湖南省长沙市雅礼中学2019届高三上学期月考二数学(理)试题(精编含解析)
【2019届高考数学】湖南省长沙市雅礼中学2019届高三上学期月考(六)理科数学(PDF版)
# $ ' ! $ " ! <! <"
! +分"
# #* # & ( ! " 由! " 可得 9! ; 0! " ! 0 " $ " " * ! ) 1 ' " ! # " ! 0 " " * ! ) 0 # $ ' " ! 1! " $ & # #" <! <" < <" <! <" < <0
# #& " * ! $! ; " " * ! ) 1 0! " ! " !! " ! 0! Ř <" <" < <"
" & $! ; # $ ' ! $ 1 " ! #1 <! <" 所以 ; # 的分布列为 )
; # $
' " ! # " ! <" <!
" " * ! )
& 因为有两个交点& 所以" $
# #" ! + ' 6 : & : ! # ! 分" 则2 2 2 "0 #1! " #1 # 2 # ! + " 0 ' 6 6 " 0 '
# # # # ! " 0 " 0 " 0 *+ 1 槡 6 2 2 6 2 2 ' 2 2 6 "! # 1 槡 "0 #"! " #1 槡 槡
湖南省雅礼中学2019届高三高考模拟卷(二)数学(文)试题 含解析
【点睛】本题 考点是数列的应用，主要考查的数列的求和，由于已知的数列 即不是等差数列，又不是等比数列，故无法直接采用公式法，我们可以采用分组求和法．
16.已知三棱锥 的各顶点都在球面上， , 平面 , ， ,若该球的体积为 ，则三棱锥 的表面积为__________．
【答案】27
【解析】
【解析】
【分析】
（1）推导出PQ⊥平面ABCD，PQ⊥AD，CD∥BQ，从而BQ⊥AD，进而AD⊥平面PBQ，由此能证明平面PQB⊥平面PAD．
（2）连接AC与BQ交于点N，则N为AC中点，则点M到平面PAB的距离是点C到平面PAB的距离的 ，求出三棱锥P-ABC的体积V= ，PAB的面积为 ，设点M到平面PAB的距离为d，由VC-PAB=VP-ABC，能求出点M到平面PAB的距离．
A. B.
C. D.
【答案】D
【解析】
【分析】
利用函数的奇偶性排除选项，利用特殊值定义点的位置判断选项即可．
【详解】函数 是偶函数，排除选项B，当x=2时，f（2）= ＜0，对应点在第四象限，排除A，C；
故选：D．
【点睛】本题考查函数的图象的判断，考查数形结合以及计算能力．
6.“ ”是“方程 为椭圆”的（ ）
【详解】如图：
由双曲线C的方程可知：a2=1，b2=8，∴c2=a2+b2=1+8=9，∴c=3，∴左焦点E（-3，0），右焦点F（3，0），
∵|AF|= ，所以当三角形APF的周长最小时，|PA|+|PF|最小．
由双曲线的性质得|PF|-|PE|=2a=2，∴|PF|=|PE|+2，
又|PE|+|PA|≥|AE|=|AF|=15，当且仅当A，P，E三点共线时，等号成立．
2019届湖南省长沙市雅礼中学高三上学期月考二数学(文)试题
雅礼中学2019届高三月考试卷（二）数学（文科）本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分，共8页。
时量 120分钟。
满分150分★祝你考试顺利★注意事项：1、考试范围：高考考查范围。
2、答题前，请先将自己的姓名、准考证号用0.5毫米黑色签字笔填写在试题卷和答题卡上的相应位置，并将准考证号条形码粘贴在答题卡上的指定位置。
用2B 铅笔将答题卡上试卷类型A 后的方框涂黑。
3、选择题的作答：每个小题选出答案后，用2B 铅笔把答题卡上对应题目的答案标号涂黑。
写在试题卷、草稿纸和答题卡上的非选择题答题区域的答案一律无效。
4、主观题的作答：用0.5毫米黑色签字笔直接答在答题卡上对应的答题区域内。
写在试题卷、草稿纸和答题卡上的非主观题答题区域的答案一律无效。
5、选考题的作答：先把所选题目的题号在答题卡上指定的位置用2B 铅笔涂黑。
答案用0.5毫米黑色签字笔写在答题卡上对应的答题区域内，写在试题卷、草稿纸和答题卡上的非选修题答题区域的答案一律无效。
6、本科目考试结束后，请将本试题卷、答题卡、草稿纸一并依序排列上交。
第Ⅰ卷一、选择题：本大题共12个小题，毎小题5分，共60分．在每小题给出的四个选项中，只有一个选项是符合题目要求的 1．已知命题p ：2,0x R x ∀∈>，则A ．命题p ⌝：2,0x R x ∀∈≤，为假命题B ．命题p ⌝：2,0x R x ∀∈≤，为真命题C ．命题p ⌝：200,0x R x ∃∈≤，为假命题D ．命题p ⌝：200x ∃≤，为真命题2．已知i 是虚数单位，则41()1i i+-等于A ．iB ．—iC ．1D ．—1 3．“上医医国”出自《国语・晋语八》，比喻高贤能治理好国家．现把这四个字分别写在四张卡片上，其中“上”字已经排好，某幼童把剩余的三张卡片进行排列，则该幼童能将这句话排列正确的概率是 A ．13B ．16C ．14D ．1124．中心在原点，焦点在x 轴上的双曲线的一条渐近线经过点（4，一2），则它 的离心率为A B C 2D 25．已知△ABC 是边长为1的等边三角形，D 为BC 中点，则()()A B A C A B D B +⋅-的值为A ．32-B ．32C ．34-D ．346．已知0x 是11()()2xf x x=+的一个零点，1020(,),(,0)x x x x ∈-∞∈，则A ．f (x 1)<0,f (x 2)<0B ．f (x 1)>0,f (x 2)>0C ．f (x 1)>0,f (x 2)<0D ．f (x 1)<0,f (x 2)>07．已知等比数列{}n a 中，各项都是正数，且a 1、12a 3、2a 2成等差数列，则91078____a a a a +=+A ．3+B ．1-C ．1+D ．3-8．函数2s in 2xy x =的部分图象可能是9．正四棱锥的顶点都在同一球面上．若该棱锥的高为4，底面边长为2，则该球的表面积为 A ．814π B ．16π C ．9π D ．274π10若函数()s in (2)o s (2)()2f x x x πθθθ=+++<的图象关于点(,0)6π对称，则f （x ）的单调速增区间为 A ．5[,],36k k k z ππππ++∈ B ．[,],63k k k z ππππ-++∈ C ．7[,],1212k k k z ππππ-+-+∈ D ．5[,],1212k k k z ππππ-++∈11．设函数22()()(),,()xf x x t e t x R f x b =-+-∀∈≥恒成立，则实数b 的最大值为A 2B ．12C ．1D ．e12．设O 为坐标原点，P 是以F 为焦点的抛物线y 2＝2px （p ＞0）上任意一点，M 是线段PF 上的点，且2P M M F =，则直线OM 的斜率的最大值为A ．3B ．23C ．1D ．2第Ⅱ卷本卷包括必考题和选考题两部分．第13～21題为必考题，每个试题考生都必须作答．第22～23題为选考题，考生根据要求作答二、填空题：本大题共4个小题，每小题5分，共20分 13．已知函数2()2()lo g xa f x +=，若f （2）＝0，则a ＝_____。
湖南省雅礼中学高三上学期月考试题20页word文档
湖南省雅礼中学2019届高三月考英语试题Part One: Listening Comprehension (30 points)omittedPart two: language KnowledgeSection A (15 points)Directions: Beneath each of the following sentences there are 4 choices marked A, B, C and D. Choose the one answer that best completes the sentence.21．---Where did you come across our chemistry teacher ?--- It was in the supermarket ______I purchased mooncakes．A．that B．which C．where D．when22. A series of stimulus policies and supportive measures taken by the government _____ to promote change in the economic environment in this area.A. are expectingB. are expectedC. is expectingD. is expected23. With all the novels he was interested in _______, he left the library and went back to his dorm.A. borrowedB. borrowingC. to borrowD. borrow24.---The research on the new bird flu virus vaccine is challenging and demanding. Who do you think can do the job?---____ my students have a try?A. MayB. MustC. WillD. Shall25. Between the two periods of classes is a break, we can have a short rest.A．then B．where C．when D．which26. “If" he added, “________ to car ry out the plan, we would surely make a big profit for our company."A．to permit B．to be permitted C．permitting D．