外研版高中英语必修三【教学设计】Module 4
Module 4 Sandstorms in Asia
本模块以Sandstorms
为话题，旨在让学生深入了解沙尘暴的起因和对我国乃至整个亚洲的危害，并通过以“沙尘暴
”和“环境保护”为话题的各种任务或活动，让学生掌握与沙尘暴和环境有关的词汇，了解沙尘暴方面的知识。
培养学生用英语谈论沙尘暴及环保的语言技能，
根据上述教材的分析特征，满足《高中英语教学大纲》对英语阅读的要求以及素质教育中要培养学生综合素质能力的要求，结合学生的英语能力普遍薄弱这一学情，
我为这一课确定了如下三项目标：
（1） 知识与能力：首先帮助学生复习掌握必要的生词及培养学生掌握良好的阅读习惯和阅读方法---跳读、略读和详读等。
同时注意开发和培养学生的记忆能力，观察能力、想象、比较和分析能力，以及实践运用能力等。
（2） 过程与方法：以课文整体教学为中心，让学生通过group work 、pair work 等小组合作形式，运用不同的阅读方法，创设不同的情境，设置各种任务，使不同层次的学生都能够积极主动参与到课堂的各项活动中；充分发挥多媒体的作用，使课堂内容丰富，形象直观，从而为完成本节课的教学目标奠定基础。
（3） 情感态度与价值观：了解沙尘暴方面的知识。
同时提高学生的环保意识。
【教学重点】
(1) 掌握一些与沙尘暴和环保有关的词汇。
(2) 学习表达有关沙尘暴和环保的话题。
【教学难点】
(1) 谈论沙尘暴和环保，写有关环保的短文。
(2) 掌握阅读技巧， 了解文章大意。
多媒体课件辅助
Period 1 Lead in
Step 1. Warming up
Lead the new topic SANDSTORMS in by reviewing what we have learned in Module 3. （2m）
h u r r i c a n e
e a r t h q u a k e
t o r n a d o
N a t u r a l D i s a st e r s
s a n d st o r m
v o l c a n i c e r u p t i o
l i g h t n i n g
Period 2 Information about sandstorms.
Ask students to show and introduce their mind mapping about sandstorms. （10m）
Period 3. Reading skills
Step1 Fast reading （5m）
Match the main idea with each.paragraph
Para.1 Para.2 Para.3 Para.4 Para.5 Para.6A. the description of sandstorms
B. the effects of sandstorms to
Beijing.
C. the measures the government
takes to prevent sandstorms D. Sandstorms have been a major
disaster.
E. the advice the weather experts
give to people
F. the causes of the sandstorms in
China.
description
effects
measures
a major
disaster
advice
causes
Step2 Listening and Detailed reading (10m)
Do the exercises.
Period 4: Discussion
What can we do to protect our earth?(10m)
Period 5: Summary and Homework. (3m)
Write a short passage about what we can do to protect our earth, according to the suggestions above.
EXERCISE
A sandstorm refers to a high amount of wind occurring in sandy areas, usually in deserts, where the wind speed is able to lift the top layer (层) of sand from the ground, and push it in every direction. The sand involved in the sandstorm can reach heights of about 3.05m—15.24m.
It is very dangerous to experience a sandstorm. Sand can get into the nose, eyes, mouth and lungs. If you happen to be caught in sandstorm, you must protect yourself by wearing masks, scarves(围巾) and so on.
If you’re driving when such a storm approaches, it’s advised that you pull off the road, since it’s difficult to continue driving. This is also important since vehicles can fail in during sandstorms and you could end up stuck on the road.
Most sandstorms occour in spring, and during the daytime. Many of the areas around the Persian Gulf and the Sahara Desert are associated with the most serious storms. Since it’s a natural phenomenon(现象), it can’t be entirely controlled. In areas that are natural desert regions, you can’t always prevent a sandstorm. There’s much evidence that the planet Mars(火星) has dust storms, and clearly, no human intervention(介入)is responsible for such. Though it can move whole sand dunes and destroy crops, a sandstorm is not without benefit(益处).
1.If you’re driving in a sandstorm, you’d better_______.
A.stop your car in the middle of the road.
B.continue to make your way
C.stop and ask for help
D.stop your car on the side of the road
2.The underlined sentence shows that, anyway, sandstorms are________.
eful
B. useless
C. harmful
D. powerful
3.According to the writer, a sandstorm ___________.
A.is the result of human activities.
B.can be prevented
C.can’t completely disappear on the earth
D.can’t be forecast
4.What will be talked about if there is a fifth paragraph?
A.the cause of sandstorms
B.how to prevent sandstorms
C.the benefit of sandstorms
D.the forecast of sandstorm。
英语必修ⅲ外研版module4period4教案
Module 4 Sandstorms in AsiaPeriod Three Listening, everyday English, function & writing （1）三维目标A．Knowledge and skills1)Make students learn to write a paragraph describing environmental problems.2)Make students practice some useful expressions.B．Process and methods1)Make students learn how to use some simple Everyday English in a conversation.2)Through the analysis of the steps in writing a short paragraph about environmental problem, students may learn some strategies on describing environmental problems.C. Emotion, attitude and valuesThrough the study of this period, ask students to love our only earth and protect environment.（2）教学重点Learn to describe one environmental problem.（3）教学难点1. Use what we have learned to give some solutions.2. How to express what we are thinking about.（4）教学建议Practice & explanation.新课导入设计Sample 1Step 1：Background materials about the environment protection.People today all over the world are beginning to hear and learn more and more about the problem of pollution. Pollution is caused either by the release of completely new and often artificial substances into the environment or by releasing greatly increased amounts of a natural substance, such as oil from oil tankers into the sea. With the development of modern industry, many of the goods and machines we need and use in our daily lives are creating a number of waste products which upset the environment balance. Many of these waste products can be prevented if people pay more attention, but clearly while more and more new goods are produced and made complex, there will be new dangerous wastes to be thrown away, for example, the waste products from nuclear power stations. Many people, therefore, see pollution as only part of a larger and more complex problem.There is no doubt that much of the pollution caused could be controlled if only companies, individuals and government would make more efforts. At home there is an obvious need to control litter and waste. Food comes wrapped up three or four times in packages that all have to be got rid of; drinks are increasingly sold in bottles or tins which cannot be reused. This not only causes a litter problem, but also is a great waste of resources, in terms of glass, metals and paper. Advertising has helped this process by persuading many of us not only to buy things we neither want nor need, but also to throw away much of what we do have. Pollution and waste combine to be a problem everyone can help to solve by cutting unnecessary buying, over consumption(消费)and careless release of the products we use in our daily lives.→ Step 2 WritingStep 1: Lead-in1)Collect the names of types of environment pollution.Students can give a lot on this problem.The teacher can collect the answers on the blackboard.Suggested answers:water pollution, air pollution, noise pollution, desertification, garbage in everyday life2)Give an introduction about the serious pollution you think.Suggestions:(1)what you are worried about(2)the present serious condition(3)cause and result(4)present your solutionSample 2板书设计Step 1: Everyday EnglishWhile learning English, we usually encounter some confusing expressions. If we don’t know their meanings, we’ll misunderstand the speaker. So it’s important for us to learn Everyday English. There are some expressions for you to learn. Choose correct answers for each sentence.1. in a nutshell means_____________ .A. in my opinionB. to explain something very simply2. It’s scary means_____________ .A. It’s frighteningB. It’s interesting3. I’ll do my best means_____________ .A. This is the best(explanation)B. I’ll try as hard as I can4. From what I understand means_____________ .A. This is what I understandB. I think I understand5. You’re absolutely right means_____________ .A. You’re completely rightB. You’re almos t right.Suggested answers:1. B2. A3. B4. A5. AStep 2:In this period, we’ll describe an environmental problem and say what we should to about it.Maybe it’s a little bit difficult for you. So you can follow the steps and example on Page 38.Show a sample:Natural Disaster—Earthquake1. An earthquake is caused by a sudden slip on a fault(断层). A fault is a fracture(断裂)in the crust(地壳)of the earth along which rocks on one side have moved relative to those on the other side. Stresses in the earth’s oute r layer push the sides of the fault together, builds up and the rocks slips suddenly, releasing energy in waves that travel through the rock to cause the shaking that we feel during an earthquake.Earthquakes tend to be concentrated in narrow zones. There are 7 major crustal plates on earth, about 80 km(50 miles)thick, all in constant motion relative to one another. They move at between 10 and 130 mm(from less than one half to 5 inches)per year. It is estimated that there are several million earthquakes in the world each year. Many of these earthquakes go undetected because they occur in remote areas or have very small magnitudes(震级). The USGS Earthquake Info Center locates 12 000 to 14 000 earthquakes each year(about 35 per day). On average, about 60 earthquakes per year are classified as significant, with 19classified as major. A significant earthquake is one of magnitude 6. 5 or higher or one of lesser magnitude that causes casualties or considerable damage. Major earthquakes havea magnitude larger than 7. 0.2. Ask students to read through the steps on Page 38 with the whole class and ensure them to know what to write down next. And discuss the structure of their short passage.First, briefly describe the problem with a partner, taking down notes and key words. Then, give students about 15 minutes to write down a short passage individually. Try to use the suggestions given.After that, exchange their writing with each other to correct mistakes.At last, the teacher displays some excellent writing for the whole class to enjoy.Some samples about this topic.