高一第二学期期中试题

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济宁市第一中学2023-2024学年度第二学期高一期中检测物理试题Word版

注意事项：济宁市第一中学2023-2024 学年度第二学期高一期中测试物理试卷考试时间：90 分钟1.答题前填写好自己的姓名、班级、考号等信息2.请将答案正确填写在答题卡上一、单项选择题:本题共 8 小题，每小题 3 分，共 24 分，每个小题只有一个选项符合题目要求。

1.下列说法正确的是（）A.开普勒在第谷观测的天文数据基础上得到了开普勒行星运动定律B ．20 世纪初建立的量子力学理论，使人们认识到牛顿力学理论也适用于微观粒子的运动C.开普勒第一定律认为，所有行星围绕太阳运动的轨迹是椭圆，太阳位于椭圆轨道中心D.牛顿发现了万有引力定律，随后卡文迪什进行了“月-地检验”将万有引力定律推广至自然界所有物体之间2.下列四幅图是有关生活中的圆周运动的实例分析，其中说法正确的是（）A.汽车通过凹形桥的最低点时，速度越快越容易爆胎B.铁路的转弯处，外轨比内轨高是为了利用轮缘与内轨的侧压力来帮助火车转弯C ．图中所示是圆锥摆，减小θ，但保持圆锥的高不变，则圆锥摆的角速度变大D ．洗衣机的脱水是利用了失重现象3.如图，运动员将质量为 m 的篮球从 h 高处投出，篮球进入离地面 H 高处的篮筐时速度为 v ，若以篮球投出时位置所在水平面为零势能面，将篮球看成质点，忽略空气阻力，对于篮球，下列说法正确的是（）A.进入篮筐时势能为 mgHB.在刚被投出时动能为mgH + 1 mv 22C.进入篮筐时机械能为mgH + 1mv 22D.经过途中 P 点时的机械能为mgH - mgh + 1mv 224.如图所示，中国自行研制、具有完全知识产权的“神舟”飞船某次发射过程简化如下：飞船在酒泉卫星发射中心发射，由“长征”运载火箭送入近地点为 A 、远地点为 B 的椭圆轨道上，在 B 点通过变轨进入预定圆轨道。

则（）A.在椭圆轨道上运行时，飞船在 A 点的速度比 B 点的小B.在椭圆轨道上运行时，飞船在 A 点的加速度比 B 点的大C.在 B 点变轨前后，飞船的机械能不变D.在 B 点飞船通过减速从椭圆轨道进入预定圆轨道5.如图所示是一簇未标明方向、由单一点电荷产生的电场线，虚线是某一带电粒子通过该电场区域时的运动轨迹，a 、b 是轨迹上的两点。

高一下学期期中考试语文试卷含答案(共3套)

高一下学期期中考试语文试卷含答案(共3套)高一第二学期期中考试语文试题（满分：150分；考试时间：150分钟）（一）论述类文本阅读（本题共3小题，9分）文化软实力，是指一个国家或地区基于文化而具有的凝聚力、生命力、创新力、传播力和影响力。

“文化软实力”的说法源自XXX的软实力理论。

一般来说，软实力是一种隐形的力量，蕴含在文化、政治价值观、外交政策和国际形象四个载体中。

在这四个载体中，文化是核心，其他三个组成部分也都深深地烙上了文化的影子。

甚至有人直接把软实力解释成文化力。

基于此，文化软实力就有了广义和狭义之分，广义的文化软实力就是指“软实力”；狭义的文化软实力，则是构成软实力的文化要素。

文化软实力的形成必须依赖先进的文化，而这种文化只有与时俱进才能更好地服务于相应的时代和社会，才能更好地促进个人全面自由的发展，才能体现出强大的吸引力和感染力。

文化软实力的作用，主要体现在国内和国际两个方面。

在国内，它通过文化建设不断增强本国文化的认同感，抵御国外一些敌对文化理念的侵袭，增强国内民众的凝聚力。

通过吸收国外先进文化元素和不断改造本国文化中落后的成分，使本国文化更加适应当前形势，更好地指导经济建设，更好地彰显本国文化的强劲生命力。

在国际政治舞台上，兼容并蓄、富有活力的本国文化必将为国外受众所认可，使本国所奉行的理念得到传播，从而提升国家形象和影响力。

文化软气力产生于一定的文化资本。

这些资本包括国家价值寻求、社会理念、宗教崇奉、品德规范，还包括风俗惯、民族精神、国民素质、文学艺术等，还与教育、科技、文化财产的开展水平密切相干。

文化软气力产生的根本是人们对本国中心价值体系的认同和接受。

与传统手段相比，非强制手段是文化软气力完成的手段，而国家的综合国力是文化软气力的力量施展阐发形式。

在现实社会中，往往存在重器不重道的现象。

它表现在国家综合实力的建设上，就是重视提升硬实力而不重视提升文化软实力。

重视提升硬实力是对的，文化软实力也一定要以硬实力为基础。

江西省南昌市第二中学2023-2024学年高一下学期5月期中英语试题(解析版)

南昌二中2023-2024学年度下学期高一期中考试英语试卷第一部分：听力理解（共两节，满分30分）第一节（共5小题；每小题1.5分，满分7.5分）听下面5段对话，每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题，每段对话仅读一遍。

1.What are the speakers talking about?A.A floodB. A fireC. A car accident2.How many tickets does the woman need to buy?A.7B.6C.53.What do we know about the man?A. He just bought a new house.B. He doesn’t get along with his roommates.C. He is a man of bad temper.4.What time is it now?A.9:00B. 9:10C.9:405.What does the man say about the woman?A. She should have been more active.B. She was very talkative.C. She danced very well.第二节（共15小题；每小题1.5分，满分22.5分）听下面5段对话或独白,每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。

听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，每小题将给出5秒钟的作答时间。

每段对话或独白读两遍。

听第6段材料，回答第6、7题。

6.Where does the woman come from?A. Australia.B. EnglandC. Brazil.7.What does the woman do ?A. She’s a trader.B. She’s a student.C. She’s a receptionist.听第7段材料,回答第8至9题。

高一期中考试试题及答案

高一期中考试试题及答案一、选择题（每题3分，共30分）1. 下列关于细胞结构的描述，正确的是：A. 细胞壁只存在于植物细胞B. 细胞膜是细胞的外层结构C. 细胞核是细胞的能量转换器D. 线粒体是细胞的遗传物质储存地答案：B2. 光合作用中，水分子分解发生在：A. 光反应阶段B. 暗反应阶段C. 光反应和暗反应阶段D. 细胞呼吸阶段答案：A3. 人体细胞中，负责合成蛋白质的结构是：A. 线粒体B. 核糖体C. 内质网D. 高尔基体答案：B4. 以下哪种元素不属于人体必需的微量元素？A. 铁B. 锌C. 钙D. 碘答案：C5. 细胞分裂过程中，染色体数目加倍发生在：A. 有丝分裂前期B. 有丝分裂中期C. 有丝分裂后期D. 减数分裂第一次分裂答案：C6. 下列关于酶的描述，错误的是：A. 酶是活细胞产生的B. 酶是蛋白质或RNAC. 酶可以提高化学反应速率D. 酶在反应后被消耗答案：D7. 人体中，血红蛋白的主要功能是：A. 运输氧气B. 运输二氧化碳C. 调节酸碱平衡D. 储存能量答案：A8. 以下哪种激素不属于内分泌腺分泌的激素？A. 胰岛素B. 甲状腺激素C. 肾上腺素D. 消化酶答案：D9. 人体免疫系统中，负责识别和攻击外来病原体的是：A. 红细胞B. 白细胞C. 血小板D. 血浆答案：B10. 人体细胞中，负责储存遗传信息的是：A. 线粒体B. 核糖体C. 内质网D. 细胞核答案：D二、填空题（每空2分，共20分）1. 细胞膜的主要功能是________和________。

答案：保护细胞内部结构；控制物质进出2. 人体中，负责合成和分泌胰岛素的腺体是________。

答案：胰腺3. 光合作用中，光能被转化为________和________。

答案：化学能；热能4. 人体中，负责运输氧气的蛋白质是________。

答案：血红蛋白5. 人体免疫系统中，负责识别和攻击外来病原体的细胞是________。

上海中学2023-2024学年高一下学期期中考试英语试题(含答案)

