山西省长治市太行中学2018-2019学年高二下学期期末考试英语试题 含答案

2018—2019学年第二学期高二第一次月考英语试题【本试卷满分150分，考试时间120分钟】第Ⅰ卷（选择题共100分）第一部分听力（共两节，满分20分）第一节（共5小题，每小题1分，满分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. Why is the play delayed?A. The main actor hasn’t c ome.B. The electricity has failed.C. The director is stuck in a traffic jam.2. What is the woman trying to find?A. The campus.B. The church.C. The garden.3. What is the woman doing now?A. Leaving for a holiday.B. Taking a vacation.C. Eating out.4. Where are the speakers?A. At a hotel.B. At an airport.C. At a hospital.5. What are the speakers talking about?A. A movie.B. A novel.C. A TV play.第二节听下面5段对话或独白。

每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。

听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。

每段对话或独白读两遍。

听第6段材料，回答第6、7题。

6. Where does the conversation probably take place?A. At Jack’s home.B. At the man’s home.C. At the wo man’s home.7. Why will the woman have only a little cake?A. She is full.B. She dislikes the cake.C. She is trying to lose weight.听第7段材料，回答第8、9题。

山西省长治市太行中学2018-2019学年高二英语下学期期末考试试题第一部分听力（共两节，满分20分）第一节（共5小题；每小题1分，满分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；你将有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.＄19.15B. ＄9.18C. ＄9.15答案是C。

1.What does the woman think of the movie?A.It's amusing.B. It's exciting.C. It's disappointing.2.How will Susan spend most of the time in France.A.Traveling aroundB.Studying at a schoolC.Looking after her3.What are the speakers talking about?A.Going outB.Ordering drinksC.Preparing for a party4. Where are the speakers?A.In a classroomB. In a libraryC. In a bookstore5. What is the man going to do?A.Go on the InternetB.Make a phone callC.Take a train trip第二节（共15小题；每小题1分，满分15分）听下面5段对话或独白[.每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。

听每段对话或独白前，你将有时间阋读各个小题.每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。

山西省长治市2023-2024学年高二下学期6月期末英语试题一、阅读理解Want to have an art trip? The first thing you might think of is museums. And while they’re must-sees, these art galleries in Barcelona are equally as interesting. From limited exhibitions to displays of local Barcelona artists, these galleries allow for fresh takes on art.SendaThis historical gallery of Barcelona was founded in 1993 and recently moved to Trafalgar Street in 2015. The gallery supports young artists, but also known names from the national and international levels. It speaks all kinds of artistic languages.Ramon ArtThis gallery was founded in 2003. It has its origins in a large antique shop and focuses on paintings and drawings. Ramon Art has a modernized and cozy space offering contemporary approaches to unique and high-quality artwork, as well as a private gallery space with some pieces available to buy, which is a major attraction to visitors.MarlboroughThe Marlborough family of galleries was founded in London in 1946 and praised for being the first gallery to show the German Expressionists like Henry Moore and Francis Bacon. Then some branch galleries were established around the world. In 1962, the New York gallery was opened, followed by Tokyo and Madrid. They also have spaces in Chile, Florida and Barcelona, which was opened in 2006.Sala ParésIt was the first to open in all of Spain. In 1991, contemporary art gallery Galeria Trama opened in the same street, sharing an address with the Sala Parés. This gallery features realistic paintings as well as other contemporary works such as sculpture, photography, video art and other styles.1．What is an advantage of Ramon Art?A．It is located in Barcelona.B．It has a public gallery space.C．It focuses on modern paintings.D．It offers some artworks to buy.2．Where is the main Marlborough gallery?A．In London.B．In New York.C．In Tokyo.D．In Barcelona. 3．Which of the following galleries was the first to open in Barcelona?A．Senda.B．Ramon Art.C．Sala Parés.D．Galeria Trama.Jake was working on a roof installing solar panels as usual when he heard something urgent. Below him, parents, neighbors, and volunteers were gathering. They were looking for a 5-year-old girl, who had disappeared from her home. Dropping his tools and climbing down, Jake joined the search party.The air was thick with anxiety. Contrary to others, Jake found himself drawn towards a rural trail winding along a stream that led to a nearby marsh (湿地). The search had spread out in all directions, but it was this path that called to him.His steps were quick, driven by an intuition (直觉) that he couldn’t quite explain. He hadn’t gone far when a sight struck him. There, in the shallow water of the stream was a T-shirt. Jake’s heart sank. As his eyes swept the watery expanse along with another volunteer named Brendan, they spotted the little girl standing in the water.Thankfully, she was alive. But, as he called out, he realized she wasn’t listening. Without hesitation, Jake lifted the little girl up from the water and passed her to Brendan. She was scared, no doubt, but safe now. “I just had this feeling,” Jake recalled. It was a mix of modesty, wonder and pride in his voice, but above all it was a relief to him and the girl’s parents, neighbors as well as volunteers.The community’s gratitude was immense. Jake, a simple man working on a roof, had become an unexpected hero in the search for a young girl. His willingness to set his work aside to help a group of strangers shows how powerful community and intuition challenge us to act beyond ourselves. Sometimes, heroes come from the most ordinary circumstances as they’re driven by the purest desire to do good deeds.4．Why did Jake decide to walk along a stream?A．He knew where the missing girl was.B．He wanted to make a difference.C．He did it out of his sixth sense D．He had noticed something unusual. 5．What’s Jake’s main feeling when recalling his experience of saving the girl?A．Relief.B．Fear.C．Regret.D．Pride.6．What do we know about the people looking for the girl?A．They were Jake’s neighbors.B．They were strangers to Jake.C．They didn’t know each other.D．They were a group of volunteers.7．What is a suitable title for the text?A．Willingness to Help Others is Fulfilled B．An Ordinary Person Makes a WonderC．An Unexpected Hero in a Search and Rescue D．The Reward to Rescuing Others in DangerEach day, millions of people make a cup of coffee in the morning to help get their day started. Like most things in history, someone had to be the first to think of roasting beans for their caffeine kick. According to legend, it was a 9th-century Ethiopian goat-herder named Kaldi.Kaldi observed his goats behaving energetically after eating the red berries from a nearby tree. He tried some of them himself and was soon acting as hyper as his herd. He then brought some to a monastery (修道院), where their stimulating effects during long hours of prayer were cause for concern. The monks thought that these beans were to blame and threw the tree’s beans onto a fire to destroy them, but the pleasant smell convinced them to give coffee a second chance. They put the roasted beans into warm water and coffee was born.However, it’s widely believed that the practice of chewing coffee beans as a stimulant had been around for centuries. People would break them to mix with butter and animal fat to preserve and eat on long journeys. Similarly, Sudanese people s chewed on coffee beans to help them survive their difficult voyages on trade routes.The cultivation and trade of the beans for the drink began in Arabic countries in the 14th century and spread throughout Egypt, Syria, and Turkey. It’s said not a single coffee plant existed outside of Arabia or Africa until the 1600s. In 1616, Pieter Broeck brought some coffee back to Amsterdam. Soon, the Dutch took possession of the European trade, followed by the French in the Caribbean, the Spanish in Central America, and the Portuguese in Brazil. The drink eventually made its way to America.Today, the average American spends about $2000 a year on coffee. And while Kaldi may not be a well-known name like Folgers, he still gets his due. The St. Louis-based Kaldi’s Coffeetakes its name from the most energetic goat herder in history.8．What does the underlined word “hyper” in Paragraph 2 mean?A．Embarrassed.B．Shocked.C．Excited.D．Amused.9．How did people use coffee beans before Kaldi’s discovery?A．By mixing them with animal fat.B．By chewing some to keep them energetic.C．By breaking them to mix with butter.D．By making them a product to sell. 10．Who took over the trade of coffee in Brazil?A．The French.B．The Dutch.C．The Spanish.D．The Portuguese. 11．What can we infer about Kaldi from the text?A．He created a world-known brand of coffee.B．He was the first to trade roasted beans.C．He changed the average American’s lifestyle.D．He deserved to be honored for hiscontribution.An ancient species of great ape likely disappeared hundreds of thousands of years ago when climate change put their favorite fruits out of reach during dry seasons.The species is known as Gigantopithecus blacki, who once lived in southern China. It stood 3 meters tall and weighed up to 295 kilograms. It represents the largest great ape known to scientists. “It’s just a massive animal — just really, really big. When food starts to be scarce, it’s so big it can’t climb trees to explore new food sources,” said Renaud White, a researcher at Australia’s Southern Cross University, who helped write the study.The huge apes likely looked similar to the modern orangutan. It survived for around 2 million years in the forested land of China’s Guangxi area. They ate plants that included fruits and flowers — until the environment began to change.Starting about 600,000 years ago, Guangxi’s forests began producing fewer fruits. The area was experiencing more periods of dry weather. Researchers examined sediment (沉积物) found in underground areas called caves to learn more about the changes and their effects. The giant apes did not disappear quickly. They likely went extinct sometime between 215,000 and 295,000 years ago.As the climate changed, smaller apes may have been able to climb trees to search for different food. But the giant apes ate more food that provided fewer nutrients, including tree barkand thin grasses called reeds. When the forest changed, there was not enough food preferred by the species.Most of what scientists know about the extinct great apes comes from studying their remains. The fossilized bones they studied included teeth and four large lower jaw bones. All of the fossils were found in southern China. No complete skeletons (骨架) have been found. Between around 2 million and 22 million years ago, many species of great apes lived in Africa, Europe, and Asia. Today, only gorillas, chimpanzees, bonobos, orangutans and humans remain.12．Why did Gigantopithecus blacki go extinct?A．For a lack of their companions.B．For a lack of their new food.C．As a result of habitat loss.D．As a result of climate change.13．How did researchers learn about the changes from the text?A．By comparing the recorded data.B．By studying the remains of these apes.C．By unearthing the buried caves.D．By counting the bones of the skeletons. 14．What can we learn about great apes from the text?A．All remains of them have been destroyed.B．They once got close to humans in southern China.C．Apes tended to live in the less developed countries.D．There were diverse species of great apes ever living on earth.15．What does the text focus on?A．The effect of climate change on apes.B．The evolution of some species of apes.C．The change of natural habitats.D．The food preferred by some species of apes.Practicing self-care every day can have a big impact on mental health. To fulfill that, you can create a personal mental-health list. When you feel anxious or upset, instead of scrolling through social media, you can pick something off the list. 16 The following ideas may get you started.Get a little exercise. Go for a walk, or a run. Do some jumping jacks. Play with your dog. Dance alone in your room. It doesn’t matter what it is, getting up and moving can be a great way to “reset” your brain. Research shows that daily exercise can improve mood, prevent depression and help deal with anxiety and anger. 17Connect with nature. Spending time in nature is a part of self-care practice. 18 A review of research on young people has found that spending time outside can reduce stress, make you more resilient, improve quality of life and even help with ADHD symptoms. In other words: Go touch some grass.19 Just finding the songs and noticing how you react to them can be very powerful. Listening to music can light up different parts of your brain. Research shows that listening to music can even improve your mood. There are music therapists who help clients improve their well-being through listening to or perhaps making music.Make art. You can go free-form, or even use an adult coloring book. Maybe you’ll want to fill in mandalas. 20 When you start to feel bad, grab these art supplies. Use these media instead of reaching for your phone to try and relieve your mood with social media.A．Try to take breaks when you need.B．Try to do at least one thing from the list.C．Keep some paper and art supplies beside you.D．List some cheerful songs and keep listening to them.E．When you are feeling anxious, have a good memory of it.F．You can go for walks, water you plants and watch them grow.G．It can even change the structure of your brain and boost memory.二、完形填空When I started my Ph. D．, I knew my work was producing much waste, but I took it for granted. That all 21 one day when I saw plastic waste piled against the wall.I went to my adviser and decided to create 3D-printed lab 22 out of our waste. But the project didn’t go smoothly. After months of 23 , I felt worried about my dream.It was a relief when my colleagues were 24 to join us. We created a group devoted to 25 other greener ways. We began meeting every month to discuss some 26 . We introduced new recycling bins to each lab after learning that some waste could be recycled if it was sorted 27 . And we also tracked the energy consumption of lab equipment. By doing these, we could create 28 on how to use each device.Our most energy-hungry devices were the ultra-low-temperature freezers, each of which consumed more energy than a typical household. So, we started an institutewide (全院的) freezer 29 , asking labs to remove samples that were not 30 anymore and combine what remained in fewer freezers. Through those efforts, we managed to turn off several freezers. We also 31 the temperature of several freezers after realizing some samples didn’t have to be stored so 32 .I’m still disappointed that I couldn’t 33 my 3D-printing dream, and I’m determined enough to keep trying. I’ve also learned that if one 34 isn’t working, sometimes it’s best to take a step back and look for other solutions. I’m 35 that with my colleagues’ help, we were able to do that.21．A．happened B．worked C．changed D．passed 22．A．tools B．experiments C．tests D．buildings 23．A．preparing B．delaying C．dreaming D．struggling 24．A．hesitant B．eager C．likely D．nervous 25．A．getting through B．setting down C．searching for D．setting off 26．A．solutions B．topics C．articles D．samples 27．A．properly B．effortlessly C．casually D．slightly 28．A．questions B．pictures C．instructions D．signs 29．A．game B．evaluation C．design D．challenge 30．A．involved B．needed C．issued D．licensed 31．A．increase B．set C．control D．keep 32．A．long B．deep C．cold D．fresh 33．A．forget B．achieve C．abandon D．find 34．A．position B．power C．direction D．approach 35．A．anxious B．curious C．grateful D．hopeful三、语法填空阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式。

