2019-2020年上海市建平中学高一上9月月考
0653-建平中学高一月考(2019.09)
建平中学高一月考数学卷2019.09一. 填空题1. 已知{2,3,5}{2,3,5,7,11,13}A ⊆⊂，那么满足条件的集合A 的个数是2. 将集合U A C B ð在右图中用阴影部分表示出来 AB =∅，则实数的，则用列举法表示集合 {3}A B =，{9}U B =ð”活动正如火如荼准备中，高一某班学生参加大舞台和 数比参加风情秀的人数多3人；两个节目都参加的人数比两个节目都不参加的学生人数少7 人，则此班的人数为9. 已知集合{1,2,3}A =，{|}B E E A =⊆，令||E 表示数集E 中所有元素的和，对集合B 中所有元素均求||E ，则这些||E 的值的和为二. 选择题10. 若“不积硅步，无以至千里”是真命题，则下面的命题一定是真命题的是（ ）A. 积硅步一定可以至千里B. 不积硅步也可能至千里C. 要想至千里一定要积硅步D. 不想至千里就不用积硅步11. 若U 为全集，B A 、为非空集合，下面四个命题：（1）A B A =；（2）A B B =；（3）U A B =∅ð；（4）UA B U =ð. 其中与命题B A ⊆等价的命题个数有（ ）A. 1个B. 2个C. 3个D. 4个12. 已知集合{|2,}A x x k k ==∈Z ，{|21,}B x x k k ==+∈Z ，{|41,}C x x k k ==+∈Z ，又a A ∈，b B ∈，则必有（ ）A. a b A +∈B. a b B +∈C. a b C +∈D. 以上都不对三. 解答题13. 证明：“已知a 、b ∈R ，若02222≠-++++b a b ab a ，则1≠+b a .”为真命题.14. 已知全集为R ，集合{|1}A x x a =<-，{|2}B x x a =>+，{|1C x x =≤或4}x >. 若()AB C C =R ð，求实数a 的取值范围.15. 已知命题:p 关于x 的不等式10mx -≥的解集为A ，且2A ∈；命题:q 关于x 的方程220x x m -+=有两个不相等的正实数根.（1）若命题p 为真命题，求实数m 的范围；（2）若命题p 和命题q 中至少有一个是假命题，求实数m 的范围.}n 12(1,2)n a a a n ≤<⋅⋅⋅<≥具有性质P ：如果对任意的 i 两数中至少有一个属于A . （是否具有性质P ；（,}n a 12(1,2)n a a a n ≤<⋅⋅⋅<≥具有性质P ，证明：对任意1i n ≤≤（i ∈*N ），i a 都是n a 的因数； （3）求30n a =时n 的最大值参考答案一. 填空题1. 72. 略3. 若1a ≠或2b ≠，则5a b +≥4. 15. {1,0,1}-6. 11{,0,}23- 7. {3,9} 8. 40人 9. 24二. 选择题10. C 11. D三. 解答题13. 逆否命题+因式分解+14. 1a ≤-或5a >.15. （1）12m ≥16. （1）{1,3,6}不满足；{（2）略（分类讨论或者反证法）（3）4；301235=⨯⨯⨯，其中且2、3、5。
上海市浦东新区建平中学2019_2020学年高一语文上学期期中试题(含解析)
上海市浦东新区建平中学2019-2020学年高一语文上学期期中试题（含解析）一、积累与运用1.按题目要求填空。
（1）_____，悠悠我心。
（曹操《短歌行》）（2）谢公宿处今尚在，__________________。
（李白《梦游天姥吟留别》）（3）银瓶乍破水浆迸，__________________。
（白居易《琵琶行》）（4）苏轼的《念奴娇·赤壁怀古》中，表现周瑜临战潇洒从容的气度和辉煌战功的句子是：“__________________，__________________。
”【答案】 (1). 青青子衿 (2). 渌水荡漾清猿啼 (3). 铁骑突出刀枪鸣 (4). 谈笑间 (5). 樯橹灰飞烟灭【解析】【详解】本题主要考查默写常见的名句名篇的能力。
名句默写分为两大类，一是给出语境的理解性默写，二是给出上句写下句的直接默写。
此类试题解答时，默写要注意字形，而字形与字义分不开，学生应借助字义来识记字形。
注意重点字的写法。
如“衿”“漾”“樯橹”要理解字义去记忆。
学生记忆的时候应该结合诗句的意思。
2.在下面一段话的空缺处依次填入词语，最恰当的一组是我们说乡下人土气，虽则似乎带着几分__________的意味，但这个“土”字却用得很好。
土字的__________意义是指泥土。
乡下人离不了泥土，因为在乡下住，种地是最普通的谋生办法。
远在西伯利亚，中国人住下了，不管天气如何，还是要下些种子，试试看能不能种地。
从土里长出过光荣的历史，自然也会受到土的__________，现在很有些飞不上天的样子。
A. 鄙视基础制约B. 藐视基本束缚C. 轻视原本压制D. 蔑视本来约束【答案】B【解析】【详解】本题考核正确使用词语的能力。
此类试题答题时，首先明确词语的意思，然后结合语境辨析正误。
鄙视：意思是表示轻蔑、看不起的意思；对人一种很不尊重的口头用语，小看人、轻视、看不起对方。
藐视：意思是认为“某种事物”很卑贱、渺小、是没有价值或令人厌恶，从而对它加以轻视，加以嘲笑。
2019-2020学年上海市浦东新区建平中学高一(上)9月月考数学试卷
2019-2020学年上海市浦东新区建平中学高一（上）9月月考数学试卷一、填空题1. 已知{2, 3, 5}⊆A⫋{2, 3, 5, 7, 11, 13}，那么满足条件的集合A 的个数是________．2. 将集合A ∩C ∩∁U B 在图中用阴影部分表示出来．3. 命题“若a ＝1且b ＝2，则a +b <5．”的否命题是________．4. 已知A ＝{(x, y)|x +y −4＝0}B ＝{(x, y)|x +ay −1＝0}，若A ∩B ＝⌀，则实数a 的值为________．5. 设集合A ＝{x, xy, xy −1}其中x ∈Z ，y ∈Z 且y ≠0．若0∈A ，则用列举法表示集合A ＝________．6. 设集合A ＝{x|x 2+x −6＝0}，B ＝{x|mx +1＝0}，则满足B ⊆A 的实数m 的值所成集合为________13，−12} ．7. 已知A ，B 均为集合U ＝{1, 3, 5, 7, 9}的子集，且A ∩B ＝{3}，(∁U B)∩A ＝{9}，则A ＝________．8. 建平中学2019年的“庆国庆930”活动正如火如茶准备中，高一某班学生参加大舞台和风情秀两个节目情况如下：参加风情秀的人数占该班全体人数的八分之三；参加大舞台的人数比参加风情秀的人数多3人：两个节目都参加的人数比两个节目都不参加的学生人数少7人，则此班的人数为________．9. 已知集合A ＝{1, 2, 3}，B ＝{E|E ⊆A}，令|E|表示数集E 中所有元素的和，对集合B 中所有元素均求|E|，则这些|E|的值的和为________．二.选择题若“不积硅步，无以至千里”是真命题，则下面的命题一定是真命题的是（ ）A.不积硅步也可能至千里B.积硅步一定可以至千里C.不想至千里就不用积硅步D.要想至千里一定要积硅步若U为全集，A、B为非空集合，下面四个命题：A∩B＝A；（2）A∪B＝B；（3）A∩∁U B＝⌀；(4)∁U A∪B＝U．其中与命题A⊆B等价的命题个数有（）A.2个B.1个C.4个D.3个A={x|x=2k, k∈Z}，B={x|x=2k+1, k∈Z}，C={x|x=4k+1, k∈Z}，又a∈A，b∈B，则（）A.a+b∈BB.a+b∈AC.a+b∈CD.a+b∈A，B，C中的任一个三.解答题证明：“已知a、b∈R，若a2+2ab+b2+a+b−2≠0，则a+b≠1．”为真命题．已知全集为R，集合A＝{x|x<a−1, B＝{x|x>a+2}，C＝{x|x≤1或x>4}．若∁R(A∪B)∪C＝C，求实数a的取值范围．已知命题p：关于x的不等式mx−1≥0的解集为A，且2∈A；命题q：关于x的方程x2−2x+m＝0有两个不相等的正实数根．（1）若命题p为真命题，求实数m的范围；（2）若命题P和命题q中至少有一个是假命题，求实数m的范围．称正整数集合A＝{a1, a2, ..., a n}(1≤a1<a2<...<a n, n≥2)具有性质P：如果对两数中至少有一个属于A．任意的i，j(1≤i≤j≤n)，a i a j与a ja i（1）分别判断集合{1, 3, 6}与{1, 3, 4, 12}是否具有性质P；（2）设正整数集合A＝{a1, a2, ..., a n}(1≤a1<a2<...<a n, n≥2)具有性质P．证明：对任意1≤i≤n(i∈N∗)，a i都是a n的因数；（3）求a n＝30时n的最大值．参考答案与试题解析2019-2020学年上海市浦东新区建平中学高一（上）9月月考数学试卷一、填空题1.【答案】此题暂无答案【解析】此题暂无解析【解答】此题暂无解答2.【答案】此题暂无答案【解析】此题暂无解析【解答】此题暂无解答3.【答案】此题暂无答案【解析】此题暂无解析【解答】此题暂无解答4.【答案】此题暂无答案【解析】此题暂无解析【解答】此题暂无解答5.【答案】此题暂无答案【解析】此题暂无解析【解答】此题暂无解答6.【答案】此题暂无答案【解析】此题暂无解析【解答】此题暂无解答7.【答案】此题暂无答案【解析】此题暂无解析【解答】此题暂无解答8.【答案】此题暂无答案【解析】此题暂无解析【解答】此题暂无解答9.【答案】此题暂无答案【解析】此题暂无解析【解答】此题暂无解答二.选择题【答案】此题暂无答案【解析】此题暂无解析【解答】此题暂无解答【答案】此题暂无答案【解析】此题暂无解析【解答】此题暂无解答【答案】此题暂无答案【解析】此题暂无解析【解答】此题暂无解答三.解答题【答案】此题暂无答案【解析】此题暂无解析【解答】此题暂无解答【答案】此题暂无答案【解析】此题暂无解析【解答】此题暂无解答【答案】此题暂无答案【解析】此题暂无解析【解答】此题暂无解答【答案】此题暂无答案【解析】此题暂无解析【解答】此题暂无解答。
2019-2020年高一上学期9月月考英语试题 含答案
2019-2020年高一上学期9月月考英语试题含答案一. 阅读理解（每小题2分，共40分）（A）American schools begin in September after a long summer holiday. There are two terms in a school year. The first term is from September to January and the second is from February to June. Most American children begin to go to school when they are five years old . Most students are seventeen or eighteen years old when they finish high school.High school students take only four or five subjects each term. They usually go to the same class every day , and they have homework for every class . After class ,they do many interesting things.After high school , many students go to college.They can go to a small one or a large one . They usually have to pay a lot of money . So many college students work after class to get the money for their studies.In American high school , most students take English , science , math and history. These are basic courses and each course is as useful as the others. In English class , the students study grammar and read famous literature . In science class, they study biology , chemistry or physics. History is more interesting to some students because they learn about important events and places in the United States . Students take other courses , too . These are electives . Some of them are music , home economics and computer science . Students needn’t take all of these courses . Some study computer science because they think it is more practical . In each class , teachers give students exams . Some exams are difficult than others, but a good student can always do well.1.In two school years, there are _____ terms in American schools .A. twoB. fourC. sixD. five2.After high school ,many American students go_________.A. homeB. to middle schoolC. to collegeD. to work3.Many college students get the money for their studies by _______.A. themselvesB. their parentsC. their teachersD. their friends4.In science class , American high students study __________ .A. history , physics or biologyB. chemistry , geography or mathC. Chinese , math or EnglishD. physics ,biology or chemistry5.The main idea of the passage is __________.A. American high school and courses.B. American college school .C. In each class , teachers give students examsD. Students needn’t take all of these courses.(B)My twin sister is my best friend . We look, speak and think alike. However, things weren’t always this way. When we were younger, we often competed over who learned how to do things first .Unluckily, I was always the second since I am the younger one by four minutes.My sister was the “leader”when we played. I didn’t care because it was better to play with a bossy sister than to play alone.We grew out of our “leader/ follower” stage in Grade 3. She wasn’t learning as fast as I was , so I taught her in the spare time . I felt needed .She was very nice to me when she needed my help. But I didn’t take advantage of her because I knew that if she was asking me for help , it was serious and I needed to do my best to help her . Through helping her, we because closer.Going through the same experiences has also brought us closer, in Grade 4, we went to the doctor together and found out that we both needed glass as. When we were 11, we learned how to ride bikes together and later we developed our artistic skills by learning from each other . In Grade 8 ,we both got graces and felt the same pain.I feel lucky to have someone to share the same experiences with.I love being a twin because I know that as long as she lives, I’ll never be alone and she’ll always love me back.6. We know when the writer and her sister were younger,___________ .A. they didn’t look alike.B. they hated each otherC. they liked competing with each otherD. both of them learnt very fast7. If someone is bossy , we probably mean he /she ______.A. is good at doing many thingsB. is afraid of people around him/herC. likes asking other people for adviceD. likes asking others to do this or that8. What did the writer do when her twin sister needed her ?______A. She took advantage of herB. She asked her sister to be nice to her.C. She tried her best to help her .D. She refused to offer her any help9. What is Paragraph 4 mainly about?_______A. Some experiences that the writer and her sister went through together.B. Some things that the writer was looking forward to doingC. Some experiences that the writer and her sister didn’t want to rememberD. Some experiences that made the writer feel she was lucky to have many friends.10. After reading the passage , we learn that the writer _________.A. feels very lonely all the timeB. isn’t as smart as her twin sisterC. likes making friends with others.D. feels lucky to have a twin sister(C)I was tired and hungry after a long day of work. When I walked into the living room , my 12-year-old son looked up at me and said , “I love you.”I did not know what to say , and I just stood there , looking down at him. My first thought was thathe must need help with his homework . Then I asked, “What was that all about ?”“Nothing,” he said , “my teacher said we should tell our par ents we love them and see what they say.”The next day I called his teacher to find out more about what my son said and how the other parents had reacted . “Most of the fathers had the same response as you did .”the teacher said , “ When I first suggested that we try this, I asked the children what they thought their parents could say .Some of them thought their parents would have heart trouble.”Then the teacher explained ,I want my students to know that feeling love is an important part of health. I’m trying to tell them it’s too bad that we don’t express our feelings. A boy should tell his father or mother he loves him or her .”The teacher understands that sometimes it is difficult for some of us to say something that is good for us to say.That evening when my son came to me , I took him in my arms and held on for an extra moment, saying, “Hey , I love you ,too.”I don’t know if saying that made either of us healthier, but it did feel pretty good.11. The writer was tired and hungry for _______.A. her son’s homeworkB. a long day of workC. her bossD. her husband12. The boy’s teacher said ________.A. that he should see what his parents say.B. that he loves him.C. where his parents workD. his parents should take care of his homework13. Some children thought their parents would have _______.A. their workB. heart problemC. their friendsD. their family14. The teacher said his students knew that ______ is very important.A their study B. money C. health D. their homework15. In the passage, “either of us” refers to _______.A. mother and fatherB. teacher and motherC. teacher and sonD. mother and son（D）The Blacks are American tourists. The whole family are visiting Beijing now. This is their first visit to China. They are going to stay in China for three months. They want to visit some big cities and villages. They hope to learn some Chinese, too.Mr. Black is a taxi driver. He likes to drive in Beijing. Mrs. Black is a school teacher in Canada. She is visiting a city school today and a village school tomorrow. Their daughter is a middle school student. She is going to meet some Chinese students. They are taking a lot of pictures in China. When they return to America, they are going to show the pictures to their friends. They want the American people to know more about China.16. The Blacks are staying in________ now.A. UKB. USAC. CanadaD. China17. Mr. Black is ________.A. a teacherB. a doctorC. a taxi driverD. a worker18. There are____ _people in Mr. Black's family.A. twoB. threeC. fourD. five19. Why are they going to show the pictures to their friends?A.The pictures are beautiful.B.They want the Americans to come to China.C. They like China.D. Let the American people to know more about China.20. The word “village” means ________ in Chinese.A. 城市B. 村庄C. 山D. 草原二. 