上海市杨浦、虹口、宝山、普陀、松江五区2021届九年级上学期期末(中考一模)英语分类汇编：书面表达
上海市杨浦、虹口、宝山、普陀、松江五区
2021届九年级上学期期末（一模）英语试题分类汇编
书面表达
上海市杨浦区2020-2021学年度第一学期九年级期末质量调研英语试题 VII. Writing(作文)
78. Write at least 60 words on the given situation.(根据以下情境写一篇不少于 60 个词的短文， 标点符号不占格。
)
法国“蜘蛛人“ 阿兰.罗伯特的经历告诉我们， 战胜恐惧也可以是一种勇敢。
你对勇敢的理解是如何的呢? 请以“The time I was bra ve(那次我很勇敢)” 为题，根据自身的经历谈谈你对勇敢的理解。
（注意： 1，短文中不得出现考生的姓名、校名等个人信息，否则不予评分。
2
，
照
抄
阅
读额
语篇不得 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 答案： 上海市虹口区
2021届九年级上学期期终学生学习能力诊断测试（一模）英语试题 V Ⅱ. Writing.
78. Write at least 60 words on the topic “Happiness does n’t always disappear during
difficult times ”
（以“在困难时期，幸福感不一定会消失”为题写一篇不少于 60 个词的短文，标点符号不占格）
小到个人，大到团队、城市、国家，都会有困难时期，但即便是困难时期，人们还是能感受生活中的小喜悦，感受幸福温馨的片刻，请结合自己或他人的经历，说说困难时期的幸福感。
（注意：短文中不得出现任何人名、校名及其他相关信息，否则不予计分）
（题目）
_______________________________________________________________________________________________________________________________________________________________________________________________________________
答案：
上海市宝山区2021届九年级上学期期末（一模）英语试题
VII. Writing (作文）（共20 分）
94.Write at least 60 words about the topic “ An act of kindness”.(以“一个善意的举动”为题写一篇不少于60 个词的短文，标点符号不占格。
）
“ 赠人玫瑰，手有余香”。
意思是一件很平凡微小的事情，哪怕如同赠人一只玫瑰般微不足道，但它带来的温馨都会在赠花人和爱花人的心底慢慢升腾、弥漫。
因此，善待他人也是善待自己，请结合生活中的一次真实经历，谈一谈你对善良的看法。
（注意：1. 短文中不得出现任何真实人名、校名及其它相关信息，否则不予评分。
2. 照搬阅读语篇内容不得分。
）
The following is for reference only. (以下表达仅供参考）
●have trouble with/doing
●give a help hand....
●treat sb with kindness.....
_______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 答案：
上海市普陀区2021届九年级上学期质量调研（一模）英语试题
VI. Writing （作文）（共20 分）
84. Write at least 60 words on the topic "I can be a winner"【以"我可以成为赢家"为题, 写一篇不少于60 词的短文, 标点符号不占格】
提示∶马拉松爱好者Allen的人生经历告诉我们∶每个人都能够在某方面取得成功。
请结合具体自己的经历谈谈你对这一观点的认识。
（注意∶短文中不得出现任何人名、校名及其他相关信息, 否则不予评分。
照抄语篇不得分）
_______________________________________________________________________________ _______________________________________________________________________________
_______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________答案：
1.审题:
这次普陀区一模"I can be a winner"是全命题式的作文，在审题时要注意人祢〔I）、时态和文体〔夹叙夹议）三个方面。
本次作文对中考有很大参考意义的一点在于出题思路，在2020中考中，阅读的D篇与作文主题一脉相承，同时文体上也是夹叙夹议，要求考生结合
自己的经历谈看法，考试中如果没有结合具体的事例，只是空谈想法和道埋，将会失分很多。
2结构与表达∶参考表达结构
松江区2020学年度九年级第一学期英语期末试卷
VII. Writing （作文）（共20分）
94. Write at least 60 words according to the following information.
虽然写给地球人的一封信中所提及到的问题确实存在, 但是我们人类正在努力改变现状。
相
信你也看到身边的变化或感受到自己的变化了。
请选取其中的一个题目A change around me （我身边的变化）或A change about me（我的变化）, 写一篇不少于60词的短文, 标点符号不占格。
注意∶1、短文中不得出现真实姓名和校名及其它相关信息, 否则不予评分。
2、照抄阅读语篇不得分。
_______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________。
上海市松江区2021—2022学年九年级上学期期末(中考一模)考试语文试卷(word版 含答案)
上海市松江区2021—2022学年九年级上学期期末（中考一模）考试语文试卷（满分：150分，完成时间：100分钟，在答题纸上完成）2022.1一、文言文（36分）（一）默写（12分）1.东风不与周郎便，（杜牧《赤壁》）2.知困，（《虽有嘉肴》）3. ，一任群芳妒。
（陆游《卜算子·咏梅》）4.问君何能尔？（陶渊明《饮酒》）5.深秋的早晨，同学们看到田野和房屋上薄雾缭绕，而东方已是一片绯红。
甲生说：这便是《答谢中书书》中描绘的“”的画面；乙生说：可惜没有文中早晨“”的热闹场景啊。
（二）阅读下列诗文，完成第6-12题（24分）【甲】石壕吏（节选）暮投石壕村，有吏夜捉人。
老翁逾墙走，老妇出门看。
吏呼一何怒！妇啼一何苦！听妇前致词：三男邺城戍。
一男附书至，二男新战死。
存者且偷生，死者长已矣！室中更无人，惟有乳下孙。
有孙母未去，出入无完裙。
【乙】（节选）见渔人，乃大惊，问所从来。
具答之。
便要还家，设酒杀鸡作食。
村中闻有此人，咸来问讯。
自云先世避秦时乱，率妻子邑人来此绝境，不复出焉，遂与外人间隔。
问今是何世，乃不知有汉，无论魏晋。
此人一一为具言所闻，皆叹惋。
余人各复延至其家，皆出酒食。
停数日，辞去。
此中人语云：“不足为外人道也。
”【丙】子奇治阿子奇年十六，齐君使治阿①.既行，齐君悔之，遣使追。
追者反曰：“子奇必能治阿，共载皆白首也。
夫以老者之智，以少者决之，必能治阿矣！”子奇至阿，铸库兵以作耕器，出仓廪以赈贫穷，阿县大治。
魏闻童子治邑，库无兵，仓无粟，乃起兵击之。
阿人父率子，兄率弟，以私兵战，遂败魏师。
【注】①阿：地名，今山东阿县。
②白首：老年人。
③决：决断（政事）。
6.甲诗的作者是（人名），乙节选语段出自课文《》。
（2分）7.解释下列句中加粗词（4分）（1)遣使追（）（2)铸库兵以作耕器（）8.用现代汉语翻译下面的句子（3分）余人各复延至其家9.对文中划线句翻译正确的一项是（）（3分）A 走出粮仓去救济贫穷的百姓，全面治理阿县。
2021年上海中考英语一模阅读B篇完型填空汇编
上海市16区2021届九年级上学期期末（一模）英语试题分类汇编完形填空上海市杨浦区2020-2021学年度第一学期九年级期末质量调研英语试题B.Choose the best answer and complete the passage.Shawn and his class were working on a new assignment. They were writing persuasive（劝说的）articles. When Shaw first learned about the assignment, he was 65 . Shawn disliked writing articles, and he wasn’t sure how to go about planning and writing a powerful article that would persuade someone to do something. So he asked Mr. Matthews for extra help planning his article.Mr. Matthews suggested that Shawn begin by selecting a 66 that wasimportant to him. Shawn wanted to be on the football team, so he decided towrite a paper explaining why he should be on the team. 67 , Mr. Matthewssuggested that Shawn list the strongest and best reasons that would persuadepeople. When Shawn had listed his reasons, he was ready to start writing.Shawn began with his main point—that he should be allowed to be on the football team. Then, he explained why he should be on the team, using the reasons he had listed. After that, he wrote the 68 -end of the paper. After Shawn had his draft（草稿）finished, he was ready to revise what he had written.Shawn read the paper to himself and to his parents. His mom and dad suggested ways and ideas that he could revise the paper to make his arguments stronger. Then, Shawn read the paper again. This time, he 69 a few ideas himself. After the revision was finished, it was time to edit.Shawn read the paper 70 to be certain that he had spelled everything the way it should be spelled. He also checked his paper for grammatical mistakes.The paper was written well enough that Mr. Matthews gave him a very good grade. The football coach read Shawn’s paper, too, and was so convinced by Shawn’s reasons tha t he permitted Shawn to work with the team!65. A. relaxed B. unhappy C. confident D. embarrassed66. A. hobby B. team C. topic D. character67. A. Next B. In addition C. However D. As a result68. A. plots B. details C. title D. conclusion69. A. reported B. thought of C. arranged D. focused on70. A. aloud B. properly C. carefully D. immediately答案：65-70 BCADBC上海市虹口区2021届九年级上学期期终学生学习能力诊断测试（一模）英语试题B. Choose the words or expressions and complete the passage.Arrest Report Sheet NAME OF SUSPECT（嫌疑犯）：Mr. John A. Berry65 FOR ARREST：Use of bad language in a public place.●Wasting a police off icer’s time.●Damaging property and causing 66 to the public.●There was something I didn’t like about him.DETAILED REPORT OF THE EVENTS LEADING UP TO THE ARRESTThe suspect came into Mean Street Police Station at 4:37 p.m. on Wednesday, February 15th, claiming（声称）to have lost his car. Of course, this story did not satisfy a police officer like myself, and I 67 started to question the suspect. After about 45 minutes, he changed his story, claiming that the car had been stolen. Something about this story, too, 68 extremely unlikely and I refused to accept it.The suspect kept telling his story. Luckily, I took a useful and 69 training course last weekend. So I used the active questioning skills from the course to get the real truth out of him.When he finally 70 under my questioning, he admitted that he had parked his car in a no-parking zone, and then blown it up（爆炸）. I have not yet worked out why he did this; my theory is that he is a mentally ill terrorist who sees parking rules as a symbol of everything he hates most in modern society.SignedDetective—Inspector Philip E. Morris65. A. REASONS B. CAUSES C. SUGGESTIONS D. EXCUSES66. A. excitement B. surprise C. danger D. variety67. A. politely B. immediately C. suddenly D. correctly68. A. looked B. tasted C. felt D. sounded69. A. noisy B. boring C. comfortable D. enjoyable70. A. broke down B. woke up C. shut up D. calmed down答案：65-70ACADDA上海市宝山区2021届九年级上学期期末（一模）英语试题B.Choose the words or expressions to complete the passage.Most people hate change, which is sad since we often go throughchanges in life. And for some of us, even the Smallest changes can upsetour day. So, the question is: Why do most of us find making adjustments（调整）to our lives so hard?Why we dislike changeFear of change is 75 new. Over a century ago, people in Paris were unhappy over an unusual addition to their city: the Eiffel Tower. In fact, the citizens were so angry about the plans for the tower that they were against its construction（建造）. As strange as it may seem, their anger was completely76 . They were given no choice about the huge change that was going to be made, so they became angry. But we get upset over changes even when we do have to a say in the matter. Changes are brought about every day by the decisions we make: which school to attend, which job to take. V oluntary（出于自愿的）changes also make most of us uneasy because we don’t know how those changes will 77 our future.How we can overcome our fear of changePeople have discovered that the key to overcoming the fear of change is to be flexible. When people are flexible, they can 78 new situations more easily. Being flexible is especially important in the 21st century as technology makes change occur faster than ever before. Those who were against change, especially with technology in the workplace, may end up finding themselves out of a job.When change comes, and you have no choice but to 79 it. A positive（积极的）attitude helps a lot. In fact, the change may turn out to be the best thing for you. That new job you got may end up being much better than your old one. You may make the best friends of your life in the new city you moved to. 80 , don’t just focus on how you feel about change. You should learn to accept the change. The change is the reality and it’s up to you to decide whether the change will be a success or a failure. You never know—your next change may be your life’s Eiffel Tower!75. A. something B. anything C. everything D. nothing76. A. important B. natural C. unusual D. ordinary77. A. assist B. reward C. affect D. arrange78. A. be aware of B. get used to C. be interested in D. get rid of79. A. forget