杭州二中2011学年第一学期高二期中考英语卷
浙江省杭州市西湖高级中学2011-2012学年高二开学考试(英语).pdf
线段的比较方法 2.从“形”出发，利用线段移动叠合 的方法 A B A C 1.从“数” 出发，通过度量长度进行 数值大 小比较。
45° 60° A o B D E F 所以:∠AOB＜∠DEF 读数为45 读数为60 如何比较角的大小？ ED落在∠ABC的外部，则∠DEF ＞ ∠ABC。
把∠DEF移动，使它的顶点E和∠ABC的顶点B重合，一边EF和BC重合，另一边ED和BA落在BC的同旁。
A B C D E F （ ） （ ） 比较∠ABC 和 ∠DEF的大小 例如： ED落在∠ABC的内部，则∠DEF ＜ ∠ABC 把∠DEF移动，使它的顶点E和∠ABC的顶点B重合，一边EF和BC重合，另一边ED和BA落在BC的同旁。
A B C D E F （ ） （ ） 比较∠ABC 和 ∠DEF的大小 1 O A B 2 C B O A 1 B O O B C 2 顶点与一边重合角的和差 1 O A B 2 C B O A 1 B O O B C 2 AOC为 1 和 2 的和 记作 AOC=1 + 2 （） AOC为 1 和 2 的差 记作 AOC=1 2 （ ） 顶点与一边重合 角的和差 O A C B 思考：下图中共有几个角？它们有什么关系？ 完成下列问题： 1、图中共有＿＿个角，它们分别是＿＿＿＿＿＿＿＿＿＿＿＿＿＿ 2、∠AOB＝＿＿＿＿+＿＿＿＿＿ 3、∠AOC＝＿＿＿＿－＿＿＿＿＿ 4、∠BOC＝＿＿＿＿－＿＿＿＿＿ 3 ∠AOB ，∠AOC， ∠BOC ∠AOC ∠BOC ∠AOB ∠BOC∠AOB ∠AOC 按图1填空： 4）∠A0B＋∠BOC＝ 5）∠A0C＋∠COD＝ 6）∠B0D－∠COD＝ 7）∠A0D－＝∠A0B O D C B A 图1 ∠AOC ∠AOD ∠BOC ∠BOD 1） ∠D0B ∠BOC 2） ∠C0B ∠AOC 3）∠DOC＋∠COB ∠B0D ＞ ＜ ＝ 同类练习1： １５° 75° 实践活动： 借助一副三角尺，大家都能画出哪些度 数的角？ O C B 例1 如图：O是直线AB上一点，∠AOC＝53°17′ 求∠BOC的度数 解：∵∠AOB是平角，∠AOB＝∠AOC+∠BOC ∴∠BOC＝∠AOB－∠AOC ＝180°－53°17′＝126°43′ A A B D C ( 1 ) ∠DAB=∠DAC+∠ ( 2 ) ∠ACB=∠DCB CAB ∠DCA （ 1）∠ABC=∠ABD ∠CBD （ 2 ）∠BDC=∠ADC ∠BDA + A B D C A B D C A B D C 2 1 2 1 B O A C O 当 1=2 时，射线OB 把 AOC分成两个相等的角 ，这时OB叫做 AOC 的平 分线，也可以说OB平分∠AOC 定义：在角的内部，自顶点引一条射线把 这个角分成两个相等的角，那么，这条射线叫做角的平分线。
浙江省杭州市第二中学2020┄2021学年高二上学期期中考试 英语试卷
杭州二中2020-2021学年第一学期高二年级期中考试英语试卷 11命题：方贤良陈雁赵岚校对、审核：鲍信良本卷分第I卷（选择题）和第II卷（非选择题）两部分，共100分，考试时间90分钟第I卷（共68分）第一部分：听力（共两节，满分15分）第一节（共5小题，每小题1分，满分5分）听下面5段对话。
每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1. What are the speakers talking about？A. How to get to Chicago.B. Whether to buy tickets onlineC. Why to cut down the expenses.2. How does the woman feel about the man’s leaving？A. Uncomfortable.B. Annoyed.C. Glad.3. How does the man feel at the moment？A. Great.B. Terrible.C. Better.4. What is Maggie’s greatest talent？A. Ability of solving problems.B. Leadership.C. Discovering new talent.5. What will Fred do at the library？A. He will borrow the books for Mary.B. He will look up the books on the list.C. He will copy the book list for Mary.第二节（共1小题，每小题1分，满分10分）听下面3段对话或独白。
2011年杭州市各类高中招生文化考试英语模拟试卷3
2011年杭州市各类高中招生文化考试英语模拟试卷3考生须知：1、本试卷满分120分，考试时间100分钟。
2、答题前，在答题纸上写姓名和准考证号。
3、必须在答题纸的对应答题位置上答题，写在其他地方无效。
1至60小题在答题纸上涂黑作答，答题方式详见答题纸上的说明。
4、做听力题时，先将答案划在试卷上。
录音内容结束后，你将有一分钟的时间将试卷上的答案转涂到答题纸上。
5、考试结束后，试题卷和答题纸一并上交。
试题卷I. 听力部分（25分）14.听短对话，回答问题（共5小题，计5分）原创听下面5段对话。
每段对话后有一个小题。
从题中所给的A、B、C三个选项中选出最佳选项，并标在试题的相应位置。
听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1. How did the man go to work today ?A. by busB.by bikeC. by car2. What does the man’ cousin do ？A. doctorB. policemanC. teacher3. what’s the relationship between the two speakers?A.workmateB.teacher and studentC. classmates4. what’s the woman looking for?A. FootballB. BasketballC.Baseball5. Where did this dialogue probably happen?A. In a theatreB. In a restaurantC.In a classroom二、听较长对话，回答问题（共6小题，计12分）由2010年东阳中考卷改编听下面一段对话，回答第6至第8三个小题。
现在，你有15秒钟的时间阅读这两个小题。
6. Why does the woman feel nervous before going to Switzerland ?A.Because she doesn’t know the language .B.Because she has never been abroad .C.Because she doesn’t know the custom there .7. What are famous in Switzerland ?A. Watches .B. Time .C. Culture .8. What should the woman do if she goes to a party in Switzerland ?A.She can’t be late .B.She should buy a present.C.She should take some flowers .听下面一段对话，回答第9至第11三个小题。
浙江省杭州地区(含周边)重点中学2021-2022学年高二上学期期中考试英语(原卷版)
