BJU Writing and Grammar Grade 12 美国十二年级英语
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2024北京怀柔高二(上)期末英语注意事项:1.考生要认真填写姓名和考号。
2.本试卷共11页,分为三部分。
考试时间90分钟,满分100分。
3.试题所有答案必须填涂或书写在答题卡的对应位置........。
选择题必须用2B ......................,在试卷上作答无效铅笔作答;书面表达部分必须用黑色字迹的签字笔作答。
4.考试结束后,考生应将试卷和答题卡放在桌面上,待监考员收回。
第一部分:知识运用(共两节,30分)第一节完形填空(共10小题;每小题1.5分,共15分)阅读下面短文,掌握其大意,然后从各题所给的A、B、C、D四个选项中,选出最佳选项,并在答题卡上将该项涂黑。
The story of Jennifer Bricker is one of the most amazing story, which is full of both great surprises and life lessons.Jennifer was born in Romania without any legs. She was later ____1____ by a loving American family, the Brickers, and raised in the small town of Hardinville, Illinois.The Brickers never let this ____2____ stop her from achieving her dreams. Her new parents gave her a simple rule, “Never say can’t”! They did whatever they could to make her life a success.The girl was ____3____ just like the Brickers’ own children. She was encouraged to play with the other normal boys and girls and became good at many ____4____, including volleyball, softball and basketball.But it was tumbling (翻腾运动) that was her true love. When she was a little girl, she was a big ____5____ of the Olympic gold medalist--- Dominque Moceanu. She would copy her on TV whenever Dominque Moceanu ____6____in the tumbling programs and continue practicing afterwards.As she grew older Jennifer began ____7____ against professional tumbling athletes around Illinois. Not only did she compete, but she even went on to become a State Champion! Jennifer and her family always believed she could do whatever she wanted to and that her positive attitude and hard work would make it another ____8____.If her story was not amazing enough already, when Jennifer turned 16, she got the most ____9____ news in her life. She learned that her beloved Dominque Moceanu was actually her biological sister! Now Jennifer is touring the country as a(n)_____10_____ speaker to encourage more disabled youngsters.1. A. adopted B. injured C. sold D. seen2. A. disability B. gift C. excuse D. failure3. A. signed up B. brought up C. put up D. kept up4. A. roles B. instruments C. sports D. tricks5. A. audience B. athlete C. member D. fan6. A. performed B. appeared C. hosted D. challenged7. A. competing B. fighting C. acting D. going8. A. pity B. topic C. challenge D. success9. A. disturbing B. popular C. unbelievable D. reliable10. A. fluent B. loud C. silent D. inspiring第二节(共10小题;每小题1.5分,共15分)阅读下列短文,根据短文内容填空。
英语十二单元课文Unit 12 of the English textbook covers a wide range of topics and skills that are essential for effective communication and language proficiency. This unit delves into various aspects of the English language such as vocabulary development vocabulary in context grammar usage reading comprehension and writing techniques Each section within this unit is designed to challenge students and help them enhance their overall English language abilitiesThe first section of Unit 12 focuses on vocabulary development Expanding one's vocabulary is crucial for improving language skills as it allows individuals to express themselves more precisely and fluently This section introduces a variety of new words that are commonly used in everyday conversations as well as in academic and professional settings Students are encouraged to learn the meanings definitions and proper usage of these words through engaging exercises and activities This not only enhances their lexical knowledge but also helps them become more comfortable and confident in using these words in their own speech and writingIn addition to vocabulary development Unit 12 also emphasizes the importance of understanding vocabulary in context This section highlights how the meaning of a word can change depending on the context in which it is used Students are presented with sentences or short passages that contain unfamiliar words and are tasked with determining the meaning of these words based on the surrounding context cues This skill is particularly valuable as it enables learners to decipher the meaning of unknown words without solely relying on dictionary definitions which can often be limiting or incompleteAnother key component of Unit 12 is grammar usage This section delves into the intricacies of English grammar covering topics such as parts of speech sentence structure verb tenses and subject verb agreement Students are provided with clear explanations and examples of grammatical concepts and then given opportunities to apply these principles through various exercises and practice activities Mastering grammar is essential for producing coherent and well-structured written and oral communication which is a crucial skill in academic professional and personal contextsThe reading comprehension section of Unit 12 challenges students to engage with a variety of text types ranging from informative articles to literary excerpts Learners are required to demonstrate their understanding of the main ideas supporting details and overall message of the given texts through a series of questions andactivities This not only enhances their reading skills but also reinforces their ability to critically analyze and interpret written information an invaluable skill in today's information-driven worldFinally Unit 12 also focuses on developing effective writing techniques This section covers various writing genres such as persuasive essays narrative compositions and research reports Students are guided through the writing process from brainstorming and outlining to drafting and revising their work They learn strategies for crafting well-organized and coherent written pieces that effectively convey their intended message to the reader Strong writing skills are essential for academic success professional advancement and personal expressionOverall Unit 12 of the English textbook provides a comprehensive and multifaceted approach to language learning By addressing vocabulary development vocabulary in context grammar usage reading comprehension and writing techniques this unit equips students with the necessary skills and knowledge to become proficient and confident communicators in the English language The diverse range of topics and activities within this unit challenges learners to expand their linguistic abilities and prepares them for success in various academic professional and personal endeavors。
2024-2025学年吉林省初二英语上册素质检查试卷班级:________________ 学号:________________ 姓名:______________一、听力题(每题3分)Question 1:Listen to the dialogue and choose the correct answer.Dialogue:(Man) Good morning, Lucy. What’s your favorite subject?(Woman) Good morning, Mr.Smith. My favorite subject is English. I enjoy readingEnglish stories.Answer: A. Her favorite subject is math.B. Her favorite subject is English.C. She doesn’t like any subjects.Answer: BQuestion 2:Listen to the conversation and select the activity they are talking about.Conversation:(Boy) Are you going to join the school basketball team this year, Tom?