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1 专题15 热点话题
“热点话题”是高中新课程标准24话题之一，亦是高考英语热点话题。本话题主要包括全球变暖、节约能源、环境保护、交通问题、人口问题等。通过本话题的学习和高考的考查，帮助学生学习有关气候、能源和环保的有关知识，树立“节约能源，保护环境”的主人翁意识。
“热点话题”在高考英语当中通常以阅读理解、完形填空、七选五或书面表达的形式出现，例如：2018年北京卷阅读理解C 、D 篇，2018年江苏卷阅读理解C 篇，2018年浙江卷B 、C 篇，2018年天津卷阅读理解A 篇；2017年新课标卷II 阅读理解C 篇；2017年北京卷阅读理解B 篇，江苏卷阅读理解D 篇；2016年北京卷阅读理解B 篇、2014年新课标全国卷Ⅱ阅读理解B 篇等。
Passage 1（2018年·新课标II 卷） 体裁
话题 词数 难度 建议时间 议论文 放下手机，与人沟通 330 ★★☆☆☆ 5分钟
We’ve all been there: in a lift, in line at the bank or on an airplane, surrounded by people who are, like us, deepl y focused on their smartphones or, worse, struggling with the uncomfortable silence.
What’s the problem? It’s possible that we all have compromised conversational intelligence. It’s more likely that none of us start a conversation because it’s awkward and challenging, or we think it’s annoying and unnecessary. But the next time you find yourself among strangers, consider that small talk is worth the trouble. Experts say it’s an invaluable social practice that results in big benefits.
Dismissing small tal k as unimportant is easy, but we can’t forget that deep relationships wouldn’t
even exist if it weren’t for casual conversation. Small talk is the grease(润滑剂) for social communication, says
2020年中考英语阅读理解专题练习《热点话题》 新科技 Passage1(2019台州) Brooke wanted a doll house and some sugar cookies. So the 6yearold asked Alexa to get them. Alexa wasn't her mom or babysitter. It was a voiceactivated home assistant powered by AI(人工智能). And it made Brooke's wishes come true. A few days later, much to her parents' surprise, a $170 dollhouse and four pounds of cookies showed up. They ate the cookies and gave away the dollhouse to a local hospital. And that's not the end of the story. When a news reporter told the story of what happened on TV, Alexa devices(设备)in many listeners' homes woke up and tried to order dollhouses! Alexa isn't the only AI willing to serve you. Apple Homepod has Siri, Google Home has its Assistant, and the upcoming Galaxy Home device will have Bixby. People who have these devices use them mainly for listening to music, checking the weather, and setting timers. According to a report from The Information, nowadays voice shopping is rare. But many scientists predict a boom(增长) in voice shopping in the near future. Is that a good thing ________. You can shout out an order as soon as you think of it, even if you are cooking, cleaning, o r driving. In addition, people with disabilities who are unable to use a keyboard or mouse can shop without any help. But voice shopping has its disadvantages. Unwanted dollhouses aren't the biggest problem. It's usually very easy to cancel an order or return products. The thing t hat worries some people is that these assistants are always listening. They have