2020届湖南长沙雅礼中学高三第2次月考试卷-英语(含答案)
湖南省雅礼中学2023-2024学年高三上学期月考卷(三)英语试题
湖南省雅礼中学2023-2024学年高三上学期月考卷（三）英语试题学校:___________姓名：___________班级：___________考号：___________一、短对话1．Where will the woman spend her vacation this year?A．On the beach.B．In the forest.C．In the mountain. 2．When did Mr. Robin start the meeting?A．At 10: 30 a. m.B．At 11:30 a. m.C．At 1: 30 p. m. 3．What is the probable relationship between the speakers?A．Husband and wife.B．Colleagues.C．Repairman andcustomer.4．What is the woman's opinion about her old laptop?A．It is heavy.B．It doesn't work properly.C．It is slow to start. 5．What are the speakers talking about?A．Looking for a job.B．Designing a website.C．Renting an apartment.二、长对话听下面一段较长对话，回答以下小题。
6．What is Sally’s problem?A．She lost Jake’s files.B．She broke Jake’s computer.C．She doesn’t get along well with Jake.7．What does the man speaker suggest Sally do?A．Download the files.B．Have a talk with Jake.C．Learn more about computers.听下面一段较长对话，回答以下小题。
湖南省长沙市第一中学2023-2024学年高三上学期第二次月考英语试题
湖南省长沙市第一中学2023-2024学年高三上学期第二次月考英语试题学校:___________姓名：___________班级：___________考号：___________一、阅读理解“Unfortunately, 85 percent of what makes us attractive or less to mosquitoes(蚊子) is hardwired in our genetic circuit board,” says Winegard, author of The Mosquito: A Human History of Our Deadliest Predator. Still, there are ways to outsmart summer’s most annoying party crashers, especially if all you want is to enjoy an evening on your patio (露台).Know your blood typeOnly female mosquitoes feed on humans, and for good reason: The proteins in your blood help them grow and mature their eggs. “She’s just being a good mom,” Wineguard says. “People with blood type O are her top of choice. They get bitten twice as much as people with blood type A, with blood type B falling in between.”Stay cool“Mosquitoes hunt by both smell and sight,” Wineguard says. “They can smell the carbon dioxide and see the heat signature of their target.” Avoiding alcohol can keep your body temperature lower— making you harder to find — so consider choosing a cocktail instead.Wear light colorsAvoiding dark clothing can also keep you cooler, but that’s not the only reason it may offer relief. Mosquitoes, like many biting flies, are attracted to darker colors. The thinking behind this is that the animals they typically feed upon are larger, dark-bodied mammals(哺乳动物).Get rid of standing waterEven a glass of drinking water left on the deck can become a breeding ground for mosquito eggs — and mother mosquitoes lay about 100 eggs at a time. “They don’t need very much at all to breed. It can be a backyard toy , like a truck that has a bit of water in it, or a crushed pop can,” says Winegard. If you get rid of it, they’ll go somewhere else to lay their eggs.1．What’s the intention of this text?A．To introduce a new book.B．To offer professional tips.C．To analyze a study of insects.D．To suggest throwing a party.2．Why does a female mosquito feed on human blood?A．To hatch more eggs.B．To raise a large family.C．To identify blood types.D．To fully develop her body.3．What can we learn about mosquitoes according to Winegard?A．They can trace the smell of alcohol.B．They have energy-locating abilities.C．They feed off dark-bodied animals.D．They need abundant water to breed.The Malaysian actress, Michelle Yeoh, 60, shared some wisdom with the American Film Institute’s newest graduating class in a speech as she accepted an honorary doctorate of fine arts at the class of 2022 graduation ceremony.She recalled her early years in the industry. After an injury dashed her dreams of going into ballet, Yeoh bounced back at a gym where several stuntmen(特技替身演员)trained and ended up learning some tricks of the trade from them.“The first thing they taught me what to do was to tuck and roll, then how to fall on my side, and then how to fall on my back. And after a while, it dawned on me that they were teaching me how to fall,” she recalled. “And they said to me, ‘How are you going to go up if you don’t know how to come down?’” “That lesson sticks with me to this day. I had to learn how to fall. Well, you could say I learned it in my bones, literally,” Yeoh added.The actress mentioned jumping off a 20-foot highway overpass for one stunt, in which she over-rotated (旋转), causing her back to fold in half and a stunt went wrong. “I didn’t land properly, but I completed the scene,” she said.“These moments taught me perseverance, courage and humility,” she said. “They also taught me to hone my skills and eventually progress to the point where I was running on rooftops and jumping onto moving trains. I’m not asking you all to do that, okay? What I want to share with you today is that our slips and stumbles(绊跌)are the secrets to our flight. Trust me, that’s part of the deal. Success without failure is called luck. It cannot really be repeated or relied upon. It is from failure that we learn and grow,” Yeoh continued.The Crazy Rich Asians star concluded her speech: “Be courageous, take chances, break barriers, be proud of what makes you unique.” “And most importantly, don’t be afraid to fall, for you are learning to fly,” Yeoh said.4．What can we learn about Michelle Yeoh from the first two paragraphs?A．She was tricked by several stuntmen.B．She was passionate about working out in a gym.C．She won a doctor’s degree in fine arts despite her old age.D．She was terribly defeated by an injury and discouraged in her early years.5．What lesson did Michelle Yeoh learn from the stuntmen?A．God helps those who help themselves.B．Misfortune might be a blessing in disguise.C．Successful people are learning experiences with others.D．The greatest glory is not in never falling, but in rising every time we fall.6．What does the underlined word “hone”in paragraph 5 mean?A．Believe.B．Sharpen.C．Restore.D．Dominate. 7．What are the keys to our success according to the text?A．Mistakes and failure.B．Luck and humility.C．Courage and pride.D．Opportunities and skills.