2020年1月学考选考浙江省绍兴一中2019学年第一学期高三期末教学质量检测数学试题及参考答案
2020年1月学考选考浙江省绍兴一中2019学年第一学期高三期末教学质量检测数学试题
绍兴一中2019学年第一学期高三期末考试(数学)命题:高三数学备课组一、选择题(本大题共10小题,每小题4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⎭⎬⎫⎩⎨⎧=ππcos 2sin ，A ,⎭⎬⎫⎩⎨⎧-+-+-=x x ，x x B sin sin 2cos cos ,则A B I 为( ▲ ) A ． {0,1}- B ．{1,1}- C ．{1}- D ．{0} 2．若复数()()14i t i +-的模为52,则实数t 的值为( ▲ )A ． 1B ． 2C ． 2±D ．3±3．某几何体的三视图如下图所示,它的体积为( ▲ )A ． π192B ．π240C ． π384D ．π5764．设等比数列{a n }的前n 项和为S n ,若S 5＝2 S 10,则5151052S S S S +=-( ▲ ) A ． 52 B ． 92- C ． 72 D ． 112- 5．已知A 、B 是抛物线x y 42=上异于原点O 的两点,则“·=0”是“直线AB 恒过定点(0,4)”的( ▲ ) A ．充分非必要条件 B ．充要条件C ．必要非充分条件D ．非充分非必要条件6．数列921,,,a a a ⋅⋅⋅中,恰好有6个7,3个4,则不相同的数列共有( ▲ )个A ．67CB ．49C C ．39CD ．36C 7．已知双曲线]2,2[)0,0(12222∈>>=-e b a by a x 的离心率,则一条渐近线与实轴所构成的角的取值范围是( ▲ )A ．⎥⎦⎤⎢⎣⎡4,6ππB ．⎥⎦⎤⎢⎣⎡3,6ππC ．⎥⎦⎤⎢⎣⎡3,4ππD ． ⎥⎦⎤⎢⎣⎡2,3ππ 8．已知函数()()242log ,041234(4)x x f x x x x ⎧<≤⎪=⎨⎪-+>⎩，若方程()(=∈f x t t )R 有四个不同的实数 根1x ,2x ,3x ,4x ,则1x 2x 3x 4x 的取值范围为( ▲ )A ．(30,34)B ．(30,36)C ．(32,34)D ．(32,36)9．已知,x y 都是正实数,则44x y x y x y +++的最大值为( ▲ ) A ．32 B ．43 C ． 52 D ． 5410.已知在矩形ABCD 中,2AB =,4AD =,E ,F 分别在边AD ,BC 上,且1AE =,3BF =,如图所示, 沿EF 将四边形AEFB 翻折成A EFB '',则在翻折过程中,二面角B CD E '--的大小为θ,则tan θ的最大值为( ▲ )A ．325 33B.5 32C.4 33D.4 非选择题部分二、填空题(本大题7小题,多空题每题6分,单空题每题4分,共36分.)11．已知函数()ln 2020f x x x =+,则()1f '= ▲ ,0(12)(1)limx f x f x∆→-∆-∆的值等于 ▲ . 12．已知点P(x,y)满足条件y x z k k y x x y x 3),(02,,0+=⎪⎩⎪⎨⎧≤++≤≥若为常数的最大值为12, 则k = ▲ .13．如果x ＋x 2＋x 3＋……＋x 9＋x 10＝a 0＋a 1(1＋x )＋a 2(1＋x )2＋……＋a 9(1＋x )9＋a 10(1＋x )10,则a 9＝______ _,10a = ▲ .14．已知A 袋内有大小相同的1个红球和3个白球,B 袋内有大小相同的2个红球和4个白球．现从A 、B 两个袋内各任取2个球,设取出的4个球中红球的个数为ξ,则(1)P ξ== ▲ ,ξ的数学期望为 ▲ .15．抛物线x y 22=顶点为O ,焦点为F ,M 是抛物线上的动点,则MF MO 取最大值时M 点的横坐标为 ▲ . 16.已知ABC ∆中,BC 中点为M,()⊥+,⋅=--2222, CA CN 31=3=AB ,则 B ∠= ▲ ,=MN ▲ . 17.已知函数()222sin 2,2cos 2a a f a a a θθθ++=++()0,,≠∈a R a θ,则函数(),f a θ的值域是 ▲ .三、解答题(本大题共5小题,共74分.解答应写出文字说明、证明过程或演算步骤.)18．(本题满分14分)在ABC ∆中,,,A B C 所对边分别为,,a b c .已知3,b =2()4cos 23sin 23,f x x x =+- (Ⅰ)求()f x 单调递减区间和最大值M ；(Ⅱ)若(),f B M =求ABC ∆面积的最大值.19．(本小题满分15分)如图,ABEF 是等腰梯形, EF AB //,BF AF ⊥,矩形ABCD 和ABEF 所在的平面互相垂直．已知2=AB ,1=EF ．(Ⅰ)求证：平面⊥DAF 平面CBF ；(Ⅱ)求直线AB 与平面CBF 所成角的正弦值.20、(本小题满分15分)已知数列{}n a 的前n 项和n S 满足：()121--=n n a S ． (Ⅰ)求{}n a 的通项公式； (Ⅱ)设11111n n n c a a +=++-,数列{}n c 的前n 项和为T n . 求证：123n T n >-．21、(本小题满分15分)已知圆S ：020422=-++y x x ,T 是抛物线x y 82=的焦点,点P 是圆S 上的动点,Q 为PT 的中点,过Q 作Q G ⊥PT 交PS 于G(1)求点G 的轨迹C 的方程；(2)过抛物线x y 82—=的焦点E 的直线l 交G 的轨迹C 于点M 、N,且满足 364sin =∠⋅MON ON OM ,(O 为坐标原点),求直线l 的方程.22．(本小题满分15分) 对于定义在I 上的函数()y f x =,若存在0x I ∈,对任意的x I ∈,都有()()0f x f x m ≥=或者()()0f x f x M ≤=,则称0()f x 为函数()f x 在区间I 上的“最小值m ”或“最大值M ”． (Ⅰ)求函数2()ln(2)f x x x =-+在]1,0[上的最小值；(Ⅱ)若把“最大值M ”减去“最小值m ”的差称为函数()f x 在I 上的“和谐度G ”, 试求函数()23F x x x a a =-+>（0）在[1,2]上的“和谐度G ”；(Ⅲ)类比函数()f x 的“和谐度G ”的概念, 请求出(,)(1)(1)11x y x y x y y xϕ=--++++在{}(,),[0,1]I x y x y =∈上的“和谐度G ”．。
2019-2020学年绍兴市第一中学高中部高三英语期末考试试卷及答案
2019-2020学年绍兴市第一中学高中部高三英语期末考试试卷及答案第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项ABob and Sue Harvey spent nine years as resident fellows in a dormitory at Sanford and in their bookVirtual Reality and The College Freshman, they write “The Freshman oftenfaces an identity problem during the first semester.” College is a more pressured environment than it used to be, in part because the academic gap between high school and college has increased. Many college freshmen have never had to make independent decisions about sex, drugs and alcohol. Most don’t know how to manage their time or money. They often feel lonely and overwhelmed, resulting in anxiety and depression.Nancy Corbin, director of clinical service for student-counseling (咨询) services at Iowa State University, says her office is seeing a significant increase in requests for counseling from freshmen who are having trouble making the adjustment to college life. She says older teenagers increasingly lack the skills to deal with personal problems that aren’t easily defined or fixed. And they get homesick but have a hard time admitting it.Parents and high schools can make things easier on freshmen by preparing them differently. For example, by teaching them to budget their hours and dollars. The Harveys think high schools should offer a college-life course. “Parents need to focus more on relationship and personal issues and less on how many sheets and towels to take,” they say. Many homesick freshmen think they’ll be regarded as failures if they come home before Thanksgiving. So parents can help by letting them know they’re welcome to return if they feel the need. In the meantime, parents have to find new ways to keep in touch with their college kids. One of the best ways is e-mail. It’s less unpleasant and less expensive than constant phone calls and is more likely to be answered than a handwritten letter.1. Why is the first semester difficult for freshmen in college?A. Because they often fail in exams.B. Because they lack time and money.C. Because they are too homesick to make new friends.D. Because they have to settle personal issues on their own.2. In the last paragraph, it is suggested that ________.A. parents should stop buying anything for their kidsB. parents should develop a good relationship with their kidsC. parents should be taught how to send e-mails to their kidsD. parents should work with high schools in college-life courses3. Which of the following might be the best title for the passage?A. Hard Life of College FreshmenB. Approaches to Trouble in CollegeC. Freshmen’s Adaptation ProblemsD. A Strange Phenomenon in CollegeBWhat about your emotions? How do they help you to understand what you are reading?In Jane Yolan'sOwl Moon,a girl explores with her father on a