上海市华二附中2017-2018学年初三第一学期期中考试英语试卷(word版,附答案无听力部分)

华师二附中2017 学年第一学期九年级期中质量检测英语试卷Part 2 Phonetics, Vocabulary and GrammarII.Choose the best answer26.I could see he was carrying a gun. Which of the following is correct for the underlined word in the sentence?A./gu:n/B. /gʌn/C. /gɔn/D. /gən/27.Which of the following underlined parts is different in pronunciation from others?A.He has a good memory for words.B. The man goes from west to eastC. Shanghai has changed a lot in recent years.D. He had a pain in the neck.st week I bought USB flash disk to store my articles.A.aB. anC. theD. /29.Five students of the Dancing Club come from Grade 7, all come from Grade 8.A.anotherB. othersC. the otherD. the others30.Smart phones have become an important part of people’s life.A.dailyB. happilyC. recentlyD. quicklying different memorizing methods can enable you to remember things .A.wiseB. correctC. easilyD. faithfully32.95% of the passengers ay they are satisfied the public transport service.A.inB. forC. toD. with33.the government has promised to improve road safety, little has been achieved so far.A.IfB. AlthoughC. UnlessD. Because34.Jane is very shy. She never starts a conversation she is spoken to.A.ifB. whenC. unlessD. because35.In order to finish the task in time, John kept for four hours without rest.A.workB. to workC. worksD. working36.Flora looked out of the window and found it heavily.A.snowsB. snowedC. has snowedD. was snowing37.The Red Cross is always the first help to victims when a disaster happens.A.provideB. providingC. to provideD. to providing38.here quickly, Alice. I have something exciting to tell you.ingB. ComesC. ComeD. To come39.Practice football, and you will do better in the match.A.playingB. playC. to playD. played40.Soon a nursing home in our neighborhood for the elderly living alone.A.has set upB. will set upC. has been set upD. will be set up41.Linda has decided at that restaurant as there were so many people in the queue.A.not eatingB. not to eatC. not eatD. to not eat42.--Can you tell me your online shopping will arrive?--In three days, I think.A.how fastB. how longC. how oftenD. how soon43. exciting program Tint Running Man is!A. WhatB. What aC. What anD. How44.--Thank you so much for the wonderful party. I really had a great time.--A.You are kind.B. I’m glad you like it.C. It doesn’t matter.D. That’s right.45.--I missed the lecture this morning because of the traffic jam.--A.What a pity!B. Don’t worry.C. Of course not.D. Watch out.plete the following passage with the words in the box. Each word can only be used onceA. deal withB. quickerC. as soon asD. clearlyE. untilThe most important thing when calling 110 is to keep calm. You need to say your name, location, your phone number and describe the situation as 46 as possible. If you are too nervous to say anything, just follow the telephone operator’s instructions.If the phone is busy, don’t hang up. You should hold on 47 the operator answers it.As well as China, almost every country has its own emergency number. In the US, 911 links callers to emergency services including police, fire and ambulance (救护车). The system is able to provide the physical location of mobile telephones, which makes it 48 to get to the scene. In the UK, people call 999 when they are in an emergency.Next are some figures about the figure 110:●“110” is a 24-hour emergency number.●On average, every telephone operator answers 800 to 1,000 emergency calls every day.●Operators should 49 an emergency call in 57 seconds.●Police set off no more than one minute after receiving information from telephone operators. In cities,police are required to get to the scene in five minutes. In suburbs, it is ten minutes.●In China, 95 percent of cities and towns have 110 emergency centers.●There are more than 24,000 telephone operators around the country.A. completeB. fifthC. problemD. instead ofE. complainApple started the service with China Union Pay on Feb 18, making China the the 50 country in which the service can be used after the US, the UK, Canada and Australia.Apple Pay users can 51 a deal by just moving their devices near point of sale (POS) terminals 52 scanning a bar code which is required by mobile payment services. The near-field communication technology or NFC allows the contactless data exchange between the user’s device and the POS terminal.People may pay close attention to Apple Pay at first, but the main 53 for Apple Pay is how to attract more people in the run.IV.. Complete the sentences with the given words in their proper forms54.The solider is brave enough to fight against those . (enemy)55.She has bought a new flat in this building and it’s on the floor. (twelve)56.Jane was happy to find that her little son could sing an English song all by . (he)57.It is everyone’s to take care of our earth. (responsible)58.In the educational program four players will with animals for food. (competition)59. A large number of houses were destroyed in the heavy storm. (serious)60.Get yourselves ready, and you are sure to in the coming tests. (success)61.They boys was because he was a new comer and had no friends here. (happily)V.Rewrite the following sentences as required.62.Mr Smith has saved some money to buy a house in the countryside. （改为一般疑问句）Mr Smith saved money to buy a house in the countryside?63.It is half an hour’s ride from our school to Chenshan Botanical Garden. （划线部分提问）is it from your school to Chenshan Botanical Garden?64.The boys like having sports better than chatting with their friends on QQ. （保持句意不变）The boys having sports chatting with their friends on QQ.65.The houses in the city are too expensive. Most people can’t afford one. （保持句意不变）The houses in the city are expensive most people can’t afford one.66. A little boy invented a housework robot for his mother last month. （改为被动语态）A housework robot by a little boy last month.67.“Will you take part in the sports meeting this year, Jimmy?” Susan asked. （改为宾语从句）Susan asked Jimmy he take part in the sports meeting this year.68.can, you, the difference, seeing and hearing, between, tell （连词成句）Part 3 Reading and WritingVI.Reading comprehensionA. Choose the best answerThe next time you sit down to a delicious dinner, ask yourself, “How much food will I be able to eat?”If you think about only taking as much food as you can eat, it will help cut down on waste. Every day, a large amount of food goes uneaten and ends up in the garbage. This is very sad considering that many people can’t even afford to have one meal every day. The problem of waste happens all over the world. People often feel the need to spend more than they can manage. This often results in waste and it can be a big problem. However, there are many things that we can do to help cut down on garbage and waste.The most important thing to remember is to be friendly to the environment. Only take as much food as you can eat, buy things in environment friendly packaging such as paper or cardboard, and leave garbage in its proper place. If every person could cut down on waste, even just a little, the overall effect would be great.Garbage and waste can be a big problem in large cities. If garbage or food is left in the streets, it can make the city dirty and may also lead to a bad smell in the streets. We all need to be responsible to clean up this problem and make the city more pleasant.It is impossible to get rid of waste completely, but we can greatly reduce it. No one is perfect, but if we pay more attention to what kinds of effect our waste has on the environment, we can work together to control the problem.69.If you think about only taking as much food as you can eat, .A.you can eat healthilyB. you can eat lessC. it will make you have more foodD. it will help cut down on waste70.People often feel the need to .A.keep the food they haveB.spend more than they can manageC.finish the food as quickly as they canD.make the food delicious71.We must leave garbage .A.at each cornerB. in its proper placeC. on the roadsD. in the streets72.in large cities.A.People left garbage or food in the streetsB.Students make the city dirtyC.Garbage and waste can be a big problemD.Food leads to a bad smell everywhere73.We all need to be responsible to .A.pay more attention to the foodB.get rid of bad food completelyC.make the city more pleasantD.reduce the food we eat greatly74.From the passage we know that .A.everybody can do something to stop wastingB.it is possible to get rid of waste completelyC.we can control the environment and the problemD.we must remember to eat more food every mealB.Choose the words or expressions to complete the passageA mobile phone app（应用软件）has recently become very popular at the Middle School Attached to Guangzhou University. It is named Health Helper. Put your weight, height and 75 into the app, and it will give you suggestions on how to get healthier. 76 , the app is not designed by a company but by two Junior 3 boys from the school.The two boys are Yang Chengxi and Yang Zhenglin, both 14 years old. They learned to design apps by taking part in the school’s app-making course, which started last year.“Electronic products are becoming increasingly popular,” said Wang Xiaopeng, the teacher of the app- making course. “It’s unpractical to block（阻隔）students from them. So why not guide them to use it in a 77 way?”As expected, the course has 78 many student including Yang Chengxi and Yang Zhenglin. As cell phone game lovers, the two brought great enthusiasm（热情）into their app-making project.“I t is much cooler to design a game than just playing a game,” said Yang Chengxi. They decided to create an app to keep fit since obesity（肥胖）has become a problem for many teenagers.They searched standard health information on the Internet, put them in the app and wrote simple programs to make it work. 79 app-making software, the two boys finished their Health Helper app after three weeks of hard work.The taste of 80 is exciting. After Health Helper, the two now plan to go a step further. They are working on a robot that can be controlled by cell phone Bluetooth. Wish them good luck.75. A. name B. class number C. address D. age76. A. Clearly B. Surprisingly C. Luckily D. Terribly77. A. more wonderful B. more difficult C. more creative D. more fashionable78. A. accepted B. attracted C. asked D. amazed79. A. With the help of B. According to C. As a result of D. In return for80. A. hobby B. achieving C. success D. lifeC.Read the passage and fill in the blanks with proper wordsLast Friday a storm swept through two villages in the New Territories, destroying fourteen homes. Seven others were so badly damaged that their o__81__ had to leave them, and fifteen others had brokenwindows or broken roofs. One person was killed, several were badly hurt and taken to hospital, and a number of other people received smaller hurt. Altogether over two hundred people were h 82 after the storm. They didn’t know where to go.A farmer, Bob, said that the storm b 83 early in the morning and lasted for over an hour.“I was eating with my wife and children,” he said, “When we heard a loud noise. A few minutes later our house f 84 down on top of us. We tried our best to climb out but then I saw that one of my children was missing. I went back inside and found him, s 85 but very fright ened.”Bob continued, “My boy cried out immediately when he saw me. I wanted to give him a hand It that time, but failed. We both tried and finally he managed to find his way out.”Mrs. Woo Mei Fong said that her husband had just l 86 for work when she felt that her house was moving. She ran outside at once with her children. “There was no time to take a__87__,” she said, “A few minutes later, the roof came down.”Rescue workers helped to take people out of the flooded area and the welfare department brought them food, clothes and shelter.D.Answer the questionsMalls are popular places for Americans to go. Some people spend so much time at malls that they are called mall rats.People like malls for many reasons. They don’t feel any danger around them because malls have police stations or private security guards. Parking is usually free, and the weather inside is always fine. The newest malls have beautiful rest places with waterfalls and large green trees.The largest mall in the United States is the Mall of America in Minnesota. It covers 4.2 million square feet. It has 350 stores, eight night clubs, and a seven-acre park! There are parking spaces for 12,750 cars. About 750,000 people shop there every week. The first indoor mall in the United States was built in 1965 in Edina, Minnesota. People love doing all their shopping in one place. More malls are built all over the country. Now, malls are like town centers where people come to do many things. They shop, of course. They also eat in food houses that have food from all over the world. They see films at the theaters. Some people even get their daily exercise by doing the new sport mall walking. Others go to malls to meet friends. In some malls, people can see a doctor or a dentist and even attend church. In other words, people can do just everything in malls. Now residents can actually live in their favorite shopping center.88.Why are some people in America called mall rats?89.What is the purpose of having police stations inside the malls?90.How many cars can the parking spaces of the largest mall in the United States hold?91.When and where was the first indoor mall set up in the United States?92.Why were more malls built all over the country?93.Do you prefer to have a one-day trip to such malls? Give at least two reasons.VII.Writing94.Write at least 60 words on the topic “A person helped/encouraged… me before”（以“曾经过我的人”为题，写一篇不少于60 个词的短文，标点符号不占格）很多人曾经出现在你的成长旅程中，他们或帮助你，或鼓励你，或爱护你，… 请你描述他（她）是怎样的人，以及发生在你和他（她）之间的故事，并谈谈他（她）对你的影响。

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武汉华中师范大学第一附属中学2017-2018学年高一下学期期中考试英语试题含答案

华中师大一附中2017—2018学年度第二学期期中检测高一年级英语试题时间：120分钟满分：150分第一部分听力（共两节，满分30分）做题时，先将答案标在试卷上，录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。

