浙江省杭州市2020届高三英语上学期五校联考试题(含解析)
浙江省杭州市2020届高三年级教学质量检测英语含答案
浙江省杭州市2020届高三年级教学质量检测英语试题注意事项：1.答卷前，考生务必将自己的姓名、准考证号填写在答题卡上。
2.选出每小题答案后，用铅笔把答题卡上对应题目的答案标号涂黑。
如需改动，用橡及擦资干净后，再选涂其他答案标号。
不能答在本试卷上，否则无效。
第一部分：听力（共两节，满分30分）做题时，先将答案标在试卷上。
录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。
第一节（共5小题，每小题1.5分，满分7.5分）听下面5段对话。
每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1.What is the man planning to do?A.Take a photography course.B.Take a nice photo.C.Make a photo album.2.How did the woman learn to make the cake?A.From a cookbook.B.From the man's wife..C.From a food market.3.How much did the man pay for the jacket?A.40$.B.20$.C.10$.4.Who will go to the movie at last?A.The man.B.The woman.C.The woman's sister.5.Where does the conversation probably take place?A.In a post office.B.In a book store.C.In a library第二节（共15小题：每小题1.5分，共22.5分）听下面可，或独自。
每段对的或班日后有儿个小题，从题中所给的A、B、C三个选项对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各中选出最佳选项。
2020届杭州市高级中学高三英语第三次联考试题及答案解析
2020届杭州市高级中学高三英语第三次联考试题及答案解析第一部分阅读（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AFour Best Cities to Visit in WinterCold rains, icy sidewalks and gray skies can make winter travel a trial. But here are four cities around the world that make for a great cold-weather destination:Prague,Czech RepublicWith its snow-capped spires and winding streets,Pragueis a fairytale city that remains ly tourist-free in winter.The amazing architecture looks even prettier under a sheet of snow, with one of the most beautiful areas being the old town, with its Romanesque vaults. Gas street lamps have been placed throughout the city center, adding a romantic color1 to evenings. Cafes here are ideal for escaping the bitter cold.Salzburg,AustriaWith its Christmas songs and traditional markets, this is a perfect city for a winter break. “Silent Night” was performed for the first time in thechurchofOberndorfon the border ofSalzburgon Christmas Eve in 1818.The city's main market is held in the shadow ofSalzburg'sHohensalzburgCastle, but the one held inMirabell Squareis especially popular with food lovers who come to taste local food such as halusky—pieces of dumpling mixed with fried bacon.Tromso,NorwayTromso is widely regarded asNorway's most beautiful city and is a base for spoiling the northern lights. There are several attractive museums, including thePolarMuseum, which offers an insight into the history of Arctic expeditions, and theTromsoMuseum, which is famous for its Sami exhibitions.Amsterdam,NetherlandsIn winter,Amsterdam' s museums are much less crowded, making it the time to visit attractions such as Rijksmuseum or the Anne Frank House. Built originally to house a circus, the Royal Carre Theater is more than 130 years old. Children will love the spectacular performances.1. What can you do inPrague?A. Enjoy the fascinating architecture.B. Taste local food halusky.C. Appreciate Sami exhibitions.D. Watch a circus performance.2. Where was “Silent Night” first performed?A. In thechurchofOberndorf.B. InHohensalzburgCastle.C. InMirabell Square.D. In the Polar Museum.3. Which city will you choose if you want to see the northern lights?A. Prague.B. Salzburg.C. Tromso.D.Amsterdam.BA company called Neuralink has shared a video which appears to show a monkey playing a video game, but what makes the video even stranger is that themonkey is playing the video game with just its mind.Neuralink is a company owned by Elon Musk, which is working to develop devices that could allow people to control things using just their brains. The monkey in the video is called Pager, having special "Link" devices inside his brain. These devices are connected to 2,048 wires which lead to the parts of Pager's brain that control movements of the arms and hands.Scientists taught Pager to play a video game using a banana juice as a reward when he playedthe game correctly. Soon Pager was eager to play well in order to get more smoothie. At first, Pager controlled the video game using a joystick (操纵杆). But as Pager played, his Link devices wirelessly sent out information about the signals his brain was using to control his arms and hands. Neuralink's scientists recorded all of these signals.Then they used computers to match up the signals from Pager's brain to the movements that his hands were actually doing. This was challenging work and the scientists counted on artificial