专题4 专题过关检测
八年级数学专题 二元一次方程组重难点(参数问题、实际应用问题)(北师大版)
ì3x - 2 y = -1
ìx =1 ìm + 5 =1
ìm = -4
íî3x + 2 y = 7
，解得
í î
y
=
2
，即
íîn
+
3
=
2
，解得
íîn
=
-1
．
(1)学以致用，模仿乐乐同学的“整体换元”的方法，解方程组
ì ïï í ï ïî
x x
+ 3 + 3
y y
+ -
x x
5 5
y y
= =
4 ．
-2
试卷第 2 页，共 9 页
义，否则，若把 y=ax+b 代入变形的原方程，必然得到一个恒等式； ③用代入法求出一个未知数的值后，再求另一个未知数时，一般代入变形后得到的方
程比较简单．
2．加减消元法
把方程组的两个方程（或先作适当变形）相加或相减，消去其中一个未知数，从而把
解二元一次方程组转化为解一元一次方程．这种解方程组的方法叫做加减消元法，简
联立成方程组，求出未知数的值，然后代入含有参数的方程即可求出参数的值．
四、列方程组解应用题步骤
1．列方程组解应用题是把“未知”转化为“已知”的重要方法，它的关键是把已知量和未 知量联系起来，找出题目中的相等关系．一般来说，有几个未知量就必须列出几个方
程，所列方程必须满足：
①方程两边表示的是同类量；②同类量的单位要统一；③方程两边的数值要相等．
y
=
与 41
íî2
x
+
3
y
=
-7
有相同的解，求
a，b
的值．
2020年春牛津版英语中考专题复习八年级Unit 4过关检测(Word版附答案)
Unit 4过关检测时间:60分钟满分:100分一、单项填空(每小题1分,共10分)1.—Could you please show me how to use the washing machine?—Please follow the .A. instructionsB. introductionsC. inventionsD. invitations2.—How does Lily want to design the birthday card?—She doesn't want to do it by herself. She plans to ask someone else to do it, .A. yetB. insteadC. tooD. either3.The bottle is full water. Who has filled it water?A. of; ofB. with; ofC. with; withD. of; with4.Something when they decorated the room.A. cut outB. went wrongC. tidied upD. made a mistake5.Yangyang's mother bought two pens for him. One is blue, and is black.A. the otherB. otherC. anotherD. others6.—Would you please the meeting instead of me, Cindy?—I'll be glad to, but I have an after-school activity to .A. join; attendB. take part; join inC. attend; take part inD. attend; take part7. —Some young people play with mobile phones all day instead of reading books.—That's too bad. Everyone be a book lover. Reading is more enjoyable.A. wouldB. mayC. shouldD. need8.—Jenny, you'd better your kid into the music hall. Maybe he is a bit noisy but he can learn a lot from the concert.—OK, I got it.A. takeB. not takeC. not to takeD. not taking9.—Do you think most people in Nanjing can talk with foreigners in English?—Yes, I think so. a young child an old person is learning to speak English.A. Either; orB. Neither; norC. Both; andD. Not only; but also10.—Can you help me repair the bike?—. Come and get it in half an hour.A. No problemB. I'm sorry I can'tC. Not at allD. It's a pleasure二、完形填空(每小题1分,共10分)Six-year-old Brandon decided one morning to make his parents pancakes. He found a big bowl and a spoon, pulled a chair to the table, opened the cupboard and pulled out the heavy flour(面粉)bag. He put some flour 11the bowl with his hands, mixed in a cup of milk and 12some sugar.Soon Brandon was covered with flour and getting frustrated(懊恼的). He wanted this to be something 13for Mum and Dad, but it was getting very bad. He didn't know what to do 14.Suddenly he saw his cat near the bowl and went to push her away, 15the egg box to the floor. He tried to clean up but slipped(滑倒)on the eggs, getting his clothes 16. Just then, he saw his dad 17at the door.Brandon's eyes were full of tears. All he wanted to do was something good, but now he was sure his dad would beat(揍)him, but his father didn't. 18, he picked up his crying son and kissed him.That's what we sometimes face in life. We try to do something good, but it turns into a mess(一团糟). Sometimes we just stand there in tears 19we can't think of anything else to do. Hopefully, someone close to us picks us up, loves us and forgives us. But we can't 20 trying to "make pancakes" for Dad or for others. Sooner or later we'll get it right, and then they'll be glad we tried.11.A. above B. at C. into D. under12.A. bought B. tasted C. gave D. added13.A. terrible B. forgettable C. good D. interesting14.A. certainly B. already C. recently D. next15.A. falling B. breaking C. knocking D. sending16.A. clean B. big C. cheap D. dirty17.A. standing B. sitting C. looking D. pushing18.A. Therefore B. Finally C. Instead D. But19.A. because B. though C. whenever D. so that20.A. stop B. keep C. mind D. finish三、阅读理解(每小题2分,共30分)AIn my spare time, I paint designs(图案) on T-shirts. I got the idea two years ago for my brother's birthday present. The shop wanted $20 for a special design on a T-shirt, so I decided to do it myself. I bought a white cotton T-shirt for $6 and some paints, and I painted a lion on the front. My brother loved it!Painting T-shirts is great fun. You needn't be a great artist, and you can just paint shapes(形状) and lines(线条). The T-shirts are the most expensive part of my hobby. You have to use special paints because they can last a long time. Brushes are not really expensive but you need to buy ones of good quality.I love my hobby because I can make quite different T-shirts for others. I give a lot of them away as presents to my family and friends. Sometimes, I sell them. Since I started, I've made about 60 T-shirts and each one is different.21.Two years ago the writer decided to .A. buy a T-shirt with a special designB. paint a special design on a T-shirtC. sell a T-shirt with a special designD. write a special word on a T-shirt22.How much did it cost the writer to buy a white cotton T-shirt ?A.