2017届杨浦区高三数学一模(含答案)
(完整版)2017届上海市杨浦区高三二模数学卷(含答案)
- - - 1 -杨浦区2016学年度第二学期高三年级质量调研 数学学科试卷 2017.4考生注意： 1．答卷前，考生务必在答题纸写上姓名、考号, 并将核对后的条形码贴在指定位置上．2．本试卷共有21道题，满分150分，考试时间120分钟．一．填空题（本大题满分54分）本大题共有12题，1-6每题4分，7-12每题5分。
考生应在答题纸相应编号的空格内直接填写结果，每个空格填对得4分，否则一律得零分．1. 行列式123456789中, 元素5的代数余子式的值为_________.2. 设实数0ω>, 若函数()cos()sin()f x x x ωω=+的最小正周期为π, 则ω=_________.3. 已知圆锥的底面半径和高均为1, 则该圆锥的侧面积为_________.4. 设向量(2,3)a =r, 向量(6,)b t =r . 若a r 与b r 的夹角为钝角, 则实数t 的取值范围为 _________.5. 集合2{1,3,}A a =, 集合{1,2}B a a =++. 若B A A ⋃=, 则实数 a =_______.6. 设12,z z 是方程2230z z ++=的两根, 则12||z z -= _________.7. 设()f x 是定义在R 上的奇函数, 当0x >时, 3()2xf x =-. 则不等式()5f x <-的解为________.- - - 2 -8. 若变量,x y 满足约束条件12,20,20,x y x y x y +≤⎧⎪-≥⎨⎪-≤⎩则z y x =-的最小值为_________.9. 小明和小红各自掷一颗均匀的正方体骰子, 两人相互独立地进行. 则小明掷出的点 数不大于2或小红掷出的点数不小于3的概率为_________.10. 设A 是椭圆()22221 04x y a a a +=>-上的动点, 点F 的坐标为(2,0)-, 若满足||10AF =的点A 有且仅有两个, 则实数a 的取值范围为_________.11. 已知0a >, 0b >, 当21(4)a b ab++取到最小值时, b =_________. 12. 设函数()||||a f x x x a =+-. 当a 在实数范围内变化时, 在圆盘221x y +≤内,且不在任一()a f x 的图像上的点的全体组成的图形的面积为_________.二、选择题（本大题满分20分）本大题共有4题，每题有且只有一个正确答案，考生应在答题纸的相应编号上，填上正确的答案，选对得5分，否则一律得零分. 13. 设z ∈C 且0z ≠. “z 是纯虚数”是“2z ∈R ”的 ( )(A) 充分非必要条件 (B) 必要非充分条件(C) 充要条件(D) 既非充分又非必要条件14．设等差数列{}n a 的公差为d , 0d ≠. 若{}n a 的前10项之和大于其 前21项之和, 则 ()(A) 0d <(B) 0d > (C) 160a <(D) 160a >- - - 3 -S15．如图, N 、S 是球O 直径的两个端点. 圆1C 是经过N 和S 点的大圆, 圆2C 和圆3C 分别是所在平面与NS 垂直的大圆和小圆. 圆1C 和2C 交于点A 、B , 圆1C 和3C 交于点C 、D .设a 、b 、c 分别表示圆1C 上劣弧CND 的弧长、圆2C 上半圆弧AB 的弧长、圆3C 上半圆弧CD 的弧长. 则,,a b c 的大小关系为 ()(A) b a c >= (B) b c a => (C) b a c >>(D) b c a >>16．对于定义在R 上的函数()f x , 若存在正常数,a b , 使得()()f x a f x b +≤+对一切x ∈R 均成立, 则称()f x 是“控制增长函数”。
杨浦区2017学年度第一学期高三模拟高质量调研
杨浦区2017学年度第一学期高三模拟质量调研英语学科试卷2017. 12 本试卷分为第I卷（第1-11页）和第II卷（第12页）两部分。
全卷共12页。
满分140分。
考试时间120分钟。
考生注意：1．答第I卷前，考生务必将条形码粘贴在答题纸的指定区域内。
2. 第I卷（1-20小题，31---70小题）由机器阅卷，答案必须全部涂写在答题卡上。
考生应将代表正确答案的小方格用铅笔涂黑。
注意试题题号和答题卡编号一一对应，不能错位。
答案需要更改时，必须将原选项用橡皮擦去，重新选择。
答案写在试卷上一律不给分。
第I卷中的第21-30小题，IV. Summary Writing部分和第II卷的试题，其答案用钢笔或水笔写在答题纸的规定区域内，如用铅笔答题，或写在试卷上则无效。
第I卷（共100分）I. Listening ComprehensionSection 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. In a professor's office. B. In a second-hand book shop.C. In a library.D. In a hospital.2. A. 10 yuan. B. 20 yuan.C. 30 yuan.D. 50 yuan.3. A. House agent and customer. B. Shop assistant and customer.C. Car mechanic and car owner.D. Employer and employee.4. A. The man doesn't believe what the woman says.B. The weather report spoils the man's good mood.C. They will cancel the hiking due to the bad weather.D. The man thinks it unnecessary to give up the adventure.5. A. She always talks bad about her colleagues.B. She has a good reputation among her colleagues.C. She is good at handling complicated relationships.D. She has good relations with her colleagues and boss.6. A. Harmony in a community. B. Safety in the neighborhood.C. Preparation for Christmas.D. Ways to save electricity.7. A. Watching advertisements may help ease eyestrain（眼疲劳）.B. It's a great chance to break the habit of watching TV.C. The advertisements are long enough for her to have a nap.D. Focusing eyes on the screen for a long time is harmful to eyes.8. A. The man decides to go home by rail.B. Most people travel by car during the festival.C. Most people arrive beyond the scheduled time.D. The man will have a sound sleep on the bus.9. A. He is not a bit overweight.B. He likes his fitness instructor.C. She has set too many rules for him.D. She should talk with his personal trainer.10. A. Greeks are not allowed to get married before 18.B. Greek kids are not as independent as American kids.C. American parents don’t pay for children's wedding.D. Greek parents will take care of children until they are 18.Section BDirections: In Section B, you will hear several longer conversation(s) and short passage(s), and you will be asked several questions on each of the conversation(s) and the passage(s). The conversation(s) and passage(s) 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. The burn is 20 millimeters across.B. The burn is small but very painful.C. The burn takes away the victim's feeling.D. The burn is small but the skin is damaged.12. A. Use a clean plastic bag to keep warm.B. Bind up the burn with bandage or cloth.C. Treat the burned area with cold running water.D. Flush（冲洗）the burn with ice water for several minutes.13. A. To avoid infection. B. To ease pain.C. To speed recovery.D. To reduce stickiness. Questions 14 through 16 are based on the following passage.14. A. A cell phone. B. A leather wallet.C. A mini camera.D. An alarm clock.15. A. The wallet will sound an alarm.B. It will track the thief with GPS system.C. It will contact the bank to block balance.D. Its owner will receive a picture of the thief.16. A. It's out-dated in this digital age.B. It can text messages automatically.C. It is a multifunctional wallet.D. It is unique in appearance and function.Questions 17 through 20 are based on the following conversation.17. A. The concert is beyond her curfew(宵禁).B. She can’t go out on school night.C. Her mother is not available.D. She doesn’t like the band.18. A. His parents set a strict rule for him.B. His parents don’t care when he is back.C. He is self-disciplined and trustworthy.D. He envies those who have curfews.19. A. Promoting maturity. B. Giving sense of security.C. Improving sense of responsibility.D. Discouraging independence.20. A. It’s a severe punishment. B. It’s for her good.C. It’s a ridiculous practice.D. It’s an exceptional case.II. Grammar and VocabularySection ADirections: After reading the passage below, fill in the blanks to make the passages 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.It’s interesting when you think about how Japan is a nation (21) ______ appreciates the virtues of silence and good manners, and yet when it comes to eating noodles, Japanese people can be (22) ______ (loud) in the world.According to lifestyle website grapee.jp, slurping (发出"哧溜"声) when eating noodles (23) ______ (encourage) in Japanese culture. It’s believed that taking air into your mouth (24) ______ enhance the flavor of the noodles, and that it helps cool down the noodles. It’s also considered to be a way to show appreciation for the dish. Sometimes, just making the noise alone seems to make the noodles more enjoyable.It wasn’t until a new expression –“noodle harassment（骚扰）”-- came out last year on social media (25) ______ Japanese people started to realize that the slurping noise is making some foreign visitors uncomfortable.(26) ______ a response, Japanese instant noodle maker Nissin introduced a so-called noise-canceling fork last month. The fork, which looks like an electric toothbrush, is connected wirelessly to a smart phone. When the person using the fork starts to slurp, the fork sends asignal to the person’s phone, (27) ______ (make) it play a sound to mask the slurping noise.But is it really necessary? Dining traditions do vary. (28) ______ is considered to be proper table manners in one country is likely to be seen as rude in another. In India, people eat with their hands (29) ______ they think in this way they build a connection with the food. However, people who are used to eating with forks might find it uncomfortable to get their hands (30) ______ (cover) in oil and bits of food. But this eating method is part of Indian's culture, just like Japan's slurping is part of its own.