(Girl) No, I’m more interested in the science club. We’re planning an experiment next week.Answer: A. Joining the music band.B. Participating in a science experiment.C. Watching a basketball game.Answer: BQuestion 3:Listen to the news report and tell where the event will take place. News Report:This weekend, the city’s annual book fair will be held at the Hengyang Convention and Exhibition Center. Visitors can expect a wide range of books, authors’ signings, and cultural activities.Answer: A. The city library.B. The Hengyang Convention and Exhibition Center.C. The local park.Answer: BQuestion 4:Listen to the instructions and identify the item you need to bring to class tomorrow.Teacher’s Instructions:“Class, please remember to bring your science textbooks and your lab coats to our next class. We’ll be conducting a practical experiment.”Answer: A. Math notebooks.B. Science textbooks and lab coats.C. Art supplies.Answer: BQuestion 5:Listen to the time announcement and write down the correct time.Announcement:“Attention, all students. The school gates will close at 5:30 p.m. sharp.Please make sure you leave the campus before then.”Answer: A. 4:30 p.m.B. 5:00 p.m.C. 5:30 p.m.Answer: C二、单选题(每题3分)Question 1:Which of the following is the correct pronunciation of the word “beautiful”?A. /ˈbjuːtɪfl/B. /ˈbjuːdɪfl/C. /ˈbjuːtɪpəl/D. /ˈbjuːtəfl/Answer: AQuestion 2:She usually_______her homework before dinner, but yesterday she watched TV instead.A. doesB. doC. didD. is doingAnswer: A (Note: While the sentence context suggests a habitual action, the blank should ideally be filled with “does” to match the usual tense. However, if strictly adhering to the sentence’s time reference “yesterday,” “did” would technically be more accurate, but considering the choice of answers provided, “A” is the most logical given the intended format.)Question 3:I’m going to the library to_______some books about history.A. borrowB. lendC. keepD. returnAnswer: AQuestion 4:The_______of the concert was fantastic, and everyone enjoyed it.A. atmosphereB. weatherC. temperatureD. situationAnswer: AQuestion 5:If it_______tomorrow, we’ll have to cancel the picnic.A. rainsB. rainC. will rainD. is rainingAnswer: A (Using the conditional tense, “if it rains” is the correct form for the subjunctive mood in English, indicating an uncertain future event that would result in a certain outcome.)三、多选题(每题4分)Question 1:Which of the following activities are commonly associated with preparing for theEnglish exam in Grade 9 in Hunan Province?A. Reviewing grammar rules and sentence structures.B. Participating in mock debates to improve speaking skills.C. Practicing reading comprehension passages on diverse topics.D. Memorizing mathematical formulas for quick calculations.E. Writing essays on personal experiences and opinions.Answers: A, B, CQuestion 2:Identify the three parts of speech that are frequently tested in the English upper volume examination for Grade 9 students in Hengyang, Hunan.A. NounsB. VerbsC. AdjectivesD. ConjunctionsE. AdverbsAnswers: A, B, CQuestion 3:Which three strategies can help students enhance their vocabulary for the English exam in Grade 9?A. Reading widely from different genres of books and articles.B. Keeping a vocabulary journal to record new words and their meanings.C. Using flashcards or mobile apps for quick vocabulary review.D. Focusing solely on memorizing grammar rules.E. Engaging in regular writing exercises to apply new words in context. Answers: A, B, CQuestion 4:Which three aspects of English listening comprehension are essential for success in the Grade 9 English upper volume exam?A. Understanding main ideas and details from audio recordings.B. Identifying speakers’ emotions and attitudes.C. Responding verbally to questions based on the audio content.D. Recognizing different accents and dialects.E. Memorizing exact word-for-word sequences.Answers: A, B, DQuestion 5:What are three good habits that Grade 9 students in Hunan Province can cultivate to improve their English writing skills for the upper volume exam?A. Planning and outlining their essays before writing.B. Using a variety of sentence structures and vocabulary.C. Proofreading and revising their work for errors.D. Memorizing pre-written templates for different essay types.E. Regularly writing in a journal to express thoughts and ideas.Answers: A, B, C四、阅读理解(每题4分)Title: “Exploring the Wonders of the Great Barrier Reef”The Great Barrier Reef, stretching over 2,300 kilometers along the northeastern coast of Australia, is the largest coral reef system in the world. It is home to an incrediblediversity of marine life, from colorful fish to giant sea turtles and even some of theworld’s smallest sea creatures. This natural wonder is not only a haven for wildlife but also a significant attraction for tourists from all over the globe.Diving and snorkeling are the most popular activities among visitors, allowing them to experience the reef’s underwater beauty firsthand. The vibrant coral formations, which act as nurseries for countless species, create a mesmerizing landscape that seems to defy description. The reef’s health, however, is threatened by a range of factors, including climate change, pollution, and overfishing.Efforts to protect this fragile ecosystem are ongoing, with conservation organizations, governments, and local communities working together to mitigate the impacts of these threats. Initiatives such as coral reef restoration projects, sustainable tourism practices, and public education campaigns are helping to preserve the Great Barrier Reef for future generations.Questions:1.What is the Great Barrier Reef famous for being? (4 points)•Answer: The Great Barrier Reef is famous for being the largest coral reef system in the world.2.Which two activities are particularly popular among tourists visiting the GreatBarrier Reef? (4 points)•Answer: Diving and snorkeling are particularly popular among tourists visiting the Great Barrier Reef.3.How does the passage describe the role of coral formations in the reef? (4 points)•Answer: The passage describes coral formations as nurseries for countless species, creating a mesmerizing underwater landscape.4.List two main threats to the health of the Great Barrier Reef. (4 points)•Answer: The two main threats to the health of the Great Barrier Reef are climate change and pollution.5.What are some of the measures being taken to protect the Great Barrier Reef? (4points)•Answer: Some of the measures being taken to protect the Great Barrier Reef include coral reef restoration projects, sustainable tourism practices, and publiceducation campaigns.五、作文(30分)Title: The Importance of Perseverance in My LifeIn the tapestry of life, perseverance stands as a golden thread, weaving together the fragments of dreams and aspirations into a vibrant picture. For me, perseverance has been a beacon of light, guiding me through the darkest hours and illuminating the path towards success.My journey with perseverance began with a simple yet daunting task – mastering the piano. As a young student, I was fascinated by the melodies that flowed effortlessly from the keys. However, as I delved deeper into the world of music, I realized thatmastery required endless hours of practice and dedication. There were days when my fingers ached from repetitive scales, and nights when discouragement threatened to engulf me. But it was perseverance that kept me going, reminding me that everystruggle was a step closer to my goal.Through perseverance, I discovered the true meaning of resilience. When faced with challenges, I learned not to give up but to find new ways to approach the problem. This mindset has not only enriched my musical pursuits but also permeated every aspect of my life. In academics, perseverance helped me conquer difficult subjects and achieveacademic excellence. In sports, it fueled my determination to push beyond my limits and excel on the field.Perhaps the greatest lesson I’ve learned from perseverance is that success rarely comes easily. It is often wrapped in layers of hardship and setbacks. But with unwavering dedication and a steadfast spirit, these obstacles can be transformed into stepping stones towards greatness.In conclusion, perseverance is the cornerstone of my life. It has taught me that every failure is a lesson, every setback an opportunity for growth. As I continue on my journey, I am grateful for this invaluable gift that has shaped me into the person I am today. With perseverance as my compass, I am confident that I can conquer any mountain and turn my dreams into reality.。
