同济大学网络教育学院 学年第 学期期终考试

上海市同济大学第一附属中学2024-2025学年高三上学期期中考试数学测试卷一、填空题1．不等式021x x ≤-+的解集是．2．已知复数1i z =+（i 是虚数单位），则1i z -=.3．已知0,0,1x y xy >>=，则12x y+的最小值为.4．若π3(,π),cos(π)25αα∈-=，则tan α=.5．若()()()1,23,45,A B C m -、、三点不能构成三角形，则m =.6．某市高考新政规定每位学生在物理､化学､生物､历史､政治､地理中选择三门作为等级考试科目，则甲､乙两位学生等级考试科目恰有一门相同的不同选择共有种.（用数字作答）7．已知{}n a 为等差数列，其前n 项和n S ，若11a =，35a =，64n S =，则n =8．过直线y x =上的一点作圆22(5)(1)2x y -+-=的两条切线1l ，2l ，当直线1l ，2l 关于y x =对称时，它们之间的夹角为．9．已知函数()ln 2f x x ax =--在区间(1,2)上不单调，则实数a 的取值范围为.10．如图，正六边形的边长为2，圆O 的圆心为正六形的中心，半径为1，若点M 在正六边形的边上运动，动点A B 、在圆O 上运动且关于圆心O 对称，则MA MB ⋅的取值范围是.11．已知()()505025001250120242024x x a a x a x a x ++-=++++，若{}00,1,2,,50k a k <∈ ，，则实数k 的最大值为.12．已知数列{}n a 满足：对于任意正整数n 有π0,2n a ⎛⎫∈ ⎪⎝⎭，且1π4a =，1()n f a +=其中()tan f x x =，若1(1)tan tan nn n nb a a +-=-，数列{}n b 的前n 项和为n T ，则440T =.二、单选题13．下列说法正确的是（）A ．如果直线l 不平行于平面α，那么平面α内不存在与l 平行的直线B ．如果直线l //平面α，平面α//平面β，那么直线l //平面βC ．如果直线l 与平面α相交，平面α//平面β，那么直线l 与平面β也相交D ．如果平面α⊥平面γ，平面β⊥平面γ，那么平面α//平面β14．某单位为了解该单位党员开展学习党史知识活动情况，随机抽取了部分党员，对他们一周的党史学习时间进行了统计，统计数据如下表所示：党史学习时间(小时)7891011党员人数610987则该单位党员一周学习党史时间的众数及第40百分位数分别是（）A ．8，8.5B ．8，8C ．9，8D ．8，915．已知椭圆2222:1x y C a b+=，过点(,0)a -且倾斜角为3π4的光线，经直线y b =-反射后过C 的右焦点，则C 的离心率为（）A ．35B ．23C ．34D ．4516．定义：如果函数()y f x =在区间[],a b 上存在()1212,x x a x x b <<<，满足()()()'1f b f a f x b a -=-，()()()'2f b f a f x b a-=-，则称函数()y f x =是在区间[],a b 上的一个双中值函数，已知函数()3265f x x x =-是区间[]0,t 上的双中值函数，则实数t 的取值范围是A ．36,55⎛⎫ ⎪⎝⎭B ．26,55⎛⎫ ⎪⎝⎭C ．23,55⎛⎫⎪⎝⎭D ．61,5⎛⎫ ⎪⎝⎭三、解答题17．如图，在四棱锥P ABCD -中，底面ABCD 是矩形，,M N 分别为棱,PD PC 的中点，PA AD =，平面PAD ⊥平面ABCD .求证：(1)//MN 平面PAB ；(2)AM ⊥平面PCD ．18．已知向量,2sin 22x x m ⎛⎫=- ⎪⎝⎭ ，cos ,cos 22x x n ⎛⎫= ⎪⎝⎭ ，函数()y f x m n ==⋅ .(1)设ππ,22θ⎡⎤∈-⎢⎥⎣⎦，且()1f θ=，求θ的值；(2)在ABC V 中，1AB =，()1f C =，且ABC Vsin sin A B +的值.19．某群体的人均通勤时间，是指单日内该群体中成员从居住地到工作地的平均用时．某地上班族S 中的成员仅以自驾或公交方式通勤．分析显示：当S 中%x （0100x <<）的成员自驾时，自驾群体的人均通勤时间为()30030180029030100x f x x x x <≤⎧⎪=⎨+-<<⎪⎩，，（单位：分钟），而公交群体的人均通勤时间不受x 影响，恒为40分钟，试根据上述分析结果回答下列问题：（1）当x 在什么范围内时，公交群体的人均通勤时间少于自驾群体的人均通勤时间？（2）求该地上班族S 的人均通勤时间()g x 的表达式；讨论()g x 的单调性，并说明其实际意义．20．已知椭圆222:1(1)x C y t t+=>的左､右焦点分别为12F F 、，直线:(0)l y kx m m =+≠与椭圆C交于M ､N 两点，（点M 在点N 的上方），与y 轴交于点E .(1)当2t =时，点A 为椭圆C 上除顶点外任一点，求12AF F △的周长；(2)当3t =且直线l 过点(1,0)D -时，设,EM DM EN DN λμ==，求证：λμ+为定值，并求出该值；(3)若椭圆C当k 为何值时，22||||OM ON +恒为定值，并求此时三角形MON 面积的最大值.21．对于函数()y f x =的导函数()y f x ''=，若在其定义域内存在实数0x 和t ，使得()()()001f x t t f x +=+'⋅成立，则称()y f x =是“跃点”函数，并称0x 是函数()y f x =的“t 跃点”.(1)若函数()sin R y x m x =-∈是“π2跃点”函数，求实数m 的取值范围；(2)若函数21y x ax =-+是定义在()1,3-上的“1跃点”函数，且在定义域内存在两个不同的“1跃点”，求实数a 的取值范围；(3)若函数()e xy bx x =+∈R 是“1跃点”函数，且在定义域内恰存在一个“1跃点”，求实数b 的取值范围.。

2020-2021学年同济高级中学高三英语期中考试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AGet up to 19% off the cover pricePlus, get digital access with your paid print subscription●Up-to-date news that touches your lifeFrom money-saving tips and quick reports on the latest healthcare, to inspiring articles on world events, you'll discover hundreds of ideas for living a richer, more satisfying life.●Read it anytime, anywhereGet a l-year-print subscription ofReader's Digestmagazine today and you'll also get free digital instantly. With digital access, you can read the latest issue ofReader's Digestanytime, anywhere! Plus, you can quickly access your past issues online, too.●Continuous renewal serviceYour subscription will automatically renew at the end of each term until you cancel. You authorize us to charge you credit/debit cardat the discounted rate on the renewal service unless you cancel. You may cancel at anytime by visiting Customer Care and receive a refund on all unmailed issues.●Other informationThe cover price ofReader's Digestis $3.99 per issue and it is currently published 10 times annually. Please check the confirmation page and your mailbox to download detailed instructions.1. What is the annual fee for subscription?A. $32. 3.B. $39. 9.C. $40.D. $47. 9.2. Which of the following words best describes the content inReader's Digest?A. Touching and amusing.B. Inspiring and practical.C. Amazing and entertaining.D. Educational and theoretical.3. If you subscribe toReader’s Digest, you can ________.A. have as many issues as possible every yearB. renew your subscription at the original rateC. get back your money for the issues not mailedD. obtain all the past issues online anytime, anywhereBHumans have found an easy way to tell if others are lying. Recent research shows that the best way so far is being clever at how you ask questions and listen to the answers.Much of this research is based on the idea that telling a lie is simply harder mental work than telling the truth. Making up a story takes more effort than simply recording something that happened. And like a writer, a liar has to keep all the unreal details in his memory and sound believable when he explains them.One method that seems to work is asking them to tell their story in reverse order. This is harder when the story isn't true and makes it easier for you to tell they are lying. An even more basic way that helps is to just ask more questions, especially unexpected ones. Truth-tellers can easily find more to say, but it's a challenge for a liar to come up with something that's not in his prepared story.Researchers suggest that you shouldn't lay all your cards on the table at the start, but only gradually present what proof you have. The liars' stories may not agree with that proof, making it clear that they're lying.So it looks like there are ways to increase the chances of catching a liar; we've just been basing our methods on the wrong stories. Low-tech ways of causing people to make mistakes in conversation seem to work better than any science about eye movement or machines used to recognize a liar. To find a liar, watch less and listen more.4. Why does the author mention the writer?A. To show it's hard to make up lies.B. To show it's hard to recognise a liar.C. To show writers know liars best.D. To show writers are very clever.5. What do we know about liars?A. They often have much to say.B. They often ask many questions.C. They usually prepare a made-up story.D. They usually feel good about themselves.6. What advice is given to help people catch liars?A. Asking them to set their stories down.B. Presenting your proof one by one.C. Telling different stories to them.D. Letting them ask questions.7. Which can be the best title for the text?A. Why People LieB. How to Stop People LyingC. Low-tech Ways to Find a LiarD. LiarsAre Smarter than ThoughtCUK physicist Isaac Newton once said, ''Nature is pleased with simplicity and nature is no dummy (傻子). ''Indeed, Mother Nature can provide almost everything human beings need if we follow her rules. But if we break the rules, she is likely to be cruel andlash out at us.The outbreak of the novel coronavirus pneumonia (新型冠状病毒肺炎, NCP) in China and some other countries at the beginning of this year is an example. According to Xinhua News Agency, the new coronavirus is similar to a virus found in a bat in 2017 and probably has an intermediate host (中间宿主). It's believed that the virus originated from the Huanan Seafood Market in Wuhan, Hubei province, where live wild animals were sold.The Wall Street Journal reported that Dr Peter Daszak, president of the US-based health organization EcoHealth Alliance, said, ''This outbreak is a lesson for us. On a global scale, human population density, wildlife diversity, and land use change are what drive new pandemics (流行病). ''In ancient times, people needed to rely on nature to survive so they held it in awe (敬畏). For example, the American Indians believed that humans are a part of nature and nature is a part of humans. Chinese ancients always pursued the harmony between nature and human beings.However, as human beings master more knowledge and make more advanced tools, people try to change and even conquer nature. They use more land to make buildings, genetically modify (改变) plants, capture some wild and rare animals to suit their own needs. In this process, humans gradually lose contact with nature and even throw it out of balance. For example, cutting a large number of forests means carbon dioxide must build up in the atmosphere and it contributes to global warming.Although we don't know for sure what first caused the NCP outbreak, Brian Lamacraft at Medium said it's time for people to ''reflect on our relationship with our planet'' and ''reconnect with this world and everything that we've been given''. After all, according to US poet Gary Snyder, ''Nature is not the place to visit. It's our home. ''8. What does the phrase ''lash out at'' in Paragraph 1 probably mean?A. punishB. controlC. testD. challenge9. What lesson did Daszak think human beings should learn from the NCP outbreak?A. Bats are one of the most dangerous wild animals.B. It's impossible to prevent new pandemics globally.C. We should stop the wildlife trade around the world.D. Humans should live peacefully with nature.10. What is the main idea of Paragraph 5?A. How human beings become their own masters.B. How human activities cause global warming.C. How human beings break the balance of nature.D. How humans use technology to improve their lives.11. What is the author's purpose in writing this article?A. To reflect on the NCP outbreak.B. To explain what led to the NCP outbreak.C. To describe experts' predictions on new pandemics.D. To compare ancient and modern attitudes toward nature.DHidden beneath the surface in the roots of Earths astonishing and diverse plant life, there exists a biological superhighway linking together the members of the plant kingdom in what researchers call the "wood wide web".The network is comprised of thin threads of fungus (真菌) that grow outwards underground up to a few meters from its partnering plant, meaning that all of the plant life within a region likely connected to one another. The partnership is beneficial for both parties involved, plants provide carbohydrates (碳水化合物) to the funguses and in exchange, the funguses aid in gathering water and providing nutrients to its partnering plant.A study conducted by Rensen Zeng of theSouthChinaAgriculturalUniversityfound that this also allowed for plants to warn one another of potential harm. The study showed Broad Beans used the fungal network to spy on one another for upcoming danger.Like our Internet, this fungal connectivity is also full of crime. Some plants, such as Golden Marigolds have been found to release poisons into the network to slow down the growth of surrounding plants in the fight for water and light. Other plants, such as the Phantom Orchid, do not have the chlorophyll (叶绿素) and must get the necessary nutrients from surrounding plants.Research suggests that animals such as insects and worms may be able to detect slight exchanges of nutrients through the network, allowing them to more easily find delicious roots to feed on; however, this has not been conclusively made clear in experimentation. The more we learn about this phenomenon, the more our understanding of the plant life of our planet will continue to change. Perhaps one day, we may be able to map out these complex networks entirely.12. What is the function of the first paragraph?A.To explain the aim of the web.B. To introduce the main topic.C. To give definition of diverse life.D. To show the importance of plants.13. The criminal behavior of plants can be seen as a way to________.A. compete for survivalB. gather more waterC. take in sunlightD. break natural rules14. What does the last paragraph suggest?A. Animals can also feed on the fungus.B. Nutrient exchanges are too slight to detect.C. No experiment can prove the phenomenon.D. More needs to be done to work out the network.15. Which can be the best title for the text?A. The Partnership between PlantsB. The Unknown Roots of the EarthC. The Superhighway Linking the PlantsD. The Mysterious Map Changing the World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。

