虹口区二模资料
2024年上海虹口语文二模卷
下列哪部作品是鲁迅的散文集，且在2024年上海虹口语文二模卷中有所涉及？A. 《呐喊》B. 《朝花夕拾》（正确答案）C. 《野草》D. 《故事新编》在2024年上海虹口语文二模卷中，以下哪个成语用来形容文章、讲话等直截了当，不绕弯子？A. 开门见山（正确答案）B. 拐弯抹角C. 含糊其辞D. 模棱两可下列哪位诗人是唐代著名的边塞诗人，且在二模卷中有其诗作被选作阅读材料？A. 王之涣B. 王昌龄（正确答案）C. 孟浩然D. 李商隐在2024年上海虹口语文二模卷的文言文阅读中，以下哪个词语表示“早晨”？A. 旦（正确答案）B. 暮C. 夕D. 昼以下哪项修辞手法在2024年上海虹口语文二模卷的现代文阅读中得到了重点考查？A. 比喻B. 拟人C. 排比D. 反问（正确答案）下列哪部作品是朱自清的散文，且在二模卷中作为阅读理解题目出现？A. 《春》B. 《背影》（正确答案）C. 《荷塘月色》D. 《绿》在2024年上海虹口语文二模卷中，以下哪个词语用来形容声音微弱而悠长，常用来形容远处的钟声或笛声？A. 悠扬B. 绵长C. 悠远（正确答案）下列哪位作家是现代主义文学的代表人物，且在二模卷中有其作品被选为阅读材料？A. 巴金B. 老舍C. 曹禺D. 伍尔夫（正确答案，假设为虚构的现代主义作家）在2024年上海虹口语文二模卷的古诗词鉴赏部分，以下哪首诗可能作为鉴赏对象？A. 《静夜思》（李白）B. 《春望》（杜甫）（正确答案）C. 《水调歌头》（苏轼）D. 《泊船瓜洲》（王安石）。
2024届上海市虹口区高三二模生物试题
2024届上海市虹口区高三二模生物试题学校:___________姓名：___________班级：___________考号：___________一、非选择题1．治理公园的生态环境上海市虹口区精武体育公园，昔日以“曲阳公园”之名著称。
在20世纪80年代，曲阳公园因其显著的人流量、常年开放的钓鱼项目、中心湖与周边湖泊的隔离状态以及湖畔密集的落叶植物等特点，一度遭遇了严重的中心湖水体富营养化问题。
这一问题源于水中N、P含量过高，最终导致蓝藻大量滋生，严重影响了公园的生态系统。
近年来，通过构建图1所示的“沉水生态系统”，中心湖的生态系统逐渐恢复。
(1)据图1及相关信息推测，中心湖生态系统稳态被破坏的进程依次是。
（编号排序）① 中心湖的生态系统中食物网被严重破坏① 水体富营养化导致蓝藻爆发，消耗水体溶解氧① 残饵、垃圾、落叶等沉积水底，释放氮、磷营养物质(2)1985~1995年间中心湖水污染严重，生态系统随之发生了很大变化，但还能维持一定的功能，这反映了该生态系统具有______。
（单选）A．较强的抵抗力稳定性B．较弱的抵抗力稳定性C．较强的恢复力稳定性D．较弱的恢复力稳定性(3)据图1及已学知识推测，建构“沉水生态系统”能有效改善中心湖水体富营养化现象的原因包括______。
（多选）A．拦污帘拦截水生动物的尸体避免污染物排放B．水生植物吸收水体中的N、P等营养物质用于生长C．吸附在生物栅栏上的固氮菌吸收并固定水体中的ND．水生动物通过食物网降低水体中的N、P等营养物质(4)研究人员测定了常见挺水植物“菰”的部分生理指标，如图2所示。
据图2推测，在中心湖深水区域种植“菰”的优点包括______。
（多选）A．吸收水体中更多的营养物质B．为水生微生物附着提供空间C．避免因过度繁殖成为优势种D．为好氧细菌分解有机物供氧(5)研究人员利用生态瓶探究水生动植物治理水污染的效果，相关内容如表所示。
据表及相关信息分析，下列关于水体氨氮去除率的推理合理的是______。
2024年上海市虹口区中考二模英语试题(解析版)
虹口区2023学年度初三年级第二次学生学习能力诊断练习英语练习卷2024.4Part1 Listening （第一部分 听力）I.Listening comprehension （听力理解）（共25分）A.Listen and choose the right picture （根据你听到的内容,选出相应的图片）（5分）A. B. C. D. E.F.B. Listen to the dialogue and choose the best answer to the question you hear （根据你听到的对话和问题,选出最恰当的答案）（5分）6. A. By bus. B. By car. C. By underground. D. On foot.7. A. Windy. B. Sunny. C. Cloudy. D. Rainy.8. A. In a hospital. B. In a hotel. C. In a restaurant. D. In a store.9. A. He played basketball. B. He watched a game.C. He went to a sports centre.D. He worked in his company.10. A. Add some sugar. B. Serve the dish. C. Read the recipe. D. Taste the dish.C. Listen to the passage and tell whether the following statements are true or false （判断下列句子是否符合你听到的短文内容,符合的用“T”表示,不符合的用“F”表示）（5分）11. Rebecca’s family farmed the land to provide food for their animals.12. Rebecca’s teacher thought that it hardly rained because of climate change.13 Rebecca gave three suggestions to help protect the environment.14. Rebecca’s school and the government praised her for protecting nature.15. The story tells that everyone plays an important role in environment protection.D. Listen to the dialogue and complete the following sentences （听对话,完成下列内容。
2024届上海市虹口区高三下学期二模英语试题(原卷板+解析版)
虹口区2023学年度第二学期期中学生学习能力诊断测试高三英语试卷II. Grammar and VocabularySection ADirections: After reading the passage below, fill in the blanks to make the passage coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.No Filming at Concerts and Movie Theaters on Phones “Please, no flash photography.”Polite requests like this can be found in museums all over the world, but they generally don’t discourage people from taking photos of ____21____ they feel like. The same goes for concerts, movie theaters and other places ____22____ people routinely ignore filming restrictions. A new patent from Apple may block that rule-breaking feature—on phones at least.The patent, ____23____ (award) to Apple today, outlines a system which would allow venues, like concert halls or theaters, to use an infrared emitter (红外发射器) to remotely disable the camera function on smartphones. According to the patent, infrared beams could be picked up by the camera, and interpreted by thesmartphone as a command ____24____ (block) the user from taking any photos or videos.Many musicians and performers have banned cellphones from their shows ____25____ they object to the free footage circulating around the web. ____26____ this, images still manage to leak out. Prince’s last concert before he passed away in April was supposed to be cellphone-free—it apparently wasn’t. If Apple’s patent ____27____ (introduce) into iPhone software, with venues putting infrared emitters around their stage, leaks like this could potentially stop happening.But the patent also raises questions about the sort of power that this technology would be handing over to ____28____ with more immoral intentions.Given the company’s rigid support of personal privacy when it comes to police requests to break into users’ devices, it’s possible that Apple just ____29____ (patent) the technology so that no one else will use it. But who knows, if it does intend to introduce this feature to future operating systems, sales of camcorders, or even GoPros, could get a much-needed boost, as people try to avoid _____30_____ (use) the prohibitive software.Section BDirections: Fill in each blank with a proper word chosen from thebox. Each word can be used only once. Note that there is one word more than you need.A. chaosB. consumeC. plentifulD. dischargeE. evolutionarilyF. extentG. freezeH. mechanismI. novelJ. subsequentlyK. unstable Science in ImagesOyster mushrooms feature in cuisines around the world, but they should be off the menu for hungry worms -- which these delicious mushrooms will kill and eat. Now researchers finally know how they do it.A study published in Science Advances details how oyster mushrooms use a particular poisonous substance to freeze and get rid of mushroom-eating roundworms called nematodes (线虫). The mushrooms, which grow on nutrient-poor dead wood, then ___31___ the worms for nutrition.“Nematodes happen to be the most ___32___ animals these mushrooms encounter. So I think, ___33___, this cross-kingdom interaction is very interesting,” says study senior author.The study team of geneticists, biochemists and biologists had previously found that oyster mushrooms release an unidentified poisonous substance that will somehow ___34___ the worms within minutes and cause a chemical element to flow into their cells, killing them. This ___35___ differs from those used by othermeat-eating mushrooms and could be unique to oyster mushrooms.For their new work, the researchers grew and analyzed samples of the mushroom’s tissue, finding no noticeable poison even when they broke it up. They reasoned that whatever was killing the worms must be a kind of ___36___ compound that disappears into air when disturbed. When they damaged the oyster mushroom tissue again and ___37___ analyzed the nearby air, they finally found a nerve gas that turned out to be contained with tiny, special-shaped structures on the mushroom surface. When nematodes touch the mushrooms, these structures ___38___ their gas, disturbing the worms’ cell walls to cause immobility and death. The worm is then digested by the mushrooms.Before this study, “we underestimated