(samples 1)Many students are taking part in the practice of improving the environment through selling used paper and planting trees. They even set up a website to help others take practice in protecting the environment. Although people care much about the environment problems but they don’t know how. So some organizations also published measures to encourage public participation in environment protection. The measures tell us what we can do to protect the environment.We surely cared much about the environment protection but didn’t do much. Actually there is much we can do in our daily life. Buy less to reduce waste. Don’t throw away things before we have made the most use of them. Use electricity, water and gas only when necessary. Switch them off when we don’t need them. Everyone can participate in making the planet suitable for future generations. Everybody can join in and make our world more fantastic. Just do it!(samples 2)Besides giving off gases and dusts into the air, humans produce waste that is poured on the environment. Often, this waste produced by major industries and people is harmful to both nature and human life.Every year, major health problems result from dangerous waste. Sadly, it is often only after someone has died or become seriously ill that the governments will take measures to reduce levels of harmful waste.Some governments have realized how serious the dangerous waste problem is and are now trying to settle this problem. They are also trying to limit the amount of waste industries are allowed to produce.Not only governments but ordinary people as well must work together to solve the problem. They can choose not to buy those products which require the production of dangerous waste, and produce less harmful waste themselves. Many scientists think that waste production can be cut. The waste can be reduced by at least one third using existing technologies and methods.。
外研版高中英语必修三【教学设计】Module-4
Module 4 Sandstorms in Asia本模块以Sandstorms为话题，旨在让学生深入了解沙尘暴的起因和对我国乃至整个亚洲的危害，并通过以“沙尘暴”和“环境保护”为话题的各种任务或活动，让学生掌握与沙尘暴和环境有关的词汇，了解沙尘暴方面的知识。
培养学生用英语谈论沙尘暴及环保的语言技根据上述教材的分析特征，满足《高中英语教学大纲》对英语阅读的要求以及素质教育中要培养学生综合素质能力的要求，结合学生的英语能力普遍薄弱这一学情，我为这一课确定了如下三项目标：（1） 知识与能力：首先帮助学生复习掌握必要的生词及培养学生掌握良好的阅读习惯和阅读方法---跳读、略读和详读等。
同时注意开发和培养学生的记忆能力，观察能力、想象、比较和分析能力，以及实践运用能力等。
（2） 过程与方法：以课文整体教学为中心，让学生通过group work 、pair work 等小组合作形式，运用不同的阅读方法，创设不同的情境，设置各种任务，使不同层次的学生都能够积极主动参与到课堂的各项活动中；充分发挥多媒体的作用，使课堂内容丰富，形象直观，从而为完成本节课的教学目标奠定基础。
【教学重点】(1) 掌握一些与沙尘暴和环保有关的词汇。
(2) 学习表达有关沙尘暴和环保的话题。
【教学难点】(1) 谈论沙尘暴和环保，写有关环保的短文。
多媒体课件辅助Period 1 Lead inStep 1. Warming upLead the new topic SANDSTORMS in by reviewing what we have learned in Module 3. （2m）hurricaneearthquake tornadoNatural Disasterssandstormvolcanic eruptionlightningPeriod 2 Information about sandstorms.Ask students to show and introduce their mind mapping about sandstorms. （10m）Period 3. Reading skillsStep1 Fast reading （5m）Match the main idea with each .paragraphPara.1 Para.2 Para.3 Para.4 Para.5 Para.6A. the description of sandstormsB. the effects of sandstorms toBeijing.C. the measures the governmenttakes to prevent sandstorms D. Sandstorms have been a majordisaster.E. the advice the weather expertsgive to peopleF. the causes of the sandstorms inChina.descriptioneffectsmeasuresa majordisasteradvicecausesStep2 Listening and Detailed reading (10m)Do the exercises.Period 4: DiscussionWhat can we do to protect our earth?(10m)Period 5: Summary and Homework. (3m)Write a short passage about what we can do to protect our earth, according to the suggestions above.EXERCISEA sandstorm refers to a high amount of wind occurring in sandy areas, usually in deserts, where the wind speed is able to lift the top layer (层) of sand from the ground, and push it in every direction. The sand involved in the sandstorm can reach heights of about 3.05m—15.24m.It is very dangerous to experience a sandstorm. Sand can get into the nose, eyes, mouth and lungs. If you happen to be caught in sandstorm, you must protect yourself by wearing masks, scarves(围巾) and so on.If you’re driving when such a storm approaches, it’s advised that you pull off the road, since it’s difficult to continue driving. This is also important since vehicles can fail in during sandstorms and you could end up stuck on the road.Most sandstorms occour in spring, and during the daytime. Many of the areas around the Persian Gulf and the Sahara Desert are associated with the most serious storms. Since it’s a natural phenomenon(现象), it can’t be entirely controlled. In areas that are natural desert regions, you can’talways prevent a sandstorm. There’s much evidence that the planet Mars(火星) has dust storms, and clearly, no human intervention(介入)is responsible for such. Though it can move whole sand dunes and destroy crops, a sandstorm is not without benefit(益处).1.If you’re driving in a sandstorm, you’d better_______.A.stop your car in the middle of the road.B.continue to make your wayC.stop and ask for helpD.stop your car on the side of the road2.The underlined sentence shows that, anyway, sandstorms are________.efulB. uselessC. harmfulD. powerful3.According to the writer, a sandstorm ___________.A.is the result of human activities.B.can be preventedC.can’t completely disappear on the earthD.can’t be forecast4.What will be talked about if there is a fifth paragraph?A.the cause of sandstormsB.how to prevent sandstormsC.the benefit of sandstormsD.the forecast of sandstormTHANKS !!!致力为企业和个人提供合同协议，策划案计划书，学习课件等等打造全网一站式需求欢迎您的下载，资料仅供参考E.。
外研版高中英语必修三 Module4 Period 1教案-新版
Module4 Period 1教案Introduction speaking and everyday English课型：Vocabulary：Teaching Aims:1, Word list and names and places of Module 42, Exercises related to vocabularyTeaching Important Point：Make the students practice speaking freelyTeaching Difficult Point：Correctly pronounce the long wordsTeaching Methods：Listening, reading and practicingTeaching Aids：the blackboard, the multi-mediaTeaching Procedures:Step1 IntroductionWe have learned many kinds of natural disasters such as Tornados, hurricanes and earthquakes, and we know that we can’t stop them from happening, but we can reduce the damage they bring by studying them. Do you know that there is other kind of disasters caused by both climate changes and human beings? (Leave a few seconds for the students to think.) Sandstorms are one of these kinds of disaster. In this module, we will talk about sandstorms. First, let’s deal with the new words in this module.Step 2 PresentationPage 114, Word list of module 4;Play the tape of the word list, Module 4 for the students to follow at least twice. Listen to the long words a few times more for the students to listen more clearly and repeat.Step 3 PracticeAllow the students at most ten minutes to practice reading these words and then check the pronunciation. While checking, the students read the words one by one, and each student reads only one word. Meanwhile, correct the wrong pronunciations together with the students.Step 4 PresentationBriefly explain a few words, such as desertification, forecast, and so on. Write them on the blackboardStep 5 PracticePage 31, Part 1 and 2; Page 33, Part 2 and 3; Page 35, Part 1.Allow the students enough time to practice, when most of them have finished, check the answers.Step 6 speaking-- Group workWe have learned from the previous class that some European countries are better than us at looking after the environment. It’s high time for us to realize the importance of protecting our planet and do something that is actually helpful. Now please turn to Page 37, look at Speaking 2, Exercise 1, andlet’s discuss how the things in the first box are bad for the environment, using the words in the second box to help you. Using “We need to…”, “We must…”, “We should…” to discuss solutions. Divide the class into groups of four to discuss in the charge of the group leaders. Each group chooses only one of the five topics. While they are discussing, the group leaders keep records. After about ten minutes, ask two group leaders to give a short talk about their discussion to the class.Step 7 Everyday EnglishStudents do pair work to discuss the right answers and then check the answers. Answers: 1b, 2 a, 3 b, 4 a, 5a.Step 8 Homework1Read the word again.2Preview the text.Step 9 Teaching reflectionsMost of the students can read the word list correctly and fluently. Encourage the quick students to help those who have difficulties in pronouncing.板书设计：Word list of Module four1desert n. 沙漠------desertification n. 沙漠化;2forecast n./v. forecast(ed) a weather forecast 天气预报3concerned adj. 1) be concerned about 关心……2) as far as I’m concerned 我认为/就我来说。
Unit4AmazingArt大单元教学设计高中英语
分析
作为这个单元的第一个课时，这节课主要是为了帮助学生，激活已有的背景知识以及激发对话题的兴趣。学生可能已经知道一些之前的学过描述艺术的语言，但是可能不太记得了，需要激活。同时，学生对于课程中的艺术内容可能略有了解，但是对于他们的具体事迹还是不太清楚，需要教师给予学生一些背景知识的启发和引导。
教学
3.思维品质
能思考人类艺术创作的价值，初步培养艺术鉴赏力。
4.学习能力
能够运用各种学习策略，在自主学习、合作学习与探究式学习的过程中，结合单元所提供的反思性和评价性问题，不断监控、评价、反思和调整自己的学习内容和进程，激发英语学习的兴趣，提高自己的理解和表达能力，最终促进自身语言能力、文化意识、思维品质和学习能力的综合提升。
教学重难点
教学重点：1.Enable the Ss to grasp more words and expressions by listening and speaking
2..plete the questionsand share the answer the answers with the class.
2.Can you think of some examples of each type?
3.What impress you most aboutthe stage?