完型填空题 ( 每小题1.5分，共30分）Four days ago, I was taking a taxi. On the way, I just had the 21 stop ata store to buy something. A woman 22 me to let her hitchhike (免费搭车).I 23 and picked this woman up. I thought she was too fat; she 24 about 120 kg. But she was very sweet and kind-hearted, so I didn’t 25 .She was talking to me 26 while going back to her place about how she got everything for her 27 .So I thought to myself she must have a happy family. But nothing special 28 yet.I got to her apartment 29 she needed help getting all the things she got to her place . I just helped her out and while I was 30 the stuff inside her house,I 31 that her husband walked in from the back of the apartment. So she was talking to him in her 32 voice. “Honey , I got you this ; Honey, I got you that.”But what I came to notice was that her husband was 33 . And then I looked closeto how they were together and I know for that moment I was seeing “TRUE 34 .”They cared for each other so 35 and what they looked liking was not 36 at all.I was just deeply 37 by the true love between them.Sometimes I think about going back to the apartment and tell them what I 38 in them and to thank them for sharing their 39 with me , even it is for a few40I like the blind couple care about each other ; it is a very happy and romantic thing.21. A. stranger B. waiter C. passenger D. driver22. A. reminded B. allowed C. asked D. helped23. A. nodded B. promised C. hesitated D. explained24. A. carried B. weighted C. supported D. lifted25. A. remember B. mind C. worry D. leave26. A. gladly B. nervously C. slowly D. calmly27. A. friend B. husband C. stopped D. happened29. A. unless B. if C. because D. although30. A. moving B. searching C. arranging D. observing31. A. imaged B. noticed C. believed D. expected32. A. police B. tired C. high D. sweet33. A. painful B. foolish C. blind D. ill34. A. LOVE B. FRIENDSHIP C. JUDGMENT D. STORY35. A. frequently B. deeply C. thankfully D. quietly36. A. useful B. clear C. secret D. important37. A. encouraged B. surprised C. touched D. shocked38. A. hid B. built C. put D. saw39. A. lives B. troubles C. food D. memory40. A. days B. hours C. minutes D. seconds答题卡班级：姓名：得分：一. 阅读理解 (每小题2分，共40分）二. 完型填空题 ( 每小题1.5分，共30分）三、单词拼写（每小题2分，共20分）1) The teacher (留印象) his students with the sense of humor.2) You should give clear (说明)for all the exercises.3) Canada is divided into (省)instead of states.4) She is pleased with her child’s (行为).5) Mr. Wang made some (改正) in my homework.6) She felt (尴尬) at first when seeing you.7) People enjoy a high level of high (技术).8) You should clear up the (误解).9) I love reading good (叙述)10) Thank you so much. My exam is really____________ ( 失望的)四、语法填空（每小题2分，共20分）A student (call) Li Hua from Gui Zhou talks about his first day at junior High school. He thinks （high） of his new school for the reason as follows. First, the teachers (be) very enthusiastic and friendly. Besides, every classroom has a computer,which is (amaze).What’s (much), the physics classis (real) interesting because her teaching method is different from that of the biology teacher at his Junior High school. The most important is that there are three (time) more girls than boys, but they are (hard-working) than those he has ever (meet). He looks forward to (get) along well with everyone here.五.改错题：（短文中有十处错误，划出来并且把正确的写在下边）（15分）Dear President,I am a Chinese students in Russia. With the 2018 World Cup drawer near, I can not help writing to you .Firstly , I’ll like to suggesting that all the construction work be completed in time so that the players can complete in desirable fields. What’s more ,I did hope that the government can take measures to make the competition safe and our citizens more civilized so that the image of Russia can be protect.Secondly , I want to express his desire to be a volunteer . It is clear that there will be many Chinese football fans then but Chinese is my native language . In addition, I was good at communicating with others and I have good knowledge of Russia . Therefore, I can be a qualified volunteer. I am looking forward to yours reply.Sincerely yours,Qian Wei六. 书面表达（25分）要求：1.字迹工整整洁。
上海建平中学2019-2020学年高三上学期第一次月考数学卷
上海建平中学2019-2020学年高三上学期第一次月考数学卷一、填空题1．（5分）已知集合A={x|x ＜1}，B={x|x ≥0}，则A ∩B= ． 2．（5分）函数f （x ）=log 2（x ﹣1）的定义域为 ． 3．（5分）当x ＞0时，函数f （x ）=x+x ﹣1的值域为 ．4．（5分）“x ＞1”是“x ＞a ”的充分不必要条件，则实数a 的取值范围是 ． 5．（5分）若函数f （x ）是奇函数，且x ＜0时，f （x ）=x ﹣2，则f ﹣1（3）= ． 6．（5分）已知集合A={x|x 2﹣3x+2≤0，x ∈Z}，B={t|at ﹣1=0}，若A ∪B=A ，则实数a 的取值集合为 ．7．（5分）已知函数f （x ）=lg （ax 2﹣4x+5）在（1，2）上为减函数，则实数a 的取值集合为 ． 8．（5分）已知不等式≤1的解集为A ，若1∉A ，则实数a 的取值范围是 ．9．（5分）设函数f （x ）=ln （1+|x|）﹣，若f （a ）＞f （2a ﹣1），则实数a 的取值范围是 ．10．（5分）若集合A={x|x 2+4x+a=0}，集合B={t|函数f （x ）=4x 2﹣8x+t （4﹣t ）至多有一个零点}，则A ∪B 的元素之和的函数关系式f （a ）= ． 11．（5分）当m ＞0时，方程（mx ﹣1）2﹣=m 在x ∈[0，1]上有且只有一个实根，则实数m 的取值范围是 ． 12．（5分）已知函数f （x ）=，记函数g （x ）=f （x ）﹣t ，若存在实数t ，使得函数g （x ）有四个零点，则实数a 的取值范围是 ．二、选择题13.关于的二元一次方程组，其中行列式为（ ）A ．B ．C ．D ． 14.“要使函数成立，只要不在区间内就可以了”等价于（ ）x y 、50234x y x y +=⎧⎨+=⎩x D 0543-102405430543-()0f x ≥x [],a bA.如果，则B.如果，则C.如果，则D.如果，则15.参数方程 （为参数）所表示的函数是（ ） A.图像关于原点对称 B.图像关于直线对称C.周期为的周期函数D.周期为的周期函数 16.已知椭圆，直线，点，直线交椭圆于两点，则的值为( ) A ．B ．C ．D ． 三、解答题17.如图，在长方体中，.（1）证明直线平行于平面； （2）求直线到平面的距离.18.的内角的对边分别为，已知的面积为.（1）求；（2）若，求的周长19. （1）请根据对数函数来指出函数的基本性质（结论不要求证明），并画出图像；（2）拉普拉斯称赞对数是一项“使天文学家寿命倍増”的发明.对数可以将大数之间的乘除运算简化为加减运算，请证明：；（3）2017年5月23日至27日，围棋世界冠军柯洁与DeepMind 公司开发的程序“AlphaGo ”进行三局人机对弈，以复杂的围棋来测试人工智能.围棋复杂度的上限约为，而根据有()0f x ≥[],x a b ∉[],x a b ∈()0f x <()0f x <[],x a b ∈[],x a b ∉()0f x ≥()()sin 1cos x a t t y a t ⎧=-⎪⎨=-⎪⎩0,a t >()y f x =x π=2a π2aπ22:143x y C +=:1l y x =-()1,0P l C A B 、22PA PB+321493244932749330491111ABCD A B C D -12,1,1AB AD A A ===1BC 1D AC 1BC 1D AC ABC ∆,,A B C ,,a b c ABC ∆23sin a Asin sin B C ⋅6cos cos 1,3B C a ⋅==ABC ∆()()1a x log x a f >=((1))x g x log a a >=0,1,,0()()a a a log x y log x log a a x y y +>≠>=⋅3613M =关资料，可观测宇宙中普通物质的原子总数约为.甲、乙两个同学都估算了的近似值，甲认为是,乙认为是.现有两种定义： ①若实数满足，则称比接近；②若实数，且，满足，则称比接近；请你任选取其中一种定义来判断哪个同学的近似值更接近，并说明理由.20.已知数列和的通项公式分别为，将集合中的元素从小到大依次排列，构成数列；将集合中的元素从小到大依次排列，构成数列.（1）求数列的通项公式； （2）求数列的通项公式；（3）设数列的前项和为，求数列的通项公式.21.如图，已知曲线，曲线，是平面上一点，若存在过点的直线与都有公共点，则称为“型点”.（1）证明：的左焦点是“型点”；8010N =MN73109310x y 、x m y m ->-y x m x y m 、、10,10,10s t u x y m ===s u t u ->-y x m MN{}n a {}n b ()*36,27n n a n b n n N =+=+∈{}*,n x x a n N =∈⋃{}*,nx x b n N =∈123,,,,,n c c c c {}*,n x x a n N =∈⋂{}*,nx x b n N =∈123,,,,,n d d d d {}n d ()h n {}n c ()f n {}n c n n S {}n S ()g n 221:12x C y -=2:1C y x =+P P 12C C 、P 12C C-1C 12C C -（2）设直线与有公共点，求证：，进而证明原点不是“型点”； （3）求证：内的点都不是“型点”.上海建平中学2019-2020学年高三上学期第一次月考数学卷试卷答案一、填空题1．（5分）已知集合A={x|x ＜1}，B={x|x ≥0}，则A ∩B= [0，1） ． 【分析】根据交集的定义写出A ∩B ． 【解答】解：集合A={x|x ＜1}， B={x|x ≥0}，则A ∩B={x|0≤x ＜1}=[0，1）． 故答案为：[0，1）．2．（5分）函数f （x ）=log 2（x ﹣1）的定义域为 （1，+∞） ． 【分析】根据对数函数的真数大于0，列出不等式求解集即可． 【解答】解：对数函数f （x ）=log 2（x ﹣1）中， x ﹣1＞0， 解得x ＞1；∴f （x ）的定义域为（1，+∞）． 故答案为：（1，+∞）．3．（5分）当x ＞0时，函数f （x ）=x+x ﹣1的值域为 [2，+∞） ． 【分析】直接利用基本不等式求得函数f （x ）=x+x ﹣1的最小值得答案． 【解答】解：∵x ＞0， ∴f （x ）=x+x ﹣1=x+．当且仅当x=1时，上式“=”成立． ∴函数f （x ）=x+x ﹣1的值域为[2，+∞）． 故答案为：[2，+∞）．4．（5分）“x ＞1”是“x ＞a ”的充分不必要条件，则实数a 的取值范围是 a ＜1 ．y kx =2C 1k >12C C -(){},1x y x y +<12C C -【分析】根据充分条件和必要条件的定义结合不等式的关系进行判断即可．【解答】解：若“x＞1”是“x＞a”的充分不必要条件，则a＜1，故答案为：a＜1．5．（5分）若函数f（x）是奇函数，且x＜0时，f（x）=x﹣2，则f﹣1（3）= 1 ．【分析】由已知可得x＞0时，f（x）=x+2，若f﹣1（3）=a，则f（a）=3，进而得到答案．【解答】解：∵函数f（x）是奇函数，且x＜0时，f（x）=x﹣2，故x＞0时，﹣x＜0，f（﹣x）=﹣x﹣2=﹣f（x），即f（x）=x+2，若f﹣1（3）=a，则f（a）=3，当a＜0时，f（a）=a﹣2=3，即a=5（舍去）当a＞0时，f（a）=a+2=3，即a=1，故f﹣1（3）=1故答案为：16．（5分）已知集合A={x|x2﹣3x+2≤0，x∈Z}，B={t|at﹣1=0}，若A∪B=A，则实数a的取值集合为{0，，1} ．【分析】求出集合A={1，2}，B={t|at﹣1=0}，A∪B=A，从而B⊆A，当a=0时，B=∅，成立；当a≠0时，B={}，由B⊆A，得=1或，由此能求出实数a的取值集合．【解答】解：∵集合A={x|x2﹣3x+2≤0，x∈Z}={x|1≤x≤2}={1，2}，B={t|at﹣1=0}，A∪B=A，∴B⊆A，当a=0时，B=∅，成立；当a≠0时，B={}，∵B⊆A，∴=1或，解得a=1或a=，∴实数a的取值集合为{0，，1}．故答案为：{0，，1}．7．（5分）已知函数f（x）=lg（ax2﹣4x+5）在（1，2）上为减函数，则实数a的取值集合为（，1] ．【分析】讨论a=0、a＞0和a＜0时，函数f（x）在（1，2）上为减函数实数a满足的条件是什么．【解答】解：a=0时，函数f（x）=lg（﹣4x+5），应满足﹣4x+5＞0，解得x＜，不满足题意；a＞0时，由题意知，解得＜a≤1；a＜0时，由题意知，此时无解；综上，函数f（x）=lg（ax2﹣4x+5）在（1，2）上为减函数，实数a的取值集合是（，1]．故答案为：（，1]．8．（5分）已知不等式≤1的解集为A，若1∉A，则实数a的取值范围是（0，1] ．【分析】求出不等式中x的范围，根据1∉A，求出a的范围即可．【解答】解：∵≤1，∴≤0，∴或，解得：0＜x＜a，而1∉A，故a∈（0，1]，故答案为：（0，1]．9．（5分）设函数f（x）=ln（1+|x|）﹣，若f（a）＞f（2a﹣1），则实数a的取值范围是（，1）．【分析】根据题意，分析可得函数f（x）为偶函数，且在区间（0，+∞）上为增函数，据此可以将不等式f（a）＞f（2a﹣1）转化为|a|＞|2a﹣1|，解可得a的取值范围，即可得答案．【解答】解：根据题意，函数f（x）=ln（1+|x|）﹣，分析可得f（﹣x）=f（x），即函数f（x）为偶函数，又由当x＞0时，y=ln（1+|x|）=ln（1+x）和y=﹣都是增函数，则函数f（x）在（0，+∞）上为增函数，若f（a）＞f（2a﹣1），则有|a|＞|2a﹣1|，变形可得：a2＞4a2﹣4a+1，解可得＜a＜1，即a的取值范围是（，1）；故答案为：（，1）．10．（5分）若集合A={x|x2+4x+a=0}，集合B={t|函数f（x）=4x2﹣8x+t（4﹣t）至多有一个零点}，则A∪B的元素之和的函数关系式f（a）= ．【分析】求出集合B，讨论a的取值，求出集合A，再求函数f（a）的表达式．【解答】解：集合A={x|x2+4x+A=0}，集合B={t|函数f（x）=4x2﹣8x+t（4﹣t）至多有一个零点}={t|64﹣16t（4﹣t）≤0}={t|t=2}={2}，△=16﹣4a，a＞4时，△＜0，方程x2+4x+a=0无解，A=∅；f（a）=2；a=4时，△=0，方程x2+4x+a=0有一解﹣2，A={﹣2}；f（a）=﹣2+2=0；a=﹣12时，△=64，方程x2+4x+a=0有两解﹣6和2，A={2，﹣6}；f（a）=2﹣6=﹣4；a∈（﹣∞，﹣12）∪（﹣12，4）时，△=16﹣4a，方程x2+4x+a=0有两解﹣2﹣和﹣2+，A={﹣2﹣，﹣2+}；f（a）=（﹣2﹣）+（﹣2+）+2=2∴函数f（a）=．故答案为：．11．（5分）当m＞0时，方程（mx﹣1）2﹣=m在x∈[0，1]上有且只有一个实根，则实数m的取值范围是（0，1]∪[3，+∞）．【分析】根据题意，由函数的解析式求出f（0）、f（1）的值，由函数零点判定定理可得f （0）f（1）=（1﹣m）（m2﹣3m）≤0，解可得m的取值范围，即可得答案．【解答】解：根据题意，令f（x）=m2x2﹣2mx﹣+1﹣m，有f（0）=1﹣m，f（1）=m2﹣3m，若方程（mx﹣1）2﹣=m在x∈[0，1]上有且只有一个实根，即函数f（x）在区间[0，1]上有且只有一个零点，有f（0）f（1）=（1﹣m）（m2﹣3m）≤0，又由m为正实数，则（1﹣m）（m2﹣3m）≤0⇒（1﹣m）（m﹣3）≤0，解可得0＜m≤1或m≥3，即m的取值范围是（0，1]∪[3，+∞）；故答案为：（0，1]∪[3，+∞）．12．（5分）已知函数f（x）=，记函数g（x）=f（x）﹣t，若存在实数t，使得函数g（x）有四个零点，则实数a的取值范围是（，）．【分析】若存在实数t，使得函数g（x）有四个零点，则a≥t＞0，且a2﹣4a2+4a＞t＞0且，解得答案．【解答】解：若存在实数t，使得函数g（x）有四个零点，则函数y=f（x）与y=t有四个交点，即|x|=t，x≤a，与x2﹣4ax+4a=t各有两个解，故a≥t＞0，且a2﹣4a2+4a＞t＞0且解得：a∈（，），故答案为：（，）二、选择题 13-16: CDCB 三、解答题17. 解：因为为长方体，故，故为平行四边形，故，显然不在平面上，于是直线平行于平面，（2）直线到平面的距离即为点到平面的距离设为考虑三棱锥的体积，以面为底面，可得而中，所以，，即直线到平面的距离为. 18．解：（1）由题意可得，化简可得，根据正弦定理化简可得：（2）由 由余弦定理 又所以故而三角形的周长为19.解:， 基本性质为：定义域：；值域：；单调减区间和 (判断奇偶性、周期性不予给分)1111ABCD A B C D -1111//,AB C D AB C D =11ABC D 11//BC AD B 1D AC 1BC 1D AC 1BC 1D AC B 1D AC h 1ABCD ABC 111121323V ⎛⎫=⨯⨯⨯⨯= ⎪⎝⎭1AD C ∆11AC D C AD ===132AD C S ∆=1312=3233V h h =⨯⨯⇒=1BC 1D AC 2321sin 23sin ABC a S bc A A∆==2223sin a bc A =2222sin 3sin sin sin sin sin 3A B C A B C =⇒=2sin sin 31cos cos 6B C B C ⎧=⎪⎪⇒⎨⎪=⎪⎩()1cos cos sin sin cos cos 2A B B C B C B C =-+=-=3A π⇒=()22221cos 9322b c a A b c bc bc +-==⇒+-=224sin sin sin sin 8sin a bc R B C B C A ⎛⎫=== ⎪⎝⎭b c +=3+()1log log x a g x a x==()()0,11,⋃+∞()(),00,-∞⋃+∞()0,1()1,+∞(渐近线画出和原点挖去，需要都画好才能给满分）（2）证明： 设 即证明完毕（3）采用定义（Ⅰ）:而所以甲同学的近似值更接近 采用定义（Ⅱ）：甲的估值 ，乙的估值 因为， 所以乙同学的近似值更接近20．解：（1 )设，则，即 假设，等式左侧为偶数，右侧为奇数，矛盾， 所以， （2） ∴log ,log ,N M a a N x M y x a y a ==⇒==()log N M N M a x y a a a N M x y +⇒⋅==⇒+=⋅()log log log a a a x y x y ⋅=+361803lg 361lg38092.2410M M N N =⇒=⋅-≈73931010MN⇒<<()361173lg 23lg2361lg3172.54173lg10⋅=+⋅≈<=3611733611731532310231010⇒⋅<⇒⋅<+36136136193739393808080333210101010101010⇒⋅<+⇒-<-MN361803lg 361lg38092.2410M MN N=⇒=⋅-≈737310lg1073⇒=939310lg1093⇒=7393lg10lglg10lg M MN N->-MN()2132166327n k a n n b k -=-+=+==+32k n =-213n n a b --=26627n k a n b k =+==+{}2n n a b ∉()2163n h n a n -==+21323123n n n n n a b b a b ---=<<<4321423141243,,,n n n n n n n n c a c b c a c b -----====∴数列的通项公式 等价形式:，（3）令，由（2）得知：是等差数列 ∴①当时，②当时，③当时，④当时，∴ 等价形式：21．解：（1）的左焦点为， 过的直线与交于，与交于，故的左焦点为“型点”，且直线可以为；（2）直线与有交点，则， 若方程组有解，则必须；{}n c ()()()()()*63436542,6641674k n k k n k f n k N k n k k n k⎧+=-⎪+=-⎪=∈⎨+=-⎪⎪+=⎩()()()()*36216542,674k n k f n k n k k N k n k +=-⎧⎪=+=-∈⎨⎪+=⎩()()()()*31521231642,231442n n k n f n n k k N n n k +⎧=-⎪⎪+⎪==-∈⎨⎪+⎪=⎪⎩43424n n n n e c c c --=++{}n e ()*4n k k N =∈2241233312334n k k n nS S e e e k k +==+++=+=()*41n k k N =-∈21133324n n n n n S S c ++++=-=()*42n k k N =-∈22233324n n n n n S S c ++++=-=()*43n k k N=-∈233213334n n n n n n nS S c c c +++++=---=()()()2*2*333,4,4343332,41,424n nn k k k N g n n n n k k k N ⎧+=-∈⎪⎪=⎨++⎪=--∈⎪⎩()22*221233,412277,41,122113,42121518,43k k n k k k n k g n k N k k n k k k n k ⎧+=⎪+-=-⎪=∈⎨+-=-⎪⎪+-=-⎩1C ()FF x =1C ⎛⎝⎭2C )()1±1C 12C C-x =y kx =2C ()111y kxk x y x =⎧⎪⇒-=⎨=+⎪⎩|1|k >直线与有交点，则， 若方程组有解，则必须故直线至多与曲线和中的一条有交点，即原点不是“型点” （3）以为边界的正方形区域记为.1）若点在的边界上，则该边所在直线与相切，与有公共部分，即边界上的点都是“型点”；2）设是区域内的点，即，假设是“型点”，则存在过点的直线与都有公共点.ⅰ)若直线与有公共点，直线的方程化为，假设，则，可知直线在之间，与无公共点，这与“直线与有公共点”矛盾，所以得到：与有公共点的直线的斜率满足.ⅱ)假设与也有公共点，则方程组有实数解.从方程组得，，由，因为y kx =1C ()222212222y kxk x x y =⎧⇒-=⎨-=⎩212k <y kx =1C 2C 12C C -1x y +=D P Ω1C 2C Ω12C C -()00,P x y Ω001x y +<()00,P x y 12C C -P ()00:l y y k x x -=-12C C、l 2C l 00y kx y kx =+-|1|k ≤0000001kx y kx kx y kx x y x x +-≤++≤++<+l 2:1C y x =+2C l 2C 2C l k |1|k >l 1C 002212y kx y kx x y =+-⎧⎪⎨-=⎪⎩2220000()(124)0)(21k x k y kx x y kx ⎡⎤-----+=⎣⎦()222200222000082128()1y kx y k x k y kx k k ⎡⎤-+∆=-++---⎣=⎦|1|k >001x y +<()()000000011y kx y k x y k y k y k k -≤+⋅<+⋅-=+-<()2200y kx k ⇒-<所以，，即直线与没有公共点，与“直线与有公共点”矛盾，于是可知不是“型点”. 证明完毕另解：令，因为，所以|，即.于是可知的图像是开口向下的抛物线，且对称轴方程为是，因为， 所以在区间上为增函数，在上为减函数.因为，，所以对任意，都有，即直线与没有公共点，与“直线与有公共点”矛盾，于是可知不是“型点”. 证明完毕.2220008)1(y kx k k ⎡⎤--+-<⎣⎦∆=l 1C l 1C P 12C C -()222200002128y kx y k x k ++∆--=()()222000012f k x k kx y y =--+001x y +<01x <2010x -<()f k 00201x y k x =-()()()0000200011111x x x y x x x ⋅-<<--⋅+()f k (),1-∞-()1,+∞()()220000111f x y x y =--≤+-<0()()220000111f x y x y -=+-≤+-<0|1|k >()()20,810f k f k k ⎡⎤<∆=+-<⎣⎦l 1C l 1C P 12C C -。
