【全国百强校】江苏省南京市金陵中学 2017-2018 学年第二学期期末考试高二数学试题

金陵中学2017-2018学年度第二学期期末考试高二数学试卷数学I一、填空题:本大题共14小题,每小题5分,共70分.请把答案填在答题卡相应位置上.1.设集合,,则 .2.已知复数,其中是虚数单位,则的值是 .3.某校共有教师200人,男学生1200人,女学生1000人.现用分层抽样的方法从所有师生中抽取一个容量为的样本,已知从女学生中抽取的人数为50人,那么的值为 .4.如图是一算法的伪代码,则输出值为 .5.如图,在长方体中, ,,则三棱锥的体积为 .6.在平面直角坐标系中,若双曲线的一条渐近线方程为,则实数的值为 .7.设各项均为正数的等比数列的前项和为，若,则数列的通项公式为 .8.将一颗均匀的骰子连续抛掷2次,向上的点数依次记为,则“”的概率是 .9.若实数满足条件则的取值范围为 .10.在平面直角坐标系中,已知,,两曲线与在区间上交点为.若两曲线在点处的切线与轴分别相交于两点,则线段的为 .11.如图,在平面四边形中, 是对角线的中点,且，. 若,则的值为 .12.若对满足的任意正实数,都有,则实数的取值范围为 .13.在平面直角坐标系中,记椭圆的左右焦点分别为，若该椭圆上恰好有6个不同的点,使得为等腰三角形,则该椭圆的离心率的取值范围是 .14.对于任意的实数,记为中的最小值.设函数，，函数,若在恰有一个零点,则实数的取值范围是 .二、解答题:本大题共6小题,共计90分.解答时应写出文字说明、证明过程.15.在平面直角坐标系中,设向量,.(1)当时,求的值；(2)若，且.求的值.16.如图,在四棱锥中,底面是矩形,平面平面,,点在棱上, ,点是棱的中点,求证：(1) 平面;(2) 平面.17.如图,在一个水平面内,河流的两岸平行,河宽1(单位:千米)村庄和供电站恰位于一个边长为2(单位:千米)的等边三角形的三个顶点处,且位于河流的两岸,村庄侧的河岸所在直线恰经过的中点.现欲在河岸上之间取一点,分别修建电缆和,.设,记电缆总长度为 (单位:千米).(1)求的解析式；(2)当为多大时,电缆的总长度最小,并求出最小值.18.如图,在平面直角坐标系中,已知椭圆的离心率为,且过点.设为椭圆的右焦点, 为椭圆上关于原点对称的两点,连结并延长,分别交椭圆于两点.(1)求椭圆的标准方程；(2)设直线的斜率分别为,是否存在实数,使得?若存在,求出实数的值;若不存在,请说明理由.19.设数列的前项的和为,且满足,对,都有 (其中常数),数列满足.(1)求证:数列是等比数列；(2)若,求的值；(3)若,使得,记,求数列的前项的和.20.在平面直角坐标系中,已知函数的图像与直线相切,其中是自然对数的底数.(1)求实数的值；(2)设函数在区间内有两个极值点.①求实数的取值范围；②设函数的极大值和极小值的差为,求实数的取值范围 .高二数学Ⅱ(附加题)21.已知矩阵，.(1)求；(2)在平面直角坐标系中,求直线在对应的变换作用下所得直线的方程.22.在直角坐标系中,以原点为极点,以轴的非负半轴为极轴,取与直角坐标系相同的长度单位,建立极坐标系.设曲线的参数方程为,(为参数, ),直线的极坐标方程为.(1)写出曲线的普通方程和直线的直角坐标方程；(2)求曲线上的点到直线的最大距离.23.假定某篮球运动员每次投篮命中率均为.现有3次投篮机会,并规定连续两次投篮均不中即终止投篮,已知该运动员不放弃任何一次投篮机会,且恰好用完3次投篮机会的概率是.(1)求的值；(2)设该运动员投篮命中次数为,求的概率分布及数学期望.24.如图,已知正四棱柱的底面边长为2,侧棱长为3, ,垂足为,交于点.(1)求证: ⊥平面;(2)记直线与平面所成的角,求的值.试卷答案一、填空题.1. 2. 3. 4.5. 6. 7. 8.9. 10. 11. 12.13. 14. 或二、解答题.15. 解(1)当时，，，所以.(2)，若.则，即.因为，所以，所以，所以.16.证明(1)因为在中, ，所以点是棱的中点.又点是棱的中点,所以是的中位线,所以.因为底面是矩形,以,所以.又平面, 平面,所以平面.(2)因为平面平面, 平面，平面平面，所以平面.又平面,所以.因为,, ,平面,平面, 所以平面.17.解(1)易得垂直平分，则，，，于是，因为在之间,所以，故，.(2) ，，令,得，故当，，递减,当,,递增,所以,当时, .答:当时, 最小值为.18.解(1)设椭圆的方程为，，由题意知解得所以椭圆的方程为.(2)设,则,,又,所以直线的方程为.由消去，得.因为是该方程的一个解,所以点的横坐标. 又点在直线上，所以，从而点的坐标为同理,点的坐标为，所以，即存在,使得.19.(1)证明:因为,都有，所以两式相减得,即，当时，所以，又因为,所以，所以数列是常数列, ，所以是以2为首项, 为公比的等比数列.(2)由(1)得.所以.(3)由(1)得.. 因为，所以当时, ，当时，.因此数列的前项的和.20. (1)设直线与函数相切于点，函数在点处的切线方程为: ，，把代入上式得.所以,实数的值为.(2)①由(1)知,设函数在区间内有两个极值点，令,则,设,因为,故只需,所以, .②因为,所以，由,得,且..设,,令，，(在上单调递减,从而，所以,实数的取值范围是.高二数学Ⅱ（附加题）21. 解(1)由题知，所以，根据逆矩阵公式,得.(2)设由上的任意一点在作用下得到上对应点.由，即解得，因为,所以，即.即直线的方程为.22.解(1)由得，由，得,即.(2)在上任取一点，则点到直线的距离为，，当，即时，.23. 解(1)设事件:“恰用完3次投篮机会”,则其对立事件:“前两次投篮均不中”, 依题意, ，解得.(2)依题意, 的所有可能值为,且,，，故.的概率分布列为:数学期望.24.解(1)如图,以为坐标原点,分别以直线所在直线为轴, 轴, 轴,建立空间直角坐标系，易得,设,则，因为,所以，解得,即,又,,所以,所以, 且，所以，又，所以平面.(2) ，，，设平面的一个法向量，则即令，则，即，.。