to be able to respond when you want them. So they listen for “Alexa” or “OK Google” or another order. When they hear it, they start recording the conversation. Some have worried about what happens to these recordings. Should companies be allowed to use them to learn about people's shopping habits And what if someone hacks(入侵) the device The CIA found a way to hack smart TVs to turn them into spies that listen all the time. Others could do the same with any smart device. What do you think Are you ready to start voice shopping ( )1. From the passage, we know that Alexa ________． A. can look after the baby B. can cook delicious food C. is a toy doll sold online D. is one kind of AI device ( )2. The underlined word “rare” in Paragraph 2 probably means ________． A. unusual B. expensive C. harmful D. impossible ( )3. Which of the following is the best to fill in the “________” in Paragraph 3 A. Convenience is the main advantage of voice shopping B. The cost of voice shopping is lower than other ways C. The popularity of voice shopping is increasing D. The technology of voice shopping needs improving ( )4. Paragraph 4 mainly tells us that ________ when people try voice shopping. A. AI sometimes forgets people's orders B. personal information might be hacked C. it's difficult to cancel or return products D. the needs for products can't be satisfied Passage2(2019宿迁) Technology is developing fast and it has become an important part of our life. Then what will
小希老师给同学们总结了2018高考英语真题所有阅读理解的A篇，适合高中各个年级的学生练习及备考使用。 【全国Ⅰ卷】 A Washington, . Bicycle Tours Cherry Blossom Bike Tour in Washington, . Duration: 3 hours This small group bike tour is a fantastic way to see the world-famous cherry trees with beautiful flowers of Washington, . Your guide will provide a history lesson about the trees and the famous monuments where they blossom. Reserve your spot before availability – and the cherry blossoms – disappear! Washington Capital Monuments Bicycle Tour Duration: 3 hours (4 miles) Join a guided bike tour and view some of the most popular monuments in Washington, . Explore the monuments and memorials on the National Mall as your guide shares unique facts and history at each stop. Guided tour includes bike, helmet, cookies and bottled water. Capital City Bike Tour in Washington, . Duration: 3 hours Morning or Afternoon, this bike tour is the perfect tour for . newcomers and locals looking to experience Washington, . in a healthy way with minimum effort. Knowledgeable guides will entertain you with the most interesting stories about Presidents, Congress, memorials, and parks. Comfortable bikes and a smooth tour route (路线) make cycling between the sites fun and relaxing. Washington Capital Sites at Night Bicycle Tour
