湖南省雅礼中学2011届高三第四次月考(数学理)
长沙市雅礼中学2011年高三第一次月考试卷
2011届高三第一次月考PART TWO: LANGUAGE KNOWLEDGESECTION ADirections : Beneath each of the following sentences there are 4 choices marked A,B,C and D.Choose one answer that best completes the sentence .21．What do you mean _________ saying that I’m lucky?A．at B．on C．by D．of22．I told them not everybody could do it , _________?A．could they B．couldn’t they C．did I D．didn’t I.23．--Where did you see him for the first time?-- It was in the factory _________ we worked.A．that B．where C．which D．when24．_________ is known to us all is that the 2012 Olympic Games will take place in London.A．As B．What C．That D．It25．–It’s really a pity that I didn’t see you in Shanghai.-- I _________ to see you in the hotel, but I was too busy.A．hope B．had hoped C．hoped D．am hoping26．More than one student in our class _________ to Shanghai Expo.A．has been B．have been C．is D．are27．All things _________, her suggestion is of greater value than yours.A．consideration B．considering C．considered D．are considered28．-- _________ you called yesterday?-- Tom．Why?A．Who it is that B．Who is it that C．Who was it that D．Who it was that29．-- I’m so sorry for breaking the plate, Mom.-- It doesn’t matter．_________ careful next time.A．Being B．Do be C．Do D．To be30．It was unwise of him to _________ the unreliable data in his speech.A．refer to B．add to C．belong to D．point to31．_________ it rain, the crops would be saved.A．Will B．Should C．Would D．Could32．--Which of the two films do you prefer?-- To tel l you the truth,, I don’t like _________.A．neither of them B．both of themC．either of them D．none of them33．Tom has been absent for two days．Do you know what _________ to him?A．has happened B．would happen C．was happened D．had happened34．Rose _________ tell her mother that she didn’t pass the exam.A．dare not to B．doesn’t dare to C．ddoesn’t dare D．dares not35．_________ the extremely hot weather, we continued having classes．A．Thanks to B．In addition to C．In defence of D．Regardless ofSECTION B (18 points)Directions: For each blank in the following passage there are four words or phrases marked A, B, C and DThis year’s Cannes Film Festival threw actress Fan Bingbing int o the international spotlight–thanks to her performance on the red carpet, not on the big screen．36 a string of fancy dresses may have impressed many, the film featuring her -–director Wang Xiaoshuai’s Chongqing Blues–failed to take home an award．Chongqing Blues, based on a real story, is about a captain and 37 (Wang Xueqi) who has been 38 with work __39___ neglects his family．When he learns that his son was killed by police because of a kidnapping, he goes 40 from Rizhao to Chongqing to discover the truth, while reflecting on his own faults during the trip．In the judges’ eyes, 41 , the film was just not artsy enough．In an interview with after the award presentation, Wang Xiaoshuai admitted that the main reason why the film 42 was because it was a bit too commercial for the judges．―Yes, it’s a pity．But a film can’t just fulfill a director’s ambition．It should also 43 a market, and keep the investors’ needs 44 , ‖ Wang said．―So, we had to add some commercial elements into this film.‖Wang Xiaoshuai and the main actors 45 Wang Xueqi and Fan Bingbing in this film, have got a modest attitude．―We didn’t 46 too much when we came,‖ said Fan in a press conference．―This time we’ve 47 great communication with filmmakers around the world–that’s what we came here for.‖ 36．A．While B．When C．Because D．For37．A．father B．mother C．teacher D．doctor38．A．angry B．busy C．familiar D．popular39．A．and B．then C．so D．or40．A．in no way B．by the way C．all the way D．in the way 41．A．meanwhile B．fortunately C．therefore D．however42．A．lost B．succeeded C．won D．missed43．A．take to B．take on C．appeal to D．apply for44．A．out of mind B．in mind C．never mind D．to mind45．A．as B．like C．