高二周练15期末复习4(14区统考)
14—15学年上学期高二期末考试语文试题(附答案)
2014-2015学年第一学期惠来一中高二年级语文期末考试注意事项:1.答卷前,考生务必用黑色字迹的钢笔或签字笔将自己的姓名、班级、试室、试室座位号和准考证号准确填涂在答题卡上。
2.所有的题目必须用黑色字迹的钢笔或签字笔作答(除选择题用铅笔将答案涂在相应区域外),答案必须写在答题卡各题目指定区域内相应位置上;如需改动,先划掉原来的答案,然后再写上新的答案;不准使用铅笔和涂改液。
不按以上要求作答的答案无效。
3.所有选择题的答案都必须涂在答题卡选择题区相应的位置上,否则答案无效。
一、本大题4小题,每小题3分,共12分。
1.下列词语中加点字,每对读音都不.相同..的一组是A.宦.官/豢.养竹竿./蒿.菜落.落大方/丢三落.四B.莅.临/乖戾.对弈./肄.业抛头露.面/露.出马脚C.足癣./朝鲜.嗔.怪/瞠.目苦心孤诣./雄关险隘.D.羡.慕/汗腺.畜.力/体恤.谄.媚阿谀借花献.佛2.下列句子加点的词语,使用恰当的一项是A.多年前,集团首席执行官就感觉自己如临深渊....,在集团迅猛发展、国际市场不断拓展的今天,他的危机感丝毫未减。
B.有人多次为芦山灾区慷慨解囊,倾尽全部积蓄;也有人声明自己将细大不捐....,以抗议某些慈善机构运作缺乏透明度。
C.泰山几千年来都是文人墨客们向往的圣地,在浩如烟海....的中华典籍中,留下了众多颂扬泰山的诗词文章。
D.家庭条件的优越和父母的溺爱,养成了他傲慢狂妄的个性,不管对谁都侧目而视....,一副天不怕地不怕的小霸王样子。
3.下列句子中,没有语病的一项是A.对于传说中这类拥有异常可怕力量的动物,尚武的古代欧洲人的真实心态恐怕还是敬畏多于憎恶的。
B.近年来,在秀丽的南粤大地上,拔地而起的九洲城、海南琼苑、风城大厦等一批多功能新型建筑物,令人流连忘返,构思奇特,巧夺天工。
C.对这部小说的人物塑造,作者没有很好地深入生活、体验生活,凭主观想象加了一些不恰当的情节,反而大大减弱了作品的感染力。
高二英语下学期第十四次周练试题高二全册英语试题
得夺市安庆阳光实验学校高阳中学高二英语下学期第十四次周练试题第一部分英语知识运用(共两节,满分45分)第一节单项填空(共15小题;每小题1分,满分15分)1. —Shall we make an appointment at 10:00 tomorrow morning?— . Maybe we can make it some other time.A. I’d like toB. No, I shall be busy thenC. Don’t mention itD. See you then2. I think you got wrong end of the stick. It’s Tony rather than David who has good nose for news.A. /; theB. /; aC. the; theD. the; a3. —He could have won first place in the speaking competition.—But he too badly at the last minute.A. performsB. has performedC. performedD. had performed4. My parents don’t of my traveling outside alone during the summer holidays.A. submitB. approveC. rejectD. suspect5. If you’re unable to come to the interview, you should us immediately.A. remindB. informC. rememberD. impress6. Much with the newly-developed software, the manager treated us to a big dinner last night.A. delightedB. delightingC. to be delightedD. being delighted7. With so much noise outside, I couldn’t my work and wondered what was happening.A. leave outB. concentrate onC. look afterD. watch over8. My neighbor accused me affecting his sleep, but now he often assists me looking after the sick dogs.A. of; onB. of; inC. with; onD. with; in9. — Why did you turn off your cellphone this morning?— be disturbed while we were having a meeting.A. So as not toB. So as to notC. In order not toD. In order to not10. I have had such a case a boy whispered to his classmate now and then while I was having lessons.A. asB. thatC. whichD. where11. Only when he failed again in the examination how much time he had wasted.A. realized heB. he had realizedC. did he realizeD. has he realized12. — Could I call on you tonight?— Sorry, you . I will be preparing an important lecture.A. mustn’tB. needn’tC. can’tD. won’t13. — How long should we exercise every day?— The length of time spent exercising can be different personal need and pu rpose.A. depending onB. carrying onC. agreeing onD. looking on14. — Do you believe the report on the Internet?— Of course not. I am highly about most of its contents.A. guiltyB. curiousC. scepticalD. cautious15. The boss looked very worried and demanded that the work before we went home.A. would be finishedB. was finishedC. must be finishedD. be finished第二节完形填空(共20小题;每小题1.5分,满分30分)Once, a group of schoolchildren were on an outing. Almost all of them were playing ball except Monty, who seemed a bit 16 . He didn’t like fights or sports. He wouldn’t even 17 himself when others hit him. He was so strange that he didn’t play football with the others at the beginning. When he finally 18 the ball that day, it ended up in a little cave. When they went to get the ball, they found a box 19 an enormous book. The book was 20 a magical shine. The children gave the 21 to the teacher, who was attracted by it.The book was called The Great Gifts, and there were 22 stories about great inventors, artists, writers and explorers. With each story the children became more wide-eyed, and they were 23 by all those characters with special gifts.They 24 reached the last page of the book, which 25 the origin of those great people. The teacher read:“There’s a(n) 26 in heaven called the fountain(源泉) of hearts, where, before birth, each heart is assigned (赋予) its special gifts. They use a little bit of everything to make normal people. But, sometimes, something goes 27 , and some hearts end up much emptier than normal. In those cases, the 28 fill up with a last gift which makes the person exceptional(杰出的). They may 29 many other qualities; in many ways they will be different, and they may be seen as 30 children. However, when their special gift is discovered, their 31 will become part of books like this one.”When the teacher finished, there was a long 32 . Suddenly Monty came into their mind, and they 33 that he was exactly one of the special cases, 34 the book had described. They felt 35 about every time they had laughed at him.16. A. foolish B. honest C. clever D. brave17. A. warn B. defend C. forget D. remind18. A. found B. kicked C. moved D. invented19. A. arranging B. describing C. publishing D. containing20. A. turning off B. turning up C. giving off D. giving up21. A. book B. ball C. box D. gift22. A. magical B. common C. wonderful D. severe23. A. attracted B. moved C. pleased D. amused24. A. easily B. finally C. actually D. carefully25. A. set about B. brought about C. searched for D. spoke about26. A. book B. invention C. place D. gift27. A. wrong B. special C. lucky D. familiar28. A. people B. hearts C. bodies D. fountains29. A. have B. develop C. lack D. learn30. A. smart B. humorous C. difficult D. strange31. A. ambition B. motivation C. techniques D. achievements32. A. silence B. darkness C. laugh D. quarrel33. A. ignored B. imagined C. understood D. promised34. A. if B. as C. after D. until35. A. pride B. delight C. pity D. regret第二部分阅读理解(共20小题;每小题2分,满分40分)ATraveling can be a very fun and exciting way to vacation with your family, but it does not always turn out as expected. I have traveled a lot with my family over the years, but some experiences were worth forgetting altogether. I remember a particular traveling experience I had with my dad and stepmother, which sticks out in my mind for the wrong reason s.My dad and stepmother had decided to drive to California for our family vacation. This was supposed to provide educational value, since we would be able to stop along the way and look at various sites in each state. Everything was going as planned until we decided to take a break and stop at the Grand Canyon (大峡谷). I had always wanted to see this exciting place and had decided to write a report on it for the eighth-grade English class. We got out of the car and were walking on one of the paths to get to a cliff(悬崖) so we could take a family photo when I slipped and fell.I fell on a piece of rock, and immediately felt the pain shot up my leg. My dad took me to the nearest hospital and after an eight-hour wait in the emergency room, found out that my two bones in my foot broken.Needless to say, our vacation was no fun for me because I was in pain and had a plastic cast on my foot during the whole two-week trip. I ended up making an appointment the day we got home to see an orthopedist. That was definitely not what I consider fun or a great vacation, and it reallyput a dent in our sightseeing plans. Who knew that trying to take a family picture would ruin my family vacation? I make up my mind I’ll have to put safety first whenever I have a trip in future.36. Why does the author always remember the particular traveling experience?A. Because he wrote a good report on it.B. Because a terrible accident during the trip taught him a lesson.C. Because the sites there provided special educational value for him.D. Because they drove to California for the first time.37. The author slipped and fell when he was .A. talking to his fatherB. walking on a path to the cliffC. taking a photo of their familyD. overlooking the Grand Canyon38. From the text we can learn that .A. the bones of the author’s two legs were brokenB. the author waited for 8 hours before the treatmentC. the author was taken to the hospital near his homeD. the author’s trip lasted about half a month39. What does the underlined word “orthopedist” in Paragraph 3 probably mean?A. The man who helps comfort whoever is unhappy.B. The man who helps improve somebody’s studies.C. The man who helps prevent bone shapes being unnatural.D. The d octor who helps save one’s life by operation.BFor people who don’t fear death and love large angry hairy animals, the Pamplona Bull Run is the perfect festival for them. The running of the bulls is part of the San Fermin Festival, which begins on 6th, July and lasts until 14th, July every year in Pamplona, Spain. People run through streets with angry bulls running after them. A bit of advice, if you happen to fall while doing the run, curl into a ball and hope for the best.Every year on 21st, August in the El