天津市第一中学2017-2018学年高一上学期期末考试数学试卷 含解析

专题10压轴题题型汇总压轴题型一、保值函数型“保值函数”，又称为“k 倍值函数”，“和谐函数”，“美好区间”等等。

1、现阶段主要是一元二次函数为主的。

核心思路是转化为“根的分布”。

2、函数单调性是解决问题的入口之一。

3、方程和函数思想。

特别是通过两个端点值构造对应的方程，再提炼出对应的方程的根的关系。

如第1题1.（江苏省连云港市市区三星普通高中2020-2021学年高一上学期期中联考）对于区间[,]a b 和函数()y f x =，若同时满足：①()f x 在[,]a b 上是单调函数；②函数(),[,]y f x x a b =∈的值域还是[,]a b ，则称区间[,]a b 为函数()f x 的“不变”区间.（1）求函数2(0)y x x =≥的所有“不变”区间；（2）函数2(0)y x m x =+≥是否存在“不变”区间？若存在，求出实数m 的取值范围；若不存在，请说明理由.2.（北京市昌平区2020-2021学年高一上学期期中质量抽测）已知函数2()f x x k =-.若存在实数,m n ，使得函数()f x 在区间上的值域为，则实数k 的取值范围为（）A ．(1,0]-B ．(1,)-+∞C ．2,0]D ．(2,)-+∞3.（广东省广州市第一中学2020-2021学年高一上学期11月考试）已知函数221()x f x x-=.（1）判断函数()f x 的奇偶性并证明；（2）若不等式23()1x f x kx x +-≥在1,14x ⎡⎤∈⎢⎥⎣⎦上恒成立，求实数k 的取值范围；（3）当11,(0,0)x m n m n ⎡⎤∈>>⎢⎥⎣⎦时，函数()()1(0)g x tf x t =+>的值域为[23,23]m n --，求实数t 的取值范围.4.(江苏省盐城市实验高级中学2020-2021学年高一上学期期中）一般地，若()f x 的定义域为[],a b ，值域为[],ka kb ，则称[],a b 为()f x 的“k 倍跟随区间”；特别地，若()f x 的定义域为[],a b ，值域也为[],a b ，则称[],a b 为()f x 的“跟随区间”，（1）若[]1,b 为2()22f x x x =-+的跟随区间，则b =______；（2）若函数()f x m =m的取值范围是______.压轴题型二、方程根的个数1.一元二次型“根的分布”是期中考试的一个难点和热点。

第一套：满分150分2020-2021年天津市第一中学初升高自主招生数学模拟卷一．选择题（共8小题，满分48分）1．（6分）如图，△ABC中，D、E是BC边上的点，BD：DE：EC=3：2：1，M在AC边上，CM：MA=1：2，BM交AD，AE于H，G，则BH：HG：GM=（）A．3：2：1 B．5：3：1C．25：12：5 D．51：24：102.（6分）若关于x的一元二次方程（x－2）（x－3）=m有实数根x1,x2，且x1≠x2，有下列结论：①x1=2，x2=3；②1> ；m4③二次函数y=（x－x1）（x－x2）＋m的图象与x轴交点的坐标为（2，0）和（3，0）．其中，正确结论的个数是【】A.0B.1C.2D.33.（6分）已知长方形的面积为20cm2，设该长方形一边长为ycm，另一边的长为xcm，则y与x之间的函数图象大致是（）A. B. C. D.4.（6分）如图，在平面直角坐标系中，⊙O 的半径为1，则直线y x 2=-与⊙O 的位置关系是（ ）A ．相离B ．相切C ．相交D ．以上三种情况都有可能 5．（6分）若一直角三角形的斜边长为c ，内切圆半径是r ，则内切圆的面积与三角形面积之比是（ ）A ．B ．C ．D ．6．（6分）如图，Rt △ABC 中，BC=，∠ACB=90°，∠A=30°，D 1是斜边AB 的中点，过D 1作D 1E 1⊥AC 于E 1，连结BE 1交CD 1于D 2；过D 2作D 2E 2⊥AC 于E 2，连结BE 2交CD 1于D 3；过D 3作D 3E 3⊥AC 于E 3，…，如此继续，可以依次得到点E 4、E 5、…、E 2013，分别记△BCE 1、△BCE 2、△BCE 3、…、△BCE 2013的面积为S 1、S 2、S 3、…、S 2013．则S 2013的大小为（ ） A.31003 B.320136 C.310073 D.67147．（6分）抛物线y=ax 2与直线x=1，x=2，y=1，y=2围成的正方形有公共点，则实数a 的取值范围是（ ）A ．≤a ≤1B ．≤a ≤2C ．≤a ≤1D ．≤a ≤28．（6分）如图，矩形ABCD 的面积为5，它的两条对角线交于点O 1，以AB ，AO 1为两邻边作平行四边形ABC 1O 1，平行四边形ABC 1O 1的对角线交BD 于点02，同样以AB ，AO 2为两邻边作平行四边形ABC 2O 2．…，依此类推，则平行四边形ABC 2009O 2009的面积为（ ）A.n 25 B.n 22 C.n 31 D.n 23二．填空题：（每题7分，满分42分）9．（7分）方程组的解是 ．10．（7分）若对任意实数x 不等式ax ＞b 都成立，那么a ，b 的取值范围为 ．11．（7分）如图，圆锥的母线长是3，底面半径是1，A 是底面圆周上一点，从A 点出发绕侧面一周，再回到A 点的最短的路线长是 ．12．（7分）有一张矩形纸片ABCD ，AD=9，AB=12，将纸片折叠使A 、C 两点重合，那么折痕长是 ．13．（7分）设﹣1≤x ≤2，则|x ﹣2|﹣|x|+|x+2|的最大值与最小值之差为 ．14．（7分）两个反比例函数y=，y=在第一象限内的图象如图所示．点P 1，P 2，P 3、…、P 2007在反比例函数y=上，它们的横坐标分别为x 1、x 2、x 3、…、x 2007，纵坐标分别是1，3，5…共2007个连续奇数，过P 1，P 2，P 3、…、P 2007分别作y 轴的平行线，与y=的图象交点依次为Q 1（x 1′，y 1′）、Q 1（x 2′，y 2′）、…、Q 2（x 2007′，y 2007′），则|P 2007Q 2007|= ．三．解答题：（每天12分，满分60分）15.(12分).已知正实数,,x y z 满足：1xy yz zx ++≠ ,且222222(1)(1)(1)(1)(1)(1)4x y y z z x xy yz zx------++= .(1) 求111xy yz zx++的值. (2) 证明:9()()()8()x y y z z x xyz xy yz zx +++≥++.16．（12分）如图，ABC △是等腰直角三角形，CA CB =，点N 在线段AB 上（与A 、B 不重合），点M 在射线BA 上，且45NCM ∠=︒。

2015年天津卷高考真题英语试卷-学生用卷一、单项选择1、【来源】 2015年高考真题天津卷第1题2020~2021学年天津和平区天津市第二南开学校高一上学期期中第22题0.5分2017~2018学年天津高一期末联考第9题1分2018~2019学年天津静海区天津市静海区第一中学高二上学期期中第16题1分—Sorry, Liz. I think I was a bit rude to you.—______, but don't do that again!A. Go aheadB. Forget itC. It dependsD. With pleasure2、【来源】 2015年高考真题天津卷第2题The quality of education in this small school is better than ______ in some larger schools.A. thatB. oneC. itD. this3、【来源】 2015年高考真题天津卷第3题2016~2017学年广东广州高二上学期期中五校联考第17题1分2018~2019学年吉林长春朝阳区吉林省实验中学高二下学期期末第30题1分Only when Lily walked into the office that she had left the contract at home.A. she realizedB. has she realizedC. she has realizedD. did she realize4、【来源】 2015年高考真题天津卷第4题—Jack, you seem excited.—______? I won the first prize.A. Guess whatB. So whatC. Pardon meD. Who cares5、【来源】 2015年高考真题天津卷第5题2018~2019学年10月广东深圳福田区深圳市高级中学高中部高二月考第47题1分2019~2020学年广东深圳罗湖区深圳市翠园中学高二上学期期中第6题1分2019~2020学年陕西西安长安区西安交通大学附属中学航天学校高三上学期段考（四诊）第22题1分2017~2018学年北京海淀区北京市十一学校高二上学期期末第49题0.5分in painting, John didn't notice evening approaching.A. To absorbB. To be absorbedC. AbsorbedD. Absorbing6、【来源】 2015年高考真题天津卷第6题2016~2017学年天津高一下学期期末第22题0.5分2017~2018学年天津和平区天津市第一中学高一下学期期末第25题1分2019~2020学年陕西西安长安区西安交通大学附属中学航天学校高三上学期段考（四诊）第23题1分2016~2017学年北京海淀区北京一零一中学高二下学期期中第22题1分Jane can't attend the meeting at 3 o'clock this afternoon because she a class at that time.A. will teachB. would teachC. has taughtD. will be teaching7、【来源】 2015年高考真题天津卷第7题2019~2020学年3月天津河西区高三下学期月考第14题1分I ______ have worried before I came to the new school, for my classmates here are very friendly to me.A. mightn'tB. mustn'tC. needn'tD. couldn't8、【来源】 2015年高考真题天津卷第8题2018~2019学年10月天津和平区天津市双菱中学高二上学期月考第26题1分2018~2019学年10月广东深圳福田区深圳市高级中学高中部高二月考第48题1分2019~2020学年3月天津河西区高三下学期月考第11题1分2019~2020学年广东深圳福田区深圳市高级中学高中部高一下学期期中第15题1.5分______ for two days, Steve managed to finish his report on schedule.A. To workB. WorkedC. To be workingD. Having worked9、【来源】 2015年高考真题天津卷第9题2019~2020学年12月江苏南京玄武区南京市第九中学高一上学期月考第63题1分2018~2019学年陕西西安未央区西安中学高一上学期期末第26题1分2017~2018学年北京东城区北京汇文中学高二上学期期中第35题1分2017~2018学年广东深圳福田区深圳市高级中学高中部高一下学期期中第53题1分Despite the previous rounds of talks, no agreement so far by the two sides.A. has been reachedB. was reachedC. will reachD. will have reached10、【来源】 2015年高考真题天津卷第10题2019~2020学年陕西西安长安区西安交通大学附属中学航天学校高三上学期段考（四诊）第25题1分Tom had to the invitation to the party last weekend because he was too busy.A. turn inB. turn downC. turn overD. turn to11、【来源】 2015年高考真题天津卷第11题2019~2020学年天津南开区高三上学期期末第6题1分If you have any doubts about your health, you'd better______ your doctor at once.A. convinceB. consultC. avoidD. affect12、【来源】 2015年高考真题天津卷第12题We need to get to the root of the problem we can solve it.A. whileB. afterC. beforeD. as13、【来源】 2015年高考真题天津卷第13题2015~2016学年北京西城区北京师范大学第二附属中学高二上学期期中第5题I wish I ______ at my sister's wedding last Tuesday, but I was on a business trip in New York then.A. will beB. would beC. have beenD. had been14、【来源】 2015年高考真题天津卷(部分区联考)第14题2016~2017学年天津高一下学期期末第13题1分See, your computer has broken down again! It doesn't ______ sense to buy the cheapest brand of computer just to save a few dollars.A. haveB. makeC. displayD. bring15、【来源】 2015年高考真题天津卷第15题2018~2019学年广东深圳宝安区宝安第一外国语学校高二下学期期中第62题1分2017~2018学年天津和平区天津市第一中学高二上学期期末第16题1分The boss of the company is trying to create an easy atmosphere his employees enjoy their work.A. whereB. whichC. whenD. who二、完型填空16、【来源】 2015年高考真题天津卷第16题2017~2018学年12月河南洛阳洛龙区洛阳市第一高级中学高二上学期月考第36~55题20分2019~2020学年高一下学期单元测试第30~49题2017~2018学年黑龙江大庆红岗区大庆市铁人中学高二上学期期中第41~60题30分My fiance （未婚夫） and I were excited about shopping for our first home. But our fundswere1, and none of the houses in our price range seemed satisfactory.One agent2 a house in particular. Although her description sounded wonderful, the price was3our range, so we declined. But she kept urging us to have a look4.We finally did and it was5at first sight. It was Our Home, small and charming, overlooking a quiet lake. Walking through the rooms and talking with the owners, a nice elderly couple, we felt the warmth and6of the marriage within that home. As perfect as it was, the price remained too high for us. But every day, we would sit by the lake, looking at the house and dreaming of7it would be like to live there.Days later, we made a(n)8—far below the asking price. Surprisingly, they didn't9us. They renewed their offer10. It was also much more than we could afford, but far11than the original asking price.The next day, we got a12message that another buyer had offered a much higher price. Even so, we decided to talk with the13directly. We made our final offer, which14was thousands of dollars less than the other buyer's bid. We knew it,15we had to try.