“It’s a natural question,”Dr. Holt-Lunstad said the “ideal”number of friends. “Just like we have guidelines and recommendations for the amount of sleep we get and how physically active we are, this is health relevant.” While she and other friendship researchers admit there aren’t many studies that have specifically tackled the question of how many friends people should aim for, those that have been done offer a range.Dr. Degges-white recently conducted a survey of 297 adults, which has not been published or subject to peer review but found that 55 percent of participants believed two to three close friends was ideal, while 31 percent thought four to six was was the goal. But friendship and intimacy are subjective, and there isn’t a widely used scale researchers share to define those concepts across studies. It’s also unclear how social media factors into all of this, as research suggests the size of a person’s online network may not have any meaningful impact on their perceived well-being.While friendship research offers some standards, it may be more useful for most of us to consider if you need more friends. Dr. Marisa Franco recommends starting with a fairly obvious but powerful question: Do I feel lonely? “Also, different people bring out different parts of us. So when you have a larger friend group, you’re able to experience this side of yourself that loves golf, and this side that loves cars,” she added. “If you feel like your identity has sort of shrunk, or you’re not feeling quite like yourself, that might indicate youneed different types of friends.”Of course, making friends in adulthood isn’t always easy. Research shows people struggle with it because they find it difficult to trust new people. For those reasons, it is often easier to start by reawakening old relationships. The amount of time you actually spend with your friends matters, too. Franco suggests that on average, very close friendships tend to take around 200 hours to develop. But spending time with friends you feel ambivalent (情绪复杂的) about — because they’re unreliable, critical, competitive or any of the many reasons people get under our skin — can be bad for your health.8．Which statement would Dr. Holt-Lunstad probably agree with?A．Healthy friendships contribute to quality sleep.B．There have been guidelines for making friends.C．Two to six close friends may be the most ideal.D．Friendships can be crucial factor in well-being.9．How was Dr. Degges-White’s survey?A．It summarized the statistics in previous studies.B．It set standards on the exact number of friends.C．It distinguished between friendship and intimacy.D．It dismissed the influences of social media factors.10．According to Franco, you have to make new friends if _________.A．your friend circle is large enough B．you have a wide range of hobbiesC．your personal identities are restricted D．you lead an unhappy adulthood life 11．What matters in maintaining close friendships according to Franco?A．Quantities of time.B．Meeting frequency.C．Your healthy moods.D．Personalities of friends.Many robots track objects by “sight” as they work with them, but optical (视觉的) sensors can’t take in an item’s entire shape when it’s in the dark or partially blocked from view. Now a new low-cost technique lets a robotic hand “feel” an unfamiliar object’s form — and skillfully handle it based on this information alone.Roboticist, Xiaolong Wang in University of California, San Diego and his team wanted to find out if complex coordination (协调) could be achieved in robotics using only simple touch data. The researcher attached 16 contact sensors, each costing about $12, to the palmand fingers of a four -fingered robot hand. These sensors simply indicate if an object is touching the hand or not. “While one sensor doesn’t catch much, a lot of them can help you capture different aspects of the object,” Wang says. In this case, the robot’s task was to rotate (旋转) items placed in its palm.The researchers first connected a large volume of touch data as a virtual robot hand practiced rotating objects, including ball. Using binary contact information (“touch” or “no touch”) from each sensor, the team built a computer model that determines an object’s position at every step of the handling process and moves the fingers to rotate it smoothly and stably.Next they transferred this capability to operate a real robot hand, which successfully manipulated (操纵) previously unencountered objects such as apples, tomatoes, soup cans and rubber ducks. Transferring the computer model to the real world was relatively easy because the binary sensor data were so simple; the model didn’t rely on accurate measurements.Digging into what the robot hand perceives, Wang and his colleagues found that it can re-create the entire object’s form from touch data, informing its actions. He and his team are set to present thier handiwork at an international conference called Robotics: Science and Systems.New York University’s Lerrel Pinto, who studies robots’ interactions with the real world, wonders whether the system would become less effective at more complicated tasks including opening a bottle cap. Wang’s group aims to tackle more complex movements in future work as well as to add sensors in places such as the sides of the fingers. The researchers will also try adding vision to improve touch data for handling complicated shapes.12．What may contribute to the ineffectiveness of the optical sensors?A．Poor visibility.B．Blocked roads.C．Complicated tasks.D．Inaccurate calculation.13．What do paragraphs 3-4 focus on?A．Stimulating the robot fingers to move the items steadily.B．Increasing the precision of touch of the robot hand.C．Comparing the computer world with the real circumstances.D．Testing if touch information can facilitate the formation of the object shape. 14．What is the attitude of Lerrel Pinto towards the system?A．Neutral.B．Suspicious.C．Favorable.D．Pessimistic.15．What is the best title for the text?A．Robotics: Science and SystemB．New Robot Rotates Items SkillfullyC．New Robot Hand Works by Feel, Not SightD．