最新通州区2019—2020学年高三一模考试试卷答案(三稿)

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2019-2020学年北京市通州区第二中学高三英语一模试卷及参考答案

2019-2020学年北京市通州区第二中学高三英语一模试卷及参考答案第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AIn the age of social distancing, using robots for some health care interactions is a promising way to reduce in-person contact between health care workers and sick patients. However, a key question is how patients will react to a robot entering the room. Researchers from MIT and Brigham and Women’s Hospital recently set out to answer that question.In a study, the team found that a large majority of patients reported that interacting with a health care provider through a video screen fixed on a robot was similar to an in-person interaction with a health care worker.“We’re working on robots that can help provide care to ensure the safety of the patient and the health care workforce. The results of this study give us some confidence that people are ready and willing to join us. In a larger online survey carried out nationwide, we also found that a majority of respondents were open to having robots perform small tasks such as taking a nose swab (拭子).” says Giovanni Traverso, an MIT assistant professor and the senior author of the study.After the COVID-19 pandemic began early last year, Traverso and his colleagues turned their attention toward new strategies to reduce interactions between potentially sick patients and health care workers. To that end, they created a mobile robot that could interact with patients as they waited in the emergency department. The robots were equipped with sensors that allow them to measure vital signs, including skin temperature, breathing rate, and pulse(脉搏) rate. The robots also carried an iPad for remote video communication with a health care provider.The study suggests that it could be worthwhile to develop robots that can perform tasks that currently require a lot of human effort, such as turning a patient over in bed. These days, turning COVID-19 patients onto their stomachs requires several people. Doing Covid-19 tests is another task that takes a lot of time and effort from health care workers, who could be arranged for other tasks if robots could help.1. Why did the researchers from MIT and BWH carry out the studies?A. To shorten the social distance between doctors and patients.B. To figure out the response of patients to robotic doctors.C. To reduce the risk of being infected with coronavirus.D. To ensure the safety of patients during the pandemic.2. What could be learned from the study?A. Robots are not welcomed by patients.B. Robots will soon replace doctors.C. Robots may help to deal with Covid-19 patients.D. Robots can operate on different patients.3. Which of the following is the best title for the text?A. StrengthsAnd Weaknesses In Robot CareB. The Robotic Doctor Will See You NowC. The Robots Speed Up COVID-19 TestingD. The Development Of Robots In HospitalsBSmart speakers have proven to be handy devices in hospitals, allowing patients to control independently . And now, researchers from theUniversityofWashingtonhave developed an artificial intelligence system that enables these devices to monitor heartbeats.Using technology to remotely monitor heart rates isn't new. These days most smartwatches and fitness trackers are capable of it. The good thing here is that researchers have figured out a way to use the microphones in smart speakers to do it without requiring physical contact.In a study published inCommunications Biology, the researchers had the smart speakers send out signals that couldn't be heard which were then reflected off a person's body. They then analyzed these signals to identify small chest wall motions related to heartbeats, as well as separate those signals from surrounding noise and breathing.For this particular proof — of — concept setup, the researchers tested this smart speaker on 26 healthy participants and 24 hospitalized patients with various heart conditions, including atrial fibrillation（心房颤动）and heart failure. In both cases, the smart speaker was within 28 -30 milliseconds of an ECG（心电图）,the gold standard used in hospitals to discover arrhythmia（心律不齐）.Like smartwatches with advanced heart features, using smart speakers in this way opens up the possibility for passive, remote heart monitoring. ECGs, while highly accurate, require a visit to the doctor and several electrodes （电极）to be placed on the body. They,re not capable of continuous monitoring so you're limited to what it picks up at that exact moment in time ——one reason why heart arrhythmia can be so hard to discover.Smartwatches are capable of passive, remote, continuous monitoring, but they require you to wear the device at all times to be effective. It's not something that's comfortable for everyone, especially when it comes tosleep and for those with highly sensitive skin. Another issue is that these advanced smartwatches are expensive, while smart speakers are much cheaper.“If you have a device like this, you can monitor a patient on an extended basis and then develop corresponding care plans that satisfy the patient' s needs,“ said Dr. Arun Sridhar, co — senior author on the study. "And the beauty of using this kind of devices is that they are already in people's homes.”4. What does the author focus on in Paragraph 3?A. How the smart speaker works.B. Why the smart speaker is useful.C. The advantages of smart speakers.D. The importance of the study.5. Why is heart arrhythmia difficult to find?A. ECGs are not highly accurate.B. ECGs can't monitor continuously.C. Doctors know little about heart arrhythmia.D. An ECG test is hard to operate and expensive.6. Which statement best explains the characteristics of smartwatches?A. They are comfortable to wear.B. They are friendly to sensitive skin.C. They are effective and cheap.D. They are able to monitor remotely.7. What can we infer from the last paragraph?A. We need to invent more smart devices.B. Care plans are vital to patients with heart failure.C. Smart speakers could be contactless heart monitors.D. Different devices are needed to meet patients,demands.COwning a dog is associated with a significantly lower risk of heart disease and death, according to a comprehensive new study published by a team of Swedish researchers on Friday in the journal Scientific Reports.The scientists followed 3.4 million people over the course of 12 years and found that adults who lived alone and owned a dog were 33 percent less likely to die during the study than adults who lived alone without dogs. Inaddition, the single adults with dogs were 36 percent less likely to die from heart disease.“Dog ownership was especiallyprominentas a protective factor in persons living alone, which is a group reported previously to be at higher risk of heart disease and death than those living in a multi-person household,” Mwenya Mubanga, a Ph.D. student at Uppsala University in Uppsala, Sweden, and the lead junior author of the study, said in a statement announcing its findings. The link between dog ownership and lower mortality(死亡率)was less pronounced in adults who lived either with family members or partners, but still present, according to the study. “Perhaps a dog may stand in as an important family member in the single households,” Mubanga added. “Another interesting findingwas that owners of dogs which were intended originally for hunting were most protected.”The study, which is the largest to date on the health relations of owning a dog, suggested that some of the reasons dog owners may have a lower risk of mortality and heart disease were because dog owners walk more. “These kind of epidemiological (流行病学的)studies look for associations in large populations but do not provide answers on whether and how dogs could protect their owners from heart disease,” Tove Fall, a senior author of the study and a professor at Uppsala University, said in a statement“We know that dog owners in general have a higher level of physical activity, which could be one explanation to the observed results,” Fall added. “Other explanations include an increased well-being and social contacts or effects of the dog on the bacterial microbiome(微生物菌群) in the owner.” Fall added that because all participants of dog owners in Sweden or other “European populations with similar culture regarding dog ownership.”8. Why did the researchers do the study related to 3.4 million people’s health and the dogs?A. To help Europeans,B. To find their association.C. To protect unhealthy adults.D. To reduce risk of heart disease.9. What does the underlined word “prominent” probably mean in Para.3?A. Universal.B. Confusing.C. Appealing.D. Important10. What’s the main idea of the text?A. Adults living with dogs are less likely to die.B. Swedish people are very fond of animal pets.C. Keeping a dog is a popular and healthy hobby.D. Owning dogs reduces the risk of heart disease.11. What’s the writer’s attitude towards owning a dog?A. Positive.B. Negative.C. Objective.D. Contradictory.DA study has found that a lifetime of regular exercise and activity can slow down the aging process (衰老过程). Researchers say that getting older should not necessarily mean becoming more weak or sick. Their research shows that a devotion to a life of movement and exercise may help us live not only longer, but also healthier.For their study, the researchers looked at two groups. The first group was made up of 125 non-professional cyclists between the ages of 55 to 79. This group included 84 healthy men and 41 healthy women. We will call this group the “cyclists”.Researchers then found 130 people to make up a second group. Within this group, 75 people were aged from 57 to 80. The other 55 were between the ages of 20 and 36. The people in this group were also healthy, but they did not exercise regularly. We will call this group the “non-exercisers”. Smokers, heavy drinkers of alcohol and people with other health issues were not included in the study.Then, researchers gave both groups a series of tests. They tested their muscle mass (肌肉质量), muscular strength, percentage of body fat and the strength of their immune (免疫的) systems. Then the researchers compared the results of the two groups.Results showed that the cyclists did not experience body changes usually regarded as a normal aging process. For example, they did not lose muscle mass or muscular strength. Also, their body fat did not increase with age.The researchers also found something they had not expected. The study showed that the immune systems of the cyclists did not age either.The researchers advise us all to find an exercise that we like in our lives.12. How did the researchers carry out the study?A. By comparing.B. By discussing.C. By imagining.D. By reasoning.13. Which of the following is a result of the research?A. The cyclists kept a thin body shape.B. The non-exercisers gained weight easily.C. The cyclists’ muscles remained strong with age.D. The non-exercisers usually had health problems.14. Which is an unexpected result for the researchers?A. The cyclists had normal aging process.B. The cyclists’ immune systems didn’t age.C. The cyclists lost nearly all their fat.D. Everyone needed an exercise in their lives.15. Which of the following can be the best title for the text?A. Healthy People Need More ExerciseB. Take an Exercise, the Harder, the BetterC. Cycling Is the Best Way to Prevent AgingD. A Lifetime of Exercise Slows Aging Process第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。

2019-2020学年通州区第三中学高三英语第一次联考试卷及答案解析

2019-2020学年通州区第三中学高三英语第一次联考试卷及答案解析第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AMy mother and her best friend Martha were in their mid-80s when they saw each other for the last time.They had been friends since they were 18, both of them students atWesleyanCollegeinMacon,Georgia. My mother was the dreamy one, who loved to read and dream herself as an actress. Martha, however, was more practical. I’m not sure what they had in common except that they trusted each other, helped each other, and stayed in touch even when life separated them.Martha spent most of her adulthood inAtlanta, where she raised three kids. My mother, meanwhile, raised eight children, and moved many times during her financially and emotionally troubled marriage, which included several months living with her family inseedymotels.I sensed my mother hid her troubles from most people, but not from Martha, and I knew from my mother that Martha carried her own sorrows. Their willingness to share sorrow without judgment was part of what bond them.The best friendships can also withstand (抵挡) periods without communication. They didn’t communicate a lot — this was before the ease of emails and texts and yet I knew they were always in each other’s minds.One day in 2008, 1 drove my mother to Martha’s house for their final visit. The moment my mother hobbled (蹒跚) into Martha’s house, they threw their arms around each other and went to sit out in the garden, laughing until they were dizzy. I snapped a photo, and spotted something joyous, young and free on my mom, which existed only in the presence of her best friend.Two years later, my mother died. Of all the people I had to tell, Martha was the hardest because I felt it erased her past. After that, we lost touch. But I still think of her and how that friendship strengthened my mother.1. What does the underlined word “seedy” in Paragraph 3 probably mean?A. largeB. dirtyC. urbanD. bright2. The author’s mother and Martha had a lasting friendship partly because they________.A. were willing to shareB. were constantly in touchC. had much in commonD. had a likeness in personality3. What is the author’s purpose in writing the text?A. To tell the importance of friendship.B. To express his gratitude to his mother.C. To share his standard of choosing a friend.D. To praise the friendship between Martha and his mother.BIt was very cold and I had been watching a homeless man make himself comfortable in a “shelter” on the river bank. His “shelter” was a tarpaulin (油布)tied to rocks to keep the wind from blowing it away. He had been living there for over a month. I never saw him with warm clothing or food. I knew what I wanted to do.When I told my parents what I wanted to do they werealarmed. They said I could be putting myself at risk, taking a box to a homeless person at night! But I knew, in my deep heart, that I would be safe.I got a box. My parents watched as I added warm gloves, a heavy blanket ... into the box until it was full! Then, I put a Christmas card on top. It said, “Even though we hardly know each other, I want to wish you a Merry Christmas!” I put ten one-dollar bills inside it as well.My father insisted he went there with me as it was 10 pm on Christmas Eve. I said he could drive me but he had to stay in the car. He agreed.I took the box and walked towards his “house”. I called, “Sir, I have a Christmas box for you!”“Go away!” he shouted.“Sir,” I repeated.“Go away!” he shouted.“Why?” I asked him.He walked over and I expected to see an angry face. Instead I saw two of the most beautiful, gentle, blue eyes I have ever seen.“Merry Christmas!” I said.“Why are you doing this?” he asked.“Because you matter to me,” I said. With that I gave him the box.Tears came to his eyes and he thanked me. I got back to the car and watched him carry the box like it was filled with gold. I didn’t want to embarrass (使困窘) him by watching him any more so Dad and I left.4. The underlined word “alarmed” can best be replaced by _____.A. pleasedB. worriedC. disappointedD. surprised5. Why did the author ask his father to stay in the car?A. Because he wanted to prove he was brave.B. Because he believed the homeless man was bad.C. Because he wanted to protect his father from being hurt.D. Because he didn’t want the homeless man to feel bad.6. When the homeless man saw the author first, he was _____.A. quite angryB. very excitedC. quite puzzledD. very curious7. The author’s purpose in writing the text is to tell readers that _____.A. it is easier said than doneB. poverty is the mother of healthC. where there is a will, there is a wayD. a willing helper doesnot wait until he is askedCAbout a month after I joined Facebook, I got a call from Lori Goler, a highly regarded senior director of marketing at eBay. She made it clear this was a business call. “I want to apply to work with you at Facebook,” she said. “Instead of recommending myself, I want to ask you: What is your biggest problem, and how can I solve it?”My jaw hit the floor. I had hired thousands of people over the previous decade and no one had ever said anything remotely like that. People usually focus on finding the right role for themselves, with the implication that their skills will help the company. Lori put Facebook’s needs front and center. It was a killer approach. I responded, “Recruiting is my biggest problem. And, yes, you can solve it.”Lori never dreamed she would work in recruiting, but she jumped in. She even agreed to trade earnings for acquiring new skills in a new field. Lori did a great job running recruiting and within months was promoted to her current job, leading People@Facebook.The most common metaphor for careers is a ladder, but this concept no longer applies to most workers. As of 2010, the average American had eleven jobs from the ages of eighteen to forty-six alone. Lori often quotes Pattie Sellers, who came up with a much better metaphor: “Careers are a jungle gym, not a ladder.”As Lori describes it, there’s only one way to get to the top of a ladder, but there are many ways to get to the top of a jungle gym. The jungle gym model benefits everyone, but especially women who might be starting careers, switching careers, getting blocked by external barriers, or reentering the workforce after taking time off. Theability to create a unique path with occasional dips, detours (弯路), and even dead ends presents great views of many people, not just those at the top. On a ladder, most climbers are stuck staring at the butt of the person above.8. Why did Lori make the call?A. She helped Facebook to solve the biggest problem.B. She wanted to make a business deal with Facebook.C. She tried to ask for a pay rise in Facebook.D. She wanted to become an employee in Facebook.9. What impressed “I” by Lori?A. Lori was good at running recruiting.B. Lori attached great importance to Facebook’s needs.C. Lori jumped in Facebook with no adequate experience.D. Lori was skilled in marketing at eBay.10. What can we infer from the passage?A. Now all people don’t tend to climb the ladder.B. None on the ladder can enjoy the great views.C. Jungle gyms offer limited exploration for employees.D. A pregnant woman, jobless, benefits little from the jungle gyms.11. What is the best title of the passage?A. It’s a Jungle Gym, Not a Ladder.B. Facebook’s Biggest Problem.C. Applying for a Job in Facebook.D. A Jungle Gym is Better than a Ladder.DAt the World Economic Forum last month, President Trump drew claps when he announced the United States would respond to the forum's proposal to plant one trillion(万亿) trees to fight climate change. The trillion-tree idea won wide attention last summer after a study published in the journal Science concluded thatplanting so many trees was “the most effective climate change solution to date”.If only it were true. But it isn't. Planting trees would slow down the planet's warming, but the only thing that will save us and future generations from paying a huge price in dollars, lives and damage to nature is rapid andconsiderable reductions in carbon release from fossil fuels, to net zero by 2050.Focusing on trees as the big solution to climate change is a dangerous diversion(偏离). Worse still, it takes attention away from those responsible for the carbon release that are pushing us toward disaster. For example, in the Netherlands, you can pay Shell an additional 1 euro cent for each liter of regular gasoline you put in your tank, to plant trees to balance the carbon release from your driving. That's clearly no more than disaster slightly delayed. The only way to stop this planet from overheating is through political, economic, technological and social solutions that end the use of fossil fuels.There is no way that planting trees, even across a global area the size of theUnited States, can absorb the huge amounts of fossil carbon released from industrial societies. Trees do take up carbon from the atmosphere as they grow. But this uptake merely replaces carbon lost when forests were cleared in the first place, usually long ago. Regrowing forests where they once grew can undo some damage done in the past, but even a trillion trees can't store enough carbon to head off dramatic climate changes this century.In a sharp counter argument to last summer's Paper in Science, Justin Gillis wrote in the same journal in October that the study's findings were inconsistent with the dynamics of the global carbon cycle. He warned that “the claimthat global tree restoration(复原) is our most effective climate solution is simply scientifically incorrect and dangerously misleading”.12. What do we know about the trillion-tree idea?A. It was published in a journal.B. It was proposed last summer.C. It was put forward by Trump.D. It drew lots of public attention.13. What is paragraph 3 mainly about?A. A drawback of the tree planting strategy.B. An example of balancing carbon release.C. An anecdote of making a purchase at Shell.D. A responsibility for politicians and economists.14. What was Justin Gillis's attitude towards global tree restoration?A. Indifferent.B. Opposed.C. Hesitant.D. Supportive.15. What is the best title for the text?A. Contradictory Ideas on Tree Planting.B. A Trillion Trees Come to the Rescue.C. Planting Trees Won't Save the World.D. The Best Solution to Climate Change.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。