第一节（共5小题；每小题1.5分，满分7.5分）听下面5段对话，每段对话后有一个小题。

从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

例：How much is the shirt?A.£19.15B.£9.15C.£9.18答案是B.1.Why will the man go to the airport?A.To meet someone.B.To see a girl off.C.To catch Flight587.2.What had they planned to do before they heard the storm warning?A.To go boating.B.To play tennis.C.To go bicycling.3.What do we know about the man?A.He is disabled.B.The man has been in China on business.C.It’s the eighth time that he has been to China.4.Where does this conversation most probably take place?A.At a railway station.B.At a hospital.C.At an interview.5.What do we know about the woman?A.She moves about in the city a lot.B.She knows nothing about the city.C.She has been in the city for a year.第二节（共15小题；每小题1.5分，满分22.5分）听下面5段对话或独白。

2017-2018年度高二第一学期期中考试英语试卷(含答案)

2017-2018年度高二第一学期期中考试英语试题本试卷共10页，满分135分，考试用时120分钟注意事项：1.本试卷分为阅读理解、英语知识运用、写作三部分。

2.答卷前，考生务必用黑色字迹的钢笔或签字笔将自己的姓名和考生号、试室号、座位号填写在答题卡上。

3.选择题每小题选出答案后，用2B铅笔把答题卡上对应题目选项的答案信息点涂黑，如需改动，用橡皮擦干净后，再选涂其他答案，答案答在试卷上无效。

4.非选择题必须用黑色字迹的钢笔或签字笔作答，答案必须写在答题卡各题目指定区域内相应位置上，如需改动，先划掉原来的答案，再写上新的答案，不准使用铅笔和涂改液。

不按以上要求作答的答案无效。

5.考生必须保持答题卡的整洁。

考试结束后，将答题卷和机改答题卡一并交回。

第一部分阅读理解（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的四个选项（A、B、C和D）中，选出最佳选项，并在答题卡上将该项涂黑。

AThe Hawaii V olcanoes (火山) National ParkThe Hawaii V olcanoes National Park, on the island of Hawaii, has two active volcanoes：Mauna Loa, which last erupted in 1984, is 13,677 feet (4.17km) above sea level; the other is Kilauea that is next to Mauna Loa and it has been erupting since January 3rd, 1983. it is 4,190 feet(1.23km) above sea level.When to visit:The park is open 24 hours a day year round. There are no plants or trees on the lava(火山岩) fields and no protection from the sun, so you must bring sunglasses and sunscreen(防晒霜).How to get there:The best way to get to the park is to take Highway 11. From the airport at Hilo, Highway 11 will take you southward across the eastern part of the island.Things to see:If you want to know more about the park, the Kilauea Visitor Center is surely a stop to make. It is a quarter of a mile (402m) from the park entrance. There, you can see a great movie about real lava and learn about the island’s geological, natural, and cultural history. The center is open from 7:45 am to 5:00 pm. There are also many guided walks and hikes around the park. You must check weather conditions and volcanic before hiking alone. If possible, you may drive down Chain of Craters Road to see lava flowing into the ocean.Tickets:Entrance to the park is $10.00 for each vehicle including people, $5.00 for those who travel on foot or ride a bicycle. Children under the age of 15 are free.1. Different from Mauna Loa, Kilauea _______.A. will disappear soon.B. is closed to visitors.C. is much bigger.D. erupts more often.2. The Kilauea Visitor Center_______.A. lets visitors learn about the park.B. is next to the park entrance.C. offers all kinds of movies.D. is open for 8hours every day.3. If a family of three drives a car into the park, they need to pay_______.A. $5.00B. $10.00C. $15.00D. $20.004. The text is most probably taken from_______.A. A travel magazine.B. A geography textbook.C. A newspaper report.D. A research paper.BIt was raining as I ran out of the church, eager to get home and play with the gifts Father Christmas sent me. Across the street was a gas station, which was closed for Christmas, but I noticed a family standing under the narrow overhang to keep dry. I wondered briefly why they were there but then forgot about them as I couldn’t wait to see my gifts.Once I got home, there was hardly any time to enjoy my gifts. My grandparents were still waiting for us to have Christmas dinner together at their house. As we drove down the highway, I noticed that the family was still there.The closer we got to my grandparents’ house, the slower the car went. Suddenly, my father U-turned and said, “I can’t stand it!” “What?” asked my mother. “It’s those people back there at the gas station, standing in the rain.”When my father pulled into the station, I saw there were five of them: the parents and three children—two girls and a small boy. Then we learned that the family was waiting for the bus to Birmingham, where the man planned to find a job.“Well, that bus won’t come along for several hours. Winborn’s just a few milesaway, and there is a shed (棚) with a cover there,” my father advised. “I will run you up there.”Then they climbed into our car,. My father looked back and asked the children if Father Christmas had found them. Three sad faces gave him his answer.“Well, Father Christmas said he was having trouble finding you, so he just left your toys at my house this morning. Let’s go to get them first,” my father said. All at once, the three children’s faces lit up.When we arrived at our house, one girl spied a lovely doll, that little boy took a ball, and the other girl picked up something else. That was the Christmas when I learned the joy of making others happy.5. At the gas station the family might feel______.A. frightenedB. disappointedC. anxiousD. delighted6. The three children received Christmas gifts thanks to_______.A. the authorB. the author’s fatherC. their parentsD. their grandparents7. We can learn from the text that the author’s father_____.A. knew that family very wellB. got lost on the way to WinbornC. was happy to help those in troubleD. sent that family to Birmingham8. What would be the best title for the text?A. Father Christmas saved usB. My father never gives upC. A hard-working familyD. Special Christmas giftsCShe was returning from teaching out in a small community (社区). It was a moonless night, and a heavy snow was falling.She remembered back to when she had first started teaching out in small communities. In those days she had always picked up hitchhikers (搭便车者), until the day her sister told her of a friend who had been killed by a hitchhiker, all because she had stopped out of kindness to help him during a storm. Her family worried about her safety over the hitchhikers until the family heard her promise: “No more hitchhikers!”Then, one night, she saw a man waving. She slowed down for him, but now as he ran toward the car in the dark she shook with fear. Yet she thought that if he was truly in need she couldn’t leave him here in this storm.The stranger explained that his car was broken, and she told him to get in the car. They drove for an hour into the next city and she took him to a telephone booth (公用电话亭). When he reported back to her that a family member would soon come for him, she wished him well and left.Tears fell on her cheeks as she drove away. She felt as though she had beenholding her breath for an hour. “I hope they’ll understand why I had to break my promise,” she thought.9. What can we learn about the woman?A. She taught in small communities.B. She used to be a hitchhiker.C. She was a taxi driver.D. She seldom picked up strangers.10. What made her family worried about her safety?A. She had been hurt by a hitchhiker.B. Her sister’s friend was killed by a hitchhiker.C. There were often snowstorms on her way home.D. Her car often broke down on her way home.11. We can infer from the underlined sentence in the last paragraph that _________.A. She regretted picking up the stranger.B. She felt too tired to breathe.C. She had been afraid being with the stranger.D. She had been too careful driving in the storm.12. We can infer from the passage that the woman is___________.A. kind-heartedB. outstandingC. cautiousD. carelessDMany parents worry that their children’s eating habits may not be good enough to keep healthy. Some children ask for the same food over and over again, some may refuse to try anything new, and some may keep asking for snacks(点心). Therefore, having healthy eating habits becomes one of the most important lessons that a child should learn. Most parents struggle with managing good eating habits and nutrition(营养) for their children. Parents should make a plan for their children’s nutritional needs.Start your child’s day with a good breakfast. Breakfast is necessary to provide the nutrition for an active day. Studies show that children do better in study when they begin a day with a good breakfast.Allow your child to help you plan and prepare a meal. He will be glad to eat foods that he has helped to put on the table.The mealtime environment has a lot to do with how your child will feel about food. Try to serve your meals at the same place at the same time of a day. Keep the meal itself as the main event and leave the toys and television for later use.Snacks are also important. We can give our body and brain energy by eating snacks between meals. Children are often hungriest in the afternoon after school andin the evening.Offer snacks at regular time between meals. This way, your child won’t refuse a meal because he knows a snack is soon to follow. More importantly, when offering snacks, you should be careful with what to choose.13. The main idea of the second paragraph is that ___ .A. Most children go to school without eating breakfast.B. One shouldn’t eat too much for breakfast.C. A good breakfast is important to children.D. Most people haven’t realized the importance of having a good breakfast.14. To help their children form healthy eating habits, parents ____ .A. should encourage their children to eat more often at school.B. can ask the children to help with meal planning and preparation.C. must make the mealtime environment as quiet as possible.D. should serve some snacks while having a meal.15. What would most probably be talked about in the next paragraph of the passage?A. What to eat for lunch and supper.B. Why snacks are important.C. Advice on how to keep healthy.D. Examples of healthy snacks.第二节（共5小题；每小题2分，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。