snowy night. She longs for this special night.And she's amazed when she sees an owl.Have you felt longing before? Amazement? Well, if you have, it helps you have a sense of agreement. When we can put ourselves inside a story we can understand it better. Our brain tells us,"Oh, this girl's experience is a bit like mine."And boom! We can relate to her.But this skill is not born in us.So young kids have to learn it.Pictures and images help young readers to understand and recognize feelings.Readers feel joy when seeing the smiling faces of friends.They feel fear when turning the page to find a scary monster. They are just pictures,but the feelings are real. This skill, to understand the thinking and feeling of others, is what researchers call "theory of mind".For example, think about the faces of people and animals in stories. The Big Bad Wolf's scary teeth. The 'o' shape of a surprised character's mouth. Or big, wide eyes like the girl inOwl Moon.By noticing the faces,readers can start to figure out what it feels like to be that character.And that helps to figure out how people feel and think in real life.But most young readers don't go into deep,scary woods.And some may not go to the beach or play basketball.In the bookYo!Yes?two kids meet and play ball. The kids start the story on opposite pages.But as the story goes on,they get closer until they are together.Some young readers might not play basketball, but they can read the clues on the page to figure out how the kids are feeling.And some readers might not like the game,but they can feel excited for the characters because of how the characters look and move.4. What can we learn from the second paragraph?A.Owl Moontalks about the exploration of the Moon.B. The feeling of"amazement"is a sense of agreement.C. Readers are blessed with the ability to interpret others.D. Readers with similar experience understand the story better.5. Which of the following might help readers develop"theory of mind"?A. True feelings.B. Smiling faces.C. Picture books.D. Reading skills.6. Young readers can go deeper into a story by________.A. tracking the plotB. developing new skillsC. sharing similar hobbiesD. analyzing the background7. What is the text mainly about?A. How thinking influences reading.B. How readers improve reading skills.C. How emotions help enhance reading.D. How kids figure out the clues of stories.CTen years ago, I set out to examine luck. I wanted to know why some people were always in the right place at the right time, while others consistently experienced ill fortune. I placed advertisements in national newspapers asking for people who felt consistently lucky or unlucky. Hundreds of extraordinary men and women volunteered for my research. Over the years I have interviewed them, monitored their lives and had them take part in various experiments.In one of the experiments, I gave both lucky and unlucky people a newspaper, asking them to look through it and tell me how many photographs were inside. I had secretly placed a large message halfway through the newspaper, saying, “Tell the experimenter you have seen this and you will win $50.” This message took up half of the page and was written in type that was more than two inches high. It was staring everyone in the face, but the unlucky people tended to miss it and the lucky people tended to spot it.Unlucky people are generally more nervous than lucky people, and this anxiety affects their ability to notice the unexpected. As a result, they miss opportunities because they are too focused on looking for something else. They go to gatherings concentrating on finding their perfect partners and miss opportunities to make good friends. They look through newspapers determined to find certain types of job advertisements and miss other types of jobs.Lucky people are more relaxed and open, and therefore see what is there rather than just what they are looking for. My research eventually showed that lucky people are skilled at noticing opportunities, make lucky decisions by listening to their intuition (直觉), are open to new experiences, and adopt a never-say-die attitude that transforms bad luck into good luck.8. What’s the purpose of the author’s research?A. To discover what luck means to people.B. To find lucky people and unlucky people.C. To distinguish between good luck and bad luck.D. To figure out why people are always lucky or unlucky.9. Why did the unlucky people miss the message in the experiment?A. There was too much information to be read in detail.B. They were too focused on looking for photographs.C. It took too much time to go through newspapers.D. The words were too small to be noticed.10. What leads to lucky people’s good fortune?A. Their ability to spot opportunities.B. Their ability to become relaxed.C. Their ability to communicate.D. Their ability to make friends.11. What’s the key message of the last paragraph?A. What lucky people are looking for.B. How lucky people generate good luck.C. What lucky people can do with opportunities.D How lucky people transform bad luck into good luck.DMasks that helped save lives during the Covid-19 pandemic（疫情）are proving a deadly risk for wildlife, with birds and sea creatures trapped in many facial coverings in animal habitats.Single-use masks have been found on the ground, waterways and beaches worldwide since countries required（heir use in public places to slow the pandemic's spread. Worn once, the thin protective materials can take hundreds of years to break down. "Face masks aren't going away any time soon-but when we throw them away, these items can harm the environment