2020年广东高考名校联考信息优化卷3

2020届广东省名校联盟高三第三次联考物理试卷★祝考试顺利★注意事项：1、考试范围：高考范围。

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14．如图所示，质量为m 的小车在与竖直方向成α角的恒定拉力F 作用下，沿水平地面向左运动一段距离L ．在此过程中，小车受到的阻力大小恒为f ，则下列说法正确的是A ．拉力对小车做功为FL cos αB ．支持力对小车做功FL sin αC ．阻力对小车做功fL sin αD ．小车动能的改变量小于拉力所做的功15．一位质量为m 的同学从下蹲状态向上跳起，经△t 时间，身体伸直并刚好离开地面，速度为ν，已知重力加速度为g ，在此过程中地面对他的支持力的冲量为A ．mv +mg △tB ．mv －mg △tC ．mvD ．mg △t 16．如图所示，是美国的“卡西尼”号探测器经过长达7年的“艰苦”旅行，进入绕土星飞行的轨道．若“卡西尼”号探测器在半径为R 的土星上空离土星表面高h 的圆形轨道上绕土星飞行，环绕一周飞行时间为T ，已知引力常量为G ，则下列关于土星质量M 和平均密度ρ的表达式正确的是A ．222243,R M GT GT ππρ== B ．2322234()3(),R h R h M GT GT R ππρ++== C ．2332234()3(),R h R h M GT GT Rππρ++== D ．2232334()3(),T R h T R h M G GRππρ++==17．如图所示，一倾角为θ的粗糙斜面放在水平地面上，细绳跨过定滑轮的两边系着两个物体A 和B ，整个装置处于静止状态．现用一个水平向右的拉力F 作用在物体B 上，将B 缓慢拉起到某一位置，整个过程中A 、C 均始终保持静止，在这个过程中，下列说法正确的是A ．水平拉力F 不断变小B ．斜面对A 的支持力不断减小C ．地面对C 的摩擦力保持不变D ．地面对C 的摩擦力变大18．一个面积S =4×10-2m 2、匝数n =100匝的线圈放在匀强磁场中，磁场方向垂直于线圈平面，磁感应强度B 随时间t 变化的规律如图所示，则下列判断正确的是A ．在开始的2s 内穿过线圈的磁通量变化率大小等于0.04Wb/sB ．在幵始的2s 内穿过线圈的磁通量的变化量等于零C ．在开始的2s 内线圈中产生的感应电动势大小等于8VD ．在第3s 末线圈中的感应电动势等于零第18题图 第19题图19．甲与乙赛跑的位移—时间图象如图所示，X m 为赛程的总位移，①为甲的x -t 图象，②为乙的x -t 图象，下面描述正确的是A ．甲做的是匀加速直线运动B ．甲与乙在比赛过程中，相遇过二次C ．甲先到达终点D ．t 3时刻甲和乙的速度相等20．如图，三根相互平行的固定长直导线L 1、L 2和L 3两两等距，垂直纸面放置，均通有大小相等的电流I ，L 1、L 2中电流方向垂直纸面向里，L 3中电流方向垂直纸面外．下列说法错误．．的是A ．L 1、L 2在L 3处产生的合磁感应强度方向与L 1、L 2连线垂直B ．L 2、L 3在L 1处产生的合磁感应强度方向与L 2、L 3连线垂直C ．L 1、L 2和L 3单位长度所受的磁场作用力大小之比为D ．L 1、L 2和L 3第20题图 第21题图21．如图所示，长为L 、倾角θ=30°的光滑绝缘斜面处于电场中，一带电荷量为+q 、质量为m的小球，以初速度v 0由斜面底端的A 点开始沿斜面上滑，到达斜面顶端的速度仍为v 0，则A ．小球在B 点的电势能一定大于小球在A 点的电势能B ．A 、B 两点间的电势差一定为2mgL qCD．若该电场是AC边中点处的点电荷Q产生的，则Q可能是负电荷三、非选择题：包括必考题和选考题两部分．第22题～第32题为必考题，每个试题考生都必须做答．第33题～第40题为选考题，考生根据要求做答．（一）必考题（11题，共129分）22．（6分）某中学有一实验小组对一电流计进行改装．已知电流计的内阻是150Ω，满偏电流是1mA，则电流计的满偏电压为V，若将它改装成量程为3V的电压表，则应（填“串”或“并”）联一个阻值为Ω的电阻．23．（9分）物理小组在一次探究活动中测量滑块与木板之间的动摩擦因数．实验装置如图1，一表面粗糙的木板固定在水平桌面上，一端装有定滑轮；木板上有一滑块，其一端与电磁打点计时器的纸带相连，另一端通过跨过定滑轮的细线与托盘连接．打点计时器使用的交流电源的频率为50Hz．开始实验时，在托盘中放入适量砝码，滑块开始做匀加速运动，在纸带上打出一系列小点．（1）滑块做匀加速运动过程中托盘受到细线的拉力（填“小于”、“等于”或“大于”）托盘及砝码的总重力．（2）如图2给出的是实验中获取的一条纸带的一部分：0、1、2、3、4、5、6是计数点，每相邻两计数点间还有4个计时点（图中未标出），计数点间的距离如图2所示．根据图中数据计算的加速度a＝（保留三位有效数字）．（3）为测量动摩擦因数，还需要测量出滑块的质量m2 与托盘和砝码的总质量m3，则滑块与木板间的动摩擦因数μ＝（用m2、m3、a、重力加速度g表示），与真实值相比，测量的动摩擦因数（填“偏大”或“偏小”）．24．（12分）如图所示，一竖直平面内斜面与粗糙的水平桌面平滑连接（即物块经过时没有能量损失），滑块B静止在斜面底端．现将滑块A从斜面顶端无初速度释放，已知斜面高H=0.33 m，与水平面之间的夹角为α = 37°，A和B的质量相同，A与斜面、桌面，B与桌面之间的动摩擦因数均为0.2．滑块A、B可视为质点，取g=10 m/s2．（1）求A在斜面上运动的加速度以及运动到斜面底端前一瞬间的速度大小；（2）若A在斜面底端与B发生弹性正碰，求B物体在桌面上运动的最大距离L．25．(20分)如图所示，平面直角坐标系xOy上有P、Q两点，P点在x轴上，OP＝2L，Q点在y轴负半轴上某处．第Ⅰ象限内有平行于y轴方向向y轴负向的匀强电场，第Ⅱ象限内有一圆形区域，与x、y轴分别相切于A、C两点，AO＝L，第Ⅳ象限内有一未知的矩形区域（图中未画出），圆形区域和矩形区域内均有相同的匀强磁场，磁场方向垂直于xOy 平面（图中未画出）．电荷量为+q、质量为m、速度大小为v0的a粒子束从A点沿y轴正方向发射，先后经过C点和P v0，电荷量为﹣q、质量为m的粒子束b从Q点沿与y轴正方向成45°角射入第Ⅳ象限，而后进入未知矩形磁场区域，离开该区域后与从P点射出的a粒子束发生正碰，即相碰时两束粒子速度在同一直线上．不计粒子的重力和粒子间相互作用力．求：（1）圆形区域内磁场感应强度B的大小、方向；（2）第Ⅰ象限内匀强电场的场强大小E；（3）矩形区域的最小面积S．33．【物理选修3-3】（1）（5分）关于热现象和热学规律，下列说法正确的是(填正确答案标号．选对1个得2分，选对2个得4分，选对3个得5分．每选错1个扣3分，最低得分为0分) A．布朗运动表明了构成悬浮微粒的分子在做无规则运动B．两个分子的间距从极近逐渐增大到10r0（r0为平衡位置时分子间距）的过程中，分子间的引力和斥力都在减小C．物体的内能变化时，它的温度一定改变D．封闭气体对容器壁的压强是由于气体分子对容器壁的碰撞引起的E．晶体熔化过程中，晶体分子平均动能不变，晶体分子势能总和增加（2）（10分）如图所示，一个内壁光滑、导热性能良好的汽缸放在水平桌面上开口向上．质量与厚度均不计、导热性能良好的活塞横截面积为S=2×10-3m2，与汽缸底部之间封闭了一定质量的理想气体，此时活塞与汽缸底部之间的距离h=24cm．汽缸所处环境的温度为300K，大气压强p0=1.0×105Pa，取g=10m/s2．现将质量为m=4kg的物块放在活塞中央位置上，活塞下移，求稳定后：①气体的压强；②缓慢加热气体使活塞回到原位置,此过程中气体吸收了20J热量，求其内能增加量．34．【物理选修3-4】（1）（5分）如图所示，一列横波在x轴上沿x轴正方向传播，实线表示t =0时刻的波形图，虚线是t = 0.5s时刻的波形图，已知该列波的周期T >1s，下列说法正确的是(填正确答案标号．选对1个得2分，选对2个得4分，选对3个得5分．每选错1个扣3分，最低得分为0分)A．质点的振动周期一定是2.0sB．该波的波速可能是20m/sC．t=0时刻，x=4m处的质点振动方向向上D．t=1.0s时刻，x=6m处的质点恰好位于波峰E．在0〜0.5s时间内，x = 3m处的质点运动的路程为5cm（2）（10分）如图所示为边长L的等边玻璃三棱镜，某单色光束射到界面AB中点上，入射角为i1=45°，玻璃对单色光的折射率为n．不考虑光在界面AC上的反射，已知该单色光在真空中传播的速度为c，求：①单色光在玻璃中传播的时间t；②从界面AC出射的光线与入射到界面AB上的光线的夹角θ．物理部分14．D 解析：根据做功方程可知，拉力做功为：，错误；支持力始终与位移垂直，所以不做功，B错误；C.阻力对小车做功为-fL，C错误；D.由动能定理：-0，D正确。

