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人教版高中数学选修3二项式定理教学设计
二项式定理形式上的特点(1)二项展开式有n+1项,而不是n项.(2)二项式系数都是C_n^k(k=0,1,2,…,n),它与二项展开式中某一项的系数不一定相等.(3)二项展开式中的二项式系数的和等于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的降幂排列,从第一项起,次数由n次逐项减少1次直到0次,同时字母b按升幂排列,次数由0次逐项增加1次直到n次.1．判断(正确的打“√”，错误的打“×”)(1)(a＋b)n展开式中共有n项． ( )(2)在公式中，交换a，b的顺序对各项没有影响． ( )(3)Cknan－kbk是(a＋b)n展开式中的第k项． ( )(4)(a－b)n与(a＋b)n的二项式展开式的二项式系数相同． ( )[解析] (1)× 因为(a＋b)n展开式中共有n＋1项．(2)× 因为二项式的第k＋1项Cknan－kbk和(b＋a)n的展开式的第k＋1项Cknbn－kak是不同的，其中的a，b是不能随便交换的．(3)× 因为Cknan－kbk是(a＋b)n展开式中的第k＋1项．(4)√ 因为(a－b)n与(a＋b)n的二项式展开式的二项式系数都是Crn.[答案] (1)× (2)× (3)× (4)√
人教版高中数学选修3全概率公式教学设计
2.某小组有20名射手，其中1，2，3，4级射手分别为2，6，9，3名.又若选1，2，3，4级射手参加比赛，则在比赛中射中目标的概率分别为0.85，0.64，0.45，0.32，今随机选一人参加比赛，则该小组比赛中射中目标的概率为________. 【解析】设B表示“该小组比赛中射中目标”，Ai(i=1，2，3，4)表示“选i级射手参加比赛”，则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 53.两批相同的产品各有12件和10件，每批产品中各有1件废品，现在先从第1批产品中任取1件放入第2批中，然后从第2批中任取1件，则取到废品的概率为________. 【解析】设A表示“取到废品”，B表示“从第1批中取到废品”，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．有一批同一型号的产品，已知其中由一厂生产的占 30%, 二厂生产的占 50% , 三厂生产的占 20%, 又知这三个厂的产品次品率分别为2% , 1%, 1%，问从这批产品中任取一件是次品的概率是多少？
人教版高中数学选修3条件概率教学设计
(2)方法一:第一次取到一件不合格品,还剩下99件产品,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为4/99,由于这是一个条件概率,所以P(B|A)=4/99.方法二:根据条件概率的定义,先求出事件A,B同时发生的概率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.在某次考试中,要从20道题中随机地抽出6道题,若考生至少答对其中的4道题即可通过;若至少答对其中5道题就获得优秀.已知某考生能答对其中10道题,并且知道他在这次考试中已经通过,求他获得优秀成绩的概率.解:设事件A为“该考生6道题全答对”,事件B为“该考生答对了其中5道题而另一道答错”,事件C为“该考生答对了其中4道题而另2道题答错”,事件D为“该考生在这次考试中通过”,事件E为“该考生在这次考试中获得优秀”,则A,B,C两两互斥,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,即所求概率为13/58.
人教版高中数学选修3正态分布教学设计
3.某县农民月均收入服从N(500,202)的正态分布,则此县农民月均收入在500元到520元间人数的百分比约为 . 解析:因为月收入服从正态分布N(500,202),所以μ=500,σ=20,μ-σ=480,μ+σ=520.所以月均收入在[480,520]范围内的概率为0.683.由图像的对称性可知,此县农民月均收入在500到520元间人数的百分比约为34.15%.答案:34.15%4.某种零件的尺寸ξ(单位:cm)服从正态分布N(3,12),则不属于区间[1,5]这个尺寸范围的零件数约占总数的 . 解析:零件尺寸属于区间[μ-2σ,μ+2σ],即零件尺寸在[1,5]内取值的概率约为95.4%,故零件尺寸不属于区间[1,5]内的概率为1-95.4%=4.6%.答案:4.6%5. 设在一次数学考试中,某班学生的分数X~N(110,202),且知试卷满分150分,这个班的学生共54人,求这个班在这次数学考试中及格(即90分及90分以上)的人数和130分以上的人数.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分以上的人数约为9人.