上海中学2023学年第二学期期中考试英语试题高一______班学号______ 姓名______ 成绩______Ⅰ．Listening ComprehensionSection ADirections: In Section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and a question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.1．A．15 dollars. B．20 dollars. C．25 dollars. D．45 dollars.2．A．To the gallery. B．To the dentist’s.C．To her flat. D．To the garage.3．A．She was fired by the company. B．She broke the law.C．She is on leave right now. D．She is replacing the company’s website.4．A．Patient and doctor. B．Resident and government official.C．Customer and insurance agent. D．Boss and secretary.5．A．He was sitting opposite Mr. Johnson. B．He is planning a farewell party for Mr. Johnson.C．All the tasks that Mr. Johnson did failed. D．He is glad Mr. Johnson left the company.6．A．She prefers dogs to cats.B．She had a close relationship with the man’s daughter.C．She used to sorrow over her dog’s death.D．She is always in low spirits.7．A．The woman should get the chips herself. B．The woman shouldn’t eat chips.C．The woman used to have several heart attacks. D．The woman warned the man against heart attacks. 8．A．They plan to have the meeting in another place.B．The availability of the meeting room will be discussed.C．They have already had the meeting.D They will have the meeting sometime later.9．A．The car’s demand greatly exceeds supply.B．The woman has listed the car’s advantages.C．The woman received a car a month ago. D．The woman didn’t like the car.10．A．She won’t do the presentation.B．She needs to collect a lot of data for the presentation.C．She is still at an early stage of preparation for the presentation.D．The topic is most important for the presentation.Section BDirections: In Section B, you will hear two short passages and a longer conversation, and you will be asked some questions on the passages and the conversation. The passages and the conversation will be read twice, but thequestions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one is the best answer to the question you’ve heard.Questions 11 through 13 are based on the following passage.11．A．The type of food you freeze. B．The way you warm up the frozen food.C．Whether the freezer bags are sealed. D．What temperature you set your freezer to. 12．A．Because they can be easily stocked.B．Because they fit well in the fridge.C．Because they come in different sizes and shapes. D．Because they help to keep the dry food dry 13．A．Prevent people from eating too much food.B．Stop people from removing food that hasn’t gone bad.C．Make people become cautious about eating unhealthy food.D．Make people become ambitious in making use of leftover food.Questions 14 through 17 are based on the following passage.14．A．Postpone retirement age. B．Involve more women in work.C．Hire more foreign workers. D．Attract workers with high salaries.15．A．Relieve pressure on human nursing care.B．Take care of children and the elderly.C．Finally replace humans in workforce. D．Give humans more time to r creative work. 16．A．Robots can’t do certain work. B．Some people don’t accept robots.C．The expenses for robots are still high. D．The functions of robots need improving.17．A．Japan struggles to fight workforce shortage.B．Japanese attitudes towards robots change a lot.C．Robots have played a major role in Japan’s industry.D．Robots can help in Japanese workforce shortage.Questions 18 through 20 are based on the following conversation.18．A．The cruise liner will provide all sorts of food and entertainment.B．Only half of the cabins will be filled up.C．The prices of unsold tickets will be reduced.D．Everyone will be able to afford the ticket.19．A．Book tickets as soon as they are available. B．Closely watch the changes of ticket prices C．Compare deals from different sources. D．Keep in contact with a travel age n you can trust. 20．A．Because cruise tours are only suitable for people who have much free time.B．Because he can work part-time to earn money to pay for the tour.C．Because doing price research and comparing takes time.D．Because he can sail shortly after buying the cheap ticket.Ⅱ．Grammar and VocabularySection A Multiple Choice21．No man is useless in this world ______ lightens the burden of someone else.A．which B．that C．who D．as22．______ be considered for the role of team leader in our upcoming project?A．Who do you suggest that should B．Who do you suggestC．Whom do you suggest should D．Do you suggest who should23．I’m now applying to graduate school, ______ means someday I’ll return to a profession ______people need to be nice to me in order to get what they want.A．which, as B．which, which C．which, where D．as, in which24．The reason ______ she gave for her resignation was ______ she wanted to pursue her passion for travel and exploration.A．that, that B．why, that C．why, because D．/, because25．It might be years ______ we ______ the creation of artificial intelligence systems capable of true human-like cognition.A．since, made possible B．before, make possibleC．since, made possible that D．before, make it possible26．The budget for the project ended up being twice ______, causing unexpected financial strain on the company. A．how it intended to B．that it had intended toC．as it intended to D．what it was intended to27．It was ______ she took her first step onto foreign soil ______ signaled the beginning of a journey filled with unknown adventures and unforgettable experiences.A．the moment, that B．the moment, whenC．the moment when, that D．the moment when, which28．The complexities of the English language are ______ even native speakers cannot always communicate effectively, ______ almost every American learns on his first day in Britain.A．so that, as B．such that, as C．so that, with D．such that, in that29．His confidence and strong will clearly show that he is no longer ______ he used to be the first time ______ he undertook such a demanding task.A．who, when B．who, / C．what, / D．what, that30．It was not so much her talent ______ her perseverance and determination ______ motivated her to the top of her field.A but. that B．as, that C．nor, which D．like, which31．______ the children tracked mud all over them again.A．No sooner did he sweep the floors clean than B．Hardly had he sweep the floors clean whenC．Barely he had swept the floors clean than D．Scarcely had he swept the floors clean when32．Although the suspect insisted ______ alone during the time of the crime, the court still demanded ______ evidence to support his alibi.A．being at home, he should provide B．he be at home, he providedC．he was at home, be provide D．he was at home, he providing33．Visitors are permitted to take photographs for personal use only, ______ stated otherwise by the museum staff. A．though B．if C．as D．unless34．The recipe book features helpful ______, making it easier for learners to visualize the cooking process.A．explanation B．demonstrations C．illustrations D．presentations35．The heroic idea that ______ qualities such as excellence, generosity courage, loyalty and dignity is highly valued and modeled.A．embraces B．identifies C．examines D．criticizes36．______ by the work pressure, he has been experiencing serious physical symptoms of stress and had to turn to a therapist for help.A．Overwhelmed B．Disappointed C．Frustrated D．Shocked37．After witnessing her tireless dedication to practice every day, the parents were ______ her enthusiasm for playing the piano.A．concerned with B．committed to C．informed of D convinced of38．When we ______ the data further, we can identify specific trends and patterns that may not be evident at first glance.A．break up B．break out C．break through D．break down39．The temptation for a declining church to ______ old privileges is strong.A．hang on to B．settle for C．pass up D．sign for40．After signing the contract, every employee is ______ fulfill their duties and conform to the rules made by the company.A．reluctant to B．obliged to C．motivated to D．honored to41．Due to the long-term environmental and financial benefits, renewable energy technologies are ______ A．worthwhile to develop B．worth being developedC．worthy to be developed D．worthy of developingSection B VocabularyDirections: Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.Stressed out? Get chewing: can a wellness rebrand make Americans buy gum again?When was the last time you saw someone chewing gum? 1998, maybe? 2007? Chances are, it probably wasn’t recently. Like high heels and affordable housing, chewing gum appears to be going 42Gum’s popularity has been fading globally thanks to increased competition from products like breath mints and mobile phones distracting us from impulse purchases while shopping. The pandemic, moreover, 43 ·accelerated gum’s decline.Even after people 44 from lockdown, sales didn’t recover. Gum sales worldwide in 2023 were 10% below 2018 figures. In the US, the drop has been particularly pronounced: last year 1.2 billion units of gum were sold in the US, 32% fewer than in 2018.However, chewing gum, in various forms, is one of the oldest habits there is. Stone age teenagers were chewing birch bar k tar possibly for pleasure, medicinal purposes, or to use it as a glue. Gum has also been loaded with culturalmeaning and the subject of various 45 panics. Some people believe it is a marker of the bad kids or a habit of the lower class.Despite a certain amount of social stigma（污名）attached to gum, it has - until relatively recently -been a wildly successful product. That’s thanks to William Wrigley Jr, who was a marketing and advertising genius. Wrigley always 46 to find a way to make gum relevant and insert it into consumer culture. For example, Wrigley advertised the idea that chewing gum was a health aid that would help digestion and would relieve stress.This year the Wrigley brand’s owner —Mars—came out with an ad campaign it hopes will revive gum’s 47 by positioning it as an almost instant stress reliever. Linking gum with wellness worked in the 1910s, but is it going to work now? Alex Hayes at the food consultancy is 48 optimistic. “The global well ness market is estimated to be worth more than $1.5 trillion, so it’s no surprise that Mars wants a piece of the pie,” Hayes says. “We’ve seen the success of categories such as tea promoting their products via functional 49 and messaging-teas for good sleep, mental clarity, stress relief, etc. So it comes as no surprise that Mars is risking the same 50 .” But he also notes, customers are increasingly worried about processed foods and are eager to move away from artificial 51 . There’s still ongoing discussion on just how effective repositioning chewable plastic as a health supplement is going to be. Ⅲ．Reading ComprehensionSection A ClozeDirections: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.It’s safe to say Jeremy Scott is having a lucky year. In March while working as a chauffeur, he told his boss about his plans to set up a driving business. By the end of the journey, Scott’s boss had offered to 52 his idea-a starting capital along with the gift of a £110,000 limousine（豪车）to kick start the business.Of course, there’s an element of luck to everyone’s career. Whether you’re a chief executive or an artist — your 53 won’t be based on hard work alone. For example, the place you were born 54 your education. It determines whether you learn to read, write or complete qualifications, which 55 limits your career choices.Many people believe success is down to talent and hard work, but “this is because most people underestimate the role of 56 ”, says psychologist Dr Elizabeth Nutt Williams. “We do a lot of work to prepare for ourcareers-education, training, taking advantage of mentoring-all of which tend to be in our control.” People don’t like to acknowledge the role of luck in their work, as it 57 this feeling of being in control, adds Williams.Everyone remembers working hard, so people are more likely to overestimate how much of their success is down to diligence than something much more 58 like luck.The reality of success （at least in terms of 59 ）is less clear cut. In the UK, studies show where you are born is likely to determine how much you earn.2017 research found that there is a “class pay gap’’, where professional employers from 60 backgrounds are paid almost £7,000 less a year — despite having the same role, education and experience as colleagues from more privileged families. 61 , black graduates earn up to 23% less per hour than white university leavers, whereas woman in the UK earn 14% less on average than men.Socio-economic status also plays a big role in the 62 you enter. A recent study by the Debrett’s Foundation found seven in every 10 young people aged 16-25 use 63 to get their first job. While research has shown that less able, richer children are 35% more likely to become high earners than their brighter. poorer peers.The truth is: chance and coincidences 64 our careers more than we like to think. Realizing that parts of your career are out of your control sounds 65 , but being grateful for the role of luck in your career can actually make you more fortunate.This is because when you acknowledge the role of luck in your work, you become prepared to take advantage of more fortunate moments. “Chance events occur·but it is all about the individual’s 66 to see those events as possibilities and their willingness to take a risk,” says Williams.52．A．challenge B．adopt C．finance D．reject53．A．performances B．accomplishments C．assessments D．outcomes54．A．accounts for B．applies to C．makes up for D．depends on55．A．in reward B．after all C．in turn D．by nature56．A．chance B．accident C．education D．diligence57．A．emphasizes B．overlooks C．maintains D．weakens58．A．manageable B．vital C．slippery D．minor59．A．reputation B．income C．education D．occupation60．A．wealthier B．poorer C．unique D．diverse61．A．Nevertheless B．Contrarily C．Consequently D．Similarly62．A．profession B．circle C．community D．university63．A．certificates B．online platforms C．career fairs D．family connections64．A．contribute to B．result from C．add to D．hold back65．A．inspiring B．encouraging C．appealing D．discouraging66．A．reluctance B．eagerness C．readiness D．resolutionSection B Passages（A）When you think about coffee alternatives, garlic is probably one of the last things that comes to mind, but that is exactly the ingredient that one Japanese inventor used to create a drink that looks and tastes like coffee.74-year-old Yokitomo Shimotai, a coffee shop owner in Aomori Prefecture, Japan, claims that his unique “garlic coffee” is the result of a cooking blunder he made over 30 years ago, when he burned a steak and garlic while waiting tables at the same time. Intrigued by the burnt garlic’s smell, he mashed it up with a spoon and mixed it with hot water. The resulting drink looked and tasted a lot like coffee. Making a mental note of his discovery, Yokimoto carried on with his job and only started researching garlic coffee again after he retired.Committed to turning his weird drink into a commercial product, Yokitomo Shimotai spent years optimizing the formula, and about five years ago, he finally achieved a result he was satisfied with. To make his dissolvable garlic grounds, he roasts the cloves（蒜瓣）in an electric oven, and after they’ve cooled off, smashes them into fine particles and pac ks them in dripbags.“My drink is probably the world’s first of its kind,” the garlic coffee inventor told Kyodo News. “It contains no caffeine so it’s good for those who would like to drink coffee at night or pregnant women.”“The bitterness of burned garl ic apparently helps create the coffee-like flavor,” Shimotai adds. He claims that, although his garlic coffee does give off an aroma of roasted garlic, it doesn’t cause bad breath, because the garlic isthoroughly cooked. And if you can get past the smell, the drink apparently does taste a lot like actual coffee. If decaf isn’t good enough for you, and you’re in the mood for something new, you can try Yokitomo Shimotai’s garlic coffee at his shop, in the city of Ninohc, lwate Prefecture, or buy your own dripbags for just 324 yen（$2.8）. 67．Which word is the closest in meaning to the underlined word “blunder” in the second paragraph?A mistake B．show C．mixture D．brand68．Who is NOT suitable to drink garlic coffee?A．A student having trouble with sleep B．A woman bearing a baby.C．A cleaner working on a day shift. D．A young lady sick of garlic.69．Which of the following is NOT characteristic of garlic coffee?A．It is caffeine-free. B．Garlic powder dissolves in waterC．The burnt garlic create s bitterness. D．It is an improvement on a garlic dish.70．Which of the following can be used to describe Yokitomo Shimotai?A．Venturous and greedy B．Innovative and perseverantC．Hardworking and cautious D．Observant and helpful（B）71．By “how they stacked up” in paragraph 1, the author probably means “how they ______.”A．make sense to manufacturers B．get stuck in storesC are compared with each other D．are piled up together72．Which of the following devices favourably reacts to users?A．Dreampad pillow B．Eight sleep trackerC．Smart Nora Wireless Snoring Solution D．Nightingale Smart Home Sleep System73．Which of the following statements is true according to the passage?A．The Eight keeps the entire bed at the same temperature.B．The Nightinga, is an economical but perfect device.C．Soft music is applied to all these four devices.D．One in three people suffer from sleep problem.（C）One way to divide up the world is between people who like to explore new possibilities and those who stick to the tried and true. In fact, the tension between betting on a sure thing and taking a chance that something unexpected and wonderful might happen troubles human and nonhuman animals alike.Take songbirds, for example. The half-dozen finches（雀）resting at my desk feeder all summer know exactly what they’ll find there: black sunflower seed, and lots of it. Meanwhile, the warblers（莺）exploring the woods nearby don’t depend on this predictable food source in fine weather. As food hunters, they enjoy less exposure to predators and, as a bonus, the chance to meet the perfect mate flying from tree to tree.This “explore-exploit” trade-off（权衡）has prompted scores of lab studies, computer simulations and algorithms （算法）, trying to determine which strategy brings in the greatest reward. Now a new study of human behavior in the real world, published last month in the journal Nature Communications, shows that in good times, there isn’t much of a difference between pursuing novelty and sticking to the status quo（原状）. When the going gets tough. however, explorers are the winners.The new study, led by Shay O’Farrell and James Sanchirico, both of the Univ ersity of California, Davis, along with Orr Spiegel of Tel Aviv University, examined the routes and results of nearly 2,500 commercial fishing trips in the Gulf of Mexico over a period of 2.5 years. The study focused on “bottom longline” fishing, a system where hundreds of lines are attached to a horizontal bar that is then lowered to reach the sea bed. Dr. O’Farrell explained the procedure this way: Go to a location and put the line down. Stay for a few hours. The lines are a mile long and have a buoy （浮标）at either end. When they pull that up, they assess the catch, and then decide if they will stay or move on to a different spot.Over two years of collecting data under various climate conditions, the researchers discovered that the fishermen were fairly c onsistent. “The exploiters would go to a smaller set of locations over and over, and go with what theyknow,” Dr. O’Farrell said. The explorers would constantly try a wider range; they’d sample new places.In the long run, there wasn’t a huge difference in payoffs between the two groups, perhaps due to the sharing information between fishing crews, said Dr. O’Farrell. But in challenging times, the study’s message was clear: “You can try new things in the face of uncertainty.”74．The author takes the songbird as an example to indicate that ______.A．like birds, humans tend to be satisfied with the predictableB．some birds are used to looking for food instead of being fedC．there exist the conservative and the adventurous like humansD．birds choose different ways to look for food in different weather75．According to the third paragraph, people who mastered “explore-exploit” trade-off ______.A．will choose either to pursue novelty or keep the status quoB．are ready to risk in time of difficultyC．will be tough in good times and bad timesD．will grow to be experts in lab studies76．Which can be inferred from the new study led by Shay O’Farrell and James Sanchirico?A．The two groups react to the unexpected differently.B．The “explore-exploit” trade-off helps scientific research a lot.C．The exploiters are used to fishing based solely on their experience.D．The explorers tend to achieve more than the exploiters in the long run.77．Which of the following can be the best title for passage?A．How the Exploiter differs from the Explorer B．How to Become a Productive FishermanC．What is “Explore-Exploit” Trade-off D．When to take risks mattersSection CDirections: Read the following passage. Fill in each blank with a proper sentence given in the Each sentence can be used only once. Note that there are two more sentences than you need.The Maya loved cacao so much that they used the beans as currency. They also believed it is good for you—which many people still say today about cacao’s most famous byproduct, chocolate. 78 . While some have suggested that less than an ounce of dark chocolate might improve heart health, much of the research doesn’t involve eating actual chocolate but rather its components — flavanol, especially.79 . In a clinical trial of 21,000 adults, they found that the half of the group that took500mg of. cocoaflavanol supplements daily had a significantly lower risk of death from cardiovascular disease than those who had taken a placebo（安慰剂）.Flavanols may also boost insulin sensitivity, according to some studies, which might be helpful in reducing the risk of type 2 diabetes（糖尿病）. 80 . Those at risk of diabetes might be wise to choose a cacao-inspired supplement instead of eating chocolate—and the sugar it contains. Other research suggests that the flavanols found in cacao （also present in fruits, vegetables, and tea）could slow cognitive decline during aging, or even boost brain performance by improving blood flow to the cerebral cortex.What these findings mean for chocolate is limited, however. Participants would have had to eat multiple fat and sugar filled chocolate bars a day to source 500mg of flavanols. 81 . So understanding why certain types of chocolate are healthier than the rest is the focus of further research.Ⅳ．Fill in the BlanksHow sneaker culture took over the worldSneakers have come a long way from when they were first invented in 1860s England for the upper-class playing croquet（槌球）and tennis.Long worn for function 82 82 fashion, today sneakers have become an entire culture—both a form of self-expression and a high art found in museum exhibits and designer auction houses.83 transformed sneaker culture into a true phenomenon was the 1985 release of Nike’s Air Jordan 1s. In 1984, Michael Jordan was a talented rookie who had yet to play in a professional game. 84 that, Nike saw Jordan as the future of their brand, signing him to a five-year, $2.5 million endorsement（代言）deal. 85 Jordan matured into one of the greatest basketball players of all time, the sneaker’s popularity skyrocketed.Meanwhile, another cultural shift 86 （take）place with casual Fridays introduced in white-collar businesses. It was when men were allowed to put aside their suits and wear something one day a week that showed people who they really were.As sneakers became increasingly desired, footwear companies turned to 87 （generate）even more publicity by collaborating with celebrities and luxury brands, as well as releasing small batches of limited-edition shoes with eye-pop ping designs.Celebrities also started their collaborations with sneaker brands, which helped target a whole new demographic of people to experience sneaker culture. It was a blending of high and low fashion, 88 the shoe industry has never really seen before. A pair that Jordan wore in his legendary final NBA season 89 （sell ）even for $2.2 mllion, making them the most expensive sneakers ever to appear at auction.By the mid-2010s, speakers 90 （become）solid gold status symbols. Wearing rare and cool sneakers became an expression of one’s social status. But not until recently, sneakers are finally getting their due as part of our cultural heritage—and particularly how Black culture has shaped that heritage. It took decades for the sneaker industry to recognize that 91 these Black athletes or artists that championed their products there would be no sneaker culture.Ⅴ．Translations92．结果看来这项传统的确值得传承给我们的后代。

