高考专题格致中学二〇一二第一学期第一次测验.docx

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2021年上海市格致中学高三上学期第一次检测数学试题

4．若行列式中，元素的代数余子式大于 ,则满足的条件是__________．
5．在复平面内，抛物线的焦点所对应的复数是，则 __________．
6．二项式的展开式中的二项式系数和为，各项系数和为，且，则的值是__________．
7．若，则它的反函数是 ________.
8．若一个圆锥的侧面展开图是面积为的半圆面，则该圆锥的体积为.
二、单选题
14．已知、、满足且，则下列选项中不一定能成立的是（）
A． B．
C． D．
15．已知数据 , , ，是上海普通职 ( ， )个人的年收入，设这个数据的中位数为，平均数为，方差为，如果再加上世界首富的年收入，则这个数据中，下列说法正确（）
A．年收入平均数大大增大，中位数一定变大，方差可能不变
9．如图中个点，任意三点构成三角形的概率为__________．
10．在平面直角坐标系中，为双曲线右支上的一个动点．若点到直线的距离大于c恒成立，则是实数c的最大值为
11．定义为数列的“均值”,已知数列的“均值” ，记数列的前项和为，若对任意正整数恒成立，则实数的范围为__________．
故答案为：
【点睛】
本题主要考查代数余子式的相关计算，熟记概念即可，属于基础题型.
5．
【分析】
先由抛物线方程得到焦点坐标，求出复数，进而可求出结果.
【详解】
因为抛物线的焦点为，
所以其所对应的复数为，
因此 .
故答案为
【点睛】
本题主要考查求复数的模，熟记复数的几何意义，以及抛物线的焦点即可，属于常考题型.
(1)求异面直线与所成角的大小(结果用反三角表示)；

高考专题格致中学二〇一一第二学期高考模拟考试.docx

高中数学学习材料马鸣风萧萧*整理制作格致中学二〇一一学年度第二学期高考模拟考试高三年级数学(理科)试卷（共4页）(测试120分钟内完成，总分150分，试后交答题卷)友情提示：昨天，你既然经历了艰苦的学习，今天，你必将赢得可喜的收获！祝你：诚实守信，沉着冷静，细致踏实，自信自强，去迎接胜利！一、填空题：（本大题共14小题，每小题4分，满分56分）。

把答案直接填写在答题卷的相应位置上。

1、已知集合{}0,1,A a =，{}0,3,3B a =，若{}0,3A B =，则A B =_____________。

2、复数2a ii+-在复平面内所对应的点在虚轴上，则实数a =________。

3、在等比数列{}n a 中，18a =，435a a a =⋅，则此数列前n 项和为_________。

4、已知偶函数()f x 在(0,)+∞上为减函数，且(2)0f =，则不等式()()0f x f x x+->的解集为_____________。

5、如图程序框图，若实数a 的值为5，则输出k 的值为_____。

6、在极坐标系中，圆2=ρ与直线cos sin 2ρθρθ+=交于,A B 两点，O 为极点，则OA OB ⋅=_________。

7、下图是底面半径为1，母线长均为2的圆锥和圆柱的组合体，则该组合体的体积为__________。

___姓名________________学号____________准考证号______________2nn =31n n=+开始n =a ，k =0n 为偶数n =1 输出k结束k =k +1是否是否8、若二项式na x x ⎛⎫+ ⎪⎝⎭的展开式中第四项与第六项的二项式系数相等，且第四项的系数与第六项的系数之比为1:4，则其常数项为___________。

9、某类产品按工艺共分10个档次，最低档次产品每件利润为8元.每提高一个档次，每件利润增加2元。

上海市格致中学高一下学期第一次测验数学试题

格致中学二〇二〇学年度第二学期第一次测验高一年级数学试卷（共4页）（测试90分钟内完成，总分100分，试后交答题卷）一、填空题（本题共12题，每题3分，满分36分）.1.已知13sin ,,322ππαα⎛⎫=∈ ⎪⎝⎭，则tan α=________； 2.在与弧度数为2021角终边相同的角中，绝对值最小的角是________；3.方程2cos210x -=的解集是________；4.已知角α的终边上的一点(4,3)(0)t t t ->，则2sin cos αα+=_______；5.若扇形的圆心角是3π，则该扇形面积与其内切圆面积的比值是________；6. sin x x -化成cos()0,02A x A πωϕϕ⎛⎫+><< ⎪⎝⎭的形式为________； 7. 在ABC 中，若52,,124AB B C ππ=∠=∠=，则BC =________； 8. 在ABC 中，4cos b a C a b+=，则cos C 取最小值时，C ∠=________；9.已知,R α∈ sin 2cos 2αα+=tan 2α的值是________； 10. 如果锐角θ满足sin log tan θθ+4cot ,3θ=- 则tan log cos θθ的值是________； 11. 已知(,)αππ∈-，满足tan α是关于方程2210cos x x α++=的两个根中较小的根，则α 的值为________；12. 在ABC 中, 90,C M ∠=是BC 的中点，若1sin ,3BAM ∠= 则sin BAC ∠=________；二、选择题（本题共4小题，每题4分，满分16分）.13 已知角α的终边经过()sin15,cos15P ︒︒-，则2sin α=A. 0B.34C .124- D.124+ 14.一台“傻瓜”计算器只会做以下运算：1减去输入的数并将得到的差取倒数，然后将输出的结果再次输入这台“傻瓜”计算器，如此不断地的进行下去。

