中考英语阅读理解知识点总结经典
一、初三英语阅读理解（含答案详细解析）
1．根据短文内容选择正确答案。
B
Shu Pulong has helped at least 1000 people bitten by snakes. “It was seeing people with snake bites that led me to this career,” he said.
In 1963, after his army service, Shu entered a medical school and later became a doctor of Chinese medicine. As part of his studies he had to work in the mountains. There he often heard of people who had their arms and legs cut off after a snake bite in order to save their lives.
“I was greatly upset when they told me the story of an old farmer I met. It was a very hot afternoon. The old man was pulling grass in his fields when he felt a pain in his left hand. He at once realized he had been bitten by a poisonous snake. In no time he wrapped（缠绕）a cloth tightly around his arm to stop the poison（毒）getting to his heart. Running home he shouted, `Bring me the knife' Minutes later the man lost his arm forever.”
“The heartbroken story touched me so much that I decided to devote myself to helping people bitten by sna kes.” Shu added, “I worked very hard and tried my best to make a good snake doctor.” And at last he made it.
（1）The best headline（标题）for this newspaper article is .
A. Amazing Medicine
B. Farmer Loses Arm
C. Dangerous Bites
D. Snake Doctor （2）Shu decided to devote himself to snake medicine because .
A. he wanted to save people's arms and legs
B. he had studied it at a medical school
C. he had seen snakes biting people
D. his army service had finished
（3）Why did Shu go into the mountains?
A. He wanted to study snake bites.
B. He wanted to help the farmers.
C. He was being trained to be a doctor.
D. He was expected to serve in the army.
（4）Which of the following can explain the word upset in the third paragraph?
A. sad
B. surprised
C. interested
D. frightened
【答案】（1）D
（2）A
（3）C
（4）A
【解析】【分析】这篇文章主要介绍了著名蛇医苏普隆的故事，文中介绍了他从医的经历和原因，1963年他服完兵役以后，上医学院，稍后成为一名中医，无意中他听说当地很多农民被蛇袭击，为了保全性命，切断胳膊或大腿，因此他决定研究蛇药，取得了巨大成就。
（1）考查主旨大意题。短文主要介绍了著名蛇医苏普隆的故事。故选D。
（2）考查细节理解题。句意为什么决定从事研发蛇药的事业。根据文中There he often heard of people who had their arms and legs cut off after a snake bite in order to save their lives.描述可知。故选A。
（3）考查细节理解题。句意他为什么进山？根据文中As part of his studies he had to work in the mountains.描述可知。作为学习的一项内容他不得不进山。故选C。
（4）词义猜测。句意：当他们跟我讲了老农的故事后我非常的不安。sad伤心的；surprised吃惊的；interested感兴趣的；frightened害怕的。故选A。
【点评】阅读理解考查对篇章的把握和对细节的识别能力，答题时注意紧扣问题中的关键词，在文章中寻找答案。
2．阅读理解
It's hard to turn down a tasty banana. They taste good and you don't have to wash them before eating them. However, British scientists say that the fruit may disappear by 2050.
One reason for this is climate（气候） change. Scientists at the University of Exeter collected data（数据）from 27 countries and regions that produce 86 percent of the world's bananas. They found that climate change has improved growing conditions in 21 of these countries. In the past 60 years, the average yield（平均产量） has reached 1.37 tons of bananas per hectare（公顷）.
However, if temperatures keep rising, this advantage will disappear. Ten of the countries, including India, the world's biggest producer of bananas, will produce fewer bananas. By 2050, the fruit may die out.
Shouldn't bananas grow more easily if it's hotter outside? In fact, the perfect temperature range for growing bananas is between 24 and 32 C. If temperatures get too high, they will stop growing.
Diseases are another danger to bananas. Unlike other crops, the bananas we grow come from shoot cuttings（茎段）rather than seeds. This means that all banana plants have the same genotype（基因型）. In other words, if a disease is able to kill one plant, it could kill them all.
One serious disease is called Panama. Caused by fungus（真菌） in the soil, it spreads easily. It has spread across South Asia, Africa, the Middle East, and Australia. If one banana plantation（种植园）suffers from the disease, it will take 30 years until it is able to grow bananas again. Scientists have yet to find a cure for this disease.
（1）What does the underlined word "this" in Paragraph 2 refer to?
A. People's love for bananas.
B. The taste of bananas.
C. The convenience of eating bananas.
D. The future disappearance of bananas.
（2）What might happen if temperatures keep going higher?
A. More countries will start to grow bananas.
B. Bananas will grow better in most countries.
C. Bananas will not be able to grow any more.
D. Bananas won't be as tasty as before.
（3）What does Paragraph 5 tell us?
A. What diseases bananas may suffer from.
B. How bananas are grown.
C. How diseases can easily kill bananas.
D. Which diseases can kill bananas.
（4）The passage is written to ________.
A. offer tips for growing bananas
B. explain why bananas may die out
C. show the difficulties of growing bananas
D. describe bananas' growing conditions
【答案】（1）D
（2）C
（3）C
（4）B
【解析】【分析】主要讲了香蕉可能消失的原因。
（1）推断题。根据前句However, British scientists say that the fruit may disappear by 2050.可知介绍了香蕉可能消失的原因，所以this代指香蕉消失，故选D。
（2）细节题。根据However, if temperatures keep rising, this advantage will disappear. Ten of the countries, including India, the world's biggest producer of bananas, will produce fewer bananas. By 2050, the fruit may die out可知温度持续上升，香蕉将更少，最终可能消失，即不能生长，故选C。
（3）细节题。根据Diseases are another danger to bananas.可知疾病是香蕉的另一个危险，即疾病是怎样杀死香蕉的，故选C。
（4）主旨题。根据全文可知主要讲了香蕉可能消失的原因，故选B。
【点评】考查阅读理解。本文涉及细节题、推断题和主旨题三种常考题型，细节题要注意从文中寻找答案；推断题需要联系上下文，推断出需要的信息；主旨题需要通读全文，了解大意之后找出中心思想。
3．阅读理解
Once there was an emperor. He had a beautiful garden. In the garden, there was a little nightingale（夜莺） singing very beautifully.
One day, the emperor heard about this little bird's beautiful voice. He asked his guards to bring her to him. When the emperor heard the nightingale's voice, he said, "Put her in a golden cage, so she can stay and sing for me whenever I want to hear her."
The little bird was so unhappy about being kept in the cage that she stopped singing one day. The emperor was very angry. He ordered the scientists in his palace to make a robot bird for him. The bird could sing very beautifully too. The emperor was pleased.
Soon the robot bird became old. It no longer sang beautiful songs. Just at that time, the emperor was ill and he became very weak. One morning, while lying in bed, the emperor wanted it to sing once again. But the robot bird could not sing any more. Suddenly, the nightingale landed on the window. She began to sing her most beautiful song. The emperor was very happy! He became better and better each day.
After the emperor was well, he changed a lot and became kind to his people. From then on, all his people cherished（爱戴） him for his love and kindness.
（1）Why did the little bird stop singing?
A. Because she was ill.
B. Because she was not free.
C. Because she was hungry.
D. Because she was too excited.
（2）What made the emperor become better and better?
A. The robot's beautiful voice.
B. His men's voice.
C. The little bird's nice dance.
D. The little bird's beautiful song.
（3）According to the passage, which of the following is TRUE?
A. A little nightingale lived in the emperor's beautiful garden.
B. The nightingale went on singing songs for the emperor after she was kept in a cage.
C. One day, the robot bird was broken and it couldn't sing.
D. The emperor gave up listening to songs after he got sick.
（4）What can we learn from the passage?
A. If we keep a bird, we can enjoy the beautiful songs.
B. Don't make a robot because it can get broken easily.
C. A bird can help people get away from illness.
D. If we are kind to someone, he or she will be also kind to us.
【答案】（1）B
（2）D
（3）A
（4）D
【解析】【分析】主要讲了国王因为小夜莺动听的歌声把小鸟关在笼子里，结果小鸟难过不再唱歌，国王让科学家做了一只机器小鸟，一天机器小鸟也不唱歌了，国王病了，原来的小鸟唱了最动听的歌，国王变得越来越好了，并且变得对他的人民友好了。
（1）细节题。根据The little bird was so unhappy about being kept in the cage that she stopped singing one day.可知小鸟被关在笼子里不高兴，所以停止唱歌，故选B。
（2）细节题。根据Suddenly, the nightingale landed on the window. She began to sing her most beautiful song. The emperor was very happy! He became better and better each day.可知小鸟动听的歌曲让国王好起来，故选D。
（3）细节题。根据In the garden, there was a little nightingale（夜莺）singing very beautifully.可知小夜莺住在花园里，故选A。
（4）细节题。根据全文可知国王在小夜莺的帮助下慢慢好起来，最终对人民友好，所以我们可以学到如果我们对他人友好，他人也会对我们友好，故选D。
【点评】考查阅读理解，主要考查细节题，注意从文中仔细寻找答案。
4．阅读理解
Great changes have taken place in family life because of science and industry（工业）. In the past, when most Americans lived on farms, the typical family had many children. In a farm family, parents and their children often lived with grandparents. Usually, uncles and aunts lived nearby. But when industry became more important than agriculture in American life, families became smaller because industry requires workers who are ready and able to move off the land and move again whenever necessary. And large families cannot move from place to place as smaller families. So, at present people tend to have smaller families.
In the future, because of industrialization, a typical family will be required to move even more often than now, so families will be even smaller. The typical family may remain childless and consist only of a man and a woman. A small number of families may take raising children as their chief work. At the same time they may also raise other people's children, leaving those families free to move from job to job.
（1）Which of the following topics is discussed in the passage?
A. The development of science and industry in America.
B. The influence of science and industry on American families.
C. Harmful effect of industrialization.
D. Social problems resulting from the highly-developed science and industry in America.
（2）What kinds of families are described in the passage?
A. Families of the past and the present.
B. Families of the present and the future.
C. Families of the past and the future.
D. Families of the past, the present and the future.（3）What is one of the reasons that families are getting smaller in America?
