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新人教版高中英语必修2Unit 5 Music-Reading and Thinking教案一
This section focuses on "learning about experiencing music Online". This virtual choir is a new form of music performance. Members from all over the world don't need to love to come to a place. Instead, they use the new technology to model the various parts and wonderful virtual harmony group of music in the family. Students need to understand the main meaning of each paragraph. Finding topic sentences is an important way to understand the general idea of a paragraph. After the topic sentence, it is usually the detail sentence that supports and explains the topic sentence. Some paragraphs have obvious subject sentences, for example, the first sentence of the second paragraph is the subject sentence of the paragraph, and the following sentenceStudents need to pay attention to the topic sentences and key sentences, and then pay attention to how the sentences after the meaning explain, explain and support the topic sentences or key sentences before.1.Guide students to learn about experiencing music online2.Guide students to scan and circle the information in the text.3.Guide students to find the numbers and dates to fill in the timeline.4.Guide students to learn more about music by completing the sentences with the correct forms of the words and phrases. And then make a mind map about the outline of the passage.1. Guide students to pay attention to reading strategies, such as prediction, self-questioning and scanning.2. Help students sort out the main meaning of each paragraph and understand the narrative characteristics of "timeline” in illustrative style.3. Lead students to understand the changes that have been caused by the Internet.
新人教版高中英语必修2Unit 5 Music-Reading for Writing教案二
The Internet celebrity Gao Yifeng. Years ago, he owned 5 companies and the staffs over 1,000, but during the economy crisis, he became nothing but debt. He was so worried that his hair became white overnight. There was a time when he wanted to killed himself. But after listening to the song Start Over by Liu Huan, he decided to cheer himself up. He started a steamed bun shop and gradually became a national chain shops. Now he became successful again.Walter Haddon said, “Music is the medicine of a troubled mind.” Music contains such a pleasant and inspiring force. Music gave him courage and bravery. When he listened to the song, it made his spirit fly like a kite in the wind. Music gave him strength and brought him relief. It was the rock I leant on to become strong and to get through those hard times. I hope none of us have to go through the same kind of suffering that he did. At the same time, we all go through various periods when we feel sad or alone. During those times, music can help us in the same way that it helped him. I hope we all will somehow begin to treasure music and make it a part of our life. Thank you for your listening !5.Revise your writing each other.Does he/she explain how music has changed his/her/someone else’s life?Are some of the rhetorical devices included and used properly ?Does he/she talk about how music makes him/her/someone feel?Is the first word in each sentences capitalised?Does he/she use correct punctuation ?
新人教版高中英语选修1Unit 2 Looking into the Future教案
【设计意图】以“新科技是一把双刃剑”为主题开展讨论活动。这个话题比较大，所以给了一定的限制，首先需要以智能家居为例来阐述科技发展对未来生活产生的影响，然后列举其优点和缺点，最后就以上现象发表自己的观点。这个活动是对整个文本的创意性总结与意义的升华，留给学生一定的想象空间，学生借此机会可以运用文本内容和语言表达自己对科技发展的看法和态度。Assignments:1. Finish Exercise 4 on Page 15 of the textbook.A smart home is one that integrated computers into the structure of the building itself. In this way, many of the things that we now do ourselves become automatic. For example, the smart home could control the air conditioning and lights so that you would no longer have to turn switches on and off, and so that your home would be more energy-efficient. The smart home could also monitor itself to make sure that everything is working as it should, and send you warnings if there is a problem. Such smart homes could even be programmed to detect your health problems, and then give you reasonable advice as to the food you should eat or if you should see a doctor. So, in a sense, smart homes will lead us to living smarter lives.2.Create a smart function for your home, and share your creation in the next period.