Salvadorian town of Nejapa, the festival Bolas de Fuego is held. Men on opposing teams throw burning clothes at each other. It is surely a dangerous act. However, it is a tradition that dates back as far as 1685 after a volcano erupted (爆发) in this town.The Baby Jumping Festival takes place in June each year in Castrillo de Murcia, Spain. It is a truly crazy Spanish practice that dates all the way back to 1620. Grown men dressed as the devil jump over babies born in the last 12 months of the year. The main aim of the festival is to protect babies against illness and evil spirits.Now this is one for all cheese lovers. On the Spring Bank Holiday in May, the British gather on the top of Coopers Hill and from the top they roll down a 4-kg round of Double Gloucester cheese and then run afterit. The first person over the finish line without injuries wins the cheese. The cheese can reach a speed of 112 km/h. Injuries are common. Luckily, doctors are waiting just beyond the finish line.The mud festival held every year at Boryeong in South Korea is a bit dirty as it sounds. However, for lovers of mud-wrestling, this is the festival that is not to be missed.There are many other odd festivals around the world. I’d like to introduce you some more next time.40. Grown men dressed as the devil jump over babies in order to .A. celebrate the birth of new livesB. teach babies to become braveC. celebrate new babies’ first birthdayD. protect babies against illness and evil spirits41. What can we learn about the festival mentioned in Paragraph 4?A. Participants are very likely to get injured.B. It is a festival mainly held for doctors in Britain.C. Those who find the heaviest cheese win the game.D. A participant has to reach a speed of 112 km/h in order to win.42. Which of the following pictures shows the festival that is held in South Korea?A. B. C. D. 43. The writer wrote this passage mainly to .A. tell us the history of several strange festivalsB. introduce several strange festivals around the worldC. show that people like doing strange things in their free timeD. tell us what festivals to avoid when we travel abroadCIf your high school doesn’t have a newspaper,you can help start one online. If your high school already has a printed newspaper, adding an online version can help you reach new audiences and add new content. It’s also cheaper to show than a printed version. A digital newspaper can be a chance for high school students to gain experience with journalism and with working online.Discuss with other student journalists to decide what kind of online newspaper you want. If your news site will only have an article or two a day, you may want to use a blog template(模板). If you plan to publish a more magazine-style weekly edition with more stories, you will probably want a m ore complicated front page to show what’s in each issue. Your website will also need to support any additional features such as slide shows (幻灯片放映) and polls.After you have decided what you want your newspaper to look like, try to collect some money. Although it’s possible to launch a website for free, even $50 will help your newspaper buy a memorable website address.These expenses can be made back later through online advertising.Create content for your newspaper. Along with written articles, an online newspaper is a great place for multimedia and interactive content such as photo slide shows, videos, polls, forums and calendars. Use a mix of content and a variety of voices to encourage more page views.Market your newspaper. You can promote it through old-fashioned announcements such as flyers (宣传单) and word of mouth, but it might be better to advertise through e-mails or messages and posts on social networking sites such as Facebook, Myspace and Twitter.44. You can use a blog template if .A. you want to have an interaction with othersB. you want to receive comments from readersC. you have just a few articles a dayD. you have many articles a day45. What can we infer from the third paragraph?A. It’s possible to attract advertising to online newspapers.B. You can use a memorable website address for free.C. It takes only $50 to start an online newspaper.D. Advertising is free in online newspapers.46. What’s the purpose of using a mix of content and a variety of voices?A. To get more useful advice.B. To collect more money.C. To attract more authors.D. To attract more viewers. 47. Why does the author suggest using Facebook, Myspace and Twitter?A. To make your newspapers more popular.B. To make more friends through them.C. To borrow some articles from them.D. To learn from them.DBy far the most important factor is how much time you are immersed in the language. The more time you spend with the language, the faster you will learn. This means listening, reading, writing, speaking, and studying words and phrases. This does not mean sitting in class looking out of the window, nor listening to other students who do not speak well. This means spending time enjoyably connecting to the language you are learning.Listen wherever you are on your MP3 player. Read what you are listening to. Listen to and read things that you like, things that you can mostly understand, or even partly understand. If you keep listening and reading, you will get used to the language. One hour of listening or reading is more effective than many hours of class time.Build up your vocabulary; you’ll need lots. Start to notice words and how they come together as phrases. Learn these words and phrases through your listening and reading. Read online, use online dictionaries, and make your own vocabulary lists for review. Gradually you will be ableto use them. Do not worry about how accurately you speak until you have accumulated (积累) plenty of words through listening and reading.Choose content of interest that you want to listen to and read. Seek out the words and phrases that you need to understand. Do not wait for someone else to show you the language, nor to tell you what to do. Discover the language by yourself, like a child growing up. Talk when you feel like it. Write when you feel like it. A teacher cannot teach you to become fluent, but you can learn to become fluent if you want to.Do not worry about what you cannot remember, or cannot yet understand, or cannot yet say. It does not matter. You are learning and improving. The language will gradually become clearer in your brain. So sit back and enjoy. Just make sure you spend enough time with the language. That is the greatest guarantee of success.48. What should we do to learn a foreign language well?A. Listen to other students whether they speak well or not.B. Speak a language accurately from the very beginning.C. Discover a language by yourself, like a child growing up.D. Ask your parents or a teacher to tell you what to do.49. Where should we listen to a language?A. In the classroom.B. Wherever we are.C. On the Internet.D. In the street.50. The text is mainly intended for .A. parentsB. teachersC. language learnersD. school leaders51. What’s the best title of the passage?A. The importance of learning a foreign languageB. How to learn a foreign languageC. Why to learn a foreign languageD. When to learn a foreign languageEAlex Scott, a brave young girl with a strong mind, wanted to make a difference for all children who have cancer with her lemonade stands and left a legacy (遗赠) of hope. This reminds us of the power one person can have by taking a stand for a worthy cause.Alex was born to Jay and Liz Scott from Manchester, CT. Before her first birthday she was diagnosed (诊断) with neuroblastoma, a childhood cancer. This type of cancer affects the nervous system. Jay and Liz were told by doctors that if Alex beat the cancer she would most likely never walk again. Challenging the doctors’ prediction, Alex was crawling(爬) by her second birthday and able to stand up. She continued to gain strength and to learn how to walk. This was just the start of her unstoppable spirit.Withi n the next year, Alex’s tumors (肿瘤) started to grow again, and, in the year 2000, a day after her fourth birthday, she received astem cell transplant(移植). She informed her mother that when she left the hospital she would have a lemonade stand to help doctors find a cure for childhood cancer.True to her words, Alex had her first lemonade stand later that year. She raised $2,000 for her hospital, a remarkable achievement. Alex continued to hold lemonade stands annually in her front yard, while battling can cer. When the news spread of this extraordinary young girl’s helping other sick children, people all over the world became inspired to hold their own stands and donated the income to Alex’s Lemonade Stand Foundation.When Alex passed away in August 2004, at the age of 8, she had raised over $1 million for childhood cancer research with the help of others. Liz and Jay, along with their