A. Children tend to leave their parents and grandparents when they grow up.
B. People stop caring for children.
C. The need for workers who are able to move at any time has been increasing.
D. Both old and young people prefer to live by themselves.
（4）What can you infer from the passage?
A. Science and industry have caused thousands of families to split（破裂）.
B. Children do not live with their parents or grandparents.
C. Large families can hardly survive in modern society.
D. Americans are very choosy about their jobs.
【答案】（1）B
（2）D
（3）C
（4）C
【解析】【分析】文章大意：由于工业的发展，家庭也受到了影响，原来的家庭孩子多，而现在的家庭孩子少，由于工业的发展家庭会总是搬动，有的家庭只有一个孩子或者没有孩子。
（1）细节理解题，根据Great changes have taken place in family life because of science and industry（工业）.可知家庭受到了科学和工业发展的影响，故答案是B。
（2）细节理解题，根据文章内容可知，短文涉及到了过去的家庭，现在的家庭和将来的家庭，故答案是D。
（3）细节理解题，根据In the future, because of industrialization, a typical family will be required to move even more often than now, so families will be even smaller. 可知对于工人们能够随时搬动的需求，所以家庭变得原来越小，故答案是C。
（4）逻辑推理题，根据文章内容可知，工人们可能会随时要搬家，大的家庭就没有这样的便捷，所以大家庭就不适于生存在现代的社会，故答案是C。
【点评】考查阅读理解。本文涉及细节理解题和逻辑推理题。细节理解题可以直接从文中寻找答案；逻辑推理题需要结合具体语境，由已知内容推出未知的可能的事实。
5．阅读理解
Mail, games, music, news, chat rooms and shopping！The Internet is part of the way we live today. "It's easy to get onto the Internet. The only thing we need to do is use a modem which is used for connecting a computer to a telephone line. The Internet is changing and growing all the time. More and more people have computers and use the Internet. Using the Internet means surfing the World Wide Web（That's the "www" you always hear about.）.The Web has large numbers of websites in it. They are the places you go to get information and do things.
Where do these websites come from？They are made by web designers. What happens when you click on a word or a picture？You are sent to another page. It's all because of the web designer. Web designers do a lot of work by using a computer programming（程序编辑）language.
Is Web design all about computer programming? No. It's about making something new. Web designers must imagine a lot when they are making a website. It must look good and be fun to use. A big part of Web design is art. They choose the best pictures and colours to make the website look good. They also write the things that you see on the website. An important part of their job is to share ideas with the website manager about how to design the website well.
（1）This passage is mainly about .
A. computer programming languages
B. the Web designers' work
C. the website manager's work
D. the way to get onto the Internet
（2）More and more people are using the Internet because it's .
A. easy and useful
B. beautiful and funny
C. colourful and hopeful
D. changing and colourful
（3）It's possible for us to change websites by just a click because of .
A. the modem's help
B. the telephone line's help
C. the Web designers' work
D. the website manager's work
（4）Which of the following is WRONG？
A. "Www" means "World Wide Web".
B. There are a few websites on the web.
C. The Internet has changed people's lives.
D. We can do things like shopping on the Internet.
【答案】（1）B
（2）A
（3）C
（4）B
【解析】【分析】本文介绍了互联网是我们今天生活方式的一部分，网页设计的工作的重要性。
（1）主旨题。根据本文介绍了互联网是我们今天生活方式的一部分，网页设计的工作的重要性可知文章主要讲网页设计师的工作，故选B。
（2）细节题。根据It's easy to get onto the Internet可知越来越多的人在使用互联网，因为它简单有用，故选A。
（3）推理题。根据They are made by web designers. What happens when you click on a word or a picture You are sent to another page它们是由网页设计师制作的。当你点击一个单词或图片会发生什么？您将被发送到另一页可知，因为网页设计师的工作我们只需点击一下就可以改变网站，故选C。
（4）细节题。根据The Web has large numbers of websites in it 网络中有大量的网站可知网上有几个网站是错误的，故选B。
【点评】考查阅读理解。本文涉及细节题、推断题，和主旨题，细节题要注意从文中寻找答案；推断题需要联系上下文，推断出需要的信息，主旨题需要通读全文，了解大意之后找出中心思想。
6．阅读理解
For more than six million American children, coming home after school means coming to an empty house. Some deal with the situation by watching TV. Some may hide. But all of them have something in common. They spend part of each day alone. They are called "latchkey children". They're children who look after themselves while their parents are working. And their bad condition has become a subject of concern.
Lynette Long was once the headmistress of an elementary school. She said, "We had a school rule against wearing jewellery. A lot of kids had chains around their necks with keys fastened. I was constantly telling them to put them inside their shirts. There were so many keys. It never came to my mind what they meant," Slowly, she learned they were house keys.
She and her husband began talking to the children who had them. They learned of the impact （影响） working couples and single parents were having on their children. Fear is the biggest problem faced by children at home alone. One in each three latchkey children the Longs talked to reported being scared. Many had nightmares and were worried about their own safety.
The most common way latchkey children deal with their fears is by hiding. It might be in a shower stall, under a bed, or in a closet. The second is TV. They'll often play it at high volume. It's hard to get statistics（统计数据）on latchkey children, the Longs learned. Most parents are slow to admit they leave their children alone.
（1）The main idea about latchkey children is that they _________________.
A. are growing in numbers
B. suffer problems from being left alone
C. watch too much TV during the day
D. are also found in middle class neighbourhoods （2）Which sentence in the second paragraph is the topic sentence?
A. We had a school rule against wearing jewellery.
B. A lot of kids had chains around their necks with keys fastened.
C. Slowly, she learned they were house keys.
D. I was constantly telling them to put them inside their shirts.
（3）he main feeling these children have when they are at home by themselves is _________________.
A. tiredness
B. freedom
C. loneliness
D. fear
（4）The Longs' study was mainly on _________________.
A. lonely children who have single parents
B. children whose parents are working or who have one parent only
C. children who have the problem of fear
D. parents who are working far from their homes
（5）We may draw a conclusion（结论） that _________________.
A. it's difficult to find out how many latchkey children there are
B. latchkey children try to hide their feelings
C. latchkey children often watch TV with their parents
D. latchkey children enjoy having such a large amount of time alone
【答案】（1）B
（2）C
（3）D
（4）B
（5）A
【解析】【分析】本文介绍了美国一些“钥匙儿童”的生活情况这一社会问题。
（1）推理题。根据 their bad condition has become a subject of concern 他们的糟糕状况已经成为人们关注的话题可知，关于钥匙儿童的主要观点是他们独自一人会有问题，故选B。（2）主旨题。根据 Slowly, she learned they were house keys 可知，慢慢地，她了解到它们是房子的钥匙是第二段的主题句子，故选C。
（3）细节题。根据 Fear is the biggest problem faced by children at home alone 可知，这些孩子独自在家时的主要感觉是害怕，故选D。
（4）细节题。根据They learned of the impact（影响）working couples and single parents were having on their children 可知，主要研究父母在工作或只有一个父母的孩子，故选B。（5）推理题。根据 It's hard to get statistics（统计数据） on latchkey children 可知，结论是很难查出有多少挂钥匙的孩子，故选A。
【点评】考查阅读理解。本文涉及细节题、推断题，主旨题，细节题要注意从文中寻找答案；推断题需要联系上下文，推断出需要的信息，主旨题需要通读全文，了解大意之后找出中心思想。
7．阅读理解
Bob was only seven years old. One night Bob was at home alone while his parents were out for a party. He had often stayed alone before, so he wasn't afraid. As he waited for his parents to return home, he watched a film on TV. His eyes became heavier and heavier as time passed by.
Suddenly Bob's eyes opened wide- what was the sound in the next room? Bob heard the window being opened slowly. For a minute, Bob was so frightened that he could not move, and his body felt like ice. He knew that he couldn't lose his head and began to think of the things he could do.
Again he heard the sound of someone trying to climb into his home through the window.
Bob's drums were standing in the corner near the TV. "Wait, maybe there is something I can do," thought Bob. He beat his drums as hard as he could. The sound was so terrible that Bob surprised even himself. He also surprised the man in the window, who ran away as fast as possible. How clever he was!
（1）What did Bob do when he waited for his parents?
A. He played the drums.
B. He watched TV.
C. He fell asleep.
D. He did nothing.（2）The person who wanted to come into the room might be _________________.
A. a friend
B. a stranger
C. an animal
D. a thief （贼）（3）What does the underlined phrase "lose his head" mean in Chinese?
A. 冷静
B. 生气
C. 惊慌失措
D. 喜出望外（4）What did Bob do to make the man run away?
A. He turned up the TV.
B. He called the police.
C. He beat his drums.
D. He asked his parents for help.
（5）What do you think of Bob?
A. Foolish.
B. Lovely.
C. Funny.
D. Clever.
【答案】（1）B
（2）D
（3）C
（4）C
（5）D
【解析】【分析】本文介绍了Bob用敲鼓的方式吓跑了小偷的故事。
（1）细节题。根据As he waited for his parents to return home, he watched a film on TV 当他等待父母回家时，他在电视上看了一部电影，可知鲍勃等父母时看了电视，故选B。（2）推理题。根据Again he heard the sound of someone trying to climb into his home through the window.他再次听到有人试图从窗户爬进他家的声音可知，想进房间的人可能是小偷，故选D。
（3）词义猜测题。根据Bob was so frightened that he could not move, and his body felt like ice.鲍勃吓得动弹不得，他的身体感觉像冰一样，可知lose his head是惊慌失措，故选C。
（4）细节题。根据He beat his drums as hard as he could. The sound was so terrible
that Bob surprised even himself. He also surprised the man in the window, who ran away as fast as possible他尽最大努力敲鼓。声音太可怕了，鲍勃甚至连自己都感到惊讶。他还让橱窗里的那个人大吃一惊，那个人跑好，可知他敲鼓吓跑了小偷，故选C。
（5）细节题。根据How clever he was，可知鲍勃很聪明，故选D。
【点评】考查阅读理解。本文涉及细节题、推断题，词义猜测题，细节题要注意从文中寻找答案；推断题需要联系上下文，推断出需要的信息，词义猜测题需要根据上下文提炼相关信息锁定词意。
8．阅读理解
Want to enjoy some extreme sports（极限运动）? Here are a small number of the extreme sport clubs across universities in the UK.
