2017年复旦附中新高一闯关练习解析版(含答案)

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2017-2018学年上海复旦附中高一(上)期末数学试卷(解析版)

2017-2018学年上海复旦附中高一（上）期末数学试卷一、选择题（本大题共4小题，共12.0分）1.下列函数中，在区间（0，+∞）上为增函数的是（）A. B. C. D.2.已知函数y=x2-2x+3在闭区间[0，m]上有最大值3，最小值2，则m的取值范围是（）A. B. C. D.3.如果函数y=f（x）图象上任意一点的坐标（x，y）都满足方程 lg（x+y）=lg x+lg y，那么正确的选项是（）A. 是区间上的减函数，且B. 是区间上的增函数，且C. 是区间上的减函数，且D. 是区间上的减函数，且4.若函数f（x）的反函数为f-1（x），则函数f（x-1）与f-1（x-1）的图象可能是（）A. B. C. D.二、填空题（本大题共12小题，共48.0分）5.函数f（x）=的定义域是______．6.函数y=x2+2（-1≤x≤0）的反函数是f-1（x）=______．7.设，，则f（x）•g（x）=______．8.若正数a、b满足log a（4b）=-1，则a+b的最小值为______．9.幂函数f（x）=（t3-t+1）x3t+1是奇函数，则f（2）=______．10.函数的单调递减区间是______．11.函数y=的值域是______．12.设关于x的方程|x2-6x+5|=a的不同实数解的个数为n，当实数a变化时，n的可能取值组合的集合为______．13.对于函数f（x）=x2+ax+4，若存在x0∈R，使得f（x0）=x0，则称x0是f（x）的一个不动点，已知f（x）在x∈[1，3]恒有两个不同的不动点，则实数a的取值范围______．14.若函数f（x）=|x-1|+m|x-2|+6|x-3|在x=2时取得最小值，则实数m的取值范围是______．15.已知函数f（x）是定义在R上的奇函数，当x＞0时，f（x）=x2-ax+a，其中a∈R．①f（-1）=______；②若f（x）的值域是R，则a的取值范围是______．16.已知函数，x∈[1，2]的最大值为f（t），则f（t）的解析式为f（t）=______．三、解答题（本大题共5小题，共60.0分）17.已知关于x的不等式log2（-2x2+3x+t）＜0，其中t∈R．（1）当t=0时，求该不等式的解；（2）若该不等式有解，求实数t的取值范围．18.已知函数（x＞0）．（1）求函数f（x）的反函数f-1（x）；（2）若x≥2时，不等式＞恒成立，求实数a的范围．19.某市环保部门对市中心每天的环境污染情况进行调查研究后，发现一天中环境综合污染指数f（x）与时刻x（时）的关系为，x∈[0，24），其中a是与气象有关的参数，且∈，．若用每天f（x）的最大值为当天的综合污染指数，并记作M（a）．（1）令t=，x∈[0，24），求t的取值范围；（2）求M（a）的表达式，并规定当M（a）≤2时为综合污染指数不超标，求当a 在什么范围内时，该市市中心的综合污染指数不超标．20.指数函数y=g（x）满足g（2）=4，且定义域为R的函数是奇函数．（1）求实数m、n的值；（2）若存在实数t，使得不等式f（t2-2t）+f（2t2-k）＞0成立，求实数k的取值范围．21.设集合M为下述条件的函数f（x）的集合：①定义域为R；②对任意实数x1、x2（x1≠x2），都有＜．（1）判断函数f（x）=x2是否为M中元素，并说明理由；（2）若函数f（x）是奇函数，证明：f（x）∉M；（3）设f（x）和g（x）都是M中的元素，求证：F（x）=＜也是M中的元素，并举例说明，G（x）=＞不一定是M中的元素．答案和解析1.【答案】A【解析】解：A.在（0，+∞）上是增函数，满足条件，B．y=（x-1）2在（-∞，1]上为减函数，在[1，+∞）上为增函数，不满足条件．C．y=x-2在（0，+∞）上为减函数，不满足条件．D．y=log0.5（x+1）在（0，+∞）上为减函数，不满足条件．故选：A根据函数单调性的性质分别进行判断即可．本题主要考查函数单调性的判断，根据常见函数的单调性是解决本题的关键．比较基础．2.【答案】C【解析】解：作出函数f（x）的图象，如图所示，当x=1时，y最小，最小值是2，当x=2时，y=3，函数f（x）=x2-2x+3在闭区间[0，m]上上有最大值3，最小值2，则实数m的取值范围是[1，2]．故选：C．本题利用数形结合法解决，作出函数f（x）的图象，如图所示，当x=1时，y最小，最小值是2，当x=2时，y=3，欲使函数f（x）=x2-2x+3在闭区间[0，m]上的上有最大值3，最小值2，则实数m的取值范围要大于等于1而小于等于2即可．本题考查二次函数的值域问题，其中要特别注意它的对称性及图象的应用，属于中档题．3.【答案】C【解析】解：由lg（x+y）=lgx+lgy，得，由x+y=xy得：，解得：x+y≥4．再由x+y=xy得：（x≠1）．设x1＞x2＞1，则=．因为x1＞x2＞1，所以x2-x10，x2-1＞0．则，即f（x1）＜f（x2）．所以y=f（x）是区间（1，+∞）上的减函数，综上，y=f（x）是区间（1，+∞）上的减函数，且x+y≥4．故选：C．由给出的方程得到函数y=f（x）图象上任意一点的横纵坐标x，y的关系式，利用基本不等式求出x+y的范围，利用函数单调性的定义证明函数在（1，+∞）上的增减性，二者结合可得正确答案．本题考查了函数单调性的判断与证明，考查了利用基本不等式求最值，训练了利用单调性定义证明函数单调性的方法，是基础题．4.【答案】A【解析】解：函数f（x-1）是由f（x）向右平移一个单位得到，f-1（x-1）由f-1（x）向右平移一个单位得到，而f（x）和f-1（x）关于y=x对称，从而f（x-1）与f-1（x-1）的对称轴也是由原对称轴向右平移一个单位得到即y=x-1，排除B，D；A，C选项中各有一个函数图象过点（2，0），则平移前的点坐标为（1，0），则反函数必过点（0，1），平移后的反函数必过点（1，1），由此得：A选项有可能，C 选项排除；故选：A．f（x）和f-1（x）关于y=x对称是反函数的重要性质；而将f（x）的图象向右平移a 个单位后，得到的图象的解析式为f（x-a）而原函数和反函数的图象同时平移时，他们的对称轴也相应平移．用整体平移的思想看问题，是解决本题的关键．5.【答案】{x|x≥-2且x≠1}【解析】解：由题意，要使函数有意义，则，解得，x≠1且x≥-2；故函数的定义域为：{x|x≥-2且x≠1}，故答案为：{x|x≥-2且x≠1}．由题意即分母不为零、偶次根号下大于等于零，列出不等式组求解，最后要用集合或区间的形式表示．本题考查了求函数的定义域，最后要用集合或区间的形式表示，这是容易出错的地方．6.【答案】，x∈[2，3]【解析】解：∵y=x2+2（-1≤x≤0）∴x=-，2≤y≤3，故反函数为，x∈[2，3]．故答案为：，x∈[2，3]．由原函数的解析式解出自变量x的解析式，再把x和y交换位置，注明反函数的定义域（即原函数的值域）．本题考查反函数的求法，考查计算能力，是基础题，反函数的定义域容易疏忽出错，注意反函数的定义域是原函数的值域．7.【答案】x，x∈（1，+∞）【解析】解：∵，，∴f（x）的定义域是（1，+∞），g（x）的定义域是[1，+∞），∴f（x）•g（x）=x，x∈（1，+∞），故答案为：x，x∈（1，+∞）．根据f（x），g（x）的解析式求出f（x）•g（x）的解析式即可．本题考查了求函数的解析式问题，考查函数的定义域，是一道基础题．8.【答案】1【解析】解：根据题意，若正数a、b满足log a（4b）=-1，则有a=，即ab=，则a+b≥2=1，即a+b的最小值为1；故答案为：1．根据题意，由对数的运算性质可得a=，即ab=，进而由基本不等式的性质可得a+b≥2=1，即可得答案．本题考查基本不等式的性质以及应用，涉及对数的运算性质，关键是分析a、b的关系．9.【答案】2【解析】解：函数f（x）=（t3-t+1）x3t+1是幂函数，∴t3-t+1=1，解得t=0或t=±1；当t=0时，f（x）=x是奇函数，满足题意；当t=1时，f（x）=x4是偶函数，不满足题意；当t=-1时，f（x）=x-2是偶函数，不满足题意；综上，f（x）=x；∴f（2）=2．故答案为：2．根据幂函数的定义求出t的值，再验证f（x）是否为奇函数，从而求出f（2）的值．本题考查了幂函数的定义与应用问题，是基础题．10.【答案】（-2，1]【解析】解：要求函数的单调递减区间，需求函数y=，（8+2x-x2＞0）的增区间，由8+2x-x2＞0可得-2＜x＜4，对应的二次函数，开口向下，增区间为：（1，4），减区间为：（-2，1]．由复合函数的单调性可知：函数的单调递减区间是：（-2，1]．故答案为：（-2，1]．由对数函数为增函数，要求复合函数的减区间，需求真数的减区间，分式的分母的增区间，利用函数的定义域以及二次函数的单调性转化求解即可．本题考查复合函数的单调性，分式函数、二次函数和对数函数的单调性，是中档题．11.【答案】（-1，）【解析】解：函数y===-1．∵2x+3＞3，∴0＜．∴函数y=的值域是（-1，）故答案为（-1，）分离常数后，根据指数函数的值域即可求函数y的范围．本题考查分离常数法转化为指数函数的值域的运用，属于基础题．12.【答案】{0，2，3，4}【解析】解：关于x的方程|x2-6x+5|=a，分别画出y=|x2-6x+5|与y=a的图象，如图：①若该方程没有实数根，则a＜0；n=0；②若a=0，则该方程恰有两个实数解，n=2；③若a=4时，该方程有三个不同的实数根，n=3；④当0＜a＜4，该方程有四个不同的实数根，n=4；⑤当a＞4，该方程有两个不同的实数根，n=2；n的可能取值组合的集合为{0，2，3，4}故答案为：{0，2，3，4}．将方程|x2-6x+5|=a的实数解的个数问题转化为函数图象的交点问题，作图分析即得答案．本题考查了根的存在性及根的个数判断．华罗庚曾说过：“数缺形时少直观，形缺数时难入微．数形结合百般好，隔离分家万事非．”数形结合是数学解题中常用的思想方法，能够变抽象思维为形象思维，有助于把握数学问题的本质．13.【答案】，【解析】解：根据题意，f（x）=x2+ax+4在[1，3]恒有两个不同的不动点，得x=x2+ax+4在[1，3]有两个实数根，即x2+（a-1）x+4=0在[1，3]有两个不同实数根，令g（x）=x2+（a-1）x+4．在[1，3]有两个不同交点，∴，即，解得：a∈[-，-3）；故答案为：[-，-3）．不动点实际上就是方程f（x0）=x0的实数根．二次函数f（x）=x2+ax+4有不动点，是指方程x=x2+ax+4有实根．即方程x=x2+ax+4有两个不同实根，然后根据根列出不等式解答即可．本题考查了二次函数图象上点的坐标特征、函数与方程的综合运用，解答该题时，借用了一元二次方程的根的判别式与根这一知识点．14.【答案】[5，+∞）【解析】解：当x＜1时，f（x）=1-x+2m-mx+18-6x=19+2m-（m+7）x，当1≤x＜2时，f（x）=x-1+2m-m，x+18-6x=17+2m-（m+5）x，f（1）=12+m，2≤x＜3时，f（x）=x-1+mx-2m+18-6x=17-2m+（m-5）x，f（2）=7，当x≥3时，f（x）=x-1+mz-2m+6x-18=-19-2m+（m+7）x，f（3）=m+2，若函数f（x）=|x-1|+m|x-2|+6|x-3|在x=2时取得最小值，则解得m≥5，故m的取值范围为[5，+∞），故答案为：[5，+∞），根据条件可得，化为分段函数，根据函数的单调性和函数值即可得到则解得即可．本题考查了函数最值和绝对值函数，并考查了函数的单调性，属于中档题．15.【答案】-1；（-∞，0]∪[4，+∞）【解析】解：①函数f（x）是定义在R上的奇函数，当x＞0时，f（x）=x2-ax+a，其中a∈R，f（-1）=-f（1）=-（1-a+a）=-1；②若f（x）的值域是R，由f（x）的图象关于原点对称，可得当x＞0时，f（x）=x2-ax+a，图象与x轴有交点，可得△=a2-4a≥0，解得a≥4或a≤0，即a的取值范围是（-∞，0]∪[4，+∞）．故答案为：①-1 ②（-∞，0]∪[4，+∞）．①运用奇函数的定义，计算即可得到所求值；②由f（x）的图象关于原点对称，以及二次函数的图象与x轴有交点，由判别式不小于0，解不等式即可得到所求范围．本题考查函数的奇偶性的运用，考查函数的值域的应用，注意运用二次函数的性质和对称性，考查运算能力，属于中档题．16.【答案】，，＜＜，【解析】解：根据题意，函数，其导数g′（x）=（t-1）+=，令h（x）=（t-1）x2+4，令h（x）=0，即（t-1）x2+4=0可得，x2=，分5种情况讨论，①，t＞1时，h（x）=（t-1）x2+4为开口向上的二次函数，在[1，2]上，有h（x）＞0，则有g′（x）＞0，函数g（x）为增函数，则g（x）在[1，2]上的最大值为g（2）=2（t-1）-=2t-4，②，t=1时，h（x）=4，在[1，2]上，有h（x）＞0，则有g′（x）＞0，函数g（x）为增函数，则g（x）在[1，2]上的最大值为g（2）=2（t-1）-=2t-4，③，0≤t＜1时，h（x）=（t-1）x2+4为开口向下的二次函数，且h（0）=4，且h（2）=t ＞0，则在[1，2]上，有h（x）＞0，则有g′（x）＞0，函数g（x）为增函数，则g（x）在[1，2]上的最大值为g（2）=2（t-1）-=2t-4，④，当-3＜t＜0时，h（x）=（t-1）x2+4为开口向下的二次函数，令h（x）=0，即（t-1）x2+4=0可得x=±，有1＜＜2，则有在[1，）上，有h（x）＞0，则有g′（x）＞0，函数g（x）为增函数，在（，2]上，有h（x）＜0，则有g′（x）＜0，函数g（x）为减函数，此时g（x）在[1，2]上的最大值为g（）=-4，⑤，当t≤-3时，h（x）=（t-1）x2+4为开口向下的二次函数，令h（x）=0，即（t-1）x2+4=0可得x=±，此时≤1，在[1，2]上，有h（x）＜0，则有g′（x）＜0，函数g（x）为减函数，此时g（x）在[1，2]上的最大值为g（1）=t-5；综合可得：；故答案为：．根据题意，由函数g（x）的解析式，对其求导可得数g′（x）=（t-1）+=，令h（x）=（t-1）x2+4，结合二次函数的性质，对t分5种情况讨论，每种情况下，分析h（x）的符号，即可得g′（x）的符号，分析可得函数g（x）的单调性，即可得g（x）在区间[1，2]上的最大值，综合即可得答案．本题考查函数最值的计算，涉及函数导数的性质以及应用，注意对k进行分类讨论．17.【答案】解：（1）关于x的不等式log2（-2x2+3x+t）＜0，当t=0时，不等式为log2（-2x2+3x）＜0，即0＜-2x2+3x＜1，等价于，解得＜＜＜或＞，即0＜x＜或1＜x＜；∴不等式的解集为（0，）∪（1，）；（2）不等式log2（-2x2+3x+t）＜0有解，∴0＜-2x2+3x+t＜1，化为2x2-3x＜t＜2x2-3x+1；设f（x）=2x2-3x，x∈R，∴f（x）min=f（）=-，且f（x）无最大值；∴实数t的取值范围是（-，+∞）．【解析】（1）t=0时不等式为log2（-2x2+3x）＜0，化为0＜-2x2+3x＜1，求出解集即可；（2）由不等式log2（-2x2+3x+t）＜0有解，得出0＜-2x2+3x+t＜1，化为2x2-3x＜t＜2x2-3x+1；设f（x）=2x2-3x，求出f（x）min即可得出结论．本题考查了对数函数的定义与不等式的解法和应用问题，是中档题．18.【答案】解：（1）∵y=（）2=（1+）2（x＞0）．∴y＞1（2分）由原式有：=，∴x+1=x∴x=（2分）∴f-1（x）=，x∈（1，+∞）（2分）（2）∵（x-1）f-1（x）＞a（a-）∴（x-1）＞a（a-）（x＞0）∴（+1）（-1）＞a（a-）∴+1＞a2-a∴（a+1）＞a2-1（2分）①当a+1＞0即a＞-1时＞a-1对x≥2恒成立-1＜a＜+1②当a+1＜0即a＜-1时＜a-1对x≥2恒成立∴a＞+1此时无解（3分）综上-1＜a＜+1．（1分）a∈，．【解析】（1）从条件中函数式f（x）=（）2=y，（x＞0）中反解出x，再将x，y互换即得f（x）的反函数f-1（x）．（2）利用（1）的结论，将不等式（x-1）f-1（x）＞a（a-）化成（a+1）＞a2-1，下面对a分类讨论：①当a+1＞0；②当a+1＜0．分别求出求实数a的取值范围，最后求它们的并集即可．本小题主要考查反函数、函数恒成立问题等基础知识，考查运算求解能力．求反函数，一般应分以下步骤：（1）由已知解析式y=f（x）反求出x=Ф（y）；（2）交换x=Ф（y）中x、y的位置；（3）求出反函数的定义域（一般可通过求原函数的值域的方法求反函数的定义域）．19.【答案】（本题满分14分）本题共有2个小题，第1小题满分（5分），第2小题满分（9分）．解：（1）当x=0时，t=0；…（2分）当0＜x＜24时，因为x2+1≥2x＞0，所以＜，…（4分）即t的取值范围是，．…（5分）（2）当∈，时，由（1），令，则∈，，…（1分）所以=，，＜…（3分）于是，g（t）在t∈[0，a]时是关于t的减函数，在∈，时是增函数，因为，，由，所以，当时，；当＜时，，即，，＜…（6分）由M（a）≤2，解得．…（8分）所以，当∈，时，综合污染指数不超标．…（9分）【解析】（1）利用取倒数，求导数，确定函数的单调性，可得t的取值范围；（2）分段求出每天的综合放射性污染指数不超过2时a的范围，即可得到结论．本题主要考查了函数模型的选择与应用及分类讨论的思想，考查学生分析解决问题的能力，属于中档题．20.【答案】解：（1）∵指数函数y=g（x）满足：g（2）=4，∴g（x）=2x；∴f（x）=是奇函数．∵f（x）是奇函数，∴f（0）=0，即=0，∴n=1；∴f（x）=，又由f（1）=-f（-1）知=-，∴m=2；（2）由（1）知f（x）==-=-+易知f（x）在（-∞，+∞）上为减函数．又∵f（x）是奇函数，从而不等式：f（t2-2t）+f（2t2-k）＞0等价于f（t2-2t）＞-f（2t2-k）=f（k-2t2），∵f（x）为减函数，∴t2-2t＜k-2t2，∴k＞3t2-2t=3（t-）2-，∴k＞-．【解析】（1）根据指数函数y=g（x）满足：g（2）=4，即可求出y=g（x）的解析式；由题意知f（0）=0，f（1）=-f（-1），解方程组即可求出m，n的值；（2）由已知易知函数f（x）在定义域f（x）在（-∞，+∞）上为减函数．我们可将f （t2-2t）+f（2t2-k）＞0转化为k＞3t2-2t，根据二次函数的性质即可得到实数k的取值范围．本题考查的知识点：待定系数法求指数函数的解析式，函数的奇偶性和函数单调性的性质，体现了转化的思想，考查了运算能力和灵活应用知识分析解决问题的能力，属中档题．21.【答案】解：（1）函数f（x）=x2的定义域为R，由f（x1）+f（x2）=x12+x22，f（x1+x2）=（x1+x2）2=x12+x1x2+x22，f（x1+x2）-f（x1）-f（x2）=-x12+x1x2-x22=-（x1-x2）2＜0，即有f（x1+x2）＜f（x1）+f（x2），则函数f（x）=x2为M中元素；（2）证明：函数f（x）是奇函数，定义域为R，且f（-x）=-f（x），图象关于原点对称，若x＞0时，f（x1+x2）＜f（x1）+f（x2），则x＜0时，f（x1+x2）＞f（x1）+f（x2），则条件②不满足，则f（x）∉M；（3）证明：设f（x）和g（x）都是M中的元素，当x1，x2对应的点在f（x）或g（x）的图象上，由题设可得结论成立；若x1，x2对应的点一个在f（x）图象上，一个在g（x）的图象上，由f（x1）+g（x2）＞g（x1）+g（x2）＞g（x1+x2），或f（x1）+g（x2）＞f（x1）+f（x2）＞f（x1+x2），由题设可得结论成立，综上可得F（x）=＜也是M中的元素；比如：f（x）=x2，g（x）=（x+3）2，如x≥-1.5，可得G（x）=x2，x＜-1.5，可得G（x）=（x+3）2，取x1=-2，x2=-1，可得x1+x2=-，G（-）=，f（x1）+f（x2）=+=1，可得f（x1+x2）＞f（x1）+f（x2），则G（x）不一定为M中的元素．【解析】（1）函数f（x）=x2的定义域为R，运用作差法结合新定义，即可得到结论；（2）运用奇函数的图象关于宇原点对称，即可得证；（3）运用新定义和分类讨论，即可得证；举例f（x）=x2，g（x）=（x+3）2，如x≥-1.5，可得G（x）=x2，x＜-1.5，可得G（x）=（x+3）2，取x1=-2，x2=-1，即可得到结论．本题考查新定义的理解和运用，考查作差法和举反例法，考查推理能力和运算能力，属于中档题．。

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年复旦附中浦东分校高一摸底考试(含答案+阅读部分解析)