From the Computer Model to the Real Robot Hand二、七选五Which is more important for people, book learning or experience? Some have spent their lives studying and gradually acquiring valuable deep knowledge. They are afraid to start andthe book, make mistakes, and learn from this experience.The debate between book learning and experience has been going on for a long time. There is no clear “right answer” yet, but there is strong evidence that experience gives us important skills that can’t be learned in books.17 Of course, reading the best books on learning gives someone knowledge, but experience gives know-how. It comes from practicing again and again. Professionals can make themselves because they devote their work, practice, and time to obtaining this position instead of managing to read books only. This distinguishes them from all the others.Reading more books about something doesn’t lead to success. You can acquire a lot of knowledge by reading, but there are also ways to accumulate knowledge through experience. Knowledge is theoretical, but experience is distinguished by the fact that you can put into practice what you have learned in a book. 18Book learning to understand a concept is important. But if you can’t understand the application of the concept in real time, the concept is useless. Experience allows you to put the learned concepts into practice. 19 You can’t effectively learn important skills without applying these concepts to real life.Certainly, the experience can lead to failure. But you can also learn from that failure and lead to success. 20 Therefore, experience is your greatest ally(盟友) in professional development if you want to understand the theory behind the concept, become an expert inthis field, keep the technique in mind, and gain valuable insights through failure.A．In contrast, others don’t worry about anything.B．You can learn a lot from books on self-learning.C．Of course, with these concepts, experience is acquired.D．This is valuable knowledge that is not found in any book.E．It is also an opportunity to test and challenge your knowledge.F．Through experience, you can also learn how to interact with people.G．Neither scientists nor doctors have read books only and become experts.三、完形填空Growing up in New Delhi, I saw Barbie as more than just a doll. She was the centralbedroom floor.As much as I loved Barbie, our time together could only last so long. Eventually, I grew 23 that I still played with my Barbie dolls while my middle-school friends had all moved onto more “mature” 24 . Barbie became similar with being a fake, “plastic” girl, whose bright pink clothing 25 my friends and me.By the tender age of 12, my friends and I had become 26 all girlish things, and Barbie topped our list of items to grow out of. Every 27 we took up instead seemed either gender-neutral or traditionally masculine (男子气概). For a 28 period I took up watching football to look cool (say exactly a month).Looking back, I feel like we were missing the point: Barbie was simply a blank canvas upon which to draw our ideas. It was our own 29 that we had come to abuse her for wearing pink clothes and having blond hair. That is why I appreciate the way the Barbie movie is being 30 . The movie 31 and Barbie’s bright pink colors are everywhere — there are 100 or more co-brand products, and you can get everything Barbie-pink from sports facilities to make-up and shoes. In Malibu, there is a pink hotel 32 after Barbie’s pink Dream House.In an interview, the director Gerwig said the team had many meetings just to settle on the correct 33 of pink for the movie — one that was beautiful but “not too fashionable”, she said, “because when I was a little girl, I loved the pinkest, brightest things”,without a hint of the 34 that I and my peers had of Barbie all those years ago, which would have been really important to me as an adolescent girl who often felt 35 in her femininity (女子气质).21．A．theme B．character C．argument D．conflict 22．A．assigned B．gathered C．created D．staged 23．A．embarrassed B．satisfied C．curious D．aware 24．A．peers B．hobbies C．ladies D．companies 25．A．involved B．caught C．offended D．connected 26．A．worried about B．passionate for C．content with D．dismissive of 27．A．appointment B．journey C．recreation D．challenge 28．A．difficult B．contemporary C．brief D．spare 29．A．fault B．memory C．experience D．selection 30．A．marketed B．captured C．illustrated D．filmed 31．A．settings B．promotions C．results D．witnesses 32．A．operated B．managed C．organized D．modeled 33．A．symbol B．design C．image D．shade 34．A．imagination B．judgment C．ignorance D．appreciation 35．A．interrupted B．sympathetic C．unsettled D．familiar四、用单词的适当形式完成短文阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式。
雅礼中学2023届高三月考英语试卷(二)
雅礼中学2023届高三月考试卷（二）英语命题人、审题人：高三英语备课组得分：本试题卷分为听力、阅读、语言运用和写作四个部分，共10页。
时量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。
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 are the speakers mainly talking about?A.How to protect eyes.B.When to use the computer.C.Which eye drops to choose.2. What does the woman want the man to do?A.Take a picture.B.Have some cheese.C.Lend his camera.3. What is the original price of the jeans?A.20 dollars.B.40 dollars.C.80 dollars.4.What is the woman doing?A.Doing some shopping.B.Sending a letter.C.Asking the way.5.How does the woman sound in the end?A.Pleased.B.Surprised.C.Grateful.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。
湖南省长沙市雅礼中学2024届高三下学期二模 英语试题(含解析)
雅礼中学2024届高三综合自主测试(4月)英语注意事项：1. 答卷前，考生务必将自己的姓名、准考证号填写在答题卡上。
2. 回答选择题时，选出每小题答案后，用铅笔把答题卡上对应题目的答案标号涂黑。
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)1．What’s the probable relationship between the speakers?A．Boss and secretary.B．Guide and tourist.C．Teacher and student. 2．How is the weather at present?A．Sunny.B．Rainy.C．Cloudy.3．How old is the man’s son?A．11.B．13.C．15.4．What is the man’s opinion?A．Most websites are safe.B．Most websites steal money.C．More and more people shop online.5．How did the man feel when the woman guessed it?A．Nervous.B．Shocked.C．Disappointed.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。
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。
2024学年湖南雅礼中学高考压轴卷英语试卷(含解析)
2024学年湖南雅礼中学高考压轴卷英语试卷考生请注意：1．答题前请将考场、试室号、座位号、考生号、姓名写在试卷密封线内，不得在试卷上作任何标记。
2．第一部分选择题每小题选出答案后，需将答案写在试卷指定的括号内，第二部分非选择题答案写在试卷题目指定的位置上。
3．考生必须保证答题卡的整洁。
考试结束后，请将本试卷和答题卡一并交回。
