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人教版高中數(shù)學選修3超幾何分布教學設計

  • 新人教版高中英語選修2Unit 4 Learning about Language教學設計

    新人教版高中英語選修2Unit 4 Learning about Language教學設計

    This section guides students to pay attention to the typical context of vocabulary use, helps students accumulate vocabulary around the key vocabulary of this unit, and uses the learned words and word chunks in different contexts to deeply understand their meaning and usage, so as to achieve the purpose of review and consolidation.The teaching design activities aim to guide students to pay attention to the typical context in which the target vocabulary is used, as well as the common vocabulary used in collocation, so that students can complete the sentence with correct words. In terms of vocabulary learning strategies, this unit focuses on cultivating students' ability to pay attention to collocation of words and to use word blocks to express meaning.For vocabulary learning, it is not enough just to know the meaning of a single word, but the most important thing is to master the common collocations of words, namely word blocks.Teachers should timely guide students to summarize common vocabulary collocation, such as verb and noun collocation, verb and preposition collocation, preposition and noun collocation, and so on.1. Guide students to understand and consolidate the meaning and usage of the vocabulary in the context, 2. Guide the students to use the unit topic vocabulary in a richer context3. Let the students sort out and accumulate the accumulated vocabulary, establishes the semantic connection between the vocabulary,4. Enable students to understand and master the vocabulary more effectivelyGuiding the Ss to use unit topic words and the sentence patterns in a richer context.

  • 新人教版高中英語選修2Unit 4 Reading and thinking教學設計

    新人教版高中英語選修2Unit 4 Reading and thinking教學設計

    【詞匯精講】highlight n.最好或最精彩的部分 vt.突出;強調(diào);使醒目One of the highlights of the trip was seeing the Taj Mahal.這次旅行的亮點之一是參觀泰姬陵。Your resume should highlight your skills and achievements.你的簡歷應該突出你的技能和成就。The report highlights the major problems facing society today.報告強調(diào)了當今社會所面臨的主要問題。I’ve highlighted the important passages in yellow.我用黃色標出了重要段落。7.Edmonton is freezing cold in winter,with daily temperatures averaging -10 ℃.埃德蒙頓冬季寒冷,日平均氣溫為-10°C?!驹~匯精講】freezing adj.極冷的;冰凍的Leave a basin of water outside in freezing weather.在冰凍的天氣里,放一盆水在室外。It’s freezing cold outside so wear a warm coat.外面超冷的,所以穿一個暖和一點的外套吧。8.It was not until 9:30 a.m.that they finally reached the capital of Ontario,Toronto.直到上午9時30分,他們才終于到達多倫多的首府安大略省。【句式剖析】本句是一個強調(diào)句,強調(diào)的是句子的時間狀語until 9:30。含有not...until...的句子的強調(diào)句為It is not until...that...,that后面的句子要用肯定形式。It was not until then that I suddenly realized nobody was happier than I was.直到那時我才突然意識到?jīng)]有人比我更幸福了。

  • 新人教版高中英語選修2Unit 2 Reading for writing教學設計

    新人教版高中英語選修2Unit 2 Reading for writing教學設計

    The theme of this section is to express people's views on studying abroad. With the continuous development of Chinese economic construction, especially the general improvement of people's living standards, the number of Chinese students studying abroad at their own expense is on the rise. Many students and parents turn their attention to the world and regard studying abroad as an effective way to improve their quality, broaden their horizons and master the world's advanced scientific knowledge, which is very important for the fever of going abroad. Studying abroad is also an important decision made by a family for their children. Therefore, it is of great social significance to discuss this issue. The theme of this section is the column discussion in the newspaper: the advantages and disadvantages of studying abroad. The discourse is about two parents' contribution letters on this issue. They respectively express their own positions. One thinks that the disadvantages outweigh the advantages, and the other thinks that the advantages outweigh the disadvantages. The two parents' arguments are well founded and logical. It is worth noting that the two authors do not express their views on studying abroad from an individual point of view, but from a national or even global point of view. These two articles have the characteristics of both letters and argumentative essays1.Guide the students to read these two articles, and understand the author's point of view and argument ideas2.Help the students to summarize the structure and writing methods of argumentative writing, and guides students to correctly understand the advantages and disadvantages of studying abroad3.Cultivate students' ability to analyze problems objectively, comprehensively and deeply

