阅读理解新题型
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阅读理解新题型分析一、阅读理解新题型说明:近年统考中,阅读理解题目增加了一种新题型,即每篇短文后有5个正误判断题,每题后有两个选项,T为“正确”,F为“错误”,请结合文章判断正误。
二、阅读理解正误判断题判断方法:1. 如果考题在文中原句照抄一定是T;或者如果考题句与文中相关语句近义替换是T;2.如果考题句子与文中语句矛盾,则判断为F;或者如果考题句子与文中表达不一致为F。
三、例题分析:每篇短文后有5个正误判断题,从每题后的两个选项中选出正确答案。
1. The workers who brought the girl to the orphanage (孤儿院) knew little about her. The streets where they found her had been her home for many years. Her parents were unknown. They left her long ago. At the orphanage, the girl, like all the children there, was taught to read and write. While she was studying at the orphanage,she learned something else-to be independent. At twenty-one,she left the orphanage and began work as a secretary. And then,in 1975, while she was still working as an ordinary secretary, something special happened. She entered the Miss Hong Kong competition and won it. This was the turning point in her life. Now her name,Mary Cheung,was known to everybody.Mary entered the competition because she wanted to show that orphanage girls could be something. Winning the competition gave her the chance to start a new life. This led her first into television and then into business as a manager. When she was working as a manager,she had trouble with her reports. "My English just wasn't good enough." she says. Luckily,she had a boyfriend (who later became her husband) to help her.Mary studied management at Hong Kong Polytechnic and graduated in 1980. She started her own business in 1985. But she did not stop developing herself. She then studied at the University of Hong Kong. Since 1987,she had spent a lot of time on photography. She has held several exhibitions of her work in many places-China, New Zealand and Paris. She still found time, however, to work on TV, write for newspapers and bring up her family.The girl from the street has come a long way, but her journey is not finished yet.(1)、Before Mary Cheung was brought to the orphanage, she had lived in the streets for many years.A:TB:F答案: A原句近义替换,只是把名字替换过来。
Passage 1When a man is taller and stronger than other men, he is sometimes called a giant. Many people think of Chamberlain as a giant. He is so tall that he has a special, extra-long bed to sleep in and a special car with enough space for his long legs. During his playing days, Wilt was paid about $200 000 a year. That was what the president of the United States earned for being president. At that time, it was more than any other athlete in the entire history of sports had ever been paid.Wilt played for the Los Angeles Lakers team. He helped to make it the best team in the Western Division of the National Basketball Association, which is a group of the very finest professional teams in the world. Wilt owns a beautiful apartment building in Los Angeles and another one in New York. He owns racehorses (赛马). He wears fine clothes. He owns an English Bentley car.When Wilt was just seven years old, he took a job. He did not tell his mother or father, but one day his mother found out. She looked out into the street and saw Wilt lifting crates for a milkman. Mrs- Chamberlain told the milkman that Wilt was only seven. She said he shouldn't be lifting those