such that D．so that46．A．expect B．think C．hope D．wish47．A．made B．founded C．built D．establishedSECTION C (12 points)Directions: Complete the following passage by filling in each blank with one word that best fitsthe context.On the first day of classes at a Los Angeles high school, several American boys came up to a Chinese boy and said: ―Hi, what’s up?‖ 48 hearing their greeting, the boy, 49 had just moved to the US with his parents, raised his head and looked at the sky.This is a story told by David Chen, 50 31-year-old actor in Taiwan who recently launched a Sinamini-blog, on which he teaches easy English expressions.― 51 me, the mini-blog is like a mirror．When I read the comments, I see myself more clearly.‖Chen made a breakthrough last year 52 he had a double-eyelid surgery．―I like making changes and I think it’s necessary,‖ he said．―I know many fans like my pretty boy image．But now I’m growing up, I want to look rougher and 53 mature.‖―When you have a new haircut, you do not need to explain it．__54___ is just like changing your mood to do so–if you feel happy, that’s great,‖ said Chen．―Young people should realiz ethat sometimes you can just do what you want to do．You will eventually get support from others if you dare to be 55 .‖PART THREE READING COMPREHENSIONstatements．For each of them there are four choices marked with A, B, C and D．choose the one that fits best according to the information given in the passage.ATayka Hotel De SalWhere: Tahua, BoliviaHow much: About $95 a nightWhy it’s cool: You’ve stayed at hotels made of brick or wood, but salt? That’s something few can claim．Tayka Hotel de Sal is made totally of salt—including the beds (though you’ll sleep on regular mattresses (床垫) and blankets)．The hotel sits on the Salar de Uyuni, a prehistoric dried-up lake that’s the world’s biggest salt flat．Builders use the salt from the 4,633-square-mile flat to make the bricks, and glue them together with a paste of wet salt that hardens when it dries．When rain starts to dissolve the hotel, the owners just mix up more salt paste to strengthen the bricks.Green Magic Nature ResortWhere: Vythiri, IndiaHow much: About $240 a nightWhy it’s cool: Ridding a pulley(滑轮)-operated lift 86 feet to your treetop room is just the start of your adventure．As you look out of your open window—there is no glass!—you watch monkeys and birds in the rain forest canopy．Later you might test your fear of heights by crossing the handmade rope bridge to the main part of the hotel, or just sit on your bamboo bed and read．You don’t even have to come down for breakfast—the hotel will send it up on the pulley-drawn ―elevator‖.Dog Bark Park Inn B&BWhere: Cottonwood, IdahoHow much: $92 a nightWhy it’s cool: This doghouse isn’t just for the family pet．Sweet Willy is a 30-foot-tall dog with guest rooms in his belly．Climb the wooden stairs beside his hind leg to enter the door in his side．You can relax in the main bedroom, go up a ffew steps ot the loft in Willy’s head, or hang out inside his nose．Cotta ―go‖(想要方便一下)? Although you have a full private bathroom in your quarters, there is also a toilet in the 12-foot-tall fire hydrant outside.Gamirasu Cave HotelWhere: Ayvali, TurkeyHow much: Between $130 and $475 a night.Why it’s cool: This is caveman cool! Experience what it wa s like 5,000 years ago, when people lived in these mountain caves formed by volcanic ash．But your stay will be much more modern．Bathrooms and electricity provide what you expect from a modern hotel, and the white volcanic ash, called tufa, keeps the rooms cool, about 65℉in summer．(Don’t worry—there is heat in winter.)56．Which of the following about Tayka Hotel de Sal is true?A．The hotel is the cheapest among the four mentioned.B．Everything in the hotel is made of salt.C．It is on an island in the Pacific Ocean.D．It is located on a prehistoric lake.57．