江苏省南通市如东县2023-2024学年高三上学期期初学情检测英语试卷(含答案 无听力音频 含听力
江苏省南京市2023-2024学年九年级下学期3月份月考英语试卷(含答案)
2023—2024学年度第一学期期末学情练习卷九年级英语考试时间：120分钟满分：120分（将答案按序号填在答卷纸上）选择题(共60分)一、听力（共20小题；每小题1分, 满分20分）第一部分听对话，回答问题。
本部分共有10道小题，每小题你将听到一段对话, 每段对话听两遍。
在听每段对话前，你将有5秒钟的时间阅读题目；听完后，你仍有5秒钟的时间选出你认为最合适的备选答案，并在答题卡上将答案涂黑。
1.What does Peter like doingA. B. C.2. What time will the opera beginA. B. C.3. What instrument can the boy playA. B. C.4. What is the weather like in Suzhou nowA. B. C.5. What will the man do this afternoonA. B. C.6.Who is the woman in a white dressA. A singer.B. A film star.C. A film director.7.How many times has the woman seen the filmA. Twice.B. Four times.C. Eight times.8.What does the man use to communicate with his friendsA. Phones.B. Emails.C. Letters.9.Why does the man prefer magazines to booksA. They are cheaper.B. They are more interesting.They can be finished more quickly.10. Where did Sally do in the afternoonA. She went for a bike ride.B. She stayed in the library.C. She had her bike repaired.第二部分听对话或独白，回答问题。
福建漳州市2023-2024学年七年级上学期1月期末考试英语试题(A卷)(含答案,无听力原文及音频)
2023—2024 学年上学期教学质量检测(A 卷)七年级英语试卷(总分:150分;考试时间:120分钟)友情提示：请把答案填涂到答题纸上！请不要错位、越界答题！！Ⅰ. 听力 (共三节,每小题1.5分,满分30分)第一节听句子听下面五个句子，从每小题所给的三幅图中选出与句子内容相符的选项。
(每个句子读两遍)第二节听对话听下面七段对话，从每小题所给的 A 、B、C三个选项中选出正确答案。
(每段对话读两遍)听第1段对话，完成第6 小题。
6. Who is the girl in red?A. Jane.B. Linda.C. Mary.听第2段对话，完成第7 小题。
7. What class is Sally in?A. In Class Three.B. In Class Four.C. In Class Five.听第3 段对话，完成第8 小题。
8. Where is Bob now?A. In America.B. In England.C. In China.听第4段对话，完成第9 小题。
9. What does Lisa look like?A. She has a long face.B. She has a small mouth.C. She has big eyes.听第5段对话，完成第10 、11 小题。
10. What does the man want to eat?A. Some rice.B. Some bread.C. Some chicken.11. How much does the man need to pay(付款)?A. ¥3.B. ¥6.C. ¥8.听第6段对话，完成第12 、13 小题。
12. What will Peter do?A. Do some shopping.B. Do some reading.C. Do some homework.13. Who are the two speakers?A. Mother and son.B. Father and daughter.C. Teacher and student.听第7段对话，完成第14 、15 小题。
2023-2024学年度上学期福建省泉州市高中教学质量跟踪监测试卷高一英语试题参考答案
2023—2024学年上学期泉州市高中教学质量跟踪监测试卷高一英语试题参考答案及评分标准第一部分听力（共两节，满分30分）1—5 CACBA 6—10 BCAAB 11—15 BABBC 16—20 CAABC第二部分阅读（共两节，满分50分）第一节（共15小题；每小题2.5分，满分37.5分）21—25 BDBDC 26—30 DCCAA 31—35 BBADC第二节（共5小题；每小题2.5分，满分12.5分）36—40 FGCAD第三部分语言运用（共三节，满分45分）第一节完形填空（共20小题；每小题1分，满分20分）41—45 DDCBA 46—50 BADAB 51—55 CABDC 56—60 ADBCC第二节选词填空（共5小题；每小题2分，满分10分）61—65 FBGAC第三节（共10小题；每小题1.5分，满分15分）66. which/that 67. is believed 68. the 69. highly 70. were71. honouring/honoring 72. to celebrate 73. variety 74. to 75. activities第四部分读后续写（满分25分）一、评分原则1. 本题总分为25分，分五个档次进行评分。
2. 评分时，应主要从内容、词汇语法和篇章结构三个方面考虑。
具体为：（1）续写内容的质量、完整性以及与原文情境的融洽度。
（2）所使用词汇和语法结构的准确性，恰当性和多样性。
（3）上下文的衔接和全文的连贯性3. 评分时，应先根据作答的整体情况确定其所属档次，然后以该档次的要求来综合衡量确定或调整档次，最后给分。
4. 评分时还应注意（1）词数少于80的，酌情扣分。
（2）书写较差，以至影响交际的酌情扣分。
（3）单词拼写和标点符号是写作规范的重要方面，评分时应视其对交际的影响程度予以考虑，英、美拼写及词汇用法均可接受。
二、各档次的给分范围和要求作答示例:It was not until bedtime that we realized we should turn off the TV. Maddy was shocked to find we had wasted time and stuck on the screen for the valuable Saturday. “I am sorry to invite you to watch the show.” she said. I replied with smiles, saying, “Never mind. I too was attracted to the delicious mysteries but I would never watch another episode.” We laughed at that and decided to make the most of the resting Sunday. With care and shared wishes, we expected the next day to be spent in our singing together and cooking cookies.Luckily, we made a wonderful Sunday completing what we chose last night. Picking out the songs we shared interest in, we let our voices spread around the house. Preparing the materials and working with joint efforts, we managed to bring good-looking and delicious-smelling cookies. The day saw our laughter and friendship. When it was time to leave, Maddy gave me a warm hug, “Thank you. Do come next time.” I said “Of course” and invited her to visit my family, too. So next time you want to treasure a friendship formed since childhood, turn off your TV and create quality time together.泉州市2023—2024学年度上学期高中教学质量跟踪监测英语听力部分录音稿Text 1M: I’m crazy about cooking programs and talk shows. If they are on, I could be in front of the TV for hours. What about you?W: I mostly watch programs about sports.Text 2W: How much did we pay for the repairs of the house?M: I had expected it to cost us around 500 dollars, but I actually spent twice as much on it.2. How much did they pay for the repairs of their house?Text 3W: Ian, you went to France last week, didn’t you?M: Yes, but that was a business trip. My holiday was three weeks in China and it was great.W: How interesting! Can you bring in some photos tomorrow?M: Fine, and you must show me your holiday photos of Spain.Text 4M: The Internet is fantastic!W: Yeah. You can easily find whatever information you need. Just type a keyword into a search engine, and you get a huge list of websites.M: Yes, it’s so convenient.Text 5W: Welcome to Hua wei. We’d like you to tell us a bout your work experience.M: I worked at Microsoft for two years.W: Can you tell us why you left?M: I left because I went back to study and get my master’s degree.Text 6M: What do you have planned for this weekend?W: I have to work in my community’s book fair.M: Again? Didn’t you volunteer at it at our school last year?W: Yeah, and the year before that. I love book fairs.M: Me too, actually.W: You should stop by if you’re free this weekend.M: Thanks for inviting me. But I am scheduled to go to library for review with my sister.Text 7W: John, what are you doing after work today?M: I am going to go jogging by the riverside.W: That’s not like the John I know who goes home and plays video games.M: I need to change my lifestyle.W: Why did you make the change?M: I had my annual health checkup three weeks ago and I got the results last week. I have too much body fat, and have high blood pressure. The doctor strongly recommends that I exercise at least three times a week for 30 minutes.W: That makes sense.Text 8M: Hello, Vivian.W: Hi, Chris. You look a bit down. What’s up?M: I’ve been struggling with physics lately, especially with exams coming up. I’ve been impressed with your ability to learn physics so well. I admire you so much.W: W ell, it wasn’t easy for me either. I had a hard time following the teacher at first.M: Oh? You too?W: Yes. But luckily, I managed to get through it. At that time, I spent 15 to 20 minutes every day reviewing physics. Whenever I was working on a problem, I would write down all the steps to catch my mistakes.M: Those tips sound great. Thanks for sharing.W: Also, I strongly recommend online study groups. Sometimes their explanations can be very helpful. M: Wow, that’s fantastic! I’ll give it a try. Th anks, Vivian.Text 9M: Hi, Cathy.W: Hi, Jonny. How are you doing? Busy?M: No, not at all. I’ve been killing time by wondering in the shopping center. Oh, by the way, did you hear the news?W: No, what is it?M: They are going to turn the city square into an entertainment park.W: Wonderful. I am glad that big and ugly thing will be gone.M: Really? In my opinion, the square is better than any entertainment park.W: I don’t see why.M: The square is a symbol of our city and is a nice place to have a walk for everyone.W: Well, I don’t know if that huge and boring thing can be our symbol, but I know for sure the city has tens of parks where you can take a nice walk.M: I know what you mean. But don’t you think that we will no longer have peac e and quiet once the entertainment park opens?W: To me, the entertainment park means more jobs and that can benefit our people.Text 10Hi, Tina, this is Jason. I heard that during the Chinese Spring Festival holiday you won’t g o back to your hometown in the United States and will go to Spain for some traveling and then come back to China. I’m leaving you this voice message to invite you to come to our family’s Chinese New Year’s Eve dinner, say, on February 4th. My mother and I will start making dumplings around 4 p.m. and we’ll probably start having dinner at 6 p.m. If you’re interested in making dumplings, feel free to join us at 4 p.m. I’m afraid there will be very few buses or taxis running tomorrow afternoon. My father is happy to pick you up from your place. Just send me your address and tell me when you can come. After dinner, we will watch some Spring Festival shows on TV. The most interesting show starts at around 8 p.m. We usually stay up very late, so don’t worry about staying too long. Just let me know when you want to go back to your place. Looking forward to your earliest reply.。
