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2012东城二模 第一篇_2012年北京市东城区二模理综试题及答案

北京市东城区

2011—2012学年度第二学期高三综合练习（二）

理科综合能力测试

本试卷共300分。考试时长150分钟。考生务必将答案答在答题卡上，在试卷上作答无效。考试结束后，将本试卷和答题卡一并交回。 以下数据可供解题时参考：

可能用到的相对原子质量：H 1 C12 O16 Mg 24 Al 27

第一部分（选择题共120分）

本部分共20小题，每小题6分，共120分。在每小题列出的四个选项中，选出最符合题目要求的一项。

1．下图表示科学家利用小鼠的纤维母细胞培养体系培养多种细胞的过程，下列叙述正确的

是

A．与纤维母细胞相比，经过程①形成的诱导性干细胞的全能性较低 B．过程②的结果说明，诱导性干细胞中遗传信息的表达情况不同 C．诱导性干细胞与上皮细胞在功能上有差异，形态上没有差异 D．上述细胞中具有细胞周期的是诱导性干细胞和神经细胞

2．下图为转基因抗冻番茄培育过程的示意图（其中ampr为抗氨苄青霉素基因）。下列叙述

不正确的是

．．．

A．可同时选用限制酶PstI、Sma I对含目的基因的DNA进行切割

B．过程②可采用农杆菌转化法将含目的基因的表达载体导入受体细胞

C．质粒上的抗性基因有利于筛选含目的基因的细胞和促进目的基因的表达

D．图中过程④可以利用放射性同位素标记的目的基因作为探针进行筛选

3．为研究CO2浓度对针叶树光合作用的影响，研究人员将红松、红皮云杉和长白落叶松的

幼苗盆栽于模拟自然光照和人工调节CO2浓度为400和700μmol·mol-1的气室内，利用仪器测定了各树种的相关数值（光补偿点表示光合速率等于呼吸速率时的光照辐射强

度，光饱和点表示光合速率开始达到最大时的光照辐射强度），结果如下表。下列叙述不正确的是

．．．

A．随着环境中CO2浓度的升高，三种植物均在更弱的光照下达到光补偿点 B．当环境CO2浓度为400μmol·mol-1时，长白落叶松有机物积累量最多

C．随着环境中CO2浓度的增加，最大净光合速率增加幅度最大的是红松

D．从光饱和点的变化推测，CO2浓度的增加会使光合速率因暗反应速率的加快而提高 4．甘氨酸是脊髓中主要的抑制性神经递质，能使突触后膜的Cl—通道开放，使Cl—内流。下

列叙述正确的是 A．脊髓神经元细胞静息状态时膜内外没有离子进出 B．甘氨酸以自由扩散的方式经突触前膜释放到突触间隙 C．甘氨酸与突触后膜上受体结合后引起膜外电位由正变负 D．某种毒素可阻止神经末梢释放甘氨酸，从而引起肌肉痉挛 5．利用下列实验方法不能实现相应目的的是

．．

6．下列说法正确的是

A．碘、铁都是人体必需的微量元素

B．淀粉和纤维素互为同分异构体，均可水解得到葡萄糖 C．碳酸钡、碳酸氢钠、氢氧化镁等均可作为抗酸药物使用 D．聚氯乙烯塑料制品可用于食品包装 7．下列说法不正确的是 ．．．

A．46 g C2H6O中共用电子对数为8×6．02×10

B．20 g重水（D2O）中含有的电子数为10×6．02×1023

23

C．100 mL 2．0 mol·L-1 NH4HCO3溶液中NH4+ 数为0．2×6．02×1023

D．标准状况下，22．4 L NO与CO的混合气体中含有的原子数为2×6．02×1023 A．漂白粉和明矾都常用于自来水的处理 B．乙烯可使溴水或酸性高锰酸钾溶液褪色 C．铁片和铝片置于冷的浓硫酸中均无明显现象 D．苯酚和氢氧化钠溶液在空气中久置均会变质

A K X

B 食盐水

Fe

A．若X为碳棒，开关K置于A处可减缓铁的腐蚀 B．若X为锌棒，开关K置于A或B处均可减缓铁的腐蚀 C．若X为锌棒，开关K置于B处时，铁电极上发生的反应为 2H++2e—=H2↑