intelligence (AI) to help them decode (解码) Pager's brain signals.The next step was to have a computer make moves in the video game as if Pager had actually moved the joystick. If Pager thought about moving the joystick up, the computer would send an "up"signal to the video game. Thus Pager was able to play the video game using just his brain.When people are paralyzed (瘫痪的), it's often because the brain has lost the ability to send signals to nerves and muscles in certain parts of the body. Neuralink hopes that one day, its system will be ableto send this information in a different way, allowing paralyzed people to use their arms or legs again.4. What does Neuralink aim to do?A. To make monkeys much smarter.B. To solve complex problems with monkeys.C. To create a device linking monkeys and people.D. To make people control things with their brains.5. How does the author introduce the process of the research?A. In order of time.B. By making a comparison.C. By giving examples.D. In order of space.6. What played an important role in the success of the research?A. The joystick.B. Artificial intelligence.C. The video game.D. The banana smoothie.7. Which is the most suitable title of the test?A. Neuralink Posts an Unusual VideoB. Disabled People Have a Bright FutureC. Monkey Plays Video Games with His MindD. Neuralink, a Creative and Competitive CompanyCIn Colombia a group, named WebConserva, is carrying out a project in the San Lucas Mountains with the help of coffee growers.The San Lucas area is one of the most unexplored places in Colombia, which is home to many thousands of species of animals and plants. Yet gold mining and coca farming have dealt a blow to its ecosystem. To limit additional development in the San Lucas area, the group helps coffee growers by linking them with processors from around the country.Colombia has more different kinds of living things than any other country except neighboring Brazil. In 2016, the Colombian government signed a peace deal with the Revolutionary Armed Forces of Colombia ending years of civil war. As a result, more land became accessible for use, with deforestation(毁林) coming along. Government information shows that in 2017, almost 220,000 hectares of forest were destroyed compared to around 124,000 hectares in 2015.To date, the project includes 10 families who farm 400 hectares of coffee plants, which costs about $77,000 dollars a year. WebConserva hopes that, in time, 200 families will be included. At that level, 20,000 hectares of untouched forest could be protected. In San Lucas, the families promise not to cut down trees to expand their crops or to hunt wild animals from the forests. In return, they receive $ 250 to $ 300 per 125 kilograms of coffee, an enviable amount there. Arcadio Barajas is among those taking part. His new coffee plantation(种植园) makes a barrier between cattle farms and forests where wild animals like the jaguar live and hunt. In this way, he doesn't have to kill wild animals to protect his cattle.Barajas said that pulling down the forest to plant coca and killing wildlife were against his will. Now he feels that growing coffee lets him be astewardof the land. "I'm taking care of the environment, the forest and the animals," he said.8. Why does WebConserva set up the project?A. To help local farmers make money.B. To expand areas of coffee growing.C. To link processors with coffee growers.D. To conserve biodiversity in the Mountains.9. What happened after Colombia’s civil war was over?A. Colombia helped many needy families.B. Colombia lost lots of areas of forests.C. Colombia started to save damaged forests.D. Colombia became more peaceful than Brazil.10. Which is probably a function of Barajas's coffee plantation?A. A method of protecting cattle and wildlife.B. A substitute for hunting of wild animals.C. A barrier between man and wild animals.D. A shelter for cattle against human hunters.11. What does the underlined word "steward" mean in the last paragraph?A. Farmer.B. Master.C. Guardian.D. Explorer.DLas Vegascity inNevadais built in a desert. The city may be known to the outside world for its partying. But officials have found that there are 21 square kilometers of useless grass. The grass is never laid on, played on or even stepped on. The grass is only there to look nice.Now, the city is asking theNevadastate legislature