  • 新人教版高中英語選修2Unit 5 Reading and thinking教學設計

    新人教版高中英語選修2Unit 5 Reading and thinking教學設計

    The theme of this activity is to learn the first aid knowledge of burns. Burns is common in life, but there are some misunderstandings in manual treatment. This activity provides students with correct first aid methods, so as not to take them for granted in an emergency. This section guides students to analyze the causes of scald and help students avoid such things. From the perspective of text structure and collaborative features, the text is expository. Expository, with explanation as the main way of expression, transmits knowledge and information to readers by analyzing concepts and elaborating examples. This text arranges the information in logical order, clearly presents three parts of the content through the subtitle, accurately describes the causes, types, characteristics and first aid measures of burns, and some paragraphs use topic sentences to summarize the main idea, and the level is very clear.1. Guide students to understand the causes, types, characteristics and first aid methods of burns, through reading2. Enhance students’ ability to deal withburnss and their awareness of burns prevention3. Enable students to improve the ability to judge the types of texts accurately and to master the characteristics and writing techniques of expository texts.Guide students to understand the causes, types, characteristics and first aid methods of burns, through readingStep1: Lead in by discussing the related topic:1. What first-aid techniques do you know of ?CPR; mouth to mouth artificial respiration; the Heimlich Manoeuvre

  • 新人教版高中英語選修2Unit 2 Learning about Language教學設計

    新人教版高中英語選修2Unit 2 Learning about Language教學設計

    The activity theme of this section is to design various activities around the key words in the first text. Therefore, the activities require students to pay attention to the spelling of words. On the other hand, let students grasp the meaning of words more accurately through sentences and short texts. This kind of teaching design also helps to improve the ability of using English thinking.1. Cultivating students' ability to use word formation to induce and memorize vocabulary, and the ability to use lexical chunks to express meaning.2. Guide the students to think independently and use the correct form of words to complete sentences3. Cultivate students' habit of using lexical chunks to express language completely, guide students to draw words in sentences quickly, pay attention to word collocation, so as to accumulate more authentic expressions4. Instruct students to create sentences with the chunks.1. Enable students to use the language points in the real situation or specific contexts flexibly and appropriately.2. Guiding the Ss to use unit topic words and the sentence patterns in a richer context.Step1: Think of a word that best fits each definition.1. to remember sth2.to accept, admit, or recognize sth or the truth/existence of sth3. the process of changing sth or yourself to suit a new situation4 .to make sb feel less worried or unhappy5. a strong desire to achieve sth

  • 新人教版高中英語選修2Unit 5 Reading for writing教學設計

    新人教版高中英語選修2Unit 5 Reading for writing教學設計

    你校英語報計劃出版一期急救常識???現(xiàn)面向全校學生公開征集稿件,你有意參加。請你根據(jù)下面提示內(nèi)容,用英語寫一篇短文,介紹在車禍現(xiàn)場對傷者進行急救的方法和步驟。1.確?,F(xiàn)場的安全;2.詢問傷者,確保其呼吸正常;3.檢查傷口,如流血則應采取止血措施;4.如需急救,確保其處于康復位置。注意:1.詞數(shù)80左右;2.可以適當增加細節(jié),以使行文連貫。參考詞匯:康復位置 recovery positionAs we all know, having a knowledge of first aid can make a great difference in our daily life. If a traffic accident happens and someone is injured, the following steps can be used to treat the injured.In the first place, we should make sure that the accident scene is safe so that we won’t get hurt. We should ask the injured person if he is OK, and see if he is breathing. What’s more, we should check for cuts and wounds. If he is bleeding badly, it is vital that we should try to stop the bleeding by applying pressure to the injury. This is because if a person loses too much blood, he may die. If necessary, take the injured person to the hospital as soon as possible.Do remember: when giving first aid, please be sure to place the person in a recovery position.