2019年中考英语作文题目（热门话题）汇总 学术文化篇 ①沉迷网络游戏 题目：李华沉迷于电脑游戏中，影响了学习。作为他的好朋友，你打算怎么帮他呢?请用下面所给的提示词写一篇不少于80字的短文。字迹工整，语言流畅。 提示词：give up concentrate on be (become)interested in ★范文 Li Hua spent too much time playing computer games and he fell behind others. As a good friend of his, I must do something to help him. Firstly, I think it’s very important for him to learn lessons well. He should spend most of his time on his study instead of computer games. Secondly, I must tell him that playing computer games too much is bad for his health, especially for his eyes. So he must give it up. I can play more sports with him after school. Maybe he will become more interested in sports than computer games. And then I'll ask him to concentrate more on his study. Of course, I will try my best to help him with all his subjects. I think I can do it in many fun ways and let him find much fun in studying. At the same time, I'll ask both his parents and our teachers to help him, too. If I try these, I'm sure he will make great progress soon. ②怎样学好英语
高考化学专题训练及解析： 无机框图题 （含标准答案及解析） 时间：45分钟分值：100分 1．从物质A的水溶液出发，有如图所示的一系列变化(参加反应或反应生成的H2O没有表示出来)。 试完成下列问题： (1)写出下列物质的化学式： A，E，X，Y。 (2)写出步骤①②发生反应的离子方程式： ①________________________________________________________________________； ②________________________________________________________________________。2．甲、乙、丙为常见单质。A、B、C、D、E、F、G、H均为中学化学中常见的化合物，其中B、G的焰色反应均为黄色，C能使品红溶液褪色。在一定条件下，各物质相互转化关系如图所示。 请回答下列问题： (1)用化学式表示：丙为__________，H为__________。 (2)A的电子式为__________________________________________________________。 (3)电解E的水溶液时，E起到的作用是_____________________________________。 (4)写出B＋C―→D的化学方程式：_________________________________________； 写出E＋G―→F的离子方程式：____________________________________________ 3．A、B、C、D、E为中学化学常见的单质或化合物，相互转化关系如图所示(部分产物略去)。 (1)若A是能使湿润红色石蕊试纸变蓝的气体；C、D均为空气的主要成分；E是一种有 毒气体。 ①C的电子式为______________。
2019年中考英语阅读理解真题汇编 (带详细解析过程) (名师精讲解题方法与技巧+实战训练，建议下载练习) 【考点分析】 阅读理解旨在考查学生阅读、理解的能力。近几年来，中考英语题中的阅读理解材料新颖，题材丰富，考查学生综合推断能力、根据语篇猜单词意思的能力 的力度加大，考查学生关注细节的能力占很大部分。所以学生往往要么没能正确 理解语篇中某些句子的意思，在细节题上丢分，要么就是对语篇的整体把握不够，在综合题或者推断题方面丢分。那么到底怎么做好阅读理解这一题型呢？ 一、解题思路 （一）先读问题，弄清考查要点，以便能带着问题看文章，这样会心中有数，有 的放矢。 （二）快速浏览全文，掌握全貌，注意发现与问题有关的信息，如果时间紧，至 少要扫视一下起首段和尾段。再把标题和文章内容结合起来想一想，这样全文大意便清楚了。此时，不要忙于答题。 （三）细读原文，捕捉相关信息词，掌握短文细节内容。这是解题的关键，应特 别注意以下几点： 1．抓住四个"W"和一个"H"，就是边读边用铅笔做些标记，把What (事件)，When （时间），Where（地点），Why（原因），How（经过）划出来。抓住了四个“W”和一个“H”，就抓住了文章的全貌，一些直接性的问题便可解决。 2．抓住连接词及起关键作用的副词、代词、介词、插入语等。因为这些词具有 因果，让步，递进，转折，指代，列举及承上启下等各种连接上下文的特殊功能。 这对考生分清文章层次，辨明各种关系，了解人物心理，推断作者意图，进行逻 辑推理等手段来分析难点，都具有举足轻重的作用。 3．注意领会文章的寓意。
4．根据题意，初选答案。这一步须仔细审题，领会测试要求，确定解题方法。 对那些明显的，有把握的题可以断然确定，不必把其余三个答案再作推敲而浪费 时间：有些略难的题，应再查阅短文（不是重读一遍），迅速找出依据，予以排 除。常用的解题方法有如下几种： ①直接解题法。即从原文中直接找出答案。 ②归纳解题法。对于不能从原文中直接找出答案的可在把握全文中心和线 索的前题下进行概括、归纳得出正确答案。 ③综合推理法。读者需统观全文，认真分析，综合推理及至计算，最后归纳出 正确答案。 题干中有"suggest, conclude, conclusion, probably, reason, because, according to“等字眼时，属于推断概括型，考查内容着眼于全篇，考生应具备一 定的分析归纳，推理等逻辑思维能力。 ④捕捉关键词。在阅读时应该注意与问题相关的同义词，近义词，反义词 或同位词等信息词来得出正确答案。 ⑤转换解题法。即原文这么说，而在问题和所给选项中则用另外的词去转 换一种说法，但仍表示同一含义。 ⑥排除法。根据语言，句法结构，信息词和常识，在没有把握的选项中用 排除法得出正确答案。 四、重读原文，仔细斟酌核对答案。在解完最后一道题后，如果时间允许，再 将原文读一遍；用全文的主题思想统率各思考题，研究其内在联系和逻辑关系， 目的在于对所做答案进一步审查，推出未解答的题，以便减少失误。
