THREE PROBLEMS IN SEARCHING FOR A MOVING TARGET BETWEEN TWO SITES

在数学上求助的英语作文Mathematics has always been a subject that has challenged and intrigued me. From a young age, I have been fascinated by the patterns, logic, and problem-solving nature of this discipline. However, as I progressed through my academic journey, I encountered moments where I found myself struggling to grasp certain mathematical concepts or solve complex problems. In these instances, seeking help became a crucial step in my learning process.One of the primary reasons I have sought help in mathematics is the inherent complexity of the subject. Mathematics often involves abstract concepts, intricate formulas, and multifaceted problem-solving strategies. While I strive to understand these elements on my own, there are times when the material becomes overwhelming, and I find myself needing additional guidance and support.When faced with such challenges, I have learned to identify the specific areas where I require assistance. This could be anything from understanding a new theorem, mastering a particular calculation technique, or applying mathematical principles to real-worldproblems. By pinpointing the specific areas of difficulty, I can then seek help from various sources that can provide the necessary clarification and instruction.One of the most valuable resources I have found in seeking help in mathematics is my instructors. Whether it's my classroom teacher, a professor, or a teaching assistant, these individuals possess a deep understanding of the subject matter and are typically more than willing to offer their expertise and support. I have found that scheduling one-on-one meetings or attending office hours can be particularly beneficial, as it allows me to engage in a personalized dialogue and receive tailored guidance.In addition to seeking help from my instructors, I have also found success in utilizing online resources and learning platforms. The internet has revolutionized the way we access and acquire knowledge, and this is particularly true in the realm of mathematics. Websites, forums, and educational platforms offer a wealth of resources, from video tutorials and interactive simulations to step-by-step explanations and practice problems. These online tools have been invaluable in supplementing my classroom learning and providing me with additional support when I need it.Furthermore, I have discovered the value of collaborative learning in mathematics. Working with my peers, either in study groups orthrough online discussion forums, has proven to be a highly effective strategy. By exchanging ideas, sharing insights, and collectively tackling challenging problems, I have been able to deepen my understanding and gain new perspectives on mathematical concepts. The collective knowledge and diverse approaches of my peers have been instrumental in helping me overcome obstacles and improve my mathematical skills.One of the key benefits I have experienced in seeking help in mathematics is the opportunity to develop a deeper understanding of the subject matter. When I struggle with a particular concept or problem, the process of seeking assistance often leads me to uncover the underlying principles and connections that I may have initially overlooked. By engaging with instructors, online resources, or my peers, I am able to gain a more comprehensive and nuanced understanding of the mathematical concepts, which in turn enhances my overall competence and confidence in the subject.Moreover, the act of seeking help has also helped me cultivate important learning skills, such as critical thinking, problem-solving, and self-advocacy. When I encounter a challenge in mathematics, I am forced to analyze the problem, identify the areas of difficulty, and actively seek out the necessary resources and support. This process encourages me to develop a growth mindset, where I view obstacles as opportunities for learning and improvement, rather than asinsurmountable barriers.Additionally, seeking help in mathematics has allowed me to build valuable relationships and networks. By interacting with instructors, tutors, and peers, I have been able to establish connections that extend beyond the immediate learning context. These relationships have not only provided me with academic support but have also opened up opportunities for mentorship, collaboration, and personal growth.In conclusion, seeking help in mathematics has been a crucial aspect of my academic journey. The inherent complexity of the subject, the need for personalized guidance, and the value of collaborative learning have all contributed to my decision to actively seek assistance when faced with challenges. Through this process, I have not only improved my mathematical skills but have also developed essential learning strategies, cultivated meaningful relationships, and gained a deeper appreciation for the subject. As I continue to pursue my academic and professional goals, I am confident that my willingness to seek help in mathematics will continue to be a valuable asset in my growth and development.。

英文灵魂三问Soul-searching: Three Essential QuestionsIntroduction:In the journey of self-discovery and personal growth, there are moments when we ponder the deeper meaning of life and search for answers that resonate with our souls. These three fundamental questions, when explored with an open heart and mind, can help guide us towards a greater understanding of our existence. Let us delve into these questions and contemplate the wisdom they offer.Question 1: Who am I?Deep within each of us lies a divine essence, waiting to be understood and unleashed. Knowing who we truly are goes beyond societal roles and external labels; it involves connecting with our authentic self. Discovering our passions, values, and unique qualities enables us to align our actions with our inner desires. Introspection and self-reflection help unravel the layers of conditioning and societal expectations, allowing our true selves to shine through.To explore our identity, we can embark on a journey of self-discovery through various means such as journaling, meditation, and engaging in activities that bring us joy. Embracing our strengths and weaknesses, acknowledging our past experiences, and aligning with our core values form the pillars of self-awareness. When we firmly grasp our authentic identity, we gain the confidence to live life with purpose and authenticity.Question 2: Why am I here?The question of purpose often arises when we contemplate our existence. We yearn for significance and meaning in our lives, seeking a higher purpose beyond the mundane routines. Discovering our life's purpose brings clarity and direction, lending a sense of fulfillment and contentment.Finding our purpose can involve exploring our passions, values, and talents. What brings us joy? What change do we wish to bring to the world? What impact do we desire to leave behind? These queries ignite the flame within us and propel us towards a purpose-driven life. Connecting with our passions and aligning them with actions that serve others cultivates a sense of fulfillment and contributes to the greater good.Question 3: What is the meaning of love?Love, a universal language that transcends boundaries, is an innate desire within every human soul. As we navigate through life, understanding the true essence of love becomes essential for our emotional well-being and the well-being of others.Love encompasses more than romantic relationships; it encompasses compassion, kindness, and empathy. It involves embracing diversity, cherishing connections, and fostering harmony. Love is a force that can heal, uplift, and connect us at the deepest level. Cultivating love within ourselves and extending it towards others opens up doors to profound joy and fulfillment. It is through love that we can create a more compassionate and harmonious world.Conclusion:As we travel along the path of self-discovery, these three soul-searching questions guide us towards a deeper understanding of our true selves and our place in the world. By exploring our identity, uncovering our life's purpose, and embracing the power of love, we embark on a transformative journey of growth, connection, and personal fulfillment. So, let us embark on this beautiful quest and embrace the wisdom that lies within these essential questions.。

三体专有名词中英文对照IntroductionThe Chinese science fiction novel "The Three-Body Problem" by Liu Cixin has gained worldwide recognition and popularity. As non-Chinese speakers delve into this fascinating story, one challenge they face is understanding the numerous specialized terms used in the book. This article provides a comprehensive list of the most important Three-Body Problem terms, presented with their English translations. By familiarizing ourselves with these terms, we can fully immerse ourselves in the world of "The Three-Body Problem" and appreciate its intricate details.1. Trisolarans - 地球人 (Dìqiú rén)Trisolarans refer to beings from the Trisolaris system, which is located 4.22 light-years away from Earth. They face the threat of their own star system being destroyed, leading them to search for a new home.2. Three-Body Problem - 三体问题(Sāntǐ wèntí)The Three-Body Problem is a mathematical problem concerned with predicting the motion of three celestial bodies influenced by their mutual gravitational attraction. In Liu Cixin's novel, it serves as a metaphor for the chaotic nature of the Trisolaran civilization.3. Sophons - 理论粒子(Lǐlùn lìzi)Sophons are microscopic particles created by the Trisolarans with extensive technological capabilities. They are used for surveillance and communication purposes between Trisolaris and Earth.4. ETO - 地球三体组织(Dìqiú Sāntǐ Zǔzhī)ETE, short for Earth-Trisolaris Organization, is a secret society established by individuals who sympathize with the Trisolaran civilization. Their goal is to help facilitate the Trisolarans' conquest of Earth.5. Wallfacer Project - 遮蔽士计划(Zhēbì shì jìhuà)This project is initiated to counter the potential invasion by the Trisolarans. Four individuals are selected as Wallfacers, with the authority to use any means to protect humanity while keeping their plans and strategies secret.6. Wallbreakers - 破壁人 (Pò bì rén)Wallbreakers are individuals assigned to penetrate the Wallfacer's defenses and uncover their secrets. They are chosen from the ETO to obstruct the Wallfacer Project.7. Dark Forest Theory - 黑暗森林理论(Hēi'àn sēnlín lǐlùn)The Dark Forest Theory is a concept that originated from the trilogy. It suggests that in the universe, civilizations are fearful and kill other potentially dangerous civilizations before being discovered.8. Droplet - 微滴(Wēi dī)Droplets are miniature spaceships used by the Trisolarans to explore the universe through virtual reality.9. Swordholder - 剑持 (Jiàn chí)The Swordholder is a position created within the Trisolaran civilization to avoid conflicts by concentrating all power in one person. The Swordholder has the authority to make all important decisions.10. Blue Space - 蓝岸 (Lán'àn)Blue Space is the virtual reality world created by the Trisolarans as a safe space for their civilization. It serves as a means of communication and interaction between Trisolaris and Earth.Conclusion"The Three-Body Problem" transcends cultural boundaries, offering readers an imaginative and thought-provoking journey through space and time. Understanding the specialized terms used in the novel enhances the reading experience for non-Chinese speakers. This article has provided a detailed list of the most important terms in "The Three-Body Problem," allowing readers to navigate the story and its complexities with ease. Whether it's the Trisolarans, the Wallfacer Project, or the Dark Forest Theory, immersing ourselves in these concepts brings us closer to the brilliance of Liu Cixin's masterpiece.。

