()2f x x =-，若不等式|(3)|()f x f x m +>+对任意实数x 恒成立，则m 的取值范围是__________12.对于实数A 和正数B ，称满足不等式||x A B -<(,0)A B ∈>R 的实数x 的集合叫做A 的B 邻域，已知t 为给定的正数，a 、b 为正数，若a b t +-的a b +领域是一个关于原点对称的区间，则22a b +的最小值为__________二.选择题13.已知1a ，1b ，2a ，2b R ∈且都不为零，则“1122a b a b =”是“110a x b +>与220a x b +>解集相同”的A.充分非必要条件B.必要非充分条件C.充要条件D.既非充分又非必要条件14.解析式为221y x =+，值域为{}5,19的函数有A .4 B.6 C.8 D.915.设()f x 是定义在正整数集上的函数，且()f x 满足：“当2()f x x >成立时，总可以推出2(1)(1)f x x +>+成立”，给出以下四个命题：①若(3)9f ≥，则(4)16f ≥；②若(3)10f =，则(5)25f >；③若(5)25f =，则(4)16f ≤；④若2()(1)f x x ≥+，则2(1)f x x +≥.其中真命题的个数为（）个A.1 B.2 C.3 D.416.设a ，b ，c 为实数，22()()(),()(1)(1),f x x a x bx cg x ax cx bx =+++=+++记集合{}{}|()0,,|()0,,S x f x x R T x g x x R ==∈==∈若{S }，{T }分别为集合S ，T 的元素个数，则下列结论不可能的是（）A.{S }=1且{T }=0 B.{S }=1且{T }=1 C.{S }=2且{T }=2 D.{S }=2且{T }=3三.解答题17.已知集合2{|(1)320}=-+-=A x m x x ，是否存在这样的实数m ，使得集合A 有且仅有两个子集？若存在，求出所有的m 的值组成的集合M ；若不存在，请说明理由.18.我校第二教学楼在建造过程中，需建一座长方体形的净水处理池，该长方体的底面积为200平方米，池的深度为5米，如图，该处理池由左右两部分组成，中间是一条间隔的墙壁，池的外围周壁建造单价为400元/平方米，中间的墙壁（不需考虑该墙壁的左右两面）建造单价为100元/平方米，池底建造单价为60元/平方米，池壁厚度忽略不计，问净水池的长AB 为多少时，可使总造价最低？最低价为多少？19.已知a ∈R ，集合26{|0}1x x A x x --=≤+，集合{||2|1}B x x a a =+≤+.（1）求集合A 与集合B ；（2）若A B B = ，求实数a 的取值范围.20.已知函数2|1|()4x m f x x +-=-，0m >，满足(2)2f =-.（1）求实数m 的值；（2）在平面直角坐标系中，作出函数()f x 的图像，并且根据图像判断：若关于x 的方程()f x k =有两个不同实数解，求实数k 的取值范围（直接写结论）21.已知M 是满足下列性质的所有函数()f x 组成的集合：对任何12,f x x D ∈（其中f D 为函数()f x 的定义域），均有1212()()||f x f x x x -≤-成立.（1）已知函数2()1f x x =+，11[,]22x ∈-，判断()f x 与集合M 的关系，并说明理由；（2）是否存在实数a ，使得()2a p x x =+，[1,)x ∈-+∞属于集合M ？若存在，求a 的取值范围，若不存在，请说明理由；（3）对于实数a 、b ()a b <，用[,]a b M 表示集合M 中定义域为区间[,]a b 的函数的集合.定义：已知()h x 是定义在[,]p q 上的函数，如果存在常数0T >，对区间[,]p q 的任意划分：011n n p x x x x q -=<<⋅⋅⋅<<=，和式11|()()|ni i i h x h x T -=-≤∑恒成立，则称()h x 为[,]p q 上的“绝对差有界函数”，其中常数T 称为()h x 的“绝对差上界”，T 的最小值称为()h x 的“绝对差上确界”，符号121n i n i tt t t ==++⋅⋅⋅+∑；求证：集合[1009,1008]M -中的函数()h x 是“绝对差有界函数”，并求()h x 的“绝对差上确界”.2017学年复旦附中高一上期中一.填空题1.已知全集U =R ，{1,0,1,2}A =-，2{|}B x x x ==，则U A C B = __________【答案】{1,2}-【分析】先求出集合B ，再求出U C B ，最后求出U A C B ⋂．【详解】由题意得{}{}2|0,1B x x x ===，∴()()(),00,11,U C B ∞=-⋃⋃+∞，∴{}1,2U A C B ⋂=-．故答案为{}1,2-．【点睛】本题考查集合的运算，解题时根据集合运算的顺序进行求解即可，属于基础题．2.命题“如果0a b +>，那么0a >且0b >”的否命题是__________命题（填“真”或“假”）【答案】真【分析】根据原命题的逆命题和其否命题为等价命题判断命题的真假．【详解】由题意得命题“如果0a b +>，那么0a >且0b >”的逆命题为“如果0a >且0b >，那么0a b +>”，其真命题，所以否命题为真命题．故答案为“真”．【点睛】判断命题的真假时，可通过命题直接进行判断也可通过其等价命题的真假来判断，解题时要根据条件选择合理的方法进行求解．3.已知集合2{|23}A y y x x ==--，2{|213}B y y x x ==-++，则A B = __________【答案】[4,14]-【分析】分别求出集合,A B ，然后再求出A B ⋂即可．【详解】由题意得{}(){}{}22|23|14|4A y y x x y y x y y ==--==--=≥-，{}{}{}22|213|(1)14|14B y y x x y y x y y ==-++==--+=≤，∴[]4,14A B ⋂=-．故答案为[]4,14-．【点睛】本题考查集合的交集运算，解题的关键是正确求出集合,A B ，属于简单题．4.已知“12a x a ≤≤+”是“1232a x a -<<+”的充分不必要条件，则实数a 的取值范围是__________【答案】13a >【分析】将充分不必要条件转化为集合间的包含关系求解可得结论．【详解】设{}1|,|12322A x a x a B x a x a ⎧⎫=≤≤+=-<<+⎨⎬⎩⎭，∵“12a x a ≤≤+”是“1232a x a -<<+”的充分不必要条件，∴A B ，∴1232121322a a a a a a ⎧⎪-<+⎪-<⎨⎪⎪+<+⎩，解得13a >，∴实数a 的取值范围是1,3⎛⎫+∞ ⎪⎝⎭．故答案为1,3⎛⎫+∞ ⎪⎝⎭．【点睛】根据充要条件求解参数范围的方法步骤(1)把充分条件、必要条件或充要条件转化为集合间的关系；(2)根据集合关系画数轴或Venn 图，由图写出关于参数的不等式(组)，求解．注意：求解参数的取值范围时，一定要注意区间端点值的检验，尤其是利用两个集合之间的关系求解参数的取值范围时，不等式是否能够取等号决定端点值的取舍，处理不当容易出现漏解或增解的现象．5.设M={a,b}，则满足M ∪N ⊆{a,b,c}的非空集合N 的个数为______________．【答案】4【详解】根据M ∪N ⊆{a ，b ，c}而M 中没有c 元素，所以N 集合中一定要有c 元素，可能有a,b 元素且N 为非空集合，所以N 可以为{c}，{a ，c}，{b ，c}，{a ，b ，c}共4个．故答案为46.函数()f x =的定义域为[2,1]-，则a 的值为__________【答案】2【分析】由题意得不等式()()2213160ax a x -+-+≥的解集为[]2,1-，然后根据“三个二次”间的关系求解即可得到结论．【详解】∵函数()f x =的定义域为[]2,1-，∴不等式()()2213160a x a x -+-+≥的解集为[]2,1-，∴2,1x x =-=是方程()()2213160a x a x -+-+=的两个根，∴()()()()2241616013160a a a a ⎧---+=⎪⎨-+-+=⎪⎩，整理得2223203100a a a a ⎧--=⎨+-=⎩，解得2a =．故答案为2．【点睛】本题以函数的定义域为载体，考查一元二次方程、二次函数、二次不等式间的关系，解题的关键是根据题意得到方程的两根，然后再根据方程的有关概念求出a 的值，考查转化能力和运算能力，属于基础题．7.已知函数()(1)23f x m x m =-+-，无论m 取什么实数，函数()f x 的图像始终过一个定点，该定点的坐标为__________【答案】()2,1--【分析】将函数解析式变形为()230x m x y +---=，然后令20x +=且30x y ---=，求得方程组的解后即可定点的坐标．【详解】由()123y m x m =-+-变形得()230x m x y +---=，解方程组2030x x y +=⎧⎨---=⎩得21x y =-⎧⎨=-⎩，所以函数()f x 的图象过的定点的坐标为()2,1--．故答案为()2,1--．【点睛】本题考查一次函数的图象过定点的问题，解题时可把函数解析式化为(,)(,)0kf x y g x y +=（k 为参数）的形式，则以方程组(,)0(,)0f x y g x y =⎧⎨=⎩的解为坐标的点即为定点．8.已知关于x 的方程2240x kx k k +++-=有两个实数根，且一根大于1，一根小于1，则实数k 的取值范围为__________【答案】(3,1)-【分析】根据一元二次方程根的分布求解，令()224f x x kx k k =+++-，则有()10f <，解不等式可得所求范围．【详解】令()224f x x kx k k =+++-，∵方程的一个实数根大于1，另一个实数根小于1，∴()21140f k k k =+++-<，即2230k k +-<，解得31k -<<，∴实数k 的取值范围为()3,1-．故答案为()3,1-．【点睛】本题考查根据方程根的情况求参数的取值范围，解题时根据方程根的分布将问题转化为不等式求解，体现了转化和数形结合的思想方法在解题中的应用．9.给出下列四个命题：（1）若a b >，c d >，则a d b c ->-；（2）若22a x a y >，则x y >；（3）若a b >，则11a b a>-；（4）110a b <<，则2ab b <.其中正确命题是________.（填所有正确命题的序号）【答案】（1）（2）（4）【分析】根据不等式的性质，以及特殊值验证，逐项判断，即可得出结果.【详解】（1）若a b >，c d >，则a c b d +>+，因此a d b c ->-，即（1）正确；（2）若22a x a y >，根据不等式性质，可得x y >；即（2）正确；（3）若1a =，1b =-，满足a b >，但不满足11a b a>-；（3）错误；（4）若110a b <<，则0b a <<，因此()20ab b b a b -=-<，即2ab b <；故（4）正确；故答案为：（1）（2）（4）【点睛】本题主要考查判定命题的真假，考查由不等式性质判定所给结论是否正确，属于基础题型.10.若(,2)x ∈-∞，则2542-+-x x x的最小值为__________【答案】2【分析】将原式变形后根据基本不等式求解．【详解】∵2x <，∴20x ->．由题意得2254(2)11==(2)+2222x x x x x x x -+-+-≥=---，当且仅当122x x-=-，即1x =时等号成立．∴2542x x x-+-的最小值为2.故答案为2.【点睛】应用基本不等式求最值时一定要注意“一正二定三相等”这三个条件缺一不可，当不满足不等式使用的条件时，可通过适当的变形使得出现定值的形式，这是解题中常遇到的情形．11.设函数()2f x x =-，若不等式|(3)|()f x f x m +>+对任意实数x 恒成立，则m 的取值范围是__________【答案】3m <-【分析】12x x +--表示数轴上的x 对应点到-1对应点的距离减去它到2对应点的距离，其最小值为-3，故有m<-3，由此求得m 的取值范围．【详解】∵()2f x x =-，不等式()()3f x f x m +>+对任意实数x 恒成立，∴12m x x <+--对任意实数x 恒成立，又12x x +--表示数轴上的x 对应点到-1对应点的距离减去它到2对应点的距离，∴123x x +--≥-，∴3m <-，∴实数m 的取值范围是(),3-∞-．故答案为(),3-∞-．【点睛】本题考查恒成立问题，解题的关键是根据绝对值的几何意义求出12x x +--的最小值，考查转化和数形结合思想的运用能力．12.对于实数A 和正数B ，称满足不等式||x A B -<(,0)A B ∈>R 的实数x 的集合叫做A 的B 邻域，已知t 为给定的正数，a 、b 为正数，若a b t +-的a b +领域是一个关于原点对称的区间，则22a b +的最小值为__________【答案】22t 【分析】先根据条件求出()2t x a b t -<<+-；再结合邻域是一个关于原点对称的区间得到a b t +=，最后结合不等式的知识可求出22a b +的最小值．【详解】∵A 的B 邻域在数轴上表示以A 为中心，B 为半径的区域，∴()x a b t a b -+-<+，∴()a b x a b t a b --<-+-<+，解得()2t x a b t -<<+-．∵邻域是一个关于原点对称的区间，∴()220a b t +-=，∴a b t +=．∵222a b ab +≥，∴()()22222222a ba b ab a b t +≥++=+=，∴2222t a b +≥，当且仅当a b =时等号成立，∴22a b +的最小值为22t ．故答案为22t ．【点睛】本题以新概念为载体考查重要不等式的应用，考查变换能力和阅读理解能力．解题的关键是根据题意得到a b t +=这一结论，然后再通过变形得到所求的最小值．二.选择题13.已知1a ，1b ，2a ，2b R ∈且都不为零，则“1122a b a b =”是“110a x b +>与220a x b +>解集相同”的A.充分非必要条件B.必要非充分条件C.充要条件D.既非充分又非必要条件【答案】B【分析】根据充分条件和必要条件的定义，结合不等式的性质进行判断即可.【详解】若1122a b a b =，取111a b ==，221a b ==-，则10x +>与10x -->的解集不同，所以“1122a b a b =”不是“110a x b +>与220a x b +>解集相同”的充分条件；若1a ，1b ，2a ，2b R ∈且都不为零，且110a x b +>与220a x b +>的解集相同，此时必有1212b b a a -=-，所以1122a b a b =成立，所以“1122a b a b =”是“110a x b +>与220a x b +>解集相同”的必要条件.综上，“1122a b a b =”是“110a x b +>与220a x b +>解集相同”的必要不充分条件.故选：B.【点睛】本题主要考查充分条件和必要条件的判断，属于常考题.14.解析式为221y x =+，值域为{}5,19的函数有A.4B.6C.8D.9【答案】D【分析】根据y 的值求出相应的x 的值，再根据函数的有关概念得到定义域的不同形式，进而可得结论．【详解】由2215x +=，解得x =；由22119x +=，解得3x =±．所以函数的定义域可为}}{}{}{}{},3,,3,,3,----{}}{}3,3,3,3,3,3---，共9种情况．故选D ．【点睛】本题考查函数的概念，考查分析理解问题的能力，解题的关键是深刻理解函数的概念，根据对应关系求出x 的取值，然后再根据定义域中元素的个数确定出函数定义域的不同情形．15.设()f x 是定义在正整数集上的函数，且()f x 满足：“当2()f x x >成立时，总可以推出2(1)(1)f x x +>+成立”，给出以下四个命题：①若(3)9f ≥，则(4)16f ≥；②若(3)10f =，则(5)25f >；③若(5)25f =，则(4)16f ≤；④若2()(1)f x x ≥+，则2(1)f x x +≥.其中真命题的个数为（）个A.1B.2C.3D.4【答案】C【分析】根据题意对给出的四个命题分别进行分析、排除后可得正确的结论．【详解】对于①，由于f(3)=9时，可以使得f(4)<16，这并不与题设矛盾，所以当f(3)≥9时，由题设不一定得到f(4)≥16成立，所以①为假命题．对于②，∵f(3)=10>9，∴f(4)>4²，∴f(5)>5²=25，所以②为真命题；对于③，若f(4)>16，则f(5)>25，这与f(5)=25矛盾，所以f(4)≤16，所以③为真命题；对于④，∵f(x)≥(x+1)²>x ²，∴f(x+1)>(x+1)²>x ²，即有f(x+1)≥x²，所以④为真命题．综上可得②③④为真命题．故选C ．【点睛】本题考查推理论证能力，解题的关键是根据条件“当()2f x x >成立时，总可以推出()()211f x x +>+成立”进行判断，注意解题方法的选择，如直接推理、利用反证法判断等．16.设a ，b ，c 为实数，22()()(),()(1)(1),f x x a x bx cg x ax cx bx =+++=+++记集合{}{}|()0,,|()0,,S x f x x R T x g x x R ==∈==∈若{S }，{T }分别为集合S ，T 的元素个数，则下列结论不可能的是（）A.{S }=1且{T }=0B.{S }=1且{T }=1C.{S }=2且{T }=2D.{S }=2且{T }=3【答案】D【详解】∵2()()(),f x x a x bx c =+++当()0f x =时至少有一个根x a =-，当240b c -=时，()0f x =还有一根2b x =-，只要b ≠﹣2a ，()0f x =就有2个根；当b =﹣2a ，()0f x =是一个根当240b c -<时，()0f x =只有一个根；当240b c ->时，()0f x =只有二个根或三个根；当a =b =c =0时{S }=1，{T }=0当a ＞0，b =0，c ＞0时，{S }=1且{T }=1当a =c =1，b =﹣2时，有{S }=2且{T }=2故选：D 三.解答题17.已知集合2{|(1)320}=-+-=A x m x x ，是否存在这样的实数m ，使得集合A 有且仅有两个子集？若存在，求出所有的m 的值组成的集合M ；若不存在，请说明理由.【答案】11,8M ⎧⎫=-⎨⎬⎩⎭【分析】若集合A 有且仅有两个子集，则A 有且仅有一个元素，即方程()21320m x x -+-=只有一个根，进而可得答案【详解】存在11,8M ⎧⎫=⎨⎬⎩⎭满足条件．理由如下：若集合A 有且仅有两个子集，则A 有且仅有一个元素，即方程()21320m x x -+-=只有一个根，①当10m -=，即=1m 时，由320x -=，解得23x =，满足题意．②当10m -≠，由A 有且仅有一个元素得()10Δ=9+81=0m m -≠-⎧⎨⎩，解得18m =-．综上可得=1m 或18m =-，∴所有的m 的值组成的集合11,8M ⎧⎫=-⎨⎬⎩⎭．【点睛】本题考查集合元素个数的问题，考查分析问题的能力，解题的关键是由题意得到方程根的个数，然后通过对方程类型的分类讨论得到所求的参数．18.我校第二教学楼在建造过程中，需建一座长方体形的净水处理池，该长方体的底面积为200平方米，池的深度为5米，如图，该处理池由左右两部分组成，中间是一条间隔的墙壁，池的外围周壁建造单价为400元/平方米，中间的墙壁（不需考虑该墙壁的左右两面）建造单价为100元/平方米，池底建造单价为60元/平方米，池壁厚度忽略不计，问净水池的长AB 为多少时，可使总造价最低？最低价为多少？【答案】15AB =时，总造价最低为132000元.【分析】设AB 的长为x 米，进而得到宽BC 为200x 米，根据题意得到总造价的表达式，然后根据基本不等式求出造价的最小值即可．【详解】设AB 的长为x 米，则宽BC 为200x 米，由题意得总造价为200200400(22)5100560200y x x x =+⨯⨯+⨯⨯+⨯450(2)12000x x=++12000≥+132000=，当且仅当4502x x=，即15x =时等号成立．所以当净水池的长15AB =米时，可使总造价最低，最低价为132000元．【点睛】基本不等式为求最值提供了工具，在利用基本不等式求最值时，一定要注意使用基本不等式的条件，即“一正二定三相等”，且三个条件缺一不可，当题目中不满足使用不等式的条件时，则需经过变形得到所需要的形式及条件．19.已知a ∈R ，集合26{|0}1x x A x x --=≤+，集合{||2|1}B x x a a =+≤+.（1）求集合A 与集合B ；（2）若A B B = ，求实数a 的取值范围.【答案】（1）(,2](1,3]A =-∞-⋃-，当1a >-，[31,1]B a a =---+，当1a =-，{2}B =，当1a <-，B =∅；（2）(,0)[3,)-∞⋃+∞.【分析】（1）解不等式得出集合A 、B ；（2）根据A∩B=B 得出B ⊆A ，讨论B=∅和B≠∅时，求出满足条件的实数a 的取值范围．【详解】（1）由题意得()()(](]2236|0|0,21,311x x x x A x x x x ⎧⎫+-⎧⎫--=≤=≤=-∞-⋃-⎨⎬⎨⎬++⎩⎭⎩⎭．当10a +<，即1a <-时，B =∅；当10a +=，即1a =-时，{}2B =；当10a +>，即1a >-时，{}[]|12131,1B x a x a a a a =--≤+≤+=---+．（2）∵A B B ⋂=，∴B ⊆A ．①当1a <-时，B =∅，满足B ⊆A ；②当1a =-时，{}2B =，满足B ⊆A ；③当1a >-时，[]31,1B a a =---+，由B ⊆A 得31113a a -->-⎧⎨-+≤⎩或12a -+≤-，解得20a -≤<或3a ≥，又1a >-，∴10a -<<或3a ≥．综上可得0a <或3a ≥，∴实数a 的取值范围为()[),03,-∞⋃+∞．【点睛】根据集合间的包含关系求参数的取值范围时，一般要借助于数轴进行求解，根据集合端点值的大小关系转化为不等式（组）求解，解题时要注意不等式中的等号是否成立，这是解题中容易出现错误的地方．20.已知函数2|1|()4x m f x x +-=-，0m >，满足(2)2f =-.（1）求实数m 的值；（2）在平面直角坐标系中，作出函数()f x 的图像，并且根据图像判断：若关于x 的方程()f x k =有两个不同实数解，求实数k 的取值范围（直接写结论）【答案】（1）1m =；（2）图象见解析，()2,0-.【分析】（1）直接由f （2）=-2求得m 的值；（2）把m 值代入函数解析式，写出分段函数，根据函数的单调性作出图象，然后利用数形结合即可求得使关于x 的方程f （x ）=k 有两个不同实数解的实数k 的取值范围．【详解】（1）∵()214x m f x x +-=-，0m >，且()22f =-，∴221224m +-=--，即12m +=，解得1m =或3m =-，又0m >，∴1m =．（2）由（1）得()2,042424,04x x x x x f x x x x x ⎧≥≠⎪⎪-==⎨-⎪-<⎪-⎩且，当04x x ≥≠且时，()22(4)882444x x f x x x x -+===+---，∴函数()f x 在[0,4)和(4,)+∞上为减函数；当0x <时，()22(4)882444x x f x x x x -+=-=-=-----，∴函数()f x 在(,0)-∞上为增函数，且()()200f x f -<<=．画出函数图象如下图：由图可知，要使关于x 的方程()f x k =有两个不同实数解，则20k -<<，∴实数k 的取值范围是()2,0-．【点睛】（1）描点法画函数图象的步骤：①确定函数的定义域；②化简函数的解析式；③讨论函数的性质，即奇偶性、周期性、单调性、最值(甚至变化趋势)等；④描点连线，画出函数的图象．（2）利用函数图象确定方程或不等式的解，形象直观，体现了数形结合思想，解题的关键是正确的作出函数的图象．21.已知M 是满足下列性质的所有函数()f x 组成的集合：对任何12,f x x D ∈（其中f D 为函数()f x 的定义域），均有1212()()||f x f x x x -≤-成立.（1）已知函数2()1f x x =+，11[,]22x ∈-，判断()f x 与集合M 的关系，并说明理由；（2）是否存在实数a ，使得()2a p x x =+，[1,)x ∈-+∞属于集合M ？若存在，求a 的取值范围，若不存在，请说明理由；（3）对于实数a 、b ()a b <，用[,]a b M 表示集合M 中定义域为区间[,]a b 的函数的集合.定义：已知()h x 是定义在[,]p q 上的函数，如果存在常数0T >，对区间[,]p q 的任意划分：011n n p x x x x q -=<<⋅⋅⋅<<=，和式11|()()|ni i i h x h x T -=-≤∑恒成立，则称()h x 为[,]p q 上的“绝对差有界函数”，其中常数T 称为()h x 的“绝对差上界”，T 的最小值称为()h x 的“绝对差上确界”，符号121n i n i tt t t ==++⋅⋅⋅+∑；求证：集合[1009,1008]M -中的函数()h x 是“绝对差有界函数”，并求()h x 的“绝对差上确界”.【答案】（1）()f x 属于集合M ；（2）[1,1]-；（3）略.【分析】（1）利用已知条件，通过任取1211,,22x x ⎡⎤∈-⎢⎥⎣⎦，证明()()1212f x f x x x -≤-成立，说明f （x ）属于集合M ．（2）若p （x ）∈M ，则有121222a a x x x x -≤-++，然后可求出当[]1,1a ∈-时，p （x ）∈M ．（3）直接利用新定义加以证明，并求出h （x ）的“绝对差上确界”T 的值．【详解】（1）设1211,,22x x ⎡⎤∈-⎢⎥⎣⎦，则()()2212121212f x f x x x x x x x -=-=-+，∵121111,2222x x -≤≤-≤≤，∴1211x x -≤+≤，∴1201x x ≤+≤∴()()221212121212f x f x x x x x x x x x -=-=-+≤-，∴函数()f x 属于集合M ．（2）若函数()2a p x x =+，[)1,x ∈-+∞属于集合M ，则当[)12,1,x x ∈-+∞时，()()1212p x p x x x -≤-恒成立，即121222a a x x x x -≤-++对[)12,1,x x ∈-+∞恒成立，∴12(2)(2)a x x ≤++对[)12,1,x x ∈-+∞恒成立．∵[)12,1,x x ∈-+∞，∴12(2)(2)1x x ++≥，∴||1a ≤，解得11a -≤≤，∴存在实数a ，使得()2a p x x =+，[)1,x ∈-+∞属于集合M ，且实数a 的取值范围为[1,1]-．（3）取1009,1008p q =-=，则对区间[]1009,1008-的任意划分：01110091008n n x x x x --=<<⋅⋅⋅<<=，和式()()()()()()()()1110211i i i n n n h x h x h x h x h x h x h x h x =--∑-=-+-++-10211n n x x x x x x -≤-+-++- 10211=()()()n n x x x x x x --+-++- 0n x x =-1008(1009)=--2017=，∴集合[]1009,1008M -中的函数()h x 是“绝对差有界函数”，且()h x 的“绝对差上确界”2017T =．【点睛】本题考查新信息问题，考查阅读理解和应用能力，具有一定的综合性，解题的关键是弄懂给出的定义，解题时始终要围绕着给出的定义进行验证、求解等．。
2017-2018年复旦大学附属中学高一上期中物理试卷解析版
复旦大学附属中学2017学年度第一学期高一年级物理期中考试试卷（时间：60分钟，满分100分,g取10m/s2）一、单项选择题（每题4分，共40分）1.下列说法正确的是（C）A.若物体的加速度均匀增加，则物体做匀加速直线运动B.若物体的加速度增加，则物体不可能做减速运动C.只要物体的加速度不为零，它的速度总是在发生变化的D.只要物体做直线运动，位移的大小和路程就一定相等2.三个质点A、B、C的运动轨迹如图2所示,同时从N点出发,同时到达M点,下列说法中正确的是(C)A.三个质点任意时刻的速度方向都相同B.三个质点从N点出发到M的任意时刻速度大小都相同C.三个质点从N点到M点的平均速度大小和方向均相同D.三个质点从N点到M点的平均速率相同【解析】平均速度等于位移比时间，三个质点的位移相同，故平均速度相同。
而平均速率等于路程比时间，三个质点的路程不相等。
3.如图所示，各接触面均光滑，A、B间无弹力作用的是（A）A．B．C．D．4.如图所示,某人用手握住一个保温杯,则下列说法中正确的是(B)A.若保持保温杯始终静止，则手握得越紧，保温杯受到摩擦力越大B.握着保温杯匀速向上运动，保温杯所受的摩擦力向上C.握着保温杯匀速向下运动，保温杯所受的摩擦力向下D.握着保温杯水平匀速运动，保温杯不受摩擦力5.某质点以20m/s 的初速度竖直向上运动,其加速度保持不变,经2s 到达最高点,上升高度为20m,又经过2s 回到出发点时,速度大小仍为20m/s,关于这一运动过程的下列说法中不正确的是(C )A ．质点运动的加速度大小为10m/s 2,方向竖直向下B ．最高点时速度为零,加速度不为零C ．质点在上升过程中速度的变化量大小相等20m/s ，方向竖直向上D ．质点在上升过程中和下降过程中速度的变化量大小相等方向相同6.用轻绳系住一小球静止在光滑斜面上,如图所示.若要按力的实际作用效果来分解小球的重力,则重力的两个分力的方向分别是图中的(C )A .1和5B .2和5C .3和5D.3和2【解析】小球重力产生两个效果。
2017-2018上海复旦附中高一上期 中考试
2017-2018 上海市复旦附中高一上学期期中考试Grammar and Vocabulary: (18%)Section A (8%)Directions: Beneath each of the following sentences there are four choices marked A, B, C and D. Choose the one answer that best completes the sentence.21. The discovery of gold in Australia led thousands to believe that a fortune_________.A, had been making B. was making C. was to be made D. would make 22. The president hopes that people will be better off when he quits than when he _________.A. has startedB. startsC. will startD. started23. Travellers to that area can carry disease to their own countries that have never experienced _________.A. themB. itC. themselvesD. itself24. No one can tell the exact number of U.S. pilots and fighter planes ________were lost in the Pearl Harbor air attack.A. whoB. whichC. thatD. what25. ____________, the climbers, who had already conquered many high mountains before, determined to reach the top of the mountain.A. However it was highB. How high it wasC. However high it wasD. However high was it26. They will not allow others to decide the future of their country, _________.A. which is to be knownB. as is to be knownC. as is known to allD. as what is known to all27. We have come to realize that the brain must “ forget” some pieces of information ________it can remember others.A. whenB. sinceC. so thatD. if28. They are our school’s volunteers _______to help elderly people cross the streets every day.A. whose task it isB. it is whose taskC. to whom is the taskD. whose task wasSection B (10%)Directions: Complete the following passage by using the words in the box. Each word can be only used once. Note that there is one word more than youneed.A. journeyingB. foundingC. educationalD. marvelous AB.viewAC. undoubtedly AD. thrill BC. existed BD. sights CD. surprisingly ABC. soilSept 27 is World Tourism Day. Of course, travel isn’t a new discovery. Imagine how Italian traveler Marco Polo must have felt when he found himself on Chinese ____29_____, seeing a way of life quite different from anything he’d seen before.And how ___30______ must it have been to listen to Zhang Qian when he returned to China from his journey through Central Asia and West Asia? His brain must have been packed with everything he’d seen and heard, leading to the ____31_____ of the Silk Road.Travel is one of the most exciting experiences a human being can have. Nowadays, more people are traveling than ever before. By train, plane and car, people all around the globe are ____32_____ to places that people didn’t even know ____33_____ a few centuries ago, or only knew from books.Some people have traveled all over the world, and travel is a way of life to them. They perhaps know what to expect before they travel. That’s why the best travel is when it’s for the first time. Imagine a person who has always wanted to travel to the United States. Of course, they’ve probably seen the Statue of Liberty a thousand times on the TV, and the White House, and all the other famous _______34__. But none of that would compare to the ___35______ of looking out of the cabin window as the plane lands, watching the cities and streets of the real America come into_____36____.Although travel is often just for fun, it’s also ____37_____. We may not know that we are getting an education, but we still are.We’re learning every day: new words in a new language, new people, and new ways of life. But this learning takes place in the school of the world, not the classroom. One of the lessons we learn is ____38_____ a moral one. As we get to know foreign places, we come to understand that there are many different ways to live, and that the way we live isn’t necessarily the best way. The British politician Benjamin Disraeli summed this up well when he said,“Travel teaches toleration.”