“Sold!” said the owner. Then he16: He'd seen us sitting by the lake all those times; he knew how much we loved the place and that we'd17the years of work they had put into their home; he realized he would take a18by selling it to us, but it was worthwhile; we were the people they wanted to live there. He told us to consider the19in the price “an early wedding present.”That's how we found our home and how I learned that when peopleare20they are not strangers, only friends we haven't yet met.A. neededB. limitedC. enoughD. largeA. recommendedB. decoratedC. soldD. rentedA. belowB. withinC. beyondD. betweenA. at leastB. at mostC. at timesD. at handA. reliefB. concernC. loveD. curiosityA. prideB. happinessC. challengeD. desireA. whichB. whyC. thatD. whatA. effortB. offerC. promiseD. profitA. come acrossB. look afterC. depend onD. laugh atA. insteadB. indeedC. asideD. apartA. worseB. betterC. lessD. higherA. relaxingB. disappointingC. pleasantD. regularA. agentsB. buyersC. managersD. ownersA. alreadyB. stillC. generallyD. everA. soB. orC. forD. butA. apologizedB. complainedC. criticizedD. explainedA. checkB. analyzeC. appreciateD. ignoreA. lossB. riskC. chanceD. leadA. increaseB. differenceC. interestD. averageA. kindB. politeC. smartD. energetic三、阅读理解17、【来源】 2015年高考真题天津卷（A篇）第17题University Room RegulationsApproved and Prohibited ItemsThe following items are approved for use in residential （住宿的） rooms: electric blankets, hair dryers, personal computers, radios, televisions and DVD players. Items that are not allowed in student rooms include: candles, ceiling fans, fireworks, waterbeds, sun lamps and wireless routers. Please note that any prohibited items will be taken away by the Office of Residence Life.Access to Residential RoomsStudents are provided with a combination （组合密码） for their room door locks upon check-in. Do not share your room door lock combination with anyone. The Office of Residence Life may change the door lock combination at any time at the expense of the resident if it is found that the student has shared the combination with others. The fee is $25 to change a room combination.Cooking PolicyStudents living in buildings that have kitchens are only permitted to cook in the kitchen. Students must clean up after cooking. This is not the responsibility of housekeeping staff. Kitchens that are not kept clean may be closed for use. With the exception of using a small microwave oven （微波炉） to heat food, students are not permitted to cook in their rooms.Pet PolicyNo pets except fish are permitted in student rooms. Students who are found with pets, whether visiting or owned by the student, are subject to an initial fine of ＄100 and a continuing fine of ＄50 a day per pet. Students receive written notice when the fine goes into effect. If, one week from the date of written notice, the pet is not removed, the student is referred to the Student Court.Quiet HoursResidential buildings must maintain an atmosphere that supports the academic mission of the University. Minimum quiet hours in all campus residences are 11:00 pm to 8:00 am Sunday through Thursday. Quiet hours on Friday and Saturday nights are 1:00 am to 8:00 am. Students who violate quiet hours are subject to a fine of $25.(1) Which of the following items are allowed in student rooms?A. Ceiling fans and waterbeds.B. Wireless routers and radios.C. Hair dryers and candles.D. TVs and electric blankets.(2) What if a student is found to have told his combination to others?A. The combination should be changed.B. The Office should be charged.C. He should replace the door lock.D. He should check out of the room.(3) What do we know about the cooking policy?A. A microwave oven can be used.B. Cooking in student rooms is permitted.C. A housekeeper is to clean up the kitchen.D. Students are to close kitchen doors after cooking.(4) If a student has kept a cat in his room for a week since the warning, he will face _____.A. parent visitsB. a fine of $100C. the Student CourtD. a written notice(5) When can students enjoy a party in residences?A. 7:00 am, Sunday.B. 7:30 am, Thursday.C. 11:30 pm, Monday.D. 00:30 am, Saturday.18、【来源】 2015年高考真题天津卷第18题Whether in the home or the workplace, social robots are going to become a lot more common in the next few years. Social robots are about to bring technology to the everyday world in a more humanized way, said Cynthia Breazeal, chief scientist at the robot company Jibo.While household robots today do the normal housework, social robots will be much more like companions than mere tools. For example, these robots will be able to distinguish when someone is happy or sad. This allows them to respond more appropriately to the user.The Jibo robot, arranged to ship later this year, is designed to be a personalized assistant. You can talk to the robot, ask it questions, and make requests for it to perform different tasks. The robot doesn't just deliver general answers to questions; it responds based on what it learns about each individual in the household. It can do things such as reminding an elderly family member to take medicine or taking family photos.Social robots are not just finding their way into the home. They have potential applications in everything from education to health care and are already finding their way into some of these spaces.Fellow Robots is one company bringing social robots to the market. The company's "Oshbot" robot is built to assist customers in a store, which can help the customers find items and help guide them to the product's location in the store. It can also speak different languages and make recommendations for different items based on what the customer is shopping for.The more interaction the robot has with humans, the more it learns. But Oshbot, like other social robots, is not intended to replace workers, but to work alongside other employees. "We have technologies to train social robots to do things not for us, but with us, " said Breazeal.(1) How are social robots different from household robots?A. They can control their emotions.B. They are more like humans.C. They do the normal housework.D. They respond to users more slowly.(2) What can a Jibo robot do according to Paragraph 3?A. Communicate with you and perform operations.B. Answer your questions and make requests.C. Take your family pictures and deliver milk.D. Obey your orders and remind you to take pills.(3) What can Oshbot work as?A. A language teacher.B. A tour guide.C. A shop assistant.D. A private nurse.(4) We can learn from the last paragraph that social robots will.A. train employeesB. be our workmatesC. improve technologiesD. take the place of workers(5) What does the passage mainly present?A. A new design idea of household robots.B. Marketing strategies for social robots.C. Information on household robots.D. An introduction to social robots.19、【来源】 2015年高考真题天津卷第19题2017~2018学年12月河南洛阳洛龙区洛阳市第一高级中学高二上学期月考第21~25题10分2017~2018学年陕西西安雁塔区陕西师范大学附属中学高三上学期开学考试第24~28题10分One day when I was 12, my mother gave me an order: I was to walk to the public library, and borrow at least one book for the summer. This was one more weapon for her to defeat my strange problem—inability to read.In the library, I found my way into the "Children's Room."I sat down on the floor and pulled a few books off the shelf at random. The cover of a book caught my eye. It presented a picture of a beagle. I had recently had a beagle, the first and only animal companion I ever had as a child. He was my secret sharer, but one morning, he was gone, given away to someone who had the space and the money to care for him. I never forgot my beagle.There on the book's cover was a beagle which looked identical to my dog. I ran my fingers over the picture of the dog on the cover. My eyes ran across the title, Amos, the Beagle with a Plan. Unknowingly, I had read the title. Without opening the book, I borrowed it from the library for the summer.Under the shade of a bush, I started to read about Amos. I read very, very slowly with difficulty. Though pages were turned slowly, I got the main idea of the story about a dog who, like mine, had been separated from his family and who finally found his way back home. That dog was my dog, and I was the little boy in the book. At the end of the story, my mind continued the final scene of reunion, on and on, until my own lost dog and I were, in my mind, running together.My mother's call returned me to the real world. I suddenly realized something: I had read a book, and I had loved reading that book. Everyone knew I could not read. But I had read it. Books could be incredibly wonderful and I was going to read them.I never told my mother about my "miraculous"（奇迹般地）experience that summer, but she sawa slow but remarkable improvement in my classroom performance during the next year. And years later, she was proud that her son had read thousands of books, was awarded a PhD in literature, and authored his own books, articles, poetry and fiction. The power of the words has held.