北京市通州区2019-2020学年高考一诊数学试题含解析

北京市通州区2019-2020学年高考一诊数学试题一、选择题：本题共12小题，每小题5分，共60分。

在每小题给出的四个选项中，只有一项是符合题目要求的。

1．从5名学生中选出4名分别参加数学，物理，化学，生物四科竞赛，其中甲不能参加生物竞赛，则不同的参赛方案种数为 A ．48 B ．72 C ．90 D ．96【答案】D 【解析】因甲不参加生物竞赛，则安排甲参加另外3场比赛或甲学生不参加任何比赛①当甲参加另外3场比赛时，共有13C •34A =72种选择方案；②当甲学生不参加任何比赛时，共有44A =24种选择方案．综上所述，所有参赛方案有72+24=96种故答案为：96点睛：本题以选择学生参加比赛为载体，考查了分类计数原理、排列数与组合数公式等知识，属于基础题． 2．《九章算术》勾股章有一“引葭赴岸”问题“今有饼池径丈，葭生其中，出水两尺，引葭赴岸，适与岸齐，问水深，葭各几何？”，其意思是：有一个直径为一丈的圆柱形水池，池中心生有一颗类似芦苇的植物，露出水面两尺，若把它引向岸边，正好与岸边齐，问水有多深，该植物有多高？其中一丈等于十尺，如图若从该葭上随机取一点，则该点取自水下的概率为（）A ．1213B ．1314C ．2129D ．1415【答案】C 【解析】【分析】由题意知：2BC =，'5B C =，设AC x =，则2AB AB x '==+，在Rt ACB 'V 中，列勾股方程可解得x ，然后由P 2xx =+得出答案. 【详解】解：由题意知：2BC =，'5B C =，设AC x =，则2AB AB x '==+ 在Rt ACB 'V 中，列勾股方程得：()22252x x +=+，解得214x =所以从该葭上随机取一点，则该点取自水下的概率为21214P 2122924x x ===++ 故选C. 【点睛】本题考查了几何概型中的长度型，属于基础题. 3．下列函数中，值域为R 且为奇函数的是（） A ．2y x =+ B ．y sinx =C ．3y x x =-D ．2x y =【答案】C 【解析】【分析】依次判断函数的值域和奇偶性得到答案. 【详解】A. 2y x =+，值域为R ，非奇非偶函数，排除；B. y sinx =，值域为[]1,1-，奇函数，排除；C. 3y x x =-，值域为R ，奇函数，满足；D. 2x y =，值域为()0,∞+，非奇非偶函数，排除；故选：C . 【点睛】本题考查了函数的值域和奇偶性，意在考查学生对于函数知识的综合应用.4．在正方体1111ABCD A B C D -中，点E ，F ，G 分别为棱11A D ，1D D ，11A B 的中点，给出下列命题：①1AC EG ⊥；②//GC ED ；③1B F ⊥平面1BGC ；④EF 和1BB 成角为4π.正确命题的个数是（） A ．0 B ．1C ．2D ．3【答案】C 【解析】【分析】建立空间直角坐标系，利用向量的方法对四个命题逐一分析，由此得出正确命题的个数. 【详解】设正方体边长为2，建立空间直角坐标系如下图所示，()()()12,0,0,0,2,2,2,1,2AC G ，()()()()()()10,2,0,1,0,2,0,0,0,2,2,2,0,0,1,2,2,0C E D B F B .①，()()112,2,2,1,1,0,2200AC EG AC EG =-=⋅=-++=u u u u r u u u r u u u u r u u u r，所以1AC EG ⊥，故①正确.②，()()2,1,2,1,0,2GC ED =--=--u u u r u u u r ，不存在实数λ使GC ED λ=u u u r u u u r，故//GC ED 不成立，故②错误. ③，()()()112,2,1,0,1,2,2,0,2B F BG BC =---=-=-u u u u r u u u r u u u u r ，1110,20B F BG B F BC ⋅=⋅=≠u u u u r u u u r u u u u r u u u u r，故1B F ⊥平面1BGC 不成立，故③错误.④，()()11,0,1,0,0,2EF BB =--=u u u r u u u r ，设EF 和1BB 成角为θ，则1122cos222EF BB EF BB θ⋅-===⨯⋅u u u r u u u ru u ur u u u r ，由于0,2πθ⎛⎤∈ ⎥⎝⎦，所以4πθ=，故④正确.综上所述，正确的命题有2个. 故选：C【点睛】本小题主要考查空间线线、线面位置关系的向量判断方法，考查运算求解能力，属于中档题.5．若x ∈（0，1），a ＝lnx ，b ＝ln 12x⎛⎫ ⎪⎝⎭，c ＝e lnx ，则a ，b ，c 的大小关系为（）A ．b ＞c ＞aB ．c ＞b ＞aC ．a ＞b ＞cD ．b ＞a ＞c【答案】A 【解析】【分析】利用指数函数、对数函数的单调性直接求解．【详解】 ∵x ∈（0，1）， ∴a ＝lnx ＜0， b ＝（12）lnx ＞（12）0＝1，0＜c ＝e lnx ＜e 0＝1，∴a ，b ，c 的大小关系为b ＞c ＞a ．故选：A ．【点睛】本题考查三个数的大小的判断，考查指数函数、对数函数的单调性等基础知识，考查运算求解能力，是基础题．6．如图是一个算法流程图，则输出的结果是（）A ．3B ．4C ．5D ．6【答案】A 【解析】【分析】执行程序框图，逐次计算，根据判断条件终止循环，即可求解，得到答案．【详解】由题意，执行上述的程序框图：第1次循环：满足判断条件，2,1x y ==；第2次循环：满足判断条件，4,2x y ==；第3次循环：满足判断条件，8,3x y ==；不满足判断条件，输出计算结果3y =，故选A ．【点睛】本题主要考查了循环结构的程序框图的结果的计算与输出，其中解答中执行程序框图，逐次计算，根据判断条件终止循环是解答的关键，着重考查了运算与求解能力，属于基础题．7．等比数列{}n a 的前n 项和为n S ，若0n a >，1q >，3520a a +=，2664a a =，则5S =（） A ．48B ．36C ．42D ．31试题分析：由于在等比数列{}n a 中，由2664a a =可得：352664a a a a ==，又因为3520a a +=，所以有：35,a a 是方程220640x x -+=的二实根，又0n a >，1q >，所以35a a <，故解得：354,16a a ==，从而公比5132,1a q a a ===；那么55213121S -==-，故选D ．考点：等比数列．8． “角谷猜想”的内容是：对于任意一个大于1的整数n ，如果n 为偶数就除以2，如果n 是奇数，就将其乘3再加1，执行如图所示的程序框图，若输入10n =，则输出i 的（）A ．6B ．7C ．8D ．9【答案】B 【解析】【分析】模拟程序运行，观察变量值可得结论．【详解】循环前1,10i n ==，循环时：5,2n i ==，不满足条件1n =；16,3n i ==，不满足条件1n =；8,4n i ==，不满足条件1n =；4,5n i ==，不满足条件1n =；2,6n i ==，不满足条件1n =；1,7n i ==，满足条件1n =，退出循环，输出7i =．本题考查程序框图，考查循环结构，解题时可模拟程序运行，观察变量值，从而得出结论．9．近年来，随着4G 网络的普及和智能手机的更新换代，各种方便的app 相继出世，其功能也是五花八门.某大学为了调查在校大学生使用app 的主要用途，随机抽取了56290名大学生进行调查，各主要用途与对应人数的结果统计如图所示，现有如下说法：①可以估计使用app 主要听音乐的大学生人数多于主要看社区、新闻、资讯的大学生人数； ②可以估计不足10%的大学生使用app 主要玩游戏； ③可以估计使用app 主要找人聊天的大学生超过总数的14. 其中正确的个数为（）A ．0B ．1C ．2D ．3【答案】C 【解析】【分析】根据利用app 主要听音乐的人数和使用app 主要看社区、新闻、资讯的人数作大小比较，可判断①的正误；计算使用app 主要玩游戏的大学生所占的比例，可判断②的正误；计算使用app 主要找人聊天的大学生所占的比例，可判断③的正误.综合得出结论. 【详解】使用app 主要听音乐的人数为5380，使用app 主要看社区、新闻、资讯的人数为4450，所以①正确；使用app 主要玩游戏的人数为8130，而调查的总人数为56290，81300.1456290≈，故超过10%的大学生使用app 主要玩游戏，所以②错误；使用app 主要找人聊天的大学生人数为16540，因为165401562904>，所以③正确.故选：C. 【点睛】本题考查统计中相关命题真假的判断，计算出相应的频数与频率是关键，考查数据处理能力，属于基础题. 10．命题p ：2(1,2],20()x x x a a ∀∈--+≥∈R 的否定为A ．2000(1,2],20()x x x a a ∃∈--+≥∈R B ．2(1,2],20()x x x a a ∀∈--+<∈R C ．2000(1,2],20()x x x a a ∃∈--+<∈R D ．2(1,2],20()x x x a a ∀∉--+<∈R【答案】C 【解析】【分析】【详解】命题p 为全称命题，它的否定为特称命题，将全称量词改为存在量词，并将结论否定，可知命题p 的否定为2000(1,2],20()x x x a a ∃∈--+<∈R ，故选C ． 11．做抛掷一枚骰子的试验，当出现1点或2点时，就说这次试验成功，假设骰子是质地均匀的.则在3次这样的试验中成功次数X 的期望为（） A ． B ．C ．1D ．2【答案】C 【解析】【分析】每一次成功的概率为，服从二项分布，计算得到答案.【详解】每一次成功的概率为，服从二项分布，故.故选：. 【点睛】本题考查了二项分布求数学期望，意在考查学生的计算能力和应用能力. 12．已知集合(){}*,|4,M x y x y x y N =+<∈、，则集合M 的非空子集个数是（）A ．2B ．3C ．7D ．8【答案】C 【解析】【分析】先确定集合M 中元素，可得非空子集个数．【详解】由题意{(1,1),(1,2),(2,1)}M =，共3个元素，其子集个数为328=，非空子集有7个．故选：C ．【点睛】本题考查集合的概念，考查子集的概念，含有n 个元素的集合其子集个数为2n ，非空子集有21n -个．二、填空题：本题共4小题，每小题5分，共20分。

2019-2020学年江苏省南通市通州区高三(上)第一次调研物理试卷 (含答案解析)

2019-2020学年江苏省南通市通州区高三（上）第一次调研物理试卷一、单选题（本大题共5小题，共15.0分）1.在电磁学发展过程中，许多科学家做出了贡献．下列说法正确的是()A. 奥斯特经过多年研究，发现了电磁感应现象B. 美国物理学家劳伦斯发明了回旋加速器，能在实验室中产生大量的高能粒子C. 欧姆发现大多数金属温度降到某一值时，都会出现电阻突然降为零的超导现象D. 库仑通过实验精确测定了元电荷e的数值2.班里两个同学做电学实验，手里分别拿着带绝缘柄相同的金属小球，它们分别带有−Q和3Q的电荷量，两球相距为r的两处，两带电小球均可视为点电荷，它们间的库仑力大小为F.两小球接触后放回原处，两球间的库仑力大小变为()A. F12B. 3F4C. F3D. 12F3.一辆货车在满载情况下，以恒定功率P匀速经过一平直路段，速率为v；当货车空载再次经过同一路段的某位置时，功率为P2，速率仍为v，此时加速度为g10。

已知重力加速度为g，货车所受阻力是货车对地面压力的15，则货车满载与空载时的质量之比为()A. 5:2B. 5:1C. 3:1D. 3:24.如图所示，重力均为G的两小球用等长的细绳a、b悬挂在O点，两小球之间用一根轻弹簧连接，两小球均处于静止状态，两细绳a、b与轻弹簧c恰构成一正三角形。

现用一水平力F缓慢拉动右侧小球，使细绳a最终竖直，并保持两小球处于静止状态，则下列说法正确的是()A. 最终状态与初态相比，细绳a的拉力变大B. 最终状态与初态相比，细绳b的拉力变大C. 最终状态与初态相比，轻弹簧c的弹力变大D. 最终状态时，水平拉力F等于√3G5.如图所示，质量为2.5kg的物体紧靠着竖直墙面，并受到一个与竖直方向夹角为37°、大小为25N的力F作用，若物体与墙面间的动摩擦因数为0.4，则物体的加速度大小不可能是()A. 0B. 0.4m/s2 C. 4m/s2 D. 4.4m/s2二、多选题（本大题共4小题，共16.0分）6.“嫦娥二号”曾飞向距离地球150万公里外的“第二拉格朗日点”(图中M)，在太阳和地球引力共同作用下，“嫦娥二号”能在M点与地球一起绕太阳运动(视为圆周运动)。

2019-2020学年通州区运河中学高三英语一模试题及参考答案

2019-2020学年通州区运河中学高三英语一模试题及参考答案第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AConsumer Electronics Show (CES) is a global stage where the world’s next-generation inventions are introduced towards the marketplace, and lots of companies are participating. Here are several of the amazing inventions that were introduced at the showin 2020.August Wi-Fi Smart LockIt's an intelligent door lock to protect your home, and it works on Wi-Fi. The lock doesn’t require any additional hardware to attach to it and can be used with the existing door lock. The owner can remotely access the door from anywhere to lock or unlock and can provide guest keys to family or friends. It keeps statistics and records of your door’s “lock”, “unlock”, and who have visited.Motion PillowIt’s a pillow developed for anyone who has a snoring (打鼾) problem. The solution box detects, records, and analyses the sleeping person’s snoring patterns. By changing the internal airbag’s pressure, it fixes the position of the sleeping person’s neck and head gently to improve his breathing. Three layers of noise-reducing material minimize the user’s sleeping disturbance.Ao AirIt’s a high-tech face-covering wearable air purifier with no tight seal on the mouth and nose. The purifier pulls air inside through a filtration (过滤) process and uses fans to createa clean area in front of the device. It’s designed in such a way that it can clean more than 98 % of PM2.5 through filtration.Transparent HoodThe company Continental showed off this revolutionary invention at CES 2020 that got the Best Vehicle Intelligence and Transportation Award. It’s a technology that gives the driver the ability to see barriers and blind spots from the driving seat. Four cameras take surrounding pictures so that the driver can see the real-time blind spots and prevent even parking damage too.1.Who is the text mainly intended for?A.The general public.B.The science lovers.C.The electronic companies.D.The college students.2.Which of the following descriptions of Motion pillow is correct?A.It’s intended for all those who can’t sleep well.B.It can help sleepers breathe smoothly.C.It can remove the noise around to help people sleep.D.Its pressure is changed by sleepers themselves.3.What can we infer from the text?A.August Wi-Fi Smart Lock helps improve the safety of homes.B.Ao Air produces fresh air for its users.C.Motion Pillow reduces material to minimize sleeping disturbance.D.Transparent Hood helps make driving safer and easier.BIn 2002, young Elon Musk tried unsuccessfully to buy Russian rockets to help him send mice to Mars and back. Afterwards, the youngmillionaire decided to build his own rockets.Musk went to Southern California and started hiring people to help bring his dream to life. In a very short time, and despite some failures, his company SpaceX launched Falcon 1, the first successful privately-built liquid fuel rocket, into Earth's orbit in 2008.As the first Falcon rocket began testing, development was already underway for the Falcon 9. This much larger rocket, which uses nine engines to lift heavy payloads（有效载荷）into orbit, is engineered to return to Earth, ready to be reused for another flight.For Musk, space is the final destination. To help people get there, his company Neuralink is developing devices that will link people's brains with computers. A similar device has been developed at the University of Utah. It consists of a chip（芯片）with 256 threads（线程）that is placed between a person's skin and brain. The threads attach directly to brain tissue（脑组织）.Patients who have the device are able to use only their minds to communicate with one another through computers.Neuralink's chips will have about 1,000 threads. A robot developed by the company will place up to ten chips under a person's skin. The chips will communicate without wires but with a tiny device that will be worn behind the person's ear. That device, in turn, will communicate with computers. The primary market for the technology will be for people that, because of injuries or birth defects, cannot control their hands and arms. With Neuralink^ product, they'll be able to mentally command a computer to type messages for them or carry out other tasks.4. According to this article, what was the first Falcon 1 able to do?A. Launch big satellites.B. Reach distant moons.C. Move around our planet.D. Study the universe.5. What does the article explain about Neuralink's chips?A. How they'll be set up.B. What safety features they'll have.C. How much money they'll earn.D. Where they'll be produced.6. According to this article, who is Neuralink going to market its product to first?A. Those who own great wealth.B. Those who are physically disabled.C. Those who travel internationally.D. Those who do research on plants.7. In which publication is this article most likely to appear?A. The Journal of Environmental Studies.B. Advances in Business and Technology.C. Digest of Fashion and Entertainment News,D. Consumer's Guide to Outdoor Recreation.CTwo years ago, I decided to study at theUniversityofSt. Edwardsin the city ofAustin,Texas. When I was on my research to find the perfect place to study in, I considered many aspects: a safe place, a city where there were companies devoted to marketing or technology, a place where speaking Spanish and English was an advantage and a school where I could learn about digital strategies (数字策略). After comparing and evaluating many cities and universities. I finally decided onAustin.Since I arrived inAustin,Texas. I had been living inside the university where I had a private room and shared common areas with more students. University life was not very different from the life inMexicoand classes weresemblableand the way of socializing too. However, in theUnited States, the classes were more practical and teachers encouraged you to be self-responsible and complete your tasks.The classes that I was taking were related to social media, digital marketing and advertising. I was very excited to be able to study technology-related courses.What I liked most about the experience was being able to live with students from many places, which allowed me to learn from other cultures and to share mine with other students. Also, international student services usually organized events and tours that helped me to get to know the city and the school.I certainly think that studying abroad is a beneficial experience. It makes us capable of understanding cultural differences and accepting diversity. Personally, I would suggest that you first determine what your goals are by going abroad, research the opportunities and lifestyle, evaluate your universities,and finally decide on the one where you feel more comfortable, connecting with your values and way of seeing life.8. Which of the following can best describe the author according to paragraph 1？A. Casual.B. Cautious.C. Changeable.D. Adventurous.9.What does the underlined word “semblable” in paragraph 2 probably mean?A. Worthwhile.B. Practical.C. Same.D. Similar.10. What made the author most pleased?A. Speaking Spanish and English inAustin,Texas.B. Working as a designer in a technology company.C. Having a chance to learn about different cultures.D. Organizing many events and tours independently.11. What are the students who intend to study abroad advised to do?A. Be careful to choose the university to study in.B. Set no limits on theiracademic performances.C. Study where they're familiar with everything.D. Adjust personal lifestyles for the university.DExperts are warning about the risks of extremely picky(挑剔的)eating after a teenager living on a diet of chips and crisps developed lasting sight loss. Eye doctors inBristolcared for the 17-year-old after his sight had gone to the point of blindness. Tests showed he had serious vitamin deficiency(缺乏). Dr. Denize Atan, who treated him at the hospital, said, “His diet was basically a portion of chips from the local fish and chip shop every day. He also used to snack on crisps and sometimes white bread and ham, and not really any fruit and vegetables.”The teenager saw his doctor at the age of 14 because he had been feeling tired and unwell. At that time he suffered from vitamin B12 deficiency, but he did not stick with the treatment or improve his poor diet. Three years later, he was taken to theBristolEyeHospitalbecause of progressive sight loss.He was not overweight or underweight, but he had lost minerals from his bones, which was really quite shocking for a boy of his age. In terms of his sight loss, he met the standards of being blind. “He had blind spotsright in the middle of his sight,” said Dr Denize Atan, “That means he can’t drive and would find it reallyarduousto read, watch TV or recognize faces.”Dr Denize Atan said that parents should learn about the harm that can be caused by picky eating, and turn to experts for help. For those who are concerned , she advised, “It’s best not to be anxious about picky eating , and instead calmly introduce one or two new foods with every meal.” She said multivitamin tablets can supplement(补充) a diet, but cannot take the place of eating healthily. “It’s much better to take in vitamins through a varied and balanced diet,” she said, adding that too manycertain vitamins , including vitamin A, can be harmful ,“so you don’t want to overdo it.”12. What does Dr Denize Atan imply in paragraph 1?A. The diet of the boy is not balanced.B. Fruit and vegetables are rich in vitamins.C. Picky eating is common among teenagers.D. The cause of the boy’s disease is unknown.13. Why did the boy go to see his doctor at the age of 14?A. To improve his poor diet.B. To get some help to lose weight.C. To be treated for his discomfort.D. To slow down his progressive sight loss.14. What does the underlined word “arduous” in paragraph 3 probably mean?A. Important.B. Easy.C. Necessary.D. Difficult.15. What does the last paragraph mainly talk about?A. Reasons why the boy is seriously ill.B.Suggestions for the boy’s family to care for him.C. Advice for parents worried about picky eating.D. Waysof taking in enough vitamins and minerals.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。