2017-2018学年华东师大版九年级上期中检测试卷含答案解析

期中数学试卷一、选择题（共10小题，每小题3分，共30分）下列各题中均由四个备选答案，其中有且只有一个正确，请将各题正确答案的代号填入到答题卷相应的答题栏中1．一元二次方程3x2﹣8x﹣10=0中的一次项系数为（）A．3 B．8 C．﹣8 D．﹣102．如果﹣2是方程x2﹣m=0的一个根，则m的值为（）A．2 B．﹣4 C．3 D．43．下列正多边形中，绕其中心旋转72°后，能和自身重合的是（）A．正方形B．正五边形C．正六边形D．正八边形4．将二次函数y=x2的图象向下平移一个单位，则平移以后的二次函数的解析式为（）A．y=x2﹣1 B．y=x2+1 C．y=（x﹣1）2D．y=（x+1）25．电脑病毒传播快，如果一台电脑被感染，经过两轮感染后就会有81台电脑被感染，若每轮感染中平均一台电脑会感染x台电脑，下列方程正确的是（）A．x（x+1）=81 B．1+x+x2=81 C．1+x+x（x+1）=81 D．1+（x+1）2=81 6．一元二次方程x2+x﹣6=0的根的情况是（）A．有两个相等的实根B．没有实数根C．有两个不相等的实根D．无法确定7．如图，在同一平面内，将△ABC绕点A旋转到△AED的位置，若AE⊥BC，∠ADC=65°，则∠ABC的度数为（）A．30°B．40°C．50°D．60°8．对于抛物线y=ax2﹣4ax+3a下列说法：①对称轴为x=2；②抛物线与x轴两交点的坐标分别为（1，0），（3，0）；③顶点坐标为（2，﹣a）；④若a＜0，当x＞2时，函数y随x的增大而增大，其中正确的结论有（）个．A．1个B．2个C．3个D．4个9．如图，矩形ABCD的两边BC、CD分别在x轴、y轴上，点C与原点重合，点A（﹣1，2），将矩形ABC D沿x轴向右翻滚，经过一次翻滚点A对应点记为A1，经过第二次翻滚点A对应点记为A2…依此类推，经过5次翻滚后点A对应点A5的坐标为（）A．C．10．如图，等边△ABC的边长为3，F为BC边上的动点，FD⊥AB于D，FE⊥AC于E，则DE的长为（）A．随F点运动，其值不变B．随F点运动而变化，最大值为C．随F点运动而变化，最小值为D．随F点运动而变化，最小值为二、填空题（每小题3分，共18分）11．x2﹣6x+（______）=（x﹣______）212．二次函数y=x2﹣2x﹣3的图象的顶点坐标是______．13．若m、n是方程x2+6x﹣5=0的两根，则3m+3n﹣2mn=______．14．如图是二次函数y=ax2+bx+c图象的一部分，图象过点A（﹣3，0），该抛物线的对称轴为直线x=﹣1，若点C（﹣，y1），D（﹣，y2），E（，y3）均为函数图象上的点，则y1，y2，y3的大小关系为_ _____．15．已知点C为线段AB上一点，且AC2=BCAB，则=______．16．在△ABC中，AC=BC，∠ACB=90°，将△ABC绕点A旋转60°到△ADE的位置，点C的对应点为E，连接CD，若AC=BC=1，则CD的长为______．三、解答题（共72分）17．选择适当方法解方程：2x2﹣x﹣3=0．18．已知关于x的方程x2﹣4x+1﹣p2=0．（1）若p=2，求原方程的根；（2）求证：无论p为何值，方程总有两个不相等的实数根．19．已知抛物线y=ax2+bx+c过点A（﹣1，0），B（3，0），C（2，﹣）（1）求此抛物线的解析式；（2）当y＜0时，x的取值范围是______（直接写出结果）20．如图，线段AB两个端点的坐标分别为A（1，﹣1），B（3，1），将线段AB绕点O逆时针旋转90°到对应线段CD（点A与点C对应，点B与D对应）．（1）请在图中画出线段CD；（2）请直接写出点A、B的对应点坐标C（______，______），D（______，______）；（3）在x轴上求作一点P，使△PCD的周长最小，并直接写出点P的坐标（______，______）．21．如图，在△ABC中，AB=AC，点D为BC上一点，以AD为腰作等腰△ADE，AD=AE，∠BAC=∠DAE，连接CE．（1）求证：BD=CE；（2）已知BC=8，∠BAC=∠DAE=30°，若△DCE的面积为1，求线段BD的长．22．某宾馆有50个房间可供游客居住，当每个房间每天的定价为180元时，房间会全部住满，当每个房间每天的定价增加10元时，就会有一个房间空闲，如果游客居住房间，宾馆需对每个房间每天支出20元的各种费用，设每个房间的定价增加x元（x为10的整数倍），此时入住的房间数为y间，宾馆每天的利润为w元．（1）直接写出y（间）与x（元）之间的函数关系；（2）如何定价才能使宾馆每天的利润w（元）最大？（3）若宾馆每天的利润为10800元，则每个房间每天的定价为多少元？23．如图，在正方形ABCD中，将正方形的边AD绕点A顺时针旋转到AE，连接BE、DE，过点A作AF⊥BE于F，交直线DE于P．（1）如图①，若∠DAE=40°，求∠P的度数；（2）如图②，若90°＜∠DAE＜180°，其它条件不变，试探究线段AP、DP、EP之间的数量关系，并说明理由；（3）继续旋转线段AD，若旋转角180°＜∠DAE＜270°，则线段AP、DP、EP之间的数量关系为______（直接写出结果）24．在平面直角坐标系中，抛物线C1：y=ax2+4x+4a（0＜a＜2）（1）当C1与x轴有唯一一个交点时，求此时C1的解析式；（2）如图①，若A（1，y A），B（0，y B），C（﹣1，y C）三点均在C1上，连BC作AE∥BC交抛物线C1于E，求点E到y轴的距离；（3）若a=1，将抛物线C1先向右平移3个单位，再向下平移2个单位得到抛物线C2，如图②，抛物线C2与x 轴相交于点M、N（M点在N点的左边），抛物线的对称轴交x轴于点F，过点F的直线l与抛物线C2相交于P ，Q（P在第四象限）且S△FMQ=2S△FNP，求直线l的解析式．2015-2016学年湖北省武汉市黄陂区九年级（上）期中数学试卷参考答案与试题解析一、选择题（共10小题，每小题3分，共30分）下列各题中均由四个备选答案，其中有且只有一个正确，请将各题正确答案的代号填入到答题卷相应的答题栏中1．一元二次方程3x2﹣8x﹣10=0中的一次项系数为（）A．3 B．8 C．﹣8 D．﹣10【考点】一元二次方程的一般形式．【分析】找出方程的一次项系数即可．【解答】解：一元二次方程3x2﹣8x﹣10=0中的一次项系数为﹣8，故选C2．如果﹣2是方程x2﹣m=0的一个根，则m的值为（）A．2 B．﹣4 C．3 D．4【考点】一元二次方程的解．【分析】把x=﹣2代入方程，得到关于m的一元一次方程，可以求出m的值．【解答】解：∵x=﹣2是方程的根，∴x=﹣2代入方程有：4﹣m=0，解得：m=4．故选D．3．下列正多边形中，绕其中心旋转72°后，能和自身重合的是（）A．正方形B．正五边形C．正六边形D．正八边形【考点】旋转对称图形．【分析】求出各个选项图形的最小旋转角度，即可做出判断．【解答】解：A、正方形的最小旋转角度为90°，故本选项错误；B、正五边形的最小旋转角度为=72°，故本选项正确；C、正六边形的最小旋转角度为=60°，故本选项错误；D、正八边形的最小旋转角度为=45°，故本选项错误；故选B．4．将二次函数y=x2的图象向下平移一个单位，则平移以后的二次函数的解析式为（）A．y=x2﹣1 B．y=x2+1 C．y=（x﹣1）2D．y=（x+1）2【考点】二次函数图象与几何变换．【分析】直接根据上加下减的原则进行解答即可．【解答】解：由“上加下减”的原则可知，将二次函数y=x2的图象向下平移一个单位，则平移以后的二次函数的解析式为：y=x2﹣1．故选A．5．电脑病毒传播快，如果一台电脑被感染，经过两轮感染后就会有81台电脑被感染，若每轮感染中平均一台电脑会感染x台电脑，下列方程正确的是（）A．x（x+1）=81 B．1+x+x2=81 C．1+x+x（x+1）=81 D．1+（x+1）2=81【考点】由实际问题抽象出一元二次方程．【分析】首先设每轮感染中平均一台电脑会感染x台电脑．则经过一轮感染，1台电脑感染给了x台电脑，这（x+1）台电脑又感染给了x（1+x）台电脑．利用等量关系：经过两轮感染后就会有81台电脑被感染得出即可．【解答】解：设每轮感染中平均一台电脑会感染x台电脑．根据题意，得：1+x+x（1+x）=81，故选：C．6．一元二次方程x2+x﹣6=0的根的情况是（）A．有两个相等的实根B．没有实数根C．有两个不相等的实根D．无法确定【考点】根的判别式．【分析】由根的判别式△=b2﹣4ac，即可判定一元二次方程x2+x﹣6=0的根的情况．【解答】解：∵△=b2﹣4ac=12﹣4×1×（﹣6）=25＞0，∴有两个不相等的实根．故选C．7．如图，在同一平面内，将△ABC绕点A旋转到△AED的位置，若AE⊥BC，∠ADC=65°，则∠ABC的度数为（）A．30°B．40°C．50°D．60°【考点】旋转的性质．【分析】先根据旋转的性质得AD=AC，∠BAE=∠CAD，再根据等腰三角形的性质和三角形内角和计算出∠CAD=50°，则∠BAE=50°，然后利用互余计算∠ABC的度数．【解答】解：∵△ABC绕点A旋转到△AED的位置，∴AD=AC，∠BAE=∠CAD，∵AD=AC，∴∠ACD=∠ADC=65°，∴∠CAD=180°﹣65°﹣65°=50°，∴∠BAE=50°，∵AE⊥BC，∴∠ABC=90°﹣∠BAE=40°．故选B．8．对于抛物线y=ax2﹣4ax+3a下列说法：①对称轴为x=2；②抛物线与x轴两交点的坐标分别为（1，0），（3，0）；③顶点坐标为（2，﹣a）；④若a＜0，当x＞2时，函数y随x的增大而增大，其中正确的结论有（）个．A．1个B．2个C．3个D．4个【考点】二次函数的性质．【分析】根据对称轴公式x=﹣，进行计算即可；令y=0，求得方程ax2﹣4ax+3a=0的解即可；根据顶点坐标公式计算即可；由a＜0，得出对称轴的左侧，函数y随x的增大而增大．【解答】解：对称轴x=﹣=﹣=2，故①正确；令y=0，得ax2﹣4ax+3a=0，解得x=1或3，∴抛物线与x轴两交点的坐标分别为（1，0），（3，0），故②正确；==﹣1，∴顶点坐标为（2，﹣1），故③错误；当a＜0，当x＜2时，函数y随x的增大而增大，故④错误，故选B．9．如图，矩形ABCD的两边BC、CD分别在x轴、y轴上，点C与原点重合，点A（﹣1，2），将矩形ABC D沿x轴向右翻滚，经过一次翻滚点A对应点记为A1，经过第二次翻滚点A对应点记为A2…依此类推，经过5次翻滚后点A对应点A5的坐标为（）A．C．【考点】规律型：点的坐标．【分析】根据题意可以画出相应的图形，然后观察图形即可得到经过5次翻滚后点A对应点A5的坐标，从而解答本题．【解答】解：如下图所示：由题意可得上图，经过5次翻滚后点A对应点A5的坐标对应上图中的坐标，故A5的坐标为：（8，1）．故选项A错误，选项B错误，选项C错误，选项D正确．故选D．10．如图，等边△ABC的边长为3，F为BC边上的动点，FD⊥AB于D，FE⊥AC于E，则DE的长为（）A．随F点运动，其值不变B．随F点运动而变化，最大值为C．随F点运动而变化，最小值为D．随F点运动而变化，最小值为【考点】等边三角形的性质．【分析】作AG⊥BC于G，根据等边三角形的性质得出∠B=60°，解直角三角形求得AG=，根据S△ABF+S△ACF=S△ABC即可得出DF+EF=AG=，再根据三角形三边关系即可求解．【解答】解：作AG⊥BC于G，∵△ABC是等边三角形，∴∠B=60°，∴AG=AB=，∵S△ABF+S△ACF=S△ABC，∴ABDF+ACEF=BCAG，∵AB=AC=BC=2，∴DF+EF=AG=，∵△DEF中，DE＜DF+EF，∴DE的长随F点运动而变化，最小值为．故选：D．二、填空题（每小题3分，共18分）11．x2﹣6x+（9 ）=（x﹣ 3 ）2【考点】完全平方式．【分析】先根据乘积二倍项确定出后一个数为3，再根据完全平方公式a2±2ab+b2=（a±b）2即可解答．【解答】解：∵（x﹣3）2=x2﹣6x+32=x2﹣6x+9，故答案为：9，3．12．二次函数y=x2﹣2x﹣3的图象的顶点坐标是（1，﹣4）．【考点】二次函数的性质．【分析】已知二次函数y=x2﹣2x﹣3为一般式，运用配方法转化为顶点式，可求顶点坐标．【解答】解：∵y=x2﹣2x﹣3=（x﹣1）2﹣4，∴抛物线顶点坐标为（1，﹣4）．13．若m、n是方程x2+6x﹣5=0的两根，则3m+3n﹣2mn= ﹣8 ．【考点】根与系数的关系．【分析】根据根与系数的关系直接得到（m+n）、mn的值，然后将其代入所求的代数式进行求值．【解答】解：∵m、n是方程x2+6x﹣5=0的两根，∴m+n=﹣6，mn=﹣5，∴3m+3n﹣2mn=3（m+n）﹣2mn=3×（﹣6）﹣2×（﹣5）=﹣8．故答案是：﹣8．14．如图是二次函数y=ax2+bx+c图象的一部分，图象过点A（﹣3，0），该抛物线的对称轴为直线x=﹣1，若点C（﹣，y1），D（﹣，y2），E（，y3）均为函数图象上的点，则y1，y2，y3的大小关系为y3＜y1＜y2．【考点】二次函数图象上点的坐标特征．【分析】由于抛物线开口向上，对称轴是直线x=﹣1，然后利用两点离对称轴的远近比较函数值的大小．【解答】解：∵抛物线y=ax2+bx+c（a≠0）的对称轴是直线x=﹣1，开口向下，∴离对称轴近的点的函数值大，∵|﹣+1|＜|﹣+1|＜|+1|∴y3＜y1＜y2．故答案为y3＜y1＜y2．15．已知点C为线段AB上一点，且AC2=BCAB，则= ．【考点】黄金分割．【分析】根据黄金分割的概念得到点C为线段AB的黄金分割点，根据黄金比值得到答案．【解答】解：∵点C为线段AB上一点，AC2=BCAB，∴点C为线段AB的黄金分割点，∴=，故答案为：．16．在△ABC中，AC=BC，∠ACB=90°，将△ABC绕点A旋转60°到△ADE的位置，点C的对应点为E，连接CD，若AC=BC=1，则CD的长为或．