“So, if your are eating noodles, whether that’s ramen, uudon, or soba, please slurp,” wrote reporter Brian Ashcraft on blog Kotaku. “If anyone gets annoyed while you are doing that, pay them no mind because they're missing the point entirely.”Section BDirections: Fill in each blank with a proper word chosen from the box. Each word can only be used once. Note that there is one word more than you need.A. tissueB. treatedC. potentialD. engineeringE. environmentF. limitedG. procedure H. commercial I. promising J. expanding K. internalScientists have developed a new surgical glue that could transform emergency treatments by sealing up critical wounds in the skin or the organs, without the need for staples or sutures（钉合或缝合）.It’s called MeTro. It was developed by researchers from both Harvard Medical School and the University of Sydney, led by Nasim Annabi, an assistant professor of chemical __31__. The glue is made from a modified （改良的）human protein that responds to UV light, allowing the application and drying of the gel-like substance in just a minute.According to the international team of researchers behind the glue,it could quite literally be a lifesaver, sealing up wounds in 60 seconds without stopping the natural __32__ and relaxing of the organ or the skin it’s applied to. Wounds __33__ with MeTro can heal up in half the time compared with stitches or staples, the researchers claim, and if surgeryis required then MeTro can simplify that __34__ too. It's also one of several ways researchers are exploring to engineer our body's own natural substances to help repair it when needed.The __35__ applications are powerful – from treating serious __36__ wounds at emergency sites such as following car accidents and in war zones, as well as improving hospital surgeries.MeTro is simple to apply, can be easily stored, and works closely with natural __37__ to heal a wound. What’s more, it degrades without leaving any kind of poisonous leftovers in the body.For now the trials are __38__ to animal models. But human trials are in the works, and the results to date are incredibly __39__. If the MeTro can be further developed into a __40__ product, it could become an essential part of a first responder’s toolkit.III. Reading ComprehensionSection ADirections:For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.Competition is good for businesses. In the world of navigation（导航） systems, however, competition is also a necessity --- it may not be wise to rely on foreign systems for positioning and tracking services. Now, ___41___ remarkable accuracy and reliability, China’s BeiDou system has made its presence felt.The BeiDou project was set up in 1994. The first BeiDou satellite was not launched until 2000. Now, ___42___, there are already more than 20 BeiDou satellites in orbit (轨道) . They form a ___43___ network that provides positioning, navigation and timing services for China and several other Asian countries.This “home-grown" system is now ___44___ a major upgrade. Earlier this month, two BeiDou-3 satellites, the first of China’s most powerful ___45___of navigation satellites, were launched into space. The launch marks the beginning of the global ___46___ of the BeiDou navigation system. Over the next three years, China plans to send up 30 more BeiDou-3 satellites; The expanded navigation system will ___47___ create a network that is able to support military and civilian applications around the world.Scientists involved in the project said the new system would give civilian users an accuracy of 2.5 meters to five meters, overtaking that of the ___48___ positioning technologies. BeiDou’s chief designer said the new satellites would be able to __49___ which lane a car is using on a motorway and __50___ the swing of a building in high winds. It will also be able to guide fire trucks to the nearest water hydrant (消防栓).The Chinese military, meanwhile, will be able to use coded signals for millimeter（毫米）___51___ .China is only the third country in the world to develop a navigation system on its own, after the United States (GPS) and Russia (GLONASS). Developing BeiDou is a necessity. The system __52___ national security by ending a reliance on foreign systems. Moreover, it enhances China’s international reputation for technological ___53___.For most of us, the benefits of the new satellite system will be felt in a couple of years when more phones are ___54___ with BeiDou chips (芯片). Many smartphones today still use GPS and GLONASS. That’ll soon change with the development of BeiDou. One product manager ___55___ mostsmartphones to be able to receive BeiDou signals. He says: “In three years’time, people may still say ‘I’m using GPS’, but in fact, their phone is tune in to BeiDou. ”41. A. dominating B. boasting C. shifting D. inputting42. A. however B. afterwards C. moreover D. therefore43. A. continental B. local C. domestic D. regional44. A. enduring B. encountering C. undergoing D. processing45. A. generation B. information C. examination D. revolution46. A. extension B. expansion C. interaction D. invasion47. A. objectively B. eventually C. sufficiently D. essentially48. A. existing B. progressing C. upcoming D. everlasting49. A. explore B. investigate C. spot D. remind50. A. detect B. prevent C. protect D. adjust51. A. privacy B. accuracy C. fluency D.currency52. A. convinces B. insures C. highlights D. strengthens53. A. innovation B. consumption C. emission D. exhibition54. A. decorated B. furnished C. equipped D. connected55. A. respects B. instructs C. inspects D. expectsSection BDirections: Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.(A)A Swedish power plant is taking reuse and recycle to the next level by burning unusable clothing instead of coal, Bloomberg reports.Retail giant Hennes & Mauritz, more commonly known as H&M, is helping the utility transition away from coal through its moldy (发霉的) or otherwise unsalable clothing.The multi-fuel power and heating station in Västerås, central Sweden, is planning to be completely fossil-fuel free by 2020. It’s thelargest station of its kind and Sweden claims it’s one of Europe’s cleanest. To kick its coal habit, the station is turning instead to other burnable materials including recycled wood, rubbish and yes, clothes.“Our goal is to use only renewable and recycled fuels,” Jens Neren, head of fuel supplies at the utility company which owns and operates the Västerås plant, told Bloomberg.Johanna Dahl, head of communications for H&M in Sweden, told Bloomberg that the company allows only the burning of clothes which are no longer safe to use.“It is our legal obligation to make sure that clothes that contain mold or do not meet the requirements of our strict restriction on chemicals are destroyed,” she said.The Västerås plant has burned around 15 tons of old H&M clothes so far this year, compared with about 400,000 tons of rubbish, Neren told Bloomberg.Sweden has one of the world’s greener energy generating systems, and has invested in bioenergy, solar power and electric buses. In 2015, the Scandinavian country announced an ambitious aim to become one of the first nations in the world to end its dependence on fossil fuels. According to the Swedish government, the country has already heavily reduced its dependence on oil, which accounted for 75% of the energy supply in 1970, and now makes up a 20% share.56. Which of the following can serve as fuel in the Västerås plant?A. Fashionable coats in H&M chain store.B. Old TV sets deserted as rubbish.C. Wooden furniture in second-hand shop.D. H&M clothes unsuitable for sale.57. The underlined word in the last paragraph “generating” is closestin meaning to ______.A. eliminatingB. adjustingC. producingD. circulating58. What can we learn from the passage?A. The Swedish government discourages the development of bioenergy.B. Clothes only take up a small proportion of the burning material.C. Sweden’s fossil-fuel free plan is almost accomplished by now.D. Sweden has an ambition to be the cleanest country in the world.59. What is the main idea of the passage?A. A Swedish power plant is burning unusable H&M clothes for fuel.B. The Swedish government aims high and is taking effective action.C. H&M is looking for a new way to strengthen its position in fashion.D. Coal and oil are no longer regarded as the primary fuels in Sweden.