2017-2018年上海市南模中学高三上周测卷(10月)

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2017-2018学年上海市徐汇区南模中学高三(上)10月月考数学试卷(解析版)

2017-2018学年上海市徐汇区南模中学高三（上）10月月考数学试卷一、填空题1．若α是第四象限角，则所在是象限是第象限．2．已知集合A={x|k，k∈Z}，B={x|4﹣x2≥0}，则A∩B=．3．函数y=的值域为．4．已知tanα=2，则sinαcos2α=．5．函数f （x）=的单调递增区间为．6．f（x）=sin2ωx+1（ω＞0）在区间[﹣，]上为增函数，则ω的最大值为．7．有一个解三角形的题因纸张破损有一个条件不清，具体如下：“在△ABC中，角A、B、C所对的边分别为a、b、c，已知a=，B=45°，，求角A：“经推断破损处的条件为三角形一边的长度，且答案提示A=60°，试将条件补充完整．8．函数f（x）=，f（x）max=M，f（x）min=m，则M+m=．9．已知函数f（x）=sin2x﹣cos2x+1，若f（x）≥log2t对x∈R恒成立，则t 的取值范围为．10．设a1、a2∈R，且，则|10π﹣a1﹣a2|的最小值等于．11．设a，b∈R，c∈[0，2π），若对于任意实数x都有2sin（3x﹣）=asin（bx+c），则满足条件的有序实数组（a，b，c）的组数为．12．关于x的方程=|sin|在[﹣2016，2016]上解的个数为．二、选择题13．在△ABC中，sin2A≤sin2B+sin2C﹣sinBsinC，则A的取值范围是（）A．（0，]B．[，π）C．（0，]D．[，π）14．把y=（cos2x﹣sin2x）的图象平移后得到y=sin2x的图象（）A．向右平移个单位 B．向左平移个单位C．向右平移个单位 D．向左平移个单位15．函数y=﹣的图象按向量=（1，0）平移之后得到的函数图象与函数y=2sinπx （﹣2≤x≤4）的图象所有交点的橫坐标之和等于（）A．2 B．4 C．6 D．816．存在函数f（x）满足，对任意x∈R都有（）A．f（sin2x）=sinx B．f（sin2x）=x2+x C．f（x2+1）=|x+1| D．f（x2+2x）=|x+1|三、解答题17．已知函数f（x）=cos2x﹣sin2x+，x∈（0，π）．（1）求f（x）的单调递增区间；（2）设△ABC为锐角三角形，角A所对边a=，角B所对边b=5，若f（A）=0，求△ABC的面积．18．设函数f（x）=cos（2x+）+sin2x．（1）求函数f（x）的最小周期；（2）设函数g（x）对任意x∈R，有g（x+）=g（x），且当x∈[0，]时，g（x）=﹣f（x）．求函数g（x）在[﹣π，0]上的解析式．19．如图所示：湖面上甲、乙、丙三艘船沿着同一条直线航行，某一时刻，甲船在最前面的A点处，乙船在中间B点处，丙船在最后面的C点处，且BC：AB=3：1．一架无人机在空中的P点处对它们进行数据测量，在同一时刻测得∠APB=30°，∠BPC=90°．（船只与无人机的大小及其它因素忽略不计）（1）求此时无人机到甲、丙两船的距离之比；（2）若此时甲、乙两船相距100米，求无人机到丙船的距离．（精确到1米）20．如图，某园林单位准备绿化一块直径为BC的半圆形空地，△ABC的外面种草，△ABC的内接正方形PQRS为一水池，其余的地方种花，若BC=a，∠ABC=θ，设△ABC的面积为S1，正方形的面积为S2．（1）用a，θ表示S1和S2；（2）当a固定，θ变化时，求取最小值时的角．21．已知函数y=f（x），x∈D，y∈A；g（x）=x2﹣（4）x+1，（1）当f（x）=sin（x+φ）为偶函数时，求φ的值．（2）当f（x）=sin（2x+）+sin（2x+）时，g（x）在A上是单调递增函数，求θ的取值范围．（3）当f（x）=a1sin（ωx+φ1）+a2sin（ωx+φ2）+…+a n sin（ωx+φn）时，（其中a i∈R，i=1，2，3…n，ω＞0），若f2（0）+f2（）≠0，且函数f（x）的图象关于点（，0）对称，在x=π处取得最小值，试探讨ω应该满足的条件．2017-2018学年上海市徐汇区南模中学高三（上）10月月考数学试卷参考答案与试题解析一、填空题1．若α是第四象限角，则所在是象限是第一或三象限．【分析】用不等式表示第四象限角α，再利用不等式的性质求出满足的不等式，从而确定角的终边在的象限．解：∵α是第四象限角，∴+2kπ＜α＜2π+2kπ，k∈Z，∴+kπ＜＜π+kπ，k∈Z，∴+kπ＜﹣＜+kπ，k∈Z，当k为偶数时，属于第一象限，当k为奇数时，属于第三象限，故答案为：一或三【点评】本题考查象限角的表示方法，不等式性质的应用，通过角满足的不等式，判断角的终边所在的象限．2．已知集合A={x|k，k∈Z}，B={x|4﹣x2≥0}，则A∩B={x|﹣2≤x＜﹣或≤x＜} ．【分析】化简集合B，根据交集的定义写出A∩B．解：集合A={x|k，k∈Z}，B={x|4﹣x2≥0}={x|﹣2≤x≤2}，则A∩B={x|﹣2≤x＜﹣或≤x＜}．故答案为：{x|﹣2≤x＜﹣或≤x＜}．【点评】本题考查了集合的化简与运算问题，是基础题．3．函数y=的值域为[，2] ．【分析】把已知函数解析式变形，分离常数，可得y=，由cosx的范围得答案．解：y==．∵﹣1≤cosx≤1，∴2≤cosx+3≤4，∴[]，则∈[，2]．故答案为：[，2]．【点评】本题考查函数值域的求法，训练了利用分离参数法求解函数值域，是中档题．4．已知tanα=2，则sinαcos2α=±．【分析】根据同角三角函数的基本关系、以及三角函数在各个象限中的符号，分类讨论求得要求式子的值．解：∵tanα==2，∴α为第一象限角或α为第三象限角，再根据sin2α+cos2α=1，若α为第一象限角，则sinα=，cosα=，则sinαcos2α=•=．若α为第三象限角，则sinα=﹣，cosα=﹣，则sinαcos2α=﹣•=﹣，故答案为：±．【点评】本题主要考查同角三角函数的基本关系、以及三角函数在各个象限中的符号，属于基础题．5．函数 f （x）=的单调递增区间为，k∈Z．【分析】利用复合函数的单调性的规律：同增异减将原函数的单调性转化为t的单调性，利用三角函数的单调性的处理方法：整体数学求出单调区间．解：∵y=log0.5t为减函数，所以函数f （x）=的单调递增区间为即为单调减区间且令解得故答案为（k∈Z）【点评】本题考查复合函数的单调性的规律、三角函数的单调区间的求法．6．f（x）=sin2ωx+1（ω＞0）在区间[﹣，]上为增函数，则ω的最大值为．【分析】由题意可得可得﹣•2ω≥2kπ﹣，且•2ω≤2kπ+，k∈z，求得ω的最大值．解：∵f（x）=sin2ωx+1（ω＞0）在区间[﹣，]上为增函数，可得﹣•2ω≥2kπ﹣，且•2ω≤2kπ+，k∈z，求得ω≤，故ω的最大值为，故答案为：．【点评】本题主要考查求正弦函数的单调性，属于基础题．7．有一个解三角形的题因纸张破损有一个条件不清，具体如下：“在△ABC中，角A、B、C所对的边分别为a、b、c，已知a=，B=45°，c=，求角A：“经推断破损处的条件为三角形一边的长度，且答案提示A=60°，试将条件补充完整．【分析】先把A=60°当做已知条件根据正弦定理计算出b，c，然后把b，c当做已知条件利用正弦定理解出A进行验证．解：∵A=60°，B=45°，∴C=75°．由正弦定理得，即，解得b=，c=．若条件为b=，则由正弦定理得，解得sinA=，∴A=60°或A=120°，答案不唯一，不符合题意．故答案为：c=．【点评】本题考查了正弦定理，解三角形，属于中档题．8．函数f（x）=，f（x）max=M，f（x）min=m，则M+m=2．【分析】利用分离法化简f（x），构造函数g（x），讨论g（x）的奇偶性，求解最值，即可求解M+m的值．解：函数f（x）==1+，令函数g（x）=的最大值为N，最小值为n，那么f（x）max=1+N=M，f（x）min=1+n=m，∵g（﹣x）=﹣=﹣g（x），则函数g（x）是奇函数，∴n+N=0．则M+m=2．故答案为：2．【点评】本题主要考查函数最值的求解，根据分离后构造新函数，求解最值是解决本题的关键．9．已知函数f（x）=sin2x﹣cos2x+1，若f（x）≥log2t对x∈R恒成立，则t 的取值范围为（0，1] ．【分析】先化简函数解析式，f（x）≥log2t恒成立，只需求出f（x）的最小值大于log2t，求出t的范围即可．解：f（x）=sin2x﹣cos2x+1=sin（2x﹣）+1，函数f（x）=sin（2x﹣）+1的最小值为：0，若f（x）≥log2t恒成立，只需0≥log2t恒成立，所以t∈（0，1]．所以t的取值范围：（0，1]．故答案为：（0，1]．【点评】本题是基础题，考查三角函数的基本性质，三角函数的化简，恒成立问题的应用，考查计算能力，逻辑推理能力，属于常考题型、基本知识的考查．10．设a1、a2∈R，且，则|10π﹣a1﹣a2|的最小值等于．【分析】由题意，要使+=2，可得sinα1=﹣1，sin2α2=﹣1．求出α1和α2，即可求出|10π﹣α1﹣α2|的最小值解：根据三角函数的性质，可知sinα1，sin2α2的范围在[﹣1，1]，要使+=2，∴sinα1=﹣1，sin2α2=﹣1．则：，k1∈Z．，即，k2∈Z．那么：α1+α2=（2k1+k2）π，k1、k2∈Z．∴|10π﹣α1﹣α2|=|10π﹣（2k1+k2）π|的最小值为．故答案为：．【点评】本题主要考察三角函数性质，有界限的范围的灵活应用，属于基本知识的考查．11．设a，b∈R，c∈[0，2π），若对于任意实数x都有2sin（3x﹣）=asin（bx+c），则满足条件的有序实数组（a，b，c）的组数为4．【分析】根据三角函数恒成立，则对应的图象完全相同．解：∵对于任意实数x都有2sin（3x﹣）=asin（bx+c），∴必有|a|=2，若a=2，则方程等价为sin（3x﹣）=sin（bx+c），则函数的周期相同，若b=3，此时C=，若b=﹣3，则C=，若a=﹣2，则方程等价为sin（3x﹣）=﹣sin（bx+c）=sin（﹣bx﹣c），若b=﹣3，则C=，若b=3，则C=，综上满足条件的有序实数组（a，b，c）为（2，3，），（2，﹣3，），（﹣2，﹣3，），（﹣2，3，），共有4组，故答案为：4．【点评】本题主要考查三角函数的图象和性质，结合三角函数恒成立，利用三角函数的性质，结合三角函数的诱导公式进行转化是解决本题的关键．12．关于x的方程=|sin|在[﹣2016，2016]上解的个数为4031．【分析】根据函数与方程的关系转化为两个函数的交点个数问题，作出两个函数的图象，利用数形结合进行求解即可得到结论．解：y==，作函数y=与y=|sinπx|在[﹣2016，2016]上的图象如下，由图象知函数y=|sin|的周期是2，两个函数都关于x=1对称，当x≤0时，两个函数在每个周期内都有两个交点，此时在[﹣2016，0]内有1008×2=2016个交点，在[0，2]内两个函数只有一个交点，当x≥2时，两个函数在每个周期内都有两个交点，此时在[2，2016]内有1007×2=2014个交点，则在[﹣2016，2016]上解的个数为2016+1+2014=4031，故答案为：4031【点评】本题主要考查方程根式的个数的求解，利用函数与方程的关系转化为两个函数的交点个数，利用数形结合进行求解是解决本题的关键．综合性较强，有一定的难度．二、选择题13．在△ABC中，sin2A≤sin2B+sin2C﹣sinBsinC，则A的取值范围是（）A．（0，]B．[，π）C．（0，]D．[，π）【分析】先利用正弦定理把不等式中正弦的值转化成边，进而代入到余弦定理公式中求得cosA的范围，进而求得A的范围．解：由正弦定理可知a=2RsinA，b=2RsinB，c=2RsinC，∵sin2A≤sin2B+sin2C﹣sinBsinC，∴a2≤b2+c2﹣bc，∴bc≤b2+c2﹣a2∴cosA=≥∴A≤∵A＞0∴A的取值范围是（0，]故选：C．【点评】本题主要考查了正弦定理和余弦定理的应用．作为解三角形中常用的两个定理，考生应能熟练记忆．14．把y=（cos2x﹣sin2x）的图象平移后得到y=sin2x的图象（）A．向右平移个单位 B．向左平移个单位C．向右平移个单位 D．向左平移个单位【分析】化函数y为正弦型函数，再根据函数图象平移法则得出答案．解：函数y=（cos2x﹣sin2x）=cos2x﹣sin2x=cos（2x+）=sin（2x++）=sin（2x+）=sin2（x+），把函数y=（cos2x﹣sin2x）的图象向右平移个单位后得到y=sin2x的图象．故选：A．【点评】本题考查了三角函数的图象平移问题，也考查了三角恒等变换问题，是中档题．15．函数y=﹣的图象按向量=（1，0）平移之后得到的函数图象与函数y=2sinπx （﹣2≤x≤4）的图象所有交点的橫坐标之和等于（）A．2 B．4 C．6 D．8【分析】y1=的图象由奇函数y=﹣的图象向右平移1个单位而得，所以它的图象关于点（1，0）中心对称，再由正弦函数的对称中心公式，可得函数y2=2sinπx 的图象的一个对称中心也是点（1，0），故交点个数为偶数，且每一对对称点的横坐标之和为2．由此不难得到正确答案．解：函数y=﹣的图象按向量=（1，0）平移之后得到函数y1=，y2=2sinπx 的图象有公共的对称中心（1，0），作出两个函数的图象如图：当1＜x≤4时，y1＜0，而函数y2在（1，4）上出现1.5个周期的图象，在（1，）和（，）上是减函数；在（，）和（，4）上是增函数．∴函数y1在（1，4）上函数值为负数，且与y2的图象有四个交点E、F、G、H，相应地，y1在（﹣2，1）上函数值为正数，且与y2的图象有四个交点A、B、C、D，且：x A+x H=x B+x G═x C+x F=x D+x E=2，故所求的横坐标之和为8，故选：D．【点评】发现两个图象公共的对称中心是解决本题的入口，讨论函数y2=2sinπx 的单调性找出区间（1，4）上的交点个数是本题的难点所在．16．存在函数f（x）满足，对任意x∈R都有（）A．f（sin2x）=sinx B．f（sin2x）=x2+x C．f（x2+1）=|x+1| D．f（x2+2x）=|x+1|【分析】利用x取特殊值，通过函数的定义判断正误即可．解：A．取x=0，则sin2x=0，∴f（0）=0；取x=，则sin2x=0，∴f（0）=1；∴f（0）=0，和1，不符合函数的定义；∴不存在函数f（x），对任意x∈R都有f（sin2x）=sinx；B．取x=0，则f（0）=0；取x=π，则f（0）=π2+π；∴f（0）有两个值，不符合函数的定义；∴该选项错误；C．取x=1，则f（2）=2，取x=﹣1，则f（2）=0；这样f（2）有两个值，不符合函数的定义；∴该选项错误；D．令x+1=t，则f（x2+2x）=|x+1|，化为f（t2﹣1）=|t|；令t2﹣1=x，则t=±；∴；即存在函数f（x）=，对任意x∈R，都有f（x2+2x）=|x+1|；∴该选项正确．故选：D．【点评】本题考查函数的定义的应用，基本知识的考查，但是思考问题解决问题的方法比较难．三、解答题17．已知函数f（x）=cos2x﹣sin2x+，x∈（0，π）．（1）求f（x）的单调递增区间；（2）设△ABC为锐角三角形，角A所对边a=，角B所对边b=5，若f（A）=0，求△ABC的面积．【分析】（1）由二倍角的余弦公式和余弦函数的递增区间，解不等式可得所求增区间；（2）由f（A）=0，解得A，再由余弦定理解方程可得c，再由三角形的面积公式，计算即可得到所求值．解：（1）函数f（x）=cos2x﹣sin2x+=cos2x+，x∈（0，π），由2kπ﹣π≤2x≤2kπ，解得kπ﹣π≤x≤kπ，k∈Z，k=1时，π≤x≤π，可得f（x）的增区间为[，π）；（2）设△ABC为锐角三角形，角A所对边a=，角B所对边b=5，若f（A）=0，即有cos2A+=0，解得2A=π，即A=π，由余弦定理可得a2=b2+c2﹣2bccosA，化为c2﹣5c+6=0，解得c=2或3，若c=2，则cosB=＜0，即有B为钝角，c=2不成立，则c=3，△ABC的面积为S=bcsinA=×5×3×=．【点评】本题考查二倍角公式和余弦函数的图象和性质，考查解三角形的余弦定理和面积公式的运用，考查运算能力，属于中档题．18．设函数f（x）=cos（2x+）+sin2x．（1）求函数f（x）的最小周期；（2）设函数g（x）对任意x∈R，有g（x+）=g（x），且当x∈[0，]时，g（x）=﹣f（x）．求函数g（x）在[﹣π，0]上的解析式．【分析】（1）利用二倍角和两角和与差以及辅助角公式基本公式将函数化为y=Asin（ωx+φ）的形式，再利用周期公式求函数的最小正周期．（2）当x∈[0，]时，g（x）=﹣f（x）．在讨论x∈[，0]时，g（x）的解析式，在函数g（x）在[﹣π，0]上的解析式．解：（1）函数f（x）=cos（2x+）+sin2x化简可得：f（x）=（cos2xcos﹣sin2xsin+sin2x）=cos2x﹣sin2x cos2x=﹣sin2x∴函数f（x）的最小周期T=；（2）当x∈[0，]时，g（x）=﹣f（x）．即g（x）=（sin2x）=sin2x．当x∈[﹣，0]时，由于g（x+）=g（x），则（x+）∈[0，]那么：g（x）=sin2（x+）=sin2x．当x∈[﹣π，﹣]时，则（x+π）∈[0，]可得：g（x）=sin2（x+π）=sin2x．∴函数g（x）在[﹣π，0]上的解析式为f（x）=【点评】本题主要考查对三角函数的化简能力和三角函数的图象和性质的运用，以及分段函数的解析式的求法．利用三角函数公式将函数进行化简是解决本题的关键．属于中档题．19．如图所示：湖面上甲、乙、丙三艘船沿着同一条直线航行，某一时刻，甲船在最前面的A点处，乙船在中间B点处，丙船在最后面的C点处，且BC：AB=3：1．一架无人机在空中的P点处对它们进行数据测量，在同一时刻测得∠APB=30°，∠BPC=90°．（船只与无人机的大小及其它因素忽略不计）（1）求此时无人机到甲、丙两船的距离之比；（2）若此时甲、乙两船相距100米，求无人机到丙船的距离．（精确到1米）【分析】（1）利用正弦定理，即可求此时无人机到甲、丙两船的距离之比；（2）若此时甲、乙两船相距100米，由余弦定理求无人机到丙船的距离．解：（1）在△APB中，由正弦定理，得，，在△BPC中，由正弦定理，得，又，sin∠ABP=sin∠CBP，故．即无人机到甲、丙两船的距离之比为．（2）由BC：AB=3：1得AC=400，且∠APC=120°，由（1），可设AP=2x，则CP=3x，在△APC中，由余弦定理，得160000=（2x）2+（3x）2﹣2（2x）（3x）cos120°，解得，即无人机到丙船的距离为≈275米．【点评】本题考查利用数学知识解决实际问题，考查正弦定理、余弦定理的运用，属于中档题．20．如图，某园林单位准备绿化一块直径为BC的半圆形空地，△ABC的外面种草，△ABC的内接正方形PQRS为一水池，其余的地方种花，若BC=a，∠ABC=θ，设△ABC的面积为S1，正方形的面积为S2．（1）用a，θ表示S1和S2；（2）当a固定，θ变化时，求取最小值时的角．【分析】（1）据题知三角形ABC为直角三角形，根据三角函数分别求出AC和AB，求出三角形ABC的面积S1；设正方形PQRS的边长为x，利用三角函数分别表示出BQ和RC，利用BQ+QR+RC=a列出方程求出x，算出S2；（2）由比值称为“规划合理度”，可设t=sin2θ来化简求出S1与S2的比值，利用三角函数的增减性求出比值的最小值即可求出此时的θ．解：（1）在Rt△ABC中，AB=acosθ，AC=asinθ，设正方形的边长为x则，由BP+AP=AB，得，故所以（2），令t=sin2θ，因为，所以0＜2θ＜π，则t=sin2θ∈（0，1]所以，，所以函数g（t）在（0，1]上递减，因此当t=1时g（t）有最小值，此时所以当时，“规划合理度”最小，最小值为．【点评】考查学生会根据实际问题选择合适的函数关系的能力，以及在实际问题中建立三角函数模型的能力．21．已知函数y=f（x），x∈D，y∈A；g（x）=x2﹣（4）x+1，（1）当f（x）=sin（x+φ）为偶函数时，求φ的值．（2）当f（x）=sin（2x+）+sin（2x+）时，g（x）在A上是单调递增函数，求θ的取值范围．（3）当f（x）=a1sin（ωx+φ1）+a2sin（ωx+φ2）+…+a n sin（ωx+φn）时，（其中a i∈R，i=1，2，3…n，ω＞0），若f2（0）+f2（）≠0，且函数f（x）的图象关于点（，0）对称，在x=π处取得最小值，试探讨ω应该满足的条件．【分析】（1）根据函数f（x）=sin（x+φ）为偶函数，可得sin（x+φ）=sin（﹣x+φ），化简为cosφ=0，可得φ的值．（2）利用三角恒等变换化简函数f（x）的解析式为sin（2x+α）∈[﹣，]，可得A，再根据g（x）的解析式结合题意可得tanθ≤﹣，由此可得θ的取值范围．（3）由于f（x）的解析式以及f2（0）+f2（）≠0，可得f（x）=msinωx+ncosωx=sin（ωx+φ），且m2+n2≠0．由函数f（x）的图象关于点（，0）对称，可得ω+φ=kπ，k∈z ①．又函数f（x）在x=π处取得最小值，可得ωπ+φ=2k′π+，k′∈z ②．由①②可得ω 满足的条件．解：（1）因为函数f（x）=sin（x+φ）为偶函数，所以，sin（x+φ）=sin（﹣x+φ），化简为2sinxcosφ=0，∴cosφ=0，所以φ=kπ+，k∈z．（2）∵函数f（x）=sin（2x+）+sin（2x+）=sin2x+2cos2x=sin（2x+α）∈[﹣，]，其中，sinα=，cosα=，所以A=[﹣，]．g（x）=x2﹣（4tanθ）x+1=+1﹣28tan2θ，由题意可知：2tanθ≤﹣，tanθ≤﹣，∴kπ﹣≤θ≤kπ﹣arctan，k∈z，即θ的取值范围是[kπ﹣，kπ﹣arctan]，k∈z．（3）由于f（x）=a1sin（ωx+φ1）+a2sin（ωx+φ2）+…+a n sin（ωx+φn）=a1（sinωxcosφ1 +cosωxsinφ1）+a2（sinωxcosφ2 +cosωxsinφ2）+…+a n（sinωxcosφn+cosωxsinφn）=sinωx （a1•cosφ1+a2•cosφ2+…+a n•cosφn）+cosωx（a1•sinφ1+a2•sinφ2+…+a n•sinφn）．∵f2（0）+f2（）≠0，∴a1•cosφ1+a2•cosφ2+…+a n•cosφn =0与a1•sinφ1+a2•sinφ2+…+a n•sinφn =0 不能同时成立．不妨设a1•cosφ1+a2•cosφ2+…+a n•cosφn =m，a1•sinφ1+a2•sinφ2+…+a n•sinφn =n，则f（x）=msinωx+ncosωx==sin（ωx+φ），且m2+n2≠0．由函数f（x）的图象关于点（，0）对称，可得sin（ω+φ）=0，故ω+φ=kπ，k∈z ①．又函数f（x）在x=π处取得最小值，∴sin（ωπ+φ）=﹣1，∴ωπ+φ=2k′π+，k′∈z ②．由①②可得，ω=（4k′﹣2k）+3．由于k和k′都是整数，故4k′﹣2k为偶数，∴ω=2h+1，h∈N．【点评】本题主要考查三角函数的恒等变换和化简求值，复合三角函数的单调性和对称性，属于中档题．。