2020年12月英语四级真题及参考答案完整版四六级试卷采用多题多卷形式，大家核对答案时，请找具体选项内容，忽略套数。

搜集整理了各个版本(有文字也有图片，图片可以自由拉伸)，仅供大家参考。

【网络综合版】听力News report 1(1) A poisonous fish which has a sting strong enough to kill a human is invading the Mediterranean, warn the scientist.The International Union for the Conservation of Nature has raised concerns after the poisonous fish was spotted in the waters around Turkey, Cyprus and the eastern Mediterranean.Native to the South Pacific and Indian Ocean, the potentially deadly fish has poisonous barbs and an painful sting capable of killing people.Although fatalities are rare, the stings can cause extreme pain, and stop people breathing.The fish, also known as the Devil Firefish, is a highly invasive a species, (2) and environmentalists fear its arrival could endanger other types of marine life.After being spotted in the Med, a marine scientist says: "The fish is spreading, and that's a cause for concern.”Q1: What is reported in the news?D. A deadly fish has been spotted in the Mediterranean waters.Q2: What is the environmentalist concern about the spread of devil fire fish in the Mediterranean?B. It could pose a threat to other marine species.News Report 2(3)Almost half the center of Paris will be accessible only by foot or bicycle this Sunday to mark World-Car-Free Day. (4) This is in response to rising air pollution that made Paris the most polluted city in the world for a brief time. Mayor Ann Ethogo promoted the first World-Car-Free Day last year. Ethogo also has supporteda Pairs-briefs-Day on the first Sunday of every month. Paris clears traffic from eight lanes of the main road. About 400 miles of streets will be closed to cars. It is expected to bring significant reduction in pollution levels. (4) Last year's Car-Free Day showed a 40% drop in pollution levels in some parts of the city. According to an independent air pollution monitor, reports the guardian and sound levels dropped by 50% in the city center.Q3: What will happen on World-Car-Free-Day in Paris?C. About half of its city center will be closed to cars.Q4: What motivated the mayor of Paris to promote the first World-Car-Free Day in her city?D. The rising air pollution in Paris.News Report 3(5) A Philippine fisherman was feeling down on his luck when a house fire forced him to clear out his possessions and change locations. Then, a good luck charm that he kept under his bed changed his life. The unidentified man fished out a giant pearl from the ocean when his anchor got stuck on the rock while sailing off a coastal island in the Philippines 10 years ago. (6) When he was forced to sell it, (7) the shocked tourist agent at Puerto Francesca told him that the £77 giant pearl that he had kept hidden in his run-down wooden house was the biggest pile in the world, which was valued at £76 million. The pearl of Allah, which is currently on display in a New York Museum, only weighs 14 pounds. That is 5 times smaller than the pearl that the fisherman just handed in. The monstrous pearl, measured at 1 foot wide and 2.2 feet long, is going to be verified by local experts and international authorities before hopefully going on display to attract more tourists in the little town.Question 5. What happened to the Philippine fisherman one day?A.His house was burnt down in a fire.Question 6. What was the fisherman forced to do?C. Sell the pearl he had kept for years.Question 7. What did the fisherman learn from the tourist agent?B. His monstrous pearl was extremely valuable.Conversation 1W: Mr. Smith, it's a pleasure meeting you.M: Nice to meet you,too. What can I do for you?W: Well, I'm here to show you what our firm can do for you. Astro Consultant has branches in over 50 countries, offering different business services. (8) We area global company with 75 years of history and our clients include some of theworld's largest companies.M: Thank you, Mrs. Houston. I know Astro Consultant is a famous company, but you said you would show me what you could do for me. Well, what exactly can your firm do for my company?W: We advise businesses on all matters—from market analysis to legal issues.Anything of business like yours could need, our firm offers expert advice. CouldI ask you, Mr. Smith, to tell me a little about your company and the challengesyou face? That way, I could better respond as to how we can help you.M: OK, sure. (9) This is a family business started by my grandfather in 1950. We employed just over 100 people. We manufacture an export stone for buildings and other constructions. Our clients usually want a special kind of stone cut in a special design. That's what we do in our factory. (10) Our main challenge is that our national currency is rising and we're losing competitive advantage to stone producers in India.W: I see. that's very interesting. (11) I would suggest that you let us first conducta financial analysis of your company, together with an analysis of yourcompetitors in India. That way we could offer the best advice on different ways forward for you.Q8. What do we learn about the woman's company?A. It boasts a fairly long history.Q9. What does the man say about his own company?D. It is a family business.Q10. What is the main problem with the man's company?B. Losing the competitive edge.Q11. What does the woman suggest doing to help the man’s company?D. Conducting a financial analysis for it.Conversation 2W: (12) Wow, Congratulations, Simon. The place looks absolutely amazing.M: Really? You think so?W: Of course, I love it! It looks like you had a professional interior designer.But you didn't, did you?M: No. I did it all by myself—with a little help from my brother Greg. He's actually in the construction business, which was really helpful.W: Well, honestly, I'm impressed. I knew I could probably repaint the walls in my house over a weekend or something, but not a full renovation. Where did you get your ideas? I wouldn't know where to start.M: (13) Well, for a while now, I've been regularly buying home design magazines every now and then, and say the picture I liked. Believe it or not, I had a full notebook of magazine pages. Since my overall style was quite minimal, I thought and hoped the whole renovation wouldn't be too difficult. And sure enough, with Greg's help,it was very achievable.W: Was it very expensive? I imagine a project like this could be.M: (14) Actually, it was surprisingly affordable. I managed to sell a lot of my old furniture, and put that extra money towards the new material. Greg was also able to get some discount of materials from a recent project he was working on as well. W: Great. If you don't mind, I'd like to pick your brain a bit more. Jonathan andI are thinking of renovating our sitting room, not the whole house—not yet anyway.(15) And we'd love to get some inspiration from your experience. Are you freeto come over for a coffee early next week?Question 12. What do we learn about the woman from the conversation?B. She is really impressed by the man’s house.Question 13. Where did the man get his ideas for the project?C. From home design magazines.Question 14. What did the man say about the project he recently completed?A. The cost was affordable.Question 15. Why does the woman invite the man to her house next week?D. She wants him to share his renovation experience with her.Passage 1(16) Removing foreign objects from ears and noses costs England almost￡3 million a year, a study suggests. Children were responsible for the vast majority of cases. 95% of objects removed from noses, and 85% from ears. Every year, an average of 1,218 nose，and 2,479 ear removals took place between 2010 and 2016. (17) According to England's hospital episodes statistics, children aged 1 to 4 were the most likely to need help from doctors for a foreign object in their nose. 5 to 9 -year-olds come to the hospital with something in their ears the most.Jewelry items accounted for up to 40% of cases in both the ears and noses of children. Paper and plastic toys for the items removed next most from noses. Cotton buds, and pencils were also found in years.(18) According to the study, the occurrence of foreign objects in children is generally attributed to curiosity. Children have an impulse to explore their noses and ears. This results in the accidental entry of foreign objects. Any ear, nose and throat surgeon has many weird stories about wonderful objects found in the noses and ears of children and adults. Batteries can pose a particular danger. In all cases, prevention is better than cure. This is why many toys contain warnings about small parts. Recognizing problems early and seeking medical attention is important.Question16 What does England spend an annual￡3 million on?C. Removing objects from patients’ noses and ears.Question17 What do we learn from England's hospital episodes statistics?B. Five-to nine-year-olds are the most likely to put things in their ears. Question18 What is generally believed to account for children putting things in their ears or noses?D. They are curious about these body parts.Passage 2(21) Good morning. Today, I would like to talk to you about my charity Re-bicycle.But before that, let me introduce someone. This is Layla Rahimi. She was so scared when she first moved to new Zealand. Does she struggled to leave the house? I would spend days working up the courage to walk to the supermarket for basic supplies.