2021届同济大学实验学校高三英语上学期期中考试试题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AThere have been many great painters in the rich history of Chinese art. Here are four of the greatest painters from China.Li Cheng (919—967, Five Dynasties and early Song Dynasty)Li Cheng contributed greatly to one of the golden ages of landscape paintings in world history. During his time, he was considered the best landscape painter ever. He is remembered especially for the winter landscapes he created and for simple compositions of tall, old evergreens set against a dry landscape. Several of his paintings are in thin ink which gives them a foggy appearance.Fan Kuan (990—1020 , Song Dynasty)Fan Kuan began his career by modeling Li Cheng's work but later created his own style, claiming that the only true teacher was nature. His finest workTravelers among Mountains and Streamsis a masterpiece of landscape painting and many future artists turned to it for inspiration.Qi Baishi (1864-1957)One of the greatest contemporary Chinese painters, Qi Baishi is known for not being influenced by Western styles like most painters of his time. He can be considered as the last great traditional painter of China. He painted almost everything from insects to landscapes. He is regarded highly in Chinese art for the freshness that he brought to the familiar types of birds and flowers, insects and grass.Wu Guanzhong (1919—2010)Widely considered as the founder of modern Chinese painting , Wu Guanzhong has painted various aspects of China, like its architecture, plants, animals, people and landscapes. Wu went on to combine Western and Chinese styles to create a unique form of modem art. In 1992, he became the first living Chinese artist whose work was exhibited at the British Museum.1.What do we know about Li Cheng?A.He loved landscape paintings.B.He copied many artists' work.C.His work gained worldwide recognition.D.He was considered as Fan Kuan's teacher.2.What is the main feature of Qi Baishi's paintings?A.They have foggy appearances.B.They lack diversity in the theme.C.They come under Western influence.D.They show advanced traditional painting skills.3.What did the four Chinese painters have in common?A.They were all modern painters.B.They all created landscape paintings.C.They were all impacted by Western art.D.They were all pioneers intraditional art history.BVolunteer DayWhat better way is there to enjoy your own hobbies while helping others at the same time? Come to Volunteer Day and choose which activity you’d like to join for the day. See below for a schedule of events on Volunteer Day.Volunteer Day schedule:7:30am.: Meet at the Community (社区) Center for juice and bagels.8:00—8:30 a.m.: Choose which activity you’d like to help with for the day.8:30 a.m.: Board the bus to your activity site.9:00 a.m.—3:30 p.m.: Work as a volunteer.3:30 p.m.: Board the bus that will take you back to the Community Center.See below for a list of volunteer opportunities for Volunteer Day so you can begin thinking about which activity you might want to join.A list of volunteer activities:Paint houses: Do you enjoy making art? If so, this volunteer opportunity might be just right for you! Happy Homes is a local organization that provides home repairs for needy people in the form of painting. For elderly or physically disabled people who cannot do repairs to their homes, Happy Homes provides volunteer painters to repaint old homes; outside or in. Happy Homes also provides painters to create beautiful wall paintings inside schools or community centers.Plant flowers: Do you enjoy being outside in nature? City Parks Association has many great opportunities for people who love to be outdoors. Help plant flowers and bushes in city parks; help lay paths at Cave Springs Park, or help pick up rubbish around the river banks. These activities are very active, so remember to be prepared with plenty of drinking water!Read to children: Do you enjoy working with young children? Do you like books? Love and Learning is an organization that provides volunteers to help children with learning disabilities. Read books out loud to groups of children four to six years old, or read one-on-one with struggling readers seven to eight years old.Play with animals: Do you love animals? Lovely Friends is an organization that visits local animal shelters and provides volunteers to spend time with the animals while their cages are being cleaned. Play with puppies, snuggle with cats, or hand-feed rabbits.4. At what time do volunteers leave for their activity sites?A. 7:30 a.m..B. 8:00 a.m.C. 8:30 a.m.D. 9:00 a.m.5. An outdoor lover probably takes part in ______.A. Plant flowersB. Paint housesC. Read to childrenD. Play with animals6. What do Lovely Friends volunteers do?A. Read books to children.B. Spend time with animals.C. Help plant bushes in parks.D. Pick up garbage along the river.7. The purpose of the passage is to _________.A. educate childrenB. attract volunteersC. comfort the elderlyD. encourage the disabledCIdentifying the chemical makeup of pigment (色素) used in ancient documents, paintings, and watercolor1 s is criticalto restoring and conserving the precious artworks. However, despite numerous efforts, scientists had been unable to determine the source of folium, a popular blue dye used to color1 manuscripts (手稿) in Europe during the middle ages — from the 5th to the 15th century. Now, a team of researchers fromPortugalhas finally uncovered the mysterious ingredient responsible for the gorgeous blueish-purple color1 that helped bring ancient illustrations and texts to life.The research team began byporing overinstructions penned by European dye makers from the 12th, 14th,and 15th centuries. They found what they were seeking in a 15th-century text entitledThe Book on How to Make All the Color Paints for Illuminating Books. However, translating the instructions was no easy task. It was written in the now extinct Judaeo-Portuguese language, and though the source of the dye was traced back to a plant, no name was mentioned.However, by piecing together suggestions from the text, the scientists were able to determine that the dye was made from the bluish-green berries of the chrozophora tinctoria plant. After an extensive search, the team found a few varieties of the plant growing along the roadside near the town ofMonsarazin southPortugal.The detailed instructions gave the researchers critical clues — including the best time to pick the berries. “You need to squeeze the fruits, being careful not to break the seeds, and then to put them on linen (亚麻).” The scientist says the detail was important since broken seeds polluted the pigment, producing an inferior quality ink. The dyed linen, which was left to dry, was an efficient way to store and transport the pigment during ancient times. When needed, the artist would simply cut off a piece of the cloth and dip it with water to squeeze out the blue color1 .Once the key ingredient had been identified, the researchers began to determine the dye’s molecular structure. To their surprise, they found that folium was not like any other known permanent blue dyes — it was an entirely new class of color1 , one they named chrozophoridin. “Chrozophoridin was used in ancient times to make a beautiful blue dye for painting.” the team wrote in the study. “Thus, we believe that this will not be our final word on this amazing plant and its story and that further discoveries will follow soon.”8. The primary purpose of the study is to ________.A. restore and conserve ancient precious artworksB. determine the substance making up the foliumC. prove the ancient dye-making technique was organicD. identify which class of color1 folium belongs to9. The underlined phrase “poring over”in the second paragraph means ________.A. discussing publiclyB. testing repeatedlyC. passing directlyD. reading carefully10. What can be learned about the blue dye folium?A. It was essentially an inferior type of ink.B. It was the only kind made from wild berries.C. It could be carried and used easily.D. It was carefully squeezed from broken seeds.11. The article is mainly about _________.A. how the mystery ofa thousand-year-old blue dye was solvedB. why the researchers took the trouble to recreate the dyeC. what needs to be done to make an organic dye from a plantD. when and where the discovery of the dye was madeDUntil quarantine (隔离期) ends, we are left picturing what sport we might do: working out at the gym, playing on a competitive sports team, swimming, biking, or rock climbing. However, we don’t often think of martial arts as possible activities; instead, we rule it out because we think it’s dangerous, uncommon, and even, impossible. Martial arts aren’t considered a sport, right?Well, here’s some good news: you’re wrong! Martial arts aren’t much more common than people think, and you can start learning at any age. Practicing martial arts is a great way to keep in shape, both physically and mentally. They’re much less boring and much lessarduoussport than they’re usually described as in movies, so do not worry that they need a lot of effort.Martial arts generally require you to focus on the position and movement of every one of your legs and arms, sometimes even your breathing too. Think about it: when you leave the gym, your mental state has improved and you are much calmer. This is because you’ve only paid attention to one activity. It is a great way to clear your head. Andpracticing it can help you learn to stay more focused, which is the greatest advantage of martial arts training.Martial arts also improve your coordination (协调性), and greatly improve your posture (姿势). I have personally seen students go from slouching (没精打采) to walking tall with their shoulders back in just a couple of months.There are many styles and countless kinds of martial arts. Whichever one you like better, know that all of them are good choices.12. What can we know about martial arts from the first two paragraphs?A. They often have people hurt.B. They are difficult to practice.C. People have a wrong view on it.D. People practice them more often.13. What does the underlined word “arduous” in paragraph 2 mean?A. Interesting.B. Difficult.C. Friendly.D. Exciting.14. What is the biggest benefit of practicing martial arts?A. Adjusting the breath.B. Enjoying one’s free time.C. Correcting the movement.D. Keeping one’s attention.15. What does the writer think of martial arts?A. They are notsports.B. They attracted many teenagers.C. They are beneficial and helpful.D. They were invented to protect others.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。