江西省赣州市于都中学2023-2024学年高一下学期期中考试语文试题(原卷版)

于都中学2023～2024学年度第二学期期中考试高一语文试卷2024年4月考生注意：1.答题前，考生务必将自己的准考证号、姓名填写在答题卡上。

考生要认真核对答题卡上粘贴的条形码的“准考证号、姓名、考试科目”与考生本人是否一致。

2.回答选择题时，选出每小题答案后，用铅笔把答题卡上对应题目的答案标号涂黑。

如需改动，用橡皮擦干净后，再选涂其他答案标号。

回答非选择题时，将答案写在答题卡上。

写在本试卷上无效。

3.考试结束，监考员将试题卷和答题卡一并收回。

一、现代文阅读（35分）（一）现代文阅读Ⅰ（本题共5小题，19分）阅读下面的文字，完成小题。

儒家思想的建立孔子身处的时代，礼崩乐坏，西周的封建制度随着西周本土的沦陷，只剩下一个空名。

在大崩溃的时候，孔子致力于重建超越时空限制的普世价值观念，将依据理性道德建立的系统作为自己安身立命之所，也作为世界可以遵行的、他所盼望的行为准则。

孔子教诲门下，并不像后世所谓的学校，而是与来自各方的同人和朋友们随机讨论问题，共同建立和发展一套思想体系。

从一开始，孔子注意的就不是个人“独善其身”的道德，而是人与人之间的相处之道——这相处之道又建立在道德之上。

“道”在孔子心目中是永恒而且普世的原则，即使是至高无上的神明“天”，也不过是“道”的显现，“天”和“道”是一体两面。

神的力量和永恒、普世的原则，虽然抽象，但“道”不只存在于人与人的相处之中，它还存在于万事之中。

因此，儒家思想落实在人间事务上，是主导人间关系的大原则、确立人和人之间相处的尺寸与尺度。

孔子将中国后世几千年的思想脉络一锤定音，这是一门人间与社会的学问，而非今天学术界的认知学问。

这个特点我们必须记得，它乃是中国和西方制度方向上最大的差异。

儒家思想中的“安人”与“安百姓”孔子认为门下的弟子分别属于四个门类：德行、政事、语言、文学。

这四科各有出色的代表人物。

德行是修身，政事是为人服务，语言是处理社会事务和传达信息，文学是书写能力，与语言同为传达信息之用。

河南省商丘市一中2021-2022学年高一下学期期中语文试题

商丘市一高2021—2022学年第二学期期中考试试题高一语文试卷命题人：审题人：一、现代文阅读（36分）（一）论述类文本阅读（本题共3小题，9分）阅读下面的文字，完成下面小题。

文化是一个国家凝聚力、生命力和影响力的集中体现，并且用一种更基本、更深沉、更持久的方式深刻影响着这个世界。

一直以来，中国始终致力于与世界各国勠力同心，共建人类命运共同体。

然而，一些地区的贫富分化、环境污染、资源枯竭，以及一些国家奉行的强权政治、丛林法则等不和谐因素不仅加剧了全球局势的动荡不安，更成为阻碍人类社会和平发展的重大障碍。

党的十九届五中全会旗帜鲜明地提出到2035年建成文化强国的目标，这是党中央首次明确建成文化强国的具体时间表，意味着中国文化必将以一种更加强健且丰满的姿态，参与到人类社会发展的历史进程中，成为推动构建人类命运共同体的澎湃力量。

以文化之魂，凝聚人类命运共同体意义上的价值共识。

人类命运共同体是依托于中国优秀传统文化而生成的一种价值理念。

“尚和”“天下”“大同”等思想描绘了人类命运共同体的重要特征。

在此，文化之“强”并不意味着文化霸权，而是说要对自己的文化足够自信，以至海纳百川、有容乃大，进而形成世界多元文化的合力。

正如习近平总书记所强调的，“中国共产党关注人类前途命运，同世界上一切进步力量携手前进”。

只有坚守这一原则，我们才能在诸多冲突与挑战面前，会同天下，共克时艰。

以文化之声，唱响人类命运共同体叙事中的中国故事。

人类命运共同体作为人类社会未来发展的愿景理念，体现了中华民族对世界的总体期待，凝聚了悠远厚重的中国智慧。

在此，文化之“强”，主要体现在让文化真正走进生活，让文化触手可及。

一方面，中国文化应深度融入世界文化主流，贴近各国人民的现实生活，创造出一批广泛传播的文化产品，把这种跨越时空、超越国度、富有魅力的文化精神与“中国”两字深度捆绑；另一方面，中国文化应致力于打造对话和交流的平台，完善文化交往的机制，推动微观层面的文化互动。

深圳中学2022—2023学年度第二学期期中考试高一语文试题及答案

深圳中学2022—2023学年度第二学期期中考试试题高一语文考试时长：150分钟卷而总分：150分一、单项选择题（共10小题，每小题2分，共20分）1．下列句子中，不含通假字的一组是（）（2分）A．失其所与，不知河海不择细流B．遂散六国之从盖亦反其本矣C．焉用亡郑以陪邻籍寇兵而贵盗粮D．俯足以畜妻子申之以孝悌之义2．下列加点词的解释全部正确的一组是（）（2分）A．功施．到今施：施展/王若隐．其无罪而就死地隐：隐瞒B．批．大郤，导大窾批：击/如上委．地委：散落C．臣以神遇．而不以目视遇：对待/道芷阳间．行间：秘密地D．且君尝为晋君赐．矣赐：赏赐/又欲肆．其西封肆：肆意3．对下列句中加点词的意义和用法完全一致的一组是（）（2分）A．方．六七十/且知方．也B．杀人如不能举．/举．所佩玉玦以示之者三C．度．我至军中，君乃入/道不通，度．己失期D．沛公不胜．杯杓/刑人如恐不胜．4．下列句子中加点词的意义与现代汉语相同的一组是（）（2分）A．沛公奉卮酒为寿，约为婚姻．．B．依乎天理．．，批大郤，导大窾C．三年之后，未尝．．见全牛也D．莅中国．．而抚四夷也5．成语，是古代汉语的活化石。

下列我们学过的文中原句与所选成语都有一个共同的字，它们的意思都相同的一组是（）（2分）①“料大王士卒足以当项王乎”旗鼓相当②“因人之力而敝之，不仁”因利乘便③“微夫人之力不及此”微乎其微④“何伤乎，亦各言其志也”无伤大雅⑤“肩之所倚，足之所履”削足适履⑥“今急而求子，是寡人之过也”是可忍，孰不可忍A．①②⑤⑥ B．①②④⑥ C．①③④⑤ D．②④⑤⑥6．下列加点词的活用现象相同的一组是（）（2分）A．赤也为之小．，孰能为之大．三子者出，曾皙后．B．然后从而刑．之强．公室，杜私门C．共其乏困．．越国以鄙远．D．欲辟土地，朝．秦楚王无异．于百姓之以王为爱也7．下列“而”的用法与其他项不同的一项是（）（2分）A．无恒产而有恒心者，惟士为能B．士不产于秦，而愿忠者众C．今人有大功而击之D．此惟救死而恐不赡8．下列句子中加点虚词的意义和用法相同的一组是（）（2分）A．夫我乃．行之，反而求之，不得吾心/合于《桑林》之舞，乃．中《经苜》之会B．敢以．烦执事/以．乱易整，不武C．异乎．三子者之撰/岂敢反乎．D．邹人与．楚人战，则王以为孰胜/可得闻与．9．与“百姓之不见保”句式相同的一项是（）（2分）A．若属皆且为所虏 B．臣之所好者道也C．保民而王，莫之能御也 D．宜乎百姓之谓我爱也10．下列各项对文化常识的介绍有错误的一项是（）（2分）A．寡人，即寡德之人，君王对自己的谦称，类似的还有予一人、孤、不榖、陛下等。

2023-2024学年度高一年级第二学期期中考试模拟卷历史试题(拔高提升版)(部编版专用)原卷版

2023-2024学年度高一年级第二学期期中考试模拟卷（江苏专用）历史试题（拔高提升版）（考试时间：75分钟；试卷满分：100分）注意事项：1．本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分。

答卷前，考生务必将自己的姓名、准考证号填写在答题卡上。

2．回答第Ⅰ卷时，选出每小题答案后，用2B铅笔把答题卡上对应题目的答案标号涂黑。

如需改动，用橡皮擦干净后，再选涂其他答案标号。

写在本试卷上无效。

3．回答第Ⅱ卷时，将答案写在答题卡上。

写在本试卷上无效。

4．测试范围：纲要下册第1~15课。

5．难度系数：0.4。

6．考试结束后，将本试卷和答题卡一并交回。

第Ⅰ卷一、选择题：本题共16小题，每小题3分，共48分。

1．以下为古代主要文明示意图。

据此可知，在人类早期文明的产生中起决定作用的是（）A．文化与文明交融B．生产方式的进步C．国家机关的建立D．人口跨区域流动2．形成于古印度西北部地区的犍陀罗艺术，伴随佛教传入中国，对中国隋唐美术影响很大，成就了云冈石窟、龙门石窟、敦煌石窟等一批中国古代艺术瑰宝，其特色是面容呈椭圆形，鼻梁如剑一般高而长，身着希腊式服装，衣褶多由左肩下垂。

据此推断，该艺术是（）A．希腊城邦海外殖民产生的影响B．古代罗马帝国对外征服的结果C．亚历山大远征交流碰撞的产物D．阿拉伯帝国融合东西方的结晶3．俄国铁腕女皇叶卡捷琳娜二世，自诩“开明君主”，实行开明专制。

1767年，她召开了新法典编纂委员会，并为这个委员会写了《圣谕》，标榜法律面前人人平等。

这反映了（）A．王权有限原则的确立B．统一民族国家的形成C．启蒙时代社会的进步D．法律至上观念的成熟4．如表是1444年—1481年奥斯曼帝国艾克银币的重量变化情况，由此可推断奥斯曼帝国（）年份1444年1451年1460年1470年1475年1481年重量（克） 1.06 1.01 0.96 0.93 0.77 0.75 A．控制商路国内通货膨胀严重B．受到新航路开辟的剧烈冲击C．连年扩张导致国力持续消耗D．攻占君士坦丁堡的军事消耗5．玛雅文字的组成原则和苏美尔文字的组成原则基本类似，都利用了语标和语言符号。

山西省太原市2023-2024学年高一下学期期中物理试题(解析版)

2023～2024学年第二学期高一年级期中学业诊断物理试卷(考试时间：下午4：30-6：0)说明：本试卷为闭卷笔答，答题时间90分钟，满分100分。

一、单项选择题：本题包含10小题，每小题3分，共30分。

请将正确选项前的字母填入表内相应位置。

1. 运动员正在短道速滑比赛中沿着弯道滑行，下列说法正确的是（）A. 运动员的加速度可能为零B. 运动员所受合力一定为恒力C. 运动员所受合力一定指向弯道内侧D. 运动员加速度方向与运动方向可能在同一直线上【答案】C【解析】【详解】A．运动员做曲线运动，则加速度不可能为零，选项A错误；B．运动员沿弯道运动，所受合力方向一定变化，则合力一定为变力，选项B错误；C．根据曲线运动的特点可知，运动员所受合力一定指向弯道内侧，选项C正确；D．运动员做曲线运动，加速度方向与运动方向一定不在同一直线上，选项D错误。

