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人教A版高中數(shù)學(xué)必修一函數(shù)的零點(diǎn)與方程的解教學(xué)設(shè)計(jì)（2）
本章通過學(xué)習(xí)用二分法求方程近似解的的方法，使學(xué)生體會(huì)函數(shù)與方程之間的關(guān)系，通過一些函數(shù)模型的實(shí)例，讓學(xué)生感受建立函數(shù)模型的過程和方法，體會(huì)函數(shù)在數(shù)學(xué)和其他學(xué)科中的廣泛應(yīng)用，進(jìn)一步認(rèn)識(shí)到函數(shù)是描述客觀世界變化規(guī)律的基本數(shù)學(xué)模型，能初步運(yùn)用函數(shù)思想解決一些生活中的簡單問題。1.了解函數(shù)的零點(diǎn)、方程的根與圖象交點(diǎn)三者之間的聯(lián)系.2.會(huì)借助零點(diǎn)存在性定理判斷函數(shù)的零點(diǎn)所在的大致區(qū)間.3.能借助函數(shù)單調(diào)性及圖象判斷零點(diǎn)個(gè)數(shù)．?dāng)?shù)學(xué)學(xué)科素養(yǎng)1.數(shù)學(xué)抽象：函數(shù)零點(diǎn)的概念；2.邏輯推理：借助圖像判斷零點(diǎn)個(gè)數(shù)；3.數(shù)學(xué)運(yùn)算：求函數(shù)零點(diǎn)或零點(diǎn)所在區(qū)間；4.數(shù)學(xué)建模：通過由抽象到具體，由具體到一般的思想總結(jié)函數(shù)零點(diǎn)概念.重點(diǎn)：零點(diǎn)的概念，及零點(diǎn)與方程根的聯(lián)系；難點(diǎn)：零點(diǎn)的概念的形成．
人教A版高中數(shù)學(xué)必修一簡單的三角恒等變換教學(xué)設(shè)計(jì)（2）
它位于三角函數(shù)與數(shù)學(xué)變換的結(jié)合點(diǎn)上，能較好反應(yīng)三角函數(shù)及變換之間的內(nèi)在聯(lián)系和相互轉(zhuǎn)換，本節(jié)課內(nèi)容的地位體現(xiàn)在它的基礎(chǔ)性上。作用體現(xiàn)在它的工具性上。前面學(xué)生已經(jīng)掌握了兩角和與差的正弦、余弦、正切公式以及二倍角公式，并能通過這些公式進(jìn)行求值、化簡、證明，雖然學(xué)生已經(jīng)具備了一定的推理、運(yùn)算能力，但在數(shù)學(xué)的應(yīng)用意識(shí)與應(yīng)用能力方面尚需進(jìn)一步培養(yǎng).課程目標(biāo)1.能用二倍角公式推導(dǎo)出半角公式，體會(huì)三角恒等變換的基本思想方法，以及進(jìn)行簡單的應(yīng)用． 2.了解三角恒等變換的特點(diǎn)、變換技巧，掌握三角恒等變換的基本思想方法． 3.能利用三角恒等變換的技巧進(jìn)行三角函數(shù)式的化簡、求值以及證明，進(jìn)而進(jìn)行簡單的應(yīng)用． 數(shù)學(xué)學(xué)科素養(yǎng)1.邏輯推理： 三角恒等式的證明； 2.數(shù)據(jù)分析：三角函數(shù)式的化簡； 3.數(shù)學(xué)運(yùn)算：三角函數(shù)式的求值.