2017-2018年上海市南模中学高三上十月月考

2017学年南模中学高三年级十月份月考试卷2017.10一、填空题1. 若α是第四象限角，则22απ-所在象限是第________象限2. 已知集合2|,,{|40}32A x k x k k Z B x x ππππ⎧⎫=+≤<+∈=-≥⎨⎬⎩⎭，则A B =____________. 3. 函数3cos 3cos xy x-=+的值域为____________.4. 已知tan 2α=，则2sin cos αα=____________.5. 函数12()log cos 34x f x π⎛⎫=+⎪⎝⎭的单调递增区间为____________. 6.若()21(0)f x x ωω+>在区间3,22ππ⎡⎤-⎢⎥⎣⎦上为增函数，则ω的最大值是____________. 7. 有一个解三角形的题因纸张破损有一个条件不清，具体如下“在ABC 中，角,,A B C 所对的边分别为,,a b c，已知4a B π==，__________. 求角A ”。

经推断破损处的条件为三角形的一边的长度，且答案提示3A π=，试将条件补充完整8. 函数2max min 2(1)sin (),(),()1x xf x f x M f x m x ++===+，则M m +=____________. 9.已知函数1()sin 22122f x x x =-+，若2()log f x t ≥对x R ∈恒成立，则t 的取值范围为____________. 10. 设12,R αα∈，且121122sin 2sin(2)αα+=++，则12|10|παα--的最小值等于____________.11. 设,,[0,2)a b R c π∈∈，若对任意实数x 都有2sin 3sin()3x a bx c π⎛⎫-=+ ⎪⎝⎭，则满足条件的有序实数组(,,)a b c 的组数为____________. 12. 关于x 的方程11|sin ||1|12x x π=--在[2016,2016]-上解的个数是____________.13. 在ABC 中，222sin sin sin sin sin A B C B C ≤+-，则角A 的取值范围是（）A. (0,]6πB. [,)6ππC. (0,]3πD. [,)3ππ14. 把2sin 2)y x x =-的图像作适当的移动得sin 2y x =的图像，这样的移动可以是（） A. 向右平移38π个单位 B. 向左平移38π个单位 C. 向右平移34π个单位 D. 向左平移34π个单位 15. 将函数1y x=-的图像按向量(1,0)a =平移，得到的函数图像与函数2sin (24)y x x π=-≤≤的图像的所有交点的横坐标之和等于（） A. 2 B. 4C. 6D. 816. 存在函数()f x 满足：对任意x R ∈都有（） A. (sin 2)sin f x x = B. 2(sin 2)f x x x =+C. 2(1)|1|f x x +=+D. 2(2)|1|f x x x +=+三、解答题17. 已知函数221()cos sin ,(0,)2f x x x x π=-+∈ （1）求()f x 的单调递增区间；（2）设ABC 为锐角三角形，角A 所对边a =B 所对边5b =，若()0f A =，求ABC 的面积18. 设函数2()2sin 4f x x x π⎛⎫=++ ⎪⎝⎭ （1）求函数()f x 的最小正周期；（2）设函数()g x 对任意x R ∈，有()2g x g x π⎛⎫+= ⎪⎝⎭，且当0,2x π⎡⎤∈⎢⎥⎣⎦时，1()()2g x f x =-，求函数()g x 在[,0]π-上的解析式19. 如图所示，湖面上甲、乙、丙三艘船沿着同一条直线航行，某一时刻，甲船在最前面的A 点处，乙船在中间的B 点处，丙船在最后的C 点处，且:3:1BC AB =，一架无人机在空中的P 点处对它们进行数据测量，在同一时刻测得30,90APB BPC ∠=︒∠=︒（船只与无人机的大小及其他因素忽略不计）（1）求此时无人机到甲、丙两船的距离之比；（2）若此时甲、乙两船相距100米，求无人机到丙船的距离（精确到1米）20. 如图，某园林单位准备绿化一块直径为BC 的半圆形空地，ABC 外的地方种草，ABC 的内接正方体PQRS 为一水池，其余的地方种花，若,BC a ABC θ=∠=，设ABC 的面积为1S ，正方形的面积为2S （1）用,a θ表示1S 和2S ；（2）当a 固定，θ变化时，求12S S 取最小值时的角θ21.已知函数2(),,;())1y f x x D y A g x x x θ=∈∈=-+ （1）当()sin()f x x ϕ=+为偶函数时，求ϕ的值；（2）当()sin 2263f x x x ππ⎛⎫⎛⎫=++ ⎪ ⎪⎝⎭⎝⎭时，()g x 在A 上是单调递减函数，求θ的取值范围；（3）当1122()s i n ()s i n ()s i n()n n f x a x a x a x ωϕωϕωϕ=++++++时，（,1,2,3,,0i a R i n ω∈=>），若22(0)02f f πω⎛⎫+≠ ⎪⎝⎭，且函数()f x 的图像关于点,02π⎛⎫ ⎪⎝⎭对称，在x π=处取得最小值，试探讨论ω应该满足的条件参考答案一、填空题 1. 一、三2. [2,)[,)232πππ--3. 1,22⎡⎤⎢⎥⎣⎦4.225 5. 36,6,4k k k Z πππ⎛⎫+∈ ⎪⎝⎭6.147.8. 29. [0,1]10. 1,13⎡⎤⎢⎥⎣⎦11. 412. 4031二、选择题 13-16 CADD三、解答题 17. （1）,2ππ⎛⎫⎪⎝⎭；（2 18. （1）π；（2）1sin 2,,22()1sin(2),(,0]22x x g x x x πππ⎧⎡⎤∈--⎪⎢⎥⎪⎣⎦=⎨⎪-∈-⎪⎩19. （1）23；（2）275 20. （1）2221221sin 2sin 2,44sin 24sin 2a S a S θθθθ==++；（2）9421. （1）,2k k Z πϕπ=+∈；（2）1,arctan ,22k k k Z πθππ⎡⎤∈--∈⎢⎥⎣⎦；（3）*21,k k N ω=+∈。

