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人教版高中数学选择性必修二等比数列的前n项和公式 (1) 教学设计
新知探究国际象棋起源于古代印度.相传国王要奖赏国际象棋的发明者，问他想要什么.发明者说：“请在棋盘的第1个格子里放上1颗麦粒，第2个格子里放上2颗麦粒，第3个格子里放上4颗麦粒，依次类推，每个格子里放的麦粒都是前一个格子里放的麦粒数的2倍，直到第64个格子.请给我足够的麦粒以实现上述要求.”国王觉得这个要求不高，就欣然同意了.假定千粒麦粒的质量为40克，据查，2016--2017年度世界年度小麦产量约为7.5亿吨，根据以上数据，判断国王是否能实现他的诺言.问题1：每个格子里放的麦粒数可以构成一个数列,请判断分析这个数列是否是等比数列?并写出这个等比数列的通项公式.是等比数列,首项是1，公比是2，共64项. 通项公式为〖a_n=2〗^(n-1)问题2：请将发明者的要求表述成数学问题.
人教版高中数学选择性必修二等差数列的概念（2）教学设计
二、典例解析例3.某公司购置了一台价值为220万元的设备，随着设备在使用过程中老化，其价值会逐年减少.经验表明，每经过一年其价值会减少d(d为正常数）万元.已知这台设备的使用年限为10年，超过10年 ，它的价值将低于购进价值的5%，设备将报废.请确定d的范围.分析：该设备使用n年后的价值构成数列{an}，由题意可知，an＝an－1－d (n≥2). 即：an－an－1＝－d.所以{an}为公差为－d的等差数列.10年之内（含10年），该设备的价值不小于（220×5%=）11万元；10年后，该设备的价值需小于11万元．利用{an}的通项公式列不等式求解．解：设使用n年后，这台设备的价值为an万元，则可得数列{an}．由已知条件，得an＝an－1－d（n≥2）．所以数列{an}是一个公差为－d的等差数列.因为a1＝220－d，所以an＝220－d＋(n－1)(－d)＝220－nd. 由题意，得a10≥11，a11＜11. 即：{█("220－10d≥11" @"220－11d＜11" )┤解得19<d≤20.9所以，d的求值范围为19<d≤20.9
人教版高中数学选择性必修二等比数列的前n项和公式 (2) 教学设计
二、典例解析例10. 如图，正方形ABCD 的边长为5cm ，取正方形ABCD 各边的中点E,F,G,H, 作第2个正方形 EFGH，然后再取正方形EFGH各边的中点I,J,K,L，作第3个正方形IJKL ，依此方法一直继续下去. (1) 求从正方形ABCD 开始，连续10个正方形的面积之和；(2) 如果这个作图过程可以一直继续下去，那么所有这些正方形的面积之和将趋近于多少？分析：可以利用数列表示各正方形的面积，根据条件可知，这是一个等比数列。解：设正方形的面积为a_1，后续各正方形的面积依次为a_2, a_(3, ) 〖…,a〗_n,…，则a_1=25,由于第k+1个正方形的顶点分别是第k个正方形各边的中点，所以a_(k+1)=〖1/2 a〗_k,因此{a_n}，是以25为首项，1/2为公比的等比数列.设{a_n}的前项和为S_n（1）S_10=(25×[1-(1/2)^10 ] )/("1 " -1/2)=50×[1-(1/2)^10 ]=25575/512所以，前10个正方形的面积之和为25575/512cm^2.(2)当无限增大时，无限趋近于所有正方形的面积和
人教版高中数学选择性必修二数列的概念（1）教学设计
情景导学古语云:“勤学如春起之苗,不见其增,日有所长”如果对“春起之苗”每日用精密仪器度量,则每日的高度值按日期排在一起,可组成一个数列. 那么什么叫数列呢?二、问题探究1. 王芳从一岁到17岁，每年生日那天测量身高，将这些身高数据（单位：厘米）依次排成一列数：75,87,96,103,110,116,120,128,138，145,153,158,160,162,163,165,168 ①记王芳第i岁的身高为 h_i ，那么h_1=75 , h_2=87, 〖"…" ，h〗_17=168.我们发现h_i中的i反映了身高按岁数从1到17的顺序排列时的确定位置，即h_1=75 是排在第1位的数，h_2=87是排在第2位的数〖"…" ，h〗_17 =168是排在第17位的数，它们之间不能交换位置，所以①具有确定顺序的一列数。2. 在两河流域发掘的一块泥板（编号K90，约生产于公元前7世纪）上，有一列依次表示一个月中从第1天到第15天，每天月亮可见部分的数：5,10,20,40,80,96,112,128,144,160,176,192,208,224,240. ②
人教版高中数学选择性必修二导数的四则运算法则教学设计