Unit One:EducationText:In Praise of the F Word对F的赞美Tens of thousands of 18-year-olds will graduate this year and be handed meaningless diplomas. These diplomas won’t look any different from those awarded their luckier classmates.Their validity will be questioned only when their employers discover that these graduates are semiliterate.今年,将有成千上万的18岁学生毕业并被授于毫无意义的文凭。
这些文凭对每个人都是一样的 ,没有一点差别,而不管学生的成绩如何.但当雇主发现他们没有实际能力时,文凭的有效性就会被质疑。
Eventually a fortunate few will find their way into educational repair shops-adult-literacy programs, such as the one where I teach basic grammar and writing. There, high school graduates and high school dropouts pursuing graduate-equivalency certificates will learn the skills they should have learned in school . They will also discover they have been cheated by our educational system.即使少数幸运的人找到了成人进修的地方,像我教语法和写作的地方。
北京师范大学第二学位考试真题英语Part I Listening Comprehension (20 minutes)Section ADirections: In this section, you will hear 10 short conversations。
At the end of each conversation a question will be asked about what was said。
Both the conversation and the question will be spoken only once。
After each question there will be a pause。
During the pause, you must read the four choices marked A, B, C and D, and decide which is the best answer。
Then mark the corresponding letter on the Answer Sheet with a single line through the center。
1。
A。
The man doesn’t want to see Mr。
Williams。
B。
Mr。
Jones is in an inferior position than Mr。
Williams。
C。
Mr。
Jones used to be in charge。
D。
Mr。
Williams doesn’t want to work tomorrow。
2。
A。
They need to make more efforts。
B。
They’ll have more work to do tomorrow。
C。
The others have done the greater part of it。
2021届北京市第十二中学高中分校高三英语下学期期末试卷及答案第一部分阅读(共两节,满分40分)第一节(共15小题;每小题2分,满分30分)阅读下列短文,从每题所给的A、B、C、D四个选项中选出最佳选项AThis online course is designed to provide you with work-ready skills including responding to job advertisements,writing application letters and resumes(简历)and developing inter-view skills.What topics will it cover?● The recruitment(招聘)and selection process● The job application● Planning for the interview● Developing interview skillsWhat will you achieve?By the end of the course,you'll be able to...● Assess the recruitment and selection process from an employer's point of view● Interpret an advertisement,job description and selection criteria correctly● Model a well-written job application● Plan for a job interviewWho is the course for?While this course appeals to trainees and graduates,it also applies to job seekersin the broader community looking to increasing their confidence and success rate when applying for work.Who develops the course?Central Queensland University.It is Australia's leading regional university.Our courses are designed alongside industry andmany include hands-on learning experiences and project-based learning.Our commitment to making real-world knowledge and skills accessible to all has seen us being awarded global recognition.1. What will students learn if they take the online course?A. The way to write a resume.B. The way to put an advertisement.C. The skills of talking with others.D. The skills of improving reading.2. Who is the online course intended for?A. Trainers.B. Interviewers.C. Job seekers.D. College students.3. Which ofthe following best describes the online course?A Cheap. B. Practical. C. Long-standing. D. World-class.BGerardo Ixcoy is a 27-year-old teacher in Guatemala. He teaches in the area where having electricity is something of a luxury and students have no access to mobile apps or computers, which became a problem when Guatemalan government had to choosedistance education for students at home because of COVID-19 inmid-March.Gerardo Ixcoy felt that he had to teach those children living far from the digital world. After all, education is a universal right. But what was the solution?Gerardo bought himself a secondhand tricycle with his savings. Once he had the tricycle, the next step was to change it into a classroom on wheels. He put a roof with a solar panel(太阳能电池板)on it, along with a screen to avoid the spread of COVID-19. He fixed a whiteboard on it so he could explain to the students the basics of primary education:math, the local language and the national language Spanish.The purpose of the solar panelis to provide constant power for a small loudspeaker so he can teach from a distance. It's a matter of respecting the healthy distance required to be safe from the virus. He, the teacher, stays outside, and the student participates from his or her house.He tries to visit his students at least twice a week, riding his classroom — cycle. The children he serves say that, although he visits them for only a few hours a week, they look forward to it. They appreciate his visit because they know he has limited time he can devote to them. They must take advantage of it to learn.4. What happened to Gerardo Ixcoy's students because of COVID-19?A. They chose to have classes in groups.B. They had to stop all the classes.C. They continued to have classes online.D. They started to learn about computers.5. Why does the teacher stay from a distance while teaching?A. Because healthy distance is reqired.B. Because he doesn't want to see his students.C. Because he wants to show his authority.D. Because the local custom reqiries him to.6. Where did Gerardo Ixcoy teach his students?A. In his own house.B. In his student's house.C. On the school playground.D. Outside his student's house.7. What can be the best title of the story?A. Love breaks down barriers.B. Hard work pays off.C. Time is money.D. Education is the key to success.CA team of researchers from several institutions in the UK and one in Estonia has created a type of buoy(浮标)that has proven to be effective at frightening seabirds, thus preventing them from getting caught in gillnets—a type of vertical fishing net that is made of a material that makes it nearly invisible underwater.Every year, hundreds of thousands of seabirds die when they get caught in gillnets. Some estimates suggest that up to a half-million birds are caught in them each year. Over the years, researchers have created devices(装置)to prevent the birds from trying to catch fish near or in gillnets, but those didn't work well.To find a way that would work for all seabirds, the researchers first studied seabirds in a general sense, looking to find things that they would avoid. They noted that seabirds avoided eye contact with other creatures. Then the researchers came up with a simple idea—they put a small pole to a regular buoy and then attached a pair of googly eyes(金鱼眼)to the top of it. They made the eyes big enough so that even birds with poor eyesight, such as geese, would see them. Adding to the effectiveness of the device, waves made the eyes move back and forth. And the wind made the buoy spin very slowly, making sure that birds from every direction would get a good look at the eyes.To test their idea, the researchers selected several sites near gillnets and counted how many birds approached and how many attempted to catch fish near the nets. They then set up their googly-eyed buoys and once again counted birds. Over the course of 62 days, they found the number of birds that tried to catch fish near the gillnets dropped by approximately 25% for a distance of up to 50 meters. They also found that the birds were less likely to fish near where the buoys had been for up to three weeks after they had been removed.8. What is the function of paragraph 2?A. Introducing a new topic to discuss.B. Providing background information.C. Summarizing