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新人教版高中英語選修2Unit 1 Science and Scientists-Learning about Language教學(xué)設(shè)計
Step 7: complete the discourse according to the grammar rules.Cholera used to be one of the most 1.__________ (fear) diseases in the world. In the early 19th century, _2_________ an outbreak of cholera hit Europe, millions of people died. But neither its cause, 3__________ its cure was understood. A British doctor, John Snow, wanted to solve the problem and he knew that cholera would not be controlled _4_________ its cause was found. In general, there were two contradictory theories 5 __________ explained how cholera spread. The first suggested that bad air caused the disease. The second was that cholera was caused by an _6_________(infect) from germs in food or water. John Snow thought that the second theory was correct but he needed proof. So when another outbreak of cholera hit London in 1854, he began to investigate. Later, with all the evidence he _7_________ (gather), John Snow was able to announce that the pump water carried cholera germs. Therefore, he had the handle of the pump _8_________ (remove) so that it couldn't be used. Through his intervention，the disease was stopped in its tracks. What is more, John Snow found that some companies sold water from the River Thames that __9__________________ (pollute) by raw waste. The people who drank this water were much more likely _10_________ (get) cholera than those who drank pure or boiled water. Through John Snow's efforts, the _11_________ (threaten) of cholera around the world saw a substantial increase. Keys： 1.feared 2.when 3. nor 4.unless 5.that/which 6.infection 7.had gathered 8.removed 9.was polluted 10.to get 11. threat
新人教版高中英語選修2Unit 1 Science and Scientists-Discovering useful structures教學(xué)設(shè)計
The grammatical structure of this unit is predicative clause. Like object clause and subject clause, predicative clause is one of Nominal Clauses. The leading words of predicative clauses are that, what, how, what, where, as if, because, etc.The design of teaching activities aims to guide students to perceive the structural features of predicative clauses and think about their ideographic functions. Beyond that, students should be guided to use this grammar in the context apporpriately and flexibly.1. Enable the Ss to master the usage of the predicative clauses in this unit.2. Enable the Ss to use the predicative patterns flexibly.3. Train the Ss to apply some skills by doing the relevant exercises.1.Guide students to perceive the structural features of predicative clauses and think about their ideographic functions.2.Strengthen students' ability of using predicative clauses in context, but also cultivate their ability of text analysis and logical reasoning competence.Step1: Underline all the examples in the reading passage, where noun clauses are used as the predicative. Then state their meaning and functions.1) One theory was that bad air caused the disease.2) Another theory was that cholera was caused by an infection from germs in food or water.3) The truth was that the water from the Broad Street had been infected by waste.Sum up the rules of grammar:1. 以上黑體部分在句中作表語。2. 句1、2、3中的that在從句中不作成分，只起連接作用。 Step2: Review the basic components of predicative clauses1.Definition