【考点】旋转的性质．【分析】分类讨论：当△ABC绕点A逆时针旋转60°得到△ADE的位置，如图1，作CH⊥ED于H，连结CE，根据旋转的性质得∠EAC=60°，∠AED=∠ACB=90°，AE=ED=AC=1，则可判断△AEC为等边三角形，所以∠AEC=60°，EC=CA=1，易得∠DEC=30°，然后在Rt△CEH中，利用含30度的直角三角形三边的关系可计算出CH=CE=，EH=CH=，所以DH=ED﹣E H=1﹣，于是在Rt△CHD中，利用勾股定理可计算出CD；当△ABC绕点A顺时针旋转60°得到△ADE的位置，如图2，连结CE，作DH⊥CE于H，同样可证明△AEC为等边三角形得到∠AEC=60°，EC=CA=1，则∠DEC=150°，所以∠DEH=30°，利用含30度的直角三角形三边的关系在Rt△DEH中可计算出DH=DE=，EH=DH=，则CH=CE+EH=1+，然后在Rt△CHD中，利用勾股定理计算CD．【解答】解：当△ABC绕点A逆时针旋转60°得到△ADE的位置，如图1，作CH⊥ED于H，连结CE，则∠EAC=60°，∠AED=∠ACB=90°，AE=ED=AC=1，∴△AEC为等边三角形，∴∠AEC=60°，EC=CA=1，∴∠DEC=30°，在Rt△CEH中，CH=CE=，EH=CH=，∴DH=ED﹣EH=1﹣，在Rt△CHD中，CD===；当△ABC绕点A顺时针旋转60°得到△ADE的位置，如图2，连结CE，作DH⊥CE于H，则∠EAC=60°，∠AED=∠ACB=90°，AE=ED=AC=1，∴△AEC为等边三角形，∴∠AEC=60°，EC=CA=1，∴∠DEC=150°，∴∠DEH=30°，在Rt△DEH中，DH=DE=，EH=DH=，∴CH=CE+EH=1+，在Rt△CHD中，CD===，纵上所述，CD的长为或=．故答案为或=．三、解答题（共72分）17．选择适当方法解方程：2x2﹣x﹣3=0．【考点】解一元二次方程-因式分解法．【分析】利用因式分解法解方程．【解答】解：2x2﹣x﹣3=0，（2x﹣3）（x+1）=0，2x﹣3=0或x+1=0，所以x1=，x2=﹣1．18．已知关于x的方程x2﹣4x+1﹣p2=0．（1）若p=2，求原方程的根；（2）求证：无论p为何值，方程总有两个不相等的实数根．【考点】根的判别式；一元二次方程的解．【分析】（1）把p=2代入方程，解方程即可；（2）利用根的判别式判定即可．【解答】解：（1）若p=2，原方程为x2﹣4x﹣3=0，解得：x1=2+，x2=2﹣；（2）△=（﹣4）2﹣4×1×（1﹣p2）=4p2+12，∵p2≥0，∴4p2+12＞0，∴无论p为何值，方程总有两个不相等的实数根．19．已知抛物线y=ax2+bx+c过点A（﹣1，0），B（3，0），C（2，﹣）（1）求此抛物线的解析式；（2）当y＜0时，x的取值范围是﹣1＜x＜3 （直接写出结果）【考点】待定系数法求二次函数解析式．【分析】（1）已知抛物线上三点坐标，代入一般式，列三元一次方程组，求a、b、c的值，确定抛物线解析式，再求抛物线与y轴交点的纵坐标．（2）根据抛物线的性质和与x轴的交点坐标求得即可．【解答】解：（1）把A（﹣1，0），B（3，0），C（2，﹣）代入抛物线解析式，得解得∴该函数的解析式为：y=x2﹣x﹣．（2）由抛物线开口向上，交点为A（﹣1，0），B（3，0）可知，当y＜0时，x的取值范围是﹣1＜x＜3；故答案为﹣1＜x＜3．20．如图，线段AB两个端点的坐标分别为A（1，﹣1），B（3，1），将线段AB绕点O逆时针旋转90°到对应线段CD（点A与点C对应，点B与D对应）．（1）请在图中画出线段CD；（2）请直接写出点A、B的对应点坐标C（ 1 ， 1 ），D（﹣1 ， 4 ）；（3）在x轴上求作一点P，使△PCD的周长最小，并直接写出点P的坐标（0.5 ，0 ）．【考点】作图-旋转变换；轴对称-最短路线问题．【分析】（1）利用网格特征和旋转的性质画出A点和B点的对应点；（2）根据第一、二象限内点的坐标特征写出C点和D点坐标；（3）A点与C点关于x轴对称，连结DA交x轴于点P，利用两点之间线段最短和判断此时△PCD的周长最小，于是可得到满足条件的P点坐标．【解答】解：（1）如图，CD为所作；（2）C（1，1），D（﹣1，4）；（3）P（0.5，0）．故答案为1，1；﹣1，4；0.5，0．21．如图，在△ABC中，AB=AC，点D为BC上一点，以AD为腰作等腰△ADE，AD=AE，∠BAC=∠DAE，连接CE．（1）求证：BD=CE；（2）已知BC=8，∠BAC=∠DAE=30°，若△DCE的面积为1，求线段BD的长．【考点】全等三角形的判定与性质．【分析】（1）易证∠BAD=∠EAC，即可证明△ABD≌△ACE，即可得到结论；（2）过D作DF⊥EC交EC的延长线于F，由△ABD≌△ACE，得到∠ACE=∠B，根据∠BAC=30°，于是得到∠B+∠ACB=150°，等量代换得到∠BCE=∠ACB+∠ACE=150°，由邻补角的性质得到∠DCF=30°，根据直角三角形的性质得到DF=CD=（BC﹣BD）=（8﹣BD），根据△DCE的面积为1，列方程即可得到结论．【解答】（1）证明：∵∠BAC=∠DAE，∴∠BAC﹣∠DAC=∠DAE﹣∠DAC，∴∠BAD=∠EAC，在△ABD和△ACE中，，∴△ABD≌△ACE（SAS），∴BD=CE；（2）过D作DF⊥EC交EC的延长线于F，∵△ABD≌△ACE，∴∠ACE=∠B，∵∠BAC=30°，∴∠B+∠ACB=150°，∴∠BCE=∠ACB+∠ACE=150°，∴∠DCF=30°，∴DF=CD=（BC﹣BD）=（8﹣BD），∵CE=BD，∴DF=4﹣CE，∵△DCE的面积为1，∴DFCE=CFBD=（8﹣BD）BD=1，解得：BD=4﹣，BD=4+（不合题意，舍去）．22．某宾馆有50个房间可供游客居住，当每个房间每天的定价为180元时，房间会全部住满，当每个房间每天的定价增加10元时，就会有一个房间空闲，如果游客居住房间，宾馆需对每个房间每天支出20元的各种费用，设每个房间的定价增加x元（x为10的整数倍），此时入住的房间数为y间，宾馆每天的利润为w元．（1）直接写出y（间）与x（元）之间的函数关系；（2）如何定价才能使宾馆每天的利润w（元）最大？（3）若宾馆每天的利润为10800元，则每个房间每天的定价为多少元？【考点】二次函数的应用．【分析】（1）用一共有的房间减去房价增长减少的房间数即可；（2）利用房间数乘每一间房间的利润即可得到函数解析式，配方法求得最大值即可．（3）令w=10800，得到一元二次方程求解即可．【解答】解：（1）y=50﹣x（0≤x≤100，且x是10的整数倍）；（2）w=（50﹣x）（180+x﹣20）=﹣x2+34x+8000；=﹣（x﹣170）2+10890∴当x=170时，w最大为10890．∴当定价为170元时利润最大．（3）令w=﹣（x﹣170）2+10890=10800解得：x=200或x=140．答：若宾馆每天的利润为10800元，则每个房间每天的定价为200或140元．23．如图，在正方形ABCD中，将正方形的边AD绕点A顺时针旋转到AE，连接BE、DE，过点A作AF⊥BE于F，交直线DE于P．（1）如图①，若∠DAE=40°，求∠P的度数；（2）如图②，若90°＜∠DAE＜180°，其它条件不变，试探究线段AP、DP、EP之间的数量关系，并说明理由；（3）继续旋转线段AD，若旋转角180°＜∠DAE＜270°，则线段AP、DP、EP之间的数量关系为PE=PD+PA （直接写出结果）【考点】四边形综合题．【分析】（1）根据正方形的性质得到AD=AB，∠BAD=90°，由AD绕点A顺时针旋转到AE，得到AD=AE，根据等腰三角形的性质得到∠ADE=∠AED=70°，∠BAE=50°，∠FAE=∠FAB=25°，根据三角形的外角的性质即可得到结论；（2）如图2，过A作AQ⊥DE于Q，于是得到∠PAQ=∠BAQ+∠FAB，根据等腰三角形的性质得到∠FAE=∠BAF，由外角的性质得到∠APQ=∠EAF+∠AEP于是得到∠APQ=∠PAQ=45°，求出PQ=AP，由于PE+PQ=PD﹣PQ，即PE+AP=PD﹣AP，于是得到结论；（3）如图3，过A作AQ⊥DE于Q，则∠AQP=90°，由AD=AE，得到DQ=EQ，∠AEQ=∠ADQ，同理得到∠3=∠FAB，根据外角的性质得到∠APQ=∠3﹣∠AEQ=∠3﹣∠ADQ，等量代换得到∠2=90°﹣∠1﹣∠ADP=90°﹣（90°﹣∠3）﹣∠AEP=∠3﹣∠AEP，求得∠2=∠APQ=45°，于是得到PQ=AP，然后由PD+PQ=PE﹣PQ，即可得到结论：PE=PD+PA．【解答】解：（1）∵四边形ABCD是正方形，∴AD=AB，∠BAD=90°，∵AD绕点A顺时针旋转到AE，∴AD=AE，∵∠DAE=40°，∴∠ADE=∠AED=70°，∠BAE=50°，∵AF⊥BE，∴∠FAE=∠FAB=25°，∴∠P=∠AED﹣∠PAE=45°；（2）如图2，过A作AQ⊥DE于Q，则∠PAQ=∠BAQ+∠FAB，∵AE=AB，AF⊥BE，∴∠FAE=∠BAF，∴∠APQ=∠EAF+∠AEP，∵∠BAD=∠AQP=90°，∴∠BAQ=∠ADQ，∵AE=AD，∴∠ADQ=∠AEP，∴∠BAQ=∠AEP，∴∠APQ=∠PAQ=45°，∴PQ=AP，∴PE+PQ=PD﹣PQ，即PE+AP=PD﹣AP，∴PD=AP+PE；（3）如图3，过A作AQ⊥DE于Q，则∠AQP=90°，∵AD=AE，∴DQ=EQ，∠AEQ=∠ADQ，∵AE=AB，AF⊥BE，∴∠3=∠FAB，∵∠APQ=∠3﹣∠AEQ=∠3﹣∠ADQ，∵∠1+∠FAB=∠FAB+∠ABF=90°，∴∠1=∠ABF=∠AEF，∴∠2=90°﹣∠1﹣∠ADP=90°﹣（90°﹣∠3）﹣∠AEP=∠3﹣∠AEP，∴∠2=∠APQ=45°，∴PQ=AP，∴PD+PQ=PE﹣PQ，即PD+PA=PE﹣PA，∴PE=PD+PA．故答案为：PE=PD+PA．24．在平面直角坐标系中，抛物线C1：y=ax2+4x+4a（0＜a＜2）（1）当C1与x轴有唯一一个交点时，求此时C1的解析式；（2）如图①，若A（1，y A），B（0，y B），C（﹣1，y C）三点均在C1上，连BC作AE∥BC交抛物线C1于E，求点E到y轴的距离；（3）若a=1，将抛物线C1先向右平移3个单位，再向下平移2个单位得到抛物线C2，如图②，抛物线C2与x 轴相交于点M、N（M点在N点的左边），抛物线的对称轴交x轴于点F，过点F的直线l与抛物线C2相交于P ，Q（P在第四象限）且S△FMQ=2S△FNP，求直线l的解析式．【考点】二次函数综合题．【分析】（1）根据△的意义和抛物线与x轴的交点问题得△=42﹣4a4a=0，然后解方程求出满足条件的a的值，从而得到此时C1的解析式；（2）先用a表示出A（1，5a+4），B（0，4a），C（﹣1，5a﹣4），再利用待定系数法得到直线BC的解析式为y=（4﹣a）x+4a，根据两直线平行问题，AE的解析式可设为y=（4﹣a）x+n，则把A（1，5a+4）代入得n=6a，所以直线AE的解析式为y=（4﹣a）x+6a，通过解方程组可得E点和A点坐标，消去y得x2+x﹣2=0，然后解方程求出x即可得到E点的横坐标，从而得到点E到y轴的距离；（3）作QA⊥x轴于A，PB⊥x轴于B，如图，当a=1时，y=（x+2）2，则抛物线C1的顶点坐标为（﹣2，0），利用抛物线的几何变换得到抛物线C2的解析式为y=（x﹣1）2﹣2，即y=x2﹣2x﹣1，F（1，0），利用抛物线的对称性得FM=FN，再利用三角形面积公式可得QA=2PB，利用平行线分线段成比例定理得FA=2BF，设P（t，t2﹣2t﹣1），则BF=t﹣1，AF=2（t﹣1），则OA=2（t﹣1）﹣1=2t﹣3，所以Q[3﹣2t，（3﹣2t）2﹣2（3﹣2t）﹣1]，然后利用AQ=2PB得到（3﹣2t）2﹣2（3﹣2t）﹣1=﹣2（t2﹣2t﹣1），解得t1=0（舍去），t2=2，于是得到P（2，﹣1），Q（﹣1，2），最后利用待定系数法确定直线l的解析式．【解答】解：（1）根据题意得△=42﹣4a4a=0，解得a1=1，a2=﹣1，而0＜a＜2，所以a=1，所以此时C1的解析式为y=x2+4x+4；（2）根据题意得A（1，5a+4），B（0，4a），C（﹣1，5a﹣4），设直线BC的解析式为y=kx+4a，把C（﹣1，5a﹣4）代入得﹣k+4a=5a﹣4，解得k=4﹣a，∴直线BC的解析式为y=（4﹣a）x+4a，∵BC∥AE，∴AE的解析式可设为y=（4﹣a）x+n，把A（1，5a+4）代入得4﹣a+n=5a+4，解得n=6a，∴直线AE的解析式为y=（4﹣a）x+6a，方程组消去y得x2+x﹣2=0，解得x1=1，x2=﹣2，∴E点的横坐标为﹣2，∴点E到y轴的距离为2；（3）作QA⊥x轴于A，PB⊥x轴于B，如图，当a=1时，y=x2+4x+4=（x+2）2，抛物线C1的顶点坐标为（﹣2，0），把点（﹣2，0）先向右平移3个单位，再向下平移2个单位得到对应点的坐标为（1，﹣2），所以抛物线C2的解析式为y=（x﹣1）2﹣2，即y=x2﹣2x﹣1，则抛物线的对称轴为直线x=1，所以F（1，0）∵抛物线C2与x轴相交于点M、N（M点在N点的左边），∴FM=FN，∵S△FMQ=2S△FNP，∴QA=2PB，∵AQ∥PB，∴==2，即FA=2BF，设P（t，t2﹣2t﹣1），则BF=t﹣1，∴AF=2（t﹣1），∴OA=2（t﹣1）﹣1=2t﹣3，∴Q[3﹣2t，（3﹣2t）2﹣2（3﹣2t）﹣1]∴（3﹣2t）2﹣2（3﹣2t）﹣1=﹣2（t2﹣2t﹣1），整理得t2﹣2t=0，解得t1=0（舍去），t2=2，∴P（2，﹣1），Q（﹣1，2），设直线PQ的解析式为y=px+q，把P（2，﹣1），Q（﹣1，2）代入得，解得，∴直线l的解析式为y=﹣x+1．。