2017-2018学年江苏省南京市鼓楼区金陵中学高二（下）期末英语试卷第一部分英语知识运用（共三节）第一节听力理解（满分10.0分）1．Why is Ann so upset？A．She failed one of her exams．B．She is worrying about other lessons．C．She has no time to do her math homework．2．What type of food does the woman eat？A．Junk food．B．Healthy food．C．Delivered food．3．What will the man probably do to stay warm？A．Use a blanket．B．Turn on the heater．C．Drink some hot chocolate．4．What are the speakers mainly talking about？A．The man's career．B．The man's travel plan．C．The man's plan after graduating．5．What are the speakers' opinions about the painting？A．It's simple．B．It's colorful．C．It's complex．6．（1）Where does the conversation take place？A．In an office downtown．B．In an apartment downtown．C．In an apartment in the Hast End．（2）What does the man want to do now？A．Get to work．B．Go to a restaurant．C．Visit the woman's company．7．（1）How do the speakers know each other？A．They are family members．B．They go to the same school．C．They teach at the same school．（2）How has the man tried to reach his brother？A．He sent him a text．B．He went to his house．C．He left him a voicemail．8．（1）Which subject is difficult for the woman？A．Math．B．History．C．Chemistry．（2）When can the woman have tutoring？A．On Tuesdays．B．On Thursdays．C．On Fridays．（3）Who is in charge of the Gifted Program？A．Mr．Jennings．B．Mr．Hobart．C．Mrs．Lee．9．（1）What might the woman's job be？A．She's a diver．B．She's a lifeguard．C．She's a swimming instructor．（2）Who called the ambulance？A．The woman．B．One of the students．C．The man's colleague．（3）When did the ambulance arrive？A．Immediately．B．Ten minutes later．C．Twenty minutes later．（4）How did the girl react when she awoke？A．She didn't know what happened．B．She went back in the pool．C．She cried．10．（1）Who is making the announcement？A．The student government．B．The school newspaper．C．The football team．（2）How many new teams are added this year？A．Four．B．Three．C．Two．（3）What do the music club members do？A．They organize trips．B．They attend concerts．C．They have dancing nights．（4）Why should a student join a campus group？A．To have friends．B．To make good grades．C．To keep up with world news．第二节单项选择（共20题，每小题1分，满分20分）11．A survey shows that the firm hasn't broken the rules，but _____________responsibly．（）A．it has neither acted B．so has it actedC．neither has it acted D．it has so acted12．There are some health problems that，when ________ in time，can become bigger ones later on．（）A．not treatedB．not being treatedC．not to be treatedD．not having been treated13．We just wonder ________ bargaining enjoys a real love and great appreciation among many people．（）A．why is it that B．what is it thatC．what it is that D．why it is that14．Never before ________ the famous museum was just a stone's thro away from their school，so out ________．（）A．had they known；went all theyB．they had known；went all theyC．had they known；they all wentD．they had known；they all went15．I would have gone to visit him in the hotel had it been at all possible，but I ________ fully occupied．（）A．were B．had been C．have been D．was16．When travelers arrived there，the village seemed deserted，the only sign of life ________ one or two dogs lying under some trees．（）A．was B．were C．being D．had been17．The customer left the waiter a ________ tip because he had been especially friendly and helpful．（）A．moderate B．liberal C．handy D．conscious18．Our leader officially ________ the plan to develop the Bay Area in his government work report delivered at the start of the National People's Congress session in March．（）A．laid out B．laid off C．laid down D．laid up19．A number of questions ________ by parents at the meeting，but the school leaders could not ________ any proper answer．（）A．came out；end up withB．came up；come up withC．put up；come up withD．put forward；come down with20．The Mp3 ________ young people ________ a bit of decline recently with the appearance of the Mp4．（）A．intending to；has entered intoB．intended for；has gone intoC．meant to；takes onD．meant for；opens up21．I know this is not quite the right word，but I can't be_____ to think of a better one．（）A．disturbed B．bothered C．troubled D．worried22．﹣Shall I ________ some music？﹣You'd better not．I'm ________ on my lessons．（）A．put on；bent B．put up；bendingC．put in；bent D．put out；bending23．It was a matter of ________ would take the position．（）A．who B．whoever C．whom D．whomever 24．Distinguished guests and friends，welcome to our school，the ceremony of the 50th Anniversary this morning are our alumni （校友）from home and abroad．（）A．Attend B．To attendC．Attending D．Having attended25．Two lawyers have donated $50，000 to ________ our school's campaign"Help the Needy"，which was started by our former headmaster three years ago．（）A．sponsor B．launch C．organize D．plan26．They seem to care little about others，shut down communication and ________ their own words．（）A．subject to B．subscribe toC．bring in D．indulge in27．What the media should not do is to ________ people's natural fears to create panic．（）A．exploit B．explore C．extend D．express28．The company lost 7 USD million this quarter ________ a profit of ﹩6.2 million a year earlier．（）A．in contrast to B．with regard toC．in favor of D．at the sacrifice of29．It was such a beautiful expression of being the change﹣a celebration of self﹣responsibility that rarely is ________ in young people's lives today．（）A．polished B．portrayed C．progressed D．proposed30．A good competitor will cause you to grow．He will ________ you beyond your former skill level．If you want to get good at chess，play against somebody better at chess than you are．（）A．serve B．shelter C．stretch D．support第三节完形填空（满分20分）31．Every Sunday morning I take a light walking around a park near my home．There's a lake （1）in one corner of the park．Each time I （2）by this lake，I see the same elderly woman sitting at the water's （3）with a small metal cage sitting beside her．This past Sunday my （4）got the best of me，so l stopped jogging and walked （5）to her．（6）I got closer，I realized that the metal cage was （7） a small trap．There were three turtles，unharmed，slowly walking around the base of the trap．She had a fourth turtle in her lap （8）she was （9）scrubbing with a spongy brush．"Hello，" I said．"If you don't mind my （10），I'd love to know what you're doing with these turtles．"She smiled．"I'm cleaning off their shells，" she replied．" （11）on a turtle's shell，like algae or scum，（12）the turtle's ability to absorb heat and impedes its ability to swim．It can also （13）and weaken the shell over time．"She went on："I spend a couple of hours each Sunday morning ，relaxing by this lake and helping these little guys out．It's my own （14）way of making a difference．""But don't most freshwater turtles live their whole lives with algae and scum（15）from their shells？" I asked．"Yep，（16），they do，" she replied．"Well then，don't you think your time could be better spent？And 99% of these turtles don't have kind people like you to help them clean off their shells．So，no （17）…but how exactly are your localized （18）here truly making a difference？"The woman giggled aloud．She then（19）at the turtle in her lap，scrubbed off the last piece of algae from its shell，and said，"Sweetie，if this little guy （20）talk，he'd tell you I just made all the differencein the world．（1）A．being located B．locating C．located D．having located （2）A．reach B．hike C．wander D．jog（3）A．surface B．bottom C．position D．edge（4）A．curiosity B．passion C．enthusiasm D．caution（5）A．down B．over C．up D．around（6）A．Until B．As C．While D．After（7）A．in particular B．in return C．in chaos D．in effect（8）A．that B．where C．which D．what（9）A．attentively B．gradually C．directly D．alternatively （10）A．request B．permission C．doubt D．nosiness（11）A．Something B．Anything C．Nothing D．Everything （12）A．broadens B．strengthens C．lowers D．enlarges（13）A．weather B．address C．choke D．split（14）A．common B．unique C．explicit D．potential（15）A．attached B．tied C．hanging D．potential（16）A．fortunately B．basically C．sadly D．absolutely （17）A．wonder B．problem C．offense D．excuse（18）A．contributions B．efforts C．sacrifices D．arrangements （19）A．looked down B．drove away C．tore up D．thought back （20）A．would B．might C．shall D．should第二部分阅读理解（满分26分）32．（6分）Culture can affect not just language and customs，but also how people experience the world on surprisingly basic levels．Researchers，with the help of brain scans，have uncovered shocking differences in perception（感知）between Westerners and Asians，what they see when they look at a city street，for example，oreven how they perceive a simple line in a square，according to findings published in a leading science journal．In western countries，culture makes people think of themselves as highly independent individuals．When looking at scenes，Westerners tend to focus more on central objects than on their surroundings．East Asian cultures，however，emphasize inter﹣dependence．When Easterners look at a scene，they tend to focus on surroundings as well as the object．Using an experiment involving two tasks，Dr Hedden asked subjects to look at a line simply to estimate its length，a task that is played to American strengths．In another，they estimated the line's length relative to the size of a square，an easier task for the Asians．The level of brain activity，by tracking blood flow，was then measured by Brain Scanners．The experiment found that although there was no difference in performance，and the tasks were very easy，the levels of activity in the subjects' brains were different．For the Americans，areas linked to attention lit up more，when they worked on the task they tended to find more difficult﹣estimating the line's size relative to the square．For the Asians，the attention areas lit up more during the harder task also﹣estimating the line's length without comparing it to the square．The findings are a reflection of more than ten years of previous experimental research into East﹣West differences．In one study，for instance，researchers offered people a choice among five pens；four red and one green，Easterners were more likely to choose a red pen while Westerners were more likely to choose the green one．Culture is not affecting how you see the world，but how you choose to understand and internalize（使内化）it．But such habits can be changed．Some psychological studies suggest that when an Easterner goes to the West or vice versa，habits of thought and perception also begin to change．Such research gives us clues on how our brain works and is hopeful for us to develop programs to improve our memory，memory techniques and enhance and accelerate our learning skills．（1）According to the passage，Chinese people are most likely to．A．more emphasize independent thinkingB．always focus more on their surroundingsC．focus on the context as well as the objectD．think of Westerners as highly independent units（2）We know from the passage that people's brains will be more active when．A．the task is much easierB．the blood flow is trackedC．people begin to choose colorsD．the task is more difficult（3）What does Dr Hedden's experiment in Paragraph 4﹣5indicate？A．Culture has a great impact on the way people talk and behave．B．Easterners and Westerners perceive the world differently．C．People's perception of the world can be changed．D．Americans are better at calculating than the Asians．33．（10分）Edgar Alan Poe was and is an abnormal figure among the major American writers of his period．It seems to have been true of Poe that no one could look at him without seeing more than they would wish．Poe published The Narrative of Arthur Gordon Pym of Nantucket in 1838，his only novel．Its importance is suggested by the fact that his major work comes after it．The Narrative's shortcomings are sometimes considered to be the fact that it was written for money，as it surely was，and as almost everything else Poe wrote was also．This is not exceptional among writers anywhere，though in the case of Poe it is often treated as if his having done so were disgraceful．Be that as it may，the Narrative makes its way to a peak as strange and powerful as anything to be found in his greatest tales．The word that reoccurs most importantly in Poe's fictions is horror．His stories are often shaped to bring the narrator and the reader to a place where the use of the word is reasonable，where the word and the experience it arouses are explored or by implication defined．Perhaps it is because Poe's tales test the limits of mental health and good manners that he is both popular and criticized．The Narrative of Arthur Gordon Pym has the grand scale of the nineteenth﹣century voyage of discovery，and a different and larger scale in the suggestions that appear as the voyage goes on．The Narrative is frequently compared with Moby﹣Dick，published thirteen years later，after Poe's death．Poe uses whiteness as a highly ambiguous symbol，by no means to be interpreted as purity or holiness or by association with any other positive value．There is blackness，too，in The Narrative，specifically associated with the populations that live in the regions nearest the South Pole．The nativepeople in Tasmania，the island south of Australia，were said by explorers and settlers to be black，and were in any case，with the word "black，" swept into the large category of those related to displacement，exploitation，and worse．Something very like the occupation of Kentucky by white settlers lies behind the events that bring Pym to the far﹣sighted conclusion of his narrative．In the early years of the nineteenth century the British began what made the native people of Tasmania die out，who had tried to resist white invasion of their island．Such occupations were，of course，a major business of Europeans，or whites，almost everywhere in the world at the time Poe wrote．