2020-2021学年格致中学高一下英语第一次测试

格致中学二〇二〇学年度第二学期第一次测验高一年级英语试卷（共9页）(测试100分钟内完成，总分100分，试后交答题卷)I. Listening Comprehension (18% 1-16题每题1分，17-20题每题0.5分)Section ADirections: In Section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.1. A. Worried and frightened. B. Relaxed and happy.C. Quite embarrassed.D. Deeply ashamed.2. A. Bill has never used a calculator. B. Bill can work better without a calculator.C. Bill is working with a calculator.D. Bill needs a calculator for this work.3. A. To cut his jeans short. B. To go on a diet.C. To wear fitted clothes.D. To buy a pair of jeans.4. A. Having an interview. B. Filling out a form.C. Talking with a friend.D. Asking for information.5. A. Put her report on his desk. B. Read some papers he recommended.C. Mail her report to the publisher.D. Improve some parts of her paper.6. A. Make some coffee. B. Meet the woman at the library.C. Continue to read.D. Go out with some friends.7. A. The man should buy a different meal ticket every month.B. Buying the meal ticket won’t save the man any money.C. It is better for the man to pay for each meal separately.D. The price of a meal may vary from month to month.8. A. She’s upset that she missed the television program.B. She doesn’t think the television program was funny.C. She doesn’t like talking about television programs.D. She watched the television program at a friend’s house.9. A. He doubts the woman’s words. B. He hasn’t read the novel yet.C. He enjoyed reading the novel a lot.D. He is not interested in the novel at all.10. A. The talks haven’t started yet. B. They have come to a general agreement.C. The talks haven’t achieved much.D. The talks broke down and went no further.Section BDirections: In Section B, you will hear two short passages and one longer conversation, and you will be asked several questions on each of the passages and the conversation. The passages and the conversation班级____________姓名________________学号____________准考证号_____________will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. They learn singing and dancing. B. They attend outdoor music festivals.C. They work on the farm for charity.D. They volunteer to work for others.12. A. On the beach. B. In a park. C. On a farm. D. In a stadium.13. A. It is run on a profit-making basis. B. It has achieved growing success.C. Fans can have free lunch there.D. Only superstars are invited to perform. Questions 14 through 16 are based on the following passage.14. A. The number of refugees is increasing sharply.B. Most refugees cannot get necessary services.C. Many refugee children cannot receive education.D. More children cannot afford to go to university.15. A. No host nations want to change education systems.B. It is impossible to find so many extra teachers.C. Parents can’t afford to send their kids to school.D. The refugee population grows but there’s not enough money.16. A. The necessity of education.B. The prohibition of child labor.C. The victims of armed conflicts.D. The living conditions of the poor.Questions 17 through 20 are based on the following conversation.17. A. It has started a week-long promotion campaign.B. It has just launched its annual anniversary sales.C. It offers regular weekend sales all the year round.D. It specializes in the sale of men’s suits.18. A. Price reductions for its frequent customers.B. Gift cards for customers with any purchases.C. Free delivery of purchases for senior customers.D. Price adjustments within seven days of purchase.19. A. Mail a gift card to her. B. Allow her to buy on credit.C. Credit it to her account.D. Give her cash directly.20. A. It has already been sold out. B. It will be sent to the woman by mail.C. It is not available for the moment.D. It is one of the items on sale.II. Grammar and Vocabulary I (17%)Section A (10%)Directions: Beneath each of the following sentences there are four choices marked A, B. C and D. Choose the one answer that best completes the sentence.21.It’s no use _________ without taking any action.A. complainB. tocomplain C. complaining D. beingcomplaining22.The rare fish, _________ from the cooking pot, has been returned to the sea.A. rescuedB. was rescuedC. being rescuedD. rescuing23.Is this museum _________ they visited last month?A.whichB.whereC. the oneD.in which24.I’ll see to it _________ everything is ready in time.A.ifB. whetherC.whatD.that25. When we first arrive in _________ New District twenty years ago, the area was covered with grass.A. what is nowB.nowC. which is nowD. now is26. You’ll find taxis waiting at the bus station _________ you can hire to reach your host family.A. whichB. whereC. whenD. as27. It wasn’t quite certain _________ , but possibly he had gone to sleep while he was driving.A. how he had crashedB. why he had crashedC. why had he crashedD. how had he crashed28.When Peter speaks in public, he always has trouble _________ the right things to say.A. to think ofB. thinking ofC. thought ofD. think of29. She does not stick to her exercise and a balanced diet. If she _________ , she would remain slim and healthy.A. doesB. would doC. didD. should30. Fears have been haunting him constantly during the past five days_________ he would be expelled from school.A. whenB. whichC. wheneverD. thatSection B (7%)Directions:Fill in each blank with a proper word chosen from the box. Each word can only be used once.Bill transition. For millenniums most people’s lives had a certain ___31___. You went to school to learn a trade or a skill-baking, farming or accounting. Then you could go into the workforce and make a good living repeating the same skill over the course of your career.But these days machines can do pretty much anything that’s ___32___. The new world requires a different sort of person. Drayton calls this new sort of personal changemaker.Changemakers are people who can see the patterns around them, identify the problems in any situation, figure out ways to solve the problem, organize fluid teams, lead collective action and then ___33___ adapt as situations change.For example, Ashoka fellow Andrés Gallardo is a Mexican who lived in a high crime neighborhood. He created an app, called Haus, that allows people to ___34___ with their neighbors. The app has a panic button that helps ___35___ everybody in the neighborhood when a crime is happening. It allows neighbors to organize, chat, share crime statistics and work together.To form and lead this community of communities, Gallardo had to possess what Drayton calls “cognitive empathy-based living for the good of all.” Cognitive empathy is the ability to perceive how people are feeling in evolving circumstances. “For the good of all” is the capacity to build teams.The central challenge of our time, Drayton says, is to make everyone a changemaker. In an earlier era, he says, society realized it needed universal ___36___. Today, schools have to develop thecurriculums and assessments to make the changemaking mentality universal. They have to understand this is their criteria for success.Ashoka has studied social movements to find out how this kind of ___37___ shift can be promoted. It turns out that successful movements take similar steps.III. Reading Comprehension (33%)Section A (15%)Directions: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.You’ve been painting for a few years, and maybe you have even sold a painting or two. Are you ready to ___38___ the title of an amateur artist?Distinguishing green hand from professional artists is a ___39___ task. It is not just a matter of your ability to create nice paintings. It’s not only about painting techniques. And for most cases, it doesn’t happen ___40___. Very few artists become overnight success without years of struggle and suffering.To turn professional, people find it critical to develop a personal style. What makes your paintings ___41___ among other paintings out there? Are your paintings standing out unmistakably directed to you as the creator? A personal style comes along with technique, painting medium, and subject and it tends to develop gradually over time. You ___42___ it through unconscious and constant exploring and self-shaping. Style does not mean that you are painting the same subject or using the same painting medium. Salvador Dali used to use many artistic media, but they all have a ___43___ Dali style. Style refers to the emotions and thoughts delivered by your paintings, which people can identify with. Their ___44___ of the painter is then a sure thing.Artists talk about their ___45___ all of the time. What gets you out of bed every morning to paint? How do you find the energy to have all your time devoted to painting? ___46___, we all love to do what we do and we get a satisfaction out of creating. For the professional artist, it goes beyond that. Some artists wish to convey a deep message concerning life, society or even politics. Others simply seek ___47___ returns to cover kids’ tuition fees or pay family bills. Yet, all professional artists know that they have to keep working to achieve the goals.Many amateur artists passively wait for ___48___ to come. If they are not in the mood, they do not bother wasting the time. They sometimes allow themselves to be occupied by events like parties.Professionals are never easily ___49___ or torn away from their art work in progress. Focused on their work so much, some even regard spending time outside their ___50___ as crime. ___51___ is their secret to high productivity.Besides, professional artists are constantly prepared to grab new ideas for the next painting, which they believe is sure to be better than the previous one. The belief that there is always room for ___52___ keeps driving them forward in the art world where many masters have come along.38. A. step beyond B. turn off C. see through D. make up39. A. rewarding B. tricky C. formal D. temporary40. A. individually B. thoroughly C. instantly D. sincerely41. A. unique B. superior C. practical D. reliable42. A. acquire B. transfer C. imitate D. analyze43. A. recent B. distinct C. modest D. logical44. A. preservation B. employment C. adaption D. recognition45. A. background B. significance C. motivation D. routine46. A. To sum up B. In contrast C. In addition D. In general47. A. academic B. global C. financial D. original48. A. inspiration B. fame C. guidance D. solution49. A. offended B. dominated C. distracted D. rewarded50. A. studio B. bedroom C. garage D. garden51. A. Reflection B. Devotion C. Creativity D. Illustration52. A. negotiation B. profit C. criticism D. improvementSection B (18% 53-59题每题2分，60-63题每题1分)Directions: Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.（A）An American exploration company, the Nauticos Corporation, has found the wreck of an ancient Greek ship in a very deep area of the Mediterranean Sea. It may be the deepest ancient shipwreck ever found. The discovery questions a long-held idea that ancient sailors didn’t have skills needed to guide ships in open seas.The ancient ship lay more than 3,000 meters below the surface of the Mediterranean. The wreck was more than 489 kilometers from the Island of Corsica. Scientists believe the ship is about 2,300 years old.The company was looking for an Israeli submarine that had disappeared more than thirty years ago. Nauticos official Thomas Dettweiler said two company ships were searching for the Israeli submarine. He supervised the operation from a ship with sonar equipment. A sonar system uses sound waves to find and identify objects under the water. A second ship carried a vehicle for deep-sea searches.During the search, one ship’s sonar began making strange sounds. Mr. Dettweiler thought this meant they had found the lost submarine. He ordered the other ship to send down the deep-sea vehicle to search.But a video camera on the vehicle did not show a submarine. Instead, it showed many large clay containers lying on the bottom of the sea. These containers are called amphoras. Mr. Dettweiler was excited. He says he knew that the 2,000 amphoras they had found meant they had discovered an important shipwreck. In ancient times such containers held wine, olive oil and other goods.Nauticos and the scientists hope to do more research in the area soon. Mr. Dettweiler believes four other ancient ships may be nearby. He says finding shipwrecks from different time periods could be especially important. It could be the first evidence of continued open-sea trading in the ancient world.53. Which of the following statements is NOT true?A. It is still believed that ancient sailors didn’t know how to guide ships in open sea.B. The ancient ship was discovered by an American exploration company.C. The exploration company happened to find the ancient ship in the sea.D. More ancient ships were likely to be discovered in the neighborhood of the wreck.54. A sonar system ______.A. helps people to find any objectB. can only be used to look for shipsC. is a technology related to sea wavesD. can only be used under the water55. The company knew they had found an ancient shipwreck when ______.A. The sonar system began to make soundsB. The video camera showed the picture of a wrecked shipC. They found amphoras, clay containers for wine or oilD. They found wine, olive oil and other products under the sea56.Mr. Dettweiler hopes to find more ancient ships because ______.A. the ancient ships are useful even for today’s tradingB. these ancient ships show the importance of trading in open seasC. they are important in the Greek historyD. they may prove there was open-sea trading in ancient times(B)Memory expert Professor Jemima Gryaznov answers your most common questions about memory.1. ____________We remember the things that have strong connections in our mind, especially emotional connections. Childhood memories are often very emotional: we experience things for the first time so we have strong feelings of fear or excitement. Retelling events also helps to fix them in our memories and interesting or funny stories from our childhood are often told again and again!2. Do some people really have a photographic memory?It is well known that some people have an extraordinary memory. Daniel Tammet, for example, can remember the first 22,500 digits of pi and Stephen Wiltshire can draw a detailed picture of a city from memory after flying over it in a helicopter. However, neither Daniel nor Stephen have a photographic memory. They are good at remembering particular things for a limited time. A person with a photographic memory could remember every detail of a picture, a book or an event many years later. No one has yet proved that they have a photographic memory in a scientific test.3. Is computer memory better than human memory?That depends on what you mean by ‘better’! Information in a computer is stored in separate pieces. Human memory is stored in a different way. Each piece of information is connected to many other pieces. That’s why a particular smell can bring back memories of a holiday or a person. The problem with human memory is that it is messy and not very accurate. The problem with computer memory is that it can’t make connections between pieces of information—it isn’t creative.4. I’m 24. Is my memory getting worse?Not yet, but it will do soon. Our memory reaches its full power at the age of 25. At that point we can remember up to 200 pieces of information a second. After this age, however, the brain starts to get smaller. By the age of 40 we are losing 10,000 brain cells every day. By middle age our memory is significantly worse than when we were young.5. Is it possible to remember early childhood?Scientists used to believe that it was impossible to remember very early childhood, but recent research shows that babies are much cleverer than we previously thought. Some people really can remember being a baby. Others, however, remember nothing before the age of five or even ten!57. Which of the following questions best fits the blank in the passage?A. What can we do to improve our memory as we grow older?B. Can childhood memories help us remember what has happened recently?C. How do we establish emotional connections with our childhood experiences?D. Why can I remember events in my childhood but not what happened last week?58. What can we learn about photographic memory?A. Only some of us can benefit from it.B. There is no reliable evidence that it exists.C. We cannot acquire it without specialized training.D. It enables us to remember details in a limited time.59. Which of the following statements is True according to the passage?A. In most cases information is separately stored in human memory.B. Human’s ability to memorize things declines as the brain gets smaller.C. Computer memory is better than human memory from many perspectives.D. Whether we can remember our early-childhood needs more scientific research.（C）Of all the components of a good night’s sleep, dreams seem to be least within our control. In dreams, a window opens into a world where logic is suspended and dead people speak. A century ago, Freud stated his revolutionary theory that dreams were the disguised(伪装的) shadows of our unconscious desires and fears; by the late 1970s neurologists had switched to thinking of them as just mental noise —— the random byproducts of the neural-repair work that goes on during sleep. Now researchers suspect that dreams are part of the mind’s emotional thermostat, regulating moods while the brain is “off-line". And one leading authority says that these intensely powerful mental events can be not only influenced but actually brought under conscious control, to help us sleep and feel better. “It's your dream,” says Rosalind Cartwright, chair of psychology at Chicago’s Medical Center. “If you don't like it, change it.”The link between dreams and emotions shows up among the patients in Cartwright’s clinic. Most people seem to have more bad dreams early in the night, progressing toward happier ones before awakening, suggesting that they are working through negative feelings generated(产生) during the day. Because our conscious mind is occupied with daily life, we don’t always think about the emotional significance of the day’s events——until, it appears, we begin to dream.And this process need not be left to the unconscious. Cartwight believes one can exercise conscious control over repeated bad dreams. As soon as you awaken, identify what is upsetting about the dream. Visualize how you would like it to end instead; the next time it occurs, try to wake up just enough to control its course. With much practice people can learn to, literally, do it in their sleep.At the end of the day, there’s probably little reason to pay attention to our dreams at all unless they keep us from sleeping or “we wake up in a panic,” Cartwright says. Terrorism, economic uncertainties and general feelings of insecurity have increased people’s anxiety. Those suffering from persistent nightmares should seek help from a therapist. For the rest of us, the brain has its ways of working through bad feeling. Sleep or rather dream on it and you'll feel better in the morning.60. By saying that “dreams are part of mind’s emotion thermostat” in paragraph 1, the researchers mean that ____________.A. dreams can help us keep our mood comparatively stableB. dreams can be brought under conscious controlC. dreams represent our unconscious desires and fearsD. we can think logically in the dreams too61. The negative feelings generated during the day tend to ____________.A. become worse in our unconscious mindB. develop into happy dreamsC. persist till the time we fall asleepD. show up in dreams early at night62. Cartwright believed with much practice, we can learn to ____________.A. control what dreams to dreamB. sleep well without any dreamsC. wake up in time to stop the bad dreamsD. identify what is upsetting about the dreams63. Cartwright might advise those who sometimes, have bad dreams to ____________.A. lead their life as usualB. seek professional helpC. exercise conscious controlD. avoid anxiety in the daytimeSection C (4%)Directions: Read the passage carefully. 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.Bad news sells. If it bleeds, it leads. No news is good news, and good news is no news. Those are the classic rules for the evening broadcasts and the morning papers. ______64______ By tracking people’s e-mails and online posts, scientists have found that good news can spread faster and farther than disasters and sad stories.“The ‘if it bleeds’ rule works for mass media,” says Jonah Berger, a scholar at the University of Pennsylvania. “______65______ But when you share a story with your friends, you care a lot more how they react. You don’t want them to think of you as a Debbie Downer.”Researchers analyzing word-of-mouth communication—e-mails, Web posts and reviews, face-to-face conversations—found that it tended to be more positive than negative. ______66______ Was positive news shared more often simply because people experienced more good things than bad things? To test for that possibility, Dr. Berger looked at how people spread a particular set of news stories: thousands of articles on New York Times’ website. He and a Penn colleague analyzed the “most e-mailed” list for six months. One of his first findings was that articles in the science section were much more likely to make the list than non-science articles. He found that science amazed Times’ readers and made them want to share this positive feeling with others.Readers also tended to share articles that were exciting or funny, or that inspired negative feelings like anger or anxiety, but not articles that left them merely sad. ______67______ The more positive an article, the more likely it was to be shared, as Dr. Berger explains in his new book, “Why Things Catch On.”IV. Grammar (8%)Directions: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.Ernest Miller Hemingway (July 21, 1899—July 2, 1961) was an American writer and journalist. His writing style had a strong influence on 20th-century fiction, his life of adventure and his public image (68) __________ (affect) later generations. Hemingway produced most of his works between the mid-1920s and the mid-1950s, and won the Nobel Prize for Literature in 1954.(69) ____________ (raise) in Illinois, Hemingway later left for the Italian front to enlist with the World War I ambulance drivers. In 1918, he (70) ____________ (wound) and returned home. In 1922, he married Hadley Richardson. The couple moved to Paris, where he worked as a foreign journalist. Advised and encouraged by other American writers in Paris—F. Scott Fitzgerald, Gertrude Stein, Ezra Pound, he began to see his work (71) __________ (appear)in print there, and in 1925 his first important book, a collection of stories called In Our Time, was published. A year later, he published The Sun Also Rises, a novel with which he scored his first solid success. The writing of books occupied Hemingway for most of the postwar years. He remained based in Paris, but he traveled widely for bullfighting, fishing, and hunting that by then (72) __________ (become) part of his life and formed the background for much of his writing. Hemingway’s love of Spain and bullfighting resulted in Death in the Afternoon (1932). His position (73) __________ a master of short fiction had been advanced by Men Without Women in 1927. The harvest of Hemingway’s considerable experience of Spain in war and peace was the novel For Whom the Bell Tolls (1940). In the public view; however, it is the novel A Farewell to Arms(1929) (74) __________ overshadowed such works.Shortly after he published The Old Man and the Sea in 1952, Hemingway went to Africa, (75) __________ he was almost killed in a plane crash that left him in pain or ill-health for much of the rest of his life. Hemingway lived in Florida and Cuba during the 1930s and 1940s, but in 1959 he moved from Cuba to Ketchum, Idaho, where ended his life in the summer of 1961.V. Translation (20%)Section A (5%)Directions:Complete the following sentences according to the Chinese given.76.没有一辆车目前是闲着的。

