南师附中2015-2016期中考试题
南京师大附中2015-2016学年度第1学期
高二年级期中考试英语试卷
第一节单项选择(共15小题；每小题1分，满分15分)
21. -- Why don't we save ourselves the trouble and use the stairs, Steven?
-- Come on! Man invented the lift so that we don’t have to act like cavemen.
-- Ok, Steven, if you ______ insist on being lazy.
A. can
B. should
C. shall
D. must
22. ______ ―killer robots‖ can help reduce battlefield deaths, they may also make countries more
likely to go into battle, which will lead to more deaths.
A. Whether
B. Where
C. While
D. What
23. Students living off campus ______ pay a little less for housing than students living in college
dormitories, but their cost of transportation is higher.
A. in general
B. in addition
C. in demand
D. in need
24. It is required that food makers remove trans fats from products, since trans fats are not widely
______ as safe.
A. adopted
B. harvested
C. recognized
D. operated
25. Desertification, the name for ______ happens when land ______ can be used to grow crops turns
into desert, is a growing world problem.
A. which; that
B. what; how
C. what; that
D. how; which
26. The Three-Body Problem has quickly become the best-selling Asian work of literature on
https://www.360docs.net/doc/065518006.html,, ______ that China also has a successful science fiction scene.
A. proving
B. to prove
C. to be proved
D. will prove
27. As Alan Turing believed, a computer would deserve ______ intelligent if it could fool a human
into believing that it was human.
A. called
B. to be called
C. having been called
D. calls
28. During the heated discussion, I ______ that blogs are better than books for their convenience,
lower price, and larger range of writing.
A. picked out
B. worked out
C. ran out
D. pointed out
29. The university is saving $300,000 per year by its energy ______ efforts, aimed to build a more
energy-efficient university.
A. consumption
B. conservation
C. consideration
D. correction
30. These measures include better administration of areas that are likely to turn into desert, and
______ people in how to use water without wasting it.
A. train
B. to train
C. training
D. trained
31. -- Good day, Bell Electronics. This is Jane speaking. How may I help you today?
-- Oh… uh, I ______ Myers Icecream Company. Sorry about that.
A. looked for
B. am looking for
C. was looking for
D. have been looking for
32. ______ with what may be his most impossible mission yet, Hunt gets together his team and joins
forces with Ilsa Faust, a female former British secret agent.
A. Facing
B. Having faced
C. Faced
D. To face
33. He doesn’t own an NBA championship ring, ______ in the face with champagne(香槟) after the
NBA finals.
A. he has neither been sprayed
B. nor has he been sprayed
C. either has he been sprayed
D. so he has been sprayed
34. Considering the fact that the relationship between neighbors in rural area is closer than ______ in
cities, I prefer to live in the countryside.
A. that
B. the one
C. those
D. them
35. In Alice Munro’s novel, Carla, trapped in a bad marriage, ______, decides to flee.
A. her unhappiness built into desperation
B. her unhappiness has built into desperation
C. her unhappiness building into desperation
D. her unhappiness builds into desperation
第二节完型填空(共20小题；每题1分，满分20分)
With their visas in hand and their bags packed, students may feel prepared for their study abroad experiences. __36__ once they set foot in foreign lands, some students realize that they don’t have the skills to communicate their thoughts and feelings in their __37__ culture.
Guo Yichen, a student at the Fashion Institute of Design and Merchandising in Los Angeles, observed a(an) __38__ of poor communication during her time abroad.
When Guo first got to the US, she stayed in the house of a 63-year-old lady, with another Chinese girl. Guo and her housemate were __39__ to take turns tidying up the bathroom. But the housemate never __40__, because she didn’t know how. Her mother had always cleaned the bathroom for her back home. And when the landlord asked about it, the housemate __41__ replied, ―I never needed to do housework back home, and I won’t do it here __42__.‖
―I was shocked by how __43__ her answer was,‖ said Guo. ―She could have explained it in a better way.‖ It was __44__ surprise that the girl was asked to move out almost immediately.
In fact, ―difficulty in __45__‖ is among the three major psychological problems that ZMN Education, an agency on overseas education, __46__ among Chinese students studying abroad, the other two being ―fear of class discussion‖ and ―fear of homework based on critical thinking‖.
A professor at the University of California, Berkeley, once told the agency that many of his Chinese students only came to see him when they got __47__ scores. They should have talked to him after each class to get a better grade __48__, he said.
According to the agency, studying abroad itself may trigger(引发) certain mental problems because it is a ―__49__ and stressful shift to new environments and __50__‖. It has been found that students are 23 times more likely to __51__ a mental health condition than business travelers headed abroad.
And during this period of major life transitions(过渡), __52__ better communication skills is particularly vital. It helps you get assistance and solve problems.
Students need to understand the value of empathy – the effective awareness of the emotions of others–as well as __53__ themselves clearly, especially in cross-cultural communications. It would be better if students participate in a(an) __54__ abroad program during vacations before trying year-long overseas study. That way, they could have __55__ coping with a strange world independently.
A. And
B. Therefore
C. But
D. Otherwise
37. A. unique B. host C. national D. superb
38.A. conflict B. trial C. debate D. case
39.A. appreciated B. represented C. fueled D. supposed
40.A. bought her story B. did her part
C. kept her word
D. followed her heart
41.A. actually B. eventually C. pleasantly D. simply
42.A. either B. rather C. too D. neither
43.A. sensitive B. serious C. straightforward D. stubborn
44.A. great B. no C. major D. exact
45.A. communication B. explanation C. opposition D. indication
46.A. impressed B. ignored C. identified D. inspired
47.A. unfortunate B. unsatisfactory C. unwelcome D. unequal
48.A. in the first place B. in other words C. in this case D. in the end
49.A. similar B. superb C. sudden D. sensitive
50.A. influences B. routines C. manners D. policies
51.A. result from B. benefit from C. suffer from D. flee from
52.A. tolerating B. simplifying C. requesting D. developing
53.A. expressing B. blaming C. committing D. advancing
54.A. affordable B. long-distance C. short-term D. trustworthy
55.A. difficulty B. experience C. leadership D. survival
第三节：阅读理解(共16小题；每小题1.5分，满分24分)
A
When it comes to romance, no one does it better than the French. This is believed to be true of their movies, too. Unlike the Hollywood blockbusters(大片) you may be used to, French films are ―usually a more artistic statement about being in the world‖, noted The Guardian.
From Oct 8 to Oct 29, in cooperation with the French embassy(大使馆) in China, the China Film Archive and China National Film Museum are presenting classic and critically acclaimed(备受赞誉的) French movies, including Le Havre (2011), Mia et le Migou (2008), and Le Voyage dans la Lune (1902).
Sha Dan, curator(策展人) of the China Film Archive, explained to the media what to expect from the film series, and revealed how first-time viewers can best appreciate French movies.
Q: Why should I watch French movies?
A: French films have a lot of virtues. For one thing, they use dialogue and plot, instead of visual effects, to drive the story. For another, they stress diversity(多元). While Hollywood movies are often about universal values, French movies have French culture or regional cultures deeply rooted in them. You have to understand them in their cultural context. That’s what sometimes makes French movies difficult to understand.
Q: How can a Chinese audience appreciate French movies?
A: You need to get used to their way of filming. When shooting two people talking to each other, the traditional way is to film each person face-forward as they take turns speaking. However, French movies are filmed in more experimental ways, like switching from a close shot to a long shot. Also, you should search for background information. The movie’s title and its director can reflect its ideas and storyline. For example, Les Enfants du Paradis (1945), also known as Children of Paradise, tells the story of beautiful Garance and the four men who love her in their own ways. Garance meets these men in a theater, and the ―Paradis‖ in the movie title is an informal French name for a theater’s gallery.