permitted27. ---How do you think I can make up with Qiong?---Put aside_____ you disagree and try to find_____ you have in common.A. what, whatB. where, whatC. what, whetherD. where, whether28. _______ the calculation is right, scientists can never be sure that they have included all variables and modeled them accurately.A. Even ifB. As far asC. If onlyD. So long as29. I ______ him in time, otherwise he would have fallen off the bike.A. had supportedB. supportedC. have supportedD. support30.May 12th，2019 is a special day，________, I think，that will be remembered by the Chinese forever.A. oneB. itC. whichD. that31. --- Could you introduce me a high quality car?--- My pleasure. _______ well even on wet roads, this kind of car is very popular.A. HandledB. To handleC. HandlingD. Being handled32. Only when he returned _________ that the war had ended and the army had come back. 2A. we tellB. we toldC. did we tellD. were we told33. According to the report, the American government didn’t intend to have itstroops____of war zone.A. pulled outB. dropped outC. driven outD. run out34. The bus was crowded with passengers going home from market, most of ________ carrying heavy bags and baskets full of fruit and vegetables they had bought there.A. whomB. themC. whoD. which35. Our society insists on regular habits, timekeeping and punctuality, and whether we like it or not, ______ we mean to make our way in society, we have to comply ( to act in accordance with a demand, rule, etc.) its demands.A. whetherB. afterC. ifD. untilSection B (18 points)Directions: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with word or phrases that best fits the context.Everyone wants to win a first-place blue ribbon, to be the best in something. Even kids in Kindergarten want that blue ribbon. In sports, I was never a blue-ribbon person. In a race, I was always 36 . In baseball I was likely to be 37 on the head or drop the ball. During the spring of my kindergarten year, our class had a field trip to a park in a town about twenty miles away. Making that drive now is no big 38 but when you’re six and you’ve lived in a town of 300 people all your life, going to a big town of a couple of thousand people is really something.I don’t remember too much about it. But there was one that I will never forget -----the __39__ race. The parents tied our feet together. One little boy got me fora 40 . He was the second most 41 boy in our class so he usually won at everything and I knew that with me tied to him he didn’t have a chance. And I’m sure he knew he was in trouble. The gun sounded and we were off. Some couples were falling and stumbling all around us, 42 we stayed on our feet and made it to the other side. 43 , when we turned around and headed back for home, we were in the lead! Only one couple had a chance to win, and they were a good several yards behind us.A few feet from the finish line, disaster struck: I tripped and fell. We were 44 enough that my partner could have easily dragged me across the finish line and won. But he didn’t. Instead he stopped, 45 down and helped me up ------ just at the other couple crossed the finish line. As a result, we received a small red ribbon for coming in second.I still remember that moment when the young boy decided that helping a friend get on her feet was more important than winning a blue ribbon. And 13 years later, I still have that little ribbon because it’s a 46 that a friend like this boy is one who really 47 .36. A. last B. first C. quick D. successful37. A. touched B. felt C. hit D. beaten38. A. question B. event C. one D. deal39. A. one-legged B. two-legged C. three-legged D.four-legged40. A. partner B. helper C. supporter D. competitor41. A. tallest B. youngest C. athletic D. handsome42. A. but B. therefore C. however D. and43. A. Obviously B. Unbelievably C. Secretly D. Undoubtedly44. A. strong B. brave C. clever D. close45. A. lay B. slowed C. moved D. reached46. A. warning B. reminder C. gift D. notice47. A. depends B. counts C. supports D. worthy Section C (12 points)Directions: Complete the following passage by filling in each blank with one word t hat best fits the context.There was a new guy in the office. When we walked by each other in the hallway, we smiled and said " hi". Actually, he said, "Hi, Joe." 48But I just said "hi" because... well... I didn't know his name, and was embarrassed to ask.I passed him in the hall again yesterday. As I was continuing down the hall, feeling pretty good about how well I was coping 49with not knowing his name, when I heard a familiar voice behind me. "I don't know you!" It was Sylvia, one of the kindest people I know. Sylvia was friendly and warm, a welcoming mother to everyone in the office. She was walking a few paces behind me, and evidently she didn't know the new guy 50yet .But rather than just smile and say "hi," Sylvia did what she did. Not only 52did she announce that she didn't know him, but asked him his name, 51toldhim hers and engaged him in conversation. Before 53that they were chatting like old friends about some things they had in 54common . And suddenly for Sylvia, the new guy wasn't the new guy anymore. He was Mitch, a colleague with children, hobbies, interests and a little shared history.I was stunned -- and a little embarrassed by the ease with 55how Sylvia negotiated that transition. It doesn't take much to turn an unfamiliar face in into a friend. You just have to get over yourself and reach out a little. Ask a question. Learn a name. And just like that -- no more new guyPart Three: Reading Comprehension (30 points)AWhat incident began the series of traffic accidents?As time slid by, we have too much to reflect on. We have all experienced days when everything goes wrong, A day may begin well enough, but suddenly everything seems to get out of control. What happens is that a great number of things choose to go wrong at the same moment, as if a single unimportant eventThis is no joke, already, in most people’s daily life.Let us suppose that you are preparing a meal and keeping an eye on the baby at the same time. The telephone rings and this marks a series of catastrophes. While you are on the phone, the baby pulls the tablecloth off the table, breaking half of your best glasses and cutting himself. You hang up hurriedly and attend to your baby, glasses, etc. Meanwhile, the meal gets burnt, as if this were not enough to reduce you to tears, your husband arrives, unexpectedly bringing three guests to dinner.Things can go wrong on a big scale, as a number of people recently discovered in Parramatta, a suburb of Sydney on the 10th of August, 2009. During the rush hour two cars collided (撞车) and both drivers began to argue. The woman immediately behind the two cars happened to be a learner. She suddenly got into a panic and stopped her car right away. This made the driver who was following her brake hard. His wife was sitting beside him with a large cake in her hands, paying no attention to the sudden change. As she was thrown forward, the cake went right through the windscreen and landed on the road. Seeing a cake flying through the air, a lorry driver who was drawing up alongside the car pulled up all of a sudden. The lorry was loaded with empty beer bottles and hundreds of them slid off the back of the vehicle and on to the road. This led to yet another angry argument. Meanwhile, the traffic piled up behind. It took the police nearly an hour to get the traffic on the move again. In the meantime, the lorry driver had to sweep up hundreds of broken bottles. Only two stray(迷路的) dogs benefited from all this confusion, for they greedily ate up what was left of the cake. It was just one of those days.56.“Let’s suppose that you are preparing a meal and keeping an eye on the baby at the same time.” What does the underlined part mean?A.putting one of your eyes on the baby.B.making sure the baby is safe.C.playing together with the baby.D.watching the baby playing.57.Why did the writer use the story that took place in Sydney?A. He wanted to tell how terrible the traffic is in Sydney.B. He wanted to state that being a driver is a terrible thing.C. He wanted to use it as an example to support his idea.D. He wanted to warn the readers not to sit beside the driver.58. According to the passage, which of the following could be the main cause to block the traffic?A. Two cars collided and both drivers began to argue.B. The woman behind was a learner and stopped her car suddenly.C. The lorry driver pulled up all of a sudden.D. There were dogs in the way.59. Which of the following is NOT true according to the passage?A. A