2019-2020学年建平中学高三上一次月考
2019-2020学年建平中学高三英语质量检测I. Listening ComprehensionSection ADirections: In Section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.e a ladder to help her reach the cup. B.See a doctor about her shoulder.C.Put the cup on a lower shelf.D.Buy a new cupboard.2. A. He has already called Harry. B. Harry knows most of the facts.C. He needs to talk to Harry soon.D. Harry doesn’t have a telephone.3.A.The new doctor lacks experience.B.She disagrees with what the man said.C.The man had better talk with the patients first.D.Patients usually cannot offer a fair evaluation.4. A. Take the man to the station. B. Look after the man’s things.C. Find out when the next bus leaves.D. Show the man the way to the station.5.A.He was good at fixing up bookshelves. B.He helped James build up the furniture.C.James helped him arrange the furniture.D.James helped him with some of the work.6. A. It’s difficult to take photographs indoors.B. The photo album is in the living room.C. Mary has lost the photo album.D. Mary is a good photographer.7. A. The job’s short hours make it impossible for her to refuse.1/ 22B. The job is turning into an excellent opportunity for her.C. She’s looking forward to meeting her new colleagues.D. She refused the position because of the low salary.8. A. He had to do what is necessary in order to learn.B. He doesn’t have to memorize all the vocabulary.C. He knows the whole vocabulary list already.D. He cannot learn much by just memorizing.9. A. It’s not the one he likes. B. He needs a smaller shirt.C. It doesn’t fit him very well.D. He hasn’t had time to try it on yet.10. A. The line for concert tickets is too busy. B. He’s too busy to go to the concert.C. Carl knows the concert is at eight.D. He hasn’t been able to reach Carl.Section B: Passages 15%Directions: In Section B, you will hear two short passages, and one longer conversation and you will be asked several questions on each of the passages and the longer conversation. The passages and the longer conversation will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. In the 19th century. B. In about 1800s.C. In the 18th century.D. In about 2400 BC.12. A. The language used. B. The targeted readers.C. The reputation.D. The length.13. A. The evolution of self-study books.B. The importance of self-study books.C. The difference among self-study books.D. The famous writers of self-study books.2/ 22Questions 14 through 16 are based on the following passage.14. A. The reasons railroad regulations in the U.S.A were changed.B. The safety record of the railroad industry in the U.S.A.C. The financing of railroad construction in the U.S.A.D. The evolution of the railroad industry in the U.S.A.15. A. Safety problems with railroad tracks.B. The growth of the automotive industry.C. The use of oversized freight containers.D. The high cost of meeting various regulations.16. A. It causes less air pollution than other means of transport.B. Its competitors are less considerate of customers.C. It creates great personal fortunes for investors.D. Its business is kept in a traditional way.Questions 17 through 20 are based on the following longer conversation.17. A. To earn money for her tuition.B. To make her dream come true.C. To make preparations for her future job.D. To ensure that she has time for acting work.18. A. Serious. B. Funny. C. Experienced. D. Demanding.19. A. It involves many theories. B. He must get an advanced camera.C. He hasn’t learned physics before.D. It occupies much of his spare time.20. A. He is more willing to do something. B. He has stopped working late.C. He can go to sleep early.D. He feels more relaxed.3/ 22II. Grammar and VocabularySection ADirections: After reading the passage below, fill in the blanks to make the passage coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.Back to School ReformFor schools in the New York City, this school year was met by a particular reform issue. It began in June of 2018, when, as part of an effort to fight the enduring problem of segregation(种族隔离), Mayor Bill de Blasio announced his intention (21) __________the testing requirement should be discontinued for admission to the city’s eight selective “élite” high schools. Then, late last month, the Advisory Group released a report (22) __________ (suggest) that the city rethink its entire approach (23) __________ identifying and educating high-achieving children. More accurately, it recommended replacing the gifted-and-talented programs with new initiatives (24) ___________challenge premature children without relying on a test or academic tracking. However, Asian-American parents fearing that the proposed change (25) __________(disadvantage) their children filed a lawsuit to block it.Testing holds great attraction (26) _________ it is neutral, indifferent to a student’s background and wealth. But this is not (27) __________the current system functions. Success is closely related to socioeconomic advantages and access to test preparation. For example, Asian-American students tend (28) _________(rate) lower on the most subjective parts of college admissions evaluations.It’s not clear what the result of the current debate will be. One thing, however, is certain: the competition for places at New York’s élite schools (29) __________(drive), in part, by a lack of faith in the quality of education in other parts of the system. Also, it is seen as a conflict between different social groups fighting for a system in which their children are (30) ________(likely) to be restricted by discrimination.Section BDirections: Fill in each blanks with a proper word chosen from the box. Each word can be used only once. Note that there is one word more than you need.The Danger of Sharenting4/ 22For the vast majority of people, checking social media involves a mix of expectation and curiosity. The app feeds on a collective ____31____ that we are missing out on something, whether it’s a fabulous party, a pop-up sale, or the mere concept of vacation. But the same dynamic doesn’t quite ____32____ to parents sharing pictures of their young children online. There certainly may be an element of proud boasting: “Admire my little son’s taste in jazz,” etc. But these carefully chosen photos often do little more than help parents escape from a harsh day _____33_____. The isolation of parenthood delivers one to strange places, and you need your tribe. Sharing images on social media makes the experience ____34____, connecting one to a larger world.In his new book Why We Should Think Before We Talk About Our Kids Online, Leah Plunkett, a Harvard psychology professor, argues that “sharenting” happens when an adult transmits private details about a child via digital channels. It ____35_____ a child’s entry into “digital life.” Studies estimate that by 2030 nearly two-thirds of identity-fraud cases affecting today’s children will have been caused by sharenting.For Plunkett, there are a couple of reasons to be concerned about sharenting. On a philosophical level, sharenting exposes children to the larger digital world without their permission, ____36_____ them of a kind of privacy. This feeds into Plunkett’s second, much broader concern. The _____37_____ problem with sharenting is the same with many adult-world privacy issues: the bargain we have made in exchange for these services is that we surrender our data and choose not to imagine the worst-case scenarios. Could things that parents post about children produce real-world ____38_____, in terms of bullying, professional reputation, or future prospects? Today, long before children take their first step, their digital data already travels to “thousands, likely tens of thousands, of human and machine users.” How long will it be until someone ___39_____ the power to predict who a child will become as an adult based on these data points?Plunkett’s concerns made parents reconsider their choices. In the end, Plunkett’s advice is to “make more mindful choices” about digital lives though parenthood is often so ____40____ vague that mindfulness seems impossible.III. Reading ComprehensionSection ADirections: For each blank in the following passage there are four words or phrases marked A,B,C and D. Fill in each blank with the word or phrase that best fits the context.The Last Robot-Proof Job in America?You can get most food, such as warm cookies or vodka, to your doorstep in minutes. But try getting a red snapper (红鲷鱼). Until recently, if you could obtain it, it would likely have been pre-frozen and shipped in from overseas.A new tech startup is aiming to _____41_____this situation. Based inside the Fulton Fish Market, a seafood wholesale market, the startup, called , allows customers across the whole country, both restaurants and individuals, to buy from the market. The fish is shipped _____42_____, rather than frozen, thanks to5/ 22an Amazon advanced logistics system. Mike Spindler, the company’s C.E.O., said recently, “I can get a fish to Warren Buffett, that’s as fresh as if he’d walked down to the pier (码头) and bought it that morning.”There is one thing, _____43_____, that the sophisticated logistics system cannot do: pick out a fish. If Warren Buffett orders a red snapper, the company needs to _____44_____ that his fish is actually red snapper, and not some other. According to the ocean-conservation organization, more than 20% of the seafood in restaurants and grocery stores in America is ____45_____. For this task, the company has employed Robert DiGregorio, a forty-seven-year veteran of the business, who possesses a blend of judgement and ____46_____ knowledge that, so far, computers have yet to replicate.“_____47____ the food-safety stuff, our business could be any market from the last three thousand years of human history,” Spindler told me. He is experienced in the ____48_____ business. When he arrived at the fish market in 2014, people were cautious. “They thought selling fish on the Internet was_____49____.” DiGregorio said, speaking for the fishmongers(鱼贩). “They didn’t see how it could possibly work.” Five years ago, DeGregorio didn’t know how to use a computer, but when the Web-site people arrived at the market, he sensed an opportunity. Together, they’ve created a human-machine fish-buying operation.By 1 a.m. each night, the company collects ____50____ from around the country and sends them to DiGregorio. He heads into the market, carrying his tablet computer. The company’s algorithms（算法）_____51____ data on their sources and can tell DiGregorio, for example, which stall to go to get the best tuna (金枪鱼). The computer is a “learning system,”, so if DiGregorio makes a choice it didn’t ____52_____, it asks,“Was the fish not available? Was it damaged?” All that information is fed back in for next time.Then, what can a fishmonger see that a computer can’t? DeGregorio showed me his part of the _____53____ process. “I’m assessing a few things,” he said. First, _____54____. Fish should have “nice” slime(粘液). Then, smell. He sniffed the air above the box. “when fish goes bad, it smells like ammonia.” Besides, to get the best stuff, “Fishmongers have to have a relationship with you. To trust you.” He added.Is he ever ____55____being replaced by the learning system of computers? DiGregorio shrugged. “By the time they invent a computer that can do what I can do,” he said, “I’ll be dead.”41. A. maintain B. remedy C. substitute D. recognize42. A. free B. overseas C. separate D. fresh43. A. therefore B. otherwise C. however D. thus44. A. ensure B. propose C concede D. remind45. A. overpriced B. misidentified C. displaced D. modified46. A. computer B. cuisine C. fish D. marketing6/ 2247. A. Rather than B. Thanks to C. Except for D. Prior to48. A. fund-raising B. online-grocery C. fish-selling D. non-profit49. A. significant B. worthy C. responsible D. ridiculous50. A. sales B. orders C. alternatives D. statistics51. A. analyze B. supply C. prioritize D. feed52. A. require B. process C. predict D. value53. A. calculation B. decoding C. correction D. selection54. A. smash B. touch C. wipe D. roll55. A. concerned about B. eager forC. delighted withD. capable ofSection BDirections: Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.