新试卷--2[1]

第一部分：听力理解Section A（共5小题，每小题2分，满分10分）1. W: Excuse me, could you tell me where the nearest post office is?M: Sure, it's just down the street, on the corner.Q: What does the man mean?2. M: I'm sorry, I didn't catch what you said. Could you repeat that?W: No problem. I said I'm going to the library to study for the exam.Q: What is the woman going to do?3. W: I can't believe it's already 6 o'clock. Time flies when you're having fun.M: Absolutely. I can't wait to go on vacation next week.Q: What can we infer from the conversation?4. M: I think we should take a break now. It's been a long day.W: I agree. Let's go for a coffee and relax for a while.Q: What are the speakers planning to do?5. W: How was your trip to Beijing?M: It was amazing. The food, the sights, and the people were all great.Q: What does the man think about his trip to Beijing?Section B（共5小题，每小题2分，满分10分）6. Listen to the passage and answer the following question.What is the main idea of the passage?7. Listen to the passage and fill in the blanks with the words you hear.The city has many _______ places to visit, such as the _______ and the _______.8. Listen to the passage and match the people with their professions.A. TeacherB. DoctorC. EngineerD. Artist9. Listen to the passage and choose the best answer to complete the sentence.The lecture will be _______ at 2:00 pm.10. Listen to the passage and answer the following question.Why is the woman going to the library?第二部分：阅读理解Section A（共10小题，每小题2分，满分20分）Passage 1Last year, I decided to take up running as a hobby. I had always been a bit of a couch potato, but I wanted to get in better shape and meet new people. I started running three times a week, and gradually, I began to notice some changes. My energy levels increased, and I started feeling more confident about myself. I also made some great friends who shared my passion for running. Running has become an integral part of my life, and I couldn't imagine going back to my old sedentary lifestyle.Passage 2The Internet has revolutionized the way we communicate and access information. With just a few clicks, we can connect with people from all over the world and learn about events happening in real-time. However, this convenience comes with a price. The Internet has also made it easier for people to spread misinformation and engage in cyberbullying. It's important to use the Internet responsibly and be mindful of the potential negative consequences.Passage 3Environmental conservation is a global issue that requires immediate action. Deforestation, pollution, and climate change are just a few of the problems we face. As individuals, we can make a difference by reducing our carbon footprint, recycling, and supporting sustainable practices. Governments and corporations also have a responsibility to implement policies that protect our planet for future generations.Section B（共5小题，每小题3分，满分15分）11. What is the author's main purpose in writing the first passage?12. According to the second passage, what are some of the negative effects of the Internet?13. What actions can individuals take to contribute to environmental conservation?14. What is the main idea of the third passage?15. How does the author conclude the first passage?第三部分：英语知识运用Section A（共15小题，每小题2分，满分30分）16. The meeting is scheduled to ________ next Tuesday at 10:00 am.17. If you ________ to the store, could you please pick up some milk?18. The students were ________ when they heard the news about the scholarship.19. The museum ________ its doors to the public last year.20. The doctor suggested that she ________ a healthy diet and exercise regularly.21. He ________ a degree in computer science from the University of Technology.22. The experiment ________ a lot of time and effort.23. She ________ her birthday party next weekend.24. The government has implemented several ________ to reduce air pollution.25. The teacher ________ the students to work together and help each other.Section B（共5小题，每小题3分，满分15分）26. Choose the correct word to complete the sentence.a. Although / While / Since / Because27. Choose the correct word to complete the sentence.a. Although / But / However / So28. Choose the correct word to complete the sentence.a. Because / Therefore / So / However29. Choose the correct word to complete the sentence.a. Although / While / Because / Since30. Choose the correct word to complete the sentence.a. Because / Although / However / So第四部分：书面表达31. Write an essay of about 100 words describing your favorite hobby. Explain why you enjoy it and what benefits you get from it.中文翻译：31. 写一篇大约100字的作文，描述你的最喜欢的爱好。

2021年高考数学试卷新高考2卷含参考答案解析2021年普通高等学校招生全国统一考试数学试卷（新高考2卷）注意事项：1.在答题卡上填写姓名、考生号、考场号和座位号。