A. She likes oranges.B. She loves meat.C. She is on a diet.
第二部分：阅读(共两节，满分50分)
第一节：(共15小题；每小题2.5分，满分37.5分)
阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项。
C. She has different interests from her friends.
16. Why doesn’t te?
A. She is too young.B. She has no time.C. She doesn’t loveto do that.
2021学年第一学期期中杭州地区(含周边)重点中学
高二年级英语学科试题
第Ⅰ卷选择题部分
第一部分：听力(共两节，满分30分)
第一节：(共5小题；每小题1.5分，满分7.5分)
听下面5段对话。每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项。听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。每段对话仅读一遍。
A. have some working experienceB. speak several languages
C. present good teaching plansD. know how to use computers
23. Before going to Japan, you need ________.
▪Applicants will teach their first language only.
▪Excellent teacher training programs.
2011年高二上学期第一次阶段考试试题终稿
岳阳县一中2011年高二上学期第一次阶段考试英语试题命题: 高二英语备课组总分:150分时量:120分钟本试卷分为四个部分,包括听力、语言知识运用、阅读理解和书面表达。
请将选择题的答案用2B铅笔涂在答题卡上,主观题的答案用0.5mm签字笔填在答题卡相应的位置。
第一部分: 听力(共两节, 满分30分)Section ADirections: In this section, you‟ll hear 6 conversations between 2 speakers. For each conversation there are several questions, and each questions is followed by 3 choices. Listen to the conversations carefully and then answer the questions by marking the corresponding letter A, B or C on the question booklet.You will hear each conversation twice.Conversation 1( )1.Where did the man want to smoke at first?A.In the another office.B.In the office next door.C.In the entrance hall.( )2.Where can the man smoke?A.In the office next door.B.In one of the offices.C.Outside.Conversation 2( )3.What is the woman going to do?A.To buy a ticket.B.To take a plane.C.To meet a friend at the airport. ( )4.How can the woman get to the ticket counter?A.Walk 3 yards and turn left at the end.B.Turn left at the end and walk further to a sign.C.Turn right at the end counter and walk 300 yards.Conversation 3( )5.What program does the man like?rmation about flights.B.Weather reports.C.Introduction to interesting places. ( )6.What will the weather be like in the next three days?A.Rainy.B.Sunny.C.Snowy.Conversation 4( )7.What is Mr Smith doing?A .Answering the phone. B.Having a meeting. C.Working in the office. ( )8.When will Mr Smith return to the office?A.After two o‟clock.B. In an hour.C.At three o‟clock.( )9.What can we infer according to the dialogue?A.The man will take a message for Mr Smith.B.Anne will ring the office again.C.Mr Smith will ring Anne back.Conversation 5( )10.What was the weather like last week?A. Nice and sunny.B. Very warm.C. Neither hot nor cold.( )11.What season is it now?A. Summer.B. Winter.C. Autumn.( )12.What does the man think the weather will be like this weekend?A.He thinks it‟ll rain.B.He doesn‟t think it‟ll rain.C.He thinks it‟ll be fine.Conversation 6( )13.Where is the woman?A. In First street.B. In Main Street.C.At the bus-stop.( )14.Where is the Burns Park?A.At the first crossing.B.On the other side of Main Street.C.At the corner of Lincoln and Fifth.( )15.How can the woman get to the park when she is at the crossing of First Street and Lin-coln Street?A.Turn right and go straight.B.Go along First Street for a few minutes.C.Turn left and walk two blocks.Section BDirections: In this section, you will hear a mini-talk. Listen carefully and then fill in the numbered blanks with the information you‟ve got. Fill in each blank with no more than 3 words. You will hear the mini-talk twice.第二部分：英语知识运用（共三节, 满分45分）第一节：语法填空（共15小题；每小题1分,满分15分）从A、B、C、D四个选项中,选出可以填入空白处的最佳选项,并在答题卡上将该项涂黑。
2011年杭州市各类高中招生文化考试英语模拟试卷21
2011年杭州市各类高中招生文化考试英语模拟试卷21考生须知：1．本试卷分试题卷和答题卷两部分。
满分为120分，考试时间为100分钟。
2．答题时，必须在答题卷的密封区内写明班级、姓名、学号、试场号和座位号。
3．所有答案都必须写在答题卷标定的位置上，务必注意试题序号和答题序号相对应。
4．考试结束后，上交答题卷。
听力部分（25%）一、听短对话回答问题。
（共5题，计5分）听下面5段对话，每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试题的相应位置。