山西省长治市学院附属太行中学2018-2019学年高三英语上学期期末试卷含解析一、选择题1. It was in such a good place _____ everyone wanted to go and visit _____ I came across the old lady．A．that, that B．where, as C．as, that D．as, as参考答案：C2. Glancing _____ his shoulder, Eric could see the dog was running after him.A. overB. acrossC. throughD. onto参考答案：A3. Advertising doesn’t work well for all products and services under all conditions．A．partly B．equally C．simply D．merely参考答案：B4. The suggestion they all objected to________to be effective finally. A．proving B．prove C．had proved D．proved参考答案：18．D试题分析：句意：他们都反对的那个建议最终证明是有效的。

这里they all objected to 是定语从句，先行词是suggestion，关系词作宾语在这里省略了，空格处缺少整个句子的谓语动词，故排除AB，过去完成时是一个相对的时态，必须有一个它的参照的过去式，而这里没有，根据句意故选D。

考点：考查动词时态的用法。

点评：本题难度适中。

动词时态是高中阶段的重难点之一，高中要求掌握的时态需要考生牢记它们的用法，但是时态必须要结合一定的语境才能做出正确的判断。

即学即练：——Bob has gone to California.——Oh, can you tell me when he ?A. has leftB. leftC. is leavingD. would leave解析：B。

2018-2019学年第二学期高二期末考试英语试卷(考试时间:120分钟试卷满分:150分)第1卷(选择题，共100分)第一部分听力(共两节，满分30分)第一节(共5小题;每小题15分，满分75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秒钟的时间来回管有关小题和阅读下面小题，。

每段对话仅读一遍。

1. What probably is the woman?A. A waitressB. A secretaryC. A saleswoman2. What is the woman probably going to do?A. Take exerciseB. Give a speechC. Go out for a walk3. How's the weather now?A. Rainy.B. CloudyC. Sunny.4. How much does each ticket cost?A.3.60 pounds.B.4.60 pounds.C.7.20 pounds.5. What can we learn from the conversation?A. The woman doesn't like pop music.B. The man doesnt't like pop musicC. The woman is quite young第二节(共15小题:每小题15分，满分22.5分)听下面5段对话或独白。

每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置，听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟:听完后，各小题将给出5秒钟的作答时间，每段对话或独白读两遍。

听第6段材料，回答第6-7题6. Why did Mr,Carter go to Los Angeles?A. To visit a friendB. To attend a meetingC. To have a vacation.7. When does the man want to discuss the new market with Mr. Carter?A. Next Tuesday morning.B. Next Tuesday afternoon.C. Next Thursday afternoon. 听第7段材料，回答第8-10题8. Why does the man need his notebook?A. To study about the show.B. To study for the test.C. To write notes in9. When does the conversation take place?A. Before the showB. During the show.C. After the show10. What will the two speakers do after the show?A. Have dinner togetherB. Go to the man's homeC. Go to the woman's home 听第8段材料，回答第11-13题，11. How many days has the man got for his vacation?A. 25 daysB. 15 daysC. 10 days12. Why does the man go to Hawaii for his vacation with his family?A. To broaden his visionB. To relax themselvesC. To visit friends13. Where is the woman going this summer?A. EgyptB. Canada.C. The United States听第9段材料，回答第14-17题14. When did the fight happen?A. At 7B. At 11C. At 1215. What did the young man take?A. A clockB. A mobile phoneC. A shelf16. Who was injured in the fight?A. A young manB. The womanC. The shopkeeper.17. What does the man want to do now?A. Look for the young man.B. Go shopping.C. Help the woman.听第10段材料，回答第18-20题。

姓名，年级：时间：铜仁一中2018—2019学年度第二学期高二期末考试英语试题考试时间为120分钟，满分为150分。

第一部分听力（共两节，满分30分)第一节（共5小题;每小题1。

5分，满分7.5分）请听下面5段对话，选出最佳选项。

1。

What is the man doing now?A。

Answering the phone. B. Having a bath。

C. Cooking supper。

2。

What does the woman mean？A。

She needs more time to fix the iPad.B. She doesn’t know how to fix the iPad。

C. The man can have his iPad back by tomorrow。

3。

What do we know about the woman?A. She got a pay raise recently.B. S he hasn’t been feeling well recently.C. She has been late for work quite often recently.4。

