北京市通州区2019—2020学年高三一模考试试卷答案(三稿)
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。
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。
北京市通州区2019届高三一模考试英语试卷Word版含解析
通州区2019年高三年级模拟考试英语第一节语法填空（共10小题；每小题1.5分，共15分）阅读下列短文，根据短文内容填空。
在未给提示词的空白处仅填写1个适当的单词，在给出提示词的空白处用括号内所给词的正确形式填空。
AI have been to many places as a news reporter. In India, I visited a city where there were many ___1___ (home) children. Some were as young as four years old. They lived in the streets ___2___ survived by begging or stealing. But then a wonderful lady ___3___ (call) Rosa opened a home for them. Within one year, she was looking after two hundred children. She clothed them, fed them and taught them. She gave them hope.【答案】1. homeless2. and3. calledBOnline shopping ___4___ (welcome) by most people due to various reasons. For the consumers, it can save some time for the people ___5___don’t have muc h spare time. Just clicking the mouse, they can get what they want ___6___ staying at home. For the sellers, it can cut some costs for those without enough circulating funds. Compared with the traditional trade mode, they don’t have to spend money in ___7___ (rent) a house.【答案】4. is welcomed5. who/that6. while/ when7. rentingCPeter worked ___8___ a night watchman in a small factory. One morning his boss came in with a suitcase. He said to Peter, I’m going to New York tomorrow. See you. Peter said, “Oh, you mustn’t go. The factory owner asked him why. Peter answered that he ___9___ (have) a nightmare the night before. In the dream, he had seen the next day’s plane to New York crash over the Atlantic Ocean. Peter’s boss ___10___ (immediate) cancelled his ticket and stayed in the office. The plane crashed; the boss thanked Peter and gave him a big present. Then he fired him.【答案】8. as 9. had had10. immediately第二节完形填空（共20小题；每小题1.5分，共30分）阅读下面短文，掌握其大意，从每题所给的A、B、C、D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。
2019年北京通州高三一模数学理科答案.doc
通州区高三年级第一次模拟考试 数学（理科）试卷参考答案及评分标准第一部分（选择题 共40分）第二部分（非选择题 共110分）二、填空题：本大题共6小题，每小题5分，共30分． 9．三 10．7 11．112．()()21f x x =-(答案不唯一) 13．48 14． ① ③ , (]0-∞，三、解答题：本大题共6小题，共80分．15．解：（Ⅰ）()()22sin cos 2cos 1f x x xx =π-+-2s i n c o s c o s x x x =+sin 2cos 2x x =+………………3分2222x x ⎫=+⎪⎪⎭………………4分 s i n 24x π⎛⎫=+ ⎪⎝⎭， ………………5分 所以最小正周期22T π==π； ………………6分 （Ⅱ）因为,44x ππ⎡⎤∈-⎢⎥⎣⎦， 2019.4所以2,22x ππ⎡⎤∈-⎢⎥⎣⎦，32,444x πππ⎡⎤+∈-⎢⎥⎣⎦． ………………7分所以当244x ππ+=-，即4x π=-时，sin 24x π⎛⎫+ ⎪⎝⎭有最小值2-10分 所以()f x 有最小值1-． ………………11分 因为当,44x ππ⎡⎤∈-⎢⎥⎣⎦时()f x m ≥恒成立， 所以1m ≤-，即m 的取值范围是(]1-∞-，． …………13分16．解：（Ⅰ）设“职工甲和职工乙微信记步数都不低于10000”为事件A ． ..........1分从3月1日至3月7日这七天中，3月2日，3月5日，3月7日这三天职工甲和职工乙微信记步数都不低于10000，所以()37P A =； ..........3分 （Ⅱ）X 的所有可能取值为0，1，2， ..........4分()0P X ==712723=C C ，()1P X ==74C 271314=⋅C C ，()2P X ==722724=C C ．..........7分 X 的分布列为..........8分()14280127777E X =⨯+⨯+⨯=；..........10分（Ⅲ）3月3日． ..........13分由直方图知，微信记步数落在[20,25]，[15,20)，[10,15)，[5,10)，[0,5)（单位：千步）区间内的人数依次为300.15200=⨯人，500.25200=⨯人，600.3200=⨯人，400.2200=⨯人，人．由甲微信记步数排名第68，可知当天甲微信记步数在15000---20000之间，根据折线图知，这只有3月2日、3月3日和3月7日；而由乙微信记步数排名第142，可知当天乙微信记步数在5000---10000之间，根据折200.1200=⨯线图知，这只有3月3日和3月6日. 所以只有3月3日符合要求．17．（Ⅰ）证明：在菱形ABCD 中，因为DE ⊥AB ，所以DE ⊥AE ，DE ⊥EB ．所以 ． ………………1分 因为 , ， 平面 ， 平面 ，所以 平面 ． ………………3分 因为 平面 ，所以平面 平面 ． ………………4分 （Ⅱ）解：由（Ⅰ）知 ， ， ，如图建立空间直角坐标系E-xyz ，则 ………………5分 E (0,0,0)，B (2,0,0)， ， ，所以，， . ………………6分 设平面 的法向量 ，由 ， ，………………7分 得， ，所以， ．令 ，则 ， ．所以 ． ………………8分 所以， 又 ， ，所以cos ,A E A E A E '⋅'<>==='⋅n n n………………9分所以直线 与平面 . ………………10分 （Ⅲ）由（Ⅱ）可知， ， ，设 ，则 ………………11分． ………………12分 因为EF //平面 ，所以， 即 ． ………………13分所以，即．所以1DFFA='. ………………14分 18．解：（Ⅰ）由已知，得，所以3c e a ===． ..........3分 又，所以 ..........4分所以椭圆C 的标准方程为，离心率e = ..........5分 （Ⅱ）设．①当直线l 与x 轴垂直时，点A ,B 的坐标分别为(0，(0． 因为()0,m m MA x y =- ，()0m m MB x y =-，()0,0mmMO x y=--，所以(3,3)m m MA MB MO x y ++=--=0．所以0m x =，0m y =，即点M 与原点重合． ..........6分 ②当直线l 与x 轴不垂直时，设直线l 的方程为1y kx =+． .......... ..........7分由221321x y y kx ⎧+=⎪⎨⎪=+⎩，， 得()2232630k x kx ++-=， .......... ..........8分()22236123272240k k k ∆=++=+>．所以，1224032y y k +=>+． .......... ..........9分因为，，， 所以1212(03,03)0m m MA MB MO x x x y y y ++=++-++-=．a =1c =222a b c =+b =22132x y +=11(,)m m MA x x y y =--22(,)m m MB x x y y =--(0,0)m m MO x y =--所以12123,3m m x x x y y y +=+=．2232m k x k -=+，243032m y k =>+． .......... ..........11分消去k 得()2223200m m m m x y y y +-=>．综上，点M 构成的曲线L 的方程为222320x y y +-=． .......... ..........12分 对于曲线L 的任意一点(),M x y ，它关于直线13y =的对称点为2,3M x y ⎛⎫'- ⎪⎝⎭．把2,3M x y ⎛⎫'- ⎪⎝⎭的坐标代入曲线L 的方程的左端： 2222222244232243223203333x y y x y y y x y y ⎛⎫⎛⎫+---=+-+-+=+-= ⎪ ⎪⎝⎭⎝⎭．所以点M '也在曲线L 上．所以由点M 构成的曲线L 关于直线13y =对称． ......... ......... ......14分19．解: （Ⅰ）当0k =时，()221f x x x -==，()3322f x x x -'=-=-. ..........1分 所以()12f '-=， ()11f -=. .........2分所以曲线()y f x =在点()()11f --，处的切线方程为 ()()()()111y f f x ⎡⎤'--=---⎣⎦， .....................................3分即230x y -+=； .....................................4分 （Ⅱ）0k ≠时，（ⅰ）()f x =，定义域为， ..........................5分所以()f x '==． .......... ........ ..............7分 2xe kx{}0|≠x x 422x x e x ke kx kx ⋅-⋅42)2xx kx e kx -⋅（令()0f x '=，得2x k=． .......... ........ ..........8分 ①当0k >时，在()0-∞，和，()0f x '>；在，()0f x '<． 所以()f x 的单调递增区间为()0-∞，和，单调递减区间为；.........9分 ②当0k <时，在，()0f x '>；在和，()0f x '<． 所以()f x 的单调递增区间为，单调递减区间为2k ⎛⎫-∞ ⎪⎝⎭，和()0+∞，；....10分 （ⅱ）由()f x 在区间()01，内单调递减， ①当0k >时，()01，，有，所以； ..........11分 ②当0k <时, ()f x 在递减，符合题意． ..........12分 综上k 的取值范围是()(]002,,-∞． ..........13分20. 解：（Ⅰ）集合()S S T --的所有元素是:248163264，，，，，； ............................2分 （Ⅱ）当首项是1，末项是100时，公差最大为11，即11D =．这样的数列只有1个：1，12，23，34，45，56，67，78，89，100； ............................4分 当选取的10个数是连续自然数时，公差最小为1，即1d =．这样的数列首项可以是12391，，，，中的任何一个，因此共有91个公差为1的等差数列．......... ......... .......6分S假设存在含有10个元素的集合A ，使得S -A 中不含10个元素组成的等差数列．显然每连续10个元素中必有集合A 中的唯一一个元素，即表的每行、每列中必有集合A 中的唯一一个元素．),2(+∞k)2,0(k),2(+∞k)2,0(k）（0,2k），（k 2-∞），（∞+0）（0,2k⊆)2,0(k12≥k20≤<k ），（∞+0记表中第i行第j列的数为(),i j．若第i(1≤i≤9)行中集合A的唯一元素为(i,j)，则第i+1行中(i+1,1),(i+1,2),┈(i+1,j)中必有集合A中元素．若第i(1≤i≤9)行的第一个数在集合A中，则此行余下九个数和下一行第一个数可以组成等差数列，与假设矛盾．因此，第一列中集合A的唯一元素只可能在第十行．同理，若第i(1≤i≤8)行的第二个数在集合A中，则此行余下八个数和下一行前两个数可以组成等差数列，与假设矛盾．因此，第二列中集合A的唯一元素只可能在第九行．依此类推，得A={10，19，28，37，46，55，64，73，82，91}．此时，另一条对角线上的十个元素{1，12，23，34，45，56，67，78，89，100}构成等差数列，与假设矛盾．综上，原命题成立．...........................13分注：解答题学生若有其它解法，请酌情给分．。