Octopush（水中曲棍球）
Oxford, York. Aberdeen and Warwick are only some of the
universities that offer this rather unusual sport. Anyone who is
able to swim can play. It is played by two teams of six players.
Everyone wears a mask and carries a small wooden stick.
Skiing and snowboarding
Nearly every university in the UK has a skiing and snowboarding
club. For example, Brumski 8. Board Club of Birmingham
University has run for 30 years and has about 500 members.
They hold Christmas and Easter ski trips every year and take
part in competitions.
Skateboarding
Warwick University is home to the Longboarding Club. A
longboard is two or three feet longer than a usual skateboard
and has a wider wheel base. Instead of offering club T-shirts, the
Longboarding Club lets members have their personal socks.
BASE jumping
The University of Lincoln offers BASE jumping. In BASE jumping,
players jump from fixed objects and use a parachute（降落
伞）to break their fall. They go on weekly trips to Skydive
Hibaldstow.
_________________.
A. ski
B. swim
C. skate
D. skydive
（2）How many members are there in Brumski &. Board Club?
A. About 30.
B. About 300.
C. About 50.
D. About 500.（3）A usual skateboard is _________________than a longboard.
A. shorter
B. longer
C. wider
D. bigger
（4）Which university offers BASE jumping?
A. Oxford.
B. York.
C. Lincoln.
D. Warwick.
（5）According to the passage, which of the following is the most common sport in UK universities?
A. Octopush.
B. Snowboarding.
C. Skateboarding.
D. BASE jumping.
【答案】（1）B
（2）D
（3）A
（4）C
（5）B
【解析】【分析】本文介绍了英国各大学的少数极限运动俱乐部。
（1）细节题。根据水中曲棍球的介绍 Anyone who is able to swim can play可知如果一个学生想参加水中曲棍球，他或她应该会游泳，故选B。
（2）细节题。根据 Brumski 8. Board Club of Birmingham University has run for 30 years and has about 500 members 布鲁姆斯基8和伯明翰大学董事会俱乐部已经运作了30年，可知大约有500名成员，故选D。
（3）推理题。根据 A longboard is two or three feet longer than a usual skateboard 长板比普通滑板长两到三英尺可知普通的滑板比长板短，故选A。
（4）细节题。根据The University of Lincoln offers BASE jumping 可知Lincoln 提供基础跳跃，故选C。
（5）推理题。根据They hold Christmas and Easter ski trips every year and take part in competitions他们每年都举行圣诞节和复活节滑雪旅行，并参加比赛可知滑雪板运动是英国大学最常见的运动，故选B。
【点评】考查阅读理解。本文涉及细节题、推断题，细节题要注意从文中寻找答案；推断题需要联系上下文，推断出需要的信息。
9．阅读理解
Aged between 18 and 40 years?
Can you work 8 hours a day to help sort parcels （分拣包裹）from late
January to the end of February？
Pay rates
7:00 am---6:00 pm ￥12/ hour
6:00 pm---7:00 am ￥15/ hour
If you are careful and can work well with others, please join us.
For more information, call 400-889-5543.
A. ￥60
B. ￥75
C. ￥96
D. ￥120（2）Which of the following is TRUE?
A. People working at night get more money.
B. Any person under 45 can apply for the job.
C. People have to start to work at the end of February.
D. The job is to get parcels to Sto Express.
（3）The material may be from a _____________.
A. book
B. notice
C. maganize
D. newspaper
【答案】（1）C
（2）A
（3）D
【解析】【分析】文章大意：这是申通快递招聘广告，年龄，工作时间及报酬。
（1）细节理解题，根据广告中7:00 am---6:00 pm ￥12/ hour可知从上午9点到下午5点，共八个小时，每小时12美元，一天能挣96美元，故选C。
（2）细节理解题，根据7:00 am---6:00 pm ￥12/ hour从上午7点到下午6点每小时12美元； 6:00 pm---7:00 am ￥15/ hour从下午6点到早晨7点每小时15美元，通过对比可知晚上工作挣钱更多，故选A。
（3）推理判断题，这是一则广告，所以这个材料可能登在报纸上，故选D。
【点评】考查阅读理解，本文是一则广告，主要涉及细节理解题，在文中找到答案的依据。
10．阅读理解
At my primary school, I was one of the smartest kids there. I never studied, but always got perfect scores. I thought I was born clever. At least I believed so. I was also a prodigy in music according to myself. I could sing better than almost everyone else in my school. I was pretty sure that once I got to the sixth grade, everyone would be surprised by me.
But actually, they weren't.
When I arrived at my new class, I couldn't wait to show everyone what I could do. However, there was always someone else who could do better than me. My grades began to suffer. More talented（有天资的）girls often sang solos（独唱）. I believed I wasn't smart. I believed I wasn't talented. I believed I was a failure.
Over the next two years, I had to work very hard. Every prize for the best singer was given to me for hard work and effort. Grades were still very poor but they improved little by little. I worked really hard. However, I was never the best at everything.
I haven't realized until recently that I really don't have to be the best at everything. I was too hard on myself. In fact, when I did badly in a test, my classmates never laughed at me.
No one is perfect. There will probably always be someone better than me at something. Anyway, there are about seven billion people in this world. I will never be the No.1 at everything, and that's really okay.
（1）What does the underlined part "a prodigy" probably mean in English?
A. A smart kid.
B. A crazy fan.
C. A common child.
D. A lazy girl.
（2）When the writer was at the new class, ___________.
A. she lost her interest in music
B. she had difficulty in learning
C. she surprised everyone in the class
D. she got separated from her friends
（3）What has the writer realized recently?
A. There is no success without effort.
B. Being talented is the key to success.
C. Don't expect too much of yourself.
D. It's not necessary to care about the result.
（4）Which would be the best title for this passage?
A. When I wasn't perfect
B. My past life as a young girl
C. Hard work doesn't work
D. What to do when you're not perfect
【答案】（1）A
（2）B
（3）C
（4）A
【解析】【分析】文章大意：作者通过对自己学习经历的叙述，阐述了"人无完人"的人生道理。
（1）词义猜测题。根据文中句子I could sing better than almost everyone else in my school．可以推断出作者在音乐方面也是一个聪明的孩子，选A。
（2）理解推断题。根据文中的语句When I arrived at my new class, I couldn't wait to show everyone what I could do. However, there was always someone else who could do better than me. My grades began to suffer. 理解可知，作者在新学校，在学习上遇到了困难，故选B。（3）细节理解题。根据文章的第五段I really don't have to be the best at everything．可推断出，作者意识到不要对自己期望太高，故选C。
（4）归纳概括题。本文主要叙述了作者尽力使自己在各方面都很突出，力求完美，结果失败的故事．故选A。
【点评】考查阅读理解。本文考查细节题，词义推断题，推理判断题和主旨题等常考题型，细节题要注意从文中抓住关键词寻找答案；主旨题，词义推断题以及判断题都需要通读全文，了解大意之后找出正确选项。
11．阅读理解
In Britain. Boxing Day is usually celebrated on December 26th, which is the following day after Christmas Day. However, strictly speaking, Boxing Day is the first weekday after Christmas. Like Christmas Day, Boxing Day is a public holiday. This means it's a non-working day in the whole of Britain. When Boxing Day falls on a Saturday or Sunday, the following Monday is the public holiday.
The exact origin（起源）of the holiday is unclear. One of the thoughts is that during the Middle Ages, when great sailing ships were setting off to discover new land, a Christmas Box was placed by a priest（神父）on each ship. Those sailors who wanted to ensure a safe return would drop money into the box. It was sealed up and kept on board until the ship came home safely. Then the box was handed over to the priest in exchange for the saying of a mass of thanks for the success of the sailing. The priest wouldn't open it to share the contents with the poor until Christmas.
One more thought is about the "Alms Box" placed in every church on Christmas Day. Worshippers（做礼拜的人） put gifts for the poor into it. These boxes were always opened the day after Christmas. That is why that day became known as Boxing Day.
Today, many businesses, organizations and families try to keep the traditional spirit of Boxing Day alive by donating（捐赠） their time, services and money to aid Food Banks, providing gifts for the poor, or helping families in need. Besides, spending time with family and shopping are popular Boxing Day activities now.
（1）If Christmas Day is on a Saturday, Boxing Day will be celebrated on____________. A. December 25th B. December 26th C. December 27th D. December 28th （2）Sailors dropped money into the Christmas Box in order to____________.
A. save the poor
B. pay for the priest
C. discover new land
D. pray for sailing safety （3）What does the underlined phrase“sealed up" mean in Chinese?
A. 密封
B. 悬挂
C. 归还
D. 传递（4）The purpose of the passage is____________.
A. to praise the kindness of priests
B. to introduce the origins of Boxing Day
C. to call on people to help the poor
D. to compare Boxing Day with Christmas Day
【答案】（1）C
（2）D
（3）A
（4）B
【解析】【分析】文章大意：在英国。节礼日通常在12月26日举行，这是圣诞节后的第二天。但是，严格来说，节礼日是圣诞节后的第一个工作日。像圣诞节一样，节礼日也是一个公共假日。这意味着这是整个英国的非工作日。当节礼日是星期六或星期日时，下一个星期一是公共假日。
（1）细节理解题，根据When Boxing Day falls on a Saturday or Sunday, the following Monday is the public holiday.可知，如果圣诞节在星期六，节礼日就在星期一，也就是十二月二十七日，故答案是C。
（2）细节理解题，根据Those sailors who wanted to ensure a safe return would drop money into the box.可知水手往节礼箱里方硬币是为了祈求航行安全，故答案是D。
（3）词义猜测题，根据The priest wouldn't open it to share the contents with the poor until Christmas.可知回来之后让神父打开箱子，可知之前箱子被密封了，故答案是A。
（4）主旨大意题，根据文章介绍了节礼日的起源，故答案是B。
【点评】考查阅读理解。本文涉及细节理解题、词义猜测题和主旨大意题。细节理解题要
可以直接从文中寻找答案；词义猜测题，需要根据单词所在的语境，进行合理想象，确定单词的意思；主旨题需要通读全文，了解大意之后找出中心思想。
12．阅读理解
In Canada and the United States, there is a new group of children called "satellite kids", who live in one place but whose parents live in another place.
