2016上海高考模拟试题

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上海市2016届高考数学模拟测试试题理(新疆班)

某某市某某班2016届高考模拟测试数学（理科）试题一、填空题（本大题共有14题，满分56分）考生应在答题纸相应编号的空格内直接填写结果，每个空格填对得4分，否则一律得零分。

1.方程的解为．2. 若线性方程组的增广矩阵为、解为，则16 ．3.设全集为实数集, ,, 则图中阴影部分所表示的集合是．4. 若，则．5.把三阶行列式中元素7的代数余子式记为，若关于的不等式的解集为，则实数 1 .6.已知曲线C的极坐标方程为，则C与极轴的交点到极点的距离是 .7.执行如图2所示的程序框图，若输入数据，，，，，，则输出的结果为。

8. 一个袋中装有5个球，编号为1，2，3，4，5，从中任取3个，用表示取出的3个球中最大编号，则=．9. 在平面直角坐标系中，，点是以原点为圆心的单位圆上的动点，则的最大值是 3 ．开始输出结束是否输入12,,,,nn a a a0,1S i==()1ii S aSi-⋅+=1i i=+?i n>S10.已知函数存在反函数，若函数的图像经过点，则函数的图像必过点.11.已知是上的奇函数,对都有成立,若,则等于.12.在等比数列中，是的等差中项，公比满足如下条件：（为原点）中，，，为锐角，则公比等于－2．13.已知点及抛物线上一动点，则的最小值为2 ．14.设函数的定义域为，其中.若函数在区间上的最大值为6，最小值为3，则在区间上的最大值与最小值之和为或.二、选择题（本大题共4题，每题5分，共20分，每题有且只有一个正确答案，考生应在答案纸的相应编号上，填上正确的答案，选对得5分，否则一律得零分.）15.设，，则“、中至少有一个数是虚数”是“是虚数”的（B ）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16.将的图像向右平移个单位，则平移后图像的一个对称中心是（A ）A．B．C．D．17.设与是定义在同一区间上的两个函数，若函数在上有两个不同的零点，则称和在上是“关联函数”，区间称为“关联区间”．若与在上是“关联函数”，则的取值X围为（A ）A. B. C. D.18．记方程①x2+a1x+1=0，②x2+a2x+1=0，③x2+a3x+1=0，其中a1，a2，a3是正实数，当a1，a2，a3成等比数列，下列选项中，正确的是（C ）A．若方程②③都有实根则方程①无实根;B．若方程②③都有实根则方程①有实根;C．若方程②无实根但方程③有实根时,则方程①无实根;D．若方程②无实根但方程③有实根时,则方程①有实根;三、解答题：（本大题满分74分，解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤 .）19.（本题满分12分）本题共有2个小题，第（1）小题满分5分，第（2）小题满分7分.如图，正方形所在平面与圆所在平面相交于，为圆的直径，线段为圆的弦，垂直于圆所在平面．（1）求证：平面；（2）设异面直线与所成的角为且，将（及其内部）绕所在直线旋转一周形成一几何体，求该几何体的体积．解：（1）证明：因为为圆的直径，所以，即…………2分又因为垂直于圆所在平面，所以……4分又所以平面……………5分（2）由题意知，将（及其内部）绕所在直线旋转一周形成一几何体的体积是两圆锥的体积之差．因为异面直线与所成的角为，且，所以，……………7分又因为，所以，在中，，………………………9分在中，，，所以…………………………10分所以该几何体的体积……………………12分20. （本题满分14分）第1小题满分6分，第2小题满分8分．在中，角的对边分别为，向量，，且．（1）求的值；（2）若，求角的大小及向量在方向上的投影．解：（1）由…3分又，则…6分（2）由…8分又…10分由余弦定理，得或（舍）…12分则在方向上的投影为…14分21.（本题满分14分）已知抛物线（）的焦点为，点是抛物线上横坐标为的点，且到抛物线焦点的距离等于．（1）求抛物线的方程；（2）过抛物线的焦点作互相垂直的两条直线，，与抛物线交于、两点，BP与抛物线交于、两点，、分别是线段、的中点，求△面积的最小值．（1）抛物线（）的准线为，（1分）由题意，，．………………（4分）所以所求抛物线的方程为．…………………（5分）（2），由题意，直线、的斜率都存在且不为，（1分）设直线的方向向量为（），则也是直线的一个法向量，所以直线的方程为，即，…………………（2分）直线的方程为，即．……………………（3分）由得，…………………………（4分）则．………………………………………………………（5分）同理可得．………………………………………………（6分）所以，．…………………………………………………………（8分）所以，当且仅当时，△的面积取最小值．…………………（9分）22.（16分）已知函数，若在定义域内存在，使得成立，则称为函数的局部对称点.（1）若、R且，证明：函数必有局部对称点；（2）若函数在区间内有局部对称点，某某数的取值X围；（3）若函数在R上有局部对称点，某某数的取值X围.解: （1）由得……1分代入得，，得到关于的方程（），……2分其中，由于且，所以恒成立……3分所以函数（）必有局部对称点。

2016年上海市奉贤区高考数学二模试卷(理科)含答案解析

2016年上海市奉贤区高考数学二模试卷（理科）一.填空题（本大题满分56分）本大题共有14题，考生应在答题纸相应编号的空格内直接写结果，1-14题每个空格填对得4分）1．若i（bi+1）是纯虚数，i是虚数单位，则实数b=______．2．函数y=的定义域是______．3．在△ABC中，||=2，||=3，•＜0，且△ABC的面积为，则∠BAC=______．4．双曲线4x2﹣y2=1的一条渐近线与直线tx+y+1=0垂直，则t=______．5．已知抛物线y2=4x上一点M（x0，2），则点M到抛物线焦点的距离为______．6．无穷等比数列首项为1，公比为q（q＞0）的等边数列前n项和为S n，则S n=2，则q=______．7．在一个水平放置的底面半径为cm的圆柱形量杯中装有适量的水，现放入一个半径为Rcm的实心铁球，球完全浸没于水中且无水溢出，若水面高度恰好上升Rcm，则R=______cm．8．从4名男生和3名女生中选出4人参加某个座谈会，若这4人中必须既有男生又有女生，则不同的选法种数共有______．（用数字作答）9．在平面直角坐标系xOy中，将点A（2，1）绕原点O逆时针旋转到点B，若直线OB 的倾斜角为α，则cosα的值为______．10．已知函数f（x）=2x﹣a•2﹣x的反函数是f﹣1（x），f﹣1（x）在定义域上是奇函数，则正实数a=______．11．把极坐标方程ρ=sinθ+cosθ化成直角坐标标准方程是______．12．在（x++1）6展开式中的常数项是______（用数值作答）13．在棱长为1的正方体ABCD﹣A1B1C1D1中，若点P是棱上一点，则满足|PA|+|PC1|=2的点P的个数为______．14．若数列{a n}前n项和S n满足S n+S n=2n2+1（n≥2，n∈N+），且满足a1=x，{a n}单调﹣1递增，则x的取值范围是______．二．选择题（本大题满分20分）本大题共有4题，每题有且只有一个正确答案，考生应在答题纸的相应编号上，将代表答案的小方格涂黑，选对得5分，否则一律得零分.15．平面α的斜线与平面α所成的角是35°，则与平面α内所有不过斜足的直线所成的角的范围是（）A．（0°，35°]B．（0°，90°]C．[35°，90°）D．[35°，90°]16．已知log2x，log2y，2成等差数列，则M（x，y）的轨迹的图象为（）A．B．C．D．17．设，那么以|z1|为直径的圆的面积为（）A．πB．4πC．8πD．16π18．方程9x+|3x+b|=5（b∈R）有两个负实数解，则b的取值范囤为（）A．（3，5） B．（﹣5.25，﹣5）C．[﹣5.25，﹣5）D．前三个都不正确三．解答题（本大题满分74分）本大题共有5题，解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤.19．（13分）（2016•奉贤区一模）平面外ABC的一点P，AP、AB、AC两两互相垂直，过AC的中点D做ED⊥面ABC，且ED=1，PA=2，AC=2，连接BP，BE，多面体B﹣PADE的体积是；（1）画出面PBE与面ABC的交线，说明理由；（2）求面PBE与面ABC所成的锐二面角的大小．20．（13分）（2016•奉贤区一模）已知椭圆C：=1（a＞b＞0）的长轴长是短轴长的两倍，焦距为2．（1）求椭圆C的标准方程；（2）不过原点O的直线l与椭圆C交于两点M，N，且直线OM，MN，ON的斜率依次成等比数列，问：直线l是否定向的，请说明理由．21．（14分）（2016•奉贤区一模）如图所示，A，B是两个垃圾中转站，B在A的正东方向16千米处，AB的南面为居民生活区，为了妥善处理生活垃圾，政府决定在AB的背面建一个垃圾发电厂P，垃圾发电厂P的选址拟满足以下两个要求（A，B，P可看成三个点）：①垃圾发电厂到两个中转站的距离与它们每天集中的生活垃圾量成反比，比例系数相同；②垃圾发电厂应尽量远离居民区（这里参考的指标是点P到直线AB的距离要尽可能大），现估测得A，B两个中转站每天集中的生活垃圾量分别约为30吨和50吨，设|PA|=5x＞0．（1）求cos∠PAB（用x的表达式表示）（2）问垃圾发电厂该如何选址才能同时满足上述要求？22．（16分）（2016•奉贤区一模）（1）已知0＜x1＜x2，求证：；（2）已知f（x）=lg（x+1）﹣log3x，求证：f（x）在定义域内是单调递减函数；（3）在（2）的条件下，求集合M={n|f（n2﹣214n﹣1998）≥0，n∈Z}的子集个数．23．（18分）（2016•奉贤区一模）数列{a n}，{b n}满足，a1＞0，b1＞0；（1）求证：{a n•b n}是常数列；（2）若{a n}是递减数列，求a1与b1的关系；（3）设a1=4，b1=1，当n≥2时，求a n的取值范围．2016年上海市奉贤区高考数学二模试卷（理科）参考答案与试题解析一.填空题（本大题满分56分）本大题共有14题，考生应在答题纸相应编号的空格内直接写结果，1-14题每个空格填对得4分）1．若i（bi+1）是纯虚数，i是虚数单位，则实数b=0．【考点】复数的基本概念．【分析】由i（bi+1）=﹣b+i，又i（bi+1）是纯虚数，即可得到实部等于0，则b可求．【解答】解：i（bi+1）=﹣b+i，又i（bi+1）是纯虚数，则﹣b=0，即b=0．故答案为：0．【点评】本题考查了复数代数形式的乘除运算，考查了复数的基本概念，是基础题．2．函数y=的定义域是[0，+∞）．【考点】函数的定义域及其求法．【分析】根据二次根式的性质，被开方数大于等于0，可知：2n﹣1≥0，解得n的范围即可．【解答】解：根据题意得：2n﹣1≥0，解得：n≥0．∴函数y=的定义域是[0，+∞）．故答案为：[0，+∞）．【点评】本题考查的是函数自变量取值范围的求法．注意偶次开方一定非负．3．在△ABC中，||=2，||=3，•＜0，且△ABC的面积为，则∠BAC=150°．【考点】平面向量数量积的运算．【分析】由题意可得∠BAC 为钝角，再由×2×3×sin∠BAC=，解得sin∠BAC=，从而得到∠BAC的值．【解答】解：∵在△ABC中，||=2，||=3，且△ABC的面积为，∴=，即，解得sin∠BAC=，又•＜0，∴，∴∠BAC=150°．故答案为：150°．【点评】本题主要考查两个向量的数量积的定义及三角形的面积公式，考查已知三角函数值求角的大小，是基础题．4．双曲线4x2﹣y2=1的一条渐近线与直线tx+y+1=0垂直，则t=±．【考点】双曲线的简单性质．【分析】求得双曲线的渐近线方程，直线tx+y+1=0的斜率为﹣t，运用两直线垂直的条件：斜率之积为﹣1，计算即可得到所求值．【解答】解：双曲线4x2﹣y2=1即为﹣y2=1，可得渐近线为y=±2x，直线tx+y+1=0的斜率为﹣t，而渐近线的斜率为±2，由两直线垂直的条件：斜率之积为﹣1，可得﹣t=±，即有t=±．故答案为：±．【点评】本题考查双曲线的渐近线方程的运用，考查两直线垂直的条件：斜率之积为﹣1，考查运算能力，属于基础题．5．已知抛物线y2=4x上一点M（x0，2），则点M到抛物线焦点的距离为4．【考点】抛物线的简单性质．【分析】把点M （x 0，2）代入抛物线方程，解得x 0．利用抛物线的定义可得：点M 到抛物线焦点的距离=x 0+1．【解答】解：把点M （x 0，2）代入抛物线方程可得：=4x 0，解得x 0=3．∴点M 到抛物线焦点的距离=x 0+1=4．故答案为：4．【点评】本题考查了抛物线的定义标准方程及其性质，考查了推理能力与计算能力，属于中档题．6．无穷等比数列首项为1，公比为q （q ＞0）的等边数列前n 项和为S n ，则S n =2，则q=．【考点】等比数列的通项公式．【分析】由无穷递缩等比数列的各项和可得=2，解方程可得．【解答】解：∵无穷等比数列首项为1，公比为q （q ＞0）的等边数列前n 项和为S n ，且S n =2，∴=2，解得q=，故答案为：．【点评】本题考查等比数列的通项公式和无穷递缩等比数列的各项和，属基础题．7．在一个水平放置的底面半径为cm 的圆柱形量杯中装有适量的水，现放入一个半径为Rcm 的实心铁球，球完全浸没于水中且无水溢出，若水面高度恰好上升Rcm ，则R= cm ．【考点】球的体积和表面积；棱柱、棱锥、棱台的体积．【分析】求出球的体积等于水面高度恰好上升Rcm 的体积，即可求出R 的值．【解答】解：在一个水平放置的底面半径为cm 的圆柱形量杯中装有适量的水，现放入一个半径为Rcm 的实心铁球，球完全浸没于水中且无水溢出，若水面高度恰好上升Rcm ，所以，，所以R=（cm ）；故答案为：．【点评】本题是基础题，考查球的体积，圆柱的体积的求法，考查计算能力．8．从4名男生和3名女生中选出4人参加某个座谈会，若这4人中必须既有男生又有女生，则不同的选法种数共有34．（用数字作答）【考点】组合及组合数公式；排列、组合的实际应用．【分析】根据题意，选用排除法；分3步，①计算从7人中，任取4人参加某个座谈会的选法，②计算选出的全部为男生或女生的情况数目，③由事件间的关系，计算可得答案．【解答】解：分3步来计算，①从7人中，任取4人参加某个座谈会，分析可得，这是组合问题，共C74=35种情况；②选出的4人都为男生时，有1种情况，因女生只有3人，故不会都是女生，③根据排除法，可得符合题意的选法共35﹣1=34种；故答案为34．【点评】本题考查组合数公式的运用，解本题采用排除法较为简单．9．在平面直角坐标系xOy中，将点A（2，1）绕原点O逆时针旋转到点B，若直线OB的倾斜角为α，则cosα的值为．【考点】直线的倾斜角．【分析】设直线OA的倾斜角为θ，则tanθ=，tanα==，cosα=．【解答】解：设直线OA的倾斜角为θ，则tanθ=，则tanα====3，∴cosα===．故答案为：．【点评】本题考查了直线的倾斜角与斜率的关系、三角函数求值，考查了推理能力与计算能力，属于中档题．10．已知函数f（x）=2x﹣a•2﹣x的反函数是f﹣1（x），f﹣1（x）在定义域上是奇函数，则正实数a=1．【考点】反函数．【分析】f﹣1（x）在定义域上是奇函数，可得：原函数f（x）在定义域上也是奇函数，利用f（0）=0即可得出．【解答】解：∵f﹣1（x）在定义域上是奇函数，∴原函数f（x）在定义域上也是奇函数，∴f（0）=1﹣a=0，解得a=1，∴f（x）=，经过验证函数f（x）是奇函数．故答案为：1．【点评】本题考查了反函数的性质，考查了推理能力与计算能力，属于中档题．11．把极坐标方程ρ=sinθ+cosθ化成直角坐标标准方程是（x﹣）2+（y﹣）2=．【考点】简单曲线的极坐标方程；点的极坐标和直角坐标的互化．【分析】先在极坐标方程ρ=sinθ+cosθ的两边同乘以ρ，再利用直角坐标与极坐标间的关系，即利用ρcosθ=x，ρsinθ=y，ρ2=x2+y2，进行代换即得．【解答】解：∵ρ=sinθ+cosθ，∴ρ2=ρsinθ+ρcosθ，∴x2+y2=y+x，即x2+y2﹣x﹣y=0．即（x﹣）2+（y﹣）2=．故答案为：（x﹣）2+（y﹣）2=．【点评】本题考查点的极坐标和直角坐标的互化，能在极坐标系中用极坐标刻画点的位置，体会在极坐标系和平面直角坐标系中刻画点的位置的区别，能进行极坐标和直角坐标的互化．12．在（x++1）6展开式中的常数项是581（用数值作答）【考点】二项式系数的性质．=，（r=0，1，…，6），令的展开式的通项公式【分析】T r+1==2k x r﹣2k，令r﹣2k=0，对k，r分类讨论即可得出．T′k+1=，（r=0，1，…，6），【解答】解：T r+1==2k x r﹣2k，令的展开式的通项公式T′k+1令r﹣2k=0，k=0，r=0时，可得：T1=1．k=1，r=2时，可得：T3=，T′2=，∴=60．k=2，r=4时，可得：T5=，T′3==24，∴×24=360．k=3，r=6时，可得：T7=，T′4==160，∴×160=160．∴（x++1）6展开式中的常数项是1+60+360+160=581．故答案为：581．【点评】本题考查了二项式定理的应用，考查了分类讨论方法、推理能力与计算能力，属于中档题．13．在棱长为1的正方体ABCD﹣A1B1C1D1中，若点P是棱上一点，则满足|PA|+|PC1|=2的点P的个数为6．【考点】棱柱的结构特征．【分析】由题意可得点P是以2c=为焦距，以a=1为长半轴，为短半轴的椭圆与正方体与棱的交点，可求．【解答】解：∵正方体的棱长为1∴AC1=，∵|PA|+|PC1|=2，∴点P是以2c=为焦距，以a=1为长半轴，以为短半轴的椭圆，∵P在正方体的棱上，∴P应是椭圆与正方体与棱的交点，结合正方体的性质可知，满足条件的点应该在棱B1C1，C1D1，CC1，AA1，AB，AD上各有一点满足条件．故答案为：6．【点评】本题以正方体为载体，主要考查了椭圆定义的灵活应用，属于综合性试题．14．若数列{a n}前n项和S n满足S n﹣1+S n=2n2+1（n≥2，n∈N+），且满足a1=x，{a n}单调递增，则x的取值范围是（2，3）．【考点】数列递推式．【分析】根据条件求出与a n的有关的关系式，利用条件，{a n}单调递增，建立条件，即可得到结论．【解答】解：由条件S n﹣1+S n=2n2+1（n≥2）得S n+S n+1=2（n+1）2+1，两式相减得a n+1+a n=4n+2，故a n+2+a n+1=4n+6，两式再相减得a n+2﹣a n=4，得{a n+2}是公差d=4的等差数列，由n=2得a1+a2+a1=9，a2=9﹣2x，从而a2n=4n+5﹣2x；n=3得a1+a2+a3+a1+a2=19，a3=1+2x，从而a2n+1=4n﹣3+2x，由条件得，解得2＜x＜3，故x的取值范围为（2，3），故答案为：（2，3）．【点评】本题主要考查参数的取值范围的求解，根据条件求出与a n的有关的关系式是解决本题的关键，有一定的难度．二．选择题（本大题满分20分）本大题共有4题，每题有且只有一个正确答案，考生应在答题纸的相应编号上，将代表答案的小方格涂黑，选对得5分，否则一律得零分.15．平面α的斜线与平面α所成的角是35°，则与平面α内所有不过斜足的直线所成的角的范围是（）A．（0°，35°]B．（0°，90°]C．[35°，90°）D．[35°，90°]【考点】直线与平面所成的角．【分析】做出斜线与射影所确定的平面，则当α内的直线与射影平行时．夹角最小为35°，当直线与射影垂直时，夹角最大为90°．【解答】解：设平面α的斜线的斜足为B，过斜线上A点做平面α的垂线，垂足为C，则∠ABC=35°，∴当α内的直线与BC平行时，直线与斜线所成的角为35°，当α内的直线与BC垂直时，则此直线与平面ABC垂直，∴直线与斜线所成的角为90°，故选：D．【点评】本题考查了线面角的定义，异面直线所成的角的计算，属于中档题．16．已知log2x，log2y，2成等差数列，则M（x，y）的轨迹的图象为（）A．B．C．D．【考点】函数的图象．【分析】根据等差中项，得到2log2y=2+log2x，继而得到y2=4x，x＞0，y＞0，问题得以解决．【解答】解：∵log2x，log2y，2成等差数列，∴2log2y=2+log2x，∴y2=4x，x＞0，y＞0，∴M（x，y）的轨迹的图象为焦点为（1，0）的抛物线的一部分，x＞0，y＞0，故选：A．【点评】本题考查了等差中项和对数的运算性质，以及抛物线的问题，属于基础题．17．设，那么以|z1|为直径的圆的面积为（）A．πB．4πC．8πD．16π【考点】复数求模．【分析】由已知可得： +4=0，解得=i，即可得出．【解答】解：∵，∴+4=0，解得==i，∴|z1|=|z2||1i|=4，∴以|z1|为直径的圆的面积为22π=4π．故选：B．【点评】本题考查了实系数一元二次方程的解法、复数的几何意义、圆的面积计算公式，考查了推理能力与计算能力，属于中档题．18．方程9x+|3x+b|=5（b∈R）有两个负实数解，则b的取值范囤为（）A．（3，5） B．（﹣5.25，﹣5）C．[﹣5.25，﹣5）D．前三个都不正确【考点】根的存在性及根的个数判断．【分析】化简9x+|3x+b|=5可得3x+b=5﹣9x或3x+b=﹣5+9x，从而讨论以确定方程的根的个数，从而解得．【解答】解：∵9x+|3x+b|=5，∴|3x+b|=5﹣9x，∴3x+b=5﹣9x或3x+b=﹣5+9x，①若3x+b=5﹣9x，则b=5﹣3x﹣9x，其在（﹣∞，0）上单调递减，故当b≤3时，无解，当3＜b＜5时，有一个解，当b≥5时，无解；②若3x+b=﹣5+9x，则b=﹣5﹣3x+9x=（3x﹣）2﹣，∵x∈（﹣∞，0）时，0＜3x＜1，∴当﹣＜b＜﹣5时，有两个不同解；当b=﹣时，有一个解；综上所述，b的取值范围为（﹣5.25，﹣5），故选B．【点评】本题考查了绝对值方程的解法与应用，属于中档题．三．解答题（本大题满分74分）本大题共有5题，解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤.19．（13分）（2016•奉贤区一模）平面外ABC的一点P，AP、AB、AC两两互相垂直，过AC的中点D做ED⊥面ABC，且ED=1，PA=2，AC=2，连接BP，BE，多面体B﹣PADE的体积是；（1）画出面PBE与面ABC的交线，说明理由；（2）求面PBE与面ABC所成的锐二面角的大小．【考点】二面角的平面角及求法．【分析】（1）延长PE交AC于F，可证F与C重合，故直线BC即为面PBE与面ABC的交线；（2）以A为原点，AB为x轴，AC为y轴，AP为z轴，建立空间直角坐标系，利用向量法能求出面PBE与面ABC所成的锐二面角的大小．【解答】解：（1）延长PE交AC于F，直线BC即为面PBE与面ABC的交线；理由如下：∵AP 、AB 、AC 两两互相垂直， ∴PA ⊥平面ABC ， ∵DE ⊥平面ABC ， ∴DE ∥PA ，∴=，∴F 与C 重合．∵C ∈PE ，C ∈AC ，PE ⊂平面PBE ，AC ⊂平面ABC ， ∴C 是平面PBE 和平面ABC 的公共点，又B 是平面PBE 和平面ABC 的公共点， ∴BC 是面PBE 与面ABC 的交线．（2）∵AP 、AB 、AC 两两互相垂直，∴AB ⊥平面PAC ，∴V B ﹣PADE =S 梯形ADEP •AB=（1+2）×1×AB=，解得AB=．以A 为原点，AB 为x 轴，AC 为y 轴，AP 为z 轴，建立空间直角坐标系，B （，0，0），P （0，0，2），E （0，1，1），=（，0，2），=（0，1，﹣1），设二面角PBE 的法向量=（x ，y ，z ），则，取y=1，得=（﹣，1，1），平面ABC 的法向量=（0，0，1），∴cos ＜＞===，∴面PBE 与面ABC 所成的锐二面角的大小为arccos ．【点评】本题考查了平面的性质，二面角的计算，属于中档题，解题时要认真审题，注意向量法的合理运用．20．（13分）（2016•奉贤区一模）已知椭圆C：=1（a＞b＞0）的长轴长是短轴长的两倍，焦距为2．（1）求椭圆C的标准方程；（2）不过原点O的直线l与椭圆C交于两点M，N，且直线OM，MN，ON的斜率依次成等比数列，问：直线l是否定向的，请说明理由．【考点】直线与圆锥曲线的综合问题；椭圆的标准方程．【分析】（1）由椭圆的长轴长是短轴长的两倍，焦距为2，列出方程组能求出椭圆C的标准方程．（2）由题意设直线l的方程为y=kx+m，（km≠0），联立，得（1+4k2）x2+4kmx+4（m2﹣1）=0，由此利用根的判别式、韦达定理、等比数列、椭圆性质，结合已知条件能求出直线l不定向．【解答】解：（1）∵椭圆C：=1（a＞b＞0）的长轴长是短轴长的两倍，焦距为2，∴，解得a=2，b=1，∴椭圆C的标准方程为．（2）由题意设直线l的方程为y=kx+m，（km≠0），联立，得（1+4k2）x2+4kmx+4（m2﹣1）=0，△=16（4k2﹣m2+1）＞0，设M（x1，y1），N（x2，y2），则，，∴y1y2=（kx1+m）（kx2+m）=，∵直线OM，MN，ON的斜率依次成等比数列，∴=k2，∴﹣+m2=0，∵m≠0，∴k2=，方向向量=（±2，1）．∴直线l不定向．【点评】本题考查椭圆方程的求法，考查直线是否定向的判断与求法，是中档题，解题时要认真审题，注意根的判别式、韦达定理、等比数列、椭圆性质的合理运用．21．（14分）（2016•奉贤区一模）如图所示，A，B是两个垃圾中转站，B在A的正东方向16千米处，AB的南面为居民生活区，为了妥善处理生活垃圾，政府决定在AB的背面建一个垃圾发电厂P，垃圾发电厂P的选址拟满足以下两个要求（A，B，P可看成三个点）：①垃圾发电厂到两个中转站的距离与它们每天集中的生活垃圾量成反比，比例系数相同；②垃圾发电厂应尽量远离居民区（这里参考的指标是点P到直线AB的距离要尽可能大），现估测得A，B两个中转站每天集中的生活垃圾量分别约为30吨和50吨，设|PA|=5x＞0．（1）求cos∠PAB（用x的表达式表示）（2）问垃圾发电厂该如何选址才能同时满足上述要求？【考点】余弦定理的应用．【分析】（1）由条件可设PA=5x，PB=3x，运用余弦定理，即可得到cos∠PAB；（2）由同角的平方关系可得sin∠PAB，求得点P到直线AB的距离h=PAsin∠PAB，化简整理配方，由二次函数的最值的求法，即可得到所求最大值及PA，PB的值．【解答】解：（1）由条件①，得，∵PA=5x，∴PB=3x，则，可得；（2）由同角的平方关系可得，所以点P到直线AB的距离h=PAsin∠PAB，=，∵cos∠PAB≤1，∴，∴2≤x≤8，所以当x2=34，即时，h取得最大值15千米．即选址应满足千米，千米．【点评】本题考查解三角形的数学模型的解法，注意运用余弦定理和同角的平方关系和二次函数的最值的求法，考查化简整理的运算能力，属于中档题．22．（16分）（2016•奉贤区一模）（1）已知0＜x1＜x2，求证：；（2）已知f（x）=lg（x+1）﹣log3x，求证：f（x）在定义域内是单调递减函数；（3）在（2）的条件下，求集合M={n|f（n2﹣214n﹣1998）≥0，n∈Z}的子集个数．【考点】对数函数的图象与性质；子集与真子集．【分析】（1）使用分析法证明；（2）设0＜x1＜x2，利用（1）的结论和对数函数的性质化简f（x1）﹣f（x2）判断其符号，得出结论；（3）由（2）的结论及f（9）=0列出不等式组，解出n即可得出M中元素的个数．【解答】（1）证明：∵x2+1＞0，x2＞0，欲证：，只需证：x2（x1+1）＞x1（x2+1），即证：x1x2+x2＞x1x2+x1，只需证：x2＞x1，显然x2＞x1成立，∴．（2）解：f（x）的定义域为（0，+∞）．设0＜x1＜x2，则f（x1）﹣f（x2）=lg（x1+1）﹣lg（x2+1）+log3x2﹣log3x1=lg+log3=lg﹣log．∵0＜x1＜x2，∴0＜＜＜1，∴lg＞log＞log，∴f（x1）﹣f（x2）=lg﹣log＞log﹣log=0．∴f（x1）＞f（x2），∴f（x）在定义域（0，+∞）上是减函数．（3）解：由（2）知f（x）是定义在（0，+∞）上的减函数，且f（9）=0，∵f（n2﹣214n﹣1998）≥0，∴0＜n 2﹣214n ﹣1998≤9． ∴13447＜（n ﹣107）2≤13456．∵115＜＜116，=116，n ∈Z ，∴n ﹣107=116或n ﹣107=﹣116． ∴集合M 有两个元素． ∴集合M 有4个子集．【点评】本题考查了不等式的证明，对数函数的性质，函数单调性的应用，属于中档题．23．（18分）（2016•奉贤区一模）数列{a n }，{b n }满足，a 1＞0，b 1＞0；（1）求证：{a n •b n }是常数列；（2）若{a n }是递减数列，求a 1与b 1的关系；（3）设a 1=4，b 1=1，当n ≥2时，求a n 的取值范围．【考点】数列递推式．【分析】（1）由题意可知a n •b n =a n ﹣1•b n ﹣1=…=a 1•b 1，故问题得以证明；（2）根据{a n }是递减数列，得到（a 1﹣b 1）2＞0，a n ＞b n ，得到a 1＞b 1恒成立，（3）先判断a n +1＞2，再根据a n +1﹣a n =，得到a n +1﹣a n ＜0，{a n }是递减数列，即可得到a n ﹣a 2＜0，求出a n 的取值范围．【解答】解：（1）∵，∴2a n +1=a n +b n ，=，∴b n +1=，∴a n +1b n +1=a n •b n ，∴a n •b n =a n ﹣1•b n ﹣1=…=a 1•b 1，∴{a n •b n }是常数列；（2）{a n }是递减数列，a n +1﹣a n ＜0，∵a 2﹣a 1=（a 1+b 1）﹣a 1=（b 1﹣a 1）＜0∴a 1＞b 1，∵a 3﹣a 2=（b 2﹣a 2）＜0，∴a 2＞b 2，∵（a 1+b 1）＞，∴（a 1﹣b 1）2＞0，猜想a n +1﹣a n =（b n ﹣a n ）＜0，∴a n ＞b n ，∴a 1＞b 1恒成立，∵a k +2﹣a k +1=（b k +1﹣a k +1）==＜0， ∴a 1＞b 1时，{a n }是递减数列．（3）整理得a n +1=（a n +），a 1=4，∴a 2=，∴a 1＞0⇒a 2＞0⇒a 3＞0⇒…⇒a n ＞0，当n ≥2时，a n +1﹣2=（a n +）﹣2=＞0， ∴a n +1＞2，∴a n +1﹣a n =（b n ﹣a n ）==， ∵a n ＞2，∴a n +1﹣a n ＜0，∴{a n }是递减数列，∴a n ﹣a 2＜0，∴a n∈（2，]【点评】本题考查了递推数列的，常数列，数列的函数特征，以及a n的取值范围，培养了学生的运算能力，转化能力，属于难题．。