heavy milk crates. “I thought he was twelve”,said the milkman.6.According to the passage, people called Wilt Chamberlain a giant.A.TB. F7.Wilt Chamberlain played for the Seattle Seahawks.A.TB. F8.The president of the United States earned as much money doing his job each year as Wilt earned playing basketball.A.TB. F9.Wilt Chamberlain could be such a famous basketball player only because he played for the finest professional team.A.TB. F10.According to the passage, the word “honesty” best describes Wilfs desire to work when he was seven.A.TB. FPassage 2Before you go to another country it is a great help if you know the language and some of the customs of the country.When people meet each other for the first time in Britain, they say “How do you do?v and shake hands. Usually they do not shake hands when they just meet or say goodbye. But they shake hands after they haven't met for a long time or when they willbe away from each other for a long time.Last year a group of German students went to England for a holiday. Their teacher told them that the English people hardly shake hands. So when they met their English friends at the station, they kept their hands behind their backs, the English students had learned that the Germans shake hands as often as possible, so they put their hands in front and got ready to shake hands with them. It make both of them laugh.6.It is very helpful if you know the language and some of the customs of the country.A.TB. F7.English people usually shake hands when they meet every time.A.TB. Fually English people dorft shake hands when they just meet or say goodbye・A.TB. F9.English people like shaking hands very much.A.TB. F10.This story is about languages and customs.A.TB. FPassage 3Gladys Holm was a secretary (秘书).She worked in an office all her life. Gladys earned (挣)about $ 15,000 a yea匚She died when she was 86 years old. And she left a big surprise - $ 18 million! She gave the money to a children^ hospital.Gladys Holm never got married or had any children. But she always liked children, and she wanted to help them. When her friend's daughter was ill in hospital, Gladys brought her a teddy bear. After that, she visited the hospital many times. Every time she visited, she brought teddy bears for those children. After that, people started to call Gladys the “Teddy Bear Lady".Gladys always gave toys and presents to her friends and family but no one knew she had a lot of money. She lived in a small house outside Chicago. Everyone was very surprised when they learned she was a millionaire. A family friend said, “She always gave us nice presents and things, but we didn^t know she was rich.How did Gladys get so much money? She asked her boss how to earn more money, and she listened to what he said. She bought the stocks (股票)that he told her to buy, and she got very rich. Before she died, she talked to her friends about “giving something to the children^ hospital^. No one knew that the “something” was $ 18 million!6.Gladys Holm often visited the hospital and gave children teddy bears because she had a lot of teddy bears.A.TB. F7.People started to call Gladys the “Teddy Bear Lady,' after she died.A.TB. F& Everyone was surprised