$20.B.$8.C.$6.D.$2.23.What was the writer's first design?A. A shape.B. A line.C. A lion.D. A T-shirt.24.are necessary (必要的) if you want to paint a design on a T-shirt.A. Special paints and good-quality brushesB. Special paints and cheap brushesC. Good-quality brushes and good painting skillsD. Good painting skills and cheap paints25.The writer loves his hobby because .A. he can give away the T-shirts as presentsB. he can wear many cheap and beautiful T-shirtsC. he can make quite different T-shirts for othersD. he can have many beautiful T-shirts26. You can join the class if you like to .A. offer some recipesB. teach how to cookC. make desserts yourselfD. get some surprises27. You will in the class.A. eat the meal with the teacherB. celebrate the special daysC. learn 2-3 recipes each lessonD. have a hands-on experience28. You will pay for five lessons.A.$30B.$60C.$120D.$15029. How can you attend the class?A. Make a phone call to them.B. Send them an e-mail.C. Get information from parents.D. Come to the class directly.30.Where can we read this passage?A. On the Internet.B. In a magazine.C. In a storybook.D. In a travel guide.CThis morning I got an email from Roy. It seems that my boy really enjoys his new life at Harvard University.The email made me think of the first day when we moved into this house.Little Roy ran around the new house with great excitement and tried to move his own things into the house such as his toys, books and clothes. Suddenly his little hand knocked over a bottle of paint on the shelf. The paint made the tidy floor and white wall a terrible mess. "Oh!" My wife rushed in angrily. I looked at my son, and his small face was filled with fear.I smiled and held his hand, "Take it easy, Roy. Now let's do something to make it look nice."I took out a brush. "You see, Dad is a magician. I can change it into a big tree."His mother soon joined us and helped paint some flowers on the wall.We spent the whole afternoon painting and laughing. The wall became a beautiful forest with plants, birds and small animals. Blue sky and white clouds were also painted by Roy. On that day, everyone in the house knew something special happened.The night before Roy left for Harvard, he asked me if I still remembered the day when he had knocked over the paint. "Since then I've never worried about making mistakes," he continued, "I believe I can always find out ways to solve the problems."That's for sure. Mistakes are unavoidable(不可避免的), making mistakes is part of life. When we make a mistake, what we shouldn't do is to run away from it. The mistake can be valuable if we can make full use of it. In fact, our attitudes(态度) towards them may make a difference.31.When the bottle of paint was knocked over, .A. Roy felt down and hurt himselfB. the whole family became a messC. Roy's mother cleaned the floor at onceD. Roy's father did something special to Roy32.What did the father do with the paint?A. To give a magic show.B. To teach his son to draw.C. To draw a forest on the floor.D. To paint some pictures on the wall.33.How did Roy feel that whole afternoon?A. Excited but tired.B. Busy but happy.C. Useless and bored.D. Afraid and worried.34.From the passage, we know Roy .A. learn a lot from his fatherB. will become braver to face difficultiesC. will try to avoid making mistakesD. has a bad relationship with his mother35.What does the writer mainly want to tell us in the passage?A. It is natural for a person to make mistakes.B. Everyone must learn to pay for their mistakes.C. We should never be afraid of making mistakes.D. One's attitude towards mistakes is very important.