湖北省华中师大一附中2012届高三上学期期中检测英语试题

2019-2020学年华中师范大学第一附属中学高三英语上学期期中考试试题及答案第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AWhat to Eat—and What to Skip—When It Comes to Takeout FoodIf the burden on your wallet doesn't bother you much, the effect your takeout habit can have on your waistline just might arouse your attention. Here's the best and worst of the lot for your belly.Steamed Vegetable Dumplings: Order This.When she orders Chinese, registered dietitian nutritionist Elisa Zied gets an order of steamed vegetable dumplings. "I often pair them with either chicken and broccoli in brown sauce（I ask for a little saucemade without sugar）or steamed shrimp dumplings," she tells us.Crab Wontons: Not That!When you deconstruct crab wontons, it's easy to see why they're a "Not That!" The inside is filled with crabmeat and cream cheese（which is just a fancy, spreadable fat）.The wonton is made of refined flour, egg and salt and the crispy（脆的）coating is a result of a deep oil bath.Peking Duck: Order This.Most of the fat from the skin flows out of the duck over the course of cooking, making this a healthier choice than most of the stir-fry dishes available. Order a side of steamed vegetables and serve it with a small scoop of brown rice. Done and done!Sweet and Sour Anything: Not That!Anything with “sweet and sour” in its title is a powerful cue that something has been deep-fried and covered in a sickly-sweet pink sauce. If you pair your selection with a side of rice, you're looking at a 1,000-calorie meal.Summer Roll: Order This.Summer rolls are steamed instead of fried—and typically filled with lean proteins and vegetables, making them a winning appetizer in our book. Pair them with an order of edamame（毛豆）and a broth-based soup for a satisfying, filling meal.Spring Roll: Not That!Spring=deep-fried, which is why we say to skip them! They're filled with fat and calories your belly doesn'tneed.1.What kind of cooking method should be skipped according to the text?A.Steaming.B.Stir-frying.C.Deep-frying.D.Boiling.2.Which of the following suits as a good starter for a meal?A.Chicken and broccoli.B.Steamed vegetable dumplings.C.Peking duck.D.Summer rolls.3.Where can the text be found?A.In a recipe.B.In a guidebook.C.In a science fiction.D.In a health magazine.BAlaska—The American city Anchorage is recovering from a powerful earthquake Friday that damaged public buildings, homes and roads.The 7.0 earthquake caused buildings to slake. But there have been no reports of deaths, serious injuries or damage. Officials say the quake has not affected transportation of food and her supplies. “The ships are coming in on schedule, the supply lines are at this point working well,” the government told reporters Sunday.The Glenn Highway was probably the road hit hardest by the earthquake. It connects the state's largest city to other parts in the north. Traffic has been heavy and slow—moving since the quake. Drivers are being guided. Groups of workers are trying to rebuild areas where the quake left large holes in the road.People who are still nervous after the major quake have been more upset by more than 1, 700 aftershocks. “Anything that moves, you feel terrified”said David, whose home suffered structural(结构)damage, including a sunken foundation(地基). Actually, Alaska came up with strict building rules after a 9. 2 earthquake in 1964. That was the second most powerful earthquake on record.Government officials said a public health center promises that moneyfor medical treatment will continue to come. Mental healthy service(心理健康服务)is also available for people hurt by the disaster.Earthquake experts say there is a 4 percent chance of another 7. 0 earthquake or greater in the following week. "The chance is very small, but its not impossible, ” said the expert, Paul Caruso.4. What was the result of the earthquake?A. Buildings were damaged.B. Food supply was cut off.C. Many people were killedD. The ships could not come in.5. Why is the traffic slow on the Glenn Highway?A. Because small quakes hit the city.B. Because falling rocks are a danger.C. Because the highway is badly damaged.D. Because drivers are misled.6. What can you learn from Paul Caruso?A. Another greater earthquake is on the way.B. Chances still exists of another earthquake.C. It will be safe in the 1th week after the quake.D. There is no possibility for more quakes.7. Where can your possibly read the passage?A. Ina story book.B. In a travel journal.C. In a poster.D. In a newspaper.CHundreds of millions of people watched on television on July 20, 1969, when American astronauts Neil Armstrong and Buzz Aldrin became the first humans to land on the moon. Back then, businesses sold many products connected to the event and many such products are now on sales again — in celebration of the moon landing’s 50th anniversary.A limited number of Omega’s gold Speedmaster watches — the same kind that Buzz Aldrin wore on the moon — will be sold at $34,600. Omega Speedmaster watches have been an important part of space travel since NASA chose them for its moon landing in 1965. Other watches had failed required tests. Omega gave its gold Speedmasters to the astronauts at a dinner in 1969 before the landing. Another less costly type of silver Speedmasters will be sold at $ 9,650. It carries a picture of Aldrin stepping down from the moon lander.Something for children-as well as adults — is the NASA Apollo 11 moon lander set. Made by Lego, it is a group of small pieces to put together to make a model of the moon lander.Other things for sale include the anti-gravity Fisher Space Pens,developed just for the Apollo 11 mission. They work even when writing upside down. Now Fisher Space Pen Company has a limited-edition pen for sale at anout-of this-worldprice: $700, with real material from the Apollo 11 spacecraft.Back in 1969, companies were quick to show their Apollo 11 connections with media and advertisements. The food company Stouffer’s made sure consumers knew it provided food for Apollo 11 astronauts once they returned to Earth. It started the ad campaign “Everybody who’s been to the moon is eating Stouffer’s”. Fifty years later, the company is celebrating with a media campaign to share some recipes from 1969.Marketing experts David Meerman Scott says, “Since 1972,we’ve gone around and around the earth many times, and it is not interesting to people any more. I’m not sure whether they can accept such crazy prices. Now NASA has had plans to go to Mars in the 2030s and marketing efforts for a NASA Mars mission should be in development.”8. What can we learn about the gold Speedmaster watch?A. It will be sold at $34,600.B. NASA bought itats9,650.C. It has Aldrin’s picture inside.D. It was chosen by NASA in 1969.9. What does the underlined word “out-of-this-world” in paragraph 4 mean?A. Extremely fair.B. Surprisingly high.C. Really low.D. Truly worthwhile.10. What does David Meerman Scott mean?A. It is a waste of money to go around and around the moon.B. People will be interested in the products connected to Apollo.C. Since 1972,governments have lost interest in moon explorations.D. The event of going to Mars will be another good chance to advertise.11. What is the author’s main purpose in writing the text?A. To show how to design the best advertisement.B. To forecast the sales of the products in the text.C. To introduce some of the products connected to Apollo 11.D. To celebrate the 50th anniversary of the first moon landing.DChina's Mars probe Tianwen-1 successfully landed on the surface of the red planet on May 15, 2021, leaving a Chinese footprint on Mars for the first time and in its first attempt, becoming the only other nation besides theUSto get such an achievement. The Tianwen-1 probe touched down at its pre-selected landing area in the southern part of Utopia Planitia, a wide plain on Mars, at 7:18 a.m.(Beijing Time), after three months scanning the whole planet on Mars docking orbit, the China National Space Administration(CNSA) announced.Tianwen-1, including an orbiter, a lander and a rover, was launched from the 'Wenchang Spacecraft Launch Site on the coast of southernChinas islandprovinceofHainanon July 23, 2020. It was the first step inChina's planetary exploration of the solar system, with the aim of completing orbiting, landing and roving on the red planet in one mission. According to the administration, the country's first Martian probe will conduct scientificinvestigations about the Martian soil, environment, atmosphere as well as water.China's planetary exploration program has been named “Tianwen”, which was named after a long poem by the famous ancient poet Qu Yuan. The name represents the Chinese nation's willpower in pursuing truth, the country's cultural inheritance of its understanding of nature and universe, as well as the unending exploration in science and technology.China's first Mars rover has been named “Zhurong”, which means the god of fire in an ancient Chinese story. The name indicates Chinese people's blessing for the rover to light the flame ofChina's planetary exploration. The rover has six wheels and four solar panels, and carries 13 scientific instruments. According to the CNSA, Zhurong has started its scientific exploration after moving from the landing platform onto the Red Planet's surface on May 22.More than 40 Mars missions have been launched since the 1960s, but only about half have succeeded. It is the first time in the world that orbiting, landing and roving on Mars has been completed in one launch mission, andChinahas come to the forefront of Mars exploration in the world.12. What can we learn from the first two paragraphs?A. China is the only nation to launch a probe to Mars.B. Tianwen-1 landed in the northern part of the planet.C. Tianwen-1 scanned the southern part of the planet.D. The Mars probe will carry out scientific investigations.13. How did the planetary exploration program get its name?A. From a long poem by Qu Yuan.B. From an ancient Chinese story.C. From Chinese nation's willpower.D. From theChinaNational Space Administration.14. Why does the author sayChinahas come to the leading position of Mars exploration?A. The rover carried many scientific instruments.B. China completed three tasks in one attempt.C. The rover successfully moved from the landing platform onto Mars.D. The CNSA is continuously exploring science and technology.15. What is the text mainly about?A. Tianwen-1 completed its mission.B. Tianwen-1 represented the god of fire.C. Tianwen-1 successfully landed on Mars.D. Tianwen-1 was launched from Wenchang.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。

华中师大一附中2020届高三阶段检测（四）英语试题本试卷共8页。

全卷满分150分。

考试用时120分钟。

注意事项：1. 答卷前，考生务必将自己的姓名和座位号填写在答题卡上。

2. 回答选择题时，选出每小题答案后，用2B铅笔把答题卡对应的答案标号涂黑。

如需改动，用橡皮擦干净后，再选涂其他答案标号。

回答非选择题时，将答案写在答题卡上。

写在本试卷上无效。

3. 考生结束后，将本试卷和答题卡一并交回。

第一部分听力（共两节，满分30分）做题时，先将答案标在试卷上。

录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。

第一节（共5小题；每小题 1.5分，满分7.5分）听下面5段对话。

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

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1. When will the film probably start?A. At 11: 45.B. At 12: 00.C. At 12: 452. What did the woman buy for her husband?A. A book.B. A watch.C. A case for coin collection.3. Where did the man know his flight had been canceled?A. At the airport.B. At the meeting.C. At the international fair.4. Why can’t the woman contact the man?A. He just had a long phone conversation.B. His phone is out of order.C. The connection on the phone line is poor.5. What is the man doing?A. Taking an exam.B. Reading a book.C. Having a class.第二节（共15小题；每小题 1.5分，满分22.5分）听下面5段对话或独白。