新人教版高中英语选修3Unit 2 Healthy Lifestyle教案
Activity 4: Figuring out the structure and the writing purpose 本活动为实现课时目标2。 1.Read Paragraph 6 and think about its main idea and the writer’s writing purpose. Q1: If you were the author, how would you end your article? “For young people, there is plenty of time to change bad habits. However, there is no “magic pill” or delete button that will help you; you have to think about your bad habits and decide on some changes. You have the power to build a happy and healthy life full of good habits!” Q2: What is Paragraph 6 mainly about? (Possible answer: to appeal to young people including teenagers to change bad habits and live a happy and healthy life.) 2.Think about the writer’s writing purpose and share opinions. Q1: What is the writing purpose? Work in pairs and figure it out. (Possible answer: On the one hand, the passage is written to help teenagers change their bad habits and live a healthy lifestyle. On the other hand, it provides us with a scientific way to identify and analyse our problems objectively, thus strengthening our resolve to tackle the seemingly common yet tough problems in our lives.) 【设计意图】 步骤1旨在预测和验证文章最后一段主要内容，梳理完整的语篇结构，步骤2旨在思考和讨论作者的写作目的。教师也可根据学生课堂反应情况融入对语篇人称多次转换的思考。
新人教版高中英语选修4Unit 2 Iconic Attractions教案
帮助学生通过讨论与对主题的提升，反思自己的旅游方式，以便做出更优化的安排，在今后的旅程中有更多的收益。 Activity 2: Further discussion of the 6 elements above and supplement of more background knowledge 本活动为实现课时教学目标2。 1.Target Q: The writer’s clear target of traveling, meeting the people and experiencing the culture, is closely related to his major in social studies. Then what is social studies? Social studies is a part of a school or college curriculum concerned with the study of social relationships and the functioning of society and usually made up of courses in history, government, economics, civics, sociology, geography, and anthropology. （Dictionary by Merriam-Webster） Reflection: When you go out to travel, what targets do you usually have in mind? 2.Research Q: Suppose you are traveling to Hangzhou during the school holidays, how will you do research on the city? (surf the internet, read books or travel brochures, consult friends, ...) What information will you be interested to know? (location, iconic sites, local cuisines, interesting customs, shopping malls ...) 3.Abandonment To make the most of time, we have to learn to abandon so that we can accomplish our plan. What will you be interested in doing if you go to Hangzhou if you have a week’s time? What if you only have 2 days? 4~5. Venturing & Experiencing Q: What did he venture to do during the trip? What new experiences did he have? In Sydney: attend his first open-air barbecue, enjoy many different but yummy meals In Catherine: observe the life and customs of the aborigines appreciate their music & try the musical instruments: the didgeridoo
新人教版高中英语必修1Unit 2 Travelling Around–Listening and Speaking教案
无论她说什么都不会对我们的安排有影响。Answers: for, arrangement3) Parents arrange everything for their children and spare no effort to pave the way for their success.父母为孩子安排好一切，不遗余力地为他们的成功铺路。4. extremely adv 极其，非常extreme adj 非常的1) Mary found it extremely difficult to get a job.2) I’m extremely sorry to have troubled you.Answers:玛丽发现找工作极其困难。给你添了麻烦，我十分抱歉。3) It had white-painted tunnels and bright red carriages, and proved _________ (extreme) popular with the public.它有白色的隧道和明亮的红色车厢，结果证明它非常受大众的欢迎。Answers: extremelyExercises1. I am continuing to apply_______ jobs though I have failed several times.2. All this had an _______ (extremely) bad effect on the criminal justice system.3. The invention would have wide ______ (apply) in industry.4. She’s happy with her unusual living _________ (arrange).5. I was banging so loudly that I’m ___________ (amaze) that they didn’t hear me.6. You haven’t changed at all you still look ___________ (exact) the same.7. “Was it what you expected?” “Yes, _________ (definite).”8. He was looking forward to______ (work) with the newPrime Minister. Answers: for extreme application arrangement amazed exactly definitely looking单句写作：1. _______________ (你要说些什么) when you get on the platform to accept the reward?2. Since_____________________(我们为这些事情做好了准备), we have nothing to worry about.
新人教版高中英语必修1Unit 2 Travelling Around-Reading and Thinking教案
Good expressions that students can choose to use: help the travelers choose which tour to take1. In my opinion, you could/might choose…, because you prefer to…2. …could be a perfect choice for you, for…3. As far as I am concerned, you would enjoy…, for…4. …would probably suit you, because you enjoy/love/hate doing…Step 5 Passage ConsolidationLanguage appreciation:1. You can then spend three days exploring the rainforest with a local guide and enjoying the plants and animals unique to the rainforest. 在接下来的三天里，您可以在当地导游的陪同下，深入雨林进行探索，欣赏雨林特有的动植物。本句主体结构为spend some time doing sth. 2. Inca builders cut stones to exact sizes so that nothing was needed to hold walls together other than the perfect fit of the stones. 印加的建筑工人将石头切割成精确的尺寸，仅仅凭着石头间的完美契合，即可稳固墙体。本句为so that引导的结果状语从句。nothing与the perfect fit为并列成分; other than在句中意为“除了”。Step 6 HomeworkSuppose you will travel to Peru, write a short essay about your three-day tour plan.