(19) After a few months of being quite down and unhappy, she was invited to joina local bike club. At this time, Re-bicycle got involved and gave Layla a second-hand bicycle. Within weeks, her depression had begun to ease as she cycled. The bicycle totally changed her life, giving her hope and a true feeling of freedom. (20) To date, Re-bicycle has donated more than 200 bikes to those in need and is now expanding bike-riding lessons as a demand source. With a bike, new comers here can travel farther but for almost no cost. The 3 hours a day they used to spend walking to and from English language lessons has been reduced to just 1hour.(21) Our bike riding lessons are so successful that we are urgently looking for more volunteers, learning to ride a bike is almost always more difficult for an adult. And this can take days and weeks rather than hours. So if any of you have some free time during the weekend, please come join us at Re-bicycle and make a difference in someone’s life.Question 19. What did Re-bicycle do to help Layla Rahimi?A. It gave her a used bicycle.Question 20. What is Re-bicycle doing to help those in need?A. Expanding bike-riding lessons.Question 21. What do we learn from the passage about Re-bicycle?D. It is a charity organization.Passage 3Thanks to the international space station, (22) we know quite a bit about the effects of low gravity on the human body, but NASA scientists want to learn more.To that end, they have been studying how other species deal with low gravity, specifically focusing on mice. The results are both interesting and humorous. The scientists first sent some mice and especially designed cage to the international space station.The cage allowed them to study the behavior of the mice remotely from earth, via video.As you’ll notice in the video, (23) the mice definitely seem uncomfortable at the beginning of the experiment.They move around clumsily, drifting within the small confines of the cage and do their best to figure out which way is up, but without success. However, it’s not long before the mice begin to catch on.They adapt remarkably well to their new environment, and even use the lack of gravity to their advantage as they push themselves around the cage. That’s when things really get wild. (24) The 11th day of the experiment shows the mice are not just dealing with the gravity change, but actually seem to be enjoying it. Several of the mice are observed running around the cage walls. The scientists wanted to see whether the mice would continue doing the same kinds of activities they were observed doing on earth.(25) The study showed that the mice kept much of the routines intact, including cleaning themselves and eating when hungry.Question 22 : What do NASA scientists want to learn about?A. How animals deal with lack of gravity.Question 23: What does the passage say about the mice at the beginning of the experiment?C. They were not used to the low-gravity environment.Question 24: What was observed about the mice on the 11th day of the experiment?B. They already felt at home in the new environment.Question 25: What did the scientists find about the mice from the experiment? B.They behaved as if they were on Earth.Questions 1 and 2 are based on the news report you have just heard.1. A) A deadly fish has been spotted in the Mediterranean waters.B) Invasive species are driving away certain native species.C) The Mediterranean is a natural habitat of Devil Firefish.D) Many people have been attacked by Devil Firefish.2. A) It could add to greenhouse emissions.B) It could disrupt the food chains there.C) It could pose a threat to other marine species.D) It could badly pollute the surrounding waters.Questions 3 and 4 are based on the news report you have just heard.3. A) Cars will not be allowed to enter the city.B) About half of its city center will be closed to cars.C) Buses will be the only vehicles allowed on its streets.D) Pedestrians will have free access to the city.4. A) The rising air pollution in Paris.B) The worsening global warming.C) The ever-growing cost of petrol.D) The unbearable traffic noise.Questions 5 and 7 are based on the news report you have just heard.5. A) Many of his possessions were stolen.B) His house was burnt down in a fire.C) His fishing boat got wrecked on a rock.D) His good luck charm sank into the sea.6. A) Change his fishing locations.B) Find a job in a travel agency.C) Spend a few nights on a small island.D) Sell the pearl he had kept for years.7. A) A New York museum...B) The largest pearl in the world...C) His monstrous pearl was extremely valuable.D) His pearl could be displayed in a museum.Questions 8 and 11 are based on the conversation you have just heard.8. A) It boast a fairly long history.B) It produces construction materials.C) It has 75 offices around the world.D) It has over 50 business partners.9. A) It has about 50 employees.B) It was started by his father.C) It has a family business.D) It is over 100 years old.10. A) Shortage of raw material supply.B) Legal disputes in many countries.C) Outdated product design.D) Loss of competitive edge.11. A) Conducting a financial analysis for it.B) Providing training for its staff members.C) Seeking new ways to increase its exports.D) Introducing innovative marketing strategies.Questions 12 and 15 are based on the conversation you have just heard.12. A) She is a real expert at house decorations.B) She is well informed about the design business.C) She is attracted by the color of the sitting room.D) She is really impressed by the man’s house.13. A) From his younger brother Greg.B) From home design magazines.C) From a construction businessman.D) From a professional interior designer.14. A) The effort was worthwhile.B) The style was fashionable.C) The cost was affordable.D) The effect was unexpected.15. A) She’d like him to talk with Jonathan about a new project.B) She wants him to share his renovation experience with her.C) She wants to discuss the house decoration budget with him.D) She’d l ike to show him around her newly-renovated house.Questions 16 to 18 are based on the passage you have just heard.16. A) Providing routine care for small childrenB) Paying hospital bills for emergency cases.C) Doing research on ear, nose and throat diseases.D) Removing objects from patients’noses and ears.17. A) Many children like to smell things they find or play with.B) Many children like to put foreign objects in their mouth.C) Five-to nine-year-olds are the most likely to put things in their ears.D) Children aged one to four are often more curious than older children.18. A) They tend to act out of impulse.B) They want to attract attentions.C) They are unaware of the potential risks.D) They are curious about these body parts.Questions 19 to 21 are based on the passage you have just heard.19. A) It paid for her English lessons.B) It gave her a used bicycle.C) It delivered her daily necessities.D) It provided her with physical therapy.20. A) Expanding bike-riding lessons.B) Asking local people for donations.C) Providing free public transport.D) Offering walking tours to visitors.21. A) It is a language school.B) It is a charity organization.C) It is a counseling center.D) It is a sports club.Questions 22 to 25 are based on the passage you have just heard.22. A) How mice imitate human behavior in space.B) How low gravity affects the human body.C) How mice interact in a new environment.D) How animals deal with lack of gravity.23. A) They were not used to the low-gravity environment.B) They found it difficult to figure out where they were.C)They found the space in the cage too small to stay in.D) They were not sensitive to the changed environment.24.A) They tried everything possible to escape from the cage.B) They continued to behave as they did in the beginning.C) They already felt at home in the new environment.D) They had found a lot more activities to engage in.25.A) They repeated their activities every day.B) They behaved as if they were on Earth.C) They begin to eat less after some time.D) They changed their routines in space.听力第一套1. D. A deadly fish has been spotted in the Mediterranean waters.2. B. It could pose a threat to other marine species.3. C. About half of its city center will be closed to cars.4. D. The rising air pollution in Paris.5. A. His house was burnt down in a fire.6. C. Sell the pearl he had kept for years.7. B. His monstrous pearl was extremely valuable.8. A. It boasts a fairly long history.9. D. It is a family business.10. B. Loss the competitive edge.11. D. Conducting a financial analysis for it.12. B. She is really impressed by the man’s house.13. C. From home design magazines.14. A. The cost was affordable.15. D. She wants him to share his renovation experience with her.16. C. Removing objects from patients’noses and ears.17. B. Five-to nine-year-olds are the most likely to put things in their ears.18. D. They are curious about these body parts.19. A. It gave her a used bicycle.20. A. Expanding bike-riding lessons.21. D. It is a charity organization.22. A. How animals deal with lack of gravity.23. C. They were not used to the low-gravity environment.24. B. They already felt at home in the new environment.25. C. They behaved as if they were on Earth.听力第二套1. D) He did an unusual good deed.2. C) Give some money to the waiter.3. A) Whether or not to move to the state’s mainland.4. B) It costs too much money.5. A) To investigate whether people are grateful for help.6. C) They held doors open for people at various places.7. B) Most people express gratitude for help.8. C) To enquire about solar panel installations.9. D) He has a large family.10. B) The cost of a solar panel installation.11. D) About five year.12. A) At a travel agency.13. D) She wanted to spend more time with her family.14. D) Two weeks.15. A) Choosing some activities herself.16. D) Pay a green tax upon arrival.17. A) It has not been doing a good job in recycling.18. B) To ban single-use plastic bags and straws on Bali island.19. D) Its population is now showing signs of increase.20. C) Commercial hunting.21. D) To seek breeding grounds.22. C) They consume less milk these days.23. A) It is not as healthy as once thought.24. C) They lack the necessary proteins to digest it.25. B) It provides some necessary nutrients.翻译【翻译第一套】鱼是春节前夕餐桌上不可或缺的一道菜，因为汉语中“鱼”字的发音与“余”字的发音相同。