Ⅲ.Reading Comprehension (40%)Section ADirections : For each blank in the following passages there are four words or phrases marked A,B,C and D. Fill in each blank with the word or phrases that best fits the context.( A )Leif Erickson reached North America around the year 1000, but the attempt to explore was started slowly. It would be five centuries __(39)__ other Europeans landed on that continent.Why were Europeans the ones to __(40)__ to the American? The Chinese and Arabs had the _(41)__ and technology to sail across the seas. __(42)__ of them tool regular voyages in the Indian Ocean and the Asian Pacific for trade. But exploration? By the mid-15th century China had followed the closed-door policy to __(43)__ itself from the rest of the world. The Arabs, with access to the minerals and spices (香料) of Africa and the Far East, saw no __(44)__ to journey into the unknown.Europe, ____(45)________ needed gold and silver; its mines could not meet the demand for coinage. Ottoman Turks blocked the routes across the land to Asia. Only the sea held the ___(46)_____of new wealth.With the return of Magellan’s ships in 1522 from its voyage around the world, the belief was __(47)__ that the oceans were interconnected, promising the age of discovery. The English, as well as the Spanish, Portuguese and French, __(48)__ themselves to finding the “river of the west” through North America to the east.39. A. after B. since C .before D .when40. A .push B .pull C .draw D .drive41. A .sources B .resources C .substances D .matters42. A .Neither B .Both C .Any D .None43. A .prevent B .protect C .isolate D .differ44. A .access B .admission C .application D .association45. A .as a matter of fact B . in other wordsC. for one thing D .on the other hand46. A .symbol B .impression C .promise D .reflection47. A .extended B .estimated C .attracted D .accepted48. A .contributed B .devoted C .referred D .connected( B )Those who keep their word become the most important members of an organization. People come to rely on and trust them. They can be____(49)____.___(50)______you make a promise , be sure to keep it. When you keep your promise, no matter how much ___(51)_______it takes, you will be rewarded.Whenever you say no, stand upon that as well. In a way, a no is also a promise. A good, _____(52)____no can be very important in building trust. Agreements are also important. Whenever you enter an agreement, live by it, ______(53)____you are not too happy with the deal after making the deal, you still live by it. In the long run, your integrity will _____(54)____.Victoria was the manager of a supermarket. She set out to do that____(55)_____. She was very careful, however, of not _____(56)_____. When she did, she moved mountains to make sure that she came through. After a while, the stone employee came to trust and respect her like no______(57)_____they had ever had. The teamwork became magical. People followed her example by living up to their word. She ____(58)______what she said, and people appreciated that.49. A. counted B. counted on C. depended D. numbered50.A. As far as B. Though C. Whenever D. However51.A. pain B. ache C. effort D. money52. A. loud B. clean C. sharp D. loose53. A. As B. As if C. Just as D. Even if54. A. set off B. show off C. pay off D. take off55. A. thoroughly B. entirely C. wholly D. totally56. A. lying B. overpromising C. underestimating D. overlooking57. A. manager B. employee C. supermarket D. others58. A. believed B. trusted C. meant D. promisedSection BDirections :Read the following passages. Each passage is followed byquestions 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 few years ago, Paul Gerner began to gather a group of architects in Las Vegas to ask them what it would take to design a public school that used 50 percent less energy, cost much less to build and obviously improved student learning. “I think half of them fell off their chairs,” Gerner says.Gerner manages school facilities for Clark County, Nevada, a district roughly the size of Massachusetts. By 2018, 143,000 additional students will enter the already crowded public-education system. Gerner needs 73 new schools to house them. Four architecture teams have nearly finished designing primary school prototypes （原型）; they plan to construct their schools starting in 2009. The district will then assess how well the schools perform, and three winners will copy those designs in 50 to 70 new buildings.Green schools are appearing all over, but in Clark County, which stands out for its vastness(广阔), such aggressive targets are difficult because design requirements like more natural light for students go against the realities of a desert climate. “One of the biggest challenges is getting the right site orientation,” Mark McGinty, a director at SH Architecture, says. His firm recently completed a high school in Las Vegas. ”You have the same building, same set of windows, but if its orientation is incorrect and it faces the sun, it will be really expensive to cool.”Surprisingly, the man responsible for one of the most progressive green-design competitions has doubts about ideas of eco-friendly buildings. “I don’t believe in the new green religion,” Gerner says. “Some of the building technologies that you get are impractical. I’m interested in those that work.”But he wouldn’t mind if some green features inspire students. He says he hopes to set up green energy systems that allow them to learn about the process of harvesting wind and solar power. “You never know what’s going to start the interest of a child to study math and science,” he says.59. How did the architects react to Gerner’s design requirements?A .They lost balance in excitement.B .They showed strong disbelief.C .They expressed little interest.D .They burst into cheers.60. Which order of steps is followed in carrying out the project?A .Assessment — Prototype — Design — Construction.B .Assessment — Design — Prototype — Construction.C .Design — Assessment — Prototype — Construction.D .Design — Prototype — Assessment — Construction.61 What makes it difficult to build green schools in Clark County?A .The large size.B .Limited facilities.C .The desert climate.D .Poor natural resources.62. What does Gerner think of the ideas of green schools?A .They are questionable.B .They are out of date.C .They are advanced.D .They are practical.(B)Spring is in the air, as is romance. Perhaps you're even thinking of taking the plunge and making a honey trip with your significant other?Before you do, why not take a look at a list of the top three places in the world to propose(求婚)? With suggestions for traditionalists and private types, you just might find the perfect spot to pop the question.New YorkIf you pay attention to romantic comedies, New York is the place for romance. Ever since the Dutch first entered this harbor in 1624 it has become a historic landmark and a must visit dreamland. Every stretch of this island is packed full of fun that will keep everyone busy. Take a leaf out of sleepless in Seattle and head to the top of the Empire State Building at night, or how about run to your loved one on the streets of NYC this New Years even like in when harry Met Sally?ParisSweeping views? Check. Grand old stately home? Check. Luxurious spots to propose? check. pack your passports and say goodbye to your daily routine life-it's less than three hours to Paris from London by Eurostar. Famous for its breathtaking architecture, and many cultural attractions, France's capital is a must-see destination. While we're not suggesting you climb the Eiffel Tower for the big moment. There's a reason why this is the city of love, if you keep your proposal original. So gentleman, take your lady to the Louvre, turn your back on the Mona Lisa and declare she is more beautiful than thefamous work of art.Las VegasDo you want to bundle the proposal and wedding all-in-one? plead to. Las Vegas, get down on one knee, show your love and get married in less time than it takes to order 'honeymoon suit’ and if it doesn't work out. There's still plenty of entertain. Once the playground of the rich and famous, from Elvis Presley to Marilyn Monroe, Las Vegas now attracts millions of visitors by its bright lights and thrills each year. Whether you're to try your luck at the casinos (赌场), or watch a show, there's a wonder to explore in Las Vegas. 63. Which of the following city on the top-3 list would be the ideal place for film fans to propose?A. New YorkB. Paris.C. Las Vegas.D. None.64. Which place is recommended for a proposal in the passage?A. On the top of the Eiffel TowerB. In the Eurostar train from LondonC. Any luxurious spot in PairsD. In front of the Mona Lisa in the Louvre64. As a perfect place for propose, Las Vegas will provide you with all the following EXCEPT.A. a honeymoon suiteB. a package weddingC. a bundle of flowersD. various ways to entertain( C )Do you look happy? angry? Have you ever wondered how you know what another person’s mood is just by looking at his or her face? Studies have shown that one instantaneously (瞬间地) and subconsciously makes a determination of another person’s mood just by glancing at the position and appearance of both the eyebrows and mouth. But what if only the position of the eyebrows was varied , and not the mouth? Would you still be able to determine his or her mood or personality just by seeing the eyebrows?Observe the four faces shown below. Notice how each face has exactly the same shape. the same smile, and the same eyes. The only difference between each of the faces is the position of the eyebrows.Low, flat eyebrows that hang over the eyes indicate tiredness, while an eyebrow that is highest in the middle denotes sadness. Downward slanting eyebrows show anger, while highly arched eyebrows show happiness.Frequently, malposition of the eyebrows, such as eyebrow sagging(下垂) and upper eyelid fullness, can be overlooked when considering facial aging and expression. Furthermore, the heavy eyebrow skin pushed the eyelid down causing a tired appearance.To avoid eyebrow sagging, many people raise their eyebrows to remove the brow and eyelid skin from their visual space. These people eventually develop wrinkles in the forehead due to the constant movement of the muscles that raise the eyebrow. In addition, there are those who are sensitive to light and frequently’ squint(斜视) and squeeze’ their eyes. This effectively pulls the eyebrows down and leads to wrinkles between the eyebrows and at the corners of the eyes.Botox is an effective measure for fine lines of the forehead and lines between the eyebrows. Botox works by freezing the muscle movement for several months. For the purpose of creating a more pleasant appearance, the best corrective measure is brow-lift surgery.66. What can this passage be?A. An advertisementB. A magazine articleC. A business reportD. A scientific report67. A person’s eyebrows that hang over the eyes low and flat can cause a(n) _________appearance.A. sadB. tiredC. happyD. angry68. What is the purpose of the passage?A. To explain the fact that varied eye position can tell a person’s mood.B. To arouse people’s interest in the best way of removing wrinkles in the forehead and between the eyebrows.C. To explain what leads to wrinkles in the forehead and near the eyebrow.D. To enable people to know how to avoid developing fine lines on their faces.69. If the passage continues, what would the writer most likely discuss in the next paragraph?A. Facial agingB. Eye operationC. Brow life surgeryD. Face-lifts.( D )The past ages of man have all been carefully labeled by anthropologists. Descriptions like ‘Palaeolithic Man’, ‘Neolithic Man’, etc., neatly sum up whole periods. When the time comes for anthropologists to turn their attention to the twentieth century, they will surely choose the label ‘Legless Man’. Histories of the time will go something like this: ‘in the twentieth century, people forgot how to use their legs. Men and women moved about in cars, buses and trains from a very early age. There were lifts and escalators in all large buildings to prevent people from walking. This situation was forced upon earth dwellers of that time because of miles each day. But the surprising thing is that they didn’t use their legs even when they went on holiday. They built cable railways, ski-lifts and roads to the top of every huge mountain. All the beauty spots on earth were ruined by the presence of large car parks.’The future history books might also record that we were deprived of the use of our eyes. In our hurry to get from one place to another, we failed to see anything on the way. Air travel gives you a bird’s-eye view of the world—or even less if the wing of the aircraft happens to get in your way. When you travel by car or train a blurred (="not" clear) image of the countryside constantly smears the windows. Car drivers, in particular, are forever obsessed with the urge to go on and on: they never want to stop. Is it the lure of the great motorways, or what? And as for sea travel, it hardly deserves mention. It is perfectly summed up in the words of the old song: ‘I joined the navy to see the world, and what did I see? I saw the sea.’ The typical twentieth-century traveler is the man who always says ‘I’ve been there. ’You mention the remotest, most evocative (引起记忆的) place-names in the world like El Dorado, Kabul, Irkutsk and someone is bound to say ‘I’ve been there’—meaning, ‘I drove through it at 100 miles an hour on the way to somewhere else.’When you travel at high speeds, the present means nothing: you live mainly in the future because you spend most of your time looking forward to arriving at some other place. But actual arrival, when it is achieved, is meaningless.You want to move on again. By traveling like this, y ou suspend all experience; the present ceases to be a reality: you might just as well be dead. The traveler on foot, on the other hand, lives constantly in the present. For him traveling and arriving are one and the same thing: he arrives somewhere with every step he makes. He experiences the present moment with his eyes, his ears and the whole of his body. At the end of his journey he feels a delicious physical weariness. He knows that sound. Satisfying sleep will be his: the just reward of all true travellers.70. Anthropologists label nowadays’ men ‘Legless’ because _________.A. people forget how to use his legs.B. people prefer cars, buses and trains.C. lifts and escalators prevent people from walking.D. there are a lot of transportation devices.71.Why does the author say ‘we are deprived of the use of our eyes’?A. People won’t use their eyes.B. In traveling at high speeds, eyes become useless.C. People can’t see anything on his way of travel.D. People want to sleep during travelling.72. Travelling at high speed means _________.A. people’s focus on the futureB. a pleasureC. satisfying drivers’ great thrillD. a necessity of life73.What's the best title of the passage?A. More haste, less speedB. Modern means of transportation make the world a small placeC. Eyes open and mind broadenD. The only way to travel is on foot.( 以下各题请务必做在答卷纸上)Ⅰ. Grammar (8%)\One of the main points of traveling is to relax and take a break from your normal daily life. (1)__________the truth is, we’re not always free to do what we like when travelling to a foreign country, and a US tourist learned that the hard way.On Aug 12, the unnamed 41-year-old man was beaten by a passerby after he was seen giving Nazi salutes(纳粹礼) again and again on a street inDresden, Germany.Ever since the end of World WarⅡ, Germany has strict laws (2)_________(forbid) the Nazi salute, as well as other symbols of Nazism.In fact, most countries have their own taboos. If you plan to travel overseas, it’s best to get familiar with these taboos(3)______________you start touring local sites. Below, TEENS gives some examples.SingaporeYou can get (4) ________(fine) fore a lot things in Singapore, including feeding birds, spitting , urinating (小便)in public, smoking in public , not flushing a public toilet after you use it, and eating or drinking on buses or trains.JapanYou’re not supposed to wear your shoes in someone’s house, but you’re not supposed to take your shoes off (5)________the house either. Instead, there’s a small areas inside the door called a “ genkan” which is (6)__________your shoes should go. If you’re still not sure where that is , pay attention to what other people do and do the same.FranceFrench people don’t like (7)________when you talk about money. It’s OK if you say that you want to quit a job because you (8)___________(pay) little money, but you should never say the exact amount. Money is a “ dirty” topic in France.Ⅱ. Recitation (4%)In western cultures, (1)_______eye contact in conversation is necessary. As a matter of fact, a westerner might consider a lack of eye contact as a lack of interest. In Spain, Italy and Greece, where people stand close together talking to each other, eye contact is more frequent and lasts longer.In many Asian cultures, people avoid eye contact to show respect. It is done when talking with anyone in (2)__________or with anyone older.Habits like this can cause problems when people do not understand them. For example, an Asian person might close his or her eyes in (3) ___________ or look down while listening to a speaker. A Western speaker might thing the person is not interested.Eye contact is a (4) ___________ thing. A lack of eye contact may be considered impolite. But if you stare at others, it is also considered rude and should be avoided.Ⅲ. Translation (20%)1. 在炎热的夏日，将食物放在冰箱被认为是保藏食物最行之有效的方法。