听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1. What do they agree to do?A. They agree to visit Aunt Bush.B. They agree to find a good idea.C. They agree to go to the park.2. What will the woman do?A. She’ll go to have a walk with the man.B. She will do some housework.C. She’ll do some washing.3. What’s the time now?A. 4:50B. 4:55C. 5:004. What’s the girl most likely?A. An English teacher.B. A student.C. A farmer.5. What are they talking about?A. About the weather.B. About traffic.C. About jobs.二、听对话回答问题(共6小题, 计12分)听下面一段对话, 回答第6-8三个小题。
现在, 你有10秒钟的时间阅读这两题。
6. What happened?A. A car accident.B. A car exhibition.C. A car race.7. How many people were there in the blue car?A. Four.B. Five.C. Six.8.Which car should be responsible for the accident?A. The blue car.B. The red car.C. The black car.听下面一段对话，回答第9—11三个小题。
2011-2012学年浙江省杭州市杭州二中树兰实验学校初三第二学期统测英语试卷(答案+解析)
2011-2012学年浙江省杭州市杭州二中树兰实验学校初三第二学期统测英语试卷学校:___________姓名：___________班级：___________考号：___________一、单选题1．This is the song I’ve told you about. Isn’t it _____ beautiful one?A．a B．an C．the D．/2．Jim has a _____. He is going to the USA to visit his sister.A．two-months holiday B．two months’ holidaysC．two-month holiday D．two months holiday3．The traffic accident _____ last Sunday morning.A．was happened B．happened C．had happened D．happening4．I have never heard______.A．so wonderful a music B．so wonderful musicC．such a wonderful music D．such wonderful music5．5．_____ people in the world are sending are receiving e-mails every day.A．Million of B．Many millions ofC．Several millions’ D．Several millions6．——Don’t put the bike_______the teaching building.——Sorry, I won’t.A．on B．under C．around D．of7．——I haven’t got a camera.——I think you should buy_______. It’s useful for you.A．one B．this C．that D．it8．I called Mary many times yesterday evening. But I couldn’t get through. Her brother _____ on the phone all the time.A．talked B．had talked C．has talked D．was talking 9．9．—TV and computer are so popular these days.—Yes, they can______ our eyes to the outside world.A．call up B．open up C．turn up D．take up10．——Must I park my car behind the building?——No, you needn’t. You _____ park it here.A．need B．must C．may D．should11．I’m new here. Could you please tell me ________ ?A．what is the building used for B．when does the first class begin C．where is the dining hall D．how many classes our school has 12．12．——Have the police caught the thieves _____ the bank last week?——Yes, they were caught yesterday.A．that robbed B．which robbed C．robbed D．who have robbed 13．—Why is the classroom so dirty?—Sorry，sir. It yesterday, We forgot to do it.A．doesn’t clean B．didn’t cleanC．isn’t cleaned D．wasn’t cleaned 14．14．——Would you mind turning down the music?——_____.A．Yes, I would B．Yes, I do C．No, of course. D．No, not at all., 15．——The dining room is dirty. Can anyone clean it?——________ I do it all the time.A．Don’t mention it.B．Why you? C．Not sure D．Not me again.二、完型填空In the depths of my memory, many things I did with my father still live. I call these things16 and love.I don’t remember my father ever getting into a swimming pool. But he did17 the water. Any kind of 18 ride seemed to give him pleasure 19 he loved to fish; sometimes he took me along.But I never really liked being on the water, the way my father did. I liked being 20 the water, moving through it, having it all around me. I was not a strong 21 , or one who learned to swim early, for I had my 22 But I loved being in the swimming pool close to my father’s office and23 those summer days with my father, who 24 come by ona break. I needed him to see what I could do. My father would stand there in his suit, the25 person not in swimsuit.After swimming, I would go 26 his office and sit on the wooden chair in front of his big desk, where he let me 27 anything I found in his top desk drawer. Sometimes, if I was left alone at his desk while he worked in the lab, an assistant or a student might come in and tell me perhaps I shouldn’t be playing with his28 But my father always showed up andsaid easily, “Oh, no, it’s fine.” Sometimes he handed me coins and told me to get29 an ice cream…A poet once said, “We look at life once, in childhood; the rest is memory.” And I think it is not only what we “look at once, in childhood” that determines our memories, but30 , in that childhood, look at us.16．