2021学年余姚中学自主招生模拟试卷
浙江省宁波市余姚实验中学2020-2021学年高三语文模拟试题含解析
浙江省宁波市余姚实验中学2020-2021学年高三语文模拟试题含解析一、现代文阅读（35分，共3题）1. 阅读下面的文字，完成各题。
①文化自信不仅在于自己的决心有多大，声音有多高，历史有多久，还在于人家是否信服，有没有“他信”。
在当今时代，面对大发展大变革的世界格局，面对各种思想文化更加频繁的交流、交融、交锋，谁占据了文化发展的制高点，谁就能够更好地在激烈的国际竞争中掌握主动权。
②近些年来，西方学术界逐渐认识到，人类中心主义是导致包括生态危机在内的全球性危机的罪魁祸首。
人类中心主义以人的利益为认识、实践的出发点和归宿，认为自然的价值在于其对人类的有用性，而没有给予自然足够的人文关怀。
生态思想家帕斯莫尔认为，基督教鼓励人们把自己当作自然的绝对主人，对人来说所有的存在物都是为他安排的。
这正是当今西方文化的死穴。
人类文明今天已走到由量变到质变的临界点，克服人类中心主义成为人类文明发展的当务之急。
英国历史学家汤因比指出：避免人类自杀之路，在这一点上现在各民族中具有最充分准备的，是两千年来培育了独特思维方法的中华民族。
什么是“独特思维方法”？就是以“中”为度、以“和”为贵。
《中庸》有云:“中者，天下之大本也；和者，天下之达道也。
”“中”“和”二字是中华文化的精髓所在。
③在如何摆正人与自然关系方面，中华文化积累了丰富的中道智慧，是克服人类中心主义的一剂良方。
中华文化一方面注重人在天地之间的地位与作用，强调“惟人，万物之灵”；另一方面注重天地本身的价值，所谓“人法地，地法天，天法道，道法自然”，认为人必须遵从自然规律。
中华文明之所以能成为数千年未曾中断的文明，根源正在于“顶天立地”、中正通达，正在于我们将“与天地参”而不是将征服自然、改造天地、满足欲望作为人类的使命，正在于我们摆正了人在天地之间的位置。
④在中国的传统文化中，我们都把“和”视作天下之大道，希望万国安宁、和谐共处。
当今中国倡导建构人类命运共同体，坚持在追求自身利益时兼顾他方利益，在寻求自身发展时促进共同发展。
浙江省余姚市小曹娥镇初级中学2021届九年级3月自主招生联考科学试题
浙江省余姚市小曹娥镇初级中学【最新】九年级3月自主招生联考科学试题学校:___________姓名：___________班级：___________考号：___________一、选择题1．由CO、HCOOH和H2COHOOH三种物质混合的蒸汽中，测得其中H元素的质量分数为a，则混合物中碳元素的质量分数为（）A．2(1-9a)/7B．2(1-7a)/9C．1-7a D．3(1-9a)/7 2．下表记录了t℃时4份相同的硫酸铜溶液中加入无水硫酸铜的质量以及析出的硫酸铜晶体（胆矾）的质量（温度维持不变）的实验数据。
当加入4.6g无水硫酸铜时，析出硫酸铜晶体的质量为（）A．3.42g B．3.88g C．6.82g D．2.56g3．有在空气中暴露过的KOH固体，经分析知其中含H2O 7.32%， K2CO3 2.48%，KOH 90.2%。
若将此样品W(g)克加入到98g20%的稀硫酸中，过量的酸再用20g10% 的KOH溶液中和，恰好完全反应。
将中和后溶液蒸发，可以得到的固体质量是（）A．17.4 g B．30.8 g C．34.8 g D．30.8——34.8 g 4．如图所示电路中，电源为恒流源，能始终提供大小恒定的电流，R0为定值电阻，移动滑动变阻器R的滑片，则下列表示电压表示数U、电路总功率P随电流表示数I变化的关系图线中，可能正确的是（）A．B．C．D．5．如图是一个足够长，粗细均匀的U形管，先从A端注入密度为ρA的液体，再从B端注入密度为ρB、长度为L的液柱，平衡时左右两管的液面高度差为L/2。
现再从A端注入密度为ρC液体，且ρC =1/2ρB，要使左右两管的液面相平，则注入的液柱长度为( )A．2L/3 B．3L/4 C．4L/5 D．L6．如图所示，密度分布均匀的圆柱形棒的一端悬挂一个小铁块并一起浸入水中。
平衡时，棒浮出水面的长度是浸在水中长度的n倍。
若水的密度为ρ，则棒的密度为（）A．11nρ+B．1nnρ+C．()211nρ+D．()221nnρ+二、填空题7．利用伏安法测量电阻时，由于使用的不是理想电表，造成测量结果有误差。
浙江省余姚中学高三语文选考科目模拟卷(一)
浙江省余姚中学2021年高三语文选考科目模拟卷〔一〕一、语言文字运用3分〕〔共20分，其中选择题每题1.以下各句中，没有错别字且加点的字的注音全都正确的一项为哪一(3项分〕A.卡尔纽波特在他的?深度工作?中表达了对于网络的批判，也展示了对于当代人“互联网化生存〞的担忧。
以此形成一个不良后果，人们总是在做一些不痛不痒(yáng)的浅薄工作，形成一种毫无价值的“外表性忙碌〞。
B.这是一个荒唐〔miù〕的螺旋，它无非验证了人类是多么脑子不清楚的生物。
对于未有之物心向往之，对于已有之物嗤之以鼻。
每一次对当下的无视，都是在糟塌这个不断流逝的当下。
每一次思绪上的分裂，都在暗示一件事：那个人从未真正拥有过他的生命。
C.雪越来越大。
棉絮般的雪花旋转〔zhuǎn〕着飘落下来。
透过雪层，阿隆靴子触到一大块新翻过的松软的土地。
他敏感地感觉到他们迷路了，而且也分不清东西南北了。
D.每个人都是自己“人生回忆片〞的导演和剪缉。
未来的人生你预期不了，过往的日子你却可以自我编排诠释：你可以把回忆像美丽的珍珠串起来，或者把它当成石头，不断地扔掷自己，直到遍体鳞(líng)伤。
阅读下面的文字，完成后面2—3题。
【甲】张爱玲是上海滩那一辈小说家中最早奇装异服，肖像上画报，宣传自己的女文人。
这种附庸群众文化的炒作，自非革命文学家愿意干的事。
她晚年孤寂，与少女时成名趁早、．．红唇时髦成了极大比照。
【乙】如果张爱玲一开始采取的不是画报型的宣传策略，走个严肃路线，她的文学是否仍拥有今日相同的经典地位？张爱玲本人与作品都成了传奇，互为叠印，世要够乱，才能出佳人。
那个战火中唯一最无国仇家恨、只求纸醉金迷的上海孤岛，出现一名明哲保身的乱世佳人，恻然轻怨的文字，．．．．竟给以了中国人在战火中避世的唯一的慰藉。
．．．．香奈儿出身比张爱玲穷困，也因此更没有道德包袱。
一切只为了表现她们的旷世奇才，除此之外别无生存准那么。
【丙】这两个女人皆活在大萧条时代，乱世里经营自己，有时也被逼到不择手段的地步。
浙江省余姚市余姚中学高中自主招生考试 化学模拟试题
浙江省余姚市余姚中学高中自主招生考试化学模拟试题一、选择题CaCl、KCl的固体混合物，可选用的一组试剂是1．分离2A．水、硝酸银、盐酸B．水、碳酸钠、盐酸C．水、碳酸钾、硫酸D．水、碳酸钾、盐酸2．氧烛是一种便携式供氧设备(如下图)。
产氧药块由氯酸钠(分解时吸收热量为QkJ·g-1)、金属粉末(燃烧时提供氯酸钠分解所需的热量)和少量催化剂组成。
某兴趣小组拟自制氧烛，火帽为确定每100g氯酸钠需要添加金属粉末的质量[m(金属)]，查得下表数据：金属铁铝镁燃烧放出热量/（KJ•g-1） 4.7331.0224.74下列说法正确的是A．m(金属)只能采用不同比例的金属和氯酸钠在空气中实验获得B．m(金属)只能通过氯酸钠分解吸收热量与金属燃烧放出热量进行理论药块计算确定C．m(金属)过小将使氧烛中反应无法持续进行，过大将减小产氧量D．不用催化剂时，分别使用铁、铝、镁作燃料，m(Fe)最小3．将铝和镁组成的混合物 10g 加入到 200g 稀盐酸中恰好完全反应后得到溶液 209g，再向溶液中加入足量的氢氧化钠溶液，最终生成沉淀的质量为（）A．12g B．14.25g C．17.25g D．27g4．下列曲线正确的是A．向盐酸中加水B．浓H2SO4加入水中C．煅烧CaCO3D．O2在水中的溶解性5．甲烷和水反应可以制备水煤气（混合气体），其反应的微观示意图如图所示，根据微观示意图得出的结论中，正确的是（）A．反应前后碳元素化合价没有发生变化B．反应中甲和丙的质量之比为4：7C．水煤气的成分是一氧化碳和氧气D．反应中含氢元素的化合物有三种6．将10g氧化铜粉末加入到100g一定质量分数的稀硫酸中，微热到氧化铜全部溶解，再向溶液中加入ag铁粉，使溶液中的溶质完全反应后，过滤，将滤渣在低温下烘干，得到干燥固体质量仍然为ag，下列分析不正确的是A．稀硫酸中溶质质量分数为12.25%B．滤渣中一定含有铜，可能含有铁C．加入铁粉后有红色固体产生，还有少量气泡产生D．a的取值范围：a≥87．有NaHCO3与NaCl的混合物20.0g，加热一段时间，得剩余固体16.9g。
2020-2021学年宁波市余姚中学高三英语模拟试卷及参考答案
2020-2021学年宁波市余姚中学高三英语模拟试卷及参考答案第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30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AFour Online EventsThe handshake：an anthropologist’s guideWhat is its biological purpose？What are the best and worst handshakes？In this talk，scientist Ella Al-Shamahi examines the power of touch and argues the handshake is at least 7 million years old．This event will start at 18:00 pm on 25 March and will last one hour．Standard ticket price：£15(A 20％discount for those who buy the ticket before March 20.)A rescue plan for natureWhat do we need to do to restore the planet 's biodiversity and preventthe next pandemic (疫情)？