2018年上海普陀区高三一模试题(附答案)

2018届上海市普陀区高三质量调研(一模)物理试题及答案1 精品

2018届上海市普陀区高考物理一模试卷参考答案与试题解析一．单项选择题（共16分，每題2分，每题只有一个正确选项．）1．“韦/米2”为磁感应强度的单位，它和下面哪个单位相同（）A．牛/（安•米）B．牛•安/米C．牛•安/米2D．牛/（安•米2）分析：“韦/米2”为磁感应强度的单位，在国际单位制中磁感应强度的单位是T，根据磁感应强度的定义式B=分析单位关系．解答：解：在国际单位制中磁感应强度的单位是T，1特=1韦/米2，根据磁感应强度的定义式B=可知，1特=1牛/（安•米）．故A正确，BCD错误．故选：A点评：对于单位关系，往往要根据物理规律即公式进行推导．2．关于惯性，下列说法中正确的是（）A．静止的物体没有惯性B．物体运动速度大时惯性大C．航天员在空间站中失去惯性 D．物体在任何情况下都有惯性考点：惯性．分析：一切物体在任何情况下都有惯性，惯性的大小只与物体的质量有关．解答：解：A、惯性大小只与物体的质量有关，而与其他因素无关，故A错误；B、惯性的大小只与物体的质量有关，与速度无关，故B错误；C、任何物体在任何情况下都有惯性，那么就不存在没有惯性的物体，故C错误；D、任何物体在任何情况下都有惯性，故D正确；故选：D点评：惯性是物理学中的一个性质，它描述的是物体能够保持原来的运动状态的性质，不能和生活中的习惯等混在一起．解答此题要注意：一切物体任何情况下都具有惯性．惯性只有在受力将要改变运动状态时才体现出来．3．对于万有引力定律的表达式，下列说法正确的是（）A．G是引力常量，是人为规定的B．当r等于零时，万有引力为无穷大C．两物体受到的引力总是大小相等，与两物体质量是否相等无关D．r是两物体间最近的距离考点：万有引力定律及其应用．专题：万有引力定律的应用专题．分析：1、万有引力定律内容：自然界中任何两个物体都相互吸引，引力的方向在它们的连线上，引力的大小与物体的质量m1和m2的乘积成正比、与它们之间距离r的二次方成反比．2、表达式：F=G，G为引力常量：G=6.67×10﹣11N•m2/kg2．3、适用条件：（1）公式适用于质点间的相互作用．当两物体间的距离远远大于物体本身的大小时，物体可视为质点．（2）质量分布均匀的球体可视为质点，r是两球心间的距离．解答：解：A、公式中引力常量G的值是卡文迪许在实验室里用实验测定的，而不是人为规定的，故A错误；B、当两个物体间的距离趋近于0时，两个物体就不能视为质点了，万有引力公式不再适用，故B错误；C、力是物体间的相互作用，万有引力同样适用于牛顿第三定律，即两物体受到的引力总是大小相等，与两物体是否相等无关，故C正确；D、r是两质点间的距离；质量分布均匀的球体可视为质点，r 是两球心间的距离；故D错误；故选：C．点评：本题关键明确万有引力定律的适用条件和万有引力常量的测量，基础题．4．如图，当逻辑电路中的A、B两端分别输入电信号“1”和“0”时，在C和D端输出的电信号分别为（）5．（2分）（2018•普陀区一模）如图，一颗小弹丸从离水面不高处落入水中，溅起的几个小水珠可以跳得很高（不计能量损失），下列说法正确的是（）6．（2分）（2018•普陀区一模）如图，一辆轿车正在水平路面上转弯时，下列说法正确的是（）7．（2分）（2018•普陀区一模）如图，绝缘金属小球A、B带同种电荷，用丝线相连．A球固定不动，B球从丝线处于水平位置由静止开始释放．下列说法正确的是（）8．（2分）（2018•普陀区一模）如图，在水平放置的螺线管的中央，放着一个可绕水平轴OO′自由转动的闭合线圈abcd，轴OO′与螺线管的轴线垂直，ab边在OO′轴的左上方，闭合k的瞬间，关于线圈的运动情况，下列说法正确的是（）二、单项选择题（共24分，每题3分，每题只有一个正确选项．）9．（3分）（2018•普陀区一模）如图，水平桌面上叠放着甲、乙两个物体，拉力F作用在乙上，甲、乙一起相对桌面向右做匀减速直线运动，乙物体受到的作用力有（）10．（3分）（2018•普陀区一模）如图，是质点做直线运动的速度﹣时间图象，该质点（），故=1m11．（3分）（2018•普陀区一模）如图，有一轻圆环和插栓，在甲、乙、丙三个力作用下平衡时，圆环紧靠着插栓．不计圆环与插栓间的摩擦，若只调整两个力的大小，欲移动圆环使插栓位于圆环中心，下列说法正确的是（）12．（3分）（2018•普陀区一模）如果闭合电路中电源的电动势为12V，外电压为10V，当有0.5C电量通过电路时，下列结论正确的是（）13．（3分）（2018•普陀区一模）在高度h=45m处竖直上抛一小球，比与它同时在同一高度自由下落的另一小球迟t=1s落到地上，不计空气阻力，则竖直上抛小球的初速度为（）h=gth=t=h=45=414．（3分）（2018•普陀区一模）如图，用一根螺钉、一节电池、一根导线、一块钕磁铁，可以做一个电动机．先把螺钉和钕磁铁连起来，并把它一头吸在电池的一极上，再用导线把电池和螺钉尾端的钕磁铁连接起来，螺钉就会转动．下列说法正确的是（）15．（3分）（2018•普陀区一模）如图，由均匀的电阻丝组成的等边三角形导体框，垂直磁场放置，将AB两点接入电压恒定的电源两端，通电时，线框受到的安培力为F，若将ACB边移走，则余下线框受到的安培力大小为（）F F F FL==16．（3分）（2018•普陀区一模）一质点做匀加速直线运动时，速度变化△v时发生位移x1，紧接着速度变化同样的△v时发生位移x2，则该质点的加速度为（））a=三．多项选择题（共16分，每小题4分，每小题有二个或三个正确选项，全选对的，得4分，选对但不全的，得2分，有选错或不答的，得0分．）17．（4分）（2018•普陀区一模）如图，将两根吸管串接起来，再取一根牙签置于吸管中，前方挂一张薄纸，用同样的力对吸管吹气，牙签加速射出，击中薄纸．若牙签开始是放在吸管的出口处，则牙签吹在纸上即被阻挡落地；若牙签开始时放在近嘴处，则牙签将穿入薄纸中，有时甚至射穿薄纸．下列说法正确的是（）mv18．（4分）（2018•普陀区一模）如图，矩形abcd为匀强磁场区域，磁场方向竖直向下，圆形闭合金属线圈以一定的速度沿光滑绝缘水平面向磁场区域运动．下图是线圈的四个可能到达的位置，则线圈的动能可能为零的位置是（）19．（4分）（2018•普陀区一模）小球从高处下落到竖直放置的轻弹簧上（如图甲），在刚接触轻弹簧的瞬间（如图乙），速度是5m/s，将弹簧压缩到最短（如图丙）的整个过程中，小球的速度v和弹簧缩短的长度△x之间的关系如图丁所示，其中A为曲线的最高点．已知该小球重为2N，弹簧在受到撞击至压缩到最短的过程中始终发生弹性形变，弹簧的弹力大小与形变成正比．下列说法正确的是（）20．（4分）（2018•普陀区一模）如图甲，固定在光滑水平面上的正三角形金属线框，匝数n=20，总电阻R=2.5Ω，边长L=0.3m ，处在两个半径均为r=的圆形匀强磁场区域中．线框顶点与右侧圆中心重合，线框底边中点与左侧圆中心重合．磁感应强度B 1垂直水平面向外，大小不变；B 2垂直水平面向里，大小随时间变化，B 1、B 2的值如图乙所示．（）=1×0.5×q=t=Rt==四．填空题（共20分，每小题4分．）21．（4分）（2018•普陀区一模）如图，一棵树上与A等高处有两个质量均为0.2kg的苹果，其中一个落入B处的篮子里，若以沟底D处为零势能参考面，则此时该苹果的重力势能为8.8 J；另一个落到沟底的D处，若以C处为零势能参考面，则此时该苹果的重力势能为﹣6 J．22．（4分）（2018•普陀区一模）在如图所示的电路中，已知定值电阻为R，电源内阻为r，电表均为理想电表．将滑动变阻器滑片向下滑动，电流表A示数变化量的绝对值为△I，则电压表V1示数变化量的绝对值△U1= △IR，电压表V2示数变化量的绝对值△U2= △I•r ．，则得：23．（4分）（2018•普陀区一模）如图，P是水平放置的足够大的圆盘，绕经过圆心O点的竖直轴匀速转动，在圆盘上方固定的水平钢架上，吊有盛水小桶的滑轮带动小桶一起以v=0.1m/s的速度匀速向右运动，小桶底部与圆盘上表面的高度差为h=5m．t=0时，小桶运动到O点正上方且滴出第一滴水，以后每当一滴水刚好落在圆盘上时桶中恰好再滴出一滴水，不计空气阻力，若要使水滴都落在圆盘上的同一条直径上，圆盘角速度的最小值为ω，则ω=πrad/s，第二、三滴水落点的最大距离为d，则d= 0.5 m．t=rad/s=π rad/s．24．（4分）（2018•普陀区一模）如图，光滑绝缘细管与水平面成30°角，在管的上方P点固定一个点电荷+Q，P点与细管在同一竖直平面内，管的顶端A与P点连线水平，PB⊥AC，AB=BC=15cm，B是AC的中点．电荷量为+q的小球（小球直径略小于细管内径）从管中A处以速度v=1m/s开始沿管向下运动，在A处时小球的加速度为a=4m/s2．则小球运动到C处速度大小为 2 m/s，加速度大小为 6 m/s2．mg25．（4分）（2018•普陀区一模）如图，重为G 的物体，用绳子挂在支架的滑轮B 上，绳子的另一端接在绞车D 上．转动绞车，物体便能升起．设滑轮的大小及轴承的摩擦略去不计，杆AB和BC 的质量不计，A 、B 、C 三处均用铰链连接．当物体处于平衡状态时，杆AB 所受力的大小为 2.73G ，杆BC 所受力的大小为 3.73G ．五．实验题（共24分）26．（4分）（2018•普陀区一模）1825年，科拉顿做了这样一个实验，他将一个磁铁插入连有灵敏电流计的闭合线圈，观察在线圈中是否有电流产生．在实验时，科拉顿为了排除磁铁移动时对灵敏电流计的影响，他通过很长的导线把接在闭合线圈上的灵敏电流计放到隔壁房间．科拉顿在两个房间之间来回跑，始终没看到电流计指针动一下．科拉顿没能看到电流计指针发生偏转的原因是他认为电流是稳定的．若要使科拉顿能看到电流计指针发生偏转，请你提出一种改进的方法将电表等器材置于同一房间．27．（5分）（2018•普陀区一模）在“用DIS研究机械能守恒定律”的实验中，（1）请按正确的实验顺序填写下列步骤：②①④③⑤⑥．①开启电源，运行DIS应用软件，点击实验条目中的“研究机械能守恒定律”软件界面②卸下“定位挡片”和“小标尺盘”，安装光电门传感器并接入数据采集器③摆锤置于A点，点击“开始记录”，同时释放摆锤，摆锤通过D点的速度将自动记录在表格的对应处④把光电门传感器放在大标尺盘最底端的D点，并以此作为零势能点．A、B、C点相对于D点的高度已事先输入，作为计算机的默认值⑤点击“数据计算”，计算D点的势能、动能和机械能⑥依次将光电门传感器放在标尺盘的C、B点，重复实验，得到相应的数据（2）（多选题）除了以上实验步骤，该实验还需要测量的物理量有BCA．摆线的长度 B．摆锤的直径 C．摆锤的质量 D．摆锤下落的时间．28．（7分）（2018•普陀区一模）在研究共点力的合成实验中，（1）甲、乙和丙三位同学在做这个实验时，所用弹簧秤的量程均为0～5N，且事先均调整好了零刻度．如图，他们都把橡皮条的一端固定在木板上的A点，用两个弹簧秤分别钩住橡皮条另一端的细绳套，互成角度地将橡皮条拉到某一确定的O 点，此时细绳都与制图板平行，用F1和F2表示两个弹簧秤的拉力．其中，甲图：F1和F2的方向互相垂直，F1=3.0N、F2=3.8N；乙图：F1和F2方向间的夹角约为60°，F1=F2=4.0N；丙图：F1和F2方向间的夹角约为120°，F1=F2=4.0N．这三位同学中操作不合适的是哪一位？为什么？操作不合适的是乙同学，因为他这两个力的合力超过了弹簧秤刻度的最大值5N，下面再用一个弹簧测力计拉时拉不到O点（2）丁图是一位同学某次实验用两弹簧秤通过细线Oa、Ob 拉橡皮筋OO’的情况，其操作错误或不妥当之处有：细线Oa太短和两细线夹角太小．（至少写两条）≈4.8N．对于乙29．（8分）（2018•普陀区一模）在用多用表测量电阻、电流和电压的实验中，（1）若旋转选择开关，使尖端对准直流电流档，可测出通过A、B两灯的电流．请按要求连接实物图（要求电路中导线不能交叉）．（2）若旋转选择开关，使尖端对准欧姆档，可测出A、B两灯串联的总电阻．请按要求连接实物图（要求电路中导线不能交叉）．（3）如图为用多用电表测未知电阻R的原理图．已知电源电动势为E、内阻为r，滑动变阻器的阻值为R1，灵敏电流计的内阻为Rg．请根据以上物理量说明：当R越小时，相同的电阻变化量对应的电流变化量越大．考点：用多用电表测电阻．专题：实验题．分析：（1）电流表应与被测电路串联，电流从正接线柱流入，从负接线柱流出，根据题目要求连接实物电路图．（2）用欧姆表测电阻，欧姆表与待测电阻并联．（3）欧姆表的工作原理是闭合电路的欧姆定律，应用欧姆定律分析答题．解答：解：（1）电流表测通过A、B两灯的电流，两灯泡与电流表串联，实验电路图如图所示：（2）用多用电表测测出A、B两灯串联的总电阻，两灯泡串联，多用电表选择欧姆档，欧姆表并联在灯泡两端，如图所示：（3）电流变化量：△I=I2﹣I1=﹣=，由上述推导可得，当△R一定时，被测电阻R的阻值越小，|△I|就越大．所以，当R越小时，相同的电阻变化量对应的电流变化量越大．故答案为：（1）如图所示；（2）如图所示；（3）如上所述．点评：本题考查了多用电表的用法，知道电流表、欧姆表的使用方法、应用闭合电路的欧姆定律即可正确解题．六．计算题（共50分）30．（10分）（2018•普陀区一模）跳伞员常常采用“加速自由降落”（即AFF）的方法跳伞．如果一个质量为50kg的运动员在3658m的高度从飞机上跳出，自由降落40s时，竖直向下的速度达到50m/s，然后再打开降落伞（开伞时间不计），假设这一运动是匀加速直线运动．求：（1）运动员平均空气阻力为多大？（2）在开伞时，他离地面的高度是多少？考点：牛顿第二定律；自由落体运动．专题：牛顿运动定律综合专题．分析：根据加速度的定义式求加速度，由牛顿第二定律求阻力；根据运动学公式求高度．解答：解：（1）加速度平均阻力为f，mg﹣f=ma所以f=（50×10﹣50×1.25）=437.5N （2）自由降落的位移为h，开伞时的高度为H，H=H0﹣h=3658﹣1000=2658m答：（1）运动员平均空气阻力为437.5N（2）在开伞时，他离地面的高度是2658m点评：本题综合考查了牛顿第二定律、自由落体公式的联合应用，难度中等．31．（12分）（2018•普陀区一模）一辆车通过一根跨过定滑轮的绳PQ提升井中质量m=10kg的物体．如图，绳的P端拴在车后的挂钩上，Q端拴在物体上．设绳的总长不变，绳的质量、定滑轮的质量和尺寸、滑轮上的摩擦都忽略不计．开始时，车在A点，左右两侧绳都已绷紧并且是竖直的，左侧绳长H=1m．提升时，车加速向左运动，沿水平方向从A经过B驶向C．设A到B的距离H=1m，车经过B点时的速度为v B=5m/s．求：（1）当车运动到B点时，物体升高的高度h；（2）车由A移到B的过程中，绳Q端的拉力对物体做的功W．某同学的解法为：W﹣mgh=mv，代入h和vB的数据，即可求出拉力对物体做的功W．你若认为该同学的结论正确，计算该功大小；你若认为该同学的结论错误，说明理由并求出该功的大小．考点：动能定理；运动的合成和分解．专题：动能定理的应用专题．分析：（1）根据几何关系求解物体升高的高度h．（2）该同学的结论是错误的．因为汽车经过B点时的速度与此时物体的速度不等，应根据速度的分解得到物体的速度，再由动能定理求解功．解答：解：（1）当车运动到B点时，物体升高的高度为：h=﹣H=（﹣1）m=0.41m （2）该同学的结论是错误的．因为绳总长不变，物体的速度与车在同一时刻沿绳方向的速度大小相等，而此刻车的速度方向不沿绳的方向，所以两者的速度大小不相等．如图，将车的速度v沿绳的方向和垂直于绳的方向分解，得：v1=v B cosθ绳Q端拉力对物体是变力做功，可用动能定理求解．则有：W﹣mgh=得：W=mgh+=（10×10×0.41+10×52×cos245°）J=103.5J答：（1）当车运动到B点时，物体升高的高度h是0.41m；（2）该同学的结论是错误的．因为绳总长不变，物体的速度与车在同一时刻沿绳方向的速度大小相等，而此刻车的速度方向不沿绳的方向，所以两者的速度大小不相等．该功的大小为103.5J．点评：本题考查了动能定理和速度的合成和分解综合运用，难度中等，知道汽车沿绳子方向的分速度等于物体的速度．32．（14分）（2018•普陀区一模）如图，A、B是两块竖直放置的平行金属板，相距为2L，两板间有场强为E的匀强电场．A 板上有一小孔（忽略它对两板间电场分布的影响），C、D为水平光滑绝缘轨道．轨道C端有一固定挡板，长为L的轻弹簧左端固定在挡板上，右端固定一块轻小的绝缘薄板Q．一个质量为m，电荷量为q（q＞0）的小球，在电场力作用下由静止开始从两板间的中点P向左运动，穿过小孔后（不与金属板A 接触）与薄板Q一起压缩弹簧．小球从接触Q开始，经历一段时间把弹簧压缩至最短，然后又被弹簧弹回．由于薄板Q的绝缘性能有所欠缺，使得小球每次离开Q瞬间，它的电荷量变成刚与Q接触时电荷量的k倍（k＜1）．不计机械能损失．（1）求弹簧第一次被压缩到最左边时的弹性势能；（2）设小球第n次离开Q向右运动（最远处没有到达B板），速度由v减为零所需时间为t n，求n为多少？（3）设A板的电势为零，当k=时，若小孔右侧的轨道粗糙，且与带电小球间的滑动摩擦力f=qE，求带电小球初、末状态的电势能变化量．考点：电势差与电场强度的关系；弹性势能；功能关系．专题：电场力与电势的性质专题．分析：（1）根据能的转化和守恒定律，即小球在电场力作用下获得动能，与Q接触过程中，全部转化成弹簧的弹性势能．（2）分析知，小球每次离开Q时的速度大小相同，等于小球第一次与Q接触时速度大小v，运动学公式即可求的n．（3）利用动能定理求的弹回两板间后向右运动最远距A板的距离，利用E=qEl求的电势能得变化解答：解：（1）当P由静止释放到弹簧第一次被压缩到最左边的过程中，根据能的转化和守恒定律可得弹性势能为：E P=qEL（2）小球第n次离开Q时，产生的加速度为：a=小球做减速运动所需时间为：t n=小球所带电荷量为：联立解得：所以有：（3）将小球第一次弹回两板间后向右运动最远距A板的距离为L1，则：（qE﹣f）L﹣（kqE+f）L1=0﹣0，L1=L设小球第2次弹回两板间后向右运动最远距A板的距离为L2，则有：，当时，电场力为，即小球将可以保持静止．所以带电小球初、末状态的电势能变化量为：答：（1）求弹簧第一次被压缩到最左边时的弹性势能qEL；（2）n为（3）带电小球初、末状态的电势能变化量为．点评：了解研究对象的运动过程是解决问题的前提，根据题目已知条件和求解的物理量选择物理规律解决问题．要注意小球运动过程中各个物理量的变化．33．（14分）（2018•普陀区一模）光滑的平行金属导轨水平放置，电阻不计，导轨间距为l=1m，左侧接R=0.3Ω的电阻．区域cdef内存在垂直轨道平面向下的有界匀强磁场，磁感应强度B=1T，磁场宽度为s=1.5m．一质量m=1kg，电阻r=0.2Ω的金属棒MN置于导轨上，与导轨垂直且接触良好．金属棒受到水平力F的作用，从磁场的左边界由静止开始做匀加速运动，加速度a=0.5m/s2．（1）求水平力F与速度v的关系；（2）若在金属棒未出磁场区域时撤去外力，此后棒的速度v 随位移x的变化规律满足v=v0﹣x，且棒运动到ef处时恰好静止．①通过计算证明金属棒在撤去外力后的过程满足动能定理．②画出金属棒在整个运动过程中速度随位移的变化所对应的图线（要求有解析过程，并在坐标轴上标出关键点）．考点：导体切割磁感线时的感应电动势；动能定理．专题：电磁感应与电路结合．分析：（1）根据感应电动势、欧姆定律得到电阻R两端的电压与金属棒速度v的关系式，根据速度均匀增大，求出棒的加速度，并解得B．（2）①从这角度去分析证明：安培力做功等于动能的该变量②求出加速阶段的末速度和位移，作出棒在整个运动过程中速度v随位移x变化的图线．解答：解：（1）金属棒受到水平力F的作用，从磁场的左边界由静止开始做匀加速运动，由牛顿第二定律得：F﹣BIl=ma而I=，E=Blv故有：F=+ma=。