that Gladys had so much money.A.TB. F9.Gladys did what the boss told her to do, so she got rich.A.TB. F10.When Gladys Holm became a millionaire, she stopped working.A.TB. FPassage 4Language is always changing. In a society where life continues year after year with few changes, the languages do not change eithe匚The earliest known languages had difficult grammar but a small, limited vocabulary. Over the century, the grammar changed, and the vocabulary grew. For example, the English and Spanish people who came to America during the sixteenth century gave names to all the new plants and animals they found. In this way, hundreds of new words were introduced into English and Spanish vocabularies. Today life is changing very fast, and language is changing fast too.There are several major language families in the world. Some scientists say there are nine main families, but other scientists divided them differently. The languages in each family are connected, and scientists think that they came from the same parent language. About 3% of the people in the world speak languages that are not in these major families-6.The early language had many words and easy grammar.A.TB. F7.In the next few hundred years we can expect language to change a great deal.A.TB. F8.This article shows that language changes with changes in society.A.TB. F9.From this article we can know that language will become easier and easie匚A.TB. F10.The first English and Spanish people arrived in America more than 400-500 years ago.A.TB.FPassage 5Most dog owners feel that their dogs are their best friends. Almost everyone likesdogs because they try hard to please their owners. One of my favorite stories is about a dog that wanted his owner to please him.One of my friends has a large German shepherd named Jack. These dogs are often very intelligent. Every Sunday afternoon, my friend takes Jack for a walk in the park. Jack likes these long walks very much.One Sunday afternoon, a young man came to visit my friend. He stayed a long time, and he talked and talked. So it was time for my friend to take Jack for his walk, but the visitor didn,t leave. Jack became very worried about his walk in the park. He walked around the room several times and then sat down directly in front of the visitor and looked at him. But the visitor paid no attention. He continued talking. Finally, Jack couldn't stand it any longe匚He went out the room and came back a few minutes later. He sat down again in front of the visitor, but this time he held the man's hat in his mouth.German shepherds aren't the only intelligent dogs. Another intelligent dog is a Seeing Eye dog. This is a special dog, which helps blind people walk along the streets and do many other things. We call these dogs Seeing Eye dogs because they are the “eyes" of the blind people and they help them to “see”. Seeing Eye dogs generally go to special schools for several years to learn to help blind people.6.Like many other dogs, Jack tried to please its owner maste匚A.TB. F7.Jack came to sit in front of the visitor in order to invite him for a walk.A.TB. F8."Finally, Jack couldn^t stand it any longer'9 means that Jack could no longer put up with the visitor.A.TB. F9.Seeing Eye dogs help and see for blind people.A.TB. F10.Famous Dogs in Germany would be the most suitable for this passage・A.TB. FPassage 11. A2.B3. A4. B5. B Passage 21. A2. B3. A4. B5. B Passage 31. B2. B3. A4.A 4. B Passage 41. B2. A3. A4. B5. A Passage 51. B2. B3. A4. A5. B。