How many foreign languages does the man speak？A。

3。

B. 4. C. 5.5. What does the man think of the woman?A。

Considerate B。

Careless C。

Rude第二节(共15小题；每小题1。

5分，满分22。

5分）请听下面5段对话或独白，选出最佳选项.请听第6段材料，回答第6、7题.6.Where is the woman now probably?A。

In a hotel。

B. In a restaurant C。

In a coffee bar。

7. What does the wo man want?A. One egg, some bread and a glass of milk。

2019-2020学年山西省长治学院附属太行中学高三英语期末试题及参考答案第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AFour Best Hikes in the WorldThere's nothing like getting out and getting some fresh air on a hike. No matter whether your idea of a hike is a leisure walk or climbing the highest mountain on Earth, we've got you covered. Below are four best hikes inthe world.Torres del Paine W CircuitLocation (位置): Patagonia. ChileDistance: 37 + milesTime: 5~6 daysBest time to go: October to JanuaryThe W Circuit is one of the most recommended hikes you'll find. Not only will you appreciate the diverse landscapes and striking granite pillars (花岗岩柱子), but you'll probably meet some new friends along the way.Grand Canyon Rim - to - Rim HikeLocation: Arizona, the United StatesDistance: 48 milesTime: 1~3 daysBest time to go: May to June, September to OctoberThere's no better way to experience one of the greatest wonders in the world. Located in one of the USA's most beautiful parks, the views are ly appealing. Just make sure you're prepared for the challenge.Trek to PetraLocation: JordanDistance: 47 milesTime: 5~ 6 daysBest time to go: October to AprilTake the road less traveled through the Kingdom of Jordan and experience one of the seven wonders of theworld. Hike through canyons, gorges and ridges, and see tombs and temples along the way all while avoiding crowds of tourists.Yosemite Grand TraverseLocation: California, the United StatesDistance: 60 milesTime: 6~7 daysBest time to go: July to SeptemberKnown for some of the best hiking in the world, Yosemite National Park is famous for its views and huge sequoia (红杉) trees. Praised byNational Geographic, the Yosemite Grand Traverse will take you through waterfalls and green mountaintops.1.Which of the following is the best time for the hike in Patagonia, Chile?A.AprilB.MayC.AugustD.December2.Where should you go for a less crowded hike?A.JordanB.Patagonia, ChileC.Arizona, the United StatesD.California, the United States3.What can you do along the Yosemite Grand Traverse?A.Plant sequoia treesB.Appreciate waterfallsC.Visit local templesD.Climb granite pillarsBPlastic is piling up in ecosystems all over the world. Although its harmful impacts on both species and ecosystems have been documented, a few animals—like bowerbirds and hermit crabs—are doing what they can to recycle it. And according to a recent study, wild bees in Canada have joined the effort, which is a rare observation of behavioral flexibility in species especially insects, in increasingly plastic-rich environments.The researchers found two species of leafcutter bees putting plastic into their nests. One of the bees they studied, the alfalfa leafcutter bee, normally bites off pieces of leaves and flowers while the second bee gathers sticky substances from trees. Leafcutter bees don't build big nests or store honey like honeybees, choosing instead small nests in underground holes, tree holes or cracks（裂缝）in buildings. But the researchers found that three of eight brood cells（育雏巢室）contained pieces of plastic bags, replacing 23 percent of the cut leaves in each cell on average.While they don't make honey,alfalfa leafcutter bees still make money for theU. S. and Canadian farmers bypollinating（给......传授花粉）crops including alfalfa , carrots and melons. The European insects were introduced to North America in the 1930s for that purpose, and they've since become wild, joining the continent's many native species of leafcutter bees.In a separate study conducted in Argentina between 2017 and 2018, researchers found a bee nest made entirely of plastic, which consisted of three separate cells. It's the first known example of such construction worldwide. Compared to the other nests the researchers examined, which were made of natural materials, this one had a pretty lower success rate of the bees' survival. One of the cells had a dead baby bee , another seemed to have housed an adult that had left the nest, and the third was unfinished.4. What does the animals' use of plastic show according to the study?A. How widely plastic is used.B. How strange the behavior of wildlife is.C. How some wildlife is adapting to plastic.D. How plastic pollution has harmed them.5. What do leaves mean to alfalfa leafcutter bees?A. Food.B. Shelter.C A plastic substitute. D. Traditional nest materials.6. Which is one characteristic of leafcutter bees?A. They have great economic value.B. They store honey like honeybees.C. They prefer to live in tree holes.D. They have evolved into a new species.7. What was the nest made entirely of plastic like?A. It might be warmer.B. It might be unhealthy.C. It might be easy to finish.D. It might be recyclable.CA satellite is about to demonstrate a new way of capturing space junk with magnets for the first time. With the frequency of space launches dramatically increasing in recent years, the potential for a disastrous collision above Earth is continually growing. Now, Japanese orbital clean-up company Astroscale is testing a potential solution.The firm's End-of-Life Services by Astroscale demonstration mission is scheduled to lift off on 20 Marchaboard a Russian Soyuz rocket. It consists of two spacecraft: a smal “client” satellite and a larger “servicer” satellite, or “chaser”. The smaller satellite is equipped with a magnetic (磁力的) plate which allows the chaser todock withit.The two stacked spacecraft will perform three tests once in orbit, each of which will involve the servicer satellite releasing and then recapturing the client satellite. The first test will be the simplest, with the client satellite drifting a short distance away and then being recaptured. In the second test, the servicer satellite will set the client satellite tumbling before catching up with it and matching its motion to grab it.Finally, if those two tests go well, the chaser will live up to its name by letting the client satellite float a few hundred metres away before finding it and attaching to it. All of these tests will be performed autonomously, with little to no human input once they are set in motion.“These kinds of demonstrations have never been done before in space - they are very different to, say, an astronaut controlling a robotic arm on the International Space Station,” says Jason Forshaw at AstroscaleUK.“This is more of an autonomous mission.” At the end of the tests, both spacecraft will burn up in Earth's atmosphere.If companies wanted to use this capability, they would have to attach a magnetic plate to their satellites so they could be captured later. Because of the growing space garbage problem, many countries now require firms to have a way to bring back their satellites once they run out of fuel or fail, so this could be a fairly simple likely plan, Forshaw says. Right now, each chaser can only nab one satellite, but Astroscale is working on a version that could drag three or four out of orbit at once.8. Which of the following can replace the underlined word "dock with" in Paragraph 2?A. Deal with.B. Keep up with.C. Join together.D. Crash.9. Why many countries now require firms to have a way to bring back their satellites?A. Because of the growing space waste problem.B. Because the frequency of space launches are dramatically increasing.C. Because they can earn large profits from it.D. Because Astroscale has found a new method of capturing the space garbage.10. What will Astroscale do to solve the space junk problem?A. An astronaut controls a robotic arm on the International Space to capture the “client” satellite.B. Through a magnetic plate remotely controlled by humans on the ground to catch the “client” satellite.C. Finding the "client "satellite and attaching to it with a magnetic plate automatically.D. Tumbling to match the motion of “client satellite the drag three or four satellites out of its orbit into atmosphere.11. What can we infer from the passage?A. People will bum the space junk up in Earth's atmosphere in the future.B. Japan andRussiawill conduct space debris cleanup experiment together.C. These kinds of demonstrations have never been done before.D. The demonstration mission will be divided into three phases.DTwo years ago, I decided to study at theUniversityofSt. Edwardsin the city ofAustin,Texas. When I was on my research to find the perfect place to study in, I considered many aspects: a safe place, a city where there were companies devoted to marketing or technology, a place where speaking Spanish and English was an advantage and a school where I could learn about digital strategies (数字策略). After comparing and evaluating many cities and universities. I finally decided onAustin.Since I arrived inAustin,Texas. I had been living inside the university where I had a private room and shared common areas with more students. University life was not very different from the life inMexicoand classes weresemblableand the way of socializing too. However, in theUnited States, the classes were more practical and teachers encouraged you to be self-responsible and complete your tasks.The classes that I was taking were related to social media, digital marketing and advertising. I was very excited to be able to study technology-related courses.What I liked most about the experience was being able to live with students from many places, which allowed me to learn from other cultures and to share mine with other students. Also, international student services usually organized events and tours that helped me to get to know the city and the school.I certainly think that studying abroad is a beneficial experience. It makes us capable of understanding cultural differences and accepting diversity. Personally, I would suggest that you first determine what your goals are by going abroad, research the opportunities and lifestyle, evaluate your universities,and finally decide on the one where you feel more comfortable, connecting with your values and way of seeing life.12. Which of the following can best describe the author according to paragraph 1？A. Casual.B. Cautious.C. Changeable.D. Adventurous.13.What does the underlined word “semblable” in paragraph 2 probably mean?A. Worthwhile.B. Practical.C. Same.D. Similar.14. What made the author most pleased?A. Speaking Spanish and English inAustin,Texas.B. Working as a designer in a technology company.C. Having a chance to learn about different cultures.D. Organizing many events and tours independently.15. What are the students who intend to study abroad advised to do?A. Be careful to choose the university to study in.B. Set no limits on theiracademic performances.C. Study where they're familiar with everything.D. Adjust personal lifestyles for the university.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学年山西省长治学院附属太行中学高三英语下学期期末考试试题及参考答案第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项ANothing beats live music, but the venue makes a difference. When you're able to score tickets to an incredible concert in an incredible place, you won't forget the experience. Here are some of the coolest music venues from around the world. If you haven't been to any of these, you've got some traveling to do.Red Rocks, Morrison, the United StatesRed Rocks might be the most beautiful and famous venue in the United States. At 6,450 feet above sea level, Red Rocks is a geologically formed natural stage. Its massive sandstone provides a perfect stage for jam bands. If you're into the blues and jazz, you'll have no trouble finding something in line with your interests.Meet Factory, Prague, Czech RepublicSmallest venues on this list, Meet Factory is an art gallery, theater, and music venue. The venue only accommodates 1,000 people, so you won't see any huge names come through. Still, it's a great place to see up-and-coming local acts, and if you've got an eye for contemporary art, you'll love your time here.Arena of NÎmes, NÎmes, FranceOriginally built around A. D. 70, the Arena of Nimes presents concertgoers with an interesting question: Should they enjoy the music, or marvel at the architecture? The Arena is, after all, one of the world's best-preserved Roman theaters. Many major touring acts plan stops at the Arena of Nimes, especially during the venue's annual festival.Sydney Opera House, Sydney, AustraliaThe Sydney Opera House is one of the world's most famous performing venues. I's also one of the most distinctive buildings in Sydney, thanks to the breathtaking design by Danish architect Utzon. It hosts about 40 events per week, so whether you're into jazz, rock, classical music, or opera, you'll find something to watch.1.Where can you enjoy music in natural beauty?A.At Red Rocks.B.At Meet Factory.C.At Arena of Nimes.D.At Sydney Opera House.2.What is special about Meet Factory?A.It enjoys breathtaking scenery.B.It hosts both musical and artistic events.C.It is the largest venue of all.D.It is famous for contemporary music.3.What do the listed music venues have in common?A.They have a long history.B.They are built near the sea.C.They accommodate thousands of people.D.They are beautiful tourist attractions.BWhether for a special holiday, as a way of showing gratitude or just a way of letting someone know you care, gift giving is a universal custom Though the purpose may be similar from place to place, traditions vary widely from one country to the next. A behavior that shows respect in one place might be consideredoffensivesomewhere else. Take a look at unique gifting traditions from around the world.Here in theUS, a set of kitchen knives seems like the perfect gift idea for a wedding. However, in certain European countries likeGermany, people believe that a knife presented as a gift will cut off your friendship. There is a way to break it: Tie a coin to the knife or gift box. The receiver then returns the coin to you as a “payment”to remove the bad luck.There's a well-known Italian wedding tradition where the groom's (新郎) tie is cut into a number of tiny pieces. Wedding guests can then "buy” these tie pieces in exchange for cash. It's a fun way to give money to the new couple thatleaves guests with a wedding souvenir.As left hands are considered unclean in Indian culture, behaviors such as touching, passing money, or giving gifts are to be done with the right hand. Different from some other cultures , an odd number (奇数) of thingsor currency represents good luck. For example, £11 should be given rather than £10.InZimbabwe, it is common to directly ask for a gift. When you receive a gift without asking for it, even if the giver's family is poor, it's the worst way to reject the offering. Also, expressing thanks with actions is better than giving thanks orally (口头地).These may include jumping up and down, dancing, or whistling.4. What does the underlined word “offensive“ in paragraph 1 refer to?A. Rude.B. Creative.C. Suitable.D. Caring.5. How do people prevent friendship breaking down when giving gifts like knives?A. The guests cut the groom's tie into pieces.B. The receiver returns the coin to the giver.C. The giver gives gifts with the right hand.D. The receiver expresses thanks by dancing.6. What can we learn about the gift giving inZimbabwe?A. It is not proper to ask for a gift directly.B. It's better to reject a gift from a poor family.C. One can express thanks by writing letters.D. Showing gratitude with