求函数的导数的策略(1)先区分函数的运算特点，即函数的和、差、积、商，再根据导数的运算法则求导数；(2)对于三个以上函数的积、商的导数，依次转化为“两个”函数的积、商的导数计算．跟踪训练1 求下列函数的导数：(1)y＝x2＋log3x； (2)y＝x3·ex； (3)y＝cos xx.[解] (1)y′＝(x2＋log3x)′＝(x2)′＋(log3x)′＝2x＋1xln 3.(2)y′＝(x3·ex)′＝(x3)′·ex＋x3·(ex)′＝3x2·ex＋x3·ex＝ex(x3＋3x2)．(3)y′＝cos xx′＝?cos x?′·x－cos x·?x?′x2＝－x·sin x－cos xx2＝－xsin x＋cos xx2.跟踪训练2 求下列函数的导数（1）y＝tan x； （2）y＝2sin x2cos x2解析：（1）y＝tan x＝sin xcos x，故y′＝?sin x?′cos x－?cos x?′sin x?cos x?2＝cos2x＋sin2xcos2x＝1cos2x.（2）y＝2sin x2cos x2＝sin x，故y′＝cos x.例5 日常生活中的饮用水通常是经过净化的，随着水的纯净度的提高，所需进化费用不断增加，已知将1t水进化到纯净度为x%所需费用（单位：元），为c(x)=5284/(100-x) (80<x<100)求进化到下列纯净度时，所需进化费用的瞬时变化率：（1） 90% ；（2） 98%解：净化费用的瞬时变化率就是净化费用函数的导数；c^' (x)=〖(5284/(100-x))〗^'=(5284^’×(100-x)-"5284 " 〖(100-x)〗^’)/〖(100-x)〗^2 =(0×(100-x)-"5284 " ×(-1))/〖(100-x)〗^2 ="5284 " /〖(100-x)〗^2
人教版高中数学选择性必修二导数的概念及其几何意义教学设计
新知探究前面我们研究了两类变化率问题：一类是物理学中的问题，涉及平均速度和瞬时速度；另一类是几何学中的问题，涉及割线斜率和切线斜率。这两类问题来自不同的学科领域，但在解决问题时，都采用了由“平均变化率”逼近“瞬时变化率”的思想方法；问题的答案也是一样的表示形式。下面我们用上述思想方法研究更一般的问题。探究1： 对于函数y=f(x) ，设自变量x从x_0变化到x_0+ ?x ，相应地，函数值y就从f(x_0)变化到f(〖x+x〗_0) 。这时， x的变化量为?x，y的变化量为?y=f(x_0+?x)-f(x_0)我们把比值?y/?x，即?y/?x=(f(x_0+?x)-f(x_0)" " )/?x叫做函数从x_0到x_0+?x的平均变化率。1．导数的概念如果当Δx→0时，平均变化率ΔyΔx无限趋近于一个确定的值，即ΔyΔx有极限，则称y＝f (x)在x＝x0处____，并把这个________叫做y＝f (x)在x＝x0处的导数(也称为__________)，记作f ′(x0)或________，即
人教版高中数学选择性必修二等比数列的概念 (2) 教学设计
二、典例解析例4. 用 10 000元购买某个理财产品一年.（1）若以月利率0.400%的复利计息，12个月能获得多少利息（精确到1元）？（2）若以季度复利计息，存4个季度，则当每季度利率为多少时，按季结算的利息不少于按月结算的利息（精确到10^(-5)）？分析：复利是指把前一期的利息与本金之和算作本金，再计算下一期的利息.所以若原始本金为a元，每期的利率为r ，则从第一期开始，各期的本利和a , a(1+r)，a(1+r)^2…构成等比数列.解：（1）设这笔钱存 n 个月以后的本利和组成一个数列{a_n }，则{a_n }是等比数列，首项a_1=10^4 (1+0.400%)，公比 q=1+0.400%，所以a_12=a_1 q^11 〖=10〗^4 (1+0.400%)^12≈10 490.7.所以，12个月后的利息为10 490.7-10^4≈491（元）.解：（2）设季度利率为 r ，这笔钱存 n 个季度以后的本利和组成一个数列{b_n }，则{b_n }也是一个等比数列，首项 b_1=10^4 (1+r)，公比为1+r，于是 b_4=10^4 (1+r)^4.
人教版高中数学选择性必修二函数的单调性(1) 教学设计
1．判断正误(正确的打“√”，错误的打“×”)(1)函数f (x)在区间(a，b)上都有f ′(x)＜0，则函数f (x)在这个区间上单调递减． ( )(2)函数在某一点的导数越大，函数在该点处的切线越“陡峭”． ( )(3)函数在某个区间上变化越快，函数在这个区间上导数的绝对值越大．( )(4)判断函数单调性时，在区间内的个别点f ′(x)＝0，不影响函数在此区间的单调性．( )[解析] (1)√ 函数f (x)在区间(a，b)上都有f ′(x)＜0，所以函数f (x)在这个区间上单调递减，故正确．(2)× 切线的“陡峭”程度与|f ′(x)|的大小有关，故错误．(3)√ 函数在某个区间上变化的快慢，和函数导数的绝对值大小一致．(4)√ 若f ′(x)≥0(≤0)，则函数f (x)在区间内单调递增(减)，故f ′(x)＝0不影响函数单调性．[答案] (1)√ (2)× (3)√ (4)√例1. 利用导数判断下列函数的单调性:（1）f(x)=x^3+3x; （2） f(x)=sinx-x,x∈(0,π); (3)f(x)=(x-1)/x解: (1) 因为f(x)=x^3+3x, 所以f^' (x)=〖3x〗^2+3=3(x^2+1)>0所以f(x)=x^3+3x ，函数在R上单调递增，如图（1）所示