2019-2020学年广东省六校联盟高三（下）第三次联考数学试卷（文科）一、选择题：本题共12小题，每小题5分，共60分.1．（5分）已知集合A＝{1，2，3}，B＝{x|（x+1）（x﹣2）＜0，x∈Z}，则A∪B等于（）A．{1}B．{1，2}C．{0，1，2，3}D．{﹣1，0，1，2，3}2．（5分）若复数z满足z（1+i）＝2i（i为虚数单位），则|z|＝（）A．1B．2C．D．3．（5分）已知向量＝（1，m），＝（3，﹣2），且（+）⊥，则m＝（）A．﹣8B．﹣6C．6D．84．（5分）AQI是表示空气质量的指数，AQI指数值越小，表明空气质量越好，当AQI指数值不大于100时称空气质量为“优良”．如图是某地4月1日到12日AQI指数值的统计数据，图中点A表示4月1日的AQI指数值为201，则下列叙述不正确的是（）A．这12天中有6天空气质量为“优良”B．这12天中空气质量最好的是4月9日C．这12天的AQI指数值的中位数是90D．从4日到9日，空气质量越来越好5．（5分）已知直线11：x+（m+1）y+m＝0，l2：mx+2y+1＝0，则11∥l2“的一个必要不充分条件是（）A．m＝﹣2B．m＝1C．m＝﹣2或m＝1D．m＝2或m＝16．（5分）已知a＞0，b＞0，并且，，成等差数列，则a+9b的最小值为（）A．16B．9C．5D．47．（5分）宋元时期数学名著《算学启蒙》中有关于“松竹并生”的问题：松长五尺，竹长两尺，松日自半，竹日自倍，松竹何日而长等．如图是源于其思想的一个程序框图，若输入的a，b分别为5，2，则输出的n＝（）A．5B．4C．3D．28．（5分）若将函数f（x）＝sin2x+cos2x的图象向左平移φ（φ＞0）个单位，所得的图象关于y轴对称，则φ的最小值是（）A．B．C．D．9．（5分）在正四棱锥S﹣ABCD中，E，M，N分别是BC，CD，SC的中点，动点P在线段MN上运动时，下列四个结论，不一定成立的为（）①EP⊥AC；②EP∥BD；③EP∥平面SBD；④EP⊥平面SAC．A．①③B．③④C．①②D．②④10．（5分）已知函数f（x）＝，则y＝f（x）的图象大致为（）A．B．C．D．11．（5分）设F为双曲线C：﹣＝1（a＞0，b＞0）的右焦点，过F且斜率为的直线1与双曲线C的两条渐近线分别交于A，B两点，且||＝2||，则双曲线C的离心率为（）A．2B．C．或2D．或212．（5分）已知求O的表面积为64π，A，B，C在球面上，且线段AB的长为4，记AB 的中点为D，若OD与平面ABC的所成角为60°，则三棱锥O﹣ABC外接球的体积为（）A．πB．πC．πD．π二、填空题：本题共4小题，每小题5分，共20分.13．（5分）曲线f（x）＝在点（1，﹣2）处的切线方程为．14．（5分）在数列{a n}中，a1＝3，a n+1＝a n+，则通项公式a n＝．15．（5分）如图，△ABC上，D是BC上的点，且AC＝CD，2AC＝AD，AB＝2AD，则sin B等于．16．（5分）设函数f（x）＝x2﹣9lnx在区间[a﹣1，a+1]上单调递减，则实数a的取值范围是．三、解答题：共70分.解答应写出文字说明、证明过程或演算步骤.第17至21题为必考题，每位考生都必须作答.第22、23题为选考题，考生根据要求作答.（一）必考题：共60分. 17．（12分）等比数列{a n}中，已知a1＝2，a4＝16．（1）求数列{a n}的通项公式；（2）若a3，a5分别为等差数列{b n}的第3项和第5项，试求数列{b n}的通项公式及前n 项和S n．18．（12分）等腰直角三角形ABC中，∠BAC＝90°，D为AC的中点，正方形BCC1B1与三角形ABC所在的平面互相垂直．（1）求证：AB1∥平面DBC1；（2）若AB＝2，求点D到平面ABC1的距离．19．（12分）某校学生营养餐由A和B两家配餐公司配送．学校为了解学生对这两家配餐公司的满意度，采用问卷的形式，随机抽取了40名学生对两家公司分别评分．根据收集的80份问卷的评分，得到如图A公司满意度评分的频率分布直方图和如表B公司满意度评分的频数分布表：频数满意度评分分组[50，60）2[60，70）8[70，80）14[80，90）14[90，100]2（Ⅰ）根据A公司的频率分布直方图，估计该公司满意度评分的中位数；（Ⅱ）从满意度高于90分的问卷中随机抽取两份，求这两份问卷都是给A公司评分的概率；（Ⅲ）请从统计角度，对A、B两家公司做出评价．20．（12分）已知椭圆（a＞b＞0）的右焦点为F（1，0），短轴长为2，过定点P（0，2）的直线l交椭圆C于不同的两点A、B（点B在点A、P之间）．（1）求椭圆C的方程；（2）若，求实数λ的取值范围；（3）若射线BO交椭圆C于点M（O为原点），求△ABM面积的最大值．21．（12分）已知函数f（x）＝px﹣﹣2lnx．（Ⅰ）若函数f（x）在其定义域内为单调函数，求p的取值范围；（Ⅱ）设函数g（x）＝，若在[1，e]上至少存在一点x0，使得f（x0）＞g（x0）成立，求实数p的取值范围．（二）选考题：共10分.请考生在第22、23题中任选一题作答.如果多做，则按所做的第-题计分.[选修4-4：坐标系与参数方程]22．（10分）在直角坐标系xOy中，直线l的参数方程为（t为参数），再以原点为极点，以x正半轴为极轴建立极坐标系，并使得它与直角坐标系有相同的长度单位，在该极坐标系中圆C的方程为ρ＝4sinθ．（1）求圆C的直角坐标方程；（2）设圆C与直线l将于点A、B，若点M的坐标为（1，4），求|MA|+|MB|的值．[选修4-5：不等式选讲]（10分）23．若a，b，c∈R+，且满足a+b+c＝2．（1）求abc的最大值；（2）求++的最小值．2019-2020学年广东省六校联盟高三（下）第三次联考数学试卷（文科）参考答案与试题解析一、选择题：本题共12小题，每小题5分，共60分.1．（5分）已知集合A＝{1，2，3}，B＝{x|（x+1）（x﹣2）＜0，x∈Z}，则A∪B等于（）A．{1}B．{1，2}C．{0，1，2，3}D．{﹣1，0，1，2，3}【解答】解：∵集合A＝{1，2，3}，B＝{x|（x+1）（x﹣2）＜0，x∈Z}＝{0，1}，∴A∪B＝{0，1，2，3}．故选：C．2．（5分）若复数z满足z（1+i）＝2i（i为虚数单位），则|z|＝（）A．1B．2C．D．【解答】解：∵复数z满足z（1+i）＝2i（i为虚数单位），∴z＝＝＝1+i，∴|z|＝＝，故选：C．3．（5分）已知向量＝（1，m），＝（3，﹣2），且（+）⊥，则m＝（）A．﹣8B．﹣6C．6D．8【解答】解：∵向量＝（1，m），＝（3，﹣2），∴+＝（4，m﹣2），又∵（+）⊥，∴12﹣2（m﹣2）＝0，解得：m＝8，故选：D．4．（5分）AQI是表示空气质量的指数，AQI指数值越小，表明空气质量越好，当AQI指数值不大于100时称空气质量为“优良”．如图是某地4月1日到12日AQI指数值的统计数据，图中点A表示4月1日的AQI指数值为201，则下列叙述不正确的是（）A．这12天中有6天空气质量为“优良”B．这12天中空气质量最好的是4月9日C．这12天的AQI指数值的中位数是90D．从4日到9日，空气质量越来越好【解答】解：这12天中，空气质量为“优良”的有95，85，77，67，72，92，故A正确；这12天中空气质量最好的是4月9日，AQI指数值为67，故B正确；这12天的AQI指数值的中位数是＝99.5，故C不正确；从4日到9日，AQI数值越来越低，空气质量越来越好，故D正确，故选：C．5．（5分）已知直线11：x+（m+1）y+m＝0，l2：mx+2y+1＝0，则11∥l2“的一个必要不充分条件是（）A．m＝﹣2B．m＝1C．m＝﹣2或m＝1D．m＝2或m＝1【解答】解：∵直线l1：x+（m+1）y+m＝0，l2：mx+2y+1＝0，若l1∥l2，则m（m+1）﹣2＝0，解得：m＝﹣2或m＝1当m＝1时，l1与l2重合，故“l1∥l2”⇔“m＝﹣2”，故“l1∥l2”的必要不充分条件是“m＝﹣2或m＝1”，故选：C．6．（5分）已知a＞0，b＞0，并且，，成等差数列，则a+9b的最小值为（）A．16B．9C．5D．4【解答】解：根据题意，a＞0，b＞0，且，，成等差数列，则+＝2×＝1；则a+9b＝（a+9b）（+）＝10++≥10+2＝16；即则a+9b的最小值为16；故选：A．7．（5分）宋元时期数学名著《算学启蒙》中有关于“松竹并生”的问题：松长五尺，竹长两尺，松日自半，竹日自倍，松竹何日而长等．如图是源于其思想的一个程序框图，若输入的a，b分别为5，2，则输出的n＝（）A．5B．4C．3D．2【解答】解：当n＝1时，a＝，b＝4，满足进行循环的条件，当n＝2时，a＝，b＝8满足进行循环的条件，当n＝3时，a＝，b＝16满足进行循环的条件，当n＝4时，a＝，b＝32不满足进行循环的条件，故输出的n值为4，故选：B．8．（5分）若将函数f（x）＝sin2x+cos2x的图象向左平移φ（φ＞0）个单位，所得的图象关于y轴对称，则φ的最小值是（）A．B．C．D．【解答】解：函数f（x）＝sin2x+cos2x＝图象向左平移φ可得：sin （2x+2φ）图象关于y轴对称，即2φ＝（k∈Z）解得：φ＝．∵φ＞0，当k＝0时，φ的值最小值为．故选：C．9．（5分）在正四棱锥S﹣ABCD中，E，M，N分别是BC，CD，SC的中点，动点P在线段MN上运动时，下列四个结论，不一定成立的为（）①EP⊥AC；②EP∥BD；③EP∥平面SBD；④EP⊥平面SAC．A．①③B．③④C．①②D．②④【解答】解：如图所示，连接AC、BD相交于点O，连接EM，EN．在①中：由正四棱锥S﹣ABCD，可得SO⊥底面ABCD，AC⊥BD，∴SO⊥AC．∵SO∩BD＝O，∴AC⊥平面SBD，∵E，M，N分别是BC，CD，SC的中点，∴EM∥BD，MN∥SD，而EM∩MN＝N，∴平面EMN∥平面SBD，∴AC⊥平面EMN，∴AC⊥EP．故正确．在②中：由异面直线的定义可知：EP与BD是异面直线，不可能EP∥BD，因此不正确；在③中：由①可知平面EMN∥平面SBD，∴EP∥平面SBD，因此正确．在④中：由①同理可得：EM⊥平面SAC，若EP⊥平面SAC，则EP∥EM，与EP∩EM＝E相矛盾，因此当P与M不重合时，EP与平面SAC不垂直．即不正确．∴恒不一定成立的结论是：②④．故选：D．10．（5分）已知函数f（x）＝，则y＝f（x）的图象大致为（）A．B．C．D．【解答】解：令g（x）＝x﹣lnx﹣1，则，由g'（x）＞0，得x＞1，即函数g（x）在（1，+∞）上单调递增，由g'（x）＜0得0＜x＜1，即函数g（x）在（0，1）上单调递减，所以当x＝1时，函数g（x）有最小值，g（x）min＝g（0）＝0，于是对任意的x∈（0，1）∪（1，+∞），有g（x）≥0，故排除B、D，因函数g（x）在（0，1）上单调递减，则函数f（x）在（0，1）上递增，故排除C，故选：A．11．（5分）设F为双曲线C：﹣＝1（a＞0，b＞0）的右焦点，过F且斜率为的直线1与双曲线C的两条渐近线分别交于A，B两点，且||＝2||，则双曲线C的离心率为（）A．2B．C．或2D．或2【解答】解：设F（c，0），则C：﹣＝1（a＞0，b＞0）的右焦点且斜率为的直线l：y＝（x﹣c），而渐近线的方程是：y＝±x，由得：A（﹣，），由得，B（，），∵||＝2||，∴＝，可得：3a2＝b2，∴＝3，∴e＝＝＝＝＝2．同理，当点A、B在x轴下方时，e＝．综上所述，双曲线C的离心率为2或．故选：D．12．（5分）已知求O的表面积为64π，A，B，C在球面上，且线段AB的长为4，记AB 的中点为D，若OD与平面ABC的所成角为60°，则三棱锥O﹣ABC外接球的体积为（）A．πB．πC．πD．π【解答】解：设△ABC所在截面圆的圆心为O1，AB中点为D，连接OD，O1D，OA＝OB，所以OD⊥AB，同理OD1⊥AB，所以∠ODO1即为OD与平面ABC所成的角，故∠ODO1＝60°；因为OA＝OB＝4，AB＝4，所以△OAB是等腰直角三角形，所以OD＝2，在Rt△ODO1中，由，得，由勾股定理得：，因为O 1到A、B、C三点的距离相等，所以三棱锥O﹣ABC外接球的球心E在射线OO1上，设四面体OABC外接球半径为R，在Rt△O1BE中，＝，BE＝R，，由勾股定理可得：，即10+，解得R＝，故所求球体积V＝，故选：D．二、填空题：本题共4小题，每小题5分，共20分.13．（5分）曲线f（x）＝在点（1，﹣2）处的切线方程为x﹣y﹣3＝0．【解答】解：∵f（x）＝＝﹣2，∴f′（x）＝，∴f′（1）＝1，又f（1）＝﹣2，∴曲线f（x）＝在点（1，﹣2）处的切线方程为：y﹣（﹣2）＝（x﹣1），整理得：x﹣y﹣3＝0，故答案为：x﹣y﹣3＝0．14．（5分）在数列{a n}中，a1＝3，a n+1＝a n+，则通项公式a n＝4﹣．【解答】解：∵a n+1﹣a n＝＝∴…a n﹣a n﹣1＝以上n﹣1个式子相加可得，a n﹣a1＝∵a1＝3，∴故答案为：4﹣15．（5分）如图，△ABC上，D是BC上的点，且AC＝CD，2AC＝AD，AB＝2AD，则sin B等于．【解答】解：由题意设AD＝2x，则AC＝CD＝x，AB＝4x，在△ADC中由余弦定理可得cos∠ADC＝＝，∴sin∠ADB＝sin∠ADC＝＝，∴在△ADB中由正弦定理可得sin B＝＝＝，故答案为：16．（5分）设函数f（x）＝x2﹣9lnx在区间[a﹣1，a+1]上单调递减，则实数a的取值范围是（1，2]．【解答】解：根据题意，函数，其导数f′（x）＝x﹣＝，（x ＞0）若f′（x）＝≤0，解可得0＜x≤3，即f（x）的递减区间为（0，3]；若函数f（x）在[a﹣1，a+1]上单调递减，则有，解可得：1＜a≤2，即a的取值范围为（1，2]；故答案为：（1，2]三、解答题：共70分.解答应写出文字说明、证明过程或演算步骤.第17至21题为必考题，每位考生都必须作答.第22、23题为选考题，考生根据要求作答.（一）必考题：共60分. 17．（12分）等比数列{a n}中，已知a1＝2，a4＝16．（1）求数列{a n}的通项公式；（2）若a3，a5分别为等差数列{b n}的第3项和第5项，试求数列{b n}的通项公式及前n 项和S n．【解答】解：（1）设{a n}的公比为q，由已知得16＝2q3，解得q＝2，∴a n＝2n．（2）由（1）得a3＝8，a5＝32，则b3＝8，b5＝32．设{b n}的公差为d，则，解得从而b n＝﹣16+12（n﹣1）＝12n﹣28，所以数列{b n}的前n项和S n＝＝6n2﹣22n．18．（12分）等腰直角三角形ABC中，∠BAC＝90°，D为AC的中点，正方形BCC1B1与三角形ABC所在的平面互相垂直．（1）求证：AB1∥平面DBC1；（2）若AB＝2，求点D到平面ABC1的距离．【解答】解：（1）证明：连结B1C，设B1C∩BC1＝O，连结OD，如图，∵O是B1C的中点，D为AC的中点，∴OD∥AB1，∵OD⊂面BDC1，AB1⊄面BDC1，∴AB1∥平面DBC1．（2）解：∵等腰直角三角形ABC中，∠BAC＝90°，∴BA⊥AC，∵BA⊥CC1，∴BA⊥平面ACC1，∴BA⊥AC1，设点D到平面ABC1的距离为h，由＝，代入可得：＝，解得点D到平面ABC1的距离为．19．（12分）某校学生营养餐由A和B两家配餐公司配送．学校为了解学生对这两家配餐公司的满意度，采用问卷的形式，随机抽取了40名学生对两家公司分别评分．根据收集的80份问卷的评分，得到如图A公司满意度评分的频率分布直方图和如表B公司满意度评分的频数分布表：频数满意度评分分组[50，60）2[60，70）8[70，80）14[80，90）14[90，100]2（Ⅰ）根据A公司的频率分布直方图，估计该公司满意度评分的中位数；（Ⅱ）从满意度高于90分的问卷中随机抽取两份，求这两份问卷都是给A公司评分的概率；（Ⅲ）请从统计角度，对A、B两家公司做出评价．【解答】解：（Ⅰ）设A公司调查的40份问卷的中位数为x，则有0.015×10+0.025×10+0.03×（x﹣70）＝0.5解得：x≈73.3所以，估计该公司满意度得分的中位数为73.3 …（4分）（Ⅱ）满意度高于9（0分）的问卷共有6份，其中4份评价A公司，设为a1，a2，a3，a4，2份评价B公司，设为b1，b2．从这6份问卷中随机取2份，所有可能的结果有：（a1，a2），（a1，a3），（a1，a4），（a1，b1），（a1，b2），（a2，a3），（a2，a4），（a2，b1），（a2，b2），（a3，a4），（a3，b1），（a3，b2），（a4，b1），（a4，b2），（b1，b2），共有15种．其中2份问卷都评价A公司的有以下6种：（a1，a2），（a1，a3），（a1，a4），（a2，a3），（a2，a4），（a3，a4）．设两份问卷均是评价A公司为事件C，则有．…（9分）（Ⅲ）由所给两个公司的调查满意度得分知：A公司得分的中位数低于B公司得分的中位数，A公司得分集中在[70，80）这组，而B公司得分集中在[70，80）和[80，90）两个组，A公司得分的平均数数低于B公司得分的平均数，A公司得分比较分散，而B公司得分相对集中，即A公司得分的方差高于B公司得分的方差．…（13分）20．（12分）已知椭圆（a＞b＞0）的右焦点为F（1，0），短轴长为2，过定点P（0，2）的直线l交椭圆C于不同的两点A、B（点B在点A、P之间）．（1）求椭圆C的方程；（2）若，求实数λ的取值范围；（3）若射线BO交椭圆C于点M（O为原点），求△ABM面积的最大值．【解答】解：（1）由题得c＝1，b＝1，所以a2＝1+1＝2，则椭圆C的方程为：；（2）①当直线l斜率不存在时，其方程为x＝0，此时A（0，﹣1），B（0，1），所以＝（0，﹣1），＝（0，﹣3），因为，则λ＝；②当直线l斜率存在时，设直线l的方程为y＝kx+2（k≠0），A（x1，y1），B（x2，y2），则＝（x1，y1﹣2），＝（x2，y2﹣2），由，得，整理得，联立，得x2+2（kx+2）2＝2，即（1+2k2）x2+8kx+6＝0，△＝64k2﹣24（1+2k2）＞0，解得k2＞，且x1+x2＝，x1x2＝，代入（1）中得，因为k2＞，所以2＜＜，解得，又因为B在A、P之间，所以，综上：；（3）由椭圆对称性可知BO＝MO，S△ABM＝2S△AOB，设O到直线l的距离为d，则S△AOB＝＝××|x2﹣x1|×＝|x2﹣x1|＝＝＝＝＝＝≤，当且仅当2k2﹣3＝（k2＞）时取“＝”，所以△ABM面积的最大值＝2△AOB面积的最大值＝，即．21．（12分）已知函数f（x）＝px﹣﹣2lnx．（Ⅰ）若函数f（x）在其定义域内为单调函数，求p的取值范围；（Ⅱ）设函数g（x）＝，若在[1，e]上至少存在一点x0，使得f（x0）＞g（x0）成立，求实数p的取值范围．【解答】解：（1）f′（x）＝p+﹣＝，令h（x）＝px2﹣2x+p，要使f（x）在其定义域（0，+∞）内是单调函数，只需h（x）在（0，+∞）内，满足：h（x）≥0或h（x）≤0恒成立，当且仅当p（x2+1）≥2x时，h（x）≥0，p（x2+1）≤2x时，h（x）≤0，因为x2+1＞0，所以当且仅当p≥时，h（x）≥0，p≤时，h（x）≤0，因为在（0，+∞）内有0＜＝＝≤1，当且仅当x＝即x＝1时取等号，所以当p≥1时，h（x）≥0，f′（x）≥0，此时f（x）在（0，+∞）单调递增，当p≤0时，h（x）≤0，f′（x）≤0，此时f（x）在（0，+∞）单调递减，综上，p的取值范围为p≥1或p≤0．（2）因为g（x）＝在[1，e]上是减函数，所以x＝e时，g（x）min＝2；x＝1时，g（x）max＝2e，即g（x）∈[2，2e]，①当p≤0时，由（1）知f（x）在[1，e]上递减，所以f（x）max＝f（1）＝0＜2，不合题意，②当0＜p＜1时，由x∈[1，e]⇒x﹣≥0，由（1）知当p＝1时，f（x）在[1，e]上单调递增，所以f（x）＝p（x﹣）﹣2lnx≤x﹣﹣2lnx≤e﹣﹣2lne＝e﹣﹣2＜2，不合题意，③当p≥1时，φ（x）＝f（x）﹣g（x），x∈[1，e]，由题意可得，只需x∈[1，e]时，φ（x）max≥0，即可，由（1）知f（x）在[1，e]上是增函数，f（1）＝0＜2，又g（x）在[1，e]上是增函数，则φ（x）max＝f（x）max﹣g（x）min，x∈[1，e]，而f（x）max＝f（e）＝p（e﹣）﹣2lne，g（x）min＝2，只需φ（x）max＝p（e﹣）﹣2lne﹣2＞0，解得p＞，综上p的取值范围是（，+∞）．（二）选考题：共10分.请考生在第22、23题中任选一题作答.如果多做，则按所做的第-题计分.[选修4-4：坐标系与参数方程]22．（10分）在直角坐标系xOy中，直线l的参数方程为（t为参数），再以原点为极点，以x正半轴为极轴建立极坐标系，并使得它与直角坐标系有相同的长度单位，在该极坐标系中圆C的方程为ρ＝4sinθ．（1）求圆C的直角坐标方程；（2）设圆C与直线l将于点A、B，若点M的坐标为（1，4），求|MA|+|MB|的值．【解答】解：（1）圆C的方程为ρ＝4sinθ，∴ρ2＝4ρsinθ，∴圆C的直角坐标方程为x2+y2﹣4y＝0．即x2+（y﹣2）2＝4．（2）将直线l的参数方程代入圆的方程，整理，得t2﹣3t+1＝0，△＝18﹣4＝14＞0，设t1，t2为方程的两个实根，则t1+t2＝3，t1t2＝1，∴t1，t2均为正数，又直线l过M（1，4），由t的几何意义得：|MA|+|MB|＝|t1|+|t2|＝t1+t2＝3．[选修4-5：不等式选讲]（10分）23．若a，b，c∈R+，且满足a+b+c＝2．（1）求abc的最大值；（2）求++的最小值．【解答】解：a，b，c∈R+，且满足a+b+c＝2．（1）∴abc≤＝，当且仅当a＝b＝c时取等号，故abc的最大值；（2）∵++＝＝（3）（3+2+2+2）＝，当且仅当a＝b＝c时取等号∴++的最小值．。