Join scientist Cristian Samper as he talks about how our ignoring nature caused the pandemic-and how we can seize a unique opportunity to build back better．This free event will start at 18:00 pm on 15 April．Origins of lifeWhy is the planet the way it is？How did we get here？Does everything happen for a reason or are some things left to chance？Research shows we live in a world driven by chance．In this talk，biologist Sean B Carroll will tell the stories of the mother of all accidents，and the surprising power of chance in our lives and the world．This event will start at 19:30 pm on 22 April and will last two hours．Standard ticket price：£18(A 10％discount for those who buy the ticket before April 17.)The truth about exerciseShould we all be hitting the gym three times a week？Should we worry about sitting to omuch？If you are strong and fit，can you get away with being inactive？In this talk，specialist Jason Gill introduces what science can really tell us about how much we need to move to live a healthy life．This event will start at 19:00 pm on May 13 and will last one hour，Standard ticket price：£12(A 15％discount for those who buy the ticket before May 8.)1.How much should you at least spend on the event about the handshake？A.£10.2．B.£12．C.£13．D.£16.2．2.From whom can you learn about the origins of life？A.Ella Al-Shamahi．B.Cristian Samper．C.Sean B Carroll．D.Jason Gill．3.What does the four online talks have in common？A.They are science-based．B.They are about cultures．C.They are related to nature．D.They are intended for the young．BA former UPS driver and his wife have made history by donating $20 million to Morgan State University – the largest gift any historically black college or university (HBCU) has ever received from a former student. The money, pledged by Calvin Tyler Jr and his wife Tina, will fund scholarships that were established under the Tylers’ name in 2002.Tyler grew up in a low-income family and was forced to drop out of Morgan State University in 1963 because he could no longer afford to study. The following year, Tyler saw a job advertisement in a Baltimore newspaper from United Parcel Service and got a job with the company as a driver. He rose through the ranks during his 34-year career at the global shipping company to become its senior vice president of US operations and a member of the board of directors before retiring in 1998.Tyler and his wife, also a Baltimore native, have lived all across the country but he said they have never forgotten their humble beginnings.Their latest pledge follows a $5million commitment they made in 2016 for the fund, which to date has supported 222 students with full or partial scholarships.Marybeth Gasman, a professor at Rutgers University who studies HBCUs, said the gift is significant because public HBCU’s like Morgan State University tend to have a lower alumni giving rate compared to private ones.“For a long time, they weren’t asking alumni to give,” she said. But that has changed in the past couple of decades, she added, and the schools have “started asking alumni to give and creating a culture of philanthropy (慈善) on campus.”David K. Wilson, the president of Morgan State University, said the money will help students for years to come. “Morgan is so proud to call this son and daughter of the great city of Baltimore our own,” he said in a statement. “Through their historic giving, the doors of higher education will most certainly be kept open for generations of aspiring leaders whose financial shortfalls may have kept them from realizing their academic dreams.”“We are forever indebted to the Tylers”.4. Why is Tyler’s donation historic?A. He was a former UPS driver.B. The donation is large enough.C. The donation will fund his scholarships.D. He used to be a student at the university.5. What is a driving force of Tyler’s donation?A. His working experiences.B. His career achievements.C. His promise to the university.D. His past embarrassing situations.6. Which is true about HBCUs according to Gasman?A. They are mainly public universities.B. They are encouraging alumni to donate.C. They rarely accept help from the alumni.D. They have changed little over the decades.7. What can be inferred about Tyler from Wilson’s comments?A. He’s helped many city leaders.B. He’s grateful to his university.C. He’s made great contributions.D. He’s proud of his son and daughter.CThe history of the flying car is almost as old as that of powered flight itself. It started with the Curtiss Autoplane of 1917, an awkward-looking machine with removable wings. It never left the ground. Later machines made it into the skies but failed to take off commercially. Money is now pouring into flying taxis. On March 30th Lilium, a German company that develops them, announced a merger with SPAC, an acquisition company that values it at $3. 