They，were boasted of as progress．It would have required unusual sensibility in Poe to have taken a different，very dark view of the phenomenon．But he was an unusual man．And the horror that fascinated him and gave such dreadful unity to his tales is often the unavoidable，conflict of the self by a perfect justice，the exposure of a guilty act in a form that makes its reveal a falling back of the mind against itself．Young Pym is simply telling a story of a kind popular at the time，a voyage adventure lived out beyond the farthest reaches of exploration．The story is disturbed by its own deeper tendencies，the rising through this surface of the kind of recognition that must find expression in another form of literature．As his ship approaches the region of the South Pole，Pym notes the mildness of the climate，coolly listing the resources of the islands，which were assumed by such voyagers to be there for the taking．If The Narrative were a conventional story，the immense roar and the towering flames might attract the notice of a passing sail﹣and there would be no need for a note explaining its lacking an ending．But the force of the narrative carries it beyond the fate of individuals，toward an engagement with a reality beyond any temporary human drama．（1）What does the underlined part in Paragraph 1 mean？A．Allan Poe was a famous America writer of his period．B．People expect too much of the American writer﹣Alan Poe．C．Unlike other writers，Allan Poe is a unique and unusual writer．D．People think Poe is a popular novelist like other famous writers．（2）Where is the novel The Narrative of Arthur Gordon Pym probably set？A．In the South Pacific．B．In Australia．C．At the South Pole．D．In Kentucky．（3）Which of the following can describe the characteristic of The Narrative of Arthur Gordon Pym？A．Poverty is the main theme of the novel．B．The novel is full of justice elements．C．Blackness can possibly be felt in the novel．D．Whiteness is the obvious symbol of the novel．（4）Which of the following might be taken from the novel The Narrative？A．"One of these adventures was related by way of introduction to a longer narrative．"B．"Gordon Pym's father was a respectable trader at Nantucket，where Pym was born．"C．"The wind，as I before said，blew freshly from the southwest．The night was very cold．" D．"Pym at length hit upon the idea of working on the terrors and guilty conscience of the mate．"（5）Which of the following statements is True according to the passage？A．The Narrative is an adventurous story written in a conventional way．B．The Narrative is considered one of Alan Poe's famous novels．C．Allan Poe was misunderstood to write The Narrative for money．D．Readers might not understand why The Narrative ended so abruptly．34．（10分）Until recently，scientists and authors were in absolute disagreement over the point of crying．In King Henry VI，Shakespeare wrote，"…，to weep is to make less the depth of grief"，and the American writer Lemony Snicket said "unless you have been very，very lucky，you know thata good，long session of weeping can often make you feel better，even if your circumstances have notchanged one bit"．Charles Darwin，on the other hand，thought that shedding tears （the act of crying）was merely a useless side effect of the way that the muscles around the eye worked．For him，those muscles had to contract（收缩）from time to time so that they didn't overflow with blood；the expulsion of tears was simply an unintended consequence of that evolved physiological（生理学的）process．He did acknowledge that crying could help young infants attract the attention of their parents，though．We now know that crying﹣at least，the sort that adults do﹣is a complex physiological response to some kind of emotional stimulus．The most noticeable feature is of course the shedding of tears，butit also includes changes in facial expressions and breathing patterns．From a scientific perspective，crying is different from shedding the kind of tears like when you accidentally rub your eyes after eating spicy foods．Even the tears themselves are different．In 1981，Minnesota psychiatrist William H Frey II discovered that tears flowing due to sad movies had more protein in them than those that flowed in response to some freshly chopped onions．If you shed tears of laughter when seeing a funny comedy show or you're moved to tears when listening to a bridegroom's wedding vows to his bride，you may know that emotional tears aren't limited to feelings of deep sadness．While all of us are familiar with the feelings that are associated with crying，whether for joy or sorrow，we know little about why we do it as adults﹣but there are plenty of ideas．One idea is that adult crying isn't actually all that different from the sort that babies do，at least when it comes to its social nature．In other words，perhaps weeping is a literal cry for attention，a means of soliciting support and help from our friends when we need it the most．It's a way of communicating our inner emotional state at a time when we may not be able to express it clearly．While this may explain some forms of crying，many researchers have found that adults often cry when they're completely alone．Another possibility is that crying might serve as a means of "secondary appraisal，" helping people to realize just how upset they are，a way of just how upset they are and helping them understand their own feelings．Another idea is that crying provides relief from stressful situations．The idea is consistent not only with the words of Shakespeare，but also with the words of Roman Poet Ovid，who wrote，"It is some relief to weep；grief is satisfied and carried off by tears．" The Greek Philosopher Aristotle also wrote that crying "cleanses the mind"．In a 1986 study of popular US magazines and newspapers，one psychologist found that 94% of articles about crying suggested that it helped to relieve psychological tension．Indeed，a 2008 study of nearly 4，300 young adults from 30 countries found that most reported improvements in both their mental and physical well﹣being after a short period of crying，but not all．Some reported no change after a crying session，and some even said that they felt worse afterwards．The difference seems to lie in the social context：if a person felt embarrassed about crying in public，for example，they might feel less resolved than if they cried alone or with a friend．The study alsofound that when people tried to suppress or hide their crying，they ended up feeling less relieved afterwards．So the notion of having "a good cry" is not without merit．In the end，adults might just cry for the same reason as human infants：to seek help from their friends and family．（1）According to Darwin，shedding tears was．A．the same thing as cryingB．aimed at attracting other's attentionC．nothing but a physiological processD．an effective way to get rid of negative emotions（2）What can we learn from the passage about crying？A．It can benefit people's eye muscles．B．It is a response to the stimulus to eyes．C．It is usually caused by painful emotions．D．It can cause changes in people's outward features．（3）The underlined word "soliciting" in Paragraph 6 can be best replaced by ""．A．refusingB．seekingC．providingD．receiving（4）Who doesn't share the same idea with Shakespeare about crying？A．Lemony Snicket．B．Ovid．C．Aristotle．D．Charles Darwin．（5）What is the best title of the passage？A．Why do people cryB．Experiments on cryingC．Different types of cryingD．Is having a cry good for us第三部分词汇及句型运用（共三节）第一节单词填空及完成句子（共6题，每空0.5分，满分4.0分）35．With the border agreement signed，the t between the two countries began to case off．36．Economist John Robertson says the finance minister was wrong to expect IMF to be（仁慈的）to Zimbabwe．37．Readers who don't shy away from political，philosophical，or religious topics of all kinds will be fascinated by Tolstoy's grasp of Napoleonic historical forces mixed with（change）but fascinating human individuals．38．He is a liar．His actions are in obvious c with his promises made in his inaugural address（就职演讲）．39．他们被控告滥用权力，人为拾高物价．They were accused of to artificially keep prices high．40．任何卖国投敌的人都将会被判死刑．Whoever betrays his country to the enemy will be to．第二节名著短语填空（只填字母）（共5题，每小题5分，满分5分）41．（1）"When you face the sun，" wrote Helen Keller，"the shadows always you．"（2）In the days our meeting he'll jot down subjects he wants to be sure he remembers to talk to me about while we are together．（3）After a month，Mr．McAyley called me and said that they have to it to two candidates，and I was one of them．（4）Only human beings have come to a point where they know why they exist．They don't use their brains and they have forgotten the secret knowledge of their bodies，their senses，or their dreams．（5）Not only can I some of the mystery books she has recommended，but I've begun to find out more about what good mystery does to the intellectual energy of the human mind．第三节名著翻译（共5题，每小题1分，满分5分）42．It was Plato who said that his definition of thinking was "the soul talking to itself"．43．Competition，if confronted enthusiastically，can be the greatest self﹣motivating experience in the world．44．Helen Keller didn't complain about not being given enough money from the government to compensate her for her disability．45．The secret to a happy life is a sound mind in a sound body．46．A vision should be judged by these criteria，the criteria of power and effectiveness．第四部分任务型阅读（满分10分）请认真阅读下列短文，并根据所读内容在文章后表格中的空格里填入一个最恰当的单词．注意：每个空格只填1个单词．请将答案写在答题纸上相应题号的横线上．47．I love indoor plants；I really do﹣but you would never know it by looking at my t rack record with them．I am always killing succulents．I decided to consult an expert on the matter．I've grown tired of killing plants．It shouldn't be rocketscience，but maybe，to some，it is．As it tums out，succulents are not as low﹣maintenance as they're often marketed to seem，but they're not impossible to care for，either．Here's what I've learned after asking a garden shop staff a thousand and one questions．HOW TO AVOID KILLING YOUR SUCCULENTS1．Use loose "cactus（仙人掌）" soil．Succulents need to drain well．They won't survive in sand or rock，and some other soils hold too much moisture．You can purchase cactus potting soil from your local garden shop．Stick with that stuff．2．Expose it to reasonable sun，shade，and temperaturesAll plants need sunshine （remember photosynthesis（光合作用），just varying levels of it．Succulents are flexible，but they won't do well in darkness or in sweltering direct sun．Moving the succulent in and out of reasonable levels of sunlight will help it thrive．3．Don't over﹣water．As a rookie like me，a person lacking in experience，this was definitely one of my mistakes﹣too much TLC （Tender Love Caring）．The problem is，no one can really tell you how often to water your succulent；you have to monitor it yourself．Depending on your climate，the soil will dry out at varying speeds．Water only when the soil has completely dried from the previous watering．Succulents won't quickly die for lack of water，but they do need it．Allowing the water to drain completely through the soil is the best way to avoid root rot．Otherwise，a misting bottle can be helpful to regulate water quantities．4．"Plant food" is not a joke．I used to think that "plant food" was just a marketing ploy（营销手段）．It's not．Since these plants aren't growing in their natural habitats，they can't absorb the nutrients （e．g，calcium）that they naturally need．Cactus/succulent food is cheap and will last a long time；you only need one drop for every gallon of water．5．Give them air circulation．Contrary to popular belief，succulents won't thrive in a closed container （like a terrarium with a lid）．They need air．6．They need room to grow．Little succulents are cute and cheap，but they'll stay that size unless you occasionally repot them．Some succulents can grow to be over ten feet tall，while others will comfortably grow within a foot or two．Occasionally repotting them might mean re﹣creating a pretty arrangement，but it will help the plants live longer．Unless the dirt is already damp，give the succulents some water before repotting．The new potting soil will be pretty dry，so the extra water will spread out．Best of lucky，everyone! May you have a beautiful windowsill with succulents that thrive!第五部分书面表达（共1小题，满分20分）48．请阅读下面短文．并按照要求用英语写一篇150词左右的文章．The national box office set a record in 2017，almost 56 billion yuan，up 13 percent from 2016．Last year，there were 92 films whose revenue（收入）exceeded 100 million yuan each including 51 Chinese films．About 1.62 billion tickets were bought，up 18 percent year﹣on﹣year．In 2017，the Chinese film industry produced 798 dramas，32 animation films and 44 documentaries in all．Fifteen films earned more than 1billion yuan each at the box office，up from nine in 2016．In the coming days，records will likely be broken and history will be made as China's film industry appears to be on the turning point of a new era，industry insiders said．This year，the number of new film releases，box﹣office earnings，and even stock﹣market performance of shares listed entertainment companies and expected to be higher，they said．Filmgoers' reviews have had an increasingly significant impact on the box office more than other factors such as the participation of pop celebrities in pre﹣release promotions，a media professor said．Also，viewers are no longer getting influenced by big names alone．They don't care whether the film is Chinese，Hollywood，European，or Indian，as long as it has substance（内容）．Evena low﹣budget film with little﹣known cast and crew could emerge as a hit，industry observers said．【写作内容】。