新人教版高中英语必修1Unit 2 Travelling Around-Reading for Writing教案
Is there a clear purpose for the trip? :Does each paragraph have a clear main idea? Does the writer use the present continuous tense for future plans?Does the writer use commas, stops, and question marks correctly? Are all the words spelt correctly?Are all the proper nouns capitalized?Revise your draft according to your partner's comments.Step 5:The summary of how to write a travel plan.旅游计划是一种常见的应用文写作。旅游可分为观光游、文化游、美食游及探险游等不同类型，因此旅游计划也要根据不同的旅游目的进行设计。常规的旅游计划需要明确以下几个方面的问题:Travel planWhen will you leave for？ Where is your the destination?How will you get there?What will you do there?How long will you there?Is there a clear purpose for the trip? 为了提升旅行计划的层级，还需注意以下几个方面的问题:1.每段是否有明确清晰的主题;2.用一般现在时代替一般将来时；3.用更高级的形容词词汇。例如:表达“好”时，不要总用“nice”,我们还可以用“smart, clean, excellent, exciting, beautiful, wonderful, clever, famous, grand”等表达更具有指向性的词汇；4.用更高级的动词词汇。比如:我们可以用“seem stand, lie .get stay, remain, look . sound, become . keep, grow”等代替"be";
新人教版高中英语必修2Unit 1 Cultural Heritage-Discovering Useful Structure教案一
This teaching period mainly deals with grammar “restrictive relative clauses.” To begin with, teachers should lead students to revise what they have learned about the relative pronouns and relative adverbs. And then, teachers move on to stress more special cases concerning this grammar, such as the “preposition+ relative pronouns which and whom” and cases where we can omit the relative pronouns. This period carries considerable significance to the cultivation of students’ writing competence and lays a solid foundation for the basic appreciation of language beauty. The teacher is expected to enable students to master this period thoroughly and consolidate the knowledge by doing some exercises. 1. Guide students to review the basic usages of relative pronouns and adverbs of attributive clauses.2. Lead students to learn to use some special cases concerning restrictive relative clauses flexibly.2. Enable students to use the basic phrases structures flexibly.3. Strengthen students’ great interest in grammar learning.1. Help students to appreciate the function of relative pronouns and adverbs of attributive clauses in a sentence2. Instruct students to write essays using the proper relative pronouns and adverbs of attributive clauses.本节语法思考：定语从句在复合句中的作用是什么？ 关系词有哪些？定语从句在复合句中的作用相当于形容词，它在句中作定语修饰名词或代词。他们在先行词和定语从句之间起到联系作用，同时在意义上代表先行词并在定语从句中担任一个成分。被定语从句所修饰的词称先行词，定语从句一般放在先行词的后面。
新人教版高中英语必修2Unit 1 Cultural Heritage-Reading For Writing教案
This report is short, concise and has typical news content and language features. The title uses the verb phrases, embodying the characteristics of being concise and general. The introduction is the first two sentences in the first paragraph, describing the general situation of the cultural heritage protection project, including time, place, characters, events and other news elements, so that readers can see the main points of the news report at a glance. The main body is the second and third paragraphs, which report the important historical and cultural value of Mogao Grottoes and the production of Mogao Grottoes Material digital photos, which are of great significance to the inheritance of historical culture and the promotion of international cultural understanding, exchange and cooperation. Direct citation is used in the report, as well as background introduction and other news writing techniques.1. Get students to have a good understanding of some features about a news report by reading the text.2. Instruct students to write a summary about a news report properly using some newly acquired writing skills in this period.3. Develop students’ writing and cooperating abilities.4. Strengthen students’ great interest in writing discourses.1. Stimulate students to have a good understanding of how to a summary about a news report 2. Cultivate students to write a news report properly and concisely.Step 1: Lead in Do you think it is necessary for us to circulate our cultural heritage to the world? Why or why not?Do we need to learn more about other countries’ cultural heritage? Why or why not?Step 2: Read to discover details concerning the main body of the news report.
