山西省运城市2022-2023学年高二上学期期末调研测试英语试题含答案

高二英语(外研版)试题注意事项：1.答卷前，考生务必将自己的姓名、准考证号等填写在答题卡和试卷指定位置上。

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，将答题卡交回。

第一部分听力(共两节，满分15分)做题时，先将答案标在试卷上，录音内容结束后，你将有一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.Where does Lucy come from?A.Canada.B.Australia.C.New Zealand.2.What is the time now?A.5:35.B.6:15.C.7:55.3.Which sport does the man probably like?A.Volleyball.B.Basketball.C.Football.4.What has happened to Bob?A.He has retired.B.He has fallen ill.C.He has gone on a business trip.5.What does the man suggest the woman do?A.Quit the band.B.Help him with his stuff.C.Ask John to join the band.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。

吕梁市2022-2023学年第一学期期末调研测试高三英语试题2023.本试题满分150分，考试时间120分钟。

答案一律写在答题卡上。

注意事项：1.答题前，考生务必先将自己的姓名、准考证号填写在答题卡上，认真核对条形码上的姓名、准考证号，并将条形码粘贴在答题卡的指定位置上。

2.答题时使用0.5毫米的黑色中性（签字）笔或碳素笔书写，字体工整、笔迹清楚。

3.请按照题号在各题的答题区域（黑色线框）内作答，超出答题区域书写的答案无效。

4.保持卡面清洁，不折叠，不破损。

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。

听力部分不计入总分。

第一节（共5小题；每小题1.5分，满分7.5分）听下面5段对话。

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

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

例如：How much is the shirt?A.£ 19.15.答案是B。

1.Who is the woman?A.A bus driver.B.£ 9. 15.B.A policewoman.2.When does the woman want to take the class?A.On Thursday.B.On Friday.3.What did the speakers do last weekend?A.They studied at home.B.They went hiking.4.Where are the speakers?A.In a library.B.In a study room.5.What will the woman do next?A.Stand on the hill alone.B.Take a picture for the man.C.Visit Chicago with the man.高三英语试题第1页（共10页）C.£ 9. 18.C.A passenger. C.On Saturday. C.They played tennis.C.In a bookstore.运城市2022-2023学年度高三第一学期期末调研测试英语参考答案第一部分听力1-5AACCB6-10BBCAA11-15BBAAC16-20CBBCA第二部分阅读理解A:21-23BCD B:24-27:BADD C:28-31BADB D:32-35:CDCB36-40EABFG第三部分语言知识运用41-45.CDACB46-50.CBCBD51-55.CADDA56.gathering57.the58.have seen59.and60.with61.who62.looking63.kicked64.planned65.approximately 第四部分写作第一节书面表达Dear Jim,I am quite disturbed these days as I have a disagreement with my parents over my career choice.I just can’t help writing to tell about it and ask for your advice.I have always dreamed of being a tourist guide,which will offer me great opportunities to broaden my horizon and enrich my experience.However,my parents hope that I should go in for professions with a secure income and stable life like teachers or doctors.I am caught in a dilemma.Is it better to obey my parents and take a career that I don’t enjoy but guarantee long-term stability?Or should I go against my parents’will and pursuit a career that brings me happiness and satisfaction?What would you do if you were in my position?I really hope that you can give me some advice.Yours,Li Hua【分析】本文是一篇应用文，由于和父母在未来职业选择上意见不一，于是写信给国外朋友Jim写信倾诉自己的苦恼并请他给提些建议。

山西省运城市教育发展联盟2023-2024学年高二上学期10月调研测试数学试题学校:___________姓名：___________班级：___________考号：___________一、单选题二、多选题三、填空题四、解答题(1)以{},,a b c为基底表示OQ (2)若||||1,||2,a b c OAB ∠===18．已知圆C 经过()()0,2,1,1A B ，且圆心在直线1:240l x y +-=上.(1)求圆C 的方程；(2)若从点()3,5M 发出的光线经过直线2:10l x y +-=反射后恰好平分圆C 的圆周，求反射光线所在直线的方程.19．如图，在三棱柱111ABC A B C -中，底面三角形ABC 是边长为4的正三角形，侧面11ACC A 是菱形，且平面11ACC A ⊥平面,,ABC E F 分别是棱11,A C BC 的中点，12C G GC = .(1)证明：EF 平面11ABB A ；(2)若①三棱锥1C ABC -的体积为8；②1C C 与底面ABC 所成角为60 ；③异面直线1B B 与AE 所成的角的大小为30 .请选择一个条件求平面EFG 与平面11ABB A 所成角（锐角）的余弦值.20．一副三角板如图（1），将其中的ABC 沿BC 折起，构造出如图（2）所示的三棱锥，E 为CD 的中点，连接AE ，使得AE BD =.(1)取BC 中点O ，连接,OE OA ，设平面DBA ⋂平面AEO l =，求证：//l BD ；(2)证明：平面ABC ⊥平面BCD ；(3)求直线AE 与平面ABD 所成角的正弦值.21．直线()():121740l m x m y m +++--=，圆22:6430C x y x y +---=.(1)证明：直线l 恒过定点P ，并求出定点P 的坐标；(2)当直线l 被圆C 截得的弦最短时，求此时l 的方程；(3)设直线l 与圆C 交于,A B 两点，当ABC 的面积最大时，求直线l 方程.22．如图，四棱锥P ABCD -中，四边形ABCD 为直角梯形，平面ABCD ⊥平面,PAB AB CD ∥，,22,2CD BC BC CD AB PD PA ⊥====.(1)若ABP 与DCP 相似，三棱锥A PBC -的外接球的球心恰为PC 中点，求AB 与平面PCA 所成角的正弦值；(2)求四棱锥P ABCD -体积的最大值.。