(时间:100分钟总分:120分)命题:夏广平审核:徐钱一、单项选择题(本题共12小题,每小题3分,共36分,每小题只有一个．．．．选项符合题意.)1.关于布朗运动,下列说法中正确的是（）A.温度越高,布朗运动越剧烈B.颗粒越大,布朗运动越剧烈C.阳光下看到灰尘飞舞,灰尘的运动就是布朗运动D.打开香水瓶香味充满房间,这是因为香水分子在做布朗运动2.在甲、乙、丙三种固体薄片上涂上蜂蜡薄层,用烧热的针接触其背面上的某一点,蜡熔化的范围如图(甲)、(乙)、(丙)所示,甲、乙、丙三种固体在熔化过程中温度随加热时间变化的图象如图(丁)所示,则（）A.甲、乙为非晶体,丙是晶体B.甲、丙为非晶体,乙是晶体C.甲、丙为晶体,乙是非晶体D.甲为单晶体,乙为非晶体,丙为多晶体3.关于液晶和液体表面张力,下列说法中正确的是（）A.液晶是液体和晶体的混合物B.液晶既具有流动性,又具有光学性质各向异性C.水黾能够停在水面上,是由于它受到水的浮力大于其重力的缘故D.小草上的露珠呈球形,是由于液体表面张力使其表面积具有扩张到最大趋势的缘故4.关于热力学定律,下列说法中正确的是（）A.做功和热传递在改变内能的方式上是不同的B.只要对内燃机不断改进,就可以把内燃机得到的内能全部转化为机械能C.满足能量守恒定律的物理过程都能自发进行D.热量只能从高温物体传到低温物体,不能从低温物体传到高温物体5.若用1||E 表示氢原子处于基态时能量的绝对值,处于第n 能级的能量为12n E E n=,则在下列各能量值中,可能是氢原子从激发态向基态跃迁时辐射出来的能量的是（ ） A. 1||4E B.13||4E C.17||8E D.1||16E 6.14C 是一种半衰期是5730年的放射性同位素,若考古工作者探测到某古木中14C 的含量为原来的14,则该古树死亡的时间距今大约（ ） A. 22920年B. 2856年C. 5730年D. 11460年7.关于饱和汽和相对湿度,下列说法中错误的是（ ） A.使未饱和汽变成饱和汽,可采用降低温度的方法B.空气的相对湿度越大,空气中水蒸气的压强越接近饱和汽压C.密闭容器中装有某种液体及其饱和蒸汽,若温度升高,同时增大容器的容积,容器中仍有液体,饱和汽压可能会减小D.相对湿度过小时,人会感觉空气干燥8.如图所示,一个向右开口的汽缸放置在水平地面上,活塞可无摩擦移动且不漏气,汽缸中间位置有小挡板.初始时,外界大气压为0p ,活塞紧压小挡板处,现缓慢升高缸内气体温度,则如图所示的p T -图象能正确反应缸内气体压强变化情况的是（ ）9.用不同频率的光分别照射钨(W )和锌(Zn ),产生光电效应,根据实验可画出光电子的最大初动能k E 随入射光频率v 变化的k E v -图线.已知钨的逸出功是4.54eV ,锌的逸出功为4.62eV ,若将二者的图线画在同一个k E v -坐标系中,则正确的图是（ ）10.如图所示,在光滑水平面上,有质量分别为2m 和m 的A B 、两滑块,它们中间夹着一根处于压缩状态的轻质弹簧(弹簧与A B 、不拴连),由于被一根细绳拉着而处于静止状态.当剪断细绳,在两滑块脱离弹簧之后,下述说法正确的是（ ）A.两滑块的动量大小之比:2:1A B p p =B.两滑块的速度大小之比:2:1A B v v =C.两滑块的动能之比:1:2kA kB E E =D.弹簧对两滑块做功之比:1:1A B W W =11.如图所示,光滑水平面上有两个大小相同的钢球A B 、,A 球的质量大于B 球的质量.开始时A 球以一定的速度向右运动, B 球处于静止状态.两球碰撞后均向右运动.设碰前A 球的德布罗意波长为1λ,碰后A B 、两球的德布罗意波长分别为2λ和3λ,则下列关系正确的是（ ）A. 123λλλ==B. 123λλλ=+C. 23123λλλλλ=-D. 23123λλλλλ=+12.绿色植物在光合作用中,每放出1个氧分子要吸收8个波长为76.8810m -⨯的光量子,每放出l mol 的氧气,同时植物储存469kJ 的能量,则绿色植物能量转换效率为(普朗克常量346.6310J s h -=⨯⋅)（ ）A. 79%B. 56%C. 34%D. 9%二.多项选择题(本题共8小题,每小题4分,共32分,每小题有多个选项．．．．．符合题意.全部选对的得4分,选对但不全的得2分,有选错或不答的得0分.) 13.下列叙述中符合物理学史的有（ ） A.汤姆孙通过研究阴极射线实验,发现了电子B.卢瑟福通过对α粒子散射实验现象的分析,证实了原子核是可以再分的C.巴耳末根据对氢原子可见光区的谱线分析,总结出了氢原子光谱可见光区波长公式D.玻尔提出的原子模型,彻底否定了卢瑟福的原子核式结构学说14.用0r 表示分子引力与斥力平衡时两分子间的距离,下列各图中可以定性反映分子作用力F 或分子势能P E 随分子间距离r 变化关系的图线是（ ）15.如图所示是一定质量的理想气体的p V -图线,若其状态由A B C A →→→,且A B →等容,B C →等压, C A →等温,则气体在A B C 、、三个状态时（ ）A.单位体积内气体的分子数A B C n n n ==B.气体分子的平均速率A B C v v v >>C.气体分子在单位时间内,对器壁的平均作用力,A B B C F F F F >=D.气体分子在单位时间内,对器壁单位面积碰撞的次数是,A B A C N N N N >> 16.下列现象中,属于克服分子力做功的是（ ） A.手用力撕纸做功 B.将吸在墙上的吸盘用力拉下 C.用力压缩液体D.人压打气筒给自行车打气17.一定质量的理想气体经历一个等压变化从状态1变化到状态2。