  • 新人教版高中英語選修2Unit 2 Reading and thinking教學設計

    新人教版高中英語選修2Unit 2 Reading and thinking教學設計

    Her tutor told her to acknowledge __________ other people had said if she cited their ideas, and advised her _______(read) lots of information in order to form __________wise opinion of her own.Now halfway __________ her exchange year, Xie Lei felt much more at home in the UK. She said __________ (engage) in British culture had helped and that she had been__________ (involve) in social activities. She also said while learning about business, she was acting as a cultural messenger __________(build) a bridge between the two countries. keys:Xie Lei, a 19­year­old Chinese student, said goodbye to her family and friends in China and boarded (board) a plane for London six months ago in order to get a business qualification. She was ambitious(ambition) to set up a business after graduation. It was the first time that she had left (leave) home.At first, Xie Lei had to adapt to life in a different country. She chose to live with a host family, who can help with her adaptation (adapt) to the new culture. When she missed home, she felt comforted (comfort) to have a second family. Also Xie Lei had to satisfy academic requirements. Her tutor told her to acknowledge what other people had said if she cited their ideas, and advised her to read lots of information in order to form a wise opinion of her own.Now halfway through her exchange year, Xie Lei felt much more at home in the UK. She said engaging (engage) in British culture had helped and that she had been involved (involve) in social activities. She also said while learning about business, she was acting as a cultural messenger building a bridge between the two countries.

  • 新人教版高中英語選修2Unit 4 Reading for writing教學設計

    新人教版高中英語選修2Unit 4 Reading for writing教學設計

    假定你是英國的Jack,打算來中國旅行,請你給你的中國筆友李華寫一封信,要點如下:1.你的旅行計劃:北京→泰山→杭州;2.征求建議并詢問他是否愿意充當你的導游。注意:1.詞數(shù)80左右(開頭和結(jié)尾已給出,不計入總詞數(shù));2.可以適當增加細節(jié),以使行文連貫。參考詞匯:故宮 the Forbidden City;泰山 Mount TaiDear Li Hua,I'm glad to tell you that 'm going to visit China.First,I am planning to visit Beijing,the capitalof China,where I am looking forward to enjoying the Great Wall,the Forbidden City and somebeautiful parks.Then I intend to go to visit Mount Tai in Shandong Province.I've heard that it is one ofthe most famous mountains in China and I can't wait to enjoy the amazing sunrise there.After that,I amalso going to Hangzhou.It is said that it is a beautiful modern city with breathtaking natural sights,among which the West Lake is a well- known tourist attraction.What do you think of my travel plan? Will you act as my guide? Hope to hear from you soon.

  • 新人教版高中英語選修2Unit 4 Using langauge-Listening教學設計

    新人教版高中英語選修2Unit 4 Using langauge-Listening教學設計

    The theme of the listening section is " talking about scenery and culture along a journey."The part is designed to further lead the students to understand Canadian natural geography and social environment, and integrated into the cultural contrast by mentioning the long train journey from Beijing to Moscow routes. On this basis, the part activates students related travel experience, lets the student serial dialogue, guides the student to explore further the pleasure and meaning of the long journey, and Chinese and foreign cultural comparison.The part also provides a framework for the continuation of the dialogue, which is designed to provide a framework for students to successfully complete their oral expressions, and to incorporate an important trading strategy to end the dialogue naturally.1. Help students to understand and master some common English idioms in the context, and experience the expression effect of English idioms.2. Guide the students to understand the identity of different people in the listening context, and finish the dialogue according to their own experience.3. Instruct the students to use appropriate language to express surprise and curiosity about space and place in the dialogue, and master the oral strategy of ending the dialogue naturally.1. Instruct students to grasp the key information and important details of the dialogue.2. Instruct students to conduct a similar talk on the relevant topic.

  • 新人教版高中英語選修2Unit 5 Learning about Language教學設計

    新人教版高中英語選修2Unit 5 Learning about Language教學設計

    The purpose of this section of vocabulary exercises is to consolidate the key words in the first part of the reading text, let the students write the words according to the English definition, and focus on the detection of the meaning and spelling of the new words. The teaching design includes use English definition to explain words, which is conducive to improving students' interest in vocabulary learning, cultivating their sense of English language and thinking in English, and making students willing to use this method to better grasp the meaning of words, expand their vocabulary, and improve their ability of vocabulary application. Besides, the design offers more context including sentences and short passage for students to practice words flexibly.1. Guide students to understand and consolidate the meaning and usage of the vocabulary in the context, 2. Guide the students to use the unit topic vocabulary in a richer context3. Let the students sort out and accumulate the accumulated vocabulary, establishes the semantic connection between the vocabulary,4. Enable students to understand and master the vocabulary more effectivelyGuiding the Ss to use unit topic words and the sentence patterns in a richer context.Step1: Read the passage about chemical burns and fill in the blanks with the correct forms of the words in the box.