three sons, Patrick, Eddie and Joey, continue the promise to Alex and all children with cancer, the promise of hope for a cure.Since 2004, because of Alex’s giving nature, adults and children have joined in the fight for a cure hosting over 8,000 Alex’s Lemonade Stands across the country. These stands represent different groups of devoted volunteers from large and small businesses, inner city school children, senior centers, pre-school aged children, middle school students, college students, and a group of homeless people.The lesson, according to the website of Alex’s Lemonade Stand Foundation, that everyone learns from holding their own lemonade stands is simple but powerful —every person can make a difference in the world.In the spirit of Martin Luther King’s famous quote, “Everybody can be great, because anybody can serve. You don’t have to have a college degree to serve. You don’t have to make your subject and verb agree to serve … You only need a heart full of grace, a soul generated by love.”Alex’s Lemonade Stand Foundation shares the vision of its founder and creator, Alexandra “Alex” Scott — a cure for all children with cancer. You can hold your own Alex’s Lemonade Stand to help raise funds for childhood cancer research. This is a great way to teach children about the virtue(美德) of service in a fun, easy and inexpensive way. For more information, contact Alex’s Lemona de Stand Foundation.52. When Alex decided to hold a lemonade stand, she wanted to .A. battle cancer in a special wayB. raise money for her future treatmentC. raise money for childhood cancer researchD. spread news of an extraordinary girl53. Before Alex’s death, her family had promised that they would .A. join the cancer research groupB. look after other sick children in hospitalC. donate more to Alex’s Lemonade Stand FoundationD. continue her hope for a cure of childhood cancer54. What can we learn from Alex’s story?A. Everyone can make a difference.B. Many hands make light work.C. Each of us could have a lemonade stand.D. The good are all rewarded.55. What is the best title of this passage?A. Alex’s Battl ing Against Childhood CancerB.How to Cure Childhood CancerC. Alex’s Lemonade Stand FoundationD. Ways to Seek Help from Alex’s Lemonade Stand Foundation第三部分书面表达(共两节,满分35分)第一节阅读表达(共5小题;每小题2分,满分10分)阅读下面的短文,并根据短文后的要求答题。
高二物理下学期第四周周练试题(2021年整理)
江西省上饶市横峰县2016-2017学年高二物理下学期第四周周练试题编辑整理:尊敬的读者朋友们:这里是精品文档编辑中心,本文档内容是由我和我的同事精心编辑整理后发布的,发布之前我们对文中内容进行仔细校对,但是难免会有疏漏的地方,但是任然希望(江西省上饶市横峰县2016-2017学年高二物理下学期第四周周练试题)的内容能够给您的工作和学习带来便利。
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江西省上饶市横峰县2016-2017学年高二物理下学期第四周周练试题一、选择每题8分(1-3题为单选,4—6题为多选)1、如图所示,在跨过一光滑定轮的轻绳两端分别挂着质量为m1、m2的两个物体,已知m2>m1.若m2以加速度a向下加速运动时,阻力不计,则()A.m1、m2的总机械能不守恒B.m2的机械能守恒C.m1、m2的总机械能守恒、动量也守恒D.m1、m2的总机械能守恒、动量不守恒2、高空作业须系安全带。
如果质量为m的高空作业人员不慎跌落,从开始跌落到安全带对人刚产生作用力前人下落的距离为h(可视为自由落体运动).此后经历时间t安全带达到最大伸长,若在此过程中该作用力始终竖直向上,则该段时间安全带对人的平均作用力大小为( )A.2m ghmg+B。
2m ghmg-C。
m ghmg+D。
m ghmg-3、在如图中,长木板M放在光滑水平面上,木块m放在木板左端,当木板与木块同时以速率V0沿相反方向运动到木板与木块有共同速度的过程中,木板对木块的摩擦力做功的情况是(设M >m)()A.一直做负功B.一直做正功C.先做正功、后做负功D.先做负功、后做正功4、质量为m 的物体静止在光滑水平面上,从t=0时刻开始受到水平力的作用,力的大小F 与时间t 的关系如图所示,力的方向保持不变,则( )A 、03t 时刻的瞬时功率为20015F t mB 、03t 时刻的瞬时功率为20010F t mC 、在t=0到03t 这段时间内,水平力的平均功率为200234F t mD 、在t=0到03t 这段时间内,水平力的平均功率为200254F t m5、如图所示,一水平传送带以速度v 匀速运动,将质量为m 的小工件轻轻放到水平传送带上,工件在传送带上滑动一段时间后与传送带保持相对静止,在上述过程中( )A .工件对传送带做功为﹣mv 2B .传送带与工件间摩擦产生热量为mv 2C .传送带因为传送工件需要多做的功为mv 2D .传送带对工件做的功为mv 26、如图所示,两水平线间存在垂直纸面向里的有界匀强磁场,磁感应强度为B,磁场高度为h,竖直平面内有质量为m ,电阻为R 的等边三角形线框,线框高为2h ,该线框从如图所示位置由静止下落,已知A 刚出磁场时所受的安培力等于线框的重力,则从A 出磁场到CD 边进磁场前的过程中,下列说法正确的是( )A .线框中有顺时针方向的感应电流B.A出磁场瞬间,线框中感应电动势的大小为C.A出磁场瞬间,线框下落的速度为D.全过程中产生的焦耳热为mgh123456二计算题(16,16,20分)7、如图所示,光滑水平面上有一长木板,板长为L=1m,板上右端放一质量为m=1kg的物块,物块与长木板间的动摩擦因数为μ=0。
2021年高二上学期第四次周考英语试题 含答案
信丰二中高二年级上学期英语学科第14周第4次周考卷(D卷)卢玉琴王玉萍一、阅读理解(每题4分,共60分)2021年高二上学期第四次周考英语试题含答案My friend, Dick, has a large police dog. Its name is Jack. Every Saturday afternoon Dick takes Jack for a long walk in the park. Jack likes these long walks very much.One Saturday afternoon, a young man came to visit my friend. He stayed a long time. He talked and talked. Soon it was time for my friend to take Jack for a walk. But the man was still there. Jack became very worried. He walked around the room several times and then sat down in front of the man and looked at him. But the man kept talking. Finally Jack could stand it no longer. He went out of the room and came back a few minutes later. He sat down again in front of the man, but this time he held the man’s hat in his mouth.1. From the story, we know that Jack is ________.A Dick’s good friendB a large police dogC a young man2. Where does Dick walk with his dog every Saturday afternoon?A In his roomB In the streetC In the park3. Jack became very worried one afternoon because ______.A he couldn’t be taken out for a walk at the usual time.B a young man came to visit Dick that afternoon.C Dick walked around his room several times.4. What does the word “stand” mean i n the passage?A 站立 B理解 C忍受5. Why did Jack sit down again in front of the man with the hat in his mouth?A. Try to take the man laugh. B Like the young man very much.C Ask the young man to leave.(B)This is a tale of two friends --- one is blind, the other has no arms. On their own, the two are “disabled”. But together, they are a powerful team that has changed part of their village in North China’s Hebei Province into a rich, green forest. Meet 53-year-old Jia Haixia and Jia Wenqi!Their story began in xx, when Haixia, who was already blind in his right eye, lost his left one after an illness. Wenqi lost his arms in an accident when he was just three. Neither could find a job, so the two decided to team up. They rented some poor land and began to plant trees. In return,the local officials paid them a small fee. Haixia and Wenqi never imagined that they would end up creating an environmental paradise. Their forest now has over 10,000 trees, hundreds of birds and many other wild animals. In addition, it saves the village from river flooding during the rainy season. When the friends work together, they focus on their strengths not their disabilities. Their day begins at 7 a.m. when the sightless Haixia carries Wenqi across the river to get to their worksite. Since they cannot afford to buy young trees to plant, the two use branches from existing trees. Haixia climbs to the tree-top and with Wenqi’s direction, selects the perfect branch. He then digs a hole and carefully plants it. Finally Wenqi waters the area.Though hard-working, the men don’t make much money. But as Wenqi puts it, “We stand on our own feet, so the fruits of our work taste sweeter.” Neither Haixia nor Wenqi cares about money. Together, they already have everything they need --- a perfect pair of eyes, two strong hands, and the best friendship in the world!6. Why did Haixia and Wenqi start working together?A. Haixia needed someone to help him.B. They both needed a way to make money.C. They wanted to improve the environment.D. They were required to do so by local officials.7. Haixia and Wenqi’s forest has helped the village by______ .A. stopping floods in the rainy seasonB. increasing the number of touristsC. making the villagers richerD. providing more farmland8. Why do Haixia and Wenqi plant tree branches?A. They are easy to get.B. They do not cost money.C. They can grow very quickly.D. They are preferred by animals.9. In paragraph 5, when Wenqi says “We stand on our own feet, so the fruits of our work taste sweeter”, he means that “______”.A. they hope to make the forest even betterB. the fruits from their trees are very sweetC. they are proud not to depend on othersD. they are able to do any difficult work10. What can we learn from this story?A. Never give up and you will succeed.B. We should help the disabled to work.C. Try your best when facing difficulties.D. We can achieve more with teamwork.