上海市普陀区2018届高三物理上学期期末质量抽测(一模)

2018学年度普陀区第一学期高三质量调研物理卷 2018.12.本试卷分第I 卷和第II 卷两部分。

满分150分。

考试时间120分钟。

本试卷g 取10m/s 2，sin37°＝0.6，cos37°＝0.8。

第I 卷(共56分)考生注意：1．答第一卷前，考生务必在答题卡上用钢笔或圆珠笔填写学校、班级、姓名、学生考试编号，并用铅笔正确涂写学生考试编号。

答第二卷前，也务必将自己的学校、班级、姓名、学生考试编号等项目内容在答题纸密封线内的相应位置上填写清楚。

2．第一卷（1—20小题），由机器阅卷，答案必须全部涂写在答题卡上。

考生应将代表正确答案的小方格用2B 铅笔涂黑。

注意试题题号和答题卡上的编号一一对应，不能错位。

答案需要更改时，必须将原选项用橡皮擦去，重新涂写。

答案写在试卷上一律不给分。

一．单项选择题.（共16分，每小題2分，每小题只有一个正确选项，请将答案涂写在答题卡上。

）1．把一根长直导线平行地放在如图所示磁针的正上方附近，当导线中有电流通过时，磁针会发生偏转。

首先观察到这个实验现象的物理学家是（）（A ）奥斯特（B ）爱因斯坦（C ）牛顿（D ）伽利略2．物理学在研究实际问题时，常常进行科学抽象，即抓住研究问题的主要特征，不考虑与当前研究问题无关或影响很小的因素，建立理想化模型．下列选项中不属于物理学中的理想化模型的有（）（A ）质点（B ）力的合成（C ）自由落体运动（D ）点电荷3. 如图所示，某小车司机在行驶途中遇到小狗突然刹车，则下列说法中正确的是（）（A ）刹车时，小车没有惯性（B ）刹车后，小车的动能增加（C ）刹车后，小车没有受到力的作用（D ）以小车为参照物，小狗是运动的4．许多同学都看过杂技演员表演的“水流星”节目，演员将一根细绳系着盛水的杯子，让杯子在竖直平面内做圆周运动，水不从杯里洒出，甚至当杯子运动到最高点时，已经杯口朝下，水也不会从杯子里洒出来。