(1) The author's mother told him to borrow a book in order to.A. encourage him to do more walkingB. let him spend a meaningful summerC. help cure him of his reading problemD. make him learn more about weapons(2) The book caught the author's eye because.A. it contained pretty pictures of animalsB. it reminded him of his own dogC. he found its title easy to understandD. he liked children's stories very much(3) Why could the author manage to read the book throughA. He was forced by his mother to read it.B. He identified with the story in the book.C. The book told the story of his pet dog.D. The happy ending of the story attracted him.(4) What can be inferred from the last paragraph?A. The author has become a successful writer.B. The author's mother read the same book.C. The author's mother rewarded him with books.D. The author has had happy summers ever since.(5) Which one could be the best title of the passage?A. The Charm of a BookB. Mum's Strict OrderC. Reunion with My BeagleD. My Passion for Reading20、【来源】 2015年高考真题天津卷第20题DOnce when I was facing a decision that involved high risk, I went to a friend. He looked at me for a moment, and then wrote a sentence containing the best advice I've ever had: Be bold and brave — and mighty (强大的) forces will come to your aid.Those words made me see clearly that when I had fallen short in the past, it was seldom because I had tried and failed. It was usually because I had let fear of failure stop me from trying at all. On the other hand, whenever I had plunged into deep water, forced by courage or circumstance, I had always been able to swim until I got my feet on the ground again.Boldness means a decision tobite off more than you can eat. And there is nothing mysterious about the mighty forces. They are potential powers we possess: energy, skill, sound judgment, creative ideas —even physical strength greater than most of us realize.Admittedly, those mighty forces are spiritual ones. But they are more important than physical ones. A college classmate of mine, Tim, was an excellent football player, even though he weighed much less than the average player. “In one game I suddenly found myself confronting a huge player, who had nothing but me between him and our goal line,” said Tim. “I was so frightened that I closed my eyes and desperately threw myself at that guy like a bullet — and stopped him cold.”Boldness — a willingness to extend yourself to the extreme—is not one that can be acquired overnight. But it can be taught to children and developed in adults. Confidence builds up. Surely, there will be setbacks (挫折) and disappointments in life; boldness in itself is no guarantee of success. But the person who tries to do something and fails is a lot better off than the person who tries to do nothing and succeeds.So, always try to live a little bit beyond your abilities—and you'll find your abilities are greater than you ever dreamed.(6) Why was the author sometimes unable to reach his goal in the past?A. He faced huge risks.B. He lacked mighty forces.C. Fear prevented him from trying.D. Failure blocked his way to success.(7) What is the implied meaning of the underlined part?A. Swallow more than you can digest.B. Act slightly above your abilities.C. Develop more mysterious powers.D. Learn to make creative decisions.(8) What was especially important for Tim’s successful defense in the football game?A. His physical strength.B. His basic skill.C. His real fear.D. His spiritual force.(9) What can be learned from Paragraph 5?A. Confidence grows more rapidly in adults.B. Trying without success is meaningless.C. Repeated failure creates a better life.D. Boldness can be gained little by little.(10) What is the author’s purpose in writing this passage?A. To encourage people to be courageous.B. To advise people to build up physical power.C. To tell people the ways to guarantee success.D. To recommend people to develop more abilities.四、任务型阅读21、【来源】 2015年高考真题天津卷第21题Six days a week, up and down the red hills of northeast Georgia, my grandfather brought the mail to the folks there. At age 68, he retired from the post office, but he never stopped serving the community.On his 80th birthday, I sent him a letter, noting the things we all should be thankful for — good health, good friends and good outcomes. By most measurements he was a happy man. Then I suggested it was time for him to slow down. At long last, in a comfortable home, with a generous pension, he should learn to take things easy.“Thank you for your nice words,” he wrote in his letter back, “and I know what you meant, but slowing down scares me. Life isn't having it made; it's getting it made.”“The finest and happiest years of our lives were not when all the debts were paid, and all difficult experiences had passed, and we had settled into a comfortable home. No. I go back years ago, when we lived in a three-room house, when we got up before daylight and worked till after dark to make ends meet.I rarely had more than four hours of sleep. But what I still can't figure out is why I never got tired, never felt better in my life. I guess the answer is, we were fighting for survival, protecting and providing for those we loved. What matters are not the great moments, but the partial victories, the waiting, and even the defeats. It's the journey, not the arrival, that counts.”The letter ended with a personal request: “Boy, on my next birthday, just tell me to wake up and get going, because I will have one less year to do things — and there are ten million things waiting to be done.”Christina Rossetti, an English poet, once said: “Does the road wind uphill all the way? Yes, to the very end.” Today, at 96, my grandfather is still on that long road, climbing.(6) What was the author’s grandfather before he retired? (no more than 5 words)(7) What did the author advise his grandfather to do in his letter? (no more than 10 words)(8) What is the grandfather’s view on life according to his letter back? (no more than 10 words)(9) How do you understand the underlined sentence in the last paragraph? (no more than 10 words)(10) Do you agree with the grandfather’s view on life? Give reasons in your own words, (no more than 20 words)五、书面表达22、【来源】 2015年高考真题天津卷第22题假设你是晨光中学学生会主席李津，你校拟向美国友好交流学校的中文班捐赠一批图书。