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”。
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。
北京市通州区2019届高三一模考试英语试卷含解析
通州区2019年高三年级模拟考试英语第一节语法填空（共10小题；每小题 1.5分，共15分）阅读下列短文，根据短文内容填空。
在未给提示词的空白处仅填写1个适当的单词，在给出提示词的空白处用括号内所给词的正确形式填空。
AI have been to many places as a news reporter. In India, I visited a city where there were many___1___ (home) children. Some were as young as four years old. They lived in the streets ___2___survived by begging or stealing. But then a wonderful lady ___3___ (call) Rosa opened a home forthem. Within one year, she was looking after two hundred children. She clothed them, fed them andtaught them. She gave them hope.【答案】1. homeless2. and3. calledBOnline shopping ___4___ (welcome) by most people due to various reasons. For theconsumers, it can save some time for the people ___5___don’t have muc h spare time. Just clickingthe mouse, they can get what they want ___6___ staying at home. For the sellers, it can cut somecosts for those without enough circulating funds. Compared with the traditional trade mode, theydon’t have to spend money in ___7___ (rent) a house.【答案】4. is welcomed5. who/that6. while/ when7. rentingCPeter worked ___8___ a night watchman in a small factory. One morning his boss came inwith a suitcase. He said to Peter, I’m going to New York tomorrow. See you. Peter said, “mustn’t go. The factory owner asked him why. Peter answered that he ___9___ (have) a nightmarethe night before. In the dream, he had seen the next day’s plane to New York crash over the Atlantic ___10___ (immediate) cancelled his ticket and stayed in the office. The planeOcean. Peter’s bosscrashed; the boss thanked Peter and gave him a big present. Then he fired him.【答案】8. as 9. had had10. immediately第二节完形填空（共20小题；每小题 1.5分，共30分）阅读下面短文，掌握其大意，从每题所给的A、B、C、D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。
2020年通州高三一模英语试题及答案
通州区2019—2020学年第二学期高三一模考试英语试卷2020年4月一、阅读理解（本大题共15小题，共30.0分）AI was in the seventh grade，and we had moved to New Jersey in November．By then，everyone already had their own friends，and no one wanted to talk to a new girl．To make things worse，they put me in"Section L"．I found out later that everyone called Section L"Loserville"．It was sort of an open secret that it was the section for troublemakers and not-so-smart kids．When I found out，I wanted to scream．I had always been a good student and had amazing friends，andnow everyone thought I was a loser!I did text my friends in Illinois almost every night，especially my best friend，Ana．At firstmy friends wanted to hear all about it．But then some stopped texting back once I said something about how miserable I was．One night when I was texting with Ana，I complained about another friend who had just done that．Ana's texts came really fast for the next few minutes and they surprised me．She said that shewas tired of hearing about how bad everything was in New Jersey，too．She said she did not want to hurt my feelings but that I needed to stop feeling so sorry for myself all the time，I had to try to make things better．The next day，I thought a lot about what Ana had said．She was right!I wish I could say that everything changed overnight after that，but it didn't．I was still stuck in "Loserville"，and some people were still mean to me，even though I tried to just stay out of their way．But what did change was me-I stopped feeling so sorry for myself and did something about making friends．I signed up to make sets for the school play．I met a lot of new people there，and suddenly I had friends to say hi to in the halls!I still miss Illinois sometimes，but life in New Jersey isn't so hard anymore．Even though I couldn't change my situation，I could change my attitude-and that made all the difference．1."Loserville"is a section for______．A.failuresB.good studentsC.class secretsD.newcomers2.The writer complained all the time in the new environment because______．A.Ana didn't text back to herB.her friends hurt her feelingsC.she was unfairly treatedD.she was a good student3.What made a difference in changing the situation？______A.She went back to Illinois．B.She ended friendship with Ana．C.She fought back with her classmates．D.She began to make friends with others．4.The best title for the passage can be______．sting FriendshipB.An Incidence at SchoolC.Say Goodbye to"Loserville"D.Unhappiness in"Loserville"BThese days everyone is worried about the size of their carbon footprint．In order to reduce global warming，we need to make our carbon footprints smaller．But how much CO are we responsible for？A new book by Mike Berners-Lee（a leading expert in carbon foot-printing）might be able to help．The Carbon Foot print of Everything looks at the different things we do and buy，and calculates the amount of CO2they produce，including the ingredients，the electricity，the equipment，the transport and the packaging．And it's frightening how much carbon dioxide everything produces．But all of this can help us decide which beer to drink．From Berners-Lee's calculations，it's clear that a pint（568ml）of locally-brewed（酿制的）beer has a smaller carbon footprint than a bottle of imported beer．This is because the imported beer has been transported from far away，and it uses more packaging．The local beer only produces300g of CO2-but the imported beer produces900 g!So，one pint of local beer is better for the environment than three cans of cheap foreign beer from the supermarket．Berners-Lee has even calculated the carbon footprint of cycling to work．Nothing is more environmentally-friendly than riding a bike，surely？Well，it depends on what you've had to eat before．To ride a bike we need energy and for energy we need food．So，if we eat a banana and then ride a kilometer and a half，our footprint is65g of CO2．However，if we eat bacon before the bike ride，it's200g．In fact，bananas are good in general because they don't need packaging．