2023-2024学年高考英语专项真题复习——定语从句(含解析)
2023-2024学年高考英语专项真题试卷复习——定语从句1.（湖南师范大学附属中学2023-2024学年高三试题）Often short and plainspoken, these poems contain profound topics, won him wide acclaim（称赞）both at home and abroad.2.（湘豫名校联考2023-2024学年高三试题）This graceful dialogue, has been flowing from brushed fingertips and travelling for thousands of years, is continuing to this day.3.（湖南省常德市临澧一中2023-2024学年高三试题）Pan, a silversmith (银匠) in Maliao village in Guizhou Province, used to dream of people living an abundant life in his village, nobody has to work far away from home and customers go for beautiful silver jewellery.4.（湖北省武汉市硚口区2023-2024学年高三质检）Tsering Yangdron, a 25-year-old Monba, one of the ethnic groups live in this region, skillfully makes her way through the garden, carefully picking tender tea leaves and tossing them into a bamboo basket tied to her waist.5.（湖北省黄冈市2023-2024学年高三调研试题）The lifestyle, however, was laid down by two historical men of letters. One was Bai Juyi, rebuilt the West Lake and made a new bank to benefit the locals.6.（江苏省2023-2024学年高三名校联考检测试题）An unconventional “teen romance”, it follows Suzume, a 16-year-old mother was killed in an earthquake some years ago.7.（江苏省2023-2024学年高三名校联考检测试题）With its “stark warnings about the real risk of ecological disaster”, Suzume is a “powerful coming-of-age tale ____ plucks at the heartstrings” while delivering some real laughs along the way.8.（江苏省前黄高级中学2023-2024学年高三学情检测）The center was launched in June on Zhenxing Road to help relieve the pressure on many of those running its 435 street stalls, many of are migrant workers from around the country without local relatives to help take care of their children.9.（江苏省2023-2024学年高三学情调研试题）Independence is another word for freedom, isa universal value cherished by all people. Freedom is like the drifting of white clouds in the open sky and the happy blooming of a flower in the woods.10.（江苏省镇江市2023-2024学年高三试题）The story of the deep friendship between poet Gao Shi and the master of romantic poetry Li Bai offers a glimpse into the star-studded history of the Tang era,_____ is often seen as a golden age in Chinese history due to its economic prosperity and culturalintegration and advancement.11.（2024届江苏省徐州市沛县高三模拟）The second introduces The Garden of Forking Paths, artist Kang’s painting, title is inspired from Jorge Borges’ novel.12.（江苏省百校联考2023-2024学年高三试题）He has been practising it since he was six years old under the guidance of his uncles, Chen Xiaowang and Chen Xiaoxing, are two iconic figures of Chen-style taijiquan in Henan Province.13.（江苏省常熟市2023-2024学年高三10月抽测试题）The French brand was criticized due to the incident. The controversy spread not only on Chinese social media platform Sina Weibo, but also among Chinese nationals around the world, a series of activities erupted among people to speak up and defend Chinese culture.14.（江苏省常州市八校2023年高三10月联合调研）Beside scientific missions, the crew also gave two live science lectures from the ce station, during ______ they conducted various experiments and answered questions from students watching the class on Earth.15.（江苏省常州市联盟校2023-2024学年高三10月调研试题）Unlike contentious hearings with other tech CEOs, lawmakers “appeared in a listening mood” with Altman, company developed the breakthrough AI chatbot ChatGPT.16.（江苏省灌南高级中学2023-2024学年高三试卷）To avoid getting taken in, be cautious about advertisements offering bargains and rewards seem too good to be true.17.（江苏省连云港高级中学2023-2024学年高三试题）The Yi people think fire possesses a superhuman power____ can drive away evil and frighten off ghosts.18.（江苏省连云港外国语学校2023-2024学年高三试题）Yet, the form of the fable still has values today,_______ Rachel Carson says in “A Fable for Tomorrow.”19.（江苏省连云港外国语学校2023-2024学年高三试题）“There was once a town in the heart of America, _______ all life seemed to enjoy peaceful existence with its surroundings,” her fable begins, borrowing some familiar words from many age-old fables.20.（江苏省南通市2023-2024学年高三统考试题）The bronze was discovered in July last year, but archaeologists successfully lifted it out of the pit a year later, they were sorting out all other bronze objects piled on the top of the statue.21.（江苏省南通市如皋市2023-2024学年度高三调研试题）Dai suggested prioritizing academic travel for young people, health-focused tourism for the elderly as well as introducing tourism products meet visitors’ budgets while suiting their preference.22.（江苏省苏州中学校2023-2024学年高三试题) It is a symbol makes the Guilin landscape what it is.23.（2024届河北省百师联盟高三联考）The 19th China International Cultural Industries Fair kicked off in Shenzhen in South China's Guangdong province on June 7, 2023, is expected to promote the development of the country's cultural industry.24.（河北省衡水市第二中学2023-2024学年高三检测试题）In addition to his studies, Walker plays for his high school’s football team and is working to develop a wrist device to help people are blind and deaf with communication.25.（2023-2024学年河北省省级联测高三试题）In particular, the Ling Si Hall, the rituals(典礼)are held, is a treasure of ancient architecture.26.（2024届河北省邯郸市高三第一次调研试题）Being an important transportation center, Handan possesses the integrated transport means of railway, highway and aviation, ___ can serve 13 cities nearby with a population of about 70 million.27.（河北省保定市重点高中2023-2024学年高三试题）The Prints-A Riot of Colors, an exhibition featuring some 130 prints created by generations of Chinese artists, the oldest one of dates back to the 1930s, opened on Monday at the Guardian Art Center in Beijing.28.（河北省2023-2024学年高三全过程纵向评价试题）At first, Minguez performed house calls, but demand increased to the point he decided to open a practice in his living room. But this, too, soon proved insufficient to care for all the people coming in and so he went on to set up a clinic.29.（河北省2023-2024学年高三试题）In fact, there is a Lanzhou Beef Noodles restaurant right downstairs, is about 100 yards from our Beijing apartment, My niece Kim came to visit us in Beijing this summer, and after visiting many fancy restaurants, she declared this bowl of noodles to be the best thing she had eaten in China ever.30.（河北省部分重点高中2023-2024学年高三综测试题）Up to now, Beijing Tianqiao Performing Arts Center,______ aim is to emphasize the inheritance, promotion, development and popularization oftraditional Chinese culture and arts, has also held many exhibitions related to traditional drama, and established the Peking Opera inheritance class to popularize the traditional art to children.31.（河北省高碑店市崇德实验中学2023年高三试题）But every spring, a small number of Sami still follow their reindeer into the valleys of Sarek, they live in tents and enjoy their traditions. 32.（河北省任丘市第一中学2023年高三试题）Taoism holds that there are basic, everlasting and supernatural principles in the earth are called “Tao”, suggesting softness, quietness, emptiness and harmony.33.（河北省新时代NT教育2023-2024学年高三试题）China’s national parks are specific land or sea areas ______main purpose is to preserve the nationally representative natural ecosystems of the country and realize the scientific protection and reasonable use of natural resources.34.（2024届福建省三明市等5地高三一模试题）Within six months, she was assigned to a higher position ________usually took four years to achieve.35.（辽宁省六校2023-2024学年高三联考试卷）Shyness is a force prevents us from realizing our potential and enjoying the company of other people.36.（辽宁省重点高中2023-2024学年高三10月试题）Volunteer travel, also known as voluntourism, refers to taking a trip purpose is to participate in an arranged service opportunity to give back to the local community and make a difference.37.（辽宁省朝阳市辽宁名校2023-2024学年高三试题）For instance, knowledge of places the surface-ocean microbial ecosystem is changing might be useful for identifying regions of the open ocean to set up marine protected areas.38.（福建省宁德第一中学2023-2024学年高三检测试题）The mortise and tenon technique, is the primary construction method used in ancient Chinese architecture and represents the core of traditional Chinese woodworking, is gaining increasing recognition among the public.39.（广东省新高考高中联合质量测评省级联考试题）Each woman’s story was vastly different,______ gave me the confidence to give my walk a try,” Maxwell told the BBC．