上海市崇明县2016届高三第二次高考模拟考试英语试题(含答案和听力稿)

崇明县2016届第二次高考模拟考试试卷英语（考试时间120分钟，满分150分。

请将答案填写在答题纸上）第Ⅰ卷 (共103分)I. Listening ComprehensionSection ADirections: In Section A, you will hear ten short conversations between two speak e rs. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.1. A. In a gallery. B. In a classroom. C. In a bookstore. D. In a museum.2. A. Boss and employee. B. Father and daughter.C. T eacher and student.D. Shop assistant and customer.3. A. 5 minutes. B. 8 minutes. C. 10 minutes. D. 15 minutes.4. A. The shirt is too large. B. The price of the shirt is wrong.C. The shirt is too expensive.D. Other shops don’t sell this shirt.5. A. Watching TV. B. Parents’ involvement.C. Playing video games.D. Teachers’ substitution.6. A. A place for a meal. B. Their good friends.C. A tip for choosing food.D. Their plan to eat out.7. A. She doesn’t know where the manager is.B. She doesn’t know where the man heard the news.C. She doesn’t know where she will be working this month.D. She doesn’t know where she can find the work schedule.8. A. The time is not convenient. B. Her house is not big enough.C. A few people won’t turn up.D. There won’t be enough food.9. A. It is rather cool in the lecture hall. B. No one will be able to see what he is wearing.C. The air-conditioner doesn’t work.D. He expects the weather to change later in the day.10. A. The film cost too much despite its high quality.B. The man didn’t like the film but the woman did.C. The man missed the film because of the woman.D. The man saw the film upon the advice of the woman.Section BDirections: In Section B, you will hear two short passages, and you will be asked three questions on each of the passages. The passages will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. A special room. B. A series of textbooks.C. A comprehension program.D. A rewritten masterpiece.12. A. Experts on English reading. B. Beginners of English learning.C. Native speakers of English.D. Editors of English textbooks.13. A. It is designed for different levels. B. It contains original masterpieces.C. It can bring back the childhood.D. It helps to improve memory.Questions 14 through 16 are based on the following passage.14. A. Work efficiency is what we pursue. B. It’s possible for us to work harder.C. Our brain is our most important tool.D. It’s wise to take a rest if our body needs it.15. A. To focus on something new. B. To ignore the limitations.C. To refresh the concentration.D. To lengthen the attention.16. A. Changing jobs from time to time. B. Doing new tasks in different work areas.C. Making a list of all your tasks.D. Eating popcorn while taking a break.Section CDirections:In Section C, you will hear two longer conversations. The conversations will be read twice. After you hear each conversation, you are required to fill in the numbered blanks with the information you have heard. Write your answers on your answer sheet.Blanks 17 through 20 are based on the following conversation.Complete the form. Write ONE WORD for each answer.Blanks 21 through 24 are based on the following conversation.Complete the form. Write NO MORE THAN THREE WORDS for each answer.II. Grammar and VocabularySection ADirections:After reading the passages below, fill in the blanks to make the passages coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.(A)Happiness Is an AttitudeThe 92-year-ol d confident and proud lady, who is fully dressed each morning by eight o’clock, with her hair fashionably combed and makeup perfectly applied, (25)_____ _____ she’s legally blind, move d to a nursing home today.Her husband of 70 years recently passed away, (26)_____ (make) the move necessary.After many hours of waiting patiently in the hall of the nursing home, she (27)_____ (smile) sweetly when told her room was ready. As she got into the elevator (28)_____ her wheelchair, I provided a description of her tiny room.“I love it,” she started with the enthusiasm of (29)_____ eight-year-old child having just been presented with a new dog.“Mrs. Jones, you haven’t seen the room…just wait.”“That ha s (30)_____ to do with it,” she replied. “Happiness is something you decide on ahead of time.(31)_____ I like my room or not doesn’t depend on how the furniture is arranged…it’s how I arrange my mind. I already decided to love it. It’s a decision I make every morning when I wake up. I have a choice; I can spend the day in bed recounting the difficulty I have with the parts of my body (32)_____ no longer work or get out of bed and be thankful for the ones working. Each day is a gift, and (33)_____ _____ _____ my eyes open, I’ll focus on the new day and all the happy memories I’ve stored away…just for this time in my life.”(B)Sculptor B uilds Dubai’s Soaring Burj Khalifa Skyscraper out of Toothpicks to Bag World RecordA sculptor has scaled new heights by building the world’s tallest toothpick (牙签) model.Stanley Hayes Munro, 45, from Syracuse, New York, is a toothpick engineer, who (34)_____ (hook) by toothpick models since he built his first sculpture in school when creating a structure that (35)_____ support the weight of an egg.Now, he has won the world record for the tallest toothpick structure with a sculpture of the Burj Kahlifa, Dubai. For Stanley though, he has always been more concerned with the integrity(完整性) of his work. Stanley said: “I’ve never cared for counting toothpicks, wasting toothpicks, or the number of toothpicks (36)_____ (use) in any construction. But an engineering problem you’ve got to create a strong structure is a problem worth (37)_____(solve).” “I made my first toothpick structure in an art class when Iwas in Grade 5,” he continued. “The assignment was to build something 25 centimeters tall and to have it (38)_____ (hold) the weight of an egg. Mine held my desk and from that point I bec ame interested in it.”“Everybody likes to ask whether my sculptures will collapse when I build them, but they are much(39)_____ (strong) than people think,” he said. “It was not really the height but the shape of the outer walls(40)_____ was the biggest challenge with Burj Khalifa. There wasn’t a flat surface anywhere and I had to individually construct each level,” he said.Section BDirections: Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.A second part of the experiment involved those watching the film being fitted with headsets(耳机) that 48 brain activity and this too showed heightened activity when watching 3D. According to the results, participants were seven percent more engaged with what they were watching, adding to the argument that 3D movies are more like watching real-life-something. “A seven percent rise in emotional engagement is 49 remarkable. Watching in 3D gives the viewer such an enriched and quality experience, as these results show,” he said. “In evolutionary 50 , the results of both parts of the test certainly make sense. 3D films are more likely to heighten the senses and cause emotional arousal—this, in turn, makes the brain run at quicker speeds,” Dr Fagan added.III. Reading ComprehensionSection ADirections: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.Researchers recently find women likely fa ce work environments that push against the “having it all” mentality, leading to feelings of guilt and depression.Trying to have it all could be bad for your mental health, according to a new study that finds that “supermoms” have higher rates of depressi on compared with working moms who let things 51 .The research, presented Aug. 20 at the annual meeting of the American Sociological Association in Las Vegas, finds that working is 52 for mothers’ mental health. But among working mothers, the least depressed are those who don’t expect to 53 work and family life perfectly, said study researcher Katrina Leupp, a graduate student at the University of Washington in Seattle. “The ideal that women can do it all actually 54 the level of depressive symptoms compared to women who were more doubtful about whether or not work and family can be balanced,” Leupp told LiveScience.Leupp analyzed survey 55 from 1,600 married women who participated in a large survey called the National Longitudinal Survey of Youth. In 1987, the women answered questions to judge their support of women’s 56 , including whether they agreed with statements such as “Women are much happier if they stay at home and take care of their children.” In 1992 and 1994, the now 40-year-old women answered questions about their symptoms of depression. Like earlier studies, the survey data indicated that women who worked outside the home had fewer symptoms of depression, perhaps because outside work gives women more 57 interaction, more varied activities and a larger income, Leupp said. Among the employed women, though, the cheeriest were those who had indicated in their younger years the least 58 for women balancing career and family. The results held even after controlling for earlier levels of depression. “Somewhat 59 , women who don’t expect to be able to balance work and family have better mental health than those who do,” Leupp said.The study didn’t explain why optimistic (乐观的) views of balancing work and motherhood would60 later depression. “The reason may come down to 61 and real-world work environments,”Leupp said. “Women who expect to have it all probably come up against 62 that aren’t designed with work-life balance in mind. When they can’t balance every thing perfectly, these supermoms are more likely to feel 63 .”“I think this research really speaks to a 64 between women’s expectations and the actual structure of the workplace,” Leupp said.“The takeaway for working moms is to temper their optimi sm about balancing 65 and employment and not to blame themselves if they struggle. Recognize that if it feels difficult, it’s because it is difficult.”51. A. happen B. continue C. slide D. end52. A. good B. ready C. hard D. possible53. A. protect B. share C. illustrate D. combine54. A. increased B. assessed C. reached D. influenced55. A. questions B. responses C. solutions D. instruments56. A. pregnancy B. marriage C. employment D. education57. A. cultural B. social C. positive D. verbal58. A. support B. tolerance C. concern D. respect59. A. deliberately B. aggressively C. ironically D. similarly60. A. result from B. relate to C. hold back D. call for61. A. families B. expectations C. surroundings D. requirements62. A. clubs B. hospitals C. governments D. workplaces63. A. excited B. embarrassed C. thrilled D. frustrated64. A. mismatch B. mistreat C. misunderstanding D. misinterpretation65. A. aging B. training C. schooling D. parentingSection 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）The twenty-four horses dash around a racetrack. The thunder of their hooves (蹄) rings in the riders’ears, nearly drowning out the cheering of the crowd. After three or four minutes of suspense, one horse crosses the finish line first, winning the Melbourne Cup and earning a place in history.The horses that compete in the Melbourne Cup—one of the world’s most famous horseraces—were fated to race. Bred for speed, these horses are the few that were singled out as having potential to become champions.Preparing a racehorse to compete requires a team. A horse’s owner manages the team and decides which races to enter. A trainer determines the racehorse’s diet and exercise. Regular exercise makes a horse less likely to be injured, but overtraining tires the horse. A groomer (动物美容师) cares for the racehorse and reports any problems he discovers to the trainer. And of course, no horserace could be run without a rider. These riders train for long hours and travel constantly from one race to another. They need to make a strategy, adapt to changing conditions and communicate with their horse to guide it to victory.Australia’s most famous horserace, the Melbourne Cup, is 3,200 meters of pure excitement. Each year 300 or 400 horses are nominated(提名), but only 24 can run. The competitors are chosen based on a number of factors, but winners of certain races qualify automatically.Each racehorse receives a handicap—a certain weight it must carry to give each horse an equal chance of winning—two months before the race. Originally, horses that seemed likely to win were assigned larger handicaps. But the rules have changed, reducing the handicap for previous winners.The first Melbourne Cup in 1861 drew a crowd of 4,000 spectators, and the race’s popularity has grown since then. Held on the first Tuesday of November, the cup has become a four-day festival with fine food and entertainment.The Melbourne Cup began during a gold rush as a form of entertainment for the rich. Today it still attracts society’s upper class. They come dressed in their finest to enjoy the event in comfort.But anyway it’s all about the race—the effort of horses and riders, the suspense and the thrill of victory.66. What can be learned about the horses in the Melbourne Cup?A. They are all winners of a certain race.B. They are raised and trained by joint effort.C. They are chosen from ordinary horses.D. Their fates are determined by their trainers.67. The racehorses are given handicaps so that _____.A. they will weigh the sameB. previous winners are unlikely to winC. the race will be fair enoughD. they will be more adaptable to the race68. It can be learned from the passage that _____.A. the spectators of the Melbourne Cup must dress wellB. the Melbourne Cup was intended for wealthy peopleC. the winner of the Melbourne Cup can earn a large fortuneD. the Melbourne Cup is the best-known horserace worldwide69. The passage can most probably be found in _____.A. a sports journalB. a business newspaperC. an academic paperD. a health magazine（B）discoveries which are linked to the early missionary work of St Patrick and his followers, and to his Early ChristianThis PEACE IIIphotographs, medicalLieutenant-Colonel Alexander Silcock, which were recently donated to Down County Museum.provides an overview Rising and will explore a selection of themes including how the Rising waspolitics and society. Pre-booking essential.This exhibition displays the applied art collection of Down County Museum.陶瓷制品), textile（C）Fed up with constantly having to recharge or replace batteries in your ever-expanding electronic devices? The solution may be just a few steps away.“Energy harvesting”promises to power countless consumer devices, often with nothing more than your body’s movement or heat. Dozens of companies around the world already offer such products, but many experts believe the market for the technology could explode due to electronic devices being developed for the Internet of Things.“It’s huge,”said Graham Martin, CEO of the EnOcean Alliance, a San Ramon-based group of businesses that promotes wireless energy-harvesting technologies. With the Internet of Things expected to combine billions of devices, “if they are all battery-powered, we’ll have a problem because there’s not enough lithium (锂) in the world,” he added. “So a lot of them will have to use energy harvesting.”Among the most basic forms of the technology is body power. When certain materials are squeezed or stretched, the movement of their atoms creates an electrical charge. Automatic watches have employed the concept for decades, for example, by winding themselves when their user moves their arm. Now, the concept is being considered for a number of other devices.In a contest seeking visionary ideas for wearable technologies, Intel awarded $5,000 for a concept to change the temperature difference between a person’s body and a special piece of clothing they’d wear into electricity for mobile devices.Using sound to power devices is another energy-harvesting variation. Stanford University engineers are testing smart microchips (芯片) that create electricity from ultrasound (超声波) to power implantable (可植入的) devices that can analyze a person’s nervous system or treat their diseases.A textile (纺织品) research association in Spain is proposing to obtain electricity from radio waves that flow around everyone to power sensors sewn into clothes, which can monitor a person’s heartbeat or other vital signs.Research firm IDTechEx has estimated that annual global sales of energy-harvesting products could hit $2.6 billion by 2024, while WinterGreen Research predicts sales of $4.2 billion by 2019.Obtaining stable energy from devices can be complex, however. For one thing, the motion that generates the electricity has to be constant to be useful. Moreover, the amount of power the devices produce depends on the person using them, according to a Columbia University study. It determined that taller people on average provide about 20 percent more power than shorter ones when walking, running or cycling.It’s also unclear how eagerly consumers might welcome energy-harvesting products. While such devices are expected to cost less than battery-powered alternatives when compared over many years, experts say, people may continue buying ones with batteries merely because those would be cheaper in the short term.74. Which “explode”in the following sentences has the most similar meaning to the word “explode”inParagraph 2?A. They were clearing up when the second bomb exploded.B. The continued tension could explode into more violence.C. The population exploded to 40,000 during the last tourist season.D. The boss exploded when he heard of the resignation of the secretary.75. What makes “energy harvesting” necessary according to the passage?A. The waste of lithium in the world.B. The increasing number of electronic devices.C. The development of technology.D. The pollution caused by batteries.76. It can be learned from the passage that _____.A. energy-harvesting products save money in the long runB. taller people can surely produce a larger amount of powerC. automatic watches harvest energy from the user s’ body heatD. two ways of harvesting energy are mentioned in the passage77. Which of the following might be the best title for the passage?A. Energy harvesting: a low-risk technologyB. Energy harvesting: a high-profit technologyC. Energy harvesting: a problem-free technologyD. Energy harvesting: an environment-friendly technologySection CDirections: Read the passage carefully. Then answer the questions or complete the statements in the fewest possible words.Want to attract and keep top talent? Here’s a suggestion: Make a flexible work schedule part of the deal.A survey this summer of 1,215 U.S. managers and employees across a variety of industries, by EY (formerly Ernst & Young), found those aged 18 to 32 rank flexibility among the perks(特殊待遇) they want most, with 33% saying they wouldn’t work anywhere that didn’t offer it. But it seems those aged 33 to 48 value flextime even more: 38% of them consider it non-negotiable, with men who said so, at 40%, slightly outnumbering women (37%).“Companies first started offering flexible schedules, in the late 80s and the 90s, as a way to recruit (招募) and keep talent ed women, but it’s gone way beyond that now,” observes Karyn Twaronite, an EY partner who came up through the tax side of the business.Noting that both men and women, in all age groups, ranked flextime(弹性工作制) tops among non-cash perks, Twaronite adds, “That result mirrors exactly what we’re seeing here at EY.” The accounting and consulting giant, No. 57 on Fortune’s Best Companies to Work For, has had thousands of employees working flexible schedules for years—including, since 2004, six weeks’ of paid lea ve for new dads.“Flextime may have started out as a women’s issue, but it’s changed into something that people of both sexes have come to expect,” he adds. “I think it’s partly because of the large number of two-career households now, where people have to adapt to two demanding professional schedules instead of just one.”The EY survey suggests that, in the next decade or so, the opportunity for a life outside the office will become an even bigger draw than it already is. Most of those surveyed still work a set schedule, the report notes, but “respondents expect a shift in the coming years to more flexible hours, as 62% currently work standard office hours and only 50% expect to do so in five to ten years.”That doesn’t surprise Twaronite. “Work is changing,” she observes. “The technology to connect anywhere and anytime means that people are expected to be on call 24 hours a day, especially in globalcompanies that operate across different time zones. The other side of that is that employers are adapting to people’s lives outside of work—because they have to be.”(Note: Answer the questions or complete the statements in NO MORE THAN TEN WORDS.)78. What is the main finding of the survey?79. Flextime was originally aimed at _____.80. The result of the survey is caused by the fact that _____.81. What makes flextime possible according to Twaronite?第Ⅱ卷（共47分）I. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.1. 出国对于这个高中生来讲根本没有吸引力。

2016届上海市虹口区高三4月高考练习(二模)数学(理)试题(2016.04)