2024年上海市同济中学物理高三第一学期期中复习检测试题考生须知：1．全卷分选择题和非选择题两部分，全部在答题纸上作答。

选择题必须用2B铅笔填涂；非选择题的答案必须用黑色字迹的钢笔或答字笔写在“答题纸”相应位置上。

2．请用黑色字迹的钢笔或答字笔在“答题纸”上先填写姓名和准考证号。

3．保持卡面清洁，不要折叠，不要弄破、弄皱，在草稿纸、试题卷上答题无效。

一、单项选择题：本题共6小题，每小题4分，共24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。

1、下列有关牛顿运动定律的说法，其中正确的是（）A．惯性就是物体保持静止状态的性质B．一对作用力和反作用力的作用效果总相同C．物体运动状态改变的难易程度就是加速度D．力的国际制单位“牛顿”是根据牛顿第二定律定义的2、某宇航员登陆水星后，测得水星的半径是地球半径的12，水星的质量是地球质量的19，已知地球表面的重力加速度是g，地球的半径为R，该宇航员在地球表面能向上竖直跳起的最大高度是h，忽略自转的影响，下列说法正确的是A．水星的平均密度为23gGRB．水星表面的重力加速度是2 3 gC．水星的第一宇宙速度与地球的第一宇宙速度相等D．该宇航员以与在地球上相同的初速度在水星上起跳后，能达到的最大高度是4 9 h3、一静止的铀核放出一个α粒子衰变成钍核，衰变方程为U→Th＋He，下列说法正确的是A．衰变后钍核的动能等于α粒子的动能B．衰变后钍核的动量大小等于α粒子的动量大小C．铀核的半衰期等于其放出一个α粒子所经历的时间D．衰变后α粒子与钍核的质量之和等于衰变前铀核的质量4、如图，质量为m、带电量为q的小球B用绝缘细线悬挂，处于固定的带电体A产生的电场中，A可视为点电荷，B为试探电荷。

当小球B静止时，A、B等高，细线偏离竖直方向的夹角为θ。

已知重力加速度为g。

则点电荷A在B处所产生的场强大小为（）A ．tan mg θB ．sin mg q θC ．cos mg q θD ．tan mg qθ 5、下列叙述符合物理学史实的是（ ）A ．牛顿提出了万有引力定律，并用实验测量了万有引力常量B ．库仑最早引入了电场概念，并提出用电场线表示电场C ．奥斯特对电磁感应现象的研究，将人类带人了电气化时代D ．安培提出了分子电流假说，解释了磁铁的磁场和电流的磁场在本质上相同6、如图所示，A 是一质量为M 的盒子，B 的质量为35M ，用细绳相连，跨过光滑的定滑轮，A 置于倾角为θ=30°的斜面上，B 悬于斜面之外，处于静止状态.现在向A 中缓慢地加入沙子，整个系统始终 保持静止，则在加入沙子的过程中下列说法错误的是A ．绳子拉力大小不变，恒等于35Mg B ．A 对斜面的压力逐渐增大C ．A 所受的摩擦力逐渐增大D ．A 所受的摩擦力先减小后增大二、多项选择题：本题共4小题，每小题5分，共20分。

同济大学网络教育学院200 -200 学年第学期期终考试管理学概论课程考试题（卷）学号一. 单选（共30题,共30分）1. 高层管理计划着重组织（）。

A.在环境中的定位和确定与环境的能量互换关系B.内部各个组成部分的定位和相互关系的确定C.每一个岗位、每一个人员、每一个时间的工作安排和协调D.内、外条件的评估和协调2. 计划工作的核心是（）A.确定目标B.估量机会C.决策D.确定计划前提条件3. 合理决策必须具备的三个条件不包括（）。

A.目标合理B.可靠的信息情报C. 有限合理D.决策结果满足预定目标的要求4. 决策树的构成要素是（）。

A.概率枝、方案枝、决策点、状态结点B.方案、概率、期望值、自然状态C.决策点、方案枝、概率枝、自然状态D.方案、决策点、概率、状态结点5. 职能部门化的一个主要缺点是（）。

A.需要较多的综合管理人员B.易产生本位主义C.管理成本上升D.使高层管理部门增加了困难6. 统一命令原则是（）。

A.每人只能有一个上司B.权责对等C.责任不可委任D.反映组织系统的相互关系7. 人力资源管理包括（）。

A.人力资源的战略计划与人力资源供求预测B.招聘、挑选与安置C.培训、发展与评价D.以上全部8. 组织招聘中，职务规范与职务描述是在（）的基础上提出的。

A.工作描述B.工作估值C.工作分析D.动作研究9. 在员工考绩中，允许员工参与确定自身绩效目标和评价自己工作情况的方法是（）。

A.排队法B.两两比较法C.关键事件法D.目标评定法10. 通过组织中等级制度所赋予的权力是（）。

A.法定权力B.表率权力C.专家权力D.奖惩权力11. 领导与非领导的差异在于领导具有一些可被确认的基本特性。

持这种观点的理论被称为（）。

A.领导行为连续统一体理论B.管理方格图理论C.领导特性理论D. 归因理论12. “大棒”是最为传统的激励手段之一。

以下现象中不属于由“大棒”产生的消极效应是（）。

A.消极怠工B.一切向钱看C.生产劣质产品D.对工作漠不关心13. 马斯洛需要层次理论中最基本的需要是（）。

同济大学课程考试试卷〔A卷〕2007-2021学年第一学期命题教师签字：审核教师签字：课号：14019 课名：口腔正畸学考试考查：考查此卷选为：期中考试〔〕、期终考试〔〕、重考考试〔〕年级 ___________ 专业_____________ 学号_____________ _____________ 得分_____________一、名词解释(共计32分，4分一个)1. 个别正常合〔英文名称：〕：2. 面横平面或眼耳平面〔英文名称：〕：3. 开牙合4. 牙齿的过度矫治5. 早期矫治6. 咬合重建7. 旋转中心8. 间接骨吸收二、简答题〔共计24分，8分一个〕1．简述人体不同组织系统发育与年龄的关系。

2．前牙深覆盖按病因机制可分为哪几类？3. 根据作用力类型简述早期生长控制的常见治疗方法。

三、问答题〔共计44分，第一题12分，第二、三题每题16分〕1. 在正畸拔牙时应考虑的因素有哪些？2. 试述下颌骨的三向生长？3 功能矫治器的作用原理、共同特点和适应症？07/08学年第一学期2004级口腔医学本科生口腔正畸学〔A卷答案〕一、名词解释(共计32分，4分一个)1. 个别正常合〔英文名称：individual normal occlusion〕：凡轻微的错牙合畸形，对于生理过程无大阻碍者，都可列入正常牙合范畴。