40.（广东省湛江市第一中学2023-2024学年高三试题）The 150-metre-tall bridge crosses a deep, narrow valley, __ aim is to bring in thrill-seeking tourists.41.（广东省深圳市富源学校2023-2024学年调研试题）It lands on a certain figure isinspired by nature or wildlife in forms of a dragon, fish, monkey, bird or flower basket.42.（广东省2023-2024学年6校高三联考）The local medicine expert meeting was organized here on April 28 in most years of the Qing Dynasty, during all kinds of talented people performed, and the vocal music lasted for more than ten days, said Wang Jianping, an expert in literature and history of the county.43.（广东省六校2023-2024学年高三第一次联考试题）Like many undergraduate biology students, Wang Fang was taught that pandas are a prime example of an umbrella species—a well-known and usually endangered animal protection benefits an entire ecosystem.44.（广东省广州市2023-2024学年高三训练试卷）The story centers around the deep friendship between poet Gao Shi and the romantic poet Li Bai offering a brief look into the glorious history of the Tang era, is known for its economic prosperity and cultural advancement.45.（广东省广东省四校联考2023-2024学年高三9月试题）The study, appeared in the journal PLOS Medicine, indicates that individuals who take in higher-than-average amounts of artificial sweetener are 13% more likely to suffer from cancer.46.（广东省2023-2024学年新高三联考试题）A closer encounter with the Great Barrier Reef’s impressive coral gardens reveals many extremely amazing underwater attractions, include the world’s largest collection of corals, coral sponges, rays, dolphins, over 1,500 species of tropical fish, more than 200 types of birds, etc.47.（2023年广东省佛山市顺德区均安中学高三拉练试题）Bamboo shoots, a root vegetable with few calories but lots of fiber, are widely harvested and eaten in Zhejiang and Sichuan provinces the climate is ideal for bamboo growth.48.（广东省湛江市第一中学2023-2024学年高三试题）The 150-metre-tall bridge crosses a deep, narrow valley,_____ aim is to bring in thrill-seeking tourists.49.（广东省江门市新会一中2023-2024学年高三试题）The simple truth is that singing makes you happy. It releases endorphins(内啡肽), a chemical reduces pain.50.（2024届广东省四校高三第一次联考试题）It has become a cultural landmark of the Yellow River Basin___ visitors can view the river passing through the city and watch exhibitions showing its long history’ and diverse cultures.二单项选择1．Among the performers in the circus were some boys, ___________the youngest was only seven.A．of whom B．which C．that D．of those2．Stephen Hawking believes that the earth is unlikely to be the only planet ______ life has developed gradually.A．what B．that C．where D．which3．John, a professor at the King’s College London, is one of the small but growing minority ______ are cutting back on their air travel because of climate change.A．what B．which C．where D．who4．A Disney-themed airplane, ________ body huge Mickey Mouse figures were painted, appeared in Shanghai.A．of which B．across whose C．across which D．of whose5．A way to raise your spirits is to think of a situation ________ you did something you are proud of.A．which B．where C．what D．as6．I first met my new teacher in the park, _________ was located by the sea.A．which B．that C．where D．who7．That boy was rude to the conductor, ______ of course, made things even worse.A．who B．whom C．what D．which8．This is one of the most exciting football games ________I have ever seen.A．when B．why C．which D．that9．I still remember the day ________I first visited the Great Wall.A．which B．that C．where D．when10．Written Chinese has also become an important means China’s present is connected with its past.A．for which B．on which C．by which D．on that11．Celeste Ng’s latest book, plot is quite new and original, has received a lot of attention.A．which B．where C．whose D．that12．My mother is grateful to the surgeon, without________ first aid she would never rose to her feet again.A．whom B．his.C．which D．whose13．She is half-way through the preparation years, ________ most foreign students completes before applying for a degree course.A．in which B．which C．of which D．when14．It was in the street _______ I went shopping with you last week ________ I met Zhang Hua, our old classmate.A．where ; that B．which ; when C．that ; that D．that ; which 15．Endurance, perseverance, industry and talent are the means ________ men can achieve great ends A．in which B．by which C．of which D．on which16．The fire started on the first floor of the hospital, patients were elderly people.A．many of whose B．whose many C．many whose D．many of whom17．Longji Rice Terraces provide a perfect environment for birds and fish, some of which feed on insects ______ can harm the rice crops.A．what B．where C．that D．whom18．The film brought the hours back to me ________ I was taken good care of in that far-away village.A．when B．until C．that D．where19．—Where did you meet her for the first time?—It was in the garden _______ we did the morning reading.A．which B．that C．there D．where20．Mrs. Wu, a dorm keeper at the university, delivered a wonderful speech, _______ of great significance to students.A．I think it was B．which I think was C．what I think was D．which I think it was 21．The last place we visited was Chaoshan Custom Museum.A．where B．that C．when D．why22．We are living in an age________ information is available with greater ease than ever before.A．which B．that C．whose D．when23．Over the past decade, the central government has established thousands of natural reserves ________ ecological “red lines” are drawn up to restrict human and industrial activities.A．which B．where C．after D．what24．On Sundays there were a lot of children playing in the park, ________ parents sat together joking.A．their B．whose C．which D．that25．I am interested in ________ you have told me about “Education in Canada”.A．which B．all C．that D．everything which26．The English play ________ my students acted at the New Year’s party was a great success.A．for which B．at which C．in which D．on which27．The museum will open in the spring with an exhibition and a viewing platform visitors can watch the big glasshouses being built.A．which B．that C．where D．when28．This national park is the unique area __________ live both wild Siberian tigers and Siberian leopards.A．where B．whichC．as D．who29．________is reported in the newper, the economic of our country has increased in the last year.A．Which B．It C．As D．What30．Mr. Li has two sons, ________are college students.A．both of them B．neither of who C．both of whom D．neither of whom三语篇填空Passage 1（2023·重庆八中阶段练习）阅读下面材料，在空白处填入1个适当的单词或括号内单词的正确形式。
江苏省镇江市2023-2024学年高三下学期期初考试数学试卷(解析版)
2023~2024学年度第二学期高三期初试卷数学注意事项：1．答卷前，考生务必将自己的姓名、考生号、考场号、座位号填写在答题卡上.2．回答选择题时，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．本卷满分150分，考试时间120分钟.考试结束后，将答题卡交回.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.1.一组数据从小到大的顺序排列如下：9，10，12，15，17，18，22，26，经计算，则75%分位数是（）A.18B.20C.21D.22【答案】B 【解析】【分析】根据百分位数的定义计算即可.【详解】因为875%6⨯=，故75%分位数是第6个和第7个的平均数，则1822202+=，故选：B.2.已知复数z 满足1i 1iz +=-，则20232024zz +=（）A.0B.1C.D.2【答案】C 【解析】【分析】由复数乘除法以及复数模的运算公式即可求解.【详解】由题意()()()21i 1ii 1i 1i 1i z ++===--+，所以20232024i 1z z +=+==.故选：C.3.在ABC 中，2π23A AC ==，，且ABC 的面积为2，则BC =（）A.B.C.2D.3【答案】B 【解析】【分析】利用面积公式求出AB ，再由余弦定理可得答案.【详解】因为12πsin232 ABC S AC AB =创=，所以22AB ´=，解得1AB =，由余弦定理可得2222π2cos73BC AC AB AC AB =+-创=，所以BC =故选：B.4.已知正数,a b 满足1a b +=，则14a b+的最小值为（）A.6B.7C.8D.9【答案】D 【解析】【分析】利用乘“1”法及基本不等式计算可得.【详解】因为正数,a b 满足1a b +=，所以()14144559b a a b a b a b a b ⎛⎫+=++=++≥+ ⎪⎝⎭，当且仅当4b a a b =，即13a =、23b =时取等号.故选：D5.已知平面内的向量a 在向量b 上的投影向量为12b，且1a b == ，则2a b - 的值为（）A.B.1C.34D.2【答案】A 【解析】【分析】先根据条件，确定向量的夹角，再根据向量数量积的性质求模.【详解】因为2·1·2a b b b b = ⇒2·12a b b= ，又1a b == ，所以·12·a b a b =⇒1cos ,2a b = ⇒,60a b =︒ .所以：()2222a b a b-=-=2214·41411432a ab b -+=-⨯⨯⨯+=，所以2a b -=.故选：A6.等差数列{}n a 的首项为1，公差不为0，若236,,a a a 成等比数列，则{}n a 的前5项的和为（）A.15-B.5- C.5D.25【答案】A 【解析】【分析】设等差数列{}n a 的公差为d ，根据题意列出方程，求得2d =-，结合等差数列的求和公式，即可求解.【详解】设等差数列{}n a 的公差为d 且0d ≠，且11a =，因为236,,a a a 成等比数列，可得2326a a a =，即2(12)(1)(15)d d d +=++，即2d =-或0d =（舍去），所以55451(2)152S ⨯=⨯+⨯-=-.故选：A.7.已知()()π140,cos ,sin 255βααβαβ<<<+=-=，则tan tan αβ的值为（）A.12B.35C.53D.2【答案】A 【解析】【分析】根据同角三角函数的基本关系式、两角和与差的余弦、正弦公式并进行弦化切求得正确答案.【详解】()1cos cos cos sin sin 5αβαβαβ+=-=，()4sin sin cos cos sin 5αβαβαβ-=-=，1sin cos cos sin 4cos cos sin sin ααβαβαββ-=-，分子分母同时除以cos cos αβ得：1tan tan 41tan tan αβαβ=--①，由于π02βα<<<，所以0π02π02αββα⎧⎪->⎪⎪-<-<⎨⎪⎪<<⎪⎩，所以π02αβ<-<，所以()3cos 5αβ-=，所以()()()sin 4tan cos 3αβαβαβ--==-，即sin cos cos sin 4cos cos sin sin 3αβαβαβαβ-=+，分子分母同时除以cos cos αβ得：即tan tan 444,tan tan tan tan 1tan tan 333αβαβαβαβ-=-=++，代入①得：14441t n a t n ta an tan 33βααβ=+-，解得1tan tan 2αβ=.