（第11题图）CBOFAy xOBAC虹口区2016年高考模拟数学试卷（理合卷）2016.4考生注意：1.本试卷共4页，23道试题，满分150分，考试时间120分钟.2.本考试分设试卷和答题纸. 作答必须涂（选择题）或写（非选择题）在答题纸上，在试卷上作答一律不得分.一、填空题（本大题满分56分）本大题共14题，只要求在答题纸相应题号的空格内直接填写结果，每个空格填对得4分，否则一律得零分.1．设集合{}2M x x x ==，{}20N x log x =≤，则=N M __________.2．已知虚数1+2i 是方程20()x ax b a b R ++=∈、的一个根，则_______.a b += 3. 在报名的5名男生和4名女生中，选取5人参加志愿者服务，要求男、女生都有，则不同的选取方式的种数为（结果用数值表示）. 4．已知复数z 在复平面上对应的点在曲线2y x=上运动，则z 的最小值等于__________. 5.已知函数()f x 的对应关系如下表：x2-1- 01 2()f x32-15m若函数()f x 不存在反函数，则实数m 的取值集合为___________. 6.在正项等比数列{}n a 中，132341,,3a a a a =+=则12lim()n n a a a →∞+++= ___________.7.已知()2sin (0)f x x ωω=>在0,3π⎡⎤⎢⎥⎣⎦单调递增，则实数ω的最大值为___________.8.若行列式124cos()20116x π+-中的元素4的代数余子式的值等于32，则实数x 的取值集合为____________.9. 若二项式1(2)nx x-展开式中的第5项为常数项，则展开式中各项的二项式系数之和为__________.10 .已知A 、B 是球O 的球面上两点，90AOB ∠=，C 为该球面上的动点，若三棱锥ABC O -体积的最大值为323， ( 第10题图) 则球O的表面积为___________.11. 如图, 2222+1(0)x yA B a b a b =>>、为椭圆的两个顶点，过椭圆的右焦点F 作x 轴的垂线，与其交于点 C. 若//AB OC (O 为坐标原点)，则直线AB 的斜率为___________.12. 若经过抛物线 24y x =焦点的直线 l 与圆22(4)4x y -+= 相切，则直线l 的方程为___________.13.（理）假设某10张奖券中有一等奖1张，奖品价值100元；有二等奖3张，每份奖品价值50元；其余6张没有奖. 现从这10张奖券中任意抽取2张，获得奖品的总价值ξ 不少于其数学期望E ξ的概率为_________.14. （理）已知对任意的[](,0)(0,),1,1x y ∈-∞⋃+∞∈-，不等式222168210x xy y a x x+----≥恒成立，则实数a 的取值范围为_________.二、选择题（本大题共4题，满分20分）每题有且只有一个正确答案，考生应在答题纸的相应题号上，将所选答案的代号涂黑，选对得 5分，否则一律零分.15． 3a =“”是“直线2(2)0a a x y -+=和直线310x y ++=平行”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16．（理）已知抛物线21:4C y x =的焦点F 恰好是椭圆22222:1(0)x y C a b a b+=>>的右焦点，且两条曲线12C C 与交点的连线过点F ，则椭圆2C 的长轴长等于 ( )（A ）21+ （B ）2 （C ） 222+ （D ）4 17. 在ABC ∆中，a b c 、、分别是内角A B C 、、所对的边，若2224ABC a b c S ∆+-=（其中)ABC S ABC ∆∆表示的面积，且0,AB AC BC AB AC ⎛⎫ ⎪+⋅= ⎪⎝⎭则ABC ∆的形状是 ( ) （第16题图）（A ）有一个角为30︒的等腰三角形（B ）等边三角形（C ）直角三角形（D ）等腰直角三角形18．（理）已知点列(,)()n n n A a b n N *∈均在函数(0,1)x y a a a =>≠的图像上，点列(,0)n B n 满足1.n n n n A B A B +=若数列{}n b 中任意连续三项能构成三角形的三边，则a 的取值范围为（）QA DCBP （第20题图）（A ）51510,,22⎛⎫⎛⎫-+⋃+∞ ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭ （B ）5151,11,22⎛⎫⎛⎫-+⋃ ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭（C ）31310,,22⎛⎫⎛⎫-+⋃+∞ ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭（D ）3131,11,22⎛⎫⎛⎫-+⋃ ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭三、解答题（本大题共5题，满分74分）解答下列各题必须在答题纸的规定区域内写出必要的步骤. 19．(本题满分12分) 本题共2个小题，每小题6分. 在锐角ABC ∆中， 2sin sin sin()sin().44A B B B ππ=++-(1) 求角A 的值；(2) 若12,AB AC ⋅=求ABC ∆的面积.20．(本题满分14分) 本题共2个小题，每小题7分. （理）如图，在四棱锥ABCD P -中，已知⊥PA 平面ABCD ，且四边形ABCD 为直角梯形，90ABC BAD ∠=∠=︒，2AB AD AP ===，1BC =.(1) 求点A 到平面PCD 的距离；(2) 若点Q 为线段BP 的中点，求直线CQ 与平面ADQ 所成角的大小.21．(本题满分14分) 本题共2个小题，每小题7分.已知函数131()log 1ax f x x -⎛⎫= ⎪-⎝⎭满足(2)1f -=，其中a 为实常数. （1）求a 的值，并判定函数()f x 的奇偶性；（2）若不等式1()2xf x t ⎛⎫>+ ⎪⎝⎭在[]2,3x ∈恒成立，求实数t 的取值范围.22. (本题满分16分) 本题共3个小题，第1小题5分，第2小题5分，第3小题6分.已知直线2y x =是双曲线2222:1x y C a b-=的一条渐近线，点(1,0)(,)A M m n 、(0)n ≠（第22题图）P NQxOAMy都在双曲线C 上，直线AM 与y 轴相交于点P ，设坐标原点为O ．(1) 求双曲线C 的方程，并求出点P 的坐标（用m 、n 表示）； (2) 设点M 关于y 轴的对称点为N ，直线AN 与y 轴相交于点Q ．问：在x 轴上是否存在定点T ，使得TP TQ ⊥？若存在，求出点T 的坐标；若不存在，请说明理由．(3) 若过点(0,2)D 的直线l 与双曲线C 交于R S 、两点，且OR OS RS +=，试求直线l 的方程．23. (本题满分18分)（理）本题共3个小题，每小题6分.设数列{}n a 的前n 项和为,n S 且2(1)().n n n S a S n N *-=∈（1）求123S S S 、、的值，并求出n S 及数列{}n a 的通项公式；（2）设121(1)(1)(),n n n n b n a a n N +*+=-+⋅∈求数列{}n b 的前n 项和.n T（3）设(1)(),n n c n a n N *=+⋅∈在数列{}n c 中取出(,3)m m N m *∈≥为常数项，按照原来的顺序排成一列，构成等比数列{}n d .若对任意的数列{}n d ，均有123,m d d d d M ++++≤ 试求M 的最小值.虹口区2016年高考模拟数学试卷参考答案与评分标准2016年4月一、填空题（本大题共14题,每题4分,满分56分）1．[]0,1 2． 3 3．125 4． 2 5． {}3,2,1,5- 6.92 7. 32 8． 2,3x x k k Z ππ⎧⎫=±∈⎨⎬⎩⎭9. 64 10．64π 11．2212. 5102x y ±-=QA D CBP （第20题解答图）z yx 13．（理）23； 14．（理）(,842⎤-∞-⎦；二、选择题（本大题共4题，每题5分，满分20分）15. A 16. C 17. D 18. B 三、解答题（本大题共5题，满分74分）19．(本题满分12分) 本题共2个小题，每小题6分.()2222sin sin sin()sin()sin sin()cos()4444111sin sin(2)sin cos 1242222A B B B B B B B B B B πππππ=++-=+++=++=+=解：因分故由ABC ∆为锐角三角形，得.6A π=……6分（2）由（1）知3cos ,2A =由已知，有 312cos ,2AB AC cb A bc =⋅=⋅= 故8 3.bc = ……9分从而111sin 832 3.222ABC S bc A ∆=⋅=⋅⋅= ……12分20．(本题满分14分) 本题共2个小题，每小题7分.（理）解：(1)以},,{AP AD AB 为正交基底建立空间直角坐标系xyz A -，则相关点的坐标为B （2,0,0），(2,1,0),(0,2,0),(0,0,2).C D P ……2分设平面PCD 的法向量为(,,),n x y z =由(2,1,0),DC =- (0,2,2),DP =- (0,2,0).DA =-则202,2.220n DC x y y x z x n DPy z ìïì?-==ïïïÞ眄镲=?-+=ïîïî 令1x =，则(1,2,2)n = . ……5分所以点A 到平面PCD 的距离为：(0,2,0)(1,2,2)4.(1,2,2)3DA n d n×-?=== ……7分 (2) 由条件，得(1,0,1),Q =(0,2,0),(1,0,1),AD AQ ==且(1,1,1).CQ=-- 设平面ADQ 的法向量为0000(,,),n x y z = 则00000000200,.0n AD y y z x n AQ x z ìïì?==ïï镲Þ眄镲=-?+=ïïîî 令01x =，则0(1,0,1)n =-. ……10分设直线CQ 与平面ADQ 所成角为,θ则00026sin cos ,.332CQ n CQ n CQ n θ⋅=<>===⋅故直线CQ 与平面ADQ 所成角的大小为6sin.3arc ……14分注：第（1）小题也可用等积法来做.21．(本题满分14分) 本题共2个小题，每小题7分. 解：（1）由1312121(2)log 1,,2133a a f ++-==-=--得解得 1.a =- ……3分于是131()log 1x f x x +⎛⎫=⎪-⎝⎭，其定义域为(,1)(1,).D =-∞-⋃+∞ ……4分对于任意的(,1)(1,),x ∈-∞-⋃+∞有111133331111()+()log log log log 10,1111x x x x f x f x x x x x +-++-+⎛⎫⎛⎫⎛⎫-=+=⋅== ⎪ ⎪ ⎪------⎝⎭⎝⎭⎝⎭故()f x 为奇函数. ……7分（2）由1()2x f x t ⎛⎫>+ ⎪⎝⎭，得[]1()2,32xt f x ⎛⎫<- ⎪⎝⎭在恒成立.由12111x x x +=+--在(,1)-∞-及(1,)+∞上均递减，且13()log g u u =在(0,)+∞上也递减，故函数()f x 在区间(,1)(1,)-∞-+∞及均单调递增. ……10分由()f x 及12xy ⎛⎫=- ⎪⎝⎭在区间[]2,3均单调递增，知[]1()()2,32xx f x ϕ⎛⎫=- ⎪⎝⎭在单调递增， ……12分故2min15()(2)(2).24x f ϕϕ⎛⎫==-=- ⎪⎝⎭因此，实数t 的取值范围为5(,).4-∞- ……14分22. (本题满分16分) 本题共3个小题，第1小题5分，第2小题5分，第3小题6分.解：（1）由已知，得11,2,2a a b b a=⎧=⎧⎪⇒⎨⎨==⎩⎪⎩故双曲线C 的方程为 22 1.4y x -= ……3分 (1,)AM m n =-为直线AM 的一个方向向量，∴直线AM 的方程为1,1x y m n -=-它与y 轴的交点为(0,).1nP m- ……5分（2）由条件，得(,),N m n -且(1,)AN m n =--为直线AN 的一个方向向量，故直线AN 的方程为1,1x ym n -=--它与y 轴的交点为(0,).1n Q m+ ……7分假设在x 轴上存在定点0(,0)T x ，使得TP TQ ⊥,则由0(,),1n TP x m =--0(,),1n TQ x m =--+ 及221,4n m -=得 0(,)1n T P T Q x m ⋅=-⋅- 22222000022(,)40.11(1)14n n n x x x x n m m --=-=-=-=+-+- 故02,x =±即存在定点T ，其坐标为(2,0)或(2,0),-满足题设条件. ……10分(3) 由OR OS RS +=知，以OR OS 、为邻边的平行四边形的对角线的长相等，故此四边形为矩形，从而.OR OS ⊥……12分由已知，可设直线l 的方程为2,y kx =+并设1122(,),(,),R x y S x y则由222,1,4y kx y x =+⎧⎪⎨-=⎪⎩ 得 22(4)480.k x kx -++= 由2221632(4)16(8)0,k k k ∆=--=->及240,k -≠得2284k k <≠且（*）由121212122248,,(2)(2),44k x x x x y y k x k x k k +=-==++-- ……14分得2222121212122228(1)84(2)(1)2()440444k k k OR OS x x y y k x x k x x k k k +-⋅=+=++++=-+==---故22,k =符合约束条件（*）.因此，所求直线l 的方程为2 2.y x =±+ ……16分 23.（理） (本题满分18分) 本题共3个小题，每小题6分. 解：（1）当1n =时， 22111111(1);2S a S S S -==⇒=当2n =时， 222222212(1)();23S a S S S S -==-⇒=当3n =时， 233333323(1)().34S a S S S S -==-⇒= ……2分由此，猜测： ().1n nS n N n *=∈+ 下面用数学归纳法证明：（i ）当1n =时，结论显然成立；（ii ）假设当()n k k N *=∈时，1k kS k =+；则当1n k =+时，由条件，得 21111111(1)().2221k k k k k k k k k k k S a S S S S S k S k k +++++++-==-⇒===-+-+即当1n k =+时，结论也成立.于是，由（i ），（ii ）可知，对任意的,.1n nn N S n *∈=+均有……4分当1112,.1(1)n n n n n n a S S n n n n --≥=-=-=++时又1111,212a S ===⨯ 于是数列{}n a 的通项公式为:1().(1)n a n N n n *=∈+ ……6分 (2)因 121111111(1)(1)(1)(1)(),(2)22n n n n n n b n a a n n n n ++++=-+⋅=-⋅=-⋅-++……8分当n 为奇数时， 12111111111111(1)()()()()()232435461121111111(1)?221222(1)(2)n n T b b b n n n n n n n n ⎡⎤=+++=---+---+--+-⎢⎥-++⎣⎦⎡⎤=-+-=+⎢⎥++++⎣⎦分当n为偶数时，12111111111111(1)()()()()()232435461121111111(1).221222(1)(2)n n T b b b n n n n n n n n ⎡⎤=+++=---+---++---⎢⎥-++⎣⎦⎡⎤=--+=-⎢⎥++++⎣⎦故111,(22(1)(2)11(1)=.22(1)(2)111,(22(1)(2)nnn n n T n n n n n ⎧⎡⎤+⎪⎢⎥++⎡⎤-⎪⎣⎦=-⎨⎢⎥++⎡⎤⎣⎦⎪-⎢⎥⎪++⎣⎦⎩当为奇数)当为偶数)……12分（3）因1(1),n n c n a n =+⋅=由于数列{}n c 的(3)m m ≥项子列{}n d 构成等比数列，设其公比为,q 则 211231(1).m m d d d d d q q q -++++=++++11,1,(),q Q q d a N a +*∈<=∈因且设(,,2,,).vq u v N u u v u *=∈≥且互质（i ）当1v =时，因11,2q u =≤故 2112312111111(1)12.2222m m m m d d d d d q q q ---++++=++++≤++++=- ……15分（ii ）当1v ≠时，因11111m m m m v d d q a u---==⋅是数列{}n c 中的项，故1().m a v a a N -*''=⋅∈2112311232211232211232211111(1)111111()111111111122323233121()321232(3).223213m m m m m m m m m m m m m m m m m m m m m m d d d d d q q q a v v u v u vu u v v u v u vu u m --------------------++++=++++=+++++'≤+++++≤+++++⋅⋅⋅⎡⎤-⎢⎥⎣⎦==-<-≥- 从而综合（i ），（ii ），得：在数列{}n c 中的所有(3)m m ≥项等比子数列{}n d 中，其和最大的是：211111.222m - ，，，，故由题意知：M 的最小值为112.2m -- ……18分另解（3）：因1(1),n n c n a n =+⋅=由于数列{}n c 的(3)m m ≥项子列{}n d 构成等比数列，设其公比为,q 则 211231(1).m m d d d d d q q q -++++=++++11,1,().q Q q d a N a +*∈<=∈因且（i ）当1a =时，因1,2q ≤故 211232111111112.2222m m m m d d d d q q q ---++++=++++≤++++=- ……15分（ii ）当2a ≥时，因11,11a a q a a+≤=+ 故2112311111(1)111312(3).22m m m d d d d q q q a a a aa m --++++=++++<⋅=+-+≤<-≥综合（i ），（ii ），得：在数列{}n c 中的所有(3)m m ≥项等比子数列{}n d 中，其和最大的是：211111.222m - ，，，，故由题意知：M 的最小值为112.2m -- ……18分。

【高考模拟】上海市崇明县2016届高三第二次高考模拟考试英语试题 Word版含解析

崇明县2016届第二次高考模拟考试试卷英语（考试时间120分钟，满分150分。

上海市2016届高考化学模拟测试试题(新疆班)

上海市新疆班2016届高考模拟测试化学试卷（时间120分钟，满分150分）考生注意：1．本试卷满分150分，考试时间120分钟。

2. 本考试设试卷和答题纸两部分，试卷包括试题与答题要求；所有答题必须涂（选择题）或写（非选择题）在答题纸上；做在试卷上一律不得分。

3. 答题前，考生务必在答题纸上用钢笔或圆珠笔清楚填写姓名、准考证号，并将核对后的条形码贴在指定位置上。

4. 答题纸与试卷在试题编号上是一一对应的，答题时应特别注意，不能错位。

相对原子质量： H-1 Na-23 S-32 O-16 C-12 Cl-35.5 Br-80 Se-79 N-14Fe-56第I 卷（共66分）一、选择题（本题共10分。

每小题2分，每题只有一个正确选项） 1、化学与生产、生活、环境等社会实际密切相关。

下列叙述正确的是A ．生吃新鲜蔬菜要比熟吃时维生素C 的损失大B ．水体中植物营养物质过多积累会引起水体富营养化C ．加强化石燃料的开采利用，能从根本上解决能源危机D ．推广使用煤液化技术，可减少二氧化碳等温室气体的排放 2、下列物质对应的用途不正确．．．的是3、下列氧化物中，能与水反应生成酸的是A ．SiO 2B ．NOC ．SO 3D ．Al 2O 34、下列化学用语正确的是A ．甲基的电子式是B ．硫的原子结构示意图是C. 188O表示中子数是18的氧原子 D. 过氧化氢的结构式是 H —O —O —H5、下列有关晶体的说法中正确的是A.晶体中分子间作用力越大，分子越稳定B.原子晶体中共价键越强，熔点越高C.冰融化时水分子中共价键发生断裂D.氯化钠熔化时离子键未被破坏二、选择题（本题共36分，每小题3分，每题只有一个正确选项）6、已知16S、52Te位于同一主族，下列关系正确的是A．原子半径：Te > Cl > S B．热稳定性：H2Te > H2S > PH3C．酸性：HClO4 > H2SO4 >H2TeO4 D．还原性：Cl- >S2- > Te2-7、下列各种关于酸的使用，其中正确的是A．检验氯乙烷中的氯元素，水解后再用硫酸酸化B．为了增强KMnO4溶液的氧化能力，用浓盐酸酸化C．为了抑制Fe2+的水解，用稀硝酸酸化D．检验溶液中是否含有SO-24时，先用盐酸酸化8、25℃时，1 mol/L醋酸加水稀释至0.01 mol/L，关于稀释前后的下列变化正确的是A．溶液中c(OH—)减小 B．pH的变化值等于2C．溶液中H+的个数增大 D．Kw的值减小9、下列有机物命名正确的是10、用下图所示装置进行实验，实验现象对应的结论正确的是11、向H2S的水溶液中通入一定量的Cl2，下列图像所示的变化正确的是12、已知H 2O 2在催化剂作用下分解速率加快，其能量随反应进程的变化如下图所示。

2016年上海高考语文模拟试题及答案高考语文模拟试题及答案

2016年上海高考语文模拟试题及答案高考语文模拟试题及答案几度播洒汗水，即将迎来收获;几度辛勤耕耘，即将结出硕果;几度怀揣梦想，即将放飞希望;成功已在招手，只等最后拼搏。

高考加油，期待奏响凯歌!高考网为大家提供2016年上海高考语文模拟试题及答案，更多高考语文试卷及高考语文答案请关注我们网站的更新!2016年上海高考语文模拟试题及答案一、名句名篇默写(6分)1.补写出下列名句名篇中的空缺部分。

(1)芳与泽其杂糅兮，________________________。

(屈原《离骚》)(2)________________________，列坐其次。

(王羲之《兰亭集序》)(3)舞幽壑之潜蛟，________________________。

(苏轼《赤壁赋》)(4)________________________，风烟望五津。

(王勃《送杜少府之任蜀州》)(5)________________________;处江湖之远则忧其君。

(范仲淹《岳阳楼记》)(6)________________________，飞鸟相与还。

(陶渊明《饮酒》)答案(1)唯昭质其犹未亏(2)引以为流觞曲水(3)泣孤舟之嫠妇(4)城阙辅三秦(5)居庙堂之高则忧其民(6)山气日夕佳二、语言文字运用(15分)2.阅读下面的文字，完成后面的题目。

(4分)①世界文学________(cuǐ càn)的星空中又一颗巨星陨落了!②马尔克斯的去世引发了互联网世界几乎是排山倒海般的缅怀。

③但这似乎与逝者没有多大关系，因为真正能打开《百年孤独》沉下心读完全书的人恐怕只是凤毛鳞角。

④而纪念一个作家最好的方式莫过于亲近他的作品，从这个意义上说，通过马尔克斯离世这件事，让人们更加意识到自己的感情已变得多么空洞苍白。

(1)根据括号内的拼音填写正确的汉字。

(1分)(2)文中有一个错别字，请指出并加以修改。

(1分)答：(3)材料中有一处语病，请写出序号并加以改正。

【中学生报】2016年上海高考英语模拟试卷(含答案)(图片版)

2016年上海高考英语模拟试卷（含答案）命题：建平中学徐锋载于5月27日《上海中学生报·高招周刊》参考答案第I卷1-24 略25. may/might/must 26. what 27. which 28. that29. concerning 30. more capable 31.has 32. Though/Although/While 33. Investigating 34. made 35. in 36. to minimize37. are used/are being used 38. a 39. that 40. before41—50 IBDFA GKJEC51—65 BABBA CDACA CCABC66—77 DBAD CAB ACADC78. the expansion of farmland79. Climate change80. (Because) urban areas provide various flowering plants and an extended flowering season81. pesticides, climate change and disease第II卷I.Translation1. Never has our school been so well-known to the public as it is now.2. His insisting on his own idea caused many people to be infected with the disease.3. Though there seems nothing special about it, the electronic watch helps the wearer to manage time and improve efficiency.4. Not having traveled alone before, he decided to conceal his plan from his parents in case they may feel worried.5. It is common for us Chinese to prepare a lot of delicious food to entertain foreign guests so as to show them our friendship and hospitality.II.略。

2016年虹口区高三数学二模(文、理)试卷.

