福建省宁化城东中学2020届九年级英语上学期第13周周练试题(无答案) 仁爱版
城东中学2020学年上学期九年级英语第十三周周测
（Unit 4 Topic 1）
一.单词：(29分 )
1.火箭11.列清单21. [ɡ?n]
2.金属12.彩色铅笔22.机器人
3.卫星13.[ θ?:t ]23.键盘
4.宇宙飞船14.愚蠢的24.探险者
5.锁15. 标示,做标记25. 体系
6.电灯泡16.估值26.brainstorm
7.飞机17.detailed 27.man-made
8.hard-wearing 18.重新设计https://www.360docs.net/doc/121947246.html,ptop
9.韩国19.想象力29.concentrate
10. [ in'ven??n ]20.气球
二.词组练习: （16分）
1. Many people ______________________ (嘲笑)the Wright brothers and said they would never fly. 2，I hope your dream will _________________________(实现)
3,The paper _________________________(由------制成) the wood.
4, It _________________________(被用来)writin g on.
5, _________________________(据说)he invented more than two thousand things during his life.. 6,It’s _________________________________(与…..不同)today’s.
7.The stars can be seen clearly _______________(只要) the weather is good.
8. ______________ your invention ______________ (和…分享) others..
三. 单项选择。(10分)
( )1.He _________play computer games unless he finished his homework.
A. was allowed to
B. was not allowed to
C. allow to
( )2.We all know that paper ________wood.
A. is made of
B. is made into
C. is made from
( )3.This kind of machine _________in 2020.
A. is invented
B. is made
C. was invented
( )4.A(An)___________is used for taking photos.
A .Camera B. Lift C. MP3 player
( )5 .We should spend more time ___________because it’s too important.
A .to learn English B. learning English C. in English
( ) 6. A big supermarket ____________in our city last year.
A. is built
B. were built
C. was built
( ) 7.Could you tell me who __________ the radio?
A. invents
B. invented
C. was invented
( ) 8. Many trees and flowers ____ in our school last year. They made our school more beautiful.
A. have planted
B. were planted
C. planted
( ) 9.The children ____ swim last month and they can swim very well now.
A. are taught
B. were taught
C. were taught to
( )10.It is said that potato chips _____by mistake about one hundred years ago.
A. were invented
B. invented
C. are invented
三，补全对话(10分)
Kangkang: Look, the laptop is very beautiful.
Maria: Yes. My father gave it to me as my birthday present .
Kangkang: _________________________________________________
Maria: Plastic.
Kangkang: _________________________________________________.
Maria: It is used for studying.
Kangkang: _________________________________________________
Maria: It was developed in Japan in 1985
Kangkang: Do you use it often?
Maria: _________________________. I like it very much.
Kangkang: Who m ade it?
Maria: ______________________________.Let’s ask Mr. Brown for help, he can tell us. Kangkang: Let’s go.
四. 完形填空。(10分)
The computer is a very wonderful machine today, and it’s so 1 that it seems that we 2 live or work without it. Computers are used in many 3 , such as offices, factories, big shops, schools and even homes. With the computer people are living a better 4 .
The computer is one of the greatest inventions in the 5 century. The first computer was built in America in 1946 whic h was named ENIAC, and it was not only very 6 , but also quite heavy. It was as big as ten ordinary (普通的) rooms!
But the computer is developing very fast. Today they’re becoming smaller and smaller, lighter and lighter, and 7 faster and faster. There are so many kinds of different computers in the market that you can choose one that you like best.
The computer can do a lot of things for people, and it also helps us to learn about the real world. With the computer you can 8 an e-mail just in a few seconds to your friend far away, but if you post the letter, it will take your friend quite a long time to receive your 9 .
Now you can see the computer really gives us a very nice picture about the world of tomorrow. So as a student in the 21st century, you have to work hard and learn how to 10 the computer very well. Don’t you think so?
( )1.A.beautiful B. interesting C. useful
( )2.A.can B. can’t C. must
( )3.A.roads B. streets C. places
( )4.A.life B. friend C. family
( )5.A.18th B.19th C.20th
( )https://www.360docs.net/doc/121947246.html,eful B. large C. small
( )7.A.studying B. teaching C. working
( )8.A.give B. tak e C. send
( )9.A.letter B. book C. help
( )10.A.get B. use C. read
五.阅读理解。（10分）
“Tom? Are you in bed yet?” called Mrs. White. There was no answer. Mrs. White put down her book and went to her 14-year-old son’s room. Tom was sitting in front of a bright computer screen on which a motorbike was running fast.