故选：A.8.已知过坐标原点O 且异于坐标轴的直线交椭圆22221(0)x y a b a b +=>>于,P M 两点，Q 为OP 中点，过Q 作x 轴垂线，垂足为B ，直线MB 交椭圆于另一点N ，直线,PM PN 的斜率分别为12,k k ，若1212k k =-，则椭圆离心率为（）A.12B.3C.2D.3【答案】D 【解析】【分析】由题意设出各个点的坐标，注意到22MN PN b k k a⋅=-，结合1212k k =-，两式相比结合斜率公式即可求解.【详解】如图所示：设(),P m n ，则(),,,,,0222m n m M m n Q B ⎛⎫⎛⎫-- ⎪ ⎪⎝⎭⎝⎭，而()()2222222222222222N N N N MN PNN N N N b b a x a m y n y n y n b a a k k x m x m x m x m a---+--⋅=⋅==-+---，又因为12PM PN k k =-⋅，所以223222PMMNn a m nk b m m k ===+，解得2213b a =，所以椭圆离心率为3c e a ===.故选：D.【点睛】关键点点睛：关键是发现22MN PNb k k a⋅=-，由此即可顺利得解.二、选择题：本题共3小题，每小题6分，共18分.在每小题给出的选项中，有多项符合题目要求.全部选对的得6分，部分选对的得部分分，有选错的得0分.9.已知()2f x x x m =++，下列命题正确的是（）A.命题“0x ∀>，()0f x >”的否定是“0x ∃≤，使得()0f x ≤成立”B.若命题“x ∀∈R ，()0f x >恒成立”为真命题，则14m >C.“0m <”是“方程()0f x =有实数解”的充分不必要条件D.若命题“()1,1x ∃∈-，()0f x >”为真命题，则2m >-【答案】BCD 【解析】【分析】对于A ：根据全称命题的否定是特称命题分析判断；对于B ：根据恒成立问题结合二次函数分析求解；对于C ：根据二次方程的根的判别式结合充分、必要条件分析判断；对于D ：根据存在性问题结合二次函数的性质分析求解.【详解】对于选项A ：命题“0x ∀>，()0f x >”的否定是“0x ∃>，使得()0f x ≤成立”，故A 错误；对于选项B ：若命题“x ∀∈R ，()0f x >恒成立”为真命题，注意到()2f x x x m =++的图象开口向上，则140m ∆=-<，解得14m >，故B 正确；对于选项C ：若0m <，则1410m ∆=->>，可知方程()0f x =有实数解，即充分性成立；例如0m =，方程()20f x x x =+=有实数解1,0-，不满足0m <，即必要性不成立，所以“0m <”是“方程()0f x =有实数解”的充分不必要条件，故C 正确；对于选项D ：若命题“()1,1x ∃∈-，()0f x >”为真命题，注意到()2f x x x m =++的图象开口向上，对称轴为12x =-，则110m ++>，解得2m >-，故D 正确；故选：BCD.10.正方体1111A B C D ABCD -的8个顶点中的4个不共面顶点可以确定一个四面体，所有这些四面体构成集合V ，则（）A.V 中元素的个数为58B.V 中每个四面体的体积值构成集合S ，则S 中的元素个数为2C.V 中每个四面体的外接球构成集合O ，则O 中只有1个元素D.V 中不存在四个表面都是直角三角形的四面体【答案】ABC 【解析】【分析】由8个顶点中选取4个不共面顶点，确定V 中元素的个数判断选项A ；由每个四面体的结构特征，计算体积值判断选项B ；由每个四面体的外接球特征判断选项C ；寻找四个表面都是直角三角形的四面体判断选项D.【详解】正方体1111A B C D ABCD -的8个顶点中任取4个，共有48C 70=种情况，其中四点共面的有六个表面和六个对角面共12种情况，不构成四面体，所以V 中元素的个数为58，A 选项正确；四面体的体积有以下两种情况：第一种情况如下图所示，四面体的四点在相对面且异面的对角线上，如四面体11D B AC -，若正方体棱长为a ，则四面体体积为331114323a a a a a -⨯⨯⋅⋅=，第二种情况如下图所示，四面体的四点中有三个点在一个侧面上，另一个点在相对侧面上，如四面体1B ABC -，若正方体棱长为a ，则四面体体积为3111326a a a a ⨯⋅⋅=，所以V 中每个四面体的体积值构成集合S ，则S 中的元素个数为2，B 选项正确；每个四面体的外接球都是原正方体的外接球，O 中只有1个元素，C 选项正确；如下图，四面体1B ABD -的每个面都是直角三角形，D 选项错误.故选：ABC11.已知函数()sin cos2f x x x =+，则下列说法正确的是（）A.2π是()f x 的一个周期B.()f x 的最小值是2-C.存在唯一实数()0,2a ∈，使得()f x a +是偶函数D.()f x 在[]0,π上有3个极大值点【答案】ACD 【解析】【分析】对于A ，直接验算()()2π,f x f x +是否相等即可；对于B ，通过放缩即可判断；对于C ，利用偶函数性质求解并建议即可；对于D ，设()()sin cos 2,sin cos 2p x x x q x x x =+=-，通过连续求导来说明()f x 在ππ3π3π0,,,,,π4444⎛⎫⎛⎫⎛⎫⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭上各有一个极大值点即可.【详解】对于A ，()()()()s 2π2πsin cos2in cos 2π2f x x x x x f x +=+++=+=，所以2π是()f x 的一个周期；对于B ，()sin cos2sin 12f x x x x =+≥≥->-，故B 错误；对于C ，若()()f a x f a x +=-，则ππ22f a f a ⎛⎫⎛⎫+=- ⎪ ⎪⎝⎭⎝⎭，即cos cos2cos cos2a a a a +=-+，所以cos 0a =，又()0,2a ∈，所以π2a =，经检验符合题意，故C 正确；对于D ，设()()sin cos 2,sin cos 2p x x x q x x x =+=-，则()()cos 2sin 2,cos 2sin 2p x x x q x x x ''=-=+，令()()()(),m x p x n x q x ''==，则()sin 4cos 2m x x x '=--在π3π0,,,π44⎛⎫⎛⎫ ⎪⎪⎝⎭⎝⎭上的函数值小于0，()sin 4cos 2n x x x '=-+在π3π,44⎛⎫⎪⎝⎭上的函数值小于0，故所有上面的极值点都是极大值点，同时，()ππ3π0102,202244224p p q q ⎛⎫⎛⎫⎛⎫''''=>>-==+>>--= ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭，()3π201π42p p ⎛⎫''=-+>>-= ⎪⎝⎭，所以()f x 在ππ3π3π0,,,,,π4444⎛⎫⎛⎫⎛⎫⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭上各有一个极大值点，从而有三个极大值点，故D 正确.故选：ACD.【点睛】关键点点睛：判断D 选项的关键是连续求导，由此即可顺利得解.三、填空题：本题共3小题，每小题5分，共15分.12.与圆221x y +=和圆22((9x y -+-=都相切的直线方程是______．【答案】0x y +=【解析】【分析】根据题意，判断两圆的位置关系内切，联立方程组求得公切线方程.【详解】设圆221x y +=的圆心为1C ，半径为r ，则()10,0C ，1r =，设圆((229x y +-=的院系为2C ，半径为R，则2C ，3R =，所以122C C R r ==-，所以两圆内切.联立方程((222219x y x y ⎧+=⎪⎨+-=⎪⎩，解得0x y +=，所以两圆的公切线方程为0x y ++=.故答案为：0x y +=.13.已知AB 是圆锥PO 的底面直径，C是底面圆周上的一点，2,PC AB AC ===，则二面角A PBC --的余弦值为______．【答案】5【解析】【分析】根据题意，建立空间直角坐标系利用向量法求解.【详解】如图，以点O 为坐标原点，,OB OP 分别为,y z 轴，过点O 垂直AB 为x 轴，建立空间直角坐标系，点C 为底面圆周上一点，则o 90ACB ∠=，又AC =2AB PC ==，1BC ∴=，PO =，()0,1,0A ∴-，()0,1,0B，(P，1,,022C ⎛⎫⎪ ⎪⎝⎭，(0,1,PB =，1,,22PC ⎛= ⎝ ，设平面CPB 的一个法向量为(),,m x y z = ，则0m PB m PC ⎧⋅=⎪⎨⋅=⎪⎩，即01022y x y ⎧=+=⎩，令1z =，得1x =，y =()m ∴= ，又易知平面APB 的一个法向量为()1,0,0n =，cos ,5m nm n m n ⋅∴====，如图，锐二面角A PB C --的余弦值为5.故答案为：14.如果函数()f x 在区间[],a b 上为增函数，则记为[],()a b f x ，函数()f x 在区间[],a b 上为减函数，则记为[],()a b f x ．已知[],34m x x ⎛⎫+ ⎪⎝⎭，则实数m 的最小值为______；函数()3223121f x x ax x =-++，且[][]2,31,2(),()f x f x ，则实数=a ______．【答案】①.2②.3【解析】【分析】第一空：由对勾函数性质即可得解；第二空由取极值的必要条件即可得解.【详解】对于第一空：由题意()4g x x x=+在[],3m 上单调递增，首先有03m <<，（若0m ≤，则当0x =时，()f x 无意义），由对勾函数性质得当0x >时，()4g x x x=+的单调递增区间为()2,+∞，所以23m ≤<，即实数m 的最小值为2；对于第二空：()f x 显然可导，()26612f x x ax '=-+，由题意()f x 在[]1,2上单调递减，在[]2,3上单调递增，即2x =是函数()f x 的极值点，所以()()642202f a '=-+=，解得3a =，经检验3a =满足题意.故答案为：2，3.四、解答题：本题共5小题，共77分．解答应写出文字说明、证明过程或演算步骤．15.在如图所示的圆台中，AB 是下底面圆O 的直径，11A B 是上底面圆1O 的直径，11AB A B ∥，1124AB A B ==，1OO =，ACD 为圆O 的内接正三角形.（1）证明：1OO ∥平面1B CD ；（2）求直线CD 与平面1AB D 所成角的正弦值.【答案】15.证明见解析16.7【解析】【分析】(1)记AB 与CD 交于点F ，连接1,B F OC ，要证明1OO ∥平面1B CD ，只需证明11//OO FB ;(2)建立空间直角坐标系，找到平面1AB D 的法向量为(m =，利用线面角的向量算法求解即可.【小问1详解】记AB 与CD 交于点F ，连接1,B F OC ，因为AB 是下底面圆O 的直径，且ACD 为圆O 的内接正三角形，所以AB 垂直平分CD，2,4sin 60ACOC AC CF ==⇒== ，Rt OCF 中，1OF ==,因为11AB A B ∥，1124AB A B ==，所以1111//,,OF O B OF O B =故四边形11OFB O 为平行四边形，故11//OO FB ，又1OO ⊄平面1B CD ,1FB ⊂平面1B CD ,故1//OO 平面1B CD .【小问2详解】由（1）知，11//OO FB ，则1FB ⊥面ACBD ,如图建立空间直角坐标系：则()()()1030,,,A B C D ，，,(),CD=-设平面1AB D 的法向量为()111,,,m x y z =则11111300030y AB m AD m y ⎧⎧-+=⋅=⎪⎪⇒⇒⎨⎨⋅=-=⎪⎪⎩⎩令11y =，则(m =，记直线CD 与平面1AB D 所成角为θ，则sin cos ,7CD m CD m CD mθ⋅===⋅，故直线CD 与平面1AB D 所成角的正弦值为7.16.为了释放学生压力，某校进行了一个投篮游戏．甲、乙两人轮流进行篮球定点投篮比赛每人各投一次为一轮．每人投一次篮，两人中只有1人命中，命中者得1分，未命中者得1-分；两人都命中或都未命中，两人均得0分．设甲每次投篮命中的概率为13，乙每次投篮命中的概率为12，且各次投篮结果互不影响．（1）经过1轮投篮，记甲的得分为X ，求X 的分布列及数学期望；（2）用i p 表示经过第i 轮投篮后，甲的累计得分高于乙的累计得分的概率，求23,p p ．【答案】（1）X 的分布列见详解，()16E X =-（2）2736p =，343216p =【解析】【分析】（1）X 的可能取值为1,0,1-．由独立乘法、互斥加法以及对立事件概率公式分别求得对应的概率，由此即可得分布列以及数学期望；（2）如果经过两轮，甲的累计得分高于乙的累计得分，则120X X +>，由此可得此时有二种情况：一是甲两轮都得1分；二是两轮中有一轮甲得1分而另一轮甲得0分，从而可得相应的概率，如果经过三轮，甲的累计得分高于乙的累计得分，同理123X X X ++有四种情况：()111,110,111,100++++++-++，由此即可求解.【小问1详解】X 的可能取值为1,0,1-．()11111323P X ⎛⎫=-=-⨯= ⎪⎝⎭；()1111101123232P X ⎛⎫⎛⎫==⨯+-⨯-= ⎪ ⎪⎝⎭⎝⎭；()11111326P X ⎛⎫==⨯-= ⎪⎝⎭．所以X 的分布列为：X1-01P131216则X 的数学期望为()11111013266E X =-⨯+⨯+⨯=-．【小问2详解】设每轮比赛甲乙得分分别为(),1,2,3i i X Y i =，则0i i X Y +=，如果经过两轮，甲的累计得分高于乙的累计得分，则1212X X Y Y +>+，代入0i i X Y +=，即120X X +>，而i X 的可能取值为1,0,1-．所以1211X X +=+，或者1210X X +=+．此时有二种情况：一是甲两轮都得1分；二是两轮中有一轮甲得1分而另一轮甲得0分．所以12211117C 666236p =⨯+⨯⨯=．如果经过三轮，甲的累计得分高于乙的累计得分，同理有得1230X X X ++>，同理123X X X ++有四种情况：()111,110,111,100++++++-++．所以32222213333111111143C C C 6626362216p ⎛⎫⎛⎫⎛⎫⎛⎫⎛⎫=+⨯+⨯+⨯= ⎪ ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭⎝⎭⎝⎭．17.已知函数()()cos ln 11f x x x =++-．（1）判断函数()f x 在区间0,2π⎛⎫⎪⎝⎭上极值点和零点的个数，并给出证明；（2）若()f x ax ≤恒成立，求实数a ．【答案】（1）一个零点，一个极大值点，证明见详解（2）1a =【解析】【分析】（1）令()()1sin 1h x f x x x '==-++，可得()21cos (1)h x x x =--+'，当0,2x π⎛⎫∈ ⎪⎝⎭时，()0h x '<，则()f x '在0,2π⎛⎫ ⎪⎝⎭上单调递减，又()00'>f ，02f π⎛⎫< ⎪⎝⎭'，则存在唯一零点00,2x π⎛⎫∈ ⎪⎝⎭，使()00f x '=，进而得到()f x 的单调性，从而得到极值点和零点个数；（2）由()f x ax ≤，得()cos ln 110x x ax ++--≤，令()()cos ln 11g x x x ax =++--，()1,x ∈-+∞，则()00g =，只需0x =是()g x 的一个极大值点，由()1sin 1g x x a x'=-+-+，则()010g a ='-=，解得1a =，从而证明当1a =时，()()cos ln 110g x x x x =++--≤恒成立即可.【小问1详解】由题可得()1sin 1f x x x=-++'令()()1sin 1h x f x x x'==-++，则()21cos (1)h x x x =--+'因为0,2x π⎛⎫∈ ⎪⎝⎭，所以cos 0x >，2(1)0x +>,则()0h x '<．所以()f x '在0,2π⎛⎫⎪⎝⎭上单调递减．()010'=>f ，110212f ππ⎛⎫='-+< ⎪⎝⎭+且()f x 和()f x '在0,2π⎛⎫ ⎪⎝⎭上连续，由零点存在定理知存在唯一零点00,2x π⎛⎫∈ ⎪⎝⎭，使()00f x '=．所以()00,x x ∈时，()00f x '>，()f x 在()00,x 单调递增；0,2x x π⎛⎫∈ ⎪⎝⎭时，()00f x '<，()f x 在0,2x π⎛⎫⎪⎝⎭单调递减，所以()f x 在0,2π⎛⎫⎪⎝⎭上只有一个极值点，且为极大值点．因为()00,x x ∈时，()()00f x f >=，则()00,x x ∈时，()f x 无零点．又因为()()000f x f >=，且20ln 11ln ln10222e f πππ+⎛⎫⎛⎫=++-=<= ⎪ ⎪⎝⎭⎝⎭，因为()f x 在0,2x π⎛⎫ ⎪⎝⎭单调递减，则存在唯一零点10,2x x π⎛⎫∈ ⎪⎝⎭，使()10f x =．所以()f x 在0,2π⎛⎫⎪⎝⎭上只有一个零点，只有一个极大值点．【小问2详解】令()()()cos ln 11g x f x ax x x ax =-=++--，()1,x ∈-+∞由()0g x ≤恒成立，得max ()0g x ≤．因为()()00,g g x =图象在定义域上连续不间断，只需0x =是()g x 的一个极大值点．因为()1sin 1g x x a x'=-+-+，则()010g a ='-=，解得1a =．下证：当1a =时，()()cos ln 110g x x x x =++--≤恒成立．因为()1sin 1sin 11x g x x x x x =-+=-+'--+．（1）当(]1,0x ∈-时，sin 0x -≥，01xx -≥+，()0g x '≥，()g x 在(]1,0-上单调递增，所以()()00g x g ≤=．（2）当[)0,x ∈+∞时，()()()cos 1ln 1g x x x x =-++-⎡⎤⎣⎦令()()ln 1x x x ϕ=+-，[)0,x ∈+∞，()1101x x ϕ=-≤+'则()x ϕ在[)0,∞+单调递减，则()()00x ϕϕ≤=．()ln 10x x +-≤，又因为cos 10x -≤所以当[)0,x ∈+∞时，()()()cos 1ln 10g x x x x =-++-≤⎡⎤⎣⎦综上，当1a =时，()f x ax ≤恒成立．18.已知双曲线2222:1(0,0)x y C a b a b-=>>的两条渐近线分别为12,,l l C上一点(A 到12,l l 的距离之积为45．