人大附中2013—2014学年初二第二学期期中考试

2023-2024学年北京市海淀区中国人民大学附属中学下学期八年级期中物理试卷一、单选题：本大题共15小题，共30分。

1.在国际单位制中，压强的单位是()A.牛顿B.帕斯卡C.千克D.摄氏度2.下列所举实例中，物体运动状态没有改变的是()A.自由下落的苹果B.正在加速起飞的飞机C.沿直线匀速运动的公共汽车D.随传送带一起匀速转弯的食物3.如图所示的四种情景下，属于通过减小受力面积来增大压强的是()A.切熟鸡蛋的钢丝很细B.载重车装有很多车轮C.图钉帽做成较大圆形D.书包背带做得较宽4.下列关于重力说法正确的是()A.普通中学生所受的重力约为60NB.重力是物体本身具有的力，没有施力物体C.重力的大小可以用弹簧测力计间接测量D.物体的重心一定在物体上5.下列现象不是利用大气压工作的是()A.用注射器吸药液B.吸附在玻璃上的塑料挂衣钩C.用吸管吸饮料D.把打气筒中的气充进自行车车胎6.如图所示，分别用大小相等的力拉和压同一弹簧。

该实验表明，弹簧受力产生的效果与力的()A.大小有关B.方向有关C.作用点有关D.大小、方向、作用点都有关7.下列关于惯性的说法正确的是()A.阻力越小，物体做匀速直线运动的时间越长，所以物体惯性越大B.踢出足球后，由于足球受到惯性作用，足球可以在空中继续飞行C.急刹车时，正确佩戴安全带可以减小乘客惯性来提高安全性D.质量大的物体，其惯性一定大8.如图所示，人沿着水平方向推装满沙子的车，但没有推动，下列说法正确的是()A.人推车的作用力小于车对人的作用力B.人对车的推力小于地面对车的摩擦力C.人对车的推力与地面对车的摩擦力是一对平衡力D.车对地面的压力与地面对车的支持力是一对平衡力9.图所示，粗玻璃管两端开口处，箍着相同的橡皮膜，且绷紧程度相同，将此装置置于水中，四幅图能正确反映橡皮膜凹凸情况的是A. B. C. D.10.利用托里拆利实验测量某地的大气压，测量数据如图所示，则大气压值应该是()A.750mmHgB.760mmHgC.770mmHgD.755mmHg11.关于力和运动的关系，下列说法正确的是()A.任何两个力都可以找到其合力B.物体受到力的作用，其运动状态可能不会改变C.竖直向上抛出一个石块，在最高点处石块静止，所以它在该处处于平衡状态D.如果两个力的作用点，大小，方向完全相同，那么它们一定是相互作用力12.小明为了演示浮力的方向，做了如图所示的实验。

2013-2014学年度人大附中八年级下英语期中考试四、单项选择(共11分, 每小题1分)21. The Taylors were watching a soccer game ______ 8:45 last night.A. onB. atC. inD. during22. Don’t push the kids too hard. They need to have time to relax and think for ______ .A. theirB. themC. themselvesD. they23. How exciting! I can’t wait ______ the gift boxes!A. to openB. openingC. for openingD. and open24. ______ some reading or writing is a good way to lower stress.A. DoB. DidC. DoingD. To doing25. ______ you please pass me the salt shaker?A. DoB. WouldC. MayD. Should26. We need to make it ______ that everyone should try their best in order to win the game.A. more clearlyB. clearestC. clearD. clearly27. The kids are having too many classes. We need to ______ a few of their activities.A. cut offB. cut upC. cut inD. put out28. We have to get up at 5 tomorrow ______ we can catch the first flight.A. untilB. so thatC. althoughD. and29. I do mind ______ in non-smoking areas in public places.A. others’ smokingB. other’ s smokeC. other’ s smokingD.others smoke30. I don’t like doing chores. ______ my sister.A. Neither doesB. So doesC. Neither isD. So is31. He never told us ______ on the trip alone last week.A. why did he goB. why would he goC. why was he goingD. why he went五、完形填空(共12分、每小题1分)VolunteeringEvery year, more and more students become volunteers. The projects may be with their school, neighborhood, or town, but the work of all volunteers is important. Students find that there are ______ (32) benefits to volunteering.First, volunteering helps others. Many people complain about ______ (33) in our society. Volunteers are part of the ______ (34) to the problems! While it is easy to complain or whine about things that are not right, the volunteer ______ (35) rather than complaining. When a student spends time working at old people’s home, ______ (36) a park, or tutoring a younger student, the volunteer ______ (37) the world a better place.Second, being a volunteer makes students feel good about themselves. When a student volunteer knows that his or her efforts have made someone else, s life better, the volunteer feels ______ (38). Students always hear people ______ (39) that everyone should care about other people. Volunteers make it ______ (40). Although some volunteer work is long or tiring, student volunteers end the day knowing they did the right thing. Their parents, teachers, and community are proud of them. Knowing they did the right thing makes them feel better, even if they are ______ (41).Finally, students learn that volunteering is fun. A group of students might volunteer to clean up a riverbed in early spring. It is fun to be with their friends, to enjoy the weather, and to picnic later in a beautiful, clean area. ______ (42) might read to young children in a preschool. It is fun to spend time with children and to have them smile and laugh. No matter what their ages or abilities are, every student ______ (43) he a volunteer. The work of student volunteers is apowerful force that makes America a better place.32. A. few B. much C. many D. little33. A. problems B. things C. fights D. arguments34. A. way B. answer C. suggestion D. solution35. A. fights back B. takes action C. gives up D. tries hard36. A. cleaning up B. clean C. to clean D. cleans up37. A. helps B. makes C. builds D. develops38. A. great B. well C. worried D. thankful39. A. speak B. talking C. say D. saying40. A. to happen B. happen C. happening D. happens41. A. proud B. happy C. tired D. right42. A. The others B. Others C. Another D. Else43. A. should B. will C. may D. can六、阅读理解(共20分、每小题2分)(A)1550 North AvenueSavannah, GA 31401April 30Dear Zachary,How are you? I am fine, but very busy. I am doing a research project for school that is due at i the end of May. The reason I am writing is that I need your help. I know that you and your dad are | great jazz fans. Maybe you and your dad can help me.The research project that I’m doing is about jazz music I went to the library and found the books I needed on jazz history. I was surprised to learn that jazz music was originally a part of the gospel song (福音欹) tradition, which is also a part of the blues. What really surprised me is that rap music has its roots in jazz, too.For my project I have to write a paper. That’s a requirement. I don’t have achoice with that. Our teacher gave us the choice of working in a group or doing something on our own for the performance part of the project. Because this is a music appreciation class, there are lots of kids who are going to sing or perform in groups. What I want to do is to play a few of Duke Ellington’s songs that I have on tape. Then, I want to play a few bars on the piano to show the class his interesting sounds.I am really excited about this project. I know that your dad has a great jazz collection. He I must have a few Ellington CDs, records, or tapes. I bought an Ellington piano book and some CDs, but I don’t have the music for two of the songs I want to use.This is where I need your help. Could you see if your dad has any Ellington piano songs in his collection? The songs that I am looking for that are in my piano book are “Solitude” and “Black Butterfly.”I hope that you can find them. I trust your dad’s collection and hope that they’ll be there. If you tape them, I’ll pay you for the tapes. I can give you a call in a week to see if you have found them. We can also talk about your plans to come and stay here for a few weeks this summer.I hope everything is fine with you and all of your family. I’m looking forward to talking with you soon.Your friend,Paul44. What is Paul planning to do FIRST for the performance part of his project?A. He will read his paper.B. He will play the piano.C. He will perform with his friends.D. He will play tapes.45. What does Paul need from Zachary’s dad?A. a book about jazz.B. Ellington music.C. Ellington videos.D. a new CD.46. While doing research, what did Paul learn about rap music?A. It is in Zachary’s dad’s collection.B. It is a part of the gospel and jazz tradition.C. His teacher is interested in itD. He is not permitted to write about it(B)Mary Cassatt: American ArtistBy the young age of sixteen, Mary Cassatt had decided she wanted to become an artist. Unlike the other women painters of the time, she did not want to be an amateur－she wanted to make a living with her art. From 1860 to 1862, Mary studied drawing at the Pennsylvania Academy of Fine Art, which was near her home. What she really wanted to do, however, was go to Europe to study the works of famous painters, known as the “old masters”At first, Mary’s parents were opposed to the idea of her going to Europe, but she eventually changed their minds. Mary moved to Paris when she was 22 years old. After studying the old masters for a while, she began to believe that if she was to become a good artist, she would have to develop her own style.In the early 1870s, the painter Edgar Degas asked Mary to join the group called the Impressionists. The Impressionists were a group of painters who had broken from the style of the old masters. Rather than painting only sitting or standing models, the Impressionists often painted from real life. Rather than painting in only dark colors, the Impressionists experimented with bright colors and the effect of light on color.Mary Cassatt became quite successful as an Impressionist painter. In later years, however, she also worked in dry point. The process of dry point consisted of three steps. The first step was to draw a picture. She did this byscratching (刮) a sharp needle onto a sheet of copper (铜), called a plate, Next she applied ink to the plate with a roller. Then she pressed the plate onto a sheet of paper. Even later, Mary Cassatt began painting pictures of mothers with their children. These are some of Cassatt’s best—known paintings. In the 1890s, Mary Cassatt had many one-woman art shows in both the United States and Europe. Her works were well respected and sold very well. She bought a summer home in the country outside of Paris, where she lived until her death in 1926.47. Mary wanted to be different from many women painters of her time by ______.A. becoming a professional artistB. traveling to London to study other artistsC. working with the Impressionist paintersD. learning from “old masters”48. The underlined word “amateur” means ______.A. 艺术家B. 业余爱好者C. 家庭妇女D. 职业画家49. How was the style of the Impressionists different from that of the old masters?A. The paintings featured only posed models.B. The artists pressed down on plates.C. The pictures showed scenes from real life.D. The painters used only dark colors.(C)Passenger ships, trade ships, and fishing boats are a normal part of life on the open sea. However, all their activity creates a great deal of noise underwater.Scientists from the United States and Canada recently reported their observations(观察) that the ocean is getting noisier.Scientists at the University of Victoria have studied the recordingsrecorded with equipment placed underwater near the busy shipping lanes off Vancouver Island in Canada. They say engine(发动机) noise is continuous during the day, and a little less strong at night. Scientists say it is likely that whales must call out more loudly to be heard over this noise. The noise could make it more difficult for orca whales to find food. The orcas find fish by producing clicking sounds and other noises. Loud engine noise could be interfering with their efforts.Michael Jasny is a policy expert for the Natural Resources Defense Council. He says the rise of underwater noise is limiting the ability of whales to communicate.Shipping noise falls across the same frequencies(频率) that these animals use for all their vital(生死攸关的) behaviors - for feeding, for finding mates, for avoiding predators(捕食者) and for going ahead.Mr. Jasny says sound travels very effectively underwater. And it is not just whales he is worried about.“The whole web of life in the oceans depends on sound. And as more and more research has been done, it’s been very clear that what we have on our hands is really a major problem. It’s a serious problem. It’s a global problem. Fortunately, in shipping we have a problem that has a solution.”One answer is to design quieter ships. America’s National Oceanic and Atmospheric Administration, or NOAA, has four new ships that are made to be quieter. Michael Bahtiarian works for Noise Control Engineering, the company which helped design the boats.Mr. Bahtiarian says the main source of noise pollution is the propeller(螺旋桨). Better shaped propellers and ship designs can help to reduce noise. NOAA’s ships also have costly engines, which produce less noise. Mr. Bahtiarian says the technology to make quieter ships does exist and has been used in the military for some time.50. The underlined phrase “interfering with”in Paragraph 3 probably means______.A. controllingB. disturbingC. encouragingD. stopping51. We can tell that whales depend on sound for ______.A. communicating with their matesB. stopping predators from fishingC. fighting against the shipping noiseD. telling the night time from the day52. From the passage we can learn that ______.A. expensive engines produce less noise in the oceanB. people should stop making big ships in order to save whalesC. the other animals in the ocean also depend on sound for livingD. it is difficult to find a way to stop noise pollution in the ocean53. What is the purpose in writing the passage?A. To tell people that ocean is getting noisier.B. To tell people about whales and ships in the ocean.C. To tell people that whales are facing a serious problem.D. To tell people that quiet ships are needed in the ocean.七、还原句子(共4分、每小题1分)Warm Up to Keep Your Game UpDon’t rush into any sport or exercise without warming up first—muscles(肌肉) that haven’t been exercised can be injured more easily.______ (54). These activities get your muscles going. Follow your warm-up with some stretches (伸展). Stretching works best after a warm-up because your body is ready to exercise.In addition to light activities and stretches, practice is also excellent preparation for most sports or activities. ______ (55). This will help you and your teammates work together and put you in top physical condition.Even if you don’t belong to a team, you can use regular workouts and practices to improve your performance anckreduce the chance of injuries.Remember, if a tool isn’t used, it gets rusty (生锈的). ______ (56). For example, try shooting some baskets or play a quick game. Practice gets your brain and body to work together while improving your performance.Although you should practice regularly, don’t work too hard. ______ (57). Your doctor or coach can help you develop a training and conditioning program that’s fit for your age and level of development.A. So keep yourself in top shape with regular practice.B. Sudden increases in training might lead to injuries.C. Don't eat too much before you start doing exercise.D. If you belong to a team, practice as much as possible.E. Start out with some light activities, such as jogging or jumping八、阅读与表达(共8分、每小题2分)Today, people care about their health much more than before and want to get a well-toned body shape, this is because when we are in good shape, it makes us feel fit and healthy. We feel good about ourselves and feel much more confident than before. When you want to tone up your body, just workouts will not do. You have to take care of your overall health by eating proper food, doing the right kind of exercises and keeping yourself happy.The first thing that needs to be done is to reduce the intake (摄入) of calories (卡路里). The calories content (含量) of each meal should not be higher than 400 calories. Ideally, one is well advised to have six meals in a day. There should be a gap(间隔) of three hours between each meal. Fresh vegetables, fruits, egg white, fish, chicken breast are some of the food that can provide you with the right nutrients (养分), at the same time will help you to get in shape.Many people make the mistake of avoiding strength training when they are trying for weight loss. They think that strength training will increase their body weight. However, this is not true. Be careful not to over exercise in order tolose weight fast. Too much of exercise can cause injury to you.Drinking 8-10 glasses of water can help in reducing fat. If you drink ice cold water, then it will burn out some extra calories from your body. This is because when you are drinking cold water; your body needs to raise the temperature of the water up to your body temperature. In this process, almost one calorie of fat gets burned from the body. Drinking a glass of water before a meal will be helpful in this regard.You can get a healthy body only if your mind is free from stress. Stress can also lead to other health problems like high blood pressure, upset stomach, headaches, etc. For all these reasons, special efforts need to be taken to relax your mind.58. Is too much exercise good for health?59. The good body shape can make people feel60. How many meals are advised to have in a day?61. According to the writer, how can we have overall health?九、完成句子(共10分每小题2分)62. 为什么不和你父母谈谈你的问题？他们也许能想出好主意帮到你。