  • 新人教版高中英語選修2Unit 5 Using langauge-Listening教學設計

    新人教版高中英語選修2Unit 5 Using langauge-Listening教學設計

    The theme of this section is to learn how to make emergency calls. Students should learn how to make emergency calls not only in China, but also in foreign countries in English, so that they can be prepared for future situations outside the home.The emergency telephone number is a vital hotline, which should be the most clear, rapid and effective communication with the acute operator.This section helps students to understand the emergency calls in some countries and the precautions for making emergency calls. Through the study of this section, students can accumulate common expressions and sentence patterns in this context. 1.Help students accumulate emergency telephone numbers in different countries and learn more about first aid2.Guide the students to understand the contents and instructions of the telephone, grasp the characteristics of the emergency telephone and the requirements of the emergency telephone.3.Guide students to understand the first aid instructions of the operators.4.Enable Ss to make simulated emergency calls with their partners in the language they have learned1. Instruct students to grasp the key information and important details of the dialogue.2. Instruct students to conduct a similar talk on the relevant topic.Step1:Look and discuss:Match the pictures below to the medical emergencies, and then discuss the questions in groups.

  • 新人教版高中英語選修2Unit 3 Food and Culture-Discovering useful structures教學設計

    新人教版高中英語選修2Unit 3 Food and Culture-Discovering useful structures教學設計

    The newspaper reported more than 100 people had been killed in the thunderstorm.報紙報道說有一百多人在暴風雨中喪生。(2)before、when、by the time、until、after、once等引導的時間狀語從句的謂語是一般過去時,以及by、before后面接過去的時間時,主句動作發(fā)生在從句的動作或過去的時間之前且表示被動時,要用過去完成時的被動語態(tài)。By the time my brother was 10, he had been sent to Italy.我弟弟10歲前就已經(jīng)被送到意大利了。Tons of rice had been produced by the end of last month. 到上月底已生產(chǎn)了好幾噸大米。(3) It was the first/second/last ... time that ...句中that引導的定語從句中,主語與謂語構(gòu)成被動關(guān)系時,要用過去完成時的被動語態(tài)。It was the first time that I had seen the night fact to face in one and a half years. 這是我一年半以來第一次親眼目睹夜晚的景色。(4)在虛擬語氣中,條件句表示與過去事實相反,且主語與謂語構(gòu)成被動關(guān)系時,要用過去完成時的被動語態(tài)。If I had been instructed by him earlier, I would have finished the task.如果我早一點得到他的指示,我早就完成這項任務了。If I had hurried, I wouldn't have missed the train.如果我快點的話,我就不會誤了火車。If you had been at the party, you would have met him. 如果你去了晚會,你就會見到他的。

  • 新人教版高中英語選修2Unit 3 Food and Culture-Reading and thinking教學設計

    新人教版高中英語選修2Unit 3 Food and Culture-Reading and thinking教學設計

    The discourse explores the link between food and culture from a foreign’s perspective and it records some authentic Chinese food and illustrates the cultural meaning, gerography features and historic tradition that the food reflects. It is aimed to lead students to understand and think about the connection between food and culture. While teaching, the teacher should instruct students to find out the writing order and the writer’s experieces and feelings towards Chinese food and culture.1.Guide the students to read the text, sort out the information and dig out the topic.2.Understand the cultural connotation, regional characteristics and historical tradition of Chinese cuisine3.Understand and explore the relationship between food and people's personality4.Guide the students to use the cohesive words in the text5.Lead students to accurately grasp the real meaning of the information and improve the overall understanding ability by understanding the implied meaning behind the text.1. Enable the Ss to understand the structure and the writing style of the passage well.2. Lead the Ss to understand and think further about the connection between food and geography and local character traits.Step1: Prediction before reading. Before you read, look at the title, and the picture. What do you think this article is about?keys:It is about various culture and cuisine about a place or some countries.