【全国百强校】上海复旦大学附属中学2017-2018学年高一上学期期中考试数学试题(解析版)
2017学年复旦附中高一上期中填空题1.已知全集U=R, A={T,0,l,2}, B = {x|x2 = x},则A A =【答案】{-1,2}【解析】【分析】先求出集合B,再求出CuB,最后求出AHCuB.【详解】由题意得B={X|X2= X}=(0.1},■,- CuB = (.")u((M)u(]. + s),.•.AnCyBT-1,2}.故答案为{-1.2).【点晴】本题考査集合的运算，解题时根据集合运算的顺序进行求解即可，属于基础題.2.命题“如果a + b>0,那么a>0且b>0”的否命题是命题(填“真”或“假”)【答案】真【解析】【分析】根据原命题的逆命题和其否命题为等价命题判断命题的真假.【详解】由题意得命题"如果a+b>0,那么a>0且b>0”的逆命题为“如果a>0且b>0,那么a + b>0” 其真命题，所以否命题为真命题. 故答案为“真”.【点晴】判断命题的真假时，可通过命题直接进行判断也可通过其等价命题的真假来判断，解題时要根据条件选择合理的方法进行求解.3.已知集合A = {y|y = x2-2x-3}, B = (y|y = -x2 + 2x+13},则A AB-【答案】[-4,14]【解析】【分析】分别求出集合A.B,然后再求出AQB即可.【详解】由题意得A-{y|y = x2・2x・3}-{y|y=(x-l)2.4} = {y|yN -4},B = {y I y = . x2 + 2x + 13} = {y I y = - (x -1)2 + 14j = {y I y < 14},•・ AC1B = [.4,14].故答案为[.4,14].【点睛】本题考査集合的交集运算，解题的关键是正确求出集合AB,属于简单题.4.已知“aga +孑是“ l・2a<x<3a + 2”的充分不必要条件，则实数a的取值范围是【答案】aR3【解析】【分析】将充分不必要条件转化为集合间的包含关系求解可得结论.【详解】设A= x a<x<a + - B = {x| 1 - 2a <x <3a + 2},*a<x<a + ^是'l.2a<x〈3a + 2”的充分不必要条件,l-2a〈3a + 2l-2a <a 1•• 1 ，解得a>;,a+ —〈3a + 2 32实数a的取值范围是（? + 8）.故答案为@ + oo）.【点睛】根据充要条件求解参数范围的方法步骤⑴把充分条件、必要条件或充要条件转化为集合间的关系；（2）根据集合关系画数轴或Venn图，由图写出关于参数的不等式（组），求解.注意：求解参数的取值范围时，一定要注意区间端点值的检验，尤其是利用两个集合之间的关系求解参数的取值范围时，不等式是否能够取等号决定端点值的取舍，处理不当容易出现漏解或增解的现象.5.设M = {&b},则满足MUNG^b.c}的集合N的个数为【答案】8【解析J盼析】分别写出満足条件的集合N后可得所求集合的个数.【详解】由题意得，满足题意得集合N为0, {a}, {b},{c}, (a,c}, {b,c}, (a,b} , {a,b,c},共8个.故答案为8.【点睛】解题时要根据集合N中元素的个数为标准进行求解，考査理解能力和判断能力，属于基础題.6.函数f(x) = ((12)x2+3(1*+ 6的定义域为[-2,1 J,则a的值为【答案】2【解析】【分析】由题意得不等式(l-a2)x2+ 3(l.a)x + 6>0的解集为[-2,1],然后根据“三个二次”间的关系求解即可得到结论.【详解】.•函数f(x) = J(1 - a* + 3(1 - a)x + 6的定义域为[-2,1],••不等式(1“浓2 + 3(1.必+ 6?0的解集为[-2,1],.. x = - 2,x = I是方程(]. a2)x2 + 3(1 - a)x + 6 = 0的两个根,.4(l-a2)-6(l-a) + 6 = 0(l-a2) + 3(l-a) + 6 = 0，整理得！矿了#「解得a = 2 .Ia~ + 3a-10 = 0故答案为2.【点睛】本题以函数的定义域为载体，考査一元二次方程、二次函数、二次不等式间的关系，解题的关蚀是根据题意得到方程的两根，然后再根据方程的有关概念求出a的俏，考査转化能力和运算能力，属于基础题.7.已知函数f(x)=(m-l)x + 2m-3,无论m取什么实数，函数f(x)的图像始终过一个定点，该定点的坐标为【答案】(-2,-1)【解析】【分析】将函数解析式变形为(x + 2)m・x.y.3 = O,然后令x + 2 =0旦・x . y . 3 = 0,求得方程组的解后即可定点的坐标.【详解】由y・(m・l)x+2m-3变形得(x+2)m - x-y- 3-0,解方程组&篇％得疝彳，所以函数f(x)的图象过的定点的坐标为(-2,-1).故答案为(-2,-1).【点睛】本题考査一次函数的图象过定点的问题，解题时可把函数解析式化为kf(x.y) + g(%y) = 0 (k为参数)的形式，则以方程组｛；修与号的解为坐标的点即为定点.8.已知关于x的方程x2 + kx + k2 + k-4 = 0有两个实数根，且一根大于1, 一根小于1,则实数k的取值范围为【答案】(-3.1)【解析】【分析】根据一元二次方程根的分布求解，令f(x)=x2 + kx + k2+k-4,则有解不等式可得所求范围【详解】令f(x)=x2+kx + k2 + k-4,方程的一个实数根大于1,另一个实数根小于1,1 + k+k2 + k-4<0.即k2+2k-3<0>解得-3<k<l,实数g取值范围为(-3,1).故答案为(-3,1).【点晴】本题考査根据方程根的情况求参数的取值范围，解题时根据方程根的分布将问题转化为不等式求解，体现了转化和数形结合的思想方法在解题中的应用.9-给出下列四个命题：(1)若a > b,c a d,则a-d > b-c;(2)若a2x>a2y .则x>y;(3)a>b,则二a-b a(4)若以<0,则abvb，.a b其中正确命题的是.(填所冇正确命题的序号)【答案J (1) (2) (4)【解析】试题分析：(3)中a = 0时不等式不成立，故正确的只有(1) (2) (4).考点：不等式的基本性质10.若xe(-oo,2),则5—4X + X 的最小值为2-x【答案】2【解析】【分析】将原式变形后根据基本不等式求解.【详解】..•x<2, •••2-x>0.当且仅当2-x = d-，即x = l 时等号成立. 2-x••5~4X + X2的最小值为2. 2-x故答案为2.【点睛】应用基本不等式求最值时一定要注意“一正二定三相等.这三个条件缺一不可，当不满足不等式使用的条件时，可通过适当的变形使得出现定值的形式，这是解题中常遇到的情形. 11.设函数f(x)=x-2,若不等式|Rx+3)1 > |f(x)|十m 对任意实数x 恒成立，则m 的取值范围是【答案】mv-3 【解析】【分析】 |x+l|-|x-2|表示数轴上的x 对应点到-1对应点的距离减去它到2对应点的距离，其最小值为-3,故有m<-3, 由此求得m 的取值范围.【详解】I f(x) = x - 2,不等式|f(x + 3)|> |f(x)| + m 对任意实数x 恒成立，二n 】Y|xi 1| -|x-2对任意实数X 恒成立，乂 |x+l|・X ・2|表示数轴上的x 对应点到・1对应点的距离减去它到2对应点的距离，.・.|x+l|・|x ・2|N ・3,二 m v • 3二实数m 的取值范围是(・皿・3).故答案为(・s ，・3).【点睛】本题考査恒成立问题，解题的关键是根据绝对值的儿何意义求出|x +l|-|x-2|的最小值，考査转化和数形结合思想的运用能力. 12.对于实数A 和正数B,称满足不等式|x-A|<B (AGR,B>0)9!I 实数x 的集合叫做A 的B 邻域，已知t 为给定的 正数，a 、b 为正数，若a +由题意得2—x 5—4x + x~ (2-x)~+ 1 —=^=(2-x)+ 2,b-t的a + b领域是一个关于原点对称的区间，则a2 + b2的最小值为【答案】L2【解析】【分析】先根据条件求出-t<x<2(a+b)-t;再结合邻域是一个关于原点对称的区间得到 a + b = t ,最后结合不等式的知识可求出a2+ b2的最小值.【详解】.. A的B邻域在数轴上表示以A为中心，B为半径的区域，|x - (a + b -1)| < a + b,二- a- bvx-(a + b-t)va + b,解得-t<x<2(a + b)-t.邻域是一个关于原点对称的区间，二2(a + b) - 2t = 0,二a + b = t., a2 + b* > 2ab,.•・ 2(a2 + b2) > a2 + b2 + 2ab = (a+ b)2 = t2,•,•a2+ b2>-,当且仅当a = b时等号成立，2二a2 + b2M最小值为2故答案为2【点睛】本题以新概念为载体考査重要不等式的应用，考査变换能力和阅读理解能力.解题的美綻足根据题意得到a + b-t这-结论，然后再通过变形得到所求的最小值.二.选择題侣.设实数勺、全、b卜3不为0,则了禹成如是“关于满不等式"心。
上海市复旦附中高一上期中精编版
2017学年复旦附中高一上期中2017.11一. 填空题1. 已知全集U =R ，{1,0,1,2}A =-，2{|}B x x x ==，则U A C B =2. 命题 “如果0a b +>，那么0a >且0b >”的否命题是 命题（填“真”或“假”）3. 已知集合2{|23}A y y x x ==--，2{|213}B y y x x ==-++，则AB = 4. 已知“12a x a ≤≤+”是“1232a x a -<<+”的充分不必要条件，则实数a 的取值范 围是5. 设{,}M a b =，则满足{,,}M N a b c ⊆的集合N 的个数为6.函数()f x 的定义域为[2,1]-，则a 的值为7. 已知函数()(1)23f x m x m =-+-，无论m 取什么实数，函数()f x 的图像始终过一个定点，该定点的坐标为8. 已知关于x 的方程2240x kx k k +++-=有两个实数根，且一根大于1，一根小于1，则实数k 的取值范围为9. 给出下列四个命题：① 若a b >，c d >，则a d b c ->-；② 若22a x a y >，则x y >；③ 若a b >，则11a b a >-；④ 若110a b<<，则2ab b <. 其中正确命题是 （填所有正确命题的序号）10. 若(,2)x ∈-∞，则2542x x x-+-的最小值为 11. 设函数()2f x x =-，若不等式|(3)||()|f x f x m +>+对任意实数x 恒成立，则m 的取值范围是12. 对于实数A 和正数B ，称满足不等式||x A B -<(,0)A B ∈>R 的实数x 的集合叫做A 的B 领域，已知t 为给定的正数，a 、b 为正数，若a b t +-的a b +领域是一个关于原点对称的区间，则22a b +的最小值为二. 选择题13. 设实数1a 、2a 、1b 、2b 均不为0，则“1122a b a b =成立”是“关于x 的不等式110a x b +> 与220a x b +>的解集相同”的（ ）条件A. 充分不必要B. 必要不充分C. 充要D. 既不充分也不必要14. 解析式为221y x =+，值域为{5,19}的函数有（ ）个A. 4B. 6C. 8D. 915. 设()f x 是定义在正整数集上的函数，且()f x 满足：“当2()f x x >成立时，总可以推出2(1)(1)f x x +>+成立”，给出以下四个命题：① 若(3)9f ≥，则(4)16f ≥； ② 若(3)10f =，则(5)25f >；③ 若(5)25f =，则(4)16f ≤； ④ 若2()(1)f x x ≥+，则2(1)f x x +≥.其中真命题的个数为（ ）个A. 1B. 2C. 3D. 416. 设a 、b 、c 为实数，2()()()f x x a x bx c =+++，2()(1)(1)g x ax cx bx =+++，记集合{|()0,}S x f x x ==∈R ，{|()0,}T x g x x ==∈R ，若||S 、||T 分别为集合S 、T 的元素个数，则下列结论不可能是（ ）A. ||1S =且||0T =B. ||1S =且||1T =C. ||2S =且||2T =D. ||2S =且||3T =三. 解答题17. 已知集合2{|(1)320}A x m x x =-+-=，是否存在这样的实数m ，使得集合A 有且仅有两个子集？若存在，求出所有的m 的值组成的集合M ；若不存在，请说明理由.18. 我校第二教学楼在建造过程中，需建一座长方体形的净水处理池，该长方体的底面积为200平方米，池的深度为5米，如图，该处理池由左右两部分组成，中间是一条间隔的墙壁，池的外围周壁建造单价为400元/平方米，中间的墙壁（不需考虑该墙壁的左右两面）建造单价为100元/平方米，池底建造单价为60元/平方米，池壁厚度忽略不计，问净水池的长AB 为多少时，可使总造价最低？最低价为多少？19. 已知a ∈R ，集合26{|0}1x x A x x --=≤+，集合{||2|1}B x x a a =+≤+. （1）求集合A 与集合B ；（2）若AB B =，求实数a 的取值范围.20. 已知函数2|1|()4x m f x x +-=-，0m >，满足(2)2f =-. （1）求实数m 的值；（2）在平面直角坐标系中，作出函数()f x 的图像，并且根据图像判断：若关于x 的方程()f x k =有两个不同实数解，求实数k 的取值范围（直接写结论）21. 已知M 是满足下列性质的所有函数()f x 组成的集合：对任何12,f x x D ∈（其中f D 为函数()f x 的定义域），均有1212|()()|||f x f x x x -≤-成立.（1）已知函数2()1f x x =+，11[,]22x ∈-，判断()f x 与集合M 的关系，并说明理由；（2）是否存在实数a ，使得()2a p x x =+，[1,)x ∈-+∞属于集合M ？若存在，求a 的取值 范围，若不存在，请说明理由；（3）对于实数a 、b ()a b <，用[,]a b M 表示集合M 中定义域为区间[,]a b 的函数的集合.定义：已知()h x 是定义在[,]p q 上的函数，如果存在常数0T >，对区间[,]p q 的任意划分：011n n p x x x x q -=<<⋅⋅⋅<<=，和式11|()()|ni i i h x h x T -=-≤∑恒成立，则称()h x 为[,]p q 上的“绝对差有界函数”，其中常数T 称为()h x 的“绝对差上界”，T 的最小值称为()h x 的“绝对差上确界”，符号121n i n i tt t t ==++⋅⋅⋅+∑；求证：集合[1009,1008]M -中的函数()h x 是“绝对差有界函数”，并求()h x 的“绝对差上确界”.参考答案一. 填空题1. {1,2}-2. 真3. [4,14]-4. 13a > 5. 8 6. 2 7. (2,1)- 8. (3,1)- 9. ①②④ 10. 2 11. 3m <- 12. 22t二. 选择题13. B 14. D 15. C 16. D三. 解答题 17. 1{1,}8M =.18. 15AB =时，总造价最低为132000元. 19.（1）(,2](1,3]A =-∞--，当1a >-，[31,1]B a a =---+，当1a =-，{2}B =，当1a <-，B =∅；（2）(,0)[3,)-∞+∞.20.（1）1m =；（2）(2,0)-.21.（1）()f x 属于集合M ；（2）[1,1]-；（3）略.。
2017-2018复旦附中高一第一学期化学期中(答案版)
【试卷分析】1、考点分布：复旦大学附属中学2017 学年第一学期高一年级化学期中考试试卷原子结构：1、2、3、8、24、25物质的量及物质的量浓度：17、21、31、33气体摩尔体积：4、5、6、15、18、26、27、28、34氯气及氯化氢（含粗盐提纯）：9、12、13、14、16、20、22、30、32离子反应方程式：7氧还：10、11、19、23、29集中考察氯气和氯化氢，包括氯气基础性质、氯碱工业、氯化氢的制备和喷泉实验，其中氯气和碱的反应考察较多（选择题22、实验题32），选择的考察较基础，填空题个别小题结合氧还对学生要求较高，实验题32 题将氯气的实验室制备和氯气与碱的反应结合考察，较综合；气体摩尔体积部分比重仅次于氯气，考察学生计算能力以及十字交叉法等计算方法；氧还部分考察四类物质和简单计算，整体不难。
2、本试卷的难点及易错点：第18 题气体摩尔体积结合物质的量计算，较综合第21 题涉及字母的物质的量浓度计算，学生易错第22 题考察守恒思想第32 题实验探究题，考察学生信息读取和运用能力，对学生要求较高1 复旦大学附属中学 2017 学年第一学期高一年级化学期中考试试卷（总分 100 分，时间 60 分钟）一、选择题（每题只有一个正确答案，共 36 分）1. 1993 年 8 月，我国科学家利用超高真空扫描隧道显微镜，在一块晶体硅的表面通过探针的作用搬走原子，写下了“中国”两个字。
下列说法中，错误的是A. 上述操作中发生了化学变化B. 这两个汉字是目前世界上最小的汉字C. 上述操作中只发生了物理变化D. 这标志着我国科学家已进入操作原子的阶段 【答案】 A2. 下列说法中正确的是A. 人们已知道了 107 种元素，即已经知道了 107 种原子B. 互为同位素的原子，它们原子核内的中子数一定不相等C. 40K 和 40Ca 原子中的中子数相等D. 质子数相同的微粒，核外电子数一定相同，但化学性质不一定相同 【答案】B3. 化学科学需要借助化学专用语言描述，下列有关化学用语正确的是A. 硫离子的电子式：S 2-B. Cl 原子结构示意图：C. 质量数为 3 的超重氢原子： 3 HD. 次氯酸钙的化学式：CaClO 【答案】C4. 下列物质中质量最大的是A. 1mol 硫酸B. 22.4L （S.T.P ）水C. 44.8L(S.T.P)O 2D. 12.04×10 23 个 NH 3 分子【答案】 B5.下列示意图中，白球代表氢原子，黑球代表氦原子，方框代表容器，容器中间有一个可以上下滑动的隔板（其质量忽略不记）。
2017-2018学年上海市上海中学高一上学期期中考试英语试题
2017-2018学年上海市上海中学高一上学期期中考试英语试题20171109高三_____班学号_________ 姓名____________ 成绩_________________第I卷(110分)I.I. Listening ComprehensionPart A Short ConversationsDirections: In Part 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 question you have heard.1. A. Angry. B. Tired. C. Hungry.D. Disappointed.2. A. She did a survey a week ago. B. She completed her survey quickly.C. She will help him on Thursday.D. She thinks she can reduce the cost.3. A. In a grocery. B. In a warehouse.C. In a shopping mall.D. In a fashion designer's studio.4. A. He wrote it last semester. B. He'll finish it ina few minutes.C. He never does assignments early.D. He isn't going towrite it.5. A. Boss and secretary. B. Coach and athlete.C. Doctor and patient.D. Teacher and student.6. A. 10:00. B. 10:10. C. 10:20.D. 10:30.7. A. The electrician came to repair the lamp. B. The lamp was taken to the repairshop.C. She had Mike fix the lamp.D. The lamp was replaced.8. A. Studying. B. Watching television.C. Coming upstairs.D. Going to the movies.9. A. She had gone to photography class instead.B. She has not chosen a picture for it.C. She had broken her camera.D. She was unable to have her picture taken.10. A. Dick is practically the only one who thinks so.B. Most people play football differently.C. Few people are optimistic about the team's chances of winning.D. Dick is disappointed in football games.Part B PassagesDirections: In Section B, you will hear one short passage and two longer conversations. After each passage or conversation, you will be asked several questions. The passage and the conversations will be read twice, but the questionswill be spoken only once. When you hear a question, read the four possible answerson your paper and decide which one would be the best answer to the question you haveheard.Questions 11 through 13 are based on the following passage.11. A. When directions are long. B. When directions are short.C. When homework is given.D. When your mother talks.12. A. Your pen and paper. B. A few words.C. Your mind and ears.D. Some pictures.13. A Topics or page numbers. B. Key words or a picture in mind.C. Some details.D. School assignments.Questions 14 through 16 are based on the following passage.14. A. The teenagers' strange behaviour.B. The teenagers' criticism of their parents.C. The dominance of the parents over their children.D. Misunderstanding between teenagers and their parents. .15. A. Because they want to make their parents angry.B. Because they have no other way to enjoy themselves.C. Because they have a strong desire to be leaders in style and taste.D. Because they want to show their existence by creating a culture of their own.16. A. They should be obedient. B. They should be responsible. .C. They should be cooperative.D. They should be independent. Questions 17 through 20 are based on the following conversation.17．A. He hadn’t found the job.B. He found a job as a teacher.C. He was preparing for final exams.D. he found a job as a writer.18. A. Writers. B. Interviewers.C. Newspaper reporters.D. Teachers.19. A. New York. B. Boston.C. California.D. Los Angeles.20. A. Continue his education. B. Start a newspaper.C. Write a book.D. Continue to find jobs.II. Grammar and VocabularySection ADirections: Beneath each of the following sentences there are four choices marked A, B, C and D. Choose the one answer that best completes the sentence.21.Understanding the cultural habits of another nation, especially _______ containing as many different subcultures as the United States, is a complex task.A. oneB. the oneC. thatD. those22. Because he could not find the right theme ______, his explanation was vague and unconvincing.A. which to center his thought aroundB. around which his thoughts to centerC. on which to center his thoughtsD. which he centers his thoughts on23.A: The research on the new virus vaccine is challenging and demanding. Who do you think can do the job?B: ______ my students have a try?A. ShallB. MustC. WillD. May24.I will be surprised if you can get Calvin, who is a close-fisted man, ______ these donation draw tickets from you.A. buyB. buyingC. buysD. to buy25. The man got up and shouted that he was the equal ______ any boxer at the Fair.A. atB. toC. withD. of26. The architects of the temples of ancient Rome and Greece worked anonymously (匿名地), ________the builders of the medieval cathedrals in Europe.A. as didB. as haveC. as ifD. as27.The Qingming Festival, now a national holiday, allows more people to pay their respects to dead relatives on ______ would otherwise be a workday like Friday.A. whereB. thatC. whenD. what28. In the United States and some other countries, it is the driver’s responsibility to make sure that children under fourteen do not ride in the front seat ______ they are wearing a seat belt of some kind.A. whileB. evenC. untilD. unless29.______ the U.S. has been busy consuming, Asia, China in particular, has been investing in factories and technologies, so it can produce even more goods and services to sell abroad.A. AsB. Even ifC. WhileD. Whether30.The text and dialogues below focus on cultural differences between Chinese and Western societies which can create misunderstanding if ______.A. ignoreB. to be ignoredC. ignoringD. ignored Directions: 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.From classics to moviesHe can recite Shakespeare’s Hamlet from memory. His favorite ancient myth is The Odyssey. Tom Hiddleston, 32, could have been a popular professor teaching English Literature at a university, but the well-educated British man chose (31) __________(do) something that he loved even more: acting.He’s well-known around the world as the villain Loki from the Hollywood films Thor (2011), The Avengers (2012) and now Thor: The Dark World, which will come out in China on Nov 8. Hiddleston’s role as Thor’s evil brother has led to his fans —“Hiddlestoners”— (32) __________ (refer) to him as “the most charming villain”in cinema.