actions is better than words.7. Which can be a suitable title for the text?A. The Wayof Showing GratitudeB. A Fun Behavior to Respect PeopleC. Various Gift Giving TraditionsD. A Special Custom of Gift GivingCStarting at university or college can be a big challenge, especially if you’re living away from home for the first time. You arefaced with big questions such as, “Who’s going to do my washing?” “Who’s going to tidy my room?” And, most importantly, “How am I going to eat?” Yes, living on your own means cooking for yourself, and when you’re living a student lifestyle, this could be a recipe for disaster.Students, in the UK at least, often rely on generally available food such as baked beans or cheese on toast. And for the more adventurous, there’s “spag bol” — spaghetti bolognaise(肉酱意粉), that is, cooked spaghetti served with a ground beef and tomato sauce — a budget-friendly solution. If you make a huge pan of it, it can probably last you a whole week! Other low-cost options include jar sauces and oven pizzas.Recently, a British supermarket suggested that rose harissa paste, organic cider vinegar and Swiss bouillon powder were the important food materials needed for the “student cupboard”. But are these items considered essential and affordable for someone on a budget?As a matter of fact, living on a budget is certainly one barrier to eating a well-balanced diet. What’s more, some young people don’t know much about cooking, and for many young students, there are more fun things to go and do than just stay inside and cook. That’s where takeaways and microwave meals come in.What should a health-conscious student really have in his or her food cupboard? Jack Monroe, a food writer and campaigner, has words to say: baked beans, lemon juice, canned tomatoes and tomato ketchup, described as“salt, sugar, vinegar and tomato all in one handy squeezy bottle”. And should that not appeal, you can always wait till your next visit to your mum and dad for a square meal!8. What does the author indicate by “this could be a recipe for disaster”?A. Cooking is difficult for a student.B. Students must cook if they live alone.C. It is important to live independently.D. Learning to cook will cause disasters.9. What is the feature of “spag bol”?A. It is delicious.B. It is healthy.C. It saves money.D. It needs little skill.10. What is paragraph 4 mainly about?A. How well-balanced diets can be realized.B. How students can eat healthily with limited money.C. Why living on a budget is common among students.D Why students choose takeaways and microwave meals.11. Why does the author write the last paragraph?A. To advocate visiting parents.B. To offer some tips.C. To promote health consciousness.D. To introduce a writer.DIn 1990, Hal Donaldson was 23 years old, fresh out of college and found himself in Calcutta, India, where he was asked to interview Mother Teresa.Donaldson says about the great woman famed for feeding the hungry, “She wasn't wearing shoes and her ankles were swollen. She sat down with me and was very polite.” After the interview, Mother Teresa asked him, “What are you doing to help the poor?” Donaldson admitted that he was young and wasn't focused on helping others. With a smile on her face, Mother Teresa said, “Everyone can do something.”Those words deeply struck Donaldson and forced him to face some hard truths about himself.Hal Donaldson grew up in the San Francisco Bay area. When he was 12 years old, his parents were hit by a drunk driver; his father died, and his mother was seriously injured. To make ends meet, they went on welfare. Donaldson says, “I had holes in my shoes and clothes. When you're teased at school for that, you just want to escape.”He managed to do just that. Donaldson got into college and turned his focus to making money for himself He says, “I was just trying to find my way out of insignificance. However, it's easy to overlook others along the way. Iwas the guy that would see a homeless person and cross the street, so I didn'thave to confront (面对) him. My focus was on climbing to the top instead of helping those trying to climb with me.”Donaldson returned home from India with a different thought. He traveled to eight cities in America and stayed on the streets and listened tostories of the homeless. “My heart broke,” he says. “I knew I could no longer just live for myself.”Inspired by Mother Teresa's words and the stories he'd heard across America. Donaldson loaded a pick-up truck with $300 worth of groceries and handed them out to anyone who needed help. In 1994, Donaldson created the nonprofit organization, Convoy for Hope, which works with communities across America and around the world. Their work focuses on feeding children, women's empowerment, helping farmers and disaster services.12. What did 23-year-old Hal Donaldson do in India?A. He attended an interview for a college.B. He fed the hungry with Mother Teresa.C. He interviewed Mother Teresa.D. He did something to help the poor.13. What can we learn about Hal Donaldson from paragraph 4?A. He was born with disability.B. He led a hard life as a child.C. He was well treated at school.D. He survived as a parentless boy.14. How does Hal Donaldson describe himself in college?A. Self-centered.B. Sympathetic.C. Popular.D. Casual.15. How did Hal Donaldson change after he returned home from India?A. He preferred traveling to volunteering.B. He suddenly fell in love with journalism.C. He turned his focus to living for himself.D. He gradually devoted himself to helping others.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学年山西省长治学院附属太行中学高三英语期末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AIt looks like 2017 is shaping up to be a record-breaking year in movie History. Here is a list of some of the year’s biggest blockbusters so far.Kong: Skull IslandA reboot (重启) of King Kong would normally get laughed at in this day and age, but it looks like this modem version of the story will be worth watching. With US actress Brie Larson and UK actor Tom Hiddleston in the mix, this film is set to be this year’s biggest monster tale.Release Date:3/10/17Beauty and the BeastDirector Bill Condon is bringing back a part of our childhood in live action, complete with the songs we all remember and love. With British stars Emma Watson and Dan Stevens leading thecast, the classic Walt Disney story already sounds like it’ll be a delight for both children and adults.Release Date:3/17/17The Fate of the FuriousThere was doubt that we’d even get a Fast 8, especially after the fitting ending US actor Paul Walker’s character was given at the end of Furious 7. Fans thought they’d never see Dom and the rest of the crew back in action, but thankfully, US star Vin Diesel himself confirmed that The Fate of the Furious is fueling up for another go.Release Date:4/14/17Spider-Man: HomecomingSpider Man is heading home to Marvel Studios for the first time. The movie will show us Peter Parker’s high school days, and will continue the threads we saw formed during his initial appearance in Captain America: Civil War. We know that Michael Keaton is playing The Vulture in this story, and that both Happy Hogan and Tony Stark, played by US actors Jon Favreau and Robert Downey Jr., are along for the ride.Release Date:7/7/171.Which of the following movies can’t you see on May Day?A.Kong: Skull Island.B.Beauty and the Beast.C.The Fate of the Furious.D.Spider-Man: Homecoming.2.What can we know about Beauty and the Beast?A.It is fueling up for another go.B.It is produced by Marvel StudiosC.It’ll show us Peter Parker’s school days.D.It’ll be enjoyable for both children and adults.3.What does the underlined word “cast” probably mean?A.Characters.B.Actors.C.Directors.D.Teachers.BExperts are warning about the risks of extremely picky(挑剔的)eating after a teenager living on a diet of chips and crisps developed lasting sight loss. Eye doctors inBristolcared for the 17-year-old after his sight had gone to the point of blindness. Tests showed he had serious vitamin deficiency(缺乏). Dr. Denize Atan, who treated him at the hospital, said, “His diet was basically a portion of chips from the local fish and chip shop every day. He also used to snack on crisps and sometimes white bread and ham, and not really any fruit and vegetables.”The teenager saw his doctor at the age of 14 because he had been feeling tired and unwell. At that time he suffered from vitamin B12 deficiency, but he did not stick with the treatment or improve his poor diet. Three years later, he was taken to theBristolEyeHospitalbecause of progressive sight loss.He was not overweight or underweight, but he had lost minerals from his bones, which was really quite shocking for a boy of his age. In terms of his sight loss, he met the standards of being blind. “He had blind spots right in the middle of his sight,” said Dr Denize Atan, “That means he can’t drive and would find it reallyarduousto read, watch TV or recognize faces.”Dr Denize Atan said that parents should learn about the harm that can be caused by picky eating, and turn to experts for help. For those who are concerned , she advised, “It’s best not to be anxious about picky eating , and instead calmly introduce one or two new foods with every meal.” She said multivitamin tablets can supplement(补充) a diet, but cannot take the place of eating healthily. “It’s much better to take in vitamins through a varied and balanced diet,” she said, adding that too manycertain vitamins , including vitamin A, can be harmful ,“so you don’t want to overdo it.”4. What does Dr Denize Atan imply in paragraph 1?A. The diet of the boy is not balanced.B. Fruit and vegetables are rich in vitamins.C. Picky eating is common among teenagers.D. The cause of the boy’s disease is unknown.5. Why did the boy go to see his doctor at the age of 14?A. To improve his poor diet.B. To get some help to lose weight.C. To be treated for his discomfort.D. To slow down his progressive sight loss.6. What does the underlined word “arduous” in paragraph 3 probably mean?A. Important.B. Easy.C. Necessary.D. Difficult.7. What does the last paragraph mainly talk about?A. Reasons why the boy is seriously ill.B.Suggestions for the boy’s family to care for him.C. Advice for parents worried about picky eating.D. Waysof taking in enough vitamins and minerals.CMany of us were delighted to learn that a high school senior Kwasi Enin was accepted to all eight Ivy League universities. To our surprise, he wasn't excited as expected, but appeared extra calm. He announced that he would revisit the universities to find the best suitable in music or medicine. He also wanted to compare their financial aid packages.Kwasi's success story is rare, but his reaction is not. After the admission letters arrive at home, students have 30 days to really think about what kind of school would help them grow as a person, which school would best prepare them for the future, and at which school they would be happiest. And they also have to think about whether they can afford the school they choose.But how to answer the questions about which school is the best suitable university? Some young people are attracted to large universities with great school spirit and a list of offerings. But besides those advantages, many of these universities focus on graduate work and research, with undergraduates taught mostly by part-time instructors. Others are attracted to smaller boarding schools with discussion-based classes. But some of theseschools will have much limitation for students who want a high-energy city life experience.Many students today seem to think they should pick the university where they will get the diploma that will help them get the most highly paid job. This is a sad misunderstanding of what a college education should provide.A good college education should prepare them to overcome any difficulty andthrivein society. It helps them to form the habit of creative mind and spirit that will continue to develop far beyond their university years. So when you choose college, you should consider if it is filled with useful learning to help create new spaces for different possibilities of growth.8. What can we know about Kwasi Enin from paragraph 1?A. He was from a very poor family.B. He would choose the top university.C. He was too excited to calm himself at the good news.D. He considered his interests when choosing his university.9. What can you infer from paragraph 2?A. Few students can be admitted to university.B. Many students face the choices like Kwasi.C. Top universities are the first choice for most students.D. American students can afford their university by themselves.10. Which of the following can best explain the underlined word “thrive” in paragraph 4?A. FailB. SucceedC. ResearchD. Work11. What should the best university be like according to the text?A. Very large and have good instructors.B. Small boarding schools with discussion-based classes.C. It will offerthe diploma to get the most highly paid job.D. It will help continue to develop far beyond university years.DHave you ever done something that was really dangerous just because you thought it was safe？Maybe you did a dangerous trick on your bicycle or skateboard because you were wearing a helmet and thought you couldn’t get hurt. The psychology(心理) of this sort of behavior is called the Peltzman Effect, named after Sam Peltzman, professor of economics at the University of Chicago. Peltzman believes that those moments when people think they are the safest are the times when they act most dangerously.Peltzman said that people drove more dangerously when they wore seat belts(安全带) . Driving a large four-wheel drive vehicle has a similar effect on drivers’ behavior. Because drivers of large vehicles sit up higher and can see better, they feel they can make better judgments when they drive. They are better protected in accidents,so they act more dangerously. This makes driving morehazardousto other drivers.The Peltzman Effect isn’t just limited to driving. In 1972, the American Food and Drug Administration (FDA) passed a law requiring child safety caps on most medicine bottles. The safety caps were designed to prevent children from accidentally taking the medicine, especially painkillers such as aspirin. Requiring safety caps sounded like a great idea, but there was an unexpected side effect. Because the safety caps are so hardto take off, some people leave them off altogether．Worse, some parents leave the bottles where kids can reach them because they feel that it is safe because of the cap. A study on the Peltzman Effect showed that more than 3,500 children have been harmedby aspirin because of the safety caps.The Peltzman Effect describes how we’re likely to take more risks and act more dangerously when we feel safest. What’s more, the effects of these behaviors can be quite different from what we expect.12. What is the Peltzman Effect？A. People behave less safely when they feel safe．B. People feel safest when they are under protection．C. Something that seems dangerous turns out to be safe．D. People who act dangerously are likely to be together．13. What does the underlined word“hazardous”in Paragraph 2 mean？A. Interesting．B. Expensive．C. Dangerous．D. Important．14. Medicine bottles with safety caps ________．A. are required throughout the worldB. meet the demands of the Peltzman EffectC. sell well in the worldD. are not completely safe15. What would be the best title for the text？A. Unsafe Safety MeasuresB. Types of Decision MakingC. People’s Fear of Taking RisksD. Different Behaviors of People in Danger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。