北京市通州区2019-2020学年高考第一次模拟数学试题含解析

北京市通州区2019-2020学年高考第一次模拟数学试题一、选择题：本题共12小题，每小题5分，共60分。

在每小题给出的四个选项中，只有一项是符合题目要求的。

1．已知定点,A B 都在平面α内，定点,,P PB C αα∉⊥是α内异于,A B 的动点，且PC AC ⊥，那么动点C 在平面α内的轨迹是（） A ．圆，但要去掉两个点 B ．椭圆，但要去掉两个点 C ．双曲线，但要去掉两个点 D ．抛物线，但要去掉两个点【答案】A 【解析】【分析】根据题意可得AC BC ⊥,即知C 在以AB 为直径的圆上. 【详解】PB α⊥Q ,AC α⊂，PB AC ∴⊥,又PC AC ⊥，PB PC P ⋂=,AC ∴⊥平面PBC ,又BC ⊂平面PBC AC BC ∴⊥，故C 在以AB 为直径的圆上，又C 是α内异于,A B 的动点，所以C 的轨迹是圆，但要去掉两个点A,B 故选：A 【点睛】本题主要考查了线面垂直、线线垂直的判定，圆的性质，轨迹问题，属于中档题.2．已知向量a r 与b r 的夹角为θ，定义a b ⨯r r 为a r 与b r 的“向量积”，且a b ⨯r r是一个向量，它的长度sin a b a b θ⨯=r r r r ，若()2,0u =r ，(1,u v -=r r ，则()u u v ⨯+=r r r（）A ．BC ．6D ．【答案】D 【解析】【分析】先根据向量坐标运算求出(u v +=r r和cos ,u u v +r r r ，进而求出sin ,u u v +r r r ，代入题中给的定义即可求解. 【详解】由题意()(v u u v =--=r r r r ，则(u v +=r r ，cos ,2u u v +=r r r ，得1sin ,2u u v +=r r r ，由定义知()1sin ,22u u v u u v u u v ⨯+=⋅++=⨯=r r r r r r r r r ，故选:D. 【点睛】此题考查向量的坐标运算，引入新定义，属于简单题目. 3．231+=-ii （） A ．15i 22-+ B ．1522i -- C ．5522i + D ．5122i - 【答案】A 【解析】【分析】分子分母同乘1i +,即根据复数的除法法则求解即可. 【详解】解:23(23)(1)151(1)(1)22i i i i i i i +++==-+--+, 故选:A 【点睛】本题考查复数的除法运算,属于基础题.4．2-31ii =+（） A ．15-22i B ．15--22iC ．15+22i D ．15-+22i 【答案】B 【解析】【分析】利用复数代数形式的乘除运算化简得答案．【详解】()()()()231231515111222i i i i z i i i i -----====--++-．故选B ．【点睛】本题考查复数代数形式的乘除运算，考查了复数的基本概念，是基础题．5．等腰直角三角形ABE的斜边AB为正四面体ABCD侧棱，直角边AE绕斜边AB旋转，则在旋转的过程中，有下列说法：（1）四面体E-BCD的体积有最大值和最小值；⊥；（2）存在某个位置，使得AE BDθ≥∠；（3）设二面角D AB E--的平面角为θ，则DAE（4）AE的中点M与AB的中点N连线交平面BCD于点P，则点P的轨迹为椭圆.其中，正确说法的个数是（）A．1 B．2 C．3 D．4【答案】C【解析】【分析】【详解】解：对于（1），当CD⊥平面ABE，且E在AB的右上方时，E到平面BCD的距离最大，当CD⊥平面ABE，且E在AB的左下方时，E到平面BCD的距离最小，∴四面体E﹣BCD的体积有最大值和最小值，故（1）正确；对于（2），连接DE，若存在某个位置，使得AE⊥BD，又AE⊥BE，则AE⊥平面BDE，可得AE⊥DE，进一步可得AE＝DE，此时E﹣ABD为正三棱锥，故（2）正确；对于（3），取AB中点O，连接DO，EO，则∠DOE为二面角D﹣AB﹣E的平面角，为θ，直角边AE绕斜边AB旋转，则在旋转的过程中，θ∈[0，π），∠DAE∈[，π），所以θ≥∠DAE不成立．（3）不正确；对于（4）AE的中点M与AB的中点N连线交平面BCD于点P，P到BC的距离为：d P﹣BC，因为＜1，所以点P的轨迹为椭圆．（4）正确．故选：C．点睛：该题考查的是有关多面体和旋转体对应的特征，以几何体为载体，考查相关的空间关系，在解题的过程中，需要认真分析，得到结果，注意对知识点的灵活运用. 6．已知函数()cos ||sin f x x x =+，则下列结论中正确的是 ①函数()f x 的最小正周期为π； ②函数()f x 的图象是轴对称图形； ③函数()f x 2； ④函数()f x 的最小值为1-． A ．①③ B ．②④ C ．②③ D ．②③④【答案】D 【解析】【分析】【详解】因为(π)cos(π)sin(π)|cos ||sin (|)f x x x x x f x +=+++=-≠，所以①不正确；因为()cos ||sin f x x x =+，所以 cos sin ()|()|(sin |22c )|os 2x x x f x x πππ+++==++， ()2f x π-=cos sin sin |c |()|()|22os ππ++--=x x x x ，所以() ()22f x f x ππ+=-，所以函数()f x 的图象是轴对称图形，②正确；易知函数()f x 的最小正周期为2π，因为函数()f x 的图象关于直线2x π=对称，所以只需研究函数()f x 在3[,]22ππ上的极大值与最小值即可．当322x ππ≤≤时，()cos sin 2)4f x x x x π=-+=-，且5444x πππ≤-≤，令42x ππ-=，得34x π=，可知函数()f x 在34x π=2，③正确；因为5444x πππ≤-≤，所以12)24x π-≤-≤()f x 的最小值为1-，④正确．故选D ．7．己知全集为实数集R ，集合A={x|x 2 +2x-8>0}，B={x|log 2x<1}，则()R A B ⋂ð等于（） A ．[-4,2] B ．[-4,2)C ．(-4,2)D ．(0,2)【答案】D 【解析】【分析】求解一元二次不等式化简A ，求解对数不等式化简B ，然后利用补集与交集的运算得答案. 【详解】解：由x 2 +2x-8>0，得x ＜-4或x ＞2， ∴A={x|x 2 +2x-8>0}＝{x| x ＜-4或x ＞2}，由log 2x<1，x ＞0，得0＜x ＜2， ∴B={x|log 2x<1}＝{ x |0＜x ＜2}，则{}|42R A x x =-≤≤ð， ∴()()0,2R A B =I ð. 故选：D. 【点睛】本题考查了交、并、补集的混合运算，考查了对数不等式，二次不等式的求法，是基础题.8．我国著名数学家陈景润在哥德巴赫猜想的研究中取得了世界瞩目的成就，哥德巴赫猜想内容是“每个大于2的偶数可以表示为两个素数的和”（注：如果一个大于1的整数除了1和自身外无其他正因数，则称这个整数为素数），在不超过15的素数中，随机选取2个不同的素数a 、b ，则3a b -<的概率是（） A ．15B ．415C ．13D ．25【答案】B 【解析】【分析】先列举出不超过15的素数，并列举出所有的基本事件以及事件“在不超过15的素数中，随机选取2个不同的素数a 、b ，满足3a b -<”所包含的基本事件，利用古典概型的概率公式可求得所求事件的概率. 【详解】不超过15的素数有：2、3、5、7、11、13，在不超过15的素数中，随机选取2个不同的素数，所有的基本事件有：()2,3、()2,5、()2,7、12()()f x f x -、()2,13、()3,5、()3,7、()3,11、()3,13、()5,7、()5,11、()5,13、()7,11、()7,13、()11,13，共15种情况，其中，事件“在不超过15的素数中，随机选取2个不同的素数a 、b ，且3a b -<”包含的基本事件有：()2,3、()3,5、()5,7、()11,13，共4种情况，因此，所求事件的概率为415P =. 故选：B. 【点睛】本题考查古典概型概率的计算，一般利用列举法列举出基本事件，考查计算能力，属于基础题.9．已知椭圆2222:1x y C a b+=的短轴长为2，焦距为12F F 、分别是椭圆的左、右焦点，若点P 为C 上的任意一点，则1211PF PF +的取值范围为（） A ．[]1,2 B． C．⎤⎦D ．[]1,4【答案】D 【解析】【分析】先求出椭圆方程，再利用椭圆的定义得到124PF PF +=，利用二次函数的性质可求1214PF PF ≤≤，从而可得1211PF PF +的取值范围. 【详解】由题设有1,b c ==2a =，故椭圆22:14x C y +=，因为点P 为C 上的任意一点，故124PF PF +=.又()12121212111144=4PF PF PF PF PF PF PF PF PF PF ++==-，因为122PF ≤≤，故()11144PF PF ≤-≤，所以121114PF PF ≤+≤. 故选：D. 【点睛】本题考查椭圆的几何性质，一般地，如果椭圆()2222:10x y C a b a b+=>>的左、右焦点分别是12F F 、，点P 为C 上的任意一点，则有122PF PF a +=，我们常用这个性质来考虑与焦点三角形有关的问题，本题属于基础题.10．如图所示的“数字塔”有以下规律：每一层最左与最右的数字均为2，除此之外每个数字均为其两肩的数字之积，则该“数字塔”前10层的所有数字之积最接近()lg 20.3≈（）A ．30010B ．40010C ．50010D ．60010【答案】A 【解析】【分析】结合所给数字特征，我们可将每层数字表示成2的指数的形式，观察可知，每层指数的和成等比数列分布，结合等比数列前n 项和公式和对数恒等式即可求解【详解】如图，将数字塔中的数写成指数形式，可发现其指数恰好构成“杨辉三角”，前10层的指数之和为29101222211023+++⋅⋅⋅+=-=，所以原数字塔中前10层所有数字之积为10231023lg230021010=≈.故选：A 【点睛】本题考查与“杨辉三角”有关的规律求解问题，逻辑推理，等比数列前n 项和公式应用，属于中档题 11．下列命题为真命题的个数是（）（其中π，e 为无理数） 32e >；②2ln 3π<；③3ln 3e<. A ．0 B ．1C ．2D ．3【答案】C 【解析】【分析】对于①中，根据指数幂的运算性质和不等式的性质，可判定值正确的；对于②中，构造新函数()2ln ,03f x x x =->，利用导数得到函数为单调递增函数，进而得到()()f f e π>，即可判定是错误的；对于③中，构造新函数()ln ,0f x e x x x =->，利用导数求得函数的最大值为()0f e =，进而得到()30f <，即可判定是正确的.【详解】由题意，对于①中，由239(),() 2.2524e e ===，可得 2.25e >，根据不等式的性质，可得32e >成立，所以是正确的；对于②中，设函数()2ln ,03f x x x =->，则()10f x x'=>，所以函数为单调递增函数，因为e π>，则()()ff e π>又由()221ln 10333f e e =-=-=>，所以()0f π>，即2ln 3π>，所以②不正确；对于③中，设函数()ln ,0f x e x x x =->，则()1e e xf x x x-'=-=，当(0,)x e ∈时，()0f x '>，函数()f x 单调递增，当(,)x e ∈+∞时，()0f x '<，函数()f x 单调递减，所以当x e =时，函数取得最大值，最大值为()ln 0f e e e e =-=，所以()3ln330f e =-<，即ln33e <，即3ln 3e<，所以是正确的. 故选：C. 【点睛】本题主要考查了不等式的性质，以及导数在函数中的综合应用，其中解答中根据题意，合理构造新函数，利用导数求得函数的单调性和最值是解答的关键，着重考查了构造思想，以及推理与运算能力，属于中档试题.12．如图是一个算法流程图，则输出的结果是（）A ．3B ．4C ．5D ．6【答案】A 【解析】执行程序框图，逐次计算，根据判断条件终止循环，即可求解，得到答案．【详解】由题意，执行上述的程序框图：第1次循环：满足判断条件，2,1x y ==；第2次循环：满足判断条件，4,2x y ==；第3次循环：满足判断条件，8,3x y ==；不满足判断条件，输出计算结果3y =，故选A ．【点睛】本题主要考查了循环结构的程序框图的结果的计算与输出，其中解答中执行程序框图，逐次计算，根据判断条件终止循环是解答的关键，着重考查了运算与求解能力，属于基础题．二、填空题：本题共4小题，每小题5分，共20分。