B. make C. face D. refuse80. A. However B. What’s more C. Besides D. Therefore答案：75-80DBCBCD上海市普陀区2021届九年级上学期质量调研（一模）英语试题B. Choose the best answer and complete the passage （选择最恰当的选项完成短文）（12分）If you live on the streets with little food and money, what will you do with a bag filled with snacks and nearly￡500 in cash in front of you? To most people. it would be a source of temptation （诱惑）Something that happened last month has made the actions of the homeless Roy Kaufman out of the ordinary.Roy saw a 65 on the front seat inside a parked car with its window down. He stood guard inthe rain for along time waiting for the owner to_66 . Because of the coldness, he reached inside and pulled the bag out. He hoped to find some cards with its owner's name or phone numbers so that he could 67_ the driver. But he only discovered it contained some bars of chocolates and￡435 in notes, with another￡50 in spare change beside it.He then took it to a nearby police station after leaving a note behind to let the owner know it was 68 . When the car's owner Mr. Anderson returned to the car, he was shocked to find two policemen standing next to it and he was told what Roy Kaufman did.Mr. Anderson was later able to thank Mr. Smith for his _69_ and said, "I couldn't believe that the man never took a penny. The man has nothing and yet he didn't take the money for himself. He thought about others instead of himself. It's unbelievable. It just proves there are _70_ men out there. "Roy Kaufman's act drew much of the public's attention. He also won praise from social media users after Mr. Anderson posted about the story on Facebook.Now Mr. Anderson has set up an organization to raise money for other homeless people in the area. For Roy Kaufman, this is a possible life-changingchance. The story once again ells us that one good turn deserves another.65. A) report B) bag C) list D) symbol66. A) apologize B) drop C) investigate D) return67. A) contact B) reward C) refuse D) greet68. A) strange B) lost C) safe D) empty69. A) encouragement B) support C) kindness D) opinion70. A) generous B) honest C) poor D) polite答案：65 B 66 D 67 A 68 C 69 C 70 B松江区2020学年度九年级第一学期英语期末试卷B. Choose the best words and complete the passage（选择最恰当的单词完成短文）（12分）Amy and Susan both live an average life. They have an average house, an average job and an average family. There is really nothing _75_ about their lives, but there is also nothing really negative （负面的）about their lives.However, when they are both happy, it always seems that Amy is happier than Susan. It looks like nothing can _76_ Amy. She is the life of the party and always has a big smile on her face.Susan can't stop thinking about this. How is Amy so happy when they both lead such _77_ lives? They go to the same stores, watch the same movies, and even have the same schedules! How can Amy be so carefree when life is so stressful?Between one's daily life and personal dreams, there is no way one can be so happy and stress free all the time. There are always a million things going on.But when Susan asks Amy about this, Amy says, "I just take life as it comes. It seems pretty easythen. "So what is the _78_ between these two friends? How is it that Amy's life seems so much better most of the time?The problem with Susan is that she spreads herself too thin（试图同时干太多的工作）. Not _79_, but in her own head. But although Amy tries to do everything at once and think about everything at once, she takes everything one step _80_. She is where she is, stays present in the moment and allows herself to focus on just one thing.When you live each moment to its fullest, when you deal with where you are and are present in the now, most of your stress will go away.75. A) boring B) common C) special D) disappointing76. A) attract B) trouble C) change D) encourage77. A) similar B)successful C) traditional D)wonderful78. A) link B)relationship C) contact D)difference79. A)physically B) rarely C) correctly D) suddenly80. A) on time B)for the time being C) at a time D) from time to time答案：75.C 76. B 77.A 78.D 79.A 80.C2021奉贤一模Choose the words and complete the passage（选择最恰当的单词，完成短文）Dogs bury bones. Squirrels gather nuts to last through the winter. Camels store food and water so that they can travel many days across deserts. But do pigs save anything? No, pigs save nothing. So why do we save coins in a piggy bank? Because someone made a mistakeDuring the Middle Ages（中世纪）, in about the fifteenth century, metal was 65 and seldom used for household wares（家用器具）. Instead, dishes and pots were made of a kind of economical clay called pygg. Whenever housewives could save an extra coin, they dropped it into one of their clay jars. They call this their pygg bank or pyggy bank.Around the eighteenth century, the spelling of pygg changed. The word 66 the same as the word for the animal pig. Over the following 200 to 300 years, people 67 that pygg meant the clay. And the term "pygg jar" gradually changed into pig bank, or piggy bank.In the nineteenth century, when English potters received requests for piggy banks, they misunderstood. They produced jars shaped like a pig. 68 , the pigs became popular among customers and delighted children.Another reason for the name "piggy bank" is 69 the idea that the coin given to the piggy bank represent the food fed to a pig by a farmer. It costs the farmer money to feed the pig and he doesn't 70 until the pig is slaughtered（屠宰）for meant, which is known as "breaking the piggy bank."Today, pigs are still one of the most popular forms of coin banks sold in gift shops.65. A. cheap B. expensive C. heavy D. light66. A. looked B. smelt C. sounded D. felt67. A. forgot B. forgave C. remembered D. realized68. A. Importantly B. Suddenly C. Sadly D. Certainly69. A. similar to B. based on C. famous for D. made of70. A. turn it over B. take it awayC. get it back D. work it out答案：65-70 BCADBC2021崇明一模B. Choose the words or expressions and complete the passage (选择最恰当的单词或词语完成短文) (12分)Animals can move from place to place, but plants cannot. When an animal is under attack, it can run away or 65. Plants certainly cannot run away, and they have no teeth or claws. But plants can protect themselves by using both physical and chemical means(方法)Some plants have their own ways to keep animals 66 For example, the leaves of the holly plant have sharp points that discourage (打消:阻止) grass eating animals. Holly leaves on lower branches have more sham points than leaves on upper branches. This is because the lower leaves are 67 for most animals to reach,Some plants, such as the oak tree, have special ways to discourage leaf-cating animals. They have thick and hard leaves that are 68 for animals to eat Some grasses may contain a sandy material; eating such grasses wears down the animal’s teeth.Many plants also have chemical defenses. Some plants produce chemicals that taste bitter or cause an unpleasant reaction Some plants may fight against a(n) 69 by increasing the production of these chemicals. When an insert bites a tobacco leaf, the leaf produces a chemical messenger(信使) This messenger sends to the roots the information to produce more nicotine The higher levels of nicotine discourage the insect.Many plants 70 both physical and chemical defenses A certain plant in China, for example, has sharp leaves, and each sharp leaf contains p oisonous venom (毒液) A single experience with this kind of plant will leach an animal not to eat the leaves of it in the future.65. A) calm down B) come back C) fall asleep D) fight back66. A) away B) warm C) safe D) crazy67. A) sweeter B) easier C) bigger D) greener68. A) important B) convenient C) difficult D) delicious69. A) attack B) illness C) storm D) flood70. A) pay for B) learn from C) search for D) rely onKey: DABCAD黄浦一模B. Choose the best answer and complete the passage(选择最恰当的选项完成短文)(1 分)The National Gallery in London has introduced an “art route” that people must follow round the gallery. Are set routes actually a better way to enjoy museums and galleries? Or should people be 75 to view exhibitions in any order they choose? What do you think - are set routes better?Yes - people will get more from their visitExperts spend years learning about the items in their museums and galleries. They know the best order in which people should see the exhibits, so that visitors can enjoy and learn about them. 76. if there was an exhibition of a painter, the works could be arranged to show visitors how their style developed through their career. If a person is on an art route, they won’t 77 any important pictures, and will be guaranteed to see everything. The experience will be enjoyable for the visitor, and they will have their own space in which to appreciate great works.No - freedom is part of the funMost exhibitions are already 78 in some kind of order. However, not everyone wants to look at the same things in the same way. Some visitors just want to enjoy a few pieces and then leave. Besides, if everyone follows the same route, some people might take a long time looking at one object and 79 everyone down. Equally, if a visitor wants to study something for more time, they may feel pressured by people behind them. One of the great joys of exhibitions is 80 noticing something. When a visitor is drawn to an object, it can feel special and they can learn about it by themselves. If everyone is following the same route, this is less likely to happen, so the experience will not be as much fun.75. A) ready B) able C) free D) thankful76. A) In fact B) For example C) In addition D) That is to say 77. A) forget B) fail C) lose D) miss78. A) laid out B) put away C) dealt with D) turned on 79. A) put B) slow C) take D) break 80. A) carefully B) silently C) suddenly D) peacefully Key:75. C 76. B 77. D 78. A 79. B 80. C2021嘉定一模B. Choose the words or expressions to complete the passage (选择最恰当的单词或词语，完成 短文)(12分)Some people volunteer to gain experience. Some people volunteer to make themselves feel better. Some people volunteer to help those who were (65)______. However; I volunteer to thank my community. I am thankful for the help I received from others.When I was in high school, I took part in the Upward Bound Program. Through Upward Bound, I was able to gain skills and opportunities that have helped me become the man that I am today. So I now often give back to enable kids to have the same(66)______ at life that I have had.V olunteering is the best way to thank those who helped me on the road to success. I remember asking a counselor(顾问)when I was in Upward Bound how I could repay him. He smiled and said, "Shawn, you can help me by helping others?