金陵中学2017-2018学年度第二学期期末考试高二数学试卷数学I一、填空题:本大题共14小题,每小题5分,共70分.请把答案填在答题卡相应位置上. 1.设集合{2,4}A =,{2,6,8}B =,则AB = .2.已知复数2(12i)z =-,其中i 是虚数单位,则||z 的值是 .3.某校共有教师200人,男学生1200人,女学生1000人.现用分层抽样的方法从所有师生中抽取一个容量为n 的样本,已知从女学生中抽取的人数为50人,那么n 的值为 .4.如图是一算法的伪代码,则输出值为 .5.如图,在长方体1111ABCD A B C D -中, 3cm AB AD ==,12cm AA =,则三棱锥111A AB D -的体积为 .6.在平面直角坐标系xOy 中,若双曲线2221(0)x y m m-=>的一条渐近线方程为0x +=,则实数m 的值为 .7.设各项均为正数的等比数列{}n a 的前n 项和为n S ，若52378,13a a S -==,则数列{}n a 的通项公式为n a = .8.将一颗均匀的骰子连续抛掷2次,向上的点数依次记为,m n ,则“2m n >”的概率是 .9.若实数,x y 满足条件14,23,x y x y -≤+≤⎧⎨≤-≤⎩则42z x y =-的取值范围为 .10.在平面直角坐标系xOy 中,已知()cos f x x =,()g x x =,两曲线()y f x =与()y g x =在区间(0,)2π上交点为A .若两曲线在点A 处的切线与x 轴分别相交于,B C 两点,则线段BC 的为 .11.如图,在平面四边形ABCD 中, O 是对角线AC 的中点,且10OB =，6OD =. 若28DA DC ⋅=-,则BA BC ⋅的值为 .12.若对满足64x y xy ++=的任意正实数,x y ,都有22210x xy y ax ay ++--+≥,则实数a 的取值范围为 .13.在平面直角坐标系xOy 中,记椭圆22221(0)x y a b a b+=>>的左右焦点分别为12,F F ，若该椭圆上恰好有6个不同的点P ,使得12F F P ∆为等腰三角形,则该椭圆的离心率的取值范围是 .14.对于任意的实数,m n ,记min{,}m n 为,m n 中的最小值.设函数21()4f x x a x=++，()ln g x x =-，函数()min{(),()}h x f x g x =,若()h x 在(0,)+∞恰有一个零点,则实数a 的取值范围是 .二、解答题:本大题共6小题,共计90分.解答时应写出文字说明、证明过程.15.在平面直角坐标系xOy 中,设向量(sin ,1)m x =-,2(3cos ,cos )n x x =.(1)当3x π=时,求m n ⋅的值；(2)若[0,]4x π∈，且132m n ⋅=-.求cos2x 的值. 16.如图,在四棱锥P ABCD -中,底面ABCD 是矩形,平面PAD ⊥平面ABCD ,AP AD =,点M 在棱PD 上, AM PD ⊥,点N 是棱PC 的中点,求证：(1) MN ∥平面PAB ; (2) AM ⊥平面PCD .17.如图,在一个水平面内,河流的两岸平行,河宽1(单位:千米)村庄,A B 和供电站C 恰位于一个边长为2(单位:千米)的等边三角形的三个顶点处,且,A C 位于河流的两岸,村庄A 侧的河岸所在直线恰经过BC 的中点D .现欲在河岸上,A D 之间取一点E ,分别修建电缆CE 和EA ,EB .设DCE θ∠=,记电缆总长度为()f θ (单位:千米).(1)求()f θ的解析式；(2)当DCE ∠为多大时,电缆的总长度()f θ最小,并求出最小值.18.如图,在平面直角坐标系xOy 中,已知椭圆22221(0)x y a b a b+=>>的离心率为2,且过点1)2.设F 为椭圆的右焦点, ,A B 为椭圆上关于原点对称的两点,连结,AF BF 并延长,分别交椭圆于,C D 两点.(1)求椭圆的标准方程；(2)设直线,AB CD 的斜率分别为12,k k ,是否存在实数m ,使得21k mk =?若存在,求出实数m 的值;若不存在,请说明理由.19.设数列{}n a 的前n 项的和为n S ,且满足12a =,对*n N ∀∈,都有1(1)2n n a p S +=-+ (其中常数1p >),数列{}n b 满足2121log ()n n b a a a n=.(1)求证:数列{}n a 是等比数列； (2)若220172p =,求2018b 的值；(3)若*k N ∃∈,使得2212k p +=,记3||2n n c b =-,求数列{}n c 的前2(1)k +项的和. 20.在平面直角坐标系xOy 中,已知函数()1n (R)f x c x c =∈的图像与直线2y x e=相切,其中e 是自然对数的底数.(1)求实数c 的值； (2)设函数()()a h x ax g x x =--在区间1(,e)e内有两个极值点. ①求实数a 的取值范围；②设函数()h x 的极大值和极小值的差为M ,求实数M 的取值范围 .高二数学Ⅱ(附加题)21.已知矩阵 2 11 3M -⎡⎤=⎢⎥⎣⎦， 1 12 1N ⎡⎤=⎢⎥-⎣⎦. (1)求1()MN -；(2)在平面直角坐标系xOy 中,求直线:210L x y +-=在M 对应的变换T 作用下所得直线L '的方程.22.在直角坐标系xOy 中,以原点O 为极点,以x 轴的非负半轴为极轴,取与直角坐标系xOy相同的长度单位,建立极坐标系.设曲线C 的参数方程为sin x y θθ⎧=⎪⎨=⎪⎩,(θ为参数,[0,2]θπ∈),直线l 的极坐标方程为cos()4p πθ-=(1)写出曲线C 的普通方程和直线l 的直角坐标方程；(2)求曲线C 上的点到直线l 的最大距离.23.假定某篮球运动员每次投篮命中率均为(01)p p <<.现有3次投篮机会,并规定连续两次投篮均不中即终止投篮,已知该运动员不放弃任何一次投篮机会,且恰好用完3次投篮机会的概率是2125. (1)求p 的值；(2)设该运动员投篮命中次数为X ,求X 的概率分布及数学期望()E X .24.如图,已知正四棱柱1111ABCD A B C D -的底面边长为2,侧棱长为3, 1AE A B ⊥,垂足为F ,AE 交1B B 于点E .(1)求证: 1D B ⊥平面AEC ;(2)记直线AE 与平面1ACD 所成的角θ,求sin θ的值.试卷答案一、填空题. 1. {2,4,6,8} 2. 5 3. 120 4. 45. 37. 31n-8.169. [5,13] 10.311. 36 12. 10(,]3-∞ 13. 111(,)(,1)32214. 5{|4a a <-或3}4a >- 二、解答题.15. 解(1)当3x π=时，1]m =-，1]4n =， 所以311442m n ⋅=-=.(2) 2cos cos m n x x x ⋅=-112cos2222x x =-- 1sin[2]62x π=--，若122m n ⋅=-.则11sin[2]6222x π--=-，即sin[2]6x π-=. 因为[0,]4x π∈，所以2663x πππ-≤-≤，所以cos[2]6x π-= 所以cos2cos[[2]]66x x ππ=-+cos[2]6x π=--1sin[2]62x π-⨯12=-=16.证明(1)因为在PAD ∆中, ,AP AD AM PD =⊥， 所以点M 是棱PD 的中点. 又点N 是棱PC 的中点, 所以MN 是PDC ∆的中位线, 所以MN DC ∥. 因为底面ABCD 是矩形, 以AB DC ∥, 所以MN AB ∥.又AB ⊂平面PAB , MN ⊄平面PAB ,所以MN ∥平面PAB . (2)因为平面PAD ⊥平面ABCD , CD ⊂平面ABCD ， 平面PAD平面,ABCD AD CD AD =⊥，所以CD ⊥平面PAD .又AM ⊂平面PAD ,所以CD AM ⊥. 因为CD AD ⊥,CD AM ⊥, CD PD D =,CD ⊂平面PCD ,PD ⊂平面PCD ,所以AM ⊥平面PCD .17.解(1)易得AD 垂直平分BC ，1CD BD ==则1cos CE EB θ==，tan ED θ=，tan AE θ=，于是11()cos cos f θθθ=++2sin tan cos θθθ-=+因为E 在CD 之间,所以03πθ<<，故2sin ()cos f θθθ-=+，03πθ<<.(2) 22cos (2sin )(sin )()cos f θθθθθ----=，03πθ<<， 令()0f θ=,得1sin ,26πθθ==， 故当06πθ<<，()0f θ<，()f θ递减,当sin 62ππθ<<,()0f θ>,()f θ递增,所以,当6πθ=时, min ()()6f f πθ==12-+=答:当6DCE π∠=时, ()f θ最小值为18.解(1)设椭圆的方程为22221(0)x y a b a b+=>>，c =，由题意知22311,4c a a b ⎧=⎪⎪⎨⎪+=⎪⎩ 解得2,1,a b =⎧⎨=⎩所以椭圆的方程为2214x y +=. (2)设00(,)A x y ,则00(,)B x y --,010y k x =,又F , 所以直线AF的方程为y x =-.由221,4y x x y ⎧=-⎪⎪⎨⎪+=⎪⎩消去y ，得2200(7)x x --20070x -+=.因为0x x =是该方程的一个解,所以点C的横坐标C x =又点(,)C C C x y在直线y x =-上，所以C C y x =-=C的坐标为 同理,点D的坐标为，所以2k =101472y k x ==， 即存在7m =,使得217k k =.19.(1)证明:因为*n N ∀∈,都有1(1)2n n a p S +=-+，21(1)2n n a p S ++=-+所以两式相减得211(1)n n n a a p a +++-=-, 即21n n a pa ++=，当1n =时211(1)2a p a pa =-+=，所以*1,()n n a pa n N +=∈，又因为1p >,所以11n nn n a a p p++=， 所以数列{}n na p是常数列, 112,2n n n n a a a p p p p -===， 所以{}n a 是以2为首项, p 为公比的等比数列.(2)由(1)得12n n a p -=.2121log ()n n b a a a n==(1)221log (2)n n np n -=1(1)()2017n n n n -+所以20182b =.(3)由(1)得12n n a p -=.2121log ()n n b a a a n==(1)221log (2)n n n p n -=(1)2121log (22)n n n k n -+1121n k -=++. 因为322322(21)n n k b k ---=+， 所以当11n k ≤≤+时, 32n n c b =-，当2n k ≥+时，32n n c b =-. 因此数列{}n c 的前2(21)k +项的和22k T +121()k b b b +=-++++2222()k k k b b b ++++++0121k k +++=-++(1)(2)2+121k k k k ++++++ (1)221k k k +=-++2(1)(22)(1)22121k k k k k k ++++=++. 20. (1)设直线2y x e =与函数()1n f x c x =相切于点00(,1n )P x c x ，函数()1n f x c x =在点00(,1n )P x c x 处的切线方程为: 0001()c y c nx x x x -=-，02c x e=， 把0,0x y ==代入上式得0,2x e c ==. 所以,实数c 的值为2. (2)①由(1)知()21n ah x ax x x=--, 设函数()h x 在区间1(,e)e内有两个极值点1212,()x x x x <，令22()a a h x a x x x'=+--2220ax x ax -+==, 则220ax x a -+=,设2()2m x ax x a =-+,因为121x x =,故只需0,20,()0,am e ∆>⎧⎪⎪>⎨⎪>⎪⎩,所以, 2211e a e <<+.②因为121x x =,所以，121()()M f x f x ax =-=1221221n (21n )a ax ax x x x ----- 11121n a ax x x =---1111(21n )a ax x x -- 21112221n aax x x =--由21120ax x a -+=,得12121x a x =+,且111x e<<. 12111211222121x x x M x x x +=-+222111211121n 4(1n )12x x x x --=-+. 设21x t =,211t e <<,令11()4(1n )+12t t t t ϕ-=-， 221()4()(+1)2t t t ϕ'=-222(1)0(1)t t t --=<+， ()t ϕ(在21(,1)e 上单调递减,从而21(1)()()t e ϕϕϕ<<， 所以,实数M 的取值范围是28(0,)1e +. 高二数学Ⅱ（附加题）21. 解(1)由题知 2 11 3MN -⎡⎤=⎢⎥⎣⎦ 1 10 32 17 2⎡⎤⎡⎤=⎢⎥⎢⎥--⎣⎦⎣⎦，所以0 3)2l 7 det(2MN ⎡⎤==-⎢⎥-⎣⎦， 根据逆矩阵公式,得121 217)1 03(MN -⎡⎤⎢⎥=⎢⎥⎢⎥⎢⎥⎣⎦.(2)设由L 上的任意一点(,)P x y '''在T 作用下得到L '上对应点(,)p x y .由 2 11 3x x y y '-⎡⎤⎡⎤⎡⎤=⎢⎥⎢⎥⎢⎥'⎣⎦⎣⎦⎣⎦，即2,3'x y x x y y ''-=⎧⎨''+=⎩解得3+72'7x y x y x y ⎧'=⎪⎪⎨-⎪=⎪⎩，因为210x y ''+-=,所以3221077x y y x +-⨯+-=，即5470x y +-=.即直线L 的方程为5470x y +-=. 22.解(1)由,sin ,x y θθ⎧=⎪⎨=⎪⎩得22:13x C y +=，由cos ()4p πθθ-=cos sin 4p p θθ+=,即:40l x y +-=.(2)在22:13x C y +=上任取一点,sin )P θθ(02)θπ≤≤，则点P 到直线l的距离为d=|2sin()4|πθ+-=，02θπ≤≤， 当sin()13πθ+=-，即76πθ=时，max d =23. 解(1)设事件A :“恰用完3次投篮机会”,则其对立事件A :“前两次投篮均不中”, 依题意, ()1()P A P A =-2211(1)25p =--=， 解得35p =.(2)依题意, X 的所有可能值为0,1,2,3, 且24(0)(1)25P X p ==-=, 2(1)(1)P X p p ==-24(1)(1)125p p p +--=， 327(3)125P X p ===， 故(2)1(0)P X P X ==-=54(1)(3)125P X P X -=-==. X 的概率分布列为:数学期望24()2125E X =+⨯54272133125125125+⨯=.24.解(1)如图,以D 为坐标原点,分别以直线1,,DA DC DD 所在直线为x 轴, y 轴, z 轴,建立空间直角坐标系D xyz -，易得1(0,2,3)A B =-,设BE a =,则(0,2,)AE a =，因为1A B AE ⊥,所以1(0,2,3)AB AE ⋅=- (0,2,)430a a ⋅=-=， 解得43a =,即4(0,2,)3AE =, 又1(2,2,3)D B =-,(2,2,0)AC =-, 所以1(2,23)D B AE ⋅=-4 (0,2,)03⋅=,所以1D B AE ⊥, 且1(2,2,3)(2,2,0)0D B AC ⋅=-⋅-=，所以1D B AC ⊥，又AE AC A =，所以1D B ⊥平面AEC . (2) 4(0,2,)3AE =，1(2,0,3)D A =-，1(0,2,3)DC =-， 设平面1ACD 的一个法向量(,,)n x y z =， 则110,0,D A n D C n ⎧⋅=⎪⎨⋅=⎪⎩即230,230,x z y z -=⎧⎨-=⎩令0z =，则3x y ==，即(3,3,2)n =，sin |cos ,AE θ=<|||||AE n n AE n ⋅>=⋅423=2⨯⨯==22.。