中考英语阅读新题型技巧单选题50题1. The passage is mainly about _____.A. a funny storyB. a trip to a new placeC. how to learn EnglishD. the history of a city答案:B。
本题主要考查对文章主旨大意的理解。
通过阅读文章,我们可以发现文中主要描述了一次去新地方的经历,包含了所见所闻和感受。
选项A 只是提到了一个有趣的故事,但文章并非重点讲述故事;选项 C 如何学习英语并非文章的主题;选项 D 城市的历史在文中未提及。
2. What is the main idea of the text?A. The benefits of exerciseB. A famous person's lifeC. Different kinds of animalsD. A new technology答案:A。
文章中多次提到运动对身体和心理的好处,围绕运动的益处展开论述。
选项B 名人的生活在文中未涉及;选项C 不同种类的动物并非文章重点;选项D 新技术并非文章的核心内容。
3. The passage mainly tells us _____.A. a delicious recipeB. a beautiful gardenC. the importance of friendshipD. the changes in a city答案:C。
文中通过多个事例和描述强调了友谊的重要性。
选项A 美味的食谱不是文章主题;选项B 美丽的花园并非文章重点;选项D 城市的变化在文中未体现。
4. What is the main topic of the article?A. A popular movieB. An exciting gameC. Saving the environmentD. A fashion show答案:C。
高考语文2024新题型概览
一、文学常识应用题
文学常识应用题主要考察学生对中外文学名著、文学流派、文学常识的基本了解。
这类题型要求学生在掌握基本的文学知识基础上,能够将这些知识应用到具体的语境中。
二、阅读理解新题型
阅读理解新题型包括散文、小说、议论文等多种文体,要求学生对文章的主旨、结构、语言特色有深刻的理解。
这类题型不仅要求学生有较高的阅读理解能力,还需要学生具备一定的批判性思维。
三、古文阅读题
古文阅读题主要考察学生对古代汉语的掌握程度,包括对文言文句子的理解、对古代文化背景的了解等。
这类题型要求学生具备扎实的古文基础,同时还需要具备一定的历史文化素养。
四、作文新题型
作文新题型包括材料作文、命题作文等多种形式,要求学生在深入理解题目材料的基础上,能够运用自己的观点和语言清晰地表达出来。
这类题型对学生的思维能力、语言表达能力和写作技巧都有较高的要求。
五、语法和词汇选择题
语法和词汇选择题主要考察学生对英语语法的掌握程度,包括时态、语态、语气、非谓语动词等。
这类题型要求学生能够准确判断句子中的语法错误和词汇选择,同时也需要学生具备一定的语言分析能力。
六、现代文阅读简答题
现代文阅读简答题主要考察学生对现代文的理解和表达能力,题目通常涉及议论文、说明文等文体。
这类题型要求学生能够准确理解文章内容,同时还需要学生能够用简练的语言回答问题。
七、文化背景填空题
文化背景填空题主要考察学生对中外文化背景的了解程度,题目通常涉及历史事件、文化传统等方面。
这类题型要求学生能够准确识记相关的文化背景知识,同时还需要学生能够将这些知识应用到具体的语
境中。
考研英语一2023新题型随着2023年考研英语一的临近,新题型成为了考生们关注的焦点。
新题型作为一种新型考试形式,旨在全面考察考生的英语综合能力。
本文将对2023年考研英语一新题型进行深度解析,并提供备考策略,帮助考生们更好地应对这一挑战。
一、新题型解析1. 阅读理解阅读理解是新题型的重要组成部分,主要考察考生对英文文献的阅读、理解和分析能力。
与往年相比,2023年的阅读理解文章篇幅更长,难度更大。
文章题材多样,涉及社会、文化、科技等多个领域。
考生需要在有限的时间内快速理解文章主旨,并完成相关问题。
2. 翻译翻译部分要求考生将英文文献翻译成中文,考察考生的语言转换能力和对英文句子结构的理解。
2023年的翻译文章涉及多种文体,包括议论文、说明文和记叙文等。
考生需要在准确传达原文意思的同时,保证译文流畅、通顺。
3. 写作写作部分要求考生根据给定的主题撰写一篇议论文或说明文,考察考生的语言表达能力和逻辑思维能力。
2023年的写作题目更加注重实际应用,要求考生结合自身经历或社会现象进行分析。
考生需要审题清晰,观点明确,论据充分。
二、备考策略1. 提升阅读能力针对阅读理解部分的难度增加,考生应加强阅读训练,提高阅读速度和理解能力。
建议考生多读英文原版书籍、新闻报道和学术论文等,以扩大词汇量、熟悉不同文体和语境。
同时,要注重阅读技巧的训练,如快速定位关键信息和筛选无关信息等。
2. 提高翻译水平翻译部分要求考生具备良好的中英文表达能力。
考生应注重训练自己的语言转换能力,通过大量翻译实践提高对英文句子结构的理解和组织。
此外,考生还应加强对中英文语言差异的认识,避免出现中式英语等常见错误。
3. 强化写作训练写作部分需要考生具备一定的逻辑思维能力和表达能力。
考生应多写、多练,通过模拟试题和历年真题进行写作训练。
在写作过程中,要注重审题、构思和语言表达等方面的训练,力求做到观点鲜明、逻辑严密、表达清晰。
此外,考生还可以通过阅读优秀范文和模仿优秀文章来提高自己的写作水平。
揭秘2024年高考语文新题型随着时代的发展,高考的题型也在不断地变化和更新。
2024年高考语文科目也将迎来一种新的题型,下面我们来揭秘一下这个新的题型。
2024年高考语文新题型是“多模态阅读理解”。
所谓多模态阅读理解,是指考生需要在给定的文本材料中,同时理解并运用多种模态,包括文字、图片、声音、视频等来进行阅读和理解。
这种题型要求考生不仅要能够准确地理解文本的含义,还要能够通过多种模态进行综合分析和判断。
在这种题型中,考生将会遇到一篇篇有关不同话题的文章,每篇文章都会以多种模态的形式出现,包括文字描述、图片、声音和视频。
考生需要仔细阅读文本,同时观察、聆听、触摸和感受多种模态的信息。
通过综合运用这些模态,考生需要理解文章的主旨、推理作者的意图、把握文章的情感色彩等。
这种题型要求考生具备全面的阅读理解能力,能够从多个角度进行综合分析和判断。
多模态阅读理解题的出现,旨在培养考生的多元智能和多模态信息处理能力。
在信息爆炸的时代,人们需要能够通过多种模态的信息获取和处理能力来更好地适应和应对社会的变化。
而语文科目作为高考的一部分,也需要紧跟时代的步伐,培养学生的多模态信息处理能力。