Asians are immigrating （移居） to Canada and the United States in larger numbers than ever before. Most Asians immigrate because they believe that they can give their children a better education in the west. In Asia, especially in China, Japan and Korea, it is difficult to go to university. Students must first pass the strict national examination. However, in Canada and the United States, it is easy to go to university, and anyone who wants to go can go. As a result, Asian parents decide to leave their countries so that their children can go to university.
The problem is that when Asians arrive, they discover that finding a job and making money are more difficult in the west. So these children become "satellite kids", and most of their parents do not know how sad it is to be a "satellite kid".
Only until now are Canadians and Americans discovering the "satellite kids" problem. Because these children do not speak English and because their parents are not there to take care of them, they are often absent from school. To be a "satellite kid" means growing up in such a country, where you know you are different and you can't make friends because you do not speak English well. Also, it means growing up alone, because your parents are not there.
（1）"Satellite kids" refer to （指代） the Asian kids .
A. without parents
B. living abroad alone
C. with university education
D. not speaking English
（2）Some Asian immigrant children become "satellite kids" because their parents .
A. want to leave their own country
B. want them to go to university
C. return to their countries to work
D. want them to depend on themselves
（3）The following problems of "satellites kids" are right except .
A. they grow up alone
B. they don't often go to school
C. they can make friends easily
D. their parents can not look after them
（4）What is the main idea of the passage?
A. Parents feel lonely abroad.
B. Parents want a better education for their kids.
C. Canadians and Americans' kids can't find jobs easily.
D. Kids in foreign countries alone are very in need of care from families.
【答案】（1）B
（2）B
（3）C
（4）D
【解析】【分析】本文讲述了在美国和加拿大“Satellite kids”他们远离父母，现在很多亚洲孩子去美国和加拿大上学，在学习和生活上有很多的问题，他们需要父母的关爱。
（1）细节理解题。
In Canada and the United States, there is a new group of children called "satellite kids", who live in one place but whose parents live in another place.在加拿大和美国，有一群新的孩子们被称为“卫星孩子”，他们居住在一个地方，父母居住在另一个地方，可知这些亚洲孩子们单独居住在国外，故选B。
（2）细节理解题。根据 As a result, Asian parents decide to leave their countries so that their children can go to university. 结果，亚洲父母决定离开国家以便于他们的孩子们能上大学。可知父母让他们去美国和加拿大是为了上大学。故选B。
（3）细节理解题。根据 Because these children do not speak English and because their parents are not there to take care of them, they are often absent from school. To be a "satellite kid" means growing up in such a country, where you know you are different and you can't make friends because you do not speak English well. Also, it means growing up alone, because your parents are not there. 可知父母不能好好照顾他们，他们经常旷课，因为他们英语说不好，不能交朋友。因为父母不在那里，他们单独长大。可知选项C的叙述和短文不符，故选C。
（4）推理判断题。从短文内容可知，这篇文章主要讲的是在外国学习的孩子们缺少父母的陪伴造成的一系列问题，可知这些孩子们需要家庭的关注。故选D。
【点评】此题考查阅读理解。这篇短文内容简单，容易理解。通过分析问题，找到问题的关键，然后仔细阅读短文，从短文的细节中找到和问题相关的句子，确定问题答案。对于推理判断题要根据文章的主要内容和作者的观点进行判断，不能主观臆断。
13．阅读理解
Have you found this? Sometimes, on grey, rainy days, your mood level is lower than on bright, sunny days. Is this a coincidence（巧合）, or is there some science behind this? Would you like to know more about how the weather can affect how you feel?
According to a recent study, there is a connection between weather and moods. Going to a warm place in the middle of winter can make our moods better. Pleasant weather has been proved to improve moods and memory. However, extremely hot weather can actually make us feel more tired and bored, spoiling our moods.
In the study, people who spent time outdoors in warm weather were happier than those who spent all day inside.
The best temperature for humans is about 22.2℃. That explains why people in southern California are happy all the time. To improve his or her moods, a person must spend at least 30 minutes outside in warm, sunny weather. Spending time indoors when the weather outside is so nice tends to lower moods.
Maybe just the activities connected with being outside affect our moods. Warm weather is connected with the beach, fun outdoor sports and so on. It brings back childhood memories of playing outside all day. Who doesn't love that?
Of course, we can wake up every day and decide how we will feel that day. If it's rainy, that won't necessarily make us unhappy. We'll just have to bring our umbrellas out and cheer up those who are feeling sad!
（1）According to the study, we may feel on extremely hot days.
A. happier
B. more bored
C. more excited
D. more pleased （2）Warm weather can help improve our moods and according to the passage.
A. sight
B. memory
C. height
D. hearing
（3）Why are people in southern California happy all the time?
A. Because the weather there is always cold.
B. Because people there don't like doing sports.
C. Because the temperature there is the best for humans.
D. Because the weather there is extremely hot all the year round.
（4）What is the best title for the passage?
A. Rainy Days Make Us Sad
B. The Best Temperature for Humans
C. Go Outside on Sunny Days
D. How the Weather Affects Our Moods
【答案】（1）B
（2）B
（3）C
（4）D
【解析】【分析】文章大意：本文主要介绍了天气怎样影响人的心情的。
（1）细节理解题。根据文中的语句However, extremely hot weather can actually make us feel more tired and bored, spoiling our moods.理解可知，极端炎热的天气实际上会让我们感到更加疲倦和无聊，破坏我们的心情。故选B。
（2）细节理解题。根据文中的语句 Pleasant weather has been proved to improve moods and memory. 理解可知，宜人的天气有助于改善情绪和记忆力。故选B。
（3）细节理解题。根据文中的语句The best temperature for humans is about 22.2℃. That explains why people in southern California are happy all the time. 可知，那里的气温最适宜于人类，故选C。
（4）标题归纳题。通读全文可知此文主要介绍了天气怎样影响人的情绪的，故选D。
【点评】考查阅读理解。本文考查细节题和主旨题等常考题型，细节题要注意从文中抓住关键词寻找答案；主旨题需要通读全文，了解大意之后找出主题句。
14．阅读理解
Hundreds of foreigners got together in a small neighborhood in Qingdao on the afternoon of April 20 because of the Neighbor Day, an 18-day event celebrated across Qingdao. They learned the arts of Chinese handwriting, dumpling making, paper cutting, and discovered the culture of Chinese family trees.
The festival started 12 years ago after a 10-year-old girl called Sun Ruihan was refused when paying a New Year's visit to her neighbor. Upset by this incident, she wrote to the Shibei district government of Qingdao, suggesting that they should introduce a "Neighbor Day" to encourage
greater spirit.
As the birthplace of the festival, Shibei hosted the opening ceremony of this year's Neighbor Day on April 19. With the theme of" ▲ ", people from across the city got together to share their homemade food and discuss the family stories. They also set up a mobile neighbors' library to share books.
Sarah from the United States said she had a great time with her neighbors as she experienced the art of Chinese paper cutting for the first time. Masha from Russia, who is studying Chinese at the Ocean University of China, described the event as a great chance to make friends with her Chinese neighbors and learn about the local culture with them. She tried her best at Chinese handwriting and also had great fun learning how to make dumplings. "I love eating dumplings but I never knew how to make them before, "she said." Now I can come to my neighbors' homes and learn in their kitchens."
Neighbor Day grew from the needs of the people. With the big support from the government, it has become another culture symbol of Qingdao.
（1）Neighbor Day in Qingdao is a festival to .
A. welcome foreigners to Qingdao
B. learn different western cultures
C. make friends with neighbors
D. help neighbors out of trouble
（2）The underlined word "incident" in Paragraph 2 probably means in Chinese.
A. 事件
B. 行动
C. 过程
D. 意外（3）Which of the following can be best put into the blank" ▲ "?
A. Foreigners as friends
B. Neighbors as family
C. Living with foreigners
D. Working with neighbors
（4）Which of the following shows the right structure of the passage?（P=Paragraph）
A. B. C. D.
【答案】（1）C
（2）A
（3）B
（4）C
【解析】【分析】本文讲述了青岛的邻居节。
（1）推理题。根据described the event as a great chance to make friends with her Chinese neighbors 可知邻居节是为了和邻居交朋友，故选C。
（2）词义猜测题。根据Sun Ruihan was refused when paying a New Year's visit to her neighbor. Upset by this incident, she wrote to......可知incident是事件的意思，故选A。
（3）推理题。根据 people from across the city got together to share their homemade food and discuss the family stories. 来自全市各地的人们聚在一起分享他们自制的食物和谈论家庭故事，可知Neighbors as family把邻居当做家人，适合作为活动主题，故选B。
（4）细节题。根据全文描述可知，文章的五段以第一段是提出这个节日，2,3,4段描述节日，第五段总结，故正确结构的是C，故选C。
【点评】考查阅读理解。本文涉及细节题、推断题，词义猜测题3种常考题型，细节题要注意从文中寻找答案；推断题需要联系上下文，推断出需要的信息，词义猜测题需要根据上下文提炼相关信息锁定词意。
15．阅读理解
Improve Your Learning Skills!
Want higher marks?
Have an important exam soon?
Come to the workshop and learn how to:
?Read faster
?Take better notes
?Improve your spelling
Wednesday, March 13, 3 pm-5 pm, Room 314
Bring a notebook, a dictionary, and a pencil.
See you there.
A. reading
B. grammar
C. speaking
D. pronunciation
（2）People need to stay in the workshop for ______.
A. one hour
B. two hours
C. three hours
D. four hours
（3）People should bring ______ if they go to the workshop.