2017-2018学年天津一中高一（上）期末数学试卷一、选择题（本大题共10小题，共30.0分）1.若tanα=3，则的值等于（）A. 2B. 3C. 4D. 62.设函数f（x）=sin2（x+）-cos2（x+）（x∈R），则函数f（x）是（）A. 最小正周期为的奇函数B. 最小正周期为的偶函数C. 最小正周期为的奇函数D. 最小正周期为的偶函数3.设函数f（x）=sin（ωx+φ）+cos（ωx+φ）＞，＜的最小正周期为π，且f（-x）=f（x），则（）A. 在单调递减B. 在单调递减C. 在单调递增D. 在单调递增4.设函数f（x）=cosωx（ω＞0），将y=f（x）的图象向右平移个单位长度后，所得的图象与原图象重合，则ω的最小值等于（）A. B. 3 C. 6 D. 95.在△ABC中，根据下列条件解三角形，其中有两个解的是（）A. ，，B. ，，C. ，，D. ，，6.在△ABC中，sin2A≤sin2B+sin2C-sin B sin C，则A的取值范围是（）A. B. C. D.7.函数，＜向左平移个单位后是奇函数，则函数f（x）在，上的最小值为（）A. B. C. D.8.已知函数y=sin x+a cos x的图象关于对称，则函数y=a sin x+cos x的图象的一条对称轴是（）A. B. C. D.9.设函数f（x）=4sin（2x+1）-x，则在下列区间中函数f（x）不存在零点的是（）A. B. C. D.10.已知函数f（x）=2x+log2x，g（x）=2-x+log2x，h（x）=2x•log2x-1的零点分别为a，b，c，则a，b，c的大小关系为（）A. B. C. D.二、填空题（本大题共6小题，共24.0分）11.已知a=log54．b=（log53）2，c=log45，则a，b，c从小到大的关系是______．12.已知α∈（，π），sinα=，则tan2α=______．13.已知tan（α+β）=，tan（）=-1，则tan（）=______．14.在△ABC中的内角A、B、C所对的边a、b、c，a=4，b=5，c=6，则=______．15.在△ABC中，内角A，B，C所对的边分别为a，b，c．已知△ABC的面积为3，b-c=2，cos A=-，则a的值为______．16.在平面四边形ABCD中，∠A=∠B=∠C=75°．BC=2，则AB的取值范围是______．三、解答题（本大题共4小题，共46.0分）17.已知函数f（x）=2sin x cosx+2cos2x-1．（1）求函数f（x）的最小正周期及在区间[0，]上的最大值和最小值；（2）若f（x）=，x0∈[，]，求cos2x0的值．18.在△ABC中，a，b，c分别为内角A，B，C的对边，且2a sin A=（2b+c）sin B+（2c+b）sin C．（Ⅰ）求A的大小；（Ⅱ）求sin B+sin C的最大值．19.已知函数f（x）=（1+）sin2x+m sin（x+）sin（x-）（1）当m=0时，求f（x）在区间[，]上的取值范围；（2）当t a na=2时，f（a）=，求m的值．20.在△ABC中，sin（A-B）=sin C-sin B，D是边BC的一个三等分点（靠近点B），记 ∠．∠ （1）求A的大小；（2）当t取最大值时，求tan∠ACD的值．答案和解析1.【答案】D【解析】解：==2tanα=6故选D利用两角和公式把原式的分母展开后化简，把tanα的值代入即可．本题主要考查了三角函数的恒等变换及化简求值．考查了基础知识的运用．2.【答案】A【解析】【分析】本题考查的知识点是三角函数中的恒等变换，三角函数的周期性，三角函数的奇偶性，其中利用倍角公式及诱导公式，化简函数的解析式，是解答本题的关键．利用倍角公式及诱导公式，化简函数的解析式，进而求出其周期，并判断其奇偶性，可得答案．【解答】解：∵f（x）=sin2（x+）-cos2（x+）=-cos2（x+）=-cos（2x+）=sin2x，∵ω=2，∴函数f（x）的最小正周期T=π，又∵f（-x）=sin（-2x）=-sin2x=-f（x），故f（x）为奇函数．故函数f（x）是最小正周期为π的奇函数．故选A．3.【答案】A【解析】解：由于f（x）=sin（ωx+ϕ）+cos（ωx+ϕ）=，由于该函数的最小正周期为T=，得出ω=2，又根据f（-x）=f（x），得φ+=+kπ（k∈Z），以及|φ|＜，得出φ=．因此，f（x）=cos2x，若x∈，则2x∈（0，π），从而f（x）在单调递减，若x ∈（，），则2x ∈（，），该区间不为余弦函数的单调区间，故B ，C ，D 都错，A 正确． 故选：A ．利用辅助角公式将函数表达式进行化简，根据周期与ω的关系确定出ω的值，根据函数的偶函数性质确定出φ的值，再对各个选项进行考查筛选．本题考查三角函数解析式的确定问题，考查辅助角公式的运用，考查三角恒等变换公式的逆用等问题，考查学生分析问题解决问题的能力和意识，考查学生的整体思想和余弦曲线的认识和把握．属于三角中的基本题型． 4.【答案】C【解析】解：f （x ）的周期T=，函数图象平移个单位长度后，所得的图象与原图象重合，说明函数平移整数个周期，所以，k ∈Z ．令k=1，可得ω=6．故选：C ．函数图象平移个单位长度后，所得的图象与原图象重合，说明函数平移整数个周期，容易得到结果． 本题是基础题，考查三角函数的图象的平移，三角函数的周期定义的理解，考查技术能力，常考题型． 5.【答案】D【解析】解：A 、∵A=45°，C=70°，∴B=65°，又b=10，∴由正弦定理==得：a==，c=，此时三角形只有一解，不合题意； B 、∵a=60，c=48，B=60°，∴由余弦定理得：b 2=a 2+c 2-2accosB=3600+2304-2880=3024＞0，∴此时三角形有一解，不合题意； C 、∵a=7，b=5，A=80°，∴由正弦定理=得：sinB=，又b ＜a ，∴B ＜A=80°，∴B只有一解，不合题意；D、∵a=14，b=16，A=45°，∴由正弦定理=得：sinB==＞，∵a＜b，∴45°=A＜B，∴B有两解，符合题意，故选：D．A、由A和C的度数，利用三角形内角和定理求出B的度数，再由b的值，利用正弦定理求出a与c，得到此时三角形只有一解，不合题意；B、由a，c及cosB的值，利用余弦定理列出关系式，得到b2小于0，无解，此时三角形无解，不合题意；C、由a，b及sinA的值，利用正弦定理求出sinB的值，由a大于b得到A大于B，可得出此时B只有一解，不合题意；D、由a，b及sinA的值，利用正弦定理求出sinB的值，由a小于b得到A小于B，可得出此时B有两解，符合题意．此题考查了正弦、余弦定理，三角形的边角关系，以及三角形的内角和定理，熟练掌握正弦、余弦定理是解本题的关键．6.【答案】C【解析】解：由正弦定理可知a=2RsinA，b=2RsinB，c=2RsinC，∵sin2A≤sin2B+sin2C-sinBsinC，∴a2≤b2+c2-bc，∴bc≤b2+c2-a2∴cosA=≥∴A≤∵A＞0∴A的取值范围是（0，]故选：C．先利用正弦定理把不等式中正弦的值转化成边，进而代入到余弦定理公式中求得cosA的范围，进而求得A的范围．本题主要考查了正弦定理和余弦定理的应用．作为解三角形中常用的两个定理，考生应能熟练记忆．7.【答案】A【解析】解：把函数y=sin（2x+φ）的图象向左平移个单位得到函数y=sin（2x++φ）的图象，因为函数y=sin（2x++φ）为奇函数，故+φ=kπ，因为，故φ的最小值是-．所以函数为y=sin（2x-）．x∈，所以2x-∈[-，]，x=0时，函数取得最小值为．故选：A．根据图象变换规律，把函数y=sin（2x+φ）的图象向左平移个单位得到函数y=sin（2（x++φ））的图象，要使所得到的图象对应的函数为奇函数，求得φ的值，然后函数f（x）在上的最小值．本题考查了三角函数的图象变换以及三角函数的奇偶性，三角函数的值域的应用，属于中档题．8.【答案】A【解析】解：y=sinx+acosx变为y=sin（x+∅），（令tan∅=a）又图象关于对称，∴+∅=kπ+，k∈z，可求得∅=kπ-，由此可求得a=tan∅=tan（kπ-）=-，∴函数y=-sinx+cosx=sin（x+θ），（tanθ=-）其对称轴方程是x+θ=kπ+，k∈z，即x=kπ+-θ又tanθ=-，故θ=k1π-，k1∈z故函数y=asinx+cosx的图象的对称轴方程为x=（k-k1）π++=（k-k1）π+，k-k1∈z，当k-k1=1时，对称轴方程为x=故选：A．函数y=sinx+acosx变为y=sin（x+∅），tan∅=a又图象关于对称，+∅=kπ+，k∈z，可求得∅=kπ-，由此可求得a=tan∅=tan（kπ-）=-，将其代入函数y=asinx+cosx化简后求对称轴即可．本题考查三角恒等变形以及正弦类函数的对称性质，是三角函数中综合性比较强的题目，比较全面地考查了三角函数的图象与性质．9.【答案】A【解析】解：在同一坐标系中画出g（x）=4sin（2x+1）与h（x）=x的图象如下图示：由图可知g（x）=4sin（2x+1）与h（x）=x的图象在区间[-4，-2]上无交点，由图可知函数f（x）=4sin（2x+1）-x在区间[-4，-2]上没有零点故选：A．将函数f（x）的零点转化为函数g（x）=4sin（2x+1）与h（x）=x的交点，在同一坐标系中画出g（x）=4sin（2x+1）与h（x）=x的图象，数形结合对各个区间进行讨论，即可得到答案本题主要考查了三角函数图象的平移和函数与方程的相关知识点，突出了对转化思想和数形结合思想的考查，对能力要求较高，属较难题．函数F（x）=f（x）-g（x）有两个零点，即函数f（x）的图象与函数g（x）的图形有两个交点．10.【答案】D【解析】解：f（x）=2x+log2x=0，可得log2x=-2x，g（x）=2-x+log2x=0，可得log2x=-2-x，h（x）=2x log2x-1=0，可得log2x=2-x，∵函数f（x），g（x），h（x）的零点分别为a，b，c，作出函数y=log2x，y=-2x，y=-2-x，y=2-x的图象如图，由图可知：a＜b＜c．故选：D．由题意画出图形，数形结合得答案．本题考查函数零点的判定，考查数形结合的解题思想方法，是中档题．11.【答案】b＜a＜c【解析】解：∵log45＞1，0＜log54＜1，0＜log53＜1，∴log54＞log53＞（log53）2，即b＜a＜c，故答案为：b＜a＜c根据对数的性质进行估算即可．本题主要考查对数值的大小比较，根据对数的性质进行估算是解决本题的关键．12.【答案】-【解析】解：由α∈（，π），sinα=，得cosα=-，tanα==∴tan2α==-故答案为：-利用题目提供的α的范围和正弦值，可求得余弦值从而求得正切值，然后利用二倍角的正切求得tan2α．本题考查了二倍角的正切与同角三角函数间的基本关系，是个基础题．13.【答案】5【解析】解：∵已知tan（α+β）=，tan（）=-1，∴tan（）===5，故答案为：5．由题意利用两角差的正切公式，求得tan（）的值．本题主要考查两角差的正切公式的应用，属于基础题．14.【答案】1【解析】解：∵a=4，b=5，c=6，∴======1．故答案为：1．由已知及正弦定理，余弦定理，二倍角的正弦函数公式化简所求即可计算得解．本题主要考查了正弦定理，余弦定理，二倍角的正弦函数公式在解三角形中的应用，考查了计算能力和转化思想，属于基础题．15.【答案】8【解析】解：∵A∈（0，π），∴sinA==．∵S△ABC==bc=，化为bc=24，又b-c=2，解得b=6，c=4．由余弦定理可得：a2=b2+c2-2bccosA=36+16-48×=64．解得a=8．故答案为：8．由cosA=-，A∈（0，π），可得sinA=．利用S△ABC==，化为bc=24，又b-c=2，解得b，c．由余弦定理可得：a2=b2+c2-2bccosA即可得出．本题考查了余弦定理、同角三角函数基本关系式、三角形面积计算公式，考查了推理能力与计算能力，属于中档题．16.【答案】（-，+）【解析】解：方法一：如图所示，延长BA，CD交于点E，则在△ADE中，∠DAE=105°，∠ADE=45°，∠E=30°，∴设AD=x，AE=x，DE=x，CD=m，∵BC=2，∴（x+m）sin15°=1，∴x+m=+，∴0＜x＜4，而AB=x+m-x=+-x，∴AB的取值范围是（-，+）．故答案为：（-，+）．方法二：如下图，作出底边BC=2的等腰三角形EBC，B=C=75°，倾斜角为150°的直线在平面内移动，分别交EB、EC于A、D，则四边形ABCD即为满足题意的四边形；当直线移动时，运用极限思想，①直线接近点C时，AB趋近最小，为-；②直线接近点E时，AB趋近最大值，为+；故答案为：（-，+）．如图所示，延长BA，CD交于点E，设AD=x，AE=x，DE=x，CD=m，求出x+m=+，即可求出AB的取值范围．本题考查求AB的取值范围，考查三角形中的几何计算，考查学生的计算能力，属于中档题．17.【答案】解：（1）函数f（x）=2sin x cosx+2cos2x-1．=，=，所以函数的最小正周期为：．由于x∈[0，]，则：∈，，所以函数的最大值2，函数的最小值1;（2）由于f（x）=，，所以：∈，则：，=+，=，=.【解析】（1）直接利用三角函数关系是的恒等变换，把函数的关系式变形成正弦型函数，进一步求出函数的最值．（2）利用整体的角的恒等变换求出结果．本题考查的知识要点：三角函数关系式的恒等变变换，正弦型函数的性质的应用，角的恒等变换的应用．18.【答案】解：（Ⅰ）设则a=2R sin A，b=2R sin B，c=2R sin C∵2a sin A=（2b+c）sin B+（2c+b）sin C方程两边同乘以2R∴2a2=（2b+c）b+（2c+b）c整理得a2=b2+c2+bc∵由余弦定理得a2=b2+c2-2bc cos A故cos A=-，A=120°（Ⅱ）由（Ⅰ）得：sin B+sin C=sin B+sin（60°-B）=cos B+sin B=sin（60°+B）故当B=30°时，sin B+sin C取得最大值1．【解析】（Ⅰ）根据正弦定理，设，把sinA，sinB，sinC代入2asinA=（2b+c）sinB+（2c+b）sinC求出a2=b2+c2+bc再与余弦定理联立方程，可求出cosA的值，进而求出A的值．（Ⅱ）根据（Ⅰ）中A的值，可知c=60°-B，化简得sin（60°+B）根据三角函数的性质，得出最大值．本题主要考查了余弦函数的应用．其主要用来解决三角形中边、角问题，故应熟练掌握．19.【答案】解：（1）当m=0时，函数f（x）=（1+）sin2x=•sin2x=sin2x+sin x cosx=+sin2x=+sin （2x-）．∵≤x≤，∴0≤2x-≤，∴-≤sin（2x-）≤1，0≤f（x）≤，故f（x）在区间[，]上的取值范围为[0，]．（2）∵当t a na=2时，f（a）=，∴sin2a=，cos2a=．再由f（a）=（1+）sin2a+m sin（a+）sin（a-）=sin2a+m（sin2a-cos2a）=，可得=，解得m=-2．【解析】（1）当m=0时，利用三角函数的恒等变换化简函数f（x）的解析式为+sin（2x-），再根据x的范围，利用正弦函数的定义域和值域，求得f（x）在区间[，]上的取值范围．（2）由tana=2时，f（a）=，利用同角三角函数的基本关系求得sin2a=，cos2a=．化简tan（a）等于，可得=，由此解得m的值．本题主要考查三角函数的恒等变换及化简求值，正弦函数的定于域和值域，属于中档题．20.【答案】解：（1）因为sin（A-B）=sin C-sin B，所以sin B=sin C-sin（A-B），即sin B=sin（A+B）-sin（A-B），整理得sin B=2cos A sin B．又sin B≠0，所以，即．（2）设BD=x，∠BAD=θ，∈，，则DC=2x，sin B=t sinθ．由正弦定理得AD=tx，∠ ．又，由，得．因为，所以，=，=．因为∈，，所以＜＜．所以当，即时，t取得最大值，此时，所以，∠ ．【解析】（1）直接利用已知条件，对三角函数的关系式进行恒等变换，进一步求出结果．（2）利用（1）的结论，进一步利用已知条件和正弦定理建立联系，最后求出最值．本题考查的知识要点：三角函数关系式的恒等变换，正弦定理的应用及函数的最值问题．。