对于考生来说,要应对2024年高考语文新题型,需要进行一些针对性的准备。
首先,考生需要加强对不同模态的阅读能力。
平时可以多接触不同形式的文本,包括文字、图片、视频等,培养自己的多模态信息处理能力。
其次,考生需要注意细节的捕捉和理解。
在多模态的题型中,可能会有很多细节需要考生去观察和理解,因此,考生需要提高对细节的敏感度和把握能力。
最后,考生需要提高综合分析和判断的能力。
多模态的阅读理解题目要求考生能够从多个角度进行分析和判断,因此,考生需要培养综合分析和判断的能力。
总的来说,2024年高考语文新题型的多模态阅读理解要求考生在阅读理解的基础上,通过多种模态的信息进行综合分析和判断。
这种题型的出现旨在培养考生的多元智能和多模态信息处理能力。
2022年考研英语一真题答案之阅读理解真题新题型(附完整版答案)2022年考研英语一阅读理解真题Part BDirections:In the following text, some sentences have been removed. For Questions 41~45, choose the most suitable one from the list A~G to fit into each of the numbered blanks. There are two extra choices, which do not fit in any of the blanks. Mark your answers on the ANSWER SHEET. (10 points)In the movies and on television, artificial intelligence is typically depicted as something sinister that will upend our way of life. When it comes to AI in business, we often hear about it in relation to automation and the impending loss of jobs, but in what ways is AI changing companies and the larger economy that don’t involve doom-and-gloom mass unemployment predictions?A recent survey of manufacturing and service industries from Tata Consultancy Services found that companies currently use AI more often in computer-to-computer activities than in automating human activities. One common application? Preventing electronic security breaches, which, rather than eliminating IT jobs, actually makes those personnel more valuable to employers, because they help firms prevent hacking attempts.Here are a few other ways AI is aiding companies without replacing employees: Better hiring practicesCompanies are using artificial intelligence to remove some of the unconscious bias from hiring decisions. “There are experiments that show that, naturally, the results of interviews are much more biased than what AI does,” says Pedro Domingos, author of The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World and a computer science professor at the University of Washington. In addition, “41. _______________” One company that’s doing this iscalled Blendoor. It uses analytics to help identify where there may be bias in the hiring process.More effective marketingSome AI software can analyze and optimize marketing email subject lines to increase open rates. One company in the UK, Phrasee, claims their software can outperform humans by up to 10 percent when it comes to email open rates. This can mean millions more in revenue. 42. _______________ These are “tools that help people use data, not a replacement for people,” says Patrick H. Winston, a professor of artificial intelligence and computer science at MIT.Saving customers moneyEnergy companies can use AI to help customers reduce their electricity bills, saving them money while helping the environment. Companies can also optimize their own energy use and cut down on the cost of electricity. Insurance companies, meanwhile, can base their premiums on AI models that more accurately access risk. Domingos says, “43. _______________”Improved accuracy“Machine learning often provides a more reliable form of statistics, which makes data more valuable,” says Winston. It “helps people make smarter decisions.” 