A．hope B．joy C．anger D．worry 17．A．hate B．refuse C．praise D．love 18．A．boat B．bus C．train D．bike 19．A．But B．Then C．And D．Still 20．A．on B．off C．by D．in 21．A．swimmer B．rider C．walker D．runner 22．A．hopes B．likes C．rights D．fears23．A．spending B．savingC．wasting D．destroying24．A．should B．would C．had to D．could 25．A．next B．only C．other D．last 26．A．away from B．out of C．by D．inside 27．A．put up B．break down C．play with D．work out28．A．fishing net B．office thingsC．wooden chair D．lab equipment29．A．the student B．the assistant C．myself D．himself 30．A．which B．who C．what D．whose三、阅读单选Lisa never had the chance to know her father. He and her mother divorced when she was just a young child. Even though he didn’t move far, he never came to visit his children.Lisa often wondered about her father. What did he looked like and what he was doing. All she knew was his name: Jeff White.After Lisa grew up, she became a nurse at a hospital, where she would help provide medicine and comfort for patients in their final days. A few weeks ago, she receieved a new patientwhose name was Jeff White.When Jeff came into his room, Lisa asked him if he had any children. Jeff told her that he had two da ughters, Lisa and Elly. Lisa couldn’t hold her tears back. She told him, “ I am Lisa, your daughter.”Jeff embraced her, saying that he was not a good father. And the daghter held his hand and kissed him. Then Jeff began to sing This Magic Moment.Jeff could have just weeks left to live, so Lisa wanted to make the most of the time she had with him. Lisa also brought her kids to the hospital to meet their grandfather. The kid made cards for him with the words, “ I love you.”Forgiveness is also a kind of love.31．what happened to Lisa when she was young?A．Her father lost his job.B．Her mother died.C．Her family moved to another country.D．Her father left the family.32．What did Lisa know about her father?A．Her father’s looksB．Her father’s nameC．Her father’s hobbyD．Her father’s job33．What does the underlined word “patient” mean in this passage?A．医生B．病人C．家属D．手术34．From the passage we know that__________A．Lisa has a brother.B．Lisa hates his father.C．Lisa has a sister.D．Lisa’s father hates her daughter.35．This passage mainly tells us that _______A．Kids should love their father.B．The father should love his kids.C．Forgiveness is also a kind of love.D．Fathers shouldn’t leave their families.New York is one of the last large American cities to have some of its policemen on horseback. The New York police have 170 horses working in certain parts of the city. The horses are expensive to feed, but it is even more expensive to look after them. Because the horses must walk on the streets, they need special horseshoes. In fact, they need more than 8,000 of them each year. Every police horse in New York gets new shoes every month. Keeping these shoes in good repair is the job of six blacksmiths(铁匠). There are only about thirty-five of these blacksmiths in the whole United States. The cost of shoeing a horse is between twenty dollars and thirty-five dollars, and it takes a good blacksmith two or three hours to do the job.A blacksmith’s job is not an easy one. He must be able to shape a shoe from a piece of metal and then fit it to the horse’s foot. The blacksmith must bend over all the time when he is fitting the shoe and must hold the weight of the horse’s leg while he works. Clearly, a blacksmith must be very strong. But even more important, he must be able to deal with horses---for before the blacksmith can begin his work, he has to get the horse to lift its leg. One of the blacksmiths in New York is James Corbin. He came to the country from Ireland in 1948. He not only makes horseshoes for the police but also works for a group of horse owners near the city. Corbin became interested in blacksmithing because his father did it, and, as he puts it, “It’s a good way to make a living.”36．