英语试卷共10页，卷面满分120分，折算成135分计入总分。

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第一部分阅读理解（共两节；满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的四个选项（A、B、C和D）中，选出最佳选项，并在答题卡上将该项涂黑。

AShotinmorethan40locationsinL.A.,themusicalLaLaLandis“alovelettertothecity”.Tocoincidewi thUKrelease,weaskedalocalwritertopicks omeofthefilm’samazingsettings.JudgeHarryPregersonInterchangeLaLaLand’sopeningsceneisasix-minutedancethatplaysoutinL.A.’sbadtraffic.Itisalsowherethef ilm’sleadingroles,strugglingactressMiaandjazzpianistSebastian,firstencountereachother–inaroadangerin cident.ThesceneissaidtohavebeenfilmedovertwohotdaysinsouthL.A..SmokehouseRestaurant,BurbankThisisthesettingforthesceneinwhichMiadiscoversSebastian’stalentforthepiano.ThefictionalLip ton’srestaurant–wherejazzpianistSebastianwasreluctanttoplayChristmasmusic–isinrealityaplacelongfreq uentedbyactors,producersandothershowbusinesstypes.Ithasbeenonthisspot,acrossthestreetfromtheWarn erBrosstudio,since1949.Inthefilm,theouterwallofLipton’sisthe YouaretheStar mural(壁画),whichfeaturesMarilynMonroe,CharlieChaplinandothers,whichisonthecornerofHollywoodBoulevard andWicoxAvenueinHollywoodinreality.WarnerBrosStudio,BurbankMiaworksatthestudio’scoffeeshop,whereSebastiancomestomeether.Astheywanderthestudio’sl ot,Miapointsout“the window that Humphrey Bogart and Ingrid Bergman looked out in Casablanca.”It’soneofthefilm’snumerousnodstomoviehistory.WarnerBrosisstillaworkingstudio,with35s oundstages,14exteriorsetsandvisitortours.Cathy’sCorner,MountHollywoodDriveThissectionoftheroadthatwindsthroughGriffthParkisthesettingoftheirdanceplay.Itoverlooksthe SanFernandoValleyandfeaturesonthefilmposter.Cathy’sCornerisnearfamedMulholandDrive,butpreparef ordisappointmentifyou’reexpectingaparkbenchandstreetlamps,whichonlyexistinthemovie.21.Inordertoencountersomefilmstars,youmaygoto .A.JudgeHarryPregersonInterchangeB.SmokehouseRestaurantC.WarnerBrosStudioD.Cathy’sCorner22.Miamentionedtheunderlinedsentencesoasto .A.stressWarnerBrosisstillinfunctionB.showrespectformoviesofpreviousgenerationsC.illustrateLaLaLandwasfilmedatHollywoodCenterStudiospareMiaandSebastian’slovestorywithHumphreyandIngrid23.Inwhichsectionofawebsitecanyoumostprobablyfindthispassage?A.NatureandEnvironment.B.CityandTransport.C.TravelandRecreation.D.FoodandHealth.BInacareerthatlastedmorethanhalfacentury,TomWolfewrotefictionandnonfictionbest-sellersincluding TheElectricKool-AidAcidTest and TheBonfireoftheVanities.Alongtheway,hecreatedanewtypeofjournalism andcoinedphrasesthatbecamepartoftheAmericanvocabulary.Wolfebeganworkingasanewspaperreporter,firstfor TheWashingtonPost,thenthe NewYorkHeraldTrib une.Hedevelopedaliterarystyleinnonfictionthatbecameknownasthe“NewJournalism”.“I’vealwaysagreed onatheoreticallevelthatthetechniquesforfictionandnonfictionareinterchangeable,”hesaid.“Thethingsthat workinnonfictionwouldworkinfiction,andviceversa.”“WhenTomWolfe’svoicebrokeintotheworldofnonfiction,itwasatimewhenalotofwriters,andalotofarti stsingeneral,wereturninginwards,”saysLevGrossman,bookcriticfor Time magazine.“Wolfedidn’tdothat.W olfeturnedoutwards.Hewasaguywhowasinterestedinotherpeople.”Wolfewasinterestedinhowtheythought, howtheydidthingsandhowthethingstheydidaffectedtheworldaroundthem.In1979,Wolfepublished TheRightStuff,anaccountofthemilitarytestpilotswhobecameAmerica’sfirstas tronauts.Fouryearslater,thebookwasadaptedasafeaturefilm.“TheRightStuff wasthebookforme”,saysCross man.“Itremindedme,incase I’dforgotten,thattheworldisanincredibleplace.”In TheRightStuff,Wolfepopularizedthephrase“pushingtheenvelope.”InaNewYorkmagazinearticle,W olfedescribedthe1970sas“The‘Me’Decade.”GrossmansaysthesephrasesbecamepartoftheAmericanidiom becausetheywereaccurate.“Hewasanenormouslyforcefulobserver,andhewasnotafraidofmakingstrongclaimsaboutwhatwashap peninginreality,”Grossmansays.“Hediditwellandpeopleheardhim.Andtheyrepeatedwhathesaidbecausehe wasright.”Allthosewordsstartedarevolutioninnonfictionthatisstillgoingon.24.The“NewJournalism”isastyleofjournalismthat .A.changesitsnewswritingtechniquesfrequentlyB.popularizesnewAmericanidiomsinaliterarywaybinesnovelistictechniqueswithtraditionalreportingD.reportsvariousnewseventsfromatheoreticalperspective25.Itcanbelearnedfromthepassagethat TheRightStuff .A.isafilmdirectedbyLevGrossmanB.isaninfluentialbookbyTomWolfeC.accountsforpopularAmericanphrasesD.dealswithincredibleplacesintheworld26.Accordingtothepassage,TomWolfe .A.wasgoodatwritingfromarealisticperspectiveB.preferredmakingclaimsabouteventstowritingbooksC.wasfondofcommentingonotherpeople’sthoughtsD.likedanalyzingsocialproblemsfromtheoutside27.Whichofthefollowingisthebesttitleforthepassage?A.AProfessionalPhraseCoinerB.AForcefulObserverandNovelistC.ATheoreticalCreatorinLiteratureD.AnInnovativeJournalistandWriterCAgainstthesuppositionthatforestfiresinAlaska,CanadaandSiberiawarmtheclimate,scientistshavedisc overedthatcoolingmayoccurinareaswhereburnttreesallowmoresnowtomirrormoresunlightintospace.Thisfindingsuggeststhattakingstepstopreventnorthernforestfirestolimitthereleaseofgreenhousegase uallylargefiresdestroyedforestsintheseareasoverthepastdecad e.Scientistspredictthatwithclimatewarming,firesmayoccurmorefrequentlyovernextseveralcenturiesasare sultofalongerfireseason.Sunlightabsorbedbytheearthtendstocausewarming,whileheatmirroredbackintosp acetendstocausecooling.Thisisthefirststudytoanalyzeallaspectsofhownorthernfiresinfluenceclimate.Earlierstudiesbyothersci entistshavesuggestedthatfireinnorthernregionsspeedupclimatewarmingbecausegreenhousegasesfrombur ningtreesandplantsarereleasedintotheatmosphereandthustrapheat.Scientistsfoundthatrightafterthefire,largeamountsofgreenhousegasesenteredtheatmosphereandcaus edwarming.Ozone（臭氧）levelsincreased,andashfromthefirefellonfar-offseaice,darkeningthesurfaceandcausingmoreradiationfrom thesuntobeabsorbed.Thefollowingspring,however,thelandwithintheareaofthefirewasbrighterthanbeforet hefire,becausefewertreescoveredtheground.Snowonthegroundmirroredmoresunlightbackintospace,leadi ngtocooling.“Weneedtofindoutallpossiblewaystoreducethegrowthofgreenhousegasesintheatmosphere.”Scient is tstrackedthechangeinamountofradiationenteringandleavingtheclimatesystemasaresultofthefire,andfound ameasurementcloselyrelatedtotheglobalairtemperature.Typically,fireinnorthernregionsoccursinthesame areaevery80to150years.Scientists,however,foundthatwhenfireoccursmorefrequently,moreradiationislost fromtheearthandcoolingresults.Specifically,theydeterminedwhenfirereturns20yearsearlierthanpredicate d,0.5wattspersquaremeterofareaburnedare soakedup bytheearthfromgreenhousegases,but0.9wattspersquaremeterwillbesentbackintospace.Theneteffectisc ooling.Wattsareusedtomeasuretherateatwhichenergyisgainedorlostfromtheearth.28.Accordingtothenewfindings,takingstepstopreventnorthernforestfiresmay .A.resultinawarmingclimateB.causetheforestfirestooccurmorefrequentlyC.leadtoalongerfireseasonD.protecttheforestsandtheenvironmentthere29.Earlierstudiesaboutnorthernforestfires .A.analyzeallaspectsofhownorthernfiresinfluenceclimateB.indicatethatforestfireswillpollutetheatmosphereC.suggestthatpeopleshouldtakemeasurestoprotectenvironmentD.suggestthatthefireswillspeedupclimatewarming30.Theunderlinedphrase“soakedup”inthelastparagraphprobablymeans .A.madeupB.takeninC.givenoffD.handedout31.FromthepassagewecandrawaconclusionthatforestfiresinAlaska,CanadaandSiberiamay .A.warmtheclimateasthesuppositiongoesbecauseofmoregreenhousegasesB.allowmoresnowtoreflectmoresunlightintospaceandthuscooltheclimateC.destroylargeareasofforestsandpollutethefar-offseaiceD.helptogainmoreenergyratherthanreleasemoreenergyDAsapersonwhowritesaboutfoodanddrinkforaliving,Icouldn’ttellyouthefirstthingaboutBillPerryorw hetherthebeershesellsarethatgreat.ButIcantellyouthatIlikethisguy.That’sbecauseheplanstobantippinginfa vorofpayinghisserversanactuallivingwage.Ihatetippingbec auseit’sanobligationdisguisedasanoption.Ihateitforthepost-dinnermathitrequiresof me.Butmostly,IhateitbecauseIbelieveIwouldbeinabetterplaceifpaydecisionsregardingemployeeswerejus tleftuptotheiremployers,asisthecustomineveryotherindustry.Mostofyoumaythinkthatyouhatetippingtoo.Researchsuggestsotherwise.Youinfactlovetipping!Yo uliketofeelthatyouhaveavoiceinhowmuchmoneyyourservermakes.Nomatterhowthemathworksout,youal waysviewrestaurantswithvoluntarytippingsystemsasbeingabettervalue,whichmakesitextremelydifficultf orrestaurantsandbarstodoawaywiththetippingsystem.Oneargumentthatyoutendtohearalotfromthepro-tippingcrowdseemslogicalenough:theserviceisbetter whenwaitersdependontips,becausetheyseeabenefittosuccessfullyhidingtheirignoranceofyou.Well,ifthiswer etrue,wewouldallbeslippingafew100-dollarbillstoourdoctorsonthewayouttheirdoors,too.Butasitturnsout,w aitersseeonlyatinyriseintipswhentheydoanexceptionaljobcomparedtoapassableone.Waiters,keenobservers ofhumanitythattheyare,arecatchingontothis.Inonepoll,afull30%saidtheydidn’t believethejobtheydidhadanyi mpactonthetipstheyreceived.Socomeon,folks:getonboardwithabandoningtheoutdatedtipsystem.Payalittlemoreupfrontforyourb eerorburger.SupportBillPerry’spub,andanyotherbarorrestaurantthatdoesn’taskyoutododrunkenmath.32.WhatcanwelearnaboutBillPerryfromthepassage?A.Herunsapubthatservesexcellentbeer.B.Heintendstogetridofthetippingpractice.C.Hegiveshisstaffaconsiderablesumfortips.D.Helivesincomfortwithoutgettinganytips.33.Whatisthemainreasonwhytheauthorhatestipping?A.Itsetsabadexampleforotherindustries.B.Itaddstotheburdenofordinarycustomers.C.ThecustomerisforcedtomakeituptothewaiterD.Thecustomerisposedagreatchallengetodothemath.34.Whydomanypeoplelovetippingaccordingtotheauthor?A.Theyhelpimprovethequalityoftherestaurantstheydinein.B.Theybelievewaitersdeservesuchrewardsforgoodservice.C.Theywanttopreserveawonderfultraditionoftheindustry.D.Theycanhavesomesayinhowmuchtheirserversearn.35.Whatdoestheauthorargueforinthepassage?A.Restaurantsshouldcalculatethetipsforcustomers.B.Customersshouldpaymoretipstohelpimproveservice.C.Waitersdeservebetterthanjustrelyingontipsforaliving.D.Waitersshouldbepaidbyemployersinsteadofcustomers.第二节（共5小题；每小题2分，满分10分）根据短文内容，从短文后的选项中选出能填入空白处的最佳选项。