56. What is the author’s purpose in writing this text?
A. To recommend some classic French movies.
B. To help readers to better appreciate French movies.
C. To compare French movies with Hollywood blockbusters.
D. To describe the development and features of French movies in great detail.
57. Which of the following is a characteristic of French movies?
A. They are often about universal values.
B. They usually have really good visual effects.
C. They attach a lot of importance to French culture and French regional cultures.
D. They are sometimes hard to understand because of their complex plots.
58. Which of the following is TRUE about French movies according to the text?
A. They are mostly romances and are usually artistic.
B. They often involve more close shots than long shots.
C. They prefer to use the traditional way of shooting two people talking to each other.
D. Their titles and directors can help viewers learn background information.
B
Many of us remember being in awe(敬畏) when we saw cloned dinosaurs running wild in the film Jurassic Park. And the idea of using technology to revive(恢复) extinct species has long fascinated not only writers and directors, but scientists as well.
According to The Telegraph, woolly mammoths(长毛猛犸象), which featured in the popular Ice Age animated movie series, ―may walk the earth once more‖ now that scientists have taken another step toward realizing a long-held dream—recreating their DNA.
Mammoths became extinct around 10,000 years ago. However, since the discovery of near-perfect preserved remains in Arctic permafrost(北极冻土带) in May 2013, a variety of research studies have been carried out since.
Geneticists from Harvard University analyzed DNA from the remains, looking for genes which separated mammoths from elephants, such as hairiness and ear size. They then used the results to reproduce exact copies of 14 mammoth genes. ―It is the first time that mammoth genes have been alive—although so far it has only been done in the lab,‖ George Church,lead researcher of the project, told the Sunday Times.
Church then used a new technique which allows scientists to edit DNA carefully, replacing sections of elephant DNA with the mammoth genes. So ―we now have functioning elephant cells with mammoth DNA i n them,‖ he said.
However, Church ruled out the possibility of bringing the mammoths back to life via cloning from frozen remains. He said he ―preferred to focus on rebuilding the full mammoth genome(基因组) by analyzing DNA from preserved remains and putting it into the cells of its closest living relative –the Asian elephant,‖ reported The Telegraph.
Church argued that the return of the woolly mammoth—or rather, the return of something very similar—could help bring back fragile(脆弱的) ecosystems. However, some scientists believe that bringing back the mammoth would be unethical.
Professor Alex Greenwood, an expert on ancient DNA, said: ―We may face the extinction of African and Asian elephants. Why bring back another elephant from extinction when we cannot even keep the ones that are not extinct around?‖ he told the Sunday Times. ―What is the message? We can be as irresponsible with the environment as we want. Then we’ll just clone things back?‖―Money would be better spent focusing on conserving what we do hav e than spending it on an animal that has been extinct for thousands of years,‖ he said.
59. We can learn from the article that ______.
A. cloned mammoths followed cloned dinosaurs to get revived
B. the technology to revive mammoth genes is already mature
C. George Church and his colleagues tried to reproduce mammoth DNA
D. Church and his team managed to list all the genes that separate mammoths from elephants
60. According to Church, what is the significance of his study?
A. It could help prevent the extinction of the Asian elephant.
B. It could help people better tell elephant DNA from mammoth genes.
C. It could help bring back some extinct species and save fragile ecosystems.
D. It could help bring mammoths back to life via cloning from frozen remains.
61. The underlined word ―unethical‖ in Paragraph 7 is closest in meaning to ______.
A. unacceptable
B. misled
C. impractical
D. illegal
62. According to the article, Professor Alex Greenwood believes that _______.
A. there is no need to worry about the extinction of African and Asian elephants at present
B. it’s necessary to bring back species that are beneficial to human beings from extinction
C. the return of the woolly mammoth would help to balance ecosystems
D. it’s more important to protect present species than to bring back extinct ones
C
Each year, 500 million people from 164 countries celebrate World Environment Day on 5 June. It may seem like there is not much that an individual can do to save the world, but there is. One of the first steps is to understand the problems and their solutions.
Try to learn about your ecosystem, endangered animals and pollution. If you are well-informed, you can make better decisions about how to save energy and produce less waste. You can also learn how to be a better consumer and not buy products made from endangered animals or which have too much packaging. Also share your concerns with others and find ways to promote environmental education. Help educate people in your community about ways in which they can help protect the environment. The Earth is our only home. We should take good care of it.
Recycle
Make a list of all the things you can recycle at home and at school and start recycling. In some cases, you can sell the things you recycle. In others, you can turn unwanted items into something useful for another purpose, such as using old plastic bottles for growing plants. Most bottles and jars contain at least 25% recycled glass. And recycling aluminum cans saves 95% of the energy needed to make aluminum from bauxite ore. Recycling one ton of paper saves 17 trees, 26,000 liters of water, 1,700 liters of oil, 266 kilograms of air pollution and 2.3 cubic meters of rubbish dump space.
Use less energy
The easiest way to save energy is to cycle or walk whenever possible instead of using public transportation. At home and at school, you should only use electric lights and electrical appliances when you need them. There are many other less obvious ways of saving energy. For example, try to ask your mum to buy food which has been grown locally. Why? When people buy food from far away, it takes extra energy to package and ship it by boat, train, truck or plane.
Save water
You can save water by helping your Dad repair leaking pipes and toilets. Take short showers instead of baths. Some waste water from baths can be used for other purposes, such as watering plants or
washing outdoor spaces. It is important to help preserve the local water quality by not pouring dangerous household chemicals down the drain or into the ground. Dispose of them properly.
63. The target readers of this passage could mostly probably be ________．
A. housewives
B. car drivers
C. businessmen
D. students
64. Which of the following is NOT mentioned to protect the Earth?
A. Don't buy products made from endangered animals.
B. Don't buy food produced in faraway places.
C. Don't order more than you can eat at a restaurant.
D. Don't buy goods with heavy packaging.
65. According to the passage, the underlined words ―bauxite ore‖ in the third paragraph refers to ________．
A. a metal which can be used to make cans
B. a mineral from which a certain metal can be obtained
C. a container in which a certain material can be stored
D. a matter which can be used to produce energy
66. Which of the following is the best title for this passage?
A. You can do these!
B. Recycling to save the Earth
C. Celebrate the World Environment Day!
D. Use less water and energy
D
Charles Dickens was one of the most beloved storytellers in the English language. His novels made him famous in his own time, and continue as classics in ours.
Dickens began his literary career with almost no formal education. He was born in Landport, on Feb. 7, 1812, the second of eight children. When he was 12, his father was sent to debtor's prison. Dickens was forced to quit school and work in a London blacking factory. He would rework that terrible experience into his fiction for the rest of his life.
―He was a social reformer,‖ says actor Simon Callow, author of a new biography called Charles Dickens and the Great Theatre of the World. ―He knew what poverty was. He knew what it was to be rejected, to be cast aside, to live in squalor(悲惨).‖
And so Dickens wrote with great sympathy for the suffering of innocent and vulnerable(易受攻击的) children—characters like David Copperfield, Little Dorrit and the orphan, Oliver Twist：With his slice of bread in his hand, and his little brown parish cap on his head, Oliver was now led away from the wretched(苦难的) home, where one kind word or look never lighted the gloom of his infant(幼儿) days.
Yet he burst into an agony of childish grief as the cottage gate closed after him. Wretched as were the little companions in misery he was now leaving behind him, they were the only friends he had ever had.
His first book Sketches by Boz came out in 1836. With the appearance of Oliver Twist in London periodicals in 1837, the 25-year-old Dickens became the most popular writer in England. But his first love was theater, and he considered becoming an actor.
―When he was actually writing, he became his characters,‖ says Peter Ackroyd, author of Dickens: Public Life and Private Passion. ―He would get up from his desk, go over to the mirror and
mouth the words—do the expressions, grimaces(鬼脸), whatever, and then laugh, chuckle to himself, then go back to his desk and write it down.‖
Dickens created 989 named characters, which increased his popularity. Every one of his major works has been adapted for either stage or screen. A Christmas Carol inspired more than a dozen films, from Alistair Sims' Scrooge in 1951 to Jim Carrey's voicing of the same character in Disney's 2009, 3-D animated film.
The original 1843 manuscript(手稿) of A Christmas Carol is on display at the Morgan Library. Dickens wrote everything by hand, in tiny script, with a quill pen. Remarkably, the manuscript is both the first and the final draft, says Kiely, the curator. You can see where Dickens has changed the name of the first chapter from ―Old Marley's Ghost‖ to ―Marley's Ghost‖. Further down the page, he has canceled an entire section.