2015年高考英语全国卷 第二部分阅读理解 第一节 A 【语篇导读】这是一篇广告文体类阅读材料。介绍了四则伦敦运河博物馆每月（八月除外）的第一个星期四的报告主题。 21. C 事实细节题。由第一则报告的首句可知，Chris Lewis所做的报告“运河先驱”中，James Brindley被公认为早期最重要的运河设计师。由此可知C项正确。 22. D 事实细节题。由题干中的“February”可将答案锁定在“February 6th”的话题“An Update on the Costwold Canals”中。显然答案为D。 23. A 事实细节题。根据题干中的关键词islands, the Thames可知答案在“March 6th”中。Miranda Vickers 在其报告“Eyots and Aits—Thames Islands”中对泰晤士河中的岛屿做了一个全景的回顾。因此答案为A。 B 【语篇导读】这是一篇记叙文。“我”生活在美国东北部的纽约，那儿的冬季实在让人难以忍受。一次去佛罗里达的Sarasota度周末的机会让“我”深切感受到了宜人的气候是多么令人惬意。尤其是那又大、又软又圆的西红柿。 24. B．推理判断题。由第一段最后一句“dulled by months of cold-weather root vegetables”所提供的信息尤其是dulled一词的意义可以推测纽约寒冷的冬季是令人厌烦的。故答案为B。 25. D。事实细节题。根据首段末句可知，让作者最感惬意的事情是逛一逛早七点的农贸市场。因此D项为最佳答案。 26. B。推理判断题。根据第三段第二句可知，作者之所以不再购买冬季的西红柿是因为不论商店里的西红柿看起来多么诱人，买到家里就会变得又干又硬，索然无味。故选B项。 27. C。推理判断题。由最后一段所述可知，Brown’s Grove Farm是新开业的一家餐馆。Jack Dusty是供货方之一。再结合“I was planning to have dinner that very night.”一句可知作者打算去那儿用餐。因此答案为C。 C 【语篇导读】这篇短文主要介绍了现代著名艺术家Dali的作品风格及the world of Dali中的展品情况。28. B。推理判断题。短文首段介绍了艺术家Dali的作品。由“…with an exhibition bring together over 200 paintings, sculptures, drawings and more.”一句可知，Dali的作品众多，是一个多产画家。故答案为B。29. A。推理判断题。根据第一段“…the visitors will find the best pieces, most importantly the Persistence of Memory”可知，该作品在Dali的最佳作品中是最重要的，由此可以推断它是Dali的杰作之一。 30. D。事实细节题。根据第二段末句中的“…follo ws a path of time and subject.”可知，Dali的作品是按时间和主题进行布展的。答案选D。 31. A。词义猜测题。由最后一段可知，展出的作品主要来源于两个途径：一是与马德里的一家艺术馆密切合作；一是靠像Salvador Dali Museum这样的机构的捐赠。联系全文大意及前一分句不难推测其它机构捐赠的是艺术作品。因此答案为A。 D 【语篇导读】这是一篇议论文。作者从La Chope咖啡馆的经营特色谈起，介绍了巴黎的一些主题咖啡馆经营理念的变化及其大受欢迎的原因。 32. D。推理判断题。根据短文第一段第二句“”可知，顾客在这里可以学着与他们内心的真实情感取得联系。亦即将自己的真实情感表达出来。故答案为D。 33. A。推理判断题。由第二段“Over the years, Parisian cafes have fallen victim to changes in the French lifestyle…”一句可知，在过去的几年里，巴黎咖啡馆的生意因法国人生活方式的变化而受损。由此可以推断，人们不再那么频繁地光顾咖啡馆了。因此答案为A。
英语作文热点话题及写作范文 英语话题作文，是英语考试最常见的一种题目类型。备考是一种经历，也是一种体验。每天进步一点点，基础扎实一点点，通过考试就会更容易一点点。今天小编在这给大家整理了英语话题作文，接下来随着小编一起来看看吧! 英语话题作文(一) 人们常说：“没有规矩，不成方圆”，合理的校规对于学生的健康成长至关重要。请你根据以下所给内容要点，以“Our school rules”为题写一篇英文短文，谈谈你们的校规。 内容要点：1.你们学校有哪些校规; 2.谈谈你对这些校规的看法; 3.请说说你的好建议; 4.…… 要求：1.文中必须包括所给提示中1-3项内容，可展开思路，适当发挥; 2.文中不能出现真实的校名、人名和其他真实信息; 3.不少于80词。 【参考范文】 Our School Rules There are many rules in our school. From Monday to Friday，we have to get to school before 7：00 in the morning. We must wear school uniforms，and I think it is good for us because uniforms can make us look smart. We must listen to our teachers carefully in class and finish our homework after school. We are not allowed to use mobile phones in class. I think the rules are very strict but useful，and we should follow them. However，we have so much homework that we have little free time to do what we love to do. In my opinion，we should have more free time to take part in all kinds of activities and improve our abilities. 英语话题作文(二) 共享单车无疑是今年的火爆热点之一，它为我们的生活带来了极大的便利。 【预测题目】