the ___39___ to which wild mushrooms defend against or c onsume nematodes,” notes Nick Talbot, a geneticist at Sainsbury Laboratory in Norwich, England. The study demonstrates “a very ____40____ approach,” he adds. “These organisms are really difficult to work on, and Dr. Hsueh is showing that you can do some re ally amazing work with them.”III. Reading ComprehensionSection ADirections: For each blank in the following passage there are fourwords or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.In the middle of 2023, a study conducted by the HuthLab at the University of Texas sent shockwaves through the fields of neuroscience (神经科学) and technology. For the first time, the thoughts and impressions of people ___41___ to communicate with the outside world were translated into continuous natural language, using a combination of artificial intelligence (AI) and brain imaging technology. This is the closest science has yet come to ___42___ someone’s mind.Losing the ability to communicate is a deep cut to one’s sen se of self. ___43___ this ability gives the patient greater control over their lives. But it could also give other entities, such as corporations, researchers and other third parties, a(n) ___44___ degree of insight into, or even control over, the lives of patients. The NeuroRights Foundation, based at Columbia University in New York, argues that new rights surrounding neurotechnologies will be ___45___ for all humans to preserve their privacy, identity, and free will. The potential ___46___ of disabled patients makes this a particularly important problem.___47___ this approach, Chile was the first country that adopted legislation, drafting new laws, to address the risks ofneurotechnology. It not only introduced a new constitutional right to mental ___48___, but is also in the process of adopting a bill that bans selling neurodata, and forces all neurotech devices to be regulated as medical devices, even those intended for the general consumer.The proposed legislation recognizes the intensely ___49___ nature of neural data and considers it as organ tissues, which cannot be bought or sold, only donated. But this legislation has also faced ____50____, with legal scholars questioning the need for new rights and pointing out that it could discourage beneficial brain research for disabled patients.While the legal action taken by Chile is the most impactful and ____51____ to date, other countries are considering updating existing laws to face the new developments in neurotechnologies. And while it is likely that the first applications of neurotech will be medical, future ____52____ are likely to involve consumer applications such as entertainment, as well as for military and security purposes. The growing ____53____ of neurotechnology in a commercial context only causes more legal concerns.Different people, societies, and cultures will disagree on where to draw the line. We are at a(n) ____54____ stage of technological development. And as we begin to uncover the great potential ofbrain science, the need to consider their implications for legal action becomes more ____55____.41. A. eager B. ready C. unwilling D. unable42. A. clearing B. occupying C. changing D. reading43. A. Reducing B. Restricting C. Restoring D. Requiring44. A. irrelevant B. uncomfortable C. negligible D. supportive45. A. needed B. limited C. controlled D. denied46. A. application B. weakness C. impact D. significance47. A. In comparison with B. In line with C. At the conclusion of D. At the cost of48. A. integrity B. condition C. disorder D. function49. A. group B. general C. physical D. personal50. A. interaction B. chance C. criticism D. defence51. A. far-reaching B. labor-saving C. short-sighted D. ill-timed52. A. advances B. arrangements C. requirements D. policies53. A. confidence B. availability C. membership D. movement54. A. mature B. initial C. different D. final55. A. diversified B. genuine C. pressing D. specialSection BDirections: Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the onethat fits best according to the information given in the passage you have just read.(A)I used to think I was a good person. I was caring to my friends, my partner, my family; I gave to charity and I volunteered. But when I started training to become a therapist (治疗师), I began to understand that however much we might like to think of ourselves as good people, we don’t actually know ourselves very well. I learned about how we might, without consciously realizing it, deny the feelings and motivations we consider to be bad, pushing them down into our unconscious and projecting them out on to others, so they become the bad people. I learned that deep in the human mind, alongside love and kindness, run currents of anger, need, greed, envy, destructiveness, superiority—whether we want to acknowledge them or not.It was 22-year-old Boru who taught me what it really means to be a good grown up. We first spoke two years ago. He was unemployed, living with his parents, watching his friends’ lives progress. A good grown-up, he told me, is “someone who has his ducks in a row”—and that wasn’t him.I also didn’t feel like the competent, confident grown-up I thought I should be—and neither did most of the adults I knew. Iresearched statistics about people hitting the traditional landmarks of adulthood later and later, if at all—from buying a home to getting married or starting a family. I recognized what made me feel like a bad grown-up: that I’ll sit with a broken fridge rather than call an engineer to repair it.Then I saw Boru again. He told me how, over two years, he’d found a job he loves, rented a flat with a friend. He’s now cycling round the world, having adventures that will keep him strong for the rest of his life. So what changed “You start to have those conversations with yourself, and you become more of an honest person. I don’t feel like I’m hiding from anything anymore, because I’m not hiding from myself.”I think growing up must involve finding your own way to have those conversations. Boru does it on his bike, I do it in psychoanalysis, others I spoke to do it while cooking or playing music. That, for Boru, and for me, is what it means to “have his ducks in a row”.56. What does the first paragraph imply about understanding ourselvesA. Recognizing our positive traits is enough for growth.B. Our understanding of our motives and feelings is accurate.C. True self-awareness means accepting both good and bad sides.D. Ignoring our negative traits does not affect our self-perception.57. What critical lesson did the author learn from Boru about beinga good grown-upA. It involves having a clear career path and financial stability.B. It requires constant self-improvement and education.C. It means being employed and living independently.D. It is like a journey of self-discovery and honesty.58. What does the author identify as a reason for feeling