2018 上海市南模中学高三月考数学试卷

2018 上海市南模中学高三月考数学试卷2017.10一. 填空题1. 已知集合2{|0}5x A x x -=<+，2{|230,}B x x x x R =--≥∈，则A B = 2. 已知函数()arcsin(21)f x x =+，则1()6f π-=3. 在(0,2)π内，使sin cos x x ≤成立的x 的取值范围为4. 函数212()log (32)f x x x =-+-的单调递增区间为5. 函数||y x x =的反函数为6. 若对任意x R ∈，不等式2sin 22sin 0x x m +-<恒成立，则m 的取值范围为7. 设数列{}n a 的前n 项和为n S ，若11a =，114n n S a +=（*n N ∈），则n S = 8. 数列{}n x 中，10x =，111n n n x x n n++=+（*n N ∈），则数列的通项公式n x = 9. 设()f x 是定义域为R 的奇函数，()g x 是定义域为R 的偶函数，若函数()()f x g x +的值域为[1,3)，则函数()()f x g x -的值域为10. 已知()sin()f x A x A ωϕ=++（0ω>），若两个不相等的实数12,{|()}2Ax x x f x ∈=，且12min ||x x π-=，则()f x 的最小正周期为 11. 函数2()|2|4sin4xf x x x π=-+-（16x ≤≤）的值域为12. 函数()2|}f x x =-，其中min{,}a a ba b b a b ≤⎧=⎨>⎩，若动直线y m =与函数()y f x =的图像有三个不同的交点，它们的横坐标分别为1x 、2x 、3x ，则1x 、2x 、3x 是否存在最大值？若存在，在横线处填写其最大值；若不存在，直接填写“不存在”二. 选择题13. 已知x R ∈，则“1x ≠”是“2430x x -+≠”的（） A. 充分不必要条件 B. 必要不充分条件C. 充要条件D. 既不充分也不必要条件14. 若||a c h -<，||b c h -<，则下列不等式一定成立的是（）A. ||2a b h -<B. ||2a b h ->C. ||a b h -<D. ||a b h -> 15. 已知ABC ∆内接于单位圆，则长为sin A 、sin B 、sin C 的三条线段（） A. 能构成一个三角形，其面积大于ABC ∆面积的一半 B. 能构成一个三角形，其面积等于ABC ∆面积的一半 C. 能构成一个三角形，其面积小于ABC ∆面积的一半 D. 不一定能构成一个三角形16. 已知函数()21x x e mf x +=+，若对任意123,,x x x R ∈，总有1()f x 、2()f x 、3()f x 为某一个三角形的边长，则实数m 的取值范围是（）A. 1[,1]2B. [0,1]C. [1,2]D. 1[,2]2三. 解答题17. 已知()2f x kx =+，不等式|()|3f x <的解集为(1,5)-，不等式1()xf x ≥的解集为A ；（1）求集合A ；（2）设22()log (22)g x ax x =-+的定义域为B ，若B A ≠∅，求实数a 的取值范围；18. 右图为函数()sin()f x A x ωϕ=+（0A >，0ω>，02πϕ<<）的部分图像，M 、N是它与x 轴的两个交点，D 、C 分别为它的最高点和最低点，(0,1)E 是线段MD 的中点，且OME ∆为等腰直角三角形；（1）求()f x 的解析式；（2）将函数()f x 图像上的每个点的横坐标缩短为原来的一半，再向左平移12的单位长度得到()y g x =的图像，求()g x 的解析式及单调增区间，对称中心；19. 在ABC ∆中，a 、b 、c 分别为内角A 、B 、C 所对的边，且满足(2)cos cos b A C =；（1）求A 的大小；（2）现给出三个条件：（1）2a =；（2）4B π=；（3）c =，试从中选出两个可以确定ABC ∆的条件，写出你的选择，并以此为依据求ABC ∆的面积；（需写出所有可行的方案）20. 对于函数1()f x 、2()f x 、()h x ，如果存在实数a 、b 使得12()()()h x a f x b f x =⋅+⋅，那么称()h x 为1()f x 、2()f x 的生成函数；（1）若1()sin f x x =，2()cos f x x =，()sin()3h x x π=+，则()h x 是否分别为1()f x 、2()f x的生成函数？并说明理由；（2）设12()log f x x =，212()log f x x =，2a =，1b =，生成函数()h x ，若不等式(4)(2)0h x th x +<在[2,4]x ∈上有解，求实数t 的取值范围；（3）设1()f x x =（0x >），21()f x x=（0x >）取0a >，0b >，生成函数()h x 图象的最低点坐标为(2,8)，若对于任意正实数1x 、2x 且121x x +=，试问是否存在最大的常数m ，使12()()h x h x m ≥恒成立？如果存在，求出这个m 的值；如果不存在，请说明理由；21. 对于给定的正整数k ，若数列{}n a 满足11(21)n k n k n k n k n a a a a k a --++-+++⋅⋅⋅++=+对任意正整数n ()n k >恒成立，则称数列{}n a 是()AP k 数列，若正数项数列{}n b ，满足2111()k n k n k n k n k n b b b b b +--++-+⋅⋅⋅=对任意正整数)(k n n >恒成立，则称{}n b 是()GP k 数列；（1）已知正数项数列{}n a 是(3)GP 数列，且前五项分别为4、2a 、2、4a 、1，求4a 的值；（2）若2sin n a n n ω=+（0ω>）为常数，且{}n a 是(2)AP 数列，求ω的最小值；（3）对于下列两种情形，只要选作一种，满分分别是 ① 7分，② 8分，若选择了多于一种情形，则按照序号较小的解答积分；① 证明：数列{}n a 是等差数列的充要条件为“{}n a 既是(2)AP 数列，又是(3)AP 数列”； ② 证明：正数项数列{}n b 是等比数列的充要条件为“数列{}n b 既是(2)GP 数列，又是(3)AP 数列”；参考答案一. 填空题1. (,2)[3,)-∞+∞2. 14-3. 5(0,][,2)44πππ4. 3(,2)25. 10()x f x x -⎧≥⎪=⎨<⎪⎩ 6. 1,)+∞ 7. 15n -（*n N ∈）8. 1n -（*n N ∈） 9. (3,1]-- 10. 3π 11. [3,29] 12. 1二. 选择题13. B 14. A 15. C 16. D三. 解答题17.（1）[1,2)A =；（2）(0,)a ∈+∞； 18.（1）()2sin()44f x x ππ=+；（2）()2cos 2g x x π=；增区间：[42,4]k k -（*n N ∈）；对称中心：(21,0)k +（k Z ∈）； 19.（1）6A π=；（2）选（1）（3），得S =1）（2），得1S =）；20.（1）是，12a =，b =；（2）4(,)3-∞-；（3）289；21.（1）2±；（2）2ωπ=；（3）略。

2017徐汇区上海中学高三上学期10月周测试卷

上海中学高三周考（）II. Grammar (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.A great deal of attention (1)_________ (pay) today to the so-called digital divide--the division of the world into the info(information) rich and the info poor at present. And that divide does exist today. My wife and I lectured about this looming danger twenty years ago. What was(2)_______ (visible) then, however, were the new, positive forces that work against the digital divide. There are reasons to be optimistic.There are technological reasons to hope the digital divide will narrow. (3)______ the Internet becomes more and more commercialized, it is in the interest of business to universalize access-after all, the more people online, the more potential customers there are. More and more governments, afraid their countries will be left behind, want to spread Internet access. Within the next decade or two, one to two billion people on the planet (4)_______(net) together. As a result, I now believe the digital divide will narrow (5)______ ______widen in the years ahead. And that is very good news because the Internet(6)______well be the most powerful tool for combating world poverty that we've ever had.Of course, the use of the Internet isn't the only way to defeat poverty. And the Internet is not the only tool we have. But it has enormous potential.(7)_________(take)advantage of this tool, some impoverished countries will have to get over their outdated anti-colonial prejudices with respect to foreign investment. Countries(8)________ still think foreign investment is an invasion of their sovereignty might well study the history of infrastructure(the basic structural foundations of a society) in the United States. When the United States built(9)________industrial infrastructure, it didn't have the capital to do so. And that is(10)_______ America's Second Wave infrastructure- including roads, harbors, highways, ports and so on-were built with foreign investment.【答案】1.is being paid 2.less visible 3.As 4.will be netted 5.rather than6.may7.To take8. that9.its 10.why【分析】(1).分析可知，此处应为被动语态，”today”提示为现在进行时。

上海市上海中学2018届高三上学期周练英语试题一含答

上海中学高三周考II. Grammar and vocabularySection 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.There seems never ____21___ (be) a civilization without toys, but when and how they developedis unknown. They probably came about just to give children something to do.In the ancient world, as is today, most boys ____22_____ (play) with some kinds of toys and most girls with others. In societies ___23_____ social roles are rigidly determined, boys pattern their play after the activitiesof their fathers and girls _____24______ (prepare), even in play, to step into the roles and responsibilitiesof the adult world._____25____ is remarkable about the history of toys is not so much how they changed over the centuriesbut how much they have remained the same. The changes have been mostly _____26_____ craftsmanship, mechanics, and technology.It is the universality (普遍性) of toys with regard to their development inall parts of the world and their persistence to the present ____27____ is amazing. In Egypt, America, China, Japan and among the Arctic (北极的) people, generally the same kinds of toys appeared. Variationsdepended on local customs and ways of life ______28_____ toys imitate their surroundings. Nearly every civilization had dolls, little weapons, toy soldiers, tiny animals and vehicles.Because toys ___29_____ be generally regarded as a kind of art form, they have not been subject to technological leaps that characterize inventions for adult use. The progress from the wheel to the cart to the automobile is a direct line of ways up. The progress from a rattle (拨浪鼓) used by ababy in 3,000 BC to ____30______ used by an infant today, however, is not characterized by inventiveness (独创性). Each rattle is the product of the artistic tastes of the times and subject to the limitations of available materials.Section BDirections: Fill in each blank with a proper word chosen from the box. Each word can be used only once. Note that there is one word more than you need.and for which we are willing if necessary to pay a price. Common addictions involve alcohol cigarettes food drugs gambling etc. This article discusses the concepts which can be ____31___ in coping with addictive behavior._____32______ minor addictions such as watching too much television or lying in bed on weekend mornings are often not even considered addictions because the price paid for engaging in them is not high. On the other hand we tend to use the term “addict” to describe the person who at least in the eyes of others continues to be addicted in a behavior long after it has become ______33____ that the substantial price being paid was not worth the benefit. The individual who has lost career house family and friends because of cocaine (可卡因) use but is _____34___ to consider stopping is an unfortunate example.Negative addictions range from those with very minor negative consequences to those as serious as the cocaine addict just mentioned with much ___35____ in between. Although it is not ____36_____ true that a negative addiction grows stronger over time yet a constant level of addictive behavior (e.g. overspending $ 200 a week ) can lead to an increasing level of negative consequences.You may be ___37___ to learn that addictions can also be considered positive. Positive addictions are those in which the benefits outweigh the price. A common example would be the habit of regular exercise. The price of membership in a gym the time involved and any clothing expense is outweighed by the benefits of better health energy self-confidence and appearance. As with negative addictions positive addictions may not get stronger over time and there is a broad ___38___ of how much benefit is actually obtained.What is common to both positive and negative addictions is the urge to engage in the addictive behavior and the satisfaction that is ____39_____ when the urge is acted upon. The urge is a state of ____40_____ and expectation that is experienced uncomfortably as a desire for the substance or activity. Because we experience reliefwhen the urge is acted upon there is an increased likelihood that we will act on the urge again.III. Reading comprehensionSection ADirections: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.The importance of liking people is the subject of an article in the Harvard Business. Review，which has carried out an experiment to find out who we'd rather work with. Hardly surprisingly, the people we want most as our workmates are both: __41__ at their job and delightful human beings. And the people we want least are both unpleasant and useless.More interestingly, the autors found that, given the choice between working with lovable folls and comptent jerks (性情古怪的人), we irresistibly choose the __42___. Anyway, who likes those who ___43___ or hurt other people? We might insist that competence matters more, but our __44__ shows we stay close to the people we like, sharing information with them.What companies should __45__ do is get people to like each other more. The trick here is apparently to make sure that stuffs come across each other as often as possible during day. They also should be sent on bonding courses and so on to encourage friendliness and __46__ displeasure.__47__, more outdoor-activity weekends and shared coffee machines inspire no confidence at all. The __48__ is that people either like each other or they don’t. You can’t force it. Possibly you can make offices fridendlier by tolerating a lot of chat, but there is a __49__ cost to that. In my experience, the question of lovable fool against competent jerk may not be the right one. The two are interrelated: we tend not to like our workmates when they are completely __50__. I was once quite friendly with a woman whom I later worked with. I found her to be so __51__ bad at her job that I lost respect for her and ended up not really liking her at all. Then is there anything that companies should be doing about it?By far the most effective strategy would be to hire people who are all pretty much the same, given that __52__ is one of the main determinants of whether we like each other. I think this is a pretty good ides, but no one __53__ recommend this anymorewithout offending the diversity lobby group (游说团体). There is only one acceptable view on this subject: teams of similar people are bad because they stop creativity. This may be true, though I have never seen any conclusive proof of it.Not only do we like similar people, we like people who like us. So if companies want to __54__ more liking, they should encourage a culture where we are all nice to each other. The __55__ is that this needs to be done with some skill.41.A. strange B. brilliant C. surprised D. absent-minded42.A. former B. latter C. majority D. minority43.A. hate B. fear C. doubt D. annoy44.A. thought B. behavior C. expression D. appearance45.A. further B. nevertheless C. therefore D. instead46.A. break down B. talk to C. pick out D. hold out47.A. besides B. Furthermore C. However D. Hence48.A. impression B. reality C. practice D. custom49.A. investment B. production C. operation D. productivity50.A. valueless B. disabled C. hopeless D. careless51.A. outstandingly B. inevitably C. hopefully D. forgetfully52.A. appearance B. effectiveness C. distinction D. similarity53.A. need B. dare C. must D. should54.A. create B. discover C. promote D. place55.A. strategy B. standard C. hope D. troubleSection BDirections: Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.AAs a father of four, I’m concerned about how to lead my children to be good young men and women in such a turbulent time. I have studied philosophy, mysticism, and religion my entire life. They provide great lessons in responsibility and growth. However, I also recognize that, at least at this point in their lives, my children are not terribly interested in such subjects.While I was reflecting on this, I was reminded of a a line in a song I had heard recently. It goes: “If you had only onechance to say something, what would it be?”That night, I found my tow oldest kids lounging on the couch watching a TV show that featured violence, cursing and even s ome “adult scenes”. I quietly sat on a chair next to them. I saw my boy straighten up, and my girl pretended to ignore me.I didn’t make any usual comments about the pointlessness of such programs. I didn’t even roll my eyes, although this took some effort. I simply asked: Can you tell me how this will make you a batter person?Without a word, I got up and left the room. About ten minutes later, to my surprise, the children were in their rooms doing their homework and the television was silent. Remarkable.This philosophy can change the way we live our lives. For example, whenever I feel angry and get the urge to lash out, I ask myself: “How does this acting or feeling the way I do right now make me a better person?” I began to realize that rarely did my thoughts or actions result in self-improvement, so I made conscious effort to change my mindset and behavior.We all want to be better fathers, mothers, sons and daughters. Better workers, better leaders, better lovers...... this list goes on. Sometimes succeeding in these roles can be tough. But one question aligns us with all those duties we possess to society and ourselves: “Is this making me a better person?”Whatever I said, it worked. My daughter has begun watching nature programs instead of violent TV shows, and she decided to go to school to become a counselor. My son told me he wants to be a police officer. I’ve since thrown away all those parenting magazines and books I’ve collected over the years because I made more progress witha single questi on than I did with hundreds of pages of “experts” advice.56. When the writer found his kids watching inappropriate TV programs that night, he appeared_______.A .calm B. indifferent C.critical D. anxious57.How can this philosophy change the way we live our lives?A.By calming ourselves down when we are angryB. By raising a question about our current action and feelingC.By helping us realize our need for self-improvementD.By providing us with new mindset and behavior58. Why did the writer throw away his parenting magazines and books?A.Because his kids had grown out of themB.Because they didn’t offer him any help.C.Because that single question was more usefulD.Because the expert advice was too much to follow59.The wrote this passage to_______A. convince teenagers of the downsides to watching TVB.introduce a life philosophy by telling a parenting storyrm the readers of how he helped hid kids set good goalsD.call on other other parents to trust themselves instead of experts.BWhen the people you know run more, you run more. And now there's data to prove it.A new study published today in Nature Communications of the daily-recorded exercise patterns of more than one million runners over five years shows that exercise is socially contagious. Your knowledge of what your friends are doing can and will motivate you to do more. The work marks a watershed moment in the use of detailed fitness tracking data to understand health behavior and causal behavior change."Knowing the running behaviors of your friends as shared on social networks can cause you to run farther, faster, and longer," said MIT Sloan Professor Sinan Aral, an author of "Exercise contagion in a global social network."Aral and colleague Christos Nicolaides, a postdoctoral fellow at MIT Sloan, used a data set that recorded the geographic location, social network ties, and daily running patterns of more than one million people who ran 359 million combined kilometers (223 million miles) and logged those runs digitally in a global social network of runners over five years. The data contain the daily distance, duration, pace, and calories burned by the runners, recorded by digital fitness tracking devices. The results, said Aral, revealed "strong contagion effects.""On the same day, on average, an additional kilometer run by friends can inspire someone to run an additional three-tenths of a kilometer and an additional ten minutes run by friends can inspire someone to run three minutes longer," the authors wrote.Historically, in the context of exercise, a debate exists about whether we make upward comparisons to those performing better than ourselves or downward comparisonsto those performing worse than ourselves. Comparisons to those ahead of us may motivate our own self-improvement, while comparisons to those behind us may create "competitive behavior to protect one's superiority." According to Aral, there is evidence for both trajectories in the study, but comparisons to those better than us are more powerful.Gender matters too. The contagion is most pronounced among men, with men influencing other men to run farther and faster. In this regard, men may be more competitive and, specifically, more competitive with each other. Influence among same sex pairs is strong while influence among mixed sex pairs is weaker. Both men and women influence men. However, only women influence women who have reported, in earlier studies, being more influenced by self-regulation and individual planning than by their peers.60. The word “contagious” in paragraph 2 most probably means______A.infectiousmunicativeC. motivatedD.available61.Jack and Tom both are friends and like running. They post their runs every day on social media. According to the research, if one day Jack ran for an hour and a half and Tom an hour, them how long would Tom most probably run the next day?A.30 minutesB.63minutesC.69minutesD.90 minutes62.Which runner tends to get the most powerful influence?A.A man making upward comparisons to his female friends.B.A man making upward comparisons to his male friends.C.A competitive women making comparisons to her peersD.A self-regulated woman who prefer individual planningCThe study of psychology is facing a crisis. The Research Excellence Framework (the Ref) has led to a research culture which is holding back attempts to stabilize psychology in particular, and science in general. The Ref encourages universities to push for groundbreaking innovative, and exciting research in the form of 4* papers, but it does not reward the efforts of those who replicate studies.The point of replicating a study is to test whether a statistically significant result will appear again if the experiments is repeated. Of course, a similar result may not appear – casting into questions the validity of the results from the firstexperiment.Last year, the Open Science Collaboration attempted to replicate 100 studies from highly ranked psychological journalists. While 97% of the original studies had a statistically significant result, just 36% of the replications had the same outcome. Equally worrying: when an effect did appear, it was often much smaller than previously thought.Recent data calls into question some widely influential findings in psychological science. These problems are not confined to psychology however – many findings published in scientific literature may actually be false.Science is supposed to be self-correcting and reproducibility is a cornerstone o f the scientific method. Yet, we simply aren’t invested in replicating findings. We all want to be good researchers and understand more about how the world works. So why are we so reluctant to check our conclusions are valid?Because no incentive is provided by the system we carry out our research in. In the UK, the Ref ranks the published works of researchers according to their originality (how innovative is the research?), significance (does it have practical or commercial importance?), and rigour (is the research technically right?). Outputs are then awarded one to four stars. 4* papers are considered world-leading. The cumulative total of 3* and 4* papers determines research funding allocation and has a knock-on effect on institutional position in league tables (排名表)and therefore attractiveness to students. Obviously, the more publications the better.Worrying, many academics admit to engaging in at least one questionable research practice in order to achieve publication. Examples of this include: coming up with a theory after data is collected, stopping collecting data when an effect appears in case it disappears later, or only reporting the significant effects from collected data. Others simply fabricate data – Dutch psychologist Diederik Stapel shockingly falsified data from more than 50 studies.The Ref completely harms our efforts to produce a reliable body of knowledge. Why? The focus on originality – publications exploring new areas of research using new paradigms, and avoiding testing well-established theories –is the exact opposite of what science needs to be doing to solve the troubling replication crisis. According to Ref standards, replicating an already published piece of work is simply uninteresting.With the next Ref submission just four years away, many researchers areeffectively faced with a choice: be a good scientist, or be a successful academic who gets funding and a promotion.63. What crisis the study of psychology facing?A. The Ref has led to a revolution in not only psychology but also science.B. The universities are encouraged to generate more groundbreaking research.C. The Ref tends to set up a different standard for replications of studies.D. The Ref’s indifference to replications of studies has led to worrying eff ects.64. The Ref’s focus on originality has brought about .A. a reliable body of knowledgeB. publications exploring new areasC. tests of well-established theoriesD. uninteresting replications of studies65. We can infer from the passage that the Ref .A. is a system for assessing the quality of research in UK universitiesB. provides UK researchers with funding and job opportunitiesC. recognizes researchers’ work and adds to their attractiveness to studentsD. is planning to change its standard before the next Ref submission66. What does the writer mean by saying “be a good scientist”?A. Contribute to the solution to the replication crisis.B. Reform the standards that have been set up by the Ref.C. Give up possible funding and promotion given by universities.D. Avoid using false research practices to test old theories.Section CDirections: Read the following passage. Fill in each blank with a proper sentence given in the box. Each sentence can be used only once. Note that there are two more sentences than you need.A.The parents’ refusal to admit these changes when the child knows them to be truemakes impossible.B.Most children have such a high ideal of their parents, unless the parents themselveshave been unsatisfactory, that it can hardly hope to stand up to a realistic evaluation.C.They may even make some unpleasant remark’s about the friends’ parents, and thinkof them as disloyalty.D.Today we tend to go to the other extreme, but on the whole this is a healthier attitudeboth for the child and the parent.E.What the child cannot forgive is the parent’s refusal to admit these charges if thechild knows them to be true.67F.They may even accuse them of disloyalty, or make some unpleasant remarks about thefriends’ par ents.Parents are often upset when their children praise the homes of their friends and regard it as a slur (诋毁) on their own cooking, or cleaning, or furniture, and often are foolish enough to let the teenagers see that they are annoyed. 67 Sucha loss of dignity and a kind of childish behavior on the part of the adults deeplyshocks the teenager, and makes them decide that in future they will not talk to their parents about the place or people they visit. Before very long the parents will be complaining that the child is so secretive and never tells them anything, but they seldom realize that they have brought this on themselves.Disillusionment(醒悟) with the parents, however good and adequate they may be both as parents and as individuals, is to some degree inevitable.68 Parents would be greatly surprised and deeply touched if they realized howmuch belief their children usually have in their character and correctness, and how much this faith means to a child. If parents were prepared for this teen-aged reaction, and realized that it was a sign that the child was growing up and developing valuable powers of observation and independent judgment, they would not be so hurt, and therefore would not drive the child into opposition by offending and resisting it.The teenagers, with his passion for sincerity, always respects a parent who admits that he is wrong, or ignorant, or even that he has been unfair or unjust. 69 Victorian parents believed that they kept their dignity by retreating（伪装） behind an unreasoning authoritarian attitude; in fact they did nothing of the kind, but children were then too frightened to let them know how they really felt. 70 It is always wiser and safer to face up to reality, however painful it may be at the moment.IV. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.71. 新任的总统因军事危机而忧心忡忡。

