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(20)（本小题满分14分）
解：（Ⅰ）10a1?(2a1?1)(a1?2)，得2a12?5a1?2?0，解得a1?2，或a1?由于a1?1，所以a1?2．
因为10Sn?(2an?1)(an?3)，所以10Sn?2an2?5an?2. 故10an?1?10Sn?1?10Sn?2an?12?5an?1?2?2an2?5an?2，
整理，得2(an?12?an2)?5(an?1?an)?0，即(an?1?an)[2(an?1?an)?5]?0． 因为?an?是递增数列，且a1?2，故an?1?an?0，因此an?1?an?则数列?an?是以2为首项，所以an?2?1． 25． 25为公差的等差数列. 251(n?1)?(5n?1).??????????????????5分 22（Ⅱ）满足条件的正整数m, n, k不存在，证明如下： 假设存在m, n, k?N，使得2(am?an)?ak， *1(5k?1)． 23整理，得2m?2n?k?， ① 5则5m?1?5n?1? 显然，左边为整数，所以①式不成立． 故满足条件的正整数m, n, k不存在． ????9分 （Ⅲ）bn?an?n?31n?3?(5n?1)??2n?1， 2222(n?3)an2(n?3)5n?1cn????n?3． 5n?15n?12不等式5 m1?≤0可转化为 111cn?1?n?131(1?)(1?)?(1?)b1b2bn5 m≤31(1?111)(1?)?(1?)b1b2bn cn?1?n?1?4682n?21b1?1b2?1b3?1bn?11． ???????????2n?12n?3b1b2b3bncn?1?n?1357 第 21 页 共 21 页
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设f(n)?4682n?21， ??????3572n?12n?34682n?22n?41??????f(n?1)3572n?12n?32n?5?则 4682n?21f(n)??????3572n?12n?3?2n?42n?32n?4 ??2n?32n?5(2n?3)(2n?5)2n?44n2?16n?15?2n?44n2?16n?16?2n?4(2n?4)2?2n?4?1. 2n?4?所以f(n?1)?f(n)，即当n增大时，f(n)也增大． 要使不等式5 m1*?≤0对于任意的n?N恒成立，111cn?1?n?131(1?)(1?)?(1?)b1b2bn只需5 m≤f(n)min即可． 315 m454145≤，所以， ??31153515因为f(n)min?f(1)?即m≤4?311244??8. 151515所以，正整数m的最大值为8． ????14分
（考生务必将所有题目的答案答在答题卡上，在试卷上作答无效） 北京市朝阳区2010届高三第二学期统一考试（二）
英语
2010.05
本试卷共50分。考试时长120分钟。考生务必将答案答在答题卡上，在试卷上
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作答无效。考试结束后，将本试卷和答题卡一并交回。 第一部分：听力理解（共三节，30分）
第一节（共5小题；每小题1．5分，共7．5分） 听下面5段对话。每段对话后有-道小题，从每题所给的A、B、C三个选项中选出最佳选项。听完每段对话后，你将有10秒钟的时间来回答有关小题和阅读下一小题。每段对话 你将听一遍。
1．What does the woman like about the film'? A．The dialogue． B．The music． C．The story． 2．How does the man feel about the book? A．Puzzled． B．Disappointed． C．Curious． 3．Which one of the following is Sharon?