2018年上海市普陀区高考数学一模试卷

2018年上海市普陀区高考数学一模试卷一.填空题（本大题共12题，1-6每题4分，7-12每题5分，共54分）1. 设全集U ={1, 2, 3, 4, 5}，若集合A ={3, 4, 5}，则∁U A =________．【答案】 {1, 2} 【考点】补集及其运算【解析】利用补集定义直接求解．【解答】∵ 全集U ={1, 2, 3, 4, 5}，集合A ={3, 4, 5}， ∴ ∁U A ={1, 2}．2. 若sinθ=14，则cos(3π2+θ)=________．【答案】14【考点】三角函数的恒等变换及化简求值【解析】由已知利用诱导公式即可化简求值得解．【解答】 sinθ=14，∴ cos(3π2+θ)=sinθ=14．3. 方程log 2(2−x)+log 2(3−x)=log 212的解x =________．【答案】 −1【考点】对数的运算性质【解析】利用对数的性质、运算法则直接求解．【解答】∵ 方程log 2(2−x)+log 2(3−x)=log 212， ∴ {2−x >03−x >0(2−x)(3−x)=12 ，即{x <2x 2−5x −6=0 ，解得x =−1．4. (√x −1x )9的二项展开式中的常数项的值为________．【考点】二项式定理的应用【解析】写出二项展开式的通项，由x 的指数为0求得r 值，则答案可求．【解答】二项展开式的通项T r+1=C 9r ∗(√x)9−r∗(−1x )r=(−1)r∗C 9r ∗x9−3r 2，由9−3r 2=0，得r =3．∴ (√x −1x )9的二项展开式中的常数项为T 4=(−1)3∗C 93=−84．5. 不等式1|x−1|≥1的解集为________．【答案】[0, 1)∪(1, 2] 【考点】其他不等式的解法【解析】去绝对值求出不等式的解集即可．【解答】由题意得：{x −1≠0|x −1|≤1 ，解得：0≤x <1或1<x ≤2，6. 函数f(x)=√3sinx +2cos 2x2的值域为________．【答案】 [−1, 3] 【考点】三角函数的恒等变换及化简求值【解析】由二倍角的余弦函数公式，两角和的正弦函数公式化简函数解析式，利用正弦函数的图象和性质即可得解．【解答】∵ f(x)=√3sinx +2cos 2x2=√3sinx +cosx +1=2sin(x +π6)+1， ∵ sin(x +π6)∈[−1, 1]，∴ f(x)=2sin(x +π6)+1∈[−1, 3]．7. 已知i 是虚数单位，z 是复数z 的共轭复数，若|z 1+i12i |=0，则z 在复平面内所对应的点所在的象限为第________象限．【考点】二阶矩阵【解析】根据二阶行列的展开式，求得z×2i−(1+i)=0，设z=a+bi，代入即可求得a和b 的值，求得z，即可判断z在复平面内所对应的点所在的象限．【解答】|z1+i12i|=0，设z=a+bi，则z×2i−(1+i)=0，即(a+bi)×2i−1−i=0，则2ai−2b−1−i=0，∴−2b−1+(2a−1)i=0，则{2a−1=0−2b−1=0，则{a=12b=−12，∴z=12−12i，则z=12+12i，∴则z在复平面内所对应的点位于第一象限，8. 若数列{a n}的前n项和S n=−3n2+2n+1(n∈N∗)，则limn→∞a n3n=________．【答案】−2【考点】数列的极限【解析】由数列的递推式：n=1时，a1=S1，当n≥2时，a n=S n−S n−1，可得通项a n，再由数列的极限的求法，即可得到所求极限．【解答】数列{a n}的前n项和S n=−3n2+2n+1(n∈N∗)，可得n=1时，a1=S1=−3+2+1=0；当n≥2时，a n=S n−S n−1=−3n2+2n+1+3(n−1)2−2n+2−1=−6n+5，则limn→∞a n3n=limn→∞5−6n3n=limn→∞(−2+53n)=−2+0=−2．9. 若直线l:x+y=5与曲线C:x2+y2=16交于两点A(x1, y1)、B(x2, y2)，则x1y2+x2y1的值为________．【答案】16【考点】直线与圆的位置关系【解析】直接利用圆与直线的位置关系，建立一元二次方程根与系数的关系，进一步求出结果．【解答】直线l:x+y=5与曲线C:x2+y2=16交于两点A(x1, y1)、B(x2, y2)，则：{x +y =5x 2+y 2=16，所以：2x 2−10x +9=0，则：x 1+x 2=5，x 1x 2=92，则：x 1y 2+x 2y 1=x 1(5−x 2)+x 2(5−x 1)， =5(x 1+x 2)−2x 1x 2， =25−9， =16．10. 设a 1、a 2、a 3、a 4是1，2，3，4的一个排列，若至少有一个i(i =1, 2, 3, 4)使得a i =i 成立，则满足此条件的不同排列的个数为________．【答案】 15【考点】排列、组合及简单计数问题【解析】根据题意，用间接法分析：先a 1、a 2、a 3、a 4计算所有的排列数，再用分步计数原理计算不存在i(i =1, 2, 3, 4)使得a i =i 成立的情况数，两者相减即可得答案．【解答】根据题意，a 1、a 2、a 3、a 4是1，2，3，4的一个排列，则所有的排列有A 44=24个，假设不存在i(i =1, 2, 3, 4)使得a i =i 成立，则a 1可以在第2、3、4位置，有3种情况，假设a 1在第二个位置，则a 1可以在第1、3、4位置，也有3种情况，此时a 3、a 4只有1种排法，剩余的两个数在其余两个位置，有1种情况，则不存在i(i =1, 2, 3, 4)使得a i =i 成立的情况有3×3=9种，则至少有一个i(i =1, 2, 3, 4)使得a i =i 成立排列数有24−9=15个；11. 已知正三角形ABC 的边长为√3，点M 是△ABC 所在平面内的任一动点，若|MA →|=1，则|MA →+MB →+MC →|的取值范围为________．【答案】 [0, 6] 【考点】平面向量数量积的性质及其运算律【解析】以A 点为原点，建立如图所示的平面直角坐标系，不妨设M(cosθ, sinθ)，根据向量的坐标运算和向量的模可得|MA →+MB →+MC →|2=18−18sin(θ+π3)，再根据三角函数的性质即可求出范围【解答】以A 点为原点，建立如图所示的平面直角坐标系，则A(0, 0)，B(√3, 0)，C(√32, 32)，∵ |MA →|=1，不妨设M(cosθ, sinθ)，∴MA→+MB→+MC→=(−cosθ, −sinθ)+(√3−cosθ, −sinθ)+(√32−cosθ, 32−sinθ)=(3√32−3cosθ, 32−3sinθ)，∴|MA→+MB→+MC→|2=(3√32−3cosθ)2+(32−3sinθ)2=9(2−√3cosθ−sinθ)=18−18sin(θ+π3)，∵−1≤sin(θ+π3)≤1，∴0≤18−18sin(θ+π3)≤36，∴|MA→+MB→+MC→|的取值范围为[0, 6]，12. 双曲线x23−y2=1绕坐标原点O旋转适当角度可以成为函数f(x)的图象，关于此函数f(x)有如下四个命题：①f(x)是奇函数；②f(x)的图象过点(√32,32)或(√32,−32)；③f(x)的值域是(−∞,−32brack∪[32,+∞)；④函数y=f(x)−x有两个零点；则其中所有真命题的序号为________．【答案】①②【考点】双曲线的特性【解析】求出双曲线的对称中心和顶点坐标和渐近线方程，画出f(x)的图象（位于一三象限），对选项一一判断，由对称性可得f(x)的图象在二四象限的情况，即可得到答案．【解答】双曲线x23−y2=1关于坐标原点对称，可得旋转后得到的函数f(x)的图象关于原点对称，即有f(x)为奇函数，故①对；由双曲线的顶点为(±√3, 0)，渐近线方程为y=±√33x，可得f(x)的图象的渐近线为x=0和y=±√33x，图象关于直线y=√3x对称，可得f(x)的图象过点(√32,32)，或(√32,−32)，由对称性可得f(x)的图象按逆时针60∘旋转位于一三象限；按顺时针旋转60∘位于二四象限；故②对；f(x)的图象按逆时针旋转60∘位于一三象限，由图象可得顶点为点(√32,32)，或(√32,−32)，不是极值点，则f(x)的值域不是(−∞,−32brack ∪[32,+∞)； f(x)的图象按顺时针旋转60∘位于二四象限，由对称性可得f(x)的值域也不是(−∞,−32brack ∪[32,+∞)．故③不对；当f(x)的图象位于一三象限时，f(x)的图象与直线y =x 有两个交点，函数y =f(x)−x 有两个零点；当f(x)的图象位于二四象限时，f(x)的图象与直线y =x 没有交点，函数y =f(x)−x 没有零点．故④错．二.选择题（本大题共4题，每题5分，共20分）若数列{a n }(n ∈N ∗)是等比数列，则矩阵(a 1a 2a 4a 5a 6a 8)所表示方程组的解的个数是（）A.0个B.1个C.无数个D.不确定【答案】 C【考点】等比数列的性质等比数列的通项公式线性方程组解的存在性，唯一性【解析】根据题意，分析矩阵所表示的方程组为{a 1x +a 2y =a4a 5x +a 6y =a 8，进而由等比数列的性质可得a 1a 5=a 2a 6=a 4a 8=1q 4，进而分析可得方程组的解的个数，即可得答案．【解答】根据题意，矩阵(a 1a 2a 4a5a 6a 8)所表示方程组为{a 1x +a 2y =a 4a 5x +a 6y =a 8 ，又由数列{a n }(n ∈N ∗)是等比数列，则有a1a 5=a2a 6=a4a 8=1q 4，则方程组{a 1x +a 2y =a4a 5x +a 6y =a 8的解有无数个；“m >0”是“函数f(x)=|x(mx +2)|在区间(0, +∞)上为增函数”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【答案】 A【考点】必要条件、充分条件与充要条件的判断【解析】m >0，函数f(x)=|x(mx +2)|=|mx 2+2x|，由f(0)=0，得到f(x)在区间(0, +∞)上为增函数”；由函数f(x)=|x(mx +2)|=|mx 2+2x|在区间(0, +∞)上为增函数，得到m ∈R ，由此能求出结果．【解答】 ∵ m >0，∴ 函数f(x)=|x(mx +2)|=|mx 2+2x|，∵ f(0)=0，∴ f(x)在区间(0, +∞)上为增函数”；∵ 函数f(x)=|x(mx +2)|=|mx 2+2x|在区间(0, +∞)上为增函数， f(0)=0， ∴ m ∈R ，∴ “m >0”是“函数f(x)=|x(mx +2)|在区间(0, +∞)上为增函数”的充分非必要条件．用长度分别为2、3、5、6、9（单位：cm ）的五根木棒连接（只允许连接，不允许折断），组成共顶点的长方体的三条棱，则能够得到的长方体的最大表面积为（） A.258cm 2 B.414cm 2 C.416cm 2 D.418cm 2 【答案】 C【考点】柱体、锥体、台体的体积计算【解析】设长方体的三条棱分别为a ，b ，c ，则长方体的表面积S =2(ab +bc +ac)，由不等式的基本性质可知，当a ，b ，c 最接近时能够得到的长方体的表面积最大，由此可得用2、6连接，3、5连接各为一条棱，第三条棱为9组成长方体，则最大表面积可求．【解答】设长方体的三条棱分别为a ，b ，c ，则长方体的表面积S =2(ab +bc +ac)≤(a +b)2+(b +c)2+(a +c)2，当且仅当a =b =c 时上式“=”成立．由题意可知，a ，b ，c 不可能相等，故考虑当a ，b ，c 三边长最接近时面积最大，此时三边长为8，8，9，用2、6连接，3、5连接各为一条棱，第三条棱为9组成长方体，此时能够得到的长方体的最大表面积为2(8×8+8×9+8×9)=416(cm 2)．定义在R 上的函数f(x)满足f(x)={2x +20≤x <14−2−x −1≤x <0 ，且f(x −1)=f(x +1)，则函数g(x)=f(x)−3x−5x−2在区间[−1, 5]上的所有零点之和为（）A.4B.5C.7D.8 【答案】 B【考点】函数零点的判定定理【解析】把方程f(x)=g(x)在区间[−1, 5]上的根转化为函数y =f(x)和y =g(x)的交点横坐标，画出函数图象，数形结合得答案．【解答】∵ 函数f(x)={2x +20≤x <14−2−x −1≤x <0 ，且f(x −1)=f(x +1)，函数的周期为2，函数g(x)=f(x)−3x−5x−2，的零点，就是y =f(x)与y =3x−5x−2图象的交点的横坐标，∴ y =f(x)关于点(0, 3)中心对称，将函数两次向右平移2个单位，得到函数y =f(x)在[−1, 5]上的图象，每段曲线不包含右端点（如下图），去掉端点后关于(2, 3)中心对称．又∵ y =3x−5x−2=3+1x−2关于(2, 3)中心对称，故方程f(x)=g(x)在区间[−1, 5]上的根就是函数y =f(x)和y =g(x)的交点横坐标，共有三个交点，自左向右横坐标分别为x 1，x 2，x 3，其中x 1和x 3关于(2, 3)中心对称， ∴ x 1+x 3=4，x 2=1，故x 1+x 2+x 3=5．三.解答题（本大题共5题，共14+14+14+16+18=76分）如图所示的圆锥的体积为√33π，底面直径AB =2，点C 是弧AB^的中点，点D 是母线PA 的中点．（1）求该圆锥的侧面积；（2）求异面直线PB 与CD 所成角的大小．【答案】∵ 圆锥的体积为√33π，底面直径AB =2，∴ 13π×12×PO =√33π，解得PO =√3，∴ PA =√(√3)2+12=2，∴ 该圆锥的侧面积S =πrl =π×1×2=2π． ∵ 圆锥的体积为√33π，底面直径AB =2，点C 是弧AB^的中点，点D 是母线PA 的中点． ∴ PO ⊥平面ABC ，OC ⊥AB ，∴ 以O 为原点，OC 为x 轴，OB 为y 轴，OP 为z 轴，建立空间直角坐标系，则A(0, −1, 0)，P(0, 0, √3)，D(0, −12, √32)，B(0, 1, 0)，C(1, 0, 0)，PB →=(0, 1, −√3)，CD →=(−1, −12, √32)，设异面直线PB 与CD 所成角为θ，则cosθ=|PB →∗CD →||PB →|∗|CD →|=2√2=√22， ∴ θ=π4．∴ 异面直线PB 与CD 所成角为π4．【考点】旋转体（圆柱、圆锥、圆台）异面直线及其所成的角【解析】（1）由圆锥的体积为√33π，底面直径AB =2，求出PO =√3，从而PA =2，由此能求出该圆锥的侧面积．（2）以O 为原点，OC 为x 轴，OB 为y 轴，OP 为z 轴，建立空间直角坐标系，利用向量法能求出异面直线PB 与CD 所成角．【解答】∵ 圆锥的体积为√33π，底面直径AB =2，∴ 13π×12×PO =√33π，解得PO =√3，∴ PA =√(√3)2+12=2，∴ 该圆锥的侧面积S =πrl =π×1×2=2π． ∵ 圆锥的体积为√33π，底面直径AB =2，点C 是弧AB^的中点，点D 是母线PA 的中点． ∴ PO ⊥平面ABC ，OC ⊥AB ，∴ 以O 为原点，OC 为x 轴，OB 为y 轴，OP 为z 轴，建立空间直角坐标系，则A(0, −1, 0)，P(0, 0, √3)，D(0, −12, √32)，B(0, 1, 0)，C(1, 0, 0)，PB →=(0, 1, −√3)，CD →=(−1, −12, √32)，设异面直线PB 与CD 所成角为θ，则cosθ=|PB →∗CD →||PB →|∗|CD →|=2√2=√22， ∴ θ=π4．∴ 异面直线PB 与CD 所成角为π4．某快递公司在某市的货物转运中心，拟引进智能机器人分拣系统，以提高分拣效率和降低物流成本，已知购买x 台机器人的总成本p(x)=1600x 2+x +150万元．(1)若使每台机器人的平均成本最低，问应买多少台？(2)现按(1)中的数量购买机器人，需要安排m 人将邮件放在机器人上，机器人将邮件送达指定落袋格口完成分拣（如图），经实验知，每台机器人的日平均分拣量q(m)={815m(60−m),(1≤m ≤30),480,(m >30)（单位：件），已知传统人工分拣每人每日的平均分拣量为1200件，问引进机器人后，日平均分拣量达最大值时，用人数量比引进机器人前的用人数量最多可减少百分之几？【答案】解：(1)由总成本p(x)=1600x 2+x +150万元，可得每台机器人的平均成本y=p(x)x =1600x2+x+150x=1600x+150x+1≥2√1600x⋅150x+1=2．当且仅当1600x=150x，即x=300时，上式等号成立．∴若使每台机器人的平均成本最低，应买300台；(2)引进机器人后，每台机器人的日平均分拣量q(m)={815m(60−m),(1≤m≤30), 480,(m>30),当1≤m≤30时，300台机器人的日平均分拣量为160m(60−m)=−160m2+9600m，∴当m=30时，日平均分拣量有最大值144000．当m>30时，日平均分拣量为480×300=144000．∴300台机器人的日平均分拣量的最大值为144000件．若传统人工分拣144000件，则需要人数为1440001200=120人．∴日平均分拣量达最大值时，用人数量比引进机器人前的用人数量最多可减少120−30120=75%．【考点】基本不等式在最值问题中的应用根据实际问题选择函数类型【解析】（1）由总成本p(x)=1600x2+x+150万元，可得每台机器人的平均成本y=p(x)x，然后利用基本不等式求最值；（2）引进机器人后，每台机器人的日平均分拣量q(m)={815m(60−m)(1≤m≤30)480(m>30)，分段求出300台机器人的日平均分拣量的最大值及所用人数，再由最大值除以1200，可得分拣量达最大值时所需传统分拣需要人数，则答案可求．【解答】解：(1)由总成本p(x)=1600x2+x+150万元，可得每台机器人的平均成本y=p(x)x =1600x2+x+150x=1600x+150x+1≥2√1600x⋅150x+1=2．当且仅当1600x=150x，即x=300时，上式等号成立．∴若使每台机器人的平均成本最低，应买300台；(2)引进机器人后，每台机器人的日平均分拣量q(m)={815m(60−m),(1≤m≤30), 480,(m>30),当1≤m≤30时，300台机器人的日平均分拣量为160m(60−m)=−160m2+9600m，∴当m=30时，日平均分拣量有最大值144000．当m>30时，日平均分拣量为480×300=144000．∴300台机器人的日平均分拣量的最大值为144000件．若传统人工分拣144000件，则需要人数为1440001200=120人．∴日平均分拣量达最大值时，用人数量比引进机器人前的用人数量最多可减少120−30120=75%．设函数f(x)=sin(ωx+φ)(ω>0, |φ|<π2)，已知角φ的终边经过点(1,−√3)，点M(x1, y1)、N(x2, y2)是函数f(x)图象上的任意两点，当|f(x1)−f(x2)|=2时，|x1−x2|的最小值是π2．（1）求函数y=f(x)的解析式；（2）已知△ABC面积为5√3，角C所对的边c=2√5，cosC=f(π4)，求△ABC的周长．【答案】已知角φ的终边经过点(1,−√3)，且|ϕ|<π2，则：φ=−π3，点M(x1, y1)、N(x2, y2)是函数f(x)图象上的任意两点，当|f(x1)−f(x2)|=2时，|x1−x2|的最小值是π2．则：T=π，所以：ω=2ππ=2，所以：f(x)=sin(2x−π3)；由于：cosC=f(π4)=sin(π2−π3)=12，且0<C<π，解得：C=π3，△ABC面积为5√3，所以：12absinC=5√3，解得：ab=20．由于：c2=a2+b2−2abcosC，c=2√5，所以：20=(a+b)2−3ab，解得：a+b=4√5，所以：C△ABC=a+b+c=6√5．【考点】正弦函数的图象【解析】（1）直接利用已知条件和函数的图象求出函数的解析式，（2）利用函数的解析式求出C的值，进一步利用余弦定理和三角形的面积公式求出结果．【解答】已知角φ的终边经过点(1,−√3)，且|ϕ|<π2，则：φ=−π3，点M(x 1, y 1)、N(x 2, y 2)是函数f(x)图象上的任意两点，当|f(x 1)−f(x 2)|=2时，|x 1−x 2|的最小值是π2．则：T =π，所以：ω=2ππ=2，所以：f(x)=sin(2x −π3)；由于：cosC =f(π4)=sin(π2−π3)=12，且0<C <π，解得：C =π3， △ABC 面积为5√3，所以：12absinC =5√3，解得：ab =20．由于：c 2=a 2+b 2−2abcosC ，c =2√5，所以：20=(a +b)2−3ab ，解得：a +b =4√5，所以：C △ABC =a +b +c =6√5．设点F 1、F 2分别是椭圆C:x 22t 2+y 2t 2=1(t >0)的左、右焦点，且椭圆C 上的点到点F 2的距离的最小值为2√2−2，点M 、N 是椭圆C 上位于x 轴上方的两点，且向量F 1M →与向量F 2N →平行．（1）求椭圆C 的方程；（2）当F 1N →∗F 2N →=0时，求△F 1MN 的面积；（3）当|F 2N →|−|F 1M →|=√6时，求直线F 2N 的方程．【答案】点F 1、F 2分别是椭圆C:x 22t 2+y 2t 2=1(t >0)的左、右焦点，∴ a =√2t ，c =t ，∵ 椭圆C 上的点到点F 2的距离的最小值为2√2−2， ∴ a −c =√2t −t =2√2−2，解得t =2， ∴ 椭圆的方程为x 28+y 24=1，由（1）可得F 1(−2, 0)，F 2(2, 0)，点M 、N 是椭圆C 上位于x 轴上方的两点，可设N(2√2cosθ, 2sinθ)，∴ F 1N →=(2√2cosθ+2, 2sinθ)，F 2N →=(2√2cosθ−2, 2sinθ)， ∵ F 1N →∗F 2N →=0，∴ (2√2cosθ+2)(2√2cosθ−2)+4sin 2θ=0，解得cosθ=0，sinθ=1， ∴ N(0, 2)， ∴ F 2N →=(−2, 2)， ∴ kF 2N =22=−1，∵ 向量F 1M →与向量F 2N →平行， ∴ 直线F 1M 的斜率为−1， ∴ 直线方程为y =−x −2，联立方程组{y =−x −2x 28+y 24=1，解得x =0，y =−2（舍去），或x =−83，y =23，∴ M(−83, 23)，∴ |F 1M|=√(−83+2)2+(23)2=2√23，点N 到直线直线y =−x −2的距离为d =√2=2√2， ∴ △F 1MN 的面积=12|F 1M|⋅d =12×2√23×2√2=43，∵ 向量F 1M →与向量F 2N →平行， ∴ λF 1M →=F 2N →， ∴ |F 2N →|−|F 1M →|=√6， ∴ (λ−1)|F 1M →|=√6，即λ>1，设M(x 1, y 1)，N(x 2, y 2)，∴ λ(x 1+2)=x 2−2，y 2=λy 1， ∴ x 2=λx 1+2(λ+1) ∵x 28+y 24=1，∴ x 22+2y 22=8，∴ [λx 1+2(λ+1)]2+2λ2y 12=12λ2+8λ+4+4λ(λ+1)x 1=8，∴ 4λ(λ+1)x 1=(1−3λ)(λ+1)， ∴ x 1=1−3λλ=1λ−3，∴ y 12=4−(1−3λ)22λ，∴ |F 1M →|2=(x 1+2)2+y 12=(1λ−3+2)2+4−(1−3λ)22λ=(λ+1)22λ2，∴ |F 1M →|=√2λ， ∴ (λ−1)2λ=√6，∴ λ2−2√3λ−1=0解得λ=2+√3，或λ=2−√3（舍去） ∴ x 1=1λ−3=2+√33=−1−√3，∴ y 12=4−(−1−√3)22=2−√3=4−2√32=(√3−1)22， ∴ y 1=√3−1√2，∴ kF 1M=√3−1√2−0−1−√3+2=−√22， ∴ 直线F 2N 的方程为y −0=−√22(x −2)，即为x +√2y −2=0 【考点】椭圆的定义【解析】（1）根据椭圆的简单性质可得a −c =√2t −t =2√2−2，解得即可，（2）可设N(2√2cosθ, 2sinθ)，根据向量的数量积求出点N 的坐标，再根据直线平行，求出M 的坐标，利用两点间的距离公式和点到直线的距离公式和三角形的面积公式计算即可，（3）向量F 1M →与向量F 2N →平行，不妨设λF 1M →=F 2N →，设M(x 1, y 1)，N(x 2, y 2)，根据坐标之间的关系，求得M 的坐标，再根据向量的模，即可求出λ的值，根据斜率公式求出直线的斜率，根据直线平行和点斜式即可求出直线方程．【解答】点F 1、F 2分别是椭圆C:x 22t 2+y 2t 2=1(t >0)的左、右焦点，∴ a =√2t ，c =t ，∵ 椭圆C 上的点到点F 2的距离的最小值为2√2−2， ∴ a −c =√2t −t =2√2−2，解得t =2， ∴ 椭圆的方程为x 28+y 24=1，由（1）可得F 1(−2, 0)，F 2(2, 0)，点M 、N 是椭圆C 上位于x 轴上方的两点，可设N(2√2cosθ, 2sinθ)，∴ F 1N →=(2√2cosθ+2, 2sinθ)，F 2N →=(2√2cosθ−2, 2sinθ)， ∵ F 1N →∗F 2N →=0，∴ (2√2cosθ+2)(2√2cosθ−2)+4sin 2θ=0，解得cosθ=0，sinθ=1， ∴ N(0, 2)， ∴ F 2N →=(−2, 2)， ∴ kF 2N =22=−1，∵ 向量F 1M →与向量F 2N →平行， ∴ 直线F 1M 的斜率为−1， ∴ 直线方程为y =−x −2，联立方程组{y =−x −2x 28+y 24=1 ，解得x =0，y =−2（舍去），或x =−83，y =23，∴ M(−83, 23)，∴ |F 1M|=√(−83+2)2+(23)2=2√23，点N 到直线直线y =−x −2的距离为d =√2=2√2， ∴ △F 1MN 的面积=12|F 1M|⋅d =12×2√23×2√2=43，∵ 向量F 1M →与向量F 2N →平行， ∴ λF 1M →=F 2N →， ∴ |F 2N →|−|F 1M →|=√6， ∴ (λ−1)|F 1M →|=√6，即λ>1，设M(x 1, y 1)，N(x 2, y 2)，∴ λ(x 1+2)=x 2−2，y 2=λy 1， ∴ x 2=λx 1+2(λ+1) ∵x 28+y 24=1，∴ x 22+2y 22=8，∴ [λx 1+2(λ+1)]2+2λ2y 12=12λ2+8λ+4+4λ(λ+1)x 1=8，∴ 4λ(λ+1)x 1=(1−3λ)(λ+1)，∴ x 1=1−3λλ=1λ−3，∴ y 12=4−(1−3λ)22λ，∴ |F 1M →|2=(x 1+2)2+y 12=(1λ−3+2)2+4−(1−3λ)22λ=(λ+1)22λ2，∴ |F 1M →|=√2λ， ∴ (λ−1)√2λ=√6，∴ λ2−2√3λ−1=0解得λ=2+√3，或λ=2−√3（舍去） ∴ x 1=1λ−3=2+√33=−1−√3，∴ y 12=4−(−1−√3)22=2−√3=4−2√32=(√3−1)22， ∴ y 1=√3−1√2，∴ kF 1M=√3−1√2−0−1−√3+2=−√22，∴ 直线F 2N 的方程为y −0=−√22(x −2)，即为x +√2y −2=0设d 为等差数列{a n }的公差，数列{b n }的前n 项和T n ，满足T n +12n =(−1)n b n (n ∈N ∗)，且d =a 5=b 2，若实数m ∈P k ={x|a k−2<x <a k+3}(k ∈N ∗, k ≥3)，则称m 具有性质P k ．（1）请判断b 1、b 2是否具有性质P 6，并说明理由；（2）设S n 为数列{a n }的前n 项和，若{S n −2λa n }是单调递增数列，求证：对任意的k(k ∈N ∗, k ≥3)，实数λ都不具有性质P k ；（3）设H n 是数列{T n }的前n 项和，若对任意的n ∈N ∗，H 2n−1都具有性质P k ，求所有满足条件的k 的值．【答案】T n +12n =(−1)n b n (n ∈N ∗)，可得n =1时，T 1+12=−b 1=−T 1，解得b 1=−14，T 2+14=b 2=−14+b 2+14=b 2，T 3+18=−b 3=−14+b 2+b 3+18，即b 2+2b 3=18， T 4+116=b 4=−14+b 2+b 3+b 4+116，即b 2+b 3=316，解得b 2=14，b 3=−116，同理可得b 4=116，b 5=−164， b 6=164，b 7=−1256，…，b 2n−1=−14n ，d =a 5=b 2，可得d =a 1+4d =14，解得a 1=−34，d =14，a n =n−44，P 6={x|a 4<x <a 9}(k ∈N ∗, k ≥3)={x|0<x <54}，则b 1不具有性质P 6，b 2具有性质P 6；证明：设S n 为数列{a n }的前n 项和，若{S n −2λa n }是单调递增数列，可得S n+1−2λa n+1≥S n −2λa n ，即为(n+1)2−7(n+1)−4λ(n+1)+16λ8≥n 2−7n−4λn+16λ8，化为4λ+6≤2n 对n 为一切自然数成立，即有4λ+6≤2，可得λ≤−1，又P k ={x|a k−2<x <a k+3}(k ∈N ∗, k ≥3)，且a 1=−34，d >0，可得P k 中的元素大于−1，则对任意的k(k ∈N ∗, k ≥3)，实数λ都不具有性质P k ；设H n 是数列{T n }的前n 项和，若对任意的n ∈N ∗，H 2n−1都具有性质P k ，由于H 1=T 1=b 1=−14，H 3=T 1+T 2+T 3=−516，H 5=T 1+T 2+T 3+T 4+T 5=−2164， H 7=−2164+0−1256=−85256，…，H 2n−1=H 2n−3+b 2n−1，(n ≥2)，当k =3时，P 3={x|a 1<x <a 6}={x|−34<x <12}，当k =4时，P 4={x|a 2<x <a 7}={x|−12<x <34}，当k =5时，P 5={x|a 3<x <a 8}={x|−14<x <1}，当k =6时，P 3={x|a 4<x <a 9}={x|0<x <54}，显然k =5，6不成立，故所有满足条件的k 的值为3，4．【考点】数列的求和【解析】（1）求得n =1，2，3，4，5，6，7时，数列{b n }的前7项，可得d 和首项a 1，得到等差数列{a n }的通项，即可判断b 1、b 2是否具有性质P 6；（2）由题意可得S n+1−2λa n+1≥S n −2λa n ，代入等差数列{a n }的通项公式和求和公式，化简整理可得λ≤−1，结合集合中元素的特点，即可得证；（3）求得n =1，2，3，4，H 2n−1的特点，结合k =3，4，5，6，集合的特点，即可得到所求取值．【解答】T n +12n =(−1)n b n (n ∈N ∗)，可得n =1时，T 1+12=−b 1=−T 1，解得b 1=−14，T 2+14=b 2=−14+b 2+14=b 2，T 3+18=−b 3=−14+b 2+b 3+18，即b 2+2b 3=18，T 4+116=b 4=−14+b 2+b 3+b 4+116，即b 2+b 3=316，解得b 2=14，b 3=−116，同理可得b 4=116，b 5=−164， b 6=164，b 7=−1256， …，b 2n−1=−14n ，d =a 5=b 2，可得d =a 1+4d =14，解得a 1=−34，d =14，a n =n−44，P 6={x|a 4<x <a 9}(k ∈N ∗, k ≥3)={x|0<x <54}，则b 1不具有性质P 6，b 2具有性质P 6；证明：设S n 为数列{a n }的前n 项和，若{S n −2λa n }是单调递增数列，可得S n+1−2λa n+1≥S n −2λa n ，即为(n+1)2−7(n+1)−4λ(n+1)+16λ8≥n 2−7n−4λn+16λ8，化为4λ+6≤2n 对n 为一切自然数成立，即有4λ+6≤2，可得λ≤−1，又P k ={x|a k−2<x <a k+3}(k ∈N ∗, k ≥3)，且a 1=−34，d >0，可得P k 中的元素大于−1，则对任意的k(k ∈N ∗, k ≥3)，实数λ都不具有性质P k ；设H n 是数列{T n }的前n 项和，若对任意的n ∈N ∗，H 2n−1都具有性质P k ，由于H 1=T 1=b 1=−14，H 3=T 1+T 2+T 3=−516，H 5=T 1+T 2+T 3+T 4+T 5=−2164，H 7=−2164+0−1256=−85256，…，H 2n−1=H 2n−3+b 2n−1，(n ≥2)，当k =3时，P 3={x|a 1<x <a 6}={x|−34<x <12}，当k =4时，P 4={x|a 2<x <a 7}={x|−12<x <34}，当k =5时，P 5={x|a 3<x <a 8}={x|−14<x <1}，}，当k=6时，P3={x|a4<x<a9}={x|0<x<54显然k=5，6不成立，故所有满足条件的k的值为3，4．。