用2B铅笔将试卷类型填涂在答题卡相应位置上，并将条形码横贴在答题卡右上角“条形码粘贴处”。

2.作答选择题时，用2B铅笔在答题卡上对应题目的答案信息点涂黑。

如需改动，用橡皮擦干净后再涂其他答案。

不要在试卷上作答。

3.非选择题必须用黑色字迹的钢笔或签字笔作答，答案必须写在答题卡各题目指定区域内相应位置上。

如需改动，先划掉原来的答案，然后再写上新答案。

不准使用铅笔和涂改液。

不按以上要求作答无效。

4.考生必须保持答题卡的整洁。

考试结束后，将试卷和答题卡一并交回。

单选题：1.复数2-i在复平面内对应的点所在的象限为（）。

A．第一象限 B．第二象限 C．第三象限 D．第四象限2.设集合U={1,2,3,4,5,6}，A={1,3,6}，B={2,3,4}，则A∪B的结果为（）。

A．{3} B．{1,6} C．{5,6} D．{1,3}3.抛物线y2=2px(p>0)的焦点到直线y=x+1的距离为2，则p=（）。

A．1 B．2 C．22 D．44.北斗三号全球卫星导航系统是我国航天事业的重要成果，其中地球静止同步卫星的轨道位于地球赤道所在平面，轨道高度为km。

将地球看作是一个球心为O，半径r为6400km的球，其上点A的纬度是指OA与赤道平面所成角的度数。

地球表面上能直接观测到一颗地球静止同步轨道卫星点的纬度最大值为α，记卫星信号覆盖地球表面的表面积为S=2πr2(1-cosα)（单位：km2）。

则S占地球表面积的百分比约为（）。

A．26% B．34% C．42% D．50%5.正四棱台的上底面和下底面的边长分别为2和4，侧棱长为2，则其体积为（）。

A．20+123 B．282 C．56√3/2 D．282√3/36.某物理量的测量结果服从正态分布N(10,σ)，下列结论中不正确的是（）。

2022年辽宁省普通高等学校招生全国统一考试数 学注意事项：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。

2．答选择题时，选出每小题答案后，用铅笔把答题卡上对应题目的答案标号涂黑。

如需改动，用橡皮擦干净后，再选涂其他答案标号。

回答非选择题时，将答案写在答题卡上。

写在本试卷上无效。

3．考试结束后，将本试卷和答题卡一并交回。

一、选择题：本题共8小题，每小题5分，共40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．已知集合A ＝{－1，1，2，4}，B ＝{x ||x －1|≤1}，则A ∩B ＝A ．{－1，2}B ．{1，2}C ．{1，4}D ．{－1，4}2．(2＋2i)(1－2i)＝A ．－2＋4iB ．－2－4iC ．6＋2iD ．6－2i3．图1是中国的古建筑中的举架结构，AA /，BB ，CC /，DD /是桁，相邻桁的水平距离称 为步，垂直距离称为举．图2是某古建筑屋顶截面示意图，其中DD 1，CC 1，BB 1，AA 1是举，OD 1，DC 1，CB 1，BA 1是相等的步，相邻桁的举步之比分别为DD 1OD 1＝0.5，CC 1DC 1＝k 1，BB 1CB 1＝k 2，AA 1BA 1＝k 3，已知k 1，k 2，k 3是公差为0.1的等差数列，且直线OA 的斜率为0.725，则k 3＝A ．0.75B ．0.8C ．0.85D ．0.94．已知向量a ＝(3，4)，b ＝(1，0)，c ＝a ＋t b ，若＜a ，c ＞＝＜b ，c ＞，则t ＝A ．－6B ．－5C ．5D ．65．甲乙丙丁戊5名同学站成一排参加文艺汇演，若甲不站在两端，丙和丁相邻，则不同排列方式共有 A ．12种 B ．24种 C ．36种 D ．48种按秘密级事项管理6．若sin(α＋β)＋cos(α＋β)＝22cos(α＋π4)sin β，则A ．tan(α－β)＝1B ．tan(α＋β)＝1C ．tan(α－β)＝－1D ．tan(α＋β)＝－1 7．已知正三棱台的高为1，上、下底面的边长分别为33和43，其顶点都在同一球面上，则该球的表面积为 A ．100π B ．128π C ．144π D ．192π8．若函数f (x )的定义域为R ，且f (x ＋y )＋f (x －y )＝f (x )f (y )，f (1)＝1，则 k ＝122f (k )＝A ．－3B ．－2C ．0D ．1二、选择题：本题共4小题，每小题5分，共20分．在每小题给出的选项中，有多项符合题目要求。

2021年全国高考新高考2卷英语试题（含答案）2021年全国高考新高考2卷英语试题本试卷共11页，共100分.考试时长90分钟.考生务必在答题卡指定区域作答，在试卷上作答无效.考试结束后，将本试卷和答题卡一并交回.第一部分听力(共两节，满分30分)做题时，先将答案标在试卷上。