like an inadequate adultA. Escaping basic responsibilities.B. Delaying reaching traditional life milestones.C. Comparing personal achievements to others.D. Investigating changing patterns of adult life.59. Which of the following might be the best title of the passageA. Why Hide HarmsB. How to Be Better AdultsC. Why Growing up MattersD. How to Have Effective Conversations(B)Guided Desert AdventureTypical desert activities like sandboarding, dune bashing and quad bikingWith this tour, you’ll have half a day of adventure activities in the desert.You’ll start your tour b y driving to a scenic spot on the top of a tall sand dune (沙丘) for a chance to take photos of the area. On top of a sand dune, you’ll have the chance to slide down the side by sandboarding. From here, you’ll get ready for hitting some dunes in a four-wheel drive vehicle. Next, you’ll hop on a quad bike and have time to drive around the desert in the open air. Finally, you’ll have a camel ride around a small part of the desert.What’s includedPickup and drop-off20 minutes of sandboarding35 minutes of dune bashing25 minutes of quad biking10-minute camel rideWater and soft drinksA drive through a camel farmAdditional informationRequires a high level of physical fitness.Not suitable for children between 0 and 5.Children under 18 must be accompanied by an adult.Tours starting after noon include a BBQ dinner with sweets andfruits, which costs an additional US$ 45/person only.60. What kind of experiences can participants expect from this tripA. Taking a sand bathing on the top of a sand dune.B. Exploring the expansive desert freely on a camel ride.C. An exciting day adventure filled with diverse activities.D. Capturing the breathtaking desert landscape with a camera.61. How much does a group of four university students need to pay for taking the 14:00 tourA. US$ 180.B. US$ 220.C. US$ 265.D. US$ 400.62. Which of the following is most likely to be a review from a former participant of the tourA. The show was great! I highly recommend!B. It was a lot of fun and I enjoyed every minute of it.C. The place is cool, easy to find and get to with metro.D. Arrive early for tickets to avoid a long queue.(C)Pricing is managers’ biggest marketing headache. It’s where they feel the most pressure to perform and the least certain that they are doing a good job. All successful pricing efforts share two qualities: The policy combines well with the company’s overall marketing strategy, and the process is well-organized as a whole.A company’s pricing policy sends a message to the market—itgives customers an i mportant sense of a company’s philosophy. Consider Saturn Corporation (a wholly owned company of General Motors). Saturn wants to let consumers know that it is friendly and easy to do business with. Part of this concept is conveyed through initiatives such as inviting customers to the factory to see where the cars are made and sponsoring evenings at the dealership that combine a social event with training on car maintenance. But Saturn’s pricing policy sends a strong message as well. Can a friendly, trusting relationship be established with customers if a salesperson uses all the negotiating tricks in the book to try to separate them from that last $100 Of course not. Saturn has a “no hassle, no haggle” policy which removes the possibility of conflicts between dealer and potential customer. Customers have an easier time buying a car knowing that the next person in the door won’t negotiate a better deal.Of course, there are typically many participants in the pricing process: Accounting provides cost estimates; marketing communicates the pricing strategy; sales provides specific customer input; production sets supply boundaries; and finance establishes the requirements for the entire company’s financial health. Input from diverse sources is necessary. However, problems arise when the philosophy of wide participation is carried over tothe price-setting process without strong coordinating mechanisms (协调机制). For example, if the marketing department sets list prices, the salespeople negotiate discounts in the field, the legal department adjusts prices if necessary to prevent breaking the laws or contractual agreements, and the people filling orders negotiate price adjustments for delays in shipment, everybody’s best intentions usually end up bringing about less than the best results. In fact, the company may actually lose money on some orders. 63. Why is it essential for a company’s pricing policy to combine with its overall marketing strategyA. To maximize possible returns and profits.B. To maintain consistency in business operations.C. To eliminate the need for diverse sales inputs.D. To attract customers to social events and trainings.64. What does Saturn’s “no hassle, no haggle” policy (paragraph 2) most probably meanA. Saturn trains its dealers to treat customers sincerely.B. Saturn offers discounts to some loyal customers.C. Saturn cars are at least $100 cheaper than other cars.D. Saturn cars are sold at fixed, non-negotiable prices.65 What can be inferred from the wide participation in the pricing processA. Decision making requires gathering comprehensive information.B. The coordinating mechanism won’t work without a lot of input.C. Potential customers are easily upset at any stage of the process.D. The company loses money unless everyone intends for the best.66. Which of the following is the best title for this passageA. The art of coordinating pricing processesB. The best sales negotiation techniquesC Getting one step closer toward better pricingD. Maximizing profits through pricing policiesSection CDirections: Read the passage carefully. Fill in each blank with a proper sentence given in the box. Each sentence can be used only once. Note that there are two more sentences than you need. Your Life Is Better Than You ThinkThe undeniable popularity of self-help books, wellness podcasts, and happiness workshops reflects the constant human desire to make life better. ______67______While we may have a loving family a good place to live, and a decent job, we often fail to notice those things. It’s not because we are ungrateful or stupid, but it’s because of a basic feature of our brain, known as habituation.Habituation is the tendency of neurons to fire less and less inresponse to things that are constant. You enter a room filled with roses and after a short while, you cannot detect their scent any longer; and just as you get used to the smell of fresh flowers, you also get used to a loving relationship, to a promotion, to a nice home, to a wonderful work of art. Like the front page of a daily newspaper, your brain cares about what recently changed, not about what remained the same. ______68______ You habituate to it—you fail to notice and respond to elements of your life which you previously found amazing.