这种正常范畴内的个体牙合，彼此之间又有所不同，故称之为个别正常牙合。

2. 面横平面或眼耳平面〔英文名称：FH. Frankfort horizontal plane〕：由耳点和眶点连线组成。

大局部个体在正常头位时，眼耳平面与地面平行。

3. 开牙合开颌主要是上下牙弓及颌骨垂直象发育异常，具体表现在前段牙、牙槽和颌骨高度发育缺乏，后段牙，牙槽或颌骨高度发育过度，或二者皆而有之。

其临床表现是上下颌牙在正中颌位及下颌功能运动时无颌接触。

4. 牙齿的过度矫治对错位严重且容易复发的牙颌畸形，在矫治过程中实行的一种有效预防复发的手段。

2019-2020学年同济高级中学高三英语上学期期中考试试题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AIn his 402nd anniversary year, Shakespeare is still rightly celebrated as a great language master and writer. But he was not the only great master of play writing to die in 1616, and he is certainly not the only writer to have left a lasting influence on theater.While less known worldwide, Tang Xianzu is considered one of Chinas greatest playwrights and is highly spoken of in that country of ancient literary and dramatic traditions.Tang was born in 1550 inLinchuan,Jiangxiprovince. Unlike Shakespeare's large body of plays,poems and sonnets (十四行诗), Tang wrote only four major plays: The Purple Hairpin, Peony Pavilion (《牡丹亭》), A Dream under the Southern bough, and Dream of Handan. The latter three were constructed around a dream narrative, a way through which Tang unlocked the emotional dimension of human desires and ambitions and explored human nature beyond the social and political limits of that time.Similar to Shakespeare, Tang's success rode the wave of a renaissance (复兴) in theater as an artistic practice. As in Shakespeare'sEngland, Tang's works became hugely popular inChinatoo. During Tang'sChina, his plays were enjoyed performed, and changed. Kunqu Opera, a form of musical drama, spread from southernChinato the whole nation and became a symbol of Chinese culture. Combining northern tune and southern music, kunqu Opera was known for its poetic language, music, dance movements and gestures. Tang's works benefited greatly from the popularity of kunqu Opera, and his plays are considered classics of kunqu Opera.While Tang and Shakespeare lived in a world away from each other, there are many things they share in common, such e humanity of their drama, their heroic figures, their love for poetic language, a lasting popularity and the anniversary during which we still celebrate them.1. Why is Shakespeare mentioned in the first paragraph?A. To describe Shakespeare's anniversary.B. To introduce the existence of Tang Xianzu.C. To explain the importance of Shakespeare.D. To suggest the less popularity of Tang Xianzu.2. What's possibly one of the main theme of Tang's works?A. Social reality.B. Female dreams.C. Human emotions.D. Political environment.3. What does the author mainly tell us in Paragraph 4?A. The influence of Kunqu Opera on Tang's works.B. Tang's success in copying Shakespeare's styles.C. The way Kunqu Opera became a symbol of Chinese culture.D. Tang's popularity for his poetic language and music.BEvery racehorse has different abilities．Like humans，some are short- distance runners，while others are marathoners．Figuring out which is which and how to pace them can be the difference between failure in the finish and taking the award home．Jockeys（赛马骑师）and trainers have traditionally relied on centuries of experience and data from previous races to plan their races．Amandine Aftalion，a mathematician in Paris，thought she could add to that．Since 2013，she has been analyzing the performances of world champion runners like Usain Bolt．She has found that short-distance runners tend to win when they start strong and gradually slow down toward the finish line．Butin medium-distance races，runners perform better when they start strong，settle down，and finish with a burst of speed．Her model shows how those winning strategies maximize the energy output of muscles reliant on two different pathways：powerful aerobic（有氧的）ones that require oxygen，which can be in limited supply during a race，and anaerobic ones，which don't need oxygen but build up waste products that lead to tiredness．Aftalion wondered which strategy would be best for horses．So she and Quentin Mercier，anothermathematician，took advantage of a new GPS tracking tool inserted in French racing saddles（马鞍）．The two studied patterns in many races at the Chantilly racetracks north of Paris and developed a model that accounted for winning strategies for three different races：a short one(1，300 meters)，a medium one (1,900 meters)，and a slightly longer one (2,100 meters)，all with different starting points on the same track．The model takes into account not just different race distances，but also the size or friction fromthe track surface．The results might surprise jockeys who hold horses back early for bursts of energy in the last finish．Instead，a strong start leads to a better finish，the team found．“That doesn't mean those jockeys are wrong，though．If the start is too strong，it can bedevastatingas well，leaving the horse tired by the end，” Aftalion says．4. What should a runner do to get an award according to the text?A. Make a good start．B. Plan for the race early．C. Run slowly on the starting line．D. Try runningquickly all the time．5. What formed the basis for Aftalion's studying horse race?A The experience and data from previous horse races．B. The benefit of knowing horses' different abilities．C. The success in studying runners' winning strategies．D. The performance of horses on different race distances．6. What does the underlined word“devastating”in the last paragraph mean?A. Boring．B. Damaging．C. Astonishing．D. Puzling．7. What can we infer from the text?A. Runners have the same energy output of muscles．B. Aftalion's findings may help horses to win the race．C. What Jockeys and trainers do makes no sense to horses．D. World champion runners made a contribution to the study．CAmerican football was the fastest-growing sport for US young players last year, according to a survey sponsored by the sport's governing body.But it was the game's no tackle variety that showed the biggest increase－a finding that may reflect concerns about injury. In American football, a tackle (抢断球) refers to an attempt to stop an opponent by forcing them to the ground.The number of participants in football grew in 2015 while most other sport, except baseball, posted a decline, USA Football said on Monday, citing(引用) the findings of a survey of 30,000 children and teenagers.Participation in flag football (a no-tackle type of football) increased by 8.7 percent among children aged 6 to 14, while tackle football rose by 1.9 percent. For that age group, the only other sport that grew was baseball, with a 3. 3 percent increase.In the 15-to-18 age group, flag football rose by 10. 5 percent, while tackle grew by 2.5 percent.Basketball was the third, with a 1. 1 percent increase. Participation in all other sports declined.Tom Farrey, executive director of the Aspen Institute's Sports & Society Program, said he was surprised that flag football participation rose so much.“The trend suggests that parents aremarching to the beat of a different drummer, in pursuing flagas analternative for their kids," he said.The findings come at a time of increasing concern about the risk associated with youth sports, particularly hockey (曲棍球) and football, where medical researchers have warned about the risk of concussions (damagesto the brain caused by violent blows to the head) and death linked to brain injury.USA Football, anIndianapolis,Indianabased nonprofit funded in part by the National Football League, believed that the increases resulted from better safety and health education."Football participation increases, even modest increases, may signal that programs such as our Heads Up Football program and practice guidelines are making a positive difference," said Scot Hallenbeck, USA Football chief executive, in a statement.Robert Cantu, aBostonUniversityneurosurgery professor and investigator at the school's chronic Traumatic Encephalopathy (CTE) Center said the increase in fag football participation signaled that more parents were directing children to a safe alternative8. What can we learn about the two age groups?A. Flag football grew the fastest in the 6-to-18 group.B. Tackle football grew he fastest in the 6-to-14 group.C. Participation in baseball declined the most in both groupsD. Participation in tackle football increased the most in both groups.9. The underlined part probably means ________.A working at a different paceB. behaving in a different wayC. ignoring the major differencesD. trying to accept different opinions10. The popularity of flag football is inked with the fact thatA. its rules have been adapted for young playersB. it receives more funds than other varietiesC. tackle football is an old-fashioned gameD. experts worry about children's safety11. What is the cause of football growth according to USA Football?A. Their safety programs are successful.B. More children show interest in the game.C. Football is less likely to cause concussions.D. There are different types of football to choose from.DAn afternoon nap(午睡)is one of the joys of life, although too much napping could signal all is not well. In some cultures, people will have a daily nap — thisis fine. The warning comes when people start sleeping during the daytime, when they did not before. There is certainly a good reason to believe that daytime sleepiness — as in the Alzheimer's study — can be a marker of an underlying condition.For most people, napping during the day is mainly a sign that you are not getting enough sleep at night, says Dr. Neil Stanley, a sleep expert. "If you feel sleepy during the day, you should think about taking a nap. That is what the body needs — it doesn't need to be kept awake with caffeine, it needs sleep. "The feeling to notice is "sleepiness", he says, not "tiredness", which could be more psychological and linked to stress.So how do you nap well? The key thing, says Stanley, is how long your nap lasts. Choose either a 20-or 90-minute nap. "When you fall asleep, you'll quickly go through the lighter stages of sleep into your first period of deep sleep. You don't want to wake up in deep sleep because that's when you wake and feel worse than you did before. "Napping for 20 minutes means you will wake up before you go into deep sleep; napping for 90 minutes means you'll complete a sleep cycle.Once you factor in the time it takes to fall asleep — some people are better at napping than others but, says Stanley, "a healthy adult will fall asleep in between 5 and 12 minutes" — you can set an alarm, allowing a 30- to 40-minute period for a short nap, and up to two hours for a longer one.A good time to nap is during the body's natural dip in the afternoon, between 2 pm and 4 pm. "You don't really want to be napping much pastthatbecause then you are going to be eating into your night-time sleep," Stanley says. The point, he stresses, is to get good night-time sleep, which would ensure you probably don't need to nap at all.12. What does an afternoon nap indicate for most people?A. Caffeine addiction.B. Psychological stress.C. Insufficient night sleep.D. Potential physical illness.13. What is the key to a good nap?A. Duration.B. Surroundings.C. Health.D. Stages.14. What does the underlined word "that" in the last paragraph refer to?A. A 30- to 40- minute period.B. Between 2 pm and 4 pm.C. Between 5 and 12 minutes.D. A 20- to 90-minute period.15. Which of the following can be the best title for the text?A. Why to phase a napB. When to take a good napC. What to learn from a napD. How to have a successful nap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。