2017-2018 学年天津市部分区高一（上）期末数学试卷一、选择题（本题共 10 小题，每小题 4 分，共 40 分）1．（4.00 分）设集合 U={1，2，3，4，5}，集合 A={1，2，3}，则 U A=（ ）A ．{1，2，3}B ．{4，5}C ．{1，2，3，4，5}D ．∁24.00 60°=1 =2 •= ．（分）已知向量 ， 的夹角为 ，且| || ，则 （ ） ，| ∅ A ． B ．C ．1 D ．23．（4.00 分）下列运算的结果正确的是（）A ．log 43=2log 23B ．（﹣a 2）3=﹣a 6C ．（ ﹣1）0=0 D ．lg2+lg3=lg54．（4.00 分）函数 f （x ）= ﹣x +1 的零点所在的区间是（ ） A ．（0，1） B ．（1，2） C ．（2，3） D ．（3，4）5．（4.00 分）将函数 y=sin2x 的图象上所有点向左平移个单位长度，再把所得各点的横坐标伸长为原来的 2 倍（纵坐标不变），所得图象对应的函数解析式是（ ）A ．y=sin （x +）B ．y=sin （2x +） C ．y=sin （x +） D ．y=sin （x +）6．（4.00 分）已知函数 f （x ）=a x（a ＞0，a ≠1），若 f （﹣2）＜f （﹣3），则 a的取值范围是（ ）A ．2＜a ＜3B ．＜a ＜C ．a ＞1D ．0＜a ＜17．（4.00 分）若非零向量 ， 满足| + |=| ﹣ |，则（ ）A ． ⊥B ． ∥C ．| |=| |D ．| |≥| |8．（4.00 分）若α为第二象限的角，且 tanα=﹣ ，则 cosα=（ ）A ．B ．﹣C ．D ．﹣9．（4.00 分）已知集合 P={x |y= }，Q={x |y=lg （x ﹣1）}，则 P ∩Q=（） A ．{x |1≤x ≤3}B ．{x |1＜x ＜3}C ．{x |1＜x ≤3}D ．{x |x ＜1，或 x ≥3}10．（4.00 分）已知偶函数 f （x ）在[0，+∞）上单调递减，若 a=f （ln2.1），b=f（1.11.1），c=f （﹣3），则 a ，b ，c 的大小关系是（ ）A．a＜b＜c B．c＜b＜a C．c＜a＜b D．b＜a＜c二、填空题（本大题共 5 小题，每小题 4 分，共 20 分）11．（4.00 分）sin（﹣）= ．12．（4.00 分）已知幂函数 f（x）经过点（2，8），则 f（3）= ．13．（4.00 分）设集合 A={x|2＜x＜3}，B={x|x＞a}，若 A∪B=B，则实数 a 的取值范围是．14．（4.00 分）已知 sin（α﹣）=，则sin（﹣α）=．15．（4.00 分）在平行四边形 ABCD 中，AB=8，AD=6，∠BAD=60°，点 P 在 CD 上，且=3，则•=．三、解答题（本大题共 60 分）16．（12.00 分）已知向量=（1，2），=（2，λ），=（﹣3，2）．（1）若∥，求实数λ的值；（2）若 k+与﹣2垂直，求实数k的值．17．（12.00 分）已知函数 f（x）=．（1）求 f（2）及 f（f（﹣1））的值；（2）若 f（x）≥4，求 x 的取值范围．18．（12.00 分）已知在△ABC 中，sinA=，cosB=﹣．（1）求 sin2A 的值；（2）求 cosC 的值．19．（12.00 分）已知函数 f（x）=是奇函数，且f（1）=1．（1）求 a，b 的值；（2）判断函数 f（x）在（0，+∞）上的单调性，并用定义证明．20．（12.00 分）已知函数 f（x）=2sinxcos（x+）+．（1）求 f（x）的最小正周期；（2）求 f（x）在区间[﹣，]上的最大值．2017-2018 学年天津市部分区高一（上）期末数学试卷参考答案与试题解析一、选择题（本题共 10 小题，每小题 4 分，共 40 分）∅1．（4.00 分）设集合 U={1，2，3，4，5}，集合 A={1，2，3}，则U A=（）A．{1，2，3} B．{4，5} C．{1，2，3，4，5} D．∁【分析】由集合的补集的定义，即由 U 中不属于 A 的元素构成的集合，即可得到所求．【解答】解：集合 U={1，2，3，4，5}，集∁合A={1，2，3}，则U A={4，5}．故选：B．2．（4.00 分）已知向量，的夹角为60°，且||=1，||=2，则•=（）A． B． C．1D．2【分析】利用已知条件，通过向量的数量积公式求解即可．【解答】解：向量，的夹角为60°，且| |=1，| |=2，则•===1．故选：C．3．（4.00 分）下列运算的结果正确的是（）A．log43=2log23 B．（﹣a2）3=﹣a6C．（﹣1）0=0D．lg2+lg3=lg5【分析】利用有理指数幂的运算性质及对数的运算性质逐一核对四个选项得答案．【解答】解：∵log43=，∴选项A错误；∵（﹣a2）3=﹣（a2）3=﹣a6，∴选项 B 正确；由 a0=1（a≠0），可得（﹣1）0=1，故C错误；∵lg2+lg3=lg（2×3）=lg6，∴D 错误．∴计算结果正确的是（﹣a2）3=﹣a6，故选：B．4．（4.00 分）函数 f（x）=﹣x+1的零点所在的区间是（）A．（0，1） B．（1，2） C．（2，3） D．（3，4）【分析】据函数零点的判定定理，判断 f（2），f（3）的符号，即可求得结论．【解答】解：函数 f（x）=﹣x+1是连续函数，f（2）=﹣2+1＞0，f（3）=＜0，故有 f（2）•f（3）＜0，由零点的存在性定理可知：函数 f（x）=﹣x+1的零点所在的区间是（2，3）故选：C．5．（4.00 分）将函数 y=sin2x 的图象上所有点向左平移个单位长度，再把所得各点的横坐标伸长为原来的 2 倍（纵坐标不变），所得图象对应的函数解析式是（）A．y=sin（x+）B．y=sin（2x+）C．y=sin（x+）D．y=sin（x+）【分析】按照题目所给条件，先求把函数y=sin2x 的图象向左平移个单位长度，函数解析式，再把所得图象上所有点的横坐标伸长到原来的 2 倍（纵坐标不变），求出解析式即可．【解答】解：把函数 y=sin2x 的图象向左平移个单位长度，得y=sin2（x+）=sin（2x+）的图象，再把所得各点的横坐标伸长到原来的 2 倍（纵坐标不变），得到 y=sin（x+）的图象；故选：A．6．（4.00 分）已知函数 f（x）=a x（a＞0，a≠1），若 f（﹣2）＜f（﹣3），则 a 的取值范围是（）A．2＜a＜3 B．＜a＜ C．a＞1D．0＜a＜1【分析】根据指数函数的单调性即可得出 a 的取值范围．【解答】解：函数 f（x）=a x（a＞0，a≠1），若f（﹣2）＜f（﹣3），则 f（x）是单调减函数，∴a 的取值范围是 0＜a＜1．故选：D．7．（4.00 分）若非零向量，满足|+|=|﹣|，则（）A．⊥ B．∥ C．||=||D．||≥||【分析】利用向量的几何意义解答．【解答】解：如图，设=，=，则|+|=||，|﹣|=||，则||=||，所以四边形 ABCD 为矩形，所以 AB⊥BC，所以⊥．故选：A．8．（4.00 分）若α为第二象限的角，且tanα=﹣，则cosα=（）A． B．﹣ C． D．﹣【分析】利用同角三角函数的基本关系，以及三角函数在各个象限中的符号，求得cosα的值．【解答】解：∵α是第二象限角，且tanα==﹣，∴sinα=﹣cosα，∵cosα＜0，sinα＞0，sin2α+cos2α=1，∴（﹣cosα）2+cos2α=1，可得：cosα=﹣，故选：D．9．（4.00 分）已知集合 P={x|y=}，Q={x|y=lg（x﹣1）}，则P∩Q=（）A．{x|1≤x≤3}B．{x|1＜x＜3}C．{x|1＜x≤3}D．{x|x＜1，或 x≥3}【分析】由偶次根式被开方式非负，化简集合 P，对数的真数大于 0，化简集合Q，再由交集的定义，即可得到所求集合．【解答】解：集合 P={x|y=}={x|3﹣x≥0}={x|x≤3}，Q={x|y=lg（x﹣1）}={x|x﹣1＞0}={x|x＞1}，则P∩Q={x|1＜x≤3}，故选：C．10．（4.00 分）已知偶函数 f（x）在[0，+∞）上单调递减，若 a=f（ln2.1），b=f （1.11.1），c=f（﹣3），则 a，b，c 的大小关系是（）A．a＜b＜c B．c＜b＜a C．c＜a＜b D．b＜a＜c【分析】根据函数奇偶性和单调性的性质，进行转化求解即可．【解答】解：∵偶函数 f（x）在[0，+∞）上单调递减，∴a=f（ln2.1），b=f（1.11.1），c=f（﹣3）=f（3），∵0＜ln2.1＜1，1＜1.11.1＜3，则0＜ln2.1＜1.11.1＜3，∴f（ln2.1）＜f（1.11.1）＜f（3），即f（ln2.1）＜f（1.11.1）＜f（﹣3），则 c＜b＜a，故选：B．二、填空题（本大题共 5 小题，每小题 4 分，共 20 分）11．（4.00 分）sin（﹣）=﹣．【分析】由条件利用诱导公式化简所给的三角函数式，可得结果．【解答】解：sin（﹣）=sin（﹣）=﹣sin=﹣，故答案为：﹣．12．（4.00 分）已知幂函数 f（x）经过点（2，8），则 f（3）= 27．【分析】设 f（x）=x n，代入（2，8），求得 n，再计算 f（3），即可得到所求值．【解答】解：设 f（x）=x n，由题意可得2n=8，解得 n=3，则f（x）=x3，f（3）=33=27，故答案为：27．13．（4.00 分）设集合 A={x|2＜x＜3}，B={x|x＞a}，若 A∪B=B，则实数 a 的取值范围是a≤2．⊆【分析】根据 A∪B=B 得出 A B，从而写出实数 a 的取值范围．【解答】解：集合⊆ A={x|2＜x＜3}，B={x|x＞a}，若 A∪B=B，则A B，∴a≤2，∴实数 a 的取值范围是 a≤2．故答案为：a≤2．14．（4.00 分）已知 sin（α﹣）=，则sin（﹣α）= ．【分析】由已知直接利用三角函数的诱导公式化简求值．【解答】解：∵sin（α﹣）=，∴sin（﹣α）=sin（π+﹣α）=﹣sin（）=sin（α﹣）=，故答案为：．15．（4.00 分）在平行四边形 ABCD 中，AB=8，AD=6，∠BAD=60°，点 P 在 CD上，且=3，则•=12．【分析】建立坐标系，求出各向量坐标，再计算数量积．【解答】解：以 A 为原点建立坐标系，则 A（0，0），B（8，0），D（3，3），∵=3，∴DP=2，即P（5，3），∴=（5，3），=（﹣3，3），∴=﹣15+27=12．故答案为：12．三、解答题（本大题共 60 分）16．（12.00 分）已知向量=（1，2），=（2，λ），=（﹣3，2）．（1）若∥，求实数λ的值；（2）若 k+与﹣2垂直，求实数k的值．【分析】（1）利用向量平行的性质能出实数λ的值；（2）先利用平面向量坐标运算法则求出 k+，﹣2，由此利用向量垂直的性质能求出实数 k 的值．【解答】解：（1）∵向量=（1，2），=（2，λ），=（﹣3，2）．∥，∴，解得实数λ=4．（2）k+=（k﹣3，2k+2），=（7，﹣2），∵k+与﹣2垂直，∴（k）•（）=7k﹣21﹣4k﹣4=0，解得实数 k=．17．（12.00 分）已知函数 f（x）=．（1）求 f（2）及 f（f（﹣1））的值；（2）若 f（x）≥4，求 x 的取值范围．【分析】（1）根据分段函数的表达式，利用代入法进行求解即可．（2）根据分段函数的表达式，讨论 x 的取值范围进行求解即可．【解答】解：（1）f（2）=﹣2×2+8=﹣4+8=4，f（f（﹣1））=f（﹣1+5）=f（4）= ﹣2×4+8=0．（2）若 x≤1，由 f（x）≥4 得 x+5≥4，即 x≥﹣1，此时﹣1≤x≤1，若x＞1，由 f（x）≥4 得﹣2x+8≥4，即 x≤2，此时 1＜x≤2，综上﹣1≤x≤2．18．（12.00 分）已知在△ABC 中，sinA=，cosB=﹣．（1）求 sin2A 的值；（2）求 cosC 的值．【分析】（1）由已知可得 B 为钝角，分别求出 sinB，cosA 的值，由二倍角公式求得 sin2A；（2）利用三角形内角和定理可得 cosC=cos[π﹣（A+B）]=﹣cos（A+B），展开两角和的余弦得答案．【解答】解：（ 1 ）在△ ABC 中，由 cosB= ﹣，可知B为钝角，且sinB=，又sinA=，得cosA=．∴sin2A=2sinAcosA=2×；（2）cosC=cos[π﹣（A+B）]=﹣cos（A+B）=﹣cosAcocB+sinAsinB=﹣+=．19．（12.00 分）已知函数 f（x）=是奇函数，且f（1）=1．（1）求 a，b 的值；（2）判断函数 f（x）在（0，+∞）上的单调性，并用定义证明．【分析】（1）根据函数奇偶性的性质和定义建立方程进行求解即可．（2）根据函数单调性的定义进行证明即可．【解答】解：（1）∵f（1）=1，∴f（1）==1，即 a﹣1=1+b，则 a=2+b，则f（﹣x）=﹣f（x），即=﹣，即﹣x+b=﹣x﹣b，则b=﹣b，b=0，得a=2．（2）∵b=0，a=2，∴f（x）==2x1﹣﹣2x2+=2（x1﹣x2）+=（x1﹣x2）（2+）∵x1，x2为（0，+∞）上任意两个自变量，且 x1＜x2∴x1﹣x2＜0，2+＞0，∴（x1﹣x2）（2+）＜0，∴f（x1）﹣f（x2）＜0，即 f（x1）＜f（x2）第 11页（共 12页）∴函数 f（x）在（0，+∞）上为增函数．20．（12.00 分）已知函数 f（x）=2sinxcos（x+）+．（1）求 f（x）的最小正周期；（2）求 f（x）在区间[﹣，]上的最大值．【分析】展开两角和的余弦，再由辅助角公式化积．（1）直接利用周期公式求周期；（2）由 x 的范围求得相位的取值范围，则 f（x）在区间[﹣，]上的最大值可求．【解答】解：f（x）=2sinxcos（x+）+=2sinx（cosxcos）+=2sinx（）=sin2x﹣===．（1）f（x）的最小正周期 T=；（2）由，得0，∴sin（）∈[0，1]，则∈[﹣，1﹣]，∈则 f（x）在区间[﹣，]上的最大值为．第 12页（共 12页）。

2010年湖北卷高考真题英语试卷-学生用卷一、单项选择1、【来源】 2010年高考真题湖北卷第1题2010年高考真题湖北卷第21题1分2017~2018学年天津红桥区高三上学期期中第9题1分2016~2017学年宁夏石嘴山大武口区石嘴山市第三中学高一下学期期末第24题1分2018~2019学年5月天津河西区天津市新华中学高三下学期月考第11题1分This restaurant has become popular for its wide_____of foods that suit all tastes and pockets.A. divisionB. areaC. rangeD. circle2、【来源】 2010年高考真题湖北卷第2题2010年高考真题湖北卷第22题1分2017~2018学年黑龙江哈尔滨道里区哈尔滨市第九中学校高一上学期期中第63题0.5分After the earthquake, the first thing the local government did was to provide ______for the homeless families.A. accommodationB. occupationC. equipmentD. furniture3、【来源】 2010年高考真题湖北卷第3题2010年高考真题湖北卷第23题1分2019~2020学年7月湖北武汉武昌区武汉市第十四中学高一下学期月考第28题1分In this lecture, I can only give you a purely view of how we can live life to the full and make some suggestions about the future.A. privateB. personalC. uniqueD. different4、【来源】 2010年高考真题湖北卷第24题1分2010年高考真题湖北卷第4题Mistakes don't just happen; they occur for a reason. Find out the reason and then making the mistake becomes.A. favourableB. preciousC. essentialD. worthwhile5、【来源】 2010年高考真题湖北卷第25题1分2010年高考真题湖北卷第5题2018年天津和平区天津市耀华中学高三二模第6题1分If I find someone who looks like the suspect, my reaction will be to tell the police.A. physicalB. immediateC. sensitiveD. sudden6、【来源】 2010年高考真题湖北卷第6题2016~2017学年3月北京海淀区北京市育英中学高二下学期月考第27题1分I wasn't blaming anyone; I said errors like this could be avoided.A. merelyB. mostlyC. rarelyD. nearly7、【来源】 2010年高考真题湖北卷第7题2010年高考真题湖北卷第27题1分Duty is an act or a course of action that people______ you to take by social customs, law or religion.A. persuadeB. requestC. instructD. expect8、【来源】 2010年高考真题湖北卷第8题2010年高考真题湖北卷第28题1分2017~2018学年天津河西区高二上学期期末第19题Just as the clothes a person wears, the food he eats and the friends with whom he spends his time, his house_____ his personality.A. resemblesB. strengthensC. reflectsD. shapes9、【来源】 2010年高考真题湖北卷第9题2018~2019学年黑龙江哈尔滨香坊区哈尔滨市第六中学高二上学期期末第64题0.5分Had she her promise, she would have made it to Yale University.A. looked up toB. lived up toC. kept up withD. come up with10、【来源】 2010年高考真题湖北卷第10题2010年高考真题湖北卷第30题1分2018~2019学年辽宁大连沙河口区大连育明高级中学高一上学期期中第15题1分2018~2019学年天津和平区天津市第一中学高一下学期期中第7题1分2018~2019学年12月江苏扬州江都区江苏省江都中学高一上学期月考（华罗庚中学、句容中学、溧水中学等五校联考）第25题1分It is illegal for a public official to ask people for gifts or money favors to them.A. in preference toB. in place ofC. in agreement withD. in exchange for二、完形填空11、【来源】 2010年高考真题湖北卷第31~50题30分(每题1.5分)2010年高考真题湖北卷第11题2018~2019学年广西南宁青秀区南宁市第二中学高二上学期期末第41~60题30分The passengers on the bus watched with sympathy as Susan made her way carefully up the steps. She paid the driver and then, using her hands to 1the seats, settled in one of them.It