常考问题5 导数的综合应用 (建议用时：50分钟) 1．若函数y ＝－4 3x 3＋bx 有三个单调区间，则b 的取值范围是________． 解析 由条件y ′＝－4x 2＋b ，∴Δ＝0＋16b ＞0，得b ＞0. 答案 (－2，－1) 2．已知函数f (x )＝13x 3 －2x 2＋3m ，x ∈[0，＋∞)，若f (x )＋5≥0恒成立，则实数 m 的取值范围是________． 解析 f ′(x )＝x 2－4x ，由f ′(x )>0，得x >4或x <0. ∴f (x )在(0,4)上递减，在(4，＋∞)上递增，∴当x ∈[0，＋∞)时，f (x )min ＝f (4)．∴要使f (x )＋5≥0恒成立，只需f (4)＋5≥0恒成立即可，代入解之得m ≥179. 答案 ???? ?? 179，＋∞ 3．下面四个图象中，有一个是函数f (x )＝1 3x 3＋ax 2＋(a 2－1)x ＋1(a ∈R)的导函数 y ＝f ′(x )图象，则f (－1)等于________． 解析 ∵f ′(x )＝x 2＋2ax ＋a 2－1，∴f ′(x )的图象开口向上，则②，④排除．若图象不过原点，则f ′(x )的图象为①，此时a ＝0，f (－1)＝5 3；若图象过原点，则f ′(x )的图象为③，此时a 2－1＝0，又对称轴x ＝－a >0，∴a ＝－1， ∴f (－1)＝－1 3. 答案 －13或5 3 4．(2013·南通调研)设P 是函数y ＝x (x ＋1)图象上异于原点的动点，且该图象在
点P 处的切线的倾斜角为θ，则θ的取值范围是________． 解析 因为y ′＝12x －12(x ＋1)＋x ＝3x 2＋1 2x ≥2 34＝3，(当且仅当x ＝13 时，“＝”成立)设点P (x ，y )(x ＞0)，则在点P 处的切线的斜率k ≥3，所以tan θ≥3，又θ∈[0，π)，故θ∈?????? π3，π2. 答案 ???? ?? π3，π2 5．函数f (x )的定义域是R ，f (0)＝2，对任意x ∈R ，f (x )＋f ′(x )>1，则不等式e x ·f (x )>e x ＋1的解集为______． 解析 构造函数g (x )＝e x ·f (x )－e x ，因为g ′(x )＝e x ·f (x )＋e x ·f ′(x )－e x ＝e x [f (x )＋f ′(x )]－e x >e x －e x ＝0，所以g (x )＝e x ·f (x )－e x 为R 上的增函数．又因为g (0)＝e 0·f (0)－e 0＝1，所以原不等式转化为g (x )>g (0)，解得x >0. 答案 (0，＋∞) 6．(2013·温州模拟)关于x 的方程x 3－3x 2－a ＝0有三个不同的实数解，则实数a 的取值范围是________． 解析 由题意知使函数f (x )＝x 3－3x 2－a 的极大值大于0且极小值小于0即可，又f ′(x )＝3x 2－6x ＝3x (x －2)，令f ′(x )＝0，得x 1＝0，x 2＝2.当x ＜0时，f ′(x )＞0；当0＜x ＜2时，f ′(x )＜0；当x ＞2时，f ′(x )＞0，所以当x ＝0时，f (x )取得极大值，即f (x )极大值＝f (0)＝－a ；当x ＝2时，f (x )取得极小值，即f (x )极小值＝f (2)＝－4－a ，所以{ －a ＞0，－4－a ＜0，解得－4＜a ＜0. 答案 (－4,0) 7．若函数f (x )＝－1 2x 2＋4x －3ln x 在[t ，t ＋1]上不单调，则t 的取值范围是______． 解析 对f (x )求导，得f ′(x )＝－x ＋4－3x ＝－x 2 ＋4x －3 x ＝－(x －1)(x －3)x .由 f ′(x )＝0得函数f (x )的两个极值点为1,3，则只要这两个极值点有一个在区间(t ，t ＋1)内，函数f (x )在区间[t ，t ＋1]上就不单调，所以t <1 Topic Topical issues Reading Class：Name：Group：No： Learning Objectives： 1.Review the important words and expressions in the reading material: 2. Learn the reading skills: scanning and skimming Learning Key Points： 1.Grasp the important words and expressions in the reading material 2.Master the reading skills: scanning and skimming Learning Difficult Points： Improve the reading ability Learning Procedures： I.【Pre-class homework】 Read the passage and choose the best answer (1) T he first Earth Day in 1970, Americans have gotten a lot ―greener‖ toward the environment（环境）. ―We didn’t know at that time there even was an environment, let alone that there was a problem with it,‖ says Bruce Anderson, president of Earth Day USA. But what began as nothing important in public affairs has grown into a social movement. Business people, political