广东六校联盟2020届高三第三次联考语文参考答案一、现代文阅读（36分）（一）论述类文本阅读（本题共3小题，9分）1．（3分）【答案】B【解析】扩大范围，唐诗宋词可以流传至今的是一些典范作品。

2．（3分）【答案】B【解析】主要采用“对比论证”手法，于文无据。

3．（3分）【答案】D【解析】A项我们要继承的是先人“正面”的思维方式、生活态度和价值追求；B项诗歌“情志一也”；C项《梦游天姥吟留别》并没有讴歌现实美好的事物，也未积极关注民生和干预现实，文中也未提及。

（二）实用类文本阅读（本题共3小题，12分）4．（3分）【答案】D【解析】材料四提到“类脑计算可以处理的任务越来越多，但是要看到这些任务都有严苛的先决条件。

”5．（3分）【答案】C【解析】材料三是“预测2018-2020年中国人工智能芯片市场规模及增长情况”，C项把未然变已然。

6.（6分）【参考答案】①努力实现类脑芯片的两个突破，即突破传统“执行程序”计算范式的局限，形成“自主认知”的新范式和突破传统计算机体系结构的局限，实现数据并行传送、分布式处理，能够以极低功耗实时处理海量数据。

②提高类脑芯片的任务性处理能力和算力水平。

③降低神经元模拟的工艺与技术成本，找到可以代替晶体管的，属于类脑计算的新材料。

④研究好适配类脑计算的架构、算法、编程方案等。

⑤警惕类脑芯片虚假繁荣带来的危险。

（每点2分，答出三点给6分。

）（三）文学类文本阅读（本题共3小题，15分）7．（3分）【答案】B【解析】小说批判对老人的漠视，并没有表现“当下年轻人工作、学习忙碌”和“无暇顾及老人”的内容。

8．（6分）【参考答案】①与前文埋下的伏笔相呼应。

上文中多处埋下伏笔，暗示老人身份的可疑，比如：（老人多次行走在同一条路上，却无目的地；老人行动极其艰难、缓慢，却一直无人陪同；老人行走的人行道，其狭窄程度并不符合生活真实；以及文中对老人行走动作和细节的刻画）等等，这样处理揭示了伏笔，照应了上文，使情节更符合艺术真实。

绝密★启用前2020届六校联盟高三第三次联考理科数学本试卷共5页，23小题，满分150分.考试用时120分钟.一、选择题：本题共12小题，每小题5分，共60分.在每小题给出的四个选项中，只有一项是符合题目要求的.1. 满足z +(i 为虚数单位的复数z =( )A .1122i + B . 1122i - C . 1122i -+ D . 1122i -- 2. 已知集合{}(){}22|1,|lg 2y y x B x y x x A ==-==-，则A . 1[0,)2B . (,0)-∞∪1[,+)2∞C . 1(0,)2D . (,0] -∞∪1[,+)2∞3. 设a R ∈，0b >，则3a b >是3log a b >的( )A . 充分而不必要条件B . 必要而不充分条件C . 充要条件D . 既不充分也不必要条件4. 根据历年气象统计资料，某地四月份吹东风的概率为730，既吹东风又下雨的概率为110.则在吹东风的条件下下雨的概率为( )A .311 B . 37C .711D .1105. 设等差数列的前n 项和为()n S n N *∈，当首项和公差d 变化时，若是定值，则下列各项中为定值的是( )A . 15SB . 16SC . 17SD . 18S6. 设的内角A ，B ，C 所对边分别为a ，b ，c 若，，3A π=，则B =( )A .6πB .23π C .6π或56π D .4π7. 已知椭圆C ：22221(0)x y a b a b+=>>的左、右焦点分别为1F 、2F ，离心率为，过2F 的直线l 交C 于A 、B 两点，若的周长为，则C 的方程为( )A . 22132x y +=B . 2213x y +=C . 221128x y +=D . 221124x y +=8. 已知向量()cos ,sin a θθ=r ，()1,2b =r ，若a r 与b r 的夹角为6π，则||a b -r r =( )A . 2B . 3C . 2D . 19. 函数sin ()=2xxf x e的图象的大致形状是( ) A . B .C .D .10. 已知双曲线22221x y a b-=(0,0a b >>)的左，右焦点分别为1F 、2F ，点A 在双曲线上，且2AF x⊥轴，若的内切圆半径为，则其离心率为( )A 3B . 2C . 31D . 2311. 设函数()()sin f x x ωϕ=+，若7()()()663f f f πππ==-，则ω的最小正值是( ) A . 1 B .65C . 2D . 6 12. 在我国古代数学名著九章算术中将底面为直角三角形，且侧棱垂直于底面的三棱柱称之为堑堵如图，在堑堵111ABC A B C -中，AB BC =，1AA AB >，堑堵的顶点1C 到直线1A C 的距离为m ，1C到平面1A BC 的距离为n ，则mn的取值范围是 A . 23(1,) B . 223(,)2 C . 23(,3) D . 23(,2)二、填空题：本题共4小题，每小题5分，共20分.13. 已知函数1()sin 2sin 33f x a x x =-（a 为常数）在3x π=处取得极值，则a 值为______.14. 若2020220200122020(1)(1)(1)xa a x a x a x =+-+-+⋅⋅⋅+-，则20201222020333a a a ++⋅⋅⋅+=______． 15. 若函数()=(0)axb f xc cxd +≠+，其图象的对称中心为(,)d a c c -，现已知22()=21xf x x --，数列{}n a 的通项公式为()()2020n na f n N *=∈，则此数列前2020项的和为______． 16. 已知正方体1111ABCD A B C D -的棱长为1，以顶点A 为球心，23为半径作一个球，则球面与正方体的表面相交所得到的曲线的长等于______．三、解答题：共70分.解答应写出文字说明、证明过程或演算步骤.第17～21题为必考题，每个试题考生都必须作答.第22、23题为选考题，考生根据要求作答. （一）必考题：共60分.17. （本小题满分12分）已知函数 ． (1)若 ，求函数()f x 的值域；(2)设的三个内角A ，B ，C 所对的边分别为a ，b ，c ，若A 为锐角且3()=f A ，，3c =，求的值．18. （本小题满分12分）如图，四棱锥P ABCD -中，底面ABCD 是直角梯形，90DAB ∠=o ,AD ∥BC ，侧面PAB ，是等边三角形，，，E 是线段AB的中点．()2sin()cos 3f x x x π=+02x π≤≤1)求证：；2)求PC 与平面PDE 所成角的正弦值．19. （本小题满分12分）已知O 为坐标原点，过点()1,0M 的直线l 与抛物线C ：22(0)y px p =>交于A ，B 两点，且3OA OB u u u r u u u r⋅=-．(1)求抛物线C 的方程；(2)过点M 作直线'l l ⊥交抛物线C 于P ，Q 两点，记OAB ∆，OPQ ∆的面积分别为1S ，2S ，证明：221211S S +为定值.20. （本小题满分12分）十九大以来，某贫困地区扶贫办积极贯彻落实国家精准扶贫的政策要求，带领广大农村地区人民群众脱贫奔小康．经过不懈的奋力拼搏，新农村建设取得巨大进步，农民收入也逐年增加．为了更好的制定2019年关于加快提升农民年收入力争早日脱贫的工作计划，该地扶贫办统计了2018年50位农民的年收入并制成如下频率分布直方图：根据频率分布直方图估计50位农民的年平均收入单位：千元同一组数据用该组数据区间的中点值表示；由频率分布直方图可以认为该贫困地区农民年收入X 服从正态分布，其中近似为年平均收入，近似为样本方差，经计算得：，利用该正态分布，求：()i 在2019年脱贫攻坚工作中，若使该地区约有占总农民人数的的农民的年收入高于扶贫办制定的最低年收入标准，则最低年收入大约为多少千元？()ii 为了调研“精准扶贫，不落一人”的政策要求落实情况，扶贫办随机走访了1000位农民．若每个农民的年收人相互独立，问：这1000位农民中的年收入不少于千元的人数最有可能是多少？附：参考数据与公式，若2(,)X N μσ~，则；21. （本小题满分12分）已知函数1)1()(-+=tx x f 的定义域为()+∞,1-，其中实数t 满足10≠≠t t 且.直线:l )(x g y =是)(x f 的图像在0=x 处的切线.(1)求l 的方程)(x g y =；(2)若)()(x g x f ≥恒成立，试确定t 的取值范围； (3)若()1,0,21∈a a ，求证：12212121aaaaa a a a +≥+.（二）选考题：共10分.请考生在第22、23题中任选一题作答.如果多做，则按所做的第一题计分.22. [选修4 ― 4：坐标系与参数方程]（本小题满分10分）在平面直角坐标系xOy 中，曲线1C 的参数方程为cos 1sin x t y t αα=⎧⎨=+⎩，以原点O 为极点，x 轴正半轴为极轴建立极坐标系，曲线2C 的极坐标方程为2cos ρθ=．若曲线1C 方程中的参数是，且1C 与2C 有且只有一个公共点，求1C 的普通方程；已知点()0,1A ，若曲线1C 方程中的参数是t ，，且1C 与2C 相交于P ，Q 两个不同点，求11||||AP AQ +的最大值．23. [选修4 ― 5：不等式选讲]（本小题满分10分） 已知函数()|1|||()f x x x a a N *=--+∈，恒成立． (1)求a 的值； (2)若正数x ，y 满足12a x y +=，证明：1122x y xy ++≥。