and the animals who share our planet," Ashley from anima! rights group PETA said.Monkeys have been found playing with used masks in the hills outsideMalaysia's capitalKuala Lumpur. And in an incident inBritain, a seagull was saved inChelmsfordafter its legs got caught in an abandoned mask for a week.However, the biggest influence is in the water. More than 1.5 billion masks made their way into the world's oceans last year, accounting for around 6200 extra tons of ocean plastic pollution, according to environmentalgroup OceansAsia. “Masks and gloves are particularlyproblematicfor sea creatures," says George Leonard, chief scientist from NGO. "When those plastics break down in the environment, they form smaller and smaller particles （颗粒）.Those particles then enter the food chain and influence the entire ecosystem,“ he added.Campaigners have urged people to deal with masks properly after using them. OceansAsia has also called on governments to increase punishment for littering and encourage the use of washable masks.12. What bring（s）a great danger to wildlife now?A. Waste masks.B. Covid-19.C. Polluted water.D. Damaged habitats.13. What does the underlined word “problematic”in paragraph 4 mean?A. Important.B. Attractive.C. Common.D. Troubling.14. What can we infer from the text?A. Monkeys learned to wear masks from humans.B. Plastics are less harmful after becoming particles.C. Used masks have a worse effect on sea creatures.D. Waste masks arc the main ocean plastic pollution.15. How should we solve the problem from the last paragraph?A. Keep masks after they' re used.B. Call on governments to stop littering.C. Punish those who wear single-use masks.D. Put used masks in the recycling box.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。
2019-2020学年绍兴市第一中学分校高三语文期末考试试卷及答案
2019-2020学年绍兴市第一中学分校高三语文期末考试试卷及答案一、现代文阅读（36分）(一)现代文阅读I(9分)阅读下面的文字，完成下面小题。
材料一：苗绣，苗族的刺绣。
其历史可以追溯到楚绣、与湘绩、汉绣同流而异源。
古代苗族妇女养蚕主要是为了获得制作刺绣使用的丝线。
苗绣主要用于装饰衣服，也用在裤脚和鞋面。
在衣服上以栏杆形式围在肩膀和袖口。
黔东南苗族的盛装刺绣，衣饰部位不是栏杆形式。
苗绣针法有平绣、辫绣、结绣、缠绣、绉绣、贴花、抽花、打子、堆花等十几种，其中辫绣、结绣是苗绣中特有。
辫绣是先将8根或12根同色丝线纳成“辫子”，然后再回旋缀于底布成花，多用于“男性之衣”（“鸟爸”）的盛装中，绣品风格粗犷凝重。
结绣则将丝线在针头挽数结，然后抽针，如此反复插满成花。
苗绣图案多是鸟、鱼、花、果子。
在盛装的大型图案中，出现庞大、凶猛的动物，如龙、大象、狮子等。
龙在苗绣中有虫龙、水龙、牛龙等形态。
黔东南苗绣图案中的蝴蝶多被解释为与神话传说中的图腾有关。
苗绣一般先在绣布上绘或贴上图案。
黔东南苗族妇女不直接在衣物上刺绣，而是先制成与装饰部位大小相同的绣件，再缀到衣物上相关部位，这样一方面便于操作，也便于单独取下来保护或替换。
（摘编自《中国少数民族文化大辞典·西南地区卷》）材料二：苗绣是苗族人的文化读本。
从启蒙开始，苗族人就可以从苗绣里学习生活常识，认识草木动物，学习纺线耕田，了解节日习俗，解读神话、宇宙天体等，无所不可。
乍一看这本“书”，罗列的事物真不少，率性随意，缺乏归纳，但如果仔细阅读，你便会发现，它所表现的内容也都是经过了严格选择的，而且不乏思想深度。
苗族先人把祖祖辈辈获得的人生智慧，都隐藏在一个个生动鲜活的苗绣故事中。
苗绣一直无声无息深藏不露，20世纪后半叶才逐渐被发现。
有趣的是，它被发现的时间与读图时代几乎同步，苗绣本身的艺术特质和读图时代的美学趣味显然不谋而合。
神秘的气息，独特的想象，呆萌的造型，饱满的情感，让我们惊叹相见恨晚。
绍兴市第一中学2019学年第一学期期末测试
绍兴市第一中学2019-2020学年第一学期期末测试英语答案及评分参考第一部分：听力（共两节，满分30分）第一节(共5小题；每小题1.5分，满分7.5分)1—5 ABBCA第二节(共15小题；每小题1.5分，满分22.5分)6—7 AC 8—9CA 10—12BCB 13—16ABBC 17—20BCCA第二部分：阅读理解（共两节，满分35分）第一节（共10小题；每小题2.5分，满分25分）21—23CDC 24—26DDB 27—30ADBC第二节（共5小题；每小题2分，满分10分）31—35 CAFGB第三部分：语言运用（共两节，满分45分）第一节：完形填空（共20小题；每小题1.5分，满分30分）36—40 ACBAC 41—45 DABBC 46—50 ADBAD 51—55 ACBDC第二节：语言运用（10个小题；每小题1.5分，满分15分）56. choices 57. to 58. debating 59. are left 60. when 61. What/All 62. successful 63. to accomplish 64. either 65. the第四部分：写作（共两节，满分40分）第一节：应用文写作（满分15分）一、评分原则1. 本题总分为15分，按5个档次给分。
2. 评分时，先根据文章的内容和语言初步确定其所属档次，然后以该档次的要求来衡量、确定或调整档次，最后给分。
3. 词数少于60和多于100的，从总分中减去2分。
4. 评分时，应注意的主要内容为：内容要点、应用词汇和语法结构的丰富性和准确性及上下文的连贯性。
5. 拼写与标点符号是语言准确性的一个方面，评分时，应视其对交际的影响程度予以考虑。
英美拼写及词汇用法均可接受。
6. 如书写较差，以至影响交际，将分数降低一个档次。
One Possible Version:Dear Bruce,I am writing to invite you to give our class a lecture on western culture. We all show great interest in your lessons and are particularly curious about the customs and traditions in your country. They are so mysterious and fantastic. Therefore, we would appreciate it if you could deliver a lecture on all of them, especially something related to your traditional festivals. The time scheduled for the lecture is 4pm—5pm next Wednesday.I am looking forward to receiving your early reply.Li Hua第二节：概要写作（满分25分）一、评分原则1. 本题总分为25分，按5个档次给分。
2019-2020学年绍兴市第一中学高中部高三英语期末考试试卷及答案
2019-2020学年绍兴市第一中学高中部高三英语期末考试试卷及答案第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AI started working with my hands at a young age. The youngest of five brothers, I took on the role as a “maintenance (维修) man” at an early age for our family’s small grocery store. Often my dad wouldn’t give me a clear idea of how something shouldbe done, so I just had to figure it out by researching or through trial and error.Fast forward to 2016 and those problem-solving skills would become the focus of Tippecanoe High School’s Homebuilding class. I knew I wanted to teach the students skills that went beyond just being able to hammer nails or cut pieces of two-by-fours. The problem was that we didn’t have the resources at the time to do much else. The idea of attracting some type of funding seemed very important. Designing, building and selling a tiny house on wheels seemed like the perfect project to accomplishthe task. I reached out to a number of local businesses and most of them responded with the greatest support for what x k w we were doing.This year we added a new element to the program. Through one of our partners, we were able to connect with the nonprofit Veteran’s Ananda Incorporated. Students in the Homebuilding class are leading the design and production of micro houses to be donated to this organization. The new partnership gives the students another focus to consider when designing and building the houses.There has been no shortage of students since our first year. Three years ago we had 41 students, the next 191, and this year it was