(B)60. Before an adventure, a trekker should ______.A. tell the park officials his destination and time scheduleB. pack up some jungle fruit juice and pre-cooked mealsC. consult a local guide about the most adventurous routeD. have his fitness level assessed at the tourist center61. Which of the following is NOT suitable for a rainforest trekking?A. Long-sleeved cotton shirts.B. Tight sports shorts.C. Hiking boots.D. A wide brimmed hat.62. If a trekker starts out at dawn, he may ______.A. escape being caught in the rainB. sight scared wildlifeC. enjoy the heat of the tropical sunD. see animals seeking food(C)The largest genetic study of mosquitoes has found their ability to resist insecticides is evolving rapidly and spreading across Africa, putting millions of people at higher risk of contracting malaria（疟疾）.British scientists who led the work said mosquitoes' growing resistance to control tools such as insecticide-treated bed nets and insecticide spraying, which have helped cut malaria cases since 2000, now threatens “to disturb malaria control” in Africa.“Our study highlights the severe challenges facing public efforts to control mosquitoes and to manage and limit insecticide resistance,” said Martin Donnelly of the Liverpool School of Tropical Medicine, who worked on the study with a team from Britain’s Wellcome Trust Sanger Institute.Latest World Health Organization (WHO) data show that 216 million people were infected last year with the malaria parasite(寄生虫), which is transmitted by blood-sucking Anopheles mosquitoes.The disease killed 445,000 people in 2016, and the majority of them were children in sub-Saharan Africa.To understand how mosquitoes are evolving, the researchers sequenced the DNA of 765 wild Anopheles mosquitoes taken from 15 locations across eight African countries. Their work, published in the journal Nature on Wednesday, created the largest data resource on natural genetic variation for any species of insect.Analyzing the data, the scientists found that the Anopheles gambiae mosquitoes（冈比亚疟蚊）were extremely genetically diverse （多样化的）compared with most other animal species. This high genetic diversity enables rapid evolution, they said, and helps to explain how mosquitoes develop insecticide resistance so quickly.The data also showed the rapid evolution of insecticide resistance appeared to be due to many previously unknown genetic variants（变体）within certain genes. The scientists said these genetic variants for insecticide resistance were not only emerging independently in different parts of Africa, but were also being spread across the continent by mosquito migration.Michael Chew, an expert at Britain’s Wellcome Trust global health charity which helped fund the research, said the finds underlined the importance of pushing scientific research ahead to control malaria.Global efforts to control malaria through effective vaccine, insecticides and the best drug combinations require urgent, united action by scientists, drug companies, governments and the WHO.63. Which of the following is scientists’ headache?A. The number of mosquitoes in Africa is growing rapidly.B. Some genetic variants of mosquitoes are still unknown.C. The existing insecticides aren’t as effective as they used to be.D. Millions of African people have resistance to medicines for malaria.64. Malaria cases can be cut by ______.A. threatening drug companiesB. spraying insecticidesC. limiting blood donationD. transmitting data65. What CANNOT be concluded from the passage?A. Children are more likely to be bit by mosquitoes.B. Many previously unknown variants are found in the study.C. The mosquito migration contributes to the spread of variants.D. Anopheles mosquitoes have great genetic diversity.66. Which is FALSE about the genetic study of mosquitoes?A. It created the largest data on natural genetic variation for any insect species.B. It found the possible causes for the rapid evolution of insecticide resistance.C. It discovered where the genetic variants emerged and how they were spread.D. It highlighted the public efforts and appealed to limit the use of insecticides.Section CDirections: Read the following passage. Fill in each blank with a proper sentence given in the box. Each sentence can be used only once. Note that there are two more sentences than you need.Imagine you're standing in line to buy an afterschool snack at a store. You step up to the counter and the cashier scans your food. Next, you have to pay. But instead of scanning a QR code with your smartphone, you just hold out your hand so the cashier can scan your fingerprint. Or, a camera scans your face, your eyes or even your ear.__________67__________ As technology companies move away from traditional password, biometric（生物识别） security, which includes fingerprint, face and voice ID, is becoming increasingly popular.In 2013, Apple introduced the iPhone 5s, one of the first smartphones with a fingerprint scanner. Since then, using one’s fingerprint to unlock a phone and make mobile payments has become commonplace, bringing convenience to our lives. And since last year, Samsung has featured eye-scanning technology in its top smartphones, while Apple’s new iPhone X can even scan a user’s face.__________68__________ “Biometrics, ideally, are good,”John Michener, a biometric expert, told tech website Inverse. “In practice, not so much.”When introducing the new iPhone’s Face ID feature at Apple’s Keynote Event in September, Phil Schiller, Apple’s senior vice president, said, “__________69__________”But it’s already been done. In a video posted on community website Reddit on Nov 3, two brothers showed how they were each able to unlock the same iPhone X using their own face, Quartz reported. And they aren’t even twins.“We may expect too much from biometrics,” Anil Jain, a computer science professor at Michigan State University, told CBS news. “No security systems are perfect.”Earlier this year, Jain found a way to trick biometric security. Using a printed copy of a thumbprint, she was able to unlock a dead person's smartphone for police.“It’s good to see biometrics being used more,” Jain told CBS News, “because it adds another factor for security. __________70__________”IV. Summary WritingDirections: Read the following passage. Summarize the main idea and the main point(s) of the passage in no more than 60 words. Use your own words as far as possible.It’s a common sight to see food delivery workers riding electric bikes through big cities in China. Most of them seem to be in a hurry, as they run red lights to deliver their meals in time. However, such reckless （鲁莽的）behavior often causes serious problems.In the first half of this year, food delivery drivers had 76 traffic accidents in Shanghai alone, according to the Shanghai Public Security Bureau. This means that on average, there is a food delivery worker that gets hurt or even dies on the road in Shanghai every 2.5 days.Other cities also share similar problems. In Nanjing, three people died and 2,473 were injured in road accidents related to food delivery workers in the same period, according to the Ministry of Public Security.The rise of reckless behavior among food delivery workers is closely related to the growing demand for their service, reported People’s Daily. About 150 million people in China use food delivery services, according to China Radio International (CRI). Such a big market has led to a large demand for food delivery workers, with some companies offering high salaries to attract new workers.However, food delivery workers are often under high pressure from their employers. They face company fines of 20 yuan for delivering food late and upwards of 200 yuan for receiving complaints, reported CRI. Moreover, the more orders they take, the more commission（佣金）they can earn, leading to some workers checking their mobile phones for new orders while they're riding their bikes.While most companies have measures requiring delivery workers to follow traffic rules, “there remains a problem of whether these requirements and rules for delivery workers are truly entering their ears, brains and hearts,” Wang Liang, deputy head of the Traffic Police Security Bureau, told news website The Paper.To solve the problem, some cities have taken action. Shanghai has asked companies to train their workers on traffic rules and safety. Now in Shenzhen, if a delivery worker gets caught breaking traffic rules more than twice, he or she will be banned from driving food delivery vehicles for a whole year.第II卷（共40分）I. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.1.这个比赛旨在鼓励年轻人继承中国文化的传统。