（1）求双曲线C 的方程；（2）设双曲线C 的左、右两个顶点分别为12,,A A T 为直线:1l x =上的动点，且T 不在x 轴上，直线1TA 与C 的另一个交点为M ，直线2TA 与C 的另一个交点为N ，直线MN 与x 轴的交点为P ，直线l 与MN 的交点为Q ，证明PM QM PNQN=．【答案】（1）2214x y -=（2）证明见详解【解析】【分析】（1）根据点到直线距离分别求出点A 到1l ，2l的距离可得45=，即2222163b a a b -=，再结合点(A 在双曲线上，从而可求解.（2）分别设()()()11221,,,,,T s M x y N x y ，求出相应斜率后可得1214MA MA k k ⋅=，再设直线:MN x my t =+，然后与2214x y -=联立利用韦达定理得到()()()2326328320t t t m t +-+--+=，从而求得4t =，然后结合条件从而求解.【小问1详解】因为(A 在22221x y a b-=上，则221631a b -=①．因为12,l l 的方程分别为0,0bx ay bx ay -=+=．(A 到12,l l 的距离之积为4545=②，由①②解得224,1a b ==，所以双曲线C 的方程为2214x y -=③．【小问2详解】因为()()122,0,2,0A A -，设()()()11221,,,,,T s M x y N x y ，则11221212,2321MA A T NA A T y y s sk k k k x x ======+--，所以213NA MA k k =-④，因为1221112111224MA MA y y y k k x x x ⋅=⨯=+--，且M 在双曲线上，则221114x y =-，代入上式得：1214MA MA k k ⋅=，把④代入上式得：2234NA MA k k ⋅=-⑤．设直线:MN x my t =+，代入③得：()2224240m y mty t -++-=，则：12224mt y y m -+=-⑥，212244t y y m -=-⑦，由⑤得：12123422y y x x --⋅=-，即：()()()22121234323(2)0m y y m t y y t ++-++-=，把⑥⑦代入上式得：()()()()222222234323(2)044t t mtm m t t m m +--+⨯+-⨯+-=--，因为2t ≠，所以()()()2326328320t t t m t +-+--+=，则832,4t t ==．则:4MN l x my =+，所以P 点坐标为()4,0．不妨设12,0y y >，因1PM ==，同理2PN =，令41x my =+=，则3Q y m=-，同理：1233,QM y QN y m m ⎫⎫=--=+⎪⎪⎭⎭，要证明PM QM PN QN =，只需证明：112233y y m y y m--=+，即证明：()1212320y y y y m++=，将4t =和⑥⑦代入上式显然成立，所以PM QM PNQN=．【点睛】方法点睛：利用韦达定理法解决直线与圆锥曲线相交问题的基本步骤如下：（1）设直线方程，设交点坐标为()11,x y ,()22,x y ；（2）联立直线与圆锥曲线的方程，得到关于x （或y ）的一元二次方程，注意∆的判断；（3）列出韦达定理；（4）将所求问题或题中的关系转化为12x x +、12x x （或12y y +、12y y ）的形式；（5）代入韦达定理求解.19.对于数列{}()*n a n ∈N，记1Δnn n aa a +=-，称数列{}Δn a 为数列{}n a 的一阶差分数列；记()21ΔΔΔΔΔn n n n a a a a +==-，称数列{}2Δn a 为数列{}n a 的二阶差分数列，…，一般地，对于k ∈N ，记()11ΔΔΔΔΔk k k k n n n n a a a a ++==-，规定：01Δ,ΔΔn n n n a a a a ==，称{}Δk n a 为数列{}n a 的k 阶差分数列．对于数列{}n a ，如果Δ0kn a d =≠（d 为常数），则称数列{}n a 为k 阶等差数列．（1）数列{}2n是否为k 阶等差数列，如果是，求k 值，如果不是，请说明为什么？（2）请用231111,Δ,Δ,Δ,a a a a 表示34,a a ，并归纳出表示n a 的正确结论（不要求证明）；（3）请你用（2）归纳的正确结论，证明：如果数列{}n a 为k 阶等差数列，则其前n 项和为123211111C C ΔC ΔC Δk k n n n n n S a a a a +=++++ ；（4）某同学用大小一样的球堆积了一个“正三棱锥”，巧合用了2024个球．第1层有1个球，第2层有3个，第3层有6个球，…，每层都摆放成“正三角形”，从第2层起，每层“正三角形”的“边”都比上一层的“边”多1个球，问：这位同学共堆积了多少层？【答案】（1）数列{}2n是二阶等差数列，2（2）231112ΔΔa a a a =++，4a =2311113Δ3ΔΔa a a a +++，1221111111ΔC ΔC Δk k n n n n a a C a a a ---=++++ （3）证明见详解（4）22【解析】【分析】（1）由新定义可直接证明数列{}2n 是二阶等差数列；（2）由()12112111ΔΔΔΔ0,ΔΔ0k k k k n a a a a a ++-=-==== 的关系，递推可得答案；（3）首先证明数列1230,,,,,n S S S S ⋅⋅⋅为1k +阶等差数列，再结合（2）可得123211111C C ΔC ΔC Δk k n n n n n S a a a a +=++++ ；（4）由（3）得：2222123n ++++ ()()11216n n n =++，方法一：结合等差数列的前n 项和公式可得答案；方法二：结合组合数的性质可得答案.【小问1详解】因为221Δ(1)21n n n a a a n n n +=-=+-=+，而()()()()2ΔΔΔΔ212112120n n a a n n n ==+=++-+=≠，所以2k =，数列{}2n 是二阶等差数列．【小问2详解】因为数列{}n a 为k 阶等差数列，则Δ0kn a d =≠，则()12112111ΔΔΔΔ0,ΔΔ0k k k k n a a a a a ++-=-==== ，则211Δa a a =+，()()223221111111ΔΔΔΔ2ΔΔa a a a a a a a a a =+=+++=++，()()2243311122Δ2ΔΔΔΔa a a a a a a a =+=++++()()()222311111112ΔΔΔΔΔΔa a a a a a a =++++++2311113Δ3ΔΔa a a a =+++．归纳得一般结论：1221111111C ΔC ΔC Δkkn n n n a a a a a ---=++++ ①．【小问3详解】设数列：1230,,,,,n S S S S ⋅⋅⋅，因为()11111Δ2,Δ0n n n n a S S S n S S a --=-=≥=-=，所以数列1230,,,,,n S S S S ⋅⋅⋅为1k +阶等差数列，由（2）中①得：122111110C ΔC ΔC Δk k n n n n S S S S ++=-+++ ，因为()1111ΔΔΔΔk k k S S a +==所以123211111C C ΔC ΔC Δk kn n n n n S a a a a +=++++ ．【小问4详解】由（1）知数列{}2n为二阶等差数列，且()()()()211213221Δ413,ΔΔΔ94412a a a a a a a a =-==-=---=---=，则由（3）得：2222123n ++++ ()()()123112C 1C 3C 23226n n n n n n n n n ---=⨯+⨯+⨯=+⨯+⨯()()11216n n n =++②．设共堆积了n 层，第n 层共有n a 个球，第1层有1个球，因为每层的“边”比上一层多1个球，所以第n 层的“边”共有n 个球，则第n 层的球数为()11232n n n a n +=++++=．则这n 层所有球的个数为()11362n n n S +=++++ ．【法一】由②式得：()()()22221113612312322n n n S n n +⎡⎤=++++=++++++++⎣⎦ ()()()111211202462n n n n n =++++=．解得：22n =．答：这位同学共堆积了22层．【法二】()222223411136C C C C 2n n n n S ++=++++=++++ 32223223223341441551C C C C C C +C C C C n n n +++=++++=++⋅⋅⋅=+++ ()()3221C 20246n n n n+++==== ．解得：22n =．答：这位同学共堆积了22层．【点睛】涉及数列新定义问题，关键是正确理解给出的定义，由给定的数列结合新定义探求数列的相关性质，并进行合理的计算、分析、推理等方法综合解决.。
江苏省泰州市姜堰区2023-2024学年七年级上学期期中学情调查英语试卷(含答案)
江苏省泰州市姜堰区2023-2024学年七年级上学期期中学情调查英语试卷学校：___________姓名：___________班级：___________考号：___________一、单选题1．—Kate,are you __________only child in your family?—Yes,but __________new baby is on the way.A.a;theB.an;theC.the;aD.the;the2．He often watches TV __________Sundays,but he wants to go to the cinema __________this Sunday.A.on;/B.on;onC./;onD.at;on3．Benny,I can't __________you clearly.Could you please __________that again?A.listen to;sayB.hear;speakC.listen to;speakD.hear;say4．How __________they are at the party!They all enjoy__________A.happily;dancingB.happy;to danceC.happy;dancingD.happily;to dance5．November 11 is coming.Sandy, __________other girls, _____shopping on Taobao.A.like;likeB.likes;likeC.like;likesD.likes;likes6．—Are there __________eggs in the fridge?—Yes,but only __________A.some;fewB.any;a fewC.some;littleD.any;a little7．—Who is your English teacher?—The woman __________glasses over there is her.Look!She is __________a blue dresstoday.A.wears;inB.with;wearsC.wears;onD.with;in8．—Daniel,do you know the man over there?—Oh,yes.He is Mr.Wu.He teaches ______English this term.We all like. ____.A.our;him;him;herD.our;her9．—Thank you so much for showing me the way.It's nice of you.A.Don't say so.B.NevermindC.You're welcomeD.It doesn't matter. 10．Here are Sandy's notes for a short writing.What does she want to introduce?A.Her familyB.Her schoolC.Her friendsD.Her hobbies.二、完形填空On a working day in late April,a large open space with 10 barbecue(烧烤)restaurants inout-of-town visitors.”Huang Yang is also a native of Zibo.And he works outside his hometown.He recently(最four different restaurants.great interest in it.They come to Zibo to study how Zibo's barbecue industry(产业)becomes11．A.buses B.cooks C.tables D.desks12．A.inside B.outside C.behind D.before13．zy B.free C.happy D.busy14．A.seldom B.always C.often ually 15．A.until B.before C.if D.after 16．A.none B.few C.most D.all 17．A.returns B.gets C.leaves D.arrives 18．A.to B.from C.on D.in 19．e B.go C.leave D.start 20．A.weekdays B.Tuesday C.Sunday D.weekends 21．A.she B.he C.it D.they 22．A.something B.somebody C.anything D.anybody 23．A.asks B.answers C.tells D.shows 24．A.countries B.cities C.schools D.offices25．A.cute B.popular C.cheap D.delicious三、阅读理解Do you love flowers?At Harrington SchoolSaturday and Sunday,May 12 and 13,8 a.m.-3 p.m.Outside on the playgroundIf you have questions about the flower sale,call Frank at 555-0216 or Sue at 555-0924 26．Where is the flower sale?A.In a gardenB.On the playground.C.At someone's home.D.At a school.27．When is the flower sale?A.On a weekend.B.In the winter.C.During the summer holiday.D.On the weekdays.28．Where can you go to buy plant food?A.The playground.B.A classroom.C.A gardenD.Your home.29．You can buy both flowers and__________.A.seedsB.vegetablesC.pictures of flowersD.pictures of friends30．This passage is probably from__________.A.a magazine about flowersB.a magazine about childrenC.an advertisement for flowersD.an advertisement for plantsA big group of sheep are eating grass outside.A wolf comes and catches a lamb.There is a bag on the lamb's back. The lamb tries hard to get away but it can not.When the wolf is about to eat the lamb,the lamb gets an idea.It asks,“Mr Wolf,will you be kind and give me my last wish?”The wolf asks,"What is your last wish?"The lamb says,“I like music.I wis h to hear you play the flute(笛子).It's in the bag on my back.”The wolf thinks it is easy and plays the flute.When the wolf stops,the lamb says,“Oh! What beautiful music!Will you play louder(大声一点),please?You play far better than myowner."The wolf is happy to hear that and starts to play louder.At the same time,the owner and the dogs are looking for the missing lamb.When they hear the sound,they begin running and catch the wolf.The lamb happily runs back to its group. 31．What is a lamb?A.A young sheepB.A young boy.C.A little dogD.Another kind of wolf32．Why docs the lamb ask the wolf to play the flute?A.To become friends with the wolf.B.To learn how to play the flute.C.To make use of the wolf's playing.D.To listen to the flute music again.33．What happens after the wolf plays the flute louder?A.The lamb starts to dance to the music.B.The owner and the dogs come and catch it.C.The lamb runs away as fast as possible.D.The other sheep all come back to join them.34．From the story,we can learn that the lamb is_______A.badB.kindC.cleverD.funny35．