阅读理解题专题
部编版七年级语文现代文阅读专题训练 试卷【含答案】
部编七年级语文现代文阅读专题训练阅读下面文章，完成1-4题笑靥千秋舒婷(1)记忆中最温柔的笑容莫过于妈嫣然一笑，这就是童年时代的最高奖赏。
仿佛我在普通话比赛中获奖，我在学校歌咏大会的领唱，每周成绩通知单上的“全优”，都是为了获得妈展颜微笑。
(2)妈牙齿细密整齐，只是牙龈偏低，每逢她开怀大笑，就虚握拳头遮羞，像扶着麦克风，那姿势有些可笑，却又令我向往。
因为，当时在我们的生活里，能让妈妈如此忘情的开心事总是鲜于遇见。
(3)这是母亲的笑容，每个亲情笃至的儿女都能在自己母亲的脸上汲取这种光辉。
(4)我在插队时的女伴长相可以说很一般：小眼睛、塌鼻梁，生气时两片嘴唇一堵，活像两扇厚墙门，那几颗雀斑简直要暴出来。
但她有足够的聪明才智，在那样单调的生活中，不仅自己笑声不断，同时让小集体洋溢欢乐的气氛。
(5)我怀念她笑起来的样子：眼睛弯如新月，连乌黑的长眉都有感情，露出一口整齐的皓齿，要多甜有多甜!为这笑容，村村队队有多少小伙子夜间在桥头为她弹吉他。
(6)这是青春无畏的笑容，不知何时，它们已在我们的脸上凋谢。
但我们仍能从周围少男少女们的幸福中一再欣赏这些芬芳的花朵。
(7)我的师傅是位极普通的女工。
善良、勤劳、刚愎和自信混合一起的个性，使她所在的班组烽烟不息。
我成为她的徒弟，不少人为我捏一把汗。
但三年中，我和她相处得很亲密，甚至成了班组的避雷针。
我喜欢她的笑容，常常逗她乐得前仰后合。
她的沧桑的前额舒展开来，疲倦的大眼睛又有了温暖的光彩，拉成长沟的颊上有当年酒窝的影子。
她一定非常美丽过，但乡下跑出来的灰姑娘和拣到她的士兵丈夫，似乎从来不曾意识到。
(8)这种质朴的笑容让人想到野地的花，随时可见，又总被忽略。
它既单纯又丰富，使你联想到劳动的艰巨与欢欣，想到生命的漫长与短暂，想到源与本，想到忘与记之间我们那些无法言喻的模糊冲动、情感的濡湿。
(9)还有一种女政治家的笑容。
女人，又是政治家。
(10)笑容于她们像男政治家当年的中山装当今的西装一样，是必备的披挂。
阅读理解题-2022年中考化学真题分项汇编(全国通用)(第01期)(解析版)
专题25 阅读理解题1．（2022年湖南省衡阳市中考）阅读下面科普短文：2004年，科学家成功地从石墨中分离出单层的石墨片(有人称为石墨烯)，其层内微观结构如图1.这种单层的石墨片有优异的导电、导热性和其他奇特性质。
石墨烯是由碳原子构成的一层或几层原子厚度的晶体，在电子、复合材料、医疗健康等多领域具有广泛应用，不同领域的应用分布如图2纺织领域是石墨烯应用的新兴领域。
纺织面料掺入石墨烯后，在低温情况下，石墨烯可将来自远红外线的热量传送给人体，改善人体微循环系统，促进新陈代谢。
另外，纺织面料中的石墨烯片层结构中含有丰富的含氧基团，影响菌体的正常代谢，从而使菌体无法吸收养分直至死亡。
随着科技水平的提升，石墨烯作为一种基本材料，其应用会有越来越多的可能。
请依据文章内容回答下列问题：(1)石墨烯的物理性质有_______。
(任写一条)(2)石墨烯应用占比最高的领域是_______。
(3)纺织面料掺入石墨烯后具有的优点有_______。
(任写一条)【答案】(1)导电性(或者导热性等)(2)电子领域(3)在低温情况下，石墨烯可将来自远红外线的热量传送给人体，改善人体微循环系统，促进新陈代谢【解析】(1)根据文章内容可知石墨烯在电子领域有广泛应用，且能将热量传送给人体，故其物理性质有导电性、导热性。
(2)根据图2信息可知，石墨烯在电子领域应用占比27%，在该领域占比最高。
(3)文章内容中已给出：纺织面料掺入石墨烯后，在低温情况下，石墨烯可将来自远红外线的热量传送给人体，改善人体微循环系统，促进新陈代谢。
2．（2022年安徽省中考）阅读下列科技短文并回答问题。
过氧化氢可用于消毒杀菌，具有不稳定性。
将水蒸气冷凝在硅，玻璃，塑料、金属等材料表面，均发现了过氧化氢的存在。
研究显示：水蒸气冷凝为粒径小于10微米的液滴时，部分水分子会转化为过氧化氢分子。
水微滴中形成的过氧化氢含量随液滴尺寸的增大而减少。
过氧化氢的产生量与温度，温度等环境条件密切相关。
小学英语语文小升初阅读理解专题练习(附答案)
