浙江省杭州第二中学2015-2016学年高一下学期期中考试英语试卷 Word版含解析
杭州二中2015学年第二学期高一年级期中考英语试卷2016. 4本试卷分为第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65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l0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 man advise the woman to do?A. Collect her books.B. Throw out her books.C. Give away her books.2. When does the woman want to go to the museum?A. Right after breakfast.B. After her mother leaves.C. Before she goes shopping.3. What does the man actually think of Twitter?A. Incorrect.B. Modern.C. Out-of-date.4. What is the woman trying to do?A. Create a game.B. Send an email.C. Strengthen her memory.5. What are the speakers talking about?A. A photo.B. The man‟s brother.C. Th e woman‟s hair.第二节（共10小题；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至7题。
6. Who is the man waiting for?A. His girlfriend.B. His sister.C. His wife.7. Where does this conversation most likely take place?A. At a concert.B. At a cinema.C. At a railway station.听第7段材料，回答第8至9题。
8. Why did the woman call the man?A. To cancel a booking.B. To make a reservation.C. To change her trip.9. When is the woman likely to be free?A. In February.B. In March.C. In half a year.听第8段材料，回答第10至12题。
10. Why is the woman moving?A. To save money.B. To build a career.C. To escape cold weather.11. What happened to the clubs in San Francisco?A. They were burned down.B. They were pulled down.C. They were turned into restaurants.12. What is the woman‟s dream?A. Becoming famous.B. Getting married.C. Attending performances.听第9段材料，回答第13至15题。
13. What attracts most tourists to Mexico City?A. Delicious food.B. Various activities.C.Colorfulnightlife.14. Why does the speaker mainly suggest walking around?A. To do shopping.B. To kill time.C. To talk with people.15. What is the purpose of this talk?A. To inform students of the city.B. To encourage people to visit.C. To introduce a different culture.第二部分：语言运用（共三节，满分30分）第一节：词汇单选（共10个小题；每小题0.5分，满分5分）16. Scientists have found that heavy drinking can cause _______ brain damage inteenagers,which may never recover.A. permanentB. addictedC. obviousD. diverse17. State leaders joined the discussions with the country‟s political advisors yesterday, calling for efforts to _______ the global financial crisis (危机).A. try out forB. stick withC. blow awayD. pull through18. China can _______ a global role in improving public health by sharing some of its vaccines(疫苗) with other developing countries.A. take effectB. fix upC. take onD. pile up19. Vice-Premier Li Keqiang said that more effort should be made to save land and _______ inorder to reduce consumption (消耗) and improvethe efficiency (效益) of the economy.A. conflictsB. resourcesC. agenciesD. expenses20. A man namedDaredevil Nik Wallenda _______ his lifelong dream and became the firstperson to walk across Niagara Falls on a high wire.A. possessedB. contributedC. fulfilledD. charged21. Carrying a plastic shopping bag is quite normal in China, but in Rwanda it‟s illegal. Such anact will_______.A. get along well with itB. get you in hot waterC. get the hang of itD. get you across the river22. Could you please make a move? You‟re throwing a _______ on my book so I can‟t see the words clearly.A. blockB. bondC. titleD. shadow23. Signs of “Bus Only, 7:00-9:00, 16:30-18:30” are painted in white to prevent vehicles fromusing the bus _______ during rush hours every day.A. lanesB. pavementC. systemD. station24. The International Olympic Committee (IOC) once expressed concern over Rio‟s ability tobuild all thenecessary _______ for the 2016 Summer Olympics in time.A. appliancesB. facilitiesC. toolsD. devices25. The director was facing a lot of doubts. In _______, he simply posted on weibo calling onpeople to concern more about his movies.A. practiceB. responseC. turnD. theory第二节：完形填空（共15个小题；每小题1分，满分15分）阅读下面的短文，从短文后所给的A、B、C、D四个选项中，选出可以填入空白处的最佳选项。
A woman named Emily renewing her driver‟s license at the County C lerk‟s office was asked to state her occupation. She __26__, uncertain how to classify herself.“What I mean is,” explained the recorder, “do you have a job, or are you just a …”“__27__ I have a job,” said Emily. “I‟m a mother.”“We don‟t list …mother‟ as an occupation… …housewife‟ __28__it,” said the recorder.One day I found myself in the same __29__. The clerk was obviously a career woman, efficient, confident and possessed of a high sounding title like, “Official Interrogator”or “Town Registrar. ” “What is your occupation?” she asked.Somehow, the words simply __30__. “I‟m a R esearch Associate in the field of Child Development and Human Relations.”The clerk paused, ballpoint pen __31__ in midair, and looked up as though she had not heard right.I repeated the __32__ slowly, then I stared __33__ as my statement was written in bold, black ink on the official questionnaire.“Might I ask,” said the clerk with new interest, “j ust what you do in this field?”__34__, without any trace of panic in my voice, I heard myself reply, “I have a continuing program of research (what mother doe sn‟t), in the lab and in the field (normally I __35__ indoors and out). Of course, the job is one of the most demanding in the humanities(any mother care to disagree?), and I often work 14 hours a day (24 is more like __36__), but rewards are more of a satisfaction __37__just money.”There was an increasing __38__ of respect in the clerk‟s voice as she completed the form, stood up, and showed me out.As I drove into our driveway, buoyed up(受鼓舞) by my glamorous new career, I was greeted by my lab assistants--ages 13, 7, and 3.Upstairs I could hear our new experimental model (a 6 month old baby), in the child-development program, __39__ a new vocal pattern.I felt proud! I had gone on the official records as someone more distinguished and indispensable(不可缺少的) to mankind than “just another mother.”Motherhood…What a glorious career! __40__ when there‟s a title on the door.26. A. doubted B. interrupted C. hesitated D. admired27. A. Above all B. Of course C. In reality D. For example28. A. covers B. lists C. replaces D. means29. A. office B. way C. lab D. situation30. A. mixed up B. faded away C. spread about D. popped out31. A. frozen B. shaking C. dropped D. flying32. A. career B. title C. field D. question33. A. with anger B. in despair C. with wonder D. in curiosity34. A. Fortunately B. Excitedly C. Obviously D. Coolly35. A. would have said B. dare say C. must have said D. could say36. A. them B. it C. one D. others37. A. other than B. together with C. rather than D. instead of38. A. note B. sound C. amount D. praise39. A. accounting for B. getting away with C. testing out D. playing jokes on40. A. Certainly B. Unexpectedly C. Usually D. Especially第三部分：阅读理解（共两节，满分30分）第一节（共11个小题；每小题2分，满分22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。
浙江省杭州市第二中学2015-2016学年高一上学期期末考试英语试卷Word版含答案.doc