四、任务型阅读(每小题2分,共10分)Tanghulu, is fruit covered with sugar on a stick, a traditional snack from northern China. It's also a necessary snack during the Chinese New Year season. Recently, in northern China, people welcome the return of spring by holding the Tanghulu Fair (庙会).Many Chinese still remember eating Tanghulu when they were young. It is said that the fair has a 500-year-old history. Nowadays, Tanghulu is not only a kind of snack, it is also a sweet memory of our childhood. Every year, a large number of Tanghulu sellers get together to start delicious Tanghulu Competition during the Spring Festival holidays. In the past, this traditional snack only used haws(山楂果), but now it also uses grapes, oranges, strawberries and so on. But people like Haw Tanghulu best. They are rich in vitamin (维他命) C and E. Do you know how to make Haw Tanghulu? First, wash the large haws clean, dig the seeds (籽) out, and pierce (刺破) ten haws on a stick. Then they heat the sugar, put the sticks of haws into heated sugar and quickly pull them out. When the sugar on the haws cools down and becomes a candy coat, the Tanghulu is done. Tanghulu is very popular in China, especially in Beijing. It also makes many foreigners want to taste it.We hope Tanghulu will become one of the most popular snacks in the world.根据短文内容回答下列问题36.Where is Tanghulu from?_______________________________________________________________________________ _________37.How do people welcome the return of spring in northern China?_______________________________________________________________________________ _________38.What do the Tanghulu sellers get together to do during the Spring Festival holidays every year? _______________________________________________________________________________ _________39.What kind of vitamin is the Haw Tanghulu rich in?_______________________________________________________________________________ _________40.What is the passage mainly about?_______________________________________________________________________________ _________五、词汇运用(每小题1分,共10分)(A)根据句意及汉语提示写出单词41.My teacher often (建议) everyone to buy a dictionary.42.The workers still kept (修补) cars at lunchtime.43.There was a (可怕的) wind last week and some trees were even blown down.44.Don't make so many (错误) in your homework next time.45.The book with a green (封面) may tell you a lot about DIY.(B)用所给单词的适当形式填空46.The books on those (shelf) are all about science.47.Tom, don't (cut) the ball open. It will be broken.48.Can you show me how (stick) a rose on the card?49.Not only Lucy but also Lily (have) got many friends in China.50.You'd better not (add) too much sugar to the dish or it will be too sweet.六、根据短文内容及首字母提示补全短文(每小题1分,共10分)An old carpenter was ready to retire(退休). His boss was sorry(难过的) to see the good worker go. He asked the carpenter if he could b51just one more house. The carpenter said yes, but his m52was not on his work any more.He used poor materials and worked on the house c53. When the carpenter finished his work, the boss handed the front-door key to him."This is your house,"he said. "A g54for you."What a surprise! What a shame! I55he had known he was building his own house, he would have done it differently. Now he had to live in the home he had poorly built. So it is with us. S56, we build our lives carelessly. At important points we do not try our b57. Then with a shame we look at the situation we have created(创造). We find that we are now living in the house we have poorly built. But we don't have a chance to make it all over a58.Think of y59as the carpenter. Think about your life. Build it wisely. It is the only life you will ever build. Life is a do-it-yourself project.Your life today is the r60of your attitudes and choices(选择) you made in thepast.Your life tomorrow will be that of your attitudes and choices you make today.51. 52. 53. 54. 55.56. 57. 58. 59. 60.七、书面表达(20分)大家都知道早餐很重要,你早餐吃什么呢?你会做鸡蛋煎饼(egg pancakes)吗?你能给英国留学生介绍一下如何制作鸡蛋煎饼吗?提示:1.食材:两杯牛奶,四个鸡蛋,一茶匙盐(salt),一些面粉(flour),一茶匙油(oil)。
2020年春外研版英语中考素养提升专题复习八年级Unit 4过关检测(Word版附答案)
Module 4过关检测时间:60分钟满分:100分一、单项填空(每小题1分,共10分)1.— will they go to Shanghai next week?—They will take a train there.A. WhenB. WhoC. HowD. Why2. you travel,your life experience will be.A. The less; the moreB. The more; the lessC. The more; the richerD. The less; the richer3.—Don't use the car for short .—I agree. We can travel in greener ways.A. seasonsB. sportsC. gamesD. journeys4.She often goes to school a bike, but sometimes she goes bus.A. by; byB. on; onC. on; byD. by; on5.—How do you go to school?—My school is my house, so I go to school on foot.A. close toB. different fromC. famous forD. far from6.—There are so many people in the room. It's very . Let's go outside. —OK. Let's go.A. warmB. crowdedC. bigD. dark7.Cola is an unhealthy drink., many children still like drinking it.A. ButB. AsC. SoD. However8.—Do you know the price of the ticket?—Yes. Each ￥180.A. paysB. costsC. takesD. spends9.—Home is place wherever you go.—East or west, home is the best.A. warmB. warmerC. warmestD. the warmest10.—Oh, no! We've missed the 9 o'clock train!