“Oh, Tom. You’re still playing that computer game. You must stop now, because it’s half past eleven. If you don’t go to bed soon, you’ll be very tired tomorrow. ” said Mrs. White.
“But I’ve nea rly won the game. ” Tom said to Mrs. White. She could see the excitement on his face. She sat down beside him.
“You’re always playing on the computer. You spend more time on this machine than on your homework. ”
Today more and more families have computers. Parents hope computers can help their children improve their study at school. But many of their children use computers to play games and watch videos instead of studying. We often see that computer net bars are crowded with people, especially young boys. They spend a lot of money competing(竞争) with the computerized (用计算机控制的) machines. The more they lose, the more they want to win. The result is that they don’t want to work or study.
In some countries, even scientists hate computers. They say computers cause millions of people to lose their jobs or cause them a lot of trouble. Computer game addiction(瘾) is a serious problem in social(社会的) life. Something should have to be done to solve the problem.
( )1.How did Mrs. White feel when she saw her son playing late?
A. She felt excited.
B. She felt happy.
C. She felt worried. . ( )2.Parents hope computers can _____.
A. help their children improve their study at school
B. help their children play well
C. help their children know a lot of Internet knowledge
( )3.Many children use computers to _____.
A. watch videos
B. listen to songs
C..A and B
( )4.The writer thinks _____.
A. the boys can go to the computer net bars, but the girls can’t
B. the computer net bars are very useful
C. the children spend too much money on computer games
D. the children should play computer games
( )5.Why do some scientists hate computers?
A. They think computers cause millions of people to lose their jobs.
B. They think computers cause them a lot of trouble.
C. Both A and B.
五．综合填空（10分）
People have 1________(居住) on the earth for only about 2 million years. But the human beings have changed the 2_________ ['pl?n?t] in many ways. For example, we have done many bad things to 3 p the earth. One hu ndred years ago, people 4__________ [?n'vent?d]cars so that they can go anywhere 5 (容易地) in a short time. Soon there are more and more people 6_________(驾驶) cars. And the 7________ has become much more heavier. Cars have polluted the
air. And many people in cities are in bad 8_________[ helθ ]. Can we stop people from driving cars? Of course not. We should do something 9 u_______ to make the pollution less and less. Let’s try our best to 10 p the earth, it’s our home.
1.__________
2.___________
3.____________
4.____________
5._____________
6.__________
7.___________
8.____________
9.____________ 10.____________
六，写作训练。（5分）
请根据以下提示，写一篇70字左右的文章。（电话的发明）
1 What: the telephone
2 Who: Bell
3 When: in 1876
4 Where: in the USA
5 funtion(功能)：talk to each other easily
2017 2018上海市上海中学高一上学期周练英语试题
上海中学2017-2018学年第学期高一英语试题 Choice 21.The impact__________ high technology draws worldwide attention. A.on 22.________________,the more expansive gestures you should employ when you deliver a speech. A.The more audience there is B.The more the audience are C.As much audience as there is D.The larger the audience is 23.John is really an independent boy and he tries his best to settle every problem_______. A.of his own his own C,for his own his own 24.The queen,__________ an old woman, made a poisonous apple and came to the cottage to tempt Snow White to eat it. A,dressed in was dressing like like had clothes on as 25.It is reported that __________schools in the west of China are improving their study environment. A.a great many of large number of B..a great amount of large number of you really mean_________a basketball player? Do you know that training to be a basketball player means_____________at least eight hours every day? ,practicing be,practicing be,to practice ,to practice the workload of a _________job alongside a course of study can be difficult, so there is an increasing tendency for people to give up work and go back to school. 28. I couldn't resist having another piece of cake ____________I was supposed to be on a diet and lose weight. if 29. Your children will not follow your advice to ____________business management as his major if you ___________. up,force him to up,force him on,force him to on,force him 30.The students of class 8____________a farewell party for their retired class teacher