杨浦区2017度第一学期高三模拟质量调研汇编
杨浦区 2017 学年度第一学期高三模拟质量调研英语学科试卷 2017. 12 本试卷分为第 I 卷（第1-11页）和第 II 卷（第 12 页）两部分。
全卷共 12 页。
满分 140 分。
考试时间 120分钟。
考生注意：1． 答第 I 卷前，考生务必将条形码粘贴在答题纸的指定区域内。
2. 第 I 卷（1-20 小题，31---70小题）由机器阅卷，答案必须全部涂写在答题卡 上。
考生应将代表正确答案的小方格用铅笔涂黑。
注意试题题号和答题卡编 号一一对应，不能错位。
答案需要更改时，必须将原选项用橡皮擦去，重新 选择。
答案写在试卷上一律不给分。
第I 卷中的第21-30小题，IV. Summary Writing 部分和第 II 卷的试题， 其答案用钢笔或水笔写在答题纸的规定区域 内，如用铅笔答题，或写在试卷上则无效。
第I 卷（共100分）I. Listening ComprehensionSection 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. Theconversations and the questions will be spoken only once. After you hear a conversationand the question about it, read the four possible answers on your paper, and decidewhich one is the best answer to the question you have heard.A. In a professor's office.C. In a library. A. 10 yuan.C. 30 yuan. A. House agent and customer. C. Car mechanic and car owner.A. The man doesn't believe what thewoman says.B. The weather report spoils the man's good mood.C. They will cancel the hiking due to the bad weather.D. The man thinks it unnecessary to give up the adventure. A. She always talks bad about her colleagues.B. She has a good reputation among her colleagues.C. She is good at handling complicated relationships.D. She has good relations with her colleagues and boss.A. Harmony in a community.B. Safety in the neighborhood.C. Preparation forChristmas. D. Ways to save electricity.A. Watching advertisements may help eas e yestrain （眼疲劳）B. It's a great chance to break the habit of watching T.VC. The advertisements are long enough for her to have a nap.D. Focusing eyes on the screen for a long time is harmful to eyes. A. The man decides to go home by rail.B. Most people travel by car during the festival.1. 2. 3. 4. 5. 6. 7. 8. B. In a second-hand book shop. D. In a hospital.B. 20 yuan. D. 50 yuan. B. Shop assistant and customer. D. Employer and employee.C. Most people arrive beyond the scheduled time.D. The man will have a sound sleep on the bus.9. A. He is not a bit overweight.B. He likes his fitness instructor.C. She has set too many rules for him.D. She should talk with his personal trainer.10. A. Greeks are not allowed to get married before 18.B. Greek kids are not as independent as American kids.C. American parents don't pay for children's wedding.D. Greek parents will take care of children until they are 18.Section BDirections: In Section B, you will hear several longer conversation(s) and short passage(s), and you will be asked several questions on each of the conversation(s) and the passage(s). The conversation(s) and passage(s) 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. The burn is 20 millimeters across.B. The burn is small but very painful.C. The burn takes away the victim's feeling.D. The burn is small but the skin is damaged.12. A. Use a clean plastic bag to keep warm.B. Bind up the burn with bandage or cloth.C. Treat the burned area with cold running water.D. Flush (冲洗)the burn with ice water for several minutes.13. A. To avoid infection. B. To ease pain.C. To speed recovery.D. To reduce stickiness.Questions 14 through 16 are based on the following passage.14. A. A cell phone. B. A leather wallet.C. A mini camera.D. An alarm clock.15. A. The wallet will sound an alarm.B. It will track the thief with GPS system.C. It will contact the bank to block balance.D. Its owner will receive a picture of the thief.16. A. It's out-dated in this digital age.B. It can text messages automatically.C. It is a multifunctional wallet.D. It is unique in appearance and function.Questions 17 through 20 are based on the following conversation.17. A. The concert is bey ond hercurfew (宵禁).B. She cantgo out on school ni ght.C. Her mother is not available.D. She doesntlike the band.18. A. His pare nts set a strict rule for him.B. His pare nts dontcare whe n he is back.C. He is self-discipli ned and trustworthy.D. He env ies those who have curfews.19. A. Promoting maturity.C. Impro ving sense of resp on sibility.20. A. It 's a severe puni shme nt.C. It 's a ridiculous practice.II. Grammar and VocabularySection ADirections: After reading the passage below, fill in the blanks to make the passagescohere nt and grammatically correct. For the bla nks with a give n word, fill in each blank with the proper form of the give n word; for the other bla nks, use one word that bestfits each bla nk.It's interesting when you think about how Japan is a nation (21) ____________appreciates the virtues of silence and good manners, and yet when it comes to eatingno odles, Japa nese people can be (22) _____ (loud) in the world.According to lifestyle website grapee.jp, slurping (发出"哧溜"声)when eatingnoodles (23) ______ (encourage) in Japanese culture. ' believed that taking air intoyour mouth (24) _______ e nhance the flavor of the noodles, and that it helps cooldown the noodles. It's also considered to be a way to show appreciation for the dish.Sometimes, just making the no ise alone seems to make the no odles more enjoyable.It wasn'tuntil a new expression — noodle harassment (骚扰) ”-came out last yearon social media (25) _________ Japa nese people started to realize that the slurp ingno ise is maki ng some foreig n visitors un comfortable.(26) _____ a response, Japaneseinstant noodle maker Nissin introduced aso-called noise-canceling fork last month. The fork, which looks like an electrictoothbrush, is connected wirelessly to a smart phone. When the person using the forkstarts to slurp, the fork sends a signal to the person ' phone, (27) ______ (make) itplay a sound to mask the slurp ing no ise.But is it really necessary? Dining traditions do vary. (28) _____ is considered tobe proper table manners in one country is likely to be see n as rude in ano ther. I n India, people eat with their hands (29) __ they thi nk in this way they build a connectionwith the food. However, people who are used to eating with forks might find it uncomfortable to get their hands (30) ________ (cover) in oil and bits of food. But thiseating method is part of Indian's culture, just like Japan's slurping is part of its own.So, if your are eating noodles, whether that's ramen, uudon, or soba, please slurp,”wrote reporter Brian Ashcraft on blog Kotaku. ff anyone gets annoyed while you are B. Giving sense of security. D. Discourag ing in depe ndence. B. It's for her good. D. It 'san excepti onal case.doing that, pay them no mind because they're miss ing the point en tirel y.Section BDirections: Fill in each bla nk with a proper word chose n from the box. Each word can only be used on ce. Note that there is one word more tha n you n eed.A. tissueB. treatedC. potentialD. engineeringE. environmentF. limitedG. procedure H. commercial I. promising J. expanding K. internalScien tists have developed a new surgical glue that could tran sform emerge ncy treatments by sealing up critical wounds in the skin or the organs, without the need for staples or sutures （钉合或缝合）.It ' called MeTro. It was developed by researchers from both Harvard Medical School and the Uni versity of Sydn ey, led by Nasim Ann abi, an assista nt professor of chemical __31__. The glue is made from a modified （改良的）human protein that resp onds to UV light, allow ing the applicati on and drying of the gel-like substa nee in just a mi nute.According to the international team of researchers behind the glue, it could quite literally be a lifesaver, sealing up wounds in 60 seconds without stopping the natural __32__ and relaxing of the organ or the skin it's applied to. Wounds __33__ with MeTro can heal up in half the time compared with stitches or staples, the researchers claim, and if surgery is required then MeTro can simplify that __34__ too. It's also one of several ways researchers are explori ng to engin eer our body's own n atural substa nces to help repair it whe n n eeded.The __35__ applicati ons are powerful -from treati ng serious __36__ wounds at emergency sites such as following car accidents and in war zones, as well as improvi ng hospital surgeries.MeTro is simple to apply, can be easily stored, and works closely with natural __37__ to heal a wound. What's more, it degrades without leaving any kind of pois onous leftovers in the body.For now the trials are __38__ to animal models. But human trials are in the works, and the results to date are in credibly __39__. If the MeTro can be further developed into a __40__ product, it could become an essetial part of a first resp on ders toolkit. 