宁夏高考卷
2020年宁夏高考英语试卷(新课标Ⅱ)及解析
2020年宁夏高考英语试卷（新课标Ⅱ）及解析第二部分：阅读理解（共两节）第一节（共4题，满分30分）阅读下面短文，从每题所给的A、B、C和D四个选项中，选出最佳选项．)1. The Lake District Attractions GuideDalemain Mansion & Historic GardensHistory, Culture & Landscape（景观）．Discover and enjoy 4 centuries of history, 5 acresof celebrated and award﹣winning gardens with parkland walk．Owned by the Hasell family since 1679, home to the International Marmalade Festival．Gifts and antiques, plant sales, museums & Mediaeval Hall Tearoom．Open: 29 Mar﹣29 Oct, Sun to Thurs．Tearoom, Gardens & Gift Shop: 10.30﹣ 17.00（16.00 in Oct）．House: 11.15﹣ 16.00（15.00 in Oct）．Town: Pooley Bridge & PenrithAbbot Hall Art Gallery & MuseumThose viewing the quality of Abbot Hall's temporary exhibitions may be forgiven for thinking they are in a city gallery．The impressive permanent collection includes Turnersand Romneys and the temporary exhibition programme has Canaletto and the artists from St Ives．Open: Mon to Sat and Summer Sundays．10.30﹣17.00 Summer．10.30﹣16.00 Winter． Town: KendalTullie House Museum & Art GalleryDiscover, explore and enjoy award﹣winning Tullie House, where historiccollections, contemporary art and family fun are brought together in one impressive museum and art gallery．There are four fantastic galleries to visit from fine art to interactive fun, so there's something for everyone!Open: High Season 1 Apr﹣31 Oct: Mon to Sat 10.00﹣17.00, Sun 11.00﹣ 17.00．Low Season 1 Nov﹣31 Mar: Mon to Sat 10.00﹣16.30, Sun 12.00﹣ 16.30．Town: CarlisleDove Cottage & The Wordsworth MuseumDiscover William Wordsworth's inspirational home．Take a tour of his Lakelandcottage, walk through his hillside garden and explore the riches of the collection in the Museum．Visit the shop and relax in the café．Exhibitions, events and family activities throughout the year．Open: Daily, 09.30﹣17.30（last admission 17.00）．Town: Grasmere（1）When is the House at Dalemain Mansion & Historic Gardens open on Sundays in July？________A.09.30﹣17.30．B.10.30﹣16.00．C.11.15﹣16.00．D.12.00﹣16.30．．（2）What can visitors do at Abbot Hall Art Gallery & Museum？________A.Enjoy Romney's works．B.Have some interactive fun．C.Attend a famous festival．D.Learn the history of a family．．（3）Where should visitors go if they want to explore Wordsworth's life？________A.Penrith．B.Kendal．C.Carlisle．D.Grasmere．2. Some parents will buy any high﹣tech toy if they think it will help their child, but researchers said puzzles help children with math﹣related skills．Psychologist Susan Levine, an expert on mathematics development in young children at the University of Chicago, found children who play with puzzles between ages 2 and 4 later develop better spatial skills．Puzzle play was found to be a significant predictor of cognition （认知）after controlling for differences in parents' income, education and the amount of parent talk, Levine said．The researchers analyzed video recordings of 53 child﹣parent pairs during everyday activities at home and found children who play with puzzles between 26 and 46 months of age have better spatial skills when assessed at 54 months of age．"The children who played with puzzles performed better than those who did not, on tasks that assessed their ability to rotate（旋转）and translate shapes, " Levine said in a statement．The parents were asked to interact with their children as they normally would, and about half of the children in the study played with puzzles at one time．Higher﹣income parents tended to have children play with puzzles more frequently, and both boys and girls who played with puzzles had better spatial skills．However, boys tended to play with more complex puzzles than girls, and the parents of boys provided more spatial language and were more active during puzzle play than the parents of girls．The findings were published in the journal Developmental Science．（1）In which aspect do children benefit from puzzle play？________A.Building confidence．B.Developing spatial skills．C.Learning self﹣control．D.Gaining high﹣tech knowledge．．（2）What did Levine take into consideration when designing her experiment？________A.Parents' age．B.Children's imagination．C.Parents' education．D.Child﹣parent relationship．．（3）How do boys differ from girls in puzzle play？________A.They play with puzzles more often．B.They tend to talk less during the game．C.They prefer to use more spatial language．D.They are likely to play with tougher puzzles．．（4）What is the text mainly about？________A.A mathematical method．B.A scientific study．C.A woman psychologist．D.A teaching program．3. When you were trying to figure out what to buy for the environmentalist on your holiday list, fur probably didn't cross your mind．But some ecologists and fashion（时装）enthusiasts are trying to bring back the market for fur made from nutria（海狸鼠）．Unusual fashion shows in New Orleans and Brooklyn have showcased nutria fur made into clothes in different styles．"It sounds crazy to talk about guilt﹣free fur ﹣unless you understand that the nutria are destroying vast wetlands every year, " says CreeMcCree, project director of Righteous Fur．Scientists in Louisiana were so concerned that they decided to pay hunters $5 a tail．Some of the fur ends up in the fashion shows like the one in Brooklyn last month．Nutria were brought there from Argentina by fur farmers and let go into the wild．"The ecosystem down there can't handle this non﹣native species（物种）．It's destroying the environment．It's them or us, " says Michael Massimi, an expert in this field．The fur trade kept nutria in check for decades, but when the market for nutria ________ in the late 1980s, the cat﹣sized animals multiplied like crazy．Biologist Edmond Mouton runs the nutria control program for Louisiana．He says it's not easy to convince people that nutria fur is green, but he has no doubt about it．Hunters bring in more than 300, 000 nutria tails a year, so part of Mouton's job these days is trying to promote fur．Then there's Righteous Fur and its unusual fashions．Model Paige Morgan says, "To give people a guilt﹣free option that they can wear without someone throwing paint on them ﹣I think that's going to be a massive thing, at least here in New York．" Designer Jennifer Anderson admits it took her a while to come around to the opinion that using nutria fur for her creations is morally acceptable．She's trying to come up with a label to attach to nutria fashions to show it is eco﹣friendly．（1）What is the purpose of the fashion shows in New Orleans and Brooklyn？________A. To promote guilt﹣free fur．B. To expand the fashion market．C. To introduce a new brand．