年普陀区高考数学一模试卷含答案

2018年普陀区高考数学一模试卷含答案2017.１２一. 填空题(本大题共12题,1-６每题４分,７-12每题5分，共54分） 1. 设全集{1,2,3,4,5}U =，若集合{3,4,5}A =,则U C A = 2. 若1sin 4θ=,则3cos()2πθ+= 3. 方程222log (2)log (3)log 12x x -+-=的解x =4. 91)x的二项展开式中的常数项的值为5. 不等式11|1|x ≥-的解集为6. 函数2()2cos 2xf x x =+的值域为7. 已知i 是虚数单位，z 是复数z 的共轭复数,若1012z ii+=，则z 在复平面内所对应的点所在的象限为第象限8．若数列{}n a 的前n 项和2321n S n n =-++(*n N ∈)，则lim3nn a n→∞=9. 若直线:5l x y +=与曲线22:16C x y +=交于两点11(,)A x y 、22(,)B x y ,则1221x y x y +的值为１0．设1a 、2a 、3a 、4a 是1,2,3，４的一个排列,若至少有一个i (1,2,3,4i =）使得i a i =成立，则满足此条件的不同排列的个数为11. 已知正三角形ABC 点M 是ABC ∆所在平面内的任一动点,若||1MA =, 则||MA MB MC ++的取值范围为1２. 双曲线2213x y -=绕坐标原点O 旋转适当角度可以成为函数()f x 的图像，关于此函数()f x 有如下四个命题：① ()f x 是奇函数；② ()f x 的图像过点3()22或3)22-； ③ ()f x 的值域是33(,][,)22-∞-+∞；④ 函数()y f x x =-有两个零点；则其中所有真命题的序号为二．选择题（本大题共4题,每题５分,共20分) 13. 若数列{}n a （*n N ∈)是等比数列,则矩阵124568a a a a a a ⎛⎫⎪⎝⎭所表示方程组的解的个数是( ）A ． 0个 B. 1个Ｃ．无数个 D. 不确定１４． “0m >”是“函数()|(2)|f x x mx =+在区间(0,)+∞上为增函数”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. 用长度分别为2、３、5、6、9(单位:cm )的五根木棒连接（只允许连接,不允许折断)，组成共顶点的长方体的三条棱,则能够得到的长方体的最大表面积为（）A. 2582cm Ｂ. 4142cm C. ４162cm D ． 41８2cm1６. 定义在R 上的函数()f x 满足2201()4210x xx f x x -⎧+≤<=⎨--≤<⎩，且(1)(1)f x f x -=+,则函数35()()2x g x f x x -=--在区间[1,5]-上的所有零点之和为( ）A. ４Ｂ. 5 Ｃ. 7 D. 8三. 解答题(本大题共5题,共14+14＋14+1６+1８＝76分) １7.,底面直径2AB =,点C 是弧AB 的中点，点D 是母线PA 的中点. (１)求该圆锥的侧面积;(2）求异面直线PB 与CD 所成角的大小.18. 某快递公司在某市的货物转运中心,拟引进智能机器人分拣系统，以提高分拣效率和降低物流成本,已知购买x 台机器人的总成本21()150600p x x x =++万元. (１）若使每台机器人的平均成本最低,问应买多少台？（2)现按（1）中的数量购买机器人,需要安排m 人将邮件放在机器人上，机器人将邮件送达指定落袋格口完成分拣(如图），经实验知，每台机器人的日平均分拣量8(60)(130)()15480(30)m m m q m m ⎧-≤≤⎪=⎨⎪>⎩(单位：件）,已知传统人工分拣每人每日的平均分拣量为120０件，问引进机器人后,日平均分拣量达最大值时，用人数量比引进机器人前的用人数量最多可减少百分之几?１9. 设函数()sin()f x x ωϕ=+（0ω>,||2πϕ<)，已知角ϕ的终边经过点(1,3)-,点11(,)M x y 、22(,)N x y 是函数()f x 图像上的任意两点，当12|()()|2f x f x -=时,12||x x -的最小值是2π. （1）求函数()y f x =的解析式;（２)已知ABC ∆面积为53，角C 所对的边25c =,cos ()4C f π=,求ABC ∆的周长.20. 设点1F 、2F 分别是椭圆2222:12x y C t t+=（0t >）的左、右焦点，且椭圆C 上的点到点2F 的距离的最小值为2-,点M 、N 是椭圆C 上位于x 轴上方的两点,且向量1F M 与向量2F N 平行. (1)求椭圆C 的方程;（２）当120F N F N ⋅=时，求1F MN ∆的面积； (3）当21||||6F N F M -=时，求直线2F N 的方程.21. 设d 为等差数列{}n a 的公差，数列{}n b 的前n 项和n T ，满足1(1)2nn n n T b +=- （*n N ∈),且52d a b ==,若实数23{|}k k k m P x a x a -+∈=<<(*k N ∈，3k ≥)，则称m 具有性质k P .（1）请判断1b 、2b 是否具有性质6P ，并说明理由；(2)设n S 为数列{}n a 的前n 项和，若{2}n n S a λ-是单调递增数列,求证：对任意的k (*k N ∈，3k ≥),实数λ都不具有性质k P ;(3)设n H 是数列{}n T 的前n 项和，若对任意的*n N ∈,21n H -都具有性质k P ,求所有满足条件的k 的值.参考答案一．填空题１． {1,2} 2.143. 1-4. 84-5. [0,1)(1,2]6. [1,3]- ７. 一 8. 2- 9. １6 10．１511. [0,6] 12. ①②二．选择题13． C 14. A １５. C 16. B三. 解答题 17.(1)2π;(２)4π. 18.(1）３00;(２）75%.1９.（1)()sin(2)3f x x π=-;（２）ABC C ∆=２0.（１)22184x y +=；(２)43;（3）2x =+. 21.（1）2b 具有性质6P ，1b 不具有性质6P ；（２）证明略；(3)3和4.。

2018届上海市普陀区高三12月质量调研(一模)理科数学试题及答案精品

2018学年第一学期普陀区高三理科数学质量调研卷考生注意：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道题，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的相．．．．．．．．．应位置，本卷上任何解答都不作评分依据．．．．．．．．．．．．．．．．．．. 一、填空题（本大题满分56分）本大题共有14小题，要求直接将结果填写在答题纸对应的空格中.每个空格填对得4分，填错或不填在正确的位置一律得零分. 1. 若集合}1lg |{<=x x A ，∈==x x y y B ,sin |{R}，则=B A .2. 若1lim =+∞→an ann，则常数=a . 3. 若1>x ，则函数112-+-=x x x y4. 函数⎪⎭⎫⎝⎛-π=x y 4tan 5. 方程1)7lg(lg =-+x x 的解集为 . 6. 如图，正三棱柱的底面边长为2，体积为3，则直线C B 1与底面ABC所成的角的大小为（结果用反三角函数值表示）.1第6题7. 若方程132||22=-+-ky k x 表示双曲线，则实数k 的取值范围是 .8. 函数22)(2+-=x x x f （0≤x ）的反函数是 . 9. 在二项式81⎪⎪⎭⎫ ⎝⎛-x x 的展开式中，含2x 项的系数为（结果用数值表示）. 10. 若抛物线mx y 42=（0>m ）的焦点在圆122=+y x 内，则实数m 的取值范围是 .11. 在ABC ∆中，三个内角A 、B 、C 的对边分别为a 、b 、c ，若32=a ，2=c ， 120=A ，则=∆ABC S . 12. 若无穷等比数列}{n a 的各项和等于公比q ，则首项1a 的最大值是 .13. 设a 为大于1的常数，函数⎩⎨⎧≤>=+00log )(1x ax x x f x a ，若关于x 的方程0)()(2=⋅-x f b x f恰有三个不同的实数解，则实数b的取是 .14. 如图，点1P ,2P ,… ,10P 分别是四面体的顶点或其棱的中点，则在同一平面内的四点组()k j i P P P P ,,,1 （101≤<<<k j i ）共有个.二、选择题（本大题满分20分）本大题共有4题，每题有且只有一个结论是正确的，必须把正确结论的代号写在答题纸3 498第14题相应的空格中. 每题选对得5分，不选、选错或选出的代号超过一个（不论是否都写在空格内），或者没有填写在题号对应的空格内，一律得零分. 15．设a、∈b R ，且<ab ，则…………………………………………………………………………（）)(A ||||b a b a -<+ )(B ||||b a b a ->+ )(C ||||||b a b a -<- )(D ||||||b a b a +<- 16.“点M 在曲线x y 42=上”是“点M 的坐标满足方程02=+y x ”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17.要得到函数x y 2sin =的图像，只需将函数⎪⎫ ⎝⎛-=42cos πx y 的图像………………………………（）)(A 向左平移8π个单位 )(B 位)(C 向左平移4π个单位 )(D 向右平移4π个单位131-n 2k 第18题18. 若在边长为1的正三角形ABC 的边BC 上有n (∈n N *，2≥n )等分点，沿向量的方向依次为121,,,-n P P P ，记AP AP T n n ⋅++⋅+⋅=-1211 ，若给出四个数值:①429 ②1091 ③18197 ④33232，则n T 的值不可能的共有…………………（）)(A 1个 )(B 2个 )(C 3个)(D 4个三、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规定的方框内写出必要的步骤. 19. (本题满分12分) 已知P 是椭圆12422=+y x 上的一点，求P 到)0,(m M （0>m ）的距离的最小值.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6分．已知函数x x b x a x f cos sin sin )(2+=满足2)23()6(==ππf f（1）求实数b a ,的值以及函数)(x f 的最小正周期；（2）记)()(t x f x g +=，若函数)(x g 是偶函数，求实数t 的值.21. (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．如图，在两块钢板上打孔，用钉帽呈半球形、钉身为圆柱形的铆钉（图1）穿在一起，在没有帽的一端锤打出一个帽，使得与钉帽的大小相等，铆合的两块钢板，成为某种钢结构的配件，其截面图如图2.（单位：mm ）.（加工中不计损失）. （1）若钉身长度是钉帽高度的2倍，求铆钉的表面积；（2）若每块钢板的厚度为12mm ，求钉身的长度（结果精确到1mm ）.22. （本题满分16分）本题共有3个小题，第（1）小题5分，第（2）小题6分，第（3）小题5分已知数列}{n a 的前n 项和为n S ，且4=+n n a S ，∈n N *（1）求数列}{n a 的通项公式；（2）已知32+=n c n （∈n N *），记=n d n C n a c log +(0>C 且1≠C )，是否存在这样的常数C ，使得数列}{n d 是常数列，若存在，求出C 的值；若不存在，请说明理由. （3）若数列}{n b ，对于任意的正整数n ，均有2221123121+-⎪⎭⎫ ⎝⎛=++++--n a b a b a b a b nn n n n 成立，求证：数列}{n b 是等差数列；23. （本题满分18分）本题共有3个小题，第（1）小题4分，第（2）小题6分，第（3）小题8分已知函数)(x f y =，若在定义域内存在0x ，使得)()(00x f x f -=-成立，则称0x 为函数)(x f 的局部对称点.（1）若a 、∈b R 且0≠a ，证明：函数a bx ax x f -+=2)(必有局部对称点；（2）若函数c x f x +=2)(在区间]2,1[-内有局部对称点，求实数c的取值范围；（3）若函数324)(21-+⋅-=+m m x f x x 在R 上有局部对称点，求实数m 的取值范围.2014学年第一学期普陀区高三理科数学质量调研卷参考答案一、填空题（本大题满分56分）本大题共有14小题，要求直接将结果填写在答题纸对应的空格中.每个空格填对得4分，填错或不填在正确的位置一律得零分. 1.)10,1[- 2.1 3.34.⎪⎭⎫⎝⎛+-43.4ππππk k （Z k ∈） 5.}5,2{6.21arctan7.),3()2,2(+∞-8.)2(11)(1≥--=-x x x f9.70 10.1>m 11.312.41 13. a b ≤<014. 33二、选择题（本大题满分20分）本大题共有4题，每题有且只有一个结论是正确的，必须把正确结论的代号写在答题纸相应的空格中. 每题选对得5分，不选、选错或选出的代号超过一个（不论是否都写在空格内），或者没有填写在题号对应的空格内，一律得零分.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规定的方框内写出必要的步骤. 19. (本题满分12分)【解】设),(y x P ，其中22≤≤-x ……………………2分则222)(||y m x PM +-==2221212)(2222++-=-+-m mx x x m x ……5分222)2(21m m x -+-=，对称轴m x 2=0>……7分（1）若220<<m ，即10<<m ，此时当mx 2=时，2min 2||m PM -=；……9分（2）若22≥m ，即1≥m ，此时当2=x 时，|2|44||2min -=+-=m m m PM ； (11)分综上所述，⎪⎩⎪⎨⎧≥-<<-=1|,2|10,2||2min m m m m PM (12)分分，第2小题满分8分．【解】（1）由⎪⎪⎩⎪⎪⎨⎧==2)23(2)6(ππf f 得，⎩⎨⎧==+283a b a ……2分，解得⎩⎨⎧==322b a ……3分将2=a ，34=b 代入xx b x a x f cos sin sin )(2+=得x x x x f cos sin 32sin 2)(2+=所以)(x f x x 2sin 32cos 1+-= (4)分)62sin(21π-+=x (5)分所以函数)(x f 的最小正周期ππ==22T …………6分（2）由（1）得，1]6)(2sin[2)(+-+=+πt x t x f ，所以1622sin 2)(+⎪⎭⎫ ⎝⎛-+=πt x x g (8)分函数)(x g 是偶函数，则对于任意的实数x ，均有)()(x g x g =-成立。

2018届上海市普陀区高三一模语文试题WORD版含解析

2018届上海市普陀区高三一模语文试题（解析版）一、积累运用1. 按题目要求填空（1）________________________，其可怪也欤！（韩愈《师说》）（2）郴江幸自绕郴山，________________________。

（秦观《________·郴州旅馆》）（3）李商隐《夜雨寄北》中“何当共剪西窗烛，却话巴山夜雨时”以虚写的手法表达无限思念，杜甫《月夜》中同样虚写相聚情景的两句是“___________________，___________________。

”【答案】(1). 今其智乃反不能及(2). 为谁流下潇湘去(3). 踏莎行(4). 何时依虚幌(5). 双照泪痕干【解析】试题分析：名句默写要注意字形，而字形与字义分不开，学生应借助字义来识记字形。

注意重点字的写法。

如“潇湘”“幌”。

要理解字义去记忆。

学生记忆的时候应该结合诗句的意思。

每句1分，句中有误该句不得分。

要求学生养成回头望的习惯，避免笔误。

按题目要求选择。

2. 小明宣传“节俭用餐不浪费”，要在学校食堂张贴标语，以下句子合适的一项是（）。

A. 由俭入奢易，由奢入俭难。

B. 为俭可以助廉，惟恕可以成德。

C. 俭，德之共也；侈，恶之大也。

D. 奢者狼藉俭者安，一凶一吉在眼前。

【答案】C【解析】试题分析：本题考查用语要得体。

本题要注意宣传的主题是“节俭用餐不浪费”，地点是学校食堂。

A指：由俭朴节约的生活转变成奢华富裕的生活比较容易，而由过惯了奢华富裕的生活变成俭朴节约的日子会比较难。

强调的是一种勤俭持家的生活之道。

适合贴在家里。

B项大意:只有节俭可以使人廉洁奉公,只有宽容可以使人养成好的品德。

强调的是俭和廉之间的关系，不适合贴在食堂。

D项大意：简朴的人和奢侈的人各有所报。

强调俭和奢对一个人，甚至一个国家的影响。

贴在食堂，语义太重了。

C项意思：节俭是一切美德中最大的大德，奢侈，是邪恶中最大的恶。

强调俭和奢的一般作用，适合贴在食堂。

2018届普陀区高考英语一模(含答案与详细解析)

普陀区2017学年度第一学期期终教学质量监控测试高三英语试卷考生注意：1. 考试时间120分钟，试卷满分140分。

2. 本考试设试卷和答题纸两部分。

所有答題必须涂（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. 答題前，务必在答題纸上填写准考证号和姓名，并将核对后的条形码貼在指定位置上，在答題纸反面清楚地填写姓名。

第 I 卷I.Listening Comprehension Section A 10%Directions: 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. Mother and child. B. Teacher and student.C. Husband and wife.D. Boss and secretary.2.A. They like reading today’s paper.B. They are interested in today’s paper.C. They found nothing interesting in today’s paper.D. They have no idea what the paper is about.3.A. In the concert. B. In the theatre. C. In the exhibition. D. In the studio.4.A. Getting ready to board a plane.B. Queuing up for the check-in.C. Meeting friends at the arrivals.D. Waiting at the baggage claim area.5.A. The man doesn’t care which colour is chosen.B. The woman prefers the colour.C. The man is concerned about the colour.D. The man intends to choose a different colour.6.A. Doing a lot of homework. B. Staying focused in class.C. Sleeping for a short break.D. Devoting all her spare time to learning.7. A. He was chairman of the club.B. He wanted to learn a new language.C. He wanted to know more about the club.D. He was interested in international advertisement.8.A. The man should work hard. B. The man should turn down the job offer.C. The man may have another chance.D. The man can apply for the job again.9.A. Its ending is not good enough. B. Its structure is not satisfying.C. It deserves an award.D. It is good except for the writing skills.10.A. She likes watching instead of playing. B. She is a good team sports player.C. She doesn’t like any kind of sports.D. She likes taking part in team sports.Section B 15%Directions: In Section B, you will hear two short passages and one longer conversation, and you will be asked several questions on each of the passages and the conversation. The passages and the conversation 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. It contains protein. B. It contains water.C. It helps the brain work properly.D. A full stomach leads to a good sleep.12. A. Sleep helps the brain control the senses.B. Sleep promotes rest.C. Sleep helps the brain revise and store information.D. Sleep reduces tiredness.13. A. Factors related to memory development. B. The importance of a good memory.C. The importance of improving memory.D. The misery caused by a poor memory.Questions 14 through 16 are based on the following weather forecast.14. A. Mountainous Area. B. Northern Europe.C. Eastern Europe.D. Southern Europe.15. A. Snowy. B. Cloudy.C. Rainy.D. Fine.16. A. Northern parts of the Mediterranean.B. Eastern parts of the Mediterranean.C. Central parts of the Mediterranean.D. Southern parts of the Mediterranean.Questions 17 through 20 are based on the following conversation.1. A. A university tutor. B. An insurance adviser.C. An overseas study officer.D. A visa officer.18. A. It is purchased in the country you will travel.B. It provides just a few kinds of medical services.C. It provides doctors who may speak your native language.D. It offers sufficient cash to pay the entire bill on the spot.19. A. It must be purchased in one’s home country before going abroad.B. It does not cover the minor medical expenses.C. It only recommends native doctors when you are aboard.D. It features personal paying first and getting money later.20.A. Consult other insurance companies.B. Buy the student health insurance.C. Get the international travel insurance.D. Choose neither insurance since it is not a must.II.Grammar and vocabulary Section A 10%Directions: After reading the passage below, fill in the blanks to make the passage coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.Recreational Vehicles (房车): On the RoadRecreational vehicles (RVs) are a typically American invention. Nationally, sales rose to 430,000 units last year, a 40-year high. At the inexpensive end, they sell for as little as $5,000 for a caravan (大篷车); deluxe versions cost up to $1,000,000 and are typically equipped with a bedroom, kitchen and bathroom that are bigger than ones in many European flats. The share prices of Thor Industries, the biggest RV-manufacturer in America, and Winnebago, the third-largest, (21) _________ (rise) by 43% and 17%, respectively so far.That is a big change. During the 2008-09 recession, notes Mr. Troiano, the owner of Continental RV, RV dealerships everywhere closed down, leaving his shop among the very few (22) _____________(leave) serving the New York metropolitan area. Mr. Troiano is on track (23) _________ (sell) more RVs this year than in any other since the early 2000s. The current rebound (反弹) is mostly (24) _________the economy’s recovery, but it also springs from the fact that new types of customer are embracing the lifestyle.A decade ago, the average age of an RV-owner was 49, and over 90% were white, says Kevin Broom of the Recreational Vehicle Industry Association (RVIA), which doesn’t indicate a bright futu re. Another boost comes from sufficient immigrants, (25) _________are keen to experience long, self-planned road trips in America. Mr. Troiano’s most recent big sale was to (26) _________ rich Asian family.The industry hopes that its poor record with foreign sales — last year less than 1% of RVs produced domestically (27) _________ (ship) to foreign markets —may improve, too. China’s government, for example, has planned to build 2,000 campgrounds by 2020, up from an estimated 300 today, in a bid to promote domestic tourism, particularly to remote rural regions. Chinese firms such as Yutong Bus make RVs, but not of the quality that many Chinese want. The country imported 1,000 vehicles last year, over half of them American.RV manufacturers are also marketing the concept (28) _________their motor homes can be commercial as well as leisure vehicles. They (29) _________allow travelling salesmen, businessmen to save on food and hotel costs. (30) _________you park it, it can be your office, as well as your home.【答案】 21. have risen22. left23. to sell24. due to/ owing to25. who26. a 27. were shipped 28. that 29. can 30. Wherever 【解析】21,考查动词，so far 表示迄今为止，时态用现在完成时，rise 是不及物动词无被动语态，故为have risen 22，考查动词，句意为“留下他在纽约大都会区为数不多的几家商店。