上海市格致中学2022-2023学年高三上学期第一次验测化学试卷(原卷版)

A.用装置氧化废液中的溴化氢
B.用装置分离油层和水层
C.用装置分离四氯化碳和液溴
D.用仪器密封存放单质溴
13.下列实验中的颜色变化，与氧化还原反应无关的是（）
A
B
C
D
实验
Na2O2露置在空气中
石蕊溶液滴入氯水中
Na2S溶液滴入AgCl浊液中
热铜丝插入稀硝酸中
现象
淡黄色固体最终变为白色固体
溶液变红，随后迅速褪色
猜想②生成白色沉淀是因为：Cu++SCN-→CuSCN↓。再请结合步骤ii溶液出现红色的现象，解释生成沉淀的可能原因：___________(用离子方程式表示)。
第二组：水合肼(N2H4·H2O)和碱性铜氨([Cu(NH3)4]2+)溶液混合反应生成铜。
（5）水合肼溶液显弱碱性，其电离与NH3·H2O相似，写出水合肼的电离方程式：___________。
实验二：
试管中的液体
现象
a．0.1mol/L SO2溶液(pH=2)
溶液逐渐变浅，约90s后完全褪色
b．0.1mol/L NaHSO3溶液(pH=5)
溶液立即变浅，约15s后完全褪色
c．0.1mol/L Na2SO3溶液(pH=10)
溶液立即褪色
d色
e．pH=2 H2SO4溶液
（2）写出本题试管1中发生反应的离子方程式：___________。
（3）试管2，预测步骤ii后溶液不应呈红色，依据是___________写出发生反应的离子方程式：______。
（4）经测定试管②中得到的白色沉淀是CuSCN。对生成CuSCN有两种猜测：
猜测①Cu2+和SCN-反应生成CuSCN，根据___________，推知这一猜测错误。