新人教版高中英语选修2Unit 5 Learning about Language教学设计
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.
新人教版高中英语选修2Unit 5 Reading and thinking教学设计
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
新人教版高中英语选修2Unit 5 Using langauge-Listening教学设计
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.
新人教版高中英语选修2Unit 2 Learning about Language教学设计
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
新人教版高中英语选修2Unit 2 Reading and thinking教学设计
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.
新人教版高中英语选修2Unit 2 Using langauge-Listening教学设计
? B: Absolutely! Getting involved with Chinese cultural activities there definitely helped a lot. I got to practice my Chinese on a daily basis, and I could learn how native Chinese speakers spoke.? A: What do you feel is your biggest achievement?? B: Learning Chinese characters! I have learnt about 1,500 so far. When I first started, I didn't think it was even going to be possible to learn so many, but now I find that I can read signs, menus, and even some easy newspaper articles.? A: What are you most keen on?? B: I've really become keen on learning more about the Chinese culture, in particular Chinese calligraphy. As I have learnt Chinese characters, I have developed a great appreciation for their meaning. I want to explore Chinese characters by learning how to write them in a more beautiful way. ? A: Finally, what do you want to say to anyone interested in learning Chinese?? I have really become keen on learning more about the Chinese culture, in particular Chinese Calligraphy. As I have learnt Chinese character, I have developed a great appreciation for their meaning. I want to explore Chinese characters by learning how to write them in a more beautiful way.? A: Finally, what do you want to say to anyone interested in learning Chinese?? B: I'd say, give it a shot! While some aspects may be difficult, it is quite rewarding and you will be happy that you tried.? A: Thanks for your time. ? B:You're welcome.