2024学年同济大学二附中高二数学第一学期期中考试卷满分：150分，完成时间：120分钟一、填空题（本题满分54分，共12小题，第1-6题每题4分，7-12题每题5分）1.在空间中，如果两条直线没有交点，那么这两条直线的位置关系是___________.2.半径为2的球的表面积为________.3.已知长方体1111ABCD A B C D -的棱11AD AA ==，2AB =，则异面直线BD 与11B C 所成角的余弦值为______．4.在四面体P ABC -中，若底面ABC 的一个法向量为()1,1,0n = ，且()2,2,1CP =- ，则顶点P 到底面ABC 的距离为_____________．5.已知一圆锥侧面展开图是一半径为2的半圆，则该圆锥的侧面积为___________.6.如图，一个水平放置的平面图形的斜二测直观图是直角梯形OA B C '''，且//OA B C '''，24OA B C '''==，2A B ''=，则该平面图形的面积为_________.7.三棱锥P ABC -中，三条侧棱PA PB PC ==，则顶点P 在平面ABC 内的射影O 是ABC V 的______．（填“内心”、“外心”、“重心”、“垂心”）8.在空间四边形ABCD 中，E ，F ，G ，H 分别是边AB ，BC ，CD ，DA 的中点，若四边形对角线2==AC BD ，对角线AC 与BD 所成的角为π3，则FH =______．9.如图，在圆柱O 1O 2内有一个球O ，该球与圆柱的上、下底面及母线均相切．记圆柱O 1O 2的体积为V 1,球O 的体积为V 2，则12V V 的值是_____10.已知二面角AB αβ--为30°，P 是半平面α内一点，点P 到平面β的距离是1，则点P 在平面β内的投影到AB 的距离是_________．11.如图是底面半径为3的圆锥，将其放倒在一平面上，使圆锥在此平面内绕圆锥顶点S 滚动，当这个圆锥在平面内转回原位置时，圆锥本身恰好滚动了4周，则圆锥的母线长为_____12.如图，正方体1111ABCD A B C D -的棱长为4，点P 在正方形ABCD 的边界及其内部运动.平面区域W 由所有满足14A P ≤≤的点P 组成，则四面体1P A BC -的体积的取值范围_________.二、选择题（共4小题，第13、14题每题4分，15、16题每题5分）13.已知直线l 和平面α，则“l 垂直于α内的两条直线”是“l α⊥”的（）．A.充分非必要条件 B.必要非充分条件 C.充要条件 D.非充分非必要条件14.把一个圆锥截成圆台，已知圆台的上、下底面半径的比为1:4，母线（原圆锥母线在圆台中的部分）长为12，则原圆锥的母线长为（）A.16 B.18 C.20 D.2215.m n 、为空间中两条直线，αβ、为空间中两个不同平面，下列命题中正确的个数为（）①二面角的范围是[)0,π；②经过3个点有且只有一个平面；③若m n 、为两条异面直线，,,//m n m αββ⊂⊂，则//n α．④若m n 、为两条异面直线，且//,//,//,//m n m n ααββ，则//αβ．A.0B.1C.2D.316.《九章算术》中将底面为直角三角形且侧棱垂直于底面的三棱柱称为“堑堵”；底面为矩形，一条侧棱垂直于底面的四棱锥称之为“阳马”；四个面均为直角三角形的四面体称为“鳖臑”.如图，在堑堵111ABC A B C -中，AC BC ⊥，且12AA AB ==.下列说法错误．．的是（）A.四棱锥11B A ACC -为“阳马”B.四面体11AC CB 为“鳖臑”C.四棱锥11B A ACC -体积的最大值为23D.过A 点作1AE A B ⊥于点E ，过E 点作1EF A B ⊥于点F ，则1A B ⊥面AEF三、解答题（本题满分78分，共5小题）17.如图，棱长为2的正方体1111ABCD A B C D -中，M N P 、、分别是1111C D CC AA 、、的中点．（1）证明：//MN 平面11ABB A ．（2）求异面直线1PD 与MN 所成角的大小．（结果用反三角表示）18.如图，已知PA ＝AC ＝PC ＝AB ＝a ，PA AB ⊥，AC AB ⊥，M 为AC 的中点．（1）求证：PM ⊥平面ABC ；（2）求直线PB 与平面ABC 所成角的大小．19.现需要设计一个仓库，由上、下两部分组成，上部的形状是正四棱锥1111P A B C D -，下部的形状是正四棱柱1111ABCD A B C D -(如图所示)，并要求正四棱柱的高1O O 是正四棱锥的高1PO 的4倍.（1）若m 6AB =，12m PO =，则仓库的容积是多少？（2）若正四棱锥的侧棱长为6m ，当1PO 为多少时，下部的正四棱柱侧面积最大，最大面积是多少？20.如图，AB 是圆柱的底面直径，2AB =，PA 是圆柱的母线且2PA =，点C 是圆柱底面圆周上的点．（1）求圆柱的表面积；（2）证明：平面PBC ⊥平面PAC ；（3）若1AC =，D 是PB 的中点，点E 在线段PA 上，求CE ED +的最小值．21.已知点P 是边长为2的菱形ABCD 所在平面外一点，且点P 在底面ABCD 上的射影是AC 与BD 的交点O ，已知60BAD ∠=︒，PDB △是等边三角形.（1）求证：AC PD ⊥；（2）求点D 到平面PBC 的距离；（3）若点E 是线段AD 上的动点，问：点E 在何处时，直线PE 与平面PBC 所成的角最大？求出最大角的正弦值，并说明点E 此时所在的位置.同济大学第二附属中学2024学年第一学期期中考试高二年级数学学科试卷满分：150分，完成时间：120分钟一、填空题（本题满分54分，共12小题，第1-6题每题4分，7-12题每题5分）1.在空间中，如果两条直线没有交点，那么这两条直线的位置关系是___________.【答案】平行或异面【解析】【分析】根据空间中两直线的位置关系即可判断.【详解】空间中的直线没有公共点，则两直线要么平行，要么是异面直线.故答案为：平行或异面2.半径为2的球的表面积为________.【答案】16π【解析】【分析】代入球的表面积公式:2=4S R π表即可求得.【详解】2R = ，∴由球的表面积2=4S R π表公式可得,2=42=16S ππ⨯⨯球表,故答案为:16π【点睛】本题考查球的表面积公式;属于基础题.3.已知长方体1111ABCD A B C D -的棱11AD AA ==，2AB =，则异面直线BD 与11B C 所成角的余弦值为______．【答案】5【解析】【分析】由定义说明DBC ∠是异面直线BD 与11B C 所成角或其补角，然后计算．【详解】因为11//B C BC ，所以DBC ∠是异面直线BD 与11B C 所成角或其补角，在直角BDC中，BD ==，5cos 5BC CBD BD ∠===，故答案为：5．4.在四面体P ABC -中，若底面ABC 的一个法向量为()1,1,0n = ，且()2,2,1CP =- ，则顶点P 到底面ABC 的距离为_____________．【答案】【解析】【分析】根据点面距公式代入计算即可得.【详解】由点面距公式得d n CP n ==⋅==故答案为：5.已知一圆锥侧面展开图是一半径为2的半圆，则该圆锥的侧面积为___________.【答案】2π【解析】【分析】根据圆锥侧面展开图与圆锥侧面的关系求出圆锥底面圆半径即可计算得解.【详解】设圆锥底面圆半径为r ，则该圆锥底面圆周长为2r π，因圆锥侧面展开图是一半径为2的半圆，则半圆弧长为2π，依题意，22ππ=r ，解得1r =，显然圆锥的母线长2l =，则圆锥侧面积2S rl ππ==，所以圆锥的侧面积为2π.故答案为：2π6.如图，一个水平放置的平面图形的斜二测直观图是直角梯形OA B C '''，且//OA B C '''，24OA B C '''==，2A B ''=，则该平面图形的面积为_________.【答案】122【解析】【分析】首先求出OC '，再画出平面图形，从而求出其面积.【详解】因为24OA B C '''==，2A B ''=，所以()2242222OC '=-+=由直观图可得如下平面图形，则24OA BC ==，242OC OC '==，所以()124222OABC S =⨯+⨯=.故答案为：1227.三棱锥P ABC -中，三条侧棱PA PB PC ==，则顶点P 在平面ABC 内的射影O 是ABC V 的______．（填“内心”、“外心”、“重心”、“垂心”）【答案】外心【解析】【分析】由已知可得顶点P 在底面ABC 上的射影O 到底面三角形三个顶点的距离相等，即O 为ABC V 的外心.【详解】如图，设顶点P 在底面ABC 内的射影为O ，则⊥PO 平面ABC ，连接OA ，OB ，OC ，OA ，OB ，OC 在平面ABC 内，∴PO OA ⊥，PO OB ⊥，PO OC ⊥，∴POA ，POB V ，POC △都是直角三角形，PA PB PC ==，∴POA ，POB V 和POC △三个三角形全等，从而有OA OB OC ==，所以O 为ABC V 的外心.故答案为：外心.8.在空间四边形ABCD 中，E ，F ，G ，H 分别是边AB ，BC ，CD ，DA 的中点，若四边形对角线2==AC BD ，对角线AC 与BD 所成的角为π3，则FH =______．【答案】1【解析】【分析】由题意可知四边形EFGH 为菱形，且知菱形相邻的两个角分别为π2π,33，再由所给边长即可求得FH 的长.【详解】如图，由,,,E F G H 分别是,,,AB BC CD DA 的中点，得1////,12EF AC HG EF HG AC ===，1////,12EH BD FG EH FG BD ===，则四边形EFGH 为菱形，又AC 与BD 所成的角为π3，于是直线EF 与EH 所成角为π3，即菱形EFGH 的边长为1，相邻两个内角分别为π2π,33，即π3FEH ∠=或2π3FEH ∠=，当π3FEH ∠=时，1FH EF ==,当2π3FEH ∠=时，2sin60FH EF ==所以1FH =或FH =故答案为：19.如图，在圆柱O 1O 2内有一个球O ，该球与圆柱的上、下底面及母线均相切．记圆柱O 1O 2的体积为V 1,球O 的体积为V 2，则12V V 的值是_____【答案】32【解析】【详解】设球半径为r ，则12=B 2×243B 3=32．故答案为32．点睛:空间几何体体积问题的常见类型及解题策略：①若给定的几何体是可直接用公式求解的柱体、锥体或台体，则可直接利用公式进行求解；②若所给定的几何体的体积不能直接利用公式得出，则常用转换法、分割法、补形法等方法进行求解．10.已知二面角AB αβ--为30°，P 是半平面α内一点，点P 到平面β的距离是1，则点P 在平面β内的投影到AB 的距离是_________．【解析】【分析】设点P 在平面β内的投影为点Q ，作PO AB ⊥于点O ，连接OQ ，证明POQ ∠即为二面角AB αβ--的平面角，再解Rt POQ △即可.【详解】如图，设点P 在平面β内的投影为点Q ，则PQ β⊥，1PQ =，作PO AB ⊥于点O ，连接OQ ，因为PQ β⊥，,OQ AB β⊂，所以,PQ AB PQ OQ ⊥⊥，又,,,PO AB PO PQ P PQ PO ⊥⋂=⊂平面POQ ，所以AB ⊥平面POQ ，又OQ ⊂平面POQ ，所以AB OQ ⊥，所以POQ ∠即为二面角AB αβ--的平面角，所以30POQ ∠=︒，在Rt POQ △中，30,1POQ PQ ∠=︒=，所以OQ =即点P 在平面β内的投影到AB11.如图是底面半径为3的圆锥，将其放倒在一平面上，使圆锥在此平面内绕圆锥顶点S 滚动，当这个圆锥在平面内转回原位置时，圆锥本身恰好滚动了4周，则圆锥的母线长为_____【答案】12【解析】【分析】设圆锥的母线长为l,求出以S 为圆心，SA 为半径的圆的面积以及圆锥的侧面积，根据题意，列出方程即可求得答案.【详解】设圆锥的母线长为l,则以S 为圆心，SA 为半径的圆的面积为2πl ，又圆锥的侧面积为π33πl l ⨯⨯=，因为当这个圆锥在平面内转回原位置时，圆锥本身恰好滚动了4周，所以2π43πl l =⨯，解得12l =，故答案为：1212.如图，正方体1111ABCD A B C D -的棱长为4，点P 在正方形ABCD 的边界及其内部运动.平面区域W 由所有满足14A P ≤≤的点P 组成，则四面体1P A BC -的体积的取值范围_________.【答案】1632,33⎡⎤⎢⎥⎣⎦【解析】【分析】连接AP ，由线面垂直的性质得到1A A AP ⊥，再由勾股定理求出0||2AP ≤≤，即可得到P 以A 为圆心2为半径的14圆面上，再根据1111,3P A BC A PBC PBC V V AA S --==⋅ 得到当P 在边AD 上时四面体的体积最大，当P 在边AB 的中点时四面体的体积最小，再根据面体的体积公式计算可得取值范围.【详解】连接AP ，如图所示，因为1A A ⊥平面ABCD ，AP ⊂平面ABCD ，所以1A A AP ⊥，∵14A A =，由145A P ≤≤2211||A P AP AA =+，则0||2AP ≤≤；所以P 在以A 为圆心2为半径的14圆面上，由题意可知，11113P A BC A PBC PBC V V AA S --==⋅ ，所以当P 在边AD 上时，四面体1P A BC -的体积的最大值是1132444323⨯⨯⨯⨯=.所以当P 在边AB 的中点时，PBC S 的面积取得最小值，此时14242PBC S =⨯⨯=△，所以四面体1P A BC -的体积的最小值是1164433⨯⨯=，所以11632,33P A BC V -⎡⎤∈⎢⎥⎣⎦，故答案为：1632,33⎡⎤⎢⎥⎣⎦.