上海市延安中学2017-2018学年高三上学期10月月考数学试题

○…………外○…………内绝密★启用前上海市延安中学2017-2018学年高三上学期10月月考数学试题试卷副标题注意事项：1．答题前填写好自己的姓名、班级、考号等信息 2．请将答案正确填写在答题卡上第I 卷（选择题)请点击修改第I 卷的文字说明一、单选题1．已知,a b 都是实数，那么“22a b >”是“a b >”的（） A ．充分不必要条件 B ．必要不充分条件 C ．充要条件 D ．既不充分也不必要条件2．若数列{}n a 的通项公式1,1,211,3,3n nn n a n n N *⎧=⎪⎪+=⎨⎪≥∈⎪⎩前n 项和为n S ，则下列结论中正确的是（） A ．lim n n a →∞不存在 B ．8lim 9n n S →∞=C ．lim 0n n a →∞=或1lim 3n n a →∞=D ．1lim 18n n S →∞=3．有一塔形几何体由若干个正方体构成，构成方式如图所示，上层正方体下底面的四个顶点是下层正方体上底面各边的中点．已知最底层正方体的棱长为2，且该塔形的表面积(含最底层正方体的底面面积)超过39，则该塔形中正方体的个数至少是○…………外○…………内4．对任意一个复数z ，定义集合{}21,n z M z n N αα-==∈，设12ω=-+（i 为虚数单位），则集合M ω与2M ω的关系是（） A ．{}21,M M ωωω=I B ．2M M ωω⊆ C ．2M M ωω= D ．M ω和2M ω没有关系第II 卷（非选择题)请点击修改第II 卷的文字说明二、填空题5．已知集合{}{}1,3,,3,4A m B ==，且B A ⊆，则实数m 的值是__________. 6．函数()f x =的定义域是_________. 7．如果圆锥的底面积为π，母线长为2，那么该圆锥的高为___________. 8．在()1521x +的二项展开式中，含5x 的项是二项展开式的第__________项.9．已知复数03z i =+（i 为虚数单位），复数z 满足003z z z z ⋅=+，则z =__________. 10．等差数列{a n }的前10项和为30，则14710a a a a +++=________11．已知双曲线与椭圆221166x y +=有相同的焦点，且双曲线的渐进线方程为12y x =±，则此双曲线方程为_________12．某班从4位男生和3位女生志愿者选出4人参加校运会的点名签到工作，则选出的志愿者中既有男生又有女生的概率的是__________.（结果用最简分数表示） 13．如图，将四个边长为1的小正方形拼成一个大正方形，,A B 是原来小正方形的其中两个顶点，()1,2,7i P i =L 是小正方形的其余顶点，在所有()1,2,7i AB AP i ⋅=u u u r u u u rL 中，不同的数值有__________个.……○…………订________班级：___________考……○…………订14．函数()()()1,01,0x x x f x x x x ⎧-≥⎪=⎨-+<⎪⎩，()()21g x f x =-+，若()3g a =，则()4g a -=__________.15．已知实数数列{}n a 满足()2123n n n a a a n N *+=-+∈，n S 是数列{}n a 的前n 项和.若()32k a k N *=∈，则2017k S +=__________. 16．已知a b vv、是平面内两个互相垂直的单位向量，且此平面内另一向量c v在满足()()340a c b c +-=v v v v，均能使c b k v v -≤成立，则k 的最小值是_________.三、解答题17．如图，在直三棱柱111ABC A B C -中，12AA AB BC ===，且AB BC ⊥.求：（1）四棱锥11C ABB A -的体积；（2）AC 与平面11A B C 所成角的大小.18．设函数()4sin ,0,3f x x x x π⎡⎤=+∈⎢⎥⎣⎦.（1）求函数()f x 的单调递减区间；（2）ABC ∆中，1,2AB AC ==,且()f A =ABC ∆为直角三角形. 19．某公司进行共享单车的投放与损耗统计，到去年2016年底单车的市场保有量（已投入市场且能正常使用的单车数量）为10000辆，预计今后每年新增单车1000辆，随着单车的频繁使用，估计每年将有200辆车的损耗，并且今后若干年内，年平均损耗在上一年损耗基础上增加10％.（1）预计2019年底单车的市场保有量是多少？（2）到哪一年底，市场的单车保有量达到最多？该年的单车保有量是多少辆（最后结…………线……………………线…………20．如图，过抛物线24y x=焦点F的直线与抛物线交于,A B（其中A点在x轴的上方）两点.（1）若线段AF的长为3，求O到直线AB的距离；（2）证明：OAB∆为钝角三角形；（3）已知AF FBλ=uu u r uu r且[]2,3λ∈，求三角形OAB的面积S的取值范围.21．A是定义在[]1,2上且满足如下条件的函数()xϕ组成的集合：①对任意的[]1,2x∈，都有()()1,2xϕ∈；②存在常数()01L L<<，使得对任意的[]12,1,2x x∈，都有()()1212x x L x xϕϕ-≤-.（1）设()[]211,1,25x x xϕ=+∈，问()xϕ是否属于A？说明你的判断理由；（2）若()x Aϕ∈，如果存在()1,2x∈，使得()00x xϕ=，证明这样的x是唯一的；（3）设,k b为正实数，是否存在函数()[]1,2x xϕ=∈，使()x Aϕ∈？作出你的判断，并说明理由.参考答案1．D 【解析】【分析】举反例说明既不充分也不必要. 【详解】当2,1a b =-=时，满足22a b >，但a b >不成立；所以不充分；当1,2a b ==-时，满足a b >，但22a b >不成立；所以不必要；故选：D 【点睛】本题考查充要关系的判定，考查基本分析判断能力，属基础题. 2．B 【解析】【分析】先利用等比数列求和公式求和，再求极限得结果. 【详解】1lim lim03n nn n a →∞→∞==3234211(1)11111551133+++(1)1233336618313n n n n S ---=++=+=+--L因此2511518lim lim[(1)]61836189n n n n S -→∞→∞=+-=+=故选：B 【点睛】本题考查数列解析以及等比数列求和公式，考查基本分析求解能力，属中档题. 3．C 【解析】【分析】根据相邻正方体的关系得出个正方体的棱长为等比数列，求出塔形表面积n S 的通项公式，令39n S >，即可得出n 的范围．【详解】设从最底层开始的第n 层的正方体棱长为n a ，则{}n a 是以2为首项，以2为公比的等比数列. ∴{}2na 是以4为首项，以12为公比的等比数列 ∴塔形的表面积为222222222123123114(1)32264444444248401212n n n n n S a a a a a a a a a -=+++⋅⋅⋅=+++⋅⋅⋅+=⨯+=--. 令3240392n ->，解得5n >. ∴塔形正方体最少为6个. 故选C. 【点睛】此题考查了立体图形的表面积问题以及等比数列求和公式的应用．解决本题的关键是得到上下正方体的棱长之间的关系，从而即可得出依次排列的正方体的一个面的面积，这里还要注意把最下面的正方体看做是6个面之外，上面的正方体都是露出了4个面． 4．C 【解析】【分析】根据ω的性质化简集合M ω与2M ω，再进行判定选择. 【详解】因为12ω=-，所以231,12ωω=-={}{}212,,1,n M n N ωααωωω-==∈=，{}{}2422,,1,n M n N ωααωωω-==∈=所以2M M ωω=，故选：C 【点睛】本题考查ω的性质以及集合相等的判定，考查基本分析化简判断能力，属基础题. 5．4 【解析】【分析】根据集合包含关系确定方程，解得结果. 【详解】因为B A ⊆，所以{3,4}{1,3,}4m m ⊆∴= 故答案为：4 【点睛】本题考查根据集合包含关系求参数，考查基本分析求解能力，属基础题. 6．()[),02,-∞+∞U 【解析】【分析】由210x -≥，化为20x x-≥,解分式不等式可得结果. 【详解】要使函数()f x =有意义，则210x -≥，即20x x-≥,解得0x <或2x ≥,即函数()f x =的定义域是()[),02,-∞+∞U ，故答案为()[),02,-∞+∞U . 【点睛】本题主要考查抽象函数的定义域、不等式的解法，属于中档题.定义域的三种类型及求法：(1)已知函数的解析式，则构造使解析式有意义的不等式(组)求解；(2) 对实际问题：由实际意义及使解析式有意义构成的不等式(组)求解；(3) 若已知函数()f x 的定义域为[],a b ，则函数()()f g x 的定义域由不等式()a g x b ≤≤求出.7【解析】【分析】由底面积求出底面半径，利用勾股定理可得结果. 【详解】设圆锥底面半径为r , 因为圆锥的底面积为π，所以21,r r ππ=⇒=又因为母线长为2=【点睛】本题主要考查圆锥的性质，意在考查对基础知识的掌握情况，考查了空间想象能力，属于基础题. 8．11 【解析】【分析】根据二项展开式通项公式即可确定结果. 【详解】15115(2)15510rr r T C x r r -+=∴-=∴=Q ,即含5x 的项是二项展开式的第11项.故答案为：11 【点睛】本题考查二项展开式通项公式，考查基本分析求解能力，属基础题. 9【解析】【分析】变形003z z z z ⋅=+可得0033z iz z i+==-，分子分母同乘以i ，可得13i z =-，利用复数模的公式可得结果.Q 复数03z i =+，复数z 满足003z z z z ⋅=+，()020333i iz i z z i i ++∴===-13131ii -+==--，z ==.【点睛】复数是高考中的必考知识，主要考查复数的概念及复数的运算．要注意对实部、虚部的理解，掌握纯虚数、共轭复数、复数的模这些重要概念，复数的运算主要考查除法运算，通过分母实数化转化为复数的乘法，运算时特别要注意多项式相乘后的化简，防止简单问题出错，造成不必要的失分. 10．12 【解析】【分析】利用等差数列的前n 项和公式即可得到a 1+a 10=6．由等差数列的性质可得a 1+a 10=a 4+a 7，进而可得答案．【详解】∵等差数列{a n }的前10项和为30，∴()11010302a a +=，解得a 1+a 10=6．由等差数列的性质可得a 1+a 10=a 4+a 7， ∴a 1+a 4+a 7+a 10=2（a 1+a 10）=2×6=12． ∴a 1+a 4+a 7+a 10=12．故答案为12．【点睛】熟练掌握等差数列的前n 项和公式、等差数列的性质是解题的关键．11．22182x y -=【分析】根据双曲线的渐进线方程为12y x =±，设双曲线222214x y b b-=，计算椭圆焦点为()，根据双曲线焦点公式得到答案. 【详解】221166x y +=的焦点为：()双曲线的渐进线方程为12y x =±，则设双曲线方程为：222214x y b b-=，焦点为()故2224102b b b +=∴= ，双曲线方程为22182x y -=故答案为：22182x y -=【点睛】本题考查了求双曲线方程，根据渐近线设双曲线为222214x y b b-=是解题的关键.12．3435【解析】【分析】“4位男生和3位女生志愿者选出4人参加校运会的点名签到工作，若这4人中必须既有男生又有女生”的对立事件是“只有男生”，利用组合知识求出总事件数，根据古典概型概率公式以及对立事件的概率公式可得结果. 【详解】“4位男生和3位女生志愿者选出4人参加校运会的点名签到工作，若这4人中必须既有男生又有女生”的对立事件是“只有男生”，事件“只有男生”只包含一个基本事件，而总的基本事件数是4735C =，故事件“只有男生”的概率是135，事件“4位男生和3位女生志愿者选出4人参加校运会的点名签到工作，若这4人中必须既有男生又有女生”的概率是13413535-=，故答案为3435. 【点睛】本题主要考查对立事件的概率公式以及古典古典概型概率公式的应用，属于基础题. 在求解有关古典概型概率的问题时，首先求出样本空间中基本事件的总数n ，其次求出概率事件中含有多少个基本事件m ，然后根据公式mP n=求得概率. 13．5 【解析】【分析】建立直角坐标系，根据向量数量积坐标计算，再统计不同结果个数. 【详解】建立如图所示直角坐标系，则123(2,1)(2,0)4,(2,1)(0,1)1,(2,1)(1,1)3,AB AP AB AP AB AP ⋅=⋅=⋅=⋅=⋅=⋅=u u u r u u u r u u u r u u u u r u u u r u u u r 4567(2,1)(1,0)2,(2,1)(0,2)2,(2,1)(1,2)4,(2,1)(2,2)6,AB AP AB AP AB AP AB AP ⋅=⋅=⋅=⋅=⋅=⋅=⋅=⋅=u u u r u u u u r u u u r u u u r u u u r u u u u r u u u r u u u u r所以有5个不同的数值，故答案为：5 【点睛】本题考查向量数量积坐标计算，考查基本分析求解能力，属基础题. 14．1- 【解析】【分析】先根据分段函数求a 的值，再代入求()2f a -的值，即得结果. 【详解】因为()3g a =，所以()()()21322g a f a f a =-+=∴-=因此20(2)(3)2a a a -≥⎧⎨--=⎩或20(2)(1)2a a a -<⎧⎨---=⎩解得4a =或a ∈∅从而()()()2(2)24211f a f g a f a -=-=-∴-=-+=- 故答案为：1- 【点睛】本题考查求分段函数值，考查基本分析求解能力，属基础题. 15．32【解析】【分析】根据递推关系求各项，再求和. 【详解】2211323232()02n n n k k k k k a a a a a a a a ++=-+∴=-+=--=Q当1n k ≥+时，0n a =若2k ≥，则由2123n n n a a a +=-+得2211111323232k k k k k k a a a a a a -----=-+∴-+=∴∈∅，因此=1k ，从而20173,133+02220,2n k n a S n +⎧=⎪=∴==⎨⎪≥⎩，故答案为：32【点睛】本题考查根据递推关系求通项，考查基本分析求解能力，属中档题. 16．52+ 【解析】根据题意，()()()1,0,0,1,,a b c x y v v v===，利用()()340a c b c +⋅-=r r r r ，求得,x y 的关系，利用圆的几何性质，再求出c b -vv 的最大值，从而求出k 的最小值.【详解】因为a b v v 、是平面内两个互相垂直的单位向量，所以可设 ()()()1,0,0,1,,a b c x y v v v===， ()33,a c x y ∴+=+r r， ()4,4b c x y -=--r r，又()()340a c b c +⋅-=r r r r，()()340x x y y ∴-++-=，即()22325224x y ⎛⎫++-= ⎪⎝⎭，它表示的圆心在3,22M ⎛⎫-⎪⎝⎭，半径为52的圆，c b -vv 表示圆上的点到(0,1)B 的距离，圆心M 到点(0,1)B 的距离为d =c b ∴-r r的最大值为52=，要使c b k -≤r r 恒成立，52k +≥即k 的最小值是52+，故答案为52. 【点睛】本题主要考查向量模的几何意义、轨迹方程的应用以及圆的几何意义，考查了转化思想的应用，属于难题. 转化是数学解题的灵魂，合理的转化不仅仅使问题得到了解决，还可以使解决问题的难度大大降低，本题将不等式恒成立问题转化为圆上动点到定点距离的最值问题是17．（1）83；（2）6π【解析】【分析】（1）先证线面垂直得高，再根据锥体体积公式求结果；（2）先补成正方体，再根据线面垂直确定线面角，最后解三角形得结果. 【详解】（1）因为直三棱柱111ABC A B C -，所以1AA ⊥平面ABC ∴1AA BC ⊥1,AB BC AB AA A BC ⊥=∴⊥Q I 平面11ABB A因此四棱锥11C ABB A -的体积为11118=222333ABB A BC S ⋅⋅⨯⨯⨯=矩形；（2）先补成正方体1111ABCD A B C D -,则AC 与平面11A B C 所成角为AC 与平面11A B CD 所成角，因为1AD ⊥平面11A B CD ,设11A O AD D =I ,则ACO ∠为AC 与平面11A B C 所成角, 因为1sin 26AO ACO ACO AC π∠==∴∠=,因此AC 与平面11A B C 所成角为6π.【点睛】本题考查锥体体积公式、线面角以及线面垂直判定定理，考查基本分析求解能力，属中档题.18．（1）766ππ⎡⎤⎢⎥⎣⎦，（2）详见解析【解析】【分析】（1）先根据辅助角公式化简函数，再根据正弦函数性质求单调区间；（2）先根据()f A A ，再根据余弦定理求BC ，最后根据勾股定理证结论. 【详解】（1）()sin 2sin(),3f x x x x π==+由322,()232k x k k Z πππππ+≤+≤+∈得722,()66k x k k Z ππππ+≤≤+∈ 因为40,3x π⎡⎤∈⎢⎥⎣⎦，所以7,66x ππ⎡⎤∈⎢⎥⎣⎦，即单调递减区间为766ππ⎡⎤⎢⎥⎣⎦，；（2）因为()f A =2sin()sin()33A A ππ+=+因为(0,)A π∈，所以2333A A πππ+=∴= 222211221232BC AC AB ∴=+-⨯⨯⨯==- 因此ABC ∆为直角三角形. 【点睛】本题考查辅助角公式、正弦函数性质以及余弦定理，考查基本分析求解能力，属基础题. 19．（1）12338（2）2033年底；最多18891辆【解析】【分析】（1）根据等差数列与等比数列进行列式计算；（2）根据题意先列市场的单车保有量函数关系式，再根据数列单调性确定单车保有量最大值. 【详解】（1）2019年底单车的市场保有量是210000+10003200200 1.1200 1.112338⨯--⨯-⨯=（2）到2016n +年底，市场的单车保有量为2110000+1000200200 1.1200 1.1200 1.1n n a n -=⨯--⨯-⨯--⨯L1 1.110000+100020010200+10002000 1.11 1.1n n n n -=-⨯=-⨯-11000200 1.1200(5 1.1)n n n n a a +-=-⨯=-Q1116,;17,;n n n n n a a n a a ++∴≤>≥<即17,n n a =取最大值18891，此时为2033年底；即到2033年底，市场的单车保有量达到最多，为18891辆. 【点睛】本题考查数列单调性以及等比数列再实际问题中的应用，考查综合分析求解能力，属中档题.20．（1（2）详见解析；（3）⎣⎦ 【解析】【分析】（1）先根据抛物线定义求出A 点坐标，再根据点斜式求直线AB 的方程，最后根据点到直线距离公式求结果；（2）先设直线方程，与抛物线方程联立，结合韦达定理化简OA OB ⋅u u u r u u u r ,根据OA OB ⋅u u u r u u u r为负证明结果；（3）先设直线方程，与抛物线方程联立，结合韦达定理以及面积公式表示三角形OAB 的面积S ，再根据对勾函数单调性求值域. 【详解】（1）设111(,),(0)A x y y >，因为3AF =，所以111132x x y +=∴=∴=因此:(1),021AB y x y =----从而O 到直线AB3=；（2）设直线AB 的方程为1x my =+，11122(,),(0)(,),A x y y B x y ，>由214x my y x=+⎧⎨=⎩得211124404,4y my y y m y y --=∴+==- 从而22121212123016y y OA OBx x y y y y u u u r u u u r ?+=+=-<，因此OAB ∆为钝角三角形；（3）因为AF FB λ=uu u r uu r，所以12y y λ=-，由（2）得124y y =-，所以2224|y y λ=，12211||1(1)||22S y y y λ=-⨯=+==因为[]2,3λ∈，而1y tt =+在上单调递增，所以S ∈= 【点睛】本题考查抛物线定义、点到直线距离公式、抛物线中三角形面积以及直线与抛物线位置关系，考查综合分析求解与论证能力，属中档题.21．（1）是，详见解析（2）详见解析（3）详见解析【解析】【分析】（1）根据定义逐一验证，即求函数在[]1,2上值域，再判断是否为()1,2子集；根据不等式寻找满足条件的常数()01L L <<；（2）利用反证法，假设存在两个，根据条件得到1L ≥，即假设不成立，原命题成立；（3）先根据条件①解不等式确定13k <<，再根据条件②利用恒成立转化为对应函数最值，再解不等式确定12k <<.b 的条件由k 确定. 【详解】（1）因为()2115x x ϕ=+在[]1,2上单调递增，所以()69[,](1,2)55x ϕ∈⊆；()()121212121455x x x x x x x x ϕϕ-=-+≤-Q ，所以存在常数45，使得对任意的[]12,1,2x x ∈，都有()()121245x x x x ϕϕ-≤-，综上()x ϕ属于A ；（2）设存在()12121,,2,x x x x ≠∈，满足()()1122,x x x x ϕϕ==，因为()x A ϕ∈，所以存在常数()01L L <<，使得()()1212x x L x x ϕϕ-≤-，即12121201x x L x x x x L -≤-->∴≥Q ，与01L <<矛盾，因此满足条件的0x 是唯一的；（3）假设存在，则因为()x A ϕ∈，且()x ϕ=[]1,2上单调递增，所以12<121210222b bb k k b b ∴+<<+∴>+>+∴<<，2411243k b k k k k ∴-<<-∴->-∴<，因此13k <<；存在常数()01L L <<，使得对任意的[]12,1,2x x ∈，12L x x ≤-，12L x x ≤-，所以k ≤<，≥>=因此2416022k k k k <+-<∴--<<从而12k <<即当12241,0k k b k b <<-<<->，时存在函数()[]1,2x x ϕ=∈，使()x A ϕ∈；否则不存在.【点睛】本题考查函数新定义、反证证以及恒成立问题，考查综合分析求解与论证能力，属难题.。