杭州二中2015学年第一学期高一年级期终考试（2016.01）英语命题、审核、校对：朱旭峰王添添沈一频第Ⅰ卷第一部分听力（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. Which suit does the woman suggest buying?A. The black suit.B. The dark blue suit.C. The grey suit.2. What did the man do this morning?A. He took a photo.B. He had an interview.C. He went to the theatre.3. Where will the woman probably go next?A. Back to her hotel.B. To a bank around the corner.C. Somewhere near the train station.4. Who might Amanda be?A. The man’s wife.B. The man’s best friend.C. The man’s girlfriend.5. What will the man do about his sore (疼痛的) throat?A. Drink some hot tea.B. Take some medicine.C. Stay home from work and rest.第二节（共10小题；每小题1分，满分10分）听下面4段对话。
每段对话后有2—4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。
浙江省杭州二中2015-2016学年高一下学期期中数学试卷 Word版含解析
2015-2016学年浙江省杭州二中高一（下）期中数学试卷一、选择题：本大题共10小题，每小题3分，共30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．1．在△ABC 中，AB=，AC=1，B=，则△ABC 的面积是（ ）A ．B ．C ．或D ．或2．已知P 是边长为2的正△ABC 的边BC 上的动点，则（ ）A ．最大值为8B ．是定值6C ．最小值为2D ．是定值23．数列{a n }满足a 1=2，，则a 2016=（ ）A ．﹣2B ．﹣1C ．2D ．4．在平面直角坐标系中，角α的顶点与原点重合，始边与x 轴的非负半轴重合，终边过点P （sin ，cos ），则sin （2α﹣）=（ ）A ．B ．﹣C ．D ．﹣5．若0＜α＜，﹣＜β＜0，cos （+α）=，cos （﹣）=，则cos （α+）=（ ）A ．B ．﹣C ．D ．﹣6．在△ABC 中，若acosA=bcosB ，则△ABC 的形状是（ ）A ．等腰三角形B ．直角三角形C ．等腰直角三角形D ．等腰或直角三角形7．已知函数f （x ）=asinx ﹣bcosx （a ，b 为常数，x ∈R ）在x=处取得最小值，则函数y=f（﹣x ）的图象关于（ ）中心对称．A ．（，0） B ．（，0）C ．（，0）D ．（，0）8．若A ，B 是锐角三角形ABC 的两个内角，则以下选项中正确的是（ ） A ．sinA ＜sinB B ．sinA ＜cosB C ．tanAtanB ＞1 D ．tanAtanB ＜19．已知两个等差数列{a n }和{b n }的前n 项和分别为A n 和B n ，且=，则使得为整数的正整数n 的个数是（ ） A ．5 B ．4 C ．3 D ．210．扇形OAB 中，∠AOB=90°，OA=2，其中C 是OA 的中点，P 是上的动点（含端点），若实数λ，μ满足=λ+μ，则λ+μ的取值范围是（ ）A．[1，]B．[1，]C．[1，2]D．[1，]二、填空题：本大题共6小题，每小题4分，共24分．11． +=．12．已知数列{a n}是等差数列，a2+a7=12，a4a5=35，则a n=．13．已知α，β∈（0，π），且cosα=，sin（α+β）=，则cosβ=．14．在△ABC中，O为△ABC的外心，满足15+8+17=，则∠C=．15．已知Rt△ABC中，两直角边分别为a、b，斜边和斜边上的高分别为c、h，则的取值范围是．16．若正实数x，y，z满足x2+y2=9，x2+z2+xz=16，y2+z2+yz=25，则2xy+xz+yz=．三、解答题：本大题共4小题．共46分．解答应写出文字说明、证明过程或演算步骤．17．在△ABC中，角A，B，C的对边分别为a，b，c，且．（1）求角A的值；（2）若∠B=，BC边上中线AM=，求△ABC的面积．18．己知等差数列{a n}，设其前n项和为S n，满足S5=20，S8=﹣4．（1）求a n与S n；（2）设c n=a n a n+1a n+2，T n是数列{c n}的前n项和，若对任意n∈N+，T n≤恒成立，求实数m的取值范围．19．如图，某房产开发商计划在一正方形土地ABCD内建造一个三角形住宅区，在其余土地种植绿化，住宅区形状为三角形APQ，其中P位于边CB上，Q位于边CD上．已知，∠PAQ=，设∠PAB=θ，记绿化率L=1﹣，若L越大，则住宅区绿化越好．（1）求L（θ）关于θ的函数解析式；（2）问当θ取何值时，L有最大值？并求出L的最大值．20．已知=（sinx，cosx），=（sinx，k），=（﹣2cosx，sinx﹣k）．（1）当x∈[0，]时，求|+|的取值范围；（2）若g（x）=（+）•，求当k为何值时，g（x）的最小值为﹣．2015-2016学年浙江省杭州二中高一（下）期中数学试卷参考答案与试题解析一、选择题：本大题共10小题，每小题3分，共30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．1．在△ABC中，AB=，AC=1，B=，则△ABC的面积是（）A．B．C．或 D．或【考点】正弦定理．【分析】先由正弦定理求得sinC的值，进而求得C，根据三角形内角和求得A，最后利用三角形面积公式求得答案．【解答】解：由正弦定理知=，∴sinC==，∴C=，A=，S=AB•ACsinA=或C=，A=，S=AB•ACsinA=．故选D2．已知P是边长为2的正△ABC的边BC上的动点，则（）A．最大值为8 B．是定值6 C．最小值为2 D．是定值2【考点】向量在几何中的应用．【分析】先设=，=，=t，然后用和表示出，再由=+将=、=t代入可用和表示出，最后根据向量的线性运算和数量积运算可求得的值，从而可得到答案．【解答】解：设===t则=﹣=﹣，2=4=2•=2×2×cos60°=2=+=+t﹙﹣﹚=﹙1﹣t﹚+t+=+•﹙+﹚=﹙﹙1﹣t﹚+t﹚•﹙+﹚=﹙1﹣t﹚2+[﹙1﹣t﹚+t] +t2=﹙1﹣t﹚×4+2+t×4=6故选B．3．数列{a n}满足a1=2，，则a2016=（）A．﹣2 B．﹣1 C．2 D．【考点】数列递推式．【分析】数列{a n}满足a1=2，，求出前4项即可得出周期性．【解答】解：∵数列{a n}满足a1=2，，∴a2==﹣1，a3==，a4==2，…，∴a n+3=a n．则a2016=a3×672=a3=．故选：D．4．在平面直角坐标系中，角α的顶点与原点重合，始边与x轴的非负半轴重合，终边过点P（sin，cos），则sin（2α﹣）=（）A．B．﹣C．D．﹣【考点】任意角的三角函数的定义．【分析】利用三角函数的定义确定α，再代入计算即可．【解答】解：∵角α的终边过点P（sin，cos），∴sinα=cos，cosα=sin，∴α=+2kπ，∴sin（2α﹣）=sin（4kπ+﹣）=sin=．故选：A．5．若0＜α＜，﹣＜β＜0，cos（+α）=，cos（﹣）=，则cos（α+）=（）A．B．﹣C．D．﹣【考点】三角函数的恒等变换及化简求值．【分析】先利用同角三角函数的基本关系分别求得sin（+α）和sin（﹣）的值，进而利用cos（α+）=cos[（+α）﹣（﹣）]通过余弦的两角和公式求得答案．【解答】解：∵0＜α＜，﹣＜β＜0，∴＜+α＜，＜﹣＜∴sin（+α）==，sin（﹣）==∴cos（α+）=cos[（+α）﹣（﹣）]=cos（+α）cos（﹣）+sin（+α）sin（﹣）=故选C6．在△ABC中，若acosA=bcosB，则△ABC的形状是（）A．等腰三角形B．直角三角形C．等腰直角三角形D．等腰或直角三角形【考点】三角形的形状判断．【分析】利用正弦定理化简已知的等式，再根据二倍角的正弦函数公式变形后，得到sin2A=sin2B，由A和B都为三角形的内角，可得A=B或A+B=90°，从而得到三角形ABC 为等腰三角形或直角三角形．【解答】解：由正弦定理asinA=bsinB化简已知的等式得：sinAcosA=sinBcosB，∴sin2A=sin2B，∴sin2A=sin2B，又A和B都为三角形的内角，∴2A=2B或2A+2B=π，即A=B或A+B=，则△ABC为等腰或直角三角形．故选D7．已知函数f（x）=asinx﹣bcosx（a，b为常数，x∈R）在x=处取得最小值，则函数y=f（﹣x）的图象关于（）中心对称．A．（，0）B．（，0）C．（，0）D．（，0）【考点】正弦函数的图象．【分析】由条件利用三角恒等变换化简函数的解析式，再利用正弦函数的图象的对称性，得出结论．【解答】解：∵函数f（x）=asinx﹣bcosx=sin（x+θ），其中，cosθ=，sinθ=，在x=处取得最小值，∴+θ=2kπ﹣，k∈Z，即θ=2kπ﹣．则函数y=f（﹣x）=sin（x+2kπ﹣）=sin（x﹣），故有f（）=0，故它的图象关于（，0）对称，故选：A．8．若A，B是锐角三角形ABC的两个内角，则以下选项中正确的是（）A．sinA＜sinB B．sinA＜cosB C．tanAtanB＞1 D．tanAtanB＜1【考点】任意角的三角函数的定义；三角函数线．【分析】根据题意，用特殊值代入法，即可判断选项的正误．【解答】解：因为A，B是锐角三角形ABC的两个内角，不妨令A=B=，则sinA=sinB，A错误；sinA＞cosB，B错误；tanAtanB=3＞1，D错误，C正确．故选：C．9．已知两个等差数列{a n}和{b n}的前n项和分别为A n和B n，且=，则使得为整数的正整数n的个数是（）A．5 B．4 C．3 D．2【考点】等差数列的前n项和．【分析】由于==6+，n的取值只要使得为正整数即可得出．【解答】解：=====6+，当n=1，2，4，10时，为正整数，即使得为整数的正整数n的值只有4个．故选：B．10．扇形OAB中，∠AOB=90°，OA=2，其中C是OA的中点，P是上的动点（含端点），若实数λ，μ满足=λ+μ，则λ+μ的取值范围是（）A．[1，]B．[1，]C．[1，2]D．[1，]【考点】平面向量的基本定理及其意义．【分析】建立直角坐标系，分别表示向量=（1，0），=（0，2），由题意可知，=cosθ，u=sinθ，θ∈[0，]，λ+μ=2cosθ+sinθ=sin（θ+φ），即可求得其最大值，当P与B重合时，即可求得其最小值．【解答】解：以所在的直线为x轴，以所在的直线为y轴，建立直角坐标系，A（2，0），B（0，2），C（1，0），=（1，0），=（0，2），设P（x，y），P在圆x2+y2=4，=λ+μ，∴（x，y）=（λ，0）+（0，2μ），∴，0≤λ≤2，0≤μ≤1，设=cosθ，u=sinθ，θ∈[0，]，∴λ=2cosθ，u=sinθ，λ+μ=2cosθ+sinθ=sin（θ+φ），tanφ=2，当θ+φ=时，λ+μ的最大值为，当P在B点时，μ=1，λ=0时λ+μ取最小值为1，故选：D．二、填空题：本大题共6小题，每小题4分，共24分．11． +=2sin1．【考点】三角函数的化简求值．【分析】利用二倍角公式，同角三角函数基本关系式，平方差（和）公式化简可得原式等于+，去根号可得：|sin1﹣cos1|+|sin1+cos1|，利用sin1＞cos1＞0去绝对值即可计算得解．【解答】解：∵180°=π，可得：45°＜1＜60°，∴sin1＞cos1＞0，∴+=+=|sin1﹣cos1|+|sin1+cos1|=sin1﹣cos1+sin1+cos1=2sin1．故答案为：2sin1．12．已知数列{a n}是等差数列，a2+a7=12，a4a5=35，则a n=2n﹣3或15﹣2n．【考点】等差数列的通项公式．【分析】由已知得a4+a5=12，从而a4，a5是方程x2﹣12x+35=0的两个根，解方程x2﹣12x+35=0得a4=5，a5=7或a4=7，a5=5，由此能求出a n．【解答】解：∵数列{a n}是等差数列，a2+a7=12，a4a5=35，∴a4+a5=12，∴a4，a5是方程x2﹣12x+35=0的两个根，解方程x2﹣12x+35=0得a4=5，a5=7或a4=7，a5=5，当a4=5，a5=7时，a1=﹣1，d=2，a n=﹣1+（n﹣1）×2=2n﹣3；a4=7，a5=5时，a1=13，d=﹣2，a n=13+（n﹣1）×（﹣2）=15﹣2n．故答案为：2n﹣3或15﹣2n．13．已知α，β∈（0，π），且cosα=，sin（α+β）=，则cosβ=．【考点】两角和与差的余弦函数．【分析】利用同角三角函数的基本关系求得sinα、cos（α+β）的值，再利用两角差的余弦公式求得cosβ=cos[（α+β）﹣α]的值．【解答】解：∵α，β∈（0，π），且cosα=，∴sinα==，∵sin（α+β）=，∴sinα＞sin（α+β），∴α+β为钝角，∴cos（α+β）=﹣=﹣，则cosβ=cos[（α+β）﹣α]=cos（α+β）cosα+sin（α+β）sinα=﹣•+•=，故答案为：．14．在△ABC中，O为△ABC的外心，满足15+8+17=，则∠C=．【考点】向量的线性运算性质及几何意义．【分析】设外接圆的半径为R，根据题意得15+8=﹣17，两边平方得出•=0，即∠AOB=，再根据圆心角等于同弧所对的圆周的关系，得出角C的值．【解答】解：设外接圆的半径为R，O为△ABC的外心，且15+8+17=，所以15+8=﹣17，∴（15+8）2=（17）2，∴289R2+240•=289R2，∴•=0，∴∠AOB=，根据圆心角等于同弧所对的圆周的关系，如图所示：所以△ABC中内角C的值为．故答案为：．15．已知Rt△ABC中，两直角边分别为a、b，斜边和斜边上的高分别为c、h，则的取值范围是（1，]．【考点】正弦定理．【分析】设A=θ，则h=bsinθ，a=btanθ，c=，代入所求，利用三角函数恒等变换的应用化简可得sin（），根据角θ的范围，利用正弦函数的图象和性质即可得解其范围．【解答】解：如图所示，设A=θ，h=bsinθ，a=btanθ，c=．∴====sinθ+cosθ=sin（），∵θ∈（0，），∴θ+∈（，），∴sin（）∈（，1]，sin（）∈（1，]．∴的取值范围是（1，]．故答案为：（1，]．16．若正实数x，y，z满足x2+y2=9，x2+z2+xz=16，y2+z2+yz=25，则2xy+xz+yz=18．【考点】根式与分数指数幂的互化及其化简运算．【分析】设=（x，y），=（x+，），=（y+，），则所求为，利用数量积公式可得所求．【解答】解：由已知设=（x，y），=（x+，），=（y+，），则由x2+y2=9，x2+z2+xz=16，y2+z2+yz=25，得到2=9，=16，2=25，9+16=25，所以，所以=xy++==3×5×，所以2xy+xz+yz=2×9=18；故答案为：18．三、解答题：本大题共4小题．共46分．解答应写出文字说明、证明过程或演算步骤．17．在△ABC中，角A，B，C的对边分别为a，b，c，且．（1）求角A的值；（2）若∠B=，BC边上中线AM=，求△ABC的面积．【考点】正弦定理．【分析】（1）利用正弦定理化边为角可求得cosA=，从而可得A；（2）易求角C，可知△ABC为等腰三角形，在△AMC中利用余弦定理可求b，再由三角形面积公式可求结果；【解答】解：（1）∵．∴由正弦定理，得，化简得cosA=，∴A=；（2）∵∠B=，∴C=π﹣A﹣B=，可知△ABC为等腰三角形，在△AMC中，由余弦定理，得AM2=AC2+MC2﹣2AC•MCcos120°，即7=，解得b=2，∴△ABC的面积S=b2sinC==．