D．若X为碳棒，开关K置于A处时，铁电极上发生的反应为 2H++2e—=H2↑

、

8．下列事实可以用同一原理解释的是

9．模拟铁的电化学防护的实验装置如右图所示，下列说法不正确的是 ．．．

10．氢化热是指一定条件下，1 mol 不饱和化合物加氢时放出的热量。表中是环己烯

下列说法正确的是

A．环己二烯与H2的反应最剧烈

B．环己烯、环己二烯和苯有相同的官能团 C．三种化合物中环己二烯的稳定性最强D．上述条件下，1 mol

转变为

时放热113 kJ

11．T ℃时，将6 mol CO2和8 mol H2充入2 L密闭容器中，n(H2)/mol

发生反应CO2（g）＋3H2（g） CH3OH（g）＋H2O8 （g），容器中H2的物质的量随时间变化如图中实线所a

(1,6) 6

示。图中虚线表示仅改变某一反应条件时，H2的物质的

量随时间的变化。下列说法正确的是 A．反应开始至a点时v（H2）＝1 mol·L-1·min-1 B．若曲线Ⅰ对应的条件改变是升温，则该反应H＞0 C．曲线Ⅱ对应的条件改变是降低压强

D．T ℃时，该反应的化学平衡常数为0．125

4 2

Ⅰ

(8,2) (11,2)

c b

Ⅱ

t/min

2 4 6 8 10

12．根据表中信息判断，下列选项不正确的是

A．第①组反应的其余产物为H2O和 O2

B．第②组反应中Cl2 与 FeBr2的物质的量之比为1︰2 C．第③组反应中生成1mol Cl2，转移电子2mol

D．氧化性由强到弱顺序为MnO4- > Cl2 > Fe3+ > Br2

13．氢原子核外电子在能级间跃迁时发出a、b两种频率的光，经同一双缝干涉装置得到的

干涉图样分别如甲、乙两图所示。若a 光是氢原子核外电子从n=3的能级向n=1的能级跃迁时释放的，则b光可能是

A．从n=4的能级向n=3的能级跃迁时释放的 B．从n=3的能级向n=2的能级跃迁时释放的 C．从n=2的能级向n=1的能级跃迁时释放的 D．从n=4的能级向n=1的能级跃迁时释放的