OBAC虹口区2016年高考模拟数学试卷（文理合卷）2016.4考生注意：1.本试卷共4页，23道试题，满分150分，考试时间120分钟.2.本考试分设试卷和答题纸. 作答必须涂（选择题）或写（非选择题）在答题纸上，在试卷上作答一律不得分.一、填空题（本大题满分56分）本大题共14题，只要求在答题纸相应题号的空格内直接填写结果，每个空格填对得4分，否则一律得零分.1．设集合{}2M x x x ==，{}20N x log x =≤，则=N M __________.2．已知虚数1+2i 是方程20()x ax b a b R ++=∈、的一个根，则_______.a b +=3. 在报名的5名男生和4名女生中，选取5人参加志愿者服务，要求男、女生都有，则不同的选取方式的种数为（结果用数值表示）. 4．已知复数z 在复平面上对应的点在曲线2y x=上运动，则z 的最小值等于__________. 5.已知函数()f x 的对应关系如下表：若函数()f x 不存在反函数，则实数m 的取值集合为___________. 6.在正项等比数列{}n a 中，132341,,3a a a a =+=则12lim()n n a a a →∞+++=___________.7.已知()2sin (0)f x x ωω=>在0,3π⎡⎤⎢⎥⎣⎦单调递增，则实数ω的最大值为___________.8.若行列式124cos()20116x π+-中的元素4的代数余子式的值等于32，则实数x的取值集合为____________.9. 若二项式(2nx 展开式中的第5项为常数项，则展开式中各项的二项式系数之和为__________.10 .已知A 、B 是球O 的球面上两点，90AOB ∠=，C 为该球面上的动点，若三棱锥ABC O -体积的最大值为323，则球O 的表面积为___________. ( 第10题图 )11. 如图, 2222+1(0)x y A B a b a b=>>、为椭圆的两个顶点，过椭圆的右焦点F 作x 轴的垂线，与其交于点C. 若//AB OC (O 为坐标原点)，则直线AB 的斜率为___________.12. 若经过抛物线 24y x =焦点的直线 l 与圆22(4)4x y -+=相切，则直线l 的方程为___________.13.（理）假设某10张奖券中有一等奖1张，奖品价值100元；有二等奖3张，每份奖品价值50元；其余6张没有奖. 现从这10张奖券中任意抽取2张，获得奖品的总价值ξ 不少于其数学期望E ξ的概率为_________.（文）设函数2,1()(0,1),2,1x a x f x a a x x x ⎧<⎪=>≠⎨-≥⎪⎩其中若不等式()3f x ≤的解集为(],3,-∞则实数a 的取值范围为___________.14. （理）已知对任意的[](,0)(0,),1,1xy ∈-∞⋃+∞∈-，不等式221620x xy a x +-≥恒成立，则实数a 的取值范围为_________.（文）在直角坐标平面，已知两定点(1,0)(1,1)A B 、和一动点(,)M x y 满足01,02OM OA OM OB ⎧≤⋅≤⎪⎨≤⋅≤⎪⎩ 则点(,)P x y x y +-构成的区域的面积为_________.二、选择题（本大题共4题，满分20分）每题有且只有一个正确答案，考生应在答题纸的相应题号上，将所选答案的代号涂黑，选对得 5分，否则一律零分.15． 3a =“”是“直线2(2)0a a x y -+=和直线310x y ++=平行”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16．（理）已知抛物线21:4C y x =的焦点F 恰好是椭圆22222:1(0)x yC a b a b +=>>的右焦点，且两条曲线12C C 与交点的连线过点F ，则椭圆2C 的长轴长等于 ()（A 1 （B ）2（C ） 2 （D ）4俯视图左视图（文）一个几何体的三视图如图所示，则该几何体的表面积为（）（A ）π3（B ）π4（C ）43+π （D ） 42+π 17. 在ABC ∆中，a b c 、、分别是内角A B C 、、所对的边，若2224ABC a b c S ∆+-=（其中)ABC S ABC ∆∆表示的面积，且0,AB AC BC AB AC ⎛⎫ ⎪+⋅= ⎪⎝⎭则ABC ∆的形状是 ( ) （第16题图）（A ）有一个角为30︒的等腰三角形（B ）等边三角形（C ）直角三角形（D ）等腰直角三角形18．（理）已知点列(,)()n n n A a b n N *∈均在函数(0,1)x y a a a =>≠的图像上，点列(,0)n B n 满足1.n n n n A B A B +=若数列{}n b 中任意连续三项能构成三角形的三边，则a 的取值范围为（）（A ）0,⎛⎫⋃+∞ ⎪ ⎪⎝⎭⎝⎭（B ）11,⎫⎛⋃⎪ ⎪ ⎝⎭⎝⎭（C ）0,⎛⎫⋃+∞ ⎪ ⎪⎝⎭⎝⎭（D ）11,⎫⎛⋃⎪ ⎪ ⎝⎭⎝⎭（文）已知抛物线27y x =-上存在关于直线0=+y x 对称的相异两点A 、B ，则AB 等于 ( ) （A ）5 （B ）（C）6 （D ）三、解答题（本大题共5题，满分74分）解答下列各题必须在答题纸的规定区域内写出必要的步骤.19．(本题满分12分) 本题共2个小题，每小题6分. 在锐角ABC ∆中， 2sin sin sin()sin().44A B B B ππ=++-(1) 求角A 的值；(2) 若12,AB AC ⋅=求ABC ∆的面积.QA DCBP （第20题图）（第20题图）PBCDA 20．(本题满分14分) 本题共2个小题，每小题7分. （理）如图，在四棱锥ABCD P -中，已知⊥PA 平面ABCD ，且四边形ABCD 为直角梯形，90ABC BAD ∠=∠=︒，2AB AD AP ===，1BC =.(1) 求点A 到平面PCD 的距离；(2) 若点Q 为线段BP 的中点，求直线CQ 与平面ADQ 所成角的大小.（文）如图，在四棱锥ABCD P -中，已知⊥PA 平面ABCD ，且四边形ABCD 为直角梯形，90ABC BAD ∠=∠=︒，2AB AD AP ===，1BC =. 求：(1) 异面直线PC AD 与所成角的大小； (2) 四棱锥ABCD P -的体积与侧面积.21．(本题满分14分) 本题共2个小题，每小题7分.已知函数131()log 1ax f x x -⎛⎫= ⎪-⎝⎭满足(2)1f -=，其中a 为实常数. （1）求a 的值，并判定函数()f x 的奇偶性；（2）若不等式1()2xf x t ⎛⎫>+ ⎪⎝⎭在[]2,3x ∈恒成立，求实数t 的取值范围.22. (本题满分16分) 本题共3个小题，第1小题5分，第2小题5分，第3小题6分.已知直线2y x =是双曲线2222:1x y C a b-=的一条渐近线，点(1,0)(,)A M m n 、(0)n ≠都在双曲线C 上，直线AM 与y 轴相交于点P ，设坐标原点为O ．(1) 求双曲线C 的方程，并求出点P 的坐标（用m 、n 表示）；(2) 设点M 关于y 轴的对称点为N ，直线AN 与y 轴相交于点Q ．问：在x 轴上是否存在定点T ，使得TP TQ ⊥？若存在，求出点T 的坐标；若不存在，请说明理由．(3) 若过点(0,2)D 的直线l 与双曲线C 交于R S 、两点，且OR OS RS +=，试求直线l 的方程．23. (本题满分18分)（理）本题共3个小题，每小题6分.设数列{}n a 的前n 项和为,n S 且2(1)().n n n S a S n N *-=∈（1）求123S S S 、、的值，并求出n S 及数列{}n a 的通项公式；（2）设121(1)(1)(),n n n n b n a a n N +*+=-+⋅∈求数列{}n b 的前n 项和.n T（3）设(1)(),n n c n a n N *=+⋅∈在数列{}n c 中取出(,3)m m N m *∈≥为常数项，按照原来的顺序排成一列，构成等比数列{}n d .若对任意的数列{}n d ，均有123,m d d d d M ++++≤试求M 的最小值.（文）本题共3个小题，第1小题5分，第2小题5分，第3小题8分.已知数列{}n a 的奇数项是首项为1的等差数列，偶数项是首项为2的等比数列. 设数列{}n a 的前n 项和为,n S 且满足43934.a S a a a ==+，（1）求数列{}n a 的通项公式；（2）若12,k k k a a a ++=求正整数k 的值；（3）是否存在正整数k ，使得221kk S S -恰好为数列{}n a 的一项？若存在，求出所有满足条件的正整数k ；若不存在，请说明理由．（第20题解答图）虹口区2016年高考模拟数学试卷参考答案与评分标准2016年4月一、填空题（本大题共14题,每题4分,满分56分）1．[]0,1 2． 3 3．125 4． 2 5． {}3,2,1,5- 6.92 7. 32 8． 2,3x x k k Z ππ⎧⎫=±∈⎨⎬⎩⎭9. 64 10．64π 1112. 10x y ±-= 13．（理）23；（文）(]1,3 14．（理）(,8-∞-；（文）4二、选择题（本大题共4题，每题5分，满分20分）15. A 16. C 17. D 18. B 三、解答题（本大题共5题，满分74分）19．(本题满分12分) 本题共2个小题，每小题6分.()2222sin sin sin()sin()sin sin()cos()4444111sin sin(2)sin cos 1242222A B B B B B B B B B B πππππ=++-=+++=++=+=解：因分故由ABC ∆为锐角三角形，得.6A π=……6分（2）由（1）知cos 2A =由已知，有12cos ,2AB AC cb A bc =⋅=⋅=故bc = ……9分从而111sin 222ABC S bc A ∆=⋅=⋅= ……12分20．(本题满分14分) 本题共2个小题，每小题7分.（理）解：(1)以},,{为正交基底建立空间直角坐标系xyz A -，则相关点的坐标为B （2,0,0），(2,1,0),(0,2,0),(0,0,2).C D P ……2分设平面PCD 的法向量为(,,),n x y z =由（第20题图）PBCDA (2,1,0),DC =-(0,2,2),DP =-(0,2,0).DA =-则202,2.220n DC x y y x z x n DPyz令1x =，则(1,2,2)n =. ……5分所以点A 到平面PCD 的距离为：(0,2,0)(1,2,2)4.(1,2,2)3DA n dn……7分 (2) 由条件，得(1,0,1),Q(0,2,0),(1,0,1),AD AQ ==且(1,1,1).CQ设平面ADQ 的法向量为0000(,,),n x y z =则0000000200,.n AD y y z x n AQx z令01x =，则0(1,0,1)n =-. ……10分设直线CQ 与平面ADQ 所成角为,θ则000sin cos ,3CQ n CQ n CQ n θ⋅=<>===故直线CQ 与平面ADQ 所成角的大小为arc ……14分注：第（1）小题也可用等积法来做.（文）解：（1）由已知，有//,BC AD AD PAB ⊥面，故BC 与PC 所成的角PCB ∠等于AD 与PC 所成的角，且.BC PB ⊥……3分因1,BC =易知PB =故tan PCPCB BC∠== 故异面直线BC 与PC 所成角的大小为tan arc …7分1(2)31111()(21)22 2.103232PABCD ABCD V S APAD BC AB AP -=⋅=⋅+⋅⋅=⋅+⋅⋅=⋯梯形分容易求得：3,PD CD PC ===故由余弦定理，得222cos 2CD PC PD PCD CD PC+-∠==⋅从而 11sin 33.22PCD S CD PC PCD ∆=⋅⋅∠=⋅= ……12分又2,PAB PAD PBC S S S ∆∆∆== 因此=+++7PAB PAD PBC PCD P ABCD S S S S S ∆∆∆∆-=四棱锥侧面积 ……14分21．(本题满分14分) 本题共2个小题，每小题7分. 解：（1）由1312121(2)log 1,,2133a a f ++-==-=--得解得 1.a =- ……3分于是131()log 1x f x x +⎛⎫=⎪-⎝⎭，其定义域为(,1)(1,).D =-∞-⋃+∞ ……4分对于任意的(,1)(1,),x ∈-∞-⋃+∞有111133331111()+()log log log log 10,1111x x x x f x f x x x x x +-++-+⎛⎫⎛⎫⎛⎫-=+=⋅== ⎪ ⎪ ⎪------⎝⎭⎝⎭⎝⎭故()f x 为奇函数. ……7分（2）由1()2x f x t ⎛⎫>+ ⎪⎝⎭，得[]1()2,32xt f x ⎛⎫<- ⎪⎝⎭在恒成立. 由12111x x x +=+--在(,1)-∞-及(1,)+∞上均递减，且13()log g u u =在(0,)+∞上也递减，故函数()f x 在区间(,1)(1,)-∞-+∞及均单调递增. ……10分由()f x 及12xy ⎛⎫=- ⎪⎝⎭在区间[]2,3均单调递增，知[]1()()2,32xx f x ϕ⎛⎫=- ⎪⎝⎭在单调递增， ……12分故2min15()(2)(2).24x f ϕϕ⎛⎫==-=- ⎪⎝⎭因此，实数t 的取值范围为5(,).4-∞- ……14分22. (本题满分16分) 本题共3个小题，第1小题5分，第2小题5分，第3小题6分.解：（1）由已知，得11,2,2a a b b a=⎧=⎧⎪⇒⎨⎨==⎩⎪⎩故双曲线C 的方程为 22 1.4y x -= ……3分(1,)AM m n =-为直线AM 的一个方向向量， ∴直线AM 的方程为1,1x y m n -=-它与y 轴的交点为(0,).1n P m- ……5分（2）由条件，得(,),N m n -且(1,)AN m n =--为直线AN 的一个方向向量，故直线AN 的方程为1,1x ym n-=--它与y 轴的交点为(0,).1n Q m + ……7分假设在x 轴上存在定点0(,0)T x ，使得TP TQ ⊥,则由0(,),1n TP x m =--0(,),1n TQ x m =--+及221,4n m -=得 0(,)1n TP TQ x m ⋅=-⋅-22222000022(,)40.11(1)14n n n x x x x n m m --=-=-=-=+-+- 故02,x =±即存在定点T ，其坐标为(2,0)或(2,0),-满足题设条件. ……10分 (3) 由OR OS RS +=知，以OR OS 、为邻边的平行四边形的对角线的长相等，故此四边形为矩形，从而.OR OS ⊥ ……12分由已知，可设直线l 的方程为2,y kx =+并设1122(,),(,),R x y S x y则由222,1,4y kx y x =+⎧⎪⎨-=⎪⎩ 得 22(4)480.k x kx -++= 由2221632(4)16(8)0,k k k ∆=--=->及240,k -≠得2284k k <≠且（*）由121212122248,,(2)(2),44k x x x x y y k x k x k k +=-==++-- ……14分得2222121212122228(1)84(2)(1)2()440444k k k OR OS x x y y k x x k x x k k k +-⋅=+=++++=-+==--- 故22,k =符合约束条件（*）.因此，所求直线l 的方程为 2.y =+ ……16分23.（理） (本题满分18分) 本题共3个小题，每小题6分.解：（1）当1n =时， 22111111(1);2S a S S S -==⇒= 当2n =时， 222222212(1)();23S a S S S S -==-⇒=当3n =时， 233333323(1)().34S a S S S S -==-⇒= ……2分由此，猜测： ().1n nS n N n *=∈+下面用数学归纳法证明：（i ）当1n =时，结论显然成立；（ii ）假设当()n k k N *=∈时，1k kS k =+；则当1n k =+时，由条件，得 21111111(1)().2221k k k k k k k k k k k S a S S S S S k S k k +++++++-==-⇒===-+-+即当1n k =+时，结论也成立.于是，由（i ），（ii ）可知，对任意的,.1n nn N S n *∈=+均有……4分当1112,.1(1)n n n n n n a S S n n n n --≥=-=-=++时又1111,212a S ===⨯ 于是数列{}n a 的通项公式为:1().(1)n a n N n n *=∈+ ……6分 (2)因 121111111(1)(1)(1)(1)(),(2)22n n n n n n b n a a n n n n ++++=-+⋅=-⋅=-⋅-++……8分当n 为奇数时， 12111111111111(1)()()()()()232435461121111111(1)?10221222(1)(2)n n T b b b n n n n n n n n ⎡⎤=+++=---+---+--+-⎢⎥-++⎣⎦⎡⎤=-+-=+⎢⎥++++⎣⎦分当n 为偶数时，12111111111111(1)()()()()()232435461121111111(1).221222(1)(2)n n T b b b n n n n n n n n ⎡⎤=+++=---+---++---⎢⎥-++⎣⎦⎡⎤=--+=-⎢⎥++++⎣⎦故111,(22(1)(2)11(1)=.22(1)(2)111,(22(1)(2)nnn n n T n n n n n ⎧⎡⎤+⎪⎢⎥++⎡⎤-⎪⎣⎦=-⎨⎢⎥++⎡⎤⎣⎦⎪-⎢⎥⎪++⎣⎦⎩当为奇数)当为偶数)……12分（3）因1(1),n n c n a n=+⋅=由于数列{}n c 的(3)m m ≥项子列{}n d 构成等比数列，设其公比为,q 则 211231(1).m m d d d d d q q q -++++=++++11,1,(),q Q q d a N a +*∈<=∈因且设(,,2,,).vq u v N u u v u *=∈≥且互质（i ）当1v =时，因11,2q u =≤故 2112312111111(1)12.2222m m m m d d d d d q q q ---++++=++++≤++++=-……15分（ii ）当1v ≠时，因11111m m m m v d d q a u---==⋅是数列{}n c 中的项，故1().m a v a a N -*''=⋅∈2112311232211232211232211111(1)111111()111111111122323233121()321232(3).223213m m m m m m m m m m m m m m m m m m m m m m d d d d d q q q a v v u v u vu u v v u v u vu u m --------------------++++=++++=+++++'≤+++++≤+++++⋅⋅⋅⎡⎤-⎢⎥⎣⎦==-<-≥-从而综合（i ），（ii ），得：在数列{}n c 中的所有(3)m m ≥项等比子数列{}n d 中，其和最大的是：211111.222m -，，，，故由题意知：M 的最小值为112.2m -- ……18分另解（3）：因1(1),n n c n a n=+⋅=由于数列{}n c 的(3)m m ≥项子列{}n d 构成等比数列，设其公比为,q 则 211231(1).m m d d d d d q q q -++++=++++11,1,().q Q q d a N a +*∈<=∈因且（i ）当1a =时，因1,2q ≤故 211232111111112.2222m m m m d d d d q q q ---++++=++++≤++++=-……15分（ii ）当2a ≥时，因11,11a a q a a+≤=+ 故2112311111(1)111312(3).22m m m d d d d q q q a aa aa m --++++=++++<⋅=+-+≤<-≥综合（i ），（ii ），得：在数列{}n c 中的所有(3)m m ≥项等比子数列{}n d 中，其和最大的是：211111.222m -，，，，故由题意知：M 的最小值为112.2m -- ……18分23.（文）本题共3个小题，第1小题5分，第2小题5分，第3小题8分.解：（1）设{}n a 的奇数项构成的等差数列的公差为,d 偶数项构成的等比数列的公比为,q 则12121(1),2.n n n a n d a q --=+-=由已知，得2(2)22,14(1)2 3.q d d d d q q =++=⎧⎧⇒⎨⎨+=++=⎩⎩ ……3分故数列{}n a 的通项公式为：22,(.23,(n n n n a n -⎧⎪=⎨⎪⋅⎩当为奇数)当为偶数) ……5分（2）当k 为奇数时，由12,k k k a a a ++=得 112222323.2k k k k k k--+⋅⋅=+⇒=由于1223,22k k N k k k-*+∈=而仅在时为正整数，与为奇数矛盾！ ……7分当k 为偶数时，由12,k k k a a a ++=得 22223+123 2.k kk k -⋅⋅=⋅⇒=（）综上，得 2.k = ……10分（3）由(1)可求得[]212213(21)2(1333)31,k k k S k k -=+++-+++++=+- 1221223 1.k k k k S S a k --=-=+-若221kk S S -为数列{}n a 中的一项，则22222121()23().m k k k k S S m m m S S ---==⋅为正奇数，或为正偶数 ……13分（i ）若221()kk S m m S -=为正奇数，则2121231(3)3(1)(1).31k k k k m m m k k --+-=⇒-=--+- 当1k =时，3m =，结论成立；当1k ≠时，1231,13k m k m --=--由12310,0,13,13k m m k m-->><<--得解得由于m 为正奇数，故此时满足条件的正整数k 不存在.……15分（ii ）若2222123(),m kk S m S --=⋅为正偶数显然1k ≠，则2222212122222122231323123(323)3(1)(231).311323m m m m k k k m k k k k k --------+-⋅-=⋅⇒-⋅=-⋅-⇒=+---⋅ 由1k >得2212222232310,0123 3.1323m m k m k ----⋅->>⇒<⋅<--⋅得 22,23m m -⋅由为正偶数得为正偶数，因此22232m -⋅=，从而1122313 1.1k k k k --=⇒=-- 121223133 1.k k k k k k --==-≥>-当时，；下面用数学归纳法证明：当时，①12331k k k -=>-当时，显然；②123311l k l l k l -=≥>-=+假设当时，有；当时，2222(1)112233(1)(1)1(1)(4)0,3333(1)(1) 1.l l l l l l l l l +--⎡⎤≥--+-=-+->⎣⎦=⋅>->+-由得故即1k l =+当时，结论成立.由①，②知：1233 1.k k k -≥>-当时，综合（i ），（ii ）得：存在两个正整数k ,k =1或2，使221k k SS -为数列{}n a 中的项.……18分。

上海市普陀区2016学年第二次高考模拟高三数学试卷--含答案

2016学年第二学期普陀区高三数学质量调研2017.4考生注意:1. 本试卷共4页，21道试题，满分150分. 考试时间120分钟.2. 本考试分试卷和答题纸. 试卷包括试题与答题要求. 作答必须涂（选择题）或写（非选择题）在答题纸上，在试卷上作答一律不得分.3. 答卷前，务必用钢笔或圆珠笔在答题纸正面清楚地填写姓名、准考证号，并将核对后的条码贴在指定位置上，在答题纸反面清楚地填写姓名.一、填空题（本大题共有12题，满分54分）考生应在答题纸相应编号的空格内直接填写结果，每个空格填对前6题得4分、后6题得5分，否则一律得零分.1. 计算：=⎪⎭⎫⎝⎛+∞→311lim n n .2. 函数⎪⎭⎫⎝⎛-=x y 11log 2的定义域为 . 3. 若παπ<<2，53sin =α，则=2tan α. 4. 若复数()21i i z ⋅+=（i 表示虚数单位），则=z . 5. 曲线C ：⎩⎨⎧==θθtan sec y x （θ为参数）的两个顶点之间的距离为 .6. 若从一副52张的扑克牌中随机抽取2张，则在放回抽取的情形下，两张牌都是K 的概率为（结果用最简分数表示）.7. 若关于x 的方程0cos sin =-+m x x 在区间⎥⎦⎤⎢⎣⎡2,0π上有解，则实数m 的取值范围是 . 8. 若一个圆锥的母线与底面所成的角为6π,体积为π125,则此圆锥的高为 . 9. 若函数1log log )(222+-=x x x f （2≥x ）的反函数为)(1x f-，则)3(1-f= .10. 若三棱锥ABC S -的所有的顶点都在球O 的球面上，⊥SA 平面ABC ，2==AB SA ，4=AC ，3π=∠BAC ，则球O 的表面积为 .11.设0<a ，若不等式01cos )1(sin 22≥-+-+a x a x 对于任意的R ∈x 恒成立，则a 的取值范围是 .12.在△ABC 中，D 、E 分别是AB 、AC 的中点，M 是直线DE 上的动点.若△ABC 的面积为1，则2BC MC MB +⋅的最小值为 .二、选择题（本大题共有4题，满分20分）每题有且只有一个正确答案，考生应在答题纸的相应编号上，将代表答案的小方格涂黑，选对得5分，否则一律得零分.13. 动点P 在抛物线122+=x y 上移动，若P 与点()1,0-Q 连线的中点为M ，则动点M 的轨迹方程为……………………………………………………………………………………………………………（）)A ( 22x y = ()B 24x y = ()C 26x y = ()D 28x y =14. 若α、β∈R ，则“βα≠”是“βαtan tan ≠”成立的……………………………………（）)A (充分非必要条件 ()B 必要非充分条件()C 充要条件 ()D 既非充分也非必要条件15. 设l 、m 是不同的直线，α、β是不同的平面，下列命题中的真命题为…………………………（）)A ( 若α//l ，β⊥m ，m l ⊥，则βα⊥ ()B 若α//l ，β⊥m ，m l ⊥，则 βα//()C 若α//l ，β⊥m ，m l //，则βα⊥ ()D 若α//l ，β⊥m ，m l //，则βα//16. 关于函数x y 2sin =的判断，正确的是……………………………………………………………（）)A (最小正周期为π2，值域为[]1,1-，在区间⎥⎦⎤⎢⎣⎡-2,2ππ上是单调减函数()B 最小正周期为π，值域为[]1,1-，在区间⎥⎦⎤⎢⎣⎡2,0π上是单调减函数()C 最小正周期为π，值域为[]1,0，在区间⎥⎦⎤⎢⎣⎡2,0π上是单调增函数()D 最小正周期为π2，值域为[]1,0，在区间⎥⎦⎤⎢⎣⎡-2,2ππ上是单调增函数三、解答题（本大题共有5题，满分76分）解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤17. （本题满分14分）本题共有2个小题，第1小题满分6分，第2小题满分8分在正方体1111D C B A ABCD -中，E 、F 分别是BC 、11D A 的中点. （1）求证：四边形EDF B 1是菱形；（2）求异面直线C A 1与DE 所成角的大小 (结果用反三角函数值表示) .18.（本题满分14分）本题共有2个小题，第1小题满分6分，第2小题满分8分已知函数x b x a x f cos sin )(+=（a 、b 为常数且0≠a ，R ∈x ）.当4π=x 时，)(x f 取得最大值.（1）计算⎪⎭⎫⎝⎛411πf 的值；（2）设⎪⎭⎫⎝⎛-=x f x g 4)(π，判断函数)(x g 的奇偶性，并说明理由.19.（本题满分14分）本题共有2个小题，第1小题满分6分，第2小题满分8分某人上午7时乘船出发，以匀速v 海里/小时（54≤≤v ）从A 港前往相距50海里的B 港，然后乘汽车以匀速ω千米/小时（10030≤≤ω）自B 港前往相距300千米的C 市，计划当天下午4到9时到达C 市.设乘船和汽车的所要的时间分别为x 、y 小时，如果所需要的经费()()y x P -+-+=853100（单位：元）（1）试用含有v 、ω的代数式表示P ；（2）要使得所需经费P 最少，求x 和y 的值，并求出此时的费用.20. （本题满分16分）本题共有3小题，第1小题4分，第2小题6分，第3小题6分.1A 1B 1C 1D B D A C EF xyo已知曲线Γ：13422=+y x ，直线l 经过点()0,m P 与Γ相交于A 、B 两点. （1）若()3,0-C 且2=PC ，求证：P 必为Γ的焦点；（2）设0>m ，若点D 在Γ上，且PD 的最大值为3，求m 的值；（3）设O 为坐标原点，若3=m ，直线l 的一个法向量为()k n ,1=，求∆AOB 面积的最大值.21.（本题满分18分）本题共有3小题，第1小题4分，第2小题6分，第3小题8分.已知数列{}n a （*N ∈n ），若{}1++n n a a 为等比数列，则称{}n a 具有性质P .（1）若数列{}n a 具有性质P ，且3,1321===a a a ，求4a 、5a 的值；（2）若()nn n b 12-+=，求证：数列{}n b 具有性质P ；（3）设=+++n c c c 21n n +2，数列{}n d 具有性质P ，其中11=d ，123c d d =-，232c d d =+，若310>m d ，求正整数m 的取值范围.2016学年第二学期普陀区高三数学质量调研一、填空题（本大题共有12题，满分54分）考生应在答题纸相应编号的空格内直接填写结果，每个空格填对前6题得4分、后6题得5分，否则一律得零分.1.12. ()()+∞∞-,10,3.34. i +-15.26.1691 7. 21≤≤m . 8. 5 9. 4 10.π20 11. 2-≤a 12. 3二、选择题（本大题共有4题，满分20分）每题有且只有一个正确答案，考生应在答题纸的相应编号上，将代表答案的小方格涂黑，选对得5分，否则一律得零分.三、解答题（本大题共有5题，满分76分）解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤17. （本题满分14分）本题共有2个小题，第1小题满分6分，第2小题满分8分【解】设正方体的棱长为1，建立空间直角坐标系，如图所示：则()1,0,11B ,⎪⎭⎫ ⎝⎛0,21,1E ,()0,1,0D ,⎪⎭⎫⎝⎛1,21,0F ……1分⎪⎭⎫⎝⎛-=0,21,1,⎪⎭⎫ ⎝⎛-=0,21,11FB ……2分所以1FB =,即1//FB DE 且1FB DE =,故四边形EDF B 1是平行四边形……3分又因为⎪⎭⎫ ⎝⎛-=1,21,01E B ,25==……5分故平行四边形EDF B 1是菱形……6分（2）因为()0,1,11=A ()()1,1,101,0--=-,⎪⎭⎫⎝⎛-=0,21,1……8分设异面直线C A 1与DE 所成的角的大小为θ……9分cos =θ……10分()()15152111110121)1(11222222=+⎪⎭⎫ ⎝⎛-+⋅+-+-⨯+⎪⎭⎫⎝⎛-⨯-+⨯-=……12分所以1515arccos=θ……13分, 故异面直线C A 1与DE 所成的角的大小为1515arccos ……14分 18.（本题满分14分）本题共有2个小题，第1小题满分6分，第2小题满分8分【解】（1）x b x a x f cos sin )(+=()ϕ++=x b a sin 22，其中abarctan =ϕ……2分根据题设条件可得，224b a f +=⎪⎭⎫⎝⎛π 即()2222b a b a +=+ ……4分化简得()()2222b a b a +=+，所以0222=+-b ab a即()02=-b a ，故0=-b a ……………5分所以()022411cos 411sin411=-=+=⎪⎭⎫⎝⎛b a b a f πππ……………6分（2）由（1）可得，b a =，即()⎪⎭⎫ ⎝⎛+=+=4sin 2cos sin )(πx a x x a x f ……8分故x a x a x a x f x g cos 22sin 244sin 24)(=⎪⎭⎫⎝⎛-=⎪⎭⎫ ⎝⎛+-=⎪⎭⎫⎝⎛-=ππππ所以x a x g cos 2)(=（R ∈x ）…………10分对于任意的R ∈x ，x a x a x g cos 2)cos(2)(=-=-（0≠a ）……12分即)()(x g x g =-，所以)(x g 是偶函数.…………14分19.（本题满分14分）本题共有2个小题，第1小题满分6分，第2小题满分8分【解】（1）v x 50=，204≤≤v ，得22510≤≤x ……2分 ω300=y ，10030≤≤ω，得103≤≤y ……4分()()y x P -+-+=853100⎪⎭⎫ ⎝⎛-+⎪⎭⎫ ⎝⎛-+=ω30085053100v所以ω300150123--=v P （其中204≤≤v ，10030≤≤ω）……6分（2）()()y x P -+-+=853100)3(123y x +-=其中⎪⎪⎩⎪⎪⎨⎧≤≤≤≤≤+≤10322510149y x y x ，……9分x令目标函数y x k +=3, 可行域的端点分别为()3,11，)10,4(，⎪⎭⎫ ⎝⎛10,25，⎪⎭⎫⎝⎛213,25，()3,6 …12分则当3,11==y x 时，36333max =+=k 所以8736123min =-=P （元）,此时115050==x v ，1003300==ω答：当3,11==y x 时，所需要的费用最少，为87元。