* A sentence so simple, yet so (67)______in its meaning.When I got my first volunteer position as a junior counselor at my local Boys and Girls Chib, I was eager to be a great role model for kids. But things did not work out as I thought at first I got so (68)______ .By the time I was ready to (69)______ , the kids looked for me everywhere that day. They said they liked having me around.My desire to give back to the community came back. Now the feeling that I can shape someone's life for the better is amazing.So it is a good idea for everyone to find a(an)(70)______ and volunteer. In this way not only will you be helping others, you will be helping yourself as well. Key:65-70 CAB BCC 2021金山一模B. Choose the best answer and complete the passage(选择最恰当的单词或短语，完成短文)（12分）Most people have heard of the Great Wall of China, but not many foreigners know about the Grand Canal. This man-made waterway —known in China as DaYunhe —is 1,700 kilometers long and some parts of it are more than 2,000 years old. It (65) the north of China with Hangzhou, a city in the southern part of the country. It's the longest man-made waterway in the world.It was built as a(66) to transport grain from the rich agricultural land in China's south to cities in the north. In fact, it's not one canal, but a system of canals and rivers linked (67) . It's still an important part of the transport system in China.Thousands of boats use it every day to transport grain and many other types of cargo.65. A) active B) honest C) unfortunate D) helpful 66. A) chance B) courage C) decision D) stress 67. A) strange B) deep C) funny D) different 68. A) excited B) disappointed C) satisfied D) proud 69. A) turn up B) wake up C) give up D)put up 70. A) exampleB)causeC) excuseD)solutionNow the Chinese government is doing new work on the Grand Canal.It is making parts of it (68) , so bigger ships can use it. The canal will also help to move water. There is a lot of (69) in the south of China, but not (as much) in the north. The canal will carry millions of liters of water from the south to the north.The Grand Canal is much(70) than the Great Wall, and not very many tourists visit(it). But it's possible to go on a cruise along some of the oldest parts of the canal. Passengers on these cruises see beautiful parts of China that other visitors don't see.60.A. compares B. connects C. controls D. communicates61.A. result B. trick C. way D. sample62.A. together B. instead C. along D.forward63.A. cleaner B. prettier C. longer D. deeper64.A. food B. population C. rain D. electricity70. A. smaller B. narrower C.less modem D.less famousKey:65-70 BCADCD2021静安一模B. Choose the words or expressions and complete the passage (选择最恰当的单词或词语完成短文)(12分)You can think of a memory, as a photograph. Our brain is like an app on the phone that stores useful photographs lor a long time. But il 75 useless photographs. Some people have always been able to recall(回想起)the smallest details about their lives. The experts are now studying Brad Williams and a woman named A.J. The two share the same talent. The goal of the study is to gain a deeper 76 of memory and how it works.Dr. James found 51-year-old Williams’ memory to be 77 perfect. He can usually tell you what he did on a certain date 40 years ago. He can also recall what was in the news. He can even tell you what the weather was like.Dr. James had seen this level of ability before. In 2006, he studied a woman named A.J. She too was able to recall tiny details from her life. These details 78 notes she had written in journals decades earlier.However, they view the ability differently. Williams enjoys having his memory tested. A.J., however, said her memories often flood her mind in an unpleasant way. “Most have called it a gift, but I call it a burden,” A.J wrote. “I run my entire life through my head every day and it makes me 79 !!!”Now, doctors are testing Williams and A.J. They want to know what sets the two apart from others. Williams and A.J. both perform well. But they perform best on topics that interest them. This fact causes doubt among some scientists. They suggest that Williams and A.J. are not so special 80. Some scientists say that people with truly special memories should be able to remember all kinds of information, not just what interests them.Dr. James hopes that his study will provide answers for both those who doubt and those who surprise at what Williams and A.J. are able to do. “The human brain is the most important machinery in the known universe,” he said. “My aim is to decrease the mystery of this surprising machinery.”75. A) gives up B) gets rid of C) picks up D) keeps off76. A) confidence B) entrance C) speed D) understanding77. A) rarely B) exactly C) nearly D) mainly78. A) created B) recorded C) added D) matched79. A) crazy B) excited C) flexible D) pale80. A) after all B) at present C) in the end D) at a timeKey:75-80 BDCDAA2021闵行一模B. Choose the words or expressions and complete the passage (选择最恰当的单词或词语完成短文)(12分)Manners Around the WorldEvery culture has set rules about how people should act. Patterns of good behavior, or manners, show respect and care for others. Yet the details of 65 to express respect are so different.Greeting people cheerfully is almost always considered polite. But ifs more important in some cultures than others. For example, when you enter a store in France, you, should always greet the person working there. Other cultures also 66 greeting people. But of course the greetings vary as people speak different languages.When I was growing up in the United States, I once, took part in a performance at my church. Afterwards, someone gave me a compliment；but I felt like I had done a bad job. So I tried to refuse the compliment, saying, "No, I didn’t do that well." My mother stopped me and told me that was very 67. Later I learned that refusing a compliment is accepted in China.Some of the biggest cultural differences have to do with 68. In North America, ifs polite to eat as quietly as possible. That means chewing with your mouth closed and not slurping your soup. The same goes for burping (打嗝).But in parts of Asia, slurping shows that you are enjoying your meal. And burping is a sign of being full and content.There are also differences in how people，eat across cultures. 69, in North America and Europe people use forks to bring food to their mouths. But in Thailand, a fork is only used to push food onto a spoon. In India and the Middle East, people eat with their hands. But eating with the left hand is frowned upon. This is because the left hand is considered unclean.Yet there are also similar points across cultures. Saying “please” and “thank you” is almost always polite. If you show appreciation and try to 70 local customs, people will generally respond well. Showing kindness can bring people together, no matter what culture they come from.()65. A) what B) how C) when D) where()66. A) mind B) avoid C) imagine D) value()67. A) rude B) simple C) common D) accurate()68. A) family parties B) table manners C) fashion tastes D) instruction signs()69. A) What’s more B) In short C) For example D) Above all()70. A) change B) develop C) follow D) mentionKey: BDABCC2021浦东一模B. Choose the best answer and complete the passage(选择最恰当的选项完成短文)（12分）One night before bed, Christine Carter was sitting with her daughter in her bedroom. They were making a list, "Three Good Things of the Day."Her daughter said," Mom, chatting with you is one of my three good things."Making a list was their way to think of things they were (65) ______ for. It's a skill in the research of happiness.Carter is a professor at the University of California. She studies how schools and families build up positive attitudes and help kids lead (66) ______ lives. This has become especially important during the coronavirus pandemic (新冠病毒引发的流行病). Many kids have missed important events. Some even have lost people in their lives.Finding the positive things sometimes doesn’t mean people won’t be sad any more. You' ll find it natural to fee l sad, but it passes more (67) ______ if we notice the good things in life."This is really about mental health,"Carter says."We can practise bringing happiness to ourselves. It's like putting money in the bank. We can deal with hard times in the future."Expressing thanks is also important. Carter says,"Let’s say you