人教A版高中数学必修一幂函数教学设计（2）
幂函数是在继一次函数、反比例函数、二次函数之后，又学习了单调性、最值、奇偶性的基础上，借助实例，总结出幂函数的概念，再借助图像研究幂函数的性质.课程目标1、理解幂函数的概念，会画幂函数y=x，y=x2，y=x3，y=x－1，y=x 的图象；2、结合这几个幂函数的图象，理解幂函数图象的变化情况和性质；3、通过观察、总结幂函数的性质，培养学生概括抽象和识图能力．数学学科素养1.数学抽象：用数学语言表示函数幂函数；2.逻辑推理：常见幂函数的性质；3.数学运算：利用幂函数的概念求参数；4.数据分析：比较幂函数大小；5.数学建模：在具体问题情境中，运用数形结合思想，利用幂函数性质、图像特点解决实际问题。重点：常见幂函数的概念、图象和性质；难点：幂函数的单调性及比较两个幂值的大小．
人教版高中数学选修3离散型随机变量及其分布列(1)教学设计
4.写出下列随机变量可能取的值，并说明随机变量所取的值表示的随机试验的结果．(1)一个袋中装有8个红球，3个白球，从中任取5个球，其中所含白球的个数为X.(2)一个袋中有5个同样大小的黑球，编号为1,2,3,4,5，从中任取3个球，取出的球的最大号码记为X.(3). 在本例(1)条件下，规定取出一个红球赢2元，而每取出一个白球输1元，以ξ表示赢得的钱数，结果如何？[解] (1)X可取0,1,2,3.X＝0表示取5个球全是红球；X＝1表示取1个白球，4个红球；X＝2表示取2个白球，3个红球；X＝3表示取3个白球，2个红球．(2)X可取3,4,5.X＝3表示取出的球编号为1,2,3；X＝4表示取出的球编号为1,2,4；1,3,4或2,3,4.X＝5表示取出的球编号为1,2,5；1,3,5；1,4,5；2,3,5；2,4,5或3,4,5.(3) ξ＝10表示取5个球全是红球；ξ＝7表示取1个白球，4个红球；ξ＝4表示取2个白球，3个红球；ξ＝1表示取3个白球，2个红球．
人教A版高中数学必修一单调性与最大（小）值教学设计（1）
《函数的单调性与最大（小）值}》系人教A版高中数学必修第一册第三章第二节的内容,本节包括函数的单调性的定义与判断及其证明、函数最大（小）值的求法。在初中学习函数时,借助图像的直观性研究了一些函数的增减性,这节内容是初中有关内容的深化、延伸和提高函数的单调性是函数众多性质中的重要性质之一,函数的单调性一节中的知识是前一节内容函数的概念和图像知识的延续,它和后面的函数奇偶性,合称为函数的简单性质,是今后研究指数函数、对数函数、幂函数及其他函数单调性的理论基础;在解决函数值域、定义域、不等式、比较两数大小等具体问需用到函数的单调性;同时在这一节中利用函数图象来研究函数性质的救开结合思想将贯穿于我们整个高中数学教学。
人教A版高中数学必修一用二分法求方程的近似解教学设计（1）
《数学1必修本（A版）》的第五章4.5.2用二分法求方程的近似解．本节课要求学生根据具体的函数图象能够借助计算机或信息技术工具计算器用二分法求相应方程的近似解，了解这种方法是求方程近似解的常用方法，从中体会函数与方程之间的联系；它既是本册书中的重点内容，又是对函数知识的拓展，既体现了函数在解方程中的重要应用，同时又为高中数学中函数与方程思想、数形结合思想、二分法的算法思想打下了基础，因此决定了它的重要地位．发展学生数学直观、数学抽象、逻辑推理和数学建模的核心素养。课程目标 学科素养1.通过具体实例理解二分法的概念及其使用条件．2.了解二分法是求方程近似解的常用方法，能借助计算器用二分法求方程的近似解．3.会用二分法求一个函数在给定区间内的零点，从而求得方程的近似解． a.数学抽象：二分法的概念；b.逻辑推理：运用二分法求近似解的原理；
人教版高中数学选修3一元线性回归模型及其应用教学设计
1.确定研究对象，明确哪个是解释变量，哪个是响应变量；2.由经验确定非线性经验回归方程的模型；3.通过变换，将非线性经验回归模型转化为线性经验回归模型；4.按照公式计算经验回归方程中的参数，得到经验回归方程；5.消去新元，得到非线性经验回归方程；6.得出结果后分析残差图是否有异常 ．跟踪训练1.一只药用昆虫的产卵数y与一定范围内的温度x有关，现收集了6组观测数据列于表中： 经计算得： 线性回归残差的平方和: ∑_(i=1)^6?〖(y_i-(y_i ) ?)〗^2=236,64,e^8.0605≈3167.其中 分别为观测数据中的温度和产卵数，i=1,2,3,4,5,6.(1)若用线性回归模型拟合，求y关于x的回归方程 (精确到0.1）；(2)若用非线性回归模型拟合，求得y关于x回归方程为 且相关指数R2＝0.9522． ①试与(1)中的线性回归模型相比较，用R2说明哪种模型的拟合效果更好 ?②用拟合效果好的模型预测温度为35℃时该种药用昆虫的产卵数.(结果取整数).