新人教版高中英語選修2Unit 4 Journey Across a Vast Land教學(xué)設(shè)計
當(dāng)孩子們由父母陪同時，他們才被允許進入這個運動場。3．過去分詞(短語)作狀語時的幾種特殊情況(1)過去分詞(短語)在句中作時間、條件、原因、讓步狀語時，相當(dāng)于對應(yīng)的時間、條件、原因及讓步狀語從句。Seen from the top of the mountain (＝When it is seen from the top of the mountain), the whole town looks more beautiful.從山頂上看，整個城市看起來更美了。Given ten more minutes (＝If we are given ten more minutes), we will finish the work perfectly.如果多給十分鐘，我們會完美地完成這項工作。Greatly touched by his words (＝Because she was greatly touched by his words), she was full of tears.由于被他的話深深地感動，她滿眼淚花。Warned of the storm (＝Though they were warned of the storm), the farmers were still working on the farm.盡管被警告了風(fēng)暴的到來，但農(nóng)民們?nèi)栽谵r(nóng)場干活。(2)過去分詞(短語)在句中作伴隨、方式等狀語時，可改為句子的并列謂語或改為并列分句。The teacher came into the room, followed by two students (＝and was followed by two students)．后面跟著兩個學(xué)生，老師走進了房間。He spent the whole afternoon, accompanied by his mom(＝and was accompanied by his mom)．他由母親陪著度過了一整個下午。
新人教版高中英語選修2Unit 1 Science and Scientists-Reading and thinking教學(xué)設(shè)計
Step 5： After learning the text, discuss with your peers about the following questions:1.John Snow believed Idea 2 was right. How did he finally prove it?2. Do you think John Snow would have solved this problem without the map?3. Cholera is a 19th century disease. What disease do you think is similar to cholera today?SARS and Covid-19 because they are both deadly and fatally infectious, have an unknown cause and need serious public health care to solve them urgently.keys:1. John Snow finally proved his idea because he found an outbreak that was clearly related to cholera, collected information and was able to tie cases outside the area to the polluted water.2. No. The map helped John Snow organize his ideas. He was able to identify those households that had had many deaths and check their water-drinking habits. He identified those houses that had had no deaths and surveyed their drinking habits. The evidence clearly pointed to the polluted water being the cause.3. SARS and Covid-19 because they are both deadly and fatally infectious, have an unknown cause and need serious public health care to solve them urgently.Step 6: Consolidate what you have learned by filling in the blanks:John Snow was a well-known _1___ in London in the _2__ century. He wanted to find the _3_____ of cholera in order to help people ___4_____ it. In 1854 when a cholera __5__ London, he began to gather information. He ___6__ on a map ___7___ all the dead people had lived and he found that many people who had ___8____ (drink) the dirty water from the __9____ died. So he decided that the polluted water ___10____ cholera. He suggested that the ___11__ of all water supplies should be _12______ and new methods of dealing with ____13___ water be found. Finally, “King Cholera” was __14_____.Keys: 1. doctor 2. 19th 3.cause 4.infected with 5.hit 6.marked 7.where 8.drunk 9.pump 10.carried 11.source 12.examined 13.polluted 14.defeatedHomework: Retell the text after class and preview its language points