2020届高三六校第三次联考英语试题试卷共10页，卷面满分120分，折算成135分计入总分。

考试用时120分钟。

注意事项：1.答题前，先将自己的姓名、准考证号填写在答题卡上。

2.选择题的作答：每小题选出答案后，用2B铅笔把答题卡上对应题目的答案标号涂黑。

写在试题卷、草稿纸和答题卡的非答题区域均无效。

3.非选择题的作答：用签字笔直接答在答题卡上对应的答题区域内。

写在试题卷、草稿纸和答题卡的非答题区域均无效。

4.考试结束后，请将本试卷和答题卡一并上交。

第一部分阅读理解（共两节，满分40分）第一节(共15小题；每小题2分，满分30分)阅读下列短文，从短文后每题所给的A、B、C和D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。

AHow cool can libraries be in an era of iPods and Kindles? More than you think. Only if you know where to go.Central Library: Seattle, Washington, United StatesThe Central Library in Seattle is modern and fashionable and has tourists from around the world paying visits and taking tours. It was designed by Dutch architect Rem Koolhaas and American designer Joshua Ramus. Tours began in 2006, two years after its opening. The library holds various art exhibitions, book signings and other events, while visitors can stop by the Chocolate cart for a coffee and scan through the gift shop anytime.Trinity College Library: Dublin, IrelandThe Trinity College Library in Dublin is in Ireland, founded at the end of the 16th century by Queen Elizabeth I. It is the largest single library in the world, also known as the Long Room, which contains more than 200,000 of the library's oldest books. The Long Room houses one of the oldest harps（竖琴）in Ireland.Dating to the 15th century, the old harp is the model for the symbol foreland.Geisel Library, University of California: San Diego, United StatesAt first glance, it looks like a spaceship. Architect William Pereira, who helped design actual space launch facilities at Cape Canaveral in Houston, Texas, designed the library in 1970. It has been featured in sci-fi films, short stories and novels. The library hosts “Dinner in the Library,” which invites readers for cocktails, and also special speeches from distinguished authors．TU Delft Library: The NetherlandsThe library at the Delft University of Technology was constructed in 1997 and has more than 862,000 books, 16,000 magazine subscriptions and its own museum. The building itself exists beneath the ground, so you can't really see the actual Library. What makes it interesting is the roof, which is a grassy hill. The roof covers 5,500 square meters. And it has become one of the most striking and greenest structures in the area.1. Which of the four libraries has the longest history?A. Central LibraryB. Trinity College LibraryC. Geisel LibraryD. TU Delft Library2. What makes Geisel Library different from the others is that _____.A. a spaceship designer founded the libraryB. it has a roof of grassy hillC. famous writers often deliver speeches thereD. it is the largest single library in the world3. In Central Library, you can _____.A. drink cocktailsB. buy souvenirsC. create paintingsD. book eventsBThe cracked step four years ago was the start of it. That day, I awoke tired—the children were tiny and needing so much—and I had a golden afternoon of rest ahead, my mother stepping in to allow me to catch up on my sleep. I dropped them off and drove home—the sun shining and my bed signaling. As I was about to enter the house, I caught sight of a deep crack beneath my feet.Without thinking, I turned around, walked back to the car and drove to a DIY store. Four hours later, I had all the tools, mixed my own cement, filled in the crack and repaired the foundation. Perfect. As I stood up to take a photo of my handiwork, I realized that I was trembling. I’d forgotten my shot at a nice long nap, and my children were already on their way home. That sleep... that promise to self was broken, because I had focused, instead, on the crack in the step.Suddenly, everything started to hurt. My head, my throat, my back. I couldn’t stop shaking. Whatearned then is that when we break the promises we make to our bodies they will not be silenced. This is when we overwork and overthink to the point of breaking down. Ironically (讽刺地), for many of us, it is only when we have no choice— when we fall ill—that we learn to listen. For me, when that crack ended in a hospital stay which sent me to bed for two unmoving weeks when my body worked to clear two different infections, the lesson is ever present. I did it to myself—a whole twisted spin on DIY.Sadly it took another two ridiculous DIY projects to finally get through. The cracks will never be fully filled. Focus, then, on your own inner core, the feeding of light, fire and strength.4．What made the author so sleepy in the first place?A. Taking care of the kids.B. Asking her mother for help.C. Driving to her mother’s houseD. Dealing with DIY projects.5．How did the author feel as soon as she finished her repair work?A. RegretfulB. UpsetC. ProudD. Thankful6．What can be implied from Paragraph 3?A. Our health is ignored deliberately.B. Our body will respond to what we do.C. The author took her mother’s advice.D. The author was infected before the DIY.7．What is the author’s purpose in writing the text?A. To describe an unfortunate event.B. To show the danger of DIY.C. To stress the importance of sleep.D. To encourage focusing on oneself.CI used to think the whole purpose of life was pursuing happiness. Everyone said the path to happiness was success, so I searched for that ideal job, that perfect boyfriend, and that beautiful apartment. But instead of ever feeling fulfilled, I felt anxious and lost. Eventually. I decided to go to graduate school for positive psychology to learn what truly makes people happy.And what's the difference between being happy and having meaning in life? Many psychologists describe happiness as a state of comfort and ease, feeling good in the moment. Meaning, though, is deeper. The famous psychologist Martin Seligman says meaning comes from belonging to and serving something beyond yourself and from developing the best within you. Our culture is obsessed with happiness, but Icame to see that seeking meaning is the more fulfilling path.There are four pillars of a meaningful life.The first pillar is belonging. Belonging comes from being in relationships where you're valued for who you are and where you value others as well. For many people, belonging is the most essential source of meaning.For others, the key to meaning is the second pillar: purpose. Finding your purpose is not the same thing as finding that job that makes you happy. A doctor told me her purpose is healing sick people. Many parents tell me, “My purpose is raising my children.” The key to purpose is using your strengths to serve others. Without something worthwhile to do, people flounder, thus losing the aim of life.The third pillar of meaning is also about stepping beyond yourself, but in a completely different way: transcendence (超然). Transcendent experiences can change you. Transcendent states are those rare moments when you're lifted above the hustle and bustle of daily life, your sense of self fades away, and you feel connected to a high er reality. For me, I’m a writer, and it happens through writing. Sometimes I get so in the zone that I lose all sense of time and place.The fourth pillar is storytelling, the story you tell yourself about yourself. Creating a narrative from the events of your life brings clarity. It helps you understand how you became you. But we don’t always realize that we're the authors of our stories and can change the way we’re telling them. Your life isn't just a list of events. You can edit, interpret and retell your story, even as you're constrained by the facts.That’s the power of meaning. Happiness comes and goes. But when life is really good and when things are really bad, having meaning gives you something to hold on to.8. What can we know from the first two paragraphs？A. Life might be fulfilled by landing ideal jobs．B. Life dilemma is challenging for us to get out of．C. Meaning is highly valued in our culture．D. Happiness is what most people try to achieve．9. Which word is the closest to the underlined word?A. ConfusedB. DistractedC. DisappointedD. Saddened10. Which pillar can describe an artist obsessed with her work despite repeated failures?A. BelongingB. PurposeC. TranscendenceD. Storytelling11. The passage aims to tell us that _______________．A. meaning is superior to happinessB. meaning is the way to successC. chasing meaning can make people happyD. meaning has deeper psychological significanceDIt often happens that a number of applicants with almost identical qualifications and experience all apply for the same position. In their educational background, special skills and work experience, there is little, if anything, to choose between half a dozen candidates. How then does the employer make a choice? Usually on the basis of an interview.There are many arguments about the interview as a selection procedure. One argument is that it gives rise to a wholly subjective decision. As often as not, employers do not choose the best candidate, but the one who makes a good first impression on them. Some employers, of course, reply to this argument by saying that they have become so experienced in interviewing staff that they are able to make a sound assessment of each candidate’s likely perfor mance. Unfortunately, both for the employers and applicants, there are many people of great ability who simply do not interview well. There are also, of course, people who interview extremely well, but are later found to be very unsatisfactory employees.Those in favour of the interview insist that the well-structured procedure is valid in assessing a candidate’s ability, an essential guarantee for the future job. They also argue that an employer is concerned not only with a candidate’s ability, but with th e suitability of his or her personality for the particular work situation. Many employers, for example, will overlook occasional inefficiencies from their secretary so long as she has a pleasant personality. Perhaps the real purpose of an interview is not to assess the assessable aspects of each candidate but to make a guess at the more intangible things, such as personality and social ability.Today, interview is still a common section of the entire selection procedure, though different employers have different standards for competence. Generally speaking, candidates who interview well tend to be quietly confident, but never boastful; direct and straight-forward in their questions and answers; cheerful and friendly, but never over-familiar; and sincerely enthusiastic and optimistic. Candidates who interview badly tend to be at either end of the spectrum of human behaviour. They are either very shy or over-confident. They show either a lack of enthusiasm or an excess of it. They either talk too little or never stop talking. They are either over-polite or rudely abrupt.12. According to the passage, which of the following statements is TRUE?A. Employers are experienced in assessing the interviewees’ performance.B. Interview is not always recognized as a sensible way to choose employees.C. The interview helps the employers to pick the desired employees.D. The remarkable candidates often distinguish themselves in an interview.13. Which may not be considered in an interview?A. PersonalityB. Communication skillsC. BackgroundD. Capability14. What is the author’s attitude towards the interview as a selection procedure?A. SupportiveB. NegativeC. ObjectiveD. Unconcerned15. The last paragraph indicates _________________.A. a link between success in interview and characterB. connections between work abilities and characterC. differences in interview experienceD. differences in personal behaviour第二节(共5小题；每小题2分，满分10分)根据短文内容，从短文后的选项中选出能填入空白处的最佳选项。