人教A版高中數(shù)學(xué)必修一正弦函數(shù)、余弦函數(shù)的性質(zhì)教學(xué)設(shè)計(jì)（2）
本節(jié)課是正弦函數(shù)、余弦函數(shù)圖像的繼續(xù)，本課是正弦曲線、余弦曲線這兩種曲線的特點(diǎn)得出正弦函數(shù)、余弦函數(shù)的性質(zhì). 課程目標(biāo)1.了解周期函數(shù)與最小正周期的意義;2.了解三角函數(shù)的周期性和奇偶性;3.會(huì)利用周期性定義和誘導(dǎo)公式求簡單三角函數(shù)的周期;4.借助圖象直觀理解正、余弦函數(shù)在[0,2π]上的性質(zhì)(單調(diào)性、最值、圖象與x軸的交點(diǎn)等);5.能利用性質(zhì)解決一些簡單問題. 數(shù)學(xué)學(xué)科素養(yǎng)1.數(shù)學(xué)抽象：理解周期函數(shù)、周期、最小正周期等的含義； 2.邏輯推理： 求正弦、余弦形函數(shù)的單調(diào)區(qū)間；3.數(shù)學(xué)運(yùn)算：利用性質(zhì)求周期、比較大小、最值、值域及判斷奇偶性.4.數(shù)學(xué)建模：讓學(xué)生借助數(shù)形結(jié)合的思想，通過圖像探究正、余弦函數(shù)的性質(zhì).重點(diǎn)：通過正弦曲線、余弦曲線這兩種曲線探究正弦函數(shù)、余弦函數(shù)的性質(zhì)； 難點(diǎn)：應(yīng)用正、余弦函數(shù)的性質(zhì)來求含有cosx,sinx的函數(shù)的單調(diào)性、最值、值域及對稱性.
人教版高中數(shù)學(xué)選修3二項(xiàng)式定理教學(xué)設(shè)計(jì)
二項(xiàng)式定理形式上的特點(diǎn)(1)二項(xiàng)展開式有n+1項(xiàng),而不是n項(xiàng).(2)二項(xiàng)式系數(shù)都是C_n^k(k=0,1,2,…,n),它與二項(xiàng)展開式中某一項(xiàng)的系數(shù)不一定相等.(3)二項(xiàng)展開式中的二項(xiàng)式系數(shù)的和等于2n,即C_n^0+C_n^1+C_n^2+…+C_n^n=2n.(4)在排列方式上,按照字母a的降冪排列,從第一項(xiàng)起,次數(shù)由n次逐項(xiàng)減少1次直到0次,同時(shí)字母b按升冪排列,次數(shù)由0次逐項(xiàng)增加1次直到n次.1．判斷(正確的打“√”，錯(cuò)誤的打“×”)(1)(a＋b)n展開式中共有n項(xiàng)． ( )(2)在公式中，交換a，b的順序?qū)Ω黜?xiàng)沒有影響． ( )(3)Cknan－kbk是(a＋b)n展開式中的第k項(xiàng)． ( )(4)(a－b)n與(a＋b)n的二項(xiàng)式展開式的二項(xiàng)式系數(shù)相同． ( )[解析] (1)× 因?yàn)?a＋b)n展開式中共有n＋1項(xiàng)．(2)× 因?yàn)槎?xiàng)式的第k＋1項(xiàng)Cknan－kbk和(b＋a)n的展開式的第k＋1項(xiàng)Cknbn－kak是不同的，其中的a，b是不能隨便交換的．(3)× 因?yàn)镃knan－kbk是(a＋b)n展開式中的第k＋1項(xiàng)．(4)√ 因?yàn)?a－b)n與(a＋b)n的二項(xiàng)式展開式的二項(xiàng)式系數(shù)都是Crn.[答案] (1)× (2)× (3)× (4)√
新人教版高中英語必修2Unit 2 Wildlife Protection-Reading and Thinking教案二
The theme of this unit is human and nature, focusing on the theme of wildlife protection. Nature is a complex ecosystem, in which there are delicate balance between animals and plants. Because of the role of the food chain, the extinction of one species will produce influence, causing a series of chain reaction. Large scale extinction of species will have a serious and even irreversible impact on the ecosystem, resulting in immeasurable losses. Therefore, it is of great significance to protect wild species. To protect wild species is to protect human beings themselves. The motto of this unit is "when the buying stops, the killing can too,” which is a public service advertising slogan to protect wildlife. It tells people that every rhinoceros horn, every fur, every bowl of shark fin soup, every Ivory product, and every tiger bone product, etc. consumed by human beings, are innocent wild animals slaughtered behind them. The mission of wild aid is to ban illegal trade in endangered wildlife and mitigate climate change. It aims to educate the public to reduce the consumption demand for endangered wildlife products through public publicity and improve the awareness of environmental protection.1. Improve the awareness of wildlife protection by acquiring the knowledge of wildlife protection.2. Focus on environmental protection and protection of all lives.3. Analysis of the living environment of wild animals with appropriate thinking mode.4. Skillfully use the vocabulary and grammar knowledge of this unit to cultivate self-study ability according to the unit content5. Develop cooperative learning ability through discussion and other ways1. Enable the Ss to talk about the current situation of wild animals.2. Guide the Ss to summarize the main idea of each paragraph as well as the main idea of the text.