18．己知等差数列{a n}，设其前n项和为S n，满足S5=20，S8=﹣4．（1）求a n与S n；（2）设c n=a n a n+1a n+2，T n是数列{c n}的前n项和，若对任意n∈N+，T n≤恒成立，求实数m的取值范围．【考点】数列的求和．【分析】（1）根据等差数列的性质建立方程组求出首项和公差即可求a n与S n；（2）求出c n=a n a n+1a n+2，的值，将T n≤恒成立转化为求（T n）max≤恒成立即可．【解答】解：（1）∵S5=20，S8=﹣4．∴，即，得，则a n=10﹣3（n﹣1）=13﹣3n，S n=10n+×（﹣3）=n2+．（2）设c n=a n a n+1a n+2=（13﹣3n）（10﹣3n）（7﹣3n），要使若对任意n∈N+，T n≤恒成立，则只要若对任意n∈N+，（T n）max≤恒成立，则a1=10，a2=7，a3=4，a4=1，a5=﹣2，a6=﹣5，a7=﹣8，a8=﹣11，则c1=a1a2a3=280，c2=a2a3a4=28，c3=a3a4a5=﹣8，c4=a4a5a6=10，c5=a5a6a7=﹣80，则当n≥5时，c n＜0，则当n=4时，前四项和最大，此时T4=280+28﹣8+10=310，则由310≤得m≥1396，即实数m的取值范围是[1396，+∞）．19．如图，某房产开发商计划在一正方形土地ABCD内建造一个三角形住宅区，在其余土地种植绿化，住宅区形状为三角形APQ，其中P位于边CB上，Q位于边CD上．已知，∠PAQ=，设∠PAB=θ，记绿化率L=1﹣，若L越大，则住宅区绿化越好．（1）求L（θ）关于θ的函数解析式；（2）问当θ取何值时，L有最大值？并求出L的最大值．【考点】函数的最值及其几何意义；函数解析式的求解及常用方法．【分析】（1）设正方形的边长为a，由解直角三角形的余弦函数，求得AP，AQ，运用三角形的面积公式和正方形的面积，即可得到所求函数L的解析式，注意定义域；（2）由正弦函数的值域，可得2θ+=，计算即可得到所求最大值及相应的θ的取值．【解答】解：（1）设正方形的边长为a，在直角三角形APB中，AP==，在直角三角形ADQ中，AQ==，可得L（θ）=1﹣=1﹣=1﹣•=1﹣•=1﹣=1﹣=1﹣，0≤θ≤，（2）由（1）可得L（θ）=1﹣，0≤θ≤，由2θ+=，即θ=∈[0，]时，L（θ）取得最大值，且为1﹣=2﹣．则当θ取 [时，L有最大值2﹣．20．已知=（sinx，cosx），=（sinx，k），=（﹣2cosx，sinx﹣k）．（1）当x∈[0，]时，求|+|的取值范围；（2）若g（x）=（+）•，求当k为何值时，g（x）的最小值为﹣．【考点】三角函数中的恒等变换应用；平面向量的坐标运算；平面向量数量积的运算．【分析】（1）由已知利用平面向量的坐标运算可得=（sinx﹣2cosx，sinx），利用三角函数恒等变换的应用可得||2=cos（2x+φ）+3，其中，tanφ=2，又x∈[0，]，可求，利用余弦函数的单调性即可得解|+|的取值范围；（2）利用平面向量数量积的运算可得g（x）=﹣3sinxcosx+k（sinx﹣cosx）﹣k2，令t=sinx﹣cosx=sin（x﹣），则g（x）可化为，对称轴．利用二次函数的图象和性质分类讨论即可得解．【解答】解：（1）=（sinx﹣2cosx，sinx），||2=（sinx﹣2cosx，sinx）2=2sin2x﹣4sinxcosx+4cos2x=2cos2x﹣4sinxcosx+2=cos2x﹣2sin2x+3=cos（2x+φ）+3，其中，tanφ=2，又∵x∈[0，]，∴，∴在上单调递减，∴|cos（2x+φ）|2∈[1，4]，∴|+|∈[1，2]．（2）=（2sinx，cosx+k），g（x）=（）=﹣4sinxcosx+（cosx+k）（sinx﹣k）=﹣3sinxcosx+k（sinx﹣cosx）﹣k2令t=sinx﹣cosx=sin（x﹣），则t∈[﹣，]，且t2=sin2x+cos2x﹣2sinxcosx=1﹣2sinxcosx，所以．所以g（x）可化为，对称轴．①当，即时，，由，得，所以．因为，所以此时无解．②当，即时，．由﹣﹣=﹣，得k=0∈[﹣3，3]．③当﹣，即k＜﹣3时，g（x）min=h（）=﹣k2+k+，由﹣k2+k+=﹣，得k2﹣k﹣3=0，所以k=．因为k，所以此时无解．综上所述，当k=0时，g（x）的最小值为﹣．2016年8月26日。
浙江省杭州第二中学2015-2016学年高二英语下学期期中试题(无答案)
杭州二中2016学年第二学期高二年级期中考试英语试卷 2016. 04第I 卷第一部分：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，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 is the woman’s opinion on the research paper?A. It’s perfect.B. It needs revising.C. Its topic is too wide.2. How will the woman go to the People’s Square?A. By bus.B. On foot.C. By subway.3. What’s wrong with the man’s phone?A. It was out of service.B. It was set on silent mode.C. It w as power off.4. How much should the woman pay for the food and drinks?A. $30.B. $20.C. $10.5. Why didn’t Jack sleep well last night?A. He was awakened by the terrible noise.B. He met with a traffic accident.C. He had to work.第二节（共15小题；每小题1.5分，满分22.5分）听下面5段对话或独白。
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，各小题将给出5秒钟的作答时间。
2015-2016学年浙江省诸暨中学高一下学期期中考试英语试卷 word版
诸暨中学2015学年第二学期高一年级英语期中试题卷第一部分:阅读理解(共15小题，每小题2分，满分30分)。
阅读下列材料，从每题所给的选项（A、B、C和D）中，选出最佳选项，并在答题纸上将该选项答案涂黑。
AWhen other nine-year-old kids were playing games, she was working at a petrol station. When other teens were studying or going out, she struggled to find a place to sleep on the street. But she overcame these terrible setbacks to win a highly competitive scholarship and gain entry to Harvard University. And her amazing story has inspired a movie, ― Homeless to Harvard: The Liz Murray Story‖, shown in late April.Liz Murray，a 22-year-old American girl, has been writing a real-life story of willpower and determination. Liz grew up in the shadow of two drug-addicted parents. There was never enough food or warm clothes in the house. Liz was the only member who had a job. Her mother had AIDS and died when Liz was just 15 years old. The effect of that loss became a turning point in her life. Connecting the environment in which she had grown up with how her mother had died, she decided to do something about it.Liz went back to school. She threw herself into her studies, never telling her teachers that she was homeless. At night, she lived on the streets. ― What drove me to live on had something to do with understanding, by understanding that there was a whole other way of being. I had only experienced a small part of the society,‖ she wrote in her book Breaking Night.She admitted that she used envy to drive herself on. She used the benefits that come easily to others such as a safe living environment, to encourage herself that ―next to nothing could hold me down‖. She finished high school in just two years and won a full scholarship to study at Harvard University. But Liz decided to leave her top university a couple of months earlier this year in orde r to take care of her father, who has also developed AIDS. ―I love my parents so much. They are drug addicts. But I never forget that they loved me all the time.‖Liz wants moviegoers to come away with the idea that changing your life is ―as simple as maki ng a decision‖.1．The main idea of the passage is __________ .A. how Liz managed to enter Harvard UniversityB. What a hard time Liz had in her childhoodC. why Liz loved her parents so muchD. how Liz struggled to change her life2．In which order did the following things happen to Liz ?a. Her mother died of AIDS.b. She worked at a petrol station.c. She got admission into Harvard University.d. The movie about her life was put on.e. She had trouble about finding a place to sleep.A. b, a , e , c, dB. a , b , c , e , dC. e , d, b , a , cD. b , e , a , d , c3．What actually made her go towards her goal?A. Envy and encouragement.B. Willpower and determination .C. Decisions and understanding.D. Love and respect for her parents.4．When she wrote ―What drove me to live on … I had only experienced a small part of the society‖, she meant that __________ .A. she had little experience of social life.B. she could hardly understand the society.C. she would do something for her own life.D. she needed to travel more around the world.BFour people in England back in 1953, stared at Photo 51,It wasn’t much—a picture showing a black X. But three of these people won the Nobel Prize for figuring out what the photo really showed –the shape of DNA The discovery brought fame and fortune to scientists James Watson, Francis Crick, and Maurice Wilkins. The fourth, the one who actually made the picture, was left out.Her name was Rosalind Franklin.‖ She should have been up there,‖ sa ys historian（历史学家）Mary Bowden.‖ If her photos hadn’t been there, the others couldn’t have come up with the structure.