小学英语语文小升初阅读理解专题练习(附答案)一、阅读理解1．阅读理解阅读理解It's a sunny morning. It's warm but not hot. Jack sees an old man with a black umbrella walking on the street.Jack is very curious (好奇的). So he asks the old man, "Hello. Would you tell me why you bring the umbrella?" The old man answers, "My legs are not strong. If I carry a walking stick, people will say, 'How poor the man is!' I don't like this. So I carry an umbrella to help me. When people see I'm walking with an umbrella in a fine day, they will only say, ‘How foolish the man is!' "（1）The weather is ________ that morning.A. snowB. windyC. warm（2）Jack sees an old man with ________.A. a red coatB. a black umbrellaC. a black coat（3）The old man's legs are ________.A. strongB. weakC. long（4）The old man carries an umbrella to ________.A. help himselfB. avoid the rainC. play with（5）Is the old man foolish?A. Yes, he is.B. No, he isn't.C. He can walk.【答案】（1）C（2）B（3）B（4）A（5）B【考点】阅读理解【解析】【分析】这是一篇讲述一位老人带伞的故事。
中考语文：典型阅读理解10篇专题一(含答案解析)
中考语文：典型阅读理解10篇专题一（含答案解析）学校:___________姓名：___________班级：___________考号：___________第一篇：阅读下面的文章，完成下列小题。
细水长流蓝雪冰儿①父亲说，以前有个算命先生说过，他是个苦命的娃。
也的确，父亲十二岁丧父，不得不辍学到石灰窑工作，一干就是一辈子。
②后来，有人说，老刘命好，三个闺女乖巧孝顺；也有人说，老刘命好，夫妻俩没红过脸，恩爱有加；还有人说，老刘命好，从来不跟人闹意见。
父亲乐呵呵地说，细水长流嘛。
别人不懂父亲这话是什么意思，摸着脑瓜皮说，老刘可真逗，说你命好，你还不乐意咋的？是啊，别人觉得，细水长流和命好放在一起，这是哪跟哪啊？但我最明白，父亲的意思是说，人不要太计较利益得失，水长流，情才会长在。
③初为人妻，继为人母，我也喜欢把“细水长流”挂在嘴上，当然，我收获的也是幸福和快乐。
但是，今年夏天，父亲的“细水长流”刚一出口，就被母亲一句话给噎回去了。
④这个夏天，老天爷太吝啬了，一场痛快淋漓的大雨也不下，弄得棒子苗干渴得黄了叶子，打了蔫。
视地如命的母亲看着很多人家都浇了地，心急如焚。
可是，我们家的地和左右两家的紧挨着，根本修不出渠来。
再说，那两家都到城里去住了，平时见不到人。
⑤当管理水渠的人告诉母亲可以去浇地时，母亲要父亲别去上班。
父亲得令而行，两人不顾炎炎烈日，在棒子地里穿梭，割伤了脸，衣服都湿透了。
最终用三个小时，浇了三家的地。
中午，我赶回娘家，替父母准备好午饭。
母亲向来身体不好，回到家，已经没有了说话的力气，一个劲擦汗；一向强壮的父亲一屁股坐在椅子上，喘着粗气。
我埋怨他们，这么大的岁数了，别把地看得比命还重要，就是旱死了，不就一年没收成吗？母亲一听，跟我急了，庄稼人能眼看着种下的庄稼死在地里啊？我不敢再接话，闷着头把午饭端上桌。
母亲便自言自语，三个小时，差点把命搭进去，不知道那两家知不知情。
父亲说，干了就啥也别说，细水长流。
新高考英语真题分项汇编专题：阅读理解应用文(解析版)
A.It gives children a discount.B.It of offers many types of bikes.