第一部分（共20小题，每小题1.5分，满分30分）1．—He is eager to try something he has never tried before.—Oh, I see. That’s _______ he’s different from others.A．when B．where C．how D．what2．I have no doubt that Anna will ________ it, but I wonder whether she is really ready enough.A．dig B．hit C．make D．lift3．What matters in life is working hard ________ hardly working.A．as well as B．less thanC．rather than D．other than4．Computers can do nothing．But once ______what to do, they show extraordinary power to do a great deal．A．to program B．being programmedC．programmed D．having programmed5．People ________ with anyone who is always talking about how wonderful he is.A．fall in B．keep company C．catch up D．get fed up6．Self- confidence is a kind of quality and that is it takes to do everything well.A．why B．thatC．what D．which7．Mike was usually so careful, this time he made a small mistake.A．yet B．still C．even D．thus8．—I am wondering ________ makes you study so hard?—To go to my dream university.A．what is it that B．that is whatC．what is that D．what it is that9．The house caught fire last week, with little of the original building _________.A．remain B．remained C．remains D．remaining10．He is such an unselfish man. You cannot help but ________ him.A．respect B．to respect C．neglect D．to neglect11．— Y ou should have come to the party last Saturday evening. It was really fantastic.— But a friend an unexpected visit to me.A．paid B．had paid C．would pay D．has paid12．The conference aims to develop business and let people think about _______ they can have a positive influence on the planet.A．why B．thatC．what D．how13．-- Alison, I'm sorry. I can't come to the wedding with you tomorrow morning. -- ________?-- My grandma was severely ill, so I have to stay in the hospital to look after her.A．How is it B．How come C．So what D．What's the problem14．If I _____it with my own eyes ,I wouldn’t have believed it.A．didn’t see B．weren’t seeingC．wouldn’t see D．hadn’t seen15．—Kevin, time for the next destination!—No hurry! Another 15 minutes and we _____ all the exhibition rooms of the museum.A．am exploring B．have exploredC．will explore D．will have explored16．Y oung couples will be happy to see their babies _______ with good health and intelligence when they are born. A．to bless B．blessingC．blessed D．being blessed17．---May! How is your plan? I heard you started it last Sunday.---Oh! I for it, but I haven’t decided where to start it.A．have prepared B．had prepared C．have been preparing D．was preparing18．---Can you help me with my English homework? You're a genius.---__________, but I'll try to help you. What's your problem?A．Far from it B．Sounds goodC．By all means D．It's out of question19．With more forests being destroyed, huge quantities of good earth ________ each year.A．is washing away B．is being washed awayC．are washing away D．are being washed away20．—OK，here ___________.—Thank you for your lift. See you later.A．are we B．is itC．we are D．comes it第二部分阅读理解（满分40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。
湖南省长沙市雅礼中学2024-2025学年高三上学期(9月)综合自主测试地理试题及答案
雅礼中学2025届高三综合自主测试（9月）地理时量：75分钟；分值：100分注意事项：1、答卷前，考生务将自己的姓名、准考证号填写在答题卡上。
2、回答选择题时，选出每小题答案后，用铅笔把答题卡上对应题目的答案标号涂黑。
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、考试结束后，将本试卷和答题卡一并交回。
一、选择题（本题共16小题，每小题3分，共48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）20世纪60年代，广西横县和茉莉花产生交集。
到了1997年，经过几十年的发展，横县拥有190多家茉莉花茶加工企业。
欣欣向荣的背后，危机四伏。
2000年，横县成了“中国茉莉之乡”，也是这一年横县成立了茉莉花产业发展委员会、茉莉花产业管理局和茉莉花研究所。
如今，横县开始在茉莉花产业上“横向”发展（如下图），并取代了称霸茉莉花茶几百年的福州，变成了真正的茉莉花产业中心。
据此完成下面小题。
1. 横县茉莉花产业能取代福州主要得益于（ ）A 先进技术 B. 土地面积广阔 C. 拓宽产业渠道 D. 培植优良品种2. 2000年横县成立各种机构的主要目的是（ ）A. 提高生产能力B. 扩大产业规模C. 规范产业方向D. 打造品牌效应碳汇是指清除或减少大气中二氧化碳的过程及机制，是实现碳中和目标的重要途径。
人工地质碳汇技术将二氧化碳注入地下枯竭油气田中，在封存二氧化碳的同时，也能提高采油率，我国已通过运用此技术实现了经济与社会效益的双赢。
下图示意二氧化碳的驱油过程。
据此完成下面小题。
.3. 常规油气田地区运用人工地质碳汇技术对二氧化碳进行封存的必备条件为（）A. 向斜构造广泛分布B. 盖层岩石孔隙度较小C. 地表断裂发育较好D. 前期勘探开发程度低4. 人工地质碳汇技术能提高采油率主要是因为二氧化碳注入后可导致储集层中的原油（）①黏度降低②黏度提高③流动性减弱④流动性增强A. ①③B. ②④C. ②③D. ①④冻雨是过冷雨滴（温度低于0℃但未冻结成冰，其外观与雨滴基本相同）在降落过程中遇到温度低于0℃的物体或地面，迅速冻结成冰的天气现象，在我国南方地区发生频率较高。
2020-2021学年湖南省雅礼中学高三(下)第二次月考数学试卷(理科) Word版含解析
2022-2021学年湖南省雅礼中学高三（下）其次次月考数学试卷（理科）一．选择题：（本大题共10小题，每小题5分，共50分．在每小题给出的四个选项中，只有一项是符合要求的.把答案填在答题卡中对应题号的框框内.）1．已知集合A={﹣2，﹣1，0，1，2，3}，集合，则A∩B等于（）A．{﹣2，﹣1，0，1} B．{﹣1，0，1} C．{﹣1，0，1，2} D．{﹣1，0，1，2，3}2．若A、B均是非空集合，则A∩B≠∅是A⊆B的（）A．充分不必要条件B．必要不充分条件C．充要条件D．即不充分也不必要条件3．（中诱导公式、基本公式）已知，且，则tan（2π﹣α）的值为（）A．B．C．D．4．如图，水平放置的三棱柱的侧棱长和底边长均为2，且侧棱AA1⊥面A1B1C1，正视图是边长为2的正方形，俯视图为一个等边三角形，该三棱柱的左视图面积为（）A．2B．C．2D．45．已知向量满足：，与的夹角为，则=（）A．2 B．4 C．2D．86．设x，y 满足约束条件，则目标函数z=的最小值为（）A．2 B．1 C．D．﹣27．设f（x）定义如下面数表，{x n}满足x0=5，且对任意自然数n均有x n+1=f（x n），则x2022的值为（）x 1 234 5f（x）4 135 2A．4 B．1 C．3 D．28．如图，长沙河西先导区某广场要划定一矩形区域ABCD，并在该区域内开拓出三块外形大小相同的矩形绿化区，这三块绿化区四周和绿化区之间设有1米宽的走道．已知三块绿化区的总面积为800平方米，则该矩形区域ABCD占地面积的最小值为（）平方米．A．900 B．920 C．948 D．9689．已知函数，若存在x1＜x2，使得f（x1）=f（x2），则x1•f（x2）的取值范围为（）A．B．C．D．10．设定义在R上的偶函数f（x）满足f（x+2）=f（x），f′（x）是f（x）的导函数，当x∈[0，1]时，0≤f（x）≤1；当x∈（0，2）且x≠1时，x（x﹣1）f′（x）＜0．则方程f（x）=lg|x|根的个数为（）A．12 B．1 6 C．18 D．20二．填空题：本大题共1小题，考生作答5小题，每小题5分，共25分，把答案填在答题卡中对应题号后的横线上．（一）选做题（请考生在第11、12、13题中任选两题作答，假如全做，则按前两题给分）【几何证明选讲】11．如图，PC切⊙O于点C，割线PAB经过圆心O，弦CD⊥AB于点E，已知⊙O的半径为3，PA=2，则OE=．【极坐标系与参数方程选讲】12．已知曲线C的参数方程为（θ为参数），直线l的极坐标方程为，它们的交点在平面直角坐标系中的坐标为．【不等式选讲】1011•天津）已知集合A={x∈R||x+3|+|x﹣4|≤9}，B=，则集合A∩B=．（二）必做题（14～16题）14．设（其中e为自然对数的底数），则的值为．15．动点A（x，y）在圆x2+y2=1上绕坐标原点沿逆时针方向匀速旋转，12秒旋转一周．已知时间t=0时，点A的坐标是，则当0≤t≤12时，动点A的纵坐标y关于t（单位：秒）的函数的单调递增区间是．16．已知数列{a n}的前n项和S n=（﹣1）n •n，若对任意正整数n，（a n+1﹣p）（a n﹣p ）＜0恒成立，则实数P 的取值范围是．三．解答题：本大题共6小题，共75分.解答应写出必要的文字说明，证明过程或演算步骤．17．设函数．（Ⅰ）求f（x）的最小正周期；（Ⅱ）当时，求函数f（x）的最大值和最小值．18．设数列{a n}的前n项和为S n，已知对任意正整数n，都有S n+2=2a n成立．（1）求数列{a n}的通项公式；（2）设，数列{b n}的前n项和为T n，求证：T n＜3．19．如图所示，在平面四边形ABCD中，，与的夹角为，与的夹角为．（1）求△CDE的面积S；（2）求．20．已知函数f（x ）=lnx﹣ax+﹣1（a∈R）（1）当a=﹣1时，求曲线y=f（x）在点（2，f（2））处的切线方程；（2）当a≤时，争辩f（x）的单调性．21．若数列{a n}（n∈N*）满足：①a n≥0；②a n﹣2a n+1+a n+2≥0；③a1+a2+…+a n≤1，则称数列{a n}为“和谐”数列．（1）已知数列{a n}，（n∈N*），推断{a n}是否为“和谐”数列，说明理由；（2）若数列{a n}为“和谐”数列，证明：．（n∈N*）22．已知函数f（x）=（1）当x＞0时，证明：f（x）＞；（2）当x＞﹣1且x≠0时，不等式f（x）＜恒成立，求实数k的值．2022-2021学年湖南省雅礼中学高三（下）其次次月考数学试卷（理科）参考答案与试题解析一．选择题：（本大题共10小题，每小题5分，共50分．在每小题给出的四个选项中，只有一项是符合要求的.把答案填在答题卡中对应题号的框框内.）1．已知集合A={﹣2，﹣1，0，1，2，3}，集合，则A∩B等于（）A．{﹣2，﹣1，0，1} B．{﹣1，0，1} C．{﹣1，0，1，2} D．{﹣1，0，1，2，3}考点：交集及其运算．专题：集合．分析：依据集合的基本运算进行求解即可．解答：解：∵A={﹣2，﹣1，0，1，2，3}，集合，∴A∩B={﹣1，0，1}，故选：B点评：本题主要考查集合的基本运算，比较基础．2．若A、B均是非空集合，则A∩B≠∅是A⊆B的（）A．充分不必要条件B．必要不充分条件C．充要条件D．即不充分也不必要条件考点：必要条件、充分条件与充要条件的推断．专题：规律型．分析：推断出“A∩B≠∅”成立推不出“A⊆B”反之，若“A⊆B”成立，则能推出A∩B≠∅”确定成立，利用充要条件的有关定义得到结论．解答：解：若“A∩B≠∅”成立推不出“A⊆B”反之，若“A⊆B”成立，则有A∩B=A≠∅，所以A∩B≠∅”确定成立，所以A∩B≠∅是A⊆B的必要不充分条件，故选B．点评：本题考查推断一个条件是另一个的什么条件，应当先化简各个条件，若条件是数集的形式，常转化为推断集合间的包含关系．3．（中诱导公式、基本公式）已知，且，则tan（2π﹣α）的值为（）A．B．C．D．考点：同角三角函数基本关系的运用．专题：计算题．分析：先依据诱导公式化简已知条件，得到sinα的值，然后由α的范围，利用同角三角函数间的基本关系求出cosα的值，把所求的式子利用诱导公式化简后，再依据同角三角函数间的基本关系把切化弦后，将sinα和cosα的值代入即可求出值．解答：解：由，又，得，则．故选B点评：此题考查同学机敏运用诱导公式及同角三角函数间的基本关系化简求值，是一道中档题．同学在求cosα的值时应留意α的范围．4．如图，水平放置的三棱柱的侧棱长和底边长均为2，且侧棱AA1⊥面A1B1C1，正视图是边长为2的正方形，俯视图为一个等边三角形，该三棱柱的左视图面积为（）A．2B．C．2D．4考点：简洁空间图形的三视图．专题：计算题；空间位置关系与距离．分析：三棱柱的左视图是一个矩形，矩形的长是三棱柱的侧棱长，宽是底面三角形的一条边上的高，在边长是2的等边三角形中做出底边上的高的长度，得到结果．解答：解：由题意知三棱柱的左视图是一个矩形，矩形的长是三棱柱的侧棱长，宽是底面三角形的一条边上的高，在边长是2的等边三角形中，底边上的高是，∴侧视图的面积是2故选：A．点评：本题考查简洁的空间图形三视图，考查三视图的面积的计算，考查通过原图观看三视图的大小，比较基础．5．已知向量满足：，与的夹角为，则=（）A．2 B．4 C．2D．8考点：平面对量数量积的运算．。