2022-2023学年山西省名校联考高二（上）期末英语试卷APlanning on watching a Premier League match，an FA Cup or a fierce England clash（比赛）？Head to one of these football friendly pubs and bars，where you can score wonderful surrounding with a cold beer and some delicious food.The Belushi's Sports Bar，London BridgeStudent-styled bar with lots of large screens，plus filling burgers and bar snacks.They're strict with IDs，so bring one.Other Belushi's can be found around London （Camden，Shepherd's Bush，Hammersmith，Greenwich）.The Belushi's Sports Bar，161-165，Borough High Street，SEll HRPub on the Park，HackneyTrue to its name，you can pretty much watch the match in the park-the gardens here are furnished with TVs and heaters.Admirable range of beers for a sports establishment.Pub on the Park，19 Martello Street，E8 3 PEThree Compasses，DalstonSpacious gastro（美食的）pub with a few screens.You can enjoy home-made beer and award-winning burgers here （made with Angus beef we're told）.Three Compasses，99 Dalston Lane，E8 1 NHFamous Three Kings，HammersmithWinner of various sports pub awards.Screens everywhere you look.One of the gardens shows football when it's warm enough.This is a Liverpool pub，but all comers are welcome.Famous Three Kings，171 North End Road，W14 9 NLSports Bar & Grill，Old Street，Canary WharfBook a table for individual screens.A bit anti-social maybe，but one way to guarantee you're not stretching your neck for 90 minutes.The food isn't cheap.There are other Sports Bar & Grills across London （Marylebone，Canary Wharf，Clapham Junction，Farringdon，Victoria），not all with the private TV option—which is why we recommend this one.Sports Bar & Grill，174-180 Old Street1. Which bar has strict requirements on IDs？______A. Sports Bar & Grill.B. Famous Three Kings.C. The Belushi's Sports Bar.D. Clissold Park Tavern.2. Which place is your best choice if you are a burger lover？______A. 99 Dalston Lane.B. 19 Martello Street.C. 171 North End Road.D. 174-180 Old Street.3. What do the Belushi's Sports Bar and Sports Bar &Grill have in common？______A. They offer large private screen.B. They have other chain bars across London.C. They are winners of various sports pub awards.D. They have gardens furnished with TVs and heaters.BAn open-air swimming pool in Bedfordshire，England，proved very popular this winter.The Woburn Lido is usually open from May to September，but this year it stayed open to swimmers throughout the autumn and winter months too.Until the lockdown（封锁）for England was announced on 4 January，outdoor pools were allowed to remain open. "Demand has taken us by surprise." said Murray Heining，a volunteer at the Woburn Lido.Over Christmas and New Year，in order to keep up with the demand from swimmers，the lido（露天游泳）had to offer extra slots for people to dive in.Cold-water swimming has grown in popularity in the UK over the past few years.A survey found that 7.5 million people in England had swum in outdoor pools，as well as lakes，rivers and the sea，in 2018.In some areas，such as the river Wharfe in Yorkshire，this new trend has prompted environmental groups to ensure that the water is cleared of pollution and clean enough for bathers.Some people make it a regular practice；others just enjoy a thrilling dip on Christmas Day，Boxing Day or New Year's Day.Every year around the UK，people are photographed jumping into icy water，often in fancy dress，and the recent festive period was no exception，despite freezing temperatures.The Outdoor Swimming Society classifies temperatures below 6℃ as "Baltic" and from 6-11℃ as "freezing".They advise people to get in the water gradually，so as not to shock the body.Likewise，they recommend warming up gradually，and not rushing the process by leaping into a hot bath when you get out.Instead，they suggest layering up and drinking something warm.It wasn't just the water that was cold—many people experienced a white Christmas；snow fell in several counties including Yorkshire and Suffolk.Paul Davies，the UK Met Office's chief meteorologist （a scientist who studies the weather），said the forecast indicates "the likelihood of the cold conditions experienced recently continuing through January".4. Which of the following can replace the word "slots" in Paragraph 2？______A. Volunteers.B. Solutions.C. Opportunities.D. Positions.5. What can we learn about cold-water swimming in the UK？______A. It is beneficial to environmental protection.B. It has won people's affections in recent years.C. People only go cold-water swimming in festive period.D. People go cold-water swimming to show off their fancy dresses.6. What does the Outdoor Swimming Society advise people to do？______A. Shock the body gradually.B. Have some warm drinks when they get out.C. Take a hot bath immediately.D. Avoid swimming in freezing temperatures.7. What is the best title of this passage？______A. Swimmers Enjoy Chilly DipsB. Freezing Weather Hits BritainC. The Woburn Lido Wins PopularityD. The UK Recovers from the LockdownCWe humans have an outsize influence on this planet，and our winged，finned，and four-legged neighbors are in their tough time.Many animals have died out in response to the pressures，but some survivors are adapting.Some animals are showing off never-before-seen behaviors，shifting their diets，and even evolving different shapes，sizes，and colors.The shifts can't be avoided and are likely permanent：There's no going back to when wildlife was still completely wild. "There's no place anywhere on the planet in its original condition.There are micro plastics at the bottom of the ocean，and Antarctica is melting.The world has changed because we're in it，" says Tag Engstrom，a biologist at California State University.African elephants in Mozambique's Gorongosa National Park are some daring members of the animal kingdom，who have found a will and a way to change right along with it.Normally elephants use their 6-foot-long tusks to dig wells in search of water，lift objects，rip bark off trees，and even battle lions.In other words，the ivory appendages （附属品）are not just impressive to look at — they are highly useful tools.So it might seem strange that a significant number of African elephants in Mozambique's Gorongosa National Park，once an illegal hunting wildlife area，are now being born without tusks.According to a 2021 DNA analysis published in the journal Science，that the elephants are born without tusks is no coincidence.After decades of being shot by ivory brokers，the leading elephants in some herds have passed down a trait that prevents the females' prize possessions from growing in — and helps them avoid being hunted.No one knows yet how widespread these genes might be in the greater population ofAfrican elephants，or how the loss of tusks might affect the mammals' survival overall.But the findings area powerful，if depressing，reminder of the extremes a species might endure to escape from extinction.8. How do the animals respond to humans influence？______A. Many animals have evolved four legs.B. Animals can survive despite the tough time.C. Some animals are developing different shapes.D. Animals live in harmony with human beings.9. Why are the shifts likely permanent？______A. We human beings are evolving.B. Wildlife are not going back to the wild.C. Plastics appear at the bottom of the ocean.D. The planet is no longer what it was like before.10. What can we infer from the 2021 DNA analysis？______A. The elephants evolve the new trait by chance.B. Elephants in some herds are all born without tusks.C. Genes will be widespread in the greater population.D. The new trait may help elephants survive the extinction.11. In which column of a magazine can we most likely to find the text？______A. Travel.B. Science.C. Puzzles.D. Well-being.DDo you see a bird right now？Can you hear one singing？If so，you might be getting a mental health boost.A recent study found that being in the presence of birds made people feel more positive.Andrea Mechelli，a psychologist at King's College London and one of the paper's authors，admitted himself studying the natural world by accident. "I don't have a particular agenda focused on nature myself.I wasn't thinking we were going to demonstrate nature has a strong effect，" says Mechelli.Instead，he was searching for answers to why people who live in cities seem to be more likely to suffer from mental illness，particularly psychosis（精神病）.In 2015，he created the smartphone app Urban Mind to search for patterns in users' environments.How crowded was their city？Did they feel safe in their neighborhood？Could they see trees？"Our first finding was that nature has a very powerful effect，" says Mechelli.He and his colleagues then wondered if some aspects of nature were more beneficial than others.Their latest study included 1，292 participants，mainly in the United Kingdom and Europe，some of whom revealed a professional mental health diagnosis such as depression.For two weeks，study participants using Urban Mind were reminded to fill out a questionnaire three times a day.They were asked questionsabout their surrounding environment and their mental state.The data were recorded at the same time. With the data collected，Mechelli performed a statistical analysis that found an obvious improvement in well-being when birds were present，even when removing other factors like the presence of trees or waterways.The mental health benefit was true both for people with diagnosed depression and those without any diagnosed mental health conditions.Nature，Mechelli notes，isn't a cure all.The presence of trees and birds，for example，didn't result in a better sense of well-being if participants also noted their neighborhood felt unsafe.12. Why does the author ask questions in the first paragraph？______A. To offer examples.B. To make comparisons.C. To introduce the topic.D. To support the conclusion.13. What is Paragraph 2 mainly about？______A. The process of the research.B. The purpose of the research.C. The findings of the research.D. The influence of the research.14. The following would be investigated by Urban Mind EXCEPT ______ .A. the sight of treesB. the crowdedness of a cityC. the pressure from their workD. the security of a neighborhood15. What can we know about participants in the latest study？______A. They all came from the UK.B. They were diagnosed with depression.C. They recorded their feelings by themselves.D. They were required to answer different questions.According to a latest theory，people each have their own "happy weight". (1) Fortunately，you would be able to maintain your "happy weight" with ease by enjoying a balanced lifestyle and feel great：you sleep well and your mood is generally stable.Your "happy weight" doesn't require you to follow a crazy diet，remove your favorite foods or punish your body with endless exercise.It can be reached and maintained by adjusting yourself to your natural hunger and fullness cues，enjoying healthy foods 80% of the time and spoiling yourself 20% of the time and taking up exercise that brings you joy. (2)Throw away the scale. (3) Choose to no longer let the number on the scale define your progress，mood for the day or your self-worth.(4) If you find yourself constantly dieting，or feeling stressed about food，take some time to reflect on our relationship with food.You can work with a dietitian to support you to heal your relationship with food. Start engaging in movement and exercise you enjoy.If you've always viewed exercise as punishment，it's time to change your mindset and start exploring sports you actually enjoy.Try new activities，join new sporting groups，or sign up for online sports apps you've been wanting to try. (5)In summary，when you're at your "happy weight"，you feel great，confident and present in life.You havea healthy relationship with food—but most of all，you no longer allow the number on the scale to decide your worth and happiness.A．Always maintain a strict diet.B．Work on your relationship with food.C．You'll regain the joy in moving your body.D．Here are some tips to help find "happy weight".E．Then，you will achieve a so-called "happy weight".F．Your health is not defined by the exact number on the scale.G．It can be described as the weight where an adult body functions best.16. A. A B. B C. C D. D E. EF. FG. GH. H17. A. A B. B C. C D. D E. EF. FG. GH. H18. A. A B. B C. C D. D E. EF. FG. GH. H19. A. A B. B C. C D. D E. EF. FG. GH. H20. A. A B. B C. C D. D E. EF. FG. GH. HI was fresh out of college and just started my career.I moved to a new place and my family (21) to congratulate me just before Christmas.However，I was out of luck right before my first (22) trip.That morning，I said goodbye to my visiting family and left for the airport — or I (23) to reach the airport.My car battery was (24).I dropped my phone by accident.As a result，it (25) and wouldn't work.Worse still，my (26) had already left my new place.I didn't know anyone in the area and there were no taxis.It was my first real job.I was supposed to meet the managers at the airport and (27) the plane together.Panicked，I started(28)the 3 miles to the office，wishing to find some help there.It was dark and (29).I must have been a (30)：a suit walking along a snowy road at 5：30 a.m.，(31) with my luggage and briefcase.Before long，a motorist stopped and (32) offered me a ride to the company.Fortunately，I(33) it to the airport on ughter replaced my fear of getting (34)when I shared the tale of my crazy morning with the happy (35)，thanks to the kindness of a stranger.21. A. visited B. called C. planned D. prepared22. A. family B. business C. study D. field23. A. decided B. asked C. tried D. managed24. A. bad B. little C. short D. dead25. A. broke down B. broke up C. broke in D. broke out26. A. friends B. family C. classmates D. managers27. A. board B. launch C. fly D. book28. A. skiing B. driving C. walking D. wandering29. A. snowing B. raining C. fogging D. blowing30. A. character B. sight C. memory D. scenery31. A. doing B. meeting C. struggling D. fighting32. A. gently B. seriously C. hesitantly D. warmly33. A. made B. led C. showed D. delivered34. A. paid B. abused C. fired D. lost35. A. content B. outcome C. climax D. flight36. So，you are interested in becoming a good journalist but don't know where to start？Well，there are a couple of things you should put on your list of (1) （priority）.Firstly，you need to be skilled at writing.The information (2) （involve）in a complex story may come from dozens of sources.Good journalists need to organize dozens of information clearly to give an (3) （accuracy）account of what is happening.Secondly，you must have a natural curiosity about things (4) are happening，even though they may appear to be minor matters.When something newsworthy comes (5) ，it may escape the attention of ordinary people. (6) ，good journalists are sensitive enough (7) （notice）the event and draw public attention to it.Finally，good journalists are committed to (8) （reveal）the truth.According to Noam Chomsky，"The duty of journalists is to tell the truth.Journalism (9) （mean）you go back to the actual facts，you look at the documents，you discover what the record is，and you report it that way." To do this，journalists need to investigate an event (10) （thorough）.To sum up，being a good journalist requires writing skills，curiosity and commitment to finding the truth.Good luck!(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)37. 假如你是李华，你校英语报社为即将举行的校音乐节展开了"My Favorite Band/ Musician"为题的征文比赛。