四川省成都市第七中学高一英语4月第3周周练试题(扫描版,无答案)
四川省成都市第七中学2014-2015学年高一英语4月第3周周练试题 （扫描版，无答案） Module 3 The Violence of Nature What Is a Tornado? A tornado is a 1)___________(rotate) column of air from a thunderstorm to the ground. The most 2) _______________ (violence) have winds of more than 400 kilometres 3) _______ hour. Almost all of them occur in the US, in the area from Texas in the southeast to South Dakota in the north. Tornadoes can pick 4) ___________ cars, trains and even houses and put them down in the next street – or even in the next town. They can take the fur 5) __________ the back of a cat and the feathers 6) ___________ a chicken. They can destroy houses, but leave the furniture inside exactly where it was. 7) __________ average, there are 800 tornadoes in the US each year, 8) ___________(cause) about 80 9)__________(die) and 1,500 10) ____________(injured). The worst tornado of all time 11) _____________(occur) in 1925, 12)______________(affect) three US states: Missouri, Illinois and Indiana. By the time it ended, more than 700 people 13) _____________________(kill) and 2,700 had been injured. What Is a Hurricane? Hurricanes are strong tropical storms, and they usually occur in the southern Atlantic Ocean, the Caribbean Sea and the Gulf of Mexico. There are violent winds of 120 kilometres per hour or more, 14) ____________ cause huge waves, heavy rain and floods. There are on average six Atlantic hurricanes each year and they usually affect the east coast of US from Texas to Maine. The worst hurricane disaster of all time occurred 15) ________ the 8th September 1900 in Galveston, Texas. Winds of 200 kilometres per hour and five-metre high waves hit the city. The disaster killed 6,000 people in a population of 37,000 and destroyed 3,600 buildings. An Extraordinary Event This is a story about the 1900 Galveston hurricane. Charles Coghlan was 16)________ nineteenth-century Irish actor 17) ________ went to live in Canada. He then moved to New York, 18) _________________ he became famous. 19)______ the 1890s, he had moved to Galveston, where he died in 1899, a year before the hurricane 20) ________ (strike). The cemetery 19) _____________ Coghlan was buried was destroyed by the hurricane and Cohglan’s coffin ended up in the sea. - 1 -
2018-2019学年上海中学高三上英语期中英语试卷
II.Grammar and Vocabulary Section B Recently,I flew to Las Vegas to attend a meeting.As we were about to arrive,the pilot announced with apology that there would be a slight delay before setting down.High desert winds had forced the airport to close all but one runway.He said that we would be circling the city for a few minutes waiting to land.We were also told to remain in our seats meanwhile with our seat belts(21)________(fasten) because there might be a few bumps.Well,that few minutes turned into about forty-five minutes, including a ride that would make a roller coaster(22)________(pale)by comparison. The movement was so sudden(23)________several passengers felt sick and had to use airsickness bags.(24)________you might guess,that’s not good thing to happen in a narrow space because it only serves to increase the discomfort of the situation. About twenty minutes into the adventure,the entire airplane became very quiet.There was now a sense of anxiety and fear that could be distinctly noticed.Every passenger simply held on for dear life… (25)________one.A baby was having a good time!With each bump of the aircraft,he(26)________let out a giggle of happiness.As I observed this,I realized that he didn’t know he was supposed to be afraid and worried about his safety.He(27)________thought about the past nor about the future.Those are (28)________we grown-ups have learned from experience.He was enjoying the ride because he (29)________(not teach)to fear it.