(33) __________ his charm, Hiddleston had a tough time (34) __________ (persuade) his scientist father that acting was a worthwhile job. As a student at Eton, a private school for upper-class kids in England, Hiddleston performed in a lot of school plays. At 18, he appeared on stage at the Edinburgh International Festival. “It was the first time that people I knew and loved and respected had come up to me after the show and said: ‘You could really do this (35) __________ you wanted to’,” Hiddleston told the Daily Mail.He said that as a teenager he didn’t have much self-esteem, but acting gave him confidence. “It was when they started saying I could do it (36) __________ I really committed to it as a possibility,” he continued. However, his father did not approve, believing his polite and bright son should be using his brains for (37) __________ else. “You’ve been educated, so why do you want to spend your life pretending to be someone else when you could be your own man?” the father told the son.So, instead of going to drama school, Hiddleston went to Cambridge, (38)__________ he studied classics. There, he continued to appear in student plays and even landed some roles on TV and in local theaters. He managed to balance his acting and his studies so well that he graduated with (39) __________ first-class degree.But Hiddleston’s international breakthrough came when he auditioned for the 2011 film Thor. He was desperate to play the title superhero, but the director decided that he was (40) __________ (suitable) for the part of the villain, Loki.In the end, his dark and powerful performance won over his father. It also earned him some important fans in the film industry: Steven Spielberg and Woody Allen. The two world-famous directors asked him to star in their award-winning films War Horse (2011) and Midnight in Paris (2011), respectively.Section BDirections: Complete the following passage by using the word in the box. Each word can only be used once. Note that there is one word more than you need.What is it about Americans and food? We love to eat, but we feel ____41______ about it afterward. We say we want only the best, but we strangely enjoy junk food. We’re obsessed with health and weight loss but face an unprecedented epidemic of obesity(肥胖). Perhaps the ____42______ to this ambivalence(矛盾情结) lies in our history. The first Europeans came to this continent searching for new spices but went in vain. The first cash crop(经济作物) wasn’t eaten but smoked. Then there was Prohibition, _____43_____ to prohibit drinking but actually encouraging more ____44______ ways of doing it.The immigrant experience, too, has been one of inharmony. Do as Romans do means eating what “real Americans” eat, but our nation’s food has come to be _____45_____ by imports — pizza, say, or hot dogs. And some of the country’s most treasured cooking comes from people who arrived here in shackles.Perhaps it should come as no surprise then that food has been a medium for thenation’s defining struggles, whether at the Boston Tea Party or the sit-ins at southern lunch counters. It is integral to our concepts of health and even morality whether one refrains from alcohol for religious reasons or evades meat as a political ____46______.But strong opinions have not brought ____47______. Americans are ambivalent （矛盾的） about what they put in their mouths. We have become ____48______ of our foods, especially as we learn more about what they contain.The ____49______ in food is still prosperous in the American consciousness. It’s no coincidence, then, that the first Thanksgiving holds the American imagination in such bondage(束缚). It’s what we eat — and how we _____50_____ it with friends, family, and strangers — that help define America as a community today.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.Now elsewhere in the world, Iceland may be spoken of, somewhat breathlessly, as western Europe's last pristine wilderness. But the truth is, once you're off the 51 track of the low-lying coastal areas where everyone lives, the roads are few, and they're all bad, 52 Iceland's natural wonders have been out of reach and unknown even to its own 53 . For them the land has always just been there, something that had to be dealt with and, if possible, 54 —the mind-set being one of land as commodity rather than land as, well, priceless art on the scale of the " Mona Lisa".When the opportunity arose in 2003 for the national power company to enter into a 40-year 55 with the American aluminum company Alcoa to supply hydroelectric power for a new smelter （冶炼厂）, those who had been dreaming of something like this for decades 56 the opportunity. For a long time, life here had meant little more than a hut, dark all winter, cold, no hope, children dying left and right, plagues, starvation, volcanoes erupting and destroying all vegetation and livestock,all spirit— a world 57 almost entirely around the welfare of one's sheep and, later, on how good the cod catch was. In the outlying regions, it still largely does. Ostensibly, the Alcoa project was intended to save one of these dying regions — the remote and sparsely populated east— where the way of life had steadily 58 to a point of desperation and gloom. After fishing quotas (定额) were 59 in the early 1980s to protect fish stocks, many individual boat owners sold their allotments or gave them away, fishing rights ended up mostly in the hands of a few companies and small fishermen were virtually 60 . Technological advances drained away even more jobs previously done by human hands, and the people were seeing everything they had worked for all their lives turn out to be 61 and their children move away. With the old way of life doomed, aluminum projects like this one had come to be perceived, wisely or not, as a last chance. "Smelter or death."The contract with Alcoa would infuse the region with foreign 62 , an estimated 400 jobs, and spin-off service industries. It also was a way for Iceland to develop expertise that 63 could be sold to the rest of the world and 64 an economy historically dependent on fish. “We have to live,” Halldor Asgrimsson said. Halldor, a former prime minister and longtime member of parliament from the region, was a driving 65 behind the project. “We have a right to live.”51. A. beaten B. explored C. expired D. centered52. A. so B. when C. if D. as53. A. government B. inhabitants C. countryside D. scale54. A. designed B. retained C. exploited D.preserved55. A. stage B. contract C. transition D. prosperity56. A. gave up B. jumped at C. rushed to D. made up57. A. revolving B. developing C. Stirring D. Initiating58. A. transferred B. declined C. grew D. reformed59. A. preferred B. presented C. resisted D. imposed60. A. wiped out B. held up C. kept down D. put aside61. A. priceless B. superficial C. worthless D. negative62. A. investment B. Exclusion C. invasion D. landscape63. A. socially B. immediately C. accidentally D. potentially64. A. stabilize B. wreck C. diversifyD. consolidate65. A. force B. wheel C. instructor D. signalSection 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 )If you intend to use humor in your talk to make people smile, you must know how to identify shared experiences and problems. Your humor must be relevant to the audience and should help to show them that you are one of them or that you understand their situation and are in sympathy with their point of view. Depending on whom you are addressing, the problems will be different. If you are talking to a group of managers, you may refer to the disorganized methods of their secretaries; alternatively if you are addressing secretaries, you may want to comment on their disorganized bosses.Here is an example, which I heard at a nurses' convention, of a story which workswell because the audience all shared the same view of doctors. A man arrives in heaven and is being shown around by St. Peter. He sees wonderful accommodations, beautiful gardens, sunny weather, and so on. Everyone is very peaceful, polite and friendly until, waiting in a line for lunch, the new arrival is suddenly pushed aside by a man in a white coat, who rushes to the head of the line, grabs his food and stomps over to a table by himself. “Who is that?” the new arrival asked St. Peter. “Oh, that's God,” came the reply, “but sometimes he thinks he's a doctor.”If you are part of the group which you are addressing, you will be in a position to know the experiences and problems which are common to all of you and it'll be appropriate for you to make a passing remark about the inedible canteen food or the chairman's notorious bad taste in ties. With other audiences you mustn't attempt to cut in with humor as they will resent an outsider making disparaging remarks about their canteen or their chairman. You will be on safer ground if you stick to scapegoats like the Post Office or the telephone system.If you feel awkward being humorous, you must practice so that it becomes more natural, include a few casual and apparently off-the-cuff remarks which you can deliver in a relaxed and unforced manner. Often it's the delivery which causes the audience to smile, so speak slowly and remember that a raised eyebrow or an unbelieving look may help to show that you are making a light-hearted remark.Look for the humor. It often comes from the unexpected. A twist on a familiar quote “If at first you don't succeed, give up” or a play on words or on a situation. Search for exaggeration and understatements. Look at your talk and pick out a few words or sentences which you can turn about and inject with humor.66. To make your humor work, you should_________.A. take advantage of different kinds of audienceB. make fun of the disorganized peopleC. address different problems to different peopleD. show sympathy for your listeners67. The joke about doctors implies that, in the eyes of nurses, they are________.A. impolite to new arrivalsB. very conscious of their godlike roleC. entitled to no privilegesD. very busy even during lunch hours68. It can be inferred from the text that public services______.A. have benefited many peopleB. are the focus of public attentionC. are an inappropriate subject for humorD. have often been the laughing stock( B )Of all the changes that have taken place in English-language newspapers during the past quarter-century, perhaps the most far-reaching has been the inexorable decline in the scope and seriousness of their arts coverage.It is difficult to the point of impossibility for the average reader under the age of forty to imagine a time when high-quality arts criticism could be found in most big-city newspapers. Yet a considerable number of the most significant collections of criticism published in the 20th century consisted in large part of newspaper reviews. To read such books today is to marvel at the fact that their learned contents were once deemed suitable for publication in general-circulation dailies.We are even farther removed from the unfocused newspaper reviews published in England between the turn of the 20th century and the eve of World War II, at a time when newsprint was dirt-cheap and stylish arts criticism was considered an ornament to the publications in which it appeared. In those far-off days, it was taken for granted that the critics of major papers would write in detail and at length about the events they covered. Theirs was a serious business, and even those reviews who wore (展示) their learning lightly, like George Bernard Shaw and Ernest Newman, could be trusted to know what they were about. These men believed in journalism as a calling （使命）, and were proud to be published in the daily press. 'So few authors have brains enough or literary gift enough to keep their own end up in journalism,' Newmanwrote “that I am tempted to define” journalism “as a term of contempt（轻蔑）applied by writers who are not read to writers who are”.Unfortunately, these critics are virtually forgotten. Neville Cardus, who wrote for the Manchester Guardian from 1917 until shortly before his death in 1975, is now known solely as a writer of essays on the game of cricket. During his lifetime, though, he was also one of England's foremost classical-music critics, and a stylist so widely admired that his Autobiography (1947) became a best-seller. He was knighted in 1967, the first music critic to be so honored. Yet only one of his books is now in print, and his vast body of writings on music is unknown save to specialists.Is there any chance that Cardus's criticism will enjoy a revival? The prospect seems remote. Journalistic tastes had changed long before his death, and postmodern readers have little use for the richly polished Vicwardian（维多利亚和爱德华时代）prose in which he specialized. Moreover, the amateur tradition in music criticism has been in headlong retreat.69. It is indicated in Paragraphs 1 and 2 thatA. arts criticism has disappeared from big-city newspapers.B. English-language newspapers used to carry more arts reviews.C. high-quality newspapers retain a large body of readers.D. young readers doubt the suitability of criticism on dailies.70. Newspaper reviews in England before World War 2 were characterized by ___________.A. free themes.B. casual style.C. elaborate layout.D.radical viewpoints71. Which of the following would Shaw and Newman most probably agree on?A. It is writers' duty to fulfill journalistic goals.B. It is contemptible for writers to be journalists.C. Writers are likely to be tempted into journalism.D. Not all writers are capable of journalistic writing.72. What can be learned about Cardus according to the last two paragraphs?A. His music criticism may not appeal to readers today.B. His reputation as a music critic has long been in dispute.C. His style caters largely to modern specialists.D. His writings fail to follow the amateur tradition.( C )The most prevalent use of intelligence test scores is to predict degree of academic success. Such scores are used in some communities as bases for admitting able children to schools at ages younger than normal, and they are very generally used to determine admissions to schools beyond public secondary school. Another use common in elementary schools involves comparing such scores with performances in various subjects to identify children who are working below capacity.The greatest problem in using intelligence tests for the purpose of prediction is that no dependable criterion(标准) of their accuracy exists. The ideal criteria would be objective and reliable achievement tests following instruction in each subject, but there are few such tests, especially at the college level. Studies have shown that correlations(相关度) between intelligence tests and achievement tests in various subjects through secondary school range roughly from 0.5 to 0.8. Such correlations are fairly high, but they do not suggest anywhere near complete agreement.At the college level there are two major tests used as criteria of admission. By far the more important is the College Entrance Examination, constructed by the Educational Testing Service authorized by the College Entrance Examination Board. These tests are returned to the Educational Testing Service for scoring, and the results are then made available to the various colleges authorized by the students to receive them. The second test of this type is the American College Test, which operates in essentially the same fashion.Both tests constitute measures of certain skills, abilities, and knowledge that have been found to be related to success in college. Their correlations with academic success are limited for three outstanding reasons. First, measures of achievement in college are themselves perhaps no more reliable than those in elementary and secondary schools. Second, intellectual factors do not alone determine academicsuccess, especially at the college level. Many students drop out of schools because they are inadequately motivated or because they dislike the instructional program. Third, correlations are lowered because the use of such tests for denying admission to some students means that the range of scores for those admitted is restricted, and such restrictions tend to reduce correlation.73. The intelligence scores can be used in the following way EXCEPT ______.A. telling in advance the degree of academic successB．admitting intelligent children to school at the age younger than ordinary C．finding out children working below capacity in primary schoolsD．selecting pupils by public secondary schools74.What can be inferred from the second paragraph?A. The standards for the evaluation of college students’ academic achievements need to be improved.B. The correlations between intelligence and achievement tests in middle schools are not as high as predicted.C. Intelligence test scores can help predict accurately the degree of students’academic success.D. The high correlations can prove that the results of academic tests exactly agree with intelligence test scores.75.What can we learn about the two major tests for college admission?A. The papers of the College Entrance Examination are set by the College Entrance Examination Board.B. The American College Test is of the same importance as the College Entrance Examination.C. The results of the two examinations will be sent to colleges with the students’permission.D. The College Entrance Examination is as fashionable as the American College Test.76.Which of the following does not account for the reduction of the correlation between the two admission tests and the academic success in college?A. Measures of students’ achievements in collegeB. Students’ motivations for and interest in their studyC. Some students’ being refused the admission to the collegeD. The popular use of the intelligence testSection 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 sentence than you need.Most people look forward to retirement as a time when they can finally take up activities that they never had the time or energy to pursue before. ___77____. They suggest that retirees are more likely to suffer from depression and possibly higher rates of other diseases such as heart disease and high blood pressure. That’s why a new study of French workers is welcome news.Led by Hugo Westerlund, a professor of psychology at Stockholm University, the study of more than 14,000 workers found lower rates of depression and fatigue in people after they got retired than while they were still employed. ___78____. They found in the year immediately after retirement, the volunteers reported 40% fewer depressive symptoms than they had in the year before their retirement. The researchers also found an 81% drop in reports of both mental and physical fatigueover the same time period.