故选C。

2. 如图所示，红嘴鸥捕食时自右向左沿曲线减速，在轨迹最低点，速度v与空气作用力F的方向可能正确的是（）A. B.C. D.【答案】D【解析】【详解】红嘴鸥捕食时自右向左沿曲线减速，在轨迹最低点，速度方向沿轨迹切线向左，由于红嘴鸥受到重力与空气作用力两个力的作用，这两个力的合力方向指向轨迹的内侧，又由于红嘴鸥做减速运动，则合力的方向与速度方向夹角为钝角，即合力方向斜向右上方，根据力的合成规律可知，速度v与空气作用力F的方向只有第四个选择项符合要求。

故选D。

3. 关于运动的合成，下列说法正确的是（）A. 物体做曲线运动的速度可以不变B. 物体在恒定合外力作用下不可能做匀速圆周运动C. 合运动的加速度一定比每一个分运动的加速度大D. 两个互成角度的匀加速直线运动的合运动一定是匀加速直线运动【答案】B【解析】【详解】A．物体做曲线运动的速度的方向一定改变，故A错误；B．物体在恒定合外力作用下不可能做匀速圆周运动，因为匀速圆周运动合外力提供向心力，向心力方向时刻在改变，所以恒力作用下物体不可能做匀速圆周运动，故B正确；C．合加速度等于分加速度的矢量和，由平行四边形定则可知，合加速度的大小可能比分加速度大，可能比分加速度小，可能与分加速度相等，故C错误；D．两个互成角度的匀加速直线运动的合运动不一定是匀加速直线运动，如果合加速度与合速度不共线，则为匀加速曲线运动，故D错误。

福建省福州高一下学期期中考试语文试题

第二学期期中考试高一语文试卷（满分：150 分；考试时间：150分钟）班级姓名座号一、现代文阅读（一）非连续性文本阅读阅读下面的文字，完成下列小题。

材料一：近日，一段云南傈僳族小伙录制的视频“我是云南的，云南怒江的……”由于过于“魔性”在网络平台走红，引得各地网友纷纷模仿。

事实上这不是云南方言首次“出圈”，“方言版”村规民约、大喇叭方言播报疫情都在网上引发关注热议。

“不是自己呢东西不能偷、也不能整烂，偷着么要被抓呢，整烂么要赔呢。

”2018年，云南开远市一张贴在墙上的村规民约走红网络，十二条内容除了以极具特色的当地方言来表述外，读起来还朗朗上口，言简意赅。

当地村委会主任称，因当地村民文化程度普遍不高，所以才以大家熟悉的方言形式来公示村规。

专家表示，村干部用通俗易懂、甚至稍带俏皮的语言来表述村规，是一种喜闻乐见的创新之举，更容易深入人心。

2020年春节期间，在全民防控新冠肺炎疫情阻击战中，曲靖硬核“老村长”大喇叭方言喊话爆红网络，刷爆微信朋友圈。

“老村长”一口土味地道的曲靖沾益方言，通过大喇叭宣传疫情防控工作，既接地气又幽默诙谐，成为打通防控疫情信息“最后一公里”著有成效的好经验和做法。

方言是地域文化的乡土记忆的聚合与凝结，但方言走到今天面临传承乏人的困境。

据联合国教科文组织几年前的一次调查，全球有6000多种语言处境堪忧，每两周就有一种语言（主要是方言）消失，超过了很多动物的灭绝速度。

如今“为家乡上分”等系列视频能够在新媒体语境中爆火，在新时代焕发出新的生机，这确实是一件好事。

节选自《“我是云南的”背后的方言困境》材料二：关键词：短视频时代互联网时代，短视频开始碾压过去娱乐方式，成为全民娱乐首选。

此前的“山东菏泽曹县666”“蓝瘦香菇”等都是通过短视频传播。

国内权威移动大数据公司极光发布的《2021年Q2国内移动互联网报告》指出，当前国内移动网民人均每日APP使用时长为5.1小时，而网民使用时长最高的就是短视频App，用户使用时长占比达29.8%，约人均每天1.5小时。

江苏省泰州市姜堰区2023-2024学年高一下学期4月期中英语试题

2023～2024学年度第二学期期中考试高一英语试题（考试时间：120分钟；总分：150分）注意事项：1．答卷前，考生务必将自己的姓名、考试号等填写在答题卡指定位置上。

2．回答选择题时，选出每小题答案后，用铅笔把答题卡上对应题目的答案标号涂黑。

如需改动，用橡皮擦干净后，再选涂其他答案标号。

回答非选择题时，将答案写在答题卡上。

写在本试卷上无效。

3．考试结束后，将答题卡交回。

第一部分听力（共两节，满分30分）做题时，先将答案标在试卷上。

录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题纸上。

第一节（共5小题；每小题1.5分，满分7.5分）听下面5段对话。

每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1．How does the man usually get to his office?A．By bus.B．By bicycle.C．On foot.2．What is the normal price of the T-shirt?A．$15.B．$30.C．$50.3．Where is the blue T-shirt?A．In the drawer.B．In the cupboard.C．In the washing machine.4．What did the woman notice about the man?A．He was unpleasant.B．He was unsure.C．He was helpful.5．What is the relationship between the speakers?A．Friends.B．Security guard and driver.C．Salesman and customer.第二节（共15小题，每小题1.5分，满分22.5分）听下面5段对话或读白。