人教版高中英语必修3Festivals around the World说课稿3篇
Teaching plan for Unit 1 book3Good morning, teachers. It’s my great pleasure to be here because I can share my lesson with you and I can learn a lot from it. I’ll begin my lesson from the following four parts， the teaching material, the teaching methods, the studying methods and the teaching procedure.Firstly, let me talk about the teaching material. The content of my lesson is the reading passage festivals and celebrations of Unit 1 Festivals around the world. This passage is about festivals and celebrations. By studying this passage, we’ll enable the students to know that festivals exit everywhere, and many of festivals in different countries celebrate similar ideas. As we all know, the reading passage is the center of each unit. If the Ss can learn it well, it will be helpful to make the Ss learn the rest of this unit.After studying the teaching material, I think the teaching aims are as the followings:1. Knowledge aims:(1) The Ss can master the usage of the important words andexpressions.(2)The Ss can use the __________________ (grammar) in the proper situation.Make students know about the festivals all over the world and the detail of the festivals, such as origin, content, and the date of the holiday festivals.2. Ability aims:(1) Students can talk about festivals and celebrations in English(2) To improve the student’s reading ability, especially their skimming and scanning ability.3. Emotion aims:Make the Ss know about the foreign festivals, and respect other countries’ custom.Next, let’s come to the important points and the difficult points.The important point is how to make the Ss understand the text better and the difficult point is how can they talk about it. secondly， Teaching Methods:1. task-based Language Teaching2. Computer assisted language teaching.3. question-and–answer methodThirdly， Studying Methods:
人教A版高中数学必修二有限样本空间与随机事件事件的关系和运算教学设计
新知讲授（一）——随机试验 我们把对随机现象的实现和对它的观察称为随机试验，简称试验，常用字母E表示。我们通常研究以下特点的随机试验：（1）试验可以在相同条件下重复进行；（2）试验的所有可能结果是明确可知的，并且不止一个；（3）每次试验总是恰好出现这些可能结果中的一个，但事先不确定出现哪个结果。新知讲授（二）——样本空间思考一：体育彩票摇奖时，将10个质地和大小完全相同、分别标号0，1，2，...，9的球放入摇奖器中，经过充分搅拌后摇出一个球，观察这个球的号码。这个随机试验共有多少个可能结果？如何表示这些结果？根据球的号码，共有10种可能结果。如果用m表示“摇出的球的号码为m”这一结果，那么所有可能结果可用集合表示{0，1，2，3，4，5，6，7，8，9}.我们把随机试验E的每个可能的基本结果称为样本点，全体样本点的集合称为试验E的样本空间。
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 and Thinking教案一
The theme of the reading and thinking is about “Understanding how a problem was solved”.The Listening & Speaking & Talking is about international co-work to protect the Mount Tai, in which the students from seven countries came up with many solutions even create the Mount Tai App. This section aims at showing how to solve a difficult and even tough problem about protecting the cultural heritage by the international co-work. So in this section, cultivating students’ international awareness is very clear and important. Concretely, with the economic development, how to balance the protection of cultural relics and social development is a big challenge for human. In the 1950s, the Egyptian government wanted to build the Aswan Dam across the Nile to control floods, produce electricity and water farms. But the proposal led to protests because it would destroy a lot of cultural relics. The Egyptian had no choice but ask the UN for help. Therefore, a international cooperation about how to protect the cultural relics began, which involved the time length about 20 years and a large amount of fund. Then, the problems was solved. 1. Read quickly to get the main idea and the structure of the article; read careful to get detailed information.2. Learn to use the reading strategy---making a timeline3. Learn how to solve a tough problem by asking for help and cooperation4. Have the international awareness and understand the great strength of international cooperation.1. Read quickly to get the main idea and the structure of the article; read careful to get detailed information.2. Learn to use the reading strategy---making a timeline.3. Learn how to solve a tough problem by asking for help and cooperation.