数学高三一模2019~2020试卷通州区含答案

通州区高三年级一模考试数学试卷2020年4月第一部分（选择题共40分）一、选择题：本大题共10小题，每小题4分，共40分.在每小题列出的四个选项中，只有一项是符合题目要求的. 1. 已知集合{}02A x x =<≤，{}13B x x =<<，则AB =A. {}03x x << B . {}23x x << C . {}01x x <≤ D . {}12x x <≤2. 已知复数=i(2i)z + （i 是虚数单位），则z =A. 1 B . 2 C.D . 33. 函数()sin 2cos 2f x x x =+的最小正周期是（）Ａ．π2Ｂ．πＣ．2π Ｄ．4π4. 已知()f x 为定义在R 上的奇函数，且(1)2f =，下列一定在函数()f x 图象上的点是A. （1，-2） B . （-1，-2） C . （-1，2） D . （2，1） 5. 已知a ，3，b ，9，c 成等比数列，且a >0，则33log log b c -等于 A. 1- B . 12- C . 12D . 16. 已知抛物线22(0)y px p =>的焦点与双曲线2213x y -=的右焦点重合，则p =A.B . 2C .D . 47. 在6(2)1x x-的展开式中，常数项是A. -160 B . -20 C . 20 D . 1608．在平面直角坐标系中，O 为坐标原点，已知两点(cos ,sin )A αα，(cos(),sin())33B ππαα++.则OA OB +=A.1 B.C . 2D . 与α有关9. 若a >0，b >0，则“ab ≥1”是 “a+b ≥2”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10. 某同学在数学探究活动中确定研究主题是“(1,N )n a a n *>∈是几位数”，他以2(N )n n *∈为例做研试用该同学的研究结论判断504是几位数（参考数据lg20.3010≈） A. 101 B . 50 C . 31 D . 30第二部分（非选择题共110分）二、填空题：本大题共5小题，每小题5分，共25分．11. 已知向量(1,2)=-a ，(3,)m =-b ，其中m ∈R ．若,a b 共线，则m 等于 ___________.12. 圆()1122=+-y x 的圆心到直线10x +=的距离为 .13.某三棱锥的三视图如图所示，则该三棱锥的体积等于 .14．中国古代数学著作《孙子算经》中有这样一道算术题：“今有物不知其数，三三数之余二，五五数之余三，问物几何？” ，将上述问题的所有正整数答案从小到大组成一个数列 {}n a ，则1a = ； n a = . （注：三三数之余二是指此数被3除余2，例如“5”）15.给出下列四个函数，①21y x =+；②12y x x =+++；③21x y =+；④2cos y x x =+ 其中值域为[1)+∞，的函数的序号是 .三、解答题：本大题共6小题，共85分．解答应写出文字说明，演算步骤或证明过程．16.（本小题14分）已知△ABC ，满足a =2b =，，判断△ABC 的面积2S >是否成立？说明理由.从①3A =π ， ② cos B =这两个条件中任选一个，补充到上面问题条件中的空格处并做答.注：如果选择多个条件分别解答，按第一个解答计分.17．（本小题14分）2019年1月1日，我国开始施行《个人所得税专项附加扣除操作办法》，附加扣除的专项包括子女教育、继续教育、大病医疗、住房贷款利息、住房租金、赡养老人．某单位有老年员工140人，中年员工180人，青年员工80人，现采用分层抽样的方法，从该单位员工中抽取20人，调查享受个人所得税专项附加扣除的情况，并按照员工类别进行各专项人数汇总（Ⅰ）在抽取的20人中，老年员工、中年员工、青年员工各有多少人；（Ⅱ）从上表享受住房贷款利息专项扣除的员工中随机选取2人，记X 为选出的中年员工的人数，求X 的分布列和数学期望.18. （本小题15分）如图，已知四边形ABCD 为菱形，且060=∠A ，取AD 中点为E .现将四边形EBCD 沿BE 折起至EBHG ，使得90AEG ∠=.(Ⅰ)求证：⊥AE 平面EBHG ； (Ⅱ)求二面角A -GH -B 的余弦值；(Ⅲ)若点F 满足AB λAF =，当//EF 平面AGH 时，求λ的值.19．（本小题14分）已知椭圆C ：)0(12222>>=+b a by a x 的离心率为22，点A (0，1)在椭圆C 上．（Ⅰ）求椭圆 C 的方程；（Ⅱ）设O 为原点，过原点的直线（不与x 轴垂直）与椭圆C 交于M 、N 两点，直线AM 、AN 与x 轴分别交于点E 、F ．问： y 轴上是否存在定点G ，使得∠OGE =∠OFG ？若存在，求点G 的坐标；若不存在，说明理由．20．（本小题14分）已知函数()()e x f x x a x a =-++，设()()g x f x '=.（Ⅰ）求()g x 的极小值；（Ⅱ）若()0f x >在(0,)+∞上恒成立，求a 的取值范围.21．（本小题14分）用[x ]表示一个小于或等于x 的最大整数.如：[2]=2，[4.1]=4，[-3.1]=-4.已知实数列 ,,10a a 对于所有非负整数i 满足])[(][1i i i i a a a a -⋅=+，其中0a 是任意一个非零实数. (Ⅰ) 若6.20-=a ，写出a 1,a 2,a 3； (Ⅱ)若00>a ，求数列]}{[i a 的最小值；(Ⅲ)证明：存在非负整数k ，使得当k i ≥时，2+=i i a a .ECDBAEGHBA通州区高三年级一模考试数学试卷参考答案及评分标准 2020年4月一、选择题：（每小题4分，共40分.）二、填空题（每道小题5分，共25分）11．6 ； 12. 1；13； 14．8；15n -7；（第一空2分，第二空3分） 15．①②④ （答对一个给1分，答对两个给3分，全对给5分，出现一个错误不得分.）三、解答题：本大题共6小题，共85分．解答应写出文字说明，演算步骤或证明过程．16．（本小题14分）解：选○1，△ABC 的面积2S >成立，理由如下:当3A =π时，2147cos 222c A c +-==⋅， …………… 4分所以2230c c --=，所以3c =， …………… 6分则△ABC 的面积11sin 23sin 223S bc A π==⨯⨯⨯=分2=>=， …………… 12分所以2S >成立. ……………14分选○2，△ABC 的面积2S >不成立，理由如下：当cos B =222cos 2a c b B ac +-==…………… 4分2=整理得，230c -+=，所以c = …………… 6分因2227,437a b c =+=+=， …………… 8分所以△ABC 是A 为直角的三角形， …………… 10分所以△ABC 的面积112222S bc ==⨯=，…………… 12分所以不成立. …………… 14分17. （本小题14分）解：（Ⅰ）该单位员工共140+180+80=400人，抽取的老年员工201407400⨯=人，中年员工201809400⨯=人，青年员工20804400⨯=人 ……………… 4分（Ⅱ）X 的可取值为0,1,2 ……………… 5分23283(X=0)28C P C ==，11352815(X=1)28C C P C ==，252810(X=2)28C P C == ……………… 11分5(X)4E =. ……………… 14分18. （本小题15分）(Ⅰ)证明：在左图中，△ABD 为等边三角形，E 为AD 中点所以BE ⊥AD ， ……………… 2分所以BE ⊥AE 因为90AEG ∠=，所以GE ⊥AE . ……………… 3分因为GE ⊥AE ，BE ⊥AE ，GE ∩BE =E所以⊥AE 平面EBHG . ……………… 4分 (Ⅱ) 设菱形ABCD 的边长为2，由(Ⅰ)可知GE ⊥AE ，BE ⊥AE ，GE ⊥BE.所以以E 为原点，EA ,EB ,EG 所在直线分别为x ,y ,z 轴，建立如图空间坐标系可得(1,0,0)A ，B ，(0,0,1)G ，H .……………… 6分=(1,0,1)AG -，=(AH -设平面AGH 的法向量为),,(z y x n =所以 00n AG n AH ⎧⋅=⎪⎨⋅=⎪⎩，即020x z x z -+=⎧⎪⎨-++=⎪⎩. 令x =1，则)1,33,1(-=n ………………8分平面EBHG 的法向量为(1,0,0)EA = ……………… 9分设二面角A -GH -B 的大小为)90(0<θθ721,cos |cos >=<=EA n θ ……………… 11分 (Ⅲ) 由AF AB =λ，则(1,0)F -λ所以)0,3,1(λλEF -= ……………… 12分因为//EF 平面AGH ，则 0=⋅EF n ……………… 13分即120-λ= ……………… 14分所以21=λ ……………… 15分19. （本小题14分）解：（Ⅰ）由题意得c e a ==………………1分 b =1,又222a b c =+解得1a c = ……………… 4分所以椭圆方程为2212x y += ……………… 5分（Ⅱ）设00(,)M x y ，由题意及椭圆的对称性可知000(,)(1)N x y y --≠±……………… 6分则直线AM 的方程为0011y y x x -=+ ……………… 7分直线AN 的方程为0011y y x x +=+ ……………… 8分则E 点坐标为00(,0)1x y -，F 点坐标为00(,0)1x y -+ ……………… 10分假设存在定点G （0，n ）使得∠OGE =∠OFG ，即tan ∠OGE =tan ∠OFG （也可以转化为斜率来求）……………… 11分即OE OG OGOF=即2OG OE OF = ……………… 12分即220221x n y ==-所以n = ……………… 13分所以存在点G 坐标为(0,满足条件. ……………… 14分20. （本小题14分）解：（Ⅰ）()(1)1x f x x a e '=-++ ……………… 1分由题意可知()(1)1x g x x a e =-++，所以()(2)x g x x a e '=-+ ……………… 2分当2x a >-时()0g x '>，()g x 在(2,)a -+∞上单调递增；……………… 3分当2x a <-时()0g x '<，()g x 在(,2)a -∞-上单调递减……………… 4分所以()g x 在2x a =-处取得极小值，为2(2)1a g a e --=-+……………… 5分（Ⅱ）由（Ⅰ）得2()()1a f x g x e -'=≥-+当2a ≤时2()10a f x e -'≥-+>， ……………… 6分所以()f x 在单调递增，所以()(0)0f x f >= ……………… 7分即2a ≤时()0f x >在(0,)+∞恒成立. ……………… 8分当2a >时(0)(0)20f g a '==-<， ………………9分又()()10a f a g a e '==+>， ……………… 10分又由于()f x '在(2,)a -+∞上单调递增；在(0,2)a -上单调递减；所以在(0,)a 上一定存在0x 使得0()0f x '=， ……………… 11分所以()f x 在0(0,)x 递减，在0(,)x +∞递增，所以0()(0)0f x f <= ……………… 12分所以在(0,)+∞存在0x ，使得0()0f x <， ……………… 13分所以当2a >时，()0f x >在(0,)+∞上不恒成立所以a 的取值范围为(],2-∞. ………………14分21. （本小题14分）解：(Ⅰ) 2.11-=a 、6.12-=a 、8.03-=a . ……………… 3分分分分分4,3, (13)令k=m，满足当ki≥时，2+=iiaa.综上，存在非负整数k，使得当ki≥时，2+=iiaa.………………14分。

通州区2019—2020学年高三一模考试试卷答案答案详解

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2019-2020学年北京育才学校通州分校高三英语一模试题及参考答案

2019-2020学年北京育才学校通州分校高三英语一模试题及参考答案第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项ABritain's brilliant bridges have aided trade and brought communities together and are always the most exciting part of the journey. These must-see bridges are now tourist attractions in their own right.Clifton Suspension Bridge, BristolDescribed byits legendary engineer Isambard Kingdom Brunel as “my first love, my darling”, in was originally designed for horse-drawn traffic. Now, more than four million vehicles a year cross the 1,352ft-Jong toll (收费) bridge over the Avon Gorge. The £ l toll for every journey pays for its repair. The history of the bridge, dating back to 1864, is kept alive through a programme of tours, events and exhibitions.Infinity Bridge, Stockton-On-TeesA pedestrian and cycle footbridge across the River Tees, its working title was the North Shore Footbridge, before it was given its grander name when opened in 2009. It is particularly spectacular (壮观) at night. The arches of the bridge are also lit white and, on calm nights, their reflection in the water appears as an infinity symbol, thereby inspiring the name which was chosen by the public.Tower Bridge, LondonAn engineering wonder built from thousands of tons of Cornish granite, Portland stone and steel, it took construction workers eight years to complete. More than 120 years old, it's a popular tourist attraction, as well as a functional bridge. Visitors can take in the views over the capital and experience seeing London life through the Glass Floor.Iron Bridge, ShropshireOpened in 1781, this is the first arch bridge in the world to be made out of cast iron. Recognised as one of the great symbols of the industrial revolution, it transformed the cart of bridge building and was a crucial factor in the development of the iron trade in Shropshire.1.Which bridge has the longest history?A.Clifton Suspension Bridge.B.Infinity Bridge.C.Tower Bridge.D.Iron Bridge.2.What can we know about Infinity Bridge?A.People can just walk on it.B.The public give it two names.C.It's well worth visiting at night.D.It's arch is the biggest on the earth.3.What do Clifton Suspension Bridge and Tower Bridge have in common?A.They are both over 120 years old.B.Visitors should pay for passing them.C.They have the same original design.D.Visitors can have a good view of London on them.BSince I was born and brought up in a rural town, I have a great interest in nature. Using the chance of studying abroad in my second year at college, I decided to go toCanadajust because I wanted to see the beautiful phenomena there So after I finished the study program, I went toYellowknifein theNorthwest Territories.I clearly remember the sixth night inYellowknife. Suddenly my host mother came to my room around 8 p.m. and told me to change clothes and go outside quickly carrying her camera.The northern lights were flickering (闪烁) in the sky! I was shocked and just stood there with my mouth open.I forgot to take pictures of the mysterious lights.Since that night, whenever it was sunny, I went outside at night and looked at the sky. It was so cold that I lost all feeling in myhands and feet.As I took pictures of the northern lights, I came to find a characteristic movement of the lights. They first appear in the north part of the sky and then they gradually come down to the south part of the sky. After that, suddenly, they come in the middle of the north and south only for a while, which is the time when the best northern lights can be seen. Since it is only a few seconds for the northern lights to come down to the middle of the sky, it is very hard to get good pictures.The stronger the sun acts, the better and stronger the northern lights flicker in the sky. That’s because they come about from the collisions (碰撞) between atmospheric gases and the solar wind. Much more solar wind comes to the earth when the sun is active, whichleads to the best northern lights. And the color1 s of the northern lights depend on the height of the collisions and the kinds of gases.4. Why did the host mother ask the author to go out?A. She wanted to take a picture of him.B. She wanted to take a walk with him.C. She wanted to tell him something important.D. She wanted him to see the northern lights.5. The author forgot to take pictures after going out because ______.A. the host mother didn’t remind him to take the cameraB. he was shocked by the wonderful sightC. the lights flickering in the sky disappeared too soonD. he lost all feeling in his hands and feet6. When is the best time to see the northern lights?A. When they appear in the north part of the sky.B. When they come down to the south part of the sky.C. When they are between the north and south.D. When they rise in the east part of the sky.7. What does the last paragraph mainly tell us?A. Waysto take good pictures.B. The relationship between the sun and the northern lights.C.The color1 s of the northern lights.D. The time of the best northern lights.CWhen Chip heard the mail truck arriving on his sixth birthday, herushed out—not knowing that he’d come back with a treasure.Outside the house, which was decorated with birthday balloons, postwoman Shelley held a pile of boxes. One was marked with Chip’s name and a greeting for his Special day, November 5.“So,” when he came running out the door, she said, “You must be Chip!” And he said,“Yes.” She said, “Today’s your birthday?” And he started smiling. Shelley said, “So, let me see if I can find you something for your birthday.”She checked her pocket and surprised him with a gift: a dollar bill and four quarters.On this day, the 42-year-old postwoman made one little boy very happy. “He was very excited,” said his mom, Bonnie. “He came running back in the house just waving his money.” Chip is saving up to buy a Spider-man action figure.“Our family has had money problems since I lost my job. Gestures like that are valuable memories.” Her hope is that Chip and his eight-year-old sister, Bennett, will remember this when they grow up. “Not the ugly that is out there right now, but the good and the kind and the giving.”A photo of a smiling Chip and Shelley next to the mail truck has been shared widely on social media. Shelley said she was just trying to give back, because people are often nice to her eight-year-old son, Joshua.On a recent day, Chip heard the mail truck and rushed out again, this time to deliver an envelope with a thank-you card for his favorite mail carrier. Since that day, the families have kept in contact. Shelley has struggled to find someone who can take care of her son, and Bonnie has agreed to watch him at her home while his mom is on her mail route.8. Why did Chip rush out when he heard the mail truck the first time?A. To thank the postwoman.B. To get a gift box mailed to him.C. To receive birthday wishes from the driver.D. To watch the mail truck.9. What did Shelley do to make Chip happy?A. She gave him some pocket money.B. She sent him some birthday balloons.C. She presented him with a greeting card.D. She bought him a Spider-man action figure.10. What is Chip’s mother’s attitude towards Shelley?A. Grateful.B. Curious.C. Doubtful.D. Indifferent.11. What does Chip’s mother do to help Shelley?A. She offers to deliver the mails for her.B. She often helps drive her mail truck.C. She looks after her son when she is at work.D. She posts pictures of her mail truck on social media.DThose who are concerned that robots are taking over the world can rest easy—for now. Though the androids have proved useful at performing ordinary tasks, they are not ready for the greatest time. At least that appears to be the case atJapan’s Henn-na Hotel chain where over half of the robot staff are being replaced by humans.The first location of the unique hotel opened in July 2015 was atNagasaki’s Huis Ten Bosch Theme Park. The hotel’s owner, Hideo Sawada, promised the hotel to be managed primarily by robots. Guests were greeted and checked-in by a dinosaur robot, while a cute android called Churi, placed inside each room, provided information about attractions. Not surprisingly, the lodging, recognized in 2016 as the world’s first robot-staffed hotel by Guinness World Records, drew in curious visitors from all around the world.But as the years have passed, the hotel’s main draw is becoming less novel and more unsatisfactory. Also as therobots are “aging”, they are costing more to repair. Among the 283 androids being replaced are the chain’s two dinosaur receptionists. In addition to scaring young guests, they are also unable to photocopy guests’ passports, forcing human employees to step in each time. Also out are the cute Churi robots, which annoyed guests by interrupting their conversations. For example, one guest told The Wall Street Journal that Churi mistook his snoring for a command and kept asking him to repeat his request all night.Sawada told The Wall Street Journal, “When you actually use robots you realize there are places where they aren’t needed—or just annoy people.” While Sawada may be cutting back on his use of androids, the recently-opened Smart LYZ Hotel and the Fly Zoo Hotel inChina, are run entirely by robots, with not a human in sight. Whether the employees have more competence than those “hired” by the Henn-na Hotel chain remains to be seen.12. What makesJapan’s Henn-na Hotel unique?A. Its robot employees.B. Its advanced equipment.C. Its convenient location.D. Its successful management.13. What is the author’s purpose with the example in paragraph 3?A. To entertain readers.B. To prove Churi’s drawback.C. To introduce Churi’s functions.D. To persuade people not to book the hotel.14. What does the owner ofJapan’s Henn-na Hotel think of his robot staff now?A. Attractive.B. Costly.C. Pioneering.D. Disappointing.15. What is the best title for the text?A. Robots Are Taking Over the World.B. The Boom of Robots-staffed Hotel.C. Robot Staff Are Fired For No Competence.D. The First Robots-staffed Hotel Won Guinness World Record.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。

