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天津市第二十中学2023-2024学年高三上学期12月月考英语试题

天津市第二十中学2023-2024学年高三上学期12月月考英语试题

天津市第二十中学2023-2024学年高三上学期12月月考英语试题一、单项选择1．—Linda, do you know Jia Ling has become the highest grossing female film director in China after directing her first film?—Wow, ________.A．go for it B．good for her C．all the best D．what a coincidence 2．________ the 24 Solar Terms on Chinese lunar calendar, the farmers in ancient China accomplished the great astronomical and meteorological achievement with their intelligence and experience.A．Basing B．Based C．To base.D．Having been based 3．Crowds of people ________ to watch the charity of performance last night.A．worked out B．turned out C．made out D．reached out4．In order to make her 45th birthday impressive, I intend to buy her a wonderful present, that is not expensive but very meaningful.A．it B．one C．the one D．this5．They are hoping for a return to normal ______ the war is over.A．now that B．even if C．as though D．in case6．________ is often the case, I assume, is the fact that when looking back, the bittersweet senior life is always one’s highlight in pursuit of dream.A．As B．Which C．That D．What7．I ________ a new alarm clock the other day at Taylor’s when I heard someone singing a familiar song.A．bought B．was buying C．has bought D．would buy 8．There _______ a six percent drop in the consumption of such drinks by the end of last month.A．is B．was C．will be D．had been 9．Reading materials for children entered schools to help them develop the habit of financial management at a young age.A．having intended B．intending C．intended D．having been intended 10．According to a newly released regulation on online video services, no one _____ generate, release or spread fake news or information by using such technologies.A．can B．shall C．will D．may11．Ann was much kinder to Peter than she was to the others, ________, of course, made all the others upset.A．which B．who C．what D．that12．After talking to Lucia about the advantages of the new robotic vacuum cleaner for hours, she was finally ________ buying one next month.A．in need of B．in defence of C．in place of D．in favor of13．At minus 130℃, a living cell can be ________ for a thousand years.A．preserved B．protected C．spared D．developed 14．History is the best teacher. It ________ records the development path of each country and foretells the future to us.A．apparently B．conventionally C．faithfully D．eventually 15．—The student union is looking for volunteers for the promotion of rubbish-sorting Would you like to join in?—________. Everyone should do his bit.A．You asked for it B．You betC．You have my word D．You’ve got me there二、完形填空On Christmas of 2017, I was born again. We like to spend our Christmas holidays somewhere warm abroad, and that year we 16 Uganda. Nature, wildlife, and sunny days were a 17 when it was so 18 and dark in Europe. Life was beautiful, and we had a rental car and a busy schedule ahead to explore the country.This is where this short travel story turns into one of my most 19 travel experiences. At Murchinson Falls National Park, we had a car accident. I lost 20 of the car, and it rolled over, destroying windows, chassis (底盘), and the engine. But we were alive! My right arm was 21 injured, but we 22 to walk to our lodge (旅馆)，not far inside the 23 . In the lodge,I was 24 to learn that there was a pretty decent American hospital in Masindi that was just a one-hour drive away. Moreover, one of the lodge’s guests was a nurse who 25 to the wound while we were waiting for the taxi. The hospital took care of us and after a couple of injections and stitches (缝合), I was 26 to head to our new hotel in Masindi; however, my wound required daily 27 and more injections, so we were 28 to stay in town for a few days.The town’s highlights were the market and our 29 visit to the hospital, so we 30 looking for the small things, 31 mod with the medical staff and the people in the market, and learning more about their customs.We learned to slow down. When we were allowed to 32 we took a road trip through the country to see something else. We did not care about our travel bucket 33 anymore—we were 34 , and we wanted to enjoy Uganda’s unique nature and its people. In the end, our Uganda trip was not about the places that we saw, but the people that we met. It was travel for 35 more than sightseeing.16．A．recommended B．chose C．predicted D．informed 17．A．blessing B．barrier C．limitation D．balance 18．A．complicated B．mysterious C．crowded D．cold 19．A．doubtful B．wonderful C．scary D．imaginary 20．A．sense B．sight C．control D．direction 21．A．severely B．permanently C．partly D．deliberately 22．A．discovered B．failed C．continued D．managed 23．A．spot B．accident C．country D．park 24．A．curious B．happy C．shocked D．creative 25．A．cleaned B．cured C．swept D．repaired 26．A．fortunate B．grateful C．ready D．relieved 27．A．movement B．dressing C．suffering D．exercise 28．A．asked B．forbidden C．permitted D．taught 29．A．occasional B．daily C．risky D．awful 30．A．put off B．carried on C．insisted on D．ended up 31．A．chatting B．arguing C．bargaining D．meeting32．A．exercise B．wander C．leave D．escape 33．A．guide B．list C．approach D．memory 34．A．awake B．sensitive C．allergic D．alive 35．A．experiment B．explanation C．experience D．reflection三、阅读理解Give a little sunshine!The Council on Aging (COA) runs a telephone friendship project called the Sunshine Call Program, matching over-60s with a friendly volunteer for a daily chat over the phone. The aim is simple — to help ease the loneliness and repair social networks.Are you ready to add a little sunshine to a senior’s life?The Sunshine Call Program initially links a volunteer with an isolate (独居的) senior for a daily call When comfortable the volunteer introduces a second senior to the call. Then another, until there are four seniors to one volunteer on what is essentially a conference call. Without having to leave the house, you will help the seniors meet and make new friends. They will then exchange phone numbers to chat on their own and reduce their isolation.What are the volunteer qualifications?V olunteers must have access to the Internet and be willing to be trained on the use of a chat app. COA will provide all supplies required to make the calls. Besides, volunteers must agree to participate in monthly meetings with other volunteers and guest speakers. All volunteers must be willing to provide a recent Criminal Record Check, the cost of which will be borne by COA．Andthe most important volunteer qualification is a sense of caring and a desire to help seniors in the community!If you wish to volunteer with our Sunshine Call program, never hesitate! Just CLICK HERE to fill out the application form.36．Why does the passage mention Sheila’s experience?A．To show her lonelinessB．To share a sweet memory.C．To stress the value of COA．D．To praise Rianne’s kindness.37．One of the responsibilities of volunteers is__________.A．making weekly calls to seniorsB．visiting seniors during holidaysC．introducing new friends to seniorsD．teaching seniors to use smart phones38．If you want to be a volunteer, what are you required to do?A．Learn the use of a chat app.B．Prepare a computer by yourself.C．Offer a letter of recommendation.D．Have relevant working experience.39．What is the purpose of the passage?A．To inform the readers of COA．B．To invite seniors to sign up for COAC．To introduce volunteer work in COA．D．To advertise for new volunteers for COA．40．Which of the following is the passage probably taken from?A．A newspaper for teenagers.B．A website of an organization.C．A guide for travelers.D．A magazine for the elderly.It probably was not easy to translate the tough talks at the high-level meeting between the U.S. and China in Anchorage. Chinese female translator Zhang Jing became an online hit in China for remaining unflustered(从容不迫的), graceful, and accurate.One video of the first session of the diplomatic talks shows how Yang Jiechi starts his response to the American side at 8.30 minutes, going on until the 24.36-minute mark. Next to him, interpreter Zhang Jing is fiercely taking notes. When Yang finishes speaking, he glances to foreign minister Wang Yi on his right to let him speak, after which Zhang says, “Shall I first translate?” While the U.S. side was awaiting the translation, Yang then says: “Ok, you translate,” adding in English: “It’s a test for the interpreter,” after which the American side says “We’re gonna give the translator a raise!” Zhang then goes ahead and calmly translates Yang’s entire 15-minute speech.To give a speedy translation of such a lengthy off-the-record speech is seen as a sign of Zhang’s utmost professionalism as an interpreter, which many on Weibo praise. “She’s my idol,” multiple people write.On Sunday, the hashtag “China-U.S. Talks Female Interpreter Zhang Jing” had reached 200 million views, but it is not the first time for Zhang, who was previously called “the most beautiful interpreter” of the National Congress in 2013.Being an interpreter is generally regarded an exciting and attractive job by many netizens, as the career involves much traveling and international contacts. But the ability to master another language than Chinese is also often admired.“Translators are usually the ‘heroes behind the scenes’, “one commenter writes, pointing out how rare it is for an interpreter to hit the limelight (聚光灯) like this.“There are still people saying it’s not important to learn English,” another Weibo user writes: “But if that were true, how could we educate brilliant interpreters like her? How else could we quarrel with Americans at the conference table?!”Many who write about Zhang on Weibo say that she is an example or a role model to them: “I hope that my spoken English one day would be as excellent as hers. This motivates me to try even harder.”41．We can infer that during the first session of the talk, ________.A．Zhang Jing seemed fierce because of Yang Jiechi’s long talkB．Zhang Jing wrote down fierce words in response to the US sideC．it was beyond Zhang Jing’s ability to follow Yang JiechiD．Zhang Jing concentrated on translating in an intense atmosphere.42．What does the underlined “it” in the fourth paragraph refer to?A．Zhang Jing was called “the most beautiful interpreter”.B．Zhang Jing became an online hit several years ago.C．Zhang Jing interpreted for the China-U.S. diplomatic talk.D．Zhang Jing gave a speedy translation of a long speech.43．Why did the American side say “We’re gonna give the translator a raise!“A．Because the American side wanted to employ Zhang Jing due to her talent.B．Because the American side thought Zhang Jing got a low salary.C．Because the American side considered Zhang Jing’s job quite tough.D．Because it was impossible for Zhang Jing to assume the task except by a pay rise. 44．Zhang Jing is taken as a good example of________.A．quarrelling with the American sidesB．enjoying an exciting and attractive jobC．showing the significance of learning English wellD．stressing the importance of educating brilliant interpreters45．Where does the passage least possibly taken from?A．Science report.B．The Internet.C．Wechat official account.D．Newspaper.As people are becoming more socially conscious about where their food comes from and how it impacts the planet, they are choosing animal-free plant-based options. Cow-free meat has been around for quite some time and the popularity of brands like Beyond Meat and cultivated meat from Aleph Farms and others are soaring. While there are a large number of plant-based milk substitutes, none of them have the same taste of cow’s milk. Now, an Israeli food-tech startup Remilk created real dairy products without harming a single cow or the planet.The company stresses that their product Remilk is not a milk substitute but rather is the realdeal. Made from a special process called microbial fermentation (微生物发酵), milk is manufactured in a lab instead of in a cow. And the end product is very healthy. “In a very simple way, we take the gene that encodes for the milk protein,” said Aviv Wolff, CEO of Remilk.”The gene functions as an instruction book for the production of the protein it encodes. And so, we insert the gene into a microbe that we’ve developed and it instructs our microbe to produce the specific protein in a very efficient way.”The company says that the lab-produced milk tastes identical to the real thing and they hope to eventually replace cows by creating every dairy product sold. They expect to roll out plant-based cheese and yogurt in addition to milk. “Remilk was founded with the mission to stop using animals to produce our food because, as dairy lovers, we realize that giving up on milk is not an option,” Wolff said. “But today’s milk comes with an unreasonable price tag. The dairy industry is destructive to our planet, our health, and our animals, and is simply not sustainable anymore.”The environmental price tag of dairy farming is way too high. According to the World Wildlife Fund, dairy cows add a huge amount of greenhouse gasses to the atmosphere and contribute to global warming and climate change as well as foul the air around them. Dairy operations consume large amounts of water and run-off of manure (粪肥) and fertilizers from these farms get into local waterways. The production of Remilk uses only 5 percent of the resources and produces only 1 percent of the waste of producing cow’s milk according to the company. And they accomplish this by being 100 percent cruelty-free unlike dairy farms. 46．What distinguishes Remilk from other milk substitutes?A．It enjoys broad popularity.B．It has the highest output.C．It comes in various flavours.D．It tastes the same as cow’s milk.47．What is paragraph 2 mainly about?A．The production of Remilk.B．The nutritional value of Remilk.C．The role of gene in making protein.D．The process of microbial fermentation.48．What can we know from Wolff’s words in paragraph 3?A．Remilk was set up for animal protection.B．Dairy industries should be shut down.C．Remilk aims to produce animal-free food.D．Prices of cow’s milk are soaring these days.49．What does the underlined word “foul” probably mean in the last paragraph?A．Clean.B．Heat.C．Pollute.D．Consume.50．What can we infer from the passage?A．Drawing on gene technology, Remilk has developed a variety of dairy products.B．Conventional dairy industry is anything but eco-friendly.C．The new technology adopted by Remilk transforms the gene of cows.D．It’ll be some time before the public get accustomed to the milk substitutes.“Girls are weak, and boys are strong. This is what is being subconsciously communicated to hundreds of millions of young boys and girls all over the world, just like it was with me,” said American actor Justin Baldoni. As a boy, all he wanted was to be accepted by other people. That acceptance meant he had to pretend to be strong when he was weak, confident when he felt insecure, and tough when he was actually hurting.Is that a healthy lifestyle? A member of the CPPCC Standing Committee might say “yes”. In his proposal, he spoke of a need to “prevent the feminization of male youths”. In response to his call, China’s Ministry of Education has recently demanded that schools should hire more physical education teachers and improve teaching methods to cultivate masculinity in students.The response has been widely debated online, with many people saying that it reinforces gender stereotypes. The state broadcaster CCTV wrote on its Weibo account, “Education is not simply about cultivating men and women. It’s more important to develop a willingness to take responsibility.” You might be wondering now: What is masculinity, and why is this so controversial?Well, by itself, “masculinity” refers to the qualities traditionally considered to be typical of men. While there is not really a single “correct” set of qualities, the term is often associated withstrength, courage, assertiveness, and emotional control. Sometimes, however, these seemingly admirable qualities can be extended in unrealistic ways. But boys are also human. Blindly asking them to control their feelings “like a man” can only increase their stress when they grow up.As an educator who has spent years teaching in China, I agree that attaching more importance to physical education would definitely benefit students. Sports provide opportunities for physical fitness. More importantly, they can help develop lifelong skills, such as leadership and communication skills. However, putting the emphasis on masculinity is far from a sound reason for which to do so.It is unnecessary for all boys to build up their muscles, but it is essential that they all learn how to be strong inside. It is also fine for boys to cry and to show their weakness. Schools should work on equipping students with the skills and values they will need to be successful in life, not reinforcing stereotypes of masculinity borrowed from a bygone age.51．Why did young Justin Baldoni think it necessary to pretend to be what he was actually not?A．He was trying to be strong and confident.B．He wanted to be accepted as a real man.C．It was necessary for an actor to be strong and tough.D．He felt it secure and safe to do so.52．The underlined expression “masculinity” in Paragraph 2 most probably means “__________”A．manly qualities B．potential abilitiesC．self-centredness D．steady strength53．What is the argument against the demand of China’s Ministry of Education?A．It is necessary to prevent the feminization of male youths.B．Physical education should be paid more attention to.C．We should teach students according to their individual qualities.D．Importance should be attached to developing students’ sense of responsibility. 54．What can we learn from the passage?A．Masculinity is out of date.B．Masculinity is overstated.C．Masculinity shows physical strength.D．Masculinity only focuses on physical fitness.55．What does the author want to say in the article?A．We should do everything we can to guarantee students’ health.B．Schools should differentiate between boys and girls while educating them.C．It is important to prepare students with necessary skills and right values.D．It is time to weaken stereotypes of masculinity.阅读下面短文，按照要求用英语回答问题。