―He realizes he's not writing a novel, and he only has a very short time in which to write this,‖ Kiely explains. ―He's got to keep it tight, in order for it to be published in time for Christmas.‖Dickens wrote all the time. He traveled with a portable inkwell and a supply of quill pens. He was working on his last novel, Our Mutual Friend, en route from France to London when the train he was on crashed.
Dickens died five years later in 1870, after a stroke at age 58. As a comic talent and a social reformer, Dickens' achievement was extraordinary, says novelist T. C. Boyle, who earned a doctorate in Victorian literature.
―He achieved what any great artist achieves—a body of work that has entertained and delighted and instructed people down through the ages. That's what we all hope for,‖ says Boyle.
But Dickens' greatest fiction was his own character, says Callow, the biographer：―People think of him as a cheerful man... but he was increasingly suffering from depression and a sense of hopelessness. And that's worth knowing. I think it's always good to know that great creative individuals have their struggle, their drama.‖
67. What can probably be reflected in Dickens' works?
A. His love for his family.
B. His childhood sufferings.
C. His desire for formal education.
D. His reason to choose literary career.
68. The author quotes Dickens' description of Oliver Twist mainly to show ________．
A. that Dickens was full of pity for poor children
B. that Dickens knew well about poor children
C. what real poverty was like in his days
D. what kind of life Oliver Twist lived
69. It can be inferred from the passage that ________．
A. Sketches by Boz is nothing but a complete failure
B. Oliver Twist made Dickens first known to the public
C. A Christmas Carol proved Dickens an efficient writer
D. Our Mutual Friend came into being on a train
70. We can learn from the passage that ________．
A. all the characters created by Dickens are popular
B. people prefer films based on Dickens' novels to his works
C. once Dickens was more interested in performing than in writing
D. the films and plays based on Dickens' novels raise his popularity
71. What did Dickens intend to do by telling his stories?
A. To amuse his readers and change society.
B. To analyze the nature of society he was in.
C. To make an attack on the upper class of the time.
D. To get rid of his depression and sense of hopelessness.
第二卷(非选择题，共31分)
第一部分：任务型阅读(共10小题；每小题1分，满分10分)
The most wonderful time of the year (the Christmas season) is also the most stressful for lots of people struggling to fit in increased end-of-the-year workloads, holiday parties, shopping, guest hosting, t ravel, and seeing friends and relatives who you’d otherwise avoid. Luckily, the same coping mechanisms that can help relieve stress and find better balance during the year also work for this holiday.
Here are four tips to finding work—life balance during this season.
1. Know and avoid your stressors(压力源).
If cooking for a large group, baking cookies, or Christmas shopping are your key stressors, don’t do them. Lots of grocery stores will help cater your next holiday meal. Bakeries exist for a reason, and gift cards are much appreciated by all. Sto p trying to live up to someone else’s expectations of the holidays and stay merry by outsourcing the pain points.
2. Get flexible at work.
If you normally travel an hour each way at work, see if your boss will let you work from home in this special season to save time, get more done, and reduce your stress. Or ask if you can start work from home in the mornings and come to the office later in the day to avoid peak hours. Leave early and finish your day from the comfort of home, too.
3. Make your own list and check it twice.
Make a to-do list for yourself, for both work and life, then divide it up into categories like ―must do,‖ ―want to do,‖ and ―feel obligated to do.‖ If you can remove any or all of your required list, the rest of your to-dos will start to look a lot easier.
Once you have your lists in order, it’s time to start crossing things off. In between your must-dos tasks, include a want-to-do task to break things up and re-energize yourself. Yes, this holiday is a time to give back to oth ers and be selfless, but there’s still a bit of ―self‖ in selflessness, isn’t there?
4. If you start to feel a cold coming on, come to a full and complete stop.
The best way to stop a cold from exploding into a weeks-long sickness is to stop it at the start. Unless a task or activity is an absolute necessity, cancel your plans, put away your to-do lists, and settle in for a long winter’s nap. A day of rest and enough sleep is the only thing you NEED right now. Feel bad about declining holiday invitation s from your friends and family? You’re doing them a favor. Once people hear that you’re sick, they’ll be glad you stayed away —they don’t want to come down with a cold during the holiday any more than you do!
It is certain that you can feel less stressed in this hectic season when you stop expecting so much from yourself, because nobody puts so much expectation on you as you do to yourself. Trying to satisfy clients, co-workers, friends and family can be draining and can finally negatively impact you in many ways. When you simplify things up front, you relieve the stress off of yourself and
everyone else in the process. Stop focusing on what you feel like you’re obligated to do, and start focusing on what you want and need to do, the load will get lighter and you will feel a lot merrier under the Christmas tree.
每小题1分，满分10分)
1. If we toy with nature, we may be on our way to ______ (produce) a real-life Frankenstein’s monster.
2. The problem is believed ______ (discuss) at the meeting two weeks ago.
3. According to the national law, a man who ______ (break) the law will have to be punished.
4. The plan was that the two parties should first reach an agreement on the basic principle, the details ______ (work out) later.
5. The water ______ (feel) cool when I jumped into the pool for morning exercise.
6. The applicant wrote a letter of application, ______ (express) his preference to be admitted to this well-known university.
7. The flowers were so lovely that they ______ (sell) in no time.
8. Many people believe that the problems ______ (create) by cloning will soon be solved.
9. This project resulted in farmers ______ (replace) their crops with trees or grass.
10. The firefighters rushed into the building, only ______ (inform) that a kid set off the alarm by accident.
第三部分：阅读下列句子并根据所给的首字母用适当的单词填空(共10小题；每小题0.5分，满分5分)
1. There was an a______ moment when she didn't know whether to shake his hand or kiss his cheek.
2. He tried to stay calm, but his trembling hands b______ his nervousness.
3. The group recommended the young man for the position without h______, since his performance in the interview was so impressive.
4. The lecturer spoke so fast that I wasn’t able to a______ everything that he said.
5. Her husband was reserved and c______, never making a swift decision about anything.
6. Many believe that poverty is one of the direct c______ of overpopulation.
7. Anny described how she got into an a______ with one of her classmates, whom she thought was being very ridiculous.
8. The magazine promotes effective language teaching and is i______ for foreign language teachers in China.
9. Local people have mixed feelings about t______ the city of Nanjing into an international metropolis(大都会).
10. According to the reporters, a fire c______ most of the town and much of the castle.
第四部分：阅读下列句子并根据所给中文翻译用适当的词组填空(共6小题；每小题1分，满分6分)
1. 北京的几个天然气田正在建设中。
Construction work is ______ ______ at several gas fields in Beijing.
2. 如果身体没有足够的胆固醇，我们不可能生存。从另外一方面讲，如果身体的胆固醇过高，健康肯定会受影响。
If the body doesn't have enough cholesterol, we would not be able to survive. ______ ______ ______ ______, if the body has too much cholesterol, our health is sure to be harmed.
3. 在解决关于长江的各种问题上，我们任重道远。
We still have a long way to go to solve all the problems ______ ______ ______ the Yangtze River. 4. 真是一场精彩的音乐会；我尤其喜欢最后一支曲子。
It was a good concert; I enjoyed the last song ______ ______.
5. 你会有一种满足感, 因为你知道自己为帮助解决气候变化问题尽了一份力。
You will find ______ ______ ______ ______ knowing that you did your part to help solve the problem of climate change.
6. 中国正在进行资源税制的改革，这凸显出北京按照五年计划推动环保改革的决心。
China is moving to reform its resources tax system, which underlines Beijing’s determination to ______ ______ ______ environmental reforms under its five-year plan.
The End!
Good luck!