—. There's another one in half an hour.A. Don't worryB. Hurry upC. Give me a breakD. Don't mention it二、完形填空(每小题1.5分,共15分)I live in a town that trains go by, fast or slowly. Lots of people take trains tovisit their friends. I like11 by train.It is very comfortable and cheap.It goes very fast.It's about 350 kilometres per hour.First you have to buy a ticket.Then youmust wait12 the waiting room.When the train 13,you can go with your ticket.Usually there are a lot of people on the train.You can play 14 and play chess,but you can't smoke because it is not15 for the other people.You can also read books or talk with your friends or the other people.But you can't talk 16.I like watchingout of the window and enjoying the mountains, trees and rivers. Besides, you may see some 17 working in the fields.You can eat something on the train such as rice,eggs, noodles,18 you can't throw your things here and there.You must put 19 in abag.The workers on the train are very20.They will help you if you have any problems.11.A. driving B. travellingC. flyingD. walking12.A. in B. onC. nearD. for13.A. goes B. arrivesC. callsD. works14.A. football B. basketballC. waterD. cards15.A. bad B. goodC. easyD. popular16.A. loudly B. clearlyC. quicklyD. slowly17.A. doctors B. teachersC. policemenD. farmers18.A. and B. butC. orD. so19.A. it B. herC. themD. his20.A. careful B. friendlyC. happyD. lucky三、阅读理解(每小题2分,共30分)ATravelling is very interesting. Many people love travelling.There are many ways to travel: by plane,by train,by ship or by car.Everyone has their favourite way.Greg: My favourite way of travelling is by car.I can bring my pet dog along.I cantravel three hundred miles or only fifty miles a day.I can stop at a good restaurant to enjoy a good meal or at a hotel to spend the night.Eliza:I love travelling by train best.It's very exciting.I travelled most of Europein 5 months by train.It's the best way to talk with the local people and make new friends on the way.Trains make even the longest trip enjoyable and the train ride to me is just like a big moving party. I also like travelling by ship. It is a great way to spend aholiday. I can go to parties,watch movies on the ship,and enjoy the blue sky and water.Danny: Travelling by plane is my favourite. It's the fastest way. I can quickly getto another country. Planes have very comfortable seats. I can have something to drink and eat.I can also read some free magazines and newspapers.21.How many ways of travelling are mentioned in the passage?A. Three.B. Four.C. Five.D. Six.22.Greg loves travelling best.A. by shipB. by carC. by trainD. by plane23.What does Eliza think of travelling by train?A. Comfortable.B. Slow.C. Boring.D. Exciting.24.Danny likes travelling by plane because.A. it's the fastest wayB. he can make new friendsC. he likes planes very muchD. he likes the blue sky25.Which of the following is TRUE according to the passage?A. Danny often sleeps when travelling.B. Eliza travelled most of Europe by ship.C. Eliza thinks the car ride is like a moving party.D. Greg likes to bring his pet dog along when travelling.BI am Mike Smith,a doctor from London. I really feel that life in China is changing so quickly. Recently(最近)I had a business trip to Tianjin. I left my Beijing apartment and walked half a street to the subway station. About twelve stops later,I reached the high-speed rail station. After two minutes of security(安检),I picked up my ticket,which I had bought on my phone while on the subway. Then I walked to the terminal(终点) andgot on the train. Twenty-eight minutes later I was in the center of a beautiful city —Tianjin. I could enjoy a nice walk along the riverside towards my hotel. It is amazingthat the whole experience(经历)took no more than a few hours,with no cars,no airports, no credit cards(信用卡) and no long lines, just my smart phone, only a few US dollars and comfortable walking shoes. In most places in the developed world, there is no experience like this. But China is different.So in my opinion, if we think highly of China's modern wonders, I believe its high-speed rail system must be one of them. And it's one symbol(象征) of a new China and a sign of China's strength(实力) as well.26.Mike Smith is from .A. AmericaB. the UKC. AustraliaD. Canada27.Mike bought his ticket to Tianjin.A. on his phoneB. from the high-speed rail ticket officeC. from the subway ticket officeD. with the help of his friend28.How many traffic tools did Mike use from his apartment to his hotel in Tianjin?A. One.B. Two.C. Three.D. Four.29.According to the passage, which of the