Step4After viewing
1.Word study
2.plete the questionsand share your answers with the class
教学准备
blackboard PPT视频图片翻页笔
教学过程
教师活动
学生活动
设计意图
Step 1:Lead in
外研版高中英语必修三【教学设计】Module 4
Module 4 Sandstorms in Asia本模块以Sandstorms为话题，旨在让学生深入了解沙尘暴的起因和对我国乃至整个亚洲的危害，并通过以“沙尘暴”和“环境保护”为话题的各种任务或活动，让学生掌握与沙尘暴和环境有关的词汇，了解沙尘暴方面的知识。
培养学生用英语谈论沙尘暴及环保的语言技能，根据上述教材的分析特征，根据《高中英语教学大纲》对英语阅读的要求，根据素质教育中要培养学生综合素质能力的要求，我为这一课确定了如下三项目标：（1） 知识与能力：首先帮助学生复习掌握必要的生词及培养学生掌握良好的阅读习惯和阅读方法---跳读、略读和详读等。
同时注意开发和培养学生的记忆能力，观察能力、想象、比较和分析能力，以及实践运用能力等。
（2） 过程与方法：以课文整体教学为中心，让学生通过group work 、pair work 等小组合作形式，运用不同的阅读方法，创设不同的情境，设置各种任务，使学生积极主动参与到课堂的各项活动中；充分发挥多媒体的作用，使课堂内容丰富，形象直观，从而为完成本节课的教学目标奠定基础。
（3） 情感态度与价值观：了解沙尘暴方面的知识。
同时提高学生的环保意识。
【教学重点】(1) 掌握一些与沙尘暴和环保有关的词汇。
(2) 学习不定式的各种形式。
(3) 学习表达有关沙尘暴和环保的话题。
【教学难点】(1) 掌握不定式的各种形式。
(2) 谈论沙尘暴和环保。
(3) 写有关环保的短文多媒体课件辅助Step 1. Warming upDescribe the picture in your own words.Step 2 Introduction 1 1. Complete the sentences using the correct form of the words.blow bury frightening last(v) sandstormThere has been a _______. It ________for ten hours and was very___________. The wind _________the sand high around the houses, and some cars were almost completely ___________by the sand .2. Look at the pictures and answer the questions.1).What is happening?2).What is the cyclist wearing and why?3).What do you think happens to traffic in this situation? Why?Keys:1)There is a sandstorm blowing.2)They’ve wearing hoods, masks and glasses to protect themselves.3)It moves very slowly. Because it is not clear to see everything on the road and peoplemust take great care.Discussion ：Where in China do sandstorms begin?Xinjiang, Gansu and Western Inner MongoliaBeijing and Northeast Inner MongoliaStep 3 : Introduction-2: discuss these statements and decide which statement is false.1)Sandstorms begin in desert areas.2)Deserts are created by climate changes.3)Deserts are also created because people cut down trees and dig up grass.4)Sandstorms from Asia have blown across the Pacific Ocean to America.5)Sandstorms can’t be prevented. ×6)The inland region has more sandstorms than the one near the sea.Step 4. Fast readingTask 1: Read the text and tell the definition of sandstormSandstorms are strong dry winds that carry sand.Task 2: What other aspects are mentioned in this passage?causes and effects suggestions measures …Task 3. How many parts can this article be divided into ?Part 1(para1) major disaster in Asia- SandstormPart 2(para2_5) description: cause influence suggestionPart 3(para6) measures to prevent sandstormsTask 4. Fill in the form with the detailsThink about : any other measures?Step 5 detailed readingTask 1. Choose the correct answer1. sand dunes means _____a) plants growing in sand b) sand hills2. affect means _____a) to kill b) to cause a change3. You wear a mask over your _____a) face b) body4. strength is the noun of _____a) strong b) strange5. desertification (in Paragraph 3) means _____a) making land desert; b) throwing sth awaykeys: bbaaaTask 2. Describe the feeling of Ren JianboIt is a ________ experience, the most _________ and the most dangerous ________. Task 3.analyze the cause of sandstormsThe cause of sandstorms is ______________(a_______ in which land becomes desert).A. ________ changesB. People __________ trees and _________ grass.Task 4 . think about the harm of sandstorms to citizens.A. Thick _ ______ covers the city.B. ________ moves very slowly.C. To be ________ in a sandstorm is frightening.D. ________ makes people breathe difficult.Task 5. The measures of reducing the harm of sandstormsA.________ a sandstorm before it occurs.B. Take ________ advice and do not go out.C. Wear a ________.D. Plant trees to ________ it coming nearer.Task 6. General structure of the passageStep 6. Group work“A Press Conference （记者招待会）about Sandstorms”Suppose you are attending a press conference about sandstorms. Some are government spokesmen , some are journalists and citizens. Now work in groups of 4. You can refer to the following problems ..sandstorm of last month in Beijing.the cause of sandstorm.effect of sandstorms.measures to prevent sandstormPeriod 2 Language points in reading原文再现(Reading)1.一个主要的灾难2.大规模的战役/运动3.被困在沙尘暴中4.次数好像增加了5.伐树挖草6.醒来看到昏黄的天空和夹杂着黄沙在城里肆虐的狂风7.车辆行驶很慢因为浓浓的尘埃降低了能见度8.建议人们不要出门9.阻止其接近10.计划继续种树11.一个接一个发生12.清扫走；卷走1.a major disaster2.a mass campaign3.be caught in the sandstorm4.appear to have increased5. cut down trees and dig up…6.wake up to an orange sky and strong winds that cover the city in a thick…dust7.traffic moves very slowly because the thick dust makes it difficult to see.8. advise people not to go out9. prevent it coming near10. plan to c ontinue planting…11.happen one after another12. sweep away1. 1. major: adj. 主要的，重大的What do you see as a major problem with the environment?One of the major aims of reading about sandstorms is to raise awareness of environmental protection.China now ____________________ in international affairs.minor: 次要的a minor illnessEnglish was my major in university.= I majored in English in university.majority: 多数，大部分(n.)the majority of sth/sb = most of sth/sbminority: 少数；少数民族2. A mass campaign has been started to help solve it.1)mass: adj. 大规模的, 大众的mass productionmass destruction weaponsmass media 大众传媒mass n. n. 1. 大团/块/群2. 质量3. 体积4. 众多; 大量, 大宗[(+of)]a mass of/masses of = a lot of/lots of + C n./U n.I’ve got masses o f work to do and masses of books to read.the masses 群众2) anti-smoking campaignan advertising campaign3.Para.2When asked about his experience in a sandstorm, Ren Jianbo said. “__________________________ a sandstorm was terrible and it was the most ____________ andthe most dangerous ___________ I’ve ever been _____. There was nothing ____________.”(bite)“___________________by a dog was not a delightful experience,” he told the doctor.bite) In the countryside _________________ by a dog is common occurrence.To have been caught in such a traffic jam was a terrible experience.(特定情况)Being caught in such a traffic jam is a common occurrence in cities.(一般情况)be/get caught in sth. 被困在…中=be/get trapped/stuck inOn seeing their car _______________,the police came to their rescue.He was late because he had been caught in a traffic jam.= _______ in a traffic jam, he was late.4.Cut downPeople in the poor village have to cut down trees to make a living.Russia and America have agreed on cutting down nuclear weapons.“The article is too long,” said the editor. “Could you cut it down to 2000 words?”响应“绿色出行”号召，很多市民减少了开车上班。
外研版高中英语必修三教学设计Module4
Module 4 Sandstorms in AsiaPeriod 1 Introduction设计思路说明【Pre-learning】通过图片讨论沙尘暴的危害。
【While-learning】学习关于沙尘暴词汇以及讨论沙尘暴的起因。
【Post-learning】讨论应对沙尘暴的方法。