3 bn -- a sign that investors think the business will fly.Thanks to better batteries and lightweight materials, some of them are ready to carry passengers. Up to 300 firms are working on short-range battery-powered craft that take off and land vertically. Carmakers, tech companies and others are investing money into the field. The government isoffering a glide pathto certification.America's Federal Aviation Administration is engaged in the process with around 30 firms, says Natasha Santha of LEK, a consulting company.Midway between a cab and a helicopter, flying taxis have distinct advantages over both. Quiet electric motors allow them to operate frequent services. They require only a patch of concrete to land, unlike noisy helicopters, which face severe operating restrictions in most cities. They can fly four or five times faster than a cab can drive and do not get stuck in traffic. Prices can be kept low by ride-sharing. Joby, based inCalifornia, says its five-seatermachine will enter commercial service in 2024. The firm calculates the initial cost of around $4 per person per mile may soon fall by 25%. A trip fromManhattanto JFK airport would then cost $30-40 per passenger.The real revolution will come when full autonomy takes out the cost of a pilot. Archer hopes to run such aircraft by 2028. They face fewer obstacles in the air than earth-bound cars do on the road; airliners mostly fly on autopilot as it is. Still, as one industry insider puts it, it is probably best to accustom passengers and regulators to airborne taxis before getting rid of the driver.8. What can we learn from Paragraph 1?A. The flying car can date back to the 1920s.B. Investors see the potential of the business of the flying car.C. The flying car never left the ground successfully in history.D. A German company has launched a new flying car into the market.9. What does "offering a glide path" in Paragraph 2 probably refer to?A. Giving the green light.B. Providing timely assistance.C. Presenting legal guidance.D. Conducting strict management.10. Which of the following is the strength of flying taxis?A. Costing as little as cabs.B. Saving passengers from the traffic jam.C. Reducing air pollution.D. Having no operating restrictions.11. What can be inferred about the flying taxis from the last paragraph?A. They will develop faster than cars.B. Passengers will quickly get used to taking them.C. The regulators will take measures to promote them.D. Autopilot flying taxis will probably replace those with pilots.DAsk a classroom of children to draw a scientist, and you’ll see plenty of color1 ed lab coats and glasses. The image (画像) hasn't changed much since the 1960s, but the person wearing the lab coat is changing.A new analysis finds that more female scientists have appeared in kids? drawings in recent decades — going from nearly nonexistent in the 1960s to about a third in 2016.The first of many “ draw-a-scientist ’’ studies asked nearly 5,000 children to draw a scientist between 1966 and 1977. Of those 5,000 drawings, only 28 drew female scientists. That was just 0.56 percent. Today, female scientists are being presented more in the media. For example, in a content analysis, 13 percent of peoplepictured in science feature stories of the 1960s were women or girls, compared with 44 percent in the 2000s. “That might really affect children’s idea on what a scientist should be like, ” says Miller, a Ph. D. candidate in psychology.To look for changes in children'sperceptionover time, the researchers conducted a meta-analysis ,combining data from 78 studies that included a total of more than 20,000 children from kindergarten to the 12th grade.On average, 28 percent of children drew female scientists in studies conducted from 1965 to 2016.What hasn’t changed much: kids pick up stereotypes (模式化观念）by gender (性别）as they grow up. At age 6, about 70 percent of the girls in the more recent studiesdrew female scientists. By age 16, 75 percent drew male scientists. This