to ban useless grass. It is trying to become the first place inAmericato ban that kind of grass often seen between streets, in housing developments and in office parks.It is estimated that useless grass makes up 40% of all the grass inLas Vegasand it needs a lot of water to survive. Grass needs four times more water than dry climate plants like cactus. By tearing out the grass, the city could reduce yearly water usage by 15%.In 2003, the Southern Nevada Water Authority banned developers from planting grass in front of new homes. It also offered homeowners $ 30 for each square meter of grass they tear out. But fewer people are now using the program. Water usage has increased in southernNevadaby 9% since 2019. And last year,Las Vegaswent a record 240 days without major rainfall. The Colorado River provides much ofNevada's drinking water. The river could lose more water as climate change affects it.Water officials in other dry cities said water usage needs to be reduced. But they fear the reaction to reforms like the ones inLas Vegasif their communities do not accept them. Cynthia Campbell is the water resources adviser for the city ofPhoenixinArizona. “There might come a point when city restrictions get too severe for some residents. They'll say that is the point of no return for them,”Campbellsaid. “For some people, it's a pool. For some people, it's grass.”12. Why doesLas Vegascity try to ban useless grass?A. To protect the local people.B. To beautify the city.C. To reduce water usage.D. To reduce waste.13. What program was carried out inLas Vegasin 2003?A. Allowing planting grass before new houses.B. Encouraging the residents to tear out grass.C. Praising those who signed on the program.D. Awarding those who reduced water usage.14. What is implied inCampbell's words in the last paragraph?A. Many residents won't follow the ban.B. Reaction to the reform will vary personally.C. Other measures should be taken to protect wetter.D. Water officials should take many factors into account.15. What is the best title for the text?s VegasPlans to Ban Useless GrassB. A Method Is Adopted to SaveLas VegasC. Choices between Beauty and PracticeD. Grass Is Important but Useless inLas Vegas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2020届高三英语联考试题
高三英语联考试题本试卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)注意事项：1.本卷满分150分，考试时间120分钟；2.答第I卷前，考生务必将自己的姓名、准考证号填写在答题卡上。
3.选出每小题答案后，用铅笔把答题卡上对应题目的答案标号涂黑。
如需改动，用橡皮擦干净后，再选涂其他答案标号。
不能答在本试卷上，否则无效。
第Ⅰ卷第一部分：听力(共两节，满分30分)做题时，先将答案标在试卷上。
录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题纸上。
第一节：(共5个小题；每小题1.5分，满分7.5分)听下面5段对话，每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1. When will the woman's brother have the wedding?A. On July 4.B. On July 11.C. On July 182. What is Lucia doing?A. Cleaning the house.B. Doing her homework.C. Watching TV.3. What's the possible relationship between the speakers?A. Teacher and pupil.B. Father and daughter.C. Mother and son.4. What attracts the woman to the restaurant?A. The bread.B. The soup.C. The ice cream.5. Why won't the man's cellphone work?A. He forgot to turn it on.B. The battery needs recharging.C. Something is wrong with it.第二节：(共15小题：每小题1.5分，满分22.5分)听下面5段对话或独白，每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
2020年浙江省杭州市第五高中高三英语联考试题含解析
2020年浙江省杭州市第五高中高三英语联考试题含解析一、选择题1. We can’t________ the fact that there is still a long way to go before we can get rid of pollution.A．ignore B．neglectC．realize D．recognize参考答案：A2. All the football fans shouted and cheered so much that you could hardly hear _______ else.A. somethingB. everythingC. anythingD. nothing参考答案：C3. Most highways are lined with billboards of advertisement，which __________ by passing car-drivers.A．are intended to be read B．are intended to be readingC．are intending to reading D．are intending to read参考答案：A4. Music treatment involves a specialist playing an instrument or sing ________ the patient’s mood.A. by means ofB. with regard toC. in response toD. on account of参考答案：C【详解】考查介词短语。
句意：音乐疗法就是一位专家根据患者的心情来弹奏一门乐器或者唱歌。
A. by means of通过，借助；B. with regard to关于；C. in response to回应；D. on account of由于。
2020届浙江省名校协作体高三上学期联考英语试卷及答案
2020届浙江省名校协作体高三上学期联考英语试卷考生须知：1.本卷满分150分，考试时间120分钟；2.答题前，在答题卷指定区域填写学校、班级、姓名、试场号、座位号及准考证号。
3.所有答案必须写在答题卷上，写在试卷上无效；4.考试结束后，只需上交答题卷。
第Ⅰ卷(选择题部分，共95分)第一部分听力(共两节，满分30分)第一节短对话(共5小题：每小题1.5分，满分7.5分)听下面5段对话。