教材分析本模块以Sandstorms为话题，通过本模块的几篇阅读材料使学生对Sandstorms有所了解，并通过文章中提出的一些深刻的问题，比如，The desert is only 250 kilometers away to the west of Beijing使学生更好地了解我们的地球和我们的生活环境正遭受的破坏，并引发对“我们应该如何保护环境”的热烈讨论，通过这些讨论会激发学生对环境保护的了解和实施的自觉性。
通过讨论Sandstorms，让学生表达对沙尘暴的看法，以及我们应采取何种措施来提高环境质量。
并能就此设计海报来呼吁人们保护环境。
INTRODUCTION 复习和学习有关自然灾害的词汇,呈现了一些自然灾害的起因以及造成的危害,使学生对沙尘暴有初步了解。
教学目标【知识与能力目标】Enable the students to talk about the sandstorms, the reasons for causing sandstorms and theimportant of protecting environment.【过程与方法目标】Help students to learn how to talk about the sandstorms, the reasons for causing sandstorms and the important of protecting environment.【情感态度价值观目标】To realize the importance of protecting environment.教学重难点【教学重点】How to describe sandstorms & environmental protection.【教学难点】How to express one’s opinions.课前准备1. A projector2. A computer教学过程Step I. Pre-learningT: Good morning, everyone! Today we are going to learn a new module, Module 4 Sandstorms in Asia. Look at the screen please. I will show you some pictures. Talk about them in your own words. (Show them the pictures of sandstorms.)S1: In the first picture I can see a man is riding a bike hard. The sky is yellow.T: Can you see the buildings clearly?S1: No, they are not clear.T: Thank you, sit down please.S2: In the second one I can find some buildings, but I cannot see them clearly. May be the city is in the sand or anything like that.S3: In the third one I can see a very tall building only. There is much sand in the sky.T: Very good. Thank you.S4: In the next picture, I can see many people riding bikes wearing masks. The weather is very cold, because they wear gloves and more clothes.T: How about the air? Is it clean?S4: The air is not clean. There is something like sand in the air.T: Quite right!S5: In the fifth picture, there is a strong wind carrying sand. It looks like smoke.S6: In the last one, there are some buildings covered with thick, yellow dust.T: Excellent job! Thank you every much. Now, who can tell us why there is so much sand in the sky? The wind that carry sand are called…S7: Sandstorm.T: Very good. Yes, they are called sandstorm. If you want to know more about sandstorm, let’s come to Module 4 Sandstorms in Asia.Step II. While-learningT: Open your books on page 31. Look at the picture in your books, what can you see in the picture?S1: There is a strong wind carrying sand in the sky, and a car covered with sand running slowly.T: Right. Now, complete the sentences using the correct form of words in the box. Three minutes.T: From this short paragraph, we can see the sandstorm is frightening. Have you ever experienced the sandstorm? How does it be created? Before we discuss these questions, let’s look at some words on the screen.into several groups to discuss questions in activity 2. Then call back the answers)S1: Most of the sandstorms begin in desert areas. Because there are no trees and grasses in the desert areas. The wind is very strong.S2: Climate changing can create deserts, but nowadays, the deserts are being enlarged because of humanity.S3: Deserts are also created because people cut down trees and dig up grass.T: Why people cut down trees?S3: They want to get wood or to plant crops.S4: Few years ago, Japan was affected by the sandstorms coming from northwest China. And America is also affected by sandstorms. Some are caused by humanity; some are from Asia blown across the Pacific Ocean. Sandstorm has been a global issue.T: Very good, thank you. Can we prevent it?S5: Yes. At present, our China has carried out many plans to prevent sandstorm. For example, China has formed a professor committee to study how to prevent sandstorms. We have planted many trees every year. Cutting down the trees is unlawful. The degree of sandstorm is on decline. So we can prevent it. We believe ourselves.T: Quite right. I believe too. Where does the sandstorm often happen?S6: the inland region has more sandstorms than the one near the sea. Because the inland is drier than the one near the sea.T: Can you give us the reason?S6: Dry weather is one of the main reasons for sandstorms.Step III. Post-learningT: Quite right. You’ve done very well. From this activity, you’ve got much information on sandstorms. Sandstorm is very bad. It pollutes the air, affects our daily life. If you are in a sandstorm what should you do? Now work in pairs to discuss the questions in activity 3.(5 minutes later, call back the answers)S1: If I am in a sandstorm I will wear a mask to protect my mouth and throat, wear a pair of glasses to protect my eyes.S2: Besides mask and glasses I will wear a hat. Because there is much sand in the air, it will make my hair dirty.T: You are right. In a sandstorm, you should wear a mask and a hat, a pair of glasses is also necessary. Which one is more dangerous, earthquake and sandstorm?S3: I think earthquake. Because in sandstorm we can stay at home to protect us, but in earthquake everywhere is dangerous.T: I agree with you. Where in China do sandstorms usually happen? What is the first sign?S4: In the west and northwest China.S5: But it also happens in Beijing often.S6: Before the sandstorm, there is usually a heavy wind and dry weather.S7: The sky is yellow.S8: One afternoon of last spring, when I was at school, the sky was yellow. There was much sand in the sky. The wind was very strong with some drops of rain. In fact, it was not rain. It was mud. At that time, I thought the earthquake was coming. It was very terrible.T: It was really terrible. Thank you. Now I think all of you have known about something of sandstorm. The sandstorm is terrible and harmful. We should work hard to protect our environment.Homework:1. Recite the new words.2. Preview the passage in Reading and V ocabulary.教学反思略Period 2 Reading and Vocabulary设计思路说明【Pre-reading】Show some pictures of sandstorms to the students and let them to describe the pictures so as to arouse the students’ interest and learn some words)【While-reading】Get the students to have an idea of the organization of the whole text and let the students know more detailed information about sandstorms to train the students’ ability of seeking the needed information.【Post-reading】Have the students watch a video of a sandstorm that happened in Inner Mongolia and ask them to work in pairs to prepare an interview about the sandstorm.教材分析本模块以Sandstorms为话题，通过本模块的几篇阅读材料使学生对Sandstorms有所了解，并通过文章中提出的一些深刻的问题，比如，The desert is only 250 kilometers away to the west of Beijing使学生更好地了解我们的地球和我们的生活环境正遭受的破坏，并引发对“我们应该如何保护环境”的热烈讨论，通过这些讨论会激发学生对环境保护的了解和实施的自觉性。
外研版高中英语必修三模块四全套教案