C.It organizes free cБайду номын сангаасcle tours.D.It has over 2,500 rental shops.
2.（2023年新高考II卷A篇）
Yellowstone National Park offers a variety of ranger programs throughout the park, and throughout the year. The following are descriptions of the ranger programs this summer.
The 2.5-hour tour covers the Gooyer Windmill, the Skinny Bridge, the Rijksmuseum, Heineken Brewery and much more. The tour departs from Dam Square every hour on the hour, starting at 1:00 pm every day. You can buy your ticket in a MacBike shop or book online.
6/19 — Waterfalls &Wide Angles: meet at Artist Point.
7/10 — Wildflowers &White Balance: meet at Washburn Trailhead in Chittenden parking area.
【英语】 英语阅读理解专题练习(及答案)含解析
【英语】英语阅读理解专题练习(及答案)含解析一、阅读理解1．阅读理解"Without music, life would be a mistake, "famous German philosopher（哲学家）Friedrich Nietzsche said over a century ago. Music is a big part of our lives. But in recent years, some American schools have cut music classes to control budgets（预算）.For example, Chicago public schools hurt arts education when it fired over 1, 000 teachers. Among them, 10 percent of the teachers taught art or music, according to The Washington Times. In fact, this is not just a problem in the US. In other countries, such as China and the UK, music classes are not thought to be as important as ones like science, math and history. That's partly because music is not seen as a very important life skill, and it isn't tested. Many students are busy with schoolwork, so parents and students choose to focus on subjects that are tested more often. However, learning music is beneficial（有益的）in many ways.When playing music, you need different abilities to work together. It is not as simple as it looks, according to Kenneth K. Guilmartin of Music Together, an early childhood music development program. For example, when playing the piano, people see music notes and decode（解码）them in their brains. They also use their fingers to make sounds. You need to deal with all these things at the same time.Music has a special connection with science as well. You can see that many scientists are good at playing music：Einstein played the violin and German physicist Max Planck was talented in playing the piano.（1）Some schools in the US cut music classes, because ____.A. they were too difficult to learnB. students in the US weren't interested in musicC. the schools wanted to control budgetsD. there weren't enough music teachers in the US （2）In Paragraph 2, what does the underlined word "them" refer to（指代）?A. Students in Chicago.B. Public schools.C. Parents in Chicago.D. Fired teachers.（3）How many scientists who are good at playing music are mentioned in this passage? A. One. B. Two. C. Three. D. Four.（4）What's the writer's opinion according to this passage?A. Music is as simple as it looks.B. Music classes should be cut in some schools.C. Music is a big part of our lives.D. Music isn't a very important life skill for us.【答案】（1）C（2）D（3）B（4）C【解析】【分析】本文介绍了很多地区削减了音乐课以控制预算，这是不合适的，因为音乐在许多方面都是有益的。
高考阅读理解专题训练一
高考阅读理解专题训练一 1 When the explorers first set foot upon the continent of North America, the skies and lands were alive with an astonishing variety of wildlife. Native Americans have taken care of these precious natural resources wisely. Unfortunately, it took the explorers and the settlers who followed only a few decades to decimate a large part of these resources. Millions of waterfowl（水禽）were killed at the hands of market hunters and a handful of overly ambitious sportsmen. Millions of acres of wetlands were dried to feed and house the ever-increasing populations, greatly reducing waterfowl habitat（栖息地）.