重庆市沙坪坝区2024届高三上学期12月月考数学试题含答案

重庆市沙坪坝区2024届高三上学期12月月考数学试题含答案

2023年重庆高2024届12月月考数学试题卷（答案在最后）注意事项：1．答卷前，考生务必将自己的姓名、准考证号码填写在答题卡上．2．作答时，务必将答案写在答题卡上，写在本试卷及草稿纸上无效．3．考试结束后，将答题卡交回．一、单项选择题（本大题共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2101x A x x ⎧⎫+=≤⎨⎬-⎩⎭，集合(){}2ln 22B y y x x ==++，则A B = （）A.[]0,1 B.[)0,1 C.1,2⎡⎫-+∞⎪⎢⎣⎭D.1,12⎡⎤-⎢⎥⎣⎦【答案】B 【解析】【分析】解分式不等式求集合A ，求对数复合函数的值域求集合B ，应用集合交运算求结果.【详解】由(21)(1)0211011012x x x x x x +-≤⎧+≤⇒⇒-≤<⎨-≠-⎩，即1[,1)2A =-，由()2222111x x x ++=++≥，故[0,)B =+∞，所以[0,1)A B = .故选：B2.已知p ：双曲线C 的方程为22194x y -=，q ：双曲线C 的渐近线方程为23y x =±，则（）A.p 是q 的充要条件B.p 是q 的充分不必要条件C.p 是q 的必要不充分条件D.p 是q 的既不充分也不必要条件【答案】B 【解析】【分析】根据双曲线的性质，判断充分必要条件，即可判断选项.【详解】若双曲线C 的方程为22194x y -=，则渐近线方程为23y x =±，若双曲线C 的渐近线方程为23y x =±，则双曲线的方程为()22094x y λλ-=≠，所以p q ⇒，但q p ⇒/，所以p 是q 的充分不必要条件.故选：B3.()1:sin3010l a x y +︒++=，)2:20l x y +︒+=，若12l l ⊥，则实数a 的值为（）A.72-B.56-C.52D.16【答案】C 【解析】【分析】由直线垂直的充要条件列出方程结合特殊三角函数值运算即可.【详解】由题意12l l ⊥，则当且仅当()sin 3011tan1200a +⨯+=，即1302a +-=，解得52a =.故选：C.4.设22tan22.51tan 22.5a ︒=-︒，sin861cos86b ︒=+︒，c =，则有（）A.b a c <<B.a c b <<C.c b a <<D.b c a<<【答案】C 【解析】【分析】由倍角公式化简为正切函数，再结合正切函数的单调性可得出答案.【详解】22tan22.5=tan 451tan 22.5a ︒=︒-︒，22sin862sin43cos432sin43cos43=tan 431cos8612cos 4312cos 43b ︒︒︒︒︒===︒+︒+︒-︒，cos 47.5sin 42.5=sin 47.5cos 42.5c ︒︒=︒︒因为tan y x =在π0,2⎛⎫⎪⎝⎭上单调递增，所以tan 42.5tan 43tan 45︒<︒<︒，即c b a <<，故选：C .5.已知在四面体-P ABC 中，底面ABC，D 为PA 的中点，则直线BP 与直线CD 所成角的余弦值为（）A.24-B.24C.14-D.14【答案】B 【解析】【分析】利用中位线将异面直线所成角转化为相交直线DE 与DC 所成角，再利用余弦定理解三角形即可.【详解】取AB 中点E ，连接DE ，由D 为PA 中点，则//DE PB，且122DE PB ==；则EDC ∠（或其补角）即为直线BP 与直线CD 所成角.又底面三角形ABC是边长为的等边三角形，则中线长31522CE ==；在PAC △中，设中线长DC m =，则cos cos 0ADC PDC ∠+∠=，由余弦定理得,222222022DA DC AC DP DC PC DA DC DP DC +-+-+=⋅⋅，所以222222202m ⎛⎫+--= ⎪ ⎪⎝⎭，化简得23m =，解得m =，则有DC =，在DEC 中，由余弦定理得,222115324cos 224DE DC EC EDC DE DC +-+-∠==-⋅,直线BP 与直线CD 所成角为锐角，则余弦值为24.故选：B .6.教务处准备给高三某班的学生排周六的课表，上午五节课，下午三节课．若准备英语、物理、化学、地理各排一节课，数学、语文各排两节课连堂，且数学不排上午的第一节课，则不同的排课方式有（）A.216种B.384种C.408种D.432种【答案】D 【解析】【分析】由数学、语文不能同时安排在下午，分为数学（连堂）或语文（连堂）安排在下午、数学、语文都安排在上午，再应用分步计数及排列组合求不同的排课方式.【详解】由题意，数学、语文不能同时安排在下午，若数学（连堂）安排在下午，在英语、物理、化学、地理中选一种安排在下午有1242C A 8=种，再把余下的三科与语文（连堂）安排在上午，把上午看作四节课，则有44A 24=种，此时共有824192´=种；若语文（连堂）安排在下午，在英语、物理、化学、地理中选一种安排在下午有1242C A 8=种，再把余下的三科与数学（连堂）安排在上午，且数学不排上午的第一节课，把上午看作四节课，数学只能安排在后三节有13C 3=种，其余三科全排有33A 6=种，此时共有836144⨯⨯=种；若数学、语文都安排在上午，在英语、物理、化学、地理中选一种安排在上午有14C 4=种，将上午看作三节课，且数学不排上午的第一节课，有1222C A 4=种，再把余下的三科安排在下午作全排有33A 6=种，此时共有44696⨯⨯=种；综上，共有19214496432++=种.故选：D7.已知{}n a 为正项等比数列，且10121a =，若函数()212ln 1x f x x x -=-+，则()()()122023f a f a f a ++⋅⋅⋅+=（）A.2023B.2024C.20232D.1012【答案】A 【解析】【分析】由等比数列的性质可得222311202322012020211a a a a a a a ⋅=⋅=⋅===L ，再由题意可得出()12f x f x ⎛⎫+= ⎪⎝⎭，由倒序相加法可求出答案.【详解】因为{}n a 为正项等比数列，且10121a =，所以222311202322012020211a a a a a a a ⋅=⋅=⋅===L ，由()212ln 1x f x x x -=-+可得22111112ln 12ln 11x x f x x x x x⎛⎫- ⎪-⎛⎫⎝⎭=-+=++ ⎪⎝⎭，所以()12f x f x ⎛⎫+=⎪⎝⎭，所以设()()()122023S f a f a f a =++⋅⋅⋅+，则()()()202320221S f a f a f a =++⋅⋅⋅+，所以两式相加可得：222023S =⨯，故2023S =，故选：A .8.已知a = ，1= b ，0a b ⋅= ，4c a c a ++-= ，2430d b d -⋅+= ，则c d - 的最大值为（）A.22113+ B.4C.23+ D.313【答案】A 【解析】【分析】由题意首先得出c d -为两外切的圆和椭圆上的两点间的距离，再由三角形三边关系将问题转换为椭圆上点到另一个圆的圆心的最大值即可.【详解】如图所示：不妨设)()()()()13,0,0,1,,,,,3,0a OA b OB OC m n OD p q A ======-，满足3a = ，1= b ，0a b ⋅= ，又4c a c a ++-=()()22221334223m n m n a c A A ++-+=>=，由椭圆的定义可知点C 在以1,A A 为焦点，长轴长为4的椭圆上运动，222,3,431a c b a c ===--，所以该椭圆方程为2214x y +=，而2430d b d -⋅+= ，即22430p q q +-+=，即()2221p q +-=，这表明了点D 在圆()2221x y +-=上面运动，其中点()0,2E为圆心，1r =为半径，又1c d OC OD CD CE ED CE -=-=≤+=+，等号成立当且仅当,,C D E 三点共线，故只需求CE 的最大值即可，因为点C 2214x y +=在椭圆上面运动，所以不妨设()2cos ,sin C θθ，所以()()222224cos sin 241sin sin 4sin 43sin 4sin 8CE θθθθθθθ=+--+-+--+，所以当()42sin 233θ-=-=-⨯-且,,C D E 三点共线时，c d - 有最大值max113CE +==+.故选：A.【点睛】关键点睛：解题的关键是将向量问题转换为圆锥曲线中的最值问题来做，通过数学结合的方法巧妙的将几何问题融入代数方法，从而顺利得解.二、多项选择题（本大题共4小题，每小题5分，共20分．在每小题给出的四个选项中，有多项是符合题目要求的．全部选对的得5分，部分选对的得2分，有选错的得0分）9.已知左、右焦点分别为1F ，2F 的椭圆222:13x y C a +=的长轴长为4，过1F 的直线交椭圆于P ，Q 两点，则（）A.离心率2e =B.若线段PQ 垂直于x 轴，则3PQ =C.2PQF 的周长为8D.2PQF 的内切圆半径为1【答案】BC 【解析】【分析】首先由题意把参数a 求出来，根据平方关系、离心率公式运算即可判断A ；由题意将=1x -代入椭圆方程求出弦长即可判断B ；由椭圆定义即可判断C ；由2PQF 的周长是定值，但面积会随着直线的倾斜程度而变化，由此即可判断D.【详解】对于A ，由题意椭圆222:13x y C a +=的长轴长为4，所以124a =，解得22112,43a a b ==>=，所以12,1a a c =====，离心率为12c e a ==，故A 错误；对于B ，由A 可知椭圆方程为22143x y +=，由题意若直线PQ 的方程为=1x -，将其代入椭圆方程可得32y =±，即33322PQ ⎛⎫=--= ⎪⎝⎭，故B 正确；对于C ，2PQF 的周长为()()2212122248PQ QF F P PF PF QF QF a a a ++=+++=+==，故C 正确；对于D ，由题意直线PQ 斜率不为0且经过点()1,0-，不妨设直线()()1122:1,,,,PQ x my P x y Q x y =-，将其与椭圆方程22143x y +=联立消去x 得()2234690m y my +--=，()()2221212226936363414410,,3434m m m m y y y y m m -∆=++=+>+==++，一方面()()()()222221212121222222363413612142343434PQF m m m S F F y y y y y y m m m ++=-=+-++++ ，另一方面，由C 选项分析可知228PQ QF F P ++=，不妨设2PQF 的内切圆的半径为r ，所以()222142PQF S PQ QF F P r r =++= ，对比两式可知223134m r m +=+，即r 与m 有关，故D 错误.故选：BC.10.与二项式定理()0C nnk n k k n k a b a b -=+=∑类似，有莱布尼兹公式：()()()()()()()()()()()()0112200120C C C C C nn n n n n n k kn k nnnnn n uv u vuv uv u vuv ---==+++⋅⋅⋅+=∑，其中()k u （0,1k =，2，…，n ）为u 的k 阶导数，()0u u =，()0v v =，则（）A.1C2nknnk ==∑ B.1351C C C 2n n n n -+++⋅⋅⋅=C.()()()()nnuv vu = D.()6e x f x x =，则()()606!f =【答案】BCD 【解析】【分析】由二项式定理，分别赋值,a b ，即可判断AB ；再根据莱布尼兹公式，结合组合数公式和性质，即可判断CD .【详解】A.由二项式定理可知，当1a b ==时，()0C 1111C 2nnnnk n k k k nn k k -==+===∑∑，1C221nkn n k n n C ==-=-∑，故A 错误；B.由二项式定理可知，当1,1a b ==-时，()012345.1C C C C C C .1.nn n n n n n =-+-+-+-()()024135C C C ...C C C ...0n n n n n n =+++-+++=，所以024135C C C ...C C C ...n n n n n n +++=+++又由A 可知，012345C C C C C C ...2nn n n n n n ++++++=，所以1351C C C 2n n n n -+++⋅⋅⋅=，故B 正确；C.()()()()()()()()()()011220012C C C ...C nn n n n n n n n n uv u v u v u v u v--=++++()()()()()()()()()()011220012C C C ...C nn n n n n n n n n vu v u v u v u v u--=++++，由组合数的性质可知，0C C n n n =，11C C n n n -=，22C C n n n -=，……，可知，()()()()n nuv vu =，故C 正确；D.()()()()()()()()()()()()()()()()()()6605142066061626666666e C e C e C e ...C e x xx xx x x x x x =++++，因为()()e e n xx =，()()066x x =，()()1656x x =，()()26465x x =⋅⋅，()()363654x x =⋅⋅⋅，()()4626543x x =⋅⋅⋅⋅，()()5665432x x =⋅⋅⋅⋅⋅，()()666543216!x =⋅⋅⋅⋅⋅=，所以()()606!f =，故D 正确.故选：BCD11.全球有0.5%的人是高智商，他们当中有95%的人是游戏高手．在非高智商人群中，95%的人不是游戏高手．下列说法正确的有（）A.全球游戏高手占比不超过10%B.某人既是游戏高手，也是高智商的概率低于0.1%C.如果某人是游戏高手，那么他也是高智商的概率高于8%D.如果某人是游戏高手，那么他也是高智商的概率低于8.5%【答案】AC 【解析】【分析】利用全概率公式和条件概率定义进行计算.【详解】A 项，高智商中有的人是游戏高手概率为0.0050.950.00475⨯=，非高智商人群中是游戏高手的概率为0.9950.050.04975⨯=，所以全球游戏高手占比为0.004750.049750.05450.1+=<，所以A 项正确；B 项，既是游戏高手，也是高智商的概率为0.0050.950.004750.001⨯=>，所以B 项错误；C 项，设事件A 为某人是游戏高手，事件B 为某人是高智商，则()0.0545P A =，则()()()0.0050.9519|0.0870.080.0545218P AB P B A P A ⨯===≈>，所以C 项正确；D 项，由C 项知，()19|0.0870.085218P B A =≈>，所以D 项错误.故选：AC.12.已知定义在()0,∞+上的函数()f x 满足()()2ln ln 2xf x f x x x +'+=，()11f =，且实数()a f x <对任意0x >都成立（ln20.693≈，ln3 1.098≈），则（）A.()18f ''= B.()f x 有极小值，无极大值C.()f x 既有极小值，也有极大值D.23<a 【答案】ABD 【解析】【分析】将题设条件化为()222[][ln ]x f x x x ''=，进而有()222ln x f x x x C =+，其中C 为常数，()0,x ∈+∞，根据已知求得()221ln f x x x =+，对函数求导判断A 、B 、C ；问题化为()0,x ∈+∞上()min a f x <，结合()f x 的极值()2200222000111ln (f x x x x x =+=+且0(1,2)x ∈求参数范围判断D.【详解】由题设()()222(ln ln )f x xf x x x =+'+，则()()2222(ln ln )xf x x f x x x x x +'+=，所以()222[][ln ]x f x x x ''=，故()222ln x f x x x C =+，其中C 为常数，()0,x ∈+∞，又()11f =，则()11f C ==，所以()222ln 1x f x x x =+，即()221ln f x x x=+，所以()32ln 2x f x x x '=-，故()242(1ln )6x f x x x-''=+，则()18f ''=，A 对；由()232(ln 1)x x f x x -'=且()0,x ∈+∞，令21ln ()x x x g =-在()0,x ∈+∞上递增，(1)10g =-<，1ln 20.4430)4(2g -=≈>，故0(1,2)x ∃∈使0()0g x =，即0201ln x x =，0(0,)x 上()0g x <，即()0f x '<，()f x 递减；0(,)x +∞上()0g x >，即()0f x ¢>，()f x 递增；所以()f x 有极小值，无极大值，B 对，C 错；由题设，()0,x ∈+∞上()min a f x <，即()2200222000111ln ()f x x a x x x =+=+>，令2011(,1)4t x =∈，则()20f x y t t ==+在1(,1)4t ∈上递增，故()05(,2)16f x y =∈，所以52163a ≤<，D 对.故选：ABD【点睛】关键点睛：根据题设条件得到()222[][ln ]x f x x x ''=，进而求得()221ln f x x x =+为关键.三、填空题（本大题共4小题，每小题5分，共20分）13.已知数列{}n a 满足211n n n a a a +-+=，且113a =，则9a =______．【答案】13【解析】【分析】先求得数列的周期性，再应用周期性求值即可.【详解】由211n n n a a a +-+=，得2421111211211nn n nn n n n n a a a a a a a a a +++---+====-+++，则95113a a a ===.故答案为：13.14.已知()220x x m m -+=∈R 的两共轭虚根为1x ，2x，且12x x +=，则m =______．【答案】3【解析】【分析】由根与系数关系有12122x x mx x =⎧⎨+=⎩，设11i x a =+，21i x a =-且R a ∈，结合题设和复数模长、乘法运算求参数.【详解】由题设12122x x mx x =⎧⎨+=⎩，可令11i x a =+，21i x a =-且R a ∈，所以2122x x a +==⇒=，所以21213x x a m =+==.故答案为：315.已知圆()()22:344C x y -+-=，过直线:4310l x y ++=上一动点P 作圆C 的两条切线，切点分别为A ，B ，则PA PB +的最小值为______．【答案】425【解析】【分析】首先利用图形，解决向量的运算，再利用PC 的最小值，即可求解.【详解】如图，连结,CA CB ，CA PA ⊥，CB PB ⊥，AB 和CP 交于点D ，2PA PB PD += ，因为2PA PD PC =，所以2244PAPC PD PC PCPCPC-===-,设4y x x=-，易知其在()0,∞+为增函数，则PC 的最小值为圆心()3,4C 到直线:4310l x y ++=的距离5d ==，所以PD 的最小值为421555-=，那么PA PB + 的最小值为425.故答案为：42516.正方体1111ABCD A B C D -棱长为2，E ，F 分别是棱CD ，1DD 的中点，M 是正方体的表面上一动点，当四面体BEFM 的体积最大时，四面体BEFM 的外接球的表面积为______．【答案】11π【解析】【分析】根据题意只需M 点离平面1BEFA 最远即可，构建空间直角坐标系，应用向量法求各点到面1BEFA 距离得到M 与1C 重合，再将1EFC △置于如下直角坐标系中求1EFC △外接圆圆心，进而确定空间坐标系中外接球球心O 坐标，即可求球的表面积.【详解】如下图，11////EF CD BA ，即1,,,B E F A 四点共面，要使四面体BEFM 的体积最大，只需M 点离平面1BEFA 最远即可，显然点D 、线段1CD 上点到平面1BEFA 距离都相等，构建下图空间直角坐标系D xyz -，则(0,1,0),(0,0,1),(2,2,0)E F B ，所以(0,1,1),(2,1,0)EF EB =-= ，若面1BEFA 的一个法向量为(,,)m x y z =，则020EF m y z EB m x y ⎧⋅=-+=⎪⎨⋅=+=⎪⎩ ，令2y =，则(1,2,2)m =- ，而11(0,2,0),(0,2,2),(2,0,0),(2,2,2)C C A B ，则(0,2,0)AB = ，(0,1,0)EC =，1(0,1,2)EC = ，1(0,0,2)BB =，所以A 到面1BEFA 距离为||43||m AB m ⋅= ，C 到面1BEFA 距离为||23||m EC m ⋅= ，1C 到面1BEFA 距离为1||2||m EC m ⋅= ，1B 到面1BEFA 距离为1||43||m BB m ⋅=，综上，正方体的表面上1C 到面1BEFA 距离最远，故四面体BEFM 的体积最大，M 与1C重合，首先确定1EFC △外接圆圆心1O 坐标，将1EFC △置于如下直角坐标系中，则1(2,2),(0,1),(1,0)C F E ，则1O 是直线1:DC y x =与1FC 的垂直平分线l 的交点，由112FC k =，则2l k =-，且1FC 中点为3(1,)2，故3:2(1)2l y x -=--，即:4270l x y +-=，联立76427076x y x x y y ⎧=⎪=⎧⎪⇒⎨⎨+-=⎩⎪=⎪⎩，即177(,)66O 对应到空间直角坐标系的坐标为177(0,,66O ，由四面体BEFM 的外接球球心O 在过1O 垂直于面1EFC 的直线上，设77(,,66O n ，由||||OB OE ==76n =，=24π11π⨯=.故答案为：11π【点睛】关键点点睛：利用向量法求出正方体的表面上到面1BEFA 距离最远的点为关键.四、解答题（共70分．解答应写出文字说明，证明过程或演算步骤）17.疫情结束之后，演唱会异常火爆．为了调查“喜欢看演唱会和学科是否有关”，对本年级的100名老师进行了调查．附：()()()()()22n ad bc a b c d a c b d χ-=++++，其中n a b c d =+++．()20P k χ≥0.0500.0100.0010k 3.8416.63510.828（1）完成下列22⨯列联表，并判断是否有95%的把握认为本年级老师“喜欢看演唱会”与“学科”有关；喜欢看演唱会不喜欢看演唱会合计文科老师30理科老师40合计50（2）三楼大办公室中有11名老师，有4名老师喜欢看演唱会，现从这11名老师中随机抽取3人，求抽到的3人中恰有1人喜欢看演唱会的概率．【答案】（1）列联表见解析，有95%的把握认为本年级老师“喜欢看演唱会”与“学科”有关（2）2855【解析】【分析】（1）根据表格进行运算即可得到完整的列联表，再根据卡方计算公式运算对比临界值即可求解.（2）根据超几何分布的概率计算公式进行运算即可求解.【小问1详解】由表可知喜欢看演唱会的理科老师有503020-=人，理科老师共有204060+=人，文科老师共有1006040-=人，不喜欢看演唱会的文科老师有403010-=人，不喜欢看演唱会的人有104050+=人，完成22⨯列联表如下表所示：喜欢看演唱会不喜欢看演唱会合计文科老师301040理科老师204060合计5050100()()()()()()22210012002005016.667 3.841406050503n ad bc a b c d a c b d χ-⨯-===≈>++++⨯⨯⨯，故有95%的把握认为本年级老师“喜欢看演唱会”与“学科”有关.【小问2详解】由题意11名老师中，有4名老师喜欢看演唱会，有7名老师不喜欢看演唱会，若从这11名老师中随机抽取3人，求抽到的3人中恰有1人喜欢看演唱会，则只能从4名喜欢看演唱会的老师中抽取1人，从7名不喜欢看演唱会的老师中抽取2人，即所求的概率为1247311C C 42128C 16555p ⨯===.18.如图，在直三棱柱111ABC A B C -中，18AA =，6AB =，E ，F 为1CC 上分别靠近C 和1C 的四等分点，若多面体11AA B BEF 的体积为40．（1）求EF 到平面11AA B B 的距离；（2）求二面角1E AB B --的大小．【答案】（1）2；（2）π4.【解析】【分析】（1）由直三棱柱结构特征有11//CC AA ，应用线面平行判定证1//CC 面11AA B B ，问题化为求C 到面11AA B B 的距离，再结合面ABC ⊥面11AA B B ，进一步化为求ABC 中AB 上的高h ，根据多面体体积列方程求结果；（2）过C 作CD AB ⊥于D ，过E 作EH ⊥面11AA B B 于H ，连接,DH DE ，证AB ⊥面CEHD ，进而有EDH ∠为二面角1E AB B --的平面角，即可求大小.【小问1详解】直三棱柱111ABC A B C -中11//CC AA ，1CC ⊄面11AA B B ，1AA ⊂面11AA B B ，所以1//CC 面11AA B B ，即//EF 面11AA B B ，只需求C 到面11AA B B 的距离，又面ABC⊥面11AA B B ，面ABC ⋂面11AA B B AB =，则C 在面11AA B B 上的射影在直线AB 上，即C 到面11AA B B 距离为ABC 中AB 上的高h ，又E ，F 为1CC 上分别靠近C 和1C 的四等分点，且多面体11AA B BEF 的体积为40，所以111118622640232AA B BEF V h h =⨯⨯-⨯⨯⨯⨯=，可得2h =，即EF 到平面11AA B B 的距离为2.【小问2详解】过C 作CD AB ⊥于D ，过E 作EH ⊥面11AA B B 于H ，连接,DH DE ，由（1）分析易知：,//CD EH CD EH =，即四边形CEHD 为平行四边形，由1CC ⊥面ABC ，AB ⊂面ABC ，则1CC AB ⊥，由1CD CC C = ，1,CD CC ⊂面CEHD ，则AB ⊥面CEHD ，而,DE DH ⊂面CEHD ，则AB DH ⊥，AB DE ⊥，故EDH ∠为二面角1E AB B --的平面角，由（1）知：2EH CD h ===，2CE DH ==，所以tan 1EH EDH DH ∠==，故锐二面角1E AB B --为π4.19.已知数列{}n a 满足12a =，23a =，且()*2123n n n a a a n +++=∈N．（1）求证：数列{}1n n a a +-为等比数列；（2）若()1111nn n n b a a +⎛⎫=-+⎪⎝⎭，求数列{}n b 的前n 项的和n S ．【答案】（1）证明见解析（2）1(1)221n n--++【解析】【分析】（1）根据已知等式变形得()2112n n n n a a a a +++-=-，利用等比数列的定义证明即可；（2）对项数n 分奇偶讨论，由裂项相消法求和可得.【小问1详解】()*2123n n n a a a n +++=∈N ，且12a =，23a =，()()*2112n n n n a a a a n +++∴=-∈-N ，且2110a a -=≠，()*2112n n n na a n a a +++=--∈∴N ，故数列{}1n n a a +-是以1为首项，2为公比的等比数列.【小问2详解】由（1）知，112n n n a a -+-=，则有211a a -=，322a a -=，21,2n n n a a ---= ，各式相加得122111212222112n n n n a a ----=++++==--- ，又12a =，则121n n a -=+.()1111n n n n b a a +⎛⎫=-+ ⎪⎝⎭，则当n 为奇数时，122334111111111111n n n n n a a a S a a a a a a a -+⎛⎫⎛⎫⎛⎫⎛⎫⎛⎫=-+++-+++-+ ⎪ ⎪ ⎪ ⎪⎪⎝⎭⎝⎭⎝⎭⎝⎭⎝⎭111111221n n a a +=--=--+；当n 为偶数时，122334111111111111n n n n n a a a S a a a a a a a -+⎛⎫⎛⎫⎛⎫⎛⎫⎛⎫=-+++-++-++⎪ ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭⎝⎭⎝⎭ 111111221n n a a +=-+=-++；综上所述，1(1)221n n n S -=-++.20.在锐角ABC 中，角A ，B ，C 所对的边分别为a ，b ，c ，且a ，b ，a c +成等比数列．（1）若π5A =，求角C ；（2）若ABC 的面积为S ，求2Sa 的取值范围．【答案】（1）2π5C =；（2）13(,22.【解析】【分析】（1）由题设可得22b a ac -=，结合余弦定理可得2cos c a a B =+，应用正弦边角关系、三角恒等变换可得sin()sin B A A -=，进而有B A A -=，即可求角C ；（2）由（1）有2B A =，结合锐角三角形得ππ64A <<，应用三角形面积公式、三角恒等变换可得2222tan (3tan )(1tan )S A A a A -=+，令tan 3t A =∈，利用导数求等式右侧单调性，再求值域即得范围.【小问1详解】由题设2()b a a c =+，即22b a ac -=，且π()C A B =-+，由2222cos 2cos b a c ac B a c a B =+-⇒=-，即2cos c a a B =+，所以sin sin 2sin cos C A A B =+，即sin()sin 2sin cos A B A A B +=+，所以cos sin sin sin cos A B A A B =+，故sin()sin B A A -=，所以B A A -=或πB A A -=-（舍），可得2π25B A ==，故2π5C =.【小问2详解】由（1）知2B A =，ABC 为锐角三角形，则π02π022π0π32A A A ⎧<<⎪⎪⎪<<⎨⎪⎪<-<⎪⎩，可得ππ64A <<，又1sin 2S ac B =，则2sin sin sin sin(3)sin(2)22sin 2sin S c B C B A A a a A A===，所以221sin(3)cos sin cos cos 2cos sin 2sin 2(cos 2)2S A A A A A A A A A a ==+=+，又22tan sin 21tan A A A =+，221tan cos 21tan A A A -=+，故22222tan 1tan 1()1tan 1tan 2S A A a A A -=⨯+++，整理得2222tan (3tan )(1tan )S A A a A -=+，令3tan 3t A =∈，则32223()(1)S t t f t a t -==+，所以2423312()(1)t t f t t -+'=+，令42()123g t t t =-+，则2()4(6)0g t t t '=-<，故()g t在,1)3t ∈上递减，8()()039g t g <=-<，即()0f t '<，所以()f t在(,1)3t ∈上递减，故322231()(,)(1)22S t t f t a t -==∈+.21.已知抛物线2:4y x Γ=的准线l 交x 轴于M ，过()1,1P -作斜率为1k 的直线1l 交Γ于,C D ，过()1,1Q --作斜率为2k 的直线2l 交Γ于,E G ．（1）若抛物线的焦点2F l ∈，判断直线l 与以EG 为直径的圆的位置关系，并证明；（2）若,,C E M 三点共线，①证明：21k k -为定值；②求直线1l 与2l 夹角θ的余弦值的最小值．【答案】（1）相切，证明见解析（2）①1；②35【解析】【分析】（1）将直线EG 和抛物线联立，利用韦达定理，求出线段EG 的中点和长度，即可得以EG 为直径的圆的方程，通过判断圆心与直线l 的距离与半径的大小关系来去顶直线与圆的位置关系；（2）①设221212,,,44y y C y E y ⎛⎫⎛⎫ ⎪ ⎪⎝⎭⎝⎭，通过,,C E M 三点共线即斜率相等可得124y y =，再将其代入21212221111144y y k k y y +--=-++计算即可；②设直线12,l l 的倾斜角分别为,αβ，()2121tan tan tan tan 1tan tan 1k k k k βαθβαβα--=-==++，通过21,k k 的关系代入消2k ，通过直线和抛物型线相交，利用判别式求出1k 的范围，进而可得最值.【小问1详解】若抛物线的焦点2F l ∈，则直线EG 即为直线QF ，又()1,0F 故()10:111EG l y x --=---，整理得:210EG l x y --=联立22104x y y x--=⎧⎨=⎩，消去x 得2840y y --=，6416800D =+=>则8E G y y +=，124y y =-，所以()2218E G E G x x y y +=++=，且20EG =，故以EG 为直径的圆的圆的方程为()()2294100x y -+-=，其圆心为()9,4，半径为10，所以以EG 为直径的圆的圆心到直线l 的距离为9110+=，故直线l 与以EG 为直径的圆相切；【小问2详解】①设221212,,,44y y C y E y ⎛⎫⎛⎫ ⎪ ⎪⎝⎭⎝⎭，又()()()1,0,1,1,1,1M P Q ----，因为,,C E M 三点共线，所以CE CM k k =，即1212221211444y y y y y y -=-+，整理得124y y =，所以()()2212212121222221211111441111114444y y y y y y k k y y y y ⎛⎫⎛⎫++--+ ⎪ ⎪+-⎝⎭⎝⎭-=-=⎛⎫⎛⎫++++ ⎪⎪⎝⎭⎝⎭()222212112212122122222211221112444444121441644y y y y y y y y y y y y y y y y y y ⎛⎫+++-+-- ⎪++⎝⎭===+++++,即21k k -为定值1；②设直线12,l l 的倾斜角分别为,αβ，则()()21221111tan tan 11tan tan 1tan tan 1111324k k k k k k k βαθβαβα--=-====++++⎛⎫++ ⎪⎝⎭由已知可得()11:11l y k x =++，联立()12114y k x y x⎧=++⎨=⎩，消去x 得2114440y y k k -++=，所以21144440k k ⎛⎫⎛⎫∆=-+> ⎪ ⎪⎝⎭⎝⎭，解得11122k ---+<<，当112k =-时，()max 14tan 334θ==，此时θ最大，cos θ最小，此时由22sin 4cos 3sin cos 1θθθθ⎧=⎪⎨⎪+=⎩，解得3cos 5θ=.即直线1l 与2l 夹角θ的余弦值的最小值为35.【点睛】关键点睛：本题关键是在解答第（2）①中设出点的坐标，将条件和目标式都坐标化，从而可以真正的通过计算得出结论.22.已知()()()2341e 3x f x x kx kx k =--+∈R （1）当0k =时，求()f x 过点()()1,1f 的切线方程；（2）若对[]1,2k ∀∈，[]0,x k ∈，不等式()f x a ≤恒成立，求实数a 的取值范围．[参考不等式：()21e 102x x x x ≥++≥]【答案】（1）22e e 0x y --=；（2）452e 3a ≥-.【解析】【分析】（1）利用导数的几何意义求切线方程；（2）构造()2()1e x g x x =-、343()kx kx h x =-并应用导数研究单调性，进而判断[]0,x k ∈上()()()f x g x h x =-最大值所在区间，利用导数研究()f x 在1(,]2x k ∈的最值，得到242max 4()(1)e 3k f x k k k =--+，利用导数求右侧最大值，即可得参数范围.【小问1详解】由题设()()21e x f x x =-，则()()221e xf x x '=-，所以()10f =，()21e f '=，故过点()()1,1f 的切线方程为2(e 1)y x =-，即为22e e 0x y --=.【小问2详解】下述过程均在[]1,2k ∈且[]0,x k ∈条件下，令()2()1e x g x x =-，则()2()21e xg x x '=-，令1()02g x x '=⇒=，故1[0,)2x ∈上()0g x '<，()g x 递减，1(,]2x k ∈上()0g x '>，()g x 递增，且21e (0)1,(,()(1)e 22k g g g k k =-=-=-，令343()kx kx h x =-，则2)()(41x h x k '-=，令1()02h x x '=⇒=，故1[0,)2x ∈上()0h x '<，()h x 递减，1(,]2x k ∈上()0h x '>，()h x 递增，且2214(0)0,(),()(1)233k h h h k k k ==-=-，由()()()f x g x h x =-，而11(0)((0)()22h h g g >>>，故1[0,2x ∈上()0f x <，32k =时33e 39()()()()2222g k g h k h ==>==，故1(,]2x k ∈上可能存在()0f x >（特殊值法判断最大值可能区间），要使不等式()f x a ≤恒成立，即max ()a f x ≥，只需找到1(,]2x k ∈上max ()f x ，在1(,]2x k ∈上2(21)(e 2)()x f x kx k x =-'--，显然210x ->，且()010f =-<，令22()e x kx k x ϕ=--且1(,]2x k ∈，则2e )0()2(x x k ϕ=->'且为增函数，若e [1,]2k ∈时01()()22e k x ϕϕ>=≥-，即()0f x '≥，()f x 递增，则max ()()f x f k =；若e (,2]2k ∈时e 01()22k ϕ=<-，22112(220))12(k k k k k k ϕ≥++⋅--=+>，所以01(,]2x k ∃∈使0200e 20()x x k x k ϕ--==，即020e 2x kx k =+，此时01(,)2x x ∈上()0f x '<，()f x 递减，0(,]x x k ∈上()0f x '>，()f x 递增，1e 0232k f ⎛⎫=-< ⎪⎝⎭，故01(,)2x x ∈上()0f x <，只需()0f k >则必为最大值，此时max ()f x 在0(,]x x k ∈上右侧端点上取得；综上，在[]1,2k ∈上确定2424()(1)e 3kf k k k k =--+的最大值即可，令2424()(1)e 3k k k k k φ=--+，[]1,2k ∈，则2316()(21)e 23k k k k k φ'=--+，令()()k k ηφ'=，则2()4(e 4)2k k k k η'=-+，对于2e 4k y k =-有22e 40k y '=->，即2e 4k y k =-在[]1,2k ∈上递增，所以22e 4e 40k y k =->->，即()0k η'>，则()()k k ηφ'=递增，所以216()(1)e 203k φφ''>=+->，即()k φ递增，则4max 52()(2)e 3k φφ==-，故4max 52()e 3f x =-，即452e 3a ≥-.【点睛】关键点睛：第二问，构造中间函数研究()f x 最大值位置，进而得到max ()f x 关于参数k 的表达式为关键.。