《上海市普陀区届高三上学期期末质量抽测(一模)(化学)》

普陀区2018学年度第一学期高三质量调研化学试卷2018.12本试卷分为第I卷和第Ⅱ卷两部分。

全卷共9页。

满分150分。

考试时间120分钟第I卷（共66分）考生注意：1、答第I卷前，考生务必在答题卡上用钢笔或圆珠笔清楚填写学校、班级、姓名、学生考试编号，并用2B铅笔正确涂写学生考试编号。

2、第I卷（1—22小题），由机器阅卷，答案必须全部涂写在答题卡上。

考生应将代表正确答案的小方格用2B铅笔涂黑。

注意试卷题号和答题卡上的编号一一对应，不能错位。

答案需要更改时，必须将原选项用橡皮擦去，重新选择。

答案不能写在试卷上，写在试卷上一律不给分。

相对原子质量： H—1 C—12 N—14 O—16 Na—23 S—32Cl－35.5 K－39 Fe—56 Cu—64 Br—80一、选择题：（本题共10分），每小题2分，只有一个正确选项，答案涂写在答题卡上。

1、化学在生活中无处不在，其中不科学的是A．含食品添加剂的食品都不属于绿色食品B．维生素C具有还原性，在人体内起抗氧化作用C．为防止月饼等富脂食品氧化变质，常在包装袋中放入硫酸亚铁D．地震后防疫人员在震区周围撒石灰，其作用是进行环境消毒，防止灾后出现疫情2、不能确定为磷元素的化学用语是A．3s23p3B．C．(n+1)sn(n+1) pn+1D．3、智利硝石与浓硫酸可用于制硝酸：NaNO3 + H2SO4(浓)−−微热−→NaHSO4+HNO3↑。

该反应说明A．硫酸比硝酸稳定B．硫酸的沸点比硝酸高C．H2SO4的酸性比硝酸强D．浓硫酸的氧化性比硝酸强4、利用海水资源能达到相关目标的是A．用潮汐发电，将化学能转化为电能B．不需富集，直接提取海水中的溴C．用海水中的NaCl制取烧碱和纯碱D．只需使海水中的碘升华就能得到碘单质5、下列判断正确的是A．氧化物中的氧元素一定呈 - 2价 B．酸性氧化物可能是金属氧化物C．化学键只存在于晶体中D．正四面体分子中键角不可能是600二、选择题（本题共36分），每小题3分，只有一个正确选项，答案涂写在答题卡上。

普陀区2018学年第一学期高三数学教学质量检测试卷

普陀区2018学年第一学期高三数学教学质量检测试卷2018.12一. 填空题（本大题共12题，1-6每题4分，7-12每题5分，共54分）1、函数21fx xx的定义城为 .2、若1sin3,则cos=2.3、设11{,,1,2,3}32，若()f x x 为偶函数，则.4、若直线l经过抛物线2C y x ：=4的焦点且其一个方向向量为1,1d ,则直线l 的方程为 .5、若一个球的体积是其半径的43倍,则该球的表面积为.6、在一个袋中装有大小、质地均相同的9只球,其中红色、黑色、白色各3只,若从袋中随机取出两个球,则至少有一个红球的概率为 .（结果用最简分数表示）7、设52360123611x x a a x a x a xa x ，则3a . (结果用数值表示)8、设0a 且1a,若log sin cos 0a xx，则88sin cos x x.9、如图,正四棱柱1111ABCDA B C D 的底面边长为4,记1111=AC B D F ，11=E BC B C ，则此棱柱的体积为.10、某人的月工资由基础工资和绩效工资组成2010年每月的基础工资为2100元、绩效工资为2000元从2011年起每月基础工资比上一年增加210元、绩效工资为上一年的110%.照此推算,此人2019年的年薪为 .万元(结果精确到0.1)11、已知点2,0A ,设BC 、是圆22:+1O x y上的两个不同的动点,且向量1OB tOA t OC（其中t为实数）,则=AB AC .12.设a 为常数,记函数1log 2ax f x a x（0a且1,0a x a ）的反函数为1fx ，则1121fa 111232++=212121a fffa aa.二. 选择题（本大题共4题，每题5分，共20分）13、下列关于双曲线22163x y：的判断，正确的是（）.A 渐近线方程为20x y .B 焦点坐标为30，.C 实轴长为12.D 顶点坐标为60，14、函数2cos 24yx的图像（）.A 关于原点对称.B 关于点3,08.C 关于y 轴对称.D 关于直线=4x 轴对称15、若a b c 、、表示直线，、表示平面，则“//a b ”成立的一个充分非必要条件是（）.A a b b c ，.B //,//a b .C a b，.D //a c bc，16、设f x 是定义在R 上的周期为4的函数，且2sin 2,012log ,14x x f xx x，记g x f x a ，若102a ，则函数g x 在区间-45，上零点的个数是（）.A 5.B 6.C 7.D 8三. 解答题（本大题共5题，共14+14+14+16+18=76分）17.在ABC 中，三个内角,,A B C 所对的边依次为,,a b c ，且1cos 4C. （1）求22cos +2sin 22A BC 的值；（2）设2c，求ab 的取值范围.18.已知曲线22:11612yx的左、右顶点分别为,A B ，设P 是曲线上的任意一点.（1）当P 异于,A B 时，记直线,PA PB 的斜率分别为12,k k ，求证：12k k 是定值；（2）设点C 满足0ACCB，且PC 的最大值为7，求的值.19.如图所示，某地出土的一种“钉”是由四条线段组成，其结构能使它任意抛至水平面后，总有一端所在的直线竖直向上，并记组成该“钉”的四条线段的公共点为O ，钉尖为1,2,3,4i A i.（1）设0iOA a a，当123,,A A A 在同一水平面内时，求1OA 与平面123A A A 所成角的大小（结果用反三角函数值表示）；（2）若该“钉”的三个钉尖所确定的三角形的面积为232cm ，要用某种线型材料复制100枚这种“钉”（损耗忽略不计），共需要该种材料多少米？xyOBAO4A 1A 2A 3A20.设数列n a 满足1133,52nnna a a n Na .（1）求23,a a 的值；（2）求证：11na 是等比数列，并求12111lim+nnn a a a 的值；（3）记n a 的前n 项和为n S ，是否存在正整数k ，使得对于任意的n （n N 且2n ）均有n S k 成立？若存在，求出k 的值；若不存在，说明理由.21. 已知函数()2xf x （xR ），记()()()g x f x f x .（1）解不等式：(2)()6f x f x ；（2）设k 为实数，若存在实数0(1,2]x ，使得200(2)()1g x k g x 成立，求k 取值范围；（3）记()(22)()h x f x a f x b （其中a 、b 均为实数），若对于任意[0,1]x ，均有1|()|2h x ，求a 、b 的值.参考答案一. 填空题1. (,0)(0,1] 2. 13 3. 24. 1y x 5. 4 6.7127. 08. 1 9. 32210. 10.4 11. 312. 2a二. 选择题13. B14. B15. C16. D三. 解答题17.（1）6158；（2）463(2,]3.18.（1）34；（2）7或17.19.（1）22arccos3（2）34200.6.20.（1）2913a ，32735a ；（2）2；（3）1k .21.（1）2(,log 3]；（2）27119[,)2259；（3）12a，172b.6158；（2）463(2,]3.17.（1）3 4；（2）7或17.18.（1）19.（1）22arccos3（2）34200.6.20、（1）由已知条件，可得：29 13a，327 35a；------4分20.（2）2；（3）1k.故不等式的解集为：2(,log3]；12a ，172b.。

6.-2018普陀高三英语一模卷

2018.1 普陀区高三英语第一学期期末质量抽查试卷(满分：140分考试时间：120分钟)第I卷(共100分)I. Listening ComprehensionSection A (10分)Directions: 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. Mother and child. B. Teacher and student.C. Husband and wife.D. Boss and secretary.2. A. They like reading today's paper.B. They are interested in today's paper.C. They found nothing interesting in today's paper.D. They have no idea what the paper is about.3. A. In the concert. B. In the theatre. C. In the exhibition. D. In the studio.4. A. Getting ready to board a plane. B. Queuing up for the check-in.C. Meeting friends at the arrivals.D. Waiting at the baggage claim area.5. A. The man doesn't care which colour is chosen.B. The woman prefers the colour.C. The man is concemed about the colour.D. The man intends to choose a different colour.6. A. Doing a lot of homework. B. Staying focused in class.C. Sleeping for a short break.D. Devoting all her spare time to learning.7. A. He was chairman of the club.B. He wanted to learn a new language.C. He wanted to know more about the club.D. He was interested in international advertisement.8. A. The man should work hard. B. The man should turn down the job offer.C. The man may have another chance.D. The man can apply for the job again.9. A. Its ending is not good enough. B. Its structure is not satisfying.C. It deserves an award.D. It is good except for the writing skills.10. A. She likes watching instead of playing. B. She is a good team sports player.C. She doesn't like any kind of sports.D. She likes taking part in team sports.Section B (15分)Directions:In Section B, you will hear two short passages and a longer conversation, and you will be asked several questions on each of the passages and the conversation. The passages and the conversation 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 is the best answer to the question you have heardQuestions 11 through 13 are based on the following news.11. A. It contains protein. B. It contains water.C. It helps the brain work properly.D. A full stomach leads to a good sleep.12. A. Sleep helps the brain control the senses.B. Sleep promotes rest.C. Sleep helps the brain revise and store information.D. Sleep reduces tiredness.13. A. Factors related to memory development. B. The importance of a good memory.C. The importance of improving memory.D. The misery caused by a poor memory.Questions 14 through 16 are based on the following weather forecast.14. A. Mountainous Area. B. Northern Europe.C. Eastern Europe.D. Southern Europe.15. A. Snowy. B. Cloudy. C. Rainy. D. Fine.16. A. Northern parts of the Mediterranean.B. Eastern parts of the Mediterranean.C. Central parts of the Mediterranean.D. Southern parts of the Mediterranean.Questions 17 through 20 are based on the following conversation.17. A. A university tutor. B. An insurance adviser.C. An overseas study officer.D. A visa officer.18. A. It is purchased in the country you will travel.B. It provides just a few kinds of medical services.C. It provides doctors who may speak your native language.D. It offers sufficien.t cash to pay the entire bill on the spot.19. A. It must be purchased in one's home country before going abroad.B. It does not cover the minor medical expenses.C. It only recommends native doctors when you are aboard.D. It features personal paying first and getting money later.20. A. Consult other insurance companies.B. Buy the student health insurance.C. Get the international travel insurance.D. Choose neither insurance since it is not a must.II. Grammar and VocabularySection A (10分)Directions: After reading the passage below, /ill in the blanks to make the passage coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.Recreational Vehicles (房车): On the RoadRecreational vehicles (RVs) are a typically American invention. Nationally, sales rose to 430,000 units last year, a 40-year high. At the inexpensive end, they sell for as little as $5,000 for acaravan (大篷车); deluxe versions cost up to $1,000:000 and are typically equipped with a bedroom, kitchen and bathroom that are bigger than ones in many European flats. The share prices of Thor Industries, the biggest RV-manufacturer in America, and Winnebago, the third-largest, (21)__________ (rise) by 43% and 17%, respectively so far.Continental RV, RV dealerships everywhere closed down4 leaving his shop among the very few (22)__________ (leave) serving the New York metropolitan area. Mr. Troiano is on-track (23)__________ (sell) more RVs this year than in any other since the early 2000s. The current rebound (反弹) is mostly (24)__________ __________ the economy's recovery, but it also springs from the fact that new types of customer are embracing the lifestyle.A decade ago, the average age of an RV-owner was 49, and over 90% were white, says Kevin Broom of the Recreational Vehicle Industry Association (RVIA), which doesn't indicate a bright future. Another boost comes from sufficient immigrants, (25)__________ are keen to experience long, self-planned road trips in America. Mr. Troiano's most recent big sale was to (26)__________ rich Asian family.The industry hopes that its poor record with foreign sales-last year less than 1% of RVs produced domestically (27)__________ (ship) to foreign markets - may improve, too. China's government, for example, has planned to build 2,000 campgrounds by 2020, up from an estimated 300 today, in a bid to promote domestic tourism, particularly to remote rural regions. Chinese firms such as Yutong Bus make RVs, but not of the quality that many Chinese want. The country imported 1,000 vehicles last year, over half of them American.RV manufacturers are also marketing the concept (28)__________ their motor homes can be commercial as well as leisure vehicles They (29)__________ allow travelling salesmen, businessmen to save on food and hotel costs. (30) __________you park it, it can be your office, as .well as your home.Section B (10分)Directions: Fill in each blank with. a proper word chosen from the box. Each word can be usedThe din(喧嚣) of a loud restaurant or party can make conversation difficult for anyone--but for the elderly, these settings can make it nearly impossible. The mechanics of hearing 31 with age, but the latest research focuses on another part of the problem--the slower 32 speed of aging brains, which have to work harder to translate sound into intelligible(可理解的) language.Research shows that musicians are better able to pick out speech from surrounding noise as they age compared to non-musicians. And a new study of auditory training with a 33 available brain training program suggests that most people who are hard of hearing can develop the same skills. The scientists showed that people trained for 40 hours over 8 weeks with Posit Science's "Brain Fitness" were able to pick out 41% more words from background noise compared to those who watched educational DVDs and were quizzed on their 34 after the same amount of time. The authors .received no funding from the makers of the program; the study was 35 by the National Institutes of Health.. iThe research included 67 older adults between 55 and 70, with an average age of 63. The auditory training came in the form of 36 hearing tasks that primed the participants to hear better by requiring them to identify various speech sounds and 37 between similar sounding syllables (音节), for example, as well as repeating back words and remembering stories.Both those who received the training and those who watched the DVDs were tested on short term memory, brain processing speed and the ability to hear speech in noisy settings. All of the participants showed improvement in these three 38 , but for the first time, the scientists also documented that the sharper hearing was 39 by earlier signaling in the brainstem.As the authors write in their paper, the training not only improved the ability to decode speech in noisy situations, but also sped up the brain's ability to 40 to the sound--bringing it to more "youthful" levels.III. Reading ComprehensionSection A (15分)Directions: 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 content.Depression: Second Biggest Cause of Disability in the World Depression is the second most common cause of disability worldwide after back pain, according to a review of research. The disease must be treated as a global public health 41 , experts report in the journal PL.OS Medicine. The study 42 clinical depression with more than 200 other diseas6s and injuries as 'a cause of disability. Globally, only a small proportion of patients have 43 to treatment the World Health Organization says.Depression was 44 at number two as a global cause of disability; but its impact varies in different countries and regions 45 , rates of major depression were highest in Afghanistan and lowest in Japan. Iii the UK, depression was rated at number three 46 years lived with a disability.Dr. Alize Ferrari from the University of Queensland's School of Population Health led the study. "Depression is a big problem and we 47 need to pay more attention to it than we are now," she told BBC News. There's still more work to be done in arousing awareness of the disease and also in 48 successful ways of treating it."The burden is different between countries, so it tends to be higher in 1ow and middle income countries and 49 in high income countries." Policy-makers had made an effort to bring depression to the forefront, but there was a lot more work to be done, she added. "There's lots of stigma (病症) we know 50 with mental health," she explained."What one person recognizes as disabling might be different to another person and might be different across countries as well. There are lots of cultural 51 and interpretations that come in place, which makes it all the more important to 52 awareness of the size of the problem and also signs and how to 53 it."The data -- for the year 2010 -- follows similar studies in 1990 and 2000 looking at the global burden of depression.Commenting on the study, Dr. Daniel Chisholm, a health economist at the department for mental health and substance abuse at the World Health Organization said depression was a very disabling condition. "It's a big public health 54 and a big problem to be reflected on but not enough is being done." Around the world only a tiny 55 of people get any sort of treatment or diagnosis.The WHO recently launched a global mental health action plan to raise awareness among policy-makers.41. A. concern B. issue C. priority D. discussion42. A. compared B. combined C. confused D. contacted43. A. objection B. access C. adaptation D. contribution44. A. considered B. evaluated C. determined D. ranked45. A. For example B. In addition C. In other words D. All in all46. A. in regard of B. in name of C. in terms of D. in face of47. A. probably B. definitely C. significantly D. randomly .48. A. coming up with B. making up C. putting up with D. consisting of49. A. severer B. heavier C. lighter D. lower50. A. related B. associated C. relevant D. close5l. A. ingredients B. interactions C. implications D. identities52. A. remove B. recreate C. raise D. rise53. A. avoid B. treat C. cure D. detect54. A. challenge B. agreement C. prediction D. outcome55. A. amount B. proportion C. quantity D. populationSection B (22分)Directions: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)Digital Etiquette (礼节)Digital Etiquette, or netiquette, is a set of rules for how to behave online. It's a lot like life etiquette, which is basically having good manners and treating others with respect. It's just as important in our digital lives, including how we act in online games-or how we communicate in emails, texts, instant messages and on social networking websites. All of these platforms let us talk and share instantly wherever we are.Unfortunately, some people can lose control the second they jump online. When they disagree with someone, or have strong feeling about a topic, they end up saying stuff they'd never say in person! They may send ruder emails and IMs or try to start arguments on message boards. That's called flaming, and it can lead to full-on flame wars, insulting arguments between two or more users.On the Internet, it's pretty easy to stay anonymous, or unidentified. Having a secret identity to hide behind can make people pretty brave. And when all they see of you is screen name or a funny icon, they might forget that they're dealing with a real human being!The principle is simple: Just like in real life, you should treat other people the way you want to be treated. You wouldn't want somebody to be rude to you, so don’t be rude to anyone else.Of course, netiquette isn't just about being nice; it's also about communicating clearly. That means keeping emails and IMs clear, and to the point. It also means making your messages easy to read and understand, which can depend on your audience: For-instance, some abbreviations and emoticons may be fine with friends. But they're generally not appropriate in formal communication. And whatever you do, don't write in all capital letters! Writing in all caps makes it seem like you're yelling.Lastly, make sure you ask permission before posting anything about your friends on a blog or a social networking site. People's personal information is private, and you can really ruin relationships if you post something that a friend - or a friend's parents - don't want on the web. And keep in mind that the Internet is not a private place; if you wouldn't want a parent, teacher or future employer to see something you post, don't post it!56. According to the passage, the users of social media are advised ______.A. to trigger arguments on message boardsB. to behave online with common courtesyC. to be respectful of others online rather than offlineD. to apply abbreviations and emoticons as many as possible57. Why might an anonymous Internet user feel bold enough to say horrible things in response to ablog post?A. Because he can make more friends if he says mean things.B. Because he knows his friends will recognize him and think better of him.C. Because he can insult others and not worry about revenge.D. Because he can impress older, smarter people with his remarks.58. Which of the following is the best way to text your uncle to say you'll be back in an hour?A. BC. D.59. Which of the following is a clear rule about posting photos online?A. If you take a photograph, it is yours to do as you please online.B. Information about your friends, including photographs, is private.C. It's illegal to post pictures online without permission from people in the pictures.D. You should always avoid posting images on the internet.(B)60. What can the employer distribute to motivate staff to recycle more?A. Educational posters.B. Annual reports.C. Regular newsletters.D. Competition rules.61. What can be bought to cut down on the waste produced by staff refreshments?A. Disposable goods.B. Writing notes.C. Envelopes.D. Ceramic tableware.62. Which of the following is NOT included in the hints?A. Unwanted PCs can be sent to charities if the company has to buy new ones:B. Waste paper can be used as envelopes for internal mails before being thrown away.C. One of the staff should be assigned to be responsible for the recycling issue.D. Educational posters can be displayed in the workplace to publicize the recycling scheme.(C)Given how valuable intelligence and automation are, we will continue to improve our technology if we are at all able to. At a certain point, we will build machines that are smarter than we are. Once we have machines that are smarter than we are, they will begin to improve themselves. And then we risk what the mathematician IJ Good called an "intelligence explosion". The process could get out of control.The concern is really that we will build machines that are much more competent than we are. And the slightest divergence between their goals and our own could destroy us. Just think about how we relate to ants. We don't hate them. We don't go out of our way to harm them. In fact, sometimes we take pains not to harm them. We step over them on the sidewalk. But whenever their presence seriously conflicts with one of our goals, we will kill them without hesitation. The concern is that we will one day build machines that, whether they're conscious or not, could treat us with similar disregard.The bare fact is that we will continue to improve our intelligent machines. We have problems that we desperately need to solve. So we will do this, if we can. The train is already out of the station, and there's no brake to pull. If we build machines that are more intelligent than we are, they will very likely develop in ways that we can't imagine, and exceed us in ways that we can't imagine.So imagine we hit upon a design of super intelligent AI that has no safety concerns. This machine would be the perfect labor-saving device. It can design the machine that can build the machine which can do any physical work, powered by sunlight, more or less for the cost of raw materials. So we're talking about the end of human labour. We're also talking about the end of most intellectual work. So what would apes like ourselves do in this circumstance?What would some nations do if they heard that some company in Silicon Valley was about to deploy (配置) a super intelligent AI? This machine would be capable of starting war, whether terrestrial (陆地的) or cyber, with unbelievable power.Given that the companies and governments building super intelligent AI are likely to perceive(感知) themselves as being in a race against all others, and that to win this race is to win the world, it seems likely that whatever is easier to do will get done first unless it is destroyed in the next moment.But the moment we admit that information processing is the source of intelligence, we have to admit that we are in the process of building some sort of god. Now would be a good time to make sure it's a god we can live with.63. When an intelligent machine becomes smarter than humanity, ______A. it will make itself better and may go beyond human controlB. it will help people to the fullest, especially in physical workC. it will threaten people by robbing them of jobsD. it will view itself as human race64. The underlined word "divergence" in Paragraph 2 almost means the same as "______".A. connectionB. hatredC. competitionD. disagreement65. How is the passage mainly developed?A. By making comparisons.B. By showing valid evidence.C. By giving assumptions.D. By analyzing statistics.66. Which of the following is the best title of the passage?A. For the God's sake, stop AI and be yourselves!B. Can we build AI without losing control over it?C. For or against AI, that is the question!D. How does super intelligence serve the people?Section C (8分)Directions:Read the following passage. Fill in each blank with a proper sentence given in the box.Women are insecure because there is no commonly accepted idea of what it means to be a good mother. Fathers have it easier in this regard; they just have to show up and they are automatically considered "good", whereas mothers are always trying to prove to themselves and the world that they aren't "bad". 67In some ways, things are getting worse. Years ago, a woman was allowed five years to shape her child's personality. In recent years, however, some psychologists tell mothers that the first three years of life are the most important, while others think that all critical events happen during the first year.Ironically, this panic about doing the right thing to produce the perfect child is probably the worst thing for the child and the parent. 68 Here is why.First, it is not harmful to children if their mothers work. Mothers who neglect their own need and abilities for the sake of their children do not benefit their children, their marriage or themselves.Second, there is no crucial moment or stage in early childhood in which a child's fate is determined forever. 69 Children are more flexible than that.Research also finds that some children who have had the best parental care and guidance later give in to drugs, addiction, mental illness or violence. 70 Between the parents' best efforts and the resulting child lie other factors: the child's nature, genetically influenced characters, experiences outside the family and the child's knowledge of events. Parents can help an inborn shy child learn to cope better in situations that make the child anxious, but they aren't going to turn her into Britney Spears.IV. Summary Writing (10分)Directions: Read the following passage. Summarize the main idea and the main point(s) of the passage in no more than 60 words. Use your own words as far as possible:"Where You Go" Doesn't Matter So MuchDuring the fall months at high school guidance counseling programs, juniors run to the stage to participate in an exercise to try and help them understand that it is not "where you go" that matters. They hold posters featuring the names and faces of famous people while their peers and parents shout out with confidence the names of elite colleges (名校) they assume the celebrities attended.The "oohs" and "aahs" follow as the audience learn that Steven Spielberg, Steve Jobs and Bill Gates dropped out of college and that Ken Burns graduated from Hampshire College. If even a few stressed students and their anxious parents benefit from this information, it is a worthwhile exercise.Even better is giving the students an assignment to identify the happy, successful people intheir own circle of family, friends, co-workers and neighbors and challenging them to go and ask "if or where they went to college?" as a means of broadening the conversation in their search for a life after high school.The key to success in college and beyond has more to do with what students do with their time during college than what college they choose to attend. A long-term study of 6,335 college graduates published by the National Bureau of Economic Research found that graduating from a college where entering students have higher SAT scores - one marker of elite colleges - didn't pay off in higher post-graduation income. Researchers found that students who applied to several elite schools but didn't attend them - either because of rejection or by their own choice - are more likely to earn high incomes later than students who actually attended elite schools.In a summary of the findings, the bureau says that "evidently, students' motivation, ambition and desire to learn have a much stronger effect on their later success than average academic ability of their classmates."V. Translation (15分)Directions:Translate the following sentences into English, using the words given in the brackets.72. 众所周知，与他人和睦相处是生活幸福的要素之一。