In 1934, with the passage of the Migratory Bird Hunting Stamp Act (Act), an increasingly concerned nation took firm action to stop the destruction of migratory（迁徙的）waterfowl and the wetlands so vital to their survival. Under this Act, all waterfowl hunters 16 years of age and over must annually purchase and carry a Federal Duck Stamp. The very first Federal Duck Stamp was designed by J.N. "Ding" Darling, a political cartoonist from Des Moines, lowa, who at that time was appointed by President Franklin Roosevelt as Director of the Bureau of Biological Survey. Hunters willingly pay the stamp price to ensure the survival of our natural resources. About 98 cents of every duck stamp dollar goes directly into the Migratory Bird Conservation Fund to purchase wetlands and wildlife habitat for inclusion into the National Wildlife Refuge System—a fact that ensures this land will be protected and available for all generations to come. Since 1934, better than half a billion dollars has gone into that Fund to purchase more than 5 million acres of habitat. Little wonder the Federal Duck Stamp Program has been called one of the most successful conservation programs ever initiated.
小学四年级西师大语文下学期阅读理解专题练习题含答案
小学四年级西师大语文下学期阅读理解专题练习题含答案班级：__________ 姓名：__________一、阅读语段，完成练习。
周恩来和同学一路上左顾右盼，忽然发现巡警局门前围着一群人。
他们凑了过去，只见人群中有个女人正在哭诉着什么。
一问才知道，这个女人的亲人被外国人的汽车轧死了，她原本（希望盼望指望）巡警局给她撑腰，惩处这个外国人，谁知中国巡警不但不惩处肇事的外国人，反而（训斥谴责批评）她。
围观的中国人都紧握着拳头，但这是在外国人的地盘里，谁又敢怎么样呢？大家只能劝慰这个不幸的女人。
此时的周恩来才真正体会到“中华不振”这四个字的沉重分量。
1．在语段中的括号里选择恰当的词语，打上“√”。
2．给语段中画“”的句子换一种说法，意思不变。
________________________________________________________3．“这个不幸的女人”的“不幸”遭遇是（）A．在外国人的地盘里，她的亲人因病而死。
B．在中国被外国人占据的地方，她的亲人被外国人的汽车轧死，中国巡警不但不惩处肇事的外国人，反而训斥她。
4．理解语段，选一选，填一填。
（填序号）A．为虎作伥 B．怒不敢言 C．哭诉无助 D．得意扬扬周恩来亲眼见到：妇女的（______），洋人的（______），警察的（______），群众的（______），让人真切感受到“中华不振”。
5．“此时的周恩来才真正体会到‘中华不振’这四个字的沉重分量”中的“中华不振”指的是（）A．中华人民不凶狠。
B．中国贫穷落后，遭受帝国主义欺凌。
C．中国不强势，没有话语权。
D．中华民族萎靡不振，没有生气。
二、课内阅读。
魏校长听了为之一振！他怎么也没想到，一个十二三岁的孩子，竟然有如此抱负和胸怀！他睁大眼睛又追问了一句：“你再说一遍，为什么而读书？”“为中华之崛起而读书！”魏校长听了，高兴地连声赞叹：“好哇！为中华之崛起，有志者当效（xiào）此生！”正当周恩来和同学左顾右盼时，忽然发现巡警局门前围着一群人。
英语阅读理解专题练习(及答案)含解析
英语阅读理解专题练习(及答案)含解析一、高中英语阅读理解1．阅读下列短文，从短文后每题所给的A、B、C和D四个选项中，选出最佳选项。
A new technology is going to ripe, one that could transform our daily lives, help to form new industries, even remove world economic powers from their present positions. Unlike the wave of industrialization that began in the West and spread later to the rest of the world, the new developments are taking place in research labs all over the globe—and Asians are in the forefront. Physicists are creating a new class of materials that display an amazing property unforeseen even two years ago—superconductivity (超导体技术).Used today only in specialized equipment, super conductors have the potential to radically change most of the electrical and electronic appliances found in the home, making them smaller, more powerful and efficient. They could free our cities of pollution by replacing petrol and diesel (柴油) vehicles with electric cars, and cut the cost of electricity. The new materials do something that even the best of conductors such as copper and silver