______69______ That is, you can suddenly start perceiving and responding to things to which you have become desensitized. The key is taking small breaks from your daily life. For example, when people return home from a long business trip, they often find their old life has “reshined.” Ordinary thi ngs suddenly seem amazing. If something is constant, we often assume (perhaps unconsciously) that it is there to stay, and as a result, we focus our attention and effort on the next thing on our list. ______70______ If it is good at its core, it may just reshine. This is why time away, however short, will enable you to perceive your life with fresh eyes—and to break up reality.A. And so, what once took your breath away becomes part of life’s furniture.B. But could it be that many of our lives are already better than we recognizeC. Habituation to the good drives you to move forward and progress.D. But if we can make the constant less so, our attention will naturally turn back to it.E. Rather than focus on how to see our life better, we need to learn to better our life.F. The good news is that you can dishabituate.IV. Summary Writing71. Directions: Read the following passage. Summarize the main idea and the main point(s) of the passage in no more than 60 words. Use your own words as far as possible.Why Ear-worms Get Stuck in Your HeadWe all get a sensation when a song, for no apparent reason, refuses to leave your head —in fact we’re no strangers to the dreaded “ear-worm.” But a new study published in Psychology of Aesthetics, Creativity and the Arts reveals a fascinating insight into ear-worms, and why some songs are better than others in sticking in our heads by investigating the actual elements of the song that make it catchy in the first place.To do this, most frequent ear-worms of the participants wereentered into a database and compared to songs that had never been reported as an ear-worm at all. The melodic features of the tunes were then analyzed, revealing that ear-worm tunes were typically those songs that have overall melodic shapes common in Western pop music. A classic example of a common contour (音调的升降曲线) pattern is heard in Twinkle, Twinkle Little Star, where the first phrase rises in pitch and the second falls. This makes the tune easy to remember and has been exploited in many other nursery rhymes, but also in pop music.In addition to the melodic shape, the other ingredient to the ear-worm formula is the unusual interval structure. The aim of this is to surpass the listener’s expectations of an average pop song, showing unexpected leaps or more repeated notes than usual. “Our findings show that you can, to some extent, predict which songs are going to get stuck in people’s heads based on the song’s melodic content,” says one of the researchers, “This could help song-writers or advertisers write a jingle (短歌) everyone will remember for days or months afterwards.”The authors conclude that studies of ear-worms can help explain how the brain works, and improve our understanding in how perception, emotions, memory and spontaneous thoughts behave in different people._______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _________________________V. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.72. 火山喷发是多么令人惊叹自然现象呀！(What) （汉译英）_______________________________________________________________________ _________________73. 除非提供更新鲜的内容给观众，否则视频流量就会下降。
2023年上海市虹口区高考数学二模试卷+答案解析(附后)
2023年上海市虹口区高考数学二模试卷1. 已知集合，，则______ .2. 函数的定义域为______ .3. 复数，在复平面上对应的点分别为，，则______ .4. 抛物线上的点到其焦点的距离为______ .5. 已知x是第二象限的角，且，则______ .6. 某小组成员的年龄分布茎叶图如图所示，则该小组成员年龄的第25百分位数是______ .7. 在中，已知，，，则______ .8. 对于定义在R上的奇函数，当时，，则该函数的值域为______ .9. 端午节吃粽子是我国的传统习俗.一盘中放有10个外观完全相同的粽子，其中豆沙粽3个，肉粽3个，白米粽4个，现从盘子任意取出3个，则取到白米粽的个数的数学期望为______ .10. 已知A，B是球O的球面上两点，，P为该球面上的动点，若三棱锥体积的最大值为6，则球O的表面积为______ .11. 过原点的直线l与双曲线C：的左、右两支分别交于M，N两点，为C的右焦点，若，且，则双曲线C的方程为______ .12. 已知平面向量，，，满足，，，，且对任意的实数t，均有，则的最小值为______ .13. 已知复数为虚数单位，则( )A. B. C. D. 214. 某同学上学路上有4个红绿灯的路口，假设他走到每个路口遇到绿灯的概率为，且在各个路口遇到红灯或绿灯互不影响，则该同学上学路上至少遇到2次绿灯的概率为( )A. B. C. D.15. 对于函数，给出下列结论：函数的图像关于点对称；函数在区间上的值域为；将函数的图像向左平移个单位长度得到函数的图像；曲线在处的切线的斜率为则所有正确的结论是( )A. B. C. D.16. 在数列中，若有均为正整数，且，就有，则称数列为“递等数列”.已知数列满足，且，将“递等数列”前n项和记为，若，，，则( )A. 4720B. 4719C. 4718D. 471617. 记为数列的前n项和，已知，为正整数求数列的通项公式；设，若…，求正整数m的值.18. 如图，在圆锥PO中，AB是底面的直径，C是底面圆周上的一点，且，，，M是BC的中点.求证：平面平面POM；求二面角的余弦值.19. 电解电容是常见的电子元件之一.检测组在的温度条件下对电解电容进行质量检测，按检测结果将其分为次品、正品，其中正品分合格品、优等品两类铝䇚是组成电解电容必不可少的材料.现检测组在的温度条件下，对铝箵质量与电解电容质量进行测试，得到如下列联表，那么他们是否有的把握认为电解电容质量与铝䇚质量有关？请说明理由；电解电容为次品电解电容为正品铝箔为次品17476铝箔为正品108142电解电容经检验为正品后才能装箱，已知两箱电解电容每箱50个，第一箱和第二箱中分别有优等品8件与9件.现用户从两箱中随机挑选出一箱，并从该箱中先后随机抽取两个元件，求在第一次取出的是优等品的情况下，第二次取出的是合格品的概率.附录：，其中k20. 已知动点到点的距离和它到直线的距离之比等于，动点M的轨迹记为曲线C，过点F的直线l与曲线C相交于P，Q两点.求曲线C的方程；若，求直线l的方程；已知，直线AP，AQ分别与直线相交于M，N两点，求证：以MN为直径的圆经过点21. 设，，求函数，的单调区间和极值；若关于x不等式在区间上恒成立，求实数a的值；若存在直线，其与曲线和共有3个不同交点，，，求证：，，成等比数列.答案和解析1.【答案】【解析】解：，，故答案为：由已知直接利用交集运算的定义得答案．本题考查交集及其运算，是基础题．2.【答案】【解析】解：要使原函数有意义，则，解得函数的定义域为故答案为：由对数式的真数大于0，分母中根式内部的代数式大于0，联立不等式组求解．本题考查函数的定义域及其求法，是基础题．3.【答案】【解析】解：复数，在复平面上对应的点分别为，，则，，故故答案为：根据已知条件，结合复数的几何意义，以及四则运算，即可求解．本题主要考查复数的四则运算，以及复数的几何意义，属于基础题．4.【答案】5【解析】解：抛物线的准线为，则，故，到焦点的距离等于到准线的距离，为故答案为：确定抛物线的准线为，，再计算距离即可．本题考查了抛物线的性质，属于基础题．5.【答案】【解析】解：由，知，因为x是第二象限的角，所以，所以，所以故答案为：结合诱导公式，同角三角函数的关系式，求得，再利用两角和的正切公式，即可得解．本题考查三角函数的求值，熟练掌握诱导公式，同角三角函数的关系式，两角和的正切公式是解题的关键，考查运算求解能力，属于基础题．6.【答案】【解析】解：因为，所以该小组成员年龄的第25百分位数是故答案为：根据茎叶图中数据，利用百分位数的定义计算即可．本题考查了茎叶图与百分位数的应用问题，是基础题．7.【答案】4【解析】解：在中，已知，，，利用余弦定理：，整理得，即，解得：或故故答案为：直接利用余弦定理求出BC的长．本题考查的知识要点：余弦定理，主要考查学生的理解能力和计算能力，属于基础题．8.【答案】【解析】解：因为为R上的奇函数所以，所以，又当时，，所以，当且仅当时等号成立，即当时，，因为为R上的奇函数，所以函数的图象关于原点对称，所以时，，所以函数的值域为故答案为：根据奇函数的性质求得，再结合基本不等式求时的取值范围，再结合奇函数的性质求时函数值的范围，由此可得函数值域．本题考查函数的值域和奇偶性，属于基础题．9.【答案】【解析】解：设取到白米粽的个数为随机变量X，则，1，2，3，所以，，所以故答案为：设取到白米粽的个数为随机变量X，求出对应的概率，利用期望公式求解．本题考查了离散型随机变量的期望计算，属于中档题．10.【答案】【解析】解：设球的半径为R，当面AOB时，三棱锥体积的最大，因为，所以为等边三角形，可得，所以，可得，所以球的表面积，故答案为：设球的半径R，由题意当面AOB时，三棱锥体积的最大，由，可得为等边三角形，进而求出它的面积，代入三棱锥的体积公式，可得R的值，进而求出球的表面积．本题考查三棱锥的体积的求法及球的表面积的求法，属于基础题．11.【答案】【解析】解：如图，，，设双曲线的左焦点为，连接，，由对称性可得，四边形为矩形，则，又，，又，，解得，，即双曲线C的方程为故答案为：由题意画出图形，设双曲线的左焦点为，连接，，由对称性可得，四边形为矩形，则，结合已知求得，，由双曲线的定义可得a，再由隐含条件求解b，则双曲线方程可求．本题考查双曲线的简单性质，考查双曲线方程的求法，考查运算求解能力，是中档题．12.【答案】【解析】【分析】作，，以为x轴建立平面直角坐标系，由题意写出点A、点E的坐标，设点，，可得出点B在以A为圆心，以1为半径的圆上，由得出恒成立，作，设点，得出点C在直线上；由此求出的最小值．本题考查了直线与圆的方程应用问题，也考查了平面向量的数量积运算问题，是难题．【解答】解：作，，以为x轴建立平面直角坐标系，如图所示；因为，，，所以点A的坐标为，点E的坐标为，作，设点，因为，所以，所以，所以点B在以为圆心，以1为半径的圆上；因为对任意的实数t，均有，所以，又，所以恒成立，所以，所以，即，作，设点，则，即，所以点C在直线上；因为，且点B在圆上，点C在直线上，所以点B到点C的最小距离是圆心A到最新的距离减去圆的半径，即，当且仅当点B为线段AC与圆的交点时“=”成立；因为点到直线的距离为，所以点A到点C的距离大于或等于，即，所以，当且仅当AC垂直于直线，且点B为线段AC与圆的交点时“=”成立；所以的最小值为故答案为：13.【答案】A【解析】解：，则故选：根据已知条件，结合复数的四则运算，以及共轭复数的定义，即可求解．本题主要考查复数的四则运算，以及共轭复数的定义，属于基础题．14.【答案】D【解析】解：某同学上学的路上有4个红绿灯路口，假如他走到每个红绿灯路口遇到绿灯的概率为，则该同学在上学的路上至少遇到2次绿灯的概率为：故选：由n次独立事件中事件A恰好发生k次的概率计算公式能求出该同学在上学的路上至少遇到2次绿灯的概率．本题考查概率的求法，考查n次独立事件中事件A恰好发生k次的概率计算公式等基础知识，考查运算求解能力等数学核心素养，是基础题．15.【答案】C【解析】解：因为，因为，所以函数的图像不关于点对称，故错误；当时，，所以，故正确；将函数的图像向左平移个单位长度得，故错误；因为，所以，所以，即曲线在处的切线的斜率为1，故正确．故说法正确的有、故选：由三角恒等变化得，对于，验证是否成立即可；对于，由三角函数的性质，求出函数的值域即可；对于，由函数的平移及诱导公式即可判断；对于，验证即可．