‖ One reason Franklin was missing was that she had died of cancer four years before the Nobel decision. But now scholars（学者）doubt that Franklin was not only robbed of her life by disease but robbed of credit by her competitorsAt Cambridge University in the 1950s, Watson and Click tried to make models by cutting up shapes of DNA’s parts and then putting them together. In the meantime, at King’s College in London, Franklin and Wilkins shone X-rays at the molecule(分子). The rays produced patterns reflection the shape.But Wilkins and Franklin’s relationship was a lot rockier than the celebrated teamwork of Watson and Crick, Wilkins thought Franklin was hired to be his assistant .But the college actually employed her to take over the DNA project.What she did was produce X-ray pictures that told Watson and Crick that one of their early models was inside out. And she was not shy about saying so. That angered Watson, who attacked her in return, ―Mere inspection suggested that she would not easily bend. Clearly she had to to go or be put in her place.‖As Franklin’s competitors, Wilkins, Watson and Crick had much to gain by cutting her out of the little group of researchers, says historian Pnina Abir-Am. In 1962 at the Nobel Prize awarding ceremony, Wilkins thanked 13 colleagues by name before he mentioned Franklin, Watson wrote his book laughing at her. Crick wrote in 1974 that ―Franklin was only t wo steps away from the solution.‖No, Franklin was the solution. ―She contributed more than any other player to solving the structure of DNA . She must be considered a co-discoverer,‖ Abir-Am says. This was backed up by Aaron Klug, who worked with Franklin and later won a Nobel Prize himself. Once described as the ―Dark Lady of DNA‖, Franklin is finally coming into the light.5. What is the text mainly about?A. The disagreements among DNA researchers.B. The unfair treatment of Franklin.C. The process of discovering DNA.D. The race between two teams of scientists.6. Watson was angry with Franklin because she .A. took the lead in the competitionB. kept her results from himC. proved some of his findings wrongD. shared her data with other scientists7. Why is Franklin described as ―Dark Lady of DNA‖?A. She developed pictures in dark labs.B. She discovered the black X-the shape of DNA.C. Her name was forgotten after her death.D. Her contribution was unknown to the public.8. What is the writer’s attitude toward Wilkins, Watson and Crick?A. Disapproving.B. Respectful.C. Admiring.D. Doubtful.CE-reading and e-books are slowly conquering the world. Compared to traditional paper books, e-books in some schools and universities attract more interest because the information flow seems much easier to manage and comes in a greatly higher quantity.Japan is known for the reform-minded attitude towards the gadget(精巧装置)world and for the fact that it is one of the first countries that encouraged in the educational system the emailing of homework.The digital textbook looks like the logical step in the world of learning. It is natural but it is also completely untraditional.The plan of the largest publishing companies to get in line with the trend is to save a large quantity of paper and make the kids become interested in learning using a cool gadget. Many USA universities and colleges have made students be used to the procedure of downloading the courses and of course the procedure involves interactive software and also the chance of using the computer.The traditional education system is still unwilling when it comes to giving up books. The standard approach of information taught out of a book and Shakespeare read out of an old school novel makes studying English as traditional as it can be.In a world where kids would rather see the movie than read a book, the digital age has brought along a completely different flavor to reading. Bringing that flavor in school will make teaching a greener and also a completely different matter.9. Why are e-books so popular in the world?A. It’s cheap to buy.B. It’s effective to use.C. It’s convenient to bring.D. It’s the lates t fashion.10. Which of the following words can best take the place of the word ―reform-minded‖ in the second paragraph?A. Old-fashioned.B. Aggressive.C. Rejecting.D. Progressive.11. In America, the students are encouraged to.A. apply the procedure of downloading the coursesB. communicate with their teachers using computersC. research some interactive software for their studiesD. do their homework in computer instead of in paper12. What’s the author’s attitude to the digital textbo oks?A. Being against.B. Being for.C. Not mentioned.D. Being neutral.DTea drinking was common in China for nearly one thousand years before anyone in Europe had ever heard about tea. People in Britain were much slower in finding out what tea was like, mainly because tea was very expensive. It could not be bought in shops and even those people who could afford to have it sent from Holland did so only because it was a fashionable curiosity. Some of them were not sure how to use it. They thought it was a vegetable and tried cooking the leaves. Then they served them mixed with butter and salt. They soon discovered their mistake but many people used to spread the used tea leaves on bread and give them to their children as sandwiches.Tea remained scarce and very expensive in England until the ships of the East India Company began to bring it direct from China early in the seventeenth century. During the next few years so much tea came into the country that the price fell and many people could afford to buy it.At the same time people on the Continent were becoming more and more fond of tea. Until then tea had been drunk without milk in it, but one day a famous French lady named Madame de Sevigne decided to see what tea tasted like when milk was added. She found it so pleasant that she would never again drink it without milk. Because she was such a great lady that her friends thought they must copy everything she did, they also drank their tea with milk in it. Slowly this habit spread until it reached England and today only very few Britons drink tea without milk.At first, tea was usually drunk after dinner in the evening. No one ever thought of drinking tea in the afternoon until a duchess（公爵夫人）found that a cup of tea and a piece of cake at three or fou r o’clock stopped her getting ―a sinking feeling‖ as she called it. She invited her friends to have this new meal with her and so, tea-time was born .13. This passage mainly discusses .A. the history of tea drinking in BritainB. how tea became a popular drink in BritainC. how the Britons got the habit of drinking teaD. how tea-time was born14.Tea became a popular drink in Britain .A. in the sixteenth centuryB. in the seventeenth centuryC. in the eighteenth centuryD. in the late seventeenth century15. We may infer from the passage that the habit of drinking tea in Britain was mostly due to the influence of .A. a famous French ladyB. the ancient ChineseC. the upper(上层的) social classD. people in Holland第二部分:完型填空（共20题，每小题1.5分，满分30分）Some years ago when I was in my first year in college, I heard Salome Bey sing for the first time. The moment was exciting. Salome’s16filled the room and brought the theater to life. I was so17that I decided to write an article about her.I18Salome Bey, telling her I was from Essence magazine, and