cannot—they do away with all electrical resistance. The significances for energy storage are great.The technology is in its early stage, still accessible to countries that decide to invest brains and money. For 75 years it had remained little more than a scientific curiosity with limited practical use because the phenomenon occurred only at extremely low temperatures. It was first observed in 1911 by a Dutch scientist named Heike Kamerlingh Onnes, who cooled mercury (水银) to temperatures below -269℃ with liquid helium (氦). Then in January last year, two IBM scientists, K. Alex Muller and J. George Bednorz, found a metal oxide ceramic (氧化陶瓷) that superconducted at -243℃. Their report went largely unnoticed until last December, when it was confirmed at a scientific meeting in Boston. Today Japan, India, China and other Asian countries all have their share of experts who spend their days and nights in labs, acting as midwives (助产士) to a new technology.（1）As is indicated in the passage, the technology of superconductivity ____________. A. has already been developed B. is still under developmentC. will be used only in specialized equipmentD. will be used in daily lives in a few years（2）The new technology differs from the others in that ____________.A. it began in the East and spread later to the rest of the worldB. it began in the West and spread later to the rest of the worldC. it is being cultivated in research labs around the worldD. it is accessible to physicists who are intelligent and rich（3）From the passage, we may conclude that ____________.A. Asian scientists gain the lead in the growth of the new technologyB. Dutch scientists kept reporting new findings for the last 75 yearsC. IBM scientists' report receive immediate attention all over the worldD. the West was astonished at the new technology developed by the Asians（4）Which of the following would be the best title for the passage?A. The Prospect of a New TechnologyB. Superconductivity: A New TechnologyC. A New Technology: The Key to Change the Way of Our LivesD. A New Technology: A Joint Effort of Many Countries【答案】（1）B（2）C（3）A（4）B【解析】【分析】本文是一篇说明文，介绍了超导体技术的发展潜能和发展状况。
中考英语阅读理解专题(含答案)(word)
中考英语阅读理解专题(含答案)（word）一、初三英语阅读理解（含答案详细解析）1．阅读理解As far back as he could remember, Larry had wanted to go to Hollywood and become a film star. The young man's hopes for success were broken again and again. However, Hollywood was just everything to him. When he first came to California? Larry had decided never to give up and return home without success. Therefore, he kept on trying. "Some day," he told himself, "my big chance would come."Larry found a job—parking cars at one of Hollywood's big restaurants. His pay was low, but since the guests were kind enough to give him more money, he managed to make a living. One day he recognized an important film director driving into the parking lot and getting out of his car. Larry had recently heard that the man was ready to make a new picture.Larry got into the car and prepared to drive it on into the lot and park it. Then he stopped, jumped out, and ran over to the director. "Excuse me, sir, but I think it's only fair to tell you that it's now or never if you want me in your next picture. A lot of big companies are after me." Instead of pushing away the boy, the director laughed, then wrote something on a card and handed it to the young man. "Come and see me tomorrow."Larry got a small part in the director's next film. He was on his way!