南京师大附中2015-2016学年度第一学期
高二年级期中考试英语答案
单项选择：
21-25：DCACC 26-30：ABDBC 31-35：CCBAC
完形填空：
36-40: CBDDB 41-45: DACBA 46-50: CBACB 51-55: CDACB
阅读理解：
A: BCD B: CCAD C: DCBA D: BACCA
任务型阅读:
1.Topic / Title / Subject
2. season / holiday
3. stress
4. avoided
5. expectations
6. flexible
7. matters/ counts
8. down
9. necessary 10. focusing
语法填空(10’)
1. producing
2. to have been discussed
3. breaks
4. to be worked out
5. felt
6. expressing
7. were sold 8. created 9. replacing 10. to be informed
单词拼写(5’)
1. awkward
2. betrayed
3. hesitation
4. absorb/ analyze
5. cautious
6. consequences
7. argument
8. intended
9. transforming 10. consumed
完成句子(6’)
1.under way
2. On the other hand
3. in/with regard to; in connection with
4. in particular
5. a sense/ feeling of satisfaction
6. push ahead with
江苏省南京市南师附中2019-2020学年高二下学期期中数学试题(解析版)
南京师大附中2019-2020学年度第2学期 高二年级期中考试数学试卷 注意事项： 1.本试卷共4页，包括单选题（第1题~第8题）、多选题（第9题~第12题）、填空题（第13题~第题18题）、解答题（第19题~第23题）四部分，本试卷满分为150分，考试时间为120分钟. 2.答题前，请务必将自己的姓名、班级、学号写在答题纸的密封线内，试题的答案写在答题纸上相应题目的答题区内，考试结束后，交回答题纸. 一、单项选择题：本题共8小题，每小题5分，共40分.在每小题给出的四个选项中，只有一项是符合题目要求的. 1.若2 20n =A ，则n 的值为（ ） A. 2 B. 3 C. 4 D. 5 【答案】D 【解析】 【分析】 根据排列数公式可得出关于n 的二次方程，进而可解得正整数n 的值. 【详解】由排列数公式可得()2 120n A n n =-=，即2200n n --=， n N *∈Q ，解得5n =. 故选：D. 【点睛】本题考查排列数方程的求解，考查排列数公式的应用，考查计算能力，属于基础题. 2.函数()sin 2f x x =的导数是（ ） A. 2cos2x B. 2cos2x - C. 2sin2x D. 2sin 2x - 【答案】A 【解析】 【分析】 利用复合函数的求导公式可求得()f x '，进而可得出结果. 【详解】()sin 2f x x =Q ，()()()sin 22cos22cos2f x x x x x ∴'='='=.
故选：A. 【点睛】本题考查复合函数求导，考查计算能力，属于基础题. 3.若i 为虚数单位，复数z 满足()134z i i +=+，则z 的 虚部为（ ） A. 52 i B. 52 C. 52 i - D. 52 - 【答案】D 【解析】 【分析】 利用复数的模长公式和复数的除法法则可求得复数z ，进而可得出复数z 的虚部. 【详解】()1345z i i +=+=Q ，因此，()515551222 i z i i -= ==-+. 因此，复数z 的虚部为5 2 -. 故选：D. 【点睛】本题考查复数虚部的求解，同时也考查了复数的运算、复数的模、复数的实部虚部，考查计算能力，属于基础题. 4.已知等差数列{}n a ，若2a 、4038a 是函数()32 113 f x x x mx =-++的极值点，则2020a 的值为（ ） A. 1 B. 1- C. ±1 D. 0 【答案】A 【解析】 【分析】 求得()f x '，利用韦达定理和等差中项的性质可求得2020a 的值. 【详解】()3 2113 f x x x mx =-++Q ，()22f x x x m ∴-'=+， 由韦达定理240382a a +=，又()2020240381 2 a a a =+，所以20201a =. 故选：A. 【点睛】本题考查利用极值点求参数，同时也考查了等差中项性质的应用，考查计算能力，属于基础题. 5.已知复数z 满足11z -=，则z 的最大值为（ ） A. 1 B. 2 C. 3 D. 4
南师附中2020届高三年级第二学期期初检测试卷 数学(含附加题)数学参考答案及评分标准
南师附中2020届高三年级第二学期期初检测试卷 数学试题参考答案及评分标准 第Ⅰ卷（必做题，160分） 一、填空题（本大题共14小题，每小题5分，计70分．不需写出解答过程，请把答案写在答题纸的指定位置上） 1．[]2,4- 2．二 3．6 4．5 5．()2,0 6． 58 7．3 8．252 9．12 10．120, 5?? ???? 11．[)4,+∞ 12．19 13．[]1,11- 14．3ln 2,02?? - - ??? 二、解答题（本大题共6小题，计90分．解答应写出必要的文字说明，证明过程或演算步骤，请把答案写在答题纸的指定区域内） 15．（本小题满分14分） 解：（1）由正弦定理 a sin A ＝ b sin B ＝ c sin C ＝2R ，得a ＝2R sin A ，b ＝2R sin B ，c ＝2R sin C ， 代入a cos B ＋b cos A ＝c cos A cos C ，得 (sin A cos B ＋sin B cos A ) cos C ＝sin C cos A ，…………2分 即sin(A ＋B )cos C ＝sin C cos A ． 因为A ＋B ＝π－C ，所以sin(A ＋B )＝sin C ， 所以sin C cos C ＝sin C cos A ，…………4分 因为C 是ⅠABC 的内角，所以sin C ≠0，所以cos C ＝cos A ．
又因为A ，C 是ⅠABC 的内角，所以A ＝C ．…………6分 （2）由（1）知，因为A ＝C ，所以a ＝c ，所以cos B ＝a 2＋c 2－b 22ac ＝a 2－2 a 2．…………8分 因为BA →·BC → ＝1，所以a 2cos B ＝a 2－2＝1，所以a 2＝3．…………10分 所以cos B ＝1 3 ．…………12分 因为B Ⅰ(0，π)，所以sin B ＝1－cos 2B ＝22 3．…………14分 16．（本小题满分14分） 解：（1）因为AD Ⅰ平面BCC 1B 1，AD ?平面ABCD ，平面BCC 1B 1∩平面ABCD ＝BC ， 所以AD ⅠBC ．…………4分 又因为BC ?平面ADD 1A 1，AD ?平面ADD 1A 1， 所以BC Ⅰ平面ADD 1A 1．…………6分 （2）由（1）知AD ⅠBC ，因为AD ⅠDB ，所以BC ⅠDB ，…………8分 在直四棱柱ABCD －A 1B 1C 1D 1中DD 1Ⅰ平面ABCD ，BC ?底面ABCD ， 所以DD 1ⅠBC ，…………10分 又因为DD 1?平面BDD 1B 1，DB ?平面BDD 1B 1，DD 1∩DB ＝D ， 所以BC Ⅰ平面BDD 1B 1，…………12分 因为BC ?平面BCC 1B 1， 所以平面BCC 1B 1Ⅰ平面BDD 1B 1．…………14分 17．（本小题满分14分） 解：（1）连接AB ，因为正方形边长为10米，
江苏省南师附中2020年高三考前模拟最后一卷数学试卷含答案
南京师大附中2020届高三年级模拟考试 数学. 观 注意事项: 1. 本试卷共4页，包括填空题(第1题?第14题)、解答题(第15题?第20题)两部分?本 试卷滚分为160分，考试时间为120分钟. 2. 答题前?请务必将口己的姓名■学校、班级、学号写在答题卡的相应位置?试题的答案 写在答题卡上对应题目的答案空格内.考试结束后.交回答题卡. ? ? ? 参考公式： 1 n 一 一 1 丿 样本数据x/2,￡的方差疋=丄》(兀yr,其中“一乂兀. n /-I n /=i 锥体的体积V^-Sh,其中S 是锥体的底面积，力是锥体的髙. 3 球体的表面积S=4寸2,其中，?是球体的半径. 一、填空题:本大题共14小题，每小题5分，共计70分.不需写出解答过程，请把答案写在 爾 卡相轆單上. 1. 已知集合 A={x^x\ < L xeZ}, B={—l,0,l,6},则 AQB= A . 2. 已知复数z=(l - 2i)(a + i), 其中i 是虚数单位.若z 的实部为0,则实数a 的值为 ▲ ? 3?样本数据6, 7, 10, 14, 8, 9的方差是 ▲ ? 4. 下图是?一个算法流程图.若输入的x 的值为1,则输出S 的值为 第4题图 5. 将一颗质地均匀的骰子(一种各个面上分别标有1, 2, 3, 4, 5, 6个点的正方体玩具)先 后抛掷2次，则出现向上的点数之和为6的倍数的概率是▲. 6. 己知函数尸sin(2x+^)(--<^<-)的图象关于点(丝，0)对称，则。的值是▲ ? 2 2 3 7. 已躲P-ABC 是正三棱锥，其外接球O 的表面积为16兀，且ZAPO = ZBPO = ZCPO = 30° , 则该三棱锥的体积为▲ ? 8. 若双曲线C ： 4-4 = ,(^>0^ b>?的离心率为3,则抛物线y = ^x 2 的焦点到双曲线 a 2 b 2 4 C 的渐近线距离为▲? 2020.06 /输出S /