chain of reactions are usually caused by something that happens unexpectedly.B. The woman following behind the two cars was an experienced driver.C. A chain of reactions might be caused by something unimportant in our daily life.D. Some small happenings may cause great confusion.60. What can we infer from the passage?We should be careful no matter where we areA single unimportant event surely results in a chain of reactionsStray dogs always block trafficSomething terrible always happens unexpectedly.AB“Tear them apart!” “Kill the damn fool!” “Murder the referee ( 裁判)!” “Whydon’t do something there, you idiot!”These are common comments one may hear at various sporting events. At the time they are made, they may seem innocent enough. But we should not kid ourselves. They have been known to influence behavior in such a way as to lead to real bloodshed (流血). So many stories have been written about the way words affect us .It has been shown that words having certain meanings may cause us to react in ways quite foreign to what we consider to be our usual humanistic behavior.I see the term “opponent” as one of those words . Perhaps the time has come to delete it from sports terms.The dictionary meaning of the term “opponent” is “adversary”: “enemy”; “one who opposes your interests.” Thus, when a player meets an opponent, he or she may tend to treat that opponent as an enemy. At such times, winning may control one’s knowledge and intellectual ability, and every action, no matter how gross, may be considered justifiable. I recall an incident in a handball game when a referee refused a player’s request for a time out for a glove change because he did not considered then wet enough. The player went on to rub his gloves across his wet T-shirt and then stated loudly. “Are they wet enough now?”In the heat of battle, players have been observed to throw themselves across the court without considering the consequences that such a move might have on anyone in their way. I have also witnessed a player reacting to his opponent’s international and illegal blocking by deliberately hitting him with the ball as hard as he could during the game. Off the court, they are good friends. Does that make any sense? It certainly gives proof of a court attitude which departs from normal behavior.Therefore, I believe it is time we elevated(提升)the game to the level where it belongs thereby setting an example to the rest of the sporting world . Replacing the term “opponent” with “associate” could be an ideal way to start.The dictionary meaning of the term “associate” is “colleague”; “friend”; “companion.” Reflect a moment! You may soon see and possibly feel the difference in your reaction to the term “associate” rather than “opponent.”61. Which of the following statements best expresses the author’s view?A. Aggressive behavior in sports can have serious consequencesB. The words people use can influence their behaviorC. Unpleasant words in sports are often used by foreign athletesD. Unfair judgments by referees will lead to violence on the sports field62. Harsh words are spoken during games because the players _______A. are too eager to winB. are usually short-tempered and easily offendedC. cannot afford to be polite in fierce competitionD. treat their contestants as enemies63. What did the handball player do when he was not allowed a time out to change his gloves?A. He refused to continue the gameB. He angrily hit the referee with a ballC. He claimed that the referee was unfairD. He wet his gloves by rubbing them across his T-shirt64. According to the passage, players, in a game , may _______A. deliberately throw the ball at anyone illegally blocking their wayB. keep on screaming and shouting throughout the gameC. lie down on the ground as an act of protestD. kick the ball across the court with force65. What is the main idea of the passage?A.The author calling on raising the referee’s sense of responsibilityB.The author calling on players to use clean language on the courtC.The author calling on changing the attitude of players on the sports fieldD.The author calling on regulating the relationship between players and refereesCIn Japan many workers who work in large corporations have a guarantee of lifetime employment. During their employment, they will not be laid off during