Book3Module4 Sandstorms in AsiaTeaching Aims:1. Knowledge and Skilla.Get the students to review the violence of nature and know more about sandstorms and how to protectthe environment.b.Through discussion and the comprehension of Reading, develop the st udents’ listening, speaking,reading and writing, mainly reading.c.Encourage the students to search the information on the Internet to gain more knowledge ofsandstorms and environmental protection.d.Improve the students’ ability to read for specific facts.e.To grasp the usage of infinitive, pay more attention to the usage of but + infinitive.2.Emotion and Valuesa.Enable the students to talk about the cause and influence of sandstorms，and the ways to solve theproblem in order to increase their sense of protecting the environment.b.To encourage the Ss to talk about the damage caused by sandstorm and their own feelings about it.3. Cross-cultural awareness:a.Understand the environmental protection of the whole world and strengthen their awareness ofenvironment protection.4. Character-building:a.To strengthen their confidence of protecting the environment we are living in.b.Enable the students to talk about the sandstorms, the reasons for causing sandstorms and theimportance of protecting environmentDifficulties and Importance:a. Conclude and collect the words and phrases related to environment and environmental protection.b. Ask students to think ways to protect the environment.c.Improve the student’s ability of grasping the general idea of the passage.Teaching Method:a.Task-based methodologymunicative ApproachTeaching Time:Five periods:Period 1 vocabulary and WritingSpeaking 1Period 2 Reading and V ocabularyPeriod 3 Grammar 1 InfinitiveListening and V ocabularyPeriod 4 Grammar 2 but + infinitiveEveryday EnglishPeriod 5 Cultural cornerSpeaking 2WritingTeaching Procedures:Period 1Step 1. Warming upLook at the picture. Complete the sentences using the correct form of these words Then answer the following questions.blow bury frightening last sandstormThere has been a ______. It _____ for ten hours and wasvery _______. The wind _______the sand high aroundthe houses, and some cars were almost completely ______by the sand.Suggested answers:1. sandstorm2. has been blowing / has lasted3. frightening4. was blowing5. buriedQ1. What is a sandstorm?Q2. What’s the weather like when a sandstorm occurs?Q3. What’s the bad influence of a sandstorm?Suggested answers:Q1. Sandstorm is a kind of bad weather, which is becoming increasingly common in Northwestern China, and it usually happens in spring and fall. When a sandstorm comes, the wind blows strongly with dust and sand.Q2. There is strong, dry wind and the sky is yellow.Q3. cars slow down and have to turn on headlight;the visibility dropsdifficult for us to breathedangerous to go out or driveStep 2 Further understandingWork in pairs. Discuss the following statements and decide whether it is true or false.1.Sandstorms begin in desert areas.2.Deserts are created by climate changes.3.Deserts are also created because people cut down trees and dig up grass.4.Sandstorms from Asia have blown across the Pacific Ocean to America.5.Sandstorms can’t be prevented.6.The inland region has more sandstorms than the one near the sea.Suggested answers:1,2,3,4,6 T 5, FStep 3 DiscussionsQ1. What’s the cause of sandstorm?Q2. What should you do in a sandstorm to protect yourself?Suggested answers:Q1. climate changes; trees cut down; desertification; serious air and water pollution;the growing population of the world and so on.Q2: This is an open question.Step 4 SpeakingWork in pairs. Suppose there has been a bad sandstorm in your city.A: You are a reporter. You interview a man who has cycled to work in the sandstorm. Before you do the interview, write down the questions you want to ask.B: You felt frightened but you put on a mask and cycled to work in the sandstorm. Tell the reporter how you feel about the sandstorm. Describe how things looked in the sandstorm.Homework:1.Memorize the new words related to sandstorms.2.Preview the passage of Sandstorms in Asia.Period 2Step 1 Pre-readinga. Look at the photo and answer the following questions.1. Get Ss to come up with as many words as possiblewhile looking at the picture.2. What is happening?3. What is the cyclist wearing and why?4. What do you think happened to traffic in this situation?Why?5. What do you think experts advise people to do in thissituation?Suggested answers:1. mask cycle cyclist dustcitizen frightening sandstorm2. There is a sandstorm blowing.3. She is wearing hoods, masks and glasses.4. The traffic moves slowly. Because it’s not clear to see everything on the road and people must take great care.5. Experts advise people to stay at home in this situation.b. PredicationIf you are to write the article named “Sandstorms in Asia”, how many parts will you include in it? What will you write in each part?Step 2 While-readinga.Skimming and scanningRead the passage quickly and fill in the diagram with one proper word.Part 1(Para1) d__________Part 2(Para2-5) c_______d_______S_______i________s________Part 3(Para.6) m________Suggested answers:Part 1 disasterPart 2 Sandstorm cause description influence suggestionsPart 3 measuresb.Detailed Reading1)Read the passage carefully and answer the following question.1 What are sandstorms?2 In what places do they often happen?3 What does Ren Ji anbo’s example tell us?4 Are there sandstorms in China? Where?5 Have sandstorms in China increased or decreased recently? Why?6 Why does traffic move slowly during the sandstorm?7 What does the government do to protect Beijing from sandstorms?Suggested answers:1.Sandstorms are strong, dry winds that carry sand.2.Central Asia, North America, Central Africa and Australia.3.It is dangerous to go out when a sandstorm occurs.4.Yes. Northwest China.5.Increased. As a result of desertification.6.Because the thick dust makes it difficult to see.7.Plant more trees.2) Read the passage carefully and then fill in the chart with suitable words.Suggested answersa. Decide if the following statements are true( T ) or false( F ).①Scientists have tried many ways to deal with sandstorms②Land becomes desert only because people cut down trees and dig up grass.③The Chinese Central West Station can not forecast sandstorm before it comes.④The desert is 25o kilometers away to the west of Beijing. So there is no need to take somemeasures.⑤Southwest China is part of the sandstorm center in Central Asia.Suggested answers:1.T2. F3. F4. F5. Fb. Read the text again and complete the following sentences1.The winds in a sandstorm can sometimes______________________________2.When Ren jianbo was living in Inner Mongolia ______________________________3.Sandstorms in China appear to have increased ______________________________4.Cutting down trees and digging up grass can______________________________5. Traffic moved slowly because ______________________________6.The government is planting trees to the west of Beijing to______________________________ Suggested answers:1. prevent you from seeing the sun2.he experienced a terrible sandstorm3.because of desertification4.cause deserts and sandstorms to increase5.the drivers can’t see6.prevent the desert coming nearerStep 4 language explanations1. blow v. (blew ,blown) (风，空气等)吹，吹动n.强风，风暴；(用拳、武器等)重击,殴打；打击。