北京市2023-2024学年高一下学期期中考试数学试题含答案

2023—2024学年度第二学期北京市高一数学期中考试试卷（答案在最后）一､选择题（本大题共10小题，每小题4分，共40分）1.11πsin3的值为（）A.2B.2-C.2D.2【答案】A 【解析】【分析】利用诱导公式及特殊角的三角函数值计算可得.【详解】11πππsin sin 4πsin 3332⎛⎫=-=-=-⎪⎝⎭.故选：A2.下列函数中，最小正周期为π且是偶函数的是（）A.πsin 4y x ⎛⎫=+ ⎪⎝⎭B.tan y x =C.cos 2y x =D.sin 2y x=【答案】C 【解析】【分析】由三角函数的最小正周期公式和函数奇偶性对选项一一判断即可得出答案.【详解】对于A ，πsin 4y x ⎛⎫=+⎪⎝⎭的最小正周期为：2π2π1T ==，故A 不正确；对于B ，tan y x =的最小正周期为：ππ1T ==，tan y x =的定义域为ππ,Z 2x x k k ⎧⎫≠+∈⎨⎬⎩⎭，关于原点对称，令()tan f x x =，则()()()tan tan f x x x f x -=-=-=-，所以tan y x =为奇函数，故B 不正确；对于C ，cos 2y x =的最小正周期为：2ππ2T ==，令()cos 2g x x =的定义域为R 关于原点对称，则()()()cos 2cos 2g x x x g x -=-==，所以cos 2y x =为偶函数，故C 正确；对于D ，sin 2y x =的最小正周期为：2ππ2T ==，sin 2y x =的定义域为R ，关于原点对称，令()sin 2h x x =，则()()()sin 2sin 2h x x x h x -=-=-=-，所以sin 2y x =为奇函数，故D 不正确.故选：C .3.设向量()()3,4,1,2a b ==- ，则cos ,a b 〈〉=（）A.5-B.5C.5-D.5【答案】D 【解析】【分析】根据给定条件，利用向量夹角的坐标表示求解即得.【详解】向量()()3,4,1,2a b ==-，则cos ,5||||a b a b a b ⋅〈〉==.故选：D4.在△ABC 中，已知1cos 3A =，a =，3b =，则c =（）A.1B.C.2D.3【答案】D 【解析】【分析】直接利用余弦定理求解即可【详解】因为在△ABC 中，1cos 3A =，a =，3b =，所以由余弦定理得2222cos a b c bc A =+-，2112963c c =+-⨯，得2230c c --=，解得3c =，或1c =-（舍去），故选：D5.函数()()sin f x A x =+ωϕ(其中0A >，0ω>，0ϕπ<<)的图像的一部分如图所示，则此函数的解析式是（）A.()3sin 42f x x ππ⎛⎫=+⎪⎝⎭ B.3()3sin 44f x x ππ⎛⎫=+⎪⎝⎭C.()3sin 84f x x ππ⎛⎫=+ ⎪⎝⎭ D.3()3sin 84f x x ππ⎛⎫=+⎪⎝⎭【答案】C 【解析】【分析】根据图象可以求出最大值，结合函数的零点，根据正弦型函数的最小正周期公式，结合特殊值法进行求解即可.【详解】由函数图象可知函数的最大值为3，所以3A =，由函数图象可知函数的最小正周期为4(62)16⨯-=，因为0ω>，所以24(62)168ππωω⨯-==⇒=，所以()3sin 8f x x πϕ⎛⎫=+ ⎪⎝⎭，由图象可知：(2)3f =，即3sin 32()2()4424k k Z k k Z ππππϕϕπϕπ⎛⎫+=⇒+=+∈⇒=+∈ ⎪⎝⎭，因为0ϕπ<<，所以令0k =，所以4πϕ=，因此()3sin 84f x x ππ⎛⎫=+ ⎪⎝⎭，故选：C6.函数ππ()sin(2),[0,]62f x x x =+∈的最大值和最小值分别为（）A.11,2-B.31,2-C.1,12- D.1,1-【答案】A 【解析】【分析】根据给定条件，求出相位的范围，再利用正弦函数的性质求解即得.【详解】由π[0,2x ∈，得ππ7π2[,666x +∈，则当ππ262x +=，即π6x =时，max ()1f x =，当π7π266x +=，即π2x =时，min 1()2f x =-，所以所求最大值、最小值分别为11,2-.故选：A7.已知向量,,a b c在正方形网格中的位置如图所示.若网格纸上小正方形的边长为1，则()a b c +⋅= （）A.2B.2- C.1 D.1-【答案】B 【解析】【分析】根据给定信息，利用向量数量的运算律，结合数量积的定义计算得解.【详解】依题意，π3π|||2,||2,,,,,44a b c a b b c a c ===〈〉=⊥〈〉= ，因此3π||||cos2(242a c a c ⋅==⨯-=-，0b c ⋅= ，所以()2a b c a c b c +⋅=⋅+⋅=-.故选：B8.在ABC 中，已知cos cos 2cos a B b A c A +=，则A =（）A.π6B.π4C.π3 D.π2【答案】C 【解析】【分析】根据给定条件，利用正弦定理边化角，再逆用和角的正弦求出即得.【详解】在ABC 中，由cos cos 2cos a B b A c A +=及正弦定理，得sin cos sin cos 2sin cos A B B A C A +=，则sin()2sin cos A B C A +=，即sin 2sin cos C C A =，而sin 0C >，因此1cos 2A =，而0πA <<，所以π3A =.故选：C9.已知函数()()π2sin 03⎛⎫=+> ⎪⎝⎭f x x ωω，则“()f x 在π0,3⎡⎤⎢⎥⎣⎦上既不是增函数也不是减函数”是“1ω>”的（）A.充分不必要条件B.必要不充分条件C.充分必要条件D.既不充分也不必要条件【答案】B 【解析】【分析】以π3x ω+为整体结合正弦函数的性质可得12ω>，进而根据充分、必要条件分析判断.【详解】因为π0,3x ⎡⎤∈⎢⎥⎣⎦且0ω>，则ππππ,3333x ωω⎡⎤+∈+⎢⎥⎣⎦，若()f x 在π0,3⎡⎤⎢⎣⎦上既不是增函数也不是减函数，则2πππ33ω+>，解得12ω>，又因为()1,+∞1,2⎛⎫+∞ ⎪⎝⎭，所以“()f x 在π0,3⎡⎤⎢⎥⎣⎦上既不是增函数也不是减函数”是“1ω>”的必要不充分条件.故选：B.10.如图，正方形ABCD 的边长为2，P 为正方形ABCD 四条边上的一个动点，则PA PB ⋅的取值范围是（）A.[]1,2-B.[]0,2 C.[]0,4 D.[]1,4-【答案】D 【解析】【分析】建立平面直角坐标系，分点P 在CD 上，点P 在BC 上，点P 在AB 上，点P 在AD 上，利用数量积的坐标运算求解.【详解】解：建立如图所示平面直角坐标系：则()()0,2,2,2A B ，当点P 在CD 上时，设()(),002Px x ≤≤，则()(),2,2,2PA x PB x =-=--，所以()()224133,4PA PB x x x ⎡⎤⋅=-+=-+∈⎣⎦ ；当点P 在BC 上时，设()()2,02P yy ≤≤，则()()2,2,0,2PA y PB y =-=-，所以()220,4PA PB y ⎡⎤⋅=-∈⎣⎦ ；当点P 在AB 上时，设()(),202Px x ≤≤，则()(),0,2,0PA x PB x ==-，所以()()22111,0PA PB x x x ⎡⎤⋅=-=--∈-⎣⎦ ；当点P 在AD 上时，设()()0,02P y y ≤≤，则()()0,2,2,2PA y PB y=-=--，所以()220,4PA PB y ⎡⎤⋅=-∈⎣⎦ ；综上：PA PB ⋅的取值范围是[]1,4-.故选：D二､填空题（本大题共5小题，每小题5分，共25分）11.已知圆的半径为2，则60 的圆心角的弧度数为__________；所对的弧长为__________.【答案】①.π3##1π3②.2π3##2π3【解析】【分析】利用度与弧度的互化关系，弧长计算公式求解即可.【详解】60 的圆心角的弧度数为ππ601803⨯=；所对的弧长为π2π233⨯=.故答案为：π3；2π312.已知向量()2,3a =- ，(),6b x =- .若//a b ，则a =r __________，x =__________.【答案】①.②.4【解析】【分析】利用坐标法求出向量的模，再根据向量共线的坐标表示求出x .【详解】因为向量()2,3a =- ，所以a == ，又(),6b x =- 且//a b ，所以()326x =-⨯-，解得4x =.；4.13.若函数()sin f x A x x =的一个零点为π3，则A =__________；将函数()f x 的图象向左至少平移__________个单位，得到函数2sin y x =的图象.【答案】①.1②.π3##1π3【解析】【分析】利用零点的意义求出A ；利用辅助角公式化简函数()f x ，再借助平移变换求解即得.【详解】函数()sin f x A x x =的一个零点为π3，得ππsin 033A =，解得1A =；则π()sin 2sin()3f x x x x =-=-，显然πππ(2sin[()]2sin 333f x x x +=+-=，所以()f x 的图象向左至少平移π3个单位，得到函数2sin y x =的图象.故答案为：1；π314.设平面向量,,a b c 为非零向量，且(1,0)a = .能够说明“若a b a c ⋅=⋅ ，则b c = ”是假命题的一组向量,b c的坐标依次为__________.【答案】(0,1),(0,1)-（答案不唯一）【解析】【分析】令向量,b c 与向量a 都垂直，且b c ≠即可得解.【详解】令(0,1),(0,1)b c ==- ，显然0a b a c ⋅==⋅，而b c ≠ ，因此(0,1),(0,1)b c ==- 能说明“若a b a c ⋅=⋅ ，则b c = ”是假命题，所以向量,b c的坐标依次为(0,1),(0,1)-.故答案为：(0,1),(0,1)-15.已知函数()2cosπ1xf x x =+，给出下列四个结论：①函数()f x 是奇函数；②函数()f x 有无数个零点；③函数()f x 的最大值为1；④函数()f x 没有最小值.其中，所有正确结论的序号为__________.【答案】②③【解析】【分析】根据偶函数的定义判断①，令()0f x =求出函数的零点，即可判断②，求出函数的最大值即可判断③，根据函数值的特征判断④.【详解】函数()2cosπ1xf x x =+的定义域为R ，又22cos(π)cos π()()()11x x f x f x x x --===-++，所以()2cosπ1xf x x =+为偶函数，故①错误；令2cos ππ1()0cos π0ππ(Z)(Z)122x f x x x k k x k k x ==⇒=⇒=+∈⇒=+∈+，所以函数()f x 有无数个零点，故②正确；因为cos π1x ≤，当ππ(Z)x k k =∈，即(Z)x k k =∈时取等号，又因为211x +≥，当且仅当0x =时取等号，所以有21011x <≤+，当且仅当0x =时取等号，所以有2cos π11x x ≤+，当且仅当0x =时取等号，因此有()2cos π11xf x x =≤+，即()()max 01f x f ==，故③正确；因为()2cosπ1xf x x =+为偶函数，函数图象关于y 轴对称，只需研究函数在()0,∞+上的情况即可，当x →+∞时2101x →+，又1cosπ1x -≤≤，所以当x →+∞时()0f x →，又()()max 01f x f ==，当102x <<时cos π0x >，210x +>，所以()0f x >，当1322x <<时1cos π0x -≤<，210x +>，所以()0f x <，当1x >时212x +>，0cos π1x ≤≤，所以()12f x <，又()112f =-，102f ⎛⎫= ⎪⎝⎭，302f ⎛⎫= ⎪⎝⎭，且()f x 为连续函数，所以()f x 存在最小值，事实上()f x 的图象如下所示：由图可知()f x 存在最小值，故④错误.故答案为：②③三､解答题（本大题共6小题，共85分）16.在平面直角坐标系xOy 中，角θ以Ox 为始边，终边经过点()1,2--.（1）求tan θ，tan2θ的值；（2）求πsin ,cos ,cos 4θθθ⎛⎫+⎪⎝⎭的值.【答案】（1）tan 2θ=，4tan 23θ=-（2）sin 5θ-=，cos 5θ=，π10cos 410θ⎛⎫+=⎪⎝⎭【解析】【分析】（1）由三角函数的定义求出tan θ，再由二倍角正切公式求出tan 2θ；（2）由三角函数的定义求出sin θ，cos θ，再由两角和的余弦公式计算可得.【小问1详解】因为角θ以Ox 为始边，终边经过点()1,2--，所以2tan 21θ-==-，则222tan 224tan 21tan 123θθθ⨯===---.【小问2详解】因为角θ以Ox 为始边，终边经过点()1,2--，所以sin 5θ-==，cos 5θ==，所以πππcos cos cos sin sin 444θθθ⎛⎫+=- ⎪⎝⎭2520555210221⎛⎫- =⨯-⨯=⎪ ⎪⎝⎭.17.已知平面向量,,2,3,a b a b a == 与b的夹角为60 ，（1）求22,,a b a b ⋅；（2）求(2)(3)a b a b -⋅+的值：（3）当x 为何值时，xa b -与3a b +rr 垂直.【答案】（1）4，9，3；（2）4-；（3）3013x =.【解析】【分析】（1）利用数量积的定义计算即得.（2）利用数量积的运算律计算即得.（3）利用垂直关系的向量表示，数量积的运算律求解即得.【小问1详解】向量,,2,3,a b a b a == 与b 的夹角为60 ，所以2222|4,|9,3||||c |os 0|6a a b b a b a b ===⋅=== .【小问2详解】依题意，2222(2)(3)2352233534a b a b a b a b -⋅+=-+⋅=⨯-⨯+⨯=- .【小问3详解】由()(3)0xa b a b -⋅+= ，得223(31)4273(31)13300xa b x a b x x x -+-⋅=-+-=-= ，解得3013x =，所以当3013x =时，xa b - 与3a b +r r 垂直.18.已知函数()sin2cos2f x x x =+.（1）求(0)f ；（2）求函数()f x 的最小正周期及对称轴方程；（3）求函数()f x 的单调递增区间.【答案】（1）1；（2）π，ππ,Z 82k x k =+∈；（3）()3πππ,πZ 88k k k ⎡⎤-++∈⎢⎥⎣⎦.【解析】【分析】（1）代入计算求出函数值.（2）（3）利用辅助角公式化简函数()f x ，再结合正弦函数的图象与性质求解即得.【小问1详解】函数()sin2cos2f x x x =+，所以(0)sin0cos01f =+=.【小问2详解】函数π())4f x x =+，所以函数()f x 的最小正周期2ππ2T ==；由ππ2π,Z 42x k k +=+∈，解得ππ,Z 82k x k =+∈，所以函数()f x 图象的对称轴方程为ππ,Z 82k x k =+∈.【小问3详解】由πππ2π22π,Z 242k x k k -+≤+≤+∈，得3ππππ,Z 88k x k k -+≤≤+∈，所以函数()f x 的单调递增区间是()3πππ,πZ 88k k k ⎡⎤-++∈⎢⎥⎣⎦.19.在△ABC 中，7a =，8b =，再从条件①、条件②这两个条件中选择一个作为已知．（1）求A ∠；（2）求ABC 的面积．条件①：3c =；条件②：1cos 7B =-．注：如果选择条件①和条件②分别解答，按第一个解答计分．【答案】（1）选①②答案相同，3A π∠=；（2）选①②答案相同，ABC 的面积为【解析】【分析】（1）选①，用余弦定理得到cos A ，从而得到答案；选②：先用余弦定理求出3c =，再用余弦定理求出cos A ，得到答案；（2）选①，先求出sin 2A =，使用面积公式即可；选②：先用sin sin()C A B =+求出sin C ，再使用面积公式即可.【小问1详解】选条件①：3c =．在△ABC 中，因为7a =，8b =，3c =，由余弦定理，得222cos 2b c a A bc+-=64949283+-=⨯⨯12=．因为()0,πA ∈，所以π3A ∠=；选条件②：1cos 7B =-由余弦定理得：222249641cos 2147a cbc B ac c +-+-===-，解得：3c =或5-（舍去）由余弦定理，得222cos 2b c a A bc+-=64949283+-=⨯⨯12=．因为()0,πA ∈，所以π3A ∠=；【小问2详解】选条件①：3c =由（1）可得sin 2A =．所以ABC 的面积11sin 8322S bc A ==⨯⨯=选条件②：1cos 7B =-．由（1）可得1cos 2A =．因为sin sin[()]C A B =π-+sin()A B =+sin cos cos sin A B A B=+11()72=-+⨯3314=，所以ABC 的面积11sin 7822S ab C ==⨯⨯=．．20.已知函数()2π2cos cos 213f x x x ⎛⎫=+-- ⎪⎝⎭.（1）求π6f ⎛⎫ ⎪⎝⎭的值；（2）求函数()f x 的在[]0,π上单调递减区间；（3）若函数()f x 在区间[]0,m 上有且只有两个零点，求m 的取值范围.【答案】（1）32（2）π7π,1212⎡⎤⎢⎥⎣⎦（3）3564π,π⎡⎫⎪⎢⎣⎭【解析】【分析】（1）利用二倍角公式及和差角公式化简函数解析式，再代入计算可得；（2）由x 的取值范围求出π23x +的范围，再根据正弦函数的性质得到ππ3π2232x ≤+≤，解得即可；（3）由x 的取值范围求出π23x +的范围，再根据正弦函数的性质得到不等式组，解得即可.【小问1详解】因为()2π2cos cos 213f x x x ⎛⎫=+-- ⎪⎝⎭ππcos2cos2cossin 2sin 33x x x =++3cos2sin 222x x =+1cos2sin 222x x ⎫=+⎪⎪⎭π23x ⎛⎫=+ ⎪⎝⎭，所以πππ2π3266332f ⎛⎫⎛⎫=⨯+== ⎪ ⎪⎝⎭⎝⎭.【小问2详解】当[]0,πx ∈时ππ7π2,333x ⎡⎤+∈⎢⎥⎣⎦，令ππ3π2232x ≤+≤，解得π7π1212x ≤≤，所以函数()f x 的在[]0,π上的单调递减区间为π7π,1212⎡⎤⎢⎥⎣⎦.【小问3详解】当[]0,x m ∈时，πππ2,2333x m ⎡⎤+∈+⎢⎥⎣⎦，又函数()f x 在区间[]0,m 上有且只有两个零点，所以π2π23π3m ≤<+，解得5π4π63m ≤<，即m 的取值范围为3564π,π⎡⎫⎪⎢⎣⎭.21.某地进行老旧小区改造，有半径为60米，圆心角为π3的一块扇形空置地（如图），现欲从中规划出一块三角形绿地PQR ，其中P 在 BC 上，PQ AB ⊥，垂足为Q ，PR AC ⊥，垂足为R ，设π0,3PAB α⎛⎫∠=∈ ⎪⎝⎭；（1）求PQ ，PR （用α表示）；（2）当P 在BC 上运动时，这块三角形绿地的最大面积，以及取到最大面积时α的值.【答案】（1）60sin PQ α=，π60sin 3PR α⎛⎫=- ⎪⎝⎭（2）三角形绿地的最大面积是平方米，此时π6α=【解析】【分析】（1）利用锐角三角函数表示出PQ 、PR ；（2）依题意可得2π3QPR ∠=，则1sin 2PQR S PQ PR QPR =⋅⋅⋅∠ ，利用三角恒等变换公式化简，再结合正弦函数的性质求出最大值.【小问1详解】在Rt PAQ 中，π0,3PAB ∠α⎛⎫=∈ ⎪⎝⎭，60AP =，∴sin 60sin PQ AP αα==（米），又π3BAC ∠=，所以π3PAR α∠=-，在Rt PAR 中，可得πsin 60sin 3PR PAR AP α⎛⎫==-⎪⎝⎭∠（米）.【小问2详解】由题可知2π3QPR ∠=，∴PQR 的面积1sin 2PQR S PQ PR QPR =⋅⋅⋅∠1π2π60sin 60sin sin 233αα⎛⎫=⨯⨯-⨯ ⎪⎝⎭πsin3αα⎛⎫=- ⎪⎝⎭ππsin cos cos sin 33ααα⎛⎫=- ⎪⎝⎭112cos 222αα⎫=+-⎪⎪⎭π1sin 262α⎡⎤⎛⎫=+- ⎪⎢⎥⎝⎭⎣⎦，又π0,3α⎛⎫∈ ⎪⎝⎭，526πππ,66α⎛⎫+∈ ⎪⎝⎭，∴当ππ262α+=，即π6α=时，PQR 的面积有最大值即三角形绿地的最大面积是π6α=.。