湖北省武汉市2023-2024学年高三12月月考生物试题含解析

湖北省武汉市2023-2024学年高三12月月考生物试题含解析

2023-2024学年度水果湖高中生物12月月考卷（答案在最后）考试时间：75分钟；注意事项：1．答题前填写好自己的姓名、班级、考号等信息2．请将答案正确填写在答题卡上第I卷（选择题）一、单选题1.蓝细菌和酵母菌的相同之处是A.都有拟核B.均能进行需（有）氧呼吸C.都有线粒体D.均能进行光合作用【答案】B【解析】【详解】蓝细菌为原核生物，酵母菌为真核生物。

原核生物无真正细胞核，只有拟核，真核生物有真正细胞核，故A错误；蓝细菌进行有氧呼吸供能，酵母菌为兼性厌氧，可以进行有氧呼吸和无氧呼吸，故B正确。

原核生物只有核糖体，无其他细胞器，故C错误；蓝细菌有光合色素，可以光合作用，酵母菌无光合色素和叶绿体，不能光合作用，故D错误。

【点睛】本题考查原核生物和真核生物相关知识，意在考查考生能理解所学知识的要点，把握知识间的内在联系，形成知识的网络结构能力。

2.关于细胞学说的建立过程及内容要点，叙述正确的有几项（）①细胞是一个有机体，一切动植物都由细胞发育而来，并由细胞和细胞产物所构成②细胞学说揭示了细胞的多样性和生物体结构的统一性③施莱登和施旺是细胞学说的建立者④细胞学说认为细胞分为原核细胞和真核细胞⑤列文虎克发现并命名了细胞⑥细胞学说的建立，标志着生物学研究由细胞水平进入了分子水平⑦魏尔肖提出所有的细胞都来源于先前存在的细胞A.6项B.5项C.4项D.3项【答案】D【解析】【分析】细胞学说的主要内容：①细胞是一个有机体，一切动植物都由细胞发育而来，并由细胞和细胞产物所构成。

②细胞是一个相对独立的单位，既有它自己的生命，又对与其他细胞共同组成的整体生命起作用。

③新细胞由老细胞分裂产生。

【详解】①细胞学说的主要内容之一是：细胞是一个有机体，一切动植物都由细胞发育而来，并由细胞和细胞产物所构成，①正确；②细胞是生物体的结构和功能的基本单位，细胞学说揭示了细胞的统一性，没有揭示细胞的多样性，②错误；③细胞学说的主要建立者是施莱登和施旺，③正确；④细胞学说并未对细胞进行原核细胞和真核细胞的分类，④错误；⑤发现并命名细胞的是罗伯特⋅胡克，⑤错误；⑥细胞学说的建立，标志着生物学研究进入了细胞水平，⑥错误；⑦所有的细胞都来源于先前存在的细胞，是魏尔肖对细胞学说的补充，属于细胞学说的内容，⑦正确。

江苏省海安高级中学2023-2024学年高三上学期12月月考英语试题

江苏省海安高级中学2023-2024学年高三上学期12月月考英语试题

江苏省海安高级中学2023-2024学年高三上学期12月月考英语试题学校:___________姓名：___________班级：___________考号：___________一、阅读选择Four of the best films to watch in this winterThe Hunger Games: The Ballad of Songbirds and SnakesIt’s prequel time again. Based on the dystopian YA (Young Adult Fiction) by Suzanne Collins, the prequel is set 64 years before the previous Hunger Games films. Donald Sutherland’s character, Coriolanus Snow, is now a teenager played by Tom Blyth, and Rachel Zegler is the woman he has to train for the Capitol’s 10th annual death match.Released internationally from 15 NovemberThe MarvelsBrie Larson’s Captain Marvel returns to save the planet from evil aliens, but her job is made considerably harder this time by a cosmic fault that links her to two other super heroines. Every time she uses her powers, she swaps places with cither Photon (Teyonah Parris) or Ms Marvel (lman Vellani). “The worlds we go to in this movie are worlds unlike others you’ve seen in the MCU. Bright worlds that you haven’t seen before, “ the Director Nia DaCosta told Total film.Released internationally from 8 NovemberWishWalt Disney celebrates its 100th anniversary with a cartoon that includes the themes and animation styles of the studio’s first century. Directed by Chris Buck (co-director of Frozen) and Fawn Veerasunthorn, Mish is a musical fairy tale set in a magical land where King Magnifico(Chris Pine) can grant his citizens’ wishes. But a 17-year-old girl, Asha (Ariana DeBose), questions whether the king should keep that power all to himself. She wishes on a star-and the star then falls from the sky to help her. Buck told Jackson Murphy at Animation Scoop that the film is “kind of our love letter to Disney, to Walt.”Released internationally from 22 November.NapoleonRidley Scott’s 28th film is an epic biopic of Napoleon Bonaparte, with Joaquin Phoenix as the French general, and V anessa Kirby as his wife Josephine. It’s reported to be three hourslong, with six major battle sequences-although it’s as much a character-driven drama as it is a war movie.On general release from 22 November1．Which of the four films was released earliest?A．The Hunger Games.B．The Marvels.C．Wish.D．Napoleon.2．Which of the following is TRUE according to the passage?A．Ridley Scott was cast as the famous French general.B．Donald Sutherland is now a teenager played by Tom Blyth.C．Elements of the studio’s first century will be displayed in Wish.D．Captain Marvel’s job is easier with the help of two other super heroines.3．In which column will you probably find this passage?A．Lifestyle.B．Business.C．Affairs.D．Entertainment.Somewhere my acquaintance with the computer started when I was working on my thesis. I was initiated into it, quite unintentionally, when I was looking for a convenient way to store my research material. I have since been busy communicating with my readers and students through the net. I can hardly believe it myself that a technophobe like me could somehow get engaged with the most modern technology!Our son has left for university and our spoilt daughter has gone overseas. Since they left home the net has become the best way for our family to communicate and share our feelings.We started off sending messages by email only -just to say hello, to seek help and to caution. Messages such as: “Please have a look at this email. I can’t open it. “Or, one that I sent to my daughter says: “So you rang to say you’d lost your credit card. The very thing that I’ve been worrying about! If you don’t try hard to mend your careless ways, you’ll wake up one morning and find that you’ve lost your brain as well.”And my son’s messages are typical in their sensational (耸人听闻的) headings, such as “Help me please!” “Help again, please!” They are always about money, no different from the notes he left when he was young. My daughter, on the other hand, would persuade her elder brother like a grand old lady: “Don’t upset Mum when I’m not home. Go back to see Mum and Dad every now and then. They’ve only got you and me.”Recently, our son has been emailing me all kinds of articles: funny, touching,intellectual. . . the lot. Recommended rending, he said, which would help me understand my students’ ideas and keep abreast of the times, so I wouldn’t be written off as over-the-hill too soon. I read the articles religiously, like an obedient pupil. I appreciate my son’s good will with mixed feelings. The kid I was bombarding with newspaper clippings not that long ago has now become my mentor! He must be thinking that his mother is still willing to embrace new ideas. That makes me fecl proud, despite the confusing sense of role reversal that I have.Through the net, we chat, exchange ideas and encourage each other with a gentle and beautiful language we seldom use. Every time I sit in front of the computer and read those instant messages, I feel warmth welling up in my heart and a profound gratitude to modem technology.4．The author got acquainted with the net initially to ________.A．keep pace with the times B．communicate with her readersC．meet academic needs D．exchange ideas with her children 5．Why did the author mention so many messages in paragraph 3?A．To show her daughter’s immaturity.B．To indicate the net’s influence on her.C．To blame her daughter’s carelessness.D．To express her love for her children.6．Which of the following can best describe the author in the son’s eyes?A．Flexible.B．Well-educated.C．Obedient.D．Old-fashioned. 7．Which of the following is the best title for the passage?A．It Is the Power of the Net B．Technology Changes LifeC．Here Comes a Cyber Mum D．Mum’s Role ChangesYoung children are always watching-including when people swap spit through actions like food sharing. Such behavior helps babies infer who is in close relationships with one another, a study suggests.Typically, people are more likely to engage in activities that can lead to an exchange of saliva (唾液), such as kissing or sharing an ice cream, with family members or close friends than with an acquaintance. So saliva sharing can be a marker of “thick relationships, “ or people with strong attachments, says MIT developmental psychologist Ashley Thomas.To see if young children might use saliva sharing as a social cue for close bonds,Thomas and colleagues ran experiments of people engaging with puppets(木偶). When shown a puppet seemingly crying, kids of 8 months old were more likely to look at an adult who had previously shared saliva with the puppet than an adult who hadn’t, the team reports.Scientists, of course, can’t know exactly babies’ thought. But tracking where they look offers hints. The team used where the kids looked first when a puppet showed distress as an indicator of their understanding of the relationship.In some experiments, the team showed 8-to 10-month-olds or 16-to 18-month-olds videos of a woman sharing an orange slice with a puppet. A second video depicted another woman and the puppet playing with a ball. During a final video, which showed the puppet crying while seated between the two women, the kids’ eyes were more often drawn to the woman who had shared the orange.The team saw similar results in another experiment. One woman stuck her finger in her mouth and then in one puppet’s mouth to share saliva. For the other, she touched only her forehead and then the puppet’s forehead. After the woman showed distress, kids spent more time looking at the puppet that had seemingly swapped saliva.It’s unclear how the findings relate to children’s daily lives. Future studies could switch out actresses for family members to better understand the role saliva may play in distinguishing relationships. Other cues, such as hugging, may also play a role, Thomas says. 8．What is the main finding of the study?A．Saliva-sharing behavior is a cultural phenomenon.B．Saliva-sharing is an indicator of trust between individuals.C．Saliva-sharing can help children distinguish close relationship.D．Children can understand relationships through saliva-sharing behavior.9．What does Ashley Thomas think of saliva sharing?A．It is a natural behavior for young children.B．It can be an indicator of strong attachments between people.C．It is a cultural behavior young children learn from their parents.D．It is a result of the development of young children’s social skills.10．Which method do the scientists apply when conducting the experiments?A．Comparison.B．Reference.C．Inference.D．Description. 11．What may be discussed in the following paragraph?A．The limitations of the current study.B．The importance of saliva in social relationships.C．The role of other cues in distinguishing relationships.D．Saliva sharing can affect children’s social development.After Alexander Pushkin was shot in a duel (决斗) in 1837, crowds of mourners formed in Saint Petersburg. When the wagon carrying the much loved poet’s body reached Pskov province, where he was to be buried, admirers tried to pull the vehicle themselves.Today’s celebrity funerals tend to involve the public largely digitally rather than in person. But people are passionate all the same. In the past few months, grief has coursed around the internet for Milan Kundera, and most recently, Michael Gambon. If you stop to think about it, such expressions of strong feelings for writers and actors are odd, even irrational.Unlike other kinds of grief, this one is not rooted in personal intimacy (亲密关系). If you ever interacted with a cherished author, it was probably during a book tour when she signed your copy of her novel. Maybe you once locked eyes with a musician during a live concert and he smiled at you, but actually he did not even know you.Objectively, sorrow makes sense when a star dies young or violently. Had she not died at 27, who knows what music Amy Winehouse would have added to her already impressive collections of work? The death of a long-lived and fulfilled artist, however, is far from the saddest item in an average day’s headlines. And while most ordinary people sink into oblivion, these celebrities live on in their output. Why, then, are these losses felt so widely and keenly?One interpretation is that departed celebrities are merely the messengers. Part of your past —the years in which the musician was the soundtrack, the writer your ally (盟友) — can seem to fade away with them. The grief can be seen as a form of gratitude for the harmony and joy they supplied.More importantly, the passing of an artist is an occasion for exchanges of ideas. In an atomized age, in which the default (默认) tone is critical, a beloved figure’s death is a chance to share positive feelings and memories with fellow admirers. These sad occasions are the parting gifts of these artists.12．Why does the author mention Milan Kundera and Michael Gambon in paragraph 2?A．To prove that celebrities’ funerals tend to attract wider public attention.B．To illustrate why people express their sadness at the loss of those celebrities.C．To demonstrate that people’s mourning for celebrities seems strange andunreasonable.D．To show that people’s grief over celebrities’ death is ridiculous and impractical. 13．The underlined phrase “sink into oblivion” in paragraph 4 probably means ________.A．are upset B．are desperate C．are helpless D．are forgotten 14．What can we learn from the passage?A．People won’t mourn for celebrities unless they have intimate relationships withcelebrities.B．It’s natural that people mourn for celebrities dying young but not for those long-lived ones.C．People feel sad for the passing of celebrities because of the mental nourishmentreceived.D．People attend celebrities’ funerals, either in person or on the Internet, to express their loyalty.15．What’s the author’s attitude towards public mourning for the celebrities?A．Supportive.B．Disapproving.C．Skeptical.D．Concerned.When you look ahead at the year to come, I hope you focus on all the positives even if the negatives exist, because positive thinking can help you get where you want to go.Positive thinking is not the same as optimism. Being optimistic means believing that everything is going to work out great. But positive thinking is more than that. It’s a mindset or a way of looking at the world and what you do. 16To think positively, first of all, we need to look at problems, mistakes and failures as normal. Imagine you bomb a big job interview. A negative thinker will be upset by the fact that he didn’t get the job. 17 He will analyze what he did and figure out how to do it better next time. And he’ll also think about what he did well and try to repeat and improve on those successes. This means focusing on the big picture.One trick to positive thinking is to imagine how you’ll think back to things that are happening now. 18 There are bad things that happened last year that you can probably laugh about now. You understand what was a big deal and what was not. Try to do that in the present.19 A negative thinker will focus on the past, especially past failures. But the pastcannot be changed. It’s done and dusted. The future, however, is yet to be written. And that’s where the positive thinker will focus his attention.Positive thinking is a mental habit. It takes practice. Sometimes, we have to remind ourselves to focus on the future and on possibility. 20 But if you can do it, there are some great payoffs: greater confidence, a better chance of success, better health condition as well as a better quality of life.A．A positive thinker will learn from the experience.B．Negative thinkers will look at failures as end points.C．Positive thinking often means separating the past and the future.D．It’s a belief in possibility, solutions to problems and the big picture.E．Sometimes, it’s hard to learn from our failures or see the big picture.F．We can see the power of positive thinking when it comes to problem-solving.G．You know from experience that the passing of time brings a fresh perspective.二、完形填空Having been a teacher for 25 years, I think I’ve taught my students the importance of good citizenship, to play by the 21 . But most of the time, I embrace my role as a pupil.One morning when I reached the intersection before my school, traffic was at a standstill (停). What was really 22 was that I could see the school.Up ahead, the tum lane into the school’s parking lot was 23 . If I could just turn to the right, the only thing between me and the turn lane was a long stretch of field. As I sat in my motionless vehicle, I heard that field call to me. I 24 the car out of the line of traffic and headed for the freedom of that open land 25 I heard a wail of siren (警笛) from behind.An officer came up to me, and I handed him my 26 without even looking up. He glanced at it, and asked, “What’s going on, Madam?”I started murmuring. “Well, I overslept, and…” Here my voice 27 a sad, pleading tone, the very quality I advise my students to 28 --“I just wanted to get to school. I have to…”“So you’re a teacher?” he 29 .“Yes, and I need…”A car drove by, and I recognized one of my eighth-graders waving at me, 30 my name, pointing me out to his mother. As she drove by, I heard the police officer say it: “You wanted to be 31 because you’re a good teacher. “ At that point he paused before adding, “You were when I had you.”And then I did look at him. I read the name badge on his chest. A 32 7th-- grade student of mine. All grown up. Keeping people safe. Trying to keep me safe 33 myself.He gave me a 34 --not too different from ones I’d given him years ago--and sent me on my way. And at last I arrived at my classroom, wondering what I would 35 next.21．A．wills B．rules C．orders D．lessons 22．A．amusing B．confusing C．annoying D．surprising 23．A．blocked B．broad C．crowded D．empty 24．A．pushed B．guided C．parked D．nosed 25．A．since B．when C．until D．while 26．A．license B．book C．contract D．certificate 27．A．picked up B．took on C．showed up D．carried on 28．A．practise B．avoid C．adopt D．try 29．A．interrupted B．explained C．wondered D．complained 30．A．gesturing B．addressing C．announcing D．mouthing 31．A．at risk B．in charge C．on time D．under arrest 32．A．familiar B．former C．mature D．distant 33．A．by B．to C．from D．about 34．A．warning B．ticket C．hand D．favor 35．A．appreciate B．propose C．understand D．learn三、语法填空阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式。

2023届福建省南安市柳城中学高三上学期12月月考数学试题(解析版)

2023届福建省南安市柳城中学高三上学期12月月考数学试题(解析版)