太行中学2018—2019学年第二学期期末考试高二数学试题（理）命题：李跃青 审题：朱会驰一、选择题：（本大题共12个小题每小题5分，共60分.在每小题给出的四个选项中只有项是符合题目要求的.）1.已知集合{}2|1log A x N x k =∈<<，集合A 中至少有3个元素，则（ ） A. 8k >B. 8k ≥C. 16k >D. 16k ≥2.复数()634i i i-+-的实部与虚部之差为（ ）A. -1B. 1C. 75-D.753.已知()cos 2cos 2παπα⎛⎫+=- ⎪⎝⎭，则tan 4πα⎛⎫-= ⎪⎝⎭（ ）A. 4-B. 4C. 13-D. 134.已知|a v |＝1，|b v|，且a v ⊥(a v －b v )，则向量a v 在b v 方向上的投影为( )A. 1B.C.12D. 25.某医院拟派2名内科医生、3名外科医生和3名护士共8人组成两个医疗分队，平均分到甲、乙两个村进行义务巡诊，其中每个分队都必须有内科医生、外科医生和护士，则不同的分配方案有 A. 72种B. 36种C. 24种D. 18种6.当a 输入a 值为16，b 的值为12时，执行如图所示的程序框图，则输出的a 的结果是( )A. 2B. 3C. 4D. 67.已知函数()21f x x lnx =--，则y ＝f （x ）的图象大致为（ ）A.B.C.D.8.如图，在棱长为a 的正方体1111ABCD A B C D -中，P 为11A D 的中点，Q 为11A B 上任意一点，E 、F 为CD 上两点，且EF 的长为定值，则下面四个值中不是定值的是（ ）A. 点P 到平面QEF 的距离B. 直线PQ 与平面PEF 所成的角C. 三棱锥P QEF -的体积D. △QEF 的面积 9.已知函数()cos sin 4f x x x π⎛⎫=+⎪⎝⎭，则函数()f x 满足（ ） A. 最小正周期为2T π=B.图像关于点,8π⎛⎝⎭对称 C. 在区间0,8π⎛⎫⎪⎝⎭上为减函数D. 图像关于直线8x π=对称10.设锐角ABC ∆的三个内角,,A B C 的对边分别为,,a b c 且1c =，2A C =，则ABC ∆周长的取值范围为（ ）A. (0,2+B. (0,3+C. (2++D. (2+11.已知函数()f x 满足对任意实数,m n ，都有()()()1f m n f m f n +=+-，设()()(0,1)1xx a g x f x a a a =+>≠+，(ln 2019)2018g =，1ln 2019g ⎛⎫= ⎪⎝⎭（ ）A. 2018B. 2017C. -2016D. -201512.已知函数,0()2(1),0xx m e mx x f x e x x -⎧++<⎪=⎨⎪-≥⎩（e 为自然对数的底），若方程()()0f x f x -+=有且仅有四个不同的解，则实数m 的取值范围是（ ）． A. (0,)eB. (,)e +∞C. (0,2)eD. (2,)e +∞第Ⅱ卷（共90分）二、填空题（每题5分，满分20分，将答案填在答题纸上）13.已知点(,)P x y 在不等式组20,10,220x y x y -≤⎧⎪-≤⎨⎪+-≥⎩，表示的平面区域上运动，则z x y =-的取值范围是__________14.已知点(22,0)Q 及抛物线24x y =上的动点(,)P x y ，则y PQ +的最小值为______. 15.已知数列{}n a 为正项的递增等比数列，1582a a +=，2481a a ⋅=，记数列2n a ⎧⎫⎨⎬⎩⎭的前n 项和为n T ，则使不等式12019113n T ->成立的最大正整数n 的值是_______． 16.已知函数()sin cos x f x x x =-，23,34x ππ⎡⎤∈⎢⎥⎣⎦，则()f x 的最小值是__________ 三、解答题（解答应写出文字说明、证明过程或演算步骤.）17.已知数列{}n a 的前n 项和为n S ，且221n n n S na a =+-． （1）求数列{}n a 的通项公式； （2）若数列21n a ⎧⎫⎨⎬⎩⎭的前n 项和为n T ，证明：4nT <． 18.如图（1），等腰梯形ABCD ，2AB =，6CD =，22AD =，E ，F 分别是CD 的两个三等分点，若把等腰梯形沿虚线AF 、BE 折起，使得点C 和点D 重合，记为点P ， 如图（2）．（1）求证：平面PEF ⊥平面ABEF ；（2）求平面PAE 与平面PAB 所成锐二面角的余弦值．19.某企业对设备进行升级改造，现从设备改造前后生产大量产品中各抽取了100件产品作为样本，检测一项质量指标值，若该项指标值落在[20,40)内的产品视为合格品，否则为不合格品，图1是设备改造前样本的频率分布直方图，表1是设备改造后的频数分布表.表1，设备改造后样本的频数分布表: 质量指标值 [)15,20[)20,25[)25,30[)30,35[)35,40[)40,45频数 2184814162（1）请估计该企业在设备改造前的产品质量指标的平均数；（2）企业将不合格品全部销毁后，并对合格品进行等级细分，质量指标值落在[25，30)内的定为一等品，每件售价240元，质量指标值落在[20，25)或[30，35)内的定为二等品，每件售价180元，其它的合格品定为三等品，每件售价120元.根据表1的数据，用该组样本中一等品、二等品、三等品各自在合格品中的频率代替从所有产品中抽到一件相应等级产品的概率，现有一名顾客随机购买两件产品，设其支付的费用为X （单位：元），求X 得分布列和数学期望.20.设椭圆()2222:10x y C a b a b +=>>2，圆22:2O x y +=与x 轴正半轴交于点A ，圆O 在点A 处的切线被椭圆C 截得的弦长为22 （1）求椭圆C 的方程；（2）设圆O 上任意一点P 处的切线交椭圆C 于点,M N ，试判断·PM PN 是否为定值？若为定值，求出该定值；若不是定值，请说明理由． 21.已知函数21()4ln 22f x x a x x =---，其中a 为实数. （1）求函数()y f x =的单调区间；（2）若函数()y f x =有两个极值点12,x x ，求证：()()126ln f x f x a +<-.请考生在22、23两题中任选一题作答，如果多做，则按所做的第一题记分. 选修4-4：坐标系与参数方程22.在直角坐标系xOy 中，以坐标原点为极点，x 轴正半轴为极轴建立极坐标系，曲线1C 的极坐标方程为4cos (0)ρθρ=>.M 为曲线1C 上的动点，点P 在射线OM 上，且满足||||20OM OP ⋅=.（Ⅰ）求点P 的轨迹2C 的直角坐标方程；（Ⅱ）设2C 与x 轴交于点D ，过点D 且倾斜角为56π的直线l 与1C 相交于,A B 两点，求||||DA DB ⋅的值. 选修4-5：不等式选讲23.已知函数1()||()3f x x a a =-∈R .（1）当2a =时，解不等式1()13x f x -+≥； （2）设不等式1()3x f x x -+≤的解集为M ，若11,32M ⎡⎤⊆⎢⎥⎣⎦，求实数a 的取值范围.太行中学2018—2019学年第二学期期末考试高二数学试题（理）命题：李跃青 审题：朱会驰一、选择题：（本大题共12个小题每小题5分，共60分.在每小题给出的四个选项中只有项是符合题目要求的.）1.已知集合{}2|1log A x N x k =∈<<，集合A 中至少有3个元素，则（ ） A. 8k > B. 8k ≥C. 16k >D. 16k ≥【答案】C 【解析】试题分析：因为{}2|1log A x N x k =∈<<中到少有3个元素，即集合A 中一定有2,3,4三个元素，所以4216k >=，故选C.考点：1.集合的运算；2.对数函数的性质.2.复数()634i i i-+-的实部与虚部之差为（ ）A. -1B. 1C. 75-D.75【答案】B 【解析】 试题分析：,故选B.考点：复数的运算. 3.已知()cos 2cos 2παπα⎛⎫+=- ⎪⎝⎭，则tan 4πα⎛⎫-= ⎪⎝⎭（ ）A. 4-B. 4C. 13-D.13【答案】C 【解析】 因为cos()2cos()2παπα+=-，所以sin 2cos tan 2ααα-=-⇒=，所以1tan 1tan()41tan 3πααα--==-+，故选C .4.已知|a v |＝1，|b v|2，且a v ⊥(a v －b v )，则向量a v 在b v 方向上的投影为( )A. 1B.2C.12D.22【答案】D 【解析】【详解】设a r 与b r 的夹角为θ，由a r ⊥(a r －b r )，得a r ·(a r －b r )＝0，即a r 2－a r ·b r ＝0，即a r 2－|a r |·|b r|cosθ＝0，所以2cos =2θ，所以向量a r 在b r 方向上的投影为2||cos 2a θ=r ．故选D. 5.某医院拟派2名内科医生、3名外科医生和3名护士共8人组成两个医疗分队，平均分到甲、乙两个村进行义务巡诊，其中每个分队都必须有内科医生、外科医生和护士，则不同的分配方案有A. 72种B. 36种C. 24种D. 18种【答案】B【解析】【分析】根据条件2名内科医生，每个村一名，3名外科医生和3名护士，平均分成两组，则分1名外科，2名护士和2名外科医生和1名护士，根据排列组合进行计算即可．【详解】2名内科医生，每个村一名，有2种方法，3名外科医生和3名护士，平均分成两组，要求外科医生和护士都有，则分1名外科，2名护士和2名外科医生和1名护士，若甲村有1外科,2名护士,则有1233339C C=⨯=，其余的分到乙村，若甲村有2外科,1名护士,则有2133339C C=⨯=，其余的分到乙村，则总共的分配方案为2×(9+9)=2×18=36种，故选B.【点睛】本题主要考查了分组分配问题，解决这类问题的关键是先分组再分配，属于常考题型.6.当a输入a的值为16，b的值为12时，执行如图所示的程序框图，则输出的a的结果是( )A. 2B. 3C. 4D. 6【答案】C 【解析】 【分析】模拟程序的运行，根据程序流程，依次判断写出a ，b 的值，可得当a=b=4时，不满足条件a≠b，输出a 的值为4，即可得解．