江苏南师附中2021届高三年级联考试题(数学)
江苏南师附中2021届高三年级联考试题 数 学 参考公式： 1．随机变量X 的方差()()2 1n i i i D X x p μ=-∑＝，其中μ为随机变量X 的数学期望． 2．球的体积公式：3 3 4R V π= ． 一、单项选择题：本题共8 小题，每小题5分，共40分.在每小题给出的四个选项中，只有一项是符合题目要求的. 1．已知集合M ＝{x |﹣4＜x ＜2}，N ＝{x |x 2﹣5x ﹣6＜0}，则M N = （ ） A ．{x |﹣1＜x ＜2} B ．{x |﹣4＜x ＜2} C ．{x |﹣4＜x ＜6} D ．{x |2＜x ＜6} 2．若z=2+i ，则|z 2–2z |=（ ） A ．0 B ．5 C ．2 D ．13 3．已知,a b ∈R ，下列四个条件中，使a b <成立的充分不必要的条件是（ ） A ．1a b <- B ．1a b <+ C ．22a b < D ．33a b < 4．赵爽是我国古代数学家、天文学家．约公元222年，赵爽为《周髀 算经》一书作序时，介绍了“勾股圆方图”，亦称“赵爽弦图”，它是 由四个全等的直角三角形与一个小正方形拼成的一个大正方形．如 图是一张弦图，已知大正方形的面积为25，小正方形的面积为1，若 直角三角形较小的锐角为α，则tan2α的值为（ ） A ．34 B ．2425 C ．127 D ．247 5．函数ln || ()x f x x x =- 的图象大致为（ ） 6．已知随机变量X －1 a 1 P 16 13 12 当a 在()11-， 内增大时，方差()D X 的变化为（ ） A ．增大 B ．减小 C ．先增大再减小 D ．先减小再增大 D
2020届江苏省南师附中、淮阴中学、姜堰中学、海门中学高三下学期四校4月联考数学理
绝密★启用前 江苏省南师附中、淮阴中学、姜堰中学、海门中学 2020届高三下学期四校4月联考 注意事项：1、答题前填写好自己的姓名、班级、考号等信息2、请将答案正确填写在答题卡上 一、填空题:本大题共14小题,每小题5分,共70分?请把答案填写在答题卡相应位置上. 1.已知集合A={x|-1
江苏省南师附中、天一、淮中、海门中学2017届高三下期初四校联考理科数学试卷
南师附中、天一、淮中、海门中学四校联考数学理科 一、填空题：本大题共14小题，每小题5分，共70分.请把答案填写在答题卡相应位置上．．．．．．．． . 1．已知全集,6}{1,2,3,4,5=I ，集合{1,3,5}=A ，{2,3,6}=B ，则(?I A )=B ▲ ． 2．复数21i +1 +的实部为 ▲ ． 3．下图是一个算法流程图，则输出的n 的值是 ▲ ． 4．某校在市统测后，从高三年级的1000名学生中随机抽出100名学生的数学成绩作为样本进行分析，得到 样本频率分布直方图，如图所示．则估计该校高三学生中数学成绩在[110,140)之间的人数为 ▲ ． 5．若双曲线22 221x y a b -=的一条渐近线过点()2,1，则双曲线的离心率为 ▲ ． 6．现有5张分别标有数字1，2，3，4，5的卡片，它们大小和颜色完全相同．从中随机抽取2张组成两位 数，则两位数为偶数的概率为 ▲ ． 7．已知点P (y x ，)满足?? ???≥≥≤+14x x y y x ，则x y z =的最大值为 ▲ ． 8．设正项等比数列{a n }满足4352a a a -=．若存在两项a n 、a m ，使得m n a a a ?=41，则n m +的值为 ▲ ． 9．在正方体1111ABCD A BC D -中， P 为1AA 中点，Q 为1CC 中点，AB = 2，则三棱锥B-PQD 的体积为 ▲ ． 10．已知f (x )是定义在R 上的奇函数．当x ＜0时，f (x )＝x 2－2x ＋1．不等式2(3)(2)f x f x ->的解集用区 间表示为 ▲ ． 11．在平面直角坐标系xOy 中，设直线0(0)x y m m -+=>与圆228x y +=交于不同的两点A ，B ，若圆上存在 点C ，使得△ABC 为等边三角形，则正数m 的值为 ▲ ． 12．已知P 是曲线x x y ln 21412-=上的动点，Q 是直线14 3-=x y 上的动点，则PQ 的最小值为 ▲ ． 13．矩形ABCD 中，P 为矩形ABCD 所在平面内一点，且满足P A = 3，PC = 4．矩形对角线AC = 6，则 ?= ▲ ． 14．在△ABC 中，若 tan tan 3tan tan A A B C +=，则sin A 的最大值为 ▲ ． （第4题图）
南师附中2014届高三数学第一轮复习课课练04函数解析式(教师版)
§04 函数的解析式 姓名 等级 一．填空题： 1．已知2 (1)21f x x +=+，则(1)__________f x -=．2 289x x -+ 2．已知()f x 是二次函数，且()02f =，()()11f x f x x +-=-，则()f x = 213 222 x x -+ 3．函数f (x )＝ 若f (a )＝1 2，则a = ．-1 4．已知定义在),0[+∞的函数???<≤≥+=)20()2(2)(2x x x x x f , 若425 )))(((=k f f f ，则实 数= k 2 3 5. 已知()2 1cos sin f x x -=，则()f x = ．[]()2 20,2x x x -∈ 6．若f (x )＋ 21f (x 1)＝x , 则 f (x )＝ ．x x 3234- 7．已知函数()()x g x f ,分别由下表给出： 则()[]1g f 的值 ；满足()[]()[]x f g x g f >的x 的值 . 8. 已知22 11()x x f x x x +++=，则()f x =__________________；2 1x x -+，x R ∈且0x ≠ 9. 已知定义在R 上的奇函数()f x 和偶函数()g x 满足2 ()()21f x g x x x +=+-， 则()f x =____________________，()g x =__________________.2x ，2 1x - 10. 已知函数2 ()f x x x =+与()y g x =的图像关于直线2x =对称，求()g x 的解析式 为 ．2 920x x -+ 二．解答题 11．已知()f x 是一次函数，且满足3(1)2(1)217f x f x x +--=+，求()f x ； 解：设()(0)f x ax b a =+≠， 则3(1)2(1)333222f x f x ax a b ax a b +--=++-+-5217ax b a x =++=+， ???≤>., ,,log 0202x x x x
2018届南师附中、天一、海门、淮阴四校联考期初高三数学调研测试试题(含详细解答)
｛冷｝的前科项和，则总二 A 2018届南师附中、天一、海门、淮阴四校联 考期初高三数学调研测试试题 I 必做題部分 注慮事项 苇生在答蠅前请认莫闻爆本注盘爭琨恳备題答越宴求 1. 本试卷扶4頁包含战宅蛊￡弟1理一第“題）、解浮題f 第沽題一第20題）.事卷满分 160分*考试时间为no 分钟.考试站虑后谥将裁鬆卡交冋. 2. 答廳前诸您的必将自己的姓".廉专吒号用03亳能朋色團水的签宁笔壇斗在试雄戾答昭 I ：的规址位賈一 乱请在答题卡卜战照脚存存对晦的袴題区域内作欝.衣共他位置作菩一律尤效.作答愛薇用 0.5老贰/色眾水的徒了遼.请注盘字怵工整乜址消建? 4. 如盂杵：圈锁用2BM 笔绘.写仙楚线峯、符号弊锁加黑、加UL 5. 请保持裁題卜左面時洁不輕折?. tt-tn ， 押不准使川般带紙、髀止液、叮擦洗的岡珠笔. 躊考金式 植那的徉积食“十討八氏中为3施邯的底面积”"为植协的向. 、埴宁題；羸大題共M 小4T 每?卜趣F 分”共刑分.请把茬案塡吁在警趣卡相应位总上. 1.已A = ｛1^｝, B = ｛13）,且/口左=｛3｝,刚实数应的值是 ______________ A Z 已如^7 = — ,其中f 是虚樹单位』贝虹餉丈邹是 ▲ ?- 1 — i 3. 根据如匱餅示的伪代與，可知输出的结異￡为 鱼 ?. 门二2 I 5^0 ! While U 1+2 ；End while I Print 5 ;Jiod 4. 如图所环，二面旦销害店根播以往 某种面色的銷售记弧，绘制“日销匡里的頻率井布直方图?若 —个月以迫天计算，估计这冢面迈店一个月内日销WslOO 个到20D 个的天数为 企 一 5. 有一个质地均匀的正四面体木块电于面分别标有数字1,乙鼻眼椅此木抉在水平桌面二抽两次， 则两女看卞到前数宇部大于2的概車为 ▲ . * b.已 Mlzn 二亠H 二」：测 bill - d co J '肖力 ▲ ?? 化设数列｛务｝为等差数列』?列数列｛乐｝的前理呗和，已^3. =9, = 225 f 色為数別 5.〔第3强圏）*