  • 拋物線及其標準方程教學設計人教A版高中數(shù)學選擇性必修第一冊

    拋物線及其標準方程教學設計人教A版高中數(shù)學選擇性必修第一冊

    本節(jié)課選自《2019人教A版高中數(shù)學選擇性必修第一冊》第二章《直線和圓的方程》,本節(jié)課主要學習拋物線及其標準方程在經(jīng)歷了橢圓和雙曲線的學習后再學習拋物線,是在學生原有認知的基礎上從幾何與代數(shù)兩 個角度去認識拋物線.教材在拋物線的定義這個內(nèi)容的安排上是:先從直觀上認識拋物線,再從畫法中提煉出拋物線的幾何特征,由此抽象概括出拋物線的定義,最后是拋物線定義的簡單應用.這樣的安排不僅體現(xiàn)出《課程標準》中要求通過豐富的實例展開教學的理念,而且符合學生從具體到抽象的認知規(guī)律,有利于學生對概念的學習和理解.坐標法的教學貫穿了整個“圓錐曲線方程”一章,是學生應重點掌握的基本數(shù)學方法 運動變化和對立統(tǒng)一的思想觀點在這節(jié)知識中得到了突出體現(xiàn),我們必須充分利用好這部分教材進行教學

  • 用空間向量研究直線、平面的位置關(guān)系(1)教學設計人教A版高中數(shù)學選擇性必修第一冊

    用空間向量研究直線、平面的位置關(guān)系(1)教學設計人教A版高中數(shù)學選擇性必修第一冊

    二、探究新知一、空間中點、直線和平面的向量表示1.點的位置向量在空間中,我們?nèi)∫欢cO作為基點,那么空間中任意一點P就可以用向量(OP) ?來表示.我們把向量(OP) ?稱為點P的位置向量.如圖.2.空間直線的向量表示式如圖①,a是直線l的方向向量,在直線l上取(AB) ?=a,設P是直線l上的任意一點,則點P在直線l上的充要條件是存在實數(shù)t,使得(AP) ?=ta,即(AP) ?=t(AB) ?.如圖②,取定空間中的任意一點O,可以得到點P在直線l上的充要條件是存在實數(shù)t,使(OP) ?=(OA) ?+ta, ①或(OP) ?=(OA) ?+t(AB) ?. ②①式和②式都稱為空間直線的向量表示式.由此可知,空間任意直線由直線上一點及直線的方向向量唯一確定.1.下列說法中正確的是( )A.直線的方向向量是唯一的B.與一個平面的法向量共線的非零向量都是該平面的法向量C.直線的方向向量有兩個D.平面的法向量是唯一的答案:B 解析:由平面法向量的定義可知,B項正確.