2017学年第一学期南洋模范中学高三年级完整版

2017学年第一学期南洋模中学高三年级期中试卷II. Grammar and V ocabularySection A （10%）Over the last few hours, hundreds of delegates from all over the world have been arriving for the J12 meeting of leading industrialized nations ,which this year is taking place in the quiet Canadian mountain resort of Kanalgirie.The Canadian President (21)____________(deliver)the operating address (22)__________the conference opens tomorrow morning. The Canadian police, who have been preparing for the event (23)____________late last year,are taking huge safety measures to avoid the violence which (24)_________(mark) last year’s summit in Berlin. They have thrown 18km security line around the area,and last night they were not allowing (25)____________to pass through—including journalists who actually have full access to the delegates. From tomorrow, police will also be blocking all mobile phone signals---to prevent bombs (26)_____________(set)off by remote control ,a police spokesmen said last night.“The politicians here seem to be isolating (27)_________from the free press,”said one journalist .”There’s no doubt that governments are becoming more and more security conscious and less and less concerned(28)____________personal freedom. It’s getting harder and harder for us to gain access to the people who,(29)________the next few days, will be making decisions which will affect all our lives…and that’s something (30)___________should concern us all.bestselling novel as it is to the science that supports the book.It’s hard to find any other science-fiction film that has stuck so___31_______to the practical challenges of living and surviving in space since Ron Howard’s Apollo 13.The film manages to create a cinematic experience, and a(an)____32________plot based on the idea that man can survive on Mars as long as he’s done the math.It sounds dry, but Ridley Scott pulls it off with magnificence.During a month-long mission on Mars ,the five-man crew of Ares 3___33_____a storm they didn’t plan for ,and the team is called home. The craft’s commander in chief Mellisa Lewis orders a(n)___34______withdrawal. In the process, Mark Watney , one of the five crew members gets injured by a flying communication antenna（天线）.Lost in the storm his fellow crewmen leave him behind for dead.NASA chief Teddy Sanders announces Mark Watney’s death to the media. His fellow crewmen and guilt-ridden commander ____35______for his loss; the only problem is that Watney is very much alive. But the question is :for how long?Based on the food and water the crew left behind ,Watney __36______he has supplies for 31 days. Due to the storm, he has no way to make contact with NASA ground control.But the movie, which is a celebration of human____37________,makes this justanother challenge for Watney,a clever and skillful scientist specializing in botany.The _38_______loner simply decides to survive and works out a plan to grow food and water on a bare, dusty planet where nothing grows.Meanwhile he is working on establishing ___39__________methods of communication with Earth. When he finally reaches NASA, and a(n)___40_____plan is worked out. But he has to survive a whole year before help arrives.On the red planet, things can go wrong at any moment and they do.III. Reading ComprehensionShould we dismiss an entire good idea just because some people abuse it ? You know how this one goes: a story is published someone with 17 children who’s living on welfare, and “getting ”38000 a year, and the piece goes on to discuss the total welfare bill, before ____41___that ,because the system is being “abused”,___42___ should be abolished.（废除）The thing is ,if we talked about abolishing everything that was abused ,then where would we stop? We would have abolished the Houses of Parliament during the political scandals. Likewise schools, given the amount of abuse that has happened there, both state and _____43____.We’d be talking about abolishing marriage, because women are abused ,in____44_______. Likewise parenthood, given the numbers of parents who abuse their_____45______.The simple truth is, people will abuse any_____46____. There’s a pro portion of humanity that will always play the system, whatever it is. That’s what humans do. We’re just monkeys,_____47_____ a stick to poke in a hole to get ants. Or monkeys who will_____48____ someone else’s stick, and ants.The question is: is the fundamental concept that is being ____49____good? Right? Moral?You don’t just ___50______when people abuse a system. Instead, you make the system better. Anyone wanting to ____51__a perfectly decent idea—indeed, a necessary, moral and transformative one—because someone else took___52____ of it is basically saying,“I am too ____53____to do all the admin to improve this. I’m busy with paperwork. I am staying away from management change in ___54_____of SETTING FIRE TO EVERYTHING AND RUNNING AWAY.”We must never___55____anyone who confuses “an idea” with “how that idea was predictably abused by a tiny percentage of the population.”41.A.deciding B.conducting C.approving D.concluding42.A.welfare anization C.bill D.interst43.A.national B.private C.regional D.global44.A.issues B.parterships C.relationships D.conditions45.A.students B.partners C.children D.lovers46.A.fact B.system C.power D.relation47.A.looking for B.looking after C.looking into D.Looking at48.A.move B.steal C.sweep D.adopt49.A.updated B.improved C.employed D.abused50.A.pick out B.take in C.get rid of D.give in51.A.give up B.revenge on C.give rise to D.participate ine B.benefit C.operation D.advantage53.A.catious B.moral zy D.conscious54.A.favour B.exchange C.opposition D.judgement55.A.hear from B.listen to C.see through D.look toSection(B)(A)There was a time,not that long ago,when women were considered smart if they played dumb(愚蠢的)to get a man ,and women who went to college were more interested in getting a “Mr.Degree”than a bachelor’s(学士)。

上海市延安中学2017-2018学年高三上学期周测(十)英语试题-十一选十 Word版含答案

2017-2018学年上海市延安中学英语试卷Section B (10)Directions: Complete the sentences with the words or phrases in the box. Each word can only be used once. There is one extra which you do not need.(F=BC，G=ABC，H=AB，I=AD，J=BD，K=ABD)In 2003, the Gates Foundation launched a project called Grand Challenges Global Health. What I like about it is the way the Gates Foundation approached solving thi s problem. They didn’t say, "We, the rich Western foundation, will now ___41___ and then ___42___instructions and write some checks. They said, “Let’s cooperate horizontally on defining both the problem and the solutions ---- let's create value that way ---- and then [the foundation] will ___43___ our money in the solutions we both define.” So the Gates Foundation placed ads on the Web and in more ___44____ channels across both the developed and the developing worlds, asking scientists to respond to one big question: What .are the biggest problems that, if science attended to them and solved them, could most dramatically change the fate of the several billion people trapped in the evil cycle of high ___45___ death rate, low life expectancy, and disease? The foundation got about eight thousand pages of ideas from hundreds of scientists from around the world, including Nobel Prize winners. It then collected through them and cut them down to a list of fourteen Grand Challenge ---- challenge where a technological innovation could remove a ___46___ barrier to the solving of an important health problem in the developing world.In the fall of 2003, these fourteen Grand Challenges worldwide. They include the following: How to create effective single-dose (单剂量) vaccines (疫苗) that can be used soon after birth, how to prepare vaccines that do not require refrigeration, how to develop needle-free deliver systems for vaccines, how to better understand which immunological(免疫系统的) responses ___47___ protective immunity, how to better control insects that carry agents of disease, how to develop a ___48___ or chemical strategy to disable an infectious insect population, how to create a full range of the most favorable bioavailable nutrients in a single staple plant species, and how tocreate immunological methods that can ___49___ chronic (慢性的) infections. Within a year, the foundation received sixteen proposals for ways to meet these ___50___ from scientists in seventy-five countries, and the foundation is now in the process of funding the best proposals with $250 million in cash.Keys: IGCKH DBEFA。