(C)In Western society, especially in the English-speaking world, the chance for young people to see the other countries and experience life is considered important. Many young people, when they finish school at the age of 18, take a gap year before they go to university.Parents often want their children to grow up a little and see what the real world is like when they finish school. Although they are worried about their safety, many think that the advantages of independence and experience are worth the worries. Children are encouraged to be brave, independent and to explore the world on their own or with friends.Young people also want to experience freedom and see what life is like on the other side. This other side could be the other side of the world or just the other side of life. For example, if they have a rich life, they may want to see how people in poor areas live.A gap year after school is also an important chance for young people to spend time thinking about what they want to do with their lives. A little bit of growing up and experience will help them make their important career decisions, especially when they are unsure about what they want to study.Another reason for going straight after school is to get a break from studying before they start the next few years of university. So anywhere you travel in the world, you will meet young European people exploring the world.So much of the world has been travelled and explored. The young people are now looking for more worthy experiences. Some of them work as volunteers to do something for the country they are visiting. Many gap year volunteers are now spending a few months teaching English in Thailand, helping feed giant pandas in China or building a well(井) in a village in Africa.These young people’s wish to ex plore the world is an expression of the values of the societies that they are part of. Both discovering the world and making a positive difference in it are important parts of the Western mind.11. In Western society, the chance for young people to see the othercountries and experience life is considered .A. rare B .unimportant C. important D. useful12. Which is NOT a reason for young people to take a gap year?A. Young people want to take a break from studying.B. Young people want to be sure about what to study.C. Parents encourage them to be brave and independent.D. Parents encourage them to live a free and wealthy life.13. Now a gap year volunteer might do something more valuable like .A. experiencing different culturesB. helping protect rainforests in BrazilC. making friends with more peopleD. enjoying traditional local food14. By taking a gap year, young people may .A. stay with their parents all the timeB. make money for their further studyC. help change the world for the betterD. change the Western mind pletely15. The purpose of writing this article is to .A. show different opinions about gap yearB. offer readers information about gap yearC. discover new ways to take a gap yearD. tell young people when to take a gap year二、完形填空(每空2分,共20分)Few people like changing their habits, good or bad. Whether it is smoking, drinking or over-eating, they 16 “enjoying” them to the end.On every packet of cigarettes(香烟), people are warned against the 17 of smoking: “Warning: Cigarette Smoking Is Dangerous to Your Health”.18 , millions of them start smoking or go on smoking. Why?Facts show that families and surroundings(环境) play a very important part in 19 smokers. All those smokers e from smoking families or have smoking 20 or relatives. Films and TV plays also play a part. People 21 their “heroes” on TV drinking alcohol(酒) or smoking cigarettes. “Heroes” seem to fear 22 , neither killing themselves nor killing others with alcohol and cigarettes. If they are not afraid of the harm of smoking and drinking, 23 should mon people be afraid?The simple warning on the cigarette packet does not influence smokers’habits. Even 24 warnings, like showing pictures of smokers who have died of cancer, don’t seem to work.Knowing and believing seem to be two 25 things. If smoking is really as harmful as doctors say, it is time for smokers to think about it and try to give it up!16. A. stop B. continue C. finish D. avoid17. A. chances B. excuses C. causes D. dangers18. A. Moreover B. Also C. However D. Otherwise19. A. influencing B. explaining C. improving D. describing20. A. parents B. uncles C. brothers D. friends21. A. hear B. catch C. watch D. face22. A. something B. nothing C. anything D. everything23. A. what B. how C. when D. why24. A. stronger B. worse C. longer D. harder25. A. similar B. pleasant C. different D. boring三、语法填空(每空2分,共20分)Everyone needs to sleep. During the day you work and play; at nightyou sleep. Your body rests while you are 26 (sleep).In the morning youare ready to 27 (work).study or play again. If you sleep 28 (good) at night, you can work or learn better in the day.Your body grows more while you are asleep. No one can live without sleeping. If a child is tired, he needs 29 (much) sleep than usual. You will be tired or will not be able to listen to your teachers in classor can’t work well if you do not have enough sleep at night. A baby willcry loudly 30 you wake him or her up when he or she is sleeping. Youwill be able to work harder at your lessons if you 31 (have) enough rest. Many students hope to learn more before rests, so they study until 32 (late) at night. 33 they feel very tired in the day and they may forget more.Boys and girls of eight or nine need ten 34 (hour) of sleep every night. Get enough sleep if you want to be strong and 35 . (heath)答题区班级:姓名:座号:得分:一、阅读理解(每题4分,共60分)二、完形填空(每空2分,共20分)三、语法填空(每空2分,共20分)26. 27. 28. 29. 30.31. 32. 33. 34. 35.参考答案:(特长班周考卷)阅读理解 (A). 1-5 BCACC; (B) 6-10 BABCD (C) 11-15 CDBCB完形填空 16-20. BDCA D 21-25. CBDAC选词填空26. sleeping 27. work 28. well 29.more 30. if31. have 32. late 33.But 34. hours 35. healthy25109 6215 戕K37442 9242 鉂38781 977D 靽024131 5E43 幃 36995 9083 邃H30020 7544 畄'35209 8989 覉a20559 504F 偏K。
辽宁省2023-2024学年高二下学期7月期末联考试题 语文含答案
2023-2024学年度下学期期末考试高二年级语文科试卷(答案在最后)命题学校:一、现代文阅读(35分)(一)现代文阅读I(本题共5小题,18分)阅读下面的文字,完成1~5题。
材料一:有关全球变暖的讨论向来层出不穷。
乐观主义者简称,在过去百年来,全球温度只上升了1%,对人类没有造成负面影响。
而悲观主义者认为,全球变暖将是人类社会在50万年来面临的最大危机。
在气候这个赌场里,真相究竟是怎样的?经济学作为一门人文社会学科,其切入气候变化议题的原因在哪里呢?诺德豪斯给出了两点理由:一方面,旨在减少温室气体排放的政策措施,必须经由经济系统才可起作用;另一方面,气候变化也会对经济系统的生产过程和最终产出发生影响,比如干旱导致粮食歉收。
还有一个更深层的理由,那就是自然学科在做预测时,往往使用简单的外推法,比如把二氧化碳排放量与GDP相挂钩。
这样的处理方法忽略了微观主体对经济环境变化的适应能力。
如果气候变得干旱了,农场主可以不种植小麦,而改种对水分要求更少的玉米。
类似地,如果政府出台碳税,企业可寻求替代能源,从而在二氧化碳排放量下降的同时,GDP增速并不一定放慢。
可见,固然自然学科在探索地球生态系统的规律上起着基础性的作用,但是如果涉及遏制气候变暖的政策实践,就绕不开经济学。
(节选自《〈气候赌场〉:全球变暖使地球处于危险》《中国青年报》2019-09-03)材料二:在气候变化领域有一个常见的荒谬现象:科学家讲政治,政治家讲科学。
世界顶级经济学家,2018年度诺贝尔经济学奖获得者威廉·诺德豪斯并没有忽视自然科学的强大力量,只是从经济学的视角出发,带领你认识碳排放的经济本质,估算全球变暖的经济影响和减缓气候变化的成本,并且设计可以实现合意减排的政策工具。
应对全球变暖,必须坚持减排成本与减排收益平衡的原则。
现阶段,应对气候变化主要有三种方法:学会与气候变化并存的适应法、“冷却地球”的地球工程、通过减排缓解气候变化的减缓法。
2021-2022年高二上学期第十四次周练物理试题word版含答案
2021年高二上学期第十四次周练物理试题word版含答案1.关于多用电表上的电阻刻度线,下列说法正确的是()A.零电阻刻度线与零电流刻度线重合B.零电阻刻度线与电流表满偏刻度线重合C.电阻刻度是不均匀的,电阻值越大,刻度线越密D.电阻刻度是不均匀的,电阻值越小,刻度线越密2.用多用电表欧姆档测电阻时,下列说法正确的是()A.测量前必须调零,而且每测一次电阻都要重新调零B.为了使测量值比较准确,应该用两手分别将两表笔与待测电阻两端紧紧捏在一起,以使表笔与待测电阻接触良好C.待测电阻若是连接在电路中,应当先把它与其它元件断开后再测量D.使用完毕应当拔出表笔,并把选择开关旋到OFF档或交流电压最高档3.用多用表测直流电压U或测电阻R时,若红表笔插入多用表的正(+)插孔,则A.前者(测电压U)电流从红表笔流人多用电表,后者(测电阻)从红表笔流出多用电表B.两者电流都从红表笔流入多用表C.两者电流都从红表笔流出多用表D.前者电流从红表笔流出多用表,后者电流从红表笔流入多用表4.下列说法中正确的是()A.欧姆表的每一档的测量范围是0~∞B.用不同档的欧姆表测量同一电阻的阻值时,误差大小是一样的C.用欧姆表测电阻时,指针越接近刻度盘中央,误差越大D.用欧姆表测电阻,选不同量程时,指针越靠近右边误差越小5.把一个量程为5mA的电流表改装成欧姆表R×1档,电流表的内阻是50Ω,电池的电动势是1.5V,经过调零之后测电阻,当欧姆表指针指到满偏的3/4位置时,被测电阻的阻值是()A.50ΩB.100ΩC.16.7ΩD.400Ω6.一个标有“220V,40W”的白炽灯泡,当用多用电表的欧姆档去测量它们的电阻时,测得的阻值()A.接近1210ΩB.接近5.5ΩC.明显大于1210ΩD.明显小于1210Ω7.如图2-49 (a)所示足一个欧姆表的外部构造示意图,其正、负插孔内分别插有红、黑表笔,则虚线内的电路图应是(b)图中的图( ).图2-498.用多用电表的欧姆档(×1KΩ)检查性能良好的晶体二极管,发现多用电表的表针向右偏转角度很小,这说明()A.二极管加有正向电压,故测得电阻很小B.二极管加有反向电压,故测得电阻很大C.此时红表笔接的是二极管的正极D.此时红表笔接的是二极管的负极9.欧姆表电路及刻度盘如图2-50所示,现因表头损坏,换用一个新表头.甲表头满偏电流为原来表头的2倍,内阻与原表头相同;乙表头满偏电流与原表头相同,内阻为原表头的2倍,则换用甲表头和换用乙表头后刻度盘的中值电阻分别为( )A.100Ω,100ΩB.200Ω,100ΩC.50Ω,100ΩD.100Ω,200Ω10.一个多用电表内的电池已使用很久了,但是转动调零旋钮时,仍可使表针调至零欧姆刻度处.用这只多用表测出的电阻值R’,与被测电阻的真实值R相比( )A.R’=R B.R’>RC.R’<R D.无法确定11.一只灵敏电流表满偏电流为200μA,把它改装成欧姆表后,用它测量10kΩ电阻时,表针恰好指在100μA处,用它测量另一只电阻R x时,表针指在50μA处,则R x= 。
高二下学期英语期末考试试卷第14套真题
高二下学期英语期末考试试卷一、阅读理解1. 阅读理解FOUR BEST BOOKSHOPS IN LONDONLooking for something to read while inLondon? If so, you’re in luck: the British capital happens to have anincredible collection of bookshops.DauntBooksAre you going on a trip and want to read anovel or nonfiction book set in the place you’re headed? This bookshop arrangesbooks by country, so it’s easy to find anything by place.FoylesBooksDig, if you will, the picture: four miles of shelves holdingup to 200,000 books. This legendary bookshop is impossible to leaveempty-handed. It was once listed in the Guinness Book of World Records as thebiggest bookshop on the planet.HatchardsIn the year 1797, this London bookshop—theoldest in the city today—first flicked on its lights. It stocks an excellentselection of fiction, nonfiction, history and other genres.LondonReview BookshopThere’s an excellent selection of history,philosophy, politics, new fictionand many other genres here. Plus, there’s anice cafe in which you can crack open that tome for the first time and start reading.(1)Which bookstore was listed in the Guinness Book of World Records?A . Daunt Books.B . Foyles Books.C . Hatchards.D . London Review Bookshop.(2)What is special about Hatchards?A . It has a long history.B . It has 200,000 books.C . It has a cafe.D . It has both fiction and nonfiction books.(3)Which place should you go to if you want to enjoy reading with a coffee?A . 83 Marylebone High Street.B . 107 Charing Cross Road.C . 187 Piccadilly Street.D . 14 Bury Place.2. 阅读理解Do you want to live another100 years or more? Some experts say that scientific advances will one dayenable humans to last tens of years beyond what is now seen as the naturallimit of the human life span.