___79___. The decline in depressive symptoms suggests that retirement may be having a positive mental effect, too, which may have a lot to do with the generous pensions that French workers enjoy. Most retirees in that country still benefit from about 80% of their yearly salaries.“The economic or financial situation in retirement is very important,”Westerlund says. “We don’t know if the decrease in fatigue and depressive symptoms is because of the removal of something bad while in work or the addition of something good while in retirement. But no matter the reason, if life in retirement is not comfortable, then we won’t see the improvements we did.”_____80_____ With less of a financial safety net, workers may no longer seem so mentally and physically happy to be out of work.IV．Summary Writing (10%)Directions:Read the following passage. Summarize the main point(s) of the passage in no more than 60 words. Use your own words as far as possible.It is a common sight on campus or in the streets: a young person rides by on an electric scooter, traveling quickly and proudly. But Beijing’s traffic authorities have said that starting on Sept.5, people who are caught riding electric scooters on public roads or bicycle lanes will be fined 10 yuan. They will also be given a warning not to use the vehicles on public roads again.The announcement was made after traffic police in Shanghai started a campaign to get electric scooters off public roads, with police officers stopping riders because the scooters could cause traffic problems.The Beijing Consumer Association said it had tested more than 20 electric scooters of different brands recently and found that most had substandard brakes. It added that 16 of the tested scooters could go faster than the maximum 20 km per hour set for electric bikes. According to the traffic police, people who ride electric scooters at certain speeds can easily bump into the vehicles in the vehicle lane and hurt people who walk in the bicycle lanes.But seeing the benefits that electric scooters have brought to young people,。
2017-2018学年上海复旦大学附属中学高一上学期期中考试数学试题(解析版)
2017-2018学年上海复旦大学附属中学高一上学期期中考试数学试题一、单选题1．设实数、、、均不为0，则“成立”是“关于的不等式与的解集相同”的（）条件A．充分不必要B．必要不充分C．充要D．既不充分也不必要【答案】B【解析】根据充分条件和必要条件的定义结合不等式的性质进行判断即可．【详解】（1）若，则，所以不等式即为，若，则可化为，所以两个不等式的解集相同，若，则可化为，此时两个不等式的解集不相同，所以充分性不成立．（2）若关于x的不等式与的解集相同，则，由于、、、均不为0，①若，则不等式的解为，由两不等式的解集相同可得，可得，即必要性成立．②若，同理可得，即必要性成立．综上可得“成立”是“关于的不等式与的解集相同”的的必要不充分条件．故选B．【点睛】解答本题的关键有两个：一个是准确把握充分必要条件的判断方法，解题时要结合定义求解；二是注意分类讨论思想方法在解题中的应用．本题具有综合性，考查分析问题和解决问题的能力．2．解析式为，值域为的函数有（）A．4 B．6 C．8 D．9【答案】D【解析】根据的值求出相应的的值，再根据函数的有关概念得到定义域的不同形式，进而可得结论．【详解】由，解得；由，解得．所以函数的定义域可为，共9种情况．故选D．【点睛】本题考查函数的概念，考查分析理解问题的能力，解题的关键是深刻理解函数的概念，根据对应关系求出x的取值，然后再根据定义域中元素的个数确定出函数定义域的不同情形．3．设是定义在正整数集上的函数，且满足：“当成立时，总可以推出成立”，给出以下四个命题：① 若，则；② 若，则；③ 若，则；④ 若，则.其中真命题的个数为（）个A．1 B．2 C．3 D．4【答案】C【解析】根据题意对给出的四个命题分别进行分析、排除后可得正确的结论．【详解】对于①，由于f(3)=9时，可以使得f(4)<16，这并不与题设矛盾，所以当f(3)≥9时，由题设不一定得到f(4)≥16成立，所以①为假命题．对于②，∵f(3)=10>9，∴f(4)>4²，∴f(5)>5²=25，所以②为真命题；对于③，若f(4)>16，则f(5)>25，这与f(5)=25矛盾，所以f(4)≤16，所以③为真命题；对于④，∵f(x)≥(x+1)²>x²，∴f(x+1)>(x+1)²>x²，即有f(x+1)≥x²，所以④为真命题．综上可得②③④为真命题．故选C．【点睛】本题考查推理论证能力，解题的关键是根据条件“当成立时，总可以推出成立”进行判断，注意解题方法的选择，如直接推理、利用反证法判断等．4．设、、为实数，，，记集合，，若、分别为集合、的元素个数，则下列结论不可能是（）A．且B．且C．且D．且【答案】D【解析】分和两种情况对方程根的个数进行进行分析后可得正确的结论，进而得到不可能的结论．【详解】①若，,，当时，；当时，；当时，．②若，,，则当时，；当时，；当时，．所以只有D不可能．故选D．【点睛】解答本题的关键是由方程根的情况得到、取值的所有可能，然后再根据选项进行判断，考查分析问题和分类讨论在解题中的应用，具有一定的综合性和难度．二、填空题5．已知全集，，，则__________【答案】【解析】先求出集合，再求出，最后求出．【详解】由题意得，∴，∴．故答案为．【点睛】本题考查集合的运算，解题时根据集合运算的顺序进行求解即可，属于基础题．6．命题“如果，那么且”的否命题是__________命题（填“真”或“假”）【答案】真【解析】根据原命题的逆命题和其否命题为等价命题判断命题的真假．【详解】由题意得命题“如果，那么且”的逆命题为“如果且，那么”，其真命题，所以否命题为真命题．故答案为“真”．【点睛】判断命题的真假时，可通过命题直接进行判断也可通过其等价命题的真假来判断，解题时要根据条件选择合理的方法进行求解．7．已知集合，，则__________【答案】【解析】分别求出集合，然后再求出即可．【详解】由题意得，，∴．故答案为．【点睛】本题考查集合的交集运算，解题的关键是正确求出集合，属于简单题．8．已知“”是“”的充分不必要条件，则实数的取值范围是__________【答案】【解析】将充分不必要条件转化为集合间的包含关系求解可得结论．【详解】设，∵“”是“”的充分不必要条件，∴ ，∴，解得，∴实数的取值范围是．故答案为．【点睛】根据充要条件求解参数范围的方法步骤(1)把充分条件、必要条件或充要条件转化为集合间的关系；(2)根据集合关系画数轴或Venn图，由图写出关于参数的不等式(组)，求解．注意：求解参数的取值范围时，一定要注意区间端点值的检验，尤其是利用两个集合之间的关系求解参数的取值范围时，不等式是否能够取等号决定端点值的取舍，处理不当容易出现漏解或增解的现象．9．设，则满足的集合的个数为__________【答案】8【解析】分别写出满足条件的集合后可得所求集合的个数．【详解】由题意得，满足题意得集合为，，，，，，共8个．故答案为8．【点睛】解题时要根据集合中元素的个数为标准进行求解，考查理解能力和判断能力，属于基础题．10．函数的定义域为，则的值为__________【答案】2【解析】由题意得不等式的解集为，然后根据“三个二次”间的关系求解即可得到结论．【详解】∵函数的定义域为，∴不等式的解集为，∴是方程的两个根，∴，整理得，解得．故答案为2．【点睛】本题以函数的定义域为载体，考查一元二次方程、二次函数、二次不等式间的关系，解题的关键是根据题意得到方程的两根，然后再根据方程的有关概念求出的值，考查转化能力和运算能力，属于基础题．11．已知函数，无论取什么实数，函数的图像始终过一个定点，该定点的坐标为__________【答案】【解析】将函数解析式变形为，然后令且，求得方程组的解后即可定点的坐标．【详解】由变形得，解方程组得，所以函数的图象过的定点的坐标为．故答案为．【点睛】本题考查一次函数的图象过定点的问题，解题时可把函数解析式化为（为参数）的形式，则以方程组的解为坐标的点即为定点．12．已知关于的方程有两个实数根，且一根大于1，一根小于1，则实数的取值范围为__________【答案】【解析】根据一元二次方程根的分布求解，令，则有，解不等式可得所求范围．【详解】令，∵方程的一个实数根大于1，另一个实数根小于1，∴，即，解得，∴实数的取值范围为．故答案为．【点睛】本题考查根据方程根的情况求参数的取值范围，解题时根据方程根的分布将问题转化为不等式求解，体现了转化和数形结合的思想方法在解题中的应用．13．给出下列四个命题：（1）若，则；（2）若，则；（3），则；（4）若，则．其中正确命题的是．（填所有正确命题的序号）【答案】（1）（2）（4）【解析】试题分析：（3）中时不等式不成立，故正确的只有（1）（2）（4）.【考点】不等式的基本性质.14．若，则的最小值为__________【答案】2【解析】将原式变形后根据基本不等式求解．∵，∴．由题意得，当且仅当，即时等号成立．∴的最小值为2.故答案为2.【点睛】应用基本不等式求最值时一定要注意“一正二定三相等”这三个条件缺一不可，当不满足不等式使用的条件时，可通过适当的变形使得出现定值的形式，这是解题中常遇到的情形．15．设函数，若不等式对任意实数恒成立，则的取值范围是__________【答案】【解析】表示数轴上的对应点到1对应点的距离减去它到2对应点的距离，其最小值为3，故有m<-3，由此求得m的取值范围．【详解】∵，不等式对任意实数恒成立，∴对任意实数恒成立，又表示数轴上的对应点到1对应点的距离减去它到2对应点的距离，∴，∴，∴实数的取值范围是．故答案为．本题考查恒成立问题，解题的关键是根据绝对值的几何意义求出的最小值，考查转化和数形结合思想的运用能力．16．对于实数和正数，称满足不等式的实数的集合叫做的邻域，已知为给定的正数，、为正数，若的领域是一个关于原点对称的区间，则的最小值为__________【答案】【解析】先根据条件求出；再结合邻域是一个关于原点对称的区间得到，最后结合不等式的知识可求出的最小值．【详解】∵A的B邻域在数轴上表示以A为中心，B为半径的区域，∴，∴，解得．∵邻域是一个关于原点对称的区间，∴，∴．∵，∴，∴，当且仅当时等号成立，∴的最小值为．故答案为．【点睛】本题以新概念为载体考查重要不等式的应用，考查变换能力和阅读理解能力．解题的关键是根据题意得到这一结论，然后再通过变形得到所求的最小值．三、解答题17．已知集合，是否存在这样的实数，使得集合有且仅有两个子集？若存在，求出所有的的值组成的集合；若不存在，请说明理由.【答案】【解析】若集合A有且仅有两个子集，则A有且仅有一个元素，即方程只有一个根，进而可得答案【详解】存在满足条件．理由如下：若集合A有且仅有两个子集，则A有且仅有一个元素，即方程只有一个根，①当，即时，由，解得，满足题意．②当，由A有且仅有一个元素得，解得．综上可得或，∴所有的的值组成的集合．【点睛】本题考查集合元素个数的问题，考查分析问题的能力，解题的关键是由题意得到方程根的个数，然后通过对方程类型的分类讨论得到所求的参数．18．我校第二教学楼在建造过程中，需建一座长方体形的净水处理池，该长方体的底面积为200平方米，池的深度为5米，如图，该处理池由左右两部分组成，中间是一条间隔的墙壁，池的外围周壁建造单价为400元/平方米，中间的墙壁（不需考虑该墙壁的左右两面）建造单价为100元/平方米，池底建造单价为60元/平方米，池壁厚度忽略不计，问净水池的长为多少时，可使总造价最低？最低价为多少？【答案】时，总造价最低为132000元.【解析】设的长为米，进而得到宽为米，根据题意得到总造价的表达式，然后根据基本不等式求出造价的最小值即可．【详解】设的长为米，则宽为米，由题意得总造价为，当且仅当，即时等号成立．所以当净水池的长米时，可使总造价最低，最低价为132000元．【点睛】基本不等式为求最值提供了工具，在利用基本不等式求最值时，一定要注意使用基本不等式的条件，即“一正二定三相等”，且三个条件缺一不可，当题目中不满足使用不等式的条件时，则需经过变形得到所需要的形式及条件．19．已知，集合，集合.（1）求集合与集合；（2）若，求实数的取值范围.【答案】（1），当，，当，，当，；（2）.【解析】（1）解不等式得出集合A、B；（2）根据A∩B=B得出B⊆A，讨论B=和B≠时，求出满足条件的实数的取值范围．【详解】（1）由题意得．当，即时，；当，即时，；当，即时，．（2）∵，∴B⊆A．①当时，，满足B⊆A；②当时，，满足B⊆A；③当时，，由B⊆A得或，解得或，又，∴或．综上可得或，∴实数的取值范围为．【点睛】根据集合间的包含关系求参数的取值范围时，一般要借助于数轴进行求解，根据集合端点值的大小关系转化为不等式（组）求解，解题时要注意不等式中的等号是否成立，这是解题中容易出现错误的地方．20．已知函数，，满足.（1）求实数的值；（2）在平面直角坐标系中，作出函数的图像，并且根据图像判断：若关于的方程有两个不同实数解，求实数的取值范围（直接写结论）【答案】（1）；（2）图象见解析，.【解析】（1）直接由f（2）=-2求得m的值；（2）把m值代入函数解析式，写出分段函数，根据函数的单调性作出图象，然后利用数形结合即可求得使关于x的方程f（x）=k有两个不同实数解的实数k的取值范围．【详解】（1）∵，，且，∴，即，解得或，又，∴．（2）由（1）得，当时，，∴函数在和上为减函数；当时，，∴函数在上为增函数，且．画出函数图象如下图：由图可知，要使关于x的方程有两个不同实数解，则，∴实数k的取值范围是．【点睛】（1）描点法画函数图象的步骤：①确定函数的定义域；②化简函数的解析式；③讨论函数的性质，即奇偶性、周期性、单调性、最值(甚至变化趋势)等；④描点连线，画出函数的图象．（2）利用函数图象确定方程或不等式的解，形象直观，体现了数形结合思想，解题的关键是正确的作出函数的图象．21．已知是满足下列性质的所有函数组成的集合：对任何（其中为函数的定义域），均有成立.（1）已知函数，，判断与集合的关系，并说明理由；（2）是否存在实数，使得，属于集合？若存在，求的取值范围，若不存在，请说明理由；（3）对于实数、，用表示集合中定义域为区间的函数的集合.定义：已知是定义在上的函数，如果存在常数，对区间的任意划分：，和式恒成立，则称为上的“绝对差有界函数”，其中常数称为的“绝对差上界”，的最小值称为的“绝对差上确界”，符号；求证：集合中的函数是“绝对差有界函数”，并求的“绝对差上确界”.【答案】（1）属于集合；（2）；（3）略.【解析】（1）利用已知条件，通过任取，证明成立，说明f（x）属于集合M．（2）若p（x）∈M，则有，然后可求出当时，p（x）∈M．（3）直接利用新定义加以证明，并求出h（x）的“绝对差上确界”T的值．【详解】（1）设，则，∵，∴，∴∴，∴函数属于集合．（2）若函数，属于集合，则当时，恒成立，即对恒成立，∴对恒成立．∵，∴，∴，解得，∴存在实数，使得，属于集合，且实数的取值范围为．（3）取，则对区间的任意划分：，和式，∴集合中的函数是“绝对差有界函数”，且的“绝对差上确界”．【点睛】本题考查新信息问题，考查阅读理解和应用能力，具有一定的综合性，解题的关键是弄懂给出的定义，解题时始终要围绕着给出的定义进行验证、求解等．。
上海市复旦大学附属中学2017-2018学年高三上学期期中考试英语试题 Word版含答案
复旦大学附属中学2017-2018学年第一学期高三年级英语期中考试试卷第I卷（共103分）I. Listening ComprehensionSection ADirections: 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 conversation and the question 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 question you have heard.1. A. This afternoon. B. Tomorrow. C. Next week. D. Next month.2. A. She doesn‟t play tennis well. B. She likes other sports as well.C. She is an enthusiastic tennis player.D. She is a professional athlete.3. A. At a paint store. B. At an oil market.C. At a science museum.D. At a gallery.4. A. Work in the yard. B. Buy some wood.C. Go to the bookstore.D. Take a walk.5. A. A taxi driver. B. A passenger. C. A car cleaner. D. A mechanic.6. A. Call a repairman. B. Get out the paper stuck.C. Turn to her colleague for help.D. Restart the machine.7. A. There are not enough gardens. B. Parking areas are full before 10:00.C. Parking areas are closed after 10:00.D. All classes begin at 10:00.8. A. The presentation will begin at noon.B. She‟ll present her work to the man.C. She‟d like to invite the man for lunch.D. She suggests working on the presentation at 12:00.9. A. The dormitory hours. B. The problem with the rules.C. The door number of the dormitory.D. The time to open the dormitory.10. A. The chairs didn‟t need to be painted.B. He doesn‟t like the color of the chairs.C. The park could have avoided the problem.D. The woman should have been more careful.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. Worried B. Surprised. C. Satisfied. D. Uninterested.12. A. It spoiled Juana‟s reputation. B. It copied her ideas without permission.C. It bought Juana‟s dishwashers.D. It wanted to share the dishwasher market.13. A. A successful business case. B. Juana‟s waterless laundry.C. A case against a global company.D. The worldwide dishwasher market.Questions 14 through 16 are based on the following passage.14. A. Footprints. B. Food. C. Living insects. D. Orange seeds.15. A. Don‟t touch animals under any circumstances.B. Don‟t take away any natural objects from the park.C. Don‟t leave litter in the park or throw any off the boat.D. Don‟t transport animals from one island to another.16. A. To protect the guide‟s interest. B. To improve the unique environment.C. To ensure a trouble-free visit.D. To get rid of illegal behaviors.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. (本题做在答题纸上)Write onlyII. 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)Libraries are my world. I've been a patron all my life, and for the past nine years I (25) ______ (work) at multiple libraries and archives in and around Detroit. The library (26) ______ an institution has many roles, but as our country struggles through an economic crisis, I have watched the library where I work evolve into a career and business center, a community gathering place and a bastion for hope.In the spring of 2007 I got a library internship at the Southfield Public Library, just north of Detroit. Summers at SPL (27) ______ (be) usually slow, but that year, we experienced a library that hustled and bustled like science-fair project week, midterms or tax season. Yet patrons weren't looking for Mosby's Nursing Drug Reference or 1040 forms. They were coming for information on entrepreneurship and growing their small business.I interpreted people's interest in our business collection as the first step to (28) ______ (pursue) their dreams, but these patrons were not motivated by dreams. They were responding to reality, and they were looking for Plan B.Things worsened in 2008, and in 2009 the economic crisis continues to suffocate Michigan. Last year, we put up a display with a variety of job resources that we restocked every hour. Each night the library closed, the display was bare. (29) ______ we normally keep displays up for a week, we kept the job resources display up for months.Then there's the tightening credit market. People see the writing on the wall and they want to get educated. They can't afford a financial adviser, but checking books out is free. Some of (30) ______(popular) titles now are "Rich Dad, Poor Dad," "Think and Grow Rich," and "Suze Orman's 2009 Action Plan."The economic downturn affects us all. I have had to work long hours and don't get to see (31) ______ of my boyfriend or experience any kind of social life lately, but I am thankful to be in a position where I can help people overcome this struggle. In Michigan, we haven't lost hope. (32) ______ ______ ______ there are libraries here, there will always be hope.(B)It‟s estimated that 300 million people in China are studying, or (33) ______ (study), English. That‟s an impressive number and I can‟t think of any other country in the world where one quarter of the population is so dedicated to (34) ______ (learn) a second language. But some people are questioning whether this “craze” for studying English is worthwhile.Professor Zhang Shuhua of the Chinese Academy of Social Sciences says that too much emphasis is placed on learning English and that it is a waste of education resources as well as a threat to the study of Chinese. He says that having English as a compulsory course in university “has distracted much of students‟attention (35) ______ specialized subjects,”and that some students have been denied access to postgraduate education because they failed English. Others have admitted that studying so much English has made them (36) ______ (poor) Chinese speakers.Both of these criticisms are legitimate, but they beg the question of why so many Chinese still want to learn English. English, (37) ______ recognize, is the lingua franca of the modern world. It is the language of business and has become the language of international relations and culture. When people from different countries get together, they frequently speak in English rather than try to translate their native languages. It seems that everyone everywhere can speak at least some English.For China to be part of that international conversation, it is necessary that some level ofEnglish proficiency (38) ______ be achieved. But what, you may ask, about those who will never speak a word of English once they leave school? Well, for good or ill, they will still be surrounded by English. It is there in signs, in music, in movies and in the casual conversations they overhear of the increasing number of foreigners on the city streets. To know English is to be included in the rest of the world, (39) ______ ______ your world is limited to China.I agree with Professor Zhang on one point, (40) ______. English should not be a compulsory subject in university. For most, passing the CET is just the endless drudgery of memorizing word lists. There is little emphasis placed on communication. And if you can‟t communicate in English after years of study in primary school, middle school and high school, a few more years in university probably won‟t help.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.For writers in Western cultures, autumn is a difficult season to describe. On the one hand, it is the end of the summer, and therefore a little sad. The nights draw in, and when you wake in the morning, there‟s mist and it‟s co oler: Winter is around the ___41___. American writer Ernest Hemingway wrote in his book A Moveable Feast: “You expected to be sad in the fall. Part of you died each year when the leaves fell from the trees and their branches were ___42___against the wind a nd the cold, wintry light.”On the other hand, autumn has its good side. There are so many changes in nature at this time of year, such as the reds and browns that the leaves change to, and the ___43___ they fall from the trees. French writer Albert Camus even though autumn was a second spring: “Autumn is a second spring when every leaf is a flower.” It‟s a view you can also find in the most famous autumn poem in English literature, To Autumn by John Keats. In that poem Keats says that the autumn has its own songs, just like spring.Another autumn theme is wisdom. The arrival of the season is thought to be similar to a person becoming ___44___. Their summer peak may have been and gone, but old age has not yet come. At this time it‟s thought that people have ___45___ a thing or two about life. The great Irish poet W.B. Yeats takes up this theme in his poem The Wild Swans at Coole. Yeats puts together a picture for the reader out of the ___46___ of the changing seasons in Coole Park in the west of Ireland, a place he knew well. Seeing and counting 59 swans, he remembers first making the count 19 years ago. He ___47___ whether he can still love like the lover swans do.Of course, many other themes and subject matters can play a part in the literature of autumn. For example, it‟s the beginning of a new term of the school year. As you would expect, autumncan___48___ in writing for children and young people. But autumn writing usually ___49___ on the changes in nature that we see, which writers often use as a ___50___ for changes in human life.