that I wanted to meet her to talk about her career. She19and told me to come to her studio next Tuesday. WhenI hung up, I was scared out of mind. I20I was lying. I was not a writer at all and hadn’t even written a grocery list.I interviewed Salome Bey the next Tuesday. I sat there21, taking notes and asking questions that all began with, ―Can you tell me. . . ? ‖I s oon realized that22Salome Bey was one thing, but writing a story for a national magazine was just impossible. The23 was almost unbearable. I struggled for days24 draft(草稿)after draft. Finally I put my manuscript(手稿)into a large envelope and dropped it into a mailbox.It didn’t take long. My manuscript25. How stupid of me! I thought. How could I 26 in a world of professional writers? Knowing I couldn’t27the rejection letter, I threw the unopened envelope into a drawer.Five years later, I was moving to California. While28my apartment, I came across the unopened envelope. This time I opened it and read the editor’s letter in29:Ms Profit,Your story on Salome Bey is fantastic. Yet we need some30materials. Please add those and return the article immediately. We would like to31your story soon. Shocked, it took me a long time to32. Fear of rejection cost me greatly. I lost at least five hundred dollars and the chance of having my article appear in a major magazine. More importantly, I lost years of33writing. Today, I have become a full-time writer. Looking back on this34, I learned a very important lesson: You can’t35to doubt yourself.16. A. joy B. voice C. speech D. smile17. A. proud B. active C. satisfied D. moved18. A. visited B. emailed C. phoned D. interviewed19. A. agreed B. refused C. hesitated D. paused20. A. replied B. discovered C. explained D. knew21. A. seriously B. patiently C. nervously D. quietly22. A. blaming B. fooling C. inviting D. urging23. A. hardship B. Failure C. comment D. pressure24. A. with B. by C. on D. in25. A. disappeared B. returned C. spread D. improved26. A. compare B. Struggle C. survive D. compete27. A. ignore B. deliver C. face D. receive28. A. decorating B. repairing C. cleaning D. leaving29. A. surprise B. anxiety C. horror D. trouble30. A. subjective B. detailed C. private D. complex31. A. broadcast B. create C. publish D. assess32. A. recover B. prepare C. escape D. concentrate33. A. energetic B. Endless C. typical D. enjoyable34. A. experience B. Success C. benefit D. accident35. A. attempt B. afford C. expect D. pretend第三部分:七选五阅读（共5题，每小题2分，满分10分）根据短文内容，从短文后的选项中选出能填入空白处的最佳选项。
浙江省杭州二中2016-2017学年高一下学期期中考英语试卷 精品
杭州二中2016学年第二学期高一年级期中考英语试卷本试卷分第I卷（选择题）和第II卷（非选择题），共100分，考试时间90分钟。
命题、校对：李陈珠、张绮审核：何玲第I卷第一部分：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 does the man promise to do at the weekend?A. Play football with MatthewB. Watch a game with the woman.C. Wash the car for the woman2. Where is the shopping center?A. Opposite a parking lot.B. On the left of a drugstore.C. Next to a sports center.3. What are the speakers mainly talking about?A. An ancient bookB. A valuable libraryC. A piece of research4. How long has the woman been working in the company?A. 4 yearsB. 5 years.C. 6 years.5. What animal did the woman fail to see?A. LionsB. MonkeysC. Elephants.第二节（共10小题，每小题1分，满分10分）听下面3段对话或独白。
每段对话或独白后面有几个小题，从题中所组的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
(完整版)浙江省杭州市第二中学2015-2016学年高一上学期期末考试英语试卷Word版含答案.doc
杭州二中2015学年第一学期高一年级期终考试（2016.01）英语命题、审核、校对：朱旭峰王添添沈一频第Ⅰ卷第一部分听力（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. Which suit does the woman suggest buying?A. The black suit.B. The dark blue suit.C. The grey suit.2. What did the man do this morning?A. He took a photo.B. He had an interview.C. He went to the theatre.3. Where will the woman probably go next?A. Back to her hotel.B. To a bank around the corner.C. Somewhere near the train station.4. Who might Amanda be?A. The man’s wife.B. The man’s best friend.C. The man’s girlfriend.5. What will the man do about his sore (疼痛的) throat?A. Drink some hot tea.B. Take some medicine.C. Stay home from work and rest.第二节（共10小题；每小题1分，满分10分）听下面4段对话。
每段对话后有2—4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。
浙江省杭州二中2015-2016学年高二上学期期中考试数学试卷Word版含答案
杭州二中2015学年第一学期高二年级期中考试数学试卷命题：李 鸽 校对：金 迪 审核：徐存旭时间：100分钟注意：本试卷不得使用计算器参考公式： 球的表面积公式 S =4πR 2 球的体积公式 V =43πR 3 其中R 表示球的半径 锥体的体积公式V =13Sh 其中S 表示锥体的底面积, h 表示锥体的高柱体的体积公式 V=Sh其中S 表示柱体的底面积, h 表示柱体的高 台体的体积公式()1213V h S S =其中S 1, S 2分别表示台体的上、下底面积, h 表示台体的高一、选择题：本大题共8小题，每小题3分，共24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.1. 不等式0322>++-x x 的解集是A.)1,3(-B. )3,1(-C. ),3()1,(+∞⋃--∞D. ),1()3,(+∞⋃--∞ 2.已知0,>ba ，且13=+b a ，则ab 的取值范围是A.),63[+∞ B. ]121,0( C. ]121,241( D. ]63,0( 3. 设m 为一条直线,βα,为两个不同的平面,则下列说法正确的是A ．若ββαα//,//,//m m 则B ．若,m αβα⊥⊥，则m β⊥C ．若ββαα⊥⊥m m 则,,//D ．若ββαα⊥⊥m m 则,//,4. 在等差数列}{n a 中，已知201=a ，前n 项和为n S ，且1510S S =，则n S 的最大值是 A ．110B ．120C ．130D ．1405. 若关于x 的不等式220x ax +->在区间[]1,5上有解,则实数a 的取值范围为 A ．),523(+∞-B ．]1,523[-C ．(1,+∞)D ．)1,(--∞6.已知各棱长均为1的四面体ABCD 中， E 是AD 的中点，P ∈直线CE ，则|BP|＋|DP|的最小值为A.1＋63B.1＋63 C.1＋32 D.1＋327.若y x a y x +≤+2对+∈R y x ,恒成立，则实数a 的最小值是 A.2 B.3 C. 5 D. 28.设三个底面半径都为1的圆柱侧面两两相切，且它们的轴两两互相垂直，则与这三个圆柱侧面都相切的球的半径最小值等于 A. 12- B. 13- C. 25- D. 1二、填空题：本大题共7小题，每小题4分，共28分.9. 已知圆锥的底面半径为1，高为1，则圆锥的侧面面积=S .10.右图是某三棱锥的三视图，各个视图是全等的等腰直角三角形，且直 角边长为1，则这个三棱锥外接球的表面积是 .11.在等比数列{a n }中，各项均为正值，且4862142=+a a a a ,693=a a ,则=+84a a .12.设函数x x x f +-=11log )(21，则不等式)21()(log 21f x f ->的解集是 . 13.空间四边形ABCD 中，AB ＝CD 且AB 与CD 所成的角为30°，E 、F 分别为BC 、AD 的中点，则EF 与AB 所成角的大小为 . 14.对一切实数x ，二次函数c bx ax x f ++=2)(的值均为非负实数，则cba +的最小值是 .15.已知三棱锥BCD A -，DC DB DA ,,两两垂直，且90=∠+∠+∠CAD BAC DAB ，则二面角D BC A --的余弦值的最大值为 .杭州二中2015学年第一学期高二年级期中考试数学答题卷一、选择题：本大题共8小题，每小题3分，共24分.在每小题给出的四个选项中，只有一项二、填空题：本大题共7小题，每小题4分，共28分.把答案填在题中的横线上．9． 10．11． 12．13. 14.15.三、解答题：本大题共4小题．共48分.解答应写出文字说明、证明过程或演算步骤. 16. （本小题满分12分）如图：已知四棱柱1111D CB A ABCD -的底面是菱形，该菱形的边长为1，60=∠ABC ，AC AA 平面⊥1.（1）设棱形ABCD 的对角线的交点为O ，求证： O A 1//平面C D B 11; （2）若四棱柱的体积23=V ，求C C 1与平面C D B 11所成角的正弦值.1B17.（本小题满分12分）（1）求关于x 的不等式)(012R a a x ax ∈>+--的解集. （2）求证：))(()(22222d c b a bd ac ++≤+，R d c b a ∈,,,.18.（本小题满足12分） 如图：已知正六边形ABCDEF 边长为1，把四边形CDEF 沿着FC 向上翻折成一个立体图形F E ABCD 11. （1）求证：A E FC 1⊥；（2）若1E B =时，求二面角C FB E --1的正切值.19.（本小题满足12分）数列{}n a 满足341=a ，2*11(N )n n n a a a n +=-+∈. （1）求证：n n a a >+1； （2）设201521111a a a m +++= ，求不超过m 的最大整数.杭州二中2015学年第一学期高二年级期中考试数学答案一．选择题：本大题共8小题，每小题3分，共24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.二．填空题：本大题共7小题，每小题4分，共28分.把答案填在题中的横线上．910． π311． 12． )2,21(13. 12512ππ或 14. -115.31三、解答题：本大题共4小题．共48分.解答应写出文字说明、证明过程或演算步骤. 16. （本小题满分10分）如图：已知四棱锥1111D C B A ABCD -的底面是棱形，该棱形的边长为1，60=∠ABC ，AC AA 平面⊥1.（1）设棱形ABCD 的对角线的交点为O ，求证： O A 1//平面C D B 11;（2）若四棱柱的体积23=V ，求C C 1与平面C D B 11所成角的正弦值.（1）证明：连接1111,D B C A 交于点G，连接GC ，因为CO G A CO G A =11,//，于是四边形GCO A 1是平行四边形，故11BOG O A //1，又C D B OG 11平面⊂，故C D B O A 111//平面（2）解：设h AA =1，因为23sin =∠⋅⋅=ABC BC AB S 底，所以23==Sh V ，所以1=h . 因为1111C A D B ⊥，A A D B 111⊥，所以C A D B 111平面⊥所以C A C D B 111平面平面⊥，过GC H C ⊥1，于是C D B H C 111平面⊥所以CG C 1∠为所求角，且55sin 11==∠GC G C CG C .17.