广东省六校联盟2020届高三下学期第三次联考数学试题（理）一、选择题：本题共12小题，每小题5分，共60分.在每小题给出的四个选项中，只有一项是符合题目要求的.1.满足z iz+＝i(i为虚数单位)的复数z＝（）A. 1122i+ B.1122i- C.1122-+i D.1122i--『答案』B『解析』易得z＋i＝z i，所以(1－i)z＝－i，解得z＝1i i--＝1122i-.故选：B.2.已知集合A＝{y|y，B＝{x|y＝lg（x﹣2x2）}，则∁R（A∩B）＝（）A. 『0，12） B. （﹣∞，0）∪『12，+∞）C. （0，12） D. （﹣∞，0』∪『12，+∞）『答案』D『解析』集合A＝{y|y=}＝{y|y≥0}＝『0，+∞）；B＝{x|y＝lg（x﹣2x2）}＝{x|x﹣2x2＞0}＝{x|0＜x12＜}＝（0，12），∴A∩B＝（0，12），∴∁R（A∩B）＝（﹣∞，0』∪『12，+∞）.故选：D.3.设a∈R，b＞0，则3a＞b是a＞log3b的（）A. 充分而不必要条件B. 必要而不充分条件C. 充要条件D. 既不充分也不必要条件『答案』C『解析』a∈R，b＞0，则3a＞b，利用对数函数y＝log3x的图象和性质左右两侧同时取对数可得：a＞log3b；故3a ＞b ，能推出a ＞log 3b ； a ∈R ，b ＞0，若a ＞log 3b 时，利用指数函数y ＝3x 的图象和性质左右两侧同时取指数幂可得：3a ＞b ； 故a ＞log 3b 能推出a ＞log 3b ；根据充分条件和必要条件的定义分别进行判断即可知C 正确. 故选：C.4.根据历年气象统计资料，某地四月份吹东风的概率为730，既吹东风又下雨的概率为110.则在吹东风的条件下下雨的概率为（ ） A.311B.37C.711D.110『答案』B『解析』设事件A 表示四月份吹东风，事件B 表示吹东风又下雨，根据条件概率计算公式可得在吹东风的条件下下雨的概率1310(|)7730P B A ==．故选：B ．5.设等差数列{}n a 的前n 项和为S n ()1n ≥，当首项a 1和公差d 变化时，若a 1+ a 8+ a 15是定值，则下列各项中为定值的是（ ） A. S 15 B. S 16C. S 17D. S 18『答案』A『解析』由等差数列的性质可得181583a a a a ++=为定值， 再由求和公式可得()11515815152a a S a +==，故当1815a a a ++为定值时，15S 为定值. 故选A.6.设ΔABC 的内角A,B,C 所对的边分别为a,b,c ，若πa 3,b A 3===，则B =（ ） A.π5π66或 B.π6C.5π6D. 2π3『答案』B『解析』由正弦定理得sin sin a b A B=，∴sin 12sin 32b AB a===． 又b a <， ∴B 为锐角， ∴6B π=．故选B ．7.已知椭圆C ：22221(0)x y a b a b +=>>的左右焦点为F 1,F 2，过F 2的直线l 交C 与A ,B 两点，若△AF 1B的周长为C 的方程为( )A. 22132x y +=B. 2213x y +=C. 221128x y +=D. 221124x y +=『答案』A『解析』若△AF 1B 的周长为,由椭圆的定义可知4a =,a ∴=c e a ==1c ∴=, 22b ∴=，所以方程为22132x y +=，故选A.8.已知向量(cos ,sin )a θθ=，(1,2)b =，若a 与b 的夹角为6π，则||a b -=( ) A.2B.C.D. 1『答案』D9.函数sin ()2xxf x e =的图象的大致形状是 A.B.C. D.『答案』A『解析』令x =0可得()00f =，则排除C 、D ；()cos sin '2e xx xf x -=当π0,4x ⎛⎫∈ ⎪⎝⎭时，()cos sin '02exx xf x -=>， 当ππ,42x ⎛⎫∈ ⎪⎝⎭时，()cos sin '02e xx x f x -=<，故排除B ， 本题选择A 选项.10.已知双曲线22221(0,0)x y a b a b-=>>的左，右焦点分别为1F ，2F ，点A 在双曲线上，且2AF x ⊥轴，若12AF F ∆的内切圆半径为1)a ，则其离心率为（ ）A.B. 2C.1D. 『答案』A『解析』∵由122AF AF a -=，∴12Rt AF F ∆内切圆半径为)212122122AF F F AF c ac a a +--==-=c ⇒=，∴离心率e =故选A 11.设函数f （x ）＝sin （ωx +φ），若f （6π）＝f （76π）＝﹣f （3π），则ω的最小正值是（ ） A. 1 B.65C. 2D. 6『答案』B 『解析』由f （6π）＝f （76π）＝﹣f （3π），且7636πππ<<并且73663ππππ-<-， 所以要使ω最小，即周期最大，,且726623πππ+=，6324πππ+= 结合正弦曲线特征，可得()f x 的图象满足关于直线23x π=成轴对称，关于点（4π，0）成中心对称对称， 且对称轴和对称中心是相邻的， 即2543412T πππ=-=，即T 53π=， 又T 253ππω==， 得ω65=， 故选：B.12.在我国古代数学名著《九章算术》中将底面为直角三角形，且侧棱垂直于底面的三棱柱称之为堑堵，如图，在堑堵ABC ﹣A 1B 1C 1中，AB ＝BC ，AA 1＞AB ，堑堵的顶点C 1到直线A 1C 的距离为m ，C 1到平面A 1BC 的距离为n ，则mn的取值范围是（ ）A . （1） B .）C .（3） D .（3『答案』D『解析』设AB ＝BC ＝1，则AC ＝A 1C1=AA 1＝a ，则CC 1＝a ，∴A 1C =的∴C 1到直线A 1C 的距离m 1111AC CC AC ⋅==，∵B 1C 1∥BC ，BC ⊂平面A 1BC ，B 1C 1⊄平面A 1BC ， ∴B 1C 1∥平面A 1BC ，∴C 1到平面A 1BC 的距离等于B 1到平面A 1BC 的距离， ∴11113B A BC A BCV S n -=⋅，∵BC ⊥AB ，BC ⊥BB 1，AB ∩BB 1＝B ， ∴BC ⊥平面ABB 1A 1， ∴BC ⊥A 1B，∴11111222A BCSBC A B =⋅⋅=⨯=，又1111111113326B A BC C ABB ABB a VV V S BC a --==⋅=⨯⨯⨯⨯=，∴13•2•n 6a =，∴n =.∴m n === ∵AA 1＞AB ，∴a ＞1， ∴022223a +＜＜，故选：D .二、填空题：本题共4小题，每小题5分，共20分. 13.已知函数1()sin 2sin 33f x a x x =-（a 为常数）在3x π=处取得极值，则a 值为______.『答案』1.『解析』因为()2cos 2cos3f x a x x '=-，所以根据函数在3x π=处取得极值应有 03f π⎛⎫'=⎪⎝⎭， 即22coscos 31033a a ππ⎛⎫-⨯=-+= ⎪⎝⎭，解得1a =， 故答案为114.若x 2020＝a 0+a 1（x ﹣1）+a 2（x ﹣1）2+…+a 2020（x ﹣1）2020，则20201222020333a a a +++=_____. 『答案』2020413⎛⎫- ⎪⎝⎭『解析』∵x 2020＝a 0+a 1（x ﹣1）+a 2（x ﹣1）2+…+a 2020（x ﹣1）2020， 令x ＝1得：a 0＝1； 令x 43=得： （43）2020＝a 020201222020333a a a ++++； ∴20202020122202043333a a a ⎛⎫+++=- ⎪⎝⎭1；故答案为：202043⎛⎫- ⎪⎝⎭115.若函数f （x ）ax b cx d +=+（c ≠0），其图象的对称中心为（d c -，a c ），现已知f （x ）2221xx -=-，数列{a n }的通项公式为a n ＝f （2020n）（n ∈N +），则此数列前2020项的和为_____.『答案』2019-『解析』∵函数f （x ）ax b cx d +=+（c ≠0），其图象的对称中心为（d c -，ac），∴f （x ）2221x x -=-，其图象的对称中心为1(,1)2-，即()(1)2f x f x +-=-，∵数列{a n }的通项公式为a n ＝f （2020n）（n ∈N +），∴此数列前2020项的和为： S 2020＝f （12020）+f （22020）+…﹣f （20192020）+f （1），∴S 2020＝f （20192020）+f （20182020）+…+f （12020）+ f （1）， 两式相加，得：2S 2020＝『f （12020）+f （20192020）』+『f （22020）+f （20182020）』+…+2f （1）()()()2019222=-+-++-+个0＝﹣2×2019，故答案为：﹣2019.16.已知正方体1111ABCD A B C D -的棱长为1，以顶点A 则球面与正方体的表面相交所得到的曲线的长等于______．『答案』6． 『解析』如图，球面与正方体的六个面都相交，所得的交线分为两类：一类在顶点A 所在的三个面上，即面11AA B B 、面ABCD 和面11AA D D 上；另一类在不过顶点A 的三个面上，即面11BB C C 、面11CC D D 和面1111D C B A 上．在面11AA B B 上，交线为弧EF 且在过球心A 的大圆上，因为113AE AA ==，则16A AE π∠=．同理6BAF π∠=，所以6EAF π∠=，故弧EF 的长为369π=，而这样的弧共有三条．在面11BB C C 上，交线为弧FG 且在距球心为1的平面与球面相交所得的小圆上，此时，小圆的圆心为B ，半径为3，所以弧FG 2π=．这样的弧也有三条．于是，所得的曲线长33+=． 三、解答题：共70分.解答应写出文字说明、证明过程或演算步骤.第17～21题为必考题，每个试题考生都必须作答.第22、23题为选考题，考生根据要求作答.（1）必考题：共60分.17.已知函数()2sin ?cos 3f x x x π⎛⎫=+ ⎪⎝⎭． （1）若02x π≤≤，求函数()f x 的值域；（2）设ABC ∆的三个内角,,A B C 所对的边分别为,,a b c ，若A 为锐角且(),2,32f A b c ===，求()cos A B -的值．解：（1）()()2sin cos sin cos f x x x x x x x ==+1sin 2cos 2sin 222232x x x π⎛⎫=++=++ ⎪⎝⎭由02x π≤≤得，42333x πππ≤+≤，sin 2123x π⎛⎫-≤+≤ ⎪⎝⎭．∴0sin 213x π⎛⎫≤++≤ ⎪⎝⎭()f x 的值域为0,1⎡+⎢⎣⎦．（2）由()sin 23f A A π⎛⎫=++= ⎪⎝⎭sin 203A π⎛⎫+= ⎪⎝⎭， 又由02A π<<，∴42333A πππ<+<，∴2,33A A πππ+==．在ABC ∆中，由余弦定理2222cos 7a b c bc A =+-=，得a =由正弦定理sin sin a b A B =，得sin sin 7b A B a ==，∵b a <，∴B A <，∴cos B =∴()1cos cos cos sin sin 2A B A B A B -=+=+=考点：两角和与差的正弦公式，二倍角公式，正弦定理与余弦定理．18.如图，四棱锥P﹣ABCD中，底面ABCD是直角梯形，∠DAB＝90°AD∥BC，AD⊥侧面P AB，△P AB是等边三角形，DA＝AB＝2，BC12AD=，E是线段AB的中点.（1）求证：PE⊥CD；（2）求PC与平面PDE所成角的正弦值.（1）证明：∵AD⊥侧面P AB，PE⊂平面P AB，∴AD⊥EP.又∵△P AB是等边三角形，E是线段AB的中点，∴AB⊥EP.∵AD∩AB＝A，∴PE⊥平面ABCD.∵CD⊂平面ABCD，∴PE⊥CD.（2）解：以E为原点，EA、EP分别为y、z轴，建立如图所示空间直角坐标系.则E（0，0，0），C（1，﹣1，0），D（2，1，0），P（0，0）.ED =（2，1，0），EP =（0，0），PC =（1，﹣1，.设n =（x，y，z）为平面PDE的一个法向量.由2030 n ED x yn EP z⎧⋅=+=⎪⎨⋅==⎪⎩，令x＝1，可得n=（1，﹣2，0）设PC与平面PDE所成的角为θ，得的35PC n sin cos PC n PC n θ⋅=⋅==⋅＜＞ 所以PC 与平面PDE 所成角的正弦值为35. 19.已知O 为坐标原点，过点M （1，0）的直线l 与抛物线C ：y 2＝2px （p ＞0）交于A ，B 两点，且3OA OB ⋅=-.（1）求抛物线C 的方程；（2）过点M 作直线l '⊥l 交抛物线C 于两点，记△OAB ，△OPQ 的面积分别为S 1，S 2，证明：221211S S +为定值. （1）解：设直线l 的方程为：x ＝my +1，与抛物线C ：y 2＝2px （p ＞0）联立，消去x 得：y 2﹣2pmy ﹣2p ＝0；设A （x 1，y 1），B （x 2，y 2），则y 1+y 2＝2pm ，y 1y 2═﹣2p ；由3OA OB ⋅=-，得x 1x 2+y 1y 2＝（my 1+1）（my 2+1）+y 1y 2＝（1+m 2）y 1y 2+（y 1+y 2）m +1＝（1+m 2）•（﹣2p ）+2pm 2+1＝﹣2p +1＝﹣3，解得p ＝2，∴抛物线C 的方程为y 2＝4x ；（2）证明：由（1）知，点M （1，0）是抛物线C 的焦点，所以|AB |＝x 1+x 2+p ＝my 1+my 2+2+p ＝4m 2+4，又原点到直线l 的距离为d =，所以△OAB 的面积为S112=4（m 2+1）＝ 又直线l ′过点M ，且l '⊥l ，所以△OPQ 的面积为S 2＝=所以()()2222212111144141m S S m m +=+=++， 即221211S S +为定值. 20.十九大以来，某贫困地区扶贫办积极贯彻落实国家精准扶贫的政策要求，带领广大农村地区人民群众脱贫奔小康．经过不懈的奋力拼搏，新农村建设取得巨大进步，农民年收入也逐年增加．为了更好的制定2019年关于加快提升农民年收人力争早日脱贫的工作计划，该地扶贫办统计了2018年50位农民的年收人并制成如下频率分布直方图：（1）根据频率分布直方图，估计50位农民的年平均收入x （单位：千元）（同一组数据用该组数据区间的中点值表示）；（2）由频率分布直方图，可以认为该贫困地区农民年收入X 服从正态分布()2,N μσ，其中μ近似为年平均收入x ，2σ近似为样本方差2s ，经计算得2 6.92s =.利用该正态分布，求:(i )在2019年脱贫攻坚工作中，若使该地区约有占总农民人数的84.14%的农民的年收入高于扶贫办制定的最低年收入标准，则最低年收入大约为多少千元？（ii ）为了调研“精准扶贫，不落一人”的政策要求落实情况，扶贫办随机走访了1000位农民．若每个农民的年收人相互独立，问：这1000位农民中的年收入不少于12.14千元的人数最有可能是多少？22.63()~,X N μσ≈,则①()0.6827P X μσμσ-<≤+=；②()220.9545P X μσμσ-<≤+=；③3309().973P X μσμσ-<≤+=.解：()1120.04140.12160.2818036200.10x =⨯+⨯+⨯+⨯+⨯220.06240.0417.40+⨯+⨯=千元.()2由题意，~17.40,62().9X N .（i ）()10.68270.841422P x μσ>-=+≈17.40 2.6314.77μσ∴-=-=时，满足题意即最低年收入大约为14.77千元（ii ）由12.14(()2)P X P X μσ≥=≥-0.95450.50.97732=+≈，得 每个农民的年收入不少于12.14千元的事件概率为0.9773，记1000个农民的年收入不少于12.14千元的人数为ζ，则()3~10,B p ζ，其中0.9773p =， 于是恰好有k 个农民的年收入不少于12.14千元的事件概率是()()3310101k kk C p P k p ξ-=-=从而由()()()()1001111P k k p P k k p ξξ=-⨯=>=-⨯-，得1001k p < 而1001978.2773p =，所以，当0978k ≤≤时， ()()1,P k P k ζζ=-<=当9791000k ≤≤时，()()1,P k P k ζζ=->=由此可知，在所走访的1000位农民中，年收入不少于12.14千元的人数最有可能是978 21.已知函数f （x ）＝（1+x ）t ﹣1的定义域为（﹣1，+∞），其中实数t 满足t ≠0且t ≠1.直线l ：y ＝g （x ）是f （x ）的图象在x ＝0处的切线.（1）求l 的方程：y ＝g （x ）；（2）若f （x ）≥g （x ）恒成立，试确定t 的取值范围；（3）若a 1，a 2∈（0，1），求证： 12212121++a a a a a a a a ≥.注：当α为实数时，有求导公式（x α）′＝αx α﹣1.解：（1）∵f （x ）＝（1+x ）t ﹣1∴f '（x ）＝t （1+x ）x ﹣1，∴f '（0）＝t ，又f （0）＝0，∴l 的方程为：y ＝tx ；（2）令h （x ）＝f （x ）﹣g （x ）＝（1+x ）t ﹣tx ﹣1，h '（x ）＝t （1+x ）t ﹣1﹣t ＝t 『（1+x ）t ﹣1﹣1』当t ＜0时，（1+x ）t ﹣1﹣1单调递减，当x ＝0时，h '（x ）＝0当x ∈（﹣1，0），h '（x ）＜0，h （x ）单调递减； 当x ∈（0，+∞），h '（x ）＞0，h （x ）单调递增.∴x ＝0是h （x ）的唯一极小值点，∴h （x ）≥h （0）＝0，f （x ）≥g （x ）恒成立；当0＜t ＜1时，（1+x ）t ﹣1﹣1单调递减， 当x ＝0时，h '（x ）＝0当x ∈（﹣1，0），h '（x ）＞0，h （x ）单调递增； 当x ∈（0，+∞），h '（x ）＜0，h （x ）单调递减∴x ＝0是h （x ）的唯一极大值点，∴h （x ）≤h （0）＝0，不满足f （x ）≥g （x ）恒成立； 当t ＞1时，（1+x ）t ﹣1﹣1单调递增，当x ＝0时，h '（x ）＝0当x ∈（﹣1，0），h '（x ）＜0，h （x ）单调递减； 当x ∈（0，+∞），h '（x ）＞0，h （x ）单调递增.∴x ＝0是h （x ）的唯一极小值点，∴h （x ）≥h （0）＝0，f （x ）≥g （x ）恒成立；综上，t ∈（﹣∞，0）∪（1，+∞）；证明：（3）当a 1＝a 2，不等式显然成立；当a 1≠a 2时，不妨设a 1＜a 2则12211212a a a a a a a a ++＞⇔12121122a a a a a a a a --＞ 令()12a ax x x ϕ=-，x ∈『a 1，a 2』 .下证φ（x ）是单调减函数：∵()1221211121211'a a a a a a x a x a x a x x a ϕ----⎛⎫=-=- ⎪⎝⎭ 易知a 1﹣a 2∈（﹣1，0），1+a 1﹣a 2∈（0，1），12111a a +-＞ 由（2）知当t ＞1，（1+x ）t ＞1+tx ，x ∈『a 1，a 2』 ∴()121211112122112121[11]111a a a a a a a a a a a a a +-+--=+-+=+-+-＞＞ ∴12121a a a a +-＞ ∴1212211a a a a a a x a --≥＞ ∴φ'（x ）＜0，∴φ（x ）在『a 1，a 2』上单调递减.∴φ（a 1）＞φ（a 2），即12121122a a a a a a a a --＞∴12211212a a a a a a a a ++＞.综上，12211212a a a a a a a a +≥+成立.22.在平面直角坐标系xOy 中，曲线C 1的参数方程为1x tcos y tsin αα=⎧⎨=+⎩，以原点O 为极点，x 轴的正半轴为极轴建立极坐标系，曲线C 2的极坐标方程为ρ＝2cos θ. （1）若曲线C 1方程中的参数是α，且C 1与C 2有且只有一个公共点，求C 1的普通方程； （2）已知点A （0，1），若曲线C 1方程中的参数是t ，0＜α＜π，且C 1与C 2相交于P ，Q 两个不同点，求11AP AQ+的最大值. 解：（1）∵ρ＝2cos θ，∴曲线C 2的直角坐标方程为∴（x ﹣1）2+y 2＝1，∵α是曲线C 1：1x tcos y tsin αα=⎧⎨=+⎩的参数，∴C 1的普通方程为x 2+（y ﹣1）2＝t 2， ∵C 1与C 2有且只有一个公共点，∴|t|=1或|t|=1，∴C 1的普通方程为x 2+（y ﹣1）21）2或x 2+（y ﹣1）21）2 （2）∵t 是曲线C 1：1x tcos y tsin αα=⎧⎨=+⎩的参数，∴C 1是过点A （0，1）的一条直线， 设与点P ，Q 相对应的参数分别是t 1，t 2，把1x tcos y tsin αα=⎧⎨=+⎩，代入（x ﹣1）2+y 2＝1得t 2+2（sin α﹣cos α）t +1＝0，∴121241t t t t πα⎧⎛⎫+=--⎪ ⎪⎝⎭⎨⎪=⎩ ∴121111AP AQ t t +=+=|t 1|+|t 2|＝|t 1+t 2|＝2|sin （α4π-）， 当α34π=时，△＝4（sin α﹣cos α）2﹣4＝4＞0， 11AP AQ+取最大值. 23.已知函数f （x ）＝|x ﹣1|﹣|x +a |（a ∈N *），f （x ）≤2恒成立. （1）求a 的值；（2）若正数x ，y 满足12a x y +=.证明：112x y xy ++≥解：（1）由f （x ）＝|x ﹣1|﹣|x +a |≤|x ﹣1﹣x ﹣a |＝|a +1|， 又f （x ）≤2恒成立，∴|a +1|≤2，∴﹣3≤a ≤1，∵a ∈N *，∴a ＝1；（2）由（1）知12x y +=1， ∴2x +y ＝xy ，∴111122x y xy xy xy ++=+≥=。