They can be transported by boat and they grow in natural sunlight．So，does this mean that cycling is bad for the environment？Absolutely not．If you cycle，you don t use your car；and the fewer cars on the road，the fewer traffic jams．And cars in trafficjams produce three times more CO2than cars travelling at speed．Cycling also makes you healthy and less likely to go to a hospital．And hospitals have very big carbon footprints!So，maybe it's time for us all to start making some changes．Pass me a banana and a pint of local beer，please．5.Which of the followings produces the smallest carbon footprints？______A.A pint of local beer．B.A bottle of imported beer．C.A banana before a1.5km bike ride．D.Bacon before a1.5km bike ride．6.According to the article，the author suggests choosing the local food because it is______．A.more tastyB.easier to buyC.better packagedD.more energy-saving7.The purpose of writing this article is to______．A.promote a new bookB.advertise the imported beerC.instruct how to measure the carbon footprintD.encourage people to reduce the production of CO2CMost adults firmly believe that as kids reach their teens，they start to take crazy risks that get them in trouble．Do teenagers simply love taking all risks much more than adults？A recent study suggests otherwise．Scientists designed a simple experiment involving33teenagers and three other age groups．In the experiment，the researchers tried to distinguish between two very different kinds of risk-taking．The first they called a willingness to take known risks（when the probability of winning is clear）and the second they called a willingness to take unknown risks（when the possibility of success is uncertain）．The study offered participants the opportunity to play two kinds of games．They had the chance to win money，with one game offering a known risk and the other offering an unknown risk．On each round of the game，each participant had to choose between taking a sure﹩5and known or unknown risks of winning a lot more．If on one particular round they had picked the﹩5for sure choice，then they got﹩5．But if on that round they had chosen to take a risk，the rules of the gamewill determine whether or not they had won．If they did win，they went home with between﹩8and ﹩125．And，of course，if they lost，they went home with nothing．What the scientists found was really quite surprising．It turned out that the average teenager was very hesitant when risks were known-more careful than college students or parents-aged adults，and about as careful as grandparent-aged adults．This means that when the risks were known，teenagers were not risky in their behavior at all．Only when the risks were unclear did teenagers choose them more often than other groups．Under those kinds of conditions，they were much more willing to take a risk than any other group．So，what does all of this mean？The research suggests that adults should probably focus more energy on trying to educate teenagers about risks than limiting them．Teenagers who understand the risks associated with a decision are more likely to be careful in their behavior．8.This experiment was carried out by______A.dividing the teens into three groupsparing the reactions to different risksC.giving equal amount of awards to the participantsD.observing the emotional changes of the teenager9.When facing known risks，teenagers tended to be______．A.ambitsB.cautiousC.anxiousD.curious10.Which group in the study were more likely to take unknown risks？______A.Teenagers．B.College students．C.Parent-aged adults．D.Grandparent-aged adults．11.According to the study，parents should focus on______．A.guaranteeing children to be carefulB.setting age limits on dangerous activitiesC.respecting teens to make their own choicesD.guiding teens to learn more about the effect of risksDShark attacks not only disturb beach activities，but can affect associated tourist industries．Shark nets are a common solution to preventing shark attacks on beaches，but they cause dangers to sea ecosystems．Seeking a cost-effective way to monitor beach safety over large areas，we have developed a system called Shark Spotter．It combines artificial intelligence（AI），computing power，anddrone（无人机）technology to identify and warn lifesavers to sharks near swimmers．The project is a cooperation between the University of Technology Sydney and The Ripper Group，which is pioneering the use of drones-called"Westpac Little Ripper Lifesavers"-in the search and rescue movement in Australia．SharkSpotter can detect sharks and other potential threats using real-time aerial imagery．The system analyses video from a camera attached to a drone to monitor beaches for sharks，send warnings，and conduct rescues．Developed with techniques known as"deep learning"，the Shark Spotter system receives imagery from the drone camera and attempts to identify all objects in the scene．Once certain objects are detected，they are put into one of16categories：shark，whale，dolphin，rays，different types of boats，surfers，and swimmers．If a shark is detected，Shark Spotter provides both a visual sign on the computer screen and an audible warning to the operator．The operator confirms the warning and sends text messages from the Shark Spotter system to the Surf Life Savers for further action．In an emergency，the drone is equipped with a lifesaving flotation pod（漂浮仓）together with an electronic shark repellent（驱逐装置）that can be dropped into the water in cases where swimmers are in severe trouble，trapped in a rip，or if there are sharks close by．In January2018，the Westpac Little Ripper Lifesavers was used to rescue two young swimmers caught in a rip at Lennox Head，NSW．The drone flew down the beach some800meters from the lifeguard station，and a lifesaving flotation pod was dropped from the drone．The complete rescue operation took70seconds．We believe Shark Spotter is a win-win for both marine life and beachgoers．