复旦附中浦东分校高一摸底（2017.09）时间：90分钟满分：100Ⅰ.Choice(30%)1. ----What are you worrying about?-----_________you can return the book to me in time.A. IfB. WhetherC. WhenD. Where2. ---When did you your uncle arrive________China?---He got to Guangzhou the morning of the 16th of April.A. at……inB. in…..inC. to….onD. in….on3. The family _________at the lunch table when someone came to tell them what had happened at _____________.A. was sitting ……..Mr. BrownB. were sitting…..Mr. Brown’sC. was sitting……..Mr. BrownD. was sitting …….Mr. Brown’s4. I am going to Florida and stay for a week.___________you are there, would you please buy some stamps for me?A. IfB. WhileC. SinceD. As soon as5. Could you give me ________second chance please?A. anB. /C. theD. a6. Black, ___________father of _______Tom, lost his new watch.A. /……. /B. the ……theC. the……/D. /…..the7. The book __________you want is on the desk. Which of the following isn’t right?A. thatB. whichC. /D. it8. The number of people who __________cars of their own is increasing.A. hasB. haveC. there isD. there are9. The train _________she was travelling was five minutes late.A. thatB. on thatC. by whichD. on which10. ________either you or I good at drawing?A. AmB. AreC. IsD. Do11. Last month Miss Han ________a doctor.A. married withB. married toC. was married withD. got married to12. In our country every boy and every girl __________the right to receive school education.A, has B. have C. is D. are13. This kind of T-shirt is __________.A. easily worn outB. easy worn outC. easy to worn outD. easily to be worn out14. The buses ________over 2 thousand people a day.A. takeB. bringC. carryD. sent15. The boy said he wouldn’t eat _______.A. any longerB. no longerC. any moreD. no more16. They_________3000 English words by the end of next month.A. learnedB. had learnedC. will learnD. will have learned16. They _________3000 English words by the end of next month.A. learnedB. had learnedC. will learnD. will have learned17. We can’t buy ________much mutton with _______little money.A. so……muchB. such…..soC. so……soD. such ……such18. -----Look! The man at the gate ________be our headmaster. He is always standing there every morning.-------No, it ________be him. He is holding a meeting in the office now.A. must……can’tB. must …….mustn’tC. can’t……can’tD. can’t mustn’t19. __________the teacher in their school is about 200 and one fourth of them are __________teachers.A. A number of ……..womenB. A number of ……womanC. The number of …….womenD. The number of …….woman20. He is an expert at chemistry. We all call him a _____________.A. chemistryB. chemicalC. chemistD. physician21. My TV is out of order. Can you tell me what the __________news about Irap War is?A. latelyB. latestC. laterD. latter22. She __________her living by playing the piano in a nightclub. Which of the following is wrong?A. earnedB. madeC. gainedD. obtained23. When anything goes wrong, the blames usually __________the youngest brother.A. goes intoB. comes downC. falls behindD. falls on24. In spite of the hard winter the rosebush still stays _________.A. livingB. aliveC.livelyD. live25. After being questioned for hours, the criminal __________his guilty to the police at last.A. admittedB. admiredC. affectedD.affected D. allowed26. There must be misunderstanding between them. Their quarrel just __________it.A. originated inB. resulted inC. led toD. brought in27. On hearing the favorable news, his anger _________and he burst out laughing.A. vanishedB. fadedC. burstD. exploded28. This detective story keeps you in ________till the last chapter.A. supplyB.supportC. suspenseD. surprise29. What is the most important of all is the way _________you communicate with people.A. /B. in whereC. in thatD. which30. ___________others is considered rude and should be avoided as soon as possible.A. ObservingB. Looking atC. Staring atD. WatchingⅡ.ClozeI realized I was holding an apple tree in the palm of my land. A little ___31___with the potential to become a beautiful big tree-----a tree that could ____32___thousands of apples in its lifetime. Thousands of apples, each _____33____several seeds, each capable of growing a new tree which again could ___34_______thousands of apples. Why then the world wasn’t filled with apples trees?It is a rule of nature that only a few of these seeds grow. Most never do or are destroyed early on in their ____35_____.And it came to my mind it’s quite often so with people’s dreams also. Wonderful ideas come to our minds but they die too soon-------we don’t tend to the little saplings, we don’t protest tem as we should. And then one day we ____36_____what happened to our dreams -----why did they never come true?I put the apple seed on the table, and ____37_____to see how the light was reflected from it, this nature’s tiny wonder. I wondered when someone was ____38_____growing apples , how many times they had to try to get a seed to germinate (发芽)? How much did it _____39_____?Maybe it was like with our___40______: the seeds of your dreams did not automatically grow. Planting an apple tree, it might take many tries, You might meet dozens of people until you met the true______41_____.But if you kept on snowing the seeds of your dream, one day you would succeed. And after that others comment you were lucky to be successful---when in fact you probably __42______more often than you would like to _____43_____.But you were good at falling -----you learned, you adapted, and then with your new knowledge you tried again. And again. And again. And one day ___44_____was yours.I picked up the apple seed again----but instead of throwing it away I took an empty flower pot, ____45_____some earth into it and planted the seed. Maybe one day it would grow into a proud tree. I’d never know if I didn’t try.31. A. water B. seed C. soil D. peel32.. A. plant B. explore C. increase D. grow33. A. folding B. covering C. containing D. eating34. A. produce B. pollute C. consume D. accomplish35. A. process B. growth C. product D. relation36. A. conclude B. argue C. affirm D. wonder37. A. look up B. peer at C. bent down D. faced up38. A. thoughtfully B. seriously C. definitely D. desperately39. A. inqure B. require C. decline D. establish40. A. purchase B. desire C. approaches D. dreams41. A. apples B. emotion C. friend D. rival42. A. disappeared B. emerged C. admitted D. failed43. A. describe B. write C. accompany D. count44. A. appreciation B. devotion C. success D. tiredness45.A. carried B. held C. picked D. pouredⅢ.Reading (30%)(A)There's something rotten in Rio里约（巴西旧首都）and the smell is coming from the huge stacks of rubbish pried up（撬开）on sidewalks all over the city. Rio's street sweepers chose the carnival holiday to demand better salaries. Their wages start at roughly $400 a month.There could hardly be a better time for them to prove their importance. The streets were left a mess after hundreds of carnival parades and now, rubbish pries up in both poor and uptown neighborhoods and in tourist areas like Ipanema（伊巴内玛）（巴西城市）or Copacabana beach.（科帕卡巴纳滩）The president of Rio's rubbish collecting company has even appealed to the population to store rubbish at home whenever possible. He says 30% of the city's sweepers have gone on strike. Some of those who have been working have been threatened by the strike movement so now the police has been deployed alongside rubbish collectors to keep them sage（他们的安全）as they go about their business.The strike has divided opinions in Rio. On social media, many support the sweepers' demands for better salaries. Others say they are opportunists and the situation is a big embarrassment to the city.But Brazil's culture of littering the streets doesn't help. A video that went viral online shows that even authorities have a problem with that. Rio's mayor, Eduardo Paes, is seen throwing what seemed to be the rest of an apple on the sidewalk--and now promised to impose himself a fine for his wrongdoing. His government recently created a programme to keep Rio's residents from littering the streets.46. Rio's street cleaners go on strike to______________.A．prove their importance B．threaten the governmentC．ask for higher salaries D．appeal to the public not to litter47. The reason why the police are involved is that______________A．the police are called out to put down the riotB．the police are required to protect some cleanersC．the police are to collect rubbish for the time beingD．the police are sent to arrest people who litter around48. The author's attitude to Brazil's culture of littering is _____________________. A．hopeless B．approving C．critical D．optimistic(B)As a senior, my future is always on my mind. To be exact, thoughts of the future have kept me up countless nights and made me worry enough to do poorly on more than one test. Because of this, words of wisdom are a source of comfort. Steve Jobs gave a speech to Stanford’s graduating class in 2005 and his words resound repeatedly in my mind whenever I think about my future.It wasn’t always like that, though. It started when I became a junior, when college came into view. It’s the first big step to making your life your own. So when Jobs discussed his life as a student, some fears were eased. He, too, felt the need to attend college to make something of himself. He faced what many are extremely afraid of: uncertainty. His lack of understanding caused him to stop attending college and focus on what he felt was important. His story had a happy ending, of course, since he certainly turned out well.This doesn’t mean that students shouldn’t attend college, but rather that they shouldn’t worry so much. You’ll get where you need to go, even if your path is a bit more winding（蜿蜒的）than you’d like.Jobs talked about the hardships in his work. His love of his work helped him carry on and he got where he was meant to be, which restates the point: don’t panic.One particular part of his speech stayed with me. Steve Jobs quoted（引用）the saying “Stay hungry, stay foolish” （好学若饥、谦卑若愚）and it has become my motto. Staying foolish is realizing that you are still a fool, no matter how much you’ve learned or experienced. There is always more to explore. Staying hungry is wanting to find those things about which you are still uneducated.Steve Jobs’s level of success is attainable, and I aim to prove that. With the will power to go into the world living every day like it’s my last and allowing the future to take care of itself, I will do great things. In the last moments of my life, I’ll be proud of what I have done and hope to have all the wisdom a person could wish for.49. The author felt worried when _________.A．he had to take tests at schoolB．he thought about his futureC．he had lots of sleepless nightsD．he searched for words of wisdom50. It is suggested in Paragraphs 1 and 2 that _________.A．Steve Jobs didn’t attend collegeB．Steve Jobs failed because of his decisionC．the author is a college studentD．the author cares much about his future51. What did the author gain from Jobs’s speech?A．Courage to drop out of school.B．Confidence in defeating Jobs.C．Interest in computer industry.D．Bravery to face uncertainties.52. What did NOT Steve Jobs encourage students to do in his speech?A．Have the desire to learn more.B．Be content with what they know.C．Stay calm in the face of hardships.D．Be modest so as to learn more.(C)DEPARTMENT OF HEALTHHONG KONGIMPORTANT NOTICE TO ALL PERSONSARRIVING IN HONG KONGDuring your stay outside Hong Kong, you may have been exposed to certain infectious （感染）diseases without your knowledge.In case you develop any symptom (症状) such as fever, chills, skin troubles or vomiting within 14 days of your arrival in Hong Kong, you should consult a doctor or attend an accident & emergency department/general out-patient clinic.Please bring along this card.CHIEF PORT HEALTH OFFICERThe Port Health OfficeTheir staff (clerks) are glad to answer your questions about travel health.Please enquire at :―Hong Kong Island18/F Wu Chung House, 213 Queen's Rd. East, Wanchai.Tel: 2961 8840-----KowloonRoom 905, Government Offices, Canton RoadTel: 2368336153. According to the passage, you may get some infectious disease___________.A. when arriving in Hong KongB. before you understanding themC. within 2weeks of your arriving in Hong Kong.D. before arriving in Hong Kong54. If you find any symptom, which of the following places is not the place where you should go?A. The hospitalB. The accident & emergency departmentC. The Port Health OfficeD. The clinic55. Where can a foreigner read this kind of notice?A. At the CustomsB. At hospitalC. On 18 F, Wu Chung House, 213 Queen’s Rd, East, WanchaiD. In Room 905, Government Offices, Canton Road, Kowloon.56. Which of the following is NOT true?A. Skin rash is an infections diseaseB. There are two Departments of Health, one in Hong Kong Island and the other in Kowloon.C. You may have some trouble without this card when you go to hospital.D. It is very possible that you get some infectious disease but you don’t know.(D)A man may usually be known by the books he reads as well as by the company he keeps, for there is a companionship of books as well as of men; and one should always live in the best company , whether it be of books or of men.A good book may be among the best of friends. It is the most patient and cheerful ofcompanions. It always receives us with the same kindness; amusing and instructing us in youth, and comforting us in age.Men often discover their similarity to each other by the common love they have for a book just as two persons sometimes discover a friend by the admiration which both entertain for a third. There is an old proverb, “Love me, love my dog.” But there is more wisdom in this: “Love my, love my book.” The book is a truer and higher bond of union. Men can think, feel, and sympathize with each other through their favorite author. They live in him together, and he in them.A good book is often the best container of a life preserving the best that life could think out; for the world of a man’s life is, for the most part, but the world of his thoughts. Thus the best books are treasuries of good words, the golden thoughts, which become our steady companions and comforters.Books are by far the most lasting products of human effort. Temples and statues decay, but good books survive. Time is of no account with great thoughts, which are as fresh today as when they first passed through their author’s minds, ages ago.The great and good do not die, even in this world. Preserved in books, their spirits walked abroad. The book is a living voice. It is an intellect(智者) to which one still listens.57. The writer introduces the topic of the passage by_____________.A．describing life experience of great writersB．telling his own story of reading good booksC．presenting the best thoughts in good booksD．comparing good books to good friends in life58. What does the underlined sentence in Paragraph 3 mean?A．Readers feel sympathy for the author.B．Readers live together with the author.C．Readers and the author share the same feeling.D．Readers are the author’s companions and comforters.59. Which of the following is TRUE according to the passage?A．We can learn about the great and good through books.B．The most important part of a man’s life is his treasures.C．Good books help us to know about their authors’ friends.D．Books are often regarded as best containers in our life.60. The passage mainly tells us that _____________ .A. one should have some good friendsB one should read as many books as possibleC. one should keep company with good booksD books are the most lasting products of human effortsⅣ.Fill in the blanks with words given in their proper forms (10%)1. ________ (judge) from his accent, he must be from Guangdong.2. Those who commit crimes, ___________ (bring) to justice sooner or later.3. When the audience heard the funny story , they ________（burst）into laughter.4. I ________ （try）my best to overcome difficulties instead of waiting for others to help me.5. When I was at college I _________(speak) three foreign languages, but I_________(forget) all except for a few words of each.6. ------Have you moved into the new house?-------Not yet. The rooms __________(pair).7. The police found that the houses __________（break）into and a lot of things ________(steal).8. The volleyball match will be put off if it _________ (rain).Ⅴ.Translation (15%)1. 他好像已经得了感冒。

【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。

上海复旦大学附属中学2017-2018学年高一下学期期末考试英语试题详解

复旦大学附属中学2017学年第二学期高一年级英语期末考试试卷II.Grammar and vocabulary(31’)Section ADirections:Beneath each of the following sentences there are four choices marked A,B,C andD.Choose the one answer that best completes the sentence.1.As a modest person,the woman scientist,though renowned worldwide,is___________to take all the praises and honors.A.reluctantB.contentC.hesitantD.welcome2.Universal themes like“love conquers all”,“good vs.evil”and“from rags to riches”etc.enhance the timelessness of great works of literature,because they are___________to us all.A.belongedB.relatedC.adaptedD.added3.A classic is a book that has stood the___________of time,a book that men and women all over the world would want to keep all their lives for its special enlightenment and insights.A.testB.limitC.journeyD.loss4.I'd like a friendship that might lead to something deeper,but I wouldn't want to myself too soon.A.expressB.sparemitD.excuse5.In the face of President Richard Nixon’s___________efforts to cut back on welfare and other federal programmers for the needy,Edward emerged as the persistent champion of the poor.binedB.determinedC.requiredD.endured6.Back in the days when energy was cheap,home builders didn’t worry much about___________cracks in the wall,thanks to which the air in the room was replaced by fresh outdoor air.A.uncoveredB.unsealedC.untouchedD.unfinished7.Motorists are being warned to take extra care on minor roads across the county as many remain as___________as old.A.obviousB.adventurousC.distractingD.treacherous8.Most of the locals hold the view that great changes___________when the new recycling system is introduced.A.will be bound to occurB.are bound to occurC.will be bound to be occurredD.are bound to be occurred9.A weak currency reduces household___________power by making imports expensive,thereby___________import-competing state-owned enterprises and boosting exports’profits.A.manufacturing…guardingB.consuming…hurtingC.producing…defendingD.purchasing…protecting10.When diseases tear away at your body,you can have confidence in a healing system that is beautifully designed to meet its problems and has___________of value to offer in the treatment.A.somehowB.somewhatC.sometimesD.something11.So much of interest___________that most visitors simply run out of time before seeing it all.A.offers the cityB.for the city to offerC.does the city offerD.the city does offer12.The“one country,two system”policy is an unprecedented political and social formula___________are capitalist and socialist systems found coexisting under“one country”today.A.never everB.so farC.nowhere elseD.no longer13.When the recorded data of the scandal about the president was collected,the length of tapes was___________ the Atlantic Ocean.A.as deep as35timesB.as35times deep asC.35times the depth ofD.35times the depth as14.At the personal level,the main health problem is apparently lack of activity.___________that the problem of obesity causes a variety of illness,including heart attack.A.No less is the fact obviousB.No less obvious is the factC.Less is the fact obviousD.Less obvious is the fact15.The only thing___________spend money on that will make you richer is traveling.A.you canB.can youC.you wouldD.would you16.The Christmas of1949we didn’t have a tree.My dad had as much pride as anybody,so,I suppose,he___________just say that we___________one.A.had better…couldn’t have affordedB.oughtn’t to…couldn’t have affordedC.wouldn’t…couldn’t affordD.would rather…couldn’t afford17.Celebrities and people in the news have___________been targets of privacy invasion,concerns about which, however,have redoubled in the Internet age.A.recentlyB.soonC.previouslyD.long18.Despite our celebrity-driven culture,fame is anything but a(n)___________source of happiness,whichdepends much more on our basic sense of self,and connection with other people.A.permanentB.alternativeC.enjoyableD.primary19.The Road of Death in Bolivia gets its scary name because of the high accident rate.___________,it seems like tourists will continue visiting this weird road.WHICH IS WRONG?A.NeverthelessB.StillC.MeanwhileD.All the same20.The clergyman often preaches his religion to the people___________measure of your life will not be in what you accumulate,but what you___________.A.where…pick upB.that…give awayC.where...set asideD.that…live up to21.The popular internet slang“foxi”somewhat reflects a“demotivational culture”,___________people pretend to keep a wise attitude toward failure___________because they’re incapable of succeeding.A.that...especiallyB.in that...excessivelyC.where...simplyD.so that...mainlySection B(10’)Directions:（Complete the following passage by using the words in the box.Each word can only be used once.Note that there is one word more than you need.）A.voiceB.preferredC.conveyD.identity AB.featuring AC.advertised AD.wardrobe BC.media BD.united CD.practical ABC.recentNow that the temperature has started to rise,it’s time to put on our casual and cool T-shirts.But to stand out from the crowd this season,you should consider adding a slogan(标语)T-shirt to your_____22_____.From headlines and hashtags(贴文标签)to popular quotes,many words have leapt from_____23_____onto our clothing.In April,New York magazine came up with a creative idea–turning headlines from its fashion section into slogan T-shirts.But slogan T-shirts certainly aren't_____24_____creations.Although they're believed to have been the idea of small1960s London fashion store Mr.Freedom,British designer Katherine Hamnett first introduced them to the wider world in the1980s.''The slogan T-shirt was something to give you a(n)_____25_____...in one,you could be read from200yards(about183meters)away,''she recently told the BBC.However,people have been using_____26_____ways to send political messages far before slogan T-shirts came along.''In the19th century before women had the vote,they would use umbrellas that represented their_____27_____candidate,''Steven Fielding,professor of political history at the University of Nottingham,told Elle magazine.Indeed,fashion has always been about self-expression.And slogan items have become a way to_____28_____messages without the need to scream and shout.''Sometimes we talk about serious stuff,and sometimes fun things,''Swedish designer Annika Berger told the Guardian.British designer Viet Tran shared his story of making fun T-shirts with Elle.Graduating from college,he couldn't afford a cool T-shirt,so he and his friends just made their own,_____29_____slogans such as,''He's your man.''Tran told the magazine.''It was an inside joke that_____30_____us as a group.''British fashion expert Natalie Kingham also agreed that slogan items provide a(n)______31______platform.So,if you want to share your thoughts with the world,a slogan T-shirt is certainly a good way to start.III.Reading Comprehension(43’)Section A(15’)Directions: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 phrase that best fits the context.Take a Chance:Seize That Opportunity in4Steps1Get yourself prepared(and keep your eyes open).Malcolm Gladwell said it in Outliers,and I’ll say it again:It takes time,about10,000hours of practice,to make perfect.This is no small___32___of your life energy,however,it___33___to spend time thinking about the kinds of opportunities you want to prepare yourself for.If you’re an advocate,what do you want to say to those senators? Start saying it now,even if you’re speaking to an empty room.Once you’ve put in the time___34___,discerning what kind of opportunity you’re seeking,keep your eyes open,because opportunity has an unexpected way of___35___.2Realize that you’ll never be totally___36___(In other words,you may fail.)Even if you’re a professional figure skater who has put in10,000hours of ice time,it will still feel___37___ to take the ice for your Olympic program-you may hit a rough patch and fall flat.Most of the world will see your stumble as a reason for you to give up.However,the best skaters take a___38___and keep going with a smile.I’s tough to smile right after you’ve made a mistake,but think of it this way:Is there anything a(n)___39___loves better than a good comeback?Asauthor Mark Batterson writes,“Our best days often start out as our worst days.And our greatest opportunities are often___40___as our biggest problems.”3Anthropomorphize the critical voices and then put a lid on them.“You can’t do it”and“You’re ridiculous to even____41____.”...The critical voices of your teachers and the not-so-____42____friends are all in your head when you’re trying to seize an opportunity.Instead of letting their negativity take control,try to____43____one of the voices and imagine it as a mouse. Pick it up by the tail and drop it into a container.Then another...And so on...Then put the lid on,and watch all these mouse people,clawing at the glass,jabbering away...”4Put up a fight and believe.(Let your second self have a turn on the chance floor.)If you want to influence a senator’s vote,or win an Olympic gold medal,you cannot allow doubts and fears to drag you down.Let something else guide you.True,you do have a self that wants to flee from a challenge.Yet you____44____have a self that wants to meet that same challenge head-on.As Martha Beck,Ph.D.writes in Steering by Starlight,“Scholars...who study human happiness hold that we are most joyful when we’re intensely____45____on something that is almost too tough to do...”Get to know that second self.Befriend it as you would a new____46____.Chances are that second self will be the one turning the knob when opportunity knocks.32.A.loss B.source C.business D.investment33.A.averages B.pays C.happens D.matters34.A.generously B.anywhere C.beforehand D.efficiently35.A.showing up B.turning around C.slipping away D.giving in36.A.satisfied B.dissuaded C.conquered D.prepared37.A.honorable B.painful C.terrifying D.privileged38.A.chance B.step C.fall D.turn39.A.winner B.audience C.professional D.opponent40.A.mistaken B.disguised C.sought D.skipped41.A.deny B.ask C.risk D.try42.A.supportive B.ridiculous C.reliable D.practical43.A.isolate B.identify C.enclose D.drown44.A.partly B.actually C.also D.seldom45.A.judging B.deciding C.concentrating D.agreeing46.A.acquaintance B.appearance C.presence D.circumstanceSection B(24’)Directions: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)Dear Cutie-Pie,Recently,I was searching for an answer on Google.Half way through entering the question.Google returned a list of the most popular searches in the world.At the top of the list was“How to keep him interested.”Surprised a lot,1scanned several of the countless articles about how to be sexy and sexual,when to bring him a beer versus a sandwich,and the ways to make him feel smart and superior.And I got angry.Little One,it is not,has never been,and never will be your job to“keep him interested.”Little One,your only task is to know deeply in your soul—in that unshakeable place that isn’t upset by rejection and loss-that you are worthy of interest.If you can trust your worth in this way,you will be attractive in the most important sense of the world:you will attract a boy who is both capable of interest and who wants to spend his one life investing all of his interest in you.Little One,I want to tell you about the boy who doesn’t need to be kept interested,because he knows you are interesting.I don’t care if he can’t play a bit of golf with me—as long as he can play with the children you give him and revel in all the glorious and frustrating ways they are just like you.I don’t care if he doesn’t follow his wallet—as long as he follows his heart and it always leads him back to you.I don’t care if he is strong—as long as he gives you the space to exercise the strength that is in your heart.I couldn’t care less how he votes—as long as he wakes up every morning and daily elects you to a place of honor in your home and a place of respect in his heart.I don’t care about the color of his skin.I don’t care if he was raised in this religion or that religion or no religion.Little One,if you come across a man like that and he and I have nothing else in common,we will have the most important thing in common:You.Because in the end,Little One,the only thing you should have to do to“keep him interested”is to be you.Your eternally interested guy47.What annoyed the writer when he was surfing on the Internet?A.“How to keep him interested”is most frequently searched,B.Girls are rejected constantly even if they try to please boys.C.The upsetting list of know-how to please boys provided for girls.D.People think girls should give priority to pleasing their boys.48.According to the writer,to attract a boy,the girl just needs to__________.A.add to her own sexual attractionB.have full confidence in her own worthC.invest time in caring for her loved oneD.find a boy to interest her for her lifetime49.What is of fundamental importance that the boy is expected to have in common with the writer?A.He will be responsible for the girl.B.He will like the girl for what she is.C.He will hold the girl in high respect.D.He will earn enough to support his family.50.The writer of the letter is__________of the addressee Cutie-pie.A.the counselorB.the boy friendC.the fatherD.a net friend(B)EssayRailair Link Railair LinkHeathrow Airport(All terminals)→Reading Valid from Dec1st,2014to Jan.31st,2015Reading→Heathrow Airport(All terminals) Valid from Dec1st,2014to Jan,31st,2015Mondays to Fridays Mondays to FridaysTerminal Terminal Terminal Terminal Reading Reading Terminal Terminal Terminal Terminal 4depart2depart3depart1depart arrive depart1arrive2arrive3arrive4arrive06350645065207000750 07300720072707350835 07500800080708150905 08200830083708450935then at the same minutes past each hour until 21502200220722152305 2250230023072315000505300615061706200630 06000645064706500700 06300730073207350745 07000800080208050815 07300830083208350845 08000900090209050915 0845093009320935094509151000100210051015then at the same minutes past each hour until2045213021322135214521452230223222352245 Saturdays and Sundays(Also Bank Holidays)Saturdays and Sundays(Also Bank Holidays)Terminal 4Terminal Terminal Terminal Reading Reading Terminal Terminal TerminalTerminal4depart2depart3depart1depart arrive depart1arrive2arrive3arrive arrive06500700070707150805 07200730073707450835 07500800080708150905then at the same minutes past each hour until 21502200220722152305 2250230023072315000505450630063206350645 06150700070207050715 06450730073207350745then at the same minutes past each hour until 20452130213221352145 21452230223222352245For more information please telephone Reading0734-*******The British Railway Board accepts no responsibility for any inaccuracy in the information contained in this guide, which may be altered at any time without notice. Published by InterCity,a business section of the British Railway Board.Customers should check in at the Railair waiting-room at Reading Station at least15minutes before departure of the coach.Please purchase a ticket before boarding the coach.51.On December25th,2014,the earliest service from Heathrow Terminal1to Reading is available at__________.A.7:15B.7:00C.6:50D.6:3552.If you are to reach Terminal2of the Heathrow Airport before10:00a.m.,you need to get to Reading Station not later than__________.A.8:20a.m.B.8:45a.m.C.9:00a.m.D.9:15a.m.53.What services are the timetables for?A.InterCity ticket offices at Heathrow airport and Reading station.B.Coaches between Heathrow airport terminals and Reading station:C.Shuttle buses between the four terminals of Heathrow Airport.D.Trains of Railair Link between Heathrow Airport and Reading.(C)Have you ever noticed how the recital(叙说)of an adventure always finds ready audience?The man with a story of some stirring adventure always takes the floor Men will stop the most important discussion to listen. Women will forget to rock the cradle.Boys and girls will neglect any sport or game.Try it sometime and see how it grips all kinds and all ages.And the reason is that none of us ever really grows up.We are always boys and girls,a little older in years,but with the same nature—alert to the new,questioning,investigating,growing,living;stirred by martial music;thrilled by the sight of the fire-houses dashing madly down the street;lured by tales of subtle intrigue(阴谋)and splendid daring.It would be sad if men and women ever lost this capacity to be attracted by tales of heroism.The man whose heart leaps for joy at the sight of a heroic deed is the man who will act the hero when his turn comes.No,the love of adventure will never be lost.It is a fundamental part of human nature,just as sentiment(感情)is.So we reasoned that a magazine edited for this universal hunger of human nature for adventure ought to have a wide appreciation and appeal,and we decided to publish such a magazine and call it ADVENTURE.It is published as a magazine wherein thousands of men and women can find adventure without being obliged to read through large amounts of stuff they care little about for the sake of getting a little they care a lot about, which is frankly made for the hours when the reader cannot work,or does not wish to,or is too weary to work and made for the reader’s recreation rather than his or her creative hours.If you care for stirring stories(and who does not?)—if you wish to get away for a brief time from the hard grind of the daily mill so that you can come back to it again with renewed passion and courage to walk through the knotty problems and nagging limitations,get a copy of Adventure.You can get away for such a trip every month for15cents or you can get a season ticket entitling you to twelve trips for$1.50.No other kind of story in the magazine;just Adventure Stories.Fact-stories as well as fictionstories.If you don’t like that kind,don’t buy;but if you do like that kind,Adventure is sure to delight you.54.Which of the following statement is TURE about man’s sense of adventure?A.People are increasingly attracted by adventures as they grow.B.The sense of adventure is rooted in a childhood curiosity.C.Adventure stories are more attractive when told with sentiment.D.Only children with curiosity grow into adults fond of adventures.55.What’s the meaning of“grip”in the first paragraph?A.to draw a clear line betweenB.to capture the attention ofC.to affect the way people thinkD.to give equal treatment to56.In what way does the writer think the magazine ADVENTURE can affect its readers?A.It reminds its work-burdened life driven readers of good old days.B.It helps them regain their adventurous selves lost in tough life.C.It offers a refreshing escape from long weary working hours.D.It encourages them to face the toughness of life and work.57.What is NOT TRUE about the purchase of Adventure?A.One can buy one copy for15cents.B.Adventure is available one issue a month,C.It contains fictional and true stories.D.Season ticket holders can enjoy free tours.58.What is the main purpose of this article?A.To instruct publishers in how to produce a popular magazine.B.To explore the psychological cause and impact of adventure.C.To attract potential readers by giving the editorial philosophy.D.To recommend to working people a refreshing way of recreation.Section C(4’)Directions:（Read the following passage.Fill in each blank with a proper sentence given in the box.Each sentence can be used only once.Note that there are two more sentences than you need.）Many of today’s young people have a difficult time seeing any moral element in their actions.There are a number of reasons why that’s true,but none more influential than an approach that fails to teach children the traditional moral values that bind our country together as a society and a culture.That failed approach,called “decision-making”introduced25years ago,tells children to decide for themselves what is right and what is wrong. It replaced“character education”,which encouraged them to practice habits of courage,justice and self-control._____59_____.Decision-making curriculums pose moral dilemmas(两难)to students,leaving them with the impression that all questions of right and wrong are in dispute._____60_____.The assumption behind this method is that students will arrive at good moral conclusions if only they are given the chance.But the actual result is moral confusion.A recent national study revealed that a majority of boys considered rape to be acceptable under certain conditions. Astoundingly,many of the girls agreed.This kind of moral illiteracy is further encouraged by values-education programs that are little more than courses in self-esteem.______61______.But it is just as reasonable to make an opposite assumption:namely,that a child who has uncritical self-regard will conclude that he or she can’t do anything bad.Such naive self-acceptance results in large part from the non-directive,non-judgmental,as-long-as-you-feel-comfortable-with-your-choices mindset that has dominated public education for the last two and one-half decades.Many of today’s drug education,sex education and values-education courses are based on the same1960s philosophy that helped fuel the explosion in teen drug use and sexual activity in the first place.It is time to throw the trend of“decision making”and“non-judgmentalism”to the ash heap of failed policies and return to a proved method.Character education provides a much more realistic approach to moral formation. ______62______.A.A common approach of these programs is to provide a list of principles,pillars,values or virtues,around which themed activities are planned.B.These programs are based on the questionable assumption that a child who feels good about himself or herself won’t want to do anything wrong.C.A person who exhibits personal qualities a society considers desirable is considered to have good character--and developing such qualities is often seen as a purpose of education.D.In the1940s,when character education prevailed,teachers worried about students chewing gum;today they worry about robbery and rape.E.Youngsters are encouraged to question values and virtues they’ve never acquired in the first place or upon which they have only a weak hold.F.It is built on an understanding that we learn morality not by debating it but by practicing it.IV.Grammar in passage(10)Directions:（After reading the passage below,fill in the blanks to make the passage coherent and grammatically correct.For the blanks with a given word,fill in each blank with the proper form of the given word;for the other blanks,useone word that best fits each blank.）For many of us,it’s easy to tell if it’s a computer that is calling you on your phone.Its voice makes it obvious ______63______it has the chance to finish telling you that you can get a free loan or that you are invited for a customer survey.It’s also easy to hang up-it’s just a computer,after all.______64______Google Duplex,an artificial intelligence(AI)voice assistant,has shown that computers are able to“conduct a natural conversation with a human over the phone and complete simple real-world tasks,”reported tech site Wired.On May8during its annual developer conference Google IO,the company showed Duplex making phone calls and having full conversations,______65______it made an appointment with a hair dresser,before making a reservation at a restaurant.As CNET noted,not only has Google changed the typical______66______(computerize)voice,but the company has taken“extra steps to disguise the system to sound______67______(much)like a human”.Duplex comes with imperfections-“umms”and“uhhs”-and uses typical human phrasing such as“Oh,gotcha.”As a result,“the receptionists on the other end of the call have no idea they are conversing back and forth______68______AI,”commented CNET.Some see Duplex as quite_____69_____breakthrough-it will be able to help humans cut down on boring tasks.But for the rest,it“straddles(跨越)a fine line between being convenient and deceptive,”as Wired wrote. People have a hard enough time knowing whether news is real or fake,or what photos are______70______(trust). And now,we may not be able to trust our own ears.Google also mentioned that soon,Duplex will be able to imitate the owner’s voice.While this is a great step forward in AI,it also raises many concerns.For example,students______71______use Duplex to call their school to pretend they’re sick by using their mother’s or father’s voice.Since people are shocked by the fact that a machine can imitate a human so well,Google has promised that in the future the voice will tell the listener that it’s not a real person.According to Alexander Rudnicky,a researcher of human-computer speech interaction at Carnegie Mellon University,technology like this is________72________that people are only going to become more aware of."We just assimilate(吸收this interaction into our culture,"he told Wired.V.Translation(3+4+4+5=16’)Directions:Translate the following sentences into English,using the words given in the brackets.73.就像苦口的良药，中肯的建议往往不受最需要它的人欢迎。