高一英语综合提高班第十一周Listening ComprehensionUniversal Design：Good for Everybody (035)一．Listen to the passage for the first time, and choose the right answer.1.Universal design is based on the idea that society should be open to all people, regardless of________. Which is not right?A. AgeB. AbilityC. ProfessionD. Gender2.Which universal design does the passage not mention?A. Door handles.B. Elevator.C. No-step b uses.D. Adjustable bathroom.3.Now a bus can let ________ get on and off easily.A. The old passengerB. Disabled passengerC. Young childrenD. Any passenger4.According to the passage, which is the right description?A. Unlike a regular, round doorknob, a universally designed door handle works for special people.B. Th no-step system is convenient to use and promotes the idea that we are all equally valued in society.C. In the fascinating bathroom, almost everything cannot be moved as needed.D. Universal design allows us to reach back to our traditional value of showing respect for the children.CBDB二．Now, lets tell the following statements true or false; put “F” for false, “T” for true.1. It is aimed at creating products and environments that people find easy to use, just the strong, the tall, or the young. ( )2. You can use your hand, your elbow, or even your foot to open the door.( )3. Senior citizens or people with special needs can sit down to take a shower.( )4. This bathroom is designed to be as comfortable and safe as possible for special people.( )FTTF三．Listen to the passage for the third time and try to answer the following questions.1. What does universal design try to achieve?________________________________________________________________________________________ 2. What are the advantages of no-step buses?1.It tries to create products and environments that everybody finds easy to use, not just the strong, th tall or the young.2.It can let any passenger get on and off easily.四．Listen to the passage again and again, and complete the following blanks.Universal design is a new way of making things “user-friendly”. It ____________________________ and environments that everybody finds easy to use, not just the strong, the tall, or the young. Universal design is ____________________________ life. Let’s take a look at some____________________________ .Universally designed door handles.____________________________, a universally designed door handle works for everybody. You can use your hand, your _______, or even your foot to open it. This means that people who have____________________________ can open the door in a way that is easier and ____________________________for them.No -step busesUntil recently, it has been difficult for some people to use buses or other____________________________ . Even when ____________________________, it took extra time and effort to let ____________________________ people on and off, causing delays and embarrassment. Now a bus can let any passenger get on and off easily. The no-step system is convenient to use and promotes the idea that we are all____________________________ .The adjustable bathroomWouldn’t you like to have a bathroom like this in your house? In this ____________________________, almost everything can be moved as needed. Tall people can have things high up, and shorter people can have things ____________________________, more comfortable level. ____________________________ or people with special needs can sit down to take a shower. Young children can____________________________ . This bathroom is designed to be as comfortable and safe as possible for everybody.Universal design might seem like a ____________________________, but it has really helped us to look ____________________________ and to ____________________________. It allows some people to be ____________________________, makes things easier to use, and makes environments more ____________________________. It also allows us to reach back to our design is being welcomed as a beautiful and ____________________________ life better for everyone.forms of public transportation special buses were availablefascinating bathroom at a lower elbowis aimed at creating products fast becoming a part of everydaytrouble using their hands more convenientphysically challenged equally valued in societysenior citizens reach the sink easilysimple concept beyond physical differencesexciting examples Unlike a regular, round doorknobpromote the value of equality more independentaccessible and comfortable practical way to make单项选择21. Chen Zhijiang is ____ paper-cutting expert whom I interviewed for my article on _____Chinese Art.A. a; theB. an; /C. a; /D. an; the22. They set off early on Tuesday morning _______ at the destination three days later.A. arrivingB. arrivedC. and arrivedD. would arrive23. Excited to see you back safe and sound from Libya. How long _____in Libya?A. have you stayedB. did you stayC. had you stayedD. would you stay24. We need a persuasive talker and a good organizer. But she is, by____, a person of a few words, therefore, she is unsuitable for the position.A. characteristicB. natureC. qualityD. character25. The UK government claims(声称) that the economy is improving, but this survey suggests_____.A. otherwiseB. thereforeC. moreoverD. meanwhile26.Charlie is going to have problems finding a job ______ he gets his A levels.A. even ifB. now thatC. as thoughD. so that27. Any foreigner who commits a crime in China _____ get into trouble eventually.A. canB. mayC. shallD. would28. Hi Sally! How are you! Glad to meet you here. We ____ called to see you last Sunday.A. prettyB. extremelyC. nearlyD. almost29. It was Xu Beihong _____ developed the tradition of combining poetry with painting ____had a leading position in the history of modern Chinese folk art.A. that; thatB. what; thatC. which; thatD. who; that30. With her eyes_____ the work attentively, she didn’t know what was happening outside.A. fixed onB. focusedC. fixing onD. focusing31.The naughty boy is a bit hard to deal with, which _____ the trouble adapting to the newenvironment.A. makes forB. adds toC. contributes toD. devotes to32. With more than 17000 islands, ______ only 6000 are inhabited, Indonesia is the world’s largest archipelago(岛国).A. on whichB. for whichC. of whichD. along which[来源33. With the mid-term examination approaching, students should _____ to stay energetic.A. work outB. pull outC. give outD. figure out34. At that moment, I was just standing by the window in my room, _____ I could see whatwas occurring on the street.A. from whichB. from whoseC. from thatD. from where35. Mother told me that it was two years _______Macy left for China to learn Chineseand the eastern culture.A. beforeB. sinceC. afterD. when单项选择21---25 CCBBA26---30 ACCDA31---35 BCADA完型填空阅读下面短文，从短文后各题所给的四个选项(A、B、C和D)中，选出可以填人空白处的最佳选项When my mother died, I was 16.As I walked out of the church after the funeral, it 36them—it was his upbringing, I guess.Paul and I now have three kids, and grandfather is part of their life too. Every Thanksgiving and Christmas36. A. injured B. harmed C. hurt D. hit37. A. reports B. talks C. lectures D. meetings38. A. missing B. losing . C. touching D owning39. A. public B. valuable C. free D. personal40. A. on his hands B. off his hands C. on all hands D. out of hand41. A. get along with B. deal with C. escape from D. keep away from42. A. often B. always C. frequently D. seldom43. A. away B. out C. up D. down44. A. the minute B. before C. while D. in the meanwhile45. A. referred B. turned C. pointed D. applied46. A. friend B. man C. mom D. dad47. A. get married B. be separated C. make friends D. keep in touch48. A. anxious B. uncomfortable C. worried D. happy49. A. long before B. long ago C. right after D. shortly after50. A. thinking B. talking C. laughing D. crying51. A. friends' B. Dad's C. brother's D. sister’s52. A. with B. without C. within D. beside53. A. examine B. observe C. see D. watch54. A. either B. another C. others D. the other55. A. more than B. other than C. better than D. rather than完型填空36---40 DBADA BDCAB46----55 CADCD BACCA阅读理解We may all have had the embarrassing moment: Getting half-way through a story only to realize that we’ve told this exact tale before, to the same person. Why do we make such memory mistakes?According to a research published in Psychological Science, it may have to do with the way our brains process different types of memory.Researchers Nigel Gopie, of the Rotman Research Institute in Toronto, and Colin Macleod, of the University of Waterloo, divided memory into two kinds. The first was source memory, or the ability to keep track of where information is coming from. The second was destination memory, or the ability to recall who we have given information to.They found that source memory functions better than destination memory, in part because of the direction inwhich that information is travelling.To study the differences between source and destination memory, the researchers did an experiment on 60 university students, according to a New York Times report. The students were asked to associate 50 random facts with the faces of 50 famous people. Half of the students “told” each fact to one of the faces, reading it aloud when the celebrity’s (名人的) picture appeared on a computer screen. The other half read each fact silently and saw a different celebrity picture afterward.When later asked to recall which facts went with which faces, the students who were giving information out (destination memory) scored about 16% lower on memory performance compared with the students receiving information (source memory).The researchers concluded that out-going information was less associated with its environmental context(背景）—that is, the person—than was incoming information.This makes sense given what is known about attention. A person who is giving information, even little facts, will devote some mental resources to thinking about what is being said. Because our attention is limited, we give less attention to the person we are giving information to.After a second experiment with another group of 40 students, the researchers concluded that self-focus is another factor that undermines(gradually lessen) destination memory.They asked half the students to continue giving out random information, while the other told things about themselves. This time around, those who were talking about themselves did 15% worse than those giving random information.