(A)On the morning of 19 April 1966, a hooded figure was hiding in the bushes near the start line of the Boston Marathon. When the gun went off to start the race, the mysterious person allowed the faster competitors to pass before joining the main group of runners. It wasn’t long before the others noticed that their new companion was a woman.The infiltrator(渗入者) was 23-year-old graduate Roberta ’Bobbi’ Gibb, an experienced runner who had had her application to run denied on the grounds that the Boston Marathon was a Men’s Division race only. Her rejection letter categorically stated: Women aren’t allowed and furthermore are not physiologically able. Having run up to 30 miles a day nearly every day for the two years leading up to the race, Gibb knew that this was not true. She decided it was time attitudes towards women changed, and bought a bus ticket to Boston.Contrary to her father’s fears that she would get hurt in the race, Gibb’s male counterparts showed her nothing but kindness. Once reporters got wind of her participation, the radio began broadcasting news of her progress. Encouraged by adrenalin and the delighted spectators, Gibb was heading for an under three-hour time for the best7/ 22part of the course, but then she began running out of steam. Starved of food and water, her legs began to falter, and her feet became almost too painful to run on. If she hadn’t known that dropping out would have set women’s running back 20 or 30 years, she may not have completed the course. However, the cheering crowds on the last leg of the course succeeded in lifting her spirits, and she sprinted to the finish in a very respectable time of just under three hours and 22 minutes.On finishing the race, Gibb was treated as a hero: she was met by the governor of Massachusetts, her parents were interviewed, newspapers ran articles on her and she was invited to a TV game show. More importantly for her, she had broken the stereotype that women didn’t run marathons. She began getting calls from inspired women who had taken up running themselves, and in 1967 a second female runner competed in the Boston Marathon alongside Gibb. The following year there were five female entrants, and by 1972, the rules had been changed to allow women to compete in all US marathons. However, by then, if you had asked anyone who was the first woman to run the Boston Marathon, they would have given you a completely different name: Kathy Switzer.Twenty-year-old journalist Kathrine Switzer shot to fame after competing against Gibb in the 1967 Boston Marathon. On discovering Switzer had entered the race by pretending to be a man, race director Jock Semple tried to physically remove her, and it was this image of Switzer being attacked while running that stuck in people’s minds. Switzer continued running, finishing second in the 1975 Boston Marathon. Moreover, she became a successful media personality. It took Gibb decade of writing letters to magazines, TV stations and book publishers to set the record straight. But in the end, she succeeded in gaining her due recognition and was retroactively awarded first-place medals for her 1966, 1967 and 1968 races.56.The woman is hiding in the bushes __________.A.to cheer on the best participantsB. so as not to be seen at the starting line.C. in order to watch the race unfoldD. so that she has a better view of the field57. What ultimately drove Gibb to finish the race?A. She didn’t want her plan to backfire(发生意外).B. She wanted her parents to be proud of her.C. She wasn’t willing to disappoint the crowd.D. She couldn’t take the shame of failure.8/ 2258. What does the writer mean when he describes Gibb’s running time as ’respectable’?A. He thinks she could have done better.B. He considers it a standard to aim at.C. He regards it as a good time.D. He can’t believe she ran so well.59. What does the reader discover about Gibb in the fourth paragraph?A. Her reputation grew as the years went by.B. She was corrupted by fame.C. She became a household name.D. Her glory was short-lived9/ 22(B)60.When you find a gift in a geocache, you _________.A.make a note of the gift on the website.B.can borrow the gift, but have to return it.C.are allowed to take the gift if you replace it with something else.D.take a photo of the gift as proof that you have found it10/ 2261.The writer thinks that the most enjoyable kind of geocaching is when _______.A.you have to find a public webcam.B.you have to find a series of geocaches.C.you have to find a geocache and then hide it in a different place.D.you simply have to find one geocache.62. The writer has written the blog mainly to _________.A. suggest that people try geocaching.B. publicise a geocaching event in Sweden.C. warn the reader that geocaching is addictive.D. explain the differences between letterboxing and geocaching.(C)The Occupy Wall Street protest movement has raised serious questions about the role of capitalist institutions, particularly corporations in American society. Well before the first protester set foot in Zucotti Park, a heckler(扰乱分子) urged Mitt Romney to tax corporations rather than people. Romney’s response-- “Corporations are people” stirred a brief but intense controversy. Now thousands of demonstrators have in effect joined the heckler, denouncing(抨击) corporations as “enemies of the people.”Far more important than questions about what corporations are is the question of what attitude we should have toward them. Should we, as corporate public relations statements often suggest, think of them as friends (if we buy and are satisfied with their products) or as family (if we work for them)? Does it make sense to be loyal to a corporation as either a customer or as an employee？More generally, even granted that corporations are not fully persons in the way that individuals are, do they have some important moral standing in our society？My answer to all these questions is no, because corporations have no core dedication to fundamental human values. Such corporations exist as instruments of profit for their shareholders. In fact, left to themselves, they can be serious threats to human values that conflict with the goal of corporate profit. Corporations are a particular threat to truth, a value essential in a democracy, which places a premium on the informed decisions of individual citizens. The corporate threat is most apparent in advertising, which explicitly aims at convincing us to prefer a product regardless of its actual merit. Their defining goal is to generate profit. There are cases when telling the truth is the best means11/ 22to advance corporate profits. In 1982, when seven people in Chicago died from poisoned Tylenol, Johnson & Johnson appealed to its credo, which makes concern for its customers primary corporate goal，and told the entire truth about what had happened. This honesty turned a potential public-relations disaster into a triumph. But Johnson & Johnson’s impressive corporate credo ends by saying, “Our final responsibility is to our stockholders and must make solid profit. The credo is unclear about what happens when there is a conflict between responsible action and long-term profit.None of this means that corporations are evil or that socialism should replace the free-enterprise system. As Michel Foucault said of all power structures, it’s not that corporations are bad but that they are dangerous. The self-serving corporate speech that fills our media and halls of government is particularly dangerous for our democracy. At least for this reason, the Occupy Wall Street protesters are right to distrust corporations.63. Mitt Romney most probably believes that ___________.A. individuals should pay more taxes than corporationsB. corporations should not be forced to pay more taxesC. people should care more about corporations’ developmentD. corporations should enjoy all the legal rights as people do64. According to Paragraphs 2 and 3, it can be inferred that corporations ___________.A. should be set as moral examples of the societyB. take employees’ faithfulness as part of their goalsC.contribute little to the most essential human valuesD.are actually means by which people share profits65. The 1982 event is cited in Paragraph 3 to illustrate that _____________A. corporations always make profits at the expense of people’s healthB. customers should always keep an eye on the quality of any productC. corporations take economic profit as their priority essentiallyD. corporation profit is always in contradiction with customer interests12/ 2266. Which of the following is the best title for the text?A.Corporations, People and TruthB.Corporations Are Different from PeopleC.Corporations Are UntrustworthyD.The Occupy Wall Street ProtestSection CDirections: Read the following passage. Fill in each blank with a proper sentence given in the box. Each sentence can be used only once. Note that there are two more sentences than you need.A Different Type of Phone BookAlthough books are still popular with teenagers, most of them spend more of their leisure time staring at their phone than reading a paperback. And the more versatile phones become, the more reasons young people have for looking at them. 67. _______ Instead of publishing whole book at once, they produce very short chapters, which they send once a week to their readers by text message. Some even claim that this style of writing represents a new literary genre: the ‘cell phone novel’.Although the idea originated in Japan, cell phone novels have also sprung up in the rest of East Asia, Europe and Africa. Many are written by high school or university students who are very familiar with the topics that teenagers are interested in. Common themes are love, tragedy and betrayal, and the stories often deal with difficult or13/ 22controversial issues. Twenty-one-year-old Rin said that she started her novel If You during her final year at high school and explained that was the tragic love story of two childhood friends.Rin wrote her novel over a six-month period in spare moments, often while commuting on the train. 68. __________Readers then voted her novel the best that year and she was offered book contract. Her book sold 40,000 copies and was number five in the Japanese bestseller list. Rin said that her mother had had no idea that she had been writing a novel and was therefore very surprised when she saw a book with her daughter’s name on it.The style of cell phone novels has evolved to suit the medium. Chapters have no more than 200 words, and often just 50-100 words. 69. __________ The text mostly consists of dialogue and the language is direct, conveying a lot in a few words. Many cell phone novelists had never written fiction before and many of their readers have never read normal novel. Other rules have evolved; for example, authors only have one name and that is a pseudonym or pen name.In 2009, a young Japanese writer called Takatsu, who lives in Canada, began writing the first English language cell phone novel, Secondhand Memories. Each instalment appeared on , a website dedicated to cell phone stories. Takatsu had read an English translation of Rin’s story If You and had been impressed by its simple and emotional language. It was a feature he deliberately copied when he started writing Secondhand Memories. 70. ___________ He now believes that, in English, cell phone novels have a powerful and poetic identity of their own. Takatsu sees himself, and the other writers who contribute to , as part of a literary movement which blends drama, technology, pop culture and social media. Cell phone novels encourage young people to engage in fiction, even those who would not normally pick up a book. They could be described as teen novels for the 21st century.IV. Summary WritingDirections: Read the following passage. Summarize the main idea and the main point(s) of the passage in no more than 60 words. Use your own words as far as possible.71. Early Adopters Fall into a Costly TrapBeing among the first to try out a new piece of technology is cool. When you’re the only member of your social circle with the latest hot device, people stare in fascination. However, people tend to underestimate the costs of this temporary coolness, which they pay in more ways. Frankly speaking, early adoption is a bad investment. The earliest versions of devices are not only expensive, they are also the most expensive that those devices will ever be. Companies are attempting to recover the cost of production as fast as they can, and once the profits from early adopters’ purchases are safely in their hands, they can cut the price and shift to the next marketing stage: selling the product to everyone else. This is why the cost of the original iPhone dropped about $200 only eight months after its14/ 22release.Those who are first to leap into a new technology also risk wasting money and time on something that will never catch on. In 2006, HD DVDs, a new format for video, entered the market. A few eager consumers bought HD DVD players that were discontinued in early 2008. The early adopters were then stuck with pricey devices that just sat on their shelves collecting dust.Another good reason to resist the early adoption temptation is that the first version of a product typically has imperfections. For example, when Microsoft’s game machine, Xbox One, was first released in 2013, users immediately began to complain of problems. Devoted gamers worked to find and share solutions to these issues. Such problems are so common with new technology that early adopters are basically unpaid testers.So don’t join the first wave of consumers who invest in the latest version of device; instead, wait and see.V. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.72. 每个人都应该为慈善出一份力，这无关地位和财富。