录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。

第一节(共5小题;每小题1.5分，满分7.5分)听下面5段对话。

每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

例：How much is the shirt?A. ￡19.15.B. ￡9.18.C. ￡9.15.答案是C。

1. Why did the woman go to Mallorca?A. To teach Spanish.B. To look for a job.C. To see a friend.2. What does the man ask the woman to do?A. Take him to hospital.B. Go to a class with him.C. Submit a report for him.3. Who will look after the children?A. Jennifer.B. Suzy.C. Marie.4. What are the speakers going to do?A. Drive home.B. Go shoppingC. Eat out.5. What are the speakers talking about?A. How to fry fish.B. How to make coffee.C. How to remove a bad smell.第二节(共15小题;每小题1.5分，满分22.5分)听下面5段对话或独白。

一、听力理解（共25小题，每小题2分，满分50分）Section A1. How does the man feel about the weather today?A. Cold.B. Warm.C. Hot.D. Cool.2. What does the woman suggest doing next weekend?A. Going to the beach.B. Visiting a museum.C. Having a picnic.D. Staying at home.3. What is the man's major in college?A. Economics.B. History.C. English.D. Physics.4. Why does the woman cancel the meeting?A. She is sick.B. She has a family emergency.C. She is traveling.D. She is busy with work.5. What is the man's plan for the weekend?A. Visiting his friends.B. Attending a concert.C. Going shopping.D. Watching a movie.Section B6. What is the main topic of the passage?A. The importance of exercise.B. The benefits of healthy eating.C. The causes of obesity.D. The impact of technology on health.7. According to the passage, what is one of the reasons for the rise in obesity rates?A. Increased fast food consumption.B. Decreased physical activity.C. Improved medical care.D. Increased education.8. How does the passage describe the relationship between exercise and mental health?A. Exercise improves mental health.B. Mental health has no impact on exercise.C. Exercise has no effect on mental health.D. Mental health improves with exercise.9. What is the author's main argument in the passage?A. Exercise is the only solution to obesity.B. Healthy eating is more important than exercise.C. Both exercise and healthy eating are important.D. There is no evidence to support the benefits of exercise.Section C10. What is the main purpose of the conversation?A. To discuss the man's job interview.B. To plan a vacation.C. To review the man's application.D. To offer advice on job interviews.11. According to the conversation, what is one of the man's strengths?A. His ability to work under pressure.B. His experience in sales.C. His good communication skills.D. His technical knowledge.12. What does the woman suggest the man do to prepare for the interview?A. Research the company.B. Practice his answers.C. Dress formally.D. Bring a portfolio.二、阅读理解（共20小题，每小题2分，满分40分）Passage 1In recent years, the Internet has become an integral part of our daily lives. While it offers numerous benefits, it also brings about certainchallenges. One of the most pressing issues is the negative impact of social media on young people.Social media platforms, such as Facebook, Twitter, and Instagram, have become popular among teenagers. However, excessive use of these platforms can lead to several problems. Firstly, it can cause mental health issues, such as anxiety and depression. Secondly, it can lead to poor academic performance, as students spend more time on social media than studying. Lastly, it can expose young people to cyberbullying and other harmful content.To address these issues, schools and parents should take appropriate measures. Schools can organize workshops and campaigns to raise awareness about the negative effects of social media. Parents should monitor their children's online activities and encourage them to spend more time on productive activities.13. What is the main topic of the passage?A. The benefits of social media.B. The challenges of social media.C. The importance of online privacy.D. The role of parents in managing social media.14. What is one of the negative effects of social media mentioned in the passage?A. Improved communication skills.B. Increased self-esteem.C. Better academic performance.D. Mental health issues.15. What is the author's recommendation to address the challenges of social media?A. Ban social media in schools.B. Limit the time children spend on social media.C. Ban all forms of technology.D. Ignore the negative effects and continue using social media.Passage 2Climate change is one of the most pressing issues facing our planet today. The increase in greenhouse gas emissions has led to rising global temperatures, extreme weather events, and other environmental consequences. To combat climate change, it is crucial for individuals, communities, and governments to take action.One way to address climate change is by reducing our carbon footprint. This can be achieved by adopting sustainable practices, such as using public transportation, recycling, and reducing energy consumption. Additionally, investing in renewable energy sources, such as solar and wind power, can help reduce our reliance on fossil fuels.Governments also play a vital role in combating climate change. They can implement policies that promote clean energy and energy efficiency, as well as regulate emissions from industries. Furthermore, international cooperation is essential in addressing the global nature of the issue.16. What is the main topic of the passage?A. The causes of climate change.B. The effects of climate change.C. Solutions to climate change.D. The role of individuals in addressing climate change.17. What is one of the actions individuals can take to reduce their carbon footprint?A. Flying frequently.B. Driving a car.C. Using public transportation.D. Buying new electronic devices.18. What is the role of governments in combating climate change?A. Promoting the use of renewable energy.B. Regulating emissions from industries.C. Encouraging international cooperation.D. All of the above.三、完形填空（共20小题，每小题1.5分，满分30分）19. It was a beautiful day, and the sun was shining brightly. Suddenly, the clouds gathered, and a ___________ storm began.A. violentB. mildC. gentleD. strong20. The teacher asked the students to ___________ their homework before the next class.A. submitB. turn inC. hand inD. give21. The company has ___________ a new product line to increase its market share.A. introducedB. developedC. createdD. designed22. She ___________ her phone and checked the message from her friend.A. turned offB. turned onC. turned upD. turned down23. The doctor ___________ the patient's blood pressure and found it was normal.A. measuredB. checkedC. examinedD. observed24. The students were ___________ in the library, reading their textbooks.A. gatheredB. collectedC. assembledD. accumulated25. The ___________ of the movie was so intense that it made me feel uncomfortable.A. sceneB. partC. chapterD. book四、写作（共1题，满分25分）Write an essay of about 150 words on the following topic:Describe a person who has had a significant impact on your life. Explain why this person is important to you and how they have influenced you.（略）。