2016-2017学年上海市复旦大学附属中学高一上学期期中考试数学试卷含详解

复旦附中高一期中数学卷一.填空题1.集合{1,2,3,,2015,2016}⋅⋅⋅的子集个数为________2.已知全集U =R ，集合{|1}A x x =≤，集合{|2}B x x =≥，则()U C A B =________3.已知集合{|12}A x x =≤≤，集合{|}B x x a =≤，若A B ⋂≠∅，则实数a 的取值范围是________4.如果全集{,,,,,}U a b c d e f =，{,,,}A a b c d =，{}A B a = ，(){}U C A B f = ，则B =________5.已知210a a >>，210b b >>，且12121a a b b +=+=，记1122A a b a b =+，1221B a b a b =+，12C =，则、、A B C按从小到大的顺序排列是________.6.已知Rt ABC ∆的周长为定值2，则它的面积最大值为__________.7.我们将b a -称为集合{|}M x a x b =≤≤的“长度”，若集合2{|}3M x m x m =≤≤+，{|0.5}N x n x n =-≤≤，且集合M 和集合N 都是集合{|01}x x ≤≤的子集，则集合M N ⋂的“长度”的最小值是________8.已知{}A x x =>，{|(3)(3)0}B x x x x =-+>，则A B = ________9.对任意两个集合X 与Y ，定义①{X Y x x X-=∈且}x Y ∉，②()()X Y X Y Y X∆=-- ，已知{}2,A y y x x R==∈，{}22B y y =-≤≤，则A B ∆=_________.10.已知常数a 是正整数，集合1{|||,}2A x x a a x Z =-<+∈，{|||2,}B x x a x Z =<∈，则集合A B ⋃中所有元素之和为________11.非空集合G 关于运算*满足：①对任意,a b G ∈，都有a b G *∈；②存在e G ∈使对一切a G ∈都有a e e a a *=*=，则称G 是关于运算*的融洽集，现有下列集合及运算：①G 是非负整数集，*运算：实数的加法；②G 是偶数集，*运算：实数的乘法；③G 是所有二次三项式组成的集合，*运算：多项式的乘法；④{|,}G x x a a b Q ==+∈，*运算：实数的乘法；其中为融洽集的是________12.集合(){},,R A x y y a x x ==∈，(){},,R B x y y x a x ==+∈，已知集合A B ⋂中有且仅有一个元素，则常数a 的取值范围是______________．二.选择题13.已知集合{1,2,3,,2015,2016}A =⋅⋅⋅，集合{|31,}B x x k k Z ==+∈，则A B ⋂中的最大元素是（）A.2014B.2015C.2016D.以上答案都不对14.已知全集U =A B ⋃中有m 个元素，()()U U A B ⋃痧中有n 个元素．若A B ⋂非空，则A B ⋂的元素个数为A.mnB.m n+ C.n m- D.m n-15.命题“已知,x y R ∈，若220x y +=，则0x =且0y =”的逆否命题是（）A.已知,x y R ∈，若220x y +≠，则0x ≠且0y ≠B.已知,x y R ∈，若220x y +≠，则0x ≠或0y ≠C.已知,x y R ∈，若0x ≠且0y ≠，则220x y +≠D.已知,x y R ∈，若0x ≠或0y ≠，则22x y +≠16.对任意实数,,a b c ，给出下列命题：①“a b =”是“ac bc =”的充要条件；②“5a +是无理数”是“a 是无理数”的充要条件；③“a b >”是“22a b >”的充分条件；④“4a <”是“3a <”的必要条件；其中真命题的个数是（）A.1个B.2个C.3个D.4个三.解答题17.已知集合{1,2,3}A =，2{|(1)0,}B x x a x a x R =-++=∈，若A B A ⋃=，求实数a ；18.已知,,a b c R +∈，求证：3332222222()a b c ab a b bc b c ac a c ++≥+++++；19.设正有理数1a21211a a =++，求证：（11a 与2a 之间；（2）2a 比1a20.已知对任意实数x ，不等式2(3)10mx m x --+>成立或不等式0mx >成立，求实数m 的取值范围；21.已知关于x 的不等式2(4129)(211)0kx k k x ---->，其中R k ∈；（1）试求不等式的解集A ；（2）对于不等式的解集A ，记B A Z = （其中Z 为整数集），若集合B 为有限集，求实数k 的取值范围，使得集合B中元素个数最少，并用列举法表示集合B；复旦附中高一期中数学卷一.填空题1.集合{1,2,3,,2015,2016}⋅⋅⋅的子集个数为________【答案】20162【分析】若集合中有n 个元素,则该集合有2n 个子集,显然,集合中的元素有2016个,即2016n =,代入2n 中即可【详解】由题,集合中有2016个元素,所以该集合有20162个子集,故答案为:20162【点睛】本题考查集合的子集个数,属于基础题2.已知全集U =R ，集合{|1}A x x =≤，集合{|2}B x x =≥，则()U C A B = ________【答案】{|12}x x <<【分析】先求的A B ⋃,再求得补集即可【详解】由题,{|1A B x x ⋃=≤或}2x ≥,所以(){}U |12A B x x ⋃=<<ð,故答案为:{|12}x x <<【点睛】本题考查集合的并集、补集运算,属于基础题3.已知集合{|12}A x x =≤≤，集合{|}B x x a =≤，若A B ⋂≠∅，则实数a 的取值范围是________【答案】1a ≥【分析】由A B ⋂≠∅,画出数轴,表示出集合,即可求解【详解】因为A B ⋂≠∅,则画出数轴,并表示出集合,如下:可得1a ≥,故答案为:1a ≥【点睛】本题考查已知交集结果求参数范围,属于基础题4.如果全集{,,,,,}U a b c d e f =，{,,,}A a b c d =，{}A B a = ，(){}U C A B f = ，则B =________【答案】{,}a e 【分析】由题,用维恩图来表示集合,由图即可得到B 集合【详解】由题,将集合用维恩图表示,则{},B a e =,故答案为:{,}a e 【点睛】本题考查图示法处理集合问题,属于基础题5.已知210a a >>，210b b >>，且12121a a b b +=+=，记1122A a b a b =+，1221B a b a b =+，12C =，则、、A B C 按从小到大的顺序排列是________.【答案】B ＜C ＜A【分析】根据题设，取符合题设的特殊值即可快速判断，或者采用排序原理也可判断.【详解】方法一：212112120,0,1a a b b a a b b >>>>+=+= ，不妨令12121212,,,3333a ab b ====，11221221145224,999999A a b a bB a b a b =+=+==+=+=，1 4.529C == ，B C A \<<，故答案为：B ＜C ＜A .方法二：∵210a a >>，210b b >>，∴由排序原理可知：22112112a b a b a b a b +>+，∵12121,1a a b b +=+=，()()1212111221221a a b b a b a b a b a b ∴=++=+++()()()2211211222112a b a b a b a b a b a b =+++<+221112a b a b ∴+>，∴A ＞C ＞B ﹒故答案为：B ＜C ＜A .6.已知Rt ABC ∆的周长为定值2，则它的面积最大值为__________.【答案】3-.【分析】设出三角形的边长，根据周长和勾股定理列方程组，利用基本不等式求得ab 的最大值，进而求得三角形面积的最大值.【详解】设Rt ABC ∆三条边长分别为,,a b c ，其中c 为斜边长，所以2222a b c c a b++=⎧⎨=+⎩，2a b +=，2≥，2≤=-，所以6ab ≤-则三角形的面积132ABC S ab ∆=≤-.故答案为3-.【点睛】本小题主要考查利用基本不等式求三角形面积的最大值，考查直角三角形的性质，考查化归与转化的数学思想方法，属于中档题.7.我们将b a -称为集合{|}M x a x b =≤≤的“长度”，若集合2{|}3M x m x m =≤≤+，{|0.5}N x n x n =-≤≤，且集合M 和集合N 都是集合{|01}x x ≤≤的子集，则集合M N ⋂的“长度”的最小值是________【答案】16【分析】当集合M N ⋂的“长度”的最小值时,M 与N 应分别在区间[]0,1的左右两端,由此能求出M N ⋂的“长度”的最小值【详解】由题,M 的“长度”为23,N 的“长度”为12,当集合M N ⋂的“长度”的最小值时,M 与N 应分别在区间[]0,1的左右两端,故M N ⋂的“长度”的最小值是2111326+-=,故答案为:16【点睛】本题考查交集的“长度”的最小值的求法,考查新定义的合理运用8.已知{}A x x =>，{|(3)(3)0}B x x x x =-+>，则A B = ________【答案】{|30}-<<x x【分析】先分别求解集合中元素的所满足的不等式,再由交集的定义求解即可【详解】由题,因为20xx >-≥⎪⎩,解得1x <,则{}|1A x x =<,因为()()330x x x -+>,解得30x -<<或3x >,则{|30B x x =-<<或}3x >,所以{}|30A B x x ⋂=-<<,故答案为:{|30}-<<x x 【点睛】本题考查集合的交集运算,考查含根式的不等式的运算,考查解高次不等式9.对任意两个集合X 与Y ，定义①{X Y x x X -=∈且}x Y ∉，②()()X Y X Y Y X ∆=-- ，已知{}2,A y y x x R ==∈，{}22B y y =-≤≤，则A B ∆=_________.【答案】[)()2,02-+∞ ，【分析】由A ＝{y |y ＝x 2，x ∈R }＝{y |y ≥0}，B ＝{y |﹣2≤y ≤2}，先求出A ﹣B ＝{y |y ＞2}，B ﹣A ＝{y |﹣2≤y ＜0}，再求A △B 的值．【详解】∵A ＝{y |y ＝x 2，x ∈R }＝{y |y ≥0}，B ＝{y |﹣2≤y ≤2}，∴A ﹣B ＝{y |y ＞2}，B ﹣A ＝{y |﹣2≤y ＜0}，∴A △B ＝{y |y ＞2}∪{y |﹣2≤y ＜0}，故答案为[﹣2，0）∪（2，+∞）．【点睛】本题考查集合的交、并、补集的运算，解题时要认真审题，仔细解答，注意正确理解X ﹣Y ＝{x |x ∈X 且x ∉Y }、X △Y ＝（X ﹣Y ）∪（Y ﹣X ）．10.已知常数a 是正整数，集合1{|||,}2A x x a a x Z =-<+∈，{|||2,}B x x a x Z =<∈，则集合A B ⋃中所有元素之和为________【答案】2a【分析】分别求出集合A 、B 中的元素,再求出集合A 、B 的并集,即可求解【详解】由题,因为12x a a -<+,所以11222x a -<<+,则11|2,22A x x a x Z ⎧⎫=-<<+∈⎨⎬⎩⎭；因为2x a <,所以22a x a -<<,则{}|22,B x a x a x Z =-<<∈,因为常数a 是正整数,所以{}0,,,,2A a a = ,{}21,,0,,21B a a =-+- ,所以{}21,,0,,21,2A B a a a ⋃=-+- ,所以A B ⋃中所有元素之和是2a ,故答案为:2a【点睛】本题考查集合的并集,考查解含绝对值的不等式11.非空集合G 关于运算*满足：①对任意,a b G ∈，都有a b G *∈；②存在e G ∈使对一切a G ∈都有a e e a a *=*=，则称G 是关于运算*的融洽集，现有下列集合及运算：①G 是非负整数集，*运算：实数的加法；②G 是偶数集，*运算：实数的乘法；③G 是所有二次三项式组成的集合，*运算：多项式的乘法；④{|,}G x x a a b Q ==+∈，*运算：实数的乘法；其中为融洽集的是________【答案】①④【分析】逐一验证几个选项是否分别满足“融洽集”的两个条件,若两个条件都满足,是“融洽集”,有一个不满足,则不是“融洽集”【详解】①对于任意非负整数,a b ,则a b +仍为非负整数,即a b G +∈；取0e =,则00a a a +=+=,故①符合题意；②对于任意偶数,a b ,则ab 仍为偶数,即ab G ∈；但是不存在e G ∈,使对一切a G ∈都有ae ea a ==,故②不符合题意；③对于G 是所有二次三项式组成的集合,若,a b G ∈,ab 不再是二次三项式,故③不符合题意；④对于{|,}G x x a a b Q ==+∈,设1x a =+2x c =+,则()(122x x ac bd ad bc ⋅=+++,即12x x G ⋅∈；取1e =,则11a a a ⨯=⨯=,故④符合题意,故答案为:①④【点睛】本题考查对新定义“融洽集”的理解,考查理解分析能力12.集合(){},,R A x y y a x x ==∈，(){},,R B x y y x a x ==+∈，已知集合A B ⋂中有且仅有一个元素，则常数a 的取值范围是______________．【答案】[]1,1-【分析】将A B ⋂中有且仅有一个元素，转化为方程只有一个解，分情况讨论，确定参数范围.【详解】由集合(){},,R A x y y a x x ==∈，(){},,R B x y y x a x ==+∈，且A B ⋂中有且仅有一个元素，a x x a ∴=+只有1个解，若0x ≥，则ax x a =+，1a x a =-，若0x <，则ax x a -=+，1ax a =-+，所以0101a a a a ⎧≥⎪⎪-⎨⎪-≥⎪+⎩或0101aa a a ⎧≤⎪⎪-⎨⎪-≤⎪+⎩或101a a a =⎧⎪⎨-<⎪+⎩或011a a a ⎧≥⎪-⎨⎪=-⎩，解得11a -≤≤，故答案为：[]1,1-.二.选择题13.已知集合{1,2,3,,2015,2016}A =⋅⋅⋅，集合{|31,}B x x k k Z ==+∈，则A B ⋂中的最大元素是（）A.2014B.2015C.2016D.以上答案都不对【答案】A【分析】由题意可知集合B 表示整数的3倍且大1的数的集合,则找到集合A 中符合条件的最大元素即可【详解】由题,因为{|31,}B x x k k Z ==+∈,即为整数的3倍且大1的数的集合,则A B ⋂中的最大元素为2014,故选:A【点睛】本题考查集合的交集定义,属于基础题14.已知全集U =A B ⋃中有m 个元素，()()U U A B ⋃痧中有n 个元素．若A B ⋂非空，则A B ⋂的元素个数为A.mnB.m n+ C.n m- D.m n-【答案】D【详解】因为()()()U UUB A B A ⋃=⋂痧所以()()U UU A B A B ⋂=⋃⎡⎤⎣⎦痧，所以A B ⋂共有m n -个元素，故选D ．15.命题“已知,x y R ∈，若220x y +=，则0x =且0y =”的逆否命题是（）A.已知,x y R ∈，若220x y +≠，则0x ≠且0y ≠B.已知,x y R ∈，若220x y +≠，则0x ≠或0y ≠C.已知,x y R ∈，若0x ≠且0y ≠，则220x y +≠D.已知,x y R ∈，若0x ≠或0y ≠，则22x y +≠【答案】D【分析】直接利用逆否命题的定义得到答案.【详解】己知,x y R ∈，若220x y +=，则0x =且0y =”的逆否命题是：己知,x y R ∈，若0x ≠或0y ≠，则220x y +≠故选D【点睛】本题考查了命题的逆否命题，意在考查学生对于命题基础知识的掌握情况.16.对任意实数,,a b c ，给出下列命题：①“a b =”是“ac bc =”的充要条件；②“5a +是无理数”是“a 是无理数”的充要条件；③“a b >”是“22a b >”的充分条件；④“4a <”是“3a <”的必要条件；其中真命题的个数是（）A.1个B.2个C.3个D.4个【答案】B【分析】利用等式与不等式的性质逐一验证命题的真假即可【详解】①“a b =”⇒“ac bc =”,但当0c =时,“ac bc =”无法推出“a b =”,则“a b =”是“ac bc =”的充分不必要条件,故①是假命题；②“5a +是无理数”⇒“a 是无理数”,且“a 是无理数”⇒“5a +是无理数”,则“5a +是无理数”是“a 是无理数”的充要条件,故②是真命题；③当12a b =>-=时,2214a b =<=,即“a b >”无法推出“22a b >”,且当2241a b =>=时,21a b =-<=,即“22a b >”无法推出“a b >”,则“a b >”是“22a b >”的既不充分也不必要条件,故③是假命题；④因为{}|3a a <{}|4a a <,所以“4a <”是“3a <”的必要条件,故④是真命题；综上,真命题有2个,故选:B【点睛】本题考查命题的真假的判断,考查两命题的充分性和必要性的判断,考查等式与不等式的性质的应用三.解答题17.已知集合{1,2,3}A =，2{|(1)0,}B x x a x a x R =-++=∈，若A B A ⋃=，求实数a ；【答案】1a =或2或3【分析】由A B A ⋃=可得B A ⊆,分别讨论B =∅与B ≠∅的情况,进而求解即可【详解】由A B A ⋃=可得B A ⊆,若B =∅,则()2140a a ∆=+-<,解得a ∈∅；若B ≠∅,则()()10x a x --=,解得1x a =,21x =,①当1a =,则{}1B =,符合题意；②当2a =,则{}1,2B =,符合题意；③当3a =,则{}1,3B =,符合题意；综上,1a =或2或3【点睛】本题考查已知集合的包含关系求参数,考查分类讨论思想18.已知,,a b c R +∈，求证：3332222222()a b c ab a b bc b c ac a c ++≥+++++；【答案】证明见解析【分析】先对33+a b 与22a b ab +作差证明3322a b a b ab +≥+,同理证明3322a c a c ac +≥+,3322b c b c bc +≥+,再求和即可得证【详解】证明:()()()()()()()()233222222a b a b ab a a b b b a a b a b a b a b +-+=-+-=--=+-,因为,,a b c R +∈,所以0a b +>,()20a b -≥,所以()()33220a b a b ab +-+≥,即3322a b a b ab +≥+,同理,3322a c a c ac +≥+,3322b c b c bc +≥+,所以333333222222a b b c a c a b ab b c bc a c ac +++++≥+++++,即3332222222()a b c ab a b bc b c ac a c++≥+++++【点睛】本题考查作差法证明不等式,考查推理论证能力19.设正有理数1a21211a a =++，求证：（11a 与2a 之间；（2）2a 比1a【答案】（1）证明见解析（2）证明见解析【分析】（1）作差(12111a a a -=+,讨论1a2a （2）整理问题为21a a <-,进而求证即可【详解】证明:（1）(121112111a a a a --=+-++,因为若1a >,则10a >,又10<,则2a <；若1a <则10a <,又10-<,则2a >,介于1a 与2a 之间（2）12111121a a a a a a ----=--+,因为10a >20-<,10a>,所以210a a -<,所以21a a -<-所以2a 比1a 【点睛】本题考查不等式的证明,考查运算能力与分类讨论思想20.已知对任意实数x ，不等式2(3)10mx m x --+>成立或不等式0mx >成立，求实数m 的取值范围；【答案】19m <<【分析】①对任意实数x ,不等式2(3)10mx m x --+>成立,讨论0m =与0m ≠的情况,进而求解；②对任意实数x ,不等式0mx >成立,则m ∈∅,二者求并集即可【详解】解:①由题,对任意实数x ,不等式2(3)10mx m x --+>成立,当0m =时,不等式为310x -+>不成立,舍去；当0m ≠时,()20340m m m >⎧⎪⎨∆=--<⎪⎩,解得19m <<；②对任意实数x ,不等式0mx >成立,则m ∈∅,综上,19m <<【点睛】本题考查含参的一元二次不等式恒成立问题,考查分类讨论思想21.已知关于x 的不等式2(4129)(211)0kx k k x ---->，其中R k ∈；（1）试求不等式的解集A ；（2）对于不等式的解集A ，记B A Z = （其中Z 为整数集），若集合B 为有限集，求实数k 的取值范围，使得集合B 中元素个数最少，并用列举法表示集合B ；【答案】（1）答案见解析（2）[44k ∈--+，{2,3,4,5}B =【分析】（1）对k 进行分类讨论,分别讨论0k =,0k <,01k <<或9k >,19k ≤≤的情况,进而求解即可；（2）由（1）可知当0k <时,集合B 为有限集,利用对勾函数可知933442k k ++≤,当且仅当3k =-时等号成立,进而求解即可【详解】（1）当0k =,11{|}2A x x =<；当0k ≠时,令21291142k k k ++=,解得1k =或9k =,则当1k <或9k >时,9113442k k ++<,当19k <<时,9113442k k ++>,①当0k <,911{|3}442k A x x k =++<<；②当01k <<或9k >,11{|2A x x =<或93}44k x k >++；③当19k ≤≤,9{|344k A x x k =<++或11}2x >；（2）因为B A Z = （其中Z 为整数集）,由（1）,当0k ≥时,集合B 中的元素的个数无限；当0k <时,集合B 中的元素的个数有限,此时集合B 为有限集,因为0k <,所以9933333444422k k k k ⎛⎫++=---+≤-+= ⎪⎝⎭,当且仅当944k k -=-,即3k =-时等号成立,所以{2,3,4,5}B =且93144k k++≥，所以2890k k ++≤，所以[44k ∈--+【点睛】本题考查解含参的不等式,考查交集的定义的应用,考查分类讨论思想。