is an important period in which kids are learning stereotypes. It’s important that teachers and parents present diverse examples of both male and female scientists.12. What’s the picture of scientists drawn by a 1960s, kid like?A. A man with long curly hair.B. A woman with lab glasses.C. A woman in a formal lab suit.D. A man in a color1 ed lab coat.13. What may contribute to the changes in kids’ drawings?A. The improvement of women^ social status.B. The kids are affected by teachers and parents.C. More female scientists appear in the media.D. The increasing number of female scientists.14. What does the underlined word “ perception” in Paragraph 4 most probably mean?A. Belief.B. Idea.C. Habit.D. Growth.15. It can be inferred from the last paragraph that .A. it's a stereotype that scientists are generally malesB. girls are more influenced by stereotypes than boysC. some children are born with certain stereotypesD. most children tend to prefer female scientists第二节（共5小题；每小题2分，满分10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。
余姚提前招生英语试卷
浙江省余姚中学自主招生英语模拟试题卷总分：100分时间：70分钟一、单项选择（20分，共20小题）1. You’d better take this sweater. It’s very good _____it’s a bit expensive.A. butB. andC. thoughD. so2. Until he told me yesterday, I know ______of what happened to him.A. everythingB. anythingC. nothingD. something3. After the weather _____ fine for three days, it rained again.A. seemedB. lookedC. becameD. stayed4. For David, this was the beginning of a new life, ______ he thought he would never see.A. thatB. whatC. itD. one5. ---- Could you help me post the letter? ---- _______, but I’m quite busy.A. I’d love toB. I think soC. I hope soD. I’m afraid6. It was _____ back home after the experiment.A. not until midnight did he goB. until midnight that he didn’t goC. not until midnight that he wentD. until midnight when he didn’t go7. ---- Who closed the door? ---- Nobody. It ________.A. was closed by itselfB. had closed itselfC. was closed itselfD. closed itself8. ---- How do you like that dress? ---- Very much. It _____ soft and nice.A. feelsB. is feltC. is feelingD. felt9. ---- Do you know Mary quarreled with her mother? ---- I don’t know, _________.A. nor don’t I careB. nor do I careC. so do I careD. I don’t care neither10. The old man dropped the ______ and broke it.A. cup of coffeeB. coffee’s cupC. cup for coffeeD. coffee cup11. ---- Thank you for seeing me off. ----________.A. Never mindB. See you laterC. Have a good journeyD. Don’t say so12. High school is _______ time of discovery and learning, and it is also _______ very enjoyable andvaluable experience for every one of us.A. a, aB. a, /C. /, aD. a, the13. --- People have reported seeing a wild man-like creature in the Himalayas called a Yeti.--- Did you see _______ when you were traveling there?A. itB. oneC. thatD. them14. With snow-covered mountains, lakes and vast grasslands, Shangri-la is a heavenly world _______people live in harmony with nature.A. thatB. in thatC. whereD. which15. --- I hear that Amy is trying to lose weight by taking weight-loss pills.--- In my opinion, looking good is important, but _______, staying healthy is far more important.A. after allB. in allC. at allD. above all16. The concert will begin soon, so Rose _______the other performers ______ busy getting everythingready.A. as well as; isB. and; isC. as well as; areD. with, are17. Maria is said ______on a novel these days. She plans to finish it next month.A. to workB. workC. to be workingD. working18. –--- What are you reading, Tom? ---- I’m not really reading, just ___ the pages.A. turning offB. turning aroundC. turning overD. turning up19. Modern equipment and no smoking are two of the things I like ____ working here.A. withB. overC. atD. about20. She is looking forward as much to his return as he himself to ________ her.A. have seenB. seeingC. seeD. seen二、完形填空（15分，共15小题）From the time each of my children started school, I packed their lunches. And in each lunch, I ___21___ a note. Often written on a napkin , it might be a thank-you for a special moment, a reminder of something we were happily expecting, or a bit of __22___ for the coming test or sporting event.In early grade school they loved their notes. But as children grow older they becomes self-conscious(有自我意识的), and __23____ he reached high school, my older son, Marc, informed me he no longer 24 my daily notes. Telling him