leaders, university professors, and especially millions of grass-roots Americans are taking part in the movement. ―The understanding has increased many, many times,‖ says Gaylord Nelson, the former governor from Wisconsin, who thought up the first Earth Day. According to US government reports, emissions（排放）from cars and trucks have dropped from 10.3 million tons a year to 5.5 tons .The number of cities producing CO beyond the standard has been reduced from 40 to 9 .Although serious problems still remain and ne ed to be dealt with , the world is a safer and healthier place .A kind of ―Green thinking ‖ has become part of practices . Great improvement has been achieved .In 1988 there were only - 1 - 2017届全国高考英语阅读理解汇编（1）英语试卷SYS201708100601 一、阅读理解 详细信息 1. 难度：中等 阅读理解。 Many of us still tend to think that emotions can affect reasonable thought，and sometimes land us in trouble. But in recent years psychologists have taken quite a different view. Keith Oatley，Professor of Psychology at Glasgow University，is involved in the research which shows the fundamental importance of emotions. He believes we are very ambivalent about them：we think of our emotions as being unreasonable，but we also consider them as essential to being human.For example，Mr Spock，a character in the television series Star Trek，is superintelligent and he has no emotions at all.However，he is never made captain of the spaceship.Maybe，this is because Mr Spock is not the kind of person you can share your feelings with—a person who shows his emotions. As Professor Oatley points out，our emotions have very important functions，for example，fear.If we cross the road and a car approaches，we usually stop moving or step back.We stop what we are doing，check what we have done and pay very careful attention to the environment.The emotion of fear makes us take this small series of actions which，on average，help preserve our safety. On the other hand，if things are going well and small problems come up，we find we can solve them with the resources we have to hand.As a consequence，we tend to feel happy and usually continue doing the job. Anger is an emotion that tends to occur when someone is preventing us from doing something.Then this small “kit” of reactions enables us to prepare ourselves to be quite aggressive to that person，or to try harder，and so on. Professor Oatley believes emotions generally occur at these important moments in actions.With fear and anger our emotions make us decide to start doing something else，while with happiness they “suggest” we continue what we are already doing. 1.What’s Keith Oatley’s opinion about emotions? A．They affect reasonable thought. B．They get us into trouble. C．They are helpful to us. D．They are reasonable. 2.What does the underlined part “we are very ambivalent about them”in Paragraph 2 mean? A．