(30)________(understand)this,I took a deep breath and sat back into my seat,pretending I was really on a roller coaster.I smiled for the rest of the flight.I even managed to giggle once or twice,which is much to the chagrin of the man sitting next to me holding the airsickness bag. C Section People become quite illogical when they try to decide what can be eaten and what cannot be eaten.If you lived in the Mediterranean,for instance,you would consider octopus a great__31__.You would not be able to understand why some people find it repulsive.On the other hand,your stomach would__32__ at the idea of frying potatoes in animal fat---the__33__accepted practice in many northern countries.The sad truth is that most of us have been brought up to eat certain foods and we__34__to them all our lives. No creature has received more praise and abuse than the common garden snail.Cooked in wine, snails are a great luxury in various parts of the world.There are countless people who,ever since their early years,have learned to__35__snails with food.My friend,Robert,lives in a country where snails are despised.As his flat is in a large town,he has no garden of his own.For years he has been asking me to collect snails from my garden and take them to him.The idea never appealed to me very much,but one day,after a heavy__36__,I happened to be walking in my garden when I noticed a huge number of snails taking a stroll on some of my__37__plants.Acting on a sudden impulse,I collected several dozen,put them in a paper bag,and took them to Robert.Robert was delighted to see me and__38__pleased with my little gift.I left the bag in the hall and Robert and I went into the living room where we talked for a couple of hours.I had forgotten all about the snails when Robert suddenly said that I must stay to dinner. 第1页/共8页
上海中学高一周练10(2019.12)
上海中学高一周练数学试卷10 2019.12 一. 填空题 1. 函数2lg(23)y x x =--的定义域为 ，单调递减区间为 2. 函数2413x x y -+-=的单调递增区间为 ，值域为 3. 若函数1()21 x f x a =+ -是奇函数，则a 的值为 4. 若lg lg 2x y +=，则1100x y +的最小值为 5. 若log 2a x =，log 3b x =，log 4c x =，则log abc x 的值为 6. 已知幂函数2()(57)m f x m m x =-+是R 上的增函数，则m 的值为 7. 若关于x 的方程3 23()25x a a +=-有负根，则实数a 的取值范围为 8. 已知偶函数()f x 是以2为周期的周期函数，且当(0,1)x ∈时，()21x f x =-，则 2(log 10)f 的值为 9. 已知13()1 x f x x -=+，函数()y g x =的图像与1(1)y f x -=+的图像关于直线y x =对称， 则(3)g 的值为 10. 已知0x >，定义()f x 表示不小于x 的最小整数，若1(3())(6)31x f x f x f +=+ +，则 正数x 的取值范围为 11. 对于函数1()42x x f x m +=-?，若存在实数0x ，使得00()()f x f x -=-成立，则实数m 的取值范围为 12. 设函数()f x =a ∈R ，e 为自然对数的底数），若曲线221x y +=上存在00(,)x y 使得00(())f f y y =，则a 的取值范围为 二. 选择题 13. 函数|24|()x f x a -=（0a >且1a ≠），满足1(1)9 f =，则()f x 的单调递减区间为（ ） A. (,2]-∞ B. [2,)+∞ C. [2,)-+∞ D. (,2]-∞- 14. 奇函数()y f x =的反函数为函数1()y f x -=，函数1()y f x -=在[0,)+∞上是减函数， 则函数()y f x =-在(,0)-∞上为（ ） A. 增函数 B. 减函数 C. 非单调函数 D. 不能确定
高中英语上学期第7周周练题(无答案)
四川省宜宾市一中2018-2019学年高中英语上学期第7周周练题第一部分阅读理解（共两节，满分40分） 第一节（共7小题；每小题2分，满分14分） 阅读下列短文，从每题所给的四个选项（A、B、C和D）中，选出最佳选项，并在答题卡上将该项涂黑。 A Every one of us has been hurt by others – either by their words or actions. In those moments, you may feel so much anger that you want to hurt the other person too. But we all know that revenge(报复) doesn’t get us anywhere. So, in order to live a happy life, the best way to deal with the problem is, perhaps, as the old saying goes, to “forgive and forget”. The wisdom of this saying has even been proven in scientific studies. “It is well established that learning to forgive others can have positive benefits for one’s physical and mental Health,”Saima Noreen, a scientist at the University of St Andrews, Uk, told the Huffington Post. And now, Noreen and her research team may have found one more reason that you should stick to this principle – forgiving somebody who has hurt you makes it easier for you to forget the unhappy memory, according to their new study. In the study, researchers asked volunteers to read descriptions of 40 different situations that contained bad actions such as stealing, lying and cheating.
上海市名校数学真题之上海中学高一周练1(2017.3)
上海中学高一周练数学卷 2017.3.2 一. 填空题 1. 若角α的终边过点(12,35)-，则s i n α= ；cos α= ； tan α= ； cot α= ；sec α= ；csc α= ； 2. 已知20tan 21 α=，且α是第三象限角，则sin α= ；cos α= ； cot α= ；sec α= ；csc α= ； 3. 角度制与弧度制互化：大小为105?的角的弧度数是 ；大小为3?的角的弧度数是 ；弧度数为20 π的角，其大小用角度制表示是 ； 4. 在一个半径为2的圆中，两条半径将圆周分成一段劣弧和一段优弧，其中劣弧长为2，则 劣弧所在的扇形与优弧所在的扇形的面积之比为 5. 若sin |cos ||sin |cos αααα=，则α的取值范围是 6. 已知02απ≤<，(cos 4,sin 4)--是角α终边上的一点，则α = 7. 已知集合{|,}3m A m Z παα==∈，集合{|,}4 n B n Z πββ==∈，则A B = 8. 已知sin cos αα-=，(0,)απ∈，则tan α= 9. 在下列四个命题中，正确命题的序号是 ① 若α角与β角的终边关于原点对称，则sin sin 0αβ+=，cos cos 0αβ+=； ② 若α角与β角的终边关于x 轴对称，则sin sin 0αβ+=，cos cos 0αβ+=； ③ 若α角与β角的终边关于y 轴对称，则sin sin 0αβ+=，cos cos 0αβ+=； ④ 若cos cos αβ=且sin sin αβ=，则α角与β角的终边相同； 10. 化简：sin(31)tan(747)cos(684)tan(27)cos(36)sin(329) αααααα??????++-=++- 11. 已知AB 是平面Γ内一条长度为2的线段，集合{|M M ψ=∈Γ且至少存在一个半径 为2的圆，使得M 、A 、B 中的每一点，都是或者在此圆内，或者在此圆周上}，则ψ中 的点形成的平面区域的面积为 二. 选择题 1. 记cos(100)k ?=，那么tan 80?=（ ） A. B. C. D.