每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1. Why does the boy refuse the girl’s offer?A. He wants to get a better grade.B. He is busy with a reading group.C. He has to get to school early.2. What has the man been doing?A. Reading a book.B. Writing a report.C. Fixing the power.3. What are the speakers mainly talking about?A. A road.B. A shop.C. A product.4. How much will the woman pay for the tickets?A.$15.B. $20.C. $30.5. What is the relationship between the speakers?A. Friends.B. Co-workers. C Sister and brother.第二节(共15小题；每小题15分，满分22.5分)听下面5段对话或独白。
每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
浙江省杭州市五校联盟2020┄2021届高三上学期第一次诊断考试 英语试题
2020-2021学年杭州市五校联盟高三年级第一次诊断考试英语试卷选择题部分（共80分）第一部分：英语知识运用（共两节，满分30分）第一节：单项填空（共20小题；每小题0.5分，满分10分）从A、B、C和D四个选项中，选出可以填入空白处的最佳选项，并在答题纸上将该选项标号涂黑。
1．--Kim, give me your report by 1O am.--__ have you been in charge of this project？A. Since whenB. By whomC. For whatD. From where2．Life is like __________ ocean; only __________ strong-willed can reach the other shore.A. an; theB. the; aC. the; /D. /; a3．—Where would you like to sit？ In the corner or near the platform？—______．I would like to sit by the piano so that I can watch the musician play．A． Either B． NeitherC． None D． Both4．It may be necessary to stop _____ in the learning process and go back to the difficult points in the lessons．A． at intervals B． at randomC． at ease D． at length5．If a friend snaps at you or is unfriendly， step back， and with a sense of compassion， try to experience life from his____．A． perspective B．priorityC．privilege D． policy6．Over the years, people have learned from ants that teamwork and perseverance are indeed two key ______ to success.A. certificatesB. ingredientsC. approachesD. instructions7．If you completely ____ foods and drinks that you love， you'll only set yourself up to go on a large amount of those items later．A．take out B．cut out C．give out D．put out8．The exhibition _____ such endangered animals as the giant panda and the Siberian tiger and describes the work being done to protect them．A． exploits B． featuresC． demonstrates D． inspects9．We will have six-day holiday during the coming APEC meetings traffic on the roads．A． to ease B． easingC． ease D． having eased10．_____ with so much trouble，we failed to complete the task on time．A． Faced B． Face C． Facing D． To face11．-Mum，I always feel everything is unfair to me．--Complaints in life ________ no sense，for things will be what they should be．A． make B． have madeC． will make D． are making12．--- Do you remember when I first met you？---- Of course. I ___________ at Oxford University.A. studiedB. had studiedC. have studiedD. was studying13．Just be patient．You _____ expect the world to change so soon．A． can’t B． may not C． needn’t D． didn’t14．The woman burst into tears ________she was announced the winner.A. thatB. instantlyC. unlessD. in case15．English is a language shared by several diverse cultures, __________ uses it differently.A. all of whichB. each of whichC. all of themD. each of them16．It is the third time that she has won the race, ______ has surprised us all．A．that B．where C．which D．what17．No matter how much knowledge you have, if your subject is at all ______, be careful when discussing it during your speech, or you may well offend your audience.A. diverseB. sensitiveC. abstractD. original18．— I’m sorry．I ________ at you the other day．— Forget it．I was a bit out of control myself．A． shouldn’t shout B． shouldn’t have shoutedC． mustn’t shout D． mustn’t have shouted19．—I’m worried about the coming test!—______, you can do it!A. Don’t mention itB. come onC. Well doneD. Not likely20．---Don’t tell me you’ll have a dinner date again.---______.I didn’t mean to.A. You meant it.B. You made it.C. You guessed it.D. You deserved it.第二节：完形填空（共20小题；每小题1分，满分20分）阅读下面短文，掌握其大意，然后从21 ~ 40各题所给的四个选项（A、B、C、D）中，选出最佳选项，并在答题纸上将该选项标号涂黑。
2020-2021学年高三年级第一学期第一次五校联考五校联考试卷(定稿)