2019-2020学年通州区运河中学高三英语一模试卷及答案解析

2019-2020学年通州区运河中学高三英语一模试卷及答案解析第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AChildren under the age of 18 will be allowed up to three hours per week to play video games, according to a notice issued by China's National Press and Publication Administration. Online game companies are required to provide services to minors — from8 to 9 p. m. on Fridays, Saturdays, Sundays and legal holidays — as a way to safeguard their physical and mental health. Children are playing more and more online games these days. Is it time to limit their online gaming time? What role do parents have? Readers share their opinions.RizlaredOnline games are addictive, but if children are taught how to manage in a sensible and responsible manner then it is no longer a threat(威胁).To achieve this, parents need to set examples for not being glued to their phones. Teaching is and always will be the best solution to such problems.AndrewGood policy. By limiting time spent on online games, kids can spend time doing more useful things to develop their potential. They can go outside and run, jump and swim instead of sitting on a couch at home and playing with a smart phone.AdamIt is often seen that parents argue with children over cellphones. Most parents can hardly set and enforce the time limit for its daily usage. Some forcibly take away their cellphones, but it will ruin trust and relationship. Even worse, it will make their kids hate them.PinkExcessive(过度的）gaming is purely a waste of time and energy for minors and has a negative effect on both physical and mental health. The gaming industry should not put profit- flaking interests as its priority (优先事项) . They should act in a socially responsible way toprovide an environment for children to ensure their well-being and development.LaurenThere would be a loophole(漏洞). Children could use their parents’ or other adults’ IDs to avoid real-name registration, thus making it impossible to put this policy in effect. Parents ly need to strengthen guidance andsupervision to keep their children from gaming addiction.1. What should kids do according to Andrew?A. Play online games.B. Play with a smart phone.C. Study all the time.D. Go in for outside activities.2. What does Pink advise the gaming industry to do?A. Pay attention to its profit.B. Focus on kids’ health.C. Be responsible for kids’ surroundings.D. Persuade kids lo play more games.3. What role do parents have according to the passage?A. They keep hold of their phones.B. They set examples for their kids.C. They limit their kids’ time.D. They blame kids for addiction.BBe it from the mouths of foreigners who have lived here for a few years or from stories on travel websites, one of the most common qualities that people list about Shanghai is the infectious energy that courses through the city.For some, this energy is defined by the way of life—Shanghai is a city that never sleeps. In the day, the streets arc always bustling with people from all over the world. After all, the city has long been China’s most cosmopolitan city, having been the epicenter of trade and cultural exchange between Chinese and foreigners since the city was forced to open its door to the world in 1843 after the First Opium War (1840-42).Shanghai’s ubiquitous delivery people can be found on the roads even past midnight, rushing from point to point on their trusty electric scooters to satiate the hunger of night owls. Even before the break of dawn, pensioners can be found gathering in parks, ready to kick start their day with a tai chi session.For others, this energy is generated from the friction between the contrasts the city has. Indeed, it does not take long for one to realize that Shanghai's charmlies in it being a binary of old and new.Here, charming neoclassical architecture and art deco structures stand alongside modem buildings with shimmering glass and metal facades, rustic (质朴的)lane houses and shikumen buildings. Humble mom-and-pop shops that look stuck in time can often be found right next tohipdining venues or industrial-chic fashion stores selling designer apparel.One of the best places to get an overview of these surreal contrasts is none other than the tallest building in the city — the Shanghai Tower in Lujiazui. Measuring a dizzying 632 meters in height, this architectural marvel boasts having the world's highest observation deck within a building or structure. It also comes with the world'sfastest elevators which would get you from the bottom to the top at 20.5 meters per second.On the other side of the Huangpu River is where you would find the Bund, which is home to magnificent neoclassical buildings. The Bund is to Shanghai what Times Square is to New York or what the Champs-61ysees is to Paris. A trip to Shanghai would not be complete without exploring this iconic waterfront promenade.Autumn is the best time to experience Shanghai on foot, not merely because the weather is conducive for walking, but because this is when the roads and sidewalks in many areas are blanketed with a layer of color1 ful fallen leaves.4. Why is the example of delivery man mentioned?A. To make a contrast with pensioners’ biological clock.B. To illustrate the vibrant energy of modern Shanghai.C. To highlight the diligence and consideration of delivery man.D. To feature the courier delivery service in full swing.5. Which of the following is TRUE about the contrast of Shanghai?A. The contrast mainly arises from the First Opium War.B. The design of the Shanghai Tower stands for a contrast.C. A marked contrast is shown in the use of building materials.D. The dishes served in mom-and-pop shops represent the outdated flavor.6. The underlined word “hip” in paragraph 5 is closest in meaning to________.A. photographicB. modestC. peculiarD. stylish7. Which of the following will be most probably discussed following the last paragraph?A. Stunning views of the Shanghai skyline.B. The best places to view the seasonal spectacle.C. The walking path thathugs the Huangpu River.D. Must-try dishes and food items typical of Shanghai.CAt the age of 50, Nina Schoen expects to have a long lifeahead of her, but has thought a lot about death—and why people are so reluctant to talk about it: “It’s going to happen to all of us,” she says, “but it should be a more positive experience than the fear we put into it.”When she first heard about a new end-of-life process that turns the body into compost (堆肥), “I was really moved by the idea,” says Schoen, who became one of the first to reserve a spot with a Seattle-based companycalled Recompose, the county’s first funeral home to offer human composting.Last year Recompose began transforming bodies to soil, more formally known as natural organic reduction. Before that, end-of-life options in the U.S. were limited to burial or cremation (火化), both of which come with environmental costs—U.S. cremations alone dump 1.7 billion pounds of carbon dioxide into theatmosphere every year.Katrina Spade pioneering the composting movement has spent a decade developing the process in hopes of offering people a greener option for death care. “I wondered, ‘What if we had a choice that helps the planet rather than harms it?’” Spade tells PEOPLE. “To know that the last gesture you’ll make will be gentle and beneficial and it just feels like the right thing to do.”After she had her own two sons, she began to wonder what she might do with her body after death. A friend who knew her interest in the topic reminded her that farmers sometimes compost the body of cows, and thatsparkedan idea for her theory: “If you can compost a cow, you can probably compost a human,” she thought, and she set about designing a facility to do just that.“This is about giving people another choice,” Spade says. “At first, people react with shock—‘You really can do that?’ But so many people today are looking at their impact on the Earth. This is a popular thing because when you die, you can give back to the planet.”8. How do people react when it comes to death according to paragraph 1?A. They are unwilling to comment.B. They can face it without fear.C. They feel it a positive experience.D. They would like to compost their bodies.9. What can we know about the company Recompose?A. Its CEO is Katrina Spade.B. It is located in Seattle.C. It was founded to resist cremation.D. It has spent 10 years composting bodies.10. What does the underlined word “sparked” probably mean?A. Changed.B. Compromised.C. Quitted.D. Inspired.11. What message does the author seem to convey in the text?A. A little things in our life can bring in big outcomes.B. We human beings should do all we can to help the earth.C. Composting is so popular that we should reserve a spot soon.D. We should reject burial because of its harm to environment.DWhat will people die of 100 years from now? If you think that is a simple question，you have not been paying attention to the revolution that is taking place in bio-technology（生物技术）. With the help of new medicine，the human body will last a very long time. Death will come mainly from accidents，murder and war. Today’s leading killers，such as heart disease，cancer，and aging itself，will become distant memories.In discussion of technological changes，the Internet gets most of the attention these days. But the change in medicine can be the real technological event of our times. How long can humans live? Human brains were known to decide the final death. Cells（细胞）are the basic units of all living things，and until recently，scientists were sure that the life of cells could not go much beyond 120 years because the basic materials of cells，such as those of brain cells，would not last forever. But the upper limits will be broken by new medicine. Sometime between 2050 and 2100，medicine will have advanced to the point at which every 10 years or so，people will beable to take medicine to repair their organs（器官）. The medicine，made up of the basic building materials of life，will build new brain cells，heart cells，and so on－in much the same way our bodies make new skin cells to take the place of old ones.It is exciting to imagine that the advance in technology may be changing the most basic condition of human existence，but many technical problems still must be cleared up on the way to this wonderful future.12. According to the passage，human death is now mainly caused by ________.A. diseases and agingB. accidents and warC. accidents and agingD. heart disease and war13. In the author’s opinion，today’s most important advance in technology lies in（在于）________.A. the InternetB. medicineC. brain cellsD. human organs14. Humans may live longer in the future because ________.A. heart disease will be far away from usB. human brains can decide the final deathC. the basic materials of cells will last foreverD. human organs can be repaired by new medicine15. How long can humans live in the future according to the passage?A. Over 100 years.B. More than 120 years.C. About 150 years.D. The passage doesn’t tell us.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。

北京市通州区2019—2020学年高三一模考试试卷答案(三稿)

通州区2020年高三模拟考试语文试卷参考答案及评分标准2020年5月一、本大题共5小题，共18分。

1.（3分）B2.（3分）A3．（3分）D4．（3分）C5.（6分）材料一：我国古代风筝可用于军事活动，也可用于民间娱乐。

材料二：放风筝是我国重要的民俗之一，人们通过放风筝来抒发内心情感和愿望。

材料三：“风筝”具有特殊的文学意象，用于文学创作，可表情达意。

【评分说明：6分。

每个要点2分；意思对，即可给分】二、本大题共6小题，共24分。

6．（3分）B（子：古代对男子的美称，也用以尊称对方，相当于“您”）7．（3分）C（C 项两句中的“而”均为连词，表示顺承关系。

A 项第一句中的“之”为代词，“聚集的百姓”；第二句中的“之”为代词，“燕国”。

B 项第一句中的“以”同“已”，意思为“已经”；第二句中的“以”是连词，表目的，“用来”。

D项第一句中的“于”为介词，“对”；第二句中的“于”为介词，“在”）8．（3分）D（看到它的根本就知道它的末梢了）9．（4分）①和百姓立下的誓约，不是一天积累成的。

②这就将使晋国的将士，舍弃仁义而追随奸佞。

【评分说明：4分，每句翻译1分，其中“约信”要准确，①句中的否定句要准确。

②实词、句意翻译要准确。

其余表述意思对，即可给分】10．（5分）答案要点：藏富于民；取信于民；不能滥用民力；不完全依据结果赏罚；不任用奸佞。

【评分说明：5分，每个要点1分。

意思对，即可给分】11．（6分）①（2分）“切、磋、琢、磨”本义是指骨角玉石等加工工艺。

在文中“如切如磋，如琢如磨”比喻道德学问方面相互研讨勉励。

或指共同研究学习，互相取长补短。

【评分说明：2分，本义，1分；引申义，1分。

要解释准确，意思对，即可给分】②（4分）《诗》是雅言，即规范语言。

（1分）在诵读《诗》《书》，述说礼仪时，都要用规范语言。

（1分）学习《诗》，不仅学习其中道理，还要学习其中的语言表达，这样就可以提高语言的表达能力。

（2分）所以孔子说“不学诗，无以言”。

通州区2019—2020学年高三一模考试试卷答案(三稿)

通州区2020年高三模拟考试语文试卷参考答案及评分标准2020年5月一、本大题共5小题，共18分。

1.（3分）B2.（3分）A3．（3分）D4．（3分）C5.（6分）材料一：我国古代风筝可用于军事活动，也可用于民间娱乐。

材料二：放风筝是我国重要的民俗之一，人们通过放风筝来抒发内心情感和愿望。

材料三：“风筝”具有特殊的文学意象，用于文学创作，可表情达意。

【评分说明：6分。

每个要点2分；意思对，即可给分】二、本大题共6小题，共24分。

6．（3分）B（子：古代对男子的美称，也用以尊称对方，相当于“您”）7．（3分）C（C 项两句中的“而”均为连词，表示顺承关系。

A 项第一句中的“之”为代词，“聚集的百姓”；第二句中的“之”为代词，“燕国”。

B 项第一句中的“以”同“已”，意思为“已经”；第二句中的“以”是连词，表目的，“用来”。

②这就将使晋国的将士，舍弃仁义而追随奸佞。

【评分说明：4分，每句翻译1分，其中“约信”要准确，①句中的否定句要准确。

②实词、句意翻译要准确。

其余表述意思对，即可给分】10．（5分）答案要点：藏富于民；取信于民；不能滥用民力；不完全依据结果赏罚；不任用奸佞。

【评分说明：5分，每个要点1分。

意思对，即可给分】11．（6分）①（2分）“切、磋、琢、磨”本义是指骨角玉石等加工工艺。

在文中“如切如磋，如琢如磨”比喻道德学问方面相互研讨勉励。

或指共同研究学习，互相取长补短。

【评分说明：2分，本义，1分；引申义，1分。

要解释准确，意思对，即可给分】②（4分）《诗》是雅言，即规范语言。

（1分）在诵读《诗》《书》，述说礼仪时，都要用规范语言。

（1分）学习《诗》，不仅学习其中道理，还要学习其中的语言表达，这样就可以提高语言的表达能力。

（2分）所以孔子说“不学诗，无以言”。

2019-2020学年通州区第三中学高三英语一模试题及答案解析

2019-2020学年通州区第三中学高三英语一模试题及答案解析第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AI started working with my hands at a young age. The youngest of five brothers, I took on the role as a “maintenance (维修) man” at an early age for our family’s small grocery store. Often my dad wouldn’t give me a clear idea of how something shouldbe done, so I just had to figure it out by researching or through trial and error.Fast forward to 2016 and those problem-solving skills would become the focus of Tippecanoe High School’s Homebuilding class. I knew I wanted to teach the students skills that went beyond just being able to hammer nails or cut pieces of two-by-fours. The problem was that we didn’t have the resources at the time to do much else. The idea of attracting some type of funding seemed very important. Designing, building and selling a tiny house on wheels seemed like the perfect project to accomplishthe task. I reached out to a number of local businesses and most of them responded with the greatest support for what x k w we were doing.This year we added a new element to the program. Through one of our partners, we were able to connect with the nonprofit Veteran’s Ananda Incorporated. Students in the Homebuilding class are leading the design and production of micro houses to be donated to this organization. The new partnership gives the students another focus to consider when designing and building the houses.There has been no shortage of students since our first year. Three years ago we had 41 students, the next 191, and this year it was limited to just over 160 students so we could have a safe and manageable classroom environment. The number of girls taking the class has risen steadily over the last few years as well. This class offers something for everyone and the skills are universal.1. How can we describe the young author?A. He opened a small grocery store.B. He did a lot of research in the lab.C. He enjoyed doing hands-on activities.D. He learnt about maintenance from his father.2. What do the underlined words “the task” in paragraph 2 refer to?A. Getting some financial support.B. Selling a tiny house on wheels.C. Reaching out to many local businesses.D. Offering the students some problem-solving skills.3. What can be inferred about the Homebuilding class from the last paragraph?A. Its size needs increasing.B. Itis popular with the students.C. It has caused some safety concerns.D. Its classroom environment is hard to manage.B“One person’s trash is another person’s treasure.” That’s a common expression, but the next time you throw something away, think about a twist on the old saying. What if your trash could become your own treasure? Many creative, thrifty, and environmentally minded people have come up with a way to makethathappen. It’s called upcycling. Our world would be a better place if everyone would begin upcycling.Upcycling is the practice of taking an unwanted item and turning it into something useful. For example, how about that pair of jeans with a hole in one knee? It could become a new pillow for your bedroom.Upcycling is not the same as recycling. Upcycling is actually much better for the environment. Recycling takes an item made of glass, paper, metal, or plastic, breaks it down to its base material, and then uses that material to make another product. This requires a great deal of energy. On the other hand, when you choose to upcycle, the only energy you use is your own. And upcycling not only reduces the amount of trash that goes into our landfills, but it also protects natural resources, such as oil and gas. Recycling is good for the environment, but upcycling is even better.Upcycling also makes a family’s budget stretch further. Of course, the idea of reusing items to save money is not new. During the Great Depression in the 1930s, many families lived on a tight budget. People had to use what they already had in order to meet their needs.As responsible citizens, we should all be concerned with protecting our environment and budgeting our resources. Upcycling is a fun and creative way to help. The next time you go to toss something into the trash can, stop and think about what it could become. Chances are, there’s a brand-new item in your hand just waiting to be upcycled.4. Why does the author mention an old saying in the first paragraph?A. To arise reader’s awareness of upcycling.B. To stress the importance of upcycling.C. To lead in the topic of upcycling.D. To show the idea of upcycling.5. Which one below belongs to upcycling?A. An old ladder is transformed into a bookshelf.B. Old tin cans are transported to landfill.C. A broken wooden door is chopped up.D. Old cloth is made into a paper bed.6. What is the difference between recycling and upcycling?A. Upcycling is much more creative.B. Recycling is much easier to achieve.C. Recycling is much more cost-saving.D. Upcycling is much more energy-efficient.7. What can be inferred from the text?A. Upcycling is popular at present.B. Upcycling is replacing recycling.C. Upcycling is worth recommending.D. Upcycling is a tradition in daily life.CEvery day, millions of shoppers hit the stores in full force, searching wildly for the perfect gift.Aside from purchasing holiday gifts, most people regularly buy presents for other occasions throughout the year, including weddings, birthdays, anniversaries, and graduations. This frequent experience of gift-giving cancause uncertain feelings in gift-givers. Many enjoy the opportunity to buy presents because gift-giving offers a powerful means to build stronger bonds, while many worry that their purchases will disappoint rather than delight the intended recipients (接受者).Anthropologists describe gift-giving as a positive social process, serving various political, religious, and psychological functions. Economists, however, offer a less favorable view. According to Waldfogel, gift-giving represents an objective wasteof resources. People buy gifts that recipients would not choose to buy on their own, or at least not spend as much money to purchase (a phenomenon referred to as‘‘the deadweight loss of Christmas”).What is surprising is that gift-givers have much experience acting as both gift-givers and gift-recipients, butnevertheless tend to overspend each time they set out to purchase a meaningful gift. In the present research, we propose a unique psychological explanation for this overspending problem — gift-givers link how much they spend with how much recipients will appreciate the gift. Though it seems natural to gift-givers, such an assumption may be unfounded. Indeed, we propose that gift-recipients will be less likely to base their feelings of appreciation on the value of a gift than givers assume.Why do gift-givers assume that gift price is closely linked to gift-recipients’ feelings of appreciation? Perhaps givers believe that more expensive gifts communicate a stronger sense ofthoughtfulness and consideration. According to Camerer and others, gift-giving represents a symbolic ritual (习俗), by which gift-givers attempt to signal their positive attitudes towards the recipient and their willingness to invest resources in a futurerelationship. In this sense, gift-givers may be motivated to spend more money on a gift in order to send a “stronger signal”. As for gift-recipients, they may not interpret smaller and larger gifts as representing smaller and larger signals of thoughtfulness and consideration.The idea of gift-givers and gift-recipients being unable to account for the other party’s viewpoint seems confusing because people slip in and out of these roles every day. Yet, despite the experience as both givers and receivers, people often struggle to apply information gained from one role in another. In theoretical terms, people fail to use information about their own preferences and experiences to produce more efficient outcomes in their exchange relations. In practical terms, people spend hundreds of dollars each year on gifts, but somehow never learn to estimate their gift expense according to personal insight.8. The author uses “the deadweight loss of Christmas” in Paragraph 2 to express ________.A. gift-givers don’t spend much money during holidaysB. gift-givers don’t ask recipients what gifts they preferC. gift-givers buy improper and expensive giftsD. gift-givers have difficulty in choosing gifts9. According to the passage, people buy gifts to ________.A. receive gifts in returnB. enjoy the feeling of shoppingC. help recipients to save moneyD. better relationships with recipients10. What can we learn from the passage?A. People’s high living standards require expensive gifts.B. Gift-givers buy gifts based on their experiences as recipients.C. Anthropologists think gift-giving meets different human needs.D. Recipients judge the depth of friendship according to the gift price.11. Why did the author write this article?A. To criticize people’s gift-buying habits.B. To analyze people’s gift-giving behaviors.C. To offer advice on how to improve relationships.D. To remind people not to overlook others’ preferences.DTen years ago, I set out to examine luck. I wanted to know why some people were always in the right place at the right time, while others consistently experienced ill fortune. I placed advertisements in national newspapers asking for people who felt consistently lucky or unlucky. Hundreds of extraordinary men and women volunteered for my research. Over the years I have interviewed them, monitored their lives and had them take part in various experiments.In one of the experiments, I gave both lucky and unlucky people a newspaper, asking them to look through it and tell me how many photographs were inside. I had secretly placed a large message halfway through the newspaper, saying, “Tell the experimenter you have seen this and you will win $50.” This message took up half of the page and was written in type that was more than two inches high. It was staring everyone in the face, but the unlucky people tended to miss it and the lucky people tended to spot it.Unlucky people are generally more nervous than lucky people, and this anxiety affects their ability to notice the unexpected. As a result, they miss opportunities because they are too focused on looking for something else. They go to gatherings concentrating on finding their perfect partners and miss opportunities to make good friends. They look through newspapers determined to find certain types of job advertisements and miss other types of jobs.Lucky people are more relaxed and open, and therefore see what is there rather than just what they are looking for. My research eventually showed that lucky people are skilled at noticing opportunities, make lucky decisions by listening to their intuition (直觉), are open to new experiences, and adopt a never-say-die attitude that transforms bad luck into good luck.12. What’s the purpose of the author’s research?A. To discover what luck means to people.B. To find lucky people and unlucky people.C. To distinguish between good luck and bad luck.D. To figure out why people are always lucky or unlucky.13. Why did the unlucky people miss the message in the experiment?A. There was too much information to be read in detail.B. They were too focused on looking for photographs.C. It took too much time to go through newspapers.D. The words were too small to be noticed.14. What leads to lucky people’s good fortune?A. Their ability to spot opportunities.B. Their ability to become relaxed.C. Their ability to communicate.D. Their ability to make friends.15. What’s the key message of the last paragraph?A. What lucky people are looking for.B. How lucky people generate good luck.C. What lucky people can do with opportunities.D How lucky people transform bad luck into good luck.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。