limited to just over 160 students so we could have a safe and manageable classroom environment. The number of girls taking the class has risen steadily over the last few years as well. This class offers something for everyone and the skills are universal.1. How can we describe the young author?A. He opened a small grocery store.B. He did a lot of research in the lab.C. He enjoyed doing hands-on activities.D. He learnt about maintenance from his father.2. What do the underlined words “the task” in paragraph 2 refer to?A. Getting some financial support.B. Selling a tiny house on wheels.C. Reaching out to many local businesses.D. Offering the students some problem-solving skills.3. What can be inferred about the Homebuilding class from the last paragraph?A. Its size needs increasing.B. Itis popular with the students.C. It has caused some safety concerns.D. Its classroom environment is hard to manage.BCraig Blackburn, a father and car fan, built a Batmobile for his son’s hope for using the vehicle to brighten the lives of sick children. And now he hopes to use it for more than just his sons hope after seeing the childrens reaction to the Batmobile.Based on the number of failures he had seen in car groups, he estimated that only about one in 50 attempted constructions was actually finished and he realized what an incredible opportunity he had.Mr. Blackburn started the project at the beginning of 2018 after hearing a friend in the US was doing the same thing. It started with importing an outer shell overseas, before picking brains of a friend who had a background as a worker in a car factory to gain knowledge of how to build the car. With the help of his friend, Mr. Blackburn built the Batmobile in 18 months with the cost reaching six figures.Mr.Blackburn hoped to add a flamethrower(喷火器)onto the back of the vehicle and said he had thought about building the more recent Batman Tumbler from the series film Dark Knight. Though Mr. Blackburn encountered plenty of difficulties to get over during the construction, in September 2019, the carmade its first show at the Carnival of Flowers in Toowoomba, before being used by Blackburn’s son for his hope.“It was great. It was so good to see the kids’ and adults’ excitement at seeing the Batmobile.” Mr. Blackburn said. As a result, the car lovers hope to make the car work on the roads as soon as possible, so he can visit sick children and take them out with his son.4. What is Craig Blackburn’s initial purpose of making the Batmobile?A. To realize his son’s dream.B. To donate it to sick children.C. To pay his respects to the film Dark Knight.D. To show off at the Carnival of Flowers in Toowoomba.5. How did Blackburn feel about the car-making at first?A. Hopeful.B. Confused.C. Impossible.D. Unsure.6. How did Blackburn’s friend help him?A. By making an outer shell for him.B. By offering him financial support.C. By sharing the knowledge of building cars.D. By telling him the background of the car factory.7. What is the car lovers’ expectation of the Batmobile?A. It will be driven soon on the roads.B. It can be displayed around the world.C. It can change the lives of sick children.D. It will appear in the next film about Batman.CIn sportthe sexes are separate. Women and men do not run or swim in the same races. Women are less strong than men.That at least is what people say.Women are called the weaker sex, or, if men want to please them, the fair sex. But boys and girls are taught together at schools and universities. There are women who are famous Prime Ministers, scientists and writers. And women live longer than men. A European woman can expect to live until the age of 74, a man only until he is 68. Are women’s bodies really weaker?The fastest men can run a mile in under 4 minutes. The best women need 4.5 minutes. Women’s time is always slower than men’s, but some facts are a surprise. Some of the fastest women swimmers today are teenage girls. One of them swam 400 meters in 4 minutes 21.2 seconds when she was only 16. The first ‘Tartan’ in film was an Olympic swimmer, Johnny Weissmuller. His fastest 400 meters was 4 minutes 49.1 seconds, which is 37.9 seconds slower than a girl 50 years later! This does not mean that women are catching men up. Conditions are very different now and sport is much more serious. It is so serious that some women athletes are given hormone injections. At the Olympics a doctor has to check whether the women athletes are really women or not. It seems sad that sport has such problems. Life can be very complicated when there are two separate sexes!8. Women are called the weaker sex because _________.A. women do as much as menB. people think women are weaker than menC. sport is easier for men than for womenD. in sport the two sexes are always together9. Which of the following is true?A. Boys and girls study separately everywhere.B Women do not run or swim in races with men.C. Famous Prime Ministers are women.D. Men can expect to live longer than women in Europe.10. The underlined part “That at least is what people say” means people _________.A. say other things, tooB. don’t say this muchC. say this but may not think soD. only think this11. In this passage the author implies that _________.A. womenare weaker than men, but fasterB. women are slower than men, but strongerC. men are not always stronger and faster than womenD. men are faster and stronger than womenDSam, I say to myself as I start across the bridge, you must stop these thoughts and start thinking about what to do now that you have lost your falcon, Frightful.Life, my friend Ban do once said, is