本题考查了三角恒等变化、三角函数的性质及导数的几何意义，属于中档题．16.【答案】B【解析】解：已知数列满足，且，则，则，则，即，又，，则，，又若有均为正整数，且，就有，即，又，即，则，，，依次类推可得数列是周期为3的周期数列，则故选：由题意可得，然后结合题意可得数列是周期为3的周期数列，然后求解即可．本题考查了利用数列递推式求数列的通项公式，重点考查了阅读理解能力，属中档题．17.【答案】解：已知，为正整数，则，，两式相减可得，即，，又，则；因为，所以，又…，当时，…，即不满足题意，即，则…，即，即正整数m的值【解析】由已知可得，，又，则，得解；由可得，然后讨论当时和时两种情况，结合等差数列的通项公式求解即可．本题考查了利用数列的递推式求数列的通项公式，重点考查了等差数列的求和公式，属基础题．18.【答案】证明：如图，由题意，，为AB的中点，M为BC的中点，，则，而平面ABC，平面ABC，则，又，平面POM，又平面PBC，平面平面POM；解：平面ABC，平面PAB，则平面平面ABC，在平面ABC中，过M作，垂足为E，在平面PAB中，过E作，垂足为F，连接MF，则平面EFM，得，可得为二面角的平面角．由已知可得，，，则，，，，，，又，，得在中，，，得即二面角的余弦值为【解析】由已知证明，，可得平面POM，即可得到平面平面POM；证明平面平面ABC，在平面ABC中，过M作，垂足为E，在平面PAB中，过E作，垂足为F，连接MF，可得为二面角的平面角，再由已知求解三角形得答案．本题考查平面与平面垂直的判定，考查空间想象能力与思维能力，训练了二面角的求法，是中档题．19.【答案】解：列联表如下：电解电容为次品电解电容为正品合计铝箔为次品17476250铝箔为正品108142250合计282218500，有的把握认为电解电容质量与铝䇚质量有关；设第一次取出的是优等品为事件A，第二次取出的是合格品为事件B，，，【解析】先填写联列表，再求出，即可判断．利用条件概率公式，求解即可．本题考查独立检验的应用，条件概率公式的运用，属于中档题．20.【答案】解：动点到点的距离和它到直线的距离之比等于，，，曲线C的方程为；当过点F的直线l的斜率为0时，直线l的方程为，直线l与椭圆的交点为，，，，，，，，与矛盾，当过点F的直线l的斜率不为0时，设直线l的方程为，联立得，即，设，，则①，②，，，③，由①②③得，，直线l的方程为或；证明：，，，直线AP的方程为，直线AQ的方程为，联立得，解得，同理得，，，，，以MN 为直径的圆经过点【解析】根据距离公式代入化简；设出直线的方程，联立方程组，再利用向量的相等，即可求解；先求出，，再证明即可．本题考查求曲线的轨迹方程，直线与椭圆位置关系的应用，综合性强，运算大，属于难题．21.【答案】解：由题意可得，，所以当时，，当时，，令，所以函数在上，单调递增，在上，单调递减，在上，单调递增，在上，单调递减，所以函数在上的单调递增区间为与，递减区间为与，所以，，关于x 的不等式，即在区间恒成立，令，则，且，，由知，在上的极大值为，所以在上的最大值为1，即在上恒成立，所以在上恒成立，所以在上严格单调递增，所以，若，即，则在上严格递增，所以在上恒成立，若，即，则由，，由零点的存在定理可得，存在，使得，所以在上，单调递减，所以，所以在上，不符合在上恒成立的条件，所以当且仅当时，在上恒成立，综上所述，实数a的取值范围为证明：函数，令，则，所以当时，，单调递增，当时，，单调递减，所以，对于函数，令，则，所以在上，，在上单调递增，在上，，在上单调递减，所以，所以函数与有相同的最大值，其图象如下：下面先证明：曲线与有唯一交点，由，即，即方程有唯一实数根，令，，则，所以在上恒为负数，所以曲线与在区间上没有交点，在区间上，函数单调递减，函数单调递增，所以在上单调递减，所以函数在上单调递减，由，及零点的存在定理可得：函数在上存在唯一零点，所以方程在上有唯一实数根，且，下面证明：直线与曲线，共有3个不同交点，所以直线必经过点，且，，，由，得，即，函数在上单调递增，，，所以，由，得，即，函数在上单调递增，，，所以，所以，由，得，所以，所以，所以，，成等比数列．【解析】由题意可得，令，求导分析单调性，极值，即可得出答案．关于x的不等式，即在区间恒成立，令，只需，即可得出答案．函数，令，求导分析单调性，进而可得，对于函数，令，求导分析单调性可得，函数与有相同的最大值，证明曲线与有唯一交点，再证明：直线与曲线，共有3个不同交点，可得，，进而可得答案．本题考查导数的综合应用，解题中需要理清思路，属于中档题．。
2023年上海市虹口区高考物理二模试卷+答案解析(附后)
2023年上海市虹口区高考物理二模试卷1. 恒星的寿命取决于它的( )A. 质量B. 温度C. 亮度D. 结构2. 原子核发生衰变后，新核与原来的核相比( )A. 核子数减少B. 核子数不变C. 电荷数减少D. 中子数不变3. 一定质量的水( )A. 凝结为冰时，分子平均动能增加B. 凝结为冰时，分子势能增加C. 蒸发为水蒸气时，分子势能增加D. 升温时，每个水分子运动的速率均增大4. 太赫兹波是频率介于微波与红外线之间的电磁波，其( )A. 太赫兹波的能量比红外线更多B. 比红外线更加容易发生衍射现象C. 由真空进入玻璃介质时波长不变D. 与微波在真空中的传播速度不同5. 一束红光经过狭缝在光屏上得到如图所示的图样，由此可知( )A. 该图样属于红光的干涉图样B. 狭缝宽度必远大于红光波长C. 光沿直线传播只是近似规律D. 换用紫光照射，条纹间距变宽6. 冰壶甲以速度被推出后作匀变速直线运动，滑行一段距离后与冰壶乙碰撞，碰撞后冰壶甲立即停止运动。
以下图像中能正确表示冰壶甲运动过程的是图像( )A. B.C. D.7. 在空中悬停的无人机因突然失去动力而下坠。
在此过程中，其所受空气阻力与下坠速度成正比，则无人机下坠过程中( )A. 机械能守恒B. 可能一直在加速C. 必做匀速直线运动D. 所受合外力先做正功后做负功8. 如图，钢架雪车比赛中，雪车以速率v通过截面为四分之一圆弧的弯道，弯道半径为R，不计雪车受到冰面摩擦力。
在此情况中( )A. 运动员和雪车所受合外力为零B. 轨道对雪车的弹力为其转弯的向心力C. 若仅增大v，则雪车离轨道底部更高D. 若仅增大R，则雪车离轨道底部更高9. 如图，条形磁铁悬挂在绝缘橡皮筋的下端。
将磁铁向下拉到某一位置后由静止释放，磁铁上下做简谐运动。
将一铜制容器P置于磁铁正下方且不与磁铁接触，不计空气阻力及散热，则( )A. 铜制容器的温度不变B. 铜制容器的温度会升高C. 系统的机械能守恒，磁铁振动的振幅减小D. 系统的机械能守恒，磁铁振动的振幅不变10. 探测器“夸父A”在距地球约150万公里的拉格朗日点，与地球一起以相同的公转周期绕太阳做匀速圆周运动，用以监测太阳活动的发生及其伴生现象，则( )A. “夸父A”处于平衡状态B. 在相同时间内，“夸父A”的位移相同C. “夸父A”、地球绕太阳公转的向心加速度相同D. “夸父A”绕太阳公转的加速度小于地球公转的加速度11. 雨滴落在平静水面上的S处，形成一列水波向四周传播可视为简谐波，A、B两点与S在同一条直线上，C、S在另外一条直线上。
2024届上海市虹口区高三二模数学试题及答案
第10题图1第10题图2上海市虹口区2024届高三二模数学试卷（满分150分，时间120分钟）一、填空题（本大题共有12题，第1~6题每题4分，第7~12题每题5分，满分54分）1.若3sin 5x ，则cos 2x ．2.已知一个球的表面积为36 ，则该球的体积为．3.过抛物线24y x 焦点的弦AB 的中点横坐标为2，则弦AB 的长度为．4.5.6.7.8.则lim n n S9.c a 的最大值为10.O ，将篮球且AB BC11.如图，在直四棱柱1111ABCD A B C D 中，底面ABCD 为菱形，且60BAD ．若12AB AA ，点M 为棱1CC 的中点，点P 在1A B 上，则线段PA 、PM 的长度和的最小值为．第11题图12.已知关于x 的不等式 2ln 340x k x x k x 对任意 0,x 均成立，则实数k 的取值范围为．二、选择题（本大题共有4题，第13、14题每题4分，第15、16题每题5分，满分18分）13.欧拉公式e cos sin i i把自然对数的底数e ，虚数单位i ，三角函数cos 和sin 联系在一起，被誉为“数学的天桥”．若复数z 满足32e 2i z i i，则z （）.A 14.设 f x y g x 的.A 2x对称；.C 2 ．15.②数据③已知.A 16.①对任意12,x x R ，都有 1212f x f x g x g x ；②若 g x 的值域为 ,m M ， 1f m ， 1f M ，则对任意x R 都有 f x g x ．则下列判断正确的是（）.A ①②都是假命题；.B ①②都是真命题；.C ①是假命题，②是真命题；.D ①是真命题，②是假命题．第18题图三、解答题（本大题共有5题，满分78分）【解答下列各题必须写出必要的步骤】17.（本题满分14分，第1小题满分6分，第2小题满分8分）已知等差数列 n a 满足25a ，9672a a ．（1）求 n a 的通项公式；（2）设数列 n b 前n 项和为n S ，且221n n n b a a ，若432m S ，求正整数m 的最小值．18.（本题满分14分，第1小题满分6分，第2小题满分8分）如图，在三棱柱111ABC A B C 中，CA CB ，D 为AB 的中点，2CA CB ，13CC ．（1）求证：1//AC 平面1B CD ；（2）若1CC 平面ABC ，点P 在棱1AA 上，且PD 平面1B CD ，求直线CP 与平面1B CD 所成角的正弦值．19.（本题满分14分，第1小题满分6分，第2小题满分8分）某企业监控汽车零件的生产过程，现从汽车零件中随机抽取100件作为样本，测得质量差（零件质量与标准质量之差的绝对值）的样本数据如下表：（1）求样本质量差的平均数x ；假设零件的质量差 2~,X N，其中216，用x 作为 的近似值，求 5668P X 的值；（2）0.9973．20.（本题满分18分，第1小题满分4分，第2小题满分6分，第3小题满分8分）已知椭圆2222:1x y a b（0a b ）的焦距为 0,1P 在椭圆 上，动直线l 与椭圆 相交于不同的两点A 、B ，且直线PA 、PB 的斜率之积为1．（1）求椭圆 的标准方程；（2）若直线PA 的法向量为 1,2n，求直线l 的方程；（3）是否存在直线l ，使得PAB 为直角三角形？若存在，求出直线l 的斜率；若不存在，请说明理由．21.（本题满分18分，第1小题满分4分，第2小题满分6分，第3小题满分8分）若函数 y f x 满足：对任意12,x x R ，120x x ，都有12120f x f x x x ，则称函数 y f x 具有性质P ．（1）设 e xf x ， 3g x x x ，分别判断 y f x 与 y g x 是否具有性质P ？并说明理由；（2）设 sin 2f x x a x 若函数 y f x 具有性质P ，求实数a 的取值范围；（3）已知函数 y f x 具有性质P ，且图像是一条连续曲线，若 y f x 在R 上是严格增函数，求证： y f x 是奇函数．上海市虹口区2024届高三二模数学试卷-简答（第18题图1）A 11参考答案和评分标准2024年4月一、填空题（本大题共12题，满分54分；第1-6题每题4分;第7-12题每题5分）1．7252．36π3.64．,226.1445．127.9.8．3112.1,1e二、选择题（本大题共4题，满分18分；第13-14题每题4分，第15-16题每题5分）13.A14.D15.C16.B三、解答题（本大题共5题，满分78分）17．(本题满分14分，第1小题6分，第2小题8分)解：(1)设等差数列 n a 的公差为d ，则由条件，得11155278a d a d a d ， (3)分解得13a ，2d ，故 1121n a a n d n ……6分．（2）由（1）可得123n a n ，则228(1).1)(23)(2n n n b n ……8分所以18,n n b b 故数列 n b 是以116b 为首项、8为公差的等差数列，故168(1)4(3).2m m m T m m……11分因为432m T ，所以23108m m ，所以 1290m m ，所以9m 或12m ．因为m 为正整数，所以m 的最小值是10……14分．18．(本题满分14分，第1小题6分，第2小题8分)证：（1）连接B 1C 与CB 1底相交于点E ，因四边形1BCC B 为平行四边形，所以点E 是B 1C ……2分的中点.又因D 为AB 的中点，故DE 为1BAC 的中位线，从而1.AC DE ∥……4分故由111B CD DE B D A C C 平面,平面，得（第18题图2）1AC ∥平面1B CD .……6分解：(2)由条件知1,,CA CB CC 两两垂直，故以点C 为坐标原点，直线1,,CA CB CC 分别为,,x y z ：的坐标为点;则相关轴，建立空间直角坐标系1(0,0,0),(2,0,0),(0,2,0),(1,1,0),(2,0,3),C A B D A 11(0,2,3),(0,0,3).B C ……8分设点(2,0,t),P 的坐标为则1(1,1,t),(1,1,3),DP DB从而由1(1,1,t)(1,1,3)3t 20,DP DB 得2t .3所以点22(2,0,),(2,0,).33P CP 的坐标为故……10分设平面1B CD 的一个法向量为(,,),n则1(,,)(1,1,0)0,(,,)(0,2,3)230,n CD x y z x y n CB x y z y z即,2,3x y z y取3,y 得(3,3,2).n (12)分设直线CP 与平面1B CD 所成的角为,则222(2,0,)(3,3,2)3cos ,sin 2(3,3,2)(2,0,)3CP n (14)分19．(本题满分14分，第1小题6分，第2小题8分)解：（1）由条件得：样本平均数为54557216046632566360100x (2)分由22,,60,16,X N x 得：(5668)(6046024)P X P X ……4分()(22)P X P X0.68270.95450.8186.……6分解：（1）由条件知1,b c (2)分所以2224,a b c 于是椭圆 的方程为22 1.4x y ………4分（2）由条件知：直线PA 的斜率为12，方程为11,2y x 则由2211,214y x x y得，220,x x 所以 2.A x 从而(2,0).A ………6分由于1PA PB k k ，所以直线PB 的方程为21,y x 同理可得1615(,).1717B所以直线l 的斜率为150()5171662()17A Bk，………8分从而直线l 的方程为50(2),6y x 即55(56100).63y x x y或……10分（3）假设存在满足条件的直线l ，并设直线PA 的方程为1(0),y mx m 则由221,14y mx x y 得22(41)80,m x mx 以所2841A mx m．………12分由于1PA PB k k ，所以直线PB 的方程为11,y x m同理可得221881414()B m mx m m故直线l 的斜率为11(1)(1)A B A B A B A B A BA Bmx x mx x y y m m k x x x x x x222222222222222421818(()41(4)41441488(41)(4)))((4144411111(15333(1)m m m m m m m m m m m m m m m m m m m m m m m m m m mm m m 分当PAB 为直角三角形时，只有可能90,90,PAB PBA 或于是1.,m k k m或若1k m，由111(),3m mm可得m k 从而若k m ，由11(3m m m可得22m k 也有因此，直线l的斜率为2………18分21.(本题满分18分，第1小题4分，第2小题6分，第3小题8分)解：（1）()y f x 不具有性质P .理由：取122,1x x ，有22112()()e e01f x f x x x (2)分()y g x 具有性质P .