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.After the college-board examinations in June, Basil Duke Lee and five other boys from St. Regis School ___51___ the train for the West. Two got out at Pittsburgh, one slanted south toward St. Louis and two stayed in Chicago; from then on Basil was alone. It was the first time in his life that he had ever felt the need of tranquility, but now he took long breaths of it; for, though things had gone better toward the end, he had had a / an ___52___ year at school.He wore one of those extremely flat derbies (常礼帽) in vogue during the twelfth year of the century, and a blue business suit became a little too short for his constantly ___53___ body. Within he was by turns a disembodied (空洞的) spirit, almost ___54___ of his person and moving in a mist of impressions and emotions, and a fiercely competitive individual trying ___55___ to control the rush of events that were the steps in his own ___56___ from child to man. He believed that everything was a matter of ___57___ — the current principle of American education — and his fantastic ___58___ was continually leading him to expect too much. He wanted to be a great athlete, popular, brilliant and always happy. During this year at school, where he had been punished for his “freshness,” for fifteen years of thorough spoiling at hom e, he had grown uselessly introspective, and this ___59___ with that observation of others which is the beginning of wisdom. It was apparent that before he obtained much success in dealing with the world he would know that he‟d been in a fight.Fifteen is of all ages the most difficult to ___60___———to put one‟s fingers on and say, “That‟s the way I was.” And all one can know is that somewhere between thirteen, boyhood‟s___61___, and seventeen, when one is a sort of counterfeit young man, there is a time when youth ___62___ hourly between one world and another —— pushed ceaselessly forward into unprecedented experiences and ___63___ trying to struggle back to the days when nothing had to be ___64___ for. Fortunately none of our contemporaries remember much more than we do of how we behaved in those days; nevertheless the ___65___ is about to be drawn aside for an inspection of Basil‟s madness that summer.51. A. boarded B. missed C. jumped D.followed52. A. happy B. unhappy C.memorableD.favourable53. A. swelling B. bending C. lengthening D.strengthening54. A. aware B.fond C. critical D.unconscious55. A. randomly B. desperately C. particularly D.indifferently56. A. evolution B. revolution C. solutionD.introduction57. A. fact B. opinion C. course D. effort58. A. fashion B. ambition C. character D.treasure59. A. contacted B. associated C. interfered D.smashed60. A. digest B.describe C. deal D. locate61. A. majority B. minority C. senior D. junior62. A. floats B. varies C. fluctuates D. ranges63. A. successfully B. vainly C. wildly D. gently64. A. hunted B. provided C. compensated D. paid65. A.curtain B. adolescence C. portrait D. ceilingSection 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)There are people in Italy who can‟t stand soccer. Not all Canadians love hockey. A similar situation exists in America, where there are those individuals you may be one of them who yawn or even frown when somebody mentions baseball. Baseball to them means boring hours watching grown men in funny tight outfits standing around in a field staring away while very little of an ything happens. They tell you it‟s a game better suited to the 19th century, slow, quiet, gentlemanly. These are the same people you may be one of them who love football because there‟s the sport that glorifies “the hit”.By contrast, baseball seems abstract, cool, silent, still.On TV the game is fractured into a dozen perspectives, replays, close ups. The geometry of the game, however, is essential to understanding it. You will contemplate the game from one point as a painter does his subject; you may, of course, project yourself into the game. It is in this projection that the game affords so much space and time for involvement. The TV won‟t do it for you.Take, for example, the third baseman. You sit behind the third base dugout and you watch him watching home plate. His legs are apart, knees flexed. His arms hang loose. He does a lot of this. The skeptic still cannot think of any other sports so still, so passive. But watch what happens every time the pitcher throws: the third baseman goes up on his toes, flexes his arms or brings the glove to a point in front of him, takes a step right or left, backward or forward, perhaps he glances across the field to check his first baseman‟s position. Suppose the pitch is a ball. “Nothing happened,” you say. “I could have had my eyes closed.”The skeptic and the innocent must play the game. And this involvement in the stands is no more intellectual than listening to music is. Watch the third baseman. Smooth the dirt in front of you with one foot; smooth the pocket in your glove; watch the eyes of the batter, the speed of the bat, the sound of horsehide on wood. If football is a symphony of movement and theatre, baseball is chamber music, a spacious interlocking of notes, chores and responses.66. Those who don‟t like baseball may complain that ______.A. it is only to the taste of the oldB. it involves fewer players than footballC. it is not exciting enoughD. it is pretentious and looks funny67. The author admits that ______.A. baseball is too peaceful for the youngB. baseball may seem boring when watched on TVC. football is more attracting than baseballD. baseball is more interesting than football68. By stating …I could have had my eyes closed.‟ the author means (4th paragraph last sentence):A. The third baseman would rather sleep than play the game.B. Even if the third baseman closed his eyes a moment ago, it could make no difference to theresult.C. The third baseman is so good at baseball that he could finish the game with eyes closed allthe time and do his work well.D. The consequence was too bad he could not bear to see it.69. We can safely conclude that the author ______.A. likes footballB. hates footballC. hates baseballD. likes baseball(B)Some of the world‟s most signifi cant problems never hit headlines. One example comes from agriculture. Food riots and hunger make news. But the trend lying behind these matters is rarely talked about. This is the decline in the growth in yields of some of the world‟s major crops. A new study by the University of Minnesota and McGill University in Montreal looks at where, and how far, this decline is occurring.The authors take a vast number of data points for the four most important crops: rice, wheat corn and soybeans. They find that on between 24% and 39% of all harvested areas, the improvement in yields that took place before the 1980s slowed down in the 1990s and 2000s.There are two worrying features of the slowdown. One is that it has been particularly sharp in the world‟s most p opulous countries, India and China. Their ability to feed themselves has been an important source of relative stability both within the countries and on world food markets. That self-sufficiency cannot be taken for granted if yields continue to slow down or reverse.Second, yield growth has been lower in wheat and rice than in corn and soya beans. This is problematic because wheat and rice are more important as foods, accounting for around half of all calories consumed. Corn and soybeans are more important as feed grains. The authors note that “we have preferentially focused our crop improvement efforts on feeding animals and cars rather than on crops that feed people and are the basis of food security in much of the world.”The report qualifies the more optimistic findings of another new paper which suggests that the world will not have to dig up a lot more land for farming in order to feed 9 billion people in 2050, as the Food and Agriculture Organization has argued.Instead, it says, thanks to slowing population growth, land currently ploughed up for crops might be able to revert to forest or wilderness. This could happen. The trouble is that the forecast assumes continued improvements in yields, which may not actually happen.70. What does the author try to draw attention to?A. Food riots and hunger in the world.B. News headlines in the leading media.C. The decline of the grain yield growth.D. The food supply in populous countries.71. Why does the author mention India and China in particular?A. Their self-sufficiency is vital to the stability of world food markets.B. Their food yields have begun to decrease sharply in recent years.C. Their big populations are causing worldwide concerns.D. Their food self-sufficiency has been taken for granted.72. What does the new study by the two universities say about recent crop improvement efforts?A. They fail to produce the same remarkable results as before the 1980s.B. They contribute a lot to the improvement of human food production.C. They play a major role in guaranteeing the food security of the world.D. They focus more on the increase of animal feed than human food grains.73. What does the Food and Agriculture Organization say about world food production in the coming decades?A. The growing population will greatly increase the pressure on world food supplies.B. The optimistic prediction about food production should be viewed with caution.C. The slowdown of the growth in yields of major food crops will be reversed.D. The world will be able to feed its population without increasing farmland.(C)Among the more colorful characters of Leadville‟s golden age were H.A.W. Tabor and his second wife, Elizabeth McCourt, better known as “Baby Doe”. Their history is fast becoming one of the legends of the Old West. Horace Austin Warner Tabor was a school teacher in Vermont. With his first wife and two children he left Vermont by covered wagon in 1855 to homestead in Kansas. Perhaps he did not find farming to his liking, or perhaps he was tempted by rumors of fortunes to be made in Colorado mines. At any rate, a few years later he moved west to the small Colorado mining camp known as California Gulch, which he later renamed Leadville when he became its leading citizen. “Great deposits of lead are sure to be found here.” he said.As it turned out, it was silver, not lead, that was to make Leadville‟s fortune and wealth. Tabor knew little about mining himself, so he opened a general store, which sold everything from boots to salt, flour, and tobacco. It was his custom to “grubstake” prospective miners, in other words, to supply them with food and supplies, or “grub”, while they looked for ore, in return for which he would get a share in the mine if one was discovered. He did this for a number of years, but no one that he aided ever found anything of value.Finally one day in the year 1878, so the story goes, two miners came in and asked for “grub”. Tabor had decided to quit supplying it because he had lost too much money that way. These werepersistent, howe ver, and Tabor was too busy to argue with them. “Oh help yourself. One more time won‟t make any difference,” He said and went on selling shoes and hats to other customers.The two miners took $17 worth of supplies, in return for which they gave Tabor a one-third interest in their findings. They picked a barren place on the mountain side and began to dig. After nine days they struck a rich vein of silver. Tabor bought the shares of the other two men, and sothe mine belonged to him alone. This mine, known as the “Pittsburgh Mine,” made 1 300 000 for Tabor in return for his $17 investment.Later Tabor bought the Matchless Mine on another barren hillside just outside the town for $117 000. This turned out to be even more fabulous than the Pittsburgh, yielding $35 000 worth of silver per day at one time. Leadville grew. Tabor became its first mayor, and later became lieutenant governor of the state.74. Leadville got its name for the following reasons EXCEPT ______.A. because Tabor became its leading citizenB. because great deposits of lead is expected to be found thereC. because it could bring good fortune to TaborD. because Tabor renamed it so75. The word “grubstake” in paragraph 2 means ______.A. to supply miners with food and suppliesB. to open a general storeC. to do one‟s contribution to the development of the mineD. to supply miners with food and supplies and in return get a share in the mine, if one wasdiscovered76. Tabor made his first fortune ______.A. by supplying two prospective miners and getting in return a one-third interest in the findingsB. because he was persuaded by the two miners to quit supplyingC. by buying the shares of the otherD. as a land speculator77. The underlying reason for Tabor‟s life career is ______.A. purely accidentalB.based on the analysis of miner‟s being very poor and their possibility of discoveringprofitable mining siteC. through the help from his second wifeD. he planned well and accomplished targets step by stepSection CDirections: Read the passage carefully. Then answer the questions or complete the statements inthe fewest possible words.When the Internet powerhouse Yahoo wanted to teach ethics to its employees, it faced a challenge familiar to multinational companies.Yahoo employs nearly 14,000 people at 25 sites worldwide. They would feel bored at sitting down in front of a dated video in which actors with 1980s haircuts tell them what to do. So it hired a company called The Network to design a game. In the game, the truck where Yahoo wasfounded traveled the world, turning into a boat and a helicopter along the way as it visited some of Yahoo's foreign offices. Participants play in game show-like scenarios that quiz them about conflicts of interest and doing business fairly. And employees note: Yahoo is tracking how well they do.Such activities draw more enthusiastic participation and teach more effectively than traditional methods. They are described as alternative-reality games (ARGs), involving both interactive and real-world elements. Besides teaching employees, ARGs have also been used in many areas for a number of different purposes.From a marketing perspective, a number of very successful ARGs have been written as a way to build product awareness. A very popular ARG called I Love Bees was produced to market the 2004 video game Halo 2. At its height, I Love Bees received between two to three million unique visitors over the course of three months.ARGs are more than just a fun way to learn. They have also been used to solve real world problems. An ARG called World Without Oil was created to obtain collective input from players about dealing with the world's dependency on oil. World without Oil simulates the first 32 days of a global oil crisis and anybody could play by creating a personal story that recorded the imagined reality of their life in the crisis. World Without Oil's success on a small budget has opened the door for similar games to engage mainstream Internet users with climate change, education reform, governmental policy and other timely, vital issues.(Note: Answer the questions or complete the statements in NO MORE THAN TEN WORDS.)78.What challenge did yahoo face in teaching ethics to its employees?79.In the game designed for yahoo, participants had to answer questions about ________.80.What are the three major functions of ARG mentioned in the passage?81.The success of World Without Oil suggests that ARGs can ________.第II卷（共47分）I. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.1.没有人不希望和平。
上海市复旦大学附属中学2017-2018学年高一上学期期中考试物理试题(解析版)