绝密★启用前江苏省南京市金陵中学2017-2018 学年第二学期期末考试高二数学试题一、单选题1,,____________.【解析】分析：求出A处切线方程，又因为A又因为A所以线段BC的长度为点睛：熟练记忆导函数公式是解导数题的前提条件，导数的几何意义是在曲线上某一点处的导数就等于该点处切线斜率，是解决曲线切线的关键，要灵活掌握.第II卷（非选择题）请点击修改第II卷的文字说明二、填空题2,【答案】{2,4,6,8}详解：A集合和B集合“加”起来的元素，重复的元点睛：在求集合并集时要注意集合的互异性.3,____________.【答案】5【解析】分析：先将复数z右边化为.4．某校共有教师200人,男学生1200人,女学生1000人.现用分层抽样的方法从所有师,已知从女学生中抽取的人数为50人,____________.【答案】120【解析】分析：根据分层抽样的原则先算出总体中女学生的比例，再根据抽取到女学生的人数计算样本容量n详解：因为共有教师200人,男学生1200人,女学生1000人女学生中抽取的人数为50人所以n=120点睛：分层抽样的实质为按比例抽，所以在计算时要算出各层所占比例再乘以样本容量即为该层所抽取的个数.5．如图是一算法的伪代码,则输出值为____________.【答案】4【解析】分析：按照循环体执行，直到跳出循环详解：第一次循环后：S=7，n=6；第二次循环后：S=13，n=5；第三次循环后：S=18，n=4；所以输出值为4点睛：程序题目在分析的时候一定要注意结束条件，逐次执行程序即可.6．如图,,为____________.【答案】3,=33点睛：在求解三棱锥体积问题时，如果所求椎体高不好确定时，往往要通过等体积转化，找到合适的高所对应的椎体进行计算，体现了数学中的转化与化归思想，要深刻体会.7,____________.x的值为x轴上，又因为该双曲线一条渐近线方程为所以的值为点睛：双曲线渐近线方程：当焦点在x y轴上时为8．，若则数列的通【解析】分析：根据基本量直接计算点睛：在等比数列问题中的未知量为首项和公比，求解这两个未知量需要两个方程，所以如果已知条件可以构造出来两个方程，则一定可以解出首项和公比，进而可以解决其他问题，因此基本量求解是这类问题的基本解法.9．将一颗均匀的骰子连续抛掷2次,则的概率是____________.【解析】分析：骰子连续抛掷2次共有366种详解：一颗均匀的骰子连续抛掷2次,(3,1)，(4,1)，(5,1)，(6,1)，(5,2)，(6,2)6种点睛：古典概型概率要准确求出总的事件个数和基本事件个数，然后根据概率公式.10____________.A点处取得最小值，在C点处取得最大值所以的取值范围为点睛：点睛：线性规划要能够准确画出可行域，尤其是判断每一个不等式代表的是直线的左侧还是右侧时不能出错，常用带点方法判断比较准确。