（本小题满分12分）（1）求关于x 的不等式R a a x ax ∈>+--,012的解集.解：若0<a ，解集为)1,11(-a；若0=a ，解集为)1,(-∞；若210<<a ，解集为),11()1,(+∞-⋃-∞a ；若21=a ，解集为),1()1,(+∞⋃-∞；若21>a ，解集为),1()11,(+∞⋃--∞a；（2）求证：))(()(22222d c b a bd ac ++≤+，其中d c b a ,,,都是实数.证明：0)(2))(()(2222222222≤--=--=++-+bc ad c b d a acbd d c b a bd ac 故))(()(22222d c b a bd ac ++≤+. 18.（本小题满足12分）如图：已知正六边形''''''F E D C B A ，边长为1，沿着''C F 向上翻折成一个立体图形ABCDEF. （1）求证：EA FC ⊥；F1B（2）若210=EB 时，求二面角E-FB-C 的正切值. （1）证明：过E 作FC EH ⊥，连接AH ，于是FC AH ⊥又H EH AH =⋂，于是AHE FC 平面⊥，又AEH EA 平面⊂，故EA FC ⊥.（2）解：连接HB ，计算可得：23=EH ， 2760cos 222=⋅-+=CB CH CB CH BH由210=EB ，故222EB EH BH =+，所以HB EH ⊥，又FC EH ⊥，H FC HB =⋂，所以ABCF EH 平面⊥ 过H 作FB SH ⊥，连接ES ，则ESH ∠为所求角. 在ESH ∆中，23,41==EH SH ，32tan ==∠HSEH ESH . 19.数列{}n a 满足143a =，2*11(N )n n n a a a n +=-+∈. （1）求证：n n a a >+1；（2）设122013111m a a a =+++，求不超过m 的最大整数. （1）因为1341>=a ，故1)1()1()1()()()(1222221112211>+-++-+-=+-++-+-=-----a a a a a a a a a a a a n n n n n n n ，于是n n n n n n a a a a a a =->+-=+2121.（2）解：)1(11-=-+n n n a a a ，于是nn n n n a a a a a 111)1(1111--=-=-+所以111111---=+n n n a a a 于是113)1111()1111()1111(2014201420133221--=---++---+---=a a a a a a a m 当2≥n 时，31341)1(1->+-=+n n n n a a a a ，于是)1(3411->-+n n a a ，故F21)34(3120142014>+⋅>a ，所以11102014<-<a ，所以不超过m 的最大整数是2.。
【英语】浙江省杭州市七校2015-2016学年高一下学期期中考试
2015学年第二学期期中杭州地区七校联考高一年级英语学科试题第一部分：听力理解（共20小题；每小题1分，满分20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。
现在你有5秒钟的时间阅读第1小题有关内容。
1. What are the two speakers talking about?A. Taking a walk.B. Taking a bus.C. Animals in the zoo.2. What relation is the woman to Jack?A. His roommate.B. His wife.C. His mother.3. How does the woman get along with her work?A. Badly.B. Well.C. Just so-so.4. What is the woman?A. A saleswoman.B. A waitress.C. An inspector.5. Why does the man want his money back?A. He wants to use the money to buy some furniture.B. The machine doesn’t have the functions he wanted.C. The machine went wrong within a week.第二节（共15小题；每小题1分，满分15分）听下面5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，各小题将给出5秒钟的作答时间。
浙江省杭州市第二中学2024-2025学年高二上学期期中考试英语试卷 Word版无答案
杭州二中2024学年第一学期高二年级期中考英语试卷本试卷分为第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分，共150分，考试时间120分钟。
第Ⅰ卷选择题（共95分）第一部分听力（共两节，满分30分）做题时，先将答案标在试卷上。
录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题纸上。
第一节（共5小题；每小题1.5分，满分7.5分）听下面5段对话。
每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项。
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 will the speakers probably do next?A. Cook at home.B. Explore a street.C. Eat out.2. Which desk is the man going to buy?A. The one with two drawers.B. The one with three drawers.C. The one with two pen holders.3. How does the woman describe her move?A. Stressful.B. Smooth.C. Unexpected.4. Where are the speakers?A. In a bank.B. In a bookstore.C. In a post office.5. What are the speakers discussing?A. A course.B. An instrument.C. A sport.第二节（共15小题；每小题1.5分，满分22.5分）听下面5段对话或独白。
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。
听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。
浙江省杭州第二中学等四校联盟2022-2023学年高一下学期期中考试英语试卷
浙江省杭州第二中学等四校联盟2022-2023学年高一下学期期中考试英语试卷学校:___________姓名：___________班级：___________考号：___________一、阅读理解Four Great Musicals for YouDrama 101Preparing a party for their beloved high school drama teacher on the eve of her retirement, a group of students describe how she changed their lives in this heartwarming and inspiring musical. This musical features a cast of young artists aged 13-19. It’s sure to touch the hearts of theatre kids of every age.TITA JokesThe show centers around the women in our lives like our aunts, moms, daughters and partners. Through this musical, many of you will see more clearly their struggles and heartaches, and also how they deal with comedy and songs. In the musical, the performers sing and dance. They’re humorous, enjoying m aking jokes.Be Kind, RewindWhen fifteen-year-old Deirdre is sent to live with her cousins in 1995, she gets a job at the local video store where she falls in love with movies. The story is funny and heartwarming. This musical shines a light on growing up in the mid-90’s and honors thenow-extinct video store. For those who are missing life in the 90’s, like songs and movies at that time, this show will touch them.Unravelled: A New MusicalThree of the greatest love stories of all time (Romeo & Juliet, Orpheus & Eurydice, Della & Jim in The Gift of the Magi) are wonderfully retold and re-imagined to create an entirely new story of love. All three stories begin as they always have, but quickly intertwine (紧密相连) “The idea of writing one musical w ith all three separate stories never occurred to me until I wanted to write a completely different show,” said the director, Andrew Seok.1．Who is the target audience for the musical Drama 101?A．College theatre majors. B．Adults interested in theatre.C．High school drama enthusiasts. D．Theatre professionals of all ages.2．What is the inspiration behind Unravelled: A New Musical?A．The lack of creativity in classic musical.B．The director’s desire to create a new show.C．The popularity of three famous love storiesD．The need to update classic love stories for modern audiences.3．Which musicals are suitable for someone who wants to seek fun?A．Drama 101 & TITA Jokes. B．TITA Jokes & Be Kind, Rewind. C．Drama 101 & Be Kind, Rewind. D．TITA Jokes & Unravelled: A New Musical.Demi Gene Moore was born on November 11th, 1962 in Roswell, New Mexico. Her childhood is covered in shadows and misery. She never knew her biological father, as he abandoned the family months before Demi was born. To make things worse, she experienced kidney dysfunction (肾脏机能障碍) and was cross-eyed.Her stepfather had troubles of his own. He had to shift from one job to another, which made the family relocate frequently. During this period, her parents were becoming violent and alcoholics. The effect was severe on Demi and her two half-brothers but they summoned the courage to press through the pain and suffering. The family eventually managed to build themselves up during the 1970s.She enrolled at Fairfax High School, where she attended classes with other future celebrities like Timothy Hutton. This enhanced her acting skills and fueled her passion for acting. She married singer Freddie Moore after dropping out of high school. Demi found herself working as a model and eventually that led to her first movie role — Parasite in 1982, after which Demi landed acting roles in various movies. Her most prominent that earned her immense fame was in the Blockbuster hit Ghost in the 1990s. But her marriage with Freddie Moore failed over time and then married Bruce Willis in 1987, with whom she had three daughters.Her presence in Hollywood skyrocketed ever since. She starred in many A-List movies along with actors Tom Cruise and Jack Nicholson. Her second marriage ended in 2000 and then her motives went to community service for a while, but she still took on small acting roles from time to time. After dating for two years, she married actor Ashton Kutcher Most recently, Demi Moore walked the Fendi Runway for Paris Haute Couture FashionWeek.4．