“When you start telling these personal facts compared with non-self facts, suddenly destination memory goes down more,. suggesting that it is the self-focus component (成分) that's reducing the memory,” Gopie told Live Science.68. The point of this article is to __________.A. give advice on how to improve memoryB. say what causes the memory to worsenC. explain why we repeat stories to those we've already told them toD. discuss the differences between source and destination memory69. What can we learn from the article?A. Source memory helps us remember who we have told the information to.B. One’s limited attention is one of the reasons why those reading aloud to the celebrity’s pictures perform worse on the memory test.C. Silent reading is a better way to remember information than reading aloud.D. It tends to be more difficult for people to link incoming information with its environmental context than outgoing information70. What did the scientists conclude from the second experiment?A. Destination memory is weaker than source memory.B. Focusing attention on oneself leads to relatively poor source memory performance.C. Associating personal experience with information helps people memorize better.D. Self-focus is responsible for giving information twice or more to the same person.CBD七选五根据短文内容，从短文后的选项中选出能填入空白处的最佳选项，选项中有两项为多余选项There is an English saying : “71” Until recently, few people took the saying seriously. Now, however,Tests were carried out to study the effects of laughter on the body. People watched funny films while doctors checked their hearts, blood pressure, breathing and muscles. It was found that laughter has similar effects toOther tests have shown that laughter appears to be able to reduce the effect of pain on the body. In oneenough to produce beneficial effects similar to those caused by laughter.A. Laughter can prolong one's life.B. As a result of these discoveries,some doctors in the United States now hold laughter clinics in which they help to improve their patients’ condition by encouraging them to laugh.C. The reason why laughter can reduce pain seems to be that it helps to produce a kind of chemicals in the brain which diminish both stress and pain.D. It increases blood pressure, the heart beating and breathing; it also works several groups of muscles in the face, the stomach and even the feet.E. Although laughter helps cure the disease, doctors still can not put this theory into clinic practice.F. Laughter is the best medicine.G. They have found that laughter really can improve people's health.71---75FGDCB短文改错注意：1．每处错误及其修改均仅限一词；2．只允许修改10处，多者（从第11处起）不计分Our government is trying hardly to build an energy-saving society. It is everyone duty to help reach this goal. However, not everybody have realized the importance of it. For example, sometimes lights and computers are still on after the classes. Some students even forget to turn off the tap after using it and have water running all the time. Usually only one side of our paper is used , caused much waste.It’s time we did something to avoid this kinds of waste. Remember to turn off the tap immediately after using them. Make sure that all the lights and other electric facilities are turned off when we leave the rooms. What’s more, paper should be printed and written on both sides.In a word, if everybody has the aware of reducing waste and saving energy, we can contribute our society.书面表达假如你是南阳中学学生李越，曾在英国学习三个月，现已回国。

2024届福建省福州时代中学中考英语适应性模拟试题含答案注意事项：1．答卷前，考生务必将自己的姓名、准考证号填写在答题卡上。

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回答非选择题时，将答案写在答题卡上，写在本试卷上无效。

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Ⅰ. 单项选择1、Which of the following words has different sounds from the underlined letter of the word “brea th e”? A．thousand B．though C．smooth2、--- ______ do you volunteer at the old people’s home?--- Once a month.A．How long B．How soon C．How far D．How often3、Richard Gere ________ a super model called Cindy Crawford in 1991, but they ended their marriage in 1995. Actually, they _________ only for four years since they fell in love with each other.A．was married to; got married B．got married to; have marriedC．married; have been married D．got married with; are married4、— Got any information about High School Examination?— Well, I was trying to, but found .A．one B．no one C．none D．some5、---Can you tell me how to have a good relationship with parents?---Certainly. If you often talk about your ideas with them, they will talk about with you, too.A．their B．them C．theirs6、--- Where has Jack gone?--- He _____ has gone to the library to return his books, because I saw him holding some books and running out of his room.A．probably B．especially C．completely7、Music helps us _______ /rɪ'læks/ a lot when we feel tired .A．read B．red C．rest D．relax8、- My bike is broken. Can you help me _____ it?- Sure.A．repair B．recycle C．store D．invent9、All of the students think the test is very easy. _____ there are still so me ones who can’t pass it.A．But B．And C．So D．Or10、On such cold winter days, I prefer ____ at home reading rather than ____.A．to stay; hang out B．stay; hang outC．to stay; to hang out D．staying; hang outⅡ. 完形填空11、Mary was ill, so she went to see 1 .“Doctor, I’m not feeling 2 ,” said Mary. “Every time I do my homework, I feel 3 . If I go to school on foot, I have to sit down and 4 for a few times.”The doctor looked over her 5 . At last he said, “ 6 serious（严重的）, but I’m afraid you are eating too much.” “I don’t understand. What do you mean（意思）?” asked Mary.“I mean you eat 7 food,” said the doctor.“Oh! You mean I’m too8 That’s a problem,” said Mary. “What should I do?”“The answer is easy,” said the doctor. “If you eat a lot of food and also do much9 , you 10 thinner and healthier”1．A．her mother B．the teacher C．the doctor D．her friend2．A．terrible B．ill C．good D．well3．A．hungry B．thirsty C．tired D．happy4．A．stand up B．lie down C．eat food D．have a rest5．A．carelessly B．careless C．carefully D．careful6．A．Something B．Anything C．Everything D．Nothing7．A．too many B．many too C．too much D．much too8．A．thin B．healthy C．stressed out D．heavy9．A．housework B．homework C．shopping D．exercise10．A．are B．will C．will be D．shouldⅢ. 语法填空12、A long time ago, there was an emperor. He had a beautiful garden. In the garden, there was a little nightingale(夜莺) singing very1．(beauty).One day the emperor heard about this little bird's beautiful voice. He asked his guards to bring her to him. As soon as the emperor heard the nightingale's voice, he said, "Put her in a golden cage, 2．she can stay and sing for me whenever I want to hear her. "The little bird was so3．(happy) about being kept in the cage that she4．(stop) singing one day. The emperor was very angry. He ordered the scientists in his palace to make a robot bird 5．him. The bird could sing very beautifully,6．. The emperor was pleased.Soon the robot bird became old. It no longer sang beautiful songs. Just at that time, the emperor became very weak. One morning, while7．(lie) in bed, the emperor wanted it to sing once again.8．the robot bird couldn't sing any more.Suddenly the nightingale landed on the window. She began to sing her9．beautiful song. The emperor was very happy! He became better and better each day.After the emperor was well，he changed a lot and became kind to his people. From then on, all his people cherished(爱戴) him for his love and10．(kind).Ⅳ. 阅读理解A13、Is there a way to quickly remember information just before taking an exam? Walking backwards might bea way to solve this problem. Scientists from the University of Roehampton in the UK said this activity can help people improve their short-term memory.Researchers asked 114 volunteers to watch a video. After watching the video, volunteers were divided into three groups. One group was told to walk 10 metres forward. The second group walked 10 metres backward. The third group stood in one place. All three groups were then asked 20 questions about what they saw in the video.The scientists found that the backward- walking group got two more.answers correct on average than the other groups.This suggests that the relationship between the concepts(概念）of time and space is important considering how our minds form memories. "Time is really expressed via(通过）space,”Aleksandar Aksentijevic, who led the study, told The Daily Mail. When you walk backward, you see things from a different way compared to walking forward. This difference helps people recall things that happened in the past.And walking backward is not just good for our brains. It is also good for the rest of our body. Compared to walking forward, walking backward is more challenging. This can ameliorate our health, according to New Scientist, Walking backward uses more energy in a short time and burns more calories.Besides, walking backward is less stressful for our knees. It could.be helpful for people who often have pain in their knees, according to researchers from the Unegon in the US. Walking backward also keeps our spines（脊柱）strong, which can help to reduce pain in the lower back. This might be why many old people like walking backward.1．In the experiment, the first group was asked to_________.A．walk 10 metres forwardB．walk 10 metres backwardC．keep on moving aroundD．stand in one place2．The experiment shows that walking backward____________.A．puts less tress on our kneesB．helps with the rest of our bodyC．uses more energy in a short time .D．improves the short-term memory3．The underlined word “ameliorate” in the passage means"_______________."A．harm B．improve C．control D．spread4．According to New Scientist,why is walking backward helpful?A．It helps people remember informationB．It helps people burn more calories.C．It reduces pain in people's knees and backs.D．It allows people to solve problems in different ways5．What is the best title for this passage?A．Let's exercise our brain B．Let's do an experimentC．Let's walk backward D．Let's do more exerciseB14、阅读下列短文，从每题A、B、C、D四个选项中，选出一个能回答所提问题或完成所给句子的最佳答案。