This unique technology combines dynamic video image processing AI and advanced drone technology to creatively deal with the global challenge of ensuring safe beaches，protecting environments，and promoting tourism．12.A Shark Spotter is______．A.a solution to monitor sharksB.an equipment to identify lifesaversC.a technology to prevent shark attacksD.a project to pioneer the use of drones13.When a shark is spotted near a swimmer，the system will______．A.take timely actionB.analyze the visual dataC.classify the identified objectsD.turn on"deep learning"mode14.The example in the5th paragraph shows us that the system is______．A.efficient in saving livesB.effective in detecting sharksC.smart in driving sharks awayD.practical over the whole sea area15.What is the author's attitude towards the future of SharkSpotter？______A.Doubtful．B.Optimistic．C.Negative．D.Objective．二、阅读七选五（本大题共5小题，共10.0分）Nowadays，WeChat is about expressing our opinions and Weibo is about collecting things we like．Both of them develop our self-focus．Self-focus simply means you pay attention to how you feel，think and behave．Self-focus isn't naturally a bad thing．Particularly in individualistic（个人主义的）cultures，we value our ability to be self-aware．(1)Unfortunately，when you are regularly focusing on yourself，you'll notice any dissatisfaction，anxiety，or general discomfort you might not have otherwise．(2)As a result，self-focus contributes to a wide range of mental health problems like anxiety．But quitting technology is no longer a practical solution．(3)For example，don't post about things you did，which focuses your attention on yourself．Instead，you could share advice and words of support from your smart phone．As a result，you'll feel better，and so will the people around you．Do you like to take selfies（自拍）？It's easy to take a quick picture of yourself to show what you re doing，or how you re feeling．But paying attention to ourselves often makes us feel worse．(4)Do your best to highlight（突出）the wonderful things that make them special．In this way，you won't focus so much on your bad hair day，and you will get along better with your friends．(5)But if we can learn to move the focus off ourselves and onto doing good for others，technology can help us grow．Anyway，the point is that it's up to you to handle the ability of yourself-focus．A．Too much self-focus means few friends．B．Self-focus is generally helpful in daily life．C．Therefore，try taking pictures of your friends．D．In fact，we can use technology in ways that are less self-focused．E．By bringing your attention to those negative emotions，you strengthen them．F．We want to know who we are and why we do what we do to uncover possible ways to improve our lives．G．Technology-when used in certain ways is having negative effects on our mental health and well-being．16. A.A B.B C.C D.D E.E F.F G.G17. A.A B.B C.C D.D E.E F.F G.G18. A.A B.B C.C D.D E.E F.F G.G19. A.A B.B C.C D.D E.E F.F G.G20. A.A B.B C.C D.D E.E F.F G.G三、完形填空（本大题共20小题，共30.0分）"Sara，don't forget your promise to me that you will mow（割草）Mrs．Martin's yard this weekend，"said Dad．"Don't let me down．"Sara was the oldest child in the family，and one of her chores was to mow their yard．Mrs．Martin，their(21)neighbor，was unable to take care of her yard in her70s，so Sara's dad had(22)Sara for this job．(23)Mrs．Martin's yard was not big，Sara knew the job would go quickly．However，she still disliked her dad's(24)．"Why didn't you ask me first？"Sara had(25)．"Did you ask me first when you volunteered me to be in the school festival last fall？"asked Sara's father．"Well，no，I didn't ask you first，(26)you would have done those things anyway．You're always(27)to help．""I(28)when I can．"Dad answered．"Sara，we have known Mrs．Martin for a very long time．She has often(29)our family．Now we can do something for her．(30)，the feeling you get from helping someone makes you(31)who is really helping whom．""I don't know，Dad，"said Sara．"The only feeling I get from mowing our yard is(32)．""Just you wait and see，"said DadAfter breakfast，Sara made her way to Mrs．Martin's yard．She was good at her job and soon had Mrs．Martins yard looking(33)．Mrs．Martin came outside with a big glass of orange juice and (34)it to her．Sara stopped her work and(35)enjoyed the drink，while Mrs．Martin talked to her about all of the flowers in her yard．Seeing the(36)in Mrs．Martin's eyes，Sara began to understand how much the yard(37)to Mrs．Martin．After finishing her drink，Sara returned to work with a new(38)．A warm feeling began to(39) through her body．Her dad was(40)．It was hard to tell who was helping whom!21. A.strange B.new C.aged D.faithful22. A.guided B.volunteered C.ordered D.forced23. A.Once B.Since C.Unless D.Although24. A.promise B.argument C.permission D.introduction25. A.replied B.suggested plained D.announced26. A.but B.so C.or D.for27. A.proud B.willing C.afraid D.fortunate28. A.choose B.succeed C.hesitate D.try29. A.respected B.changed C.protected D.helped30. A.Besides B.Instead C.Therefore D.Otherwise31. A.imagine B.explore C.worry D.wonder32. A.scared B.moved C.tired D.relaxed33. A.tidy B.alive C.empty D.messy34. A.threw B.delivered C.offered D.sold35. A.eagerly B.generously C.carefully D.gratefully36. A.determination B.peace C.curiosity D.joy37. A.related B.meant C.belonged D.referred38. A.attitude B.wisdom C.inspiration D.expectation39. A.exist B.fly C.spread D.break40. A.unusual B.right C.serious D.helpful四、语法填空（本大题共3小题，共15.0分）I have been to many places as a news reporter．In India，I visited a city where there were many(1)（home）children．Some were as young as four years old．They lived in the streets(2) survived by begging or stealing．But then a wonderful lady(3)（call）Rosa opened a home for them．Within one year，she was looking after two hundred children．She clothed them，fed them and taught them．She gave them hope．Online shopping(1)（welcome）by most people due to various reasons．For the consumers，it can save some time for the people(2)don't have much spare time．Just clicking the mouse，they can get what they want(3)staying at home．