According to the reading passage, a blacksmith must be likely a ________________ man. A．clever B．rich C．strong D．lucky37．James Corbin became a blacksmith because he ________________.A．was interested in horsesB．was needed by the policemenC．drew a picture of the horseshoeD．had to make a living38．In the reading pa ssage “to shape a shoe” is to ________________.A．fit it on the horse’s footB．use it for two or three hoursC．make the form of a horseshoe from a piece of metalD．draw a picture of the shoe39．The best title for the passage is “________________”.A．Policemen on HorsebackB．Blacksmiths and HorseshoeingC．James Corbin, a BlacksmithD．Horseshoeing is a Good Way to Make a Living40．Which of the following is true?A．Only a few large American cities have some policemen on horseback.B．New York is the only city in America to have some policemen on horseback. C．Policemen on horseback enjoy travelling around the United States.D．Policemen on horseback are less expensive than those in cars.四、信息匹配电视已经走进了千家万户，是我们生活的重要组成部分。
浙江省杭州二中2011-2012学年高二上学期期中试题(数学文)
浙江省杭州二中2011-2012学年高二上学期期中试题（数学文）参考公式：球的表面积公式 柱体的体积公式 24S R π= V Sh=球的体积公式 其中S 表示柱体的底面积，h 表示柱体的高334R V π=台体的体积公式其中R 表示球的半径 )(312211S S S S h V ++=锥体的体积公式 其中S 1、S 2分别表示台体的上、下底面积13V Sh = h 表示台体的高其中S 表示锥体的底面积，h 表示锥体的高.一、选择题（本大题共10小题，每小题4分，共40分，在每小题给出的四个选项中，只有一项是符合题目要求的，把答案填在答卷相应空格中）1．,,a b c 是三条直线，如果,a c b c ⊥⊥，则,a b 的位置关系是（ ）A ．相交B ．平行C ．异面D ．以上答案都有可能 2． 已知直线,a b 和平面α，下列推论错误的是（ ）A ． a a b b αα⊥⎫⇒⊥⎬⊂⎭B ． //a b a b a b αα⊥⎫⇒⊂⎬⊥⎭或C ．////a a b b αα⎫⇒⎬⊂⎭ D ． //a b b a αα⎫⇒⊥⎬⊥⎭3．已知一水平放置的三角形的平面直观图是边长为1的正三角形，那么原三角形的面积为（ ）A ．23 B ．2 C ．4 D ．164． 直线1l 的倾斜角为30°，直线2l ⊥1l ，则直线2l 的倾斜角为（ ） A ．30 B ．60 C ．120 D ．1505．直线3480x y ++=在x 轴上的截距是（ ） A 83-B 83C 2D 2- 6．若直线10x ay ++=和10ax y +-=互相平行，那实数a 的值是（ ） A 1 B 1或－1 C －1 D 07．若一个正方体的棱长为1，则其外接球的体积为（ ）A ．6πBC ．43π D8．某几何体的正视图与侧视图如图所示，若该几何体的体积为31，则该几何体的俯视图可以是（ ）9．a 、b 是异面直线，P 为空间一点，下列命题： （1）过P 总可以作一条直线与a 、b 都垂直； （2）过P 总可以作一条直线与a 、b 都垂直相交；（3）过P 总可以作一条直线与a 、b 之一垂直与另一条相交； （4）过点P 总可以作一平面与a 、b 同时垂直；（5）过P 总可以作一平面与a 、b 之一垂直与另一条平行，其中正确命题的个数是（ ） A ．0 B ．1 C ．2 D ．310．一个斜三棱柱的底面是边长为4的正三角形，侧棱长5，若其中一条侧棱与底面三角形的相邻两边都成45˚角，则这个三棱柱的侧面积是（ ）A ．60 B． C．20 D．20二、填空题（本大题共4小题，每小题4分，共16分，把答案填在答卷中相应横线上） 11.经过原点且与直线3420x y ++=平行的直线方程为 ▲ ．12.若直线l 经过点24(,), 且其在x 轴和y 轴上的截距相等, 则直线l 的方程是▲ ． 13．空间四边形ABCD 中，2====CD BC AD AB ，AD 和BC 所成角为60o，FE 、分别为CD AB 、 中点，则EF 的长度为 ▲ ．14.如图所示，在三棱柱ABC －A 1B 1C 1中，AA 1⊥底面A 1B 1C 1，底面为直角三角形，∠ACB ＝90°，AC，BC ＝CC 1＝1，P 是BC 1上一动点，则A 1P ＋PC 的最小值是 ▲ ．三、解答题（本大题共5小题，共44分，解答应写出文字说明,证明过程或演算步骤） 15．（本小题8分）已知R m ∈, 点A （m ，-1），B （22-m ，4），C （-2，2），D （4，（第14题）A BCD主视图 侧视图（第8题）m ），直线AB 与CD 垂直, 求实数m 的值.16．（本题8分）如图1，在三棱锥P －ABC 中，平面PAC ⊥平面ABC ，AB ⊥BC ，AB ＝BC ＝PA ＝PC ，点O 、D 分别是AC 、PC 的中点.（I ）求证：//OD 平面PAB ； （II ）求PB 与平面ABC 所成角．图1 17．（本题8分）如图2，在四棱锥P －ABCD 中，PA ⊥平面ABCD ，底面ABCD 是菱形，AB=2，∠BAD= 60.(Ⅰ) 求证：BD ⊥平面PAC; 图2 （Ⅱ）若PA=AB, 求PB 与AC 所成角的余弦值.18．（本题8分）在直角△ABC 中，∠C 为直角，点A 、B 的坐标分别A(3，6) ，B(1，0)，斜边AB 上的中线所在的直线的斜率为31.（I ）求点C 的坐标；（II ）若点C 在第二象限，求此时BC 边上的中线所在的直线方程．19．（本题12分）如图3，在四面体ABOC中，OC⊥OA，OC⊥OB，∠AOB＝120°，且OA ＝OB＝OC＝1．(I) 求二面角O－AB－C的平面角的正切值；(II) 设P为AC的中点．证明：在AB上存在一点Q，使PQ⊥OA，并计算ABAQ的值.图3杭州二中2011学年第一学期高二年级期中考试数学答题卷（文科）二、填空题（本大题共4小题，每小题4分，共16分）11．．12．．13．．14．．三、解答题（本大题共5小题，共44分，解答应写出文字说明,证明过程或演算步骤）15．16．图117．图218．19．图3杭州二中2011学年第一学期高二年级期中考试数学答题卷（文科）二、填空题（本大题共4小题，每小题4分，共16分）11． 340x y += ． 12．x y y x 206==-+或.13 14三、解答题（本大题共5小题，共44分．解答应写出文字说明,证明过程或演算步骤） 15． 解:由题意可知k CD 肯定存在,但k AB 不一定存在(1)若k AB 不存在,则m= m 2-2,即m=2或者-1, 当m=2时, k CD =0,则符合题意当m=-1时, k CD =12-,则不符合题意,舍去 (2)若k AB 存在,则m ≠ m 2-2,即m ≠2且m ≠-1,则kAB k CD =252126m m m -=---,化简得到26220m m --=,解得2611=-=m m 或又因为m ≠2且m ≠-1,故116m =-(3)综上所述, 2611=-=m m 或16．解：（Ⅰ）∵O 、D 分别为AC 、PC 中点，∴OD ∥PA 又PA //平面PAB ∴OD ∥平面PAB（Ⅱ）连接PO ，OB 图1 ∵PA ＝PC ∴PO ⊥AC又∵平面PAC ⊥平面ABC ∴PO ⊥平面ABC ∴∠PBO 是直线PB 与平面ABC 所成角 设AB ＝BC ＝PA ＝PC ＝1，则∵AB ⊥BC∴0B=0C=2 2=∴tan ∠PBO ＝POOB=1 ∴∠PBO ＝45 ∴PB 与平面ABC 所成角为4517．证明：（Ⅰ）因为四边形ABCD 是菱形，所以AC ⊥BD. 图2 又因为PA ⊥平面ABCD. 所以PA ⊥BD.所以BD ⊥平面PAC.