often argue with a brother or a sister. Think about whether they did something good for you or with you. Remember the good times. This makes it likely you’ll (68) ______ better tomorrow."A key step toward happiness is learning how to describe emotions, even negative ones. It' better to face your emotions than to (69) ______ them. Ask yourself, "How do I feel? Where in my body am I feeling it? Does it have a color or a shape?"The surest way to happiness is (70) ______,"Helping others gives life purpose because you are changing the world" Carter says, "Besides, people have a sense of connection and satisfaction. We are comfortable when were connected with other people."65.A. sorry B. ready C. famous D. thankful66. A. richer B. healthier C. busier D. freer67. A. quickly B. patiently C. strongly D. heavily68. A. go out B. get along C. show off D. grow up69 A. disturb B. forgive C. operate D. ignore70. A. entertainment B. ambition C. kindness D. freedomB篇：65-70 DBABDC2021青浦一模B. Choose the words or expressions and complete the passage(选择最恰当的单词或词语，完成短文)(12分)When you think of a journalist, do you see a reporter with a pen and paper? Writing is one way to tell a story, but some stories are told without (65)__________.Photojournalists are reporters too. They use a camera to capture a story in photographs (66)__________ a pen and paper. You can see their work in the pictures that appear with an article. Pictures help readers visualize the things being described. Photojournalists also create photo essays, which tell a story with photosAlice Aedy is a photojournalist and documentary filmmaker based in London, England. She specializes in stories about social justice and human rights, but she also covers (67)_________issues. Aedy said that she's “passionate about climate change” because of how it affects peoples livesPhotojoumalism helps people (68)__________current events by giving context to important moments in history. So photojournalists aren't just photographers. Theyre storytellers. Like other reporters, they need to be on the scene and able to interview people about what's happeningAedy has traveled the world to do her reporting. While working, she spends as much time as she can in the country where a story is taking place and does lots of interviews to get the full story. “I want my photos to build empathy(共鸣),” she says，“and make people care.”Aedy says that photography, like all forms of media, should be viewed “with a (69)________ eye.” Viewers sh ould ask themselves questions like “What is the context of the photo? When and where was it taken? Was the photo taken with the permission of its subjects? Why was it taken?”It's also important for viewers to take time to think about how a photograph make s them (70)__________. “We’re bombarded(轰炸) with images every day, ” Aedy says，“So my hope is that whatever you're looking at, you just truly engage.”65. A)words B)pens C)pictures D) writers66. A)in addition to B)instead of C)except for D)because of67. A)business B)environment C)technology D) entertainment68.A)watch B)hear C) explain D)understand69.A)critical B) close C)friendly D)real70.A)judge B)decide C)feel D) observeB篇：65-70ABBDAC2021徐汇一模B.Choose the words or expressions and complete the passage.Dan and Michelle sat at a picnic table in the park on a beautiful fall afternoon. The air around them was filled。
上海市宝山区2020-2021学年九年级上学期期末(中考一模)数学试卷带讲解
上海市宝山区2021届初三一模数学试卷一、选择题1. 如果C 是线段AB 延长线上一点，且:3:1AC BC =，那么:AB BC 等于（ ）．A. 2:1B. 1:2C. 4:1D. 1:4 【答案】A【分析】先画出图形，设BC 为k ，然后用k 表示出AB ，最后求出:AB BC 即可．【详解】解：根据题意可画出下图：∵:3:1AC BC =，设BC 为k ，∴AC=3k ，∴AB=AC-BC=2k ，∴:AB BC =2k∴k=2∶1．故答案为A ．【点睛】本题主要考查了线段的和差，根据题意画出图形成为解答本题的关键．2. 在Rt ABC △中，90C ∠=︒，5AB =，3BC =，那么sin A 的值为（ ）． A. 35 B. 34 C. 45 D. 43【答案】A【分析】根据正弦的定义解答即可．【详解】解：在Rt △ABC 中，∠C=90°，AB=5，BC=3，则sinA=35BC AB =， 故选：A ．【点睛】本题考查了锐角三角函数的定义，掌握锐角A 的对边a 与斜边c 的比叫做∠A 的正弦是解题的关键．3. 如图，//AB DE ，//BC DF ，已知::AF FB m n =，BC a =，那么CE 等于（ ）．A. am nB. an mC. am m n +D. an m n+【答案】D【分析】先证明：四边形DEBF 是平行四边形，可得DF BE =，利用::AF FB m n =，再求解AF m AB m n=+，再证明ADF ACB ∽，利用相似三角形的性质求解BE ，再利用线段的和差可得答案． 【详解】解： //AB DE ，//BC DF ，∴ 四边形DEBF 是平行四边形， DF BE ∴=，::AF FB m n =，AF m AB m n∴=+， //DF BC ，ADF ACB ∴∽AF DF AD AB BC AC∴==, //AB DE ，BE AD m BC AC m n∴==+， BC a =，ma BE m n∴=+， .ma na CE a m n m n ∴=-=++ 故选：.D4. 已知点M 是线段AB 的中点，那么下列结论中，正确的是（ ）． A. AM BM = B. 12AM AB = C. 12BM AB = D. 0AM BM +=【答案】B【分析】根据题意画出图形，因为点M 是线段AB 的中点，所以根据线段中点的定义解答．【详解】解：A 、AM MB =，故本选项错误；B 、12AM AB =，故本选项正确；C 、12BM BA =，故本选项错误； D 、0AM BM +=，，故本选项错误．5. 若将抛物线2y x 先向右平移1个单位长度，再向上平移2个单位长度，就得到抛物线（ ） A. 2(1)2y x =-+B. 2(1)2y x =--C. 2(1)2y x =++D. 2(1)2y x =+- 【答案】A【分析】根据二次函数图象左加右减，上加下减的平移规律进行解答即可．【详解】解：将抛物线2y x 先向右平移1个单位长度，再向上平移2个单位长度，就得到抛物线：()212y x =-+ 故答案为：A ．【点睛】本题考查二次函数的图象与性质，图象平移规律“左加右减，上加下减”是解题关键．6. 如图所示是二次函数()20y ax bx c a =++≠图像的一部分，那么下列说法中不正确的是（ ）．A. 0ac <B. 抛物线的对称轴为直线1x =C. 0a b c -+=D. 点()12,y -和()22,y 在拋物线上，则12y y >【答案】B 【分析】根据图象分别求出a 、c 的符号，即可判断A ；根据抛物线与x 轴的两个交点可判断出该抛物线的对称轴不是x =1，即可判断B ；把x =-1代入二次函数的解析式，再根据图象即可判断C ；将x =-2与x =2带入二次函数，可得出y 1与y 2的值，即可判断D ．【详解】解：∴二次函数图象开口向上，∴a ＞0，∴二次函数的图象交y 轴的负半轴于一点，∴c ＜0，∴ac ＜0 选项A 正确；∴由图像可看出，抛物线与x 轴的交点一个为x=-1，另一个在x=2和x=3中间，不关于x=1对称，∴抛物线的对称轴不是x=1 选项B 错误；把x=-1代入y=ax 2+bx+c 得：y=a-b+c ，由图像可知，x=-1时y=0，∴a-b+c=0 选项C 正确；把x=-2和x=2代入y=ax 2+bx+c 中，由图像可知，y 1＞0，y 2＜0，∴y 1＞y 2 选项D 正确；故选：B ．【点睛】本题考查二次函数的性质，解题的关键时熟练运用抛物线的图像判断系数a 、b 、c 之间的关系，同时注意特殊点与对称轴之间的关系，属于中等题型．二、填空题7. 如果2x ＝3y ，那么x y y+=___． 【答案】52【分析】直接利用已知得出x =32y ，进而代入得出答案． 【详解】解：∵2x =3y ，∴x =32y ， ∴3522y y x y y y ++==． 故答案为：52． 【点睛】本题主要考查了比例的性质，正确将已知变形是解题关键．8. 已知线段2a =厘米，8c =厘米，那么线段a 和c 的比例中项b 的长度为______厘米．【答案】4【分析】根据线段的比例中项可直接进行列式求解．【详解】解：由题意可得：22816b ac ==⨯=，∴4b =cm ；故答案为4．【点睛】本题主要考查比例中项，熟练掌握比例中项是解题的关键．9. 如果线段AB 的长为2，点P 是线段AB 的黄金分割点，那么较短的线段AP =______．【答案】3【分析】设较短的线段AP x =，则BP AB AP =-，根据黄金分割点的性质列方程并求解，即可得到答案．【详解】设较短的线段AP x =∵AB 的长为2∴2BP AB AP x =-=- ∴BP AP AB BP= ∴222x x x-=- ∴()222x x -=∴3x =+3（经检验均为方程的根）32+>，故舍去∵(22310x -=-=≠∴3x =-∴较短的线段3AP =故答案为：3【点睛】本题考查了黄金分割点、分式方程、一元二次方程、二次根式的知识；解题的关键是熟练掌握黄金分割点、分式方程、一元二次方程、二次根式的性质，从而完成求解．10. 计算：32a ba b ______． 【答案】54a b -【分析】根据向量的表示方法可直接进行解答．【详解】解：326354a ba b a b a b a b ， 故答案为：54a b -．【点睛】本题考查的是平面向量的知识，熟悉相关性质是解题的关键．11. 已知等腰梯形上底为5，高为4，底角的余弦值为35，那么其周长为______． 【答案】26【分析】作DF ⊥BC 于F ，AE ⊥BC 于E ，根据等腰梯形的性质就可以得出△AEB ≌△DFC 就可以求出FC=BE ，然后根据底角的余弦值为35，求得BE ，AB ，从而求出周长． 【详解】解：如图示，作DF⊥BC 于F ，AE⊥BC 于E ，∵四边形ABCD 是等腰梯形，∴∠B=∠C ，AB=CD ，AD ∥BC ，∴∠ADF=∠DFC=90°，∴∠AEF=∠DFE=∠ADF=90°，∴四边形AEFD 是矩形，5EF AD ，△AEB 和△DFC 中BC AEBDFC AE DF ， ∴△AEB ≌△DFC （AAS ），∴BE=CF ； ∵35cos E ABB B ， 设3BE x =，则5AB x =， 根据勾股定理，有：2222534AE AB BE x x ，解之得：1x =（取正值），∴3BE =，5AB =，∴3FCBE ，5DC AB ==， ⊥周长AB BE EF FC CD AD 53535526，故答案是：26．【点睛】本题考查了等腰梯形的性质的运用，三角函数，矩形的判定及性质的运用，等腰三角形的性质的运用，全等三角形的判定及性质的运用，能熟练应用相关性质是解题的关键．12. 某公司10月份的产值是100万元，如果该公司第四季度每个月产值的增长率相同，都为0)x x >（，12月份的产值为y 万元，那么y 关于x 的函数解析式是______．【答案】()21001y x =+；【分析】根据：现有量=原有量×(1+增长率)n ,即可列方程求解．详解】依题意得：()21001y x =+故答案为：()21001y x =+【点睛】考查了一元二次方程的应用，可直接套公式：原有量×(1+增长率)n =现有量，n 表示增长的次数． 13. 如果抛物线()21y m x m =++（m 是常数）的顶点坐标在第二象限，那么它的开口方向______． 【答案】向上【分析】根据解析式写出顶点，根据顶点坐标在第二象限求出m 的取值故可求解．【详解】∵抛物线()21y m x m =++的得到为（-1，m ）又顶点坐标在第二象限∴m ＞0∴开口向上故答案为：向上．【点睛】此题主要考查二次函数的性质，解题的关键是熟知顶点式的特点．14. 已知一条抛物线具有以下特征：（1）经过原点；（2）在y 轴左侧的部分，图像上升，在y 轴右侧的部分，图像下降；试写出一个符合要求的抛物线的表达式：______．【答案】2y x =-（答案不唯一）【分析】设出符合条件的函数解析式，再根据二次函数的图象在y 轴左侧部分是上升的，在y 轴右侧部分是下降的可知该函数图象的开口向下，对称轴为y 轴，即0a <，0b =，再把()0,0A 代入，得出符合条件的函数解析式即可．【详解】解：设出符合条件的函数解析式为：()20y ax bx c a =++≠， ∵二次函数的图象在y 轴左侧部分是上升的，在y 轴右侧部分是下降的，∴该函数图象的开口向下，对称轴为y 轴，即0a <，0b =，∵函数图象经过()0,0A ，∴0c ，∴符合条件的二次函数解析式可以为：2y x =-（答案不唯一）．故答案为：2y x =-（答案不唯一）．【点睛】本题考查的是二次函数的性质，先根据题意设出函数解析式，再根据二次函数的性质判断出a 的符号及对称轴是解答此题的关键，此题属开放性题目，答案不唯一．15. 如图，已知ABC 中，//EF AB ，12AF FC =，如果四边形ABEF 的面积为25，那么ABC 的面积为______．【答案】45【分析】根据//EF AB ，易得∴CFE ∽△CAB ，再依据相似三角形的面积比等于相似比的平方，即可求出三角形ABC 的面积．【详解】解：∵//EF AB∴△CFE ∽△CAB 又∵12AF FC = ∴32ACFC=， ∴94ABC FEC S S =△△ 设∴ABC 的面积为x 则9254x x =-， 解得，x=45，经检验x=45是原方程的根故答案为：45【点睛】本题考查了相似三角形的判定与性质，依据相似三角形面积比是相似比的平方，构建方程，是解决问题关键．16. 在一块直角三角形铁皮上截一块正方形铁皮，如图，已有的铁皮是Rt ABC △，90C ∠=︒，要截得的正方形EFGD 的边FG 在AB 上，顶点E 、D 分别在边CA 、CB 上，如果4AF =，9GB =，那么正方形铁皮的边长为______．【答案】6【分析】设正方形铁皮的边长为x ，证明△AEF ∽△DBG ，得到EF AF BG DG =，49x x=，求解即可． 【详解】设正方形铁皮的边长为x ，∵90C ∠=︒，∴∠A+∠B=90︒，在正方形EFGD 中，EF=DG=FG=x ，∠EFG=∠DGF=90︒,∴∠AFE=∠BGD=90︒，∴∠A+∠AEF=90︒,∴∠AEF=∠B ，∴△AEF ∽△DBG ， ∴EF AF BG DG=， ∴49x x =， 解得x=6（负值舍去），故答案为：6．【点睛】此题考查正方形的性质，相似三角形的判定及性质，根据已知条件证明△AEF ∽△DBG 是解题的关键．17. 如图，某堤坝的坝高为12米，如果迎水坡的坡度为1:0.75，那么该大坝迎水坡AB 的长度为______米．【答案】15【分析】过点B 作BC ⊥AC 于C ，由迎水坡的坡度为1:0.75，得到tan ∠BAC=43=BC AC ，求出AC=9米，再利用勾股定理求出答案．【详解】过点B 作BC ⊥AC 于C ，∵迎水坡的坡度为1:0.75，∴tan ∠BAC=43=BC AC ， ∵BC=12米，∴AC=9米，∴米)，故答案为：15．．【点睛】此题考查坡度的定义，解直角三角形的实际应用，勾股定理，正确理解迎水坡的坡度为1:0.75得到tan ∠BAC=43=BC AC 是解题的关键． 18. 在Rt ABC △中，90ACB ∠=︒，AC BC =，点E 、F 分别是边CA 、CB 的中点，已知点P 在线段EF 上，联结AP ，将线段AP 绕点P 逆时针旋转90°得到线段DP ，如果点P 、D 、C 在同一直线上，那么tan CAP ∠=______．1．【分析】分两种情形：⊥当点D 在线段PC 上时，延长AD 交BC 的延长线于H ．证明AD ＝DC 即可解决问题．【详解】解：⊥如图2中，当点D 在线段PC 上时，延长AD 交BC 的延长线于H ．⊥CE ＝EA ，CF ＝FB ，∴EF ∥AB ，∵AC ＝AB ，∠ACB ＝90°⊥⊥CEF ＝⊥CAB ＝45°，∵PD ＝P A ，∠APD ＝90°⊥⊥PAD ＝⊥PDA ＝45°，⊥⊥HDC ＝⊥PDA ＝45°，∵点E 是边CA 的中点，⊥EA ＝EP ＝EC⊥⊥EPC ＝⊥CEP ，∵∠HDC ＝∠DCA+∠DAC ＝45°，∠CEF ＝∠DCA+∠EPC ＝45°，⊥⊥DAC ＝⊥EPC ＝⊥ECP ，∴DA ＝DC ，设AP ＝a ，则DA DC =,∴)1PC a =∴)1tan 1a PC CAP PAa∠===②如图3中，当点P 在线段CD 上时，由①可知，EF ∥AB ，∠CAB ＝∠PDA ＝45°， ∴∠CAD ＝180°-∠ACD-45°， ∠COA ＝180°-∠ACO-45° ∴∠CAD ＝∠COA ， ∵EF ∥AB ， ∴∠CPE ＝∠COA ， ∴∠CPE ＝∠CAD ， ∵点E 是边CA 的中点， ⊥EA ＝EP ＝EC ∴∠ECP ＝∠CPE ， ∴∠ECP ＝∠CAD ，∴DA ＝DC ，设AP ＝a ，则PD ＝a ，DA DC ==,∴)1PC a =∴)1tan 1a PC CAP PAa∠===:点P 在线段EF 上，情况⊥不满足条件,情况⊥满足条件，综上所述，tan CAP ∠1．【点睛】本题考查了旋转变换，等腰直角三角形的性质，中位线的性质，外角的性质，三角形内角和，勾股定理和三角函数等知识，熟悉相关性质是解题的关键．