上海市黄浦区2023-2024学年高一下学期期中统考数学试题

黄浦区2023学年第二学期高一年级数学期中统考2024.05一、填空题(本大题共有12小题,满分42分)1.当手表比标准时间慢10分钟时，只需将分针旋转弧度就可以调节准确.2.方程12cosx =-在[]0x ,∈π内的解为x =.3.在ABC ∆中,2,3a B π==,其面积为,则边c =.cos α+α化为()(0)Asin A α+ϕ>的形式.5.在ABC ∆中,已知::2:3:4sinA sinB sinC =,则该三角形最小角的余弦值为.6.若3tan α=,则()()222cos cos sin sin π⎛⎫-α-π-α ⎪⎝⎭=π⎛⎫π+α-+α ⎪⎝⎭.7.若α为第一象限角,则()21tan log cos +αα=.8.已知等腰三角形的底角的余弦值为45,则该三角形顶角的正弦值为.9.若,αβ为锐角,()1114sin cos α=α+β=-,则sin β=.10.在平面直角坐标系中,角α的顶点与坐标原点重合,始边与x 轴的正半轴重合,其终边过点()34,-,角β的终边与角α的终边关于直线y x =对称,则tan β=.11.若41225sin πα⎛⎫-= ⎪⎝⎭,则23cos π⎛⎫α-= ⎪⎝⎭.12.在ABC ∆中,若2,3AC B π==,且928sinAsinC =,则ABC ∆的周长为.二、选择题（本大题共有4题,满分14分,第13,14题每题3分,第15,16题每题4分）13.若02,π⎛⎫α∈- ⎪⎝⎭,则点()cos ,tan αα在第（）象限.A.一 B.二C.三D.四14.下列命题中，真命题的个数为（）.(1)若角α的终边经过点()()20P a,a a ≠,则cos α=；(2)同时满足1,2sin cos α=α=的角6πα=(3)不存在角α和β使得等式()cos cos cos α-β=α-β成立;(4)任意的角α和β都满足等式()()2cos cos sin sin α+β-α-β=-αβA.1个B.2个C.3个D.4个15.在ABC ∆中,“cos 2sinA B π⎛⎫>- ⎪⎝⎭”是“A B >”的（）.A.充分非必要条件B.必要非充分条件C.充要条件D.既非充分也非必要条件16.李善兰是中国近代著名数学家,辅助角公式是他提出来的一种三角公式,其主要作用是将多个三角函数化成单个三角函数。

高一下语文期中测试题

高一下语文期中测试题一、单项选择题1.对下面语段中的四句话是否有语病的分析，不正确．．．的一项是（）在今天，①拥有一部电脑就如同好比拥有整个世界。

于是，有的人开始厌倦纸质图书，更愿意在网上快速阅读。

但是网上阅读好像乘火车出差，直来直去，毫无悬念；而阅读纸质图书则好像坐牛车去姥姥家，慢悠悠地观景赏花，心含喜悦。

②对纸质图书的命运，即使怎样担忧，我都始终抱有希望，因为只要你想借助阅读享受快乐，这种传统阅读方式就永远不会消亡。

而且，③随着整个社会浮躁心态的改变，使传统阅读方式将会受到大众的钟爱。

目前，④古典著作图书受到读者追逐，就是最好的印证。

A.第①句没有语病。

B.第②句中关联词使用错误。

C.第③句成分残缺。

D.第④句搭配不当。

2.下列各句中加点的词语与括号内的词语替换，不正确．．．的一项是（）A.希望大家不要再为难他了，不要再对他为什么受伤这件事刨根．．问底．．了。

（打破砂锅问到底）B.现实生活中，常常有些干部便是“能交差就行”，对工作中出现的问题不求甚解，将自己的工作看成是一种负担，得过且过．．．．，说到底这都是工作态度问题。

（当一天和尚撞一天钟）C.拖泥带水．．．．、支离破碎、死气沉沉的语文课堂依然存在，因此，语文教育呼唤一种生命化、创新化、最优化的课堂教学形式。

（拔出萝卜带出泥）D.学习是一个滴水石．．．穿．、循序渐进的过程，这不像其他事情可以来个突击行动，就可以有质的提升。

（冰冻三尺非一日之寒）3.下列词语或句子中没有．．错别字的一项是（）A.倜怅锲而不舍蜿蜒无精打彩B.风声谈笑风声质疑不容置疑C.改革开放三十年，湖州地区发生了天翻地复的变化。

D这种东西没有流行到市面上来，很快就销声匿迹了。

4.对下列广告语的赏析，不正确．．．的一项是（）A.飞利浦电动剃须刀：显然刚被飞利浦吻了一下。

——用了拟人的手法，将剃须刀人格化，赋予剃须刀人情味。

一个”吻”字”吻”出了须刀的温柔体贴，”吻”出了顾客対剃须刀的品质的信赖。

高一必修期中试题及答案

高一必修期中试题及答案一、选择题（每题2分，共20分）1. 下列哪项不是细胞的基本结构？A. 细胞膜B. 细胞核C. 细胞壁D. 细胞质2. 光合作用的主要场所是：A. 线粒体B. 叶绿体C. 细胞核D. 细胞质3. 以下哪种元素不属于人体必需微量元素？A. 铁B. 锌C. 钙D. 碘4. 人体最大的器官是：A. 肝脏B. 皮肤C. 心脏D. 肺5. 以下哪种物质不属于蛋白质？A. 胰岛素B. 血红蛋白C. 淀粉D. 胶原蛋白6. 人体中含量最多的无机盐是：A. 钙B. 钠C. 钾D. 镁7. 以下哪种维生素是脂溶性的？A. 维生素CB. 维生素BC. 维生素AD. 维生素D8. 人体中主要的遗传物质是：A. DNAB. RNAC. 蛋白质D. 脂肪9. 以下哪种激素是由胰腺分泌的？A. 胰岛素B. 甲状腺素C. 肾上腺素D. 促性腺激素10. 人体中负责免疫反应的细胞是：A. 红细胞B. 白细胞C. 血小板D. 淋巴细胞二、填空题（每题2分，共20分）1. 细胞的基本结构包括____、____和____。