（Ⅱ）取AB 、BC 、PA 中点，分别记为E 、F 、G ， 则EG ∥PB ，EF ∥AC所以∠GEF 即为 PB 与AC 所成角 ∵PA ⊥平面ABCD ∴PA ⊥AB, PA ⊥AF又∵PA=AB ＝2，∠BAD= 60 ∴∴== ∴cos ∠∴PB 与AC所成角的余弦值418．解：（I ）由题意，设AB 的中点为D ，则D 的坐标为D(2,3),则斜边AB 上的中线方程为CD:1323()y x -=-，即1733y x =+ 由于C 点在AB 的中线上，所以可设点C 的坐标为1733(,)m m +若m ＝1，C 点坐标为813(,)，直线BC 的斜率不存在，但直线AC 的斜率为53，其乘积不为－1，则BC 与AC 不垂直，不合题意，舍去 若m ＝3，C 点坐标为1033(,)，直线AC 的斜率不存在，但直线BC 的斜率为53，其乘积不为－1，则BC 与AC 不垂直，不合题意，舍去所以31≠≠m m 且，所以AC 的斜率是76113339m m m m +--=--，BC 的斜率是773133m m m m +-+=--，则由于AC ⊥BC, 所以13379311-=-+⋅--m m m m ，化简得2450m m --=，解得15-==m m 或，所以点C 的坐标为54(,)或12(,)-.（II ）若点C 在第二象限，则有上题可知，点C 坐标为12(,)-，则BC 的中点坐标为01(,)，则BC 上的中线经过BC 的中点坐标为01(,)和A 点36(,)，可以根据两点式，得到106130y x --=--，化简得到5330x y -+=，即为所求的直线方程. 19．解：（I ）取AB 的中点D,连接OD,CD ，则由于OA=OB,所以OD ⊥AB ， 图3又由于OC ⊥OA ，OC ⊥OB ，所以OC ⊥平面OAB ，所以OC ⊥AB 又因为OD∩OC ＝O ，所以AB ⊥平面OCD ，所以AB ⊥CD,所以∠ODC 就是所求的二面角O －AB －C 的平面角又因为∠AOB ＝120°，且OA ＝OB ＝OC ＝1，在直角△ODA 中， ∠ OAD ＝30°，所以OD ＝12， 所以tan ∠ODC=1212OC OD ==,所以二面角O －AB －C 的平面角的正切值为2. （II ）在平面OAB 内作ON ⊥OA 交AB 于N ，连结N C ．又OA ⊥OC ，∴OA ⊥平面ON C ． ∵NC ⊂平面ONC ，∴OA ⊥N C ． 取Q 为AN 的中点，则PQ ∥NC ， ∴PQ ⊥O A ．在等腰△AOB 中，∠AOB ＝120°， ∴∠OAB ＝∠OBA ＝30°． 在Rt △AON 中，∠OAN ＝30°， ∴ON ＝12AN ＝AQ ．在△ONB 中，∠NOB ＝120°－90°＝30°＝∠NBO ，∴NB ＝ON ＝AQ ，∴ABAQ ＝3。
杭州二中2011学年第一学期高一期中考数学卷
杭州二中2011学年第一学期高一年级期中考试数学试卷命题 叶加群 校对 陆华兵 审核 孙惠华本试卷分为第Ⅰ卷（选择题和填空题）和第Ⅱ卷（答题卷）两部分， 满分100 分，考试时间 90 分钟.一、选择题（本大题共10小题，每小题4分，共40分，在每小题给出的四个选项中，只有一项是符合题目要求的．把答案填在答卷．．相应空格中） 1. 满足{}1,1{1,0,1}A -=- 的集合A 共有（ ）A.2个B. 4个C. 8个D. 16个2. 三个数20.520.5,log 0.5,2a b c ===之间的大小关系是 （ ） A ．a c b << B. b c a << C. b a c << D. a b c <<3.下列函数中是偶函数的是 ( )A .3y x=-B.]3,3(,22-∈+=x x yC.x y 2log =D.2-=x y4. 已知⎩⎨⎧>-<+=044)(x x x x x f ，则)3([-f f ]的值为 （ ）A ．－2B ．2C ．－3D ．35. 已知函数()833-+=x x f x ，用二分法求方程()33801,3xx x +-=∈在内近似解的过程中，取区间中点02x =，那么下一个有根区间为 ( ) A ．（1,2） B ．（2,3） C ．（1,2）或（2,3）都可以 D ．不能确定6. 函数y =）A ．[1,)+∞B ．2(,)3+∞C ．(,1]-∞D ．2(,1]37. 已知()f x 为R 上奇函数，当0x ≥时,2()2f x x x =+，则当0x <时，()f x =( ).A.22x x - B. 22x x -+ C. 22x x + D. 22x x -- 8. 甲、乙二人从A 地沿同一方向去B 地，途中都使用两种不同的速度1v 与2v （1v ＜2v ）.甲前一半的路程使用速度1v ，后一半的路程使用速度2v ；乙前一半的时间使用速度1v ，后一半时间使用速度2v .关于甲、乙二人从A 地到达B 地的路程与时间的函数图象及关系，有如图所示的四个不同的图示分析（其中横轴t 表示时间，纵轴s 表示路程，C 是AB 的中点），则其中可能正确的图示分析为 （ ）A .（1） B. （2） C.（3） D . （4） 9. 已知函数(31)4,1()log ,1aa x a x f x x x -+<⎧=⎨≥⎩满足:对任意实数21,x x ,当12x x <时,总有12()()0f x f x ->,那么实数a 的取值范围是 （ ）A ． [11,)73B ． 1(0,)3C ．11(,)73D ．[1,1)710. 定义：区间[]()1212,x x x x <的长度为21x x -．已知函数||2x y =的定义域为[],a b ，值域为[]1,2，记区间[],a b 的最大长度为m , 最小长度为n ．则函数)2()(n x m x g x +-=的零点个数是 （ ）A ．1B ．2C ．0D ．3二、填空题（本大题共7小题，每小题3分，共21分 ．把答案填在答卷中相应横线上） 11.函数2y =的值域是 ▲ . 12. 已知集合{}{222,,M y y x x x R N x y ==-++∈==，那么集合M N 为 ▲ .13. 设函数2 0()() 0.x x f x g x x ⎧<=⎨>⎩，，，，若()f x 是奇函数，则(2)g 的值是 ▲ .14. 方程2240x ax -+=的两根均大于1，则实数a 的范围是 ▲ .15. 已知偶函数)(x f 在区间),0[+∞上单调递增，则满足)31()12(f x f <-的x 的取值范围是 ▲ . 16. 定义运算()()a ab a b b a b ≤⎧*=⎨>⎩，例如，121*=，则函数2()(1)f x x x =*-的最大值为▲ . 17. 下列说法：①函数()212log 23y x x =--的单调增区间是(),1-∞；②若函数()y f x =定义域为R 且满足()()11f x f x -=+，则它的图象关于y 轴对称；③函数()()1||xf x x R x =∈+的值域为(1,1)-；④函数2|3|y x =-的图象和直线 ()y a a R =∈的公共点个数是m ，则m 的值可能是0,2,3,4；⑤若函数2()25(1)f x x ax a =-+>在[]1,3x ∈上有零点，则实数a 的取值范围是,3]. 其中正确的序号是 ▲ .杭州二中2011学年第一学期高一年级期中考试数学答题卷一、 选择题（本大题共10小题，每小题4分，共40分）二、填空题（本大题共7小题，每小题3分，共21分）11. . 12. . 13. . 14. .15. . 16. . 17. .三、解答题（本大题共4小题，共39分．解答应写出文字说明,证明过程或演算步骤） 18. ( 本小题满分8分）(Ⅰ) 计算：2213log lg14812lg1)27100-⎛⎫-++ ⎪⎝⎭（Ⅱ）已知11223x x-+=，求22123x x x x --+-+-的值.19. （本小题满分8分）若集合2{|log (2)2,01}a A x x x a a =--<>≠且， （Ⅰ）若2=a ，求集合A ；（Ⅱ）若3A ∈，求实数a 的取值范围．20. （本小题满分11分）已知函数4()nf x x x=-，且(4)3f =. （Ⅰ）判断()f x 的奇偶性并说明理由；（Ⅱ）判断()f x 在区间()0,+∞上的单调性，并证明你的结论；（Ⅲ）若在区间[1,3]上，不等式()221f x x m >++恒成立，试确定实数m 的取值范围.21. （本小题满分12分）已知幂函数(2)(1)(),k k f x x k Z -+=∈，且()f x 在()0,+∞上单调递增.（Ⅰ）求实数k 的值，并写出相应的函数()f x 的解析式；（II ）若()2()43F x f x x =-+在区间[2,1]a a +上不单调．．．，求实数a 的取值范围； （III ）试判断是否存在正数q ，使函数()1()(21)g x qf x q x =-+-在区间[1,2]-上的值域为17[4,]8-. 若存在，求出q 的值；若不存在，请说明理由.杭州二中2011学年第一学期高一年级期中考试数学答案一、选择题（本大题共10小题，每小题4分，共40分）二、填空题（本大题共7小题，每小题3分，共21分）11. [02]，. 12. []3,2- . 13. 14-. 14. 5[2,)2.15. 12{|}33x x <<. 17. ③ ④ ⑤.三、解答题（本大题共4小题，共39分．