2016-2017学年上海市复旦大学附中高一上学期开学考英语试卷含详解

上海市复旦大学附中2016-2017学年高一上学期开学考试英语试卷I. Choice1．Rather than read the science fiction alone in the classroom he preferred______the performance put on by the American student’s choir.A．watching B．watch C．having watched D．to watch2．Eggs in the shopping center are sold ______.A．by dozen B．by the dozen C．in dozens D．in the dozens3．The Chinese government has decided to boycott the imported beef from UK for the purpose of ______ the local citizen from mad cow disease.A．protecting B．preserving C．reserving D．releasing4．Paper produced every year is ______ the world’s production of vehicles.A．as three times heavy as B．the three time weight ofC．three times the weight of D．three times heavier as5．Don’t worry about it. My dog will ______ the gate of my house when I am away.A．defend B．protect C．save D．guard6．He set aside much money for his tuition each month and only a ______ amount of money went to his living expense. A．little B．small C．tiny D．few7．This clever boy absorbed almost all ______ his teacher could give him.A．which B．/C．what D．as8．______ in thought, he failed to realize his mother’s approach.A．Losing B．Being lost C．Lost D．To be lost9．The whereabouts of Bin Laden has become a focus of media’s _____.A．observation B．notice C．intention D．attention10．Walk ______ of the street, and you can see a post office just around the corner.A．at the end B．in the end C．to the end D．to an end11．You really don’t know what to do ______ your mother’s kindness.A．in place of B．instead of C．ahead of D．in return for12．The panda ______ to China is threatened with extinction. Something must be done to save her from danger. A．natural B．local C．native D．rural13．Many searchlights were used to ______ the missing passengers on the spot the air crash occurred.A．situate….which B．search ….. whereC．search for….which D．locate ….where14．V enus Fly-Trap has two special leaves and ______ leaf has several hairs in the middle.A．any B．either C．both D．none15．It was ______ late to catch a bus after the party, ______, we called a taxi.A．too much…..moreover B．too much ….. thereforeC．much too …. therefore D．much too…. moreover16．It is believed that ______ type of tree grows ______ than the Giant Redwood.A．not any ….. more highly B．no other …. higherC．no other ….more highly D．not any….. higher17．Too much rainfall failed to ______ the growth of these plants.A．encourage B．discourage C．disappoint D．appoint18．Our English monitor can sing ______, if not better than, Mary.A．as good as B．as well as C．so well as D．so good as19．We know for sure that the Venus Fly-Trap ______ insects for food.A．catches B．holds C．masters D．kidnaps 20．Admission will be free to ______ wears the school uniform and the school badge.A．anyone B．who C．whoever D．whom21．The first prize ______ to Mr. Brown for his outstanding design of his banknote counting machine. A．rewarded B．awarded C．presented D．went22．Nurseries are the areas where plants are grown to be sold or ______ in other places.A．being planted B．to plant C．plant D．planted 23．Ecology is the study of the relationship between plants, animal, people and their ______. A．condition B．situation C．environment D．atmosphere24．We parted from each other at the crossroads and returned to our ______ houses. A．respected B．respectful C．respectable D．respective 25．Mimosa, 15 cm in height, is a sensitive small plant, which will close when ______. A．touching B．touched C．is touched D．to be touched26．As a matter of fact ______, we raise at home are collected from the wild forest.A．most the plants B．most of plants C．most of the plants D．most of plant27．I thought that they were unhappy at the party when they got nothing to eat, ______?A．didn’t I B．do I C．were they D．weren’t they28．______ I referred to in class is the weird world of plants.A．Knowing to be the best chapter B．Known as the best chapterC．The best-known chapter D．To know it as the best chapter29．—Will professor Brown attend her wedding ceremony?—It will not be ______ so.A．particularly B．necessarily C．commonly D．regularly30．—How are we going to make our language teaching more efficient?—______ the teaching methodology.A．To improve B．Improving C．Having improved D．By improvingⅡ.Close Test(A)31 to us all, Martin Luther King was the black leader in America, who devoted his life to the racial equality, and died for his beliefs. The following is a(n) 32 from his famous speech delivered in the large audience of American people. The speech is called “I have a dream”.I say to you today, my friend, even though we face the difficulties of today and tomorrow, I will have a dream. It is a dream deeply 33 in the American dream. I have a dream that one day this 34 will rise up and live out the true meaning of its belief that “all men are 35 equal”.I have a dream that the sons of 36 slaves and the sons of former slave owners will be able to sit down together at the table of 37 . I have a dream that one day even the state of Mississippi, a state sweltering with the heat of injustice, sweltering with the heat of oppression, will be transformed into an oasis(绿洲) of freedom and justice. I have a dream that my four little children will one day live in a nation 38 they will not be judged by the color of their skin39 by the content of their character.I have a dream that one day little black boys and black girls will be able to join hands with little white boys and white girls as sisters and brothers. This is our hope and faith. 40 this faith, we will work together, pray together, struggle together, go to jail together, stand up for freedom together, knowing that we will be free one day.31．A．It is known B．As it is known C．As is known D．We all know32．A．story B．fiction C．speech D．excerpt33．A．rooted B．mixed C．rested D．grown34．A．state B．nation C．government D．community35．A．discovered B．invented C．created D．born36．A．latter B．former C．late D．previous37．A．manhood B．brotherhood C．boyhood D．sisterhood38．A．which B．where C．that D．what39．A．and B．either C．but D．though40．A．As B．With C．For D．By(B)A 25-year-old architectural designer spends at least five hours a day 41 on the Internet, but not just for work42 sending e-mails to friends. To him, the most important thing is 43 he can have on-line talks with his girlfriends, a primary school teacher in south China.A shy young man is active in the virtual world. 44 his girlfriend, he has many on- line good friends .“It’s not a45 thing for net chatters to have on-line friends of the opposite sex or even 46 a girlfriend or a boyfriend, ”said a graduate student of Beijing university. “Many of 47 classmates and friends have had such an experience.”He and his girlfriend surnamed Wang first met on the Internet, and on-line discussions became the starting 48 of their love story. Nowadays “Net-love” is no longer a strange 49 to many young Chinese, and on-line recreational activities have sprung up.Evidences show that the number of net chatter in China 50 79.5 million by the end of last year.and 32.2 percent of the them said that the purpose of surfing on the Internet was to have fun and make friends.41．A．to surf B．having surfed C．surf D．surfing42．A．or B．and C．either D．neither43．A．which B．what C．that D．whom44．A．Except that B．except C．In addition D．Besides45．A．fair B．bare C．usual D．rare46．A．to chat B．to search C．to hunt D．to locate47．A．his B．her C．my D．their48．A．top B．point C．tip D．spot49．A．word B．vocabulary C．phrase D．letter50．A．had reached B．had arrived C．would rise D．would raise(A)I arrived in the United States on February 6, 1966, but I remember my first day here very clearly. My friend was waiting for me when my plane landed at Kennedy Airport at three o'clock in the afternoon. The weather was very cold and it was snowing, but I was too excited to mind. From the airport, my friend and I took a taxi to my hotel. On the way, I saw the skyline of Manhattan for the first time and I stared in astonishment at the famous skyscrapers and their man-made beauty. My friend helped me unpack at the hotel and then left me because he had to go back to work. He promised to return the next day.Shortly after my friend had left, I went to a restaurant near the hotel to get something to eat. Because I couldn’t speak aword of English, I couldn’t tell the waiter what I wanted. I was very upset and started to make some gestures, but the waiter didn’t understand me. Finally, I ordered the same thing the man at the next table was eating. After dinner, I started to walk along Broadway until I came to Times Square with its movie theatres, neon lights, and huge crowds of people. I did not feel tired, so I continued to walk around the city. I wanted to see everything on my first day. I knew it was impossible, but I wanted to try.When I returned to the hotel, I was exhausted, but I couldn’t sleep because I kept hearing the fire and police sirens during the night. I lay awake and thought about New York. It was a very big and interesting city with many tall buildings and big cars, and full of noise and busy people. I also decided right then that I had to learn to speak English.51．He did not have what he really wanted, because _______.A．he only made some gesturesB．he did not order at allC．he could not make himself understoodD．the waiter was unwilling to serve52．The waiter _______.A．knew what he orderedB．finally understood what he saidC．took the order through his gesturesD．served the same thing the man at the next table was having53．After dinner, he _______.A．walked back to the hotel right awayB．had a walking tour about the cityC．went to the moviesD．did some shopping on Broadway54．That night he could not sleep because _______.A．he did not know what to do the next dayB．he was not tired at allC．he kept hearing the fire and police sirensD．he was thinking about the great city（B）Dear Doctor,My husband and I got married in 1965 and for the first ten years of our marriage I was very happy to stay home and raise our three children. Then four years ago, our youngest child went to school and I thought I might go back to work.My husband was very supportive and helped me to make my decision. He emphasized all of the things I can do around the house, and said he thought I could be a great success in business.After several weeks of job-hunting, I found my present job, which is working for a small public relations firm. At first, my husband was very proud of me and would tell his friends, “My clever little wife can run that company she’s working for.”But as his joking remark approached reality, my husband stopped talking to me about my job. I have received several promotions and pay increases, and I am now making more money than he is. I can buy my own clothes and a new car. Because of our combined incomes, my husband and I can do many things that we had always dreamed of, but we don’t do these things because he is very unhappy.We fight about little things and my husband is very critical of me in front of our friends. For the first time in our marriage, I think there is a possibility that our marriage may come to an end.I love my husband very much, and I don’t want him to feel inferior, but I also love my job. I think I can be a good wife and a working woman, but I don’t know how. Can you give me some advice? Will I have to choose one or the other or can I keep both my husband and my new career?Please help.55．What do you think shows her husband was supportive?A．He took up all the work she used to do.B．He made all the decisions for her.C．He gave her encouragement.D．All of the above.56．As her income increased _______.A．she found a gap emerged between her and her husbandB．she bought more clothes and a new houseC．she did many things she had dreamed forD．she felt very proud of herself57．The dilemma of the working woman is a choice between _______.A．husband and childrenB．children and workC．career and moneyD．job and marriage（C）If we are observant(善于观察的), we can find that most of the flowers in nature are red, orange and yellow. If we haveseen a black flower, it is a chance in a million. People have made census (统计) to colors of more than four thousand kinds of flowers and discovered that only eight of them are black. Why are black flowers so rare?As we know, sunlight is formed by seven different kinds of colored light. The wave length of each light changes, so the quantity of heat in each light changes, too. Flowers, especially their petals (花瓣) , are very weak and easy to the harm caused by high temperature. Black flowers can take in all the light waves, which cause the flowers to dry up in a high temperature. So the black flowers can hardly continue their lives. While red flowers, orange flowers and yellow ones can protect themselves from sunlight by reflecting（反射）the red light, orange light and yellow light, each of which has a large quantity of heat.That is why red, orange and yellow flowers are very common in nature while black flowers are so unusual.58．It is a chance in a million” means______.A．something commonB．something luckyC．something extremely rareD．something impossible59．Sunlight is formed by _____.A．many different kinds of colored lightB．three different kinds of colored light—red, orange and yellowC．seven different kinds of colored lightD．four thousand kinds of colored light60．Black flowers are so rare because ______.A．they are so weak that it’s difficult for them to grow upB．there are actually no black flowers in the worldC．the petals of black flowers are very delicate（易碎的）D．they can take in the light of all wave length which make the flowers dry up because of high temperature.61．Which of the following statements is NOT true?A．Red, orange and yellow flowers can absorb the light of all wave lengths.B．People have found that only a few kinds of flowers are black.C．Most of the flowers are resistant（有抵抗力的）to high temperature owing to their bright colors.D．The black flowers cannot protect themselves from sunlight.62．幸运的是，今天的天气很适合野营。

上海市复旦大学附属中学2017-2018学年高一10月月考英语试题 Word版含答案

复旦大学附属中学2017-2018学年第一学期试卷高一英语 2018/10（满分150分，答卷时间120分钟）第I卷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 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 you paper, and decide which one is the best answer to the question you have heard.1. A. At 10:00 B. At 10:10 C. At 10:20 D. At 10:302. A. Sandwiches B. Bread and butter C.Eggs D. Coffee3. A. 30 yuan B. 40 yuan C. 60 yuan D. 100 yuan4. A. Boating and swimming B. SwimmingC. SkatingD. Boating5. A. Daughter and son B. Father and daughterC. Husband and wifeD. Mother and son6. A. Help the man repair his car B. Give the man a ride to workC. Cancel the man’s appointmentD. Take the man to his doctor’s office7. A. She attended the party. B. She visited th e man’s home.C. She stayed home with a visitor.D. She went out to meet her friend.8. A. Her college life us relaxingB. Her college life is out of her expectationC. She is always available in the college.D. She is very pleased with her college life9. A. Jack is the best student.B. Jack is second to AnnC. Jack is as good as anyoneD. Jack is the second best student in the class10. A. Go on playing the games B. Have a good restC. Review his lessonsD. Stop watching videoSection 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. The care for the people B. Payment for the damage done by dogsC. Medical care for dogsD. Insurance for dog owners12. A. The owner of the car . B. The owner of the dogC. The insurance companyD. The government13. A. Dogs are welcome in public places B. Keeping dogs means asking for troubleC. Many car accidents are caused by dogsD. People take overall responsibility for their dogs Questions 14 through 16 are based on the following news.14. A. One B. TwoC. ThreeD. Four15. A. It is made up of five collegesB. Its students are mainly undergraduatesC. It provides housing for all undergraduate studentsD. All the faculty members are expected to teach and research16. A. Princeton offers two undergraduate degreesB. An academic year lasts about nine months in Princeton UniversityC. Undergraduates should spend their first two years in one of five colleges.D. It’s about an hour’s train ride from Princeton University to the north of New York City. Section CDirections: In Section C, you will hear tow longer conversations. The conversations will be read twice. After you hear each conversation, you are required to fill in the numbered blanks with theinformation you have heard. Write your answersBlanks 17 through 20 are based on the following conversation.What is the person in the next room doing? The person is 17 the piano.What does the woman think of herself? She doesn’t have any music18What music does the man like? All kinds of music, from 19 to pop. What’s the man’s answer to the woman’s suggestion? To20 the woman to the concert, Complete the form. Write ONE WORD for each answer.Blanks 21 through 24 are based on the following conversation.What were the overseas students from last year?They were from African countries, the Far East, 21 and Latin America..What did the woman do before she became an assistant director?She was secretary of 22 at Birmingham.What does the man ask the woman to imagine?23 a different kind of responsibility or doing something else.What will the woman’s new job be like?There is going to be more 24Complete the form. Write NO MORE THAN THREE WORDS for each answer.II. Grammar and vocabularySection A：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.25.-Look out , you were almost hit by the truck. - Oh, thank you. But I __________ about a math problem .A. had been thinkingB. thoughtC. was thinkingD. am thinking26. I didn’t like Mr. Li, who ___________ without warning and brining complaints about my school life to my parents.A. always turned upB. has always turned upC. was always turning upD. was always turned up27.I arrived late; I ____________ the road to be so icy.A. wouldn’t expectB. haven’t expectedC. hadn’t expectedD. wasn’t expecting28.The general announced yesterday that by the end of the next month, the army ___________ the occupied area.A. will have leftB. will leaveC. would have leftD. had left29.He will have learned English for eight years by the time he _________ from the university next year.A. will graduateB. graduatedC. graduatesD. is to graduate30.They asked me to have a drink with them. I said it was at least ten years since I _________ a good drink.A. had enjoyedB. was enjoyingC. enjoyedD. had been enjoying31.The man opened the box only _________ there was nothing in it.A. foundB. to findC. had foundD. have found32.Something _________ these years to prevent the rivers in our city from being polluted.A. has been doneB. have doneC. doneD. being done33. Every few years, the coal workers ___________ their lungs X-rayed to ensure their health.A. are havingB. haveC. have hadD. had had34.The church tower which __________will be open to tourists soon. The work is almost finished.A. has restoredB. has been restored C .is restoring D. is being restored35. Wind power is an ancient source of energy________ we may return in the near future.A. on whichB. by whichC. to whichD. from which36. Today we have chat rooms, text messaging, emailing… but we seem ______ the art ofcommunicating face-to-face.A. losingB. to be losingC. to be lostD. having lost37. The police officers in our city work hard ______ the rest of us can live a safe life.A. in caseB. as ifC. in order thatD. only if38. There is much truth in the idea _ kindness is usually served by frankness.A. whyB. whichC. thatD. whether39. Some parents argue that it is their job to get their kids _____ in community service.A. to involveB. involvedC. involvingD. involve40. Whether or not your role models are famous, they should be people worth _____.A . to copyB . to be copied C. copying D. being copiedKeys: 25-30 CCCCCA 31-35 BABDC 36-40 BCCBCSection BDirections: 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）When 41_____________ （ask）to point out one or two things that are most important to themselves, many put friends ahead 42 ___________ homes, jobs, clothes and cars.A true friendship carries a long history of experience that determines who we are and 43 __________ （keep）us connected. It is a treasure we should protect. Unfortunately, the better friends you are, the 44 ________ （probable）you’ll have disagreements. And the result can be what you don’t want— an end to the relationship.The good news is 45 _________ most troubled friendships can be mended. First, don’t let your pride get in your way. Most of us can forgive each other when differences are brought out in the open. Second, 46 _________ （apologize）when you’re wrong --–47 _____ _____ you’ve been wronged. Over the course of a friendship, even the best people make mistakes. Sometimes, it may be best if the wronged person takes the lead and apologizes. When you apologize, give your friend a chance to admit that he has been wrong. Third, see things from your friend’s point of view. And finally, accept that friendships change as our needs and lifestyle change. Makingfriends can sometimes seem easy. The hard part is keeping the connections strong during the natural ups and downs that have an effect on all relationships. My suggestion: Consider friendship 48 _________ honor and a gift, and worth the effort to treasure and nurture 培养.Keys：41.asked，42.of，43.keeps，44.more probable，45.the，46.apologize，47.even if，48.an（B）Fear 49 __________ be felt in the heart as well as in the head, according to a study that has found a link between the cycles of a beating heart and the chance of someone feeling fear. Tests on healthy volunteers found that they were more likely to feel a sense of fear at the moment when their hearts are contracting（收缩）and pumping blood around their bodies, compared with the point 50 ________ the heartbeat is relaxed. Scientists say the results suggested that the heart is able to influence 51 ___________ the brain responds to a fearful event, depending on which point it is at in its regular cycle of contraction and relaxation. Sarah Garfinkel at the Brighton and Sussex Medical School said, “Our study show for the first time that the way 52 _____ ______ we deal with fear is different, depending on when we see fearful pictures in relation to our heart. The study tested 20 healthy volunteers on their reactions to fear as they were shown pictures of fearful faces. Dr. Garfinkel said, “The study showed that fearful faces are better noticed when the heart is pumping 53 _________ when it is relaxed. Thus our hearts can also affect what we see and what we don’t see —and guide whether we see fear.” 54 _________ （understand）this relationship further, the scientists also used a brain scanner to show how the brain influences the way the heart changes a person’s feeling of fear. “So far we 55 ___________ （find）an important mechanism by which the heart and brain ‘speak’ to each other to change our feelings and reduce fear” Dr. Garfinkel said. “We hope that by increasing our understanding about how fear is dealt with and ways that it could be reduced, we may be able to develop more successful treatments for anxiety, disorders, and also for 56 __________ who are suffering from serious stress disorder.” Keys: 49.may 50.when 51.how 52.in which 53.than 54.To understand 55.have found 56.thoseSection CDirections: Complete the following passage by using the words in the box. Each word can only beused once. Note that there is one word more than you need.Walking, if you do it vigorously enough, is the overall best exercise for regular physical activity. It requires no equipment, everyone knows how to do it and it carries the 57 risk of injury. The human body is designed to walk. You can walk in parks or along a river or in your neighborhood. To get 58 benefit from walking, aim for 45 minutes a day, an average of five days a week. Strength training is another important 59 of physical activity. Its purpose is to build and 60 bone and muscle mass, both of which shrink with age. In general, you will want to do strength training two or three days a week , 61 recovery days between sessions.Finally, flexibility and balance training are 62 important as the body ages. Aches and pains are high on the list of complaints in old age. The result of constant muscle tension and stiffness of joints, many of them are 63 and simple flexibility training can 64 these by making muscles stronger and keeping joints lubricated 润滑. Some of this you do whenever you stretch. If you watch dogs and cats, you’ll get an idea of how natural it is. The general65 is simple: whenever the body has been in one position for a while, it is good to 66 stretch it in an opposite position.Keys: 57 H 58 J 59 D 60 I 61 A 62 G 63 B 64 K 65 E 66 CIII. 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.The responsibilities of job, home and family all too often transform the daily routine into a huge burden. Enjoying quality leisure time becomes 67 .True leisure means engaging in a 68 and rewarding activity without being 69 by other aspects of your life. Sometimes, the 70 you experience during the week makeyou place great emphasis on weekends and other days off. You hope to relax, but the stress is 71 .You can't rest even when you have the time to do so. When time is limited, leisure activities areusually the first items to 72 from the daily schedule.If you routinely 73 your leisure time because you have "more important things to do," you may be underestimating how much time the things 74 take. Most people routinely shortchange themselves on the amount of time required to complete a given task. The problem isa 75 to evaluate performance honestly.76 , simplifying your life will let you have more windows of opportunity to do stuff just for fun. Maybe you need to relearn to relax.Spare Time for Your 77 : Devote one afternoon or evening per week 78 to doing something that you enjoy, listening to music, assembling a jigsaw puzzle. Do whatever you always wish to but never seem to find time for. And do it where there's nothing to remind you of other 79 .Choose Low-Tech: The popular fascination with technological advances in all areas of life has diverted 偏离attention from the simple pleasures of many 80 pastimes. People think they must have the best, most up-to-date equipment available to enjoy themselves. When keeping up with trends becomes the ., the pure pleasure of leisure is lost.67. A. difficult B. essential C. noticeable D. incapable68.A. reluctant B. pleasurable C. delicate D. disgusting69.A. cultivated B. ashamed C. preoccupied D. oppressed70.A. favour B. risk C. stress D. thirst71.A. reasonable B. enormous C. ignorant D. adjusted72.A. destroy B. consider C. recognize D. disappear73.A. estimate B. fulfill C. abandon D. expand74.A. constantly B. actually C. initially D. equally75.A. variety B. delay C. failure D. record76.A. Consequently B. However C. Moreover D. Therefore77.A. Instincts B. Images C. Desires D. Tasks78.A. occasionally B. entirely C. primarily D. dramatically79.A. duties B. expectations C. stimulations D. limitations80.A. uncommon B. individual C. traditional D. physical81.A. focus B. depression C. source D. threatKey:67-71 ABCCB 72-76 DCBCB 77-81 CBACASection 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)Here is one of the world’s largest indoor ski-slopes. It covers an area of 22,500m2, about the same size as three football fields, and the temperature is a constant -1℃to -2℃. However, the strangest thing about this place is that it’s in the middle of the desert! It’s called Ski Dubai and the outside temperature s can rise to more than 40℃!It sounds crazy, but it just shows how serious people are about having fun. We spend huge sums on sports facilities. We pay our sports stars ridiculous amounts of money. And we spend hour after hour playing games! I wonder if all the sports - lovers and game - players in the world aren’t a little crazy. I know I am. I was once driving past a football field where some kids were playing. I turned to watch and crashed my car. I know it’s stupid but I can do nothing about it. As someone said, “Football isn’t a matter of life and death. It’s much more important than that!”Of course, it isn’t that important really. No game is. But the problem is that games are addictive. From the tennis court to the golf course, you’ll find participants and spectators who can’t live without the drug of their choice. It could be a good thing. After all, despite being addictive, it’s true that sports and games help us to relax. Maybe if it wasn’t for sport, our societies would be more violent. Perhaps sport is a substitute for war? It’s hard t o think of a quieter, more peaceful game than chess, and what’s the objective? Capturing your opponent’s king, and surely, it’s better to have wars in athletics stadiums rather than on battlefields.What’s more, playing is natural. Kittens chase balls of w ool and puppies pretend to fight. Games help us perfect ours kills and prepare us for the serious contest of survival.But do all games help us relax and stay away from violence? What about computer games? A recent article in New Scientist suggest s that playing violent video games and most of them are extremely violent makes people more aggressive and more likely to commit violent crimes.Are these games a rehearsal for life or a substitute for life? Do we play instead of facing up toour real problems? I don’t know. But what I do know is that I need a break, something to help me relax. Skiing would be nice. I wonder how much it costs to get to Dubai?82. According to the author, the most surprising thing about Ski Dubai is its _____.A. slopesB. sizeC. locationD. facilities83. The expression “the drug of their choice” in the 3rd paragraph refers to _____.A. the game they are keen onB. the medicine they takeC. the activity good for healthD. the sport in place of war84. Which of the following statements does the author most probably agree with?A. Sports stars should be paid more to play well.B. Sports are more important than life and death.C. Chess is too peaceful to be considered a sport.D. Games can make one relaxed as well as violent.85. What does the author mainly talk about in the passage ?A. The relationship between games and crimes .B. Human natural craze for having fun with games.C. Serious concerns about time that is spent on games.D. Real problems facing game players in everyday life.Keys: C A D B（B）Across the rich world, well-educated people increasingly work longer than the less-skilled. Some 65% of American men aged 62-74 with a professional degree are in the workforce, compared with 32% of men with only a high-school certificate. This gap is part of a deepening divide between the well-education well off and the unskilled poor. Rapid technological advance has raised the incomes of the highly skilled while squeezing those of the unskilled. The consequences, for individual and society, are profound.The world is facing as astonishing rise in the number of old people, and they will live longer than ever before. Over the next 20 years the global population of those aged 65 or more will almost double, from 600 million to 1.1 billion. The experience of the 20th century, when greater longevity 长寿translated into more years in retirement rather than more years at work, haspersuaded many observers that this shift will lead to slower economic growth, while the swelling ranks of pensioners will create government budget problems.But the notion of a sharp division between the working young and the idle old misses a new trend, the growing gap between the skilled and the unskilled. Employment rates are falling among younger unskilled people, whereas older skilled folk are working longer. The divide is most extreme in America, where well-educated baby-boomers are putting off retirement while many less-skilled younger people have dropped out of the workforce.That even the better-off must work longer to have a comfortable retirement. But the changing nature of work also plays a big role. Pay has risen sharply for the highly educated, and those people continue to reap rich rewards into old age because these days the educated elderly are more productive than the preceding generation. Technological change may well reinforce that shift: the skills that complement computers, from management knowhow to creativity. Do not necessarily decline with age.86.what is happening in the workforce in rich countries?A. younger people are replacing the elderlyB. well-educated people tend to work longerC. unemployment rates are rising year after yearD. people with no college degree do not easily find work87.what do many observers predict in view of the experience of the 20th century?A. Economic growth will slow down.B. Government budgets will increase.C. More people will try to pursue higher educationD. There will be more competition in the job market.88.What is the result of policy changes in European countries?A. Unskilled workers may choose to retire early.B. more people have to receive in-service training.C. Even wealthy people must work longer to live comfortably in retirement.D. People may be able to enjoy generous defined-benefits from pension?plans.89.What is characteristic of work in the 21st century?A. Computers will do more complicated work.B. More will be taken by the educated young.C. Most jobs to be done will be creative ones.D. Skills are highly valued regardless of age.Keys: B A C D（C）At the heart of the debate over illegal immigration lies one key question: are immigrants good or bad for the economy? The American public overwhelmingly thinks they're bad. Yet the consensus among most economists is that immigration, both legal and illegal, provides a small net boost to the economy. Immigrants provide cheap labor, lower the prices of everything from farm produce to new homes, and leave consumers with a little more money in their pockets. So why is there such a discrepancy between the perception of immigrants' impact on the economy and the realityThere are a number of familiar theories. Some argue that people are anxious and feel threatened by an inflow of new workers. Others highlight the strain that undocumented immigrants place on public services, like schools, hospitals, and jails. Still others emphasize the role of race, arguing that foreigners add to the nation's fears and insecurities. There's some truth to all these explanations, but they aren't quite sufficient.To get a better understanding of what's going on, consider the way immigration's impact is felt. Though its overall effect may be positive, its costs and benefits are distributed unevenly. David Card, an economist at UC Berkeley, notes that the ones who profit most directly from immigrants' low-cost labor are businesses and employers – meatpacking plants in Nebraska, for instance, or agricultural businesses in California. Granted, these producers' savings probably translate into lower prices at the grocery store, but how many consumers make that mental connection at the checkout counter? As for the drawbacks of illegal immigration, these, too, are concentrated. Native low-skilled workers suffer most from the competition of foreign labor. According to a study by George Borjas, a Harvard economist, immigration reduced the wages of American high-school dropouts by 9% between 1980-2000.Among high-skilled, better-educated employees, however, opposition was strongest in states with both high numbers of immigrants and relatively generous social services. What worried them most, in other words, was the?fiscal? 财政的burden of immigration. That conclusion wasreinforced by another finding: that their opposition appeared to soften when that fiscal burden decreased, as occurred with welfare reform in the 1990s, which curbed immigrants' access to certain benefits.The irony is that for all the overexcited debate, the net effect of immigration is minimal. Even for those most acutely affected –say, low-skilled workers, or California residents –the impact isn't all that dramatic. "The unpleasant voices have tended to dominate our perceptions," says Daniel Tichenor, a political science professor at the University of Oregon. "But when all those factors are put together and the economists calculate the numbers, it ends up being a net positive, but a small one." Too bad most people don't realize it.90. What can we learn from the first paragraph?A .Whether immigrants are good or bad for the economy has been puzzling economists.B .The American economy used to thrive on immigration but now it's a different story.C .The consensus among economists is that immigration should not be encouraged.D .The general public thinks differently from most economists on the impact of immigration.91. In what way does the author think ordinary Americans benefit from immigration?A .They can access all kinds of public services.B .They can get consumer goods at lower prices.C .They can mix with people of different cultures.D .They can avoid doing much of the manual labor.92. What is the chief concern of native high-skilled, better-educated employees about the inflow of immigrants?A .It may change the existing social structure.B .It may pose a threat to their economic status.C .It may lead to social instability in the country.D .It may place a great strain on the state budget.93. What is the irony about the debate over immigration?A .Even economists can't reach a consensus about its impact.B .Those who are opposed to it turn out to benefit most from it.C .People are making too big a fuss about something of small impact.D .There is no essential difference between seemingly opposite opinions.Keys: D B D ASection CDirections: Read the following passage carefully. In the passage there are four sentences missing. Choose the best one from the six sentences.ForgivenessTo forgive is a virtue, but no one has ever said it is easy. When someone has deeply hurt you, it can be extremely difficult to let go of your hate. However, forgiveness is possible, and it can be surprisingly beneficial to your physical and mental health. People who forgive show less sadness, anger and stress and more hopefulness, according to a recent research.____1____ Try the following steps:Calm yourself. ____2____ You can take a couple of breaths and think of something that gives you pleasure: a beautiful scene in nature, or someone you love.Don't wait for an apology. Many times the person who hurt you does not intend to apologize. They may have wanted to hurt you or they just don't see things the same way. If you wait for people to apologize, you could be waiting an awfully long time. Keep in mind that forgiveness does not necessarily mean becoming friends again with the person who upset you.Take the control away from your offender(冒犯者). Rethinking about your hurt gives power to the person who causes you pain. Instead of focusing on your wounded feelings, learn to look for the love, beauty and kindness around you.____4____ If you understand your offender, you may realize that he or she was acting out of unawareness, fear, and even love. You may want to write a letter to yourself from your offender's point of view.Don't forget to forgive yourself. ____5____ But it can rob you of your self-confidence if you don't do it.A. Why should you forgive?B. How should you start to forgive?C. Recognize the benefits of forgiveness.D. Try to see things from your offender's angle.E. For some people, forgiving themselves is the biggest challenge.F. To make your anger die away, try a simple stress-management technique.G. Keys: B F D ESection DBased on the following passage and write a summaryFinancial setbacks in the form of pay cuts are having a trickle-down effect(涓滴效应) as the depression persists. Families across America are cutting or even axing kids’ allowance (零用钱) to reflect what’s going on with household finances and the economy as a whole .Some jobless parents are doing it out of necessity .Other parents are using allowance adjustments to teach children about economic realities and how to budget in leaner times.“Try to use relevant news to explain the reasons behind the depression and how it’s hitting home. If they see it obvious in their own allowance, they’ll feel the impact and see how it all ties in, ”says financial consultant Antwone Harris.Any reduction in allowance should be understood in age-appropriate communication, says Dr. Tony Meyer, a child psychiatrist(精神科医生) and medical director of Aurora Psychiatric Hospital. Six to 12-year-olds are mature enough for a frank talk, but don’t set them back with a lot of details. It’s sufficient to say their allowance is lower because Mom and Dad is getting paid less at work ,so there’s less money for the family to spend. With 12 to 18-year-olds, you can broaden the discussion to include the banking crisis and other factors that contributed to the depression, Meyer says. Younger kids have the idea that they’re at the center of things, and adolescents by nature are especially self-concerned . “They’ll think they’re responsible, ”Meyer says.A cut in allowance might seem punishing , so the message that the child is not at fault needs to come across. Depending on the child’s age, “You can also ask them to bring some income by working a job or helping more around the house so Mom or Dad can work more,” he says. Kids can also contribute by means of taking over landscaping services previously done by a paid professional. “You’ll pay lower rates, and the money stays in the family ,”financial。