新人教版高中英語選修2Unit 1 Science and Scientists-Using langauge教學(xué)設(shè)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!
新人教版高中英語選修2Unit 2 Bridging Cultures-Discovering useful structures教學(xué)設(shè)計
The grammar of this unit is designed to review noun clauses. Sentences that use nouns in a sentence are called noun clauses. Nominal clauses can act as subject, object, predicate, appositive and other components in compound sentences. According to the above-mentioned different grammatical functions, nominal clauses are divided into subject clause, object clause, predicate clause and appositive clause. In this unit, we will review the three kinds of nominal clauses. Appositive clauses are not required to be mastered in the optional compulsory stage, so they are not involved.1. Guide the students to judge the compound sentences and determine the composition of the clauses in the sentence.2. Instruct students to try to learn grammar by generalizing grammar rules, controlling written practice, and semi-open oral output.3. Inspire the students to systematize the function and usage of noun clause1.Instruct students to try to learn grammar by generalizing grammar rules, controlling written practice, and semi-open oral output.2.Inspire the students to systematize the function and usage of noun clauseStep1: The teacher ask studetns to find out more nominal clauses from the reading passage and udnerline the nominal clauses.
新人教版高中英語選修2Unit 5 First Aid-Discovering useful structures教學(xué)設(shè)計
You have no excuse for not going.你沒有理由不去。He was punished for not having finished his homework.他因未完成作業(yè)而受到懲罰。2．動詞ing形式復(fù)合結(jié)構(gòu)由物主代詞或人稱代詞賓格、名詞所有格或普通格加動詞ing，即“sb./sb.'s＋doing”構(gòu)成。動詞ing形式的復(fù)合結(jié)構(gòu)實際上是給動詞ing形式加了一個邏輯主語。動詞ing形式的復(fù)合結(jié)構(gòu)有四種形式：①形容詞性物主代詞＋動詞ing②名詞所有格＋動詞ing③代詞賓格＋動詞ing④名詞＋動詞ingHer coming to help encouraged all of us.她來幫忙鼓舞了我們所有人。The baby was made awake by the door suddenly shutting.這個嬰兒被突然的關(guān)門聲吵醒了。Can you imagine him/Jack cooking at home?你能想象他/杰克在家做飯的樣子嗎？無生命名詞無論是作主語還是作賓語都不能用第②種形式。Tom's winning first prize last year impressed me a lot.湯姆去年得了一等獎使我印象深刻。Do you mind my/me/Jack's/Jack leaving now?你介意我/杰克現(xiàn)在離開嗎？Excuse me for my not coming on time．很抱歉我沒能按時來。His father's being ill made him worried.他父親病了，他很擔(dān)心。We are looking forward to the singer's/the singer to give us a concert.我們盼望著這位歌手來給我們舉辦一場演唱會。
人教版高中政治選修3美國的聯(lián)邦制教案
3、聯(lián)邦制的弊端：（1）、效率不高：（2）、集團分享權(quán)力，維護資產(chǎn)階級的利益，不顧人民要求。在美國實行聯(lián)邦制的二百多年問，聯(lián)邦制的弊端也顯露無遺。美國聯(lián)邦制的最大問題是效率不高，聯(lián)邦政府與州政府之間相互扯皮、推諉，各州政府之間各自為政。全國性資產(chǎn)階級利益集團與地方性資產(chǎn)階級利益集團分享權(quán)力，對于廣大人民群眾的要求，資產(chǎn)階級則利用國家結(jié)構(gòu)形式的特點相互推卸責(zé)任。當(dāng)大多數(shù)資產(chǎn)階級利益集團意見接近時，聯(lián)邦制既能保護州的靈活性，又能保證中央的權(quán)威；當(dāng)資產(chǎn)階級利益集團之間矛盾重重時，聯(lián)邦制就處于低效運轉(zhuǎn)之中。相關(guān)鏈接：1954年，美國最高法院在一項判決中宣布，公立學(xué)校實行種族隔離、拒絕黑人入學(xué)是違反憲法的。這一裁決引起南方一些州的抵制，一些州竟以暴力阻止黑人進入公立學(xué)校。
人教版高中政治選修3國際組織概觀教案