2021届上海市格致中学高三英语第一次联考试卷及参考答案

2021届上海市格致中学高三英语第一次联考试卷及参考答案第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AIt’s the time of year when we start hiking. As you pack, remember to bring your smartphone. Whether you’re going on a short walk or a long trip, there are a handful of apps that can help.MapMyHikeThis app tracks where you're hiking so you have a mapof your route at the end of the hike. It can also track other fitness information like the distance traveled, speed, pace, and even calories burned. You can save the data for your hike, so you can always access the route you look as well as track improvements to your workout. GaiaGPSYou don't always have cellphone service when hiking, but you always want to know where you are. The GaiaGPS app provides that information. Download maps of different parts of the world, and access the GaiaGPS app in the middle of even the most remote trails. The GPS function makes using the maps simple, and the app will also point to areas of interest.Backpacking ChecklistOne of the worst things is being way out on a trail only to discover you left behind something important. That's why checklists are the best. This checklist app helps you build a customized(定制的) list of things to take with you. Organize different lists based on trail lengths or requirements. Track all your essential items by weight and where you can find them.WildObsUsing WildObs, you can record your observations of plants and animals and add them to the database. You can ask the community to help you identify something and keep track of everything you've met, and most importantly, you can become a citizen scientist. By recording what you've seen with this app, you're helping scientists keep track of what's happening to the natural world.1. What can you do with MapMyHike?A. Record your walking speed.B. Design a suitable hiking route.C. Locate popular tourist attractions.D. Store the data of your daily activities.2. What is WildObs intended to do?A. To provide survival skills.B. To lead the way.C. To identify wildlife.D. To help make preparations.3. Which app is most useful before hiking?A. GaiaGPS.B. MapMyHike.C. WildObs.D. Backpacking Checklist.BItaly's fashion capital is gray — not only because of the blocks of stone buildings，but also due to its often-gray sky, which traps pollution. ButMilannow wants to change it.The city has an ambitious plan to plant 3 million new trees by 2030 - a move that experts say could offer relief from the city's hot weather. Some projects have already contributed to environmental improvements. Architect Stefano Boeri’s Vertical Forest residential (居民的) tower, completed in 2014, aims to improve not only air quality but the quality of life for Milan residents. Boeri created a smallisland of greenery in the heart ofMilan, filling every balcony with plants that absorb carbon dioxide.“I think forestation is one of the best chances that we have today. It is one of the most effective ways we have to fight climate change, because everyone can plant trees, Boeri said.Damiano Di Simine, a member of the environmental group Legambiente , said the greenMilanproject will lower temperatures in a city where the nighttime temperature can be 6 degrees Celsius higher than in the surrounding area. City show thatMilanexperiences 35 hot nights a year. Because the city lies close to theAlps, Milin gets very little wind to lower the city's temperatures. "Planting trees will help this," Di said.TheVerticalForesthas attracted more than 20 species of birds. And the shade provided by the 800 trees and 15,000 plants means that residents rarely have to put on air conditioning, even in hot summers. TheVerticalForest's total greenery- can absorb 30 metric tons of carbon dioxide every year. The presence of green trees has a very important effect on people's health and psychological state, as has already been proved.4. What change doesMilanplan to make?A. Planting more trees.B. Creating a new fashion style.C. Pulling down more gray stone buildings.D. Doing more surveys to study global wanning.5. What's Boeri's opinion on the city's plan?A. It costs a lot.B. It is unpractical.C. It fails to attract people's attention.D. It is helpful to fight against climate change.6. What is Di Simine's attitude toward the city's plan?A. Doubtful.B. Supportive.C. Disappointed.D. Unconcerned.7. What does the last paragraph focus on?A. Specifics of the city's plan.B. Challenges faced by the city.C. The aim of theVerticalForestproject.D. The positive effect of theVerticalForestproject.CThose who are concerned that robots are taking over the world can rest easy—for now. Though the androids have proved useful at performing ordinary tasks, they are not ready for the greatest time. At least that appears to be the case atJapan’s Henn-na Hotel chain where over half of the robot staff are being replaced by humans.The first location of the unique hotel opened in July 2015 was atNagasaki’s Huis Ten Bosch Theme Park. The hotel’s owner, Hideo Sawada, promised the hotel to be managed primarily by robots. Guests were greeted and checked-in by a dinosaur robot, while a cute android called Churi, placed inside each room, provided information about attractions. Not surprisingly, the lodging, recognized in 2016 as the world’s first robot-staffed hotel by Guinness World Records, drew in curious visitors from all around the world.But as the years have passed, the hotel’s main draw is becoming less novel and more unsatisfactory. Also as the robots are “aging”, they are costing more to repair. Among the 283 androids being replaced are the chain’s two dinosaur receptionists. In addition to scaring young guests, they are also unable to photocopy guests’ passports, forcing human employees to step in each time. Also out are the cute Churi robots, which annoyed guests by interrupting their conversations. For example, one guest told The Wall Street Journal that Churi mistook his snoring for a command and kept asking him to repeat his request all night.Sawada told The Wall Street Journal, “When you actually use robots you realize there are places where they aren’t needed—or just annoy people.” While Sawada may be cutting back on his use of androids, the recently-opened Smart LYZ Hotel and the Fly Zoo Hotel inChina, are run entirely by robots, with not a human in sight. Whether the employees have more competence than those “hired” by the Henn-na Hotel chain remains to be seen.8. What makesJapan’s Henn-na Hotel unique?A. Its robot employees.B. Its advanced equipment.C. Its convenient location.D. Its successful management.9. What is the author’s purpose with the example in paragraph 3?A. To entertain readers.B. To prove Churi’s drawback.C. To introduce Churi’s functions.D. To persuade people not to book the hotel.10. What does the owner ofJapan’s Henn-na Hotel think of his robot staff now?A. Attractive.B. Costly.C. Pioneering.D. Disappointing.11. What is the best title for the text?A. Robots Are Taking Over the World.B. The Boom of Robots-staffed Hotel.C. Robot Staff Are Fired For No Competence.D. The First Robots-staffed Hotel Won Guinness World Record.DElonMusk is a symbol of passion, hard work and success. A person may work hard in his life, but when hard work goes along with passion and a new idea, then something is created that astonishes the world. As the founder of big companies like PayPal, SpaceX, and Tesla Motors, Elon Musk is a guide and inspiration for the youth around the world.Elon Musk was born on June 28,1971 inPretoria,South Africa. He was the eldest of three children. His father Errol Musk, a British-born South African, was an engineer. Musk spent his childhood inSouth Africaand at the age of 9, he got his first personal computer. This got Elon interested in programming and he started to learn on his own. At the age of 12, he made his first computer game, Blaster, which earned him $500 when he sold the source code to a magazine.When he was 17, he decided to leave home and had wanted to move to theUnited Statesafter graduating from a secondary school inPretoria. However, he was unable to move to theUnited States. In 1989, Elon Musk moved toCanada, where his mother’s s lived. After obtaining Canadian citizenship, Musk went toMontreal. Due to a lack of money, he found a low-paying job. At the age of 19, he enteredQueensUniversityinKingston,Ontario, studying there for two years. Finally, in 1992, his dream came true—he moved to theUnited States.As a teenager, Musk struggled with depression. But then he realized that the most important thing waspresenting himself with the right questions. The day he started doing this, everything started to get easier.Musk thought that a human being had to expand the limits of his consciousness—to ask the right questions and get answers to them; thus he asked the best question of all: what will have the greatest impact on the future of humans? Musk found that these things were the Internet and space exploration.The life of Elon Musk is inspiring. He found success on the Internet, without much formal learning. By reading books and using his willpower and dedication, he reached a level of knowledge that is difficult to imagine. He did not give up until he achieved his dreams. Elon Musk truly stands out among other billionaires because of his leadership abilities, positive attitude, ability to know when to take risks, and belief in futuristic technologies.12. According to the passage, Elon Musk gained knowledge of computer by ________.A. teaching himselfB. learning from his fatherC. taking online coursesD. studying inQueensUniversity13. What made things easier for Elon Musk when he suffered from depression?A. Expanding knowledge by reading books.B. Asking himself the right questions.C. Achieving success on the Internet.D. Designing computer games.14. What can we learn from the passage?A. It’s never too late to learn.B. Youth means limitless possibilities.C. Where there’s a will, there’s a way.D. He who doesn’t advance falls backward.15. Which words can best describe Elon Musk according to the passage?A. Optimistic and generous.B. Ambitious and determined.C. Independent and helpful.D. Adventurous and realistic.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。