What is the main idea of this article?A．The life and career of Demi Moore. B．The history of a Hollywood actress. C．The struggle of Demi Moore’s growth.D．The rise and fall of Hollywood movies. 5．How did attending Fairfax High School help Demi Moore in her career as an actress? A．She was able to work as a model.B．She met her future husband there.C．She got to know other future celebrities.D．She learned how to act in Hollywood movies.6．Which of the following is the closest in meaning to the underlined w ord “landed” in paragraph 3?A．Dropped. B．CreatedC．Got. D．Changed.7．What did Demi’ focus turn to after her marriage to Bruce Willis ended?A．Taking on small acting roles. B．Helping out in the community. C．Starting a fashion line. D．Traveling the world.A study from 2010 said that raising prices by 1% without losing sales can increase profits by 8.7% on average. Getting the prices right can be difficult. Set them too high and you lose customers; set them too low and you leave money on the table.To make more money, shopkeepers have been turning to price-optimization (优化) systems that predict how customers will respond to price changes. These systems are becoming cleverer thanks to advances in artificial intelligence (AI). While older systems used historical sales data to estimate (估计) price sensitivity for individual goods, the latestAI-powered systems can find relationships between multiple goods. These AI-powered systems use big data to estimate price sensitivity — how much demand increases as the price falls or how much demand decreases as the price goes up-for thousands of products.Price-sensitive (价格敏感的) goods can then be discounted and price-insensitive ones marked up.All this makes pricing systems “much more three-dimensional”, observes Chad Yoes, the pricing official at Walmart, a supermarket. In February, Starbucks, a chain of coffee shops, expressed pride in its use of AI to price products “on an ongoing basis”. US Foods, a foodcompany, says its pricing system can promote sales and profits.Price-optimization may make prices change more. “Shopkeepers are pricing faster today than they ever have before,” says Matt Pavich of Revionics, a pricing-software firm. That is especially true in the fast-moving world of e-commerce. But even Walmart changes the prices of many items in its stores 2-4 times a year, says Mr Yoes. up from once or twice a few years ago.Sysco, a food company, says the AI-powered system allows it to lower prices on “key value items” and raise prices on other products. It can thus i ncrease profits by expanding sales while maintaining profits. That keeps investors content and shoppers sweet.8．What can be learned from the first paragraph?A．It is sometimes difficult to set the right prices.B．Getting the prices right can make you lose customers.C．Raising prices by 1% always leads to an 8.7% increase in profits.D．The study from 2010 suggests that you leave money on the table.9．What is the advantage of AI-powered pricing systems over older systems?A．They are more price-sensitive.B．They make prices change more.C．They can predict price sensitivity for individual goods.D．They are able to identify links between various products.10．According to the text, which of the following products will shopkeepers reduce the price of?A．Starbucks coffee. B．Price-insensitive goods. C．Walmart’s online goods.D．Sysco’s “key value items”.11．What is the best title for the text?A．Apply AI to Set Prices B．Raise Prices to Increase Profits C．Reduce Prices to Promote Sales D．Use AI to Predict Customer ResponseDespite their bad reputation, sharks are critical to the marine ecosystem and can even help fight climate change.In the shallows of Shark Bay, Western Australia, seagrass is food for the sea cows, which can weigh as much as 500kg and eat roughly 40kg of seagrass a day. Sea cows are a rich source of food for tiger sharks. By keeping the sea cow population in check, tiger sharks helpseagrass meadows (草地) thrive. A flourishing seagrass meadow stores twice as much CO2 per square mile as forests typically do on land.But tiger shark numbers are declining. Off Australia’s northeast coast of Queensland, tiger sharks are estimated to have fallen by at least 71 percent, largely due to overfishing. A reduction in tiger sharks means more seagrass consumed by herbivores (食草动物) and less carbon stored in sea vegetation. This begged the question: What if they were absent from the Shark Bay—would the seagrass-dominated ecosystem survive?To find out, researchers led by Rob Nowicki of Florida International University, spent time in Eastern Australia, where shark numbers were lower and sea cows ate seagrass largely undisturbed. “When uncontrolled, sea cows can rapidly destroy wide areas of seagrass,” said Nowicki. “When the seagrass recovers, the seagrass community looks different, with more tropical species dominating than before.”Those findings underlined the role that tiger sharks were playing in Shark Bay. If their populations continue to decline, the resilience (恢复能力) of carbon-rich ocean ecosystems will likely decrease.When it comes to boosting shark numbers, there have been movements toward more sustainable fishing, but a large percentage of the industry have not changed their methods, which is a reason why the population of many marine top predators (捕食者) continues to decline.Apart from supporting sustainable fishing, Nowicki said the only way to truly protect marine life is to reduce our global greenhouse gas emissions. “Ultimately, if we are going to conserve our ecosystems in the centuries to come, we are going to need to solve climate change while undertaking species conservation at the same time.”12．Why are tiger sharks key to the marine ecosystem?A．They feed on various sea animals. B．They can store large amounts of CO2. C．They can prevent the loss of seagrass. D．They affect marine species distribution. 13．What did Rob Nowicki’s team want to find out in Eastern Australia?A．How sea cows destroy the seagrass community.B．How shark population influences the ocean ecosystem.C．What was contributing to the declining number of tiger sharks.D．What to do to recover the seagrass-dominated ecosystem.14．What is the main reason for the decline in tiger shark numbers in Australia?A．Climate change. B．Seagrass Loss.C．Habitat destruction. D．Unsustainable fishing.15．What is important in preserving marine life and ecosystems suggested by Nowicki? A．Banning marine fishing activities. B．Addressing ocean pollution problems. C．Preserving marine top predators. D．Decreasing greenhouse gas release.