2019-2020学年上海市浦东新区建平中学高一(上)9月月考数学试卷
2019-2020学年上海市浦东新区建平中学高一（上）9月月考数学试卷试题数：16.满分：01.（填空题.3分）已知{2.3.5}⊆A⫋{2.3.5.7.11.13}.那么满足条件的集合A的个数是___ ．2.（问答题.3分）将集合A∩C∩∁U B在图中用阴影部分表示出来．3.（填空题.3分）命题“若a=1且b=2.则a+b＜5．”的否命题是___ ．4.（填空题.3分）已知A={（x.y）|x+y-4=0}B={（x.y）|x+ay-1=0}.若A∩B=∅.则实数a的值为___ ．5.（填空题.3分）设集合A={x.xy.xy-1}其中x∈Z.y∈Z且y≠0．若0∈A.则用列举法表示集合A=___ ．6.（填空题.3分）设集合A={x|x2+x-6=0}.B={x|mx+1=0}.则满足B⊆A的实数m的值所成集合为___ ．7.（填空题.3分）已知A.B均为集合U={1.3.5.7.9}的子集.且A∩B={3}.（∁U B）∩A={9}.则A=___ ．8.（填空题.3分）建平中学2019年的“庆国庆930”活动正如火如荼准备中.高一某班学生参加大舞台和风情秀两个节目情况如下：参加风情秀的人数占该班全体人数的八分之三；参加大舞台的人数比参加风情秀的人数多3人：两个节目都参加的人数比两个节目都不参加的学生人数少7人.则此班的人数为___ ．9.（填空题.3分）已知集合A={1.2.3}.B={E|E⊆A}.令|E|表示数集E中所有元素的和.对集合B中所有元素均求|E|.则这些|E|的值的和为___ ．10.（单选题.3分）若“不积跬步.无以至千里”是真命题.则下面的命题一定是真命题的是（）A.积硅步一定可以至千里B.不积跬步也可能至千里C.要想至千里一定要积硅步D.不想至千里就不用积硅步11.（单选题.3分）若U为全集.A、B为非空集合.下面四个命题：（1）A∩B=A；（2）A∪B=B；（3）A∩∁U B=∅；（4）∁U A∪B=U．其中与命题A⊆B等价的命题个数有（）A.1个B.2个C.3个D.4个12.（单选题.3分）A={x|x=2k.k∈Z}.B={x|x=2k+1.k∈Z}.C={x|x=4k+1.k∈Z}.又a∈A.b∈B.则（）A.a+b∈AB.a+b∈BC.a+b∈CD.a+b∈A.B.C中的任一个13.（问答题.0分）证明：“已知a、b∈R.若a2+2ab+b2+a+b-2≠0.则a+b≠1．”为真命题．14.（问答题.0分）已知全集为R.集合A={x|x＜a-1}.B={x|x＞a+2}.C={x|x≤1或x＞4}．若∁R （A∪B）∪C=C.求实数a的取值范围．15.（问答题.0分）已知命题p：关于x的不等式mx-1≥0的解集为A.且2∈A；命题q：关于x 的方程x2-2x+m=0有两个不相等的正实数根．（1）若命题p为真命题.求实数m的范围；（2）若命题P和命题q中至少有一个是假命题.求实数m的范围．16.（问答题.0分）称正整数集合 A={a1.a2.….a n}（1≤a1＜a2＜…＜a n.n≥2）具有性质 P：如果两数中至少有一个属于 A．对任意的i.j（1≤i≤j≤n）.a i a j与a ja i（1）分别判断集合{1.3.6}与{1.3.4.12}是否具有性质 P；（2）设正整数集合 A={a1.a2.….a n}（1≤a1＜a2＜…＜a n.n≥2）具有性质 P．证明：对任意1≤i≤n（i∈N*）.a i都是a n的因数；（3）求a n=30时n的最大值．2019-2020学年上海市浦东新区建平中学高一（上）9月月考数学试卷参考答案与试题解析试题数：16.满分：01.（填空题.3分）已知{2.3.5}⊆A⫋{2.3.5.7.11.13}.那么满足条件的集合A的个数是___ ．【正确答案】：[1]7【解析】：由题意可知.满足条件的集合A的个数相当于{7.11.13}的真子集的个数.可求【解答】：解：∵{2.3.5}⊆A⫋{2.3.5.7.11.13}.那么满足条件的集合A的个数相当于{7.11.13}的真子集的个数.有7个故答案为：7．【点评】：本题主要考查了集合的包含关系及集合子集个数的判断.属于基础试题》2.（问答题.3分）将集合A∩C∩∁U B在图中用阴影部分表示出来．【正确答案】：【解析】：根据集合的基本运算.结合Venn图进行表示即可．【解答】：解：由集合交集的定义知阴影部分位于B的外侧.同时在集合A和C的内部.对应的阴影部分如图：【点评】：本题主要考查Venn图的表示.利用Venn图表示集合关系是解决本题的关键．比较基础．3.（填空题.3分）命题“若a=1且b=2.则a+b＜5．”的否命题是___ ．【正确答案】：[1]若a≠1或b≠2.则a+b≥5【解析】：根据命题“若p.则q”的否命题是“若￢p.则￢q”.写出它的否命题即可．【解答】：解：若a=1且b=2.则a+b＜5．的否命题是：若a≠1或b≠2.则a+b≥5.故答案为：若a≠1或b≠2.则a+b≥5．【点评】：本题考查了四种命题之间的关系.解题时应熟记四种命题之间的关系是什么.是简单题．4.（填空题.3分）已知A={（x.y）|x+y-4=0}B={（x.y）|x+ay-1=0}.若A∩B=∅.则实数a的值为___ ．【正确答案】：[1]1【解析】：根据A∩B=∅即可得出：直线x+y-4=0和直线x+ay-1=0平行.从而得出a=1．【解答】：解：∵A∩B=∅.∴直线x+y-4=0和直线x+ay-1=0平行.∴a=1．故答案为：1．【点评】：考查描述法的定义.以及交集的定义及运算.直线平行时.直线的斜率相等．5.（填空题.3分）设集合A={x.xy.xy-1}其中x∈Z.y∈Z且y≠0．若0∈A.则用列举法表示集合A=___ ．【正确答案】：[1]{-1.1.0}【解析】：根据题意可得出xy=1.再根据x∈Z.y∈Z即可得出x=-1.y=-1.从而可用列举法表示集合A．【解答】：解：据题意知.xy=1.又x∈Z.y∈Z.∴x=-1.y=-1.∴A={-1.1.0}．故答案为：{-1.1.0}．【点评】：考查列举法的定义.元素与集合的关系.以及集合元素的互异性．6.（填空题.3分）设集合A={x|x2+x-6=0}.B={x|mx+1=0}.则满足B⊆A的实数m的值所成集合为___ ．【正确答案】：[1]{0. 13 .- 12}【解析】：由B⊆A.可分B=∅和B≠∅两种情况进行讨论.根据集合包含关系的判断和应用.分别求出满足条件的a值.并写成集合的形式即可得到答案．【解答】：解：∵A={x|x2+x-6=0}={-3.2}又∵B⊆A当m=0.mx+1=0无解.故B=∅.满足条件若B≠∅.则B={-3}.或B={2}.即m= 13 .或m=- 12故满足条件的实数m∈{0. 13 .- 12}故答案为{0. 13 .- 12}【点评】：本题考查的知识点是集合的包含关系判断及应用.本题有两个易错点.一是忽B=∅的情况.二是忽略题目要求求满足条件的实数a的取值集合.而把答案没用集合形式表示．7.（填空题.3分）已知A.B均为集合U={1.3.5.7.9}的子集.且A∩B={3}.（∁U B）∩A={9}.则A=___ ．【正确答案】：[1]{3.9}【解析】：由韦恩图可知.集合A=（A∩B）∪（C U B∩A）.直接写出结果即可．【解答】：解：因为A∩B={3}.所以3∈A.又因为C U B∩A={9}.所以9∈A.本题也可以用Venn图的方法帮助理解．故答案为：{3.9}．【点评】：本题考查了集合之间的关系、集合的交集、补集的运算.考查了同学们借助于Venn 图解决集合问题的能力．8.（填空题.3分）建平中学2019年的“庆国庆930”活动正如火如荼准备中.高一某班学生参加大舞台和风情秀两个节目情况如下：参加风情秀的人数占该班全体人数的八分之三；参加大舞台的人数比参加风情秀的人数多3人：两个节目都参加的人数比两个节目都不参加的学生人数少7人.则此班的人数为___ ．【正确答案】：[1]40【解析】：由card（A∪B）=card（A）+card（B）-card（A∩B）.然后根据集合的运算求解即可．【解答】：解：设U={x|x是建平中学高一某班学生}.A={x|x是该班参加大舞台的学生}.B={x|x是该班参加风情秀的学生}．设该班两个节目都参加的人数为x.只参加风情秀的人数为y．由题可知.(x+7+y+3+x+y)由图可知. x+y=38∴x+y=15.∴该班总人数为40人．故答案为：40．【点评】：本题主要考查Venn图的应用及集合的基本运算.利用图象先确定集合关系是解决本题的关键.比较基础．9.（填空题.3分）已知集合A={1.2.3}.B={E|E⊆A}.令|E|表示数集E中所有元素的和.对集合B 中所有元素均求|E|.则这些|E|的值的和为___ ．【正确答案】：[1]24【解析】：由题意可得.B={E|E⊆A}={∅.{1}.{2}.{3}.{1.2}.{1.3}.{2.3}.{1.2.3}}.即可求解．【解答】：解：由题意可得.B={E|E⊆A}={∅.{1}.{2}.{3}.{1.2}.{1.3}.{2.3}.{1.2.3}}.∴对集合B中所有元素均求|E|.可得|E|的值的和1+2+3+（1+2）+（1+3）+（2+3）+（1+2+3）=24．故答案为：24．【点评】：本题主要考查了集合包含关系的简单应用.属于基础试题．10.（单选题.3分）若“不积跬步.无以至千里”是真命题.则下面的命题一定是真命题的是（）A.积硅步一定可以至千里B.不积跬步也可能至千里C.要想至千里一定要积硅步D.不想至千里就不用积硅步【正确答案】：C【解析】：根据命题与逆否命题真假性相同.由原命题得到其逆否命题即为真命题．【解答】：解：原命题的逆否命题为：若至千里.则积硅步.故C正确.故选：C．【点评】：本题考查了四种命题及其真假性的关系.主要考查了互为逆否命题的两命题真假性相同.属于基础题．11.（单选题.3分）若U为全集.A、B为非空集合.下面四个命题：（1）A∩B=A；（2）A∪B=B；（3）A∩∁U B=∅；（4）∁U A∪B=U．其中与命题A⊆B等价的命题个数有（）A.1个B.2个C.3个D.4个【正确答案】：D【解析】：利用集合的运算性质、集合之间的关系即可判断出结论．【解答】：解：U为全集.A、B为非空集合.下面四个命题：（1）A∩B=A⇔A⊆B；（2）A∪B=B⇔A⊆B；（3）A∩∁U B=∅.∀x∈A.则x∉∁U B.∴x∈B.∴A∩∁U B=∅⇔A⊆B；（4）∁U A∪B=U.∀x∈A.则x∉∁U A.∴x∈B.∴∁U A∪B=U⇔A⊆B．其中与命题A⊆B等价的命题个数有4．故选：D．【点评】：本题考查了集合的运算性质、集合之间的关系、简易逻辑的判定方法.考查了推理能力与计算能力.属于中档题．12.（单选题.3分）A={x|x=2k.k∈Z}.B={x|x=2k+1.k∈Z}.C={x|x=4k+1.k∈Z}.又a∈A.b∈B.则（）A.a+b∈AB.a+b∈BC.a+b∈CD.a+b∈A.B.C中的任一个【正确答案】：B【解析】：利用集合元素和集合之间的关系.表示出a.b.然后进行判断即可．【解答】：解：∵a∈A.b∈B.∴设a=2k1.k1∈Z.b=2k2+1.k2∈Z.则a+b=2k1+2k2+1=2（k1+k2）+1∈B．故选：B．【点评】：本题主要考查集合元素和集合之间的关系的判断.比较基础．13.（问答题.0分）证明：“已知a、b∈R.若a2+2ab+b2+a+b-2≠0.则a+b≠1．”为真命题．【正确答案】：【解析】：原命题不好证明.利用逆否命题的等价性进行证明即可【解答】：证明：若a+b=1.则a2+2ab+b2+a+b-2=（a+b）2+（a+b）-2=1+1-2=0成立. ∴根据逆否命题的等价性可知：若a2+2ab+b2+a+b-2≠0.则a+b≠1．【点评】：本题主要考查命题的证明.利用原命题和逆否命题的等价性转换为证明逆否命题是解决本题的关键．14.（问答题.0分）已知全集为R.集合A={x|x＜a-1}.B={x|x＞a+2}.C={x|x≤1或x＞4}．若∁R （A∪B）∪C=C.求实数a的取值范围．【正确答案】：【解析】：根据集合并集运算.以及集合关系转化为∁R（A∪B）⊆C.建立不等式关系进行求解即可．【解答】：解：∵A={x|x＜a-1}.B={x|x＞a+2}.∴A∪B={x|x＜a-1或x＞a+2}.则∁R（A∪B）={x|a-1≤x≤a+2}.∵∁R（A∪B）∪C=C.∴∁R（A∪B）⊆C.则a+2≤1或a-1＞4.得a≤-1.或a＞5.即实数a的取值范围是a≤-1.或a＞5．【点评】：本题主要考查集合的基本运算.结合集合的基本运算转化为集合关系是解决本题的关键．15.（问答题.0分）已知命题p：关于x的不等式mx-1≥0的解集为A.且2∈A；命题q：关于x 的方程x2-2x+m=0有两个不相等的正实数根．（1）若命题p为真命题.求实数m的范围；（2）若命题P和命题q中至少有一个是假命题.求实数m的范围．【正确答案】：【解析】：命题p ：关于x 的不等式mx-1≥0的解集为A.且2∈A .可得2m-1≥0.解得m 范围；命题q ：关于x 的方程x 2-2x+m=0有两个不相等的正实数根.可得 {f (0)＞0f (1)＜0.解得m 范围． （1）由命题p 为真命题.即可得出实数m 的范围．（2）由命题P 和命题q 中都是真命题.解得m 范围．进而得出当命题P 和命题q 中至少有一个是假命题时的实数m 的范围．【解答】：解：命题p ：关于x 的不等式mx-1≥0的解集为A.且2∈A .则2m-1≥0.解得m ≥12 ； 命题q ：关于x 的方程x 2-2x+m=0有两个不相等的正实数根.则 {f (0)＞0f (1)＜0 .解得0＜m ＜1． （1）由命题p 为真命题.∴实数m 的范围是 [12，+∞) ；（2）由命题P 和命题q 中都是真命题.则 {m ≥120＜m ＜1.解得 12≤ m ＜1． 可得：命题P 和命题q 中至少有一个是假命题.则m ＜12 .或m≥1．∴实数m 的范围是m ＜12 .或m≥1．【点评】：本题考查了不等式的解法、函数的性质、简易逻辑的判定方法.考查了推理能力与计算能力.属于中档题．16.（问答题.0分）称正整数集合 A={a 1.a 2.….a n }（1≤a 1＜a 2＜…＜a n .n≥2）具有性质 P ：如果对任意的i.j （1≤i≤j≤n ）.a i a j 与 aj a i 两数中至少有一个属于 A ． （1）分别判断集合{1.3.6}与{1.3.4.12}是否具有性质 P ；（2）设正整数集合 A={a 1.a 2.….a n }（1≤a 1＜a 2＜…＜a n .n≥2）具有性质 P ．证明：对任意1≤i≤n （i∈N *）.a i 都是a n 的因数；（3）求a n =30时n 的最大值．【正确答案】：【解析】：（1）根据性质P ；对任意的i.j （1≤i≤j≤n ）.a i a j 与 a ja i 两数中至少有一个属于A.验证给的集合集{1.3.6}与{1.3.4.12}中的任何两个元素的积商是否为该集合中的元素；（2）运用反证法.结合A 具有性质P.即可得证；（3）运用30的质因数分解.结合性质P.即可得到n 的最大值．【解答】：解：（1）由于3×6与 63 均不属于数集{1.3.6}.∴数集{1.3.6} 不具有性质P ； 由于1×3.1×4.1×12.3×4. 123 . 124 都属于数集{1.3.4.12}.∴数集{1.3.4.12} 具有性质P ．（2）证明：设正整数集合 A={a 1.a 2.….a n }（1≤a 1＜a 2＜…＜a n .n≥2）具有性质 P ．即有对任意的i.j （1≤i≤j≤n ）.a i a j 与 a j a i 两数中至少有一个属于A ． 运用反证法证明．假设存在一个数a i 不是a n 的因数.即有a i a n 与 a i a n 或 an a i .都不属于A.这与条件A 具有性质P 矛盾． 故假设不成立．则对任意1≤i≤n （i∈N *）.a i 都是a n 的因数；（3）由（2）可知.a i 均为a n =30的因数.由于30=2×15=3×10=5×6.且对任意的i.j （1≤i≤j≤n ）.a i a j 与 aj a i 两数中至少有一个属于 A ． 由于A 中的最大数为30.最小数为1.若有2.必须含有15；若有3.必须含有10；若有5.必须含有6；不可能同时含有10.15或6.10.或6.15.或6.10.15.若A 中的元素含有5个.则与性质P 矛盾．即有n 的最大值为4．【点评】：本题考查新定义的理解和运用.考查推理能力.以及反证法的运用.组合知识的运用.属于中档题．。
上海市建平中学2019-2020学年第一学期高一数学9月月考试卷(简答)
建平中学高一月考数学卷2019.09一. 填空题1. 已知{2,3,5}{2,3,5,7,11,13}A ⊆⊂，那么满足条 件的集合A 的个数是2. 将集合UACB 在右图中用阴影部分表示出来3. 命题“若1a =且2b =，则5a b +<.”的否命题 是4. 已知{(,)|40}A x y x y =+-=，{(,)|10}B x y x ay =+-=，若A B =∅，则实数a 的值为5. 设集合{,,1}A x xy xy =-，其中x ∈Z ，y ∈Z 且0y ≠. 若0A ∈，则用列举法表示集合6. 设集合2{|60}A x x x =+-=，，若A B ⊆，则实数m 的取 值的集合为7. 已知A 、B 均为集合{1,3,5,7,9}U =的子集，且{3}A B =，{9}UAB =，则集合8. 建平中学2019年的“庆国庆930”活动正如火如荼准备中，高一某班学生参加大舞台和 风情秀两个节目情况如下：参加风情秀的人数占该班全体人数的八分之三；参加大舞台的人 数比参加风情秀的人数多3人；两个节目都参加的人数比两个节目都不参加的学生人数少7 人，则此班的人数为9. 已知集合{1,2,3}A =，{|}B E E A =⊆，令表示数集E 中所有元素的和，对集合B 中所有元素均求，则这些的值的和为二. 选择题10. 若“不积硅步，无以至千里”是真命题，则下面的命题一定是真命题的是（ ） A. 积硅步一定可以至千里 B. 不积硅步也可能至千里 C. 要想至千里一定要积硅步 D. 不想至千里就不用积硅步 11. 若U 为全集，B A 、为非空集合，下面四个命题： （1）AB A =；（2）A B B =；（3）UAB =∅；（4）UA B U =.其中与命题B A ⊆等价的命题个数有（ ）A. 1个B. 2个C. 3个D. 4个12. 已知集合{|2,}A x x k k ==∈Z ，，{|41,}C x x k k ==+∈Z ，又a A ∈，b B ∈，则必有（ ）A. a b A +∈B. a b B +∈C. a b C +∈D. 以上都不对三. 解答题13. 证明：“已知a 、，若02222≠-++++b a b ab a ，则1≠+b a .”为真命题.14. 已知全集为R ，集合{|1}A x x a =<-，{|2}B x x a =>+，{|1C x x =≤或4}x >. 若()A B C C =R，求实数a 的取值范围.15. 已知命题:p 关于x 的不等式10mx -≥的解集为A ，且2A ∈； 命题:q 关于x 的方程220x x m -+=有两个不相等的正实数根. （1）若命题p 为真命题，求实数m 的范围；（2）若命题p 和命题q 中至少有一个是假命题，求实数m 的范围. 附加题16. 称正整数集合12{,,,}n A a a a =⋅⋅⋅12(1,2)n a a a n ≤<⋅⋅⋅<≥具有性质P ：如果对任意的 、j (1)i j n ≤≤≤，j i a a 与ija a 两数中至少有一个属于A . （1）分别判断集合{1,3,6}与{1,3,4,12}是否具有性质P ；（2）设正整数集合12{,,,}n A a a a =⋅⋅⋅12(1,2)n a a a n ≤<⋅⋅⋅<≥具有性质P ，证明：对任意1i n ≤≤（i ∈*N ），i a 都是n a 的因数； （3）求30n a =时n 的最大值参考答案一. 填空题1. 72. 略3. 若1a ≠或2b ≠，则4. 15. {1,0,1}-6.7. {3,9}8. 40人9.二. 选择题10. C 11. D 12. B三. 解答题13. 逆否命题+因式分解+代入计算14. 1a ≤-或5a >.（子集与推出关系+数轴图）15. （1）12m ≥（根的分布：数形结合+韦达定理）；（2）12m <或1m ≥ 16. （1）{1,3,6}不满足；{1,3,4,12}满足；（2）略（分类讨论或者反证法）；（3）4；301235=⨯⨯⨯，其中1、30定属于集合，因此2、3、5可在可不在， 且2、3、5不可同时出现，所以最大值是4。
上海市建平中学2019-2020学年高一上学期期中考试数学试题
建平中学高一期中数学卷一. 填空题1.已知全集{}5,6,7,8,9U =，{}6,7,8A =，那么UA________.【答案】{}5,9 【解析】 【分析】根据补集的定义可得出集合UA .【详解】全集{}5,6,7,8,9U =，{}6,7,8A =，由补集的定义可得5,9UA .故答案为：{}5,9.【点睛】本题考查补集的计算，考查对补集定义的理解，属于基础题. 2.不等式2101x x +<-的解集是________. 【答案】112x x ⎧⎫-<<⎨⎬⎩⎭【解析】 【分析】将分式不等式等价变形为()()2110x x +-<，解此不等式即可. 【详解】不等式2101x x +<-等价于()()2110x x +-<，解得112x -<<， 因此，不等式2101x x +<-的解集是112x x ⎧⎫-<<⎨⎬⎩⎭.故答案为：112x x ⎧⎫-<<⎨⎬⎩⎭. 【点睛】本题考查分式不等式的求解，考查运算求解能力，属于基础题. 3.命题“若0xy ≠，则0x ≠且0y ≠”的逆否命题是________ 【答案】若0x =或0y =，则0xy =. 【解析】 【分析】根据原命题与逆否命题之间的关系可得出答案.【详解】由题意可知，命题“若0xy ≠，则0x ≠且0y ≠”的逆否命题是“若0x =或0y =，则0xy =”.故答案为：若0x =或0y =，则0xy =.【点睛】本题考查逆否命题的改写，解题时要充分了解原命题与逆否命题之间的关系，属于基础题.4.已知函数()222019,0,0x x f x x x ⎧-≤=⎨->⎩，则()2f =________.【答案】4- 【解析】 【分析】根据分段函数()y f x =的解析式可计算出()2f 的值.【详解】()222019,0,0x x f x x x ⎧-≤=⎨->⎩，()2224f ∴=-=-.故答案为：4-.【点睛】本题考查分段函数值的计算，解题时要根据自变量所满足的定义域选择合适的解析式来进行计算，考查计算能力，属于基础题.5.若“x a >”是“5x >”的充分非必要条件，则实数a 的取值范围是________. 【答案】()5,+∞ 【解析】 【分析】根据充分非必要条件关系得出()(),5,a +∞+∞，由此可得出实数a 的取值范围.【详解】“x a >”是“5x >”的充分非必要条件，()(),5,a ∴+∞+∞，则5a >.因此，实数a 的取值范围是()5,+∞. 故答案为：()5,+∞.【点睛】本题考查利用充分不必要条件求参数，一般转化为集合包含关系来求解，考查化归与转化思想的应用，属于基础题.6.若x 、y +∈R ，且4xy =，则4x y +的最小值是________.【答案】8 【解析】 【分析】直接利用基本不等式可求出4x y +的最小值.【详解】由基本不等式可得48x y +≥==，当且仅当4y x =时，等号成立. 因此，4x y +的最小值为8. 故答案为：8.【点睛】本题考查利用基本不等式求最值，在利用基本不等式求最值时，也要注意“一正、二定、三相等”条件的成立，考查计算能力，属于基础题.7.函数y =的定义域是________.【答案】()2,+∞ 【解析】 【分析】根据偶次根式被开方数非负、分式中分母不为零，列出关于x 的不等式组，解出即可得出函数的定义域.【详解】由题意可得2102520x x x -≥⎧⎨-+>⎩，解得2x >.因此，函数y =的定义域是()2,+∞.故答案为：()2,+∞.【点睛】本题考查具体函数定义域的求解，解题时要根据函数解析式有意义列不等式组进行求解，考查计算能力，属于基础题.8.设函数()246,06,0x x x f x x x ⎧-+≥=⎨+<⎩，则不等式()3f x >的解集是________.【答案】()()3,13,-+∞【解析】 【分析】分0x ≥与0x <两种情况解不等式()3f x >，得出不等式的解集与定义域取交集，然后将两段解集取并集可得出()3f x >的解集.【详解】当0x ≥时，由()3f x >，得2463x x -+>，即2430x x -+>，解得1x <或3x >， 此时，01x ≤<或3x >；当0x <时，由()3f x >，得63x +>，解得3x >-，此时，30x -<<. 综上所述，不等式()3f x >的解集是()()3,13,-+∞.故答案为：()()3,13,-+∞.【点睛】本题考查分段不等式的求解，解题时要注意对自变量的取值范围进行分类讨论，在得出不等式的解集后要注意与定义域取交集，考查运算求解能力，属于中等题.9.若函数()f x =的定义域为R ，则实数m 的取值范围是______.【答案】1,4⎡⎫+∞⎪⎢⎣⎭【解析】 【分析】由题意知，对任意的x ∈R ，不等式()221940mx m x m ++++≥恒成立，然后分0m =和m >⎧⎨∆≤⎩两种情况分析，由此可得出实数m 的取值范围. 