新人教版高中英语必修2Unit 3 The Internet-Discovering Useful Structure教案一
This unit is about the Internet, which has a great influence to our humans and our lives. During the Listening & Speaking & Talking and Reading and Thinking section, the influence in examples has been shown. Thus, use the Present Perfect Tense is appropriate. However, in order to show the justice or weaken the doer of the behavior/action, it’s better to use the Present Perfect Passive Voice than the Present Perfect Tense. Besides, having learned to use the Present Perfect Passive Voice, students can beautify their language in their writing. 1. Learn the structure of the Present Perfect Passive Voice and its functions. 2. Learn to change the sentences with the Present Perfect Passive Voice into the sentences with the Present Perfect Passive Voice. 3. Learn to write sentences with the Present Perfect Passive Voice flexibly according to the context. 1. Learn the structure of the Present Perfect Passive Voice and its functions. 2. Learn to change the sentences with the Present Perfect Passive Voice into the sentences with the Present Perfect Passive Voice. 3. Learn to write sentences with the Present Perfect Passive Voice flexibly according to the context. Step 1 Observe the following sentences, then change the sentences into passive voice.He has been selected to take part in the sports meeting．(肯定句)他已被挑选出来参加运动会。The ink has not been removed from his overcoat．(否定句)墨迹还没有从他外套上去掉。
新人教版高中英语必修2Unit 4 History and Traditions-Discovering Useful Structure教案一
Step 5 Practice一、完成下列句子。1. Judy and I _______________（把车停下来(park)）in an underground car Park near Trafalgar Square, where we could ______________________(让我们的车充电（charge)).2. When we finally reached the service desk to ask for audio guides, we heard it ___________ that there were no audio guides____________(留下，剩下）.3. We__________________________（发现自己对...很惊讶）the large number of visitors and the amount of noise at the entrance of the National Gallery.4. Judy ____________________(眼神专注于） Van Gogh’s Sunflowers. It was hard to approach the painting as there were so many people around.5. She ____________________(把这幅画的复制品装箱（box)） to ensure that it was delivered safely.答案：1.had our car parked get our car battery charged 2. announced left 3. found ourselves very surprised 4. had her eyes fixed on 5. had a copy of the painting boxed二、用过去分词对下列句子进行改写。1. Loch Ness was surrounded by beautiful natural landscape, which made it look amazing.2. Carl and his friend stayed with a generous family who offered them bread with butter and honey that was homemade.3. The family’s ancestors once attended to soldiers who were wounded in the First World War.4. The young people were attracted by the legend of Loch Ness. They watched over the lake with their cameras and binoculars, which were positioned on the hill.答案：1. Loch Ness surrounded by beautiful natural landscape looks amazing.2. Carl and his friends stayed with a generous family who offered them homemade bread with butter and honey.3. The family’s ancestors once attended to wounded soldiers in the First World War.4. The young people attracted by the legend of Loch Ness watched over the lake with their cameras and binoculars positioned on the hill.
新人教版高中英语必修2Unit 4 History and Traditions-Listening＆Speaking＆Talking教案一
This unit is about history and traditions. From the opening page, we can know that this unit will introduce the history and traditions around the world. As Marcus Garvey says “A people without the knowledge of their past history, origin and culture is like a tree without roots”, it is important for students to realize the importance and value of knowing the history and traditions and their further meanings. And this part ( listening and speaking ) is divided into two parts: Part A---share views on historic sites, Part B ---talk about a visit to a historic tourist destination. By talking with a foreigner, the speakers introduce the historic attractions and their cultures. Part A is that William, a British student, who was going to visit the Confucius Temple and a Chinese student, Xiao Kong, who was going to the Confucius Temple to meet with the members of the research group, went together and exchanged their views on the Confucius Temple, Confucius, Confucius' descendants and Confucius' educational thoughts. Part B is a conversation between Xiao Yan, a youth hostel receptionist and Paul, a backpacker about the feelings and experience after visiting the Chinese famous tourist attraction Pingyao.1. Guide students to understand the content of listening texts in terms of the whole and key details; 2. Cultivate students' ability to guess the meaning of words in listening; discuss with their peers how to talk about historic spots and great person.3. Instruct students to use functional sentences of showing one’s excitement, surprise and disappointment.1. Guide students to understand the content of listening texts in terms of the whole and key details; 2. Cultivate students' ability to discuss with their peers the related topics.3. Enable students to use the functional items of showing one’s excitement, surprise and disappointment.