2013-2014学年度北京市清华附中初二第二学期英语期中考试2013-2014学年度北京市清华附中初二第二学期英语期中考试四、单项选择（共12分，每小题1分）10. ---My little sister has a sore throat. What should I do?---You should take ________ temperature first.A.herB. sheC. hersD. she’s11. ______my opinion, it’s more important to have happy and healthy children than to have successful children.A. InB. OnC. ToD. For12. ---Can you ______me your dictionary? I left mine at home today.---No problem. Here you are.A. borrowB. returnC. lendD. send13. _______ I missed the early bus, I still arrived at school on time today.A. ButB. BecauseC. SinceD. Although14. He knocked on the door but _______ answered.A. somebodyB. anybodyC. nobodyD. everybody15. We have activities these days. Everyone in our class is as _______ as a bee.C. when does Malaysian MH 370 go missingD. when Malaysian MH 370 goes missing五．完型填空（共12分，每小题1分）（A）People’s views on whether children should help with housework vary from person to person.Some people cannot understand why parents make their kids help with chores at home. They think kids these days already have enough stress from school. ___22___ is a waste of their time. Also, when kids get older, they will have to do housework. ___23___there is no need for them to do it now.Others believes it is important for children to learn to help out around the house. They think children these days___24___on their parents too much. Doing chores helps to develop children’s independence and teaches them how to look after themselves. It also helps them to understand the idea of ___25___. Since they live in one house with their parents, they should know that everyone should do their part in keeping it clean and tidy.22.A. Homework B. Housework C. Study D. Volunteering23.A. but B. so C. if D. when24.A. call B. go C. turn D. depend25. A. love B. care C. respect D. fairness(B)For Sparky, school was almost impossible. school was almost impossible. He failed every subject in the eighth grade, physics, Latin, algebra, and English. He didn’t do much 26 in sports. Although he join the scho ol’s golf team, he soon 27 the only important match of the season.Throughout this youth, Sparky was not good with his classmates. In fact, he was not ___28___by the other students; the truth was that no one even cared. Sparky never once asked a girl to go out in high school; because he was afraid that no one would. He even felt___29___if a classmate said hello to him outside of school hours.However, one thing was important to Sparky-drawing. He was proud of his artwork. Of course,___30___else liked it. At high school, he sent some of his cartoons to the editors of the school yearbook. They were refused, but Sparky was so sure of his___31___that he decided to become a professional artist. After completing high, he___32___for Walt Disney Studios. Unluckily, his work was refused again.So Sparky decided to write his own life story in cartoons. He described his childhood self-a little boy loser. The cartoon character soon became famous all over the world. For Sparky, the boy who___33___had any success in school and whose work was rejected again and again, was Charles Schultz. He created the “Peanuts”comic strip and the little cartoon character who never succeeded in kicking a football, Charlie Brown.26. A. more B. better C. worse D. less27. A. played B. competed C. won D. lost28. A. wanted B. pushed C. imagined D. disliked29. A. surprised B. excited C. sad D. normal30. A. everyone B. someone C. no one D. anyone31. A. success B. ability C. future D. luck32. A. called up B. never C. always D. try out33. A. ever B. never C. always D. soon六、阅读理解（共20分，每小题2分）(A)King’s Summer School is a training program for students who want to improve their English. It will be from July 25 to August 15. More information is as follows:Application(申请) date CourseStudents in New York, before July 21,2014 Students of other cites, before July 16,2014 Foreign students, before July 10,2014 English Language Spoken English: 22 hours Reading and Writing : 10 hoursAmerican History: 16 hoursAmerican Culture:16 hoursSteps costA letter of self-introductionA letter of Daily lessons: $200 Sports and activities: $100 Hotel service: $400recommendation(推荐)Please write to:Thompson, Sanders1026 King StreetNew York, NY10016,USAE-mail: KC-Summer-School@34. A. When should the foreign students send their application?A. Before July 21, 2014B. Before July 16, 2014C. Before July 10, 2014D. Before July 25, 201435. You can have all these courses except(除了)___.A. Spoken EnglishB. Listening and SpeakingC. American HistoryD. American Culture36. How much will the daily lesson cost?A. $100B. $200C. $300D. $400(B)A professor began his class by holding up a glass with some water in it. He held it up for ail to see, and askedthe students,“How much do you thin this glass weighs?”“50g!”“100g”“125g”the students answered.“I really don’t know unless I weigh it,” said the professor, “but my question is what would happen if I held it up like this for a few minutes?”“Nothing,” the students said.“OK. What would happen if I held it up like this for an hour?” the professor asked. “ Your arm would begin to ache,” said one of the students.“You are right. Now, what would happen if held it for a day?”“Your arm could go numb, and then you can’t feel anything. You might have serious muscle stress. Have to go to hospital for sure!” said another student. All the students laughed.“Very good. But during all this, did the weigh of the glass change?” asked professor.“No,” the students said.“Then what caused the arm ache and the muscle stress?”The students were puzzled.“Put the glass down!” said one of the students. “Exactly!” said the professor. “The problems of lifeare something like this. Hold it for a few minutes in you head, and they seem OK. Think of then for a long time and they begin to ache. Hold it even longer and you may become paralyzed. You will not be able to do anything. It’s important to think of the challenges in your life, but it’s even more important to put them down at the end of every day before you go to sleep. That way, you are not stressed. You wake up every day fresh and strong and can deal with any problem, any challenge that comes your way!”37. What can we learn from the passage?A. The glass weighs 125g.B. The professor is good at teachingC. It’s the glass that caused the arm acheD. The weight of the glass changed when the professor held it.38. The underlined word “Paralyzed”probably means “________”.A. disabledB. weakC. triedD. painful39. What is the best title for this passage?A. Put Down the GlassB. Hold Up the WeightC. Learn to Be HopefulD. Never Give Up(C)Do you notice that though students spend the same amount of time in class, some get better grades than others? In some ways, it’s because they are different listeners. When having classes, some of them listen carefully to speakers. We call them effective listeners. Some just day dream or talk to a neighbor. They are in effective listeners.How do effective listeners try to pay close attention? First of all, they don’t allow poor circumstances, like an uncomfortable seat or a personal problem to distract them instead, they say “No”to anything that will stop them from understanding and remembering what they hear. After leaving a class or meeting, they remember what was said not the room conditions or not the poor delivery of the speaker. On the other hand, effective listeners who think they are paying attention to the message can be easily daydreaming.In order not to let probable distractions, effective listeners pay attention to the message itself. And Try not to be influenced by theirown feelings or opinions. They do not decide if the material is boring, too easy, or too difficult before listening, effective listeners accept the challenge of new ideas. To help remember difficult ideas. They write down important words and phrases.Ineffective listeners mayappear to listen but daydream instead . They don’t like to hear what they disagree with or easily understand. Moreover, they might be so busy taking too many notes that they miss the speaker’s main idea. These listeners leave a sp eech or a class with a notebook full of words, but the notesbook mean little for a teat or other purpose.Do you expect to do well in your study? Start to be an effective listener. It may help.40. To be effective listener, you'd better__________A. pay special attention to the message of itselfB. get to know all the things happening around youC. try to find out if the material is easy or difficult for youD. look up anything you have trouble understanding in a book41. Which of the following shows the listeners is notdistracted?A. Linda kept thinking about the argument with her friend in the music class.B. Ben continued paying attention to the lesson though others were making noiseC. Eric didn’t listen to the teacher when he found the math problem easy for him.D. Susan gave up listening when her group members started to play in the art class.42. The writer probably agree that____________.A. Listeners should be open to new ideas.B. Listeners can improve listening skills by taking down many things.C. Listeners should stop the speaker when whey don’t share the same opinion.D. Listeners shouldn’t accept the speaker’s idea because he’s bad at speaking.43. By writing the passage, the writer mainly wants to tell people ________.A. the listening habits of poor listenersB. the ways and advantages of effective listeningC. the differences between effective and ineffective listeners.D. the problems of ineffective listening and some suggestions.七、还原句子（共4分，每小题1分）A. The study has caused a great deal of argument.B. They also help us not to make the mistakes we made in the past any more.C. The drug stops the body releasing chemicals that fix memories in the brain.D. How can we keep memories in mind?E. Some people spend all their lives trying to forget bad experiences.NOT all memories are sweet. ___44___. Now American scientists think they are close to developing a drug, which will help people forget bad memories. After a terrible experience, people have to take the medicine right away. They hope it might reduce, or possibly erase the effect of painful memories.In November, scientists tested a drug on people in the US and France. ___45___. So far the study has suggested that only the emotional effects of memories may be reduced, not that the memories are erased.__46___. Some think it is a bad idea, while otherssupport it.Supporters say it could lead to drugs that prevent or treat soldiers' troubling memories after war. But those who are against the research say that changing memories is very dangerous, because memories, no matter whether they are terrible or not, makes us who we are. ___47___.八、词汇（共8分，每小题1分）根据句意及首字母提示补全单词，使句子完整、通顺。