recessions(经济萧条) or when the tasks they perform are taken over by robots. To some observers, this is what they call capitalism at its best, because workers are treated as people not things. Others see it as necessarily inefficient and they also believe it cannot continue if Japan is to remain competitive with foreign corporations by being more concerned about profits and less concerned about people.Defenders of the system argue that those who call it inefficient do not understand how it really works. In the first place not every Japanese worker has the guarantee of a lifetime job. The lifetime employment system includes on ly “regular employees”. Many employees are not included in this category, including all women. All businesses have many part-time and temporary employees. These workers arehired and laid off during the course of the business cycle just as employees in the United States are. These “irregular workers” make up about 10 percent of the non-agricultural work force. Additionally, Japanese firms keep some flexibility through the large-scale use of subcontractors（转承包者）. This practice is much more common in Japan than in the United States.The use of both subcontractors and temporary workers has increased remarkably in Japan since the 1974-1975 recessions. All this leads some people to argue that the Japanese system is not all that different from the American system. During recessions Japanese corporations lay off temporary workers and give less business to subcontractors. In the United States, corporations lay off those workers with the least seniority(资历). The difference then is probably less than the term “lifetime employment” suggests, but there still is a difference. And this difference cannot be understood without looking at the values of Japanese society. The relationship between employer and employee cannot be explained in purely contractual(合同的) terms. Firms hold on to the employees and employees stay with one firm. There are also practical reasons for not jumping from job to job. Most retirement benefits come from the employer. Changing jobs means losing these benefits. Also, teamwork is an essential part of Japanese production. Moving to a new firm means adapting to a different team and at least temporarily, possessing lower productivity and lower pay.66.It is stated in the second paragraph that ____.A. defenders themselves do not appreciate the systemB. about 90% of “irregular workers” are employed in agricultureC. the business cycle occurs more often in Japan and in the U.S.D. not all employees can benefit from the policy67. During recessions those who are to be fired first in the U.S. corporations are ____.A. regular employeesB. part-time workersC. junior employeesD. temporary workers68. According to the passage, Japanese firms are remarkably different from American firms in that the former ____.A. use subcontractors in larger amountB. are less flexible in terms of lifetime employmentC. hold on to the values of societyD. are more efficient in competition than the latter69. Which of the following does NOT account for the fact that a Japanese worker is unwilling to change his job?A. He will probably be low-paid.B. He will not be able to possess some job benefits.C. He has got used to the teamwork.D. He will be looked down upon by his prospective employer.70. Which of the following can be the best title for this passage?A. The guarantee of employment in JapanB. The consequence of the Japanese systemC. The advantages of lifetime employment in JapanD. The expectations of capitalismPart Four: WritingSection A (10 points)Write NO MORE THAN 3 WORDS for each answer.Many workers depend on plans offered by their employers to help pay for their retirement. There are two major kinds of retirement plans. One is defined by what is paid out, the other by what is paid in.The first is called a defined benefit plan, or pension. It provides set payments based on the number of years an employee has worked. These plans often pay for health care and other costs. They might also provide money to family members when the pensioner dies.Pensions, however, can be a big cost to employers. In the United States, the change from a manufacturing economy to a service economy has resulted in fewer and fewer traditonal plans.In 1974, the Employment Retirement