2022-2023学年中考英语模拟试卷注意事项1．考生要认真填写考场号和座位序号。

2．试题所有答案必须填涂或书写在答题卡上，在试卷上作答无效。

第一部分必须用2B 铅笔作答；第二部分必须用黑色字迹的签字笔作答。

3．考试结束后，考生须将试卷和答题卡放在桌面上，待监考员收回。

Ⅰ. 单项选择1、—Have you ________ your plan, Jimmy?—Not yet. It still needs improving.A．given up B．handed in C．thought of D．put away2、— Jane, your watch is so nice. When and where did you buy it?—In November in Hongkong. I it for only several months. I went to visit the Hongkong-Zhuhai-Macao Bridge after buying the watch.A．bought B．had C．have had3、— Did you go to the cinema last night?— Oh, no. I go to the cinema. I think the tickets are too expensive.A．always B．hardly C．usually D．often4、I have to leave now __ I can catch the last bus.A．so that B．because of C．until D．as soon as5、—How do you like the fish I cooked for you?—I haven’t had it yet. However, it ________ good.A．smells B．tastesC．sounds D．feels6、---Could you tell me_______?----In five minutes, at 10: 25.A．when did the next underground arrive B．when the next underground arrivedC．when will the next underground arrive D．when the next underground will arrive7、Bob’s first book was by four book companies, but he didn’t lose heart.A．taken down B．come down C．turned down D．written down8、________ excellent volleyball player Zhu Ting is! I really love this talented girl.A．How B．What C．What an9、Mr. Li ____ to give a talk in our school yesterday.A．invites B．is invited C．was invited D．invited10、--Peter, please send us postcards we’ll know where you have visited.--No problem.A．but B．or C．for D．soⅡ. 完形填空11、完形填空，阅读下面的短文，从短文后各题所给的选项中选出能填入空白处的最佳答案。

2022～2023学年第一学期高二年级期末考试英语试题参考答案及评分建议(满分100分)第一部分听力（共两节；每小题1分，满分15分）1.B2.B3.A4.A5.C6.C7.C8.A9.B10.C11.B12.A13.C14.A15.B第二部分阅读理解（共两节；每小题2分，满分30分）16.C17.D18.B19.B20.D21.A22.A23.C24.D25.B26.B27.A28.F29.G30.D（以下是B种题型答案）说明：22~25小题根据学生答题情况可酌情给分。

22.The convenience of on-demand viewing.23.From the entertainment that was on offer.24.It can help us find more things than what we are looking for.25.They are full of unexpected joy.第三部分完形填空（共20小题；每小题1分，满分20分）31.A32.B33.D34.B45.A36.C37.D38.A39.B40.C41.A42.C43.B44.D45.C46.A47.D48.D49.C50.B第四部分语篇填空（每小题1分，满分10分）51.fascinating52.was given53.On54.to name55.surroundings 56.valuable57.designed58.where59.an60.vitally1第五部分写作（共两节，满分25分）说明：根据学生答题情况可酌情给分。

第一节（满分10分）One possible version:Dear Roy,How is it going?I’m writing to invite you to attend a photography exhibition held in our school,whose theme is“Impressive changes around me”.Here is some detailed information.The exhibition will last for about three hours in the school hall on Feb.15th.In addition,the exhibition will feature about fifty students’works centering on the ways people live and work in this fast-developing city.You will surely be amazed by the brilliant pictures and thus more familiar with the city.I would be very joyful if you could come.I’m looking forward to your reply.Yours sincerely,Students’Union第二节（满分15分）One possible version:Obviously,the cabin was quite tiny,so it was impossible to leave each other alone.Megan sat in one chair,trying to read and Elaine sat in another,singing song after song.When Elaine’s Dad noticed the strange atmosphere,he chose to figure out what had happened.He thought of the expression“too much of a good thing”,and explained that one piece of cake tastes delicious,but 10is too much.Thanks to the expression“too much of a good thing”from Elaine’s Dad,things got better. Elaine and Megan are still great friends.They realize that even best friends need to give each other some space when they need it.What’s more,good friends need to show respect and patience.In this way,it will be easier to understand each other and maintain their friendship.书面表达评分标准一、应用文写作评分参考标准（一）参考要点：1.时间、地点；2.活动特色；3.期待。