that he no longer needed to read them but I still needed to write them, I _25___until the day he graduated.Six years after high school graduation, Marc called and asked if he could move __26__ for a couple of months. He had spent those years well, graduating from college,___27___ two internship (实习) in Washington, D.C., and 28 , becoming a technical assistant in Sacramento, 29 short vacation visits, however, he had lived away from home. With his younger sister leaving for college, I was 30 happy to have Marc back. Since I was still making lunch for his younger brother, I 31 one for Marc, too. Imagine my 32 when I got a call from my 24-yere-old son, 33 his lunch.“Did I do something 34 ? Don’t you love me any more ,Mom?” were just a few of the questions he threw at me as I __35 asked him what was wrong.“My note, Mom,” he answered. “Where’s my note?”21. A. carried B. found C. included D. held22. A. congratulation B. improvement C. explanation D. encouragement23. A. lately B. by the way C. by the time D. gradually24. A. received B. understood C. enjoyed D. collected25. A. held up B. gave up C. followed D. continued26. A. out B. home C. to college D. to Sacramento27. A. organizing B. planning C. comparing D. completing28. A. hopefully B. finally C. particularly D. certainly29. A. Because of B. Instead of C. Except for D. As for30. A. especially B. immediately C. equally D.generally 31. A. packedB. fetchedC. boughtD. filled32. A. fear B. surprise C. anger D. disappointment33. A. waiting for B. worrying about C. caring for D. asking about34. A. wrong B. funny C. strange D. smart35. A. interestingly B. bitterly C. politely D. laughingly三、阅读理解（40分，共20小题）AMany teenagers feel that the most important people in their lives are their friends. They believe that their family members, espe cially their parents, don’t know them as well as their friends do. In large families, it is often for brothers and sisters to fight with each other and then they can only go to their friends for advice. It is very important for teenagers to have one good friend or many friends. Even when they are not with their friends, they usually spend a lot of time talking among themselves on the phone. This communication is very impor tant in children’s growing up, because frien ds can discuss something difficult to say to their family members.However, parents often try to choose friends for their children. Some parents may even stop their children from meeting their good friends. The question of “choice” is an intere sting one. Have you ever thought of the following questions?Who chooses your friends?Do you choose your friends or your friends choose you?Have you got a good friend your parents don’t like?36. Many teenagers think their _________ know them better than their parents do.A. friendsB. teachersC. brothers and sistersD. classmates37. When teenagers stay alone, the usual way of communication is to _________.A. go to their friendsB. talk with their parentsC. have a discussion with their familyD. talk with their friends on the phone38. Which of the following sentences is TRUE?A. Teenagers can only go to their friends for help.B. Parents should like everything their children enjoy.C. In all families, children can choose everything they like.D. Parents should try their best to understand their children better.39. What is important in children’s growing up?A. Parents’ love.B. The communication with friends.C. Education in school.D. we don’t know.40. The main idea of this passage is that _________.A. Teenagers need good friendsB. Friends can give good adviceC. Parents often choose friends for their childrenD. Good friends can communicate with each otherBThere was a story many years ago of a school teacher--- Mrs. Thompson. She told the children on the first day that she loved them all the same. But that was a lie. There in the front row was a little boy named Teddy Stoddard. He didn’t play well with th e other children and he always needed a bath. She did not like him.Then Mrs. Thompson got to know that Teddy was actually a very good boy before the death of his mother. Mrs. Thompson was ashamed of herself. She felt even worse when, like all her other students, Teddy brought her a Christmas pr esent too. It was his mother’s perfume(香水)。
浙江省余姚市余姚中学高中自主招生考试 化学模拟试题