上海市七宝中学2016届高三考前模拟英语试题(一) Word版含答案
2016高三英语模拟考试 II. Grammar and Vocabulary Section A Directions:After reading the passages below, fill in the blanks to make the passages coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank. (A) Once just a science fiction idea, VR has now become more accessible than ever. (25) _________ (wear) a pair of VR goggles connected to your computer and you can experience a lot of things without stepping out of the room. From climbing (26) _________ (high) mountain in the world to flying a spacecraft, the things you can experience with VR are limitless. This new 'reality ' is starting to takeover China. The Report on Chinese VR Users' Behavior was released on March 18 during the 12th TFC Global Mobile Game Conference & Intelligent Entertainment Expo held in Beijing. The report is based on a survey of 5,626 people, (27) _________ (age) between 15 and 39, from across the country. It shows that up to 68.5 percent of people have heard of or are interested in VR products. But surprisingly, it isn't new technology that has made VR so popular. 'VR has been (28) _________ for many years, but it will stick this time because there's enough computer power and the price will just keep going down,' Todd Richmond, a VR group member with the Institute of Electrical and Electronic Engineers in the US, told USA Today. VR (29) _________ (expect) to change various different fields. For example, VR could be used to train pilots and miners before they had to actually risk their lives in highly dangerous working environments, or to treat patients with acrophobia(恐高症）by making them think they were standing on top of a high building. 'If you have perfect virtual reality, (30) _________ you'll be able to simulate everything that a human can experience or imagine experiencing,it's hard to imagine where you go from there,' Palmer Luckey, 23 inventor of the Oculus VR goggles, told NPR. But the technology is still far from perfect. Users report experiencing motion sickness, headaches and other discomfort while wearing VR goggles. Also, (31) _________ more and more tools are flooding the market, the software that runs VR games and simulators has yet to catch up with all the new advancements. It could take (32) _________ while for VR to be widely accepted. When every new technology is first introduced, the technology (33) _________ is the driving force. But for it to really blend into people's lives, meeting basic and practical needs should be the main aim. (B) It has become the talk of the town: A stranger allegedly attacked a woman in a Beijing hotel at night on April 3. The man is said to have clutched her by the neck and attempted to drag her into the elevator. Lodgers passed by, but no one tried to intervene until one woman did. Her actions are believed to (34) _________ (save) the victim from whatever was going to happen to her. The incident has pushed the risks of solo traveling into the spotlight. Online forums like Sina Weibo (35) _________ (flood) with advice for how women (36) _________ protect themselves
高一英语周练一
高一英语周练(一) Ⅰ. 单项填空(共15小题；每小题1分) 1. He asked me to read an article ______ the history of France ______ an American writer. A.about; from B. on; by C. from; by D. for; with 2. Like other Disney parks, Shanghai Disneyland will______ several “lands”, each offering different experiences. A. make up B. be made up of C. consist D. be consisted of 3. He had seen the film before. That is ______ he did not see it last night. A. what B. that C. why D. because 4. It is said that he is ______ a translation of a French novel. A. occupying in B. occupying with C. occupied in D. occupied with 5. It is said that the first electronic computers ______ in 1958. https://www.360docs.net/doc/121947246.html,e into being B. came into sight C. come into use D. came into existenc 6. Rising sea levels and drought caused by global warming could ______ large migrations (移民). A. led to B. lie in C. result in D. result from 7. A large quantity of pigs and chickens______ on their