What is the similarity of the four hotels?A．Being expensive. B．Being beautiful. C．Being natural. D．Being unique.58．What does the underline part ―Sweet Willy‖ refer to?A．The building of Dog Bark Park Inn B&B. B．The name of a pet dog of the hotel owner.59．Which of the hotel makes you have a feeling of living in the far past?A．Tayka Hotel De Sal B．Green Magic Nature ResortC．Dog Bark Park Inn B&B D．Gamirasu Cave Hotel60．What may be the purpose of the writer writing the passage?A．To show his wide knowledge. B．To introduce some interesting hotels.C．To develop business in tourism. D．To attract attention from the readers.BSwedish master medical photographer Lennart Nilsson is a pioneer in medical photography．In association with researchers and with the help of advanced, specially designed equipment, he has documented the inside of man down to the level of a cell with his camera.Born in Strängnäs, a satellite city of Stockholm, in 1922, Nilsson got his first camera from his father when he was 11 years old．From the early stage, he has been interested in looking at ants and taking photos of them.Throughout the years, he has devoted special attention to capturing the creation of a human being, from conception to birth.In 2006 when his photo book Life was published in both Swedish and English, he was invited to give a lecture at the Stockholm bookstore．He vividly described to the public how he took the photos so that the development process of the embryo can be understood better．Finally when he was signing his name in the book, I asked him what made him so passionate about working on this, he stopped writing and thought for a second, ―I think it is the respect for life,‖ Nilsson sa id.Nilsson began his career as a photographic journalist in the middle of the 1940s and published a number of photo-essays in Swedish and foreign magazines, including "Polar Bear Hunting in Spitzbergen" (1947) and Midwife.―When I went to the professor t o take the embryo photo, I was looking around and then I saw something which was unbelievable, it was a tiny human embryo lies in a very special place, a 10-20 millimeter embryo with hands, arms and eyes, and I got a shock,‖ Nilsson said.Nilsson began experimenting with new photographic techniques in the mid-1950s to report on the world of ants and life in the sea．His revealing macro-studies were published in his book on ants, Myror (1959), and in the Life in the Sea (1959), and in Close to Nature (1984)．In the 1960s special designed, very slim endoscopes (内窥镜))made it possible for him to photograph the blood vessels and the cavities (空洞) of the body with the necessary depth of field and, in 1970, he used a scanning electron microscope for the first time, he was also considered the pioneer for three dimension digital pictures of the body organs.After his photographs of human embryo were published, he was encouraged to continue photographing the origins of human being.Nilsson is very modest and sincere．At age of nearly 88, he is still cooperating with colleagues in Karolinska Institute where the Nobel Prize in Physiology or Medicine is selected every year.―He can forget all the other things when he is working and he is still working diligently,‖ Mrs Nilsson told People’s Daily Online.61．Why does Nilsson want to document the creation of a human being?A．Because he is a pioneer in medical photography.B．Because he has been interested in taking photos.C．Because he thinks it a way to show respect for life.D．Because he wished to win a Nobel Prize.62．What can we learn from the passage?A．Nilsson was the only expert in medical photography. B．Nilsson’s camera is specially designed.D．Nilsson has always been working alone．63．How many books written by Nilsson are mentioned in this passage?A．3．B．4. C．5. D．6.64．Which of the following word can Not be used to describe Nilsson?A．