浙江省余姚市余姚中学高中自主招生考试化学模拟试题一、选择题1．如图所示图像中，能正确反映对应变化关系的是（）A B C D向饱和石灰水中加入一定量CaO一定温下，向不饱和硝酸钾溶液中加入硝酸钾固体一定质量的红磷在密闭容器内燃烧电解水生成氢气和氧气质量A．A B．B C．C D．D2．如图是A、B、C三种固体物质的溶解度曲线，下列分析正确的是（）A．20℃时等质量的A和C两种物质的溶液中溶质的质量相等B．50℃时把50gA放入100g水中能得到A的饱和溶液，其溶质质量分数为50%C．将50℃时A、B、C三种物质的饱和溶液都降温至20℃时，这三种溶液的溶质质量分数的大小关系是B＞A＝CD．将C的饱和溶液变为不饱和溶液，可采用降温的方法3．除去下列物质中所含杂质(括号内为杂质)，所选用试剂及操作方法均正确的一组是选项物质选用的试剂操作方法A CO2(HCl)NaOH溶液洗气B FeSO4溶液(CuSO4)Al粉加过量Al粉，过滤C KNO3溶液(KOH)CuSO4溶液过滤，蒸发结晶D CaCl2溶液（HCl）CaCO3加入过量的CaCO3，再过滤A．A B．B C．C D．D4．下列各组转化中，一定条件下均能一步实现的组合是A．①②B．①③C．②③D．①②③5．将等质量的镁和铁分别放入等质量、相同质量分数的稀盐酸中，产生氢气的质量与反应时间的关系如图所示，下列说法错误的是（）A．反应结束后镁一定有剩余B．反应消耗盐酸的总质量一定相等C．O—t1时段，产生氢气的质量镁比铁大D．O—t2时段，参加反应的镁的质量与铁相等6．归纳总结能使知识系统化，有利于提高素质和能力，下面是一同学对部分化学知识的归纳，其中都正确的一项是A．A B．B C．C D．D7．下列实验方案，不能．．达到实验目的的是选项实验方案实验目的A分别取气体样品，倒入澄清石灰水比较二氧化碳气体含量B分别取少量液体，各加入二氧化锰鉴别水和过氧化氢溶液C 取一个注射器，吸入一定体积氮气，堵住针筒小孔，将活塞慢慢推入证明分子间存在间隔D分别取样品，滴加足量稀盐酸鉴别碳酸钠溶液和水A．A B．B C．C D．D8．除去下列物质中的少量杂质，所选用的试剂及操作方法错误的是选项物质(括号内为杂质)试剂操作方法A CO（CO2）氧化铜将气体通入灼热的氧化铜B FeCl2 (CuCl2溶液)过量铁粉搅拌、过滤C CuO(炭粉)不用外来试剂在空气中灼烧D Cu粉（Fe粉）足量稀盐酸过滤、洗涤、干燥A．A B．B C．C D．D9．一包固体粉末可能含有NaNO3、CaCO3、NaOH、CuCl2、NaCI和Ca(NO3)2中的一种或几种.为确定其组成，某同学设计了如下实验方案.下列判断正确的是A．该混合物中一定含有CaCO3、NaOH、CuCl2、Ca(NO3)2B．蓝色溶液B的溶质有2种C．无色溶液A呈中性D．该混合物中一定含有NaCI可能含有NaNO310．下列图像能正确反映其对应操作中各量变化关系的是A．图①是给氯酸钾和二氧化锰的混合物加热B．图②是向一定温度下的饱和氢氧化钙溶液中不断加入氧化钙固体C．图③是向pH＝1的酸溶液中不断加水D．图④是向一定质量的稀硫酸中加入锌粒11．根据图2所示的溶解度曲线判断，下列说法正确的是（）A．甲物质的溶解度大于乙物质的溶解度B．甲物质的不饱和溶液温度升高后变成饱和溶液C．将t2℃甲、乙两物质的饱和溶液温度降低到t1℃时都会析出晶体D．t2℃时，甲物质的饱和溶液和乙物质的饱和溶液中含有相等质量的溶质12．一定质量的Mg、Al、Fe的混合物，与足量稀硫酸反应，生成0.4g的H2。
2021年浙江省余姚中学自主招生九年级英语模拟试卷
2021年浙江省余姚中学自主招生九年级英语模拟试卷学校:___________姓名：___________班级：___________考号：___________一、单选题1．The driver drove _______ hit at a big tree and the car came to a stop.A．too carelessly to B．carelessly enough toC．so carelessly that he D．so careless that he2．Jack is a good friend _______, and he often comes to our home for a visit.A．of my father B．of my father’s C．for my father D．in my father’s 3．You’d better make a mark ______ you have any questions.A．at which B．at where C．the place D．where4．We didn’t plan our art exhibition like that but it _______ very well.A．worked out B．tried out C．went on D．carried out5．He was so angry at all _____ I was doing _______ he walked out.A．that; that B．what; that C．that; what D．which; what 6． If it had been possible, I would have helped him, but I ______ too busy. A．had been B．would be C．were D．was7．----You’ve never been to the village, have you?----__ __. It is the most beautiful village I’ve ever seen.A．No,never B．No,Ihave C．No,onlyonce D．Yes,onlyonce 8．---- Could you do me a favor and take the box up to the sixth floor?---- _______. No problem at all.A．With please B．My pleasure C．For pleasure D．At your pleasure 9． The number of foreign students attending Chinese universities ________ rising steadily since1990.A．is B．are C．has been D．have been10．Is this the watch you wish to __ ___?A．have it repaired B．repair it C．have repaired it D．have repaired 11．Has everything __ ___ can be done ___ ___?A．what; done B．that; been doneC．that; already done D．what; already being done12．Whom would you rather have _____ with you?A．to go B．gone C．going D．go13．How pleased the emperor was _____ what the cheat said!A．hearing B．heard C．hear D．to hear14．The students are ______ to hand in the exercises before class.A．hoped B．suggested C．agreed D．expected 15．Is this school ______ they visited the other day?A．that B．which C．where D．the one 16．They are _____ children that they can’t dress themselves.A．so little B．such little C．so small D．too small17． China is larger than _____ in Africa.A．any other country B．other countries C．any countries D．any country 18．_ ____ and I will hit you.A．If you say that again B．Say that againC．Say you that again D．You’ll say that again19．We must find a dictionary. ____ will do.A．Some B．Any C．Every D．Each20．_____ leaves the room last ought to turn off the lights.A．Anyone B．The person C．Whoever D．Who二、完型填空The word “sharp” can be __ to describe many different things in your home, classroom, and places of work. In this chapter, the writer __sharp pencils, meaning pencils with a very fine__.The writer does not like dull pencils. 。
浙江省余姚中学全国重点高中初升高自主招生化学模拟试题(含答案)
浙江省余姚中学全国重点高中初升高自主招生化学模拟试题(含答案)一、选择题1．向某硫酸和硫酸铜的混合溶液中加入某浓度的氢氧化钠溶液，产生沉淀的质量与加入氢氧化钠溶液的质量关系如图所示，下列说法正确的是（）A．加入氢氧化钠溶液的溶质质量分数为20%B．点溶液中含有两种溶质C．段发生的反应为中和反应D．混合溶液中硫酸和硫酸铜的质量比为1∶12．向一定质量的FeCl3溶液中滴加NaOH溶液一段时间后，改为滴加稀硫酸，所得沉淀质量随加入试剂总体积的变化趋势如图所示。