the previous paragraph.D. Pointing out the main idea of the text.9. Why did the researchers make the googly eyes big?A. To ensure all the seabirds can see them.B. To clearly observe seabirds' eye contact.C. To allow them to survive the strong wind.D. To effectively identify the right direction.10. What does the researchers' test result mainly suggest?A. The new device still needs improvingB. Gillnets are a death valley for seabirds.C. Seabirds hardly catch fish near the nets.D. The googly-eyed buoy proves effective.11. What is the text mainly about?A. A group of researchers interested in seabirds.B. A way to help seabirds catch fish effectively.C. A device keeping seabirds safe from gillnets.D. A googly-eyed buoy guiding seabirds to hunt.DEvery racehorse has different abilities.Like humans,some are short- distance runners,while others are marathoners.Figuring out which is which and how to pace them can be the difference between failure in the finish and taking the award home.Jockeys(赛马骑师)and trainers have traditionally relied on centuries of experience and data from previous races to plan their races.Amandine Aftalion,a mathematician in Paris,thought she could add to that.Since 2013,she has been analyzing the performances of world champion runners like Usain Bolt.She has found that short-distance runners tend to win when they start strong and gradually slow down toward the finish line.Butin medium-distance races,runners perform better when they start strong,settle down,and finish with a burst of speed.Her model shows how those winning strategies maximize the energy output of muscles reliant on two different pathways:powerful aerobic(有氧的)ones that require oxygen,which can be in limited supply during a race,and anaerobic ones,which don't need oxygen but build up waste products that lead to tiredness.Aftalion wondered which strategy would be best for horses.So she and Quentin Mercier,anothermathematician,took advantage of a new GPS tracking tool inserted in French racing saddles(马鞍).The two studied patterns in many races at the Chantilly racetracks north of Paris and developed a model that accounted for winning strategies for three different races:a short one(1,300 meters),a medium one (1,900 meters),and a slightly longer one (2,100 meters),all with different starting points on the same track.The model takes into account not just different race distances,but also the size or friction fromthe track surface.The results might surprise jockeys who hold horses back early for bursts of energy in the last finish.Instead,a strong start leads to a better finish,the team found.“That doesn't mean those jockeys are wrong,though.If the start is too strong,it can bedevastatingas well,leaving the horse tired by the end,” Aftalion says.12. What should a runner do to get an award according to the text?A. Make a good start.B. Plan for the race early.C. Run slowly on the starting line.D. Try runningquickly all the time.13. What formed the basis for Aftalion's studying horse race?A The experience and data from previous horse races.B. The benefit of knowing horses' different abilities.C. The success in studying runners' winning strategies.D. The performance of horses on different race distances.14. What does the underlined word“devastating”in the last paragraph mean?A. Boring.B. Damaging.C. Astonishing.D. Puzling.15. What can we infer from the text?A. Runners have the same energy output of muscles.B. Aftalion's findings may help horses to win the race.C. What Jockeys and trainers do makes no sense to horses.D. World champion runners made a contribution to the study.第二节(共5小题;每小题2分,满分10分)阅读下面短文,从短文后的选项中选出可以填入空白处的最佳选项。
2021年北京市第十二中学草桥分校高三英语模拟试题及参考答案第一部分阅读(共两节,满分40分)第一节(共15小题;每小题2分,满分30分)阅读下列短文,从每题所给的A、B、C、D四个选项中选出最佳选项ACanadais one of the most beautiful countries in the world. Here are 4 attractive places worth your visit.ChurchillChurchill is a town with the nickname "Polar Bear Capital of the World”, where tourists can safely view polar bears from special vehicles in the autumn and winter. Thousands of beluga whales, which move into the warmer waters of theChurchill Riverduring July and August, are a major summer attraction. Churchill is also a destination for bird watchers from late May until August.Niagara FallsNiagara Fallsis a group of three waterfalls, crossing the border betweenCanadaand theUnited States. The largest of the three is Horseshoe Falls, also known asCanadian Falls. Niagara Falls illumination(彩灯)is a must for any visitor! Every night of the year, the three waterfalls are illuminated in color1 s creating an attractive scene that can be viewed from near and far.VancouverVancouverisCanada's third-largest city, always named as one of the top five worldwide cities for its comfortable environment and quality of life.Vancouverhas an active nightlife scene, whether its food and dining, or bars and nightclubs. From mid-June to early July, the Vancouver International Jazz Festival features 300 concerts, including a free opening Downtown Jazz Weekend.OttawaThe capital ofCanadais situated on the banks of theOttawa Riverand has a lot ofEnglish buildings in it. It is a beautiful city which has the Parliament buildings on the banks and English influenced houses and parks around. There are museums and art galleries that will give you a complete knowledge of the English culture there. It is really the heart ofCanada. So if you are a history and art loverOttawais the best choice for your visit inCanada.1. If you want to watch birds, which place will you choose to visit?A. Churchill.B.Niagara Falls.C. Vancouver.D.Ottawa.2. What is the best season for visitingVancouver?A. Spring.B. Summer.C. Autumn.D. Winter.3. What doNiagara FallsandVancouverhave in common?A. They are both famous for natural scenery.B. The best visiting time are both at nights.C. They are both located inCanadaentirely.D. The tickets there are both free at weekends.BThe market for tourism in remote areas is booming as never before. Countries all across the world are actively promoting their wilderness regions-such as mountains, Arctic lands, deserts, small islands and wetlands— to high-spending tourists. The attraction of these areas is obvious: by definition, wilderness tourism requires little or no initial investment. But that does not mean that there is no cost.Once a location is established as a main tourist destination, the effects on the local community are profound. Hill-farmers can make more money from foreign travellers than working in their fields. It is not surprising that many o£ them give up their farm-work. In some hill-regions, this has led to a serious decline in farm output and a change in the local diet, because there is lacking labour to maintain terraces and irrigation systems. The result has been that many people in these regions have turned to outside supplies of rice and other foods.InArcticand desert societies, year-round survival has traditionally depended on hunting animals and fish and collecting fruit over a ly short season. However, as some inhabitants become involved in tourism, they no longer have time to collect wild food; this has led to increasing dependence on bought food and stores. What should they do if these new sources of income dry up?The physical impact of visitors is another serious problem associated with the growth in adventure tourism. Much attention has focused on erosion along major roads, but perhaps more important are the forest destruction and impacts on water supplies arising from the need to provide tourists with cooked food and hot showers. In both mountains and deserts, slow-growing trees are often the main sources of fuel and water supplies may be limited through heavy