提示词：世博会 Expo ；长三角Yangtze River Delta；文明Civilization

　 　The 41st EXPO, the theme of which is “Better city,better life” ,is being hosted in Shanghai.Different people have different ideas about the event.I think there are both advangtages and disadvantages　 of holding EXPO.

Today EXPO is the economic and cultural Olympiad of　 the world among nations.At the same time ,it is about marketing countries internationally.Throuth its existence of more than 150 years,EXPO will bring new knowledge from a specific perieod of time and trend of development,reflecting the human civilization. Holding EXPO can showcase the fantastic growth of Chinese economy.It is also the symbol of a powerful country and　 means an improvement of a　 country international position. It plays an important role in improving the life quality , the standard of civilization as well as the management of city. More importantly,not only the city of Shanghai but the economy of Yangtze River Delta will benefit from it.

However,holding EXPO has its own disadvantages.Fistly,It is reported that the main buildings of EXPO -the most expensive ones-cost 3 billion,and an authoritive statistic shows it will cost 22 billion in total.Obviously,doing so is a waste of money. What about spending the money on rural areas? It is a more important task for the government to help the poor. Besides, EXPO will last from May 1st to　 October 31th ,which makes it really a 　hard job for the soldiers and the police to maitain the safety of it for so long a time.

In my opinion, it is a more powerful country than ever that China is now,thus making us have enough money and energy.Therefore, we should host EXPO and make it have its real effect.By doing this ,we can build up the confidence and accelerate the develpment of the whole nation.　

四、虎年春晚重聚的“小虎队”大受欢迎，其表演的节目在最受欢迎歌舞类节目中当选为第一名，其成员是很多70、80甚至90后的偶象，请根据以下提示，写一篇120字左右的英语短文，发表你对崇拜明星偶像这一现象的看法。1、其成员有苏有朋AlecSu ，吴奇隆Nicholas ，陈志朋Benny ，是来自宝岛台湾的组合；2、早年给人们形象健康、积极进取的良好印象；3、歌舞具佳；4、参演多部高收视率影视作品，演技超群；5、今年是农历虎年，请“小虎队”上春晚符合中国人的风俗习惯，具有特殊意义；6、很多跟其同龄的观众，含泪观看节目，对青春岁月感慨万千,引起强烈共鸣.

提示词：偶象(idol)；小虎队　 " Little Tigers "；90后the post-90s.

Many Chinese people know that Little Tigers is a Taiwanese pop music's most popular singing group.It was formed in early years and then dismissed a few yeas later. It is a great pity for the fans who like it.

To our excitement, they showed their talent on the stage of the spring festival.And it’s worth mentioning that their performance was chosen as the most popular one 　in the programme evalution. Why are they still so popular? The reasons for it are the follows.　 .

Firstly, the singing group,made up of Alec Su, Nicholas and Benny,are attractive . They made a good impression on people by their healthy image and aggressive mind in early years . They were good at both dancing and singing and also acted as main actors in many films and TV Series which were well -recieved. So naturally they are the idols of many the post-70s,80s and even 90s.

Secondly, According to Chinese traditional lunar custom,this year is the year of　 tiger.The programme which was performed by little tigers had a special significance.

Finally, They reminded the audiences who were of the same age of their past youth.Becoming old was no longer a legend.As a result, many audiences even watched the show with tears.

In my opinion, Little Tigers has a unique personlaity affacting their fans positively. I think this is the main reason why they are still so popular. It is fortunate for us to have an outstanding idol. Having idols is not a bad thing. However, we should make it clear who are the real “heroes”. As far as I am concerned, the real heroes are those who are making the most contributions to our society, such as teachers, doctors and scientists. As young students we should learn from them. Only in this way can we become useful men and achieve our goals.

提示词：一国二制One country, two systems；珠港澳大桥Zhuhai Hong Kong and Macao Bridge，一小时经济圈One-hour economic circle

It’s well-known to us that the Zhuhai Hong Kong and Macao Bridge is being built in China. Of course it is 　not only well praised but also resulting in much doubt as well. Its advantages and the disadvantages can be listed as follows.