2019-2020学年江苏省南通市通州区高三(上)第一次调研数学试卷试题及答案(解析版)(9月份)

2019-2020学年江苏省南通市通州区高三（上）第一次调研数学试卷（9月份）一、填空题：本大题共14小题，每小题5分，共70分.请把答案填写在答題卡相应位置 1．己知集合{1A =-，1，2}，{1B =，2，4}，则A B = ．2．设i 为虚数单位，则复数3(1)i +的实部为．3．某校共有学生2400人，其中高三年级600人．为了解各年级学生的兴趣爱好情况，用分层抽样的方法从全校学生中抽取容量为100的样本，则高三年级应抽取的学生人数为． 4．若从甲乙丙丁4位同学中选出3位同学参加某个活动，则甲被选中的概率为． 5．在如图所示的算法流程图中，若输出的y 的值为2-，则输入的x 的值为6．已知双曲线2221(0)x y a a -=>的焦距为4，则a 的值为．7．不等式23122x x --<的解集为8．在棱长为2的正方体1111ABCD A B C D -中，点E 是棱1BB 的中点，则三棱锥11D DEC -的体积为．9．已知等比数列{}n a 的前n 项和为n S ．若21a =，3680a a +=，则5S 的值为． 10．将函数()sin()4f x x π=+的图象向右平移ϕ个单位，得到函数()y g x =的图象．则“34πϕ=”是“函数()g x 为偶函数”的条件．（从“充分不必要”、“必要不充分”、“充要”和“既不充分也不必要”中选填一个）11．已知函数()()x f x ax b e =+，若曲线()y f x =在点(0，(0))f 处的切线方程为310x y -+=，则f （1）的值为．12．设．0x >，0y >，24x y +=，则(4)(2)x y xy++的最小值为．13．已知()f x 是定义在R 上且周期为3的周期函数，当(0x ∈，3]时，()1|1|f x x =--．若函数()log (0a y f x x a =->且1)a ≠在(0,)+∞上有3个互不相同的零点，则实数a 的取值范围是．14．在平面直角坐标系xOy 中，(2,2)P ，(0,4)Q -为两个定点，动点M 在直线1x =-上，动点N 满足2216NO NQ +=，则||PM PN +的最小值为．二、解答题：本大题共6小题，共90分.请在答題卡指定区域内作答.解答时应写出文字说明、证明过程或演算步骤.15．如图，在四棱锥P ABCD -中，四边形ABCD 是平行四边形，AC ，BD 相交于点O ，OP OC =，E 为PC 的中点，PA PD ⊥．（1）求证：//PA 平面BDE ；（2）求证：PA ⊥平面PCD16．在ABC ∆中，角A ，B ，C 的对边分别为a ，b ，c ．已知向量(sin(),1)6a A π=+-，向量(1,cos )b A =，且12a b =．（1）求角A 的大小；（2）若4b =，5c =，求sin 2B 的值．17．设数列{}n a 的各项均为正数，{}n a 的前n 项和2*1(2),8n n S a n N =+∈（1）求数列{}n a 的通项公式；（2）设等比数列{}n b 的首项为2，公比为(0)q q >，前n 项和为n T ．若存在正整数m ，使得33m S S T =，求q 的值．18．（16分）如图，某沿海地区计划铺设一条电缆联通A ，B 两地，A 地位于东西方向的直线MN 上的陆地处，B 地位于海上一个灯塔处，在A 地用测角器测得4BAN π∠=，在A 地正西方向4km 的点C 处，用测角器测得tan 3BCN ∠=．拟定铺设方案如下：在岸MN 上选一点P ，先沿线段AP 在地下铺设，再沿线段PB 在水下铺设．预算地下、水下的电缆铺设费用分别为2万元/km 和4万元/km ，设BPN θ∠=，(,)42ππθ∈，铺设电缆的总费用为()f θ万元．（1）求函数()f θ的解析式；（2）试问点P 选在何处时，铺设的总费用最少，并说明理由．19．（16分）在平面直角坐标系xOy 中，己知椭圆2222:1(0)43x y C t t t +=>的左、右顶点为A ，B ，右焦点为F ．过点A 且斜率为(0)k k >的直线交椭圆C 于另一点P ．（1）求椭圆C 的离心率；（2）若12k =，求22PA PB 的值；（3）设直线:2l x t =，延长AP 交直线l 于点Q ，线段BQ 的中点为E ，求证：点B 关于直线EF 的对称点在直线PF 上．20．（16分）已知函数2()(1)f x x a x a =++-，()(g x x blnx a =-，)b R ∈ （1）当2b =时，求函数()g x 的单调区间；（2）设函数(),1()(),1f x x h x g x x ⎧=⎨>⎩…若0a b +=，且()0h x …在R 上恒成立，求b 的取值范围；（3）设函数()()()u x f x g x a =-+，若2a b +-…，且()u x 在(0,)+∞上存在零点，求b 的取值范围．本题包括A ，B 共1小题，每小题10分，共20分.把答案写在答题卡相应的位置上.解答时应写出文字说明、证明过程或演算步骤.[选修4-2：矩阵与变换] 21．已知矩阵23[]1M t =的一个特征値为4，求矩阵M 的逆矩阵1M -．[选修H ：极坐标与参数方程]22．在极坐标系中，曲线C 的极坐标方程是2cos ρθ=，直线l 的极坐标方程是cos()24πρθ+=．试判断直线l 与曲线C 的位置关系，并说明理由．【必做题】本题满分20分.解答时应写出文字说明'证明过程或演算步骤.23．如图，在直三棱柱111ABC A B C -中，4AC BC ==，AB =，M ，N 分别是AB ，1CC 的中点，且11A M B C ⊥．（1）求1A A 的长度；（2）求平面1B AN 与平面1B MC 所成锐二面角的余弦值．24．己知数列{}n a ．的通项公式为n n n a =-，*n N ∈记1212n n n n n n S C a C a C a =++⋯+（1）求12S S 的值；（2）求证：对任意的正整数n ，21n nn S S S +++为定值．2019-2020学年江苏省南通市通州区高三（上）第一次调研数学试卷（9月份）参考答案与试题解析一、填空题：本大题共14小题，每小题5分，共70分.请把答案填写在答題卡相应位置 1．己知集合{1A =-，1，2}，{1B =，2，4}，则AB = {1，2}【解答】解：集合{1A =-，1，2}，{1B =，2，4}， {1AB ∴=，2}．故答案为：{1，2}．2．设i 为虚数单位，则复数3(1)i +的实部为 2- ．【解答】解：32(1)(1)(1)2(1)22i i i i i i +=++=+=-+． ∴复数3(1)i +的实部为2-．故答案为：2-．3．某校共有学生2400人，其中高三年级600人．为了解各年级学生的兴趣爱好情况，用分层抽样的方法从全校学生中抽取容量为100的样本，则高三年级应抽取的学生人数为 25 【解答】解：有学生2400人，其中高三年级600人，为了解各年级学生的兴趣爱好情况，用分层抽样的方法从全校学生中抽取容量为100的样本，则抽样的比例为600124004=，则高三年级应抽取的学生人数为1100254⨯=，故答案为：25．4．若从甲乙丙丁4位同学中选出3位同学参加某个活动，则甲被选中的概率为4．【解答】解：从甲、乙、丙、丁4位同学中随机选出3名代表参加学校会议，共有344C =种方法，甲被选中，共有3种方法， ∴甲被选中的概率是34P =故答案为：34． 5．在如图所示的算法流程图中，若输出的y 的值为2-，则输入的x 的值4【解答】解：模拟执行程序框图，可得程序框图的功能是求22211x x y log x x ⎧->⎪=⎨⎪⎩…的值，2y =-，∴当1x >时，222x -=-，无解；当1x …时，2log 2x =-，解得：14x =；综上，输入的x 的值是：14．故答案为：14． 6．已知双曲线2221(0)x y a a -=>的焦距为4，则a【解答】解：由双曲线2221(0)x y a a -=>，得221ca =+，即c =又焦距为4，∴4=，得a =，又0a >，a ∴=． 7．不等式23122xx --<的解集为 (1,2)- 【解答】解：不等式23122x x --<，即不等式23122x x ---<，231x x ∴--<-，即(1)(2)0x x +-<，求得12x -<<，故答案为：(1,2)-．8．在棱长为2的正方体1111ABCD A B C D -中，点E 是棱1BB 的中点，则三棱锥11D DEC -的体积为3【解答】解：在棱长为2的正方体1111ABCD A B C D -中，点E 是棱1BB 的中点， ∴三棱锥11D DEC -的体积：11111113D DEC E DD C DD C V V BC S--==⨯⨯1122232=⨯⨯⨯⨯ 43=．故答案为：43．9．已知等比数列{}n a 的前n 项和为n S ．若21a =，3680a a +=，则5S 的值为 2．【解答】解：设等比数列{}n a 的公比为q ．21a =，3680a a +=， 11a q ∴=，33380a a q +=，解得：112a =-，2q =-，则551[1(2)]1121(2)2S ---==---．故答案为：112-． 10．将函数()sin()4f x x π=+的图象向右平移ϕ个单位，得到函数()y g x =的图象．则“34πϕ=”是“函数()g x 为偶函数”的充分不必要条件．（从“充分不必要”、“必要不充分”、“充要”和“既不充分也不必要”中选填一个）【解答】解：将函数()sin()4f x x π=+的图象向右平移ϕ个单位，得到函数()sin()4y g x x πϕ==+-的图象．若函数()g x 为偶函数，则(0)sin()14g πϕ=-=±，42k ππϕπ∴-=+，解得34k πϕπ=+． ∴ “34πϕ=”是“函数()g x 为偶函数”的充分不必要条件．故答案为：充分不必要．11．已知函数()()x f x ax b e =+，若曲线()y f x =在点(0，(0))f 处的切线方程为310x y -+=，则f （1）的值为 3e【解答】解：由题得(0)f b =，将(0，(0))f 代入切线的1b = 因为()()x f x a ax b e '=++，所以(0)3f a b '=+=，所以2a = 则f （1）()3a b e e =+= 故答案为：3e ．12．设．0x >，0y >，24x y +=，则(4)(2)x y xy++的最小值为 9【解答】解：24x y +=，0x >，0y >，24x y ∴+=…，(2x =，1y =时取等）∴112xy …， ∴(4)(2)2(2)8161189x y xy x y xy xy xy+++++==++=…．(2x =，1y =时取等）故答案为：913．已知()f x 是定义在R 上且周期为3的周期函数，当(0x ∈，3]时，()1|1|f x x =--．若函数()log (0a y f x x a =->且1)a ≠在(0,)+∞上有3个互不相同的零点，则实数a 的取值范围是 47a <<或96a <…．【解答】解：函数()log (0a y f x x a =->且1)a ≠在(0,)+∞上有3个互不相同的零点， ()y f x ∴=与log a y x =的图象有3个不同的交点， ∴14171a a a log log >⎧⎪<⎨⎪>⎩或016191a aa log log <<⎧⎪-⎨⎪<-⎩…，解得：47a <<或1196a <…．故答案为：47a <<或1196a <…．14．在平面直角坐标系xOy 中，(2,2)P ，(0,4)Q -为两个定点，动点M 在直线1x =-上，动点N 满足2216NO NQ +=，则||PM PN +的最小值为 3 ．【解答】解：2216NO NQ +=，N ∴在以OQ 为直径的圆上，不妨设(4cos 2,4sin )N θθ-，(1,)M m -，则(3,2)PM m =--，(4cos 4,4sin 2)PN θθ=--， ∴(4cos 7,4sin 4)PM PN m θθ+=-+-，2222||(4cos 7)(4sin 4)8818[(4)sin 7cos ]PM PN m m m m θθθθ∴+=-++-=-++--2(4)65)m θϕ=-++-，t =，sin()a θϕ-=，则7t …，11a -剟． 22||168PM PN t at ∴+=++，令222()168(4)1616f t t at t a a =++=++-，7t …，11a -剟， ()f t ∴在[7，)+∞上单调递增，故当7t =时，()f t 取得最小值6556a +，再令g （a ）6556a =+，11a -剟，显然g （a ）在[1-，1]上单调递增，故1a =-时，g （a ）取得最小值65569-=，综上，当7t =，1a =-时，2||PM PN +取得最小值9．故||PM PN +的最小值为3．故答案为：3．二、解答题：本大题共6小题，共90分.请在答題卡指定区域内作答.解答时应写出文字说明、证明过程或演算步骤.15．如图，在四棱锥P ABCD-中，四边形ABCD是平行四边形，AC，BD相交于点O，⊥．OP OC=，E为PC的中点，PA PD（1）求证：//PA平面BDE；（2）求证：PA⊥平面PCD【解答】解（1）证明：连接OE，四边形ABCD是平行四边形，AC，BD相交于点O，O∴为AC中点，又E为PC的中点，∴，OE PA//OE⊂面BDE，PA⊂/面BDE，PA∴平面BDE．//（2）OP OC=，E为PC的中点，∴⊥，OE PC由（1）知//OE PA，∴⊥，PA PC又PA PD⊥，PC，PD⊂面PCD，∴⊥平面PCD．PA16．在ABC ∆中，角A ，B ，C 的对边分别为a ，b ，c ．已知向量(sin(),1)6a A π=+-，向量(1,cos )b A =，且12a b =．（1）求角A 的大小；（2）若4b =，5c =，求sin 2B 的值．【解答】解：（1）111sin()cos cos cos cos sin()62262a b A A A A A A A A ππ=+-=+-=-=-=，因为0A π<<，5666A πππ-<-<，所以66A ππ-=，3A π=．（2）由余弦定理可知，2222cos a b c bc A =+-，所以22245245cos 213a π=+-⨯⨯⨯=，a ∴=由正弦定理，知sin sin a bA B =4sin 3B =，所以sin B = b c <，B C ∴<，即B 为锐角，所以cos B =sin 22sin cos 2B B B ∴===． 17．设数列{}n a 的各项均为正数，{}n a 的前n 项和2*1(2),8n n S a n N =+∈（1）求数列{}n a 的通项公式；（2）设等比数列{}n b 的首项为2，公比为(0)q q >，前n 项和为n T ．若存在正整数m ，使得33m S S T =，求q 的值．【解答】解：（1）列{}n a 的各项均为正数，且21(2)8n n S a =+，①当1n =时，2111(2)8S a =+，解得12a =．当2n …时，2111(2)8n n S a --=+，②， ①-②整理得11()(4)0n n n n a a a a --+--=，所以14n n a a --=（常数），则14(1)42n a a n n =+-=-（首项符合通项），故42n a n =-．（2）由（1）得：2(422)22n n n S n -+==，等比数列{}n b 的首项为2，公比为(0)q q >，前n项和为2(1)1n n q T q-=-．所以3232(1)2221q T q q q-==++-，假设存在正整数m 存在正整数m ，使得33m S S T =，则22912q q m=++由于0q >，所以2912m>，解得m <，由于m 是正整数，所以1m =或2．当1m =时，整理得2702q q +-=，解得q =，当2m =时，整理得2108q q +-=，解得q （负值舍去），所以q =和q =． 18．（16分）如图，某沿海地区计划铺设一条电缆联通A ，B 两地，A 地位于东西方向的直线MN 上的陆地处，B 地位于海上一个灯塔处，在A 地用测角器测得4BAN π∠=，在A 地正西方向4km 的点C 处，用测角器测得tan 3BCN ∠=．拟定铺设方案如下：在岸MN 上选一点P ，先沿线段AP 在地下铺设，再沿线段PB 在水下铺设．预算地下、水下的电缆铺设费用分别为2万元/km 和4万元/km ，设BPN θ∠=，(,)42ππθ∈，铺设电缆的总费用为()f θ万元．（1）求函数()f θ的解析式；（2）试问点P 选在何处时，铺设的总费用最少，并说明理由．【解答】解：（1）如图所示过点B 作MN 的垂线，垂足为D ，在Rt BAD ∆中，4BAD π∠=，则BD AD =．在Rt BCD ∆中，tan 3BDBCD DC∠==，所以3DB CD =．由于4AC =，所以143BD BD -=，解得6BD =．由BPN θ∠=，则6sin BP θ=，6tan DP θ=，由6AD BD ==，得到66tan AP θ=-．所以662cos ()2(6)41212tan sin sin f θθθθθ-=⨯-+⨯=+⨯其中(,)42ππθ∈．（2）设2cos ()sin h θθθ-=，(,)42ππθ∈．则222sin (2cos )cos 12cos ()sin sin h θθθθθθθ---'==．令()0h θ'=，得1cos 2θ=，所以3πθ=．所以(,)43ππθ∈时，()0h θ'<，(,)32ππθ∈时，()0h θ'>，所以当3πθ=时，函数的极小值为()3h π=所以()f θ的最小值为12+此时6AP =-即当点P 选在距离A 地(6km -处时，铺设费用最少为12+万元．19．（16分）在平面直角坐标系xOy 中，己知椭圆2222:1(0)43x y C t t t +=>的左、右顶点为A ，B ，右焦点为F ．过点A 且斜率为(0)k k >的直线交椭圆C 于另一点P ．（1）求椭圆C 的离心率；（2）若12k =，求22PA PB 的值；（3）设直线:2l x t =，延长AP 交直线l 于点Q ，线段BQ 的中点为E ，求证：点B 关于直线EF 的对称点在直线PF 上．【解答】（1）解：椭圆2222:143x y C t t +=，224a t ∴=，224b t =，22c t =，又0t >，2a t ∴=，c t =， ∴椭圆C 的离心率12c e a ==；（2）解：直线AP 的斜率12k =，且过椭圆C 的左顶点(2,0)A t -， ∴直线AP 的方程为1(2)2y x t =+，代入椭圆C 的方程，得2220x tx t +-=，解得x t =或2x t =-（舍去）．将x t =代入1(2)2y x t =+，得32y t =，∴点P 的坐标为3(,)2t t ，又椭圆C 的右顶点为(2,0)B t ，∴2222345(2)(0)24PA t t t t =++-=，2222313(2)(0)24PB t t t t =-+-=，∴224513PA PB =；（3）证明：直线AP 的方程为(2)y k x t =+，将2x t =代入(2)y k x t =+，得4y kt =，(2,4)Q t kt ∴． E 为线段BQ 的中点，(2,2)E t kt ∴，焦点F 的坐标为(,0)t ， ∴直线EF 的斜率为2k ．联立222(2)3412y k x t x y t=+⎧⎨+=⎩，得22222(34)164(43)0k x k tx k t +++-=．由于224(43)34A P k x x k -=+，2A x t =-，∴222(34)34P k tx k -=+，则P 点的坐标为222(34)(34k t k -+，212)34ktk +．∴直线PF 的斜率为2222212422342(34)141(2)34ktk kk k t k k k +==---+．而直线EF 的斜率为2k ，若设EFB θ∠=，则有tan tan 2PFB θ∠=，即2PFB EFB ∠=∠． ∴点B 关于直线EF 的对称点在直线PF 上．20．（16分）已知函数2()(1)f x x a x a =++-，()(g x x blnx a =-，)b R ∈ （1）当2b =时，求函数()g x 的单调区间；（2）设函数(),1()(),1f x x h x g x x ⎧=⎨>⎩…若0a b +=，且()0h x …在R 上恒成立，求b 的取值范围；（3）设函数()()()u x f x g x a =-+，若2a b +-…，且()u x 在(0,)+∞上存在零点，求b 的取值范围．【解答】解：（1）当2b =时，()2g x x lnx =-，所以22()1x g x x x-'=-=，令()0g x '=，得2x =，因为函数()g x 的定义域为(0,)+∞，当(0,2)x ∈时，()0g x '<；当(2,)x ∈+∞时，()0g x '>，所以函数()g x 的单调减区间为(0,2)，单调增区间为(2,)∈+∞．（2）因为0a b +=，所以2(1),1(),1x b x b x h x x blnx x ⎧--+=⎨->⎩…，当1x …时，有2()(1)0h x x b x b =--+…恒成立，则有当112b -…，即3b …时，()min h x h =（1）20=…恒成立；当112b -<，即3b <时，2161()()024min b b b h x h --+-==…，所以33b -<，综上，3b -…；当1x >时，由()0h x x blnx =-…恒成立，即xb lnx…恒成立，设()(1)xm x x lnx=>，则21()()lnx m x lnx -'=，令()0m x '=，得x e =，且当(1,)x e ∈时，()0m x '<；当(,)x e ∈+∞时，()0m x '>，所以()min m x m =（e ）e =，所以b e …，综上所述，b的取值范围是3b e -．（3）2()u x x ax blnx =++，因为()u x 在(0,)+∞上存在零点，所以20x ax blnx ++=在(0,)+∞有解，即lnx a x bx =--在(0,)+∞上有解，又因为2a b +-…，即2a b --…，所以2lnxx b b x----…在(0,)+∞上有解，设()t x lnx x =-，则11()1xt x x x-'=-=，令()0t x '=，得1x =，且当(0,1)x ∈时，()0t x '>；当(1,)x ∈+∞时，0t '<，所以()t x t …（1）10=-<，即lnx x <，所以1lnxx<，因此22x x b x lnx --…，设22()x x F x x lnx -=-，则2(1)(22)()()x x lnx F x x lnx --+'=-，同理可证：2xlnx <，所以220x lnx -+>，于是()F x 在(0,1)上单调递减，所以()min F x F =（1）1=-，故1b -…．本题包括A ，B 共1小题，每小题10分，共20分.把答案写在答题卡相应的位置上.解答时应写出文字说明、证明过程或演算步骤.[选修4-2：矩阵与变换] 21．已知矩阵23[]1M t =的一个特征値为4，求矩阵M 的逆矩阵1M -．【解答】解：矩阵M 的特征多项式为23()(2)(1)31f t t λλλλλ--==-----；因为矩阵M 的一个特征值为4，所以方程()0f λ=有一根为4；即f （4）2330t =⨯-=，解得2t =；所以2321M ⎡⎤=⎢⎥⎣⎦，设1a b M c d -⎡⎤=⎢⎥⎣⎦，则12323102201a c b d MM a c b d -++⎡⎤⎡⎤==⎢⎥⎢⎥++⎣⎦⎣⎦，由23120a c a c +=⎧⎨+=⎩，解得1412a c ⎧=-⎪⎪⎨⎪=⎪⎩；由23021b d b d +=⎧⎨+=⎩，解得3412b d ⎧=⎪⎪⎨⎪=-⎪⎩；所以113441122M -⎡⎤-⎢⎥=⎢⎥⎢⎥-⎢⎥⎣⎦． [选修H ：极坐标与参数方程]22．在极坐标系中，曲线C 的极坐标方程是2cos ρθ=，直线l 的极坐标方程是cos()24πρθ+=．试判断直线l 与曲线C 的位置关系，并说明理由．【解答】解：曲线C 的极坐标方程是2cos ρθ=，转换为直角坐标方程为22(1)1x y -+=，直线l 的极坐标方程是cos()24πρθ+=．转换为直角坐标方程为0x y --=，所以圆心(1,0)到直线l的距离21d r ==->=，所以直线与圆相离．【必做题】本题满分20分.解答时应写出文字说明'证明过程或演算步骤.23．如图，在直三棱柱111ABC A B C -中，4AC BC ==，AB =，M ，N 分别是AB ，1CC 的中点，且11A M B C ⊥．（1）求1A A 的长度；（2）求平面1B AN 与平面1B MC 所成锐二面角的余弦值．【解答】解：（1）在ABC ∆中，4AC BC ==，AB =，则222AB AC BC =+，90ACB ∴∠=︒，以C 为原点，CA ，CB ，1CC 所在直线分别为x ，y ，z 轴，建立空间直角坐标系，设1AA a =，则(4A ，0，0)，(0B ，4，0)，(0C ，0，0)，1(4A ，0，)a ，1(0B ，4，)a ，(2M ，2，0)，∴1(2A M =-，2，)a -，1(0B C =，4-，)a -，11A M B C ⊥，∴21180A M B C a =-+=，解得a =，1AA ∴的长为（2）由（1）知1(0C ，0，，由N 中1CC 的中点，得(0N ，0， ∴1(4B A =-，4，，1(0B N =，4-，，设平面1B AN 的法向量(n x =，y ，)z ，则1144040n B A x y n B N y ⎧=-++=⎪⎨=-=⎪⎩，取1x =，得(1n =，1-，，1(0B C =，4-，-，(2CM =，2，0)，设平面1B MC 的法向量(m x =，y ，)z ，则140220m B C y m CM x y ⎧=-==⎪⎨=+=⎪⎩，取1x =，得(1m =，1-，设平面1B AN 与平面1B MC 所成锐二面角为θ，则||310cos ||||10m n m n θ==∴平面1B AN 与平面1B MC24．己知数列{}n a ．的通项公式为n nn a =-，*n N ∈记1212n n n n n n S C a C a C a =++⋯+（1）求12S S 的值；（2）求证：对任意的正整数n ，21n nn S S S +++为定值．【解答】解：（1）1111S C a ==-=，1222122272S C a C a =+=+-=，则1222427S S =；（2）证明：设α=，β=，则1222122122()()()()()n n n n n n n n n n n n n n n n n S C C C C C C C C C αβαβαβαααβββ=-+-+⋯+-=++⋯+-++⋯+(1)(1)n n n nαβ=+-+=-，由1=，22112]n n n n n nn S +++++=-=-+--183n n S S +=-，则2183n n n S S S +++=为定值．。