Passionate. B．Devoted. C．Forgetful. D．Dillgent.65．What can be the title for the passage?A．Nilsson, a pioneer medical photographer B．Nilsson, a pioneer medical publisherC．Nilsson, a person of rich experience D．Nilsson, a talented photographerCSHANGHAI - Health experts in Shanghai are calling for more protection for young children as the latest research shows about half of the youngsters are suffering from secondhand smoke.About 45 percent of children suffer passive smoking in families, 50 percent in public places, and almost 6 percent on public transportation, shows a research released by the Shanghai Children's Medical Center on Tuesday."Not only adults but also children and newborn babies are at risk for the adverse effects of passive smoking," said Tang Jingyan, a doctor at the Shanghai Children's Medical Center."Actually, those young children whose bodies are still growing and developing are more sensitive to the effects of secondhand smoke."Research has shown that children who are exposed to secondhand smoke will suffer from more colds, coughs and sore throats, and they are more likely to suffer from bronchitis, pneumonia and will have a higher risk of developing cancer.Doctors even suggested that children suffering passive smoking are more likely to have behavioral problems and may not develop mentally as quickly as their peers．Other research by the Shanghai Children's Medical Center has found that more than 80 percent of child patients in the center live in a smoke-filled household, where one or both parents smoke．"Though doctors have stressed the harm of passive smoking over and over, it is still hard to reach a totally 'smoke free' home," said a pediatrician named Zhang Yiwen, noting that parents are often tempted to smoke even though they have learned the harmful effects of secondhand smoke.China has 540 million people suffering from passive smoke, 180 million of them younger than 15．The age of smokers is also getting lower, earlier reports said."There are more young smokers than before．You can see young people wearing a school uniform and carrying a schoolbag light a cigarette on the street．Some of them are even female students," said Jing Xingming, a professor of children's developmental behavior at the center."Children like to imitate adults, especially their parents．If parents often smoke at home, it is very likely children will develop a smoking habit, which can cause a vicious circle," Jin said.Reports from the Ministry of Health said China has about 350 million smokers, of whom 15 million are underage smokers．Also, around 40 million of the country's 130 million children aged between 13 and 18 had tried smoking, and 15 million had become addicted to tobacco.66．What is the main idea of the passage?A．About half of the youngsters are suffering from secondhand smoke.B．Experts are calling for more protection for youngsters from smoking.C．More and more youngsters are picking up the habit of smoking.D．Smoking does great harm to the health of the youngsters.67．What kind of the youngsters most possibly develop a habit of smoking?A．Children of non-smoking mothers B．Children of non-smoking fathers.68．Which of the following disease may not be connected with secondhand smoking?A．Cancer. B．Behavioral problemsC．Sore throats. D．Coughs.69．The underlined word ―vicious‖ in the last paragraph but one most probably means ___________.A．complete B．simple C．great D．bad70．What can be inferred from the passage?A．About 80% of the children in the Shanghai Children's Medical Center smoke heavily.B．About 45 percent of children suffer passive smoking in the Shanghai Children's Medical Center.C．About 540 million people are heavy smokers in China.D．Children aged between 13 to 18 are more likely addicted to smoking.PART FOUR WRITINGSection ADirections: Read the following passage．