2020年1月山西省(高二年级)期末调研测试英语试题注意事项：1.答题前，考生务必将自己的学校、姓名、班级、准考证号填写在答题卡上相应的位置。

2.全部答案在答题卡上完成，答在本试题上无效。

3.回答选择题时，选出每小题答案后，用2B铅笔把答题卡上对应题目的答案标号涂黑。

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，将答案用0. 5毫米及以上黑色笔迹签字笔写在答题卡上。

4.考试结束后，将本试题和答题卡一并交回。

5.听力部分满分30分，不计入总分。

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）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。

1. How will the speakers probably go to the concert hall?A. By bus.B. On foot.C. By taxi.2. What does the man mean?A. He doesn't mind the weather.B. The weather is going to be fine.C. He doesn't mind being harmed.3. What is the weather like now?A. Sunny.B. Cloudy.C. Rainy.4. Where does the conversation take place?A. At a restaurant.B. At the theatre.C. At the station.5. Where are the speakers now?A. In the plane.B. At home.C. In the car.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。

运城市2023-2024学年度高三摸底调研测试英语答案1-5 CCBCB6-10 ABACA11-15 BCACC16-20 BACAB21-25 BACDD25-30 DCBAC31-35 CCBDA36-40 GFDAE41-45 BDCAB 46-50 CADBC 51-55AADBC56. Despite 57. preserving 58. more determined 59. conservation60. outweighed 61. to digitize 62. images 63. tirelessly64. on/ forward 65. where第一节One possible version：Dear fellows,A new column for the graduating students called “My school, I have something to say to you” is set up in our school newspaper. We are expecting your theme-related articles.We set no limit to the type—poems, essays, or novels are all welcome. Your contributions should cover your authentic experiences in your school life and genuine feelings that you want to extend. They are expected to be original and within 300 words. Please submit your articles before May 20th to *************************. Works chosen, you will get a certificate and 200 yuan in prize money.Write down your stories and keep your cherished memory alive. Looking forward to your works!The Editorial SectionMay 5th, 2023第二节One possible version：Soon after, all the negative words started to destroy me. I cried myself to sleep late in the night and woke up with swollen eyes the next morning, hardly able to get out of my room. Several days later, overwhelmed by depression, I refused to go to school and talk with someone and even refused food. It seemed that I was totally trapped in darkness. Thankfully, the magazines at hand helped to relieve my stress somehow. Everything changed from that day, when I happened to read an article.I saw a quote in the journal. “Once you choose your way of life, be brave to stick it out andnever return.” Reading it, I suddenly caught what it meant. I could either let myself down in the gossip or hug it as a chance to grow up and become better. So I reread the posts and reflected on my recent experiences. I realized that I was bothered because I cared so much about people’s bad comments that I lost heart and forgot my target. It’s time to face the situation bravely and stick to what I have always dreamed to do.听力录音原文Text 1W: We haven’t seen much of you lately in the hospital. Have you been away on business? M: No, I’ve been away on holiday with my family.Text 2W: You can change planes in either Chicago or Denver.M: You mean there’s no direct flight from New York to Phoenix?Text 3M: Those tickets on Tuesday are so expensive. Can’t you find anything better before Friday? W: Well, if we want cheaper tickets, we have to leave on Thursday.Text 4W: Oh, don’t throw that away!M: Why not? It’s been used already.W: You can get a new label and put it on top of the old address, and then you can buy a bigger stamp and put it on top of the old stamp.M: Good idea!Text 5M: Can I borrow your biology textbook? Mine was gone when I went back in the classroom. W: That happened to me once. I’d almost given up on finding it until I checked it at the information desk downstairs in the lobby.M: Oh, good idea.Text 6W: Is university pretty much what you expected, Sam?M: Well, ⑥I’ve been here two months now and I’m just getting used to it, really. It’s certainly not easy. In fact, the workload is more than I expected. I’ve got to do loads of reading, for example.W: How do you find the lectures?M: Well, ⑦the professors are great speakers and they know how to hold your interest. I’ve never been bored.Text 7M: You just said ⑧you’re interested in our position of production manager. Do you have experience in this position?W: Yes, I’ve worked in a similar position for three years.M: Could you tell me about some of your achievements from your previous job?W: Well, I made full use in my job of what I had learned in university and, since my work was sati sfactory, I was promoted to be a team leader after only one year. With our team’s hard work, ⑨we were able to reduce production costs by 15%, 3% more than your company’s goal for the coming year.M: Great! Could you tell me about your educational background?W: Of course. I have a bachelor’s degree in management from Peking University.M: Hmm, not bad. I wonder how much you know about our company.W: ⑩I’ve visited your company’s website. I know that your company is one of the Global 500 and the company’s stock price has increased by 10% recently because of its outstanding performance.M: OK, thank you. We’ll call you in a week if we would like to hire you.W: Thank you very much.Text 8W: Hi! It’s nice to see you. Where have you been these days?M: I went to Beijing for business.⑪I left last week on Wednesday and returned yesterday morning. Because it was Friday yesterday and the manager wasn’t going to work on the weekend,⑫I had to spend the whole day preparing a report about my Beijing business trip. I worked on it until I got a headache, but⑫I finished the report in time to send to the manager just half an hour before the end of the workday.W: No wonder you’re looking so tired. You’ve been working much too hard.M: True. That’s why I came here to the park to relax a bit.W: How was your business in Beijing?M: I could say it was a success —I was able to return earlier than I’d planned. I had thought my trip would last two weeks and I would have to spend Christmas alone.W: Congratulations! I hope you can enjoy yourself now.⑬Let’s get together sometime. M: OK. Goodbye!Text 9W: We’re looking for someone to sell our new software products internationally. The job requires independence and ⑭most importantly, a pleasant manner with customers.M: I agree...that’s important. I’ve worked in sales for years and have always tried to really listen to my customers to find out what they need. I think I’m really good at it.W: That’s g reat. What about your experience with software programs?M: Well, I’ve trained people how to use a similar software product for the past two years at my current job, so I really feel I know the product.W: Hmm...interesting, and your sales experience?M: I’ve been with my present company for four years and ⑮in my present position since two years ago. During that time, ⑯I’ve been named salesperson of the month three times, and have taken top sales awards several times as well.W: ⑰Impressive...Text 10Women like shopping, me included of course. I used to shop with my friends almost every week. ⑱But this year I decided to try to go for a year without shopping for clothes.I have to say it has been really hard. But I don’t want to give up. ⑱So why did I decide to do that?First, it’s about money. Last year, being tired of doing the work I disliked, I left my highly-paid job and found a job that doesn’t pay that much. But I was still spending a lot of money on clothes. As a result, I didn’t have any savings. I decided to spe nd less on clothes.Second, I already have a lot of clothes. ⑲According to a study, most women wear only 20-30% of their clothes. A year without shopping for clothes gave me a chance to wearthe clothes that I haven’t tried before. I wasn’t buying any new clothes, but I still had many new clothes to wear.Third, I have less time for shopping than before. Now I’m trying to lose some weight, ⑳so I go to the gym with friends on the weekend.If I were going shopping, I’d have no time to go to the gym.。

2022—2023 学年高二上学期期末考试英语试卷参考答案详解（新高考）（公共版）英语试题第一部分听力1—5 BBCAB 6—10 BAABC 11—15 CBCAC 16—20 CBCAA第二部分阅读第一节A篇本文是一篇应用文。