人大附中2023 ~ 2024学年度第二学期初二年级语文期中练习2024年4月22日答案一．基础·运用（共20分）（一）1.（1）D （2分）2．【甲】织女还将支撑织布机的一块珍贵的石头赠给了他。

（原句多重定语顺序有误）【乙】以这个神话传说为素材进行创作的，除了文人骚客之外，艺术家们也纷纷参与其中。

（原句句式杂糅）（2分）3.藏品二：雕品为一牛呈卧姿状，圆润可感；牛背上驮一童子，手拽缰绳和拨浪鼓，表情欢愉（或憨态可掬）。

（2分）4. B （2分）5. D （2分）6. C （2分）7. D （2分）8.示例：希望大家努力学习美学知识，传承传统技艺，创新融合古今，共铸文化辉煌。

让我们行动起来吧！（用上三个词，逻辑合理，表达通顺，即可得分）。

（2分）（二）综合性学习（共4分）9. C （2分）10.示例：①风筝也会展翅翱翔（或启航、勇敢飞翔等）②因为，每一次跌宕，都是在宣告成长。

（或每一次盘旋，都是在告别迷茫。

）（每空1分，共2分）二．古诗文阅读（共17分）（一）古诗文默写。

（4分）11. 白露未已（1分）12. 气蒸云梦泽（1分）13. 俶尔远逝天涯若比邻（每空1分，共2分。

有错字该空不得分）（二）古诗阅读（共5分）14. 水鸟和鸣（或水鸟和鸣起兴）钟鼓乐之（或琴瑟友之）（每空1分，共2分）15. 示例：两首诗都运用了“重章叠句”的艺术形式。

《关雎》诗人通过对“参差荇菜”“窈窕淑女”等，反复吟咏、一唱三叹，将男子对心仪女子的热切之情层层推进，表达了对美好情感的向往和追求。

而《式微》则通过反复运用设问“式微式微，胡不归”（或反问“微君之”“胡为乎”）来表达服劳役的人民的疾苦和对统治者的怨愤。

（3分）（三）文言文阅读（共8分）16. A（2分）17. B（2分）18. ①对理想社会的向往②热情好客③申以主敬④知礼（每空1分共4分）【译文】唐大历六年（公元771年），温州人李庭带领一批人到深山老林里伐木取材，由于山林密集而迷了路，遇见了一处瀑布。

2013~2014学年度第二学期北京四中初二年级物理期中考试题及答案（考试时间共100分钟，试卷满分为100分） 班级_____学号_____________姓名____________________第Ⅰ卷（选择题40分）考 生 须 知1．本试卷共8页，共五道大题，37道小题，满分100分。

考试时间100分钟。

2．在试卷和答题卡上准确填写班级名称、姓名和学号。

3．试题答案一律填涂或书写在机读卡、答题纸上，在试卷上作答无效。

4．在机读卡、答题纸上，选择题、作图题用2B 铅笔作答，其他试题用黑色字迹签字笔作答。

5．考试结束，将本试卷、机读卡和答题纸一并交回。

一、单项选择题（下列各小题均有四个选项，其中只有一个选项符合题意。

共28分，每小题2分）1. 如图所示的物体中，重力最接近2N 的是A ．一个苹果B ．一张课桌C ．一辆汽车D ．一枚别针 2. 如图所示的实例中，目的是为了增大压强的是 3. 如图所示的四个实例中，目的是为了减小摩擦的是4. 关于力的知识，下列说法中正确的是A ．同一直线上两个力的合力，一定大于其中任意一个分力A自行车的车把上刻有条纹 汽车轮胎上刻有花纹 自行车脚蹬上刻有纹线轴承中装有滚珠 注射器针头做得很尖 A 坦克装有宽大的履带B图钉帽的面积做得较大 C 载重汽车装有很多轮子 DB．静止在水平桌面上的书，其所受重力与桌面对它的支持力是一对相互作用力C．人推车时，人也受到了车对人的推力D．如果作用在一个物体上的两个力大小相等，这两个力一定是平衡力5.下列事例中，哪一项没有利用大气压A．塑料挂衣钩紧贴在光滑墙上，就可挂衣服B．利用针管吸药液C．活塞式抽水机把水抽到高处D．水在连通器内静止时液面总相平6.将一金属块挂在竖直的弹簧测力计挂钩上，并处于静止状态，则下列说法正确的是A．金属块所受的重力跟金属块对弹簧测力计的拉力是一对平衡力B．金属块所受的重力跟弹簧测力计对金属块的拉力是一对平衡力C．弹簧测力计所受的重力跟金属块对弹簧测力计的拉力是一对平衡力D．弹簧测力计对金属块的拉力跟金属块对弹簧测力计的拉力是一对平衡力7.如图所示的装置中，甲物重10N，乙物重5N，甲、乙均保持静止状态，不计弹簧测力计自重．则甲受到的合力和弹簧测力计的示数分别是A．0 N，10 NB．0 N，5 NC．5 N，5 ND．10 N，5 N8.下面关于压力和压强的说法中正确的是A．物体质量越大，产生的压力一定越大B．压力越大，支持面受到的压强一定越大C．受力面积越小，产生的压强一定越大D．压力越大，受力面积越小，支持面受到的压强就越大9.如图所示，物体重10 N，它与竖直墙面的接触面积是0.5 dm2，现用24 N的水平力把物体按在墙上，墙面受到物体的压力和压强分别为A．10 N，2×103 Pa B．10 N，4.8×103 PaC．24 N，2×103 Pa D．24 N，4.8×103 Pa10.正方体金属块放在水平桌面上，若从高度的一半处将它沿水平方向切开，如图所示，并将上半部分拿走，则剩余部分对桌面的压力、压强与原来相比A．压力减半，压强减半B．压力不变，压强减半C．压力减半，压强不变D．压力、压强都不变11.三个完全相同的烧杯里装有相同体积的水，用细线拴好三个质量相等的实心铜块、铁块、铝块，再把它们分别浸没在烧杯内的水中，水不溢出，已知ρ铜>ρ铁>ρ铝，则水对杯底的压强变化最小的是A．放入铜块的B．放入铁块的C．放入铝块的D．无法判断12.水平地面上放一块砖A，然后在它上面再放半块同样规格的砖B，如图所示，则B对A的压强和A对地面的压强之比是A．1: 1 B.2:1 C.2 :3 D.3 :213.两个完全相同的容器中分别盛有质量相等的水和酒精，如图所示，下列说法正确的是A．液面下深度相同的两处a、b所受液体压强相等B．两容器底受到压力相等C．盛水容器底部受到压强较大D．盛水容器底部受到压强较小14.教室装有磁性黑板，由于磁体之间有吸引力，所以内部装有磁铁的黑板擦就可以被吸在黑板上的任何位置而不会掉下来。