  • 用空間向量研究直線、平面的位置關(guān)系(2)教學設計人教A版高中數(shù)學選擇性必修第一冊

    用空間向量研究直線、平面的位置關(guān)系(2)教學設計人教A版高中數(shù)學選擇性必修第一冊

    跟蹤訓練1在正方體ABCD-A1B1C1D1中,E為AC的中點.求證:(1)BD1⊥AC;(2)BD1⊥EB1.(2)∵(BD_1 ) ?=(-1,-1,1),(EB_1 ) ?=(1/2 "," 1/2 "," 1),∴(BD_1 ) ?·(EB_1 ) ?=(-1)×1/2+(-1)×1/2+1×1=0,∴(BD_1 ) ?⊥(EB_1 ) ?,∴BD1⊥EB1.證明:以D為原點,DA,DC,DD1所在直線分別為x軸、y軸、z軸,建立如圖所示的空間直角坐標系.設正方體的棱長為1,則B(1,1,0),D1(0,0,1),A(1,0,0),C(0,1,0),E(1/2 "," 1/2 "," 0),B1(1,1,1).(1)∵(BD_1 ) ?=(-1,-1,1),(AC) ?=(-1,1,0),∴(BD_1 ) ?·(AC) ?=(-1)×(-1)+(-1)×1+1×0=0.∴(BD_1 ) ?⊥(AC) ?,∴BD1⊥AC.例2在棱長為1的正方體ABCD-A1B1C1D1中,E,F,M分別為棱AB,BC,B1B的中點.求證:D1M⊥平面EFB1.思路分析一種思路是不建系,利用基向量法證明(D_1 M) ?與平面EFB1內(nèi)的兩個不共線向量都垂直,從而根據(jù)線面垂直的判定定理證得結(jié)論;另一種思路是建立空間直角坐標系,通過坐標運算證明(D_1 M) ?與平面EFB1內(nèi)的兩個不共線向量都垂直;還可以在建系的前提下,求得平面EFB1的法向量,然后說明(D_1 M) ?與法向量共線,從而證得結(jié)論.證明:(方法1)因為E,F,M分別為棱AB,BC,B1B的中點,所以(D_1 M) ?=(D_1 B_1 ) ?+(B_1 M) ?=(DA) ?+(DC) ?+1/2 (B_1 B) ?,而(B_1 E) ?=(B_1 B) ?+(BE) ?=(B_1 B) ?-1/2 (DC) ?,于是(D_1 M) ?·(B_1 E) ?=((DA) ?+(DC) ?+1/2 (B_1 B) ?)·((B_1 B) ?-1/2 (DC) ?)=0-0+0-1/2+1/2-1/4×0=0,因此(D_1 M) ?⊥(B_1 E) ?.同理(D_1 M) ?⊥(B_1 F) ?,又因為(B_1 E) ?,(B_1 F) ?不共線,因此D1M⊥平面EFB1.

  • 空間向量及其運算的坐標表示教學設計人教A版高中數(shù)學選擇性必修第一冊

    空間向量及其運算的坐標表示教學設計人教A版高中數(shù)學選擇性必修第一冊

    一、情境導學我國著名數(shù)學家吳文俊先生在《數(shù)學教育現(xiàn)代化問題》中指出:“數(shù)學研究數(shù)量關(guān)系與空間形式,簡單講就是形與數(shù),歐幾里得幾何體系的特點是排除了數(shù)量關(guān)系,對于研究空間形式,你要真正的‘騰飛’,不通過數(shù)量關(guān)系,我想不出有什么好的辦法…….”吳文俊先生明確地指出中學幾何的“騰飛”是“數(shù)量化”,也就是坐標系的引入,使得幾何問題“代數(shù)化”,為了使得空間幾何“代數(shù)化”,我們引入了坐標及其運算.二、探究新知一、空間直角坐標系與坐標表示1.空間直角坐標系在空間選定一點O和一個單位正交基底{i,j,k},以點O為原點,分別以i,j,k的方向為正方向、以它們的長為單位長度建立三條數(shù)軸:x軸、y軸、z軸,它們都叫做坐標軸.這時我們就建立了一個空間直角坐標系Oxyz,O叫做原點,i,j,k都叫做坐標向量,通過每兩個坐標軸的平面叫做坐標平面,分別稱為Oxy平面,Oyz平面,Ozx平面.

  • 雙曲線及其標準方程教學設計人教A版高中數(shù)學選擇性必修第一冊

    雙曲線及其標準方程教學設計人教A版高中數(shù)學選擇性必修第一冊

    ∵在△EFP中,|EF|=2c,EF上的高為點P的縱坐標,∴S△EFP=4/3c2=12,∴c=3,即P點坐標為(5,4).由兩點間的距離公式|PE|=√("(" 5+3")" ^2+4^2 )=4√5,|PF|=√("(" 5"-" 3")" ^2+4^2 )=2√5,∴a=√5.又b2=c2-a2=4,故所求雙曲線的方程為x^2/5-y^2/4=1.5.求適合下列條件的雙曲線的標準方程.(1)兩個焦點的坐標分別是(-5,0),(5,0),雙曲線上的點與兩焦點的距離之差的絕對值等于8;(2)以橢圓x^2/8+y^2/5=1長軸的端點為焦點,且經(jīng)過點(3,√10);(3)a=b,經(jīng)過點(3,-1).解:(1)由雙曲線的定義知,2a=8,所以a=4,又知焦點在x軸上,且c=5,所以b2=c2-a2=25-16=9,所以雙曲線的標準方程為x^2/16-y^2/9=1.(2)由題意得,雙曲線的焦點在x軸上,且c=2√2.設雙曲線的標準方程為x^2/a^2 -y^2/b^2 =1(a>0,b>0),則有a2+b2=c2=8,9/a^2 -10/b^2 =1,解得a2=3,b2=5.故所求雙曲線的標準方程為x^2/3-y^2/5=1.(3)當焦點在x軸上時,可設雙曲線方程為x2-y2=a2,將點(3,-1)代入,得32-(-1)2=a2,所以a2=b2=8.因此,所求的雙曲線的標準方程為x^2/8-y^2/8=1.當焦點在y軸上時,可設雙曲線方程為y2-x2=a2,將點(3,-1)代入,得(-1)2-32=a2,a2=-8,不可能,所以焦點不可能在y軸上.綜上,所求雙曲線的標準方程為x^2/8-y^2/8=1.

