复旦附中2017-2018学年高一期中考

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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。

上海复旦大学附属中学2017-2018学年高一上学期期中英语试题(解析版)

上海复旦大学附属中学2017-2018学年高一上学期期中英语试题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.1.The discovery of gold in Australia led thousands to believe that a fortune_ .A. had been makingB. was makingC. was to be madeD. would make【答案】C【解析】【详解】考查动词时态和非谓语动词。

句意：在澳大利亚发现的黄金使成千上万的人相信会发财。

首先主句为一般过去时，fortune 这里表示财富，因为在澳大利亚发现金子，所以在那里“将会”发财故应用be to do sth.“要做某事”，表示将来。

且fortunate与make构成被动关系，故应用to be done结构，且从句应跟随主句用一般过去时。

故选C。

2.The president hopes that the people will be better off when he quits than when he_______.A. has startedB. startsC. startedD. will start【答案】C【解析】【详解】考查时态。

句意：总统希望在他下台的时候人们要比他上台的时候更富有。

根据句意可知他已经是总统了，那么他上台是一个过去发生的事情，故使用一般过去时。

故选C项。

3.Travellers to that area can carry disease to their own countries that have neverexperienced_____.A. themB. itC. themselvesD. itself 【答案】A【解析】【详解】考查代词。

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．。

2017_2018上海复旦附中高中一年级上期中考试

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 make22. 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 t he 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 wordSept 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 havebeen 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 per haps 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 politi cian 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 worl d, 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 the m 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 b iggest 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 beli eve 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 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 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 leadsto 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. Bu t 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 seatravel, 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 tr aveler 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, 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 wasseen 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。

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)

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( )
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．
BCD、由ห้องสมุดไป่ตู้可知：BCD项肯定有弹力，因为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．F与分析不符，故C错误；
D．2 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t2时刻运动员以速度v2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（）

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）。

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