鞍山市第一中学2024年全国新课标II 卷高考数学试题最后一模注意事项1．考试结束后，请将本试卷和答题卡一并交回．2．答题前，请务必将自己的姓名、准考证号用0．5毫米黑色墨水的签字笔填写在试卷及答题卡的规定位置． 3．请认真核对监考员在答题卡上所粘贴的条形码上的姓名、准考证号与本人是否相符．4．作答选择题，必须用2B 铅笔将答题卡上对应选项的方框涂满、涂黑；如需改动，请用橡皮擦干净后，再选涂其他答案．作答非选择题，必须用05毫米黑色墨水的签字笔在答题卡上的指定位置作答，在其他位置作答一律无效． 5．如需作图，须用2B 铅笔绘、写清楚，线条、符号等须加黑、加粗．一、选择题：本题共12小题，每小题5分，共60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．设集合{}2560A x x x =--<，{}20B x x =-<，则A B =( )A ．{}32x x -<< B ．{}22x x -<< C ．{}62x x -<<D ．{}12x x -<<2．执行如图所示的程序框图，则输出S 的值为（ ）A ．16B ．48C ．96D ．1283．已知等比数列{}n a 的前n 项和为n S ，若11a =，且公比为2，则n S 与n a 的关系正确的是（ ） A ．41n n S a =- B ．21n n S a =+ C ．21n n S a =-D ．43n n S a =-4．已知向量(1,4)a =，(2,)b m =-，若||||a b a b +=-，则m =（ ） A ．12-B ．12C ．-8D ．85．定义在R 上的函数()()f x x g x =+，()22(2)g x x g x =--+--，若()f x 在区间[)1,-+∞上为增函数，且存在20t -<<，使得(0)()0f f t ⋅<.则下列不等式不一定成立的是（ ）A ．()2112f t t f ⎛⎫++> ⎪⎝⎭B ．(2)0()f f t ->>C ．(2)(1)f t f t +>+D ．(1)()f t f t +>6．已知椭圆()222210x y a b a b+=>>的左、右焦点分别为1F 、2F ，过点1F 的直线与椭圆交于P 、Q 两点.若2PF Q ∆的内切圆与线段2PF 在其中点处相切，与PQ 相切于点1F ，则椭圆的离心率为（ ） A ．22B ．32C ．23D ．337．记递增数列{}n a 的前n 项和为n S .若11a =，99a =，且对{}n a 中的任意两项i a 与j a （19i j ≤<≤），其和i j a a +，或其积i j a a ，或其商j ia a 仍是该数列中的项，则（ ）A ．593,36a S ><B ．593,36a S >>C ．693,36a S >>D ．693,36a S ><8．已知函数()222ln 02x x e f x e x x e⎧<≤=⎨+->⎩，，，存在实数123x x x <<，使得()()()123f x f x f x ==，则()12f x x 的最大值为（ ）A ．1eB ．1eC ．12eD ．21e 9．若双曲线22214x y b -=的离心率72e =，则该双曲线的焦点到其渐近线的距离为（ ） A ．23B ．2C ．3D ．110．如图示，三棱锥P ABC -的底面ABC 是等腰直角三角形，90ACB ∠=︒，且2PA PB AB ===，3PC =，则PC 与面PAB 所成角的正弦值等于（ ）A ．13B ．63C ．33D ．2311．已知函数2()2f x x x =-，集合{|()0}A x f x =≤，{}|()0B x f x '=≤，则AB =（ ）A ．[-1,0]B ．[-1,2]C ．[0,1]D ．(,1][2,)-∞⋃+∞ 12．已知i 是虚数单位，则（ ） A ．B ．C ．D ．二、填空题：本题共4小题，每小题5分，共20分。