2023届福建省南安市柳城中学高三上学期12月月考数学试题一、单选题 1．已知复数i2iz =+，i 为虚数单位，则z 的共轭复数为（ ） A ．12i 55+B ．12i 55-C ．21i 55+D ．21i 55-【答案】B【分析】根据复数的运算公式求复数z 的代数形式，再求其共轭复数即可. 【详解】()()()i 2i i 12i 12=i 2i 2i 2i 555z -+===+++-， 所以z 的共轭复数为12i 55-，故选：B.2．已知集合()(){}120A x x x =+-<，{}Z 1B x x =∈≥，则()A B =R （ ） A ．[]{}1,21⋃- B ．[]1,2C ．{}1,1,2-D ．{}1,2【答案】C【分析】解一元二次不等式求得集合A ，解绝对值不等式求得集合B ，由此求得()A B ⋂R . 【详解】由120x x，得1x <-或2x >，所以[]1,2R A =-；由1x ≥，得1x ≤-或1x ≥，所以{Z|1B x x =∈≤-或}1x ≥， 从而(){}1,1,2A B ⋂=-R ． 故选：C3．已知随机变量X 服从正态分布()23,N σ，若()()12436P X P X >=⋅<，则()23P X <<=（ ） A ．13B ．14C ．16D ．19【答案】A【分析】利用对称性可得(2)(4)P X P X <=>结合条件可求()2P X <，再由 1(2)(4)(23)2P X P X P X -<-><<=求解.【详解】因为随机变量X 服从正态分布()23,N σ，又()()12436P X P X >=⋅<， 所以1(2)(4)6P X P X <=>=， 故1111(2)(4)166(23)223P X P X P X =---<-><<==. 故选：A.4．已知某圆锥的侧面展开图为半圆，该圆锥的体积为，则该圆锥的表面积为（ ）A ．27πB ．C ．D ．16π【答案】A【分析】根据条件先算出母线长与底面半径的关系，再根据体积计算出底面半径即可.【详解】设圆锥底面半径为r ，母线长为l ，则r l 2π=π，所以2l r =，=，所以213r π⨯=，解得3r =，故其表面积291827S r rl πππππ=+=+=；故选：A ．5．将函数π()sin (0)3f x x ωω⎛⎫=+> ⎪⎝⎭的图像向左平移π2个单位长度后得到曲线C ，若C 关于y 轴对称，则ω的最小值是（ ） A ．16B ．14C ．13D ．12【答案】C【分析】先由平移求出曲线C 的解析式，再结合对称性得,232k k ωππππ+=+∈Z ，即可求出ω的最小值.【详解】由题意知：曲线C 为sin sin()2323y x x ππωππωω⎡⎤⎛⎫=++=++ ⎪⎢⎥⎝⎭⎣⎦，又C 关于y 轴对称，则,232k k ωππππ+=+∈Z ，解得12,3k k ω=+∈Z ，又0ω>，故当0k =时，ω的最小值为13.故选：C.6．已知抛物线212,,y F F =分别是双曲线22221(0,0)x y a b a b-=>>的左、右焦点，抛物线的准线过双曲线的左焦点1F ，与双曲线的渐近线交于点A ，若124F F A π∠=，则双曲线的标准方程为（ ）A ．22110x y -=B ．22116y x -=C ．2214y x -=D ．2214x y -=【答案】C【分析】由已知可得出c 的值，求出点A 的坐标，分析可得112AF F F =，由此可得出关于a 、b 、c 的方程组，解出这三个量的值，即可得出双曲线的标准方程.【详解】抛物线245y x =的准线方程为5x =-，则5c =，则()15,0F -、()25,0F ，不妨设点A 为第二象限内的点，联立b y x a x c⎧=-⎪⎨⎪=-⎩，可得x c bc y a =-⎧⎪⎨=⎪⎩，即点,bc A c a ⎫⎛- ⎪⎝⎭，因为112AF F F ⊥且124F F A π∠=，则12F F A △为等腰直角三角形，且112AF F F =，即2=bc c a，可得2ba =，所以，22225ba c c ab ⎧=⎪⎪⎪=⎨⎪=+⎪⎪⎩，解得125a b c ⎧=⎪=⎨⎪=⎩，因此，双曲线的标准方程为2214y x -=.故选：C.7．如图，在正三棱柱111ABC A B C 中，13AA =，2AB =，则异面直线1A B 与1B C 所成角的余弦值为（ ）A ．513B ．713C ．913D ．1213【答案】B【分析】在三棱锥内构造直线使其平行于1A B ，然后构造三角形，运用异面直线夹角的定义求解即可.【详解】取11A C 的中点D ，连接1BC 交1B C 于点E ，连接DE ， 则1//DE A B 且112DE A B =，则1DEB ∠为异面直线1A B 与1B C 所成的角或其补角． 易求1113A B BC =13B D ，则113DE B E ==， 所以222111113133744cos 21313132DE B E B D DEB DE B E +-+-∠===⋅⨯⨯. 故选：B ．8．已知函数()f x 是定义域为R 的偶函数()1f x +为奇函数，当[]0,1x ∈时，()2xf x k a =⋅+，若()()036f f +=，则()2log 96f =（ ）A ．2B ．0C ．-3D ．-6【答案】C【分析】根据条件，可以证明()f x 是周期为4的周期函数，计算出a 和k ，由周期性可得()()22log 961log 3f f =+ ，再利用函数的对称性即可求解.【详解】因为()1f x +为奇函数，所以()()11f x f x -+=-+，又()f x 为偶函数， 所以()()11f x f x -+=-，所以()()11f x f x -=-+，即()()2=-+f x f x ， 所以()()()42f x f x f x +=-+=，故()f x 是以4为周期的周期函数；由()()11f x f x -+=-+，易得()10f =，()()()3110f f f =-==，所以()06f =， 所以6k a +=，20k a +=，解得6k =-，12a =；所以()()()222log 965log 31log 3f f f =+=+()23log 2223log 31log 621232f f ⎛⎫⎛⎫=--=-=--⨯+=- ⎪ ⎪⎝⎭⎝⎭； 故选：C ．9．已知0a b >>，0c d <<，则（ ） A ．a b d c> B ．a b d c< C ．ac bd < D ．ac bd >【答案】BC【分析】利用不等式的基本性质判断不等关系． 【详解】因为0c d <<，所以0cd >，所以110d c <<，所以110d c->->，又0a b >>，所以a b d c ->-，所以a bd c<，故 A 错误，B 正确； 因为0a b >>，0c d ->->，所以ac bd ->-，所以.ac bd <故D 错误，C 正确． 故选：BC ．10．已知数列{}n a 的前n 项和为n S ，则（ ） A ．若22n S n n =-，则{}n a 是等差数列 B ．若121n n S +=-，则{}n a 是等比数列 C ．若{}n a 是等差数列，则202310122023S a =D ．若{}n a 是等比数列，且10a >，0q >，则221212n n n S S S -+⋅> 【答案】AC【分析】利用n a 与n S 的关系，结合等差数列与等比数列的定义，可得A 、B 的正误；根据等差中项以及等差数列求和公式，可得C 的正误；取1n =时的特殊情况验证不等式，可得D 的正误.【详解】对于A ，若22n S n n =-，则11a =，当2n ≥时，143n n n a S S n -=-=-，显然1n =时也满足43n a n =-， 故43n a n =-，由14n n a a --=，则{}n a 为等差数列，故A 正确；对于B ，若121n n S +=-，则13a =，2214a S S =-=，3328a S S =-=，显然3212a a a a ≠，所以{}n a 不是等比数列，故B 错误； 对于C ，因为{}n a 为等差数列，则()12023101220231012202320232202322a a a S a +⨯===，故C 正确；对于D ，当1n =时，()()222222132111110S S S a q q a q a q ⋅-=++-+=-<，故当1n =时，不等式不成立，即221212n n n S S S -+⋅>不成立，故D 错误．11．关于函数()()π3sin 21R 3f x x x ⎛⎫ ⎪⎝⎭=-+∈，下列说法正确的是（ ）A ．若()()121f x f x ==，则()12πZ x x k k -=∈B ．()y f x =的图像关于点2π,13⎛⎫⎪⎝⎭对称 C ．()y f x =在π0,2⎛⎫⎪⎝⎭上单调递增D ．()y f x =的图像向右平移π12个单位长度后所得图像关于y 轴对称【答案】BD【分析】对于A ，根据三角函数的对称中心性质即可判断； 对于B ，可根据对称中心对应的函数值特征即可判断； 对于C ，根据三角函数单调性判断即可；对于D ，求出平移后的解析式并根据偶函数的性质进行判断即可.【详解】对于A ，由()()121f x f x ==知()1,1x ，()2,1x 是()π3sin 213f x x ⎛⎫=-+ ⎪⎝⎭图象的两个对称中心，则12x x -是函数()f x 的最小正周期的整数倍，即()12πZ 2k x x k -=∈，故A 不正确； 对于B ，因为2π3sin π113f ⎛⎫=+= ⎪⎝⎭，所以2π,13⎛⎫⎪⎝⎭是()f x 的对称中心，故B 正确；对于C ，由()πππ2π22πZ 232k x k k -≤-≤+∈解得()π5πππZ 1212k x k k -≤≤+∈， 当0k =时，()f x 在π5π,1212⎡⎤-⎢⎥⎣⎦上单调递增，则()f x 在5π0,12⎡⎤⎢⎥⎣⎦上单调递增，在5ππ,122⎡⎤⎢⎥⎣⎦上单调递减，故C 不正确；对于D ，()y f x =的图象向右平移π12个单位长度后所得图象对应的函数ππ3sin 213cos 21123y x x ⎛⎫⎛⎫=--+=-+ ⎪ ⎪⎝⎭⎝⎭，x ∈R ()()3cos213cos21()f x x x f x ∴-=--+=-+=3cos 21y x =-+是偶函数，所以图象关于y 轴对称，故D 正确.故选：BD.12．将边长为2的正方形ABCD 沿对角线AC 折起，使点D 不在平面ABC 内，则在翻折过程中，下列结论正确的有（ ）A ．存在某个位置，使直线BD 与平面ABC 所成的角为45°B ．当二面角D AC B --为23π时，三棱锥D ABC - C ．当平面ACD ⊥平面ABC 时，异面直线AB 与CD 的夹角为60°D ．O 为AC 的中点，当二面角D AO B --为23π时，三棱锥A OBD -外接球的表面积为10π 【答案】ACD【分析】A.当当平面ACD ⊥平面ABC ，即可判断；B.根据锥体体积公式，即可求解； C.将异面直线所成的角转化为相交直线所成的角，即可求解； D.将三棱锥补体为三棱柱，即可求球心和半径.【详解】A.当平面ACD ⊥平面ABC 时，取AC 的中点O ，连接,BO DO ，DO AC ⊥，DO ∴⊥平面ABC ，DBO ∴∠为直线BD 与平面ABC 所成的角， DBO 是等腰直角三角形，45DBO ∴∠=，故A 正确；B.DO AC ⊥，BO AC ⊥，DO BO O ⋂=，AC ∴⊥平面DBO ，且23DOB π∠=， AC ⊂平面ABC ，∴平面DBO ⊥平面ABC ，且交于BO ，∴点D 在平面ABC 的射影落在BO 上，∴点D 到平面ABC 的距离6sin 602d DO =⋅=，三棱锥D ABC -的体积1166223223V =⨯⨯⨯⨯=，故B 错误；C.取,BC BD 的中点,M N ，连接,,OM ON MN ，则//OM AB ，/MN DC ，所以OMN ∠或其补角是异面直线AB 与CD 的夹角，根据A 的证明可知()()22222BD =+=，112ON BD ==，且1OM MN ==，所以OMN 是等边三角形，60OMN ∠=，故C 正确；D.由条件可知AO ⊥平面DOB ，23DOB π∠=，且DO OB =，所以可以将四棱锥A DOB -补成底面是菱形的直棱柱因为四边形OBCD 是菱形，且23BOD π∠=，所以点C 是底面OBD 外接圆的圆心，取侧棱1CC 的中点E ，则E 是四棱柱外接球的球心，连结OE ，()222221022OE OC CE ⎛⎫=+=+ ⎪ ⎪⎝⎭所以四棱锥A OBD -外接球的半径10R =2410S R ππ==，故D 正确. 故选：ACD三、填空题13．已知向量()3,1a =-，(),2b m =，且()2a a b ⊥+，则+=a b ______． 85 【分析】由向量线性运算及垂直的数量积表示可得方程解出m ，即可由坐标计算向量模. 【详解】()()()23,12,223,5a b m m +=-+=-，由()2a a b ⊥+得()()()23,123,5a a b m ⋅+=-⋅-6950m =-++=，解得73m =． 则()723,1,2,333a b ⎛⎫⎛⎫+=-+=- ⎪ ⎪⎝⎭⎝⎭，故2228533a b ⎛⎫+=-+= ⎪⎝⎭85. 14．63x x ⎛⎝展开式的常数项为______.【答案】2160【分析】根据给定条件，求出二项式展开式的通项公式，再求出常数项作答.【详解】6(3x展开式的通项公式为36662166C (3)(3(2)C ,N,6r r r r r r rr T x x r r ---+==⋅-∈≤， 令3602r -=，解得4r =，则244563(2)C 916152160T =⋅-=⨯⨯=， 所以展开式的常数项为2160. 故答案为：216015．已知函数()()()10 ln f x x x =+≥，将()f x 的图象绕原点逆时针旋转(]()0,ααθ∈角后得到曲线C ，若曲线C 仍是某个函数的图象，则θ的最大值为______．【答案】π4##1π4【分析】求得()f x 在点()0,0处的切线方程，从而求得正确答案. 【详解】依题意0x ≥， ()11f x x '=+，所以()01f '=，故函数()f x 的图象在()()0,0f 处的切线为y x =， 切线向上的方向与y 轴正方向的夹角为π4，函数()f x 的图象绕原点旋转不超过π4时，仍为某函数图象，若超过π4，y 轴与图象有两个公共点，与函数定义不符，故θ的最大值为π4．故答案为：π416．有一种投掷骰子走跳棋的游戏：棋盘上标有第1站、第2站、第3站、…、第10站，共10站，设棋子跳到第n 站的概率为n P ，若一枚棋子开始在第1站，棋手每次投掷骰子一次，棋子向前跳动一次．若骰子点数小于等于3，棋子向前跳一站；否则，棋子向前跳两站，直到棋子跳到第9站（失败）或者第10站（获胜）时，游戏结束．则3P =_________；该棋手获胜的概率为__________． 【答案】34##0.75 85256【分析】根据题意找出(38)n P n ≤≤与21,n n P P --的关系即可求解. 【详解】由题311132224P =+⨯=，因为2111(38)22n n n P P P n --=+≤≤，故11112n n n n P P P P ----=--，由2112P P -=-，所以111,22n n n P P n --⎛⎫-=-≥ ⎪⎝⎭，累加可得：2878108111118518521,1222128225612P P P ⎛⎫-- ⎪⎛⎫⎛⎫⎛⎫⎝⎭=+-+-+⋅⋅⋅+-==== ⎪ ⎪ ⎪⎛⎫⎝⎭⎝⎭⎝⎭-- ⎪⎝⎭．故答案为：34；85256.四、解答题17．在ABC 中，角A ，B ，C 的对边分别为a ，b ，c ，()22214cos a b B ab +-=-，且2cos c b B =．(1)求B ；(2)若ABC 的周长为423+，求BC 边上中线的长． 【答案】(1)π6B = (2)7．【分析】（1）已知条件结合余弦定理求得2π3C =，再由正弦定理求B . （2）由（1）求出角A ，利用三角形周长求出各边的长，再由余弦定理求BC 边上中线的长．【详解】（1）由()22214cos a b B ab +-=-，有22224cos a b b B ab +-=-，又2cos c b B =，所以2224cos c b B =，即222a b c ab +-=-， 由余弦定理，得2221cos 222a b c ab C ab ab +--===-． 又()0,πC ∈，所以2π3C =，由2cos c b B =及正弦定理，得sin 2sin cos C B B =，所以3sin 22B =， 由π0,3B ⎛⎫∈ ⎪⎝⎭，得2π20,3B ⎛⎫∈ ⎪⎝⎭，所以π23B =，解得π6B =.（2）由（1）可知π6B =，2π3C =，所以π2πππ636A =--=， 所以a b =，由2cos c b B =，得3c a =． 因为ABC 的周长为423+，所以3423a a a ++=+，解得2a =． 设BC 的中点为D ，则112CD BC ==，如图所示:AD==，所以BC．18．已知数列{}n a的前项和为n S，若()12n nnS n S+=+，且11a=.(1)求{}n a的通项公式;(2)设()2112nn nb na a-=≥，11b=，数列{}n b的前n项和为n T，求证32nT<.【答案】(1)n a n=(2)证明见解析【分析】（1）由已知等式可得12nnS nS n++=，采用累乘法可求得当2n≥时的nS，利用1n n na S S-=-可求得n a，检验首项后可得结论；（2）由（1）可得2n≥时nb的通项，由()()112122nbn n n n=<--，采用裂项相消法可求得11112nTn⎛⎫<+-⎪⎝⎭，由1n>可得结论.【详解】（1）由()12n nnS n S+=+得：12nnS nS n++=，则当2n≥时，()123211232111143123212n n n nn n nn nS S S S S S n n nS S S S S S n n n-----++-=⋅⋅⋅⋅⋅⋅⋅⋅=⋅⋅⋅⋅⋅⋅⋅⋅=---，又111S a==，()12nn nS+∴=，()()11122n n nn n n na S S n-+-∴=-=-=，经检验：11a=满足na n=；()na n n*∴=∈N.（2）由（1）得：当2n≥时，()()11111212221nbn n n n n n⎛⎫=<=-⎪---⎝⎭；123111111111112223341n n nT b b b b bn n-⎛⎫∴=+++⋅⋅⋅++<+-+-+-+⋅⋅⋅+-⎪-⎝⎭11112n⎛⎫=+-⎪⎝⎭，1n>，111n∴-<，1113111222nTn⎛⎫∴<+-<+=⎪⎝⎭.19．2018年9月10日，全国教育大会在北京召开，习近平总书记在会上提出“培养德智体美劳全面发展的社会主义建设者和接班人”.某学校贯彻大会精神，为学生开设了一门模具加工课，经过一段时间的学习，拟举行一次模具加工大赛，学生小明､小红打算报名参加大赛.(1)赛前，小明进行了一段时间的强化训练，加工完成一个模具的平均速度y (秒)与训练天数x (天)有关，经统计得到如下表数据：经研究发现，可用b y a x=+作为回归方程模型，请利用表中数据，求出该回归方程，并预测小明经过50天训练后，加工完成一个模具的平均速度y 约为多少秒？(2)小明和小红拟先举行一次模拟赛，每局比赛各加工一个模具，先加工完成模具的人获胜，两人约定先胜4局者赢得比赛.若小明每局获胜的概率为35，已知在前3局中小明胜2局，小红胜1局.若每局不存在平局，请你估计小明最终赢得比赛的概率．参考数据：(其中1i t x =) 参考公式：对于一组数据()11,u v ，()22,u v ，…，(),n n u v ，其回归直线ˆvu αβ=+的斜率和截距的最小二乘估计公式分别为1221n i ii n i i u v nu v unu β==-⋅=-∑∑，v u αβ=-⋅. 【答案】(1)100013ˆ0=+yx；150； (2)513625． 【分析】(1)令1t x =，则可利用最小二乘法估计ˆˆˆy bt a =+，从而得到ˆˆˆb y a x=+，代入x =50即可预测小明经过50天训练后，加工完成一个模具的平均速度；(2)设比赛再继续进行X 局小明最终赢得比赛，最后一局一定是小明获胜，且最多再进行4局就结束比赛分出胜负，则小明赢得比赛得概率P =P (X =2)+P (X =3)+P (X =4)．【详解】（1）由题意，()19909904503203002402105007y =++++++=，令1t x =，设y 关于t 的线性回归方程为ˆˆˆy bt a =+， 则7172217184570.37500ˆ10000.557i ii i i t y t y b tt ==-⋅-⨯⨯===-∑∑， 则ˆ50010000.37130=-⨯=a， ∴100013ˆ0=+yt ， ∴y 关于x 的回归方程为100013ˆ0=+y x， 当50x =时，ˆ150=y， ∴预测小明经过50天训练后，加工完成一个模具的平均速度y 约为150秒；（2）设比赛再继续进行X 局小明最终赢得比赛，则最后一局一定是小明获胜，由题意知，最多再进行4局就有胜负，X 的可能取值为2、3、4．当2X =时，小明4∶1胜，∴()33925525P X ==⨯=； 当3X =时，小明4∶2胜，∴()12333363C 1555125P X ⎛⎫==⨯⨯-⨯= ⎪⎝⎭； 当4X =时，小明4∶3胜，∴()2133331084C 1555625P X ⎛⎫==⨯⨯-⨯= ⎪⎝⎭． ∴小明最终赢得比赛的概率为93610851325125625625++=． 20．如图，圆台下底面圆O 的直径为AB ， C 是圆O 上异于,A B 的点，且30BAC ∠=，MN 为上底面圆O '的一条直径，MAC △是边长为23的等边三角形，4MB =.(1)证明：BC ⊥平面MAC ；(2)求平面MAC 和平面NAB 夹角的余弦值.【答案】(1)证明见解析313【分析】(1)线线垂直从而证明线面垂直.(2)利用向量法，即可求二面角的余弦值.【详解】（1）∵AB 为圆台下底面圆O 的直径，C 是圆O 上异于,A B 的点，故=90ACB ︒∠又∵=30BAC ︒∠，23AC =，∴4AB MB ==∵AC MC =，BC BC =∴ABC MBC ≅，∴=90BCM ︒∠∴BC MC ⊥，又∵BC AC ⊥，AC MCC ，,AC MC ⊂平面MAC ∴BC ⊥平面MAC（2）取AC 的中点，连接,DM DO ，则MD AC ⊥，由(1)可知，BC DM ⊥∵AC BC C =，∴DM ⊥平面ABC ， 又∵OD AC ⊥∴以D 为原点，DA 为x 轴，DO 为y 轴，DM 为z 轴，建立如下图所示的空间直角坐标系，由题意可得(3,0,0)A ，(3,2,0)B -，∵OO '⊥平面ABC ，∴//'DM OO ，四边形ODMO '为矩形，∴(0,2,3)N平面MAC 的一个法向量为1(0,1,0)n =.设平面NAB 的一条法向量为2(,,)n x y z =，(23,2,0)AB =-，(3,2,3)AN =-由2200n AB n AN ⎧⋅=⎪⎨⋅=⎪⎩ 得23203230x y x y z ⎧-+=⎪⎨++=⎪⎩ 令3x =3y =，1z =-平面NAB 的一个法向量为2(3,3,1)n =-则平面MAC 与平面NAB的夹角的余弦值为1212·3nn n n ==∴平面MAC 和平面NAB 21．已知抛物线2:2(0)C x py p =>在点()01,M y 处的切线斜率为12． (1)求抛物线C 的方程；(2)若抛物线C 上存在不同的两点关于直线:2l y x m =+对称，求实数m 的取值范围．【答案】(1)24x y =；(2)94m >.【分析】（1）根据给定条件，求出切线方程，再与抛物线C 的方程联立，借助判别式计算作答.（2）设出抛物线C 上关于l 对称的两点A ，B 的坐标，并设出直线AB 的方程，再与抛物线C 的方程联立，借助判别式及韦达定理计算作答.【详解】（1）点1(1,)2M p ，则切线方程为：11(1)22y x p -=-，由221(1)2py p x x py -=-⎧⎨=⎩消去y 并整理得： 210x px p -+-=，依题意，24(1)0p p ∆=--=，解得2p =，所以抛物线C 的方程是24x y =.（2）设抛物线C 上关于l 对称的两点为1122(,),(,)A x y B x y ，则设直线AB 方程为：12y x t =-+， 由2124y x t x y⎧=-+⎪⎨⎪=⎩消去y 并整理得：2240x x t +-=，则有4160t '∆=+>，解得14t >-， 122x x +=-，12121()2212y y x x t t +=-++=+，显然线段AB 的中点1(1,)2t -+在直线l 上， 于是得122t m +=-+，即有52t m =-，而14t >-，因此，5124m ->-，解得94m >， 所以实数m 的取值范围是94m >. 【点睛】结论点睛：抛物线22(0)x py p =≠在点200(,)2x x p 处的切线斜率0x k p =； 抛物线22(0)y px p =≠在点2000(,)(0)2y y y p ≠处的切线斜率0p k y =. 22．某品牌轿车经销商组织促销活动，给出两种优惠方案，顾客只能选择其中的一种. 方案一：每满6万元，可减6千元；方案二：金额超过6万元（含6万元），可摇号三次，其规则是依次从装有2个幸运号、2个吉祥号的一号摇号机，装有2个幸运号、2个吉祥号的二号摇号机，装有1个幸运号、3个吉祥号的三号摇号机各摇号一次，每次摇出一个号. 其优惠情况为：若摇出3个幸运号打6折；若摇出2个幸运号打7折；若摇出1个幸运号打8折；若没摇出幸运号不打折.(1)若某型号的车正好6万元，两名顾客都选方案二，求至少有一名顾客比选方案一更优惠的概率；(2)若你朋友看中一款价格为10万元的轿车，请用所学知识帮助你朋友分析一下应选择哪种优惠方案.【答案】(1)247256(2)方案二【分析】（1）设顾客三次没摇出幸运号为事件A ，由独立事件概率乘法公式求得()P A ，则利用对立事件概率得所求概率为()21P A -； （2）方案二，设付款金额为X 万元，则{}6,7,8,10X ∈，求出X 的分布列，期望与方案一比较即可.【详解】（1）方案一相当于打9折，要使选择方案二比选择方案一更优惠，则需要至少摇出1个幸运号，设顾客不打折即三次没摇出幸运号为事件A ，则()223344416P A =⨯⨯=， 故所求的概率()2232471116256P P A ⎛⎫=-=-= ⎪⎝⎭. （2）若选择方案一，则需要付款100.69.4-=（万元）若选择方案二，设付款金额为X 万元，则{}6,7,8,10X ∈， ()322116416P X ⨯⨯===，()322322122157416P X ⨯⨯+⨯⨯+⨯⨯===， ()322322322178416P X ⨯⨯+⨯⨯+⨯⨯===，()31016P X ==， 故X 的分布列为所以()1573678107.93759.416161616E X =⨯+⨯+⨯+⨯=<（万元），所以选方案二划算.。

2024届河南省青桐鸣联考高三上学期12月月考化学试题及答案

2024届河南省青桐鸣联考高三上学期12月月考化学试题及答案

2024届普通高等学校招生全国统一考试青桐鸣大联考(高三化学)注意事项：1.答卷前，考生务必将自己的姓名、班级、考场号、座位号、考生号填写在答题卡上。

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.考试结束后，将本试卷和答题卡一并交回。

4.全卷满分100分，考试时间90分钟。

可能用到的相对原子质量：H：1 N：14 O：16 S：32 Cl：35.5 Fe：56 Bi：209一、选择题：本题共14小题，每小题3分，共42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. 废物改头换面，服务日常生活。

下列说法正确的是A. 钢管表面镀锌可起到防腐的作用，镀锌层破损后，钢管腐蚀速率加快B. 生产豆奶产生的豆渣可加工成面粉和饼干，豆渣中含有的纤维素与淀粉互为同分异构体C. 废弃玻璃磨粉可代替砂子掺入混凝土建造房子，玻璃的生产原料为纯碱、石灰石和石英砂D. 废旧轮胎制成的橡胶粉可掺入沥青中铺路，橡胶均属于天然有机高分子化合物2. 芳香族化合物a、b、c是有机合成的基础原料，下列有关说法错误的是A. a、b均能与NaOH溶液反应B. a、c均能与b发生酯化反应C. b的芳香族同分异构体有3种D. 基态碳原子与氧原子核外未成对电子数相等3. 下列关于化学实验的基本操作正确的是A ．制备纯净的()2Fe OH B ．收集氨气并进行尾气处理C ．量取稀硫酸并排除滴定管中气泡D ．用该装置进行喷泉实验A. AB. BC. CD. D4. 设A N 为阿伏加德罗常数的值，下列说法正确的是A. 46 g 2NO 和24N O 的混合气体中所含原子数目为4.5AN B. 乙酸和乙醇发生酯化反应生成1 mol 2H O 时，生成C—O 键的数目为A N C. 56 g Fe 与71 g 2Cl 完全反应，转移电子数目为3A N D. 1 mol/L 23Na CO 溶液中含有+的数目为2A N 5. 下列离子方程式错误的是A. 用过量氨水吸收少量2SO 气体：2232432SO 2NH H O 2NH SO H O +-+⋅=++B. 用3FeCl 溶液腐蚀覆铜板：3222Fe Cu 2Fe Cu ++++=+C. NaClO 溶液中通入少量2SO 气体：2224ClO SO H O Cl SO 2H---+++=++D. 向硫酸酸化的4KMnO 溶液中滴加少量双氧水：2422222MnO 6H 5H O 2Mn 5O 8H O-++++=+↑+6. 通过对已知物质的性质和实验的描述进行类比推测，得出的相应结论正确的是选项已知物质的性质和实验类比推测ACuSO4溶液和过量NaOH 溶液反应生成蓝色沉淀CuSO 4溶液和过量NH 3·H 2O 反应也生成蓝色沉淀的BNaHCO 3溶液与Al 2(SO 4)3溶液反应有沉淀和气体产生NaHCO 3溶液与Fe 2(SO 4)3溶液反应也有沉淀和气体产生C 向Na 2CO 3固体中加入少量水，伴随放热现象向NaHCO 3固体中加入少量水，也伴随放热现象D 少量CO 2通入Ba(OH)2溶液中产生白色沉淀少量CO 2通入BaCl 2溶液中也产生白色沉淀A. AB. BC. CD. D7. 有机物M 和N 是合成药物的中间体，在一定条件下M 可以转化为N ，其过程如图所示，下列说法错误的是A. 该反应类型为消去反应B. 可用金属Na 鉴别M 和NC. M 的分子式为9143C H O D. N 可使酸性4KMnO 溶液褪色8. 某兴趣小组以铝土矿(主要成分为23Al O ，还含有少量23Fe O 和2SiO )为主要原料制备絮凝剂聚合氯化铝()2mAlOH Cl b a ⎡⎤⎣⎦和金属铝的流程如图所示。