4、中國積極發(fā)展與區(qū)域性國際組織的關(guān)系。中國積極發(fā)展與區(qū)域性國際組織的關(guān)系。中國與歐盟建立了領(lǐng)導(dǎo)人年度會晤機制，致力于發(fā)展全面戰(zhàn)略伙伴關(guān)系。中國重視與非洲國家的傳統(tǒng)友誼，與非洲聯(lián)盟團結(jié)合作。中國與阿拉伯國家聯(lián)盟、石油輸出國組織等發(fā)展中國家組建的國際組織發(fā)展友好關(guān)系，支持它們維護自身的正當(dāng)權(quán)益，并與它們共同為建立公正合理的國際政治經(jīng)濟新秩序而努力。新中國與國際組織關(guān)系的歷史演變大致經(jīng)歷了三個時期。從中華人民共和國建立初期到1971年：新中國被排斥在聯(lián)合國等國際組織之外，為恢復(fù)在聯(lián)合國的合法席位進行了不懈的斗爭。從1 9 7 1年到改革開放前：中國恢復(fù)了在聯(lián)合國的合法席位，并與大批國際組織建立、恢復(fù)了友好合作關(guān)系。改革開放以來：中國恢復(fù)了在世界銀行和國際貨幣基金組織的席位，加入了世界貿(mào)易組織、亞太經(jīng)合組織等經(jīng)濟組織。世界銀行出資興建的希望小學(xué)小結(jié)：4個主要特征：國際組織的四個主要特征即：①跨國性、②目的性、③組織性、④自主性。
人教版高中政治選修3國家的本質(zhì)教案
①含義：即國家管理形式，是國家政權(quán)的組織形式②政體的必要性和重要性A、行使職能B、維護其根本利益掌握國家政權(quán)的階級為實現(xiàn)政治統(tǒng)治、行使社會管理職能，必然要采取某種形式組織政權(quán)機關(guān)。統(tǒng)治階級為維護其根本利益，總是力求采用最有效的政權(quán)組織形式。3、國體與政體的關(guān)系（板書）（1）、政體的多樣性（2）、國體與政體的關(guān)系①國體決定政體，并通過一定的政體來體現(xiàn)；政體體現(xiàn)國體，并服務(wù)于特定的國體。適當(dāng)?shù)恼w能夠鞏固國體，不適當(dāng)?shù)恼w會危害國體。補充：政體由國體決定并反映國體，國體是主要的方面。但是，政體也具有一定的獨立性，影響它形成的因素主要有：歷史條件、階級力量對比、傳統(tǒng)習(xí)慣、國際環(huán)境影響等。②專政政體國體與政體，即是國家制度中內(nèi)容與形式兩個方面(3)從國體、政體兩個方面看民主制國家補充：專政即是主要依靠暴力實行的統(tǒng)治，它與民主相對立，屬于國體的范疇，而專制則與法制相對立，屬于政體的范疇。
人教版高中政治選修3美國的利益集團教案
（3）、各種利益集團內(nèi)部很少有什么民主機制，大都為少數(shù)人所控制——從利益集團內(nèi)部的管理機制看；廣大群眾常常對某些組織寄予期望，投人力量，但是他們的利益卻往往得不到關(guān)注。（4）、利益集團為政府腐敗提供了肥沃的土壤。利益集團的活動方式，在很大程度上是用金錢購買政治影響力，是一種滋養(yǎng)腐敗的行為——從利益集團對政府的負(fù)面影響看。實際上，在國會議員、政府官員與利益集團之間，已經(jīng)形成一種相互依賴的共生關(guān)系。3、利益集團機制的隱蔽性、欺騙性及其實質(zhì)：美國政壇中的利益集團機制，是資產(chǎn)階級控制國家機器的一種特殊形式，具有相當(dāng)強的隱蔽性和欺騙性。表面上看，利益集團是所謂的“民意代表”，向政府反映各階層、群體的觀點和利益，實質(zhì)上是資產(chǎn)階級在“民意”的幌子下控制權(quán)力。
人教版高中政治選修3美國的三權(quán)分立教案
國會一直在政治生活中居于主導(dǎo)地位；到了當(dāng)代，則是總統(tǒng)居于主導(dǎo)地位。由于司法機關(guān)無權(quán)直接支配社會力量和財富，相比之下，聯(lián)邦法院力量向來較弱。第二次世界大戰(zhàn)后，由于美國一直追逐全球霸權(quán)，美國總統(tǒng)的戰(zhàn)爭權(quán)力更加強化，向海外派遣軍隊的次數(shù)更加頻繁。美國人民日益覺察到這種不斷增長的“帝王般總統(tǒng)職位”可能帶來的危險。2、三權(quán)分立制的本質(zhì)——是一種資產(chǎn)階級民主制度美國的三權(quán)分立制本質(zhì)上是一種資產(chǎn)階級民主制度。二百多年的歷史經(jīng)驗表明，它有效地維護了美國資產(chǎn)階級的統(tǒng)治。但是，廣大勞動人民不可能在這種制度下享有真正的民主。雖然三大權(quán)力機關(guān)之間互相制約、平衡，卻沒有一個代表人民意志的權(quán)力機關(guān)，因而不可能實現(xiàn)人民群眾的多數(shù)人統(tǒng)治?！蟊究蝾}小結(jié)：◇3個3種權(quán)力：3種權(quán)力即立法權(quán)、行政權(quán)和司法權(quán)；3個弊端：即三權(quán)分立原則的3 個弊端；3個中央政權(quán)機構(gòu)即立法機關(guān)、行政機關(guān)和司法機關(guān)；◇2個原因：即確立三權(quán)分立原則的原因◇1個本質(zhì)：即三權(quán)分立原則的本質(zhì)
人教版高中政治選修3走進世界貿(mào)易組織教案
中國加人世貿(mào)組織承擔(dān)的義務(wù)主要包括：進一步降低關(guān)稅；取消非關(guān)稅貿(mào)易壁壘；取消被禁止的出口補貼；開放國內(nèi)市場，特別是服務(wù)市場；擴大對知識產(chǎn)權(quán)的保護范圍；放寬和改善外資政策；增加貿(mào)易政策的透明度等。履行這些義務(wù)對中國提出了挑戰(zhàn)。中國加入世貿(mào)組織后，享受多邊、無條件、穩(wěn)定的最惠國待遇和國民待遇；參與世貿(mào)組織各機構(gòu)的所有會議；參與貿(mào)易政策審議，對貿(mào)易伙伴的貿(mào)易政策進行質(zhì)詢和監(jiān)督；利用世貿(mào)組織的爭端解決機制解決貿(mào)易糾紛；參與新一輪多邊貿(mào)易談判，制定多邊貿(mào)易規(guī)則；享受發(fā)展中國家特有的權(quán)益。②意義：中國正充分行使這些權(quán)利，積極主動地參與、加強和發(fā)展多邊貿(mào)易體制，推動建立公平、合理的國際經(jīng)濟新秩序，維護國家利益。相關(guān)鏈接：2005年7月．中國倡議的WTO小型部長級會議在大連召開，世貿(mào)組織總干事和三十多個成員的代表出席會議。
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
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個不同元素中任選4個元素的排列問題,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?能被5整除的有多少個?(2)這些四位數(shù)中大于6 500的有多少個?解:(1)偶數(shù)的個位數(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,由分步乘法計數(shù)原理,知共有四位偶數(shù)A_3^1·A_6^3=360(個);能被5整除的數(shù)個位必須是5,故有A_6^3=120(個).(2)最高位上是7時大于6 500,有A_6^3種,最高位上是6時,百位上只能是7或5,故有2×A_5^2種.由分類加法計數(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).