新人教版高中英語必修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
新人教版高中英語必修2Unit 1 Cultural Heritage-Reading and Thinking教案二
1. This section focuses on "Understanding how a problem was solved”, which is aimed to guide students to analyze and discuss the challenges and problems faced by cultural heritage protection during the construction of Aswan Dam, as well as the solutions. On the basis of understanding, students should pay attention to the key role of international cooperation in solving problems, and attach importance to the balance and coordination between cultural heritage protection and social and economic development. Students are encouraged to face challenges actively, be good at cooperation, and make continuous efforts to find reasonable ways and means to solve problems.2. Enable students to understand the main information and text structure of the reading text;3. Motivate students to use the reading strategy "make a timeline" according to the appropriate text genre;4. Enable students to understand how a problem was solved;5. Enable students to understand the value of protecting cultural heritage by teamwork and global community;1. Guide students to pay attention to reading strategies, such as prediction, self-questioning and scanning.2. Help students sort out the topic language about protecting cultural relics and understand the narrative characteristics of "time-event" in illustrative style3. Lead students to understand the value of protecting cultural heritage by teamwork and global community;
新人教版高中英語必修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.
新人教版高中英語必修1Unit 5 Languages Around the World-Reading for Writing教案
Step 3: Read to sum upRead it again and sum up the problems of the three students, and then write down the advice that was given from others.Step 4: Work in pairs. List your learning problems in English and brainstorm some useful advice.Useful expressions ? I don't know how to…... Is a big difficulty for me. I cannot ...? You might try …. It's very important to…? I have no idea how/what .My biggest problem is .... ? I (also) have trouble with. My advice is …. This worked for me.? l cannot understand the teachers’ English in class.Step 5 Homework：為提高我校學(xué)生的英語口語水平，我們將舉辦英語演講比賽(English- speaking contest)，請你根據(jù)下面的信息，以學(xué)生會(huì)(the Students‘ Union)的名義寫一份海報(bào)，歡迎全校同學(xué)參加，屆時(shí)特邀本校美籍教師史密斯先生頒獎(jiǎng)。? 報(bào)名時(shí)間 9月30日以前(報(bào)名:signup)? 報(bào)名地點(diǎn) 學(xué)生會(huì)辦公室? 比賽時(shí)間 10月9日晚7:00~9:00? 比賽地點(diǎn) 學(xué)校大會(huì)議室? 獎(jiǎng)勵(lì) 前8名
人教A版高中數(shù)學(xué)必修一二次函數(shù)與一元二次方程、不等式教學(xué)設(shè)計(jì)（2）
三個(gè)“二次”即一元二次函數(shù)、一元二次方程、一元二次不等式是高中數(shù)學(xué)的重要內(nèi)容，具有豐富的內(nèi)涵和密切的聯(lián)系，同時(shí)也是研究包含二次曲線在內(nèi)的許多內(nèi)容的工具 高考試題中近一半的試題與這三個(gè)“二次”問題有關(guān) 本節(jié)主要是幫助考生理解三者之間的區(qū)別及聯(lián)系，掌握函數(shù)、方程及不等式的思想和方法。課程目標(biāo)1. 通過探索，使學(xué)生理解二次函數(shù)與一元二次方程，一元二次不等式之間的聯(lián)系。2. 使學(xué)生能夠運(yùn)用二次函數(shù)及其圖像，性質(zhì)解決實(shí)際問題． 3. 滲透數(shù)形結(jié)合思想，進(jìn)一步培養(yǎng)學(xué)生綜合解題能力。數(shù)學(xué)學(xué)科素養(yǎng)1.數(shù)學(xué)抽象：一元二次函數(shù)與一元二次方程，一元二次不等式之間的聯(lián)系；2.邏輯推理：一元二次不等式恒成立問題；3.數(shù)學(xué)運(yùn)算：解一元二次不等式；4.數(shù)據(jù)分析：一元二次不等式解決實(shí)際問題；5.數(shù)學(xué)建模：運(yùn)用數(shù)形結(jié)合的思想，逐步滲透一元二次函數(shù)與一元二次方程，一元二次不等式之間的聯(lián)系。