江苏省南京市金陵中学河西分校2017-2018学年下学期初中七年级期末考试语文试卷注意事项：1．本试卷6页，共100分，其中书写分4分。

考试时间为120分钟。

考生答题全部答在答题卷上，答在本试卷上无效。

2．答题请用0.5毫米黑色签字笔写在答题卷的指定位置，在其他位置答题一律无效。

一、积累与运用（24分）1. 用诗文原句填空（10分）（1）山际见来烟，。

（南朝·吴均《山中杂诗》）（2）深林人不知，。

（唐·王维《竹里馆》）（3），思君不见下渝州。

（唐·李白《峨眉山月歌》）（4），寒光照铁衣。

（南北朝《木兰诗》）（5）马上相逢无纸笔，。

（唐·岑参《逢入京使》）（6），野渡无人舟自横。

（唐·韦应物《滁州西涧》）（7），崔九堂前几度闻。

（唐·杜甫《江南逢李龟年》）（8）苍苍竹林寺，。

（唐·刘长卿《送灵澈上人》）（9），闲敲棋子落灯花。

（宋·赵师秀《约客》）（10），各领风骚数百年。

（清·赵翼《论诗》）2.下列加点字注音完全正确的一项是（）（2分）A.菜畦．qí祈．祷qǐ尽态极妍．yánB.秕．谷bǐ泛滥．làn 义愤填膺．yīnC.嫉．妒jì蠕．动rú略胜一筹．chóuD.讪．笑shàn 告罄．qìng 孜孜．．不倦zī3. 下列书写完全正确的一项是（）（2分）A.锤练滑稽轶序井然B.阔绰仰幕姗姗来迟C.对峙步履养精蓄锐D.赢弱惩戒纭纭众生4. 下列成语运用不恰当．．．的一项是（）（2分）A.足球是当之无愧．．．．的世界第一运动，四年一届的世界杯是全世界的狂欢节。

B.中国男足早就无缘世界杯，他们已经三次无缘亚洲十强，真是可歌可泣．．．．。

C.五届世界杯冠军得主巴西队气冲斗牛．．．．：“我们誓必在主场为巴西赢得冠军。

”D.梅西的个人能力与球队的整体配合相得益彰．．．．，这使阿根廷队夺冠成为可能。

2017-2018学年江苏省南京市金陵中学高二第二学期期末考试地理（选修）试题地理注意事项：1．答题前，先将自己的姓名、准考证号填写在试题卷和答题卡上，并将准考证号条形码粘贴在答题卡上的指定位置。

2．选择题的作答：每小题选出答案后，用2B 铅笔把答题卡上对应题目的答案标号涂黑，写在试题卷、草稿纸和答题卡上的非答题区域均无效。

3．非选择题的作答：用签字笔直接答在答题卡上对应的答题区域内。

写在试题卷、草稿纸和答题卡上的非答题区域均无效。

4．考试结束后，请将本试题卷和答题卡一并上交。

第I 卷（选择题）一、单选题下图为“黄土高原局部地区等高线图”，实线是黄土表面等高线，虚线是黄土底面(基岩表面)等高线(单位：m)。

读图，回答下面小题。

1．甲处黄土层的最大厚度可能达到（ ）A. 26mB. 34mC. 36mD. 44m2．3月21日傍晚，假如天气晴朗，最有可能看到日落的地点是（ ）A. 甲B. 乙C. 丙D. 丁下图为“我国西部地区7月平均气温示意图”。