2018届上海市普陀区高三质量调研(一模)地理试题及答案 (4)

2018学年度第一学期普陀区高三质量调研考试地理试卷本试卷共11页，满分150分，考试时间120分钟。

全卷包括两大题，第一大题为选择题，第二大题为综合分析题。

考生注意：1．答卷前，务必在答题纸上用钢笔或圆珠笔清楚填写姓名、考号等。

2．答案必须全部涂或写在答题纸上。

一、选择题（共60分，每小题2分。

每小题只有一个正确答案）（一）今年下半年来，云南鲁甸、景谷两地先后发生了6级以上地震。

1．有关云南地震成因的说法一般认为是A．大陆板块相撞挤压B．大陆板块张裂C．大陆板块与大洋板块相撞挤压D．大陆板块与大洋板块相对张裂2．景谷地震较鲁甸地震伤亡少，其原因可能是A ．震中距较小B ．震级较大C ．人口稀少D ．烈度小（二）下图为在上海郊区一个蔬菜大棚所拍摄的照片，棚顶为黑色的尼龙网, 而不是常见的白色透明的塑料或者是玻璃大棚。

3．由此推断，此时段上海的天气可能是A ．连续不断的对流雨B ．持续的伏旱天气C ．连续的霜冻天气D ．台风来临狂风暴雨4．在此季节，农民这样做的主要目的是 A ．增加大气逆辐射，提高夜间温度 B ．减少地面辐射，防止夜间温度过低 C ．增强地面辐射，提高农作物存活率 D ．削弱太阳辐射，减少农作物水分蒸腾（三）下图为“塔里木盆地南缘绿洲附近的约特干古城遗址某处地层剖面图”深度（米）剖面距今年份（年）5．约特干古城遗址文化层深埋于地下的原因是①板块运动②河流泥沙沉积③风沙沉积④冰川冰碛物堆积A．①②B．①③C．②③D．③④6．据该地层剖面图，可推知约特干古城遗址自然环境变化的特点是A．1000年以来气候稳定不变 B．2000年以来沉积速度加快C．6000年以来湿润期大于干旱期 D．距今7000年开始出现绿洲（四）下图是从南极附近上空观察到的地球局部洋流示意图，图中箭头代表洋流流向。

7．我国去南极的考察船，通常都要驶过咆哮的西风带，该带强大的西风漂流常使船员感觉非常不舒服，该带在图中的位置是A．①地附近B．②地附近 C．③地附近D．④地附近8．对图中以③为中心的环流圈的分析正确的是A．其中的一支是西澳大利亚暖流B．是南半球的中高纬环流C．是南半球的副热带环流D．位于印度洋，洋流流向会随季节而改变9．有关洋流②对地理环境的影响，叙述正确的是A．在该洋流影响下，会形成世界性大渔场B．该洋流属于补偿流，会使沿岸地区增温增湿C．该洋流会使自南向北航行的船只航速增加D．在该洋流的影响下，沿岸地区形成了沙漠气候（五）流量是指单位时间内通过某一断面的水量，常用单位为m3/s。

2018-2019学年普陀区高三年级英语一模测试卷（含答案解析版）

普陀区2018-2019学年度第一学期期末质量监控试卷高三英语（满分140分，完卷时间120分钟）I. Listening Comprehension（略）II. Grammar and vocabularySection A 10%The Best Book I’ve Ever ReadFrankly, I have read nearly all of the great works of literature, but no book has ever impressed me as deeply or directly ____1____Joel Stein‘s Man Made: A Stupid Quest for Masendinity.Haven‘t we all, on some level, been Jewish boys in New Jersey in ____2____ 1970s with only female friends, an Easy-Bake oven and a strong preference for show tunes? Haven‘t we all had a panic attack ____3____learning we‘re going to have a son, since that means we‘re going to have to figure out how to throw footballs, watch other people throw footballs and decide ____4____ to be happy or sad about the results of football th rowing? Haven‘t we all then tried to correct our lack of maleness by becoming a man, fighting fires with firefighters, ____5____ (drive) a Lamborghini and doing three days of Army training camp? I know I have.The only parts I didn‘t fully enjoy were ___6___ in which the author suffered horribly. After just three hours of training camp, he fainted weakly into the arms of a soldier. The film rights to Man Made have already been sold to Fox, and I hope it gets ____7____ (turn) into a movie with George Clooney playing the Stein role, since they remind me so much of each other.____8____this is only Stein‘s first book, I would already consider him as someone like David Sedaris, Dave Barry, James Thurber, Mark Twain and Abraham Lincoln. I ____9____ (recommend) Man Made not just to all my friends and family but also to strangers on Twitter over and over again. My one fear is ____10____ after this great achievement, Stein will lose his ability to be a cruel critic of our shallow times.【答案】1. as 2. the3. when4. whether5. driving6. those7. turned8. Though/Although/While9. have recommended10. that【解析】【分析】本文是一篇说明文。