'III. Reading ComprehensionSection ADirections: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each bla nk with the word or phrase that best fits the con text.Competiti on is good for bus in esses. In the world ofnavigati on （导航） systems, however, competition is also a necessity --- it may not be wise to rely on foreign systems for positioning and tracking services. Now, __________________________ 41 __ remarkable accuracyand reliability, China ' s BeiDou system has made its presenee felt.The BeiDou project was set up in 1994. The first BeiDou satellite was not launched until 2000. Now, _____________________ 42 __ , there are already more than 20 BeiDousatellites in orbit （轨道）.They form a __ 43 __ n etwork that provides positi oning,navigation and timing services for China and several other Asian countries.This “ hom-gerown" system is now ___44___ a major upgrade. Earlier this month, two BeiDou-3 satellites, the first of China 'ms ost powerful ___45___of navigation satellites, were launched into space.The launch marks the beginning of the global ___46___ of the BeiDou navigation system. Overthe next three years, China plans to send up 30 more BeiDou-3 satellites; The expanded navigation system will ___47___ create a network that is able to support military and civilian applications around the world.Scientists involved in the project said the new system would give civilian users an accuracy of 2.5 meters to five meters, overtaking that of the ___48___ positioning technologies. BeiDou's chief designer said the new satellites would be able to __49___ which lane a car is using on a motorway and __50___ the swing of a building in high winds. It will also be able to guide fire trucks to the nearest water hydrant （消防栓）.The Chinese military, meanwhile, will be able to use coded signals for millimeter （毫米）___51___ .China is only the third country in the world to develop a navigation system on its own, after the United States （GPS） and Russia （GLONASS）. Developing BeiDou is a necessity. The system__52___ national security by ending a reliance on foreign systems. Moreover, it enhances China'isnternational reputation for technological ___53___.For most of us, the benefits of the new satellite system will be felt in a couple of years when more phones are ___54___ with BeiDouchips （芯片）. Many smartphones today still use GPS and GLONASS. That 'lsl oon change with the development of BeiDou. One product manager ___55___ most smartphones to be able to receive BeiDou signals. He says: “In three years ' time, people may still say , ‘ I ' m using but in fact, their phone is tune into BeiDou. ”41. A. dominating B. boasting C. shifting D. i nputting42. A. however B. afterwards C. moreover D. t herefore43. A. continental B. local C. domestic D. r egional44. A. enduring B. encountering C. undergoing D. p rocessing45. A. generation B. information C. examination D. r evolution46. A. extension B. expansion C. interaction D. i nvasion47. A. objectively B. eventually C. sufficiently D. essentially48. A. existing B. progressing C. upcoming D. everlasting49. A. explore B. investigate C. spot D. r emind50. A. detect B. prevent C. protect D. adjust51. A. privacy B. accuracy C. fluency D. c urrency52. A. convinces B. insures C. highlights D. strengthens53. A. innovation B. consumption C. emission D. e xhibition54. A. decorated B. furnished C. equipped D. c onnected55. A. respects B. instructs C. inspects D. e xpectsSection BDirections: Read the following three passages. Each passage isfollowed 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)A Swedish power pla nt is tak ing reuse and recycle to the n ext level by bur ning unu sable clothi ng in stead of coal, Bloomberg reports.Retail giant Hennes & Mauritz, more commonly known as H&M, is helping the utility transition away from coal through its moldy (发霉的)or otherwise unsalable clothi ng.The multi-fuel power and heating station in V?ster$, central Sweden, is planning to be completelyfossil- fuel free by 2020. It ' s the largest station of its kindand Sweden claims it ' s one of Europe ' s cleanest. To kick its coal habit,ithe station turning in stead to other burn able materials in cludi ng recycled wood, rubbish and yes, clothes.“ Our goal is to use only renewable and recycled fuels, ” Jens Neren, head of fuesupplies at the utility company which owns and operates the V?ster? plant, told Bloomberg.Joha nna Dahl, head of com muni cati ons for H&M in Swede n, told Bloomberg that the compa ny allows only the bur ning of clothes which are no Ion ger safe to use.“ is our legal obligati on to make sure that clothes that contain mold or do not meet the requirements ofour strict restriction on chemicals are destroyed, ” she said.The V?ster?s plant has burned around 15 tons of old H&M clothes so far this year, compared with about 400,000 tons of rubbish, Neren told Bloomberg.Sweden has one of the world ' greener energy generating systems, and has in vested in bioe nergy, solar power and electric buses. In 2015, the Scandin avia n country announced an ambitious aim to become one of the first nations in the world to end its depe ndence on fossil fuels. Accord ing to the Swedish gover nment, the country has already heavily reduced its depe ndence on oil, which acco un ted for 75% of the en ergy supply in 1970, and now makes up a 20% share.56. Which of the following can serve as fuel in the V?ster? plant?A. Fashi on able coats in H&M cha in store.B. Old TV sets deserted as rubbish.C. Woode n fur niture in sec on d-ha nd shop.D. H&M clothes un suitable for sale.57. The un derl ined word in the last paragraph gen erat in g” is closest in meaning toA. elim in ati ngB. adjusti ngC. produc ingD. circulati ng58. What can we lear n from the passage?A. The Swedish gover nment discourages the developme nt of bioe nergy.B. Clothes only take up a small proporti on of the burning material.C. Swedensfossil-fuel free pla n is almost accomplished by now.D. Swede n has an ambiti on to be the clea nest country in the world.59. What is the main idea of the passage?A. A Swedish power plant is burning unusable H&M clothes for fuel.B. The Swedish gover nment aims high and is tak ing effective action.C. H&M is looking for a new way to strengthen its position in fashion.D. Coal and oil are no Ion ger regarded as the primary fuels in Swede n.