had been a year since Susan became blind. As the result of an accident she was suddenly thrown into a world of 2Susan’s husband Mark watchedher 3into hopelessness and he was 4to use every possible means to help his wife.Finally, Susan felt ready to 5to her job, but how would she get there? She used to take the bus, but she was now too 6to get around the city by herself. Mark7to ride the bus with Susan each morning andevening 8she could manage it by herself.For two weeks, Mark 9Susan to and from work each day. He taught her how to rely on her other10, specifically her hearing, to determine where she was and how to adapt to her new11At last, Susan decided that she was ready to try the trip12Monday morning arrived. Before she left, she hugged her husband 13,her eyes filled with tears of gratitude（感激）. She said good-bye and, for the first time, they wenttheir 14ways. Each day went perfectly, and a wildexcitement 15Susan.She was doing it!On Friday morning, Susan took the bus to work 16As she was getting off the bus, the driver said, “Miss, I sure17you.” Curious, Susan asked the driver18“You know, every morning for the 19week, a fine-looking gentleman in a military uniform has been standing across the corner watching you until you enter your office building safely, ” the bus driver said.Tears of happiness poured down Susan’s cheeks. She was so lucky for he had given her a gift more powerful than20, that is the gift of love that can bring light where there is darkness.A. touchB. grabC. countD. feelA. weaknessB. sicknessC. darknessD. sadnessA. runB. sinkC. jumpD. stepA. inspiredB. determinedC. honoredD. pleasedA. returnB. adjustC. contributeD. stickA. tiredB. astonishedC. depressedD. frightenedA. volunteeredB. attemptedC. continuedD. struggledA. whenB. asC. untilD. afterA. droveB. directedC. accompaniedD. sentA. feelingB. organsC. skillsD. sensesA. positionB. environmentC. statusD. roleA. on herownB. in personC. to her benefitD. on footA. politelyB. calmlyC. brieflyD. tightlyA. oppositeB. separateC. fixedD. lonelyA. tookcharge ofB. took place ofC. took advantage ofD. took hold ofA. as usualB. as a ruleC. as wellD. as a consequenceA. respectB. envyC. knowD. supportA. whatB. howC. whyD. whoA. pastB. sameC. firstD. nextA. courageB. willC. sightD. wisdom三、阅读理解12、【来源】 2010年高考真题湖北卷第12题2010年高考真题湖北卷（A篇）第51~54题8分2016~2017学年北京西城区北京师范大学附属中学高一下学期期中第31~34题8分It was a Sunday and the heavy storm had lasted all night. The morning after the storm, though, was beautiful: blue skies, warm air and a calm, inviting sea touching the shore gently.My father realized it was a good day for fishing and invited my sister and me to go with him. I was only 14 and fishing had never been my thing, but I decided to go all the same. TAL#NBSP I'm so glad I did.On the road to the harbour we could see the terrible destruction on the coast, but the harbour itself was in fairly good shape. After all, it was protected by the arms of a bay that had only one tiny channel to the sea. As we got on board, we noticed two big humps（脊背）in the distance.On approaching them, we saw it was a mother whale with her baby. We couldn't believe it—there aren't any whales along the coast here. The storm must have driven them across the ocean into the bay, in which the still water was so badly polluted that nothing could survive.The little baby whale—actually as big as our boat—was obviously stuck and could not move. The mother dived under the water and came up suddenly, making big whirlpools（漩涡）and waves. "She's trying to help her baby, but on the wrong side, "my father said. At this point, my father moved our boat in a semicircle to the other side and, heading the boat towards the baby whale, pushed it gently. With our several gentle pushes the big hump turned over and disappeared under water. Then it swam up right beside its mum. They struggled in their desperate attempts to escape but missed the exit and started heading in the wrong direction. We hurried up to the whales and tried to lead them towards the bay channel. Slowly, they let us lead them, some-times rising from the water right beside us to breathe—and to give us a trusting look with those huge eyes. Once they hit their first part of clean water flowing straight from the sea, the mum gave us a wave with her tail and off they swam into the distance.In the excitement it had felt like only a few minutes, but we had been with those wonderful animals for almost an hour and a half. That was the simple and lasting beauty of the day, Nearly four decades later,I still look back fondly to that golden day at sea.(1) The author says "I'm so glad I did." （in Para. 2） because.A. he witnessed the whole process of fishingB. he enjoyed the beauty of the calm seaC. he experienced the rescue of the whalesD. he spent the weekend with his family(2) The harbour survived the storm owing to.A. the shape of the harbourB. the arms of the bayC. the still water in the channelD. the long coast line(3) The mother whale failed to help her baby because.A. she had stayed in the polluted water for too longB. the whirl pools she had made were not big enoughC. she had no other whales around to turn to for helpD. the waves pushed her baby in the wrong direction(4) What is the theme of the story?A. Saving lives brings people a sense of happinessB. Fishing provides excitement for childrenC. It's necessary to live in harmony with animalsD. It's vital to protect the environment13、【来源】 2010年高考真题湖北卷第13题2017~2018学年广东广州海珠区广州市第六中学高三下学期期中（D篇）第32~35题8分2017~2018学年广东广州越秀区广州市第十六中学高一上学期期中第4题2016~2017学年广东广州越秀区广州市第十六中学高一上学期期中第32~35题8分For many parents, raising a teenager is like fighting a long war, but years go by without any clear winner. Like a border conflict between neighboring countries, the parent-teen war is about boundaries: Where is the line between what I control and what you do?Both sides want peace, but neither feels it has any power to stop the conflict. In part, this is because neither is willing to admit any responsibility for starting it. From the parents' point of view, the only cause of their fight is their adolescents' complete unreasonableness. And of course, TAL#NBSP the teens see it in exactly the same way, except oppositely.Both feel trapped.In this article, I'll describe three no-win situations that commonly arise between teens and parents and then suggest some ways out of the trap. The first no-win situation is quarrels over unimportant things. Examples include the color of the teen's hair, the cleanliness of the bedroom, the preferred style of clothing, the child's failure to eat a good breakfast before school, or his tendency to sleep until noon on the weekends. Second, blaming. The goal of a blaming battle is to make the other admit that his bad attitude is the reason why everything goes wrong. Third, needing to be right, It doesn't matter what the topic is—politics. The laws of physics, or the proper way to break an egg—the point of these arguments is to prove that you are right and the other person is wrong. for both wish to be considered an authority—someone who actually knows something — and therefore to command respect. Unfortunately, as long as long as parents and teens continue to assume that they know more than the other, they'll continue to fight these battles forever and never make any real progress.