上海市格致中学2022届高三上学期开学考试数学试卷含详解

上海市格致中学2021-2022年高三上开学考数学试卷一、填空题（本大题共有12小题，满分54分，第1-6题每题4分，第7-12题每题5分）1.已知集合{}{}3,1,0,1,2,1A B x x =--=>，则A B = __________.2.已知复数z 满足()12i 34i(i z -=+为虚数单位），则z 的模为__．3.如果无穷等比数列{}n a 所有奇数项的和等于所有项和的3倍，则公比q =______．4.已知函数()1(0)f x x =≥，则它的反函数1()f x -=__．5.二项式25(x +的展开式中的常数项等于___________（结果用数值表示）6.方程4sin 101cos xx=在[0,]π上的解集为__．7.正六边形的中心和顶点共7个点，以其中3个点为顶点的三角形共有_________个．8.已知双曲线2221(0)2x y a a -=>的两条渐近线的夹角为3π，则a =_________．9.设△ABC 的三个内角A 、B 、C 所对的三边分别为a,b,c ，若△ABC 的面积为22()S a b c =--，则sin 1cos AA -=______.10.已知各项为正数的等比数列{}n a 满足7652a a a =+，若存在两项,m n a a1=，则14m n +的最小值为__________．11.设定义域为R 的函数()f x 、()g x 都有反函数，且函数(1)f x +和1(2)g x --图像关于直线y x =对称，若(5)2021g =，则(6)f =__12.2021年3月30日，小米正式开始启用具备“超椭圆”数学之美的新log o ．设计师的灵感来源于曲线:||||1n n C x y +=（其中n 是一个非零实常数）．以下几个关于曲线C 的命题：①曲线C 关于原点成中心对称；②曲线C 只有两条对称轴；③当2n =-时，曲线C 上的点到原点的距离的最小值为2；④当0n >时，记曲线C 所围成图形的封闭图形的面积为n S ，则4n S <；⑤当0n >时，记曲线C 所围成图形的封闭图形的面积为nS ，则nS 关于n 单调递增.其中正确的序号是__．二、选择题（本大题共有4小题，满分20分，每题5分）13.已知实数,,αβ“+2,k k Z αβπ=∈”是“()sin +sin sin αβαβ=+”的（）A .充分而不必要条件B.必要而不充分条件C.充分必要条件D.既不充分也不必要条件14.在ABC 中，H 为直线BC 上的任意一点，M 为AH 的中点，若AM AB AC λμ=+，则λμ+=（）A.14B.12C.1D.215.如图，已知四面体ABCD 的棱//AB 平面α，且AB =，其余的棱长均为1．四面体ABCD 以AB 所在的直线为轴旋转x 弧度，且始终在水平放置的平面α上方．如果将四面体ABCD 在平面α内正投影面积看成关于x 的函数，记为()S x ，则函数()S x 的最小值为（）A.1B.2C.12D.2416.已知函数()y f x =与()y g x =满足对任意1x 、2x ∈R ，都有()()()()1212f x f x g x g x -≥-.有以下四个命题：（1）若()y g x =有反函数，则()y f x =有反函数；（2）若()y f x =是偶函数，函数()y g x =也是偶函数；（3）若()y f x =是周期函数，函数()y g x =也是周期函数；（4）若()y f x =有最大值和最小值，则()y g x =也有最大值和最小值.其中正确命题的个数是（）A.1B.2C.3D.4三、解答题（本大题共5题，满分76分）17.如图，线段OA 和OB 是以P 为顶点的圆锥的底面的两条互相垂直的半径，点M 是母线PB 的中点，已知2OA OM ==.（1）求该圆锥的体积；（2）求异面直线OM 与AP 所成角的大小18.已知0,0a ω>>，函数()sin 3f x a x x ωω=的最小正周期为π，对于任意π,()12x f x f ⎛⎫∈≤ ⎪⎝⎭R 恒成立.（1）求函数()y f x =的解析式；（2）当[0,π]x ∈，求()y f x =的零点和单调递增区间.19.已知函数()21ax f x x b+=+的图像过点(1,2)，且函数图像又关于原点对称.（1）求函数()f x 的解析式；（2）若关于x 的不等式()()()24xf x t x t >-+-在()0,∞+上恒成立，求实数t 的取值范围.20.已知椭圆2222:1(0)x y C a b a b+=>>经过点2)且焦距为4，点,A B 分别为椭圆C 的左右顶点，点P 在椭圆C 上．（1）求椭圆C 的方程；（2）设直线,AP BP 的斜率分别为12,k k ，求12k k 的值；（3）,M N 是椭圆C 上的两点，且,M N 不在坐标轴上，满足OM ∥AP ，ON ∥BP ，问MON △的面积是否是定值？如果是，请求出MON △的面积；如果不是，请你说明理由.21.若无穷数列{}n a 满足：1a 是正实数，当2n ≥时，{}1121max ,,,n n n a a a a a ---= ，则称{}n a 是“Y -数列”．（1）若{}n a 是“Y -数列”且11a =，写出4a 的所有可能值；（2）设{}n a 是“Y -数列”，证明：{}n a 是等差数列的充分必要条件是{}n a 单调递减；（3）若{}n a 是“Y -数列”且是周期数列（即存在正整数T ，使得对任意正整数n ，都有)T n n a a +=，求集合{}*1,12021,ii a a i i =≤≤∈N ∣的元素个数的所有可能取值．上海市格致中学2021-2022年高三上开学考数学试卷一、填空题（本大题共有12小题，满分54分，第1-6题每题4分，第7-12题每题5分）1.已知集合{}{}3,1,0,1,2,1A B x x =--=>，则A B = __________.【答案】{}3,2-【分析】将A 中元素逐个代入判断1x >是否成立即可得解.【详解】将A 中元素逐个代入1x >，符合的有3-、2，即{}3,2A B ⋂=-.故答案为：{}3,2-.【点睛】本题考查了描述法表示集合和集合的交集运算，属于基础题.2.已知复数z 满足()12i 34i(i z -=+为虚数单位），则z 的模为__．【答案】【分析】根据复数的运算公式求复数z 的代数形式，再由复数的模的公式求z 的模.【详解】由(12i)34i z -=+，得34i (34i)(12i)510i 12i 12i (12i)(12i)5z +++-+====-+--+，||z ==.3.如果无穷等比数列{}n a 所有奇数项的和等于所有项和的3倍，则公比q =______．【答案】23-【分析】由题意可知，所有项和11a S q =-，奇数项的和121a S q =-奇，结合已知即可求解.【详解】解：由题意可知，所有项和11a S q=-，奇数项的和121a S q=-奇，112311a aq q∴=--，解可得，23q =-或1q =(舍)故答案为23-.【点睛】本题主要考查了无穷等比数列的求和公式的简单应用，属于基础试题．4.已知函数()1(0)f x x =≥，则它的反函数1()f x -=__．【答案】2(1)x -，(1)x ≥【分析】根据反函数的概念利用()1(0)f x x =≥，得2(1)x y =-，即可得反函数()1f x -.【详解】解：因为()1(0)y f x x ==+≥，所以1y -=，(0)x ≥，所以2(1)x y =-，所以反函数12()(1)f x x -=-，(1)x ≥.故答案为：2(1)x -，(1)x ≥.5.二项式25(x+的展开式中的常数项等于___________（结果用数值表示）【答案】5【分析】由通项()111025222155rr r rr r r T C xx C x----+⎛⎫== ⎪⎝⎭,令110202r r --=,解得4r =,再代入求解即可.【详解】由题,通项()111025222155rr r rr r r T C x x C x----+⎛⎫== ⎪⎝⎭,令110202r r --=,解得4r =,则常数项为455C =,故答案为:5【点睛】本题考查二项式的常数项,属于基础题.6.方程4sin 101cos x x=在[0,]π上的解集为__．【答案】5,1212ππ⎧⎫⎨⎬⎩⎭【分析】利用行列式定义及二倍角公式化简即可.【详解】14sin cos 1,sin 22x x x ==，因为[0,]x π∈，所以2[0,2]x π∈，所以26x π=或526x π=，所以在[0,]π上的解集为5,1212ππ⎧⎫⎨⎬⎩⎭.故答案为：5,1212ππ⎧⎫⎨⎬⎩⎭.7.正六边形的中心和顶点共7个点，以其中3个点为顶点的三角形共有_________个．【答案】32【详解】7个点，任选3个，方法数有37C 35=种，其中有3种情况是三点共线的，故总的方法数有35332-=种.故答案为：32.8.已知双曲线2221(0)2x y a a -=>的两条渐近线的夹角为3π，则a =_________．【答案】3【分析】由两条渐近线的夹角得出渐近线y x a=的倾斜角为6π或3π，再由斜率得出a 的值.【详解】因为两条渐近线的夹角为3π，所以渐近线2y xa=的倾斜角为6π或3π则23tan 63a π==或2tan 3a π==a =63a =故答案为：3或9.设△ABC 的三个内角A 、B 、C 所对的三边分别为a,b,c ，若△ABC 的面积为22()S a b c =--，则sin 1cos AA-=______.【答案】4【详解】试题分析：∵ABC ∆的面积S=()221bcsinA=a 2b c --，∴2222221(b )bcsinA=2bc-(b ),sinA=4-4,22c a c a bc+-+-∴sin 1A coaA -=4.考点：（1）余弦定理；（2）三角形面积公式.10.已知各项为正数的等比数列{}n a 满足7652a a a =+，若存在两项,m n a a 1=，则14m n+的最小值为__________．【答案】116【分析】由7652a a a =+求得2q =1=可得5m n +=，结合,m n 为正整数，讨论四种情况可得14m n+的最小值.【详解】设等比数列的公比为q ,由7652a a a =+,可得到6662a a q a q=+,由于0n a >,所以21q q=+,解得2q =或1q =-.因为各项全为正,所以2q =.