2024届天津市南开中学高三上学期12月月考生物试题及答案

2024届天津市南开中学高三上学期12月月考生物试题及答案

南开中学2024届高三第二次月检测生物学科试卷考试时间：60 分钟本试卷分第Ⅰ卷(单选题) 和第Ⅱ卷(非选择题) 两部分，共100分。

注意事项：1.答题前填写好自己的姓名、班级、考号等信息2. 请将答案正确填写在答题纸上Ⅰ卷(共 48 分)一、单选题(每题4分，共48分)1.细胞是生物体结构和功能的基本单位，下列相关叙述正确的是( )A. 乳酸菌、醋酸菌、大肠杆菌、哺乳动物成熟的红细胞均无细胞核，都是原核细胞B.细胞学说揭示了生物界的统一性，但未涉及病毒和原核生物C. HIV 、肺炎支原体、烟草花叶病毒的遗传物质都是 RNAD.细胞中存在纤维素构成的细胞骨架，细胞骨架与物质运输等生命活动有关2.甲图中①②③④表示不同化学元素所组成的化合物，乙图表示由单体构成的化合物(局部)。

以下说法错误的是( )A.甲图中所示的化学元素只有大量元素，没有微量元素B.若甲图中②是储能物质，则其可能是淀粉，也可能是脂肪C. 若乙图表示蛋白质的一部分，则其变性后不能与双缩脲试剂发生紫色反应D.若乙图表示核糖核酸，则其彻底水解后，产物种类最多可达6种3.下列关于人体细胞生命历程的叙述，错误的是( )A.胚胎细胞中存在与细胞凋亡有关的基因B. 白细胞和骨骼肌细胞所含的蛋白质中有部分相同试卷第1页，共9页C. 衰老的神经细胞发生萎缩，细胞核体积也随之变小D. 机体通过免疫系统清除被新冠病毒感染的细胞属于细胞凋亡4. 研究表明，烟草细胞吸收与利用 NO −3主要是通过硝酸盐转运蛋白(NRT)完成的，过程如图所示。

下列叙述错误的是( )A. NO₃⁻通过NRT 进入烟草细胞和H⁺运出烟草细胞的方式相同B. 在一定范围内，烟草细胞吸收NO₃⁻的速率与膜内外H⁺浓度梯度呈正相关C. NRT 可以同时运输NO₃⁻和H⁺，因此其不具有特异性D.中耕松土可以促进烟草对NO ₃⁻的吸收，提高烟草的产量5.游泳时人体在水中耗能增多，呼吸运动加强，肺泡呼吸表面积扩大，肺泡壁上开放的毛细血管数量增加，从而加快肺泡内气体的扩散速度，有利于提高血氧含量，从而提高组织对氧的利用率。

北京一六一中学2023—2024 学年度上学期12月月考高三语文试题及答案

北京一六一中学2023—2024 学年度上学期12月月考高三语文试题及答案

北京一六一中学2023—2024学年度上学期12月月考高三语文2023.12一、实用类文本阅读（本大题5小题，共18分）材料一历史如潮，大道如砥。

十年砥砺前行，化作惊艳跨步。

2020年，嫦娥五号顺利从月球带回约2公斤月壤。

自立项以来，中国探月工程“一张蓝图绘到底”，“一条龙”攻关攻坚，“一盘棋”协同推进，“一体化”迭代提升。

诗歌中的婵娟从书页来到现实，中华民族“九天揽月”的千年梦想得以实现。

2021年，“天问一号”探测器着陆火星，实现了从地月系到行星际的跨越；随后，“祝融号”火星车成功驶上火星表面开始巡视探测，我国首次火星探测任务一次实现了“绕、着、巡”三个目标。

同年，随着首颗太阳探测科学技术试验卫星“羲和号”成功发射，中国迈入“探日”时代。

“效法羲和驭天马，志在长空牧群星”，沿着上古神话中的“太阳女神”羲和的脚步，中国人的宇宙探索终于拓展到这颗始终照耀着华夏儿女的璀璨星球。

“问鼎苍穹”承载着中国人探索浩瀚宇宙的雄心与浪漫；“跨山越海”则改写了神州大地的时空格局，挺起了泱泱大国的发展骨架。

“逢山开路、遇水搭桥”。

港珠澳大桥、伶仃洋大桥、泉州湾大桥……一座座跨海大桥，让“天堑变通途”，创造了“当惊世界殊”的发展成就。

“原来去澳门一天只能跑一趟，现在一天可以跑四趟；通过香港机场走的航空货，原来要提前两天到达香港仓库，现在通过大桥仅需提前半天。

”对于在珠海从事跨境电商工作的郑太龙来说，被英国《卫报》誉为“现代世界七大奇迹之一”的港珠澳大桥让他运货花的时间更少了，收益更高了。

2022年9月5日，在建世界高速公路第一长隧——全长22.035公里的乌尉天山胜利隧道进口端三洞顺利穿越全线最大断层，为隧道顺利贯通和乌尉高速公路顺利通车创造了良好条件。

乌尉高速全线共设置隧道20座、桥梁117座，桥隧比达到40.37%，其通车将意味着南北疆交通屏障完全被打破。

走天山，独库公路、巴里坤至哈密公路、乌尉高速公路分卧西、东、中三线，物畅其流的通衢大道让丝绸古道焕新颜；越沙漠，和若铁路自2018年底正式开工建设到正式通车仅用时三年多，建设跑出加速度，铁路在塔克拉玛干沙漠“画”了一个圈。

海南省海口黄冈金盘学校2024-2025学年高三上学期12月月考数学试题

海南省海口黄冈金盘学校2024-2025学年高三上学期12月月考数学试题

海南省海口黄冈金盘学校2024-2025学年高三上学期12月月考数学试题一、单选题1．已知集合{}}242{60M x x N x x x =-<<=--<，，则M N ⋂=A ．}{43x x -<<B ．}{42x x -<<-C ．}{22x x -<<D ．}{23x x <<2．在复平面内，复数()()3i 1i z =+-对应的点位于（）A ．第一象限B ．第二象限C ．第三象限D ．第四象限3．已知(2,0)a = ，(1,1)b = ，则||2a b -的值为（）A ．1B ．2C ．3D ．44．在ABC V 中，内角A ，B ，C 的对边分别为a ，b ，c ．若222a b c +=+，则tan 2A 的值为（）A ．3B ．33-C D ．5．已知()1cos πsin 03αα+=<，，则tan α=（）A ．-B ．C D ．6．函数()sin x f x =的图像大致是（）A ．B ．C ．D ．7．已知函数log (1)1a y x =-+（0a >，且1a ≠）的图象恒过定点A ，若点A 在直线()100,0mx ny m n +-=>>上，则41m n+的最小值为（）A ．13B ．C ．9+D ．88．设函数()πcos 4f x x ω⎛⎫=+ ⎪⎝⎭在区间π0,2⎛⎫ ⎪⎝⎭上恰有3个零点、2个极值点，则ω的取值范围是（）A ．79,22⎛⎤⎥⎝⎦B ．911,22⎛⎤ ⎥⎝⎦C ．913,22⎛⎤ ⎥⎝⎦D ．713,22⎛⎤ ⎥⎝⎦二、多选题9．已知α的终边过点()1,2P -，则（）A ．sin cos 12sin cos αααα-=-+B ．25sin 5α-=C ．3cos 25α=D ．π1tan 43α⎛⎫+=-⎪⎝⎭10．设函数()23ln f x x x x=--，记()f x 的极小值点为1x ，极大值点为2x ，则（）A ．123x x +=B ．12x x <C ．()f x 在()21,x x 上单调递减D ．()()123ln2f x f x +=-11．已知函数()()()2sin l 0,0πf x x ωϕωϕ=++><<的部分图象如图所示，则（）A ．π3ϕ=B ．2ω=C ．()f x 的图象关于点π,06⎛⎫⎪⎝⎭对称D ．π6f x ⎛⎫+ ⎪⎝⎭的图象关于直线π4x =对称三、填空题12．若2sin 3x =-，则cos 2x =．13．记ABC 的内角的对边分别为a，b ，c cos 1A A -=，π0,2A ⎛⎫∈ ⎪⎝⎭，则A =；若3a =，2b =，则sinB =．14．设函数()e ln a f x x x x ⎛⎫=-+ ⎪⎝⎭有两个不同极值点1x ，2x ，若12x x <，则12x x +=；a 的取值范围是．四、解答题15．设等差数列{}n a 的前n 项和为n S ，已知324a =，1133S =．(1)求数列{}n a 的通项公式；(2)求数列{}n a 的前n 项和n S ．16．已知ABC V 的内角A ，B ，C 的对边分别为a ，b ，c ，cos cos a c A b a C +=+．(1)求角C 的大小；(2)若2c =，ABC VABC V 的周长．17．如图，在棱长为1的正方体OABC O A B C ''''-中，E ，F 分别是棱AB ，BC 上的中点．(1)求证：A F C E ''⊥；(2)求平面A EF '与平面B EF '的夹角的余弦值．18．已知ABC V 的内角A ，B ，C 所对的边分别为a ，b ，c ，()2cos 2cos f x x x x =-的最大值为()f A ．(1)求()f x 的最小正周期及单调递增区间；(2)求角A ；(3)当a =2b =时，求ABC V 的面积．19．已知函数()()2ln 21f x a x a x x =-++-．(1)若12a =，求()f x 在()()1,1f 处的切线方程．(2)当1a =时，证明：()f x 有两个不同的极值点．(3)讨论()f x 的单调性．。

福建省南安名校2023届高三上学期12月月考数学试题(解析版)

福建省南安名校2023届高三上学期12月月考数学试题(解析版)