2018年上海市普陀区高考高三数学一模试卷及解析

2018年上海市普陀区高考数学一模试卷一.填空题(本大题共12题,1-6每题4分,7-12每题5分,共54分)1.(4分)设全集U＝{1,2,3,4,5},若集合A＝{3,4,5},则∁U A＝.2.(4分)若,则＝.3.(4分)方程log2(2﹣x)＋log2(3﹣x)＝log212的解x＝.4.(4分)的二项展开式中的常数项的值为.5.(4分)不等式的解集为.6.(4分)函数的值域为.7.(5分)已知i是虚数单位,是复数z的共轭复数,若,则在复平面内所对应的点所在的象限为第象限.8.(5分)若数列{a n}的前n项和(n∈N*),则＝.9.(5分)若直线l：x＋y＝5与曲线C：x2＋y2＝16交于两点A(x1,y1)、B(x2,y2),则x1y2＋x2y1的值为.10.(5分)设a1、a2、a3、a4是1,2,3,4的一个排列,若至少有一个i(i＝1,2,3,4)使得a i＝i成立,则满足此条件的不同排列的个数为.11.(5分)已知正三角形ABC的边长为,点M是△ABC所在平面内的任一动点,若,则的取值范围为.12.(5分)双曲线绕坐标原点O旋转适当角度可以成为函数f(x)的图象,关于此函数f(x)有如下四个命题：①f(x)是奇函数；②f(x)的图象过点或；③f(x)的值域是；④函数y＝f(x)﹣x有两个零点；则其中所有真命题的序号为.二.选择题(本大题共4题,每题5分,共20分)13.(5分)若数列{a n}(n∈N*)是等比数列,则矩阵所表示方程组的解的个数是()A.0个B.1个C.无数个D.不确定14.(5分)“m＞0”是“函数f(x)＝|x(mx＋2)|在区间(0,＋∞)上为增函数”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.(5分)用长度分别为2、3、5、6、9(单位：cm)的五根木棒连接(只允许连接,不允许折断),组成共顶点的长方体的三条棱,则能够得到的长方体的最大表面积为()A.258cm2B.414cm2C.416cm2D.418cm216.(5分)定义在R上的函数f(x)满足,且f(x﹣1)＝f(x＋1),则函数在区间[﹣1,5]上的所有零点之和为()A.4B.5C.7D.8三.解答题(本大题共5题,共14＋14＋14＋16＋18＝76分)17.(14分)如图所示的圆锥的体积为,底面直径AB＝2,点C是弧的中点,点D是母线PA的中点.(1)求该圆锥的侧面积；(2)求异面直线PB与CD所成角的大小.18.(14分)某快递公司在某市的货物转运中心,拟引进智能机器人分拣系统,以提高分拣效率和降低物流成本,已知购买x台机器人的总成本p(x)＝＋x＋150万元.(1)若使每台机器人的平均成本最低,问应买多少台？(2)现按(1)中的数量购买机器人,需要安排m人将邮件放在机器人上,机器人将邮件送达指定落袋格口完成分拣(如图),经实验知,每台机器人的日平均分拣量q(m)＝(单位：件),已知传统人工分拣每人每日的平均分拣量为1200件,问引进机器人后,日平均分拣量达最大值时,用人数量比引进机器人前的用人数量最多可减少百分之几？19.(14分)设函数f(x)＝sin(ωx＋φ)(ω＞0,),已知角φ的终边经过点,点M(x1,y1)、N(x2,y2)是函数f(x)图象上的任意两点,当|f(x1)﹣f(x2)|＝2时,|x1﹣x2|的最小值是.(1)求函数y＝f(x)的解析式；(2)已知△ABC面积为,角C所对的边,,求△ABC的周长. 20.(16分)设点F1、F2分别是椭圆(t＞0)的左、右焦点,且椭圆C上的点到点F2的距离的最小值为,点M、N是椭圆C上位于x轴上方的两点,且向量与向量平行.(1)求椭圆C的方程；(2)当时,求△F1MN的面积；(3)当时,求直线F2N的方程.21.(18分)设d为等差数列{a n}的公差,数列{b n}的前n项和T n,满足(n∈N*),且d＝a5＝b2,若实数m∈P k＝{x|a k﹣2＜x＜a k＋3}(k∈N*,k ≥3),则称m具有性质P k.(1)请判断b1、b2是否具有性质P6,并说明理由；(2)设S n为数列{a n}的前n项和,若{S n﹣2λa n}是单调递增数列,求证：对任意的k(k ∈N*,k≥3),实数λ都不具有性质P k；(3)设H n是数列{T n}的前n项和,若对任意的n∈N*,H2n﹣1都具有性质P k,求所有满足条件的k的值.2018年上海市普陀区高考数学一模试卷参考答案与试题解析一.填空题(本大题共12题,1-6每题4分,7-12每题5分,共54分)1.(4分)设全集U＝{1,2,3,4,5},若集合A＝{3,4,5},则∁U A＝{1,2} .【试题解答】解：∵全集U＝{1,2,3,4,5},集合A＝{3,4,5},∴∁U A＝{1,2}.故答案为：{1,2}.2.(4分)若,则＝.【试题解答】解：,∴＝.故答案为：.3.(4分)方程log2(2﹣x)＋log2(3﹣x)＝log212的解x＝﹣1.【试题解答】解：∵方程log2(2﹣x)＋log2(3﹣x)＝log212,∴,即,解得x＝﹣1.故答案为：﹣1.4.(4分)的二项展开式中的常数项的值为﹣84.【试题解答】解：二项展开式的通项＝,由,得r＝3.∴的二项展开式中的常数项为.故答案为：﹣84.5.(4分)不等式的解集为[0,1)∪(1,2] .【试题解答】解：由题意得：,解得：0≤x＜1或1＜x≤2,故答案为：[0,1)∪(1,2].6.(4分)函数的值域为[﹣1,3] .【试题解答】解：∵＝sinx＋cosx＋1＝2sin(x＋)＋1,∵sin(x＋)∈[﹣1,1],∴f(x)＝2sin(x＋)＋1∈[﹣1,3].故答案为：[﹣1,3].7.(5分)已知i是虚数单位,是复数z的共轭复数,若,则在复平面内所对应的点所在的象限为第一象限.【试题解答】解：,设z＝a＋bi,则z×2i﹣(1＋i)＝0,即(a＋bi)×2i﹣1﹣i＝0,则2ai﹣2b﹣1﹣i＝0,∴﹣2b﹣1＋(2a﹣1)i＝0,则,则,∴z＝﹣i,则＝＋i,∴则在复平面内所对应的点位于第一象限,故答案为：一.8.(5分)若数列{a n}的前n项和(n∈N*),则＝﹣2.【试题解答】解：数列{a n}的前n项和(n∈N*),可得n＝1时,a1＝S1＝﹣3＋2＋1＝0；当n≥2时,a n＝S n﹣S n＝﹣3n2＋2n＋1＋3(n﹣1)2﹣2n＋2﹣1﹣1＝﹣6n＋5,则＝＝(﹣2＋)＝﹣2＋0＝﹣2.故答案为：﹣2.9.(5分)若直线l：x＋y＝5与曲线C：x2＋y2＝16交于两点A(x1,y1)、B(x2,y2),则x1y2＋x2y1的值为16.【试题解答】解：直线l：x＋y＝5与曲线C：x2＋y2＝16交于两点A(x1,y1)、B(x2,y2),则：,所以：2x2﹣10x＋9＝0,则：x1＋x2＝5,,则：x1y2＋x2y1＝x1(5﹣x2)＋x2(5﹣x1),＝5(x1＋x2)﹣2x1x2,＝25﹣9,＝16.故答案为：16.10.(5分)设a1、a2、a3、a4是1,2,3,4的一个排列,若至少有一个i(i＝1,2,3,4)使得a i＝i成立,则满足此条件的不同排列的个数为15.【试题解答】解：根据题意,a1、a2、a3、a4是1,2,3,4的一个排列,则所有的排列有A44＝24个,假设不存在i(i＝1,2,3,4)使得a i＝i成立,则a1可以在第2、3、4位置,有3种情况,假设a1在第二个位置,则a1可以在第1、3、4位置,也有3种情况,此时a3、a4只有1种排法,剩余的两个数在其余两个位置,有1种情况,则不存在i(i＝1,2,3,4)使得a i＝i成立的情况有3×3＝9种,则至少有一个i(i＝1,2,3,4)使得a i＝i成立排列数有24﹣9＝15个；故答案为：15.11.(5分)已知正三角形ABC的边长为,点M是△ABC所在平面内的任一动点,若,则的取值范围为[0,6] .【试题解答】解：以A点为原点,建立如图所示的平面直角坐标系,则A(0,0),B(,0),C(,),∵,不妨设M(cosθ,sinθ),∴＋＋＝(﹣cosθ,﹣sinθ)＋(﹣cosθ,﹣sinθ)＋(﹣cosθ,﹣sinθ)＝(﹣3cosθ,﹣3sinθ),∴|＋＋|2＝(﹣3cosθ)2＋(﹣3sinθ)2＝9(2﹣cosθ﹣sinθ)＝18﹣18sin(θ＋),∵﹣1≤sin(θ＋)≤1,∴0≤18﹣18sin(θ＋)≤36,∴的取值范围为[0,6],故答案为：[0,6]12.(5分)双曲线绕坐标原点O旋转适当角度可以成为函数f(x)的图象,关于此函数f(x)有如下四个命题：①f(x)是奇函数；②f(x)的图象过点或；③f(x)的值域是；④函数y＝f(x)﹣x有两个零点；则其中所有真命题的序号为①②.【试题解答】解：双曲线关于坐标原点对称,可得旋转后得到的函数f(x)的图象关于原点对称,即有f(x)为奇函数,故①对；由双曲线的顶点为(±,0),渐近线方程为y＝±x,可得f(x)的图象的渐近线为x＝0和y＝±x,图象关于直线y＝x对称,可得f(x)的图象过点,或,由对称性可得f(x)的图象按逆时针60°旋转位于一三象限；按顺时针旋转60°位于二四象限；故②对；f(x)的图象按逆时针旋转60°位于一三象限,由图象可得顶点为点,或,不是极值点,则f(x)的值域不是；f(x)的图象按顺时针旋转60°位于二四象限,由对称性可得f(x)的值域也不是.故③不对；当f(x)的图象位于一三象限时,f(x)的图象与直线y＝x有两个交点,函数y＝f(x)﹣x有两个零点；当f(x)的图象位于二四象限时,f(x)的图象与直线y＝x没有交点,函数y＝f(x)﹣x没有零点.故④错.故答案为：①②.二.选择题(本大题共4题,每题5分,共20分)13.(5分)若数列{a n}(n∈N*)是等比数列,则矩阵所表示方程组的解的个数是()A.0个B.1个C.无数个D.不确定【试题解答】解：根据题意,矩阵所表示方程组为,又由数列{a n}(n∈N*)是等比数列,则有＝＝＝,则方程组的解有无数个；故选：C.14.(5分)“m＞0”是“函数f(x)＝|x(mx＋2)|在区间(0,＋∞)上为增函数”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【试题解答】解：∵m＞0,∴函数f(x)＝|x(mx＋2)|＝|mx2＋2x|,∵f(0)＝0,∴f(x)在区间(0,＋∞)上为增函数”；∵函数f(x)＝|x(mx＋2)|＝|mx2＋2x|在区间(0,＋∞)上为增函数,f(0)＝0,∴m∈R,∴“m＞0”是“函数f(x)＝|x(mx＋2)|在区间(0,＋∞)上为增函数”的充分非必要条件.故选：A.15.(5分)用长度分别为2、3、5、6、9(单位：cm)的五根木棒连接(只允许连接,不允许折断),组成共顶点的长方体的三条棱,则能够得到的长方体的最大表面积为()A.258cm2B.414cm2C.416cm2D.418cm2【试题解答】解：设长方体的三条棱分别为a,b,c,则长方体的表面积S＝2(ab＋bc＋ac)≤(a＋b)2＋(b＋c)2＋(a＋c)2,当且仅当a＝b＝c时上式“＝”成立.由题意可知,a,b,c不可能相等,故考虑当a,b,c三边长最接近时面积最大,此时三边长为8,8,9,用2、6连接,3、5连接各为一条棱,第三条棱为9组成长方体,此时能够得到的长方体的最大表面积为2(8×8＋8×9＋8×9)＝416(cm2).故选：C.16.(5分)定义在R上的函数f(x)满足,且f(x﹣1)＝f(x＋1),则函数在区间[﹣1,5]上的所有零点之和为()A.4B.5C.7D.8【试题解答】解：∵函数,且f(x﹣1)＝f(x＋1),函数的周期为2,函数,的零点,就是y＝f(x)与y＝图象的交点的横坐标,∴y＝f(x)关于点(0,3)中心对称,将函数两次向右平移2个单位,得到函数y＝f(x)在[﹣1,5]上的图象,每段曲线不包含右端点(如下图),去掉端点后关于(2,3)中心对称.又∵y＝＝3＋关于(2,3)中心对称,故方程f(x)＝g(x)在区间[﹣1,5]上的根就是函数y＝f(x)和y＝g(x)的交点横坐标,共有三个交点,自左向右横坐标分别为x1,x2,x3,其中x1和x3关于(2,3)中心对称,∴x1＋x3＝4,x2＝1,故x1＋x2＋x3＝5.故选：B.三.解答题(本大题共5题,共14＋14＋14＋16＋18＝76分)17.(14分)如图所示的圆锥的体积为,底面直径AB＝2,点C是弧的中点,点D是母线PA的中点.(1)求该圆锥的侧面积；(2)求异面直线PB与CD所成角的大小.【试题解答】解：(1)∵圆锥的体积为,底面直径AB＝2,∴,解得PO＝,∴PA＝＝2,∴该圆锥的侧面积S＝πrl＝π×1×2＝2π.(2)∵圆锥的体积为,底面直径AB＝2,点C是弧的中点,点D是母线PA的中点.∴PO⊥平面ABC,OC⊥AB,∴以O为原点,OC为x轴,OB为y轴,OP为z轴,建立空间直角坐标系,则A(0,﹣1,0),P(0,0,),D(0,﹣,),B(0,1,0),C(1,0,0),＝(0,1,﹣),＝(﹣1,﹣,),设异面直线PB与CD所成角为θ,则cosθ＝＝＝,∴θ＝.∴异面直线PB与CD所成角为.18.(14分)某快递公司在某市的货物转运中心,拟引进智能机器人分拣系统,以提高分拣效率和降低物流成本,已知购买x台机器人的总成本p(x)＝＋x＋150万元.(1)若使每台机器人的平均成本最低,问应买多少台？(2)现按(1)中的数量购买机器人,需要安排m人将邮件放在机器人上,机器人将邮件送达指定落袋格口完成分拣(如图),经实验知,每台机器人的日平均分拣量q(m)＝(单位：件),已知传统人工分拣每人每日的平均分拣量为1200件,问引进机器人后,日平均分拣量达最大值时,用人数量比引进机器人前的用人数量最多可减少百分之几？【试题解答】解：(1)由总成本p(x)＝＋x＋150万元,可得每台机器人的平均成本y＝＝2.当且仅当,即x＝300时,上式等号成立.∴若使每台机器人的平均成本最低,应买300台；(2)引进机器人后,每台机器人的日平均分拣量q(m)＝,当1≤m≤30时,300台机器人的日平均分拣量为160m(60﹣m)＝﹣160m2＋9600m,∴当m＝30时,日平均分拣量有最大值144000.当m＞30时,日平均分拣量为480×300＝144000.∴300台机器人的日平均分拣量的最大值为144000件.若传统人工分拣144000件,则需要人数为人.∴日平均分拣量达最大值时,用人数量比引进机器人前的用人数量最多可减少＝75%.19.(14分)设函数f(x)＝sin(ωx＋φ)(ω＞0,),已知角φ的终边经过点,点M(x1,y1)、N(x2,y2)是函数f(x)图象上的任意两点,当|f(x1)﹣f(x2)|＝2时,|x1﹣x2|的最小值是.(1)求函数y＝f(x)的解析式；(2)已知△ABC面积为,角C所对的边,,求△ABC的周长.【试题解答】解：(1)已知角φ的终边经过点,且,则：φ＝﹣,点M(x1,y1)、N(x2,y2)是函数f(x)图象上的任意两点,当|f(x1)﹣f(x2)|＝2时,|x1﹣x2|的最小值是.所以：ω＝,所以：；(2)由于：＝sin()＝,且0＜C＜π,解得：C＝,△ABC面积为,所以：,解得：ab＝20.由于：c2＝a2＋b2﹣2abcosC,c＝2,所以：20＝(a＋b)2﹣3ab,解得：a＋b＝4,所以：.20.(16分)设点F1、F2分别是椭圆(t＞0)的左、右焦点,且椭圆C上的点到点F2的距离的最小值为,点M、N是椭圆C上位于x轴上方的两点,且向量与向量平行.(1)求椭圆C的方程；(2)当时,求△F1MN的面积；(3)当时,求直线F2N的方程.【试题解答】解：(1)点F1、F2分别是椭圆(t＞0)的左、右焦点,∴a＝t,c＝t,∵椭圆C上的点到点F2的距离的最小值为,∴a﹣c＝t﹣t＝2﹣2,∴椭圆的方程为＋＝1,(2)由(1)可得F1(﹣2,0),F2(2,0),点M、N是椭圆C上位于x轴上方的两点,可设N(2cosθ,2sinθ),∴＝(2cosθ＋2,2sinθ),＝(2cosθ﹣2,2sinθ),∵,∴(2cosθ＋2)(2cosθ﹣2)＋4sin2θ＝0,解得cosθ＝0,sinθ＝1,∴N(0,2),∴＝(﹣2,2),∴k＝＝﹣1,∵向量与向量平行,∴直线F1M的斜率为﹣1,∴直线方程为y＝﹣x﹣2,联立方程组,解得x＝0,y＝﹣2(舍去),或x＝﹣,y＝,∴M(﹣,),∴|F1M|＝＝,点N到直线直线y＝﹣x﹣2的距离为d＝＝2,∴△F1MN的面积＝|F1M|•d＝××2＝,(3)∵向量与向量平行,∴λ＝,∴,∴(λ﹣1)||＝,即λ＞1,设M(x1,y1),N(x2,y2),∴λ(x1＋2)＝x2﹣2,y2＝λy1,∴x2＝λx1＋2(λ＋1)∵＋＝1,∴x22＋2y22＝8,∴[λx1＋2(λ＋1)]2＋2λ2y12＝12λ2＋8λ＋4＋4λ(λ＋1)x1＝8,∴4λ(λ＋1)x1＝(1﹣3λ)(λ＋1),∴x1＝＝﹣3,∴y12＝4﹣,∴||2＝(x1＋2)2＋y12＝(﹣3＋2)2＋4﹣＝,∴||＝,∴(λ﹣1)•＝,∴λ2﹣2λ﹣1＝0解得λ＝2＋,或λ＝2﹣(舍去)∴x1＝﹣3＝﹣3＝﹣1﹣,∴y12＝4﹣＝2﹣＝＝,∴y1＝,∴k＝＝﹣,∴直线F2N的方程为y﹣0＝﹣(x﹣2),即为x＋y﹣2＝021.(18分)设d为等差数列{a n}的公差,数列{b n}的前n项和T n,满足(n∈N*),且d＝a5＝b2,若实数m∈P k＝{x|a k﹣2＜x＜a k＋3}(k∈N*,k ≥3),则称m具有性质P k.(1)请判断b1、b2是否具有性质P6,并说明理由；(2)设S n为数列{a n}的前n项和,若{S n﹣2λa n}是单调递增数列,求证：对任意的k(k ∈N*,k≥3),实数λ都不具有性质P k；(3)设H n是数列{T n}的前n项和,若对任意的n∈N*,H2n﹣1都具有性质P k,求所有满足条件的k的值.【试题解答】解：(1)(n∈N*),可得n＝1时,T1＋＝﹣b1＝﹣T1,解得b1＝﹣,T2＋＝b2＝﹣＋b2＋＝b2,T3＋＝﹣b3＝﹣＋b2＋b3＋,即b2＋2b3＝,T4＋＝b4＝﹣＋b2＋b3＋b4＋,即b2＋b3＝,解得b2＝,b3＝﹣,同理可得b4＝,b5＝﹣,b6＝,b7＝﹣,…,b2n﹣1＝﹣,d＝a5＝b2,可得d＝a1＋4d＝,解得a1＝﹣,d＝,a n＝,P6＝{x|a4＜x＜a9}(k∈N*,k≥3)＝{x|0＜x＜},则b1不具有性质P6,b2具有性质P6；(2)证明：设S n为数列{a n}的前n项和,若{S n﹣2λa n}是单调递增数列,可得S n＋1﹣2λa n＋1≥S n﹣2λa n,即为≥,化为4λ＋6≤2n对n为一切自然数成立,即有4λ＋6≤2,可得λ≤﹣1,又P k＝{x|a k﹣2＜x＜a k＋3}(k∈N*,k≥3),且a1＝﹣,d＞0,可得P k中的元素大于﹣1,则对任意的k(k∈N*,k≥3),实数λ都不具有性质P k；(3)设H n是数列{T n}的前n项和,若对任意的n∈N*,H2n﹣1都具有性质P k,由于H1＝T1＝b1＝﹣,H3＝T1＋T2＋T3＝﹣,H5＝T1＋T2＋T3＋T4＋T5＝﹣, H7＝﹣＋0﹣＝﹣,…,H2n﹣1＝H2n﹣3＋b2n﹣1,(n≥2),当k＝3时,P3＝{x|a1＜x＜a6}＝{x|﹣＜x＜},当k＝4时,P4＝{x|a2＜x＜a7}＝{x|﹣＜x＜},当k＝5时,P5＝{x|a3＜x＜a8}＝{x|﹣＜x＜1},当k＝6时,P3＝{x|a4＜x＜a9}＝{x|0＜x＜},显然k＝5,6不成立,故所有满足条件的k的值为3,4.。

上海普陀高三第一次教学质量调研化学试卷(带答案)-精选文档

上海普陀2018届高三第一次教学质量调研化学试卷（带答案）化学是自然科学的一种，以下是上海普陀2018届高三第一次教学质量调研化学试卷，请考生及时联系。

一、选择题(本题共10分，每小题2分，每题只有一个正确选项)pH中起作用的离子是A.Na+ .Cl- C.HCO3- D.Fe2+2、已知的相对原子质量为34.969，下列相关说法正确的是A.氯元素的近似相对原子质量为35B.氯元素的某种同位素的质量数为35C.氯元素的中子数为18D.氯原子的质量为34.9693、水溶液受热不能分解的物质是A.HClOB.HNO3C.Ca(HCO3)2D.NaNO34、下列对有机物的性质描述正确的是A.含有羟基的有机物都能与醋酸发生酯化反应B.氨基酸、乙酸和苯酚都能与氢氧化钠溶液反应C.醇类、卤代烃都能发生消去反应D.除饱和烃之外的烃都能发生聚合反应5、2018年8月12日天津港国际物流中心内某公司危险品仓库发生严重火灾涉及的危险品包括压缩液化气体、电石和过氧化物等。

以下方法正确的是A.使用大量水B.使用泡沫灭火器C.使用黄沙D.使用干粉(3)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、能用共价键键能大小解释的是A.还原性：HIHFB.溶解度：HFHIC.沸点：HFHID.分解温度：HFHI7、勒沙特列原理是自然界一条重要的基本原理下列事实能用勒沙特列原理解释的是A.NO2压后颜色先变深后变浅B.对2HIg)H2(g)+I2(g)平衡体系加压颜色迅速变深C.合成氨工业采高温、高压提高氨的产率D.配制硫酸亚铁溶液时，常加入少量铁屑防止氧化8、下列各组物质均属于分子晶体且为化合物的是A.NH3、HD、C10H8B.PCl3、CO2、AlCl3C.SO2、SiO2、P2O5 Dl4、H2O2、Na2S9、其它条件不变仅升高温度，一定增大的是A.强碱在水中的溶解度B.吸热反应的热效应C.化学平衡常数KD.盐类水解程度10、对右图装置铁的防护)分析正确的是A.甲装置是牺牲阳极的阴极保护法B.乙装置是牺牲阳极的阴极保护法C.一段时间后甲、乙装置中pH均增大D.甲、乙装置中铁电极的电极反应式均为：2H++2eH211、《Inorganic Syntheses》中有一制备某干燥纯净气体的装置。