Which can be the title of passage?A.Cleveness wins over danger.B.Music is very beautiful.C.A big group of sheep and a wolf.D.The owner and his sheep.On Sept 5,China's 13th scientific expedition(科学考察)to the Arctic Ocean(北冰洋) reached the North Pole region(北极点区域).You may want to know:What's the difference berween doing research(研究)in the Arctic(北极)and Antarctica(南极)?Research in the Arctic is difficult but it is easy in Antarctica.Antarctica is mainly land.Soscientists can set up research stations(站点) on the land.However,the Arctic is mainly an ocean(海洋).Scientists can only set up drifing(流动的)stations or stations on boats in the Arctic.There are also other differences between the two poles.The Arctic is at the north end of Earth.Canada,Norway,Russia and five other countries have land there.Antarctica is at the south end of Earth.There are no countries there.People from all countries and regions can go there.Antarctica is very cold.The winds at the South Pole are very strong.They blow away(吹走) the winds from warm places.But winds at the North Pole are not that strong.They mix(混合) with air from warm places.36．What do we know from Paragraph 1?A.September is the best time to go to the Arctic.B.China did 12 scientific expeditions to the Arctic Ocean before Sept 5.C.Thineen Chinese scientists are in the Arctic.D.The scientists are studying the difterence between the Arctic and Antarctica.37．Why is it difficult to do studies in the Arctic?A.Because it is mainly land.B.Because there are many research stations.C.Because there are many boats in the Arctic.D.Because scientists have to use boats as research stations.38．Which of the following is TRUE about Canada?a.Part of it is in the Arcticb.It is at the south end of Earth.c.People there can go to Antarctica.d.It has land in AntarcticaA.abB.acC.bcD.bd39．Why is the Arctic not very cold?A.Because there is air from warm places.B.Because there is more water.C.Because the winds there are strong.D.Because it is south of Antarctica.40．What is the passage mainly about?A.Chinese scientists'studies of the Arctic.B.Research stations in the Arctic and Antarctica.C.Differences between the Arctic and Antarctica.D.The weather in the Arctic and Antarctica.四、填空题41．Helen, _______(stay)here and don't go anywhere.Your parents are looking for you. 42．Although Tommy is poor,he gives a nice present to his friend for his _______ (9)birthday.43．I hope you _______ (come)to my birthday party this Friday.44．Sandy with her friends often _______ (fly)kites at weekends.45．—Do you know all the _______ (play)names?—Sorry,I only know some.46．—Can you write _______ (diary)in English?—Yes,I can.47．Eating more vegetables and fruit _______ (be)good for our health.48．What great fun Millie had _______ (chat)with her friends yesterday!49．Look!Lily _______ (have)a beautiful flower in her hand.50．Can you think of a way to make the baby _______ (not cry).51．There are different outdoor activities for different seasons.In spring we can fly kites.In summer,we can go swimming or sailing.In autumn,it is a good idea to camp or hike.In winter, we can go to ski or skate because they bring us a lot of fun.They make us strong and healthy too. So it is important for people of all ages to take part in some outdoor activities at the right time.There are many group activities,like football and basketball.The members work together for the same goal(目标).So group activities need team spirit(团队精神).It is very useful for a person to have team spirit.It is good for us both in life and in work.Old people like walking and jogging.These outdoor activities don't need much strength(力气).Young people like exciting activities like diving(潜水),skiing and horse riding.Children like funny activities like flying kites.Some outdoor activities are dangerous,like climbing rocks.So we must be careful when we take part in them.backs. They follow maps on . ②_______ (they)phones.They are called backpackers(背包客).Before③_______ (leave)for a new place,backpackers would like④_______ (study)their destinations(目的地).For example,what food to eat,where to live,what to buy and how to take trains.Most backpackers usually don't take too much money with them,they choose to stay in hostels(青年旅舍)during their trips.Hostels are much cheaper than big hotels.There⑤_______ (be)six or eight beds in each room.People⑥_______different countries become friends there.Backpacking . ⑦_______ (let)travelers see more.An . ⑧_______(America)backpacker Charles Veley went to over 190. ⑨_______ (country)in 10 years!"To live is to see . ⑩_______world as much as possible,"he said.五、翻译题53．你空闲时愿意带我参观一下姜堰吗?Would you like to _______ me _______.Jiangyan in your free time?54．现在很多人向银行贷款买房子。
广东省潮州市2023-2024学年高一上学期期末考试英语试题(含答案,含听力原文,无音频)
潮州市2023-2024学年度第一学期期末高一级教学质量检测卷英语本试卷共10页; 满分 100分, 完成时间100分钟。
注意事项：1.答卷前，考生务必用黑色字迹的钢笔或签字笔将自己的姓名和考号填写在答题卡上。
2.选择题每小题选出答案后，用2B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，再选涂其它答案；不能答在试卷上。
3.非选择题必须用黑色字迹钢笔或签字笔作答，答案必须写在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，然后再写上新的答案；不准使用铅笔和涂改液。
不按以上要求作答的答案无效。
4.考生必须保持答题卡的整洁，考试结束，将答案卡交回。
一、听说考试 (共两节；满分15分)做题时先把答案写在试卷上，等听说考试结束后再把答案写在答题卡上。
第一节角色扮演(共8小题；每小题1分，满分8分)情景介绍：角色: 你是 Tom任务：(1)与同学Mary谈论阅读俱乐部的话题；(2)根据对话内容，回答另一同学的问题。
生词: detective 侦探; philosophy 哲学下面请用英语提出三个问题。
每个问题有20秒的准备时间。
当你听见“滴”声时，开始提问。
Now please ask the speaker three questions. You have twenty seconds to prepare the question. When you hear a beep, begin to ask the question.1.你如何知道这个俱乐部?2.你们有什么活动?3.你现在喜欢阅读吗?下面请用英语回答五个问题。
每小题有10秒的准备时间。
当你听见“滴”声时，开始回答。
Now please get ready to answer five questions. You are allowed ten seconds to prepare the answer. When you hear a beep, begin to answer the question.4. When did Mary join the reading club?·5. How many people are there in the reading club?·6. Who founded the reading club?7. What is the reading club's aim?————— ·8. What kind of novels does Mary like?第二节故事复述(共7小题；每小题1分，满分7分)请听下面一个故事，然后根据故事意思填空，每空一词，录音读两遍。
2024届江苏无锡市四校高三下学期期初学情调研数学试题及答案
2023-2024学年春学期期初学情调研试卷高三数学命题人： 复核人：注意事项：1. 答卷前，考生务必将自己的考生号、姓名、考场号及座位号填写在答题卡上。
2. 回答选择题时，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。
如需要改动，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。
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．设集合{|22}M x x =−<<，{0,1,2,3}N =，则M N = （ ）A. {|22}x x −<<B. {01} ，C. {012} ，，D. {|02}x x <<2．已知�aa ⃑,bb �⃑,cc ⃑�是空间的一个基底，则可以与向量pp ⃑=aa ⃑+bb �⃑，qq ⃑=aa ⃑−bb �⃑构成基底的向量是( ) A. aa ⃑B ．bb �⃑C ．aa ⃑+2bb�⃑ D ．aa ⃑+2cc ⃑3．若直线ll 12值为( )5．如图，一个底面边长为2√3ππ3cm 的正四棱柱形状的容器内装有部分水，现将一个底面半径为1cm 的铁制实心圆锥放入容器，圆锥放入后完全沉入水中，并使得水面上升了1cm ．若该容器的厚度忽略不计，则该圆锥的侧面积为（ ） A ．√17ππccmm 2 B ．4ππccmm 2 C ．3√2ππccmm 2D ．2√3ππccmm 26．某校A ，B ，C ，D ，E 五名学生分别上台演讲，若A 须在B 前面出场，且都不能在第3号位置，则不同的出场次序有( ) A ．18种B ．36种C ．60种D ．72种7．双曲线C:x 29−y 216=1的右支上一点P 在第一象限，F 1、F 2分别为双曲线C 的左、右焦点，I 为△PF 1F 2的内心，若内切圆I 的半径为1，则△PF 1F 2的面积等于( ) A. 323B. 12C. 24D. 1638．已知函数f(x)=� |x −1|, x <2,2(x −3)2−1, x ≥2, 若方程f(f(x))=12的实根个数为( ) A. 4 B. 8 C. 10 D. 12二、选择题：本题共3小题，每小题6分，共18分．在每小题给出的选项中，有多项符合题目要求．全部选对的得6分，部分选对的得部分分，有选错的得0分． 9．在△AAAAAA 中，内角AA ,AA ,AA 所对的边分别为a 、b 、c ，则下列说法正确的是( ) A ．bbsinBB =aa+bb+ccsinAA+sinBB+sinCC B ．若AA >AA ，则sin2AA >sin2AAC ．aa =bb cos AA +cc cos AAD ．若(AABB�����⃗|AABB �����⃗|+AACC�����⃗|AACC�����⃗|)⋅AAAA �����⃗=0，且AABB�����⃗|AABB �����⃗|⋅AACC�����⃗|AACC�����⃗|=12，则△AAAAAA 为等边三角形10．设a 为常数，1(0)2f =，()()()()()f x y f x f a y f y f a x +=−+−，则( ) A. 1()2f a =B. 1()2f x =恒成立C. ()2()()f x y f x f y +=D. 满足条件的()f x 不止一个11．如图，在正方体1111ABCD A B C D −中，E 为棱BC 上的动点，F 为棱1B B 的中点，则下列选项正确的是( )A ．直线11A D 与直线EF 相交B ．当E 为棱BC 上的中点时，则点E 在平面1AD F 的射影是点F C ．不存在点E ，使得直线1AD 与直线EF 所成角为30 D ．三棱锥E ADF −的体积为定值三、填空题：本题共3小题，每小题5分，共15分．12．已知αα∈(0,π),sin �αα−，则cos �2αα+13．若直线()0y kx b b =+<是曲线2e x y −=的切线，也是曲线ln y x =的切线，则b = ．14.“曼哈顿距离”是人脸识别中的一种重要测距方式，其定义如下：设A(x 1,y 1)，B(x 2,y 2)，则A ，B 两点间的曼哈顿距离d(A,B)=|x 1−x 2|+|y 1−y 2|.已知M(4,6)，点N 在圆C:x 2+y 2+6x +4y =0上运动，若点P 满足d(M,P)=2，则|PN|的最大值为 ．四、解答题：本题共5小题，共77分．解答应写出文字说明、证明过程或演算步骤． 15．（13分）在ABC 中，内角A ，B ，C 的对边分别为a ，b ，c ，已知该三角形的面积2221()sin 2S b c a A =+−．17．（15分）如图，在三棱柱AAAAAA−AA1AA1AA1中，AAAA1⊥平面AAAAAA,AAAA⊥AAAA,AAAA=AAAA=2，AAAA1=3，点DD, EE分别在棱AAAA1和棱AAAA1上，且AADD=1 AAEE=2, MM为棱AA1AA1的中点．（Ⅰ）求证：AA1MM⊥AA1DD；（Ⅱ）求二面角AA−AA1EE−DD的正弦值；（Ⅲ）求直线AAAA与平面DDAA1EE所成角的正弦值．18．（17分）已知M，N为椭圆C1:x2a2+y2=1(a>0)和双曲线C2:x2a2−y2=1的公共左、右顶点，e1，e2分别为C1和C2的离心率．(1)若e1e2=√154．