m，两球心间的距离l为球半径R的3倍。若使它们带上等量异种电荷，所带电荷量的绝对值均为Q，则a、b两球之间的万有引力F引和库仑力F库的表达式正确的是

甲

乙

14．两个相同的、质量分布均匀的金属球a和b，分别固定于绝缘支座上，设两球质量均为

A．F引G

ml

2

2

，F库k

Ql

2

2

B．F引G

ml

2

2

，F库k

2

Ql

2

2

C．F引G

ml

2

2

，F库k

Ql

2

2

D．F引G

ml

2

，F库k

Ql

2

2

15．一列沿x轴正方向传播的简谐横波，每个质点振动的振幅都

为2cm，已知在t=0时刻相距4cm的两个质点a、b的位移都【2012东城二模,】

是1cm，但速度方向相反，其中a质点的速度沿y轴负方向，

如图所示。则

A．t=0时刻，a、b两质点的加速度相同

B．a、ｂ两质点的平衡位置间的距离为半波长的奇数倍 C．a质点的速度最大时，b质点的速度为零

D．当b质点的位移为+2cm时，a质点的位移为正

/cm

16．北斗导航系统又被称为“双星定位系统”，具有导航、定位等功能。“北斗”系统中两颗

工作卫星1和2均绕地心O做匀速圆周运动，轨道半径均为r，某时刻两颗工作卫星分

别位于轨道上的A、B两位置，如图所示。若卫星均顺时针运行，地球表面处的重力加速度为g，地球半径为R，不计卫星间的相互作用力。以下判断中正确的是

A．这两颗卫星的向心加速度大小相等，均为

Rgr

22

卫星1

B．卫星l由位置A运动至位置B所需的时间为C．如果使卫星l加速，它就一定能追上卫星

2

2r3R

rg

2 B

D．卫星1由位置A运动到位置B的过程中万有引力做正功

17．在一支氖管两端加一个正弦交流电压u=50sin（314t） V。当氖管两端电压达到或超过

U0

时，氖管就能发光。则在此交流电的一个周期内氖管的发光时间为

A．0．2s

B．0．02s

C．0．01s

D．0．005s

18．有两个质量分别为m1和m2的物体A和B，并排放在水平地面上。现用同向水平拉力

F1、F2分别作用于物体A和B上，作用一段时间后撤去，两物

体各自滑行一段距离后停止。A、B两物体运动的v—t图象分

别如a、b图线所示。由图中信息可以得出

A．若m1=m2，则力F1对A所做的功小于力F2对B所做的功

B．若m1=2m2，则力F1对A所做的功小于力F2对B所做的功 C．若m1= m2，则力F1的最大瞬时功率一定是力F2的最大瞬

时功率的2倍

D．若m1=2 m2，则力F1的最大瞬时功率一定是力F2的最大瞬时功率的2倍

/s

19．如图所示，在轻弹簧的下端悬挂一个质量为m的小球A，若将

小球A从弹簧

原长位置由静止释放，小球A能够下降的最大高度为h。若将小球A换为质

量为2m的小球B，仍从弹簧原长位置由静止释放，则小球B下降h时的速 度为（重力加速度为g，不计空气阻力。）

A

B

C D．0

20．静电场方向平行于x轴，其电势φ随x的分布可简化为如图所示的折线。一质量为m、带电量为＋q的粒子（不计重力），以初速度v0从O点进入电场，沿x轴正方向运动。

下列叙述正确的是

A．粒子从O运动到x1的过程中速度逐渐增大 B．粒子从x1运动到x3的过程中，电势能先减小后增大

C．要使粒子能运动到x4处，粒子的初速度v0至少为



D．若v0第二部分（非选择题共180分）

本部分共11小题，共180分。

21．（18分）（1）在做“用双缝干涉测量光的波长”实验时，某同学调整手轮后，从测量头的目镜看去，当分划板中心刻度线对齐A条纹中心时（如图1所示），游标卡尺的示数

2012东城二模 第二篇_2012东城二模高三英语试题及答案

北京市东城区2011—2012学年度第二学期高三综合练习（二）

英语 2012.5

本试卷共150分，考试时间120分钟。考试结束后，考生务必将答题卡交回。 注意事项：

1. 考生务必将答案答在答题卡上, 在试卷上作答无效。

2. 答题前考生务必将答题卡上的姓名、准考证号用黑色字迹的签字笔填写。

3. 答题卡选择题必须用2B铅笔作答, 将选中项涂满涂黑, 黑度以盖住框内字母为准, 修改时用橡皮擦除干净。

4. 答题卡非选择题必须用黑色字迹的签字笔按照题号顺序在各题目的答题区域内作答, 未在对应的答题区域内作答或超出答题区域作答均不得分。

第一部分：听力理解（共三节，30分）

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。

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 答案是D。

D．Believe it or not

21. The boy is excited about the coming music festival and he enjoys pop music ______. A. less B. little C. most D. more 22. Before moving to Australia, the Browns______ their cars and house in the USA. A. have sold B. sold C. were selling D. sell 23. ─ Has your brother found a job?

─ Not yet. There are many jobs that he _____ do but he seems unwilling to do anything. A. shall B. could C. must D. should 24. After a long absence, I went back to college, ______ to pick up where I’d left off. A. hoping B. hope C. to hope D. hoped 25. Peter will have to change his travel plan because his flight _____. A. delays B. would delay C. has been delayed D. was delayed 26. You have a gift for art. ______ you do your best, you are sure to create fine art works. A. As soon as B. Even if C. In case D. As long as 27. She looked ______ her handbag, but her keys were not there.

A. for B. to C. at D. in 28. I wish that I _____ to go to Jim’s party, for I have to do some extra work tonight. A. hadn’t agreed B. haven’t agreed C. wouldn’t agree D. won’t agree 29. If your call is not answered within two minutes, you______ to hang up and dial again. A. would be advised B. are advised

C. have been advised D. were advised

30. Don’t have the water _____ while you brush your teeth.

A. running B. run C. to run D. ran

31. I have sent several e-mails to the company for the advertised job, none of _____ has been answered.

1

A. whom B. that C. which D. whose

32. Johnson is a new graduate. He has difficulty in dealing with ______ problems arise.

A. wherever B. whichever C. whatever D. whenever

33. We saw ______ audience clapping their hands when ______ popular singer appeared on the stage.

A. the; the B. the; 不填 C. an; a D. 不填; the 34. ______ the young man is in great need of a computer in his work is known to his boss. A. What B. That C. How D. When 35. Not until I completed the form______ that half the questions were not relevant to me. A. had I realized B. I had realized C. I realized

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。

One Monday morning, the class were excited about the rumor that the science room was on fire over the weekend. Mr. Johnson, my fifth grade teacher ___36___ it and explained that science class would be cancelled due to the ___37___. He also warned us not to go near the room ___38___ it could be dangerous.