meeting problems and solving them whether you are an amoeba or a space traveller. I have a problem. I have to provide my younger sister Alice and myself with meat. Fish, nuts, and vegetables are good and necessary, but they don't provide enough fuel for the hard physical work we do. Although we have venison now, I can't always count on getting it. So far this year, our venison has been only road kill from in front of Mrs Strawberry's farm.I decide to take the longest way home, down the flood plain of the West Branch of Delaware to Spillkill, my own name for a fast stream that cascades down the south face of the mountain range I'm on. I need time to think. Perhaps Alice and I should be like the early Eskimos. We should walk, camp and hunt, and when the seasons change, walk on to new food sources. But I love my tree and my mountaintop.Another solution would be to become farmers, like the people of the Iroquois Confederacy who once lived here. They settled in villages and planted corm and squash, bush beans and berries. We already grow groundnuts in the damp soil and squash in the poor land. But the Iroquois also hunted game. I can't do that anymore.I'm back where I started from.Slowly I climb the Spillkill. As I hop from rock to rock beneath shady basswoods and hemlocks, I hear the cry of the red-tailed hawk who nests on the mountain crest. I am reminded of Frightful and my heart aches. I can almost hear her call my name, Cree, Cree, Cree, Car-ree.Maybe I can get her back if I beg the man who is in charge of the peregrines at the university. “But it's the law,”he would say. I could write to the president of the United States and ask him to make an exception of Alice and me. That won't work. The president swore to uphold the Constitution and laws of the United States when he took office.I climb on. I must stop thinking about the impossible and solve the problem of what to do now. I must find a new way to provide for us. Frightful is going to be in good hands at the university, and she will have young.I smile at the thought of little Frightfuls and lift my reluctant feet.When I am far above the river, I take off my clothes and moccasins and bathe in a deep, clear pool until I am refreshed and thinking more clearly. Climbing up the bank, I dress and sit down. I breathe deeply of the mountain air and try to solve my problem more realistically.12. What does this excerpt main describe?A. Delicate mental activities.B. Unique story environment.C. Everchanging story events.D. Complicated character relationship.13. What is Sam's first worry?A. How to get back quicklyB. How to get enough venison.C. How to ensure the safety of Frightful.D. How to provide meat for Alice and himself.14. What do we know about Frightful?A. He left Sam and Alice due to lack of food.B. He helped Sam hunt before being taken away.C. He is living with the red-tailed hawk happily.D. He has given birth to babies in the university.15. Which of the following can best describe Sam?A. Humorous.B. Aggressive.C. Responsible.D. Unrealistic.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。
浙江省绍兴市柯桥区2019届高三上学期1月教学质量检测(期末考试)语文试题
【题文】阅读下面的文字，根据要求作文。
有人说：“好看的皮囊千篇一律，有趣的灵魂万里挑一。
”对此你有什么感想？请写一篇文章。
注意：①角度自选，立意自定，题目自拟。
②明确文体，不得写成诗歌。
③不少于800字。
④不得抄袭、套作。
【答案】有趣的灵魂，永久的魅力有人说，初识一个人，第一印象完全取决于外貌。
两个互不相识的人初次见面，漂亮的外在，是吸引别人关注的第一要素。
但随着时间的流逝，两个人是否能从陌生人发展成熟人，再变成朋友或者恋人，外在就不是先决条件了。
而有趣的灵魂，才是持续的吸引力。
有趣的灵魂，最是难能可贵。
与一个有趣的人聊天，总是充满乐趣，笑容满面。
不用担心彼此没话可说，更不用担心在一起时无聊至极。
有趣的灵魂，总是自由而又让人向往。
机械枯燥的生活，总是会让人失去初心，变得暗淡无光，变得失去自己。
而有趣的灵魂，总是如莲花一般，出淤泥而不染，保持真我，散发出沁人心脾的清香。
在浑浑噩噩的现实世界中，拥有一个有趣的灵魂，可以称之为混沌浑浊中的一股清流。
面对不那么顺心如意的现实生活，有人因此失去了自己的棱角，丧失了最后一丁点脾气，没有了自己的爱好。
于是，我们周边开始充斥着越来越多没趣的人，当人现实到可怕的程度，生活也就只剩下了苟且。
我们所说的诗和远方，大抵只有有趣的灵魂才会去追寻。
因为人们一旦向现实生活的残酷低头，就失去了憧憬美好和不放弃追求的初心。
能够笑看人生，在没趣的世界中保持有趣的灵魂的人，总是寥寥无几，难能可贵。
人和人最大的区别，不是外表而是内在。
长得好看的人总是漂亮得很相似，而有趣的灵魂，却总是独一无二、万里挑一。
人与人之间最大的区别，永远都不是外表，而是内在。
一个心灵丑恶的人，长得再漂亮，嘴脸也是招人烦；而一个外表不怎么符合主流审美的人，如若心灵足够慈善，也会散发出由内而外的真正的美感。
这个世界上，其实没有特别丑的人，只要稍微拾掇一下，长相上并无太大差异。
所以，真正能让一个人脱颖而出、与众不同的，不是千篇一律的外在，而是万里挑一的内在。
浙江省绍兴市第一中学2019届高三上学期期末考试数学试题附答案解析
浙江省绍兴市第一中学2019届高三上学期期末考试数学试题一、选择题（每小题4分，共40分）1.设全集，集合，则集合（）A. B.C. D.【答案】D【解析】【分析】先根据补集的定义求出集合A的补集，然后和集合B进行交集运算，可求【详解】因为A={x|x≥3}，所以 ={x|x＜3}，所以（）∩B═{x|0≤x＜3}．故选：D．【点睛】本题的考点是集合的补集和交集运算，比较基础．2.已知角的终边与单位圆交于点，则( )A. B. C. D.【答案】B【解析】【分析】根据三角函数的定义可直接求得结果。
【详解】由题意得：本题正确选项：【点睛】本题考查三角函数的定义，要注意区分与的具体表示形式，基础题。
3.若复数在复平面内对应的点关于y轴对称，且，则复数A. B. 1 C. D.【答案】C【解析】分析：由z1=2﹣i，复数z1，z2在复平面内对应的点关于y轴对称，求出z2，然后代入，利用复数代数形式的乘除运算化简即可．详解：∵z1=2﹣i，复数z1，z2在复平面内对应的点关于y轴对称，∴z2=﹣2﹣i．∴==，故选：C点睛：复数的运算，难点是乘除法法则，设，则，.4.设，则“”是“”的( )A. 充分而不必要条件B. 必要而不充分条件C. 充要条件D. 既不充分也不必要条件【答案】C【解析】【分析】根据充要条件的定义进行判断即可。
【详解】由得，，所以是充分条件；由可得，所以是必要条件，故“”是“”的充要条件。
答案选C。
【点睛】本题考查充分必要条件的定义，不等式的性质，属于基础题。
5.设为数列的前项和，，，若，则＝( )A. B. C. D.【答案】C【解析】【分析】根据，可列出，利用可求得数列为等比数列。
求解出的通项公式，进而解得的取值。
【详解】由可得：当时，两式作差得：，即又，满足是以为首项，为公比的等比数列，又本题正确选项：【点睛】解题关键在于利用数列的前项和求得数列的通项公式。
在利用时，要注意对数列首项是否满足所求通项公式的验证。
2019-2020学年绍兴市第一中学高中部高三英语上学期期末试卷及答案