上海市虹口区2016届高三5月模拟(三模)数学理试题-Word版含答案

2016年虹口区高考模拟试卷理科数学2016.5考生注意：1.本试卷共4页，23道试题，满分150分，考试时间120分钟。

2。

本考试分设试卷和答题纸. 作答必须涂（选择题）或写（非选择题）在答题纸上，在试卷上作答一律不得分。

一、填空题（本大题满分56分）本大题共14题,只要求在答题纸相应题号的空格内直接填写结果，每个空格填对得4分，否则一律得零分. 1．设集合103x M xx ⎧+⎫=≥⎨⎬-⎩⎭，{}21xN x =≥，则M N ⋂=__________.2．在ABC ∆中，3tan ,4A =- 则sin 2A =_________.3.已知复数()z i z z =为虚数单位，表示的共轭复数，则z z ⋅=_________.4。

若等比数列{}n a 的公比1q q <满足，且24344,3,a a a a =+=则12lim()n n a a a →∞+++=___________.5.若函数()()()f x x a x a R =-∈存在反函数1()f x -,则1(1)(4)f f -+-= _________.6 .在数学解题中,时常会碰到形如“1x yxy+-”的式子，它与“两角和的正切公式”的结构类似.若a ，b 是非零实数，且满足sincos855tan 15cos sin55a b a b πππππ+=-，则b a =________.7. 若一个球的半径与它的内接圆锥的底面半径之比为5,3且内接圆锥的轴截面为锐角三角形，则该球的体积与它的内接圆锥的体积之比等于________.8．某小区有排成一排的8个车位，现有5辆不同型号的轿车需要停放,则这5辆轿车停入车位后，剩余3个车位连在一起的概率为________(结果用最简分数表示）.9．若双曲线2221y x b-=的一个焦点到其渐近线的距离为，则该双曲线的焦距等于________.10．若复数z 满足34(z z i i +=-为虚数单位)，则z 的最小值为_______.11．在极坐标系中，圆2sin ρθ=被直线1sin()32πρθ+=截得的弦长为． 12．过抛物线28x y =的焦点F 的直线与其相交于A ，B 两点，O 为坐标原点．若6,AF = 则OAB ∆的面积为．13．若关于x 的方程21x x a x -=有三个不同实根,则实数a 的取值范围为_______.14．在平面直角坐标系中,定义11111,()(,)(,)n n nn n n n n n n n nx x y n N P x y P x y y x y +*++++=-⎧∈⎨=+⎩为点到点的一个变换，我们把它称为点变换.已知1222(1,0)(,)P P x y ，，333(,)P x y ，是经过点变换得到的一组无穷点列，设112,n n n n n a P P P P +++=⋅则满足不等式122016n a a a +++>的最小正整数n 的值为________.二、选择题（本大题共4题，满分20分）每题有且只有一个正确答案，考生应在答题纸的相应题号上,将所选答案的代号涂黑,选对得 5分，否则一律零分。

上海市崇明县2016届高三第二次高考模拟考试英语试题(含答案)

崇明县2016届第二次高考模拟考试试卷英语（考试时间120分钟，满分150分。

请将答案填写在答题纸上）第Ⅰ卷 (共103分)I. Listening ComprehensionSection ADirections: In Section A, you will hear ten short conversations between two speak e rs. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.1. A. In a gallery. B. In a classroom. C. In a bookstore. D. In a museum.2. A. Boss and employee. B. Father and daughter.C. T eacher and student.D. Shop assistant and customer.3. A. 5 minutes. B. 8 minutes. C. 10 minutes. D. 15 minutes.4. A. The shirt is too large. B. The price of the shirt is wrong.C. The shirt is too expensive.D. Other shops don’t sell this shirt.5. A. Watching TV. B. Parents’ involvement.C. Playing video games.D. Teachers’ substitution.6. A. A place for a meal. B. Their good friends.C. A tip for choosing food.D. Their plan to eat out.7. A. She doesn’t know where the manager is.B. She doesn’t know where the man heard the news.C. She doesn’t know where she will be working this month.D. She doesn’t know where she can find the work schedule.8. A. The time is not convenient. B. Her house is not big enough.C. A few people won’t turn up.D. There won’t be enough food.9. A. It is rather cool in the lecture hall. B. No one will be able to see what he is wearing.C. The air-conditioner doesn’t work.D. He expects the weather to change later in the day.10. A. The film cost too much despite its high quality.B. The man didn’t like the film but the woman did.C. The man missed the film because of the woman.D. The man saw the film upon the advice of the woman.Section BDirections: In Section B, you will hear two short passages, and you will be asked three questions on each of the passages. The passages will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. A special room. B. A series of textbooks.C. A comprehension program.D. A rewritten masterpiece.12. A. Experts on English reading. B. Beginners of English learning.C. Native speakers of English.D. Editors of English textbooks.13. A. It is designed for different levels. B. It contains original masterpieces.C. It can bring back the childhood.D. It helps to improve memory.Questions 14 through 16 are based on the following passage.14. A. Work efficiency is what we pursue. B. It’s possible for us to work harder.C. Our brain is our most important tool.D. It’s wise to take a rest if our body needs it.15. A. To focus on something new. B. To ignore the limitations.C. To refresh the concentration.D. To lengthen the attention.16. A. Changing jobs from time to time. B. Doing new tasks in different work areas.C. Making a list of all your tasks.D. Eating popcorn while taking a break.Section CDirections:In Section C, you will hear two longer conversations. The conversations will be read twice. After you hear each conversation, you are required to fill in the numbered blanks with the information you have heard. Write your answers on your answer sheet.Blanks 17 through 20 are based on the following conversation.Complete the form. Write ONE WORD for each answer.Blanks 21 through 24 are based on the following conversation.Complete the form. Write NO MORE THAN THREE WORDS for each answer.II. Grammar and VocabularySection ADirections:After reading the passages below, fill in the blanks to make the passages coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.(A)Happiness Is an AttitudeThe 92-year-ol d confident and proud lady, who is fully dressed each morning by eight o’clock, with her hair fashionably combed and makeup perfectly applied, (25)_____ _____ she’s legally blind, move d to a nursing home today.Her husband of 70 years recently passed away, (26)_____ (make) the move necessary.After many hours of waiting patiently in the hall of the nursing home, she (27)_____ (smile) sweetly when told her room was ready. As she got into the elevator (28)_____ her wheelchair, I provided a description of her tiny room.“I love it,” she started with the enthusiasm of (29)_____ eight-year-old child having just been presented with a new dog.“Mrs. Jones, you haven’t seen the room…just wait.”“That ha s (30)_____ to do with it,” she replied. “Happiness is something you decide on ahead of time.(31)_____ I like my room or not doesn’t depend on how the furniture is arranged…it’s how I arrange my mind. I already decided to love it. It’s a decision I make every morning when I wake up. I have a choice; I can spend the day in bed recounting the difficulty I have with the parts of my body (32)_____ no longer work or get out of bed and be thankful for the ones working. Each day is a gift, and (33)_____ _____ _____ my eyes open, I’ll focus on the new day and all the happy memories I’ve stored away…just for this time in my life.”(B)Sculptor B uilds Dubai’s Soaring Burj Khalifa Skyscraper out of Toothpicks to Bag World RecordA sculptor has scaled new heights by building the world’s tallest toothpick (牙签) model.Stanley Hayes Munro, 45, from Syracuse, New York, is a toothpick engineer, who (34)_____ (hook) by toothpick models since he built his first sculpture in school when creating a structure that (35)_____ support the weight of an egg.Now, he has won the world record for the tallest toothpick structure with a sculpture of the Burj Kahlifa, Dubai. For Stanley though, he has always been more concerned with the integrity(完整性) of his work. Stanley said: “I’ve never cared for counting toothpicks, wasting toothpicks, or the numbe r of toothpicks (36)_____ (use) in any construction. But an engineering problem you’ve got to create a strong structure is a problem worth (37)_____(solve).” “I made my first toothpick structure in an art class when Iwas in Grade 5,” he continued. “The as signment was to build something 25 centimeters tall and to have it (38)_____ (hold) the weight of an egg. Mine held my desk and from that point I became interested in it.”“Everybody likes to ask whether my sculptures will collapse when I build them, but t hey are much(39)_____ (strong) than people think,” he said. “It was not really the height but the shape of the outer walls(40)_____ was t he biggest challenge with Burj Khalifa. There wasn’t a flat surface anywhere and I had to individually construct each level,” he said.Section BDirections: Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.A second part of the experiment involved those watching the film being fitted with headsets(耳机) that 48 brain activity and this too showed heightened activity when watching 3D. According to the results, participants were seven percent more engaged with what they were watching, adding to the argument that 3D movies are more like watching real-life-something. “A seven percent rise in emotional engagement is 49 remarkable. Watching in 3D gives the viewer such an enriched and quality experience, as these results show,” he said. “In evolutionary 50 , the results of both parts of the test certainly make sense. 3D films are more likely to heighten the senses and cause emotional arousal—this, in turn, makes the brain run at quicker speeds,” Dr Fagan added.III. Reading ComprehensionSection ADirections: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.Researchers recently find women likely face work environments that push against the “having it all” mentality, leading to feelings of guilt and depression.Trying to have it all could be bad for your mental health, according to a new study that finds that “supermoms” have higher rates of depression compared with working moms who let thin gs 51 .The research, presented Aug. 20 at the annual meeting of the American Sociological Association in Las Vegas, finds that working is 52 for mothers’ mental health. But among working mothers, the least depressed are those who don’t expect to 53 work and family life perfectly, said study researcher Katrina Leupp, a graduate student at the University of Washington in Seattle. “The ideal that women can do it all actually 54 the level of depressive symptoms compared to women who were more doubtful about whether or not work and family can be balanced,” Leupp told LiveScience.Leupp analyzed survey 55 from 1,600 married women who participated in a large survey called the National Longitudinal Survey of Youth. In 1987, the women answered questions to judge their support of women’s 56 , including whether they agreed with statements such as “Women are much happier if they stay at home and take care of their children.” In 1992 and 1994, the now 40-year-old women answered questions about their symptoms of depression. Like earlier studies, the survey data indicated that women who worked outside the home had fewer symptoms of depression, perhaps because outside work gives women more 57 interaction, more varied activities and a larger income, Leupp said. Among the employed women, though, the cheeriest were those who had indicated in their younger years the least 58 for women balancing career and family. The results held even after controlling for earlier levels of depression. “Somewhat 59 , women who don’t expect to be able to balance work and family have better mental health than those who do,” Leupp said.The study didn’t explain why optimistic (乐观的) views of balancing work and motherhood would60 later depression. “The reason may come down to 61 and real-world work environments,”Leupp said. “Women who expect to have it all probably come up against 62 that aren’t designed with work-life balance in mind. When they can’t balance everything perfectly, these supermoms are more likely to feel 63 .”“I think this research really speaks to a 64 between women’s expectations and the actual structure of the workplace,” Leupp said.“The takeaway for working moms is to temper their optimism about balancing 65 and employment and not to blame themselves if they struggle. Recognize that if it feels difficult, it’s because it is difficult.”51. A. happen B. continue C. slide D. end52. A. good B. ready C. hard D. possible53. A. protect B. share C. illustrate D. combine54. A. increased B. assessed C. reached D. influenced55. A. questions B. responses C. solutions D. instruments56. A. pregnancy B. marriage C. employment D. education57. A. cultural B. social C. positive D. verbal58. A. support B. tolerance C. concern D. respect59. A. deliberately B. aggressively C. ironically D. similarly60. A. result from B. relate to C. hold back D. call for61. A. families B. expectations C. surroundings D. requirements62. A. clubs B. hospitals C. governments D. workplaces63. A. excited B. embarrassed C. thrilled D. frustrated64. A. mismatch B. mistreat C. misunderstanding D. misinterpretation65. A. aging B. training C. schooling D. parentingSection 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）The twenty-four horses dash around a racetrack. The thunder of their hooves (蹄) rings in the riders’ears, nearly drowning out the cheering of the crowd. After three or four minutes of suspense, one horse crosses the finish line first, winning the Melbourne Cup and earning a place in history.The horses that compete in the Melbourne Cup—one of the world’s most famous horseraces—were fated to race. Bred for speed, these horses are the few that were singled out as having potential to become champions.Preparing a racehorse to compete requires a team. A horse’s owner manages the team and decides which races to enter. A trainer determines the racehorse’s diet and exercise. Regular exercise makes a horse less likely to be injured, but overtraining tires the horse. A groomer (动物美容师) cares for the racehorse and reports any problems he discovers to the trainer. And of course, no horserace could be run without a rider. These riders train for long hours and travel constantly from one race to another. They need to make a strategy, adapt to changing conditions and communicate with their horse to guide it to victory.Australia’s most famous horserace, the Melbourne Cup, is 3,200 meters of pure excitement. Each year 300 or 400 horses are nominated(提名), but only 24 can run. The competitors are chosen based on a number of factors, but winners of certain races qualify automatically.Each racehorse receives a handicap—a certain weight it must carry to give each horse an equal chance of winning—two months before the race. Originally, horses that seemed likely to win were assigned larger handicaps. But the rules have changed, reducing the handicap for previous winners.The first Melbourne Cup in 1861 drew a crowd of 4,000 spectators, and the race’s popularity has grown since then. Held on the first Tuesday of November, the cup has become a four-day festival with fine food and entertainment.The Melbourne Cup began during a gold rush as a form of entertainment for the rich. Today it still attracts society’s upper class. They come dressed in their finest to enjoy the event in comfort.But anyway it’s all about the race—the effort of horses and riders, the suspense and the thrill of victory.66. What can be learned about the horses in the Melbourne Cup?A. They are all winners of a certain race.B. They are raised and trained by joint effort.C. They are chosen from ordinary horses.D. Their fates are determined by their trainers.67. The racehorses are given handicaps so that _____.A. they will weigh the sameB. previous winners are unlikely to winC. the race will be fair enoughD. they will be more adaptable to the race68. It can be learned from the passage that _____.A. the spectators of the Melbourne Cup must dress wellB. the Melbourne Cup was intended for wealthy peopleC. the winner of the Melbourne Cup can earn a large fortuneD. the Melbourne Cup is the best-known horserace worldwide69. The passage can most probably be found in _____.A. a sports journalB. a business newspaperC. an academic paperD. a health magazine（B）Down County Museum - Open and FreeWhat’s OnContact detailsThe Mall, Downpatrick, County Down, BT30 6AH Telephone: +44 (0) 28 4461 5218Fax: +44 (0) 28 4461 5590Email: mail@ Opening hoursMonday to Friday 10.00 am - 5.00 pmSaturdays and Sundays 1.00 pm - 5.00 pmAdmission freeThere is however a charge for some special events and for guided tours.In the Footsteps of St Patrick12 November 2015 - 24 April 2016 at Down CountyMuseumThe aim of this exhibition is to explore some of the localsites, monuments and archaeological(考古的) discoveries which are linked to the early missionary work of St Patrick and his followers, and to his Early Christian heritage (遗产) in County Down.This PEACE III funded display, featuring wonderful photographs, is in English and Polish and is accompanied by a free leaflet, also in both languages.Admission FREE.From Ballyhosset to Bengal03 February 2016 - 31 December 2016 at Down CountyMusuemThis display features a selection of documents, photographs, medical instruments and uniforms belonging to Lieutenant-Colonel Alexander Silcock, which were recently donated to Down County Museum.Admission FREE.1916 and After28 April 2016 - 01 May 2016 at Down County MuseumThis exhibition has been created by Down CountyMuseum and Newry and Mourne Museum to mark the100th anniversary of the 1916 Rising. The exhibition provides an overview Rising and will explore a selection of themes including how the Rising was reported in local newspapers and its impact on local politics and society. Pre-booking essential.Admission FREE.Essence of Form: The Applied Art Collection of DownCounty Museum03 May 2016 - 30 October 2016 at Down CountyMuseumThis exhibition displays the applied art collection of Down County Museum. Collected over 25 years, the exhibition includes ceramics (陶瓷制品), textile (纺织的) pieces, silversmithing and jewellery made by artists living and working in County Down.Admission FREE.70. Which exhibition is related to religion?A. In the Footsteps of St Patrick.B. From Ballyhosset to Bengal.C. 1916 and After.D. Essence of Form.71. Which exhibition needs to be reserved in advance?A. In the Footsteps of St Patrick.B. From Ballyhosset to Bengal.C. 1916 and After.D. Essence of Form.72. Mr. Smith, who is interested in the works of art in Down County Museum, can go to visit the museumon ______.A. April 25, 2016.B. April 29, 2016.C. June 18, 2016.D. November 3, 2016.73. It can be learned from the above introduction that _____.A. Admission to Down County Museum is always free.B. Down County Museum is open for a shorter time on weekdays.C. All the exhibitions are held by Down County Museum independently.D. The exhibits in “From Ballyhosset to Bengal” have long belonged to the museum.（C）Fed up with constantly having to recharge or replace batteries in your ever-expanding electronic devices? The solution may be just a few steps away.“Energy harvesting”promises to power countless consumer devices, often with nothing more than your body’s movement or heat. Dozens of companies around the world already offer such products, but many experts believe the market for the technology could explode due to electronic devices being developed for the Internet of Things.“It’s huge,”said Graham Martin, CEO of the EnOcean Alliance, a San Ramon-based group of businesses that promotes wireless energy-harvesting technologies. With the Internet of Things expected to combine billions of devices, “if they are all battery-powered, we’ll have a problem because there’s not enough lithium (锂) in the world,” he added. “So a lot of them will have to use energy harvesting.”Among the most basic forms of the technology is body power. When certain materials are squeezed or stretched, the movement of their atoms creates an electrical charge. Automatic watches have employed the concept for decades, for example, by winding themselves when their user moves their arm. Now, the concept is being considered for a number of other devices.In a contest seeking visionary ideas for wearable technologies, Intel awarded $5,000 for a concept to change the temperature difference between a person’s body and a special piece of clothing they’d wear into electricity for mobile devices.Using sound to power devices is another energy-harvesting variation. Stanford University engineers are testing smart microchips (芯片) that create electricity from ultrasound (超声波) to power implantable (可植入的) devices that can analyze a person’s nervous system or treat their diseases.A textile (纺织品) research association in Spain is proposing to obtain electricity from radio waves that flow around everyone to power sensors sewn into clothes, which can monitor a person’s heartbeat or other vital signs.Research firm IDTechEx has estimated that annual global sales of energy-harvesting products could hit $2.6 billion by 2024, while WinterGreen Research predicts sales of $4.2 billion by 2019.Obtaining stable energy from devices can be complex, however. For one thing, the motion that generates the electricity has to be constant to be useful. Moreover, the amount of power the devices produce depends on the person using them, according to a Columbia University study. It determined that taller people on average provide about 20 percent more power than shorter ones when walking, running or cycling.It’s also unclear how eagerly consumers might welcome energy-harvesting products. While such devices are expected to cost less than battery-powered alternatives when compared over many years, experts say, people may continue buying ones with batteries merely because those would be cheaper in the short term.74. Which “explode”in the following sentences has the most similar meaning to the word “explode”inParagraph 2?A. They were clearing up when the second bomb exploded.B. The continued tension could explode into more violence.C. The population exploded to 40,000 during the last tourist season.D. The boss exploded when he heard of the resignation of the secretary.75. What makes “energy harvesting” necessary according to the passage?A. The waste of lithium in the world.B. The increasing number of electronic devices.C. The development of technology.D. The pollution caused by batteries.76. It can be learned from the passage that _____.A. energy-harvesting products save money in the long runB. taller people can surely produce a larger amount of powerC. automatic watches harvest energy from the user s’ body heatD. two ways of harvesting energy are mentioned in the passage77. Which of the following might be the best title for the passage?A. Energy harvesting: a low-risk technologyB. Energy harvesting: a high-profit technologyC. Energy harvesting: a problem-free technologyD. Energy harvesting: an environment-friendly technologySection CDirections: Read the passage carefully. Then answer the questions or complete the statements in the fewest possible words.Want to attract and keep top talent? Here’s a suggestion: Make a flexible work schedule part of the deal.A survey this summer of 1,215 U.S. managers and employees across a variety of industries, by EY (formerly Ernst & Young), found those aged 18 to 32 rank flexibility among the perks(特殊待遇) they want most, with 33% saying they wouldn’t work anywhere that didn’t offer it. But it seems those aged 33 to 48 value flextime even more: 38% of them consider it non-negotiable, with men who said so, at 40%, slightly outnumbering women (37%).“Companies first started offering flexible schedules, in the late 80s and the 90s, as a way to recruit (招募) and keep talented women, but it’s gone way beyond that now,” observes Karyn Twaronite, an EY partner who came up through the tax side of the business.Noting that both men and women, in all age groups, ranked flextime(弹性工作制) tops among non-cash perks, Twaronite adds, “That result mirrors exactly what we’re seeing here at EY.” The accounting and consulting giant, No. 57 on Fortune’s Best Companies to Work For, has had thousands of employees working flexible schedules for years—including, since 2004, six weeks’ of paid leave for new dads.“Flextime may have started out as a women’s issue, but it’s changed into something that people of both sexes have come to expect,” he adds. “I think it’s partly because of the large number of two-career households now, where people have to adapt to two demanding professional schedules instead of just one.”The EY survey suggests that, in the next decade or so, the opportunity for a life outside the office will become an even bigger draw than it already is. Most of those surveyed still work a set schedule, the report notes, but “respondents expect a shift in the coming years to more flexible hours, as 62% currently work standard office hours and only 50% expect to do so in five to ten years.”That doesn’t surprise Twaronite. “Work is changing,” she observes. “The technology to connect anywhere and anytime means that people are expected to be on call 24 hours a day, especially in globalcompanies that operate across different time zones. The other side of that is that employers are adapting to people’s lives outside of work—because they have to be.”(Note: Answer the questions or complete the statements in NO MORE THAN TEN WORDS.)78. What is the main finding of the survey?79. Flextime was originally aimed at _____.80. The result of the survey is caused by the fact that _____.81. What makes flextime possible according to Twaronite?第Ⅱ卷（共47分）I. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.1. 出国对于这个高中生来讲根本没有吸引力。