三、解答题19. 计算：21cos 45cot 30sin 60tan 30-︒︒+︒⋅︒．【分析】根据特殊角的三角函数值进行计算求解．【详解】解：原式21112121112⎛- -=====． 【点睛】本题考查特殊角的三角函数值，解题的关键是掌握特殊角的三角函数值．20. 如图，已知ABC 中，//DE BC ，且DE 经过ABC 的重心点G ，BD a =，BC b =．（1）试用向量a 、b 表示向量BE ； （2）求作向量()233a b -（不要求写作法，但要指出图中表示结论的向量）． 【答案】（1）23BE a b =+；（2）见解析 【分析】（1）根据重心到顶点距离是它到对边中点距离的2倍，分析得到DE=23BC ，再根据向量的加法法则，首尾顺次相连，由三角形法则即可求解；（2）取AD 的中点J ，延长CB 到I ，使BI=DE ，以BJ 、BI 为邻边作平行四边形BJKI ，边接BK ，则BK 即是所求作的向量．【详解】解：（1）如图，连接AG 并延长交BC 于点F ，则GF=12AG ，AG 2=AF 3∴，DE//BC ，BC b = ADE ABC ∴△△∽， DE AG 2==BC AF 3∴， 23b DE BC =＝， 2a 3BE BD DE b ∴=+=+（2）BD a =，3BA a ∴=，作AD 的中点J ，2J=3a 23B a ∴⨯=，延长CB 到I ，使得BI=DE ，23BI b ∴=-，以BJ 、BI 为邻边作平行四边形BJKI ，则()2223a 33BK BJ BI a b b =+=-=-， ∴BK 即是所求的求作的向量【点睛】本题考查了向量的知识，掌握法则向量的平行四边形法则，向量的三角形法则是解题的关键．21. 已知二次函数()20y ax ax a =-≠的图像经过点()1,2-．（1）求该二次函数的解析式和顶点坐标；（2）能否通过所求得的抛物线的平移得到抛物线2132y x x =++？如果能，请说明怎样平移，如果不能，请说明理由． 【答案】（1）2yx x ，顶点为11,24⎛⎫- ⎪⎝⎭；（2）可以，先向左平移2个单位，再向下平移32个单位【分析】（1）把点()1,2-代入函数解析式，求出a 的值即可得到解析式，再把一般式写成顶点式得到顶点坐标； （2）把所给的函数解析式化为顶点式，根据函数图象的平移法则进行求解． 【详解】解：（1）把点()1,2-代入函数解析式，得2a a +=，解得1a =， ∴2yx x ，写成顶点式：21124y x ⎛⎫=-- ⎪⎝⎭，∴顶点坐标是11,24⎛⎫-⎪⎝⎭； （2）将2132y x x =++也写成顶点式，得23724y x ⎛⎫=+- ⎪⎝⎭，31222⎛⎫--= ⎪⎝⎭，713442-=， ∴把原抛物线先向左平移2个单位，再向下平移32个单位． 【点睛】本题考查二次函数解析式的求解和图象的平移，解题的关键是掌握解析式的求解方法和函数图象的平移方法．22. 如图，点O 是菱形ABCD 的对角线BD 上一点，联结AO 并延长，交CD 于点E ，交BC 的延长线于点F ．（1）求证：2AB DE BF =⋅； （2）如果1OE =，2EF =，求CFBF的长．【答案】（1）见解析；（2）33CF BF -=【分析】（1）根据菱形的性质证明ABO EDO ，BFO DAO ，得到AB BFED DA=，再由AB DA =，即可证明结论；（2）连接OC ，先证明()ADO CDO SAS ≅得到DAO DCO ∠=∠，就可以证明OEC OCF ，根据对应边成比例求出OC 的长，再根据ADE FCE ~，利用对应边成比例求出结果． 【详解】解：（1）∵四边形ABCD 是菱形， ∴//AB CD ，//AD BC ，AB DA =， ∴ABO EDO ，BFO DAO ，∴AB BO ED DO =，BF BODA DO =， ∴AB BFED DA=， ∵AB DA =， ∴2AB DE BF =⋅； （2）如图，连接OC ，∵四边形ABCD 是菱形， ∴AD=DC ，ADO CDO ∠=∠， 在ADO △和CDO 中，AD CD ADO CDO DO DO =⎧⎪∠=∠⎨⎪=⎩， ∴()ADO CDO SAS ≅， ∴DAO DCO ∠=∠， ∵//AD BF ， ∴DAO OFC ∠=∠， ∴DCO OFC ∠=∠，∵COE FOC ∠=∠， ∴OEC OCF ，∴OE OCOC OF=，即2OC OE OF =⋅， ∵1OE =，2EF =， ∴123OF =+=，∴OC =∴AO OC == ∵//AD CF ， ∴ADE FCE ~，∴12AD AE FC FE ==，∴12BC AD FC +==，1322BF BC CF FC FC FC =+=+=，∴(236CF BF===． 【点睛】本题考查相似三角形，解题的关键是掌握相似三角形的性质和判定．23. 某校数学活动课上，开展测量学校教学大楼()AB 高度的实践活动，三个小组设计了不同方案，测量数据如下表：（2）请选择其中一个可行方案及其测量数据，求出教学大楼的高度． 【参考数据：sin370.60︒≈，cos370.80︒≈，tan370.75︒≈】 【答案】（1）二；（2）36米【分析】（1）根据第二组只测了角度，未给出距离相关信息即可判断； （2）由锐角三角函数可求tan ABBC C =，tan AB BD ADB=∠，由BC BD CD -=，列出方程可求解． 【详解】（1）∴第二组中没有线段长度的数据，所以无法测出AB 的高度， ∴填第二组， 故答案为：二．（2）可选第一组的方案， 设AB xm =，在Rt ABC 中，90B ∠=︒，tan =ABC BC， ∴4=tan tan 373AB x BC x C ==︒，在Rt ABD △中，90B ∠=︒，tan =ABADB BD∠， ∴tan tan 45AB xBD x ADB ===∠︒，∴BC BD CD -=， ∴4123x x -=， ∴36x =．答：教学大楼高36米．【点睛】本题考查了解直角三角形的应用，利用数学知识解决实际问题是中学数学的重要内容．解决此问题的关键在于正确理解题意的基础上建立数学模型，把实际问题转化为数学问题．24. 已知抛物线()20y ax bx a =+≠经过 ()4,0A ，()1,3B -两点，抛物线的对称轴与x 轴交于点C ，点 D 与点B 关于抛物线的对称轴对称，联结BC 、BD ．（1）求该抛物线的表达式以及对称轴；（2）点E 在线段BC 上，当CED OBD =∠∠时，求点 E 的坐标；（3）点M 在对称轴上，点N 在抛物线上，当以点O 、A 、M 、N 为顶点的四边形是平行四边形时，求这个平行四边形的面积． 【答案】（1）231255y x x =-，对称轴为2x =；（2）1,1E ；（3）当OA 为边时，1445S =；当OA 为对角线时，485S =． 【分析】（1）将()4,0A ，()1,3B -代入抛物线2y ax bx =+，求解即可；（2）过B 点作BF x ⊥轴叫x 轴与点F ，过E 点作EH x ⊥轴叫x 轴与点H ，根据B 点坐标是()1,3-，对称轴为2x =，易得BCF △是等腰直角三角形，ECH 也是等腰直角三角形，求出BC =CED OBD =∠∠，点D 与点B 关于抛物线的对称轴对称，可证得OBCEDB ，DBE BCO ，则DBEBCO ，有DBEBBCOC，可得EB =EC =（3）分两种情况讨论：当OA 对角线时，当OA 为边时，分别求出N 点坐标，然后求解即可．【详解】解：（1）将()4,0A ，()1,3B -代入抛物线 2y ax bx =+，得：16403a b a b +=⎧⎨-=⎩，解之得： 35125a b ⎧=⎪⎪⎨⎪=-⎪⎩，∴该抛物线的表达式是231255y x x =-， ∴22231233124255555y x x x xx ， ∴对称轴为2x =；（2）如图示：过B 点作BF x ⊥轴叫x 轴与点F ，过E 点作 EH x ⊥轴叫x 轴与点H ，∴B 点坐标是()1,3-，对称轴为2x =， ∴3BF CF ==，∴BCF △是等腰直角三角形，则ECH 也是等腰直角三角形， ∴22223332BCBF CF ,∴CED OBD =∠∠,CED EBD EDB ∠=∠+∠,OBDEBD OBC∴OBCEDB ,∴点D 与点B 关于抛物线的对称轴对称，则D 点坐标是()5,3， ∴//BD FA∴DBE BCO ∴DBE BCO ∴DB EBBCOC, ∴6BD =,2OC =,2EB，即有EB =∴32222ECBCEB,∴ECH 是等腰直角三角形， ∴1EHHC∴1OH =即点E 的坐标是()1,1； （3）∴4OA =∴当OA 是平行四边形的边长时，如图2所示，则MN 必定在y 轴的上方，并有4MN OA ，∴点M 在对称轴上， ∴点N 的横坐标是6或-2， 又∴点N 在抛物线上， ∴当6x =时，23123666555y， ∴平行四边形OANM 的面积36144455；当2x =-时，23123622555y ， 同理可得平行四边形OANM 的面积36144455； ∴当OA 是平行四边形的对角线时，如图3所示，∵点M 在对称轴上，并MONA ∴点N 也在对称轴2x =上，∴当2x =时，23121222555y， ∴112244255OAN S ∴平行四边形OANM 的面积24482255OAN S ． 综上所述，平行四边形的面积为1445或485． 【点睛】本题考查了用待定系数法求函数解析式，二次函数坐标轴上的点，三角形的相似的判定与性质，平行四边形的判定与性质，熟悉相关性质是解题的关键．25. 如图，已知△ABC 中，∠ACB =90°，AC =BC ，点D 、E 在边AB 上，∠DCE =45°，过点A 作AB 的垂线交CE 的延长线于点M ，联结MD ．（1）求证：2CE BE DE =⋅；（2）当AC =3，AD =2BD 时，求DE 的长；（3）过点M 作射线CD 的垂线，垂足为点F ，设BD x BC =，tan ∠FMD =y ，求y 关于x 的函数关系式，并写出定义域．【答案】（1）见解析； （2）4DE =； （3）1(02y x =<<． 【分析】（1）证明两个角相等证明△CDE ∽△BCE ，列比例式可得结论；（2）如图2，过D 作DN ⊥AC 于N ，根据△ADN 是等腰直角三角形，得AN =DN ，由平行线分线段成比例定理得23AD AN AB AC ==，计算DN 和CN 的长，利用勾股定理计算CD 和BD 的长，根据（1）中的相似三角形，列比例式得：DE CE DC CE BE BC ===，设DE ，CE =3x ，代入比例式可得结论； （3）如图3，作辅助线构建全等三角形，证明△AMC ≌△BPC （ASA ），得CM =CP ，证明△MCD ≌△PCD（SAS ），得∠MDC =∠PDC =∠BDC ，证明△BCD ∽△CMD ，列比例式得BD CD BC CM=，根据三角函数的定义和等量代换可得比例式，并根据D ，E 是AB 上一点，∠DCE =45°，可知当点E 与A 重合时，BD 最大为12AB ，可得x 的取值范围．【小问1详解】证明：如图1，∵∠ACB =90°，AC =BC ，∴∠B =∠CAB =45°，∵∠DCE =45°，∴∠B =∠DCE ，∵∠CED =∠CEB ，∴△CDE ∽△BCE ， ∴CE DE BE CE=， ∴2CE BE DE =⋅；【小问2详解】解：如图2，过D 作DN ⊥AC 于N ，∴∠AND =90°，∵∠DAN =45°，∴△ADN 是等腰直角三角形，∵DN ∥BC ，AD =2BD ， ∴23AD AN AB AC ==， ∵AC =3，∴AB AN =DN =2，CN =1，∵AD =2BD ，∴BD由勾股定理得：DC =由（1）知：△CDE ∽△BCE ，∴3DE CE DC CE BE BC ===，设DE ，CE =3x ，3=，∴x ，∴DE ； 【小问3详解】解：如图3，过点C 作CP ⊥CM ，交AB 的延长线于点P ，∵∠DCE =45°，∠ACB =90°，∴∠ACM +∠BCD =45°=∠BCD +∠BCP ，∴∠BCP =∠ACM ，∵∠CBP =180°-45°=135°=∠CAM ，AC =BC ，∴△AMC ≌△BPC （ASA ），∴CM =CP ，∵∠DCM =∠DCP =45°，CD =CD ，∴△MCD ≌△PCD （SAS ），∴∠MDC =∠PDC =∠BDC ，∵∠ABC =45°=∠MCD ，∴△BCD ∽△CMD ， ∴BD BC CD CM =，即BD CD BC CM=， ∵FM ⊥FC ，∠DCE =45°，∴△CFM 是等腰直角三角形，∴CM FM ，∴y =tan ∠FMDDF MF CM==)CF CD CM-=CM -=1BD BC=x ；Rt △ABC 中，AC =BC ，∴AB BC ，∵D ，E 是AB 上一点，∠DCE =45°，∴当点E与A重合时，BD最大为12 AB，∵BDBC=x，∴0＜x∴y（0＜x＜2）．【点睛】本题是相似形的综合题，考查了全等和相似三角形的判定和性质，等腰直角三角形的性质，三角函数的定义等知识，添加恰当辅助线构造全等三角形是本题的关键．。
2021-2022学年上海市虹口区九年级上学期期末数学试卷(一模)(含答案解析)
2021-2022学年上海市虹口区九年级上学期期末数学试卷(一模)一、选择题（本大题共6小题，共24.0分）1.如图(1)所示，E为矩形ABCD的边AD上一边，动点P，Q同时从点B出发，点P沿折线BE−ED−DC运动到点C时停止，点Q沿BC运动到点C时停止，它们运动的速度都是1cm/秒，设P、Q同时出发t秒时，△BPQ的面积为ycm2.已知y与t的函数关系图象如图(2)(曲线OM为抛物线的一部分)则下列结论正确的是()A. AB：AD=3：4B. 当△BPQ是等边三角形时，t=5秒C. 当△ABE∽△QBP时，t=7秒D. 当△BPQ的面积为4cm2时，t的值是√10或47秒52.已知非零向量a⃗、b⃗ 和c⃗，下列条件中，不能判定a⃗//b⃗ 的是()A. a⃗=−2b⃗B. a⃗=c⃗，b⃗ =3c⃗C. a⃗+2b⃗ =c⃗，a⃗−b⃗ =−c⃗D. |a⃗|=2|b⃗ |3.若y=(3+m)x m2−9是开口向下的抛物线，则m的值为()A. 3B. −3C. √11D. −√114.把抛物线y=(x−2)2向左平移2个单位长度，再向上平移2个单位长度，所得到的抛物线是()A. y=x2+2B. y=x2−2C. y=(x+2)2−2D. y=(x+2)2+25.如图，小王在长江边某瞭望台D处，测得江面上的渔船A的俯角为40°，若DE=3米，CE=2米，CE平行于江面AB，迎水坡BC的坡度i=1：0.75，坡长BC=25米，则此时AB的长约为()(参考数据：sin40°≈0.64，cos40°≈0.77，tan40°≈0.84)A. 10.4米B. 12.4米C. 27.4米D. 22.4米6.如图，四边形ABCD内接于⊙O，AB为直径，AD=CD，过点D作DE⊥AB于点E.连接AC交DE于点F.若cos∠CBA=35，EF=3.则AB的长为()A. 10B. 12C. 16D. 20二、填空题（本大题共12小题，共48.0分）7.如果3x−5y=0，且y≠0，那么xy=______．8.计算：2(2a⃗+3b⃗ )−13a⃗+12b⃗ =______ ．9.如图，是抛物线y=ax2+bx+c(a≠0)图象的一部分．已知抛物线的对称轴为x=2，与x轴的一个交点是(−1,0).有下列结论：①abc>0；②4a−2b+c<0；③4a+b=0；④抛物线与x轴的另一个交点是(5,0)；⑤点(−3,y1)，(6,y2)都在抛物线上，则有y1<y2.其中正确的是。
2021年上海市宝山区九年级中考一模(上学期期末)英语试题
2021年上海市宝山区九年级中考一模（上学期期末）英语试题学校:___________姓名：___________班级：___________考号：___________一、单选题1．One function of federal government is to coin money. Which of the following is correct for the underlined word in the sentence?A．/kɔɪn/B．/keən/C．/kɪən/D．/kɔɪŋ/ 2．Which of the following underlined parts is different in pronunciation from others? A．The boy is from Chile.B．I’d like to buy a Father Christmas coat.C．Please check your homework carefully.D．It’s hard for me to choose which one is the best.3．WeChat is _________ useful tool to communicate with others nowadays.A．an B．/ C．the D．a4．Billy spoke in such a low voice that _________ in my office could hear him. A．everybody B．somebody C．anybody D．nobody 5．Fifty percent of my monthly pocket money _________ spent on entertainment.A．am B．is C．are D．be6．Is _________ riding enough for you to get there?A．thirty five minutes B．thirty-five minutes’C．thirty-five-minutes D．thirty five minute’s7．Save and protect natural resources, _________ we’ll run ou t of them in the near future. A．and B．or C．but D．so 8．Traveling by car is _________ not reliable because of too many cars during the rush hours. A．sometime B．sometimes C．some time D．some times 9．Mr. White can always make us relaxed. He is _________ teacher I have ever met. A．the most humorous B．most humorousC．more humorous D．a humorous10．I _________in London for many years, but I’ve never regretted my final decision to move back to China.A．lived B．was living C．have lived D．am living11．Nowadays many new taxi apps（打车软件）_________ to help people travel around more easily.A．are used B．use C．used D．is used 12．The organization is considering _________ some money to victims of the natural disaster. A．donate B．donating C．to donate D．to donating 13．Mum always tells me _________ any food when I have dinner at home.A．not to waste B．don’t waste C．not waste D．to not waste 14．George couldn’t wait to _________ his new car.A．put off B．set off C．take off D．show off 15．Could you tell me _________ in British schools?A．what do students wear B．to wear whatC．what students wear D．students wear what16．I don’t think he will take pride in his son’s achievement, _________?A．do I B．don’t I C．will he D．won’t he 17．Scientists say we will have no water to drink _________ we protect water resources. A．if B．when C．before D．unless18．–Would you mind explaining the word in English again, please?–___________________________.A．That’s OK B．Never mindC．Of course not. D．You should listen carefully19．What is the name of the official London residence（住所）of Queen Elizabeth Ⅱ? A．Windsor Castle B．The White HouseC．The Tower of London D．Buckingham Palace二、用单词的正确形式完成短文A．Increasing B．thinking about C．easily D．immediately E．