由于存在两项,m n a a 1=，所以,218m n a a a ⋅=,112211188m n m n a q a q a q --+-⋅=∴=，28m n q +-∴=,可得5m n +=.当1,4m n ==时,142m n +=;当2,3m n ==时，14116m n +=；当3,2m n ==时,1473m n +=;当4,1m n ==时,14174m n +=;综上可得14m n +的最小值为116,故答案为116.【点睛】本题主要考查等比数列的通项公式和性质,考查了分类讨论思想的应用,属于中档题.分类讨论思想的常见类型⑴问题中的变量或含有需讨论的参数的，要进行分类讨论的；⑵问题中的条件是分类给出的；⑶解题过程不能统一叙述，必须分类讨论的；⑷涉及几何问题时，由几何元素的形状、位置的变化需要分类讨论的.11.设定义域为R 的函数()f x 、()g x 都有反函数，且函数(1)f x +和1(2)g x --图像关于直线y x =对称，若(5)2021g =，则(6)f =__【答案】2023【分析】根据函数(1)f x +和1(2)g x --图像关于直线y x =对称列式，求得()6f 的值.【详解】依题意，令()()651f f t =+=，由于函数(1)f x +和1(2)g x --图像关于直线y x =对称，故1(2)5g t --=，()1g x -的反函数是()g x ，而(5)2021g =，故22021t -=，解得2023t =，即()62023f =故答案为:202312.2021年3月30日，小米正式开始启用具备“超椭圆”数学之美的新log o ．设计师的灵感来源于曲线:||||1n n C x y +=（其中n 是一个非零实常数）．以下几个关于曲线C 的命题：①曲线C 关于原点成中心对称；②曲线C 只有两条对称轴；③当2n =-时，曲线C 上的点到原点的距离的最小值为2；④当0n >时，记曲线C 所围成图形的封闭图形的面积为n S ，则4n S <；⑤当0n >时，记曲线C 所围成图形的封闭图形的面积为n S ，则n S 关于n 单调递增.其中正确的序号是__．【答案】①③④⑤．【分析】以x -替换x ，以y -替换y ，方程不变判断①；举例说明曲线C 的对称轴不只两条判断②；利用基本不等式求最值判断③；求得曲线在第一象限围成图形的面积的范围，结合由对称性判断④；根据曲线中(),1,1x y ∈-，若当n 变大时，仍满足:||||1n n C x y +=，则曲线向外扩展，即可判断⑤．【详解】解：对于①，在曲线:||||1n n C x y +=中，以x -替换x ，以y -替换y ，方程不变，则曲线C 关于原点成中心对称，故①正确；对于②，当n 为偶数时，例如2n =时，曲线22:1C x y +=表示圆，圆又无数条对称轴，不只有两条对称轴，故②错误；对于③，当2n =-时，:||||1n n C x y +=化为22111x y+=，由2222222211()(224y x x y x y x y ++=++≥+=，当且仅当44x y =2≥，即曲线C 上的点到原点的距离的最小值为2，故③正确；对于④，当0n >时，若点()00,x y 在曲线上，则点()()()000000,,,,,x y x y x y ----均在曲线上，则曲线C 在四个象限围成封闭图形的面积相同，取曲线C 在第一象限的面积为1S ，则14S S =，又在第一象限的曲线为1n n x y +=，所以1111S <⨯=，则4S <，故④正确．对于⑤，易得(),1,1x y ∈-，当n 变大时，若,x y 不变，则||||1n n x y +<，所以为了保持曲线:||||1n n C x y +=，图形必定要向外拓展，曲线C 所围成图形的封闭图形的面积为n S ，则n S 关于n 单调递增，故⑤正确；故正确的序号是①③④⑤．故答案为：①③④⑤．二、选择题（本大题共有4小题，满分20分，每题5分）13.已知实数,,αβ“+2,k k Z αβπ=∈”是“()sin +sin sin αβαβ=+”的（）A.充分而不必要条件B.必要而不充分条件C.充分必要条件D.既不充分也不必要条件【答案】A【分析】由条件推结论可判断充分性，由结论推条件可判断必要性.【详解】当+2,k k Z αβπ=∈时，()sin +0αβ=，且sin sin sin sin(2)sin sin 0k αβααπαα+=+-+=-=，充分性成立；当()sin +sin sin αβαβ=+时，未必有+2,k k Z αβπ=∈，例如,0απβ==时，此时()sin +sin sin 0αβαβ=+=，但不满足+2,k k Z αβπ=∈.所以实数,,αβ“+2,k k Z αβπ=∈”是“()sin +sin sin αβαβ=+”的充分而不必要条件.故选：A.14.在ABC 中，H 为直线BC 上的任意一点，M 为AH 的中点，若AM AB AC λμ=+，则λμ+=（）A.14B.12C.1D.2【答案】A【分析】根据平面向量基本定理与共线定理即可得结论.【详解】解：因为M 为AH 的中点，且AM AB AC λμ=+，所以12AM AH AB ACλμ==+ 所以22AH AB AC λμ=+，且B ，H ，C 三点共线，所以221λμ+=，则12λμ+=．故选：A ．15.如图，已知四面体ABCD 的棱//AB 平面α，且AB =，其余的棱长均为1．四面体ABCD 以AB 所在的直线为轴旋转x 弧度，且始终在水平放置的平面α上方．如果将四面体ABCD 在平面α内正投影面积看成关于x 的函数，记为()S x ，则函数()S x 的最小值为（）A.1B.22C.12D.24【答案】D【分析】方法一：根据图象的旋转过程直观的看出何时最小，代入数据即可求解；方法二：根据题干中的数据和点到面的距离可得到当CD α⊥时取最小值，代入数据即可求解.【详解】方法一：记AB 的中点E ，从侧面看，图1只需考虑ECD 绕着E 点旋转时，ECD 在直线l 上的投影.图1为初始状态.①当旋转π4时，如图2，投影最短为12，min11224S==.②旋转过程中，有如下函数关系：12πcos,022412ππ,2242123ππcos(),π2242Sθθθθθθ⎧≤<⎪⎪⎪⎪=≤<⎨⎪⎪-≤≤⎪⎪⎩，当ECD第一次旋转到图3位置时，ECD在直线l的投影又回到了图1，综上：min112224S==，故选：D.方法二：取AB的中点M，连结CM，DM，因为DA DB=，CA CB=，所以AB CM⊥，AB DM⊥，DM CM M⋂=，所以AB⊥平面CDM，因为CD⊂平面CDM，所以AB CD⊥．因为AB=，1AC BC CD===，所以AC BC⊥，22CM DM==，所以CM DM⊥，所以M到CD的距离为12．故当CDα⊥时，()S x取得最小值112224=．故选：D.16.已知函数()y f x=与()y g x=满足对任意1x、2x∈R，都有()()()()1212f x f xg x g x-≥-.有以下四个命题：（1）若()y g x=有反函数，则()y f x=有反函数；（2）若()y f x=是偶函数，函数()y g x=也是偶函数；（3）若()y f x =是周期函数，函数()y g x =也是周期函数；（4）若()y f x =有最大值和最小值，则()y g x =也有最大值和最小值.其中正确命题的个数是（）A.1B.2C.3D.4【答案】C【分析】利用反函数的定义可判断（1）的正误；取1x x =，2x x =-，利用函数奇偶性的定义可判断（2）的正误；设()y f x =的周期为T ，令1x x T =+，2x x =，利用不等式的基本性质结合函数周期性的定义可判断（3）的正误；取()arctan ,110,110,1x x f x x x ≠±⎧⎪==⎨⎪-=-⎩，()1arctan 2g x x =可判断（4）的正误.即可得出合适的选项.【详解】对于（1），若()y g x =有反函数，则x 、y 一一对应，即任取1x 、2x ∈R ，有()()12g x g x ≠，从而()()()()12120f x f x g x g x -≥->，故()()12f x f x ≠，即x 、y 一一对应，故()y f x =有反函数，故（1）正确；对于（2），若()y f x =是偶函数，则()()f x f x -=，若()()()()1212f x f x g x g x -≥-对任意1x 、2x ∈R 恒成立，令1x x =，2x x =-，则()()()()f x f x g x g x --≥--，因为()()f x f x -=，所以()()0g x g x --≤，所以()()g x g x =-，所以函数()y g x =也是偶函数，故（2）正确；对于（3），设()y f x =的周期为T ，若()()()()1212f x f x g x g x -≥-对任意1x 、2x ∈R 恒成立，令1x x T =+，2x x =，则()()()()f x T f x g x T g x +-≥+-，因为()()f x T f x +=，所以()()0g x T g x +-≤，所以()()g x T g x +=，所以函数()y g x =也是周期函数，故（3）正确；对于（4），只能说明()y g x =有界，不能说明有最值，反例如下：()arctan ,110,110,1x x f x x x ≠±⎧⎪==⎨⎪-=-⎩，()1arctan 2g x x =，则函数()f x 的最大值为10，最小值为10-，()1ππarctan ,244g x x ⎛⎫=∈- ⎪⎝⎭，对任意的1x 、2x ∈R ，()()()()1212f x f x g x g x -≥-恒成立，但函数()g x 既无最大值，也无最小值，故（4）错误；故选：C ．三、解答题（本大题共5题，满分76分）17.如图，线段OA 和OB 是以P 为顶点的圆锥的底面的两条互相垂直的半径，点M 是母线PB 的中点，已知2OA OM ==.（1）求该圆锥的体积；（2）求异面直线OM 与AP 所成角的大小【答案】（1）833（2）3arccos 4【分析】（1）由圆锥性质知4PB =，然后计算出高PO 后可得体积；（2）以OA 为x 轴正半轴，OB 为y 轴正半轴，OP 为z 轴正半轴.建立空间直角坐标系，用空间向量法示得异面直线所成的角．【详解】（1）由题可得4,PB OP ==，故体积2112333V S h ππ=⋅⋅=⋅⨯⨯=.