(ⅰ)求C2的渐近线方程;(ⅱ)过点G(4,0)的直线l交C2的右支于A，B两点，直线MA，MB与直线x=1相交于A1，B1两点，记A，B，A1，B1的坐标分别为(x1,y1)，(x2,y2)，(x3,y3)，(x4,y4)，求证：1y1+1y2=1y3+1y4;(2)从C2上的动点P(x0,y0)(x0≠±a)引C1的两条切线，经过两个切点的直线与C2的两条渐近线围成三角形的面积为S，试判断S是否为定值?若是，请求出该定值;若不是，请说明理由．19．（17分）已知A m=�a1,1a1,2⋯a1,ma2,1a2,2⋯a2,m⋮⋮⋱⋮a m,1a m,2⋯a m,m�(m≥2)是m2个正整数组成的m行m列的数表，当1≤i<s≤m,1≤j<t≤m时，记d(a i,j,a s,t)=|a i,j−a s,j|+|a s,j−a s,t|.设n∈N∗，若A m 满足如下两个性质：①a i,j∈{1,2,3;⋯,n}(i=1,2,⋯,m;j=1,2,⋯,m)；②对任意k∈{1,2,3,⋯,n}，存在i∈{1,2,⋯,m},j∈{1,2,⋯,m}使得a i,j=k，则称A m为Γn数表．(1)判断A3=�123231312�是否为Γ3数表，并求d�a1,1,a2,2�+d�a2,2,a3,3�的值；(2)若Γ2数表A4满足d�a i,j,a i+1,j+1�=1(i=1,2,3;j=1,2,3)，求A4中各数之和的最小值；(3)证明：对任意Γ4数表A10，存在1≤i<s≤10,1≤j<t≤10，使得d�a i,j,a s,t�=0．2023-2024学年春学期期初学情调研试卷参考答案1．B [试题解析]{|22}M x x =−<<，{0,1,2,3}N =，M N = {01} ，故选：B 2．D [试题解析]因为aa ⃑，pp ⃑=aa ⃑+bb �⃑，qq ⃑=aa ⃑−bb �⃑，为共面向量，所以不能构成基底，故A 错误； 因为bb �⃑，pp ⃑=aa ⃑+bb �⃑，qq ⃑=aa ⃑−bb�⃑，为共面向量，所以不能构成基底，故B 错误； 因为aa ⃑+2bb �⃑，pp ⃑=aa ⃑+bb �⃑，qq ⃑=aa ⃑−bb �⃑，为共面向量，所以不能构成基底，故C 错误； 因为aa ⃑+2cc ⃑，pp ⃑=aa ⃑+bb �⃑，qq ⃑=aa ⃑−bb�⃑，为不共面向量，所以能构成基底，故D 正确；故选：D 3．D [试题解析]∵ll 1⊥ll 2，∴aa (aa −1)+(1−aa )×(2aa +3)=0，即(aa −1)(aa +3)=0，解得aa =1或aa =−3. 故选：D ．4．B [试题解析]奇数项共有(nn +1)项，其和为aa 1+aa 2nn+12⋅(nn +1)=2aa nn+12⋅(nn +1)=290，∴(nn +1)aa nn+1=290．偶数项共有n 项，其和为aa 2+aa 2nn2⋅nn =2aa nn+12⋅nn =nnaa nn+1=261，∴aa nn+1=290−261=29．故选：B ．5．C [试题解析]依题意可得圆锥的体积VV =1×�2√3ππ3�2=4ππ3ccmm 3，又VV =13ππ×12×ℎ(ccmm 3)（其中h 为圆锥的高），则ℎ=4cm ，则圆锥的母线长为√12+42=√17cm ，故圆锥的侧面积为√17ππccmm 3．故选：A ． 6．B [试题解析]因为A 在B 的前面出场，且A ，B 都不在3号位置，则情况如下：①A 在1号位置，B有2,4,5号三种选择，有3A 33＝18种出场次序；②A 在2号位置，B 有4,5号两种选择，有2A 33＝12种出场次序；③A 在4号位置，B 有5A 33＝6种出场次序，故不同的出场次序共有18＋12＋6＝36种．故选B.7．A [试题解析]解：由题意，作图如下：设圆II 与xx 轴、PPFF 2、PPFF 1分别切于点EE 、HH 、FF ， 因为双曲线CC 的右顶点为AA (3,0)，FF 1(−5,0)，FF 2(5,0)， 所以|AAFF 1|−|AAFF 2|=(3+5)−(5−3)=6，因为|PPFF 1|−|PPFF 2|=6，所以|PPFF 1|−|PPFF 2|=(|PPFF |+|FFFF 1|)−(|PPHH |+|HHFF 2|)=|FFFF 1|−|HHFF 2|=|FF 1EE |−|EEFF 2|=6，因此切点EE 与AA 重合．又因为内切圆II 的半径为1，所以II (3,1)，又FF 1(−5,0)，FF 2(5,0)，|IIFF 1|=√ 65,|IIFF 2|=√ 5,cos ∠FF 1IIFF 2=65+5−1002√ 65×√ 5=−3√ 13, 所以tan ∠FF 1IIFF 2=−23,解得tan∠FF 1PPFF 22=32,所以SS △FF 1PPFF 2=bb2tan∠FF 1PPFF 22=323，所以△PPFF 1FF 2面积为323．8．C [试题解析]解：在同一坐标系中作yy =ff (xx )，yy =12的图象，若由图象观察可知，0<xx 1<1<xx 2<2<xx 3<3<xx 4<4， 当ff (ff (xx ))=12时，由ff (xx )=xx 1，0<xx 1<1存在4个不同根， ff (xx )=xx 2，1<xx 2<2存在2个不根，ff (xx )=xx 3，2<xx 3<3存在2个不根， ff (xx )=xx 4，3<xx 4<4，存在2个不根，综上ff (ff (xx ))=12的实根个数为10．9．ACD [试题解析]A ：由aasinAA =bbsinBB=cc sinCC，根据等比的性质有bb sinBB =aa+bb+ccsinAA+sinBB+sinCC ，正确； B ：当AA =ππ3,BB =ππ6时，有sin2AA =sin2BB ，错误；C ：sin BB cos CC +sin CC cos BB =sin(BB +CC )，而BB +CC =ππ−AA ，即sin BB cos CC +sin CC cos BB =sin AA ，由正弦定理易得aa =bb cos CC +cc cos BB ，正确；D ：如图，AAEE�����⃗=AABB�����⃗|AABB�����⃗|,AAFF �����⃗=AACC �����⃗|AACC �����⃗|是单位向量，则AABB�����⃗|AABB�����⃗|+AACC�����⃗|AACC�����⃗| =AAEE �����⃗+AAFF �����⃗=AAAA �����⃗，即AAAA �����⃗⋅BBCC �����⃗=0、AAEE �����⃗⋅AAFF �����⃗=12，则AAAA �����⃗⊥BBCC �����⃗且AAAA 平分∠BBAACC ，AAEE �����⃗,AAFF �����⃗的夹角为ππ3， 易知△AABBCC 为等边三角形，正确.故选：ACD 10．ABC [试题解析]令0xy ==，可得(0)2(0)()f f f a =，因为1(0)2f =，所以1().2f a A =正确.令0y =，可得()()()(0)()f x f x f a f f a x =+−，代入1()2f a =，1(0)2f =，可得()().f a x f x −=同理，令0x =，可得()(0)()()()f y f f a y f y f a =−+，代入1()2f a =，1(0)2f =，可得()().f a y f y −=即原等式变形为()2()()f x y f x f y +=，C 正确. 令y x =可得2(2)2[()]0f x f x = ，即函数取值非负.令y a x =−可得2()2[()]f a f x =，即21[()]4f x =，解得1()2f x =，B 正确.因此仅有一个函数关系式1()2f x =满足条件，故D 错误.故选ABC 11．CD [试题解析【详解】A ：由题意知，1111//A D B C ，11B C ⊂平面11B C CB ，11A D ⊄平面11B C CB 所以11//A D 平面11B C CB ，又EF ⊂平面11B C CB ，所以11A D 与EF 不相交，故A 错误；B ：连接111AD D F AF AE CB 、、、、，如图，当点E 为BC 的中点时，1//EF CB ，又11AD CB ⊥，所以1EF AD ⊥， 若点E 在平面1AD F 的射影为F ，则EF ⊥平面1AD F ，垂足为F ，所以EF AF ⊥，设正方体的棱长为2，则AE AF EF ===在AEF 中，222AF EF AE +≠，所以90AFE °∠≠，即EF AF ⊥不成立，故B 错误；C ：建立如图空间直角坐标系D xyz −，连接1BC ，则11//AD BC ， 所以异面直线EF 与1AD 所成角为直线EF 与1BC 所成角，设正方体的棱长为2，若存在点(,2,0)(02)E a a ≤≤使得EF 与1BC 所成角为30°，则1(2,2,0)(2,2,1)(0,2,2)B F C ，，，所以1(2,0,1)(2,0,2)EF a BC =−=−，，所以122EF BC a ⋅=− ，又11cos30EF BC EF BC °⋅= ，得22a −=，解得4a =± 符合题意，故不存在点E 使得EF 与1AD 所成角为30°，故C 错误； D ：如图，由等体积法可知E ADF F ADE V V −−=，又111332F ADE ADE V S BF AD AB BF −=⋅=×××× ，AD AB BF 、、为定值，所以F ADE V −为定值，所以三棱锥E ADF −的体积为定值，故D 正确.故选：C D .12．−4√29[试题解析]因为sin �αα−π6�=13，αα∈(0,π)，αα−π6∈�−π6,5π6�,又因为sin �αα−π6�=13<sin 5π6=12，所以αα−π6∈�0,π2�, 所以cos �αα−π6�=�1−sin 2�αα−π6�=2√23, 所以sin �2�αα−π6��=2sin �αα−π6�cos �αα−π6�=4√29, π�π�π�π�π�π��4√2. 故答案为：−4√2.解：由题意得，圆CC :(xx +3)2+(yy +2)2=13，圆心CC (−3,−2) 设点PP (xx 0,yy 0)，则|xx 0−4|+|yy 0−6|=2，故点PP 的轨迹为如下所示的正方形，其中AA (4,8)，BB (6,6)， 则|AACC |=√ 149，|BBCC |=√ 145， 则|PPPP |≤|AACC |+rr =√ 149+√ 13，�����⃗、CCBB�����⃗、CCCC1�������⃗的方向为xx轴、yy轴、zz轴的正方向建立空间直17．（15分）解：依题意，以CC为原点，分别以CCAA角坐标系（如图），可得CC(0,0,0)、AA(2,0,0)、BB(0,2,0)、CC1(0,0,3)、AA1(2,0,3)、BB1(0,2,3)、DD(2,0,1)、EE(0,0,2)、MM(1,1,3).（Ⅰ）依题意，CC MM��������⃗=(1,1,0)，BB DD�������⃗=(2,−2,−2)，从而CC 1MM ��������⃗⋅BB 1DD �������⃗=2−2+0=0，所以CC 1MM ⊥BB 1DD ； （Ⅱ）依题意，CCAA�����⃗=(2,0,0)是平面BBBB 1EE 的一个法向量， EEBB 1�������⃗=(0,2,1)，EEDD �����⃗=(2,0,−1)． 设nn�⃗=(xx ,yy ,zz )为平面DDBB 1EE 的法向量， 则{nn �⃗⋅EEBB 1�������⃗=0nn�⃗⋅EEDD �����⃗=0，即{2yy +zz =02xx −zz =0， 不妨设xx =1，可得nn�⃗=(1,−1,2)． cos <CCAA �����⃗,nn �⃗>=CCAA �����⃗⋅nn�⃗|CCAA �����⃗|⋅|nn �⃗|=22×√6=√66， ∴sin <CCAA �����⃗,nn �⃗>=�1−cos 2<CCAA �����⃗,nn �⃗>=√306．所以，二面角BB −BB 1EE −DD 的正弦值为√306； （Ⅲ）依题意，AABB�����⃗=(−2,2,0)． 由（Ⅱ）知nn �⃗=(1,−1,2)为平面DDBB 1EE 的一个法向量，于是cos <AABB �����⃗,nn �⃗>=AABB �����⃗⋅nn �⃗|AABB�����⃗|⋅|nn �⃗|=−42√2×√6=−√33． 所以，直线AABB 与平面DDBB 1EE 所成角的正弦值为√33.18．（17分）解：(1)由题意得ee 1=� aa 2−1aa，ee 2=� aa 2+1aa，所以ee 1ee 2=� aa 4−1aa 2=√ 154，又aa >0，解得aa 2=4，(ii )故双曲线CC 2的渐近线方程为yy =±12xx ；(ii ii )设直线AABB 的方程为xx =ttyy +4，则�xx =ttyy +4,xx 24−yy 2=1,消元得：(tt 2−4)yy 2+8ttyy +12=0，ΔΔ>0且tt ≠±2， 所以�yy 1+yy 2=−8tttt 2−4,yy 1yy 2=12tt 2−4,故11yy 1+yy 22tt，又直线AAAA 1的方程为yy =yy1xx 1+2(xx +2)， 所以yy 3=3yy 1xx 1+2，同理yy 4=3yy 2xx 2+2， 所以1yy 3+1yy 4=13(xx 1+2yy 1+xx 2+2yy 2)=13(tt yy 1+6yy 1+tt yy 2+6yy 2) =2tt yy 1yy 2+6(yy 1+yy 2)3yy 1yy 2=23tt +2(yy 1+yy 2)yy 1yy 2=23tt +2(1yy 1+1yy 2)=23tt −43tt =−23tt ， 故1yy 1+1yy 2=1yy 3+1yy 4．(2)设两个切点为PP 1(xx 5,yy 5)，PP 2(xx 6,yy 6)，由题意知PPPP 1，PPPP 2斜率存在， 直线PPPP 1方程为ll 1:yy =kk 1(xx −xx 5)+yy 5，联立�xx 2aa 2+yy 2=1,yy =kk 1(xx −xx 5)+yy 5,由ΔΔ=0得kk 1=−xx 5aa 2yy 5，所以ll 1:xx 5xx aa 2+yy 5yy =1，同理直线PPPP 2方程为ll 2:xx 6xx aa 2+yy 6yy =1， 由ll 1，ll 2过PP 点可得�xx 5xx 0aa 2+yy 5yy 0=1,xx 6xx 0aa 2+yy 6yy 0=1可得直线PP 1PP 2的方程为xx 0xx aa 2+yy 0yy =1， 不妨设，直线PP 1PP 2与双曲线两渐近线yy =±1aa xx 交于两点PP 1′(aa 2xx 0+aayy 0,aaxx 0+aayy 0)， PP 2′(aa 2xx 0−aayy 0,−aa xx 0−aayy 0)， 则围成三角形的面积 SS =12|aa 2xx 0+aayy 0⋅−aa xx 0−aayy 0−aa xx 0+aayy 0⋅aa 2xx 0−aayy 0|=|aa 3xx 02−aa 2yy 02|. 因PP 在双曲线CC 2上，xx 02−aa 2yy 02=aa 2，则SS =aa 3aa 2=aa 为定值．19．（17分） 解：(1) AA 3=�123231312� 是 ΓΓ3 数表，dd (aa 1,1,aa 2,2)+dd (aa 2,2,aa 3,3)=2+3=5. (2)由题可知 dd (aa ii ,jj ,aa ii+1,jj+1)=|aa ii ,jj −aa ii+1,jj |+|aa ii+1,jj −aa ii+1,jj+1|=1 (ii =1,2,3;jj =1,2,3) ． 当 aa ii+1,jj =1 时，有 dd (aa ii ,jj ,aa ii+1,jj+1)=|aa ii ,jj −1|+|aa ii+1,jj+1−1|=1 ， 所以 aa ii ,jj +aa ii+1,jj+1=3 ． 当 aa ii+1,jj =2 时，有 dd (aa ii ,jj ,aa ii+1,jj+1)=|aa ii ,jj −2|+|aa ii+1,jj+1−2|=1 ，所以 aa ii ,jj +aa ii+1,jj+1=3 ． 所以 aa ii ,jj +aa ii+1,jj+1=3(ii =1,2,3;jj =1,2,3). 所以 aa 1,1+aa 2,2+aa 3,3+aa 4,4=3+3=6, aa 1,3+aa 2,4=3,aa 3,1+aa 4,2=3. aa 1,2+aa 2,3+aa 3,4=3+1=4 或者 aa 1,2+aa 2,3+aa 3,4=3+2=5 ， aa 2,1+aa 3,2+aa 4,3=3+1=4 或者 aa 2,1+aa 3,2+aa 4,3=3+2=5 ， aa 1,4=1 或 aa 1,4=2 ， aa 4,1=1 或 aa 4,1=2 ，故各数之和 ⩾6+3+3+4+4+1+1=22 ， 当 AA 4=�1111122212111212� 时，各数之和取得最小值 22 ． (3)由于 ΓΓ4 数表 AA 10 中共 100 个数字，必然存在 kk ∈{1,2,3,4} ，使得数表中 kk 的个数满足 TT ≥25.设第 ii 行中 kk 的个数为 rr ii (ii =1,2,⋅⋅⋅,10).当 rr ii ≥2 时，将横向相邻两个 kk 用从左向右的有向线段连接， 则该行有 rr ii −1 条有向线段， 所以横向有向线段的起点总数 RR =∑ (rr ii ⩾2rr ii −1)⩾∑ii=110(rr ii −1)=TT −10. 设第 jj 列中 kk 的个数为 cc jj (jj =1,2,⋅⋅⋅ ．当 cc jj ≥2 时，将纵向相邻两个 kk 用从上到下的有向线段连接， 则该列有 cc jj −1 条有向线段，所以纵向有向线段的起点总数 CC =∑ (cc jj ⩾2cc jj −1)⩾∑jj=110(cc jj −1)=TT −10. 所以 RR +CC ≥2TT −20 ， 因为 TT ≥25 ，所以 RR +CC −TT ⩾2TT −20−TT =TT −20>0 ．所以必存在某个 kk 既是横向有向线段的起点，又是纵向有向线段的终点， 即存在 1<uu <vv ⩽10,1<pp <qq ⩽10,使得 aa uu ,pp =aa vv ,pp =aa vv ,qq =kk ，所以 dd (aa uu ,pp ,aa vv ,qq )=|aa uu ,pp −aa vv ,pp |+|aa vv ,pp −aa vv ,qq |=0 ，则命题得证．。