年广东历史高考名校联考信息优化卷(三)1．在年进行的全国1％人口抽样调查中显示，我国男女人口比例为106．30：100。

新生儿性别比例失调，这说明重男轻女观念仍然存在。

这种观念形成的历史原因有（）①宗法制②小农经济③科举制④近代新式教育的推广A．①② B．③④ C.①③ D．②④2．柳宗元说：“周之失，在于制；秦之失，在于政，不在制。

”文中两个“制”分别是指（） A分封制和郡县制 B宗法制和郡县制C分封制和专制主义中央集权制 D宗法制和专制主义中央集权制3.左图的漫画反映的是二战后跨大西洋关系的一幅漫画，画面中的医生给的药方是（）A.杜鲁门主义B.经互会C.马歇尔计划D.租借法案4．马克思说：“蒸汽大王在前一个世纪翻转了整个世界，现在他的统治已到末日，另外一种更大得无比的革命力量——电力的火花将取而代之。

”这一“革命力量”带来的影响不包括（）A．改变了人类的生活方式 B．促使第二次工业革命达到空前的深度和广度C．使世界开始走向一个整体 D．引起了一系列新兴工业部门的产生5．近代以来，在西方文明的冲击下，中国固有的传统文明受到冲击和挑战。

下列哪些是这一冲击的表现①新式学堂的兴起和科举制的废除②长袍马褂的废除，西装革履的兴起③布票、粮票的流行④“百花齐放，百家争鸣”方针的提出（）A．①② B．③④ C．②③④ D．①②③④6．“上师尧舜三代，外采东西强国，立行宪法，大开国会，以庶政与国民共之，行三权鼎立之制，则中国之治强可计日待也。

”该思想的主要特点是（）A．照搬西方资产阶级的政治学说 B．把西方资产阶级思想同儒家思想相结合C．从西方基督教教义中受到启发 D．以儒学作为变法的指导思想7．爱因斯坦在20世纪20年代初，曾两次途经上海，总共停留不到三天时间，却对上海产生了深刻的印象。

他在日记中写到：“(上海)这个城市表明欧洲人同中国人的社会地位的差别，这种差别使得近年来的革命事件特别可以理解了。

在上海，欧洲人是一个统治阶级，而中国人则是他们的奴仆。

2020届高三六校第三次联考英语试题试卷共10页，卷面满分120分，折算成135分计入总分。

考试用时120分钟。

注意事项：1.答题前，先将自己的姓名、准考证号填写在答题卡上。

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第一部分阅读理解（共两节，满分40分）第一节(共15小题；每小题2分，满分30分)阅读下列短文，从短文后每题所给的A、B、C和D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。

AHow cool can libraries be in an era of iPods and Kindles? More than you think. Only if you know where to go.Central Library: Seattle, Washington, United StatesThe Central Library in Seattle is modern and fashionable and has tourists from around the world paying visits and taking tours. It was designed by Dutch architect Rem Koolhaas and American designer Joshua Ramus. Tours began in 2006, two years after its opening. The library holds various art exhibitions, book signings and other events, while visitors can stop by the Chocolate cart for a coffee and scan through the gift shop anytime.Trinity College Library: Dublin, IrelandThe Trinity College Library in Dublin is in Ireland, founded at the end of the 16th century by Queen Elizabeth I. It is the largest single library in the world, also known as the Long Room, which contains more than 200,000 of the library's oldest books. The Long Room houses one of the oldest harps（竖琴）in Ireland.Dating to the 15th century, the old harp is the model for the symbol foreland.Geisel Library, University of California: San Diego, United StatesAt first glance, it looks like a spaceship. Architect William Pereira, who helped design actual space launch facilities at Cape Canaveral in Houston, Texas, designed the library in 1970. It has been featured in sci-fi films, short stories and novels. The library hosts “Dinner in the Library,” which invites readers for cocktails, and also special speeches from distinguished authors．TU Delft Library: The NetherlandsThe library at the Delft University of Technology was constructed in 1997 and has more than 862,000 books, 16,000 magazine subscriptions and its own museum. The building itself exists beneath the ground, so you can't really see the actual Library. What makes it interesting is the roof, which is a grassy hill. The roof covers 5,500 square meters. And it has become one of the most striking and greenest structures in the area.1. Which of the four libraries has the longest history?A. Central LibraryB. Trinity College LibraryC. Geisel LibraryD. TU Delft Library2. What makes Geisel Library different from the others is that _____.A. a spaceship designer founded the libraryB. it has a roof of grassy hillC. famous writers often deliver speeches thereD. it is the largest single library in the world3. In Central Library, you can _____.A. drink cocktailsB. buy souvenirsC. create paintingsD. book eventsBThe cracked step four years ago was the start of it. That day, I awoke tired—the children were tiny and needing so much—and I had a golden afternoon of rest ahead, my mother stepping in to allow me to catch up on my sleep. I dropped them off and drove home—the sun shining and my bed signaling. As I was about to enter the house, I caught sight of a deep crack beneath my feet.Without thinking, I turned around, walked back to the car and drove to a DIY store. Four hours later, I had all the tools, mixed my own cement, filled in the crack and repaired the foundation. Perfect. As I stood up to take a photo of my handiwork, I realized that I was trembling. I’d forgotten my shot at a nice long nap, and my children were already on their way home. That sleep... that promise to self was broken, because I had focused, instead, on the crack in the step.Suddenly, everything started to hurt. My head, my throat, my back. I couldn’t stop shaking. Whatearned then is that when we break the promises we make to our bodies they will not be silenced. This is when we overwork and overthink to the point of breaking down. Ironically (讽刺地), for many of us, it is only when we have no choice— when we fall ill—that we learn to listen. For me, when that crack ended in a hospital stay which sent me to bed for two unmoving weeks when my body worked to clear two different infections, the lesson is ever present. I did it to myself—a whole twisted spin on DIY.Sadly it took another two ridiculous DIY projects to finally get through. The cracks will never be fully filled. Focus, then, on your own inner core, the feeding of light, fire and strength.4．What made the author so sleepy in the first place?A. Taking care of the kids.B. Asking her mother for help.C. Driving to her mother’s houseD. Dealing with DIY projects.5．How did the author feel as soon as she finished her repair work?A. RegretfulB. UpsetC. ProudD. Thankful6．What can be implied from Paragraph 3?A. Our health is ignored deliberately.B. Our body will respond to what we do.C. The author took her mother’s advice.D. The author was infected before the DIY.7．What is the author’s purpose in writing the text?A. To describe an unfortunate event.B. To show the danger of DIY.C. To stress the importance of sleep.D. To encourage focusing on oneself.CI used to think the whole purpose of life was pursuing happiness. Everyone said the path to happiness was success, so I searched for that ideal job, that perfect boyfriend, and that beautiful apartment. But instead of ever feeling fulfilled, I felt anxious and lost. Eventually. I decided to go to graduate school for positive psychology to learn what truly makes people happy.And what's the difference between being happy and having meaning in life? Many psychologists describe happiness as a state of comfort and ease, feeling good in the moment. Meaning, though, is deeper. The famous psychologist Martin Seligman says meaning comes from belonging to and serving something beyond yourself and from developing the best within you. Our culture is obsessed with happiness, but Icame to see that seeking meaning is the more fulfilling path.There are four pillars of a meaningful life.The first pillar is belonging. Belonging comes from being in relationships where you're valued for who you are and where you value others as well. For many people, belonging is the most essential source of meaning.For others, the key to meaning is the second pillar: purpose. Finding your purpose is not the same thing as finding that job that makes you happy. A doctor told me her purpose is healing sick people. Many parents tell me, “My purpose is raising my children.” The key to purpose is using your strengths to serve others. Without something worthwhile to do, people flounder, thus losing the aim of life.The third pillar of meaning is also about stepping beyond yourself, but in a completely different way: transcendence (超然). Transcendent experiences can change you. Transcendent states are those rare moments when you're lifted above the hustle and bustle of daily life, your sense of self fades away, and you feel connected to a high er reality. For me, I’m a writer, and it happens through writing. Sometimes I get so in the zone that I lose all sense of time and place.The fourth pillar is storytelling, the story you tell yourself about yourself. Creating a narrative from the events of your life brings clarity. It helps you understand how you became you. But we don’t always realize that we're the authors of our stories and can change the way we’re telling them. Your life isn't just a list of events. You can edit, interpret and retell your story, even as you're constrained by the facts.That’s the power of meaning. Happiness comes and goes. But when life is really good and when things are really bad, having meaning gives you something to hold on to.8. What can we know from the first two paragraphs？A. Life might be fulfilled by landing ideal jobs．B. Life dilemma is challenging for us to get out of．C. Meaning is highly valued in our culture．D. Happiness is what most people try to achieve．9. Which word is the closest to the underlined word?A. ConfusedB. DistractedC. DisappointedD. Saddened10. Which pillar can describe an artist obsessed with her work despite repeated failures?A. BelongingB. PurposeC. TranscendenceD. Storytelling11. The passage aims to tell us that _______________．A. meaning is superior to happinessB. meaning is the way to successC. chasing meaning can make people happyD. meaning has deeper psychological significanceDIt often happens that a number of applicants with almost identical qualifications and experience all apply for the same position. In their educational background, special skills and work experience, there is little, if anything, to choose between half a dozen candidates. How then does the employer make a choice? Usually on the basis of an interview.There are many arguments about the interview as a selection procedure. One argument is that it gives rise to a wholly subjective decision. As often as not, employers do not choose the best candidate, but the one who makes a good first impression on them. Some employers, of course, reply to this argument by saying that they have become so experienced in interviewing staff that they are able to make a sound assessment of each candidate’s likely perfor mance. Unfortunately, both for the employers and applicants, there are many people of great ability who simply do not interview well. There are also, of course, people who interview extremely well, but are later found to be very unsatisfactory employees.Those in favour of the interview insist that the well-structured procedure is valid in assessing a candidate’s ability, an essential guarantee for the future job. They also argue that an employer is concerned not only with a candidate’s ability, but with th e suitability of his or her personality for the particular work situation. Many employers, for example, will overlook occasional inefficiencies from their secretary so long as she has a pleasant personality. Perhaps the real purpose of an interview is not to assess the assessable aspects of each candidate but to make a guess at the more intangible things, such as personality and social ability.Today, interview is still a common section of the entire selection procedure, though different employers have different standards for competence. Generally speaking, candidates who interview well tend to be quietly confident, but never boastful; direct and straight-forward in their questions and answers; cheerful and friendly, but never over-familiar; and sincerely enthusiastic and optimistic. Candidates who interview badly tend to be at either end of the spectrum of human behaviour. They are either very shy or over-confident. They show either a lack of enthusiasm or an excess of it. They either talk too little or never stop talking. They are either over-polite or rudely abrupt.12. According to the passage, which of the following statements is TRUE?A. Employers are experienced in assessing the interviewees’ performance.B. Interview is not always recognized as a sensible way to choose employees.C. The interview helps the employers to pick the desired employees.D. The remarkable candidates often distinguish themselves in an interview.13. Which may not be considered in an interview?A. PersonalityB. Communication skillsC. BackgroundD. Capability14. What is the author’s attitude towards the interview as a selection procedure?A. SupportiveB. NegativeC. ObjectiveD. Unconcerned15. The last paragraph indicates _________________.A. a link between success in interview and characterB. connections between work abilities and characterC. differences in interview experienceD. differences in personal behaviour第二节(共5小题；每小题2分，满分10分)根据短文内容，从短文后的选项中选出能填入空白处的最佳选项。