2021届湖北华中师范大学第一附属中学高三英语上学期期中试题及答案解析第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项ACanadais one of the most beautiful countries in the world. Here are 4 attractive places worth your visit.ChurchillChurchill is a town with the nickname "Polar Bear Capital of the World”, where tourists can safely view polar bears from special vehicles in the autumn and winter. Thousands of beluga whales, which move into the warmer waters of theChurchill Riverduring July and August, are a major summer attraction. Churchill is also a destination for bird watchers from late May until August.Niagara FallsNiagara Fallsis a group of three waterfalls, crossing the border betweenCanadaand theUnited States. The largest of the three is Horseshoe Falls, also known asCanadian Falls. Niagara Falls illumination（彩灯）is a must for any visitor! Every night of the year, the three waterfalls are illuminated in color1 s creating an attractive scene that can be viewed from near and far.VancouverVancouverisCanada's third-largest city, always named as one of the top five worldwide cities for its comfortable environment and quality of life.Vancouverhas an active nightlife scene, whether its food and dining, or bars and nightclubs. From mid-June to early July, the Vancouver International Jazz Festival features 300 concerts, including a free opening Downtown Jazz Weekend.OttawaThe capital ofCanadais situated on the banks of theOttawa Riverand has a lot ofEnglish buildings in it. It is a beautiful city which has the Parliament buildings on the banks and English influenced houses and parks around. There are museums and art galleries that will give you a complete knowledge of the English culture there. It is really the heart ofCanada. So if you are a history and art loverOttawais the best choice for your visit inCanada.1. If you want to watch birds, which place will you choose to visit?A. Churchill.B.Niagara Falls.C. Vancouver.D.Ottawa.2. What is the best season for visitingVancouver?A. Spring.B. Summer.C. Autumn.D. Winter.3. What doNiagara FallsandVancouverhave in common?A. They are both famous for natural scenery.B. The best visiting time are both at nights.C. They are both located inCanadaentirely.D. The tickets there are both free at weekends.BA Virginia teen is doing his part to make sure frontline health care workers are getting the meals they need to help them take care of themselves and others.Arul Nigam, 17, of Tyson's Corner, Va. , has had to make several adjustments since his school year ended abruptly in mid-March due to the coronavirus pandemic(新冠疫情).“We didn'thave any classes for like over a month and then after that there were a lot of technical difficulties. So I started to have a lot more free time,” he tells Yahoo Life. “It was really saddening, but it was also something that really surprised me, that our health care workers are facing something like that,” Nigam says. “So I wanted to see what I could do to help them because obviously, they're sacrificing so much and giving so much for all of us. ”In late March, the teen started fundraising efforts with the help of friends and family to help these health care workers receive much-needed meals. He also began doing research about what hospitals had the most amount of coronavirus cases, so he could prioritize those places first. He was also arranging for the orders to be fulfilled at local family-owned restaurants impacted by shutdown orders. So far, Nigam has delivered over 1,000 meals to 22 hospitals in 13 states, including New York, Massachusetts and Maryland.Nigam's efforts have not only helped health care workers, but restaurants as well. With quarantine restrictionstaking a toll onthe food industry, places like Best Coast Burrito in Oakland, Calif. , have lost business over the last few weeks. Best Coast's owner,Alvin Shen, tells Yahoo Life that being able to partner with Arul and others in efforts to feed those on the frontline has been a big help.4. What would Nigam probably do according to his words?A. Study at home by himself.B. Spend the more free time playing.C. Donate some money to health care workers.D. Do something helpful for health care workers.5. What is Nigam's priority when delivering food?A. The urgency of meals.B. The severity of the virus.C. The number of doctors.D. The position of hospitals.6. What does the phrase “taking a toll on” in the last paragraph mean?A. Turning a blind eye to.B. Keeping an eye on.C Causing lots of damage to.D. Answering completely for.7. Where can you probably read this text?A. Science fiction.B. Fashion magazine.C. Life magazine.D. Entertainment newspaper.CTwenty years ago, I became involved in pet therapy(疗法) work with our Angel. As she matured and went through professional training, we realized that she would be good at this new job.Angel is ten now and works every week. She visits two hospitals providing day care for the elderly, and our library’s PAWS forReadingprogram. At the library, six to ten dogs lie on the floor, and the kids pick a book to read to a dog. After they finish, they get a card with the dog’s picture and history. Angel also helps out at a special-needs camp. She is so popular that everywhere we go people recognize her, especially the kids she has worked with.We have seen some very special things through our pet therapy work. I brought Angel to our local hospital to visit a woman who was completely unable to move the right side of her body from a stroke(中风). One day, my husband, Jack, got Angel up into a chair next to the woman’s bed, asking her if she wanted to give Angel a treat. She nodded. Angel gently took the treat. Then the woman raised her right hand and started petting Angel. Her friend couldn’t believe her eyes.After that, every time we saw the woman, she lifted her left hand. We’d tell her she had to use her right hand, and she would. Next, you’ll fall in love with this woman’s story of rearing her own Angel later in her family andwhy she calls it the best decision she ever made.8. Who is Angel?A. A pet trainer.B. A hospitalC. A therapy dog.D. The author’s kid.9. What does Angel usually do?A. Save seriously ill people.B. Pay visits to kids in hospital.C. Protect the elderly in their homes.D. Help children at a special camp.10. Why was the woman’s friend astonished?A The woman moved her right hand.B. The woman treated Angel.C. Angel helped the woman recover.D. Angel got along with the woman.11. What does the underlined word “rearing” in the last paragraph mean?A. Accompanying.B. Raising.C. Assisting.D. Training.DA teenager in Georgia will no longer have to walk 7 miles to work after school thanks to one woman’s act of kindness.Jayden Sutton, a high school senior, went on foot each day from school to his job at a restaurant and then back home. Sutton was determined to work and make enough money to eventually buy his own vehicle.Sutton said he’d leave school at 3:30 pm, then walk miles to his job at the restaurant. After his work, which usually lasted six to eight hours, he walked home, sometimes not arriving back until almost midnight.That all changed when Myers saw him walking down the road in the rain in December. “The young man was insistently in a rush walking to work, saying ‘I can’t be late,’” Myers said. “He begged me to give him a ride. I told him I could take him as far as I was going. I began to create small talk along the way. It wasrevealedto me that his name was Jayden, 12th grader, worked 40 hours a week, walked 5 miles to work immediately after school, got off at 10:30 pm at night and walked back home another 5 miles if co-workers didn’t offer a ride.”After dropping Sutton off, Myers said his heart and determination filled her with tears. “He was smiling ingood spirits and that’s a child worth blessing,” she told Fox News. So, Myers shared Sutton’s story on the GoFundMe page, which raised more than $ 9, 000 from 186 donors.She surprised Sutton with a new car after she managed to convince the general manager to drop the price of the vehicle to meet the budget.12. Why did Sutton work so hard in his spare time?A. To gain working experience.B. To pay for his education.C. To own a car.D. To support his family.13. What difficulty did Sutton have in his work at the restaurant?A. He worked longer than other workers.B. His work was too tiring.C. His job was much less paid.D. He had to walk to work.14. What does the underlined word “revealed” in paragraph 4 mean?A. Known.B. Attached.C. Believed.D. Limited.15. What do we know about the money donated online?A. It could buy more than a new car.B. It was not enough to buy a new car.C. It was given to Myers to buy herself a new car.D It mainly came from a car sales manager.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。