文章主要介绍了英国伦敦设计博物馆和国家足球博物馆举办的一场展出——“足球：设计美丽的运动”的相关内容。

21. D 细节理解题。

根据What to expect部分中的“involve yourself in the stories ofclubs and game legends (传奇人物) ... Diego Maradona”可知，参观者在展览会上可以了解到包括梅西、贝利、乔治·贝斯特和迭戈·马拉多纳在内的足坛人物的故事。

故选D。

22. A 细节理解题。

根据Ticket information部分中的“Adult tickets are chargedfrom £16 and student tickets from £12. Meanwhile, you can save 25% on family and group tickets.”可知，成人票16英镑起，学生票12英镑起，家庭团体票可以享受七五折优惠。

因此他们至少应支付的费用为（16×2 + 12）×0.75 = 33（英镑）。

故选A。

23. A 细节理解题。

根据Ticket information部分中的“Present your exhibition entryticket for 10% off food and drink at London Grade Coffee on the ground floor.”可知，参观者在一楼咖啡厅购买食物和饮料时凭门票可享受九折优惠。

故选A。

B篇本文是一篇记叙文。

Franco Cagnoli看到太阳从罗卡卡拉西奥的城堡升起时深受震撼，于是决定并着手帮助复兴这个意大利小山村。

2022-2023学年山西省运城市教育发展联盟高二上学期12月调研数学试题一、单选题1．准线方程为2x =的抛物线的标准方程为（ ）A ．28y x =B ．28y x =-C ．28x y =D ．28x y【答案】B【分析】结合抛物线的定义求得正确答案.【详解】由于抛物线的准线方程是2x =，所以抛物线的开口向左，设抛物线的方程为()220y px p =->， 则2,282p p ==，所以抛物线的标准方程为28y x =-. 故选：B2．已知等差数列{}n a 的前n 项和为n S ，若12a =，530S =，则8a =（ ）A ．10B ．12C ．14D ．16 【答案】D【分析】首先通过已知条件求出等差数列的基本量1a 和d ，然后根据等差数列的通项公式进行求解即可.【详解】已知12a =，所以515455210302S a d d ⨯=+=⨯+=，解得2d =. 因此得81727216a a d =+=+⨯=.故选：D3．已知双曲线()222210,0y x a b a b-=>>的实轴长为4，虚轴长为6，则双曲线的渐近线方程为（ ）A ．y x =B ．32y x =±C ．23y x =±D ．y x = 【答案】C【分析】根据双曲线几何性质解决即可. 【详解】由题知双曲线()222210,0y x a b a b-=>>中24,26a b ==， 所以2,3a b ==，双曲线焦点在y 轴上，所以双曲线的渐近线方程为23y x a b x =±=±， 故选：C. 4．已知圆2260x y x +-=，过点()2,2的直线被该圆所截得的弦长的最小值为（ ）A ．1B ．2C ．3D ．4 【答案】D【分析】结合已知条件求出圆的圆心和半径，由圆的弦长公式和性质即可求解.【详解】由圆的方程2260x y x +-=可知22(3)9x y -+=，则圆心坐标(3,0)C ，半径为3，因为22(23)(20)59-+-=<，所以点()2,2D 在圆的内部，设圆心到直线的距离为d ，则过()2,2的直线与圆的相交弦长AB =显然当d 最大时，弦长最小，由圆的性质可知当CD AB ⊥时d 最大，此时max d CD ==所以弦长的最小值为4，故选：D5．已知直线l ：()()2110m x m y m ++++=经过定点P ，直线l '经过点P ，且l '的方向向量()3,2a =，则直线l '的方程为（ ）A ．2350x y -+=B ．2350x y --=C ．3250x y -+=D ．3250x y --=【答案】A【分析】直线l 方程变为()210x y m x y ++++=，可得定点P ()1,1-.根据l '的方向向量()3,2a =，可得斜率为23，代入点斜式方程，化简为一般式即可.【详解】()()2110m x m y m ++++=可变形为()210x y m x y ++++=， 解0210x y x y +=⎧⎨++=⎩得11x y =-⎧⎨=⎩，即P 点坐标为()1,1-. 因为()23,231,3a ⎛⎫== ⎪⎝⎭，所以直线l '的斜率为23，又l '过点P ()1,1-， 代入点斜式方程可得()2113y x -=+，整理可得2350x y -+=.故选：A.6．已知空间直角坐标系中的点()1,1,1P ，()2,0,1A ，()0,1,0B ，则点Р到直线AB 的距离为（ ）A B C D 【答案】D【分析】由向量在向量上的投影及勾股定理即可求. 【详解】()1,1,1P ，()2,0,1A ，()0,1,0B ，∴()2,1,1AB =--，()1,1,0AP =-，2AP =AP 在AB 上的投影为|3|AP AB AB ⋅=则点P 到直线AB 22||AP AB AP AB ⎛⎫⋅-== ⎪ ⎪⎝⎭. 故选：D ． 7．在平面直角坐标系xOy 中，已知圆A ：()22220x y -+=（圆心为A ），点()2,0B -，点Р在圆A 上运动，设线段PB 的垂直平分线和直线P A 的交点为Q ，则点Q 的轨迹方程为（ ）A ．2215x y -= B ．2215y x += C ．2215x y += D ．2215y x -= 【答案】C【分析】根据椭圆的定义求得正确答案.【详解】圆A ：()22220x y -+=的圆心()2,0A ，半径r =. 由于()221220206=--+<，所以()2,0B -在圆A 内，AB 4= 根据垂直平分线的性质可知QP QB =，所以QA QB QA QP r AB +=+==，所以Q 点的轨迹是椭圆，且24,2,1a a c c b =====，所以点Q 的轨迹方程是2215x y +=. 故选：C8．众所周知的“太极图”，其形状如对称的阴阳两鱼互抱在一起，因而也被称为“阴阳鱼太极图”.如图是放在平面直角坐标系中的“太极图”，整个图形是一个圆形，其中黑色阴影区域在y 轴右侧部分的边界为一个半圆，已知直线l ：()2y a x =-.给出以下命题：①当0a =时，若直线l 截黑色阴影区域所得两部分面积记为1S ，2S （12S S ≥），则12:3:1S S =；②当43a =-时，直线l 与黑色阴影区域有1个公共点； ③当(]0,1a ∈时，直线l 与黑色阴影区域有2个公共点.其中所有正确命题的序号是（ ） A ．①②B ．①③C ．②③D ．①②③【答案】A 【分析】由题知根据直线l ：()2y a x =-横过点(2,0) ，a 为直线的斜率 根据直线和圆的位置关系作图，数形结合逐项分析判断即可得解【详解】如图1所示，大圆的半径为2，小圆的半径为1，所以大圆的面积为4π，小圆的面积为π．对于①，当0a =时，直线l 的方程为0y =．此时直线l 将黑色阴影区域的面积分为两部分，1π3ππ22S =+=，2πππ22S =-=， 所以12:3:1S S =，故①正确．对于②，根据题意，黑色阴影区域在第一象限的边界方程为()()22110x y x +-=> 当43a =-时，直线l 的方程为()423y x =--， 即4380x y +-=，小圆圆心()0,1到直线l 的距离2238143d -==+，所以直线l 与该半圆弧相切，如图2所示， 所以直线l 与黑色阴影区域只有一个公共点，故②正确．对于③，当(]0,1a ∈时，如图3所示，直线():2l y a x =-与黑色阴影区域的边界曲线有2个公共点，当1a =时，直线:2l y x =-与黑色阴影区域的边界曲线有1个公共点，故③错误． 综上所述，①②正确．故选：A ．二、多选题9．已知双曲线C ：22197y x -=，则下列选项中正确的是（ ） A ．