A. a pen
B. a notebook
C. an English book
D. a computer
【答案】（1）A
（2）B
（3）B
【解析】【分析】本文是关于如何提高英语的广告。
（1）细节题。根据 Read faster 可知在研讨会上可以提高阅读，故选A。
（2）细节题。根据 Wednesday, March 13, 3 pm-5 pm可知人们在研讨会上待2个小时，故选B。
（3）细节题。根据 Bring a notebook 看着需要带笔记本，故选B。
【点评】考查阅读理解。本文涉及细节题，细节题要注意从文中寻找答案。
圆知识点归纳 一、圆的定义。 1、以定点为圆心，定长为半径的点组成的图形。 2、在同一平面内，到一个定点的距离都相等的点组成的图形。 二、圆的各元素。 1、半径：圆上一点与圆心的连线段。 2、直径：连接圆上两点有经过圆心的线段。 3、弦：连接圆上两点线段（直径也是弦）。 4、弧：圆上两点之间的曲线部分。半圆周也是弧。 （1）劣弧：小于半圆周的弧。 （2）优弧：大于半圆周的弧。 5、圆心角：以圆心为顶点，半径为角的边。 6、圆周角：顶点在圆周上，圆周角的两边是弦。 7、弦心距：圆心到弦的垂线段的长。 三、圆的基本性质。 1、圆的对称性。 （1）圆是轴对称图形，它的对称轴是直径所在的直线。 （2）圆是中心对称图形，它的对称中心是圆心。 （3）圆是旋转对称图形。 2、垂径定理。 （1）垂直于弦的直径平分这条弦，且平分这条弦所对的两条弧。 （2）推论： ? 平分弦（非直径）的直径，垂直于弦且平分弦所对的两条弧。 ? 平分弧的直径，垂直平分弧所对的弦。 3、圆心角的度数等于它所对弧的度数。圆周角的度数等于它所对弧度数的一半。 （1）同弧所对的圆周角相等。 （2）直径所对的圆周角是直角；圆周角为直角，它所对的弦是直径。 4、在同圆或等圆中，两条弦、两条弧、两个圆周角、两个圆心角、两条弦心距五对量中只要有一对量相等，其余四对量也分别相等。 5、夹在平行线间的两条弧相等。 6、设⊙O 的半径为r ，OP=d 。 7、（1）过两点的圆的圆心一定在两点间连线段的中垂线上。 （2）不在同一直线上的三点确定一个圆，圆心是三边中垂线的交点，它到三个点的距 离相等。 （直角三角形的外心就是斜边的中点。） 8、直线与圆的位置关系。d 表示圆心到直线的距离，r 表示圆的半径。 直线与圆有两个交点，直线与圆相交；直线与圆只有一个交点，直线与圆相切； d = r 点P 在⊙O 上 d < r （r > d 点P 在⊙O 内 d > r （r 最新中考英语知识点汇总中考英语知识点：名词所有格 【速记口诀】 名词所有格，表物是"谁的"。 若为生命词，加"‘s"即可行。 词尾有s，仅把逗号择。 并列名词后，各自和共有。 前者分别加，后者最后加。 若为无生命词，of所有格。 前后须倒置，此是硬规则。 【妙语诠释】 ①有生命的名词所有格一般加s，但如果名词以s结尾，则只加"‘"; ②并列名词所有格表示各自所有时，分别加"‘s"，如果是共有，则只在最后名词加"’s"; ③如果是无生命的名词则用of表示所有格，这里需要注意它们的顺序与汉语不同，A of B要翻译为B的A. 中考英语知识点：宾语从句用法巧记口诀 【速记口诀】 宾语从句须注意，几点事项应牢记。 一是关键引导词，不同句子词相异。 陈述句子用that;一般疑问是否(if，whether)替; 特殊问句更好办，引导还用疑问词。 二是时态常变化，主句不同从句异。 主句若为现在时，从句时态应看意; 主句若为过去时，从句时态向前移。 三是语序要记清，从句永保陈述序。 【妙语诠释】 宾语从句应注意三点： ①引导词，陈述句一般由that引导，这时的that可以省略;一般疑问句则由if或whe-ther引导;而特殊疑问句则由特殊疑问词引导。 ②时态，主句是现在时态，从句可用所需要的任何时态;但如果主句是过去时态，从句时态所表示时间一般往前移一个时间段。 ③语序，宾语从句永远要用陈述句顺序。 中考英语知识点：语法学习口诀 1、最初的简单动词的学习。 来是come，去是go.点头yes，摇头no.再见要用goodbye，谢谢要说thankyou. 2、关于Be的用法：BTH 我用am，你用are，is用在他、她、它，凡是复数都用are.不能错来，不能差。 3、关于冠词的使用：BTH 不见原因(元音)，别施恩(n)。 4、不用冠词的部分情况：BTH 季节、月份、节假日，三餐、球类和星期。 5、以-fe结尾变复数只加s的单词： gulf roof chief serf belief proof handkerchief 海湾边，屋顶上，首领奴仆两相望，谁说他们无信仰，证据写在 圆 章节知识点 一、圆的概念 集合形式的概念： 1、 圆可以看作是到定点的距离等于定长的点的集合； 2、圆的外部：可以看作是到定点的距离大于定长的点的集合； 3、圆的内部：可以看作是到定点的距离小于定长的点的集合 轨迹形式的概念： 1、圆：到定点的距离等于定长的点的轨迹就是以定点为圆心，定长为半径的圆； 二、点与圆的位置关系 1、点在圆内 ?d r ? 点A 在圆外； 三、直线与圆的位置关系 1、直线与圆相离?d r >?无交点； 2、直线与圆相切?d r =?有一个交点； 3、直线与圆相交?d r +；外切（图2）? 有一个交点?d R r =+； 相交（图3）? 有两个交点?R r d R r -<<+；内切（图4）? 有一个交点?d R r =-； 内含（图5）? 无交点 ?d R r <-； A r R d 图3 r R d 五、垂径定理 垂径定理：垂直于弦的直径平分弦且平分弦所对的弧。 推论1：（1）平分弦（不是直径）的直径垂直于弦，并且平分弦所对的两条弧； （2）弦的垂直平分线经过圆心，并且平分弦所对的两条弧； （3）平分弦所对的一条弧的直径，垂直平分弦，并且平分弦所对的另一条弧 以上共4个定理，简称2推3定理：此定理中共5个结论中，只要知道其中2个即可推出其它3个结论，即： ①AB 是直径 ②AB CD ⊥ ③CE DE = ④ 弧BC =弧BD ⑤ 弧AC =弧AD 中任意2个条件推出其他3个结论。 推论2：圆的两条平行弦所夹的弧相等。 即：在⊙O 中，∵AB ∥CD ∴弧AC =弧BD 六、圆心角定理 r R d O E D C O D A B avoid 可表示“避开”或“躲避”(keep oneself from)某人或某物；也可表示“防止”(prevent... from...)某事的发生。如： I think she is avoiding me. 我想她在躲我。 avoid+sth./doing sth.（2次）可接名词或动名词作宾语，但是不能接不定式作宾语。如： Try to avoid accidents.尽量防止发生事故。 He avoided answering my questions.他对我的问题避而不答。 happen 指偶然发生，具有不可预测性，主语一 般是某物/某事。表示“某人发生了什么事” 时用sth. happen(s) to sb.; happen 还可以表示“碰巧”，常用于“sb. happen(s) to do sth.”和“It happens+that 从句”两种结构。 注意：happen 和take place 都没有被动语态。 suggest sth. (to sb. ) （向某人）建议某事。 suggest doing sth. 建议做某事。 suggest sb. (宾格)/one’s doing sth.建议某人做某事 suggest 意为“ 暗示；表明”时，用于suggest+that从句(表示此意思的时候，一般只考查这一个用法)，此时，其宾语从句不能使用虚拟语气，而是使用陈述语气，即该用什么时态就用什么时态，只是要注意和主句suggest的时态对应即可。 suggest + that从句，表示建议……。此时that从句 要使用虚拟语气，即从句的谓语由“(should) + 动词 原形”构成，且should可以省略。 。 ①regret＋n./pron. 意为“后悔,对……表示歉意”。 如: If you don’t do it now, you’ll regret later. 如果你现在不做,以后一定会后悔的。 ②regret ＋that/wh-从句,意为“后悔,遗憾……”。如: I have deeply regretted what I said.我非常后悔说了那些话。 ③regret＋to do sth.意为“对做某事感到遗憾”。如: We regret to inform you that your application has not been successful.我们很遗憾地通 圆知识点学案 考点一、圆的相关概念 1、圆的定义 在一个平面，线段OA绕它固定的一个端点O旋转一周，另一个端点A随之旋转所形成的图形叫做圆，固定的端点O叫做圆心，线段OA叫做半径。 2、圆的几何表示 以点O为圆心的圆记作“⊙O”，读作“圆O” 考点二、弦、弧等与圆有关的定义 （1）弦 连接圆上任意两点的线段叫做弦。（如图中的AB） （2）直径 经过圆心的弦叫做直径。（如途中的CD） 直径等于半径的2倍。 （3）半圆 圆的任意一条直径的两个端点分圆成两条弧，每一条弧都叫做半圆。 （4）弧、优弧、劣弧 圆上任意两点间的部分叫做圆弧，简称弧。 弧用符号“⌒”表示，以A，B为端点的弧记作“”，读作“圆弧AB”或“弧AB”。 大于半圆的弧叫做优弧（多用三个字母表示）；小于半圆的弧叫做劣弧（多用两个字母表示） 考点三、垂径定理及其推论 垂径定理：垂直于弦的直径平分这条弦，并且平分弦所对的弧。 推论1：（1）平分弦（不是直径）的直径垂直于弦，并且平分弦所对的两条弧。（2）弦的垂直平分线经过圆心，并且平分弦所对的两条弧。 （3）平分弦所对的一条弧的直径垂直平分弦，并且平分弦所对的另一条弧。 推论2：圆的两条平行弦所夹的弧相等。 垂径定理及其推论可概括为： 过圆心 垂直于弦 直径平分弦知二推三 平分弦所对的优弧 平分弦所对的劣弧 考点四、圆的对称性 1、圆的轴对称性 圆是轴对称图形，经过圆心的每一条直线都是它的对称轴。 2、圆的中心对称性 圆是以圆心为对称中心的中心对称图形。 考点五、弧、弦、弦心距、圆心角之间的关系定理 1、圆心角 顶点在圆心的角叫做圆心角。 2、弦心距 从圆心到弦的距离叫做弦心距。 