use.4. Why are some countries promoting the wilderness regions to tourists?A. The wildness regions are accessible to tourists.B. The landscapes there are beautiful and unique.C. Developing tourism there doesn't need much investment.D. Lots of high-spending tourists prefer such remote regions.5. What is the effect of tourism on the local community?A. Many hill farmers have turned to outside supplies of foods.B. There is enough labour to maintain terraces and irrigation systems.C. Farm output there has increased and local diet has changed.D. The local people's new sources of income will dry up soon.6. Which might be the best title of the passage?A. The future of wilderness tourism.B. The impacts of wilderness tourism.C. The destruction of wilderness tourism.D. The disadvantages of wilderness tourism.7. If there is one more paragraph following the last paragraph, what will it talk about?A. The effects on local people.B. The solutions tothese problems.C. The choices of adventure tourists.D. The reasons for visiting remote areas.CCigarettes aren’t just harmful when they’re being smoked. Even when cigarette ends go out and are cold, new research has found they continue to give off harmful chemicals in the air. In the first 24 hours alone, scientists say a used cigarette end will produce 14 percent of the nicotine (尼古丁) that an actively burning cigarette would produce.While most of these chemicals are released within a day of being put out,an analysis for the United States Food and Drug Administration (FDA) found the level of nicotine fell by just 50% five days later.“I was ly surprised,” since environmental engineer Dustin Poppendieck from the United States National Institute of Standards and Technology (NIST). “The numbers are significant and could have important impacts when cigarette ends are dealt with indoors or in cars. While much attention has been paid to the health influence of first-hand, second-hand and now third-hand smoking, it is not the case when it comes to the actual cigarette end of the matter.”To measure emissions (排放) from this forgotten thing, Poppendieck and his team placed 2,100 cigarettes that were recently put out inside a special room. Once the ends weresealed away, the team measured eight chemicals commonly produced by cigarettes, four of which the FDA have their eye on for being harmful or potentially so.After setting the room’s temperature, the researchers tested how emissions changed under certain conditions. When the air temperature of the room was higher, for instance, they noticed the ends produced these chemicals at higher rates. This finding might discourage those who want to leave ashtrays (烟灰缸) out for days ata time, especially in the heat.8. What do the researchers say about cigarette ends?A They contain little nicotine.B. They produce no nicotine five days later.C. They give off nicotine for days.D. They create as much nicotine as burning cigarettes.9. What do Poppendieck’s words suggest?A. First-hand smoking does most harm.B. The findings are within his expectation.C. Cigarettes should be dealt with indoors.D. Health influence of cigarette ends is ignored.10. Which word best describes the author’s attitude to not cleaning ashtrays for days?A. Unclear.B. Disapproving.C. Unconcerned.D. Puzzled.11. What can be the best title for the text?A. Used Cigarette Ends Release Harmful ChemicalsB. Cigarettes Are More Harmful While Being SmokedC. Research Found Reasons For Cigarette Ends’ HarmD. Cigarette Ends Produce More Chemicals in the HeatDAn afternoon nap(午睡)is one of the joys of life, although too much napping could signal all is not well. In some cultures, people will have a daily nap — thisis fine. The warning comes when people start sleeping during the daytime, when they did not before. There is certainly a good reason to believe that daytime sleepiness — as in the Alzheimer's study — can be a marker of an underlying condition.For most people, napping during the day is mainly a sign that you are not getting enough sleep at night, says Dr. Neil Stanley, a sleep expert. "If you feel sleepy during the day, you should think about taking a nap. That is what the body needs — it doesn't need to be kept awake with caffeine, it needs sleep. "The feeling to notice is "sleepiness", he says, not "tiredness", which could be more psychological and linked to stress.So how do you nap well? The key thing, says Stanley, is how long your nap lasts. Choose either a 20-or 90-minute nap. "When you fall asleep, you'll quickly go through the lighter stages of sleep into your first period of deep sleep. You don't want to wake up in deep sleep because that's when you wake and feel worse than you didbefore. "Napping for 20 minutes means you will wake up before you go into deep sleep; napping for 90 minutes means you'll complete a sleep cycle.Once you factor in the time it takes to fall asleep — some people are better at napping than others but, says Stanley, "a healthy adult will fall asleep in between 5 and 12 minutes" — you can set an alarm, allowing a 30- to 40-minute period for a short nap, and up to two hours for a longer one.A good time to nap is during the body's natural dip in the afternoon, between 2 pm and 4 pm. "You don't really want to be napping much pastthatbecause then you are going to be eating into your night-time sleep," Stanley says. The point, he stresses, is to get good night-time sleep, which would ensure you probably don't need to nap at all.12. What does an afternoon nap indicate for most people?A. Caffeine addiction.B. Psychological stress.C. Insufficient night sleep.D. Potential physical illness.13. What is the key to a good nap?A. Duration.B. Surroundings.C. Health.D. Stages.14. What does the underlined word "that" in the last paragraph refer to?A. A 30- to 40- minute period.B. Between 2 pm and 4 pm.C. Between 5 and 12 minutes.D. A 20- to 90-minute period.15. Which of the following can be the best title for the text?A. Why to phase a napB. When to take a good napC. What to learn from a napD. How to have a successful nap第二节(共5小题;每小题2分,满分10分)阅读下面短文,从短文后的选项中选出可以填入空白处的最佳选项。
2020-2021学年北京第十二中学高三英语上学期期末试卷及答案解析第一部分阅读(共两节,满分40分)第一节(共15小题;每小题2分,满分30分)阅读下列短文,从每题所给的A、B、C、D四个选项中选出最佳选项AArtificial intelligence (Al) is practically everywhere today. There are so many products out there which use Al. Some are being developed, some are already in use, and some failed and are being improved, so it’s very difficult to name a few of them and regard them as the best.ViIt is an Al personal trainer which is mainly concerned with fitness and coaching. It, however, requires the use of bio-sensing earphones and other fitness tracking equipment! It can play your favourite music while you work out and all you have to worry about is the exercise you're doing.Deep TextDo you ever wonder how an ad appears suddenly just when you are looking for something similar? This is because of Deep Text. It uses real-time consumer information to produce data which in turn is used to target consumers. Thus, if you search online for flight tickets fromBangaloretoDelhi, it is very likely that an ad relating to hotels inDelhiwill soon follow.Hello EggIf you live alone and miss your mother because you always miss your breakfast or don’t know what to eat for dinner, then Hello Egg is exactly what you are looking for. A very healthy choice of the 2-minute noodles and oats, Hello Egg provides you with a detailed weekly meal plan about the needs of your body. It is truly a modern AI-powered home cooking tool for the young.WordsmithYou can put Mr. Smith into your Microsoft Excel using their free API, and let it write up detailed analysis of the stories behind your numbers. It can produce detailed reports