下列有关说法不正确的是（）A．b点时所加试剂一定是稀硫酸B．加入试剂总体积大于V1时，溶液中不存在NaOHC．c点时溶液中的溶质不止是盐D．a点时溶液中有可能存在Fe3+3．在硝酸银、硝酸铜的混合溶液中加入一定量锌粉，反应停止后过滤，滤液仍为蓝色，有关判断正确的是（）A．滤渣中一定有银、没有铜和锌B．滤渣中一定有银和锌，可能有铜C．滤液中一定有硝酸锌、硝酸铜、硝酸银D．滤液中一定有硝酸锌、硝酸铜，可能有硝酸银4．化学趣味小组在学习了金属的化学性质后，对金属R的活动性进行探究发现：将金属R 放入稀盐酸中，观察到有气泡产生（该反应的化学方程式可表示为：R+2HCl2=RCl2+H2↑），将R放入ZnSO4溶液中无任何变化。
下列化学方程式书写错误的是（）A．R+MgSO4=RSO4+Mg B．R+CuSO4=RSO4+CuC．R+H2SO4=RSO4+H2↑D．2A1+3RSO4=Al2（SO4）3+3R5．下表除去杂质的方法中，正确的是选项物质（括号内为杂质）除去杂质的方法A Cu(NO3)2溶液（AgNO3）加过量铜粉，过滤B KCl溶液（CaCl2）加适量Na2CO3溶液，过滤C Fe（Zn）加足量稀盐酸，过滤D CO（CO2）通过灼热的氧化铜粉末A．A B．B C．C D．D6．（2012年山东烟台，18题，2分）电影《黄金大劫案》上映后，里面用“王水”（浓盐酸与浓硝酸的混合液）溶解黄金的情引起了广泛的热议。
浙江省余姚中学全国重点高中初升高自主招生化学模拟试题(含答案)
浙江省余姚中学全国重点高中初升高自主招生化学模拟试题(含答案)一、选择题1．下图中“—”表示相连的两种物质能发生反应，“→”表示一种物质转化成另一种物质，部分反应物、生成物及反应条件未标出。
则不可能出现的情况是A ．AB ．BC ．CD ．D2．不能正确对应变化关系的图像是（ ）A ．A 图中横坐标既可以表示加入铁粉的质量，也可以表示加入部分变质的苛性钠质量B ．B 图中纵坐标既可以表示溶质质量，又可表示溶液的导电性C ．C 图中横坐标既可以表示反应时间，也可以表示加入二氧化锰质量D ．D 图中纵坐标既可以表示溶剂质量，又可表示溶液质量3．实验室有一包含杂质的碳酸氢钠样品50g （杂质不含钠元素，受热不变化），其中钠元素的质量分数为23%，180℃时，将样品加热一段时间后称得固体质量为43.8g ，则分解的碳酸氢钠占原碳酸氢钠的质量分数为（已知323222NaHCO Na CO +H O+CO Δ）A ．60%B ．47.3%C ．40%D ．33.6%4．下列四个图象，分别对应四种操作过程，其中正确的是（ ）A．向pH＝2的酸溶液中不断加水B．向NaOH溶液中逐滴加入稀盐酸C．向一定量的水中持续加入食盐（m表示食盐的质量，A%表示溶质质量分数）D．等质量的锌、铁与足量的稀硫酸反应，产生氢气的质量随反应时间t的变化5．已知反应前后分子变化的微观示意图如下所示，下列说法错误．．的是A．反应前后元素种类不变B．A是有机物，C、D是无机物C．点燃前要先检验A的纯度，防止爆炸D．此反应中A和B的化学计量数之比等于1：16．逻辑推理是化学学习中常用的思维方法。
下列推理正确的是A．碱溶液呈碱性，呈碱性的溶液一定是碱溶液B．单质只含一种元素，只含一种元素的纯净物一定是单质C．中和反应生成盐和水，生成盐和水的反应一定是中和反应D．有机化合物都含碳元素，含碳元素的化合物一定是有机化合物7．下图是a、b、c三种物质的溶解度曲线，下列有关叙述正确的( )A．a物质的溶解度大于b物质的溶解度B．降低温度，c物质会从其饱和溶液中析出C．t2℃时30ga物质加入到50g水中不断搅拌，能形成80g溶液。
2020-2021学年浙江省余姚市中考仿真模拟考数学试题及答案解析
2020-2021学年浙江省余姚市中考仿真模拟考数学试题及答案解析ABCD初中毕业⽣学业考试仿真模拟考数学试卷⼀、选择题（每⼩题4分，共48分） 1.已知－4的相反数是a ，则a 是（） A.41 B.41- C. 4 D. －4 2．下列运算中正确的是（）A ．2325a a a +=B ．22(2)(2)4a b a b a b +-=-C ．23622a a a ?=D ．222(2)4a b a b +=+3. 据宁波海关统计，1-4⽉宁波⼝岸进⼝消费品11.9亿元⼈民币，⽐去年同期下降11%。
其中11.9亿元⽤科学计数法表⽰为（）A.1.19×910元 B.1.19×810元 C. 11.9×810元 D. 0.119×910元 4.函数1-=x y 中,⾃变量x 的取值范围是( )A ．x ≥1B.x ＞1C.x ≠1D.x ≥05．某⼏何体的三视图如图所⽰，则这个⼏何体是（）6. 将⼆次函数y=x 2-2x +3化为y=(x -h)2+k 的形式，结果为（） A ．y=(x +1)2+4 B ．y=(x -1)2+4 C ． y=(x +1)2+2 D ．y=(x -1)2+27．如图，△ABC 中，点D 、E 分别是AB,AC 的中点，则下列结论：①BC=2DE ；②△ADE ∽△ABC ；③ACABAE AD =．其中正确的有（） A ．3个 B ．2个 C ．1个 D ．0个 8.下列说法不正确的是（） A ．某种彩票中奖的概率是11000，买1000张该种彩票⼀定会中奖. B ．了解⼀批电视机的使⽤寿命适合⽤抽样调查.C ．若甲组数据的标准差S 甲=0.31，⼄组数据的标准差S ⼄=0.25，则⼄组数据⽐甲组数据稳定.D ．在⼀个装有⽩球和绿球的袋中摸球，摸出⿊球是不可能事件.9.已知圆锥的底⾯半径为6，侧⾯积为60π，则这个圆锥的母线为( ) A ．6 B ．8 C ．10 D ．1210. 如果关于x 的⼀元⼆次⽅程0962=+-x kx 有两个不相等的实数根，那么k 的取值范围是（）A 、1k D 、1EDCBA（第7题图）11. 如图，将⼀张正三⾓形纸⽚剪成四个⼩正三⾓形，得到4个⼩正三⾓形，称为第⼀次操作；然后，将其中的⼀个正三⾓形再剪成四个⼩正三⾓形，共得到7个⼩正三⾓形，称为第⼆次操作；再将其中的⼀个正三⾓形再剪成四个⼩正三⾓形，共得到10个⼩正三⾓形，称为第三次操作；...，根据以上操作，若要得到2014个⼩正三⾓形，则需要操作的次数是( ) . A. 670 B. 671 C.672 D. 67312. 如图，平⾯直⾓坐标系中，分别以点A(2，3)、点B （3，4）为圆⼼， 1、3为半径作⊙A 、⊙B, M ，N 分别是⊙A 、⊙B 上的动点， P 为x 轴上的动点，则PM ＋PN 的最⼩值为( ) A ．52－4 B.17－1 C ．6－22 D.17⼆、填空题（每⼩题4分，共24分）13．分解因式：442+-a a = .14. ⼀个不透明的盒⼦中放着编号为1到10的10张卡⽚（编号均为正整数），这些卡⽚除了编第11题图图第12题图图号以外没有任何其他区别.盒中卡⽚已经搅匀.从中随机地抽出1张卡⽚，则“该卡⽚上的数字⼤于162”的概率是_________. 15. 如图，AB 为圆O 的直径，弦CD ⊥AB ，垂⾜为点E ，连结OC ，若OC=5， CD=8，则AE= 。
浙江省余姚中学全国重点高中初升高自主招生物理模拟试题(含答案)
浙江省余姚中学全国重点高中初升高自主招生物理模拟试题(含答案)一、选择题1．如图，两个相同的空塑料瓶，瓶口扎上橡皮膜，竖直浸没在水中，甲瓶口朝上，乙瓶口朝下，若甲瓶恰好悬浮，则（）A．乙瓶内气体密度较大B．乙瓶可能悬浮C．甲瓶内气体的压强较大D．两瓶受到的浮力相等2．我国是目前为数不多的可以生产无针注射器的国家，其中一种电动式无针注射器通电时永磁体的磁场与通电线圈相互作用，产生强大的助推力，使药液以接近声音的速度注入皮肤。
下列关于该注射器说法错误的是（）A．它的工作原理与电动机相同B．药液能注入皮肤是利用了药液的惯性C．它是利用电磁感应工作的D．它工作时将电能转化为机械能3．关于家庭电路，下列说法正确的是（）A．有人触电，立即用手拉人B．安装电路时，开关接在用电器和火线之间C．保险丝熔断，用铜丝代替保险丝D．使用测电笔时，手指不能接触笔尾的金属电极4．不允许在森林里随地丢弃瓶子，因为雨水进入透明的瓶子后，在阳光照射下就可能会引发火灾，能说明此现象发生原因的选项是（）A．B．C．D．5．关于声现象，下列说法中正确的是（）A．“闻其声而知其人”主要是根据声音的响度来判断的B．“上课回答问题要大声”是要求学生回答问题的声音音调要高一些C．用超声波能粉碎人体内的“小石头”，说明超声波能够传递信息D．临街房子的窗户装上双层玻璃，可以在传播过程中减弱噪声6．甲、乙两种物质的质量和体积关系如图所示，如分别用甲、乙两种物质制成体积相等的两实心物体a和b，放在水中静止后，则A．a漂浮，a受浮力大于b B．b漂浮，b受浮力大于aC．a沉底，a受浮力大于b D．b沉底，b受浮力大于a7．如图所示，汽车装有日间行车灯可以提高行车安全，当汽车启动时，S1闭合，日间行车灯L1立即亮起：再闭合S2车前大灯L2也亮起．符合这一情况的电路图是（）A．B． C．D．8．下列关于简单机械的理解，错误的是：（）A．木螺丝能轻松拧入木头，螺丝的螺纹可看作是一个斜面B．汽车方向盘是一个轮轴，其本质是一个等臂杠杆C．将绳子把两根光滑的木棍绕起来，可以看作是滑轮组D．蜡烛跷跷板在两端蜡烛都点燃时能上下摆动，因此可以看作是一个杠杆9．如图，在空气压缩引火仪玻璃筒的底部放一小撮干燥的棉絮，用力将活塞迅速向下压，棉絮燃烧起来。
浙江省余姚市余姚中学高中自主招生考试 物理模拟试题
浙江省余姚市余姚中学高中自主招生考试物理模拟试题一、选择题1．如图所示，甲、乙两个容器中分别盛有不同的液体，液面的高度相同，且液体对两容器底部的压力也相同。