高中思想政治人教版必修三《文化创新的途径》说课稿
二、说学情本课的教学对象为高二学生，他们思维活跃已具备一定归纳能力和分析、综合能力，能够自主地分析现实生活中的一些文化行为，但看问题往往比较偏激、片面，缺乏良好的逻辑思维能力。所以，在文化创新的途径上要对他们进行指导，以免走入误区。三、教学目标根据新课程标准、教材特点、学生的实际，我确定了如下教学目标：【知识与能力目标】1.理解文化创新的根本途径和两个基本途径;2.了解文化创新过程中需要坚持正确方向，克服错误倾向。
新人教版高中英语必修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 3 The Internet-Reading and Thinking教案一
Paragraph 3. Jan decided to start an IT club to teach old people how to use computers and the Internet. Paragraph 4. Jan has started taking online classes to learn more about how to use the Internet to make society better. Paragraph 5. Jan’s life has been greatly improved by the Internet. Step 5: Critical thinking:(1)How do you arrange your time spent on study and the Internet? Is it reasonable? I usually surf the Internet using my mobile phone for only an hour after class, and it is reasonable for me.(2)What are your online activities? Are they safe? I chat with my friends, read news and play games. I never give away my private information so I think they are safe.Step 4: summary Much has been written about the wonders of the World Wide Web. There are countless articles (1)______(tell) us how the Internet has made our lives more convenient. But the Internet has done a lot (2)_____(much) for people than simply make life more convenient. People’s lives (3) _________________(change) by online communities and social networks so far. Take Jan for example, who developed a serious illness that made her (4)_____(stick) at home with only her computer to keep (5)___(she) company. She joined an online group (6)______ she could share problems, support and advice with others. She considered the ability to remove the distance between people as one of the greatest (7)_______(benefit). She was so inspired (8)____ she started an IT club in which many people have been helped. She has started to learn more about how to use the Internet to make society better. Her next goal is to start a charity website to raise money (9)___ children in poor countries. Jan’s life has been (10)______(great) improved by the Internet. Step 5 Homework:Review what we have learned and find out the key language points in the text.
新人教版高中英语必修2Unit 3 The Internet-Reading For Writing教案一
⑦identity theft 身份盗窃⑧chat room 聊天室⑨draft your blog post 起草博客帖子⑩post embarrassing photos 张贴尴尬照片 【话题句式】 1. How do you stay safe online and avoid bad experiences on the Internet? 你如何在网上保持安全, 避免在网上的不良经历? 2. I’m not an expert, but many years as a blogger have taught me a thing or two. 我不是专家, 但作为一个博主, 我已经学了好几年了。 3. If you see or read something that makes you feel uncomfortable, leave the site immediately. 如果你看到或读到一些让你觉得不舒服的东西, 立即离开这个网站。4. Don’t give out your address or phone number. 别告诉别人你的地址或电话号码。 5. Identity theft is a common and serious problem. 身份盗窃是一个常见而严重的问题。6. Being online is no excuse for being rude, and you don’t want to become a target for a troll or cyberbully. 上网并不是无礼的借口, 你也不想成为发挑衅帖子的人或网络恶霸的目标。 7. Trolls often use several false names so that they can stay on a site. 发挑衅帖子的人经常使用几个假名, 这样他们就可以留在一个网站上。8. However, the more polite you are, the less likely it is you will be attacked. 然而, 你越有礼貌, 你被攻击的可能性就越小。
新人教版高中英语必修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.
新人教版高中英语必修1Unit 3 Sports and Fitness-Reading for Writing教案
Then have them write a short paragraph to describe and explain their changes. After that, get the Ss to exchange their drafts with their partners and use the checklist to give feedback on their drafts, and finally revise it.Step 5 Summary of how to write a wellness book1.健康书的审题步骤：第一步：明确要求该写作属于经验分享，故要用第一人称来写;时态以一股现在时为主。第二步：确定段落该类文章可以从以下三个方面人手:Para.1首先表明写作的目的Para.2自己的做法及心得体会Para.3表示期望及感谢第三步：提炼要点2.健康书常见句式：1) It is an honor for me to share my favorite sport with you,2) It makes me feel relaxed playing with my friends.3) It makes me rid myself of stress while playing with my friends.4) Moreover, it provides me a valuable chance to communicate with others.5) I we eat too little or too much, or if we choose the wrong food, we may become sick.6) We can do something to change the poor situation.Step 6Homework假如你的老师让你在班级Wellness Bok上分享自己的亲身经历及心得，请根据以下要点写一篇80字左右的文章1. 你喜欢的运动是什么？2. 你最喜欢的原因是什么？3. 你参加锻炼的体会。