复旦大学附属中学2017 学年度第一学期高一年级物理期中考试试卷一、单项选择题（每题4 分，共40 分）1. 下列说法正确的是（）A. 若物体的加速度均匀增加，则物体做匀加速直线运动B. 若物体的加速度增加，则物体不可能做减速运动C. 只要物体的加速度不为零，它的速度总是在发生变化的D. 只要物体做直线运动，位移的大小和路程就一定相等【答案】C【解析】【详解】匀加速直线运动的加速度保持不变，故A错误；当加速度的方向与速度方向相反，加速度增大而物体做减速运动，故B错误；只要有加速度，速度就变化，所以只要物体的加速度不为零，它的速度总是在发生变化的，故C正确;只有物体做单方向得直线运动时，位移的大小和路程才相等，故D错误．所以C正确，ABD错误．2. 三个质点A、B、C的运动轨迹如图所示，同时从N点出发，同时到达M点，下列说法中正确的是（）A. 三个质点任意时刻的速度方向都相同B. 三个质点从N点出发到M的任意时刻速度大小都相同C. 三个质点从N点到M点的平均速度大小和方向均相同D. 三个质点从N点到M点的平均速率相同【答案】C【解析】【详解】由题意可知任意时刻三个质点的速度大小和方向都不相同，选项AB错误；平均速度等于位移除以时间，故平均速度大小相同，平均速度的方向与位移方向相同，故平均速度方向相同，选项C正确；平均速率等于路程除以时间，三质点的路程不同，时间相同，故平均速率不同，选项D错误．综上本题选C．3. 如图所示，各接触面均光滑，A、B间无弹力作用的是（）A. B. C. D.【答案】A【解析】【详解】试题分析：弹力是物体发生形变后要恢复原状时产生的力．而形变有宏观与微观形变，所以有时接触不一定有形变，即有弹力．故弹力产生的条件是接触且形变．解：A、假设AB间有弹力，则AB两物体均不能处于平衡状态，所以要运动，然而AB两物体没有运动．故A选项没有弹力BCD、由图可知：BCD项肯定有弹力，因AB间有相互挤压，将A或者我B其中一个拿走，物体运动状态会发生变化，因此必定存在弹力．故A正确，BCD错误．故选A．4. 如图所示，某人用手握住一个保温杯，则下列说法中正确的是A. 若保持保温杯始终静止，则手握得越紧，保温杯受到的摩擦力越大B. 握着保温杯匀速向上运动，保温杯所受的摩擦力向上C. 握着保温杯匀速向下运动，保温杯所受的摩擦力向下D. 握着保温杯水平匀速运动，保温杯不受摩擦力【答案】B【解析】【详解】A.手握得越紧，保温杯受到的最大静摩擦力越大，静摩擦力不变，静摩擦力等于保温杯的重力，故A错误；B.握着保温杯匀速向上运动，保温杯所受的摩擦力与重力是一对平衡力，所以摩擦力方向向上．故B正确；C.握着保温杯匀速向下运动，保温杯所受的摩擦力与重力是一对平衡力，所以摩擦力方向向上，故C错误；D.握着保温杯匀速运动，保温杯所受的摩擦力与重力是一对平衡力，保温杯仍受摩擦力作用，故D错误．5. 某质点以20m/s的初速度竖直向上运动,其加速度保持不变,经2s到达最高点,上升高度为20m,又经过2s回到出发点时,速度大小仍为20m/s,关于这一运动过程的下列说法中不正确的是( )A. 质点运动的加速度大小为10m/s2,方向竖直向下B. 最高点时速度为零,加速度不为零C. 质点在上升过程中速度的变化量大小为20m/s，方向竖直向上D. 质点在上升过程中和下降过程中速度的变化量大小相等方向相同【答案】C【解析】【详解】A．由速度位移公式：22vxa-=代入数据解得210m sa=质点向上做匀减速直线运动，所以加速度方向竖直向下，故A正确；B．质点在最高点时速度为零，加速度不为零，仍然是10m/s2，故B正确；C．由公式∆=∆vat可知，质点在上升过程中速度的变化量大小102m/s20m/sv∆=⨯=速度变化量方向与加速度方向相同即竖直向下，故C错误；D．由公式∆=∆vat可知，质点在上升过程中和下降过程中速度的变化量大小相等，方向与加速度方向相同即竖直向下，故D正确．6. 用轻绳系住一小球静止在光滑斜面上，如图所示．若要按力的实际作用效果来分解小球的重力，则重力的两个分力的方向分别是图中的（）A. 1和5B. 2和5C. 3和5D. 3和2【答案】C【解析】【详解】小球重力产生两个效果，一是使绳子拉伸，二是使斜面受压，故应按此两个方向分解，分别是3和5，故选项C正确．【点睛】将力进行分解时，一般要按照力的实际作用效果来分解或按需要正交分解，若要按照力的实际作用效果来分解，要看力产生的实际效果．7. a 、b 、c 三个物体在同一直线上运动，其位移时间图像中，图线c 是一条x =0.4t 2的抛物线．有关这三个物体在0 -5s 内的运动，下列说法正确的是（ ）A. a 物体做匀加速直线运动B. c 物体做变加速直线运动C. t = 5s 时，a 物体速度比c 物体速度小D. a 、b 两物体都做匀速直线运动，且速度相同【答案】C 【解析】【详解】AD ．位移图象倾斜的直线表示物体做匀速直线运动，则知a 、b 两物体都做匀速直线运动，由图看出斜率看出，a 、b 两图线的斜率大小、正负相反，说明两物体的速度大小相等、方向相反，所以速度不同，故AD 错误；B ．图线c 是一条x =0.4t 2的抛物线，结合2012x v t at =+可知，c 做初速度为0，加速度为0.8m/s 2的匀加速直线运动，故B 错误；C ．图象的斜率大小等于速度大小，根据图象可知，t =5s 时，a 物体速度比c 物体速度小，故C 正确．8. 两个大小相等的共点力，当它们夹角为120︒时，合力为F ，当它们的夹角为90︒时，合力大小为（ ）A. 2FB. 2FC. FD. 22F【答案】B【解析】【详解】由题意，两个大小相等的共点力F 1和F 2，当它们的夹角为120°时合力为F ，由于当它们之间的夹角为120︒时合力如图，由等边三解形的知识可知分力是F ，当这两个力之间的夹角为90︒时，由勾股定理得合力大小为 222F F F +=A ．2F 与分析不符，故A 错误；B ．2F 与分析相符，故B 正确；C ． F 与分析不符，故C 错误；D ．22F 与分析不符，故D 错误．9. 据英国《每日邮报》2014年8月10日报道：27名跳水运动员参加了科索沃年度高空跳水比赛，自某运动员离开跳台开始计时，在t 2时刻运动员以速度v 2落水，选竖直向下为正方向，其速度随时间变化的规律如图所示，下列结论正确的是（ ）A. 该运动员在0 -t 2时间内加速度大小先减小后增大，加速度的方向不变B. 该运动员在t 2- t 3时间内加速度大小逐渐变大C. 在0-t 2时间内，平均速度v =122v v + D. 在t 2 -t 3时间内，平均速度v =202v + 【答案】C【解析】【详解】A ．运动员在0～t 2时间内加速度大小一直不变，加速度的方向一直沿正方向，说明加速度的大小和方向没有发生了变化，故A 错误；B ．在t 2～t 3时间内图象的斜率不断减小，则运动员的加速度大小逐渐减小，故B 错误；C ．在0～t 2时间内，运动员做匀变速直线运动位移，则其平均速度122v v v +=故C 正确； D ．在t 2～t 3时间内，运动员的位移小于匀减速直线运动的位移，则平均速度202v v +<故D 错误．10. 一质点做匀加速直线运动，运动10m的过程中速度增加了5m/s，再运动15m的过程中速度同样增加了5m/s，则该质点的加速度为（）A. 1m/s2B. 5m/s2C. 10m/s2D. 15m/s2【答案】B【解析】【详解】物体做匀加速直线运动，连续通过两段位移速度增加量相同，则运动的时间相等，设为T，则有：△x=aT2，即15-10=aT2，根据速度时间公式有：△v=5=aT，解得T=1s，a=5m/s2，故B正确，ACD错误．二、多项选择题（每题4 分，共16 分）11. 物体受共点力F1、F2、F3作用而做匀速直线运动，则这三个力大小的可能值是（）A. 15N，5N，16NB. 1N，2N，10NC. 3N，6N，4ND. 1N，6N，3N【答案】AC【解析】【详解】因物体做匀速直线运动，所以所受的合力为零．因为是三个力，我们可让前两个先合成，再和第三个合成：A项中前两个力的合力范围是：[10，20]，第三个力是16N，所以合力可能为零．故A正确．B项中前两个力的合力范围是：[1，3]，第三个力是10N，所以合力不可能为零．故B错误．C项中前两个力的合力范围是：[3，9]，第三个力是4N，所以合力可能为零，故C正确．D项中前两个力的合力范围是：[5，7]，第三个力是3N，所以合力不可能为零，故D错误．故选AC．【点睛】求三个力的合力时我们可以先合成前两个力，再与第三个力进行合成即可．12. 关于摩擦力的有关说法正确的是( )A. 只有静止的物体才可能受静摩擦力B. 运动的物体可能受到静摩擦力作用C. 摩擦力可能作动力D. 受到摩擦力的物体一定受到弹力【答案】BCD【解析】【详解】AB．运动物体也可以受静摩擦力，比如传送带向高处运送货物，货物受静摩擦力，故A错误，B正确；C．摩擦力可以与物体运动方向相反，作为阻力；也可以与物体运动方向相同，作为动力，故C正确；D．根据摩擦力产生条件之一需要物体间有正压力，所以有摩擦力必有弹力，而有弹力时未必有摩擦力，故D正确．13. 在H=30m高的塔顶上将一物体竖直向上抛出，抛出速度为v0=20m／s，不计空气阻力，g取10m/s2，则物体位移大小为15 m时，球离开抛出点的时间可能为（）A. 1sB. 3sC. 2+3sD. 2+7s 【答案】ABD【解析】【详解】物体在塔顶上的A点竖直向上抛出，位移大小为15m的位置有两处，如图所示，一处在A点之上，另一处在A点之下．在A点之上时，通过位移为15m处又有上升和下降两种过程．根据在A点之上时，物体的位移为15m，则，t1=1s，t2=3s在A点之下时，物体的位移为-15m，则，t=2+7s故选ABD【点睛】本题考查了竖直上抛运动规律．竖直上抛运动中位移相等，可能有三种情况，位移向上包括物体上升过程中经过；物体下降过程中经过；位移向下，物体下降到抛出点以下．根据竖直上抛运动的位移时间关系，列方程求解．14. 放在粗糙水平面上的物体A上叠放着物体B，A和B之间有一根处于压缩状态的弹簧A、B均处于静止状态，下列说法中正确的是( )A. B受到向左的摩擦力B. B对A的摩擦力向左C. 地面对A没有摩擦力D. 地面对A的摩擦力向右【答案】BC【解析】【详解】A．压缩状态的弹簧对B有向左的弹力，B有向左运动的趋势，受到向右的摩擦力，故A错误；B．A对B的摩擦力向右，根据牛顿第三定律可知，B对A的摩擦力向左，故B正确；CD．对整体研究，根据平衡条件分析可知，地面对A没有摩擦力，故C正确，D错误．三、填空题（每格2 分，共20 分）15. 汽车从制动到停止下来共用了5s，汽车前1s、前2s、前3s、前4s和全程的平均速度分别为9m/s、8m/s、7m/s、6m/s、5m/s，这五个平均速度中最接近汽车关闭油门时的瞬时速度的是____________ m/s，它比这个瞬时速度____________（选填“略大”或“略小”）．【答案】①. 9②. 略小【解析】【详解】将汽车刹车作为匀减速直线运动处理，设汽车关闭油门时的瞬时速度为9m/s，则5s末速度为0，全程的平均速度为：5/2vv m s+==，解得：v=10m/s，则第1s内的平均速度9m/s最接近汽车关闭油门时的瞬时速度，但比这个瞬时速度略小．16. 分别作出图（1）中A物体和图（2）中A、C两个物体的受力示意图．A物体在力F作用下向右匀速运动水平地面光滑其他接触面粗糙，三物块都处于静止状态【答案】【解析】【详解】图（1）中A物体匀速运动，所以物体受重力，推力，天花板的弹力，摩擦力，示意图如图图（2）中三物块都处于静止状态，整体分析可知，A物体不受墙面的弹力，所以A物体受到重力，B对A的支持力，B对A的摩擦力，C物体受到重力，地面的支持力，B对C的压力17. 如图所示,轻绳OA 一端系在天花板上,与竖直线夹角为37︒轻绳OB 水平,一端系在墙上,若O 点处挂一重为40N 的物体.则AO 、BO 的拉力各为________N 和________N ．若AO 、BO 、CO 所能承受的最大拉力均为100N,则所吊重物不能超过________N ．（sin 37︒=0.6, cos 37︒=0.8）【答案】 ①. 50N ②. 30N ③. 80N 【解析】【详解】[1][2]对结点O 受力分析，如图所示：根据共点力平衡条件，有：50N cos37AO G T ︒== tan 3730N BO T G ︒==[3]O 点受三个力作用而处于平衡状态，结合图中三角形知识，可知由于T OA ＞T OC ＞T OB 所以1cos3780N OA G T ︒==18. 物体做变速运动，初速度v 0 =6m/s .加速度随时间变化关系为a =+(4-2t )（式中a 和t 的单位分别为m/s 2和s ；t ≤4s ），经过________s 速度达到最大，最大值为________m/s.【答案】 ①. 2s ②. 10m/s 【解析】【详解】[1][2]当加速为零时，速度最大，由a =+(4-2t )可知，2s t = 加速度为零，由于加速度随时间均匀变化，所以平均加速度为2240m /s 2m /s 2a +== 此时速度为 0(622)m /s 10m /s v v at =+=+⨯=四、综合题（每题 8 分，共 24 分）19. 研究共点力的合成”的实验情况如图甲所示,其中A 为固定橡皮筋的图钉,O 为橡皮筋与细绳的结点,OB 和OC 为细绳,图乙是在白纸上根据实验结果画出的图示.(1)图乙中的F 与 F '两力中,方向一定沿AO 方向的是_________;(2)用F 1和F 2两个力或用一力拉橡皮条时，结点都必须达到O 点，这是因为_________．(3)同学们在操作过程中有如下议论，其中对减小实验误差有益的说法是___（填字母代号） A.两条细绳必须等长B.弹簧秤、细绳、橡皮条都应与木板平行C.用两弹簧秤同时拉细绳时两弹簧秤示数之差尽可能大D.拉橡皮条的细绳要长些，标记同一细绳方向的两点要远些【答案】 ①. 'F ②. 为了使两个力和一个力的作用效果相同 ③. BD【解析】【详解】(1)[1]F 是通过作图的方法得到合力的理论值，而F′是通过一个弹簧称沿AO 方向拉橡皮条，使橡皮条伸长到O 点，使得一个弹簧称的拉力与两个弹簧称的拉力效果相同，测量出的合力．故方向一定沿AO 方向的是F′(2)[2]用F 1和F 2两个力或用一力拉橡皮条时，结点都必须达到O 点，这是为了使两个力和一个力的作用效果相同；(3)[3]A ．细线的作用是能显示出力的方向，所以不必须等长，故A 错误；B ．为减小实验误差，拉橡皮条时，弹簧秤、橡皮条、细绳应贴近木板且与木板平面平行，故B 正确；C ．用弹簧秤同时拉细绳时，拉力不能太太，也不能太小，故C 错误；D ．为了更加准确的记录力的方向，拉橡皮条的细绳要长些，标记同一细绳方向的两点要远些，故D 正确．20. 在一种新的“子母球”表演中，让同一竖直线上的小球A 和小球B ，从距水平地面高度为ph （p ＞1）和h 的地方同时由静止释放，如图所示．球A 的质量为m ，球B 的质量为3m ．设球与地面碰撞后速度大小不变，方向相反，重力加速度大小为g ，忽略球的直径、空气阻力及碰撞时间．（1）求球B 第一次落地时球A 的速度大小；（2）若球B 在第一次上升过程中就能与球A 相碰，求p 的取值范围；【答案】（1）02v gh =（2）15p <<【解析】【详解】（1）由于两球同时释放，所以球B 第一次落地时A 球下落高度为h ，设此时A 球的速度大小为0v ，由202v gh =可得，02v gh =．（2）球B 第一次落地并与地发生弹性碰撞后做竖直上抛运动．若球B 上升到最大高度h 处时刚好与球A 发生碰撞，设此时球A 自由下落时间t A ，则21()22A t g h =， 此时球A 自由下落的高度212A A h gt =． 联立以上两式，可得4A h h =，则5A ph h h h =+=，所以p=5．若球B 在第一次上升过程中就能与球A 相碰，则p 的取值范围应为15p <<．【点睛】要想在上升阶段两球相碰，临界情况是B 刚好反跳回到出发点时与A 相碰，据此求出A 球的最大高度21. 一辆汽车向悬崖以加速度22m/s 做匀加速驶近时鸣喇叭，经8s t =听到来自悬崖的回声；接着再前进22s t =，第二次鸣喇叭，经36s t =又听到回声。
2017-2018学年上海中学高一(上)期中数学试卷
2017-2018学年上海中学高一（上）期中数学试卷一、填空题1．（3分）设集合A={0，2，4，6，8，10}，B={4，8}，则∁A B=．2．（3分）已知集合A={x||x|＜2}，B={﹣1，0，1，2，3}，则A∩B=．3．（3分）“若x=1且y=1，则x+y=2”的逆否命题是．4．（3分）若f（x+）=x2+，则f（3）=．5．（3分）不等式x＞的解是．6．（3分）若不等式ax2+（a+1）x+a＜0对一切x∈R恒成立，则a的取值范围是．7．（3分）不等式（x﹣3）2﹣2﹣3＜0的解是．8．（3分）已知集合A={x|﹣6≤x≤8}，B={x|x≤m}，若A∪B≠B且A∩B≠∅，则m的取值范围是．9．（3分）不等式（x+y）（+）≥25对任意正实数x，y恒成立，则正实数a 的最小值为．10．（3分）设a＞0，b＞0，且ab=a+4b+5，则ab的最小值为．11．（3分）对于二次函数f（x）=4x2﹣2（p﹣2）x﹣2p2﹣p+1，若在区间[﹣1，1]内至少存在一个数c 使得f（c）＞0，则实数p的取值范围是．12．（3分）已知a，b为正实数，且a+b=2，则+的最小值为．二、选择题13．（3分）不等x|x|＜x的解集是（）A．{x|0＜x＜1}B．{x|﹣1＜x＜1}C．{x|0＜x＜1}或{x|x＜﹣1}，D．{x|﹣1＜x＜0，x＞1}14．（3分）若A⊆B，A⊆C，B={0，1，2，3，4，5，6}，C={0，2，4，6，8，10}，则这样的A的个数为（）A．4B．15C．16D．3215．（3分）不等式ax2+bx+1＞0的解集是（﹣，），则a﹣b=（）A．﹣7B．7C．﹣5D．516．（3分）已知函数f（x）=x2+bx，则“b＜0”是“f（f（x））的最小值与f（x）的最小值相等”的（）A．充分不必要条件B．必要不充分条件C．充分必要条件D．既不充分也不必要条件三、解答题17．解不等式：（1）|x﹣2|+|2x﹣3|＜4；（2）．18．已知a，b，c，d∈R，证明下列不等式：（1）（a2+b2）（c2+d2）≥（ac+bd）2；（2）a2+b2+c2≥ab+bc+ca．19．已知二次函数f（x）=ax2+bx+1，a，b∈R，当x=﹣1时，函数f（x）取到最小值，且最小值为0；（1）求f（x）解析式；（2）关于x的方程f（x）=|x+1|﹣k+3恰有两个不相等的实数解，求实数k的取值范围．20．设关于x的二次方程px2+（p﹣1）x+p+1=0有两个不相等的正根，且一根大于另一根的两倍，求p的取值范围．21．已知二次函数f（x）=ax2+bx+c（a≠0），记f[2]（x）=f（f（x）），例：f（x）=x2+1，则f[2]（x）=（f（x））2+1=（x2+1）2+1；（1）f（x）=x2﹣x，解关于x的方程f[2]（x）=x；（2）记△=（b﹣1）2﹣4ac，若f[2]（x）=x有四个不相等的实数根，求△的取值范围．2017-2018学年上海中学高一（上）期中数学试卷参考答案与试题解析一、填空题1．（3分）设集合A={0，2，4，6，8，10}，B={4，8}，则∁A B={0，2，6，10} ．【解答】解：集合A={0，2，4，6，8，10}，B={4，8}，所以∁A B={0，2，6，10}．故答案为：{0，2，6，10}．2．（3分）已知集合A={x||x|＜2}，B={﹣1，0，1，2，3}，则A∩B={﹣1，0，1} ．【解答】解：∵A={x||x|＜2}={x|﹣2＜x＜2}，B={﹣1，0，1，2，3}，∴A∩B={﹣1，0，1}，故答案为：{﹣1，0，1}3．（3分）“若x=1且y=1，则x+y=2”的逆否命题是“若x+y≠2，则x≠1，或y ≠1”．【解答】解：“若x=1且y=1，则x+y=2”的逆否命题是“若x+y≠2，则x≠1，或y ≠1”，故答案为：“若x+y≠2，则x≠1，或y≠1”4．（3分）若f（x+）=x2+，则f（3）=7．【解答】解：f（x+）=x2+=（x+）2﹣2，所以f（x）=x2﹣2，则f（3）=7．故答案为：7．5．（3分）不等式x＞的解是（﹣3，0）∪（3，+∞）．【解答】解：原不等式等价于等价于（x+3）（x﹣3）x＞0，由穿根法得到不等式的解集为（﹣3，0）∪（3，+∞）；故答案为：（﹣3，0）∪（3，+∞）；6．（3分）若不等式ax2+（a+1）x+a＜0对一切x∈R恒成立，则a的取值范围是（﹣∞，﹣）．【解答】解：若不等式ax2+（a+1）x+a＜0对一切x∈R恒成立，则，解得：a∈（﹣∞，﹣），故答案为：（﹣∞，﹣）．7．（3分）不等式（x﹣3）2﹣2﹣3＜0的解是（0，6）．【解答】解：设=t，则原不等式化为t2﹣2t﹣3＜0，（t≥0），所以t∈[0，3），即∈[0，3），所以（x﹣3）2＜9，解得﹣3＜x﹣3＜3，所以0＜x＜6，故原不等式的解集为（0，6）；故答案为：（0，6）．8．（3分）已知集合A={x|﹣6≤x≤8}，B={x|x≤m}，若A∪B≠B且A∩B≠∅，则m的取值范围是[﹣6，8）．【解答】解：A={x|﹣6≤x≤8}，B={x|x≤m}，若A∪B≠B且A∩B≠∅，则，故答案为：[﹣6，8）．9．（3分）不等式（x+y）（+）≥25对任意正实数x，y恒成立，则正实数a 的最小值为16．【解答】解：（x+y）（+）=1+a++≥1+a+2=1+a+2=（+1）2，即（x+y）（+）的最小值为（+1）2，若不等式（x+y）（+）≥25对任意正实数x，y恒成立，∴（+1）2≥25，即+1≥5，则≥4，则a≥16，即正实数a的最小值为16，故答案为：16．10．（3分）设a＞0，b＞0，且ab=a+4b+5，则ab的最小值为25．【解答】解：∵a＞0，b＞0，∴a+4b+5=ab，可得ab≥5+2=5+4，当且仅当a=4b时取等号．∴（+1）（﹣5）≥0，∴≥5或≤﹣1（舍去）．∴ab≥25．故ab的最小值为将25；故答案为：25．11．（3分）对于二次函数f（x）=4x2﹣2（p﹣2）x﹣2p2﹣p+1，若在区间[﹣1，1]内至少存在一个数c 使得f（c）＞0，则实数p的取值范围是（﹣3，1.5）．【解答】解：二次函数f（x）在区间[﹣1，1]内至少存在一个实数c，使f（c）＞0的否定是：对于区间[﹣1，1]内的任意一个x都有f（x）≤0，∴即整理得解得p≥，或p≤﹣3，∴二次函数在区间[﹣1，1]内至少存在一个实数c，使f（c）＞0的实数p的取值范围是（﹣3，）．12．（3分）已知a，b为正实数，且a+b=2，则+的最小值为．【解答】解：∵a，b为正实数，且a+b=2，∴=a++=+a+b﹣1+=+1=f（a），0＜a＜2．f′（a）=+=，令f′（a）＞0，解得，此时函数f（a）单调递增；令f′（a）＜0，解得，此时函数f（a）单调递减．∴当且仅当a=6﹣3时函数f（a）取得极小值即最小值，=．故答案为：．二、选择题13．（3分）不等x|x|＜x的解集是（）A．{x|0＜x＜1}B．{x|﹣1＜x＜1}C．{x|0＜x＜1}或{x|x＜﹣1}，D．{x|﹣1＜x＜0，x＞1}【解答】解：不等x|x|＜x，即x（|x|﹣1）＜0，∴①，或②．解①可得0＜x＜1，解②可得x＜﹣1．把①②的解集取并集，即得原不等式的解集为{x|0＜x＜1}或{x|x＜﹣1}，故选：C．14．（3分）若A⊆B，A⊆C，B={0，1，2，3，4，5，6}，C={0，2，4，6，8，10}，则这样的A的个数为（）A．4B．15C．16D．32【解答】解：∵A⊆B，A⊆C，∴A⊆（B∩C），∵B={0，1，2，3，4，5，6}，C={0，2，4，6，8，10}，∴B∩C={0，2，4，6}，∴A的个数为16，故选：C．15．（3分）不等式ax2+bx+1＞0的解集是（﹣，），则a﹣b=（）A．﹣7B．7C．﹣5D．5【解答】解：由不等式ax2+bx+1＞0的解集是（﹣，），构造不等式（x+）（x﹣）＜0，整理得：6x2+x﹣1＜0，即﹣6x2﹣x+1＞0，与ax2+bx+1＞0对比得：a=﹣6，b=﹣1，则a﹣b=﹣6+1=﹣5，故选：C．16．（3分）已知函数f（x）=x2+bx，则“b＜0”是“f（f（x））的最小值与f（x）的最小值相等”的（）A．充分不必要条件B．必要不充分条件C．充分必要条件D．既不充分也不必要条件【解答】解：f（x）的对称轴为x=﹣，f min（x）=﹣．（1）若b＜0，则﹣＞﹣，∴当f（x）=﹣时，f（f（x））取得最小值f（﹣）=﹣，即f（f（x））的最小值与f（x）的最小值相等．∴“b＜0”是“f（f（x））的最小值与f（x）的最小值相等”的充分条件．（2）设f（x）=t，则f（f（x））=f（t），∴f（t）在（﹣，﹣）上单调递减，在（﹣，+∞）上单调递增，若f（f（x））=f（t）的最小值与f（x）的最小值相等，则﹣≤﹣，解得b≤0或b≥2．∴“b＜0”不是“f（f（x））的最小值与f（x）的最小值相等”的必要条件．故选：A．三、解答题17．解不等式：（1）|x﹣2|+|2x﹣3|＜4；（2）．【解答】解：（1）x≥2时，x﹣2+2x﹣3＜4，解得：x＜3，＜x＜2时，2﹣x+2x ﹣2＜4，解得：x＜4，x≤时，2﹣x+3﹣2x＜4，解得：x＞，故不等式的解集是：{x|＜x＜3}；（2）∵，∴≥0，∴x﹣1=0或或，解得：﹣1＜x≤0或x=1或x＞2，故不等式的解集是（﹣1，0]∪{1}∪（2，+∞）．18．已知a，b，c，d∈R，证明下列不等式：（1）（a2+b2）（c2+d2）≥（ac+bd）2；（2）a2+b2+c2≥ab+bc+ca．【解答】证明：∵（a2+b2）（c2+d2）﹣（ac+bd）2=（a2c2+a2d2+b2c2+b2d2）﹣（a2c2+2abcd+b2d2）=（ad﹣bc）2≥0，∴（a2+b2）（c2+d2）≥（ac+bd）2 成立；（2）a2+b2+c2=（a2+b2+c2+a2+b2+c2），≥（2ab+2ca+2bc）=ab+bc+ca．∴a2+b2+c2≥ab+bc+ca．19．已知二次函数f（x）=ax2+bx+1，a，b∈R，当x=﹣1时，函数f（x）取到最小值，且最小值为0；（1）求f（x）解析式；（2）关于x的方程f（x）=|x+1|﹣k+3恰有两个不相等的实数解，求实数k的取值范围．【解答】解：（1）x=﹣1时，函数f（x）取到最小值，且最小值为0，∴﹣=﹣1，f（﹣1）=a﹣b+1=0，解得a=1，b=2，∴f（x）=x2+2x+1，（2）：f（x）=|x+1|﹣k+3，∴x2+2x+1=|x+1|﹣k+3，即（x+1）2=|x+1|﹣k+3，设|x+1|=t，t≥0，∴t2﹣t+k﹣3=0，∵x的方程f（x）=|x+1|﹣k+3恰有两个不相等的实数解，∴关于t的方程由两个相等的根或有一个正根，∴△=1﹣4（k﹣3）=0，或解得k=，或k＜3，故有k的取值范围为{k|k=，或k＜3}20．设关于x的二次方程px2+（p﹣1）x+p+1=0有两个不相等的正根，且一根大于另一根的两倍，求p的取值范围．【解答】解：关于x的二次方程px2+（p﹣1）x+p+1=0有两个不相等的正根，则△=（p﹣1）2﹣4p（p+1）=﹣3p2﹣6p+1＞0，解得﹣1﹣＜p＜﹣1+，当x1+x2=＞0，及x1x2=＞0时，方程的两根为正．解之，得0＜p＜1．故0＜p＜﹣1．记x1=，x2=，由x2＞2x1，并注意p＞0，得3＞1﹣p＞0，∴28p2+52p﹣8＜0，即7p2+13p﹣2＜0．∴﹣2＜p＜．综上得p的取值范围为{p|0＜p＜}21．已知二次函数f（x）=ax2+bx+c（a≠0），记f[2]（x）=f（f（x）），例：f（x）=x2+1，则f[2]（x）=（f（x））2+1=（x2+1）2+1；（1）f（x）=x2﹣x，解关于x的方程f[2]（x）=x；（2）记△=（b﹣1）2﹣4ac，若f[2]（x）=x有四个不相等的实数根，求△的取值范围．【解答】解：（1）由题意：当f（x）=x2﹣x时，则：f[2]（x）=（x2﹣x）2﹣（x2﹣x）=x4﹣2x3+x；那么：f[2]（x）=x；即：x4﹣2x3+x=x；解得：x=0或x=2．（2）根据新类型的定义：f（f（x））=x，令f（x）﹣x=t，则f（x）﹣t=x，f（x）=t+x，则有：f（t+x）=f（x）﹣t．即a（t+x）2+b（t+x）+c=ax2+bx+c﹣t，化简可得：at2+（2ax+b+1）t=0，解得：t=0或t=．当t=0时，即ax2+bx+c=x，有两个不相同的实数根，可得（b﹣1）2﹣4ac＞0．当t=时，ax2+bx+c=x ，整理可得：，∴△==（b+1）2﹣4ac+4（b+1）=（b﹣1）2﹣4ac﹣4∵有两个不相同的实数根△＞0．∴（b﹣1）2﹣4ac﹣4＞0，即（b﹣1）2﹣4ac＞4．综上所得△=（b﹣1）2﹣4ac的取值范围是（4，+∞）．第11页（共11页）。
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2017-2018 上海市复旦附中高一上学期期中考试Grammar and Vocabulary: (18%)Section A (8%)Directions: Beneath each of the following sentences there are four choices marked A, B, C and D. Choose the one answer that best completes the sentence.21. The discovery of gold in Australia led thousands to believe that a fortune_________.A, had been making B. was making C. was to be made D. would make 22. The president hopes that people will be better off when he quits than when he _________.A. has startedB. startsC. will startD. started23. Travellers to that area can carry disease to their own countries that have never experienced _________.A. themB. itC. themselvesD. itself24. No one can tell the exact number of U.S. pilots and fighter planes ________were lost in the Pearl Harbor air attack.A. whoB. whichC. thatD. what25. ____________, the climbers, who had already conquered many high mountains before, determined to reach the top of the mountain.A. However it was highB. How high it wasC. However high it wasD. However high was it26. They will not allow others to decide the future of their country, _________.A. which is to be knownB. as is to be knownC. as is known to allD. as what is known to all27. We have come to realize that the brain must “forget”some pieces of information ________it can remember others.A. whenB. sinceC. so thatD. if28. They are our school’s volunteers _______to help elderly people cross the streets every day.A. whose task it isB. it is whose taskC. to whom is the taskD. whose task wasSection B (10%)Directions: Complete the following passage by using the words in the box. Each word can be only used once. Note that there is one word more than you need.Sept 27 is World Tourism Day. Of course, travel isn’t a new discovery. Imagine how Italian traveler Marco Polo must have felt when he found himself on Chinese ____29_____, seeing a way of life quite different from anything he’d seen before.And how ___30______ must it have been to listen to Zhang Qian when he returned to China from his journey through Central Asia and West Asia? His brainmust have been packed with everything he’d seen and heard, leading to the ____31_____ of the Silk Road.Travel is one of the most exciting experiences a human being can have. Nowadays, more people are traveling than ever before. By train, plane and car, people all around the globe are ____32_____ to places that people didn’t even know ____33_____ a few centuries ago, or only knew from books.Some people have traveled all over the world, and travel is a way of life to them. They perhaps know what to expect before they travel. That’s why the best travel is when it’s for the first time. Imagine a person who has always wanted to travel to the United States. Of course, they’ve probably seen the Statue of Liberty a thousand times on the TV, and the White House, and all the other famous _______34__. But none of that would compare to the ___35______ of looking out of the cabin window as the plane lands, watching the cities and streets of the real America come into_____36____.Although travel is often just for fun, it’s also ____37_____. We may not know that we are getting an education, but we still are.We’re learning every day: new words in a new language, new people, and new ways of life. But this learning takes place in the school of the world, not the classroom. One of the lessons we learn is ____38_____ a moral one. As we get to know foreign places, we come to understand that there are many different ways to live, and that the way we live isn’t necessarily the best way. The British politician Benjamin Disraeli summed this up well when he said, “Travel teaches toleration.”Ⅲ.Reading Comprehension (40%)Section ADirections : For each blank in the following passages there are four words or phrases marked A,B,C and D. Fill in each blank with the word or phrases that best fits the context.