解答应写出文字说明,证明过程或演算步骤）18. ( 本小题满分8分）(Ⅰ) 2213log lg1481192lg1)2132710044-⎛⎫-++=--+=- ⎪⎝⎭（Ⅱ）已知11223x x -+=，求22123x x x x --+-+-的值. 解：∵11223x x-+=，∴11222()9x x -+=，∴129x x -++=，∴17x x -+=，∴12()49x x -+=，∴2247x x -+=，∴2212472453734x x x x --+--==+--19.（本小题满分8分）若集合2{|log (2)2,01}a A x x x a a =--<>≠且， （Ⅰ）若2=a ，求集合A ；（Ⅱ）若3A ∈，求实数a 的取值范围．解:（Ⅰ）若2=a ，22log (2)2x x --<，则2024x x <--<得21x -<<-或 23x <<所以{|2123}A x x x =-<<-<<或（Ⅱ）因为3A ∈，所以2log (332)2a --<，log 42a <，当1a >时，24a >，2a ∴>； 当01a <<时，24a <，∴01a << 所以实数a 的取值范围是(0,1)(2,)+∞ .20.（本小题满分11分）已知函数4()nf x x x=-，且(4)3f =. （Ⅰ）判断()f x 的奇偶性并说明理由；（Ⅱ）判断()f x 在区间()0,+∞上的单调性，并证明你的结论；（Ⅲ）若在区间[1,3]上，不等式()221f x x m >++恒成立，试确定实数m 的取值范围. 解：（Ⅰ）由(4)3f =得： 1n = ，其定义域为()(),00,-∞+∞∴函数()f x 在()(),00,-∞+∞ 上为奇函数。
浙江省杭州二中2011-2012学年高二上学期期中试题(数学理)
主视图侧视图（第5题）浙江省杭州二中2011-2012学年高二上学期期中试题（数学理）参考公式：球的表面积公式 柱体的体积公式 24S R π= V Sh=球的体积公式 其中S 表示柱体的底面积，h 表示柱体的高334R V π=台体的体积公式其中R 表示球的半径 )(312211S S S S h V ++=锥体的体积公式 其中S 1、S 2分别表示台体的上、下底面积13V Sh = h 表示台体的高其中S 表示锥体的底面积，h 表示锥体的高.一、选择题（本大题共10小题，每小题4分，共40分，在每小题给出的四个选项中，只有一项是符合题目要求的，把答案填在答卷相应空格中） 1．已知直线a b 、是异面直线,直线c d 、分别与a b 、都相交，则直线c d 、的位置关系（ ） A.可能是平行直线 B.一定是异面直线C.可能是相交直线D.平行、相交、异面直线都有可能 2．已知m ,n 是两条不重合的直线，α,β,γ是三个两两不重合的平面,给出下列四个命题: ①若,,m m αβ⊥⊥则//αβ； ②若,,αγβγ⊥⊥则//αβ；③若,,//,m n m n αβ⊂⊂则//αβ；④若m ,n 是异面直线,,//,,//,m m n n αββα⊂⊂则//αβ。
其中正确的命题是（ ）A .①和②B .①和③C .③和④D .①和④3．已知一水平放置的三角形的平面直观图是边长为1的正三角形，那么原三角形的面积为（ ） A ．23 B．2 C．4 D．164．已知θ∈R ，则直线013sin =+-y x θ的倾斜角的取值范围是（ ） A ．]30,0[︒︒ B ．)180,150[︒︒ C ．)180,150[]30,0[︒︒⋃︒︒ D ．]150,30[︒︒5．某几何体的正视图与侧视图如图所示，若该几何体的体积为31，则该几何体的俯视图可以是（ ）A BC D6．当θ是第四象限时,两条直线0cos 1sin =-++a y x θθ和0cos 1=+-+b y x θ的位置关系是（ ）A ．平行B ．垂直C ．相交但不垂直D ．重合7．如左图已知异面线段CD AB 、, 线段BD AC 、中点的为F E 、,且6,5,8AB EF CD ===,则异面线段CD AB 、所在直线所成的角为（ ） 第题A 030 B 045 C. 060 D.090 8．点)1,1(A 到直线02sin cos =-+θθy x 的距离的最大值是（） A. 1 B. 22+C. 1+D. 29．已知直线l 过点P(2,1),且与x , y 轴所围成的面积为4,则直线l 有（ ）条 A. 1 B. 2 C. 3 D. 410．已知正ABC ∆的顶点A 在平面α内，顶点B 、C 在平面α外的同一侧，D 为BC 的中点，若ABC ∆在平面α上的投影是以A 为直角顶点的三角形，则直线AD 与平面α所成角的正弦值的范围为（ ）A .23⎛ ⎝⎭B. ,13⎫⎪⎪⎣⎭C.1,23⎛⎫ ⎪ ⎪⎝⎭D. 32 二、填空题（本大题共4小题，前3题各4分，第14题6分，共18分，把答案填在答卷中相应横线上）11. 矩形A B C D 中，43AB BC ==，，沿AC 将矩形ABCD 折成一个直二面角B AC D--，则四面体ABCD 的外接球的体积为________. 12．两条直线12++=k kx y 和042=-+y x 的交点在第四象限，则k 的取值范围是_________．13．如图,二面角l αβ--的大小是60°，线段AB α⊂，B l ∈，与l 所成的角为30°，则AB与平面β所成的角的正弦值是_________.α∙AB∙β14. 如果一个四面体的三个面是直角三角形，那么，第四个面可能是：①直角三角形；②锐角三角形；③钝角三角形；④等腰三角形；⑤等腰直角三角形；⑥等边三角形。
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杭州二中2011学年第一学期高二年级期中考试英语试题2011.11命题和校对：鲍信良赵岚方贤良第Ⅰ卷第一部分听力（共两节，满分15分）第一节（共5题；每小题1分，满分5分）听下面5段对话。
每段对话后有5个小题，从题中所给的A, B, C三个选项中选出最佳选项，并标在试卷的相应位置。
听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1. What does the woman ask the man to do?A. Make a kite for her.B. Buy a kite for her.C. Get her kite from the tree.2. How will the woman deal with the tickets?A. Return them back with a refund.B. Give them to a friend.C. Give them to the man.3. How does the man feel about the final exam questions?A. He thinks they were very difficult.B. He doesn‘t have any idea about them.C. He thinks they were fairly easy.4. Why do the speakers decide to take the subway?A. It‘s fast.B. It‘s cheap.C. It‘s direct.5. What do we know about the man‘s wife?A. She isn‘t interested in the outside view.B. She likes taking elevators.C. She wants to change to a lower floor.第二节（共10题；每小题1分，满分10分）听下面4段对话或独白。
每段对话或独白后有几个小题，从题中所给的A, B, C三个选项中选出最佳选项，并标在试卷的相应位置。
听完每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各个小题将给出5秒钟的作答时间。
每段对话或独白读两遍。
听第6段材料，回答第6，7题。
6. Where did the man get the dog?A. From his father.B. From his neighbors.C. From a pet center.7. What does the woman‘s cat like to do?A. Roll over.B. Scratch with her paws.C. Play dead.听第7段材料，回答第8，9题。
8. When should the speakers get to the cinema?A. At 9:00 p.m.B. At 9:30 p.m.C. At 10:00 p.m.9. Why should they arrive so early?A. There will be many people there waiting to see the movie.B. They need to buy tickets there.C. There‘s a ceremony before the show.听第8 段材料，回答第10至12题。