2020届湖南省长沙市雅礼中学高三上学期第二次月考数学(理)试题(解析版)
2020届湖南省长沙市雅礼中学高三上学期第二次月考数学（理）试题一、单选题1．集合{}{}{}202,1,1A a B a A B ==⋂=，，，若，则a 的值为（ ） A ．0 B ．1 C ．-1D ．±1【答案】C【解析】{}{}221,02,1,A B A a a⋂==⇒=，又{}1,B a = ，1a ∴=- ，故选C.2．已知向量()()2,1,,2a b λ==r r ，若a b ⊥r r，则实数λ= （ ）A ．4-B ．1-C ．1D ．4【答案】B【解析】由题得=0a b ⋅r r，解方程即得解.【详解】因为a b ⊥r r，所以=220,1a b λλ⋅+=∴=-r r .故选B 【点睛】本题主要考查向量垂直的坐标表示，意在考查学生对该知识的理解掌握水平和分析推理能力.3．已知ABCD 是复平面内的平行四边形，A ，B ，C 三点对应的复数分别是2i -+，1i -，22i +，则点D 对应的复数为（ ）A ．4i -B ．32i --C ．5D ．14i -+【答案】D【解析】分析：利用平行四边形的性质得到AB DC =u u u r u u u r,再把点的坐标代入计算即得点D 的坐标，再写出点D 对应的复数.详解：由题得A(-2，1),B(1，-1),C(2，2),设D(x,y)，则(3,2),(2,2),AB DC x y =-=--u u u v u u u v因为AB DC =u u u r u u u r，所以2322x y -=⎧⎨-=-⎩，解之得x=-1,y=4.所以点D 的坐标为（-1，4）， 所以点D 对应的复数为-1+4i, 故选D.点睛：本题方法比较多，但是根据AB DC =u u u r u u u r求点D 的坐标，是比较简单高效的一种方法，大家解题时，注意简洁高效. 4．已知集合2{|0}1x A x x -=<+，{|}B x x a =<，若“1a =”是“B A ⊆”的（ ） A ．充分不必要条件 B ．必要不充分条件C ．充要条件D ．既不是充分条件也不是必要条件【答案】A【解析】化简两个集合，分别讨论充分性和必要性，可选出答案. 【详解】由题意，集合()()2{|0}{|120}{|12}1x A x x x x x x x -=<=+-<=-<<+， 先来判断充分性，若1a =，则{|11}B x x =-<<，满足B A ⊆，即“1a =”是“B A ⊆”的充分条件； 再来判断必要性，若B A ⊆，①集合B =∅，0a ≤，此时符合B A ⊆；②集合B ≠∅，此时21a a a a -<⎧⎪≤⎨⎪-≥-⎩，解得01a <≤.故B A ⊆时，1a ≤，即“1a =”不是“B A ⊆”的必要条件. 所以“1a =”是“B A ⊆”的充分不必要条件. 故选：A. 【点睛】本题考查不等式的解法，考查集合的包含关系，考查充分性与必要性，考查学生的计算能力与逻辑推理能力，属于基础题.5．若关于x 的不等式2420x x a --->在区间()1,4内有解,则实数a 的取值范围是 A ．2a <- B ．2a >-C ．6a >-D ．6a <-【答案】A【解析】由题意可得224a x x +<-在区间(1,4)内成立，由224(2)4y x x x =-=--，求得顶点处的函数值和端点处的函数值，即可得到所求范围． 【详解】解：关于x 的不等式2420x x a --->在区间(1,4)内有解， 即为224a x x +<-在区间(1,4)内成立， 由224(2)4y x x x =-=--，可得2x =处函数y 取得最小值4-；1x =时，3y =-；4x =时，0y =； 则函数24y x x =-的值域为[)4,0-，可得20a +<， 解得2a <-． 故选：A ． 【点睛】本题考查不等式成立的条件，注意运用转化思想和二次函数的值域求法，考查运算能力，属于中档题．6．将函数()sin 6f x x π⎛⎫=+⎪⎝⎭的图象上各点的纵坐标不变，横坐标扩大到原来的2倍，所得函数()g x 图象的一个对称中心可以是（ ） A ．,012π⎛⎫-⎪⎝⎭B ．5,012π⎛⎫⎪⎝⎭C ．,03π⎛⎫-⎪⎝⎭D ．2,03π⎛⎫⎪⎝⎭【答案】C【解析】试题分析：()1sin 26g x x π⎛⎫=+ ⎪⎝⎭，,2,263x k x k k Z ππππ+=∴=-∈，令0,3k x π==-，∴()g x 图象的一个对称中心是,03π⎛⎫-⎪⎝⎭． 【考点】三角函数图象的平移、三角函数的对称中心．7．在正方体1111ABCD A B C D -中，E 为棱1BB 的中点，则异面直线DE 与AB 所成角的正切．．值为（ ）A ．2B C D【答案】C【解析】依据异面直线所成角的定义，结合//AB DC ，就得到异面直线DE 与AB 所成角，解三角形，即可求出异面直线DE 与AB 所成角的正切值. 【详解】如图，因为//AB DC ，所以EDC ∠（或其补角）即为异面直线DE 与AB 所成角， 连接EC ，设正方体棱长为2，利用勾股定理可以求得：2CD =，5CE =，3DE =，因此三角形DEC 是直角三角形，∴5tan EDC ∠=. 故选：C【点睛】本题考查了异面直线所成的角，属于基础题.8．已知以双曲线的两个焦点及虚轴的两个端点为顶点的四边形中，有一个内角为，则双曲线的离心率为（ ） A ． B ．C ．D ．【答案】B【解析】试题分析：由于，由题意知，，，因此，双曲线的离心率为，故选B.【考点】双曲线的离心率9．已知直线1:(3)10l mx m y +-+=，直线2:(1)10l m x my ++-=，若12l l ⊥则m =（ ）A ．0m =或1m =B ．1m =C ．32m =-D ．0m =或32m =- 【答案】A【解析】根据直线垂直的充要条件，列出等式，求解，即可得出结果. 【详解】因为直线1:(3)10l mx m y +-+=与直线2:(1)10l m x my ++-=垂直， 所以(1)(3)0m m m m ++-=，即(1)0m m -=，解得0m =或1m =. 故选A 【点睛】本题主要考查根据直线垂直求参数的问题，熟记直线垂直的充要条件即可，属于常考题型.10．已知函数2()log (46)x xf x a b =-+，满足2(1)1,(2)log 6f f ==，,a b 为正实数，则()f x 的最小值为（ ） A ．6- B ．3-C ．0D ．1【答案】D【解析】试题分析：22462{466a b a b -+=-+=，解得2{4b a ==， ∴222()log (44?26)log [(22)2]x x x f x =-+=-+，当1x =时，min ()1f x =，故选D .【考点】对数函数的性质11．直线l 是抛物线22x y =在点()2,2-处的切线，点P 是圆22420x y x y +--=上的动点，则点P 到直线l 的距离的最小值等于（ ）A 2BCD ．65【答案】C【解析】先由题意求出直线l 的方程，再求出圆22420x y x y +--=的圆心到直线的距离，减去半径，即为所求结果. 【详解】因为22x y =，所以y x '=，因此抛物线22x y =在点()2,2-处的切线斜率为22x y x =-==-'，所以直线l 的方程为22(2)y x -=-+，即22y x =--，又圆22420x y x y +--=可化为22(2)(1)5x y -+-=，所以圆心为(2,1)，半径r =则圆心到直线的距离为d ==又因点P 是圆22420x y x y +--=上的动点，所以点P 到直线l的距离的最小值等于d r -=. 故选C 【点睛】本题主要考查圆上的点到直线距离的最值问题，熟记直线与圆位置关系即可，属于常考题型.12．若对任意的1,x e e ⎡⎤∈⎢⎥⎣⎦，不等式22ln 30x x x mx +-+≥恒成立，则实数m 的最大值为（ ） A ．132e e+- B ．32e e++C ．2e 1-D ．4【答案】D【解析】通过分离变量将恒成立的不等式变为32ln m x x x≤++，由此可知当1,x e e ⎡⎤∈⎢⎥⎣⎦时，min 32ln m x x x ⎛⎫≤++ ⎪⎝⎭，通过导数求解出右侧函数在区间内的最小值，从而得到结果. 【详解】22ln 30x x x mx +-+≥ 22ln 3mx x x x ⇒≤++ 32ln m x x x⇒≤++22ln 30x x x mx +-+≥在1,x e e ⎡⎤∈⎢⎥⎣⎦上恒成立等价于min 32ln m x x x ⎛⎫≤++ ⎪⎝⎭，1,x e e ⎡⎤∈⎢⎥⎣⎦令()32ln g x x x x =++，则()22223231x x g x x x x+-'=+-= 令()0g x '=，解得13x =-，21x =则1,1x e ⎡⎫∈⎪⎢⎣⎭时，()0g x '<，()g x 单调递减；(]1,x e ∈时，()0g x '>，()g x 单调递增则1,x e e ⎡⎤∈⎢⎥⎣⎦时，()()min 12ln1134g x g ==++= 4m ∴≤ 即m 的最大值为4 本题正确选项：D 【点睛】本题考查利用恒成立问题的求解，解题关键是能够通过分离变量的方式将问题转化为所求变量与某一函数的最值比较的问题，通过求解函数最值得到所求参数的取值范围，属于恒成立问题中的常规题型.二、填空题13．已知抛物线24y x =-的准线经过椭圆2221(0)4x y b b+=>的焦点，则b =________． 【答案】3【解析】先根据抛物线的方程求得准线方程，根据椭圆的方程求得焦点，代入抛物线的准线方程求得b ． 【详解】解：依题意可得抛物线24y x =-的准线为1x =，又因为椭圆焦点为()240b ±-，所以有241b -=．即b 2＝3故b 3=． 故答案为3． 【点睛】本题主要考查了椭圆和抛物线的简单性质，椭圆的标准方程．考查了学生对圆锥曲线基础知识的掌握． 14．若实数x ，y 满足，则的取值范围是______．【答案】【解析】化简题设条件，得到的取值范围，再化简为x 的二次函数，借助二次函数的图象与性质，即可求解函数的最值，得到答案． 【详解】由题意，实数x ，y 满足，即，可得．则，则函数的对称轴为，开口向下，所以在上，时函数取得最大值6，时，函数取得最小值．所以的取值范围是．故答案为：．【点睛】本题主要考查了二次函数的图象与性质的应用问题，其中解答中根据题设条件得到变量的取值范围，再结合二次函数的图象与性质求解是解答的关键，着重考查了转化思想，以及推理与运算能力，属于基础题．15．设x，y满足约束条件20230x yx yx y--≤⎧⎪-+≥⎨⎪+≤⎩，则46yx++的取值范围是__________．【答案】[]3,1-【解析】作出不等式组对应的平面区域，利用目标函数的几何意义，由数形结合进行求解即可．【详解】作出不等式组对应的平面区域如图所示：则46yx++的几何意义是区域内的点到定点P（﹣6，﹣4）的斜率，由230x yx y-+=⎧⎨+=⎩得x＝﹣1，y＝1，即A（﹣1，1），则AP的斜率k＝1416+-+＝1，由20230x yx y--=⎧⎨-+=⎩得x＝﹣5，y＝﹣7，即B（﹣5，﹣7），则BP的斜率k＝7456-+-+＝﹣3，则46yx++的取值范围是[﹣3，1]故答案为：[﹣3，1]．【点睛】本题主要考查线性规划的应用，利用目标函数的几何意义是解决本题的关键，属于中档题.16．在数列{}n a 中，1253a a +=，()()11280n n n a na n N *+--+=∈，若()12n n n n b a a a n N *++=⋅⋅∈，则{}n b 的前n 项和取得最大值时n 的值为__________．【答案】10【解析】解法一：利用数列的递推公式，化简得122n n n a a a ++=+，得到数列{}n a 为等差数列，求得数列的通项公式313n a n =-，得到12100a a a >>>>L ，1112130a a a >>>>L ，得出所以1280b b b >>>>L ，90b <，100b >，1112130b b b >>>>L ，进而得到结论；解法二：化简得()128 11n n a a n n n n +-=---，令1n n a c n +=，求得11281n c c n ⎛⎫-=- ⎪⎝⎭，进而求得313n a n =-，再由0n b ≥，解得8n ≤或10n =，即可得到结论．【详解】解法一：因为()11280n n n a na +--+=① 所以()211280n n na n a ++-++=②，①-②，得122n n n na na na ++=+即122n n n a a a ++=+，所以数列{}n a 为等差数列． 在①中，取1n =，得1280a -+=即128a =，又1253a a +=，则225a =， 所以313n a n =-．因此12100a a a >>>>L ，1112130a a a >>>>L 所以1280b b b >>>>L ，99101180b a a a =⋅⋅=-<，10101112100b a a a =⋅⋅=>，1112130b b b >>>>L所以12389T T T T T <<L ， 9101112T T T T >>L 又1089108T T b b T =++>，所以10n =时，n T 取得最大值． 解法二：由()11280n n n a na +--+=，得()12811n n a a n n n n +-=---， 令1n n a c n +=，则11111282811n n c c n n n n -⎛⎫⎛⎫-=--=- ⎪ ⎪--⎝⎭⎝⎭，则11281n c c n ⎛⎫-=- ⎪⎝⎭，即1211281281n c c a n n ⎛⎫⎛⎫=+-=+- ⎪ ⎪⎝⎭⎝⎭，代入得()()1222812828n n a nc na n n a +==+-=+-，取1n =，得1280a -+=，解得128a =，又1253a a +=，则225a =，故1283n a n +=- 所以313n a n =-，于是()()()12313283253n n n n b a a a n n n ++=⋅⋅=---． 由0n b ≥，得()()()3132832530n n n ---≥，解得8n ≤或10n =， 又因为98b =-，1010b =， 所以10n =时，n T 取得最大值． 