【点睛】思路点睛：求解三棱锥体积的最值问题，要找准突破口，也即是按三棱锥的体积公式13V Sh =，通常会有以下两种：①如果底面积固定，则通过找高的最值来进行求解；②如果高已知确定，则求底面积的最值来进行求解（如本题）.二、选择题（共4小题，第13、14题每题4分，15、16题每题5分）13.已知直线l 和平面α，则“l 垂直于α内的两条直线”是“l α⊥”的（）．A.充分非必要条件B.必要非充分条件C.充要条件D.非充分非必要条件【答案】B【分析】利用直线与平面垂直的判定定理，即可得出结论.【详解】根据直线与平面垂直的判定定理可知：如果一条直线垂直于平面内的两条相交直线，那么这条直线垂直于这个平面.而“l 垂直于α内的两条直线”，没有满足相交，所以不一定能推出直线与平面垂直，但是如果一条直线与平面垂直，一定能推出这条直线垂直于平面内的所有直线，即可得：“l 垂直于α内的两条直线”是“l α⊥”的必要不充分条件.故选：B .14.把一个圆锥截成圆台，已知圆台的上、下底面半径的比为1:4，母线（原圆锥母线在圆台中的部分）长为12，则原圆锥的母线长为（）A.16B.18C.20D.22【答案】A【分析】根据圆台的几何特征利用三角形相似即可求得结果.【详解】由题意可得，几何体如下图所示：取轴截面可知，圆台的上、下底面半径的比为14CD AB =，且//,12CD AB BD =，设圆锥的母线长为l ，根据相似比可得1214CD ED l AB EB l -===，解得16=l ，即原圆锥的母线长为16.故选：A.15.m n 、为空间中两条直线，αβ、为空间中两个不同平面，下列命题中正确的个数为（）①二面角的范围是[)0,π；②经过3个点有且只有一个平面；③若m n 、为两条异面直线，,,//m n m αββ⊂⊂，则//n α．④若m n 、为两条异面直线，且//,//,//,//m n m n ααββ，则//αβ．A.0 B.1C.2D.3【答案】B【分析】利用二面角的取值范围可判断①，当三点共线时可判断②，利用线面平行的判定方法可判断③，利用线面平行的性质以及面面平行的判定定理可判断④【详解】对于①，二面角的范围是[]0,π，①错；对于②，若三点共线，则经过这个点有无数个平面，②错对于③，若m n 、为两条异面直线，,,//m n m αββ⊂⊂，则n 与α可能平行也可能相交，故③错误；对于④，因为//,//m m αβ，过直线m 作平面γ，使得,b a γαβγ== ，由线面平行的性质定理可得//,//m a m b ，则//a b ，因为,a b αα⊄⊂，则//a α，因为//,//αβn n ，过直线n 作平面ϕ，使得,d c ϕαβϕ== ，由线面平行的性质定理可得//,//n c n d ，则//c d ，因为,c d αα⊄⊂，则//c α，若//a c ，则//m n ，这与m n 、为两条异面直线矛盾，故,a c 相交，又因为,a c β⊂，所以//αβ，故④对，故选：B16.《九章算术》中将底面为直角三角形且侧棱垂直于底面的三棱柱称为“堑堵”；底面为矩形，一条侧棱垂直于底面的四棱锥称之为“阳马”；四个面均为直角三角形的四面体称为“鳖臑”.如图，在堑堵111ABC A B C -中，AC BC ⊥，且12AA AB ==.下列说法错误．．的是（）A.四棱锥11B A ACC -为“阳马”B.四面体11AC CB 为“鳖臑”C.四棱锥11B A ACC -体积的最大值为23D.过A 点作1AE A B ⊥于点E ，过E 点作1EF A B ⊥于点F ，则1A B ⊥面AEF 【答案】C 【解析】【分析】根据“阳马”和“鳖膈”的定义，可判断A ，B 的正误；当且仅当AC BC =时，四棱锥11B A ACC -体积有最大值，求值可判断C 的正误；根据题意可证1A B ⊥平面AEF ，进而判断D 的正误.【详解】底面为直角三角形且侧棱垂直于底面的三棱柱称为“堑堵”，∴在堑堵111ABC A B C -中，AC BC ⊥，侧棱1AA ⊥平面ABC ，A 选项，∴1AA BC ⊥，又AC BC ⊥，且1AA AC A = ，则⊥BC 平面11A ACC ，∴四棱锥11B A ACC -为“阳马”，故A 正确；B 选项，由AC BC ⊥，即11A C BC ⊥，又111AC C C ⊥且1BC C C C ⋂=，∴11A C ⊥平面11BB C C ，∴111A C BC ⊥，则11A BC V 为直角三角形，又由⊥BC 平面11AAC C ，得1A BC 为直角三角形，由“堑堵”的定义可得11AC C 为直角三角形，1CC B 为直角三角形，∴四面体11AC CB 为“鳖膈”，故B 正确；C 选项，在底面有2242AC BC AC BC =+≥⋅，即2AC BC ⋅≤，当且仅当AC BC ==1111111243333B A ACC A ACC V S BC AA AC BC AC BC -=⨯=⨯⨯=⨯≤，最大值为43，故C 错误；D 选项，因为1AE A B ⊥，1EF A B ⊥，AE EF E ⋂=，所以1A B ⊥平面AEF ，故D 正确；故选：C三、解答题（本题满分78分，共5小题）17.如图，棱长为2的正方体1111ABCD A B C D -中，M N P 、、分别是1111C D CC AA 、、的中点．（1）证明：//MN 平面11ABB A ．（2）求异面直线1PD 与MN 所成角的大小．（结果用反三角表示）【答案】（1）证明见解析（2）arccos 10【解析】【分析】（1）构造线线平行，根据线面平行的判定定理证明线面平行.（2）根据线线平行，找出异面直线所成的角，在三角形中，利用余弦定理求角的余弦.【小问1详解】如图：连接1A B ，1D C .因为1111ABCD A B C D -为正方体，所以11//A B CD .又，M 、N 分别是11C D 、1CC 的中点，所以1//MN CD ，所以1//MN A B ，1A B ⊂平面11ABB A ，MN ⊄平面11ABB A ，所以//MN 平面11ABB A .【小问2详解】如图：连接PC 、1PD 因为1//MN CD ，所以1PDC ∠即为异面直线MN 与1PD 所成的角，设为θ.在1PCD V 中，221111145PD PA A D =+=+=，122CD =，2221443PC PA AB BC =++=++=.所以2221111cos θ2D P D C PC D P D C +-=⨯⋅10102522==⨯⨯.所以异面直线1PD 与MN 所成的角为：10arccos10.18.如图，已知PA ＝AC ＝PC ＝AB ＝a ，PA AB ⊥，AC AB ⊥，M 为AC 的中点．（1）求证：PM ⊥平面ABC ；（2）求直线PB 与平面ABC 所成角的大小．【答案】（1）见解析（2）6arcsin4【解析】【分析】（1）推导出PM AC ⊥，PM AB ⊥，由此能证明PM ⊥平面ABC ；（2）连结BM ，则PBM ∠是直线PB 和平面ABC 所成的角，由此能求出直线PB 和平面ABC 所成的角．【小问1详解】证明：因为PAC 为等边三角形，且M 为AC 的中点，所以PM AC ⊥．又PA AB ⊥，AC AB ⊥，且PA AC A = ，所以BA ⊥平面PAC ．又PM 在平面PAC 内，所以BA PM ⊥．因为AB AC A ⋂=，且BA PM ⊥，PM AC ⊥，所以PM ⊥平面ABC ．【小问2详解】解：连结BM ，由（1）知PM ⊥平面ABC ，所以PBM ∠是直线PB 和平面ABC 所成的角．因为PAC 为等边三角形，所以32PM a =.又PAB 为等腰直角三角形，且π2∠=PAB ，所以PB =．因为PM BM ⊥，所以sin 4PBM PM PB ∠==，则arcsin4PBM =∠所以直线PB 和平面ABC 所成的角的大小等于6arcsin4．19.现需要设计一个仓库，由上、下两部分组成，上部的形状是正四棱锥1111P A B C D -，下部的形状是正四棱柱1111ABCD A B C D -(如图所示)，并要求正四棱柱的高1O O 是正四棱锥的高1PO 的4倍.（1）若m 6AB =，12m PO =，则仓库的容积是多少？（2）若正四棱锥的侧棱长为6m ，当1PO 为多少时，下部的正四棱柱侧面积最大，最大面积是多少？【答案】（1）3312m（2），2【解析】【分析】（1）明确柱体与锥体积公式的区别，分别代入对应公式求解；（2）先根据面积关系建立函数解析式，()S x =，然后利用二次函数性质求其最值.【小问1详解】由12PO =知1148OO PO ==.因为116A B AB ==，所以正四棱锥1111P A B C D -的体积()22311111=6224m ;33V A B PO ⋅⋅=⨯⨯=锥正四棱柱1111ABCD A B C D -的体积()2231=68288m .V AB OO ⋅=⨯=柱所以仓库的容积()324288312m V V V =+=+=锥柱.【小问2详解】设1m PO x =，下部分的侧面积为()S x ，则14m OO x =，1111A O A B ==111()46)S x A B OO x =⋅==<<，设()()()222422363618324f x xx xx x =-=-+=--+，当218x =，即x =max ()324f x =，max ()S x =即当1PO 为2.20.如图，AB 是圆柱的底面直径，2AB =，PA 是圆柱的母线且2PA =，点C 是圆柱底面圆周上的点．（1）求圆柱的表面积；（2）证明：平面PBC ⊥平面PAC ；（3）若1AC =，D 是PB 的中点，点E 在线段PA 上，求CE ED +的最小值．【答案】（1）6π（2）证明见解析（3【解析】【分析】（1）根据圆柱求表面积公式即可求解.（2）先证⊥BC 平面PAC ，再利用面面垂直的判定定理判定即可.（3）先分析得将PAC 绕着PA 旋转到PC '，使其与PAB 共面，且C '在AB 的反向延长线上，当D ，E ，C '三点共线时，CE ED +的最小值为C D '，通过解三角形求C D '即可.【小问1详解】根据题意，圆柱的底面半径12ABr ==，圆柱的高2h PA ==，圆柱的上下底面积和为222π2πS r ==底，圆柱的侧面积为2πr =4πS h =⋅侧，所以圆柱的表面积为26πS S S =+=底侧【小问2详解】由题意可知，PA ⊥底面ABC ，⊂BC 底面ABC ，则PA BC ⊥，由直径所对的圆周角为直角，可得BC AC ⊥，又PA AC A = ，PA ⊂平面PAC ，AC ⊂平面PAC ，所以⊥BC 平面PAC ，又因为⊂BC 平面PBC ，所以平面PBC ⊥平面PAC 【小问3详解】将PAC 绕着PA 旋转到PC '，使其与PAB 共面，且C '在AB 的反向延长线上，当D ，E ，C '三点共线时，CE ED +的最小值为C D '，因为2PA =，2AB =，PA AB ⊥，PB ==2tan 12PA PBA AB ∠===，所以π4PBA ∠=，12BD BP ==，213BC BA AC '=+=+=，所以在三角形C BD '中，由余弦定理可得C D ='，所以CE ED +.21.已知点P 是边长为2的菱形ABCD 所在平面外一点，且点P 在底面ABCD 上的射影是AC 与BD 的交点O ，已知60BAD ∠=︒，PDB △是等边三角形.（1）求证：AC PD ⊥；（2）求点D 到平面PBC 的距离；（3）若点E 是线段AD 上的动点，问：点E 在何处时，直线PE 与平面PBC 所成的角最大？求出最大角的正弦值，并说明点E 此时所在的位置.【答案】（1）证明见解析（2）5（3）E 在线段AD 上靠近D 点的14处，4sin 5θ=【解析】【分析】（1）由题可得⊥PO 平面ABCD ，故⊥PO AC .根据菱形的性质可得BD ⊥AC ，再根据线面垂直的判定定理与性质定理即可证明；（2）根据题干数据结合D PBC P BDC V V --=即可求解；（3）由线面平行的判定定理可得AD ∥平面PBC ，可得E 到平面PBC 的距离即为D 到平面PBC 的距离h ，过E 作垂线⊥EF 平面PBC 交于点F ，要使θ最大，则需使PE 最小，此时PE AD ⊥，从而可求解.【小问1详解】因为点P 在底面ABCD 上的射影是AC 与BD 的交点O ，所以⊥PO 平面ABCD .因为AC ⊂平面ABCD ，所以⊥PO AC .因为四边形ABCD 为菱形，所以BD ⊥AC .因为,,PO BD O PO BD ⋂=⊂平面PBD ，所以AC ⊥平面PBD .因为BD ⊂平面PBD ，所以AC PD ⊥.【小问2详解】由题意可得ABD △、BCD △与PBD △都是边长为2的等边三角形，所以PO AO CO ===，122BDC S =⨯=△.所以PC =因为2BP BC ==，所以122PBC S ==△.设点D 到平面PBC 的距离为h ，由D PBC P BDC V V --=得1133PBC BDC S h S OP ⋅=⋅△△，=5h =.故点D 到平面PBC 的距离为5.【小问3详解】设直线PE 与平面PBC 所成的角为θ，AD BC AD ⇒∥∥ 平面PBC ，∴E 到平面PBC 的距离即为D 到平面PBC 的距离h .过E 作垂线⊥EF 平面PBC 交于点F ，则EPF θ=∠，此时sin EF PE θ=θ最大，则需使PE 最小，此时PE AD ⊥.由题意可知：1,OD OA ==，因为⊥PO 平面ABCD ，且PO =，所以PA ==，2PD ==，在PAD △中，由余弦定理可得：222cos24AP AD PD PAD AP AD +-∠==⋅，所以sin 4PAD ∠=，由面积相等11sin 22PAD S AP AD PAD AD PE =⋅∠=⋅ ，即1122242PE ⨯=⨯⨯，经计算得，2PE =12DE ==，则4sin 5θ=，此时E 在线段AD 上靠近D 点的14处.。