新人教版高中英语必修2Unit 4 History and Traditions-Reading and Thinking教案二
Step 5 While reading---Task 3Read the text again and answer the following questions.Q1: How many countries does the UK consist of ?4 Q2: What are the four countries of the United Kingdom?England, Wales, Scotland and Northern Ireland Q3: Which two were the first to be joined together ?England and WalesQ4: What are the two chief advantages of studying the history of a country ?The first one is to help you understand more about the country and its traditions.The second one is to make visiting it more enjoyable.Q5: What’s the author’s attitude towards studying the history ?Supportive/positiveStep 6 Post reading---Retell the textThe United Kingdom, Great Britain, Britain, England—many people are confused by (1)_____ these different names mean. In the 16th century, the nearby country of Wales (2) __________(join) to the Kingdom of England. In the 19 th century, the Kingdom of Ireland was added to create the United Kingdom of Great Britain and Ireland. Finally, the southern part of Ireland (3) ______ (break) away from the UK, which resulted in the full name we have today. However, most people just use the (4)_________(shorten) name: the UK. The four countries (5)__________ belong to the United Kingdom work together in some areas. There were four sets of invaders and the last group were the Normans. They had castles (6)_________(build) all around England and made changes (7)__________ the legal system. Studying the history of the country will make your visit much more (8)_________(enjoy). The capital city London is (9)___ ancient port city that has a history (10)______(date) back to Roman times. 1. what 2.was joined 3.broke 4.shortened 5.that 6. built 7.to 8.enjoyable 9.an 10.dating Step 6 Homework
新人教版高中英语必修2Unit 4 History and Traditions-Reading and Thinking教案一
Features of languages1．Finally, in the 20th century, the southern part of Ireland broke away from the UK, which resulted in the full name we have today: the United Kingdom of Great Britain and Northern Ireland．该句是一个复合句。该句主句为：the southern part of Ireland broke away from the UK；which resulted in the full name we have today为which引导的定语从句代指前面整句话的内容，we have today为定语从句修饰先行词name。译文：最后，在20世纪，爱尔兰南部脱离英国，这导致了我们今天有的英国的全名：大不列颠及北爱尔兰联合王国。2．Almost everywhere you go in the UK, you will be surrounded by evidence of four different groups of people who took over at different times throughout history．该句是一个复合句。该句主句为：you will be surrounded by evidence of four different groups of people；其中Almost everywhere you go in the UK为让步状语从句； who took over at different times throughout history为定语从句修饰先行词people。译文：几乎无论你走到英国的任何地方，你都会发现历史上有四种不同的人在不同的时期统治过英国。3．The capital city London is a great place to start, as it is an ancient port city that has a history dating all the way back to Roman times．该句是一个复合句。该句主句为：The capital city London is a great place to start; as it is an ancient port city that has a history dating all the way back to Roman times．为原因状语从句；dating all the way back to Roman times为现在分词短语作定语修饰history。
新人教版高中英语必修2Unit 5 Music-Listening＆Speaking＆Talking教案
choir memberspeople to run food stands people to sell festival ticketspeople to sell music CDspeople to set up equipmentmusical performersStep 2: Listen to the announcement again and answer the questions. ? 1. What kind of songs will Grace Davis sing at the festival?? 2. Who can try out as a performer?? 3. What can those who think they do not have musical talent do?? 4. How can students volunteer to take part?? Talking about preferences:? Would you prefer doing ..?? What would you prefer to do?? Would you rather do .... or ….?? What would you rather do?? I'd prefer .... to ..? I'd rather have ... than .. Step 3: Speaking ProjectWork in groups. Role-play the conversation or make a new one.? Debbie: Where have you been? You missed the announcement about the music festival.? John: I was at the doctor's office. Music festival?? Frank: Yes, it's going to be next month on the school sports field. John, you can play the piano. How about playing it at the festival?? John: Well, I'd rather play the violin. I can play Liang Zhu.? Frank: Wow! Sounds good. What about you, Debbie? ? Debbie: Actually, I don't have much musical ability. I'd prefer just to help out with the crowds.? Frank: You can sell tickets or work at a food stand.? John: So can I assume that the aim of the festival is to raise money?? Debbie: Yes. All of the money will go to charity.
新人教版高中英语必修2Unit 5 Music-Listening and Speaking教案
This lesson is about music. Students can classify the types of music through the instruments and its sound and can talk about their preferences about music, even join some activities and play a role in them according to their musical talents. On the basis, they are guided to use the languages to express their preferences and some plosive sounds and their rules.1. Classify the music types through the instruments and its sound.2. Listen and understand what the speakers’ preferences are and the reasons; talk about their own preferences and give their own reasons, using these sentences: “What kind of music do you like? And why? “ “Because it makes/gives me energy/peaceful.../touches my heart...”.3. Learn some plosives and the rules.4. Join some activities and play a role in them according to the talents. 1. Listen and understand what the speakers’ preferences are and the reasons;2. talk about their own preferences and give their own reasons, using these sentences: “What kind of music do you like? And why? “ “Because it makes/gives me energy/peaceful.../touches my heart...”.3. Learn some plosives and incomplete plosives and its rules.Step 1 Lead inPoint at the pictures on P50 and ask Q1: What are the people doing in the pictures below?Q2: What kind of music they are?Then play the MP3s one by oneStep 2 ListeningTask 1: A reporter from the school newspaper is interviewing students about music. Listen to the interviews. Draw lines between the words to make complete sentences. Some words will not be used.