新人教版高中英語必修1Unit 3 Sports and Fitness-Reading and Thinking教案
2. Sort out detailed information about Michael Jordan.（1） Understand the transitional sentence.Q: Which part is about Michael Jordan as a master? Which part is about the example he set?（2） Have the Ss Focus on why Michael Jordan is a master and what good examples Michael Jordan set when they’re reading. And think about these questions as below:Q1: How does the author describe his impressive skills?Q2: How do you understand “time seemed to stand still”?Q3: What does “graceful” mean?Q4. Which sentence do you think best describes his mental strength?Q5. Which words is important in the sentence in describing his mental strength? Why?Q6: How do you understand “unique”?Q7: What can we learn from Michael Jordan?Step 5 Discussing and recommendingRecommend their own living legends of sports.Work in groups to choose your own living legend of sports and give the reasons of your choice. Step 6 HomeworkReview the stories of Lang Ping and Michael Jordan, and try to retell them.
新人教版高中英語必修2Unit 3 The Internet-Listening &Speaking＆Talking教案一
Listening and Speaking introduces the topic of “ask about online habits”. Many middle school students have been surfing the Internet for many years, but what they do with the Internet and how much time they spend every day may not be very clear to themselves, nor to other students. This section allows students to investigate their peers' Internet use, which is conducive to their mutual understanding and understanding of the Internet. It can also help them reflect on their own online behavior, learn from other people's good online habits, and get rid of their bad online behavior.The listening text of this section is an investigation interview. The investigators interview specific groups with the same questions to obtain information, so as to understand their views, practices or attitudes on this issue. There are two specific questions: “how much time do you spend online every day? What do you usually do online?”. The answers of the three respondents provide rich and different information, and achieve the purpose of the investigators. The oral discourse structure of survey interviews generally includes greeting and explaining the purpose of the interview, presenting the interview questions and the respondents' answers. Listening and Talking introduces the theme of “choosing the right application ". Listening text is a conversation between Laura and Xiao Bo. In this part of listening, “oink”； “piggy bank” may cause the students' hearing comprehension limitation. Oink refers to sound word and pig's sound. So, add some oink to my piggy bank is often used to describe "making a little money".1. Guide students to understand the content of listening texts in terms of listening for definitions.2. Cultivate students' ability to define words and understand an investigation interview.