following isn't Mike's ideas about his trip?A. Comfortable.B. Fast.C. Cheap.D. Boring.30.What is Mike's attitude(态度) to Chinese high-speed rail train?A. He looks down upon it.B. He dislikes it.C. He thinks highly of it.D. He hates it.CIf you want to travel from Xi'an to Chengdu by train, it will take about 16 hours. But starting this month, the new Xi'an-Chengdu high-speed railway will shorten thistravel time to three hours.The 643-kilometer line is China's first high-speed railway to run through the Qinling Mountains, which form a natural boundary (分界线)between China's north and south. With a speed of 250 km per hour, it's also the first mountain-heavy train line to provide a(提供) 4G network.Along the way,the train passes through some areas for rare(稀有的)wild animals like pandas and crested ibises(朱鹮).To reduce the railway's influence(影响) on the animals, workers and experts have designed and built the railway to be environmentally friendly,China Daily reported.In September,there were 345 wild pandas living in the Qinling Mountains. China now has 1,864 wild pandas in total, according to the Xinhua News Agency.To avoid disturbing(打扰) the pandas, the railway was designed to run through tunnels(隧道)within the area. Protective shields(防护屏)are placed near the entrance(入口) of each tunnel to stop animals from going in.To avoid hurting the thousands of crested ibises that fly near one part of the railway, protective nets have been set up along the tracks(铁轨) to make sure the birds will notfly into a train.The nets are about 32 km long and 4 meters high. Experts tested different shapes and materials for building the nets before making their final choice. (A report in December, 2017)31.From this month,it will take to travel from Xi'an to Chengdu by the high-speedtrain.A. 16 hoursB. 13 hoursC. 6 hoursD. 3 hours32.Which of the following is TRUE about the new Xi'an-Chengdu railway?A. It is China's first high-speed railway.B. It runs through the Qinling Mountains.C. It is the first mountain-heavy train line.D. It is the first train line with a 4G network.33.Why was the railway designed and built to be environmentally friendly?A. To save money and energy.B. To avoid harming wild animals.C. To avoid damaging the mountains.D. To help the train run through tunnels quietly.34.What are experts using to stop animals from going into the tunnels?A. Entrances.B. Tracks.C. Protective shields.D. Protective nets.35.This news about the new railway is reported by .A. China DailyB. the Xinhua News AgencyC. the 4G networkD. CCTV四、从方框中选择最佳选项补全对话(有两项多余)(每小题1分,共5分)A: How does your friend Jack go to school every day, David?B:36A: It's the most popular way now. Lots of students in my class ride to school, too. B:37A: No, my home is far from school, so I take a bus.B: How long does it take you to go to school by bus?A:38What about you?B: My home is much farther than yours, so I take the underground. It takes me about half an hour.A:39B: Yes, there are. Sometimes I don't feel comfortable with so many people on it. A:40B: It is the most comfortable way, but it's too expensive for me.A: Yes, I think so.五、任务型阅读(每小题2分,共10分)The train made a lot of noise as it came to a stop at the station. Martha waited for a while until her father held her hand. They walked onto the train together. Her mother and brother walked behind them.This was the first train ride for Martha and her brother Brian. They would take the train to visit their grandparents. They usually went there by car. But today, Mum andDad wanted to try a different way.They walked to the middle of the train. They found some seats and sat down. A few minutes later, the train began to move.Martha and Brian felt a little nervous,but their parents said they would enjoy theride. Dad said he liked the train ride because he didn't need to drive all the time. Mum added that she could talk to her two children face to face instead of turning around.When the children heard their parents' words, they felt relaxed."The train isn't as noisy as I thought it would be," said Martha, "and I can stand up and walk around. I believe I can see everything through the windows.""The train really goes fast," said Brian, "I like that best of all. If we get on the train in the morning, we can see grandparents before lunch. I can't wait to enjoy their apple pie!"根据短文内容回答下列问题41.According to the passage, who got on the train first?42.How did Martha and Brian usually go to visit their grandparents?43.How did Martha and Brian feel when the train began to move?44.Why did Dad like the train ride?45.What does the underlined word "that" refer to(指代)?