（1）It's clear that Larry's job—parking cars ________.A. helped him make a lot of moneyB. brought him the hope to be a film starC. made him fail again and again in getting into HollywoodD. gave him few chances to meet stars（2）The film director asked Larry to meet him the next day because _______.A. he needed a driver very muchB. Larry would become a starC. some big companies would give him a jobD. Larry expressed his hope in a wise way（3）We can learn from the story that _______.A. the film director knew Larry's hard experience beforeB. Larry managed to be a part in the new filmC. the job parking cars could bring young people everythingD. the new film was not so important for the director（4）"He was on his Way" refers to the fact that _______.A. he gave up and returned homeB. he began to work towards successC. he drove the director's car to HollywoodD. he had a long way to go to be in the film（5）The story mainly wants to tell us _______.A. it was hard for Larry, to find a job in a restaurant in HollywoodB. Larry was so lucky to meet the director in the parking lotC. why Larry could remember many things beforeD. how Larry succeeded- in his new life in Hollywood【答案】（1）B（2）D（3）B（4）B（5）D【解析】【分析】本文介绍了Larry在好莱坞寻求机会的故事。
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1
阅读理解题专题
【例1】（2010，北京朝阳，一模）请阅读下列材料
问题：如图1，在等边三角形ABC内有一点P，且PA=2， PB=3， PC=1．求
∠BPC
度数的大小和等边三角形ABC的边长．
李明同学的思路是：将△BPC绕点B逆时针旋转60°，画出旋转后的图形（如图2）．连
接PP′，可得△P′PB是等边三角形，而△PP′A又是直角三角形（由勾股定理的逆定理可证）．所
以∠AP′C=150°，∠BPC=∠AP′C=150°．进而求出等边△ABC边长为7．问题得到解决．
请你参考李明同学的思路，探究并解决下列问题：如图3，在正方形ABCD内有一点
P，且PA=5，BP=2，PC=1．求∠BPC度数的大小和正方形ABCD的边长．
变式训练、阅读下列材料：
小伟遇到这样一个问题：如图1，在梯形ABCD中，AD∥BC，对角线AC、BD交于点
O。若梯形ABCD的面积为1，试求以AC、BD、AD+BC的长度为三边长的三角形的面积。
图1 图2
小伟是这样思考的：要想解决这个为题，首先应想办法移动这些分散的线段，构造一个
三角形，在计算面积即可。他先后尝试了翻折、旋转、平移的方法后，发现通过平移可以解
决合格问题。他的方法是过点D作AC的平行线交BC的延长线于点E，得到的△BDE即是
以AC、BD、AD+BC的长度为三边长的三角形（如图2）。
请你回答：图2中△BDE的面积等于＿＿＿＿．
参考小伟同学思考问题的方法，解决下列问题：
如图3，△ABC的三条中线AD、BE、CF。
（1）在图3中利用图形变换画出并指明以AD、BE、
CF的长度为三边长的一个三角形（保留作图痕迹）；
（2）若△ABC的面积为1，则以AD、BE、CF的长度
为三边长的三角形的面积等于＿＿＿＿．
图3
图1
图2
2
图3
A
BCEFG
P
Q
2、（2010，大兴，一模）
若12,xx是关于x的一元二次方程20(0)axbxca的两个根，则方程的两个根
12
,xx
和系数,,abc有如下关系：1212,bcxxxxaa. 我们把它们称为根与系数关系定理
.
如果设二次函数2(0)yaxbxca的图象与x轴的两个交点为12(,0),(,0)AxBx.利用
根与系数关系定理我们又可以得到A、B两个交点间的距离为：
22
22
121212
2
444()4().bcbacbacABxxxxxxaaaa
请你参考以上定理和结论，解答下列问题
:
设二次函数2(0)yaxbxca的图象与x轴的两个交点为12(,0),(,0)AxBx，抛物线
的顶点为C，显然ABC为等腰三角形
.
（1）当ABC为等腰直角三角形时，求
2
4;bac的值
（2）当ABC为等边三角形时，
2
4bac
.
（3）设抛物线21yxkx与x轴的两个交点为A、B，顶点为C，且
90ACB
,
试问如何平移此抛物线，才能使60ACB？
例2. 情境观察
将矩形ABCD纸片沿对角线AC剪开，得到△ABC和△A′C′D，如图1所示.将△A′C′D
的顶点A′与点A重合，并绕点A按逆时针方向旋转，使点D、A(A′)、B在同一条直线上，
如图2所示．
观察图2可知：与BC相等的线段是 ，∠CAC′= °．
问题探究：如图3，△ABC中，AG⊥BC于点G，以A
为直角顶点，分别以AB、AC为直角边，向△ABC外作等腰
Rt△ABE和等腰Rt△ACF，过点E、F作射线GA的垂线，
垂足分别为P、Q. 试探究EP与FQ之间的数量关系，并证
明你的结论.