Income Act set rules to protect pensions. That law also created a federal agency called the Pension Benefit Guaranty Corporation. As a result, it is now responsible for the current and future pensions of more than one million workers. At the end of last September，it reported a deficit of almost twenty-three thousand million dollars in its single-employer insurance program. The agency takes control of pensions that do not have enough money to pay claims. It currently guarantees thirty thousand plans. Forty-four million Americans are in these plans. But there are limits to how much they can receive if their pension fails. The other major kind of retirement plan is called a defined contribution plan. Two things define how much a worker will get at retirement. The first is how much boththe worker and the employer paid into the plan. The other is the performance of its investments.Defined contribution plans can reduce the taxes of workers and employers. But some plans are very complex. An easier way for small employers to offer retirement savings is through a Savings Incentive Match Plan. It permits contributions of up to ten thousand dollars a year toward retirement.Title: Saving for retirement76.________Features 77._________ 78._________Saving IncentiveMatch PlanWays to bedefined79._________ 80.________81._________ 82._________ ·Amount of money paid by worker and the employer ·83._________________84._________ Likely to failgovernmentguaranty·tax – reducing·being85._______Easier for smallemployersSection B (10 points)Directions: Read the following passage. Answer the questions according to the information given in the passage and the required word limit. Write your answers onyour answer sheet.More than 300 high school students from 40 schools across the globe gathered this week at the Western Academy of Beijing, one of the capital's leading international schools, to discuss how they can "change" the world by helping to solve global problems.It is the first time an Asian country has hosted the Global Issues Network conference, which was set up in 2019 by teachers and students from six international schools in Europe. It aims to help students realize they can make a difference by empowering them to work with peers to develop solutions to global issues.The idea for the conference came from the book High Noon: Twenty Global Problems, Twenty Years to Solve Them by Jean-Francois Rischard, former World Bank vice-president for Europe, which presents a series of challenges that can be solved only through global cooperation.One of the participants at the conference was Austin Gutwein from Arizona in the United States, who was just 9 when he began raising money for children orphaned by AIDS.In 2019, the junior high school student, now 13, launched the basketball-themed Hoops of Hope, which "charged" people in his neighborhood $1 for every basket he shot.Since then, thousands of youngsters have picked up on the idea and helped raised more than $325,000 for the cause."It works because kids my age want a chance to do something great and be part of something like this," Gutwein told China Daily."I realized these kids weren't any different from me, except they were suffering and I wanted to do something to help them," he said.With the help of non-government organizations, Hoops of Hope has built a school for HIV/AIDS orphans and a medical lab in Zambia in South Africa.Another participant, Li Yeqiao, a 15-year-old student at Beijing Bayi Middle School who chairs the school's Roots & Shoots group, told the conference how the group seeks to improve the way electronic waste is disposed of, and encourages people to save water and care for animals."We have developed 3R (Reduce, Reuse and Recycle) living habits and are optimistic our initiatives will have a positive impact on the local environment," Li said.British animal behavior expert Jane Goodall introduced the Roots & Shoots concept to China in 2000 to promote environmental and humanitarian education programs to children. There are now 300 of such groups in the country.86. What kind of problems are the young students trying to solve? (no more than 2 words.)87.How does Austin Gutwein raise money for children orphaned by AIDS? (with no more than 7 words)88. What does Li Yeqiao think of their 3R? (with no more than 10 words)89. What’s the main i dea of this passage? （no more than 12words）Section C (25 points)Directions :Write an English composition according to the instructions given below in Chinese .近来，越来越多的中学生家长在学校附近租房陪读。