2020-2021学年湖北华中师范大学第一附属中学高三英语上学期期中考试试题及答案第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AWhen the sun shines brightly, it provides a great chance to get outdoor things done. Like making hay! At least, that is what farmers from the past would say. ―Make hay while the sun shines.This idiom is very old, dating back to Medieval times. Rain would often ruin the process of making hay. So, farmers had no choice but to make hay when the sun was shining.Today, we all use this expression, not just farmers. When conditions are perfect to get something done, we can say, ―It’s a good idea to make hay while the sun shines.In other words, you are taking advantage of a good situation or of good conditions. You are making the most of your opportunities. These all mean ―making hay while the sun shines.And sometimes we use this expression to mean we beat someone to the punch, or we got ahead of someone else. And other times you make hay while the sun shines to make good use of the chance to do something while it lasts. You are being opportunistic – taking advantage of a good opportunity. For example, my friend Ozzy was sick for a week and could not go to work. So, his co-worker Sarah -- who doesn’t like him -- took advantage of his illness and stole his project! Talk about making hay while the sun shines.Sometimes when you make hay while the sun shines you are staying ahead of a problem – like in this example:Hey, do you want to go hiking with me and my friends this weekend? The weather is going to be beautiful! I wish I could. But I have to finish my taxes. It’s the last weekend before they’re due.Oh, that’s too bad.Wait. What about your taxes?My taxes are done. I was off from work a couple of weeks ago and made hay while the sun shined. I got all of it done!I wish I would have taken advantage of my time off last week___1___All I did was lay around thehouse.And that’s all the time we have for these Words and Their Stories. But join us again next week. You can listen while you’re making dinner or riding to work. Yeah, make hay while the sun shines.1.Which of the following best matches ―make hay whilethe sun shines in paragraph 2?A.Sow nothing, reap nothing.B.Sharp tools make good work.C.Strike while the iron is hot.D.One swallow doesn’t make a summer.2.According to the underlined sentence, what feeling does the speaker express?A.AdmirableB.RegretfulC.AnnoyedD.Indifferent3.Where is the passage probably taken from?A.A radio programB.A magazineC.A brochureD.A novelBFrom Mozart to Metallica, tons of people enjoy listening to various types of music while they paint, write, or draw. Most believe that music helps increase creativity, but an international study conducted by English and Swedish researchers is challenging that view. The study results wereechoedby scientists fromLancasterUniversity, and theUniversityofGavle, saying their findings show music actually weakens creativity.To reach their conclusions, researchers had volunteers complete verbal problems designed to inspire creativity while sitting in a quiet room, and then again while music played in the background. They found that background music significantly weakened the volunteers’ ability to complete tasks connected with verbal creativity. The team also tested background noises like those commonly heard in a library, but found that such noises had no influence on subjects’ creativity.The tasks were simple word games. For example, volunteers were given three words, such as dress, rise, and flower. Then, they were asked to find a single word connected with all three that could be combined to form a common phrase or word. The single word, in this case, would be “sun” (sundress, sunrise, sunflower). Volunteers completed the tasks in either a quiet room, or while listening to two different types of music: rock music or light music“We found strong evidence of weakened performance when playing background music in comparison to quiet background conditions,” says co-author D. Neil McLatchie ofLancasterUniversity. He and his colleagues find that music negatively influences the verbal working memory processes of the brain, preventing creativity. Also, as far as the library background noises having seemingly no effect, the study’s authors believe that was the case because library noises create a “regular state” environment that doesn’t affect concentration.“To conclude, the findings here challenge the popular view that music increases creativity, and instead showthat music, whatever type it is, is always a disadvantage for creative performance in problem solving,” the study reads.4. The underlined word in Paragraph 1 can be replaced by ________.A. challengedB. acceptedC. doubtedD. heard5. What were the volunteers asked to do in the study?A. To play music.B. To combine given words.C. To create new words.D. To connect words with music.6. What can we infer from the study?A. Quiet background inspires creativity best.B. Library noise does no harm to creativity.C. Music has a bad effect on language ability.D. Music types matter in creative performance.7. Which is the main idea of the passage?A. Quiet Environments Prevent Concentration.B. Background NoiseAffects Concentration.C. Composing Music Weakens Creativity.D. Listening to Music Reduces Creativity.CThe Chinese philosopher (哲学家) Confucius once said, “Time flows away like the water in the river.” This is especially true as the novel coronavirus pneumonia outbreak has affected millions of people in China, andthe whole nation has been working day and night to fight the epidemic.In late January, when an increasing number of people in Wuhan were suspected to be infected, and hospitals didn't have adequate beds for them, two special hospitals—Lei shenshan Hospital and Huo shenshan Hospital were built. These two makeshift (临时的) hospitals were built to treat pneumonia patients infected with the novel coronavirus.HuoshenshanHospitalhas 1,000 beds and covers 33,900 square meters, andLeishenshanHospitalhas 1,500 beds and a total area of about 79,000 square meters. More than 4,000 workers worked 24/7 in two shifts, and nearly 1,000 large-scale pieces of equipment and transport vehicles helped the project on site. The two hospitals were built in an amazingly short time. It only took 10 days for people to build Huo shenshan, and 14 days for Lei shenshan.This certainly wowed many people overseas. “It's incredible that two hospitals with 2,500 beds can be built in a short period. It's just hard to believe,” a foreigner named Stuart told People's Daily. In the meantime, Chinese companies have also taken actions quickly in this battle.“The automobile industry is highly industrialized with strong capabilities in comprehensive manufacturing, purchasing materials, production lines and output of technologies,” Shi Jianhua, deputy secretary-general of ChinaAssociation of Automobile Manufacturers, told CCTV News. “In this special time, when the nation needs more masks, it's time for us to quickly respond and shoulder the social responsibilities.”Indeed, a fast response is crucial in any crisis. In this special time,Chinacan't afford to waste a second in the fight against the epidemic. After all, time equals life during this crisis.8. Confucius' saying “Time flows away like the water in the river.” is mentioned to ______.A. arouse readers' interest in the passage.B. introduce the subject of the passage.C. present the background information.D. stress the value of time in epidemic.9. What can we learn about Lei shenshan hospital and Huo shenshan hospital?A. They are new hospitals for health care inWuhan.B. They were built in minimal time.C. Over 4,000 workers worked continuously.D. Stuart found them too massive to believe.10. We can infer from Shi Jianhua's words that the automobile industry inChina______.A. had no medical supplies factories before.B. guarantees whoever in need enough masks.C. has capabilities to give timely response.D. has strong abilities in manufacturing.11. What does the passage mainly talk about?A. China fights epidemic against the clock.B. Twospecial hospitals were constructed.C. Chinese firms acted quickly and effectively.D. Time is crucial for people in overcoming crisis.DThe China International Search and Rescue Team(CISAR) was formed in 2001 and is now made up of several hundred rescue workers and about 20 police dogs. The team brings help and hope to those whose lives are changed by astorm, flood, earthquake, or any other natural disasters.After long and careful training, the team went on its first international rescue tasks in 2003. That year, the Chinese team helped save lives after earthquakes inAlgeriaandIran. It was the first time that a Chinese team had worked outsideChinawhose members won high praise for bravery and skill.Since then, the CISAR has completed many tasks. The list of people to whom help has been given is long. Theteam treated more than 3,000 people who were wounded in the 2006 earthquake inIndonesia, helped 2,500 wounded people after the earthquake that hitHaitiin 2010, and spent several months giving aid to over 25,000 people suffering from the 2010 floods inPakistan. On April 26, 2015, a group of 62 people from CISAR went toNepalafter the 8.1 magnitude earthquake that happened there.Rescue workers are trained to find people, treat wounds, and hand out food, water, and other supplies. They have to be able to do work that is difficult under conditions which can be very dangerous. After a disaster, there is usually no electricity or water, and there may be diseases and other dangers. Rescue workers get to save lives, but they must also bury the dead. That means they have to be strong in both body and mind.Rescue workers must have big hearts, too. It takes a lot of love and courage to risk one’s own life to save someone else’s. The members of the CISAR have plenty of both and are always ready to go wherever help is needed.12. What is the function of the numbers in Paragraph 3?A. To advertise for the CISAR.B. To add some basic information.C. To praise Recue Workers’ contributions.D. To stress the dangers Rescue Workers face.13. What is the author’s attitude towards Rescue Workers?A. Hopeful.B. Respectful.C. Curious.D. Supportive.14. What are the last two paragraphs mainly about?A. The duty rescue workers must perform.B. The qualities rescue workers must own.C. The difficulties rescue workers must go through.D. The willingness rescue workers should require.15. What may be the best title of the passage?A. China to the RescueB. How to train CISARC. Welcome to CISARD. Rescue on request第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。

2019-2020学年湖北华中师范大学第一附属中学高三英语上学期期中试卷及答案解析第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AEach year, theLas Vegasconsumer electronics show, or CES, presents the latest developments in many areas of technology. The newest products are designed to make our lives easier, fun and more productive.A car with legsOne of this year’s presentations was by South Korean carmaker Hyun-dai. The company introduced a small model of a “ walking car,” which is called Elevate. It has four movable legs that can raise the main part of the vehicle high off the ground. The electric-powered vehicle is designed to be used in search-and-rescue operations during emergencies or natural disasters.Changeable people moverGermany's Mercedes presented an experimental self-driving vehicle that it claims can revolutionize transportation for people and goods. The company says the vehicle, called Vision Urbanetic, will be able lo easily change bodies depending on its desired use. Mercedes says as a ride-sharing vehicle , the futuristic-looking car can seat 12 people.Fully electric HarleyAmerican manufacturer Harley-Davidson showed off its first fully electric motorcycle, called LiveWire. The company says the bike will be able to go 177 kilometers between charges. It can reach 96 kilometers per hour in under3.5 seconds. Although Harley is known for building powerful bikes with huge, loud motors, the LiveWire will be unusually quiet.Personal robotsOne of the new robots, called Temi, is really just a computer tablet on wheels. It is designed to be a personal electronic assistant. It moves around the home and performs commands when spoken to. It can link users to friends through voice or video, connect to video or place orders for food or goods.1. Which do you probably use to search for the injured in an earthquake?A. Elevate.B. Vision Urbanetic.C. LiveWire.D. Temi.2. What is the first fully electric motorcycle produced by Harley-Davidson?A. ElevateB. Hyun-daiC. LiveWire .D. Temi .3. Why are the four products designed?A. To ease traffic jam.B. To help us socialize.C. To improve our life.D. To protect the environment.BHappiness is not a warm phone, according to anew study exploring the link between young life satisfaction and screen time. The study was led by professor of psychology Jean M. Twenge at San Diego State University (SDSU).To research this link, Twenge, along with colleagues Gabrielle Martin at SDSU and W. Keith Campbell at the University of Georgia, dealt with data from the Monitoring the Future (MtF) study, a nationally representative survey of more than a million U. S. 8th-, 10th-, and 12th-graders. The survey asked students questions about how often they spent time on their Phones, tablets and computers, as well as questions about their face-to-face social interactions and their overall happiness.On average found that teens who spent more time in front of screen devices — playing computer games, using social media, texting and video chatting — were less happy than those who invested more time in non-screen activities like sports, reading newspapers and magazines, and face-to-face social interactions."The key to digital media use and happiness is limited use," Twenge said. "Aim to spend no more than two hours a day on digital media, and try to increase the amount of time you spend seeing friends face-to-face and exercising — two activities reliably linked to greater happiness."Looking at historical trends from the same age groups since the 1990s, it's easy to find that the increase of screen devices over time happened at the same time as a general drop-off in reported happiness inU. S.teens. Specifically, young peopled life satisfaction and happiness declined sharply after 2012. That's the year when the percentage of Americans who owned a smartphone rose above 50 percent. By far the largest change in teens' lives between 2012 and 2016 was the increase in the amount of time they spent on digital media, and the following decline in in-person social activities and sleep.4. Which method did Twenge's team use for the study?A. Calculating students' happiness.B. Asking students certain questions.C. Analyzing data from a survey.D. Doing experiments on screen time.5. How does the author develop the finding of the study in paragraph 3?A. By making a comparison.B. By giving an example.C. By making an argument.D. By introducing a concept.6. What is the purpose of the last paragraph?A. To draw a conclusion from the study.B. To offer some advice to the readers.C. To prove social activities' importance.D. To support the researchers' finding.7. Which of the following can be the best title for the text?A. Quitting Phones Equals HappinessB. Screen Time Should Be BannedC. Teens' Lives Have Changed SharplyD. Screen-addicted Teens Are UnhappierCIn recent years,people have been focusing on the quality of food that children are fed in schools. Former First Lady Michelle Obama worked hard to make school lunches healthier, resulting in new menus that featured less fat and salt, more fruits and vegetables.But high-quality nutrients count for little when there is no time to eat them. Amy Ettinger reports, "There is no national standard on how much time kids get to eat that meal. " And with schools being occupied with test scores, teachers are using every available minute for lesson time, which often leaves kids without enough eating time.This is a problem because the length of the school lunch period is a key factor (因素) in how much nutrition children actually gel. Research has found that having less than 20 minutes for lunch results in children consuming much less of their lunch than those with more than 20 minutes.This is really terrible. For many low-income kids, that cafeteria lunch can represent half their daily energy intake. There's also another terrible message that it's acceptable to wolf down food as fast as possible before rushing off to your next class. Cafeteria time should be a chance to interact with friends, to learn important social skills, to observe and share varieties of food. It should be a break in day, a chance to relax before heading into theafternoon.As Ettinger explains,some parents are hoping the National Parent Teacher Association will address this issue. This, in turn, would help parents push their kids' schools for better lunch time standards. Meanwhile, if you have a kid in this situation, you can help by packing a healthy lunch to spare them the cafeteria lineup. Make the foods easy to eat, provide non-messy snacks that can be eaten in class, put great effort into serving a hearty breakfast, and sit down as a family for dinner whenever possible.8. What did Michelle Obama make efforts to improve?A. The quality of school lunches.B. The performance of school kids.C. The school lunch time kids have.D. The eating habits of school kids.9. What happens to children in American schools?A. They are occupied with many tests.B. They fail to get along with each other.C. They consume more meat than before.D. They have less lunch time than before.10. How are low-income kids influenced by the problem at school?A. They can't go to classes on time.B. They can't have enough energy.C. They can't share different kinds of food.D. They can't hold a positive attitude toward life.11.What can parents do to solve the problem?A. Prepare a better lunch for their kids.B. Stop their kids going to the cafeteria.C. Force schools to make adjustments to lunch.D. Guide their kids on how to pack their own lunch.DAt first glance, there is nothing unusual about BingoBox’s convenience store–shelves packed with snacks line the walls, attracting passers-by through the glass windows. But upon closer look, BingoBox is no ordinary store. The door unlocks only after customers scan (扫描) aQR code to enter, and there is no cashier — just a lone checkout counter (柜台) in a corner. The Shanghai-based company is one of many unmanned store operators (运营者) opening outlets all over China, hoping to improve slim profit by reducing staff costs.“Ifstaff costs rise quickly, that puts greater pressure on low-profit businesses like convenience stores and supermarkets,” said Andrew Song, an analyst at Guotai Junan Securities. “InChina, manpower costs have beenrising ly quickly.”However, the future vision of shopping without a check-out person is still a work in progress. A Post reporter who visited a BingoBox store inShanghaiwas briefly locked in when trying to exit without buying anything. Although a sign near the exit stated that empty-handed customers can leave by scanning a QR code, no QR code was to be found. Repeated calls to the customer service hotline went unanswered.The idea of unmanned stores first caught the world’s attention in December last year. Equipped with technology such as RFID tags, mobile payment systems and facial and movement recognition, such stores collect large amounts of data that give operators a better idea of consumer preferences and buying habits, which can then be used to optimize (使最优化) operations and make more efficient inventory decisions. For companies like BingoBox, lower operating costs also mean it can afford to expand its reach to areas with less foot traffic or fewer people, according to its founder and chief executive ChenZilin.12. What makes BingoBox store look like an ordinary convenience store?A. No cashier to check out.B. A lone checkout counter.C. Shelves packed with goods.D. Entering by scanning a QR code.13. Why are unmanned stores popular with operators?A. The customers prefer mobile payment systems.B. The unmanned stores help improve profit with lower labor costs.C. The employees focus on consumer preferences and buying habits.D. The operators care more about operations and inventory decisions.14. Why is the reporter’s case mentioned in the passage?A. To show his anger and dissatisfaction.B. To warn people not to go to a BingoBox store.C. To explain unmanned stores still have a long way to go.D. To complain that QR code service is not convenient at all..15. What can we infer from the chief executive Chen Zilin?A. Nowadays all stores should be equipped with advanced technology.B. The operators collect data about consumer preferences and buying habits.C. BingoBox made wiser decisions based on the data collected in those unmanned stores.D. The operators can open unmanned supermarkets in more distant places with low cost.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。