北京师大附中2013－2014学年下学期初中八年级期中考试语文试卷试卷说明：本试卷满分120分，考试时间为120分钟。

本试卷共Ⅱ卷，五道大题，24道小题。

第Ⅰ卷（共70分）一、选择（每题2分，共20分）1. 下列加点字注音完全正确的一项是（）A. 绯．红（fēi）执．拗（zhí）诘．责（jiã）长吁．短叹（xū）B. 胆怯．（quâ）污秽．（huì）睥睨．（nì）颔．首低眉（hàn）C. 滞．留（zhì）黝．黑（yǒu）酷肖．（xiào）藏污纳垢．（hîu）D. 迸．射（bìng）憔．悴（qiáo）馈．赠（kuì）深恶．痛疾（wù）2. 下列词语没有错别字的一项是（）A. 宽恕迁徒标致诚惶诚恐B. 退尽凛冽轩昂拖泥带水C. 犀利璀璨真缔冥思遐想D. 企盼蜿蜒奥秘黯然失色3. 下列加点字词解释完全正确的一项是（）A. 匿．名（隐藏）托辞．．（拜托的言辞）B. 禁锢．．（束缚，限制）正襟危坐（整理好衣襟，端正地坐着，形容生气的样子）C. 诘责．．（眼睛斜着看，形容高傲的样子）．．（质问并责备）睥睨D. 不逊．（无礼）广袤．．无垠（古代以东西长度为广，南北长度为袤）4. 在初二年级的篮球比赛中，一班二班的比赛最引人关注。

两个班实力相当，竞争激烈，比分一直交替上升，双方拼到最后一秒才分出胜负。

赛后，体育老师请观赛的学生用一句话来评价这场比赛。

评价最恰当的一句是（）A. 学生甲：这场比赛真可谓是峰回路转。

B. 学生乙：这真是一场扣人心弦的比赛！C. 学生丙：这场比赛不能不说是峰回路转。

D. 学生丁：这难道不是一场扣人心弦的比赛吗？5. 下列句子中加点词语运用正确的一项是（）A. 武侠小说《天龙八部》情节起伏跌宕、抑扬顿挫．．．．，吸引了无数读者。

B. 以前的科幻电影中的许多设想，当时看起来是不可思议．．．．的，现在却不断变为现实。

第Ⅰ卷一. 选择题（每小题3分，共30分）1. 若正比例函数kx y =的图像经过点（-2，1），则k 的值为（ ）． A ．21-B ．－2 C．21D ．22. 如图，数轴上点A 所表示的数为a ，则a 的值是（）．A 1BCD 3. 一条直线y kx b =+其中5k b +=-，6kb =，那么该直线经过（ ）． A ．第二、四象限 B ．第一、二、三象限 C ．第一、三象限 D ．第二、三、四象限4. 已知平行四边形周长为28cm ，相邻两边的差是4cm ，则两边的长分别为（ ）．A ．4cm 、10cm B ．5cm 、9cm C ．6cm 、8cm D ．5cm 、7cm5. 若一直角三角形两边长为6和8，则第三边长为（）．A ．10 B． C ．10或 D ．102013---2014学年度北京市第十三中学分校 第二学期期中 八年级 数 学 试 卷6. 下列命题中，不正确的是（）．A．三个角的度数之比为1:3:4的三角形是直角三角形;B．三边之比为1: 3:2的三角形是直角三角形;C．三个角的度数之比为1:2:2的三角形是直角三角形;D．三边之比为2:2:2的三角形是直角三角形.7.一次函数y=kx+b与y=kbx，它们在同一坐标系内的图象可能为（）A ．B ．C ．D ．8. 已知平行四边形的一条边长为14，下列各组数中能分别作它的两条对角线长的是（）．A．10与6 B．12与16 C．20与22 D．10与189.如下图，在矩形ABCD中，动点P从点B出发，沿BC，CD，DA运动至点A停止．设点P运动的路程为x，△ABP的面积为y，如果y关于x的函数图象如图所示，则△ABC的面积是（）．A．4 B．5 C．9 D．1010. 已知直线(1)122ny xn n-+=+++（n为正整数）与坐标轴围成的三角形的面积为S n，则S1+S2+S3+…+S2014=（）．A．1007503B．5032014C．10074032D．10072016ADP第Ⅱ卷二. 填空题（每小题2分，共16分）11. 已知菱形ABCD 两对角线AC = 8 cm, BD = 6 cm, 则菱形的高为________．12. 如图，在矩形ABCD 中，AB=2BC ，N 为DC 的中点，点M 在DC 上，且AM=AB ，则∠MBN 的度数为 ． 13. 如图，矩形纸片ABCD 中，AB =4，AD =3，折叠纸片使AD 边与对角线BD 重合，折痕为DG ，则AG 的长为 ．14. 如图所示，已知边长为2的正方形OABC 在平面直角坐标系中，位于x 轴上方，OA 与x 轴正半轴的夹角为60°，则B 点坐标为__________．15.新定义：[a ，b]为一次函数y=ax+b （a ≠0，a ，b 为实数）的“关联数”．若“关联数”[1，m ﹣2]的一次函数是正比例函数，则关于x 的方程1111x m+=-的解为 ． 16. 如图是一个“羊头”形图案，其做法是：从正方形（1）开始，以它的一边为斜边，向外做等腰直角三角形，然后再以其直角边为边，分别向外做正方形（2）和2’（），...，依次类推，若正方形（1）的边长为64厘米，则正方形（7）的边长为 厘米． 17. 如图，△ABC 的周长为26，点D ，E 都在边BC 上，∠ABC 的平分线垂直于AE ，垂足为Q ，∠ACB 的平分线垂直于AD ，垂足为P ，若BC=10，则PQ 的长为 ．18. 已知点A 、B 分别在一次函数y=x ，y=8x ，的图像上，其横坐标分别为a 、b(a>0，b>O)．若直线AB 为一次函数y=kx+m 的图像，则当a b是整数时，满足条件的整数k 的值为 ．BADCMN 12题图G DBA 13题图105︒30︒8BA三．解答题(19、21题 每题5分；26、27题7分, 其余各题每题6分, 共54分 ) 19. 如图，在△ABC 中，∠B=30°, ∠BAC=105°,AB=8. 求BC 的长.20. 如图,在平面直角坐标系xOy 中,一次函数 y=kx+b 的图象与x 轴交于点A(-3,0),与y 轴交于点B,且与正比例函数43y x =的图象的交点为C(m,4).(1)求一次函数y=kx+b 的解析式.(2)若点D 在第二象限,△DAB 是以AB 为直角边的等腰直角三角形,求点D 的坐标.21. 在平行四边形ABCD 中，分别以AD 、BC 为边向内作等边△ADE 和等边△BCF ，连接BE 、DF ．求证：四边形BEDF 是平行四边形．22. 已知：矩形ABCD.（1）如图（1），P 为矩形ABCD 的边AD 上一点，求证：2222PD PB PC PA +=+.（2）如图（2），当点P 运动到矩形ABCD 外时，结论是否仍然成立？请说明你的理由.ABBC CA D DP ●●P 图（1）图（2）CA23. 已知，如图，在△ABC中，∠ABC=90°，BD⊥AC于D,CE平分∠BCA,交AB于G,请你过G作GM⊥AC,垂足为M,连结ME,判断四边形BGME的形状并证明.BGEA24.某商场筹集资金12.8万元，一次性购进空调、彩电共30台．根据市场需要，这些空调、彩电可以全部销售，全部销售后利润不少于1.5万元，其中空调、彩电的进价和设商场计划购进空调x台，空调和彩电全部销售后商场获得的利润为y元．（1）试写出y与x的函数关系式；（2）商场有哪几种进货方案可供选择？（3）选择哪种进货方案，商场获利最大？最大利润是多少元？25. 在平面直角坐标系中，矩形OACB的顶点O在坐标原点，顶点A、B分别在x轴、y轴的正半轴上，OA=3，OB=4，D为边OB的中点．（1）若E为边OA上的一个动点，当△CDE的周长最小时，点E的坐标为；（温馨提示：可以作点D关于x轴的对称点D'，连接CD'与x轴交于点E，此时△CDE的周长是最小的．）（2）若E、F为边OA上的两个动点，且EF=2，当四边形CDEF的周长最小时，求点E、F的坐标．26. 已知，在△ABC 中，∠BAC=90°，∠ABC=45°，点D 为直线BC 上一动点（点D不与点B ，C 重合）．以AD 为边做正方形ADEF ，连接CF （1）如图1，当点D 在线段BC 上时．求证CF+CD=BC ；（2）如图2，当点D 在线段BC 的延长线上时，其他条件不变，请直接写出CF ，BC ，CD 三条线段之间的关系；（3）如图3，当点D 在线段BC 的反向延长线上时，且点A ，F 分别在直线BC 的两侧，其他条件不变；①请直接写出CF ，BC ，CD 三条线段之间的关系；②若正方形ADEF的边长为AE ，DF 相交于点O ，连接OC ．求OC 的长度．27. 如图，已知直线 162y x =-+ 交x 轴于B ，交y 轴于C ，并与直线y = x 交于点A ，点P 在射线OA 上从点O 出发沿射线OA 方向以每秒1个单位长的速度运动，过P 作PQ // x 轴交直线 162y x =-+ 于Q ，以PQ 为边向下作正方形PQMN ，设点P 的运动时间为t 秒，正方形PQMN 与△AOB 的重叠部分的面积为S ． （1）直接写出点A 的坐标（2）当点P 在线段OA 上且MN 在x 轴上时，求线段PQ 的长；（3）当点Q 在第一象限内时， 求S 与t 的函数关系式，并求对应的t 的取值范围.图3图2图1CD y= -12x。