外研版必修 三module 4 教案
Module 4 Sandstorms in AsiaI．教学内容分析本模块以Sandstorms为话题，旨在让学生深入了解沙尘暴的起因和对我国乃至整个亚洲的危害，并通过以“沙尘暴”和“环境保护”为话题的各种任务或活动，让学生掌握与沙尘暴和环境有关的词汇，了解沙尘暴方面的知识。
培养学生用英语谈论沙尘暴及环保的语言技能，同时提高学生的环保意识。
Introduction 部分介绍了一些有关“沙尘暴”的词汇，要求通过练习让学生熟悉这些词汇的意义，并通过讨论问题的方式，让学生初步了解沙尘暴。
Reading and Vocabulary 部分通过阅读Sandstorms in Asia，让学生学习相关词汇，学会分析文章结构,归纳段落大意，同时增进对沙尘暴危害性的了解，为后面的说、写做准备。
Grammar 1 部分旨在让学生通过三个学习活动，发现规律，理解掌握“动词不定式”的各种时态和语态概念，以达到正确使用各种形式的目的。
Listening and Vocabulary 部分先引入大量与环境有关的词汇，然后通过给topics排序，回答问题以及用刚学词汇完成句子的活动对词汇加以巩固和掌握。
Grammar 2部分为“动词不定式”的一种特殊用法，即but后加不带to的不定式。
要求在进行活动的同时加以启发，让学生明确用法。
Pronunciation and Function部分通过听的训练让学生掌握句子的重读，同时掌握如何“表达强烈感情”，并加以练习进行巩固。
Speaking 1 部分要求学生就“沙尘暴”的话题进行访谈。
Speaking 2 部分要求教师引导学生认识了解环境污染问题，然后以“环保”为主题，进行讨论，提高学生的环保意识。
Writing部分通过四个步骤的练习掌握写作技巧，学会写有关环保的短文。
Everyday English部分出自本模块听力部分，可以在听力结束后处理本环节。
主要通过补全对话的形式使学生熟练掌握这几个表达Cultural Corner部分通过介绍欧洲一些国家的环保情况，让学生了解欧洲国家在环保方面的一些做法。
外研版高中英语必修3 Module4教学设计Teaching Resources
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（浙教版）九年级数学下册（全册）章节测试卷汇总（共4套）第1章综合达标测试卷(满分：100分 时间：90分钟)一、选择题(每小题2分，共20分)1．在Rt △ABC 中，∠C ＝90°，下列式子不一定成立的是( A ) A ．sin A ＝sin B B ．cos A ＝sin B C ．sin A ＝cos BD ．∠A ＋∠B ＝90°2．如果α是锐角，且sin α＝35，那么cos(90°－α)的值为( A )A ．35B ．45C ．34D ．433．正方形网格中，∠AOB 如图放置，则cos ∠AOB 的值为( B )A ．12B ．22C ．32D ．334．当锐角α>30°时，则cos α的值( D ) A ．大于12B ．小于12C ．大于32D ．小于325．已知∠A 为锐角，tan A 是方程x 2－2x －3＝0的一个根，则代数式tan 2A ＋2tan A ＋1的值为( A )A ．16B ．8C ．15D ．176．如图，已知∠α的一边在x 轴上，另一边经过点A (2,4)，顶点为(－1,0)，则sin α的值是( D )A ．25B ．55C ．35D ．457．如图是一个棱长为4的正方体盒子，一只蚂蚁在D 1C 1的中点M 处，它到BB 1的中点N 的最短路线是( C )A ．8B ．42C ．210D ．2＋2 58．【2016·浙江绍兴中考】如图，在Rt △ABC 中，∠B ＝90°，∠A ＝30°，以点A 为圆心，BC 长为半径画弧交AB 于点D ，分别以点A 、D 为圆心，AB 长为半径画弧，两弧交于点E ，连结AE 、DE ，则∠EAD 的余弦值是( B )A ．312 B ．36 C ．33D ．329．如图，河坝横断面迎水坡AB 的坡比是1∶3(坡比是坡面的铅直高度BC 与水平宽度AC 之比)，坝高BC ＝3 m ，则坡面AB 的长度是( B )A ．9 mB ．6 mC ．6 3 mD ．3 3 m10．【2016·广西钦州中考】如图为固定电线杆AC ，在离地面高度为6 m 的A 处引拉线AB ，使拉线AB 与地面BC 的夹角为48°，则拉线AB 的长度约为(结果精确到0．1 m ，参考数据：sin 48°≈0．74，cos 48°≈0．67，tan 48°≈1．11)( C )A ．6．7 mB ．7．2 mC ．8．1 mD ．9．0 m二、填空题(每小题3分，共24分)11．计算：2sin 30°＋2cos 60°＋3tan 45°＝__5__． 12．已知sin A ＝12，则锐角∠A ＝__30°__．13．在Rt △ABC 中，∠C ＝90°，AC ＝2，BC ＝1，则sin A ＝__55__． 14．在一个斜坡上前进5米，水平高度升高了1米，则该斜坡坡度i ＝__1∶26__． 15．如图，△ABC 的三个顶点分别在边长为1的正方形网格的格点上，则tan(α＋β) __>__tan α＋tan β．(填“＞”“<”或“＝”)16．如图，某河堤的横断面是梯形ABCD ，BC ∥AD ，迎水坡AB 长13 m ，且tan ∠BAE ＝125，则河堤的高BE ＝__12__m ．17．如图，在Rt△ABC中，∠CAB＝90°，AD是∠CAB的平分线，tan B＝12，则CD∶DB＝__1∶2__．18．如图，在A处看建筑物CD的顶端D的仰角为α，且tan α＝0．7，向前行进3米到达B处，从B处看顶端D的仰角为45°(图中各点均在同一平面内，A、B、C三点在同一条直线上，CD⊥AC)，则建筑物CD的高度为__7__米．三、解答题(共56分)19．(8分)计算：(1)cos245°＋cos 30°2sin 60°＋1－3tan 30°；解：原式＝⎝⎛⎭⎫222＋322×32＋1－3×33＝12＋3－34－1＝1－34．(2)⎝⎛⎭⎫－120＋⎝⎛⎭⎫13－1·23－|tan 45°－3|．解：原式＝1＋3×233－(3－1)＝1＋23－3＋1＝2＋3．20．(8分)如图，△ABC中，∠ACB＝90°，sin A＝45，BC＝8，D是AB中点，过点B作直线CD的垂线，垂足为点E．(1)求线段CD的长；(2)求cos∠ABE的值．解：(1)在△ABC中，∵∠ACB＝90°，∴sin A＝BCAB＝45．∵BC＝8，∴AB＝10．∵D 是AB中点，∴CD＝12AB＝5．(2)在Rt△ABC中，∵∠ACB＝90°，AB＝10，BC＝8，∴AC ＝AB 2－BC 2＝6．∵D 是AB 中点，∴BD ＝5，S △BDC ＝S △ADC ，∴S △BDC ＝12S △ABC ，即12CD·BE ＝12×12AC·BC ，∴BE ＝AC·BC 2CD ＝6×82×5＝245．在Rt △BDE 中，∵∠BED ＝90°，∴cos ∠DBE ＝BE BD ＝2455＝2425，即cos ∠ABE 的值为2425．21．(8分)【2016·四川自贡中考】某国发生8．1级强烈地震，我国积极组织抢险队赴地震灾区参与抢险工作，如图，某探测队在地面A 、B 两处均探测出建筑物下方C 处有生命迹象，已知探测线与地面的夹角分别是25°和60°，且AB ＝4米，求该生命迹象所在位置C 的深度．(结果精确到1米，参考数据：sin 25°≈0．4，cos 25°≈0．9，tan 25°≈0．5，3≈1．7)解：如图，过点C 作CD ⊥AB 交AB 延长线于点D ．设CD ＝x 米．在Rt △ADC 中，∵∠ADC ＝90°，∠DAC ＝25°，∴tan ∠DAC ＝CDAD＝0．5，∴AD ＝2x 米，∴BD ＝(2x －4)米．在Rt △BDC 中，∵∠BDC ＝90°，∠DBC ＝60°，∴tan ∠DBC ＝CD BD ＝x2x －4＝3，解得x ≈3．即生命迹象所在位置C 的深度约为3米．22．(10分)如图所示，学校在楼顶平台上安装地面接收设备，为了防雷击，在离接收设备3 m 远的地方安装避雷针，接收设备必须在避雷针顶点45°夹角范围内，才能有效避免雷击(α≤45°)．已知接收设备高80 cm ，那么避雷针至少应安装多高？解：如图，过点A 作AE ⊥CD 于点E ，AB ＝EC ＝0．8 m ，AE ＝BC ＝3 m ．在Rt △ADE 中，tan α＝AE DE ，∴DE ＝AE tan α＝3tan α．∵α≤45°，∴tan α≤1，即DE ≥3 m ，∴CD ＝CE ＋DE ≥3．8 m ．故避雷针至少应安装3．8 m 高．23．(10分)如图，将水库拦水坝背水坡的坝顶加宽2 m ，坡度由原来的1∶2改为1∶2．5，已知坝高6 m ，坝长50 m ．(1)加宽部分横断面AFEB 的面积是多少？ (2)完成这一工程需要多少立方米的土？解：(1)如图，过点A 作AG ⊥BC ，过点F 作FH ⊥BC ，垂足分别是G 、H ．根据题意，得FH ＝AG ＝6 m ，HG ＝AF ＝2 m ．在Rt △AGB 和Rt △FHE 中，∵tan ∠ABG ＝AG BG ＝12，tan ∠E＝FH EH ＝12.5，∴BG ＝2AG ＝12 m ，EH ＝2．5FH ＝15 m ，∴EB ＝EH －BH ＝15－(12－2)＝5(m)，∴S 梯形AFEB ＝12(AF ＋EB)·FH ＝12×(2＋5)×6＝21(m 2)．即加宽部分横断面AFEB 的面积为21平方米． (2)完成这一项工程需要21×50＝1050(m 3)的土．24．(12分)如图，小岛A 在港口P 的南偏西45°方向，距离港口81 n mile 处．甲船从A 出发，沿AP 方向以9 n mile/h 的速度驶向港口，乙船从港口P 出发，沿南偏东60°方向以18 n mile/h 的速度驶离港口．现两船同时出发．(1)出发后几小时两船与港口P 的距离相等？(2)出发后几小时乙船在甲船的正东方向上？(结果精确到0．1 h)解：(1)设出发后x h 两船与港口P 的距离相等．根据题意，得81－9x ＝18x ．解得x ＝3．故出发后3 h 两船与港口P 的距离相等． (2)如图，设出发后y h 乙船在甲船的正东方向上，此时甲、乙两船的位置分别在点C 、D 处，连结CD ，过点P 作PE ⊥CD ，垂足为点E ，则点E 在点P 的正南方向上．在Rt △CEP 中，∠CPE ＝45°，∴PE ＝PC·cos 45°．在Rt △PED 中，∠EPD ＝60°，∴PE ＝PD·cos 60°，∴PC·cos 45°＝PD·cos 60°，即(81－9y)·cos 45°＝18y·cos 60°．解得y ≈3．7．故出发后约3．7 h 乙船在甲船的正东方向上．第2章综合达标测试卷(满分：100分 时间：90分钟)一、选择题(每小题2分，共20分)1．一圆的半径为3，圆心到直线的距离为4，则该直线与圆的位置关系是( C ) A ．相切 B ．相交 C ．相离D ．以上都不对2．在△ABC 中，∠C ＝90°，AC ＝6，BC ＝8，则△ABC 的内切圆半径是( A ) A ．2 B ．2．5 C ．3D ．43．如图，在平面直角坐标系xOy 中，半径为2的⊙P 的圆心P 的坐标为(－3,0)，将⊙P 沿x 轴正方向平移，使⊙P 与y 轴相切，则平移的距离为( B )A ．1B ．1或5C ．3D ．54．如图，⊙B 的半径为4 cm ，∠MBN ＝60°，点A 、C 分别是射线BM 、BN 上的动点，且直线AC ⊥BN ．当AC 平移到与⊙B 相切时，AB 的长度是( A )A ．8 cmB ．6 cmC ．4 cmD ．2 cm5．如图，在Rt △ABC 中，∠ACB ＝90°，AC ＝4，BC ＝6，以斜边AB 上的一点O 为圆心所作的半圆分别与AC 、BC 相切于点D 、E ，则AD 的长为( B )A ．2．5B ．1．6C ．1．5D ．16．【2016·四川德阳中考】如图，AP 为☉O 的切线，P 为切点，若∠A ＝20°，C 、D 为圆周上两点，且∠PDC ＝60°，则∠OBC 等于( B )A ．55°B ．65°C ．70°D ．75°7．将一块三角板和半圆形量角器按图中方式叠放(三角形斜边与半圆相切)，重叠部分(阴影)的量角器圆弧(AB ︵)对应的圆心角(∠AOB )为120°，AO 的长为4 cm ，OC 的长为2 cm ，则图中阴影部分的面积为( C )A ．⎝⎛⎭⎫16π3＋2 cm 2B ．⎝⎛⎭⎫8π3＋2 cm 2C ．⎝⎛⎭⎫16π3＋23 cm 2D ．⎝⎛⎭⎫8π3＋23 cm 28．如图，在△ABC 中，AB ＝10，AC ＝8，BC ＝6，经过点C 且与边AB 相切的动圆与CA 、CB 分别相交于P 、Q 两点，则线段PQ 长度的最小值是( B )A ．4．75B ．4．8C ．5D ．4 29．如图，Rt △ABC 的内切圆⊙O 与两直角边AB 、BC 分别相切于点D 、E ，过劣弧DE (不包括端点D 、E )上任一点P 作⊙O 的切线MN 与AB 、BC 分别交于点M 、N ，若⊙O 的半径为r ，则Rt △MBN 的周长为( C )A ．rB ．32rC ．2rD ．r10．如图，⊙O 的半径为2，P 为⊙O 外一点，P A 切⊙O 于点A ，P A ＝2，若AB 为⊙O 的弦，且AB ＝22，则PB 的长为( D )A ．2B ．25C ．1或5D ．2或2 5二、填空题(每小题3分，共24分)11．如图，∠ACB ＝60°，⊙O 的圆心O 在边BC 上，⊙O 的半径为3，在圆心O 向点C运动的过程中，当CO ＝ 23 时，⊙O 与直线CA 相切．12．