华中师大一附中2019—2020学年度上学期期中检测高三年级英语试题时间：120分钟满分：150分第一部分：听力（共两节，满分30分）做题时，先将答案划在试卷上。

录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。

第一节（共5小题；每小题1.5分，满分7.5分）听下面5段对话。

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

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

例：How much is the shirt?A.￡19.15.B.￡9.15.C.￡9.18.答案是B。

1. What will the man do for the woman?A. Repair the car.B. Give her a ride.C. Pick up her aunt.2. How is the weather today?A. Cloudy and a little windy.B. Clear and a little windy.C. Rainy and cool.3. Who might Mr. Peterson be?A. A new professor.B. A department head.C. Gordon’s best friend.4. What is the probable relationship between the two speakers?A. Classmates.B. Teachers and students.C. Jobseeker and interviewer.5. Where is the man now?A. In hospital.B. At home.C. In the library.第二节（共15小题；每小题1.5分，满分22.5分）听下面5段对话或独白。

华中师大一附中2012—2013学年度上学期高三期中检测文科综合试题—政治12．最近武汉的气温转冷，某超市向顾客推荐一款标价为600元的电热取暖器。

这600元①行使着价值尺度的职能，是观念上的货币②行使着流通手段职能，是现实的货币③是取暖器的价格，是其价值的货币表现④行使着支付手段职能，是观念上的货币A．①②B．③④C．①③D．②④13．假设2011年M国一单位商品，其价值用该国货币表示为13元，1单位M国货币/1单位N国货币为1：5，如果M国2012年生产该商品的社会劳动生产率提高30%，且该国的货币价值贬值20%,2011年将该商品出口到N国，在其它条件不变的情况下，从购买力的角度，可换回N国货币多少元？A．65 B．62.5 C．50D．4014．消费是我们日常生活中不可缺少的部分，居民收入直接影响居民消费需求。

在右图中，合理表示居民收入与居民消费需求量的关系的是A．A1曲线B．A2曲线C．A3曲线D．A4曲线15．武汉东湖高新技术开发区已成为湖北省创新活力最强、经济增长最快的区域。

“十二五”期间，该区将推动企业自主创新力度，重点发展光电子信息、环保节能、高技术服务等产业。

武汉东湖高新加快自主创新①可以提高社会劳动生产率，增加商品价值量②有利于企业提升产品附加值，获得较高利润③可以提升企业市场竞争力④有利于企业降低成本，提高经济效益A．①②③B．①②④C．①③④D．②③④16．2011年12月3日，美国联邦储备委员会公布了新一轮量化宽松的货币政策，以进一步刺激美国经济复苏，美元贬值成为不争的事实。

美元贬值对我国的影响可能有①我国商品出口竞争力增强，有利于出口②加剧我国外向型制造企业的困境③导致我国的外汇储备的实际价值缩水④居民人民币存款储蓄缩水A．①②B．②③C．②④D．③④经过两年多的规划研究，武汉市雄楚大街改造方案初定。

2011年5月17日，市国土资源和规划局组织召开了“雄楚大街快速化改造规划方案”听证会，广泛听取社会各界的意见和建议。

高三年级英语试题答案1.BBBAC 6.CACBA 11CBBAC 16.ABCAC 21.ABC 24.DBAB 28.BCAC 32.CDDA 36.EBACD 41.CDABD 46.DAACB 51.ABBCC 56.CBDAD 61.What 62.cancel(l)ed 63. won 64.previously 65. as 66. to call 67accusation 68.who /and 69. exploring 70. be taken1.The 改为a2. Organize 后面加it 4. were改为was 5. variously 改为various 6. ranged 改为ranging 6. copy改为copies 7.c-o/me改为came 8. selling 改为sell 9. 去掉of 10. which改为that Dear Mr. Smith,I am Li Hua, chairman of the Student Union in our school . I am very pleased to learn that you are coming to visit our school on June 26. On behalf of our school, I am writing to express our warm welcome to you and tell you what we have arranged for you.In the morning, there will be a special lesson for the visiting students, where they are instructed to play the traditional Chinese Taiji Boxing. At noon, you are invited to have lunch in our school cafeteria with students from our school. You can taste dumplings, noodles and other Chinese foods. In the afternoon, there will be a basketball match between our guests and our school basketball team, which, I am sure, will be exciting and promote the friendship as well. After that, you will end your visit to our school.How do you like the arrangements ? I sincerely wish you a pleasant time with us.Yours sincerely，Li Hua。

华中师大一附中2017-2018学年度上学期高三年级期中检测英语试题注意事项：1.本试卷由四个部分组成。

其中，第一、二部分和第三部分的第一节为选择题。

第三部分的第二节和第四部分为非选择题。

2.答卷前，考生务必将自己的姓名、准考证号填写在答题卡上。

3.回答选择题时，选出每小题答案后，用2B铅笔把答题卡上对应题目的答案标号涂黑；回答非选择题时，将答案写在答题卡上，写在本试卷上无效。

4.考试结束后，将本试卷和答题卡一并交回。

第一部分听力(共两节，满分30分)做题时，先将答案标在试卷上。

录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。

第一节（共5小题；每小题1.5分，满分7.5分）听下面5段对话。

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

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

例：How much is the shirt?A. £ 19. 15.B. £ 9. 18.C. £ 9. 15.答案是C。

1. What’s wr ong with the woman?A. She lost her money.B. She has no money in hand.C. She couldn’t find the bank.2. What will happen to Julia and Tony?A. Julia will leave Tony.B. They will stay in love.C. Tony will quit drinking.3. What are the speakers talking about?A. Geometry.B. The shape of the house.C. The decoration of the building.4. How long will it take to complete the walk?A. 20 minutes.B. 22 minutes.C. 42 minutes.5. Where does this conversation probably take place?A. At reception.B. On the phone.C. At the hospital.第二节（共15小题；每小题1.5分，满分22.5分）听下面5段对话或独白。