on thousands of pages of spreadsheets in seconds.1. What can we learn about Vi from the text?A. It is an AI music player.B. It is a bio-sensing earphone.C. It doesn't work without bio-sensing earphones.D. It can make you more energetic while you work out.2. Which can help you improve cooking skill?A. Deep Text.B. Vi.C. Wordsmith.D. Hello Egg.3. What can Wordsmith do for us?A. Produce a detailed report.B. Provide us with a detailed meal plan.C. Book a ticket ahead of time.D. Offer us information on hotels for traveling.B36-year-old Juan Dual likes to joke that he’s empty inside. Juan’s story began when he was only 13. It was then that he was diagnosed with a terrible disease, which left him with a 99.8% chance of developing cancer of the digestive system. At age 19, right after finishing high-school, Juan underwent a tough operation to take away his colon and rectum. Sadly, it was only the beginning. By age 28, Juan’s disease had affected his stomach and gallbladder so he had to go under the knife again.Having just recovered from several serious surgeries, Juan Dual decided to accept the invitation of some friends of his parents and travel to Japan. It was there that things started to change for the better. He didn’t speak a word of Japanese, so he spent most of his time walking his dog. One day, the dog pulled harder, and Juan realized that he was still able to jog, and he started to do just that.Months later, he found himself working in a small, peaceful town in England. There was little in terms of entertainment, but the town was surrounded by hills, so he devoted even more of his time to running. He befriended some like-minded folks and told them what he’d been through, and they seemed amazed at the fact that he was still alive, let alone that he was pushing himself to exercise. That’s when the idea of focusing on motivating others took root in his mind.With the help of Pepa, a nutritionist, Juan Dual slowly relearned how to eat to keep his energy level high enough to sustain him during physical activity. Eight months after his last operation, he finished the Barcelona half marathon in two hours. He then started training for mountain running and ultra-marathons.4. Why does Juan Dual say he is empty inside?A. Because he has no desire for anything.B. Because he doesn’t have much knowledge.C. Because he always suffers from great hunger.D. Because many of his organs have been removed.5. What made Juan Dual aware that he could still run?A. His parents’ support.B. A walk with his dog.C. The idea of challenging himself.D. His quick recovery from surgeries.6. When did Juan Dual decide to inspire others with his story?A. After finishing the Barcelona half marathon.B After being introduced to a nutritionist named Pepa.C. After sharing it with his friends in an English town.D. After making friends with people with similar sufferings.7. Which of the following words can best describe Juan Dual?A. Ambitious and intelligent.B. Inspiring and responsible.C. Unfortunate but determined.D. Confident but stubborn.CAncient Dunhuang manuscripts housed abroad have been edited and published by the Institute for Overseas National Literature of Northwest Minzu University since 2006. Up till now, 9 manuscripts kept in the British Library and22 inthe National Library of France have been finished, the institute said on April 24, 2018.Tens of thousands of valuable ancient documents and cultural relics, discovered in the Mogao Grottos in Dunhuang, Gansu province, were scattered overseas in the early 20th century. Dunhuang manuscripts currently in the British Library and the National Library of France are the most important ancient national documents housed abroad.Co-edited by Institute for Overseas National Literature of Northwest Minzu University, Shanghai Classics Publishing House, the British Library and the National Library of France, these Dunhuang manuscripts return home in publication form for the first time. The institute is also preparing an online database of the manuscripts.According to Cai Rang, associate director of the institute, Dunhuang manuscripts scattered overseas in Russia, Britain, France and Japan have rich contents, including Buddhism law, social contract, history,linguisticsand art. The institute has edited and published 31 manuscripts over the past 13 years, but the work has not been finished. It plans to publish 15 from the British Library and over 30 from the National Library of France all together. In addition, it will also publish manuscripts collected by other countries.“Some manuscripts are hard to read because of the indecipherable words. So we read carefully and understand them by comparing with Buddhism documents handed down from ancient times,” Cai said. “Next, document classification and compilation will be our key work for further research.”The work done by the institute is helpful to study the history and culture of Tubo(present-day Tibet) during the period of 8th to 11th century and the history of national cultural exchanges at that time.8. When did so many valuable ancient documents, discovered in the Mogao Grottos, were scattered overseas?A. In the late 19th century.B. In the middle of the 19th century.C. At the beginning of the 19th century.D. At the beginning of the 20th century.9. How do the members of the institute understand some manuscripts that are hard to read?A. By using modern technology.B. By asking other famous experts.C. By comparing them with Buddhism documents.D. By studying the history and culture of Tubo.10. The possible meaning of the underlined word “linguistics” in paragraph 4 is “______”.A. the scientific study of languageB. the opinion that people have about someone or somethingC. something that people may have as part of their characterD. a system or method for carrying passengers or goods from one place to another11. What is the theme of the news report?A. Dunhuang manuscripts scattered overseas have rich contents.B. China publishes Dunhuang manuscripts housed overseas.C. High value of ancient documents and cultural relics in Mogao Grottos.D. Prepare an online database of Dunhuang manuscripts housed overseas.DOne rainy afternoon, I was on a crosstown bus when ayoung woman jumped on. She had a child with her who must have been about 3 or 4 years old.The bus was full, bumpy, and it soon got noisy as her kid began crying because he couldn’t sit next to his mother. There were a couple of open seats, but they weren’t together. She wasflusteredand looked embarrassed.Then another woman, a little older, stood up and moved so that the mother and child could sit together. The mom smiled as a thank-you. And then three words came out of the older woman’s mouth that elevated the entire energy of that bus ride: “I’ve been there”.Simple, undramatic and honest. In that moment, it seemed to unite people. Why? Because almost all experiences are shared human experiences. We forget that, as we forge (前进) through life, focused onour own troubles and needs—which are actually less unique than we think. How can these three words create more connection in your life? Ask yourself: “Where am I holding back?One thing I know for sure is this: Healing others helps heal yourself. I noticed this recently with my friend, Tracy, who took a new friend who had suffered a miscarriage under her wing. Tracy had three of them before having her daughter two years ago. Our intellect needs a doctor to explain the medical side of things, yes. But our souls need human connection to help us along. No one can do that better than someone who has been exactly where you are.Can the essence of these three words help you make a small difference right now? It can be as simple as volunteering your