(B)RAINFOREST ADVENTURE TIPS1. Find out about the trail and surro undin gs, be sure that youhave eno ugh time to complete the en tire route beforedarkness falls. Do not stray off the path to chase after animals.2. Use good judgme nt regard ing the fitn ess level required forthe trek (徒步跋涉)，and know your physical limits.3. Always inform the park officials or let some one know of yourpla ns and dest in ati on for the day, especially if going alone.4. Take ple nty of water and pack a few easy to eat sn acks tokeep en ergy level up. Un less trekk ing with a local guide, itis not advisable to eat jungle fruit or drink from any watersource.5. Be as quiet as possible to avoid scaring any wildlife. Gettingan early start during the dawn provides the best chanee tosight animals seeking food and the warmth of the earlymorning sun.6. Wear thin, I oose, preferably cott on cloth ing to rema incomfortable.7. Cover arms and legs with long trousers and Iong-sleevedshirts to ward off mosquitoes and to provide protect ion against thor ny pla nts.8. Be prepared for sudden rain showers by carrying a ponchothat wraps over both body and your carrying pack to keepeverythi ng dry.9. Choose footwear with proper an kle support and good traction., 10. A wide brimmed hat helps to shade a trekker from the\ heat of the tropical sun.60. Before an adventure, a trekker should _____ .A. tell the park officials his destination and time scheduleB. pack up some jungle fruit juice and pre-cooked mealsC. consult a local guide about the most adventurous routeD. have his fitness level assessed at the tourist center61. Which of the following is NOT suitable for a rainforest trekking?A. Long-sleeved cotton shirts.B. Tight sports shorts.C. Hiking boots.D. A wide brimmed hat.62. If a trekker starts out at dawn, he may _____ .A. escape being caught in the rainB. sight scared wildlifeC. enjoy the heat of the tropical sunD. see animals seeking food（C）The largest genetic study of mosquitoes has found their ability to resist insecticides is evolving rapidly and spreading across Africa, putting millions of people at higher risk of contractingmalaria （疟疾）.British scientists who led the work said mosquitoes' growing resistance to control tools such as insecticide-treated bed nets and insecticide spraying, which have helped cut malaria cases since 2000, now threaten“sto disturb malaria control”in Africa.“ Ousr tudy highlights the severe challenges facing public efforts to control mosquitoes and to manage and limit insecticideresistance, sa”id Martin Donnelly of the Liverpool School of Tropical Medicine, who worked on the study with a team from Britain 's Wellcome Trust Sanger Institute.Latest World Health Organization （WHO） data show that 216 million people were infected last year with the malaria parasite （寄生虫）, which is transmitted by blood-sucking Anopheles mosquitoes.The disease killed 445,000 people in 2016, and the majority of them were children in sub-Saharan Africa.To understand how mosquitoes are evolving, the researchers sequenced the DNA of 765 wild Anopheles mosquitoes taken from 15 locations across eight African countries. Their work, published in the journal Nature on Wednesday, created the largest data resource on natural genetic variation for any species of insect.Analyzing the data, the scientists found that the Anopheles gambiae mosquitoes （冈比亚疟蚊）were extremely geneticallydiverse （多样化的）compared with most other animal species.This high genetic diversity enables rapid evolution, they said, and helps to explain how mosquitoes develop insecticide resistance so quickly.The data also showed the rapid evolution of insecticide resistance appeared to be due to many previously unknown genetic variants （变体）within certain genes. The scientists said these genetic variants for insecticide resistance were not only emerging independently in different parts of Africa, but were also being spread across the continent by mosquito migration.Michael Chew, an expert at Britain's Wellcome Trust global health charity which helped fund the research, said the finds underlined the importance of pushing scientific research ahead to control malaria.Global efforts to con trol malaria through effective vacc ine, in secticides and the best drug comb in ati ons require urge nt, un ited action by scie ntists, drug compa ni es, gover nments and the WHO.63. Which of the following is scientists' headache?A. The nu mber of mosquitoes in Africa is grow ing rapidly.B. Some genetic variants of mosquitoes are still unknown.C. The existing insecticides arentas effective as they used to be.D. Millions of African people have resistance to medicines for malaria.64. Malaria cases can be cut by ______ .A. threate ning drug compa niesB. spray ing in secticidesC. limiti ng blood don ati onD. tran smitti ng data65. What CANNOT be concluded from the passage?A. Childre n are more likely to be bit by mosquitoes.B. Many previously unknown variants are found in the study.C. The mosquito migrati on con tributes to the spread of varia nts.D. An opheles mosquitoes have great gen etic diversity.66. Which is FALSE about the gen etic study of mosquitoes?A. It created the largest data on n atural gen etic variatio n for any in sect species.B. It found the possible causes for the rapid evolutio n of in secticide resista nce.C. It discovered where the genetic variants emerged and how they were spread.D. It highlighted the public efforts and appealed to limit the use of insecticides.Section CDirections: Read the following passage.Fill in each blank with a proper sentence give n in the box. Each sentence can be used only on ce. Note that there are two more senten ces tha n you n eed.A. But despite its popularity, experts warn that biometrics might not be as secure aswe'd imagi ned.B. Security experts don 'tthi nk it absolutely n ecessary to use biometricC. But using multiple security measures is the best defe nse.D. Now, this type of tech no logy might not be far away.E. If a person ' s biometric information is stolen, that could have extremely serious conseque nces for that in dividualF. The chance that a random person could look at your iPhone X and uniock it with hisface is about one in a million.Imagi ne you're sta nding in line to buy an afterschool sn ack at a store. You step up to the coun ter and the cashier sca ns your food. Next, you have to pay. But in stead of sca nning a QR code with your smartph one, you just hold out your hand so the cashier can scan your fingerprint. Or, a camera scans your face, your eyes or even yourear._________ 67 _________ As tech no logy compa nies move away from traditional password, biometric （生物识别）security, which includes fingerprint, face and voice ID, is beco ming in creas in gly popular.In 2013, Apple introduced the iPhone 5s, one of the first smartphones with a fingerprint scanner. Since then, using one s fingerprint to uniock a phone and make mobile payme nts has become com mon place, bringing convenience to our lives. And since last year, Sams ung has featured eye-sca nning tech no logy in its top smartph ones, while Apple' s new iPhone X can even scan a users face._________ 68 _________ Biometrics, ideally, are good,” John Michener, a biometric expert, told tech website Inv erse. In practice, not so much”When in troduci ng the new iPh one s Face ID feature at Apple s Keynote Eve nt in September, Phil Schiller, Apple' s senior vice preside nt, said,But it' s already been done. In a video posted on community website Reddit on Nov 3, two brothers showed how they were each able to uni ock the same iPho ne X using their own face, Quartz reported. And they aren t even twins.We may expect too much from biometrics,” Anil Jain, a computer scienee professor at Michigan State University, told CBS news. No security systems are perfect.”Earlier this year, Jain found a way to trick biometric security. Using a printed copy of a thumbpri nt, she was able to uni ock a dead pers on's smartpho ne for police.ft' s good to see biometrics being used more,Jain told CBS News, because itadds ano ther factor for security. _________ 70 _______ ”_IV. Summary WritingDirections: Read the following passage. Summarize the main idea and the main poin t （s） of the passage in no more tha n 60 words. Use your own words as far as possible.It' s a com mon sight to see food delivery workers riding electric bikes throughbig cities in China. Most of them seem to be in a hurry, as they run red lights to deliver their meals in time. However, such reckless （鲁莽的）behavior often causes serious problems.In the first half of this year, food delivery drivers had 76 traffic accidents inShanghai alone, according to the Shanghai Public Security Bureau. This means that on average, there is a food delivery worker that gets hurt or eve n dies on the road in Shan ghai every 2.5 days.Other cities also share similar problems. In Nanjing, three people died and 2,473 were injured in road accidents related to food delivery workers in the same period, according to the Ministry of Public Security.The