第1页，共12页2020-2021学年高三年级第一学期第一次五校联考数学试题一、单项选择题（本大题共8小题，共40.0分） 1.函数f(x)=√1−x +lg(3x −1)的定义域为( )A. ( 13,1] B. ( 0,1]C. (−∞,13)D. (0,13) 2.已知log 2a >log 2b ，则下列不等式一定成立的是( )A. 1a >1bB. log 2(a −b)>0C. (13)a<(12)bD. 2a−b <13.已知f(x)是定义在R 上的偶函数，且在[0,+∞)上是增函数，f(2)=0，则不等f(log 2x)>0的解集为( )A. (0,14)B. (4,+∞)C. (14,1)∪(4,+∞)D. (0,14)∪(4,+∞)4.我国著名数学家华罗庚先生曾说：数缺形时少直观，形缺数时难入微，数形结合百般好，隔裂分家万事休. 在数学的学习和研究中，常用函数的图象来研究函数的性质，也常用函数的解析式来琢磨函数的图象的特征，如函数(1)e sin ()e 1x x xf x =-+在区间ππ(-,)22上的图象的大致形状是( ) A ． B ．C ．D ．5.已知x >0,y >0,lg4x +lg2y =lg8，则12x +4y 的最小值是( )．A. 3B. 94C. 4615D. 96．已知函数()sin f x x x =+，x ∈R ，若()2log 3a f =，13log 2b f ⎛⎫= ⎪⎝⎭，()22c f -=则,,a b c 的大小为（ ） A ．a b c >> B ．a c b >>C ．c b a >>D ．b a c >>27．已知命题：，；命题q: ，，若、都为真命题，则实数的取值范围是（ ）A ．B ．C ．D ．8.已知函数f (x )=x (lnx −ax )有两个极值点，则实数a 的取值范围是( )A. (−∞,0)B. (0,12)C. (0,1)D. (0,+∞)二、不定项选择题（本大题共4小题，共20.0分，每小题全对得5分，部分对得3分，有错得零分）9.若直线y =12x +b 是函数f (x )图象的一条切线，则函数f (x )可以是( )A. f (x )=1xB. f (x )=x 4C. f (x )=sinxD. f (x )=e x10．设正实数mn 、满足2m n +=，则下列说法正确的是( ) A ．2n m n+的最小值为3 B ．mn 的最大值为1 C的最小值为2 D ．22m n +的最小值为211.下列命题中正确命题的是( )A .已知a ，b 是实数，则“(13)a <(13)b ”是“log 3a >log 3b ”的充分而不必要条件； B .∃x ∈(−∞,0)，使2x <3x ；C.设x =θ是函数f(x)=3sinx −cosx 的一个极值点，则sin2θ+2cos 2θ=−25 D.若角α的终边在第一象限，则sinα2|sin α2|+cosα2|cos α2|的取值集合为{−2,2}．12.高斯是德国著名的数学家，近代数学奠基者之一，享有“数学王子”的称号，他和阿基米德、牛顿并列为世界三大数学家，用其名字命名的“高斯函数”为：设，用[x ]表示不超过x 的最大整数，则y =[x]称为高斯函数，例如：[−3.5]=−4，[2.1]=2.已知函数f (x )=e x1+e x−12，则关于函数g (x )=[f (x )]的叙述中正确的是( ) A. g (x )是偶函数B. f (x )是奇函数C. f (x )在R 上是增函数D. g (x )的值域是{−1,0,1}三、填空题（本大题共4小题，共20.0分）13.已知扇形的圆心角为2π3，半径为5，则扇形的面积S =______．14.已知函数f(x)=lg(√x 2+1+x)+a ，且f(ln3)+f(ln 13)=1，则a =______． 15.已知三个函数ℎ(x )=x 2−2ln x,f(x)=ℎ′(x)−5ln x −5ln 2，g(x)=ℎ(x)+2ln x −bx +4.若∃x 1∈(0,1]，∀x 2∈[1,2]，都有f(x 1)≥g(x 2)成立，求实数b 的取值范围16.设f(x)是定义在R 上的偶函数，且f(2+x)=f(2−x)，当x ∈[−2,0]时，f(x)=(√22)x −1，若在区间(−2,6)内关于x 的方程f(x)−log a (x +2)=0(a >0)有3个不同的根，则a 的范围是 ．p x ∀∈R 220mx +>x ∃∈R 2210x mx -+≤p q m [1,)+∞(,1]-∞-(,2]-∞-[1,1]-第3页，共12页四、解答题（本大题共6小题，共70.0分） 17.（本题共10分）已知角α为第一象限角，且sinα=√55． (1)求cosα，tanα的值； (2)求3sin(π−α)−2cos(π+α)cos(π2−α)的值．18.（本题共12分）已知集合A ={x|y =log 2(−4x 2+15x −9),x ∈R }，B ={x||x −m |⩾1,x ∈R }(1)求集合A ；(2)若p ：x ∈A ，q ：x ∈B ，且p 是q 的充分不必要条件，求实数m 的取值范围． 19.（本题共12分）已知函数f(x)=ax 2+2x +c ，(a,c ∈N ∗)满足：①f(1)=5；②6<f(2)<11．(1)求函数f(x)的解析式；(2)若对任意的实数x ∈[12,32]，都有f(x)−2mx ≤1成立，求实数m 的取值范围．20. （本题共12分）已知函数f(x)=a·4x−14x+1是定义在R上的奇函数．(1)求a的值；(2)判断并证明函数f(x)的单调性，并利用结论解不等式：f(x2−2x)+f(3x−2)<0；(3)是否存在实数k，使得函数f(x)在区间[m,n]上的取值范围是[k4m ,k4n]？若存在，求出实数k的取值范围；若不存在，请说明理由．21.（本题共12分）如图，公园内直线道路旁有一半径为10米的半圆形荒地(圆心O在道路上，AB为直径)，现要在荒地的基础上改造出一处景观．在半圆上取一点C，道路上B点的右边取一点D，使OC垂直于CD，且OD的长不超过20米．在扇形区域AOC 内种植花卉，三角形区域OCD内铺设草皮．已知种植花卉的费用每平方米为200元，铺设草皮的费用每平方米为100元．(1)设∠COD=x(单位：弧度)，将总费用y表示为x的函数式，并指出x的取值范围；(2)当x为何值时，总费用最低？并求出最低费用．22.已知函数f(x)=4x−alnx−12x2−2，其中a为正实数．(1)若函数y=f(x)在x=1处的切线斜率为2，求a的值；(2)求函数y=f(x)的单调区间；(3)若函数y=f(x)有两个极值点x1，x2，求证：f(x1)+f(x2)<6−lna．4第5页，共12页五校联考试卷精选一、选择题（本大题共8小题，共40分） 1.函数f(x)=√1−x +lg(3x −1)的定义域为( )A. ( 13,1]B. ( 0,1]C. (−∞,13)D. (0,13)【答案】A2.已知log 2a >log 2b ，则下列不等式一定成立的是( )A. 1a >1bB. log 2(a −b)>0C. (13)a <(12)bD. 2a−b <1【答案】C3.已知f(x)是定义在R 上的偶函数，且在[0,+∞)上是增函数，f(2)=0，则不等f(log 2x)>0的解集为( )A. (0,14)B. (4,+∞)C. (14,1)∪(4,+∞)D. (0,14)∪(4,+∞)【答案】D4.我国著名数学家华罗庚先生曾说：数缺形时少直观，形缺数时难入微，数形结合百般好，隔裂分家万事休. 在数学的学习和研究中，常用函数的图象来研究函数的性质，也常用函数的解析式来琢磨函数的图象的特征，如函数(1)e sin ()e 1x x xf x =-+在区间ππ(-,)22上的图象的大致形状是( ) A ． B ．C ．D ．【答案】A5.已知x >0,y >0,lg4x +lg2y =lg8，则12x +4y 的最小值是( )．A. 3B. 94C. 4615D. 9【答案】A6．已知函数()sin f x x x =+，x ∈R ，若()2log 3a f =，13log 2b f ⎛⎫= ⎪⎝⎭，()22c f -=则,,a b c 的大小为（ ）6A ．a b c >>B ．a c b >>C ．c b a >>D ．b a c >>【答案】B 7．已知命题：，；命题q: ，，若、都为真命题，则实数的取值范围是（ ）A ．B ．C ．D ．【答案】A8.已知函数f (x )=x (lnx −ax )有两个极值点，则实数a 的取值范围是( )A. (−∞,0)B. (0,12)C. (0,1)D. (0,+∞)【答案】B 【解答】解：因为f(x)=x(lnx −ax)，所以f′(x)=lnx −2ax +1． 由题可知f′(x)在(0,+∞)上有两个不同的零点， 令f′(x)=0，则．令，则，所以g(x)在(0,1)上单调递增，在(1,+∞)上单调递减， 又因为当x 从右边趋近于0时，g(x)→−∞，当x →+∞时，g(x)→0，而g(x)max =g(1)=1， 所以只需0<2a <1，即0<a <12．故选B ．二、不定项选择题（本大题共4小题，共20.0分）9.若直线y =12x +b 是函数f (x )图象的一条切线，则函数f (x )可以是( )A. f (x )=1xB. f (x )=x 4C. f (x )=sinxD. f (x )=e x【答案】BCD10．设正实数m n 、满足2m n +=，则下列说法正确的是( ) A ．2n m n+的最小值为3 B ．mn 的最大值为1 C m n 的最小值为2 D ．22m n +的最小值为2【答案】ABD11.下列命题中正确命题的是( )A .已知a ，b 是实数，则“(13)a <(13)b ”是“log 3a >log 3b ”的充分而不必要条件； B .∃x ∈(−∞,0)，使2x <3x ；C.设x =θ是函数f(x)=3sinx −cosx 的一个极值点，则sin2θ+2cos 2θ=−25 D.若角α的终边在第一象限，则sinα2|sin α2|+cosα2|cos α2|的取值集合为{−2,2}．【答案】CDp x ∀∈R 220mx +>x ∃∈R 2210x mx -+≤p q m [1,)+∞(,1]-∞-(,2]-∞-[1,1]-第7页，共12页【解析】解：对于A ，若“(13)a <(13)b ”，则a >b ，若“log 3a >log 3b ”，则a >b >0． 所以“(13)a <(13)b ”，是“log 3a >log 3b ”的必要不充分条件．所以A 不正确； 对于B ，由指数函数的单调性可得x ∈(−∞,0)，使2x <3x ；不正确，所以B 不正确； 对于C. f′(x)=3cosx +sinx ，∴f′(θ)=3cosθ+sinθ=0，∴tanθ=−3，∴sin2θ+2cos 2θ=sin2θ+2cos 2θcos 2θ+sin 2θ=2tanθ+21+tan 2θ=−25．对于 D ，角α的终边在第一象限，则α2∈(kπ,kπ+π4)，k ∈Z ，α2在第一象限时，sinα2|sin α2|+cosα2|cos α2|=2，当α2在第三象限时，则sinα2|sin α2|+cosα2|cos α2|=−2．则sinα2|sin α2|+cosα2|cos α2|的取值集合为：{2,−2}.