【点睛】本题主要考查了数列的综合应用，以及数列的最值问题的求解，此类题目是数列问题中的常见题型，对考生计算能力要求较高，解答中确定通项公式是基础，合理利用数列的性质是关键，能较好的考查考生的数形结合思想、逻辑思维能力及基本计算能力等，属于中档试题.三、解答题17．在锐角ABC V 中角A ，B ，C 的对边分别是a ，b ，c ，且sin 0a B =. （1）求角A 的大小；（2）若4a =，求ABC V 面积的最大值.【答案】（1）60A =︒（2）【解析】（1）由正弦定理可得sin sin 0A B B -=，结合sin 0B ≠，可求出sin A 与A ；（2）由余弦定理可得2222cos a b c bc A =+-，结合基本不等式可得162bc bc bc ≥-=，即可求出16bc ≤，从而可求出1sin 2ABC S bc A =V 的最大值.【详解】解：（1）因为sin 0a B =，所以sin sin 0A B B =，又sin 0B ≠，所以3sin 2A=， 又ABC V 是锐角三角形，则60A =o .（2）因为2222cos a b c bc A =+-，60A =o ，4a =， 所以222211622b c bc b c bc =+-⨯=+-， 所以162bc bc bc ≥-=，即16bc ≤（当且仅当4b c ==时取等号）， 故11sin 16sin 432260ABC S bc A =≤⨯⨯=V o . 【点睛】本题考查了正弦定理、余弦定理在解三角形中的运用，考查了利用基本不等式求最值，考查了学生的计算能力，属于中档题.18．某公司为确定下一年度投入某种产品的宣传费，需了解年宣传费x （单位：千元）对年销售量y （单位：t ）和年利润z （单位：千元）的影响，对近8年的年宣传费i x 和年销售量()1,2,,8i y i =⋅⋅⋅数据作了初步处理，得到下面的散点图及一些统计量的值.xyw()821ii x x =-∑()821ii w w =-∑ ()()81iii x x y y =-⋅-∑ ()()81iii w w y y =-⋅-∑46.6 5636.8289.8 1.6 1469 108.8表中i i w x =8118i i w w ==∑.（1）根据散点图判断，y a bx =+与y c x =+哪一个适宜作为年销售量y 关于年宣传费x 的回归方程类型？（给出判断即可，不必说明理由）（2）根据（1）的判断结果及表中数据，建立y 关于x 的回归方程；（3）已知这种产品的年利润z 与x ，y 的关系为0.2z y x =-.根据（2）的结果回答下列问题：（i ）年宣传费49x =时，年销售量及年利润的预报值是多少？ （ii ）年宣传费x 为何值时，年利润的预报值最大？附：对于一组数()11,u v ，()22,u v ，…，(),n n u v ，其回归直线v u αβ=+的斜率和截距的最小二乘估计分别为µ()()()121niii nii u u v v u u β==--=-∑∑，µµv u αβ=-. 【答案】（1）y c =+适宜（2）100.6y =+3）（i ）年销售量y 的预报值576.6，年利润的预报值66.32（ii ）46.24x =【解析】（1）根据所给的两个函数解析式的特点，结合图象直接选择即可； （2）令w =y 关于w 的线性回归方程，利用表中所给的数据求解即可.（3）（i ）由（2）知，把49x =代入，100.6y =+即可；（ii ）根据（2）的结果知，求出年利润z 的预报值的函数关系式，利用配方法求出当年利润的预报值最大时，年宣传费的值. 【详解】（1）由散点图可以判断，这些点明显不在同一条直线上，也不是在一条直线的附近，所以y c =+适宜作为年销售量y 关于年宣传费x 的回归方程类型. （2）令w =y 关于w 的线性回归方程，由于()()()81821108.8681.6iii i i w w y y d w w==--===-∑∑，56368 6.8100.6cy dw =-=-⨯=$， 所以y 关于w 的线性回归方程为100.668y w =+， 因此y 关于x的回归方程为100.6y =+（3）（i ）由（2）知，当49x =时，年销售量y的预报值100.6576.6y =+=，年利润的预报值0.2576.64966.32z=⨯-=$. （ii ）根据（2）的结果知，年利润z 的预报值()0.2100.66813.620.12x x x x z=+-=-++$， 所以当13.66.82x ==，即46.24x =时，z 取得最大值. 【点睛】本题考查了根据图象选择函数的解析式，考查了求线性回归方程，考查了线性回归方程的应用，考查了数学运算能力.19． 如图，在四棱锥P ABCD -中，底面ABCD 为平行四边形，PCD △为等边三角形，平面PAC ⊥平面PCD ，PA CD ⊥，2CD =，3AD =，（Ⅰ）设G H ，分别为PB AC ，的中点，求证：GH ∥平面PAD ； （Ⅱ）求证：PA ⊥平面PCD ；（Ⅲ）求直线AD 与平面PAC 所成角的正弦值. 【答案】（I ）见解析；（II ）见解析；（III 3【解析】（I ）连接BD ，结合平行四边形的性质，以及三角形中位线的性质，得到GH PD P ，利用线面平行的判定定理证得结果；（II ）取棱PC 的中点N ，连接DN ，依题意，得DN PC ⊥，结合面面垂直的性质以及线面垂直的性质得到DN PA ⊥，利用线面垂直的判定定理证得结果；（III ）利用线面角的平面角的定义得到DAN ∠为直线AD 与平面PAC 所成的角，放在直角三角形中求得结果. 【详解】（I ）证明：连接BD ，易知AC BD H ⋂=，BH DH =，又由BG PG =，故GH PD P ，又因为GH ⊄平面PAD ，PD ⊂平面PAD ， 所以GH ∥平面PAD .（II ）证明：取棱PC 的中点N ，连接DN ，依题意，得DN PC ⊥， 又因为平面PAC ⊥平面PCD ，平面PAC I 平面PCD PC =， 所以DN ⊥平面PAC ，又PA ⊂平面PAC ，故DN PA ⊥， 又已知PA CD ⊥，CD DN D =I ， 所以PA ⊥平面PCD .（III ）解：连接AN ，由（II ）中DN ⊥平面PAC ， 可知DAN ∠为直线AD 与平面PAC 所成的角.因为PCD ∆为等边三角形，2CD =且N 为PC 的中点， 所以3DN =DN AN ⊥， 在Rt AND ∆中，3sin 3DN DAN AD ∠==， 所以，直线AD 与平面PAC 3【点睛】本小题主要考查直线与平面平行、直线与平面垂直、平面与平面垂直、直线与平面所成的角等基础知识，考查空间想象能力和推理能力.20．已知椭圆2222:1x y C a b+=的右焦点为(1,0)，且经过点(0,1)A .（Ⅰ）求椭圆C 的方程；（Ⅱ）设O 为原点，直线:(1)l y kx t t =+≠±与椭圆C 交于两个不同点P ，Q ，直线AP 与x 轴交于点M ，直线AQ 与x 轴交于点N ，若|OM |·|ON |=2，求证：直线l 经过定点.【答案】（Ⅰ）2212x y +=；（Ⅱ）见解析.【解析】(Ⅰ)由题意确定a ,b 的值即可确定椭圆方程；(Ⅱ)设出直线方程，联立直线方程与椭圆方程确定OM ,ON 的表达式，结合韦达定理确定t 的值即可证明直线恒过定点. 【详解】（Ⅰ）因为椭圆的右焦点为(1,0)，所以1225； 因为椭圆经过点(0,1)A ,所以1b =，所以2222a b c =+=，故椭圆的方程为2212x y +=.（Ⅱ）设1122(,),(,)P x y Q x y联立2212(1)x y y kx t t ⎧+=⎪⎨⎪=+≠⎩得222(12)4220k x ktx t +++-=，21212224220,,1212kt t x x x x k k -∆>+=-=++，121222()212t y y k x x t k +=++=+，222212121222()12t k y y k x x kt x x t k-=+++=+. 直线111:1y AP y x x --=，令0y =得111x x y -=-，即111x OM y -=-； 同理可得221x ON y -=-. 因为2OM ON =,所以1212121212211()1x x x x y y y y y y --==---++；221121t t t -=-+，解之得0t =，所以直线方程为y kx =，所以直线l 恒过定点(0,0). 【点睛】解决直线与椭圆的综合问题时，要注意：(1)注意观察应用题设中的每一个条件，明确确定直线、椭圆的条件；(2)强化有关直线与椭圆联立得出一元二次方程后的运算能力，重视根与系数之间的关系、弦长、斜率、三角形的面积等问题． 21．已知函数（I ）若在处的切线的斜率为，求的值；（Ⅱ），不等式恒成立，求整数的最大值.【答案】（Ⅰ）（Ⅱ）【解析】（Ⅰ）由题意得,解之即得a 的值；（Ⅱ）不等式或化为，设，再利用导数研究函数h(x)的图像和性质得解.【详解】 解：（Ⅰ），由题意得，则.（Ⅱ）不等式或化为.设，．设，当时，，则在单调递增. 又，，则在存在唯一零点满足.则当时，单调递减，当时，单调递增，则.又因为，则，因为，则，则整数的最大值为. 【点睛】本题主要考查导数的几何意义，考查利用导数研究不等式的恒成立问题，考查函数的最值、单调性、零点问题的综合应用，意在考查学生对这些知识的理解掌握水平和分析推理能力，属于难题.22．在平面直角坐标系xOy 中，曲线C 的参数方程为3cos 1sin x r y r ϕϕ⎧=⎪⎨=+⎪⎩（0r >，ϕ为参数），以坐标原点O 为极点，x 轴正半轴为极轴建立极坐标系，直线l 的坐标方程为sin 13πρθ⎛⎫-= ⎪⎝⎭，若直线l 与曲线C 相切. （1）求曲线C 的极坐标方程；（2）在曲线C 上取两点M 、N 于原点O 构成MON ∆，且满足6MON π∠=，求面积MON ∆的最大值.【答案】（1）4sin 3πρθ⎛⎫=+⎪⎝⎭； （2）2. 【解析】（1）求出直线l 的直角坐标方程为y =+2，曲线C，1），半径为r 的圆，直线l 与曲线C 相切，求出r ＝2，曲线C 的普通方程为（x 2+（y ﹣1）2＝4，由此能求出曲线C 的极坐标方程． （2）设M （ρ1，θ），N （ρ2，6πθ+），（ρ1＞0，ρ2＞0），由126MONS OM ON sin π==V u u u u r u u u r 2sin （23πθ+）△MON 面积的最大值．【详解】（1）由题意可知将直线l的直角坐标方程为2y =+，曲线C是圆心为)，半径为r 的圆，直线l 与曲线C相切，可得：2r ==；可知曲线C的方程为(()2214x y +-=，∴曲线C的极坐标方程为2cos 2sin 0ρθρθ--=，即4sin 3πρθ⎛⎫=+⎪⎝⎭. （2）由（1）不妨设()1,M ρθ，2,6N πρθ⎛⎫+⎪⎝⎭，()120,0ρρ>>21211sin ?4sin ?sin 2sin cos 26432MONS OM ON πππρρθθθθθ∆⎛⎫⎛⎫===++=+ ⎪ ⎪⎝⎭⎝⎭u u u u v u u u vsin22sin 23πθθθ⎛⎫=+=++ ⎪⎝⎭当12πθ=时，2MON S ∆≤MON ∴∆面积的最大值为2+.【点睛】本题考查曲线的极坐标方程的求法，考查三角形的面积的最大值的求法，考查参数方程、极坐标方程、直角坐标方程的互化等基础知识，考查运算求解能力，考查函数与方程思想，是中档题．23．设函数()2f x x x a =--+． (1)当1a =时，求不等式()2f x <-的解集；(2)当()()(),22x y R f y f x f y a ∈-+≤≤+时，，求的取值范围． 【答案】（1）32x x ⎧⎫>⎨⎬⎩⎭；（2）[]3,1-- 【解析】(1) 求出函数f （x ）的分段函数的形式，通过讨论x 的范围求出各个区间上的x 的范围，取并集即可；(2)()()()22f y f x f y -+≤≤+等价于()()()()max min 22f x f y f x f x ⎡⎤⎡⎤-≤⇔-≤⎣⎦⎣⎦，求出()f x 的最值即可.【详解】（1）当a =1时，()3,1,12,123,2x f x x x x ≤-⎧⎪=--<≤⎨⎪->⎩，可得()2f x <-的解集为32x x ⎧⎫>⎨⎬⎩⎭（2）当,x y R ∈时，()()()()()()()max min 2222f y f x f y f x f y f x f x ⎡⎤⎡⎤-+≤≤+⇔-≤⇔-≤⎣⎦⎣⎦,因为()()222x x a x x a a --+≤--+=+， 所以()222a a +--+≤. 所以21a +≤，所以31a -≤≤-. 所以a 的取值范围是[-3，-1] 【点睛】含绝对值不等式的解法有两个基本方法，一是运用零点分区间讨论，二是利用绝对值的几何意义求解．法一是运用分类讨论思想，法二是运用数形结合思想，将绝对值不等式与函数以及不等式恒成立交汇、渗透，解题时强化函数、数形结合与转化化归思想方法的灵活应用.。
2024-2025学年湖南省师大附中高三上学期月考(二)英语试题及答案
湖南师大附中2025届高三月考试卷(二)英语第二部分阅读(共两节，满分50分)第一节(共15小题；每小题2.5分，满分37.5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。