withoutWorld Water Day is on 22 March each year．It started in 1992．Its goal is to get people and Governments20．one of our most precious resources．For human beings，water not only is an important resource to survive and grow，but also offers fun and pleasure．Could youimagine what the world would be like21．water？Nowadays，we are facing an22．number of environmental crisis（危机）such as water pollution and water shortage．In India's capital，New Delhi，millions do not have any running water．Even in richer neighborhoods，young and old wait hours for clean water．One young woman in Ghana，like many in Africa，Asia，Latin America，and elsewhere walks kilometers for water．"I have to collect for my family five times a day．"Something must be done to save and protect water23．．The special day is a day for us to know about what we have done and what we should do．I believe the environment will become better and better if we follow the spirit of the World Water Day．A．Perhaps B．shone C．shook D．ahead E．LuckilyOn the way to my company，I was driving behind a small truck．I was a few minutes late and the two men24．of me were talking in that slow truck．They made me angry．The light turned green，but the truck was still moving very slowly．I became impatient，so I turned right to past it．Suddenly，a new blue Chevy Silverado was rushing by．I tried to stop，but it was too late．My car hit the side of the Chevy．"Pow!"I heard a big noise and then I realized that an accident happened．For a moment，just a moment…I asked if I was OK，and honestly，I was waiting for people to come over and help me．Those thoughts didn't last long，as the answer came into my mind that the air bag had saved me．25．，I was still alive．Slowly I opened the door．The warm，bright morning sunlight 26．on my face and I felt better．I saw the Chevy Silverado and I ran over to check if the driver in it was injured．"Are you OK？"I shouted loudly through the window．His head was down and he didn't answer me．At that moment，I thought I was looking at a dead man．Full of fear，I shouted again，and knocked at the window heavily once more．His eyes started to open，and he slowly27．hishead"Yes．"Once again，I said to myself，"How lucky I am !"三、用所给单词的正确形式填空Completethesentenceswiththegivenwordsintheirproperforms.28．Floods are the No．1 natural___ in the world．（kill）29．If Mary isn't satisfied with the style of uniforms，why not design them___？（she）30．Western countries didn't use paper money until the___ century．（sixteen）31．After the earthquake，thousands of people were left___．（home）32．I hope the company will___ something like homework robots in the nearest future．（product）33．Our country has developed___ in the past 40 years．（rapid）34．Our government has paid great attention to___ rights nowadays．（work）35．After learning the text，my English teacher asked me to___ it to the whole class．（tell）四、句型转换Rewritethefollowingsentencesasrequired.36．The government tried to find some ways to fight against the air pollution．（改为一般疑问句）___ the government___ to find some ways to fight against the air pollution？37．They surfed the Internet to gather some information about the earthquake．（对划线部分提问）___ they surf the Internet？38．The postman delivers letters in the late afternoon every day．（改为被动语态）Letters______ by the postman in the late afternoon every day．39．"Can earthquakes be exactly predicted？" Jack asked．（改为宾语从句）Jack wanted to know___ earthquakes___ be exactly predicted．40．I haven't decided what I will do for the summer holiday．（改为简单句）I haven't decided what______ for the summer holiday．41．When doing translation work，Johnson chose every word very carefully．（保持原句意思）When doing translation work，Johnson chose very word with______．42．electricity，for，be，water，used，producing，can（连词成句）_________________________________________________．五、阅读单选Choose the best answer (根据文章内容，选择最恰当的答案)：“Mother, may I go down to the river? It has stopped raining now!”“Very well, Tom,” replied his mother, “only, be careful, and don’t stay away long!”So, Tom ran off down the field to the river which flowed past his father’s farm in far north Queensland in Australia. It had been raining for ten days. Sometimes the rain fell fast and hard, then light showers would follow. The ground was all wet.“All hot countries, such as where we live,” Tom’s father had once told him, “may flood at times. The sun has great power in the tropics to draw up the water from the sea. You know how the vapour rises into the air. The higher the temperature of the air, the greater the amount of moisture(水分) the air can hold. When the air cools, the vapour becomes clouds, or if it is near the earth’s surface, as mist(薄雾). When the air cools gradually(逐渐地), the rain drops are small and the rain is light. However, when the vapour drops suddenly in temperature, the drops are large and the rain is heavy.”“In some tropical countries, where the sun is always at work on large bodies of water, a very large amount of vapour collects in the air, and it may take days, or even weeks, to form rain drops and fall. It may then rain for days continually. When this happens, after two or three days, the water falls does not have the time to soak(浸泡) through the soil or be carried off in the streams; so it gathers on the surface, and then we have a flood.”When Tom got to the river, where the crossing was, he found the water rising rapidly. He thought about what his father had taught him about the floods, and decided to go back home at once and tell him the news.43．What did Tom’s father probably do?A．A geography teacher. B．A scientist.C．A farmer. D．A doctor.44．How long had Tom probably stayed at home?A．Ten days. B．Two days. C．Three days. D．Several weeks. 45．The air can hold a lot of moisture when ________.A．the air cools down suddenly B．the air cools down graduallyC．the temperature is high D．the temperature is low46．Which order is RIGHT according to the passage?(1) The water from the sea rises into the air and became vapour.(2) When the air cools down, it begins to rain.(3) The vapour became clouds or mist.(4) Too much water gathers on the surface and becomes flood.A．(1)(2)(3)(4) B．(2)(1)(3)(4) C．(4)(1)(3)(2) D．(1)(3)(2)(4) 47．What was the “news” in the last sentence?A．Maybe a terrible flood was coming soon.B．They could start to work on the farm immediately.C．The rain had caused a great loss to their farm.D．He had learned how the flood came into being.48．Tom was a ________ boy according to the passage.A．hardworking B．generous C．lazy D．clever六、完型填空Choosethewordsorexpressionstocompletethepassage.Stan Lee，who helped create Spiderman，the X﹣Men，Iron Man，the Incredible Hulk （绿巨人），Black Panther（黑豹），and many other comic book heroes，has died．He was 95．Stanley Martin Lieber was born in 1922．When he was just 17，he got a job at a company that made comic books．As a writer，he started using the name "Stan Lee" （which）sounded like his first name，Stanley）．He wrote his first Captain America story in 1941．It turned out to be popular．Before he turned 19，he was 49 all writing for the company，whichbecame Marvel Comics（漫威漫画公司）in the 1960s．At the time，most superheroes were shown as being almost perfect．They were strong and smart and always knew the right thing to do．However，after working with some artists，Mr．Lee came up with some new ideas．He made it okay for comic book heroes to have 50 ．The Fantastic Four（神奇四侠）argued among themselves．The Incredible Hulk was a really nice guy until he got angry．Spider﹣Man was never sure he was doing the right thing，but he always seemed to have something funny to say to the bad guys．Besides，he also had the clever idea of having his comic book heroes 51 in each other's stories．For example．Spider﹣Man might show up in an Iron Man story．This made readers feel like there was a 52 world of Marvel superheroes．Readers loved it．Many people say that Mr．Lee's characters and stories helped make comic books popular again．In 1980，Mr．Lee moved to California．He wanted to try and get his superheroes onto TV and into the movies．He didn't have too much luck at first，53 he Incredible Hulk and X﹣Men became popular TV shows．But after the success of the X﹣Men and Spider﹣Man movies in the early 2000s，movies with Marvel heroes began to come out often．Marvel movies have now earned over ﹩24 billion．Mr．Lee has 54 a small role in most of these movies，usually showing up on screen for just a few seconds．Mr．Lee is no longer with us，but the heroes he created live on．49．A．in favour of B．proud of C．in charge of D．familiar with 50．A．trouble B．weaknesses C．strength D．purposes 51．A．work B．travel C．appear D．turn 52．A．various B．similar C．necessary D．whole 53．A．therefore B．although C．for D．unless 54．A．played B．expected C．joined D．shared七、单词填空Read the passage and fill in the blanks with proper words（在短文的空格内填入适当的词，使其内容通顺，每空格限填一词，首字母已给）Watch young children in a school class. You will often notice that there are three or four—especially boys who cannot sits s55．. They have trouble paying attention to the teacher for longer than a few minutes, and they seem to forget things the teachers tells them. What is the manner with them? Many doctors think they need medicine, so they give the children a drug c56．Ritalin(利他林). It is supposed to help them settle down and pay better attention. It works, but it is also dangerous. Ritalin has some bad side effects, and it can even kill children who take too much. Because of the serious side effects of Ritalin, many people think it is not good for children.Ritalin seems to affect both a child’s mind and body. The drug does help children calm down and focus, but some scientists claim( 声称) that Ritalin decreases the flow of blood to theb57．. This effects a child’s thinking and memory and makes it more difficult to learn. Scientists also think that the drug might l58．