人大附中2023～2024学年度第二学期初二年级数学期中练习说明：1．本试卷共6页，共两部分，三道大题，24道小题，满分100分，考试时间90分钟．2．试题答案一律填涂或书写在答题卡上，在试卷、草稿纸上作答无效．3．在答题卡上，选择题、作图题用2B 铅笔作答，其他试题用黑色字迹签字笔作答．第一部分 选择题一、选择题（共24分，每题3分）1. 以下列长度的三条线段为边能组成直角三角形的是（ ）A. 6，7，8B. 2，3，4C. 3，4，6D. 6，8，10【答案】D【解析】【分析】根据勾股定理逆定理即两短边的平方和等于最长边的平方逐一判断即可．【详解】解：．，不能构成直角三角形，故本选项错误；．，不能构成直角三角形，故本选项错误；．，不能构成直角三角形，故本选项错误；．，能构成直角三角形，故本选项正确．故选：．【点睛】本题考查的是勾股定理逆定理，熟知如果三角形的三边长，，满足，那么这个三角形就是直角三角形是解答此题的关键．2. 如图，中，于点，若，则的度数为（ ）A. B. C. D. 【答案】B【解析】【分析】由在□ABCD 中，∠EAD ＝35°，得出∠D 的度数，根据平行四边形的对角相等，即可求得∠B 的度数，继而求得答案．【详解】解：∵∠EAD ＝35°，AE ⊥CD ，∴∠D ＝55°，A 222678+≠ ∴B 222234+≠ ∴C 222346+≠ ∴D 2226810+= ∴D a b c 222+=a b c ABCD Y AE CD ⊥E 35EAD ∠=︒B ∠35︒55︒65︒125︒∴∠B ＝55°，故选：B ．【点睛】此题考查了平行四边形的性质．此题难度不大，注意掌握数形结合思想的应用．3. 下列各式中，运算正确的是（ ）A. B. C. D. 【答案】A【解析】【分析】本题考查了算术平方根，二次根式的加减运算．熟练掌握算术平方根，二次根式的加减运算是解题的关键．根据算术平方根，二次根式的加减运算求解作答即可．【详解】解：AB ．，错误，故不符合要求；C ．D，错误，故不符合要求；故选：A ．4. 在菱形中，点分别是的中点，若，则菱形的周长是（ ）A. 12B. 16C. 20D. 24【答案】D【解析】【分析】根据三角形中位线定理可得，再根据菱形的周长公式列式计算即可得到答案．【详解】解：点分别是的中点，是的中位线，，菱形的周长，=3=2=2=-=3=≠2+≠22=≠-ABCD E F ，AC DC ，3EF =ABCD 26AD EF == E F ，AC DC ，EF ∴ACD 2236AD EF ∴==⨯=∴ABCD 44624AD ==⨯=【点睛】本题主要考查了三角形中位线定理，菱形性质，熟练掌握三角形的中位线等于第三边的一半及菱形的四条边都相等，是解题的关键．5. 如图，正方形的边长为2，是的中点，，与交于点，则的长为（ ）A. B. C. D. 3【答案】A【解析】【分析】由正方形的性质得出∠DAF ＝∠B ＝90°，AB ＝AD ＝2，由E 是BC 的中点，得出BE ＝1，由勾股定理得出AEADF ≌△BAE（ASA ），即可得出答案．【详解】∵四边形ABCD是正方形，∴∠DAF ＝∠B ＝90°，BC ＝AB ＝AD ＝2，∴∠BAE ＋∠2＝90°，∵AB ＝2，E 是BC 的中点，∴BE ＝1，∴AE ，∵AD ∥BC ，∴∠1＝∠2，∵DF ⊥AE ，∴∠1＋∠ADF ＝90°，∴∠ADF ＝∠BAE ，在△ADF 和△BAE 中，，的ABCD E BC DF AE ⊥AB F DF =DAF B AD ABADF BAE ∠=∠⎧⎪=⎨⎪∠=∠⎩∴△ADF ≌△BAE （ASA ），∴DF ＝AE故选：A ．【点睛】此题主要考查了正方形的性质、全等三角形的判定和性质、勾股定理等知识；熟练掌握正方形的性质，证明三角形全等是解题的关键．6. 一个正方形的面积是22.73，估计它的边长大小在（ ）A. 2与3之间B. 3与4之间C. 4与5之间D. 5与6之间【答案】C 【解析】【分析】设正方形的边长为，根据其面积公式求出的值，估算出的取值范围即可．【详解】解：设正方形的边长为，正方形的面积是22.73，，，，它的边长大小在4与5之间，故选：C ．【点睛】本题考查的是估算无理数的大小及算术平方根，估算无理数的大小时要用有理数逼近无理数，求无理数的近似值．7. 要判断一个四边形是否为矩形，下面是4位同学拟定的方案，其中正确的是 （ ）A. 测量两组对边是否分别相等B. 测量两条对角线是否互相垂直平分C. 测量其中三个内角是作都为直角D. 测量两条对角线是否相等【答案】C【解析】【分析】根据矩形的判定和平行四边形的判定以及菱形的判定分别进行判断，即可得出结论．【详解】解：矩形的判定定理有①有三个角是直角的四边形是矩形，②对角线互相平分且相等的四边形是矩形，③有一个角是直角的平行四边形是矩形，、根据两组对边分别相等，只能得出四边形是平行四边形，故本选项错误；a a a a a ∴=1622.7325<< <<45<<∴A、根据对角线互相垂直平分得出四边形是菱形，故本选项错误；、根据矩形的判定，可得出此时四边形是矩形，故本选项正确；、根据对角线相等不能得出四边形是矩形，故本选项错误；故选：．【点睛】本题考查了矩形的判定、平行四边形和菱形的判定，主要考查学生的推理能力和辨析能力．8. 如图，点A ，B ，C 在同一条直线上，点B 在点A ，C 之间，点D ，E 在直线AC 同侧，，，，连接DE ，设，，，给出下面三个结论：①；②；．上述结论中，所有正确结论的序号是（ ）A. ①B. ①③C. ②③D. ①②③【答案】D【解析】【分析】此题考查了勾股定理，全等三角形的判定与性质，完全平方公式的应用，熟记勾股定理是解题的关键．①根据直角三角形的斜边大于任一直角边即可；②在三角形中，两边之和大于第三边，据此可解答；③将用和表示出来，再进行比较．【详解】解：①过点作，交于点；过点作，交于点．∵，，，又，，B C D C AB BC <90A C ∠=∠=︒EAB BCD ≌△△AB a =BC b =DE c =a b c +<a b +>)a b c +>c a b D DF AC ∥AE F B BG FD ⊥FD G DF AC ∥AC AE ⊥DF AE ∴⊥BG FD ⊥ BG AE ∴四边形为矩形，同理可得，四边形也为矩形，，在中，则，故①正确，符合题意；②∵，，在中，，，故②正确，符合题意；③∵，，，又，，．，，，，，．故③正确，符合题意；故选：D第二部分 非选择题二、填空题（共24分，每题3分）∴ABGF BCDG FD FG GD a b ∴=+=+∴Rt EFD DF ED<a b c +<EAB BCD ≌△△AE BC b ∴==Rt EAB△BE ==AB AE BE +>a b ∴+>EAB BCD ≌△△AEB CBD ∠∠∴=BE BD =90AEB ABE ∠+∠=︒ 90CBD ABE ∴∠+=∠︒90EBD ∴∠︒=BE BD = 45BED BDE ∴∠=∠=︒sin 45BE c ∴==⋅︒=c ∴= 22222222()2(2)2()42()a b a ab b a b ab a b +=++=++>+∴)a b +>∴)a b c +>9.有意义，则实数x 的取值范围是______．【答案】【解析】【分析】本题主要考查了二次根式有意义的条件，解题的关键是熟练掌握二次根式被开方数为非负数．有意义，∴，解得：，故答案为：．10. 如图，在中，若，点D 是的中点，，则的长度是_____．【答案】2【解析】【分析】本题考查了直角三角形的性质，利用直角三角形斜边上的中线等于斜边的一半可得的长度．【详解】解：∵在中，，点D 是的中点，，∴．故答案为：2．11. 如图，在数轴上点 A 表示的实数是_____．【解析】【分析】根据勾股定理求得的长度，即可得到的长度，根据点的位置即可得到点表示的数．【详解】解：如图，1x ≥10x -≥1x ≥1x ≥ABC 90ACB ∠=︒AB 4AB =CD CD ABC 90ACB ∠=︒AB 4AB =114222CD AB ==⨯=BD AB B A根据勾股定理得：，，点【点睛】本题考查了实数与数轴，掌握直角三角形两直角边的平方和等于斜边的平方是解题的关键．12. 如图，在四边形中，对角线相交于点O ．如果，请你添加一个条件，使得四边形成为平行四边形，这个条件可以是______________________．【答案】（答案不唯一）【解析】【分析】本题考查了平行四边形的判定．熟练掌握平行四边形的判定是解题的关键．根据平行四边形的判定作答即可．【详解】解：由题意知，可添加的条件为，∵，，∴四边形平行四边形，故答案为：．13. 如图，矩形的对角线相交于点O ，，，则矩形对角线的长为___________，边的长为___________．【答案】①. 8 ②. 【解析】【分析】本题主要考查了矩形的性质，等边三角形的性质与判定，勾股定理，先由矩形对角线相等且互相是BD ==∴AB BD ==∴A ABCD AC BD ，AB CD ∥ABCD AD BC ∥AD BC ∥AD BC ∥AB CD ∥ABCD AD BC ∥ABCD AC BD ，60AOB ∠=︒4AB =BD BC平分得到，再证明是等边三角形，得到，则，据此利用勾股定理求出的长即可．【详解】解：∵四边形是矩形，∴，∵，∴是等边三角形，∴，∴，在中，由勾股定理得故答案为：8；14. 小明用四根长度相同的木条制作了能够活动的菱形学具，他先活动学具成为图1所示的菱形，并测得，对角线的长为，接着活动学具成为图2所示的正方形，则图2中对角线的长为________．【答案】【解析】【分析】如图1，2中，连接AC ．在图2中，利用勾股定理求出BC ，在图1中，只要证明△ABC 是等边三角形即可解决问题．【详解】解：如图1，2中，连接AC ．如图1中，∵AB ＝BC ，∠B ＝60°，∴△ABC 是等边三角形，∴AB ＝BC ＝AC ＝30，在图2中，∵四边形ABCD 是正方形，2290AC BD OA BD ABC ====︒，∠AOB 4OA OB AB ===28AC BD OB ===BC ABCD 2290OA OB AC BD OA BD ABC =====︒，，∠60AOB ∠=︒AOB 4OA OB AB ===28AC BD OB ===Rt ABC △BC ===60B ∠︒AC 30cm AC cm∴AB ＝BC ，∠B ＝90°，∵AB ＝BC ＝30cm ，∴AC ＝cm ，故答案为：．【点睛】本题考查菱形的性质、正方形的性质、勾股定理等知识，解题的关键是灵活运用所学知识解决问题，属于中考常考题型．15. 如图，将菱形纸片ABCD 折叠，使点B 落在AD 边的点F 处，折痕为CE ，若∠D ＝80°，则∠ECF 的度数是________．【答案】40°【解析】【分析】根据题意由折叠的性质可得∠BCE =∠FCE ，BC =CF ，由菱形的性质可得BC ∥AD ，BC =CD ，可求∠BCF =∠CFD =80°，即可求解．【详解】解：∵将菱形纸片ABCD 折叠，使点B 落在AD 边的点F 处，∴∠BCE =∠FCE ，BC =CF ，∵四边形ABCD 是菱形，∴BC ∥AD ，BC =CD ，∴CF =CD ，∴∠CFD =∠D =80°，∵BC ∥AD ，∴∠BCF =∠CFD =80°，∴∠ECF =40°．故答案为：40°．【点睛】本题考查翻折变换以及菱形的性质，熟练掌握并运用折叠的性质是解答本题的关键．16. 图1中的直角三角形有一条直角边长为3，将四个图1中的直角三角形分别拼成如图2，图3所示的正方形，其中阴影部分的面积分别记为，，则的值为___________．【答案】9【解析】【分析】设直角三角形另一直角边为，然后分别用表示出两个阴影部分的面积，最后求解即可．本题主要考查了三角形和正方形面积的求法，解题的关键在于能够熟练地掌握相关的知识点．【详解】解：设直角三角的另一直角边为，则，，，．故答案为：9三、解答题（共52分，第17题8分，第18-19题，每题5分，第20题6分，第21题5分，第22题6分，第23题7分，第24题10分）解答应写出文字说明、演算步骤或证明过程．17. 计算：（1）；（2）．【答案】（1（2）【解析】【分析】本题考查了利用二次根式的性质进行化简，二次根式的加减运算，二次根式的混合运算．熟练掌握利用二次根式的性质进行化简，二次根式的加减运算，二次根式的混合运算是解题的关键．（1）先利用二次根式的性质进行化简，然后进行加减运算即可；1S 2S 12S S -a a a 2211(3)4392S a a a =+-⨯⨯=+22S a a a =⋅=221299S S a a ∴-=+-=(1-（2）先分别计算二次根式的乘除，然后进行加减运算即可．【小问1详解】解：【小问2详解】解：．18. 如图，四边形为平行四边形，，是直线上两点，且，连接，．求证：．【答案】见详解【解析】【分析】本题考查平行四边形的性质、平行线的性质、全等三角形的判定与性质，根据可得，再根据平行四边形的性质可得，且，即，即可证明，即可得到结论．【详解】证明：∵，∴，∴，∵四边形为平行四边形，∴，且，∴，在和中，2=⨯=(32=+1=-ABCD E F BD BE DF =AF CE AF CE =BE DF =ED FB =AB DC =AB DC =EDC FBA ∠∠()SAS DEC BFA ≌BE DF =BE BD DF BD +=+ED FB =ABCD AB DC =AB DC =EDC FBA ∠∠DEC BFA V，∴，∴．19. 已知，求的值．【答案】11【解析】【分析】本题考查了已知式子的值求代数式的值，平方差公式，先整理，再代入计算，即可作答．【详解】解：依题意，20. 如图，在中，点D 是线段的中点．求作：线段，使得点E 在线段上，且．作法：①连接，②以点A 为圆心，长为半径作弧，再以C 为圆心，长为半径作弧，两弧相交于点M ；③连接，交于点E ；所以线段即为所求的线段．（1）使用直尺和圆规，依作法补全图形（保留作图痕迹）；（2）完成下面的证明：证明：连接∵，，∴四边形是平行四边形．（①）（填推理的依据）∵交于点E ，∴，即点E 是的中点．（② ）（填推理的依据）DE BF EDC FBA DC AB =⎧⎪∠=∠⎨⎪=⎩()SAS DEC BFA ≌AF CE=1x =-227x x ++()22727x x x x ++=++()))2272711751711x x x x ++=++=⨯++=-+=ABC AB DE AC 12DE BC =CD CD AD DM AC DE AM CM ，，AM CD =AD CM =ADCM AC DM ，AE CE =AC∵点D 是AB 的中点，∴．（③ ）（填推理的依据）【答案】见详解【解析】【分析】本题考查了作图复杂作图：复杂作图是在五种基本作图的基础上进行作图，一般是结合了几何图形的性质和基本作图方法．解决此类题目的关键是熟悉基本几何图形的性质，结合几何图形的基本性质把复杂作图拆解成基本作图，逐步操作．（1）根据几何语言画出对应的几何图形即可；（2）先证明四边形是平行四边形，得出点E 是的中点，再结合然后点D 是的中点，即三角形中位线性质得到．【详解】解：（1）如图，；（2）证明：连接AM ，CM ，∵，，∴四边形是平行四边形．（①两组对边分别相等的四边形是平行四边形）（填推理的依据）∵AC ，DM 交于点E ，∴，即点E 是中点．（②平行四边形的对角线互相平分）（填推理的依据）∵点D 是的中点，∴（③中位线的性质）．故答案为：两组对边分别相等的四边形是平行四边形；平行四边形的对角线互相平分；中位线的性质．21. 如图，四边形中，，，．的12DE BC =-ADCM AC AB 12DE BC =AM CD =AD CM =ADCM AE CE =AC AB 12DE BC =ABCD 90BAD ∠=︒AB AD ==4BC =CD =（1）求的度数；（2）求四边形的面积．【答案】（1）（2）5【解析】【分析】（1）由题意得，，由勾股定理得，，由，可得是直角三角形，且，根据，计算求解即可；（2）根据，计算求解即可．【小问1详解】解：∵，∴，由勾股定理得，，∵，∴，∴是直角三角形，且，∴，∴的度数为；【小问2详解】解：由题意知，，∴四边形的面积为5．【点睛】本题考查了三角形内角和定理，等边对等角，勾股定理，勾股定理逆定理等知识．熟练掌握三角形内角和定理，等边对等角，勾股定理，勾股定理逆定理是解题的关键．ABC ∠ABCD 135︒1802BADABD ADB ︒-∠∠=∠=2BD =222BD BC CD +=BCD △90CBD ∠=︒ABC ABD CBD ∠=∠+∠1122ABD BCD ABCD S S S AB AD BC BD =+=⨯+⨯ 四边形90BAD ∠=︒AB AD ==180452BAD ABD ADB ︒-∠∠=∠==︒2BD ==(2222420+==222BD BC CD +=BCD △90CBD ∠=︒135ABC ABD CBD ∠=∠+∠=︒ABC ∠135︒11522ABD BCD ABCD S S S AB AD BC BD =+=⨯+⨯= 四边形ABCD22. 在中，，点D 是边上的一个动点，连接．作，，连接．（1）如图1，当时，求证：；（2）当四边形是菱形时，①在图2中画出四边形，并回答：点D 的位置为 ．②若，，则四边形的面积为 ．【答案】（1）见解析，（2）①见解析，为的中点；②【解析】【分析】（1）由，，可证四边形是平行四边形，由，可证四边形是矩形，进而结论得证；（2）①由题意作图如图2，由四边形是菱形，可得，则，由，可得，则，，即为的中点；②如图2，记的交点为，则，，，由勾股定理求，则，根据，计算求解即可．【小问1详解】证明：∵，，∴四边形是平行四边形，∵，∴，∴四边形是矩形，∴；【小问2详解】①解：如图2，Rt ABC △90ACB ∠=︒AB CD AE DC ∥CE AB ∥DE CD AB ⊥AC DE =ADCE ADCE 10AB =8DE =ADCE D AB 24AE DC ∥CE AB ∥AECD 90CDA ∠=︒AECD ADCE AD CD =DAC DCA ∠=∠18090B ACB DAC DCB DCA ∠=︒-∠-∠∠=︒-∠，B DCB ∠=∠CD BD =AD BD =D AB AC DE 、O 5AD =142DO DE ==AC DE ⊥3AO =26AC AO ==12ADCE S AC DE =⨯四边形AE DC ∥CE AB ∥AECD CD AB ⊥90CDA ∠=︒AECD AC DE =∵四边形是菱形，∴，∴，∵，∴，∴，∴，∴为的中点；②解：如图2，记的交点为，∵四边形是菱形，为的中点，，，∴，，，由勾股定理得，，∴，∴，故答案为：．