英语作文关于问题和烦恼的三段式示例回答如下1:In our daily lives, we often encounter various problems and difficulties that can be a source of annoyance and frustration. However, it is essential to address these challenges and find solutions to overcome them. In this essay, I will discuss three different types of problems and how to deal with them.Firstly, one common problem that many people face is time management. With numerous responsibilities, such as work, studies, and personal commitments, it is easy to become overwhelmed and feel like there are not enough hours in a day. To address this issue, it is crucial to prioritize tasks, set goals, and create a schedule. By organizing our time effectively, we can allocate specific periods for each activity and ensure that we make the most out of our day. Additionally, delegating tasks or seeking assistance from others can also help lighten the workload and reduce stress associated with time management.Secondly, interpersonal conflicts are another significant source of frustration and annoyance. Whether it be with friends,family, or colleagues, disagreements and misunderstandings can arise, leading to strained relationships. Instead of avoiding or escalating the conflict, it is important to address the issue directly and communicate honestly. By expressing our concerns, listening to the perspectives of others, and seeking to find common ground, we can work towards resolving the conflict and maintaining healthy relationships. It is also helpful to practice empathy and understand that everyone has different viewpoints and experiences.Lastly, personal doubts and insecurities can often lead to self-doubt and unhappiness. Many individuals face moments when they question their abilities, appearance, or sense ofself-worth. To address these concerns, it is crucial to practice self-care and self-acceptance. Engaging in activities that bring joy and boost self-confidence, such as exercise, hobbies, or spending time with loved ones can help combat negative thoughts. Surrounding ourselves with supportive and positive individuals can also make a significant difference in overcoming personal doubts. Moreover, seeking professional help, such as therapy or counseling, can provide guidance and support during challenging periods.In conclusion, problems and annoyances are a part of life, but it is important to address them rather than let them overwhelm us. By effectively managing our time, addressing interpersonal conflicts, and practicing self-care, we can successfully overcome these challenges and lead a more fulfilled and contented life.。

Call a -digit number geometric if it has distinct digits which, when readfrom left to right, form a geometric sequence. Find the difference between the largest and smallest geometric numbers.There is a complex number with imaginary part and a positive integersuch thatFind .A coin that comes up heads with probability and tails with probabilityindependently on each flip is flipped eight times. Suppose theprobability of three heads and five tails is equal to of the probability of fiveheads and three tails. Let , where and are relatively prime positive integers. Find .In parallelogram , point is on so that and pointis on so that . Let be the point of intersection of and. Find .Triangle has and . Points and are located onand respectively so that , and is the angle bisector ofangle . Let be the point of intersection of and , and let be thepoint on line for which is the midpoint of . If , find .How many positive integers less than are there such that the equationhas a solution for ? (The notation denotes the greatest integerthat is less than or equal to .)The sequence satisfies and for . Letbe the least integer greater than for which is an integer. Find .Let . Consider all possible positive differences of pairs of elements of . Let be the sum of all of these differences. Find theremainder when is divided by .A game show offers a contestant three prizes A,B and C, each of which is worth a whole number of dollars from $to $inclusive. The contestantwins the prizes by correctly guessing the price of each prize in the order A, B, C. As a hint, the digits of the three prices are given. On a particular day, the digits given were . Find the total number of possible guessesfor all three prizes consistent with the hint.The Annual Interplanetary Mathematics Examination (AIME) is written by a committee of five Martians, five Venusians, and five Earthlings. At meetings, committee members sit at a round table with chairs numbered from to inclockwise order. Committee rules state that a Martian must occupy chairand an Earthling must occupy chair , Furthermore, no Earthling can sitimmediately to the left of a Martian, no Martian can sit immediately to the left of a Venusian, and no Venusian can sit immediately to the left of an Earthling. The number of possible seating arrangements for the committee is. Find .Consider the set of all triangles where is the origin and and aredistinct points in the plane with nonnegative integer coordinates such that . Find the number of such distinct triangles whose area isa positive integer.In right with hypotenuse , , , and is thealtitude to . Let be the circle having as a diameter. Let be a pointoutside such that and are both tangent to circle . The ratioof the perimeter of to the length can be expressed in the form ,where and are relatively prime positive integers. Find .The terms of the sequence defined by for arepositive integers. Find the minimum possible value of .For , define , where . If and, find the minimum possible value for .In triangle , , , and . Let be a point in theinterior of . Let and denote the incenters of triangles and, respectively. The circumcircles of triangles and meet atdistinct points and . The maximum possible area of can beexpressed in the form , where , , and are positive integers andis not divisible by the square of any prime. Find .Of the students attending a school party, of the students are girls, andof the students like to dance. After these students are joined by moreboy students, all of whom like to dance, the party is now girls. How manystudents now at the party like to dance?SolutionSquare has sides of length units. Isosceles triangle has base, and the area common to triangle and square is squareunits. Find the length of the altitude to in .SolutionEd and Sue bike at equal and constant rates. Similarly, they jog at equal and constant rates, and they swim at equal and constant rates. Ed coverskilometers after biking for hours, jogging for hours, and swimming forhours, while Sue covers kilometers after jogging for hours, swimming forhours, and biking for hours. Their biking, jogging, and swimming rates areall whole numbers of kilometers per hour. Find the sum of the squares of Ed's biking, jogging, and swimming rates.SolutionThere exist unique positive integers and that satisfy the equation. Find .SolutionA right circular cone has base radius and height . The cone lies on its sideon a flat table. As the cone rolls on the surface of the table without slipping, the point where the cone's base meets the table traces a circular arc centered at the point where the vertex touches the table. The cone first returns to its original position on the table after making complete rotations. The valueof can be written in the form , where and are positive integersand is not divisible by the square of any prime. Find .A triangular array of numbers has a first row consisting of the odd integersin increasing order. Each row below the first has one fewer entrythan the row above it, and the bottom row has a single entry. Each entry in any row after the top row equals the sum of the two entries diagonally above it in the row immediately above it. How many entries in the array are multiples of ?Let be the set of all integers such that . Forexample, is the set . How many of the setsdo not contain a perfect square?Find the positive integer such thatTen identical crates each of dimensions ft ft ft. The first crate is placedflat on the floor. Each of the remaining nine crates is placed, in turn, flat on top of the previous crate, and the orientation of each crate is chosen atrandom. Let be the probability that the stack of crates is exactly ft tall,where and are relatively prime positive integers. Find .Let be an isosceles trapezoid with whose angle at thelonger base is . The diagonals have length , and point is atdistances and from vertices and , respectively. Let be thefoot of the altitude from to . The distance can be expressed in theform , where and are positive integers and is not divisible by thesquare of any prime. Find .Consider sequences that consist entirely of 's and 's and that have theproperty that every run of consecutive 's has even length, and every run ofconsecutive 's has odd length. Examples of such sequences are , ,and , while is not such a sequence. How many suchsequences have length 14?On a long straight stretch of one-way single-lane highway, cars all travel at the same speed and all obey the safety rule: the distance form the back of the car ahead to the front of the car behind is exactly one car length for each 15 kilometers per hour of speed or fraction thereof (Thus the front of a car traveling 52 kilometers per hour will be four car lengths behind the back of the car in front of it.) A photoelectric eye by the side of the road counts the number of cars that pass in one hour. Assuming that each car is 4 meters long and that the cars can travel at any speed, let be the maximum wholenumber of cars that can pass the photoelectric eye in one hour. Find the quotient when is divided by 10.Let.Suppose that.There is a point for which for all such polynomials, where , , and are positive integers, and are relatively prime, and .Find .SolutionLet be a diameter of circle . Extend through to . Point lies onso that line is tangent to . Point is the foot of the perpendicularfrom to line . Suppose , and let denote the maximumpossible length of segment . Find .SolutionA square piece of paper has sides of length . From each corner a wedgeis cut in the following manner: at each corner, the two cuts for the wedge each start at distance from the corner, and they meet on the diagonal atan angle of (see the figure below). The paper is then folded up along thelines joining the vertices of adjacent cuts. When the two edges of a cut meet, they are taped together. The result is a paper tray whose sides are not at right angles to the base. The height of the tray, that is, the perpendicular distancebetween the plane of the base and the plane formed by the upper edges, can be written in the form , where and are positive integers, ,and is not divisible by the th power of any prime. Find .How many positive perfect squares less than are multiples of 24?A 100 foot long moving walkway moves at a constant rate of 6 feet per second. Al steps onto the start of the walkway and stands. Bob steps onto the start of the walkway two seconds later and strolls forward along the walkway at a constant rate of 4 feet per second. Two seconds after that, Cy reaches the start of the walkway and walks briskly forward beside the walkway at a constant rate of 8 feet per second. At a certain time, one of these three persons is exactly halfway between the other two. At that time, find the distance in feet between the start of the walkway and the middle person.The complex number is equal to , where is a positive real