a child’s ability to grow and can cause trouble sleeping. Another problem is that children can take too much of the drug. Some children like the way the drug makes t59．feel, so they take more than they should. They know this is wrong, but they cannot stop, much the same as people who cannot stop smoking. A third problem is that doctors do not know if the drug is really safe or not. Doctors do not know what happens to children who take this drug for a long time. They do not know if these children show side effects after they grow up. Ritalin might help when children are young but are there bad effects l60．in life? Because nobody knows for sure, some scientists say that Ritalin should not be used.Today, some doctors and teachers say that there are better ways than drugs to help children with attention problems. One good idea is to give children better food and make sure they get more rest. Another way to help children with attention problems is to find teachers who have special training with a61．children. Such teachers know how to help these children learn. Another idea is for parents and teachers to simply be patient. Most children’s attention will improve naturallyas they get older. Parents and teachers just have to give these children time to develop.八、回答问题Answer the questions（根据短文内容回答下列问题）It happened about one year ago. My mom wanted to visit her sister who lived in America. Since we lived in the Ukraine(乌克兰), my mom had to get agreement from our government to go to America. After she got the agreement to go and all of the paper work was done, she was ready to go. Then came the bad part. She had to be away from my dad, my two sister, and me for about three months. From our city, my mum had to go to New York by plane. My sisters, my dad and I stood and watched the plane leave until we couldn’t see it any more.The next day, we got a call from our mom. She said that her sister met her in New York and from there, they drove to the place where my aunt lived. She also said that it was really nice in America, but she missed her very much. It was really hard to live without my mom, without her help or her advice, but I got over it.After about three months my mom was coming home. My dad and my sister went to pick my mom up from the airport. It was very far and my mom had a lot of bags. My younger sister and I waited for them at home. We waited and waited, and then it was late, but they weren’t back. Then we got a call from our dad. He said that there was a big snowstorm in New York and the plane couldn’t leave until the storm was over, so our mum would be late. When they finally got home, I was really happy. My mum had a lot of gifts for us, but she was the best one. 62．Why di d the writer’s mother fly to New York?_________________________________________________________________________. 63．How long did the writer’s mother have to be away from home?_________________________________________________________________________. 64．Who saw off the writer’s mother at the airport?_______________________________________________________________________. 65．The writer met his mother at the airport with his dad, didn’t he?________________________________________________________________________.66．Why didn’t his mother’s plane arrive on time?_________________________________________________________________________. 67．What was the best gift for the writer?_________________________________________________________________________.九、材料作文68．Writing（作文）Write at least 60 words about the topic "My Ideal Weekend"．（以"我理想的周末" 为题写一篇不少于60 个词的短文，标点符号不占格．）Use the following questions as a reference．（以下问题仅供参考）1）What's your weekend like？2）What's your ideal weekend like？3）Why do you want a weekend like that？（注意：短文中不得出现考生的姓名、校名及其他相关信息，否则不予评分）参考答案1．A【详解】句意：联邦政府的一项职能是铸造货币。
2021学年度上海杨浦区九上期末质量检测 物理学科(中考一模)
2021学年度第一学期初三期末质量检测物理学科（满分100分，时间90分钟） 2022.1 考生注意：1．本试卷物理部分含四个大题。
2．答题时，考生务必按答题要求在答题纸规定的位置上作答，在草稿纸、本试卷上答题一律无效。
一、选择题（共20分）1.下列各物理量中，可鉴别物质的是A．质量B．电阻C．体积D．密度2.研究得出“导体中电流与电压的关系”的科学家是A．牛顿B．帕斯卡C．欧姆D．伽利略3.下列生活器件中，利用连通器原理的是A．密度计B．茶壶C．抽水机D．注射器4.下列实例中，为了增大压强的是A．尖锐的逃生锤尖B．较宽的书包带C．宽大的骆驼脚掌D．有很多轮子的拖车5.九年级第一学期物理练习册共有70页，平放在水平桌面中央时，它对桌面的压强约为A．1帕B．35帕C．70帕D．140帕6.小球漂浮在酒精中，排开酒精的质量为0.2千克。
若该小球漂浮在水中，则排开水的质量A．一定大于0.2千克B．可能小于0.2千克C．一定等于0.2千克D．一定小于0.2千克7.在图1(a)(b)所示电路中，电源电压相同且不变，电路元件均完好，无论开关S1、S2同时断开，还是同时闭合，观察到电流表A1与电流表A2示数始终相同。
关于电阻R1、R2、R3的判断，以下列式中正确的是A．R3=R1+R2B．R2=R1+R3C．R1>R2>R3D．R3>R1>R28.相同柱形容器甲、乙置于水平地面上，容器内装有完全相同．．．．物块A、B，物块A与容器甲底部用一根细绳相连。
同时往两容器内注水，直至水面相平，如图2所示。
下列判断正确的是A．此时物块受到的浮力F浮A=F浮BB．此时容器对地面的压力F甲=F乙C．此时容器对地面的压强p甲>p乙D．此时水对容器底部的压力F水甲=F水乙9.在图3所示的电路中，电源电压保持不变。
闭合开关S，当滑动变阻器的滑片P由最右端向中间移动时，变小的是A．电流表 A 示数与电流表 A1 示数的差值B．电流表 A 示数与电流表 A1 示数的比值C．电压表 V 示数与电流表 A 示数的比值D．电压表 V 示数与电流表 A1 示数的比值10.如图4所示，均匀正方体甲、乙放置在水平地面上，它们的质量分别为m甲、m乙，对地面的压强分别为p甲、p乙。
2021-2022学年上海市松江区九年级上学期期末数学试卷(一模)(含答案解析)
2021-2022学年上海市松江区九年级上学期期末数学试卷(一模)一、选择题（本大题共6小题，共24.0分）1.如图，△ABC与△AEF中，AB=AE，BC=EF，∠B=∠E，AB交EF于D.给出下列结论：①∠C=∠E；②△ADE∽△FDB；③∠AFE=∠AFC；④FD=FB．其中正确的结论是()A. ①③B. ②③C. ①④D. ②④2.如图，在△ABC中，∠A=90°.若AB=12，AC=5，则cosC的值为()A. 513B. 1213C. 512D. 1253.把抛物线y=2x2先向左平移4个单位，再向下平移3个单位，所得抛物线的函数表达式为()A. y=2(x+4)2+3B. y=2(x+4)2−3C. y=2(x−4)2−3D. y=2(x−4)2+34.如图，AB//CD，EC⊥CD于C，CF交AB于B，已知∠2=29°，则∠1的度数是()A. 58°B. 59°C. 61°D. 62°5.如图，河堤横断面迎水坡AB的坡比i=1：√3，则∠BAC是()A. 60°B. 55°C. 45°D. 30°6.如图所示，在Rt△ABC中，∠A=30°，点D是斜边AB的中点，点G是Rt△ABC的重心，GE⊥AC于点E，若BC=6cm，则GE=()cm．A. 2B. 3C.D.二、填空题（本大题共12小题，共48.0分）7.已知：xy =23，那么2x−yx+y=______．8.点P为线段AB的黄金分割点(AP>BP)，若AB=4，则线段AP的长为_________ ．9.已知：锐角α满足sinα=√22，则α=．10.如图，在直角坐标系中，将矩形沿对折，使点落在处，已知，，则点的坐标是．11.一个物体重100N，物体对地面的压强P(单位：Pa)随物体与地面的接触面积S(单位：m2)变化而变化的函数关系式是______．12.若A(−3,y1)，B(−√2,y2)，C(2,y3)为二次函数y=x2+2x−5图象上的三点，则y1，y2，y3的大小关系是______．13.如图，直线AB//CD//EF，若AC=3，CE=4，则BDBF的值是______ ．14.如图，四边形BDCE内接于以BC为直径的⊙A，已知：BC=10，cos∠BCD=3，∠BCE=30°，则线段DE的长是______．515.把边长分别为1和2的两个正方形按如图所示的方式放置，则图中阴影部分的面积是______．16.如图，直角梯形ABCD中，AD//BC，AB⊥BC，AD=3.将腰CD以D为中心逆时针旋转90°至DE，连接AE、CE，△ADE的面积为6，则BC的长为______．17.如图，正方形OABC的顶点B在抛物线y=x2的第一象限部分，若B点的横坐标与纵坐标之和等于6，则正方形OABC的面积为______．AC，18.如图，在△ABC中，AB=AC=6√3，∠BAC=120°，点M，N分别在边AB，AC上，AN=13将△AMN沿MN翻折，点A落在A′处，则线段BA′长度的最小值为______ ．三、计算题（本大题共2小题，共20.0分）19.如图，在Rt△ABC中，∠ACB=90°，以AC为直径的⊙O与AB边交于点D，点E是边BC的中点．(1)求证：；(2)判断DE与⊙O位置关系，并说明理由．20. 如图，小河对岸有一座通讯信号塔AB，在点D处测得信号塔顶端A的仰角是48°，沿着射线BD方向走9米到达C处，在C处测得信号塔顶端A的仰角是39°，点A，B，C，D，E，F在同一平面内.若测角仪的高度为1.2米，求信号塔AB的高度(结果取整数)．参考数据：sin39°≈0.63，cos39°≈0.78，tan39°≈0.81，sin48°≈0.74，cos48°≈0.67，tan48°≈1.11．四、解答题（本大题共5小题，共58.0分）21. 如图，抛物线y=a(x−1)(x+3)交x轴于A、B两点，交y轴于点C，∠BAC=45°．(1)求a的值；(2)点D为第三象限内抛物线上的一点，当△DAC的面积为3时，求D点的坐标．22. 如图，在平面直角坐标系中，直线AB与x轴交于点B，与y轴交于(k≠0)的图象在第二象限交于点C，点A，与反比例函数y=kxCE⊥x轴，垂足为点E，sin∠ABO=√5，OB=2，OE=1．5(1)求反比例函数的解析式；(2)若点D是反比例函数图象在第四象限上的点，过点D作DF⊥y轴，垂足为点F，连接OD、BF，如果S△BAF=4S△DFO，求点D的坐标．23. 学校校园内有一块形状为直角梯形的空地ABCD，其中AB//DC，∠B=90°，AB=100m，BC=80m，CD=40m，现计划在上面建设一个面积为S的矩形综合楼PMBN，其中点P在线段AD上，且PM的长至少为36m(1)求边AD的长；(2)设PA=xm，求S关于X的函数关系式，并指出自变量x的取值范围；(3)若S=2800m2，求PA的长；(4)当x的值为多少时，s的值最大，最大值为多少？(5)求tan A．224. 在平面直角坐标系xOy中，已知抛物线y=mx2−3(m−1)x+2m−1(m≠0)．(1)当m=3时，求抛物线的顶点坐标；(2)已知点A(1,2).试说明抛物线总经过点A；(3)已知点B(0,2)，将点B向右平移3个单位长度，得到点C，若抛物线与线段BC只有一个公共点，求m的取值范围．25. 阅读下面材料，完成(1)−(3)题．数学课上，老师出示了这样一道题：如图1，在△ABC中，BA=BC，AB=kAC.点F在AC上，点E在BF上，BE=2EF.点D在BC延长线上，连接AD、AE，∠ACD+∠DAE=180°.探究线段AD与AE的数量关系并证明．同学们经过思考后，交流了自己的想法：小明：“通过观察和度量，发现∠CAD与∠EAB相等.”小亮：“通过观察和度量，发现∠FAE与∠D也相等.”小伟：“通过边角关系构造辅助线，经过进一步推理，可以得到线段AD与AE的数量关系.”…老师：“保留原题条件，延长图1中的AE，与BC相交于点H(如图2)，若知道DH与AH的数量关系，可以求出AB的值.”CH(1)求证：∠CAD=∠EAB；(2)求ADAE的值(用含k的式子表示)；(3)如图2，若DH=32AH，则ABCH的值为______ (用含k的式子表示)．参考答案及解析1.答案：B解析：解：在△ABC与△AEF中，{AB=AE ∠B=∠E BC=EF，∴△AEF≌△ABC，∴AF=AC，∠AFE=∠C∴∠AFC=∠C，∴∠AFE=∠AFC；由∠B=∠E，∠ADE=∠FDB，可知△ADE∽△FDB；无法得到∠C=∠E；FD=FB．综上可知：②③正确．故选：B．先根据已知条件证明△AEF≌△ABC，从中找出对应角或对应边．然后根据角之间的关系找相似，即可解答．本题考查相似三角形的性质、全等三角形的判定和性质等知识，解题的关键是正确寻找全等三角形或相似三角形解决问题，属于中考常考题型．2.答案：A解析：解：根据勾股定理得，BC=√AC2+AB2=√52+122=13，所以，cosC=ACBC =513．故选：A．利用勾股定理列式求出BC，再根据锐角的余弦等于邻边比斜边解答．本题考查锐角三角函数的定义及运用：在直角三角形中，锐角的正弦为对边比斜边，余弦为邻边比斜边，正切为对边比邻边．3.答案：B解析：解：把抛物线y=2x2先向左平移4个单位，再向下平移3个单位，所得的抛物线的解析式是y= 2(x+4)2−3，故选：B．根据“左加右减、上加下减”的原则进行解答即可．本题主要考查了二次函数的图象与几何变换，熟知函数图象平移的法则是解答此题的关键．4.答案：C解析：解：延长DC到F，∵EC⊥CD，∴∠DCE=90°，∵∠2=29°，∴∠3=61°，∵AB//CD，∴∠1=∠3=61°，故选：C．得到∠DCE=90°，根据余角的性质得到∠3=61°，根据平行线的性质即可得到结论．本题考查了平行线的性质，垂直的定义，熟练掌握平行线的性质是解题的关键．5.答案：D解析：解：∵河堤横断面迎水坡AB的坡比i=1：√3，∴tan∠BAC=BCAC =1√3=√33，∴∠BAC=30°．故选：D．直接利用锐角三角函数关系得出tan∠BAC=BCAC，进而得出答案．此题主要考查了解直角三角形的应用，正确掌握坡比的定义是解题关键．6.答案：A解析：7.答案：15解析：直接利用已知用同一未知数表示出x，y，进而代入原式求出答案．此题主要考查了比例的性质，掌握表示出x，y是解题关键．解：∵x y=23，∴设x=2a，y=3a，∴2x−yx+y =4a−3a2a+3a=15．故答案为：15．8.答案：−1解析：解析：试题分析：解：如果一点为线段的黄金分割点，那么被分割的较短的边比较大的边等于较大的边比上这一线段的长=≈0.618.∵AB=2，AP﹥BP，∴AP:AB=×2=−1．考点：黄金分割的定义。
上海市松江区2020-2021学年九年级(上)期末数学试卷(一模) 解析版