二、七选五When raindrops fall to the ground in summer, a familiar scent always follows. Many people call this the “smell of rain”. However, rain is made up of odorless (无味的) water. So, where does this smell come from?___16___ But it actually comes from wet soil. This special odor even has its own name: petrichor (潮土油), which comes from a pair of chemical reactions.The pleasant smell has long been an interest of scientists since Australian scientists first documented the formation of petrichor in 1964. According to scientists, some plants produce oils during dry periods. ___17___Yet, it’s the second reaction that creates the most petrichor. It occurs when chemicals produced by bacteria in soil are released. ___18___ These bacteria break down and change into simple chemical compounds, providing nutrition for plants. Meanwhile the process also produces geosmin (土臭素), a compound with a distinct earthy aroma (香味).Lots of animals are sensitive to geosmin but human beings are extremely sensitive to it. When it rains after a long period of dryness, drops of water hit the ground. Geosmin is then released from the surfaces. ___19___ And it finally gives raindrops their familiar scent. If it rains heavily enough, geosmin will be spread downwind, warning others of coming rain.___20___ And the next time someone mentions how much they love the smell of rain, you can prove your intelligence by explaining where that smell comes from.A．And when it rains, these oils are released into the air.B．The smell of petrichor is quite pleasant to the human nose.C．There are a group of microorganisms widely found in soils.D．Rain can refresh the soil specially when it rains heavily.E．Scientists found the distinctive smell doesn’t come from rain.F．The pleasant smell always comes into being with the flow of air.G．It is further spread around its surroundings with the aid of wind and rain.三、完形填空My mother was always knitting (针织). What a shock to me when she recently told me that knitting helped her ___21___ stresses of raising four children. And I have now ___22___ that it is true for me — and much more.My mother taught me to knit when I was about 6. But I soon ___23___ the project, as it was boring for a young child. My next knitting was restarted in Madison, where I was in graduate school and feeling the ___24___ of the studies. Miraculously, the knitting saved my soul in that stressful semester of studies and other life events of love and ___25___.Knitting during the pandemic ___26___ my despair at not being able to participate in my ___27___ volunteer activities. I knitted dozens of scarves to ___28___ to a shelter and this helped me feel ___29___ the community.Knitting scarves, shawls (披肩) and blankets for my daughter when she went away for university brought me ____30____ as I imagined every stitch (针脚) of love ____31____ my now-adult child — as once my arms ____32____ her when she was young.My mother’s legacy is vast, but the major life ____33____ she taught me through knitting is that there is a step-by-step process of building, ____34____ and rebuilding. It requires patience and a belief that stitches that are cast off (收针) can always ____35____ their way back on.21．A．get through B．get across C．get into D．get on 22．A．noticed B．remembered C．realized D．adapted 23．A．made out B．gave up C．held onto D．struggled with 24．A．delight B．feature C．importance D．pressure 25．A．grades B．health C．loss D．achievements 26．A．eased B．worsened C．improved D．strengthened 27．A．common B．usual C．ordinary D．unique 28．A．devote B．belong C．sell D．donate 29．A．concerned about B．connected to C．addicted toD．interested in30．A．sorrow B．disappointment C．comfort D．excitement31．A．preserved B．moved C．impressed D．surrounded 32．A．lifted B．balanced C．covered D．protected 33．A．lesson B．plan C．experience D．skills 34．A．checking out B．tearing down C．putting aside D．working out 35．A．push B．give C．find D．lose四、用单词的适当形式完成短文阅读下面材料, 在空白处填入适当的内容(1个单词)或括号内单词的正确形式.Hangzhou art exhibitions paint the wonders of Southern Song Dynasty Hangzhou, capital city of Zhejiang province, East China, was the political, economic and cultural center more than 800 years ago, when it ___36___ (serve)as the capital of the Southern Song Dynasty(1127-1279).A gathering of outstanding intellectuals, scholars, and artists lifted the city’s culture and art to a new peak, casting ___37___ long-standing influence in Chinese history that has lasted to present day.___38___ (mark) this booming scene, five exhibitions opened at the art museum of China Academy of Art in Hangzhou on Saturday. Paintings and calligraphic pieces from different periods of time ___39___ (be)now on show to showcase the Song era to audiences, ___40___ to help them understand how Chinese cultural traditions have been passed on throughout centuries.The center exhibition of the five is Embrace the Landscape, ___41___ brings together 37 classic paintings—10 of them dated to Song Dynasty (960-1279)—borrowed ___42___ major museums across the country. It provides an enactment(呈现)of the landscapes and ___43___ (society) and cultural lives led by people in Southern Song, in Hangzhou, then called Lin’an, and neighboring areas in Jiangnan, a term ___44___ (refer)to the lower reaches of the Yangtze River.Through these objects one will also see the cultural lineage that has been passed on since the Tang Dynasty(618-906)and has been further developed by the elite communities in Song, and how their accomplishments continued to guide and inspire artists in the following____45____ (dynasty).五、根据首字母填写单词46．I really a________ your help with this project, without which it couldn’t have been so successful.(根据首字母单词拼写)47．The water s________ has been cut off for the moment because the workers are repairing the pipes. (根据首字母拼写单词)48．I ran a marathon in the burning heat, and the sweat was s________ down my cheeks by the time I crossed the finish line. (根据首字母单词拼写)49．If you have any other questions, please feel free to c________ us at the e-mail address below. (根据首字母拼写单词)50．The performance of the talented singer left a deep i________ on the audience, and they could not stop talking about it for days. (根据首字母单词拼写)51．As the team leader, I am r________ for ensuring the project is completed on time. (根据首字母单词拼写)52．The most awkward moment came when the presenter accidentally spilled water all over herself during the live broadcast, leaving her e________ and speechless in front of the camera. (根据首字母单词拼写)53．The teacher will a________ the results of the final exam after all the answer sheets have been graded. (根据首字母单词拼写)54．It is highly r________ that you should try the new Italian restaurant that just opened up downtown — the food is absolutely delicious! (根据首字母拼写单词)55．The small business suffered a huge l________ in the fire that broke out last night, destroying the entire building, and leaving them with nothing but ashes. (根据首字母单词拼写)六、其他应用文56．上周末你参加了校学生会组织的“了解我们身边的非物质文化遗产（intangible cultural heritage）”活动，请为校英文报写篇报道，内容包括：1. 活动的过程；2. 收获与感想。