numberand . Given that the imaginary parts of and are the same, what isequal to?Three planets orbit a star circularly in the same plane. Each moves in the same direction and moves at constant speed. Their periods are , , and. The three planets and the star are currently collinear. What is the fewest number of years from now that they will all be collinear again?The formula for converting a Fahrenheit temperature to the correspondingCelsius temperature is An integer Fahrenheit temperatureis converted to Celsius, rounded to the nearest integer, converted back to Fahrenheit, and again rounded to the nearest integer.For how many integer Fahrenheit temperatures between 32 and 1000 inclusive does the original temperature equal the final temperature? Problem 6A frog is placed at the origin on the number line, and moves according to the following rule: in a given move, the frog advances to either the closest point with a greater integer coordinate that is a multiple of 3, or to the closest point with a greater integer coordinate that is a multiple of 13. A move sequence is a sequence of coordinates which correspond to valid moves, beginning with 0, and ending with 39. For example, is a movesequence. How many move sequences are possible for the frog?LetFind the remainder when is divided by 1000. (is the greatest integerless than or equal to , and is the least integer greater than or equal to.)The polynomial is cubic. What is the largest value of for which thepolynomials andare both factors of ?In right triangle with right angle , and . Its legsand are extended beyond and . Points and lie in theexterior of the triangle and are the centers of two circles with equal radii. The circle with center is tangent to the hypotenuse and to the extension of leg, the circle with center is tangent to the hypotenuse and to theextension of leg , and the circles are externally tangent to each other. Thelength of the radius of either circle can be expressed as , where andare relatively prime positive integers. Find .In a 6 x 4 grid (6 rows, 4 columns), 12 of the 24 squares are to be shaded so that there are two shaded squares in each row and three shaded squares in each column. Let be the number of shadings with this property. Find theremainder when is divided by 1000.For each positive integer , let denote the unique positive integer suchthat . For example, and . If find the remainder when is divided by 1000.In isosceles triangle , is located at the origin and is located at (20,0).Point is in the first quadrant with and angle . Iftriangle is rotated counterclockwise about point until the image oflies on the positive -axis, the area of the region common to the original andthe rotated triangle is in the form , where areintegers. Find .A square pyramid with base and vertex has eight edges of length 4.A plane passes through the midpoints of , , and . The plane'sintersection with the pyramid has an area that can be expressed as . Find.A sequence is defined over non-negative integral indexes in the followingway: , .Find the greatest integer that does not exceedLet be an equilateral triangle, and let and be points on sidesand , respectively, with and . Point lies on sidesuch that angle . The area of triangle is . The twopossible values of the length of side are , where and arerational, and is an integer not divisible by the square of a prime. Find .In quadrilateral is a right angle, diagonal is perpendicular toand Find the perimeter ofLet set be a 90-element subset of and let be the sum ofthe elements of Find the number of possible values ofFind the least positive integer such that when its leftmost digit is deleted, theresulting integer is of the original integer.Let be the number of consecutive 0's at the right end of the decimalrepresentation of the product Find the remainder whenis divided by 1000.The number can be written aswhere and are positive integers. FindLet be the set of real numbers that can be represented as repeatingdecimals of the form where are distinct digits. Find the sum of theelements ofAn angle is drawn on a set of equally spaced parallel lines as shown. The ratio of the area of shaded region to the area of shaded region is 11/5. Findthe ratio of shaded region to the area of shaded regionProblem 8Hexagon is divided into five rhombuses, and asshown. Rhombuses and are congruent, and each has areaLet be the area of rhombus Given that is a positive integer, find thenumber of possible values forThe sequence is geometric with and common ratio whereand are positive integers. Given thatfind the number of possible orderedpairsEight circles of diameter 1 are packed in the first quadrant of the coordinte plane as shown. Let region be the union of the eight circular regions. Linewith slope 3, divides into two regions of equal area. Line 's equation canbe expressed in the form where and are positive integerswhose greatest common divisor is 1. FindA collection of 8 cubes consists of one cube with edge-length for eachinteger A tower is to be built using all 8 cubes according to therules:Any cube may be the bottom cube in the tower.The cube immediately on top of a cube withedge-length must have edge-length at mostLet be the number of different towers than can be constructed. What is theremainder when is divided by 1000?Find the sum of the values of such thatwhere is measured in degrees andFor each even positive integer let denote the greatest power of 2 thatdivides For example, and For each positive integerlet Find the greatest integer less than 1000 such that isa perfect square.A tripod has three legs each of length 5 feet. When the tripod is set up, the angle between any pair of legs is equal to the angle between any other pair, and the top of the tripod is 4 feet from the ground In setting up the tripod,the lower 1 foot of one leg breaks off. Let be the height in feet of the topof the tripod from the ground when the broken tripod is set up. Then canbe written in the form where and are positive integers and is notdivisible by the square of any prime. Find (The notation denotes the greatest integer that is less than or equal to )Given that a sequence satisfies and for all integersfind the minimum possible value ofSix circles form a ring with with each circle externally tangent to two circles adjacent to it. All circles are internally tangent to a circle with radius 30. Letbe the area of the region inside circle and outside of the six circles in thering. FindFor each positive integer let denote the increasing arithmetic sequenceof integers whose first term is 1 and whose common difference is Forexample, is the sequence For how many values of doescontain the term 2005?How many positive integers have exactly three proper divisors, each of which is less than 50?The director of a marching band wishes to place the members into a formation that includes all of them and has no unfilled positions. If they are arranged in a square formation, there are 5 members left over. The director realizes that if he arranges the group in a formation with 7 more rows thancolumns, there are no members left over. Find the maximum number of members this band can have.Robert has 4 indistinguishable gold coins and 4 indistinguishable silver coins. Each coin has an engraving of one face on one side, but not on the other. He wants to stack the eight coins on a table into a single stack so that no two adjacent coins are face to face. Find the number of possible distunguishable arrangements of the 8 coins.Let be the product of the nonreal roots ofFindIn quadrilateral andGiven that where and are positiveintegers, findThe equation has three real roots. Given thattheir sum is where and are relatively prime positive integers, findTwenty seven unit cubes are painted orange on a set of four faces so that two non-painted faces share an edge. The 27 cubes are randomly arranged to form a cube. Given the probability of the entire surface area of thelarger cube is orange is where and are distinct primes andand are positive integers, findTriangle lies in the Cartesian Plane and has an area of 70. Thecoordinates of and are and respectively, and thecoordinates of are The line containing the median to side hasslope Find the largest possible value ofA semicircle with diameter is contained in a square whose sides have length8. Given the maximum value of is findFor positive integers let denote the number of positive integerdivisors of including 1 and For example, and Defineby Let denote the number of positiveintegers with odd, and let denote the number of positiveintegers with even. FindA particle moves in the Cartesian Plane according to the following rules:1.From any lattice point the particle mayonly move to or2.There are no right angle turns in the particle'spath.How many different paths can the particle take from to ?Consider the points and There is a unique square such that each of the four points is on a different side ofLet be the area of Find the remainder when is divided by 1000.Triangle has The incircle of the triangle evenly trisects themedian If the area of the triangle is where and are integersand is not divisible by the square of a prime, findThe digits of a positive integer are four consecutive integers in decreasing order when read from left to right. What is the sum of the possible remainders when is divided by 37?Set consists of consecutive integers whose sum is and set consistsof consecutive integers whose sum is The absolute value of thedifference between the greatest element of and the greatest element ofis 99. FindA convex polyhedron has 26 vertices, 60 edges, and 36 faces, 24 of whichare triangular, and 12 of which are quadrilaterals. A space diagonal is a linesegment connecting two non-adjacent vertices that do not belong to the same face. How many space diagonals does have?A square has sides of length 2. Set is the set of all line segments that havelength 2 and whose endpoints are on adjacent sides of the square. The midpoints of the line segments in set enclose a region whose area to thenearest hundredth is FindAlpha and Beta both took part in a two-day problem-solving competition. At the end of the second day, each had attempted questions worth a total of 500 points. Alpha scored 160 points out of 300 points attempted on the first day, and scored 140 points out of 200 points attempted on the second day. Beta who did not attempt 300 points on the first day, had a positive integer score on each of the two days, and Beta's daily success rate (points scored divided by points attempted) on each day was less than Alpha's on that day. Alpha's two-day