C 的焦点坐标为()4,0± B ．C 的顶点坐标为()0,3±C ．C 的离心率为43D ．C 的焦点到渐近线的距离为3【答案】BC 【分析】根据已知条件，可知双曲线的焦点在y 轴上，3a =，b =4c =，然后逐项判断双曲线的性质即可.对于D 项，根据点到直线的距离求出即可判断.【详解】由已知，双曲线的焦点在y 轴上，且29a =，27b =，则216c =， 所以3a =，b =4c =.所以C 的焦点坐标为()0,4-、()0,4，故A 项错误； 顶点坐标为()0,3、()0,3-，故B 项正确； 离心率43c e a ==，所以C 项正确；30x -=30x +=，焦点()0,430x +=23=+D 项错误. 故选：BC.10．已知等比数列{}n a 是单调数列，设n S 是其前n 项和，若1243a =，53a =，则下列结论正确的是（ ）A ．327a =±B ．63n n a -=C ．4332n n S +-=D ．121211n n a a a a a a -⋅⋅⋅=⋅⋅⋅【答案】BD【分析】利用等比数列的通项公式和前n 项和求解即可.【详解】设等比数列{}n a 的公比为q ，则有5145124333a a a q ⎧==⎨==⎩，解得13q =或13-， 当13q =-时数列{}n a 不是单调数列，所以13q =， 所以23127a a q ==，故A 错误；115611333n n n n a a q ---⎛⎫==⨯= ⎪⎝⎭，故B 正确；56611313(1)332123n n n n S a q q -⎡⎤⎛⎫-⎢⎥ ⎪⎝⎭--⎢⎥⎣⎦===-，故C 错误； (11)5462123333n n n n a a a --⨯⨯⨯⋅⋅⋅==，()11(55)(11)54521211233333n n n n n n a a a --+---+==⋅⋅⋅⨯⨯⨯=，所以121211n n a a a a a a -⋅⋅⋅=⋅⋅⋅成立，故D 正确. 故选:BD.11．如图，直三棱柱111ABC A B C 中，11AA AB ==，2AC =，5BC =．点Р在线段1B C 上（不含端点），则（ ）A ．不存在点P ，使得1AB BP ⊥B ．ABP 5C ．PA PB +5D ．三棱锥1B PAB -与三棱锥1C PAC -的体积之和为定值【答案】BD【分析】对于A 项，通过证明111AB BA C ⊥面可得出11AB BC ⊥，进而得出使得1AB BP ⊥的P 点的位置；对于B 项，通过转化，表达出三棱锥11-A A B C 的两种体积的表达式，即可求出点P 到AB 的距离的最小值，进而求出ABP 面积的最小值；对于C 项，通过对两个面的翻转和几何知识求出cos ACB ∠，进而求出PA PB +的最小值；对于D 项，通过转化，分别得到点P 到面11AA B B 的距离为点M 到面11AA B B 的距离，点P 到面11AAC C 的距离为点M 到面11AAC C 的距离，表达出三棱锥1B PAB -与三棱锥1C PAC -的体积之和，即可求出三棱锥1B PAB -与三棱锥1C PAC -的体积之和为定值.【详解】解：由题意在直三棱柱111ABC A B C 中，11AA AB ==，1AC AA ⊥， 1AB AA ⊥，11//AB A B∴11AB A B ⊥在△ABC 中，2AC =，5BC =222AB AC BC += ∴AB AC ⊥∵1AA AB A =,1AA AC A =∴11AC AA B B ⊥面，11AB AAC C ⊥面在矩形11AAC C 中，11//AC A C如下图，连接1BC ，1AB ，1A B∴1AC AB ⊥∴111AC AB ⊥∵1111A B A C A =∴111AB BA C ⊥面∴11AB BC ⊥∴当点P 为1B C 和1BC 的交点时，1AB BP ⊥， 故A 错误.连接1A C ，点P 到AB 的距离的最小值为直线AB 与1B C 之间的距离d ， ∵11//AB A B ，1111A B A B C ⊂面∴11//AB A B C 面∴点A 到面11A B C 的距离为d ，在三棱锥11-A A B C 中，1111A A B C C AA B V V --=, 即11111111151123232A ABC C AA B V d V --=⨯⨯⨯⋅==⨯⨯⨯⨯ 解得：255d = ∴min 12551255ABP S =⨯⨯=△， 故B 正确.将△1AB C 和△1BB C 沿BC 展开，连接AB 交1B C 于点D ，当点P 与点D 重合时PA PB +的值最小，如下图所示：116cos 6AC B CA B C ∠===11123sin 6AB B CA B C ∠==， 11530cos 6BC BCB B C ∠===1116sin 6BB BCB B C ∠===，()11111163036252cos cos cos cos sin sin 36366ACB ACB BCB ACB BCB ACB BCB -∠=∠+∠=∠∠-∠∠=⨯-⨯=在△1AB C 中，由余弦定理得，()22222521562cos 2522563AB AC BC AC BC ACB -+=+-⋅⋅∠=+-⨯⨯⨯= 故C 错误. 过点P 作直线1//PM CC ，交11B C 于点M ，如下图所示，∴点P 到面11AA B B 的距离为点M 到面11AA B B 的距离，设为1d ，点P 到面11AAC C 的距离为点M 到面11AAC C 的距离，设为2d .在△111A B C 中，由几何知识得，111A B =，112A C =，111tan 2A B C ∠=， ∴111122B E ME d ==∴三棱锥1B PAB -与三棱锥1C PAC -的体积之和为111112121111111111111232323233C PAC P ACC B PAB P ABB V V V V d d d d A B ----⎛⎫+=+=⨯⨯⨯⋅+⨯⨯⨯⋅=+== ⎪⎝⎭， 故D 正确.故选：BD.【点睛】考查了立体几何中的动点的相关位置关系，面积，体积和最值问题，考查空间想象力和逻辑推理能力.12．在平面四边形ABCD 中，A ，C 在BD 两侧，ABD △的面积是BCD △面积的2倍，又数列{}n a 满足12a =，恒有()()1122n n n n BD a BA aBC -+=++-，设数列{}n a 的前n 项和为n S ，则（ ）A ．{}n a 为递增数列B ．{}n a 为等比数列C ．2n n a ⎧⎫⎨⎬⎩⎭为等差数列D ．()1122n n S n +=-⋅+【答案】ACD【分析】设AC 与BD 交于点E ，由面积比得2AECE=，根据平面向量基本定理得BD 与,BA BC 关系，从而得数列{}n a 递推关系，然后根据各选项求解数列，判断结论，其中选项D 需要用错位相减法求和．【详解】设AC 与BD 交于点E ，1sin 221sin 2ABD CBDBD AE AEBS AESCE BD CE CEB ⋅∠===⋅∠， 2212()3333BE BA AE BA AC BA BC BA BA BC =+=+=+-=+， ,,B E D 共线，所以存在实数(0)λλ≠，使得BD BE λ=，所以()()1122n n n n BD a BA aBC -+=++-1233BA BC λλ=+，所以11123223n n n n a a λλ-+⎧+=⎪⎪⎨⎪-=⎪⎩，所以()11222-++=-n n n n a a ，1122n n n a a ++=+，所以11122n n n n a a ++=+，即2n na ⎧⎫⎨⎬⎩⎭是以112a =为首项，1为公差的等差数列，故C 正确； 所以()112nna n n =+-=，即·2n n a n =， 对于A ，()1112++=+n n a n ，()()11122220++-=+-=+>n n nn n a a n n n ，所以{}n a 为递增数列，故A 正确；对于B ，12a =，28a =，324a =，所以2213a a a ≠，所以{}n a 不是等比数列，故B 错误；对于D ，因为23121222322=+++=⨯+⨯+⨯++⨯n n n S a a a n ，23121222(1)22n n n S n n +=⨯+⨯++-⨯+⨯，所以两式相减得23122222n n n S n +-=++++-⨯112(12)22(1)212n n n n n ++-=-⨯=---⨯-，所以()1212+=+-⨯n n S n ，D 正确．