During the morning break, Kim and I ___39___ to check out the damage. A first hand observation would make us heroes at lunch. We safely ___40__ the science room. We stood on tiptoes(脚尖) looking hard through the door window，___41___ to see what was like inside when suddenly a firm hold on our shoulders stopped us.

“Where do you belong? Certainly not here!”

I turned around to find a teacher staring ___42___ at us, shouting. In those frozen seconds millions of ___43___flashed through my mind. My father would kill me for disobeying teachers. ___44___ than that, my mother might be so mad that she might not stop him. My spirits ___45___ even lower when I thought of how angry Mr. Johnson would be. Soon the arresting teacher led Kim and me back to the ___46___, leaving us trembling before Mr. Johnson .

But to our ___47___, there was no yelling and no anger from Mr. Johnson. ___48___, he bent slowly to look me in the eye. I was met with a look of ___49___ rather than anger. He spoke softly and carefully as he explained why he was ___50___ in my decision to go where I might have got ___51___. As I looked into the eyes of the man who could send me to unimagined consequences at home, tears ___52___ up in my eyes. The thought of disappointing Mr. Johnson ___53___ me while I felt a gentle touch of Mr. Johnson’s hand on my shoulder. I glanced up and he smiled. My ___54___ for Mr. Johnson grew greatly in the moment I discovered that he still liked me even after I’d disappointed him. I could see that he cared more about my ___55___ than the fact that I’d broken a rule. It was the first time I felt the power of forgiveness. 36. A. heard 37. A. fire 38. A. unless 39. A pretended 40. A. entered 41. A. hanging 42. A. angrily

D. did I realize

B. believed B. rumor B. because B. asked B. found B. trying B. patiently

C. confirmed D. studied C. focus D. loss C. though C. decided

D. once D. hesitated

C. examined C. happening C. silently

2

D. reached

D. waiting D. curiously

43. A. excuses 44. A. Easier

45. A. flew 46. A. school 47. A. surprise 48. A. However 49. A. concern

B. thoughts

C. words C. Later C. changed C. office C. regret C. comfort

D. feelings

D. Worse D. moved D. classroom D. sorrow D. Instead D. complaint D. disappointed D. blamed D. rounded

B. Less B. sank B. lab B. delight

B. guilt B. puzzled B. burnt B. shamed B. hope

B. Therefore C. Otherwise C. discouraged C. lost C. welled C. bored C. desire

50. A. frightened 51. A. hurt 52. A. flooded 53. A. shocked 54. A. care 55. A. safety

B. rushed

D. confused D. love

D. behaviour

B. freedom C. dignity

第三部分：阅读理解（共两节，40分）

第一节（共15小题；每小题2分，共30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，并在答题卡上将该项涂黑。

A

I recently had dinner with someone who told me that one of his best friends had been killed in a private plane crash, and something happened at the memorial service that he’ll never forget. He shared the story with me.

At the memorial service, his friend’s wife walked to the platform to speak to the gathering. She said a friend had asked her the best memory she had of their life together. At the moment, she had been too sad to answer, but she had thought about it since and wanted to answer the question. They were in their late forties when he died, and she began talking about a time in their life almost twenty years earlier. She had quit her job to obtain her master’s degree, and her husband never hesitated in his support.

and also did the cooking, cleaning, and other housework while she studied for her degree.

One time they both stayed up all night. She was finishing her paper, and he was preparing for an important business meeting. That morning, she walked out of her study, leaned against the door by the stairs, looked at her husband downstairs and just thought about how much she loved him. She knew how important this meeting was to his future, and she was feeling guilty that she didn’t even have time to make his breakfast. He took his briefcase and hurried out. She heard the garage door open and close, but much to her surprise, she heard it open again about thirty seconds later. From above, she watched her husband dash into the house and walk over to the forgotten coffee table. Marking the surface of it with his finger through the dust with the words “I love you”, then he raced back to his car.

The new widow then looked out at her audience and said, “John and I had a wonderful life together. We have been around the world several times. We’ve had everything money can buy...but nothing comes close to that moment.”

Hearing this, I was deeply moved. “Love makes life worthwhile.” 56. The service was held to ______.