20172018年度高二第一学期期中考试英语试卷(含答案)

2017-2018年度高二第一学期期中考试英语试题本试卷共10页，满分135分，考试用时120分钟注意事项：1.本试卷分为阅读理解、英语知识运用、写作三部分。

2.答卷前，考生务必用黑色字迹的钢笔或签字笔将自己的姓名和考生号、试室号、座位号填写在答题卡上。

不按以上要求作答的答案无效。

5.考生必须保持答题卡的整洁。

考试结束后，将答题卷和机改答题卡一并交回。

AThe Hawaii V olcanoes (火山) National ParkThe Hawaii V olcanoes National Park, on the island of Hawaii, has two active volcanoes：Mauna Loa, which last erupted in 1984, is 13,677 feet above sea level; the other is Kilauea that is next to Mauna Loa and it has been erupting since January 3rd, 1983. it is 4,190 feet above sea level.When to visit:The park is open 24 hours a day year round. There are no plants or trees on the lava(火山岩) fields and no protection from the sun, so you must bring sunglasses and sunscreen(防晒霜).How to get there:The best way to get to the park is to take Highway 11. From the airport at Hilo, Highway 11 will take you southward across the eastern part of the island.Things to see:If you want to know more about the park, the Kilauea Visitor Center is surely a stop to make. It is a quarter of a mile (402m) from the park entrance. There, you can see a great movie about real lava and learn about the island’s geological, natural, and cultural history. The center is open from 7:45 am to 5:00 pm. There are also many guided walks and hikes around the park. You must check weather conditions and volcanic before hiking alone. If possible, you may drive down Chain of Craters Road to see lava flowing into the ocean.Tickets:Entrance to the park is $ for each vehicle including people, $ for those who travel on foot or ride a bicycle. Children under the age of 15 are free.1. Different from Mauna Loa, Kilauea _______.A. will disappear soon.B. is closed to visitors.C. is much bigger.D. erupts more often.2. The Kilauea Visitor Center_______.A. lets visitors learn about the park.B. is next to the park entrance.C. offers all kinds of movies.D. is open for 8hours every day.3. If a family of three drives a car into the park, they need to pay_______.A. $B. $C. $D. $4. The text is most probably taken from_______.A. A travel magazine.B. A geography textbook.C. A newspaper report.D. A research paper.BIt was raining as I ran out of the church, eager to get home and play with the gifts Father Christmas sent me. Across the street was a gas station, which was closed for Christmas, but I noticed a family standing under the narrow overhang to keep dry. I wondered briefly why they were there but then forgot about them as I couldn’t wait to see my gifts.Once I got home, there was hardly any time to enjoy my gifts. My grandparents were still waiting for us to have Christmas dinner together at their house. As we drove down the highway, I noticed that the family was still there.The closer we got to my grandparents’ house, the slower the car went. Suddenly, my father U-turned and said, “I can’t stand it!” “What?” asked my mother. “It’s those people back there at the gas station, standing in the rain.”When my father pulled into the station, I saw there were five of them: the parents and three children—two girls and a small boy. Then we learned that the family was waiting for the bus to Birmingham, where the man planned to find a job.“Well, that bus won’t come along for several hours. Winborn’s just a few milesaway, and there is a shed (棚) with a cover there,” my father advised. “I will run you up there.”Then they climbed into our car,. My father looked back and asked the children if Father Christmas had found them. Three sad faces gave him his answer.“Well, Father Christmas said he was having trouble finding you, so he just left your toys at my house this morning. Let’s go to get them first,” my father said. All at once, the three children’s faces lit up.When we arrived at our house, one girl spied a lovely doll, that little boy took a ball, and the other girl picked up something else. That was the Christmas when I learned the joy of making others happy.5. At the gas station the family might feel______.A. frightenedB. disappointedC. anxiousD. delighted6. The three children received Christmas gifts thanks to_______.A. the authorB. the author’s fatherC. their parentsD. their grandparents7. We can learn from the text that the author’s father_____.A. knew that family very wellB. got lost on the way to WinbornC. was happy to help those in troubleD. sent that family to Birmingham8. What would be the best title for the text?A. Father Christmas saved usB. My father never gives upC. A hard-working familyD. Special Christmas giftsCShe was returning from teaching out in a small community (社区). It was a moonless night, and a heavy snow was falling.She remembered back to when she had first started teaching out in small communities. In those days she had always picked up hitchhikers (搭便车者), until the day her sister told her of a friend who had been killed by a hitchhiker, all because she had stopped out of kindness to help him during a storm. Her family worried about her safety over the hitchhikers until the family heard her promise: “No more hitchhikers!”Then, one night, she saw a man waving. She slowed down for him, but now as he ran toward the car in the dark she shook with fear. Yet she thought that if he was truly in need she couldn’t leave him here in this storm.The stranger explained that his car was broken, and she told him to get in the car. They drove for an hour into the next city and she took him to a telephone booth (公用电话亭). When he reported back to her that a family member would soon come for him, she wished him well and left.Tears fell on her cheeks as she drove away. She felt as though she had beenholding her breath for an hour. “I hope they’ll understand why I had to break my promise,” she thought.9. What can we learn about the woman?A. She taught in small communities.B. She used to be a hitchhiker.C. She was a taxi driver.D. She seldom picked up strangers.10. What made her family worried about her safety?A. She had been hurt by a hitchhiker.B. Her sister’s friend was killed by a hitchhiker.C. There were often snowstorms on her way home.D. Her car often broke down on her way home.11. We can infer from the underlined sentence in the last paragraph that _________.A. She regretted picking up the stranger.B. She felt too tired to breathe.C. She had been afraid being with the stranger.D. She had been too careful driving in the storm.12. We can infer from the passage that the woman is___________.A. kind-heartedB. outstandingC. cautiousD. carelessDMany parents worry that their children’s eating habits may not be good enough to keep healthy. Some children ask for the same food over and over again, some may refuse to try anything new, and some may keep asking for snacks(点心). Therefore, having healthy eating habits becomes one of the most important lessons that a child should learn. Most parents struggle with managing good eating habits and nutrition(营养) for their children. Parents should make a plan for their children’s nutritional needs.Start your child’s day with a good breakfast. Breakfast is necessary to provide the nutrition for an active day. Studies show that children do better in study when they begin a day with a good breakfast.Allow your child to help you plan and prepare a meal. He will be glad to eat foods that he has helped to put on the table.The mealtime environment has a lot to do with how your child will feel about food. Try to serve your meals at the same place at the same time of a day. Keep the meal itself as the main event and leave the toys and television for later use.Snacks are also important. We can give our body and brain energy by eating snacks between meals. Children are often hungriest in the afternoon after school andin the evening.Offer snacks at regular time between meals. This way, your child won’t refuse a meal because he knows a snack is soon to follow. More importantly, when offering snacks, you should be careful with what to choose.13. The main idea of the second paragraph is that ___ .A. Most children go to school without eating breakfast.B. One shouldn’t eat too much for breakfast.C. A good breakfast is important to children.D. Most people haven’t realized the importance of having a good breakfast.14. To help their children form healthy eating habits, parents ____ .A. should encourage their children to eat more often at school.B. can ask the children to help with meal planning and preparation.C. must make the mealtime environment as quiet as possible.D. should serve some snacks while having a meal.15. What would most probably be talked about in the next paragraph of the passage?A. What to eat for lunch and supper.B. Why snacks are important.C. Advice on how to keep healthy.D. Examples of healthy snacks.第二节（共5小题；每小题2分，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。