所以D 正确；12.高斯是德国著名的数学家，近代数学奠基者之一，享有“数学王子”的称号，他和阿基米德、牛顿并列为世界三大数学家，用其名字命名的“高斯函数”为：设，用[x ]表示不超过x 的最大整数，则y =[x]称为高斯函数，例如：[−3.5]=−4，[2.1]=2.已知函数f (x )=e x1+e x−12，则关于函数g (x )=[f (x )]的叙述中正确的是( ) A. g (x )是偶函数B. f (x )是奇函数C. f (x )在R 上是增函数D. g (x )的值域是{−1,0,1}【答案】BC【解答】 解：，定义域R ，且f(−x)=e −x1+e −x−12=11+e x −12=−f(x)， 故函数f(x)为奇函数，函数g(x)=[f(x)]，则g(−1)=[f(−1)]=−1,g(1)=[f(1)]=0， 故g(−1)≠g(1)，显然g (x )不是偶函数 ， 故A 错，B 对．，f′(x)=e x(1+e x )2>0，故f (x )在R 上是增函数，C 正确；∵1e x +1∈(0,1)，故f(x)∈(−12,12)，则g(x)∈{−1,0}，故D 错误． 故选BC ．三、填空题（本大题共4小题，共20.0分）13.已知扇形的圆心角为2π3，半径为5，则扇形的面积S =______． 【答案】25π314.已知函数f(x)=lg(√x 2+1+x)+a ，且f(ln3)+f(ln 13)=1，则a =______．8【答案】1215.已知三个函数ℎ(x )=x 2−2ln x,f(x)=ℎ′(x)−5ln x −5ln 2，g(x)=ℎ(x)+2ln x −bx +4.若∃x 1∈(0,1]，∀x 2∈[1,2]，都有f(x 1)≥g(x 2)成立，求实数b 的取值范围【答案】b ≥8 【解答】解：由题知f(x)=2x −2x −5lnx −5ln2，g(x)=x 2−bx +4． ∴f′(x)=2+2x2−5x=2x 2−5x+2x 2=(x−2)(2x−1)x 2．∴f(x)在(0,12)上单调递增；在(12,2)上单调递减， 易知f(x)在区间(0,1]上的最大值为f(12)=−3， ∃x 1∈(0,1]，∀x 2∈[1,2]，都有f(x 1)≥g(x 2)成立， 即{f(12)≥g(1)f(12)≥g(2),即{−3≥5−b −3≥8−2b ,解得b ≥8， 16.设f(x)是定义在R 上的偶函数，且f(2+x)=f(2−x)，当x ∈[−2,0]时，f(x)=(√22)x −1，若在区间(−2,6)内关于x 的方程f(x)−log a (x +2)=0(a >0)有3个不同的根，则a 的范围是 ．【答案】(4,8) 【解析】 【分析】本题考查了函数的零点与方程根的关系，函数的奇偶性及函数的周期性，函数图象的应用，属于中档题．由已知中可以得到函数f(x)是一个周期函数，且周期为4，根据函数与方程之间的关系，转化为函数f(x)的图象与函数y =log a (x +2)的图象有3个不同的交点，利用数形结合即可得到实数a 的取值范围．【解答】解：∵对于任意的x ∈R ，都有f(x −2)=f(2+x)， ∴f(x +4)=f[2+(x +2)]=f[(x +2)−2]=f(x)， ∴函数f(x)是一个周期函数，且T =4．又∵当x ∈[−2,0]时，f(x)=(√22)x −1，且函数f(x)是定义在R 上的偶函数，若在区间(−2,6)内关于x 的方程f(x)−log a (x +2)=0恰有3个不同的实数解， 则函数y =f(x)与y =log a (x +2)在区间(−2,6)上有3个不同的交点，如下图所示：第9页，共12页又f(−2)=f(2)=1，当0<a <1时，不合题意，当a >1时，则对于函数y =log a (x +2)，由题意可得，当x =2时的函数值小于1，当x =6时的函数值大于1，即{log a 4<1log a 8>1，由此解得：4<a <8， 故答案为：(4,8).四、解答题（本大题共6小题，共70.0分） 17.已知角α为第一象限角，且sinα=√55． (1)求cosα，tanα的值； (2)求3sin(π−α)−2cos(π+α)cos(π2−α)的值．【答案】(1)∵角α为第一象限角，且sinα=√55，∴cosα=√1−sin 2α=2√55，tanα=sinαcosα=12．……………………………4分 (2)3sin(π−α)−2cos(π+α)cos(π2−α)=3sinα+2cosαsinα……………………6分=3+2tanα……………………8分 =3+212=7．………………10分18.已知集合A ={x|y =log 2(−4x 2+15x −9),x ∈R }，B ={x||x −m |⩾1,x ∈R }(1)求集合A ；(2)若p ：x ∈A ，q ：x ∈B ，且p 是q 的充分不必要条件，求实数m 的取值范围． 【答案】(1)∵A ={x|y =log 2(−4x 2+15x −9),x ∈R}， ∴−4x 2+15x −9>0，则(x −3)(4x −3)<0，∴34<x <3，∴A ={x|34<x <3}．……………………6分(2)B ={x||x −m|≥1,x ∈R}，∴由|x −m|≥1可得：x −m ≥1或x −m ≤−1，∴x ≥m +1或x ≤m −1， ∴B ={x|x ≥m +1或x ≤m −1}．……………………8分 ∵p:x ∈A ，q:x ∈B ，且p 是q 的充分不必要条件， ∴A 是B 的真子集，……………………9分∴m −1≥3或m +1≤34，∴m ≥4或m ≤−14，……………………11分 ∴实数m 的取值范围是(−∞,−14]∪[4,+∞). ……………………12分19.已知函数f(x)=ax 2+2x +c ，(a,c ∈N ∗)满足：①f(1)=5；②6<f(2)<11． (1)求函数f(x)的解析式；(2)若对任意的实数x ∈[12,32]，都有f(x)−2mx ≤1成立，求实数m 的取值范围． 【答案】(1)∵f (1)=a +2+c =5，∴c =3−a.① 又∵6<f (2)<11，即6<4a +c +4<11，② 将①式代入②式，得−13<a <43，……………………3分10又∵a 、c ∈N ∗，∴a =1，c =2．∴f (x )=x 2+2x +2……………………6分 (2)证明：∵x ∈[12,32]，∴不等式f (x )−2mx ≤1恒成立⇔2(1−m )≤−(x ++1x) 在[12,32]上恒成立．……………………8分由于[−(x +1x )]min =−52，故只需2(1−m)≤−52即可．……………………10分 解得m ≥94……………………12分（注：本题有其它解法酌情给分） 20.已知函数f(x)=a·4x −14x +1是定义在R 上的奇函数．(1)求a 的值；(2)判断并证明函数f(x)的单调性，并利用结论解不等式：f(x 2−2x)+f(3x −2)<0；(3)是否存在实数k ，使得函数f(x)在区间[m,n]上的取值范围是[k4m ,k4n ]？若存在，求出实数k 的取值范围；若不存在，请说明理由． 【答案】解：(1)∵f (x )=a⋅4x −14x +1是定义在R 上的奇函数，∴f (0)=0，从而得出a =1，…………………2分 a =1时，f(x)+f(−x)=4x −14x +1+4−x −14−x +1=4x −14x +1+14x −114x+1=4x −14x +1+1−4x 1+4x=0，∴a =1；…………………4分（不证明扣2分） (2)f(x)是R 上的增函数，证明如下： 设任意x 1,x 2∈R 且x 1<x 2，=24x 2+1−24x 1+1=2(4x 1−4x 2)(4x 2+1)(4x 1+1)，∵x 1<x 2,∴4x 1<4x 2,4x 1+1>0,4x 2+1>0, ∴f(x 1)<f(x 2)，∴f (x )是在(−∞,+∞)上是单调增函数．…………………6分 ∵f (x 2−2x )+f (3x −2)<0，又∵f (x )是定义在R 上的奇函数且在(−∞,+∞)上单调递增， ∴f (x 2−2x )<f (2−3x )，∴x 2−2x <2−3x ，∴−2<x <1；…………………8分 (3)假设存在实数k ，使之满足题意， 由(2)可得函数f (x )在[m,n ]上单调递增，∴{f (m )=k4mf (n )=k 4n ,∴{4m −14m +1=k 4m 4n −14n +1=k4n, ∴m,n 为方程4x −14x +1=k4x 的两个根，即方程4x −14x +1=k4x 有两个不等的实根，令4x =t >0，即方程t 2−(1+k )t −k =0有两个不等的正根，…………………10分∴{1+k2>0Δ>0−k>0, ∴−3+2√2<k<0．∴存在实数k，使得函数f(x)在[m,n]上的取值范围是[k4m ,k4n]，并且实数k的取值范围是(−3+2√2,0)．…………………12分（注：本题有其它解法酌情给分）21.某公园内直线道路旁有一半径为10米的半圆形荒地(圆心O在道路上，AB为直径)，现要在荒地的基础上改造出一处景观．在半圆上取一点C，道路上B点的右边取一点D，使OC垂直于CD，且OD的长不超过20米．在扇形区域AOC内种植花卉，三角形区域OCD内铺设草皮．已知种植花卉的费用每平方米为200元，铺设草皮的费用每平方米为100元．(1)设∠COD=x(单位：弧度)，将总费用y表示为x的函数式，并指出x的取值范围；(2)当x为何值时，总费用最低？并求出最低费用．【答案】解：(1)因为扇形AOC的半径为10m，，且OD的长不超过20米，当OD=20m时，，故0<x⩽π3．…………………2分所以扇形AOC的面积：S扇AOC =(π−x)·1022=50(π−x)，0<x⩽π3．在Rt△COD中，OC=10，，所以△COD的面积，从而y=100S△COD+200S扇AOC，0<x⩽π3；………6分(2)设，则，f′(x)=cos2x+sin2xcos2x −2=1−2cos2xcos2x，令f′(x)=0，解得x=π4，…………………8分从而当0<x<π4时，f′(x)<0，当π4<x≤π3，f′(x)>0，因此f(x)在区间(0,π4)上单调递减，在区间(π4,π3]上单调递增，…………………10分当x=π4时，f(x)取得最小值，f(π4)=1+2π−π2=1+3π2，所以y的最小值为(5000+7500π)元，答：当x=π4时，改造景观的费用最低，最低费用为(5000+7500π)元．