D. To celebrate a winter holiday．．（2）Why are scientists concerned about nutria？________A. Nutria damage the ecosystem seriously．B. Nutria are an endangered species．C. Nutria hurt local cat﹣sized animals．D. Nutria are illegally hunted．．（3）What does the underlined word "collapsed" in paragraph 5 probably mean？________A. Boomed．B. Became mature．C. Remained stable．D. Crashed．．（4）What can we infer about wearing fur in New York according to Morgan？________A. It's formal．B. It's risky．C. It's harmful．D. It's traditional．4. I have a special place in my heart for libraries．I have for as long as I can remember．I was always an enthusiastic reader, sometimes reading up to three books a day as a child．Stories were like air to me and while other kids played ball or went to parties, I lived out adventures through the books I checked out from the library．My first job was working at the Ukiah Library when I was 16 years old． It was a dream job and I did everything from shelving books to reading to the children for story time．As I grew older and became a mother, the library took on a new place and ________ in my life． I had several children and books were our main source （来源） of entertainment． It was a big deal for us to load up and go to the local library, where my kids could pick out books to read or books they wanted me to read to them．I always read, using different voices, as though I were acting out the stories with my voice and they loved it! It was a special time to bond with my children and it filled them with the wonderment of books．Now, I see my children taking their children to the library and I love that the excitement of going to the library lives on from generation to generation．As a novelist, I've found a new relationship with libraries． I encourage readers to go to their local library when they can't afford to purchase a book． I see libraries as a safe haven （避风港）for readers and writers, a bridge that helps put together a reader with a book． Libraries, in their own way, help fight book piracy （盗版行为）and I think all writers should support libraries in a significant way when they can． Encourage readers to use the library． Share library announcements on your social media． Frequent them and talk about them when you can．（1）Which word best describes the author's relationship with books as a child？________ A. Cooperative． B. Uneasy． C. Inseparable． D. Casual．．（2）What does the underlined phrase "an added meaning" in paragraph 3 refer to？________A. Pleasure from working in the library．B. Joy of reading passed on in the family．C. Wonderment from acting out the stories．D. A closer bond developed with the readers．．（3）What does the author call on other writers to do？________A. Sponsor book fairs．B. Write for social media．C. Support libraries．D. Purchase her novels．．（4）Which can be a suitable title for the text？________A. Reading： A Source of KnowledgeB. My Idea about WritingC. Library： A Haven for the YoungD. My Love of the Library．第二节（满分10分）根据短文内容，从短文后的选项中选出能填入空白处的最佳选项．选项中有两项为多余选项．)5.Emoji （表情符号） and Workplace CommunicationIn Asia， messaging platforms are growing rapidly， with users in the hundreds of millions，both at work and play．（1）_______． It's been reported that 76 percent of employees in some western countries are using emojis at work．Written communications can often read as cold and dull． Using emojis can add humor and feeling， keeping intention clear．（2）_______， encouraging better and more frequent communication．In any given office， employees can range from age 22 to 70 and beyond， and finding common ground in communication style can be a challenge．（3）_______．While the younger generations prefer to communicate visually， for those used to working with traditional tools like email， it may feel like a learning curve （曲线）．The good news isthat it's simple to learn and can be worth the effort．There is also the matter of tone （语气）． Who hasn't received an email so annoying that it ruined an entire day？（4）_______．Emoji can help communication feel friendlier， and even a serious note can be softened with an encouraging smile．（5）_______，and emoji can contribute directly to that positive outcome． And when your employees begin adding smiling emojis to their business communication， you'll know you have succeeded in improving your work culture．A． Messages with emojis feel more conversationalB． Even a formal email can seem cold and unfriendlyC． Sending smiling faces to colleagues may seem strangeD． The popularity of these platforms is spreading globallyE． Giving employees the tools enables them to communicate honestlyF． Studies show that friendlier communication leads to a happier workplaceG． An easy way to bring all work generations together is with a chat platform第三部分英语知识运用（共两节）第一节完形填空（每小题1.5分，满分30分）阅读下面短文，从短文后各题所给的A、B、C和D四个选项中，选出可以填入空白处的最佳选项．)6. It was just after sunrise on a June morning．"Nicolo, " whose real name cannot be（1）_______to the public because of Italy's privacy laws, （2）_______working the whole nightat a factory in Turin． As he often did, he stopped by the "after work auction （拍卖）"（3）_______by the Italian police where things（4）_______on the trains were sold to the highest bidder． There, among many other things, Nicolo spotted two paintings he thought would look（5）_______above his dining room table． Nicolo and another bidder（6）_______until Nicolo finally won the paintings for ﹩32．When Nicolo retired and went to live in Sicily, he（7）_______the paintings withhim． He hung them above the same table he had（8）_______from Turin． His son, age 15, who had（9）_______an art appreciation class, thought that there was something（10）_______about the one with a young girl sitting on a garden chair． It was signed （签名）"Bonnato" or so he thought, but when he（11）_______it, he only found "Bonnard, " a French（12）_______he had never heard of．He bought a book and was（13）_______to find a picture of the artist Pierre Bonnard sitting on the same chair in the same（14）_______as his father's painting．"That's the garden in our picture, " Nicolo's son told his father． They（15）_______learned that the painting they（16）_______was called "The Girl with Two Chairs．" They（17）_______the other painting and learned that it was（18）_______Paul Gauguin's "Still Life of Fruit on a Table with a Small Dog．" The（19）_______called the Italian Culture Ministry; the official confirmed that the paintings were （20）_______and worth as much as ﹩50 million．