故选：ACD ．三、填空题13．已知数列{}n a 的前n 项和21n S n =+，则数列{}n a 的通项公式是______.【答案】2,121,2*n n a n n n N =⎧=⎨-≥∈⎩且 【分析】1n = 时,112a S ==,利用2n ≥ 时,1n n n a S S -=- 可得21n a n =-,最后验证1n =是否满足上式,不满足时候,要写成分段函数的形式. 【详解】当1n = 时, 112a S ==,当2n ≥时, 1n n n a S S -=-=221(1)121n n n +---=-, 又1n = 时,12111n a a ==⨯-=不适合,所以2,121,2n n a n n =⎧=⎨-≥⎩. 【点睛】本题考查了由n S 求n a ,注意使用1n n n a S S -=-求n a 时的条件是2n ≥,所以求出n a 后还要验证n a 适不适合1n = ,如果适合,要将两种情况合成一种情况作答,如果不适合,要用分段函数的形式作答.属于中档题.14310x y +-=与直线320x my ++=平行，则它们之间的距离是____________． 【答案】1【分析】根据两直线平行，可得2m =，然后根据两条平行线之间的距离公式即可求出距离. 3130m -⨯=，所以2m =，10y +-=与220y ++=.将直线方程220y ++=10y ++=，1=.故答案为：1.15．在平行六面体1111ABCD A B C D -中，1AA a =，AB b =，AD c =，点P 在1A C 上，且1:2:3A P PC =，则DP =___________．（用a ，b ，c 表示） 【答案】323555a b c +-【分析】利用空间向量的基本定理可得出DP 关于{},,a b c 的表达式.【详解】由平面六面体法则可知111111AC A B A D A A b c a =++=+-， ()()11112232355555DP A P A D AC AD AA b c a c a a b c =-=--=+--+=+-. 故答案为：323555a b c +-.16．已知椭圆C ：()222210x y a b a b+=>>的左、右焦点分别是1F ，2F ，斜率为12的直线l 经过左焦点1F 且交C 于A ，B 两点（点A在第一象限），设12AF F △的内切圆半径为1r ，12BF F △的内切圆半径为2r ，若122r r =，则椭圆的离心率e =___________． 【分析】由题意得122A B r y r y =-=，联立直线与椭圆方程得22244A B b c y y a b +=+，4224A B b y y a b -⋅=+，再利用()22AB A B A BB Ay y y yy y y y +=++⋅，再代入值计算即可得答案. 【详解】如图所示，由椭圆定义可得122AF AF a +=，122BF BF a +=， 设12AF F △的面积为1S ，12BF F △的面积为2S ，因为123r r =， 所以()()()111222112222221122222A A BB a c r c y S r y S r y a c r c y +⨯⨯==⇒=-=+⨯⨯-，即2A B y y =-， 设直线:2l x y c =-，则联立椭圆方程与直线l ，可得222242222222(4)40x y ca b y b cy b b x a y a b=-⎧⇒+--=⎨+=⎩， 由韦达定理得：22244A B b cy y a b+=+，4224A B b y y a b -⋅=+ 又()22A B A B A B B A y y y y y y y y +=++⋅，即2222422441122224b c a b b a b ⎛⎫⎪+⎝⎭=-+-=--+ 化简可得()222222216132442c c a a c a b =⇒=+-+，即22365c a =， 即22365c a =时，有255366e e =⇒=. 故答案为：56四、解答题17．已知圆C 过平面内三点()0,4A ，(2,25M ，(2,25N -． (1)求圆C 的标准方程；(2)若点B 也在圆C 上，且弦AB 长为43AB 的方程． 【答案】(1)()22220x y -+=(2)(264y x =+或(264y x =+【分析】（1）将三点代入圆的一般方程，求解方程组得出圆的一般方程，再将其转化为标准方程即可；（2）先求出圆心C 到直线AB 的距离，当直线AB 斜率不存在时，验证直线是否满足要求，当直线AB 斜率存在时，设出方程，根据距离公式得出斜率，进而得出AB 方程. 【详解】（1）设圆C 的方程为220x y Dx Ey F ++++=，16404202042020E F D F D F ++=⎧⎪++++=⎨⎪++-+=⎩，解得4,0,16,D E F =-⎧⎪=⎨⎪=-⎩即224160x y x +--=，故圆C 的标准方程为()22220x y -+=． （2）圆心()2,0C 到直线AB的距离d =当直线AB 斜率不存在时，AB 方程为：0x =，此时2d =，不符合题意； 当直线AB 斜率存在时，设直线AB 方程为：4y kx =+，d ==2k =∴直线AB方程为(24y x =+或(24y x =+． 18．已知数列{}n a 的前n 项和为n S ，12a =，12n n a S +=+． (1)求数列{}n a 的通项公式；(2)若数列{}n b 满足221log n n n b a a +=+，求数列{}n b 的前n 项和n T ． 【答案】(1)2n n a = (2)12222n n T n n +=++-【分析】(1)由条件结合n S 与n a 的关系，证明数列{}n a 是等比数列，从而得到数列的通项公式；(2)由(1)可知221nn b n =+-，利用分组转化为等差数列和等比数列求和.【详解】（1）∵12n n a S +=+，① ∴()122n n a S n -=+≥．②①-②得1n n n a a a +-=，即()122n n a a n +=≥ 又12a =，2124a S =+=，∴212a a =，∴()*12n na n a +=∈N ， ∴{}n a 是以2为首项，2为公比的等比数列，∴1222n nn a -=⋅=．（2）由（1）得2n n a =，212212log 2log 2221n n n n n n b a a n ++=+=+=++， ∴()()()21232325221nn n T b b b b n =+++⋅⋅⋅+=++++⋅⋅⋅+++()()22223521n n =++⋅⋅⋅++++⋅⋅⋅++()()12212321222122n n n n n n +-++=+=++--．19．如图，在四棱锥O ABCD -中，OA ⊥底面ABCD ，底面四边形ABCD 为菱形且3ABC π∠=，2OA AB ==，M 为OA 的中点，N 为BC 的中点．(1)证明：直线MN ∥平面OCD ； (2)求点B 到平面OCD 的距离． 【答案】(1)证明见解析 (2)2217【分析】由题可过点A 作垂线垂直于CD ，垂足为CD 中点，令中点为P ，分别以AB ，AP ，AO 所在直线为x ，y ，z 轴，建立空间直角坐标系，利用空间向量即可求出答案.【详解】（1）作AP CD ⊥于点P ，则P 为CD 中点，分别以AB ，AP ，AO 所在直线为x ，y ，z 轴，建立如图空间直角坐标系．则()0,0,0A ，()2,0,0B ，()3,0P ，()3,0D -，()3,0C ，()0,0,2O ，()0,0,1M ，332N ⎛⎫⎪ ⎪⎝⎭，∴3312MN ⎛⎫=- ⎪ ⎪⎝⎭，()3,2OP =-，()3,2OD =--，设平面OCD 的法向量为(),,n x y z =， 则0n OP ⋅=，0n OD ⋅=，即20,20,z x z ⎧-=⎪⎨--=⎪⎩取y =30,3,2n ⎛⎫=⎪⎝⎭；所以3301022MN n ⋅=⨯⨯=，MN ⊂平面OCD ，∴//MN 平面OCD ；（2）设点B 到平面OCD 的距离为d ，则d 为向量OB 在向量30,3,2n ⎛⎫= ⎪⎝⎭上的投影数量的绝对值，由()2,0,2OB =-，得321OB n d n⋅==，所以点B 到平面OCD 20．