英语高考模拟卷-上海市育培高中2016届自招高考模拟卷英语试题及答案

上海市育培高中2016届自招高考模拟英语试题考生注意：1. 考试时间100分钟, 试卷总分值120分。

2. 本试卷设试卷和答题卷两部分。

试卷分为第I卷和第II卷。

所有答案必须涂〔选择题〕或写〔非选择题〕在答题卷上，做在试卷上一律不得分。

3. 答题前，务必在答题卷纸上填写准考证号和，并将核对后的条形码贴在指定位置上。

Grammar and VocabularySection ADirections: After reading the passages below, fill in the blanks to make the passages coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.(A)Daniel Anderson, a famous psy chologist, believes it’s important to distinguish television’s influences on children from those of the family. We tend to blame TV___(25)____ problems it doesn’t really cause, overlooking our own roles in shaping children’s minds.One traditional belief a bout television is that it reduces a child’s ability___(26)____(understand) the world. While watching TV, children do not merely absorb words and images (影像).___(27)______, they learn both explicit and hidden meanings from what they see. Actually, children learn early the psychology of characters in TV shows. Furthermore, as many teachers agree, children understand far more when parents watch TV with them, explaining new words and ideas. Yet, most parents use an educational program as a chance to park their kids in front of the set and do something in another room.__(28)___ argument against television is that it replaces reading as__29_____ form of entertainment. But according to Anderson, the amount of time spent watching television is not related to readi ng ability. TV doesn’t take the place of reading for most children; it takes the place of similar sorts of recreation, such as listening to the radio and playing sports. Things like parents’ educational background have a stronger influence on a child’s reading. “A child’s reading ability isbest predicted by how much a parent reads.” Anderson says.Traditional wisdom also has it that heavy television-watching___30___(lower) IQ (智商) scores and affects school performance. But here, too, Anderson notes ___31_____ no studies have proved it. In fact, research suggests that it’s the other way around. “If you’re smart young, you’ll watch less TV when you’re older,” Anderson says. Yet, people of lower IQ tend to be lifelong television viewers.(B)While income worry is a rather common problem of the aged, loneliness is another problem that aged parents may face. Of all the reasons __32__ explain their loneliness, a large geographical distance between parents and their children is the major one. This phenomenon is commonly known as “Empty Nest Syndrome”(空巢综合症).In order to seek __33__(good) chances outside their countries, many young people have gone abroad, __34__(leave) their parents behind with no clear idea of when they will return home. Their parents spend countless lonely days and nights, taking care of themselves, in the hope that someday their children will come back to stay with them. The fact __35__ most of these young people have gone to Europeanized or Americanized societies makes it unlikely that they will hold as tightly to the value of duty __36__ they would have if they had not left their countries. Whatever the case, it has been noted that the values they hold do not necessarily match __37__ they actually do. This geographical and cultural distance also prevents the grown-up children from providing timely response __38__ the needs of their aged parents.The situation in which grown-up children live far away from their aged parents __39__ (describe) as “distant parent phenomenon”, __40__ is common both i n developed countries and in developing countries. Our society has not yet been well prepared for “Empty Nest Syndrome”.The fact that most of these young people have gone to Europeanized or Americanized societies makes it unlikely that they will hold as tightly to the value of duty as they would have if they had not left their countries. Whatever the case, it has been noted that the values they hold do not necessarily match what they actually do.Section BDirections: Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.It was once common to regard Britain as a society with class distinction. Each class had ___41____ characteristics.In recent years, many writers have begun to speak the '__42___ of class' and 'classless society' in Britain. And in modern day consumer society everyone is considered to be middle class.But _43___ the death of class is too early. A recent wide-ranging society of public opinion found 90 percent of people still ___44____ themselves in __45_____ class; 73 percent agreed that class was still a vital part of British society; and 52 percent thought there were still sharp class differences. Thus, class may not be culturally and politically ___46____, yet it remains an important part of British society. Britain seems to have a love of stratification.One unchanging aspect of a British person's class position is accent. The words a person speaks tell her or his class. A study of British accents during 1970s found that a voice sounding like a BBC newsreader was __47_____ as the most attractive voice, Most people said this accent sounded 'educated' and 'soft'. The accents placed at the bottom in this study, on the other hand, were regional city accents. These accents were seen as 'common' and 'ugly'. However, a similar study of British accents in the US turned these results upside down and placed some regional accents as the most attractive and BBC English as the least. This suggests that British attitudes towards accent have deep roots and are based on class___48____In recent years, however, young upper middle-class people in London, have begun to adopt some regional accents, in order to hide their class origins. This is an __49_____of class becoming unnoticed. However, the 1995 pop song 'Common People' puts forward the view that though a middle-class person may 'want to live like common people' they can never__50_____ the reality of a working-class life.III. Reading ComprehensionSection A 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.Archaeologists are scientists who search for clues that help form a clearer picture of the lives people led in the past. Archaeology is a modern science, but it has been ___51___ for centuries. More than 2,400 years ago, the Greek historian Herodotus described the Egyptian pyramids and other monuments. He may have been the first writer to consider that remains and ___52___ could provide information for ___53___ generations. For more than a thousand years, however, such ___54___ were observers rather than researchers.In the 1700s, scientists and adventurers from a variety of countries traveled ___55___ to explore ancient sites. Digs that are still ___56___ began in 1709 at Herculaneum, an Italian city buried in ash during the explosion of Mount Vesuvius in A. D. 79. The Danish scholar Carsten Niebuhr visited the ruins of Persepolis in the Middle East in 1765 to study cuneiform writing (楔形文字). ___57___, archaeology didn’t become a widely recognized science and schools didn’t recognize the subject as a scholarly pursuit until the 19th century. The term itself was ___58___ in 1837. It comes from a Latin word meaning “the study of antiquities (古物).” One of the first archaeologists to use a scientific approach to the discipline was Heinrich Schliemann of Germany, who in the late 1800s ___59___ the ancient civilization of the city of Troy.Today, archaeologists uncover the past in many different ___60___, including deserts and jungles, at sites called digs. Ancient sources, folk tales, and landscape features can suggest where archaeologists should look. Surveys of the land help them choose sites ___61___ to provide artifacts, the objects that will unlock the story of a particular people —their daily lives, their beliefs, and their ties to other cultures. A site, however, does not have to be old to be interesting to an archaeologist. Some prefer to study more ___62___ settlements. One scientist, for instance, studies coal mining camps in California by examining the garbage that miners ___63___. Archaeologists may work for universities, museums or governments, and some of them are involved in educating the public about ___64___ ancient sites. Artifact hunters who are ___65___ history rob these places and sell what they find for a few dollars to immoral dealers in antiquities.51. A. adventuring B. changing C. digging D. evolving52. A. books B. history C. ruins D. science53. A. lost B. later C. older D. several54. A. inventors B. scholars C. visitors D. writers55. A. extensively B. nationwide C. regularly D. together56. A. in progress B. in good condition C. on display D. out of control57. A. Besides B. However C. Instead D. Meanwhile58. A. coined B. considered C. recognized D. used59. A. created B. developed C. established D. investigated60. A. countries B. fields C. locations D. ways61. A. certain B. likely C. ready D. necessary62. A. honorable B. peaceful C. rural D. recent63. A. gave away B. gave off C. left behind D. left out64. A. choosing B. examining C. studying D. protecting65. A. aware of B. fed up with C. ignorant of D. familiar with Section BDirections: Read the following 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)When a consumer finds that an item she or he bought is faulty or in some other way does not live up to the manufacturer's claims, the first step is to present the warranty, or any other records which might help, at the store of purchase. In most cases, this action will produce results. However, if it does not, there are various means the consumer may use to gain satisfaction. A simple and common method used by many consumers is to complain directly to the store manager. In general, the “higher up” his or her complaint, the faster he or she can expect it to be settled. In such a case, it is usually settled in the consumer's favor, assuming he or she has a just claim. Consumers should complain in person whenever possible, but if they cannot get to the place of purchase, it is acceptable to phone or write the complaint in a letter.Complaining is usually most effective when it is done politely but firmly, and especially when the consumer can demonstrate what is wrong with the item in question. If this cannot be done, theconsumer will succeed best by presenting specific information as to what is wrong, rather than by making general statements. For example, “The left speaker does not work at all and the sound coming out of the right one is unclear” is better than “This stereo does not work”. The store manager may advice the consumer to write to the manufacturer. If so, the consumer should do this, stating the complaint as politely and firmly as possible. If a polite complaint does not achieve the desired result, the consumer can go to a step further. She or he can threaten to take the seller to court or report the seller to a private or public organization responsible for protecting consumer's rights.66. When a consumer finds that his or her in it, the first thing he or she should do is to ____.A) complain personally to the managerB) threaten to take the matter to courtC) write a firm letter of complaint to the store of purchaseD) show some written proof of the purchase to the store67. How can a consumer make his or her complaint more effective, according to the passage?A) Explain exactly what is wrong with the item.B) Threaten to take the seller to court.C) Make polite and general statements about the problem.D) Avoid having direct contact with the store manager.68. According to the passage, which of the following is suggested as the last alternative that consumers may turn to?A) Complain to the store manager in person.B) Complain to the manufacturer.C) Write a complaint letter to the manager.69.The passage tells us ____.A) how to settle a consumer’s complai nt about a faulty itemB) how to make an effective complaint about a faulty itemC) how to avoid buying a faulty itemD) how to deal with complaints from customers(B)About PISAThe Program for International Student Assessment(PISA) is a triennial international survey which aims to evaluate education systems worldwide by testing the skills and knowledge of 15-year-old students. To date, students representing more than 70 economies have participated in the assessment. What makes PISA differentPISA is unique because it develops tests which are not directly linked to the school curriculum. The tests are designed to assess to what extent students at the end of compulsory education, can apply their knowledge to real-life situations and be equipped for full participation in society. The information collected through background questionnaires also provides context which can help analysts interpret the results.What the assessment involvesSince the year 2000, every three years, fifteen-year-old students from randomly selected schools worldwide take tests in the key subjects: reading, mathematics and science, with a focus on one subject in each year of assessment. The students take a test that lasts 2 hours. The tests are a mixture of open-ended and multiple-choice questions that are organized in groups based on a passage setting out a real-life situation. A total of about 390 minutes of test items are covered. Students take different combinations of different tests. Additional PISA initiativesPISA-based Test for Schools(PTS)As interest in PISA has grown, school and local educators have been wanting to know how their individual schools compare with students and schools in education systems worldwide. To address this need, the OECD(The Organization for Economic Co-operation and Development) has developed the PISA-based test for schools. It is currently available in the United States and the OECD is in discussions with governments to make the test available in other countriessuch as England and Spain.70. PISA is different from other programmes because __________.A. its test is closely related to the school curriculum.B. its test aims to assess whether students can solve real-life problems.C. its test can equip students for full participation in school.D. test scores directly determine the analysis of the test.71. Which of the following statements is true according to the passage?A. Test-takers are carefully selected.B. Test-takers answer the same questions.C. Test-takers are tested on three key subjects.D. Test-takers spend about 390 minutes on the test.72. What can we infer from the last paragraph?A. Students of all ages will be able to take PTS in the future.B. More countries are likely to have PTS in the future.C. School and local educators show little interest in PISA at present.D. PISA provides evaluation of education system within a certain country.73. Where can we most probably find the passage?A. On the InternetB. In a newspaperC. In a magazineD. In an advertisement(C)According to a survey, which was based on the responses of over 188, 000 students, today's traditional-age college freshmen are "more materialistic and less altruistic (利他主义的) " than at any time in the 17 years of the poll.Not surprising in these hard times, the student's major objective is to be financially well off. Less important than ever is developing a meaningful philosophy of life. It follows then that today the most popular course is not literature or history but accounting.Interest in teaching, social service and the "altruistic" fields is at a low. On the other hand, enrollment in business programs, engineering and computer science is way up.While it's true that we all need a career, it is equally true that our civilization has accumulated an incredible amount of knowledge in fields far removed from our own and that we are better for our understanding of these other contributions—be they scientific or artistic. It is equally true that, in studying the diverse wisdom of others, we learn how to think. More important, perhaps, education teaches us to see the connections between things, as well as to see beyond our immediate needs.The most important argument for a broad education is that in studying the accumulated wisdom of the ages, we improve our moral sense. I saw a cartoon recently which shows a group of businessmen looking puzzled as they sit around a conference table; one of them is talking on the intercom (对讲机) : "Miss Baxter, " he says, "could you please send in someone who can distinguish right from wrong?"From the long-term point of view, that's what education really ought to be about.74. According to the author’s observation, college students ________.A) have never been so materialistic as todayB) have never been so interested in the artsC) have never been so financially well off as todayD) have never attached so much importance to moral sense75. The students’ criteria for selecting majors today have much to do with ________.A) the influences of their instructorsB) the financial goals they seek in lifeC) their own interpretations of the coursesD) their understanding of the contributions of others76. By saying “While it’s true that...be they scientific or artistic”, t he author means that ________.A) business management should be included in educational programsB) human wisdom has accumulated at an extraordinarily high speedC) human intellectual development has reached new heightsD) the importance of a broad education should not be overlooked77.Which of the following statements is true according to the passage?A) Businessmen absorbed in their career are narrow-minded.B) Managers often find it hard to tell right from wrong.C) People engaged in technical jobs lead a more rewarding life.D) Career seekers should not focus on immediate interests only.Section CDirections: Read the passage carefully. Then answer the questions or complete the statements in the fewest possible words.All of us exist in ‘bodies’ of different shapes, heights, colors and physical abilities. The main reasons for the differences are genetic, and the fact that people’s bodies change as they age. However, a huge range of research indicates that there are social factors too.Poorer people are more likely to eat ‘unhealthy’ foods, to smoke cigarettes and to be employed in physically difficult work or the opposite: boring, inactive employment. Moreover, their housing conditions and neighbourhoods tend to be worse. All of these factors impact upon the condition of a person’s health: the physical shapes of bodies are strongly influenced by social factors.These social factors are also closely linked to emotional wellbeing. People with low or no incomes are more likely to have mental health problems. It is not clear, however, whether poverty causes mental illness, or whether it is the other way around. For example, certain people with mental health issues may be at risk of becoming homeless, just as a person who is homeless may have an increased risk of illnesses such as depression.There are other types of social factors too. Bodies are young or old, short or tall, big or small, weak or strong. Whether these judgments matter and whether they are positive or negative depends on the cultural and historical context. In fact, the culture of different societies promote very different valuations of body shapes. What is considered as attractive or ugly, normal or abnormal varies enormously. Currently, for example, in rich societies the idea of slimness is highly valued, but historically this was different. In most societies the ideal body shape for a woman was a ‘full figure’, while in middle-aged man, a large stomach indicated that they were financially successful in life.Sociologists are suggesting that we should not just view bodies and minds in biological terms,but also in social terms. The physical body and what we seek to do with it change over time and society. This has important implications for medicine and ideas of health. Thus, the idea of people being ‘overweight’ is physically related to large amounts of processed food, together with lack of exercise, and is therefore a medical issue. However, it has also become a mental health issue and social problem as a result of people coming to define this particular body shape as ‘wrong’ and unhealthy.(Note: Answer the questions or complete the statements in NO MORE THAN TEN WORDS.)78. Besides social factors, what are the other two reasons for differences in bodies?79. The social factors are likely to have a great effect on people’s ______ and ______.80. Valuations of body shapes change with ______.81. The “This” in the last paragraph refers to ______.第II 卷〔共47 分〕I. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.1. 他们的建议听起来和我们的同样可行。

上海市虹口区2016届高考练习(二模)英语试卷(含答案)

虹口区2016年英语学科高考练习题第 I 卷 (共103分)I. Listening ComprehensionSection ADirections: In Section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.1. A. At 12:00. B. At 12:15. C. At 12:30. D. At 12:45.2. A. To visit a museum.C. To get married. B. To attend a wedding.D. To go to India.3. A. This afternoon.C. Next month. B. Tomorrow.D. Next week.4. A. In a tea house. B. In a school. C. In a grocery. D. In a garage.5. A. The desk lamp.C. The electricity bill. B. The dirty kitchen.D. The power failure.6. A. They’re a couple.C. They’re classmates. B. They’re neighbors.D. They’re colleagues.7. A. She saw the play more than once. B. She acted in the play.C. She visited the English Department.D. She led the drama club.8. A. Small corrections could be made. B. Major corrections are needed.C. The paper should be rewritten.D. The paper needs no correction.9. A. Mary has never collected any postcards.B. Mary didn’t receive the postcard from Germany.C. The woman will go to Germany for her holiday.D. Mary begins to take up collecting postcards.10. A. The man has left a good impression on her family.B. The man can dress casually for the family reunion.C. The man had better buy himself a new suit.D. The man’s jeans and T-shirts are fashionable.Section BDirections: In Section B, you will hear two short passages, and you will be asked three questions on each of the passages. The passages will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. He was knocked down by a bus. B. He fell ill suddenly.C. He was chased by some tough guys.D. He was robbed.12. A. A neighbour. B. A friend. C. A stranger. D. A doctor.13. A. Churchgoers are very helpful. B. Only doctors can save our lives.C. A friend in need is a friend indeed.D. Neighbours are dearer than distant relatives.Questions 14 through 16 are based on the following passage.14. A. They haven’t devoted as much energy to medicine as to space travel.B. There are too many kinds of cold viruses for them to identify.C. It is not economical to find a cure for each type of cold.D. They believe people can recover without treatment.15. A. They reveal the seriousness of the problem.B. They indicate how fast the virus spreads.C. They tell us what kind of medicine to take.D. They show our body is fighting the virus.16. A. It actually does more harm than good.B. It actually helps us to recover much sooner.C. It causes damage to some organs of our body.D. It works better when combined with other therapies.Section CDirections: In Section C, you will hear two longer conversations. The conversations will be read twice. After you hear each conversation, you are required to fill in the numbered blanks with the information you have heard. Write your answers on your answer sheet.Blanks 17 through 20 are based on the following conversation.Blanks 21 conversation.II. Grammar and VocabularySection ADirections:Read the following two passages. Fill in the blanks to make the passage coherent. For the blanks with a given word, fill in each blank with the proper form of the given word. For the other blanks, fill in each blank with one proper word. Make sure that your answers are grammatically correct.(A)“Time,” says the proverb, “is money”. This means that every moment well-spent may put some money into our pockets.If our time (25) ______ (employ) usefully, it will either turn out some useful and important piece of work which will fetch its price in the market, or it will add to our experience and increase our capacities so as to enable us to earn money when the proper opportunity comes. Let those, (26) ______ think nothing of wasting time, remember this.Our life is nothing more than our time. To kill time is therefore a form of suicide. We are shocked (27) ______ we think of death, and we spare no pains, no trouble, and no expense to preserve life.But we often care nothing about the loss of an hour or of a day, (28) ______ (forget) that our life is the sum total of the days and of the hours we live. Our life is a brief period measuring some seventy or eighty years in all. So a day or an hour (29) ______ (waste) is therefore so much life lost.But nearly one third of this has to be spent in sleep; some years have to be spent over our meals; some in watching over the sick-beds of our (30) ______ (near) relatives; some in making journeys on land and voyages by sea.Now if all these years were to be decreased from the term over which our life extends, we shall find about twenty or thirty years at our disposal (处置) for active work. (31) ______ remembers this can never willingly waste a single moment of his life.The precious hours of childhood and youth, if properly used, (32) ______ (supply) us with incalculable advantages. If we allow these morning hours of life to slip away, we shall never be able to make up for the loss.(B)Home on the WayPeople need homes: children assume their parents’ place as home; boarders call school “home” on weekdays; married couples work together (33) ______ (build) new homes; and travelers … have no place to call “home”, at least for a few nights.So how (34) ______ people who have to travel for extended periods of time? Don’t they have the right to have a home? Of course they do.Some regular travelers take their own belongings: like bed sheets, toothbrushes and family photos to make them feel like home (35) ______ ______ ______ they are; some stay for long periods in the same hotel and as a result become very familiar with service and attendants; others (36) ______ simply put some flowers by the hotel window to m ake things more homely. Furthermore, driving a camping car during one’s travels and sleeping in the vehicle at night is just like (37) ______ is generally thought of as “home” -- only mobile!And how about maintaining relationships while in transit? Some keep contact with their friends via internet; some send letters and postcards, or even photos; (38) ______ may just call and say hi, just to let their friends know that they’re still alive and well. People find ways to keep in touch. (39) ______ (make) friends on the way helps travelers feel more or less at home. Backpackers in youth hostels may become very good friends, even closer than siblings.Nowadays, fewer people are working in their local towns, so how do they develop a sense of belonging? Whenever w e step out of our local boundaries, there is always another “home” waiting to be found. Wherever we are, with just a little bit of effort and imagination, we can make (40) ______ place where we stay “home”.Section BDirections: Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.A book entitled “Jiading –Centuries of History, Decades of Change” by American writer Kate Baker has recently been published in Shanghai. New book launch was held last week at the Old China Hand Style, a major __41__ of a series of walking guide books called “Beyond the Concession: Six Walks in Shanghai’s Other Districts.” And Baker’s “Jiading” runs the fourth among the six.From a foreign point of view, the book has __42__ the history of Jiading District back between the year Tang Dynasty (618-907) and the Song Dynasty (960-1279), when Jiading had been “a leading economic and intellectual influence in the region long before Shanghai became a major trading port,” a s Baker is __43__ in her book.Baker first landed in Shanghai in 2011 with her husband, an engineer with Ford, who was sent to work in Shanghai to prepare for the __44__ of the Lincoln brand in China. “I and my husband have been traveling around the wo rld in the past 20 years,” Baker said at a(n) __45__ with Shanghai Daily. “Wherever I go, I would jump into the local history and culture quickly and deeply.”Having taken a 15-month online course of Chinese with Harvard’s “China X”, Baker started __46__ o ut on her own. An occasional excursion into the northwest of Shanghai, she “discovered” and fell in love with Jiading. Since then, she has visited Jiading __47__, bringing family, friends, and tour groups. At the end of 2013, the Jiading Tourism Bureau officially invited Baker to write a book on Jiading.With up-to-date facts, useful information and __48__ pictures, Baker's “Jiading” is a well researched guide about interesting areas less than one hour from Shanghai. There are chapters on celebrating the seasonal and agricultural festivals that are unique to the region; stories of __49__ figures living in Jiading; changes to the Nanxiang Old Town; tours to numerous gardens, museums and temples; and the development of outdoor recreational activities in Jiadin g’s Anting Town, such as the F1 car racing, horse riding and golf.With good public __50__ and enough green space, Baker sees Jiading a high growth district of Shanghai, which offers a quality of lifestyle and tourism. “I see a better-planned and forward-thinking of the district government. And I sincerely thank the people of Jiading who welcomed me to their community and trusted me with their narrative,” Baker says.III. Reading ComprehensionSection ADirections: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.Harvard LibraryIf we compare professors and students to the host of auniversity, then the library of a university can be comparedto the hallway. The quality of a university, __51__, is indirect proportion to that of its library. At Harvard, the libraryis an essential part of everybody’s life. Both the quantity andthe __52__ of the library make study a pleasant process.Harvard Library is not only the most ancient library inthe United States, but the largest university library with thelargest scale. In 1638 John Harvard __53__ his whole libraryto the then Harvard College. After 300 years of development,the library now holds 10 million books and __54__ more than 100 branch libraries. In addition to the libraries owned by each school, there are some branch libraries that are __55__ in some aspects. While most of the branch libraries are on Harvard campus, some are as far as in Washington, D.C., or even in Florence of Italy. Yenching Library is famous for its __56__ of East Asian literature. Lamont Library is the first library in the world that is __57__ for undergraduates. Widener Library is the largest library in Harvard, only second to Library of Congress.What __58__ to be mentioned is the system or rather the service of the libraries. Usually the libraries are open from 9 a.m. to 5 p.m.. The main libraries are open until 10 p.m.. The libraries for undergraduates will even be open all night during the __59__ period. The libraries also provide with students the service of __60__ reading materials for all courses. At the beginning of a semester, each teacher will give a list of books to the librarians. The librarians are __61__ to find out these books and put them at the places where students can easily find them.There is no limitation for the number of books that students can borrow. As the space for the library is limited, many books are __62__ in suburban library. Despite this, students can go to fetch the book at the __63__ library within 24 hours after they submit request for that book. Even if there is only one book to be fetched from the suburban library, the libraries on campus will send someone to do the job. This kind of __64__ which put readers in the first place is rare even in Ivy League. Therefore, study at Harvard will be a(n) __65__ experience.51.A.as a result B. to some extent C. on the contrary D. at all times52.A.influence B. discipline C. quality D. prospect53.A. donated B. assigned C. adapted D. distributed54.A.contains B. composes C. involves D. includesrmative B. different C. secure D. peculiar56.A.collections B. documents C. phenomena D. exhibitions57.A.unusually B. formally C. specially D. especially58.A.remains B. happens C. appears D. deserves59.A.examination B. experiment C. vacation D. graduation60.A.confirming B. preparing C. selecting D. designing61.A.desperate B. willing C. reluctant D. responsible62.A.exhibited B. reserved C. stored D. classified63.A.appointed B. accepted C. expected D. restricted64.A.performance B. service C. activity D. response65.A.fortunate B. creative C. positive D. enjoyableSection 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)How Would You Like to Pay?How do you pay for your coffee? Is it with change? I use my tap-and-go card. I don’t even need to enter my PIN number or a signature to approve payment. It’s quicker and everybody in the queue is happy.Contactless payments are gaining popularity. Those concerned about security will be pleased to know that the amount of money you can spend in one-go is limited –in the UK it’s currently £30. But if the card is used a few times in a row, a PIN number will be needed. If a thief gets hold of your card and goes on a crazy shopping, your bank covers you against fraud. However, if someone steals your bills, that’s your bad luck!For those who are always forgetting where they put their cards, there’s a new solution: wearable technique: clothing and devices that have combined electronic technology. Kenneth Cukier, an economist and technology expert, says: “You can simply take any wireless card and the chip (芯片) from it that your bank might issue you with, and you can put it in a coat. When you want to make a payment just wave your arm in front of the terminal and leave the coffee shop with your latte(拿铁咖啡). This is intended for people who don’t want to take their card out of their wallet, use their phone or their watch.”Good, isn’t it? And new ways of spending money a re not stopping there. The future is all about biometrics(生物识别技术). Very convenient if you are at the beach or a festival –there’s a new system in development which will make it possible to read the unique maps of veins (静脉) under the surface of your finger, and use them to confirm payments –or prove that it’s you making the payments. You just need to remember which finger you registered with.So spending money is becoming easier all the time. And the temptation to buy more stuff increases. But it’s worth bearing in mind that earning the money in the first place will still require the same effort. Back to work then!66. A thief wouldn’t be able to buy much with a stolen wireless card because ______.A. the card doesn’t permit withdrawing money more than £30B. there’s a limit to the amount of money spent at a timeC. the wireless card must be used a few times in one-goD. a PIN number is always required before payment67. The underlined word “fraud” in Paragraph 2 is closest in meaning to “______”.A. theftB. protectionC. cheatD. prevention68. What must be done before you use biometrics for payment?A. You must prove that it’s you making the payments.B. You must have a smart phone or a watch with you.C. You must have something to read your fingers.D. You must have one of your fingers registered.69. What can be learned from this passage?A. People’s banking information is kept in a small chip.B. People can only use a wireless card to consume coffee.C. Wearable technique is the safest way to make a payment.D. A tap-and-go card needs a signature to approve payment.(B)Asia TEFL and the Far Eastern English Language Teachers’ Association 14th Asia TEFL International Conference and 11th FEELTA International Conference invite proposals for their joint conference on language teaching and learning:“Connecting Professionally on ELT in Asia:Crossing the Bridge to Excellence”to be held on 30 June – 2 July, 2016 atThe Far Eastern Federal University, Vladivostok, RussiaCALL FOR PRESENTATIONSConference DescriptionThe 14th Asia TEFL and 11th FEELTA international conference places emphasis on working towards special skills or knowledge in English Language Teaching through being connected professionally in Asia and worldwide. Professional networks link teachers from a variety of educational contexts, helping to develop research, advance skills and update knowledge. We invite educators, scholars and policy makers to cooperate and share teaching theories, excellent teaching ideas and relevant practices.The meaning of the “bridge” in our theme is inspired by the place of the conference. The university campus is located on Russky Island “across the bridge” from the mainland. It also refers to new horizons and perspectives in the field of ELT that we discover when we “cross the bridge” to explore pioneering teaching ideas and stimulating experiences.Conference SubtopicsWe invite papers on the following subtopics in ELT:●ELT curriculum and design●Materials writing●Teacher education and professional development●Teaching literature and the arts●Interpreting and translation●Global Issues in Language EducationTypes of PresentationsAll presentations will be given in English. Presenters are encouraged to hand in full papers of their presentation to the Journal of Asia TEFL to be considered for publication.●Papers: 30 minutes●Workshops: 60 minutes●Poster presentations: displayed all day ---- presenters are expected to stand by their posters ready toexplain and discuss them, for 60 minutes.●Group discussions: 90 minutesProposal Submission (提交)Materials to be submitted:● a title of up to ten words●an abstract of not more than 200 words● a self-introduction of not more than 60 wordsAll proposals must be submitted online through the link: http://feelta.wl.dvfu.ru/asiatefl-feelta-2016●Presentation submission opens: November 1, 2015●Deadline for submission: February 29, 2016Questions about proposal submission can be addressed to Larisa Krainik, Abstract Committee Chair: feeltacon@70. What does the expression “Crossing the Bridge to Excellence” in the title imply?A. Exploring pioneering teaching ideas and stimulating experiences.B. the process from knowledge to skills on language teaching and learning.C. inviting proposals about new horizons and perspectives in the field of ELT.D. Coming from every country in the world to the Far Eastern Federal University.71. The joint international conference will be held to ______.A. be connected professionally in Asia and worldwideB. call for presentations of the educators, scholars and policy makersC. work towards special skills or knowledge in English Language TeachingD. provide a chance for teachers to cooperate and share theories, ideas and practices72. According to the passage, what can be learned from the conference?A. How to achieve good results in the English exams.B. Effective communication skills among teachers.C. How to help teachers to share research skills.D. Effective teaching approaches and theories.73. It can be inferred from the passage that ______.A. the presentations are most likely to have been published during the conferenceB. all presentations must be submitted formally online within the required timeC. presenters can only choose to take part in one of the types of presentationsD. presentations are required to be explained to the participants publicly(C)Scientists Detect Gravitational WavesWhat is gravitational waves(引力波)? Scientists havefor the first time observed ripples in the fabric of space time(时空涟漪) called gravitational waves, arriving at the earthfrom a severely destructive event in the distant universe. Itconfirms a major prediction of Albert Einstein’s 1915 generaltheory of relativity and opens a unique new window onto the universe, according to a group of scientists at a press conference in Washington on Thursday.“This is truly scientific moonshot. We did it. We landed on the moon,” declared David Reitz, executive director of the LIGO Laboratory at Caltech, at the conference in the National Press Club.According to the National Science Foundation (NSF) experts, gravitational waves carry information about their dramatic origins and about the nature of gravity that cannot be obtained from elsewhere. Physicists have concluded that the detected gravitational waves were produced during the final fraction of a second (千分之一秒) of the combination of two black holes to produce a single, much bigger turning black hole. This fierce shock of two black holes had been predicted but never observed by NSF.The gravitational waves were detected on Sept 14, 2015 at 5:51 am EDT by both of the twin Laser Interferometer Gravitational-wave Observatory (LIGO) detectors, located in Livingston, Louisiana, and Hanford, Washington.Based on the observed signals, LIGO scientists estimate that the black holes for this event were about 29 and 36 times the weight of the sun, and the event took place 1.3 billion years ago. About three times the weight of the sun was changed into gravitational waves in a fraction of a second -- with a peak power output about 50 times that of the whole visible universe. By looking at the time of arrival of the signals -- the detector in Livingston recorded the event 7 milliseconds (毫秒) before the detector in Hanford -- scientists can say that the source was located in the Southern Hemisphere, according to a press release from NSF, which funded the research.This new LIGO discovery is the first observation of gravitational waves themselves, made by measuring the tiny disturbances the waves make to space and time as they pass through the earth. “Our observation of gravitational waves accomplishes an ambitious goal set out over five decades ago to directly detect this puzzling phenomenon an d better understand the universe, and, properly, fulfills Einstein’s prediction on the 100th anniversary of his general theory of relativity,” Reitze said.74. By saying “This is truly scientific moonshot. We did it. We landed on the moon,” what does Davi d Reitzmean?A. We humans truly landed on the moon this time.B. The theory of relativity was not proved until today.C. Gravitational waves arrived at the earth in the end.D. Scientists successfully observed gravitational waves.75. What do NSF experts talk about in the third paragraph?A. Gravitational waves carry information about the origins of nature.B. The nature of gravity cannot be obtained from gravitational waves.C. The combination of two black holes can produce a single, much bigger turning black hole.D. Gravitational waves only appear at the final fraction of a second of the shock of two black holes.76. According to the observed signals, LIGO scientists find out that ______.A. the two black holes which brought about this event were much bigger than the sunB. about three times the weight of the sun became gravitational waves in this eventC. the event produced by the observed signals took place 1.3 billion years agoD. the peak power output was about 50 times that of the whole universe77. From this passage, a conclusion can be drawn that ______.A. gravitational waves can make disturbances to space and timeB. Einstein predicted the observed gravitational waves in the universeC. gravitational waves is not a puzzling phenomenon to the world any moreD. this new LIGO discovery was made to test the general theory of relativitySection CDirections: Read the passage carefully. Then answer the questions or complete the statements in the fewest possible words.The World Health Organization (WHO) has declaredthe spread of mosquito-born Zika virus a global publichealth emergency. On Monday, the global health agencyheld an emergency meeting in Geneva after warning thepublic that Zika is spreading “explosively” across t heAmericas. Dr. Margaret Chan, the director-general of theWHO, said after the meeting that the cases of microcephaly,which is a birth disease in which babies are born with verysmall heads and underdeveloped brains, in regions withZika cases, “become an extraordinary event and a public health threat to other parts of the world.”Last week, health officials confirmed one case of the virus in Denmark, five in Great Britain, three cases in the United States and 18 in its territory of Puerto Rico. The global health organization also predicts that Zika could infect as many as four million people in the Americas this year.The symptoms from the virus are minor. The symptoms are flu-like and include a rash (皮疹). But the results for some infected with Zika -- namely pregnant women -- are destructive. The WHO suspects the virus may have something to do with brain disorders in babies. Health experts highly suspect there may be a link between the illness and microcephaly. However, a definite link between Zika and microcephaly has not been proven.World Health Organization spokesman Gregory Hartl has this to say, “So, one of the curiosities is why we have so many neurological (神经学的) cases in the northeast of Brazil, but we have not had it in other places. So, we really need to understand what is existing that causes these microcephaly cases, for example, in children.”Hartl does not agree with claims that the Zika virus could lead to a threat similar to that of Ebola (埃博拉病毒). He says that Ebola is transmitted by contact with bodily fluids (体液) from person to person and kills about 50 percent of its victims. “Zika has never killed a person and it is transmitted by the mosquito. So, we know that there are those two basic differences at least. Let us say that Zika on its own would not be the consideration of an emergency committee. What is the concern to the international community is the possible link with neurological disorders.”(Note: Answer the questions or complete the statements in NO MORE THAN TEN WORDS)78. The cases of microcephaly are generally seen in the places ______.79. Who should pay special attention to the infection of the virus to avoid its terrible result?80. What puzzles the health experts about the cases of microcephaly?81. What causes the global concern is that the mosquito-born Zika virus may ______.第II卷（共47分）I. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.1、现在人们已经习惯于将坏天气与空气污染联想到一起。