【详解】模拟程序的运行，可得 a =16，b =12满足条件a ≠b ，满足条件a >b ，a =16−12=4， 满足条件a ≠b ，不满足条件a >b ，b =12−4=8， 满足条件a ≠b ，不满足条件a >b ，b =4−4=4， 不满足条件a ≠b ，输出a 的值为4. 故选C.【点睛】本题主要考查程序框图的循环结构流程图，属于中档题. 解决程序框图问题时一定注意以下几点：(1) 不要混淆处理框和输入框；(2) 注意区分程序框图是条件分支结构还是循环结构；(3) 注意区分当型循环结构和直到型循环结构；(4) 处理循环结构的问题时一定要正确控制循环次数；(5) 要注意各个框的顺序,（6）在给出程序框图求解输出结果的试题中只要按照程序框图规定的运算方法逐次计算，直到达到输出条件即可.7.已知函数()21f x x lnx =--，则y ＝f （x ）的图象大致为（ ）A. B.C. D.【答案】A 【解析】 【分析】利用特殊值判断函数的图象即可．【详解】令21x e =，则22222122111ln 1e f e e e e ⎛⎫== ⎪+⎝⎭--，再取1x e=，则12211ln 1f ee e e⎛⎫== ⎪⎝⎭--，显然22221e e e<+，故排除选项B 、C ； 再取x e =时，()220ln 12f e e e e ==>---，又当x →+∞时，()0f x →，故排除选项D.故选：A.【点睛】本题考查函数的图象的判断，特殊值法比利用函数的导函数判断单调性与极值方法简洁，属于基础题.8.如图，在棱长为a 的正方体1111ABCD A B C D -中，P 为11A D 的中点，Q 为11A B 上任意一点，E 、F 为CD 上两点，且EF 的长为定值，则下面四个值中不是定值的是（ ）A. 点P 到平面QEF 的距离B. 直线PQ 与平面PEF 所成的角C. 三棱锥P QEF -的体积D. △QEF 的面积 【答案】B 【解析】【详解】试题分析：将平面QEF 延展到平面11CDA B 如下图所示，由图可知，P 到平面11CDA B 的距离为定值.由于四边形11CDA B 为矩形，故三角形QEF 的面积为定值，进而三棱锥P QEF -的体积为定值.故A ，C ，D 选项为真命题，B 为假命题.考点：空间点线面位置关系.9.已知函数()cos sin 4f x x x π⎛⎫=+ ⎪⎝⎭，则函数()f x 满足（ ）A. 最小正周期为2T π=B. 图像关于点2,84π⎛- ⎝⎭对称C. 在区间0,8π⎛⎫⎪⎝⎭上为减函数 D. 图像关于直线8x π=对称【答案】D 【解析】∵函数f （x ）=cos （x +4π）sinx =（22cosx ﹣22sinx ）•sinx =24sin2x ﹣22•122cos x - =2（sin2x +cos2x 2=12sin （2x +4π）2故它的最小正周期为2π2π=，故A 不正确； 令x =8π，求得f （x ）=12222+，为函数f （x ）的最大值，故函数f （x ）的图象关于直线x=8π对称，且f （x ）的图象不关于点（8π2B 不正确、D 正确； 在区间（0，8π）上，2x +4π∈（4π，2π），f （x ）=12sin （2x +4π）+24为增函数，故C 不正确， 故选D ．10.设锐角ABC ∆的三个内角,,A B C 的对边分别为,,a b c 且1c =，2A C =，则ABC ∆周长的取值范围为（ ）A. (0,2+B. (0,3+C. (2++D. (2+【答案】C 【解析】因为△ABC 为锐角三角形，所以02A π<<，02B π<<，02C <<π，即022C π<<，022C C ππ<--<，02C <<π，所以64C ππ<<，cos 2C <<；又因为2A C =，所以sin 2sin cos A C C =，又因为1c =，所以2cos a C =；由sin sin b cB C=，即2sin sin 34cos 1sin sin c B C b C C C ===-，所以24cos 2cos a b c C C ++=+，令cos t C =，则t ∈⎝⎭，又因为函数242y t t =+在⎝⎭上单调递增，所以函数值域为(2， 故选C点睛：本题解题关键是利用正弦定理实现边角的转化得到ABC ∆周长关于角C 的函数关系，借助二次函数的单调性求最值，易错点是限制角C 的取值范围.11.已知函数()f x 满足对任意实数,m n ，都有()()()1f m n f m f n +=+-，设()()(0,1)1xx a g x f x a a a =+>≠+，(ln 2019)2018g =，1ln 2019g ⎛⎫= ⎪⎝⎭（ ）A. 2018B. 2017C. -2016D. -2015【答案】D 【解析】 【分析】通过取特殊值，可得(0)1f =，进一步可得()()2f x f x +-=，然后经过计算可得111x xx x a a a a --+=++，最后代值计算，可得结果.【详解】由题可知：()()()1f m n f m f n +=+- 令0m n ==，可得(0)1f =令,==-m x n x ，则()()()1f x x f x f x -=+--所以()()2f x f x +-=又111x x x x a a a a --+=++ 由()()1xx a g x f x a =++，所以()()()()311x xx x a a g x g x f x f x a a ---+=-+++=++又()1lnln 20192019g g ⎛⎫=- ⎪⎝⎭所以1ln (ln 2019)32019g g ⎛⎫+= ⎪⎝⎭，由(ln 2019)2018g = 所以1ln 20152019g ⎛⎫=- ⎪⎝⎭故选：D【点睛】本题考查抽象函数的应用，难点在于发现()()2f x f x +-=，111x xx x a a a a --+=++，考验观察能力以及分析问题的能力，属中档题.12.已知函数,0()2(1),0xx m e mx x f x e x x -⎧++<⎪=⎨⎪-≥⎩（e为自然对数的底），若方程()()0f x f x -+=有且仅有四个不同的解，则实数m 的取值范围是（ ）． A. (0,)e B. (,)e +∞ C. (0,2)e D. (2,)e +∞【答案】D 【解析】 【分析】首先需要根据方程特点构造函数()()()F x f x f x =+-,将方程根的问题转化为函数零点问题，并根据函数的奇偶性判断出函数()F x 在()0,+∞上的零点个数，再转化成方程1e 2xx m x ⎛⎫=-⎪⎝⎭解的问题，最后利用数形结合思想，构造两个函数，转化成求切线斜率问题，从而根据斜率的几何意义得到解.【详解】因为函数()()()F x f x f x =-+是偶函数，()00F ≠，所以零点成对出现，依题意，方程()()0f x f x -+=有两个不同的正根，又当0x >时，()e 2x mf x mx-=-+，所以方程可以化为： e e e 02x x x m mx x -++-=，即1e 2xx m x ⎛⎫=- ⎪⎝⎭，记()e (0)xg x x x =>，()()e10xg x x ='+>，设直线12y m x ⎛⎫=- ⎪⎝⎭与()g x 图像相切时的切点为(),e tt t ，则切线方程为()()e e 1tty t t x t -=+-，过点1,02⎛⎫⎪⎝⎭，所以()1e e 112t t t t t t ⎛⎫-=+-⇒= ⎪⎝⎭或12-（舍弃），所以切线的斜率为2e ，由图像可以得2e m >.选D.【点睛】本题考查函数的奇偶性、函数零点、导数的几何意义，考查函数与方程思想、数形结合思想、转化与化归思想，突显了直观想象、数学抽象、逻辑推理的考查.属中档题.第Ⅱ卷（共90分）二、填空题（每题5分，满分20分，将答案填在答题纸上）13.已知点(,)P x y 在不等式组20,10,220x y x y -≤⎧⎪-≤⎨⎪+-≥⎩，表示的平面区域上运动，则z x y =-的取值范围是__________ 【答案】[-1,2] 【解析】 【分析】画出可行域，然后利用目标函数的等值线y x =在可行域中进行平移，根据z 或含z 的式子的含义，目标函数取最值得最优解，可得结果. 【详解】如图令0z =，则y x =为目标函数的一条等值线 将等值线延y 轴正半轴方向移到到点()0,1A 则点()0,1A 是目标函数取最小值得最优解 将等值线延y 轴负半轴方向移到到点()2,0B 则点()2,0B 是目标函数取最大值得最优解 所以min max 011,202z z =-=-=-= 所以[]1,2z ∈- 故答案为：[]1,2-【点睛】本题考查线性规划，一般步骤：（1）作出可行域；（2）理解z 或含z 的式子的含义，利用等值线在可行域中移动找到目标函数取最值得最优解，属基础题.14.已知点(22,0)Q 及抛物线24x y =上的动点(,)P x y ，则y PQ +的最小值为______. 【答案】2 【解析】试题分析：设抛物线的焦点为F （0,1），由抛物线的知：=1+y PQ PF PQ +-，所以y PQ +的最小值为12FQ -=.考点：抛物线定义；两点间的距离公式．点评：把“y PQ +的最小值”应用抛物线的定义转化为“1FQ -”，是解题的关键，考查了学生分析问题、解决问题的能力．15.已知数列{}n a 为正项的递增等比数列，1582a a +=，2481a a ⋅=，记数列2n a ⎧⎫⎨⎬⎩⎭的前n 项和为n T ，则使不等式12019113n T ->成立的最大正整数n 的值是_______． 【答案】6 【解析】 【分析】设等比数列{a n }的公比q ，由于是正项的递增等比数列，可得q ＞1．由a 1+a 5=82，a 2•a 4=81=a 1a 5，∴a 1，a 5，是一元二次方程x 2﹣82x+81=0的两个实数根，解得a 1，a 5，利用通项公式可得q ，a n ．利用等比数列的求和公式可得数列{2n a }的前n 项和为T n ．代入不等式2019|13T n ﹣1|＞1，化简即可得出． 