（1）A.attachedB.allocatedC.exposedD.submitted（2）A.finishedB.delayedC.consideredD.tried（3）A.attendedB.reservedC.cancelledD.run（4）A.shownB.foundC.keptD.hidden（5）A.niceB.familiarefulD.real（6）A.battledB.debatedC.discussedD.bargained（7）A.heldB.leftC.registeredD.brought（8）A.chosenB.receivedC.orderedD.moved（9）A.missedB.failedC.takenD.led（10）A.concreteB.unusualC.unappealingD.natural（11）A.appreciatedB.touchedC.researchedD.witnessed（12）A.painterB.designerC.authorD.actor（13）A.expectedB.surprisedC.anxiousD.ready（14）A.roomB.kitchenC.hallD.garden（15）A.apparentlyB.confidentlyC.eventuallyD.temporarily（16）A.ownedB.borrowedC.soldD.stole（17）A.collectedB.cleanedC.framedD.studied（18）A.suitablyB.actuallyC.rightlyD.specifically（19）A.girlB.artistC.familyD.police（20）A.copiesB.originalsC.modelsD.presents第二节（每小题1.5分，满分15分）阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式．)7.Decorating with Plants， Fruits and Flowers for Chinese New YearChinese New Year is a （1）________（celebrate） marking the end of the winter season and the beginning of spring．This is why decorating with plants， fruits and flowers（2）________（carry） special significance．They represent the earth （3）________（come）back to life and best wishes for new beginnings．These are some of the most popular in many parts of the country：Oranges：Orange trees are more（4）________ decoration；they are a symbol of good fortune and wealth．They make great gifts and you see them many times（5）________（decorate） with red envelopes and messages of good fortune．Bamboo：Chinese love their "Lucky Bamboo" plants and you will see them often in their homes and offices．（6）________（certain） during the holiday period，this plant is a must．Bamboo plants are associated （7）________ health， abundance and a happy home．They are easy（8）________ （care） for and make great presents．Branches of Plum Blossoms （梅花）：The（9）________ （beauty） long branches covered with pink﹣colored buds （蓓蕾） make fantastic decorations．The plum trees are （10）________ first to flower even as the snow is melting （融化）．They represent the promise of spring and a renewal of life．第四部分写作（共两节）第一节短文改错（满分10分）)8. 假定英语课上老师要求同桌之间交换修改作文，请你修改你同桌写的以下信件内容．文中共有10处语言错误，每句中最多有两处．每处错误仅涉及一个单词的增加、删除或修改．增加：在缺词处加一个漏字符号（∧），并在其下面写出该加的词．删除：把多余的词用斜线（\）划掉．修改：在错的词下划一横线，并在该词下面写出修改后的词．注意： 1．每处错误及其修改均仅限一词；2．只允许修改10处，多者（从第11处起）不计分．Thank you for your letter，what really made me happy．I'm glad to know that you've comeChina to learn kung fu in a school in my hometown．I'm surely you'll have a good time．Actually， I start to learn kung fu when I was seven years old， for I have long been out of practice．Luckily，I will go home in two weeks for summer vacations．Then I can spare some time to learn it again，such that we can practice together on every day．Best of luck with yours learning kung fu in China．See you sooner．第二节书面表达（满分25分）)9. 上周末，你和同学参加了一次采摘活动．请你为班级英语角写一篇短文，介绍这次活动，内容包括：1．农场情况；2．采摘过程；3．个人感受．注意：1．词数100左右；2．题目已为你写好．题目：My Weekend参考答案与试题解析2020年宁夏高考英语试卷（新课标Ⅱ）第二部分：阅读理解（共两节）第一节（共4题，满分30分）阅读下面短文，从每题所给的A、B、C和D四个选项中，选出最佳选项．1.【答案】CAD2.【答案】BCDB3.【答案】AADB4.【答案】CBCD第二节（满分10分）根据短文内容，从短文后的选项中选出能填入空白处的最佳选项．选项中有两项为多余选项．5.【答案】D,A,G,B,F第三部分英语知识运用（共两节）第一节完形填空（每小题1.5分，满分30分）阅读下面短文，从短文后各题所给的A、B、C和D四个选项中，选出可以填入空白处的最佳选项．6.【答案】CADBAADDCBCABDCADBCB第二节（每小题1.5分，满分15分）阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式．7.【答案】celebration,carries,coming,than,decorated,Certainly,with,to care,beautiful,the第四部分写作（共两节）第一节短文改错（满分10分）8.【答案】Thank you for your letter，what really made me happy．I'm glad to know that you've come ∧China to learn kung fu in a school in my hometown．I'm surely you'll have a good time．Actually， I start to learn kung fu when I was seven years old，for I have long been out of practice．Luckily，I will go home in two weeks for summer vacations．Then I can spare some time to learn it again，such that we can practice together on every day．Best of luck with yours learning kung fu in China．See you sooner．详1．what改为which．考查定语从句．句意：谢谢你的来信，这真的让我很高兴．此处是非限制性定语从句，不能用what连接，关系词指代前面句子在从句中作主语，应用关系代词which，故将what改为which．2．China前加to．考查介词．句意：得知你来中国在我家乡的一所学校学习功夫我很高兴．come是不及物动词，表示"来到某地"时需加介词to，故在China前加to．3．surely改为sure．考查形容词．句意：我相信你一定会玩得很开心．此处应用形容词sure作表语，I'm sure （that）"我相信"，故将surely改为sure．4．start改为started．考查动词时态．句意：实际上，我七岁时就开始学功夫了，但是我已经很久没有练习了．根据时间状语when I was seven years old，主句谓语动词应用一般过去时，故将start改为started．5．for改为but/yet．考查连词．句意：实际上，我七岁时就开始学功夫了，但是我已经很久没有练习了．前后句之间表达转折关系，而不是因果关系，应用连词but或yet 连接，故将for改为but/yet．6．vacations改为vacation．考查名词的数．句意：幸运的是，两周后我将回家过暑假．vacation"假期"，指的是整个的放假时间．所以一般用单数形式，故将vacations改为vacation．7．such改为so．考查状语从句．句意：然后我可以抽出时间再学一次，这样我们就可以每天一起练习了．so that"以便"，引导目的状语从句，故将such改为so．8．去掉on．考查介词．句意：名词day前面有every修饰，不需要加介词，故去掉on．9．yours改为your．考查人称代词．句意：yours是名词性物主代词，相当于"your+名词"，而此处修饰动名词短语learning kung fu，应用形容词性物主代词，故将yours改为your．10．sooner改为soon．考查副词．句意：期待很快与您见面．sooner是soon 的比较级，而本句没有比较的对象，只表达"期待很快与您见面"之意，应用原级soon，故将sooner改为soon．第二节书面表达（满分25分）9.【答案】My WeekendLast weekend，I， together with my classmates took part in picking up fruits．（活动）The farm where we went is located in the west of our city．【高分句型一】 There are many fruits growing there， ranging from apples to peaches． We went there by bus．（农场情况）While working there， some of us climbed onto the trees with ladders and picked up the fruits． Others sorted the fruits and put them in the box． Tired as we were， we felt happy to help the farmers．【高分句型二】（采摘过程）Through this experience， I learn the importance of labour and determine to invent some useful machines to help the farmers． What a meaningful activity．（个人感受）。
2024年高考数学试卷(文)(全国甲卷)(含答案)
绝密★启用前2024年普通高等学校招生全国统一考试全国甲卷文科数学使用范围：陕西、宁夏、青海、内蒙古、四川注意事项：1．答题前，务必将自己的姓名、考籍号填写在答题卡规定的位置上．2．答选择题时，必须使用2B 铅笔将答题卡上对应题目的答案标号涂黑．如需改动，用橡皮擦擦干净后，再选涂其它答案标号．3．答非选择题时，必须使用0.5毫米黑色签字笔，将答案书写在答题卡规定的位置上．4．所有题目必须在答题卡上作答，在试题卷上答题无效．5．考试结束后，只将答题卡交回．一、选择题：本题共12小题，每小题5分，共60分．在每小题给出的四个选项中，只有一项是符合题目要求的．1. 集合{}1,2,3,4,5,9A =，{}1B x x A =+Î，则A B =I （ ）A. {}1,2,3,4B. {}1,2,3 C. {}3,4 D. {}1,2,9【答案】A 【解析】【分析】根据集合B 的定义先算出具体含有的元素，然后根据交集的定义计算.【详解】依题意得，对于集合B 中的元素x ，满足11,2,3,4,5,9x +=，则x 可能的取值为0,1,2,3,4,8，即{0,1,2,3,4,8}B =，于是{1,2,3,4}A B Ç=.故选：A2. 设z =，则z z ×=（ ）A. -iB. 1C. -1D. 2【答案】D 【解析】【分析】先根据共轭复数的定义写出z ，然后根据复数的乘法计算.【详解】依题意得，z =，故22i 2zz =-=.故选：D3. 若实数,x y 满足约束条件43302202690x y x y x y --³ìï--£íï+-£î，则5z x y =-最小值为（ ）A. 5B.12C. 2-D. 72-【答案】D 【解析】【分析】画出可行域后，利用z 的几何意义计算即可得.【详解】实数,x y 满足43302202690x y x y x y --³ìï--£íï+-£î，作出可行域如图：由5z x y =-可得1155y x z =-，即z 的几何意义为1155y x z =-的截距的15-，则该直线截距取最大值时，z 有最小值，此时直线1155y x z =-过点A ，联立43302690x y x y --=ìí+-=î，解得321x y ì=ïíï=î，即3,12A æöç÷èø，则min 375122z =-´=-.故选：D.4. 等差数列{}n a 的前n 项和为n S ，若91S =，37a a +=（ ）A. 2- B.73C. 1D.29【答案】D 【解析】的【分析】可以根据等差数列的基本量，即将题目条件全转化成1a 和d 来处理，亦可用等差数列的性质进行处理，或者特殊值法处理.【详解】方法一：利用等差数列的基本量由91S =，根据等差数列的求和公式，911989193612S a d a d ´=+=Û+=，又371111222628(936)99a a a d a d a d a d +=+++=+=+=.