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江苏省南通市如东县2023-2024学年高三上学期期初学情检测英语试卷（含答案无听力音频含听力原文）2023～2024 学年度第一学期期初学情检测高三英语参考答案及评分标准第一部分听力（共两节，满分30分）1-5 BCCBA 6- 10 ABBCA 11- 15 BABCA 16-20 BCACA第二部分阅读（共两节，满分50分）第一节(共15 小题；每小题2.5 分，满分37.5 分)21-23 CDA 24-27 BDAC 28-31 ACBD 32-35 DCAB第二节（共5 小题；每小题2.5 分，满分12.5 分）36-40 BAEGF第三部分语言运用（共两节，满分30 分）第一节（共15 小题；每小题1 分，满分15 分）41-45 CDCAB 46-50 DBACD 51-55 BACDB第二节（共10 小题；每小题1.5 分，满分15 分）56. relaxation 57. has popped 58. professionals 59. to go 60. the 61. which 62. as 63. more authentic 64. exposed 65. and第四部分写作（共两节，满分40分）第一节（满分15 分）Dear Kevin,Hearing that you want to learn Chinese mainly by watching movies, I’m writing to share with you myopinion. I believe it may not be the most appropriate choice for the following reasons.First of all, language learning involves several skills, such as listening, speaking, reading and writing.Obviously, learning Chinese mainly by watching movies is not conducive to developing your integrated skills.Besides, the language in the movie is set for the plot and may not match your language level, which mayprevent you from learning Chinese gradually and systematically. Therefore, I suggest, besides watching movies, you should read more books and communicate withnative speakers frequently to practice your Chinese. In addition, taking some Chinese courses is also a goodchoice. I am convinced that with the help of teachers, you can learn Chinese better.Thanks for considering my suggestion.Yours sincerely,Li Hua.2023～2024学年度第一学期期初学情检测高三英语参考答案第1页共4页{#{ABQAYaYUooggCiIAAgIABAABAhRChACQAUQAXCAkCGEQCkQAkCBCE CCKAgCGgRGFBAFEAoEAoAABAyByFRANBABAA=A}#=}}#}第二节读后续写（满分25 分）“How much do you have ” asked the man from Chicago. “47 cents!” Tess replied without any hesitation.To her surprise, the man said that he was a doctor and that it was a fair price for a miracle. Overcome withexcitement，Tess grasped his hand，leading him to her home. With doubt and hope，Dad and Mom hadAndrew checked by the man，who declared that he would perform an operation on the boy and promised itwouldn’t be long before he could pick himself up. Hearing his words, the whole family burst into tears of joy.The operation was completed. Hardly had Andrew been sent back home when his parents went to thankthe doctor with Tess，for they knew that 47 cents was a joke for an operation. They promised to save enoughmoney to pay for the bill only to be told that Tess had paid for it. “It’s a fair deal,” the doctor explained to theparents，and then looked into Tess’s eyes，smiling, “47 cents was what itcost—plus the faith of a little girl.”分值说明：选择题部分95 分1. 听力1-20 题，1.5 分1 题，共30 分；2. 阅读理解21-35 题，2.5 分1 题，共37.5 分；3. 阅读“七选五”36-40 题，2.5 分1 题，共12.5 分；4. 完形填空41-55 题，1 分1 题，共15 分。
非选择题部分共55 分1. 语法填空56-65 题，1.5 分1 题，共15 分；2. 应用文写作，15 分；3. 读后续写，25 分。
2023～2024学年度第一学期期初学情检测高三英语参考答案第2页共4页{#{ABAQYaYUooggCiIAAIgABAABAhRChACQAUQAXCAkCGEQCkQAkCBCE CCKAgCGgRGFBAFEAoEAoAABAyByFRANBABAA=A}#=}}#}听力材料Text 1W: Can’t you knock on the door before you enter my officeM: Sorry! It’s just because I’m in such a hurry.Text 2W: I just sat down at my computer and realized that my phone was dead. Do you have a charger I can borrowM: Yes, Catherine. I always bring an extra charger to work.W: I usually do too! But I forgot to bring mine before getting on the train this morning.Text 3M: It’s going to take me forever to finish this maths homework, and I’m really not in the mood to do my sciencehomework after that!W: At least you completed your history yesterday. If you do it a little faster, perhaps you’ll finish the scienceearlier than you thought.Text 4M: Have you seen Mr. Arnold I’ve been searching everywhere for him. W: From 3:00 p.m. to 5:00 p.m., he has a meeting. He’ll be back in his office after the meeting.M: Thanks. I’ll check there later. There’s only an hour left.Text 5W: I’m sorry, Jack. I must decline your offer. Your company looks great, but I’d need a higher salary. I hope youunderstand.M: When I got your call, I thought you were ready to begin working. But I understand your concern.Text 6M: Mom, I bought a smart phone for you. Next month I will go to work in another country. You can still connectwith me on the Internet.W: But I really don’t know how to use it. It’s hard for the old to learn new things.M: It’s OK. I’ll teach you how to have a video chat.W: All right. I will try my best to follow you. It will save a lot of money on phone bills anyway.Text 7M: Hi, Sue. Where have you beenW: Oh. Hi, Dan. I was just at the library. I have to hand in my biology paper tomorrow.M: Tomorrow Oh, no! I thought it wasn’t due till Monday.W: Don’t worry. It is indeed due on Monday. But I’m going away for the weekend and won’t be back tillMonday night.M: Oh, where are you goingW: California. We’re having a family party. It’s my grandmother’s ninetieth birthday, so all the cousins, auntsand uncles are going. She planned the whole thing herself.M: Wow. That’s great. How many people will be thereW: Around sixty. My family is big and spreads out, but we’re pretty close.Text 8M: It’s such a pleasure to meet everyone. Thanks to people like you, small businesses everywhere have manygrowth opportunities.W: Thank you, Paul. And thanks for coming to my office to explain your company. Now you can begin.M: OK. So, we all feel anxious to look our best. But clothing styles quickly change, and fashion isn’t cheap!2023～2024学年度第一学期期初学情检测高三英语参考答案第3页共4页{#{ABAQYaYUooggCiIAAIgABAABAhRChACQAUQAXCAkCGEQCkQAkCBCE CCKAgCGgRGFBAFEAoEAoAABAyByFRANBABAA=A}#=}}#}Plus, the more we buy, the more we waste. How many of us have over five clothing items that we neverwearW: Good, how will you fix thisM: Through my service, Rental Trend.W: How does it workM: It’s a website where users can rent out their clothes. Anyone who is interested in those clothes can offer aprice and rent them. There will be many types of clothes. Whether it’s for a party, photo taking or vacation,we try our best to meet people’s need.W: Interesting, Paul. Have you borrowed from any banksM: No. And because this company is only a year old, this is the first time I’ve come to sincerely invite you toput money into our website. I’m sure you will see what a big difference you make. With your help, we canbring fair fashion nationwide.Text 9W: Sorry to bother you, sir, but we’re looking into a report concerning the house opposite being broken into lastnight. We are speaking to everyone who lives in the neighborhood to investigate what happened.M: Goodness me, they’re friends of mine! Are they OK Did they take anythingW: Everyone is fine, sir. A watch and some pieces of jewelry are missing, which has been upsetting, butthankfully no one was hurt.M: How awful, but I’m glad they are okay.W: May I ask you a few questions, sirM: Of course.W: Did you see anything unusual around eleven o’clock last night Something out of the ordinary, loud noisesperhaps, or activity that you wouldn’t normally see outsideM: Now that you come to mention it, I did notice some flashing lights from the house opposite around that time.I remember thinking it was strange because they are an old couple and their lights are usually out by aroundten o’clock.W: Did you see anyoneM: I did take a look as it happened. There was a white car parked outside their house. Oh, I’m so stupid — Ishould have realized something was happening!W: Is there anything else you can remember Anything at all Even if you don’t think it is importantM: Wait a minute!W: What is itM: I forgot to say I have an outside security camera! It must have recorded everything!W: Excellent, sir! It may solve the case! Let’s take a look immediately! Text 10I’m glad so many of you have come for the gardening class. Welcome, all of you.Each week, we will be growing and looking after our plants, and I will show you all how to get the best outof them. You will all have your own small section of land where you can choose which plants to grow. Thisweek, we want a bed of flowers to brighten up the place.In the following weeks, you may wish to grow your own fruit and vegetables. I will be here to advise andencourage you. I am here every day, so it is easy to come and find me if you have any questions. All I ask inreturn is that you enjoy your time in the great outdoors. Gardening is such a wonderful thing to do. It’s goodexercise, and rewarding. Plus, when you garden in groups like this, it turns into a wonderful social event too.Right then, let me show you to your areas. Follow me.2023～2024学年度第一学期期初学情检测高三英语参考答案第4页共4页{#{ABAQYaYUooggCiIAAIgABAABAhRChACQAUQAXCAkCGEQCkQAkCBCE CCKAgCGgRGFBAFEAoEAoAABAyByFRANBABAA=A}#=}}#}如东县2023-2024学年高三上学期期初学情检测(注意事项考生在答题前请认真阅读本注意事项及各题答题要求：1.本试卷包括选择题和非选择题两部分。