福建省南安名校2023届高三上学期12月月考数学试题一、单选题1．已知集合{}21log A x N x k =∈<<，集合A 中至少有2个元素，则（ ） A ．16k ≥B ．16k >C ．8k ≥D ．8k >2．已知圆锥的轴截面是一个正三角形，则其侧面积与轴截面面积之比是（ ） A ．23B ．233πC ．23π D ．32π 3．“函数tan y x =的图象关于0(,0)x 中心对称”是“0sin 0x =”的（ ） A ．充分不必要条件 B ．必要不充分条件 C ．充分必要条件D ．既不充分也不必要条件4．若()()2i 2i 1z z -+=，则z 的最大值为（ ） A ．2B ．3C ．2D ．35．已知等差数列{}n a 和等比数列{}n b 均为递增数列，且121a b ==，26a b =，若10k a b =，则k 的最小值为（ ） A ．3B ．4C ．5D ．66．在ABC 中，点P 满足2BP PC =，过点P 的直线与AB ，AC 所在的直线分别交于点M ，N ，若AM x AB =，()0,0AN yAC x y =>>，则2x y +的最小值为（ ）A ．3B ．32C ．1D ．137．下图中的多边形均为正多边形，M ，N 是所在边的中点，双曲线均以1F ，2F 为焦点，且经过M ，N 两点．设图1，图2，图3中双曲线的离心率分别为1e ，2e ，3e ，则（ ）A ．123e e e >>B ．213e e e >>C ．321e e e >>D ．132e e e >>8．已知函数2()ln f x x x ax =+-有两个极值点m ，n ，且[1,2]m ∈，则()()f m f n -的最大值为（ ）A ．2ln 23-B ．2ln 23-C ．3ln 24-D ．3ln 24-二、多选题9．已知a ，b ，c 为非零实数，且0a b -≥，则下列结论正确的有（ ） A ．a c b c +≥+B ．-≤-a bC ．22a b ≥D ．2211ab ba ≥10．设0ω>，函数()cos f x x x ωω=+在区间0,2π⎛⎤⎥⎝⎦上有零点，则ω的值可以是（ ）A ．16B ．56C ．13D ．2311．四边形ABCD 是边长为2的正方形，E 、F 分别为BC 、CD 的中点，分别沿AE 、AF 及EF 所在直线把AEB △、AFD △和EFC 折起，使B 、C 、D 三点重合于点P ，得到三棱锥P AEF -，则下列结论中正确的有（ ）． A ．三棱锥P AEF -的体积为23B ．平面APF ⊥平面EPFC ．三棱锥中无公共端点的两条棱称为对棱，则三棱锥P AEF -中有三组对棱相互垂直D ．若M 为AF 的中点，则过点M 的平面截三棱锥P AEF -的外接球，所得截面的面积的最小值为5π412．已知实数2a >，2b >，且a b ，若b a a b =，则a b -可能等于（ ）A ．0.5B ．1C ．2D ．3三、填空题13．同时将圆221x y +=和22240x y x y +--=的面积平分的直线的斜截式方程为________．14．12233445555555C 0.998C 0.998C 0.998C 0.998C 0.998++++≈_______（精确到0.01）15．已知定义R 上的函数()f x 满足()()()63f x f x f =-+，又()πf x +的图象关于点()π,0-对称，且()12022f =，则()2023f =______16．已知抛物线2:4C y x =，点()1,2P ，,,,A B M N 是抛物线C 上的四个动点，过点P 作分别作AB ，MN 的垂线，垂足分别为E ，F ，2PA PB PM PN k k k k +=+= ,则点E F ､距离的最大值为__________. 四、解答题17．记ABC 的内角,,A B C 的对边分别为,,a b c ，2sin sin sin()A C B A =+-． (1)证明：cos a A b=； (2)若2b ac =，求cos B ．18．已知数列{}n a 满足113(1)1(1)1,22n nn n a a a +--+-==+. (1)设21n n b a -=，求数列{}n b 的通项公式； (2)求数列{}n a 的前2n 项和2n S .19．如图，在四棱锥P ABCD -中，侧面PAD 为等边三角形且垂直于底面ABCD ，//AD BC ，AB AD ⊥．24AB BC ==，E 是棱PD 上的动点（除端点外），,F M 分别为,AB CE 的中点．(1)求证：//FM 平面PAD ；(2)若直线EF 与平面PAD 所成的最大角为30°，求平面CEF 与平面PAD 所成锐二面角的余弦值．20．某中学在一次考试后，对本年级学生物理成绩进行分析，随机抽取了300名同学的物理成绩（均在50~100分之间），将抽取的成绩分组为[)5060，，[)6070，，[)7080，，[)8090，，[]90100，，得到如图所示的频率分布直方图.(1)求这300名同学物理平均成绩x 与第三四分位数的估计值；（结果精确到1）(2)已知全年级同学的物理成绩服从正态分布()2N μσ，，其中μ取（1）中的x ，经计算，σ=11，现从全年级随机选取一名同学的物理成绩，求该成绩在区间()6295，的概率（结果精确到0.1）；(3)根据（2）的条件，用频率估计概率，现从全年级随机选取n 名同学的物理成绩，若他们的成绩都在()6295，的概率不低于1%，求n 的最大值（n 为整数）. 附：lg20.301≈，若()2~N ξμσ，，则()0.68P μσξμσ-<<+≈，()220.96P μσξμσ-<<+≈.21．已知椭圆()2222:10x y E a b a b +=>>2过坐标原点O 的直线交椭圆E 于,P A两点，其中P 在第一象限，过P 作x 轴的垂线，垂足为C ，连接AC .当C 为椭圆的右焦点时，PAC △2(1)求椭圆E 的方程；(2)若B 为AC 的延长线与椭圆E 的交点，试问：APB ∠是否为定值，若是，求出这个定值；若不是，说明理由.22．某大学有A ，B 两个餐厅为学生提供午餐与晚餐服务，甲、乙两位学生每天午餐和晚餐都在学校就餐，近100天选择餐厅就餐情况统计如下： 选择餐厅情况（午餐，晚餐）(),A A(),A B(),B A(),B B甲30天20天40天10天假设甲、乙选择餐厅相互独立，用频率估计概率．(1)分别估计一天中甲午餐和晚餐都选择A 餐厅就餐的概率，乙午餐和晚餐都选择B 餐厅就餐的概率；(2)记X 为甲、乙在一天中就餐餐厅的个数，求X 的分布列和数学期望()E X ；(3)假设M 表示事件“A 餐厅推出优惠套餐”，N 表示事件“某学生去A 餐厅就餐”，()0P M >，一般来说在推出优惠套餐的情况下学生去该餐厅就餐的概率会比不推出优惠套餐的情况下去该餐厅就餐的概率要大，证明：()()P M N P M N >．福建省南安名校2023届高三上学期12月月考数学试题一、单选题1．已知集合{}21log A x N x k =∈<<，集合A 中至少有2个元素，则（ ） A ．16k ≥ B ．16k > C ．8k ≥ D ．8k >【答案】D【分析】由于集合A 中至少有2个元素，所以2log 3k >,从而可求出k 的取值范围 【详解】解：因为集合A 中至少有2个元素， 所以2log 3k >，解得8k >， 故选：D2．已知圆锥的轴截面是一个正三角形，则其侧面积与轴截面面积之比是（ ）A ．23B C D 【答案】B【分析】分别计算侧面积和面积作比即可. 【详解】设底面圆的半径为r ，则母线长为2r ， 得侧面积是212222r r r ππ⨯⨯=轴截面是一个正三角形，边长为2r ， 则其面积2122sin6032r r r ⨯⨯⨯= .故选：B3．“函数tan y x =的图象关于0(,0)x 中心对称”是“0sin 0x =”的（ ） A ．充分不必要条件 B ．必要不充分条件 C ．充分必要条件 D ．既不充分也不必要条件【答案】B【分析】分别求出tan y x =与sin y x =的对称中心，比较两个中心关系.【详解】tan y x =的对称中心为(π,0),Z 2kk ∈，sin y x =的对称中心为(π,0),Z k k ∈，tan y x=的对称中心不一定为sin y x =的对称中心；sin y x =的对称中心一定为tan y x =的对称中心. 故选：B ．4．若()()2i 2i 1z z -+=，则z 的最大值为（ ）A B C ．2 D ．3【答案】D【分析】根据题意结合共轭复数的概念运算整理的()2221b a -=+，即复数z 对应的点(),a b 在圆()2221x y +-=上，根据圆的性质求z 的最大值.【详解】设()=+i,,R z a b a b ∈，则()()2i=+2i,+2i=2i z a b z a b ----∵()()()()()222i 2i =2i 2i 21a b a b b z z a +----=⎡⎤⎡⎤=+⎣⎦+⎦⎣-∴复数z 对应的点(),a b 在圆()2221x y +-=上圆()2221x y +-=的圆心()0,2C ，半径=1r ，则z 的最大值为3OC r +=，其中O 为复平面的坐标原点 故选:D.5．已知等差数列{}n a 和等比数列{}n b 均为递增数列，且121a b ==，26a b =，若10k a b =，则k 的最小值为（ ） A ．3 B ．4 C ．5 D ．6【答案】B【分析】由等差数列和等比数列的通项公式可得3k d =+，由0d >，即可得k 的最小值. 【详解】设等差数列{}n a 公差为d ，等比数列{}n b 公比为q ， 则0d >，1q >，因为121a b ==，26a b =， 所以41d q +=①，而10k a b =， 所以81(1)k d q +-=②，由①②得：2(1)1(1)d k d +=+-， 即3k d =+，0d >，k *∈N ，所以k 的最小值为4. 故选：B6．在ABC 中，点P 满足2BP PC =，过点P 的直线与AB ，AC 所在的直线分别交于点M ，N ，若AM x AB =，()0,0AN yAC x y =>>，则2x y +的最小值为（ ）A ．3B ．32C ．1D ．13【答案】A【分析】由向量加减的几何意义可得233AB ACAP =+，结合已知有233AM AN AP x y =+，根据三点共线知21133x y+=，应用基本不等式“1”的代换即可求最值，注意等号成立的条件. 【详解】由题设，如下图示：23333BC AC AB AB ACAP AB BP AB AB -=+=+=+=+，又AM x AB =，()0,0AN yAC x y =>>，∴233AM AN AP x y=+，由,,M P N 三点共线，有21133x y +=， ∴21522522)23333333323(2)(x y x yx y y x x xy y y x +=+=⋅++≥++，当且仅当x y =时等号成立. 故选：A【点睛】关键点点睛：利用向量线性运算的几何表示，得到AP 、AM 、AN 的线性关系，根据三点共线有21133x y+=，再结合基本不等式求最值. 7．下图中的多边形均为正多边形，M ，N 是所在边的中点，双曲线均以1F ，2F 为焦点，且经过M ，N 两点．设图1，图2，图3中双曲线的离心率分别为1e ，2e ，3e ，则（ ）A ．123e e e >>B ．213e e e >>C ．321e e e >>D ．132e e e >>【答案】A【分析】由双曲线定义有122F F c =、122F N F N a -=，结合正多边形的性质求得12F N F N -关于c 的表达式，即可求各图对应双曲线的离心率.【详解】在图1中，122F F c =，又122(31)F N F N a c -==，则1232e =-在图2中，122F F c =，221210(2)2F N c c ⎛⎫=+ ⎪ ⎪⎝⎭，22F N =， 121022F N F N a --==，则2102e =-． 在图3中，122F F c =，212F N c =，由余弦定理得：2211221222cos 60F N F F F N F F F N =+-︒13=，121312F N F N a --==，则3131e =-． 因为232102131<，所以123e e e >>． 故选：A8．已知函数2()ln f x x x ax =+-有两个极值点m ，n ，且[1,2]m ∈，则()()f m f n -的最大值为（ ）A ．2ln 23-B ．2ln 23-C ．3ln 24-D ．3ln 24-【答案】C【分析】对()f x 求导得()f x '，得到m ，n 是2210x ax -+=两个根，由根与系数的关系可得m ，n 的关系，然后构造函数，利用导数求单调性，进而得最值.【详解】由2()ln f x x x ax =+-得：2121()2x ax f x x a x x-+=+-=' m ，n 是2210x ax -+=两个根，由根与系数的关系得：1,22a m n mn +==，故12n m=22222221()()ln ln lnln 24m f m f n m m am n n an m n m m n m-=+---+=-+=+-， 令[]2,1,4x m x =∈记[]1()ln 2,1,44g x x x x x =+-∈，则()222222111414()10444x x x g x x x x x----'=--==<，故()g x 在[]1,4x ∈上单调递减. ()()max 311n24g x g ==-故选：C二、多选题9．已知a ，b ，c 为非零实数，且0a b -≥，则下列结论正确的有（ ） A ．a c b c +≥+ B ．-≤-a b C ．22a b ≥ D ．2211ab ba ≥ 【答案】ABD【解析】根据不等式的性质判断，错误的命题可举反例．【详解】因为0a b -≥，所以a b ≥.根据不等式的性质可知A ，B 正确； 因为a ，b 的符号不确定，所以C 不正确； 2222110a b ab ba a b --=≥. 可得2211ab ba ≥，所以D 正确. 故选：ABD ．【点睛】本题考查不等式的性质，掌握不等式的性质是解题关键．10．设0ω>，函数()cos f x x x ωω=+在区间0,2π⎛⎤⎥⎝⎦上有零点，则ω的值可以是（ ）A ．16B ．56C ．13D ．23【答案】BCD【分析】由题得()2sin 6πω⎛⎫=-- ⎪⎝⎭f x x ，令6x k πωπ-=，求出,6k x ππωω=+解不等式062ππω<得解.【详解】由题得()cos 2sin 6f x x x x πωωω⎛⎫=+=-- ⎪⎝⎭，令6x k πωπ-=，解得,06k x ππωωω=+>，取k ＝0， 062ππω∴<，即13ω． 故选：BCD11．四边形ABCD 是边长为2的正方形，E 、F 分别为BC 、CD 的中点，分别沿AE 、AF 及EF 所在直线把AEB △、AFD △和EFC 折起，使B 、C 、D 三点重合于点P ，得到三棱锥P AEF -，则下列结论中正确的有（ ）． A ．三棱锥P AEF -的体积为23B ．平面APF ⊥平面EPFC ．三棱锥中无公共端点的两条棱称为对棱，则三棱锥P AEF -中有三组对棱相互垂直D ．若M 为AF 的中点，则过点M 的平面截三棱锥P AEF -的外接球，所得截面的面积的最小值为5π4【答案】BCD【分析】由条件结合线面垂直判定定理证明PA ⊥平面EFP ，根据面面垂直判定定理证明平面APF ⊥平面EPF ，判断B ，根据锥体体积公式求三棱锥P AEF -的体积判断A ，由线面垂直的性质判断C ，由球的截面的性质判断D.【详解】由已知22215F AE A =+22112=+=EF 翻折前AB BE ⊥，CE CF ⊥，AD DF ⊥， 翻折后，则有PA PE ⊥，PA PF ⊥，PE PF ⊥， 因为PA PE ⊥，PA PF ⊥，PE PF P =，,PE PF ⊂平面EFP ，所以PA ⊥平面EFP ，因为PA ⊥平面EFP ，PE PF ⊥，又1PE PF ==，2PA =，所以111123323P AEF A EFP EFPV V SAP --==⨯⨯=⨯⨯=，A 错误，因为PA ⊥平面EFP ，又PA ⊂平面APF ，所以平面APF ⊥平面EPF ，B 正确，因为PA ⊥平面EFP ，EF ⊂平面EFP ，所以PA EF ⊥， 因为PA PF ⊥，PE PF ⊥，PA PE P =，,PE PA ⊂平面PAE ，所以PF ⊥平面PAE ，又AE ⊂平面PAE ，所以PF ⊥AE ， 同理可证PE AF ⊥，所以三棱锥P AEF -中有三组对棱相互垂直，C 正确， 将三棱锥P AEF -补成长方体PEQA FGNH -，则三棱锥P AEF -的外接球球心O 为体对角线PN 的中点， 且2226PN PE PF PA =++O 的半径为6R =， 所以，过点M 的平面截三棱锥P AEF -的外接球所得截面圆的半径设为r ， 设球心O 到截面圆的距离为d ，则0d OM ≤≤， O 、M 分别为PN 、PH 的中点，则1122OM HN ==， 则102d ≤≤，又22r R d -12d =时，2r 取最小值54，所以过点M 的平面截三棱锥P AEF -的外接球，所得截面的面积的最小值为5π4，D 正确， 故选：BCD.12．已知实数2a >，2b >，且a b ，若b a a b =，则a b -可能等于（ ）A ．0.5B ．1C ．2D ．3【答案】AB【分析】问题可转化为,a b 是()ln xf x x=大于2的两个不同零点，利用导数研究单调性并作出图象，结合图象即可求解【详解】因为实数2a >，2b >，且a b ，若b a a b =，所以ln ln b a a b =，即ln ln b a a b =， 所以ln ln a ba b=， 令()ln xf x x=，()21ln xf x x -'=， 令0f x解得0e x <<，令()0f x '<解得e x >，所以()f x 在()0,e 单调递增，在()e,+∞上单调递减， 作出()ln xf x x=的图象如下：2a >，2b >，不妨设a b >，()()()()ln 2ln 4ln 22,4,24242f f f f ====， 由图象可知：e 4a <<，2e b <<，且422a b -<-=， 所以AB 正确，CD 错误； 故选：AB三、填空题13．同时将圆221x y +=和22240x y x y +--=的面积平分的直线的斜截式方程为________． 【答案】2y x =【分析】求出两圆圆心坐标，过两圆圆心的直线即为所求直线. 【详解】圆221x y +=的圆心为()0,0，圆22240x y x y +--=化为标准方程为：()()22125x y -+-=，其圆心为()1,2，同时将圆221x y +=和22240x y x y +--=的面积平分的直线过两圆圆心， 所以所求直线方程为()200010y x --=--，即2y x =. 故答案为：2y x =.14．12233445555555C 0.998C 0.998C 0.998C 0.998C 0.998++++≈_______（精确到0.01）【答案】30.84【分析】先利用二项式定理将原式化为5(10.998)1+-，再变形为5(20.002)1--，利用二项式定理展开，并近似计算．【详解】原式55(10.998)1(20.002)1=+-=--32051423255555555344C 2C 20.002C 20.002C 20.002C 20.002C 0.0021=-⨯+⨯-⨯+⨯-⨯-320.16130.84≈--=故答案为：30.84．15．已知定义R 上的函数()f x 满足()()()63f x f x f =-+，又()πf x +的图象关于点()π,0-对称，且()12022f =，则()2023f =______ 【答案】2022-【分析】根据()πf x +的图象关于点()π,0-对称判断函数为奇函数，再赋值法确定()3f 的值，进而得到函数是周期函数，找出()2023f 与()1f 的关系可得答案.【详解】()πf x +的图象关于点()π,0-对称，所以()f x 的图象关于点()0,0对称， 即()f x 为奇函数，在()()()63f x f x f =-+中，()()()()36333=0f f f f =-+∴，， 所以()()6f x f x =-，又()(),f x f x =--∴()()6f x f x --=-,()()6,f x f x ∴-=+()()()()612,12f x f x f x f x ∴-+=+∴=+， 所以()f x 是12T =的周期函数，()()()()()202312168776112022.f f f f f =⨯+==+=-=- 故答案为：2022-16．已知抛物线2:4C y x =，点()1,2P ，,,,A B M N 是抛物线C 上的四个动点，过点P 作分别作AB ，MN 的垂线，垂足分别为E ，F ，2PA PB PM PN k k k k +=+= ,则点E F ､距离的最大值为__________.【答案】【分析】设直线AB ，MN 的方程，与抛物线方程联立，运用韦达定理证明直线AB ，MN 是过定点的，运用几何意义即可求解.【详解】设直线AB 的方程为221212,,,,44y y x my n A y B y ⎛⎫⎛⎫=+ ⎪ ⎪⎝⎭⎝⎭，将x my n =+代入24y x =中有2440y my n --= ，故12124,4y y m y y n +==-，又1244,22PA PB k k y y ==++， 所以()()()121212124441442224212PA PB y y m k k y y y y y y m n++++=+===++++++-，解得1n =-， 故直线AB 过定点()1,0Q -.因此点E 在以PQ 为直径的圆上， 同理点F 在以PQ 为直径的圆上.PQ =； 故点E F ､距离的最大值为圆的直径故答案为：四、解答题17．记ABC 的内角,,A B C 的对边分别为,,a b c ，2sin sin sin()A C B A =+-． (1)证明：cos a A b=； (2)若2b ac =，求cos B ． 【答案】(1)证明见解析..【分析】（1）将2sin sin sin()A C B A =+-化为2sin sin()sin()A B A B A =++-，利用两角和的正弦公式化简，结合正弦定理角化边，即可证明结论;（2）利用（1）的结论和题设，结合余弦定理可推出a c =，再用222cos 2a c b B ac +-=化简求值，可得答案.【详解】（1）由题意知，2sin sin()sin()A B A B A =++-， 所以2sin sin cos cos sin sin cos cos sin A B A B A B A B A =++-， 所以2sin 2sin cos A B A =，而(0,π),sin 0B B ∈≠ ，结合正弦定理，所以sin cos sin A aA B b==. （2）由（1）知：222cos 2a b c a A b bc+-==, 所以222ac ac c a =+-，即220a c ac -+=，所以2210a ac c+-=解得a c =（舍）,所以2222211cos 11)2222a c b a c ac a c B ac ac c a +-+-⎛⎫===+-== ⎪⎝⎭. 18．已知数列{}n a 满足113(1)1(1)1,22n nn n a a a +--+-==+. (1)设21n n b a -=，求数列{}n b 的通项公式； (2)求数列{}n a 的前2n 项和2n S .【答案】(1)21nn b =-(2)123236n n S n +=⋅--【分析】（1）先化简()()1311122n nn n a a +--+-=+，再推导出111n n b b +++等于一个常数，即可求解；（2）结合第一问，先求出数列{}n a 的满足的规律，然后再求和.【详解】（1）由已知有：12=21,3(1)1(1)12,22n n n n n n a n k k Za a a n k k Z ++∈⎧--+-=+=⎨+=∈⎩，， 所以21+1+1n n b a -=，()1212212121111=2222222(1)2(1)n n n n n n n b a a a a a b ++---++=++=+=+=+=+， 其中11+1+12b a ==，所以数列{}1n b +为以2为首项，公比为2的等比数列. 所以11222n n n b -+=⨯=，得21n n b =-.（2）由（1）知：2121nn n b a -==-，22122(21)n n n a a -==-，所以1231232(21)(21)(21)(21)2[(21)(21)(21)(21)]n n n S =-+-+-++-+-+-+-++-1233[(21)(21)(21)(21)]n =-+-+-++-1233(2222)3n n =++++-2(12)3312n n -=⨯--13236n n +=⋅--.19．如图，在四棱锥P ABCD -中，侧面PAD 为等边三角形且垂直于底面ABCD ，//AD BC ，AB AD ⊥．24AB BC ==，E 是棱PD 上的动点（除端点外），,F M 分别为,AB CE 的中点．(1)求证：//FM 平面PAD ；(2)若直线EF 与平面PAD 所成的最大角为30°，求平面CEF 与平面PAD 所成锐二面角的余弦值．【答案】(1)证明见解析 (2)9331【分析】（1）取CD 中点N ，连接,MN NF ，先明平面//MNF 平面PAD ，再证明结论；（2）先根据题意，建立空间直角坐标系，利用用向量数量积计算直线与平面成角正弦值，列方程求最值解，再用向量数量积求二面角的余弦值． 【详解】（1）证明：证明：取CD 中点N ，连接,MN NF ， 因为M 为CE 中点，所以//MN DE ， 因为MN ⊄平面PAD ，DE ⊂平面PAD 所以//MN 平面PAD ，又因为//AD BC ，F 为AB 中点， 所以//FN AD ，因为FN ⊄平面PAD ，AD ⊂平面PAD 所以//FN 平面PAD ，因为MN FN N ⋂=，MN 、FN ⊂平面MNF ， 所以平面//MNF 平面PAD ， 又因为MF ⊂平面MNF ， 所以//MF 平面PAD ．（2）解：建立如图所示的空间直角坐标系， 设4AD a =，()0,43E a t t -，()0,2t a ∈，则()0,0,0A ，()2,0,0F ，()4,2,0C ， ()2,2,0FC →=，()2,4FE a t →=--，平面PAD 的法向量为()1,0,0m →=，直线EF 与平面PAD 所成的正弦值为FE mFE m→→→→⋅==⋅，当ta =1sin302=︒=， 解得1a =，(FE →=-， 设平面CEF 的法向量为(),,n x y z →=， 220230FC n x y FE n x y ⎧⋅=+=⎪⎨⋅=-+=⎪⎩，令y=)n →=，3cos ,311n m n m n m⋅===⋅⋅ 所以平面CEF 与平面PAD20．某中学在一次考试后，对本年级学生物理成绩进行分析，随机抽取了300名同学的物理成绩（均在50~100分之间），将抽取的成绩分组为[)5060，，[)6070，，[)7080，，[)8090，，[]90100，，得到如图所示的频率分布直方图.(1)求这300名同学物理平均成绩x 与第三四分位数的估计值；（结果精确到1）(2)已知全年级同学的物理成绩服从正态分布()2N μσ，，其中μ取（1）中的x ，经计算，σ=11，现从全年级随机选取一名同学的物理成绩，求该成绩在区间()6295，的概率（结果精确到0.1）；(3)根据（2）的条件，用频率估计概率，现从全年级随机选取n 名同学的物理成绩，若他们的成绩都在()6295，的概率不低于1%，求n 的最大值（n 为整数）. 附：lg20.301≈，若()2~N ξμσ，，则()0.68P μσξμσ-<<+≈，()220.96P μσξμσ-<<+≈. 【答案】(1)73；79 (2)0.8 (3)20【分析】（1）利用题给条件和平均数与第三四分位数的定义即可求得这300名同学物理平均成绩x 与第三四分位数的估计值；（2）利用正态分布的性质即可求得该成绩在区间()6295，的概率； （3）利用独立事件同时发生的概率列出关于n 的不等式，解之即可求得n 的最大值. 【详解】（1）550.1650.3750.4850.1950.173x =⨯+⨯+⨯+⨯+⨯=. 35701078.7540+⨯=， 则这300名同学物理平均成绩x 与第三四分位数的估计值分别为73，79 （2）()()11629520.680.960.820.822P P ξμσξμσ<<=-<<+≈⨯+⨯=≈，（3）()0.80.01n≥，即0.8lg0.012log 0.0120.62lg0.83lg21n -≤==≈-， 故n 的最大值为20.21．已知椭圆()2222:10x y E a b a b +=>>过坐标原点O 的直线交椭圆E 于,P A两点，其中P 在第一象限，过P 作x 轴的垂线，垂足为C ，连接AC .当C 为椭圆的右焦点时，PAC △(1)求椭圆E 的方程；(2)若B 为AC 的延长线与椭圆E 的交点，试问：APB ∠是否为定值，若是，求出这个定值；若不是，说明理由. 【答案】(1)22142x y += (2)APB ∠为定值90【分析】（1）由离心率可得,,a b c 之间关系，根据通径长可得2b PC a=，由2PACPOCS S=可构造方程求得22,a b ，由此可得椭圆方程；（2）设直线():0AP y kx k =>，结合斜率公式可求得2AC kk =，由此可得直线AC 方程，将其与椭圆方程联立，结合韦达定理可求得B 点坐标，利用向量数量积的坐标运算可求得0PA PB ⋅=，由此可得结论. 【详解】（1）椭圆离心率22c e a ==，2212c a ∴=，则222212b a c a =-=， 当C 为椭圆右焦点时，212b PC a a ==； 211122222224PACPOCSSc a ac a ==⨯⋅===，解得：24a =，22b ∴=，∴椭圆E 的方程为：22142x y +=.（2）由题意可设直线():0AP y kx k =>，()00,P x kx ，()11,B x y ， 则()00,A x kx --，()0,0C x ，0002AC kx kk x x ∴==+，∴直线()0:2k AC y x x =-； 由()0222142k y x x x y ⎧=-⎪⎪⎨⎪+=⎪⎩得：()22222002280k x k x x k x +-+-=， 2001222k x x x k ∴-+=+，则2010222k x x x k =++， ()2300110002222222k x k x k k y x x x x k k ⎛⎫∴=-=+-= ⎪++⎝⎭，23000222,22k x k x B x k k ⎛⎫∴+ ⎪++⎝⎭；2002222,22k x kx PB k k ⎛⎫∴=- ⎪++⎝⎭，又()002,2PA x kx =--，()20000222222022k x kx PA PB x kx k k ⎛⎫∴⋅=-⋅+-⋅-= ⎪++⎝⎭，则PA PB ⊥，APB ∴∠为定值90.【点睛】思路点睛：本题考查直线与椭圆综合应用中的定值问题的求解，求解此类问题的基本思路如下：①假设直线方程，与椭圆方程联立，整理为关于x 或y 的一元二次方程的形式； ②利用0∆>求得变量的取值范围，得到韦达定理的形式； ③结合韦达定理的结论表示出所求量； ④化简整理可得定值.22．某大学有A ，B 两个餐厅为学生提供午餐与晚餐服务，甲、乙两位学生每天午餐和晚餐都在学校就餐，近100天选择餐厅就餐情况统计如下：假设甲、乙选择餐厅相互独立，用频率估计概率．(1)分别估计一天中甲午餐和晚餐都选择A 餐厅就餐的概率，乙午餐和晚餐都选择B 餐厅就餐的概率；(2)记X 为甲、乙在一天中就餐餐厅的个数，求X 的分布列和数学期望()E X ；(3)假设M 表示事件“A 餐厅推出优惠套餐”，N 表示事件“某学生去A 餐厅就餐”，()0P M >，一般来说在推出优惠套餐的情况下学生去该餐厅就餐的概率会比不推出优惠套餐的情况下去该餐厅就餐的概率要大，证明：()()P M N P M N >． 【答案】(1)0.3，0.4； (2)分布列见解析，1.9； (3)证明见解析.【分析】(1)由统计表确定甲午餐和晚餐都选择A 餐厅就餐频率和乙午餐和晚餐都选择B 餐厅就餐的频率，由频率估计概率即可；(2)由条件确定随机变量X 的可能取值，再求取各值的概率，根据期望的定义求期望；(3)由条件结合条件概率公式证明()()()P NM P N P M >⋅，由此证明()()P M N P M N >.【详解】（1）设事件C 为“一天中甲员工午餐和晚餐都选择A 餐厅就餐”， 事件D 为“乙员工午餐和晚餐都选择B 餐厅就餐”，因为100个工作日中甲员工午餐和晚餐都选择A 餐厅就餐的天数为30， 乙员工午餐和晚餐都选择B 餐厅就餐的天数为40， 所以()300.3100P C ==，()400.4100P D ==． （2）由题意知，甲员工午餐和晚餐都选择B 餐厅就餐的概率为0.1， 乙员工午餐和晚餐都选择A 餐厅就餐的概率为0.2，记X 为甲、乙两员工在一天中就餐餐厅的个数，则X 的所有可能取值为1、2， 所以()10.30.20.10.40.1P X ==⨯+⨯=，()()2110.9P X P X ==-==， 所以X 的分布列为：所以X 的数学期望()10.120.9 1.9E X =⨯+⨯=． （3）由题知()()P N M P N M >，即()()()()()()()1P NM P NM P N P NM P M P M P M ->=-，即()()()P NM P N P M >⋅，即()()()()()()()P NM P N P NM P N P M P N P NM ->⋅-， 即()()()()P NM P N P N P NM ⋅>⋅，即()()()()P NM P NM P N P N >，即()()P M N P M N >．。

2024届湖北省武昌实验中学高三上学期12月月考化学试题及答案

2024届湖北省武昌实验中学高三上学期12月月考化学试题及答案

湖北省武昌实验中学高三年级12月月考化学试卷命题教师：韩雅莲考试时间：2023年12月11日下午14:30—15:45可能用到的相对原子质量H 1 Li 7 C 12 N 14 O 16 Mn 55一、选择题（本题共15小题，每小题3分，共45分。

每小题只有一个选项符合题意）1．下列描述错误的是（）A ．1869年俄国化学家门捷列夫根据相对原子质量从小到大的顺序制作了第一张元素周期表B ．1922年德国化学家施陶丁格提出了“聚合反应是大量小分子以化学键相互结合形成大分子的过程”假说，为建立高分子科学奠定了基础C ．葡萄糖在水溶液中存在链状和环状结构之间的平衡，从链状到环状发生了加成反应D ．核酸检测是诊断新冠肺炎的重要依据，核酸是生物体遗传信息的载体，通过红外光谱仪可检测其结构中存在单键、双键、氢键等化学键2．“人造太阳”可照亮地球。

“人造太阳”是通过氘(D)氘(T)核聚变反应而实现的。

这意味着人类未来的可持续发展将有新的出路，也为全世界持续多年的能源危机找到一个终极解决方案。

下列说法正确的是（）A ．氘与氚互为同素异形体B ．2D 、2T 、DT 均属于单质C ．T 转化为D 发生化学变化D ．2D 、2T 、DT 的摩尔质量相同3．下列说法正确的是（）A ．透明溶液中能大量共存的离子：224K Na Cu SO +++-、、、B ．4KHSO 在熔融状态下的电离方程式为：244KHSO =K H SO ++-++C ．右图为NaCl 固体溶解并形成水合离子的示意图：a 离子为Na +，b 离子为Cl -D ．与铝反应放出2H 的溶液中一定能大量共存的离子：43NH K Cl NO ++--、、、4．阿斯巴甜是第三代人工代糖，其甜味度是蔗糖的200倍，又几乎没有热量，常被用于制作无糖饮料，其结构简式如图。

下列说法错误的是（）下列说法错误的是（）A ．Se 的基态原子价电子排布式为244s 4p B ．该化合物的晶体类型是离子晶体C ．该化合物的化学式为86K SeBr D ．距离K 最近的Se Br -八面体有4个9．三级溴丁烷乙醇解的反应进程及势能关系如图所示，有关说法错误的是（）A ．三级溴丁烷乙醇解的反应过程中只存在极性键的断裂和形成B ．反应：()()32532533CH CBr C H OH CH COC H HBr+→+的H 0∆<C ．反应：()()3333CH CBr CH C Br +-→+的活化能最大，决定总反应的速率D ．催化剂可以降低反应的活化能，加快反应速率，降低反应的反应热10．（原题）常温下，二氯化二硫(S 2Cl 2)为橙黄色液体，遇水发生反应，工业上用于橡胶的硫化。