………12分22.已知函数f(x)=4x−alnx−12x2−2，其中a为正实数．(1)若函数y=f(x)在x=1处的切线斜率为2，求a的值；(2)求函数y=f(x)的单调区间；(3)若函数y=f(x)有两个极值点x1，x2，求证：f(x1)+f(x2)<6−lna．第11页，共12页【答案】解：(1)因为f(x)=4x−alnx−12x2−2，所以f′(x)=4−ax−x，则f′(1)=3−a=2，所以a的值为1…………………2分(2)f′(x)=4−ax −x=−x2−4x+ax，函数y=f(x)的定义域为(0,+∞)，①若16−4a≤0，即a≥4，则f′(x)≤0，此时f(x)的单调减区间为(0,+∞)；(4分)②若16−4a>0，即0<a<4，则f′(x)=0的两根为2±√4−a，此时f(x)的单调增区间为(0,2−√4−a)，(2+√4−a,+∞)，单调减区间为(2−√4−a,2+√4−a)…(6分)(3)由(2)知，当0<a<4时，函数y=f(x)有两个极值点x1，x2，且x1+x2=4，x1x2=a．因为f(x1)+f(x2)=4x1−alnx1−12x12−2+4x2−alnx2−12x22−2=4(x1+x2)−aln(x1x2)−12(x12+x22)−4=16−alna−12(42−2a)−4=4+a−alna，要证f(x1)+f(x2)<6−lna，只需证alna−a−lna+2>0…(8分)构造函数g(x)=xlnx−x−lnx+2，则g′(x)=1+lnx−1−1x =lnx−1x，g′(x)在(0,4)上单调递增，又g′(1)=−1<0，g′(2)=ln2−12>0，且g′(x)在定义域上不间断，由零点存在定理，可知g′(x)=0在(1,2)上唯一实根x0，且lnx0=1x…(10分)则g(x)在(0,x0)上递减，(x0,4)上递增，所以g(x)的最小值为g(x0)，因为g(x0)=1−x0−1x0+2=3−(x0+1x0)，当x0∈(1,2)时，x0+1x0∈(2,52)，则g(x0)>0，所以g(x)≥g(x0)>0恒成立．所以alna−a−lna+2>0，所以f(x1)+f(x2)<6−lna，得证…(12分)12。
2020学年第一学期五校联考试题高三年级英语试题
2020学年第一学期五校联考试题高三年级英语试题卷命题：杭州第二中学考生须知：1．本卷满分150分，考试时间120分钟；2．答题前，在答题卷指定区域填写学校、班级、姓名、试场号、座位号及准考证号；3．所有答案必须写在答题卷上，写在试卷上无效；4．考试结束后，只需上交答题卷。
第Ⅰ卷（选择题部分）第一部分听力（共两节，满分30分）做题时，先将答案标在试卷上。
录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题纸上。
第一节（共5小题；每小题1.5分，满分7.5分）听下面5段对话。
每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项。
听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
例如：你将听到以下内容：M: Excuse me. Can you tell me how much the shirt is？W: Yes, it’s nine fifteen.How much is the shirt?A. $ 19.15B. $ 9.5C. $ 9.151.Why is the woman going to Trader Joe’s now?A. To join the big crowds.B. To enjoy a special sale.C. To see the familiar folks.2. What is the speakers’ main activity?A. Eating food.B. Trying out furniture.C. Watching a movie.3. How does the woman probably feel?A. Happy.B. Angry.C. Shy.4. What is the relationship between the speakers?A. Boss and driver.B. Husband and wife.C. Taxi driver and passenger.5. What does the man mean?A. He didn’t put in any sugar.B. He added some natural flavor.C. He also thinks the coffee strange.第二节（共15 小题；每小题1.5 分，满分22.5 分）听下面 5 段对话或独白。
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浙江省杭州市2020届高三英语上学期五校联考试题（含解析）考生须知:1.本卷满分150分，考试时间120分钟；2.答题前，在答题卷指定区域填写学校、班级、姓名、试场号、座位号及准考证号。
3.所有答案必须写在答题卷上，写在试卷上无效；4.考试结束后，只需上交答题卷。
第Ⅰ卷(选择题部分)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)听下面5段对话，每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项。
听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题，每段对话仅读一遍。
1.What would the man like to do?A. To visit his brother.B. To have dinner with her.C. To watch films. 【答案】C【解析】【原文】此题为听力题，解析略。
2.What time is it now?A. 4 o’clock.B. 5 o’clock.C. 7 o’clock.【答案】C【解析】【原文】此题为听力题，解析略。
3.Where are the speakers?A. In a car.B. On a train.C. On a plane.【答案】A【解析】【原文】此题为听力题，解析略。
4.What does the woman mean?A. She doubts Tom’s ability to run the station.B. She hopes Tom can take over the station.C. She believes Tom can manage the station better.【答案】A【解析】【原文】此题为听力题，解析略。
5.What do we know about the woman’s notes?A. She lost her notes.B. The notes are not hers.C. Someone has borrowed her notes.【答案】C【解析】【原文】此题为听力题，解析略。
第二节(共15小题；每小题1.5分，满22.5分)听下面5段对话或独白。
每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项。
听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。
每段对话或独白读两遍。
听下面一段较长对话，回答以下小题。
6. What are the speakers talking about?A. A famous athlete and his fans.B. The woman’s unusual experience last night.C. How the woman saved the life of a famous writer.7. What did Tom Clancy do in the end?A. He took a picture with his readers.B. He gave autographs till midnight.C. He left the restaurant secretly.【答案】6. B 7. C【解析】【原文】此题为听力题，解析略。
听下面一段较长对话，回答以下小题。
8. Where did the speakers finally agree to go for dinner?A. To a cafeteria.B. To McDonald’s.C. To KFC.9. Why didn’t the girl drive?A. She was too young.B. She was a bit tired.C. She didn’t know the way.10. What can we learn from the conversation?A. The mother is a good cook.B. The girl likes fried chicken very much.C. The father will go to find the seats. 【答案】8. B 9. B 10. A 【解析】【原文】此题为听力题，解析略。
听下面一段较长对话，回答以下小题。