2024-2025学年上海市杨浦区同济大学一附中高三（上）期中数学试卷一、单选题：本题共4小题，共18分。

在每小题给出的选项中，只有一项是符合题目要求的。

1.下列说法正确的是( )A. 如果直线l 不平行于平面α，那么平面α内不存在与l 平行的直线B. 如果直线l//平面α，平面α//平面β，那么直线l//平面βC. 如果直线l 与平面α相交，平面α//平面β，那么直线l 与平面β也相交D. 如果平面α⊥平面γ，平面β⊥平面γ，那么平面α//平面β2.某单位为了解该单位党员开展学习党史知识活动情况，随机抽取了部分党员，对他们一周的党史学习时间进行了统计，统计数据如下表所示：党史学习时间(小时)7891011党员人数610987则该单位党员一周学习党史时间的众数及第40百分位数分别是( )A. 8，8.5B. 8，8C. 9，8D. 8，93.已知椭圆C ：x 2a 2+y 2b 2=1(a >b >0)，过点(−a,0)且倾斜角为34π的光线，经直线y =−b 反射后过C 的右焦点，则C 的离心率为( )A. 35B. 23C. 34D. 454.定义：如果函数y =f(x)在区间[a,b]上存在x 1，x 2(a <x 1<x 2<b)，满足f′(x 1)=f(b)−f(a)b−a，f′(x 2)=f(b)−f(a)b−a，则称函数y =f(x)是区间[a,b]上的一个双中值函数，已知函数f(x)=x 3−65x 2是区间[0,t]上的双中值函数，则实数t 的取值范围是( )A. (35,65)B. (25,65)C. (25,35)D. (1,65)二、填空题：本题共12小题，共54分。

5.不等式x−2x +1≤0的解集是______．6.已知复数z =1+i(i 是虚数单位)，则|1−iz|= ______．7.已知x >0，y >0，xy =1，则1x +2y 的最小值为______．8.若α∈(π2,π),cos (π−α)=35，则tanα= ______．9.若A(1,2)、B(−3,4)、C(5,m)三点不能构成三角形，则m = ______．10.某市高考新政规定每位学生在物理、化学、生物、历史、政治、地理中选择三门作为等级考试科目，则甲、乙两位学生等级考试科目恰有一门相同的不同选择共有______种．(用数字作答)11.已知{a n }为等差数列，其前n 项和为S n .若a 1=1，a 3=5，S n =64，则n =______．12.过直线y =x 上一点作圆(x−5)2+(y−1)2=2的两条切线l 1，l 2，当l 1，l 2关于直线y =x 对称时，l 1，l 2的夹角的大小为______．13.已知函数f(x)=lnx−ax−2在区间(1,2)上不单调，则实数a 的取值范围为______．14.如图，正六边形的边长为2，圆O 的圆心为正六边形的中心，半径为1，若点M 在正六边形的边上运动，动点A 、B 在圆O 上运动且关于圆心O 对称，则MA ⋅MB 的取值范围是______．15.已知(1+2024x )50+(2024−x )50=a 0+a 1x +a 2x 2+⋯+a 50x 50，其中a 0，a 1，a 2，…a 50∈R ，若a k <0，k ∈{0,1,2,…,50}，则实数k 的最大值为______．16.已知数列{a n }满足：对于任意正整数n 有a n ∈(0,π2)，且a 1=π4,f(a n +1)=f′(a n )，其中f(x)=tanx ，若b n =(−1)ntana n +1−tana n ，数列{b n }的前n 项和为T n ，则T 440= ______．三、解答题：本题共5小题，共78分。