“I think we are knocking atthe door of immortality ,” said Michael Zey, aMontclair State University business professor and author of two books on thefuture. “I think by 2075 we will seeit and that’s a conservative estimate .”At the conference in SanFrancisco, Donald Louria, a professor at New Jersey Medical School in Newarksaid advances in using genes as well as nanotechnology make it likely that humans will live in the future beyond whatwas possible in the past. “There is a great effort sothat people can livefrom 120 to 180 years,” he said. “Some have suggested thatthere is no limi t and that people could live to 200 or 300 or 500 years.”However, many scientistswho specialize in aging are doubtful about it and say the human body is justnot designed to last past about 120 years. Even with healthier lifestyles andless disease, they say failure of the brain and organs will finally lead allhumans to death.Scientists also differ onwhat kind of life the super aged might live. “It remains to be seen ifyou pass 120, you know; could you be healthy enough to have good quality oflife?” said Leonard Poon, director of the Universityof Georgia Gerontology Centre. “At present people who could get to that pointare not in good health at all.”(1)By saying “we are knocking at the door of immortality”, Michael Zey means_________.A . they have got some ideas about living foreverB . they believe that there is no limit of livingC . they are able to make people live past the present life spanD . they are sure to find the truth about long living(2)Donald Louria’ s attitude towards long living is that________.A . the human body is designed to last past about 120 yearsB . it is possible for humans to live longer in the futureC . it is still doubtful how long humans can liveD . people can live from 120 to 180(3)The underlined word “it” refers to________.A . a great effortB . the conservative estimateC . the idea of living from 200 to 300 yearsD . the idea of living beyond the present life span(4)What would be the best title for this text?A . No Limit for Human LifeB . Living Longer or notC . Science, Technology and Long LivingD . Healthy Lifestyle and Long Living3. 阅读理解Plastic-Eating WormsHumans produce more than300 million tons of plastic every year. Almost half of that winds up in landfills, and up to 12 million tons pollute the oceans.So far there has been no effective way to get rid of it, but a new studysuggests an answer may lie in the stomachs of some hungry worms.Researchers in Spain andEngland recently found that the worms of the greater wax moth can break downpolyethylene , which accounts for 40%of plastics. The team left 100 wax worms on a commercial polyethylene shoppingbag for 12 hours, and the worms consumed and broke down about 92 milligrams, oralmost 3% of it. To confirm that the worms’ chewing alone was not responsiblefor the polyethylene breakdown, the researchers made some worms into paste and applied it to plastic films. 14 hours later the films hadlost 13% of their mass—apparently broken down byenzymes from the worms’ stomachs.Their findings were published in Current Biology in 2017.Federica Bertocchini,co-author of the study, says the worm’s ability to break down their everydayfood beeswax also allows them to breakdown pl astic. “Wax is a complex mixture, but the basic bond in polyethylene,the carbon-carbon bond, is there as well,” she explains. “The wax worm evolveda method or system to break this bond.”Jennifer DeBruyn, amicrobiologist at the University of Tennessee, who was not involved in thestudy, says it is not surprising that such worms can break down polyethylene.But compared with previous studies, she finds the speed of breaking down inthis one exciting. The next step, DeBruyn says, will be to identify the causeof the breakdown. Is it an enzyme produced by the worm itself or by its gutmicrobes ?Bertocchini agrees andhopes her team’s findings might one day help employ the enzyme to break downplastics in landfills. But she expects using the chemical in some kind ofindustrial process—not simply “millionsof worms thrown on top of the plastic.”(1)What can we learn about the worms in the study?A . They wind up in landfills.B . They can consume plastics.C . They are newly evolved creatures.D . They take plastics as their everyday food.(2)According to Jennifer DeBruyn, the next step of the study is to_______.A . increase the breakdown speedB . confirm the research findingsC . find out the source of the enzymeD . identify other means of the breakdown (3)It can be inferred from the last paragraph that the chemical might_____.A . be produced in factories in futureB . be used to clean the oceansC . help make plastic bagsD . help to raise worms(4)What is the main purpose of the passage?A . To explain a study method on worms.B . To present a way to break down plastics.C . To introduce the diet of a special worm.D . To propose newmeans to keep eco-balance.4. 阅读理解Volunteering Is FunOne afternoon I was sittingat home feeling so bored. Instead of feeling sorry for myself, I wanted to meetpeople and have new experiences so I decided to start volunteering. I searchedon my computer and found a website where I could volunteer on a farm in France.My time working on a farmwas a new experience for me. It was basically a free holiday as food andaccommodation were provided. However, it was not my typical holiday as I had tolook after fifteen horses and sleep at the top of a tower in a castle! I was anawful farmer but it did not matter because I made some great friends. However,you do not need to go abroad to volunteer. I have had plenty of adventures athome as volunteering can become a hobby. For example, I love singing so I had agood laugh waving my arms in an attempt to conduct my local choir. I did slowlyimprove and it felt great to conduct the choir in a concert. At university, Iorganized a concert for charity with my friends. It was really fun findingbands and raising money for a cause we believe in.It is true that you feelgood volunteering but there are also other advantages. I once volunteered as aserver at a charity sports event where the organizers gave me cupcakes to thankme for my services. I also volunteered in a charity shop so I found loads ofnice cheap clothes to update my wardrobe .While this is all fun, myfavorite aspect of volunteering is creating andsharing stories. My terribleattempts at farming have given me hilarious stories to tell! Talking tovolunteers from different countries and backgrounds has also helped me learnmore about the world. I feel thankful to have had so much fun with many nicepeople thanks to volunteering.(1)Why did the author want to be volunteer?A . He wanted to taste new life and make friends.B . He felt ashamed of himself.C . He wanted to be a farmer.D . He wanted to go abroad.(2)The un derlined word “hilarious” in the last paragraph is closest in meaning to “_____”.A . sadB . criticalC . awfulD . funny(3)What volunteering work did the author do?A . Taking care of sheep.B . Helping in an Italian farm.C . Helping in a charity shop.D . Conducting a choir in a sports event.(4)How does the author feel according to the last paragraph?A . Curious.B . Anxious.C . Grateful.D . Cautious二、任务型阅读5. 根据短文内容,从短文后的选项中选出能填入空白处的最佳选项。
2021年高二下学期第四次周考物理试题(重点班) 含答案
2021年高二下学期第四次周考物理试题(重点班)含答案一、选择题(每题4分,1至8题为单选,9至12题为多选,共48分)1. 关于速度和加速度的关系,下列说法中正确的是( )A.速度变化越大,加速度就越大B.速度变化越快,加速度越大C.加速度大小不变,速度方向也保持不变D.加速度大小不断变小,速度大小也不断变小2.在一个原子核衰变为一个原子核的过程中,发生β衰变的次数为( )A.6次B.10次C.22次D.32次3.如图所示,以9.8米/秒的水平初速度抛出的物体,飞行一段时间后,垂直地撞在倾角θ为30°的斜面上.可知物体完成这段飞行的时间是( )A.秒B.秒C.秒D.2秒4.ab是长为l的均匀带电细杆,P1、P2是位于ab所在直线上的两点,位置如图6-2-8所示.ab 上电荷产生的静电场在P1处的场强大小为E1,在P2处的场强大小为E2.则以下说法正确的是( )图6-2-8A.两处的电场方向相同,E1>E2B.两处的电场方向相反,E1>E2C.两处的电场方向相同,E1<E2D.两处的电场方向相反,E1<E25.如图所示是一种理想自耦变压器示意图.线圈绕在一个圆环形的铁芯上,P是可移动的滑动触头.AB间接交流电压u,输出端接有两个相同的灯泡L1和L2,Q为滑动变阻器的滑动触头.当开关S闭合,P处于如图所示的位置时,两灯均能发光.下列说法正确的是( )A.P不动,将Q向右移动,变压器的输入功率变大B.P、Q都不动,断开开关S,L1将变暗C.P不动,将Q向左移动,两灯均变暗D.Q不动,将P沿逆时针方向移动,变压器的输入功率变大6.中国已投产运行的1000kV特高压输电是目前世界上电压最高的输电工程。
假设甲、乙两地原采用500kV的超高压输电,输电线上损耗的电功率为P。
在保持输送电功率和输电线电阻都不变的条件下,现改用1000kV特高压输电,若不考虑其他因素的影响,则输电线上损耗的电功率将变为( )A.P/4 B.P/2 C.2P D.4P7.两个电荷量相等但电性相反的带电粒子a、b分别以速度va和vb射入匀强磁场,两粒子的入射方向与磁场边界的夹角分别为30°和60°,磁场宽度为d,两粒子同时由A点出发,同时到达B点,如图所示,则( )A.a粒子带正电,b粒子带负电B.两粒子的轨道半径之比Ra∶Rb=∶1C.两粒子的质量之比ma∶mb=1∶2D.两粒子的速度之比va∶vb=1∶28.如图所示为氢原子的能级示意图,一群氢原子处于n=3的激发态,在向较低能级跃迁的过程中向外发出光子,用这些光照射逸出功为2.49eV的金属钠,说法正确的是( )A.这群氢原子能发出三种频率不同的光,其中从n=3跃迁到n=2所发出的光波长最短B.这群氢原子能发出两种频率不同的光,其中从n=3跃迁到n=1所发出的光频率最小C.金属钠表面所发出的光电子的最大初动能为9.60eVD.金属钠表面所发出的光电子的最大初动能为11.11eV9.甲、乙为两颗地球卫星,其中甲为地球同步卫星,乙的运行高度低于甲的运行高度,两卫星轨道均可视为圆轨道。
高二期末真题重组卷(三)(15+4模式)(原卷版)
期末真题重组卷(三)(测试范围:《经济与社会生活》全册测试时间:75分钟满分:100分)一、选择题(本大题共15小题,每题3分,共45分)1.(2022·江苏苏州·高二期末)明代嘉靖年间,太湖地区的“桑基鱼塘”逐渐成熟起来。
乡尺在搪基上种桑,用桑叶喂蚕、蚕沙养鱼、鱼粪肥塘、塘泥壅桑。
这种农业生产模式的发展()A.丰富了人们的食物种类B.活跃了江南的商品经济C.改变了当地的食物结构D.促进了农业生产规模化2.(2022·辽宁抚顺·高二期末)油画(巧克力)描绘了17世纪引人注意的消费体验。