Some hold the view that it is 50 kilometers long(the longest bridge in the world)and it must be　 a big challenge for the engineers to overcome the technical problems . Besides, investment of 　the whole project is up to 72.6 billion. If we use the huge money for the western poor areas, we 　can help them to live a better life in some degree. Finally, it will have a negative effect on the natural environment.

　 　However, it is true that some show much support to the project. They have sufficient reasons for it.Firstly,after finishing the project, the one-hour economic circle will be realized and the local economy of all sides can benefit from each other. Secondly,the bridge will be required to be the best one and become a landmark which is an attractive scenic spot. Most important of all, there will be a profound and significant meaning to carry out “one country, two systems”smoothly.

　 Personally speaking, building the bridge brings more advantages than disadvantages, so I am in favor of it.

No1: 选香港义工黄福荣废墟中舍命救人的占43%

NO2：选为恢复灾区供电，电力职工劳动累过度因公殉职的占24%

NO3：选深圳街头卖艺老人两次捐款灾区的占20%

NO4：选全校无一人伤亡的“玉树最牛中学”复课的占13%

请根据以上提示，写一篇120词左右的英语短文，如是你本人，你会选择哪一项，并说明你选择的理由。

提示词：ruins(废墟)；捐赠(donation)

A strong eathquake hit YuShu and destroyed it seriously.Which event in YuShu do you think is the most moving?There is a survy about this recently.The results can be listed as fowllows.

43 percent of the people choose the event that HuangFurong who came from HongKong sacrificed his own life to save the students and teachers in ruins.24% support the electricity worker who died of overwork to restore the electricity supply owing to public service.20% are in favor of an old man who made a living by performing in the street in ShenZhen but donated his money to the disaster area twice.13% choose the event that the school at which nobody was wounded in the earthquake resumed classes quickly and was called the proudest one.Different people have different ideas.I will choose the event concerned with HuangFurong.It is my honor to introduce some backgrounds about him.He once participated in the rescue of WenChuan earthquake in 2008.He himself was not healthy enough.But he insisted on public service diligently without any payment for many years .Though not rich, he tried his best to help the people who need help,especially the poor.He was awarded the honorary citizen of HongKong after his death by Government of the Hong Kong Special Administrative Region.To spread his spirit,the young in Hong Kong form an organization named after him now.He is called Afu cordially according to Chinese custom and　 will be remembered by all the Chinese people.In my view,Afu is a hero who can move me to tears .Only by learning from him and doing something to help others,can we make contributions to a better society.

22、(本小题满分14分)

解(1)∵函数图象关于原点对称，∴对任意实数，　 1分

，即恒成立，

，　

．　 3分

∵ x = 1时，取极小值－，

∴ 3a + c = 0且a + c = －，

解得a = ，c = －1．　 5分

　 (2)当时，图象上不存在这样的两点使结论成立．　 6分

假设图象上存在两点、，使得过此两点处的切线互相垂直，

则由知两点处的切线斜率分别为，

且…………(*)　 8分

∵x₁、，，　

此与(*)相矛盾，故假设不成立．　 9分

(3)证明：f^/(x) = x²－1，令f^/(x) = 0，得x = ±1，

∵ x Î (－¥,－1)或x Î (1, + ¥)时，f^/(x)>0；x Î (－1,1)时，f^/(x)<0，　 10分

上是减函数，且，　 11分

∴在[－1，1]上，有| f(x) |≤成立，　　 12分

于是当x­₁，x₂ Î [－1,1]时，．　 14分

21、(本小题满分12分)