已知数列{}n a 中，134a =，112n na a +=-（n N *∈）.（1）求证：数列1{}1na -是等差数列，并求数列{}n a 的通项公式；（2）设1()n n b a n *+=∈N ，12231n n n S b b b b b b +=+++，试比较n a 与8n S 的大小.【答案】（1）见解析；（2）当1,2n =时，有280,8(3)(4)n n n S a n n -<<++，当3n ≥时，有280,8(3)(4)n n n S a n n ->>++. 【详解】试题分析：(1)由等差数列的定义即可证得数列11n a ⎧⎫⎨⎬-⎩⎭是等差数列，进而取得求数列{}n a 的通项公式是113n a n =-+. (2)裂项求和，结合前n 项和的特点可得当1,2n =时，有()()280,834n n n S a n n -<<++，当3n ≥时，有()()280,834n n n S a n n ->>++. 试题解析： （1）解：∵134a =，112n na a +=-（*n N ∈），∴11211114,11111112n n n n na a a a a a +-=-===-------，即111111n n a a +-=---.∴11n a ⎧⎫⎨⎬-⎩⎭是首项为4-，公差为1-的等差数列. 从而113113n nn a a n =--⇒=--+.（2）∵()*1n n b a n N +=∈，由（1）知113n a n =-+. ∴1111,334n k k b b b n k k +==-+++（1,2,3,k =）∴1223111111111114556673444n n n S b b b b b b n n n +⎛⎫⎛⎫⎛⎫⎛⎫=+++=-+-+-++-=- ⎪ ⎪ ⎪ ⎪+++⎝⎭⎝⎭⎝⎭⎝⎭， 而()()2111888144334n n n S a n n n n -⎛⎫⎛⎫-=---=⎪ ⎪++++⎝⎭⎝⎭， ∴当1,2n =时，有()()280,834n n n S a n n -<<++； 当3n ≥时，有()()280,834n n n S a n n ->>++. 点睛：注意等差数列概念中的“从第2项起”与“同一个常数”的重要性.使用裂项法求和时，要注意正负项相消时消去了哪些项，保留了哪些项，切不可漏写未被消去的项，未被消去的项有前后对称的特点，实质上造成正负相消是此法的根源与目的．21．如图，平面五边形P ABCD 中，PAD 是边长为2的等边三角形，//AD BC ，AB ＝2BC ＝2，AB BC ⊥，将PAD 沿AD 翻折成四棱锥P －ABCD ，E 是棱PD 上的动点（端点除外），F ，M 分别是AB ，CE 的中点，且7PC =．(1)证明：AB FM ⊥；(2)当直线EF 与平面P AD 所成的角最大时，求平面ACE 与平面P AD 夹角的余弦值． 【答案】(1)证明详见解析(2)1717【分析】（1）建立空间直角坐标系，利用向量法证得AB FM ⊥.（2）先判断出直线EF 与平面P AD 所成的角最大时E 点是PD 的中点，然后利用向量法求得平面ACE 与平面P AD 夹角的余弦值.【详解】（1）设O 是AD 的中点，连接,OP OC ， 三角形PAD 是等边三角形，所以OP AD ⊥，3OP =. 四边形ABCD 是直角梯形，//,OA BC OA BC =，所以四边形ABCO 是平行四边形，也即是矩形，所以OC AD ⊥，2==OC AB .折叠后，7PC =222OP OC PC +=，所以OP OC ⊥， 由于,,AD OC O AD OC ⋂=⊂平面ABCD ， 所以OP ⊥平面ABCD ，则,,OC OD OP 两两相互垂直，由此建立如图所示的空间直角坐标系，()2,0,0,AB OC ==()1,1,0F -，设)()0,31,01E t t t -<<，()2,0,0C ，所以)311,,22t t M ⎛⎫- ⎪ ⎪⎝⎭，则)3120,,22t t FM ⎛⎫-+= ⎪ ⎪⎝⎭， 所以0AB FM ⋅=， 所以AB FM ⊥.（2）由于OP ⊥平面ABCD ，AB ⊂平面ABCD ，所以OP AB ⊥， 由于,,,AB AD AD OP O AD OP ⊥⋂=⊂平面PAD ，所以AB ⊥平面PAD ，由于AE ⊂平面PAD ，所以AB AE ⊥， 所以FEA ∠是直线EF 与平面PAD 所成角， 在直角三角形AEF 中，tan AF FEA AE∠=， 由于1AF =，所以当AE 最小时，tan FEA ∠最大，也即FEA ∠最大，由于三角形PAD 是等边三角形，所以当E 为PD 的中点时，AE PD ⊥，AE 取得最小值. 由于()0,0,3P ，()0,1,0D ，故此时130,,22E ⎛⎫ ⎪ ⎪⎝⎭， 平面PAD 的法向量为()1,0,0m =，()()()330,1,0,2,0,0,2,1,0,0,,22A C AC AE ⎛⎫-== ⎪ ⎪⎝⎭，设平面ACE 的法向量为(),,n x y z =，则2033022n AC x y n AE y z ⎧⋅=+=⎪⎨⋅=+=⎪⎩，故可设()1,2,23n =-， 设平面ACE 与平面PAD 的夹角为θ， 则117cos 1717m n m nθ⋅===⋅.22．已知双曲线C ：()222210,0x y a b a b-=>>2,,M N 点()1,1P -满足1PM PN ⋅=． (1)求双曲线C 的方程；(2)过点P 的直线l 与双曲线C 交于,A B 两点，直线OP （O 为坐标原点）与直线AN 交于点D ．设直线,MB MD 的斜率分别为1k ，2k ，求证：12k k 为定值． 【答案】(1)221x y -= (2)证明见解析【分析】(1)利用向量的数量积的坐标运算求出1a =即可求双曲线方程；(2) 设()11,A x y ，()22,B x y ，将直线,MB MD 的斜率1k ，2k 之积表示为1212,x x x x +的代数表达式，利用韦达定理即可证明.【详解】（1）由题意知(),0M a -，(),0N a ，又()1,1P -，所以()1,1PM a =-+-，()1,1PN a =+-，由221PM PN a ⋅=-=，可得1a =，又c e a==c =2221b c a =-=， 所以双曲线C 的方程为221x y -=；（2）因为()1,0M -，()1,1P -，若直线l 的斜率不存在，则l 与双曲线C 仅有一个公共点M ，不合题意，故l 的斜率存在， 设l ：()11y k x -=+，联立221(1)1y k x x y -=+⎧⎨-=⎩得：()()222121220k x k k x k k --+---=， 设()11,A x y ，()22,B x y ，则()122211k k x x k ++=-，2122221k k x x k ---=-． 因为()1,1P -，故OP ：y x =-，①又()11,A x y ，()1,0N ，所以AN ：()1111y y x x =--，② 联立①②，解得111111,11y y D x y x y ⎛⎫- ⎪+-+-⎝⎭， 于是()()1112121212112111121111y x y y y y k k y x x y x x y -+-=⋅=-++-+++- ()()()()()()()()()221212121121212111122211211kx k kx k k x x k k x x k x kx k x k x x x x +++++++++=-=-+++-+++++()()()()()()222222222122112111121212221111k k k k k k k k k k k k k k k k k k k +---+++++--=-=-=+-+⎛⎫⎡⎤---⎣⎦+++ ⎪--⎝⎭ 所以12k k 为定值．。