44. _______________Protecting and maintaining infrastructureA number of companies, particularly in energy and transportation, use AI image processing technology to inspect infrastructure and prevent equipment failure or leaks before they happen. “If they fail first and then you fix them, it’s very expensive,” says Domingos. “45. _______________”[A] AI replaces the boring parts of your job. If you’re doing research, you can have AI go out and look for relevant sources and information that otherwise you just wouldn’t have time for.[B] One accounting firm, EY, uses an AI system that helps review contracts during an audit. This process, along with employees reviewing the contracts, is faster and more accurate.[C] There are also companies like Acquisio, which analyzes advertising performance across multiple channels like Adwords, Bing and social media and makes adjustments or suggestions about where advertising funds will yield best results.[D] You want to pred ict if something needs attention now and point to where it’s useful for employees to go to.[E] Before, they might not insure the ones who felt like a high risk or charge them too much, or they would charge them too little and then it would cost the company money.[F]We’re also giving our customers better channels versus picking up the phone to accomplish something beyond human scale.[G] AI looks at résumés in greater numbers than humans would be able to, and selects the more promising candidates.答案:F、C、A、B、G。
中考英语阅读新题型一、引言随着中考英语考试的改革,阅读理解题型也在不断变化。
为了更好地应对这一变化,我们需要深入了解新的阅读题型及其考查重点。
本文将详细解析中考英语阅读新题型,包括文本概括与推理、细节理解与判断、词汇理解与运用、句子结构与表达、篇章结构与逻辑等方面。
二、文本概括与推理1.考查重点:考查学生对文章主旨大意的把握能力,以及根据文章内容进行推理的能力。
2.解题技巧:首先,快速浏览全文,了解文章大意;其次,仔细阅读题目,找出关键信息;最后,根据文章内容和关键信息进行推理。
三、细节理解与判断1.考查重点:考查学生对文章细节的把握能力,以及根据文章内容进行判断的能力。
2.解题技巧:首先,仔细阅读文章,找出与题目相关的细节;其次,对比题目和文章内容,判断正误。
四、词汇理解与运用1.考查重点:考查学生对词汇的理解和运用能力。
2.解题技巧:首先,根据上下文理解词汇含义;其次,运用所理解的词汇进行句子和段落的理解。
五、句子结构与表达1.考查重点:考查学生对句子结构及其表达方式的理解能力。
2.解题技巧:首先,分析句子的语法结构;其次,理解句子的含义;最后,对比原文和题目中的句子表达方式,判断正误。
六、篇章结构与逻辑1.考查重点:考查学生对文章整体结构和逻辑关系的理解能力。
2.解题技巧:首先,分析文章的整体结构;其次,理解各段落之间的逻辑关系;最后,根据文章结构和逻辑关系进行推理和判断。
七、总结中考英语阅读新题型主要考查学生的文本概括与推理、细节理解与判断、词汇理解与运用、句子结构与表达、篇章结构与逻辑等方面。
为了更好地应对这一变化,我们需要熟悉这些题型及其考查重点,掌握相应的解题技巧和方法。
同时,我们还应该注重提高自己的阅读能力和语言素养,以更好地应对中考英语考试。
考教衔接,关联教材:《荷塘月色》课内外比较阅读新题型一、阅读下面的文字,完成下面小题。
看莲杨莹①看莲要趁早,千万别过了八月才去,只剩下莲蓬头和枯叶。
也千万别到了傍晚才去,莲会睡着在夜雾里。
今日恰逢其时,正是蓬花盛开的时节,一路上听得到那花开的声音。
非专程去看蓬,也未想到会遇到莲,临时去参加一个会,中午休会,意外地听说我们被安排在一个荷塘旁就餐。
②常常,想见的人会偶遇在某个地方,这样的邂逅便带来如看莲般的喜悦。
今天随意地走近了莲,莲花在湖面上轻轻地裂开,久违了的莲,总能令人心动,这内心的喜悦,又似意外地走近了一位想念已久的人。
③荷塘边总是一种令人晕眩的燥热,蝉鸣此起彼伏,柳枝一动不动,一股燥热往上冒,心底的烦恼再次无限地蔓延开来。
这个季节里,我不自觉地染上了复杂而郁闷的情绪,陷入不想回忆的回忆。
那么多的日子里,是什么使我满怀忧伤,又满怀希望呢?那些烦恼,如莲,是切肤的,是温暖的,又是不可言说的,那苦痛是属于自己的,是与出身连在一起的。
④心烦时喝茶,心静许多,那么,心烦时看莲呢?也许与喝茶同感。
最安静地度过余生的地方该是温暖的,什么回忆也打扰不了的。
⑤湖面骄阳当头,莲,勇敢地展示着自己的美,这本身其实就是一种无声的力量。
静心现荷,无需任何语言。
⑥忽然飙来两句秽语,折杀了荷塘溢出的美,徒增使人心烦的噪音。
在湖面上生出一片莲花之前,是一池污水,而花败时污水还是污水,所以,有的人就只看得见污水,就只看见了污水,看不到大美,便只有把看见的污水反复地传说,而污水,是骂不干净的。
⑦常常,我们周围的人,我们的同行者,都不是我们自己可以选择的,这是人的一种无奈。
生活中常常忽然间就撞见了你不想见的人,为了和谐,你必须忍耐着。
⑧而那“大美”,美的时间又是那么短暂,所以,人们才记得,才惦记。
在这样谁也逃脱不了的污水中,孤独着,等待着莲花一次次开放。
每个夏天的花朵,都是寂寞的。
在这样谁也逃脱不了的污水中,没有孤独感的人,应该是可耻的,不能品味寂寞的人,也是可怜的。
阅读理解新题型
1.(2017年成都24)在平面直角坐标系xOy 中,对于不在坐标轴上的任意一点(),P x y ,我们把点11,P x y ⎛⎫
'
⎪⎝⎭
称为点P 的 “倒影点”
.直线1y x =-+上有两点,A B ,它们的倒影点
,A B ''均在反比例函数k
y x
=
的图像上.若AB =k =____________.