2017年上海市复旦附中提前自主招生数学试题答案与解析

2017年上海市复旦附中提前自主招生数学试题1.已知 a 、 b 、 c 是一个三角形的三边，则 a 4b 4c 42a 2b 22b 2c 22c 2a 2的值是（）A .恒正B .恒负C . 可正可负D .非负2. 设 m ， n 是正整数，满足 m n mn ，给出以下四个结论：① m ，n 都不等于 1；② m ，n 都不等于 2；③ m ，n 都大于 1；④ m ， n 至少有一个等于 1 ，其中正确的结论是（） A .① B .② C . ③ D . ④3. 已知关于 x 的方程 2x a x a 有一个根为 1，则实数 a 的值为（）D .以上答案都不正确4. 已知 a ， b ， c 是不完全相等的任意实数，若关于 x ， y ， z 的值，下列说法正确的是（ A .都大于 0 B .至少有一个大于 0 5. 已知 a ， b ， c 不全为无理数，则关于三个数 A .可能均为有理数 C .可能恰有一个为有理数C .都小于 0D . 至多有一个大于 0 b ，b c ， c a ，下列说法错误的是（ B . 可能均为无理数 D . 可能恰有两个为有理数6. 关于 x ， y 的方程组 (x y)( x 2y) 0 2( x y 2) 2(2x 2 的实数解有（ y 1） 2 0A .先关于 x 轴对称，再向右平移B .先关于 x 轴对称，再向右平移是（）B .m 3410. 用同样大小的一种正多边形平铺整个平面（没有重叠）隙？（）A. 2 种B. 3 种B .2 组C . 3组 D .4组2 7. 为了得到函数 y3 x 2的图像，2可以将函数 y 3x 2 6x 1的图像（ C .先关于 y 轴对称，再向右平移1 个单位，最后向上平移4个单位1 个单位，最后向下平移4 个单位C .2 B .0 8.若关于 x 的方程 2 b 的结果是（ bx a 2b c ， y a b 2c ， z 2a b c ，则 1 个单位，最后向上平移 1 4个单位 4D .先关于 y 轴对称，再向右平移D .4 9. 如果方程（x 1）（x 2 2x m ） 0的三根可以作为一个三角形的三边之长，那么实数m 的取值范围，有几种正多边形可以铺满整个平面而不留缝D.5种11. 已知对于满足： a b 3， b c 4的实数 a,b,c ，均有 2a b c k 恒成立，则实数 k 的最小值为（）A. 7B. 8 C . 9 D. 1012. 设 f （x ） x 4x 3x 2x 1，则关于 f （x ）的性质，正确的一项为（）13.已知实数 a, b,c 满足 a b 0，且 a b c 0，抛物线 y ax 2bx c 0在 x 轴上截得线段长度为 l ，则 l 的取值范围为（）A.0 l 1B. 0 l 2C.2 l 3D. 3 l 43x 2 14. 已知实数 x 、 y 满足： x y 3 0,2y 3 y 6 0 .则 y 2的值为（）.y2y x 22ax 2 x 的取值范围为1 x 1 ， y 的取值既有正值又有负值则实数 a 的取值范围为（）.1A.aB.a - 1 C .a 1或 a - 1 D. 以上答案都不正确 22 22 ③x 2cx a 0，①② 有公共根 p ，②③ 有公共根 q ，③① 有公共根 r ，则 abc （）.A.1B. 3 C . 1 D.217. 甲、乙、丙、丁四个人参加一个比赛，有两个人获奖 .在比赛结果揭晓之前，四个人做了如下猜测甲：两名获奖者在乙、丙、丁中 . 乙：我没有获奖，丙获奖了 . 丙：甲、乙两个人中有且只有一个人获奖 . 丁：乙说得对 . 已知四个人中有且只有两个人的猜测是正确的，则两名获奖者为（） . A. 甲丁 B.乙丙 C.乙丁 D .以上都不正确18.如图梯形 ABCD 中， AB ∥CD ,对角线 AC 与 BD 交于点 K ,点 L 为BD 的中点 .已知 △AKB 、 △ALD 的面积分别为 18、21 ，则 △ALC 的面积为（）.AB21L18KDCA.7B.9C.11 D .1319. 甲用 1000 元人民币购买了一手股票，随即他将这手股票转卖给已，获利 10% ，而后乙又将这手股票A.对任意实数 x ， f （ x ）总是大于 0 C.当 x 0时， f （x ） 0 B .对任意实数 x ， f （ x ）总是小于 0D .16. 已知 a 、b 、c 是互不相等的实数， 2三个方程 ①x 2 ax b 0 ； 2② x 2bx c 0 ；反卖给甲，但乙损失了10% ，最后甲按乙卖给甲的价格的九折将这手股票卖给了乙，甲在上述股票交易中（）A.甲刚好盈亏平衡B.甲盈利1元C.甲盈利9元D.甲亏本1.1元20. 对于三个一元二次方程：x 2 a b x b c 0 、x 2 b c c a 0 、2x2 c a a b 0（其中a,b, c为实数），下列说法错误的是（）A.存在实数a,b,c ，使得恰有一个方程没有实数根B.存在实数a,b,c ，使得恰有两个方程没有实数根C .存在实数a,b,c ，使得三个方程都没有实数根D.存在实数a,b,c ，使得三个方程都有实数根21. 已知在直角三角形ABC 中，C 90 ，ABC 60 ，点E 直角边AC 上，且EBC 20 ，延长BE 到点D 使得ED 2AB ，连AD ，CD ，则下列结论正确的是（）A. AD 3ABB. AD∥ BCC.CD 2ACD. AE 2EC22. 已知线段AB ，如何用尺规作出线段AB 的一个黄金分割点P ，下面给出了几种方法，其中正确的是（）A.过点B 作BC AB，使得BC AB，连AC ，在AC上截取CD CB，在AB截取AP AD ，点P 为线段AB 的一个黄金分割点1B.过点B 作BC AB，使得BC AB，连AC，在AC 上截取CD CB，在AB截取AP AD ，2点P 为线段AB 的一个黄金分割点1C.过点B 作BC AB，使得BC AB，连AC，在AC 上截取CD CB，在AB截取AP AD ，3点P 为线段AB 的一个黄金分割点1D.过点B作BC AB，使得BC AB，连AC，在AC 上截取CD CB ，在AB截取AP AD ，4点P 为线段AB 的一个黄金分割点15 2∴a2017 年上海市复旦附中提前自主招生试题答案与解析1.已知 a 、 b 、 c 是一个三角形的三边，则 a 4b 4c 42a 2b 22b 2c 22c 2a 2的值是()A .恒正B .恒负C . 可正可负D .非负解：选 B4 4 4 2 2 2 2 2 2a b c 2a b 2b c 2c a(a2 b2 c 2)24b 2c 2( a 2b 2c 22bc)( a 2b 2c 22bc) [a 2(b c)2][a 2(b c)2]( a b c)( a b c)( a b c)( a b c)∵a 、 b 、 c 是一个三角形的三边，∴a b c 0， a b c 0， a b c 0， a b c 0， ∴ (a b c)(a b c)( a b c)(a b c) 02.设 m ， n 是正整数，满足 m n mn ，给出以下四个结论：① m ，n 都不等于 1；② m ，n 都不等于 2；③ m ，n 都大于 1；④ m ， n 至少有一个等于 1 ，其中正确的结论是( ) A .① B .② C . ③ D . ④ 解：选 D由 m n mn 得 m 1 n 1 1若 m ， n 均大于 1，则 m 1 1,n 1 1, m 1 n 1 1，矛盾， ∴ m ， n 至少有一个等于 1.3. 已知关于 x 的方程 2x a x a 有一个根为 1 ，则实数 a 的值为（）1 5 1 5 A . B . 22 解：选 A将 x 1代入，得 a 2 a 1 ，21 5 两边平方，得 a2a1 0， a1 52D .以上答案都不正确x 1 不是原方程的根，舍4.已知 a ， b ， c 是不完全相等的任意实数，若 x a 2b c ， ya b 2c ，z 2a b c ，则关于 x ， y ， z 的值，下列说法正确的是（）x y z 0，若 x ， y ， z 均小于 0，则 x y z 0，矛盾；故至少有一个大于 0 .5.已知 a ， b ， c 不全为无理数，则关于三个数 A .可能均为有理数 C .可能恰有一个为有理数解：选 Db ，bc ， c a ，下列说法错误的是（B . 可能均为无理数D . 可能恰有两个为有理数若 a, b, c 均为有理数， A 正确；若 a 2， b 3 ， c 0，B 正确；若 a 2，b2， c 0，C 正确 ;即 y 3 x 1 2 4，再向右平移 1个单位，最后向上平移 4 个单位，得到 y 3x 2.27. 为了得到函数 y 3 x 2的2可以将函数 y 3x 26x 1的图像（A.先关于 x 轴对称，再向右平移 1个单位，最后向上平移 4个单位 B .先关于 x 轴对称，再向右平移 1 个单位，最后向下平移 4个单位C .先关于 y 轴对称，再向右平移1 个单位，最后向上平移4个单位D .先关于 y 轴对称，再向右平移 1 个单位，最后向下平移4个单位解：选 A由于两个函数二次项系数为相反数，故先关于 x 轴对称，得到 y 3 x 2 6 x ）1， A .都大于 0 解：选 BB .至少有一个大于 0C .都小于 0D . 至多有一个大于 06. 关于 x ， y 的方程组 (x y)( x 2y) 0 2 2 2 的实数解有( ( x y 2) 2(2x y 1) 2A . 1组解：选 B .2 组C . 3组D .4组由①得 x y 0 或 x 2y 0，由②得 x y 2 0且 2x y 1 0，∴只有 x 1一组解 .y1解：选 C2设 x 22x m 0的两根为 x 1， x 2，8.若关于 x 的方程 x 2 b a 有四个实数解， B .解：选 C画出 y x 2 b 和 y a 的函数图像， ∵有四个交点，∴ 0 a b ，ab abab ab 方法二：b a 或 x 2a b 或 x2∵原方程有四个实数解，∴ a 0，a b 0 ，b a 0， ∴ b 0 ，∴原式 1 1 1 1 29. 如果方程 ( x 1)(x 22x m) 0的三根可以作为一个三角形的三边之长，那么实数 m 的取值范围是( )B .m 34C .3 m 1 4D .3m 14则化ababb的结果是(b 的结果是(a ∴ x 2∴ x 2 b a ，b a ，b a ，A. 0 l 1B. 0 l 2 解：选CD. 3 l 4x1 x 2 1 则x1 x2 1 03解得3m 1 .410. 用同样大小的一种正多边形平铺整个平面(没有重叠) ，有几种正多边形可以铺满整个平面而不留缝隙？( )A. 2 种B.3 种C.4 种D.5 种解：选B 关键是看正多边形的内角和，如果围绕一点拼在一起的几个正多边形的内角之和恰是一个周角，则可以铺满整个平面而不留缝隙，只有正三角形、正四边形和正六边形可以 .11. 已知对于满足：a b 3，b c 4的实数a,b,c ，均有2a b c k恒成立，则实数k 的最小值为 ( )A. 7B. 8 C . 9 D. 10 解：选Da c ab bc a b b c 72a b c a b a c 10 ，所以k 最小是1043212.设f(x) x4 x3 x2 x 1，则关于f ( x )的性质，正确的一项为( )A.对任意实数x，f ( x )总是大于0 B .对任意实数x，f ( x )总是小于0C.当x 0时，f (x) 0 D .以上均不对解：选Af( x) x4 x3 x2 x 1 (x 1)2(x2 x 1) x2恒大于013.已知实数a, b,c满足a b 0，且a b c 0，抛物线y ax2 bx c 0在x轴上截得线段长度为l ，则l 的取值范围为 (a 0，b (a c)c ( a b)cb1 2 ，∴ 2 x 1 x 2 3 aa解：选 D∴ f (1) f ( 1) 0 ， ∴ (1 2a 2)(1 2a 2) 0 ，1 经检验当 a 时，不符合题意 . 216. 已知 a 、b 、c 是互不相等的实数，三个方程 ①x 2ax b 0 ； ②x 2bx c 0 ；③x 2cx a 0，①② 有公共根 p ，②③ 有公共根 q ，③① 有公共根 r ，则 abc （）.D.214. 已知实数 x 、 y 满足： x y 30,2y 3 y 6 0 .则 xy2的值为 y）.A.01B. 2C.1D.32x 2y yy3y63 32y215. 已知二次函数 y x 2ax 2 .当自变量 x 的取值范围为 1 x 1， y 的取值既有正值又有负值则实数 a 的取值范围为（）.A.a 12 B.a - 1211 C .a 或 a -22D. 以上答案都不正确解：选 D显然，二次函数与 x 轴有两个交点，令交点横坐标为x 1, x 2 ， x 1 x 2 .由韦达定理得 x 1x 2 2若1x 1 x 2 1，则 x 1x 21 与 x 1x2 2矛盾，A.11a2∴ abc ( pqr)21 ，选 A17. 甲、乙、丙、丁四个人参加一个比赛，有两个人获奖 .在比赛结果揭晓之前，四个人做了如下猜测甲：两名获奖者在乙、丙、丁中 . 乙：我没有获奖，丙获奖了丙：甲、乙两个人中有且只有一个人获奖 . 丁：乙说得对 . 已知四个人中有且只有两个人的猜测是正确的，则两名获奖者为（A. 甲丁B.乙丙解：选 D 显然乙、丁同对错① 当甲丙对，乙丁错时，② 当甲丙错，乙丁对时，18. 如图梯形 ABCD 中， △ALD 的面积分别为18、21 ，则 △ALC 的面积为（∴S△ ABl24 ,由蝴蝶定理得S△KAD S△KBC24∴S △ ALC 7，选 A19. 甲用 1000 元人民币购买了一手股票，随即他将这手股票转卖给已，获利 10% ，而后乙又将这手股票反卖给甲，但乙损失了 10% ，最后甲按乙卖给甲的价格的九折将这手股票卖给了乙，甲在上述股票交易中（）A.甲刚好盈亏平衡B.甲盈利 1元C.甲盈利 9元D.甲亏本 1.1元解：选 Bcb ab解：将 pqr 带入三个方程得 ac bc又由韦达定理得ab racpr bpq c qr a ）.C. 乙丁 D .以上都不正确乙丙或乙丁获奖无符合情况 AB ∥CD ,对角线 AC 与 BD 交于点 K ,点 L 为 BD 的中点 .已知△AKB 、）. A.7B.9C.11解：由 L 为 BD 中点可得 S △ ALBS △ALD 21，∴ S △ALKS△ALK AK S△ ABK 18S△CLKKCS△CBK24∴S△CLK甲第一次卖给乙赚了1000 10% 100 元，乙用1100 元买入股票，乙卖给甲乙亏了1100 10% 110 元，甲用990 元买入股票，甲第二次卖给乙亏了 990 10% 99元，故甲总共盈利 100 99 1元 .2220. 对于三个一元二次方程： x 2 a b x b c 0 、 x 2b c c a 0 、 2 x 2 c a a b 0（其中 a,b, c 为实数），下列说法错误的是（）A.存在实数 a,b,c ，使得恰有一个方程没有实数根B.存在实数 a,b,c ，使得恰有两个方程没有实数根C .存在实数 a,b,c ，使得三个方程都没有实数根D.存在实数 a,b,c ，使得三个方程都有实数根解：选 C 设三个方程判别式为 1, 2, 3 ，则 1 a b 2 4a b ， 2 b c 2 4 c a ， 3 c a 2 4a b ，2221 2 3 a b 2 b c 2 c a 20 故三个方程中至少有一个方程有实根 .21. 已知在直角三角形 ABC 中， C 90 ， ABC 60 ，点 E 直角边 AC 上，且 EBC 20 ，延长 BE 到点 D 使得 ED 2AB ，连 AD ，CD ，则下列结论正确的是（）A. AD 3ABB. AD ∥ BCC.CD 2ACD. AE 2EC解：选 B作 EAF 70 交 DE 于点 F .∵ AEF BAC ABE 70 EAF ，∴ AE EF ， AFE 180 EAF AEF 40 ABE ，D∴ AB AF ，∵ 2AB DE ，∴ AF EF CF∴ DAE 90∴ AD ∥ BC22. 已知线段AB ，如何用尺规作出线段AB 的一个黄金分割点P ，下面给出了几种方法，其中正确的是（）A.过点B 作BC AB，使得BC AB，连AC ，在AC上截取CD CB，在AB 截取点P 为线段AB 的一个黄金分割点点P 为线段AB 的一个黄金分割点点P 为线段AB 的一个黄金分割点点P 为线段AB 的一个黄金分割点解：选设AB 2a,BC a ，则CD BC a ，AC 5a ，AD AC CD 5 1 aAP AD 5 1 a ，AP 5 1 a 5 1AB 2a 2即点P 为线段AB 的一个黄金分割点AP ADB.过点B 作BC AB，使得BC 1 AB，连AC，在AC 上截取2CD CB ，在AB 截取AP ADC.过点B 作BC AB，使得BC 1 AB，连AC，在AC 上截取3CD CB ，在AB 截取AP ADD.过点B 作BC AB，使得BC1 AB ，连AC ，在AC 上截取CD CB ，在AB 截取APAD。

2017年复旦附中新高一闯关语法练习(含答案)

复旦附中新高一闯关练习2017.9I. Grammar and Vocabulary1.Given these conditions, there will not be ________ room left in one’s brain for ________ rational thought.A. a; theB. /; aC. /; /D. the; /2.In the workplace, e-mail has now become ________ way for employers to monitor ________ what their employees are doing and thinking.A. the other; eitherB. one; everyC. another; bothD. other; all3.He ________ the test again; in that case, his mother will be very disappointed.A. might failB. must have failedC. should failD. could have failed4.He hurt his leg climbing the mountain; otherwise he ________ the meeting.A. will attendB. had attendedC. would have attendedD. would attend5.________ the demand for fish and seafood increases, people will not need to rely on land animals for food.A. WithB. AsC. DuringD. Because of6.Stonehenge is a good example of a site that many people think ________ to change.A. needB. to needC. needsD. needing7.Every week we go to the theatre! Not once since we arrived here ________ to the movies!A. we have goneB. we have beenC. had we goneD. have we been8.Other students had poorer exam results – he is by no means ________ in the class.A. the bestB. betterC. worseD. the worst9.Fast food chains used to be found only along highways or in business areas ________ people used to grab a quick lunch before returning to work.A. whereB. whenC. for whichD. while10.All the passengers object to transferring to the next flight ________ they ________ a proper explanation.A. though; will giveB. unless; are givenC. if; have givenD. so long as; get11.The percentage of women who would stay at home full-time, ________ they could afford it, dropped from 39 percent in 1981 to 31 percent in this survey.A. ifB. untilC. even ifD. as12.You’ve switched the machine off. I told you not to, ________?A. didn’t IB. haven’t youC. will youD. did I13.The company wasted ________ investing in out of date technology.A. a million poundB. millions of poundsC. several millions of poundD. a million of pounds14.Television has many advantages. It keep us ________ about the ________ news, and also provides entertainment in the home.A. informed; latestB. to know; laterC. learning; latterD. to think; late15.It’s difficult to say ________ this portrait was painted by.A. howB. whoseC. thatD. who16. Helen had to pay extra at the airport because she had ________.A. much too luggageB. too many pieces of luggagesC. too much luggageD. too many luggages17.________, you can’t come in here unless you’re a club member.A. Strictly speakingB. Considering carefullyC. Spoken strictlyD. Carefully considered18.I’ll wait here until 6:00, so ________ here by then.A. try and beB. trying to getC. you to comeD. to be sure to reach19.Tony finished his meal, ________ the bill, and left the restaurant.A. payingB. to checkC. checkingD. paid20.The palace is heavily guarded, because inside its walls ________.A. where sit the European leadersB. sit the European leadersC. the European leaders there sitD. that the European leaders sit21.Nowadays we hear music in shops and lifts, and many people ________ their own music with them, or even listen to music when they study.A. wearB. playC. liftD. carry22.It was no ________ getting upset about it though. Shaking her head, she sighed and looked up at her husband. “I’m sorry, darling,” she said meekly.A. worthB. needC. pointD. good23.“How could you have lost all your library books?” Charles asked his wife, eyeing her angrily from ________ the kitchen table. “I suppose we’ll have to pay for them now.”A. atB. acrossC. throughD. off24.Every day we receive many letters from our readers expressing their admiration for China, their appreciation of our work, and suggestion for improving the ________ of the magazine.A. qualityB. quantityC. characterD. price25.The agreement will not only ________ impact trade relations between China and the United States. It may influence the overall relations between the two countries.A. favoriteB. favorablyC. favorableD. unfavorable26.Let Harry play with your toys as well, Clare, you must learn to ________.A. supportB. careC. spareD. share27.It is wise to have some money ________ for old age.A. put awayB. kept upC. given awayD. laid up28.If you keep on, you’ll succeed ________.A. in timeB. at one timeC. at the same timeD. on time29.His temperature is still going down, and he’s breathing more easily. I think we can safely say he’s turned the corner. The underlined phrase means “________”.A. suffered a lotB. been successfully past the dangerC. still in dangerD. no hope of living through the day30.One week after coming to Berkeley, I was living with my friend Duane; I was regularly attending classes and had found two jobs to keep my head above water. The underlined phrase means ________.A. turn knowledge into practiceB. make more friendsC. have enough money to live onD. enrich one’s experienceII. Cloze(A)There are times when you find yourself unable to work out a problem. It is at this __31__ that the way in which you use your teacher is important. With a good teacher, such times should be less _-32__ than with a bad one; so the worse the teacher, the more responsibility you have for your __33__! Whatever your luck in this __34__, one thing is most significant and stays the same. Whatever the quality of teaching you __35__: if there is something you don’t understand, you must ask, again and again if necessary, until youdo understand it –fully. __36__ though this may seem, it is almost unbelievable how many people would rather sit in silent __37__ than admit not understanding. To behave in such a way is the only truly __38__ thing a student can do; it’s a false form of pride, which is the most useless, damaging quality anyone can have, to say nothing of a student! __39__, regard your teacher as a guide or even a friend and do not sit __40__ wondering what he’s going on about.31. A. course B. point C. thought D. opportunity32. A. lucky B. remote C. frequent D. comfortable33. A. mood B. image C. intention D. success34. A. field B. period C. respect D. direction35. A. offer B. describe C. arrange D. receive36. A. Likely B. Obvious C. Difficult D. Suitable37. A. ignorance B. depression C. nervousness D. disapproval38. A. safe B. simple C. strange D. stupid39. A. Otherwise B. Furthermore C. Therefore D. Nevertheless40. A. quietly B. honestly C. separately D. gently(B)Have you seen the popular Pete Sampras poster that says: “Pardon me, is that my serve in your throat?”Sampras isn’t the only __41__ hitter in professional tennis nowadays. Many of the best players are equally strong and skillful, __42__ of hitting a ball so hard that __43__ players find it all __44__ impossible to reach the ball in time to return it.In an effort to slow superserves the International Tennis Federation (ITF) has __45__ a ball that doesn’t move as fast as the standard tennis ball. The new ball __46__ virtually the same as the old ball. Its difference __47__ in its greater diameter, or width. The new ball is 7.08 centimeters in diameter, __48__ to 6.65 centimeters for the standard ball.A larger ball has more surface area and, __49__, more drag. Drag is a backward force that __50__ on a moving object and slows it down. Drag results __51__ the friction between the air and the surface area of the moving object. The greater the surface area of a ball, the greater the drag.Various tests of the new ball done at the University of Sheffield have found that serves __52__ indeed take longer to reach a __53__. In one test, the new ball gave players __54__ of 16 milliseconds more time to reach the ball on return.The ITF will continue to test the larger ball and ask for __55__ from players until December, 2001. Then it will decide whether to make the ball compulsory in professional play.41. A. heavy B. huge C. massive D. tremendous42. A. able B. capable C. powerful D. worthy43. A. contrary B. hostile C. opposing D. opposite44. A. but B. that C. along D. around45. A. advanced B. introduced C. progressed D. promoted46. A. grades B. measures C. ranks D. weighs47. A. involves B. lies C. proves D. justifies48. A. compared B. contrasted C. related D. directed49. A. in addition B. however C. hence D. moreover50. A. acts B. exerts C. functions D. performs51. A. out of B. in C. from D. towards52. A. would B. should C. could D. do53. A. destination B. object C. goal D. target54. A. an average B. a mean C. a difference D. a space55. A. agreement B. comments C. understanding D. recommendations参考答案：1-5 CCACB 6-10 CDDAB11-15 AABAD 16-20 CAADB21-25 DDBAB 26-30 DAABCCloze答案：31-35 BCDCD 36-40 BADCA41-45 ABCAB 46-50 DBACA51-55 CDDAB。