图1 图2
C'A'BADC
ABCDBCDA(A')
C'
3
拓展延伸
如图4，△ABC中，AG⊥BC于点G，分别以AB、AC
为一边向△ABC外作矩形ABME和矩形ACNF，射线GA交
EF于点H. 若AB=k AE，AC=k AF，试探究HE与HF之间的
数量关系，并说明理由.
变式训练：数学课上，李老师出示了如下框中的题目.
在等边三角形ABC中，点E在AB上，
点D在CB的延长线上，且ED=EC，如图.
试确定线段AE与DB的大小关系，并说明
理由.
E
A
B
C
D
小敏与同桌小聪讨论后，进行了如下解答：
（1）特殊情况，探索结论
当点E为AB的中点时，如图1，确定线段AE与DB的大小关系，请你直接写出结论：
AE DB
（填“＞”，“＜”或“＝”）.
E
A
B
C
D
E
A
B
C
D
（2）特例启发，解答题目
解：题目中，AE与DB的大小关系是：AE DB（填“＞”，“＜”或“＝”）.理由如下：
如图2，过点E作//EFBC，交AC于点F.
（请你完成以下解答过程）
（3）拓展结论，设计新题
在等边三角形ABC中，点E在直线AB上，点D在直线BC上，且EDEC.若
ABC
的边长为1，2AE，求CD的长（请你直接写出结果）.
图1 图2
4
中考链接
1．(2012年贵州六盘水)定义：f(a，b)＝(b，a)，g(m，n)＝(－m，－n)，例如：f(2,3)＝(3,2)，g(－
1，－4)＝(1,4)，则g[f(－5,6)]＝( )
A．(－6,5) B．(－5，－6) C．(6，－5) D．(－5,6)
2．(2012年山东莱芜)对于非零的两个实数a，b，规定a⊕b＝1b－1a.若2⊕(2x－1)＝1，则x的值
为( )
A.56 B.54 C.32 D．－16
3．(2012年湖南湘潭)文文设计了一个关于实数运算的程序，按此程序，输入一个数后，输出的
数比输入的数的平方小1.若输入7，则输出的结果为( )
A．5 B．6 C．7 D．8
4．(2012年四川德阳)为确保信息安全，信息需加密传输，发送方由明文→密文(加密)，接收方
由密文→明文(解密)．已知加密规则为：明文a，b，c，d对应密文a＋2b,2b＋c,2c＋3d,4d.
例如：明文1,2,3,4对应密文5,7,18,16.当接收方收到密文14,9,23,28时，则解密得到的明文为
A．4,6,1,7 B．4,1,6,7 C．6,4,1,7 D．1,6,4,7
练习作业
第一部分
1．(2011山东菏泽)定义一种运算☆，其规则为a☆b＝1a＋1b，由此规则，计算2☆3的值是( )
A.56 B.15 C．5 D．6
2．(2012年湖北随州)定义：平面内的直线l1与l2相交于点O，对于该平面内任意一点M，点M
到直线l1，l2的距离分别为a，b，则称有序非负实数对(a，b)是点M的“距离坐标”．根据
上述定义，距离坐标为(2,3)的点的个数是( )
A．2个 B．1个 C．4个 D．3个
第二部分
3、几何模型：条件：如下左图，A、B是直线l同旁的两个定点．问题：在直线l上确定
一点P，使PAPB的值最小．
方法：作点A关于直线l的对称点A，连结AB交l于点P，则PAPBAB的值
最小（不必证明）．
模型应用：
（1） 如图1，正方形ABCD的边长为2，E为AB的中点，P是AC上一动点．连
结BD，由正方形对称性可知，B与D关于直线AC对称．连结ED交AC于P，则
PBPE
的最小值是___________；
（2） 如图2，O⊙的半径为2，点ABC、、在O⊙上，OAOB，60AOC°，
P
是OB 上一动点，则PAPC的最小值是___________；
（3）如图3，45AOB°，P是AOB内一点，10PO，QR、分别是
OAOB、
上
A
B
A
P
l O A B P R Q 图3 O A B C 图2 A B E C
P
D
图1
P
5
的动点，则PQR△周长的最小值是___________．