  • 用空間向量研究距離、夾角問題(1)教學設計人教A版高中數(shù)學選擇性必修第一冊

    用空間向量研究距離、夾角問題(1)教學設計人教A版高中數(shù)學選擇性必修第一冊

    二、探究新知一、點到直線的距離、兩條平行直線之間的距離1.點到直線的距離已知直線l的單位方向向量為μ,A是直線l上的定點,P是直線l外一點.設(AP) ?=a,則向量(AP) ?在直線l上的投影向量(AQ) ?=(a·μ)μ.點P到直線l的距離為PQ=√(a^2 "-(" a"·" μ")" ^2 ).2.兩條平行直線之間的距離求兩條平行直線l,m之間的距離,可在其中一條直線l上任取一點P,則兩條平行直線間的距離就等于點P到直線m的距離.點睛:點到直線的距離,即點到直線的垂線段的長度,由于直線與直線外一點確定一個平面,所以空間點到直線的距離問題可轉(zhuǎn)化為空間某一個平面內(nèi)點到直線的距離問題.1.已知正方體ABCD-A1B1C1D1的棱長為2,E,F分別是C1C,D1A1的中點,則點A到直線EF的距離為 . 答案: √174/6解析:如圖,以點D為原點,DA,DC,DD1所在直線分別為x軸、y軸、z軸建立空間直角坐標系,則A(2,0,0),E(0,2,1),F(1,0,2),(EF) ?=(1,-2,1),

  • 新人教版高中英語選修2Unit 1 Science and Scientists-Using langauge教學設計

    新人教版高中英語選修2Unit 1 Science and Scientists-Using langauge教學設計

    This happens because the dish soap molecules have a strong negative charge, and the milk molecules have a strong positive charge. Like magnets, these molecules are attracted to each other, and so they appear to move around on the plate, taking the food coloring with them, making it look like the colors are quickly moving to escape from the soap.Listening text:? Judy: Oh, I'm so sorry that you were ill and couldn't come with us on our field trip. How are you feeling now? Better?? Bill: Much better, thanks. But how was it?? Judy: Wonderful! I especially liked an area of the museum called Light Games.it was really cool. They had a hall of mirrors where I could see myself reflected thousands of times!? Bill: A hall of mirrors can be a lot of fun. What else did they have?? Judy: Well, they had an experiment where we looked at a blue screen for a while, and then suddenly we could see tiny bright lights moving around on it. You'll never guess what those bright lights were!? Bill: Come on, tell me!? Judy: They were our own blood cells. For some reason, our eyes play tricks on us when we look at a blue screen, and we can see our own blood cells moving around like little lights! But there was another thing I liked better. I stood in front of a white light, and it cast different shadows of me in every color of the rainbow!? Bill: Oh, I wish I had been there. Tell me more!? Judy: Well, they had another area for sound. They had a giant piano keyboard that you could use your feet to play. But then, instead of playing the sounds of a piano, it played the voices of classical singers! Then they had a giant dish, and when you spoke into it, it reflected the sound back and made it louder. You could use it to speak in a whisper to someone 17 meters away.? Bill: It all sounds so cool. I wish I could have gone with you? Judy: I know, but we can go together this weekend. I'd love to go there again!? Bill: That sounds like a great idea!

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