2024届天津市静海区一中高三上学期12月月考数学试题及答案

2024届天津市静海区一中高三上学期12月月考数学试题及答案

静海一中2023-2024第一学期高三数学（12月）学生学业能力调研试卷考生注意：本试卷分第Ⅰ卷基础题（133分）和第Ⅱ卷提高题（14分）两部分，共147分.3分卷面分.知 识 技 能学习能力内容集合简单逻辑函数圆锥曲线立体几何数列基本不等式平面向量三角函数复数关键环节分数10153520205518514第Ⅰ卷 基础题（共131分）一、选择题（每小题5分，共45分）1. 设集合{1,2,3,4,5,6},{1,3,6},{2,3,4}U A B ===，则()U A B = ð（ ）A. {3}B. {1,6}C. {5,6}D. {1,3}2. 设数列{}n a 的公比为q ，则“10a >且01q <<”是“{}n a 是递减数列”的（ ）A 充分不必要条件B. 必要不充分条件C. 充要条件D. 既不充分也不必要条件3. 函数()242log 2xf x x x+=-的大致图象是（ ）A. B. C. D.4. 设0.32,sin28,ln2a b c === ，则（ ）A. c b a << B. b c a <<C. a b c<< D. b a c<<5. 已知2243x y ==，则3y xxy-的值为（ ）.A. 1B. 0C. 1-D. 26. 若三棱锥-P ABC 中，已知PA ⊥底面ABC ，120BAC ∠=︒，2PA AB AC ===，若该三棱雉的顶点都在同一个球面上，则该球的表面积为（ ）A. B. 18πC. 20πD. 7. 已知函数()sin cos f x x x x =+，则下列说法不正确的是（ ）A. 函数()f x 的最小正周期为πB. 函数()f x 的图象关于点π,06⎛⎫⎪⎝⎭对称C. 函数()f x 的图象可由πsin 3y x ⎛⎫=+⎪⎝⎭的图象上所有点横坐标缩短为原来的12，纵坐标不变得到D. 函数()f x 的图象可由sin2y x =的图象上所有点向左平移π6个单位得到8. 已知12,F F 分别为双曲线22221(0,0)x y a b a b -=>>的左、右焦点，过2F 与双曲线的一条渐近线平行的直线交双曲线于点P ，若213PF PF =，则双曲线的离心率为（ ）A. 3B.C.D. 29. 设a R ∈，函数2sin 2,0()474,0x x f x x x a x π<⎧=⎨--≥⎩，若()f x 在区间(),a ∞-+内恰有5个零点，则a 取值范围是（ ）A 7511,2,424⎡⎫⎡⎫⋃⎪⎪⎢⎢⎣⎭⎣⎭B. 75,22,42⎡⎫⎛⎤⋃⎪ ⎢⎥⎣⎭⎝⎦C. 37511,,2424⎛⎤⎡⎫⋃⎪⎥⎢⎝⎦⎣⎭D. 375,2,242⎛⎤⎛⎤⋃⎥⎥⎝⎦⎝⎦二、填空题：每小题5分，共30分.10. 已知复数2i2i 1a +-是纯虚数，则实数=a ______.11. 抛物线28y x =，过焦点的弦AB 长为8，则AB 中点M 的横坐标为____.12. 已知圆()22200x ax y a =+->截直线0x y -=所得弦长是，则a 的值为______．13. 设数列 {}n a 的通项公式为()π21cos 2n n a n =-⋅，其前n 项和为n S ，则20S =__________14. 已知0m >，0n >，21m n +=，则()()11m n mn++的最小值为______.15. 如图是由两个有一个公共边的正六边形构成的平面图形Γ，其中正六边形边长为1，设的.AG xAB y AI =+ ，则x y +=______；P 是平面图形Γ边上的动点，则GE AP ⋅的取值范围是______.三、解答题：（本大题共5小题，共72分）16. 在ABC 中，角A ，B ，C 所对边分别为a ，b ，c .已知sin A C =，150B =︒，ABC 的面.（1）求a 的值；（2）求sin A 的值；（3）求sin 26A π⎛⎫+⎪⎝⎭的值.17. 如图，四棱锥P ABCD -中，底面ABCD 为平行四边形，PA ABCD ⊥面，M 是棱PD 的中点，且2AB AC PA ===，BC =（I ）求证：CD PAC ⊥面； （Ⅱ）求二面角M AB C --的大小；（Ⅲ）若N 是AB 上一点，且直线CN 与平面MAB，求AN NB 的值．18. 设椭圆22221(0)x y a b a b +=>>的右焦点为F ，左右顶点分别为A ，B ．已知椭圆的离心率为12，||3AF =．（1）求椭圆的方程；（2）已知P 为椭圆上一动点（不与端点重合），直线BP 交y 轴于点Q ，若四边形OPQA的面积是三角形的BFP 面积的3倍，求直线BP 的方程．19. 已知数列{}{},,n n n a b S 是数列{}n a 的前n 项和，已知对于任意N*n ∈，都有323n n a S =+，数列{}n b 是等差数列，131log b a =，且2465,1,3b b b ++-成等比数列.（1）求数列{}n a 和{}n b 的通项公式.（2）记211,N n n n n nb d n b b a *++-=∈，求数列{}n d 前n 项和n T .（3）记2,,n n na n cb n ⎧⎪=⎨⎪⎩为奇数为偶数，求211n k k k c c +=∑.第Ⅱ卷提高题（共14分）20. 已知函数()()e 11xf x a x =+--，其中a ∈R .（1）当3a =时，求曲线()y f x =在点()()0,0f 处的切线方程；（2）讨论函数()f x 的单调性；（3）当1a >时，证明：()cos f x x x a x >-.的静海一中2023-2024第一学期高三数学（12月）学生学业能力调研试卷命题人：李静 审题人：陈中友考生注意：本试卷分第Ⅰ卷基础题（133分）和第Ⅱ卷提高题（14分）两部分，共147分.3分卷面分.知 识 技 能学习能力内容集合简单逻辑函数圆锥曲线立体几何数列基本不等式平面向量三角函数复数关键环节分数10153520205518514第Ⅰ卷 基础题（共131分）一、选择题（每小题5分，共45分）1. 设集合{1,2,3,4,5,6},{1,3,6},{2,3,4}U A B ===，则()U A B = ð（ ）A. {3}B. {1,6}C. {5,6}D. {1,3}【答案】B 【解析】【分析】根据交集、补集的定义可求()U A B ⋂ð.【详解】由题设可得{}U 1,5,6B =ð，故(){}U 1,6A B ⋂=ð，故选：B2. 设数列{}n a 的公比为q ，则“10a >且01q <<”是“{}n a 是递减数列”的（ ）A. 充分不必要条件 B. 必要不充分条件C. 充要条件 D. 既不充分也不必要条件【答案】A 【解析】【分析】根据题意，结合等比数列的通项公式，分别验证充分性以及必要性，即可得到结果.【详解】由等比数列的通项公式可得，111n n n a a a qq q-=⋅=⋅，.当10a >且01q <<时，则10a q >，且n y q =单调递减，则1n n aa q q=⋅是递减数列，故充分性满足；当1n n a a q q =⋅是递减数列，可得1001a q >⎧⎨<<⎩或101a q <⎧⎨>⎩，故必要性不满足；所以“10a >且01q <<”是“{}n a 是递减数列”的充分不必要条件.故选：A3. 函数()242log 2xf x x x+=-的大致图象是（ ）A. B. C. D.【答案】D 【解析】【分析】方法一：根据函数的奇偶性及函数值的符号排除即可判断；方法二：根据函数的奇偶性及某个函数值的符号排除即可判断.【详解】方法一：因为202xx+>-，即()()220x x +⋅-<，所以22x -<<，所以函数()242log 2xf x x x+=-的定义域为()2,2-，关于原点对称，又()()242()log 2xf x x f x x--=-=-+，所以函数()f x 是奇函数，其图象关于原点对称，故排除B C ,；当()0,2x ∈时，212x x+>-，即42log 02xx +>-，因此()0f x >，故排除A.故选:D.方法二：由方法一，知函数()f x 是奇函数，其图象关于原点对称，故排除B C ,；又()211log 302f =>，所以排除A.故选：D.4. 设0.32,sin28,ln2a b c === ，则（ ）A. c b a<< B. b c a<<C. a b c <<D. b a c<<【答案】B 【解析】【分析】根据给定条件，利用指数、对数函数、正弦函数的性质，借助“媒介数”比较判断作答.【详解】00.32,si 2n n212i 81s 30a b >=<===2e <<，则1ln 212<<，即112c <<，所以b<c<a .故选：B5. 已知2243x y ==，则3y xxy-的值为（ ）A. 1 B. 0C. 1- D. 2【答案】C 【解析】【分析】利用指数与对数互化的公式表示出224log 3,log 3x y ==，再利用换底公式和对数的运算性质化简计算.【详解】因为2243x y ==，所以224log 3,log 3x y ==，由换底公式和对数的运算性质可得33333322433131813log 2log 24log 8log 24log log 1log 3log 3243y x xy x y -=-=-=-=-===-.故选：C6. 若三棱锥-P ABC 中，已知PA ⊥底面ABC ，120BAC ∠=︒，2PA AB AC ===，若该三棱雉的顶点都在同一个球面上，则该球的表面积为（ ）A. B. 18πC. 20πD. 【答案】C 【解析】【分析】由题设知三棱锥-P ABC 是相应正六棱柱内的一个三棱锥，由此知该三棱锥的外接球即为该六棱柱的外接球，求出正六棱柱的外接球半径即可得．【详解】三棱锥-P ABC 中，已知PA ⊥底面ABC ，120BAC ∠=︒，2PA AB AC ===，故该三棱锥为图中正六棱柱内的三棱锥-P ABC ，所以该三棱锥的外接球即为该六棱柱的外接球，所以外接球的直径2R ==，则R =所以该球的表面积为224π4π20πS R ==⋅=．故选：C ．7. 已知函数()sin cos f x x x x =+，则下列说法不正确的是（ ）A. 函数()f x 的最小正周期为πB. 函数()f x 的图象关于点π,06⎛⎫⎪⎝⎭对称C. 函数()f x 的图象可由πsin 3y x ⎛⎫=+⎪⎝⎭的图象上所有点横坐标缩短为原来的12，纵坐标不变得到D. 函数()f x 的图象可由sin2y x =的图象上所有点向左平移π6个单位得到【答案】B 【解析】【分析】首先化简函数()f x ，再根据三角函数的性质，求最小正周期判断A ，整体代入法判断对称中心判断B ，利用函数图象变换法则即可判断CD.【详解】()1πsin cos sin 22sin 223f x x x x x x x ⎛⎫===+ ⎪⎝⎭，所以函数的最小正周期2ππ2T ==，故A 正确；当π6x =时，πππ2πsin 2sin 06633f ⎛⎫⎛⎫=⨯+==≠ ⎪ ⎪⎝⎭⎝⎭，所以π,06⎛⎫⎪⎝⎭不是函数()f x 一个对称中心，故B 错误；由πsin 3y x ⎛⎫=+ ⎪⎝⎭的图象上所有点横坐标缩短为原来的12，纵坐标不变得到πsin(23y x =+，故C 正确；将sin2y x =的图象上所有点向左平移π6个单位得到ππsin[2()]sin(2)63y x x =+=+，故D 正确.故选：B的8. 已知12,F F 分别为双曲线22221(0,0)x y a b a b -=>>的左、右焦点，过2F 与双曲线的一条渐近线平行的直线交双曲线于点P ，若213PF PF =，则双曲线的离心率为（ ）A. 3B.C.D. 2【答案】C 【解析】【分析】设过2F 与双曲线的一条渐近线by x a=平行的直线交双曲线于点P ，运用双曲线的定义和条件可得1||3PF a =，2||PF a =，12||2F F c =，再由渐近线的斜率和余弦定理，结合离心率公式，计算即可得到所求值．【详解】设过2F 与双曲线的一条渐近线by x a=平行的直线交双曲线于点P ，由双曲线的定义可得12||||2PF PF a -=，由12||3||PF PF =，可得1||3PF a =，2||PF a =，12||2F F c =，由12tan bF F P a ∠=可得12cos aF F P c ∠==，在三角形12PF F 中，由余弦定理可得：222121221212||||||2||||cos PF PF F F PF F F F F P =+-⋅∠，即有2229422aa a c a c c=+-⨯⨯，化简可得223c a =，所以双曲线的离心率==ce a．故选：C ．9. 设a R ∈，函数2sin 2,0()474,0x x f x x x a x π<⎧=⎨-+-≥⎩，若()f x 在区间(),a ∞-+内恰有5个零点，则a 的取值范围是（ ）A. 7511,2,424⎡⎫⎡⎫⋃⎪⎪⎢⎢⎣⎭⎣⎭ B. 75,22,42⎡⎫⎛⎤⋃⎪ ⎢⎥⎣⎭⎝⎦C. 37511,,2424⎛⎤⎡⎫⋃⎪⎥⎢⎝⎦⎣⎭D. 375,2,242⎛⎤⎛⎤⋃⎥⎥⎝⎦⎝⎦【答案】D 【解析】【分析】解法一：利用排除法，分别令94a =和138a =求解函数的零点进行判断，解法二：分类讨论，分()f x 在区间(),0a -有5个零点且在区间[)0,∞+没有零点，()f x 在区间(),0a -有4个零点且在区间[)0,∞+有1个零点和()f x 在区间(),0a -有3个零点且在区间[)0,∞+有2个零点三种情况求解即可【详解】法一（排除法）：令94a =，则2sin 2,0()42,0x x f x x x x π<⎧=⎨--≥⎩，当0x <时，()f x 在区间9,04⎛⎫- ⎪⎝⎭有4个零点，当0x ≥时，()020f =-<，Δ240=>，()f x 在区间[)0,∞+有1个零点，综上所述，()f x 在区间(),a ∞-+内有5个零点，符合题意，排除A ､C.令138a =，则2sin 2,0()14,02x x f x x x x π<⎧⎪=⎨-+≥⎪⎩，当0x <时，()f x 在区间13,08⎛⎫- ⎪⎝⎭有3个零点，当0x ≥时，()1002f =>，Δ140=>，()f x 在区间[)0,∞+有2个零点，综上所述，()f x 在区间(),a ∞-+内有5个零点，符合题意，排除B ，故选D.法二（分类讨论）：①当()f x 在区间(),0a -有5个零点且在区间[)0,∞+没有零点时，满足0532a ∆<⎧⎪⎨-≤-<-⎪⎩，无解；②当()f x 在区间(),0a -有4个零点且在区间[)0,∞+有1个零点时，满足()000522f a ⎧⎪∆>⎪<⎨⎪⎪-≤-<-⎩，解得522a <≤；③当()f x 在区间(),0a -有3个零点且在区间[)0,∞+有2个零点时，满足()000322f a ⎧⎪∆>⎪≥⎨⎪⎪-≤-<-⎩，解得3724a <≤，综上所述，a 的取值范围是375,2,242⎛⎤⎛⎤⋃ ⎥⎥⎝⎦⎝⎦，故选：D.二、填空题：每小题5分，共30分.10. 已知复数2i2i 1a +-是纯虚数，则实数=a ______.【答案】1【解析】【分析】由复数的除法运算、纯虚数的概念即可求得参数a .【详解】由题意()()()()()()2i 2i+12241i 41i2i 222i 12i 12i+14155a a a a a a +-++++-===-----，由题意复数2i 2i 1a +-是纯虚数，则2205a-=且4105a +-=，解得1a =.故答案为：1.11. 抛物线28y x =，过焦点的弦AB 长为8，则AB 中点M 的横坐标为____.【答案】2【解析】【分析】利用梯形中位线定理，结合抛物线的定义，先求出弦AB 的中点M 到准线的距离，最后求出弦AB 的中点M 的横坐标.【详解】抛物线28y x =的准线l 的方程为：2x =-，焦点为(2,0)F ,分别过,,A B M ，作,,AC l BD l MH l ⊥⊥⊥，垂足为,,C D H ，在直角梯形ABDC 中，2AC BDMH +=，由抛物线的定义可知：,AC AF BD BF ==，因此有4222AC BDAF BFAB MH ++====，所以点M 的横坐标为422-=.故答案为：2.12. 已知圆()22200x ax y a =+->截直线0x y -=所得弦长是，则a 的值为______．【答案】2【解析】【分析】化圆的方程为标准方程，可得圆心和半径，求得圆心到直线0x y -=的距离d ，代入弦长公式，即可求得答案.【详解】圆()22200x ax y a =+->可变形为：222()x a y a -+=，所以圆心为(,0)a ，半径r a =，所以圆心到直线0x y -=的距离d ，根据弦长公式可得2==，因为0a >，解得2a =.故答案为：213. 设数列 {}n a 的通项公式为()π21cos 2n n a n =-⋅，其前n 项和为n S ，则20S =__________【答案】20【解析】【分析】先由()πcos2n f n =的周期性及函数值特点，分析数列{}n a 的特点1234n n n n a a a a ++++++=()1,5,9,13,16n = ，；再根据这个特点求解即可.【详解】由()πcos 2n f n =可得：周期为2π4π2T ==，()π1cos 02f ==，()2π2cos 12f ==-，()3π3cos 02f ==，()4π4cos 12f ==.因为()π21cos 2n n a n =-⋅，所以123n n n n a a a a ++++++()()()()()()()1π2π3ππ21cos221cos 241cos 261cos 2222n n n n n n n n +++=-⋅++-⋅++-⋅++-⋅4=，()1,5,9,13,16n = ，所以数列{}n a 的前n 项和具有周期为4的周期性，且这样一个周期内的和为 4 ，所以204520S =⨯=故答案为：20.14. 已知0m >，0n >，21m n +=，则()()11m n mn++的最小值为______.【答案】8+8+【解析】【分析】对代数式结合已知等式进行变形，再利用基本不等式进行求解即可.【详解】因为21m n +=，所以()()()()1122262238m n m m n n m n n m n mmnmnm nmn++++++⎛⎫⎛⎫==++=++ ⎪⎪⎝⎭⎝⎭，因为0m >，0n >，所以62n m m n +≥=，当且仅当62n m m n =时取等号，即23n m =-=时，()()11m nmn++有最小值8+，故答案为：8+【点睛】关键点睛：利用等式把代数式()()11m n mn++变形为628n m mn++.15. 如图是由两个有一个公共边的正六边形构成的平面图形Γ，其中正六边形边长为1，设AG xAB y AI =+ ，则x y +=______；P 是平面图形Γ边上的动点，则GE AP ⋅的取值范围是______.【答案】 ①. 1 ②. 3,32⎡⎤-⎢⎥⎣⎦【解析】【分析】以I 为原点，建立平面直角坐标系，根据,,G B I 三点共线，得到1x y +=，设(,)P x y ，求得)GE AP x ⋅=+ ，令z x =+，转化为求该直线在y 轴上截距的取值范围，得到目标函数的最优解，代入即可求解.【详解】以I 为原点，,BG IO 所在的直线分别为,x y 轴，建立平面直角坐标系，如图所示，因为,,G B I 三点共线，且AG xAB y AI =+，所以1x y +=，由正六边形的内角均为120 ，且边长为1，可得31(()22G E A -，设(,)P x y ，可得31),(22GE AP x y ==+ ，则31()22GE AP x y x ⋅=⋅+=+，令z x =，则)y x z =-，当该直线经过点C 时，截距最大，对应的z 最大，此时·GE AP最大值为3，当该直线经过点(G 时，截距最小，对应的z 最小，此时·GE AP的最小值为32-，所以·GE AP 3,32⎡⎤∈-⎢⎥⎣⎦.故答案为：1；3[,3]2-.三、解答题：（本大题共5小题，共72分）16. 在ABC 中，角A ，B ，C 所对的边分别为a ，b ，c .已知sin A C =，150B =︒，ABC 的面.（1）求a 的值；（2）求sin A 的值；（3）求sin 26A π⎛⎫+ ⎪⎝⎭的值.【答案】（1）；（2； （3）1314.【解析】【分析】(1)已知条件结合三角形面积公式和正弦定理即可求a ；(2)由余弦定理求出b ，再根据正弦定理即可求出sin A ；(3)根据sin A 求出cos A ，再由正弦和角公式、正余弦二倍角公式即可求值.【小问1详解】∵sin A C =，∴由正弦定理得a =，又ABC1sin1502ac ︒=，解得2c =，∴a =；【小问2详解】由余弦定理有2222cos150b a c ac =+-︒，∴b =.由正弦定理sin sin sin a b A A B =⇒==.【小问3详解】∵B ＝150°，∴A ＜90°，∴由sin A得，cos A =，∴sin 22sin cos A A A ==，211cos 22cos 114A A =-=.∴13sin 2sin 2cos cos 2sin 66614A A A πππ⎛⎫+=+= ⎪⎝⎭.17. 如图，四棱锥P ABCD -中，底面ABCD 为平行四边形，PA ABCD ⊥面，M 是棱PD 的中点，且2AB AC PA ===，BC =（I ）求证：CD PAC ⊥面； （Ⅱ）求二面角M AB C --的大小；（Ⅲ）若N 是AB 上一点，且直线CN 与平面MAB，求AN NB 的值．的【答案】（I ）见解析；（Ⅱ）4；（Ⅲ）1．【解析】【分析】【详解】试题分析：(I)，，所以平面PAC ；(II)建立空间直角坐标系，求出两个法向量，平面MAB 的法向量，是平面ABC 的一个法向量，求出二面角；(III)设，平面MAB 的法向量，解得答案．试题解析：证明：(I)连结AC ．因为为在中，，，所以，所以．因为AB //CD ，所以．又因为地面ABCD ，所以．因为，所以平面PAC ．(II)如图建立空间直角坐标系，则．因为M是棱PD的中点，所以．所以，．设为平面MAB的法向量，所以，即，令，则，所以平面MAB的法向量．因为平面ABCD，所以是平面ABC的一个法向量．所以．因为二面角为锐二面角，所以二面角的大小为．(III)因为N是棱AB上一点，所以设，．设直线CN与平面MAB所成角为，因为平面MAB的法向量，所以．解得，即，，所以．18. 设椭圆22221(0)x y a b a b +=>>的右焦点为F ，左右顶点分别为A ，B ．已知椭圆的离心率为12，||3AF =．（1）求椭圆的方程；（2）已知P 为椭圆上一动点（不与端点重合），直线BP 交y 轴于点Q ，若四边形OPQA 的面积是三角形BFP 面积的3倍，求直线BP 的方程．【答案】（1）22143x y +=（2）2)4y x =-【解析】【分析】（1）根据已知线段长度与离心率，求解出,a c 的值，然后根据222a b c =+求解出b 的值，则椭圆方程可求；（2）根据条件将问题转化为三角形ABQ 与三角形OBP 的面积比，由此得到关于,P Q y y 的关系式，通过联立直线与椭圆方程求得对应坐标，然后求解出参数值得P 的坐标，则可求BP 直线方程.【小问1详解】因为，12c e a ==，||3AF =，所以2,3a c a c =+=，所以2,1a c ==，所以b ==所以椭圆方程为22143x y +=；【小问2详解】如图，因为四边形OPQA 与三角形BFP 的面积之比为3:1，所以三角形ABQ 与三角形OPB 的面积比为5:2，所以152122QP AB y OB y ⋅=⋅，所以54Q P y y =，显然直线BP 的斜率不为0，设直线BP 的方程为2x my =+，联立2223412x my x y =+⎧⎨+=⎩，所以()2234120m y my ++=，所以21234P m y m =-+，2Qy m=-，所以22512434m m m -=-+，解得m =，当m =:2BP x y =+，当m =时，:2BP x y =+，故直线BP的方程为2)y x =-.19. 已知数列{}{},,n n n a b S 是数列{}n a 的前n 项和，已知对于任意N*n ∈，都有323n n a S =+，数列{}n b 是等差数列，131log b a =，且2465,1,3b b b ++-成等比数列.（1）求数列{}n a 和{}n b 的通项公式.（2）记211,N n n n n nb d n b b a *++-=∈，求数列{}n d 的前n 项和n T.（3）记2,,n n na n cb n ⎧⎪=⎨⎪⎩为奇数为偶数，求211n k k k c c +=∑.【答案】（1）3nn a =，21n b n =-（2）1122(21)3n nT n =-+⋅ （3）175402591648n n +-+⋅【解析】【分析】（1）首先根据n a 与n S 的关系得到n a ，再根据等比数列的性质即可得到n b ；（2）利用裂项相消法即可得结果；（3）将分组求和与错位相减法相结合即可得结果.【小问1详解】当1n =时，11323a a =+，解得13a =.当2n ≥时，11323n n a S --=+，所以113233n n nn n a a a a a --=⇒=-，即{}n a 是以首先13a =，公比为3的等比数列，即3nn a =.因为131log 3b ==，2465,1,3b b b ++-成等比数列，所以()()()2426153b b b +=+-，即()()()213115153d d d ++=+++-，解得2d =.所以()12121n b n n =+-=-.【小问2详解】由（1）得2112(2)2(21)(21)3n n nn n n b n d b b a n n ++-+-==-+⋅()()()()122111212132213213n n n n n n n n -⎡⎤+==-⎢⎥-+⋅-⋅+⋅⎢⎥⎣⎦，则123n nd d d d T +++⋅⋅⋅+=0112231111111111[((()(2133333535373(21)3(21)3n nn n -=-+-+-+⋅⋅⋅+-⨯⨯⨯⨯⨯⨯-⋅+⋅0111()213(21)3n n =-⨯+⋅1122(21)3nn =-+⋅【小问3详解】1223221211k k n n n k c c c c c c c c =++=+++∑ ，因为()()()()2121212221221211021332193n n nn n n n n n n c c c c c c c n n -+-+-++=+=-+=-⋅，设()219n n d n =-⋅，前n 项和为n K ，则()121939219n n K n =⨯+⨯++-⨯ ，()()23191939239219n n n K n n +=⨯+⨯++-⨯+-⨯ ，()()()()12118119892992199221919n n n n n K n n -++--=+++--⋅=+⨯--⋅- 1458593232n n n K +-=+⋅.所以211110754025931648n n n k k k c c n K +=+-==+⋅∑第Ⅱ卷提高题（共14分）20. 已知函数()()e 11x f x a x =+--，其中a ∈R .（1）当3a =时，求曲线()y f x =在点()()0,0f 处的切线方程；（2）讨论函数()f x 的单调性；（3）当1a >时，证明：()ln cos f x x x a x >-.【答案】（1）30x y -=（2）答案见解析 （3）证明见解析【解析】【分析】（1）求出()0f '，利用导数几何意义结合点斜式方程即可求出切线方程；（2）求出导函数，按照1a ≥和1a <分类讨论研究函数的单调性即可；（3）把原不等式作差变形得()()e cos 1ln 0,0,x a x x x x x x ∞++--->∈+，结合()cos cos a x x x x +>+，把不等式证明转化为e cos 1ln 0x x x x +-->问题，构造函数，求导，利用函数的单调性求得最值即可证明.【小问1详解】当3a =时，()e 21x x x f =+-，()e 2x f x '=+，所以()00e 23f '=+=，又()00e 10f =-=，由导数几何意义知，曲线()y f x =在点()()0,0f 处的切线方程为()030y x -=-，即30x y -=.【小问2详解】因为()()e 11x f x a x =+--，所以()e 1x f x a =+-'，当1a ≥时，()e 10xf x a =+->'，函数()f x 在R 上单调递增；当1a <时，由()e 10xf x a =+->'，得()ln 1x a >-，函数()f x 在区间()()ln 1,a ∞-+上单调递增，由()()e 10x f x a =+-<'，得()ln 1x a <-，函数()f x 在区间()(),ln 1a -∞-上单调递减.【小问3详解】要证()ln cos f x x x a x >-，即证()()e 11ln cos ,0,x a x x x a x x ∞+-->-∈+，即证()()e cos 1ln 0,0,xa x x x x x x ∞++--->∈+，设()cos k x x x =+，则()1sin 0k x x ='-≥故()k x 在()0,∞+上单调递增，又()010k =>，所以()1k x >，又因为1a >，所以()cos cos a x x x x +>+，所以()e cos 1ln e cos 1ln x xa x x x x x x x x ++--->+--，①当01x <≤时，因为e cos 10,ln 0x x x x +->≤，所以e cos 1ln 0x x x x +-->；②当1x >时，令()e cos ln 1x g x x x x =+--，则()e ln sin 1xg x x x '=---，设()()h x g x '=，则()1e cos x h x x x=--'，设()1e cos x m x x x =--，的则()21e sin x m x x x=++'，因为1x >，所以()0m x '>，所以()m x 即()h x '在()1,+∞上单调递增，所以()()1e 1cos10h x h >=--'>'，所以()h x 在()1,+∞上单调递增，所以()()1e sin110h x h >=-->，即()0g x '>，所以()g x 在()1,+∞上单调递增，()()1e cos110g x g >=+->，即e cos 1ln 0x x x x +-->.综上可知，当1a >时，()e cos 1ln e cos 1ln 0x xa x x x x x x x x ++--->+-->，即()ln cos f x x x a x >-.【点睛】方法点睛：利用导数证明不等式的常见形式是()()f x g x >，一般可构造“左减右”的函数，即先将不等式()()f x g x >移项，构造函数()()()h x f x g x =-，转化为证不等式()0h x >，进而转化为证明min ()0h x >，因此只需在所给区间内判断()h x '的符号，从而得到函数()h x 的单调性，并求出函数()h x 的最小值即可.。