2017年上海市复旦大学附中高一下学期期中数学试卷与解析答案

2016-2017学年上海市复旦大学附中高一（下）期中数学试卷一、填空题（每题4分，共48分）1．（4分）半径为2，圆心为300°的圆弧的长为．2．（4分）函数y=|tanx|的对称轴是．3．（4分）在平面直角坐标系中，已知角θ的顶点在坐标原点，始边与x轴正半轴重合，终边在直线y=3x上，则sin2θ=．4．（4分）求函数的单调递减区间．5．（4分）已知锐角α，β满足cosα=，cos（α+β）=﹣，求cosβ．6．（4分）已知函数，则f（x）的定义域是．7．（4分）若长度为x2+4，4x，x2+6的三条线段可以构成一个锐角三角形，则x 取值范围是．8．（4分）若f（x）=2sinωx（0＜ω＜1）在区间上的最大值是，则ω=．9．（4分）如图所示，在塔底B测得山顶C的仰角为60°，在山顶测得塔顶A的仰角为45°，已知塔高AB=20米，则山高DC=米．10．（4分）函数y=的值域为．11．（4分）已知，则f （cos100°）=．12．（4分）设a，b均为大于1的自然数，函数f（x）=a（b+sinx），g（x）=b+cosx，若存在实数m，使得f（m）=g（m），则a+b=．二、选择题（共4小题，每小题4分，满分16分）13．（4分）若MP和OM分别是角的正弦线和余弦线，则（）A．MP＜OM＜0 B．OM＞0＞MP C．OM＜MP＜0 D．MP＞0＞OM14．（4分）已知，则下列不等式一定成立的是（）A．sin（α+β）＜sinα+sinβB．sin（α+β）＞s inα+sinβC．cos（α+β）＜sinα+sinβD．cos（α+β）＞cosα+cosβ15．（4分）把函数y=sin2x的图象沿着x轴向左平移个单位，纵坐标伸长到原来的2倍（横坐标不变）后得到函数y=f（x）的图象，对于函数y=f（x）有以下四个判断：（1）该函数的解析式为；（2）该函数图象关于点对称；（3）该函数在上是增函数；（4）若函数y=f（x）+a在上的最小值为，则其中正确的判断有（）A．1个 B．2个 C．3个 D．4个16．（4分）在区间[﹣2π，2π]范围内，函数y=tanx与函数y=sinx的图象交点的个数为（）A．3 B．5 C．7 D．9三、解答题（本题共5大题，满分56分）17．（10分）已经cos（2θ﹣3π）=，且θ是第四象限角，（1）求cosθ和sinθ的值；（2）求+的值．18．（10分）已知函数f（x）=（1）若，求f（a）的值．（2）求函数f（x）的最小正周期及单调递增区间．19．（10分）设△ABC的内角A，B，C所对的边分别为a，b，c且acosC+c=b．（1）求角A的大小；（2）若a=1，求△ABC的周长l的取值范围．20．（12分）函数y=f（x）满足f（3+x）=f（1﹣x），且x1，x2∈（2，+∞）时，＞0成立，若f（cos2θ+2m2+2）＜f（sinθ+m2﹣3m﹣2）对θ∈R恒成立．（1）判断y=f（x）的单调性和对称性；（2）求m的取值范围．21．（14分）已知函数f（x），g（x）满足关系，（1）设f（x）=cosx+sinx，求g（x）的解析式；（2）当f（x）=|sinx|+cosx时，存在x1，x2∈R，对任意x∈R，g（x1）≤g（x）≤g（x2）恒成立，求|x1﹣x2|的最小值．2016-2017学年上海市复旦大学附中高一（下）期中数学试卷参考答案与试题解析一、填空题（每题4分，共48分）1．（4分）半径为2，圆心为300°的圆弧的长为．【解答】解：300°=弧度．∴半径为2，圆心为300°的圆弧的长=×2=．故答案为：．2．（4分）函数y=|tanx|的对称轴是x=，k∈Z．【解答】解：函数y=|tanx|的图象是y=tanx把x轴的下部分翻折到x轴的上方可得到的．∴函数y=|tanx|的对称轴是x=，k∈Z．故答案为：x=，k∈Z．3．（4分）在平面直角坐标系中，已知角θ的顶点在坐标原点，始边与x轴正半轴重合，终边在直线y=3x上，则sin2θ=．【解答】解：∵角θ的顶点在平面直角坐标系xOy原点O，始边为x轴正半轴，终边在直线y=3x上，∴tanθ=3∴sin2θ====，故答案为：．4．（4分）求函数的单调递减区间[kπ，kπ+]，k∈Z．【解答】解：函数=sin（﹣2x）=cos2x，令2kπ≤2x≤2kπ+π，k∈Z，解得kπ≤x≤kπ+，k∈Z，∴f（x）的单调递减区间为[kπ，kπ+]，k∈Z．故答案为：[kπ，kπ+]，k∈Z．5．（4分）已知锐角α，β满足cosα=，cos（α+β）=﹣，求cosβ．【解答】解：∵锐角α，β满足cosα=，cos（α+β）=﹣，∴sinα==，同理可得sin（α+β）==，∴cosβ=cos[（α+β）﹣α]=cos（α+β）cosα+sin（α+β）sinα==6．（4分）已知函数，则f（x）的定义域是（﹣，﹣）∪（，）．【解答】解：∵函数y=lg（tanx﹣1）+，∴tanx﹣1＞0，且9﹣x2≥0，∴，∴x∈（﹣，﹣）∪（，）故答案为：（﹣，﹣）∪（，）．7．（4分）若长度为x2+4，4x，x2+6的三条线段可以构成一个锐角三角形，则x 取值范围是x．【解答】解：∵x2+6＞x2+4≥4x＞0，可得x2+6为最大边．由于此三角形为锐角三角形，∴cosθ=＞0，化为：x2＞，x＞0，解得x．故答案为：x．8．（4分）若f（x）=2sinωx（0＜ω＜1）在区间上的最大值是，则ω=．【解答】解：，故答案为：9．（4分）如图所示，在塔底B测得山顶C的仰角为60°，在山顶测得塔顶A的仰角为45°，已知塔高AB=20米，则山高DC=10（3+）米．【解答】解：如图，设CD=x m，则AE=x﹣20 m，tan 60°=，∴BD===（m）…（6分）在△AEC中，x﹣20=x，解得x=10（3+）m．故山高CD为10（3+）m…（12分）．故答案为：10（3+）．10．（4分）函数y=的值域为[，﹣1）∪（﹣1，] ．【解答】解：函数y=，∵分母不能为零，即sinx﹣cosx≠﹣1，设t=sinx﹣cosx=sin（x﹣），∴，且t≠﹣1．则sinx•cosx=，可得函数y===（t﹣1）=根据一次函数的单调性，可得函数y的值域为[，﹣1）∪（﹣1，]．故答案为：[，﹣1）∪（﹣1，]．11．（4分）已知，则f （cos100°）=3．【解答】解：∵已知，a•sin310°+b•cos310°=1，则f（cos100°）=f（﹣sin10°）=a•（﹣sin310°）+b•（﹣cos310°）+4=﹣1+4=3，故答案为：3．12．（4分）设a，b均为大于1的自然数，函数f（x）=a（b+sinx），g（x）=b+cosx，若存在实数m，使得f（m）=g（m），则a+b=4．【解答】解：由f（m）=g（m），即a（b+sinm）=b+cosmasinm﹣cosm=b﹣ab•sin（m﹣θ）=b（1﹣a）[注：sinθ=]∵﹣1≤sin（m﹣θ）≤1∴﹣≤b，（1﹣a）≤∵a，b均为大于1的自然数∴1﹣a＜0，b（1﹣a）＜0，∴b（1﹣a）≥﹣，b（a﹣1）≤b≤=．∵a≥4时，b＜2∴a＜4当a=2时b≤，b=2当a=3时b≤无解综上：a=2，b=2a+b=4．故答案为：4．二、选择题（共4小题，每小题4分，满分16分）13．（4分）若MP和OM分别是角的正弦线和余弦线，则（）A．MP＜OM＜0 B．OM＞0＞MP C．OM＜MP＜0 D．MP＞0＞OM【解答】解：在单位圆中画出角的正弦线MP和余弦线OM，如图所示；则OM＜MP＜0．故选：C．14．（4分）已知，则下列不等式一定成立的是（）A．sin（α+β）＜sinα+sinβB．sin（α+β）＞sinα+sinβC．cos（α+β）＜sinα+sinβD．cos（α+β）＞cosα+cosβ【解答】解：∵已知，sin（α+β）=sinαcosβ+cosαsinβ，∴0＜cosβ＜1，0＜cosα＜1，∴sin（α+β）＜sinα+sinβ成立，故A正确．由于sin（α+β）=sinαcosβ+cosαsinβ，0＜cosβ＜1，0＜cosα＜1，不能推出它大于sinα+sinβ，故B不正确．由于cos（α+β）=cosαcosβ﹣sinαsinβ，0＜cosβ＜1，0＜cosα＜1，不能推出它小于sinα+sinβ，故C错误．由于cos（α+β）=cosαcosβ﹣sinαsinβ，0＜cosβ＜1，0＜cosα＜1，不能推出它大于sinα+sinβ，故D错误．故选：A．15．（4分）把函数y=sin2x的图象沿着x轴向左平移个单位，纵坐标伸长到原来的2倍（横坐标不变）后得到函数y=f（x）的图象，对于函数y=f（x）有以下四个判断：（1）该函数的解析式为；（2）该函数图象关于点对称；（3）该函数在上是增函数；（4）若函数y=f（x）+a在上的最小值为，则其中正确的判断有（）A．1个 B．2个 C．3个 D．4个【解答】解：把函数y=sin2x的图象沿着x轴向左平移个单位，可得y=sin （2x+）的图象；再把纵坐标伸长到原来的2倍（横坐标不变）后得到函数y=f（x）=2sin（2x+）的图象，对于函数y=f（x）=2sin（2x+），故选项A不正确，故（1）错误；由于当x=时，f（x）=0，故该函数图象关于点对称，故（2）正确；在上，2x+∈[，]，故f（x）该函数在[0，]上不是增函数，故（3）错误；在上，2x+∈[，]，故当2x+=时，f（x）+a该函数在上取得最小值为﹣+a=，∴a=2，故（4）正确，故选：B．16．（4分）在区间[﹣2π，2π]范围内，函数y=tanx与函数y=sinx的图象交点的个数为（）A．3 B．5 C．7 D．9【解答】解：tanx=sinx得，即sinx（）=0，即sinx=0或，∴sinx=0或cosx=1．∴在区间[﹣2π，2π]内x=﹣2π，﹣π，0，π，2π共5个值．故两个函数图象的交点个数为5个．故选：B．三、解答题（本题共5大题，满分56分）17．（10分）已经cos（2θ﹣3π）=，且θ是第四象限角，（1）求cosθ和sinθ的值；（2）求+的值．【解答】解：由cos（2θ﹣3π）=cos（﹣π+2θ）=﹣cos2θ=，即cos2θ=1﹣2sin2θ=，（1）∵θ是第四象限角，∴sinθ=﹣．∵cos2θ=2cos2θ﹣1=∵θ是第四象限角，∴cosθ=．（2）由+=====．18．（10分）已知函数f（x）=（1）若，求f（a）的值．（2）求函数f（x）的最小正周期及单调递增区间．【解答】解：函数f（x）=（1）若，则f（a）=sinαcosα+cos2α+===；（2）将函数f（x）化简可得：f（x）=sin2x+cos2x+=sin2x+cos2x+1=sin （2x+）+1．∴函数f（x）的最小正周期T=．由2x+，k∈Z．得：≤x≤．∴函数f（x）的单调递增区间为：[，]，k∈Z．19．（10分）设△ABC的内角A，B，C所对的边分别为a，b，c且acosC+c=b．（1）求角A的大小；（2）若a=1，求△ABC的周长l的取值范围．【解答】解：（1）∵acosC+c=b，由正弦定理得2RsinAcosC+2RsinC=2RsinB，即sinAcosC+sinC=sinB，又∵sinB=sin（A+C）=sinAcosC+cosAsinC，∴sinC=cosAsinC，∵sinC≠0，∴，又∵0＜A＜π，∴．（2）由正弦定理得：b==，c=，∴l=a+b+c=1+（sinB+sinC）=1+（sinB+sin（A+B））=1+2（sinB+cosB）=1+2sin（B+），∵A=，∴B，∴B+，∴，故△ABC的周长l的取值范围为（2，3]．（2）另解：周长l=a+b+c=1+b+c，由（1）及余弦定理a2=b2+c2﹣2bccosA，∴b2+c2=bc+1，∴（b+c）2=1+3bc≤1+3（）2，解得b+c≤2，又∵b+c＞a=1，∴l=a+b+c＞2，即△ABC的周长l的取值范围为（2，3]．20．（12分）函数y=f（x）满足f（3+x）=f（1﹣x），且x1，x2∈（2，+∞）时，＞0成立，若f（cos2θ+2m2+2）＜f（sinθ+m2﹣3m﹣2）对θ∈R恒成立．（1）判断y=f（x）的单调性和对称性；（2）求m的取值范围．【解答】解：（1）由f （3+x）=f （1﹣x），可得f （2+x）=f（2﹣x），∴y=f （x）的对称轴为x=2．…（2分）当2＜x 1＜x2时，f （x1）＜f （x2）；当2＜x2＜x1时，f （x2）＜f （x1）．∴y=f （x）在（2，+∝）上为增函数，在（﹣∞，2）上为减函数．…（4分）（2）由f（cos2θ+2m2+2）＜f（sinθ+m2﹣3m﹣2），可得|cos2θ+2m2|＜|sinθ+m2﹣3m﹣4|，即m2﹣3m﹣4+sinθ＞cos2θ+2m2（i），或m2﹣3m﹣4+sinθ＜﹣cos2θ﹣2m2（ii）恒成立．…（7分）由（i）得m2+3m+4＜﹣cos2θ+sinθ=（sinθ+）2﹣恒成立，∴m2+3m+4＜﹣，故4m2+12m+21＜0恒成立，m无解．…（10分）由（ii）得3m2﹣3m﹣4＜﹣cos2θ﹣sinθ=（sinθ﹣）2﹣恒成立，可得3m2﹣3m﹣4＜﹣，即12m2﹣12m﹣11＜0，解得＜m＜．…（13分）21．（14分）已知函数f（x），g（x）满足关系，（1）设f（x）=cosx+sinx，求g（x）的解析式；（2）当f（x）=|sinx|+cosx时，存在x1，x2∈R，对任意x∈R，g（x1）≤g（x）≤g（x2）恒成立，求|x1﹣x2|的最小值．【解答】解：由，（1）当f（x）=cosx+sinx，可得g（x）=（cosx+sinx）[cos（x+）+sin（x+）]=（cosx+sinx）（cosx﹣sinx）=cos2x﹣sin2x=cos2x．∴g（x）的解析式为g（x）=cos2x．（2）f（x）=|sinx|+cosx时，可得g（x）=（|sinx|+cosx）（|cosx|﹣sinx）=，k∈Z．∵存在x1，x2∈R，对任意x∈R，g（x1）≤g（x）≤g（x2）恒成立，当x1=2kπ+π或2k时，可得﹣1≤g（x）．当x2=2kπ+时，可得g（x）≤2．那么：|x1﹣x2|=|2kπ+π﹣（2kπ+）|=或者：x1﹣x2|=|2kπ+﹣（2kπ+）|=∴|x1﹣x2|的最小值为．赠送初中数学几何模型【模型三】双垂型：图形特征：运用举例：1.在Rt△ABC中，∠ACB＝90°，以斜边AB为底边向外作等腰三角形PAB，连接PC.（1）如图，当∠APB＝90°时，若AC=5，PC＝，求BC的长；（2）当∠APB＝90°时，若AB=APBC的面积是36，求△ACB的周长.2.已知：如图，B、C、E三点在一条直线上，AB＝AD，BC＝CD.（1）若∠B＝90°，AB＝6，BC＝23，求∠A的值；（2）若∠BAD＋∠BCD＝180°，cos∠DCE＝35，求ABBC的值.3.如图，在四边形ABCD中，AB=AD，∠DAB=∠BCD=90°，（1）若AB=3，BC+CD=5，求四边形ABCD的面积（2）若p= BC+CD，四边形ABCD的面积为S，试探究S与p之间的关系。

上海市复旦大学附中2016-2017学年高一上学期期中考试数学试卷(解析版)