【详解】数列{}n a 为正项的递增等比数列，1582a a +=，a 2•a 4=81=a 1a 5， 即15158281a a a a +=⎧⎨⋅=⎩解得15181a a =⎧⎨=⎩，则公比3q =，∴13n n a -=，则2122221333n n T -=++++L 11132311313n n -⎛⎫=⨯=- ⎪⎝⎭-， ∴12019113n T ->，即1201913n ⨯>，得32019n <，此时正整数n 的最大值为6. 故答案为6.【点睛】本题考查了等比数列的通项公式与求和公式、一元二次方程的解法、不等式的解法，考查了推理能力与计算能力，属于中档题． 16.已知函数()sin cos x f x x x =-，23,34x ππ⎡⎤∈⎢⎥⎣⎦，则()f x 的最小值是__________【答案】43π- 【解析】 【分析】计算导数，然后构造函数()cos sin h x x x x =+，利用导数研究该函数的单调性进而判断原函数的单调性，可得结果.【详解】由题可知：'2cos si ()cos co n s f x x xxx x =-+ 令()cos sin h x x x x =+，则()'sin sin cos cos h x x x x x x x =-++=由23,34x ππ⎡⎤∈⎢⎥⎣⎦，所以cos 0x < 所以()'0h x <，则()h x 在23,34x ππ⎡⎤∈⎢⎥⎣⎦递减 所以()min 3333cos sin 4444h x h ππππ⎛⎫==+⎪⎝⎭()min 31024h x π⎫=->⎪⎝⎭，又cos 0x < 则'2cos sin ()cos 0cos f x x x x xx=-+>所以函数()f x 在23,34x ππ⎡⎤∈⎢⎥⎣⎦递增 所以min 2223()sin 233cos 3f x f ππππ⎛⎫==- ⎪⎝⎭所以min 243()12322f x ππ=-=---故答案为：43π-【点睛】本题考查函数在区间的最值，难点在于构造函数二次求导，注意细节，需要通过判断函数在区间的单调情况才能代值计算，考查对问题的分析能力，属中档题.三、解答题（解答应写出文字说明、证明过程或演算步骤.）17.已知数列{}n a 的前n 项和为n S ，且221n n n S na a =+-． （1）求数列{}n a 的通项公式；（2）若数列21n a ⎧⎫⎨⎬⎩⎭的前n 项和为n T ，证明：4n T <．【答案】（1）1()2n n a n N *+=∀∈；（2）见解析 【解析】 【分析】(1)根据前n 项和与通项间的关系得到，221n n n S na a =+-，()1112121n n n S n a a ---=-+-，两式做差即可得到数列11n n a a n n -=+，数列1n a n ⎧⎫⎨⎬+⎩⎭为常数列，112n a n =+，即12n n a +=；（2）根据第一问得到()()22144114111n a n n n n n ⎛⎫=<=- ⎪++⎝⎭+，裂项求和即可. 【详解】（1）当1n =时，111221S a a =+-，即11a =，当2n ≥时，221n n n S na a =+- ①， ()1112121n n n S n a a ---=-+- ② -①②，得()112122n n n n n a na n a a a --=--+-，即()11n n na n a -=+，所以11n n a a n n -=+，且1122a =， 所以数列1n a n ⎧⎫⎨⎬+⎩⎭为常数列，112n a n =+，即()*12nn a n N +=∀∈． （2）由（1）得12n n a +=，所以()()22144114111n a n n n n n ⎛⎫=<=- ⎪++⎝⎭+，所以()()22224444444423412233411n T n n n =++++<++++⨯⨯⨯++L L ，11111111414142233411n n n L ⎡⎤⎛⎫⎛⎫⎛⎫⎛⎫⎛⎫=-+-+-++-=-< ⎪ ⎪ ⎪ ⎪ ⎪⎢⎥++⎝⎭⎝⎭⎝⎭⎝⎭⎝⎭⎣⎦．【点睛】这个题目考查的是数列通项公式的求法及数列求和的常用方法；数列通项的求法中有常见的已知n S 和n a 的关系，求n a 表达式，一般是写出1n S -做差得通项，但是这种方法需要检验n=1时通项公式是否适用；数列求和常用法有：错位相减，裂项求和，分组求和等．18.如图（1），等腰梯形ABCD ，2AB =，6CD =，AD =E ，F 分别是CD 的两个三等分点，若把等腰梯形沿虚线AF 、BE 折起，使得点C 和点D 重合，记为点P ， 如图（2）．（1）求证：平面PEF ⊥平面ABEF ；（2）求平面PAE 与平面PAB 所成锐二面角的余弦值． 【答案】（1）详见解析；（2）57. 【解析】 【分析】（1）推导出BE EF ⊥，BE PE ⊥，从而BF ⊥面PEF ，由此能证明平面PEF ⊥平面ABEF ； （2）过点P 作PO EF ⊥于O ，过点O 作BE 的平行线交AB 于点G ，则PO ⊥面ABEF ，以O 为原点，以OG ，OE ，OP 所在直线分别为x 轴、y 轴、z 轴建立空间直角坐标系，利用向量法能求出平面PAE 与平面PAB 所成锐二面角的余弦值．【详解】（1）证明：Q 四边形ABCD 为等腰梯形，2AB =，6CD =，22AD =，E ，F 是CD 的两个三等分点，∴四边形ABEF 是正方形，∴BE EF ⊥，Q BE PE ⊥，且PE EF E ⋂=，∴BF ⊥面PEF ，又BF ⊂平面ABEF ，∴平面PEF ⊥平面ABEF ；（2）过点P 作PO EF ⊥于点O ，过点O 作BE 的平行线交AB 于点G ，则PO ⊥面ABEF ，以O 为坐标原点，以OG ，OE ，OP 所在直线分别为x 轴、y 轴、z 轴建立空间直角坐标系，如图所示：则(2,1,0)A -，(2,1,0)B ，(0,1,0)E ，3)P ，∴(2,2,0)AE =-u u u v ,(0,3)EP =-u u u v ,(0,2,0)AB =u u u v,(2,1,3)PA =-u u u v ，设平面PAE 的法向量(,,)n x y z =v，则22030n AE x y n EP y z⎧⋅=-+=⎪⎨⋅=-+=⎪⎩u u u v v u u u v v ，取1z =，得(3,3,1)n =v ， 设平面PAB 的法向量(,,)m x y z =u v，则00m AB m PA ⎧⋅=⎨⋅=⎩u u u v v u u u v v ，∴20230y x y z =⎧⎪⎨--=⎪⎩，取3x =，得：(3,0,2)m =u v ，设平面PAE 与平面PAB 所成锐二面角为θ，则5cos 777n m n m θ⋅===⋅⋅r rr r ． ∴平面PAE 与平面PAB 所成锐二面角的余弦值为57． 【点睛】本题考查平面与平面垂直的判定以及二面角平面角的求法，属于常考题.19.某企业对设备进行升级改造，现从设备改造前后生产的大量产品中各抽取了100件产品作为样本，检测一项质量指标值，若该项指标值落在[20,40)内的产品视为合格品，否则为不合格品，图1是设备改造前样本的频率分布直方图，表1是设备改造后的频数分布表.表1，设备改造后样本的频数分布表: 质量指标值 [)15,20[)20,25[)25,30[)30,35[)35,40[)40,45频数 2184814162（1）请估计该企业在设备改造前的产品质量指标的平均数；（2）企业将不合格品全部销毁后，并对合格品进行等级细分，质量指标值落在[25，30)内的定为一等品，每件售价240元，质量指标值落在[20，25)或[30，35)内的定为二等品，每件售价180元，其它的合格品定为三等品，每件售价120元.根据表1的数据，用该组样本中一等品、二等品、三等品各自在合格品中的频率代替从所有产品中抽到一件相应等级产品的概率，现有一名顾客随机购买两件产品，设其支付的费用为X （单位：元），求X 得分布列和数学期望. 【答案】(1) 30.2；(2)分布列见解析， 400. 【解析】 【分析】（1）每个矩形的中点横坐标与该矩形的纵坐标、组距相乘后求和可得平均值；（2）X 的可能取值为：240， 300，360, 420, 480，根据直方图求出样本中一、二、三等品的频率分别为111,,236，利用独立事件与互斥事件概率公式求出各随机变量对应的概率，从而可得分布列，进而利用期望公式可得X 的数学期望. 【详解】(1)样本的质量指标平均值为0.0417.50.1622.50.427.50.1232.51837.51042.5⨯+⨯+⨯+⨯+⨯+⨯30.2=.根据样本质量指标平均值估计总体质量指标平均值为30.2 .（2）根据样本频率分布估计总体分布，样本中一、二、三等品的频率分别为111,,236， 故从所有产品中随机抽一件，是一、二、三等品的概率分别为111,,236， 随机变量X 的取值为：240， 300，360, 420, 480，()()12111111240;3006636369P X P X C ==⨯===⨯⨯=；()()112211115111360;420263318233P X C P X C ==⨯⨯+⨯===⨯⨯=，()111480224P X ==⨯=，所以随机变量X 的分布列为：()115112403003604204804003691834E X ∴=⨯+⨯+⨯+⨯+⨯=. 【点睛】本题主要考查直方图的应用，互斥事件的概率公式、独立事件同时发生的概率公式以及离散型随机变量的分布列与数学期望，属于中档题. 求解数学期望问题，首先要正确理解题意，其次要准确无误的找出随机变量的所有可能值，计算出相应的概率，写出随机变量的分布列，正确运用均值、方差的公式进行计算，也就是要过三关：（1）阅读理解关；（2）概率计算关；（3）公式应用关.20.设椭圆()2222:10x y C a b a b +=>>的离心率为2，圆22:2O x y +=与x 轴正半轴交于点A ，圆O 在点A 处的切线被椭圆C 截得的弦长为 （1）求椭圆C 的方程；（2）设圆O 上任意一点P 处的切线交椭圆C 于点,M N ，试判断·PM PN 是否为定值？若为定值，求出该定值；若不是定值，请说明理由．【答案】（1）22163x y +=； （2）见解析.【解析】 【分析】（I ）结合离心率，得到a,b,c 的关系，计算A 的坐标，计算切线与椭圆交点坐标，代入椭圆方程，计算参数，即可．