2019-2020学年绍兴市第一中学高中部高三英语上学期期末试卷及答案第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项ALocated in the beautiful Sichuan Basin, Chongqing is a magical 8D city. The natural history and cultural scenery of the area provide children with learning opportunities because they can enjoy the many wonders of this area.Fengjie Tiankeng Ground JointTiankeng Diqiao Scenic Area is located in the southern mountainous area of Fengjie County. The Tiankeng pit is 666 meters deep and is currently the deepest tiankeng in the world. The scenic spot is divided into ten areas including Xiaozhai Tiankeng, Tianjingxia Ground, Labyrinth River, and Longqiao River. There are many and weird karst cave shafts, and countless legends haunt them.Youyang Peach GardenYouyang Taohuayuan Scenic Area is a national forest park, a national 5A-level scenic spot, and a national outdoor sports training base. Located in the hinterland of Wuling Mountain. The Fuxi Cave in the scenic spot is about 3,000 meters long, with winding corridors, deep underground rivers, and color1 ful stalactites. The landscape is beautiful.Jinyun Mountain National Nature ReserveJinyun Mountain is located in Beibei District of Chongqing City, about 45 kilometers away from the Central District of Chongqing City. The nine peaks of Jinyun Mountain stand upright and rise from the ground. The ancient trees on the mountain are towering, the green bamboos form the forest, the environment is quiet, and the scenery is beautiful, so it is called "Little Emei". Among them, Yujian Peak is the highest, 1050 meters above sea level; Lion Peak is the most precipitous and spectacular, and the other peaks are also unique.Chongqing People's SquareChongqing's Great Hall of the People, one of the landmarks of Chongqing, gives people the deepest impression than its magnificent appearance resembling the Temple of Heaven. It also uses the traditional method of central axis symmetry, with colonnade-style double wings and a tower ending, plus a large green glazed roof, large red pillars, white railings, double-eave bucket arches, and painted carved beams.1.How deep is the Tiankeng Ground Joint?A.666mB.3,000mC.45kmD.1050m2.Which of the following rocks can you see in Youyang Peach Garden?A.LimestoneB.StalactiteC.MarbleD.Quartzite3.Which attraction is closest to downtown Chongqing?A.Fengjie Tiankeng Ground JointB.Jinyun Mountain National Nature ReserveC.Chongqing People's SquareD.Youyang Peach GardenBChimps use loud calls and gestures to make their feelings known but until now, the exact meaning for individual movements has remained a mystery. Now researchers believe they have translated the key gestures used in the chimp community and identified their intentions for the first time.From 4,351 gestures, experts were able to identify 66 that are used for 19 specific message meanings, including showing a foot to tell a child they can climb on their back. The researchers were able to narrow down these 66 gestures to 36 that are used intentionally to achieve 15 purposes. The translations were made by Dr Catherine Hobaiter and her colleagues at St Andrews University in Scotland.Dr Hobaiter used behavior sampling and filmed all recorded cases of gestural communication. Other gestures include stomping their feet to ask another chimp to stop what they are doing, and slapping objects together to ask another to follow them. Of the 19 meanings,17 encouraged interactions to start, or to develop, such as “move closer,” and “change play”. Some of the gestures were found to have more than one meaning. and only 10 of the 66 gestures were used for only a single meaning.Researchers collected a total of 471 video clips from two social groups of chimps at a shelter near Kinshasa, Democratic Republic of Congo. As well as identifying what the gesture means, they also discovered the technique needed to increase the chances of success.“Human children use gestures to communicate before they produce their first words, and their earliest gestures typically appear around 10 months of age,” explained the researchers. “In great apes, there is good evidence that language-trained individuals are capable of acquiring and understanding signals, but this is far less clear in their natural communication. ”4. Chimps slap the objects to____________.A. tell others to stop what they are doingB. ask others chimps to join themC. gather other chimps to move closerD. encourage interactions to start5. What did researchers find after studying 471 video clips?A. Chimps trained in language are good at understanding signals.B. Two social groups of chimps live at a shelter near Kinshasa.C. Language-trained individuals do well in natural communication.D. Chimps’earliest gestures appear around 10 months of age.6. How is the last paragraph developed?A. By analyzing causes.B. By examining differences.C By making comparisons. D. By following time order.7. What can be a suitable title for the text?A A New Research on Chimps B. Human Children and ChimpsC. Getting the Chimps Trained for LanguageD. Translating the Sign Language of ChimpsCThe World Wildlife Fund (WWF) says more than half of the world’s wildlife population has been lost, whichthe conservation group says has placed the health of the planet at risk.The WWF recently released its 10th Flagship Living Planet Report. The group warns the condition of the world's animals is worse than its earlier reports showed, indicating worldwide action is needed.The WWF is worried about the loss of and damage to Earth’s environment. The report provides information about more than 10,000 animal populations from 1970 to 2010. These populations are called “vertebrate species,” or animals with backbones — like fish, birds, mammals, amphibians and reptiles. The report shows these populations have dropped by 52 percent in just 40 years. It warns freshwater species have fallen by 76 percent, which is almost twice the loss of land and ocean species. Most of these losses are in the tropics, with the biggest drop inLatin America.Marco Lambertini, the WWF’s International Director-General said, “This is about losing natural habitats. This is aboutconvertingforests, grasslands, and wetlands into agriculture mainly, and it is about unsustainable use of wildlife. Illegal hunting has been actually increasing over the last 10 years, which definitely a driving force for extinction, particularly of large species.”The report also notes what it calls the world’s “Ecological Footprint”, that is, the effect of human activities on the planet. Mr. Lambertini says there has been an increase in carbon dioxide gases and the pouring of nitrogen intooceans and rivers from fertilizers used in agriculture, which certainly cannot continue.