【点睛】本题考查了矩形的判定与性质，等边对等角，三角形内角和定理，菱形的性质，勾股定理等知识．熟练掌握矩形的判定与性质，等边对等角，三角形内角和定理，菱形的性质，勾股定理是解题的关键．23. 如图，四边形中，，，对角线平分，过点A 作的垂线，分别交，于点E ，O ，连接．（1）求证：四边形菱形；（2）连接，若，，求的长．是ADCE AD CD =DAC DCA ∠=∠18090B ACB DAC DCB DCA ∠=︒-∠-∠∠=︒-∠，B DCB ∠=∠CD BD =AD BD =D AB AC DE 、O ADCE D AB 10AB =8DE =5AD =142DO DE ==AC DE⊥3==AO 26AC AO ==1242ADCE S AC DE =⨯=四边形24ABCD AD BC ∥90BCD ∠=︒BD ABC ∠BD AE BC BD DE ABED CO 3AB =2CE =CO【答案】（1）见解析（2）【解析】【分析】（1）先证明，再由等腰三角形的性质得，然后证，得，则四边形是平行四边形，然后由菱形的判定即可得出结论；（2）由勾股定理得，根据直角三角形斜边上的中线等于斜边的一半，即可得出【小问1详解】证明：∵，∴，∵平分，∴，∴，∴，∵，∴，∵，在和中，，，，四边形是平行四边形，又，平行四边形为菱形；【小问2详解】解：∵四边形为菱形，∴，，CO =AB AD =OB OD =()ASA OBE ODA ≌OE OA =ABED CD =BD =CO =AD BC ∥ADB DBE ∠=∠BD ABC ∠ABD DBE ∠=∠ABD ADB ∠=∠AB AD =AE BD ⊥BO DO =AD BC ∥OBE △ODA V DBE ADB OB ODBOE DOA ∠=∠⎧⎪=⎨⎪∠=∠⎩()ASA OBE ODA ∴ ≌OE OA ∴=∴ABED AB AD = ∴ABED ABED 3BE DE AB ===BO DO =∵，，，∴在中，根据勾股定理得：，∵，为直角三角形，∴．【点睛】本题考查了菱形的判定与性质、全等三角形的判定与性质、等腰三角形的性质以及勾股定理、直角三角形斜边上的中线等于斜边的一半，二次根式的混合运算等知识，熟练掌握菱形的判定与性质是解题的关键．24. 在中，，，点D 为射线上一动点（不与点B 、C 重合），点B 关于直线的对称点为E ，作射线，过点C 作的平行线，与射线交于点F ．连接（1）如图1，当点E 恰好在线段上时，用等式表示与的数量关系，并证明；（2）如图2，当点D 在线段的延长线上时，①依题意补全图形；②用等式表示和的数量关系，并证明．【答案】（1），证明见详解（2）①见详解②，证明见详解【解析】【分析】本题考查了全等三角形的判定与性质、正方形的性质与判定，矩形的性质，轴对称性质，正确掌握相关性质内容是解题的关键．（1）先由轴对称性质，得出再证明，因为，得出得证即可作答．90BCD ∠=︒CD =∴=325BC BE CE =+=+=Rt BCDBD ===BO DO =BCD△12CO BD ==ABC 90ABC ∠=︒AB BC =BC AD DE AB DE AE AF ，．AC DF BD BC ADB ∠AFE ∠2DF BD =45ADB AFE ∠+︒=∠AB AE BD ED ==，，()SSS ADE ADB ≌CF AB ∥45ECD ECF ∠=∠=︒，()ASA CED CEF ≌，（2）①根据题意的描述作图即可；②易得，过点作于点，四边形是正方形，证明，则，再通过角的运算，即可作答．【小问1详解】解：，证明如下：如图：当点E 恰好在线段上时，∵在中，∴，∵点B 关于直线的对称点为E ，∴在和中，∴，∴，∴，，∵，∴在和中，∴ADE ADB ≌A AG CF ⊥G ABCG ()Rt Rt HL AFG AFE ≌FAG FAE EAG ∠==∠2DF BD =AC ABC 90ABC AB BC∠=︒=，45BAC ACB ∠=∠=︒AD AB AE BD ED ==，，ADE V ADB AE AB ED BD AD AD =⎧⎪=⎨⎪=⎩，()SSS ADE ADB ≌90AED ABD ∠=∠=︒AC DF ⊥90CED CEF ∠=∠=︒CF AB ∥45ECF BAC ∠=∠=︒，45ECD ECF ∴∠=∠=︒，CED △CEF △CED CEF CE CEECD ECF ∠=∠⎧⎪=⎨⎪∠=∠⎩()ASA CED CEF ≌，∴ ∴，即有；【小问2详解】解：当点在线段的延长线上时①依题意补全图形如下②用等式表示和的数量关系是，证明如下∵点关于直线的对称点为E ，∴，∴，过点作于点，如上图，则，∵，∴∴四边形是矩形，∵，∴四边形是正方形，∴，在和中，∴，∴，即有，12DE EF DF ==，12BD DE DF ==2DF BD =D BC ADB ∠AFE ∠45ADB AFE ∠+︒=∠B AD ADE ADB ≌90AE AB AEF ABC =∠=∠=︒，12EAD BAD BAE ∠=∠=∠，A AG CF ⊥G 90AGF AGC ∠=∠=︒CF AB ∥90BAG AGF ABC AGC∠=∠=︒=∠=∠ABCG AB BC =ABCG AG AB AE ==Rt AFG △Rt AFE AG AE AF AF=⎧⎨=⎩()Rt Rt HL AFG AFE ≌FAG FAE EAG ∠==∠2EAG FAE ∠=∠∵∴，∴，∴∴在中，，∴∴．人大附中2023～2024学年度第二学期初二年级数学期中练习附加题说明：1．附加题共4页，共两道大题，9道小题，满分40分，考试时间30分钟．2．试题答案一律填涂或书写在答题卡上，在试卷、草稿纸上作答无效．3．在答题卡上，作图题用2B 铅笔作答，其他试题用黑色字迹签字笔作答．一、填空题（共15分，第1题4分，第2-4题，每题3分，第5题2分）25. 矩形中，，，点E 是边上一点，连接，将沿折叠，使点B 落在点处，连接．（1）如图1，当时，的长为___________．（2）如图2，当点恰好在矩形的对角线上，则的长为___________．【答案】①. 4 ②. 【解析】【分析】（1）由矩形性质得，由折叠得：，，由平行线的性质得：，，进而得出：，，即；90AFE FAE ∠+∠=︒90FAE AFE ∠=︒-∠21802EAG FAE AFE ∠=∠=︒-∠2702BAE BAG EAG AFE∠=∠+∠=︒-∠135.BAD BAE AFE ∠=∠=︒-∠Rt △ABD 90ADB BAD ∠+∠=︒13590ADB AFE ∠+︒-∠=︒45ADB AFE ∠+︒=∠ABCD 6AB =8BC =BC AE ABE AE B 'CB 'CB AE '∥BE B 'ABCD ACAE 90ABE ∠=︒B E BE '=AEB AEB '∠=∠AEB ECB '∠=∠AEB EB C ''∠=∠ECB EB C ''∠=∠B E EC '=142BE EC BC ===（2）利用勾股定理可得，由折叠得：，，，设，则，，利用勾股定理建立方程求解即可；本题是矩形综合题，考查了矩形的性质，折叠变换的性质，勾股定理等，熟练掌握相关知识，学会添加辅助线是解题关键．【详解】解：（1）四边形是矩形，，由折叠得：，，，，，，，，，，故答案为：4；（2）如图，点恰好在矩形的对角线上，四边形是矩形，，，，，由折叠得：，，，，，设，则，，在中，，10AC ===AB AB '=B E BE '=90AB E ABE '∠=∠=︒BE x =B E x '=8CE x =- ABCD 90ABE ∴∠=︒B E BE '=AEB AEB '∠=∠CB AE ' AEB ECB '∴∠=∠AEB EB C ''∠=∠ECB EB C ''∴∠=∠B E EC '∴=12BE EC BC ∴==8BC = 4BE ∴=B 'ABCD AC ABCD 90ABC ∴∠=︒=6AB 8BC=10AC ∴===AB AB '=B E BE '=90AB E ABE '∠=∠=︒1064B C AC AB ''∴=-=-=18090CB E AB E ''∠=︒-∠=︒BE x =B E x '=8CE x =-Rt CB E '△222B E B C CE ''+=，解得：，，在中，；故答案为：4，26. 如图，四边形中， ，的平分线交于点E ，连接．在以下条件：①平分；②E 为中点；③中选取两个作为题设，另外一个作为结论，组成一个命题．（1）请写出一个真命题：题设为___________，结论为___________．（填序号）（2）可以组成真命题的个数为___________．【答案】①. ②， ②. ③， ③. 6【解析】【分析】（1）根据挑选题设为②，结论为③，结合，的平分线交这个两个条件，先证明，再进行边的等量代换，即可作答．（2）注意分类讨论以及逐个分析，不管取哪个作为条件都可以证明，从而利用全等三角形的性质进行边的等量代换或者角的等量代换，即可作答．【详解】解：（1）题设为②，结论为③；理由如下：延长交的延长线于点，∵∴，()22248x x ∴+=-3x =3BE ∴=Rt ABEAE ===ABCD AD BC ∥BAD ∠CD BE BE ABC ∠CD AD BC AB +=AD BC ∥BAD ∠CD ()AAS AED FEC ≌AED FEC △≌△AE BC F AD BC∥DAE F ∠=∠∵E 为中点，∴，在和中，∴，∴，，∵的平分线交于点E ，∴，∴∴∴（2）由（1）知，题设为②，结论为③是真命题，同理：题设为③，结论为②是真命题，过程如下：延长交的延长线于点，∵的平分线交于点E∴，∵∴∴∵∴∴∵CD DE CE =AED △FEC DAE F DEA CEFDE CE ∠=∠⎧⎪∠=∠⎨⎪=⎩()AAS AED FEC ≌CF AD =AD BC CF BC BF +=+=BAD ∠CD DAE BAD ∠=∠BAD F∠=∠AB BF=AD BC AB+=AE BC F BAD ∠CD DAE BAD ∠=∠AD BC∥BAD DAE F∠=∠=∠AB BF=AD BC AB+=AD BC AB BF+==AD CF=AD BC∥∴∵∴∴即E 为中点；当题设为①，结论为②是真命题，过程如下：延长交的延长线于点，∵的平分线交于点E∴，∵∴∴∵平分∴∵∴∴即E 为中点；同理：当题设为②，结论①为是真命题，同理，∴，，∵的平分线交于点E ，∴，∴∴∴DAE F∠=∠DEA CEF∠=∠ ≌DEA CEFDE CE=CD AE BC F BAD ∠CD DAE BAD ∠=∠AD BC∥BAD DAE F∠=∠=∠AB BF=BE ABC∠EB AF AE EF⊥=，DEA CEF DAE F∠=∠∠=∠， ≌DEA CEFDE CE=CD CF AD =AD BC CF BC BF +=+=BAD ∠CD DAE BAD ∠=∠BAD F∠=∠AB BF=AD BC AB+=则当题设为①，结论为③是真命题，同理：当题设为③，结论为②是真命题，综上共有6个命题：分别是题设为②，结论为③；题设为③，结论为②；题设为①，结论为②；题设为②，结论①；题设为①，结论为③，题设为③，结论为②．【点睛】本题考查了全等三角形的判定与性质、真命题，等腰三角形的判定与性质，角平分线的定义，正确掌握相关性质内容是解题的关键．27. 如图，在正方形中，，点E 为对角线上的动点（不与A ，C 重合），以为边向外作正方形，点P 是的中点，连接，则的取值范围为___________．【解析】【分析】先取的中点O，结合正方形的性质，得证，当时，有最小值，在中，，计算即可作答．【详解】解：如图，取的中点O ，连接，∵四边形、是正方形，∴，，∴，则在和中ABCD 4AB =AC DE DEFG CD PG PG PG ≤<AD ()SAS ODE PDG ≌OEAC ⊥OE Rt AOE △2224OE AE AO +==AD OE DEFG ABCD 90ODE EDC ︒∠+∠=90PDG EDC ∠+∠=︒ODE PDG ∠=∠ODE PDG △OD OP ODE PDGDE DG =⎧⎪∠=∠⎨⎪=⎩，∴，当时，有最小值，此时为等腰直角三角形，，∵，∴，在中，，即，解得，∴．当点运动到点的时候，如图：此时即为点H 的位置，此时正方形的边长最大且为则的值最大，此时∴则．【点睛】本题考查了正方形性质，全等三角形的判定与性质，垂线段最短，勾股定理等知识，正确掌握相关性质内容是解题的关键．28.如图，正方形ABCD 边长为2，点E 是射线AC 上一动点(不与A ，C 重合)，点F 在正方形ABCD 的外角平分线CM 上，且CF=AE ，连接BE ， EF ， BF 下列说法：①的值不随点E 的运动而改变的()SAS ODE PDG ∴ ≌OE PG =OE AC ⊥OE AOE △OE AE =4AD AB ==122AO AB ==Rt AOE △2224OE AE AO +==224OE =OE =OE E C G DEFG 4CD AD ==PH PH ===PG PG ≤<PG ≤<②当B ，E ， F 三点共线时，∠CBE=22.5°；③当△BEF 是直角三角形时，∠CBE=67.5°；④点E 在线段AC 上运动时，点C 到直线EF 的距离的最大值为1；其中正确的是__________（填序号）．【答案】①②④【解析】【分析】连接、，由正方形的对称性可知，，，证明，得出，，证出，证出是等腰直角三角形得出，因此，得出①正确；当，，三点共线时，证出，，，四点共圆，由圆周角定理得出，证出，得出，求出，②正确；当是直角三角形时，证出，得出，，③不正确；当点在线段上运动时，过点作于，则，最大时，与重合，即，证出是的中位线，得出，④正确；即可得出结论．【详解】解：连接、，如图1所示：由正方形的对称性可知，，四边形是正方形，，，点是正方形外角平分线上一点，，，在和中，，，，，ED DF BE DE =CBE CDE ∠=∠()ABE CDF SAS ∆≅∆BE DF =ABE CDF ∠=∠DE DF =EDF∆EF=EF B E F E C F D BFC CDE ∠=∠CDE CBE =∠∠CBF CFB ∠=∠22.5CBF ∠=︒BEF ∆9045135BED ∠=︒+︒=︒1(36013590)67.52CBE ∠=︒-︒-︒=︒67.5CBF ∠<︒E AC C CQ EF ⊥Q CQ CH …CQ CQ CH CD EF ⊥QE ACD ∆112CQ DQ CD ===ED DF BE DE =CBE CDE∠=∠ ABCD AB CD ∴=45BAC ∠=︒ F ABCD CM 45DCF ∴∠=︒BAC DCF ∴∠=∠ABE ∆CDF ∆AB CD BAC DCF AE CF =⎧⎪∠=∠⎨⎪=⎩()ABE CDF SAS ∴∆≅∆BE DF ∴=ABE CDF ∠=∠，，，即，是等腰直角三角形，，的值不随点的运动而改变，①正确；当，，三点共线时，如图2所示：，，，，四点共圆，，，，，，，，②正确；当是直角三角形时，如图3所示：是等腰直角三角形，，DE DF ∴=90ABE CBE ∠+∠=︒ 90CDF CDE ∴∠+∠=︒90EDF ∠=︒EDF∴∆EF ∴=EF ∴=∴EF BEE B EF 90ECF EDF ∠=∠=︒ E ∴C F D BFC CDE ∴∠=∠ABE ADE ∠=∠ 90ABC ADC ∠=∠=︒CDE CBE ∴∠=∠CBF CFB ∴∠=∠45FCG CBF CFB ∠=∠+∠=︒ 22.5CBF ∴∠=︒BEF ∆EDF ∆ 9045135BED ∴∠=︒+︒=︒，，③不正确；当点在线段上运动时，如图4所示：过点作于，则，最大时，与重合，即，当时，，，是的中位线，，④正确；综上所述，①②④正确；故答案为：①②④．【点睛】本题考查了正方形的性质、全等三角形的判定与性质、等腰直角三角形的判定与性质、四点共圆、圆周角定理等知识；本题综合性强，有一定难度．29. 如图，在平行四边形中，，，，在线段上取一点E ，使，连接，点M ，N 分别是线段上的动点，连接，则的最小值为___________．1(36013590)67.52CBE ∴∠=︒-︒-︒=︒67.5CBF ∴∠<︒E AC C CQ EF ⊥Q CQ CH …CQ ∴CQ CH CD EF ⊥CD EF ⊥//EF AD CF CE AE ==QE ∴ACD ∆112CQ DQ CD ∴=== ABCD 3AB =4BC =60ABC ∠=︒AD 1DE =BE AE BE ，MN 12MN BN +【解析】【分析】如图，作于，于，于，则四边形是矩形，，由题意可求，，，则，，由，可知当三点共线且时，最小，为，求的长，进而可求最小值，【详解】解：如图，作于，于，于，则四边形是矩形，∴，∵平行四边形中，，，，，∴，，∴，∴，∴，∴，∴当三点共线且时，最小，为，∵，∴，由勾股定理得，，∴，【点睛】本题考查了平行四边形的性质，矩形的判定与性质，含的直角三角形，等边对等角，勾股定理NF BC ^F AH BC ⊥H MG BC ⊥G AHGM MG AH =3AE AB ==120BAC ∠=︒30ABE AEB ∠=∠=︒30EBC ∠=︒12NF BN =12MN BN MN NF +=+M N F 、、MF BC ⊥12MN BN +MG AH 12MN BN +NF BC ^F AH BC ⊥H MG BC ⊥G AHGM MG AH =ABCD 3AB =4BC =1DE =60ABC ∠=︒3AE AB ==120BAC ∠=︒30ABE AEB ∠=∠=︒30EBC ∠=︒12NF BN =12MN BN MN NF +=+M N F 、、MF BC ⊥12MN BN +MG =30BAH ∠︒1322BH AB ==AH ==12MN BN +30︒等知识．明确线段和最小的情况是解题的关键．二、解答题（共25分，第6题5分，第7题4分，第8-9题，每题8分）解答应写出文字说明、演算步骤或证明过程．30. 如图是由小正方形组成的网格，每个小正方形的边长为，其顶点称为格点，四边形的四个顶点都在格点上，请运用课本所学知识，仅用无刻度的直尺，在给定网格中按要求作图．（1）①线段的长为 个单位长度；②在图1中求作边的中点E ；（2）在图中求作边上一点，使平分．注：保留作图痕迹，同时标出必要的点；当你感觉方法比较复杂时，可用文字简要说明作法．【答案】（1）①；②作图见解析；（2）见解析．【解析】【分析】（1）①利用勾股定理即可求解；②取格点、，连接交于点，则点为所求；（2）取格点、，连接、相交于点，作射线交于点，则点为所求．【小问1详解】解：①，故答案为：；②如图，点为所求作图形，【小问2详解】解：如图，点为所求，87⨯1ABCD CD CD 2AB F CF BCD ∠5M N MN AC E E G H AQ DH Q CF AB FF 5CD ==5E F。