rise of reckless behavior among food delivery workers is closely related to the grow ing dema nd for their service, reported People' s Daily. About 150 millio n people in China use food delivery services, according to China Radio International (CRI). Such a big market has led to a large dema nd for food delivery workers, with some compa nies offeri ng high salaries to attract new workers.However, food delivery workers are often under high pressure from their employers. They face compa ny fines of 20 yua n for deliveri ng food late and upwards of 200 yua n for recei ving compla in ts, reported CRI. Moreover, the more orders they take, the more commissi on (佣金)they can earn, leadi ng to some workers check ing their mobile phones for new orders while they're riding their bikes.While most compa nies have measures requiri ng delivery workers to follow traffic rules, (here remains a problem of whether these requirements and rules for delivery workers are truly entering their ears, brains and hearts, Wang Liang, deputy head of the Traffic Police Security Bureau, told n ews website The Paper.To solve the problem, some cities have taken action. Shanghai has asked companies to train their workers on traffic rules and safety. Now in Shenzhen,if a delivery worker gets caught breaking traffic rules more than twice, he or she will be banned from driv ing food delivery vehicles for a whole year.第II 卷（共40 分）I. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.1. 这个比赛旨在鼓励年轻人继承中国文化的传统。
上海市杨浦高中2017届高三下学期开学考试数学试卷 Word版含答案
杨浦高中高三开学考数学试卷2017.02一、填空题：（本大题共14小题，每小题5分，共70分）1. 复数()1i i +（i 为虚数单位）的实部为 .2. 设全集U=R,集合{}{}22|log ,|10A x y x B x x ===-<，则()U C A B = .3.已知n S 是公差不为0的等差数列{}n a 的前n 项和，且124,,S S S 成等比数列， 则21a a = . 4.在614x x ⎛⎫- ⎪⎝⎭的展开式中，2x 的系数为 .5．一个圆柱形容器的轴截面尺寸如右图所示，容器内有一个实心球，球的直径等于圆柱的高，现用水将该容器注满，然后取出该球（假设球的密度大于水且操作过程中水量损失不计），则球取出后，容器内水面的高度为 cm.（精确到0.1cm ）6.双曲线()222210,0x y a b a b-=>>的渐近线为正方形OABC 的边OA,BC 所在的直线，点B 为该双曲线的焦点，若正方形OABC 的边长为2，则a = .7.袋中有形状、大小都相同的4只球，其中1只白球，1只红球，2只黄球，从中一次随机摸出2只球，则这2只球颜色不同的概率是 .8.某四棱锥的三视图如图所示，则该四棱锥的四个侧面的面积中最大值是 .9.已知函数()()2sin 0,2f x x πωϕωϕ⎛⎫=+>< ⎪⎝⎭的图象如图所示，则其所有的对称中心的坐标为 .10.已知实数,x y 满足3060x x y x y ≤⎧⎪+≥⎨⎪-+≥⎩，若z ax y =+的最大值为39a +，最小值为33a -，则实数a 的取值范围是 .11.已知函数()()2,2f x f x x =-≥⎪⎩若对于正数()n k n N *∈，直线n y k x =与函数()f x 的图象恰有21n +个不同的交点，则()22212lim n n k k k →∞+++= .12.若()f x 是定义在R 上的函数，对任意的实数x ，都有()()44f x f x +≤+和()()22f x f x +≥+且()14f =，则()2017f 的值为 .二、选择题：13．直线l 的方程为10223012xy =-，则直线l 的一个法向量是 A. ()1,2 B. ()2,1 C. ()1,2- D. ()2,1-14．已知直线l ⊥平面α，直线m ⊆平面β，给出下列命题，其中正确的是 ①//l m αβ⇒⊥；②//l m αβ⊥⇒；③//l m αβ⇒⊥；④//l m αβ⊥⇒A. ①④B. ②③④C. ①③D. ①②③15．数列{}n a 满足()1!1,,,0n n a a ra r n N r R r *+==+∈∈≠，则“1r =”是“数列为等差数列”的（ ）条件A. 充分不必要B. 必要不充分C. 充要D.既不充分也不必要16．如图，正方形ABCD 内接于圆22:2O x y +=，M,N 分别为边AB,BC 时，PM ON⋅的中点，已知点()2,0P ，当正方形ABCD 绕圆心O 旋转的取值范围是A. []1,1-B.⎡⎣C. []2,2-D. ⎡⎢⎣⎦三、解答题：解答应写出必要的文字说明或推理、验算过程.19. 如图，直四棱柱1111ABCD A BC D -中，底面ABCD 为直角梯形，//,90,AB CD BAD P ∠=是棱CD 上一点，12,3,3, 1.AB AD AA CP PD =====（1）求异面直线1A P 与1BC 所成的角； （2）求证：PB ⊥平面11BCC B .18. 已知函数()()2,.21x f x a x R a R =-∈∈+ （1）求证：()f x 在(),-∞+∞上是增函数；（2）设函数()f x 存在反函数()1f x -，且()f x 是奇函数，若方程()()12log f x x t -=+有实数根，求实数t 的取值范围.19. 某公司要在一条笔直的道路边安装路灯，要求灯柱AB 与底面垂直，灯杆BC 与灯柱AB 所在的平面与道路走向垂直，路灯C 采用锥形灯罩，射出的管线与平面ABC 部分截面如图中阴影所示，2,,33ABC ACD ππ∠=∠=路宽AD=24米，设.126BAC ππθθ⎛⎫∠=≤≤ ⎪⎝⎭ （1）求灯柱AB 的高h （用θ表示）；（2）此公司应该如何设置的值才能使制作路灯灯柱AB 和灯杆BC所用材料的总长度最小？最小值为多少？20. 已知动点P 到直线1:2l x =-的距离与到点()1,0F -的距离之比为（1）求动点P 的轨迹Γ；（2）直线l 与曲线Γ交于不同的两点A,B(A,B 在x 轴的上方)180OFA OFB ∠+∠=：①当A 为椭圆与y 轴的正半轴的交点时，求直线l 的方程；②对于动直线l ，是否存在一个定点，无论OFA ∠如何变化，直线l 总经过此定点？若存在，求出该定点的坐标；若不存在，请说明理由. .21. 定义：对于任意n N *∈，满足条件212n n n a a a +++≤且n a M ≤（M 是与n 无关的常数）的无穷数列{}n a 称为M 数列.（1）若等差数列{}n b 的前n 项和为n S ，且2253,25b S =-=-，判断数列{}n b 是否是M 数列，并说明理由；（2）若各项为正数的等比数列{}n c 的前n 项和为n T ，且3317,44c T ==，证明：数列{}n T 是M数列，并指出M 的取值范围； （3）设数列()1,1n pd n N p n*=-∈>，问数列{}n d 是否是M 数列？请说明理由.。
上海市各区2017届高三一模数学试卷
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21. 设集合 A 、 B 均为实数集 R 的子集，记： A B {a b | a A, b B} ； （1）已知 A {0,1, 2} ， B {1,3} ，试用列举法表示 A B ；
2017年上海市杨浦区高考数学一模试卷
2017年上海市杨浦区高考数学一模试卷一、填空题（本大题满分54分）共12小题，1-6题每题4分，7-12题每题5分1. 若“”，则“”是________命题（填：真、假）【答案】真【考点】命题的真假判断与应用不等式的概念与应用【解析】利用函数在是单调增函数判定．【解答】解：函数在是单调增函数，∴当，一定有，故是真命题答案为：真．2. 已知,，若，则的取值范围是________．【答案】．【考点】并集及其运算【解析】利用集合的性质直接求解，解题时要注意的是是成立的【解答】解：若，,，必有；故答案为：．3. （为虚数单位），则________．【答案】【考点】复数的模【解析】设，代入，化为：，利用复数相等即可得出．【解答】解：设，∵，∴，化为：，∴，，解得，．∴．故答案为：．4. 若中，，，则面积的最大值是________．【答案】【考点】正弦定理【解析】由条件可得的面积，再利用正弦函数的值域、基本不等式求得的最大值．【解答】解：在中，∵，，∴的面积，当且仅当时取等号，故答案为：．5. 若函数的反函数的图象经过点，则________．【答案】【考点】反函数【解析】由函数的反函数的图象经过点，得函数的图象经过点，代入计算可得结论．【解答】解：∵函数的反函数的图象经过点，∴函数的图象经过点，∴，∴，故答案为．6. 过半径为的球表面上一点作球的截面，若与该截面所成的角是，则该截面的面积是________．【答案】【考点】直线与平面所成的角球的性质【解析】充分利用球的半径、球心与截面圆心的连线、在截面圆上的射影构成的直角三角形解决即可．【解答】设截面的圆心为，由题意得：，，∴．7. 抛掷一枚均匀的骰子（刻有，，，，，）三次，得到的数字依次记作，，，则（为虚数单位）是方程的根的概率是________．【答案】【考点】古典概型及其概率计算公式【解析】基本事件总数，由（为虚数单位）是方程的根，得，，由此能求出（为虚数单位）是方程的根的概率．【解答】解：抛掷一枚均匀的骰子（刻有，，，，，）三次，得到的数字依次记作，，，基本事件总数，∵（为虚数单位）是方程的根，∴，即，∴，，∴（为虚数单位）是方程的根包含的基本事件为：，，∴（为虚数单位）是方程的根的概率是．故答案为：．8. 设常数，展开式中的系数为，则________．【答案】【考点】二项式定理的应用【解析】由，根据的系数为，求出，从而，解得，由此能求出的值．【解答】解：∵常数，展开式中的系数为，∴，当时，，∴，解得，∴，∴．故答案为：．9. 已知直线经过点且方向向量为，则原点到直线的距离为________．【答案】【考点】点到直线的距离公式【解析】通过方向向量求出直线的斜率，利用点斜式写出直线方程，通过点到直线的距离求解即可．【解答】解：直线的方向向量为，所以直线的斜率为：，直线方程为：，由点到直线的距离可知：；故答案为：．10. 若双曲线的一条渐近线为，且双曲线与抛物线的准线仅有一个公共点，则此双曲线的标准方程为________．【答案】【考点】直线与抛物线的位置关系抛物线的求解直线与双曲线的位置关系【解析】求出抛物线的准线方程，得到双曲线的实半轴的长，利用双曲线的渐近线方程，求解即可．【解答】解：抛物线的准线：，双曲线与抛物线的准线仅有一个公共点，可得双曲线实半轴长为，焦点在轴上．双曲线的一条渐近线为，∴，可得，则此双曲线的标准方程为：．故答案为：．11. 平面直角坐标系中，给出点，，若直线存在点，使得，则实数的取值范围是________．【答案】或【考点】两点间的距离公式【解析】根据题意，设出点，代入，化简得，由，求出实数的取值范围．【解答】解：设，∵，∴，∴，化简得，则，解得或，即实数的取值范围是或．故答案为：或．12. 已知偶函数满足，且在时，，若存在，，…满足，且（，则最小值为________．【答案】【考点】函数的最值及其几何意义【解析】由函数是最小正周期为的偶函数可知函数的值域为，对任意，,…,，都有，要使取得最小值，尽可能多让,…,取得最高点，然后可得的最小值．【解答】解：∵偶函数满足，∴函数是周期为4的偶函数，且当时，，∴函数的值域为，对任意，,…,，都有，若，注意到在上是单调递减函数，，，则，∴不妨设当时，，要使取得最小值，则尽可能多让,…,取得最高点与最低点，且，，，∵，且，=2018，根据，且，相应的最小值为．故答案为：．二、选择题（本大题共4题，满分20分）若与都是非零向量，则“”是“”的（）A.充分但非必要条件B.必要但非充分条件C.充要条件D.既非充分也非必要条件【答案】C【考点】平面向量数量积的运算必要条件、充分条件与充要条件的判断【解析】根据向量数量积运算和向量垂直的充要条件，可得答案．【解答】解：“”“”“”“”，故“”是“”的充要条件，故选：行列式中，元素的代数余子式的值为（）A. B. C. D.【答案】B【考点】二阶行列式的定义【解析】利用代数余子式的定义和性质求解．【解答】解：∵行列式，∴元素的代数余子式为：．故选：．一个公司有名员工，其中名员工的月工资分别为，，，，，，另两名员工数据不清楚，那么位员工月工资的中位数不可能是（）A. B. C. D.【答案】D【考点】众数、中位数、平均数【解析】由已知能求出位员工月工资的中位数的取值区间为，由此能求出结果．【解答】∵一个公司有名员工，其中名员工的月工资分别为，，，，，，∴当另外两名员工的工资都小于时，中位数为，当另外两名员工的工资都大于时，中位数为，∴位员工月工资的中位数的取值区间为，∴位员工月工资的中位数不可能是若直线通过点，则下列不等式正确的是（）A. B.C. D.【答案】D【考点】不等式比较两数大小【解析】先把点代入得到，即可得到，得到，问题得以判断【解答】解：直线通过点，∴，∴，其中，∴，∴，∴，故选：三、解答题（满分76分）共5题某柱体实心铜制零件的截面边长是长度为毫米线段和毫米的线段以及圆心为，半径为的一段圆弧构成，其中．（1）求半径的长度；（2）现知该零件的厚度为毫米，试求该零件的重量（每个立方厘米铜重克，按四舍五入精确到克）．柱底．【答案】解：（1）∵，，，．，∴在中，由余弦定理可得：，可得：，∴解得：．（2）在中，，，，，∴．∴．柱底扇形该零件的重量．【考点】弧长公式【解析】（1）在中，由余弦定理建立方程，即可求半径的长度；（2）求出柱底，即可求该零件的重．量【解答】解：（1）∵，，，．，∴在中，由余弦定理可得：，可得：，∴解得：．（2）在中，，，，，∴．∴．柱底扇形该零件的重量．如图所示，，是互相垂直的异面直线，是它们的公垂线段，点，在直线上，且位于点的两侧，在上，（1）求证：异面直线与垂直；（2）若四面体的体积，求异面直线，之间的距离．【答案】解：（1）证明：由已知，，，可得平面．由已知，，可知且．又为在平面内的射影．∴（2）∵，是它们的公垂线段，就是异面直线，之间的距离，由中垂线的性质可得，四面体的体积，可得：，∴．异面直线，之间的距离为．【考点】点、线、面间的距离计算【解析】（1）欲证，可先证面，根据线面垂直的判定定理只需证，即可；（2）判断异面直线的距离，利用体积公式求解即可．【解答】解：（1）证明：由已知，，，可得平面．由已知，，可知且．又为在平面内的射影．∴（2）∵，是它们的公垂线段，就是异面直线，之间的距离，由中垂线的性质可得，四面体的体积，可得：，∴．异面直线，之间的距离为．如图所示，椭圆，左右焦点分别记作，，过，分别作直线，交椭圆，，且．（1）当直线的斜率与直线的斜率都存在时，求证：为定值；（2）求四边形面积的最大值．【答案】（1）证明：由椭圆，得，，∴．设，则所在直线方程为，所在直线方程为，联立，得．解得，不妨取，则同理求得，．则，则；（2）解：由（1）知，，．、的距离，∴．四边形令，则，∴当时，．【考点】直线与椭圆的位置关系【解析】（1）由椭圆方程求出焦点坐标，得到直线、的方程，与椭圆方程联立求得、的坐标，求出所在直线斜率得答案；（2）由（1）结合弦长公式求得，再由两平行线间的距离公式求出边、的距离，代入平行四边形面积公式，利用换元法求得最值．【解答】（1）证明：由椭圆，得，，∴．设，则所在直线方程为，所在直线方程为，联立，得．解得，不妨取，则同理求得，．则，则；（2）解：由（1）知，，．、的距离，∴．四边形令，则，∴当时，．数列，定义为数列的一阶差分数列，其中（1）若，试判断是否是等差数列，并说明理由；（2）若，，求数列的通项公式；（3）对中的数列，是否存在等差数列，使得，对一切都成立，若存在，求出数列的通项公式，若不存在，请说明理由．【答案】解：（1）若，试判断是等差数列，理由如下：∵，∴，∵，且，∴是首项为，公差为的等差数列；（2）∵．，∴，∴，∴数列构成以为首项，为公差的等差数列，即；（3），即，∵，∴存在等差数列，，使得对一切自然都成立．【考点】数列的求和数列递推式【解析】（1）根据数列的通项公式，结合新定义，可判定是首项为，公差为的等差数列；（2）由入手能够求出数列的通项公式；（3）结合组合数的性质：进行求解．【解答】解：（1）若，试判断是等差数列，理由如下：∵，∴，∵，且，∴是首项为，公差为的等差数列；（2）∵．，∴，∴，∴数列构成以为首项，为公差的等差数列，即；（3），即，∵，∴存在等差数列，，使得对一切自然都成立．对于函数，若存在正常数，使得对任意的，都有成立，我们称函数为“同比不减函数”．（1）求证：对任意正常数，都不是“同比不减函数”；（2）若函数是“同比不减函数”，求的取值范围；（3）是否存在正常数，使得函数为“同比不减函数”；若存在，求的取值范围；若不存在，请说明理由．【答案】解：（1）∵，∴，由于与的小无法比较，∴不一定成立，∴对任意正常数，都不是“同比不减函数，（2）∵函数是“同比不减函数，∴恒成立，∴，∵，∴，（3）图象如图所示，由图象可知，只要把图象向左至少平移个单位，即对任意的，都有成立，∴．【考点】函数与方程的综合运用【解析】（1）根据同比不减函数的定义即可证明，（2）根据同比不减函数的定义，分离参数得到，根据三角形函数的性质即可求出的范围，（3）画出函数的图象，根据图象的平移即可求出的范围．【解答】解：（1）∵，∴，由于与的小无法比较，∴不一定成立，∴对任意正常数，都不是“同比不减函数，（2）∵函数是“同比不减函数，∴恒成立，∴，∵，∴，（3）图象如图所示，由图象可知，只要把图象向左至少平移个单位，即对任意的，都有成立，∴．。