10. Where does this conversation probably take place?A. In a classroom.B. In the professor‘s office. C In the school library.11. Why has the professor given the girl a failing grade on her paper?A. She should have finished it earlier.B. Her work was not completed.C. Her paper was not done individually.12. What must she do to receive credit?A. Give a talk to the class.B. Write another report.C. Take an extra exam.听第9段材料，回答第13至15题。
13. What does Sarah advise the man to do first?A. Think about his appearance.B. Find information about the company.C. Recite the answers to some questions.14. Why is it helpful for the man to get a general idea of the company?A. He‘ll get to know the hobbies and interests of the boss.B. He‘ll be able to answer the questions properly.C. He can fight all the others without defeat.15. How many things does the man have to prepare?A. TwoB. ThreeC. Four第二部分英语知识运用（共两节，满分25分）第一节：单项填空(共20小题；每小题0.5分，满分10分)从A、B、C、D四个选项中，选出可以填入空白处的最佳选项，并在答题卡上将该项涂黑。
16. Tom thought he was ______ failure for the reason that he lost ______ face in front of theaudience.A. a; /B. /; /C. a; theD. /; a17. The New York Times ______ a wide circulation in that town and that people each ______ acopy in the subway is a common occurrence.A. has; readsB. have; readC. has; readD. have; reads18. I got out of the taxi, ______ the fare and dashed into the train station.A. paidB. to payC. payingD. having paid19. ----It‘s a pity you missed the plane.----I just couldn‘t help it because all _______ to the airport were blocked!A. methodsB. approachesC. itemsD. means20. The mountain village had been ______ by the snow for almost a month before the rescue partyarrived.A. cut offB. cut upC. cut downD. cut back21. ----You've finally figured out the puzzle！----Yeah, in a complex way, _______.A. tooB. thoughC. eitherD. yet22. In the shop the lady had a preference for the latter and paid for it with the _______.A. 20 pounds remainedB. 20 pounds to remainC. remaining 20 poundsD. remained 20 pounds23. Kitty is very______ about what she wears, depending on what occasions she has to attend.A. considerateB. specialC. particularD. modest24. ---- What should I do with this digital media now?----______ the iPad Pocket Guide first.A. ReadingB. ReadC. To readD. Having read25. In the US coffee is the usual drink. Next after it, Americans are ______ to drink cola drinks,such as Coke or Pepsi, or other soft drinks.A．possible B．likely C．probable D．truly26. Much _______ Maggie‘s regret, she saw her son cross for _______.A. to; having not been invitedB. for; having not been invitedC. for; not having been invitedD. to; not having been invited27. With the help of his friends, he has ______a good business over the years.A. built upB. made upC. grown upD. picked up28. Finding her Porsche 911 stolen, ______.A. a policeman was asked to helpB. it was searched for everywhereC. she hurried to a policeman for helpD. the area was searching thoroughly29. ______ it matters, but how did you spend so much money in such a short period of time?A. Now thatB. So thatC. Only thatD. Not that30. The cartoon movie, originally ______ teenagers, has turned out to appeal to adults so much.A. crowded inB. referred toC. intended forD. set on31. ______ can you expect to get a pay rise.A. With hard workB. Although work hardC. His working hardD. Only with hard work32. Learning that their only son was sound and safe ______ the family _______.A. laid; at easeB. made; in easeC. set; with easeD. put; at ease33. The accused man ________ himself by saying that he killed the man totally out of self-defenseand it was completely an accident.A. guardedB. protectedC. defendedD. prevented34. The idea that China has been in the first ________ of world powers is more or less subjective.A. rateB. rankC. stageD. pace35. _______ with the speech ________ by the graduate, the boss determined to give him a joboffer.A. Impressed; deliveredB. Impressing; directedC. Impressed; inspiredD. Impressing; commented第二节完形填空（共15小题；每小题1分，满分15分）阅读下面短文，从短文后各题所给的A、B、C、D四个选项中，选出最佳选项。