word格式-可编辑-感谢下载支持2016-2017学年上海市复旦大学附中高一（上）期中数学试卷一.填空题1．集合{1，2，3，…，2015，2016}的子集个数为．2．已知全集U=R，集合A={x|x≤1}，集合B={x|x≥2}，则∁U（A∪B）=．3．已知集合A={x|1≤x≤2}，集合B={x|x≤a}，若A∩B≠∅，则实数a的取值范围是．4．己知集合U={a，b，c，d，e，f}，集合A={a，b，c，d}，A∩B={b}，∁U（A∪B）={f}，则集合B=．5．已知a2＞a1＞0，b2＞b1＞0，且a1+a2=b1+b2=1，记A=a1b1+a2b2，B=a1b2+a2b1，C=，则按A、B、C从小到大的顺序排列是．6．已知Rt△ABC的周长为定值2，则它的面积最大值为．7．我们将b﹣a称为集合M={x|a≤x≤b}的“长度”，若集合M={x|m≤x≤m+}，N={x|n﹣0.5≤x≤n}，且集合M和集合N都是集合{x|0≤x≤1}的子集，则集合M∩N的“长度”的最小值是．8．已知A={x|＞x}，B={x|x（x﹣3）（x+3）＞0}，则A∩B=．9．对于任意集合X与Y，定义：①X﹣Y={x|x∈X且x∉Y}，②X△Y=（X﹣Y）∪（Y﹣X），已知A={y|y=x2，x∈R}，B={y|﹣2≤y≤2}，则A△B=．10．已知常数a是正整数，集合A={x||x﹣a|＜a+，x∈Z}，B={x||x|＜2a，x∈Z}，则集合A∪B中所有元素之和为．11．非空集合G关于运算⊕满足：（1）对任意a，b∈G，都有a+b∈G；（2）存在e∈G使得对于一切a∈G都有a⊕e=e⊕a=a，则称G是关于运算⊕的融洽集，现有下列集合与运算：①G是非负整数集，⊕：实数的加法；②G是偶数集，⊕：实数的乘法；③G是所有二次三项式构成的集合，⊕：多项式的乘法；④G={x|x=a+b，a，b∈Q}，⊕：实数的乘法；其中属于融洽集的是（请填写编号）12．集合A={（x，y）|y=a|x|，x∈R}，B={（x，y）|y=x+a，x∈R}，已知集合A∩B中有且仅有一个元素，则常数a的取值范围是．二.选择题13．已知集合A={1，2，3，…，2105，2016}，集合B={x|x=3k+1，k∈Z}，则A∩B中的最大元素是（）A．2014 B．2015C．2016 D．以上答案都不对14．已知全集U=A∪B中有m个元素，（∁U A）∪（∁U B）中有n个元素．若A∩B非空，则A∩B的元素个数为（）A．mn B．m+n C．n﹣m D．m﹣n15．命题“已知x，y∈R，如果x2+y2=0，那么x=0且y=0”的逆否命题是（）A．已知x，y∈R，如果x2+y2≠0，那么x≠0且y≠0B．已知x，y∈R，如果x2+y2≠0，那么x≠0或y≠0C．已知x，y∈R，如果x≠0或y≠0，那么x2+y2≠0word格式-可编辑-感谢下载支持D．已知x，y∈R，如果x≠0且y≠0，那么x2+y2≠016．对任意实数a，b，c，给出下列命题：①“a=b”是“ac=bc”的充要条件；②“a+5是无理数”是“a是无理数”的充要条件；③“a＞b”是“a2＞b2”的充分条件；④“a＜4”是“a＜3”的必要条件；其中真命题的个数是（）A．1个B．2个C．3个D．4个三.解答题17．已知集合A={1，2，3}，B={x|x2﹣（a+1）x+a=0，x∈R}，若A∪B=A，求实数a．18．已知a，b，c∈R+，求证：2（a3+b3+c3）≥ab2+a2b+bc2+b2c+ac2+a2c．19．设正有理数a1是的一个近似值，令a2=1+，求证：（1）介于a1与a2之间；（2）a2比a1更接近于．20．已知对任意实数x，不等式mx2﹣（3﹣m）x+1＞0成立或不等式mx＞0成立，求实数m的取值范围．21．已知关于x的不等式（4kx﹣k2﹣12k﹣9）（2x﹣11）＞0，其中k∈R；（1）试求不等式的解集A；（2）对于不等式的解集A，记B=A∩Z（其中Z为整数集），若集合B为有限集，求实数k的取值范围，使得集合B中元素个数最少，并用列举法表示集合B．2016-2017学年上海市复旦大学附中高一（上）期中数学试卷参考答案与试题解析一.填空题1．（2016秋•杨浦区校级期中）集合{1，2，3，…，2015，2016}的子集个数为22016．【考点】子集与真子集．【专题】集合思想；集合．【分析】对于有限集合，我们有以下结论：若一个集合中有n个元素，则它有2n个子集．【解答】解：∵集合{1，2，3，…，2015，2016}中有2016个元素，∴集合M{1，2，3，…，2015，2016}的子集的个数为22016；故答案为：22016．【点评】本题考查了集合的子集个数，若一个集合中有n个元素，则它有2n个子集，有（2n﹣1）个真子集，属于基础题．2．（2016秋•杨浦区校级期中）已知全集U=R，集合A={x|x≤1}，集合B={x|x≥2}，则∁U（A∪B）= {x|1＜x＜2} ．【考点】交、并、补集的混合运算．【专题】集合思想；定义法；集合．【分析】根据并集与补集的定义，进行计算即可．【解答】解：全集U=R，集合A={x|x≤1}，集合B={x|x≥2}，所以A∪B={x|x≤1或x≥2}，所以∁U（A∪B）={x|1＜x＜2}．故答案为：{x|1＜x＜2}．【点评】本题考查了并集与补集的定义与应用问题，是基础题目．3．（2016秋•杨浦区校级期中）已知集合A={x|1≤x≤2}，集合B={x|x≤a}，若A∩B≠∅，则实数a的取值范围是[1，+∞）．【考点】交集及其运算．【专题】计算题；集合思想；定义法；集合．【分析】题中条件：“A∩B≠∅，”表示两个集合的交集的结果不是空集，即可求解实数a的取值范围．【解答】解：集合A={x|1≤x≤2}，集合B={x|x≤a}，因为A∩B≠∅，所以a≥1故答案为：[1，+∞）【点评】本题考查集合的关系、一元二次不等式的解法，考查运算能力，是基础题．4．（2016秋•杨浦区校级期中）己知集合U={a，b，c，d，e，f}，集合A={a，b，c，d}，A∩B={b}，∁U（A∪B）={f}，求集合B．【考点】交、并、补集的混合运算．【专题】集合思想；综合法；集合．【分析】根据全集U，以及A与B并集的补集确定出A与B的并集，再根据A与B的交集及A，确定出B即可．【解答】解：∵U={a，b，c，d，e，f}，∁U（A∪B）={f}，∴A∪B={a，b，c，d，e}，∵A∩B={b}；A={a，b，c，d}，∴b∈B，e∈B，b∉B，c∉B，d∉B，∴B={b，e}．【点评】此题考查了交、并、补集的混合运算，熟练掌握各自的定义是解本题的关键．5．（2016秋•杨浦区校级期中）已知a2＞a1＞0，b2＞b1＞0，且a1+a2=b1+b2=1，记A=a1b1+a2b2，B=a1b2+a2b1，C=，则按A、B、C从小到大的顺序排列是B＜C＜A．【考点】不等式比较大小．【专题】计算题；转化思想；转化法；不等式．【分析】不妨令a1=，a2=，b1=，b2=，分别求出A，B，比较即可【解答】解：∵a2＞a1＞0，b2＞b1＞0，且a1+a2=b1+b2=1，不妨令a1=，a2=，b1=，b2=，A=a1b1+a2b2=+=，B=a1b2+a2b1=+=，∵C==∴B＜C＜A故答案为：B＜C＜A．【点评】本题主要考查不等式与不等关系，利用特殊值代入法比较几个式子在限定条件下的大小关系，是一种简单有效的方法，属于基础题．6．（2016秋•杨浦区校级期中）已知Rt△ABC的周长为定值2，则它的面积最大值为3﹣2．【考点】正弦定理．【专题】计算题；转化思想；综合法；解三角形；不等式的解法及应用．【分析】设直角边长为a，b，则斜边长为，利用直角三角形ABC的三边之和为2，可得a+b+=2，利用基本不等式，即可求△ABC的面积的最大值．【解答】解：设直角边长为a，b，则斜边长为，∵直角三角形ABC的三边之和为2，∴a+b+=2，∴2≥2+，∴≤=2﹣，∴ab≤6﹣4，∴S=ba≤3﹣2，∴△ABC的面积的最大值为3﹣2．故答案为：3﹣2．【点评】本题考查基本不等式的运用，考查学生的计算能力，正确运用基本不等式是关键，属于中档题．7．（2016秋•杨浦区校级期中）我们将b﹣a称为集合M={x|a≤x≤b}的“长度”，若集合M={x|m≤x≤m+}，N={x|n﹣0.5≤x≤n}，且集合M和集合N都是集合{x|0≤x≤1}的子集，则集合M∩N的“长度”的最小值是．【考点】交集及其运算．【专题】计算题；新定义；转化思想；转化法；集合．【分析】当集合M∩N的长度的最小值时，M与N应分别在区间[0，1]的左右两端，由此能求出M∩N 的长度的最小值．【解答】解：根据题意，M的长度为，N的长度为，当集合M∩N的长度的最小值时，M与N应分别在区间[0，1]的左右两端，故M∩N的长度的最小值是=．故答案为：．【点评】本题考查交集的“长度”的最小值的求法，是基础题，解题时要认真审题，注意新定义的合理运用．8．（2016秋•杨浦区校级期中）已知A={x|＞x}，B={x|x（x﹣3）（x+3）＞0}，则A∩B={x|﹣3＜x＜0} ．【考点】交集及其运算．【专题】计算题；方程思想；定义法；集合．【分析】先利用不等式的性质分别求出集合A和B，由此利用交集的性质能求出A∩B．【解答】解：∵A={x|＞x}={x|﹣2≤x≤1，或x＜0}，B={x|x（x﹣3）（x+3）＞0}={x|﹣3＜x＜0或x＞3}，∴A∩B={x|﹣3＜x＜0}．故答案为：{x|﹣3＜x＜0}．【点评】本题考查交集的求法，是中档题，解题时要认真审题，注意无理不等式和高次不等式性质的合理运用．9．（2016秋•杨浦区校级期中）对于任意集合X与Y，定义：①X﹣Y={x|x∈X且x∉Y}，②X△Y=（X ﹣Y）∪（Y﹣X），已知A={y|y=x2，x∈R}，B={y|﹣2≤y≤2}，则A△B=[﹣3，0）∪（3，+∞）．【考点】子集与交集、并集运算的转换．【专题】综合题；方程思想；演绎法；集合．【分析】由A={y|y=x2，x∈R}={y|y≥0}，B={y|﹣2≤y≤2}，先求出A﹣B={y|y＞2}，B﹣A={y|﹣2≤y＜0}，再求A△B的值．【解答】解：∵A={y|y=x2，x∈R}={y|y≥0}，B={y|﹣2≤y≤2}，∴A﹣B={y|y＞2}，B﹣A={y|﹣2≤y＜0}，∴A△B={y|y＞2}∪{y|﹣2≤y＜0}，故答案为：[﹣3，0）∪（3，+∞）．【点评】本题考查集合的交、并、补集的运算，解题时要认真审题，仔细解答，注意正确理解X﹣Y={x|x ∈X且x∉Y}、X△Y=（X﹣Y）∪（Y﹣X）．10．（2016秋•杨浦区校级期中）已知常数a是正整数，集合A={x||x﹣a|＜a+，x∈Z}，B={x||x|＜2a，x∈Z}，则集合A∪B中所有元素之和为2a．【考点】并集及其运算．【专题】集合思想；转化法；集合．【分析】分别求出集合A、B中的元素，从而求出A、B的并集，求和即可．【解答】解：A={x||x﹣a|＜a+，x∈Z}={0，a，2a}，B={x||x|＜2a，x∈Z}={﹣a，0，a}，则集合A∪B={﹣a，0，a，2a}，故集合A∪B中所有元素之和是2a，故答案为：2a．【点评】本题考查了集合的运算，考查解绝对值不等式问题，是一道基础题．11．（2016秋•杨浦区校级期中）非空集合G关于运算⊕满足：（1）对任意a，b∈G，都有a+b∈G；（2）存在e∈G使得对于一切a∈G都有a⊕e=e⊕a=a，则称G是关于运算⊕的融洽集，现有下列集合与运算：①G是非负整数集，⊕：实数的加法；②G是偶数集，⊕：实数的乘法；③G是所有二次三项式构成的集合，⊕：多项式的乘法；④G={x|x=a+b，a，b∈Q}，⊕：实数的乘法；其中属于融洽集的是①④（请填写编号）【考点】元素与集合关系的判断．【专题】新定义；集合思想；集合．【分析】逐一验证几个选项是否分别满足“融洽集”的两个条件，若两个条件都满足，是“融洽集”，有一个不满足，则不是“融洽集”．【解答】解：①对于任意非负整数a，b知道：a+b仍为非负整数，所以a⊕b∈G；取e=0，及任意非负整数a，则a+0=0+a=a，因此G对于⊕为整数的加法运算来说是“融洽集”；②对于任意偶数a，b知道：a+b仍为偶数，故有a+b∈G；但是不存在e∈G，使对一切a∈G都有a⊕e=e ⊕a=a，故②的G不是“融洽集”．③对于G={二次三项式}，若a、b∈G时，a，b的两个同类项系数，则其积不再为二次三项式，故G不是和谐集，故③不正确；④G={x|x=a+b，a，b∈Q}，设x1=a+b，x2=c+d，则设x1+x2=（a+c）+（b+d），属于集合G，取e=1，a×1=1×a=a，因此G对于⊕实数的乘法运算来说是“融洽集”，故④中的G是“融洽集”．故答案为①④．【点评】本题考查了对新定义“融洽集”理解能力，及对有关知识的掌握情况．关键是看所给的数集是否满足“融洽集”的两个条件．12．（2016秋•杨浦区校级期中）集合A={（x，y）|y=a|x|，x∈R}，B={（x，y）|y=x+a，x∈R}，已知集合A∩B中有且仅有一个元素，则常数a的取值范围是[﹣1，1] ．【考点】交集及其运算．【专题】计算题；转化思想；转化法；集合．【分析】由已知得a|x|=x+a有1个解，由此能求出常数a的取值范围．【解答】解：∵集合A={（x，y）|y=a|x|，x∈R}，B={（x，y）|y=x+a，x∈R}，集合A∩B中有且仅有一个元素，∴a|x|=x+a有1个解，若x≥0，ax=x+a，x=，若x＜0，﹣ax=x+a，x=﹣，由已知得或或或，解得﹣1≤a≤1．∴常数a的取值范围是[﹣1，1]．故答案为：[﹣1，1]．【点评】本题考查常数的取值范围的求法，是基础题，解题时要认真审题，是基础题，解题时要认真审题，注意交集性质的合理运用．二.选择题13．（2016秋•杨浦区校级期中）已知集合A={1，2，3，…，2105，2016}，集合B={x|x=3k+1，k∈Z}，则A∩B中的最大元素是（）A．2014 B．2015C．2016 D．以上答案都不对【考点】交集及其运算．【专题】计算题；集合思想；定义法；集合．【分析】由题意求出A与B的交集，即可作出判断．【解答】解：∵A={1，2，3，…，2105，2016}，集合B={x|x=3k+1，k∈Z}∴则A∩B中的最大元素是2014．故选：A．【点评】此题考查了交集及其运算，熟练掌握交集的定义是解本题的关键．14．（2009•江西）已知全集U=A∪B中有m个元素，（∁U A）∪（∁U B）中有n个元素．若A∩B非空，则A∩B的元素个数为（）A．mn B．m+n C．n﹣m D．m﹣n【考点】V enn图表达集合的关系及运算．【专题】数形结合．【分析】要求A∩B的元素个数，可以根据已知绘制出满足条件的韦恩图，根据图来分析（如解法一），也可以利用德摩根定理解决（如解法二）．【解答】解法一：∵（C U A）∪（C U B）中有n个元素，如图所示阴影部分，又∵U=A∪B中有m个元素，故A∩B中有m﹣n个元素．解法二：∵（C U A）∪（C U B）=C U（A∩B）有n个元素，又∵全集U=A∪B中有m个元素，由card（A）+card（C U A）=card（U）得，card（A∩B）+card（C U（A∩B））=card（U）得，card（A∩B）=m﹣n，故选D．【点评】解答此类型题目时，要求对集合的性质及运算非常熟悉，除教材上的定义，性质，运算律外，还应熟练掌握：①（C U A）∪（C U B）=C U（A∩B）②（C U A）∩（C U B）=C U（A∪B）③card（A∪B）=card（A）+card（B）﹣card（A∩B）等．15．（2016秋•杨浦区校级期中）命题“已知x，y∈R，如果x2+y2=0，那么x=0且y=0”的逆否命题是（）A．已知x，y∈R，如果x2+y2≠0，那么x≠0且y≠0B．已知x，y∈R，如果x2+y2≠0，那么x≠0或y≠0C．已知x，y∈R，如果x≠0或y≠0，那么x2+y2≠0D．已知x，y∈R，如果x≠0且y≠0，那么x2+y2≠0【考点】四种命题间的逆否关系．【专题】定义法；简易逻辑．【分析】根据已知中原命题，写出逆否命题，可得答案．【解答】解：命题“已知x，y∈R，如果x2+y2=0，那么x=0且y=0”的逆否命题是“已知x，y∈R，如果x≠0或y≠0，那么x2+y2≠0”故选：C【点评】本题考查的知识点是四种命题，难度不大，属于基础题．16．（2016秋•杨浦区校级期中）对任意实数a，b，c，给出下列命题：①“a=b”是“ac=bc”的充要条件；②“a+5是无理数”是“a是无理数”的充要条件；③“a＞b”是“a2＞b2”的充分条件；④“a＜4”是“a＜3”的必要条件；其中真命题的个数是（）A．1个B．2个C．3个D．4个【考点】命题的真假判断与应用；必要条件、充分条件与充要条件的判断．【专题】综合法；简易逻辑．【分析】逐项判断即可．①由ac=bc不能推出a=b；②由5是有理数易判断；③根据不等式的性质可得；④根据充分必要条件的定义易得．【解答】解：①由“a=b“可得ac=bc，但当ac=bc时，不能得到a=b，故“a=b”是“ac=bc”的充分不必要条件，故①错误；②因为5是有理数，所以当a+5是无理数时，a必为无理数，反之也成立，故②正确；③取a=1，b=﹣2，此时a2＜b2，故③错误；④当a＜4时，不能推出a＜3；当a＜3时，有a＜4成立，故“a＜4”是“a＜3”的必要不充分条件，故④正确．综上可得正确的命题有2个．故选：B．【点评】本题考查充分必要条件的判断，掌握充分必要条件的定义是关键．属于基础题．三.解答题word格式-可编辑-感谢下载支持17．（2016秋•杨浦区校级期中）已知集合A={1，2，3}，B={x|x2﹣（a+1）x+a=0，x∈R}，若A∪B=A，求实数a．【考点】并集及其运算．【专题】计算题；分类讨论；集合．【分析】根据A∪B=A，得到B⊆A，然后分B为空集和不是空集讨论，A为空集时，只要二次方程的判别式小于0即可，不是空集时，分别把1和2代入二次方程求解a的范围，注意求出a后需要验证．【解答】解：由A∪B=A，得B⊆A．①若B=∅，则△=（a+1）2﹣4a＜0，解得：a∈∅；②若1∈B，△=（a+1）2﹣4a=0，此时a=1，满足12﹣a﹣1+a=0，此时B={1}，符合题意；③若2∈B，则22﹣2a﹣2+a=0，解得：a=2，此时A={2，1}，满足题意．④若3∈B，则32﹣3a﹣3+a=0，解得：a=3，此时A={3，1}，满足题意．综上所述，实数a的值为：1，2，3．【点评】本题考查了并集及其运算，考查了分类讨论的数学思想，求出a值后的验证是解答此题的关键，是基础题．18．（2016秋•杨浦区校级期中）已知a，b，c∈R+，求证：2（a3+b3+c3）≥ab2+a2b+bc2+b2c+ac2+a2c．【考点】不等式的证明．【专题】证明题；转化思想；演绎法；不等式的解法及应用．【分析】作差，因式分解，即可得到结论．【解答】证明：（a3+b3）﹣（a2b+ab2）=a2（a﹣b）+b2（b﹣a）=（a﹣b）（a2﹣b2）=（a﹣b）2（a+b）∵a＞0，b＞0，∴（a3+b3）﹣（a2b+ab2）≥0∴a3+b3≥a2b+ab2．同理b3+c3≥bc2+b2c，a3+c3≥ac2+a2c，三式相加，可得2（a3+b3+c3）≥ab2+a2b+bc2+b2c+ac2+a2c．【点评】本题考查不等式的证明，考查作差法的运用，考查学生分析解决问题的能力，属于中档题．19．（2016秋•杨浦区校级期中）设正有理数a1是的一个近似值，令a2=1+，求证：（1）介于a1与a2之间；（2）a2比a1更接近于．【考点】二分法求方程的近似解．【专题】证明题；转化思想；作差法；不等式．【分析】（1）利用作差法，再因式分解，确定其符号，即可得到结论；（2）利用作差法，判断|a2﹣|﹣|a1﹣|＜0，即可得到结论【解答】证明：（1）a2﹣=1+﹣=，∵若a1＞，∴a1﹣＞0，而1﹣＜0，∴a2＜∵若a1＜，∴a1﹣＜0，而1﹣＜0，∴a2＞，故介于a1与a2之间；word格式-可编辑-感谢下载支持（2）|a2﹣|﹣|a1﹣|=﹣|a1﹣|=|a1﹣|×，∵a1＞0，﹣2＜0，|a1﹣|＞0，∴|a2﹣|﹣|a1﹣|＜0∴|a2﹣|＜|a1﹣|∴a2比a1更接近于．【点评】本题考查不等式的证明，考查作差法的运用，确定差的符号是关键．20．（2016秋•杨浦区校级期中）已知对任意实数x，不等式mx2﹣（3﹣m）x+1＞0成立或不等式mx＞0成立，求实数m的取值范围．【考点】一元二次不等式的解法．【专题】分类讨论；转化思想；不等式的解法及应用．【分析】①对任意实数x，不等式mx2﹣（3﹣m）x+1＞0成立，对m分类讨论，m=0时，易判断出．m ≠0时，，解出即可得出．②对任意实数x，不等式mx＞0成立，m∈∅．【解答】解：①对任意实数x，不等式mx2﹣（3﹣m）x+1＞0成立，m=0时化为：﹣3x+1＞0，不成立，舍去．m≠0时，，解得．②对任意实数x，不等式mx＞0成立，m∈∅．综上可得：．∴实数m的取值范围是．【点评】本题考查了一元二次不等式的解法，考查了分类讨论方法、推理能力与计算能力，属于中档题．21．（2016秋•杨浦区校级期中）已知关于x的不等式（4kx﹣k2﹣12k﹣9）（2x﹣11）＞0，其中k∈R；（1）试求不等式的解集A；（2）对于不等式的解集A，记B=A∩Z（其中Z为整数集），若集合B为有限集，求实数k的取值范围，使得集合B中元素个数最少，并用列举法表示集合B．【考点】一元二次不等式的解法．【专题】分类讨论；不等式的解法及应用；不等式．【分析】（1）对k分类讨论，利用一元二次不等式的解法即可得出．（2）根据B=A∩Z（其中Z为整数集），集合B为有限集，即可得出．【解答】解：（1）①当k＜0，A={x|}；②当k=0，A={x|x}；③当0＜k＜1或k＞9，A={x|x，或x＞}；④当1≤k≤9，A={x|x＜，或x＞}；（2）B=A∩Z（其中Z为整数集），集合B为有限集，word格式-可编辑-感谢下载支持只有k＜0，B={2，3，4，5}．【点评】本题考查了一元二次不等式的解法，考查了分类讨论方法、推理能力与计算能力，属于中档题．。

2017-2018年上海市复旦附中高一(下)期末数学试卷(解析版)

2017-2018学年上海市复旦附中高一（下）期末数学试卷一.填空题1．（3分）在等差数列{a n}中，若a4＝0，a6+a7＝10，则a7＝2．（3分）在数列1、3、7、15、…中，按此规律，127是该数列的第项3．（3分）已知数列{a n}的前n项和S n＝n2﹣1，那么数列{a n}的通项公式为4．（3分）若在等比数列{a n}中，a1•a2…a9＝512，则a5＝5．（3分）方程（3cos x﹣1）（cos x+sin x）＝0的解集是6．（3分）若数列{a n}满足a1＝13，a n+1﹣a n＝n，则的最小值为7．（3分）若数列{a n}是等差数列，则数列（m∈N*）也为等差数列，类比上述性质，相应地，若正项数列{c n}是等比数列，则数列d n＝也是等比数列8．（3分）观察下列式子：，，，…，你可归纳出的不等式是．9．（3分）在我国古代数学著作《孙子算经》中，卷下第二十六题是：今有物，不知其数，三三数之剩二，五五数之剩三，七七数之剩二，问物几何？满足题意的答案可以用数列表示，该数列的通项公式可以表示为a n＝10．（3分）对于下列数排成的数阵：它的第10行所有数的和为11．（3分）对于数列{a n}满足：a1＝1，a n+1﹣a n∈{a1，a2，…，a n}（n∈N*），其前n项和为S n，记满足条件的所有数列{a n}中，S12的最大值为a，最小值为b，则a﹣b＝12．（3分）设n∈N*，用A n表示所有形如++…+的正整数集合，其中0≤r1＜r2＜…＜r n≤n，且r i∈N（i∈N*），b n为集合A n中的所有元素之和．则{b n}的通项公式为b n ＝．二.选择题13．（3分）“b是与的等差中项”是“b是与的等比中项”的（）A．充分不必要条件B．必要不充分条件C．充要条件D．既不充分也不必要条件14．（3分）在数列{a n}中，a1＝1，a2＝64，且数列是等比数列，其公比，则数列{a n}的最大项等于（）A．a7B．a8C．a6或a9D．a1015．（3分）若数列，若k∈N*，则在下列数列中，可取遍数列{a n}前6项值的数列为（）A．{a2k+1}B．{a3k+1}C．{a4k+1}D．{a5k+1}16．（3分）数列{a n}中，若a1＝a，，n∈N*，则下列命题中真命题个数是（）（1）若数列{a n}为常数数列，则a＝±1；（2）若a∈（0，1），数列{a n}都是单调递增数列；（3）若a∉Z，任取{a n}中的9项，，，…，（1＜k1＜k2＜…＜k9）构成数列{a n}的子数列{}，n＝1，2，…，9，则{}都是单调数列．A．0个B．1个C．2个D．3个三.解答题17．已知{a n}是一个公差大于0的等差数列，且满足a4a6＝96，a3+a7＝20，数列{b n}满足等式：（n∈N*）．（1）求数列{a n}的通项公式；（2）求数列的前n项和S n．18．已知b、c为常数且均不为零，数列{a n}的通项公式为a n＝，并且a1、a3、a2成等差数列，a1、a2、a4成等比数列．（1）求b、c的值；（2）设S n是数列{a n}前n项的和，求使得不等式S2n＞20182成立的最小正整数n．19．王某2017年12月31日向银行贷款100000元，银行贷款年利率为5%，若此贷款分十年还清（2027年12月31日还清），每年年底等额还款（每次还款金额相同），设第n年末还款后此人在银行的欠款额为a n元．（1）设每年的还款额为m元，请用m表示出a2；（2）求每年的还款额（精确到1元）．20．设数列{a n}的首项a1为常数，且a n+1＝3n﹣2a n（n∈N*）．（1）判断数列是否为等比数列，请说明理由；（2）S n是数列{a n}的前n项的和，若{S n}是递增数列，求a1的取值范围．21．如果数列{a n}对任意的n∈N*满足：a n+2+a n＞2a n+1，则称数列{a n}为“M数列”．（1）已知数列{a n}是“M数列”，设b n＝a n+1﹣a n，n∈N*，求证：数列{b n}是递增数列，并指出2（a5﹣a4）与a4﹣a2的大小关系（不需要证明）；（2）已知数列{a n}是首项为1，公差为2d的等差数列，S n是其前n项的和，若数列{|S n|}是“M数列”，求d的取值范围；（3）已知数列{a n}是各项均为正数的“M数列”，对于n取相同的正整数时，比较和的大小，并说明理由．2017-2018学年上海市复旦附中高一（下）期末数学试卷参考答案与试题解析一.填空题1．（3分）在等差数列{a n}中，若a4＝0，a6+a7＝10，则a7＝6【解答】解：在等差数列{a n}中，由a4＝0，a6+a7＝10，得2a4+5d＝10，即d＝2．∴a7＝a4+3d＝6．故答案为：6．2．（3分）在数列1、3、7、15、…中，按此规律，127是该数列的第7项【解答】解：a2﹣a1＝21，a3﹣a2＝22，a4﹣a3＝23，…依此类推可得a n﹣a n﹣1＝2n﹣1∴a2﹣a1+a3﹣a2+a4﹣a3…+a n﹣a n﹣1＝a n﹣a1＝21+22+23+…+2n﹣1＝2n﹣2∴a n﹣a1＝2n﹣2，a n＝2n﹣1，∴2n﹣1＝127，解得n＝7，故答案为：73．（3分）已知数列{a n}的前n项和S n＝n2﹣1，那么数列{a n}的通项公式为a n＝【解答】解：数列{a n}的前n项和S n＝n2﹣1，可得a1＝S1＝1﹣1＝0；n≥2时，a n＝S n﹣S n﹣1＝n2﹣1﹣（n﹣1）2+1＝2n﹣1，则a n＝，故答案为：a n＝．4．（3分）若在等比数列{a n}中，a1•a2…a9＝512，则a5＝2【解答】解：{a n}是等比数列，a m•a n＝a p•a q．由a1•a2…a9＝512，即，∴a5＝2．故答案为：2．5．（3分）方程（3cos x﹣1）（cos x+sin x）＝0的解集是【解答】解：方程（3cos x﹣1）（cos x+sin x）＝0，整理得：（3cos x﹣1）•2sin（x+）＝0．故：cos x＝或sin（x+）＝0，解得：x＝或x＝﹣（k∈Z）．故方程的解集为{x|，x＝﹣，k∈Z}故答案为：{x|}，x＝﹣，k∈Z}6．（3分）若数列{a n}满足a1＝13，a n+1﹣a n＝n，则的最小值为【解答】解：数列{a n}满足a1＝13，a n+1﹣a n＝n，可得a n＝a1+（a2﹣a1）+…+（a n﹣a n﹣1）＝13+1+2+…+（n﹣1）＝13+n（n﹣1），则＝n+﹣，由n+≥2＝，当且仅当n＝∉N*，由n＝5可得×5+﹣＝；由n＝6可得×6+﹣＝，则的最小值为．故答案为：．7．（3分）若数列{a n}是等差数列，则数列（m∈N*）也为等差数列，类比上述性质，相应地，若正项数列{c n}是等比数列，则数列d n＝也是等比数列【解答】解：在类比等差数列的性质推理等比数列的性质时，我们一般的思路有：由加法类比推理为乘法，由减法类比推理为除法，由算术平均数类比推理为几何平均数等，故我们可以由数列{a n}是等差数列，则当时，数列{b n}也是等差数列．类比推断：若数列{c n}是各项均为正数的等比数列，则当d n＝时，数列{d n}也是等比数列．故答案为：8．（3分）观察下列式子：，，，…，你可归纳出的不等式是．【解答】解：，＝，，…，可得1++ +…+＞，故答案为：1+++…+＞9．（3分）在我国古代数学著作《孙子算经》中，卷下第二十六题是：今有物，不知其数，三三数之剩二，五五数之剩三，七七数之剩二，问物几何？满足题意的答案可以用数列表示，该数列的通项公式可以表示为a n＝105n+23【解答】解：本题的意思是一个数用3除余2，用7除也余2，所以用3与7的最小公倍数21除也余2，而用21除余2的数我们首先就会想到23；23恰好被5除余3，即最小的一个数为23，同时这个数相差又是3，5，7的最小公倍数，即3×5×7＝105，即数列的通项公式可以表示为a n＝105n+23，故答案为：105n+2310．（3分）对于下列数排成的数阵：它的第10行所有数的和为﹣505【解答】解：第1行1个数，第2行2个数，则第9行9个数，故第10行的第一个数为1+＝46，第10行的最后一个数无45+10＝55，且奇数为负数，偶数为正数，故第10行所有数的和为462﹣472+482﹣492+502﹣512+522﹣532+542﹣552＝﹣（46+47+48+49+50+51+52+53+54+55）＝﹣505，故答案为：505．11．（3分）对于数列{a n}满足：a1＝1，a n+1﹣a n∈{a1，a2，…，a n}（n∈N*），其前n项和为S n，记满足条件的所有数列{a n}中，S12的最大值为a，最小值为b，则a﹣b＝4017【解答】解：由a1＝1，a n+1﹣a n∈{a1，a2，…，a n}（n∈N+），可得a2﹣a1＝a1，解得a2＝2a1＝2，又a3﹣a2∈{a1，a2}，可得a3＝a2+a1＝3或2a2＝4，又a4﹣a3∈{a1，a2，a3}，可得a4＝a3+a1＝4或5；a4＝a3+a2＝5或6；或a4＝2a3＝6或8；又a5﹣a4∈{a1，a2，a3，a4}，可得a5＝a4+a1＝5或6或7；a5＝a4+a2＝6或7或8；a5＝a4+a3＝7或8或9或10或12；a5＝2a3＝8或10或12或16．综上可得S12的最大值a＝1+2+22+23+24+…+211＝＝4095，最小值为b＝1+2+3+4+5+…+12＝＝78．则a﹣b＝4095﹣78＝4017．故答案为：4017．12．（3分）设n∈N*，用A n表示所有形如++…+的正整数集合，其中0≤r1＜r2＜…＜r n≤n，且r i∈N（i∈N*），b n为集合A n中的所有元素之和．则{b n}的通项公式为b n＝n•（2n+1﹣1）．【解答】解：由题意可知，r1、r2、…、r n是0、1、2、…、n的一个排列，且集合A n中共有n+1个数，若把集合A n中每个数表示为++…+的形式，则20、21、22、…、2n每个数都出现n次，因此，＝，故答案为：n•（2n+1﹣1）．二.选择题13．（3分）“b是与的等差中项”是“b是与的等比中项”的（）A．充分不必要条件B．必要不充分条件C．充要条件D．既不充分也不必要条件【解答】解：若b是与的等差中项，则b＝＝1，若b是与的等比中项，则b＝±＝±1，则“b是与的等差中项”是“b是与的等比中项”的充分不必要条件，故选：A．14．（3分）在数列{a n}中，a1＝1，a2＝64，且数列是等比数列，其公比，则数列{a n}的最大项等于（）A．a7B．a8C．a6或a9D．a10【解答】解：∵在数列{a n}中，a1＝1，a2＝64，且数列是等比数列，其公比，∴＝×（﹣）n﹣1＝（﹣1）n﹣1•27﹣n．∴＝1×（﹣1）0+1+……+（n﹣2）×26+5+……+（8﹣n）＝，∵＝+．由n＝7或8时，＝﹣1，n＝6或9时，a6＝220＝a9，∴数列{a n}的最大项等于a6或a9．故选：C．15．（3分）若数列，若k∈N*，则在下列数列中，可取遍数列{a n}前6项值的数列为（）A．{a2k+1}B．{a3k+1}C．{a4k+1}D．{a5k+1}【解答】解：∵数列，k∈N*，∴，，，，，＝cos，，∴{a n}是以6为周期的周期数列，∴{a5k+1}是可取遍数列{a n}前6项值的数列．故选：D．16．（3分）数列{a n}中，若a1＝a，，n∈N*，则下列命题中真命题个数是（）（1）若数列{a n}为常数数列，则a＝±1；（2）若a∈（0，1），数列{a n}都是单调递增数列；（3）若a∉Z，任取{a n}中的9项，，，…，（1＜k1＜k2＜…＜k9）构成数列{a n}的子数列{}，n＝1，2，…，9，则{}都是单调数列．A．0个B．1个C．2个D．3个【解答】解：数列{a n}中，若a1＝a，，n∈N*，（1）若数列{a n}为常数数列，则a2＝sin（a）＝a，解得a＝0或±1，故（1）不正确；（2）若a∈（0，1），a∈（0，），a2＝sin（a），由函数f（x）＝sin（x）﹣x，x∈（0，1），f′（x）＝cos（x）﹣1，由x∈（0，），可得极值点唯一且为m＝arccos，极值为f（m）＝﹣arccos＞0，由f（0）＝f（1）＝0，可得a2＞a1，则a3﹣a2＝sin（a2）﹣sin（a1）＞0，即有a3＞a2，…，由于a n∈（0，1），a n∈（0，），由正弦函数的单调性，可得a n+1＞a n，则数列{a n}都是单调递增数列，故（2）正确；（3）若a∈（0，1），任取{an}中的9项，，，…，（1＜k1＜k2＜…＜k9）构成数列{a n}的子数列{}，n＝1，2，…，9，{}是单调递增数列；由f（x）＝sin（x）﹣x，可得f（﹣x）＝﹣f（x），f（x）为奇函数；当0＜x＜1时，f（x）＞0，x＞1时，f（x）＜0；当﹣1＜x＜0时，f（x）＜0；x＜﹣1时，f（x）＞0，运用正弦函数的单调性可得0＜a＜1时，a＜﹣1时，数列{a n}单调递增；﹣1＜a＜0时，a＞1时，数列{a n}单调递减．数列{a n}都是单调递增数列，故（3）正确；故选：C．三.解答题17．已知{a n}是一个公差大于0的等差数列，且满足a4a6＝96，a3+a7＝20，数列{b n}满足等式：（n∈N*）．（1）求数列{a n}的通项公式；（2）求数列的前n项和S n．【解答】解：（1）在等差数列{a n}中，由a3+a7＝20，得a4+a6＝20，又a4a6＝96，可得或．∵d＞0，∴，则d＝．∴a n＝a4+2（n﹣4）＝2n；（2）由（n∈N*），得（n≥2），∴，即（n≥2），∵满足上式，∴．则，∴数列的前n项和S n＝（b1+b2+…+b n）+＝．18．已知b、c为常数且均不为零，数列{a n}的通项公式为a n＝，并且a1、a3、a2成等差数列，a1、a2、a4成等比数列．（1）求b、c的值；（2）设S n是数列{a n}前n项的和，求使得不等式S2n＞20182成立的最小正整数n．【解答】解：（1）∵a n＝，∴a1＝b﹣1，a2＝9c，a3＝3b﹣1，a4＝81c．∵a1、a3、a2成等差数列，a1、a2、a4成等比数列．∴2a3＝a1+a2，＝a1a4，∴2（3b﹣1）＝b﹣1+9c，81c2＝（b﹣1）×81c，b，c≠0．联立解得：b＝2，c＝1．（2）由（1）可得：a n＝，∴S2n＝（a1+a3+……+a2n﹣1）+（a2+a4+……+a2n）＝（1+5+……+4n﹣3）+（32+34+……+32n）＝+＝2n2﹣n+，由，解得n＞6．∴n＝7．19．王某2017年12月31日向银行贷款100000元，银行贷款年利率为5%，若此贷款分十年还清（2027年12月31日还清），每年年底等额还款（每次还款金额相同），设第n年末还款后此人在银行的欠款额为a n元．（1）设每年的还款额为m元，请用m表示出a2；（2）求每年的还款额（精确到1元）．【解答】解：（1）a2＝100000×（1+5%）﹣m（1+5%）2﹣m＝110250﹣2.05m．（2）a10＝100000×（1.05）10﹣m×（1.05）9﹣m×（1.05）8﹣……﹣m＝0，100000×1.0510﹣＝0，解得：m＝≈12950．20．设数列{a n}的首项a1为常数，且a n+1＝3n﹣2a n（n∈N*）．（1）判断数列是否为等比数列，请说明理由；（2）S n是数列{a n}的前n项的和，若{S n}是递增数列，求a1的取值范围．【解答】解：（1）∵a n+1＝3n﹣2a n（n∈N*），则时，＝＝＝﹣2，∴时，为等比数列，公比为﹣2．（2）由（1）可得：a n﹣＝×（﹣2）n﹣1，∴，n≥2，∴a2＞0，a3＞0，∴．21．如果数列{a n}对任意的n∈N*满足：a n+2+a n＞2a n+1，则称数列{a n}为“M数列”．（1）已知数列{a n}是“M数列”，设b n＝a n+1﹣a n，n∈N*，求证：数列{b n}是递增数列，并指出2（a5﹣a4）与a4﹣a2的大小关系（不需要证明）；（2）已知数列{a n}是首项为1，公差为2d的等差数列，S n是其前n项的和，若数列{|S n|}是“M数列”，求d的取值范围；（3）已知数列{a n}是各项均为正数的“M数列”，对于n取相同的正整数时，比较和的大小，并说明理由．【解答】解：（1）证明：数列{a n}是“M数列”，可得a n+2+a n＞2a n+1，即a n+2﹣a n+1＞a n+1﹣a n，即b n+1＞b n，可得数列{b n}是递增数列；2（a5﹣a4）＞a4﹣a2；（2）数列{|S n|}是“M数列”，可得|S3|﹣|S2|＞|S2|﹣|S1|，即|S1|+|S3|＞2|S2|，可得1+|3+6d|＞2|2+2d|，即有或或，即d≤﹣1或﹣1＜d＜﹣或d＞0，可得；（3）数列{a n}是各项均为正数的“M数列”，对于n取相同的正整数时，＞，运用数学归纳法证明：当n＝1时，u1＝，v1＝a2，显然a3﹣a2＞a2﹣a1即u1＞v1．设n＝k时，u k＞v k．即＞，可得k（a1+a3+…+a2k+1）＞（k+1）（a2+a4+…+a2k），当n＝k+1时，即证＞，即证（k+1）（a1+…+a2k+1+a2k+3）＞（k+2）（a2+a4+…+a2k+a2k+2），由（k+1）（a1+…+a2k+1+a2k+3）＝k（a1+a3+…+a2k+1）+ka2k+3+a1+…+a2k+1+a2k+3＞（k+1）（a2+a4+…+a2k）+ka2k+3+a1+…+a2k+1+a2k+3，即证（k+1）（a2+a4+…+a2k）+ka2k+3+a1+…+a2k+1+a2k+3＞（k+2）（a2+a4+…+a2k+a2k+2），即证（k+1）a2k+3+a1+…+a2k+1＞（k+1）a2k+2+a2+a4+…+a2k+a2k+2，由a1+a2k+3＞a2+a2k+2，a3+a2k+3＞a4+a2k+2，…，a2k+3+a2k+1＞a2k+2+a2k+2，相加可得（k+1）a2k+3+a1+…+a2k+1＞（k+1）a2k+2+a2+a4+…+a2k+a2k+2，则对一切n∈N*，有u n＞v n．。