3、弧、弦、弦心距、圆心角之间的关系定理 在同圆或等圆中，相等的圆心角所对的弧相等，所对的弦想等，所对的弦的弦心距相等。 推论：在同圆或等圆中，如果两个圆的圆心角、两条弧、两条弦或两条弦的弦心距中有一组量相等，那么它们所对应的其余各组量都分别相等。 考点六、圆周角定理及其推论 1、圆周角 顶点在圆上，并且两边都和圆相交的角叫做圆周角。 2、圆周角定理 一条弧所对的圆周角等于它所对的圆心角的一半。 推论1：同弧或等弧所对的圆周角相等；同圆或等圆中，相等的圆周角所对的弧也相等。 推论2：半圆（或直径）所对的圆周角是直角；90°的圆周角所对的弦是直径。推论3：如果三角形一边上的中线等于这边的一半，那么这个三角形是直角三角形。 考点七、点和圆的位置关系 设⊙O的半径是r，点P到圆心O的距离为d，则有： d 圆的知识点总结 （一）圆的有关性质 ［知识归纳］ 1. 圆的有关概念： 圆、圆心、半径、圆的内部、圆的外部、同心圆、等圆； 弦、直径、弦心距、弧、半圆、优弧、劣弧、等弧、弓形、弓形的高； 圆的内接三角形、三角形的外接圆、三角形的外心、圆内接多边形、多边形的外接圆；圆心角、圆周角、圆内接四边形的外角。 2. 圆的对称性 圆是轴对称图形，经过圆心的每一条直线都是它的对称轴，圆有无数条对称轴； 圆是以圆心为对称中心的中心对称图形； 圆具有旋转不变性。 3. 圆的确定 不在同一条直线上的三点确定一个圆。 4. 垂直于弦的直径 垂径定理垂直于弦的直径平分这条弦，并且平分弦所对的两条弧； 推论1 （1）平分弦（不是直径）的直径垂直于弦，并且平分弦所对的两条弧； （2）弦的垂直平分线经过圆心，并且平分弦所对的两条弧； （3）平分弦所对的一条弧的直径垂直平分弦，并且平分弦所对的另一条弧。 垂径定理及推论1 可理解为一个圆和一条直线具备下面五个条件中的任意两个，就 可推出另外三个：①过圆心；②垂直于弦；③平分弦（不是直径）； ④平分弦所对的优弧；⑤平分弦所对的劣弧。 1 推论2圆的两条平行弦所夹的弧相等。 5. 圆心角、弧、弦、弦心距之间的关系 定理在同圆或等圆中，相等的圆心角所对的弧相等，所对的弦相等；所对的弦的弦心距相等。 推论在同圆或等圆中，如果两个圆心角、两条弧、两条弦或两条弦的弦心距中有一组量相等，那么它们所对应的其余各组量都分别相等。 此定理和推论可以理解成：在同圆或等圆中，满足下面四个条件中的任何一个就能推出另外三个：①两个圆心角相等；②两个圆心角所对的弧相等；③两个圆 心角或两条弧所对的弦相等；④两条弦的弦心距相等。 圆心角的度数等于它所对的弧的度数。 6. 圆周角 定理一条弧所对的圆周角等于它所对的圆心角的一半； 推论1同弧或等弧所对的圆周角相等；在同圆或等圆中，相等的圆周角所对的弧也相等； 推论2半圆（或直径）所对的圆周角是直角；90°的圆周角所对的弦是直径； 推论3如果三角形一边上的中线等于这边的一半，那么这个三角形是直角三角形。 圆周角的度数等于它所对的弧的度数的一半。 7. 圆内接四边形的性质 圆内接四边形的对角互补，并且任何一个外角都等于它的内对角。 ※8. 轨迹 轨迹符合某一条件的所有的点组成的图形，叫做符合这个条件的点的轨迹。 （1）平面内，到一定点的距离等于定长的点的轨迹，是以这个定点为圆心，定长为半径的圆； （2）平面内，和已知线段两个端点的距离相等的点的轨迹，是这条线段的垂直平分线； （3）平面内，到已知角两边的距离相等的点的轨迹，是这个角的平分线。 ［例题分析］ 例1. 已知：如图1，在⊙O中，半径OM⊥弦AB于点N。 图1 ①若AB ＝，ON＝1，求MN的长； ②若半径OM＝R，∠AOB＝120°，求MN的长。 解：①∵AB ＝，半径OM⊥AB，∴AN＝BN ＝ ∵ON＝1，由勾股定理得OA＝2 ∴MN＝OM－ON＝OA－ON＝1 ②∵半径OM⊥AB，且∠AOB＝120°∴∠AOM＝60° 2 1.在一个平面内，线段OA绕它固定的一个端点O旋转一周，另 一个端点A所形成的图形叫做圆。固定的端点O叫做圆心，线段OA叫做半径。 2.连接圆上任意两点的线段叫做弦，经过圆心的弦叫做直径。 3.圆上任意两点间的部分叫作圆弧，简称弧。圆的任意一条直 径的两个端点把圆分成两条弧，每一条弧都叫做半圆。能够重合的两个圆叫做等圆。在同圆或等圆中，能够互相重合的弧叫做等弧。 4.P108圆是轴对称图形，任何一条直径所在直线都是它的对称 轴，圆心是它的对称中心（p110） 5.垂直于弦的直径平分弦，并且平分弦所对的两条弧。(逆定理： 经过弦中点的直径垂直于这条弦并且平分弦所对的两条弧) 6.推论：平分弦（不是直径）的直径垂直于弦，并且平分弦所 对的两条弧。 7.我们把顶点在圆心的角叫做圆心角。 8.定理1：在同圆或等圆中，相等的圆心角所对的弧相等，所对 的弦也相等。 9.在同圆或等圆中，相等的弧所对的圆心角相等，所对的弦相 等。 10.定理3：在同圆或等圆中，相等的弦所对的两条劣弧（优弧） 相等，相等的劣弧（优弧）所对的圆心角相等。相等的圆心角所对的弦相等的优劣弧之间的关系 11.不在同一条直线上的三个点确定一个圆（P117） 12.顶点在圆上，并且两边都与圆相交(弦)的角叫做圆周角。 13.在同圆或等圆中，同弧或等弧所对的圆周角相等，都等于这 条弧所对的圆心角的一半。(p122)4-23 14.定理：（p119-120）半圆（或直径）所对的圆周角是直角，90° 的圆周角所对的弦是直径。 15.如果一个多边形的所有顶点都在同一个圆上，这个多边形叫 做圆内接多边形，这个圆叫做这个多边形的外接圆。 16.P123推论：在同圆或等圆中，如果两个圆周角相等，他们所 对的弧一定相等。 17.圆内接四边形的对角互补，圆内接四边形的一个外角等于互 补角的内对角；对角互补的四边形内接于圆 下接PPT 18.点P在圆外——d > r 点P在圆上——d = r 点P在圆内— —d < r 中考英语知识点归纳汇总-详细 第一课时名词 一、概述 1、名词的属性：表示人或事物的名称抽象概念的词叫名词。 2、名词分普通名词和专有名词。普通名词是表示某一类人或事物，或某种物体或抽象概念的名称。如：teacher, desks, plates, milk, box等，专有名词表示某一特定的人、事物、地方团体、党派、国家机关、语言、节日等专用的名称。（运用）如：China, Chinese, Saturday, June, Green, Beijing, Olympic等。（专有名词的第一个字母要大写） 二、可数名词与不可数名词 1、可数名词是指表示人或事物，可以用数来计量的名词，有单复数之分。如：glass-----glasses; book---- books 2、不可数名词是指所表示的事物不能用数来计量。 如：paper, rice, water , milk, tea等。 3、有些名词在特定情况下由不可数变为可数名词。 Light travels faster than sound; (light：光线，不可数) The lights are on. (light：灯，可数) 4、不可数名词的量的表示 不可数名词一般无法用数来计算，前面不能用a或an或数词来表示数量，它的量往往借助于容器来表示。 如：a glass of milk ------ four glasses of milk a piece of paper------two pieces of paper a bag of rice------three bags of rice 三、可数名词的复数形式（识记、运用） 1、可数名词在应用时有单复数之分，单数变复数有规则变化和不规则变化两种。规则变化 情况 变化形式 例词 一般情况 加-s girls; books; 以s,x,ch,sh结尾的名词 2019年中考数学圆的知识点总结 一、圆及圆的相关量的定义(28个) 1.平面上到定点的距离等于定长的所有点组成的图形叫做圆。定点称为圆心，定长称为半径。 2.圆上任意两点间的部分叫做圆弧，简称弧。大于半圆的弧称为优弧，小于半圆的弧称为劣弧。连接圆上任意两点的线段叫做弦。经过圆心的弦叫做直径。 3.顶点在圆心上的角叫做圆心角。顶点在圆周上，且它的两边分别与圆有另一个交点的角叫做圆周角。 4.过三角形的三个顶点的圆叫做三角形的外接圆，其圆心叫做三角形的外心。和三角形三边都相切的圆叫做这个三角形的内切圆，其圆心称为内心。 5.直线与圆有3种位置关系：无公共点为相离;有2个公共点为相交;圆与直线有唯一公共点为相切，这条直线叫做圆的切线，这个唯一的公共点叫做切点。 6.两圆之间有5种位置关系：无公共点的，一圆在另一圆之外叫外离，在之内叫内含;有唯一公共点的，一圆在另一圆之外叫外切，在之内叫内切;有2个公共点的叫相交。两圆圆心之间的距离叫做圆心距。 7.在圆上，由2条半径和一段弧围成的图形叫做扇形。圆锥侧面展开图是一个扇形。这个扇形的半径成为圆锥的母线。 二、有关圆的字母表示方法(7个) 圆--⊙半径—r 弧--⌒直径—d 扇形弧长/圆锥母线—l 周长—C 面积—S三、有关圆的基本性质与定理(27个) 1.点P与圆O的位置关系(设P是一点，则PO是点到圆心的距离)： P在⊙O外，POP在⊙O上，PO=r;P在⊙O内，PO 2.圆是轴对称图形，其对称轴是任意一条过圆心的直线。圆也是中心对称图形，其对称中心是圆心。 3.垂径定理：垂直于弦的直径平分这条弦，并且平分弦所对的弧。逆定理：平分弦(不是直径)的直径垂直于弦，并且平分弦所对的弧。 4.在同圆或等圆中，如果2个圆心角，2个圆周角，2条弧，2条弦中有一组量相等，那么他们所对应的其余各组量都分别相等。 5.一条弧所对的圆周角等于它所对的圆心角的一半。 6.直径所对的圆周角是直角。90度的圆周角所对的弦是直径。 7.不在同一直线上的3个点确定一个圆。 8.一个三角形有唯一确定的外接圆和内切圆。外接圆圆心是三角形各边垂直平分线的交点，到三角形3个顶点距离相等;内切圆的圆心是三角形各内角平分线的交点，到三角形3边距离相等。 9.