通州区2019—2020学年高三一模考试试卷

阅读下面的材料完成 !& 题材料一
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南宋为避开金人的侵吞#偏安建康#把北宋的风筝工艺带到江南$ 那里的气候湿润#少烈风多和风$因此#江南的风筝多为仿生型风筝$ 形神兼备#动态逼真#多以鹞子的轻巧灵活的动态作为模仿 (标的 +$ 南方至今仍把风筝叫 (纸鹞 +或 (鹞子 +#例如蜈蚣风筝叫 (蜈蚣鹞子+#双斗燕儿风筝叫(双燕鹞子+$ 南通地区#风力强大#那里的工艺高手以 (板子+扎法为主#能抗大风$他们把各种不同大小的哨子拴到 (板鹞+的迎风面料上#使它受风就发出音响 $ 多少组高低音不同的哨子 #使得放到天上的风筝发出不同的音响效果 $

2019-2020学年通州区潞河中学分校高三语文第一次联考试卷及答案

2019-2020学年通州区潞河中学分校高三语文第一次联考试卷及答案一、现代文阅读（36分）(一)现代文阅读I(9分)阅读下面的文字，完成下面小题。

材料一：2018年，海外受访者对中国的整体印象为6.2分(10分制)，延续了近年来小幅稳定上升的趋势。

在中国参与全球治理的领域中，科技、经济、文化是海外受访者最为认可的三个领域。

与2017年调查相比，海外受访者对中国未来参与全球治理各领域的期待均有所提升。

同时，海外受访者普遍看好中国经济未来发展，接近半数的受访民众认为中国将成为全球第一大经济体，65%的海外受访者认为中国的国际地位和全球影响力将会持续提升。

历史悠久、充满魅力的东方大国和全球发展的贡献者仍是中国最突出的国家形象，中餐、中医药、武术被认为是最能代表中国文化的元素。

此外，海外发展中国家受访者对中国形象的评价更为正面。

值得一提的是，“人类命运共同体”理念对个人、国家、全球治理的积极意义获关注，总体来看，六成左右的海外受访者认为“人类命运共同体”理念对个人、国家、全球治理具有积极意义；“一带一路”的海外认知度不断提升，排名前五的国家分别为印度、日本、意大利、俄罗斯和韩国，海外发展中国家受访者对于“一带一路”倡议对个人、国家、地区和全球经济的积极意义更认可。

（摘编自《“中国国家形象全球调查报告”出炉：中国整体形象保持稳定》）材料二：为进一步提高我国国际影响力、感召力、塑造力，为世界和平与发展做出新的重大贡献，我们要积极开展对外宣传工作，向世界多方面展现更加丰富多彩的中国形象。