南师附中2014届高三数学第一轮复习课课练02函数的概念(教师版)
1 §02 函数的概念 一．填空题 1．函数()y f x =的图象与直线x ＝2的公共点共有 个。 0或1 2. 在函数①x y sin 1= ，② x x y ln =，③y ＝xe x ，④x x y sin =中，与函数31x y =定义域相同的函数为 ．④ 3．已知函数 ()f x 的定义域为()1,0-,则函数()21f x -的定义域为 ．1(0,)2 4．函数() f x =的定义域为 ． 5．若函数)22lo g 21y ax ax =++的定义域为R ，则a 的取值范围是 ．[ )0,1 6．已知函数f (2x ）的定义域是［-1，1］，则f (log 2x )的定义域为 ．［2，4］ 7．若函数f (x )=log a (x +1)(a ＞0，a ≠1)的定义域和值域都是［0，1］，则a 等于 ．2 8．若a b c <<,则函数()()()()()()()f x x a x b x b x c x c x a =--+--+--的两个零点分别位 于区 间 内．(),a b 和(),b c 9. 如果函数f (x )=ax -1的定义域为[－2 1，+)∞，那么实数a 的取值是 ．-2 10.若一系列函数的解析式相同值域相同但是定义域不同，则称这些函数为“孪生函数”。那 么函数解析式为y =2x 2+1,值域为{1,5}的孪生函数共有 个．3 二．解答题 11. 判断下列各组中的两个函数是否是同一函数？为什么？ （1）3 )5)(3(1+-+= x x x y ；52-=x y 解：不是同一函数，定义域不同 （2）111-?+=x x y ；)1)(1(2-+=x x y 解：不是同一函数，定义域不同 （3）2 1)52()(-=x x f ，52)(2-=x x f 解：不是同一函数，定义域、对应法则 都不同 （4） f (n )=2n -1,g (n )=2n +1,(n ∈Z ). 解：不是同一函数，对应法则不同 （5）||)(2 x x x f =， ? ??-∞∈-+∞∈=)0,(,),0(,)(t t t t t g 解：是同一函数 12．求下列函数的定义域： （1）1lg 4x y x -=-； （2）() 2lg 4y x x =- 解： （1）()1,4 ；（2 ）((() 0,2223,224??-++?? 。 13．（2013陕西）在如图所示的锐角三角形空地中, 欲建一个面积不小于300m 2的内接矩形花园(阴影部分), 求其边长x (单位m )的取值范围．[10,30]
江苏省南师附中2020届高三数学6月模拟考试试卷【含答案】
江苏省南师附中2020届高三模拟考试试卷(2020．6) 数 学 (满分160分，考试时间120分钟) 参考公式： 样本数据x 1，x 2，…，x n 的方差s 2＝1n (x i －x)2，其中x ＝1 n x i . 锥体的体积V ＝1 3 Sh ，其中S 是锥体的底面积，h 是锥体的高． 球体的表面积S ＝4πr 2，其中r 是球体的半径． 一、 填空题：本大题共14小题，每小题5分，共70分． 1. 已知集合A ＝{x||x|≤1，x ∈Z }，B ＝{x|－1，0，1，6}，则A ∩B ＝________． 2. 已知复数z ＝(1－2i)(a ＋i)，其中i 是虚数单位．若z 的实部为0，则实数a 的值为________． 3. 样本数据6，7，10，14，8，9的方差是________． 4. 右图是一个算法流程图，若输入的x 的值为1，则输出S 的值为________． 5. 将一颗质地均匀的骰子(一种各个面上分别标有1，2，3，4，5，6个点的正方体玩具)先后抛郑2次，则出现向上的点数之和为6的倍数的概率是________． 6. 已知函数y ＝sin(2x ＋φ)(－π2＜φ＜π2)的图象关于点(2π 3 ，0)对称，则φ的值是 ________． 7. 已知P-ABC 是正三棱锥，其外接球O 的表面积为16 π，且∠APO ＝∠BPO ＝∠CPO ＝30°，则该三棱锥的体积为________． 8. 若双曲线C ：x 2a 2－y 2b 2＝1(a ＞0，b ＞0)的离心率为3，则抛物线y ＝1 4 x 2的焦点到双曲线 C 的渐近线距离为________． 9. 已知函数f(x)＝sin x ＋2x ＋x 3.若f(a －6)＋f(2a 2)≤0，则实数a 的取值范围是________． 10. 设等差数列{a n }的前n 项和为S n .已知a 1＋a 2＋a 5＝47，a 3＋a 4＝28.若存在正整数k ，使得对任意的n ∈N *都有S n ≤ S k 恒成立，则k 的值为________． 11. 已知圆O ：x 2＋y 2＝m(m ＞0)，直线l ：x ＋2y ＝10与x 轴，y 轴分别交于A ，B 两点．若 圆O 上存在点P 使得△PAB 的面积为25 2 ，则实数m 的最小值为________． 12. 已知点G 为△ABC 的重心，点D ，E ，F 分别为AB ，BC ，CA 的中点．若AB →·GD →
江苏南师附中2019高三高考重点卷(十)(最后一卷)-数学
江苏南师附中2019高三高考重点卷（十）（最后一卷）-数 学 数学 (总分值160分，考试时间120分钟) 2018、5 参考公式： 锥体的体积公式为V ＝1 3Sh ，其中S 是锥体的底面积，h 是锥体的高、 【一】填空题：本大题共14小题，每题5分，共70分、 1.设集合U ＝R ，集合M ＝{x|x 2－x ≥0}，那么?U M ＝______________、 2.高三(1)班共有48人，学号依次为1，2，3，…，48，现用系统抽样的方法抽取一个容量为4的样本，学号5，29，41在样本中，那么还有一个同学的学号应为______________、 (第4题) 3.i 为虚数单位，?????? a ＋i i ＝2，那么正实数a ＝________________、 4.执行右图所示的算法流程图，假设输出的结果为1 2，那么输入的x 为________________、 5.在平面直角坐标系xOy 中，角α的始边与x 轴正半轴重合，终边在直线y ＝－3x 上，且x ＞0，那么sin α＝____________、 6.从集合{1，2，3，4，5}中随机选取一个数记为a ，从集合{2，3，4}中随机选取一个数记为b ，那么b ＞a 的概率是__________、 7.向量a ＝(x －z ，1)，b ＝(2，y －z)，且a ⊥b .假设x ，y 满足不等式组???? ?x －2y ＋2≥0， x ＋2y －2≥0， x ≤2， 那么z 的取值范围是______________、 8.“a ＝1”是“函数f(x)＝2x －a 2x ＋a 在其定义域上为奇函数”的____________条件、(填“充分不必要”“必要不充分”“充要”或“既不充分也不必要”) (第9题) 9.一个圆锥的展开图如下图，其中扇形的圆心角为120°，底面圆的半径为1，那么该圆锥的体积为__________、
南师附中2014届高三数学第一轮复习课课练07函数性质的运用(教师版)
§07 函数性质运用 姓名 等级 一、填空题： 1.①④ 2. f (2)=6 3. 函数f (x )＝|ln(2－x )|的增区间是（1,2） 4. a ＝1 2 5. （0, 0.5） 6.充要条件 7.①②④ 8. ]1,(-∞ 9. 15 4 10. {x | x ＜0或x ＞4) 二、解答题： 11. 函数()y f x =(0)x ≠是奇函数，且当(0,)x ∈+∞时是增函数，若(1)0f =，求不等式 1 [()]02 f x x -<的解集. 分析：利用函数的奇偶性及函数的单调性. 解：∵函数()y f x =(0)x ≠是奇函数，且(1)0f = ∴(1)(1)0f f =-= 由()y f x =在(0,)x ∈+∞时是增函数得：()y f x =在(,0)x ∈-∞时也是增函数 ∴ 1 [()]0 2 f x x -<1()021()12x x x x ?-????->??1 ()12 x x ?-<-或 1 ()12 x x ?->， 解得：1{|02x x x <<<< 或， ∴不等式1[()]02f x x -<的解集为：｛| x 0x << 或12x << ｝ 12．已知函数1()ln 1a f x x ax x -=-+-，当1 2a ≤时，讨论()f x 的单调性。 解： 因为1()ln 1a f x x ax x -=-+-， 所以 2' 22 111()(0,)a ax x a f x a x x x x --+-=-+=∈+∞， 令 2 ()1,(0,) h x a x x a x =-+-∈+∞， ①当12 a =时，12,()0x x h x =≥恒成立，此时' ()0f x ≤，函数 ()f x 在∞（0，+）上 单调递减；