六、根据短文内容及所给提示,在空白处填上适当的单词补全短文(每小题1分,共10分)In China, you can travel to all corners of this big country by bus or train. It's surprising what China has done in the past ten 46(year)in terms of train travel— it now has the 47(big) high-speed railway network in 48 world. The high-speed trains are great, and a l49 train journey in China is a greatway to see the country.China is a huge, fascinating(迷人的) country with so much to see. 50 a student, I love traveling 51 my parents, from big cities to seaside hot spots(地点), to high mountains, to national parks, to historical sites and to s52 villages far away. 53(get) out of your comfortable home here to some unknown places is a good experience as well. And you can eat local food, and 54(real) reach the heart of the country.I always love traveling outside of Yibin to see our 55(beauty) country —China.46.47.48.49.50.51.52.53.54.55.七、书面表达(20分)Mary准备周日去伦敦旅行。
平面解析几何三角形与圆相关课后限时作业(四)含答案新人教版高中数学名师一点通
评卷人
得分
二、解答题
3．选修4—1：几何证明选讲
如图，⊙ 为四边形 的外接圆，且 ， 是 延
长线上一点，直线 与圆 相切．
求证： ．
4．如图, 和 分别与圆 相切于点 , 经过圆心 ,且
求证: （汇编年普通高等学校招生全国统一招生考试江苏卷（数学）（已校对纯WORD版含附加题））A.[选修4-1:几何证明选讲]本小题满分10分.
5．如图，AB是⊙O的直径，C、E为⊙O上的点，且CA平分∠BAE，DC是⊙O的切线，交AE的延长线于点D。求证：CD⊥AE。
所以 ．……………………10分
6．如图，AB是圆O的直径，AC是弦，∠BAC的平分线AD交圆O于点D，DE ⊥AC且交AC的延长线于点E．
求证：DE是圆O的切线．
7．如图， 是⊙ 的一条切线，切点为 直线 , 都是⊙ 的割线，已知 求证：
8．如图， 与⊙ 相切于点 ， 为 的中点，
过点 引割线交⊙ 于 ， 两点，
求证: ．
【参考答案】***试卷处理标记，请不要删除
评卷人
得分
一、填空题
1．
2．
评卷人
得分
二、解答题
3．选修4—1：几何证明选讲
证明：连结 ． 是圆 的切线，∴ ．…………………2分
，∴ ．∴ ．…………………4分
圆 是四边形 的外接圆，∴ ．…………………6分
∴ ∽ ．…………………8分
∴ ， ，∴ ．…………………10分
4．A证明:连接OD,∵AB与BC分别与圆O相切于点D与C
平面解析几何初步直线圆的方程等一轮复习专题练习(四)含答案高中数学
高中数学专题复习《平面解析几何初步直线圆的方程等》单元过关检测经典荟萃，匠心巨制！独家原创，欢迎下载！注意事项：1．答题前填写好自己的姓名、班级、考号等信息 2．请将答案正确填写在答题卡上第I 卷（选择题）请点击修改第I 卷的文字说明 评卷人得分一、选择题1．1 ．（2020年普通高等学校招生统一考试辽宁数学（理）试题（WORD 版））使得()13nx n N nx x +⎛⎫+∈ ⎪⎝⎭的展开式中含有常数项的最小的为 （ ）A ．4B ．5C ．6D ．72．在平面直角坐标系xOy 中,直线3450x y +-=与圆224x y +=相交于A 、B 两点,则弦AB 的长等于（ ） A ．33B ．23C ．3D ．1（2020广东文）(解析几何)3．已知直线x=a （a>0）和圆（x －1）2+y 2=4相切，那么a 的值是（ ） A ．5 B ．4C ．3D ．2（2020全国文3）4．设R n m ∈,，若直线02)1()1(=-+++y n x m 与圆1)1()1(22=-+-y x 相切，则m+n 的取值范围是（A ）]31,31[+- （B ）),31[]31,(+∞+⋃--∞（C ）]222,222[+- （D ）),222[]222,(+∞+⋃--∞5．下列说法正确的是 ． [答]( ) (1)若直线l 的倾斜角为α，则0απ≤<；(2)若直线l 的一个方向向量为(,)d u v =，则直线l 的斜率v k u=； (3)若直线l 的方程为220(0)ax by c a b ++=+≠，则直线l 的一个法向量为(,)n a b =．A .(1)(2) B. (1)(3) C.(2)(3) D.(1)(2)(3)6．直线1:2l y k x ⎛⎫=+⎪⎝⎭与圆22:1C x y +=的位置关系为（ ）． Ａ．相交或相切 Ｂ．相交或相离 Ｃ．相切 Ｄ．相交7．圆x 2＋y 2＋2x ＋6y ＋9＝0与圆x 2＋y 2－6x ＋2y ＋1＝0的位置关系是 （ ）A ．相交B ．相外切C ．相离D ．相内切8．圆224460x y x y +-++=截直线50x y --=所得弦长为（ ） Ａ、6 Ｂ、522Ｃ、１ Ｄ、５9．已知点(1,2),(3,1)A B ，则线段AB 的垂直平分线的方程是（ ） A 、425x y += B 、425x y -= C 、25x y += D 、25x y -=10． 直线l 过点（-1，2）且与直线垂直，则l 的方程是 A ．3210x y +-= B.3270x y ++=C. 2350x y -+=D.2380x y -+=第II 卷（非选择题）请点击修改第II 卷的文字说明评卷人得分二、填空题11．在平面直角坐标系xOy 中，已知圆C 与x 轴交于A (1,0)，B (3,0)两点，且与直线x －y －3＝0相切，则圆C 的半径为 ▲ ． 解析：可设圆心为(2，b )，半径r ＝b 2＋1，则|－1－b |2＝b 2＋1，解得b ＝1．故r ＝2．12． 已知从点(2,1)-发出的一束光线，经x 轴反射后,反射光线恰好平分 圆:222210x y x y +--+=的圆周,则反射光线所在的直线方程为 13．圆2240x y x +-=在点(1,3)P 处的切线方程为 ▲ ．14．如果直线210mx y ++=与20x y +-=互相垂直，那么实数m ＝ ▲ ．15．两圆221:2220C x y x y +++-=与222:4210C x y x y +--+=的公切线有且仅有_____条。
平面解析几何三角形与圆相关40分钟限时练(四)带答案新高考高中数学
高中数学专题复习《平面解析几何三角形、圆相关》单元过关检测经典荟萃，匠心巨制！独家原创，欢迎下载！注意事项：1．答题前填写好自己的姓名、班级、考号等信息 2．请将答案正确填写在答题卡上 评卷人得分一、填空题1．如图,在ABC 中,090C ∠=, 060,20A AB ∠==,过C 作ABC 的外接圆的切线CD ,BD CD ⊥,BD 与外接圆交于点E ,则DE 的长为__________（汇编年普通高等学校招生统一考试重庆数学（理）试题（含答案））2．如图3，圆O 的半径为5cm ，点P 是弦AB 的中点，3OP =cm ，弦CD 过点P ，且13CP CD =，则CD 的长为 cm ．（几何证明选讲选做题）评卷人得分二、解答题3．选修4—1 几何证明选讲P OAB C D图3如图，已知⊙O 的半径为1，MN 是⊙O 的直径，过M 点作⊙O 的切线AM ，C 是AM 的中点，AN 交⊙O 于B 点，若四边形BCON 是平行四边形.求AM 的长；4．如图，圆1O 与圆2O 内切于点A ，其半径分别为1r 与212()r r r >， 圆1O 的弦AB 交圆2O 于点C （1O 不在AB 上）， 求证：:AB AC 为定值。
证明：由弦切角定理可得11212,O B r AB AO CAO B AC O C r∴== 5．过圆O 外一点A 作圆O 的两条切线AT 、AS ，切点分别为T 、S ，过点A 作圆O 的割线APN ，证明：22AT PT PSAN NT NS=．[来源:学科网ZXXK] (汇编年3月苏、锡、常、镇四市高三数学教学情况调查一) 证明：AT 是圆O 的切线，∠ATP =∠ANT ,又∠TAP =∠NAT ,∴三角形ATP 与三角形ANT ，∴AT PT AN TN =同理AS PSAN NS= 两等式相乘222,AT AS PT PSAT PT PS AT AS AN NT NSAN NT NS∙∙∙==∴=∙∙. 6．已知：如图，在△ABC 中，∠ABC ＝90°，O 是AB 上一点，以O 为圆心，OB 为半径的圆与AB 交于点E，与21-A 第图AC 切于点D ，连结DB 、DE 、OC 。
2024年新高二数学提升精品讲义圆的标准方程(思维导图+4知识点+4考点+过关检测)(原卷版)