（2）以OA 为x 轴正半轴，OB 为y 轴正半轴，OP 为z 轴正半轴建立空间直角坐标系，则(0,0,0)O，(2,0,0),M A P ，所以(OM AP ==-，设异面直线OM 与AP 所成角为θ，则||63cos 244||||OM AP OM AP θ⋅===⨯ ，故所成角为3arccos 4.【点睛】本题考查求圆锥的体积，考查用空间向量法求异面直线所成的角．掌握圆锥的性质是解题关键．18.已知0,0a ω>>，函数()sin f x a x x ωω=的最小正周期为π，对于任意π,()12x f x f ⎛⎫∈≤ ⎪⎝⎭R 恒成立.（1）求函数()y f x =的解析式；（2）当[0,π]x ∈，求()y f x =的零点和单调递增区间.【答案】（1）π()2sin 23f x x ⎛⎫=+ ⎪⎝⎭（2）零点为π3x =和5π6x =，单调递增区间为π0,12⎡⎤⎢⎥⎣⎦和7π,π12⎡⎤⎢⎥⎣⎦.【分析】(1)先利用辅助角公式化简，结合题意得周期以及max π()12f x f ⎛⎫== ⎪⎝⎭，即可判断解析式；(2)结合三角函数性质求解零点和单调递增区间即可.【小问1详解】由题意得()sin )f x a x x x ωωωϕ=+=+，因为最小正周期为π，所以2ω=，所以()()sin222f x a x x x ϕ=+=+，因为对于任意π,()12x f x f ⎛⎫∈≤ ⎪⎝⎭R 恒成立，所以max π()12f x f ⎛⎫== ⎪⎝⎭322a =+，解得1a =，所以π()sin 222sin 23f x x x x ⎛⎫=+=+⎪⎝⎭【小问2详解】令π2π,3x k k Z +=∈得ππ,26k x k Z =-∈，令πππ22π,2π+,322x k k k Z ⎡⎤+∈-∈⎢⎥⎣⎦得5πππ,π+,1212x k k k Z ⎡⎤∈-∈⎢⎥⎣⎦，又[0,π]x ∈，所以()y f x =的零点为π3x =和5π6x =，单调递增区间为π0,12⎡⎤⎢⎥⎣⎦和7π,π12⎡⎤⎢⎥⎣⎦.19.已知函数()21ax f x x b+=+的图像过点(1,2)，且函数图像又关于原点对称.（1）求函数()f x 的解析式；（2）若关于x 的不等式()()()24xf x t x t >-+-在()0,∞+上恒成立，求实数t 的取值范围.【答案】（1）21()x f x x+=；（2）(),4-∞.【分析】（1）根据图象关于原点对称得()f x 图象过点(1,2)和(1,2)--，再用待定系数即可求解；（2）将()()()24xf x t x t >-+-化为225(1)x x x t ++>+，再用分离参数法求解即可.【详解】（1）依题意，函数()f x 的图象过点(1,2)和(1,2)--.所以1(1)221111210(1)21a f a b a b a a b b f b +⎧==⎪⎧-==⎧⎪+⇒⇒⎨⎨⎨++==⎩⎩⎪-==-⎪-+⎩，故21()x f x x +=.（2）不等式()(2)(4)xf x t x t >-+-可化为225(1)x x x t ++>+.即2251x x t x ++<+对一切的()0,x ∈+∞恒成立.因为22541411x x x x x ++=++≥++，当且仅当1x =时等号成立，所以实数t 的取值范围为(),4-∞.【点睛】本题考查待定系数法求解析式，不等式恒成立问题，是中档题.根据不等式恒成立求解参数范围的两种方法：（1）分类讨论法：根据参数的临界值分类讨论参数的取值是否满足要求；（2）参变分离法：将参数从不等式中分离出来，通过函数或者不等式确定最值，由此得到参数范围.20.已知椭圆2222:1(0)x y C a b a b+=>>经过点且焦距为4，点,A B 分别为椭圆C 的左右顶点，点P 在椭圆C 上．（1）求椭圆C 的方程；（2）设直线,AP BP 的斜率分别为12,k k ，求12k k 的值；（3）,M N 是椭圆C 上的两点，且,M N 不在坐标轴上，满足OM ∥AP ，ON ∥BP ，问MON △的面积是否是定值？如果是，请求出MON △的面积；如果不是，请你说明理由.【答案】（1）22184x y +=（2）12-（3）是，【分析】（1）根据题意建立方程，联立解出22,a b 即可，（2）由题意M ，N 是椭圆C 上非顶点的两点，且OM ∥AP ，ON ∥BP，设,2sin )P θθ，然后表示出直线的斜率，化简即可得.（3）利用（2）中的结论，设直线方程，联立方程组消元，写出韦达定理，找出参数变量间的关系，利用三角形面积公式表示出MON S ，化简求出面积为定值即可.【小问1详解】椭圆2222:1(0)x y C a b a b+=>>经过点且焦距为4，得24c =，即2c =，①22421a b +=，②222a b c =+，③解得28a =，24b =，所以椭圆方程为22184x y +=．【小问2详解】由题意M ，N 是椭圆C 上非顶点的两点，且OM ∥AP ，ON ∥BP ，设,2sin )P θθ，则21224sin 18(cos 1)2k k θθ===--.【小问3详解】因为OM ∥AP ，ON ∥BP ，所以12OM ON k k =-，设直线MN 的方程为x my t =+，由22184x my t x y =+⎧⎪⎨+=⎪⎩，得222(2)280m y mty t +++-=，④设1122(,),(,)M x y N x y ，则12222mt y y m +=-+，212282t y y m-=+，12x x =22221212228()2t m m y y mt y y t m -+++=+，所以2212221228122822OM ON t y y m k k t m x x m -+===--+，得2224t m =+，又1211||||||22MON S t y y t =-=1||2t =即MON △的面积为定值.21.若无穷数列{}n a 满足：1a 是正实数，当2n ≥时，{}1121max ,,,n n n a a a a a ---= ，则称{}n a 是“Y -数列”．（1）若{}n a 是“Y -数列”且11a =，写出4a 的所有可能值；（2）设{}n a 是“Y -数列”，证明：{}n a 是等差数列的充分必要条件是{}n a 单调递减；（3）若{}n a 是“Y -数列”且是周期数列（即存在正整数T ，使得对任意正整数n ，都有)T n n a a +=，求集合{}*1,12021,i i a a i i =≤≤∈N ∣的元素个数的所有可能取值．【答案】（1）所有可能值为2-，0，2，8（2）证明见解析（3）答案见解析【分析】（1）根据定义写出234,,a a a 即可；（2）利用已知条件，证明充分条件以及必要条件即可；（3）方法1：因为{}n a 为周期数列，推出1{}n n a a --为周期数列，根据周期性推导出结果即可；方法2：设第一次出现大于1a 的项为i a ，则{}112max ,,,i i i i a a a a a a +-== ，所以121...,Z i i i a a ka a k ++=≠∈，与{}n a 为周期数列矛盾，所以{}121max ,,,i a a a a = ，后面的分析与方法1一样.【小问1详解】所有可能的情况有：22a =，0，34a =，0，1，1-，48a =，0，2，2-，2，0，0，2-，故4a 的所有可能值为2-，0，2，8．【小问2详解】因为211||a a a -=，所以20a =或12a ．当{}n a 是等差数列时，假设212a a =，则321123a a a a =-=．此时321||a a a -=，而{}121max ,2a a a =，矛盾，所以20a =．于是公差2110d a a a =-=-<，所以{}n a 单调递减；当{}n a 单调递减时，对任意2n ≥，{}1211max ,,,n a a a a -= ，又11||n n n n a a a a ---=-，所以11n n a a a --=-，从而{}n a 是等差数列；综上，{}n a 是等差数列的充分必要条件是{}n a 单调递减；【小问3详解】方法1：因为{}n a 为周期数列，所以11i i i T i T a a a a -+-+-=-，所以1{}n n a a --为周期数列，又{}1121max ,,,n n n a a a a a ---= ，所以21321n n a a a a a a --≤-≤≤-≤ 设一个周期里：11221T T i i T T a a a a a a ----≤-≤-，因为1221T T T T a a a a ---=-，所以11221T T i i T T a a a a a a ----=-=-，所以1n n a a c --=为定值，因为211||a a a -=，所以{}11121max ,,,n n n a a a a a a ---== ，取1111,0,,0,,,a a a a ，则1i a a =有2011110112+=个，取1111111,0,,2,,10081009,1008,,0,a a a a a a a ----- ，则1i a a =有1个，取1111111,0,,2,,10071008,1007,,0,,0a a a a a a a ----- ，则1i a a =有1个，取11111111,0,,2,,10061007,1006,,0,,0,a a a a a a a a ----- ，则1i a a =有2个，依次取数得到1~1010个1i a a =，个数最多有1011个.方法2：设第一次出现大于1a 的项为i a ，则{}112max ,,,i i i i a a a a a a +-== ，所以121...,Z i i i a a ka a k ++=≠∈，与{}n a 为周期数列矛盾，所以{}121max ,,,i a a a a = ，取1111,0,,0,,,a a a a ，则1i a a =有2011110112+=个，取1111111,0,,2,,10081009,1008,,0,a a a a a a a ----- ，则1i a a =有1个，取1111111,0,,2,,10071008,1007,,0,,0a a a a a a a ----- ，则1i a a =有1个，取11111111,0,,2,,10061007,1006,,0,,0,a a a a a a a a ----- ，则1i a a =有2个，依次取数得到1~1010个1i a a =，个数最多有1011个.。