3

A. listen to the woman’s story B. mourn the woman’s husband D. share the woman’s sadness

C. meet some old friends

57. Why did the woman quit her job? A. She had to support her husband. B. She had too much housework to do. C. She wanted to travel around the world.

D. She needed to concentrate on her studies.

58. “He held down his own job…” in Paragraph 4 means that ______. A. he managed to keep his job B. he needed help in his work C. he cancelled his job

D. he delayed his work

59. The woman mentioned an incident 20 years ago to show______. A. how busy their life was B. how her husband loved her C. how they improved their life

Dear Volunteers，

The service you will provide to elderly individuals in Abilene as a Meals on Wheels volunteer is deeply appreciated. I want to take this opportunity to thank you for the many miles you will travel and all of the hours you will contribute to help make this one of the best programs in the entire state.

We have our staff members make a home visit before adding each person to the program and try to visit everyone at least once every year. That is hardly enough, and we depend on your contact a great deal! It is important that you report back when you do not get an answer to your knock on the door. The person inside may be hurt or ill. They may be in hospital or out of town and fail to inform us. If they are frequently absent, we may need to determine if they still need meals.

If you find someone with a medical emergency, please call 911 to request medical assistance, and then call the Meals on Wheels office. If you find someone who needs assistance other than for a medical emergency, please call the Meals on Wheels office at 6725050, and we will try to find the appropriate agency or individual to call.

Let us know when a certain person needs extra food. We have a food preparation room of shelf stable items to share with them. Please feel free to take a few magazines when you deliver meals. Many of those we serve cannot afford magazines and enjoy reading. If someone is interested in getting books from the Abilene Public Library, let us know. We can sign them up for the Books on Wheels program. Call if you smell gas strongly when you deliver meals, or if someone needs a space heater, a blanket, or an electric fan. Please convey all needs to us, and we will try to see that they are met. Some of the elderly people who we offer our service may have cancers, liver diseases, AIDS, etc. If you do not want to deliver meals to the people with certain types of health problems, such as these, please let us know.

Sincerely,

Betty L. Bradley, LBSW,

Executive Director

60. Why does the author write this letter?

A. To express great thanks to volunteers.

4

B

D. how hard her husband worked

B. To explain how the old people get help.

C. To tell volunteers what they are tasked with.

D. To describe the life situation of the old people.

61. What can we learn about the volunteers from the passage? A. They order books for needy people. B. They design programs to help people. C. They offer medical help to sick people.

D. They deliver food to the elderly people.

62. How does the author learn about the needs of the people served? A. The volunteers report back the information to him. B. His staff members call them to get the information. C. He visits them now and then to get the information. D. The family members send the information to his office.

C

When it comes to success in business and success in life, there are few qualities as important as confidence.

People naturally have different levels of confidence. Some have a higher level of confidence than others do, but even those whose confidence is lacking can learn to build their level of confidence and reach their most important goals. Increasing self confidence is one of the most common reasons people give for seeking the help of psychologists and other professionals.

One of the many places where a greater level of confidence is useful is in the workplace. We all know how difficult it can be, for instance, to ask the boss for a raise. This process can be extremely difficult for those who lack confidence in their own abilities. After all, if you are unsure about your own abilities, how will you ever convince your boss that you deserve more money for the work you do?

Even if you are not asking for that big raise, having plenty of confidence in your abilities is important to success. If you are certain of your abilities, chances are that those around you, whether they are your coworkers, your colleagues or your superiors, will see that confidence, and that will help to assure them that you are the best at what you do.

Being thought of as the person to go to, and being seen as an expert in your chosen field, is naturally very important to success on the job. If you can make yourself the person people go to for guidance and advice, you will help to protect yourself from the ever present danger of downsizing. After all, if you are a recognized expert at the office, you will be regarded as an indispensable member of the team.

Having a high level of confidence, after all, does not mean overlooking the places where you could improve. Knowing what you do well and where you need help will help you enjoy increased success and confidence.

63. What is the passage mainly about?

A. The influence of confidence on one’s life. B. The importance of confidence to success. C. The difference of people’s confidence.

D.The judgment on one’s confidence.

64. Psychologists and other professionals can offer help to those _____. A. who think their goals are hard to reach

5

2012东城二模 第三篇_2012北京东城二模数学文科试题及答案

北京市东城区2011-2012学年度第二学期高三综合练习（二）

数学 （文科）

本试卷分第Ⅰ卷和第Ⅱ卷两部分，第Ⅰ卷1至2页，第Ⅱ卷3至5页，共150分.考试时长120分钟.考生务必将答案答在答题卡上，在试卷上作答无效.考试结束后，将本试卷和答题卡一并交回.