华中师大一附中2024-2025学年度上学期高三期中检测数学试题时限：120分钟 满分：150分一、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. 已知平面向量()1,2a =，()1,b λλ=-，a b ⊥，则实数λ=（ ）A. 1- B. 1C. 2- D. 22. 若p ：()41log 12a -<，q：2230a a --<，则p 是q （ ）A. 充分不必要条件 B. 必要不充分条件C. 充要条件D. 既不充分也不必要条件3. 己知,A B 是全集U 的两个子集，则如图所示的阴影部分所表示的集合是（ ）A. ()()U U A B⋂ðð B. ()()U U A B⋃ððC ()()U A B A B ⋃⋂⋂ð D. ()()U A B A B ⋂⋃⋃ð4. 若0.51.2a =，5log 2b =，0.20.5c =，则（ ）A. c a b>> B. a b c>> C. a c b>> D. c b a>>5. 已知α，β都是锐角，tan 3tan αβ=，()1sin 3αβ+=，则cos sin αβ=（ ）A.14B.16C.18D.1126. 已知O 为ABC V 的外接圆圆心，2BC =，30BAC ∠=︒，则AB OC ⋅的最大值为（ ）A. 4B. 6C. D. 7. 某中学数学兴趣小组为测量学校附近某建筑物的高度，在学校操场选择了同一条直线上的A ，B ，C 三点进行测量．如图，20AC =（单位：米），点B 为AC 中点，兴趣小组组长小王在A ，B ，C 三点正的.上方2米处的1A ，1B ，1C 观察建筑物最高点E 的仰角分别为α，β，γ，其中tan α=tan 2β=，tan γ=，点D 为点E 在地面上的正投影，点1D 为DE 上与1A ，1B ，1C 位于同一高度的点，则建筑物的高度DE 为（ ）米．A. 20B. 22C. 40D. 428. 设函数()()11e e sin 1x x f x x --=-+-，则关于x 的不等式()()2220f x x f x --+-≥的解集为（ ）A. []1,4- B. ][(),14,-∞-⋃+∞C. []2,1- D. ][(),21,∞∞--⋃+二、多选题：本题共3小题，每小题6分，共18分．在每小题给出的选项中，有多项符合题目要求．全部选对的得6分，部分选对的得部分分，有选错的得0分．9. 设函数()33f x x x =-+，()()1f x g x x=+，()f x 的导数为()f x '，则（ ）A. ()12f '-=B. 当()02f x '=时，01x =-C. 曲线()y g x =在点()1,4处的切线方程为50x y +-=D. 当0x >时，()()g x g x -<10. 某个简谐运动可以用函数()()sin f x x ωϕ=+（0ω>，π<ϕ），[)0,x ∈+∞来表示，部分图象如图所示，则（ ）A. 2π3AB =B. 这个简谐运动的频率为1π，初相为π6-C. 直线π8x =是曲线π23y f x ⎛⎫=+ ⎪⎝⎭的一条对称轴D. 点π,08⎛⎫⎪⎝⎭是曲线π23y f x ⎛⎫=+ ⎪⎝⎭的一个对称中心11. 已知实数x ，y 满足e 0x yyx++=，则（ ）A. 当0y <时，0x y += B. 当0x <时，0x y +=C. 当0x y +≠时，2y x -> D. 当0x y +≠时，10xy -<<三、填空题：本题共3小题，每小题5分，共15分．12. 已知向量1e ，2e 为单位向量，且1e 在2e 上的投影向量为21e 2-，则12e e -= ______．13. 若实数a ，b 满足13a b -<+<，24a b <-<，则3a b +的取值范围为______．14. 设1F ，2F 是双曲线C ：22221x y a b-=（0a >，0b >）的左、右焦点，点A 是C 右支上一点，若12AF F △的内切圆的圆心为M ，半径为a ，且λ∃∈R ，使得22AM OM OF λ+=，则C 的离心率为______．四、解答题：本题共5小题，共77分．解答应写出文字说明、证明过程或演算步骤．15. 在ABC V 中，内角A ，B ，C 的对边分别为a ，b ，csin cos C a C c b -=-．（1）求A ；（2）若角A 平分线交边BC 于点D，AD =，求ABC V 面积的最小值．16. 已知函数()()()sin cos cos 0f x a x x x a =+>，且()π6f x f ⎛⎫≤ ⎪⎝⎭恒成立．（1）求a的值；的（2）设()()sin cos sin cos g x b x x x x =+-，若1π0,4x ⎡⎤∀∈⎢⎥⎣⎦，2π,06x ⎡⎤∃∈-⎢⎥⎣⎦，使得()()12g x f x ≤，求实数b 的取值范围．17 已知函数()()ln f x ax x a =-∈R ．（1）若函数()f x 在1,1e ⎡⎤⎢⎥⎣⎦上的最小值为32，求a 的值；（2）若0a =，函数()()1e x f x g x x-=+，求()g x 的最小值．18. 已知椭圆C ：()222210+=>>x y a b a b()0,1A 在C 上，直线l 与C 交于不同于A的两点M ，N ．（1）求C 的方程；（2）若0AM AN ⋅=，求AMN 面积的最大值；（3）记直线AM ，AN 的斜率分别为1k ，2k ，若12116k k =-，证明：以MN 为直径的圆过定点，并求出定点坐标．19. 已知函数()()3sin R f x x ax x a =+-∈．（1）当0a =时，判断()f x y x=在π0,2⎛⎫⎪⎝⎭上单调性，并说明理由；（2）当0x >时，()0f x >恒成立，求a 的取值范围；（3）设()sin g x x =，在()g x 的图象上有一点列()*11,1,2,,,22i ii A g i n n ⎛⎫⎛⎫=⋅⋅⋅∈ ⎪⎪⎝⎭⎝⎭N ，直线1i i A A +的斜率为()1,2,,1,2i k i n n =⋅⋅⋅-≥，求证：11109n ii kn -=>-∑．.的华中师大一附中2024-2025学年度上学期高三期中检测数学试题时限：120分钟 满分：150分 命题人：沈宇为 审题人：胡立松一、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. 已知平面向量()1,2a =，()1,b λλ=-，a b ⊥，则实数λ=（ ）A. 1-B. 1C. 2- D. 2【答案】A 【解析】【分析】根据向量数量积的坐标表示求解即可.【详解】因为()1,2a = ，()1,b λλ=- ，a b ⊥，所以()1120a b λλ⋅=⨯-+⨯=，解得1λ=-，故选：A2. 若p ：()41log 12a -<，q：2230a a --<，则p 是q 的（ ）A. 充分不必要条件 B. 必要不充分条件C. 充要条件 D. 既不充分也不必要条件【答案】A 【解析】【分析】解两个不等式，分别得到13a <<和13a -<<，根据真包含关系，得到p 是q 的充分不必要条件.【详解】()()44421log 1log 1log 2a a -<⇒-<，故012a <-<，解得13a <<，2230a a --<，解得13a -<<，因为{}13a a <<是{}13a a -<<的真子集，所以p 是q 的充分不必要条件.故选：A3. 己知,A B 是全集U 的两个子集，则如图所示的阴影部分所表示的集合是（ ）A. ()()U U A B⋂ðð B. ()()U U A B⋃ððC. ()()U A B A B ⋃⋂⋂ð D. ()()U A B A B ⋂⋃⋃ð【答案】C 【解析】【分析】由给定的韦恩图分析出阴影部分所表示的集合中元素满足的条件，再根据集合运算的定义即可得解【详解】由图可知，阴影部分所表示的集合中的元素x A B ∈⋃且x A B ∉ ，则阴影部分所表示的集合是()()U A B A B ⋃⋂⋂ð.故选：C.4. 若0.51.2a =，5log 2b =，0.20.5c =，则（ ）A. c a b >> B. a b c>> C. a c b>> D. c b a>>【答案】C 【解析】【分析】根据指数函数、对数函数的性质判断即可.【详解】因为500.11.2 1.2a >==，5510log log 2log 21=<<=，即102b <<，10.20.50.50.50.51=<<=，即112c <<，所以a c b >>.故选：C5. 已知α，β都是锐角，tan 3tan αβ=，()1sin 3αβ+=，则cos sin αβ=（ ）A.14B.16C.18D.112【答案】D 【解析】【分析】运用两角和与差的正弦公式展开，化切为弦得sin cos 3cos sin αβαβ=，代入即可求解.【详解】由题意()1sin sin cos cos sin 3αβαβαβ+=+=，又tan 3tan αβ=，所以sin cos 3cos sin αβαβ=，即sin cos 3cos sin αβαβ=，所以14cos sin 3αβ=，所以1cos sin 12αβ=.故选：D6. 已知O 为ABC V 的外接圆圆心，2BC =，30BAC ∠=︒，则AB OC ⋅的最大值为（ ）A. 4B. 6C. D. 【答案】B 【解析】【分析】得到260BOC BAC ∠=∠=︒，OBC △为等边三角形，2OA OB OC ===，变形得到()24cos AB OC OB OA OC OB OC OA OC AOC ⋅=-⋅=⋅-⋅=-∠，当,,A O C 三点共线，即cos 1AOC ∠=-时，24cos AB OC AOC ⋅=-∠取得最大值，最大值为6.【详解】因为O 为ABC V 的外接圆圆心，30BAC ∠=︒，所以260BOC BAC ∠=∠=︒，因为OB OC =，所以OBC △为等边三角形，故2OA OB OC ===，()cos 60cos AB OC OB OA OC OB OC OA OC OB OC OA OC AOC⋅=-⋅=⋅-⋅=⋅︒-⋅∠1224cos 24cos 2AOC AOC =⨯⨯-∠=-∠，当,,A O C 三点共线，即cos 1AOC ∠=-时，24cos AB OC AOC ⋅=-∠取得最大值，最大值为246+=.故选：B7. 某中学数学兴趣小组为测量学校附近某建筑物的高度，在学校操场选择了同一条直线上的A ，B ，C三点进行测量．如图，20AC =（单位：米），点B 为AC 中点，兴趣小组组长小王在A ，B ，C 三点正上方2米处的1A ，1B ，1C 观察建筑物最高点E 的仰角分别为α，β，γ，其中tan α=tan 2β=，tan γ=，点D 为点E 在地面上的正投影，点1D 为DE 上与1A ，1B ，1C 位于同一高度的点，则建筑物的高度DE 为（ ）米．A. 20B. 22C. 40D. 42【答案】B 【解析】【分析】设1D E h =，得到11A D =112h B D =，11C D =，并得到111110A B B C ==，根据111111πA B D C B D ∠+∠=得到111111cos cos 0A B D C B D ∠+∠=，结合余弦定理得到方程，求出20h =，得到筑物的高度DE .