“We are consuming on average every year about the equivalent of about 1.5, one and a half times the resources available to the planet. That means we are cutting trees more quickly than they can be restored. We are fishing the oceans more quickly than fishing stocks can reproduce, and we are emitting in the atmosphere more CO2than the natural systems can actually absorb, which is clearly not sustainable.”Mr. Lambertini warns climate change affects almost everyone on the planet and that whole species may disappear if the world does not reduce the effects of humans on the climate.8. According to the passage, what kind of species faces the biggest drop in population?A. Land and ocean species.B. Animals with backbones.C. Freshwater species inLatin America.D. Freshwater species in the tropics.9. All the following can contribute to the loss of world’s wildlife population EXCEPT ________.A. turning wildlife habitats into agriculture land.B. making sustainable use of wildlife.C. hunting illegally.D. emitting CO2 gases and pouring nitrogen.10. Which does the underlined word “converting” in paragraph 4 mean?A. Conserving.B. Conveying.C. Exchanging.D. Transforming.11. It can be inferred from the passage that _______.A. Marco is much concerned about human’s current behaviors towards wildlife.B. what the planet provides now can satisfy human’s sustainable development.C. more than half of the world’s wildlife population has been lost.D. if humans reduce the effects on the climate, the whole species will not disappear.DIn a study published in Nature Machine Intelligence, researchers at Ohio State University show how artificial intelligence（AI）can follow clinical trials to identify drugs for repurposing, a solution that can help advance innovative treatments.Repurposing drugs is legal and not unusual. When doctors prescribe(开处方)drugs that have been approvedby the Food and Drug Administration(FDA)for purposes different from what is printed on the labels, the drugs are being used “off-label” Just because a drug is FDA-approved for a specific type of disease does not prevent it from having possible benefits for other purposes.For example, Metformin, a drug that is FDA-approved for treating type 2 diabetes, is also used to treat PCOS(a disease of women), and other diseases. Trazodone, an anti-depressant with FDA-approval to treat depression, is also prescribed by doctors to help treat patients with sleep issues.The Ohio State University research team created an AI deep learning model for predicting treatment probability with patient data including the treatment, outcomes, and potential confounders(干扰因素).Confounders are related to the exposure and outcome. For example, a connection is identified between music festivals and increases in skin rashes(红疹). Music festivals do not directly cause skin rashes. In this case, one possible confounding factor between the two may be outdoor heat, as music festivals tend to run outdoors when the temperature is high, and heat is a known cause for rashes. When working with real-world data, confounders could number in the thousands. AI deep learning is well-suited to find patterns in the complexity of potentially thousands of confounders.The researcher team used confounders including population data and co-prescribed drugs. With this proof-of-concept, now clinicians have a powerful AI tool to rapidly discover new treatments by repurposing existing medications.12. What do we know about a drug used off-label?A. It is sold without a label.B. It is available at a low price.C. Its uses extend beyond the original ones.D. Its clinical trials are rejected by doctors.13. Metformin and Trazodone are similar as both of them________.A. are used off-labelB. treat rare diseasesC. result in sleep issuesD. are medical breakthroughs14. What can be inferred about “confounders”?A. They are possible treatments.B. They are environmental factors.C. They can be easily recognized in real-world data.D. They should be taken into serious consideration.15. What is the main idea of the text?A. AI examines benefits of existing drugs.B. AI identifies off-label uses for drugs.C. AI finds new drugs for common diseases.D. AI proves the power of drug research.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。
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绍兴一中2019学年第一学期高三期末考试(数学)命题:高三数学备课组一、选择题(本大题共10小题,每小题4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⎭⎬⎫⎩⎨⎧=ππcos 2sin ，A ,⎭⎬⎫⎩⎨⎧-+-+-=x x ，x x B sin sin 2cos cos ,则A B I 为( ▲ )A ． {0,1}-B ．{1,1}-C ．{1}-D ．{0}2．若复数()()14i t i +-的模为52,则实数t 的值为( ▲ )A ． 1B ． 2C ． 2±D ．3± 3．某几何体的三视图如下图所示,它的体积为( ▲ )A ． π192B ．π240C ． π384D ．π5764．设等比数列{a n }的前n 项和为S n ,若S 5＝2 S 10,则5151052S S S S +=-( ▲ )A ． 52B ． 92-C ． 72D ． 112-5．已知A 、B 是抛物线x y 42=上异于原点O 的两点,则“·=0”是“直线AB 恒过定点(0,4)”的( ▲ )A ．充分非必要条件B ．充要条件C ．必要非充分条件D ．非充分非必要条件6．数列921,,,a a a ⋅⋅⋅中,恰好有6个7,3个4,则不相同的数列共有( ▲ )个 A ．67C B ．49C C ．39C D ．36C7．已知双曲线]2,2[)0,0(12222∈>>=-e b a by a x 的离心率,则一条渐近线与实轴所构成的角的取值范围是( ▲ )A ．⎥⎦⎤⎢⎣⎡4,6ππB ．⎥⎦⎤⎢⎣⎡3,6ππC ．⎥⎦⎤⎢⎣⎡3,4ππD ． ⎥⎦⎤⎢⎣⎡2,3ππ 8．已知函数()()242log ,041234(4)x x f x x x x ⎧<≤⎪=⎨⎪-+>⎩，若方程()(=∈f x t t )R 有四个不同的实数 根1x ,2x ,3x ,4x ,则1x 2x 3x 4x 的取值范围为( ▲ )A ．(30,34)B ．(30,36)C ．(32,34)D ．(32,36)9．