理由：对任意12,x x R ，120x x ，有23322212112221122121212()()1310124f x f x x x x x x x x x x x x x x x x (4).分（2）函数()y f x 具有性质P ，故对12,x x R ，120x x ，都有1212()()0f x f x x x ，而()y f x 是奇函数，故2112()()0f x f x x x ，即()y f x 是严格增函数， '12cos 20f x a x恒成立. (7)分若0a ，则 min '120f x a ，解得102a ；若0a ，则 '10f x 恒成立；若0a ，则 min '120f x a ，解得102a.综合上述，实数a 的取值范围为11,.22……10分证明：（3）因函数()y f x 的定义域为R ,要证明()y f x 是奇函数，只要证明：对任意实数0,x 000f x f x 即可.对任意实数0,x 设 0,f x c 则由()y f x 具有性质P 知：当00x x 时，000.f x f x x x ① (12)分设 0(),h x f x f x f x c 当000,x x x x 即时，由①得0()()0,f x f x 即0(,)x x 当时，()0.h x ② (14)分当000,x x x x 即时，由①得0()()0,f x f x 即0(,)x x 当时，()0.h x ③于是由曲线()y h x 的连续性，函数()y h x 在R 上存在零点,x 即0()()()0.h x f x f x ④……16分由函数()y f x 在R 上严格增，知：函数()y h x 在R 上严格增；所以由②知0,x x 由③知0;x x 故0.x x 故由④得：000()()()0,h x f x f x 即对任意对任意实数0,x 均有000f x f x ；因此，函数()y f x ……18分是奇函数.另证：（3）由()y f x 具有性质P ，知：当0x 时 00f x f ，当0x 时00f x f ，由零点存在定理知 000f f ，即 00f ……12分.下面用反证法证明()y f x 是奇函数.假设存在0x 使得 000f x f x ，不妨设00x ，则由()y f x 在R 上严格增，知000f x f f x .若 000f x f x ，则构造函数00()2f x f x F x f x，00000000(0)222f x f x f f x f f x F f，0000000()22f x f x f x f x F x f x，由零点存在定理知，存在0(),t x 0,使得()0F t ……14分,即000()2f x f x f t f x；而()y f x 在R 上严格增，同样由单调性知00000()()()()102f t f x f x f x t x t x ，从而有00000()()()()102f t f x f x f x t x t x ，与()y f x 具有性质P 矛盾.……16分若 000f x f x ，构造函数00()2f x f x G x f x，同理也可推出与()y f x 具有性质P 矛盾.综合上述，存在0x 使得 000f x f x 的假设不能成立，即对任意R x 都有0f x f x ，故()y f x 是奇函数.……18分。
2023年上海市虹口区中考英语二模试卷(含答案)
2023年上海市虹口区中考英语二模试卷(满分140分,考试时间 90分钟) 2023年5月Part 1 Listening (第一部分听力)I.Listening comprehension(听力理解)(共25分)A. Listen and choose the right picture(根据你听到的内容。
选出相应的图片)(5分)B. Listen to the dialogue and choose the best answer to the question hear (根据你听到的对话和问题,选出最恰当的答案)(5分)6. A)Sunny. B)Cloudy C)Rainy. D)Snowy.7. A)By bike B)By car. C)By bus. D)By underground.8. A)At home. B)At a shop. C)At school D)At a park.9. A)Alice's hobbies B)Alice's favorite booksC)Alice's birthday presents D)Alice's birthday wishes.10.A)Excited B)Bored. C)Interested. D)Worried.C. Listen to the passage and tell whether thc following statements are true or false(判断下列句子是否符合你听到的短文内容，符合的用“T”表示，不符合的用“F”表示)(5分)11.Tony’s father is an engineer who was sent to work in a university last summer.12.Father decided to take Tony with him because it was the school holiday13 Although Tony couldn’t even speak the language of the country,he was keen at first.14.Tony found out that the town was founded in 1971 by some artists and scientists.15.From the passage,we learn that Tony was amazed by this place and began to like it.D. Listen to the passage and complete the following sentences(听短文; 用听到的单词完成下列句子。
2024年上海市虹口区中考二模数学试题(解析版)
虹口区2023学年度初三年级第二次学生学习能力诊断练习数学 练习卷（满分150分，考试时间100分钟）注意：1．本练习卷含三个大题，共25题．答题时，请务必按答题要求在答题纸规定的位置上作答，在草稿纸、本练习卷上答题一律无效．2．除第一、二大题外，其余各题如无特别说明，都必须在答题纸的相应位置上写出证明或计算的主要步骤．一、选择题：（本大题共6题，每题4分，满分24分）［下列各题的四个选项中，有且只有一个选项是正确的，选择正确项的代号并填涂在答题纸的相应位置上．］1. 下列各数中，无理数是（ ）A. B. 3.14159 C. D. 【答案】C【解析】【分析】本题主要考查的是对无理数定义的应用，熟练掌握理解无理数的定义是解此题的关键．根据无理数的定义（无理数是指无限不循环小数）判断即可．【详解】解：A、是分数，不是无理数，故本选项错误；B 、3.14159是小数，不是无理数，故本选项错误；C 是无理数，故本选项正确；D 、是循环小数，不是无理数，故本选项错误；故选C ．2. 关于一元二次方程无实数根，则实数的取值范围是（ ）A. B. C. D. 【答案】D【解析】【分析】根据一元二次方程判别式与根情况的关系，列代数式求解即可．【详解】解：一元二次方程无实数根，的211 1.22111.2x 220x x m -+=m 1m <1m £m 1≥1m >220x x m -+=则判别式解得，故选：D ．【点睛】此题考查了一元二次方程判别式与根情况的关系，解题的关键是掌握相关基础知识，一元二次方程的判别式，当时有两个不相等的实数根，当时，有两个相等的实数根，当时，无实数根．3. 已知二次函数，如果函数值随自变量的增大而减小，那么的取值范围是（ ）A. B. C. D. 【答案】A【解析】【分析】本题考查二次函数的性质，熟练掌握二次函数的增减性是解题关键．根据二次函数，可得函数图象开口向下，对称轴为，函数值随自变量的增大而减小，则，得以解答．【详解】解：二次函数，，函数图象开口向下，对称轴为，时，函数值随自变量的增大而减小，故选：A ．4. 下列事件中，必然事件是（ ）A. 随机购买一张电影票，座位号恰好是偶数B. 抛掷一枚质地均匀的硬币，落地后反面朝上C. 在只装有2个黄球和3个白球的盒子中，摸出一个球是红球D. 在平面内画一个三角形，该三角形的内角和等于【答案】D【解析】【分析】本题考查是必然事件、不可能事件、随机事件的概念．必然事件指在一定条件下，一定发生的事件．不可能事件是指在一定条件下，一定不发生的事件，不确定事件即随机事件是指在一定条件下，可能发生也可能不发生的事件．根据事件发生的可能性大小判断．的()224240b ac m ∆=-=--<1m >()200ax bx c a ++=≠24b ac ∆=-0∆>Δ0=Δ0<()24y x =--y x x 4x ≥4x ≤4x ≥-4x ≤-()24y x =--()24y x =--4x =y x 4x ≥()24y x =--10-< ∴()24y x =--4x =∴4x ≥y x 180︒【详解】解：A 、随机购买一张电影票，座位号是偶数，是随机事件；B 、抛掷一枚质地均匀的硬币，反面朝下，是随机事件；C 、在只装有2个黄球和3个白球的盒子中，摸出一个球是红球，是不可能事件；D 、在平面内画一个三角形，该三角形的内角和等于，是必然事件；故选D ．5. 如图，在正方形中，点、分别在边和上，，，如果，那么的面积为（ ）A. 6B. 8C. 10D. 12【答案】B【解析】【分析】本题主要考查了正方形的性质，平行四边形的性质与判定，先根据正方形的性质得到，进而证明四边形是平行四边形，得到，则，最后根据三角形面积计算公式求解即可．【详解】解：∵四边形是正方形，∴，∵，∴四边形是平行四边形，∴，∴，∴，故选：B ．6. 在中，，．如果以顶点为圆心，为半径作，那么与边所在直线的公共点的个数是（ ）A. 3个B. 2个C. 1个D. 0个．180︒ABCD E F BC AD 2BE =6AF =AE CF ABE 90AD BC AB CD ABE =∠=︒∥，，AECF 6AF CE ==8AB BC BE CE ==+=ABCD 90AD BC AB CD ABE =∠=︒∥，，AE CF AECF 6AF CE ==8AB BC BE CE ==+=1128822ABE S AB BE =⋅=⨯⨯=△ABCD Y 5BC =20ABCD S = C BC C C AD【答案】B【解析】【分析】本题考查了平行四边形的面积，直线与圆的位置关系d 、r 法则，熟练掌握法则是解题的关键．根据面积公式计算点C 到的距离d ，比较d 与半径的大小判断即可．【详解】解：如图，∵在平行四边形中，，，设点C 到的距离为d ，∴点C 到的距离，∴直线与圆C 相交，即有2个交点，故选：B ．二、填空题：（本大题共12题，每题4分，满分48分）［请将结果直接填入答题纸的相应位置］7.=___．【答案】﹣2【解析】【分析】根据立方根的定义，求数a 的立方根，也就是求一个数x ，使得x 3=a ，则x 就是a 的立方根．【详解】∵（－2）3=－8，，故答案为：-28. 分解因式：_______．【答案】【解析】【分析】根据平方差公式因式分解即可求解．【详解】解：AD BC ABCD 5BC =20ABCD S = AD AD 2054d =÷= 45BC<=AD 2-229a b -=()()33a b a b +-229a b -=()()33a b a b +-故答案为：．【点睛】本题考查了因式分解，熟练掌握因式分解的方法是解题的关键．9. 解不等式：，的解集为________.【答案】【解析】【分析】本题主要考查的是解一元一次不等式；按照去括号、移项、合并同类项、系数化为1的步骤解一元一次不等式即可求解．【详解】解：去括号，移项，合并同类项，化系数为1，故答案为：．10. 函数的定义域是 【答案】＞【解析】【分析】定义域是指该函数的自变量的取值范围，根据二次根号下被开方数≥0；分式中分母不为0；即可解答.【详解】定义域是指该函数的自变量的取值范围，二次根号下被开方数≥0；分式中分母不为0；∴∴故答案为11. 将抛物线先向右平移3个单位，再向下平移4个单位后，所得到的新抛物线的表达式为________．【答案】【解析】【分析】本题主要考查的是二次函数的图象与几何变换，要求熟练掌握平移的规律：左加右减，上加下减．并()()33a b a b +-()5232x x +≤+2x ≤()5232x x +≤+5263+≤+x x5362x x -≤-24x ≤2x ≤2x≤y =10x +>1x >-1x >-()221y x =-+()253y x =--用规律求函数解析式．根据平移规律“左加右减，上加下减”写出新抛物线解析式．【详解】解：抛物线先向右平移3个单位，再向下平移4个单位后，所得到的新抛物线的表达式为，即．故答案为：．12. 在一个不透明袋子中，装有2个红球和一些白球，这些球除颜色外其他都一样，如果从袋中随机摸出一个球是红球的概率为，那么白球的个数是________．【答案】6【解析】【分析】本题考查了概率的定义．解题的关键与难点在于理解概率的定义，求出球的总数．随机摸出一个球是红球的概率是，可以得到球的总个数，进而得出白球的个数．【详解】解：设红、白球总共n 个，记摸出一个球是红球为事件A ，，白球有个故答案为：．13. 某校为了解该校1200名学生参加家务劳动的情况，随机抽取40名学生，调查了他们的周家务劳动时间并制作成频数分布直方图，那么估计该校周家务劳动时间不少于2小时的学生大约有________名．【答案】780【解析】【分析】本题主要考查了用样本估计总体，根据条形统计图获取信息是解题的关键．根据条形统计图直接得出家务劳动时间不少于2小时的学生有26名，进而估计该校1200名学生参加家务劳动时间不少于2小时的学生人数即可求解．()221y x =-+()22314y x =--+-()253y x =--()253y x =--0.2520.25n=()20.25P A n==8n ∴=∴826-=6【详解】解：由题意得：被调查的40人中，家务劳动时间不少于2小时的学生有26名，该校周家务劳动时间不少于2小时的学生大约有（名），故答案为：780．14. 一根蜡烛长30厘米，点燃后匀速燃烧，经过50分钟其长度恰为原长的一半．在燃烧的过程中，如果设蜡烛的长为（厘米），燃烧的时间为（分钟），那么关于的函数解析式为________（不写定义域）．【答案】【解析】【分析】本题主要考查由实际问题列一次函数的解析式，解题的关键是理解题意．根据题意先求出蜡烛燃烧的速度为（厘米/分），即可直接进行求解．【详解】解：由题意可得：蜡烛长30厘米，经过50分钟其长度恰为原长的一半，经过50分钟蜡烛燃烧的长度为15厘米，蜡烛燃烧的速度为（厘米/分），蜡烛的长为蜡烛燃烧前长度减去燃烧的长度，，故答案为：．15. 如图，正六边形螺帽的边长是，那么这个扳手的开口的值是______．【答案】【解析】【分析】本题考查解直角三角形，等腰三角形的性质，含角的直角三角形的性质．由螺帽是正六边形，可得是含角的直角三角形，再根据即可求出和．【详解】解：如图，连接,则，过点作于∴26120078040⨯=y t y t 300.3y t=-15500.3÷=∴∴15500.3÷=300.3y t \=-300.3y t =-4cm a 30︒ACD 30︒4AC =AD AB AB a AB =C CD AB ⊥D螺帽是正六边形，,．故答案为：16. 如图，在梯形中，，，点、分别是边、的中点，连接，设，，那么用向量、表示向量________．【答案】【解析】【分析】本题考查了平面向量的问题，熟练掌握三角形法则是解题的关键，根据梯形的中位线定理及向量的三角形法则解答即可．