( A )Leif Erickson reached North America around the year 1000, but the attempt to explore was started slowly. It would be five centuries __(39)__ other Europeans landed on that continent.Why were Europeans the ones to __(40)__ to the American? The Chinese and Arabs had the _(41)__ and technology to sail across the seas. __(42)__ of them tool regular voyages in the Indian Ocean and the Asian Pacific for trade. But exploration? By the mid-15th century China had followed the closed-door policy to __(43)__ itself from the rest of the world. The Arabs, with access to the minerals and spices (香料) of Africa and the Far East, saw no __(44)__ to journey into the unknown.Europe, ____(45)________ needed gold and silver; its mines could not meet the demand for coinage. Ottoman Turks blocked the routes across the land to Asia. Only the sea held the ___(46)_____of new wealth.With the return of Magellan’s ships in 1522 from its voyage around the world, the belief was __(47)__ that the oceans were interconnected, promising the age ofdiscovery. The English, as well as the Spanish, Portuguese and French, __(48)__ themselves to finding the “river of the west” through North America to the east.39. A. after B. since C .before D .when40. A .push B .pull C .draw D .drive41. A .sources B .resources C .substances D .matters42. A .Neither B .Both C .Any D .None43. A .prevent B .protect C .isolate D .differ44. A .access B .admission C .application D .association45. A .as a matter of fact B . in other wordsC. for one thing D .on the other hand46. A .symbol B .impression C .promise D .reflection47. A .extended B .estimated C .attracted D .accepted48. A .contributed B .devoted C .referred D .connected( B )Those who keep their word become the most important members of an organization. People come to rely on and trust them. They can be ____(49)____.___(50)______you make a promise , be sure to keep it. When you keep your promise, no matter how much ___(51)_______it takes, you will be rewarded.Whenever you say no, stand upon that as well. In a way, a no is also a promise. A good, _____(52)____no can be very important in building trust.Agreements are also important. Whenever you enter an agreement, live by it, ______(53)____you are not too happy with the deal after making the deal, you still live by it. In the long run, your integrity will _____(54)____.Victoria was the manager of a supermarket. She set out to do that ____(55)_____. She was very careful, however, of not _____(56)_____. When she did, she moved mountains to make sure that she came through. After a while, the stone employee came to trust and respect her like no______(57)_____they had ever had. The teamwork became magical. People followed her example by living up to their word. She ____(58)______what she said, and people appreciated that.49. A. counted B. counted on C. depended D. numbered50.A. As far as B. Though C. Whenever D. However51.A. pain B. ache C. effort D. money52. A. loud B. clean C. sharp D. loose53. A. As B. As if C. Just as D. Even if54. A. set off B. show off C. pay off D. take off55. A. thoroughly B. entirely C. wholly D. totally56. A. lying B. overpromising C. underestimating D. overlooking57. A. manager B. employee C. supermarket D. others58. A. believed B. trusted C. meant D. promisedSection BDirections : Read the following passages. Each passage is followed by 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 few years ago, Paul Gerner began to gather a group of architects in Las Vegas to ask them what it would take to design a public school that used 50 percent less energy, cost much less to build and obviously improved student learning. “I think half of them fell off their chairs,” Gerner says.Gerner manages school facilities for Clark County, Nevada, a district roughly the size of Massachusetts. By 2018, 143,000 additional students will enter the already crowded public-education system. Gerner needs 73 new schools to house them. Four architecture teams have nearly finished designing primary school prototypes （原型）; they plan to construct their schools starting in 2009. The district will then assess how well the schools perform, and three winners will copy those designs in 50 to 70 new buildings.Green schools are appearing all over, but in Clark County, which stands out forits vastness(广阔), such aggressive targets are difficult because design requirements like more natural light for students go against the realities of a desert climate. “One of the biggest challenges is getting the right site orientation,”Mark McGinty, a director at SH Architecture, says. His firm recently completed a high school in Las Vegas. ”You have the same building, same set of windows, but if its orientation is incorrect and it faces the sun, it will be really expensive to cool.”Surprisingly, the man responsible for one of the most progressive green-design competitions has doubts about ideas of eco-friendly buildings. “I don’t believe in the new green religion,” Gerner says. “Some of the building technologies that you get are impractical. I’m interested in those that work.”But he wouldn’t mind if some green features inspire students. He says he hopes to set up green energy systems that allow them to learn about the process of harvesting wind and solar power. “You never know what’s going to start the interest of a child to study math and science,” he says.59. How did the architects react to Gerner’s design requirements?A .They lost balance in excitement.B .They showed strong disbelief.C .They expressed little interest.D .They burst into cheers.60. Which order of steps is followed in carrying out the project?A .Assessment —Prototype —Design —Construction.B .Assessment —Design —Prototype —Construction.C .Design —Assessment —Prototype —Construction.D .Design —Prototype —Assessment —Construction.61 What makes it difficult to build green schools in Clark County?A .The large size.B .Limited facilities.C .The desert climate.D .Poor natural resources.62. What does Gerner think of the ideas of green schools?A .They are questionable.B .They are out of date.C .They are advanced.D .They are practical.(B)Spring is in the air, as is romance. Perhaps you're even thinking of taking the plunge and making a honey trip with your significant other?Before you do, why not take a look at a list of the top three places in the world to propose(求婚)? With suggestions for traditionalists and private types, you just might find the perfect spot to pop the question.New YorkIf you pay attention to romantic comedies, New York is the place for romance. Ever since the Dutch first entered this harbor in 1624 it has become a historiclandmark and a must visit dreamland. Every stretch of this island is packed full of fun that will keep everyone busy. T ake a leaf out of sleepless in Seattle and head to the top of the Empire State Building at night, or how about run to your loved one on the streets of NYC this New Years even like in when harry Met Sally?ParisSweeping views? Check. Grand old stately home? Check. Luxurious spots to propose? check. pack your passports and say goodbye to your daily routine life-it's less than three hours to Paris from London by Eurostar. Famous for its breathtaking architecture, and many cultural attractions, France's capital is a must-see destination. While we're not suggesting you climb the Eiffel Tower for the big moment. There's a reason why this is the city of love, if you keep your proposal original. So gentleman, take your lady to the Louvre, turn your back on the Mona Lisa and declare she is more beautiful than the famous work of art.Las VegasDo you want to bundle the proposal and wedding all-in-one? plead to. Las Vegas, get down on one knee, show your love and get married in less time than it takes to order 'honeymoon suit’ and if it doesn't work out. There's still plenty of entertain. Once the playground of the rich and famous, from Elvis Presley to Marilyn Monroe, Las Vegas now attracts millions of visitors by its bright lights and thrills each year. Whether you're to try your luck at the casinos (赌场), or watch a show, there's a wonder to explore in Las Vegas.63. Which of the following city on the top-3 list would be the ideal place for film fans to propose?A. New YorkB. Paris.C. Las Vegas.D. None.64. Which place is recommended for a proposal in the passage?A. On the top of the Eiffel TowerB. In the Eurostar train from LondonC. Any luxurious spot in PairsD. In front of the Mona Lisa in the Louvre64. As a perfect place for propose, Las Vegas will provide you with all the following EXCEPT.A. a honeymoon suiteB. a package weddingC. a bundle of flowersD. various ways to entertain( C )Do you look happy? angry? Have you ever wondered how you know what another person’s mood is just by looking at his or her face? Studies have shown that one instantaneously (瞬间地) and subconsciously makes a determination of another person’s mood just by glancing at the position and appearance of both the eyebrows and mouth. But what if only the position of the eyebrows was varied , and not the mouth? Would you still be able to determine his or her mood or personalityjust by seeing the eyebrows?Observe the four faces shown below. Notice how each face has exactly the same shape. the same smile, and the same eyes. The only difference between each of the faces is the position of the eyebrows.Low, flat eyebrows that hang over the eyes indicate tiredness, while an eyebrow that is highest in the middle denotes sadness. Downward slanting eyebrows show anger, while highly arched eyebrows show happiness.Frequently, malposition of the eyebrows, such as eyebrow sagging(下垂) and upper eyelid fullness, can be overlooked when considering facial aging and expression. Furthermore, the heavy eyebrow skin pushed the eyelid down causing a tired appearance.To avoid eyebrow sagging, many people raise their eyebrows to remove the brow and eyelid skin from their visual space. These people eventually develop wrinkles in the forehead due to the constant movement of the muscles that raise the eyebrow. In addition, there are those who are sensitive to light and frequently’squint(斜视) and squeeze’ their eyes. This effectively pulls the eyebrows down and leads to wrinkles between the eyebrows and at the corners of the eyes.Botox is an effective measure for fine lines of the forehead and lines between the eyebrows. Botox works by freezing the muscle movement for several months. For the purpose of creating a more pleasant appearance, the best correctivemeasure is brow-lift surgery.66. What can this passage be?A. An advertisementB. A magazine articleC. A business reportD. A scientific report67. A person’s eyebrows that hang over the eyes low and flat can cause a(n) _________appearance.A. sadB. tiredC. happyD. angry68. What is the purpose of the passage?A. T o explain the fact that varied eye position can tell a person’s mood.B. To arouse people’s interest in the best way of removing wrinkles in the forehead and between the eyebrows.C. T o explain what leads to wrinkles in the forehead and near the eyebrow.D. T o enable people to know how to avoid developing fine lines on their faces.69. If the passage continues, what would the writer most likely discuss in the next paragraph?A. Facial agingB. Eye operationC. Brow life surgeryD. Face-lifts.( D )The past ages of man have all been carefully labeled by anthropologists. Descriptions like ‘Palaeolithic Man’, ‘Neolithic Man’, etc., neatly sum up wholeperiods. When the time comes for anthropologists to turn their attention to the twentieth century, they will surely choose the label ‘Legless Man’. Histories of the time will go something like this: ‘in the twentieth century, people forgot how to use their legs. Men and women moved about in cars, buses and trains from a very early age. There were lifts and escalators in all large buildings to prevent people from walking. This situation was forced upon earth dwellers of that time because of miles each day. But the surprising thing is that they didn’t use their legs even when they went on holiday. They built cable railways, ski-lifts and roads to the top of every huge mountain. All the beauty spots on earth were ruined by the presence of large car parks.’The future history books might also record that we were deprived of the use of our eyes. In our hurry to get from one place to another, we failed to see anything on the way. Air travel gives you a bird’s-eye view of the world—or even less if the wing of the aircraft happens to get in your way. When you travel by car or train a blurred (="not" clear) image of the countryside constantly smears the windows. Car drivers, in particular, are forever obsessed with the urge to go on and on: they never want to stop. Is it the lure of the great motorways, or what? And as for sea travel, it hardly deserves mention. It is perfectly summed up in the words of the old song: ‘I joined the navy to see the world, and what did I see? I saw the sea.’The typical twentieth-century traveler is the man who always says ‘I’ve been there. ’You mention the remotest, most evocative (引起记忆的) place-names in the world like El Dorado, Kabul, Irkutsk and someone is bound to say ‘I’ve been there’—meaning, ‘Idrove through it at 100 miles an hour on the way to somewhere else.’When you travel at high speeds, the present means nothing: you live mainly in the future because you spend most of your time looking forward to arriving at some other place. But actual arrival, when it is achieved, is meaningless. You want to move on again. By traveling like this, you suspend all experience; the present ceases to be a reality: you might just as well be dead. The traveler on foot, on the other hand, lives constantly in the present. For him traveling and arriving are one and the same thing: he arrives somewhere with every step he makes. He experiences the present moment with his eyes, his ears and the whole of his body. At the end of his journey he feels a delicious physical weariness. He knows that sound. Satisfying sleep will be his: the just reward of all true travellers.70. Anthropologists label nowadays’ men ‘Legless’ because _________.A. people forget how to use his legs.B. people prefer cars, buses and trains.C. lifts and escalators prevent people from walking.D. there are a lot of transportation devices.71.Why does the author say ‘we are deprived of the use of our eyes’?A. People won’t use their eyes.B. In traveling at high speeds, eyes become useless.C. People can’t see anything on his way of travel.D. People want to sleep during travelling.72. Travelling at high speed means _________.A. people’s focus on the futureB. a pleasureC. satisfying drivers’ great thrillD. a necessity of life73.What's the best title of the passage?A. More haste, less speedB. Modern means of transportation make the world a small placeC. Eyes open and mind broadenD. The only way to travel is on foot.( 以下各题请务必做在答卷纸上)Ⅰ. Grammar (8%)\One of the main points of traveling is to relax and take a break from your normal daily life. (1)__________the truth is, we’re not always free to do what we like when travelling to a foreign country, and a US tourist learned that the hard way.On Aug 12, the unnamed 41-year-old man was beaten by a passerby after he was seen giving Nazi salutes(纳粹礼) again and again on a street in Dresden, Germany.Ever since the end of World WarⅡ, Germany has strict laws (2)_________(forbid) the Nazi salute, as well as other symbols of Nazism.In fact, most countries have their own taboos. If you plan to travel overseas, it’s best to get familiar with these taboos(3)______________you start touring local sites.Below, TEENS gives some examples.SingaporeYou can get (4) ________(fine) fore a lot things in Singapore, including feeding birds, spitting , urinating (小便)in public, smoking in public , not flushing a public toilet after you use it, and eating or drinking on buses or trains.JapanYou’re not supposed to wear your shoes in someone’s house, but you’re not supposed to take your shoes off (5)________the house either. Instead, there’s a small areas inside the door called a “ genkan” which is (6)__________your shoes should go. If you’re still not sure where that is , pay attention to what other people do and do the same.FranceFrench people don’t like (7)________when you talk about money. It’s OK if you say that you want to quit a job because you (8)___________(pay) little money, but you should never say the exact amount. Money is a “ dirty” topic in France.Ⅱ. Recitation (4%)In western cultures, (1)_______eye contact in conversation is necessary. As a matter of fact, a westerner might consider a lack of eye contact as a lack of interest. In Spain, Italy and Greece, where people stand close together talking to each other, eye contact is more frequent and lasts longer.In many Asian cultures, people avoid eye contact to show respect. It is done when talking with anyone in (2)__________or with anyone older.Habits like this can cause problems when people do not understand them. For example, an Asian person might close his or her eyes in (3) ___________ or look down while listening to a speaker. A Western speaker might thing the person is not interested.Eye contact is a (4) ___________ thing. A lack of eye contact may be considered impolite. But if you stare at others, it is also considered rude and should be avoided. Ⅲ. Translation (20%)1. 在炎热的夏日，将食物放在冰箱被认为是保藏食物最行之有效的方法。