目前世界经济复苏面临的挑战和压力并不少，发展不平衡不充分问题仍然普遍存在，南北发展差距依然巨大，世界上还有很多国家的民众生活在困境之中。

【甲】中国提出并实践了“创新、协调、绿色、开放、共享”新发展理念，对外积极推动经济全球化发展。

事实证明，中国同一大批国家的联动发展，使全球经济发展更加平衡。

中国改革开放持续推进，为开放型世界经济发展提供了重要动力，引领着全球发展。

通州区2020届高三一模数学试题及答案

通州区高三年级一模考试数学试卷2020年4月第一部分（选择题共40分）一、选择题：本大题共10小题，每小题4分，共40分.在每小题列出的四个选项中，只有一项是符合题目要求的.1. 已知集合{}02A x x =<≤，{}13B x x =<<，则AB =A. {}03x x << B . {}23x x << C . {}01x x <≤ D . {}12x x <≤2. 已知复数=i(2i)z + （i 是虚数单位），则z =A. 1 B . 2 C.D . 33. 函数()sin 2cos 2f x x x =+的最小正周期是（）Ａ．π2Ｂ．πＣ．2π Ｄ．4π4. 已知()f x 为定义在R 上的奇函数，且(1)2f =，下列一定在函数()f x 图象上的点是A. （1，-2） B . （-1，-2） C . （-1，2） D . （2，1） 5. 已知a ，3，b ，9，c 成等比数列，且a >0，则33log log b c -等于 A. 1- B . 12- C . 12D . 16. 已知抛物线22(0)y px p =>的焦点与双曲线2213x y -=的右焦点重合，则p =A.B . 2C .D . 47. 在6(2)1x x-的展开式中，常数项是A. -160 B . -20 C . 20 D . 1608．在平面直角坐标系中，O 为坐标原点，已知两点(cos ,sin )A αα，(cos(),sin())33B ππαα++.则OA OB +=A.1 B .C . 2D . 与α有关9. 若a >0，b >0，则“ab ≥1”是 “a+b ≥2”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10. 某同学在数学探究活动中确定研究主题是“(1,N )n a a n *>∈是几位数”，他以2(N )n n *∈为例做研究，得出相应的结论，其研究过程及部分研究数据如下表：试用该同学的研究结论判断504是几位数（参考数据lg20.3010≈） A. 101 B . 50 C . 31 D . 30第二部分（非选择题共110分）二、填空题：本大题共5小题，每小题5分，共25分．11. 已知向量(1,2)=-a ，(3,)m =-b ，其中m ∈R ．若,a b 共线，则m 等于 ___________.12. 圆()1122=+-y x的圆心到直线10x ++=的距离为 .13.某三棱锥的三视图如图所示，则该三棱锥的体积等于 .14．中国古代数学著作《孙子算经》中有这样一道算术题：“今有物不知其数，三三数之余二，五五数之余三，问物几何？” ，将上述问题的所有正整数答案从小到大组成一个数列 {}n a ，则1a = ； n a = . （注：三三数之余二是指此数被3除余2，例如“5”）15.给出下列四个函数，①21y x =+；②12y x x =+++；③21x y =+；④2cos y x x =+ 其中值域为[1)+∞，的函数的序号是 .三、解答题：本大题共6小题，共85分．解答应写出文字说明，演算步骤或证明过程．16.（本小题14分）已知△ABC，满足a =2b =，，判断△ABC 的面积2S >是否成立？说明理由.从①3A =π ，② cos B = 这两个条件中任选一个，补充到上面问题条件中的空格处并做答.注：如果选择多个条件分别解答，按第一个解答计分.17．（本小题14分）2019年1月1日，我国开始施行《个人所得税专项附加扣除操作办法》，附加扣除的专项包括子女教育、继续教育、大病医疗、住房贷款利息、住房租金、赡养老人．某单位有老年员工140人，中年员工180人，青年员工80人，现采用分层抽样的方法，从该单位员工中抽取20人，调查享受个人所得税专项附加扣除的情况，并按照员工类别进行各专项人数汇总，数据统计如下：（Ⅰ）在抽取的20人中，老年员工、中年员工、青年员工各有多少人；（Ⅱ）从上表享受住房贷款利息专项扣除的员工中随机选取2人，记X 为选出的中年员工的人数，求X 的分布列和数学期望.18. （本小题15分）俯视图如图，已知四边形ABCD 为菱形，且060=∠A ，取AD 中点为E .现将四边形EBCD 沿BE 折起至EBHG ，使得90AEG ∠=. (Ⅰ)求证：⊥AE 平面EBHG ； (Ⅱ)求二面角A -GH -B 的余弦值；(Ⅲ)若点F 满足AB λAF =，当//EF 平面AGH 时，求λ的值.19．（本小题14分）已知椭圆C ：)0(12222>>=+b a by a x 的离心率为22，点A (0，1)在椭圆C 上．（Ⅰ）求椭圆 C 的方程；（Ⅱ）设O 为原点，过原点的直线（不与x 轴垂直）与椭圆C 交于M 、N 两点，直线AM 、AN 与x 轴分别交于点E 、F ．问： y 轴上是否存在定点G ，使得∠OGE =∠OFG ？若存在，求点G 的坐标；若不存在，说明理由．20．（本小题14分）已知函数()()e x f x x a x a =-++，设()()g x f x '=. （Ⅰ）求()g x 的极小值；（Ⅱ）若()0f x >在(0,)+∞上恒成立，求a 的取值范围. 21．（本小题14分）用[x ]表示一个小于或等于x 的最大整数.如：[2]=2，[4.1]=4，[-3.1]=-4.已知实数列 ,,10a a 对于所有非负整数i 满足])[(][1i i i i a a a a -⋅=+，其中0a 是任意一个非零实数.(Ⅰ) 若6.20-=a ，写出a 1,a 2,a 3； (Ⅱ)若00>a ，求数列]}{[i a 的最小值；(Ⅲ)证明：存在非负整数k ，使得当k i ≥时，2+=i i a a .ECDBAEGHBA通州区高三年级一模考试数学试卷参考答案及评分标准 2020年4月一、选择题：（每小题4分，共40分.）二、填空题（每道小题5分，共25分）11．6 ； 12. 1；13．3； 14．8；15n -7；（第一空2分，第二空3分） 15．①②④ （答对一个给1分，答对两个给3分，全对给5分，出现一个错误不得分.）三、解答题：本大题共6小题，共85分．解答应写出文字说明，演算步骤或证明过程．16．（本小题14分）解：选○1，△ABC 的面积2S >成立，理由如下:当3A =π时，2147cos 222c A c +-==⋅， …………… 4分所以2230c c --=，所以3c =， …………… 6分则△ABC 的面积11sin 23sin 223S bc A π==⨯⨯⨯=分2=>=， …………… 12分所以2S >成立. ……………14分选○2，△ABC 的面积2S >不成立，理由如下：当cos 7B =时，222cos 27a c b B ac +-==，…………… 4分27=整理得，230c -+=，所以c = …………… 6分因2227,437a b c =+=+=， …………… 8分所以△ABC 是A 为直角的三角形， …………… 10分所以△ABC 的面积112222S bc ==⨯=<，…………… 12分所以不成立. …………… 14分17. （本小题14分）解：（Ⅰ）该单位员工共140+180+80=400人，抽取的老年员工201407400⨯=人，中年员工201809400⨯=人，青年员工20804400⨯=人 ……………… 4分（Ⅱ）X 的可取值为0,1,2 ……………… 5分23283(X=0)28C P C ==，11352815(X=1)28C C P C ==，252810(X=0)28C P C == ……………… 11分5(X)4E =. ……………… 14分18. （本小题15分）(Ⅰ)证明：在左图中，△ABD 为等边三角形，E 为AD 中点所以BE ⊥AD ， ……………… 2分所以BE ⊥AE 因为90AEG ∠=，所以GE ⊥AE . ……………… 3分因为GE ⊥AE ，BE ⊥AE ，GE ∩BE =E所以⊥AE 平面EBHG . ……………… 4分 (Ⅱ) 设菱形ABCD 的边长为2，由(Ⅰ)可知GE ⊥AE ，BE ⊥AE ，GE ⊥BE.所以以E 为原点，EA ,EB ,EG 所在直线分别为x ,y ,z 轴，建立如图空间坐标系可得(1,0,0)A ，B ，(0,0,1)G ，H .……………… 6分=(1,0,1)AG -，=(1,AH -设平面AGH 的法向量为),,(z y x n =所以 00n AG n AH ⎧⋅=⎪⎨⋅=⎪⎩，即020x z x z -+=⎧⎪⎨-+=⎪⎩. 令x =1，则)1,33,1(-=n ………………8分平面EBHG 的法向量为(1,0,0)EA = ……………… 9分设二面角A -GH -B 的大小为)90(0<θθ721,cos |cos >=<=EA n θ ……………… 11分 (Ⅲ) 由AF AB =λ，则(1,0)F -λ所以)0,3,1(λλ-= ……………… 12分因为//EF 平面AGH ，则 0=⋅ ……………… 13分即120-λ= ……………… 14分所以21=λ ……………… 15分19. （本小题14分）解：（Ⅰ）由题意得c e a ==………………1分 b =1,又222a b c =+解得1a c == ……………… 4分所以椭圆方程为2212x y += ……………… 5分（Ⅱ）设00(,)M x y ，由题意及椭圆的对称性可知000(,)(1)N x y y --≠±……………… 6分则直线AM 的方程为0011y y x x -=+ ……………… 7分直线AN 的方程为0011y y x x +=+ ……………… 8分则E 点坐标为00(,0)1x y -，F 点坐标为00(,0)1x y -+ ……………… 10分假设存在定点G （0，n ）使得∠OGE =∠OFG ，即tan ∠OGE =tan ∠OFG （也可以转化为斜率来求）……………… 11分即OE OG OGOF=即2OG OE OF = ……………… 12分即220221x n y ==-所以n = ……………… 13分所以存在点G 坐标为(0,满足条件. ……………… 14分20. （本小题14分）解：（Ⅰ）()(1)1x f x x a e '=-++ ……………… 1分由题意可知()(1)1x g x x a e =-++，所以()(2)x g x x a e '=-+ ……………… 2分当2x a >-时()0g x '>，()g x 在(2,)a -+∞上单调递增；……………… 3分当2x a <-时()0g x '<，()g x 在(,2)a -∞-上单调递减……………… 4分所以()g x 在2x a =-处取得极小值，为2(2)1a g a e --=-+……………… 5分（Ⅱ）由（Ⅰ）得2()()1a f x g x e -'=≥-+当2a ≤时2()10a f x e -'≥-+>， ……………… 6分所以()f x 在单调递增，所以()(0)0f x f >= ……………… 7分即2a ≤时()0f x >在(0,)+∞恒成立. ……………… 8分当2a >时(0)(0)20f g a '==-<， ………………9分又()()10a f a g a e '==+>， ……………… 10分又由于()f x '在(2,)a -+∞上单调递增；在(0,2)a -上单调递减；所以在(0,)a 上一定存在0x 使得0()0f x '=， ……………… 11分所以()f x 在0(0,)x 递减，在0(,)x +∞递增，所以0()(0)0f x f <= ……………… 12分所以在(0,)+∞存在0x ，使得0()0f x <， ……………… 13分所以当2a >时，()0f x >在(0,)+∞上不恒成立所以a 的取值范围为(],2-∞. ………………14分21. （本小题14分）解：(Ⅰ) 2.11-=a 、6.12-=a 、8.03-=a . ……………… 3分分分分 4,3, ……………… 13令k =m ，满足当k i ≥时，2+=i i a a .综上，存在非负整数k ，使得当k i ≥时， 2+=i i a a .………………14分。

2019-2020学年通州区潞河中学分校高三语文一模试卷及答案

2019-2020学年通州区潞河中学分校高三语文一模试卷及答案一、现代文阅读（36分）(一)现代文阅读I(9分)阅读下面的文字，完成各题。

材料一：《流浪地球》的票房奇迹，加上此前《三体》的热销，刘慈欣的作品影响巨大，但社会各界的评价却颇有两极分化之势。

刘慈欣的大多数作品都没有精巧的剧情或百转千回的人物感情，更多是直接甩出一个个宏大震撼的设定，靠设定本身为读者带来审美快感。

在他笔下，主人公与他人的情感联结不过是宇宙规律中很小的部分，和人类命运、宇宙洪荒相比，根本不值一提。

刘慈欣自称是“一个疯狂的技术主义者”，他坦承自己“喜欢文学因素较少、科幻因素较多的科幻作品，一直认为，透视现实和剖析人性不是科幻小说的任务，更不是它的优势”，甚至有过“把科幻从文学剥离出来”的激进想法。

在写作的过程中，刘慈欣却逐渐意识到需要保持“科学性与文学性的平衡、思想性与可读性的平衡、作为文学的科幻与作为商品的科幻的平衡”，他后来的作品“正是这些平衡的结果”，这“或多或少地背叛了自己的科幻理念”。

刘慈欣对文笔也并不是没有自觉。

他评价阿西莫夫的文笔，“平直、单色调、刚硬、呆板……几乎所有这类文学上的负面词都可以用来形容他的文笔”，却又话锋一转，表示“这种笔调无论如何是不适合文学的，但却很适合科幻，也使他的小说风靡世界”。

刘慈欣对于他敬仰的阿西莫夫的描述，显然也适用于他自己的文风。

(摘编自冰村《刘慈欣：黄金年代的守望者》）材料二：为什么有人认为科幻小说欠缺文学性？科幻小说描绘幻想世界，我们当然能够发现幻想世界与现实世界的某些相似性，但是在细节设置和整体结构方面，幻想世界是超出我们现在的社会结构和人的行为心理的。

一般的小说在进行情节描绘的时候，存在一种天然的便利性，作者不用浪费笔墨在整个世界的构想上，细节的描绘和推陈出新就成了这些小说的长处。

作家也不必为新的人际关系、社会行为、世界结构负责，只需直接去描绘既有世界下细微的情感波澜和社会反应即可。

北京市通州区2019-2020学年高考数学一模考试卷含解析

北京市通州区2019-2020学年高考数学一模考试卷一、选择题：本题共12小题，每小题5分，共60分。

在每小题给出的四个选项中，只有一项是符合题目要求的。

1．若复数z 满足1zi i =-（i 为虚数单位），则其共轭复数z 的虚部为（） A ．i - B ．iC ．1-D ．1【答案】D 【解析】【分析】由已知等式求出z ，再由共轭复数的概念求得z ，即可得z 的虚部. 【详解】由zi ＝1﹣i ，∴z ＝()()111·i i i i i i i ---==--- ，所以共轭复数z =-1+i ，虚部为1 故选D ．【点睛】本题考查复数代数形式的乘除运算和共轭复数的基本概念，属于基础题． 2．设x ∈R ，则“327x <”是“||3x <”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】B 【解析】【分析】先解不等式化简两个条件，利用集合法判断充分必要条件即可【详解】解不等式327x <可得3x <，解绝对值不等式||3x <可得33x -<<，由于{|33}-<<x x 为{|3}x x <的子集，据此可知“327x <”是“||3x <”的必要不充分条件．故选：B 【点睛】本题考查了必要不充分条件的判定，考查了学生数学运算，逻辑推理能力，属于基础题. 3．设i 是虚数单位，若复数103m i++（m R ∈）是纯虚数，则m 的值为（） A ．3-B ．1-C ．1D ．3【答案】A 【解析】【分析】根据复数除法运算化简，结合纯虚数定义即可求得m 的值. 【详解】由复数的除法运算化简可得1033m m i i+=+-+，因为是纯虚数，所以30m +=， ∴3m =-，故选：A. 【点睛】本题考查了复数的概念和除法运算，属于基础题.4．若函数2()x f x x e a =-恰有3个零点，则实数a 的取值范围是（） A ．24(,)e+∞ B ．24(0,)eC ．2(0,4)eD ．(0,)+∞【答案】B 【解析】【分析】求导函数，求出函数的极值，利用函数2()xf x x e a =-恰有三个零点，即可求实数a 的取值范围.【详解】函数2xy x e =的导数为2'2(2)x x xy xe x e xe x =+=+，令'0y =，则0x =或2-，20x -<<上单调递减，(,2),(0,)-∞-+∞上单调递增，所以0或2-是函数y 的极值点，函数的极值为：224(0)0,(2)4f f ee -=-==，函数2()xf x x e a =-恰有三个零点，则实数的取值范围是：24(0,)e. 故选B. 【点睛】该题考查的是有关结合函数零点个数，来确定参数的取值范围的问题，在解题的过程中，注意应用导数研究函数图象的走向，利用数形结合思想，转化为函数图象间交点个数的问题，难度不大.5．已知函数()f x 的定义域为[]0,2，则函数()()2g x f x =+ ）A ．[]0,1 B ．[]0,2 C ．[]1,2 D ．[]1,3【答案】A 【解析】试题分析：由题意，得022{820x x ≤≤-≥，解得01x ≤≤，故选A ．考点：函数的定义域．6．设函数()()ln 1f x x =-的定义域为D ，命题p ：x D ∀∈，()f x x ≤的否定是（） A ．x D ∀∈，()f x x > B ．0x D ∃∈，()00f x x ≤ C ．x D ∀∉，()f x x > D ．0x D ∃∈，()00f x x >【答案】D 【解析】【分析】根据命题的否定的定义，全称命题的否定是特称命题求解. 【详解】因为p ：x D ∀∈，()f x x ≤是全称命题，所以其否定是特称命题，即0x D ∃∈，()00f x x >. 故选：D 【点睛】本题主要考查命题的否定，还考查了理解辨析的能力，属于基础题.7．已知11()x x f x e e x --=-+，则不等式()(32)2f x f x +-≤的解集是（） A ．[)1,+∞ B ．[)0,+∞ C ．(],0-∞ D ．(],1-∞【答案】A 【解析】【分析】构造函数()()1g x f x =-，通过分析()g x 的单调性和对称性，求得不等式()(32)2f x f x +-≤的解集. 【详解】构造函数()()()11111x x g x f x ex e--=-=-+-，()g x 是单调递增函数，且向左移动一个单位得到()()11x x h x g x e x e=+=-+，()h x 的定义域为R ，且()()1xx h x e x h x e-=--=-，所以()h x 为奇函数，图像关于原点对称，所以()g x 图像关于()1,0对称. 不等式()(32)2f x f x +-≤等价于()()13210f x f x -+--≤，等价于()()320g x g x +-≤，注意到()10g =，结合()g x 图像关于()1,0对称和()g x 单调递增可知3221x x x +-≤⇒≥. 所以不等式()(32)2f x f x +-≤的解集是[)1,+∞. 故选：A 【点睛】本小题主要考查根据函数的单调性和对称性解不等式，属于中档题.8．很多关于整数规律的猜想都通俗易懂，吸引了大量的数学家和数学爱好者，有些猜想已经被数学家证明，如“费马大定理”，但大多猜想还未被证明，如“哥德巴赫猜想”、“角谷猜想”.“角谷猜想”的内容是：对于每一个正整数，如果它是奇数，则将它乘以3再加1；如果它是偶数，则将它除以2；如此循环，最终都能够得到1.下图为研究“角谷猜想”的一个程序框图.若输入n 的值为10，则输出i 的值为（）A ．5B ．6C ．7D ．8【答案】B 【解析】【分析】根据程序框图列举出程序的每一步，即可得出输出结果. 【详解】输入10n =，1n =不成立，n 是偶数成立，则1052n ==，011i =+=； 1n =不成立，n 是偶数不成立，则35116n =⨯+=，112i =+=； 1n =不成立，n 是偶数成立，则1682n ==，213i =+=； 1n =不成立，n 是偶数成立，则842n ==，314i =+=；1n =不成立，n 是偶数成立，则422n ==，415i =+=；1n =不成立，n 是偶数成立，则212n ==，516i =+=；1n =成立，跳出循环，输出i 的值为6.故选：B. 【点睛】本题考查利用程序框图计算输出结果，考查计算能力，属于基础题.9．如图，在平面四边形ABCD 中，,,120,1,AB BC AD CD BAD AB AD ⊥⊥∠===o 若点E 为边CD 上的动点，则AE BE ⋅u u u v u u u v的最小值为（）A ．2116B ．32C ．2516D ．3【答案】A 【解析】【分析】【详解】分析：由题意可得ABD △为等腰三角形，BCD V 为等边三角形，把数量积AE BE ⋅u u u v u u u v分拆，设(01)DE tDC t =≤≤u u u v u u u v，数量积转化为关于t 的函数，用函数可求得最小值。

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