湖南省长沙市雅礼中学2019届高三数学上学期月考试题(一)文
长沙市雅礼中学2019届高三月考试巻（一）数学（文科）第I 卷一、选择题：本大题共12个小题，每小题5分，共60分．在每小题给出的四个 选项中，只有一个选项是符合题目要求的1．已知集合{}{}2lg(4),2,0,1,2A x y x B ==-=-，则A B =A ．{}0,1B ．{}1,0,1-C ．{}2,0,1,2-D ．{}1,01,2-2．在复平面内，复数121i i-+的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执行如图所示的程序图，如果输入1a =，2b =，则输出的a 的值为A ．7B ．8C ．12D ．164．若变量x ，y 满足约束条件30101x y x y y +-≤⎧⎪-+≥⎨⎪≥⎩，则2z x y =+的最大值为A ．1B ．3C ．4D ．55．已知回归直线的斜率的估计值是1．23，样本点的中心为（4，5），则回归直线的方程是A ． 1.234y x ∧=+B ． 1.230.8y x ∧=+C ． 1.230.08y x ∧=+D ． 1.230.08y x ∧=-6．在数列{}n a 中，11a =，数列{}n a 是以3为公比的等比数列，则20193log a 等于 A ．2017 B ．2018 C ．2019 D ．20207．设()s i n ()c o s ()5f x a x b x παπβ=++++，且(2018)2f =，则(2019)f 等于A ．2B ．2-C ．8D ．8-8．某几何体的三视图如图所示，其中俯视图是个半圆，则该几何体的表面积为A ．32π B．π．52π+．32π+9．将函数sin 2y x =的图象向右平移16π个单位后得到的函数为()f x ，则函数()f x 的图象 A ．关于点（12π，0）对称 B ．关于直线12x π=对称 C ．关于直线512x π=对称 D ．关于点（5,012π）对称 10．若函数6,2()(03log ,2x a x x f x a x -+≤⎧=>⎨+>⎩且1a ≠）的值域是［4，＋∞），则实数a 的取值范围是A ．(1,2]B ．(0,2]C ．[2,)+∞ D．(111．已知点F 是双曲线22221(0,0)x y a b a b-=>>的左焦点，点E 是该双曲线的右顶点，过F 且垂直于x 轴的直线与双曲线交于A 、B 两点，若△ABE 是饨角三角形，则该双曲线的离心率e 的取值范围是A ．(1,)+∞B ．(1,2) C．[1,1 D ．(2,)+∞12．已知△ABC 是边长为2的等边三角形，P 为△ABC 所在平面内一点，则()PA PB PC ⋅+的最小值是A ．32-B ．2-C ．43- D ．1- 第II 卷本卷包括必考题和选考题两部分．第13～21题为必考题，每个试題考生都必须作答．第22～23题为选考题，考生根据要求作答．二、填空题：本大题共4小題，每小题5分，共20分13．锐角△ABC 中，AB ＝4，AC ＝3，△ABC的面积为BC ＝_______。
湖南省长沙市雅礼中学2019届高三上学期月考(一)数学(文)试卷(含答案)
雅礼中学2019届高三月考试卷（一）数学（文科）第I卷一、选择题：本大题共12个小题，每小题5分，共60分．在每小题给出的四个选项中，只有一个选项是符合题目要求的1.已知集合，则A. B. C. D.【答案】A【解析】【分析】化简集合A，根据交集的定义写出A∩B．【详解】，∴故选：A【点睛】在进行集合的运算时要尽可能地借助Venn图和数轴使抽象问题直观化．一般地，集合元素离散时用Venn图表示；集合元素连续时用数轴表示，用数轴表示时要注意端点值的取舍．2.在复平面内，复数的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【答案】B【解析】【分析】利用两个复数代数形式的除法，虚数单位i的幂运算性质化简复数z，求出其共轭复数，从而得到答案.【详解】∵复数===﹣1﹣3i，∴，它在复平面内对应点的坐标为（﹣1，3），故对应的点位于在第二象限，故选：B．【点睛】本题主要考查两个复数代数形式的除法，共轭复数，虚数单位i的幂运算性质，复数与复平面内对应点之间的关系，属于基础题．3.执行如图所示的程序图，如果输入，，则输出的的值为A. 7B. 8C. 12D. 16【答案】B【解析】【分析】根据程序框图，依次判断是否满足条件即可得到结论．【详解】若输入a=1，b=2，则第一次不满足条件a＞6，则a=2，第二次不满足条件a＞6，则a=2×2=4，第三次不满足条件a＞6，则a=4×2=8，此时满足条件a＞6，输出a=8，故选：B．【点睛】本题主要考查程序框图的识别和运行，依次判断是否满足条件是解决本题的关键，比较基础．4.若变量x，y满足约束条件，则的最大值为A. 1B. 3C. 4D. 5【答案】D【解析】【分析】画出满足条件的平面区域，求出A点的坐标，将z=2x+y转化为y=﹣2x+z，结合函数图象求出z的最大值即可．【详解】画出满足条件的平面区域，如图示：，由，解得：A（2，1），由z=2x+y得：y=﹣2x+z，显然直线y=﹣2x+z过（2，1）时，z最大，故z的最大值是：z=4+1=5，故选：D．【点睛】本题考查的是线性规划问题，解决线性规划问题的实质是把代数问题几何化，即数形结合思想.需要注意的是：一，准确无误地作出可行域;二，画目标函数所对应的直线时，要注意让其斜率与约束条件中的直线的斜率进行比较，避免出错;三，一般情况下，目标函数的最大值或最小值会在可行域的端点或边界上取得.5.已知回归直线的斜率的估计值是1．23，样本点的中心为（4，5），则回归直线的方程是A. B.C. D.【答案】C【解析】【分析】根据回归直线方程一定经过样本中心点这一信息，即可得到结果．【详解】由条件知，，设回归直线方程为，则.∴回归直线的方程是故选：C【点睛】求解回归方程问题的三个易误点：（1）易混淆相关关系与函数关系，两者的区别是函数关系是一种确定的关系，而相关关系是一种非确定的关系，函数关系是一种因果关系，而相关关系不一定是因果关系，也可能是伴随关系．（2）回归分析中易误认为样本数据必在回归直线上，实质上回归直线必过(，)点，可能所有的样本数据点都不在直线上．（3）利用回归方程分析问题时，所得的数据易误认为准确值，而实质上是预测值(期望值)．6.在数列中，，数列是以3为公比的等比数列，则等于A. 2017B. 2018C. 2019D. 2020【答案】B【解析】【分析】由等比数列通项公式得到，再结合对数运算得到结果.【详解】∵，数列是以3为公比的等比数列，∴∴故选：B【点睛】本题考查等比数列通项公式，考查指对运算性质，属于基础题.7.设，且，则等于A. 2B.C. 8D.【答案】C【解析】【分析】由题意利用诱导公式求得asinα+bcosβ=﹣3，再利用诱导公式求得f（2019）的值．【详解】∵∴即而=8故选：C【点睛】本题主要考查诱导公式的应用，体现了整体的思想，属于基础题．8. 某几何体的三视图如图所示，其中俯视图是个半圆，则该几何体的表面积为( )A. B. C. D.【答案】D【解析】试题分析：由三视图可知，该几何体为圆锥的一半，那么该几何体的表面积为该圆锥表面积的一半与轴截面面积的和．又该半圆锥的侧面展开图为扇形，所以侧面积为，底面积为，由三视图可知，轴截面为边长为2的正三角形，所以轴截面面积为，则该几何体的表面积为．选D考点：几何体的表面积，三视图9.将函数的图象向右平移个单位后得到的函数为，则函数的图象A. 关于点（，0）对称B. 关于直线对称C. 关于直线对称D. 关于点（）对称【答案】C【解析】【分析】利用平移变换得到，然后研究函数的对称性.【详解】将的图象右移个单位后得到图象的对应函数为，令得，，取知为其一条对称轴，故选：C.【点睛】函数的性质(1) .(2)周期(3)由求对称轴(4)由求增区间;由求减区间.10.若函数且）的值域是［4，＋∞），则实数的取值范围是A. B. C. D.【答案】A【解析】【分析】先求出当x≤2时，f（x）≥4，则根据条件得到当x＞2时，f（x）=3+log a x≥4恒成立，利用对数函数的单调性进行求解即可．【详解】当时，，要使得函数的值域为，只需的值域包含于，故，所以，解得，所以实数的取值范围是.故选：A【点睛】本题主要考查函数值域的应用，利用分段函数的表达式先求出当x≤2时的函数的值域是解决本题的关键．11.已知点是双曲线的左焦点，点是该双曲线的右顶点，过且垂直于轴的直线与双曲线交于两点，若是钝角三角形，则该双曲线的离心率的取值范围是（）A. B. C. D.【答案】D【解析】如图，根据双曲线的对称性可知，若是钝角三角形，显然为钝角，因此，由于过左焦点且垂直于轴，所以，，，则，，所以，化简整理得：，所以，即，两边同时除以得，解得或（舍），故选择D.点睛：求双曲线离心率时，将提供的双曲线的几何关系转化为关于双曲线基本量的方程或不等式，利用和转化为关于的方程或不等式，通过解方程或不等式求得离心率的值或取值范围，在列方程或不等式的过程中，要考虑到向量这一重要工具在解题中的应用.求双曲线离心率主要以选择、填空的形式考查，解答题不单独求解，穿插于其中，难度中等偏高，属于对能力的考查. 12.已知△ABC是边长为2的等边三角形，P为△ABC所在平面内一点，则的最小值是A. B. C. D.【答案】A【解析】【分析】根据条件建立坐标系，求出点的坐标，利用坐标法结合向量数量积的公式进行计算即可．【详解】以为轴，的垂直平分线为轴，为坐标原点建立坐标系，则,设，所以，所以，，故选：A【点睛】本题主要考查平面向量数量积的应用，根据条件建立坐标系，利用坐标法是解决本题的关键．第II卷本卷包括必考题和选考题两部分．第13～21题为必考题，每个试題考生都必须作答．第22～23题为选考题，考生根据要求作答．二、填空题：本大题共4小題，每小题5分，共20分13.锐角中，，△ABC的面积为，则＝_______。