success ratio was 300/500 = 3/5. The largest possibletwo-day success ratio that Beta could achieve is where and are relatively prime positive integers. What is ?An integer is called snakelike if its decimal representationsatisfies if is odd and if is even. How many snakelikeintegers between 1000 and 9999 have four distinct digits?Let be the coefficient of in the expansion of the productFindDefine a regular -pointed star to be the union of line segmentssuch thatthe points are coplanar and no threeof them are collinear,each of the line segments intersects at least oneof the other line segments at a point other than anendpoint,all of the angles at are congruent,all of the line segments arecongruent, andthe path turnscounterclockwise at an angle of less than 180degrees at each vertex.There are no regular 3-pointed, 4-pointed, or 6-pointed stars. All regular5-pointed stars are similar, but there are two non-similar regular 7-pointed stars. How many non-similar regular 1000-pointed stars are there?Let be a triangle with sides 3, 4, and 5, and be a 6-by-7rectangle. A segment is drawn to divide triangle into a triangle and atrapezoid and another segment is drawn to divide rectangle into atriangle and a trapezoid such that is similar to and is similar toThe minimum value of the area of can be written in the formwhere and are relatively prime positive integers. FindA circle of radius 1 is randomly placed in a 15-by-36 rectangle so thatthe circle lies completely within the rectangle. Given that the probability thatthe circle will not touch diagonal is where and are relativelyprime positive integers. FindA solid in the shape of a right circular cone is 4 inches tall and its base has a 3-inch radius. The entire surface of the cone, including its base, is painted. A plane parallel to the base of the cone divides the cone into two solids, a smaller cone-shaped solid and a frustum-shaped solid in such a waythat the ratio between the areas of the painted surfaces of and and theratio between the volumes of and are both equal to Given thatwhere and are relatively prime positive integers, findLet be the set of ordered pairs such that andand are both even. Given that the area of the graph ofis where and are relatively prime positive integers, findThe notation denotes the greatest integer that is less than or equal toThe polynomial has 34 complex rootsof the form withand Given thatwhere and are relatively prime positive integers, findA unicorn is tethered by a 20-foot silver rope to the base of a magician's cylindrical tower whose radius is 8 feet. The rope is attached to the tower at ground level and to the unicorn at a height of 4 feet. The unicorn has pulled the rope taut, the end of the rope is 4 feet from the nearest point on thetower, and the length of the rope that is touching the tower is feet, where and are positive integers, and is prime. FindFor all positive integers , let anddefine a sequence as follows: and for all positiveintegers . Let be the smallest such that . (For example,and .) Let be the number of positive integers suchthat . Find the sum of the distinct prime factors of .SolutionGiven thatwhere and are positive integers and is as large as possible, findOne hundred concentric circles with radii are drawn in a plane.The interior of the circle of radius 1 is colored red, and each region bounded by consecutive circles is colored either red or green, with no two adjacent regions the same color. The ratio of the total area of the green regions to thearea of the circle of radius 100 can be expressed as where and are relatively prime positive integers. FindLet the set Susan makes a list as follows: for each two-element subset of she writes on her list the greater of the set's twoelements. Find the sum of the numbers on the list.Given that and thatfindConsider the set of points that are inside or within one unit of a rectangular parallelepiped (box) that measures 3 by 4 by 5 units. Given that the volumeof this set is where and are positive integers, and andare relatively prime, findThe sum of the areas of all triangles whose vertices are also vertices of a 1 by1 by 1 cube is where and are integers. FindPoint is on with and Point is not on so thatand and are integers. Let be the sum of all possibleperimeters of FindIn an increasing sequence of four positive integers, the first three terms form an arithmetic progression, the last three terms form a geometric progression, and the first and fourth terms differ by 30. Find the sum of the four terms.An integer between 1000 and 9999, inclusive, is called balanced if the sum of its two leftmost digits equals the sum of its two rightmost digits. How many balanced integers are there?Triangle is isosceles with and Point is inthe interior of the triangle so that and Find thenumber of degrees inAn angle is chosen at random from the interval Let be theprobability that the numbers and are not the lengthsof the sides of a triangle. Given that where is the number ofdegrees in and and are positive integers withfindIn convex quadrilateral andThe perimeter of is 640. Find (The notation means thegreatest integer that is less than or equal to )Let be the number of positive integers that are less than or equal to 2003and whose base-2 representation has more 1's than 0's. Find the remainder when is divided by 1000.The decimal representation of where and are relatively prime positive integers and contains the digits 2, 5, and 1 consecutively, andin that order. Find the smallest value of for which this is possible.In and Let be the midpoint ofand let be the point on such that bisects angle Let bethe point on such that Suppose that meets atThe ratio can be written in the form where and arerelatively prime positive integers. FindMany states use a sequence of three letters followed by a sequence of three digits as their standard license-plate pattern. Given that each three-letter three-digit arrangement is equally likely, the probability that such a license plate will contain at least one palindrome (a three-letter arrangement or athree-digit arrangement that reads the same left-to-right as it doesright-to-left) is , where and are relatively prime positive integers. Find .The diagram shows twenty congruent circles arranged in three rows and enclosed in a rectangle. The circles are tangent to one another and to the sides of the rectangle as shown in the diagram. The ratio of the longer dimension of the rectangle to the shorter dimension can be written as , where and are positive integers. Find .Jane is 25 years old. Dick is older than Jane. In years, where n is a positive integer, Dick's age and Jane's age will both be two-digit number and will have the property that Jane's age is obtained by interchanging the digits ofDick's age. Let be Dick's present age. How many ordered pairs of positiveintegers are possible?Problem 4Consider the sequence defined by for . Given that, for positive integers and with , find .Let be the vertices of a regular dodecagon. How manydistinct squares in the plane of the dodecagon have at least two vertices inthe set ?The solutions to the system of equations。

《三体》英语书评：A Journey ThroughTime and SpaceIn the vast expanse of the universe, where the boundaries of science and imagination intersect, LiuCixin's "Three-Body Problem" stands as a monumental testament to the power of human creativity and curiosity. This groundbreaking science fiction novel, a winner of numerous awards and accolades, weaves a complex tapestry of ideas, ranging from astrophysics to philosophy, into a captivating narrative that takes readers on a thrillingride through the cosmos.The story begins with a mysterious signal received by Earth from a distant civilization, the Trisolaris. This signal heralds the beginning of a chain of events that upend our understanding of the universe and our placewithin it. The Trisolaris, facing extinction in their own star system, seek a new home and view Earth as a potential candidate. As the Trisolaris' technology and influence grow, so does the threat to humanity, leading to a race against time for Earth's scientists and politicians to find a wayto survive.The narrative is told through multiple perspectives, giving readers a rich and nuanced understanding of the characters and their动机. The scientific details are meticulously crafted, yet accessible to the lay reader, making the complex concepts of cosmology and quantum physics engaging and understandable. Liu's writing style is both powerful and poetic, evoking a sense of awe and wonder that is both exhilarating and thought-provoking.One of the most remarkable aspects of "Three-Body Problem" is its ability to blur the lines between science and fiction. Liu seamlessly integrates cutting-edge scientific theories and hypothetical scenarios into the narrative, creating a world that feels both real and fantastical. This blend of science and fiction not only enhances the story's credibility but also encourages readers to question their own understanding of the universe and the limits of human knowledge.The themes explored in "Three-Body Problem" are as vast and complex as the universe itself. The novel raises questions about the nature of intelligence, the role of technology in society, and the ethics of survival in theface of existential threats. Through these themes, Liu challenges readers to consider the biggest questions of our time: What is our purpose in the universe? How far shouldwe push the boundaries of science and technology? What are the costs of survival?The impact of "Three-Body Problem" extends beyond the pages of the book. It has sparked widespread interest in science fiction and astrophysics, inspiring a generation of readers to pursue further study in these fields. Thenovel's influence has also extended to the global stage,with its English translation winning numerous awards and recognition, further solidifying Liu's status as a leading figure in science fiction literature.In conclusion, "Three-Body Problem" is a remarkablefeat of literary and scientific genius. Liu Cixin'svisionary storytelling and profound insights into the human condition make this novel a must-read for anyone interested in science fiction, astrophysics, or the intersection of these fields with human thought and culture. "Three-Body Problem" is not just a story about survival in the universe; it is a story about the survival of the human spirit in theface of insurmountable challenges and the limitless possibilities of the human imagination.**《三体》英语书评：穿越时空的旅程**在宇宙的辽阔无垠中，科学与想象力的边界交汇，刘慈欣的《三体》作为人类创造力和好奇心的壮丽见证，屹立不倒。