新人教版高中英语必修3Unit 4 Space Exploration-Discovering Useful Structures导学案
【点津】 1.不定式的复合结构作目的状语 ,当不定式或不定式短语有自己的执行者时，要用不定式的复合结构?即在不定式或不定式短语之前加 for ＋名词或宾格代词?作状语。He opened the door for the children to come in. 他开门让孩子们进来。目的状语从句与不定式的转换 英语中的目的状语从句，还可以变为不定式或不定式短语作状语，从而使句子在结构上得以简化。可分为两种情况： 1?当目的状语从句中的主语与主句中的主语相同时，可以直接简化为不定式或不定式短语作状语。We'll start early in order that/so that we may arrive in time. →We'll start early in order to/so as to arrive in time. 2?当目的状语从句中的主语与主句中的主语不相同时，要用动词不定式的复合结构作状语。I came early in order that you might read my report before the meeting. →I came early in order for you to read my report before the meeting.
新人教版高中英语必修1Unit 1 Teenage Life-Reading for Writing教案
【教材分析】This teaching period mainly deals with reading for writing a letter of advice. Students are expected to learn the knowledge about how to write a suggestion letter. The teacher is expected to enable students to master some writing skills concerning suggestion letters and learn to write one.【教学目标与核心素养】1. Get students to have a good understanding of how to write a suggestion letter properly.2. Enable students to use some writing skills flexibly.3. Develop students’ writing and cooperating abilities.4. Strengthen students’ great interest in writing discourses.【教学重难点】1. How to enable students to have a good understanding of the skills of writing a suggestion letter2.How to enable students to write a good recommendation letter using some writing skills properly.【教学过程】Step 1: Lead in Begin the class with the lead-in questions: how to write a letter for advice? What kinds of aspects should be included? It is strongly recommended that the teacher should ask students to discuss the topic freely with their partners and brainstorm some ideas concerning the topic. In this way, students can come up with more ideas and avoid being nervous at the beginning of the class.Step 2: Read to discover details concerning advice letters’ writing style.The teacher is expected to ask students to read a letter offering some advice on page 18 silently and then request students to discuss the questions below.
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 2 Wildlife Protection-Reading For Writing教案一
1. 标题首先根据海报的特点、格式写明标题。海报中往往把内容作为大标题。例如: Save the earth, Save the birds。2. 正文部分不同的海报其正文部分的侧重点不同。对于介绍性的海报, 首先要引出话题, 其次列出原因, 最后是总结。对于宣传类的海报, 要写明具体内容, 如: 活动内容, 地点以及参加活动的注意事项, 主持或举办单位等。1. 图片: 要选择引人注目的图片, 与主题要相关, 色彩明亮。话题句式 1. It is a treasure of our country. 它是我国的国宝。2. Believe it or not, at present only several thousand pandas exist in the world. 信不信由你, 目前世界上仅现存几千只熊猫。 3.It’s because of human activities that tigers are endangered. 正是因为人类的活动, 老虎处于濒危的状态。4. Many wild animals are in danger of dying out. 很多野生动物面临着灭绝的危险。 5. The government has taken effective measures to protect them. 政府已采取有效的措施来保护它们。6. People should raise the awareness of the protection of wild animals. 人们应该提高保护野生动物的意识。 7. It’s amazing that there are merely less than 1, 000 finless porpoises living in China. 非常令人吃惊, 目前中国仅有不足1 000只江豚。
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!
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";