2014-2015学年人大附中八年级（下）期中物理试卷一、单项选择题（下列各小题均有四个选项，其中只有一个选项符合题意．共28分，每小题2分）1．（2分）在如图所示的物理学家中，以其名字命名压强的单位的是（）A．帕斯卡B．伽利略C．牛顿D．托里拆利2．（2分）如图所示的四个实例中，目的是为了增大摩擦的是（）A．轮胎上制有花纹B．在轴承中加滚珠C．给车轮的轴中加润滑油D．旅行箱下装有小轮3．（2分）下列所举实例中，物体运动状态不改变的是（）A．自由下落的苹果B．正在进站的公共汽车C．在空中沿直线匀速飞行的飞机D．绕地球匀速飞行的人造卫星4．（2分）如图所示的实例中，为了增大压强的是（）A．载重汽车安装了很多车轮B．铁轨铺在枕木上C．吸管的一端剪成斜口D．图钉帽的面积做得较大5．（2分）下列关于大气压的说法中正确的是（）A．大气压的数值总是不变的B．在其他条件相同时，海拔高度越高，大气压的值越大C．活塞式抽水机是利用大气压把水从低处抽到高处的D．大气压的数值与天气无关6．（2分）如图所示，从水平匀速飞行的飞机上先后落下两颗炸弹，在不计空气阻力的条件下，能正确反映飞机和两颗炸弹运动情况的是（）A．B． C． D．7．（2分）小明沿水平方向推静止在水平地面上的桌子，但没有推动。