【详解】由题意可知，对任意的x ∈R ，不等式()221940mx m x m ++++≥恒成立.①当0m =时，则有240x +≥，该不等式在R 上不恒成立；②当0m >时，由于不等式()221940mx m x m ++++≥在R 上恒成立，则()()()224149448210m m m m m ∆=+-+=⨯--+≤，即28210m m +-≥，解得12m ≤-或14m ≥，此时，14m ≥.因此，实数m 的取值范围是1,4⎡⎫+∞⎪⎢⎣⎭.故答案为：1,4⎡⎫+∞⎪⎢⎣⎭.【点睛】本题考查利用函数的定义域求参数，解题的关键就是将问题转化二次不等式在R 上恒成立问题，利用首项系数和判别式的符号来进行求解，考查化归与转化思想的应用，属于中等题.10.若(){}2210,A x x m x x R =+++=∈，且A+=∅R ，则m 的取值范围是________.【答案】()4,-+∞ 【解析】 【分析】由0A ∉，结合题意得出关于x 的方程()2210x m x +++=有负根或无实根，分二次方程有两个相等的负根、两根一正一负、两个负根以及无实根进行分类讨论，可求出实数m 的取值范围.【详解】由于0A ∉，且A+=∅R ，则关于x 的方程()2210x m x +++=有负根或无实根. ①若方程有两个相等的负根时，则()2240202m m ⎧∆=+-=⎪⎨+-<⎪⎩，解得0m =；②若方程的两根1x 、2x 一正一负，则120x x <，事实上1210x x =>，不合乎题意；③若方程的两根1x 、2x 不等，且两根均为负数，则()()212122402010m x x m x x ⎧∆=+->⎪+=-+<⎨⎪=>⎩，解得0m >；④若方程无实根，则()222440m m m ∆=+-=+<，解得40m -<<. 综上所述，实数m 的取值范围是()4,-+∞. 故答案为：()4,-+∞.【点睛】本题考查二次函数根的分布问题，解题时要结合判别式、两根之和与差的符号来进行分析，考查分类讨论思想的应用，属于中等题.11.关于x 的不等式2315x x a a +--≤-的解集不是∅，则实数a 的取值范围为______. 【答案】(][),14,-∞+∞【解析】 【分析】由题意知，存在x ∈R ，使得2315x x a a +--≤-，然后利用绝对值三角不等式求出31x x +--的最小值4-，将问题转化为解不等式254a a -≥-，解出即可.【详解】由题意知，存在x ∈R ，使得2315x x a a +--≤-，则()2min 531a a x x -≥+--.由绝对值三角不等式得()()31314x x x x +--≤+--=，4314x x ∴-≤+--≤，()2min 5314a a x x ∴-≥+--=-，即2540a a -+≥，解得1a ≤或4a ≥.因此，实数a 的取值范围是(][),14,-∞+∞.故答案为：(][),14,-∞+∞.【点睛】本题考查绝对值不等式成立问题，一般转化为绝对值不等式的最值问题，可利用绝对值三角不等式来得到，考查化归与转化思想的应用，属于中等题. 12.已知x、y +∈R ，21x y +=，可以利用不等式1ax x+≥42ay y +≥()0a >求得14x y+的最小值，则其中正数a 的值是________.【答案】9+【解析】 【分析】利用两个基本不等式等号成立的条件得出x 、y 的表达式，代入21x y +=可求出实数a 的值.详解】由基本不等式得1ax x +≥()10,0ax x a x=>>时，即当x =等号成立.由基本不等式得4242ay a y +≥，当且仅当()420,0ay y a y=>>时，即当2y a=时，等号成立. 此时，2212221x y a a a++=+==，则122a =+， 所以，()2122942a =+=+.故答案为：942+.【点睛】本题考查利用基本不等式求最值时等号成立的条件，求出对应的变量后，还应将变量代入定值条件求出参数，考查运算求解能力，属于中等题. 二. 选择题13.对于集合M 、N ，若M N ，则下面集合的运算结果一定是空集的是（ ）A. UMNB.UM NC.UUMN D. M N ⋂【答案】A 【解析】 【分析】作出韦恩图，利用韦恩图来判断出各选项集合运算的结果是否为空集. 【详解】作出韦恩图如下图所示：如上图所示，UM N =∅，UMN ≠∅，U UMN ≠∅，M N M =≠∅.故选：A.【点睛】本题考查集合的运算，在解题时可以充分利用韦恩图法来表示，考查数形结合思想的应用，属于基础题.14.如果a 、b 、c 满足c b a <<，且0ac <，那么下列选项不恒成立的是（ ） A. ab ac > B. 22cb ab < C. ()0c b a -> D. ()0ac a c -<【答案】B 【解析】试题分析：依题意可得，．不等式两边同乘以一个正数不等号方向不变，所以选项A 正确；,,所以()0c b a ->，故选项C 正确；,所以()0ac a c -<，故选项D 正确；当时，选项B 错误．故选B ．考点：证明简单的不等式（或比大小）．15.若集合{}2540A x x x =-+<，{}1B x x a =-<，则“()2,3a ∈”是“B A ⊆”的（ ）A. 充分非必要条件B. 必要非充分条件C. 充要条件D. 既非充分又不必要条件【答案】A 【解析】 【分析】解出集合A 、B ，由B A ⊆得出关于a 的不等式组，求出实数a 的取值范围，由此可判断出“()2,3a ∈”是“B A ⊆”的充分非必要条件.【详解】解不等式2540x x -+<，解得14x <<，{}14A x x ∴=<<.解不等式1x a -<，即11x a -<-<，解得11a x a -<<+，{}11B x a x a ∴=-<<+.B A ⊆，则有1114a a -≥⎧⎨+≤⎩，解得23a ≤≤.因此，“()2,3a ∈”是“B A ⊆”的充分非必要条件. 故选：A【点睛】本题考查充分非必要条件的判断，一般将问题转化为集合的包含关系来判断，考查逻辑推理能力，属于中等题.16.已知A 与B 是集合{}1,2,3,,100的两个子集，满足：A 与B 的元素个数相同，且A B为空集，若n A ∈时总有22n B +∈，则集合A B 的元素个数最多为（ ）A. 62B. 66C. 68D. 74【答案】B 【解析】 【分析】令22100n +≤，解得49n ≤，从A 中去掉形如22n +的数，此时A 中有26个元素，注意A中还可含以下7个特殊元素：10、14、18、26、32、42、46，故A 中元素最多时，A 中共有33个元素，由此可得出结论.【详解】令22100n +≤，解得49n ≤，所以，集合A 是集合{}1,2,3,,49的一个非空子集.再由AB =∅，先从A 中去掉形如()22n n N *+∈的数，由2249n +≤，可得23n ≤，492326-=，此时，A 中有26个元素.由于集合A 中已经去掉了4、6、8、12、16、20、22这7个数，而它们对应的形如22n +的数分别为10、14、18、26、32、42、46，并且10、14、18、26、32、42、46对应的形如22n +的数都在集合B 中.故集合A 中还可有以下7个特殊元素：10、14、18、26、32、42、46，故集合A 中元素最多时，集合A 中共有33个元素，对应的集合B 也有33个元素， 因此，A B 中共有66个元素.故选：B.【点睛】本题考查集合中参数的取值问题，同时也考查了集合中元素的个数问题，考查分类讨论思想的应用，属于中等题. 三. 解答题17.解不等式组()()31150x x x ⎧->⎪⎨--≥⎪⎩.【答案】[)(]1,24,5【解析】 【分析】分别解出两个不等式，然后将两个不等式解集取交集即可得出不等式组的解集.【详解】解不等式31x ->，即31x -<-或31x ->，解得2x <或4x >. 解不等式()()150x x --≥，即()()150x x --≤，解得15x ≤≤.因此，不等式组()()31150x x x ⎧->⎪⎨--≥⎪⎩的解集为[)(]1,24,5.【点睛】本题考查不等式组的解法，涉及绝对值不等式和一元二次不等式的求解，考查运算求解能力，属于基础题.18.已知：a 、b 是正实数，求证：22a ba b b a++≥.【答案】见解析. 【解析】 【分析】由基本不等式得出22a b a b+≥，22b a b a +≥，然后利用同向不等式的可加性可得出证明.【详解】由基本不等式得出2222a a b b a b b +≥⋅=，2222b b a a b a a+≥⋅=，上述两个不等式当且仅当a b =时，等号成立，由同向不等式的可加性得2222a b a b a b b a +++≥+，即22a b a b b a++≥.【点睛】本题考查不等式的证明，考查基本不等式的应用，考查推理论证能力，属于中等题.19.若()f x x x =+，()()02x x g x x--=，()()()F x f x g x =+.（1）分别求()f x 与()g x 的定义域；（2）求()F x 的定义域与值域；（3）在平面直角坐标系内画出函数()F x 的图象，并标出特殊点的坐标. 【答案】（1）()f x 的定义域为()0,∞+，()g x 的定义域为()()0,22,+∞；（2）()F x 的定义域是()()0,22,+∞，()F x 的值域是[)2,+∞；（3）图象见解析. 【解析】 【分析】（1）根据函数解析式有意义列不等式组，由此可得出函数()y f x =和()y g x =的定义域； （2）将函数()y f x =和()y g x =的定义域取交集可得出函数()y F x =的定义域，并求出函数()y F x =的解析式，利用基本不等式可得出函数()y F x =的值域； （3）根据双勾函数的图象可得出函数()y F x =在其定义域上的图象. 【详解】（1）对于函数()f x x =+0x >，则函数()f x x =+的定义域为()0,∞+.对于函数()()02x g x x -=，有20x x x -≠⎧⎪≥⎨⎪≠⎩，解得0x >且2x ≠， 所以，函数()()02x g x x-=的定义域为()()0,22,+∞；（2）()()()1F x f x g x x x x=+==+，定义域为()()0,22,+∞.由基本不等式可得()12F x x x =+≥=，当且仅当1x =时，等号成立. 因此，函数()y F x =的值域为[)2,+∞； （3）函数()1F x x x=+，()()0,22,x ∈+∞为双勾函数图象的一部分，如下图所示：【点睛】本题考查函数的定义域与值域的求解，同时也涉及到了函数图象的画法，解题时要熟悉几种常见的函数，考查分析问题和解决问题的能力，属于中等题.20.设集合{}210A x x =-=，集合{}20,B x x ax b x R =-+=∈，且B ≠∅. （1）若B A ⊆，求实数a 、b 的值； （2）若A C ⊆，且{}21,21,C m m=-+，求实数m 的值.【答案】（1）2a =，1b =或2a =-，1b =或0a =，1b =-；（2）0m =或1m =. 【解析】 【分析】（1）解出集合{}1,1A =-，分集合{}1B =-、{}1、{}1,1-三种情况讨论，结合韦达定理可得出实数a 、b 的值；（2）由A C ⊆可得出211m +=或21m =，并利用集合C 中的元素满足互异性得出实数m 的值. 【详解】（1）{}{}2101,1A x x =-==-，B A ⊆，且B ≠∅，分以下三种情况讨论：①当{}1B =-时，由韦达定理得()212211a b =-⨯=-⎧⎪⎨=-=⎪⎩； ②当{}1B =时，由韦达定理得212211a b =⨯=⎧⎨==⎩； ③当{}1,1B =-时，由韦达定理得()()110111a b ⎧=+-=⎪⎨=⨯-=-⎪⎩.综上所述，2a =，1b =或2a =-，1b =或0a =，1b =-； （2）A C ⊆，且{}21,21,C m m =-+，211m ∴+=或21m =，解得0m =或1m =±.当0m =时，{}1,1,0C =-，集合C 中的元素满足互异性，合乎题意； 当1m =-时，211m +=-，集合C 中的元素不满足互异性，舍去； 当1m =时，{}1,3,1C =-，集合C 中的元素满足互异性，合乎题意. 综上所述，0m =或1m =.【点睛】本题考查利用集合的包含关系求参数，同时也考查了一元二次方程根与系数的关系，解题时要注意有限集中的元素要满足互异性，考查分类讨论思想的应用，属于中等题. 21.按照某学者的理论，假设一个人生产某产品单件成本为a 元，如果他卖出该产品的单价为m 元，则他的满意度为m m a +，如果他买进该产品的单价为n 元，则他的满意度为nn a+，如果一个人对两种交易（卖出或买进）的满意度分别为1h 和2h ，则他对这两种交易的综合满意现假设甲生产A 、B 两种产品的单件成本分别为12元和5元，乙生产A 、B 两种产品的单件成本分别为3元和20元，设产品A 、B 的单价分别为A m 元和B m 元（根据经济学常识，212A m ≤≤，520B m ≤≤），甲买进A 与卖出B 的综合满意度为h 甲，乙卖出A 与买进B 的综合满意度为h 乙.（1）求h 甲和h 乙关于A m 、B m 的表达式，当35A B m m =时，求证：h h =甲乙； （2）设35A B m m =，当A m 、B m 分别为多少时，甲、乙两人的综合满意度均最大？最大的综合满意度为多少？（3）记（2）中最大的综合满意度为0h ，试问能否适当选取A m 、B m 的值，使得0h h ≥甲和0h h ≥乙同时成立？试说明理由.【答案】（1）见解析；（2）当6A m =，10B m =时，甲、乙两人的综合满意度均最大，最大值为23；（3）不存在满足条件的A m 、B m 的值. 【解析】 【分析】（1）表示出甲和乙的满意度，整理出最简形式，在条件35A B m m =时，表示出要证明的相等的两个式子相等；（2）在上一问表示的结果中，整理出关于变量的符合基本不等式的形式，利用基本不等式求出两个人满意度最大时的结果，并且写出等号成立的条件； （3）先写出结论：不能由（2）知023h =，因为49h h ≤甲乙，不能取到A m 、B m 的值，使得0h h ≥甲和0h h ≥乙同时成立，但等号不同时成立. 【详解】（1）甲：买进A 的满意度11212A A h m =+，卖出B 的满意度为15B B B m h m =+.所以，甲买进A 和卖出B的综合满意度为h ===甲乙：卖出A 的满意度为23A A A m h m =+，买进B 的满意度为22020B B h m =+.所以，乙卖出A 和买进B的综合满意度为h ===乙当35A B m m =时，h ==甲.h ==乙h h =甲乙；（2）设()0B m x x =>，当35A B m m =时，h h ====≤甲乙23==，当且仅当100x x =时，即当10x =时，等号成立，即31065A m =⨯=，10B m =时，甲、乙两人的综合满意度最大，最大综合满意度为23； （3）不能由（2）知023h =，因为49h h ⋅≤甲乙， 因此，不能取到A m 、B m 的值，使得0h h ≥甲和0h h ≥乙同时成立，因为等号不同时取到. 【点睛】本题考查函数模型的选择和应用，解题的关键就是理解题意，在求最值时应该根据代数式的机构合理选择，考查分析问题和解决问题的能力，属于中等题.。
上海市建平中学高三化学2020年9月月考试卷 上科版
上海市建平中学高三化学2020年9月月考试卷可能用到的相对原子质量： H-1 N-14 O-16 Cl-35.5Mg-24 Fe-56 Cu-64第Ⅰ卷(共66分)一、 选择题（每小题只有一个．．．．选项符合题意）。
1．禽流感病毒对常用消毒剂十分敏感，容易将其杀灭，如氧化剂、稀酸等等都能迅速破坏其活性。
下列不能杀灭禽流感病毒的物质是A ．H 2O 2溶液B ．NaClO 溶液C ．矿泉水D ．醋酸 2．下列说法正确的是A ．铅笔芯的主要成分是金属铅B ．CO 气体有毒，在生有炉火的居室中多放几盆水，可吸收COC ．含磷洗衣粉的大量使用会造成水体富营养化D ．绿色食品是指使用过化肥和农药生产出来的农副产品3．已知HCl 难溶于4CCl ，如图所示，下列装置中，不适宜于HCl 气体尾气吸收的是4．可以证明次氯酸为弱酸的实验事实是A ．次氯酸具有强氧化性B ．次氯酸不稳定，见光即分离C ．可与强碱发生中和反应D ．其盐可与弱酸发生复分解反应5．用两根石墨电极分别插入盛有氯化铜溶液的 U 形管中，接通电源，则关于与电源正极相连的电极描述正确的是A ．阳极，有Cl 2 放出B ．阴极，有H 2 放出C ．阳极，有O 2 放出D ．阴极，有Cu 覆盖二、 选择题（每小题只有一个．．．．选项符合题意）。
6．2020年10月16日，美国劳伦斯·利弗莫尔国家实验室宣布，美、俄科学家合作，用大量钙－48离子轰击人造元素锎－249，合成了3个新原子X 297118，其存在时间只有0.9毫秒。
下列关于X 297118的说法不正确的是A ．科学家合成了一种新元素B ．该元素X 位于第7周期C ．该元素X 属过渡金属元素D ．X 297118的中子数比电子数多61 7．下列八种试剂中：①酚酞试液 ②银氨溶液 ③稀H 2SO 4 ④Na 2SO 3溶液 ⑤FeCl 3溶液(加少量HCl) ⑥氢硫酸 ⑦Na 2CO 3溶液 ⑧石灰水 都不宜长期放置的组合是A ．②④⑥⑧B ．①②④⑥⑧C ．②③⑤⑦D ．②④⑤8．在右图装置中，烧瓶中充满于燥气体a ，将滴管中的液体b 挤入烧瓶内，轻轻振荡烧瓶，然后打开弹簧夹f ，烧杯中的液体b 呈喷泉状喷出，最终几乎充满 a （干燥气体）b （液体）A 2NO 水B 2CO L mol /4 NaOH 溶液C 2Cl 饱和NaCl 溶液 D3NH浓NaOH 溶液9．在浓度均为 3 mol/L 的盐酸和硫酸各100 mL 溶液中，分别加入等质量的铁粉，充分反应后生成气体质量之比为 3∶4 。
上海市建平中学2024-2025学年高三上学期9月月考英语试卷
上海市建平中学2024-2025学年高三上学期9月月考英语试卷一、语法填空Directions: After reading the passage below, fill in the blanks to make the passage coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.The Trouble with FriendsOn a daily basis, I teach kids. 1 “kids”, I mean teens to college- age, sometimes mid -twenties. Kids talk a lot about their friends, but don’t usually talk about their families. Sometimes I’m taken completely by surprise when, months into our knowing each other, a student mentions 2 (have) a twin. I suppose hearing the constant chatter about friends has made me consider my own, and how hard it can be 3 (maintain) these bonds as an adult. Mostly, what I notice is that I lose more friends than I make.An obvious reason for that is marriage. Friends get married and their spouses become their 4 (close) friends. My husband is now the person I spend the most time with. I tell him everything because I trust him with my thoughts, 5 stupid they may be. I used to be the same way with friends, but when I tell friends something now, I must accept the possibility that they will tell their spouses, 6 I’m friendly but not friends. A friendship is truly strained when you don’t like the spouse. Sometimes this new person is so far removed from 7 you imagined for your friend that you wonder if you knew your friend at all.After marriage, a friend who used to discuss things with you stops doing so, and 8 (update) you only on definitive good news, never the bad, the ugly, or the in- progress. She saves all of that for her partner. In other words, you’re no longer included in the problem- solving. Of course, some matters belong first to the marriage: the stuff of intimacy, finance, family. Increasingly, my friends leave me out of these big conversations, and vice versa, but when 9 outcome is certain, we do update one another, which reminds us that we’re still friends, but with the friendship 10 (reduce) to a PowerPoint.二、选词填空Directions: Fill in each blank with a proper word chosen from the box. Each word can be used only once. Note that there is one word more than you need.Dupes are wearing out Lululemon AthleticaDupes are the products that cost less than the premium (高端的) versions but are of similar style and quality. Less expensive versions of premium products have become a(n) 11 alternative, particularly for younger shoppers.That is becoming a problem for Lululemon Athletica, the company that 12 high-end sportswear and made $100 leggings the norm.“The brand logo doesn’t hold as much appeal as it used to,” said Mikayla Kitsopoulos, a 22- year- old college student. “Finding 13 is the new status symbol.” When Kitsopoulos was in high school, she wore Lululemon leggings, which cost about $100. Now, she buys her leggings on Amazon for about $30. She said the quality and fit is almost 14 , so why pay more?The heightened competition comes as Lululemon has made a series of 15 that have turned off even some of its most devoted fans. Not long ago, it removed a new type of leggings from its stores and website after customers complained about the fit. Other mistakes have included a color palette that was too 16 and not having enough of some products such as smaller size leggings. The misfires have pushed people such as Natalie Assink to 17 seek out different brands. The20-year-old college student said she switched from Lululemon to Gymshark and AYBL not just because their leggings cost less, but also because they have more color varieties.Buying cheaper versions of premium products isn’t new. Boasting about it is. Ellyn Briggs, Moring Consult’s brands analyst, 18 the growing popularity of dupes to inflation but also to the rise of social media. The No. I reason people said they bought dupes was to save money, according to Morning Consult’s survey. They also wanted to test out whether the cheaper versions were as good as the premium 19 and then post about them on TikTok or other platforms. “It’s more than just a transaction,” Briggs said. “They want to share the fact that they have 20a success.”三、完形填空People’s relationship with work is complex and complicated. 