2. 人体必需的微量元素包括铁、锌、____和____。

3. 人体中含量最多的无机盐是____，它在维持细胞内外渗透压平衡中起着重要作用。

4. 人体最大的器官是____，它覆盖在人体的表面，起到保护和调节体温的作用。

5. 蛋白质是生命活动的主要承担者，包括胰岛素、血红蛋白和____等。

6. 人体中主要的遗传物质是____，它携带着遗传信息，控制着生物体的性状。

7. 脂溶性维生素包括维生素A、D、E和____。

8. 人体中负责免疫反应的细胞是____，它们能够识别和清除体内的病原体。

三、简答题（每题10分，共30分）1. 描述光合作用的基本原理及其在生态系统中的作用。

2. 解释人体必需微量元素的功能及其缺乏时可能出现的症状。

3. 阐述胰岛素的主要功能及其在人体中的重要性。

四、计算题（每题10分，共30分）1. 假设一个细胞的体积是1立方微米，细胞膜的厚度是10纳米，请计算细胞膜的表面积。

2022-2023学年黑龙江省哈尔滨市高一下学期期中数学试题-含答案

2022-2023学年黑龙江省哈尔滨市高一下学期期中数学试题一、单选题1．在空间中，下列命题不正确的是（）A ．若两个平面有一个公共点，则它们有无数个公共点．且在一条直线上B ．若已知四个点不共面，则其中任意三点不共线C ．梯形可确定一个平面D ．任意三点能确定一个平面【答案】D【分析】利用平面的相关公理和推论逐项进行判断即可求解.【详解】对于选项A ，若两个平面有一个公共点，则它们有经过该公共点的一条直线，即两平面有无数个公共点，故选项A 正确；对于选项B ，若已知四个点不共面，则其中任意三点不共线，否则，若存在三点共线，则问题转化为一条直线与直线外一点，则四点共面，故选项B 正确；对于选项C ，因为两条平行直线确定一个平面，所以梯形可确定一个平面，故选项C 正确；对于选项D ，共线的三点不能确定一个平面，故选项D 错误；故选：D.2．已知复数满足，则的虚部为（）z (2i)24i z +=-z A ．B ．C ．D ．22i -2i 2-【答案】C【分析】计算，确定虚部得到答案.2i z =-【详解】，故虚部为.()()()()24i 2i 24i 10i2i 2i 2i 2i 5z ----====-++-2-故选：C3．在中，角A ，B ，C 所对的边分别为a ，b ，c ．已知a，b，则角A 为ABC π3B =（）A ．B ．C ．D ．或3π4π3π4π43π4【答案】C【分析】由正弦定理即可求解.【详解】由正弦定理，得sin sin a b A B =sin sin a B A b ===又，所以，所以为锐角，所以．a b <A B <A π4A =故选：C ．4．向量，，在边长为1的正方形网格中的位置如图所示，若为与同方向的单位向量，a b c ec 则（）()a b e+⋅ A ．1.5B ．2C ．-4.5D ．-3【答案】D【分析】首先建系，确定向量的坐标，根据向量数量积的坐标表示求解.【详解】如图，建立平面直角坐标系，由图可知，，，()1,1a =-()2,1b =--()1,0e =则，所以.()3,0a b +=- ()3a b e +⋅=- 故选：D5．在中，角所对的边分别为，已知，则下列结论正确的是（）ABC ,,A B C ,,a b c ::3:3:4a b c =A ．B ．sin :sin :sin 4:3:3A B C =0CA CB ⋅< C ．若，则的面积是D．若，则8c =ABC 7b c +=ABC 【答案】C【分析】根据题意，由正弦定理可判定A 错误；由余弦定理求得，结合向量的数量积的定cos 0C >义，可判定B 错误；由三角形的面积公式，可判定C 正确；由正弦定理求得外接圆的半径，可判定D 错误.【详解】由题意，在中，满足，ABC ::3:3:4a b c =对于A 中，由正弦定理，所以，sin sin sin a b cA B C ==sin :sin :sin 3:3:4A B C =所以A 不正确；对于B 中，设三边的长分别为，ABC 3,3,4a m b m c m ===由余弦定理得，222(3)(3)(4)1cos 02339m m m C m m +-==>⨯⨯所以，所以B 错误；cos 0CA CB ab C ⋅=> 对于C 中，若，可得，可得，则8c =6a b ==1cos 9C =sinC =所以的面积为C 正确；ABC 11sin 6622S ab C ==⨯⨯=对于D 中，设三边的长分别为，ABC 3,3,4a m b m c m ===由，即，可得，所以，7b c +=347m m +=1m =4c=设外接圆的半径为，则，ABC R 2sinc R C ===所以D 错误.R 故选：C.6．已知非零向量，满足，且向量在向量方向的投影向量是，则向量a b ()()a b a b +⊥- b a 12a -与的夹角是（）a bA ．B ．C ．D ．6π3π23π56π【答案】C【分析】运用数量积和投影向量的定义求解.【详解】由题意，，则，即，()()a b a b +⋅-=22a b = a b=设与的夹角为，则在方向的投影，a b θb a 1cos 2a b aa θ⋅=-，则；[]1cos ,0,π2θθ∴=-∈2π3θ=故选：C.7．=（）23sin 502cos 20--A ．BCD ．212【答案】D【分析】根据降幂公式及变名的诱导公式进行化简.【详解】.()()223sin 5023sin 503sin 503sin 5021cos 402cos 203cos 403sin 5022----====+----故选：D.8．已知函数，若存在实数，满足，且()cos f x x=12,,,n x x x ⋅⋅⋅1204πn x x x ≤<<⋅⋅⋅<≤，，，，则n 的最小值为()()()()()()122318n n f x f x f x f x f x f x --+-+⋅⋅⋅+-=2n ≥*N n ∈（）A ．4B ．5C ．6D ．7【答案】B 【分析】由的性质，根据的特()cos f x x=()()()()()()122318n n f x f x f x f x f x f x --+-++-= 点以及题意求解.【详解】由题意，n 要尽可能地小，则等式中，每一项要尽可能地大，()()()()()()122318n n f x f x f x f x f x f x --+-++-= ，显然时，n 最小，()()()1cos ,2n n f x x f x f x -=∴-≤ ()()12n n f x f x --= ，即，()()()()()()122312n n f x f x f x f x f x f x --=-==-= 814,52n n -==∴=此时不妨取，满足题意；123450,π,2π,3π,4πx x x x x =====故选：B.二、多选题9．如图，正方形ABCD 的边长为3，点E 是线段AB 的靠近点B 的一个三等分点，若边DC 上存在点F ，使得成立，则下列选项中符合题意的的值有（）EA EF λ⋅=λA ．B ．1C ．5D ．02-【答案】ABD【分析】以为基底，设，用基底表示出，根据x 的范围可求得,BA BC (01)CF xCD x =≤≤ EA EF ⋅ 的范围即可.λ【详解】记，设，,BA a BC b ==(01)CF xCD x =≤≤ 由题知，，3,0a b a b ==⋅=又因为，211,333EA a EF EB BC CF a b xa x a b⎛⎫==++=-++=-+ ⎪⎝⎭ 所以，22121623333EA EF a x a b x a x ⎡⎤⎛⎫⎛⎫⋅=⋅-+=-=- ⎪ ⎪⎢⎥⎝⎭⎝⎭⎣⎦ 因为，所以，即.01x ≤≤24EA EF -≤⋅≤24λ-≤≤故选：ABD.10．已知是函数的一个周期，则的取值可能为（）π()2sin cos 066y x x ππωωω⎛⎫⎛⎫=++≠ ⎪ ⎪⎝⎭⎝⎭ωA ．﹣2B ．1C ．D ．312【答案】ABD【分析】根据三角恒等变换公式进行化简，根据周期函数定义求出的表达式即可求解．ω【详解】依题意得，2sin cos sin 2663y x x x πππωωω⎛⎫⎛⎫⎛⎫=++=+ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭由周期函数定义得：，即： ()()f x f x π+=()sin 2sin 233x x ππωπω⎡⎤⎛⎫++=+ ⎪⎢⎥⎣⎦⎝⎭即：sin 22sin 233x x ππωωπω⎛⎫⎛⎫++=+ ⎪ ⎪⎝⎭⎝⎭222233x x k k Zππωωπωπ∴++=++∈，解得：k k Zω=∈，又0ω≠ 或1ω∴=32ω=-，故选：ABD ．11．在中，角A ，B ，C 所对的边分别为a ，b ，c ．若，内角A 的平分线交BC 于点ABC cos b c A =D ，AD =1，，以下结论正确的是（）1cos 8A =A ．B ．C ．D ．32AC =6AB =18CD BD =ABD △【答案】BCD【分析】首先根据题意结合余弦定理可得，并根据二倍角公式得到，依次计算π2C =3cos 4CAD ∠=的值，根据面积公式，分析判断选项C 和D.,AC AB 【详解】在中，ABC ∵，则，整理得，所以，cos b c A =2222b c a b c bc +-=⨯222b ac +=π2C =由二倍角公式得，解得，21cos 2cos 18BAC CAD ∠∠=-=3cos 4CAD ∠=在中，则，故选项A 错误；Rt ACD △3cos 4AC AD CAD ∠==在中，则，故选项B 正确；Rt ABC △3461cos 8ACAB BAC ===∠由题意可知：，即，CAD BAD ∠=∠sin sin CAD BAD ∠=∠由，解得，故选项C 正确；11sin 2211sin 22ACDADB CD AC AC AD CADS S BD AC ABAD BAD∠∠⋅⋅⋅==⋅⋅⋅ 18CD AC BD AB ==在中，ABD △∵，则3cos 4BAD ∠=sin BAD ∠==∴D 正确.11sin 1622ABD S AD AB BAD ∠=⋅⋅=⨯⨯= 故选：BCD.12．如图甲所示，古代中国的太极八卦图是以同圆内的圆心为界，画出相等的两个阴阳鱼，阳鱼的头部有眼，阴鱼的头部有个阳殿，表示万物都在相互转化，互相涉透，阴中有阳，阳中有阴，阴阳相合，相生相克，蕴含现代哲学中的矛盾对立统一规律，其平面图形记为图乙中的正八边形，其中，则（）ABCDEFGH 2OA =A B ．0OE OG ++= OA OD ⋅=-C ．D ．4AH EH +=4+=+AH GH 【答案】ABC【分析】分别以所在的直线为轴和轴，建立的平面直角坐标系，作，结合向,HD BF x y AM HD ⊥量的坐标运算，逐项判定，即可求解.【详解】由题意，分别以所在的直线为轴和轴，建立如图所示的平面直角坐标系，,HD BF x y 因为正八边形，所以ABCDEFGH AOH HOG AOB EOF FOG∠∠∠∠∠====，DOE COB COD =∠=∠=∠360458==作，则，AM HD ⊥OM AM =因为，所以，2OA =OM AM ==(A同理可得其余各点坐标，，，，，，()0,2B -E (G ()2,0D ()2,0H -对于A ，故A 正确；(0(0OE OG ++=-=对于B 中，，故B 正确；(2(0OA OD ⋅=⨯+⨯=-对于C 中，，，，(2AH =- (2EH =-(4,0)AH EH +=-所以，故C 正确；4AH +=对于D 中，，，，(2AH =- (2GH =-(4AH GH +=-+，故D 不正确.4AH +=- 故选：ABC.三、填空题13．若复数为纯虚数，则=___________.i1i a +-2ia +【分析】由复数除法法则化简后求得，再由复数模的定义求解．a 【详解】为纯虚数，则且，i (i)(1i)1(1)i 11i 1i (1i)(1i)222a a a a a a +++-++-+===+--+102a -=102a +≠∴，1a =，2+14．圆锥侧面展开图扇形的圆心角为60°，底面圆的半径为6，则圆锥的侧面积为______．【答案】216π【分析】运用扇形的弧长公式以及圆锥的侧面积公式计算即可求解.【详解】设圆锥的底面周长为，母线长为，则，c l 2π612πc =⨯=因为圆锥侧面展开图扇形的圆心角为，60︒所以，解得，π12π3c l l ==36l =则圆锥的侧面积为，113612π216π22lc =⨯⨯=故答案为：.216π四、双空题15．已知，是单位向量，且，设向量，当时，______；1e 2e 120e e ⋅=12a e e λμ=+ 1λμ==1,a e = 当时，的最小值为______．4λμ+=1a e -【答案】/4π45︒【分析】求出，根据夹角公式可得，将表示为关于的二次函数，求出最小值即可.a1,a e 1a e - λ【详解】当时，，1λμ==12a e e =+222112222a ee e e =+⋅+= ，()1211111cos ,e e e a e a e a e a e +⋅⋅====⨯⨯因为，所以；[]1,0,πa e ∈1π,4a e =当时，，4λμ+=()()()11212114a e e e e e λμλλ-=-+=-+-则，()()222215914222a eλλλ⎛⎫-=-+-=-+⎪⎝⎭ 当时，的最小值为，52λ=1a e - 故答案为：π4五、填空题16．在中，若AC=2，，，点D 为AB 边上的动点，有如下结论：ABC =60B ∠︒45A ∠=︒①不存在点D 使得为等边三角形 ②存在点D 使得BCD △1cos 3CDA ∠=③存在点D使得④存在点D 使得CD =1:BD DC =上述结论中正确的有______【答案】②③【分析】运用三角形的正弦定理和三角形的内角和定理、边角关系，结合正弦函数的性质，对选项一一判断，即可得到结论．【详解】若△BCD 为边长为x 的等边三角形，可得＝解得x 2，sin 45x ︒2sin 60︒满足AC ＞CD ，所以存在点D 使得为等边三角形，则①不正确；BCD △因为cos ∠CDA ＝＜＝cos60°，且0°＜∠CDA ＜180°，1312可得∠CDA ＞B ，所以AB 上存在点D ，则②正确；由＝，BD DC =：：sin sin 60BCD ︒∠BDDC可得，即有∠BCD ＝45°＜∠BCA ＝75°，则③正确；sin BCD ∠=若CD ＝1，在中可得＝，ACD sin 45CD ︒sin ACADC ∠可得sin ∠ADC1，∠ADC 不存在，则④不正确．故答案为：②③．六、解答题17．某广场内设置了一些石凳供大家休息，这些石凳是由正方体截去八个一样的四面体得到的，如图所示，若被截正方体的棱长是60cm ．(1)求石凳的体积；(2)为了美观工人准备将石凳的表面进行粉刷，已知每平方米造价50元，请问粉刷一个石凳需要多少钱？【答案】(1)3180000cm (2)元(54+【分析】（1）计算出正方体的体积减去8个小正三棱锥的体积，得到答案；（2）计算出石凳的表面积，从而求出粉刷一个石凳的钱数.【详解】（1）正方体的体积为，3360216000cm =石凳的体积为正方体的体积减去8个正三棱锥的体积，其中一个小正三棱锥的三条侧棱边长为，30cm 故一个小正三棱锥的体积为，321130304c 52m 003⨯⨯⨯=故石凳的体积为；321600045008c 180m 000-⨯=（2）石凳的表面由6个正方形和8个正三角形组成，其中正方形和正三角形的边长均为，则石凳的表面积为，(()22166081080cm 02⨯+⨯︒⨯=元.(5054=+18．角A ，B ，C 对边分别为,向量，，且ABC ,,a b c ()cos cos ,m a B b A abc =+()222,1n a b c =+--．m n ⊥ (1)求角C ；(2)若的周长为外接圆半径为2，求的面积．ABC ABC ABC 【答案】(1)3C π=(2)【分析】（1）运用数量积以及三角函数和差公式，正弦定理，余弦定理求解；（2）运用正弦定理余弦定理求出，再利用面积公式计算.ab 【详解】（1）由得：，由余弦定理知：m n ⊥ ()()222cos cos 0a B b A a b c abc ++--= ，2222cos a b c ab C +-= ，，()2cos cos cos 0ab C a B b A abc ∴+-=()0,0,2cos cos cos 0a b C a B b A c ≠≠∴+-= 由正弦定理得：，即()2cos sin cos sin cos sin 0C A B B A C +-= ，()2cos sin sin 0,2cos sin sin 0C A B C C C C +-=-= ，，；()0,πC ∈ sin 0C ∴≠∴π3C =（2）由正弦定理得，即，2,22sin c R c C =∴=⨯=a b +=由余弦定理得，()2222222cos 312c a b ab C a b ab a b ab =+-=+-=+-=，12ab ∴=1sin 2ABC S ab C ==即.ABC S = 19．已知点，，，()3,0A ()0,3B ()cos ,sin C x x Rx ∈(1)若，且，求x 的值AC BC = []0,2πx ∈(2)设函数，求的单调递增区间．()f x AC BC=⋅()f x(3)对于（2）中的函数，，求()f x ()1f α=π,02α⎛⎫∈- ⎪⎝⎭sin α【答案】(1)或π4x =5π4(2)增区间为()π5π2π,2πZ 44k k k ⎡⎤++∈⎢⎥⎣⎦(3)sin α=【分析】（1）求得，，根据模长坐标公式并化简得到(cos 3,sin )AC x x =- (cos ,sin 3)BC x x =-，结合即可求解；tan 1x =[]0,2πx ∈（2）化简得到，令，即可得到增区间；()π14f x x ⎛⎫=-++ ⎪⎝⎭ππ3π2π2π,Z242k x k k +≤+≤+∈（3）代入可得，由得到，从而得到π1sin 43α⎛⎫+= ⎪⎝⎭π,02α⎛⎫∈- ⎪⎝⎭πππ,444α⎛⎫+∈- ⎪⎝⎭，利用差角正弦公式即可求解.πcos 4α⎛⎫+= ⎪⎝⎭ππsin sin 44αα⎛⎫=+- ⎪⎝⎭【详解】（1），，(cos 3,sin )AC x x =- (cos ,sin 3)BC x x =-因为，所以，AC BC=2222(cos 3)sin cos (sin 3)x x x x -+=+-即，即，2222cos 6cos 9sin cos sin 6sin 9x x x x x x -++=+-+cos sin x x =所以，又，所以或.tan 1x =[]0,2πx ∈π4x =5π4（2）22()(cos 3)cos sin (sin 3)cos 3cos sin 3sin fx AC BC x x x x x x x x=⋅=-+-=-+- ，π3(sin cos )114x x x ⎛⎫=-++=-++ ⎪⎝⎭令，ππ3π2π2π,Z 242k x k k +≤+≤+∈解得，π5π2π2π,Z 44k x k k +≤≤+∈所以的单调递增区间为.()f x ()π5π2π,2πZ44k k k ⎡⎤++∈⎢⎥⎣⎦（3），π()114f αα⎛⎫=-++= ⎪⎝⎭π1sin 43α⎛⎫+= ⎪⎝⎭因为，所以，所以，π,02α⎛⎫∈- ⎪⎝⎭πππ,444α⎛⎫+∈- ⎪⎝⎭πcos 4α⎛⎫+== ⎪⎝⎭所以ππππππsin sin sin cos cos sin444444αααα⎛⎫⎛⎫⎛⎫=+-=+-+ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭13==20．已知函数的部分图像如图所示．，()()πsin 20,0,2f x A x A ϕωϕ⎛⎫=+>>< ⎪⎝⎭π4f ⎛⎫= ⎪⎝⎭，3π08f ⎛⎫= ⎪⎝⎭3π4f ⎛⎫= ⎪⎝⎭(1)求的解析式；()f x (2)将的图像先向右平移个单位，再将图像上所有点的横坐标变为原来的倍（纵坐标()y f x =7π2412不变），所得到的图像对应的函数为，若对于恒成立，求实数m 取()y g x =()2g x m -≤π0,4x ⎡⎤∈⎢⎥⎣⎦值范围．【答案】(1)．()π2sin 24f x x ⎛⎫=+ ⎪⎝⎭(2)0,2m ⎡∈⎣【分析】（1）根据图像求出函数的周期，进而求出ω，再由特殊点以及求出φ，然后由π||2ϕ<A ，从而得出答案；π()4f =（2）利用图像的平移伸缩变换求出，再根据三角函数的性质即可求解.()y g x =【详解】（1）由图像可得：，故，且，解得，3πππ2442T =-=2ππT ω==0ω>2ω=可得，()()sin 2f x A x ϕ=+∵的图像过点，则，()f x 3π,08⎛⎫⎪⎝⎭3π3πsin 2sin 084A A ϕϕ⎛⎫⎛⎫⨯+=+= ⎪ ⎪⎝⎭⎝⎭可得，且，则，3πsin 04ϕ⎛⎫+= ⎪⎝⎭ππ,22ϕ⎛⎫∈- ⎪⎝⎭3ππ5π,444ϕ⎛⎫+∈ ⎪⎝⎭∴，解得，3ππ4ϕ+=π4ϕ=可得，()sin π24f x A x ⎛⎫=+ ⎪⎝⎭又∵的图像过点，则，()f x π4⎛ ⎝ππ3πsin 2sin 444A A A ⎛⎫⨯+=== ⎪⎝⎭解得，2A =故.()π2sin 24f x x ⎛⎫=+ ⎪⎝⎭（2）将的图像先向右平移个单位，得到；()y f x =7π247π24ππ2sin 22sin 243y x x ⎡⎤⎛⎫⎛⎫=-+=- ⎪ ⎪⎢⎥⎝⎭⎝⎭⎣⎦再将图像上的所有点的横坐标变为原来的倍（纵坐标不变），得到，12π2sin 43y x ⎛⎫=- ⎪⎝⎭故，()π2sin 43g x x ⎛⎫=- ⎪⎝⎭∵，则，π0,4x ⎡⎤∈⎢⎥⎣⎦ππ2π4,333x ⎡⎤-∈-⎢⎥⎣⎦∴，可得，πsin 44x ⎡⎤⎛⎫-∈⎢⎥⎪⎝⎭⎣⎦()2g x ⎡⎤∈⎣⎦故在上的最大值为2，最小值为()y g x =π0,4x ⎡⎤∈⎢⎥⎣⎦因为对于恒成立，所以,可得恒成()2g x m -≤π0,4x ⎡⎤∈⎢⎥⎣⎦()22m g x m ≤≤+-()()22m g xg x -≤≤+立,,可得.()()max min 22m g x g x -≤≤+02m ≤≤0,2m ⎡∈⎣21．目前，中国已经建成全球最大的5G 网络，无论是大山深处还是广袤平原，处处都能见到5G 基站的身影.如图，某同学在一条水平公路上观测对面山顶上的一座5G 基站AB ，已知基站高，该同学眼高（眼睛到地面的距离），该同学在初始位置C 处（眼睛所在位置）测得50m AB = 1.5m 基站底部B 的仰角为37°，测得基站顶场A 的仰角为45°.(1)求出山高BE （结果保留一位小数）；(2)如图，当该同学面向基站AB 前行时（保持在同一铅垂面内），记该同学所在位置M 处（眼睛所在位置）到基站AB 所在直线的距离，且记在M 处观测基站底部B 的仰角为，观测基m MD x =α站顶端A 的仰角为.试问当x 多大时，观测基站的视角最大？βAMB ∠参考数据：，，，.sin 80.14︒≈sin 370.6︒≈sin 450.7︒≈sin1270.8︒≈【答案】(1)151.5m(2)x =【分析】（1）在中，利用正弦定理求出，再在中，求出即可；ABC BC Rt BCD BD （2）易得，分别在在和在中，求出，再根据π02AMB βα∠=<-<Rt BMD △Rt AMD △tan ,tan αβ两角和的正切公式结合基本不等式求出取得最大值时，的值，再根据正切函数的单调tan AMB ∠x 性即可得解.【详解】（1）由题意可知，，37,45,8,45BCD ACD ACB A ∠=︒∠=︒∠=︒=︒在中，，ABC sin sin AB BCACB A =∠所以，250BC =≈在中，，Rt BCD sin 2500.6150BD BC BCD =⋅∠≈⨯=所以出山高；150 1.5151.5m BE =+=（2）由题意知，且，,AMD BMD βα∠=∠=π02αβ<<<则，π02βα<-<在中，，Rt BMD △150tan BD MD x α==在中，，Rt AMD △200tan AD MD x β==则()200150tan tan tan tan 2001501tan tan 1x x AMB x x βαβαβα--∠=-==++⋅，250503000030000x x x x ==≤=++当且仅当，即30000x x =x =所以取得最大值时，tan AMB ∠x =又因为，所以此时最大，π02AMB <∠<AMB ∠所以当时，最大.x =AMB ∠22．在中，内角A ，B ，C 所对的边分别为a ，b ，c，请在；②ABC cos sin C c B =；③这三个条件中任选一个，完成下列问题．()()()c a c a b b a +-=-sin cos 2sin sin cos C CB A A =-(1)求角C 的大小；(2)若b =2，当取最大值时，求外接圆半径和内切圆半径的乘积的值；πsin cos 6B A ⎛⎫-+ ⎪⎝⎭ABC (3)若为锐角三角形，，求面积的取值范围．ABCa =ABC 【答案】(1)条件选择见解析，π3C=(2))21-(3)【分析】（1）利用正弦定理、余弦定理、三角恒等变换的知识化简已知条件，求得的大小.C （2）先求得，然后求得外接圆半径和内切圆半径，进而求得正确答案.,a c ABC（3）先求得的取值范围，然后根据三角形的面积公式求得面积的取值范围．b ABC 【详解】（1）若选，cos sin C c B =，cos sin sin B C C B =由于，0π,sin 0B B <<>sin C C =所以，则为锐角，且.tan 0C =>C π3C =若选②，()()()c a c a b b a +-=-整理得，则，222a b c ab +-=2221cos 022a b c C ab +-==>则为锐角，且.C π3C =若选③，sin cos 2sin sin cos C C B A A =-则，sin cos 2sin cos sin cos C A B C A C =-，()sin cos sin cos sin sin 2sin cos A C C A A C B B C+=+==由于，所以，0π,sin 0B B <<>1cos 02C =>则为锐角，且.C π3C =（2）由（1）得，π3C =()ππsin cos sin cos 66B A A C A ⎛⎫⎛⎫-+=+-+ ⎪ ⎪⎝⎭⎝⎭ππsin cos 36A A ⎛⎫⎛⎫=+-+ ⎪ ⎪⎝⎭⎝⎭，11sin sin sin 22A A A A A =+=由于，所以当时取得最大值为，2π03A <<π2A =πsin cos 6B A ⎛⎫-+ ⎪⎝⎭1此时，，则π6B =2b =4,a c ==所以外接圆半径为，ABC 122a=设内切圆半径为，ABCr 则，解得，(1122422r⨯⨯=⨯++⨯1r =所以外接圆半径和内切圆半径的乘积为.ABC )21（3）由（1）得，π3C =由正弦定理得，sin 3sin tan a B b A A ===+由于三角形是锐角三角形，所以，所以，ABC π02ππ32A A ⎧<<⎪⎪⎨⎪+>⎪⎩ππ62A<<所以，所以tan >A 130tan tan A A <<<<3tan A <<所以.113sin 222ABC S ab C b b ==⨯=∈。