Complete the diagram by using the information for the passage．Write NO MORE THAN 3 WORDS for each answer.United Nations officials say now fewer people than they thought are infected with the AIDS virus.Last year, the agency known as UNAIDS thought that 39.5 million people were living with HIV．On Tuesday it reduced by 16% to a little more than 33 million.Agency officials say the low number reflects better information form more countries．The agency reduced the number for five African countries: Angola, Kenya, Mozambique, Nigeria and Zimbabwe.Also, UNAIDS says it now believes the number of new HIV cases per year reached a high in the late 1990s at more than three million．This year, it thinks that 2.5 million people became infected, and 2 million people died of AIDS.Luckily, better treatments are saving lives, and more people are getting the drugs.Yet even as the number of new infections has dropped, UN officials say AIDS is still one of the leading causes of the death worldwide, and the major cause in Africa．African death rates remain high, they say, because treatment needs are not being met．Sub-Saharan Africa had almost 70% of the new cases of HIV reported this year．UNAIDS officials say this is a sharp reduction since 2001, but there is a need to further improve research method.Billions of dollars are being spent preventing and treating HIV．Experts worry that the new number may lead to a drop in financial support．But UNAIDS officials say they do not change the need for immediate action and more money．They warn that in some countries, infection rates that were falling are rising again now．Title: A New Report on (71) Infections(72) Few people are infected with AIDS.(73) ◆The number has been (74) a little over 33 million. ◆HIV infected 2.5 million and (75) 2 million last year.◆The number of infections in five (76) has fallen.Measure To reduce new infections, the organization is supplying more people with better (77) .(78) ◆That treatment needs are not being met results in(79) in Africa.◆Because of the new number, some organizations mayprovide (80) to the program.◆In some countries, the infection rates are rising again.Section Bpassage and required words limit．Write your answers on your answer sheet.Richard Wagner was a German musician who lived in the mid-19th century．He gained fame by writing opera, a form of performance combining singing, music on instruments, and drama.Wagner’s life and work have been ve ry controversial(有争议的)．While he wrote excellent music, many people think his operas are too dark and serious, lacking tile fun common in operas written before his time.Wagner, on the other hand, thought the opera of his time was too simple．He wanted to make opera a serious form of art that combined drama and music to tell deep stories that would have a strong effect on the audience.Some people thought Wagner’s new kind of music was too different from the operas they were used to hearing．Wagner agreed with them．In fact, he didn’t call his works ―operas‖ at all, using instead a German word that means ―Musical Festival‖ or ―Musical play‖.While many people today still do not like Wagner’s operas, they cannot deny that Wagner had a lot of influence on opera as a form of art．Wagner invented the tradition of turning off the lights before starting a play．He also was the first person to make the whole audience sit down for an entire play．Today, almost all operas are performed in this manner.Wagner as a man was even more controversial than Wagner as a writer of music．He hated Jewish people, slept with his friends’ wives, and made many people angry, which we would today think of as evil．Some would say he was a good musician, while others would say that he was a bad musician．But it would be difficult to say he was not an important person in music and in the world.81．What is the best word that describes Wagner? (no more than one word)82．What does the underlined word ―deep‖ in Para．3 mean? (no more than 3 words)83．W hy does the author say ―Wagner as a man was even more controversial‖? (no more than 15 words) 84．List two things that showed Wagner had a lot of influence on opera? (no more than 30 words)Section C (25)Directions :Write an English composition according to the instructions given below in Chinese .近年来选秀类的电视节目吸引了很多人的注意力。