已知,x y 都是正实数,则44x yx y x y+++的最大值为( ▲ )A ．32B ．43C ． 52D ． 5410.已知在矩形ABCD 中,2AB =,4AD =,E ,F 分别在边AD ,BC 上,且1AE =,3BF =,如图所示, 沿EF 将四边形AEFB 翻折成A EFB '',则在翻折过程中,二面角B CD E '--的大小为θ,则tan θ的最大值为( ▲ )A ．325 33B.5 32C.4 33D.4非选择题部分二、填空题(本大题7小题,多空题每题6分,单空题每题4分,共36分.) 11．已知函数()ln 2020f x x x =+,则()1f '= ▲ ,0(12)(1)lim x f x f x∆→-∆-∆的值等于 ▲ .12．已知点P(x,y)满足条件y x z k k y x x y x 3),(02,,0+=⎪⎩⎪⎨⎧≤++≤≥若为常数的最大值为12, 则k = ▲ .13．如果x ＋x 2＋x 3＋……＋x 9＋x 10＝a 0＋a 1(1＋x )＋a 2(1＋x )2＋……＋a 9(1＋x )9＋a 10(1＋x )10,则a 9＝______ _,10a = ▲ .14．已知A 袋内有大小相同的1个红球和3个白球,B 袋内有大小相同的2个红球和4个白球．现从A 、B 两个袋内各任取2个球,设取出的4个球中红球的个数为ξ,则(1)P ξ== ▲ ,ξ的数学期望为 ▲ .15．抛物线x y 22=顶点为O ,焦点为F ,M 是抛物线上的动点,则MFMO 取最大值时M 点的横坐标为 ▲ .16.已知ABC ∆中,BC 中点为M,()⊥+,⋅=--2222,CA CN 31=3=AB ,则 B ∠= ▲ ,=MN ▲ .17.已知函数()222sin 2,2cos 2a a f a a a θθθ++=++()0,,≠∈a R a θ,则函数(),f a θ的值域是▲ .三、解答题(本大题共5小题,共74分.解答应写出文字说明、证明过程或演算步骤.) 18．(本题满分14分)在ABC ∆中,,,A B C 所对边分别为,,a b c .已知3,b =2()4cos 23sin 23,f x x x =+- (Ⅰ)求()f x 单调递减区间和最大值M ；(Ⅱ)若(),f B M =求ABC ∆面积的最大值.19．(本小题满分15分)如图,ABEF 是等腰梯形, EF AB //,BF AF ⊥,矩形ABCD 和ABEF 所在的平面互相垂直．已知2=AB ,1=EF ．(Ⅰ)求证：平面⊥DAF 平面CBF ；(Ⅱ)求直线AB 与平面CBF 所成角的正弦值.20、(本小题满分15分)已知数列{}n a 的前n 项和n S 满足：()121--=n n a S ． (Ⅰ)求{}n a 的通项公式；(Ⅱ)设11111n n n c a a +=++-,数列{}n c 的前n 项和为T n . 求证：123n T n >-．21、(本小题满分15分)已知圆S ：020422=-++y x x ,T 是抛物线x y 82=的焦点,点P 是圆S 上的动点,Q 为PT 的中点,过Q 作Q G ⊥PT 交PS 于G(1)求点G 的轨迹C 的方程；(2)过抛物线x y 82—=的焦点E 的直线l 交G 的轨迹C 于点M 、N,且满足364sin =∠⋅MON ON OM ,(O 为坐标原点),求直线l 的方程.22．(本小题满分15分)对于定义在I 上的函数()y f x =,若存在0x I ∈,对任意的x I ∈,都有()()0f x f x m ≥=或者()()0f x f x M ≤=,则称0()f x 为函数()f x 在区间I 上的“最小值m ”或“最大值M ”． (Ⅰ)求函数2()ln(2)f x x x =-+在]1,0[上的最小值；(Ⅱ)若把“最大值M ”减去“最小值m ”的差称为函数()f x 在I 上的“和谐度G ”, 试求函数()23F x x x a a =-+>（0）在[1,2]上的“和谐度G ”；(Ⅲ)类比函数()f x 的“和谐度G ”的概念, 请求出(,)(1)(1)11x yx y x y y xϕ=--++++在{}(,),[0,1]I x y x y =∈上的“和谐度G ”．参考答案：CDBDB CCCBC 11．【答案】2021,-4042． 12．【答案】9- 13．【答案】－9,1 14．【答案】 7(1)15P ξ==,76E ξ= ξ可能的取值为0123，，，．1(0)5P ξ==,7(1)15P ξ==, 13224611(3)30C P C C ξ===·．从而3(2)1(0)(1)(3)10P P P P ξξξξ==-=-=-==．ξ的分布列为ξ的数学期望012351510306E ξ=⨯+⨯+⨯+⨯=．15．【答案】1．【解析】设抛物线方程为x y 22=,则顶点及焦点坐标为()00，O ,⎪⎭⎫ ⎝⎛021，F ,若设点M 坐标为(),M x y ,则2⎪⎭⎫⎝⎛MF MO ==+⎪⎭⎫ ⎝⎛-+222221y x y x =+⎪⎭⎫ ⎝⎛-+x x x x 22122241222+++x x x x 令41222+++=x x x x t 得,()()04212=+-+-t x t x t ,由0≥∆得34≤t ,由4123422+++=x x x x 得1=x 。
16.【答案】4π,210 【解析】由()⊥+得： ()0=+,即20=⋅,故BC AM ⊥。
由⋅=--2222得：()22BC AB AC =+,即224BC AM =,AM 2=,所以ABC ∆的形状为等腰直角三角形(如图)。
在CNM ∆中,由余弦定理得=MN 210。
17.【答案】23,23⎡⎤-+⎣⎦．【解析】设222sin 22cos 2a a t a a θθ++=++,则22cos 2sin (1)(2)0,at a t a θθ-+-+=所以直线222(1)(2)0,atx ay t a -+-+=与圆221x y +=有公共点,从而有221(2)121t a a t -+≤+得2212222221t a a a at -≤≤=++于是2121t t -≤+,得2410t t -+≤得2323t +≥≥-18．【解析】(Ⅰ) ()4sin(2)1,6f x x π=+-.........3分设3222,262k x k k Z πππππ+≤+≤+∈解得2,.63k x k k Z ππππ+≤≤+∈所以函数()f x 的单调减区间为2,,.63k k k Z ππππ⎡⎤++∈⎢⎥⎣⎦.........6分 函数()f x 的最大值为 3.M =.........8分(Ⅱ)(0,),B π∈Q 且当x B =时()f x 取得最大值,2,.626B B πππ∴+=∴=.........10分222292cos 323,1893,a c ac A a c ac ac ac ac =+-=+-≥-∴≤+.........12分等号当且仅当a c =时成立. 111893sin .24ABC S ac B ac ∆+∴==≤ 所以ABC ∆面积的最大值为1893.+.........14分19．(Ⅰ)证明：Θ平面⊥ABCD 平面ABEF ,平面I ABCD 平面ABEF =AB ,AB CB ⊥,⊂CB 平面ABCD , ⊥∴CB 平面ABEF ． ⊂AF Θ平面ABEF , CB AF ⊥∴, 又Θ BF AF ⊥,⊥∴AF 平面CBF ．⊂AF Θ平面ADF ,∴平面⊥DAF 平面CBF ．(Ⅱ)方法一：根据(Ⅰ)的证明,有⊥AF 平面CBF ,∴FB 为AB 在平面CBF 上的射影, 因此,ABF ∠为直线AB 与平面CBF 所成的角．EF AB //Θ,四边形ABEF 为等腰梯形,过点F 作AB FH ⊥,交AB 于H ．2=AB ,1=EF ,则212=-=EF AB AH ． 在AFB Rt ∆中,根据三角形相似(或射影定理)得AB AH AF ⋅=2,解得1=AF ．21sin ==∠AB AF ABF ． ∴直线AB 与平面CBF 所成角的大小为ο30．方法二：略20【解析】(Ⅰ)Θ()121--=n n a S ,∴()12111--=a S ,即()12111--=a a ∴311=a 当2n ≥时,()1121----=-=n n n n n a a S S a ,得311=-n n a a ,即{}n a 是等比数列； ∴1()3n n a = ．(Ⅱ)证明： 11111331131311()1()33n n n n n n n c +++=+=++-+- 111311311111131313131n n n n n n ++++--+=+=-+++-+- 1112()3131+=--+-n n ,由111111,313313n n n n ++<>+-得111111,313133n n n n ++-<-+-所以1113112()2()313133＋++=-->---n n n n n c ,从而122231111111[2()][2()][2()]333333n n n n T c c c +=+++>--+--+--L L22311111112[()()()]333333n n n +=--+-++-L11112()2333n n n +=-->-．即123n T n >-．21、【解析】(1)由题意得：T(2,0),且GQ 是PT 的中垂线.∴.||||GT PG = 又62||||||||||==+=+PS GP GS GT GS , ∴点G 的轨迹是以S 、T 为焦点的椭圆,2,6==c a∴G ∴==,2c -a b 22的轨迹C 的方程是.12622=+y x ⑵由题意得：E(-2,0),当直线l 的斜率存在时,设l ：()2+=x k y ,代入.12622=+y x 并整理得：2222(31)121260k x k x k +++-=,设1122(,) (,)M x y N x y ，, 则2212122212126, 3131k k x x x x k k -+=⋅=++,∴2122)31k MN x k +=-==+, 点O 到直线l的距离d =.∵sin OMN OM ON MON S ⋅∠==V u u u u r u u u r ,而12OMN S MN d =⋅V ,∴MN d ⋅=即22)31k k +=+解得k =,此时: 2)m y x =±+ , 当直线l 的斜率不存在时,l ：2-=x ,也有OMN S =V 故直线l 的方程为20 2x x +==-或22解：(Ⅰ) 令1()202f x x x-'=+=-,则22410x x -+=,12111x x ∴=<<= 显然,[]1,01∈x ,列表有：所以,()f x 在]1,0[上的“下确界”为 13()ln(12f x =+. ……………4分 (Ⅱ)①当102a <≤时,max ()(2)F x F =,min ()(1)F x F = , 和谐度G (2)(1)32F F a =-=-； ②当1526a <≤时,max ()(2)F x F =,min ()(2)F x F a =, 和谐度G ()(2)44F a F a a =-=-； ③当516a <≤时, max ()(1)F x F =,min ()(2)F x F a =, 和谐度G ()(2)21F a F a =-=-； ④当312a <<时,max ()()F x F a = min ()(2)F x F = , 和谐度G 2()(2)(2)F a F a =-=- ；⑤当322a ≤≤时,max ()()F x F a =,min ()(1)F x F =, 和谐度G 2()(1)(1)F a F a =-=- ；⑥当2a >时, max ()(2)F x F =, min ()(1)F x F =, 和谐度G (2)(1)23F F a =-=-.综上所述：22132, 0<21544, 26521, 163(2), 123(1), 2223, 2a a a a a a G a a a a a a ⎧-≤⎪⎪⎪-<≤⎪⎪⎪-<≤⎪=⎨⎪-<≤⎪⎪⎪-<≤⎪⎪->⎪⎩ ………………10分(每一项得1分)(Ⅲ) 因为221(1)(,)11(1)(1)(1)(1)x y x y xy xy x y x y x y ϕ+++-==-≤++++, 当0xy =或1xy =时等号成立,所以(,)x y ϕ的最大值为1． ………………11分令(1),(1)(1)xy xy T t x y -==++则2222(1)(1)(1),[0,1].1(1)1xy xy t t t t T t x y xy t t---=≤==∈+++++ 令2(1)()1t t g t t-=+,则223222((23)(1)()22()(1)(1)t t t t t t t t g t t t --+--'==++, 令()0g t '=,得12t -+=是()g t 的极大值点,也是()g t 的最大值点, ()g t g ∴≤=,从而T ≤, 所以(,)1x y ϕ≥=………………13分当x y ==时等号成立,所以(,)x y ϕ的最小值为25513-． ………………14分由此G =………………………………15分。