For the sellers，it can cut some costs for those without enough circulating funds．Compared with the traditional trade mode，they don't have to spend money in(4)（rent）a house．Peter worked(1)a night watchman in a small factory．One morning his boss came in with a suitcase．He said to Peter，I'm going to New York tomorrow．See you．Peter said，"Oh，you mustn't go．The factory owner asked him why．Peter answered that he(2)（have）a nightmare the night before．In the dream，he had seen the next day's plane to New York crash over the Atlantic Ocean．Peter's boss(3)（immediate）cancelled his ticket and stayed in the office．The plane crashed；the boss thanked Peter and gave him a big present．Then he fired him．五、书面表达（本大题共2小题，共35.0分）假设你是红星中学高三学生李华，你的英国朋友Jim对中国文化很感兴趣．他即将过生日，你给他准备了一件礼物并写信给他，内容包括：1．生日祝福；2．礼物介绍；3．选择该礼物的原因．注意：1．词数不少于50；2．信的开头和结尾已给出，不计入总词数．Dear Jim，Yours，Li Hua假设你是红星中学高三学生李华，请根据以下四幅图的先后顺序，介绍你组织戏剧社成员排演《雷雨》参加学校戏剧节的全过程，并以"Putting Thunderstorm on the School Stage"为题，给校刊"英语角"写一篇英文稿件．词数不少于60．Putting Thunderstorm on the School Stage。
通州区2019—2020学年高三一模考试试卷
风筝在古代书籍中叫风鸢#用 木 料 为 主 制 作 的 叫 木 鸢#以 帛 或 纸 做 成 的 叫 帛 鸢 或 纸 鸢$ 曹雪芹在%南鹞北鸢考工志&中有这样一段 文 字'(观 夫 史 籍 所 载 风 鸢 之 由 来 久 矣#其 可 徵)注* 者 实 寡 非 所 详 也 #惟 墨 子 作 木 鸢 三 年 而 飞 之 说 无 或 疑 焉 #盖 将 用 之 负 人 载 物 超 险 阻 而 飞 达 越 川泽而空递#所以辅舆马之不能#匡 舟 楫 之 不 逮 者 也#揆 其 初 衷 殆 欲 利 人#非 以 助 暴#夫 子 非 攻#故其法卒无所传$+从这段文字 中 可 以 看 到 前 人 考 证 风 筝 的 制 作 年 代 上 推 到 春 秋 时 期 墨 子以前#甚或还要远得多#只是没有文献可以考据#无法加以论断$ 另一方面#也告诉我们墨 子 和 公 输 子 创 作 木 鸢 和 木 鹊 都 是 为 了 用 以 负 人 载 物 #从 空 中 飞 往 要 去 的 目 的 地 #想 把 风 鸢 发 展 成 为 飞 行 工 具 #限 于 古 代 不 具 备 应 有 的 条 件 #所 以 都 没 有 成 功 $
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北京市通州区2019-2020学年高考数学第一次调研试卷含解析
北京市通州区2019-2020学年高考数学第一次调研试卷一、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．某圆柱的高为2，底面周长为16，其三视图如图所示，圆柱表面上的点M在正视图上的对应点为A，圆柱表面上的点N在左视图上的对应点为B，则在此圆柱侧面上，从M到N的路径中，最短路径的长度为（）A．17B．5C．3D．2【答案】B【解析】【分析】首先根据题中所给的三视图，得到点M和点N在圆柱上所处的位置，将圆柱的侧面展开图平铺，点M、N在其四分之一的矩形的对角线的端点处，根据平面上两点间直线段最短，利用勾股定理，求得结果. 【详解】根据圆柱的三视图以及其本身的特征，将圆柱的侧面展开图平铺,可以确定点M和点N分别在以圆柱的高为长方形的宽，圆柱底面圆周长的四分之一为长的长方形的对角线的端点处，224225+= B.点睛：该题考查的是有关几何体的表面上两点之间的最短距离的求解问题，在解题的过程中，需要明确两个点在几何体上所处的位置，再利用平面上两点间直线段最短，所以处理方法就是将面切开平铺，利用平面图形的相关特征求得结果.2．若实数x，y满足条件2502401x yx yxy+-≤⎧⎪+-≤⎪⎨≥⎪⎪≥⎩，目标函数2z x y=-，则z 的最大值为()A．52B．1 C．2 D．0【答案】C 【解析】【分析】画出可行域和目标函数，根据平移得到最大值. 【详解】若实数x ，y 满足条件25024001x y x y x y +-≤⎧⎪+-≤⎪⎨≥⎪⎪≥⎩，目标函数2z x y =-如图：当3,12x y ==时函数取最大值为2 故答案选C 【点睛】求线性目标函数(0)z ax by ab =+≠的最值:当0b >时，直线过可行域且在y 轴上截距最大时，z 值最大，在y 轴截距最小时，z 值最小； 当0b <时，直线过可行域且在y 轴上截距最大时，z 值最小，在y 轴上截距最小时，z 值最大. 3．ABC ∆ 的内角,,A B C 的对边分别为,,a b c ，已知22cos a c b A +=，则角B 的大小为（ ） A ．23π B ．3π C ．6π D ．56π 【答案】A 【解析】 【分析】先利用正弦定理将边统一化为角，然后利用三角函数公式化简，可求出解B. 【详解】由正弦定理可得sin 2sin 2sin cos A C B A +=，即sin 2sin()2sin cos A A B B A ++=，即有sin (12cos )0A B +=，因为sin 0A >，则1cos 2B =-，而(0,)B π∈，所以23B π=.故选：A 【点睛】此题考查了正弦定理和三角函数的恒等变形，属于基础题. 4．已知命题p ：,x R ∃∈使1sin 2x x <成立． 则p ⌝为（ ）A ．,x R ∀∈1sin 2x x ≥均成立 B ．,x R ∀∈1sin 2x x <均成立 C ．,x R ∃∈使1sin 2x x ≥成立D ．,x R ∃∈使1sin 2x x =成立【答案】A 【解析】试题分析：原命题为特称命题，故其否定为全称命题，即:p ⌝,sin 2x x x ∀∈≥R ． 考点：全称命题.5．已知等差数列{}n a 中，468a a +=则34567a a a a a ++++=（ ） A ．10 B ．16C ．20D ．24【答案】C 【解析】 【分析】根据等差数列性质得到46582a a a +==，再计算得到答案. 【详解】已知等差数列{}n a 中，4655824a a a a +==⇒=345675520a a a a a a ++++==故答案选C 【点睛】本题考查了等差数列的性质，是数列的常考题型.6．函数()y f x =在区间,22ππ⎛⎫- ⎪⎝⎭上的大致图象如图所示，则()f x 可能是（ ）A ．()ln sin f x x =B ．()()ln cos f x x =C ．()sin tan f x x =-D ．()tan cos f x x =- 【答案】B 【解析】【分析】根据特殊值及函数的单调性判断即可； 【详解】解：当0x =时，sin00=，ln sin0无意义，故排除A ； 又cos01=，则(0)tan cos0tan10f =-=-≠，故排除D ； 对于C ，当0,2x π⎛⎫∈ ⎪⎝⎭时，tan 0x >，所以()sin tan f x x =-不单调，故排除C ； 故选：B 【点睛】本题考查根据函数图象选择函数解析式，这类问题利用特殊值与排除法是最佳选择，属于基础题. 7．已知集合{}2|2150A x x x =-->，{}|07B x x =<<，则()R A B ðU 等于( )A ．[)5,7-B ．[)3,7-C ．()3,7-D ．()5,7-【答案】B 【解析】 【分析】解不等式确定集合A ，然后由补集、并集定义求解． 【详解】由题意{}2|2150A x x x =-->{|3x x =<-或5}x >，∴{|35}R A x x =-≤≤ð，(){|37}R A B x x =-≤<U ð．故选：B. 【点睛】本题考查集合的综合运算，以及一元二次不等式的解法，属于基础题型．8．如图，在底面边长为1，高为2的正四棱柱1111ABCD A B C D -中，点P 是平面1111D C B A 内一点，则三棱锥P BCD -的正视图与侧视图的面积之和为（ ）A ．2B ．3C ．4D ．5【答案】A 【解析】 【分析】根据几何体分析正视图和侧视图的形状，结合题干中的数据可计算出结果. 【详解】由三视图的性质和定义知，三棱锥P BCD -的正视图与侧视图都是底边长为2高为1的三角形，其面积都是11212⨯⨯=，正视图与侧视图的面积之和为112+=， 故选：A. 【点睛】本题考查几何体正视图和侧视图的面积和，解答的关键就是分析出正视图和侧视图的形状，考查空间想象能力与计算能力，属于基础题.9．设i 为数单位，z 为z 的共轭复数，若13z i=+，则z z ⋅=（ ） A ．110B ．110i C ．1100D ．1100i 【答案】A 【解析】 【分析】由复数的除法求出z ，然后计算z z ⋅． 【详解】13313(3)(3)1010i z i i i i -===-++-， ∴223131311()()()()10101010101010z z i i ⋅=-+=+=． 故选：A. 【点睛】本题考查复数的乘除法运算，考查共轭复数的概念，掌握复数的运算法则是解题关键．10．已知20,()1(0),{|()},{|(())()}a f x ax x x A x f x x B x f f x f x x >=-+>=≤=≤≤，若A B φ=≠则实数a 的取值范围是（ ） A ．(0,1] B ．3(0,]4C ．3[,1]4D ．[1,)+∞【答案】C 【解析】 【分析】根据A φ≠，得到2()1f x ax x x =-+≤有解，则440a ∆=-≥，得01a <≤，1211,x x a a+==，得到12{|()}[]11,[A x f x x x x a a -≤===，再根据{|(())()}B x f f x f x x =≤≤，有(())()f f x f x ≤，即()()22212110a ax x ax x -+--++≤，可化为()()2222110axx a x a +-+-≤，根据A B φ=≠，则2210a x a -≥+的解集包含11[,]a a+求解， 【详解】 因为A φ≠，所以2()1f x ax x x =-+≤有解， 即2()210f x ax x =-+≤有解，所以440a ∆=-≥，得01a <≤，12x x ==所以12{|()}[]11,[A x f x x x x a a-≤===， 又因为{|(())()}B x f f x f x x =≤≤， 所以(())()f f x f x ≤，即()()22212110a ax x ax x -+--++≤， 可化为()()2222110ax x a x a +-+-≤， 因为A B φ=≠，所以2210a x a -≥+的解集包含11[a a-+，所以111a aa a+---≤或111a aa a---≥，解得314a≤≤，故选：C【点睛】本题主要考查一元二次不等式的解法及集合的关系的应用，还考查了运算求解的能力，属于中档题，11．执行如图所示的程序框图，若输出的310S=，则①处应填写（）A．3?k<B．3?k…C．5?k…D．5?k<【答案】B【解析】【分析】模拟程序框图运行分析即得解.【详解】2111,0;2,0226k S k S====+=+；21113,6334k S==+=+；21134,44410k S==+=+.所以①处应填写“3?k…”故选：B【点睛】本题主要考查程序框图，意在考查学生对这些知识的理解掌握水平.12．已知a，b，Rc∈，a b c>>，0a b c++=．若实数x，y满足不等式组4xx ybx ay c≥⎧⎪+≤⎨⎪++≥⎩，则目标函数2z x y=+（）A ．有最大值，无最小值B ．有最大值，有最小值C ．无最大值，有最小值D ．无最大值，无最小值【答案】B 【解析】 【分析】判断直线0bx ay c ++=与纵轴交点的位置，画出可行解域，即可判断出目标函数的最值情况. 【详解】由0a b c ++=，a b c >>，所以可得0,0a c ><.1112,22222c c c ca b a a c b c a c c a a a a>⇒>--⇒>->⇒-->⇒<-∴-<<-⇒<-<， 所以由0b cbx ay c y x a a++=⇒=--，因此该直线在纵轴的截距为正，但是斜率有两种可能，因此可行解域如下图所示：由此可以判断该目标函数一定有最大值和最小值. 故选：B 【点睛】本题考查了目标函数最值是否存在问题，考查了数形结合思想，考查了不等式的性质应用. 二、填空题：本题共4小题，每小题5分，共20分。
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。
2020北京通州高三一模数学答案
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 a (1,2) ， b (3,m) ，其中 m R ．若 a , b 共线 ，则 m 等于