2019年高考数学二轮复习解题思维提升专题04：三角函数与解三角形小题部分训练手册含答案
专题04 三角函数与解三角形小题部分【训练目标】1、掌握三角函数的定义，角的推广及三角函数的符号判断；2、熟记同角三角函数的基本关系，诱导公式，两角和差公式，二倍角公式，降幂公式，辅助角公式，并能熟练的进行恒等变形；3、掌握正弦函数和余弦函数的图像与性质，并能正确的迁移到正弦型函数和余弦型函数；4、掌握三角函数的图像变换的规律，并能根据图像求函数解析式；5、熟记正弦定理，余弦定理及三角形的面积公式；6、能熟练，灵活的使用正弦定理与余弦定理来解三角形。
【温馨小提示】此类问题在高考中属于必考题，难度中等，要想拿下，只能有一条路，多做多总结，熟能生巧。
【名校试题荟萃】1、（福建省“永安一中、德化一中、漳平一中”2019届高三三校联考试题）已知角的顶点与原点重合，始边与轴的正半轴重合，终边在直线上， 则＝（ ）【答案】C2、（福建省上杭县第一中学2019届高三上学期期中考试）在中，内角，，所对应的边分别为，，，若，且，则________。
【答案】【解析】显然，则，则，根据两角差的正弦公式，利用降幂公式及辅助角公式得，再由正弦定理可求得αx x y 2-=α2cos .A 54-.B 53-.C 53.D 54ABC △A B C a b c =+ca b12sin 0A≠。
3、（湖南省衡阳市第八中学2019届高三上学期第四次月考试题+数学（文））的内角的对边分别为，已知，则角 ( )A.B. C. D. 【答案】D4、（江苏省南京市六校联合体2019届高三上学期12月联考试题）已知，则的值是 ．【答案】【解析】先利用两角差的正切公式可求得，结合，利用同角三角函数的基本关系可求得，则。
5、（陕西省宝鸡市宝鸡中学2019届高三上学期模拟考试（二））已知，则.【答案】ABC D ,,A B C ,,a b c C =34p 3p 6p 4p⎪⎭⎫⎝⎛∈20πα,)sin(6πα+410+3tan 4α=⎪⎭⎫⎝⎛∈20πα,13【解析】由于，根据诱导公式知。
湖南省长沙市雅礼中学2019届高三月考(七)数学(理)试题(解析版)
雅礼中学2019届高三月考试卷（七）数学（理科）注意事项：1. 本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分。
答卷前，考生务必将自己的姓名、准考证号填写在答题卡上。
2. 回答第Ⅰ卷时，选出每小题答案后，用铅笔把答题卡上对应题目的答案标号涂黑。
如需改动，用橡皮擦干净后，再选涂其它答案标号。
写在本试卷上无效。
3. 回答第Ⅱ卷时，将答案写在答题卡上，写在本试卷上无效。
4. 考试结束后，将本试卷和答题卡一并交回。
第Ⅰ卷一、选择题：本题共12小题，每小题5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，.若，则的取值范围为（）A. B. C. D.【答案】A【解析】由已知，若，则，即，故选A．2.设为虚数单位，复数满足，则共轭复数的虚部为（）A. B. C. D.【答案】C【解析】【分析】根据条件求出复数，然后再求出共轭复数，从而可得其虚部．【详解】∵，∴，∴，∴复数的虚部为．故选C．【点睛】本题考查复数的乘除法的运算及共轭复数的概念，其中正确求出复数是解题的关键，对于复数的运算，解题时一定要按照相关的运算法则求解，特别是在乘除运算中一定不要忘了．3.某中学2018年的高考考生人数是2015年高考考生人数的倍，为了更好地对比该校考生的升学情况，统计了该校2015年和2018年的高考情况，得到如图柱状图：则下列结论正确的是A. 与2015年相比，2018年一本达线人数减少B. 与2015年相比，2018年二本达线人数增加了倍C. 2015年与2018年艺体达线人数相同D. 与2015年相比，2018年不上线的人数有所增加【答案】D【解析】【分析】设2015年该校参加高考的人数为，则2018年该校参加高考的人数为.观察柱状统计图，找出各数据，再利用各数量间的关系列式计算得到答案.【详解】设2015年该校参加高考的人数为，则2018年该校参加高考的人数为.对于选项A.2015年一本达线人数为.2018年一本达线人数为，可见一本达线人数增加了，故选项A错误；对于选项B，2015年二本达线人数为，2018年二本达线人数为，显然2018年二本达线人数不是增加了0.5倍，故选项B错误；对于选项C，2015年和2018年.艺体达线率没变，但是人数是不相同的，故选项C错误；对于选项D，2015年不上线人数为.2018年不上线人数为.不达线人数有所增加.故选D. 【点睛】本题考查了柱状统计图以及用样本估计总体，观察柱状统计图，找出各数据，再利用各数量间的关系列式计算是解题的关键．4.设，，若函数为奇函数，则的解析式可以为（）A. B. C. D.【答案】B【解析】试题分析：，则，代入，得为奇函数，满足题意，故选B.考点：（1）函数的奇偶性；（2）定积分的计算.5.如图所示，在中，点在线段上，且，若，则（）A. B. C. 2 D.【答案】B【解析】分析：从A点开始沿着三角形的边转到D，则把要求的向量表示成两个向量的和，把写成的实数倍，从而得到，从而确定出，最后求得结果.详解：，所以，从而求得，故选B.点睛：该题考查的是有关向量的基本定理，在解题的过程中，需要利用向量直角的关系，结合三角形法则，求得结果.6.榫卯是在两个木构件上所采用的一种凹凸结合的连接方式，凸出部分叫榫，凹进部分叫卯，榫和卯咬合，起到连接作用，代表建筑有：北京的紫禁城、天坛祈年殿、山西悬空寺等，如图所示是一种榫卯的三视图，其表面积为（）A. B. C. D.【答案】B【解析】由三视图可知榫卯的榫为底边长为高为长方体，卯为底面半径为，高为的中空的圆柱体，设表面积为，侧面积为，上下底面积的和为，则有，故选B【点睛】本题重点是抓住榫卯的工作原理—榫凸卯凹、榫卯咬合连接，由此发现卯（中空的圆柱体）中间所缺失的上下表面积刚好由榫的上下表面积补充。
湖南省长沙市长郡中学2019届高三上学期第二次月考数学(理)答案
# 0" 6 ; 3# = # $ # #+ # ! # " # ; 3# " ; " 3#6 " = + # 0 " 6 0 # 6 0 $ # # # # # # " 时 " 易得#$ $ +# # + $#$ # $ 6> 时$ % $ < < " " 当#0 " 时取得最小值 即" # # # # 0 $ 0 $ + + + =函数$ & ? 2 30 " $ $ < 0 " < < # ! " # ! " 在 上单调递增 即< 解得##! 故选 .! =函数" $ 6> = < < # < " ! # # " " 二 填空题
理科数学试题参考答案! 长郡版" !# !
又1 #也符合& "0! 3& " 1 3! # # 3$, ! ! " #分" = 3 0! " # 参加足球社团的概率为 ! ! $ 解析% ! " 依题意& 这'个人中& 每个人参加篮球社团的概率为 & #分" " % ! " & & 设+ 这'个人中恰有-个人参加篮球社团, 为事件 ( & & & & " & 0 $ " # & ' -! ' ! # - " & ! & & & & " & 则 /! 0, ( 0 $ " # & ' -" ' & & # & & # ! 分" " " 这'个人中恰有"个人参加篮球社团的概率为 /! ( 0, ( 0 ! "" ' & & + " & & ! " 由已知得 4 的所有可能取值为$ # ' ! # # # " # + # ' # /! 40 0 0 & $" 0, ' & & + " # * & # & # ' $ " " & " ! " / 40 6, 0 & # 0, ' ' + " & & & & ' ' " * # " $ ' +分" /! 40 6, 0 ! ! '" 0, ' ' + " & & =4 的分布列为*
【精准解析】湖南省长沙市雅礼中学2020届高三上学期第2次月考数学(理)试题
设数列an 的公差为 d ，则有 2a22 a12 a32 ，即 2 (2 d )2 22 (2 2d )2 ，
解得 d 0 ，所以 an 2 ， an2 4 ，
所以 a22 a33 a44 a55 4 8 16 32 60 ，故选 A.
【点睛】本题主要考查了等差数列的定义，以及等差数列的通项公式的应用，着重考查了推
A. (0, 1 ] 2
B. (1, 0) [1 , 2) 2
C. (2, 0) [1 ,1) 2
【答案】C
【解析】
【分析】
先求解不等式化简集合 A 和 B，再根据集合的交集运算求得结果即可.
【详解】因为集合 A x | x2 x 2 0 {x | 2 x 1} ，
D. [1 ,1) 2
果是第一种奇偶奇的情况，可以从个位开始分析(3 种选择)，之后十位(2 种选择)，最后百位
(2 种选择)，共 12 种；如果是第二种情况偶奇奇，分析同理：个位(3 种情况)，十位(2 种情
-4-
况)，百位(不能是 0，一种情况)，共 6 种，因此总共 12+6=18 种情况．
8.设数列 an ， an2 ( n N * )都是等差数列，若 a1 2 ，则 a22 a33 a44 a55 等于（ ）
雅礼中学 2020 届高三月考试卷（二） 数学（理科）
本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分，共 8 页.时量 120 分钟.满分 150 分.
第Ⅰ卷 一、选择题：本大题共 12 个小题，每小题 5 分，共 60 分.在每小题给出的四个选项中，只有 一个选项是符合题目要求的.
1.集合 A x | x2 x 2 0 , B x | 1 2 ，则 A B （ ） x