We have contradictory feelings towards emotions. B．We have similar ideas of emotions. 2016高考英语作文热点话题作文 1、低碳生活现在全世界都在倡导“低碳生活”(low-carbon life)，即：降低二氧化碳的排放，采取低能量、低消耗、低开支的生活方式。低碳生活对我们大家都有好处，请你写一篇短文向一家英文报社投稿。内容包括：你的具体做法、你的感受以及建议。 提示词语：be good for, everyone, ride a bike, think, make a difference, environment, suggest, reuse ★范文 Low-carbon life is good for everyone. To help with the environment, I always walk or ride a bike to school instead of taking a car. Besides, I will try to use things that can be recycled and I never forget to turn off the lights when I leave the classroom. I think it’s my duty to live a low-carbon life. And even the simplest activities can make a real difference to the environment. So I suggest we should reuse books as long as possible. And we’d better not spend much money on expensive clothes. If everyone does something for the environment, I believe the earth will be a better place。 2. 假如你是Li Lin，你的英国笔友Eric来信询问你家乡是否有雾霾(thick haze)，情况如何。请按提示写一封不少于60词的电子邮件回复他。要求卷面整洁书写工整;内容可在包含要点的基础上适当发挥。 提示：1. 感谢他的关心; 2. 介绍:(1)去年冬天有多次雾霾; (2)空气被严重污，危害：车祸，生病等; 3. 正采取各种举措减少其发生。 Dear Erik, I’m glad to receive your letter. You asked if there is thick haze in my hometown. Thank you for your caring for the weather and my health. There was heavy haze last winter. The air is badly polluted. Many traffic accidents happened and more and more people have to go to see the doctor because of the smog. People have realized the great harm caused by the smog and the importance of protecting the environment. The government suggests people to go to work or school with the public traffic, such as the bus and the underground. Also we should plant more trees. According to me, I will go to school by bike or on foot, and I won’t throw the waste anywhere. Would you like to tell me some good ideas? I’m looking forward to your reply. 常考问题7三角恒等变换与解三角形 (建议用时：50分钟) 1．(2013·济宁二模)在△ABC中，角A，B，C所对的边分别为a，b，c，且a＝1，B＝45°，S△ABC＝2，则b等于________． 解析∵S＝1 2ac sin B＝2，∴ 1 2×1×c×sin 45°＝2. ∴c＝4 2. ∴b2＝a2＋c2－2ac cos B＝1＋32－2×1×42×cos 45°. ∴b2＝25，b＝5. 答案 5 2．(2013·北京东城区期末)在△ABC中，A，B，C为内角，且sin A cos A＝sin B cos B，则△ABC是________三角形． 解析由sin A cos A＝sin B cos B得sin 2A＝sin 2B＝sin(π－2B)，所以2A＝2B 或2A＝π－2B，即A＝B或A＋B＝π 2，所以△ABC为等腰或直角三角形． 答案等腰或直角 3．(2013·浙江卷改编)已知α∈R，sin α＋2cos α＝10 2，则tan 2α等于________． 解析∵sin α＋2cos α＝10 2， ∴sin2α＋4sin α·cos α＋4cos2α＝5 2. 化简，得4sin 2α＝－3cos 2α， ∴tan 2α＝sin 2α cos 2α＝－ 3 4. 答案－3 4 4．在△ABC中，内角A，B，C所对的边分别是a，b，c.已知8b＝5c，C＝2B，则cos C等于________． 解析先用正弦定理求出角B的余弦值，再求解． 由b sin B ＝c sin C ，且8b ＝5c ，C ＝2B ， 所以5c sin 2B ＝8c sin B ，所以cos B ＝4 5. 所以cos C ＝cos 2B ＝2cos 2 B －1＝7 25. 答案 7 25 5．已知tan β＝43，sin(α＋β)＝5 13，其中α，β∈(0，π)，则sin α的值为________． 解析 依题意得sin β＝45，cos β＝35；注意到sin(α＋β)＝5 132018届高三英语话题阅读话题《热门话题》学案含答案
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