2021年上海同济大学第一附属中学高三英语上学期期中试卷及答案第一部分阅读（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AIt’s the time of year when we start hiking. As you pack, remember to bring your smartphone. Whether you’re going on a short walk or a long trip, there are a handful of apps that can help.MapMyHikeThis app tracks where you're hiking so you have a mapof your route at the end of the hike. It can also track other fitness information like the distance traveled, speed, pace, and even calories burned. You can save the data for your hike, so you can always access the route you look as well as track improvements to your workout. GaiaGPSYou don't always have cellphone service when hiking, but you always want to know where you are. The GaiaGPS app provides that information. Download maps of different parts of the world, and access the GaiaGPS app in the middle of even the most remote trails. The GPS function makes using the maps simple, and the app will also point to areas of interest.Backpacking ChecklistOne of the worst things is being way out on a trail only to discover you left behind something important. That's why checklists are the best. This checklist app helps you build a customized(定制的) list of things to take with you. Organize different lists based on trail lengths or requirements. Track all your essential items by weight and where you can find them.WildObsUsing WildObs, you can record your observations of plants and animals and add them to the database. You can ask the community to help you identify something and keep track of everything you've met, and most importantly, you can become a citizen scientist. By recording what you've seen with this app, you're helping scientists keep track of what's happening to the natural world.1. What can you do with MapMyHike?A. Record your walking speed.B. Design a suitable hiking route.C. Locate popular tourist attractions.D. Store the data of your daily activities.2. What is WildObs intended to do?A. To provide survival skills.B. To lead the way.C. To identify wildlife.D. To help make preparations.3. Which app is most useful before hiking?A. GaiaGPS.B. MapMyHike.C. WildObs.D. Backpacking Checklist.BCuckoos don’t bother building their own nests—they just lay eggs that perfectly imitate those of other birds and take over their nests. But other birds are wishing up, evolving some seriously impressive tricks to spot the cuckoo eggs.Cuckoos are often know asparasites, meaning that they hide their eggs in the nest of other species. To avoid detection, the cuckoos have evolved so that eggs seem reproduction of those of their preferred targets. If the host bird doesn’t notice the strange egg in its nest, the little cuckoo will actually take the entire nest for itself after it comes out, taking the other eggs on its back and dropping them out of the nest.To avoid this unpleasant fate for their young, the other birds have evolved a few smart ways to spot the fakes, which we’re only now beginning to fully understand. One of the most amazing finds is that birds have an extra colour-sensitive cell in their eyes, which makes them far more sensitive to ultraviolet wavelengths and allows them to see a far greater range of colours than humans can. This allows cautious birds to detect a fake egg which might be exactly the same to our eyes.Fascinatingly, we’re actually able to observe different bird species at very different points in their evolutionary war with the cuckoos. For instance, some cuckoos lay their eggs in the nests of the redstarts. The blue eggs these cuckoos lay are practically alike to those of the redstarts, and yet they are still sometimes rejected. Compare that with cuckoos who target dunnocks. While those birds lay perfectly blue eggs, their cuckoo invaders just lay white eggs with brown irregular shaped spots. And yet dunnocks barely ever seem to notice the obvious trick.Biologists suspect these more easily fooled species like the dunnocks are on the same evolutionary path as the redstarts, but they have a long way to go until they evolve the same levels of suspicion. What’s remarkable is that the dunnocks fakes are so bad and the redstart ones so good, and yet cuckoos are still more successful with the former than the latter.It speaks to just how thoroughly a species’ behavior can be changed by the pressures of natural selection, or it might just be a bit of strategic cooperation on the part of the dunnocks. Biologists have suggested that thesebirds are willing to tolerate a parasite every so often because they don’t want to risk accidentally getting rid of one of their own eggs.4. This passage can be most likely found in a ________.A. science surveyB. nature magazineC. zoo advertisementD. travel journal5. What does the underlined word “parasite” in paragraph 2 most probably refer to?A. Animals that work together to raise young.B Small harmful animals such as worms or mice.C. Animals that can adapt to changing environments.D. Animals which live on or inside other host animals.6. Which of the following is TRUE about the dunnock according to the passage?A. It is colour-blind and therefore cannot identify foreign eggs in the nest.B. It can easily remove cuckoo eggs from the nest because fakes are so bad.C. It is a host bird that is more likely to raise a cuckoo chick than the redstart.D. It is unable to evolve and hence accepts cuckoo eggs that appear in the nest.7. Which of the following can be inferred from the passage?A. Dunnocks may eventually learn to recognise foreign eggs.B. Redstarts seem to be less suspicious compared to dunnocks.C. Cuckoo birds are good at taking responsibility for their own young.D. It is very easy for cuckoos to imitate the colouring of the dunnock’s egg.CBill Gates on how to fight future pandemicsWHEN HISTORIANS write the book on the covid-19 pandemic, what we've lived through so far will probably take up only the first third or so.The bulk of the story will be what happens next.I believe that humanity will beat this pandemic, but only when most of the population is vaccinated(接种疫苗）.Until then, life will not return to normal.As the pandemic slows in developed nations,itwill accelerate in developing ones.Their experience,however,will be worse.In poorer countries,where fewer jobs can be done remotely,distancing measures won't work as well.The virus will spread quickly,and health systems won't be able to care for the infected.Wealthy nations can help.But people in rich and poor places alike will be safe only once we have an effective medical solution for this virus,which means a vaccine.My hope is that,by the second half of 2021,facilities around the world will be manufacturing a vaccine.If that's the case,it will be a history-making achievement: the fastest humankind has ever gone from recognizing a new disease to immunizing（免疫）against it.Apart from this progress in vaccines,two other big medical breakthroughs will emerge from the pandemic.One will be in the field of diagnostics.The next time a novel virus crops up,people will probably be able to test for it at home.Researchers could have such a test ready within a few months of identifying a new disease.The third breakthrough will be in antiviral drugs.We haven't been as effective at developing drugs to fight viruses as we have those to fight bacteria.But that will Researchers will develop large diverse libraries of antivirals,which they'll be able to scan trough and quickly find effective treatments for novel viruses.All three technologies will prepare us for the next pandemic by allowing us to intervene(干预）early when the number of cases is still very low.Our progress won't be in science alone.It will also be in our ability to make sure everyone benefits from that science.In the years after 2021,I think we'll learn from the years after 1945. With the end of the Second World War, leaders built international institutions like the UN to prevent more conflicts.After covid-19, leaders will prepare institutions to prevent the next pandemic.These will be a mix of national,regional and global organizations.I expect they will participate in regular"germ games”in the same way as armed forces take part in War games.These will keep us ready for the next time a novel virus jumps from bats or birds to humans.I hope wealthy nations include poorer ones in these preparations,especially by devoting more foreign aid to building up their primary health-care systems.This pandemic has shown us that viruses don't obey border laws and that we are all connected biologically by a network of microscopic germs,whether we like it or not.The best analogy(类比）for today might be November 10th 1942.Britainhad just won its first land victory of the war,and Winston Churchill declared in a speech: “This is not the end.It is not even the beginning of the end.But it is,perhaps,the end of the beginning.”8. What are the three technologies that will prepare us for the next pandemic?①manufacturing a vaccine fast②diagnosing a virus at home③developing antiviral drugs④allowing us to intervene earlyA. ①②③B. ①②④C. ①③④D. ②③④9. As far as poorer countries areconcerned,which of the following is TRUE according to this passage?A. pandemic disease is more likely to begin in poorer countriesB. Working from home can work well in poorer countries.C. Health systems are sufficient to care for the infected in poorer countries.D. Virus will cross borders if poorer countries fail to contain it.10. Why is the Second World War mentioned in Para.8?A. The fight against the COVID-19 is similar to the Second World War.B. People are suffering just as they were in the Second World War.C. We should cooperate globally just as we did after the Second World War.D. Countries are fighting each other like in the Second World War.11. What is the tone of this passage?A. pessimisticB. optimisticC. neutralD. indifferentDScientists often compare coral reefs(珊瑚礁) to underwater rainforests, yet unlike the leafy plant base of a forest, corals are animals. The soft creatures are naturally half-transparent and get their brilliant color1 from algae(藻类) living inside them. When corals experience stress from hot temperatures or pollution, theyhaltthe interdependent relationship with algae, typically pushing them out and turning white. Corals are still alive when they are white, but they're at risk and many eventually die, turning dark brown.Scientists around the world are looking for means to protect and maybe increase corals. One common option is to create more protected areas — essentially national parks in the ocean. Beyond nature preserves, some conservationists are looking to more hands-on methods. One research center in the Florida Keys is exploring a form of natural selection to keep corals remaining. The reef system in the Keys has been hit hard by climate change and pollution, which is especially tough, because corals there help support fisheries worth $ 100 million every year.To keep the wild ecosystem alive, Erinn Muller, the center's director, and her team are harvesting samples of the corals that survived the environmental stress naturally, keeping them to make them reproduce, and thenreattaching them to the reef. They have 46,000 corals on plastic frames under the sea. So far, the center has regrown over 70,000 corals from five different species on damaged reefs.In The Bahamas, Ross Cunning, a research biologist at Chicago's Shedd Aquarium, focuses on corals with genes that could make them natural candidates for restoration projects. He published a study of two Bahamian reefs, one that survived an extreme 2015 heat wave, and one that didn't. "We think their ability to deal with these higher temperatures is built into their genes," says Cunning. There's evidence of corals evolving more quickly to resist rapidly warming climate. The big question scientists need investigate, adds Gunning, is how much more heat corals can adapt to.12. What does the underlined word "halt" in the first paragraph mean?A. End.B. Develop.C. Strengthen.D. Weaken.13. What do Muller and her team do to save corals?A. Restore the damaged reefs.B. Grow corals by hand underwater.C. Create more protected areas.D. Move corals to unpolluted areas.14. What do Gunning's words suggest?A. Many corals have been genetically improved.B. Cooling down the waters is key to rescuing corals.C. Reasons for corals surviving heat waves are shocking.D. The highest temperature corals can survive is unclear.15. Which can be a suitable title for the text?A. Relationship between corals and algaeB. Efforts made to save coralsC. Impact of climate warming on coralsD. Survival crisis faced by coral reefs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。