【详解】设1D E h =，因为tan α=tan 2β=，tan γ=，所以11tan h A D α==11tan 2h hB D β==，11tan h C D γ==因为20AC =，点B 为AC 中点，所以1120A C =，点1B 为11A C 中点，故111110A B B C ==，在111A B D 中，由余弦定理得222111251*********cos 102102h h h A B D h h +--∠==⨯⨯，在111C B D 中，由余弦定理得2221111001004312cos 102102h h h C B D h h +--∠==⨯⨯，由于111111πA B D C B D ∠+∠=，故111111cos cos 0A B D C B D ∠+∠=，即225100100121201010h h h h--+=，解得20h =，故建筑物的高度222D h E =+=（米）.故选：B8. 设函数()()11e e sin 1x x f x x --=-+-，则关于x 的不等式()()2220f x x f x --+-≥的解集为（ ）A. []1,4- B. ][(),14,-∞-⋃+∞C. []2,1- D. ][(),21,∞∞--⋃+【答案】B 【解析】【分析】令()()1e esin xxg x f x x -=+=-+，定义域R ，得到()g x 为奇函数，即()()11f x f x -+=-+，求导，得到()g x 在R 上单调递增，变形得到()()2321g x x g x --≥+，从而2321x x x --≥+，求出解集.【详解】令()()1e esin xxg x f x x -=+=-+，定义域为R ，()()()n sin e e si e e x x x x g x x g x x ---=-+-==---，故()g x 为奇函数，即()()11f x f x -+=-+，()e e cos cos 2cos 0x x g x x x x -'=++≥=+>，故()g x 在R 上单调递增，()()()()2222022f x x f x f x x f x --+-≥⇒--≥--，故()()()231211211f x x f x f x ⎡⎤⎡⎤⎡⎤--+≥---+=++⎣⎦⎣⎦⎣⎦，即()()2321g x x g x --≥+，所以2321x x x --≥+，2340x x --≥，为解得4x ≥或1x ≤-.故选：B二、多选题：本题共3小题，每小题6分，共18分．在每小题给出的选项中，有多项符合题目要求．全部选对的得6分，部分选对的得部分分，有选错的得0分．9. 设函数()33f x x x =-+，()()1f x g x x=+，()f x 的导数为()f x '，则（ ）A. ()12f '-=B. 当()02f x '=时，01x =-C. 曲线()y g x =在点()1,4处的切线方程为50x y +-=D. 当0x >时，()()g x g x -<【答案】ACD 【解析】【分析】求出()f x 的导数f ′(x )即可判断A 、B ，表示出y =g (x )，利用导数的几何意义求出切线方程，即可判断C ，利用作差法判断D.【详解】对于A ：因为()33f x x x =-+，所以()231f x x ='-，则()()213112f -=⨯--='，故A 正确；对于B ：因为()02f x '=，即20312x -=，解得01x =±，故B 错误；因为()()323311f x x x g x x xx x-+=+=+=+，则()232g x x x-'=，所以()11g '=-，则y =g (x )在点(1,4)处的切线方程为()41y x -=--，即50x y +-=，故C 正确；当0x >时g (x )=x 2+3x >0，()23g x x x-=-，令()23h x x x =-()0x >，因为2y x =与3y x=-均在(0,+∞)上单调递增，则ℎ(x )在(0,+∞)上单调递增，且()120h =-<，ℎ(2)=72>0，所以存在()01,2x ∈使得()00h x =，所以当00x x <<时ℎ(x )<0，当0x x >时ℎ(x )>0，所以()20203,3,0x x x x g x x x x x ⎧-≥⎪⎪-=⎨⎛⎫⎪--<< ⎪⎪⎝⎭⎩，所以当0x x ≥时()()223360g x g x x x x x x⎛⎫⎛⎫--=--+=-< ⎪ ⎪⎝⎭⎝⎭，所以()()g x g x -<，当00x x <<时()()2223320g x g x x x x x x ⎛⎫⎛⎫--=---+=-< ⎪ ⎪⎝⎭⎝⎭，所以()()g x g x -<，综上可得当0x >时，()()g x g x -<，故D 正确.故选：ACD10. 某个简谐运动可以用函数()()sin f x x ωϕ=+（0ω>，π<ϕ），[)0,x ∈+∞来表示，部分图象如图所示，则（ ）A. 2π3AB =B. 这个简谐运动的频率为1π，初相为π6-C. 直线π8x =是曲线π23y f x ⎛⎫=+ ⎪⎝⎭的一条对称轴D. 点π,08⎛⎫⎪⎝⎭是曲线π23y f x ⎛⎫=+ ⎪⎝⎭的一个对称中心【答案】BD 【解析】【分析】根据图象可得()πsin 26f x x ⎛⎫=-⎪⎝⎭，选项A ，利用sin y x =的图象与性质可得π3AB =，即可判断选项A 的正误；选项B ，由频率和初相的定义，结合()πsin 26f x x ⎛⎫=-⎪⎝⎭，即可求解；选项C 和D ，π2cos43y f x x ⎛⎫=+= ⎪⎝⎭，利用cos y x =性质，求出π2cos43y f x x ⎛⎫=+= ⎪⎝⎭的对称轴和对称中心，即可判断出选项C 和D 的正误.【详解】由图知()10sin 2f ϕ==-，由图象知π2π,Z 6k k ϕ=-+∈，又π<ϕ，所以π6ϕ=-，又由五点作图知，第三个点7π(,0)12，所以7πππ126ω-=，得到2ω=，所以()πsin 26f x x ⎛⎫=- ⎪⎝⎭.对于选项A ，设1211(,(,)22A x B x ，由()π1sin 262f x x ⎛⎫=-= ⎪⎝⎭，得到1ππ22π,Z 66x k k -=+∈，2π5π22π,Z 66x k k -=+∈，所以21π3AB x x =-=，故选项A 错误，对于选项B ，因为2ω=，所以频率为112ππT ω==，由()πsin 26f x x ⎛⎫=- ⎪⎝⎭知初相为π6-，所以选项B正确，对于选项C ，因为ππ2sin(4)cos432y f x x x ⎛⎫=+=+= ⎪⎝⎭，由4π,Z x k k =∈，即π,Z 4k x k =∈，所以π8x =不是曲线π23y f x ⎛⎫=+ ⎪⎝⎭的对称轴，故选项C 错误，对于选项D ，因为π2cos43y f x x ⎛⎫=+= ⎪⎝⎭，由π4π,Z 2x k k =+∈，得到ππ,Z 84k x k =+∈，令0k =，得到π8x =，所以点π,08⎛⎫ ⎪⎝⎭是曲线π23y f x ⎛⎫=+ ⎪⎝⎭的一个对称中心，故选项D 正确.故选：BD.11 已知实数x ，y 满足e0x yyx++=，则（ ）A. 当0y <时，0x y += B. 当0x <时，0x y +=C. 当0x y +≠时，2y x -> D. 当0x y +≠时，10xy -<<【答案】ACD 【解析】【分析】A 选项，0y <，所以0x >，变形为()ln ln x x y y +=-+-，令()ln f x x x =+，0x >，故为.()()f x f y =-，根据函数单调性得到0x y +=；B 选项，0x <时，0y >，变形得到()ln ln y y x x -=---，构造()ln g x x x =-，0x >，则()()g y g x =-，求导得到()g x 的单调性，()ln g x x x =-不单调，故y 不一定等于x -，即0x y +=不一定成立；CD 选项，由AB 选项知，0x y +≠时，0x <，0y >，令,y n x m =-=，则有()()g m g n =，不妨设01m n <<<，故1ln ln n m n m -=-ln ln 2n m m nn m -+<<-，从而得到2m n +>，01mn <<，故2y x ->，10xy -<<，CD 正确.【详解】A 选项，由e0x yy x++=得e 0x y yx +=>-，因为0y <，所以0x >，e 0x y y x +=>-两边取对数得，()ln ln ln y x y y x x ⎛⎫+=-=-- ⎪⎝⎭，故()ln ln x x y y +=-+-，令()ln f x x x =+，0x >，故()()f x f y =-，由于()ln f x x x =+在(0,+∞)上单调递增，故x y =-，故0x y +=，A 正确；B 选项，0x <时，0y >，故()ln ln ln y x y y x x ⎛⎫+=-=-- ⎪⎝⎭，故()ln ln y y x x -=---，令()ln g x x x =-，0x >，则()()g y g x =-，其中()111x g x x x'-=-=，当1x >时，()0g x '>，当01x <<时，()0g x '<，故()ln g x x x =-在(0,1)上单调递减，在(1,+∞)上单调递增，因为()ln g x x x =-不单调，故y 不一定等于x -，即0x y +=不一定成立，B 错误；CD 选项，由AB 选项知，0x y +≠时，0x <，0y >，令,y n x m =-=，则有()()g m g n =，不妨设01m n <<<，故1ln ln n mn m-=-，ln ln 2n m m nn m -+<<-，先证不等式右边，1ln ln 1ln 221nn m n m n m n m n m m---<⇒<++，令1n t m=>，即证11ln 12t t t -<+，令()11ln 12t q t t t -=-+，1t >，则()()()()()()22222411210212121t t t q t t t t t t t -+--=-==<+++'，故()11ln 12t q t t t -=-+在()1,t ∞∈+上单调递减，又()10q =，故11ln 12t t t -<+，所以ln ln 2n m m n n m -+<-，即12m n +<，2m n +>，故2y x ->，C 正确；ln ln n m n m -<-，即证ln ln ln n n m m -<⇒<-，1u =>，即证12ln u u u <-，令()12ln w u u u u =-+，1u >，则()()222221212110u u u w u u u u u---+-='=--=<，故()12ln w u u u u=-+在(1,+∞)上单调递减，又()10w =，故12ln u u u<-ln ln n m n m -<-，1<，所以01mn <<，故01xy <-<，所以10xy -<<，D 正确.故选：ACD121212ln ln 2x x x xx x -+<<-，在处理函数极值点偏移问题上经常用到，可先证明，再利用对数平均不等式解决相关问题，证明方法是结合1122ln ln ln x x x x -=，换元后将二元问题一元化，利用导函数进行证明三、填空题：本题共3小题，每小题5分，共15分．的12. 