【2016·安徽中考】如图，已知⊙O 的半径为2，A 为⊙O 外一点，过点A 作⊙O 的一条切线AB ，切点是B ，AO 的延长线交⊙O 于点C ，若∠BAC ＝30°，则劣弧BC 的长为__4π3__．13．如图，△ABC 内切⊙O 于点D 、E 、F ．若∠EOF ＝120°，∠DEF ＝70°，则∠C ＝__80°__．14．如图是一张电脑光盘的表面，两个圆的圆心都是O ，大圆的弦AB 所在的直线是小圆的切线，切点为C ．已知大圆的半径为5 cm ，小圆的半径为1 cm ，则弦AB 的长度为__46__cm ．15．如图，点I 是△ABC 的内心．记∠ABI 与∠ACI 的平分线的交点为I 1，∠ABI 1与∠ACI 1的平分线的交点为I 2，∠ABI 2与∠ACI 2的平分线的交点为I 3，…，依次类推．若∠A ＝20°，则∠BI 5C 的度数是__22．5°__．16．【2016·江苏苏州中考】如图，AB 是⊙O 的直径，AC 是⊙O 的弦，过点C 的切线交AB 的延长线于点D ，若∠A ＝∠D ，CD ＝3，则图中阴影部分的面积为__33－π2__．17．【山东烟台中考】如图，直线l ：y ＝－12x ＋1与坐标轴交于A 、B 两点，点M (m,0)是x 轴上一动点，以点M 为圆心，2个单位长度为半径作⊙M ，当⊙M 与直线l 相切时，则m 的值为__2－25或2＋25__．18．如图，在Rt △ABC 中，∠ACB ＝90°，点D 是AC 上一点，以CD 为直径的圆与AB 相切于点E ，若CD ＝3，tan ∠AED ＝12，则AD 的长为__1__．三、解答题(共56分)19．(8分)如图，公路MN 与公路PQ 在点P 处交汇，且∠QPN ＝30°，点A 处有一所中学，AP ＝160 m ．假设拖拉机行驶时，周围100 m 以内会受到噪音的影响，那么拖拉机在公路MN 上沿PN 方向行驶时，学校是否受到噪音影响？说明理由；如果受影响，且知拖拉机的速度为18 km/h ，那么学校受影响的时间是多少秒？解：学校受到噪音影响．理由如下：作AH ⊥MN 于点H ，如图．∵PA ＝160 m ，∠QPN ＝30°，∴AH ＝12PA ＝80 m ．而80 m ＜100 m ，∴拖拉机在公路MN 上沿PN 方向行驶时，学校受到噪音影响．以点A 为圆心，100 m 为半径作⊙A 交MN 于B 、C ，连结AB ，如图．∵AH ⊥BC ，∴BH ＝CH ．在Rt △ABH 中，AB ＝100 m ，AH ＝80 m ，∴BH ＝AB 2－AH 2＝60 m ，∴BC ＝2BH ＝120 m ．∵拖拉机的速度＝18 km/h ＝5 m/s ，∴拖拉机在BC 段行驶所需要的时间＝1205＝24(秒)，∴学校受影响的时间为24秒．20．(10分)如图，AB 是⊙O 的直径，P 为AB 延长线上一点，PD 切⊙O 于点C ，BC 和AD 的延长线相交于点E ，且AD ⊥PD ．(1)求证：AB ＝AE ；(2)当AB ∶BP 为何值时，△ABE 为等边三角形？请说明理由．(1)证明：连结OC ．∵PC 切⊙O 于点C ，∴OC ⊥PD ．又∵AD ⊥PD ，∴AD ∥OC ，∴∠E ＝∠OCB ．∵OC ＝OB ，∴∠OBC ＝∠OCB ，∴∠E ＝∠ABE ，∴AB ＝AE ．(2)解：当AB ∶BP ＝2∶1时，△ABE 为等边三角形．理由：∵AB ＝AE ，∴当∠A ＝60°时，△ABE 为等边三角形．由(1)，知AE ∥OC ，∴∠BOC ＝60°．又∵∠PCO ＝90°，∴∠P ＝30°，∴OC ＝12OP ．∵OB ＝OC ，OP ＝OB ＋BP ，∴BP ＝OB ＝AO ．故当AB ∶BP ＝2∶1时，△ABE 为等边三角形．21．(11分)【2016·浙江衢州中考】如图，AB 为⊙O 的直径，弦CD ⊥AB ，垂足为点P ，直线BF 与AD 的延长线交于点F ，且∠AFB ＝∠ABC ．(1)求证：直线BF 是⊙O 的切线；(2)若CD ＝23，OP ＝1，求线段BF 的长．(1)证明：∵∠AFB ＝∠ABC ，∠ABC ＝∠ADC ，∴∠AFB ＝∠ADC ，∴CD ∥BF ，∴∠APD ＝∠ABF ．∵CD ⊥AB ，∴AB ⊥BF ，∴直线BF 是⊙O 的切线．(2)解：连结OD ．∵CD ⊥AB, ∴PD ＝12CD ＝3．∵OP ＝1，∴OD ＝2．∵∠PAD ＝∠BAF ，∠APD ＝∠ABF ，∴△APD ∽△ABF, ∴AP AB ＝PD BF ，∴34＝3BF ， ∴BF ＝433． 22．(12分)【四川遂宁中考】如图，AB 为⊙O 的直径，直线CD 切⊙O 于点D ，AM ⊥CD 于点M ，BN ⊥CD 于点N ．(1)求证：∠ADC ＝∠ABD ； (2)求证：AD 2＝AM ·AB ；(3)若AM ＝185，sin ∠ABD ＝35，求线段BN 的长．(1)证明：连结OD ．∵直线CD 切⊙O 于点D ，∴∠CDO ＝90°．∵AB 为⊙O 的直径，∴∠ADB ＝90°，∴∠1＋∠2＝∠2＋∠3＝90°，∴∠1＝∠3．∵OB ＝OD ，∴∠3＝∠4，∴∠ADC ＝∠ABD ． (2)证明：∵AM ⊥CD ，∴∠AMD ＝∠ADB ＝90°．又∵∠1＝∠4，∴△ADM ∽△ABD ，∴AM AD ＝AD AB ，∴AD 2＝AM·AB ． (3)解：∵sin ∠ABD ＝35，∴sin ∠1＝35．∵AM ＝185，∴AD ＝6，∴AB ＝10，∴BD ＝AB 2－AD 2＝8．∵BN ⊥CD ，∴∠BND ＝90°，∴∠DBN ＋∠BDN ＝∠1＋∠BDN ＝90°，∴∠DBN ＝∠1，∴sin ∠DBN ＝35，∴DN＝245，∴BN ＝BD 2－DN 2＝325． 23．(15分)观察思考：图1是某种在同一平面内进行传动的机械装置的示意图．其工作原理是：滑块Q 在平直滑道l 上可以左右滑动，在Q 滑动的过程中，连杆PQ 也随之运动，并且PQ 带动连杆OP 绕固定点O 摆动．在摆动过程中，两连杆的接点P 在以OP 为半径的⊙O 上运动．数学兴趣小组为进一步研究其中所蕴含的数学知识，过点O 作OH ⊥l 于点H ，并测得OH ＝4 dm ，PQ ＝3 dm ，OP ＝2 dm ，如图2．解决问题：(1)点Q 与点O 间的最小距离是__4__dm ，点Q 与点O 间的最大距离是__5__dm ，点Q 在l 上滑到最左端的位置与滑到最右端的位置间的距离是__6__dm ；(2)如图3，小明同学说：“当点Q 滑动到点H 的位置时，PQ 与⊙O 是相切的．”你认为他的判断对吗？为什么？(3)①小丽同学发现：“当点P 运动到OH 上时，点P 到l 的距离最小．”事实上，还存在着点P 到l 距离最大的位置，此时，点P 到l 的距离是__3__dm ；②当OP 绕点O 左右摆动时，所扫过的区域为扇形，求这个扇形面积最大时圆心角的度数．解：(2)不对．∵OP ＝2 dm ，PQ ＝3 dm ，OQ ＝4 dm,42≠32＋22，即OQ 2≠PQ 2＋OP 2，∴OP 与PQ 不垂直，∴PQ 与⊙O 不相切．(3)②由①知⊙O 上存在点P 、P ′到l 的距离为3 dm ，此时OP 将不能再向下转动，如图．OP 在绕点O 左右摆动过程中所扫过的最大扇形就是扇形P ′OP ．连结P ′P ，交OH于点D．∵PQ、P′Q′均与l垂直，且PQ＝P′Q′，∴四边形PQQ′P′是矩形，∴OH⊥PP′，PD＝P′D．由OP＝2 dm，OD＝1 dm，得∠DOP＝60°，∴∠POP′＝120°．故所求最大圆心角的度数为120°．第3章综合达标测试卷(满分：100分时间：90分钟)一、选择题(每小题2分，共20分)1．如图所示的几何体的主视图是(A)2．如图所示的几何体的左视图是(A)3．下列四个图形中是三棱柱的表面展开图的是(A)4．电梯间或建筑物的监控器通常都装在天花板的角落里，目的是(D)A．减小盲区，减小视野B．扩大盲区，减小视野B．扩大盲区，扩大视野D．减小盲区，扩大视野5．如图所示是某几何体的三视图，则这个几何体是(D)A．三棱锥B．圆柱C．球D．圆锥6．一个几何体是由若干个相同的立方体组成，其主视图和左视图如图所示，则组成这个几何体的立方体个数不可能是(A)A．15B．13C．11D．57．图中的四个几何体的三视图为以下四组平面图形，其中与③对应的三视图是(A)8．如图是由若干个完全相同的小正方体组成的一个几何体的主视图和俯视图，则组成这个几何体的小正方体的个数是(B)A．3或4B．4或5C．5或6D．6或79．我们常用“y随x的增大而增大(或减小)”来表示两个变量之间的变化关系．有这样一个情境：如图，小王从点A经过路灯C的正下方沿直线走到点B，他与路灯C的距离y 随他与点A之间的距离x的变化而变化．下列函数中y与x之间的变化关系，最有可能与上述情境类似的是(D)A ．y ＝xB ．y ＝x ＋3C ．y ＝3xD ．y ＝(x －3)2＋310．如图，在斜坡的顶部有一铁塔AB ，B 是CD 的中点，CD 是水平的，在阳光的照射下，塔影DE 留在坡面上，已知铁塔底座宽CD ＝12 m ，塔影长DE ＝18 m ，小明和小华的身高都是1．6 m ，同一时刻，小明站在点E 处，影子在坡面上，小华站在平地上，影子也在平地上，两人影长分别为2 m 和1 m ，那么塔高AB 为( A )A ．24 mB ．22 mC ．20 mD ．18 m二、填空题(每小题3分，共24分)11．一根高为5 m 的铁栏杆，在地上的影子长为533 m 时，太阳光线与地面的夹角为__60°__．12．如图，当太阳光与地面上的树影成45°角时，树影投射在墙上的影高CD 等于2米，若树根到墙的距离BC 等于8米，则树高AB ＝__10__米．13．如图，从三个不同的方向看一个各面涂有不同颜色的立方体，那么红色的对面是__橙色__，绿色的对面是__蓝色__．14．【2016·黑龙江鹤岗中考】如图所示的扇形是一个圆锥的侧面展开图，若∠AOB ＝120°，弧AB 的长为12π cm ，则该圆锥的侧面积为__108π__cm 2．15．如图，电影胶片上每一个图片的规格为3．5 cm ×3．5 cm ，放映屏幕的规格为2 m ×2 m ，若放映机的光源S 距胶片20 cm ，那么光源S 距屏幕__807__米时，放映的图像刚好布满整个屏幕．16．如图是一个几何体的三视图，则这个几何体的表面积是__600π_cm2__．(结果保留π)17．如图是由棱长为1的正方体搭成的积木三视图，则图中棱长为1的正方体的个数是__9__．18．如图是一个包装纸盒的三视图(单位：cm)，则制作这样一个纸盒所需纸板的面积是(252＋1083) cm2．三、解答题(共56分)19．(7分)如图是由大小相同的小立方体搭成的几何体．(1)图中共有__5__个小立方体；(2)画出这个几何体的三个视图．解：如图所示．20．(8分)如图，小明和小亮在阳光下玩耍，小亮发现自己刚好踩到了小明的“脑袋”． (1)请画出此时小明和小亮在阳光下的影子；(用线段表示)(2)如果此时附近一棵2 m 高的小树的影长是2．5 m ，请计算影长是2 m 的小亮的身高．第20题(1)略 (2)1．6 m21．(9分)李航想利用太阳光测量楼高．他带着皮尺来到一栋楼下，发现对面墙上有这栋楼的影子，针对这种情况，他设计了一种测量方案，具体测量情况如下：如示意图，李航边移动边观察，发现站到点E 处时，可以使自己落在墙上的影子与这栋楼落在墙上的影子重叠，且高度恰好相同．此时，测得李航落在墙上的影子高度CD ＝1．2 m ，CE ＝0．6 m ，CA ＝30 m(点A 、E 、C 在同一直线上)．已知李航的身高EF 是1．6 m ，请你帮李航求出楼高AB ．解：过点D 作DN ⊥AB ，垂足为N ，交EF 于点M ，∴四边形CDME 、ACDN 是矩形，∴AN ＝ME ＝CD ＝1．2 m ，DN ＝AC ＝30 m ，DM ＝CE ＝0．6 m ，∴MF ＝EF －ME ＝1．6－1．2＝0．4(m)．依题意知，EF ∥AB ，∴△DFM ∽△DBN ，∴DM DN ＝MF BN ，即0.630＝0.4BN ，∴BN＝20 m ，∴AB ＝BN ＋AN ＝20＋1．2＝21．2(m)，即楼高为21．2米．22．(9分)如图所示是一个几何体的三视图，一只蚂蚁要从该几何体的顶点A 处，沿着几何体的表面到和A 相对的顶点B 处吃食物，那么它需要爬行的最短路径的长度是多少？解：该几何体为如图所示的长方体．由图知，蚂蚁有三种方式从点A 爬向点B ，且通过展开该几何体可得到蚂蚁爬行的三种路径长度分别为l 1＝32＋(4＋6)2＝109(cm)；l 2＝42＋(3＋6)2＝97(cm)；l 3＝62＋(3＋4)2＝85(cm)．通过比较，得最短路径长度是85 cm ．23．(11分)如图是一个用来盛爆米花的圆锥形纸杯，纸杯开口圆的直径EF 长为10 cm ，母线OE (OF )长为10 cm ．在母线OF 上的点A 处有一块爆米花残渣，且F A ＝2 cm ，一只苍蝇从杯口的点E 处沿圆锥表面爬行到点A ．(1)求该圆锥形纸杯的侧面积； (2)此苍蝇爬行的最短距离是多少？解：(1)由题意，得底面半径r ＝5 cm ，母线长l ＝10 cm ，则圆锥侧面积为S 侧＝πrl ＝50π(cm 2)． (2)将圆锥沿母线OE 剪开，则得到扇形的圆心角θ＝r l ·360°＝510×360°＝180°．连结AE ，如图所示，即AE 为苍蝇爬行的最短路径，且OA ＝8 cm ，OE ＝10 cm ，θ1＝12θ＝90°．故苍蝇爬行的最短距离AE ＝OA 2＋OE 2＝164＝241(cm)．24．(12分)如图所示，一幢楼房AB 背后有一台阶CD ，台阶每层高0．2米，且AC ＝17．2米，设太阳光线与水平地面的夹角为α，当α＝60°时，测得楼房在地面上的影长AE ＝10米，现有一只小猫睡在台阶上晒太阳．(1)求楼房的高度约为多少米？(结果精确到0．1米) (2)过了一会儿，当α＝45°时，小猫能否晒到太阳？ 解：(1)当α＝60°时，在Rt △ABE 中，∵tan 60°＝AB AE ＝AB10，∴AB ＝10·tan 60°＝103≈17．3(米)．即楼房的高度约为17．3米． (2)当α＝45°时，小猫仍可以晒到太阳．理由如下：假设没有台阶，当α＝45°时，从点B 射下的光线与地面AD 的交点为点F ，与MC 的交点为点H ．∵∠BFA ＝45°，∴tan 45°＝AB AF ＝1，此时的影长AF ＝AB ＝17．3米，∴CF ＝AF －AC ＝17．3－17．2＝0．1(米)，∴CH ＝CF ＝0．1米，∴大楼的影子落在台阶MC 这个侧面上，∴小猫能晒到太阳．期末综合达标测试卷(满分：120分 时间：120分钟)一、选择题(每小题3分，共30分)1．在△ABC 中，∠C ＝90°，a 、b 、c 分别是∠A 、∠B 、∠C 的对边，则有( C ) A ．b ＝a tan A B ．b ＝c sin A C ．a ＝c sin AD ．c ＝a sin A2．【2016·湖南湘西中考】在Rt △ABC 中，∠C ＝90°，BC ＝3 cm ，AC ＝4 cm ，以点C 为圆心，以2．5 cm 为半径画圆，则⊙C 与直线AB 的位置关系是( A )A ．相交B ．相切C ．相离D ．不能确定3．【2016·浙江宁波中考】如图所示的几何体的主视图为( B )4．如图是一个几何体的三视图，已知主视图和左视图都是边长为2的等边三角形，则这个几何体的全面积为( B )A ．2πB ．3πC ．23πD ．(1＋23)π5．