新人教版高中英語必修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)他已被挑選出來參加運(yùn)動(dòng)會(huì)。The ink has not been removed from his overcoat．(否定句)墨跡還沒有從他外套上去掉。
新人教版高中英語必修2Unit 3 The Internet-Reading For Writing教案一
⑦identity theft 身份盜竊⑧chat room 聊天室⑨draft your blog post 起草博客帖子⑩post embarrassing photos 張貼尷尬照片 【話題句式】 1. How do you stay safe online and avoid bad experiences on the Internet? 你如何在網(wǎng)上保持安全, 避免在網(wǎng)上的不良經(jīng)歷? 2. I’m not an expert, but many years as a blogger have taught me a thing or two. 我不是專家, 但作為一個(gè)博主, 我已經(jīng)學(xué)了好幾年了。 3. If you see or read something that makes you feel uncomfortable, leave the site immediately. 如果你看到或讀到一些讓你覺得不舒服的東西, 立即離開這個(gè)網(wǎng)站。4. Don’t give out your address or phone number. 別告訴別人你的地址或電話號(hào)碼。 5. Identity theft is a common and serious problem. 身份盜竊是一個(gè)常見而嚴(yán)重的問題。6. Being online is no excuse for being rude, and you don’t want to become a target for a troll or cyberbully. 上網(wǎng)并不是無禮的借口, 你也不想成為發(fā)挑釁帖子的人或網(wǎng)絡(luò)惡霸的目標(biāo)。 7. Trolls often use several false names so that they can stay on a site. 發(fā)挑釁帖子的人經(jīng)常使用幾個(gè)假名, 這樣他們就可以留在一個(gè)網(wǎng)站上。8. However, the more polite you are, the less likely it is you will be attacked. 然而, 你越有禮貌, 你被攻擊的可能性就越小。
人教A版高中數(shù)學(xué)必修二有限樣本空間與隨機(jī)事件事件的關(guān)系和運(yùn)算教學(xué)設(shè)計(jì)
新知講授（一）——隨機(jī)試驗(yàn) 我們把對隨機(jī)現(xiàn)象的實(shí)現(xiàn)和對它的觀察稱為隨機(jī)試驗(yàn)，簡稱試驗(yàn)，常用字母E表示。我們通常研究以下特點(diǎn)的隨機(jī)試驗(yàn)：（1）試驗(yàn)可以在相同條件下重復(fù)進(jìn)行；（2）試驗(yàn)的所有可能結(jié)果是明確可知的，并且不止一個(gè)；（3）每次試驗(yàn)總是恰好出現(xiàn)這些可能結(jié)果中的一個(gè)，但事先不確定出現(xiàn)哪個(gè)結(jié)果。新知講授（二）——樣本空間思考一：體育彩票搖獎(jiǎng)時(shí)，將10個(gè)質(zhì)地和大小完全相同、分別標(biāo)號(hào)0，1，2，...，9的球放入搖獎(jiǎng)器中，經(jīng)過充分?jǐn)嚢韬髶u出一個(gè)球，觀察這個(gè)球的號(hào)碼。這個(gè)隨機(jī)試驗(yàn)共有多少個(gè)可能結(jié)果？如何表示這些結(jié)果？根據(jù)球的號(hào)碼，共有10種可能結(jié)果。如果用m表示“搖出的球的號(hào)碼為m”這一結(jié)果，那么所有可能結(jié)果可用集合表示{0，1，2，3，4，5，6，7，8，9}.我們把隨機(jī)試驗(yàn)E的每個(gè)可能的基本結(jié)果稱為樣本點(diǎn)，全體樣本點(diǎn)的集合稱為試驗(yàn)E的樣本空間。
人教版高中數(shù)學(xué)選修3排列與排列數(shù)教學(xué)設(shè)計(jì)
4.有8種不同的菜種,任選4種種在不同土質(zhì)的4塊地里,有 種不同的種法. 解析:將4塊不同土質(zhì)的地看作4個(gè)不同的位置,從8種不同的菜種中任選4種種在4塊不同土質(zhì)的地里,則本題即為從8個(gè)不同元素中任選4個(gè)元素的排列問題,所以不同的種法共有A_8^4 =8×7×6×5=1 680(種).答案:1 6805.用1、2、3、4、5、6、7這7個(gè)數(shù)字組成沒有重復(fù)數(shù)字的四位數(shù).(1)這些四位數(shù)中偶數(shù)有多少個(gè)?能被5整除的有多少個(gè)?(2)這些四位數(shù)中大于6 500的有多少個(gè)?解:(1)偶數(shù)的個(gè)位數(shù)只能是2、4、6,有A_3^1種排法,其他位上有A_6^3種排法,由分步乘法計(jì)數(shù)原理,知共有四位偶數(shù)A_3^1·A_6^3=360(個(gè));能被5整除的數(shù)個(gè)位必須是5,故有A_6^3=120(個(gè)).(2)最高位上是7時(shí)大于6 500,有A_6^3種,最高位上是6時(shí),百位上只能是7或5,故有2×A_5^2種.由分類加法計(jì)數(shù)原理知,這些四位數(shù)中大于6 500的共有A_6^3+2×A_5^2=160(個(gè)).