第Ⅰ卷（选择题 共40分）

一、本大题共8小题，每小题5分，共40分。在每小题列出的四个选项中，选出符合题目

要求的一项。

（1）若集合Axx0，且ABB，则集合B可能是

（A）1,2（B）xx1 （C）1,0,1 （D）R





（2）“a3”是“直线ax3y0与直线2x2y3平行”的

（A）充分不必要条件 （B）必要不充分条件

（C）充要条件 （D）既不充分也不必要条件

（3）执行右图的程序框图，则第3次输出的数为

（A）4 （B）5 （C）6 （D）7

（4）已知圆x2y22xmy0上任意一点M关于直线xy0的对称点N也在圆上，则m的值为

（A）1 （B）1 （C）2 （D）2 （5）将函数ysinx的图象向右平移

象对应的函数解析式为

（A）y1sinx （B）y1sinx （C）y1cosx （D）y1cosx

（6）已知m和n是两条不同的直线，和是两个不重合的平面，那么下面给出的条件中

一定能推出m 的是

（A），且m （B）m∥n，且n （C），且m∥ （D）mn，且n∥

（7）设M(x0,y0)为抛物线C:y8x上一点，F为抛物线C的焦点，若以F为圆心，

2



个单位长度，再向上平移1个单位长度，所得的图2

FM为半径的圆和抛物线C的准线相交，则x0的取值范围是

（A）(2,) （B）(4,) （C）(0,2) （D）(0,4)

1

（8）已知函数f(x)(xa)(x2bxc),g(x)(ax1)(cx2bx1)，集合

Sxf(x)0,xR，

T

g(x)0,xR，记cardS,cardT分别为集合S,T中的元素个数，那么下列

结论不可能的是

（A）cardS1,cardT0 （B）cardS1,cardT1 （C）cardS2,cardT2 （D）cardS2,cardT3

第Ⅱ卷（共110分）

二、填空题：本大题共6小题，每小题5分，共30分。

(9) 若向量a(1,0)，向量b(1,1)，则a-ba-b与b的夹角为. (10) 设aR，且(ai)2i为实数，则a

(11)将容量为n的样本中的数据分成6组，若第一组至第六组数据的频率之比为

(12)在平面直角坐标系xOy中，将点A(3,1)绕原点O逆时针旋转90到点B，那么点B坐

标为____，若直线OB的倾斜角为，则tan2的值为 ． (13) 已知函数f(x)x,给出下列命题：

①若x1，则f(x)1；

1

2



②若0x1x2，则f(x2)f(x1)x2x1； ③若0x1x2，则x2f(x1)x1f(x2)； ④若0x1x2，则

f(x1)f(x2)xx

f(12).

22

其中，所有正确命题的序号是 .

(14) 已知四棱柱ABCDA侧棱AA底面ABCD的1BC11D1中，1底面ABCD,AA12，

边长均大于2，且DAB45，点P在底面ABCD内运动且在AB,AD上的射影分别为M，N，若PA2，则三棱锥PD1MN体积的最大值为____.

2



三、解答题：本大题共6小题，共80分。解答应写出文字说明，演算步骤或证明过程。 （15）（本小题共13分）

已知函数f(x)Asin(x)（其中xR，A0，0,图象如图所示.

（Ⅰ）求A，，的值；

（Ⅱ）已知在函数f(x)图象上的三点M,N,P的横坐标分别为1,1,3，求sinMNP的值.

（16）（本小题共13分）

ππ【2012东城二模,】

）的部分22

某校为了解学生的学科学习兴趣，对初高中学生做了一个喜欢数学和喜欢语文的抽样调查，随机抽取了100名学生，相关的数据如下表所示：

(Ⅰ) 用分层抽样的方法从喜欢语文的学生中随机抽取5名，高中学生应该抽取几名? (Ⅱ) 在(Ⅰ)中抽取的5名学生中任取2名，求恰有1名初中学生的概率．

（17）（本小题共13分）

如图，矩形AMND所在的平面与直角梯形MBCN所在的平面互相垂直，MB∥NC,MNMB．

（Ⅰ）求证：平面AMB∥平面DNC； （Ⅱ）若MCCB，求证BCAC.

3

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