故选：D方法二：利用等差数列的性质根据等差数列的性质，1937a a a a +=+，由91S =，根据等差数列的求和公式，193799()9()122a a a a S ++===，故3729a a +=.故选：D方法三：特殊值法不妨取等差数列公差0d =，则9111199S a a ==Þ=，则371229a a a +==.故选：D5. 甲、乙、丙、丁四人排成一列，丙不在排头，且甲或乙在排尾的概率是（ ）A.14B.13C.12D.23【答案】B 【解析】【分析】分类讨论甲乙的位置，得到符合条件的情况，然后根据古典概型计算公式进行求解.【详解】当甲排在排尾，乙排第一位，丙有2种排法，丁就1种，共2种；当甲排在排尾，乙排第二位或第三位，丙有1种排法，丁就1种，共2种；于是甲排在排尾共4种方法，同理乙排在排尾共4种方法，于是共8种排法符合题意；基本事件总数显然是44A 24=，根据古典概型的计算公式，丙不在排头，甲或乙在排尾的概率为81243=.故选：B6. 已知双曲线2222:1(0,0)y x C a b a b-=>>的上、下焦点分别为()()120,4,0,4F F -，点()6,4P -在该双曲线上，则该双曲线的离心率为（ ）A. 4B. 3C. 2D.【答案】C 【解析】【分析】由焦点坐标可得焦距2c ，结合双曲线定义计算可得2a ，即可得离心率.【详解】由题意，()10,4F -、()20,4F 、()6,4P -，则1228F F c ==，110PF ==，26PF ==，则1221064a PF PF =-=-=，则28224c e a ===.故选：C.7. 曲线()631f x x x =+-在()0,1-处的切线与坐标轴围成的面积为（ ）A.16B.C.12D. 【答案】A 【解析】【分析】先求出切线方程，再求出切线的截距，从而可求面积.【详解】()563f x x =¢+，所以()03f ¢=，故切线方程为3(0)131y x x =--=-，故切线的横截距为13，纵截距为1-，故切线与坐标轴围成的面积为1111236´´=故选：A.8. 函数()()2e esin xxf x x x -=-+-在区间[ 2.8,2.8]-的大致图像为（）A. B.C. D.【答案】B 【解析】【分析】利用函数的奇偶性可排除A 、C ，代入1x =可得()10f >，可排除D.【详解】()()()()()22ee sin e e sin xx x x f x x x x x f x ---=-+--=-+-=，又函数定义域为[]2.8,2.8-，故该函数为偶函数，可排除A 、C ，又()11πe 11111e sin11e sin 10e e 622e 42ef æöæö=-+->-+-=-->->ç÷ç÷èøèø，故可排除D.故选：B.9. 已知cos cos sin a a a =-πtan 4a æö+=ç÷èø（ ）A. 1+B. 1- C.D. 1【答案】B 【解析】【分析】先将cos cos sin aa -a弦化切求得tan a ，再根据两角和的正切公式即可求解.【详解】因为cos cos sin aa a=-，所以11tan =-a ，tan 1Þa =，所以tan 1tan 11tan 4a +p æö==a +ç÷-aèø，故选：B .原10题略10. 设a b 、是两个平面，m n 、是两条直线，且m a b =I .下列四个命题：①若//m n ，则//n a 或//n b ②若m n ^，则,n n a b^^③若//n a ，且//n b ，则//m n ④若n 与a 和b 所成的角相等，则m n^其中所有真命题的编号是（ ）A. ①③ B. ②④C. ①②③D. ①③④【答案】A【解析】【分析】根据线面平行的判定定理即可判断①；举反例即可判断②④；根据线面平行的性质即可判断③.【详解】对①，当n Ìa ，因为//m n ，m b Ì，则//n b ，当n b Ì，因为//m n ，m a Ì，则//n a ，当n 既不在a 也不在b 内，因为//m n ，,m m a b ÌÌ，则//n a 且//n b ，故①正确；对②，若m n ^，则n 与,a b 不一定垂直，故②错误；对③，过直线n 分别作两平面与,a b 分别相交于直线s 和直线t ，因为//n a ，过直线n 的平面与平面a 的交线为直线s ，则根据线面平行的性质定理知//n s ，同理可得//n t ，则//s t ，因为s Ë平面b ，t Ì平面b ，则//s 平面b ，因为s Ì平面a ，m a b =I ，则//s m ，又因为//n s ，则//m n ，故③正确；对④，若,m n a b Ç=与a 和b 所成的角相等，如果//,//a b n n ，则//m n ，故④错误；综上只有①③正确，故选：A.11. 在ABC V 中内角,,A B C 所对边分别为,,a b c ，若π3B =，294b ac =，则sin sin A C +=（ ）A.32B.C.D.【答案】C 【解析】【分析】利用正弦定理得1sin sin 3A C =，再利用余弦定理有22134a c ac +=，再利用正弦定理得到22sin sin A C +的值，最后代入计算即可.【详解】因为29,34B b ac p==，则由正弦定理得241sin sin sin 93A CB ==.由余弦定理可得:22294b ac ac ac =+-=，即:22134a c ac +=，根据正弦定理得221313sin sin sin sin 412A C A C +==，所以2227(sin sin )sin sin 2sin sin 4A C A C A C +=++=，因为,A C 为三角形内角，则sin sin 0A C +>，则sin sin A C +=.故选：C.二、填空题：本题共4小题，每小题5分，共20分．原13题略12. 函数()sin f x x x =在[]0,π上的最大值是______．【答案】2【解析】【分析】结合辅助角公式化简成正弦型函数，再求给定区间最值即可.【详解】()πsin 2sin 3f x x x x æö==-ç÷èø，当[]0,πx Î时，ππ2π,333x éù-Î-êúëû，当ππ32x -=时，即5π6x =时，()max 2f x =.故答案为：213. 已知1a >，8115log log 42a a -=-，则=a ______．【答案】64【解析】【分析】将8log ,log 4a a 利用换底公式转化成2log a 来表示即可求解.【详解】由题28211315log log log 4log 22a a a a -=-=-，整理得()2225log 60log a a --=，2log 1a Þ=-或2log 6a =，又1a >，所以622log 6log 2a ==，故6264a ==故答案：64.为14. 曲线33y x x =-与()21y x a =--+在()0,¥+上有两个不同的交点，则a 的取值范围为______．【答案】()2,1-【解析】【分析】将函数转化为方程，令()2331x x x a -=--+，分离参数a ，构造新函数()3251,g x x x x =+-+结合导数求得()g x 单调区间，画出大致图形数形结合即可求解.【详解】令()2331x x x a -=--+，即3251a x x x =+-+，令()()32510,g x x x x x =+-+>则()()()2325351g x x x x x =+-=+-¢，令()()00g x x ¢=>得1x =，当()0,1x Î时，()0g x ¢<，()g x 单调递减，当()1,x ¥Î+时，()0g x ¢>，()g x 单调递增，()()01,12g g ==-，因为曲线33y x x =-与()21y x a =--+在()0,¥+上有两个不同的交点，所以等价于y a =与()g x 有两个交点，所以()2,1a Î-.故答案为：()2,1-三、解答题：共70分．解答应写出文字说明，证明过程或演算步骤．第17题第21题为必考题，每个考题考生必须作答．第22、23题为选考题，考生根据要求作答．（一）必考题：共60分．15. 已知等比数列{}n a 的前n 项和为n S ，且1233n n S a +=-.（1）求{}n a 的通项公式；（2）求数列{}n S 通项公式.【答案】（1）153n n a -æö=ç÷èø的（2）353232næö-ç÷èø【解析】【分析】（1）利用退位法可求公比，再求出首项后可求通项；（2）利用等比数列的求和公式可求n S .【小问1详解】因为1233n n S a +=-,故1233n n S a -=-，所以()12332n n n a a a n +=-³即153n n a a +=故等比数列的公比为53q =，故1211523333533a a a a =-=´-=-，故11a =，故153n n a -æö=ç÷èø.【小问2详解】由等比数列求和公式得5113353523213n nn S éùæö´-êúç÷èøêúæöëû==-ç÷èø-.16. 如图，在以A ，B ，C ，D ，E ，F 为顶点的五面体中，四边形ABCD 与四边形ADEF 均为等腰梯形，//,//BC AD EF AD ，4,2AD AB BC EF ====，ED FB ==M 为AD 的中点.（1）证明：//BM 平面CDE ；（2）求点M 到ABF 的距离.【答案】（1）证明见详解； （2【解析】【分析】（1）结合已知易证四边形BCDM 为平行四边形，可证//BM CD，进而得证；（2）作FO AD ^，连接OB ，易证,,OB OD OF 三垂直，结合等体积法M ABF F ABM V V --=即可求解.【小问1详解】因为//,2,4,BC AD BC AD M ==为AD 的中点，所以//,BC MD BC MD =，四边形BCDM 为平行四边形，所以//BM CD ，又因BM Ë平面CDE ，CD Ì平面CDE ，所以//BM 平面CDE ；【小问2详解】如图所示，作BO AD ^交AD 于O ，连接OF ，因为四边形ABCD 为等腰梯形，//,4,BC AD AD =2AB BC ==，所以2CD =，结合（1）BCDM 为平行四边形，可得2BM CD ==，又2AM =，所以ABM V 为等边三角形，O 为AM中点，所以OB =，又因为四边形ADEF 为等腰梯形，M 为AD 中点，所以,//EF MD EF MD =，四边形EFMD 为平行四边形，FM ED AF ==，所以AFM △为等腰三角形，ABM V 与AFM △底边上中点O 重合，OF AM ^，3OF ==，因为222OB OF BF +=，所以OB OF ^，所以,,OB OD OF 互相垂直，由等体积法可得M ABF F ABM V V --=，2112333F ABM ABM V S FO -=×=×=△，222cos 2FA AB FBFAB FAB FA AB+-Ð===Ð=×11sin 222FAB S FA AB FAB =××Ð==△，设点M 到FAB的距离为d ，则1133M FAB F ABM FAB V V S d d --==××==△解得d =M 到ABF .为17. 已知函数()()1ln 1f x a x x =--+．（1）求()f x 的单调区间；（2）若2a £时，证明：当1x >时，()1ex f x -<恒成立．【答案】（1）见解析（2）见解析【解析】【分析】（1）求导，含参分类讨论得出导函数的符号，从而得出原函数的单调性；（2）先根据题设条件将问题可转化成证明当1x >时，1e 21ln 0x x x --++>即可.【小问1详解】()f x 定义域为(0,)+¥，11()ax f x a x x¢-=-=当0a £时，1()0ax f x x -¢=<，故()f x 在(0,)+¥上单调递减；当0a >时，1,x a ¥æöÎ+ç÷èø时，()0f x ¢>，()f x 单调递增，当10,x a æöÎç÷èø时，()0f x ¢<，()f x 单调递减.综上所述，当0a £时，()f x 在(0,)+¥上单调递减；0a >时，()f x 在1,a ¥æö+ç÷èø上单调递增，在10,a æöç÷èø上单调递减.【小问2详解】2a £，且1x >时，111e ()e (1)ln 1e 21ln x x x f x a x x x x ----=--+-³-++，令1()e 21ln (1)x g x x x x -=-++>，下证()0g x >即可.11()e 2x g x x -¢=-+，再令()()h x g x ¢=，则121()e x h x x-¢=-，显然()h x ¢在(1,)+¥上递增，则0()(1)e 10h x h ¢¢>=-=，即()()g x h x =¢在(1,)+¥上递增，故0()(1)e 210g x g ¢¢>=-+=，即()g x 在(1,)+¥上单调递增，故0()(1)e 21ln10g x g >=-++=，问题得证18. 设椭圆2222:1(0)x y C a b a b+=>>的右焦点为F ，点31,2M æöç÷èø在C 上，且MF x ^轴．（1）求C 的方程；（2）过点()4,0P 的直线与C 交于,A B 两点，N 为线段FP 的中点，直线NB 交直线MF 于点Q ，证明：AQ y ^轴．【答案】（1）22143x y += （2）证明见解析【解析】【分析】（1）设(),0F c ，根据M 的坐标及MF ^x 轴可求基本量，故可求椭圆方程.（2）设:(4)AB y k x =-，()11,A x y ，()22,B x y ，联立直线方程和椭圆方程，用,A B 的坐标表示1Q y y -，结合韦达定理化简前者可得10Q y y -=，故可证AQ y ^轴.【小问1详解】设(),0F c ，由题设有1c =且232b a =，故2132a a -=，故2a =，故b =，故椭圆方程为22143x y +=.【小问2详解】直线AB 的斜率必定存在，设:(4)AB y k x =-，()11,A x y ，()22,B x y ，由223412(4)x y y k x ì+=í=-î可得()2222343264120k x k x k +-+-=，故()()422Δ102443464120k k k =-+->，故1122k -<<，又22121222326412,3434k k x x x x k k-+==++，而5,02N æöç÷èø，故直线225:522y BN y x x æö=-ç÷èø-，故22223325252Q y y y x x --==--，所以()1222112225332525Q y x y y y y y x x ´-+-=+=--()()()12224253425k x x k x x -´-+-=-()222212122264123225825834342525k k x x x x k k k k x x -´-´+-++++==--2222212824160243234025k k k k k x --+++==-，故1Q y y =，即AQ y ^轴.