上海市南模中学2017-2018学年上学期高三周考试题-文档资料

南模中学高三周练卷2019.9一. 填空题1. 函数()y f x =的图像与x 轴有三个不同的交点(,0)m 、(,0)n 、(,0)p ，若函数()y f x = 的图像关于直线2x =对称，则m n p ++=2. 函数()y f x =的图像上所有点的纵坐标不变，横坐标变为原来的15得到函数的图像3. 函数()1x af x x a -=--的图像的对称中心是(4,1)，则a =4.函数3,0()0x x f x x ⎧≥⎪=<与函数1,()0,x d x x ⎧=⎨⎩为有理数为无理数图像的交点是5. 已知函数()y x f x =-的图像过点(1,3)，则函数(1)y f x =-的图像必过点6. 已知()f x 是定义在R 上的偶函数，且1(2)()f x f x +=-，若当23x ≤≤时，()f x x =，则(5.5)f =7. 已知函数2(1999)443f x x x +=++，x ∈R ，则()f x 的最小值为8. 已知定义在R 上的函数()f x 满足：① ()(2)0f x f x +-=；② ()(2)0f x f x ---=；③ 在[1,1]-上的表达式为[1,0]()1,(0,1]x f x x x ∈-=-∈⎪⎩；则()f x 与122,0()log ,0xx g x x x ⎧≤⎪=⎨>⎪⎩的图像在区间[3,3]-上的交点个数为9. 已知函数1|1|,20()2(2),0x x f x f x x -+-≤≤⎧=⎨->⎩，若方程()f x x a -=在区间[2,4]-内有3个不等实根，则实数a 的取值范围是10. 已知()f x 是定义在[4,4]-上的奇函数，1()(2)3g x f x =-+，当[2,0)(0,2]x ∈-时， ||1()21x g x =-，(0)0g =，则方程12()log (1)g x x =+的解的个数为11. 已知函数()||f x x x a =-，若对任意1x 、2[2,3]x ∈，恒有1212()()()22x x f x f x f ++>，则实数a 的取值范围为 12. 设函数()||||a f x x x a =+-，当a 在实数范围内变化时，在圆221x y +=内，且不在任一()a f x 的图像上的点的全体组成的图形的面积为二. 选择题13. 对于任意函数()y f x =，在同一坐标线中，函数(2)y f x =-与(2)y f x =-的图像关于（）对称A. x 轴B. y 轴C. 直线2y =D. 直线2x =14. 已知定义域为R 的函数()f x 在(8,)+∞上为减函数，且函数(8)y f x =+为偶函数，则（）A. (6)(7)f f >B. (6)(9)f f >C. (7)(9)f f >D. (7)(10)f f >15. 设函数31,1()2,1x x x f x x -<⎧⎪=⎨≥⎪⎩，则满足()(())2f a f f a =的a 的取值范围是（）A. 2[,1]3B. [0,1]C. 2[,)3+∞ D. [1,)+∞16. 设()f x 、()g x 、()h x 是定义域为R 的三个函数，对于下列命题：① 若()()f x g x +、()()f x h x +、()()g x h x +均为增函数，则()f x 、()g x 、()h x 中至少有一个增函数；② 若()()f x g x +、()()f x h x +、()()g x h x +均是以T 为周期的函数，则()f x 、()g x 、()h x 均是以T 为周期的函数，下列判断正确的是（）A. ①和②均为真命题B. ①和②均为假命题C. ①为真命题，②为假命题D. ①为假命题，②为真命题三. 解答题17. 设(21,21]k I k k =-+，k ∈Z ，定义在R 上的函数()f x 是周期函数，最小正周期为2，又0x I ∈时，2()f x x =.（1）求k x I ∈时，()f x 的解析式；（2）对于给定的正整数k ，方程()f x ax =在k I 上有两个不同的解，求a 的取值范围.18. 写出函数()||f x x a a=++为奇函数的充要条件，并证明你的结论.19. 设()f x 是R 上的函数，且(5)f x +是偶函数，(10)(10)0f x f x ++-=. 求证：（1）()f x 是周期函数；（2）()f x 是奇函数.20. 已知函数11()()2f x x x =+，11()()2g x x x=-. （1）求函数()()2()h x f x g x =+的零点；（2）若直线:0l ax by c ++=（a 、b 、c 为常数）与()f x 的图像交于不同的两点A 、B ，与()g x 的图像交于不同的两点C 、D ，求证：||||AC BD =；（3）求函数22()[()][()]n n F x f x g x =-*()n ∈N 的最小值.21. 定义：对于函数()f x ，若存在非零常数M 、T ，使()f x 对于定义域内任意实数x 都有()()f x T f x M +-=，则称函数()f x 是广义周期函数，其中称T 为广义周期，M 为周距.（1）证明函数()(1)x f x x =+-()x ∈Z 是以2为广义周期的广义周期函数，并求出函数周距M 的值；（2）试判断函数()sin()f x kx b A x ωϕ=+++(k 、A 、ω、ϕ为常数，0k ≠，0A >，0)ω>是否为广义周期函数，若是，请求出广义周期T 和周距M ，若不是，请说明理由；（3）设函数()y g x =是周期2T =的周期函数，当函数()2()f x x g x =-+在[1,3]上的值域为[3,3]-时，求()f x 在[9,9]-上的最大值和最小值.参考答案一. 填空题1. 62. (5)y f x =3. 34. (1,1)5. (2,2)-6. 2.57. 28. 69. (2,0){1}- 10. 4 11. [3,)+∞ 12. 34π 二. 选择题13. D 14. D 15. C 16. D 三. 解答题17.（1）2()(2)f x x k =-；（2）当0k <，1(,0)21a k ∈-；当0k =，(1,0)(0,1]a ∈-；当0k >，1(0,]21a k ∈+. 18. 0a <，证明略. 19.（1）20T =；（2）略.20.（1）x =；（2）略；（3）1. 21.（1）证明略，2M =；（2）是，2T πω=，2k M πω=；（3）最大值23，最小值15-.。

2017—2018学年度第一学期高三十模考试数学试卷（理科）（附答案）

2017—2018学年度第一学期高三十模考试数学试卷（理科）（附答案）2017—2018学年度第一学期高三十模考试数学试卷（理科）一、选择题（每小题5分，共60分.下列每小题所给选项只有一项符合题意，请将正确答案的序号填涂在答题卡上）1.设集合2{|log (2)}A x y x ==-，2{|320}B x x x =-+<，则A CB =（） A ．(,1)-∞ B ．(,1]-∞C ．(2,)+∞D ．[2,)+∞2.在复平面内，复数2332iz i-++对应的点的坐标为(2,2)-，则z 在复平面内对应的点位于（）A ．第一象限B ．第二象限C ．第三象限D ．第四象限3.已知ABC ?中，sin 2sin cos 0A B C +=c =，则tan A 的值是（）A4.设{(,)|0,01}A x y x m y =<<<<，s 为(1)n e +的展开式的第一项（e 为自然对数的底数），m =，若任取(,)a b A ∈，则满足1ab >的概率是（） A ．2e B ．2e C ．2e e - D ．1e e- 5.函数4lg x x y x=的图象大致是（）A ．B ．C ．D ．6.已知一个简单几何体的三视图如图所示，若该几何体的体积为2448π+，则该几何体的表面积为（）A ．2448π+B ．2490π++C ．4848π+D ．2466π++7.已知11717a =，16log b =17log c =，则a ，b ，c 的大小关系为（）A ．a b c >> B ．a c b >> C ．b a c >> D ．c b a >> 8.执行如下程序框图，则输出结果为（）A ．20200B ．5268.5-C ．5050D ．5151-9.如图，设椭圆E ：22221(0)x y a b a b+=>>的右顶点为A ，右焦点为F ，B 为椭圆在第二象限上的点，直线BO 交椭圆E 于点C ，若直线BF 平分线段AC 于M ，则椭圆E 的离心率是（） A ．12 B ．23 C ．13 D ．1410.设函数()f x 为定义域为R 的奇函数，且()(2)f x f x =-，当[0,1]x ∈时，()sin f x x =，则函数()cos()()g x x f x π=-在区间59[,]22-上的所有零点的和为（）A ．6B ．7C ．13D ．14 11.已知函数2()sin 20191xf x x =++，其中'()f x 为函数()f x 的导数，求(2018)(2018)f f +-'(2019)'(2019)f f ++-=（）A ．2B ．2019C ．2018D ．012.已知直线l ：1()y ax a a R =+-∈，若存在实数a 使得一条曲线与直线l 有两个不同的交点，且以这两个交点为端点的线段长度恰好等于a ，则称此曲线为直线l 的“绝对曲线”.下面给出的四条曲线方程：①21y x =--；②22(1)(1)1x y -+-=；③2234x y +=；④24y x =. 其中直线l 的“绝对曲线”的条数为（）A ．1B ．2C ．3D ．4二、填空题：（本大题共4小题，每题5分，共20分）13.已知实数x ，y 满足2202401x y x y y x +-≥??+-≤??≤+?，且341x y m x ++=+，则实数m 的取值范围．14.双曲线22221x y a b-=的左右焦点分别为1F 、2F ，P 是双曲线右支上一点，I 为12PF F ?的内心，PI 交x 轴于Q 点，若12FQ PF =，且:2:1PI IQ =，则双曲线的离心率e 的值为． 15.若平面向量1e ，2e 满足11232e e e =+=，则1e 在2e 方向上投影的最大值是． 16.观察下列各式：311=；3235=+； 337911=++； 3413151719=+++；……若3*()m m N ∈按上述规律展开后，发现等式右边含有“2017”这个数，则m 的值为．三、解答题：（本大题共6小题，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）17.已知等差数列{}n a 中，公差0d ≠，735S =，且2a ，5a ，11a 成等比数列. （1）求数列{}n a 的通项公式；（2）若n T 为数列11{}n n a a +的前n 项和，且存在*n N ∈，使得10n n T a λ+-≥成立，求实数λ的取值范围.18.为了解学生寒假期间学习情况，学校对某班男、女学生学习时间进行调查，学习时间按整小时统计，调查结果绘成折线图如下：（1）已知该校有400名学生，试估计全校学生中，每天学习不足4小时的人数.（2）若从学习时间不少于4小时的学生中选取4人，设选到的男生人数为X ，求随机变量X 的分布列.（3）试比较男生学习时间的方差21S 与女生学习时间方差22S 的大小.（只需写出结论）19.如图所示，四棱锥P ABCD -的底面为矩形，已知1PA PB PC BC ====，AB =，过底面对角线AC 作与PB 平行的平面交PD 于E .（1）试判定点E 的位置，并加以证明；（2）求二面角E AC D --的余弦值.20.在平面直角坐标平面中，ABC ?的两个顶点为(0,1)B -，(0,1)C ，平面内两点P 、Q 同时满足：①0PA PB PC ++=；②QA QB QC ==；③//PQ BC .（1）求顶点A 的轨迹E 的方程；（2）过点F 作两条互相垂直的直线1l ，2l ，直线1l ，2l 与A 的轨迹E 相交弦分别为11A B ，22A B ，设弦11A B ，22A B 的中点分别为M ，N . ①求四边形1212A A B B 的面积S 的最小值；②试问：直线MN 是否恒过一个定点？若过定点，请求出该定点，若不过定点，请说明理由.21.已知函数ln(1)()1x f x ax +=+.（1）当1a =，求函数()y f x =的图象在0x =处的切线方程；（2）若函数()f x 在(0,1)上单调递增，求实数a 的取值范围；（3）已知x ，y ，z 均为正实数，且1x y z ++=，求证(31)ln(1)(31)ln(1)11x x y y x y -+-++--(31)ln(1)01z z z -++≤-.请考生在22、23题中任选一题作答，如果多做，则按所做的第一题记分.22.[选修4-4：坐标系与参数方程] 在极坐标系中，曲线1C 的极坐标方程是244cos 3sin ρθθ=+，以极点为原点O ，极轴为x 轴正半轴（两坐标系取相同的单位长度）的直角坐标系xOy 中，曲线2C 的参数方程为：cos sin x y θθ=??=?（θ为参数）.（1）求曲线1C 的直角坐标方程与曲线2C 的普通方程；（2）将曲线2C 经过伸缩变换''2x y y=??=??后得到曲线3C ，若M ，N 分别是曲线1C 和曲线3C 上的动点，求MN 的最小值.23.[选修4-5：不等式选讲] 已知()21()f x x a x a R =--+∈. （1）当1a =时，解不等式()2f x >. （2）若不等式21()12f x x x a +++>-对x R ∈恒成立，求实数a 的取值范围.答案（理）一、选择题1-5: BDACD 6-10: DACCA 11、12：AC二、填空题13. [2,7] 14.15. 3- 16. 45 三、解答题17.解：（1）由题意可得12111767352(4)()(10)a d a d a d a d ??+=+=++?，即121352a d d a d +=??=?. 又因为0d ≠，所以121a d =??=?.所以1n a n =+.（2）因为111(1)(2)n n a a n n +=++1112n n =-++，所以11112334n T =-+-1112n n ++-++11222(2)nn n =-=++. 因为存在*n N ∈，使得10n n T a λ+-≥成立，所以存在*n N ∈，使得(2)02(2)nn n λ-+≥+成立，即存在*n N ∈，使得22(2)n λ≤+成立. 又2142(2)2(4)n n n n =+++，114162(4)n n≤++（当且仅当2n =时取等号），所以116λ≤.即实数λ的取值范围是1(,]16-∞.18.解：（1）由折线图可得共抽取了20人，其中男生中学习时间不足4小时的有8人，女生中学习时间不足4小时的有4人.∴可估计全校中每天学习不足4小时的人数为：1240024020=人. （2）学习时间不少于4本的学生共8人，其中男学生人数为4人，故X 的所有可能取值为0，1，2，3，4.由题意可得4448(0)C P X C ==170=；134448(1)C CP X C ==1687035==； 224448(2)C C P X C ==36187035==； 314448(3)C CP X C ==1687035==； 448(4)C P X C ==170=. 所以随机变量X 的分布列为∴均值017070EX =?+?237070+?+?4270+?=. （3）由折线图可得2212s s >. 19.解：（1）E 为PD 的中点，证明如下：连接OE ，因为//PB 平面AEC ，平面PBD平面AEC OE =，PB ?平面AEC ，所以//OE PB ，又O 为BD 的中点，所以E 为PD 的中点.（2）连接PO ，因为四边形ABCD 为矩形，所以OA OC =.因为PA PC =，所以PO AC ⊥.同理，得PO BD ⊥，所以PO ⊥平面ABCD ，以O 为原点，OP 为z 轴，过O 平行于AD 的直线为x 轴，过O 平行于CD 的直线为y 轴建立空间直角坐标系（如图所示）.易知1(,22A -，1(,22B ，1(,22C -，1(,22D --，1(0,0,)2P ，11(,)444E --，则11(,)444EA =--，1(,22OA =. 显然，OP 是平面ACD 的一个法向量.设1(,,)n x y z =是平面ACE 的一个法向量，则1100n EA n OA ??==??，即110444102x y z x y ?--=-=??，取1y =，则1(2,1n =，所以1cos ,n OP <>11n OP n OP==所以二面角EAC D --的余弦值为11. 20.（1）221(0)3x y x +=≠；（2）①S 的最小值的32，②直线MN 恒过定点4?? ? ???. 试题解析：（1）∵2PA PB PO +=，∴由①知2PC PO =-，∴P为ABC ?的重心. 设(,)A x y ，则,33x y P ??，由②知Q 是ABC ?的外心，∴Q 在x 轴上由③知,03x Q ?? ???，由QC QA=，得=221(0)3x y x +=≠. （2）解：F 恰为2213x y +=的右焦点，①当直线1l ，2l的斜率存且不为0时，设直线1l 的方程为my x=由22330my x x y ?=?+-=??22(3)10m y ?++-=，设111(,)A x y ，122(,)B x y ，则1223y y m -+=+，12213y y m -=+，①根据焦半径公式得1112)A B x x =+，又1212x x my my +=12()m y y =++223m -=++23m =+，所以1123A B m =+=22221113m A B m ?+?=+221)31m m +=+，则2222(1)6(3)(31)m S m m +=++2222(1)64(1)2m m +≥?? + ?32=，当22331m m +=+，即1m =±时取等号.②根据中点坐标公式得22,33M m m ?? ? ?++?? ，同理可求得222,3131N m m ?? ? ?++??，则直线MN的斜率为MNk =243(1)m m =-，∴直线MN的方程为y -243(1)m x m ?=- -?，整理化简得()4334ym x m +()263490ym x m y ++-=，令0y =，解得x =∴直线MN恒过定点?.②当直线1l ，2l 有一条直线斜率不存在时，另一条斜率一定为0，直线MN 即为x轴，过点4??. 综上，S 的最小值的32，直线MN恒过定点,04?? ? ???. 21.（1）当1a =时，ln(1)()1x f x x +=+则(0)0f =， 21ln(1)'()(1)x f x x -+=+则'(0)1f =，∴函数()y f x =的图象在0x =时的切线方程为y x =.（2）∵函数()f x 在(0,1)上单调递增，∴10ax +=在(0,1)上无解，当0a ≥时，10ax +=在(0,1)上无解满足，当0a <时，只需1010a a +≥?-≤<，∴1a ≥-①21ln(1)1'()(1)ax a x x f x ax +-++=+，∵函数()f x 在(0,1)上单调递增，∴'()0f x ≥在(0,1)上恒成立，即[](1)ln(1)1a x x x ++-≤在(0,1)上恒成立. 设()(1)ln(1)x x x ?=++'()ln(1)(1)x x x x ?-=+++11ln(1)1x x ?-=++，∵(0,1)x ∈，∴'()0x ?>，则()x ?在(0,1)上单调递增，∴()x ?在(0,1)上的值域为(0,2ln 21)-.∴1(1)ln(1)a x x x≤++-在(0,1)上恒成立，则12ln 21a ≤-②综合①②得实数a 的取值范围为11,2ln 21?-??-??.（3）由（2）知，当1a =-时，ln(1)()1x f x x+=-在(0,1)上单调递增，于是当103x <≤时，ln(1)()1x f x x +=-134()ln 323f ≤=，当113x ≤<时，ln(1)()1x f x x +=-134()ln 323f ≥=，∴(31)()x f x -34(31)ln 23x ≥-?，即(31)ln(1)1x x x -+-33(31)ln 24x ≤-?，同理有(31)ln(1)1y y y -+-33(31)ln 24y ≤-?，(31)ln(z 1)1z z -+-33(31)ln 24z ≤-?，三式相加得(31)ln(1)1x x x -+-(31)ln(1)1y y y -++-(31)ln(z 1)01z z -++≤-. 22.解：（1）∵1C 的极坐标方程是244cos 3sin ρθθ=+，∴4cos 3sin 24ρθρθ+=，整理得。