若把两个质量相同的小球A和B分别放入甲、乙两个容器中（小球的体积均小于容器中液体的体积，且液体都不溢出），小球都静止后，液体对两容器底部的压强相等，则小球B在液体中静止时的状态是（）A．漂浮B．悬浮C．沉底D．无法判围2．小明在探究“平面镜成像”和“凸透镜成像”两个实验中，分别把一个不透明的木板放在如图甲、乙所示的位置，以下说法错误的是（）A．甲图中，蜡烛能成像且人能看到像B．乙图中，蜡烛能成像且人能看到像C．甲图中，取走木板，将蜡烛远离平面镜，镜中的像变大D．乙图中，取走木板，蜡烛靠近凸透镜，所成的像变小3．电动平衡车是一种时尚代步工具．如图所示，当人驾驶平衡车在水平路面上匀速直线运动时，下列说法正确的是A．平衡车受到的重力与地面对它的支持力是一对平衡力B．平衡车对地面的压力与地面对它的支持力是相互作用力C．关闭电机，平衡车仍继续前进是由于其受到惯性作用D．若平衡车在运动过程中所受的力全部消失，平衡车会慢慢停下来4．如图所示，电源电压保持不变，闭合开关S，将滑动变阻滑片P向右移动，下列说法中正确的是（）A．电路消耗的总电功率变大B．电压表与电流表的示数之比变小C．电流表的示数变大，电压表的示数变小D．电流表的示数变小，电压表的示数不变5．如图所示，装有水的容器静止放在水平桌面上，正方体物块M悬浮在水中，其上表面与水面平行，则下列说法中正确的是A．M上、下表面受到水压力的合力大于M受到的浮力B．M上、下表面受到水压力的合力大小等于M受到的重力大小C．M上表面受到水的压力大于M下表面受到水的压力D．M上表面受到水的压力和M下表面受到水的压力是一对平衡力6．如图是某品牌榨汁机．为保障安全，该榨汁机设置了双重开关——电源开关S1和安全开关S2．当杯体倒扣在主机上时， S2自动闭合，此时再闭合S1，电动机才能启动，开始榨汁．下列电路图符合上述要求的是A．B．C．D．7．如图所示，将一个条形磁铁置于水平桌面上，电磁铁左端固定在竖直墙壁上并保持水平。
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2021学年余姚中学自主招生模拟试卷（数学卷）2021.11题号 一二三总分得分一、选择题（共7题，每题5分，共35分）1．二次函数2y ax bx c =++的图像如右图所示，则化简二次根式22()()a c b c ++-的结果是（ ）A ．a+bB ．-a-bC ．a-b+2cD ．-a+b-2c2.有4支队伍进行4项比赛，每项比赛的第一、第二、第三、第四名分别得到5、3、2、1分。
每队的4项比赛得分之和算作总分，如果已知各队的总分不相同，并且其中一队获得了三项比赛的第一名，问总分最少的队伍最多得多少分？（ ）A ．7B ．8C ．9D ．103．已知a 是方程3310x x +-=的一个实数根，则直线1y ax a =+-不经过（ ） A ．第一象限 B ．第二象限 C ．第三象限 D ．第四象限 4．有一种长方体集装箱，其内空长为5米，高4.5米，宽3.4米，用这样的集装箱运长为 5米，横截面的外圆直径为0.8米的圆柱形钢管，最多能运（ ）根。
A ．20根B ．21根C ．24根D ．25根5．将5个相同的球放入位于一排的8个格子中，每格至多放一个球，则3个空格相连的概 率是（ ） A ．328 B ． 528 C ． 356 D ． 5566．用[x]表示不大于x 的最大整数，则方程[]2230x x --=的解的个数是（ ） A ．1 B ．2 C ．3 D ．4 7.对每个x ，y 是x y 21=,1223,232+-=+=x y x y 三个值中的最小值，则当x 变化时，函数y 的最大值是（ ）A ． 4B ． 6C ． 8D ． 487二、填空题（共7题，每题5分，共35分） 8. 已知()21()()4b c a b c a -=--，且a ≠0,则b c a += 。
9．G 是△ABC 的重心，过G 的直线交AB 于M ，交AC 于N ， 则BM CNAM AN+= 。
10. 已知a 、b 、c 都是实数，且满足a>b>c,a+b+c=0.那么，ca的取值范围是 。
11.在△ABC 中，AB=AC ，且过△ABC 某一顶点的直线可将△ABC 分成两个等腰三角形， 则各内角的度数为 。
12．对于一切不小于2的自然数n ，关于x 的一元二次方程22(2)20x n x n -+-=的两个根记 作,n n a b (n ≥2),则223311(2)(2)(2)(2)a b a b ++----…200720071(2)(2)a b +--= 。
13. 设抛物线25(21)2(4y x a x a a =++++为常数）的图象与x 轴只有一个交点， 则186323a a -+= 。
14.如图，E ，F 是正方形ABCD 的边AD 上两个动点，满足AE=DF ．连接CF 交BD 于点G ，连接BE 交AG 于点H ．若正方形的边长为2，则线段DH 长度的最小值是 ．三、解答题（本题有4小题，共60分）15. （10分）试求实数k （ k ≠±1），使得方程 22(1)6(31)720k x k x ---+=的两根都是正整数。
16.（12分）如图1, 矩形铁片ABCD 的长为a 2, 宽为a ; 为了要让铁片能穿过直径为a 1089的圆孔, 需对铁片进行处理 (规定铁片与圆孔有接触时铁片不能穿过圆孔);(1)如图2, M 、N 、P 、Q 分别是AD 、AB 、BC 、CD 的中点, 若将矩形铁片的四个角去掉,只余下四边形MNPQ, 则此时铁片的形状是_______________, 给出证明, 并通过计 算说明此时铁片都能穿过圆孔;(2)如图3, 过矩形铁片ABCD 的中心作一条直线分别交边BC 、AD 于点E 、F(不与端点重合),沿着这条直线将矩形铁片切割成两个全等的直角梯形铁片;①当BE=DF=a 51时, 判断直角梯形铁片EBAF 能否穿过圆孔, 并说明理由;②为了能使直角梯形铁片EBAF 顺利穿过圆孔, 请直接写出线段BE 的长度的取值范围17.（14分）喜欢钻研的小亮对75°角的三角函数发生了兴趣，他想：75度虽然不是特殊角，但和特殊角有着密切的关系，能否通过特殊角的三角函数值求75°的正弦值呢？经研 究，他发现：sin75°=sin(45°+30°)=sin45°cos30°+cos45°sin30°,于是他大胆猜想：sin(+)=sin cos +cos sin αβαβαβ（αβ和为锐角）。
将图1（a ）等积变形为 图1（b ）可用于勾股定理的证明，现将这两幅图分别“压扁”成图2（a ）和图2（b ）。
如图,锐角为α的直角三角形斜边为m ，锐角为β的直角三角形斜边为n ，请你借助 图2（a ）和图2（b ）证明上述结论能成立。
图2 图1图3 D C B AQ PN M D C B A F E QD CB A18.（14分）已知菱形ABCD 的边长为1．∠ADC=60°，等边△AEF 两边分别交边DC 、CB 于点E 、F ．（1）特殊发现：如图1，若点E 、F 分别是边DC 、CB 的中点．求证：菱形ABCD 对角线AC 、BD 交点O 即为等边△AEF 的外心；（2）若点E 、F 始终分别在边DC 、CB 上移动．记等边△AEF 的外心为点P ． ①猜想验证：如图2．猜想△AEF 的外心P 落在哪一直线上，并加以证明；②拓展运用：如图3，当△AEF 面积最小时，过点P 任作一直线分别交边DA 于点M ，交边DC 的延长线于点N ，试判断DN DM 11是否为定值？若是，请求出该定值；若不是，请说明理由．自主招生模拟答卷（数学卷）班级姓名学号一、选择题（每小题5分，共35分）二、填空题（每小题6分，共35分）8． 9． 10．11． 12． 13．14．三、解答题（第15题10分，第16题12分，第17、18每题14分，共50分）15．16．17．图2图1图3DCBAQPNM DCBAFEQDCBA18．重点中学提前招生试卷（数学）答案一、选择题1. C2. B3. D4.B5. A6. C7. B 二、填空题8. 2 ；9. 1； 10. 1-2<<-2c a ；11. （45°、45°、90°）（36°、36°、108°） （36°、72°、72°）（01807、05407、05407）；12.10034016-； 13. 5796 14.15-三、解答题15.Ｋ＝２，３，7516.解：（1）是菱形，如图，过点M 作MG⊥NP 于点G ，∵M、N 、P 、Q 分别是AD 、AB 、BC 、CD 的中点， ∴△AMN≌△BPN≌△CPQ≌△DMQ， ∴MN=NP=PQ=QM， ∴四边形MNPQ 是菱形，a a MN S MG a a a MN a S S MNPQ ABCD MNPQ1089552,25)21(,21222<==∴=+=== ∴能穿过圆孔（2）①如图，过点A 作AH⊥EF 于点H ，过点E 作EK⊥AD 于点K 显然AB=a ＞a 1089，故沿着与AB 垂直的方向无法穿过圆孔， 过点A 作EF 的平行线RS ，故只需计算直线RS 与EF 之间的距离即可，aa a EF a AK AF KF a DF AD AF a AB EK a AK BE 589)58(,58,59,,5122=+==-=∴=-=====∵∠AHF=∠EKF=90°，∠AFH=∠EFK， ∴△AHF∽△EKF，a a AH EF AF EK AH 108989899,>==∴，∴该直角梯形铁片不能穿过圆孔； ②a BE a a BE 2648933964893390<<+-<<或17.如图2(a)，原来内部的正方形变成了一个平行四边形，m ，n 为相邻两边，其夹角为α＋β，得它的面积是mnsin(α＋β)（其中m 、n 分别是相邻两个直角三角形斜边的长度）．如图2(b)，原来的两个小正方形变成了两个矩形，其面积之和是msin α·ncos β＋mcos α·nsin β．与上面一样，图2(a)与图2(b)中空白部分的面积相等，所以有mnsin(α＋β)＝msin α·ncos β＋mcos α·nsin β，化简得sin(α＋β)＝sin αcos β＋sin αcos β。
18（1）证明：如图1，连接OE 、0F ， ∵四边形ABCD 是菱形，∴AC⊥BD，BD 平分∠ADC，AD=DC=BC ， ∴∠COD=∠COB=∠AOD=90°,3021︒=∠=∠ADC ADO 又∵E、F 分别为DC 、CB 中点，OA OF OE AD AO BC OF CD OE ==∴===∴,21,21,21,∴点O 即为△AEF 的外心；①猜想：外心P 一定落在直线DB 上．理由如下：如图2，分别连接PE 、PA ，过点P 分别作PI⊥CD 于I ，PJ⊥AD 于J ， ∴∠PIE=∠PJD=90°， ∵∠ADC=60°，∴∠IPJ=360°-∠PIE -∠PJD -∠JDI=120°， ∵点P 是等边△AEF 的外心， ∴∠EPA=120°，PE=PA ， ∴∠IPJ=∠EPA， ∴∠IPE=∠JPA， ∴△PIE≌△PJA， ∴PI=PJ，∴点P 在∠ADC 的平分线上，即点P 落在直线DB 上；②211=+DNDM。