如图，正方形网格中，∠AOB 如图放置，则cos ∠AOB 的值为( D )A ．255B ．2C ．12D ．556．如图，为了测量河两岸A 、B 两点的距离，在与AB 垂直方向的点C 处测得AC ＝a ，∠ACB ＝α，则AB 等于( B )A ．a ·sin αB ．a ·tan αC ．a ·cos αD ．atan α7．已知等腰直角三角形外接圆半径为5，则内切圆半径为( C ) A ．52＋5 B ．102－5 C ．52－5D ．102－108．如图，P 为⊙O 外一点，P A 切⊙O 于点A ，且OP ＝5，P A ＝4，则sin ∠APO 等于( B )A ．45B ．35C ．43D ．349．如图，王华晚上由路灯A 下的B 处走到C 处时，测得影子CD 的长为1 m ，继续往前走3 m 到达E 处时，测得影子EF 的长为2 m ．已知王华的身高是1．5 m ，则路灯A 的高度AB 等于( D )A ．4．5 mB ．6 mC ．7．2 mD ．7．5 m10．【2016·山东潍坊中考】如图，在平面直角坐标系中，⊙M 与x 轴相切于点A (8,0)，与y 轴分别交于点B (0,4)和点C (0,16)，则圆心M 到坐标原点O 的距离是( D )A ．10B ．82C ．413D ．241二、填空题(每小题4分，共32分)11．计算：－2－1＋(π－3．142)0＋2cos 230°＝__2__．12．在△ABC 中，∠C ＝90°，斜边上的中线CD ＝6，sin A ＝13，则S △ABC ＝__162__． 13．【2016·湖南株洲中考】如图，△ABC 的内切圆的三个切点分别为D 、E 、F ，∠A ＝75°，∠B ＝45°，则圆心角∠EOF ＝ __120__度．14．如图∠MAB ＝30°，P 为AB 上的点，且AP ＝6，圆P 与AM 相切，则圆P 的半径为__3__．15．如图是由几个小立方体所搭成的几何体从上方看到的图形，小正方形中的数字表示在该位置小立方体的个数，已知小立方体边长为1，则这个几何体的表面积为__34__．16．如图，小华剪了两条宽为1的纸条，交叉叠放在一起，且它们较小的交角为60°，则它们重叠部分的面积为__233__．17．如图，圆锥的高是215 cm ，底面半径是2 cm ，A 是底面圆周上一点，从点A 出发绕侧面一周，再回到点A 的最短路线的长是__82cm__．18．如图，已知⊙O 是以数轴的原点O 为圆心，半径为1的圆，∠AOB ＝45°，点P 在数轴上运动，若过点P 且与OA 平行的直线与⊙O 有公共点，设OP ＝x (x ≥0)，则x 的取值范围是__0≤x ≤2__．三、解答题(共58分)19．(6分)计算：(1)9－|cos 60°－1|＋(2)－1－(2017－π)0；解：原式＝3－⎝⎛⎭⎫1－12＋22－1＝3－1＋12＋22－1＝3＋22． (2)2－1＋12－4sin 60°－()－30． 解：原式＝12＋23－4×32－1＝12＋23－23－1＝－12． 20．(6分)如图是一个由若干个棱长相等的正方体构成的几何体的三视图．(1)请写出构成这个几何体的正方体个数；(2)请根据图中所标的尺寸，计算这个几何体的表面积．解：(1)构成这个几何体的正方体有5个．(2)S 表＝5×6a 2－10a 2＝20a 2．21．(6分)如图，防洪大堤的横断面是梯形ABCD ，其中AD ∥BC ，坡长AB ＝10 m ，坡角∠2＝60°，汛期来临前对其进行了加固，改造后的背水面坡角∠1＝45°．(1)试求出防洪大堤的横断面的高度； (2)请求出改造后的坡长AE ．解：(1)过点A 作AF ⊥BC 于点F ．在Rt △ABF 中，∠ABF ＝60°，则AF ＝ABsin 60°＝5 3 m ，即防洪大堤的横断面的高度为5 3 m ． (2)在Rt △AEF 中，∵∠E ＝45°，AF＝5 3 m ，∴AE ＝AF sin 45°＝5322＝56(m)，即改造后的坡长AE 为5 6 m ． 22．(6分)如图，AB 是⊙O 的直径，点F 、C 是⊙O 上两点，且AF ︵ ＝FC ︵ ＝CB ︵，连结AC 、AF ，过点C 作CD ⊥AF 交AF 延长线于点D ．(1)求证：CD 是⊙O 的切线；(2)若CD ＝23，求⊙O 的半径．(1)证明：如图，连结OC ．∵FC ︵ ＝CB ︵ ，∴∠FAC ＝∠BAC ． ∵OA ＝OC ，∴∠OAC ＝∠OCA ，∴∠FAC ＝∠OCA ，∴OC ∥AF ．∵CD ⊥AF ，∴OC ⊥CD ，∴CD 是⊙O 的切线．(2)解：如图，连结BC ．∵AB 为直径，∴∠ACB ＝90°．∵AF ︵ ＝FC ︵ ＝CB ︵，∴∠BOC ＝13×180°＝60°，∴∠BAC ＝30°，∴∠DAC ＝30°．在Rt △ADC 中，∵∠DAC ＝30°，CD ＝23，∴AC ＝2CD ＝43．在Rt △ACB 中，∵∠BAC ＝30°，∴BC ＝33AC ＝33×43＝4，∴AB ＝2BC ＝8，∴⊙O 的半径为4．23．(8分)如图，从地面上的点A 看一山坡上的电线杆PQ ，测得杆顶端点P 的仰角是45°，向前走9 m 到达点B ，测得杆顶端点P 和杆底端点Q 的仰角分别是60°和30°．(1)求∠BPQ 的度数；(2)求该电线杆PQ 的高度．(结果保留根号)解：(1)如图，延长PQ 交直线AB 于点E ．由题意，可知∠BEP ＝90°，∠PBE ＝60°，∠QBE ＝30°，∴∠BPQ ＝90°－∠PBE ＝90°－60°＝30°． (2)设PE ＝x 米． 在Rt △APE 中，∵∠A ＝45°，∴AE ＝PE ＝x 米． 在Rt △BPE 中，∵∠BPE ＝30°，∴BE ＝33PE ＝33x 米．∵AB ＝AE －BE ＝9米，∴x －33x ＝9，解得x ＝27＋932．则BE ＝93＋92米．在Rt △BEQ 中，∵∠QBE ＝30°，∴QE ＝33BE ＝9＋332米．∴PQ ＝PE －QE ＝27＋932－9＋332＝(9＋33)(米)．即电线杆PQ 的高度为(9＋33)米．24．(8分)如图，O 为平面直角坐标系的原点，半径为1的⊙B 经过点O ，且与x 、y 轴分别交于A 、C 两点，点A 的坐标为(－3，0)，AC 的延长线与⊙B 的切线OD 交于点D ，A 、B 、C 三点在同一条直线上．(1)求OC 的长和∠CAO 的度数；(2)求过点D 的反比例函数的表达式．解：(1)在Rt △ACO 中，∵AC ＝2，OA ＝3，∴OC ＝1，∴sin ∠CAO ＝OC AC ＝12，即∠CAO ＝30°． (2)由(1)，知OC ＝1，∴C(0,1)．又∵∠CAO ＝30°，∴直线AC 的斜率为33，∴直线AC 的解析式为y ＝33x ＋1．① 连结OB ．∵AB ＝OB ，∴∠BOA ＝30°．又∵OD 切⊙B 于点O ，∴∠BOD ＝90°，∴直线OD 的斜率为tan 60°＝3，∴直线OD 的解析式为y ＝3x ．② 由①②，得点D ⎝⎛⎭⎫32，32．设过点D 的反比例函数的解析式为y ＝k x ，则k ＝32×32＝334，∴过点D 的反比例函数的解析式为y ＝334x (x>0)． 25．(8分)如图，在直角坐标系中，以M (3,0)为圆心的⊙M 交x 轴负半轴于点A ，交x 轴正半轴于点B ，交y 轴于C 、D 两点．(1)若点C 的坐标为(0,4)，求点A 的坐标；(2)在(1)的条件下，在⊙M 上，是否存在点P ，使∠CPM ＝45°？若存在，求出满足条件的点P ；(3)过点C 作⊙M 的切线CE ，过点A 作AN ⊥CE 于点F ，交⊙M 于点N ，当⊙M 的半径大小发生变化时，AN 的长度是否变化？若变化，求出变化范围；若不变，证明并求值．解：(1)连结CM ．∵M(3,0)、C(0,4)，∴OM ＝3，OC ＝4．在Rt △COM 中，由勾股定理，得CM ＝OM 2＋OC 2＝5，即⊙M 的半径为5，∴MA ＝5．∵M(3,0)，∴A(－2,0)．(2)假设存在点P(x ，y)满足题意，则△CMP 为等腰直角三角形，且CM ＝PM ＝5，故CP ＝52．根据题意，可得⎩⎪⎨⎪⎧ (x －3)2＋y 2＝25，x 2＋(y －4)2＝50， 解得⎩⎪⎨⎪⎧ x 1＝7，y 1＝3， ⎩⎪⎨⎪⎧x 2＝－1，y 2＝－3， 即点P 1(7,3)、P 2(－1，－3)满足题意．(3)AN 的长不变．证明：如图，过点M 作MH ⊥AN 于点H ，则AH ＝NH ．易证△AMH ≌△MCO ，∴AH ＝OM ＝3，∴AN ＝2AH ＝6．26．(10分)如图，已知直线y ＝－m (x －4)(m ＞0)与x 轴、y 轴分别交于A 、B 两点，以OA 为直径作半圆，圆心为点C ．过点A 作x 轴的垂线AT ，M 是线段OB 上一动点(与点O 不重合)，过点M 作半圆的切线交直线AT 于点N ，交AB 于点F ，切点为点P ．连结CN 、CM ．(1)求证：∠MCN ＝90°；(2)设OM ＝x ，AN ＝y ，求y 关于x 的函数解析式；(3)若OM ＝1，则当m 为何值时，直线AB 恰好平分梯形OMNA 的面积．(1)证明：连结OP 、CP ．∵BM ⊥OC ，∴BM 切⊙C 于点O ．又∵MP 切⊙C 于点P ， ∴MO ＝MP ．又∵PC ＝OC ，MC ＝MC ，∴△MCO ≌△MCP ，∴∠MCO ＝∠MCP ．同理，∠NCP ＝∠NCA ，∴∠MCP ＋∠NCP ＝90°，即∠MCN ＝90°．(2)解：∵点A 为直线y ＝－m(x －4)(m>0)与x 轴的交点，∴A(4,0)，∴OA ＝4，OC ＝CP ＝AC ＝2．在Rt △MCO 中，MC 2＝OM 2＋OC 2＝x 2＋4．在Rt △ACN 中，NC 2＝AN 2＋AC 2＝y 2＋4．由(1)，可知△MCO ≌△MCP ，△ACN ≌△PCN ，∴MP ＝OM ＝x ，NP ＝AN ＝y ，∴MN ＝MP ＋PN ＝x ＋y ．在Rt △MCN 中，MN 2＝MC 2＋NC 2，即(x ＋y)2＝x 2＋y 2＋8，∴y ＝4x(x>0)． (3)解：∵OM ＝1，∴AN ＝4，∴S 梯形OMNA ＝10，∴△ANF 的面积为5．过点F 作FG ⊥AN 于点G ，则12FG·AN ＝5，∴FG ＝52，∴点F 的横坐标为4－52＝32．又∵M(0,1)、N(4,4)，∴直线MN 的解析式为y ＝34x ＋1．∵点F 在直线MN 上，∴点F 的纵坐标为34×32＋1＝178，∴F ⎝⎛⎭⎫32，178．又∵点F 在直线y ＝－m(x －4)上，∴178＝－m ⎝⎛⎭⎫32－4．解得m ＝1720．本课教学反思本节课主要采用过程教案法训练学生的听说读写。
新外研社版高中英语必修三Unit4Amazing Art整单元完整教学设计
新外研社版高中英语必修三Unit 4 Amazing artStarting out &Understanding ideas教学设计教学目标：By the end of this period,students will be able to:1.Watch a video and extract the key information from it;2.Master the language points in the text;prehend this passage by grasping key information and details;4.Improve critical thinking skills and establish proper artistic values.教学重难点：1.Instruct students to understand the basic information about the art pieces introduced in the text.2.Guide students in appreciating outstanding works of art from China and abroad.教学方法：P-W-P教学法，Task-based Teaching Method教学设计：Step ⅠLead-inActivity1Watch a videoWatch the video and answer the questions.1.What cities are introduced in the video?2.What is each city famous for in the world of art?Suggested answers:1.Florence,New York City and Beijing.2.Florence is famous for its long history of art.New York City is famous for modern art.Beijing is famous for mixing traditional and modern Chinese art.Activity2Complete the quizWork in pairs and complete the quiz.Try to guess if you are not sure of the answers.1.Where is the Louvre Museum?a.In London.b.In Paris.c.In Berlin.2.When was the original castle of the Louvre built?a.The 12th century.b.The 15th century.c.The 18th century.3.How many works of art are there in its collection?a.Around 180,000.b.Around 400,000.c.Around 480,000.4.Which work of art is among the “Big Three” attractions of the Louvre?a.The Code of Hammurabi.b.Liberty Leading the People.c.Venus de Milo.Suggested answers:1.b2.a3.b4.cStep ⅠWhile-readingActivity1Read for the main ideaChoose three tags that best describe the main idea of the passage and give reasons for your choices.Louvre art Mona Lisa exhibition museum selfie fantastic tour guide history live broadcastSuggested answers:Students’ own answers.Activity2Language points and translation1.Her head and arms are missing,but you can imagine her holding her arms uphigh,celebrating the result of an ancient battle.【翻译】虽然头部和手臂已经遗失了,但你们仍然可以想象她正高举双臂,庆祝一场古老战役的胜利。