AThe Virgin Islands National Park is a tropical(热带的)paradise on the island of St. John,which covers more than half of the small island.It is surrounded by the Atlantic Ocean to the north and the Caribbean Sea to the south,where the climate is warm all year.The island's white sand beaches and clear blue seas are considered to be among the most beautiful in the Caribbean,gaining reputation and popularity among visitors across the world.How the national park was formedLaurence Rockefeller was an American millionaire,businessman and conservationist.He visited St.John in the 1950s. He quickly fell in love with the island's clean,pure beauty.He first purchased a small resort there, Caneel Bay. He also purchased more than 2,000 hectares of the island and donated it to the government.That donation created the U.S.Virgin Islands National Park.It was officially opened as a national park on December 1,1956.How to get to the parkThe only way to reach the park is by boat.Some people arrive on their own sailboats.Others come in on large cruise ships.Visitors also arrive on water taxis from the island of St.Thomas.What to do at the parkFrom the tropical hills to the blue waters there are many things to do at the Virgin Islands National,Park.Visitors enjoy fishing,camping,sailing,scuba diving, snorkeling (浮潜),and bird watching.Of all of the park's beaches,Trunk Bay Beach is said to be the most striking.Below the clear blue water is a 200-meter snorkeling path. Hawksnest Beach is also a popular place for snorkeling.Near the shore are three small reefs of Elkhorn Coral.The Elkhorn Coral gets its name from its shape.The reef looks similar to the huge horns(角)of an animal called elk.It is a very rare kind of reef.Scientists say it is in danger of becoming extinct.The Virgin Islands National Park is often called America's paradise.It protects St. John's pristine nature,and preserves the record of human history in the Caribbean.Don't hesitate! Come here and put yourself in the paradise!1. What is most likely attractive to tourists when they visit the Virgin Islands National Park?A. Its tropical climate.B. Its location.C. Its beautiful scenery.D. Its activity.2. What can we learn about the Virgin Islands National Park?A. An animal called elk is at risk of becoming dying out.B. Visitors can choose any means of transportation to get to the park.C Laurence's donation greatly contributed to the foundation of the park..D. There is a 200-meter snorkeling path beneath the water of the Hawksnest Beach.3. Where is the text probably taken from?A. A speech script.B. A travel brochure.C. An academic essay.D. A geographic journal.BBoeing’s Starliner spacecraft landed in a New Mexico desert late on Friday,months after its original departure date and without the two astronauts it carried when it launched in early June.The Nasa astronauts Suni Williams and Butch Wilmore should have flown the Starliner back to Earth in June, a week after launching in it.But thruster (推进器) failures and helium (氦气) leaks marred their ride. Instead, they will remain at the International Space Station (ISS) for the rest of the year and will return in February aboard the SpaceX Dragon spacecraft.their empty seats and blue spacesuits along with some old station equipment.After Nasa’s space shuttles were retired more than a decade ago, Nasa hired Boeing and SpaceX for orbital (轨道的) taxi service. Boeing ran into so many problems on its first test flight with no one onboard in 2019 that it had to repeat it. The 2022 do-over uncovered even more flaws and the repair bill topped $1.5bn.The Starliner finally blasted into space on 5 June from Florida’s Cape Canaveral Space Force Station after unsuccessful launches on 6 May and 1 June. On the first launch attempt,a problem was found with a valve (阀门) on the second stage,or upper portion, of the rocket. On the second,a computer tripped an automatic hold just three minutes and 50 seconds from liftoff. That was later attributed to a single ground power supply fault within one of the launch control computers.Even after it successfully launched,helium leaks continued to trouble the spacecraft. As the Starliner approached the ISS, two leaks were detected but Nasa determined the spacecraft remained stable. What started as an eight-day mission dragged on for three months after the leaks and faulty thrusters raised safety concerns.However, Nasa and Boeing officials insisted that the astronauts were not trapped and that the technical difficulties did not threaten the mission. “We’ll come home when we’re ready,” Steve Stich, Nasa’s commercial crew program manager, said in the press conference in July.4. What does the underlined word “marred” in paragraph 2 mean?A. Underwent.B. Stimulated.C. Facilitated.D. Blocked.5. What do we know about Boeing’s spacecraft launches?A. They were filled with delays and setbacks.B. Starliner’s initial launch went smoothly.C. The 2019 manned spaceflight was a failureD. Reasons of the problems were still unidentified.6. Why didn’t the two astronauts come back to Earth on time?A. Because the project went over the original budget.B. Because they were both in serious health conditions.C. Because it was dangerous to take the Starliner then.D. Because Nasa officials failed to reach an agreement.7. What can be implied according to the last two paragraphs?A. The two astronauts would come back soon.B. Officials considered the situation within control.C. Nasa officials were pessimistic and pressed.D. The mission would be completed in 3 months.CActor Alicia Silverstone worried fans on social media recently. While on a trip to England, she posted a TikTok video of herself tasting a kind of poisonous berries she found along a sidewalk. Silverstone, who appeared in the 1995 movie Clueless, said she thought the fruit was a tomato. But when she bit into it and found that it had an unusual taste, she realized that it was not the common food.Plant expert, Jessica Damiano, recently wrote about poisonous plants that look like common foods for the Associated Press. She said the fruit that looked like a tomato appears to have been a Jerusalem cherry.Often sold as a houseplant, all parts of the Jerusalem cherry are poisonous.The American Society for the Prevention of Cruelty to Animals says the plant is not only harmful to humans but also to dogs, cats and horses.Eating large amounts can be deadly. Silverstone was lucky because she did not swallow the berries. She was also lucky because the berries were reddish orange, which meant they were ripe. While all parts of the Jerusalem cherry are poisonous, the plant’s unripe berries can be especially dangerous.They can cause problems with the central nervous and gastrointestinal (肠胃的) systems.The Jerusalem cherry is not the only toxic plant that looks like a safe one.The poisonous Carolina horsenettle fruit also looks like a tomato. It is also known as devil’s