（1）设直线方程，设交点坐标为()()1122,,,x y x y ；（2）联立直线与圆锥曲线的方程，得到关于x （或y ）的一元二次方程，注意D 的判断；（3）列出韦达定理；（4）将所求问题或题中的关系转化为12x x +、12x x （或12y y +、12y y ）的形式；（5）代入韦达定理求解.（二）选考题：共10分．请考生在第22、23题中任选一题作答，并用2B 铅笔将所选题号涂黑，多涂、错涂、漏涂均不给分，如果多做，则按所做的第一题计分．19. 在平面直角坐标系xOy 中，以坐标原点O 为极点，x 轴的正半轴为极轴建立极坐标系，曲线C 的极坐标方程为cos 1r r q =+.（1）写出C 的直角坐标方程；（2）设直线l ：x t y t a=ìí=+î（t 为参数），若C 与l 相交于A B 、两点，若2AB =，求a 的值.【答案】（1）221y x =+（2）34a =【解析】【分析】（1）根据cos xr r q ìï=í=ïî可得C 的直角方程.（2）将直线的新的参数方程代入C 的直角方程，法1：结合参数s 的几何意义可得关于a 的方程，从而可求参数a 的值；法2：将直线的直角方程与曲线的直角方程联立，结合弦长公式可求a 的值.【小问1详解】由cos 1r r q =+，将cos xr r q ìï=í=ïîcos 1r r q =+，1x =+，两边平方后可得曲线直角坐标方程为221y x =+.【小问2详解】对于直线l 的参数方程消去参数t ，得直线的普通方程为y x a =+.法1：直线l 的斜率为1故直线的参数方程可设为x y ì=ïïíïïî，s ÎR .将其代入221y x =+中得()221)210s a s a +-+-=设,A B 两点对应的参数分别为12,s s ，则)()212121,21s s a s s a +=--=-，且()()22Δ818116160a a a =---=->，故1a <，12AB s s\=-=2==，解得34a =.法2：联立221y x a y x =+ìí=+î，得22(22)10x a x a +-+-=，()22Δ(22)41880a a a =---=-+>，解得1a <，的设()()1122,,,A x y B x y ,2121222,1x x a x x a \+=-=-，则AB ==2=，解得34a =20. 实数,ab 满足3a b +³．（1）证明：2222a b a b +>+；（2）证明：22226a b b a -+-³．【答案】（1）证明见解析（2）证明见解析【解析】【分析】（1）直接利用22222()a b a b +³+即可证明.（2）根据绝对值不等式并结合（1）中结论即可证明.【小问1详解】因为()()2222222022a b a ab b a b b a -+=--++=³，当a b =时等号成立，则22222()a b a b +³+，因为3a b +³，所以22222()a b a b a b +³+>+;【小问2详解】222222222222()a b b a a b b a a b a b -+-³-+-=+-+22222()()()()(1)326a b a b a b a b a b a b =+-+³+-+=++-³´=。
宁夏银川市(新版)2024高考数学人教版能力评测(提分卷)完整试卷
宁夏银川市（新版）2024高考数学人教版能力评测(提分卷)完整试卷一、单选题：本题共8小题，每小题5分，共40分 (共8题)第(1)题2024年某校举行一场射箭比赛，甲乙等8人各射中的环数分别为:9环，4环，6环，5环，7环，10环，8环，9环.则这8个人的成绩的上四分位数是（）A．8环B．9环C．7环D．6环第(2)题已知集合，，则（）A．B．C．D．第(3)题如图，分别取与x轴，y轴正方向相同的两个单位向量作为基底，若，，则向量的坐标为（）A．B．C．D．第(4)题在中，为边的中点，，则（）A．B．C．D．第(5)题为了普及环保知识，增强环保意识，某大学随机抽取30名学生参加环保知识测试，得分如图所示，假设得分值的中位数为，众数为，平均值为，则（ ）A．B．C．D．第(6)题将3个1和3个0随机排成一行，则3个0都不相邻的概率是（）A．B．C．D．第(7)题过点作直线，使它与抛物线仅有一个公共点，这样的直线有（）A．1条B．2条C．3条D．4条第(8)题一个四棱台的三视图如图所示，其中正视图和侧视图均为上底长为4，下底长为2，腰长为的等腰梯形，则该四棱台的体积为（）A．B．C．28D．二、多选题：本题共3小题，每小题6分，共18分 (共3题)第(1)题下列函数中最小值为6的是（）A．B．C．D．第(2)题已知复数满足，且复数对应的点在第一象限，则下列结论正确的是（）A．复数的虚部为B．C．D．复数的共轭复数为第(3)题设，向量，向量，则（）A．必不互为平行向量B．必不互为垂直向量C．存在，使D．对任意三、填空题：本题共3小题，每小题5分，共15分 (共3题)第(1)题若体积为的正三棱锥的所有顶点都在同一个球面上，则该球体积的最小值为______．第(2)题已知函数（定义域为D，值域为A）有反函数，则方程有解，且的充要条件是满足______________．第(3)题已知实数满足，则的最大值为___________.四、解答题：本题共5小题，每小题15分，最后一题17分，共77分 (共5题)第(1)题已知数列的前n项和为，，且数列为等差数列．(1)求数列的通项公式；(2)定义：表示不超过x的最大整数．设，求数列的前114项和．第(2)题已知各项均为正数的数列的前n项和为，，且对任意n，恒成立.（1）求证：数列是等差数列，并求数列的通项公式；（2）设，已知，，(2＜i＜j)成等差数列，求正整数i，j.第(3)题如图，已知抛物线，其焦点为，其准线与轴交于点，以为直径的圆交抛物线于点，连接并延长交抛物线于点，且．(1)求的方程．(2)过点作轴的垂线与抛物线在第一象限交于点，若抛物线上存在点，，使得．求证：直线过定点．第(4)题如图，在多面体中，已知，，均为等边三角形，平面平面ABC，平面平面ABC，H为AB的中点．(1)判断DE与平面ABC的位置关系，并加以证明；(2)求直线DH与平面ACE所成角的正弦值．第(5)题如图所示，圆台的上､下底面圆半径分别为和为圆台的两条不同的母线.分别为圆台的上､下底面圆的圆心，且为等边三角形.(1)求证：；(2)截面与下底面所成的夹角大小为，求异面直线与所成角的余弦值.。
2024年高考语文试卷(全国甲卷)(含答案)
使用地区：四川、宁夏、内蒙古、青海、陕西 本试卷满分 150 分，考试时间 150 分钟。
一、现代文阅读（36 分） （一）论述类文本阅读（本题共 3 小题，9 分）
阅读下面的文字，完成下面小题。 2019 年 4 月 23 日，习近平主席在会见应邀出席中国人民解放军海军成立 70 周年多国海军活动的外方 代表团团长时指出： “海洋对于人类社会生存和发展具有重要意义。海洋孕育了生命、联通了世界、促进 了发展。我们人类居住的这个蓝色星球，不是被海洋分割成了各个孤岛，而是被海洋连 结成了命运共同 体，各国人民安危与共。 ”作为“人类命运共同体 ”的重要组成部分，海洋命运共同体的建设目标是打造 一个持久和平、普遍安全、共同繁荣、开放包容、清洁美丽的海洋环境。 要实现海洋的持久和平与普遍安全，各国必须摒弃传统的大国争霸思路，充分照顾彼此 的安全关切和 合理利益，联合起来打击海盗、人口走私、贩毒等海上犯罪行为，在涉及海洋权益争端时通过友 好协商的 方式来解决问题，短期内无法协商的问题可以考虑搁置争议。共同繁荣、开放包容和清洁美丽的 愿景意味 着，我们要坚持开放的自由贸易体系，同时共同应对气候变化、海洋环境保护等问题，发挥海洋 作为国际 贸易大通道的积极作用，关注发展中国家的发展诉求。随着人类技术水平的提升和各国经济发展对资源需 求的日益增加，各国都希望开发利用更多的海洋资源。如何才能在更好地利用海洋 资源的同时又促进可持 续发展、构建海洋命运共同体？习近平总书记提出海洋发展的“四个转变 ”：“要提高海洋资源开发能 力，着力推动海洋经济向质量效益型转变 ”；“要保护海洋生态环境，着力推动海洋开发方式向循环利用 型转变 ”；“要发展海洋科学技术，着力推动海洋科技向创新引领型转变 ”；“要维护国家海洋权益，着力 推动海洋维权向统筹兼顾型转变 ”。这为海洋开发利用指明了方向。 具体到全球、地区和双边层面，构建海洋命运共同体应该着眼于不同的路径，这样才更具有可行性。 在全球层面，构建海洋命运共同体主要着眼于涉海全球公共问题的治理，各国应致力于构建 更加公正 合理、稳定有效的国际法和国际规则体系。目前，发达国家和发展中国家在海洋资源的开发利用 方面仍然 存在矛盾。发达国家过于强调公海自由原则，希望利用技术上的优势开发更多的公海资源。发展 中国家更 多强调公海作为人类共同财产的原则。如果公海被确定为人类共同财产，那么它就不得被占有， 所有国家 共同参加公海管理，积极分享公海开发中获取的利益，并保障公海只用于和平目的。人类共同财 产原则更 有利于保护公海环境和对海洋资源的可持续开发利用，对于实现持久和平与共同繁荣的愿景来 说更为可 行。总的来说，全球层面的海洋命运共同体构建，应着眼于建立更加有效的合作制度体系。
1983年宁夏卷高考语文阅读真题解析
1983年宁夏卷高考语文阅读真题解析1983年，宁夏卷的语文高考阅读题给了考生们一些挑战性的内容。
本文将对该年卷上的阅读材料进行解析，帮助读者更好地理解和应对这些问题。
第一篇阅读材料是一篇关于战国时期名将孙膑的短文。
短文主要描述了他的智勇和军事才能。
通过细节描写和事例，作者生动地展示了孙膑在军事战略和战术上的杰出表现。
阅读完这篇材料后，考生应该能理解孙膑的军事才能，并能回答相关问题，如他在哪些战役中发挥了重要作用等。
第二篇阅读材料是一篇关于宁夏地理特点的描述。
短文主要介绍了宁夏地处内陆，地势较高，气候干燥，土地肥沃等特点。
通过对这些特点的描述，读者可以了解到宁夏的地理环境对当地农业和居民生活的影响。
考生需要在阅读过程中注意提取出相关信息，以便回答后续的问题，如宁夏的主要农作物是什么等。
第三篇阅读材料是一首古诗。
这首诗描述了大漠孤烟直，长河落日圆的景象，表达了作者对大自然壮丽景色的赞美之情。
考生需要通过仔细阅读，理解诗意，并注意诗中所使用的修辞手法和意象，以回答相关问题，如诗中表达的主题是什么等。
通过以上的解析，我们可以看出，1983年宁夏卷的语文高考阅读题主要涵盖了历史人物、地理特点以及文学作品等题材。
考生需要在阅读过程中注重理解和把握细节，以便准确回答问题。
同时，考生还应该对历史和文学有一定的基础知识和理解能力，以便更好地理解和分析材料。
总之，1983年宁夏卷高考语文阅读真题涉及了多个领域的内容，包括历史、地理和文学。
通过仔细阅读和理解材料，考生可以更好地应对这些问题，并找到正确答案。
对于考生来说，掌握基础知识和分析能力至关重要，只有这样才能在高考中取得好成绩。
祝愿所有考生都能以积极的态度备考，并取得优异的成绩！。
2007-2012年宁夏高考数学(理科)试卷及答案1
2007-2012年宁夏高考理科数学试卷及答案2007年（宁夏卷）数学（理科）试卷一、选择题：本大题共12小题，每小题5分，在每小题给出的四个选项中，只有一项是符合题目要求的。
1．已知命题:p x ∀∈R ，sin x ≤1，则（ ）A ．:p x ⌝∃∈R ，sin x ≥1B ．:p x ⌝∀∈R ，sin x ≥1C ．:p x ⌝∃∈R ，sin x >1D ．:p x ⌝∀∈R ，sin x >12．已知平面向量a =（1，1），b （1，－1），则向量1322-=a b （ ）A ．（－2，－1）B ．（－2，1）C ．（－1，0）D ．（－1，2）3．函数πsin 23y x ⎛⎫=- ⎪⎝⎭在区间ππ2⎡⎤-⎢⎥⎣⎦，的简图是（ ）4．已知{a n }是等差数列，a 10=10，其前10项和S 10=70，则其公差d =（ ）A ．23- B ．13- C ．13D ．235．如果执行右面的程序框图，那么输出的S=（ ）A ．2450B ．2500C ．2550D ．26526．已知抛物线22(0)y px p =>的焦点为F ，点P 1（x 1，y 1），P 2（x 2，y 2），P 3（x 3，y 3）在抛物线上，且2x 2=x 1+x 3， 则有（ ）A ．123FP FP FP +=B ．222123FP FP FP += C ．2132FP FP FP =+ D ．2213FP FP FP =·7．已知x >0，y >0，x ，a ，b ，y 成等差数列，x ，c ，d ，y 成等比数列，则2()a b cd+的最小值是（ ） A ．0 B ．1 C ．2 D ．48．已知某个几何体的三视图如下，根据图中标出的尺寸（单位：cm ），可得这个几何体的体积是（ ）A ．34000cm 3B ．38000cm 3C ．2000cm 3D ．4000cm 3 9．若cos 22π2sin 4αα=-⎛⎫- ⎪⎝⎭，则cos sin αα+的值为（ ） A ．72-B ．12-C ．12D ．72 10．曲线12e x y =在点（4，e 2）处的切线与坐标轴所围三角形的面积为（ ）A ．29e 2B ．4e 2C ．2e 2D ．e 211．甲、乙、丙三名射箭运动员在某次测试中各射箭20次，三人的测试成绩如下表s 1，s 2，s 3分别表示甲、乙、丙三名运动员这次测试成绩的标准差，则有（ ）A ．s 3>s 1>s 2B ．s 2>s 1>s 3C ．s 1>s 2>s 3D ．s 2>s 3>s 112．一个四棱锥和一个三棱锥恰好可以拼接成一个三棱柱，这个四棱锥的底面为正方形，且底面边长与各侧棱长相等，这个三棱锥的底面边长与各侧棱长也都相等。
2009年宁夏高考语文试卷
2009年宁夏高考语文试卷（1）下列对传记有关内容的分析和概括，最恰当的两项是（5分）A．陶行知全力推进城市平民教育运动，当这一运动在全国二十多个省市形成热潮的时候，他开始转向思考改造乡村教育的问题了。
B．陶行知游栖霞山时遇到张大哥，发现他对学习《平民千字课本》，几个月就能写信、记账、读报感情趣，更坚定了陶行知从事乡村教育的决心。
C．陶行知希望从师乡村教育的人都要有一颗“农民甘苦化”的心，把心献给农民，把城里人本来认为是苦的地方变为意想不到的乐趣。
D．操震球写信给陶行知，认为最急迫最重要的是提高农民的文化水平，促进农业生产，二者须同时并进，而不是急于创建乡村师范学校。
E．本文运用平实自然的语言，娓娓道来的生动叙述，讲述陶行知从事乡村教育的感人事迹，为我们再现一个平民教育家的光辉形象。
（2）陶行知由推行城市平民教育转向改造乡村教育，原因是什么？请简要分析。
（6分）（3）在给操震球的回信中，陶行知是怎样描述乡村教育“个中甘苦”的？请简要概括。
（6分）（4）文中说：“陶行知不仅是一位富于想象的浪漫主义理想家，而且是一位脚踏实地、一步一个脚印的实干家。
”（5）这句话给你什么样的启示？请结合全文，谈谈你感受最深的一点。
（8分）第Ⅱ卷表达题五、语言文字运用（20分）13.下列各句中，加点的成语使用不恰当的一项是（3分）A．新年联欢宴会在喜气洋洋的乐曲声中拉开帷幕，一时间，觥筹交错，笑语喧哗，欢乐的气氛弥漫了整个宴会大厅。
B．如果一般读者不认为我的这个小册子言不及义，编辑出版工作者又觉得它有可鉴之处，那么我就心满意足了。
C．眼下在某些地区，“走穴”正成为一些学者乐此不疲的事情，因为这既能提高知名度，又可带来不菲的经济收入。