广东省深圳市高级中学2023-2024学年高一下学期期中英语试题

深圳高级中学（集团）2023-2024学年第二学期期中测试高一英语2024.4试卷共11页，卷面满分150分。

考试用时120分钟。

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第一部分阅读理解（共15小题；每小题2.5分，满分37.5分）阅读下列短文，从每题所给的A、B、C、D 四个选项中选出最佳选项。

ABoat Rentals in VancouverGranville Island Boat Rentals, located in the heart of down town Vancouver, features the safest and most advanced lineup of boat rentals in Vancouver. It has served over half a million customers since it began renting boats in 1982.While exploring the sites Vancouver has offered, you can't miss observing wildlife like seals （海豹）, bald（秃的）eagles, sea birds along the way. Besides these, what sets us apart is the extensive selection of boat rentals weprovide, varying from different models, capacities to reasonable prices.Boats in rentalGuest Comments"…Thanks for the awesome instructions and patience. We had a great time! My 7 yr. old spotted a seal! Myhusband received a gift certificate for his 40th birthday…brilliant idea!…"—Sarah, Delta, Canada "…Great experience! The nicest, most friendly staff I've ever met in Canada. The boat was nice and handledwell. The price was very reasonable. Great way to get a different view of Vancouver. An absolute must try. Thanks guys!…"—Morten Bothmann, Copenhagen, Denmark1. What is the biggest advantage of Granville Island Boat Rentals?A. Offering various boat rentals.B. Taking tourists to different sites.C. Ensuring the highest level of safety.D. Guiding visitors in wildlife observation.2. How much does it cost to rent a boat accommodating 8 people for 5 hours on weekend?A. $ 350.B. $ 500.C. $ 700.D. $ 675.3. What do Sara's and Morten's opinions have in common?A. Easily-controlled equipment.B. Well-received service.C. Reasonable boat rental price.D. Breathtaking scenery.BWhen Belquer first joined a team to make a better live music experience for deaf and hard-of-hearing people, he was struck by how they had developed more solutions to enjoy concerts. "What they were doing at the time was holding balloons to feel the vibrations（震动）through theirfingers," Belquer said. He thought the team could make something to help hard-of-hearing people enjoy live music even more with the technology now available.Belquer, who is also a musician and theater artist, is now the "Chief Vibration Officer" of Music: Not Impossible, which uses new technology to address social issues like poverty and disability access. His team started by tying different vibrating cell phone motors to bodies, but that didn't quite work. The vibrations were all the same. Eventually, they worked with engineers to develop a light haptic （触觉的）suit with a total of 24 vibrating plates. There are 20 of them tied to a undershirt that fits tightly around the body like a hiking backpack, plus one that ties to each wrist and ankle, When you wear the suit, it's surprising how it feels.The vibrations are mixed by a haptic DJ who controls the location, frequency and intensity of feeling across the suits, just as a music DJ mixes sounds in an artful way. "What we're doing is selecting and mixing what we want and send it to different parts of the body," said the DJ. The haptic suits were just one component of the event. There were American Sign Language interpreters; the music was displayed on a screen on the stage.The suits are the star attraction. Lily Lipman, who has auditory processing disorder, lit up when asked about her experience. "It's cool, because I'm never quite sure if I'm hearing what other people are hearing, so it's amazingto get the music in my body."4. What surprised Belquer about people with hearing problems?A. The attitude they held to life.B. The way they enjoyed music.C. The love they had for balloons.D. The frequency they vibrated fingers.5. Why did the team's initial attempt fail?A. The vibrations lacked variety.B. The vibrations were irregular.C. The motors were the same.D. The motors hardly worked.6. What is paragraph 3 of the text mainly about?A. Displaying music on the stage.B. Selecting proper suits for participants.C. Mixed methods helping people feel the music.D. Interpreters with excellent sign language skills.7. What does Lily Lipman think of the suit?A. It's comforting.B. It's challenging.C. It's satisfying.D. It's disturbing.CA team in Norway recently conducted in-depth research on writing by hand and typing on a keyboard.The team invited 36 university students who had to either write or type words displayed on a screen. The study participants used a digital pen to write in cursive （草书）on a touchscreen, and they used one finger on a keyboard to type. The researchers used a special cap with 256 sensors. This cap was worn by the students, and their brain activity was recorded for five seconds each time they were asked to write or type."We show that when writing by hand, brain connectivity patterns are far more complex than when typewriting on a keyboard," says Professor Audrey van der Meer, the team leader. "Such widespread brain connectivity is known to be important for memory formation and for encoding （编码）new information and, therefore, is beneficial for learning." The researchers also note that even though the participants used digital pens for writing in the study, they believe the findings would be similar if the participants used an ink pen and paper."We've shown that the differences in brain activity are related to the careful forming of the letters when writing by hand while making more use of the senses. Since it's the movement of the fingers carried out when forming letters that promotes brain connectivity, writing in print also has similar benefits for learning as cursive writing," Audrey adds. "This also explains why children who have learned to write and read on a tablet can have difficulty differentiating between letters that are mirror images of each other, such as 'b' and 'd'. They haven't felt with their bodies what it feels like to produce those letters."Considering handwritten note-taking is becoming less common in educational settings, the researchers advocate for more opportunities for students to write by hand. "There's some evidence that students learn more and remember better when taking handwritten lecture notes, while using a computer with a keyboard may be more pragmatic when writing a long text or essay," Audrey concludes.8. What was the special cap used to do?A. Measure the participants' brain activity.B. Evaluate the participants' writing styles.C. Tell the participants when to write or type.D. Record the time the participants used to write.9. What does paragraph 3 focus on about the study?A. Its backgrounds.B. Its equipment.C. Its outcomes.D. Its process.10. What plays the key role in strengthening brain connectivity?A. Writing letters carefully by hand.B. Forming the habit of taking notes.C. Recognizing letters' mirror images.D. Learning to practice cursive writing.11. What does the underlined word "pragmatic" in the last paragraph mean?A. Difficult.B. Traditional.C. Special.D. Practical.DWhen I stepped into the Samcheong Park Library in Seoul, I saw the future. The simple building had a nice selection of books and a cafe where readers could enjoy coffee while gazing at the leaves outside. It was specifically designed without any latest technology."What's so innovative about that?" a librarian in Toronto asked when I showed her pictures. Innovation to her meant digital technology, like 3D printers. "Why couldn't they both be innovative?" I asked.We are constantly told that innovation is the most important force in our economy, without which we would be left behind. But that fear of missing out has led us to fall into the false trappings of innovation over truly innovative ideas that may be simpler and more effective. This mindset implies that if you just buy the new thing, you have innovated! Each year, businesses and individuals run around like broken toy robots, trying to figure out their strategy for the latest buzzword equipment.At best, this is a waste of resources. Devices are bought, used and abandoned, as the technology's capabilities fall short of its promise. But at its worst, this approach can truly cause damage. Schools cut field trips to purchase tablets with few proven benefits. Companies that applied AI into hiring have actually strengthened gender and racial prejudices.True innovation isn't just some magic devices. It is a continuing process of reflection and reassessment, which often means adopting "old" ideas and tools in a new context, or even returning to methods that worked in the past. Adjusted properly, these rearview（后视的）innovations have proved as transformative as novel technologies.Look no farther than the streets of New York, which have been redesigned recently to accommodate cyclists with car-free zones. The idea isn't new. It was created half a century ago, with the aim of bringing cities back to their residents. And while e-reader sales have been exploding, Penguin just announced it would publish tiny printed books, an ideal solution for a market demanding both convenience and physicality.12. Which of the following best describes Samcheong Park Library?A. Dull but convenient.B. Simple but refreshing.C. Old-fashioned but cozy.D. Unexceptional but spacious.13. What can we learn about innovation from Paragraph 3?A. Its true meaning is to buy new things.B. It is important for the growth of economy.C. It shouldn't involve simple and effective ideas.D. Its true meaning has been misread by the public.14. Which statement will the author probably agree with?A. Magic devices encourage innovation.B. Innovation should be human-centered.C. The power of technology is undervalued.D. Wasting resources are a must for innovation.15. What is the writing purpose of the text?A. To introduce some best ideas about innovation.B. To show that future lies in returning to the past.C. To convince people of the true meaning of innovation.D. To stress the important role innovation plays in economy.第二部分阅读七选五（共5小题；每小题2.5分，满分12.5分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。