21 complaining about the boredom and bureaucracy, the power-crazed bosses and disobedient colleagues, individuals need the security of a job. A century of research has shown that 22 is bad for mental health, leading to depression, anxiety and reduced self-esteem.On average, it has an even greater effect than divorce. But how much work do you need to do? A recent paper by the Centre for Business Research at Cambridge University found that people working reduced working hours or being 23 do not have poorer mental health. What was particularly surprising is how little work was needed to keep people happy. The threshold for good mental health was just one day a week — after that, it seemed to make little difference to individuals’ well-being if they worked eight hours or 48 hours a week. The 24 from working clearly comes from the feeling of purpose, from the social status it creates and from the camaraderie of colleagues engaged in the same tasks.A little bit of work may be 25 , but too much is not. An enterprising junior analyst at Goldman Sachs recently surveyed his 26 . The survey found those first-year analysts had worked an average 98 hours a week since the start of 2021, and only managed five hours of sleep a night. It found that 77% of them had been the subject of 27 , that 75% had sought, or considered seeking counselling, and that, on average, they had suffered sharp declines in mental and physical health.Nevertheless, the general reaction to the story was remarkably 28 . In some people’s eyes, the young analysts should have expected to be 29 in such a fashion; after all, that is why they were being paid so well. The well-experienced analysts of the investment-banking industry thought “It was the same in my day. Never did me any harm.” 30 , it is still hard to see why young analysts should expect to suffer. They joined a bank, not the Mafia.Nor does it make much 31 sense to have employees working so long that they only get to sleep five hours a night. They can hardly be operating 32 when they are dog-tired. That junior professional staff have always worked long hours is not a good explanationfor 33 stress on young people at the start of their careers. It smacks of the legendary navy motto: “The beatings will continue until morale improves.”Clearly, economy cannot 34 if everyone works one day a week. The need to limit excessive working hours was realised back in Victorian times. For much of the 20th century the length of the average working week fell while output continued to climb.There will be occasions when people have to work late or rise early to finish a project. Day after day, however, a long-hours lifestyle is bad for workers’ health. Some organizations may see the 35 for work as a sign of an employee’s willingness to put their job ahead of their families and friends. If so, they don’t need to have better employees. They need better managers. 21．A．With B．Despite C．Against D．Like 22．A．unemployment B．divorce C．complaint D．prosecution 23．A．employed B．suspended C．criticized D．motivated 24．A．secrets B．fatigue C．boost D．assignment 25．A．stressful B．helpless C．creative D．satisfying 26．A．peers B．superiors C．relatives D．advocates 27．A．workplace abuse B．racial discrimination C．cyber bullyingD．peer pressure28．A．predictable B．inevitable C．normal D．unsympathetic 29．A．accommodated B．treated C．paid D．fired 30．A．Conversely B．Therefore C．However D．Likewise 31．A．education B．medicine C．fitness D．business 32．A．at full efficiency B．at a loss C．in others’ shoesD．in low spirits33．A．relieving B．piling C．blaming D．experimenting 34．A．contract B．collapse C．prosper D．recover 35．A．appetite B．gift C．excuse D．strategy四、阅读理解This year, my two oldest sons asked me to sign them up for piano lessons. For certainreasons, I decided it would also be a good time for me to take up the piano again, after 30 years.As a child, I learned not just the piano, but the cello. I played in two orchestras and sang in the school choir. No one forced me to do any of it, but it wasn’t quite a free choice either. When you are the approval-addicted daughter of an over-invested mother, no one needs to apply force. My mom and I were well matched partners in the dance of unspoken expectation and approval-seeking. I did her forcing for her.For my mother, my musical industriousness wasn’t so much about achievement as identity. She was American by birth, and after marrying my university professor father and moving to London, she spent a decade working to be accepted into the impatient, fraught world of British intellectual society.In this environment, a diligent daughter lugging a giant cello was a tiny amount of cultural capital, a ticket to belonging. As much as anything could, music made me into the person my mother needed me to be, so that she could be the person she needed to be, in order to escape who she actually was.And for my part, although I never truly believed that my mother’s love was conditional, I did have the suspicion that there was a performance- related bonus in there.It was foolish to think that taking up the piano at the same time as my own children would be emotionally uncomplicated. Or perhaps the complication was exactly why I sought it out. Somehow, the piano lessons turn me into both my childhood self, seeking my mother’s approval, and into my mother herself, putting the same high expectations on my own children.My mother was lucky in that I was temperamentally (性情地) suited to the role she assigned me. My sons are not so much so. They are rambunctious and restless, not wired for lengthy sessions of sitting still and reflecting well on me.Unconditional love may be at the defining heart of parenthood, but sometimes it can feel impossible to accommodate unconditional love to the worldly practices of day- to- day parenting. The whole job seems set up for conditionality: It would be dishonest to pretend that we have no stake in wanting our children to reflect our own values and preferences.I’m disappointed when my sons won’t play their role in the script I have written for them, but deep down, I’m also a little thrilled. They are maddeningly, gloriously resistant to the pressure.A secret part of me is delighted by their raging demands for full personhood -beyond myprojections and hopes and fears. By the life they claim.36．The underlined sentence in paragraph two means ______.A．The author demanded to learn musical instruments out of pure love.B．The author forced her mum to sign her up for piano lessons against her will.C．The author’s mom pushed her to learn musical instruments for her own sake.D．The author offered to learn musical instruments to obtain her mom’s approval.37．The author’s mother think of the author’s musical industriousness as ______.A．a symbol more of family achievement than of social identityB．a way for her to fit into the British intellectual society at that timeC．proof of her ability to be a qualified mother in front of her husbandD．a result of her selfless cultivation more than the author’s own diligence38．Which of the following is TRUE from the author’s perspective?A．She doesn’t care about her sons’ levels of playing musical instruments.B．She has a mixed feeling towards her sons’ reluctance to practise musical instruments.C．She feels sorrowful because her sons are unlikely skilled at playing musical instruments.D．She is still convinced that her sons could be as talented on musical instruments as she was. 39．Which of the following might be the best title for the passage?A．Can Musical Talents Really be Inherited?B．Can We Really Force Our Children to Love Music?C．Can We Really Love Our Children Unconditionally?D．Can Playing Instruments Help Us Fit into Intellectual Society?Universal Studios SingaporeHave your fun multiplies across 6 themed zones.Universal Studios Singapore is Southeast Asia’s first and only Universal Studios theme park. Transported by adrenaline- pumping rides, you can enjoy interactive shows and a wide variety of exciting attractions based on the blockbuster movies and television series you know and love sowell. Welcome in and enjoy the ride!Rides and ShowsOperating hours may be subject to changes without prior notice. Street entertainment and selected experiences will not be available until further notice. Please click here to view the Rider’s Guide for Rider Safety and Guest with Disabilities.S. E. A．AquariumExplore the wonders of the oceans’ diverse inhabitantsand how to protect marine life.S. E. A．Aquarium is one of the world’s largest aquariums, home to more than 100,000 marine animals representing 1,000 species across more than 40 diverse habitats. The vast array of aquatic life is complemented by interactive programs, up- close animal encounters and immersive learning journeys to inspire visitors to protect the world’s oceans. S. E. A．Aquarium will be closed every Tue and Wed from 1 Jul to 31 Aug, 2 and 3 Sep, plus every Tue and Wed from 9 Sep to 30 Nov 2024. On 9 Sep, kindly be advised that S. E. A．Aquarium will be closed at 2:00 PM for the Teyvat SEA Exploration media preview. We seek your kind understanding for any inconvenience caused.Before Visit AdvisoryWe encourage cashless payments. Tap and pay with your contactless cards or digital wallets at our attractions, hotels and RWS- owned dining establishments.TicketsLatest ticket price is available in Booking page. Please click here.Adventure Cove Waterpark“Water” way to play!From thrilling water slides full of high- speed twists and turns to appealing wonders of different coves, there’s an experience waiting just for you at Adventure Cove Waterpark. For the ultimate adrenaline seeker, Riptide Rocket is an irresistible pull and on the opposite side of it is the calming trip down Adventure River.Note:Adventure Cove Waterpark will be closed on September 15 for a private event. We appreciate your understanding and apologize for any inconvenience this may cause. We look forward to welcoming you soon.Important InformationIn the event of unpleasant weather, all outdoor attractions will be suspended for your safety. Most water attractions are physically demanding and is not recommended for pregnant mothers.No outside food and beverages will be permitted. Please click here for more information of accepted swimwear prior to your visit.40．According to the passage, which of the following statements is TRUE?A．The S. E. A．Aquarium accepts only cash payments for tickets and dining.B．Three attractions are friendly for all guests even those who have been pregnant.C．Universal Studios Singapore has 6 zones themed on famous films and TV series.D．Adventure Cove Waterpark is open every day without exception throughout the year. 41．Lydia, a fan of adventure but hates getting wet, is planning for a day trip on Thursday September 15th. The most suitable attraction for her is ______.A．Universal Studios Singapore B．S. E. A．AquariumC．Adventure Cove Waterpark D．Riptide Rocket42．Where can you most probably find this passage?A．The official website of a resort.B．A travel magazine.C．The newspaper’s entertainment section.D．An update on social media.JULY 19TH was a day for help- desk heroes. A routine software update by CrowdStrike, a cyber- security company, caused computer breakdown in offices, hospitals and airports worldwide. Most white- collar workers looked miserably at their screens and realised just how useless they are if they cannot log in. People in IT came to the rescue of helpless colleagues and stranded passengers. Their work that day was full of stress— but also full of meaning.If machines can add purpose to some jobs when they fail, what about when they work properly? This is not a meaningless question. Technologies tend to spread in less dramatic ways, task by task rather than role by role. Before machines replace individuals, they change the nature of the work they do.A recent paper, from Milena Nikolova and Femke Cnossen looked at the prevalence of robots in industrial settings and how that affected workers. Robots reduced the perceived meaningfulness of jobs across the board, regardless of age, gender, skills and the type of work. In theory, machines can free up time for more interesting tasks; in practice, they seem to have had the opposite effect.In a separate paper, Ms Nikolova and Anthony Lepinteur of the University of Luxembourg,explore why this might be. They find that industrial robots make jobs less physically exhausting. But the number of tasks that remain open to humans decreases, hurting both the variety of work and people’s understanding of the production process. Work becomes more routine, not less.Machines need not have a dulling effect. In their research Ms Nikolova and her co- authors found that people did not perceive a loss of autonomy if they were working with computers, where they have more control of the machine than the other way round. And automation may well have a different impact on service industries like health caro, where less time spent on manual work might indeed mean more time with patients.A paper from 2011 by Michael Barrett of the University of Cambridge found that the introduction of drug- dispensing robots into hospital pharmacies had different effects. Pharmacists felt the quality of their jobs had improved because they had more time for patient counselling. Pharmacy assistants had a more miserable time of it, however, as their role shrank to loading medicine into the machines.It is still too early to know how AI will affect the quality of work. Some will surely enjoy using a bot to brainstorm ideas and take care of boring tasks, while others may not. The thing for managers to remember is that machines can make employees feel differently about their work. So it matters whether new technologies are introduced in collaboration with employees or imposed from above, and whether they enhance or weaken their sense of competence.43．