2.(2016年成都24)实数a ,n ,m ,b 满足a <n <m <b ,这四个数在数轴上对应的点分别
为A ,N ,M ,B (如图),若AM 2=BM •AB ,BN 2
=AN •AB ,则称m 为a ,b 的“大黄金数”,n 为a ,b 的“小黄金数”,当b ﹣a=2时,a ,b 的大黄金数与小黄金数之差m ﹣n= .
3.(2015年成都25)如果关于x 的一元二次方程20ax bx c ++=有两个实数根,且其中一个根为另一个根的2倍,则称这样的方程为“倍根方程”,以下关于倍根方程的说法,正确的是 .(写出所有正确说法的序号) ①方程220x x --=是倍根方程;
②若(2)()0x mx n -+=是倍根方程,则22450m mn n ++=; ③若点()p q ,在反比例函数2y x
=的图像上,则关于x 的方程230px x q ++=是倍根方程;
④若方程2
0ax bx c ++=是倍根方程,且相异两点(1)M t s +,,N(4)t s -,都在抛物
线2
y ax bx c =++上,则方程20ax bx c ++=的一个根为54
.
4. (2017年河北省)对于实数p ,q ,我们用符号min{p,q}表示两数中较小的数,如min{1,2}=1,
因此 若22
min{(x-1),}1x =,则x=
5. (2017年黑龙江齐齐哈尔)经过三边都不相等的三角形一个顶点的线段把三角形分成两个小三角形,如果其中一个是等腰三角形,另外一个三角形和原来三角形相似,那么把这条线段定义为原三角形的“和谐分割线”。
如图,线段CD 是的ABC ∆“和谐分割线”,ACD ∆为等腰三角形,BCD ∆和ABC ∆相似,0=46A ∠,则ACB ∠的度数是
6. (2016四川巴中)先阅读下列材料,然后解答问题:
从A,B,C 三张卡片选两张,有三种不同选法,抽象成数学问题就是从3个元素中选取2个元
素组合,记作
2332
=
=321C ⨯⨯。
一般地,从m 个元素中选取n 个元素组合,记
m (1)...(1)=
(1)...321n m m m n C n n --+-⨯⨯⨯。
例:从7个元素选5个元素,共有5
776543==21
54321C ⨯⨯⨯⨯⨯⨯⨯⨯
问题:从某学习小组10人中选取3人参加活动,不同的选法共有 种
7. (2016年广东梅州)将4个数a ,b ,c ,d 排成2行、2列,两边各加一条竖直线记成
|
|a b c
d ,定义||=ad-bc a b c d 上述记号就叫2阶行列式。
若x+1
1||=6
11
x x
x --+,则x=
8. 三个非零实数x ,y ,z 满足:只要其中一个数的倒数等于另外一个两个数的倒数和,则称
这三个实数x ,y ,z 构成“和谐三数组”。
已知123,),(1,),(1,)A t y B t y C t y -+(三点均在函数
y k
x =
(k 为常数,0k ≠)的图形上,且这三点的纵坐标构成“和谐三组数”
,则实数t 的值为
9. 当m 、n 是实数且满足m n m n -=时,就称点
,
)
m
Q m n (为“奇异点”,已知点A 、B 是
“奇异点”且都在反比例函数
2
y x =
的图象上,点O 是平面直角坐标系的原点,则OAB ∆的
面积为
10. 如图,我们把一个半圆与抛物线的一部分围成的封闭图形称为“果园”。
已知点A 、B 、C 、D 分别是“果园”与坐标轴的交点,抛物线的解析式为2
y 23x x =--,AB 为半圆的直径,则称这个“果园”被y 轴截得的弦CD 的长为
11. (2017年宜宾)规定:[x]表示不大于x 的最大整数,(x )表示不小于x 的最小整数,[)x 表示最接近x 的整数(0.5,x n ≠+n 为整数)。