直线AB与圆O的位置关系(设OP⊥AB于P，则PO是AB 初中英语中考考点大汇总 1 (see 、hear 、notice 、find 、feel 、listen to 、look at (感官动词)+ do eg :I like watching monkeys jump 2 （比较级and 比较级）表示越来越怎么样 3 a piece of cake =easy 小菜一碟（容易）补：a place of interest 名胜 4 agree with sb 赞成某人 5 all kinds of 各种各样a kind of 一样 6 all over the world = the whole world 整个世界 7 along with 同……一道，伴随…… eg : I will go along with you 我将和你一起去 the students planted trees along with their teachers 学生同老师们一起种树 8 As soon as 一怎么样就怎么样 9 as you can see 你是知道的 10 ask for ……求助向…要…（直接接想要的东西）eg : ask you for my book 11 ask sb for sth 向某人什么 12 ask sb to do sth 询问某人某事ask sb not to do 叫某人不要做某事 13 at the age of 在……岁时eg：I am sixteen I am at the age of sixteen 14 at the beginning of …………的起初；……的开始 15 at the end of +地点/+时间最后；尽头；末尾eg : At the end of the day 16 at this time of year 在每年的这个时候补：at least 至少 17 be /feel confident of sth /that clause +从句感觉/对什么有信心，自信 eg : I am / feel confident of my spoken English I feel that I can pass the test A 图5 圆的总结 一 集合： 圆：圆可以看作是到定点的距离等于定长的点的集合； 圆的外部：可以看作是到定点的距离大于定长的点的集合； 圆的内部：可以看作是到定点的距离小于定长的点的集合 二 轨迹： 1、到定点的距离等于定长的点的轨迹是：以定点为圆心，定长为半径的圆； 2、到线段两端点距离相等的点的轨迹是：线段的中垂线； 3、到角两边距离相等的点的轨迹是：角的平分线； 4、到直线的距离相等的点的轨迹是：平行于这条直线且到这条直线的距离等于定长的两条直线； 5、到两条平行线距离相等的点的轨迹是：平行于这两条平行线且到两条直线距离都相等的一条直线 三 位置关系： 1点与圆的位置关系: 点在圆内 d D B B A B A 四 垂径定理: 垂径定理：垂直于弦的直径平分弦且平分弦所对的弧 推论1：（1）平分弦（不是直径）的直径垂直于弦，并且平分弦所对的两条弧； （2）弦的垂直平分线经过圆心，并且平分弦所对的两条弧； （3）平分弦所对的一条弧的直径，垂直平分弦，并且平分弦所对的另一条弧 以上共4个定理，简称2推3定理：此定理中共5个结论中，只要知道其中2个即可推出其它3个结论，即： ①AB 是直径 ②AB ⊥CD ③CE=DE ④ ⑤ 推论2：圆的两条平行弦所夹的弧相等。 即：在⊙O 中，∵AB ∥CD 五 圆心角定理 六 圆周角定理 圆周角定理：同一条弧所对的圆周角等于它所对的圆心的角的一半 即：∵∠AOB 和∠ACB 是 所对的圆心角和圆周角 ∴∠AOB=2∠ACB 圆周角定理的推论： 推论1：同弧或等弧所对的圆周角相等；同圆或等圆中，相等的圆周角所对的弧是等弧 即：在⊙O 中，∵∠C 、∠D 都是所对的圆周角 ∴∠C=∠D 推论2：半圆或直径所对的圆周角是直角；圆周角是直角所对的弧是半圆，所对的弦是直径 即：在⊙O 中，∵AB 是直径 或∵∠C=90° ∴∠C=90° ∴ AB 是直径 推论3：三角形一边上的中线等于这边的一半，那么这个三角形是直角三角形 ??BC BD =??AC AD = 历年英语中考考点归纳 必考内容之一：被动语态 考查形式：单项，完形，完成句子题型出现，尤其是完成句子。 考察难度：考查的动词都是比较简单、拼写不会超过5个字母的单词，过去分词一般都是直接+ed出现，出题不难，要求掌握被动语态的判断、被动语态的结构和动词过去分词的正确拼写。 要点归纳： 1、结构：be+过去分词+（by+动作执行者） 2、掌握的几种形式： 一般现在时的被动语态： 一般过去时的被动语态： 现在完成时的被动语态：（理解要求） 一般将来时的被动语态： 含有情态动词的被动语态： 3、感官动词或使役动词使用省略to的不定式，主动语态中不带to，但北纬被动语态时，须 加上to Feel, hear, listen to, let, have, make, see, watch observe, notice, look at, help 口诀：十二个动词真正怪 To去to 归让人烦 主动语态时不在 被动语态却回来 例：make sb do sth = sb +be+made + to do sth 4、被动语态常考的固定搭配： Be made of Be made from Be made in Be used for Be used to do 注意下列短语和动词有“被动形式”，但没有被动的意思： be used to doing Used to do sth Be made up of Be dressed Be well-known for 5、无被动语态的不及物动词常考的有：happen, take place, begin, start, end, belong to, come true. 6、含双宾语的被动语态： 和to搭配的：give, show, pass, hand, tell, lend, bring ,ect. 和for搭配的：buy, pay, sing, wake, get, do, ect. 7、主动表被动的动词：sell, wash, write, 和五个起来：feel, smell, look, taste, sound e.g.: The pen writes well. He looks strong. 初三数学圆知识点总结 一、本章知识框架 二、本章重点 1．圆的定义： (1)线段OA绕着它的一个端点O旋转一周，另一个端点A所形成的封闭曲线，叫做圆． (2)圆是到定点的距离等于定长的点的集合． 2．判定一个点P是否在⊙O上． 设⊙O的半径为R，OP＝d，则有 d>r点P在⊙O 外； d＝r点P在⊙O 上； d (1)旋转不变性：圆是旋转对称图形，绕圆心旋转任一角度都和原来图形重合；圆是中心对称图形，对称中心是圆心． 在同圆或等圆中，两个圆心角，两条弧，两条弦，两条弦心距，这四组量中的任意一组相等，那么它所对应的其他各组分别相等． (2)轴对称：圆是轴对称图形，经过圆心的任一直线都是它的对称轴． 垂径定理及推论： (1)垂直于弦的直径平分这条弦，并且平分弦所对的两条弧． (2)平分弦(不是直径)的直径垂直于弦，并且平分弦所对的两条弧． (3)弦的垂直平分线过圆心，且平分弦对的两条弧． (4)平分一条弦所对的两条弧的直线过圆心，且垂直平分此弦． (5)平行弦夹的弧相等． 5．三角形的内心、外心、重心、垂心 (1)三角形的内心：是三角形三个角平分线的交点，它是三角形内切圆的圆心，在三角形内部，它到三角形三边的距离相等，通常用“I”表示． (2)三角形的外心：是三角形三边中垂线的交点，它是三角形外接圆的圆心，锐角三角形外心在三角形内部，直角三角形的外心是斜边中点，钝角三角形外心在三角形外部，三角形外心到三角形三个顶点的距离相等，通常用O表示．(3)三角形重心：是三角形三边中线的交点，在三角形内部；它到顶点的距离是到对边中点距离的2倍，通常用G表示． (4)垂心：是三角形三边高线的交点． 6．切线的判定、性质： (1)切线的判定： ①经过半径的外端并且垂直于这条半径的直线是圆的切线． ②到圆心的距离d等于圆的半径的直线是圆的切线． (2)切线的性质： ①圆的切线垂直于过切点的半径． ②经过圆心作圆的切线的垂线经过切点． ③经过切点作切线的垂线经过圆心． (3)切线长：从圆外一点作圆的切线，这一点和切点之间的线段的长度叫做切线长． (4)切线长定理：从圆外一点作圆的两条切线，它们的切线长相等，这一点和圆心的连线平分两条切线的夹角． 7．圆内接四边形和外切四边形 (1)四个点都在圆上的四边形叫圆的内接四边形，圆内接四边形对角互补，外角等于内对角． (2)各边都和圆相切的四边形叫圆外切四边形，圆外切四边形对边之和相等．8．直线和圆的位置关系： 设⊙O 半径为R，点O到直线l的距离为d． (1)直线和圆没有公共点直线和圆相离d>R． (2)直线和⊙O有唯一公共点直线l和⊙O相切d＝R． (3)直线l和⊙O 有两个公共点直线l和⊙O 相交d 中考英语核心知识点汇总 中考英语核心知识点汇总英语语法重点与难点 1、as…as…结构：你和汤姆是一样好的孩子。 You’re a boy as good as Tom.=You’re as good a boy as Tom. 2、(1)too…to与so…that sb. can’t…的句型转换：前者为简单句，主语只有一个，而后者为复合句，主语有两个，试比较：The man was too angry to be able to speak. The man was so angry that he wasn’t able to speak. (2) too…to…与 not enough to句型的转换： He is too young to get married.=He is not old enough to get married. The book is too difficult for me to read.= The book is not easy enough for me to read. 3、形容词原级表示比较级含义： 约翰不象迈克那么苯。 John is not so stupid as Mike. John is less stupid than Mike. John is cleverer than Mike. 4、用比较级表示最高级：约翰是班里最高的男生。 John is taller than any other boy in the class. John is the tallest boy in the class. 5、the more….. the more….