2017年上海高三数学一模中档题
7. 抛掷一枚均匀的骰子（刻有1、2、3、4、5、6）三次，得到的数字依次记作a 、b 、c ， 则a bi +（i 为虚数单位）是方程220x x c -+=的根的概率是8. 设常数0a >，9(x+展开式中6x 的系数为4，则2lim()n n a a a →∞++⋅⋅⋅+=9. 已知直线l 经过点(且方向向量为(2,1)-，则原点O 到直线l 的距离为10. 若双曲线的一条渐近线为20x y +=，且双曲线与抛物线2y x =的准线仅有一个公共 点，则此双曲线的标准方程为11.平面直角坐标系中，给出点(1,0)A 、(4,0)B ，若直线10x my +-=上存在点P ，使得 ||2||PA PB =，则实数m 的取值范围是15. 一个公司有8名员工，其中6位员工的月工资分别为5200、5300、5500、6100、6500、 6600，另两位员工数据不清楚，那么8位员工月工资的中位数不可能是（ ）A. 5800B. 6000C. 6200D. 64007. 若函数22,0(),0x x f x x m x ⎧≤⎪=⎨-+>⎪⎩的值域为(,1]-∞，则实数m 的取值范围是 8. 如图，在△ABC 中，若3AB AC ==，1cos 2BAC ∠=，2DC BD =uuu r uu u r ，则AD BC ⋅=uuu r uu u r9. 定义在R 上的偶函数()y f x =，当0x ≥时，2()lg(33)f x x x =-+，则()f x 在R 上的零点个数为 个10. 将6辆不同的小汽车和2辆不同的卡车驶入如图所示的10个车位中的某8个内，其中2辆卡车必须停在A 与B 的位置，那么不同的停车位置安排共有 种（结果用数值表示）11. 已知数列{}n a 是首项为1，公差为2m 的等差数列，前n 项和为n S ，设2n n n S b n =⋅ *()n N ∈，若数列{}n b 是递减数列，则实数m 的取值范围是18. 已知函数23sin ()cos 1x x f x x -=； （1）当[0,]2x π∈时，求()f x 的值域；（2）已知△ABC 的内角,,A B C 的对边分别为,,a b c ，若()32Af =4a =，5b c +=，求△ABC 的面积；上海市长宁、嘉定区2017届高三一模数学试卷8. 若数列{}n a 23n n =+（*n N ∈），则 1221lim ()231n n a a a n n →∞++⋅⋅⋅+=+ 9. 如图，在ABC ∆中，45B ∠=︒，D 是BC 边上的一点，5AD =，7AC =，3DC =，则AB 的长为10. 有以下命题：① 若函数()f x 既是奇函数又是偶函数，则()f x 的值域为{0}；② 若函数()f x 是偶函数，则(||)()f x f x =；③ 若函数()f x 在其定义域内不是单调函数，则()f x 不存在反函数；④ 若函数()f x 存在反函数1()f x -，且1()f x -与()f x 不完全相同，则()f x 与1()f x -图 像的公共点必在直线y x =上；其中真命题的序号是 （写出所有真命题的序号）17. 如图，已知AB ⊥平面BCD ，BC CD ⊥，AD 与平面BCD 所成的角为30°，且2AB BC ==；（1）求三棱锥A BCD -的体积；（2）设M 为BD 的中点，求异面直线AD 与CM所成角的大小（结果用反三角函数值表示）；8. 已知圆222:220C x y kx y k ++++=（k R ∈）和定点(1,1)P -，若过P 可以作两条直 线与圆C 相切，则k 的取值范围是9. 如图，在直三棱柱111ABC A B C -中，90ABC ∠=︒， 1AB BC ==，若1A C 与平面11B BCC 所成的角为6π， 则三棱锥1A ABC -的体积为 10. 掷两颗骰子得两个数，若两数的差为d ，则{2,1,0,1,2}d ∈--出现的概率的最大值 为 （结果用最简分数表示）15. 设l αβ--是直二面角，直线a 在平面α内，直线b 在平面β内，且a 、b 与l 均不垂 直，则（ ）A. a 与b 可能垂直，但不可能平行B. a 与b 可能垂直，也可能平行C. a 与b 不可能垂直，但可能平行D. a 与b 不可能垂直，也不可能平行18. 已知椭圆2222:1x y a bΓ+=（0a b >>）的左、右两个焦点分别为1F 、2F ，P 是椭圆上位于第一象限内的点，PQ x ⊥轴，垂足为Q ，且12||6F F =，12PF F ∠=12PF F ∆的面积为（1）求椭圆Γ的方程；（2）若M 是椭圆上的动点，求||MQ 的最大值，并求出||MQ 取得最大值时M 的坐标；8. 若21(2)n x x +*()n N ∈的二项展开式中的第9项是常数项，则n = 9. 已知,A B 分别是函数()2sin f x x ω=(0)ω>在y 轴右侧图像上的第一个最高点和第一 个最低点，且2AOB π∠=，则该函数的最小正周期是10. 将序号分别为1、2、3、4、5的5张参观券全部分给4人，每人至少一张，如果分给同 一人的2张参观券连号，那么不同的分法种数是15. 如图，已知椭圆C 的中心为原点O ，(F -为C 的左焦点，P 为C 上一点，满 足||||OP OF =且||4PF =，则椭圆C 的方程为（ ）A. 221255x y +=B. 2213010x y += C. 2213616x y += D. 2214525x y += 18. 在一个特定时段内，以点E 为中心的7海里以内海域被设为警戒水域，点E 正北55海 里处有一个雷达观测站A ，某时刻测得一艘匀速直线行驶的船只位于点A 北偏东45°且与点A 相距B 处，经过40分钟又测得该船已行驶到点A 北偏东45θ︒+（其中sin 26θ=，090θ︒︒<<）且与点A 相距海里的位置C 处； （1）求该船的行驶速度；（单位：海里/小时）（2）若该船不改变航行方向继续行驶，判断它是否会进入警戒水域，并说明理由；9. 已知一个底面置于水平面上的圆锥，其左视图是边长为6的正三角形，则该圆锥的侧面 积为10. 某班级要从5名男生和2名女生中选出3人参加公益活动，则在选出的3人中男、女生 均有的概率为 （结果用最简分数表示）11. 设常数0a >，若9()a x x +的二项展开式中5x 的系数为144，则a =15. 设M 、N 为两个随机事件，给出以下命题： （1）若M 、N 为互斥事件，且1()5P M =，1()4P N =，则9()20P M N =U ； （2）若1()2P M =，1()3P N =，1()6P MN =，则M 、N 为相互独立事件； （3）若1()2P M =，1()3P N =，1()6P MN =，则M 、N 为相互独立事件； （4）若1()2P M =，1()3P N =，1()6P MN =，则M 、N 为相互独立事件； （5）若1()2P M =，1()3P N =，5()6P MN =，则M 、N 为相互独立事件； 其中正确命题的个数为（ ）A. 1B. 2C. 3D. 417. 如图，已知正三棱柱111ABC A B C -的底面积为4，侧面积为36； （1）求正三棱柱111ABC A B C -的体积；（2）求异面直线1A C 与AB 所成的角的大小；上海市松江区2017届高三一模数学试卷8. 设230123(1)n n n x a a x a x a x a x +=++++⋅⋅⋅+，若2313a a =，则n = 9. 已知圆锥底面半径与球的半径都是1cm ，如果圆锥的体积与球的体积恰好也相等，那么 这个圆锥的侧面积是 2cm10. 设(,)P x y是曲线1C =上的点，1(4,0)F -，2(4,0)F ，则12||||PF PF + 的最大值为15. 若矩阵11122122a a a a ⎛⎫ ⎪⎝⎭满足：11a 、12a 、21a 、22{0,1}a ∈， 且111221220a a a a =，则这样的互不相等的矩阵共有（ ） A. 2个 B. 6个 C. 8个 D. 10个18. 已知函数21()21x x a f x ⋅-=+（a 为实数）； （1）根据a 的不同取值，讨论函数()y f x =的奇偶性，并说明理由；（2）若对任意的1x ≥，都有1()3f x ≤≤，求a 的取值范围；8. 如图，一个空间几何体的主视图、左视图、俯视图均为全等的等腰直角三角形，如果直角三角形的直角边长都为1，那么这个几何体的表面积为9. 已知互异复数0mn ≠，集合22{,}{,}m n m n =，则 m n +=10. 已知等比数列{}n a 的公比为q ，前n 项和为n S ，对任意的*n N ∈，0n S >恒成立，则 公比q 的取值范围是15. 已知函数22sin ,0()cos(),0x x x f x x x x α⎧+≥⎪=⎨-++<⎪⎩([0,2))απ∈是奇函数，则α=（ ） A. 0 B. 2π C. π D. 32π 18. 已知函数22()log (2)x x f x a a =+-(0)a >，且(1)2f =；（1）求a 和()f x 的单调区间；（2）(1)()2f x f x +->；8. 已知数列{}n a 的通项公式为2n a n bn =+，若数列{}n a 是单调递增数列，则实数b 的取值范围是9. 将边长为10的正三角形ABC ，按“斜二测”画法在水平放置的平面上画出为△A B C '''， 则△A B C '''中最短边的边长为 （精确到0.01）10. 已知点A 是圆22:4O x y +=上的一个定点，点B 是圆O 上的一个动点，若满足 ||||AO BO AO BO +=-uuu r uu u r uuu r uu u r ，则AO AB ⋅=uuu r uu u r14. 已知空间两条直线m 、n ，两个平面α、β，给出下面四个命题：①m ∥n ，m n αα⊥⇒⊥；②α∥β，m α，n β⇒m ∥n ；③m ∥n ，m ∥αn ⇒∥α；④α∥β，m ∥n ，m α⊥n β⇒⊥；其中正确的序号是（ ）A. ①④B. ②③C. ①②④D. ①③④17. 如图所示，三棱柱111ABC A B C -的侧面11ABB A 是圆柱的轴截面，C 是圆柱底面圆周 上不与A 、B 重合的一个点；（1）若圆柱的轴截面是正方形，当点C 是弧AB 的中点时，求异面直线1A C 与AB 的所成 角的大小（结果用反三角函数值表示）；（2）当点C 是弧AB 的中点时，求四棱锥111A BCC B -与圆柱的体积比；上海市浦东新区2017届高三一模数学试卷9. 过双曲线222:14x y C a -=的右焦点F 作一条垂直于x 轴的垂线交双曲线C 的两条渐近线 于A 、B 两点，O 为坐标原点，则△OAB 的面积的最小值为10. 若关于x 的不等式1|2|02x x m --<在区间[0,1]内恒成立，则实数m 的范围14. 已知函数()y f x =的反函数为1()y f x -=，则()y f x =-与1()y f x -=-图像（） A. 关于y 轴对称 B. 关于原点对称C. 关于直线0x y +=对称D. 关于直线0x y -=对称15. 设{}n a 是等差数列，下列命题中正确的是（ ）A. 若120a a +>，则230a a +>B. 若130a a +<，则120a a +<C. 若120a a <<，则2a >D. 若10a <，则2123()()0a a a a --> 18. 已知△ABC 的内角A 、B 、C 的对边分别为a 、b 、c ；（1）若3B π=，b =，△ABC 的面积2S =，求a c +的值；（2）若22cos ()C BA BC AB AC c ⋅+⋅=u u r u u u r u u u r u u u r ，求角C ；上海市闵行区2017届高三一模数学试卷7. 从单词“shadow ”中任意选取4个不同的字母排成一排，则其中含有“a ”的共有 种排法（用数字作答）8. 集合{|cos(cos )0,[0,]}x x x ππ=∈= （用列举法表示）9. 如图，已知半径为1的扇形AOB ，60AOB ∠=︒，P为弧»AB 上的一个动点，则OP AB ⋅uu u r uu u r 取值范围是10. 已知x 、y 满足曲线方程2212x y +=，则22x y +的 取值范围是17. 如图，在Rt AOB ∆中，6OAB π∠=，斜边4AB =，D 是AB 中点，现将Rt AOB ∆以直角边AO 为轴旋转一周得到一个圆锥，点C 为圆锥底面圆周上一点，且90BOC ∠=︒，（1）求圆锥的侧面积；（2）求直线CD 与平面BOC 所成的角的大小；（用反三角函数表示）上海市虹口区2017届高三一模数学试卷8. 若正项等比数列{}n a 满足：354a a +=，则4a 的最大值为9. 一个底面半径为2的圆柱被与其底面所成角是60°的平面所截，截面是一个椭圆，则该椭圆的焦距等于10. 设函数61()211x x f x x x ⎧≥=⎨--≤-⎩，则当1x ≤-时，则[()]f f x 表达式的展开式中含2x 项的系数是13. 在空间，α表示平面，m 、n 表示二条直线，则下列命题中错误的是（ ）A. 若m ∥α，m 、n 不平行，则n 与α不平行B. 若m ∥α，m 、n 不垂直，则n 与α不垂直C. 若m α⊥，m 、n 不平行，则n 与α不垂直D. 若m α⊥，m 、n 不垂直，则n 与α不平行15. 如图，在圆C 中，点A 、B 在圆上，则AB AC ⋅u u u r u u u r 的值（ ）A. 只与圆C 的半径有关B. 既与圆C 的半径有关，又与弦AB 的长度有关C. 只与弦AB 的长度有关D. 是与圆C 的半径和弦AB 的长度均无关的定值18. 如图，我海蓝船在D 岛海域例行维权巡航，某时刻航行至A 处，此时测得其北偏东30° 方向与它相距20海里的B 处有一外国船只，且D 岛位于海蓝船正东18海里处；（1）求此时该外国船只与D 岛的距离；（2）观测中发现，此外国船只正以每小时4海里的速度沿正南方航行，为了将该船拦截在 离D 岛12海里的E 处（E 在B 的正南方向），不让其进入D 岛12海里内的海域，试确定 海蓝船的航向，并求其速度的最小值（角度精确到0.1°，速度精确到0.1海里/小时）；7. 根据相关规定，机动车驾驶人血液中的酒精含量大于（等于）20毫克/100毫克的行为属 于饮酒驾驶，假设饮酒后，血液中的酒精含量为0p 毫克/100毫克，经过x 个小时，酒精含量降为p 毫克/100毫克，且满足关系式0rx p p e =⋅（r 为常数）若某人饮酒后血液中的酒精含量为89毫克/100毫克，2小时后，测得其血液中酒精含量降为61毫克/100毫克，则此人饮酒后需经过 小时方可驾车8. 已知奇函数()f x 是定义在R 上的增函数，数列{}n x 是一个公差为2的等差数列，满足 78()()0f x f x +=，则2017x 的值为9. 直角三角形ABC 中，3AB =，4AC =，5BC =，点M 是三角形ABC 外接圆上任意一点，则AB AM ⋅u u u r u u u u r 的最大值为13. 某班班会准备从含甲、乙的6名学生中选取4人发言，要求甲、乙两人至少有一人参加， 那么不同的发言顺序有（ ）A. 336种B. 320种C. 192种D. 144种17. 设双曲线22:123x y C -=，1F 、2F 为其左右两个焦点； （1）设O 为坐标原点，M 为双曲线C 右支上任意一点，求1OM F M ⋅uuu r uuu u r 的取值范围；（2）若动点P 与双曲线C 的两个焦点1F 、2F 的距离之和为定值，且12cos F PF ∠的最小值 为19-，求动点P 的轨迹方程；7. 如果实数x 、y 满足2030x y x y x -≤⎧⎪+≤⎨⎪≥⎩，则2x y +的最大值是8. 从5名学生中任选3人分别担任语文、数学、英语课代表，其中学生甲不能担任数学课 代表，共有 种不同的选法（结果用数值表示）9. 方程22242340x y tx ty t +--+-=（t 为参数）所表示的圆的圆心轨迹方程是 （结果化为普通方程）10. 若n a 是(2)n x +（*n N ∈，2n ≥，x R ∈）展开式中2x 项的二项式系数，则23111lim()n na a a →∞++⋅⋅⋅+=15. 某几何体的三视图如图所示，则它的体积是（ ）A. 283π-B. 83π- C. 82π- D. 23π17. 如图，在四棱锥P ABCD -中，底面ABCD 是矩形，PA ⊥平面ABCD ，PB 、PD 与 平面ABCD 所成的角依次是4π和1arctan 2，2AP =，E 、F 依次是PB 、PC 的中点； （1）求异面直线EC 与PD 所成角的大小；（结果用反三角函数值表示）（2）求三棱锥P AFD -的体积；。
杨浦区2017学年度第一学期高三模拟质量调研
杨浦区2017学年度第一学期高三模拟质量调研英语学科试卷2017。
12本试卷分为第I卷（第1-11页）和第II卷（第12页）两部分。
全卷共12页。
满分140分。
考试时间120分钟。
考生注意：1．答第I卷前,考生务必将条形码粘贴在答题纸的指定区域内。
2。
第I卷（1—20小题,31--—70小题)由机器阅卷，答案必须全部涂写在答题卡上。
考生应将代表正确答案的小方格用铅笔涂黑。
注意试题题号和答题卡编号一一对应,不能错位。
答案需要更改时，必须将原选项用橡皮擦去，重新选择。
答案写在试卷上一律不给分。
第I卷中的第21-30小题，IV. Summary Writing部分和第II卷的试题，其答案用钢笔或水笔写在答题纸的规定区域内,如用铅笔答题，或写在试卷上则无效。
第I卷（共100分）I。
Listening ComprehensionSection 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. In a professor’s office。
B。
In a second—hand book shop.C. In a library.D。