potato to add to the confusion.The Virginia creeper fruit also looks like blueberries, and it can be deadly if eaten.Wild parsnip has flowers like a carrot and leaves like parsley (欧芹). Simply touching it can cause a skin problem. Creeping buttercup looks like flat-leaf parsley. It can cause severe stomach pain,vomiting (呕吐) and heart problems. And Canadian moonseed can be confused with wild grape. However, its taste is so bitter that you would likely spit it out before swallowing it. This is a good thing because eating it can lead to death.If you think you have swallowed a toxic plant by mistake, contact a poison control center in your area or your doctor immediately. There is additional information on the website .Damiano advises using common sense with plants you find in the wild. If you are not completely sure that something is food, do not eat it.8. What is the purpose of the first paragraph?A. To present the author’s argument.B. To introduce the topic of the article.C. To raise the public’s attention of wild plants.D. To popularize the knowledge of medical science.9. Why was Silverstone thought to be fortunate?A. The berries she had a bite were ripe.B. She found the fruit she ate was a tomato.C. She had a good knowledge of wild plants.D. The amount of the berries she consumed was large.10. According to the description,what plants can be most harmful to people?A. Carolina horsenettle and wild parsnip.B Virginia creeper and creeping buttercup..C. Wild parsnip and Canadian moonseed.D. Canadian moonseed and Virginia creeper.11. What may be the suitable measure if someone mistakenly swallows a poisonous plant?A. Spitting it out as quickly as possible.B. Making an appointment with their doctor.C. Getting in touch with the local authority instantly.D. Searching for the relevant information on the Internet.DSuperhuman artificial intelligence has played a role in our life. When it comes to playing games like chess, or solving difficult scientific challenges like predicting protein structures, computers are well ahead of humans. But we have one superpower they aren’t close to mastering:mind reading.We are blessed with a mysterious ability to reason the goals,desires and beliefs of others, a crucial skill that means we can anticipate other people’s actions and the consequences of our own.If AIs are to become truly useful in everyday life — to cooperate effectively with us or to understand that a child might run into the road after a bouncing ball — we have to give them this gift that evolution has given us to read other people's minds.In psychology, the ability to infer another’s mental state is referred to as theory of mind. In humans, this capacity develops at a very young age. How to reproduce the capability in machines is far from clear, though.One of the main challenges is context. For instance, if someone asks whether you are going for a run and you reply “it’s raining”, they can quickly conclude the answer is no. But this requires huge amounts of background knowledge about running, weather and human preferences.Besides, whether humans or AI, the theory of mind is supposed to emerge naturally from one’s own learning process. Building prior knowledge into AI makes it reliant on our imperfect understanding of theory of mind.In addition, AI may be capable of developing approaches we could never imagine. There can be many forms of theory of mind that we don’t know about simply because we live in a human body that has certain types of senses and a certain ability to think.But we might still want AI to have a more human-like form of theory of mind. Humans can clearly explain their goals to each other using common language and ideas. While letting AI form the theory of mind in their learning process is likely to lead to developing more powerful AI,plainly building in shared ways to represent knowledge may be crucial for humans to trust and communicate with AI.It is important to remember, though, that the pursuit of machines with theory of mind is about more than just building more useful robots. It is also a stepping stone on the path towards a deeper goal for AI and robotics research: building truly self-aware machines.Whether we will ever get there remains to be seen. But along the way thinking about other people and other agents, we are on the path to learning to think about ourselves.12. According to the passage,which of the following contexts can AI understand well?A. When asked where an object is, a naughty kid points in the wrong direction.B. When a teacher asks for a boy’s homework,he answers “my dog ate it” .C. When you are treated with a hotpot for dinner, you reply “a sore throat” .D. When a mom tells her kid milk is good for health, the kid drinks it up.13. Which statement will the author agree with most about theory of mind?A. Humans’ theory of mind is far from perfect.B. Humans limit AI’s theory of mind to an extent.C. AI’s theory of mind development has been totally decoded.D. Shared forms of theory of mind result in more powerful AI.14. What is the author’s attitude toward truly self-aware machines?A. AmbiguousB. Conservative.C. Skeptical.D. Approving.15. Which would be the best title for the passage?A. AI’s Theory of Mind Will Define Our FutureB. AI with Its Own Theory of Mind Is ExpectedC. AI’s Theory of Mind — a Blessing or Suffering to HumansD. Theory of Mind Bridges the Gap Between Humans and AI第二节(共5小题；每小题2.5分，满分12.5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。
湖南省长沙市雅礼中学2024届高三下学期3月综合测试(一)英语试题
湖南省雅礼中学2024届高三综合自主测试(一)英语试卷第一部分听力(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)1.Why does the woman intend to go to Rome?A. To work.B. To study.C. To travel.2.What does the woman think of the trip?A. Worthless.B. Terrible.C. Great.3.In which city did the woman and John stay the longest?A. Vienna.B. Rome.C. Paris.4.What is “couscous”?A.A new hotel.B.A kind of food.C.A close relative.5.Where does the conversation most probably take place?A. In a park.B. In a zoo.C. In a pet store.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。
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。
听下面一段对话,回答6-7小题。
6.Where are the speakers?A. In a restaurant.B. In a bookstore.C. In a supermarket.7.What does the man have to do now?A. Sign his name.B. Wait for his turn.C. Call his friend.听下面一段对话,回答8-10小题。