已知向量1e ，2e 为单位向量，且1e 在2e 上的投影向量为21e 2-，则12e e -= ______．【解析】【分析】利用投影向量得到122e 1e ⋅=- ，先计算出()221212e e e e 3-=-= ，求出模长.【详解】由题意得122222e e e 1e 2e e ⋅⋅=-，故122e 1e ⋅=- ，()2222121211221e e e e e 2e e e 12132⎛⎫-=-=-⋅+=-⨯-+= ⎪⎝⎭，故12e e -=.13. 若实数a ，b 满足13a b -<+<，24a b <-<，则3a b +的取值范围为______．【答案】()0,10【解析】【分析】令()()3a b x a b y a b +=++-，求出x 、y ，再根据不等式的性质计算可得.【详解】令()()()()3a b x a b y a b x y a x y b +=++-=++-，所以31x y x y +=⎧⎨-=⎩，解得21x y =⎧⎨=⎩，所以()()32a b a b a b +=++-，又13a b -<+<，24a b <-<，所以()()0210a b a b <++-<，即0310a b <+<，所以3a b +的取值范围为()0,10.故答案为：()0,1014. 设1F ，2F 是双曲线C ：22221x y a b-=（0a >，0b >）的左、右焦点，点A 是C 右支上一点，若12AF F △的内切圆的圆心为M ，半径为a ，且λ∃∈R ，使得22AM OM OF λ+=，则C 的离心率为______．【答案】2【解析】【分析】设A 在第一象限，则点M 也在第一象限，根据22AM OM OF λ+=得到13a y =，由两种方法求解12AF F △的面积，得到方程，求出124AF AF c +=，结合122AF AF a -=，求出22AF c a =-，由两点间距离公式得到21x a c AF a=-，求出12x a =，故()2,3A a a ，代入双曲线方程，求出223b a=，得到离心率.【详解】不妨设A 在第一象限，则点M 也在第一象限，设()()11,,,M A x y M x a ，()2,0F c ，因为22AM OM OF λ+=，所以()()()11,,,20M M x a x a y x c λ-=-+，故13a y =，121211123322AF F S F F y c a ac =⋅=⨯⋅= ，又)()1221212122AF F S AF F F a a AF AF c =+⋅=++ ，故()121232a AF AF c ac ++=，解得124AF AF c +=，由双曲线定义得122AF AF a -=，故12AF a c =+，22AF c a =-，又2A F ====，又1x a >，故10cx a a ->，故21xa c AF a=-，又22AF c a =-，故12xa=，12x a =，故()2,3A a a ，将()2,3A a a 代入22221x y a b-=中，得22941a b -=，解得223b a =，所以C 2=.故答案为：2【点睛】方法点睛：双曲线的离心率是双曲线最重要的几何性质，求双曲线的离心率(或离心率的取值范围)，常见有两种方法：①求出,a c ，代入公式ce a=；②只需要根据一个条件得到关于,,a b c 的齐次式，结合222b c a =-转化为,a c 的齐次式，然后等式(不等式)两边分别除以a 或2a 转化为关于离心率的方程(不等式)，解方程(不等式)即可得离心率(离心率的取值范围).四、解答题：本题共5小题，共77分．解答应写出文字说明、证明过程或演算步骤．15. 在ABC V 中，内角A ，B ，C 的对边分别为a ，b ，c sin cos C a C c b -=-．（1）求A ；（2）若角A 的平分线交边BC 于点D ，AD =，求ABC V 面积的最小值．【答案】（1）2π3A =（2）【解析】【分析】（1）利用正弦定理化边为角，再根据三角形内角和定理结合两角和差的正弦公式化简即可得解；（2）根据角平分线性质，求得BAD ∠和CAD ∠，再将ABC BAD CAD S S S =+ 转化为b 与c 的关系，利用基本不等式求解即可.【小问1详解】sin cos C a C c b -=-，sin sin cos sin sin A C A C C B -=-，()sin sin cos sin sin sin sin cos cos sin A C A C C A C C A C A C -=-+=--，sin cos sin sin A C A C C +=，又sin 0C >cos 1A A +=，所以π1sin 62A ⎛⎫+= ⎪⎝⎭，又()0,πA ∈，所以ππ7π,666A ⎛⎫+∈ ⎪⎝⎭，所以π5π66A +=，所以2π3A =；【小问2详解】如图，由题意及第（1）问知，π3BAD CAD ∠=∠=，且ABC BAD CAD S S S =+ ，∴111sin sin sin 222bc BAC c AD BAD b AD CAD ∠=⨯⨯⨯∠+⨯⨯⨯∠，∴111222bc c b =⨯+⨯，化简得)bc b c =+，∵0b >，0c >，∴由基本不等式得)bc b c =+≥≥当且仅当b c ==时，等号成立，∴12bc ≥，∴11sin 1222ABC S bc BAC =∠≥⨯=△，故ABC V 的面积的最小值为.16. 已知函数()()()sin cos cos 0f x a x x x a =+>，且()π6f x f ⎛⎫≤ ⎪⎝⎭恒成立．（1）求a 的值；（2）设()()sin cos sin cos g x b x x x x =+-，若1π0,4x ⎡⎤∀∈⎢⎥⎣⎦，2π,06x ⎡⎤∃∈-⎢⎥⎣⎦，使得()()12g x f x ≤，求实数b 的取值范围．【答案】（1）a =（2）1b ≤【解析】【分析】（1）利用三角恒等变换得到()()122f x x ϕ=++，其中1tan a ϕ=，根据()π6f x f ⎛⎫≤ ⎪⎝⎭，求出πZ π2,6k k ϕ=+∈，故1πtan 2πZ 6k k a ⎛⎫=+=∈ ⎪⎝⎭，解得a =（2）1π0,4x ⎡⎤∀∈⎢⎥⎣⎦，2π,06x ⎡⎤∃∈-⎢⎥⎣⎦，使得()()12g x f x ≤，则只需()()max max g x f x ≤，求出()max1f x =，换元得到()()()221122b g x h t t b +==--+，分1b ≤，b 1<<和b ≥()max h t ，从而得到不等式，求出b 的取值范围.【小问1详解】()()211cos 2sin cos cos sin cos cos sin 222xf x a x x x a x x x a x +=+=+=+()122x ϕ=++，其中1tan a ϕ=，由于0a >，()π6f x f ⎛⎫≤ ⎪⎝⎭，故πsin 13ϕ⎛⎫+= ⎪⎝⎭，所以ππ2π,Z 32k k ϕ+=+∈，故πZ π2,6k k ϕ=+∈，1πtan 2πZ 6k k a ⎛⎫=+=∈ ⎪⎝⎭，解得a =【小问2详解】由（1）得，不妨取π6ϕ=，故()π1sin 262f x x ⎛⎫=++ ⎪⎝⎭，1π0,4x ⎡⎤∀∈⎢⎥⎣⎦，2π,06x ⎡⎤∃∈-⎢⎥⎣⎦，使得()()12g x f x ≤，则只需()()max max g x f x ≤，其中π,06x ⎡⎤∈-⎢⎥⎣⎦时，πππ2,666x ⎡⎤+∈-⎢⎥⎣⎦，故()[]π1sin 20,162f x x ⎛⎫=++∈ ⎪⎝⎭，则()max 1f x =，令sin cos x x t +=，则21sin cos 2t x x -=，则()()()222111sin cos sin cos 222t b g x b x x x x bt t b -+=+-=-=--+，其中πsin cos 4t x x x ⎛⎫=+=+ ⎪⎝⎭，因为π0,4x ⎡⎤∈⎢⎥⎣⎦，所以πππ,442x ⎡⎤+∈⎢⎥⎣⎦，π4t x ⎛⎫⎡=+∈ ⎪⎣⎝⎭，若1b ≤，此时()()221122b h t t b +=--+在t ⎡∈⎣上单调递减，故()()max 1h t h b ==，故1b ≤，若b 1<<，此时()()2max12b h t h b +==，令2112b +≤，故21b ≤，解得11b -≤≤，11b -≤≤与b 1<<取交集得∅，若b ≥()()221122b h t t b +=--+在t ⎡∈⎣上单调递增，故()max 12h t h ==-，112-≤，解得b ≤，b ≥b ≤取交集得∅，综上，1b ≤.【点睛】关键点点睛：第二问，1π0,4x ⎡⎤∀∈⎢⎥⎣⎦，2π,06x ⎡⎤∃∈-⎢⎥⎣⎦，使得()()12g x f x ≤，转化为()()max max g x f x ≤，再进行下一步的求解.17. 已知函数()()ln f x ax x a =-∈R ．（1）若函数()f x 在1,1e ⎡⎤⎢⎥⎣⎦上的最小值为32，求a 的值；（2）若0a =，函数()()1e x f x g x x-=+，求()g x 的最小值．【答案】（1；（2）1.【解析】【分析】（1）利用导数分析含参函数y =f(x)在区间上的单调性，结合函数最小值，即可求得参数值；（2）求得()g x '22e ln x x x x+=，令()2e ln (0)xh x x x x =+>，利用导数研究其隐零点，从而判断()y g x =的单调性，再结合隐零点满足的条件，即可求得函数的最小值.【小问1详解】因为()ln f x ax x =-，x ∈1,1e ⎡⎤⎢⎥⎣⎦，故可得()f x '1a x =-，[]11,e x∈，①若1a ≤，()f x '0≤，y =f(x)在1,1e ⎡⎤⎢⎥⎣⎦单调递减，()f x 的最小值为()312f a ==，不满足1a ≤；②若1e a <<，令()f x '>0，解得1,1x a ⎛⎤∈⎥⎝⎦，故y =f(x)在1,1a ⎛⎤⎥⎝⎦单调递增；令()f x '0<，解得11,e x a ⎡⎫∈⎪⎢⎣⎭，故y =f(x)在11,e a ⎡⎫⎪⎢⎣⎭单调递减；故y =f(x)的最小值为1131ln 2f a a ⎛⎫=-=⎪⎝⎭，即1ln 2a =，解得a =1e a <<；③若e a ≥，()f x '0≥，y =f(x)在1,1e ⎡⎤⎢⎥⎣⎦单调递增，()f x 的最小值为131e e 2a f ⎛⎫=+= ⎪⎝⎭，解得e2a =，不满足e a ≥；综上所述，a =【小问2详解】若0a =，()ln f x x =-，()()1e x f x g x x-=+ln 1e x x x+=-，定义域为()0,+∞，()g x '222ln e ln e x xx x xx x+=+=，令()2e ln (0)xh x x x x =+>，()h x '()()211e 2e 20x x x x x x x x=++=++>，故()y h x =在()0,+∞单调递增，又1ln 202h ⎛⎫=-<⎪⎝⎭，()1e 0h =>，故存在01,12x ⎛⎫∈⎪⎝⎭，使得()00h x =，也即0200e ln 0x x x +=，且00()g x '=，且当()00,x x ∈，()0h x <，()g x '0<，()y g x =在()00,x 单调递减；当()0,x x ∈+∞，()0h x >，()g x '>0，()y g x =在()0,x +∞单调递增；故()g x 的最小值为()0000ln 1e x x g x x +=-；由上述求解可知，020001e ln 0,,12xx x x ⎛⎫+=∈ ⎪⎝⎭，则000011e ln xx x x =，令()e ,0x m x x x =>，则()m x '()e10xx =+>，故()m x 在()0,+∞单调递增；000011e ln x x x x =，也即()001ln m x m x ⎛⎫= ⎪⎝⎭，又0010,ln 0x x >>，故001ln x x =，即001e x x =；又()000000000001ln ln 1ln 1ln 1e 1x x x x x g x x x x x x ++=-=-=-==.