一、听力（共25小题，每小题2分，满分50分）Part A1. How did the man feel about the weather yesterday?A. It was sunny.B. It was rainy.C. It was windy.D. It was cloudy.2. What does the woman want to do this weekend?A. Go shopping.B. Go to the movies.C. Go to the park.D. Go to the gym.3. What is the main topic of the conversation?A. Sports.B. Music.C. Education.D. Travel.Part B4. What does the man suggest doing?A. Going to the movies.B. Going to the park.C. Going to the gym.D. Going to the shopping mall.5. What is the woman's response to the man's suggestion?A. She agrees.B. She disagrees.C. She is not sure.D. She has no idea.Part C6. What is the man's opinion about the new technology?A. He thinks it is useful.B. He thinks it is not useful.C. He thinks it is expensive.D. He thinks it is not expensive.7. What is the woman's opinion about the new technology?A. She thinks it is useful.B. She thinks it is not useful.C. She thinks it is expensive.D. She thinks it is not expensive.二、阅读理解（共20小题，每小题2分，满分40分）Passage 1When it comes to choosing a major, many students are confused and worried. Some students are worried about their future career, while others are concerned about their interests. However, choosing a major is an important decision that can affect their future. In this article, we will discuss some tips for choosing a major.Firstly, students should consider their interests. If they are passionate about a certain subject, it is more likely that they willexcel in it. Secondly, they should think about their strengths and weaknesses. If they are good at math, they may consider a major related to engineering or finance. Thirdly, they should consider the job market. Some majors have a higher demand than others, and it is important to choose a major that has good job prospects. Finally, they should seek advice from teachers, parents, and mentors. These people can provide valuable insights and help them make a better decision.Passage 2Traveling is an exciting experience that allows people to explore new places and cultures. However, it can also be expensive. Here are sometips for saving money while traveling.Firstly, students should plan their budget carefully. They should research the cost of transportation, accommodation, food, and activities. Secondly, they should choose affordable destinations. Some countriesoffer lower prices for accommodations and food. Thirdly, they should travel in groups. Group travel can help reduce costs. Fourthly, they should use public transportation instead of taxis. Lastly, they should avoid peak travel seasons. Traveling during off-peak seasons can save money.Passage 3Exercise is important for maintaining physical and mental health. However, some people find it difficult to stay motivated. Here are some tips for staying motivated to exercise.Firstly, set realistic goals. If you aim for too much, you may become discouraged. Secondly, find a workout buddy. Exercising with a friendcan make it more enjoyable. Thirdly, vary your workouts. Doing different types of exercises can keep you engaged. Fourthly, track your progress. Seeing improvements can boost your motivation. Lastly, remember that exercise is a long-term commitment. Don't expect immediate results.三、完形填空（共20小题，每小题2分，满分40分）When I was a child, my parents always told me that reading was important. They said it would help me learn new things and improve my writing skills. As I grew older, I realized that they were right. Reading has become an integral part of my life.I remember the first book I ever read. It was a children's book about a girl who lived in a magical world. I was fascinated by the story and the characters. From that day on, I was hooked on reading. I read everything I could get my hands on, from novels to newspapers.Reading has not only helped me improve my writing skills, but it hasalso expanded my knowledge. I have learned about different cultures, history, and science. It has opened my eyes to new ideas and perspectives. Moreover, reading has taught me how to think criticallyand analyze information.In addition to reading books, I also enjoy reading online articles and watching documentaries. These sources provide me with up-to-date information and different perspectives. They help me stay informed about current events and global issues.Reading has also helped me relax and unwind. It is a great way to escape from the stress of daily life. I often read before bedtime to help mefall asleep.In conclusion, reading has had a significant impact on my life. It has helped me become a better writer, expanded my knowledge, and provided me with a way to relax. I am grateful for the lessons I have learned from reading and will continue to enjoy it for years to come.四、作文（满分25分）Write an essay of about 150 words on the following topic: The Importance of Education. You should use your own ideas and experiences and support your argument with examples.The Importance of EducationEducation is a fundamental right and plays a crucial role in the development of individuals and societies. It is essential for personalgrowth, economic prosperity, and social progress. In this essay, I will discuss the importance of education.Firstly, education provides individuals with knowledge and skills that are necessary for their personal development. It enables them to acquire a wide range of information, including history, science, literature, and arts. This knowledge helps individuals to become well-roundedindividuals and to make informed decisions in their lives.Secondly, education is essential for economic prosperity. It equips individuals with the skills and qualifications required to secure good jobs and contribute to the growth of the economy. Educated individuals are more likely to be employed, earn higher incomes, and have better job prospects.Thirdly, education promotes social progress. It fosters critical thinking, creativity, and innovation, which are essential for solving complex problems and improving the quality of life. Educated individuals are more likely to participate in democratic processes and contribute to the development of their communities.In conclusion, education is of utmost importance. It is the key to personal development, economic prosperity, and social progress. We should value education and strive to provide equal opportunities for all individuals to access quality education.。