(1) Why does the author compare the parent-teen war to a border conflict?A. Both can continue for generations.B. Both are about where to draw the lineC. Neither has any clear winnerD. Neither can be put to an end(2) What does the underlined part in Paragraph 2 mean?A. The teens blame their parents for starting the conflict.B. The teens agree with their parents on the cause of the conflictC. The teens cause their parents of misleading themD. The teens tend to have a full understanding of their parents(3) Parents and teens want to be right because they want to.A. give orders to the otherB. know more than the otherC. gain respect from the otherD. get the other to behave properly(4) What will the author most probably discuss in the paragraph that follows?A. Causes for the parent –teen conflictsB. Examples of the parent –teen war.C. Solutions for the parent –teen problemsD. Future of the parent-teen relationship14、【来源】 2010年高考真题湖北卷（C篇）第59~62题8分(每题2分)2010年高考真题湖北卷（C篇）第14题2017~2018学年北京西城区北京师范大学附属中学高二下学期期中第64~67题8分They wear the latest fashions with the most up-to-date accessories （配饰）. Yet these are girls in their teens or twenties but women in their sixties and seventies. A generation which would once only wear old-fashioned clothes is now favoring the same high street looks worn by those half their age.Professor Julia Twigg, a social policy expert, said, "Women over 75 are now shopping for clothes more frequently than they did when they were young in the 1960s. In the 1960s buying a coat for a woman was a serious matter. It was an expensive item that they would purchase only every three or four years —now you can pick one up at the supermarket whenever you wish to. Fashion is a lot cheaper and people get tired of things more quickly. "Professor Twigg analyzed family expending（支出）data and found that while the percentage of spending on clothes and shoes by women had stayed around the same—and 5 or 6 per cent of spending—the amount of clothes bought had risen sharply.The professor said, "Clothes are now 70 per cent cheaper than they were in the 1960s because of the huge expansion of production in the Far East. In the 1960s Leeds was the heart of the British fashion industry and that was where most of the clothes came from, but now almost all of our clothes are sourced elsewhere. Everyone is buying more clothes but in general we are not spending more money on them. "Fashion designer Angela Barnard, who runs her own fashion business in London, said older women were much more affected by celebrity（名流） style than in previous years.She said, "When people see stars such as Judi Dench and Helen Mirren looking attractive and fashionable in their sixties, they want to follow them. Older women are much more aware of celebrities. There's also the boom in TV programmes showing people how they can change their look, and many of my older customers do yoga to stay in shape well in their fifties. When I started my business a few years ago, my older customers tended to be very rich, but now they are what I would call ordinary women. My own mother is 61 and she wears the latest fashions in a way she would never have done ten years ago. "(1) Professor Twigg found that, compared with the 1960s,.A. the price of clothes has generally fallen by 70%B. the spending on clothes has increased by 5% or 6%C. people spend 30% less than they did on clothesD. the amount of clothes bought has risen by 5% or 6%(2) What can we learn about old women in terms of fashionA. They are often ignored by fashion designers.B. They are now more easily influenced by stars.C. They are regarded as pioneers in the latest fashion.D. They are more interested in clothes because of their old age.(3) It can be concluded that old women tend to wear the latest fashions today mainlybecauseA. they get tired of things more quicklyB. TV shows teach them how to change their lookC. they are in much better shape nowD. clothes are much cheaper than before(4) Which is the best possible title of the passage?A. Age Is No Barrier for Fashion FansB. The More Fashionable, the Less ExpensiveC. Unexpected Changes in FashionD. Boom of the British Fashion Industry15、【来源】 2010年高考真题湖北卷（D篇）第63~66题8分(每题2分)2010年高考真题湖北卷第15题This brief book is aimed at high school students, but speaks to anyone learning at any stage of life.Its formal, serious style closely matches its content, a school-masterly book on schooling. The author, W. H. Armstrong, starts with the basics: reading and writing. In his opinion, reading doesn't just mean recognizing each word on the page; it means taking in the information, digesting it and incorporating it into oneself just as one digests a sandwich and makes it a part of him. The goal is to bring the information back to life, not just to treat it as dead facts on paper from dead trees. Reading and writing cannot be completely separated from each other; in fact, the aim of reading is to express the information you have got from the text. I've seen it again and again：some-one who can't express an idea after reading a text is just as ineffective as someone who hasn't read it at all.Only a third of the book remains after that discussion, which Armstrong devotes to specific tips for studying languages, math, science and history. He generally handles these topics thoroughly（透彻地）and equally, except for some weakness in the science and math sections and a bit too much passion（激情） regarding history to his students, that was a hundred times more than my history teachers ever got across. To my disappointment, in this part of the book he ignores the arts. As a matter of fact, they demand all the concentration and study that math and science do, though the study differs slightly in kind. Although it's commonly believed that the arts can only be naturally acquired, actually, learning the arts is no more natural than learning French or mathematics.My other comment is that the text aged.The first edition apparently dates to the 1960s—none of the references（参考文献）seem newer than the late 1950s. As a result, the discussion misses the entire computer age.These are small points, though, and don't affect the main discussion. I recommend it to any student and any teacher, including the self-taught student.(1) According to Armstrong, the goal of reading is to.A. gain knowledge and expand one's viewB. understand the meaning between the linesC. experts ideas based on what one has readD. gets information and keeps it alive in memory(2) The author of the passage insists that learning the arts.A. requires great effortsB. demands real passionC. is less natural than learning mathsD. is as natural as learning a language(3) What is a shortcoming of Armstrong's work according to the author?A. Some ideas are slightly contradictory.B. There is too much discussion on studying science.C. The style is too serious.D. It lacks new information.(4) This passage can be classified as.A. an advertisementB. a book reviewC. a feature storyD. a news report16、【来源】 2010年高考真题湖北卷E篇第67~70题8分(每题2分)2010年高考真题湖北卷第16题EHave you winterized your horse yet? Even though global warming may have made our climate more mild, many animals are still hibernating(冬眠). It’s too bad that humans can’t hibernate. In fact,as a species, we almost did.Apparently, at times in the past, peasants in France liked a semi-state of human hibernation. So writes Graham Robb, a British scholar who has studied the sleeping habits of the French peasants. As soon as the weather turned cold people all over France shut themselves away and practiced the forgotten art of doing nothing at all for months on end.In line with this, Jeff Warren, a producerat CBC Radio’s The Current, tells us that the way we sleep has changed fundamentally since the invention of artificial(人造的) lighting and the electric bulb.When historians began studying texts of the Middle Ages, they noticed something referred to as “first sleep”, which was not clarified, though. Now scientists are telling us our ancestors most likely slept in separate periods. The business of eight hours’ uninterrupted sleep is a modern invention.In the past, without the artificial light of the city to bathe in, humans went to sleep when it became dark and then woke themselves around midnight. The late night period was known as “The Watch”It was when people actually kept watch against wild animals, although many of them simply moved around or visited family and neighbours.According to some sleep researchers,a short period of insomnia(失眠) at midnight is not a disorder. It is normal. Humans can experience another state of consciousness around their sleeping, which occurs in the brief period before we fall asleep or wake ourselves in the morning. This period can be an extraordinarily creative time for some people. The impressive inventor,Thomas Edison, used this state to hit upon many of his new ideas.Playing with your sleep rhythms can be adventurous, as anxiety may set in. Medical science doesn’t help much in this case. It offers us medicines for a full night’s continuous sleep, which sounds natural;however, according to Warren’s theory，it is really the opposite of what we need.