富有的欧洲人像阿兹特克上层社会人士一样把巧克力作为一种奢侈的饮料,他们从墨西哥进口昂贵的巧克力到西班牙,再用从中国进口的更品贵的瓷杯来饮用巧克力。
这幅作品可以用来说明当时()①欧亚之间开始建立商业联系②世界贸易促进饮食文化交流③中国瓷器受到欧洲贵族的追捧④资本主义世界经济体系确立A.①③B.②③C.①④D.②④3.(2022·安徽·定远县育才学校高二期末)袁隆平一生致力于杂交水稻技术的研究、应用与推广,发明“三系法”籼型杂交水稻,成功研究出“两系法”杂交水稻,创建了超级杂交稻技术体系。
袁隆平的贡献在于()A.运用科技手段战胜了饥饿对人类的威胁B.解决了中国人民的温饱和国家粮食安全C.为解决世界粮食供给作出了杰出贡献D.推动了世界和平稳定和农业科技进步4.(2022·安徽黄山·高二期末)中国古代官府对手工业工匠人户编订特别户籍制度,称之为匠籍制度,世代相袭,很多工匠因不忍受到沉重剥削,常以逃亡、怠工等方式进行反抗,明政府不得不指定适应商品经济发展的“以银代役”法,这种匠籍制度的改革()A.促进了民间手工业的发展B.体现了重农抑商的政策C.源于新式生产方式的推动D.促进了赋税制度的改革5.(2022·湖南·衡阳县第四中学高二期末)1790年代的一篇文章里举例谈到:一位每天挣30便士(伦敦劳动阶层的标准收入)的40岁花匠,每天可以买一个小麦面包、半磅肉、几盎司芝士、1品脱啤酒、一些茶和糖。
晋江二中高二理数周练14(椭圆专题)(含答案)
晋江二中高二理数周练14-椭圆专题(2014/12/05)(满分120分 时长90分钟 命卷人:林建彬)姓名____________班级___________学号____________分数______________一.选择题(共60分,请将答案抄写在选择题答案表中)1 .下列方程表示椭圆的是( )A.22199x y += B.2228x y --=- C.221259x y -= D.22(2)1x y -+= 2 .已知椭圆22159x y +=上一点P 到椭圆的一焦点的距离为3,则P 到另一焦点的距离是( )A.3B.2C.3D.63 .动点P 到两个定点1F (- 4,0).2F (4,0)的距离之和为8,则P 点的轨迹为( ) A.椭圆 B.线段12F F C.直线12F F D.不能确定4 .已知椭圆的标准方程22110y x +=,则椭圆的焦点坐标为( )A.(B.(0,C.(0,3)±D.(3,0)±5 .离心率为32,长轴长为6的椭圆的标准方程是( )(A )22195x y += (B )22195x y +=或22159x y +=(C )2213620x y += (D )2213620x y +=或2212036x y += 6 .如果22212x y a a +=+表示焦点在x 轴上的椭圆,则实数a 的取值范围为() A.(2,)-+∞ B.()()2,12,--⋃+∞ C.(,1)(2,)-∞-⋃+∞ D.任意实数R 7 .椭圆x 29+y 24+k =1的离心率为45,则k 的值为( )A .-21B .21C .-1925或21D.1925或21 8 .若一个椭圆长轴的长度、短轴的长度和焦距成等差数列,则该椭圆的离心率是( )A 54 B.53 C. 52 D. 519 .k 为何值时,直线y=kx+2 和椭圆 22236x y +=相交( ) A.3k >B.3k < C.3k ≥ D.3k ≤ 10 .点P 为椭圆22154x y +=上一点,以点P 以及焦点F 1, F 2为顶点的三角形的面积为1,则点P 的坐标是 (A )(, 1) (B ), ±1)(C ), 1) (D )(, ±1) 11 .若△ABC 顶点B , C 的坐标分别为(-4, 0), (4, 0),AC , AB 边上的中线长之和为30,则△ABC 的重心G 的轨迹方程为(A )221(0)10036x y y +=≠ (B )221(0)10084x y y +=≠ (C )221(0)10036x y x +=≠ (D )221(0)10084x y x +=≠ 12 .关于曲线的对称性的论述正确的是()A.方程220x xy y ++=的曲线关于X 轴对称B.方程330x y +=的曲线关于Y 轴对称C.方程2210x xy y -+=的曲线关于原点对称D.方程338x y -=的曲线关于原点对称二.填空题(共20分)13 .已知椭圆G 的中心在坐标原点,长轴在x 轴上,离心率为32,且G 上一点到G 的两个焦点的距离之和为12,则椭圆G 的方程为________.14 .P 为椭圆22110064x y +=上的一点,F 1和F 2是其焦点,若∠F 1PF 2=60°,则△F 1PF 2的面积为 ________.15 .椭圆12222=+by a x (a >b >0)的半焦距为c ,若直线y =2x 与椭圆的一个交点的横坐标为c ,则椭圆的离心率为 .16 .如图所示,“嫦娥一号”探月卫星沿地月转移轨道飞向月球,在月球附近一点P 变轨进入以月球球心F 为一个焦点的椭圆轨道I 绕月飞行,之后卫星在P 点第二次变轨进入仍以F 为一个焦点的椭圆轨道Ⅱ绕月飞行,最终卫星在P 点第三次变轨进入以F 为圆形轨道Ⅲ绕月飞行,若用12c 和22c 分别表示椭圆轨道I 和Ⅱ的焦距,用12a 和22a 分别表示椭圆轨道I 和Ⅱ的长轴的长,给出下列式子:①1122;a c a c +=+ ②1122;a c a c -=- ③1212;c a a c > ④1212.c c a a < 其中正确式子的序号是 三.解答题(共40分)17 .求适合下列条件的椭圆的标准方程.(1)焦距为8,离心率为0.8;(2)经过两点(6,1),(-3,-2).18 .已知椭圆的两焦点为F 1(-1,0)、F 2(1,0),P 为椭圆上一点,且2|F 1F 2|=|PF 1|+|PF 2|.(1)求此椭圆的方程;(2)若点P 在第二象限,∠F 2F 1P =120°,求△PF 1F 2的面积.19 .已知椭圆的中心在原点,焦点在x轴上,且经过点M(4,1),直线l:y=x+m交椭圆于不同的两点A,B.(1)求椭圆的方程;(2)求m的取值范围.20 .已知椭圆M:2222x ya b=1(a>b>0)的离心率为12,短轴的一个端点到右焦点的距离为2,(1)试求椭圆M的方程;(2)若斜率为12的直线l与椭圆M交于C、D两点,点P(1,32)为椭圆M上一点,记直线PC的斜率为k1,直线PD的斜率为k2,试问:k1+k2是否为定值?试证明你的结论.晋江二中高二理数周练(14)参考答案一选择题1-5 BCBCB 6-10BCBAD 11-12 BC二填空题13 答案x 236+y 29=1 14 答案3151 16②③三解答题17. 【答案】解(1)若焦点在x 轴上,设方程为x 2a 2+y 2b 2=1 (a >b >0).依题意得c =4,e =45,∴a =5,b =3.∴椭圆的标准方程为x 225+y 29=1. 若焦点在y 轴上,同理可求得椭圆的标准方程为x 29+y 225=1.因此,所求椭圆的标准方程为x 225+y 29=1或x 29+y 225=1. (2)设椭圆方程为Ax 2+By 2=1 (A >0,B >0且A ≠B ). ∵椭圆经过点(6,1)、(-3,-2),∴⎩⎨⎧6A +B =1,3A +2B =1,解得⎩⎪⎨⎪⎧A =19,B =13.∴所求椭圆方程为x 29+y 23=1.点评 第(1)易错点是,易忽略对焦点所在的坐标轴进行分类讨论.第(2)避免讨论的方法是将方程设为Ax 2+By 2=1 (A >0,B >0且A ≠B ),用待定系数法求解. 18【答案】解(1)依题意得|F 1F 2|=2,又2|F 1F 2|=|PF 1|+|PF 2|,∴|PF 1|+|PF 2|=4=2a .∴a =2,c =1,b 2=3. ∴所求椭圆的方程为x 24+y 23=1.。
2021-2022年高二下学期第四次周考数学(理)试题(重点班) 含答案
1俯视图侧视图正视图3332021年高二下学期第四次周考数学(理)试题(重点班) 含答案一、选择题(5分分)1.已知集合,则“”是“”的( A )A .充分不必要条件B .必要不充分条件C .充要条件D .既不充分也不必要条件2.若复数满足,是虚数单位,则的虚部为( D )A. B. C. D.3. 已知命题p :x 1,x 2R ,(f (x 2)f (x 1))(x 2x 1)≥0,则p 是( C )A.x 1,x 2R ,(f (x 2)f (x 1))(x 2x 1)≤0 B .x 1,x 2R ,(f (x 2)f (x 1))(x 2x 1)≤0C. x 1,x 2R ,(f (x 2)f (x 1))(x 2x 1)<0D.x 1,x 2R ,(f (x 2)f (x 1))(x 2x 1)<04、已知各项为正的等比数列中,与的等比数列中项为,则的最小值( B )A.16B.8C.D.45. 在△中,是的中点,,点在上且满足,则等于 ( D )A .-43B .49 C.43 D. -496.如图1是一个几何体的三视图,则该几何体体积是( B )A .14B .15C . 16D .18图1 图27.在如图2所示的程序框图中,若输出的值是3,则输入的取值范围是( A )A .(4, 10]B .(2,+∞)C .(2, 4]D .(4,+∞)8. 已知函数时有极大值,且为奇函数,则的一组可能值依次为( D )(A ) (B ) (C ) (D )9.设满足约束条件,若目标函数的最大值为,则实数的值为( A )A. B. 1 C. D.10.过双曲线的左焦点F 作圆的切线,设切点为M ,延长FM 交双曲线于点N ,若点M 为线段FN 的中点,则双曲线C 1的离心率为( C )A .B .C .D .11. 我国南北朝数学家何承天发明的“调日法”是程序化寻求精确分数来表示数值的算法,其理论依据是:设实数的不足近似值和过剩近似值分别为和 ,则是的更为精确的不足近似值或过剩近似值。
高二第15周周练试题 试题
卜人入州八九几市潮王学校第15周周练一、选择题〔每一小题4分,一共64分〕1.以下各句中,标点符号使用正确的一项为哪一项哪一项〔〕A.“坚决遏制局部城房价过快上涨〞。
国务院常务会议的声音刚刚传出,人们猜测已久的二套房贷新政随即出台。
B.气象专家表示,预计今明两天南方局部地区的降雨仍然较强,需加强防范城镇积涝,山洪,山体滑坡和泥石流等灾害。
C.连日来,有关这8位中国维和警察的消息,一直牵动着中国人民的心,也让人们开场关心和理解这个特殊而神密的群体:中国维和警察。
D.4月9日至11日,博鳖亚洲论坛2021年年会在中国博鳖举行,本届年会主题为绿色复苏:亚洲可持续开展的现实选择。
2、以下各项中,标点符号的使用符合标准的一项为哪一项哪一项〔〕A.身体温暖,微循环才会正常,所以清早起来第一口食物最好选择温热的,应该享用热稀饭、热燕麦粥、热羊乳、热豆花、热豆浆和芝麻糊……等,再配着吃蔬菜、面包、治、水果。
B.2021放映阶段,各大影城的观众络绎不绝。
放映一周,2021的全球票房就超过了2.5亿美元。
国产电影怎样打败2021?还是一个未知数。
C.今年的春晚大HY中,参加了教育部的身影,其中一位负责人表示“央视春晚太闹,不该安排在年三十,〞从而让教育部这台春晚成了关注热点。
D.今年面向全国公开选拔一批指导HY,HY力度大,创新措施多,多项考试测评方法在我属于首次使用,有的在全国也是第一次。
3.以下各项中,标点符号的使用符合标准的一项为哪一项哪一项〔〕A.郭沫假设在剧本里写婵娟骂宋玉:“你是没有骨气的文人!〞上演时他自己在台下听,嫌这话不够味。
有人提醒他把“是〞改为“这〞,“你这没有骨气的文人!〞就够味。
B.依我之见,少年写作文,就应该多写一点“有意思〞的事。
何必那么深化,何必那么深沉?故作高深,一本正经,老气横秋,少了童年的童趣和稚气,倒没有什么得意之处。
C.“知屋漏者在宇下,知政失者在草野〞,〔王充论衡〕HY引用这句名言意在说明:要想理解的缺失,就必须深化民间调查。
高二下学期第四次周练试题
HY中学2021-2021学年高二语文下学期第四次周练试题〔扫描版〕励志赠言经典语录精选句;挥动**,放飞梦想。
厚积薄发,一鸣惊人。
关于努力学习的语录。
自古以来就有许多文人留下如头悬梁锥刺股的经典的,而近代又有哪些经典的高中励志赠言出现呢?小编筛选了高中励志赠言句经典语录,看看是否有些帮助吧。
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含泪播种的人一定能含笑收获。
贵在坚持、难在坚持、成在坚持。
功崇惟志,业广为勤。
耕耘今天,收获明天。
成功,要靠辛勤与汗水,也要靠技巧与方法。
常说口里顺,常做手不笨。
不要自卑,你不比别人笨。
不要自满,别人不比你笨。
高三某班,青春无限,超越梦想,勇于争先。
敢闯敢拼,**协力,争创佳绩。
丰富学校体育内涵,共建时代校园文化。
奋勇冲击,永争第一。
奋斗冲刺,誓要蟾宫折桂;全心拼搏,定能金榜题名。
放心去飞,勇敢去追,追一切我们为完成的梦。
翻手为云,覆手为雨。
二人同心,其利断金。
短暂辛苦,终身幸福。
东隅已逝,桑榆非晚。
登高山,以知天之高;临深溪,以明地之厚。
大智若愚,大巧若拙。
聪明出于勤奋,天才在于积累。
把握机遇,心想事成。
奥运精神,永驻我心。
“想”要壮志凌云,“干”要脚踏实地。
**燃烧希望,励志赢来成功。
楚汉名城,喜迎城运盛会,三湘四水,欢聚体坛精英。
乘风破浪会有时,直挂云帆济沧海。
不学习,如何养活你的众多女人。
不为失败找理由,要为成功想办法。
不勤于始,将悔于终。
不苦不累,高三无味;不拼不搏,高三白活。
不经三思不求教不动笔墨不读书,人生难得几回搏,此时不搏,何时搏。
不敢高声语,恐惊读书人。
不耻下问,学以致用,锲而不舍,孜孜不倦。
博学强识,时不我待,黑发勤学,自首不悔。
播下希望,充满**,勇往直前,永不言败。
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百尺高梧,撑得起一轮月色;数椽矮屋,锁不住五夜书声。
2021年高二数学周练14 理
2021年高二数学周练14 理一. 选择题:(本大题共14小题,每小题5分,共70分.在每个小题给出的四个选项中,只有一项是符合题目要求的)1.设数列是首项大于零的等比数列,则“”是“数列是递增数列”的( ) A .充分而不必要条件B .必要而不充分条件C .充分必要条件D .既不充分也不必要条件2.在等差数列中,,则数列的前11项和( )A .24B .48C .66D .1323.下列有关命题的说法正确的是 ( ) A .命题“若,则”的否命题为:“若,则”. B .“”是“”的必要不充分条件. C .命题“使得”的否定是:“ 均有”. D ..命题“若,则”的逆否命题为真命题.4.在△ABC 中,,则k 的值是( ) A .5 B .-5 C . D .5. 已知等比数列的前三项依次为,则( ) A . B . C . D .6.若命题“”是假命题,则实数的取值范围是 ( ) A 、[-1,3] B 、[1,4] C 、(1,4) D 、7.如果,则下列不等式,,③,中成立的是( )A..①②③④ B .②④ C .①② D .③④ 8. 已知实数满足若的最小值为,则实数等于( ) A .7 B .5 C .4 D .39. 已知圆关于直线对称,则 的取值范围是( )A . B. C. D.10. 已知椭圆的两个焦点分别是F 1、F 2,P 是椭圆上的一个动点,如果延长F 1P 到Q ,使得|PQ |=|PF 2|,那么动点Q 的轨迹是( )A .圆B .椭圆C .射线D .直线11. 已知△ABC 的顶点A (0,-4),B (0,4),且4(sinB -sinA)=3sinC ,则顶点C 的轨迹方程是( ) A .x 29-y 27=1(x >3) B .x 27-y 29=1(x >7) C .y 29-x 27=1(y >3) D .y 27-x29=1(y <-7)12.如图过抛物线的焦点F 的直线l 交抛物线于点A 、B ,交其准线于点C ,若|BC|=2|BF|,且|AF|=3,则此抛物线的方程为( )A .B .C .D .13.已知抛物线焦点恰好是椭圆 x 2a 2+y2b 2=1(a>b>0)的右焦点,且两条曲线交点的连线过点,则该椭圆的离心率为( )A .B .C .D .14.已知椭圆C :x 2a 2+y 2b 2=1(a>b>0)的离心率为32.双曲线x 2-y 2=1的渐近线与椭圆C 有四个交点,以这四个交点为顶点的四边形的面积为16,则椭圆C 的方程为( )A.x 28+y 22=1B.x 212+y 26=1C.x 216+y 24=1D.x 220+y25=1 第Ⅱ卷(非选择题 共80分)二. 填空题:(本大题共5小题,每小题4分,共20分,把答案填在答题卷的相应位置上) 15. 若数列{}的前项和,则 的值为 .16. 已知数列{a n }中,a 1=2,点(a n -1,a n )(n >1且n ∈N +)满足y =2x -1,则a 1+a 2+…+a 10=________.17. 若不等式的解集是,则以下结论中:①;②;③;④;⑤,正确结论的序号是 .18. 设O 为坐标原点,点M (2,1),若点N (x ,y )满足,则的最大值为 .19. 椭圆x 2a 2+y2b2=1(a >b >0)的左、右焦点为F 1,F 2,过F 1的直线与椭圆相交于A 、B 两点.若∠AF 1F 2=60,且→AF 1·→AF 2=0,则椭圆的离心率为______.三. 解答题(本大题共5小题,共60分,把答案填在答题卷的相应位置上)20.(本小题满分10分)设数列{}的前n 项和为,点的图象上。
2023-2024学年河南省区域联考高二上册期末考试数学模拟试题(含解析)