2024年普通高等学校招生全国统一考试数学真题试卷（新课标Ⅱ卷）1.已知，则( ).1i z =--||z =A.0B.1 D.22.已知命题：，，命题，，则( ).:R p x ∀∈|1|1x +>:0q x ∃>3x x =A.p 和q 都是真命题 B.和q 都是真命题p ⌝C.p 和都是真命题D.和都是真命题q ⌝p ⌝q ⌝3.已知向量，满足，，且，则( ).a b ||1a = |2|2a b += (2)b a b -⊥ ||b =A. D.1124.某农业研究部门在面积相等的100块稻田上种植新型水稻，得到各块稻田的亩产量（单位：）并部分整理如下表所示.kg 亩产[900,950)[950,1000)[1000,1050)[1050,1150)[1150,1200)频数612182410根据表中数据，下列结论正确的是( )A.100块稻田亩产量的中位数小于1050kgB.100块稻田中的亩产量低于的稻田所占比例超过1100kg 40%C.100块稻田亩产量的极差介于到之间200kg 300kg D.100块稻田亩产量的平均值介于到之间900kg 1000kg 5.已知曲线，从C 上任意一点P 向x 轴作垂线，为垂足，则线段22:16(0)C x y y +=>PP 'P '的中点M 的轨迹方程为( ).PP 'A. B.221(0)164x y y +=>221(0)168x y y +=>C. D.221(0)164y x y +=>221(0)168y x y +=>6.设函数，，当时，曲线和2()(1)1f x a x =+-()cos 2g x x ax =+(1,1)x ∈-()y f x =恰有一个交点，则( )()y g x =a =A.-1 B. C.1 D.2127.已知正三棱台的体积为，，，则与平面ABC 所成角的正111ABC A B C -5236AB =112A B =1A A 切值为( ).A. B.1 C.2D.3128.设函数，若，则的最小值为( ).()()ln()f x x a x b =++()0f x ≥22a b +A. B. C. D.11814129.对于函数和，下列正确的有( ).()sin 2f x x =π()sin 24g x x ⎛⎫=-⎪⎝⎭A.与有相同零点B.与有相同最大值()f x ()g x ()f x ()g xC.与有相同的最小正周期D.与的图像有相同的对称轴()f x ()g x ()f x ()g x 10.拋物线的准线为l ，P 为C 上的动点，对P 作的一条切线，Q2:4C y x =22:(4)1A x y +-= 有切点，对P 作C 的垂线，垂足为B .则( ).A.l 与相切B.当P ，A ，B 三点共线时，A ||PQ =C.当时，D.满足的点A 有且仅有2个||2PB =PA AB⊥||||PA PB =11.设函数，则( ).32()231f x x ax =-+A.当时，有一个零点1a >()f x B.当时是的极大值点0a <0x =()f x C.存在a ，b 使得为曲线的对称轴x b =()y f x =D.存在a 使得点为曲线的对称中心(1,(1))f ()y f x =12.记为等差数列的前n 项和，若，，则__________.n S {}n a 347a a +=2535a a +=10S =13.已知为第一象限角，为第三象限角，，，则αβtan tan 4αβ+=tan tan 1αβ=+__________.sin()αβ+=14.在如图的方格表中选4个方格，要求每行和每列均恰有一个方格被选中，则共有44⨯__________种选法，在所有符合上述要求的选法中，选中方格的4个数之和的最大值是__________.15.记的内角A ，B ，C 的对边分别为a ，b ，c ，已知.ABC △sin 2A A +=（1）求A ；（2）若，求周长.2a =sin 2C c B =ABC △16.已知函数.3()e x f x ax a =--（1）当时，求曲线在点处的切线方程；1a =()y f x =(1,(1))f （2）若有极小值，且极小值小于0，求a 的取值范围.()f x 17.如图，平面四边形ABCD 中，，，，，，点E ，F 满足，8AB =3CD =AD =90APC ∠=︒30BAD ∠=︒25AE AD =，将沿EF 对折至，使得，12AF AB = AEF △PEF △PC =（1）证明：：EF PD ⊥（2）求面PCD 与PBF 所成的二面角的正弦值.18.某投篮比赛分为两个阶段，每个参赛队由两名队员组成，比赛具体规则如下：第一阶段由参赛队中一名队员投篮3次，若3次都未投中，则该队被淘汰，比赛成员为0分，若至少被投中一次，则该队进入第二阶段，由该队的另一名队员投篮3次，每次投中得5分，未投中得0分，该队的比赛成绩为第二阶段的得分总和.某参赛队由甲、乙两名队员组成，设甲每次投中的概率为p ，乙每次投中的概率为q ，各次投中与否相互独立.（1）若，，甲参加第一阶段比赛，求甲、乙所在队的比赛成绩不少于5的概率；0.4p =0.5q =（2）假设，0p q <<（i ）为使得甲、乙所在队的比赛成绩为15分的概率最大，则该由谁参加第一阶段的比赛？（ii ）为使得甲、乙，所在队的比赛成绩的数与期望最大，应该由谁参加第一阶段比赛？19.