___________.
12. 圆 x 12 y2 1的圆心到直线 x 3y 1 0的距离为
1. 已知集合 A x 0 x 2 ， B x 1 x 3 ，则 A B A. x 0 x 3 B. x 2 x 3 C. x 0 x 1 D. x 1 x 2
2. 已知复数 z=i (2 i) （i 是虚数单位），则 z
A. 1
B. 2 C. 5 D. 3
3. 函数 f (x) sin 2x cos 2x 的最小正周期是（ ）
A. 1 B. 1 2
C. 1 D. 1 2
6. 已知抛物线 y2 2 px( p 0) 的焦点与双曲线 x2 y2 1 的右焦点重合，则 p 3
1 / 13
A. 2
B. 2 C. 2 2 D. 4
7. 在 (2x 1 )6 的展开式中，常数项是 x
A. -160 B. -20 C. 20 D. 160
π
Ａ．
2
Ｂ． π
Ｃ． 2π
Ｄ． 4π
4. 已知 f (x) 为定义在 R 上的奇函数，且 f (1) 2 ，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 log3 b log3 c 等于
2020 北京通州高三一模
数学
1.本试卷共 4 页，满分 150 分．考试时长 120 分钟．
2019年北京市通州区高考一模考试数学(理)试卷及答案
高考数学精品复习资料2019.5通州区20xx —高三一模考试数学（理）试卷4月本试卷分第一部分和第二部分两部分，共150分．考试时间长120分钟．考生务必将答案答在答题卡上，在试卷上作答无效．考试结束后，将本试卷和答题卡一并交回.第一部分 （选择题 共40分）一、选择题：本大题共8小题，每小题5分，共40分．在每小题给出的四个选项中，选出符合题目要求的一项. 1．已知全集U =R ，集合{}|10A x x =-<，{}0,1,2B =，那么()U AB ð等于A ．{}0,1,2B ．{}1,2C ．{}0,1D ．{}22．已知x ，y 满足0,1,2,x y x x y +≥⎧⎪≤⎨⎪-≥-⎩那么2z x y =+A. 1-B. 0C. 1D. 23．执行如右图所示的程序框图，若输出m 的值是25， 则输入k 的值可以是A ．4B ．6C ．8D ．104．设131log 6a =，31log 2b =，123c -=，那么A ．c b a >>B ．c a b >>C ．a b c >>D ．a c b >>5．“x ∀∈R ,210x bx -+>成立”是“[]0,1b ∈”的A ．充分而不必要条件B ．必要而不充分条件C ．充分必要条件D ．既不充分也不必要条件6．已知抛物线28y x =的准线与圆心为C 的圆22280x y x ++-=交于A ，B 两点，那么CA CB -等于2A ．2 B． C． D．7．已知四棱锥P ABCD -的底面ABCD 是边长为2的正方形，且它的正视图如图所示， 则该四棱锥侧视图的面积是A． B ．4 C． D ．28则完成这三件原料的描金工作最少需要A ．43小时B ．46小时C ．47小时D ．49小时第二部分 （非选择题 共110分）二、填空题：本大题共6小题，每小题5分，共30分.把答案填在答题卡上． 9．已知复数()()1i 1i a -+是纯虚数，那么实数a =_______.10．若直线l 的参数方程为1,1x t y t =+⎧⎨=-+⎩(t 为参数)，则点()4,0P 到直线l 的距离是_______.11．已知数列{}n a 是等比数列，34a =，632a =，那么86a a =_______；记数列{}2n a n - 的前n 项和为n S ，则n S =_______.12．2位教师和4名学生站成一排合影，要求2位教师站在中间，学生甲不站在两边，则不同排法的种数为_______（结果用数字表示）.13．在△ABC 中，角A ，B ，C 的对边分别为a ，b ，c ，已知60B =︒，4b =， 下列判断：①若c =C 有两个解；②若12BC BA ⋅=，则AC 边上的高为③a c +不可能是9.其中判断正确的序号是_______.14．设函数2()cos f x x a x =+，a ∈R ，非空集合{}|()0,M x f x x ==∈R . ①M 中所有元素之和为_______；②若集合()(){}|0,N x f f x x ==∈R ，且M N =，则a 的值是_______.三、解答题：本大题共6小题，共80分.解答应写出文字说明，演算步骤或证明过程. 15．（本题满分13分）已知函数()2sin cos 222x x x f x π⎛⎫=-+ ⎪⎝⎭． （Ⅰ）求()f x 的最小正周期；（Ⅱ）求()f x 在区间[],0π-上的最大值和最小值．16．（本题满分13分）作为北京副中心，通州区的建设不仅成为京津冀协同发展战略的关键节点，也肩负着医治北京市“大城市病”的历史重任，因此，通州区的发展备受瞩目. 12月25日发布的《北京市通州区统计年鉴（20xx ）》显示：通州区全区完成全社会固定资产投资939.9 亿元，比上年增长17.4％，下面给出的是通州区20xx-全社会固定资产投资及增长率，如图一.又根据通州区统计局1月25日发布：通州区全区完成全社会固定资产投资1054.5亿元，比上年增长12.2％.（Ⅰ）在图二中画出通州区全区完成全社会固定资产投资（柱状图），标出增长率并补全折线图；（Ⅱ）通过计算20xx-20xx 这7年的平均增长率约为17.2％，现从20xx-20xx 这7年中随机选取2个年份，记X 为“选取的2个年份中，增长率高于17.2％的年份个数”，求X 的分布列及数学期望；（Ⅲ）设20xx-20xx 这7年全社会固定资产投资总额的中位数为0x ，平均数为x ，比较0x 与x 的大小（只需写出结论）. 17．（本题满分14分）如图所示的几何体中，平面PAD ⊥平面ABCD ,PAD △为等腰直角三角形，QBCD AP图一（亿元）（％）2011-2016年全社会固定资产投资及增长率201620152014201320122011图二201725.020.015.010.05.00.0（亿元）2011-2017年全社会固定资产投资及增长率20162015201420132012201190APD ∠=，四边形ABCD 为直角梯形，//AB DC ，AB AD ⊥，2AB AD ==，//PQ DC ，1PQ DC ==.（Ⅰ）求证：//PD 平面QBC ； （Ⅱ）求二面角Q BC A --的余弦值； （Ⅲ）在线段QB 上是否存在点M ，使得AM ⊥平面QBC ，若存在，求QMQB的值；若不存在，请说明理由. 18．（本题满分13分）已知函数x xe x f =)(,)1()(-=xe a x g ，a ∈R ．（Ⅰ）当1a =时，求证：)()(x g x f ≥；（Ⅱ）当1>a 时，求关于x 的方程)()(x g x f =的实根个数.19．（本题满分13分）已知椭圆()2222:10x y C a b a b+=>>的上、下顶点分别为A ，B ，且2AB =，离心率为O 为坐标原点. （Ⅰ）求椭圆C 的方程；（Ⅱ）设P ，Q 是椭圆C 上的两个动点（不与A ，B 重合），且关于y 轴对称，M ，N 分别是OP ，BP 的中点，直线AM 与椭圆C 的另一个交点为D . 求证：D ，N ，Q 三点共线.20．（本题满分14分）已知数列{}n a ，设()11,2,3,n n n a a a n +∆=-=，若数列{}n a ∆为单调增数列或常数列时，则{}n a 为凸数列.（Ⅰ）判断首项01>a ，公比0>q ，且1≠q 的等比数列{}n a 是否为凸数列，并说明理由；（Ⅱ）若{}n a 为凸数列，求证：对任意的1k m n ≤<<，且k ，m ，n ∈N ， 均有1n m m k m m a a a aa a n m m k+--≥-≥--，且{}1max ,m n a a a ≤；其中{}1max ,n a a 表示1a ，n a 中较大的数；（Ⅲ）若{}n a 为凸数列，且存在()1,t t n t <<∈N ，使得0t a a ≤，n t a a ≤， 求证：12n a a a ===.