湖南省长沙市高三上学期月考(四)数学(理)试题 Word版含解析
炎德∙英才大联考雅礼中学2017届高三月考试卷（四）数学（理）第Ⅰ卷（选择题）一、选择题：本大题共12小题，每小题5分，共60分.在每个小题给出的四个选项中，有且只有一项符合题目要求. 1.设集合{}⎭⎬⎫⎩⎨⎧<=-=21|1,1x x N M ，则下列结论正确的是 A. M N ⊆ B. N M ⊆ C. ∅=M N D.R N M = 2.在复平面内，复数Z 满足()i i z 311+=+，则的z 共轭复数对应的点位于A.第一象限B. 第二象限C.第三象限D.第四象限3.在一次跳伞训练中，甲、乙两位学员各跳一次，设命题p 是“甲降落在指定范围”，q 是“乙降落在指定范围”，则命题“至少有一位学员没有降落在指定范围”可表示为 A. ()()q p ⌝∧⌝ B.()q p ⌝∨ C. ()()q p ⌝∨⌝ D.q p ∨4.函数x x y 2cos 32sin -=的图象的一条对称轴方程为 A. 12π=x B. 12π-=x C. 3π-=x D.6π-=x5.一个三棱锥的正视图和俯视图如右图所示，则该三棱锥的俯视图可能为6.四位男生和两位女生排成一排，男生有且只有两位相邻，则不同的排法种数是 A. 72 B. 96 C. 144 D.2407.已知函数()0sin >+=a b ax y 的图象如图所示，则函数()b x y a +=log 的图象可能是8.从混有5张假钞的20张一百元纸币中任意抽取2张，将其中一张在验钞机上检验发现是假币，则这两张都是假钞的概率为 A.191 B. 1817 C. 194 D.172 9.公元263年左右，我国数学家刘徽发现，当圆内接四边形的边数无限增加时，多边形的面积可无限逼近圆的面积，由此创立了割圆术，利用割圆术刘徽得到了圆周率精确到小数点后面两位的近似值14.3，这就是著名的“圆率”.如图是利用刘徽的割圆术设计的程序框图，则输出的n 值为参考数据：.1305.05.7sin ,2588.015sin ,732.13===A. 12B. 24C. 48D. 9610.如图，正方体1111D C B A ABCD -的棱长为3，以顶点A 为球心，2为半径作一个球，则图中球面与正方体的表面相交所得到的两段弧长之和等于 A.65π B. 32π C. π D.67π11.P 为双曲线19422=-y x 右支上一点，21,F F 分别为其左、右焦点，且021=⋅PF ，直线2PF 交y 轴于点A ，则P AF 1∆的内切圆半径为A. 2B.3C.23D.21312.已知实数b a ,满足,,0ln 522R c b a a ∈=--则()()22c b c a ++-的最小值为A. 21B. 22C. 223D.29二、填空题：本大题共4小题，每小题5分，共20分.13.已知平面向量b a ,3,23-=⋅===+ .14. 设函数()⎪⎩⎪⎨⎧>≤-=-,0,,0,23x x x x f x ，若()10=x f ，则=0x .15. 已知y x ,满足⎪⎩⎪⎨⎧≤≥-+≤-+,1,033,032y y x y x y x z +=2的最大值为m ，若正数ba ,满足m b a =+，则ba 41+的最小值为 . 16.()()()()()x a x x a x x x x x f 14cos sin 3sin cos cos sin 21-+-+-+=在⎥⎦⎤⎢⎣⎡-0,2π上单调递增，则实数a 的取值范围为 .三、解答题：本大题共6小题，共70分.解答应写出必要的文字说明或推理、验算过程. 17.（本题满分12分）某农科所对冬季昼夜温差大小与某反季节大豆新品种发芽多少之间的关系进行分析研究，他们分别记录了12月1日到12月5日的每天昼夜温度与实验室每天每100颗种子中的发芽数，得到如下数据：该农科所确定的研究方案是：先从这5组数据中选取2组，用剩下的3组数据求线性回归方程，再对被选取的2组进行检验.（1）求选取的2组数据恰好是不相邻的2天数据的概率；（2）若选取的是12月1日与12月5日的两组数据，请根据12月2至12月4日的数据，求y 关于x 的线性回归直线方程；（3）若由线性回归方程得到的估计数据与所选取出的检验数据的误差不超过2颗，则认为得到的回归直线方程是可靠的，试问（2）中所得的线性回归方程是否可靠？18.（本题满分12分）如图，在四棱锥ABCD P -中，平⊥AB 面//,CD BCP 平面ABP.22=====CD BP CP BC AB ，（1）证明：平面⊥BAP 平面DAP ；（2）点M 为线段AB （含端点）上一点，设直线MP 与平面DCP 所成角为α，求αsin 的取值范围.19.（本题满分12分） 已知首项为23的等比数列{}n a 的前项和为()*∈N n S n ，且4324,,2S S S -成等差数列 （1）求数列{}n a 的通项公式；（2）对于数列{}n A ，若存在一个区间M 均有() ,3,2,1=i A i ，则称M 为数列{}n A 的“容值区间”，设nn n S S b 1+=，试求数列{}n b 的“容值区间”长度的最小值. （注：区间()(][)[]b a b a b a b a ,,,,,,的长度均为a b -）20.（本题满分12分）已知三点()()()1,2,1,2,0,0Q R O -，曲线C 上任意一点()y x M ,满足().2++⋅=OM（1）求曲线C 的方程；（2）若B A ,是曲线C 上分别位于点Q 两边的任意两点，过B A ,分别作曲线C 的切线交于点P ，过点Q 做曲线C 的切线分别交直线PB PA ,于E D ,两点，证明：QAB ∆与PDE ∆的面积之比为定值.21.（本题满分12分） 已知函数()().012221ln >++⎪⎭⎫ ⎝⎛+=x x ax x f （1）若0>a ，且()x f 为单调递增，求实数a 的取值范围；（2）是否存在实数a 使得()x f 最小值为1，若存在，求出实数a 的值，若不存在，请说明理由.请考生在第（22）、（23）两题中任选一题作答，如果多做，则按所做的第一题计分，作答时用2B 铅笔在答题卡上把所选题目对应题号下方的方框涂黑.22.（本题满分10分）选修4—1；坐标系与参数方程已知曲线C 的极坐标方程为10cos sin 2=+θρθρ，将曲线⎩⎨⎧==,sin ,cos :1ααy x C （α为参数），经过伸缩变换⎩⎨⎧='=',2,3y y x x 后得到曲线2C .（1）求曲线2C 的参数方程；（2）若点M 在曲线2C 上运动，试求出M 到曲线C 的距离的最小值.23（本题满分10分)选修4—5；不等式选讲 已知函数().2-++=x a x x f（1）若4-=a ，求不等式()6≥x f 的解集；（2）若()3-≤x x f 的解集包含[]1,0，求实数a 的取值范围.。
雅礼中学高三月考试卷(一)数学及答案
雅礼中学高三月考试卷(一)数学一、单项选择题：本大题共8小题，每小题5分，共40分。
在每小题给出的四个选项中，只有一项符合题目要求。
1.已知集合A =-2,0 ,B =x x 2-2x =0 ，则以下结论正确的是()A.A =BB.A ∩B =0C.A ∪B =AD.A ⊆B2.已知等比数列a n 满足a 1=1,a 3⋅a 5=4a 4-1 ，则a 7的值为()A.2B.4C.92D.63.已知复数z =a +1 -ai a ∈R ，则a =-1是z =1的()A.充分不必要条件B.必要不充分条件C.充要条件D.既不充分也不必要条件4.已知向量a =cos θ,sin θ ，b =2,-1 ，若a ⊥b ，则cos 2θ+12sin2θ的值为()A.13B.35C.45D.235.如图，在棱长为2的正方体ABCD -A 1B 1C 1D 1中，E ，F 分别是棱AA 1，CC 1的中点，过BE 的平面α与直线A 1F 平行，则平面α截该正方体所得截面的面积为()A.5B.25C.4D.56.某工厂有A ,B 两个生产车间，所生产的同一批产品合格率分别是99%和98%，已知某批产品的60%和40%分别是A ,B 两个车间生产，质量跟踪小组从中随机抽取一件，发现不合格，则该产品是由A 车间生产的概率为()A.34B.47C.12D.377.已知椭圆C ：x 2a2+y 2b 2=1(a >b >0)的左、右焦点分别为F 1,F 2，P 为椭圆上一点，且∠F 1PF 2=π3，若F 1关于∠F 1PF 2平分线的对称点在椭圆C 上，则该椭圆的离心率为()A.22B.33C.12D.138.△ABC 中，角A ,B ,C 所对的三边分别为a ,b ,c ,c =2b ，若△ABC 的面积为1，则BC 的最小值是()A.2B.3C.3D.33二、多项选择题：本大题共4个小题，每小题5分，共20分。