已知双曲线，点在C 上，k 为常数，，按照如下公式依22:(0)C x y m m -=>1(5,4)P 01k <<次构造点，过点作斜率为k 的直线与C 的左支点交于点，令为关于(2,3,)n P n = 1n P -1n Q -n P 1n Q -y 轴的对称点，记的坐标为.n P (),n n x y （1）若，求，；12k =2x 2y （2）证明：数列是公比为的等比数列；{}n n x y -11k k +-（3）设为的面积，证明：对任意的正整数n ，.n S 12n n n P P P ++△1n n S S +=2024年普通高等学校招生全国统一考试数学答案答案：C解析.||z =1.答案：B解析：时，，错误，和q 是真命题.1x =-|1|1x +<p ∴P ∴⌝2.答案：A解析：，(2)0b a b -⋅= 220b a b ∴-⋅= 又，，||1a = |2|4a b += 得.1||2b = 3.答案：C解析：中位数错误，标差介于之间，选C.200kg ~300kg ∴4.答案：A解析：设，将坐标代入原方程联立，得M 方程.(,)P x y 221(0)164x y y +=>5.答案：D解析：联立，，代入方程，恰好得到一个极点，()()f x g x =2(1)1cos 2a x x ax ∴+-=+2a =.2a ∴=6.答案：B解析：，.πtan 4α=tan 1α∴=7.答案：C 解析：，，，()()ln()f x x a x b =++()()()f x x a h x =+⋅(1)0g b -=，，10b a -+= 1a b ∴=-.222221(1)2212a b b b b b +=-+=-+=8.答案：BC 解析：A.令，，零点不同；()0f x =()0g x =B.，最大值相同；()f x ()g x C.，，C 正确；π()sin 22f x x Tf ===π()2g x =∴D.，对称轴显然不同，D 错误.()f x ()g x ∴9.答案：ABD解析：依次代入抛物线方程，联立求解，所以C 错，ABD 对.10.答案：D解析：依次带入质检即可后为直角三角形，，，，12AF F△12212c F F =≥=6C =22||8a AF AF =-=4a =.32c e a ==11.答案：95解析：命题意图是考察正确应用等差数列的通项公式和求和公式以及会解相关方程得，3412512573475a a a d a a a d +=+=⎧⎨+=+=⎩143a d =-⎧⎨=⎩10110931040135952S a ⨯⨯∴=+=-+=12.解析：考察三角恒等式变形tan tan tan()1tan tan αβαβαβ⋅+===--⋅222sin ()cos ()19cos ()1a αββαβ+++=⇒+=1cos()3αβ∴+=-1sin()3αβ⎛⎫+=--= ⎪⎝⎭13.答案：24；58解析：（1）41432124=⨯⨯⨯=（2）分别列出，13，14，15，16最大，.1314151658+++=14.答案：（1）π6A =（2）2ABC C =+△解析：（1）sin 2A A=2R ===2sin()2A φ+=π2A φ+=.tan φ=π6A =（2）24πsin 6aR ==sin 2sin cos C c B B=⋅，2cos B =π4B ∴=54sin π12c=⋅22ABC C a b c ∴=++=++=+△15.答案：（1）(e 3)2y x =-+（2）2e 8a >解析：（1）(1)e 1f =-当，时1a =1x =(1)e 3f '=-(e 1)(e 3)(1)y x --=--(e 3)3e e 1y x ∴=-+-+-；(e 3)2x =-+（2），2()e 3x f x ax '=-()0f x '=2e 30x ax -=2e 3x ax =，，()e 6x f x ax ''=-2e 3x ax = ()3(2)f x ax x ''=-时，2x =2e 12a =232(2)e 2e 8f a a=-⋅=-代入，得2222e 2e (2)e 8e e 1233k f =-⋅=-=(2)0f < 2e 80a ∴-<28e a >2e 8a >.2e ,8a ⎡⎫∴∈+∞⎪⎢⎣⎭16.答案：（1）EF PD⊥（2）正弦值为0解析：（1）证明：设A 的坐标为，则B 为，(0,0)(8,0)依次求出，，，E (4,0)F (1,EF = 152D ⎛ ⎝P 关于EF 的中点M 对称，34722M ⎛⎛+== ⎝⎝设，，(,)P xy 7(2x t =+⋅1y t =⋅15922C ⎛⎛=-= ⎝⎝PC ∴=将x ，y表达式代PC ==152PD x y ⎛⎫∴=-- ⎪ ⎪⎝⎭0EF PD ⋅= EF PD∴⊥建立坐标系求出各点坐标，再利用向量相乘之积为0证明垂直（2）(8,0)PC = 求出面PCD 与面PBF 的法向量，1a 2a 又1212sin 0||a a a a θ⋅==⋅ 正弦值为0.∴17.答案：（1）0.686（2）（i ）乙（ii ）甲18.答案：（1），23x =20y =（2）证明见解析（3）证明见解析解析：（1）设(),n n n P x y 2221n n x x a m∴-=()n n y y k x x -=-.()12n n y y x x -=--22211221n n x x y x a m⎛⎫-++ ⎪⎝⎭-=1122n y x xn yn -=-++2n nx x y =-代入得，.222()1x yn y a m+-=23x =20y =（2）()2221n n kx y kx x a m +--=22222222221n n n n n n k x kxx kx y k x y k x x a m++-+∴-=111n n x k x k++=-利用等性证明。