读图，回答下面小题。

3．下列关于甲处地形及影响其7月等温线分布因素的判断，正确的是（ ） A. 柴达木盆地，太阳辐射 B. 黄河谷地，地形 C. 秦岭山地，大气环流 D. 祁连山地，地形 4．有关乙地成为我国夏季高温中心的说法，错误的是（ ） A. 气候干旱，天气晴朗，太阳辐射强 B. 纬度较高，太阳辐射受到的削弱作用小 C. 盆地地形，热量不易散失 D. 地表缺植被保护，比热容小，升温快 格林尼治时间2016年3月17日零时18分45秒，爱尔兰天文爱好者拍摄到一颗天体碰撞木星表面的照片。

据此回答下面小题。

5．拍摄照片时，北京时间大约为（ ） A. 16日16时 B. 16日22时 C. 17日8时 D. 17日20时 6．有人称木星为“地球的盾牌”，保护着地球等其他星体。

你认为较合理的解释是，木星（ ）A. 距离太阳更近，削弱了太阳射向地球的紫外线辐射 此卷只装订不密封班级姓名准考证号考场号座位号B. 公转轨道在地球与小行星带之间，阻挡小行星撞击C. 公转方向与地球一致，构成了安全稳定的宇宙环境D. 体积、质量巨大，吸引部分可能撞向地球的小天体2016年1月6日，中国两架民航客机先后从海南省海口市美兰机场起飞，成功试飞南沙永暑礁新建机场。

金陵中学2017-2018学年度第二学期期末考试高二化学（选修）试卷选择题(共40分)单项选择题(本题包括10题，每小题2分。

共20分。

每小题只有一个选项符合题意。

)1.下列元靠第一电离能最大的是A.BB.CC.ND.O2.在分子中，羰基(-CO-)碳原子与甲基(-CH3)碳原于成键时所采取的杂化方式分别为A.sp2杂化；sp3杂化B.sp3杂化；sp3杂化C.sp3杂化: sp2杂化D.sp2杂化；sp2杂化3.下列各组物质各自形成晶体，均属于分子晶体的化合物是A.NH3、HD、C10H8B.PCl3，CO2、H2SO4C.SO2、SiO2、P2O5l4、Na2S、H2O24.下列说法正确的是A.凡是放热反应都是自发的，因为吸热反应都是非自发的B.自发反应的熵一定增大，非自发反应的熵一定减小C.常温下，反应C(s)+CO2(g)2CO(g)不能自发进行，则该反应的∆H>0D.反应2Mg(s)+CO2(g)=C(s)+2MgO(s)能自发进行，则该反应的∆H>05.加热蒸干下列溶液，之后再进一步灼烧，最終所得固体的成分和原溶液中溶质相同的是A. FeCl3溶液B.Na2CO3溶液C.NaHCO3溶液D.KMnO4溶液6.与盐类水解无关的化学应用是A.明矾用于净水B.草木灰不能与铵态氮肥混合使用C.氧化铁溶液腐蚀铜板D.用硫酸铝和碳酸氢钠溶液作为泡辣灭火器的反应物7.研究人员最近发现了一种“水”电池。

这种电池在海水中的总反应可表示为：5MnO2+2Ag+2NaCl=Na2Mn5O10+2AgCl。

下列有关“水”电池放电时的说法正确的是A.负极反应式:Ag+Cl-e-=AgC1B.AgCl是还原产物C.Na+不断向“水”电池的负极移动D.每生成1mol Na2Mn5O10转移1mol电子8.结合右图判断，下列叙述正确的是A.I和II中Fe电极均被保护B.I和II中的负极反应均为Fe-2e-=Fe2+C.I和II中的正极反应均是O2+2H2O+4e-=4OH-D.I和II中分别加入少量K3Fe(CN)6溶液，装置II中可见明显的蓝色沉淀9.常温下，下列离子浓度关系正确的是A. Na2S溶液中，c(Na+)=c(H2S)+c(HS-)+ 2c(S2-)B.将浓度均为0.1mol/L的KOH溶液和KHSO3溶液等体积混合，所得溶液中:c(OH-)=c(H+)+c(HSO3-)+2(H2SO3)C.0.1mol/LCH3COONa和0.1mol/LNaClO混合溶液中:c(Na+)=c(C10-)+c(CH3C0O-)D.常温下，加水稀释Na2CO3溶液， m(H+)增大，n(OH-)减小10.已知25℃时，CaCO3饱和溶液中c(Ca2+)=5.3×10-5mol/L；MgCO3饱和溶液中c(Mg2+)=2.6×10-3mol/L。

江苏南京金陵中学2018—2018学年第二学期期末试卷高一语文第I卷一、（8分）1、下列各组词语中，加点字的读音全都正确的一组是A、芜．杂wú镣．铐liáo 蜕．变tuì厥．词juãB、夷．平yí遏．抑â菁．华qīng 笞．刑chīC、牛虻．mãng 虫豸．zhì恫．吓dîng 悄．然qiǎoD、神甫．pǔ石栈．zhàn 吸吮．shǔn 猿猱．náo2、下列各组词语中，没有错别字的一组是A、脸颊沉湎暧昧力挽狂澜B、纯萃缄默震撼融汇贯通C、杀戳菲薄破釜沉舟烦燥D、得心应手安祥诅咒经渭分明3、下列句子中，加点成语使用恰当的一项是A、这些食品是交给姐姐保管的，可她并不是一个从长计议．．．．的人，常常领着我们将下一日的提前消耗掉，造成寅吃卯粮的局面。

B、这件事对我无异于晴天霹雳——一块珍藏多年价值连城的璧玉，顷刻变成一块一文．．不名．．的瓦片。

C、他最近出版了一本文不加点．．．．、几乎没有注释的旧体诗集子，这样的书，读起来确实累人。

D、早在30年代，他就因创作长篇小说《楚之音》而名躁一时．．．．，成为京派作家的后起之秀。

4、下面文学常识正确的一项是A、李白和杜甫都是唐代著名的诗人，分别将古典诗歌推向现实主义和浪漫主义的高峰。

前者有“诗仙”之誉，后者被称为“诗圣”。

B、王勃，字子安，少有才名，被誉为神童；与骆宾王、卢照邻、王维并称为“初唐四杰”；其作品以《滕王阁序》最为著名，本篇又题为“滕王阁诗序”。

C、《琵琶行》是一首长篇叙事诗，是唐代七言歌行体的代表作。

作者白居易为唐中期著名诗人，字乐天，号易安居士，为杜甫之后的又一位伟大的现实主义诗人。

D、李煜，字重光，南唐最后一位君主，世称李后主，与其父李璟并称“南唐二主”，俱为五代著名词人。

代表作有《虞美人》（春花秋月何时了）、《相见欢》（无言独上西楼）等。

金陵中学2017-2018学年度第二学期期末考试英语本试卷满分120分第I卷第一部分英语知识运用（共三节，满分50分）第一节听力理解（共20题，每小题0.5分，满分10分）做题时，先将答案标在试卷上。

录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。

听下面5段对话。

每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1. Why is Ann so upset?A. She failed one of her exams.B. She is worrying about other lesson.C. She has no time to do her math homework.2. What type of food does the woman cat?A. Junk food.B. Healthy food.C. Delivered food.3. What will the man probably do to stay warm?A. Use a blanket.B. Turn on the heater.C. Drink some hot chocolate.4. What are the speakers mainly talking about?A. The man’s career.B. The man’s travel plan.C. The man’s plan after graduating.5. What are the speakers’ opinions about the painting?A. It’s simple.B. It’s colorful.C. It’s complex.听下面5段对话。

每段对话后有几个小题，从题中所给的A、B、C、三个选项中选出最佳选项，并标在试卷的相应位置，听每段对话前，你将有时间阅读各个小题，每小题5秒钟：听完后，各小题给出5秒钟的作答时间。