farm, which ______ extra income. A.are raised; means B. is raised; means C. are raised; is meant D. is raised; is meant 8. Although ______ to say this, I must still cancel my dinner appointment with you this evening. A. to embarrass B. to be embarrassed C. embarrassing D. embarrassed 9. — I’m sorry. I ______ at you the other day. — Forget it. I was a bit out of control myself. A. ought not to shout B. ought not to have shouted C. mustn’t shout D. mustn’t have shouted 10. The system has been designed to give students quick and easy ______ to the digital resources of the library A. passage B. access C. way D. approach 11. If it is ______ to you, I will visit you next Tuesday. A. convenient B. fit C. easy D. comfortable 12. ______ efforts with confidence will make a full man. A. Concerning B. Occupying C. Contributing D. Combining 13. — Could you find an answer to your problem in the book I gave you? — I looked at it, but it wasn’t really ______. A. much used B. much using C. of useful D. of much use 14. Jenny nearly missed the flight ______ doing too much shopping. A. in front of B. in need of C. as a result of D. as a result 15. In many ways I agree ______ his statement. A. with B. of C. about D. on
2019届上海市各高中名校高三英语题型分类专题汇编--阅读理解B篇--老师版(带答案已校对珍藏版)
III. Reading Comprehension Section B Directions: Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read. B Kettlebells do not hurt people. People do. A kettlebell will get your respect – the easy way or the hard way. Here is the easy way. 1. Get a medical clearance. Get clearance, especially from an orthopedist and a cardiologist. The latter is no joking matter, since kettlebell training can be extremely intense. 2. Always be aware of your surroundings. Find a training area with a non-slippery surface on which you are not afraid to drop a kettlebell. The area must be clear of objects you might trip over – including other kettlebells – or that you might hit with a kettlebell. There should be no people or animals in a radius where you could injure them. 3. Train barefoot or wear shoes with a flat, thin sole and room for the toes to spread. Training barefoot is superior for health and performance reasons. If you must wear shoes, wear Converse Chuck Taylors, Vibram Five Fingers, or similar shoes that have thin soles and do not pinch the toes together. You have sensory receptors on the bottoms of your feet that make you stronger and improve balance and coordination. Wearing traditional shoes diminishes the ability of these receptors to work properly, and therefore inhibits performance and can increase the risk of injury. Go native. 4. Never contest for space with a kettlebell. Do not try to save a rep that has gone wrong. Guide the kettlebell to fall harmlessly, and move out of the way if necessary. And remember, quick feet are happy feet. 5. Practice all safety measures at all times. Respect every kettlebell, even the lightest one. Always use perfect form picking up and setting down a kettlebell. The set is not over until the bell is safely parked.
上海名校数学周周爽：上海中学高一下学期数学周周练9
上海中学高一数学周练卷 一. 填空题 1. 已知实数0a <与G ，G ，依次成等 比数列，则G = 2. 项数为k 的数列{}n a 的各项不是0就是1，而且此数列既不是只有0，也不是只有1，所 有的0相连且所有的1相连，这样的数列有 个 3. 数列{}n a 满足11a =，且11n n a a n +-=+（*n N ∈），则数列1{}n a 的前n 项和为 4. 已知数列{}n a 对任意的*n N ∈都有21n n n a a a ++=-，而11a =，23a =，则数列{}n a 的 前n 项和n S 能取得的最大值为 5. 将一条长度为1的线段三等分，抹去中间的一段，以此作为第一次操作，将第一次操作后留下的两条线段的每一条都三等分，并各自将中间的一段抹去，以此作为第二次操作，此后的每次操作都按上述方式进行，如果这样的操作进行了八次，则剩余的所有线段的长度和 为 6. 制作如图所示的一个“3步”的楼梯用了18根牙签， 如果要做成一个“10步”楼梯，还需要增加的牙签的 根数是 7. 算式9291 2(2(22(2(2(2(2(21)1)1)1)1)1)1)1)1????????+++++++++个个的值是 8. 若三角形的三边长是公差为1的等差数列，最大角是最小角的两倍，则最小角的余弦值为 9. 已知数列{}n a 和{}n b 的通项公式分别为2n a n =和2n n b =，数列{}n a 的前m 项构成集合A ，数列{}n b 的前k 项构成集合B ，且m k a b =，任取x A B ∈，则用k 表示x A B ∈的 概率为 10. 已知实数x 使得1sin a x =，2cos a x =，3tan a x =的数列{}n a 为等比数列，若 1cos n a x =+，则n = 11. 如图，互不相同的点12,,,,n A A A ??????和12,,,,n B B B ?????? 分别在角O 的两条边上，所有n n A B 相互平行，且所有梯形 11n n n n A B B A ++的面积均相等，设n n OA a =，若11a =， 22a =，则数列{}n a 的通项公式是n a = 12. 在自然数数列中，保留前4个数，划去1个数，保留5个数，划去2个数，保留6个数，