D.日出而作，日入而息，他们就这样日复一日、年复一年地劳作生活在这片广袤的土地上，真有点令人匪夷所思。
14.下列各句中，没有语病的一句是（3分）A．太阳队近来的表现不能令人满意，糟糕的防守问题一直没有改善，比赛连连失利，甚至在与弱旅勇士队比赛时，也饮恨败北。
宁夏2021届高考英语试卷和答案解析
2021年宁夏高考英语试卷AThe Biggest Stadiums in the World People have been pouring into stadiums since the days of ancient Greece. In around 8 A.D.，the Romans built the Colosseum, which remains the world's best known stadium and continues to inform contemporary design.Rome's Colosseum was 157 feet tall and had 80 entrances,seating 50，000 people.However,that was small fry compared with the city's Circus Maximus,which accommodated around 250，000 people.These days,safety regulations-not to mention the modern sports fan's desire for a good view and a comfortable seat-tend to keep stadium capacities（容量）slightly lower.Even soccer fans tend to have a seat each；gone are the days of thousands standing to watch the match.For the biggest stadiums in the world,we have used data supplied by the World Atlas list so far,which ranks them by their stated permanent capacity,as well as updated information from official stadium websites.All these stadiums are still functional,still open and still hosting the biggest events in world sport.• Rungrado 1st of May Stadium,Pyongyang,D.P.R.Korea.Capacity：150，000.Opened：May 1，1989. • Michigan Stadium, Ann Arbor,Michigan, U.S. Capacity：107，601. Opened：October 1，1927. • Beaver Stadium,State College,Pennsylvania,U.S. Capacity：106，572.Opened：September 17，1960. • Ohio Stadium, Columbus, Ohio, U.S. Capacity：104，944. Opened：October 7，1922.• Kyle Field, College Station, Texas, U.S. Capacity：102，512. Opened：September 24，1927.1. How many people could the Circus Maximus hold？______A. 104，944.B. 107，601.C. About 150，000.D. About 250，000.2. Of the following stadiums, which is the oldest？______A. Michigan Stadium.B. Beaver Stadium.C. Ohio Stadium.D. Kyle Field.3. What do the listed stadiums have in common？______A. They host big games.B. They have become tourist attractions.C. They were built by Americans.D. They are favored by architects.BWhen almost everyone has a mobile phone,why are more than half of Australian homes still paying for a landline（座机）？These days you'd be hard pressed to find anyone in Australia over the age of 15 who doesn't own a mobilephone.In fact plenty of younger kids have one in their pocket. Practically everyone can make and receive calls anywhere,anytime.Still,55 percent of Australians have a landline phone at home and only just over a quarter（29%）rely only on their smartphones,according to a survey（调查）. Of those Australians who still have a landline,a third concede that it's not really necessary and they're keeping it as a security blanket - 19 percent say they never use it while a further 13 percent keep it in case of emergencies. I think my home falls into that category. More than half of Australian homes are still choosing to stick with their home phone.Age is naturally a factor （因素）- only 58 percent of Generation Ys still use landlines now and then,compared to 84 percent of Baby Boomers who've perhaps had the same home number for 50 years.Age isn't the only factor；I'd say it's also to do with the makeup of your household.Generation Xers with young families,like my wife and I，can still find it convenient to have a home phone rather than providing a mobile phone for every family member. That said,to be honest the only people who ever ring our home phone are our Baby Boomers parents,to the point where we play a game and guess who is calling before we pick up the phone（using Caller ID would take the fun out of it）.How attached are you to your landline？How long until they go the way of gas street lamps and morning milk deliveries？4. What does paragraph 2 mainly tell us about mobile phones？______A. Their target users.B. Their wide popularity.C. Their major functions.D. Their complex design.5. What does the underlined word "concede" in paragraph 3 mean？______A. Admit.B. Argue.C. Remember.D. Remark.6. What can we say about Baby Boomers？______A. They like smartphone games.B. They enjoy guessing callers' identity.C. They keep using landline phones.D. They are attached to their family.7. What can be inferred about the landline from the last paragraph？______A. It remains a family necessity.B. It will fall out of use some day.C. It may increase daily expenses.D. It is as important as the gas light.CYou've heard that plastic is polluting the oceans-between 4.8 and 12.7 million tonnes enter ocean ecosystems every year.But does one plastic straw or cup really make a difference？Artist Benjamin Von Wong wants you to know that it does.He builds massive sculptures out of plastic garbage,forcing viewersto re-examine their relationship to single-use plastic products.At the beginning of the year,the artist built a piece called "Strawpocalypse," a pair of 10-foot-tall plastic waves,frozen mid-crash. Made of 168，000 plastic straws collected from several volunteer beach cleanups, the sculpture made its first appearance at the Estella Place shopping center in Ho Chi Minh City,Vietnam. Just 9% of global plastic waste is recycled.Plastic straws are by no means the biggest source（来源）of plastic pollution,but they've recently come under fire because most people don't need them to drink with and,because of their small size and weight, they cannot be recycled. Every straw that's part of Von Wong's artwork likely came from a drink that someone used for only a few minutes. Once the drink is gone, the straw will take centuries to disappear.In a piece from 2018，Von Wong wanted to illustrate（说明）a specific statistic：Every 60 seconds,a truckload's worth of plastic enters the ocean. For this work,titled "Truckload of Plastic," Von Wong and a group of volunteers collected more than 10，000 pieces of plastic,which were then tied together to look like they'd been dumped（倾倒）from a truck all at once.Von Wong hopes that his work will also help pressure big companies to reduce their plastic footprint.8. What are Von Wong's artworks intended for？______A. Beautifying the city he lives in.B. Introducing eco-friendly products.C. Drawing public attention to plastic waste.D. Reducing garbage on the beach.9. Why does the author discuss plastic straws in paragraph 3？______A. To show the difficulty of their recycling.B. To explain why they are useful.C. To voice his views on modern art.D. To find a substitute for them.10. What effect would "Truckload of Plastic" have on viewers？______A. Calming.B. Disturbing.C. Refreshing.D. Challenging.11. Which of the following can be the best title for the text？