2019-2020年江苏省南京市南师附中高二下学期数学期中考试
3i n 南京师大附中 2019-2020 学年度第 2 学期 高二年级期中考试数学试卷 2020.05 注意事项： 1．本试卷共 4 页，包括单选题（第 1 题~第 8 题）、多选题（第 9 题~第 12 题）、填空题（第 13 题~第题 18 题）、解答题（第 19 题~第 23 题）四部分，本试卷满分为 150 分，考试时间为 120 分钟. 2． 答题前，请务必将自己的姓名、班级、学号写在答题纸的密封线内，试题的答案写在答题纸上相应题 目的答题区内，考试结束后，交回答题纸. 一、单项选择题：本题共 8 小题，每小题 5 分，共 40 分．在每小题给出的四个选项中，只有一项是符合题目要求的． 1. 若 A 2 = 20 ，则n 的值为（ ） A. 2 B. 3 C. 4 D. 5 2. 函数 f ( x ) = sin 2 x 的导数是（ ） A. 2 c o s 2 x B. -2 cos 2 x C. 2 sin 2 x D. - 2 sin 2 x 3. 若i 为虚数单位，复数 z 满足 z (1 + i ) =| 3 + 4i | ，则 z 的虚部为（ ） A. 5 i B. 5 C. - 5 i D. - 5 2 2 2 2 4. 已知等差数列{a } ，若 a ， a 是函数 f ( x ) = 1 x 3 - x 2 + mx + 1的极值点，则 a 的值为（ ） n 2 4038 3 2020 A. 1 B. - 1 C. ± 1 D. 0 5. 已知复数 z 满足 z -1 - = 1，则 z 的最大值为（ ） A. 1 B .2 C . 3 D . 4 6. 若 ke x - x -1 ≥ 0 恒成立，则实数k 的取值范围是（ ） A .(-∞,1] B .(0,1] C .(0, +∞) D .[1, +∞) 7. 某班联欢会原定的 3 个节目已排成节目单，开演前又增加了 2 个新节目，如果将这 2 个新节目插入节目单中，那么不同的插法种数为（ ） A. 1 2 B. 20 C. . 36 D . 120 8. 定义在 R 上的可导函数 f (x ) 满足 f '(x ) < 1，若 f (m ) - f (1 - 2m ) ≥ 3m -1，则 m 的取值范围是（ ）
南师附中2012届高三高考模拟卷(最后一卷)数学试题
2012届高三模拟考试试卷(十) (南师附中) 数 学 (满分160分，考试时间120分钟) 2012．5 参考公式： 锥体的体积公式为V ＝1 3 Sh ，其中S 是锥体的底面积，h 是锥体的高． 一、 填空题：本大题共14小题，每小题5分，共70分． 1. 设集合U ＝R ，集合M ＝{x|x 2－x ≥0}，则?U M ＝______________． 2. 高三(1)班共有48人，学号依次为1，2，3，…，48，现用系统抽样的方法抽取一个容量为4的样本，已知学号5，29，41在样本中，那么还有一个同学的学号应为______________． (第4题) 3. 已知i 为虚数单位，?? ?? a ＋i i ＝2，则正实数a ＝________________． 4. 执行右图所示的算法流程图，若输出的结果为1 2 ，则输入的x 为________________． 5. 在平面直角坐标系xOy 中，角α的始边与x 轴正半轴重合，终边在直线y ＝－3x 上，且x ＞0，则sin α＝____________． 6. 从集合{1，2，3，4，5}中随机选取一个数记为a ，从集合{2，3，4}中随机选取一个数记为b ，则b ＞a 的概率是__________． 7. 已知向量a ＝(x －z ，1)，b ＝(2，y －z)，且a ⊥b .若x ，y 满足不等式组???? ?x －2y ＋2≥0， x ＋2y －2≥0， x ≤2， 则z 的取值范围是______________． 8. “a ＝1”是“函数f(x)＝2x －a 2x ＋a 在其定义域上为奇函数”的____________条件．(填“充 分不必要”“必要不充分”“充要”或“既不充分也不必要”) (第9题) 9. 已知一个圆锥的展开图如图所示，其中扇形的圆心角为120°，底面圆的半径为1，则该圆锥的体积为__________． 10. 已知F 是双曲线C ：x 2a 2－y 2 b 2＝1(a ＞0，b ＞0)的左焦点，B 1B 2是双曲线的虚轴，M 是 OB 1的中点，过F 、M 的直线交双曲线C 于A ，且FM →＝2MA → ，则双曲线C 离心率是______________． 11. 已知数列{a n }是公差不为0的等差数列，{b n }是等比数列，其中a 1＝3，b 1＝1，a 2
【高三数学】南师附中高三数学冲刺试卷
7 8 99 4 4 467 3 南师大附属中学2011届高三冲刺卷 数学试卷Ⅰ 2011.5 一、填空题（本大题共14小题，每小题5分，计70分） 1. 已知集合},3 sin |{Z n n x x A ∈==π ，则集合A 的子集的个数为_____▲______. 2. 若复数i i a 213++（a R ∈，i 为虚数单位）是纯虚数,则实 数 a 的值为______▲______. 的3. 已知条件p ：2|1|>+x ，条件q ：a x >，且p ?是q ?充分不必要条件，则a 的取值范围可以是____▲_____. 4. 右图程序运行结果是_______▲________. 5. 右图是七位评委打出的分数的茎叶统计图，去掉一个 最高分和一个最低分后，所剩数据的方差为 ▲ ． 6. 在120°的二面角内放置一个小球，它与二面角的两个面相切于A 、B 两点，这两个点的距离AB=5, 则小球的半径为_______▲________． 7. 函数)2ln()(2 x x x f -=的单调递增区间是________▲_______. 8. 将直线20x y λ-+=沿x 轴向左平移1个单位，所得直线与圆2 2 240x y x y ++-=相切，则实数λ的值为_____▲______． 9. O 是锐角?ABC 所在平面内的一定点,动点P 满足:OP OA =+u u u r u u u r 2AB AB Sin ABC λ? + ∠? u u u r u u u r a ←1 b ←1 i ←4 WHILE i ≤6 a ←a +b b ←a +b i ←i +1 END WHILE PRINT b 程序运行结果是
2014南师附中高三数学课本综合题1S
南京师大附中2014届高三数学课本综合题1 一、填空题 1.如果数集｛0，1，x +2｝中有3个元素，那么x 不能取的值是________. 2.sin 5π12cos π12 ＝________. 3.“a ＝3”是“直线ax ＋2y ＋1＝0和直线3x ＋(a －1)y －2＝0平行”的________条件. 4.已知x ＞0，y ＞0，2x ＋5y ＝20，则lg2x ＋lg y 的最大值是________. 5.三个数成等差数列，他们的和为15，他们的平方和为83，则这三个数是________. 6.已知sinα－3cosα=m －1, 则实数m 的取值范围是_________. 7.在坐标平面内，过点(1，2)的直线l 与x 轴的正半轴、y 轴的正半轴分别交于A ，B 两点，当ΔOAB 的面积最小时，直线l 的方程为_________. 8.执行如图流程图，输出的S 为_________. 9.已知sin(x ＋π6)=14, 则sin(5π6－x )+sin 2(π3－x )的值为_________. 10.已知|→a |＝1，|→b |＝ 3，→a ＋→b ＝( 3，1)， 则|→a －→b |＝_________，→a ＋→b 与→a －→b 的夹角为_________. 11.在△ABC 中，已知2a ＝b ＋c ，sin 2A ＝sin B sin C ，则△ABC 形状为_________. 12.设(5)5,(5)3,(5)4,(5)1f f g g ''====，若()2()()f x h x g x += ，则(5)h '=_________. 13.已知函数32()31f x x ax ax =-++在区间(),-∞+∞内既有极大值，又有极小值，则实数a 的取值范围是_________. 14.函数1 sin 2y x x =+在3x π=处的切线的倾斜角是_________. 15.若两个平行平面的距离等于10，夹在这两个平面间的线段AB 长为20，则AB 与这两个平面所成的角为_________.