2024年新高二数学提升精品讲义圆的标准方程（原卷版）模块一思维导图串知识模块二基础知识全梳理（吃透教材）模块三核心考点举一反三模块四小试牛刀过关测1．会用定义推导圆的标准方程，并掌握圆的标准方程的特征；2．能根据所给条件求圆的标准方程；3．掌握点与圆的位置关系并能解决相关问题.知识点1圆的定义平面内到定点的距离等于定长的点的集合叫做圆．如图，在平面直角坐标系中，⊙A 的圆心A 的坐标为(,)a b ，半径为r ，(,)M x y 为圆上任意一点，⊙A 就是集合{}P M MA r ==．定义中，定点指的是圆心，定长指的是圆的半径．知识点2圆的标准方程1、圆的标准方程：我们把()()222-+-=x a y b r 称为圆心为(),A a b ，半径长为r 的圆的标准方程．【注意】（1）所谓标准方程，是指方程的形式．圆的标准方程体现了圆的集合性质，突出了圆的几何意义：圆心位置和半径．（2）圆的标准方程的右端20r >，当方程右端小于或等于0时，对应方程不是圆的标准方程．2、圆的标准方程的推导过程（1）建系设点：建立坐标系时，原点在圆心是特殊情况，就一般情况来说，因为A 是定点，设(),A a b ，半径为r ，且设圆上任意一点M 的坐标为(,)x y ．（2）写点集：根据定义，圆就是集合{}P M MA r ==．（3r =．（4）化简方程：将上式两边平方得222()()x a y b r -+-=．3、几种特殊位置的圆的标准方程知识点3点与圆的位置关系1、几何法：点()00,M x y ，圆心(),A a b ，圆的半径r ，设M 与点A 间的距离MA d =，d r >⇔点M 在圆A 外；d r <⇔点M 在圆A 内；d r =⇔点M 在圆A 上．2、代数法：将点()00,M x y 直接代入圆的标准方程()()222-+-=x a y b r 进行判断，即若点()00,M x y 在圆外，则()()22200->+-x a y b r ；若点()00,M x y 在圆内，则()()22200x a y b r +-<-；若点()00,M x y 在圆上，则()()22200x a y b r +-=-．知识点4圆上的点到定点的最大、最小距离设圆心A 到定点C 的距离为d ，圆的半径为r ，圆上的动点为点P ．（1）若点C 在圆外时，max PC d r =+，min PC d r =-；（2）若点C 在圆上时，max 2PC r =，min 0PC =；（2）若点C 在圆内时，max PC d r =+，min PC r d =-．综上：max PC d r =+，min PC d r =-．考点一：求圆的标准方程例1．（23-24高二上·安徽马鞍山·月考）已知圆的圆心在(3,4)-，半径为5，则它的方程为（）A ．()()22345x y -+-=B ．()()223425x y +++=C ．22(3)(4)25x y ++-=D ．()()22345x y ++-=【变式1-1】（23-24高二上·山西太原·期末）已知圆C 的一条直径的两个端点坐标分别为()4,1-，()2,3，则圆C 的方程是.【变式1-2】（22-23高二上·广东东莞·期中）求经过点(2,0),(2,2)--且圆心在直线:0l x y +=上的圆的标准方程为.【变式1-3】（23-24高二下·云南玉溪·期中）过三点()()()120,01,33,1O M M ---､､的圆的标准方程是.考点二：点与圆的位置关系例2.（23-24高二上·安徽亳州·月考）（多选）已知()14,9P ，()26,3P 两点，以线段12PP为直径的圆为圆P ，则（）A ．()6,9M 在圆P 上B ．()3,3N 在圆P 内C ．()5,3Q 在圆P 内D ．()2,7R 在圆P 外【变式2-1】（23-24高二上·江苏·专题练习）已知点(,10)P a ，圆的标准方程为()()221112x y -+-=，则点P （）A ．在圆内B ．在圆上C ．在圆外D ．与a 的取值有关【变式2-2】（23-24高二上·重庆·期中）若点(),3A a 在圆()22:15C x y +-=外，则实数a 的取值范围是（）A ．(),1-∞-B ．(),1-∞C ．()(),11,-∞-⋃+∞D ．()1,1-【变式2-3】（23-24高二上·广西·期末）已知两直线2y x k =+与y x =-的交点在圆228x y +=的内部，则实数k 的取值范围是（）A ．11k -<<B ．2<<2k -C ．33k -<<D ．k <考点三：与圆有关的最值问题例3.（23-24高二上·湖北·期中）已知半径为2的圆经过点()3,4，则其圆心到原点的距离的最大值为（）A ．4B ．5C ．6D ．7【变式3-1】（23-24高二上·浙江湖州·月考）若实数x y ，满足221x y +=，则()()2234x y -+-的最大值是（）A ．5B ．6C ．25D ．36【变式3-2】（23-24高二上·上海·期末）已知P 为圆22(3)(4)4x y -+-=上一点，Q 为圆221x y +=上一点，则点Q 到点P 的距离的最大值为.【变式3-3】（23-24高二上·天津武清·月考）已知圆C :()()22124x y ++-=，点()2,0A -，()2,0B .设P 是圆C 上的动点，令22d PA PB =+，则d 的最小值为．考点四：与圆有关的对称问题例4.（23-24高二上·河南周口·期末）若曲线()()22124x y -+-=上相异两点P 、Q 关于直线20kx y --=对称，则k 的值为（）A ．1B ．2C ．3D ．4【变式4-1】（23-24高二上·云南昆明·月考）已知圆()()22124x y +++=关于直线10ax by ++=（0a >，0b >）对称，则12a b+的最小值为（）A ．52B ．9C ．4D ．8【变式4-2】（23-24高二上·河北·期中）已知圆M ：()2211x y ++=与圆N ：()()22231x y -+-=关于直线l 对称，则l 的方程为（）A ．210x y --=B ．210x y -+=C ．230x y +-=D ．230x y +-=【变式4-3】（23-24高二上·四川成都·期末）圆()()22:112C x y -+-=关于直线:1l y x =-对称后的方程为（）A ．()2222x y -+=B ．()2222x y ++=C ．()2222x y +-=D ．()2212x y ++=一、单选题1．（23-24高二上·广东湛江·期中）在平面直角坐标系中，圆心为()1,0，半径为2的圆的方程是（）A ．()2212x y -+=B ．()2212x y ++=C ．()2214x y -+=D ．()2214x y ++=2．（23-24高二上·河南开封·期末）已知圆M 经过点()()0,20,4,，且圆心M 在直线210x y --=上，则圆M 的面积为（）A ．2πB 5πC ．4πD ．5π3．（23-24高二上·安徽黄山·期末）圆22:(2)(1)1M x y -+-=与圆N 关于直线0x y -=对称，则圆N 的方程为（）A ．22(1)(2)1x y +++=B ．22(2)(1)1x y -++=C ．22(2)(1)1x y +++=D ．22(1)(2)1x y -+-=4．（23-24高二上·广东惠州·期中）点(,3)P m 与圆()()22212x y -+-=的位置关系为（）A ．点在圆外B ．点在圆内C ．点在圆上D ．与m 的值无关5．（2023高二上·全国·专题练习）点(1,1)--在圆22()()4x a y a ++-=的内部，则a 的取值范围是（）A ．11a -<<B ．01a <<C ．1a <-或1a >D ．1a =±6．（23-24高二上·浙江温州·期中）已知半径为2的圆经过点()3,4，则其圆心到原点的距离最小值为（）A ．1B ．2C ．3D ．4二、多选题7．（23-24高二上·四川宜宾·期末）已知圆C 经过点()0,0A 、()2,0B ，ABC 为直角三角形，则圆C 的方程为（）A ．()()22114x y -+-=B ．()()22112x y -++=C ．()()22112x y -+-=D ．()()22125x y -+-=8．（23-24高二上·重庆九龙坡·月考）若有一组圆k C ：()()()224R x k y k k -+-=∈，下列命题正确的是（）A ．所有圆k C 的半径均为2B ．所有的圆kC 的圆心恒在直线y x =上C ．当2k =时，点()3,0在圆k C 上D ．经过点()2,2的圆k C 有且只有一个三、填空题9．（23-24高二上·贵州毕节·期末）与圆222430x y x y +-++=有相同圆心，且过点()4,2-的圆的标准方程是.10．（22-23高二下·四川凉山·月考）若圆221:(1)9C x y -+=和圆222:(3)(2)9C x y +++=关于直线l 对称，则直线l 的方程是11．（23-24高二上·全国·专题练习）已知,x y 满足22(1)(2)16x y -+-=，则22x y +的取值范围是.四、解答题12．（23-24高二上·福建福州·期末）已知A 关于直线y x =对称，点()0,0O ，()4,0N 都在A 上.(1)求线段ON 垂直平分线的方程；(2)求A 的标准方程13．（23-24高二上·山东济南·期末）已知圆心为C 的圆经过()0,0O ，(0,A 两点，且圆心C 在直线:l y =上．(1)求圆C 的标准方程；(2)点P 在圆C 上运动，求22PO PA +的取值范围．。
4.《逻辑推理》专题过关检测卷带解析
4．《逻辑推理》专题过关检测卷A卷（50分）一、填空题（每题3分，共30分）1．甲、乙、丙三人进行跑步比赛。
A，B，C三人对比赛结果进行预测。
A说：“甲肯定是第一名。
”B说：“甲不是最后一名。
”C说：“甲肯定不是第一名。
”其中只有一人对比赛结果的预测是对的。
预测对的是_____。
2．A，B，C，D，E和F六人在一圆桌边坐下。
B是坐在A右边的第二人；C是坐在F右边的第二人；D坐在E的正对面，还有F和E不相邻。
那么，坐在A和B之间的是_____。
3．甲、乙、丙、丁与小明五位同学进入象棋决赛。
每两人都要比赛一盘，每胜一盘得2分，和一盘得1分，输一盘得0分。
到现在为止，甲赛了4盘，共得了2分；乙赛了3盘，得了4分；丙赛了2盘，得了1分；丁赛了1盘，得了2分。
那么小明现在已赛了____盘，得了____分。
4．曹、钱、刘、洪四个人出差，住在同一个招待所。
一天下午，他们分别要找一个单位去办事。
甲单位星期一不接待，乙单位星期二不接待，丙单位星期四不接待，丁单位只在星期一、三、五接待，星期日四个单位都不接待。
曹：“两天前，我去误了一次，今天再去一次，还可以与老洪同走一条路。
”钱：“今天我一定得去，要不明天人家就不接待了。
”刘：“这星期的前几天和今天我去都能办事。
”洪：“我今天和明天去，对方都接待。
”那么，这一天是星期____，刘要去____单位，钱要去____单位，曹要去____单位，洪要去____单位。
5．四位外国朋友住在十八层高的饭店里，他们分别来自埃及、法国、朝鲜和墨西哥。
(1)A住的层数比C住的层数高，但比D住的层数低；(2)B住的层数比朝鲜人住的层数低；(3)D住的层数恰好是法国人住的层数的5倍；(4)如果埃及人住的层数增加2层，他与朝鲜人相隔的层数，恰好和他与墨西哥人相隔的层数一样；(5)埃及人住的层数是法国人和朝鲜人住的层数的和。
根据上述情况，请你确定A是____人，住在____层；B是____人，住在____层；C是____人，住在____层；D是____人，住在____层。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