4．What does the man want to borrow'? A．A textbook． B．A bike． C．A key． 5．When will the woman get the computers? A．On Tuesday． B．On Wednesday． C．On Thursday 第二节（共10小题；每小题1．5分．共15分） 听下面4段对话或独白，每段对话或独白后有几道小题，从每题所给的A、B、C三个选项中选出最佳选项。昕每段对话或独㈠前，你将有5秒钟的时间阅读每小题。听完后，每小题将给出5秒钟的作答时问。每段对话或独自你将听两遍。 听第6段材料，回答第6至7题。
6．What kind of flowers does the man order? A．Red roses． B．While roses． C．Yellow roses． 7．How much will he pay? A．$32． B．$35． C．$38． 听第7段材料，回答第8至9题。
8．When is the music program for teenagers? A．From 10:30 a．m．to noon． B．From noon to 2:00 p．m． C．From 2:00 p．m．to 4:00 p．m．
9．Which will be cancelled if the weather is bad? A．Tennis． B．Skiing． C．Football. 听第8段材料，回答第10至12题。 10．Why does the woman get the job? A．Because she wants low pay． B．Because she prefers a part-time job．
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C．Because she has some experience． 11．What will the woman do after work? A．Read novels． B．Cook dinner． 12．What job is the woman probably going to do? A．A teacher． B．A nurse． C．An engineer. 听第9段材料，回答第13至15题。
13．What do we learn about Ms Rowling's first book? A．Il was written for adults． B．It made her famous soon． C．It was about a kind of animal． 14．Why does Ms Rowling consider herself so lucky? A．She can make a living by writing． B．She is loved by many people． C．She likes writing so much． 15．Where did Ms Rowling get the ideas for the Many Potter books? A．She read many books written by others． B．She collected them from daily life． C．She didn't know it herself． 第三节（共5小题；每小题1．5分，共7．5分） 听下面一段对话，完成第16题至20题，每小题仅填写一个词。听对话前，你将有20秒钟的时间阅读试题，听完后你将有60秒钟的作答时问。这段对话你将听两遍。 Information about the Rented House Location ● 16 Arawa Street, Glen Eden ●10 minutes’ walk to the 17 and 5 minutes to the train stat ion ●a house with two 18 bedrooms, 19 size ●no 20 Detailed information （请将第1 6至第20题的答案抄写在试卷第16页开放作文答题卡相应位置上） 第二部分：知识运用（共两节，45分） 第一节：单项填空（共15小题；每小题1分，共15分） 从每题所给的A、B、C、D四个选项中，选出可以填人空白处的最佳选项，并在答题卡上将该项涂黑。 例：It’s so nice to hear from her again. , we last met more than thirty years ago. A．What’s more B．That’s to say C．In other words D．Believe it or not 答案是D。 21．He raised his voice, ______ we still couldn't hear anything． A．so B．or C．but D．as
22．—What about ______ lecture you attended yesterday? —To tell the truth, it was too boring．I can't stand ______ lecture like that． A．a; the B．the; a C．the; 不填 D．the; the
23．She tried two different methods, yet ______ of them seemed to work very well． A．neither B．none C．each D．both 24．—Ring me at six tomorrow morning, will you? —Why that early? I ____.
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A．will be sleeping B．will sleep C．have slept D．have been sleeping
25．It is still unclear ______ the little boy got the CD player to work． A．where B．what C．that D．how
26．They made a great effort to prepare the exhibition, ______ to achieve a big success． A．hoped B．hoping C．to hope D．hope
27．My dog made a mess in the living room, ______ really annoyed me． A．who B．when C．that D．which
28．You have a big mouth, Tom．You ___ have told everybody the secret． A．can'1 B．mustn't C．shouldn't D．mightn't
29．I'll try it again．Never in my life _____ such a particular difficulty． A．had I met B．have I met C．I had met D．I have met 30．—Have you seen your aunt lately? —Yes, in fac t I saw her yesterday．I ______ her for several months． A．haven't see B．didn't see C．hadn't seen D．don't see 31．Just hang the towel ______ the back of the chair so that it will dry soon． A．over B．for C．with D．through
32． ______ colorful charts and graphs, he loaded a new software to help him． A．Create B．Created C．Creating D．To create 33．Students taking the course _____to finish their homework with the help of computers． A．are encouraged B．have encouraged C．are encouraging D．had been encouraged 34．You should explore your talents so us to find out ______ your real interests lie． A．what B．where C．which D．how
35．The traffic problems we are looking forward to seeing _____ have attracted the government's attention． A．solving B．solve C．solved D．to solve 第二节：完形填空（共20小题；每小题1．5分，共30分） 阅读下面短文，掌握其大意，从每题所给的A、B、C、D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。 When high school started, Becky and I became best friends．We _36__ many interests and quickly became inseparable．When high school ended, we both cried _ 37__ we would attend different colleges in the fall． Our first term of university life was _38__, We had a huge telephone bill and our e-mails were incredibly long．In the second tern-, I found some new friends with whom I felt very _39_．These were frie nds with whom I could be myself and __40__ out my feelings．I was eager to share my new friends with Becky． When Becky finally visited me at my school, we were excited．She 41 a toy bear to me as a present and told me about her college life．However, something unexpected happened when I _42__ her to my new friends．Her eyes grew dark and I could see the 43 within them．My new friends tried to share their friendship, but Becky seemed __44_ to accept it．I didn't understand __45_ the people 1 loved most couldn't love each other． Becky left．I knew she was not happy．I thought long about what had happened．After many unanswered questions, I understood that she was 46 ．She saw me with my new friends and
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