2023-2024学年河南省区域联考高二上册期末考试数学模拟试题一、单选题1.若直线410mx y -+=与直线230x y +-=平行,则实数m =().A .2B .2-C .12D .12-【正确答案】B【分析】根据直线平行的关系计算求解即可.【详解】解:两直线的斜率分别是4m,12-,由两直线平行可知142m =-,解得2m =-.故选:B .2.已知数列{}n a 满足13a =,()111n na n a*+=-∈N ,则4a =().A .23B .12-C .3D .32【正确答案】C【分析】根据递推关系直接求解即可.【详解】解:因为13a =,()111n na n a *+=-∈N ,所以,211213a a =-=,321112a a =-=-,43113a a =-=.故选:C3.若双曲线C 与双曲线2211612x y -=有相同的渐近线,且经过点(,则双曲线C 的标准方程是().A .221912y x -=B .221129x y -=C .223411313y x -=D .224311313x y -=【正确答案】A【分析】由题设双曲线C 的方程为221612x y λ-=,进而待定系数求解即可.【详解】解:由双曲线C 与双曲线2211612x y -=有相同的渐近线,故可设双曲线C 的方程为221612x y λ-=,又因为C过点(,所以8151612λ-=,解得34λ=-,所以,双曲线C 的标准方程是221912y x -=.故选:A .4.若曲线ln x ay x+=在点()1,a 处的切线与直线:250l x y -+=垂直,则实数=a ().A .12B .1C .32D .2【正确答案】C【分析】函数求导,计算()11k f =',利用切线与直线:250l x y -+=垂直,求得a 值.【详解】因为21ln x ay x --'=,所以曲线ln x ay x+=在点()1,a 处的切线的斜率为()111k f a ='=-,直线l 的斜率22k =,由切线与直线l 垂直知121k k =-,即()211a -=-,解得32a =.故选:C .5.中国共产党第二十次全国代表大会于2022年10月16日在北京召开,二十大报告提出:尊重自然、顺应自然、保护自然,是全面建设社会主义现代化国家的内在要求.必须牢固树立和践行绿水青山就是金山银山的理念,站在人与自然和谐共生的高度谋划发展.某市为了改善当地生态环境,计划通过五年时间治理市区湖泊污染,并将其建造成环湖风光带,预计第一年投入资金81万元,以后每年投入资金是上一年的43倍;第一年的旅游收入为20万元,以后每年旅游收入比上一年增加10万元,则这五年的投入资金总额与旅游收入总额分别为().A .781万元,60万元B .525万元,200万元C .781万元,200万元D .1122万元,270万元【正确答案】C【分析】根据等差数列和等比数列前n 项和求解即可.【详解】由题意知这五年投入的资金构成首项为81,公比为43,项数为5的等比数列,所以这五年投入的资金总额是548113781413⎡⎤⎛⎫⨯-⎢⎥⎪⎝⎭⎢⎥⎣⎦=-(万元).由题意知这五年的旅游收入构成首项为20,公差为10,项数为5的等差数列,所以这五年的旅游收入总额是54205102002⨯⨯+⨯=(万元).故选:C .6.如图,在平行六面体1111ABCD A B C D -中,底面ABCD 是菱形,侧面11A ADD 是正方形,且1120A AB ∠=︒,60DAB ∠=︒,2AB =,若P 是1C D 与1CD 的交点,则AP =().A .9B .7C .3D【正确答案】D【分析】由题知11122AP AB AD AA =++,进而根据计算向量的模得答案.【详解】解:在平行六面体1111ABCD A B C D -中,四边形11DD C C 是平行四边形,又P 是1C D ,1CD 的交点,所以P 是1C D 的中点,所以,()11111222AP AD DP AD DC DD AB AD AA =+=++=++,又2AB AD ⋅=,12AB AA ⋅=- ,10AD AA ⋅= ,所以2211122AP AB AD AA ⎛⎫=++ ⎪⎝⎭2221111117442AB AD AA AB AD AD AA AB AA =+++⋅+⋅+⋅=,即AP =故选:D .7.已知直线:240l x y +-=与x 轴,y 轴分别交于P ,Q 两点,点A 是圆()()()22:330C x y r r -+-=>上的动点,若APQ △的面积的取值范围是515,22⎡⎤⎢⎥⎣⎦,则r =().A B C D 【正确答案】B【分析】运用两点间距离公式求得PQ ,由三角形面积范围可得h 范围及圆与直线相离,进而可求得r 的值.【详解】由题意知()2,0P ,()0,4Q ,()3,3C ,所以PQ ==C 到直线l的距离d ==设点A 到直线l 的距离为h,则12APQ S PQ h =⨯⨯=△,因为515,22APQ S ⎡⎤∈⎢⎥⎣⎦△,所以,22h ∈⎢⎣⎦,所以直线l 与圆C 相离,所以[],h d r d r ∈-+,即h r r ⎤∈-+⎦,所以r r ⎧=⎪⎪=,解得r =.故选:B .8.已知(),0,a b ∈+∞,且221ln 4223b a a b b a =--+-,则下列不等式一定成立的是().A .21a b +<B .21a b +>C .2b a >D .2b a<【正确答案】D【分析】利用对数运算把式子化为()22ln 22ln 2b b b a a a -+<-+,构造函数,利用导数判断单调性,利用单调性求解不等式.【详解】由221ln4223b a a b b a =--+-,得()221ln ln 2223b a a a b b -=--+-,即()()2221ln 22ln 222ln 23b b b a a a aa a-+=-+-<-+,令()2ln f x x x x =-+,则()()2f b f a <.()2121210x x f x x x x-+'=-+=>,所以()f x 在()0,∞+上单调递增,又()2,0,a b ∈+∞,()()2f b f a <,所以2b a <.故选:D .二、多选题9.已知圆22:6480C x y x y ++-+=,则().A .圆C 关于直线330x y +-=对称B .圆C 的面积是25πC .点()1,4-在圆C 外D .直线3480x y --=与圆C 相切【正确答案】AC【分析】根据圆的一般方程写出圆心坐标与半径,对于选项A ,判断圆心是否在直线上即可;对于选项B ,运用圆的面积公式计算即可;对于选项C 、D ,运用几何法判断点与圆、直线与圆的位置关系即可.【详解】由226480x y x y ++-+=,得()()22325x y ++-=,所以圆心为()3,2C -,因为圆心()3,2C -在直线330x y +-=上,所以圆C 关于直线330x y +-=对称,故A 正确;C 的面积是5π,故B 错误;当=1x -,4y =时,22648116616830x y x y ++-+=+--+=>,所以点()1,4-在圆C 外,故C 正确;因为圆心()3,2C -到直线3480x y --=的距离为5d =>,所以直线3480x y --=与圆C 相离,故D 错误.故选:AC.10.已知数列{}n a 满足11a =,()131n n a a n *+=+∈N ,{}n a 的前n 项和为n S ,则().A .12n a ⎧⎫-⎨⎬⎩⎭是等比数列B .12n a ⎧⎫+⎨⎬⎩⎭是等比数列C .3122n n a =-D .3214n n n S +-=【正确答案】BC【分析】根据给定的递推公式,变形并构造数列,求出通项,再逐项判断、计算作答.【详解】数列{}n a 中,N n *∈,131n n a a +=+,则1113()22n n a a ++=+,又11322a +=,因此数列1{}2n a +是以32为首项,3为公比的等比数列,A 错误,B 正确;11333222nn n a -+=⨯=,即有3122n n a =-,C 正确;1213(13)3333232()22221324n nn n n n n S +---=+++-=-=-L ,D 错误.故选:BC11.已知抛物线2:12C y x =的焦点为F ,准线为l ,直线l 与x 轴交于点P ,过点F 的直线与抛物线C 交于M ,N 两点,O 为坐标原点,则下列说法正确的是().A .若M ,N 的横坐标之和为8,则14MN =B .以MN 为直径的圆与直线l 相交C .27OM ON ⋅=-D .直线PM ,PN 关于x 轴对称【正确答案】ACD【分析】运用抛物线定义分析选项A ,运用梯形中位线性质分析选项B ,运用韦达定理代入OM ON ⋅计算分析选项C ,运用韦达定理代入PM PN k k +计算分析选项D.【详解】如图,过M ,N 作准线l 的垂线,垂足分别为1M ,1N ,设线段MN 的中点为Q ,Q 在准线l 上的射影为1Q .118614M N MN MF NF MM NN x x p =+=+=++=+=,故A正确;在梯形11MM N N 中,()()111111222QQ MM NN MF NF MN =+=+=,因此以MN 为直径的圆与直线l 相切,故B 错误;由题意知()3,0F ,设211,12y M y ⎛⎫ ⎪⎝⎭,222,12y N y ⎛⎫⎪⎝⎭,直线MN 的方程为3x my =+,由2312x my y x=+⎧⎨=⎩得212360y my --=,所以1212y y m +=,1236y y =-,所以()22212121212,271212144y y y y OM ON y y y y ⎛⎫⎛⎫⋅=⋅=+=- ⎪ ⎪⎝⎭⎝⎭,故C 正确;由题意知()3,0P -,则1122111236312PM y y k y y ==++,2222221236312PN y y k y y ==++,所以()()()()2212211222221212123636121236363636PM PNy y y y y y k k y y y y ⎡⎤+++⎣⎦+=+=++++()()()()12122212123603636y y y y y y ++==++,所以直线PM ,PN 的倾斜角互补,即直线PM ,PN 关于x 轴对称,故D 正确.故选:ACD .12.已知函数()e sin xf x a x =-,则下列说法正确的是().A .当0a =时,过原点作曲线()y f x =的切线l ,则l 的方程为e y x =B .当1a =时,()f x 在()0,∞+上单调递增C .若()f x 在ππ,22⎛⎫- ⎪⎝⎭上单调递增,则π4a -<D .当1a =-时,()f x 在ππ,2⎛⎫-- ⎪⎝⎭上有极小值点【正确答案】ABD【分析】设切点坐标并求导及导数的几何意义可求得切线方程,运用导数研究函数的单调性、极值点.【详解】当0a =时,()e x f x =,设切点为(),e mm ,()e x f x '=,e m k =,所以():e e m ml y x m -=-,又l 过原点,则()e e m mm -=-,解得1m =,所以l 的方程为e y x =,故A 正确;当1a =时,()e sin xf x x -=,()e cos x f x x '=-,当0x >时,e 1x >,1cos 1x -≤≤,所以()0f x ¢>,所以()f x 在()0,∞+上单调递增,故B 正确;()e cos x f x a x '=-,若()f x 在ππ,22⎛⎫- ⎝⎭上单调递增,则()0f x '≥在ππ,22⎛⎫- ⎪⎝⎭上恒成立,即ecos xa x ≤在ππ,22⎛⎫- ⎪⎝⎭上恒成立,令()e cos xh x x =,则()()2e cos sin cos x x x h x x+'=,令()0h x '=,得π4x =-,当ππ,24x ⎛⎫∈-- ⎪⎝⎭时,()0h x '<,()h x 单调递减,当ππ,42x ⎛⎫∈- ⎪⎝⎭时,()0h x '>,()h x 单调递增,所以()π4min π4h h x -⎛⎫=- ⎪⎝⎭,所以π4a -≤,故C 错误;当1a =-时,()e sin x f x x =+,()e cos xf x x '=+,令()()x f x ϕ'=,则()e sin xx x ϕ'=-,当ππ,2x ⎛⎫∈-- ⎪⎝⎭时,sin 0x <,所以()e sin 0xx x ϕ'=->,所以()()x f x ϕ'=在ππ,2⎛⎫-- ⎪⎝⎭上单调递增,又()ππe 10f -'-=-<,π2πe 02f -⎛⎫'-=> ⎪⎝⎭,所以由零点存在定理可知,存在唯一的0ππ,2x ⎛⎫∈-- ⎪⎝⎭,使得()00f x '=,当()0π,x x ∈-时,()00f x '<,()f x 单调递减,当0π,2x x ⎛⎫∈- ⎪⎝⎭时,()00f x '>,()f x 单调递增,所以()f x 在ππ,2⎛⎫-- ⎪⎝⎭上有极小值点,故D 正确.故选:ABD .三、填空题13.已知等差数列{}n a 的前n 项和为n S ,若785a a +=,则14S =__________.【正确答案】35【分析】根据给定条件,利用等差数列性质结合前n 项和公式求解作答.【详解】因为{}n a 是等差数列,114785a a a a +=+=,所以()1141414352a a S +==.故3514.滑县木版画是河南安阳最传统的手工艺品,创始于明朝初期,距今已有六百多年的历史了,滑县木版画制作工艺考究,至今一直都是纯手工制作,颜色精细淡雅,色彩和谐,人物造型夸张,线条刚劲有力,极具当地的民俗特色.小华的伯伯制作滑县木版画并出售,寒假期间小华通过调研得知伯伯制作的A 系列木版画的成本为30元/套,每月的销售量()f x (单位:套)与销售价格x (单位:元/套)近似满足关系式()()290f x x =-,其中3090x <<,则当A 系列木版画销售价格定为__________元/套时,月利润最大.【正确答案】50【分析】根据题意可得月利润为()()()()2903,030,90g x x x x =-∈-,求导,利用导数判断函数单调性,进而可求最值点.【详解】设A 系列木版画的月利润为()g x ,则()()()()()2309030g x f x x x x =-=--,3090x <<,可得()()()()()()2290309039050g x x x x x x '=--+-=--,令()0g x '=,则50x =,当()30,50x ∈时,()0g x '>,当()50,90x ∈时,()0g x '<,()g x 在()30,50上单调递增,()g x 在()50,90上单调递减,所以当50x =时,利润()g x 取到极大值,也是最大值,即当A 系列木版画销售价格定为50元/套时,月利润最大.故50.15.已知椭圆22:143x y C +=的左顶点为A ,右焦点为F ,斜率为k 的直线l 过点F ,若直线l 上存在点M 满足2AM FM +=,则实数k 的取值范围是__________.【正确答案】⎡⎢⎣⎦【分析】根据题意结合向量的线性运算分析可得1NM =,转化为N 到直线l 的距离1d NM ≤=,利用点到直线的距离公式运算求解.【详解】由题意可得2,1a b c ==,则()2,0A -,()1,0F ,取AF 的中点1,02N ⎛⎫- ⎪⎝⎭,∵22AM FM NM +==uuu r uuu r uuur ,则1NM = ,即直线l 上存在点M ,使得1NM =,所以N 到直线l 的距离1d NM ≤=,又∵直线l 的方程为()1y k x =-,即kx y k 0--=,则1d =,解得k ≤≤故答案为.,55⎡-⎢⎣⎦16.已知数列{}n a 满足()22122n a a n n a n n *++++=∈N L ,数列121n n n a a +⎧⎫+⎨⎬⎩⎭的前n 项和为n T ,若()20222023k T k *<∈N ,则k 的最大值为__________.【正确答案】43【分析】根据n a 与n S 的关系可求得2n a n =,利用裂项相消法求121n n n a a +⎧⎫+⎨⎬⎩⎭的前n 项和为n T ,结合恒成立问题运算求解.【详解】因为()22122n a a n n a n n *++++=∈N L ,当2n ≥时,则()()212111212n n n a a a n --+-+++=-L ,两式相减得1n a n n =,即2n a n =;令1n =,则211112a +==,满足2n a n =,综上所述:2n a n =,n *∈N .则()()2222121211111n n n n a a n n n n +++==-++,所以()()222222211111111122311n T n n n =-+-+-=-++L ,又∵()20222023k T k *<∈N ,即()212022120231k -≤+,整理得()212023k +<,解得1k <,且k *∈N ()143,44∈,所以k 的最大值为43.故43.方法点睛:1.裂项相消的规律(1)裂项系数取决于前后两项分母的差.(2)裂项相消后前、后保留的项数一样多.2.数列与不等式的综合问题的常见题型数列常与不等式结合,如比较大小、不等式恒成立、求参数范围等问题,需要熟练应用不等式知识解决数列中的相关问题.四、解答题17.已知直线1:280l x y +-=,2:330l x y -+=的交点为P ,直线l 经过点P 与点()3,1Q --.(1)求直线l 的方程;(2)若直线l 与圆()()22:129C x y -++=交于A ,B 两点,求ABC 的面积.【正确答案】(1)210x y -+=(2)185【分析】(1)求出两直线交点坐标,运用斜率公式及直线点斜式方程即可.(2)运用几何法求圆内的弦长,进而求得三角形的面积.【详解】(1)由题意知,28033302x y x x y y +-==⎧⎧⇒⎨⎨-+==⎩⎩,即()3,2P .因为直线l 经过点P ,Q ,所以直线l 的斜率()()211332k --==--,所以直线l 的方程为()1232y x -=-,即210x y -+=.(2)圆()()22:129C x y -++=的圆心为()1,2C -,半径3r =,所以圆心C 到直线l 的距离5d ==,5AB ==,所以△ABC 的面积11825S AB d =⋅=.18.已知函数()321f x x ax bx =-++在3x =处取得极值26-.(1)求a ,b 的值;(2)若存在[]4,4x ∈-,使得()0f x t ->成立,求实数t 的取值范围.【正确答案】(1)3a =,9b =-(2)(),6-∞【分析】(1)根据已知条件可知得(3)0(3)26f f =-'=⎧⎨⎩求解即可.(2)运用分离参数求最值解决存在性问题,再运用导数研究函数的最值即可.【详解】(1)()232f x x ax b '=-+,因为函数()321f x x ax bx =-++在3x =处取到极值26-,所以(3)0(3)26f f =-'=⎧⎨⎩,即2760 2793126a b a b -+=⎧⎨-++=-⎩,解得39a b =⎧⎨=-⎩.经检验,当3a =,9b =-时,()f x 在3x =处取到极值,所以3a =,9b =-.(2)因为存在[]4,4x ∈-,使得()0f x t ->成立,所以()max t f x <,由(1)知()32391f x x x x =--+,()()()2369313f x x x x x '=--=+-,令()0f x '=,得=1x -或3x =,当[)4,1x ∈--时,()0f x ¢>,()f x 单调递增;当()1,3x ∈-时,()0f x '<,()f x 单调递减,当(]3,4x ∈时,()0f x ¢>,()f x 单调递增.所以()()16f x f =-=极大值.又()419f =-,所以()max 6f x =,所以6t <.所以实数t 的取值范围是(),6-∞.19.如图,在四棱柱1111ABCD A B C D -中,底面ABCD 是矩形,平面11AA D D ⊥平面ABCD ,点E 是AD 的中点,1122A A A D AD AB ====.(1)求证:平面1A EB ⊥平面ABCD ;(2)求直线1A D 与平面1A BC 所成角的正弦值.【正确答案】(1)证明见解析【分析】(1)根据面面垂直的判断定理和性质定理分析证明;(2)建系,利用空间向量求线面夹角.【详解】(1)因为11A A A D =,点E 是AD 的中点,所以1A E AD ⊥,又平面11AA D D ⊥平面ABCD ,平面11AA D D ⋂平面ABCD AD =,1A E ⊂平面11AA D D ,所以1A E ⊥平面ABCD ,又∵1A E ⊂平面1A EB ,所以平面1A EB ⊥平面ABCD .(2)取BC 的中点F ,连结EF ,则四边形CDEF 为正方形,所以EF AD ⊥,以E 为坐标原点,EF ,ED ,1EA 所在直线分别为x 轴,y 轴,z 轴建立空间直角坐标系如图所示,则()1,1,0B -,()1,1,0C ,()0,1,0D ,(13A ,所以()0,2,0BC =uu u r,(13BA =- ,(10,1,3A D =- .设平面1A BC 的法向量(),,m x y z =,则12030m BC y m BA x y z ⎧⋅==⎪⎨⋅=-++=⎪⎩,令1z =,则0y =,3x =所以平面1A BC 的一个法向量)3,0,1m =,设直线1A D 与平面1A BC 所成角为θ,则11133sin cos ,224m A D m A D m A Dθ-⋅====,即直线1A D 与平面1A BC 3420.已知数列{}n a 的前n 项和为n S ,()()2221n n S n n a n *-=+∈N .(1)求数列{}n a 的通项公式;(2)设()3n a n n b a n *=-⋅∈N ,求数列{}n b 的前n 项和n T .【正确答案】(1)n a n =-(2)332443n nn T +=-⋅【分析】(1)由题意结合n a 与n S 的关系分析可得数列{}n a 是首项为1-,公差为1-的等差数列,根据等差数列的通项公式运算;(2)可得13nn b n ⎛⎫=⋅ ⎪⎝⎭,利用错位相减法分析运算.【详解】(1)当1n =时,11213a a -=,所以11a =-;当2n ≥时,由()2221n n S n n a -=+,则()()2112121n n S n n a ----=-,可得()()()221212121n n n a n n n a n a --+-=+--,整理得11n n a a --=-,所以数列{}n a 是首项为1-,公差为1-的等差数列,故()11=---=-n a n n .(2)由(1)可得:133nna n nb a n ⎛⎫=-⋅=⋅ ⎪⎝⎭,则2311111233333nn T n ⎛⎫⎛⎫⎛⎫=⨯+⨯+⨯++⨯ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭L ,23411111112333333n n T n +⎛⎫⎛⎫⎛⎫⎛⎫=⨯+⨯+⨯++⨯ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭⎝⎭L ,两式相减得:231211111333333nn n T n +⎛⎫⎛⎫⎛⎫⎛⎫=++++-⨯ ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭⎝⎭L 111113311311322313nn n n n ++⎡⎤⎛⎫-⎢⎥ ⎪⎝⎭⎢⎥⎛⎫⎛⎫⎛⎫⎣⎦=-⨯=-+⎪ ⎪⎪⎝⎭⎝⎭⎝⎭-,所以332443n nn T +=-⋅.21.