Which of the following statements is TRUE according to the first and second paragraphs?A．Machines can sometimes add more purposes to jobs when they fail.B．Technologies typically spread across entire roles, replacing workers in one go.C．Potential demerits of introducing machines in the workplace have been recorded.D．A cyber- security company caused technological faults on purpose when testing thesoftware.44．What’s the conclusion of Ms Nikolova’s research in industrial settings?A．Workers feel more autonomous and in control when working with robots.B．Machines reduce the sense of purpose in human workers’ jobs in reality.C．Industrial robots replace human workers, eliminating their tasks and roles.D．Automation facilitates manual labor, increasing the variety of tasks.45．We can infer from Barrett’s research that ______.A．the introduction of robots leads to a decrease in job quality for all hospital staffB．when robots are introduced, staff tend to feel more satisfied regardless of their rolesC．in the same department, workers in different positions can feel differently to automation D．in some occupational areas, automation does constantly reduce the perceivedmeaningfulness46．Which of the following studies will others in the last paragraph cite as their evidence?A．A paper from Boris Nikolaev illustrates that many employees put a higher premium on non- monetary than monetary rewards.B．Research by Pok Man Tang of the University of Georgia suggests that workers whointeract more with AI assistants feel lonelier and long for more social contact.C．A recent Federal Reserve discussion paper surveyed American workers who had switched jobs; they found that interest in the work mattered more to people than pay and benefits.D．An experiment conducted by Eugina Leung states that a technology that cuts down on boring tasks is fine; one that threatens your sense of identity is not.How Many Devices Are You Wearing?The classic nightmare of suddenly realizing you are naked in public could soon get a futuristic twist: it might involve the horror of losing not just your modesty but also your pass codes. Scientists recently created magnetic garments that they say can store data, automatically unlock doors or control a nearby smartphone with gesture. The concept of interactive “smart clothing” has drawn attention in the past couple of years. 47 This and other smart garments are made with conductive thread and usually require an attached electronic device. To eliminate the need for such devices, researchers at the University of Washington recently took advantage of what is a previously untapped property of conductive thread: its ability to be magnetized. “Using magnetic instead of electric properties of the thread may seem like a small difference, but it is what makes this work interesting and exciting,” says Chris Harrison, a computer scientist at Carnegie Mellon University. 48The Washington team magnetized a patch of fabric embroidered with conductive thread, giving different parts of the cloth a north or south orientation that correspond to binary 1’s or0’. This step allowed the researchers to store up to 33 million different combinations — such as passcodes for doors — on a shirt sleeve. 49 The team described its findings last October at a meeting of the Association for Computing Machinery.The garments still stored data after washing, drying and ironing, but they could not escape time’s eraser; after about a week, the threads’ magnetic fields had weakened by around30 percent.50 But for now the clothes may be best suited for storing temporary codes, such as those found on hotel key cards or clothing tags in stores. Harrison says that it is “very unlikely you are ever going to achieve a comparable density to magnetic hard drives” with data-storing fabric, however.A．Custom- made thread has thus been designed so that the clothes are enabled to work longer. B．For example, Google and Levi’s created a touch- sensitive jacket that can operate a smartphone. C．Turning wearables into storage devices with the new technique was a unique thing the researchers bad done.D．The researchers suggest that using custom- made thread designed to hold stronger magnetic fields might work longer.E．The new technique allowed the researchers to do something they say is unique among wearables: turn them into storage devices.F．They also created magnetic gloves that could control a nearby smartphone with gestures.五、书面表达51．Directions: Read the following passage. Summarize the main idea and the main point(s) of the passage in no more than 60 words. Use your own words as far as possible.Work is just meeting nowIn 2016, a group of work researchers calculated that time spent in meetings had increased by 50 percent since the 1990s. Many workers were spending so much time in meetings, taking calls, and combing through their inbox that their most “critical work” often had to wait until they were home. Wall- to- wall meetings from 9 to 5 were pushing any creative or individual work to some period after dinner.In 2022, Microsoft researchers published a study that anonymously tracked workers using the company’s software. They discovered that about one-third of the workers in their study wereas likely to work at 10 p. m. as they were at 8 a. m. The reason? When the pandemic sent knowledge workers home, official meetings replaced casual interactions and made it impossible for many people to get things done unless they found time to log back online after dinner. In further research, Microsoft has found that, since 2020, workers in their sample have tripled the time they spent in meetings.If someone had to defend this phenomenon, they might point out that as firms grow, they accumulate bureaucratic habits. Departments are born, and workers within those departments develop expertise that is alien to people just down the hall. Working across these divisions requires that people spend more time getting to know and understand what their colleagues- are doing.Recent cultural changes might also be driving the surge in meeting times. In the last few years, the business world has focused much more on inclusion— letting more people’s voices be heard in decision- making. A business culture that allows more people to say their piece is one that requires people to spend more time listening to other people talk. In some decisions, that might be appropriate. At extremes, an office that requests more input is an office where talking about work can disturb efficient decision making.Today, knowledge work is, quantitatively speaking, less about creating new things than it is about talking about those things. Luckily, artificial-intelligence tools have the potential for eliminating unnecessary meetings and allowing people to focus on their work— or, even better, to cut hours of meetings that they can instead devote to leisure._______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _________________________________________________________________六、翻译52．过去80年，浦江沿岸经历了翻天覆地的变化。
上海市建平中学2019-2020学年高一上学期期中英语试题Word版含解析
【答案】A
【解析】
【详解】考查状语从句连接词。句意：在谷歌，我们把助力小企业更充分地使用技术视作我们的使命，不管是〔用技术帮助它们〕找到新的客户还是更高效地工作。A. whether是否，不管，不管；B. no matter不管怎样，不要紧；C. whatever任何事物，无论什么；D. so that以便，所以。分析句意可知，这里表达的是“不管A还是B〞，都是我们要帮助小企业更好地利用技术的两个方面，四个选项中只有whether可构成whether…or…的固定结构，且意为“不管……还是……〞，应选A。
6.A college freshman complained on her Weibo post that her mother______to give her only2000yuan each month for living expenses when she asked for 4.500 yuan, which sparked offmassive online debate.
上海市建平中学2021-2021学年高一上英语期中试题
II. Grammar and Vocabulary
Section A
Directions: Choose the best answer to complete the following sentences.
1.By the end of the 1980s. about 9.5 million elephants_________for the ivory trade inSouth Africa.
3._________Jay Chou's newly-released song "Won't Cry" met with instant financial success,public opinions have been divided. Some people insist it is unoriginal.
2020-2021学年上海市浦东新区建平中学高三(上)月考化学试卷(9月份)
2020-2021学年上海市浦东新区建平中学高三（上）月考化学试卷（9月份）一、选择题（共20小题，每小题2分，满分40分）1. 苏轼的《格物粗淡》中有这样的记载：“红柿摘下未熟，每篮用木瓜三枚放入，得气即发，并无涩味。
”按照现代科技观点，该文中的“气”是指（）A.乙烯B.甲烷C.乙酸D.甲醛2. 在预防新冠肺炎中，消毒剂发挥了重要作用。
下列试剂不常用于杀菌、消毒试剂的是（）A.75%酒精B.明矾C.漂粉精D.3%双氧水3. 用化学用语表示2H2S+302 → 2SO2+2H2O中的相关微粒，其中正确的是（）A.H2O的结构式：H−O−HB.中子数为18的硫原子：18SC.S的原子结构示意图：D.H2S的比例模型：4. 下列化合物中，只含有一种化学键的是（）A.Na2O2B.CaCl2C.Na2CO3D.(NH4)2SO45. 向漂粉精的水溶液中加入或通入少量下列物质，不能增强其漂白能力的是（）A.CaCl2粉末B.稀盐酸C.NaHCO3固体D.CO2气体6. 1.2−二苯乙烯（）具有抗老年痴呆、抗癌等功能，下列关于该有机物的说法不正确的是（）A.可以发生加成聚合反应B.难溶于水C.分子中所有原子可能共平面D.不能使高锰酸钾稀溶液褪色7. 下列物质在空气中变质，与二氧化碳无关的是（）A.生石灰B.漂粉精C.亚硫酸钠D.过氧化钠8. 下列化工生产中未使用催化剂的是（）A.合成氨B.索尔维制碱法C.SO2转化为SO3D.乙烯水化9. 工业制硫酸和合成氨生产中相同的是（）A.都用压缩机压缩原料气B.所有原料气都循环使用C.都用热交换器进行加热D.用了完全相同的催化剂10. 设N A为阿伏加德罗常数的值。
下列说法正确的是（）A.1L 0.1mol⋅L−1NaAlO2溶液中含AlO2−的数目为0.1N AB.0.1mol HClO中含H−Cl键的数目为0.1N AC.1mol苯中所含碳碳双键的数目为3N AD.78g Na2O2中阴、阳离子的总数为3N A11. 能与氢硫酸反应的非电解质是（）A.氢氧化钠B.二氧化碳C.二氧化硫D.硫酸亚铁12. 不能鉴别Fe2+和Fe3+的是（）A.盐酸B.氯水C.氢氧化钠溶液D.硫氰化钾溶液13. 实现Al3++3A1O2−+6H2O→Al(OH)3↓，正确的做法是（）A.向偏铝酸钠溶液中不断滴加盐酸B.向铝盐溶液中不断加入小苏打C.向烧碱溶液中不断滴入铝盐溶液D.向铝盐溶液中不断滴入烧碱溶液14. 关于下列转化过程分析不正确的是（）A.过程Ⅰ中每消耗58 g Fe3O4转移1 mol电子B.Fe3O4中Fe元素的化合价为+2、+3C.该过程总反应为2H2O=O2↑+2H2↑D.过程Ⅱ的化学方程式为3FeO +H 2O ====△Fe 3O 4+H 2↑15. 侯氏制碱原理：NH 3+CO 2+H 2O +NaCl =NaHCO 3↓+NH 4Cl ，经过制取氨气、制取NaHCO 3、分离及干燥NaHCO 3四个步骤，下列图示装置能达到实验目的是（ ）A.制取NaHCO 3B.制取氨气C.干燥NaHCO 3D.分离NaHCO 316. 室温下，在0.2mol/LAl 2(SO 4)3溶液中，逐滴加入1.0mol/LNaOH 溶液，实验测得溶液pH 随NaOH 溶液体积变化曲线如图，下列说法正确的是（ ）A.a ∼b 段，溶液pH 增大，促进了氢氧化铝的碱式电离B.a 点，离子方程式为：Al 3++3OH −→Al(OH)3↓C.b ∼c 段，加入的OH −主要用于生成Al(OH)3沉淀D.d 点时，Al(OH)3沉淀开始溶解17. 有一瓶澄清溶液，其中可能含有：NH 4+、K +、Mg 2+、Al 3+、Fe 2+、NO 3−、Cl −、SO 42−、CO 32−，取该溶液进行下列实验：取部分溶液，向其中逐滴滴入Ba(OH)2溶液至过量，有白色沉淀生成，沉淀量与加入Ba(OH)2溶液量的关系如图。
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2019-2020年建平中学高一上月考
一. 填空题
1. 已知{2,3,5}{2,3,5,7,11,13}A ⊆⊂，那么满足条
件的集合A 的个数是
2. 将集合U A C B ð在右图中用阴影部分表示出来
3. 命题“若1a =且2b =，则5a b +<.”的否命题
是
4. 已知{(,)|40}A x y x y =+-=，{(,)|10}B x y x ay =+-=，若A
B =∅，则实数a 的值为
5. 设集合{,,1}A x xy xy =-，其中x ∈Z ，y ∈Z 且0y ≠. 若0A ∈，则用列举法表示集合 A =
6. 设集合2{|60}A x x x =+-=，{|10,}B x mx m =+=∈R ，若A B ⊆，则实数m 的取 值的集合为
7. 已知A 、B 均为集合{1,3,5,7,9}U =的子集，且{3}A B =，{9}U A B =ð，则集合
A =
8. 建平中学2019年的“庆国庆930”活动正如火如荼准备中，高一某班学生参加大舞台和 风情秀两个节目情况如下：参加风情秀的人数占该班全体人数的八分之三；参加大舞台的人 数比参加风情秀的人数多3人；两个节目都参加的人数比两个节目都不参加的学生人数少7 人，则此班的人数为
9. 已知集合{1,2,3}A =，{|}B E E A =⊆，令||E 表示数集E 中所有元素的和，对集合B 中所有元素均求||E ，则这些||E 的值的和为
二. 选择题
10. 若“不积硅步，无以至千里”是真命题，则下面的命题一定是真命题的是（ ）
A. 积硅步一定可以至千里
B. 不积硅步也可能至千里
C. 要想至千里一定要积硅步
D. 不想至千里就不用积硅步
11. 若U 为全集，B A 、为非空集合，下面四个命题：
（1）A B A =；（2）A B B =；（3）U A B =∅ð；（4）U
A B U =ð. 其中与命题B A ⊆等价的命题个数有（ ）
A. 1个
B. 2个
C. 3个
D. 4个
12. 已知集合{|2,}A x x k k ==∈Z ，{|21,}B x x k k ==+∈Z ，{|41,}C x x k k ==+∈Z ，又a A ∈，b B ∈，则必有（ ）
A. a b A +∈
B. a b B +∈
C. a b C +∈
D. 以上都不对
三. 解答题
13. 证明：“已知a 、b ∈R ，若02222≠-++++b a b ab a ，则1≠+b a .”为真命题.
14. 已知全集为R ，集合{|1}A x x a =<-，{|2}B x x a =>+，{|1C x x =≤或4}x >. 若()A
B C C =R ð，求实数a 的取值范围.
15. 已知命题:p 关于x 的不等式10mx -≥的解集为A ，且2A ∈；
命题:q 关于x 的方程220x x m -+=有两个不相等的正实数根.
（1）若命题p 为真命题，求实数m 的范围；
（2）若命题p 和命题q 中至少有一个是假命题，求实数m 的范围.
附加题
16. 称正整数集合12{,,,}n A a a a =⋅⋅⋅12(1,2)n a a a n ≤<⋅⋅⋅<≥具有性质P ：如果对任意的 i 、j (1)i j n ≤≤≤，j i a a 与i j
a a 两数中至少有一个属于A . （1）分别判断集合{1,3,6}与{1,3,4,12}是否具有性质P ；
（2）设正整数集合12{,,,}n A a a a =⋅⋅⋅12(1,2)n a a a n ≤<⋅⋅⋅<≥具有性质P ，证明：对任意
1i n ≤≤（i ∈*N ）
，i a 都是n a 的因数； （3）求30n a =时n 的最大值
参考答案
一. 填空题
1. 7
2. 略
3. 若1a ≠或2b ≠，则5a b +≥
4. 1
5. {1,0,1}-
6. 11{,0,}23
- 7. {3,9} 8. 40人 9. 24
二. 选择题
10. C 11. D 12. B
三. 解答题
13. 逆否命题+因式分解+代入计算
14. 1a ≤-或5a >.（子集与推出关系+数轴图） 15. （1）12m ≥
（根的分布：数形结合+韦达定理）；（2）12
m <或1m ≥ 16. （1）{1,3,6}不满足；{1,3,4,12}满足； （2）略（分类讨论或者反证法）；
（3）4；301235=⨯⨯⨯，其中1、30定属于集合，因此2、3、5可在可不在， 且2、3、5不可同时出现，所以最大值是4。