上海市延安中学2017届高三上学期周测(十)英语试题-十一选十 Word版含答案

Section B (10)Directions: Complete the sentences with the words or phrases in the box. Each word can only be used once. There is one extra which you do not need.(F=BC，G=ABC，H=AB，I=AD，J=BD，K=ABD)In 2003, the Gates Foundation launched a project called Grand Challenges Global Health. What I like about it is the way the Gates Foundation approached solving this problem. They didn’t say, "We, the rich Western foundation, will now ___41___ and then ___42___instructions and write some checks. They said, “Let’s cooperate horizontally on defining both the problem and the solutions ---- let's create value that way ---- and then [the foundation] will ___43___ our money in the solutions we both define.” So the Gates Foundation placed ads on the Web and in more ___44____ channels across both the developed and the developing worlds, asking scientists to respond to one big question: What .are the biggest problems that, if science attended to them and solved them, could most dramatically change the fate of the several billion people trapped in the evil cycle of high ___45___ death rate, low life expectancy, and disease? The foundation got about eight thousand pages of ideas from hundreds of scientists from around the world, including Nobel Prize winners. It then collected through them and cut them down to a list of fourteen Grand Challenge ---- challenge where a technological innovation could remove a ___46___ barrier to the solving of an important health problem in the developing world.In the fall of 2003, these fourteen Grand Challenges worldwide. They include the following: How to create effective single-dose (单剂量) vaccines (疫苗) that can be used soon after birth, how to prepare vaccines that do not require refrigeration, how to develop needle-free deliver systems for vaccines, how to better understand which immunological(免疫系统的) responses ___47___ protective immunity, how to better control insects that carry agents of disease, how to develop a ___48___ or chemical strategy to disable an infectious insect population, how to create a full range of the most favorable bioavailable nutrients in a single staple plant species, and how to create immunological methods that can ___49___ chronic (慢性的) infections. Within a year, thefoundation received sixteen proposals for ways to meet these ___50___ from scientists in seventy-five countries, and the foundation is now in the process of funding the best proposals with $250 million in cash.Keys: IGCKH DBEFA。

上海市南洋模范中学2017-2018学年高三上学期期中考试英语试题Word版含答案

上海市南洋模范中学2017-2018学年高三上学期期中考试英语试题Word版含答案2017-2018学年南洋模范中学高三上学期期中考试试卷英语学科Section A (16 points)最新试卷多少汗水曾洒下，多少期待曾播种，终是在高考交卷的一刹尘埃落地，多少记忆梦中惦记，多少青春付与流水，人生，总有一次这样的成败，才算长大。

Directions: Read the following tow passages. Fill in the blanks to make the passages coherent. For the blanks with a given word, fill in each blank with the proper form of the given word. For the other blanks, fill in each with one proper word. Make sure that your answers are grammatically correct.Summer is almost here, which means it is time 31 （sign) your kids up for swim classes again at the Community Pool. Classes begin on Monday, May 1, and will continue 32 the summer. Fifteen swim classes are being offered. Each class 33 ten hours. A new class starts each week of the summer.Each class costs $20. The pool is big enough for six stud ents per class.Classes will increase 34 difficulty each week. The first week is for children up to six years ol d. The last week is for 35 (advance) swimmers who want to improve their race skills.Stud ents 36 sign up for as many classes as they like, but they must pass the skills l evel test. For exampl e, stud ents who sign up for Level 4 (Stroke Readiness) must show their certificate for compl eting Level 3 or must d emonstrate the front crawl and backstroke. Chil dren cannot sign up for a l evel they are not ready for. Chil dren who have never attend ed Community Pool classes must show up April 29 or 30 for a swim skills evaluation.Instructors will rate the stud ents and assign them to a particular skill l evel.Swim classes are fun for all, 37 Children l earn new skills and make new friends. Parents get to meet other parents in the community. Swimming, like bicycling, is a healthy and valuabl e skill that, 38 l earned, is never forgotten. "to teach young children is 39 attracts me and makes me happy," said Ginger, the l ead instructor for swimming programs. "More than half of them 40 (terrify) when we put them into the water the first time. Two months later,they're begging their parents to go to the pool every day."Section BDirections: Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.Developing an original and creative id ea requires that two compl etely different networks in the brain work at the same time: the associative network alongsid e the more “conservative(保守的)” network, according to new research ___41___ at the University of Haifa.The researchers ___42___ that “creative thinking apparently requires ‘checks and balances’.” According to the researchers, creativity is our ability to think in new ways to solve probl ems. But not every original solution is consid ered a creative one. If the id ea is not fully applicabl e,it is not consid ered creative, but simply one which is ___43___.The researchers assumed that for a creative id ea to be produced, the brain must ___44___ a number of different and perhaps even contradictory(矛盾的) networks. In the first part ofthe research, respond ents were given half a minute to come up with a new, original and unexpected id ea for the use of different objects. Answers provid ed with l ow frequency received a high score for originality, whil e those given ___45___ received a l ow score. In the second part, respond ents were asked to give, within half a minute, their best characteristic ___46___ of the objects. During the tests, all subjects were scanned using an FMRI d evice to examine their brain activity whil e providing the answer.The researchers found ___47___brain activity in an “associative” region among participants whose originality was high. This region, which includ es the medial brain areas, mainly works in the background when a person is not concentrating, similar to daydreaming.But the researchers found that this region did not operate alone when anoriginal answer was given. For the answer to be original, an ad ditional region worked in cooperation with the associative region—the administra tive control region, a more “conservative” region related to social norms and rul es. The researchers also found that the stronger the ___48___, the better these regions work together in parallel, the greater the l evel of originality of the answer.“On th e one hand, there is surely a need for a region that produces innovative id eas, but on the other hand there is also the need for one that will know to ___49___ how applicabl e and reasonabl e these id eas are. The ability of the brain to operate these two regions in parallel is what results in creativity. It is possibl e that the most ___50___ creations of humanity were produced by peopl e who had an especially strong connection between the two regions,” t he researchers conclud ed.Reading ComprehensionSection A (15 points)Direction: 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 phrases that best fits the context.The term "quality of life" is difficult to d efine. It 51 a very wid e scope such as living environment, health, empl oyment, food, family life, friends, education, material possessions, l eisure and52 , and so on. 53 speaking, the quality of life, especially as seen by the individual, is meaningful in 54 of the d egree to which these various are as of life are 55 or provid e satisfaction to the individual.As activity carried 56 as one thinks fit during one's spare time, l eisure has the foll owing 57: relaxation, recreation and entertainment, and personal d evel opment. The importance of these 58 according to the nature of one's job and one's lifestyl e. Thus, peopl e who need to 59 much energy in their work will find relaxation most 60 in l eisure. Those with a better education and in professional occupations may 61 more to seek recreation and personal d evel opment(e.g. 62 of skills and hobbies) in l eisure.The specific use of l eisure varies from individual to individual.63 the same l eisure activity may be used differently by different individuals. Thus, thefoll owing are possibl e uses of television watching, a(n) 64 l eisure activity, a change of experience to provid e 65 from the stress and 66 of work; to l earn more about what is happening in one's environment; to provid e an opportunity for und erstanding oneself by 67 other peopl e's life experiences as portrayed(描绘) in the programs. 68 l eisure is basically self-d etermined, one is abl e to take 69 one's interests and preferences and get70 in anactivity in ways that will bring enjoyment and satisfaction.51.A. Composes B. covers C. consists D. constitute52.A. excursion B. reservation C. recreation D. recognition53.A. place B. terms C. means D. way54.A. adaptabl e B. approachabl e C. agreeabl e D. availabl e55.A. off B. through C. away D. out56.A. d efinitions B. id entification C. operations D. functions57.A. alters B. shifts C. varies D. changes58.A. consume B. hire C. provid e D. exercise59.A. prefer B. tend C. select D. oblige60.A. still B. Yet C. So D. Even61.A. proper B. ad equate C. precise D. right62.A. separation B. flight C. escape D. isolation63.A. contrasting B. matching C. comparing D. measuring64.A. Although B. whenever C. Since D. Therefore65.A. attend ed B. involved C. participated D. empl oyedSection B (22 points)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)More mod est consumer appetites might not only save money but also reduce the amount of crime. At l east that’s the conclusion of a l eading British criminalbehavior expert.Dr. Keith Hayward, a l ecturer at the University of Kent, says antisocial behavior results from a need to experience new sensations. And, stealing a car to rid e around in it offers youngpeopl e the same thrill as shoppers get from buying goods.That d esire is encouraged among young peopl e by advertisers who use “pl easure-seeking experience” to sell their products.Advertisements teach young peopl e that they must have the next d esirabl e consumer item to feel good, Hayward said. If that need is not met, then they feel that something is missing. Some yo ung peopl e then use “the exciting possibilities offered by criminal activities” to fill the expectation gap.Hayward has written a book call ed City Limits：Crime, Consumer Culture and the Urban Experience. He says a consumer society teaches young peopl e that their needs must be met instantly. Apart from shopping, he claimed, crime was an easy way for that d esire to be fulfilled.“The current generation of youngsters,” he said,“ is getting far more advertising messages than any other group of chil dren in history.”This makes them dissatisfied with their lives and hungry for more thrills. The main motivation for street crime was not poor parenting, poverty of social exclusion, Hayward argued.It’s “a d esire for styl e, excitement and self-expression” created by the way a consumer society works.Hayward said young peopl e were repeatedly tol d that the purpose of their lives was to consume.However, he said, they rarely questi on what rol e this “language of seduction(诱惑)”plays in shaping their everyday lives.The government fail ed to und erstand the problem, he add ed. It sound be bringing in law to stop advertisers targeting young peopl e.56. Stealing a car and buying heavily-advertised goods are similar in that_____.A. They both need a big decision.B. They can offer a new experience to peopl e.C. They can satisfy peopl e’s d esire for a thrill.。

2017-2018上海市上海中学高三上学期周练英语试题(一)