人教版高中數(shù)學(xué)選修3超幾何分布教學(xué)設(shè)計(jì)
探究新知問題1：已知100件產(chǎn)品中有8件次品，現(xiàn)從中采用有放回方式隨機(jī)抽取4件．設(shè)抽取的4件產(chǎn)品中次品數(shù)為X，求隨機(jī)變量X的分布列.（1）：采用有放回抽樣，隨機(jī)變量X服從二項(xiàng)分布嗎？采用有放回抽樣，則每次抽到次品的概率為0.08，且各次抽樣的結(jié)果相互獨(dú)立,此時(shí)X服從二項(xiàng)分布,即X～B(4，0.08).（2）：如果采用不放回抽樣，抽取的4件產(chǎn)品中次品數(shù)X服從二項(xiàng)分布嗎？若不服從，那么X的分布列是什么？不服從，根據(jù)古典概型求X的分布列.解：從100件產(chǎn)品中任取4件有 C_100^4 種不同的取法，從100件產(chǎn)品中任取4件，次品數(shù)X可能取0,1,2,3,4.恰有k件次品的取法有C_8^k C_92^(4-k)種.一般地，假設(shè)一批產(chǎn)品共有N件，其中有M件次品．從N件產(chǎn)品中隨機(jī)抽取n件(不放回），用X表示抽取的n件產(chǎn)品中的次品數(shù)，則X的分布列為P(X＝k）＝CkM Cn－kN－M CnN ，k＝m，m＋1，m＋2，…，r.其中n，N，M∈N*，M≤N，n≤N，m＝max{0，n－N＋M}，r＝min{n，M}，則稱隨機(jī)變量X服從超幾何分布．
人教版高中數(shù)學(xué)選修3全概率公式教學(xué)設(shè)計(jì)
2.某小組有20名射手，其中1，2，3，4級(jí)射手分別為2，6，9，3名.又若選1，2，3，4級(jí)射手參加比賽，則在比賽中射中目標(biāo)的概率分別為0.85，0.64，0.45，0.32，今隨機(jī)選一人參加比賽，則該小組比賽中射中目標(biāo)的概率為________. 【解析】設(shè)B表示“該小組比賽中射中目標(biāo)”，Ai(i=1，2，3，4)表示“選i級(jí)射手參加比賽”，則P(B)= P(Ai)P(B|Ai)= 2/20×0.85+ 6/20 ×0.64+ 9/20×0.45+ 3/20×0.32=0.527 5.答案：0.527 53.兩批相同的產(chǎn)品各有12件和10件，每批產(chǎn)品中各有1件廢品，現(xiàn)在先從第1批產(chǎn)品中任取1件放入第2批中，然后從第2批中任取1件，則取到廢品的概率為________. 【解析】設(shè)A表示“取到廢品”，B表示“從第1批中取到廢品”，有P(B)= 112，P(A|B)= 2/11 ，P(A| )= 1/11所以P(A)=P(B)P(A|B)+P( )P(A| )4．有一批同一型號(hào)的產(chǎn)品，已知其中由一廠生產(chǎn)的占 30%, 二廠生產(chǎn)的占 50% , 三廠生產(chǎn)的占 20%, 又知這三個(gè)廠的產(chǎn)品次品率分別為2% , 1%, 1%，問從這批產(chǎn)品中任取一件是次品的概率是多少？
人教版高中數(shù)學(xué)選修3條件概率教學(xué)設(shè)計(jì)