2020-2021学年上海市松江区九年级（上）期末数学试卷（一模）一、选择题（本大题共6题，每题4分，满分24分【下列各题的四个选项中，有且只有一个选项是正确的，选择正确项的代号并填涂在答题纸的相应位置上】1．如果两个相似三角形对应边的比为1：4，那么它们的周长比是（）A．1：2B．1：4C．1：8D．1：162．在Rt△ABC中，∠C＝90°，∠A＝α，BC＝2，那么AC的长为（）A．2sinαB．2cosαC．2tanαD．2cotα3．将抛物线y＝2x2向右平移3个单位，能得到的抛物线是（）A．y＝2x2+3B．y＝2x2﹣3C．y＝2（x+3）2 D．y＝2（x﹣3）24．已知＝2，下列说法中不正确的是（）A．﹣2＝0B．与方向相同C．∥D．||＝2||5．如图，一艘船从A处向北偏东30°的方向行驶10千米到B处，再从B处向正西方向行驶20千米到C处，这时这艘船与A的距离（）A．15千米B．10千米C．10千米D．5千米6．如图，已知在Rt△ABC中，∠C＝90°，点G是△ABC的重心，GE⊥AC，垂足为E，如果CB＝8，则线段GE的长为（）A．B．C．D．二、填空题（本大题共12题，每题4分，满分48分）【请将结果直接填入答题纸的相应位置上】7．已知，则＝．8．已知线段MN的长是4cm，点P是线段MN的黄金分割点，则较长线段MP的长是cm．9．计算：sin30°•cot60°＝．10．在Rt△ABC中，∠C＝90°，AC＝6，cos A＝，那么AB的长为．11．一个边长为2厘米的正方形，如果它的边长增加x（x＞0）厘米，则面积随之增加y平方厘米，那么y关于x的函数解析式为．12．已知点A（2，y1）、B（3，y2）在抛物线y＝x2﹣2x+c（c为常数）上，则y1y2（填“＞”、“＝”或“＜”）．13．如图，已知直线l1、l2、l3分别交直线l4于点A、B、C，交直线l5于点D、E、F，且l1∥l2∥l3，AB＝4，AC＝6，DF＝10，则DE＝．14．如图，△ABC在边长为1个单位的方格纸中，△ABC的顶点在小正方形顶点位置，那么∠ABC的正弦值为．15．如图，已知点D、E分别在△ABC的边AB和AC上，DE∥BC，＝，四边形DBCE 的面积等于7，则△ADE的面积为．16．如图，在梯形ABCD中，AD∥BC，BC＝2AD，设向量＝，＝，用向量、表示为．17．如图，正方形DEFG的边EF在△ABC的边BC上，顶点D、G分别在边AB、AC上．已知△ABC的边BC＝16cm，高AH为10cm，则正方形DEFG的边长为cm．18．如图，已知矩形纸片ABCD，点E在边AB上，且BE＝1，将△CBE沿直线CE翻折，使点B落在对角线AC上的点F处，联结DF，如果点D、F、E在同一直线上，则线段AE的长为．三、解答题（本大题共7题，满分78分）19．（10分）用配方法把二次函数y＝3x2﹣6x+5化为y＝a（x+m）2+k的形式，并指出这个函数图象的开口方向、对称轴和顶点坐标．20．（10分）如图，已知AB∥CD，AD、BC相交于点E，AB＝6，BE＝4，BC＝9，联结AC．（1）求线段CD的长；（2）如果AE＝3，求线段AC的长．21．（10分）如图，已知在Rt△ABC中，∠C＝90°，sin∠ABC＝，点D在边BC上，BD ＝4，联结AD，tan∠DAC＝．（1）求边AC的长；（2）求cot∠BAD的值．22．（10分）如图，垂直于水平面的5G信号塔AB建在垂直于水平面的悬崖边B点处（点A、B、C在同一直线上）．某测量员从悬崖底C点出发沿水平方向前行60米到D点，再沿斜坡DE方向前行65米到E点（点A、B、C、D、E在同一平面内），在点E处测得5G信号塔顶端A的仰角为37°，悬崖BC的高为92米，斜坡DE的坡度i＝1：2.4．（1）求斜坡DE的高EH的长；（2）求信号塔AB的高度．（参考数据：sin37°≈0.60，cos37°≈0.80，tan37°≈0.75．）23．（12分）如图，已知在▱ABCD中，E是边AD上一点，联结BE、CE，延长BA、CE相交于点F，CE2＝DE•BC．（1）求证：∠EBC＝∠DCE；（2）求证：BE•EF＝BF•AE．24．（12分）如图，在平面直角坐标系xOy中，抛物线y＝ax2+bx﹣2经过点A（2，0）和B （﹣1，﹣1），与y轴交于点C．（1）求这个抛物线的表达式；（2）如果点P是抛物线位于第二象限上一点，PC交x轴于点D，．①求P点坐标；②点Q在x轴上，如果∠QCA＝∠PCB，求点Q的坐标．25．（14分）如图，已知在等腰△ABC中，AB＝AC＝5，tan∠ABC＝2，BF⊥AC，垂足为F，点D是边AB上一点（不与A，B重合）．（1）求边BC的长；（2）如图2，延长DF交BC的延长线于点G，如果CG＝4，求线段AD的长；（3）过点D作DE⊥BC，垂足为E，DE交BF于点Q，联结DF，如果△DQF和△ABC 相似，求线段BD的长．2020-2021学年上海市松江区九年级（上）期末数学试卷（一模）参考答案与试题解析一、选择题（本大题共6题，每题4分，满分24分【下列各题的四个选项中，有且只有一个选项是正确的，选择正确项的代号并填涂在答题纸的相应位置上】1．如果两个相似三角形对应边的比为1：4，那么它们的周长比是（）A．1：2B．1：4C．1：8D．1：16【分析】直接利用相似三角形的性质得出答案．【解答】解：∵两个相似三角形对应边的比为1：4，∴它们的周长比是：1：4．故选：B．2．在Rt△ABC中，∠C＝90°，∠A＝α，BC＝2，那么AC的长为（）A．2sinαB．2cosαC．2tanαD．2cotα【分析】根据锐角三角函数的意义求解后，再做出判断即可．【解答】解：∵cot A＝，BC＝2，∴AC＝BC•cotα＝2cotα，故选：D．3．将抛物线y＝2x2向右平移3个单位，能得到的抛物线是（）A．y＝2x2+3B．y＝2x2﹣3C．y＝2（x+3）2 D．y＝2（x﹣3）2【分析】根据“左加右减、上加下减”的原则进行解答即可．【解答】解：由“左加右减”的原则可知，抛物线y＝2x2向右平移3个单位，能得到的抛物线是y＝2（x﹣3）2．故选：D．4．已知＝2，下列说法中不正确的是（）A．﹣2＝0B．与方向相同C．∥D．||＝2||【分析】根据平面向量的性质进行一一判断．【解答】解：A、由＝2得到：﹣2＝，故本选项说法不正确．B、由＝2知，与方向相同，故本选项说法正确．C、由＝2知，与方向相同，则∥，故本选项说法正确．D、由＝2知，||＝2||，故本选项说法正确．故选：A．5．如图，一艘船从A处向北偏东30°的方向行驶10千米到B处，再从B处向正西方向行驶20千米到C处，这时这艘船与A的距离（）A．15千米B．10千米C．10千米D．5千米【分析】根据直角三角形的三角函数得出AE，BE，进而得出CE，利用勾股定理得出AC 即可．【解答】解：如图，∵BC⊥AE，∴∠AEB＝90°，∵∠EAB＝30°，AB＝10米，∴BE＝5米，AE＝5米，∴CE＝BC﹣CE＝20﹣5＝15（米），∴AC＝（米），故选：C．6．如图，已知在Rt△ABC中，∠C＝90°，点G是△ABC的重心，GE⊥AC，垂足为E，如果CB＝8，则线段GE的长为（）A．B．C．D．【分析】延长AG交BC于D，如图，利用三角形重心的性质得到CD＝BD＝4，AG＝2GD，再证明GE∥CD，则可判断△AEG∽△ACD，然后利用相似比可求出EG的长．【解答】解：延长AG交BC于D，如图，∵点G是△ABC的重心，∴CD＝BD＝BC＝4，AG＝2GD，∵GE⊥AC，∴∠AEG＝90°，而∠C＝90°，∴GE∥CD，∴△AEG∽△ACD，∴＝＝＝，∴EG＝CD＝×4＝．故选：C．二、填空题（本大题共12题，每题4分，满分48分）【请将结果直接填入答题纸的相应位置上】7．已知，则＝．【分析】根据题意，设x＝5k，y＝3k，代入即可求得的值．【解答】解：由题意，设x＝5k，y＝3k，∴＝＝．故答案为：．8．已知线段MN的长是4cm，点P是线段MN的黄金分割点，则较长线段MP的长是（2﹣2）cm．【分析】根据黄金分割的概念得到MP＝MN，把MN＝4cm代入计算即可．【解答】解：∵P是线段MN的黄金分割点，∴MP＝MN，而MN＝4cm，∴MP＝4×＝（2﹣2）cm．故答案为（2﹣2）．9．计算：sin30°•cot60°＝．【分析】直接利用特殊角的三角函数值化简得出答案．【解答】解：原式＝×＝．故答案为：．10．在Rt△ABC中，∠C＝90°，AC＝6，cos A＝，那么AB的长为8．【分析】根据锐角三角函数的意义求解后，再做出判断即可．【解答】解：∵cos A＝＝，AC＝6，∴AB＝＝8，故答案为：8．11．一个边长为2厘米的正方形，如果它的边长增加x（x＞0）厘米，则面积随之增加y平方厘米，那么y关于x的函数解析式为y＝x2+4x．【分析】根据“面积的增加量就是边长增加前后的两个正方形的面积差”可得答案．【解答】解：由题意得，y＝（2+x）2﹣22＝x2+4x，故答案为：y＝x2+4x．12．已知点A（2，y1）、B（3，y2）在抛物线y＝x2﹣2x+c（c为常数）上，则y1＜y2（填“＞”、“＝”或“＜”）．【分析】先求得开口方向和对称轴，再根据二次函数的性质进行判断即可．【解答】解：∵y＝x2﹣2x+c，∴抛物线的开口向上，对称轴是直线x＝﹣＝1，∴在对称轴的右侧，y随x的增大而增大，∵1＜2＜3，∴y1＜y2，故答案为：＜．13．如图，已知直线l1、l2、l3分别交直线l4于点A、B、C，交直线l5于点D、E、F，且l1∥l2∥l3，AB＝4，AC＝6，DF＝10，则DE＝．【分析】直接根据平行线分线段成比例定理得到＝，然后根据比例的性质可计算出DE的长．【解答】解：∵l1∥l2∥l3，∴＝，即＝，∴DE＝．故答案为．14．如图，△ABC在边长为1个单位的方格纸中，△ABC的顶点在小正方形顶点位置，那么∠ABC的正弦值为．【分析】根据题意和图形，可以求得AC、BC和AB的长，然后根据勾股定理的逆定理可以判断△ACB的形状，然后即可求得∠ABC的正弦值．【解答】解：由图可得，AC＝＝，AB＝＝，BC＝＝2，∴AC2+BC2＝AB2，∴△ACB是直角三角形，∴sin∠ABC＝＝，故答案为：．15．如图，已知点D、E分别在△ABC的边AB和AC上，DE∥BC，＝，四边形DBCE 的面积等于7，则△ADE的面积为9．【分析】由DE∥BC可判定△ADE∽△ABC，根据相似三角形的面积比等于相似比的平方，可得＝（）2＝，从而求得＝，即可求得△ADE的面积为9．【解答】解：∵DE∥BC，∴△ADE∽△ABC，∴＝（）2＝，∴＝，∵四边形DBCE的面积等于7，∴S△ADE＝9．故答案为：9．16．如图，在梯形ABCD中，AD∥BC，BC＝2AD，设向量＝，＝，用向量、表示为+2．【分析】根据梯形的性质和三角形法则解答．【解答】解：如图，在梯形ABCD中，∵AD∥BC，BC＝2AD，＝，∴＝2＝2，∴＝+＝+2，故答案是：+2．17．如图，正方形DEFG的边EF在△ABC的边BC上，顶点D、G分别在边AB、AC上．已知△ABC的边BC＝16cm，高AH为10cm，则正方形DEFG的边长为cm．【分析】设正方形DEFG的边长为xcm，则DE＝PH＝xcm，所以AP＝（10﹣x）cm，再证明△ADG∽△ABC，则利用相似比得到＝，然后根据比例的性质求出x．【解答】解：如图，设正方形DEFG的边长为xcm，则DE＝PH＝xcm，∴AP＝AH﹣PH＝（10﹣x）cm，∵DG∥BC，∴△ADG∽△ABC，∴＝，即＝，∴x＝（cm），故答案为．18．如图，已知矩形纸片ABCD，点E在边AB上，且BE＝1，将△CBE沿直线CE翻折，使点B落在对角线AC上的点F处，联结DF，如果点D、F、E在同一直线上，则线段AE的长为．【分析】根据矩形的性质得到AD＝BC，∠ADC＝∠B＝∠DAE＝90°，根据折叠的性质得到CF＝BC，∠CFE＝∠B＝90°，EF＝BE＝1，DC＝DE，证明△AEF∽△DEA，根据相似三角形的性质即可得到结论．【解答】解：∵四边形ABCD是矩形，∴AD＝BC，AB＝CD，∠ADC＝∠B＝∠DAE＝90°，∵把△BCE沿直线CE对折，使点B落在对角线AC上的点F处，∴CF＝BC，∠CFE＝∠B＝90°，EF＝BE＝1，∠CEB＝∠CEF，∵矩形ABCD中，DC∥AB，∴∠DCE＝∠CEB，∴∠CEF＝∠DCE，∴DC＝DE，设AE＝x，则AB＝CD＝DE＝x+1，∵∠AFE＝∠CFD＝90°，∴∠AFE＝∠DAE＝90°，∵∠AEF＝∠DEA，∴△AEF∽△DEA，∴，解得x＝或x＝（舍去），∴AE＝．故答案为：．三、解答题（本大题共7题，满分78分）19．（10分）用配方法把二次函数y＝3x2﹣6x+5化为y＝a（x+m）2+k的形式，并指出这个函数图象的开口方向、对称轴和顶点坐标．【分析】利用配方法把一般式化为顶点式，根据二次函数的性质解答．【解答】解：y＝3x2﹣6x+5＝3（x2﹣2x）+5＝3（x2﹣2x+1﹣1）+5＝3（x﹣1）2+2，开口向上，对称轴为直线x＝1，顶点（1，2）．20．（10分）如图，已知AB∥CD，AD、BC相交于点E，AB＝6，BE＝4，BC＝9，联结AC．（1）求线段CD的长；（2）如果AE＝3，求线段AC的长．【分析】（1）证明△ABE∽△DCE，由相似三角形的性质得出，则可得出答案；（2）由相似三角形的性质求出DE＝，证明△ABC∽△ECD，由相似三角形的性质得出，则可求出答案．【解答】解：（1）∵AB∥CD，∴△ABE∽△DCE，∴，∵AB＝6，BE＝4，BC＝9，∴CD＝；（2）∵AE＝3，△ABE∽△DCE，∴，∴，∴DE＝，∵，＝，∴，∵AB∥DC，∴∠ECD＝∠ABC，∴△ABC∽△ECD，∴，∴，∴AC＝．21．（10分）如图，已知在Rt△ABC中，∠C＝90°，sin∠ABC＝，点D在边BC上，BD ＝4，联结AD，tan∠DAC＝．（1）求边AC的长；（2）求cot∠BAD的值．【分析】（1）根据题意和锐角三角函数，可以求得AC的长；（2）根据（1）中的结果，可以得到AC、CD的长，然后根据勾股定理可以得到AD的长，再根据等面积法可以求得DE的长，从而可以求得AE的长，然后即可得到cot∠BAD 的值．【解答】解：（1）设AC＝3x，∵∠C＝90°，sin∠ABC＝，∴AB＝5x，BC＝4x，∵tan∠DAC＝，∴CD＝2x，∵BD＝4，BC＝CD+BD，∴4x＝2x+4，解得x＝2，∴AC＝3x＝6；（2）作DE⊥AB于点E，由（1）知，AB＝5x＝10，AC＝6，BD＝4，∵，∴，解得DE＝，∵AC＝6，CD＝2x＝4，∠C＝90°，∴AD＝＝2，∴AE＝＝＝，∴cot∠BAD＝＝＝，即cot∠BAD的值是．22．（10分）如图，垂直于水平面的5G信号塔AB建在垂直于水平面的悬崖边B点处（点A、B、C在同一直线上）．某测量员从悬崖底C点出发沿水平方向前行60米到D点，再沿斜坡DE方向前行65米到E点（点A、B、C、D、E在同一平面内），在点E处测得5G信号塔顶端A的仰角为37°，悬崖BC的高为92米，斜坡DE的坡度i＝1：2.4．（1）求斜坡DE的高EH的长；（2）求信号塔AB的高度．（参考数据：sin37°≈0.60，cos37°≈0.80，tan37°≈0.75．）【分析】（1）过点E作EM⊥DC交DC的延长线于点M，根据斜坡DE的坡度（或坡比）i＝1：2.4可设EH＝x，则DH＝2.4x，利用勾股定理求出x的值，进而可得出EH；（2）结合（1）得DH的长，故可得出CH的长．由矩形的判定定理得出四边形EHCM 是矩形，故可得出EM＝HC，CM＝EH，再由锐角三角函数的定义求出AM的长，进而可得出答案．【解答】解：（1）过点E作EM⊥AC于点M，∵斜坡DE的坡度（或坡比）i＝1：2.4，DE＝65米，CD＝60米，∴设EH＝x，则DH＝2.4x．在Rt△DEH中，∵EH2+DH2＝DE2，即x2+（2.4x）2＝652，解得，x＝25（米）（负值舍去），∴EH＝25米；答：斜坡DE的高EH的长为25米；（2）∵DH＝2.4x＝60（米），∴CH＝DH+DC＝60+60＝120（米）．∵EM⊥AC，AC⊥CD，EH⊥CD，∴四边形EHCM是矩形，∴EM＝CH＝120米，CM＝EH＝25米．在Rt△AEM中，∵∠AEM＝37°，∴AM＝EM•tan37°≈120×0.75＝90（米），∴AC＝AM+CM＝90+25＝115（米）．∴AB＝AC﹣BC＝115﹣92＝23（米）．答：信号塔AB的高度为23米．23．（12分）如图，已知在▱ABCD中，E是边AD上一点，联结BE、CE，延长BA、CE相交于点F，CE2＝DE•BC．（1）求证：∠EBC＝∠DCE；（2）求证：BE•EF＝BF•AE．【分析】（1）通过证明△DEC∽△ECB，可得结论；（2）通过证明△ABE∽△EBF，可得△ABE∽△EBF，可得结论．【解答】证明：（1）∵四边形ABCD是平行四边形，∴AD∥BC，∴∠DEC＝∠BCE，∵CE2＝DE•BC，∴，∴△DEC∽△ECB，∴∠EBC＝∠DCE；（2）∵AD∥BC，AB∥CD，∴∠AEB＝∠EBC，∠F＝∠ECD，∴∠AEB＝∠F，又∵∠ABE＝∠EBF，∴△ABE∽△EBF，∴，∴BE•EF＝BE•AE．24．（12分）如图，在平面直角坐标系xOy中，抛物线y＝ax2+bx﹣2经过点A（2，0）和B （﹣1，﹣1），与y轴交于点C．（1）求这个抛物线的表达式；（2）如果点P是抛物线位于第二象限上一点，PC交x轴于点D，．①求P点坐标；②点Q在x轴上，如果∠QCA＝∠PCB，求点Q的坐标．【分析】（1）由待定系数法可求解析式；（2）①过点P作PE⊥x轴于E，由平行线分线段成比例可求PE的长，代入解析式可求解；②分两种情况讨论，利用全等三角形的性质和相似三角形的性质可求解．【解答】解：（1）∵抛物线y＝ax2+bx﹣2经过点A（2，0）和B（﹣1，﹣1），∴，解得：，∴抛物线解析式为：y＝x2﹣x﹣2；（2）①如图1，过点P作PE⊥x轴于E，∵抛物线y＝ax2+bx﹣2与y轴交于点C，∴点C（0，﹣2），∴OC＝2，∵PE∥OC，∴＝，∴PE＝，∴＝x2﹣x﹣2，∴x＝﹣2或x＝（不合题意舍去），∴点P（﹣2，）；②如图2，过点B作BH⊥CO于H，由①可知DO＝＝，∵B（﹣1，﹣1），点C（0，﹣2），A（2，0）∴OA＝OC＝2，BH＝CH＝1，∴∠BCH＝45°＝∠OCA，∴∠BCA＝90°，当点Q在线段AO上时，∵∠QCA＝∠PCB，∴∠DCO＝∠QCO，又∵CO＝CO，∠DOC＝∠QOC＝90°，∴△DOC≌△QOC（ASA），∴DO＝QO＝，∴点Q坐标为（，0），当点Q'在射线OA上时，∵∠Q'CA＝∠PCB，∴∠DCQ'＝90°，∴∠CDO+∠DQ'C＝90°，∠DCO+∠CDO＝90°，∴∠DQ'C＝∠DCO，又∵∠DOC＝∠Q'OC＝90°，∴△DOC∽△COQ'，∴，∴4＝×Q'O，∴Q'O＝，∴点Q'（，0），综上所述：点Q坐标为（，0）或（，0）．25．（14分）如图，已知在等腰△ABC中，AB＝AC＝5，tan∠ABC＝2，BF⊥AC，垂足为F，点D是边AB上一点（不与A，B重合）．（1）求边BC的长；（2）如图2，延长DF交BC的延长线于点G，如果CG＝4，求线段AD的长；（3）过点D作DE⊥BC，垂足为E，DE交BF于点Q，联结DF，如果△DQF和△ABC 相似，求线段BD的长．【分析】（1）先利用等腰三角形的性质判断出BC＝2BH，再用三角函数和勾股定理求出BH，即可得出结论；（2）先利用勾股定理和三角函数求出CF，再判断出△CFK∽△AFD和△CGK∽△BGD，得出比例式，即可得出结论；（3）先求出BF＝4，再判断出△BEQ∽△BFC，得出，设EQ＝m，则BQ ＝5m，BE＝2m，进而表示出BD＝10m，DQ＝3m，∠DQF＝∠C，再分两种情况，利用相似得出比例式表示出FQ，最后用BF＝4建立方程求出m，即可得出结论．【解答】解（1）如图1，过点A作DH⊥BC于H，∴∠AHB＝90°，∵AB＝AC＝5，∴BC＝2BH，在Rt△AHB中，tan∠ABC＝＝2，∴AH＝2BH，根据勾股定理得，AH2+BH2＝AB2，∴（2BH）2+BH2＝（5）2，∴BH＝5，∴BC＝2BH＝10；（2）∵AB＝AC，∴∠ABC＝∠ACB，∵tan∠ABC＝2，∴tan∠ACB＝2，由（1）知，BC＝10，∵BF⊥AC，∴∠BFC＝90°，在Rt△BFC中，tan∠ACB＝＝2，∴BF＝2CF，根据勾股定理得，BF2+CF2＝BC2，∴（2CF）2+CF2＝102，∴CF＝2，∴AF＝AC﹣CF＝5﹣2＝3，如图2，过点C作CK∥AB交FG于K，∴△CFK∽△AFD，∴，∴＝，∴△CGK∽△BGD，∴，∴CG＝4，∴＝，∴，∴，∴AD＝AB＝×5＝；（3）如备用图，在Rt△BFC中，根据勾股定理得，BF＝＝＝4，∵DE⊥BC，∴∠BEQ＝90°＝∠BFC，∵∠EBQ＝∠FBC，∴△BEQ∽△BFC，∵CF＝2，BC＝10，∴，∴，∴设EQ＝m，则BQ＝5m，根据勾股定理得，BE＝2m，在Rt△BEQ中，tan∠ABC＝＝2，∴DE＝2BE＝4m，根据勾股定理得，BD＝10m，∴DQ＝DE﹣EQ＝3m，∵DE⊥BC，∴∠BEQ＝90°，∴∠CBF+∠BQE＝90°，∵∠BQE＝∠DQF，∴∠CBF+∠DQF＝90°，∵∠BFC＝90°，∴∠CBF+∠C＝90°，∴∠DQF＝∠C，∵AB＝AC，∴∠ABC＝∠C＝∠DQF，∵△DQF和△ABC相似，∴①当△DQF∽△ACB时，∴，∴，∴QF＝6m，∵BF＝4，∴5m+6m＝4，∴BD＝10m＝，②当△DQF∽△BCA时，，∴，∴FQ＝m，∴m+5m＝4，∴m＝，∴BD＝10m＝，即BD的长为或．。
2021-2022学年上海市松江区九年级上学期期末数学试题
∴这个二次函数的二次项系数为负数，
∴符合条件的函数有y＝﹣x2+4x+5，
答案为：y＝﹣x2+4x+5，答案不唯一．
【点睛】此题主要考查了二次函数的性质，解题的关键是会利用函数的性质确定解析式的各项系数．
13.一位运动员投掷铅球，如果铅球运行时离地面高度为y（米）关于水平距离x（米）的函数解析式为 ，那么铅球运动过程中最高点离地面的距离为______m．
2.已知在Rt ABC中，∠C＝90°，AB＝c，AC＝b，那么下列结论一定成立的是（ ）
A.b＝ctanAB.b＝ccotAC.b＝csinAD.b＝ccosA
【答案】D
【分析】根据余弦的定义解答即可．
【详解】解： Rt△ABC中，∠C＝90°，AB＝c，AC＝b，
则cosA＝ ，
∴b＝ccosA，
8.把抛物线y＝x2+1向右平移1个单位，所得新抛物线的表达式是___．
【答案】
【分析】根据平移规律得到新抛物线顶点坐标，即可得 新抛物线的表达式．
【详解】∵抛物线 的顶点坐标为 ，
∴抛物线向右平移1个单位后，所得新抛物线的表达式为 ，即 ．
故答案为： ．
【点睛】本题考查的是二次函数的图象与几何变换，熟知“上加下减，左加右减”的原则是解答此题的关键．
【详解】解：∵抛物线开口向上，
∴a＞0，
∵抛物线对称轴在y轴右侧，
∴﹣ ＞0，
∴b＜0，
∵抛物线与y轴交点在x轴下方，
∴c＜0．
故选：D．
【点睛】本题考查了二次函数的图象，解题关键是掌握二次函数的图象与系数的关系．
4.已知 ＝2 ，那么下列判断错误的是（ ）
上海市上海市虹口区2021年中考一模(暨上学期期末)语文试卷及参考答案
的起点从鲁迅到上海后的第一个居住地景云里开始。
鲁迅在景云里居住期间，与茅盾、叶圣陶、柔石、冯雪峰、陈望道等一批文化名人的往来密切。
的第二处场所，是“中国左翼作家联盟会址纪念馆”。
鲁迅在这里发表了著名的《对于左翼作家联盟的意见》，与柔石等革命青年建立了深厚的友谊。
的第三处场所，是多伦文化艺术空间，在这里可以看到《鲁迅的文化生活》专题展览。
的第四处场所，是鲁迅在虹口的第二处住所拉摩斯公寓，在这里可以看到鲁迅与瞿秋白、陈赓、陈云等共产党人密切交往的生动故事。
2. 3. 4. 5.
6. 7.。