11. What kind of clothing does Amy like most? A. Fashionable clothes. B. Expensive clothes. C. Comfortable clothes. 12. Why does she like to go shopping at the local market? A. She can buy second-hand clothes there. B. She can find good and cheap things there. C. She enjoys talking with people there. 13. What does she think of second-hand clothes? A. She likes looking at them but never buys them. B. She thinks they are real bargains.C. She seldom goes to those shops.【答案】11. C 12. B 13. A【解析】【原文】此题为听力题，解析略。
听下面一段较长对话，回答以下小题。
14. Why couldn’t Mark play basketball with the man?A. He had to study.B. He needed to go out with his girlfriend.C. He didn’t like basketball any more.15. What should Mark do according to the man?A. Be honest with him.B. Spend more time studying.C. End the relationship with his girlfriend.16. What does the man decide to do?A. Ask Mary to talk to Mark.B. End the friendship with Mark.C. Talk with Mark.17. What does the woman think of Mark’s lies?A. They’re harmless.B. They’re harmful to friendship.C. Mark made a serious mistake.【答案】14. B 15. A 16. C 17. A【解析】【原文】此题为听力题，解析略。
听下面一段独白，回答以下小题。
18. What are some of the problems brought about by global warming?A. The reduction of sea water.B. More serious earthquakes.C. Animal and plant species disappearing.19. What can people do to slow down global warming?A. Use clean energy.B. Control population growth.C. Close down factories.20. Why is it hard to get governments to pass new laws?A. They don’t care about the environment.B. They don’t want to hurt their economies.C. They can’t get their people’s support.【答案】18. C 19. A 20. B【解析】【原文】此题为听力题，解析略。
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)阅读下列短文，从每题所给的A、B、C和D四个选项中，选出最佳选项，并在答题纸上将该项涂黑。
ATwo blocks. Two very, very long blocks beyond in deep darkness. It is 1953, and I have walked these blocks many times on my way to the room I rent off campus. I get off the bus after leaving the library at ten o’clock in the evening clutching books in my arms, with a purse hanging from a strap on my shoulder.My landlady works the night shift at the hospital, so at this hour, the house will be as dark and blank as the others on this street. Everything is quiet and closed. Far ahead is a streetlight. I am thinking about a paper due in a few days. What theme should I explore? Will the professor admire or dismiss it? Why are we reading Dreiser anyway?I notice headlights coming toward me. A car is driving slowly down the street on the other side. As it passes, I glance at the driver—male, blond. I keep walking. The car slows down and stops. I hear its door slam shut. A few seconds later, I hear footsteps behind me. I keep walking; I do not speed up, because I don’t want to callattention to myself. The walker may be going to a house nearby, visiting a friend. Besides, what would be the point of hurrying, running?I still have to get my door key from my purse. When I reach my house, I will have to walk upstairs to the porch, and fumble in the dark for my key. Then he will climb the steps behind me, put his right hand over my mouth, knock me down on the porch floor, scattering my books and the contents of my purse. There is no one to see. He will hold me down with one hand squeezing my throat, search my body for any valuables with the other, and say, “Don’t fight me; don’t fight.”I am exhausted. The scene I have imagined is detailed, brutal, and unbearable.I cannot live through what I expect.I stop.I turn around and wait for him. I wait and wait until he catches up to where I stand, with nothing to defend myself but the urgency to escape not what might happen but what has already happened in my mind.He comes close, closer. I can see his eyes (or I think I can).“Will you please leave me alone.” It is neither a question nor a scream. My voice is low, conversational. Nothing can be worse than what I have imagined.He pauses. “I’m not going to bother you,” he whispers, then turns around and walks back to his car.21. What is on the author’s mind before she notices the car?A. The long way home.B. The dark and blank street.C. Her landlady’s absence.D. The theme of her paper.22. The underlined word “fumble” is closest to ___________ in meaning.A. reachB. searchC. findD. touch23. Why does the author turn around and wait for the man?A. She tries to escape what has happened in her mind.B. She wants to ask him whether he will leave her alone.C. She knows she will be safe after talking with him.D. She is so terrified of what is going to happen later.【答案】21. D 22. B 23. A【解析】这是一篇记叙文。