故()y g x =的最小值为1.【点睛】关键点点睛：解决本题第二问的关键，一是进行二次求导，从而确定()y g x =的单调性；二是熟练掌握隐零点问题的处理方法；三是能够根据000011e ln x x x x =，进行同构处理，进一步确定0x 满足的具体条件；属综合困难题.18. 已知椭圆C ：()222210+=>>x y a b a b()0,1A 在C 上，直线l 与C 交于不同于A的两点M ，N ．（1）求C 的方程；（2）若0AM AN ⋅=，求AMN 面积的最大值；（3）记直线AM ，AN 的斜率分别为1k ，2k ，若12116k k =-，证明：以MN 为直径的圆过定点，并求出定点坐标．【答案】（1）2214x y +=（2）6425（3）证明见详解，定点()0,1-【解析】【分析】（1）根据题意结合离心率列式求,,a b c ，即可得椭圆方程；（2）可知直线l 的斜率存在，设直线l ：()1y kx m m =+≠，联立方程结合韦达定理可得35m =-，进而求面积，结合单调性求最值；（3）可知直线l 的斜率存在，设直线l ：()1y kx m m =+≠，联立方程结合韦达定理可得35m =，假设过定点，根据数量积运算求解即可.【小问1详解】由题意可知：2221b c e a a b c=⎧⎪⎪==⎨⎪=+⎪⎩，解得21a b c ⎧=⎪=⎨⎪=⎩，所以椭圆C 的方程为2214x y +=.【小问2详解】若0AM AN ⋅=，可知直线l 的斜率存在，设直线l ：()1y kx m m =+≠，()()1122,,,M x y N x y ，联立方程2214y kx mx y =+⎧⎪⎨+=⎪⎩，消去y 可得()222418440k x kmx m +++-=，则()()2222Δ64441440k m k m =-+->，整理可得2241m k <+，可得2121222844,4141km m x x x x k k -+=-⋅=++，因为()0,1A ，则()()1122,1,,1AM x y AN x y =-=-，由0AM AN ⋅=，可得()()1212110x x y y +--=，则()()1212110x x kx m kx m ++-+-=，整理可得()()()()2212121110k x x k m x x m ++-++-=，则()()()()22222214481104141k m k m m m k k +---+-=++，且1m ≠，则10m -≠，可得()()()22224118104141k m k m m k k ++-+-=++，解得35m =-，且满足2241m k <+，可知直线l ：35y kx =-过定点30,5⎛⎫- ⎪⎝⎭，则AMN 面积1213125AMNS x x ⎛⎫=⨯+-=== ⎪⎝⎭令2t =≥，则22425t k -=，可得223232894254941425AMN t t S t t t t===-+⨯++V ，因为()94f t t t=+在[)2,+∞内单调递增，则()()2528f t f ≥=，所以当2,0t k ==时，AMN 面积取到最大值6425.【小问3详解】若直线l 的斜率不存在，设()()11111,,,,0M x y N x y x -≠，可得2111122111111116y y y k k x x x ----=⋅=-=-，可得221111116y x =+>，这与211y ≤相矛盾，不合题意；可知直线l 的斜率存在，设直线l ：()1y kx m m =+≠，()()1122,,,M x y N x y ，可得()()121212*********16kx m kx m y y k k x x x x +-+---=⋅==-，整理可得()()()()2212121611611610k x x k m x x m ++-++-=，则()()()()22222216144128116104141km k m m m k k +---+-=++，且1m ≠，则10m -≠，可得()()()22221611324104141km k m m k k ++-+-=++，解得35m =，设以MN 为直径的圆过定点P (x 0,y 0)，则()()10102020,,,PM x x y y PN x x y y =--=--，可得()()()()102010200PM PN x x x x y y y y ⋅=--+--=，则()()()()102010200x x x x kx m y kx m y --++-+-=，整理可得()()()()2221200120010k x x k m y x x x x m y ⎡⎤++--+++-=⎣⎦，则()()()()2222022144804141k m km k m y x x m yk k +-⎡⎤--⎣⎦-++-=++，可得()2222200000246434105255x y k x k x y ⎛⎫+-+-++-= ⎪⎝⎭，注意到上式对任意的k 均成立，则()2200220041024056430255x y x x y ⎧⎪+-=⎪⎪=⎨⎪⎪⎛⎫-++-=⎪ ⎪⎝⎭⎩，解得0001x y =⎧⎨=-⎩，所以以MN 为直径的圆过定点()0,1-.【点睛】方法点睛：利用韦达定理法解决直线与圆锥曲线相交问题的基本步骤如下：（1）设直线方程，设交点坐标为()()1122,,,x y x y ；（2）联立直线与圆锥曲线的方程，得到关于x （或y ）的一元二次方程，注意∆的判断；（3）列出韦达定理；（4）将所求问题或题中的关系转化为12x x +、21x x （或12y y +、12y y ）的形式；（5）代入韦达定理求解.19. 已知函数()()3sin R f x x ax x a =+-∈．（1）当0a =时，判断()f x y x=在π0,2⎛⎫⎪⎝⎭上的单调性，并说明理由；（2）当0x >时，()0f x >恒成立，求a 的取值范围；（3）设()sin g x x =，在()g x 的图象上有一点列()*11,1,2,,,22i ii A g i n n ⎛⎫⎛⎫=⋅⋅⋅∈ ⎪⎪⎝⎭⎝⎭N ，直线1i i A A +的斜率为()1,2,,1,2i k i n n =⋅⋅⋅-≥，求证：11109n i i k n -=>-∑．【答案】（1）()f x y x=在π0,2⎛⎫⎪⎝⎭上单调递减，理由见解析 （2）1,6⎡⎫+∞⎪⎢⎣⎭（3）证明见解析【解析】【分析】（1）利用多次求导的方法来判断出()f x y x=在π0,2⎛⎫⎪⎝⎭上的单调性.（2）利用多次求导的方法，结合()0f x >恒成立，列不等式来求得a 的取值范围.（3）根据（2）的结论，得到3sin 6x x x >-，求得i k 的不等关系式，然后根据分组求和法以及等比数列的前n 项和公式证得不等式成立.小问1详解】()f x y x=在π0,2⎛⎫⎪⎝⎭上单调递减，理由如下：当0a =时，()sin sin π102f x x x x y x xx x -⎛⎫===-<< ⎪⎝⎭，2cos sin x x x y x-'=，()cos sin cos sin cos sin 0x x x x x x x x x '-=--=-<，【所以函数cos sin y x x x =-在π0,2⎛⎫⎪⎝⎭上单调递减，当0x =时，0cos 0sin 00-=，所以cos sin 0x x x -<，所以2cos sin 0x x xy x -'=<，所以()f x y x=在π0,2⎛⎫ ⎪⎝⎭上单调递减.【小问2详解】当0x >时，f (x )=sin x +ax 3−x >0恒成立①，当0x =时，3sin 0000a +⨯-=②，()2cos 31f x x ax +'=-，设u (x )=cos x +3ax 2−1(x >0)，0x =时2cos 03010a +⨯-=，()sin 6u x x ax '=-+，设()sin 6v x x ax =-+，当0x =时，sin 0600a -+⨯=，()cos 6v x x a ='+，要使①恒成立，由于②，则需()cos 60v x x a =+≥'恒成立，所以6cos a x ≥-恒成立，所以61a ≥，16a ≥.此时()cos 60v x x a =+≥'，()sin 6v x x ax =-+在(0,+∞)上单调递增，u ′(x )=−sin x +6ax >0，u (x )=cos x +3ax 2−1(x >0)在(0,+∞)上单调递增，f ′(x )=cos x +3ax 2−1>0，()3sin f x x ax x =+-在(0,+∞)上单调递增，使得f (x )=sin x +ax 3−x >0恒成立.综上所述，a 的取值范围是1,6⎡⎫+∞⎪⎢⎣⎭.【小问3详解】由（2）可知，当0x >，16a =时，f (x )=sin x +16x 3−x >0恒成立，即0x >时，3sin 6x x x >-恒成立，下证：11109n ii kn -=>-∑，*i ∈N 时，11111111222sin sin 112222i i i i i i i ig g k ++++⎛⎫⎛⎫- ⎪ ⎪⎛⎫⎝⎭⎝⎭==- ⎪⎝⎭-11111111111122sin cos sin 2sin 2cos 122222i i i i i i i +++++++⎛⎫⎛⎫=-=- ⎪ ⎪⎝⎭⎝⎭，由上述分析可知，()2cos 102x m x x =+->，即2cos 12x x >-，则12311cos 1022i i ++>->，所以111112311112sin2cos 12sin 2112222i i i i i i ++++++⎛⎫⎛⎫⎛⎫->-- ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭=2i +1>2i==1−76×122i +2+16×124i +4>1−76×122i +2，n−1i =1ki >+126+128+⋯=n−1−76⋅1641−14=n−1−718×77179717980101721847218472729n n n n n n n =--+⨯=-+⨯>->-=-，即得证.【点睛】思路点睛：用导数分析单调性：首先对函数进行多次求导，通过分析导数符号来判断函数在不同区间的单调性，这一步为后续的不等式恒成立条件的推导奠定了基础.结合不等式求参数范围：通过设定不等式恒成立，结合函数的单调性，逐步推导出参数 a 的取值范围.利用等比数列和斜率关系进行证明：在小问3中，通过对等比数列的求和以及利用斜率条件，成功证明了所需的不等式.。