2020-2021年格致中学高三上第一次月考化学试卷

第一学期第一次测试高三年级化学试卷可能用到的相对分子质量：H-1 N-14 Fe-56 Cu-64一、选择题（本题共40分，每小题2分，每小题只有一个正确选项）1. 《本草纲目》记载的烧酒工艺：“凡酸坏之酒，皆可蒸烧”，“以烧酒复烧二次……价值数倍也”。

该方法与分离下列物质的原理相同的是A. 苯和水B. 硝酸钾和氯化钠C. 食盐水和泥沙D. 乙酸丁酯和1-丁醇2. 重水（D2O）是重要的核工业原料，下列说法错误的的A. 氘（D）原子核外有1个电子B. 1H与D互称为同位素C. H2O与D2O互称为同素异形体D. 1H218O与D216O的相对分子质量相同3. Fe为26号元素，属于第四周期，最外层有2个电子，Fe3+最外层的电子数则为A. 8B. 13C. 14D. 184. 以下关于氢气分子中的成键状况的表达错误的是A. B. C. D. H—H5. 含有非极性共价键的离子化合物是A. B. KOH C. Na2O2 D. CaCl26. 烷烃命名中常使用三套数字，甲、乙、丙……，1、2、3……，二、三……。

其中“二、三……”是说明A. 碳原子数B. 烷基位置编号C. 氢原子数D. 同种烷基数目7. 下列物质的水溶液能导电，但属于非电解质的是A. CH3COOHB. Cl2C. NH4NO3D. SO28. 按原子序号递增的顺序（稀有气体除外），对第三周期元素性质的描述正确的是A. 原子半径和离子半径均减小B. 氧化物对应的水化物碱性减弱，酸性增强C. 单质的晶体类型金属晶体，原子晶体和分子晶体D. 单质的熔点降低9. 从下列叙述中能肯定判断某平衡发生移动的是A. 混合物中分组分的浓度改变B. 混合体系中气体密度发生变化C. 正、逆反应速率改变D. 反应物的转化率改变10. 在FeCl3和CuCl2的混合溶液中加入铁屑，反应结束后滤出固体物质，滤液中存在的阳离子可能是A. Fe3+B. Fe2+和Fe3+C. Fe2+和Cu2+D. Cu2+和Fe3+11. 寒冷的冬天，经常使用暖宝宝，暖宝宝中装的是铁粉、活性炭、无机盐等物质，打开包装以后，可以连续12个小时释放热量，以下分析错误的是A. 将化学能转化为热能B. 其发热原理与钢铁的吸氧腐蚀相同C. 铁作负极，电极反应为：Fe-3e-→Fe3+D. 活性炭作正极，电极反应为；2H2O+O2 + 4e-→4OH-12. 用石墨电极电解CuCl2溶液（见右图）。

上海市格致中学2024-2025学年高一上学期第一次测验数学试卷

上海市格致中学2024-2025学年高一上学期第一次测验数学试卷一、填空题1．不等式11x≤的解集为； 2．已知关于x 的一元二次方程2310x x --=的两个实数根为12,x x ，则1211x x +的值为． 3．设a ，R b ∈，{}1,P a =，{}1,Q b =--，若P Q =，则a b -= ．4．设a ,b ∈R ，则“2b a >”是“220a b b->”的条件．（填“充分不必要”“必要不充分”“充要”“既不充分也不必要”）520y +=的解集为．（用列举法表示）6．给出下列关系式，其中正确的是（填序号）． ①{}a ∅⊆；②{}a a ⊆；③{}{}a a ⊆；④{}{},a a b ∈；⑤{}{},a ∅⊆∅．7．设集合{}21,14,M a x a x x =-=≤≤∈Z ，则集合M 的非空真子集的个数为． 8．若不等式24223x m x x +<-+恒成立，则实数m 的取值范围是. 9．已知对于实数,x y ，满足2x y +≤且3x y -≤，则3x y -的最大值为． 10．已知集合()()()()(){}0,0,0,1,1,0,0,1,1,0,{(,)|2,1,Z,Z}A B x y x y x y =--=≤≤∈∈，定义集合()()(){}12121122,,,,A B x x y y x y A x y B ⊕=++∈∈，则A B ⊕中元素的个数为．二、单选题11．用反证法证明命题“已知,x y N *∈，如果xy 可被7整除，那么,x y 至少有一个能被7整除”时，假设的内容是A ．,x y 都不能被7整除B ．,x y 都能被7整除C ．,x y 只有一个能被7整除D ．只有x 不能被7整除 12．若110a b<<，则下列结论不正确的是（） A ．0a b +< B ．22a b < C ．2ab b < D ．2ab a <13．若关于x 的不等式2x m n -<的解集为(),αβ，则αβ-的值（）．A ．与m 有关，且与n 有关B ．与m 有关，但与n 无关C ．与m 无关，且与n 无关D ．与m 无关，但与n 有关14．设01b a <<+，若关于x 的不等式()()22x b ax ->的解集中的整数解个数恰为3个，则满足条件的实数a 所在区间可以是（）A ．()1,0-B ．()0,1C ．()1,3D ．()3,5三、解答题15．已知集合{}14A x x =-≤<，{}2,R B x a x a a =≤≤+∈．(1)当2a =-时，求A B U ；(2)若A B =∅I ，求实数a 的取值范围．16．已知a ，b 是实数，求证：44221a b b --=成立的充要条件是221a b -=.17．已知关于x 的不等式2430ax x +->的解集为{}1,1x x b b <．(1)求,a b 的值；(2)当0c >时，求关于x 的一元二次不等式()20cx bc a x b --+≥的解集． 18．根据要求完成下列问题：(1)已知命题2:8200p x x -++≥，命题()22:2100q x x m m -+-≤>，若q 是p 的必要不充分条件，求实数m 的取值范围；(2)已知命题p ：关于x 的方程210x mx ++=有两个不等的负根；命题q ：关于x 的不等式2230mx mx -+>的解集为R ．若,p q 一真一假，求实数m 的取值范围．19．设集合{}12,,,n A a a a =⋅⋅⋅，其中120n a a a ≤<<⋅⋅⋅<，正整数3n ≥．若对任意(),1i j i j m ≤≤≤，i j a a +与j i a a -至少有一个属于A ，则称A 具有性质P ．(1)分别判断集合{}0,2,4C =与{}1,2,3D =是否具有性质P ，并说明理由；(2)当3n =时，若A 具有性质P ，且24a =，求集合A ；(3)记()123n na f n a a a a =+++⋅⋅⋅+，若A 具有性质P ，求()2024f 的值．。

格致中学2021学年度第一学期高三数学(理)第一次测验

格致中学2021学年度第一学期高三数学（理）第一次测验(测试 120 分钟内完成，总分150分，试后交答卷)一、填空题（本大题满分48分）本大题共有12题，只要求直接填写结果（填在答卷上），每个空格填对得4分，否则一律得零分。

1、用描述法表示直角坐标平面上不在第一，三象限内点的集合2、“1=a ”是“函数22cos sin y ax ax =-的最小正周期为π”的条件；3、已知集合(){}(){}2,1,A x y y x B x y y x m ==-==+，，若B A ⋂为单元素集合，则m 的取值范围4、执行右边的程序框图6，若p ＝0.8，则输出的n ＝ .5、已知向量(3,5)a k =-，(1,1)b =-，若3a b -不超过3，则k 的取值范围是6、若复数2(1m ii mi++是虚数单位）是纯虚数，则实数m =则所取4个球的最大号码是6的概率为8、已知()f x 在R 上是奇函数，且2(4)(),(0,2)()2,(7)f x f x x f x x f +=∈==当时，则9、函数1sin 2cos xy x+=+的值域为10、设A 是n 阶方阵，定义运算：21,(*)n n A A A AA A n N +⋅==⋅∈，称这一运算为矩阵的乘方。

显然矩阵的乘方满足：对任意的*,m n N ∈，mnm nA A A+⋅=。

设1101A ⎛⎫=⎪⎝⎭，计算234,,,A A A 并对一切*n N ∈，猜想n A =11、满足{}4,3,2,1=⋃B A 的B A ,有组图612、已知函数2()(0,)af x x x a R x=+≠∈常数，若()f x 在[)2,+∞上是增函数，则a 的取值范围是_______________。

二、选择题（本大题满分16分）本大题共有4题，每题都给出代号为A 、B 、C 、D 的四个结论，其中有且只有一个结论是正确的，必须把正确结论的代号写在答卷纸的相应位置上，选对得4分，不选、选错或者选出的代号超过一个（不论是否都写在相应位置上），一律得零分。