专题4 专题过关检测本试卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分，满分100分，考试时间90分钟。
第Ⅰ卷(选择题，共48分)一、选择题(共16个小题，每小题3分，共48分)1．下列物质的化学用语表达正确的是( )A ．甲烷的球棍模型：B ．(CH 3)3COH 的名称：2,2-二甲基乙醇C ．乙醛的结构式：CH 3CHOD ．羟基的电子式：·O ····:H 答案 D 解析 甲烷的球棍模型中碳原子的半径应大于氢原子，A 项错误；(CH 3)3COH 的正确名称为2-甲基-2-丙醇，B 项错误；CH 3CHO 是乙醛的结构简式，不是结构式，C 项错误。
2．下列说法中正确的是( )A ．含有羟基的有机物称为醇B ．能发生银镜反应的有机物都是醛C ．苯酚俗称石炭酸，酸性比碳酸强D ．酯类在碱性条件下的水解程度大于酸性条件下的水解程度答案 D解析 A 选项中要注意醇与酚的区别，醇是羟基与链烃基相连的化合物，而酚是羟基与苯环直接相连的化合物；B 选项中应是只要有醛基的物质都能发生银镜反应，如醛、甲酸、甲酸酯类以及葡萄糖、麦芽糖等都含有醛基而能发生银镜反应；C 选项中应是苯酚的酸性比碳酸弱。
3．下列每组中各有三对物质，它们都能用分液漏斗分离的是( )A ．乙酸乙酯和水、酒精和水、苯酚和水B ．二溴乙烷和水、溴苯和水、硝基苯和水C ．甘油和水、乙醛和水、乙酸和乙醇D ．油酸和水、甲苯和水、己烷和苯答案 B解析 能用分液漏斗分离的物质应该是互不相溶的物质。
酒精和水、甘油和水、乙醛和水、乙酸和乙醇、己烷和苯都能互溶。
4．下列化合物中同分异构体数目最少的是( )A ．戊烷B ．戊醇C ．戊烯D ．乙酸乙酯答案 A解析 A 项，戊烷存在正戊烷、异戊烷和新戊烷3种异构体；B 项，戊醇可看成戊烷的3种异构体中的1个H 被—OH 取代得到的产物，有8种醇类异构体，另外戊醇还有多种醚类异构体；C 项，戊烯的烯类同分异构体主链可以含5个碳原子或4个碳原子，再结合双键位置可得出5种异构体，另外戊烯还存在环烷烃类异构体；D 项，乙酸乙酯的异构体中，甲酸酯有2种，丙酸酯有1种，羧酸有2种，另外还有羟基醛、酮等多种异构体。
5．中学化学中下列各物质间不能实现(“→”表示一步完成)转化的是( )解析 A 中的CH 3COOH 不能一步转化为CH 3CH 2OH ；B 中CH 2===CH 2――→＋HBrCH 3CH 2Br ――→＋NaOH △CH 3CH 2OH ――→浓硫酸△CH 2===CH 2；C 中Cl 2――→＋H 2O HClO ――→光或热HCl ――→＋MnO 2△Cl 2；D 中C ――→＋O 2CO ――→＋O 2CO 2――→＋MgC 。
6．下列有机化合物中均含有酸性杂质，除去这些杂质的方法中正确的是( )A．苯中含苯酚杂质：加入溴水、过滤B．乙醇中含乙酸杂质：加入碳酸钠溶液洗涤，分液C．乙醛中含乙酸杂质：加入氢氧化钠溶液洗涤，分液D．乙酸乙酯中含乙酸杂质：加入碳酸钠溶液洗涤，分液答案 D解析A项中形成的三溴苯酚易溶于苯，不能用过滤法分离，错误；B项中不分层，无法分液，应加入Na2CO3溶液洗涤后再蒸馏，错误；C项中不分层，无法分液，应加入NaOH溶液洗涤后再蒸馏，错误；D项正确。
7．在有机合成中官能团的引入与转化都极为重要，下列说法正确的是() A．甲苯在光照条件下与Cl2反应时，主反应为苯环上引入氯原子B．引入羧基的方法有醛的氧化反应和酯的水解反应C．CH2===CH—CHO与酸性KMnO4溶液反应可转化为CH2===CH—COOH D．乙醇在浓硫酸作用下加热到140 ℃时生成乙烯答案 B解析甲苯在光照条件下与Cl2反应时，主要是—CH3上的氢原子被取代，A 项错误。
酸性KMnO4溶液也可将丙烯醛分子中的碳碳双键氧化，C项错误。
乙醇在浓硫酸作用下加热到140 ℃时生成乙醚，D项错误。
答案 C解析由C与乙烯加聚得到的产物的结构简式可推知C为CH2===CH—CH3，而A与NaOH的醇溶液反应生成CH2===CH—CH3，表明A是卤代烃，再由D与AgNO3溶液反应生成白色沉淀，可知卤原子是氯，故A为CH3CH2CH2Cl或。
9．下列叙述正确的是()A．甲苯既可使溴的CCl4溶液褪色，也可使KMnO4酸性溶液褪色B．有机物的消去产物有2种C．有机物A(C4H6O2)能发生加聚反应，可推知A的结构一定是CH2===CH—COOCH3D．可用溴水鉴别直馏汽油、四氯化碳和乙酸答案 D解析甲苯不能使溴的CCl4溶液褪色；CH2===CH—CH2COOH。
10．某有机物W的结构简式如下所示：，下列叙述正确的是() A．W的相对分子质量为206B．1 mol W最多能与2 mol Br2发生反应C．1 mol W最多能与5 mol NaOH反应D．1 mol W最多能与2 mol Na2CO3反应答案 D解析W的分子式为C10H8O5，它的相对分子质量为208；W分子中酚羟基邻位有2个H可以与溴发生取代反应，也可与溴发生加成反应，故1 mol W最多能与3 mol Br2发生反应；W分子中含2个酚羟基，1个酚酯基，1 mol 酚酯基消耗2 mol NaOH,2 mol酚羟基消耗2 mol NaOH，醇羟基不与NaOH反应，故1 mol W 最多与4 mol NaOH 反应；酚羟基与Na 2CO 3反应生成NaHCO 3，醇羟基和酯基不与Na 2CO 3反应，故1 mol W 最多与2 mol Na 2CO 3反应。
11．有下列几种有机物，当它们分别与足量的烧碱溶液混合共热后，最终不会出现分层现象的物质有()A ．2种B ．3种C ．4种D ．5种答案 D解析 ①⑤难溶于水，但与足量的烧碱溶液混合共热后能生成易溶于水的物质；②能与水以任意比互溶；③微溶于水，与烧碱溶液反应能生成易溶于水的物质；④易溶于水，同时也能与烧碱溶液反应。
12．满足下列条件的有机物的种类数正确的是( )解析 该有机物有四种氢原子，所以该有机物的一氯代物有4种，故A 正确；能与NaHCO 3溶液反应的有机物含有—COOH ，C 6H 12O 2可以看作C 5H 11—COOH ，C 5H 11—有8种，所以C 5H 11—COOH 有8种，故B 错误；分子式为C 5H 12O 的含有两个甲基的醇可看作C 5H 11OH ，含有两个甲基的C 5H 11—有4种，所以含有两个甲基的醇C 5H 11OH 有4种，故C 错误；分子式为C 5H 10O 2的有机物在酸性条件下会水解生成甲和乙，且甲、乙的相对分子质量相等，说明该有机物为CH3COOC3H7，丙醇有两种，所以该有机物有两种，故D错误。
13．绿原酸的结构简式如图，下列有关绿原酸的说法不正确的是()A．分子式为C16H18O9B．能与Na2CO3反应C．能发生取代反应和消去反应D．0.1 mol绿原酸最多可与0.8 mol NaOH反应答案 D解析0.1 mol绿原酸最多可与0.4 mol NaOH反应。
14．某优质甜樱桃中含有一种羟基酸(用M表示)，M的碳链结构无支链，分子式为C4H6O5；1.34 g M与足量的碳酸氢钠溶液反应，生成标准状况下的气体0.448 L。
M在一定条件下可发生如下转化：M――→浓硫酸△A――→Br2B――→足量NaOH溶液C(M、A、B、C分子中碳原子数目相同)。
下列有关说法中不正确的是()A．M的结构简式为HOOC—CHOH—CH2—COOHB．B的分子式为C4H4O4Br2C．与M的官能团种类、数量完全相同的同分异构体还有2种D．C物质不可能溶于水答案 D解析由题知M的相对分子质量为134,1.34 g M为0.01 mol，与足量的碳酸氢钠溶液反应生成0.02 mol CO2，由此可推出M分子中含二个羧基，再根据M分子无支链，可知M的结构简式为HOOCCHOHCH2COOH。
M→A是消去反应，A→B是加成反应，B→C包含—COOH与NaOH的中和反应和—Br的水解反应，C分子中含有多个亲水基，C可溶于水，D错误；符合条件的M的同分异构体还有、两种，C正确。
15．CPAE是蜂胶的主要活性成分，它可由咖啡酸合成，其合成过程如下。
下列说法不正确的是()A．1 mol CPAE与足量的NaOH溶液反应，最多消耗3 mol NaOHB．可用金属Na检测上述反应是否残留苯乙醇C．与苯乙醇互为同分异构体的酚类物质共有9种D．咖啡酸可发生聚合反应，并且其分子中含有3种官能团答案 B解析CPAE中酚羟基和酯基都能与NaOH反应，A正确。
题述反应方程式中的四种物质都能与Na反应产生氢气，所以用Na无法检验反应是否残留苯乙醇，B项错误。
与苯乙醇互为同分异构体的酚类物质共有9种，分别确。
咖啡酸中含有碳碳双键，能发生加聚反应，D项正确。
16．阿魏酸在食品、医药等方面有着广泛用途。
一种合成阿魏酸的反应可表示为下列说法正确的是()A．可用酸性KMnO4溶液检测上述反应是否有阿魏酸生成B．香兰素、阿魏酸均可与Na2CO3、NaOH溶液反应C．通常条件下，香兰素、阿魏酸都能发生取代、加成、消去反应D．与香兰素互为同分异构体，分子中有5种不同化学环境的氢，且能发生银镜反应的酚类化合物共有3种答案 B解析香兰素中含有的—OH、—CHO和阿魏酸中含有的—OH、CC均可被酸性KMnO4溶液氧化，A项不正确；香兰素中的酚羟基，阿魏酸中的酚羟基和羧基均能与Na2CO3、NaOH溶液反应，B项正确；香兰素能发生苯环上的取代反应、苯环和醛基与H2的加成反应，阿魏酸能发生苯环上的取代反应、羧基上的酯化反应、苯环和碳碳双键的加成反应，但二者均不能发生消去反应，C项不正确；符合D条件下的同分异构体有，D项不正确。
第Ⅱ卷(非选择题，共52分)二、非选择题(共4个题，共52分)17．(10分)异戊二烯是重要的有机化工原料，其结构简式为CH2===C(CH3)CH===CH2。
完成下列填空：(1)化合物X与异戊二烯具有相同的分子式，与Br2/CCl4反应后得到3-甲基-1,1,2,2-四溴丁烷。
X的结构简式为________________。
(2)异戊二烯的一种制备方法如下图所示：A 能发生的反应有________________________(填反应类型)。
B 的结构简式为________________。
(3)设计一条由异戊二烯制得有机合成中间体的合成路线。
(合成路线常用的表示方式为A ――→反应试剂反应条件B ……――→反应试剂反应条件目标产物)答案 (1)(2)加成(还原)、氧化、聚合、取代(酯化)、消去反应解析 (1)由题意可知化合物X 与异戊二烯的分子式相同，则X 的分子式为C 5H 8，X 的不饱和度Ω＝2；由X 与Br 2/CCl 4发生加成反应产物为3-甲基-1,1,2,2-四溴丁烷，则X分子中存在碳碳叁键，其结构简式为。