2016-2017学年上海市复旦附中高一(上)期末数学试卷(解析版)

2016-2017学年上海市复旦附中高一（上）期末数学试卷一、填空题（每题4分，共48分）1．（4分）函数y＝的定义域为．2．（4分）已知函数f（x）＝，则f（2017）等于．3．（4分）已知函数的定义域是非零实数，且在（﹣∞，0）上是增函数，在（0，+∞）上是减函数，则最小的自然数a等于．4．（4分）设函数y＝f（x）与y＝g（x）的图象关于直线y＝x对称，且f（x）＝，（x ≠﹣1），则g（x）＝．5．（4分）函数y＝log0.1（x2﹣x﹣2）的递增区间是．6．（4分）函数y＝lg（﹣1）的图象关于对称．7．（4分）已知lg2＝a，lg3＝b，用a，b的代数式表示log1225＝．8．（4分）函数f（x）＝log a（x+1）（a＞0，a≠1）的定义域和值域都是[0，2]，则a＝．9．（4分）已知函数f（x）＝，若关于x的方程f（x）＝k有三个不同的实根，则实数k的取值范围是．10．（4分）已知是R上的单调递增函数，则实数a的取值范围是．11．（4分）已知函数y＝f（x）是周期为2的周期函数，且当x∈[﹣1，1]时，f（x）＝2|x|﹣1，则函数F（x）＝f（x）﹣|lgx|的零点有个．12．（4分）若x1满足2x+2x＝5，x2满足2x+2log2（x﹣1）＝5，则x1+x2＝．二、选择题（每题4分，共16分）13．（4分）下列函数中，既是偶函数，又在区间（﹣∞，0）上是单调递增的是（）A．y＝B．y＝（）|x|C．y＝ln|x|D．y＝x314．（4分）关于x的方程＝x+m有两个不同的实数解，则实数m的取值范围是（）A．m≥1或m＜B．m＞1或m≤C．＜m≤1D．≤m＜1 15．（4分）已知函数f（x）＝，且y＝f﹣1（x﹣1）的图象对称中心是（0，3），则a的值为（）A．B．2C．D．316．（4分）设a，b，c均为正数，且2a＝a，（）b＝b，（）c＝log2c，则（）A．c＜a＜b B．c＜b＜a C．a＜b＜c D．b＜a＜c三、解答题（本题共5大题，满分56分)17．（10分）已知函数f（x）＝2+1og3x（1≤x≤9），求函数y＝f2（x）+f（3x）的最大值和最小值．18．（10分）设函数f（x）＝（a∈R）是R上的奇函数．（1）求a的值；（2）求函数f（x）的反函数f﹣1（x）的解析式；（3）若k∈R+，解不等式ln．19．（12分）若偶函数f（x）＝+1（m∈Z）在R+上是增函数．（1）确定函数y＝f（x）的解析式；（2）求函数y＝f（x）（x∈（∞，t]）的最小值d（t）的解析式；（3）设g（x）＝﹣ax（a＞1），证明：函数y＝g（x）在R+上是减函数．20．（12分）对于在区间[m，n]上有意义的两个函数f（x）与g（x），如果对任意x∈[m，n]均有|f（x）﹣g（x）|≤1，则称f（x）与g（x）在[m，n]上是接近的；否则称f（x）与g （x）在[m，n]上是非接近的．现有两个函数f1（x）＝log a（x﹣3a），与f2（x）＝log a （a＞0，a≠1），给定区间[a+2，a+3]．（1）若f1（x）与f1（x）在给定区间[a+2，a+3]上都有意义，求a的取值范围；（2）讨论f1（x）与f1（x）在给定区间[a+2，a+3]上是否是接近的？21．（12分）在R上的递减函数f（x）满足：当且仅当x∈M⊆R+，函数值f（x）的集合为[0，2]且f（）＝1；对M中的任意x1，x2都有f（x1•x2）＝f（x1）+f（x2）．（1）求证：∈M，而M；（2）证明：f（x）在M上的反函数f﹣1（x）满足f﹣1（x1）•f﹣1（x2）＝f﹣1（x1+x2）；（3）解不等式：f﹣1（x2+x）•f﹣1（x+2）≤，（x∈[0，2]）2016-2017学年上海市复旦附中高一（上）期末数学试卷参考答案与试题解析一、填空题（每题4分，共48分）1．【解答】解：根据函数y＝有意义可知解得：x≥1故答案为：[1，+∞）2．【解答】解：∵函数f（x）＝，∴f（2017）＝f（2）＝f（﹣3）＝＝﹣1．故答案为：﹣1．3．【解答】解：对函数求导，得，又在（﹣∞，0）上是增函数，（1）当≥1，则必须为奇数（否则为减函数），则＞0，可得，得a≤﹣5，不符合题意，舍去．（2）当1＞＞0，则﹣2＞a＞﹣5，不符合舍去．（3）当时，必须符合﹣a﹣2为负奇数，则解得a＞1故答案为：3．4．【解答】解：函数y＝f（x）与y＝g（x）的图象关于直线y＝x对称，且f（x）＝，（x≠﹣1），令y＝，解得x＝，且y≠﹣1，交换x、y，得g（x）＝，（x≠﹣1）．故答案为：（x≠﹣1）．5．【解答】解：对于函数y＝log0.1（x2﹣x﹣2），由x2﹣x﹣2＞0，求得x＜﹣1，或x＞2，故函数的定义域为{x|x＜﹣1，或x＞2}，本题即求函数t＝x2﹣x﹣2在定义域内的减区间．再利用二次函数的性质可得函数t＝x2﹣x﹣2在定义域{x|x＜﹣1，或x＞2} 内的减区间为（﹣∞，﹣1），故答案为：（﹣∞，﹣1）．6．【解答】解：∵函数y＝f（x）＝lg（﹣1）＝lg，∴函数y＝f（x）的定义域关于原点对称，又∵f（﹣x）＝lg＝lg（）﹣1＝﹣lg＝﹣f（x），故函数y＝f（x）为奇函数，故函数y＝lg（﹣1）的图象关于原点对称，故答案为：原点7．【解答】解：∵lg2＝a，lg3＝b，∴log1225＝＝＝＝．故答案为：．8．【解答】解：当a＞1时，函数f（x）＝a x﹣1（a＞0，a≠1）在[0，2]上单调递增，则，解得：a＝，当a＜1时，函数f（x）＝a x﹣1（a＞0，a≠1）在[0，2]上单调递减，则无解；故a＝．故答案为：9．【解答】解：画出函数f（x）的图象（红色曲线），如图示：，令y＝k，由图象可以读出：﹣1＜k＜0时，y＝k和f（x）有3个交点，即方程f（x）＝k有三个不同的实根，故答案为：（﹣1，0）．10．【解答】解：由题意，，解得4≤a＜8故答案为：4≤a＜811．【解答】解：函数F（x）＝f（x）﹣|lgx|的零点个数，即方程f（x）﹣|lgx|＝0的根的个数，也就是函数y＝f（x）与y＝|lgx|的交点个数，作出两函数的图象如图：由图可知，函数F（x）＝f（x）﹣|lgx|的零点有10个．故答案为：10．12．【解答】解：由题意①2x2+2log2（x2﹣1）＝5 ②所以由①得：⇒x1＝log2（5﹣2x1）即2x1＝2log2（5﹣2x1）令2x1＝7﹣2t，代入上式得7﹣2t＝2log2（2t﹣2）＝2+2log2（t﹣1）⇒5﹣2t＝2log2（t ﹣1）又∵由②式得：5﹣2x2＝2log2（x2﹣1），易知t＝x2于是2x1＝7﹣2x2即x1+x2＝故答案为：．二、选择题（每题4分，共16分）13．【解答】解：A.是奇函数，∴该选项错误；B.是偶函数；x＜0时，；∴该函数在（﹣∞，0）上是单调递增的；∴该选项正确；C．x＜0时，y＝ln|x|＝ln（﹣x）；∴该函数在（﹣∞，0）上单调递减；∴该选项错误；D．y＝x3是奇函数，∴该选项错误．故选：B．14．【解答】解：令y＝（x），则y2＝2x+1（x），其图象如图，联立，可得y2﹣2y+2m﹣1＝0．由△＝4﹣4（2m﹣1）＞0，得m＜1．又x+m≥0恒成立，得m≥﹣x恒成立，而x，∴﹣x，∴m．综上，＜1．故选：D．15．【解答】解：设，反解x＝，∴的反函数是f﹣1（x）＝，∴f﹣1（x﹣1）＝∴f﹣1（x﹣1）＝a+1+，其对称中心是（0，a+1）∵f﹣1（x﹣1）的图象的对称中心是（0，3），所以a+1＝3，所以a＝2．故选：B．16．【解答】解：在平面直角坐标系中画出函数y＝2x，y＝x，y＝（）x，y＝log2x图象，如图：可得a＜b＜c．故选：C．三、解答题（本题共5大题，满分56分)17．【解答】解：函数y＝f2（x）+f（3x），由，解得≤x≤3，可得g（x）的定义域为[，3]，又g（x）＝（2+log3x）2+（2+log33x）＝（log3x+）2+，可令t＝log3x，∵≤x≤3，∴﹣1≤t≤1，h（t）＝（t+）2+在﹣1≤t≤1递增，当t＝﹣1时，即x＝时，函数h（t）取得最小值3；当t＝1即x＝3时，h（t）取得最大值13，∴当x＝时，g（x）有最小值3；当x＝3时，g（x）有最大值13．18．【解答】解：（1）∵f（x）是R上的奇函数；∴；∴a＝1；（2）设y＝f（x），则；∴；∴；∴函数f（x）的反函数，x∈（﹣1，1）；（3）解得，﹣1＜x＜1；∴由ln得，；∴，且k＞0；∴1﹣x＜k；∴x＞1﹣k；①若﹣1＜1﹣k＜1，即0＜k＜2，则原不等式的解集为（1﹣k，1）；②若1﹣k≤﹣1，即k≥2，则原不等式的解集为（﹣1，1）．19．【解答】解：（1）因为f（x）在（0，+∞）上是增函数，所以﹣m2+m+＞0，解得：﹣1＜m＜3，又m∈Z，所以m＝0或m＝1或m＝2，当m＝0时，f（x）＝x+1不是偶函数，不合题意；当m＝1时，f（x）＝x2+1，符合题意；当m＝2时，f（x）＝x+1不是偶函数，不合题意．综上所述：f（x）＝x2+1（2）当t≤0时，f（x）在（﹣∞，t]上是减函数，所以x＝t时，d（t）＝t2+1；当t＞0时，d（t）＝1，综上所述：d（t）＝（3）g（x）＝﹣ax，（a＞1）g′（x）＝＝＝，因为，a＞1，所以g′（x）＜0，所以g（x）在（0，+∞）上是减函数．20．【解答】解：（1）要使f1（x）与f2（x）有意义，则有，要使f1（x）与f2（x）在给定区间[a+2，a+3]上都有意义，等价于：，所以0＜a＜1．（2）f1（x）与f2（x）在给定区间[a+2，a+3]上是接近的，⇔|f1（x）﹣f（x2）|≤1⇔|log a（x﹣3a）﹣|≤1⇔|log a[（x﹣3a）（x﹣a）]|≤1⇔a ≤（x﹣2a）2﹣a2对于任意x∈[a+2，a+3]恒成立．设h（x）＝（x﹣2a）2﹣a2，x∈[a+2，a+3]，且其对称轴x＝2a＜2在区间[a+2，a+3]的左边，⇔⇔⇔⇔，所以当，时，f1（x）与f2（x）在给定区间[a+2，a+3]上是接近的．21．【解答】解：（1）证明：因为∈M，又＝×，f（）＝1，所以f（）＝f（×）＝f（）+f（）＝2∈[0，2]，所以∈M，又因为f（）＝f（×）＝f（）+f（）＝3∉[0，2]，所以∉M；（2）因为y＝f（x）在M上递减，所以y＝f（x）在M有反函数y＝f﹣1（x），x∈[0，2]任取x1、x2∈[0，2]，设y1＝f﹣1（x1），y2＝f﹣1（x2），所以x1＝f（y1），x2＝f（y2）（y1、y2∈M）因为x1+x2＝f（y1）+f（y2）＝f（y1y2），所以y1y2＝f﹣1（x1+x2），又y1y2＝f﹣1（x1）f﹣1（x2），所以：f﹣1（x1）•f﹣1（x2）＝f﹣1（x1+x2）；（3）因为y＝f（x）在M上递减，所以f﹣1（x）在[0，2]上也递减，f﹣1（x2﹣x）•f﹣1（x+2）≤等价于：f﹣1（x2﹣x+x+2）≤f﹣1（2）转化为，解得，即﹣1≤x≤0；∴不等式的解集为[﹣1，0]．。

上海市复旦附中新高一闯关练习解析版(含答案)

复旦附中新高一闯关练习I. Grammar and Vocabulary1.Given these conditions, there will not be ________ room left in one’s brain for ________ rational thought.A. a; theB. /; aC. /; /D. the; /考点：冠词的填写分析：此处的room 为不可数名词，空间，相当于space, 所以前不需要加上冠词。

rational thought 意为“理性的思考” 为不可数名词，也不需要加冠词。

所以答案选C2.In the workplace, e-mail has now become ________ way for employers to monitor ________ what their employees are doing and thinking.A. the other; eitherB. one; everyC. another; bothD. other; all考点：不定代词、宾语从句分析：前一空，考察不定代词的区别，the other 用于两者中另一个，或者the other +名词的复数；other不能单独使用，后需要加名词复数，所以从one和another中选择。

后一空，monitor为监督，what引导的宾语从句，关键点在于and 的使用，应该是both….and….所以答案选C3.He ________ the test again; in that case, his mother will be very disappointed.A. might failB. must have failedC. should failD. could have failed考点：情态动词的用法分析：情态动词+do / be doing表示对现在或者未来的推测情态动词+have+done 表示对过去的推测根据后半句，时态will，所以只能从A或者C中选择should do 表示将来的推测时，是对“所希望的事情进行推测的”显然不成立，所以选A might fail4.He hurt his leg climbing the mountain; otherwise he ________ the meeting.A. will attendB. had attendedC. would have attendedD. would attend考点：虚拟语气分析：前半句用一般过去时（hurt可以推断出）；otherwise ,意为“否则的话”，虚拟语气虚拟语气对过去的推测，用would /should/could + have +done。

【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)

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．
14. 解析式为
，值域为
的函数有（）
A. 4 B. 6 C. 8 D. 9
【答案】 D
【解析】
【分析】
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
A. 充分不必要【答案】 B
B. 必要不充分
C. 充要 D. 既不充分也不必要
【解析】【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】（1）若
，则
，
与
的解集相
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．
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】【解析】
时，总造价最低为 132000 元 .
【分析】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
【详解】存在
满足条件．理由如下：
只有一个根，进而可得答
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， Nhomakorabea由
，解得
，满足题意．
②当

上海市复旦附中2017-2018学年高一9月份闯关练习含答案

上师大附中2017学年高三英语课堂练习II. Grammar and vocabularySection AYou know that business of business is making money。

What you may not realize is：__21__ simple that business is. You need two fundamental ingredients -—a good product that customers want to own, and bright, charismatic people who will __22__ sell it and，if necessary, defend it. And of the two __23__ （desire) product and competent people -- good people are，in the long run，more important than good products. You can't expect to produce one popular product after another。

You can，however，cover your bets by staffing your enterprise with superb employees who will continue to reflect the company’s strengths __24__ ______ the products are weak. It is your responsibility to keep those employees __25__ （perform) as well as they can。

They won’t remain superb __26__ reliable leadership and, in fact, there is a perfect time to address this issue. Most successful companies have a defining moment ____27______profits are skyrocketing，and business __28__ not be better. That is precisely the time to look closely at your customer service. That you are earning more money than ever before __29__ (indicate）your product is terrific, but it doesn't necessarily mean the same about yourcustomer service. It is the ideal time to examine your reputation and expand the success you are earning from your product to include customer service。

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rational thought 意为“理性的思考” 为不可数名词，也不需要加冠词。

所以正确答案为C5.________ the demand for fish and seafood increases, people will not need to rely on land animals for food.A. WithB. AsC. DuringD. Because of考点：介词、连词分析：关键点在于横线后为句子，increases 为谓语动词，所以横线处需要连词根据句意“随着对鱼类等海产品的需要增加”，所以应该填写连词as表示随着如果用介词with的话，应该接短语或者动名词所以正确答案为B6.Stonehenge is a good example of a site that many people think ________ to change.A. needB. to needC. needsD. needing考点：动词适当形式分析：that引导的定语从句，在句中指代前面的site, 在从句中作many people think the site__________to change ，所以此处选择C7.Every week we go to the theatre! Not once since we arrived here ________ to the movies!A. we have goneB. we have beenC. had we goneD. have we been考点：倒装句分析：否定词Not 放在句首，需部分倒装since结构主句应该用现在完成时，所以选D8.Other students had poorer exam results – he is by no means ________ in the class.A. the bestB. betterC. worseD. the worst考点：比较级和最高级分析：by no means 意为“绝不”前半句表示“其他学生考得差，他绝对不是班级最差的”。

所以选D9.Fast food chains used to be found only along highways or in business areas ________ people used to grab a quick lunch before returning to work.A. whereB. whenC. for whichD. while考点：定语从句分析：areas作先行词，在后面的句子中充当地点状语，所以选A10.All the passengers object to transferring to the next flight ________ they ________ a proper explanation.A. though; will giveB. unless; are givenC. if; have givenD. so long as; get 考点：状语从句/时态语态分析：前半句中”object to “表示反对，句意为“所有的乘客都反对转机，” 所以后半句表示“除非他们被给一个合理的解释。

”连词应该为unless，后句中表示被动，为are given11.The percentage of women who would stay at home full-time, ________ they could afford it, dropped from 39 percent in 1981 to 31 percent in this survey.A. ifB. untilC. even ifD. as考点：状语从句分析：“那些全职待在家里的妈妈们，……..他们能负担起的话，”中间表示条件关系，意为“如果妈妈们能负担得起话”，所以选择if12.You’ve switched the machine off. I told you not to, ________?A. didn’t IB. haven’t youC. will youD. did I考点：反义疑问句分析：注意反义后句，I told you not to，所以用didn’t I13.The company wasted ________ investing in out of date technology.A. a million poundB. millions of poundsC. several millions of poundD. a million of pounds考点：数词分析：句意为“这个家公司浪费了几百万投资过时的技术”millions of +名词复数/ 数词+million +名词复数选项C 中several 表示约数，相当于数字，应该为several million pound 所以正确答案为B millions of pounds14.Television has many advantages. It keep us ________ about the ________ news, and also provides entertainment in the home.A. informed; latestB. to know; laterC. learning; latterD. to think; late考点：非谓语动词分析：keep sb doing , 让某人一直做某事keep sb +非谓语动词，非谓语动词的形式取决于动词和sb之间的关系inform 和sb之间的关系是被动，所以被告知informed“the …….news”表示最新的信息，所以选择latest注意：latter 为形容词，后者，反义词—former 表示前者later 为副词，后来，稍后latest 为形容词，最新的15.It’s difficult to say ________ this portrait was painted by.A. howB. whoseC. thatD. who考点：宾语从句连词分析：say 后接宾语，宾语从句缺少by的宾语，所以选D16. Helen had to pay extra at the airport because she had ________.A. much too luggageB. too many pieces of luggagesC. too much luggageD. too many luggages考点：不可数名词的修饰分析：Henlen不得不付额外的费用，因为她有太多的行李。

注意：too much 表示“太多”修饰不可数名词much too 表示“太”修饰副词或者形容词所以正确答案为A17.________, you can’t come in here unless you’re a club member.A. Strictly speakingB. Considering carefullyC. Spoken strictlyD. Carefully considered考点：搭配分析：“严格来说”应该为Strictly speaking.类似的表达“一般来说”，generally speaking （副词+ 非谓语动词）所以正确答案A18.I’ll wait here until 6:00, so ________ here by then.A. try and beB. trying to getC. you to comeD. to be sure to reach考点：并列句分析：so 为连词，并列句，所以前后都是完整的句子，选A 祈使句19.Tony finished his meal, ________ the bill, and left the restaurant.A. payingB. to checkC. checkingD. paid考点：动词适当形式分析：句中and 表示并列连词，说明都是并列的谓语动词sb did sth , did sth and did sth20.The palace is heavily guarded, because inside its walls ________.A. where sit the European leadersB. sit the European leadersC. the European leaders there sitD. that the European leaders sit考点：倒装句分析，方位副词或者介词放在句首，需要全倒装。

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