(2)方法一:第一次取到一件不合格品,還剩下99件產(chǎn)品,其中有4件不合格品,95件合格品,于是第二次又取到不合格品的概率為4/99,由于這是一個(gè)條件概率,所以P(B|A)=4/99.方法二:根據(jù)條件概率的定義,先求出事件A,B同時(shí)發(fā)生的概率P(AB)=(C_5^2)/(C_100^2 )=1/495,所以P(B|A)=(P"(" AB")" )/(P"(" A")" )=(1/495)/(5/100)=4/99.6.在某次考試中,要從20道題中隨機(jī)地抽出6道題,若考生至少答對其中的4道題即可通過;若至少答對其中5道題就獲得優(yōu)秀.已知某考生能答對其中10道題,并且知道他在這次考試中已經(jīng)通過,求他獲得優(yōu)秀成績的概率.解:設(shè)事件A為“該考生6道題全答對”,事件B為“該考生答對了其中5道題而另一道答錯(cuò)”,事件C為“該考生答對了其中4道題而另2道題答錯(cuò)”,事件D為“該考生在這次考試中通過”,事件E為“該考生在這次考試中獲得優(yōu)秀”,則A,B,C兩兩互斥,且D=A∪B∪C,E=A∪B,由古典概型的概率公式及加法公式可知P(D)=P(A∪B∪C)=P(A)+P(B)+P(C)=(C_10^6)/(C_20^6 )+(C_10^5 C_10^1)/(C_20^6 )+(C_10^4 C_10^2)/(C_20^6 )=(12" " 180)/(C_20^6 ),P(E|D)=P(A∪B|D)=P(A|D)+P(B|D)=(P"(" A")" )/(P"(" D")" )+(P"(" B")" )/(P"(" D")" )=(210/(C_20^6 ))/((12" " 180)/(C_20^6 ))+((2" " 520)/(C_20^6 ))/((12" " 180)/(C_20^6 ))=13/58,即所求概率為13/58.
人教版高中數(shù)學(xué)選修3正態(tài)分布教學(xué)設(shè)計(jì)
3.某縣農(nóng)民月均收入服從N(500,202)的正態(tài)分布,則此縣農(nóng)民月均收入在500元到520元間人數(shù)的百分比約為 . 解析:因?yàn)樵率杖敕恼龖B(tài)分布N(500,202),所以μ=500,σ=20,μ-σ=480,μ+σ=520.所以月均收入在[480,520]范圍內(nèi)的概率為0.683.由圖像的對稱性可知,此縣農(nóng)民月均收入在500到520元間人數(shù)的百分比約為34.15%.答案:34.15%4.某種零件的尺寸ξ(單位:cm)服從正態(tài)分布N(3,12),則不屬于區(qū)間[1,5]這個(gè)尺寸范圍的零件數(shù)約占總數(shù)的 . 解析:零件尺寸屬于區(qū)間[μ-2σ,μ+2σ],即零件尺寸在[1,5]內(nèi)取值的概率約為95.4%,故零件尺寸不屬于區(qū)間[1,5]內(nèi)的概率為1-95.4%=4.6%.答案:4.6%5. 設(shè)在一次數(shù)學(xué)考試中,某班學(xué)生的分?jǐn)?shù)X~N(110,202),且知試卷滿分150分,這個(gè)班的學(xué)生共54人,求這個(gè)班在這次數(shù)學(xué)考試中及格(即90分及90分以上)的人數(shù)和130分以上的人數(shù).解:μ=110,σ=20,P(X≥90)=P(X-110≥-20)=P(X-μ≥-σ),∵P(X-μσ)≈2P(X-μ130)=P(X-110>20)=P(X-μ>σ),∴P(X-μσ)≈0.683+2P(X-μ>σ)=1,∴P(X-μ>σ)=0.158 5,即P(X>130)=0.158 5.∴54×0.158 5≈9(人),即130分以上的人數(shù)約為9人.