seat, sharing some helpful advice or even lightening the mood with a joke when you notice that someone’s uncomfortable—because we’re all in this together.12. The underlined word “flustered” in the second paragraph is closest in meaning to _______.A. angryB. anxiousC.scaredD. upset13. What does the woman mean by saying “ I’ve been there”in the third paragraph?A. The woman was on the bus and saw what had happened to the boy.B. The woman got to her destination and was ready to get off the bus.C. The woman once had the similar experience with that mother.D. The woman took the exact seat that the boy was on just now.14. Which of the following statements is TRUE according to the passage?A. Everyone has his or her own unique problem that is difficult to solve.B. Doctors can help us get through when we have mental or physical problems.C. The author’s friend Tracy felt better after she was comforted by her new friend.D. One can indeed make a difference to those in need of help by doing simple things.15. The passage isintended to _______.A. show a harmonious world by telling some touching storiesB. praise those who are willing to help others in emergenciesC. appeal to readers to give timely help to those in needD. illustrate some ways of helping others in detail第二节(共5小题;每小题2分,满分10分)阅读下面短文,从短文后的选项中选出可以填入空白处的最佳选项。
2019-2020学年北京市第十二中学高中分校高三英语下学期期末试题及答案解析第一部分阅读(共两节,满分40分)第一节(共15小题;每小题2分,满分30分)阅读下列短文,从每题所给的A、B、C、D四个选项中选出最佳选项AIn his 402nd anniversary year, Shakespeare is still rightly celebrated as a great language master and writer. But he was not the only great master of play writing to die in 1616, and he is certainly not the only writer to have left a lasting influence on theater.While less known worldwide, Tang Xianzu is considered one of Chinas greatest playwrights and is highly spoken of in that country of ancient literary and dramatic traditions.Tang was born in 1550 inLinchuan,Jiangxiprovince. Unlike Shakespeare's large body of plays,poems and sonnets (十四行诗), Tang wrote only four major plays: The Purple Hairpin, Peony Pavilion (《牡丹亭》), A Dream under the Southern bough, and Dream of Handan. The latter three were constructed around a dream narrative, a way through which Tang unlocked the emotional dimension of human desires and ambitions and explored human nature beyond the social and political limits of that time.Similar to Shakespeare, Tang's success rode the wave of a renaissance (复兴) in theater as an artistic practice. As in Shakespeare'sEngland, Tang's works became hugely popular inChinatoo. During Tang'sChina, his plays were enjoyed performed, and changed. Kunqu Opera, a form of musical drama, spread from southernChinato the whole nation and became a symbol of Chinese culture. Combining northern tune and southern music, kunqu Opera was known for its poetic language, music, dance movements and gestures. Tang's works benefited greatly from the popularity of kunqu Opera, and his plays are considered classics of kunqu Opera.While Tang and Shakespeare lived in a world away from each other, there are many things they share in common, such e humanity of their drama, their heroic figures, their love for poetic language, a lasting popularity and the anniversary during which we still celebrate them.1. Why is Shakespeare mentioned in the first paragraph?A. To describe Shakespeare's anniversary.B. To introduce the existence of Tang Xianzu.C. To explain the importance of Shakespeare.D. To suggest the less popularity of Tang Xianzu.2. What's possibly one of the main theme of Tang's works?A. Social reality.B. Female dreams.C. Human emotions.D. Political environment.3. What does the author mainly tell us in Paragraph 4?A. The influence of Kunqu Opera on Tang's works.B. Tang's success in copying Shakespeare's styles.C. The way Kunqu Opera became a symbol of Chinese culture.D. Tang's popularity for his poetic language and music.BTo stay healthy and fit, Chinesestudents do group exercises every day at school. Most of you probably do the same set of exercises. But some school exercises have grown popular online due to their local and innovative designs.Singing in Sichuan dialects with energetic movements and unique mask-changing is not just a Sichuan Opera performance. It’s the routine exercise for students of Mianyang Foreign Languages Experimental School in Sichuan province.“Sichuan Opera is a local opera, and it is now facing a gap in inheritance (传承). Therefore, we cooperated with Mianyang Intangible Cultural Heritage Center to create a simple and easy-to-learn Sichuan Opera exercise,” said Shen Junhua, who is in charge of organizing the school’s exercise between classes.According to Shen, this new type of exercise has been practiced since 2017 and has been popular among students. When students enroll (入学), they will spend several weeks practicing it. At present, almost all of the students and teachers have mastered it.“In fact, we had hardly heard of Sichuan Opera before teachers taught us how to do the Sichuan Opera exercise,” said Li Yangwenwen, 14, an eighth grade student who also joined the school’s Sichuan Opera club out of interest. “It’s very different from normal exercises. After practicing it, we found it very beautiful and became interested in it. Now, almost all of the students look forward to our daily exercise time and feel excited to do it.”“By combining opera with daily exercise, the daily class activity allows students to perceive and understand Sichuan Opera’s culture”, Shen said. “After years of continuous effort to spread the seeds of traditional culture, the younger generation is finally catching on.”4. What do students in Shen’s school do during the group exercise?A. They do normal exercise .B. They sing pop songs in Sichuan dialects.C. They do mask-changing in a Sichuan Opera performance.D. They combine group exercise with Sichuan Opera.5. Why do they adopt the new type of exercise?A. To attract new students to the school.B. To inherit local culture.C. To create an easy-to-learn exercise.D. To make the school’s group exercise popular.6. How do teachers and students react to the group exercise?A. Calm.B. Indifferent.C. Enthusiastic.D. Uninterested.7. What can we learn from the last paragraph?A. Shen’s continuous effort is highly praised.B. The younger generation will have a stronger body.C. The students can better understand their local culture.D. Students help to spread the seeds of traditional culture toyounger generation.CMore than 10,000 people were made homeless in Ternang when the Sungai Mas overflowed its banks yesterday after six days of continuous heavy rain.The wooden bridge across the river has been washed away. The town is cut off by flood waters. At the fifth mile, Jalan Tengkn, the water is two meters deep. It is closed to all traffic. Flooding first happened at mid-afternoon yesterday along the river banks. People trying to get to higher ground were just in time to escape the destroying of the flood. Most of the flood victims(受害者) had to leave all their things behind.The National Flood Relief(救济) Center was reported to give its help and by early evening the whole town was moved out, helped by the army, police, Red Cross Society and volunteers(志愿者).The flood victims are now housed in different simple relief centers in the nearby town of Ternang. “Everything possible is being done to help the unlucky people,” a government spokesman said, “In fact, money, food and clothing have begun to come in from public organizations and helpful people. A Disaster Relief Fund(救灾基金会) will be started as soon as possible.”According to the latest reports it is still raining heavily at Ternang. The whole town is expected to be whollycovered by the water. So far no deaths have been