2017-2018学年度第一学期期中考试八年级英语试卷

2017~2018学年度第一学期期中考试八年级英语试卷听力部分（20分）Ⅰ.听句子, 选择符合题意的图片回答问题。

（每小题1分, 共5分）( )1.Who are Lucy and Lily? ( )2.What’s Tina’s favorite subject?( )3.How are Tom and Tim different? ( )4.What is Maria better at?( )5.What do Paul and Pedro both like playing?Ⅱ.听短对话, 选择正确答案。

（每小题1分, 共5分）( )6.Where did he go on vacation?A.Beijing.B.Hangzhou.C.Zhengzhou.( )7.How often does he go to the movies?A.Twice a mont h.B.Twice a week.C.Once a month.( )8.Who dances better?A.Sally.B.Mike.C.Linda.( )9.How does he like talk shows?A.He likes them.B.He can’t stand them.C.He doesn’t mind them.( )10.Which cinema is the closest?A.Movie World.B.Screen City.C.Town Cinema.Ⅲ.听长对话, 选择正确答案。

（每小题1分, 共5分）听第一段对话, 回答第11小题。

( )11.Where is the man going tomorrow?A.To the West Lake.B.To the zoo.C.To Jim’s home.听第二段对话, 回答第12.13小题。

( )12.When is Bob’s birthday?A.October 16th.B.October 15th.C.October 14th.( )13.Where is Bob having the party?A.In a restaurant.B.At school.C.At home.听第三段对话, 回答第14.15小题。

上海市重点中学2017-2018初二第一学期英语试题(附答案)(1)培训课件

上海市重点中学2017-2018学年初二第一学期英语试题（附答案）Part1V ocabulary and GrammarI.Choose the best answerst week I wrote_______one-act play and two rhymes.A.aB.anC.theD./2.I saw a red apple in his_______hand.A.anotherB.the otherC.othersD.other3.Our headmaster,together with all the students,________morning exercise every day.A.doB.doesC.is doingD.are doing4.The Mississippi is longer than________river in the United States.A.anyB.any otherC.the otherD.other5.This pass enables me_______half-price on trains.A.to travelB.travelC.travellingD.travelled6.The game makes the students________.A.happyB.to be happyC.being happyD.are happy7.The shop is_______from morning till night.A.openB.openingC.openedD.to open8.Tom used________up late,but now he_______up early.A.to get,is used to gettingB.to get,is used to getC.to getting,is used to getD.to getting,used to getting9.Why not________？Don’t lost heart!A.trying againB.have another tryC.to do it againD.give it up10.Could you tell me what__________tomorrow?A.the weather will be likeB.will the weather be likeC.the weather will beD.will the weather be11.The teacher will teach you_________and________.A.what to do……how to do itB.what to do it…….what to not do itC.how to do……..how not to doD.what to do….what to not do12.He______down on his bed and soon______asleep.A.lied…..fally…..feltC.lied…..felly…..fell13.How many syllables(音节)are there in the word“torches”?A.OneB.TwoC.ThreeD.Four14.Y ou’d better not sleep too late,_______you?A.wouldB.didC.couldD.had15.Can you see the dark clouds over there?It________.A.is going to rainB.will rainC.is rainingD.rained16.Each year at the date that Nobel died,the prizes________to people who have done a great job in making a better world.A.gaveB.giveC.were givenD.are given17.There’s nothing left in the classroom________the air-condition.A.exceptB.except forC.besideD.besides18.Y ou look so tired.Why_______have a break?A.don’t youB.not toC.don’tD.don’t to19.My elder brother stood at the school gate,________for me.A.waitsB.waitingC.was waitingD.waited20.-----Do you mind if I use your NDSL for a while?-------______________.A.Certainly,please doB.No,you can’t use itC.No,go aheadD.Y es,of course notplete the following passage with the words or phrase in the box.Each word or phrase can only be use once.I was also_____1____nervous before I got here.But once I arrived I soon felt happy.Y ou asked me about the kinds of clothes you should bring.Y ou should bring_____2____one formal outfit(外套)for important dinners,and remember to bring lots of warm__3_____clothes,a well. Y es,I did say“warm”,because it is a bit cold here until the summer!My mum wanted to make sure that I packed lots of special food so that I would not___4____ her Chinese cooking too much.However,there are many different kinds of food in the UK,and I can buy all my favourite foods at small Chinese shops.There are also lots of cheap restaurantsAnother suggestion is to learn how to cook some of your favourite____5____before you come.Chinese food in England____6___very different to the food back home.Y ou can also go to the university canteen------eating with others is a great way to make new friends.Y ou will probably live in the halls of residence in your first year.People usually have their own room,with a desk,______7__and a bed.The bathrooms and kitchen are usually___8_____ the corridor(走廊).The kitchen is also a great place to meet the students in you hall.Good luck!I am sure you will have a wonderful time.III.Fill in the blanks with the words in their proper forms.1.People sometimes don’t________the importance of family until they lost their relative.( real)2.Let’s__________Sheshan this weekend.(unexplored)3.The young man asked himself what was the more important,________or money.(free)4.If the bank refuses to lend us money,we’re________.(finish)5.Frank________to buy the new car though it would cost him much money.(decision)6.I am sorry,could you speak a little_______?I can’t hear you clearly.(loud)7.Shanghai is so attractive and it has many tourist__________.（attract）8.My father always says to me that_______is gold.(silently)9.I can’t remember what I am going to say after a sudden________.（interrupt）10.What is your_________for being late?(explain)IV.Rewrite the sentences as required.1.Open the door,please.(改为反义疑问句)Open the door,_______________?2.I went to the USA two years ago.(保持句意)I’ve______________the USA for two years.3.Both of the twins are good at foreign languages.(改为否定句)_________of the twins_______good at foreign languages.4.Chery won the first prize with the help of the teacher.(就划线部分提问)________did Chery________the first prize?5.Rita shook the bottles before taking the medicine.(改为否定句)Rita_______________the bottle before taking the medicine.6.连词成句：Gork,turned,our,to,ice,gave a roar,blood,to,the crew,thatPart III.Reading comprehensionA.Choose the best answer.News1Have you ever thought of being able to fly around the world in a few hours thought it is about40,000kilometers?One day,maybe you st Saturday,the American X-43A airplane made its first flight.It reached a speed of8,000kilometers an hour.This makes it the fastest plane in the world.The X-43A is only three to four meters long,but it's very heavy:it weighs1,270 kilogrammes.News2Have you ever got angry at books that are full of mistakes？Don't worry,things will get better st week,China started checking textbooks,dictionaries and children's books all over the country.The government said the results of the checking would come out at the end of June. News3There will be a new"star"in the sky soon.China plans to send a satellite into space by December2009.It will stay in space for one year.It will go around the moon and take pictures.It must be very expensive,right？That's for sure-1.4billion yuan!News4Floods across the northern Mexican state of Coabuila killed at least32people and left100 more missing.It was reported on Monday.The heavy rain hit the state all night last Friday,so some banks of the river were broken.Along the river about3,000families were seriously affected.1.News1talks about_____.News1talks about_____.A.people can't go around the earth in a few hoursB.the American X-43A airplane traveled around the earth in a few hoursC.the American X-43A airplane is the fastest one in the worldD.only Americans can make such a fast plane2.If the X-43A goes around the earth,it will take about_____hours to finish the trip.A.threeB.fiveC.eightD.twelve3.Which of the following about New2is true？A.Some students have to use the books full of mistakes till the end of June.B.There are many mistakes in most of the textbooks,dictionaries and children's books.st week,Japan started checking textbooks,dictionaries and children'books.D.A few mistakes are not serious for children.4.Which of the following about the new"star"is NOT true？A.It will help us know more about the moon.B.It will go around the earth for one year.C.It will cost1.4billion yuan.D.It will be sent up by the year2009.5.Many families were affected because of_____.A.the heavy rain on MondayB.the death of132peopleC.the floods across CoabuilaD the broken banks of the riverB.Choose the words or expressions and complete the passage.Jim Carrey has become one of the most famous faces in the world.It is because of his face that he has become so famous.The funny faces that he makes and his strange behavior are what people like to____ _1_____.He was born in Canada in January17th,1962.His family was poor and____2___was difficult for him.As a teenager,he had to both work and go to school.Soon he decided to leave school.He was unhappy then___3______it helped him a great deal.He developed a wonderful sense of humor to help him live with his problems.He didn’t have any friends because he said he didn’t want any.At15,however,Jim Carrey started performing in a famous comedy(喜剧)bar in Toronto（多伦多）.Later he did the_____4___thing in America.He became very good at it.That’s the important reason why he developed into a famous comedy star many years later.Now Jim Carrey is a big famous star and he hasn’t looked back since.The__5____looks good for him,and he has millions of fans who love his wild style of films.He has proved his ability to be a great star.Carrey has come a long way from his unhappy childhood and in fact seems to be living a___6____ childhood now.Canada has been producing fine comedic talents for years,and Jim Carrey is the best of the new ones.1.A.hear B.see C.read D.look2.A.putting up B.getting up C.growing up D.looking up3.A.but B.so C.or D.for4.A.same B.different C.dirty D.wrong5.A.film B.future C.star D.school6.A.first B.second C.third D.fourthC.Read the passage and fill in the blanks with the proper words.A young boy was going to buy vegetables.On his way to the s____1___,he met a friend.“Where are you going?”asked the boy.“Wherever my legs take me.”answered his friend.Theboy thought about the answer and he was s____2____it had some deep meanings.When he returned home,he told his mother about it.His mother said,“Y ou should ask him what he would do if he had no l____3____.”The next day the boy was e____4___to see his friend coming towards him.“Where are you going?”he asked,and without w____5___for an answer,he continued,“Wherever your legs take you,right? Well,let me ask you…”“Sorry,”his friend interrupted(打断).“Today I’m going wherever the wind blows.”This answer was so d___6___from the boy’s expectation(预期)that he had nothing to ter,the boy told his mother about it.His mother said,“Y ou should ask him what he would do if there were no wind.”Some days later the boy saw his friend a____7___.He ran to his friend and asked,“Where are you going?Wherever your legs take you or wherever the wind blows?Well,let me ask you…”“No,no,”his friend interrupted.“Today I’m going to buy vegetables.”D.Answer the questionsEvery day on Amelia’s way to work she had to pass a slum(贫民窟).Though she was a social worker,she had never paid much attention to it.This changed when she met a boy named Jack.Jack knew that she was the head of social services, and was sure she could help.He reached out his hand to touch her,and said,"Can you help me?I’m looking hard for my dad."His hands were so cold that Amelia could not help holding them.She said,"What’s up?""My mom is sick and too weak to get up.Her birthday is coming.I know my father’s coming back would be the best present.W e really love him,and need him.""So what’s his name?What does he do?"Amelia asked.He said,"I’ve no idea.My mama said he had left us before I was two years old."Amelia was deeply moved and said,"Take me to your home,son."He led her to a small house.Looking around,there was nothing in it except for a small bed.A woman was sitting on it and as soon as Amelia saw her,she knew her life was near its end.She said to Amelia,"Please find a home for my son.Please don’t leave him alone in the world."With tears running from her eyes,Amelia took her hand and said,“I will take care of him and love him as my own son”.In fact,since her husband and she had no children,they had been wanting a child for a long time.Ever since Amelia took Jack into her home,life is full of joy and laughter.She got the best present in return for her kindness.1.What was Amelia?2.Where was she stopped by Jack?3.Why was Jack looking hard for his dad?4.How was Jack’s mother?5.Jack had no memory of his father,did he?6.What was the best present for Amelia？7.What can we learn from the story?参考答案：1.A2.D3.B4.B5.A6.A7.A8.A9.B10.A11.A12.D13.B14.D15.A16.D17.A18.A 19.B20.C1.B2.D3.E4.A1.B2.A3.E4.C1.realize2.explore3.freedom4.finished5.decided6.louder7.attractions8.silence9. interruption10.explanationIV.Rewrite the sentences as required.1.will you2.been in3.Neither,is4.How,win5.didn’t shake6.Gork gave a roar that turned our blood to ice.A.Choose the best answer.1.C2.B3.B4.B5.CB.Choose the words or expressions and complete the passage.1.B2.C3.A4.A5.B6.BC.Read the passage and fill in the blanks with the proper words.1.supermarket2.suspected3.legs4.excited5.waiting6.different7.again。