表示“越……越……”: The more books you read, the wider your knowledge is. The more food you eat, the fatter you are. 6、more and more….表示“越来……越……”: 初中数学——《圆》 【知识结构】 ????? ??????? ? ? ? ?? ? ? ????? ??????? ? ? ? ?? ? ?? ? ? ???????????????????????????? ???????????????????????????????????????????? ???????? ?? ????????? ?? ??侧面积、全面积计算侧面展开图定义圆柱和圆锥形面积计算圆面积、扇形、组合图形周长计算圆周长、弧长、组合图画法应用边长、面积的计算计算半径、边心距、中心角计算概念正多边形正多边形与圆内含 内切相交外切外离圆和圆的位置关系切割线定理及推论相交弦定理及推论相交性质判定相切相离直线和圆的位置关系反证法点的轨迹圆内接四边形圆周角定理距之间的关系圆心角、弧、弦、弦心垂径定理及推论基本性质三点定圆定理点与圆的位置关系定义圆的有关性质圆 一、圆及与圆相关的概念 二、圆的对称性 （1）圆既是轴对称图形，又是中心对称图形。 （2）对称轴——直径所在的直线，对称中心——圆心。 三、垂径定理 垂径定理：垂直于弦的直径平分弦且平分弦所对的弧。 推论1：平分弦（不是直径）的直径垂直于弦，并且平分弦所对的两条弧； 知2推3定理：①AB是直径②AB CD ⊥③CE DE =④弧BC=弧BD⑤弧AC=弧AD 推论2：圆的两条平行弦所夹的弧相等。 四、圆心角定理 圆心角定理：同圆或等圆中，相等的圆心角所对的弦相等，所对的弧相等，弦心距相等。 知1推3定理： ①AOB DOE ∠=∠；②AB DE =；③OC OF =；④弧BA=弧BD 五、圆周角定理 1、圆周角定理：同弧所对的圆周角等于它所对的圆心的角的一半。 2、推论： 1：同弧或等弧所对的圆周角相等；同圆或等圆中，相等的圆周角 所对的弧是等弧； 2 对的弦是直径。 3：若三角形一边上的中线等于这边的一半，那么这个三角形是直角 三角形。 六、圆内接四边形 圆的内接四边形定理：圆的内接四边形的对角互补，外角等于它的内 对角。 七、点与圆的位置关系 1、点在圆内? d r ?点A在圆外； 八、三点定圆定理——三角形外接圆 1、三点定圆：不在同一直线上的三个点确定一个圆。 2、三角形的外接圆：经过三角形的三个顶点的圆叫做三角形的外 接圆。 3、三角形的外心：三角形的外接圆的圆心是三角形三条边的垂直平分线的交点，它叫做这个三角形的外心。 九、直线与圆的位置关系 1、直线与圆相离?d r >?无交点； 2、直线与圆相切?d r =?有一个交点； 3、直线与圆相交?d r 《圆》题型分类资料 一．圆的有关概念： 1.下列说法：①直径是弦②弦是直径③半圆是弧，但弧不一定是半圆④长度相等的两条弧是等弧，正确的命题有（） A. 1个 B.2个 C.3个 D.4个 2．下列命题是假命题的是（） A．直径是圆最长的弦B．长度相等的弧是等弧 C．在同圆或等圆中，相等的圆心角所对的弧也相等 D．如果三角形一边的中线等于这条边的一半，那么这个三角形是直角三角形。 3.下列命题正确的是（） A．三点确定一个圆B．长度相等的两条弧是等弧 C．一个三角形有且只有一个外接圆D.一个圆只有一个外接三角形 4.下列说法正确的是( ) A．相等的圆周角所对的弧相等B．圆周角等于圆心角的一半 C．长度相等的弧所对的圆周角相等D．直径所对的圆周角等于90° 5.下面四个图中的角，为圆心角的是( ) A．B．C．D． 二．和圆有关的角： 1. 如图1，点O是△ABC的内心，∠A=50 ，则∠BOC=_________ 图1 图2 2.如图2，若AB是⊙O的直径，CD是⊙O的弦，∠ABD=58°，则∠BCD的度数为( ) A.116° B.64° C. 58° D.32° 3. 如图3，点O为优弧AB所在圆的圆心，∠AOC=108°，点D在AB的延长线上，BD=BC，则∠D的度数为 A 图3 图4 4. 如图4，AB、AC是⊙O的两条切线，切点分别为B、C，D是优弧BC上的一点，已知∠BAC＝80°， 那么∠BDC＝_________度． 5. 如图5，在⊙O中，BC是直径，弦BA，CD的延长线相交于点P，若∠P＝50°，则∠AOD＝． A 图5 图6 6. 如图6，A，B，C，是⊙O上的三个点，若∠AOC＝110°，则∠ABC＝°． 7.圆的内接四边形ABCD中，∠A：∠B：∠C=2：3：7，则∠D的度数为。 8. 若⊙O的弦AB所对的劣弧是优弧的 1 3 ，则∠AOB＝ . 9.如图7，AB是⊙O的直径，C、D、E都是⊙O上的点，则∠1＋∠2=________ A 图7 图8 10.如图8，△ABC是O的内接三角形，点C是优弧AB上一点（点C不与A，B重合），设OABα ∠=，Cβ ∠=（1）当35 α=时，求β的度数； （2）猜想α与β之间的关系为 11.已知：如图1，四边形ABCD内接于⊙O，延长BC至E，求证：∠A+∠B C D=180°，∠DCE=∠A； 如图2，若点C在⊙O外，且A、C两点分别在直线BD的两侧，试确定∠A+∠BCD与180°的大小关系； 中考英语重点知识归纳 一.常使用动词不定式的短语 1. It’s time to do sth.\ It’s time for sth 该作某事的时候了. 2. can’t wait to do sth. 迫不及待要作某事 3. Ask /tell sb. (not ) to do sth. 要求/告诉某人(不)作某事 4. Allow sb. to do sth. 允许某人作某事 5. Be supposed to do sth. 应该作某事 6. Would like /want (sb.) to do sth. 想要作某事 7. Have sth/nothing to do 有…时要做/与…无关 8. Find it +adj. to do sth. 发觉作某事… 9. Prefer to do sth. rather than do sth. 宁愿作某事,而不愿作某事 10. It’s +adj. for/of sb. to do sth. 作某事对某人来说… 11. It’s better /best to do sth. 最好做某事 12. It takes sb. st. to do sth. 某人做某事用了一些时间 二.常用动名词的短语 13. Enjoy /like /love/hate /be fond of doing sth. 喜欢做某事 14. Keep /keep on /carry on / go on doing sth. 继续做某事 15. Feel like doing sth. 想要做某事 16. Practice doing sth. 练习作某事 17. Give up doing sth. =stop doing Sth. 放弃作某事 18. Be good at/ do well in doing sth. 擅长作某事 19. Pay attention to doing sth. 注意作某事 20. What about/ how about doing sth. ….怎么样(好吗) 21. Thank you for doing sth. 为…感谢某人 22. Mind doing sth. 介意作某事 23. Be used for doing sth./ be used to do sth. 被用来作某事 24. Spend …(in) doing sth. 花时间作某时 25. Be busy doing/ with sth. 忙于作某事 26. Finish doing sth. 作完某时 27. Make a contribution to doing sth. 在…做贡献 28. Look forward to doing Sth. 29. Prefer doing sth. to doing sth. 喜欢…胜过… 30. Be/get used to doing sth. 习惯作某事 31. Keep / stop/ prevent sb. from doing sth. 阻止某人作某事 32. have problems/ difficulty (in) doing sth.做某事有….麻烦 三.省略动词不定式的短语 33. 一感二听三使役四看半帮助 34. See/ hear/ feel/ notice/ look at /listen to sb. do sth. 看见/听见/感觉/注意某人作某事 《圆》中考数学知识点_中考数学知识点总结 一、圆的基本性质 1.圆的定义(两种) 2.有关概念：弦、直径;弧、等弧、优弧、劣弧、半圆;弦心距;等圆、同圆、同心圆。 3.“三点定圆”定理 4.垂径定理及其推论 5.“等对等”定理及其推论 5.与圆有关的角：⑴圆心角定义(等对等定理) ⑵圆周角定义(圆周角定理，与圆心角的关系) ⑶弦切角定义(弦切角定理) 二、直线和圆的位置关系 1.三种位置及判定与性质： 2.切线的性质(重点) 3.切线的判定定理(重点)。圆的切线的判定有⑴…⑵… 4.切线长定理 三、圆换圆的位置关系 1.五种位置关系及判定与性质：(重点：相切) 2.相切(交)两圆连心线的性质定理 3.两圆的公切线：⑴定义⑵性质 四、与圆有关的比例线段 1.相交弦定理 2.切割线定理 五、与和正多边形 1.圆的内接、外切多边形(三角形、四边形) 2.三角形的外接圆、内切圆及性质 3.圆的外切四边形、内接四边形的性质 4.正多边形及计算 中心角： 内角的一半：(右图) (解Rt△OAM可求出相关元素,、等) 六、一组计算公式 1.圆周长公式 2.圆面积公式 3.扇形面积公式 4.弧长公式 5.弓形面积的计算方法 6.圆柱、圆锥的侧面展开图及相关计算 七、点的轨迹 六条基本轨迹 八、有关作图 1.作三角形的外接圆、内切圆 2.平分已知弧 3.作已知两线段的比例中项 4.等分圆周：4、8;6、3等分 九、基本图形 十、重要辅助线 1.作半径 2.见弦往往作弦心距 3.见直径往往作直径上的圆周角 4.切点圆心莫忘连 5.两圆相切公切线(连心线) 6.两圆相交公共弦 感谢您的阅读！最新中考英语知识点汇总
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