上海市崇明县2016届高三第二次高考模拟考试英语试题剖析

崇明县2016届第二次高考模拟考试试卷英语（考试时间120分钟，满分150分。

请将答案填写在答题纸上）第Ⅰ卷 (共103分)I. Listening ComprehensionSection ADirections: In Section A, you will hear ten short conversations between two speak e rs. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.1. A. In a gallery. B. In a classroom. C. In a bookstore. D. In a museum.2. A. Boss and employee. B. Father and daughter.C. T eacher and student.D. Shop assistant and customer.3. A. 5 minutes. B. 8 minutes. C. 10 minutes. D. 15 minutes.4. A. The shirt is too large. B. The price of the shirt is wrong.C. The shirt is too expensive.D. Other shops don’t sell this shirt.5. A. Watching TV. B. Parents’ involvement.C. Playing video games.D. Teachers’ substitution.6. A. A place for a meal. B. Their good friends.C. A tip for choosing food.D. Their plan to eat out.7. A. She doesn’t know where the manager is.B. She doesn’t know where the man heard the news.C. She doesn’t know where she will be working this month.D. She doesn’t know where she can find the work schedule.8. A. The time is not convenient. B. Her house is not big enough.C. A few people won’t turn up.D. There won’t be enough food.9. A. It is rather cool in the lecture hall. B. No one will be able to see what he is wearing.C. The air-conditioner doesn’t work.D. He expects the weather to change later in the day.10. A. The film cost too much despite its high quality.B. The man didn’t like the film but the woman did.C. The man missed the film because of the woman.D. The man saw the film upon the advice of the woman.Section BDirections: In Section B, you will hear two short passages, and you will be asked three questions on each of the passages. The passages will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.高三英语共10页第1页11. A. A special room. B. A series of textbooks.C. A comprehension program.D. A rewritten masterpiece.12. A. Experts on English reading. B. Beginners of English learning.C. Native speakers of English.D. Editors of English textbooks.13. A. It is designed for different levels. B. It contains original masterpieces.C. It can bring back the childhood.D. It helps to improve memory.Questions 14 through 16 are based on the following passage.14. A. Work efficiency is what we pursue. B. It’s possible for us to work harder.C. Our brain is our most important tool.D. It’s wise to take a rest if our body needs it.15. A. To focus on something new. B. To ignore the limitations.C. To refresh the concentration.D. To lengthen the attention.16. A. Changing jobs from time to time. B. Doing new tasks in different work areas.C. Making a list of all your tasks.D. Eating popcorn while taking a break.Section CDirections: In Section C, you will hear two longer conversations. The conversations will be read twice. After you hear each conversation, you are required to fill in the numbered blanks with the information you have heard. Write your answers on your answer sheet.Blanks 17 through 20 are based on the following conversation.Complete the form. Write ONE WORD for each answer.Sunshine Travel AgencyReservation FormType of tour:Destination:Name:Telephone: Number of people: Date of departure:Total price: a 4-day 17 tour LondonLisa Garcia197-6344-58294 (2 18 & 2 children)19 6th20Blanks 21 through 24 are based on the following conversation.Complete the form. Write NO MORE THAN THREE WORDS for each answer.What does the woman want the man to read in the newspaper? A report about a thief who got into people’s homes under a false identity and 21 from the homes.How did the thief manage to get into people’s homes? He pretended to be from the electricity board to check the 22 of their appliances.What is the warning from the police? The police warn people not to let anyone in 23 . What does the thief look like? He’s in his thirties and tall with dark hair and 24 .II. Grammar and VocabularySection ADirections:After reading the passages below, fill in the blanks to make the passages coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.高三英语共10页第2页(A)Happiness Is an AttitudeThe 92-year-ol d confident and proud lady, who is fully dressed each morning by eight o’clock, with her hair fashionably combed and makeup perfectly applied, (25)_____ _____ she’s legally blind, moved to a nursing home today.Her husband of 70 years recently passed away, (26)_____ (make) the move necessary.After many hours of waiting patiently in the hall of the nursing home, she (27)_____ (smile) sweetly when told her room was ready. As she got into the elevator (28)_____ her wheelchair, I provided a description of her tiny room.“I love it,” she started with the enthusiasm of (29)_____ eight-year-old child having just been presented with a new dog.“Mrs. Jones, you haven’t seen the room…just wait.”“That ha s (30)_____ to do with it,” she replied. “Happiness is something you decide on ahead of time. (31)_____ I like my room or not doesn’t depend on how the furniture is arranged…it’s how I arrange my mind. I already decided to love it. It’s a decision I make every morning when I wake up. I have a choice; I can spend the day in bed recounting the difficulty I have with the parts of my body (32)_____ no longer work or get out of bed and be thankful for the ones working. Each day is a gift, and (33)_____ _____ _____ my eyes open, I’ll focus on the new day and all the happy memories I’ve stored away…just for this time in my life.”(B)Sculptor B uilds Dubai’s Soaring Burj Khalifa Skyscraper out of Toothpicks to Bag World RecordA sculptor has scaled new heights by building the world’s tallest toothpick (牙签) model.Stanley Hayes Munro, 45, from Syracuse, New York, is a toothpick engineer, who (34)_____ (hook) by toothpick models since he built his first sculpture in school when creating a structure that (35)_____ support the weight of an egg.Now, he has won the world record for the tallest toothpick structure with a sculpture of the Burj Kahlifa, Dubai. For Stanley though, he has always been more concerned with the integrity(完整性) of his work. Stanley said: “I’ve never cared for counting toothpicks, wasting toothpicks, or the number of toothpicks (36)_____ (use) in any construction. But an engineering problem you’ve got to create a strong structure is a problem worth (37)_____(solve).” “I made my first toothpick structure in an art class when I was in Grade 5,” he continued. “The assignment was to build something 25 centimeters tall and to have it (38)_____ (hold) the weight of an egg. Mine held my desk and from that point I bec ame interested in it.”“Everybody likes to ask whether my sculptures will collapse when I build them, but they are much (39)_____ (strong) than people think,” he said. “It was not really the height but the shape of the outer walls (40)_____ was the biggest challenge with Burj Khalifa. There wasn’t a flat surface anywhere and I had to individually construct each level,” he said.Section BDirections:Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.高三英语共10页第3页A. standardB. experiencedC. potentiallyD. orderlyE. extremelyF. termsG. powerH. benefitI. comparedJ. noticeableK. scannedPaying more for a ticket to see a film in 3D is the cause of annoyance of many a cinema-goer’s life. But there may be a(n) 41 to doing so, as a study has claimed that 3D films exercise the brain and improve short-term functioning in a similar way to brain-training tests.The research was led by neuroscientist(神经科学家)Dr Patrick Fagan from Goldsmiths University in London. More than 100 people took part in the experiment, where participants watched Disney film Big Hero6in either 42 type or RealD 3D. They also carried out a brain-training-style test before and after seeing a part from the film. The test covered memory, reaction time and cognitive (认知的) function, and the results were later 43 .According to the research, participants 44 a 23 per cent increase in cognitive processing, as well as an 11 percent increase in reaction time.Dr Fagan said that the results showed enough of an improvement in brain function to suggest that 3D could play a part in improving brain 45 in the future. “These findings are more significant than you might think,” he said. “It is a fact that people are living longer and there is a(n) 46 decline in cognitive brain function in old age which can damage future quality of life. There has never been a better time to look at ways to improve brain function. The initial results of this study indicate that 3D films may 47 play a role in slowing this decline.”A second part of the experiment involved those watching the film being fitted with headsets(耳机) that 48 brain activity and this too showed heightened activity when watching 3D. According to the results, participants were seven percent more engaged with what they were watching, adding to the argument that 3D movies are more like watching real-life-something. “A seven percent rise in emotional engagement is 49 remarkable. Watching in 3D gives the viewer such an enriched and quality experience, as these results show,” he said. “In evolutionary 50 , the results of both parts of the test certainly make sense. 3D films are more likely to heighten the senses and cause emotional arousal—this, in turn, makes the brain run at quicker speeds,” Dr Fagan added.III. Reading ComprehensionSection ADirections: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.Researchers recently find women likely fa ce work environments that push against the “having it all” mentality, leading to feelings of guilt and depression.Trying to have it all could be bad for your mental health, according to a new study that finds that “supermoms” have higher rates of depressi on compared with working moms who let things 51 .The research, presented Aug. 20 at the annual meeting of the American Sociological Association in Las Vegas, finds that working is 52 for mothers’ mental health. But among working mothers, the least depressed are those who don’t expect to 53 work and family life perfectly, said study researcher Katrina Leupp, a graduate student at the University of Washington in Seattle. “The ideal that women can do it all actually 54 the level of depressive symptoms compared to women who were高三英语共10页第4页more doubtful about whether or not work and family can be balanced,” Leupp told LiveScience.Leupp analyzed survey 55 from 1,600 married women who participated in a large survey called the National Longitudinal Survey of Youth. In 1987, the women answered questions to judge their support of women’s 56 , including whether they agreed with statements such as “Women are much happier if they stay at home and take care of their children.”In 1992 and 1994, the now 40-year-old women answered questions about their symptoms of depression. Like earlier studies, the survey data indicated that women who worked outside the home had fewer symptoms of depression, perhaps because outside work gives women more 57 interaction, more varied activities and a larger income, Leupp said. Among the employed women, though, the cheeriest were those who had indicated in their younger years the least 58 for women balancing career and family. The results held even after controlling for earlier levels of depression. “Somewhat 59 , women who don’t expect to be able to balance work and family have better mental health than those who do,” Leupp said.The study didn’t explain why optimistic (乐观的) views of balancing work and motherhood would 60 later depression. “The reason may come down to 61 and real-world work environments,”Leupp said. “Women who expect to have it all probably come up against 62 that aren’t designed with work-life balance in mind. When they can’t balance every thing perfectly, these supermoms are more likely to feel 63 .”“I think this research really speaks to a 64 between women’s expectations and the actual structure of the workplace,” Leupp said.“The takeaway for working moms is to temper their optimi sm about balancing 65 and employment and not to blame themselves if they struggle. Recognize that if it feels difficult, it’s because it is difficult.”51. A. happen B. continue C. slide D. end52. A. good B. ready C. hard D. possible53. A. protect B. share C. illustrate D. combine54. A. increased B. assessed C. reached D. influenced55. A. questions B. responses C. solutions D. instruments56. A. pregnancy B. marriage C. employment D. education57. A. cultural B. social C. positive D. verbal58. A. support B. tolerance C. concern D. respect59. A. deliberately B. aggressively C. ironically D. similarly60. A. result from B. relate to C. hold back D. call for61. A. families B. expectations C. surroundings D. requirements62. A. clubs B. hospitals C. governments D. workplaces63. A. excited B. embarrassed C. thrilled D. frustrated64. A. mismatch B. mistreat C. misunderstanding D. misinterpretation65. A. aging B. training C. schooling D. parentingSection 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.高三英语共10页第5页（A）The twenty-four horses dash around a racetrack. The thunder of their hooves(蹄) rings in the riders’ ears, nearly drowning out the cheering of the crowd. After three or four minutes of suspense, one horse crosses the finish line first, winning the Melbourne Cup and earning a place in history.The horses that compete in the Melbourne Cup—one of the world’s most famous horseraces—were fated to race. Bred for speed, these horses are the few that were singled out as having potential to become champions.Preparing a racehorse to compete requires a team. A horse’s owner manages the team and decides which races to enter. A trainer determines the racehorse’s diet and exercise. Regular exercise makes a horse less likely to be injured, but overtraining tires the horse. A groomer (动物美容师) cares for the racehorse and reports any problems he discovers to the trainer. And of course, no horserace could be run without a rider. These riders train for long hours and travel constantly from one race to another. They need to make a strategy, adapt to changing conditions and communicate with their horse to guide it to victory.Australia’s most famous horserace, the Melbourne Cup, is 3,200 meters of pure excitement. Each year 300 or 400 horses are nominated (提名), but only 24 can run. The competitors are chosen based on a number of factors, but winners of certain races qualify automatically.Each racehorse receives a handicap—a certain weight it must carry to give each horse an equal chance of winning—two months before the race. Originally, horses that seemed likely to win were assigned larger handicaps. But the rules have changed, reducing the handicap for previous winners.The first Melbourne Cup in 1861 drew a crowd of 4,000 spectators, and the race’s popularity has grown since then. Held on the first Tuesday of November, the cup has become a four-day festival with fine food and entertainment.The Melbourne Cup began during a gold rush as a form of entertainment for the rich. Today it still attracts society’s upper class. They come dressed in their finest to enjoy the event in comfort.But anyway it’s all about the race—the effort of horses and riders, the suspense and the thrill of victory.66. What can be learned about the horses in the Melbourne Cup?A. They are all winners of a certain race.B. They are raised and trained by joint effort.C. They are chosen from ordinary horses.D. Their fates are determined by their trainers.67. The racehorses are given handicaps so that _____.A. they will weigh the sameB. previous winners are unlikely to winC. the race will be fair enoughD. they will be more adaptable to the race68. It can be learned from the passage that _____.A. the spectators of the Melbourne Cup must dress wellB. the Melbourne Cup was intended for wealthy peopleC. the winner of the Melbourne Cup can earn a large fortuneD. the Melbourne Cup is the best-known horserace worldwide69. The passage can most probably be found in _____.A. a sports journalB. a business newspaperC. an academic paperD. a health magazine高三英语共10页第6页（B）Down County Museum - Open and Free What’s OnContact detailsThe Mall, Downpatrick, County Down, BT30 6AH Telephone: +44 (0) 28 4461 5218Fax: +44 (0) 28 4461 5590Email: mail@ Opening hoursMonday to Friday 10.00 am - 5.00 pmSaturdays and Sundays 1.00 pm - 5.00 pmAdmission freeThere is however a charge for some special events and for guided tours.In the Footsteps of St Patrick12 November 2015 - 24 April 2016 at Down County MuseumThe aim of this exhibition is to explore some of the local sites, monumentsand archaeological(考古的) discoveries which are linked to the earlymissionary work of St Patrick and his followers, and to his Early Christian heritage (遗产) in County Down.This PEACE III funded display, featuring wonderful photographs, is in English and Polish and is accompanied by a free leaflet, also in both languages.Admission FREE.From Ballyhosset to Bengal03 February 2016 - 31 December 2016 at Down County MusuemThis display features a selection of documents, photographs, medicalinstruments and uniforms belonging to Lieutenant-Colonel Alexander Silcock,which were recently donated to Down County Museum.Admission FREE.1916 and After28 April 2016 - 01 May 2016 at Down County MuseumThis exhibition has been created by Down County Museum and Newry andMourne Museum to mark the 100th anniversary of the 1916 Rising. Theexhibition provides an overview Rising and will explore a selection of themes including how the Rising was reported in local newspapers and its impact on local politics and society. Pre-booking essential.Admission FREE.Essence of Form: The Applied Art Collection of Down County Museum03 May 2016 - 30 October 2016 at Down County MuseumThis exhibition displays the applied art collection of Down County Museum.Collected over 25 years, the exhibition includes ceramics (陶瓷制品), textile(纺织的) pieces, silversmithing and jewellery made by artists living andworking in County Down.Admission FREE.70. Which exhibition is related to religion?A. In the Footsteps of St Patrick.B. From Ballyhosset to Bengal.C. 1916 and After.D. Essence of Form.高三英语共10页第7页71. Which exhibition needs to be reserved in advance?A. In the Footsteps of St Patrick.B. From Ballyhosset to Bengal.C. 1916 and After.D. Essence of Form.72. Mr. Smith, who is interested in the works of art in Down County Museum, can go to visit themuseum on ______.A. April 25, 2016.B. April 29, 2016.C. June 18, 2016.D. November 3, 2016.73. It can be learned from the above introduction that _____.A. Admission to Down County Museum is always free.B. Down County Museum is open for a shorter time on weekdays.C. All the exhibitions are held by Down County Museum independently.D. The exhibits in “From Ballyhosset to Bengal” have long belonged to the museum.（C）Fed up with constantly having to recharge or replace batteries in your ever-expanding electronic devices? The solution may be just a few steps away.“Energy harvesting” promises to power countless consumer devices, often with nothing more than your body’s movement or heat. Dozens of companies around the world already offer such products, but many experts believe the market for the technology could explode due to electronic devices being developed for the Internet of Things.“It’s huge,”said Graham Martin, CEO of the EnOcean Alliance, a San Ramon-based group of businesses that promotes wireless energy-harvesting technologies. With the Internet of Things expected to combine billions of devices, “if they are all battery-powered, we’ll have a problem because there’s not enough lithium (锂) in the world,” he added. “So a lot of them will have to use energy harvesting.”Among the most basic forms of the technology is body power. When certain materials are squeezed or stretched, the movement of their atoms creates an electrical charge. Automatic watches have employed the concept for decades, for example, by winding themselves when their user moves their arm. Now, the concept is being considered for a number of other devices.In a contest seeking visionary ideas for wearable technologies, Intel awarded $5,000 for a concept to change the temperature difference between a person’s body and a special piece of clothing they’d wear into electricity for mobile devices.Using sound to power devices is another energy-harvesting variation. Stanford University engineers are testing smart microchips (芯片) that create electricity from ultrasound (超声波) to power implantable (可植入的) devices that can analyze a person’s nervous system or treat their diseases.A textile(纺织品) research association in Spain is proposing to obtain electricity from radio waves that flow around everyone to power sensors sewn into clothes, which can monitor a person’s heartbeat or other vital signs.Research firm IDTechEx has estimated that annual global sales of energy-harvesting products could hit $2.6 billion by 2024, while WinterGreen Research predicts sales of $4.2 billion by 2019.Obtaining stable energy from devices can be complex, however. For one thing, the motion that generates the electricity has to be constant to be useful. Moreover, the amount of power the devices produce depends on the person using them, according to a Columbia University study. It determined高三英语共10页第8页that taller people on average provide about 20 percent more power than shorter ones when walking, running or cycling.It’s also unclear how eagerly consumers might welcome energy-harvesting products. While such devices are expected to cost less than battery-powered alternatives when compared over many years, experts say, people may continue buying ones with batteries merely because those would be cheaper in the short term.74. Which “explode” in the following sentences has the most similar meaning to the word “explode” inParagraph 2?A. They were clearing up when the second bomb exploded.B. The continued tension could explode into more violence.C. The population exploded to 40,000 during the last tourist season.D. The boss exploded when he heard of the resignation of the secretary.75. What makes “energy harvesting” necessary according to the passage?A. The waste of lithium in the world.B. The increasing number of electronic devices.C. The development of technology.D. The pollution caused by batteries.76. It can be learned from the passage that _____.A. energy-harvesting products save money in the long runB. taller people can surely produce a larger amount of powerC. automatic watches harvest energy from the user s’ body heatD. two ways of harvesting energy are mentioned in the passage77. Which of the following might be the best title for the passage?A. Energy harvesting: a low-risk technologyB. Energy harvesting: a high-profit technologyC. Energy harvesting: a problem-free technologyD. Energy harvesting: an environment-friendly technologySection CDirections: Read the passage carefully. Then answer the questions or complete the statements in the fewest possible words.Want to attract and keep top talent? Here’s a suggestion: Make a flexible work schedule part of the deal.A survey this summer of 1,215 U.S. managers and employees across a variety of industries, by EY (formerly Ernst & Young), found those aged 18 to 32 rank flexibility among the perks (特殊待遇) they want most, with 33% saying they wouldn’t work anywhere that didn’t offer it.B ut it seems those aged 33 to 48 value flextime even more: 38% of them consider it non-negotiable, with men who said so, at 40%, slightly outnumbering women (37%).“Companies first started offering flexible schedules, in the late 80s and the 90s, as a way t o recruit (招募) and keep talented women, but it’s gone way beyond that now,” observes Karyn Twaronite, an EY partner who came up through the tax side of the business.Noting that both men and women, in all age groups, ranked flextime (弹性工作制) tops among non-cash perks, Twaronite adds, “That result mirrors exactly what we’re seeing here at EY.” The高三英语共10页第9页accounting and consulting giant, No. 57 on Fortune’s Best Companies to Work For, has had thousands of employees working flexible schedules for years—including, since 2004, six weeks’ of paid leave for new dads.“Flextime may have started out as a women’s issue, but it’s changed into something that people of both sexes have come to expect,” he adds. “I think it’s partly because of the large number of two-career households now, where people have to adapt to two demanding professional schedules instead of just one.”The EY survey suggests that, in the next decade or so, the opportunity for a life outside the office will become an even bigger draw than it already is. Most of those surveyed still work a set schedule, the report notes, but “respondents expect a shift in the coming years to more flexible hours, as 62% currently work standard office hours and only 50% expect to do so in five to ten years.”That doesn’t surprise Twaronite. “Work is changing,” she observes. “The technology to connect anywhere and anytime means that people are expected to be on call 24 hours a day, especially in global companies that operate across different time zones. The other side of that is that employers are adapting to people’s lives outside of work—because they have to be.”(Note: Answer the questions or complete the statements in NO MORE THAN TEN WORDS.)78. What is the main finding of the survey?79. Flextime was originally aimed at _____.80. The result of the survey is caused by the fact that _____.81. What makes flextime possible according to Twaronite?第Ⅱ卷（共47分）I. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.1. 出国对于这个高中生来讲根本没有吸引力。