解：(1) 由a₂ = 6，= 1，= 2，= 3，　 1分

解得a­₁ = 1，a₃ = 15，a₄ = 28．　 3分

(2) 由此猜想a_n = n (2n－1) ．　 4分

下面用数学归纳法加以证明：

①　　 当n = 1时，a₁ = 1×(2×1－1) = 1，结论正确；

当n = 2时，a₁ = 2×(2×2－1) = 6，结论正确． 　5分

②　　 假设n = k (k≥2)时结论正确，即a_k = k(2k－1) ．

则当n = k + 1时，∵　 = k，

∴　　 (k－1)a_{k + 1} = (k + 1)a _k－(k + 1) = (k + 1)k(2k－1)－(k + 1)

= (k + 1)(2k²－k－1) = (k + 1)(2k + 1)(k－1)，

∵　　 k－1 ≠ 0，∴　　 a_{k + 1} = (k + 1)[2(k + 1)－1]，

即当n = k + 1时，结论正确．　　　　　　　　　　 7分

由①②可知，{a_n} 的通项公式是a_n = n (2n－1) ．　 8分

(3) ∵　　 　= 　= ( －)　 10分

∴　　 (+ + ┄ + ) = (1－) = ．　 12分

20、(本小题满分12分)

解：(1)设切去正方形边长为x，则焊接成的长方体的底面边长为4－2x，高为x，　 1分

所以V=(4－2x)²·x = 4(x³－4x² + 4x)　 (0<x<2) ．　　 3分

∴　　 V^/ = 4(3x²－8x + 4)，　　 4分

令V^/ = 0，即4(3x²－8x + 4) = 0，解得x₁ = ，x₂ = 2 (舍去) ．　 6分

又当x<时，V^/>0；当<x<2时，V^/<0．　　 7分

∴　　 当x = 时，V取得最大值V₁ = ．　 8分

(2)重新设计方案如下：

如图①，在正方形的两个角处各切下一个边长为1的小正方形；如图②，将切下的小正方形焊在未切口的正方形一边的中间；如图③，将图②焊成长方体容器.新焊长方体容器底面是一个长方形，长为3，宽为2，此长方体容积V₂ = 3×2×1 = 6，显然V₂>V₁．

故第二种方案符合要求．

　　　　　 图①　　　　　　　　　　　 图②　　　　　　　　　 　　　图③

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　 12分

19、(本小题满分12分)

解：设z = a + bi (a,b Î R)，则z² = (a²－b²) + 2abi ，　 2分

　　 ∴　　 (a²－b²) + 2abi = 3 + 4i 　Û ，　 3分

　　 解得 或 ，　　 5分

　　 即z = 2 + i或z = －2－i ．　　　 6分

　　 又z³－6z + = 　= － ，　　 8分

　　 当z = 2 + i时，z³－6z + 　= －　= －+ i ；　 10分

　　 当z = －2 － i时，z³－6z + 　= －　= － i ．　 12分

18、(本小题满分12分)

解(1)从6个球中选取3个，共有A₆³种取法，　 2分

三次选取中，恰好有两次取到蓝色球，共有C₃¹C₄¹ A₂²种取法，　 4分

所以在三次选取中，恰好有两次取到蓝色球的概率为P = = ．　 6分

(2)设取球次数为随机变量x ，则x =1、2、3，　 8分

　　　 其分布列是：

　　　　　　　　　　　　　　　　　　　　　　　 10分

∴　 Ex =1×+ 2×+ 3×= 1.7．　　 12分

17、(本小题满分12分)

解：原不等式可化为(x－2)(x－a－1)≥0，　 2分

(1)　　 当a + 1>2即a>1时，解得x≥a + 1或x≤2；　　 5分

(2)　　 当a + 1 = 2即a = 1时，解得x Î R； 　7分

(3)　　 当a + 1<2即a<1时，解得x≥2或x≤a + 1；　 10分

∴　　 原不等式的解集：当a≥1时，是；当a<1时，是．

　　　　　　　　　　　　　　　　　　　　　　　　　　　　 12分

13、5　　　 14、i　　　 15、　　　　16、3x－y－11 = 0