高三数学（理科）一模考试参考答案20xx.4二、填空题9．1- 10.11. 4，221n n n ---12. 24 13. ②③ 14. 0，0三、解答题15. 解：（Ⅰ）因为()2sin cos 222x x x f x π⎛⎫=-⎪⎝⎭2sin cos 222x x x =21si 2n 2x x =++sin +3x π⎛⎫= ⎪⎝⎭． (4)分所以()f x 的最小正周期2.T π= (6)分（Ⅱ）因为[],0x π∈-，所以2+,333x πππ⎡⎤∈-⎢⎥⎣⎦.所以当33x ππ+=，即0x =时，函数)(x f 取得最大值sin3π=当32x ππ+=-，即56x π=-时，函数)(x f 取得最小值1+-所以()f x 在区间[],0π-和-……………… 13分16. 解：（Ⅰ） (4)分（Ⅱ）依题意，X 的可能取值为0，1，2. …………………… 5分24272(0)7C P X C ===，1134274(1)7C C P X C ===，23271(2)7C P X C ===. ……………… 8分所以X 的分布列为 (9)分所以X 的数学期望()2416012.7777E X =⨯+⨯+⨯=…………………… 10分 （Ⅲ）0x <. (13)分17. 解：（Ⅰ）因为//PQ CD ，PQ CD =，所以四边形PQCD 是平行四边形. 所以//.PD QC因为PD ⊄平面QBC ，QC ⊂平面QBC ，图二（％）201725.020.015.010.05.00.0（亿元）2011-2017年全社会固定资产投资及增长率201620152014201320122011所以//PD 平面.QBC (4)分（Ⅱ）取AD 的中点为O ， 因为PA PD =，所以.OP AD ⊥因为平面PAD ⊥平面ABCD ,OP ⊂平面PAD ，所以OP ⊥平面.ABCD …………………… 5分以点O 为坐标原点，分别以直线OD ，OP 为y 轴，z 轴建立空间直角坐标系Oxyz ，则x 轴在平面ABCD 内．因为90APD ∠=︒，2AB AD ===，1PQ CD ==， 所以(),,A -010，(),,B -210，(),,C 110，(),,Q 101，所以()1,1,1BQ =-，()0,1,1CQ =-. …………………… 7分设平面QBC 的法向量为(),,n x y z =，所以,,n BQ n CQ ⎧⋅=⎪⎨⋅=⎪⎩00 即,.x y z y z -++=⎧⎨-+=⎩00所以,.x y z y z =+⎧⎨=⎩令1z =，则1y =，2x =.所以()2,1,1n =. …………………… 8分 设平面ABCD 的法向量为()0,0,1m =，所以cos ,n m == 又因为二面角Q BC A --为锐角，所以二面角Q BC A --…………………… 10分 （Ⅲ）存在. 设点(),,M a b c ，QM QBλ=，[]01.λ∈,所以()1,,1QM a b c =--，()1,1,1.QB =--所以+1a λ=， b λ=-， +1c λ=-. 所以点(),,.M λλλ+--+11所以(),,.AM λλλ=+-+-+111 又平面QBC 的法向量为()2,1,1n =，AM⊥平面QBC ，所以.λλ+-+=1121所以.λ=13所以在线段QB 上存在点M ，使AM ⊥平面QBC ，且QM QB的值是.13…………… 14分18. 解：（Ⅰ）设函数()()().xxF x f x g x xe ae a =-=-+当1=a 时，()1x x F x xe e =-+，所以'()xF x xe =.所以)0(，-∞∈x 时，'()0F x <；)0(∞+∈，x 时，'()0F x >. 所以()F x 在)0(，-∞上单调递减，在)0(∞+，上单调递增. 所以当0=x 时，()F x 取得最小值(0)0F =.所以()0F x ≥，即)()(x g x f ≥． …………………… 4分（Ⅱ）当1>a 时，'()(1)xF x x a e =-+， 令'()0F x >，即(1)0xx a e -+>，解得1x a >-； 令'()0F x <，即(1)0x x a e -+<，解得 1.x a <-所以()F x 在(1)a -∞-，上单调递减，在(1)a -+∞，上单调递增. 所以当1-=a x 时，()F x 取得极小值，即1(1)a F a a e --=-. (6)分令1()a h a a e-=-，则1'()1a h a e-=-.因为1>a ，所以'()0h a <. 所以()h a 在(1,)+∞上单调递减. 所以()(1)0h a h <<. 所以(1)0F a -<.又因为()0F a a =>，所以()F x 在区间),1(a a -上存在一个零点.所以在),1[+∞-a 上存在唯一的零点. …………………… 10分又因为()F x 在区间)1,(--∞a 上单调递减，且(0)0F =，所以()F x 在区间)1,(--∞a 上存在唯一的零点0. …………………… 12分所以函数)(x h 有且仅有两个零点，即使)()(x g x f =成立的x 的个数是两个.…………………… 13分19. 解：（Ⅰ）因为椭圆的焦点在x 轴上，2AB =，离心率e =所以1b =，c a = 所以由222a b c =+，得2 4.a = 所以椭圆C 的标准方程是22 1.4x y += …………………… 3分（Ⅱ）设点P 的坐标为()00,x y ，所以Q 的坐标为()00,x y -. 因为M ，N 分别是OP ，BP 的中点， 所以M 点的坐标为00,22x y ⎛⎫ ⎪⎝⎭，N 点的坐标为001,22x y -⎛⎫⎪⎝⎭. …………………… 4分所以直线AD 的方程为0021y y x x -=+. …………………… 6分代入椭圆方程2214x y +=中，整理得()()222000042820.x y x x y x ⎡⎤+-+-=⎣⎦ 所以0x =，或()()()0000220008222=.5442x y x y x y x y --=-+-所以()2000000002222431.5454x y y y y y x y y ---+-=⋅+=--所以D 的坐标为()200000022243,5454x y y y y y -⎛⎫-+- ⎪--⎝⎭. (10)分所以000000112.32QNy y y k x x x --+==-+ 又()200000000243541.22354QD y y y y y k x y x x y -+---+==--+- 所以D ，N ，Q 三点共线. (13)分20.解：（Ⅰ）因为+12+1n n n a a a +∆=-，1n n n a a a +∆=-，所以+12+12n n n n n a a a a a +∆-∆=+-22n n n a q a a q =+-()()22121.n n a q q a q =+-=-因为，公比，且， 所以0n a >，()210.q ->所以()210.n a q ->所以等比数列{}n a 为凸数列. …………………… 3分（Ⅱ）因为数列}{n a 为凸数列，所以11=m m m m a a a a ++--，211m m m m a a a a +++-≥-，321m m m m a a a a +++-≥-，…，11.m n m m n m m m a a a a +-+--+-≥-叠加得()1()n m m m a a n m a a +-≥--. 