已知椭圆()2222:10x y C a b a b +=>>的左、右焦点分别为1F ,2F,离心率为2,点M 是C 上任意一点,且12MF F △的周长为8+(1)求椭圆C 的方程;(2)点P 是椭圆C 上一点且在第四象限,212PF F F ⊥,过点P 作倾斜角互补的两条不同直线分别与椭圆C 交于点A ,B (A ,B 与P 不重合),试判断直线AB 的斜率是否为定值,并证明你的结论.【正确答案】(1)221168x y +=(2)是,证明见解析【分析】(1)依题意可得2c a =,228a c +=+a 、c ,再求出b ,即可得解;(2)设()()00P y y<,代入椭圆方程,求出P 点坐标,设直线AP的方程为(2y k x +=-,联立直线与椭圆方程,求出A x ,同理求出B x ,再由A BAB A By y k x x -=-计算可得.【详解】(1,得c a =2c a =,由12MF F △的周长为8+228a c +=+所以4a =,c =所以b =所以椭圆C 的方程为221168x y +=.(2)解:直线AB 的斜率是定值,证明如下:因为P 是椭圆C 上一点且在第四象限,212PF F F ⊥,所以设()()000P y y<,代入椭圆C 的方程,得02y =-,即()2P -.设直线AP的方程为(2y k x +=-,与椭圆C 的方程联立,得()()2222128161680kx k x k +-+++-=,所以2216128A k k k -=++,即22128A k k x k +-=+.因为PA ,PB 的倾斜角互补,所以直线BP的方程为(2y k x +=--,同理得22812B k x k--=+.因为(2A A y k x +=-,(2B B y k x +=--,所以((A B A B ABA B A Bk x k x y y k x x x x -+--==--(221216212A B A Bk x x k k x x k -+-+===--+,因此直线AB的斜率为定值2-.22.已知函数()2ln 1f x ax x =--,()()()2g x f x a x =+-,a ∈R .(1)求函数()f x 的单调区间;(2)若对任意的()0,x ∈+∞,()0g x >恒成立,求整数a 的最小值.【正确答案】(1)当0a ≤时,函数()f x 的单调递减区间为()0,∞+;当0a >时,函数()f x 的单调递减区间为⎛ ⎝⎭,单调递增区间为⎫+∞⎪⎪⎝⎭(2)2【分析】(1)求导,分类讨论求原函数单调性;(2)根据题意分析可得2ln 21x x a x x ++>+在()0,∞+上恒成立,构建新函数()2ln 21x x x x xϕ++=+,利用导数结合零点代换求()x ϕ的最大值.【详解】(1)由题意可得:函数()f x 的定义域为()0,∞+,且()21212ax f x ax x x -'=-=,当0a ≤时,()2210ax f x x-'=<在定义域内恒成立,则函数()f x 的单调递减区间为()0,∞+;当0a >时,令()2210ax f x x -'==,则2x a =或2x a =-(舍去),当x ⎛∈ ⎝⎭时,()0f x '<,当x +∞⎫∈⎪⎪⎝⎭时,()0f x ¢>,则函数()f x的单调递减区间为0,2a ⎛ ⎝⎭,单调递增区间为2a ⎛⎫+∞ ⎪ ⎪⎝⎭;综上所述,当0a ≤时,函数()f x 的单调递减区间为()0,∞+;当0a >时,函数()f x的单调递减区间为2a ⎛ ⎝⎭,单调递增区间为,2a ⎛⎫+∞ ⎪ ⎪⎝⎭.(2)对任意的()0,x ∈+∞,()0g x >恒成立,即不等式()2ln 21a x x x x +>++恒成立,因为0x >,则20x x +>,所以原问题等价于2ln 21x x a x x++>+在()0,∞+上恒成立,设()2ln 21x x x x xϕ++=+,()0,x ∈+∞,则只需()max a x ϕ>,可得()()()()()()()()222221221ln 2121ln x x x x x x x x x x x x x x ϕ⎛⎫++-+++ ⎪+--⎝⎭'==++,令()ln h x x x =--在()0,∞+上单调递减,因为()111ln 2ln 410222h ⎛⎫=-=-> ⎪⎝⎭,()110h =-<,所以存在唯一的01,12x ⎛⎫∈ ⎪⎝⎭,使得()000ln 0h x x x =--=,即00ln x x =-,当()00,x x ∈时,()0h x >,则()0x ϕ'>,当()0,x x ∈+∞时,()0h x <,则()0x ϕ'<,则()x ϕ在()00,x 上单调递增,()x ϕ在()0,x +∞上单调递减,所以()()000000222max 0000000ln 212111x x x x x x x x x x x x x x ϕϕ++-+++=====+++,所以01a x >即可,又∵01,12x ⎛⎫∈ ⎪⎝⎭,所以()011,2x ∈,故整数a 的最小值为2.方法定睛:破解不等式的恒成立问题的常用方法:(1)分离参数法第一步:将原不等式分离参数,转化为不含参数的函数的最值问题;第二步:利用导数求该函数的最值;第三步:根据要求得所求范围.(2)函数思想法第一步将不等式转化为含待求参数的函数的最值问题;第二步:利用导数求该函数的极值;第三步:构建不等式求解.。
文科高二15周末测试.docx
文科12月17周末测试1.命题“存在0x R ∈, 020x ≤”的否定是( )A. 不存在0x R ∈, 020x >B. 存在0x R ∈, 020x ≥C. 对任意的0x R ∈, 020x ≤D. 对任意的0x R ∈, 020x > 2.已知a R ∈,则“2a >”是“22a a >”成立的( )A. 充分不必要条件B. 必要不充分条件C. 充要条件D. 既不充分也不必要条件 3.物体运动时位移s 与时间t 的函数关系是2-28s t t =+,此物体在某一时刻的速度为0,则相应的时刻为( ).A. 0t =B. 1t =C. 2t =D. 4t =4.已知正数组成的等比数列{}n a ,若318•100a a =,那么714a a +的最小值为( )A. 20B. 25C. 50D. 不存在5.设()ln ,0f x x a b =<<,若p f=, 2a b q f +⎛⎫= ⎪⎝⎭, ()()()12r f a f b =+,则下列关系式中正确的是( )A. q r p =<B. q r p =>C. p r q =<D. p r q =>6.上一点M 到左焦点1F 的距离是2, N 是1MF 的中点, O 是坐标)3 D. 27 ) A C )[1,)+∞ D ][1,)+∞8A.B. C. D.9.不等式组240{10x y x y ++≤-+≤所表示的平面区域大致为以下四幅所示的哪一个( )10.若函数()ln f x kx x =-在区间()2,+∞单调递增,则k 的取值范围是( ).A. (],2-∞- B. 1,2⎡⎫+∞⎪⎢⎣⎭ C. [)2,+∞ D. 1,2⎛⎤-∞ ⎥⎝⎦11.设圆()22125x y ++=的圆心为C , ()1,0A 是圆内一定点, Q 为圆周上任一点,线段AQ 的垂直平分线与CQ 的连线交于点M ,则M 的轨迹方程为( )A.224412125x y -= B. 224412125x y += C. 224412521x y -= D. 224412521x y += 12.已知椭圆的左焦点为1F ,右焦点为2F .若椭圆上存在一点P ,且以椭圆的短轴为直径的圆与线段2PF 相切于线段2PF 的中点,则该椭圆的离心率为( )A.13B. 23C. 36D.53 二.填空题(每空5分,共20分)13.已知函数()f x 的导函数为()f x ',且满足()()312ln f x xf x +'=,则()1f '=______. 14.抛物线y =x 24的准线方程是_____.15.若,x y 满足条件21{2 2x y x y y x -≤+≥-≤,目标函数32z x y =-+的最小值为__________.16.传说中孙悟空的“如意金箍棒”是由“定海神针”变形得来的.这定海神针在弯形时永远保持为圆柱体,其底面半径原为12cm 且以每秒1cm 等速率缩短,而长度以每秒20cm 等速率增长.已知神针的底面半径只能从12cm 缩到4cm 为止,且知在这段变形过程中,当底面半径为10cm 时其体积最大.假设孙悟空将神针体积最小时定形成金箍棒,则此时金箍棒的底面半径为__________cm . 三、解答题(17题10分,其余每题12分) 17.求下列函数的导数: (1)()()()1sin 14f x x x =+-; (2)()21x xf x x =-+.18.已知曲线382y x x =-+(1)求曲线在点0x =处的切线方程;(2)过原点作曲线的切线:l y kx =,求切线方程.19 x R ∈,求: (1)()f x 的单调增区间;(2)()f x 在[]0,2上的最小值和最大值。
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侧(左)视图正(主)视图65533556高二理科数学周练(十五)综合卷一、选择题:1.命题:“若12<x ,则11<<-x ”的逆命题是( C )A .若12≥x ,则11x x ≥≤-或 B .若11x x ≥≤-或,则12≥xC .若11<<-x ,则12<xD .若11x x ><-或,则12>x2.若命题“0R x ∃∈,使得200230x mx m ++-<”为假命题,则实数m 的取值范围是(A )(A )[2,6] (B )[6,2]--(C )(2,6) (D )(6,2)--3.“1m <”是“一元二次方程20x x m ++=有实数解”的( B )A .充分不必要条件B .必要不充分条件C .充要条件D .既不充分不必要条件 4.用斜二测画法画一个水平放置的平面图形的直观图为如图1所示的一个正方形,则原 来的图形是( A )5. 下图是某几何体的三视图,则该几何体的体积为( D )A .256323π+ B .1616π+C .32163π+D .32323π+ 6.某几何体的三视图如图所示,它的表面积为( D )(A )30π (B )36π (C )51π (D )33π 7.设l 为直线,,αβ是两个不同的平面,下列命题中 正确的是( C )A .若//l α,//l β,则//αβB .若l α⊥,//l β,则//αβC .若l α⊥,l β⊥,则//αβD .若αβ⊥,//l α,则l β⊥图1 正视图 侧视图俯视图48.直线1:230l x y +-=经过点()1,k ,若直线2l 也经过点()1,k ,且与1l 垂直,则2l 的方 程为( A ) A .210x y -+= B .230x y +-=C .230x y +-= D .210x y --=9.已知x , y 满足约束条件⎪⎩⎪⎨⎧≥--≥-≥02200y x y x y , 则11+-=x y W 的取值范围为是( D )A.〔 —1,31〕 B.〔-21,31〕 C. 〔 -21,+∞ ) D. 〔-21,1) 10.设(2,1,3)a x = ,(1,2,9)b y =-,若a 与b 为共线向量,则(C )A .1x =,1y =B .12x =,12y =-C .16x =,32y =-D .16x =-,32y =11.设F 为抛物线C :26y x =的焦点,过F 且倾斜角为30°的直线交C 于A 、B 两点,O 为坐标原点,则AOB ∆的面积为( D ) A.B . 92C .D . 912.直线4y kx =+与圆()()22334x y -+-=相交于,M N 两点,若MN ≥则k的取值范围是( B ) A .[)3,0,4⎛⎤-∞-+∞ ⎥⎝⎦ B .3,04⎡⎤-⎢⎥⎣⎦C.⎡⎢⎣⎦D .2,03⎡⎤-⎢⎥⎣⎦二、填空题:13. 命题2:,11p x R x ∀∈-≥-,则p ⌝:14.如图,在正方体1111ABCD A BC D -中, ,M N 分别是棱1,AB CC 的中点,则异面直线1A M 与DN 所成的角大小为15.已知向量(1,1,0),(0,1,),a b k == ,a b 的夹角为3π,则k 的值是16.与圆221:(2)4C x y +-=关于直线3x =对称的圆2C 的标准方程为 17.抛物线24y x =上与焦点的距离等于5的点的坐标为 18.设双曲线的一个焦点为F ;虚轴的一个端点为B ,如果直线FB 与该双曲线的一条渐三、解答题:本大题共6小题,满分80分,解答须写出文字说明、证明过程或演算步骤。
15.(12分)已知直线l经过点(1,0),A B(1)求直线l 的倾斜角;(2)若点P 在y 轴上,并且PAB ∆求点P 的坐标。
16.(12分)已知圆心为C 的圆经过坐标原点O ,半径为5,点C 在第一象限、且在直线:430l x y -=上,点A 为圆C 上的点、且8OA =,(1)求圆C 的标准方程; (2)求OA 所在直线的方程。
17.(14分)已知四棱锥P ABCD -,底面ABCD 为矩形,侧棱PA 垂直平面ABCD ,22ADPA AB ===,,E F 分别为棱,AD PC 的中点, (1)证明://EF 平面PAB ;(2)EF ⊥平面PBC ; (3)求三棱锥C BEF -的体积。
PACDEF18.(14分)已知PAB ∆的两个顶点,A B 分别为双曲线22154x y -=的左、右两个焦点,且,PA PB 所在直线斜率之积为(0)k k ≠,试探求顶点P 的轨迹。
19.(14分)已知直三棱柱111ABC A B C -中, (1)求侧棱1CC 与平面1ABC 所成角的正弦值;(2)若点,E F 分别为棱,AC BC 上的动点,且CE BF =, 当三角形CEF 面积最大时,求二面角1C EF C --的正切值。
AFE1C 1B 1A C1,2,32ACB AC BC CC π∠====参考答案及评分标准13.200,11x R x ∃∈-<- ; 14.2π; 15. 1±; 16.22(6)(2)4x y -+-=; 17. ()4,4±,18. 15.(本小题满分12分)已知直线l经过点(1,0),A B(Ⅰ)求直线l 的倾斜角;(Ⅱ)若点P 在y 轴上,并且PAB ∆求点P 坐标。
解:(Ⅰ)设直线l 的倾斜角为α,斜率为k则31203tan =--==αk …... 2分 又[)πα,0∈ ..3分3πα=∴ ....4分即直线l 的倾斜角为3π。
(Ⅱ)依题意,可设点P 的坐标为()a ,0,点P 到直线l 的距离为d由已知得直线l 的方程为()13-=x y ,即033=--y x …...….....5分23133+=+--=∴a a d ……...…...…...……………………...….....7分又()()2120322=-+-=AB ……...…...…...……………………...…..8分d AB S PAB⨯=∆21 ⨯⨯∴221323=+a ..…………………...…..9分 即323=+a 323±=+∴a3=∴a 或33-=∴a ..…..11分 即点P 的坐标为()3,0或()33,0-...…..12分16.(本小题满分12分)已知圆心为C 的圆经过坐标原点O ,半径为5,点C 在第一象限、 且在直线:430l x y -=上,点A 为圆C 上的点、且8OA =,(Ⅰ)求圆C 的标准方程;(Ⅱ)求OA 所在直线的方程。
解:(Ⅰ)依题意设圆C 的标准方程为()()2522=-+-b y a x …………...….... 1分由已知得⎪⎩⎪⎨⎧>>=+=-0,02503422b a b a b a ...3分 解方程得⎩⎨⎧==43b a ……...…....5分即圆C 的标准方程为()()254322=-+-y x …………………...…....6分(Ⅱ)①当直线OA 的斜率不存在时,其方程为0=x …………...…....7分 此时圆心(3,4)C 到OA 的距离3d =,835222=-=OA ,满足题意。
....8分②当直线OA 的斜率存在时,设斜率为k ,直线OA 的方程为kx y =即0=-y kx .….9分依题意可知:3285143222=⎪⎭⎫⎝⎛-=+-=k k d …………………...…....10分解得247=k x y 247=∴ ………………….....11分 由①②可知OA 所在直线方程为0=x 或724y x = …………………...…....12分 17.(本小题满分14分)已知四棱锥P ABCD -,(如图4)底面ABCD 为矩形,侧棱PA垂直平面ABCD ,22ADPA AB ===,,E F 分别为棱,AD PC 的中点, (Ⅰ)证明://EF 平面PAB ;(Ⅱ)EF ⊥平面PBC ;(Ⅲ)求三棱锥C BEF -体积。
解:(I )取PB 的中点H ,连FH AH ,F E , 分别是PC AD ,的中点,底面ABCD 为矩形HF ∴//BC 且BC HF 21=,BC AE //且BC AE 21= AE HF //∴且AE HF =∴四边形AEFH 为平行四边形AH EF //∴…2分又⊄EF 平面PAB ⊂AH 平面PAB ……3分//EF ∴平面PAB ……………4分(II)⊥PA 平面ABCD ,⊂BC 平面ABCD BC PA ⊥∴…………………5分又A AB PA BC AB =⊥ ,,⊂AB PA 、平面PAB ,⊥∴BC 平面PAB⊂AH 平面PAB AH BC ⊥∴……………………………………………6分 AB PA = ,H 为PB 中点AH PB ⊥∴……………………………………7分PA CDE FH M又⊂=PB BC B PB BC 、, 平面PBC ⊥∴AH 平面PBC …………………8分 由(I )知AH EF //∴⊥∴EF 平面PBC ……………………………9分 (III )设M BD AC = ,连FM底面ABCD 为矩形,M ∴为AC 中点,又F 为PC 中点 PA FM //∴…………………………………10分⊥PA 底面ABCD ,⊥∴FM 底面ABCD ,则FM 为三棱锥BEC F -的高……11分4242121=⨯⨯=⨯⨯=∆AB BC S BEC ……………………………………12分3431=⨯⨯=∴∆-FM S V BEC BEC F ………………………………………………13分BEC F BEF C V V --= ∴三棱锥BEF C -的体积为34…………………………14分18、(本小题满分14分)已知PAB ∆的两个顶点,A B 分别为双曲线22154x y -=的左、右两个焦点,且,PA PB 所在直线斜率之积为(0)k k ≠,试探求顶点P 的轨迹。
解:设点P ()y x ,, 39452=∴=+=c c .….... 1分 即()()0,3,0,3B A - ... 2分设直线PA 、PB 的斜率分别为21,k k ,则()()33,3321≠-=-≠+=x x y k x x yk ...…..3分 依题意可知:=21k k ()333±≠=-⨯+x k x yx y ………….….... 4分 化简即:()319922±≠=-x ky x …………...... 5分 ① 当0>k 时,点P 的轨迹为以()()0,13,0,13k k ++-为焦点的双曲线并去掉()()0,3,0,3-两点 …………...….... 7分② 当0<k 时(ⅰ)01<<-k 时,990<-<k ,方程可化为()()319922±≠=-+x k y xP 点的轨迹为以()()0,13,0,13k k ++-为焦点的椭圆并去掉()()0,3,0,3-两点... 10分(ⅱ)1-=k 时,方程可化为922=+y xP 点的轨迹为以原点为圆心,3为半径的圆并去掉()()0,3,0,3-两点 …...….... 12分(ⅲ)1-<k 时,99>-k ,方程可化为()()319922±≠=+-x x k yP 点的轨迹为以()()k k -----13,0,13,0为焦点的椭圆并去掉()()0,3,0,3-两点..........14分19、(本小题满分14分)已知直三棱柱111ABC A B C -中,(如图5)1,2,32ACB AC BC CC π∠====,(Ⅰ)求侧棱1CC 与平面1ABC 所成角的正弦值;(Ⅱ)若点,E F 分别为棱,AC BC 上的动点,且CE BF =,当三角形CEF 面积最大时,求二面角1C EF C --的正切值。