______A. Artists' Opinions on Plastic SafetyB. Media Interest in Contemporary ArtC. Responsibility Demanded of Big CompaniesD. Ocean Plastics Transformed into SculpturesDDuring an interview for one of my books,my interviewer said something I still think about often. Annoyed by the level of distraction（干扰）in his open office,he said,"That's why I have a membership at the coworking space across the street - so I can focus." His comment struck me as strange. After all,coworkingspaces also typically use an open office layout（布局）. But I recently came across a study that shows why his approach works.The researchers examined various levels of noise on participants as they completed tests of creative thinking. They were randomly divided into four groups and exposed to various noise levels in the background,from total silence to 50 decibels（分贝），70 decibels,and 85 decibels. The differences between most of the groups were statistically insignificant；however,the participants in the 70 decibels group - those exposed to a level of noise similar to background chatter in a coffee shop - significantly outperformed the other groups. Since the effects were small,this may suggest that our creative thinking does not differ that much in response to total silence and 85 decibels of background noise.But since the results at 70 decibels were significant,the study also suggests that the right level of background noise - not too loud and not total silence - may actually improve one's creative thinking ability. The right level of background noise may interrupt our normal patterns of thinking just enough to allow our imaginations to wander,without making it impossible to focus. This kind of "distracted focus" appears to be the best state for working on creative tasks.So why do so many of us hate our open offices？The problem may be that,in our offices,we can't stop ourselves from getting drawn into others' conversations while we're trying to focus. Indeed,the researchers found that face-to-face interactions and conversations affect the creative process,and yet a coworking space or a coffee shop provides a certain level of noise while also providing freedom from interruptions.12. Why does the interviewer prefer a coworking space？______A. It helps him concentrate.B. It blocks out background noise.C. It has a pleasant atmosphere.D. It encourages face-to-face interactions.13. Which level of background noise may promote creative thinking ability？______A. Total silence.B. 50 decibels.C. 70 decibels.D. 85 decibels.14. What makes an open office unwelcome to many people？______A. Personal privacy unprotected.B. Limited working space.C. Restrictions on group discussion.D. Constant interruptions.15. What can we infer about the author from the text？______A. He's a news reporter.B. He's an office manager.C. He's a professional designer.D. He's a published writer.According to Jessica Hagy, author of How to Be Interesting, it’s not difficult to make yourself interesting at a dinner party.(1) , if you’re out of your comfort zone or if you’re wandering into somebody’s house for the first time. So the main thing is just to show up and be adventurous, trying different foods and talking to strangers.People love to talk about themselves. If you can start the conversation with a question other than “What do you do for a living?”, you’ll be able to get a lot more interesting conversation out of whomever it is you’re talking to. (2) , it can bring in “I have this old, broken-down vehicle” or “I rode the bus with these crazy people who were laughing at silly jokes in the back.” It just opens up conversation.(3) ? If you can’t take their wine away, you should certainly try to take away their soapbox (讲台). If you’re the host, you can ask them to help you in the kitchen with something and just remove them from the situation. (4) .And what about that other dinner-party killer: awkward silence? If you’re faced with an awkward silence at a dinner party, the only thing that always gets everyone talking again is to give the host a compliment (赞扬). (5) . Just quickly turn around and say, “This cake is extremely delicious and you have to tell me all about it.”So being interesting at a dinner party isn’t that hard.A.How do you know the hostB.The first step is to go exploringC.If you ask the question “How did you get here?”D.Be prepared to have awkward conversations with strangersE.Or turn the conversation into a topic where they have little to sayF.What about that person who had too much to drink or won’t stop talkingG.He or she is the person who is feeling the weight of that awkwardness the most16. A. A B. B C. C D. D E. EF. FG. G17. A. A B. B C. C D. D E. EF. FG. G18. A. A B. B C. C D. D E. EF. FG. G19. A. A B. B C. C D. D E. EF. FG. G20. A. A B. B C. C D. D E. EF. FG. GSimply saying thank you doesn't seem enough in certain situations. I was considering this while working as a（1）______ just a few weeks ago. And it came to me then how much easier is would be if we had a range of words that express different （2）______ of gratitude（感谢）.My thoughts were soon（3）______ . We had a woman patient who was（4）______ from a knee replacement operation. One afternoon,while（5）______ to get into bed she collapsed （倒下）from what was（6）______ discovered to be a heart attack. The collapse was disastrous,（7）______ the emergency medical team and good teamwork. But she recovered,though （8）______ ，and was ready for discharge （出院）after four weeks.She was （9）______ for everything that the medical and nursing team had done for her. On her day of discharge, we shared in her（10）______ at her recovery. As she was（11）______ she was eager to say （12）______ to each of us in the nursing team. When she（13）______ one nurse,she tried to press a five-pound note into her hand. My colleague（14）______ to accept it,saying that we were all just（15）______ our job. The patient looked puzzled,and then（16）______ ："Oh this isn't for the（17）______ I had. I take that as a（18）______ .No, this is for setting my hair yesterday."And there you have it. To many people,（19）______ lives is part of the job but styling hair is an （20）______ and should be rewarded.21. A. cleaner B. chemist C. nurse D. doctor22. A. grades B. meanings C. needs D. expectations23. A. brushed aside B. put to the testC. brought under discussionD. taken into account24. A. departing B. escaping C. retiring D. recovering25. A. attempting B. choosing C. pausing D. promising26. A. eventually B. fortunately C. casually D. secretly27. A. assessing B. requiring C. forming D. proving28. A. slightly B. accidentally