所以1.n mm m a a a a n m+-≥--同理可证1.m km m a a a a m k+-≤-- 综上所述，1n m m k m m a a a aa a n m m k+--≥-≥--. (7)分 因为n m m k a a a a n m m k--≥--，所以()()()().n m m k m k a k m a n m a m n a -+-≥-+-所以()()().n k m m k a n m a n k a -+-≥-令1k =，()()11()1.n m m a n m a n a -+-≥- 所以11.11m n m n m a a a n n --⎛⎫≤+ ⎪--⎝⎭若1n a a ≤，则111()().1111m n n n n m n m m n ma a a a a a n n n n ----≤+≤+=---- 若1n a a ≥，则111111()().1111m n m n m m n ma a a a a a n n n n ----≤+≤+=---- 所以{}1max ,.m n a a a ≤ (10)分（Ⅲ）设p a 为凸数列}{n a 中任意一项， 由（Ⅱ）可知，1max{,}.p n t a a a a ≤≤再由（Ⅱ）可知，对任意的1p m n ≤<<均有1m p n m m m a a a a a a n mm p +--≥-≥--， （1）当1p t n ≤<<时，t pn ta a a a n t t p --≥--.又因为n t a a ≤，所以0.t pn ta a a a n t t p --≥≥--所以.p t a a ≥（2）当1t p n <<≤时，11p t t a a a a p t t --≥--.又因为1t a a ≤，所以10.1p t t a a a a p t t --≥≥--所以.p t a a ≥（3）当p t =时，.p t a a = 所以.p t a a ≥综上所述，.p t a a = 所以12n a a a ===. …………………… 14分。
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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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）B
2.（3分）A3．（3分）D4．（3分）C
5.（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”。
【评分说明：4分，按照答案中分项给分。
意思对，即可给分】
三、本大题共5小题，共26分。
12.（3分）B
13.（3分）C
14．（6分）孟诗主要运用侧面描写的表现手法，运用衬托手法来描写潮水。
孟诗通过人们听
到潮声后“辍弹”“连骑出”等行为表现出人们观潮的踊跃，引起读者对钱塘潮的好奇心。
用“照日秋云迥，浮天渤澥宽”营造出潮水涌来时海天湛蓝开阔的背景，以静衬动。
最后两句诗“惊涛来似雪，一座凛生寒”写观潮人的心态和神态，来衬托钱塘江潮水排空而来的雄伟壮观。
苏诗主要运用正面描写的手法来写潮水，诗人用“万人鼓噪”“浮江老阿童”两个典故来比喻钱塘江潮水的汹涌，又用设问手法，一问一答，描写江水涌起，白浪滔天，潮头似卷越山而去的令人震撼的场面。
【评分说明：孟诗运用衬托手法，举出诗句分析，3分；苏诗运用正面描写手法，举出诗句分析，3分。
意思对，即可酌情给分】
15．（8分）①东船西舫悄无言唯见江心秋月白
②雕栏玉砌应犹在只是朱颜改
③群贤毕至少长咸集
千里逢迎高朋满座
【评分说明：8分。
每空1分。
写对一句给1分，每句中只要有一处错误，该句便不给分】16．（6分）答案示例：
同意“这样修改不好”的看法：因为这段文字是“宝黛共读西厢”情节（1分）。
曹雪芹原稿要突出林黛玉聪明。
（1分）黛玉用“果然有趣”来回答宝玉的问话，表现出他们有共同一致的性格、理想及审美趣味，（1分）用“共读《西厢》”来表现二人叛逆性格和宝黛纯真爱情这一主题。
（1分）而高鄂的修改，体现不出林黛玉的聪明，也与后面“虽看完了，却只管出神，心内还默默记诵”矛盾。
(1分)“黛玉笑着点头儿”只表明她认可宝玉的观点，不能体现出他们志趣、性格一致的特点。
（1分）
不同意“这样修改不好”（即认为高鹗修改是可以）的看法：高鹗的修改也有他的道理。
这段文字是“宝黛共读西厢”情节（1分）。
在高鹗看来，林黛玉当时的年龄，在不到一顿饭的工夫，读完《西厢》是不可能的。
（1分）所以用了现实主义手法，客观描写人物。
（1分）同时用“点头不语”来体现林黛玉作为贵族小姐的含蓄、矜持的特点，（1分）也表现出她对宝玉的观点心悦诚服的心理状态。
（1分）高鹗的修改只是客观描写了宝黛共读《西厢》这件事，没有加入主观思想情感。
（1分）
【评分说明：6分，按照答案中分项给分。
意思对，即可给分】
四、本大题共4小题，共17分。
17．（3分）D（对付：勉强支撑）
18．（3分）C
19．（4分）答案要点：
①小说成就高，二十来岁就写出受到名家激赏的小说。
②诗歌成就高，歌词创作婉转深挚，自成一派；旧体诗创作俊逸潇洒，每出专业诗人之上。
③能写戏曲剧本，擅长绘画。
④读书多，学问大，老舍先生佩服。
【评分说明：4分。
每个要点1分；意思对，即可给分】
20．（7分）寓意：表达了对端木先生去世的痛惜心情，也表达了对端木先生的尊崇和缅怀之情。
（2分）
启示：答案要点：①引古文来命文章题目，点明文章的主题及内容，同时又符合中国传统文化中“避讳”的风俗。
（2分）
②从文章内容选材上，作者围绕“哲人”一词，对端木先生的才学、性情、人品给予了高度评
价。
用“哲人其萎”来概括自己失去端木这样一位可以尊崇、效仿的先辈的痛惜之情和无人可效仿学习的失望之情。
这样选材，中心突出，值处我们学习写作时借鉴。
（3分）
③从文章结构安排上，文章第一话“端木蕻良真是一位才子”和最后一句话“……，那多好！”正是围绕“哲人其萎”来组织材料、谋篇布局，这样使文章结构完整、严谨，值得我们学习写作时借鉴。
（3分）
【评分说明：7分。
寓意，2分；启示，5分，按照答案中分项给分，②③可以选择其一回答。
每点均3分。
意思对，即可酌情给分】
五、本大题共3小题，共65分。
21．（5分）①（3分）C
②（2分）你的微笑是我伤痛中一剂康复的良方，你的微笑是我绝望中一线希望
的曙光。
【评分说明：2分。
每句，1分】
22.（10分）微写作：略
23.（50分）作文：
作文评分标准
【译文】
有的人有罪而能够受到赏赐，有的人有功反而要加罪。
西门豹担任邺令时，仓库里没有积粮，府库里没有储钱，兵库里没有武器，官衙里没有账目，人们多次向魏文侯告状。
文侯亲自到这个县察看，果真像人们所说的那样。
文侯说：“翟璜任用你治理邺县，而现在一片混乱，你能有办法（改变这种局面），那么就算了；如果不能改变，我将对你施加刑罚。
”西门豹说：“我听说打算称王的君主使百姓富裕，称霸的君主使武备强盛，亡国的君主使仓库堆满。
现在君主要想成就霸业，我因此积蓄财力在百姓之中。
君主如果不相信，我请求允许登城击鼓，武
器、粮食，能够立即准备好。
”于是登上城楼击起战鼓。
一鼓声落，百姓身披铠甲，捆束箭矢，手握兵弩而奔来；第二次击鼓，百姓拉车背粮前来待命。
文侯见状，说：“让他们回去吧！”西门豹说：“和老百姓立下的誓约，不是一天积累成的。
一次击鼓欺骗了他们，以后就不能再听从指挥了。
燕国曾经侵略魏国，占领八城，我请求攻打他们，夺回被侵领土。
”于是举兵讨伐燕国，夺回侵地后才返回邺地。
这是有罪而能够受赏的例子。
解扁为魏国管理东部边界，向上交的赋税比往年增加三倍，主管官吏请求给他赏赐。
魏文侯说：“我国的土地没有扩大，人口也没增加，收入为何增加了三倍？”官吏答说：“用冬季的时间在山里伐木，堆聚起来，在春天顺河漂浮而下，然后卖掉，因此增加了收入。
”魏文侯说：“百姓春天勤力耕种，暑天尽力除草耕耘，秋天收割贮藏，冬天闲暇无事，砍伐树木积聚起来，装在车子上运到河边，顺流运往城邑，这样是使老百姓一年四季得不到休息。
百姓已经十分疲惫了，即使有三倍的收入，将来又有什么用处？”这是有功反被加罪的例子。
贤明的君主不随便求得，忠臣不随便求利，怎么能说明这个问题？晋大夫中行穆伯攻打鼓地，没有能够攻下。
这时晋臣馈闻伦进言说：“鼓地的啬夫，我知道他，（只要由他做内应），不需要劳累将士，而鼓地可以得到。
”穆伯没有表示意见。
左右的人说“不折断一件兵器，不伤害一个士卒，而鼓攻而得，你为什么不派他去呢？”穆伯说：“馈闻伦这个人巧媚而不讲仁义。
假使让他得到了鼓地，我难道不赏赐他吗？如果赏赐他，这是奖励佞人。
佞人得志，这就将使晋国的将士，舍弃仁义而追随奸佞。
即使得到鼓地，又将有什么用呢？”攻城的目的是想扩张土地。
能够得到土地而不取得，是看到它的根本而就知道它的末梢了。