(1) The example of the French peasants shows the fact that________.A. people might become lazy as a result of too much sleepB. there were signs of hibernation inhuman sleeping habitsC. people tended to sleep more peacefully in cold weatherD. winter was a season for people to sleep for months on end(2) The late night was called “The Watch” because it was a time for people______.A. to set traps to catch animalsB. to wake up their family and neighboursC. to remind others of the timeD. to guard against possible dangers(3) What does the author advise people to do?A. Sleep in the way animals do.B. Consult a doctor if they can’t sleep.C. Follow their natural sleep rhythm.D. Keep to the eight-hour sleep pattern.(4) What is the author’s purpose in writing the passage?A. To give a prescription for insomnia.B. To urge people to sleep less.C. To analyze the sleep pattern of modern people.D. To throw new light on human sleep.四、完成句子17、【来源】 2010年高考真题湖北卷第17题阅读下列各小题，根据括号内的汉语提示，用句末括号内的英语单词完成句子，并将答案写在答题卡上的相应题号后。

2017-2018学年天津市部分区高一（上）期末数学试卷一、选择题（本大题共10小题，共40.0分）1.设集合U={1，2，3，4，5}，集合A={1，2，3}，则∁U A=（）A. 2，B.C. 2，3，4，D.2.已知向量，的夹角为60°，且||=1，||=2，则•=（）A. B. C. 1 D. 23.下列运算的结果正确的是（）A. B. C. D.4.函数f（x）=-x+1的零点所在的区间是（）A. B. C. D.5.将函数y=sin2x的图象上所有点向左平移个长度，再把所得各点的横坐标伸长为原来的2倍（纵坐标不变），所得图象对应的函数解析式是（）A. B. C. D.6.已知函数f（x）=a x（a＞0，a≠1），若f（-2）＜f（-3），则a的取值范围是（）A. B. C. D.7.若非零向量，满足|+|=|-|，则（）A. B. C. D.8.若α为第二象限的角，且tanα=-，则cosα=（）A. B. C. D.9.已知集合P={x|y=}，Q={x|y=lg（x-1）}，则P∩Q=（）A. B.C. D. ，或10.已知偶函数f（x）在[0，+∞）上单调递减，若a=f（ln2.1），b=f（1.11.1），c=f（-3），则a，b，c的大小关系是（）A. B. C. D.二、填空题（本大题共5小题，共20.0分）11.sin（-）=______．12.已知幂函数f（x）经过点（2，8），则f（3）=______．13.设集合A={x|2＜x＜3}，B={x|x＞a}，若A∪B=B，则实数a的取值范围是______．14.已知sin（α-）=，则sin（-α）=______．15.在平行四边形ABCD中，AB=8，AD=6，∠BAD=60°，点P在CD上，且=3，则•=______．三、解答题（本大题共5小题，共60.0分）16.已知向量=（1，2），=（2，λ），=（-3，2）．（1）若 ∥，求实数λ的值；（2）若k+与-2垂直，求实数k的值．17.已知函数f（x）=．（1）求f（2）及f（f（-1））的值；（2）若f（x）≥4，求x的取值范围．18.已知在△ABC中，sin A=，cos B=-．（1）求sin2A的值；（2）求cos C的值．19.已知函数f（x）=是奇函数，且f（1）=1．（1）求a，b的值；（2）判断函数f（x）在（0，+∞）上的单调性，并用定义证明．20.已知函数f（x）=2sin x cos（x+）+．（1）求f（x）的最小正周期；（2）求f（x）在区间[-，]上的最大值．答案和解析1.【答案】B【解析】解：集合U={1，2，3，4，5}，集合A={1，2，3}，则∁U A={4，5}．故选：B．由集合的补集的定义，即由U中不属于A的元素构成的集合，即可得到所求．本题考查集合的运算，主要是补集的求法，运用定义法解题是关键．2.【答案】C【解析】解：向量，的夹角为60°，且||=1，||=2，则•===1．故选：C．利用已知条件，通过向量的数量积公式求解即可．本题考查平面向量的数量积的计算，考查计算能力．3.【答案】B【解析】解：∵log43=，∴选项A错误；∵（-a2）3=-（a2）3=-a6，∴选项B正确；由a0=1（a≠0），可得（-1）0=1，故C错误；∵lg2+lg3=lg（2×3）=lg6，∴D错误．∴计算结果正确的是（-a2）3=-a6，故选：B．利用有理指数幂的运算性质及对数的运算性质逐一核对四个选项得答案．本题考查命题的真假判断与应用，考查有理指数幂的运算性质及对数的运算性质，是基础题．4.【答案】C【解析】解：函数f（x）=-x+1是连续函数，f（2）=-2+1＞0，f（3）=＜0，故有f（2）•f（3）＜0，由零点的存在性定理可知：函数f（x）=-x+1的零点所在的区间是（2，3）故选：C．据函数零点的判定定理，判断f（2），f（3）的符号，即可求得结论．本题考查函数的零点的判定定理，解答关键是熟悉函数的零点存在性定理，属基础题．5.【答案】A【解析】解：把函数y=sin2x的图象向左平移个单位长度，得y=sin2（x+）=sin（2x+）的图象，再把所得各点的横坐标伸长到原来的2倍（纵坐标不变），得到y=sin（x+）的图象；故选：A．按照题目所给条件，先求把函数y=sin2x的图象向左平移个单位长度，函数解析式，再把所得图象上所有点的横坐标伸长到原来的2倍（纵坐标不变），求出解析式即可．本题考查函数y=Asin（ωx+φ）的图象变换，考查计算能力，是基础题．三角函数的平移原则为左加右减上加下减．6.【答案】D【解析】解：函数f（x）=a x（a＞0，a≠1），若f（-2）＜f（-3），则f（x）是单调减函数，∴a的取值范围是0＜a＜1．故选：D．根据指数函数的单调性即可得出a的取值范围．本题考查了指数函数的单调性问题，是基础题．7.【答案】A【解析】解：如图，设=，=，则|+|=||，|-|=||，则||=||，所以四边形ABCD为矩形，所以AB BC，所以．故选：A．利用向量的几何意义解答．本题考查了向量的模．解题时，借用了矩形的判定与性质，属于基础题．8.【答案】D【解析】【分析】本题主要考查同角三角函数的基本关系，以及三角函数在各个象限中的符号，属于基础题．【解答】解：∵α是第二象限角，且tanα==-，∴sinα=-cosα，∵cosα＜0，sinα＞0，sin2α+cos2α=1，∴（-cosα）2+cos2α=1，可得：cosα=-，故选D．9.【答案】C【解析】解：集合P={x|y=}={x|3-x≥0}={x|x≤3}，Q={x|y=lg（x-1）}={x|x-1＞0}={x|x＞1}，则P∩Q={x|1＜x≤3}，故选：C．由偶次根式被开方式非负，化简集合P，对数的真数大于0，化简集合Q，再由交集的定义，即可得到所求集合．本题考查集合的交集的求法，考查函数的定义域的求法，运用定义法解题是关键，属于基础题．10.【答案】B【解析】解：∵偶函数f（x）在[0，+∞）上单调递减，∴a=f（ln2.1），b=f（1.11.1），c=f（-3）=f（3），∵0＜ln2.1＜1，1＜1.11.1＜3，则0＜ln2.1＜1.11.1＜3，∴f（ln2.1）＜f（1.11.1）＜f（3），即f（ln2.1）>f（1.11.1）>f（-3），则c＜b＜a，故选：B．根据函数奇偶性和单调性的性质，进行转化求解即可．本题主要考查函数值的大小比较，根据函数奇偶性和单调性的关系进行转化是解决本题的关键．11.【答案】-【解析】解：sin（-）=sin（-）=-sin=-，故答案为：-．由条件利用诱导公式化简所给的三角函数式，可得结果．本题主要考查利用诱导公式进行化简求值，属于基础题．12.【答案】27【解析】解：设f（x）=x n，由题意可得2n=8，解得n=3，则f（x）=x3，f（3）=33=27，故答案为：27．设f（x）=x n，代入（2，8），求得n，再计算f（3），即可得到所求值．本题考查幂函数的解析式的求法，考查运算能力，属于基础题．13.【答案】a≤2【解析】解：集合A={x|2＜x＜3}，B={x|x＞a}，若A∪B=B，则A⊆B，∴a≤2，∴实数a的取值范围是a≤2．故答案为：a≤2．根据A∪B=B得出A⊆B，从而写出实数a的取值范围．本题考查了并集的定义与应用问题，是基础题．14.【答案】【解析】解：∵sin（α-）=，∴sin（-α）=sin（π+-α）=-sin（）=sin（α-）=，故答案为：．由已知直接利用三角函数的诱导公式化简求值．本题考查三角函数的化简求值，考查诱导公式的应用，是基础的计算题．15.【答案】12【解析】解：以A为原点建立坐标系，则A（0，0），B（8，0），D（3，3），∵=3，∴DP=2，即P（5，3），∴=（5，3），=（-3，3），∴=-15+27=12．故答案为：12．建立坐标系，求出各向量坐标，再计算数量积．本题考查了平面向量的数量积运算，建立坐标系可使计算较简单，属于中档题．16.【答案】解：（1）∵向量=（1，2），=（2，λ），=（-3，2）．∥，∴，解得实数λ=4．（2）k+=（k-3，2k+2），=（7，-2），∵k+与-2垂直，∴（k）•（）=7k-21-4k-4=0，解得实数k=．【解析】（1）利用向量平行的性质能出实数λ的值；（2）先利用平面向量坐标运算法则求出k+，-2，由此利用向量垂直的性质能求出实数k的值．本题考查实数值的求法，考查向量平行、平面向量坐标运算法则、向量垂直等基础知识，考查运算求解能力，考查函数与方程思想，是基础题．17.【答案】解：（1）f（2）=-2×2+8=-4+8=4，f（f（-1））=f（-1+5）=f（4）=-2×4+8=0．（2）若x≤1，由f（x）≥4得x+5≥4，即x≥-1，此时-1≤x≤1，若x＞1，由f（x）≥4得-2x+8≥4，即x≤2，此时1＜x≤2，综上-1≤x≤2．【解析】（1）根据分段函数的表达式，利用代入法进行求解即可．（2）根据分段函数的表达式，讨论x的取值范围进行求解即可．本题主要考查分段函数的应用，利用代入法是解决本题的关键．18.【答案】解：（1）在△ABC中，由cos B=-，可知B为钝角，且sin B=，又sin A=，得cos A=．∴sin2A=2sin A cosA=2×；（2）cos C=cos[π-（A+B）]=-cos（A+B）=-cos AcocB+sin A sin B=-+=．【解析】（1）由已知可得B为钝角，分别求出sinB，cosA的值，由二倍角公式求得sin2A；（2）利用三角形内角和定理可得cosC=cos[π-（A+B）]=-cos（A+B），展开两角和的余弦得答案．本题考查同角三角函数基本关系式的应用，考查两角和与差的余弦，是基础题．19.【答案】解：（1）∵f（1）=1，∴f（1）==1，即a-1=1+b，则a=2+b，则f（-x）=-f（x），即=-，即-x+b=-x-b，则b=-b，b=0，得a=2．（2）∵b=0，a=2，∴f（x）==2x1--2x2+=2（x1-x2）+=（x1-x2）（2+）∵x1，x2为（0，+∞）上任意两个自变量，且x1＜x2∴x1-x2＜0，2+＞0，∴（x1-x2）（2+）＜0，∴f（x1）-f（x2）＜0，即f（x1）＜f（x2）∴函数f（x）在（0，+∞）上为增函数．【解析】（1）根据函数奇偶性的性质和定义建立方程进行求解即可．（2）根据函数单调性的定义进行证明即可．本题主要考查函数奇偶性和单调性的判断，利用定义法是解决本题的关键．20.【答案】解：f（x）=2sin x cos（x+）+=2sin x（cos x cos）+=2sin x（）=sin2x-===．（1）f（x）的最小正周期T=；（2）由，得0，∴sin（）∈[0，1]，则∈[-，1-]，∴f（x）∈[-，1-]，则f（x）在区间[-，]上的最大值为．【解析】展开两角和的余弦，再由辅助角公式化积．（1）直接利用周期公式求周期；（2）由x的范围求得相位的取值范围，则f（x）在区间[-，]上的最大值可求．本题考查y=Asin（ωx+φ）型函数的图象和性质，考查两角和的余弦，是中档题．。

天津市第一中学2017-2018学年高一数学上学期期末考试试题（含解析）一、选择题（每小题3分，共30分） 1.若tan α=3，则2sin 2cos aα的值等于A. 2B. 3C. 4D. 6【答案】BD 【解析】 试题分析：原式=考点：三角函数的化简名师点睛：对于这类分式形式，上下是关于正弦和余弦的齐次形式，考虑上下同时除以，转化为的形式求值．【此处有视频，请去附件查看】2.函数22ππ()sin cos 44f x x x ⎛⎫⎛⎫=--- ⎪ ⎪⎝⎭⎝⎭是（ ）．A. 最小正周期为π的奇函数B. 最小正周期为π的偶函数C. 最小正周期为π2的奇函数 D. 最小正周期为π2的偶函数 【答案】A 【解析】 【分析】先化简函数，再利用三角函数的周期公式求周期,再判断函数的奇偶性得解.【详解】22ππ()sin cos 44f x x x ⎛⎫⎛⎫=--- ⎪ ⎪⎝⎭⎝⎭πcos 22x ⎛⎫=-- ⎪⎝⎭sin2x =-．∴sin 2y x =-最小正周期为2ππ2T ==， ()sin(2)sin2()f x x x f x -=--==-．∴函数为奇函数． 故选:A ．【点睛】本题主要考查三角恒等变换，考查三角函数奇偶性的判断和周期的计算，意在考查学生对这些知识的理解掌握水平和分析推理能力.3.设函数π()sin()cos()0,||2f x x x ωϕωϕωϕ⎛⎫=>< ⎪⎝⎭+++的最小正周期为π，且()()f x f x =-则（ ）．A. ()f x 在π0,2⎛⎫⎪⎝⎭单调递增B. ()f x 在π3π,44⎛⎫⎪⎝⎭单调递增C. ()f x 在π0,2⎛⎫⎪⎝⎭单调递减D. ()f x 在π3π,44⎛⎫⎪⎝⎭单调递减【答案】A 【解析】 【分析】三角函数()()()sin cos 4f x x x x πωϕωϕωϕ⎛⎫=+++=++ ⎪⎝⎭ ，由周期为π，可以得出2ω=；又()()0f x f x --=，即()()f x f x -=，所以函数()y f x =为偶函数，从而解得ϕ值，由此可以判断出函数的单调性。