C. slowly D. happily29. A. grateful B. thoughtful C. sorrowful D. fearful30. A. surprise B. delight C. curiosity D. disappointment31. A. operating B. thinking C. hesitating D. leaving32. A. sorry B. hello C. goodbye D. yes33. A. reached B. consulted C. introduced D. persuaded34. A. wished B. pretended C. failed D. refused35. A. enjoying B. doing C. securing D. starting36. A. repeated B. recited C. replied D. reported37. A. courage B. patience C. duty D. care38. A. goal B. given C. push D. greeting39. A. risking B. changing C. saving D. building40. A. honour B. ability C. opening D. extra41. Ecotourism is commonly regarded as low impact（影响）travel to undisturbed places. It is different from traditional tourism because it allows the traveler to become （1）______ （educate）about the areas - both in terms of geographical conditions and cultural characteristics, and often provides money for conservation and benefits the（2）______ （develop）of the local areas. Ecotourism has（3）______ （it）origin with the environmental movement of the 1970s. It was not widely accepted as a travel concept（4）______ the late 1980s. During that time,increasing environmental awareness made it desirable.Due to（5）______ growing popularity of environmentally-related and adventure travel,various types （6）______ trips are now being classified as ecotourism. Actually,a true eco-friendly trip must meet the following principles：●Minimize the impact of （7）______ （visit）the place.●Build respect for and awarene ss of the environment and cultural practices.●Provide（8）______ （finance）aid and other benefits for local peoples.●Make sure that the tourism provides positive experiences for both the visitors and the hosts. Komodo National Park,officially recognized in 1980，is popular for ecotourism because of its unique biodiversity.（9）______ （activity）there range from whale watching to hiking（远足）and accommodations aim（10）______ （have）a low impact on the natural environment.(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)42. 假定英语课上老师要求同桌之间交换修改作文，请你修改你同桌写的以下作文。
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2009年普通高等学校招生全国统一考试（宁夏卷）理综综合能力测试（物理部分）二、选择题：本题共8小题，每小题6分，在每小题给出的四个选项中，有的只有一个选项正确，有的有多个选项正确，全部选对的得6分，选对但不全的得3分，有选错的得0分。
14. (09年宁夏)在力学理论建立的过程中，有许多伟大的科学家做出了贡献。
关于科学家和他们的贡献，下列说法正确的是A. 伽利略发现了行星运动的规律B. 卡文迪许通过实验测出了引力常量C ．牛顿最早指出力不是维持物体运动的原因D ．笛卡尔对牛顿第一定律的建立做出了贡献【答案】BD15. (09年宁夏)地球和木星绕太阳运行的轨道都可以看作是圆形的。
已知木星的轨道半径约为地球轨道半径的5.2倍，则木星与地球绕太阳运行的线速度之比约为A. 0.19B. 0.44C. 2.3D. 5.2【答案】B16. (09年宁夏)医生做某些特殊手术时，利用电磁血流计来监测通过动脉的血流速度。
电磁血流计由一对电极a 和b 以及磁极N 和S 构成，磁极间的磁场是均匀的。
使用时，两电极a 、b 均与血管壁接触，两触点的连线、磁场方向和血流速度方向两两垂直，如图所示。
由于血液中的正负离子随血流一起在磁场中运动，电极a 、b 之间会有微小电势差。
在达到平衡时，血管内部的电场可看作是匀强电场，血液中的离子所受的电场力和磁场力的合力为零。
在某次监测中，两触点的距离为3.0mm ，血管壁的厚度可忽略，两触点间的电势差为160µV ，磁感应强度的大小为0.040T 。
则血流速度的近似值和电极a 、b 的正负为A. 1.3m/s ，a 正、b 负B. 2.7m/s ， a 正、b 负C ．1.3m/s ，a 负、b 正 D. 2.7m/s ， a 负、b 正【答案】A17. (09年宁夏)质量为m 的物体静止在光滑水平面上，从t=0时刻开始受到水平力的作用。
力的大小F 与时间t 的关系如图所示，力的方向保持不变，则A ．03t 时刻的瞬时功率为mt F 0205 B ．03t 时刻的瞬时功率为mt F 02015C ．在0=t 到03t 这段时间内，水平力的平均功率为mt F 423020 D. 在0=t 到03t 这段时间内，水平力的平均功率为mt F 625020 【答案】BD18. (09年宁夏)空间有一均匀强电场，在电场中建立如图所示的直角坐标系O-xyz ，M 、N 、P 为电场中的三个点，M 点的坐标(0，a ，0)，N 点的坐标为(a ，0，0)，P 点的坐标为(,,)22a a a 。
已知电场方向平行于直线MN ，M 点电势为0，N 点电势为1V ，则P 点的电势为A. C.14V D.34V【答案】D19 (09年宁夏).如图所示，一导体圆环位于纸面内，O 为圆心。
环内两个圆心角为90°的扇形区域内分别有匀强磁场，两磁场磁感应强度的大小相等，方向相反且均与纸面垂直。
导体杆OM可绕O 转动，M 端通过滑动触点与圆环良好接触。
在圆心和圆环间连有电阻R 。
杆OM 以匀角速度ω逆时针转动，t=0时恰好在图示位置。
规定从a 到b 流经电阻R 的电流方向为正，圆环和导体杆的电阻忽略不计，则杆从t=0开始转动一周的过程中，电流随t ω变化的图象是【答案】C20. (09年宁夏)如图所示，一足够长的木板静止在光滑水平面上，一物块静止在木板上，木板和物块间有摩擦。
现用水平力向右拉木板，当物块相对木板滑动了一段距离但仍有相对运动时，撤掉拉力，此后木板和物块相对于水平面的运动情况为A.物块先向左运动，再向右运动B.物块向右运动，速度逐渐增大，直到做匀速运动C.木板向右运动，速度逐渐变小，直到做匀速运动D.木板和物块的速度都逐渐变小，直到为零【答案】BC21. (09年宁夏)水平地面上有一木箱，木箱与地面之间的动摩擦因数为(01)μμ<<。
现对木箱施加一拉力F ，使木箱做匀速直线运动。
设F 的方向与水平面夹角为θ，如图，在θ从0逐渐增大到90°的过程中，木箱的速度保持不变，则A.F 先减小后增大B.F 一直增大C.F 的功率减小D.F 的功率不变【答案】AC三、非选择题：包括必考题和选考题两部分。
第22题~第32题为必考题，每个小题考生都必须做答。
第33题~第41题为选考题，考生根据要求做答。
（一）必考题（11题，共129分）22.（4分）某同学用游标卡尺测量一圆柱体的长度l ，用螺旋测微器测量该圆柱体的直径d ，示数如图。
由图可读出l = cm , d = mm【答案】2.25 6.86023.(11分) (09年宁夏)青岛奥运会帆船赛场采用风力发电给蓄电池充电，为路灯提供电能。
用光敏电阻作为传感器控制路灯电路的开关，实现自动控制。
光敏电阻的阻值随照射光的强弱而变化，作为简化模型，可以近似认为，照射光较强（如白天）时电阻几乎为0：照射光较弱（如黑天）时电阻接近于无穷大。
利用光敏电阻作为传感器，借助电磁开关，可以实现路灯自动在白天关闭，黑天打开。
电磁开关的内部结构如图所示。
1、2两接线柱之间是励磁线圈，3、4两接线柱分别与弹簧片和触点连接。
当励磁线圈中电流大于50mA时，电磁铁吸合铁片，弹簧片和触点分离，3、4断开；电流小于50mA 时，3、4接通。
励磁线圈中允许通过的最大电流为100mA 。
（1） 利用以下器材设计一个自动控制路灯的电路，画出电路原理图。
光敏电阻1R ，符号 ；灯泡L ，额定功率40W ，额定电压36V ，符号 ；保护电阻2R ，符号；电磁开关，符号蓄电池E ，电压36V ，内阻很小；开关S ，导线若干。
（2） 回答下列问题：①如果励磁线圈的电阻为200Ω，励磁线圈允许加的最大电压为 V ，保护电阻2R 的阻值范围为 Ω。
②在有些应用电磁开关的场合，为了安全，往往需要在电磁铁吸合铁片时，接线柱3、4之间从断开变为接通。
为此，电磁开关内部结构应如何改造？请结合本题中电磁开关内部结构图说明。
答： 。
③任意举出一个其它的电磁铁应用的例子。
答： 。
【答案】（1）电路原理如图所示（2）①20；160～520②把触点从弹簧片右侧移到弹簧片左侧，保证当电磁铁吸合铁片时，3、4之间接通；不吸合时，3、4之间断开③电磁起重机24．（14分）(09年宁夏)冰壶比赛是在水平冰面上进行的体育项目，比赛场地示意如图。
比赛时，运动员从起滑架处推着冰壶出发，在投掷线AB 处放手让冰壶以一定的速度滑出，使冰壶的停止位置尽量靠近圆心O.为使冰壶滑行得更远，运动员可以用毛刷擦冰壶运行前方的冰面，使冰壶与冰面间的动摩擦因数减小。
设冰壶与冰面间的动摩擦因数为1μ=0.008，用毛刷擦冰面后动摩擦因数减少至2μ=0.004.在某次比赛中，运动员使冰壶C 在投掷线中点处以2m/s 的速度沿虚线滑出。
为使冰壶C 能够沿虚线恰好到达圆心O 点，运动员用毛刷擦冰面的长度应为多少？（g 取10m/s 2）【答案】设冰壶在未被毛刷擦过的冰面上滑行的距离为S 1，所受摩擦力的大小为f 1；在被毛刷擦过的冰面上滑行的距离为S 2，所受摩擦力为f 2，则有：S S S =+21 式中S 为投掷线到圆心O 的距离。
又 mg f 11μ= mg f 22μ= R 2设冰壶的初速度为v 0，由功能关系得：20221121mv S f S f =+ 联立以上各式解得：)(22212012μμμ--=g v gS S 代入数据解得S 2＝10m25．(18分) (09年宁夏)如图所示，在第一象限有一均强电场，场强大小为E ，方向与y 轴平行；在x 轴下方有一均强磁场，磁场方向与纸面垂直。
一质量为m 、电荷量为-q(q>0)的粒子以平行于x 轴的速度从y 轴上的P 点处射入电场，在x 轴上的Q 点处进入磁场，并从坐标原点O 离开磁场。
粒子在磁场中的运动轨迹与y 轴交于M 点。
已知OP=l ,l OQ 32=。
不计重力。
求:（1）M 点与坐标原点O 间的距离；（2）粒子从P 点运动到M 点所用的时间。
【答案】（1）带电粒子在电场中做类平抛运动，在y 轴负方向上做初速为零的匀加速运动，设加速度大小为a ；在x 轴正方向上做匀速直线运动，设速度为v 0；粒子从P 点运动到Q 点所用的时间为t 1，进入磁场速度方向与x 轴正方向的夹角为θ，则：ma qE =，21021at y =，100t v x = 其中l x 320=,l y =0. 又有：01tan v at =θ 联立上式解得030=θ因为M 、O 、Q 在圆周上，∠MOQ ＝900，所以MQ 为直径，由图中的几何关系可知： l R 32=，l MO 6=（2）设粒子在磁场中运动的速度为v ，从Q 到M 点运动的时间为t 2，则有：θcos 0v v = vR t π=2 带电粒子自P 点出发到M 点所用的时间t 为 21t t t += 联立以上各式并代入数据解得：qEml t 2)123(+=π (二)选考题：共45分。
33. ［物――――选修2－2］（15分）（1）(09年宁夏)（5分）常见的传动方式有_____________、______________、__________________轮传动等。
齿轮传动的传动比是主动轮与__________的转速之比，传动 比等于___________的齿数之比。
【答案】（1）链传动；带传动；液压传动；从动轮；从动轮和主动轮（2）(09年宁夏)（10分）液压千斤顶是利用密闭容器内的液体能够把液体所受到的压强向各个方向传递的原理制成的。
图为一小型千斤顶的结构示意图。
大活塞A 的直径D 1=20 cm,小活塞B 的直径D 2=5 cm,手柄的长度OC=50 cm,小活塞与手柄的连接点到转轴O 的距离DO=10 cm 。
现用此千斤顶使质量m =4×103 kg 的重物升高了h =10 cm 。
g 取10m/s 2，求（ⅰ）者此千斤顶的效率为80％，在这一过程中人做的功为多少？（ⅱ）若此千斤顶的效率为100％，当重物上升时，人对手柄的作用力【答案】（ⅰ）将重物托起h 需做的功mgh W =1，设人对手柄做的功为W 2，则千斤顶的效率为21W W =η，代入数据可得W 2=5.0×103J. （ⅱ）设大活塞的面积为S 1，小活塞的面积为S 2，作用在小活塞上的压力为F 1，当千金顶的效率为100℅时，有：211S S F mg =，222121D D S S = 当F 1和F 2都与杠杆垂直时，手对杠杆的压力最小。
利用杠杆原理，有：OC F OD F ⋅=⋅1由以上各式解得：F ＝500N34. ［物理――――选修3－3］（15分）（1）(09年宁夏)（5分）带有活塞的气缸内封闭一定量的理想气体。