（II ）分切线斜率存在与不存在讨论，设出M,N 的坐标，设出切线方程，结合圆心到切线距离公式，得到m,k 的关系式，将直线方程代入椭圆方程，利用根与系数关系，表示OM ON ⋅u u u u r u u u r，结合三角形相似，证明结论，即可．【详解】(Ⅰ)设椭圆的半焦距为c 知，b c a ，==， ∴椭圆C 的方程可设为222212x y b b+=.易求得)A，∴点在椭圆上，∴222212b b +=， 解得2263a b ⎧=⎨=⎩，∴椭圆C方程为22163x y +=.(Ⅱ)当过点P 且与圆O 相切的切线斜率不存在时，不妨设切线方程为x =MN，-，0OM ON OM ON ==⋅=u u u u ru u u r u u u u r u u u r，，，∴OM ON ⊥.当过点P 且与圆O 相切的切线斜率存在时，可设切线的方程为y kx m =+，()()1122M x y N x y ，，，，=()2221m k =+.联立直线和椭圆的方程得()2226x kx m ++=，∴()222124260k x kmx m +++-=，得()()()222122212244122604212621km k m km x x k m x x k ⎧∆=-+->⎪⎪⎪+=-⎨+⎪⎪-=⎪+⎩.∵()()1122OM x y ON x y ==u u u u r u u u r，，，， ∴()()12121212OM ON x x y y x x kx m kx m ⋅=+=+++u u u u r u u u r，()()()22222121222264112121m km kx xkm x x m kkm m k k --=++++=+⋅+⋅+++ ()()()()2222222222222126421322663660212121k m k m m k k k mk k k k +--+++----====+++， ∴OM ON ⊥.综上所述，圆O 上任意一点P 处的切线交椭圆C 于点M N ，，都有OM ON ⊥. 在Rt OMN ∆中，由OMP ∆与NOP ∆相似得，22OP PM PN =⋅=为定值.【点睛】本道题考查了椭圆方程的求解，考查了直线与椭圆位置关系，考查了向量的坐标运算，难度偏难．21.已知函数21()4ln 22f x x a x x =---，其中a 为实数. （1）求函数()y f x =的单调区间；（2）若函数()y f x =有两个极值点12,x x ，求证：()()126ln f x f x a +<-. 【答案】（1）见解析；（2）证明见解析 【解析】 【分析】（1）计算导数，采用分类讨论的方法，4a ≥，04a <<与0a ≤，根据导数的符号判定原函数的单调性，可得结果.（2）根据（1）的结论，可得()()124ln f x f x a a a +=+-，然后构造新函数，通过导数研究新函数的单调性，并计算最值，然后与0比较大小，可得结果. 【详解】（1）函数()y f x =的定义域为(0,)+∞，24()4a x x af x x x x'-+=--=-①若1640a -≤，即4a ≥时，则()0f x '≤，此时()f x 的单调减区间为(0,)+∞； ②若1640a ->，04a <<时，令'()0f x =的两根为2±(()0,22x ∈⋃++∞，'()0f x <(2x ∈，'()0f x >所以()f x 的单调减区间为(0,2，(2)++∞，单调减区间为(22-+.③当0a ≤时，(0,2x ∈，'()0f x >(2)x ∈+∞，'()0f x <此时()f x 的单调增区间为(0,2，单调减区间为(2)++∞. （2）当04a <<时，函数()y f x =有两个极值点12,x x ， 且124x x +=，12x x a =.()()2212111222114ln 24ln 222f x f x x a x x x a x x +=---+---则()()()()()221212121214ln 42f x f x x x a x x x x +=+--+- 则()()()212116ln 4244ln 2f x f x a a a a a a +=----=+- 要证()()126ln f x f x a +<-，只需证ln ln 20a a a a --+>. 构造函数()ln ln 2g x x x x x =--+， 则'11()1ln 1ln g x x x x x=+--=-， '()g x 在(0,4)上单调递增，又'(1)10g =-<，'1(2)ln 202g =->，且'()g x 在定义域上不间断， 由零点存在定理可知：'()0g x =在(1,2)上唯一实根0x ，且001ln x x =. 则()g x 在()00,x 上递减，()0,4x 上递增， 所以()g x 的最小值为()0g x .因为()00000ln ln 2g x x x x x =--+，()0000011123g x x x x x ⎛⎫=--+=-+ ⎪⎝⎭ 当0(1,2)x ∈，00152,2x x ⎛⎫+∈ ⎪⎝⎭，则()00g x >， 所以()0()0g x g x ≥>恒成立. 所以ln ln 20a a a a --+>， 所以()()126ln f x f x a +<-，得证.【点睛】本题考查导数的综合应用，难点在于分类讨论思想的应用，同时掌握构造函数，化繁为简，考验分析能力以及极强的逻辑推理能力，综合性较强，属难题.请考生在22、23两题中任选一题作答，如果多做，则按所做的第一题记分. 选修4-4：坐标系与参数方程22.在直角坐标系xOy 中，以坐标原点为极点，x 轴正半轴为极轴建立极坐标系，曲线1C 的极坐标方程为4cos (0)ρθρ=>.M 为曲线1C 上的动点，点P 在射线OM 上，且满足||||20OM OP ⋅=.（Ⅰ）求点P 的轨迹2C 的直角坐标方程； （Ⅱ）设2C 与x 轴交于点D ，过点D 且倾斜角为56π的直线l 与1C 相交于,A B 两点，求||||DA DB ⋅的值.【答案】（Ⅰ）5x =；（Ⅱ）5. 【解析】 【分析】（Ⅰ）首先依据动点,P M 的极坐标的关系找到点P 的极坐标方程，再化为直角坐标方程；（Ⅱ）首先根据条件确定直线l 的参数方程，依据参数t 的几何意义，结合解方程，利用韦达定理得到解. 【详解】（Ⅰ）设P 的极坐标为(),(0)ρθρ>，M 的极坐标为()11,(0)ρθρ>， 由题设知1,4cos OP OM ρρθ===.所以4cos 20ρθ=， 即2C 的极坐标方程cos 5(0)ρθρ=>，所以2C 的直角坐标方程为5x =.（Ⅱ）交点()5,0D ，所以直线l的参数方程为5,212x t y t⎧=-⎪⎪⎨⎪=⎪⎩（t 为参数），曲线1C 的直角坐标方程()22400x y x x +-=≠，代入得：250t -+=，70∆=>， 设方程两根为12,t t ，则12,t t 分别是,A B 对应的参数， 所以125DA DB t t ⋅==.【点睛】本题考查直线与圆的极坐标方程、极坐标方程与直角坐标方程的互化、直线参数方程的应用，突显了直观想象的考查.选修4-5：不等式选讲23.已知函数1()||()3f x x a a =-∈R . （1）当2a =时，解不等式1()13x f x -+≥； （2）设不等式1()3x f x x -+≤的解集为M ，若11,32M ⎡⎤⊆⎢⎥⎣⎦，求实数a 的取值范围. 【答案】（1）{|0x x ≤或1}x ≥；（2）14,23⎡⎤-⎢⎥⎣⎦【解析】 【分析】（1）使用零点分段法，讨论分段的取值范围，然后取它们的并集，可得结果.（2）利用等价转化的思想，可得不等式|31|||3x x a x -+-≤在11,32⎡⎤⎢⎥⎣⎦恒成立，然后解出解集，根据集合间的包含关系，可得结果. 【详解】（1）当2a =时，原不等式可化为|31||2|3x x -+-≥. ①当13x ≤时， 则33012x x x -++-⇒≤≥，所以0x ≤； ②当123x <<时， 则32113x x x -+≥⇒≥-，所以12x ≤<； ⑧当2x ≥时，则332132x x x +≥⇒≥--，所以2x ≥. 综上所述：当2a =时，不等式的解集为{|0x x ≤或1}x ≥. （2）由1||()3x f x x -+≤， 则|31|||3x x a x -+-≤， 由题可知：|31|||3x x a x -+-≤在11,32⎡⎤⎢⎥⎣⎦恒成立，所以31||3x x a x -+-≤，即||1x a -≤， 即11a x a -≤≤+，所以1114312312a a a ⎧-≤⎪⎪⇒-≤≤⎨⎪+≥⎪⎩ 故所求实数a 的取值范围是14,23⎡⎤-⎢⎥⎣⎦.【点睛】本题考查零点分段求解含绝对值不等式，熟练使用分类讨论的方法，以及知识的交叉应用，同时掌握等价转化的思想，属中档题.。

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1.What does the woman advise the man to do?A.Buy a computer.B.Talk with his boss.C.Start his own business.2.What is the weather like?A.Windy.B.Sunny.C.Snowy.3.How does the man sound in the end?A.Surprised.B.Humorous.C.Angry.4.What does the woman mean?A.She isn’t interested in sports.B.She is very excited about the news.C.She supports another basketball team.5.What are the speakers mainly doing?A.Tasting the coffee.B.Choosing a café.C.Asking the way.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。