例如:[2.3]2,(2.3)3,[2.3)2===。
则下列说法正确的是 (写出所有正确的序号)
(1)当x=1.7时,[]()[)6x x x ++=;(2)当x=-2.1时,[]()[)-7x x x ++= (3)方程4[]3()[)11x x x ++=的解为1 1.5x <<;
(4)当-11x <<时,函数y []()x x x =++的图象与正比例函数4y x =的图象有两个交点
12. 如图,多边形的各顶点都在方格纸的格点(横竖格子线的交错点)上,这样的多边形称
“格点多边形”,它的面积S 可用公式
( 是多边形内的格点数, 是多
边形边界上的格点数)计算,这个公式称为“皮克定理”。
现有一张方格纸共有 200 个格点,画有一个格点多边形,它的面积 S=40. ( 1 )这个格点多边形边界上的格点数
= (用含
的代数式表示);
( 2 )设该格点多边形外的格点数为
,则
=
13. (2017年山东临沂)平面直角坐标系中,如果点P 的坐标是(m ,n ),向量OP 可以用点P 的坐标表示为(,)OP m n =。
已知,1122(,),(,)OA x y OB x y ==。
如果1212+y 0x x y = ,那么OA 与OB 互相垂直。
下列四组向量:(1)(2,1),(1,2)OA OB ==- (2)0
(cos30,tan 45),(1,sin60)OC OD ==;
(3)1
(32,2),(3)2OE OF =--=+;(4) 0
(,2),(2,1)OG OH π==-
其中互相垂直的是 (填上所有正确的答案序号)
14. 在平面直角系xoy 中,(t,0),(A B t ,对于线段AB 和X 轴上方的点P 给出如下定义,当0=60APB ∠时,称点P 为AB 的“等角点”
(1)若
,在点33
(0,),1)22C D E ,(,)
中,线段AB 的“等角点”是
(2)直线MN 分别交x 轴、y 轴于点M 、N ,点M 的坐标是(6,0),0
=30
O M N ∠
(a )线段AB 的“等角点”P 在直线MN 上,且0
=90ABP ∠,求点P 的坐标
(b )在(a )的条件下,过点B 作BQ PA ⊥,交MN 于点Q ,求AQB ∠的度数 (c )若线段AB 的所有“等角点”都在MON ∆内部,求t 的取值范围。
15.对任意的一个三位数n ,如果n 满足各个数位上的数字互不相同,且都不为零,那么称这个数为“相异数”,将一个“相异数”任意两个数位上的数字对调后可以得到三个不同的新三位数,把这三个新三位数的和与111的商记为F (n )。
例如n=123,对调百位与十位上的数字得到213,对调百位与个位上的数字得到321,对调十位与个位上的数字得到132,这三个新三位数的和为213+321+132=666,666111=6,所以F (123)=6.
(1)计算:F (243),F (617);
(2)若s ,t 都是“相异数”,其中s 10032,150y x t =+=+(19,19x y ≤≤≤≤,x 与y
都是正整数),规定()
k ()F s F t =
,当()()18F s F t +=时,求k 的最大值
16. (2017年北京)在平面直角坐标系中的点P 和图形M ,给出如下定义:若图形M 上存在一点Q ,使得P 、Q 两点间的距离小于或等于1,则称P 为图形M 的关联点. (1) 当O 的半径为2,
(a ) 在123
115(,0),(222
P P P ,(,0)点中,O 的关联点是
(b ) 点P 在直线y=-x 上,若P 为O 的关联点,求点P 的横坐标取值范围 (2)C 的圆心在x 轴上,半径为2,直线y=-x+1与x 轴、y 轴交于点A ,B 。
若线段AB 上的所有点都是C 的关联点,直接写出圆心C 的横坐标的取值范围。