湖北省华中师范大学第一附属中学2017-2018学年高三上学期期中考试英语试题 Word版含答案

华中师大一附中2017-2018学年度第一学期期中检测高三年级英语试题时间：120分钟满分：150分第一部分：听力（共两节，满分30分）做题时，先将答案划在试卷上。

录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。

第一节（共5小题；每小题1.5分，满分7.5分）听下面5段对话。

每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

例：How much is the shirt?A. £19.15B. £9.18C. £9.15答案是C1. What will the man do today?A. Take part in Steve’s party.B. Visit Mary.C. Have a picnic.2. Why does Emma come here?A. To attend Professor Austin’s lecture.B. To ask for help.C. To hand in her paper.3. What does the woman ask the man to do?A. Have fun on the beach.B. Throw away the garbage.C. Do community work .4. What is the woman going to do right now?A. Borrow some books.B. Revise history.C. Take an exam.5. What do we know about the woman’s parents’ house in Florida?A. It’s near the beach.B. It’s their own house.C. It has a swimming pool.第二节（共15小题；每小题1.5分，满分22.5分）听下面5段对话或独白。

上海市重点中学2017-2018学年初二第一学期英语试题(附答案)

广州市华师附中番禺学校2017-2018学年度第一学期期中初二英语试卷(含答案)

广州市华师附中番禺学校2017-2018学年度第一学期期中初二英语试卷说明:本试卷共10页，八大题。

全卷共100分;考试时间为120分钟。

注意事项：考生务必将姓名、学号填写在答题卡（卷）上,答案写在试题卷上无效。

听力部分（20分）第一节：听力理解（共15小题；每小题1分，满分15分）听下面几段对话或独白，每段对话或独白后有几个小题，从题中所给的三个选项中选出最佳选项。

每段对话或独白读两遍。

听下面一段对话，回答第1—2两个小题。

1. Where does the man want to go?A. The library.B. The cinema.C. The museum.2. How often does the woman see a film now?A. Twice a week.B. Once a week.C. Once a month.听下面一段对话，回答第3—5 三个小题。

3. What will the boy do during this holiday?A. Visit his parents for a week.B. Take a trip to Taiwan.C. Join a club.4. How long is the boy’s holiday?A. One week.B. Two weeks.C. Three weeks.5. Why is the boy not sure if his father can go with him?A. Because his father only has a one-week holiday.B. Because his father may be busy with his work.C. Because his father is in hospital.听下面一段独白，回答第6—8三个小题。

6. What do people in Scotland think about the New Year’s Eve?A. It is as important as Christmas.B. It is less important than Christmas.C. It is more important than Christmas.7. What do people do on New Year’s Eve in Scotland?A. Have a big party with friends.B. Wish each other good luck.C. Go shopping with family.8. What can we know about the New Year’s Eve in Scotland?A. All shops are open all day.B. People drink with each other in the park.C. There is a big meal in the family.听下面一段对话，回答第9—12四个小题。