【详解】解：，，，，， 120ACB ∴∠=︒CD AB ⊥AC BC=1120602ACD ∴∠=⨯︒=︒AD BD =4AC = 4AD AC ∴===22a AB AD ∴===⨯=ABCD AD BC ∥2BC AD =E F AB CD AC AB a =AC b = a b EF = 3344a b -+ AB a = AC b =BC BA AC a b \=+=-+ ,2AD BC BC AD = ∥111222AD BC a b \==-+,点、分别是边、的中点，，，，故答案为：．17. 如图，在中，，，．点在边上，，以点为圆心，为半径作．点在边上，以点为圆心，为半径作．如果和外切，那么的长为________．【答案】##【解析】【分析】本题考查的是圆和圆的位置关系、解直角三角形的知识，作于点H ，连接，先求出，设，在中，根据勾股定理列方程即可解决．【详解】解：作于点H ，连接，，，，在中，，11112222DC DA AC AD AC a b b a b \=+=-+=-+=+ E F AB CD 111222EA BA AB a \==-=- 111244DF DC a b \==+ 11111332224444EF EA AD DF a a b a b a b æöæöç÷ç÷\=++=-+-+++=-+ç÷ç÷èøèø3344a b -+ ABCD Y 7AB =8BC =4sin 5B =P AB 2AP =P AP P Q BC Q CQ Q P Q CQ 37149214PH BC ⊥PQ 43PH BH ==，CQ a =Rt QPH △PH BC ⊥PQ 7AB = 2AP =725BP \=-=Rt BPH 4sin 5B =，，设，和外切，半径为2，，在中，，，解得：，故答案为：．18. 如图，在扇形中，，，点在半径上，将沿着翻折，点的对称点恰好落在弧上，再将弧沿着翻折至弧（点是点A 的对称点），那么的长为________．【答案】##【解析】【分析】本题考查翻折性质，圆的基本性质，等边三角形判定与性质、勾股定理的应用，连接，由翻折得，证出是等边三角形，设，在中，根据勾股定理列方程并解出进而求出结论．【详解】解：连接，455PH \=43PH BH \==，CQ a =P Qe Q P 2PQ a \=+Rt QPH △4,835PH HQ a a ==--=-()()222452a a ∴+-=+3714a =3714AOB 105AOB ∠=︒8OA =C OA BOC BC O D AB AD CD 1A D 1A 1OA 8-8-+OD 1105OB BD AC A C BOC BDC ==∠=∠=︒，，OBD AC a =Rt COD AC OD由翻折得：，，，是等边三角形，，，设，则，在中，，，解得：（舍去），，故答案为：．三、解答题：（本大题共7题，满分78分）19.先化简，再求值：，其中．【答案】【解析】【分析】本题主要考查分式的化简求值，分母有理化，掌握分式的基本性质与运算法则是解题的关键，注意化简过程中能因式分解要先因式分解．先算括号内的减法，把除法变成乘法，算乘法，最后代入求值即可．【详解】解：1105OB BD AC A C BOC BDC ==∠=∠=︒，，OC CD =OB OD = OBD ∴△60OBD ∴∠=︒3601051056090OCD \Ð=°-°-°-°=°AC a =1882OC a CD A O a =-==-，Rt COD 8OC CD a ==-()()222888a a ∴-+-=12888a a =-=+>(128288OA OA AC ∴=-=--=8-22214133m m m m m -+⎛⎫÷- ⎪++⎝⎭m 1m m -22214133m m m m m -+⎛⎫÷- ⎪++⎝⎭()()2134333m m m m m m -+⎛⎫=÷- ⎪+++⎝⎭；当．20. 解方程组：【答案】【解析】【分析】将第二个方程进行因式分解得到，然后令因式和因式分别为0即可求解.【详解】解：由题意可知： 对方程②进行因式分解得：即或∴原方程组化为 或 解得或故原方程组的解为：或.【点睛】本题考查了因式分解的方法及二元方程组，熟练掌握常见的二元一次方程组的解法是解决此类题的关键.21. 如图，一次函数图像在反比例函数图像相交于点和点，与轴交于点．点在反比例函数图像上，过点作轴的垂线交一次函数图像于点．()()21133m m m m m --=÷++()()21331m m m m m -+=⨯+-1m m-=m =1m m -222-620x y x xy y =⎧⎨--=⎩121242,22x x y y ==⎧⎧⎨⎨==-⎩⎩()(2)0+-=x y x y 2x y -x y +222-620x y x xy y =⎧⎨--=⎩①②()(2)0+-=x y x y 20x y -=0x y +=2620x y x y -=⎧⎨-=⎩260x y x y -=⎧⎨+=⎩1142x y =⎧⎨=⎩2222x y =⎧⎨=-⎩1142x y =⎧⎨=⎩2222x y =⎧⎨=-⎩(),2A m ()2,4B -y C ()1,D n -D x E（1）求反比例函数和一次函数的解析式；（2）求面积．【答案】（1）反比例函数为，一次函数解析式 （2）【解析】【分析】此题考查了反比例函数综合题，涉及的知识有：待定系数法确定反比例函数和一次函数解析式，三角形面积．（）利用待定系数法求解即可；（）先分别求出、、的坐标，进而利用三角形面积公式解答即可．【小问1详解】解：设反比例函数为，把点代入得，，∴反比例函数为，把点，点代入，得，，∴，，∴点，点，设一次函数解析式，的CDE 8y x=-2y x =--9212C D E k y x=()2,4B -k y x=428k =-⨯=-8y x=-(),2A m ()1,D n -8y x =-82m =-881n =-=-4m =-8n =()4,2A -()1,8D -y cx d =+把点，点代入得，解得，∴一次函数解析式；【小问2详解】∵一次函数解析式，∴把点代入，得，∴，∴点，∵轴，∴点横坐标为，把代入得，∴∴，∴22. 根据以下素材，完成探索任务．探究斜坡上两车之间距离素材1图①是某高架入口的横断面示意图．高架路面用表示，地面用表示，斜坡用表示．已知，高架路面离地面的距离为25米，斜坡长为65米．素如图②，矩形为一辆大巴车的侧面示意图，长为10米，长为的()4,2A -()2,4B -4224c d c d-=+⎧⎨=-+⎩12c d =-⎧⎨=-⎩2y x =--2y x =--()0,2C -,()1,D n -8y x =-881n =-=-8n =()1,8D -DE x ⊥E 1-1x =-2y x =--121y =-=-()1,1E --,189DE =+=119191222CDE S DE =⋅=⨯⨯= .BM AN AB BM AN ∥BM BH AB ECKG CK EC 3.5材2米．如图③，该大巴车遇堵车后停在素材1中的斜坡上，矩形的顶点与点重合，点与指示路牌底端点之间的距离为米，且．小张驾驶一辆小轿车跟随大巴车行驶，小张的眼睛到斜坡的距离为1米．任务一如图①，求斜坡的坡比．问题解决任务二如图③，当小张正好可以看到整个指示路牌（即、、在同一条直线上）时，试求小张距大巴车尾的距离．【答案】任务一：斜坡的坡比；任务二：米【解析】【分析】本题考查的是解直角三角形坡度坡角问题及相似三角形判定与性质，矩形判定与性质，任务一：根据勾股定理求出第三边进而求出坡度；任务二：作交延长线于点O ，作于点Q ，交于点R ，通过解直角三角形结合矩形判定与性质求出相关线段长度，再证明，根据性质求出结论即可．【详解】解：任务一：如图①，由题意得：在中，25米，斜坡长为65米，（米），斜坡的坡比；任务二：如图③，作交延长线于点O ，作于点Q ，交于点R ，为ECKG K B B P BP 6.5BP BM ⊥FD AB P E F EC CD AB 1:2.4i =12.5PO DB ⊥DB FQ PO ^CE FER FPQ ∽Rt ABH △BH AB 60AH \=∴AB 251:2.460BH i AH ===PO DB ⊥DB FQ PO ^CE则四边形为矩形，四边形为矩形，米，米，，为米，，解得：米，米，米，米，，，，，，解得：，经检验，是原方程的解，米．23. 如图，在中，，延长至点，使得，过点、分别作，，与相交于点，连接．CRQO FDCR,1RQ CO FR DC FD CR OQ\=====，3.51 2.5ER\=-=,90ABH PBO O HÐ=ÐÐ=Ð=°BP 6.525cos cos6.565BOPBO ABH\Ð==Ð=2.5BO=6PO\==615PQ∴=-=10 2.512.5RQ CO==+=,EC AB PQ AB^^ER PQ\∥FER FPQ\∽ER FRPQ FQ\=2.5512.5FRFR\=+12.5FR=12.5FR=12.5CD FR\==Rt ABC△90C∠=︒CB D DB CB=A DAE BC∥DE BA∥AE DE E BE（1）求证：；（2）连接交于点，连接交于点．如果，求证：．【答案】（1）证明见解析（2）证明见解析【解析】【分析】本题考查平行四边形的判定与性质，矩形的判定与性质，勾股定理等，解题的关键是掌握平行四边形和矩形的判定方法．（1）先证四边形是平行四边形，得出从而证出四边形是矩形，即可证明结论；（2）设，算出，证明，求出 ，进而证出结论；【小问1详解】证明：，，四边形是平行四边形，，，，又，点D 在的延长线上，，四边形是平行四边形，又，四边形是矩形，；【小问2详解】解：如图，BE CD ⊥AD BE F CE AD G FBA ADB ∠=∠AG AB =AEDB AE CB =AEBC EF BF a ==AE =AEG DCG V ∽△AGAB = AE BD DE BA ∥∴AEDB ∴AE BD = BD CB =∴AE CB = AE BD CB ∴AE CB ∥∴AEBC 90C ∠=︒∴AEBC ∴BE CD ⊥四边形是平行四边形，，设，，，，，，，，，，，在中，，，，在中，，AEDB ,EF BF AF DF \==EF BF a ==FBA ADB Ð=Ð tan tan FBA ADB \Ð=ÐAE BF BE BD\=AE BD = 222AE a \=AE ∴=BD BC AE \==AE CD AEG DCG \ ∽12AE AG CD DG \==Rt DBF △DF ==AD \=AG \=Rt ABC △AB ==．24. 新定义：已知抛物线（其中），我们把抛物线称为的“轮换抛物线”．例如：抛物线的“轮换抛物线”为．已知抛物线：的“轮换抛物线”为，抛物线、与轴分别交于点、，点在点的上方，抛物线的顶点为．（1）如果点的坐标为，求抛物线的表达式；（2）设抛物线的对称轴与直线相交于点，如果四边形为平行四边形，求点的坐标；（3）已知点在抛物线上，点坐标为，当时，求的值．【答案】（1） （2） （3）或【解析】【分析】本题考查的是二次函数综合题，重点考查二次函数的性质、平行四边形性质及相似三角形性质，（1）将点代入表达式，求出m 的值，根据“轮换抛物线”定义写出即可；AG AB \=AG AB \=2y ax bx c =++0abc ≠2y cx ax b =++2y ax bx c =++2231y x x =++223y x x =++1C ()2445y mx m x m =+-+2C 1C 2C y E F E F 2C P E ()0,12C 2C 38y x =+Q PQEF E ()4,M n -2C N 12,72⎛⎫-- ⎪⎝⎭PMN PEF △∽△m 241y x x =+-20,3E ⎛⎫- ⎪⎝⎭1m =-1732()0,1E（2）根据轮换抛物线定义得出抛物线表达式及点E 、F 坐标，并求出P 、Q 坐标，根据平行四边形性质得出列方程并解出m 值，进而解决问题；（3）先求，结合求出的点P 、E 、F 坐标得出及，根据相似三角形性质得出关于m 的方程，解方程即可解决．【小问1详解】解：抛物线：与轴交于点坐标为，当，代入，得，，抛物线表达式为，抛物线的“轮换抛物线”为表达式为；【小问2详解】解：抛物线：，当时，，即与y 轴交点为，抛物线：的“轮换抛物线”为，抛物线表达式为，同理抛物线与y 轴交点为，抛物线对称轴为直线，当时，，抛物线的顶点坐标为，当时，，抛物线的对称轴与直线交点，点在点的上方，，解得：，2C PQ EF =()4,45M m --2PN 2PF 1C ()2445y mx m x m =+-+y E ()0,10x =1y =1m =451m \-=-∴1C 241y x x =-+∴1C 2C 241y x x =+-1C ()2445y mx m x m =+-+0x =y m =()0,E m 1C ()2445y mx m x m =+-+2C ∴2C ()2445y mx mx m =++-2C ()0,45F m -2C 422m x m=-=-2x =-5y =-∴2C ()25P --，2x =-382y x =+=∴2C 38y x =+()2,2Q - E F 45m m \>-53m <，四边形为平行四边形，，即，解得：，；【小问3详解】解：点在抛物线上，当时，，即，点坐标为，，，，，，，，，，解得：．25. 在梯形中，，点在射线上，点在射线上，连接、相交于点，．()4553EF m m m \=--=- PQEF PQ EF \=()2553m --=-23m =-20,3E ⎛⎫∴- ⎪⎝⎭ ()4,M n -2C 4x =-()244545y mx mx m m =++-=-()4,45M m -- N 12,72⎛⎫-- ⎪⎝⎭()25P --，()0,E m ()0,45F m -()222125225724PN æöç÷\=-++-+=ç÷èø()()22222455416PF m m =-+-+=+()115325322PEF P S EF x m m =×=-´=- ()111557242222PMN M P S PN x x æöç÷=×-=´-+´-+=ç÷èø PMN PEF ∽222PEF PMN S PF PF S PN PN æöç÷\==ç÷èø 25341652524m m -+\=12171,32m m =-=ABCD AD BC ∥E DA F AB CE DF P EPF ABC ∠=∠（1）如图①，如果，点、分别在边、上．求证：；（2）如图②，如果，，，．在射线的下方，以为直径作半圆，半圆与的另一个交点为点．设与弧的交点为．①当时，求和的长；②当点为弧的中点时，求的长．【答案】（1）见解析（2）①；；②【解析】【分析】（1）根据等腰梯形的性质可得，，，根据三角形的外角性质得出，进而可得，即可证明，根据相似三角形的性质，即可求解；（2）①同（1）证明，如图所示，过点作于点，连接，得出，，解直角三角形，分别求得，，进而根据相似三角形的性质求得的长；②根据题意画出图形，根据垂径定理得出，根据题意可设，，则，得出，设，则，则，在中，得出，根据得出，即可求解．【小问1详解】证明：∵梯形中，，，∴，，，又∵，∴AB CD =E F ADAB AF DF DE CE =AD CD ⊥5AB =10BC =3cos 5ABC ∠=DA DE O O CE G DF EG Q 6DE =EG AF Q EG AF EG =215AF =15B DCB DCE BCE ∠=∠=∠+∠A EDC ∠=∠DEC BCE ∠=∠FPE CED EDP ∠=∠+∠ADF DCE ∠=∠ADF DCE ∽ADF PDE ∽A AM BC ⊥M DG cos DEC ∠=sin DEC ∠=EG EP AF OQ EQ ⊥EPF ABC α∠=∠=ODQ OQD β∠=∠=90αβ+=︒43tan tan 34αβ==12FR a =9AR a =15AF a =Rt DFR 16DR a =1697AD DR AR a a a =-=-=1a =ABCD AD BC ∥AB CD =B DCB DCE BCE ∠=∠=∠+∠A EDC ∠=∠DEC BCE ∠=∠FPE CED EDP ∠=∠+∠EPF ABC∠=∠ADF DCE∠=∠∴，∴；【小问2详解】解：∵，∵，则∴∴∵∴又∵∴，如图所示，过点作于点，连接，∵，∴，则，，∵∴∵∴又∵∴，在中，∴∴，ADF DCE ∽AF DF DE CE=EPF ABC ∠=∠DPC EPF∠=∠180FPC DPC ∠+∠=︒180FPC B ∠+∠=︒180ECB PFB ∠+∠=︒ECB AFD∠=∠AD BC∥ECB DEC∠=∠EDP FDA∠=∠ADF PDE ∽A AM BC ⊥M DG 5AB =3cos 5ABC ∠=3BM =4AM =4sin 5AM ABC AB ∠==,AD BC AD CD⊥∥4CD AM==10BC =1037AD MC BC BM ==-=-=6DE =1AE=Rt EDC 6,4ED CD ==EC ===cos DE DEC EC ∠===sin DC DEC EC ∠===∵为直径∴∴，∴，∵∴∴②过点作于点，∵∴∵∴设，，则ED 90DGE ∠=︒cos 6EG ED DEC =⨯∠==sin 6DG ED DEC =∠==sin sin DG DG PD DPG ABC ====∠∠3cos 5PG PD DPG =∠==EP EG PG =-=ADF PDE∽AF AD PE PD=215D A PE AF PD ⋅===F FR AD ⊥R EQGQ =OQ EQ⊥OQ OD=ODQ OQD∠=∠EPF ABC α∠=∠=ODQ OQD β∠=∠=90αβ+=︒∵，则设，则∴∵∴设，则，∴，在中，∴又∵∴∴【点睛】本题考查了解直角三角形，等腰梯形的性质，相似三角形的性质与判定，垂径定理，熟练掌握以上知识是解题的关键．3cos os cos 5DPG EPF ABC ∠=∠=∠=35PG PD =3,5PG k PD k ==4GD k =43tan tan 34αβ==AD BC∥RAF α∠=12FR a =9AR a =15AF a =Rt DFR 3tan 4RF DR β==16DR a=1697AD DR AR a a a =-=-=7=1a =15AF =。