2016年全国普通高等学校招生统一考试(上海数学模拟试卷二)

2016年全国普通高等学校招生统一考试上海数学模拟试卷二 (理工农医类)考生注意：1.答卷前，务必用钢笔或圆珠笔在答题纸正面清楚地填写姓名、准考证号、，并将核对后的条形码贴在制定位置上，在答题纸反面清楚地填写姓名。

2.本试卷共有23道试题，满分150分，考试时间120分钟。

一、填空题(共14题，满分56分)1. 已知集合A=｛-2，-1,0,2｝，B=｛x|（X-1）（x+2）＜0｝,则A∩B= ．2.等比数列｛a n ｝满足a 1=3，a 1+ a 3+ a 5=21，则a 3+ a 5+ a 7 = ．3. 设向量，不平行，向量与平行，则实数_________．4. i 为虚数单位，607i 的共轭．．复数．．为．5. 在极坐标系中，点π23⎛⎫ ⎪⎝⎭‚到直线()cos 6ρθθ+=的距离为．6. 我国古代数学名著《数书九章》有“米谷粒分”题：粮仓开仓收粮，有人送来米1534 石，验得米内夹谷，抽样取米一把，数得254粒内夹谷28粒，则这批米内夹谷约为 ________.7. 已知向量OA AB ⊥，||3OA =，则OA OB ⋅= ．8. 设为等比数列的前项和，若，且成等差数列，则 . 9. 用数字0，1，2，3，4，5组成没有重复数字的五位数，其中比40000大的偶数共有 _______.10. 设a ，b 都是不等于1的正数，则“333a b>>”是“log 3log 3a b <”的条件.11. 某食品的保鲜时间y （单位：小时）与储存温度x （单位：C ）满足函数关系bkx ey +=（ 718.2=e 为自然对数的底数，k 、b 为常数）。

若该食品在0C的保鲜时间设计192小时，在22C 的保鲜时间是48小时，则该食品在33C的保鲜时间是小时.12. 如图，四边形ABCD 和ADPQ 均为正方形，它们所在的平面互相垂直，动点M 在线段PQ上，E 、F 分别为AB 、BC 的中点。

上海市2016普陀高考预测卷(文理合卷)资料

2015学年第二学期普陀区高三数学质量调研卷2016.4 考生注意:1. 答卷前,考生务必在答题纸上将姓名、考试号填写清楚，并在规定的区域贴上条形码.2. 本试卷共有23题，满分150分，考试时间120分钟.3. 本试卷另附答题纸，每道题的解答必须写在答题纸相应位置，本卷上的任何解答都不作评分依据. 一填空题（本大题共有14题，满分56分）考生应在答题及纸相应编号的空格内直接填写结果，每个空格填对得4分，否则一律得零分. 1. 若集合{}R x x y x A ∈-==,1|，{}R x x x B ∈≤=,1|||，则=B A .2. 若函数xx f 11)(+=()0>x 的反函数为)(1x f -，则不等式2)(1>-x f 的解集为 . 3.【理科】若53sin =α且α是第二象限角，则=⎪⎭⎫⎝⎛-42cot πα . 【文科】【理科】若53sin =α且α是第二象限角，则=⎪⎭⎫ ⎝⎛-4tan πα . 4. 若函数)(x f 是定义在R 上的奇函数，且满足)()2(x f x f -=+，则=)2016(f . 5. 在831⎪⎭⎫ ⎝⎛-x x 的展开式中，其常数项的值为 .6.若函数x x f 2sin )(=，⎪⎭⎫⎝⎛+=6)(πx f x g ，则函数)(x g 的单调递增区间为 . 7.【理科】设P 是曲线⎪⎩⎪⎨⎧==θθtan sec 22y x （θ为参数）上的一动点，O 为坐标原点，M 为线段OP 的中点，则点M 的轨迹的普通方程为 .【文科】设P 是曲线1222=-y x 上的一动点，O 为坐标原点，M 为线段OP 的中点，则点M 的轨迹方程为 .8.【理科】在极坐标系中，O 为极点，若⎪⎭⎫ ⎝⎛6,1πA ，⎪⎭⎫⎝⎛32,2πB ，则△AOB 的面积为 . 【文科】不等式组⎪⎩⎪⎨⎧≥+-≥+≤0203y x y x x 所表示的区域的面积为 .9.【理科】袋中装有5只大小相同的球，编号分别为5,4,3,2,1，现从该袋中随机地取出3只，被取出的球中最大的号码为ξ，则=ξE .【文科】袋中装有5只大小相同的球，编号分别为5,4,3,2,1，若从该袋中随机地取出3只，则被取出的球的编号之和为奇数的概率是（结果用最简分数表示）.10．若函数x x f 5log )(=（0>x ），则方程1)3()1(=-++x f x f 的解=x .11.某同学用球形模具自制棒棒糖.现熬制的糖浆恰好装满一圆柱形容器（底面半径为3cm ，高为10cm ），共做了20颗完全相同的棒棒糖，则每个棒棒糖的表面积为 2cm （损耗忽略不计）. 12. 如图所示，三个边长为2的等边三角形有一条边在同一直线上，边33C B 上有10个不同的点1021,,,P P P ，记i i AP AB M ⋅=2 （10,,2,1 =i ），则=+++1021M M M .13．设函数⎩⎨⎧>-≤+=-0),1(0,2)(x x f x a x f x ，记x x f x g -=)()(，若函数)(x g 有且仅有两个零点，则实数a 的取值范围是 .14. 已知*N n ∈，从集合{}n ,,3,2,1 中选出k （N k ∈,2≥k ）个数k j j j ,,,21 ，使之同时满足下面两个条件：①n j j j k ≤<<≤ 211； ②m j j i i ≥-+1（1,,2,1-=k i ），则称数组()k j j j ,,21为从n 个元素中选出k 个元素且限距为m 的组合，其组合数记为()m k n C ,. 例如根据集合{}3,2,1可得()31,23=C .给定集合{}7,6,5,4,3,2,1，可得()=2,37C .二、选择题（本大题共有4题，满分20分）每题有且只有一个正确答案，考生应在答题纸的相应编号上，将代表答案的小方格涂黑，选对得5分，否则一律得零分.15. 若a 、b 表示两条直线，α表示平面，下列命题中的真命题为（）（A ）若α⊥a ，b a ⊥，则α//b （B ）若α//a ，b a ⊥，则α⊥b （C ）若α⊥a ，α⊆b ，则b a ⊥ （D ）若α//a ，α//b ，则b a //16.过抛物线x y 82=的焦点作一条直线与抛物线相交于A 、B 两点，且这两点的横坐标之和为9，则满足条件的直线（）（A ）有且只有一条（B ）有两条（C ）有无穷多条（D ）必不存在 17.若z C ∈，则“1Im ,1Re ≤≤z z ”是“1||≤z ”成立的条件.（）（A ）充分非必要（B ）必要非充分（C ）充要（D ）既非充分又非必要18. 对于正实数α，记αM 是满足下列条件的函数)(x f 构成的集合：对于任意的实数R x x ∈21,且21x x <，都有()()121212)()(x x x f x f x x -<-<--αα成立.下列结论中正确的是（）（A ）若21)(,)(ααM x g M x f ∈∈，则21)()(αα⋅∈⋅M x g x f （B ）若21)(,)(ααM x g M x f ∈∈且0)(≠x g ，则21)()(ααM x g x f ∈ （C ）若21)(,)(ααM x g M x f ∈∈，则21)()(αα+∈+M x g x f（D ）若21)(,)(ααM x g M x f ∈∈且21αα>，则21)()(αα-∈-M x g x f三、解答题（本大题共有5题，满分74分）解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤.19.（本题满分12分）【文科】在正四棱柱1111D C B A ABCD -中，底面边长为1，体积为2，E 为AB 的中点，证明：E A 1与B C 1是异面直线，并求出它们所成的角的大小（结果用反三角函数值表示）.【理科】在正四棱柱1111D C B A ABCD -中，底面边长为1，B C 1与底面ABCD 所成的角的大小为2arctan ，如果平面11C BD 与底面ABCD所成的二面角是锐角，求出此二面角的大小（结果用反三角函数值）20.（本题满分14分）本题共有2个小题，第1小题满分6分，第2小题满分8分. 【理科】已知函数x x x f cos 3sin 2)(⋅⎪⎭⎫⎝⎛+=π 【文科】已知函数)(x f x x x 2cos 3cos sin += （1）若20π≤≤x ，求函数)(x f 的值域；（2）设ABC ∆的三个内角C B A ,,所对的边分别为c b a ,,，若A 为锐角且23)(=A f ，2=b ，3=c ，1 1AA 1A求)cos(B A -的值.21.（本题满分14分）本题共有3个小题，第1小题满分6分，第2小题满分8分，某企业参加A 项目生产的工人为1000人，平均每人每年创造利润10万元.根据现实的需要，从A 项目中调出x 人参与B 项目的售后服务工作，每人每年可以创造利润⎪⎭⎫⎝⎛-500310x a 万元（0>a ），A 项目余下的工人每人每年创造利润需要提高%2.0x（1）若要保证A 项目余下的工人创造的年总利润不低于原来1000名工人创造的年总利润，则最多调出多少人参加B 项目从事售后服务工作？（2）在（1）的条件下，当从A 项目调出的人数不能超过总人数的%40时，才能使得A 项目中留岗工人创造的年总利润始终不低于调出的工人所创造的年总利润，求实数a 的取值范围.22.（本题满分14分）本题共有2个小题，第1小题满分4分，第2小题满分6分. 第3小题满分6分.已知椭圆Γ：14522=+y x 的中心为O ，一个方向向量为),1(k d =的直线l 与Γ只有一个公共点M （1）若1=k 且点M 在第二象限，求点M 的坐标；（2）若经过O 的直线1l 与l 垂直，求证：点M 到直线1l 的距离25-≤d ；（3）若点N 、P 在椭圆上，记直线ON 的斜率为1k ，且为直线OP 的一个法向量，且541=k k 求22OP ON +的值.23.（本题满分18分）本题共有3个小题，第1小题满分4分，第2小题满分6分，第3小题满分8分.已知各项不为零的数列{}n a 的前n 项和为n S ，且11=a ，121+⋅=n n n a a S （*N n ∈）（1）求证：数列{}n a 是等差数列；（2）设数列{}n b 满足：122+-=n n a a n b ，且()3841lim 1211=+++++++∞→n n k k k k n b b b b b b ，求正整数k 的值；（3）若m 、k 均为正整数，且2≥m ，m k <，在数列{}k c 中，11=c ，11++-=k k k a mk c c ，求m c c c +++ 21.2015学年第二学期普陀区高三数学质量调研评分细则二填空题（本大题共有14题，满分56分）考生应在答题及纸相应编号的空格内直接填写结果，每个空格填对得4分，否则一律得零分.1.{}12. ⎪⎭⎫⎝⎛231， 3.【理科】2 【文科】7- 4. 0 5. 286.⎥⎦⎤⎢⎣⎡+-12,125ππππk k ，z k ∈7.14822=-y x . 8.【理科】1.【文科】16 9.【理科】29【文科】5210．4. 11.π9. 12. 180 13． 2->a 14. 10二、选择题（本大题共有4题，满分20分）每题有且只有一个正确答案，考生应在答题纸的相应编号上，将代表答案的小方格涂黑，选对得5分，否则一律得零分.三、解答题（本大题共有5题，满分74分）解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤.19.（本题满分12分）【文科】【解】根据已知条件,C C 1为正四棱柱1111D C B A ABCD -的高底面四边形11ABB A 是正方形，且面积为1, 故由sh V =2=，可得21=C C .……2分假设E A 1与B C 1不是异面直线，则它们在同一平面内由于点1A 、E 、B 在平面11ABB A 内，则点1C 也在平面11ABB A 内，这是不可能的，故E A 1与B C 1是异面直线.…………5分取11B A 的中点为E ，连接BE ,1EC ,所以E A BE 1//,1EBC ∠或其补角，即为异面直线E A 1与B C 1所成的角.……7分在1BEC ∆，51=BC ,217=BE ,251=EC ,……9分由余弦定理得，8585821752454175cos 1=⨯-+=∠EBC 0>,即85858arccos 1=∠EBC ，…11分1 1A所以异面直线E A 1与B C 1所成的角的大小为85858arccos.……12分【理科】【解】根据题意，可得⊥C C 1底面ABCD ，所以BC 是B C 1在平面ABCD 上的射影，故BC C 1∠即为直线B C 1与底面ABCD 所成的角，即BC C 1∠=2arctan .……2分在BC C RT 1∆中，2tan 11=∠⋅=BC B BC C C ……3分以D 为坐标原点，以射线1,,DD DC DA 所在的直线分别为建立空间直角坐标系，如图所示：由于D D 1⊥平面ABCD ，故1DD 是平面的一个法向量，且1DD ()0,1,1B ,()1,0,01D ,()2,1,01C ,故()2,1,11--=,()2,0,11-=……7分设()z y x ,,=是平面11C BD 的一个法向量,所以⎪⎩⎪⎨⎧=⋅=⋅0011BC n BD ,即⎩⎨⎧=-=-+0202z x z y x ,不妨取1=z ,则⎩⎨⎧==02y x ,即()1,0,2=……9分设平面11C BD 与底面ABCD 所成的二面角为θ,则5552120002cos =⨯⨯+⨯+⨯==θ, 即55arccos=θ……11分所以平面11C BD 与底面ABCD 所成的二面角大小为55arccos.……12分 20.（本题满分14分）本题共有2个小题，第1小题满分6分，第2小题满分8分. 20.【解】（1）()x x x x f cos cos 3sin )(+=x x x 2cos 3cos sin +=232cos 232sin 21++=x x 2332sin +⎪⎭⎫ ⎝⎛+=πx …………2分A1A由20π≤≤x 得，34323πππ≤+≤x ，132sin 23≤⎪⎭⎫ ⎝⎛+≤-πx …………4分 2312332sin 0+≤+⎪⎭⎫ ⎝⎛+≤πx ，所以函数)(x f 的值域为⎥⎦⎤⎢⎣⎡+231,0………6分（2）由232332sin )(=+⎪⎭⎫⎝⎛+=πA A f 得，032sin =⎪⎭⎫ ⎝⎛+πA 又由20π<<A 得，34323πππ<+<A ，只有ππ=+32A ，故3π=A .…………8分在ABC ∆中，由余弦定理得，A bc c b a cos 2222-+=73cos 32294=⨯⨯⨯-+=π,故7=a …………10分由正弦定理得，B b A a sin sin =，所以721sin sin ==a A b B 由于a b <，所以772cos =B …………12分 ()B A B A B A sin sin cos cos cos +=-14757212377221=⨯+⨯=……14分 21.（本题满分14分）本题共有3个小题，第1小题满分6分，第2小题满分8分，【解】（1）根据题意可得，()()≥⨯+-%2.010101000x x 101000⨯……3分展开并整理得，05002≤-x x ……5分解得5000≤≤x ，最多调出的人数为500人……6分（2）⎩⎨⎧⨯≤≤≤%4010005000x x ，解得4000≤≤x ……7分()()%2.010101000500310x x x x a ⨯+⋅-≤⨯⎪⎭⎫ ⎝⎛-，对于任意的[]400,0∈x 恒成立……9分即%210201010005031022x x x x ax --+⨯≤- 即10002502++≤x x ax 对于任意的[]400,0∈x 恒成立……10分当0=x 时，不等式显然成立；当4000≤<x 时，1250000250111000250+⎪⎭⎫ ⎝⎛+=++≤x x x x a ……11分令函数xx x f 250000)(+=，可知函数)(x f 在区间[]400,0上是单调递减函数……12分故()1025400)(min ==f x f ，故1.511000250≥++xx ……13分故1.50≤<a ，所以实数a 的取值范围是1.50≤<a ……14分22.（本题满分14分）本题共有2个小题，第1小题满分4分，第2小题满分6分. 第3小题满分6分. 【解】（1）设直线l ：m x y +=，根据题意可得：……1分⎪⎩⎪⎨⎧=++=14522y x mx y ，消去y 并整理得()04510922=-++m bx x ……①…………2分 ()()045941022=-⨯⨯-=∆b b ，解得92=m ，因为M 在第二象限，故3=m ，……3分代入①得0253092=++x x ，解得35-=x ，进而34=y ，故⎪⎭⎫⎝⎛-34,35M .……4分（2）根据题意可得，直线1l ：0=+ky x ……5分设直线l ：m kx y +=（0≠m ），则⎪⎩⎪⎨⎧=++=14522y x mkx y ……5分消去y 得()()0451054222=-+++m kmx xk……6分()()()0454*******=-⋅+-=∆m k km ，解得04522=+-m k ，即4522+=k m ……7分且4552+-=k km x ，4542+=k m y ，故⎪⎭⎫ ⎝⎛++-454,45522k m k kmM ……8分点M 到直线1l 的距离222221451454455kk km kk kmk km d ++=++++-=()()22541k k k++=① 当0=k 时，0=d ；……9分 ② 当0≠k 时，=d 25945122-≤++k k ，当且仅当454±=k 时等号成立. 综上①②可得，点M 到直线1l 距离25-≤d .……10分（3）根据条件可得直线OP 的斜率kk 12-=，……11分由于541=k k ，则直线ON 的斜率的k k 541=……12分于是直线ON 的方程为kx y 54=，由⎪⎪⎩⎪⎪⎨⎧==+kxy y x 5414522，可得224525k x +=……13分设点),(11y x P ，则222122121245162525161k kx k y x OP ++=⎪⎭⎫ ⎝⎛+=+=……14分同理2ON()22222245120kk y x ++=+=……15分 22ONOP +=22451625k k +++()2245120k k ++945364522=++=k k ……16分 23.（本题满分18分）本题共有3个小题，第1小题满分4分，第2小题满分6分，第3小题满分8分. 【解】（1）当1=n 时，121211==a a S ，11=a ，故22=a ；……1分当2≥n 时，=-=-1n n n S S a -⋅+121n n a a n n a a ⋅-121变形得()112-+-⋅=n n n n a a a a ，由于0≠n a ，所以211=--+n n a a ……2分所以1212-=-n a n ，n a n 22=，*N n ∈，于是n a n =，*N n ∈.……3分由于11=-+n n a a ，所以数列{}n a 是以1首项，1为公差的等差数列.…………4分（2）由（1）得n a n =，所以122+-=n n a a n b nn n ⎪⎭⎫⎝⎛⋅==+-21412)1(2……5分 52121++⎪⎭⎫ ⎝⎛=⋅n n n b b ，且128121=b b ，当2≥n 时，4111=-+n n n n b b b b …………7分故数列{}1+n n b b 是以1281为首项，41为公比的等比数列.……8分于是()=+++++++∞→1211lim n n k k k k n b b b b b b =-+4111k k b b 3841，即912-+=⋅k k b b ……9分 k kk k b b 251241321--+=⎪⎭⎫⎝⎛=⋅，故92522---=k ，解得2=k .…………10分（3）则由（1）得k a k =，11++-=k k k a m k c c 1+-=k m k ，12211c cc c c c c k k k k k ⋅⋅⋅=--- ……12分 ()()kmk k k C mk k k m k m c 1112)1()2)(1(111⋅-=⋅⋅-⋅+-+-⋅-=-- …………14分 m c c c +++ 21()[]m m m m m m C C C C m 132111--+-+-=…………16分 ()()[]m C C C C m m m m m m m 1111210=-+-+--= 故m c c c +++ 21m1=.……18分。

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