南师附中2011届高三模拟考试(数学)
南师附中2011届高三模拟考试 数 学 (满分160分，考试时间120分钟) 2011．05 一、 填空题：本大题共14小题，每小题5分，共70分． 1. 已知全集U ＝R ，集合A ＝{x |log 2x ＞1}，则?U A ＝______________. 2. 已知复数z ＝2i 1＋i ，则该复数的虚部为______________． 3. 已知双曲线过点(2,1)且一条渐近线方程为x －y ＝0，则该双曲线的标准方程为__________． 4. 在如图所示的流程图中，输出的结果是__________． (第4题) 5. 在△ABC 中，三边a 、b 、c 所对的角分别为A 、B 、C ，若A ＝30°，a ＝1，b ＝2，则B ＝____________. 6. 已知向量a 与b 的夹角为150°，且|a|＝2，|b|＝3，则(2a ＋b )·a ＝____________. 7. 已知函数f (x )＝??? x (x ≥0)，－x 2－4x (x ＜0)， 若f (x )≤3，则x 的取值范围是____________． 8. 如图是函数y ＝A sin(ωx ＋φ)? ???A ＞0，ω＞0，|φ|＜π 2图象的一部分，则此函数的表达式为____________． (第8题) 9. 某人2011年初向银行申请个人住房公积金贷款a (a ＞0)元购买住房，年利率为r (r ＞0)，按复利计算，每年等额还贷一次，并从贷款后的次年初开始还贷．如果10年还清，那么每年应还贷款__________元．(用a 、r 表示) 10. 已知函数f (x )＝x x ＋a ，若函数y ＝f (x ＋2)－1为奇函数，则实数a ＝____________. 11. 已知等差数列{a n }的公差不为零且a 3、a 5、a 8依次成等比数列，则S 5 a 9 ＝ ______________. 12. 已知椭圆C ：x 2a 2＋y 2 b 2＝1(a ＞b ＞0)的右准线与x 轴交于点A ，点B 的坐标为(0，a )， 若椭圆上的点M 满足AB →＝2AM → ，则椭圆C 的离心率为____________． 13. 在平面直角坐标系xOy 中，集合M ＝{(x ，y )|x ＋y ≤1，且x ≥0，y ≥0}，N ＝{(x －y ，
江苏省南师附中高三数学第一轮复习课课练： 函数的概念教师
§02 函数的概念 一．填空题 1．函数()y f x =的图象与直线x ＝2的公共点共有 个。 0或1 2. 在函数①x y sin 1= ，② x x y ln =，③y ＝xe x ，④x x y sin =中，与函数31x y =定义域相同的函数为 ．④ 3．已知函数 ()f x 的定义域为()1,0-,则函数()21f x -的定义域为 ．1(0,)2 4．函数() f x =的定义域为 ． 5．若函数)22lo g 21y ax ax =++的定义域为R ，则a 的取值范围是 ．[)0,1 6．已知函数f (2x ）的定义域是［-1，1］，则f (log 2x )的定义域为 ．［2，4］ 7．若函数f (x )=log a (x +1)(a ＞0，a ≠1)的定义域和值域都是［0，1］，则a 等于 ．2 8．若a b c <<,则函数()()()()()()()f x x a x b x b x c x c x a =--+--+--的两个零点分别位 于区 间 内．(),a b 和(),b c 9. 如果函数f (x )=ax -1的定义域为[－2 1，+)∞，那么实数a 的取值是 ．-2 10.若一系列函数的解析式相同值域相同但是定义域不同，则称这些函数为“孪生函数”。那么函数解析式为y =2x 2+1,值域为{1,5}的孪生函数共有 个．3 二．解答题 11. 判断下列各组中的两个函数是否是同一函数？为什么？ （1）3 )5)(3(1+-+= x x x y ；52-=x y 解：不是同一函数，定义域不同 （2）111-?+=x x y ；)1)(1(2-+=x x y 解：不是同一函数，定义域不同 （3）21)52()(-=x x f ，52)(2-=x x f 解：不是同一函数，定义域、对应法则 都不同 （4） f (n )=2n -1,g (n )=2n +1,(n ∈Z ). 解：不是同一函数，对应法则不同 （5）||)(2 x x x f =， ? ??-∞∈-+∞∈=)0,(,),0(,)(t t t t t g 解：是同一函数 12．求下列函数的定义域： （1）1lg 4x y x -=-； （2）lg 4y x x =- 解：（1）()1,4；（2）(()()0,223,23,2323,4??-++??。 13．（2013陕西）在如图所示的锐角三角形空地中, 欲建一个面积不小于300m 2的内接矩形花园(阴影部分), 求其边长x (单位m )的取值范围．[10,30]
江苏省南师附中高三数学第一轮复习课课练： 集合的概念与运算学生
§01 集合的概念 姓名 等级 一、填空题： 1．已知集合A ={1,2,4}，B ＝{2,4,6}，则A ∪B ＝ ． 2．集合{1,2,3,4}共有 个子集． 3．已知集合{1,1,2,4},{1,0,2},A B =-=- 则A ∩B ＝ ． 4．设集合A ={－1,1,3}，B ={a +2,a 2＋4}，A ∩B ={3}，则实数a ＝________． 5．如果集合A ＝{x | ax 2＋2x ＋1＝0}只有一个元素，则实数a 的值为 ． 6．已知集合{}2log 2,(,)A x x B a =≤=-∞，若A B ?则实数a 的取值范围是(,)c +∞，其 中c = ． 7．设{} {}{}2 2,3,23,|1|,2,5U U m m A m A =+-=+=，?U A ＝{5}，则m ＝ ． 8．已知{}2|230A x x x =-->，{} 2|0B x x ax b =++≤，若A ∪B =R ，(]3,4A B =，则ab ＝ ． 9．若A ={()}2137x x x -<+，则A∩Z 的元素的个数为 ． 10．己知集合2220,2(52)50x x M x x Z x k x k ???-->??=∈???+++
二、解答题： 11．已知全集I=R ，A ={x |x 2－3x ＋2≤0}，B ={x |x 2－2ax ＋a ≤0,a ∈R }，且B ?A ，求a 的取值 范围． 12．设平面点集{} 221(,)()()0,(,)(1)(1)1A x y y x y B x y x y x ? ?=--≥=-+-≤????，求A B 所表示的平面图形的面积. 13．已知全集I =R ，A ={x |x 2－x －6＜0}，B ={x |x 2＋2x －8＞0}，C ={x |x 2－4ax ＋3a 2＜0}． (1)求实数a 的取值范围，使A ∩B ?C ； (2)求实数a 的取值范围，使?I A ∩?I B ? C ． 三、反思与小结：