2024年上海市虹口区高三下学期等级考试(二模)高效提分物理试题(基础必刷)
2024年上海市虹口区高三下学期等级考试（二模）高效提分物理试题（基础必刷）学校：_______ 班级：__________姓名：_______ 考号：__________（满分：100分时间：75分钟）总分栏题号一二三四五六七总分得分评卷人得分一、单项选择题（本题包含8小题，每小题4分，共32分。
在每小题给出的四个选项中，只有一项是符合题目要求的）(共8题)第(1)题如图所示，在两端开口的U形管中，下部有一段水银柱a，右侧直管内封闭气体上有一段水银柱b、若向左侧直管中沿管壁缓慢注入高为x的水银，则平衡后（ ）A．右侧直管内封闭气体的压强减小B．右侧直管内封闭气体的体积减小C．水银柱a两侧水银面的高度差增加D．水银柱b升高第(2)题关于物理学史或物理知识在生活中的应用，下列说法正确的是（ ）A．安培在实验中首先发现电流的磁效应，揭开了电生磁的科学之门B．停在高压线上的小鸟没有被电击，是因为小鸟两脚间的电势差几乎为零C．宇航员王亚平在太空实验授课中，水球可以悬浮在空中，是因为水球不受任何外力而平衡D．牛顿通过理论和实验相结合，第一个推翻了亚里士多德之“重的物体比轻的物体下落快”的观点第(3)题用手上下抖动绳的一端，产生一列向右传播的横波，其中、、、、是绳上的五个质点，某时刻这列波恰好传播到点，如图所示。
此时质点在平衡位置，质点、、偏离平衡位置的位移大小相等，下列说法正确的是（ ）A．手开始抖动的方向竖直向上B．质点、的位移始终相等C．这五个质点中，最先到达波峰的质点是D．这五个质点中，最先到达波谷的质点是d第(4)题打印机正常情况下，进纸系统能做到每次只进一张纸，进纸系统的结构示意图如图所示，设图中刚好有20张相同的纸，每张纸的质量均为m，搓纸轮按图示方向转动带动最上面的第1张纸向右运动。
搓纸轮与纸张之间的动摩擦因数为，纸张与纸张之间、纸张与底部摩擦片之间的动摩擦因数均为，工作时搓纸轮给第1张纸压力大小为F。
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虹口区2012年英语学科中考练习题（满分150分，考试时间100分钟）2012.4考生注意：本卷有7大题，共99小题。
试题均采用连续编号，所有答案务必按照规定在答题纸上完成，做在试卷上不给分。
Part 1 Listening (第一部分听力)I. Listening Comprehension (听力理解): (共30分)A. Listen and choose the right picture (根据你听到的内容，选出相应的图片): (共6分)A B CD E F G1. ______2. ______3. ______4. ______5. ______6. ______B. Listen to the dialogue and choose the best answer to the question you hear (根据你听到的对话和问题，选出最恰当的答案): (共10分)7. A) Eggs. B) Noodles. C) Bread D) Cheese.8. A) Playing tennis. B) Cycling. C) Swimming. D) Fishing.9. A) By bus. B) By bike. C) On foot. D) By underground.10. A) She’s watching TV. B) She’s listening to music.C) She’s having a test. D) She’s going over her lessons.11. A) 2. B) 3. C) 4. D) 5.12. A) In a department store.B) At a booking office. C) At a library.D) In a restaurant.13. A) At 9:00. B) At 9:30. C) At 10:00. D) At10:30.14. A) Because bears are lovely animals. B) Because bears are funnier than monkeys.C) Because she’s heard the terrible story. D) Because she’s fond of poorthings.15. A) Teacher and student. B) Doctor and patient.C) Driver and passenger. D) Policeman and tourist.16. A) The boy’s father will keep his promise. B) It’s difficult to make sucha promise.C) She exactly remembers the times. D) The boy’s father won’t give upsmoking.C. Listen to the passage and tell whether the following statements are true or false(判断下列句子是否符合你听到的短文内容，符合的用“T”表示，不符合的用“F”表示): (共7分)17. Harry was outside his bedroom when he saw the robber(抢劫者).18. The robber took off his mask(面罩), so Harry saw his face clearly.19. Harry even knew that there was something wrong with the robber’s leg.20. The robber robbed many things including black jeans and a lady’s stocking.21. With Harry’s help, the police managed to catch the robber the next day.22. The policeman said “Well done” to Harry after he pointed out the robber easily.23. Form the passage we can know Harry was a boy who observed very carefully.D. Listen to the dialogue and complete the following sentences（听对话，完成下列内容。
每空格限填一词）:（共7分）24. Penny’s new book is for young children, about ______ years old.25. Children love Captain Fish-Eye and his amazing ______.26. Children don’t feel it’s boring to read the ______ stories.27. Young children need books with ______ colourful pictures.28. When children read stories, they see pictures in their ______.29. In Penny’s opinion, children in ______ read much more than children in many othercountries.30. There, in most families, children listen to a story before they go to ______.Part 2 Vocabulary and Grammar (第二部分词汇和语法)II. Choose the best answer (选择最恰当的答案): (共20分)31. —Do you know ________ lady in blue?—Yes. She is a teacher of a university.A) a B) an C) the D) /32. The poor couple dreamed of having a flat of ________ own some day in the future.A) they B) them C) their D) theirs33. All the boys went swimming that afternoon ________ Bob because he had a cold.A) except B) including C) besides D) with34. You needn’t tell me about this. ________ sent me a message about it three days ago.A) No one B) Anyone C) Someone D) Everyone35. How much ________ do you need to make dumplings for the family and the guests?A) potato B) pork C) egg D) vegetable36. The story in the newspaper sounds ________, but where did the woman journalist get it?A) well B) true C) loudly D) properly37. Since Jennifer is ________ girl in the class, you can find her easily in the classroom.A) tall B) taller C) tallest D) the tallest38. Dr. Sitwell took up the project on water pollution with several assistants in her ________ .A) sixty B) sixties C) sixtieth D)sixtieths39. You may fail to pass the examination ________ you do your best to go over the lessons.A) after B) because C) unless D) when40. Only you ________ do such a thing, I’m sure, and nobody else has such an ability.A) must B) should C) may D) can41. James, Catherine and I ________ friends since we were at the same primary school.A) am B) were C) will be D) have been42. My uncle will send me some local postcards and stamps after he ________ France.A) reaches B) reached C) will reach D) is reaching43. The aged people in the community ________ their eightieth birthday together last week.A) celebrate B) celebrated C) will celebrate D) have celebrated44. Don’t let such a thing happen again, ________ you will lose your job!A) and B) but C) or D) so45. He used to be a good movie director but nowadays he is only busy ________ money.A) make B) made C) to make D) making46. The mother always encouraged her baby ________ up by himself when he fell over.A) stand B) stood C) to stand D) standing47. ______ amazing performance the boy gave in the Talent Show yesterday evening!A) How B) What C) What a D) What an48. Both my husband and I think it is the most amusing story we have ________ heard.A) ever B) never C) hardly D) already49. —The music is too loud. Could you turn it down, please?—________.A) Sure, what time? B) Sorry, I didn’t notice it.C) Well, me too. D) OK, go ahead.50. — Would you like me to take a photo of you in front of the church?—________A) Yes, please. B) Well done. C) Yes, I would. D) With pleasure.III. Complete the following passage with the words or phrases in the box. Each wordcan only be used once（将下列单词或词组填入空格。