2017-2018上海市上海中学高三上学期周练英语试题(一)上海中学高三周考II.Grammar and vocabularySection 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.There seems never 21 (be) a civilization without toys, but when and how they developed is unknown. They probably came about just to give children something to do.In the ancient world, as is today, most boys 22 (play) with some kinds of toys and most girls with others. In societies 23 social roles are rigidly determined, boys pattern their play after the activities of their fathers and girls 24 (prepare), even in play, to step into the roles and responsibilities of the adult world.25 is remarkable about the history of toys is not so much how theychanged over the centuries but how much they have remained the same. The changes have been mostly 26 craftsmanship, mechanics, and technology.It is the universality (普遍性) of toys with regard to their development in all parts of theworld and their persistence to the present 27 is amazing. In Egypt, America,China, Japan and among the Arctic (北极的) people, generally the same kinds of toys appeared. Variations depended on local customs and ways of life 28toys imitate their surroundings. Nearly every civilization had dolls, little weapons, toy soldiers, tiny animals and vehicles.Because toys 29 be generally regarded as a kind of art form, they have not been subject to technological leaps that characterize inventions for adult use. The progress from the wheel to the cart to the automobile is a direct line of ways up. The progress from a rattle (拨浪鼓) used by a baby in 3,000 BC to 30 used by an infant today, however, is not characterized by inventiveness (独创性). Each rattle isused only once. Note that there is one word more than you need.forwhich we are willing if necessary to pay a price. Common addictions involve alcohol cigarettes food drugs gambling etc. This article discusses the concepts which can be31 in coping with addictive behavior.32 minor addictions such as watching too much television or lying in bed on weekend mornings are often not even considered addictions because the price paid for engaging in them is not high. On the other hand we tend to use the term “addict”to describe the person who at least in the eyes of others continues to be addicted in a behavior long after it has become 33 that the substantial price being paid was not worth the benefit.The individual who has lost career house family and friends because of cocaine (可卡因) usebut is 34 to consider stopping is an unfortunate example.Negative addictions range from those with very minor negative consequences to those as serious as the cocaine addict just mentioned with much 35 in between. Although it is not 36 true that a negative addiction grows stronger over time yet a constant level of addictive behavior (e.g. overspending $ 200 a week ) can lead to an increasing level of negative consequences.You may be 37 to learn that addictions can also be considered positive. Positive addictions are those in which the benefits outweigh the price. A common example would be the habit of regular exercise. The price of membership in a gym the time involved and any clothing expense is outweighed by the benefits of better health energy self-confidence and appearance. As with negative addictions positive addictions may not get stronger over time and there is a broad 38 of how much benefit is actually obtained.What is common to both positive and negative addictions is the urge to engage in the addictive behavior and the satisfaction that is 39 when the urge is acted upon. The urge is a state of 40 and expectation that is experienced uncomfortably as a desire for the substance or activity. Because weexperience relief when the urge is acted upon there is an increased likelihood that we will act on the urge again.III.Reading comprehensionSection ADirections: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.The importance of liking people is the subject of an article in the Harvard Business.Review，which has carried out an experiment to find out who we'd rather work with. Hardly surprisingly, the people we want most as our workmates are both: 41 at their job anddelightful human beings. And the people we want least are both unpleasant and useless. More interestingly, the autors found that, given the choice between working with lovable folls and comptent jerks (性情古怪的人), we irresistibly choose the 42 . Anyway, who likes those who 43 or hurt other people? We might insist that competence matters more, butour 44 shows we stay close to the people we like, sharing information with them.What companies should 45 do is get people to like each other more. The trickhere is apparently to make sure that stuffs come across each other as often as possible during day. They also should be sent on bonding courses and so on to encourage friendliness and46 displeasure.47 , more outdoor-activity weekends and shared coffee machines inspire no confidence at all. The 48 is that people either like each other or they don’t. You can’t force it. Possibly you can make offices fridendlier by tolerating a lot of chat, but there is a49 cost to that. In my experience, the question of lovable fool against competent jerk may not be the right one. The two are interrelated: we tend not to like our workmates when they are completely 50 . I was once quite friendly with a woman whom I later worked with. I found her to be so 51 bad at her job that I lost respect for her and ended up not really liking her at all. Then is there anything that companies should be doing about it?By far the most effective strategy would be to hire people who are all pretty much the same, given that 52 is one of the main determinants of whether we like each other. Ithink this is a pretty good ides, but no one 53 recommend this anymore withoutoffending the diversity lobby group (游说团体). There is only one acceptable view on this subject: teams of similar people are bad because they stop creativity. This may be true, though I have never seen any conclusive proof of it.Not only do we like similar people, we like people who like us. So if companies wantto54 more liking, they should encourage a culture where we are all nice to eachother. The55 is that this needs to be done with some skill.41. A. strange B. brilliant C. surprised D. absent-minded42.A. former B. latter C. majority D. minority43.A. hate B. fear C. doubt D. annoy44.A. thought B. behavior C. expression D. appearance45.A. further B. nevertheless C. therefore D. instead46.A. break down B. talk to C. pick out D. hold out47.A. besides B. Furthermore C. However D. Hence48.A. impression B. reality C. practice D. custom49.A. investment B. production C. operation D.productivity50.A. valueless B. disabled C. hopeless D. careless51.A. outstandingly B. inevitably C. hopefully D. forgetfully52.A. appearance B. effectiveness C. distinction D. similarity53.A. need B. dare C. must D. should54.A. create B. discover C. promote D. place55.A. strategy B. standard C. hope D. troubleSection BDirections: Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B,C and D. Choose the one that fits best according to the information given in the passageyou have just read.AAs a father of four, I’m concerned about how to lead my children to be good young men and women in such a turbulent time. I have studied philosophy, mysticism, and religion my entire life. They provide great lessons in responsibility and growth. However,I also recognize that, at least at this point in their lives, my children are not terriblyinterested in such subjects. While I was reflecting on this, I was reminded of a line in a song I had heard recently. It goes: “If you had only one chance to say something, what would it be?”That night, I found my tow oldest kids lounging on the couch watching a TV show that featured violence, cursing and even some “adult scenes”. I quietly sat on a chair next to them. I saw my boy straighten up, and my girl pretended to ignore me. I didn’t make any usual comments about the pointlessness of such programs. I didn’t even roll my eyes, although this took some effort. I simply asked:Can you tell me how this will make you a batter person?Without a word, I got up and left the room. About ten minutes later, to my surprise, the children were in their rooms doing their homework and the television was silent.Remarkable. This philosophy can change the way we live our lives. For example, whenever I feel angry and get the urge to lash out, I ask myself: “How does this acting or feeling the way I do right now make me a better person?” I began to realize that rarel ydid my thoughts or actions result in self-improvement, so I made conscious effort to change my mindset and behavior.We all want to be better fathers, mothers, sons and daughters. Better workers, better leaders, better lovers...... this list goes on. Sometimes succeeding in these roles can be tough. But one question aligns us with all those duties we possess to society and ourselves: “Is this making me a better person?”Whatever I said, it worked. My daughter has begun watching nature programs instead of violent TV shows, and she decided to go to school to become a counselor. My son told me he wants to be a police officer. I’ve since thrown away all those parenting magazines and books I’ve collected over the years because I made more progress with a single question than I did with hundreds of pages of “experts” advice.56.When the writer found his kids watching inappropriate TV programs thatnight, he appeared .A .calm B. indifferent C. critical D.anxious57.How can this philosophy change the way we liveour lives?A.By calming ourselves down when we are angryB.By raising a question about our current action and feelingC.By helping us realize our need for self-improvementD.By providing us with new mindset and behavior58.Why did the writer throw away his parenting magazines and books?A.Because his kids had grown out of themB.Because they didn’t offer him any help.C.Because that single question was more usefulD.Because the expert advice was too much tofollow 59.The wrote this passage toA.convince teenagers of the downsides to watching TVB.introduce a life philosophy by telling a parenting storyrm the readers of how he helped hid kids set good goalsD.call on other other parents to trust themselves instead of experts.BWhen the people you know run more, you run more. And now there's data toprove it.A new study published today in Nature Communications of the daily-recorded exercise patterns of more than one million runners over five years shows that exercise is socially contagious. Your knowledge of what your friends are doing can and will motivate you to do more. The work marks a watershed moment in the use of detailed fitness tracking data to understand health behavior and causal behavior change."Knowing the running behaviors of your friends as shared on social networks can cause you to run farther, faster, and longer," said MIT Sloan Professor Sinan Aral, an author of "Exercise contagion in a global social network."Aral and colleague Christos Nicolaides, a postdoctoral fellow at MIT Sloan, used a data set that recorded the geographic location, social network ties, and daily running patterns of more than one million people who ran 359 million combined kilometers (223 million miles) and logged those runs digitally in a global social network of runners over five years. The data contain the daily distance, duration, pace, and calories burned by the runners, recorded by digital fitness tracking devices. The results, said Aral, revealed "strong contagion effects.""On the same day, on average, an additional kilometer run by friends can inspire someone to run an additional three-tenths of a kilometer and an additional ten minutes run by friends can inspire someone to run three minutes longer," the authors wrote.Historically, in the context of exercise, a debate exists about whether we make upward comparisons to those performing better than ourselves or downward comparisons to those performing worse than ourselves. Comparisons to those ahead of us may motivate our own self-improvement, while comparisons to those behind us may create "competitive behavior to protect one's superiority." According to Aral, there is evidence for both trajectories in the study, but comparisons to those better than us are more powerful.Gender matters too. The contagion is most pronounced among men, with men influencing other men to run farther and faster. In this regard, men may be more competitive and, specifically, more competitive with each other. Influence among same sex pairs is strong while influence among mixed sex pairs is weaker. Both men andwomen influence men.However, only women influence women who have reported, in earlier studies, being more influenced by self-regulation and individual planning than by their peers.60.The word “contagious” in paragraph 2 most probably meansA.infectiousB. communicativeC. motivatedD. available61.Jack and Tom both are friends and like running. They post their runs every day onsocial media. According to the research, if one day Jack ran for an hour and a half and Tom an hour, them how long would Tom most probably run the next day?A.30 minutesB.63minutesC.69minutesD.90minutes62.Which runner tends to get the most powerful influence?A. A man making upward comparisons to his female friends.B. A man making upward comparisons to his male friends.C. A competitive women making comparisons to her peersD. A self-regulated woman who prefer individual planningCThe study of psychology is facing a crisis. The Research Excellence Framework (the Ref) has led to a research culture which is holding back attempts to stabilize psychology in particular, and science in general. The Ref encourages universities to push forgroundbreaking innovative, and exciting research in the form of 4* papers, but it does not reward the efforts of those who replicate studies.The point of replicating a study is to test whether a statistically significant result will appear again if the experiments is repeated. Of course, a similar result may not appear –casting into questions the validity of the results from the first experiment.Last year, the Open Science Collaboration attempted to replicate 100 studies from highly ranked psychological journalists. While 97% of the original studies had a statistically significant result, just 36% of the replications had the same outcome.Equally worrying: when an effect did appear, it was often much smaller than previously thought.Recent data calls into question some widely influential findings in psychological science. These problems are not confined to psychology however –many findings published in scientific literature may actually be false.Science is supposed to be self-correcting and reproducibility is a cornerstone of the scientific method. Yet, we simply aren’t invested in replicating findings. We all want to be good researchers and understand more about how the world works. So why are we so reluctant to check our conclusions are valid?Because no incentive is provided by the system we carry out our research in. In the UK,the Ref ranks the published works of researchers according to their originality(how innovative is the research?), significance (does it have practical or commercial importance?),and rigour (is the research technically right?). Outputs are then awarded one to four stars. 4* papers are considered world-leading. The cumulative total of 3* and 4* papers determines research funding allocation and has a knock-on effect on institutional position in league tables(排名表) and therefore attractiveness to students. Obviously, the more publications the better.Worrying, many academics admit to engaging in at least one questionable research practice in order to achieve publication. Examples of this include: coming up with a theory after data is collected, stopping collecting data when an effect appears in case it disappears later, or only reporting the significant effects from collected data. Others simply fabricate data– Dutch psychologist Diederik Stapel shockingly falsified data from more than 50 studies.The Ref completely harms our efforts to produce a reliable body of knowledge.Why? The focus on originality – publications exploring new areas of research using new paradigms,and avoiding testing well-established theories – is the exact opposite of what science needs to be doing to solve the troubling replication crisis. According to Ref standards, replicating an already published piece of work is simply uninteresting.With the next Ref submission just four years away, many researchers are effectively faced with a choice: be a good scientist, or be a successful academic who gets funding and a promotion.63.What crisis the study of psychology facing?A.The Ref has led to a revolution in not only psychology but also science.B.The universities are encouraged to generate more groundbreaking research.C.The Ref tends to set up a different standard for replications of studies.D.The Ref’s indifference to replications of studies has led to worrying effects.64.The Ref’s focus on originality has brought about .A.a reliable body ofknowledgeB.publications exploring new areasC.tests of well-established theoriesD.uninteresting replications of studies65.We can infer from the passage that the Ref .A.is a system for assessing the quality of research in UK universitiesB.provides UK researchers with funding and job opportunitiesC.recognizes researchers’ work and adds to their attractiveness to studentsD.is planning to change its standard before the next Ref submission66.What does the writer mean by saying “be a good scientist”?A.Contribute to the solution to the replication crisis.B.Reform the standards that have been set up by the Ref.C.Give up possible funding and promotion given by universities.D.Avoid using false research practices to test old theories.Section CDirections: Read the following passage. Fill in each blank with a proper sentence given in the box. Each sentence can be used only once. Note that there are two more sentences than you need.A.The parents’ refusal to admit these changes when the child knows them to be truemakes impossible.B.Most children have such a high ideal of their parents, unless the parents themselves havebeen unsatisfactory, that it can hardly hope to stand up to a realistic evaluation.C.They may even make some unpleasant remark’s about the friends’ parents, and think ofthem as disloyalty.D.Today we tend to go to the other extreme, but on the whole this is a healthier attitudeboth for the child and the parent.E.What the child cannot forgive is the parent’s refusal to admit these charges if the childknows them to be true.67F.They may even accuse them of disloyalty, or make some unpleasant remarks about thefriends’ parents.Parents are often upset when their children praise the homes of their friends and regard it as a slur (诋毁) on their own cooking, or cleaning, or furniture, and often are foolish enoughto let the teenagers see that they are annoyed. 67 Such a loss of dignity and a kind of childish behavior on the part of the adults deeply shocks the teenager, and makes them decide that in future they will not talk to their parents about the place or people they visit. Before very long the parents will be complaining that the child is so secretive and never tells them anything, but they seldom realize that they have brought this on themselves.Disillusionment(醒悟) with the parents, however good and adequate they may be bothas parents and as individuals, is to some degree inevitable.68 Parents would be greatly surprised and deeply touched if they realized howmuchbelief their children usually have in their character and correctness, and how much this faith means to a child. If parents were prepared for this teen-aged reaction, and realized that it was a sign that the child was growing up and developing valuable powers of observation and independent judgment, they would not be so hurt, and therefore would not drive the child into opposition by offending and resisting it. The teenagers, with his passion for sincerity, always respects a parent who admits that he is wrong, or ignorant, or even that he has been unfair or unjust. 69Victorian parents believed that they kept their dignity by retreating（伪装）behind anunreasoning authoritarian attitude; in fact they did nothing of the kind, but children were then too frightened to let them know how they really felt. 70 It is always wiser and safer to face up to reality, however painful it may be at the moment.IV.TranslationDirections: Translate the following sentences into English, using the words given in the brackets.71. 新任的总统因军事危机而忧心忡忡。

2017徐汇区上海中学高三上学期10月周测试卷

2017徐汇区上海中学⾼三上学期10⽉周测试卷上海中学⾼三周考（）II. Grammar (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.A great deal of attention (1)_________ (pay) today to the so-called digital divide--the division of the world into theinfo(information) rich and the info poor at present. And that divide does exist today. My wife and I lectured about this looming danger twenty years ago. What was(2)_______ (visible) then, however, were the new, positive forces that work against the digital divide. There are reasons to be optimistic.There are technological reasons to hope the digital divide will narrow. (3)______ the Internet becomes more and more commercialized, it is in the interest of business to universalize access-after all, the more people online, the more potential customers there are. More and more governments, afraid their countries will be left behind, want to spread Internet access. Within the next decade or two, one to two billion people on the planet (4)_______(net) together. As a result, I now believe the digital divide will narrow (5)______ ______widen in the years ahead. And that is very good news because theInternet(6)______well be the most powerful tool for combating world poverty that we've ever had.Of course, the use of the Internet isn't the only way to defeat poverty. And the Internet is not the only tool we have. But it has enormous potential.(7)_________(take)advantage of this tool, some impoverished countries will have to get over their outdated anti-colonial prejudices with respect to foreign investment. Countries(8)________ still think foreign investment is an invasion of their sovereignty might well study the history of infrastructure(the basic structural foundations of a society) in the United States. When the United States built(9)________industrial infrastructure, it didn't have the capital to do so. And that is(10)_______ America's Second Wave infrastructure- including roads, harbors, highways, ports and so on-were built with foreign investment.【答案】1.is being paid 2.less visible 3.As 4.will be netted 5.rather than6.may7.To take8. that9.its 10.why【分析】(1).分析可知，此处应为被动语态，”today”提⽰为现在进⾏时。

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2017 学年南模中学高三年级十月份月考试卷
2017.10
一、填空题
1. 若是第四象限角，则所在象限是第
象限
2. 已知集合 A x | k
2
2 x
k , k
Z
,
B
{x
|
4
x2
0}，则
A
B
.
3
2
3 cos x
3. 函数 y
的值域为
.3 cosຫໍສະໝຸດ x4. 已知 tan 2 ，则 sincos2 .
2
（1）求 f (x) 的单调递增区间；
（2）设 ABC 为锐角三角形，角 A 所对边 a 19 ，角 B 所对边 b 5 ，若 f ( A) 0 ，求 ABC 的面积
第 2页
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18.
设函数 f (x)
2 cos 2x sin 2 x
2
4
（1）求函数 f (x) 的最小正周期；
（3）当 f (x) a1 sin(x 1) a2 sin(x 2) a nsin(x n) 时，（ ai R,i 1, 2, 3,, n, 0 ），
若 f 2 (0) f 2 0 ，且函数 f (x) 的图像关于点, 0 对称，在 x 处取得最小值，试探讨论应
该满足的条件
第 4页
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参考答案
一、填空题 1. 一、三
2. [2,
2) [ , ) 32
3. 1 , 2
2
4. 2 25
6k, 6k 3, k Z
5.
4
6. 1 7. 6 2
8. 2
9. [0,1]
10. 1 ,1
4
2
3
11. 4 12. 4031
二、选择题 13-16 CADD
3
A. 向右平移个单位
8
3
B. 向左平移个单位
8
3
C. 向右平移个单位
4
3
D. 向左平移个单位
4
15. 将函数 y 1 的图像按向量 a (1,0) 平移，得到的函数图像与函数 y 2sinx(2 x 4) 的图像
x
的所有交点的横坐标之和等于（）
A. 2
B. 4
C. 6
D. 8
（1）求此时无人机到甲、丙两船的距离之比；（2）若此时甲、乙两船相距 100 米，求无人机到丙船的距离（精确到 1 米）
第 3页
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20. 如图，某园林单位准备绿化一块直径为 BC 的半圆形空地，ABC 外的地方种草，ABC 的内接正方
体 PQRS 为一水池，其余的地方种花，若 BC a, ABC ，设ABC 的面积为 S1 ，正方形的面积为 S2
.
| x 1| 1
2
二、选择题
第 1页
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13. 在 ABC 中， sin2 A sin2 B sin2 C sin B sin C ，则角 A 的取值范围是（）
A. (0, ] 6
B. [ ,)
6
C. (0, ] 3
D. [ ,)
3
14. 把 y 2 (cos 2x sin 2x) 的图像作适当的移动得 y sin 2x 的图像，这样的移动可以是（） 2
三、解答题
17. （1） , ；（2） 15 3
18. （1）；
（2） g(x)
1
2
sin 2x, x ,
1 sin(2x), x (
2
, 0]
2
2
2
19. （1）；（2）275
3
1 20. （1） S1 4 a
21. （1） k
2
a2 sin 2 2 9
sin 2, S2
,
k
Z
16. 存在函数 f (x) 满足：对任意 x R 都有（）
A. f (sin 2x) sin x
B. f (sin 2x) x 2 x
C. f (x2 1) | x 1|
D. f (x2 2x) | x 1|
三、解答题
17. 已知函数 f (x) cos2 x sin2 x 1 , x (0,)
4
答案提示 A ，试将条件补充完整
3
. 求角 A ”。经推断破损处的条件为三角形的一边的长度，且
8.
函数
f
(x)
(x
1)2 sin x2 1
x,
f
(x) max
M,
f
(x) min
m
，则 M
m
.
9. 已知函数 f (x) 1 sin 2x 3 cos 2x 1 ，若 f (x) log t 对 x R 恒成立，则 t 的取值范围为
（2）设函数 g(x) 对任意 x R ，有g x g(x) ，且当 x 0, 时，g(x) 1 f (x) ，求函数 g(x)
在[, 0]上的解析式
19. 如图所示，湖面上甲、乙、丙三艘船沿着同一条直线航行，某一时刻，甲船在最前面的 A 点处，乙船在
中间的 B 点处，丙船在最后的 C 点处，且 BC : AB 3 :1，一架无人机在空中的 P 点处对它们进行数据测量，在同一时刻测得APB 30, BPC 90（船只与无人机的大小及其他因素忽略不计）
2
2
2
.
10. 设1,2 R ，且
2
1
sin
2
1
sin(2
)
2 ，则 |101
2
| 的最小值等于
.
1
2
11. 设 a, b R, c [0, 2)，若对任意实数 x 都有2 sin 3x a sin(bx c) ，则满足条件的有序实数
组 (a, b, c) 的组数为
.
12. 关于 x 的方程 1 | sin 1x | 在[2016, 2016] 上解的个数是
；
4 sin 2
（2）
2k4s,ikn2a；rcta（n21）
4 ,k
Z
；
（3）
2k
1,
k
N
*
2
2
2
第 5页
（1）用 a,表示 S1 和 S2 ；
（2）当 a 固定，变化时，求 S1 取最小值时的角
S2
21. 已知函数 y f (x), x D, y A; g(x) x2 (4 7 tan)x 1
（1）当 f (x) sin(x )为偶函数时，求的值；
（2）当 f (x) sin 2x 3 sin 2x 时， g(x) 在 A 上是单调递减函数，求的取值范围；
5.
函数
f
(x)
log 1 2
cos
x 3
4
的单调递增区间为
.
6. 若 f (x) 3 sin 2x1( 0) 在区间 32, 2 上为增函数，则的最大值是
.
7. 有一个解三角形的题因纸张破损有一个条件不清，具体如下“在 ABC 中，角 A, B, C 所对的边分别
为 a,b, c ，已知 a 3, B ，

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