上海市普陀区2018届高三一模数学试卷

上海市普陀区2018届高三一模数学试卷一、填空题（本大题共12题，1~6每题4分，7~12每题5分，满分54分）1.设全集U{1,2,3,4,5}，若会合A{3,4,5}，则C U A；2. 若1 3sin ，则cos( ) ；4 23.方程log2(2x)log2(3x)log212的解x；4. ( 19x ) 的二项睁开式中的常数项的值为；x15.不等式1的解集为；|x1|6. 函数2 xf ( x) 3 sin x 2 cos 的值域为；2z 1 i7. 已知i 是虚数单位，z 是复数z 的共轭复数，若01 2i ，则z 在复平面内所对应的点所在的象限为第象限；2 n n N 8. 若数列{ a n } 的前n项和3 2 1( )S n n ，则a n lim ；n 3n229.若直线l:xy5与曲线C :xy16交于两点A(x1,y1)，B(x2,y2)，则x1y2x2y1的值为；10.设a1,a2,a3,a4是1,2,3,4的一个摆列，若起码有一个i(i1,2,3,4)使得a i i建立，则知足此条件的不一样摆列的个数为；11.已知正三角形ABC的边长为3，点M是ABC所在平面内的任一动点，若|MA|1，则|MAMBMC|的取值范围为；2x2 12. 双曲线y 13 绕坐标原点 O 旋转适合角度能够成为函数f ( x) 的图像，对于函数f)有以下四个命题：(x①f(x)是奇函数；②f ( x) 的图像经过点32,32或32,32；33③f(x)的值域是,,；22④函数yf(x)x有两个零点；则此中全部真命题的序号为；二、选择题（本大题共4题，每题5分，满分20分）13. 若数列{a n} ( n N ) 是等比数列，则矩阵a1a5aa26a4a8所表示方程组的解的个数是（）A.0个B.1个C.无数个D.不确立14.“m0”是“函数f(x)|x(mx2)|在区间(0,)上为增函数”的（）A.充足非必需条件B.必需非充足条件C.充要条件D.既非充足也非必需条件15.用长度分别为2、3、5、6、9（单位：cm）的五根木棒连结（只同意连结，不一样意折断），构成共极点的长方体的三条棱，则能够获得的长方体的最大表面积为（）A. 2258 cm B.2414 cm C.2416 cm D.418cm216. 定义在R上的函数f (x ) 知足f( x)x2 2, 0 x 1x4 2 , 1 x 0，且f (x 1) f ( x1) ,则函数3x5g(x)f(x)在区间[1,5]上全部零点之和为（）x2A.4B.5C.7D.8三、解答题（本大题共5题，满分76分）17.（此题满分14分，第1小题6分，第2小题8分）如图 1 所示的圆锥的体积为33，底面直径AB 2 ，点C 是弧AB的中点，点D 是母线PA的中点。

6. 2018普陀高三英语一模卷

2018.1 普陀区高三英语第一学期期末质量抽查试卷(满分：140分考试时间：120分钟)第I卷(共100分)I. Listening ComprehensionSection A (10分)Directions: 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. Mother and child. B. Teacher and student.C. Husband and wife.D. Boss and secretary.2. A. They like reading today's paper.B. They are interested in today's paper.C. They found nothing interesting in today's paper.D. They have no idea what the paper is about.3. A. In the concert. B. In the theatre. C. In the exhibition. D. In the studio.4. A. Getting ready to board a plane. B. Queuing up for the check-in.C. Meeting friends at the arrivals.D. Waiting at the baggage claim area.5. A. The man doesn't care which colour is chosen.B. The woman prefers the colour.C. The man is concemed about the colour.D. The man intends to choose a different colour.6. A. Doing a lot of homework. B. Staying focused in class.C. Sleeping for a short break.D. Devoting all her spare time to learning.7. A. He was chairman of the club.B. He wanted to learn a new language.C. He wanted to know more about the club.D. He was interested in international advertisement.8. A. The man should work hard. B. The man should turn down the job offer.C. The man may have another chance.D. The man can apply for the job again.9. A. Its ending is not good enough. B. Its structure is not satisfying.C. It deserves an award.D. It is good except for the writing skills.10. A. She likes watching instead of playing. B. She is a good team sports player.C. She doesn't like any kind of sports.D. She likes taking part in team sports.Section B (15分)Directions:In Section B, you will hear two short passages and a longer conversation, and you will be asked several questions on each of the passages and the conversation. The passages and the conversation 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 is the best answer to the question you have heardQuestions 11 through 13 are based on the following news.11. A. It contains protein. B. It contains water.C. It helps the brain work properly.D. A full stomach leads to a good sleep.12. A. Sleep helps the brain control the senses.B. Sleep promotes rest.C. Sleep helps the brain revise and store information.D. Sleep reduces tiredness.13. A. Factors related to memory development. B. The importance of a good memory.C. The importance of improving memory.D. The misery caused by a poor memory.Questions 14 through 16 are based on the following weather forecast.14. A. Mountainous Area. B. Northern Europe.C. Eastern Europe.D. Southern Europe.15. A. Snowy. B. Cloudy. C. Rainy. D. Fine.16. A. Northern parts of the Mediterranean.B. Eastern parts of the Mediterranean.C. Central parts of the Mediterranean.D. Southern parts of the Mediterranean.Questions 17 through 20 are based on the following conversation.17. A. A university tutor. B. An insurance adviser.C. An overseas study officer.D. A visa officer.18. A. It is purchased in the country you will travel.B. It provides just a few kinds of medical services.C. It provides doctors who may speak your native language.D. It offers sufficien.t cash to pay the entire bill on the spot.19. A. It must be purchased in one's home country before going abroad.B. It does not cover the minor medical expenses.C. It only recommends native doctors when you are aboard.D. It features personal paying first and getting money later.20. A. Consult other insurance companies.B. Buy the student health insurance.C. Get the international travel insurance.D. Choose neither insurance since it is not a must.II. Grammar and VocabularySection A (10分)Directions: After reading the passage below, /ill in the blanks to make the passage coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.Recreational Vehicles (房车): On the RoadRecreational vehicles (RVs) are a typically American invention. Nationally, sales rose to 430,000 units last year, a 40-year high. At the inexpensive end, they sell for as little as $5,000 for acaravan (大篷车); deluxe versions cost up to $1,000:000 and are typically equipped with a bedroom, kitchen and bathroom that are bigger than ones in many European flats. The share prices of Thor Industries, the biggest RV-manufacturer in America, and Winnebago, the third-largest, (21)__________ (rise) by 43% and 17%, respectively so far.Continental RV, RV dealerships everywhere closed down4 leaving his shop among the very few (22)__________ (leave) serving the New York metropolitan area. Mr. Troiano is on-track (23)__________ (sell) more RVs this year than in any other since the early 2000s. The current rebound (反弹) is mostly (24)__________ __________ the economy's recovery, but it also springs from the fact that new types of customer are embracing the lifestyle.A decade ago, the average age of an RV-owner was 49, and over 90% were white, says Kevin Broom of the Recreational Vehicle Industry Association (RVIA), which doesn't indicate a bright future. Another boost comes from sufficient immigrants, (25)__________ are keen to experience long, self-planned road trips in America. Mr. Troiano's most recent big sale was to (26)__________ rich Asian family.The industry hopes that its poor record with foreign sales-last year less than 1% of RVs produced domestically (27)__________ (ship) to foreign markets - may improve, too. China's government, for example, has planned to build 2,000 campgrounds by 2020, up from an estimated 300 today, in a bid to promote domestic tourism, particularly to remote rural regions. Chinese firms such as Yutong Bus make RVs, but not of the quality that many Chinese want. The country imported 1,000 vehicles last year, over half of them American.RV manufacturers are also marketing the concept (28)__________ their motor homes can be commercial as well as leisure vehicles They (29)__________ allow travelling salesmen, businessmen to save on food and hotel costs. (30) __________you park it, it can be your office, as .well as your home.Section B (10分)Directions: Fill in each blank with. a proper word chosen from the box. Each word can be usedThe din(喧嚣) of a loud restaurant or party can make conversation difficult for anyone--but for the elderly, these settings can make it nearly impossible. The mechanics of hearing 31 with age, but the latest research focuses on another part of the problem--the slower 32 speed of aging brains, which have to work harder to translate sound into intelligible(可理解的) language.Research shows that musicians are better able to pick out speech from surrounding noise as they age compared to non-musicians. And a new study of auditory training with a 33 available brain training program suggests that most people who are hard of hearing can develop the same skills. The scientists showed that people trained for 40 hours over 8 weeks with Posit Science's "Brain Fitness" were able to pick out 41% more words from background noise compared to those who watched educational DVDs and were quizzed on their 34 after the same amount of time. The authors .received no funding from the makers of the program; the study was 35 by the National Institutes of Health.. iThe research included 67 older adults between 55 and 70, with an average age of 63. The auditory training came in the form of 36 hearing tasks that primed the participants to hear better by requiring them to identify various speech sounds and 37 between similar sounding syllables (音节), for example, as well as repeating back words and remembering stories.Both those who received the training and those who watched the DVDs were tested on short term memory, brain processing speed and the ability to hear speech in noisy settings. All of the participants showed improvement in these three 38 , but for the first time, the scientists also documented that the sharper hearing was 39 by earlier signaling in the brainstem.As the authors write in their paper, the training not only improved the ability to decode speech in noisy situations, but also sped up the brain's ability to 40 to the sound--bringing it to more "youthful" levels.III. Reading ComprehensionSection A (15分)Directions: 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 content.Depression: Second Biggest Cause of Disability in the World Depression is the second most common cause of disability worldwide after back pain, according to a review of research. The disease must be treated as a global public health 41 , experts report in the journal PL.OS Medicine. The study 42 clinical depression with more than 200 other diseas6s and injuries as 'a cause of disability. Globally, only a small proportion of patients have 43 to treatment the World Health Organization says.Depression was 44 at number two as a global cause of disability; but its impact varies in different countries and regions 45 , rates of major depression were highest in Afghanistan and lowest in Japan. Iii the UK, depression was rated at number three 46 years lived with a disability.Dr. Alize Ferrari from the University of Queensland's School of Population Health led the study. "Depression is a big problem and we 47 need to pay more attention to it than we are now," she told BBC News. There's still more work to be done in arousing awareness of the disease and also in 48 successful ways of treating it."The burden is different between countries, so it tends to be higher in 1ow and middle income countries and 49 in high income countries." Policy-makers had made an effort to bring depression to the forefront, but there was a lot more work to be done, she added. "There's lots of stigma (病症) we know 50 with mental health," she explained."What one person recognizes as disabling might be different to another person and might be different across countries as well. There are lots of cultural 51 and interpretations that come in place, which makes it all the more important to 52 awareness of the size of the problem and also signs and how to 53 it."The data -- for the year 2010 -- follows similar studies in 1990 and 2000 looking at the global burden of depression.Commenting on the study, Dr. Daniel Chisholm, a health economist at the department for mental health and substance abuse at the World Health Organization said depression was a very disabling condition. "It's a big public health 54 and a big problem to be reflected on but not enough is being done." Around the world only a tiny 55 of people get any sort of treatment or diagnosis.The WHO recently launched a global mental health action plan to raise awareness among policy-makers.41. A. concern B. issue C. priority D. discussion42. A. compared B. combined C. confused D. contacted43. A. objection B. access C. adaptation D. contribution44. A. considered B. evaluated C. determined D. ranked45. A. For example B. In addition C. In other words D. All in all46. A. in regard of B. in name of C. in terms of D. in face of47. A. probably B. definitely C. significantly D. randomly .48. A. coming up with B. making up C. putting up with D. consisting of49. A. severer B. heavier C. lighter D. lower50. A. related B. associated C. relevant D. close5l. A. ingredients B. interactions C. implications D. identities52. A. remove B. recreate C. raise D. rise53. A. avoid B. treat C. cure D. detect54. A. challenge B. agreement C. prediction D. outcome55. A. amount B. proportion C. quantity D. populationSection B (22分)Directions: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)Digital Etiquette (礼节)Digital Etiquette, or netiquette, is a set of rules for how to behave online. It's a lot like life etiquette, which is basically having good manners and treating others with respect. It's just as important in our digital lives, including how we act in online games-or how we communicate in emails, texts, instant messages and on social networking websites. All of these platforms let us talk and share instantly wherever we are.Unfortunately, some people can lose control the second they jump online. When they disagree with someone, or have strong feeling about a topic, they end up saying stuff they'd never say in person! They may send ruder emails and IMs or try to start arguments on message boards. That's called flaming, and it can lead to full-on flame wars, insulting arguments between two or more users.On the Internet, it's pretty easy to stay anonymous, or unidentified. Having a secret identity to hide behind can make people pretty brave. And when all they see of you is screen name or a funny icon, they might forget that they're dealing with a real human being!The principle is simple: Just like in real life, you should treat other people the way you want to be treated. You wouldn't want somebody to be rude to you, so don’t be rude to anyone else.Of course, netiquette isn't just about being nice; it's also about communicating clearly. That means keeping emails and IMs clear, and to the point. It also means making your messages easy to read and understand, which can depend on your audience: For-instance, some abbreviations and emoticons may be fine with friends. But they're generally not appropriate in formal communication. And whatever you do, don't write in all capital letters! Writing in all caps makes it seem like you're yelling.Lastly, make sure you ask permission before posting anything about your friends on a blog or a social networking site. People's personal information is private, and you can really ruin relationships if you post something that a friend - or a friend's parents - don't want on the web. And keep in mind that the Internet is not a private place; if you wouldn't want a parent, teacher or future employer to see something you post, don't post it!56. According to the passage, the users of social media are advised ______.A. to trigger arguments on message boardsB. to behave online with common courtesyC. to be respectful of others online rather than offlineD. to apply abbreviations and emoticons as many as possible57. Why might an anonymous Internet user feel bold enough to say horrible things in response to ablog post?A. Because he can make more friends if he says mean things.B. Because he knows his friends will recognize him and think better of him.C. Because he can insult others and not worry about revenge.D. Because he can impress older, smarter people with his remarks.58. Which of the following is the best way to text your uncle to say you'll be back in an hour?A. BC. D.59. Which of the following is a clear rule about posting photos online?A. If you take a photograph, it is yours to do as you please online.B. Information about your friends, including photographs, is private.C. It's illegal to post pictures online without permission from people in the pictures.D. You should always avoid posting images on the internet.(B)60. What can the employer distribute to motivate staff to recycle more?A. Educational posters.B. Annual reports.C. Regular newsletters.D. Competition rules.61. What can be bought to cut down on the waste produced by staff refreshments?A. Disposable goods.B. Writing notes.C. Envelopes.D. Ceramic tableware.62. Which of the following is NOT included in the hints?A. Unwanted PCs can be sent to charities if the company has to buy new ones:B. Waste paper can be used as envelopes for internal mails before being thrown away.C. One of the staff should be assigned to be responsible for the recycling issue.D. Educational posters can be displayed in the workplace to publicize the recycling scheme.(C)Given how valuable intelligence and automation are, we will continue to improve our technology if we are at all able to. At a certain point, we will build machines that are smarter than we are. Once we have machines that are smarter than we are, they will begin to improve themselves. And then we risk what the mathematician IJ Good called an "intelligence explosion". The process could get out of control.The concern is really that we will build machines that are much more competent than we are. And the slightest divergence between their goals and our own could destroy us. Just think about how we relate to ants. We don't hate them. We don't go out of our way to harm them. In fact, sometimes we take pains not to harm them. We step over them on the sidewalk. But whenever their presence seriously conflicts with one of our goals, we will kill them without hesitation. The concern is that we will one day build machines that, whether they're conscious or not, could treat us with similar disregard.The bare fact is that we will continue to improve our intelligent machines. We have problems that we desperately need to solve. So we will do this, if we can. The train is already out of the station, and there's no brake to pull. If we build machines that are more intelligent than we are, they will very likely develop in ways that we can't imagine, and exceed us in ways that we can't imagine.So imagine we hit upon a design of super intelligent AI that has no safety concerns. This machine would be the perfect labor-saving device. It can design the machine that can build the machine which can do any physical work, powered by sunlight, more or less for the cost of raw materials. So we're talking about the end of human labour. We're also talking about the end of most intellectual work. So what would apes like ourselves do in this circumstance?What would some nations do if they heard that some company in Silicon Valley was about to deploy (配置) a super intelligent AI? This machine would be capable of starting war, whether terrestrial (陆地的) or cyber, with unbelievable power.Given that the companies and governments building super intelligent AI are likely to perceive(感知) themselves as being in a race against all others, and that to win this race is to win the world, it seems likely that whatever is easier to do will get done first unless it is destroyed in the next moment.But the moment we admit that information processing is the source of intelligence, we have to admit that we are in the process of building some sort of god. Now would be a good time to make sure it's a god we can live with.63. When an intelligent machine becomes smarter than humanity, ______A. it will make itself better and may go beyond human controlB. it will help people to the fullest, especially in physical workC. it will threaten people by robbing them of jobsD. it will view itself as human race64. The underlined word "divergence" in Paragraph 2 almost means the same as "______".A. connectionB. hatredC. competitionD. disagreement65. How is the passage mainly developed?A. By making comparisons.B. By showing valid evidence.C. By giving assumptions.D. By analyzing statistics.66. Which of the following is the best title of the passage?A. For the God's sake, stop AI and be yourselves!B. Can we build AI without losing control over it?C. For or against AI, that is the question!D. How does super intelligence serve the people?Section C (8分)Directions:Read the following passage. Fill in each blank with a proper sentence given in the box.Women are insecure because there is no commonly accepted idea of what it means to be a good mother. Fathers have it easier in this regard; they just have to show up and they are automatically considered "good", whereas mothers are always trying to prove to themselves and the world that they aren't "bad". 67In some ways, things are getting worse. Years ago, a woman was allowed five years to shape her child's personality. In recent years, however, some psychologists tell mothers that the first three years of life are the most important, while others think that all critical events happen during the first year.Ironically, this panic about doing the right thing to produce the perfect child is probably the worst thing for the child and the parent. 68 Here is why.First, it is not harmful to children if their mothers work. Mothers who neglect their own need and abilities for the sake of their children do not benefit their children, their marriage or themselves.Second, there is no crucial moment or stage in early childhood in which a child's fate is determined forever. 69 Children are more flexible than that.Research also finds that some children who have had the best parental care and guidance later give in to drugs, addiction, mental illness or violence. 70 Between the parents' best efforts and the resulting child lie other factors: the child's nature, genetically influenced characters, experiences outside the family and the child's knowledge of events. Parents can help an inborn shy child learn to cope better in situations that make the child anxious, but they aren't going to turn her into Britney Spears.IV. Summary Writing (10分)Directions: Read the following passage. Summarize the main idea and the main point(s) of the passage in no more than 60 words. Use your own words as far as possible:"Where You Go" Doesn't Matter So MuchDuring the fall months at high school guidance counseling programs, juniors run to the stage to participate in an exercise to try and help them understand that it is not "where you go" that matters. They hold posters featuring the names and faces of famous people while their peers and parents shout out with confidence the names of elite colleges (名校) they assume the celebrities attended.The "oohs" and "aahs" follow as the audience learn that Steven Spielberg, Steve Jobs and Bill Gates dropped out of college and that Ken Burns graduated from Hampshire College. If even a few stressed students and their anxious parents benefit from this information, it is a worthwhile exercise.Even better is giving the students an assignment to identify the happy, successful people intheir own circle of family, friends, co-workers and neighbors and challenging them to go and ask "if or where they went to college?" as a means of broadening the conversation in their search for a life after high school.The key to success in college and beyond has more to do with what students do with their time during college than what college they choose to attend. A long-term study of 6,335 college graduates published by the National Bureau of Economic Research found that graduating from a college where entering students have higher SAT scores - one marker of elite colleges - didn't pay off in higher post-graduation income. Researchers found that students who applied to several elite schools but didn't attend them - either because of rejection or by their own choice - are more likely to earn high incomes later than students who actually attended elite schools.In a summary of the findings, the bureau says that "evidently, students' motivation, ambition and desire to learn have a much stronger effect on their later success than average academic ability of their classmates."V. Translation (15分)Directions:Translate the following sentences into English, using the words given in the brackets.72. 众所周知，与他人和睦相处是生活幸福的要素之一。