外研版三年级英语下册期末试卷一、根据所给汉语选出正确的英语（20分）（）1．玩具 A. toy B. doll C. song（）2．毛线衫 A. dress B. coat C. sweater （）3．大的 A. big B. small C. tall（）4．足球 A. basketball B. football C. skipping （）5．树 A. tree B. pass C. thin（）6．面条 A. noodles B. milk C. tall（）7．时间 A. watch B. sing C. time（）8. 上床睡觉A .get up B. have dinner C. go to bed （）9. 夏天 A. cold B. summer C hot（）10.在…下面A. under B. box C. park二、找出不同类的单词，将序号写在前面的括号里。

（10分）（）1、A、bus B、car C、walk（）2、A、coat B、sport C、dress（）3、A、today B、summer C、spring（）4、A、fish B、rice C、ship（）5、A、milk B、cool C、windy三、单项选择。

将正确答案的序号写在前面的括里。

（20分）（）1、My name is Tom. What’s your name?A、Fangfang B、Yes, it is. C、Fine, thank you.（）2、Nice to meet you.A、Thank you,Lucy.B、Nice ti meet you,too. C. Hello,Bill.（）3、What do you do at the weekend?A、I like basketball.B、Yes, It is.C、I go swimming.（）4、What’s the time,please?A、I have breakfast.B、It’s half past five.C、It’s dog. ( ) 5、It's ABC song.A. the C. that( ) 6、Noodles and rice very nice.( ) 7、I have breakfast seven o'clock.( )8、、 you got a new bike?( )9、We have Christmas England.C. that( )10、It's in spring.四、选择填空（15分 3×5）1. I usually have English classes Sundays. （on/in）2. Welcome our school. （to/at）3. How many do you have on Monday? （class/classes）4. Look my new Chinese book. （at/over）5. There are seven in a week. （days/day）五、答语选择。