2017-2018学年上海市华东师范大学第二附属中学高一上学期期中考试数学试卷含详解

华二附中2017-2018高一上期中数学卷一、填空题1.若集合{}**(,)|24,,A x y x y y N x N =+=∈∈，用列举法表示：A =________________.2.函数y =__________.3.已知命题P 的逆命题是“若实数满足1a =且2b =，则4a b +<”，则命题P 的否命题是4.若()f x x =，()g x =，则()()f x g x ⋅=_________.5.设集合{}24,,3A m m m =+中实数m 的取值集合为M ，则R C M =_____.6.不等式12x<的解集是_________.7.任意两个正整数x 、y ，定义某种运算⊗：()()x y x y x y x yx y +⎧⊗=⎨⨯⎩与奇偶相同与奇偶不同，则集合{(,)|6,,}M x y x y x y =⊗=∈*N 中元素的个数是________8.若关于x 的不等式22160kx x k --+<的解集为空集，则k 的取值范围是______.9.已知函数()f x k =的定义域和值域都是[],a b ，则实数k 的取值范围是_________.10.已知函数()()y f x x I =∈，对函数()()y g x x I =∈，定义()g x 关于()f x 的“对称函数”为函数(),y h x x I =∈.即(),y h x x I =∈满足对任意x I ∈，两点()()()(),,,x h x x g x 关于点()(),x f x 对称.若()h x 是()g x =()3f x x m =+的对称函数，且()()h x g x >恒成立，则实数m 的取值范围是__________．二、选择题11.设集合2{|430}A x x x =-+<，{|230}B x x =->，则A B = （）A.3(3,2-- B.3(3,2- C.3(1,2 D.3(,3)212.设0x >，则“1a =”是“2ax x+≥恒成立”的（）A.充分不必要条件B.必要不充分条件C.充分必要条件D.既不充分也不必要条件13.下列命题中：①a b c a c b >⇒-<-；②a b >，0c cc a b>⇒<；③22ac bc a b >⇒>；④33>⇒>a b a b ，其中正确的命题个数是（）A.1个B.2个C.3个D.4个14.国际上通常用恩格尔系数衡量一个国家和地区人民生活水平的状况，它的计算公式为xn y=x 代表人均食品支出总额，y 代表人均个人消费支出总额）且2475y x =+，各种类型的家庭标准如下表：家庭类型贫困温饱小康富裕n59%n ≥50%59%n ≤<40%50%n ≤<30%40%n ≤<张先生居住区2017年比2016年食品支出下降7.5%，张先生家在2017年购买食品和2016年完全相同的情况下人均少支出75元，则张先生家2017年属于（）A.贫困B.温饱C.小康D.富裕三、解答题15.解关于x 的不等式(1)()0x x a --<，a R ∈16.已知a 、[1,1]b ∈-，求证：|||1|a b ab +≤+17.如图，某机械厂要将长6m ，宽2m 的长方形铁皮ABCD 进行裁剪．已知点F 为AD 的中点，点E 在边BC 上，裁剪时先将四边形CDFE 沿直线EF 翻折到MNFE 处（点C ，D 分别落在直线BC 下方点M ，N 处，FN 交边BC 于点)P ，再沿直线PE 裁剪．（1）当4EFP π∠=时，试判断四边形MNPE 的形状，并求其面积；（2）若使裁剪得到的四边形MNPE 面积最大，请给出裁剪方案，并说明理由．18.设集合2{1,2,3,2}n A n = ()*2,n N n ∈≥，如果对于2n A 的每一个含有m ()4m ≥个元素的子集P ，P 中必有4个元素的和等于41n +，称正整数m 为集合2n A 的一个“相关数”（1）当3n =时，判断5和6是否为集合6A 的“相关数”，说明理由；m n≥+.（2）若m为集合2n A的“相关数”，证明：3华二附中2017-2018高一上期中数学卷一、填空题1.若集合{}**(,)|24,,A x y x y y N x N =+=∈∈，用列举法表示：A =________________.【答案】(){}2,1根据**24,,x y y N x N +=∈∈解出方程，写成集合形式.【详解】由题：**24,,x y y N x N +=∈∈，根据0,0x y >>，必有04,02x y <<<<，且**,y N x N ∈∈，所以只能,12y x ==，所以(){}2,1A =.故答案为：(){}2,1【点睛】此题考查根据集合描述法求集合中的元素，准确辨析限制条件，用列举法表示，注意元素的表示形式.2.函数y =__________.【答案】[]5,1-解不等式2450x x --+≥，其解集就是函数定义域.【详解】由题：2450x x --+≥，即2450x x +-≤，()()510x x +-≤，解得：51x -≤≤，所以定义域为：[]5,1-.故答案为：[]5,1-【点睛】此题考查根据函数求定义域，关键在于准确求解不等式，结果写成集合或区间形式. 3.已知命题P 的逆命题是“若实数满足1a =且2b =，则4a b +<”，则命题P 的否命题是【答案】,4,12a b a b a b +≥≠≠若实数满足则或根据四种命题之间关系，可先由逆命题写出原命题，进而可得出其否命题.【详解】因为命题P 的逆命题是“若实数满足1a =且2b =，则4a b +<”，所以命题P ：若实数满足4a b +<，则1a =且2b =；所以其否命题为：若实数满足4a b +≥，则1a ≠或2b ≠；【点睛】本题主要考查四种命题之间关系，熟记概念即可，属于基础题型.4.若()f x x =，()g x =，则()()f x g x ⋅=_________.【答案】根据运算法则对两个函数进行乘积运算即可.【详解】由题：()f x x =，()g x =则()()f x g x x ⋅=⋅.故答案为：【点睛】此题考查求两个函数的乘积，关键在于正确计算代数式的乘积.5.设集合{}24,,3A m m m =+中实数m 的取值集合为M ，则R C M =_____.【答案】{}4,2,0,1,4--根据集合中的元素的互异性，列出不等式组求解.【详解】由题：集合{}24,,3A m m m =+，则224343m m m m m m ≠⎧⎪+≠⎨⎪+≠⎩，化简得：()()()441020m m m m m ⎧≠⎪+-≠⎨⎪+≠⎩，解得：()()()()()(),44,22,00,11,44,m ∈-∞----+∞ ，即()()()()()(),44,22,00,11,44,M =-∞----+∞ ，所以{}4,2,0,1,4R C M =--.故答案为：{}4,2,0,1,4--【点睛】此题考查根据集合中元素的互异性求参数的取值范围，需要注意不重不漏.6.不等式12x<的解集是_________.【答案】()1,0,2⎛⎫-∞+∞ ⎪⎝⎭【分析】由不等式12x <得120x -<，所以210x x->，等价于(21)0x x ->，解之得所求不等式的解集.【详解】由不等式12x <得120x -<，即120x x -<，所以210x x->，此不等式等价于(21)0x x ->，解得0x <或12x >，所以不等式的解集是：()1,0,2⎛⎫-∞+∞ ⎪⎝⎭，故填：()1,0,2⎛⎫-∞+∞ ⎪⎝⎭.【点睛】本题考查分式不等式的解法，一般的步骤是：移项、通分、分解因式、把每个因式未知数的系数化成正、转化为一元二次不等式或作简图数轴标根、得解集，属于基础题.7.任意两个正整数x 、y ，定义某种运算⊗：()()x y x y x y x y x y +⎧⊗=⎨⨯⎩与奇偶相同与奇偶不同，则集合{(,)|6,,}M x y x y x y =⊗=∈*N 中元素的个数是________【答案】9根据正整数的奇偶,讨论x y 、的不同取值情况:若一奇一偶,则取6xy =;若都是奇数或都是偶数,则取6x y +=,列举出所有可能即可.【详解】集合{(,)|6,,}M x y x y x y =⊗=∈*N 若x y 、一奇一偶,则取6xy =,此时所有个数为16x y =⎧⎨=⎩,23x y =⎧⎨=⎩,32x y =⎧⎨=⎩,61x y =⎧⎨=⎩,此时(),x y 共有4个;若x y 、都是偶数,则取6x y +=,此时所有个数为24x y =⎧⎨=⎩,42x y =⎧⎨=⎩,此时共(),x y 有2个;若x y 、都是奇数,则取6x y +=,此时所有个数为15x y =⎧⎨=⎩,33x y =⎧⎨=⎩,51x y =⎧⎨=⎩此时(),x y 共有3个;综上可知,满足条件的元素共有9个.故答案为:9【点睛】本题考查了新定义运算与集合的综合应用,注意分析题意并正确理解新定义是解决此类问题的关键,属于中档题.8.若关于x 的不等式22160kx x k --+<的解集为空集，则k 的取值范围是______.【答案】176k +≥【详解】由题意知，对每一个x R ∈，都有22160kx x k --+≥，即()2216x k f x x -≥=+，所以，(),k maxf x x R ≥∈.当1x ≥时，令1t x =-，0t ≥则()()()22227167216ttf x tt ==≤=++++，当且仅当t =，即1x =+当1x <时，令10t x t =->，，则()()()22227167216ttf x ttt +==≤+--+，当且仅当t =，即1x =-综上知，()17max 6x Rf x ∈=，故k 的取值范围是176k ≥9.已知函数()f x k =的定义域和值域都是[],a b ，则实数k 的取值范围是_________.【答案】5,14k ⎛⎤∈-- ⎥⎝⎦函数()f x k =-在定义域内是减函数，只需满足(),()f a b f b a ==，转化成方程的根的问题.【详解】由题函数()f x k =在定义域[)2,-+∞内是减函数，函数()f x k =-的定义域和值域都是[],a b ，所以(),()f a b f b a ==，即k bk a ⎧=⎪⎨=⎪⎩，2a b k -≤<≤k b k a ⎧-=⎪⎨-=⎪⎩，两式同时平方得：22222222k bk b a k ak a b ⎧-+=+⎨-+=+⎩，两式相减得：2222ak bk b a a b -+-=-，()()()2k a b a b a b a b --+-=-，所以：21a b k +=-所以22222222k bk b a k ak a b ⎧-+=+⎨-+=+⎩等价于222222122212k bk b k a k ak a k b ⎧-+=--+⎨-+=--+⎩，即()()22222121021210b k b k k a k a k k ⎧--+--=⎪⎨--+--=⎪⎩，所以可以看成,a b 是方程()2221210x k x k k --+--=在[]2,x k ∈-的两个不等实根，由根的分布可知：()()()()()()2222222142102122221221021210k k k k k k k k k k k k k ⎧∆=---->⎪⎪--<<⎪⎨⎪----+--≥⎪⎪--+--≥⎩，化简得：2450421223010k k kk k k +>⎧⎪-<-<⎪⎨++≥⎪⎪--≥⎩，解得：54321k k k ⎧>-⎪⎪⎪>-⎨⎪≤-⎪⎪⎩，所以5,14k ⎛⎤∈-- ⎥⎝⎦.故答案为：5,14k ⎛⎤∈-- ⎥⎝⎦【点睛】此题考查根据函数的单调性讨论定义域与值域的问题，将问题转化为方程的根的问题解决.10.已知函数()()y f x x I =∈，对函数()()y g x x I =∈，定义()g x 关于()f x 的“对称函数”为函数(),y h x x I =∈.即(),y h x x I =∈满足对任意x I ∈，两点()()()(),,,x h x x g x 关于点()(),x f x 对称.若()h x 是()g x =()3f x x m =+的对称函数，且()()h x g x >恒成立，则实数m 的取值范围是__________．【答案】m >由“对称函数”的定义及中点坐标公式得2()432h x x x m +-=+所以，2()624h x x m x =+--，()()h x g x >恒成立即226244x m x x +-->-，234x m x +>-恒成立，亦即直线3y x m =+位于半圆24y x =-的上方.在同一坐标系内，画出直线3y x m=+及半圆24y x =-（如图所示），当直线与2300213m⨯-+=+解得10m =，故答案为m 10>二、选择题11.设集合2{|430}A x x x =-+<，{|230}B x x =->，则A B = （）A.3(3,2-- B.3(3,2- C.3(1,2 D.3(,3)2【答案】D试卷分析：集合()(){}{}|130|13A x x x x x =--<=<<，集合，所以3|32A B x x ⎧⎫⋂=<<⎨⎬⎩⎭,故选D.考点：1、一元二次不等式；2、集合的运算.【此处有视频，请去附件查看】12.设0x >，则“1a =”是“2ax x+≥恒成立”的（）A.充分不必要条件 B.必要不充分条件C.充分必要条件 D.既不充分也不必要条件【答案】A试卷分析：由题意得，min 2(2221a a x x a a x x +≥⇔+≥⇔≥⇔≥，故“1a =”是“2ax x+≥恒成立”的充分不必要条件，故选A ．考点：1．充分必要条件；2．恒成立问题．13.下列命题中：①a b c a c b >⇒-<-；②a b >，0c cc a b>⇒<；③22ac bc a b >⇒>；④33>⇒>a b a b ，其中正确的命题个数是（）A.1个B.2个C.3个D.4个【答案】C根据不等式的性质分析①③④正确，②中若0a b >>则不成立.【详解】对于①：a b a b c a c b >⇒-<-⇒-<-，正确；对于②：若0a b >>，00c cc a b>⇒>>，所以原说法错误；对于③：22222220ac bc ac bc c a b c c>⇒>⇒>⇒>，正确；对于④：33a b a b >⇒>⇒>，正确，所以正确的命题共3个.故选：C【点睛】此题考查不等式性质的应用，对命题真假性进行判断.14.国际上通常用恩格尔系数衡量一个国家和地区人民生活水平的状况，它的计算公式为xn y=x 代表人均食品支出总额，y 代表人均个人消费支出总额）且2475y x =+，各种类型的家庭标准如下表：家庭类型贫困温饱小康富裕n59%n ≥50%59%n ≤<40%50%n ≤<30%40%n ≤<张先生居住区2017年比2016年食品支出下降7.5%，张先生家在2017年购买食品和2016年完全相同的情况下人均少支出75元，则张先生家2017年属于（）A.贫困B.温饱C.小康D.富裕【答案】D根据食品支出下降7.5%和人均支出少75元，求出2017年的食品支出和人均消费支出，即可求出系数.【详解】设2016年人均食品消费x 元，则2017年人均食品支出()17.5%92.5%x x -=，2017年人均消费支出：292.5%475x ⨯+，由题：292.5%475752475x x ⨯++=+，解得：500x =，所以92.952.50.33292.55475%292.5%5475n x x ⨯==≈⨯⨯+⨯+，所以属于富裕.故选：D【点睛】此题考查函数模型的应用，根据题目所给关系，建立函数模型求解实际问题.三、解答题15.解关于x 的不等式(1)()0x x a --<，a R∈【答案】当1a >时，不等式的解为：(1,)a ，当1a =时，不等式解为∅，当1a <时，不等式的解为：(,1)a .分类讨论当1,1,1a a a >=<三种情况的解.【详解】关于x 的不等式(1)()0x x a --<，a R∈当1a >时，不等式的解为：1x a <<，当1a =时，原不等式为2(10)x -<，不等式无解，当1a <时，不等式的解为：1<<a x ，综上所述：当1a >时，不等式的解为：(1,)a ，当1a =时，不等式解为∅，当1a <时，不等式的解为：(,1)a .【点睛】此题考查解含参数的不等式，关键在于准确进行分类讨论.16.已知a 、[1,1]b ∈-，求证：|||1|a b ab +≤+【答案】证明见解析.通过作差法证明()()()()221110ab a b ab a b ab a b +-+=++++--≥即可【详解】a 、[1,1]b ∈-，所以10,10,10,10a b a b +≥+≥-≥-≥()()()()22111ab a b ab a b ab a b +-+=++++--()()()()11110a b a b =++--≥所以()()221ab a b +-+，即1ab a b +≥+，所以|||1|a b ab +≤+.【点睛】此题考查不等式的证明，含绝对值问题可以考虑平方处理，常用作差法结合因式分解证明.17.如图，某机械厂要将长6m ，宽2m 的长方形铁皮ABCD 进行裁剪．已知点F 为AD 的中点，点E 在边BC 上，裁剪时先将四边形CDFE 沿直线EF 翻折到MNFE 处（点C ，D 分别落在直线BC 下方点M ，N 处，FN 交边BC 于点)P ，再沿直线PE 裁剪．（1）当4EFP π∠=时，试判断四边形MNPE 的形状，并求其面积；（2）若使裁剪得到的四边形MNPE 面积最大，请给出裁剪方案，并说明理由．【答案】（1）四边形MNPE 为矩形，面积22S m =．（2）当3EFD π∠=时，沿直线PE 裁剪，四边形MNPE 面积最大，最大值为26-．理由见解析.（1）当4EFP π∠=时，由条件得4EFP EFD FEP π∠=∠=∠=．可得FN BC ⊥，四边形MNPE 为矩形．即可得出．（2）设(02EFD πθθ∠=<<，由条件，知EFP EFD FEP θ∠=∠=∠=．可得22sin(2)sin 2PF πθθ==-，23sin 2NP NF PF θ=-=-，23tan ME θ=-．四边形MNPE 面积为112222()[(3)(3)]2622sin 2tan tan sin 2S NP ME MN θθθθ=+=-+-⨯=--，化简利用基本不等式的性质即可得出．【详解】解：（1）当4EFP π∠=时，由条件得4EFP EFD FEP π∠=∠=∠=．所以2FPE π∠=．所以FN BC ⊥，四边形MNPE 为矩形．所以四边形MNPE 的面积22S PN MN m == ．（2）设(0)2EFD πθθ∠=<<，由条件，知EFP EFD FEP θ∠=∠=∠=．所以22sin(2)sin 2PF πθθ==-，23sin 2NP NF PF θ=-=-，23tan ME θ=-．由230sin 2230tan 02θθπθ⎧->⎪⎪⎪->⎨⎪⎪<<⎪⎩得2sin 232tan ,(*)30.2θθπθ⎧>⎪⎪⎪>⎨⎪⎪<<⎪⎩所以四边形MNPE 面积为1()2S NP ME MN =+122[(3)(322sin 2tan θθ=-+-⨯226tan sin 2θθ=--2222(sin cos )6tan 2sin cos θθθθθ+=--36(tan tan θθ=-+66-=-．当且仅当3tan tan θθ=，即tan ,3πθθ==时取“=”．此时，(*)成立．答：当3EFD π∠=时，沿直线PE 裁剪，四边形MNPE 面积最大，最大值为26-．【点睛】本题考查了函数的性质、矩形的面积计算公式、基本不等式的性质、三角函数的单调性应与求值，考查了推理能力与计算能力，属于中档题．18.设集合2{1,2,3,2}n A n = ()*2,n N n ∈≥，如果对于2n A 的每一个含有m ()4m ≥个元素的子集P ，P 中必有4个元素的和等于41n +，称正整数m 为集合2n A 的一个“相关数”（1）当3n =时，判断5和6是否为集合6A 的“相关数”，说明理由；（2）若m 为集合2n A 的“相关数”，证明：3m n ≥+.【答案】（1）5不是集合6A 的“相关数”，6是集合6A 的“相关数”；（2）证明见解析.（1）写出6{1,2,3,4,5,6}A =，分别考虑含有5个元素的子集和含有6个元素的子集讨论其中某四个数之和是否为13即可；（2）分析2n A 的含有2n +个元素的集合，{}1,,1,2,,2n n n n n -++⋅⋅⋅，其中任意四个元素之和的最小值42n +，不可能等于41n +，所以2n +不是集合2n A 的“相关数”，分析当2,m n m N *≤+∈时，m 不是集合2n A 的“相关数”，即可得证.【详解】（1）当3n =时，6{1,2,3,4,5,6}A =，它的5个元素的子集中{2,3,4,5,6}，它的四个元素之和的最小值23451413+++=>，其中任意四个元素之和都不可能为13，所以5不是集合6A 的“相关数”，它的6个元素的子集中只能是{1,2,3,4,5,6}，存在四个元素124613+++=，所以6是集合6A 的“相关数”；（2）若m 为集合2n A 的“相关数”，假设2,m n m N *≤+∈，则448m n -≥--，分析2n A 的含有m 个元素的集合{}21,22,,2n m n m n -+-+⋅⋅⋅，其中任意四个元素之和的最小值21222324841042n m n m n m n m n m n -++-++-++-+=-+≥+，不可能等于41n +，则m 不是集合2n A 的“相关数”，与题矛盾，所以2,m n m N *>+∈，即3,m n m N *≥+∈.【点睛】此题考查对集合中元素特点分析进行辨析和证明，涉及推理与证明，利用反证法证明，对综合能力要求较高.。

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