天津市第二十五中学2024-2025学年高三上学期12月月考英语试题

天津市第二十五中学2024-2025学年高三上学期12月月考英语试题

天津市第二十五中学2024-2025学年高三上学期12月月考英语试题一、单项选择1．—I’m thinking about learning a new instrument, but I’m a bit worried I’m too old.—You’re never too old to learn something new.A．You are joking.B．Don’t mention it.C．Please yourself!D．Go for it!2．Someone is planning to move out of our building, and their apartment will be _________ for rent at the beginning of March.A．available B．normal C．competitive D．expensive3．Our special thanks go to thousands of volunteers, without ________ tireless work, none of these achievements would be possible.A．which B．whom C．whose D．that4．Caroline doesn't have a natural talent for music but she _________ it with hard work.A．lives up to B．makes up for C．reaches out to D．looks out for 5．George _________ too far. His coffee is still warm.A．must have gone B．might have goneC．can’t have gone D．needn’t have gone6．—Do you remember little Julien from Grade Two?—Well, _________, but I can’t quite think who he is.A．it’s up to you B．that’s a good pointC．I really envy you D．that name rings a bell7．The workers are determined to go through with their railway project, ________ the expenses have risen.A．as long as B．even though C．now that D．as though8．The Smiths _________ the online shopping experience in China since they moved back to New Zealand two years ago.A．had been missing B．were missingC．have been missing D．will be missing9．As a symbol of the glorious history of Chinese civilization, the Forbidden City _________ the cultural memory of the country.A．invents B．preserves C．acquires D．declares10．We were worried that there would be a lot of disagreement at the meeting, but everything went quite _________ .A．repeatedly B．endlessly C．smoothly D．urgently11．The organizers had to cancel the outdoor concert due to the sudden thunderstorm, _________ many eager fans who had been waiting for hours.A．disappointing B．to disappointC．having disappointed D．disappointed12．This online course _________, but you can still access and use the original version.A．has updated B．had updatedC．has been updated D．had been updated13．________ she couldn’t understand was ________ fewer and fewer students showed interest in her lessons.A．What；why B．That；what C．What；because D．Why；that 14．Exercise is not only good for our bodies, but it can also _________ our mood and help us deal with anxiety.A．boost B．match C．ruin D．reflect15．_________ focusing on winning the approval of others, try to understand and accept yourself.A．Because of B．Instead of C．For fear of D．In terms of 16．Coffee may cause sleep disturbance, especially when _________ in large amounts or after 2 pm.A．consumed B．being consumed C．consuming D．having consumed 17．The new model electric car should _________ many safety tests before it is released to the public.A．turn out B．bring about C．go through D．set up二、完形填空I had struggled with math since fourth grade, but worked very hard to 18 the smart students around me. In eleventh grade, much to my classmates 19 , I signed up for precalculus BC, the hardest math class. That was when I met Mr. Dena and told him I had 20 in math, yet I would try my hardest. He was convinced I could succeed 21 the doubts from my classmates.Mr. Dena kept an unforgettable 22 by Sir Isaac Newton on his chalk board: “If I have been able to see further, it is only because I stand on the shoulders of giants.” He reflected on that throughout the year and was 23 to teach us more than math.Mr. Dena occasionally gave partner tests, believing that we could solve hard problems together. He drew names out of a hat to 24 partners. Students were 25 out loud that they wouldn't be paired with me. As the “lucky” name was 26 , the class burst into laughter. My partner joked about being 27 with me. However, we worked well together and surprised everyone with our 28 on this test. I learned so much from my classmates and I realized this was really 29 we had partner tests.The final exam was Mr. Dena's final 30 to us, but I failed it. I told him I didn't understand how I could do so 31 on a test when I had studied so hard. He explained it's not about the grades; it's about true understanding. If studying didn't 32 on a test, it would someday. I knew then that 33 passing or failing tests, studying was about hard work and effort. And I 34 myself harder than I ever had.To be challenged in math really changed the way I 35 other challenges in life. I wasn't going to let a grade stop me from learning some of the best lessons of my life. Mr. Dena is one of the giants that Newton 36 . He has helped me see not only more 37 ideas than I thought possible, but who I can be.18．A．keep up with B．give in to C．stay away from D．watch out for 19．A．sorrow B．delight C．surprise D．relief 20．A．talent B．methods C．innovation D．weaknesses 21．A．in spite of B．in case of C．in view of D．in consequence of 22．A．diary B．quote C．essay D．letter 23．A．embarrassed B．determined C．astonished D．puzzled24．A．assign B．honor C．persuade D．monitor 25．A．reading B．singing C．praying D．applauding 26．A．registered B．changed C．abandoned D．picked 27．A．concerned B．stuck C．impressed D．content 28．A．negotiation B．mistake C．performance D．standard 29．A．when B．why C．where D．how 30．A．decision B．challenge C．instruction D．victory 31．A．accurately B．carefully C．effortlessly D．poorly 32．A．give out B．break down C．turn up D．pay off 33．A．beyond B．within C．upon D．across 34．A．praised B．defended C．pushed D．criticized 35．A．viewed B．created C．ignored D．presented 36．A．admires B．establishes C．measures D．describes 37．A．social B．mathematical C．psychological D．moral三、阅读理解With the rapid development of computer science, the Internet is changing quickly out of our expectations. In the past, we just had the Internet while now we have the Internet of Things (IoT), which aims to get everything and everyone talking. Attaching sensors to “things”, such as cows, cars and refrigerators, and then assigning them unique IP addresses allow them to “talk” to the Internet. Of course, the IoT will involve much more than a handful of sensors. Networking company Cisco estimates that 50 billion Internet-connected devices and objects will be sending over data by 2020.38．How do researchers get everything and everyone talking?A．By establishing the IoT and launching a handful of sensors.B．By sending people to track them day and night and collect useful data.C．By communicating with them all the time through the IoT.D．By connecting sensors with them and appointing them unique IP addresses. 39．According to the passage, which of the following is NOT TRUE?A．IoT can help people do preventive maintenance and save money.B．IoT can help people monitor energy usage and observe price changes timely.C．IoT can help people adjust their habits and use electrical appliances more wisely.D．IoT can help people investigate things and update a lot of important data. 40．Besides its probably ending up being a fashion, what else do critics worry about the IoT?A．People will lose interest in it as quckly as the thrill over last year’s smartphone.B．Whether related companies will provide long-term software updates or not.C．Refrigerators and washing machines will be replaced by other devices in a few years.D．The software provided by companies will be outdated easily and quickly.41．According to the passage, when owners of the Tesla Model S electric car received a recall notice, they ___.A．just waited in the car while the maintenance is being done through wireless updateB．were required to go to the nearest 4S store to make some adjustments or repairsC．could definitely depend on the IoT to send them the charger plug to be fixedD．had to confirm the update with the help of the equipment provided by the company 42．What would be the best title for the passage?A．Craze is disappearing!B．It’s time to change!C．It’s all connected!D．The Internet is coming!Our teacher, Miss Chevalier was a small woman, with a moon face, fatty fingers and curls that sprang straight up from her head, hence the funny name “Poodle (卷毛狗)”. She taught in our reading club. Sometimes she would look in and ask what we were reading — not to check but to know.That’s what happened the day my club was reading aloud a poem by Henry Longfellow. I guess I was better than the others, for Miss Chevalier asked a while later, “Addie, I was wondering if you would recite the whole poem to the Saturday evening’s club.” She said a famous professor was going to give a lecture about the poet, and a presentation of that poem would be a fresh way to start.She asked me to memorize it. “But that shouldn’t be a problem for a child of your ability,” she added. I’m telling you, my happy feet barely touched the ground all the way home. To me, that was the biggest thing ever and I soon learned the whole poem by heart, well prepared for our first rehearsal.I was desperately nervous when I went to her office the next day. But the good thing was she always had the smile that would make you feel like you just did something right.Halfway through the poem, Miss Chevalier stopped me and asked if I knew what “impetuous” meant. Despite her encouraging smile, I wanted to sink through the floor because I was unsure about its pronunciation as well as its meaning. Miss Chevalier pretended not to have noticed my red face and handed me a dictionary, asking me to read its definition aloud. “Impetuous has two definitions: rushing with great force or violence; acting suddenly, with littlethought. ”She asked me which one fitted the poem. I read both definitions over again, trying to figure it out, but Miss Chevalier must have read my mind. “There is no wrong answer,” she said, “I want to know your opinion, Addie.” Hesitantly, I said, “Maybe… both.”She liked that. “One has to be impetuous both ways or they wouldn’t dare to face up to any challenge. Would you call yourself impetuous?”I knew she was asking for an opinion. “My mother thinks being impetuous for girls is improper, anyway.”She said my mom was somewhat right about that. “But girls should also be wise to take up challenges when needed. I believe you are such a girl.”After that, I would never call Miss Chevalier “Poodle” again.43．Why was Addie asked to recite Longfellow’s poem to the Saturday evening’s club?A．To help with her performance.B．To get the attention of her classmates.C．To set an example for the rest of the class.D．To try a new way to warm up the coming lecture.44．Why did Addie feel happy on her way home?A．An event was going to happen.B．She was fully ready for her first rehearsal.C．She gained recognition for her performance.D．She memorized the poem sooner than others.45．What can be learned about Miss Chevalier’s personality from the way she treated Addie?A．Caring and considerate.B．Easygoing and carefree.C．Curious and open-minded.D．Disciplined and strong-willed.46．How did Miss Chevalier succeed in making Addie truly understand the word “impetuous”?A．By asking Addie to define it in her own way.B．By interpreting the two definitions separately.C．By consulting the dictionary for its definitions.D．By linking its definitions to Addie’s situations.47．What is the probable reason that Addie would never call Miss Chevalier “Poodle” again?A．She followed her mother’s advice.B．She made up her mind to be a polite girl.C．She was touched by Miss Chevalier’s trust.D．She felt Miss Chevalier’s teaching funny.Research sometimes proves, with data, what we more or less already know（e. g. Exercise is good for you, and polluted air isn’t）. Still, sometimes our assumptions are incorrect, and scientific findings surprise researchers, along with the rest of us. A recent example is the phenomenon of disappearing lakes in parts of the frozen treeless Arctic（北极的）region.You might think these lakes would be expanding, not disappearing. As climate change warms the region — melting（融化）surface snow and ice as well as the permafrost（永冻层）— there should be more surface water, forming larger lakes and even new ones. Recently, however, scientists have observed not just shrinking（缩小的）lakes but lakes that have completely gone away.Many scientists shared the commonsense expectation that as permafrost melted, lakes would at first expand with meltwater flowing into them. Eventually, researchers made a prediction that progressive warming during the 21st and 22nd centuries would dry out the Arctic, and lakes would begin to shrink. But now it looks as if Arctic lakes are disappearing a century sooner than predicted. A case in point is that some large, age-old lakes shrank dramatically in what appears to have been a matter of months. Scientists have labeled this phenomenon “disastrous lake loss”What caused this? The frozen solid ground actually contains bits of rock, mineral and organic matter, leaving spaces in between. And because these spaces are filled with solid ice, liquid water cannot readily get inside, but it can when the permafrost melts, allowing more water to get through. Soon after that, around 192 lakes in northwestern Alaska are gone from sight.Why did scientists miss this? One probable reason is that most climate models assume that the melting of permafrost is driven only by warming air.New evidence suggests, however, that rainfall — particularly increasing autumn rain — is now contributing significantly to permafrost loss. The rainfall carries heat into the ground. Yet none of the existing models includes such processes.That is a good example of why — no matter how complex our models are or may one day be — we need direct observation of the natural world.48．What does Paragraph 1 mainly tell us?A．General knowledge can at times turn out to be true.B．Commonsense assumptions can sometimes prove wrong.C．Research findings should be built on popular assumptions.D．Scientific research is inspired by an unknown phenomenon.49．Contrary to the general expectation, climate change has caused ________.A．a rapid rise of water surface B．the permafrost to melt fasterC．many Arctic lakes to grow larger D．the disappearance of many Arctic lakes 50．The disastrous climatic impacts on the Arctic region have been ________.A．proved with emerging lakes B．underestimated by scientistsC．well predicted by researchers D．shown elsewhere in the world51．Why is the frozen Arctic ground hard for water to get through?A．Because of the solid ice within it.B．Because of its unique composition.C．Because it is far away from the waters.D．Because snow rarely melts on frozen ground.52．What lesson can we learn from the passage?A．Direct observation is a must for scientific research.B．Scientific research is guaranteed by sufficient lab facilities.C．New evidence should be found to back up research findings.D．Scientific predictions should be mostly based on research models.Staring at the bookcases in my study, packed with so many great books that had remained unread, I heard a loud voice in my head — “Shame on you! How can you leave these masterpieces unread?”The first book I picked up was Montaigne's Essays. To my surprise I discovered in the margins (页边空白) what clearly was my own faded hand-writing. So I was actually reading it again, but what I was rereading seemed entirely new. I also found sentences underlined. Only this time I wondered: Why did I underline this sentence? It's the next one that is important!Clearly, my way of reading the text had shifted, and I myself had changed over the years.This raised the larger question of rereading. It comes in many forms. There’s voluntary rereading, the result of a willful decision to revisit a book one has admired, or a book that has left one with some unanswered questions. This kind of planned revisit could also be for confirming certain details in the text, or for checking on the moves of a given character. A devoted teacher might also wish to refresh his closeness to a work, and thus avoid teaching through the same old written notes with soporific (让人瞌睡的) effects.Contrarily, there’s involuntary rereading. The original reading was either forgotten or so totally absorbed that the new chance encounter with the text produced surprise and astonishment. My reaction to the renewed reading no longer corresponded to the original experience, and I was no longer sure that I recognized myself as the same reader.Then there are what one might call subconscious (潜意识的) rereadings, those that occur without the specific act of reading, much as the memory of a tune can keep coming back to the mind without its actually being heard again. This form of remembered contact with a book can accompany us during a lifetime and continue to strengthen and shape us. Much in the same manner, we may over the years recite to ourselves poems learnt by heart long ago, which have become part of our self-recognition.All of these ways of reading are valuable. Renewed contact with a novel or a poem can activate the search for a better knowledge of the self. The new reading, a form of revision, uncovers the change in us. The newness is not in the text. It is we who have evolved. In the process of rereading, our outlook has also been significantly changed. Rereading makes it possible for us to see the world around us, ourselves included, in a new light.53．What did the author find when reading Montaigne’s Essays?A．He still couldn't understand it.B．He had made notes in it.C．It was a brand new copy.D．It was his favorite work.54．According to the author, what could be a purpose of voluntary rereading?A．To improve the quality of teaching.B．To learn from admirable characters.C．To collect details for writing novels.D．To help making important decisions. 55．According to Paragraph 4, involuntary rereading can bring about?A．Unexpected reading experience.B．Total concentration on new books.C．Changed preferences for books.D．Enhanced reading skills.56．What can be learnt about subconscious rereading?A．It prevents memory from fading.B．It helps make who we are.C．It involves actual reading.D．It works best with poetry and music. 57．What could be the best title for the passage?A．Accessing Masterpieces through Rereading B．Rereading: V oluntary or Involuntary?C．Rereading: Pursuit of Truth D．Transformative Power of Rereading阅读表达Studies show teaching children how to cook at an early age helps with reading comprehension and fine motor ability, in addition to learning about nutrition and food safety. In 2015 Stephanie Drewry was looking for a cooking summer camp for her three children. To her dismay, she quickly realized such a camp didn’t exist.“I have my degree in education, but I had been staying home with my kids, ” Drewry says. “I love working with kids, so I just decided to take a spare bedroom and turn it into a one-room cooking school called Sprouts Cooking School. ”The school grew in popularity so quickly that Drewry realized she would need more space outside her home for the classes. In 2017 she moved Sprouts into a 1,400-square-foot storefront (临街店面) in Carmel, Indiana. As demand grew, Drewry opened another Sprouts in the same area in 2022.“Our classrooms are built with kids in mind. The worktops (操作台) in the classrooms are slightly lower than normal to fit in with their height,” Drewry says. “All of the cooking facilities are domestic ones. I wanted to have them feel like cooking in their own home.”The school offers activities targeted at kids aged 3 to 13. Younger kids might make cookies while older ones are cooking soup and meatballs. There are birthday parties and summer camps as well. The fun part of the activities is that the kids can eat or take home whatever they make. They can also enjoy themselves in the themed classes like Harry Potter or Winter Wonder-land Baking. With all these activities, the school is extremely popular.Teaching kids, especially those picky eaters, to cook helps a lot because they’re more willing to eat something made by themselves. More importantly, it is also about releasing children into the world with a life skill they’ll need as an adult when they’re no longer in their parents’care.58．What does the underlined word mean in Paragraph 1? (1 word)59．Why was Sprouts moved into a 1,400-square-foot storefront in 2017? (no more than 10 words)60．How does the school design the classrooms in consideration of kids’ height? (no more than 10 words)61．Why is the school so popular according to Paragraph 5? (no more than10 words)62．Besides cooking, what other life skills would you like to develop? Please give one example and explain why. (no more than 20 words)四、书信写作63．假设你是晨光中学的学生李津，学校即将举办“低碳校园，从我做起”英语主题演讲活动，你要报名参加。

辽宁省名校联盟(东北三省联考)2023-2024学年高三上学期12月月考语文试题含答案

辽宁省名校联盟(东北三省联考)2023-2024学年高三上学期12月月考语文试题含答案

2023～2024学年度上学期高三12月合考试卷语文考生注意：1.本试卷满分150分，考试时间150分钟。

2.答题前，考生务必用直径0.5毫米黑色墨水签字笔将密封线内项目填写清楚。

3.考生作答时，请将答案答在答题卡上。

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；非选择题请用直径0.5毫米黑色墨水签字笔在答题卡上各题的答题区域内作答，超出答题区域书写的答案无效，在试题卷、草稿纸上作答无效。

4.本卷命题范围：高考范围。

一、现代文阅读(35分)（一）现代文阅读I(本题共5小题，19分)阅读个厨的文学完成16题。

材料一：曾几何时，红楼IP[互联网界的“IP”可以理解为所有成名文创(文学、影视、动漫、游戏等)作品的统称]的开发与传播出现了影视改编、电视讲坛、图画动漫、网络空间、消费物品等多样化传播形式。

现在我们不得不思考经典IP《红楼梦》如何转化为当下“现象级”IP,这游需要红楼IP影视开发者转变观念，注重年轻化、时尚化、商业化。

在40多年的改革开放进移中，我们经历了消解严肃、快餐文化、读图时代等一系列时代现象，《红楼梦》的传播方式和审美批评理念不再适用于当下新兴的大众需要。

尽管学院派红学依然沉浸在文字文本里，但精英红学与大众红学的区别在于，精英红学体验的是经典的厚重与高贵，而大众红学需要的是普适与通俗，需要的是娱乐与快感。

新近发展起来的大众媒介传播技术，无论在广度还是深度上都在强势地巩固着经典文学作品的经典地位。

对于文学经典而言，大众传媒的市场力量可以说是一把双刃剑，用得好，可以使经典地位更牢固，用得不好，却会把“经典”变得畅销却“庸俗”,甚至“恶俗”。

确实，媒介技术本身是中性的，但利用其动机却有好有坏，而正是这“有好有坏”的动机，会使得搭乘媒介技术这一便利之车的文学经典驶向两个完全相反的境地。

(摘编自刘继保《红楼IP影视开发为何越来越冷》)材料二：①一部经典首先只有被阅读，然后才会产生审美价值、社会价值、哲学价值等。

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高三12月份月考理科数学试题
一、选择题：（每小题5分，共60分）
1 已知集合M 二｛m,-3｝, N 二｛x|2x
2 7x
3 ：： 0,x Z｝,如果M N “：」，则m等于（）
A 、-1B、—2C、- 2或-1D、-3
2
2、i是虚数单位，复数_1 3i=()
1 +2i
A 1 + i B、5 + 5i C、-5-5i D、-1 一
3
、
下列说法中错误的个数是（）
①命题“ -x ■ R,x2-x 0 ”的否定是“ -R,X2-X^0”；
②命题p q为真是命题p q为真的必要不充分条件；
③“若am2 ::: bm2，则a ::: b”的逆命题为真;
④若实数x,r [0,1]，则满足：x2 y2 1的概率为丄。

4
A、0
B、1
C、2
D、3
4、已知ta严=2，则刑2宀一哄―）等于（）
sin（—…'）一sin（二-n）
2
A、2
B、- 2
C、0
D、-
3
5、已知公差不为0的等差数列｛a n｝满足a1,a3,a4成等比数列，S n为｛a.｝的前n
项和，则S4 ~S2的值为（）
-S3
5 7
A、3
B、
C、
D、1
7 5
6、若向量e,©与满足3 1 = 2 61 = 2,（0 2e2）^4，则e,与e?的夹角为（
）
A、300
B、600
C、1200
D、150°
9
7、已知函数f(x)=x-4
,x ・(0,4)，当x = a 时，f(x)取得最小值b ，则 x +1
线y 二f (x)的一条切线的斜率是3，则切点的横坐标为(
) 2
A 、0
B 、In2
C 、In3
D 、2ln2
11、设函数 f (x)二 sin(，x ) . 3 cos( x J( ■ 0,0 ：：：二),f(x ) = f (—x 3)， 2 2
且f(x) • f(-x)=0，贝U 以下判断不可能的是(
)
4n
A 、f(x)的周期为——
B 、f(x)的周期为-
3
C 、f (x)在［0,二］上单调递减
D 、f (x)在［―,二］上单调递增
3
12、设S n 为数列｛a n ｝的前项和，若邑是非零常数，贝U 称该数列为“和等比数
S n
列”若数列｛C n ｝是首项为2,公差为d(d^0)的等差数列，且数列｛C n ｝是“和等 比
在(
)6的二项展开式中,
x 2的系数为
15 4
B 、
1_5 4
已知函数f (x)在［0,二)上是增函数，g(x)二-f (| x|)，若g(g x) g(1),则x 的取值范围是() 9、
A 、(0,10)
B 、(10/::)
1
C 、(护)
1
D 、(0,
) (10/-) 10
10、设 a • R ，函数 f (x) =e x ae 」
的导函数是f (x)，且f (x)是奇函数，若曲
C
B
g(xH(-)|xb| 的图象是()
a
数列”，则d =()
1
A、B、2 C、- 4 D、4
2
二、填空题：(每小题5分，共16分)
13、函数f(x) =2sin x(sinx cosx) -1的最小正周期是_________________ ;
14、已知数列｛a.｝对任意的p,q • N ”满足a p .q = ap ■ aq，且a? = -6，那么
a io = __________ ；
15、偶函数f(x)满足f(x 2)=f(x)，且当x [0,1]时，f(x)=「x・1则关于x的方
1
程f(x) N-)X在x • [0,3]上解的个数是 ______________ ；
2
16、在厶ABC中，.A不是最大的内角，且ta n彳(1 • cos A) = 3, AB-CA - -8，
2 5
则边BC长的最小值是______________ 。

三、解答题(17~21题，每题12分；选作题10分；共70分)
17、设公比为正数的等比数列｛a n｝的前n项和为S n，已知a3 =8,S2 =48，数列
a
｛b n｝满足b n =4log2 n。

( 1)求数列｛a n｝和数列｛b n｝的通项公式；
(2)设数列｛a n b n｝的前n项和为T，求T。

18、已知A、B、C是厶ABC的三个内角，且满足2sin B =sin A sinC，设B的最
大值为B。

( 1)求B。

的大小；(2)当B^3^时，求cosA-cosC的值。

4
19、某银行柜台设有一个服务窗口，假设顾客办理业务所需的时间互相独立，
且都是整数分钟，对以往顾客办理业务所需的时间统计结果如下：
从第一个顾客开始办理业务时计时.
(1)估计第三个顾客恰好等待4分钟开始办理业务的概率；
20、已知〉为锐角，且tan : = . 2 -1，函数f (x)二2xtan 2 ：T，数列｛a n｝的首项a! Ma n i "(a.)。

(1)在厶ABC中，若.A = 2：「C ,BC = 2，求△ ABC
3
的面积；(2)求数列｛a.｝的前n项和S n。

21、设a 为实数，函数f (x) =e x -2x • 2a,x・ R。

(1)求f(x)的单调区间与极值；
(2)求证：当 a • In 2 -1 且x 0 时，e x x2 - 2ax 1。

选作题：(以下两题选作一题)
D 22、选修4-1：几何证明选讲
已知AB是圆O的直径，D为圆O上一点，过D作圆O的切
线交AB延长线于点C,若DA=DC求证：AB=2BC
23、选修4-5：不等式选讲
设 f x =ln(| x -1| m|x - 2| -3) ( m R ).
(I)当m =1时，求函数f x的定义域；
(U)若当1乞xJ时，f x _0恒成立，求实数m的取值范围.。

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