新人教版高中英语必修2Unit 5 Music-Reading For Writing教案一
(4)Now we have heard a number of outstanding speeches ... 我们已经聆听了许多精彩的发言……(5)Because we wanted the nations of the world, working together, to deal with ... 因为我们希望全世界各国团结起来去应对……(6)And if we do not act ... 如果我们不采取行动……(7)Now, I share the concerns that have been expressed ... 我也同意对于……表达的担心(8)Let us show the world that by working together we can ... 让我们告诉全世界，通过一起努力我们可以……(9)It is now time for us to ... 是时候我们……(10)And I have always wished that ... 我一直希望……(11)Thank you for letting me share this day with me.感谢你们和我共度这一天。实践演练：假如你是高中生李华，你校将举办一次以“音乐”为主题的演讲比赛，请你按照主题，写下你的演讲稿。注意：词数100左右。First of all, thank you for listening to my speech. My topic is: love music like love yourself.Music is like the air we need to maintain our normal lives around us. You can't imagine how terrible a world without music would be. Movies and TV shows have no music, only dry conversations and scenes; mobile phones only vibrations; streets only noisy crowds; cafes, western restaurants only depressed meals. What a terrible world it is!As a student, I hope we all can enjoy the fun brought by music in our spare time. Instead of just listening to music, we can even make our own music. Let's enjoy the fun of music!Thanks again for your attention!
人教A版高中数学必修一对数的运算教学设计（1）
本节课是新版教材人教A版普通高中课程标准实验教科书数学必修1第四章第4.3.2节《对数的运算》。其核心是弄清楚对数的定义，掌握对数的运算性质，理解它的关键就是通过实例使学生认识对数式与指数式的关系，分析得出对数的概念及对数式与指数式的 互化，通过实例推导对数的运算性质。由于它还与后续很多内容，比如对数函数及其性质,这也是高考必考内容之一，所以在本学科有着很重要的地位。解决重点的关键是抓住对数的概念、并让学生掌握对数式与指数式的互化；通过实例推导对数的运算性质，让学生准确地运用对数运算性质进行运算，学会运用换底公式。培养学生数学运算、数学抽象、逻辑推理和数学建模的核心素养。1、理解对数的概念，能进行指数式与对数式的互化；2、了解常用对数与自然对数的意义，理解对数恒等式并能运用于有关对数计算。
双曲线的简单几何性质（1）教学设计人教A版高中数学选择性必修第一册
问题导学类比椭圆几何性质的研究，你认为应该研究双曲线x^2/a^2 -y^2/b^2 =1 (a>0，b>0)，的哪些几何性质，如何研究这些性质1、范围利用双曲线的方程求出它的范围，由方程x^2/a^2 -y^2/b^2 =1可得x^2/a^2 =1+y^2/b^2 ≥1 于是，双曲线上点的坐标（ x ， y ）都适合不等式，x^2/a^2 ≥1，y∈R所以x≥a 或x≤-a; y∈R2、对称性 x^2/a^2 -y^2/b^2 =1 (a>0，b>0)，关于x轴、y轴和原点都是对称。x轴、y轴是双曲线的对称轴，原点是对称中心，又叫做双曲线的中心。3、顶点（1）双曲线与对称轴的交点，叫做双曲线的顶点 .顶点是A_1 （-a,0）、A_2 （a,0），只有两个。（2）如图，线段A_1 A_2 叫做双曲线的实轴，它的长为2a,a叫做实半轴长；线段B_1 B_2 叫做双曲线的虚轴，它的长为2b,b叫做双曲线的虚半轴长。（3）实轴与虚轴等长的双曲线叫等轴双曲线4、渐近线（1）双曲线x^2/a^2 -y^2/b^2 =1 (a>0，b>0)，的渐近线方程为：y=±b/a x（2）利用渐近线可以较准确的画出双曲线的草图