2011届高三年级第四次月考数学试卷(理科)
2011届高三年级第四次月考数学试卷（理科）一、选择题（本大题共同10小题，每小题5分，共50分.在每个小题给出的四个选项中，只有一项是符合题目要求的.）1. 下列命题中的假命题是（ ） A.02, 1>∈∀-x R x B. 1lg , <∈∃x R xC ．()01 , 2>-∈∀*x N x D. 2tan , =∈∃x R x2.设集合}log ,5{)63(22+-=a a A ，集合},,1{b a B =若}2{=B A 则集合B A 的非空真子集的个数是（ ） A ．3个 B ．7个 C ．14个 D ．15个3．已知命题p ：存在xxx 32),,0(≥+∞∈；命题q ：ABC ∆中，若B A sin .sin >，则B A >，则下列命题为真命题的是（ ） A ．p 且qB ．（﹁p ）且qC ．p 或（﹁q ）D ．p 且（﹁q ）4．给定函数①52x y =，②)1(21log +=x y ，③|1|y x =-，④12+=x y ，其中在区间（0，1）上单调递减的函数序号是（ ）A.①②B.②③C.③④D.①④ 5．将函数()sin()f x x ωϕ=+的图象向左平移2π个单位，若所得的图象与原图象重合，则ω的值不可能等于（ ）A ．4B ．6C ．8D ．126.设等差数列}{n a 的前n 项和为n S ,若6,11641-=+-=a a a ,则当n S 取最小值时, n 等于（ ）A ．6B ．7C ．8D ．97. 已知A ，B ，C 三点的坐标分别是3(3,0),(0,3),(cos ,sin ),(,)22A B C ππααα∈若1-=⋅，则21tan 2sin sin 2ααα++的值为（ ）A. 95-B.3C.2D. 59-8、已知定义在R 上的奇函数满足(4)()f x f x -=-，且在区间[0,2]上是增函数，则（ ）A ．(25)(11)(80)f f f -<<B ．(80)(11)(25)f f f <<-C ．(11)(80)(25)f f f <<-D ．(25)(80)(11)f f f -<<9、已知P 是圆22(3)(3)1x y -+-=上或圆内的任意一点，O 为坐标原点，1(,0)2OA =，则OA OP ⋅的最小值为（ ） A ．12B ．32C ．1D ．210．在△ABC 所在平面上有三点P 、Q 、R ，满足=++，BC QC QB QA =++，CA RC RB RA =++，则△PQR 的面积与△ABC 的面积之比为 ( )A.1:2B.1:3C.1:4D.1:5二、填空题（本大题共6小题，每小题4分，共24分。
湖南省雅礼高三数学第四次月考试题理
高三月考试卷（四） 数 学 试 题（理）本试题卷包括选择题、填空题和解答题三部分。
时量120分钟。
满分150分。
一、选择题：本大题共8小题，每小题5分，共40分。
在每小题给出的四个选项中，只有一项是符合题目要求的。
1．复数12ii+（i 是虚数单位）的虚部是（ ）A ．25B ．25-C ．15-D ．152．设全集,{1,2,3,,10},{0,1,2,}U Z A B === 则右图中阴影部分表示的集合的真子集的个数为 （ ）A ．3B ．4C ．7D ．83．等差数列{}n a 的前n 项和为n S ，若31710a a +=，则19S =（ ）A ．190B ．95C ．170D ．854．命题“4x >”是命题“31x x ><-或”成立的（ ） A ．充分必要条件 B ．必要非充分条件 C ．充分非必要条件 D ．既非充分也非必要条件5．动点(,)A x y 在圆221x y +=上绕坐标原点沿逆时针方向匀速旋转，12秒旋转一周，已知时间0t =时，点A 的坐标是1(2，则当012t ≤≤秒时，动点A 的纵坐标y 关于t （单位：秒）的函数的单调递增区间是（ ） A ．[0，1] B ．[1，7] C ．[7，12]D ．[0，1]和[7，12]6．如下图所示的程序框图的输出值(]1,2y ∈，则输入值x ∈（ ）A ．(][)2log 3,11,3--B ．(][)31,log 21,2--C ．[)(]31,log 21,2--D ．[)(]2log 3,11,3--7．用0，1，2，3，4这五个数字组成无重复数字的五位数，其中恰有一个偶数数字夹在两个奇数数字之间，这样的五位数的个数有 （ ） A ．48个 B ．12个 C ．36个 D ．28个 8．定义区间[)(,),,,[,]a b a b a b 的长度均为d b a =-，多个区间并集的长度为各区间长度之和，例如，[)(1,2)3,5 的长度(21)(53) 3.d =-+-=用[x]表示不超过x 的最大整数，记{}[]x x x =-，其中x R ∈，设()[]{},()1f x x x g x x =⋅=-，若用123,,d d d 分别表示不等式()(),f x g x >方程()()f x g x =，不等式()()f x g x <解集区间的长度，则当02011x ≤≤时，有（ ） A ．1231,2,2008d d d === B ．1231,1,2009d d d ===C ．1233,5,2003d d d ===D ．1232,3,2006d d d ===二、填空题：本大题共9小题，考生作答7小题，每小题5分，共35分。
湖南长郡中学2011届高三第四次月考(数学理)
湖南长郡中学 2011届高三第四次月考数 学 试 题（理）（考试范围：集合与逻辑、算法与框图、函数、三角函数、平面向量、数列、推理与证明、不等式、计数原理、概率与统计、空间几何及空间向量、4—1、4—4、4—5）本试题卷包括选择题、填空题和解答题三部分。
时间120分钟。
满分150分。
一、选择题：本大题共8小题，每小题5分，共40分。
在每小题给出的四个选项中，只有一项是符合题目要求的。
1．已知集合{|},{|12},A x x a B x x R =<=<<表示实数集，且()U A C B R =，则实数a 的取值范围是（ ）A ．2a ≤B ．1a <C ．2a ≥D ．2a >2．已知函数()22()xxf x P x R -=+∈为奇函数，则下列结论正确的是 （ ）A ．1,()P f x =为R 上的减函数B ．1,()P f x =-为R 上的减函数C ．P=1，f （x ）为R 上的增函数D ．P=-1，f （x ）为R 上的增函数3．函数2sin()cos()((0,))36y x x x πππ=--+∈，则y（ ）A ．有最小值-1，无最大值B ．有最大值1，无最小值C ．有最小值 1D ．有最小值-14．某企业三月中旬生产A 、B 、C 三种产品共3000件，根据分层抽样的结果，企业统计员制作了如下的统计表格。
由于不小心，表格中A 、C 产品的有关数据己被污染看不清楚，统计员记得A 产品的样本容量比C 产品的样本容量多10件，根据以上信息，可得C 产品的数量是 （ ）A ．900件B ．800件C ．90件D ．80件5．如图，AC 为⊙O 的直径，BD AC ⊥于P 点，PC=2，AP=8，则BC 的长为 （ ）A B ．3C ．4D ．6．已知,,l m n 是三条不重合的直线，,,αγβ是三具不重合的平面，给出下列四个命题：①若,//,m m αβαβ⊥⊥则；②若直线m ，n 与平面α所成的角相等，则m//n ；③存在异面直线m ，n ，使得m//α，m//β，n//β，则α//β； ④若,,,//,l m n l αββγγαγ===则m//n ；A ．1B ．2C ．3D ．47．已知向量(,),(1,2),(,),//,a m n b c k t a b b ===且⊥c ，|a+c 则mt 的取值范围是（ ）A ．(,1]-∞B ．(0,1]C ．[—1，1]D ．（—1，1）8．将正整数排成下表：1 2 3 4 4 56 7 8 9 10 11 12 13 14 15 16 …… 则数表中的数2010出现在 （ ） A ．第44行第75列 B ．第45行第75列 C ．第44行第74列 D ．第45行第74列二、填空题：本大题共7小题，每小题5分，共35分，把答案填在答题卡中对应题号的横线上。
2024-2025学年湖南省长沙市雅礼中学高三(上)月考数学试卷(9月份)(含答案)