reported.8. This passage is probably taken from______.A. a storybookB. a textbookC. a magazineD. a newspaper9. It seems that the flood happened just because ______.A. the banks were too lowB. the wooden bridge is solid (坚固)C. the river was too narrowD. they had had wet days for some time10.From the passage we know that ______.A. though the town was flooded, you could still go there by busB. as soon as the water flowed over the banks, people began to go to higher landsC. the government and the whole society are taking great care of the flood victimsD. the flood hasn't brought a large loss to the town as nobody died in the flood11. What is the best title for this passage?A. A Big FloodB. Ternang Is destroyedC. Over 10,000 People Are HomelessD. Rescue Team ArrivedDOver 180 teenage girls from LixianCounty No. 1 Middle School in Longnan city, Gansu province, listened carefully to a lecture about neuroscience (神经科学). It was delivered by a director of the experimental surgery department at The Second Affiliated Hospital of the Air Force Medical University in Xi’an.The students also joined a science class to make paper rockets to launch into the sky. A plastic bottle was connected with a long pipe joined to the end of the rocket, and students stepped heavily on the middle of the bottle so hard that the air pressure shot the rocket upward.The program started in 2016 as a one-week summer camp in Beijing that invited female students to take science courses and to interact with women in science. It aims to stir (激发) an interest in science and technology among female students.“I’m excited to take the opportunity because it’s been my biggest wish to popularize science among students. They can broaden their eyes and hopefully some of them will devote themselves to the field of neuroscience,” the director says. “It’s necessary to bring more of these activities on campus. I’m willing to communicate with teenagers, some of whom ask deep and thoughtful questions that I would never think of.”The key to science popularization is to imbue (灌输) others with the spirit of science. Some scientific andtechnological workers have devoted themselves to a job in a certain field and they enjoy the pleasure of scientific research. Female Chinese scientific and technological workers sometimes have to double their efforts to receive the same treatment or recognition as those male scientific workers. However, after years of continued effort, the situation will improve, showing the increasing number of female scientists in China.12. What is the purpose of the program?A. To praise the efforts of women scientists.B. To find out how much girls love science.C. To develop interest in science among girls.D. To show love for students in Western China.13. How does the director think of the program?A. Important.B. Challenging.C. Confusing.D. Serious.14. What is the most important in science popularization?A. Enjoying the fun of scientific research.B. Filling people with the spirit of science.C. Holding more scientific activities on campus.D. Forcing students to choose scientific subjects.15. What can we learn from the text?A. One can go anywhere if he/she learns science well.B. People have a stronger sense of science than before.C. Male scientists are much easily recognized than female ones.D. Thedirector graduated from Lixian County No. 1 Middle School.第二节(共5小题;每小题2分,满分10分)阅读下面短文,从短文后的选项中选出可以填入空白处的最佳选项。
江西省南昌市2015-2016学年度第一学期期末试卷(江西师大附中使用)高三理科数学分析一、整体解读试卷紧扣教材和考试说明,从考生熟悉的基础知识入手,多角度、多层次地考查了学生的数学理性思维能力及对数学本质的理解能力,立足基础,先易后难,难易适中,强调应用,不偏不怪,达到了“考基础、考能力、考素质”的目标。
试卷所涉及的知识内容都在考试大纲的范围内,几乎覆盖了高中所学知识的全部重要内容,体现了“重点知识重点考查”的原则。
1.回归教材,注重基础试卷遵循了考查基础知识为主体的原则,尤其是考试说明中的大部分知识点均有涉及,其中应用题与抗战胜利70周年为背景,把爱国主义教育渗透到试题当中,使学生感受到了数学的育才价值,所有这些题目的设计都回归教材和中学教学实际,操作性强。
2.适当设置题目难度与区分度选择题第12题和填空题第16题以及解答题的第21题,都是综合性问题,难度较大,学生不仅要有较强的分析问题和解决问题的能力,以及扎实深厚的数学基本功,而且还要掌握必须的数学思想与方法,否则在有限的时间内,很难完成。
3.布局合理,考查全面,着重数学方法和数学思想的考察在选择题,填空题,解答题和三选一问题中,试卷均对高中数学中的重点内容进行了反复考查。
包括函数,三角函数,数列、立体几何、概率统计、解析几何、导数等几大版块问题。
这些问题都是以知识为载体,立意于能力,让数学思想方法和数学思维方式贯穿于整个试题的解答过程之中。
二、亮点试题分析1.【试卷原题】11.已知,,A B C 是单位圆上互不相同的三点,且满足AB AC →→=,则AB AC →→⋅的最小值为( )A .14-B .12-C .34-D .1-【考查方向】本题主要考查了平面向量的线性运算及向量的数量积等知识,是向量与三角的典型综合题。
解法较多,属于较难题,得分率较低。
【易错点】1.不能正确用OA ,OB ,OC 表示其它向量。
2.找不出OB 与OA 的夹角和OB 与OC 的夹角的倍数关系。
【解题思路】1.把向量用OA ,OB ,OC 表示出来。
2.把求最值问题转化为三角函数的最值求解。
【解析】设单位圆的圆心为O ,由AB AC →→=得,22()()OB OA OC OA -=-,因为1OA OB OC ===,所以有,OB OA OC OA ⋅=⋅则()()AB AC OB OA OC OA ⋅=-⋅-2OB OC OB OA OA OC OA =⋅-⋅-⋅+ 21OB OC OB OA =⋅-⋅+设OB 与OA 的夹角为α,则OB 与OC 的夹角为2α所以,cos 22cos 1AB AC αα⋅=-+2112(cos )22α=--即,AB AC ⋅的最小值为12-,故选B 。
【举一反三】【相似较难试题】【2015高考天津,理14】在等腰梯形ABCD 中,已知//,2,1,60AB DC AB BC ABC ==∠= ,动点E 和F 分别在线段BC 和DC 上,且,1,,9BE BC DF DC λλ==则AE AF ⋅的最小值为 .【试题分析】本题主要考查向量的几何运算、向量的数量积与基本不等式.运用向量的几何运算求,AE AF ,体现了数形结合的基本思想,再运用向量数量积的定义计算AE AF ⋅,体现了数学定义的运用,再利用基本不等式求最小值,体现了数学知识的综合应用能力.是思维能力与计算能力的综合体现. 【答案】2918【解析】因为1,9DF DC λ=12DC AB =,119199918CF DF DC DC DC DC AB λλλλλ--=-=-==, AE AB BE AB BC λ=+=+,19191818AF AB BC CF AB BC AB AB BC λλλλ-+=++=++=+,()221919191181818AE AF AB BC AB BC AB BC AB BCλλλλλλλλλ+++⎛⎫⎛⎫⋅=+⋅+=+++⋅⋅ ⎪ ⎪⎝⎭⎝⎭19199421cos1201818λλλλ++=⨯++⨯⨯⨯︒2117172992181818λλ=++≥+= 当且仅当2192λλ=即23λ=时AE AF ⋅的最小值为2918. 2.【试卷原题】20. (本小题满分12分)已知抛物线C 的焦点()1,0F ,其准线与x 轴的交点为K ,过点K 的直线l 与C 交于,A B 两点,点A 关于x 轴的对称点为D . (Ⅰ)证明:点F 在直线BD 上; (Ⅱ)设89FA FB →→⋅=,求BDK ∆内切圆M 的方程. 【考查方向】本题主要考查抛物线的标准方程和性质,直线与抛物线的位置关系,圆的标准方程,韦达定理,点到直线距离公式等知识,考查了解析几何设而不求和化归与转化的数学思想方法,是直线与圆锥曲线的综合问题,属于较难题。
【易错点】1.设直线l 的方程为(1)y m x =+,致使解法不严密。
2.不能正确运用韦达定理,设而不求,使得运算繁琐,最后得不到正确答案。
【解题思路】1.设出点的坐标,列出方程。
2.利用韦达定理,设而不求,简化运算过程。
3.根据圆的性质,巧用点到直线的距离公式求解。
【解析】(Ⅰ)由题可知()1,0K -,抛物线的方程为24y x =则可设直线l 的方程为1x my =-,()()()112211,,,,,A x y B x y D x y -,故214x my y x =-⎧⎨=⎩整理得2440y my -+=,故121244y y m y y +=⎧⎨=⎩则直线BD 的方程为()212221y y y y x x x x +-=--即2222144y y y x y y ⎛⎫-=- ⎪-⎝⎭令0y =,得1214y yx ==,所以()1,0F 在直线BD 上.(Ⅱ)由(Ⅰ)可知121244y y m y y +=⎧⎨=⎩,所以()()212121142x x my my m +=-+-=-,()()1211111x x my my =--= 又()111,FA x y →=-,()221,FB x y →=-故()()()21212121211584FA FB x x y y x x x x m →→⋅=--+=-++=-,则28484,93m m -=∴=±,故直线l 的方程为3430x y ++=或3430x y -+=213y y -===±,故直线BD 的方程330x -=或330x -=,又KF 为BKD ∠的平分线,故可设圆心()(),011M t t -<<,(),0M t 到直线l 及BD 的距离分别为3131,54t t +--------------10分 由313154t t +-=得19t =或9t =(舍去).故圆M 的半径为31253t r +== 所以圆M 的方程为221499x y ⎛⎫-+= ⎪⎝⎭【举一反三】【相似较难试题】【2014高考全国,22】 已知抛物线C :y 2=2px(p>0)的焦点为F ,直线y =4与y 轴的交点为P ,与C 的交点为Q ,且|QF|=54|PQ|.(1)求C 的方程;(2)过F 的直线l 与C 相交于A ,B 两点,若AB 的垂直平分线l′与C 相交于M ,N 两点,且A ,M ,B ,N 四点在同一圆上,求l 的方程.【试题分析】本题主要考查求抛物线的标准方程,直线和圆锥曲线的位置关系的应用,韦达定理,弦长公式的应用,解法及所涉及的知识和上题基本相同. 【答案】(1)y 2=4x. (2)x -y -1=0或x +y -1=0. 【解析】(1)设Q(x 0,4),代入y 2=2px ,得x 0=8p,所以|PQ|=8p ,|QF|=p 2+x 0=p 2+8p.由题设得p 2+8p =54×8p ,解得p =-2(舍去)或p =2,所以C 的方程为y 2=4x.(2)依题意知l 与坐标轴不垂直,故可设l 的方程为x =my +1(m≠0). 代入y 2=4x ,得y 2-4my -4=0. 设A(x 1,y 1),B(x 2,y 2), 则y 1+y 2=4m ,y 1y 2=-4.故线段的AB 的中点为D(2m 2+1,2m), |AB|=m 2+1|y 1-y 2|=4(m 2+1).又直线l ′的斜率为-m ,所以l ′的方程为x =-1m y +2m 2+3.将上式代入y 2=4x ,并整理得y 2+4m y -4(2m 2+3)=0.设M(x 3,y 3),N(x 4,y 4),则y 3+y 4=-4m,y 3y 4=-4(2m 2+3).故线段MN 的中点为E ⎝ ⎛⎭⎪⎫2m2+2m 2+3,-2m ,|MN|=1+1m 2|y 3-y 4|=4(m 2+1)2m 2+1m 2.由于线段MN 垂直平分线段AB ,故A ,M ,B ,N 四点在同一圆上等价于|AE|=|BE|=12|MN|,从而14|AB|2+|DE|2=14|MN|2,即 4(m 2+1)2+⎝ ⎛⎭⎪⎫2m +2m 2+⎝ ⎛⎭⎪⎫2m 2+22=4(m 2+1)2(2m 2+1)m 4,化简得m 2-1=0,解得m =1或m =-1, 故所求直线l 的方程为x -y -1=0或x +y -1=0.三、考卷比较本试卷新课标全国卷Ⅰ相比较,基本相似,具体表现在以下方面: 1. 对学生的考查要求上完全一致。
即在考查基础知识的同时,注重考查能力的原则,确立以能力立意命题的指导思想,将知识、能力和素质融为一体,全面检测考生的数学素养,既考查了考生对中学数学的基础知识、基本技能的掌握程度,又考查了对数学思想方法和数学本质的理解水平,符合考试大纲所提倡的“高考应有较高的信度、效度、必要的区分度和适当的难度”的原则. 2. 试题结构形式大体相同,即选择题12个,每题5分,填空题4 个,每题5分,解答题8个(必做题5个),其中第22,23,24题是三选一题。
题型分值完全一样。
选择题、填空题考查了复数、三角函数、简易逻辑、概率、解析几何、向量、框图、二项式定理、线性规划等知识点,大部分属于常规题型,是学生在平时训练中常见的类型.解答题中仍涵盖了数列,三角函数,立体何,解析几何,导数等重点内容。
3. 在考查范围上略有不同,如本试卷第3题,是一个积分题,尽管简单,但全国卷已经不考查了。
四、本考试卷考点分析表(考点/知识点,难易程度、分值、解题方式、易错点、是否区分度题)。