对于这一现象，下列说法中正确的是（ ）现象，下列说法中正确的是（A．因为推力小于桌子所受的重力，所以桌子未被推动B．因为推力小于桌子所受的阻力，所以桌子未被推动C．虽然桌子未被推动，但推力大小等于桌子所受的重力的大小D．虽然桌子未被推动，但推力大小等于桌子所受的阻力的大小8．（2分）放在水平桌面上的茶杯，对桌面有压力，下列有关“茶杯对桌面压力”的说法，正确的是（ ）的说法，正确的是（A．茶杯对桌面的压力是由于茶杯发生弹性形变而产生的B．茶杯对桌面的压力是作用在茶杯上的C．茶杯对桌面的压力就是重力D．茶杯对桌面的压力是由于桌面发生形变而产生的9．（2分）桌面上甲、乙两个圆柱形容器中分别装有水和酒精，实心木球和空心铁球的体积和质量都相等，如图所示。

人大附中2014—2015学年度第二学期期中一、选择题：（本题共30分，每小题3分）1、式子3x -在实数范围内有意义，则x 的取值范围是（ ）.3A x > .3B x ≥ .3C x < .3D x ≤2、一元二次方程25470x x -+=的二次项系数是（ ）.5A .1B .4C - .7D3、以下列各组数为边长，能构成直角三角形的是（ ）.2,3,3A .2,3,4B .2,3,5C .2,3,5D4如图，在矩形ABCD 中，70BAC ∠=，则ACB ∠的度数（ ）.90A .20B .70C .60D5、一次函数1y x =-的图像经过的象限是（ ）.A 第一、二、三象限 .B 第一、二、四象限 .C 第二、三、四象限 .D 第一、三、四象限6、如图ABCD 的对角线AC 、BD 相交于点O ，点E 是CD 的中点，若6AD =，则OE 的长为（ ）.6A .5B .4C .3D7、正比例函数2y x =的图像上有两个点11(,)A x y ，22(,)B x y ，其中120x x <<，则下列不等式关系成立的是（ ）12.0A y y << 21.0B y y << 12.0C y y << 21.0D y y <<8、如图，若菱形ABCD 的周长是20，6BD =，对角线AC 、BD 交于点O ，则菱形ABCD 的面积是（ ）.48A .24B .12C .6D9、用配方法解方程245x x -=，下列配方正确的是（ ）2.(2)9A x -= 2.(2)1B x -= 2.(2)9C x += 2.(2)1D x +=10、如图1，矩形ABCD 中，2AB =，1BC =，E 是边AB 的中点，一动点P 从点B 出发，沿着B —C —D 在矩形的边上作匀速运动，点M 为图1中某一定点，设点P 的运动的路程为x ，△BPM 的面积为y ，表示y 与x 的函数关系的图像大致如图2所示，则点M 的位置可能是图1中的（ ） 第4题DCBA第6题D CBAE O第8题DCBAO.A A 点 .B C 点 .C D 点 .D E 点yx311EDCBAO二、填空题（本题共20分，每空2分）11、比较大小，321912、如图，在ABC △中，90ACB ∠=，6AC =，8BC =，D 是AB 中点，则CD = 。