2020届高三六校第三次联考英语试题试卷共10页，卷面满分120分，折算成135分计入总分。

考试用时120分钟。

注意事项：1.答题前，先将自己的姓名、准考证号填写在答题卡上。

2.选择题的作答：每小题选出答案后，用2B铅笔把答题卡上对应题目的答案标号涂黑。

写在试题卷、草稿纸和答题卡的非答题区域均无效。

3.非选择题的作答：用签字笔直接答在答题卡上对应的答题区域内。

写在试题卷、草稿纸和答题卡的非答题区域均无效。

4.考试结束后，请将本试卷和答题卡一并上交。

第一部分阅读理解（共两节，满分40分）第一节(共15小题；每小题2分，满分30分)阅读下列短文，从短文后每题所给的A、B、C和D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。

AHow cool can libraries be in an era of iPods and Kindles? More than you think. Only if you know where to go.Central Library: Seattle, Washington, United StatesThe Central Library in Seattle is modern and fashionable and has tourists from around the world paying visits and taking tours. It was designed by Dutch architect Rem Koolhaas and American designer Joshua Ramus. Tours began in 2006, two years after its opening. The library holds various art exhibitions, book signings and other events, while visitors can stop by the Chocolate cart for a coffee and scan through the gift shop anytime.Trinity College Library: Dublin, IrelandThe Trinity College Library in Dublin is in Ireland, founded at the end of the 16th century by Queen Elizabeth I. It is the largest single library in the world, also known as the Long Room, which contains more than 200,000 of the library's oldest books. The Long Room houses one of the oldest harps（竖琴）in Ireland. Dating to the 15th century, the old harp is the model for the symbol foreland.Geisel Library, University of California: San Diego, United StatesAt first glance, it looks like a spaceship. Architect William Pereira, who helped design actual space launch facilities at Cape Canaveral in Houston, Texas, designed the library in 1970. It has been featured in sci-fi films, short stories and novels.The library hosts “Dinner in the Library,” which invites readers for cocktails, and also special speeches from dis tinguished authors．TU Delft Library: The NetherlandsThe library at the Delft University of Technology was constructed in 1997 and has more than 862,000 books, 16,000 magazine subscriptions and its own museum. The building itself exists beneath the ground, so you can't really see the actual Library. What makes it interesting is the roof, which is a grassy hill. The roof covers 5,500 square meters. And it hasbecome one of the most striking and greenest structures in the area.1. Which of the four libraries has the longest history?A. Central LibraryB. Trinity College LibraryC. Geisel LibraryD. TU Delft Library2. What makes Geisel Library different from the others is that _____.A. a spaceship designer founded the libraryB. it has a roof of grassy hillC. famous writers often deliver speeches thereD. it is the largest single library in the world3. In Central Library, you can _____.A. drink cocktailsB. buy souvenirsC. create paintingsD. book eventsBThe cracked step four years ago was the start of it. That day, I awoke tired—the children were tiny and needing so much—and I had a golden afternoon of rest ahead, my mother stepping in to allow me to catch up on my sleep. I dropped them off and drove home—the sun shining and my bed signaling. As I was about to enter the house, I caught sight of a deep crack beneath my feet.Without thinking, I turned around, walked back to the car and drove to a DIY store. Four hours later, I had all the tools, mixed my own cement, filled in the crack and repaired the foundation. Perfect. As I stood up to take a photo of my handiwork, I realized that I was trembling. I’d forgotten my shot at a nice long nap, and my children were already on their way home. That sleep... that promise to self was broken, because I had focused, instead, on the crack in the step.Suddenly, everything started to hurt. My head, my throat, my back. I couldn’t stop shaking. What earned then is that when we break the promises we make to our bodies they will not be silenced. This is when we overwork and overthink to the point of breaking down. Ironically (讽刺地), for many of us, it is only when we have no choice— when we fall ill—that we learn to listen. For me, when that crack ended in a hospital stay which sent me to bed for two unmoving weeks when my body worked to clear two different infections, the lesson is ever present. I did it to myself—a whole twisted spin on DIY.Sadly it took another two ridiculous DIY projects to finally get through. The cracks will never be fully filled. Focus, then, on your own inner core, the feeding of light, fire and strength.4．What made the author so sleepy in the first place?A. Taking care of the kids.B. Asking her mother for help.C. Driving to her mother’s houseD. Dealing with DIY projects.5．How did the author feel as soon as she finished her repair work?A. RegretfulB. UpsetC. ProudD. Thankful6．What can be implied from Paragraph 3?A. Our health is ignored deliberately.B. Our body will respond to what we do.C. The author took her mother’s advice.D. The author was infected before the DIY.7．What is the author’s purpose in writing the text?A. To describe an unfortunate event.B. To show the danger of DIY.C. To stress the importance of sleep.D. To encourage focusing on oneself.CI used to think the whole purpose of life was pursuing happiness. Everyone said the path to happiness was success, so I searched for that ideal job, that perfect boyfriend, and that beautiful apartment. But instead of ever feeling fulfilled, I felt anxious and lost. Eventually. I decided to go to graduate school for positive psychology to learn what truly makes people happy.And what's the difference between being happy and having meaning in life? Many psychologists describe happiness as a state of comfort and ease, feeling good in the moment. Meaning, though, is deeper. The famous psychologist Martin Seligman says meaning comes from belonging to and serving something beyond yourself and from developing the best within you. Our culture is obsessed with happiness, but I came to see that seeking meaning is the more fulfilling path.There are four pillars of a meaningful life.The first pillar is belonging. Belonging comes from being in relationships where you're valued for who you are and where you value others as well. For many people, belonging is the most essential source of meaning.For others, the key to meaning is the second pillar: purpose. Finding your purpose is not the same thing as finding that job that makes y ou happy. A doctor told me her purpose is healing sick people. Many parents tell me, “My purpose is raising my children.” The key to purpose is using your strengths to serve others. Without something worthwhile to do, people flounder, thus losing the aim of life.The third pillar of meaning is also about stepping beyond yourself, but in a completely different way: transcendence (超然). Transcendent experiences can change you. Transcendent states are those rare moments when you're lifted above the hustle and b ustle of daily life, your sense of self fades away, and you feel connected to a higher reality. For me, I’m a writer, and it happens through writing. Sometimes I get so in the zone that I lose all sense of time and place.The fourth pillar is storytelling, the story you tell yourself about yourself. Creating a narrative from the events of your life brings clarity. It helps you understand how you became you. But we don’t always realize that we're the authors of our stories and can change the way we’re tellin g them. Your life isn't just a list of events. You can edit, interpret and retell your story, even as you're constrained by the facts.That’s the power of meaning. Happiness comes and goes. But when life is really good and when things are really bad, having meaning gives you something to hold on to.8. What can we know from the first two paragraphs？A. Life might be fulfilled by landing ideal jobs．B. Life dilemma is challenging for us to get out of．C. Meaning is highly valued in our culture．D. Happiness is what most people try to achieve．9. Which word is the closest to the underlined word?A. ConfusedB. DistractedC. DisappointedD. Saddened10. Which pillar can describe an artist obsessed with her work despite repeated failures?A. BelongingB. PurposeC. TranscendenceD. Storytelling11. The passage aims to tell us that _______________．A. meaning is superior to happinessB. meaning is the way to successC. chasing meaning can make people happyD. meaning has deeper psychological significanceDIt often happens that a number of applicants with almost identical qualifications and experience all apply for the same position. In their educational background, special skills and work experience, there is little, if anything, to choose between half a dozen candidates. How then does the employer make a choice? Usually on the basis of an interview.There are many arguments about the interview as a selection procedure. One argument is that it gives rise to a wholly subjective decision. As often as not, employers do not choose the best candidate, but the one who makes a good first impression on them. Some employers, of course, reply to this argument by saying that they have become so experienced in interviewing s taff that they are able to make a sound assessment of each candidate’s likely performance. Unfortunately, both for the employers and applicants, there are many people of great ability who simply do not interview well. There are also, of course, people who interview extremely well, but are later found to be very unsatisfactory employees.Those in favour of the interview insist that the well-structured procedure is valid in assessing a candidate’s ability, an essential guarantee for the future job. They also argue that an employer is concerned not only with a candidate’s ability, but with the suitability of his or her personality for the particular work situation. Many employers, for example, will overlook occasional inefficiencies from their secretary so long as she has a pleasant personality. Perhaps the real purpose of an interview is not to assess the assessable aspects of each candidate but to make a guess at the more intangible things, such as personality and social ability.Today, interview is still a common section of the entire selection procedure, though different employers have different standards for competence. Generally speaking, candidates who interview well tend to be quietly confident, but never boastful; direct and straight-forward in their questions and answers; cheerful and friendly, but never over-familiar; and sincerely enthusiastic and optimistic. Candidates who interview badly tend to be at either end of the spectrum of human behaviour. They are either very shy or over-confident. They show either a lack of enthusiasm or an excess of it. They eithertalk too little or never stop talking. They are either over-polite or rudely abrupt.12. According to the passage, which of the following statements is TRUE?A. Employers are experienced in a ssessing the interviewees’ performance.B. Interview is not always recognized as a sensible way to choose employees.C. The interview helps the employers to pick the desired employees.D. The remarkable candidates often distinguish themselves in an interview.13. Which may not be considered in an interview?A. PersonalityB. Communication skillsC. BackgroundD. Capability14. What is the author’s attitude towards the interview as a selection procedure?A. SupportiveB. NegativeC. ObjectiveD. Unconcerned15. The last paragraph indicates _________________.A. a link between success in interview and characterB. connections between work abilities and characterC. differences in interview experienceD. differences in personal behaviour第二节(共5小题；每小题2分，满分10分)根据短文内容，从短文后的选项中选出能填入空白处的最佳选项。