2024-2025学年湖南省长沙市雅礼中学高三（上）月考数学试卷（9月份）一、单选题：本题共8小题，每小题5分，共40分。
在每小题给出的选项中，只有一项是符合题目要求的。
1.设集合A ={x|(x +1)(x−4)<0}，B ={x|2x +a <0}，且A ∩B ={x|−1<x <3}，则a =( )A. 6B. 4C. −4D. −62.已知z 1+i =1−1i ，则|−z |=( )A.2B.22C. 2D. 13.已知f(x)=sin (ωx−π3)(ω∈N)的图象与直线y =a 在区间[0,π]上存在两个交点，则当ω最大时，曲线y =f(x)的对称轴为( )A. x =π24+kπ4，k ∈Z B. x =π30+kπ5，k ∈Z C. x =5π24+kπ4，k ∈Z D. x =π6+kπ5，k ∈Z4.函数f(x)=2x +2−xln( x 2+1−x)的图象大致为( )A. B.C. D.5.若平面单位向量a ，b ，c 满足〈a ,b〉=π6，b ⋅c =0，a ⋅c <0，则|b 2c ||a +c |( )A.5B.3C.153D.536.石雕、木雕、砖雕被称为建筑三雕.源远流长的砖雕，由东周瓦当、汉代画像砖等发展而来，明清时代进入巅峰，形成北京、天津、山西、徽州、广东、临夏以及苏派砖雕七大主要流派.苏派砖雕被称为“南方之秀”，是南方地区砖雕艺术的典型代表，被广泛运用到墙壁、门窗、檐廊、栏槛等建筑中.图(1)是一个梅花砖雕，其正面是一个扇环ABCD ，如图(2)，砖雕厚度为6cm ，AD =80cm ，CD =3AB ，CD 所对的圆心角为直角，则该梅花砖雕的表面积为(单位：cm 2)( )A. 3200πB. 480π+960C. 6880π+960D. 3680π+9607.已知过抛物线C ：y 2=2px(p >0)的焦点F 的直线与C 交于A ，B 两点，线段AB 的中点为M(x 0,y 0)，且|AB|=2x 0+1，Q(t,−2−t)，若点P 在抛物线C 上，则|PQ|的最小值为( )A.3 24B.3 22C.3 34D.328.已知数列{a n }满足a 1=3,a n +1−a n =2,4b n =(−1)n +1(1a n +1a n +1)，若数列{b n }的前n 项和为T n ，不等式3T n <λ(3−5λ)(n ∈N ∗)恒成立，则λ的取值范围为( )A. (110,+∞)B. (15,+∞)C. (110,12)D. (15,25)二、多选题：本题共3小题，共18分。
2024-2025学年湖南省长沙市雅礼中学高三(上)月考数学试卷(一)(含答案)
2024-2025学年湖南省长沙市雅礼中学高三（上）月考数学试卷（一）一、单选题：本题共8小题，每小题5分，共40分。
在每小题给出的选项中，只有一项是符合题目要求的。
1.已知集合A ={x |log 2x >1}，B ={x |0<x <4}，则A ∩B =( )A. {x |2<x <4}B. {x |2⩽x <4}C. {x |0<x⩽2}D. {x |x⩽2}2.已知复数z 满足(1―i )z =2i ，且z +ai (a ∈R )为实数，则a =( )A. 1B. 2C. ―1D. ―23.设向量a =(1,0)，b =(12,12)，则下列结论中正确的是( )A. |a |=|b | B. a ⋅b = 22 C. a ―b 与b 垂直 D. a //b4.已知a 是函数f (x )=2x ―log 12x 的零点，若0<x 0<a ，则f (x 0)的值满足( )A. f (x 0)=0B. f (x 0)>0C. f (x 0)<0D. f (x 0)的符号不确定5.若sinx +cosx =13，x ∈(0,π)，则sinx ―cosx 的值为( )A. ± 173 B. ― 173 C. 13 D. 1736.用数字1，2，3，4，5组成的无重复数字的四位偶数的个数为( )A. 8B. 24C. 48D. 1207.函数y =f (x )的图象如图①所示，则如图②所示的函数图象所对应的函数解析式可能为( )A. y =f (1―12x )B. y =―f (1―12x )C. y =f (4―2x )D. y =―f (4―2x )8.刍曹是我国传统建筑造型之一，蕴含着丰富的数学元素.安装灯带可以勾勒出建筑轮廓，展现造型之美.如图，某屋顶可视为五面体ABCDEF ，四边形ABFE 和CDEF 是全等的等腰梯形，△ADE 和△BCF 是全等的等腰三角形.若AB =25m ，BC =AD =10m ，且等腰梯形所在的面、等腰三角形所在的面与底面夹角的正切值均为145.为这个模型的轮廓安装灯带(不计损耗)，则所需灯带的长度为( )A. 102mB. 112mC. 117mD. 125m二、多选题：本题共3小题，共18分。
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湖南省雅礼中学 2011届高三第四次月考
数学试题（理科）
（考试范围：集合与逻辑，函数与导数，三角，平面向量，数列，立体 几何，解析几何，计
数原理，算法初步，推理与证明，不等式，概率统计，系列4） 本试题卷包括选择题、填空题和解答题三部分，时量120分钟。
满分150分。
一、选择题：本大题共8小题，每小题5分，共40分，在每小题给出的四个选项中，只有一
项是符合题目要求的，请将所选答案填在答题卡对应位置。
1．集合2{0,2,},{1,}A a B a ==，若{0,1,2,4,16}A B ⋃=，则a 的值为 （ ）
A ．0
B ．1
C ．2
D ．4 2．“1k =”是“直线0x y k -+=与圆221x y +=相交”的
（ ） A ．充分不必要条件 B ．必要不充分条件
C ．充要条件
D ．既不充分又不必要条件
3．若实数,x y 满足
2222111,2x y x y
+=+则有
（ ）
A
．最大值3+ B
．最小值3+
C ．最大值6
D ．最小值6
4．已知函数()f x 满足21
3
2()()f x f x x
-=，则()f x 的最小值是 （ ）
A ．2
B ．3
C
．D ．4
5．已知偶函数()f x 在区间（0，+∞）单调递增，则满足1(21)()3
f x f -<的x 的范围是
（ ）
A ．12(,)33
B ．12[,)33
C ．12(,)23
D ．12[,)23
6．函数1,(10)()cos ,(0)2
x x f x x x π+-≤<⎧⎪
=⎨≤≤⎪⎩的图象与x 轴所围成的封闭图形的面积为
（ ）
A ．
12
B ．1
C ．
32
D ．2
7．如表定义函数()f x ：
对于数列112010{},4,(),2,3,4,,n n n a a a f a n a -=== 则的值是
（ ）
A ．4
B ．3
C ．2
D ．1
8．某班有一个7人小组，现任选其中4人相互调整座位，其余3人座位不变，则不同的调整
方案种数有 （ ） A ．35 B ．70 C ．105 D ．315
二、填空题：本大题共7小题，每小题5分，共35分，把答案填在答题卡中对应题号后的横
线上． 9．对任意非零实数,a b ，若a b ⊗的运算原理如图所示，则2
1lg1000()
2
-⊗= 。
10．对于数列{}n a ，定义数列1{}n n a a +-为数列{}n a 的“差数列”，若12,{}n a a =的“差数
列”的通项为2n
，则数列{}n a 的前n 项和n S = 。
11．一个篮球运动员投篮一次得3分的概率为a ，得2分的概率为b ，得0分的概率为
(,,(0,1))c a b c ∈，已知他投篮一次得分的数学期望为2（不计其他得分情况），则ab 的
最大值是 ．
12．将长度为1米的铁丝随机剪成三段，则这三段能拼成一个三角形（三段的端点相接）的
概率是 ． 13．若()(12)(13)(,)m n f x x x m n N +=+++∈的展开式中x 的系数为13，则展开式中2
x 的
系数是 。
14．已知抛物线2
4y x =与直线24y x =-交于A ，B 两点，如果在该抛物线上存在点C ，使
得OA OB OC λ+= （O 为坐标原点），则OA OB ⋅= ，实数λ= ．
15．观察下列算式，猜测由此提供的一般法则，用适当的数学式子表示它
1=1 3+5=8 7+9+11=27
13+15+17+19=64 21+23+25+27+29=125
设这些式子的第n 个为121,(,)n n n a a a b a a +++== 则 ，n b = 。
三、解答题：本大题共6小题，共75分．解答应写出文字说明，证明过程或演算步骤． 16．（本小题满分12分）
已知∆ABC 的面积为
，角A ，B ，C 所对的边分别是a ，b ，c ，且
2
22s i n s i n s i n s i n s i n
.
C A B A B =+
+
（1）求角C ；
（2）若∆ABC 的外接圆半径是2时，求a b +的值．。