人教版高中數(shù)學(xué)選修3超幾何分布教學(xué)設(shè)計
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抽取4件．設(shè)抽取的4件產(chǎn)品中次品數(shù)為X，求隨機變量X的分布列.（1）：采用有放回抽樣，隨機變量X服從二項分布嗎？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)果相互獨立,此時X服從二項分布,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}，則稱隨機變量X服從超幾何分布．
人教版高中數(shù)學(xué)選修3二項式定理教學(xué)設(shè)計
二項式定理形式上的特點(1)二項展開式有n+1項,而不是n項.(2)二項式系數(shù)都是C_n^k(k=0,1,2,…,n),它與二項展開式中某一項的系數(shù)不一定相等.(3)二項展開式中的二項式系數(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,從第一項起,次數(shù)由n次逐項減少1次直到0次,同時字母b按升冪排列,次數(shù)由0次逐項增加1次直到n次.1．判斷(正確的打“√”，錯誤的打“×”)(1)(a＋b)n展開式中共有n項． ( )(2)在公式中，交換a，b的順序?qū)Ω黜棝]有影響． ( )(3)Cknan－kbk是(a＋b)n展開式中的第k項． ( )(4)(a－b)n與(a＋b)n的二項式展開式的二項式系數(shù)相同． ( )[解析] (1)× 因為(a＋b)n展開式中共有n＋1項．(2)× 因為二項式的第k＋1項Cknan－kbk和(b＋a)n的展開式的第k＋1項Cknbn－kak是不同的，其中的a，b是不能隨便交換的．(3)× 因為Cknan－kbk是(a＋b)n展開式中的第k＋1項．(4)√ 因為(a－b)n與(a＋b)n的二項式展開式的二項式系數(shù)都是Crn.[答案] (1)× (2)× (3)× (4)√
人教版高中數(shù)學(xué)選修3全概率公式教學(xué)設(shè)計
2.某小組有20名射手，其中1，2，3，4級射手分別為2，6，9，3名.又若選1，2，3，4級射手參加比賽，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
(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”,事件C為“該考生答對了其中4道題而另2道題答錯”,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
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:因為月收入服從正態(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,這個班的學(xué)生共54人,求這個班在這次數(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.
人教版高中數(shù)學(xué)選修3組合與組合數(shù)教學(xué)設(shè)計
解析:因為減法和除法運算中交換兩個數(shù)的位置對計算結(jié)果有影響,所以屬于組合的有2個.答案:B2.若A_n^2=3C_(n"-" 1)^2,則n的值為( )A.4 B.5 C.6 D.7 解析:因為A_n^2=3C_(n"-" 1)^2,所以n(n-1)=(3"(" n"-" 1")(" n"-" 2")" )/2,解得n=6.故選C.答案:C 3.若集合A={a1,a2,a3,a4,a5},則集合A的子集中含有4個元素的子集共有 個. 解析:滿足要求的子集中含有4個元素,由集合中元素的無序性,知其子集個數(shù)為C_5^4=5.答案:54.平面內(nèi)有12個點,其中有4個點共線,此外再無任何3點共線,以這些點為頂點,可得多少個不同的三角形?解:(方法一)我們把從共線的4個點中取點的多少作為分類的標(biāo)準(zhǔn):第1類,共線的4個點中有2個點作為三角形的頂點,共有C_4^2·C_8^1=48(個)不同的三角形;第2類,共線的4個點中有1個點作為三角形的頂點,共有C_4^1·C_8^2=112(個)不同的三角形;第3類,共線的4個點中沒有點作為三角形的頂點,共有C_8^3=56(個)不同的三角形.由分類加法計數(shù)原理,不同的三角形共有48+112+56=216(個).(方法二 間接法)C_12^3-C_4^3=220-4=216(個).