Computer programmer David Jones earns￡35,000 a year designing new computer games, yet he cannot find a bank ready to let him have a credit card．Instead，he has been told to wait another two years，___1____ he is 18．The 16-year-old works for a small firm in Liverpool, where the problem of most young people ___2______his age is finding a job．David’s firm releases(推出) two new games for the fast growing computer market each month．

　 　But David’s biggest headache is what to do with his money．Even though he earns a lot, he cannot drive a car, take out a mortgage(抵押贷款)，___3_____ get credit cards．David got his job with the Liverpool-based company four months ago，a year after leaving school with six O-levels and _____4____(work) for a time in a computer shop．“I got the job because the people who run the firm knew I had already written some programs，” he said．David spends some of his money ___5_______records and clothes，and gives his mother 50 pounds __6_____week．But most of his spare time_____7______(spend) working．

“Unfortunately, computing was not part of our studies at school,” he said．“But I had been studying ___8_____in books and magazines for four years in my spare time．I knew what I wanted to do and never considered _____9_____(stay) on at school．Most people in this business are fairly young， anyway.”David added：“l would like to earn a million and I suppose early retirement is a___10___(possible)．You never know when the market might disappear．”

1. until 2.of 3.or 4.work 5.on 6.a 7.is spent 8.it 9.staying 10.possibility)

The True Story of Treasure Island

　　 It was always thought that Treasure Island was the product of Robert Louis Stevenson's imagination. However, recent research has found the true story of this exciting work.

　 Stevenson, a Scotsman, had lived abroad for many years. In 1881 he returned to Scotland for a holiday . With him were his American wife Fanny and his son Lloyd.

　 Each morning Stevenson would take them out for a long 　1　 　over the hills. They had been 　2 　this for several days before the weather suddenly took a turn for the worse. Kept indoors by the heavy rain, Lloyd felt the days dull . To keep the boy happy, Robert asked the boy to do some 　3　 .

　 　One morning, the boy came to Robert with a beautiful map of an island. 　Robert 　4___that the boy had drawn a large cross in the middle of the island . "What's that?" he asked. "That's the　 5　 　treasure'" said the boy. Robert suddenly 　6　 　something of an adventure story in the boy's 　7 　. While the rain was pouring, Robert sat down by the fire to write a story. He would make the hero a twelve-year-old boy, just like Lloyd. But who would be the pirate (海盗)?

　 Robert had a good friend named Henley, who walked around with the help of a wooden leg. Robert had always wanted to 　8 　such a man in a story. Thus Long John Silver, the pirate with a wooden leg, was born .

　 So, thanks to a　 　9　 　September in Scotland, a friend with a wooden leg, and the imagination of a twelve-year-old boy, we have one of the greatest 　10　 　stories in the English language.

1. A. talk　　　　　 　B. rest　　　　　　　 C. walk　　　　　　 D. game

2. A. attempting　　　 B. missing　 　　　　　C. planning　　　　 D. enjoying

3. A. cleaning　　　 B. writing　　　　　　 C. drawing　　　　　 D. exercising

4. A. doubted　　　　 B. noticed　　　　　　 C. decided　　　　 D. recognized

5. A. forgotten　　　 B. buried　　　　　　 C. discovered　　 　D. unexpected

6. A. saw　　　　　 B. drew　　　　　　 C. made　　　　　　 D. learned

7. A. book　　　　　 B. reply　　　　　　 C. picture　　　　　 D. mind

8. A. praise　　　　 B. produce　　　　　 C. include　　　　　 D. accept

9. A. rainy　　　　　 B. sunny　　　　　　 C. cool　　　　　　 D. windy

10. A. news　　　　 B. love　　　　　　　 C. real-life　　　　 D. adventure

(1---5 CDCBB　 6---10ACCAD)

22. 解：(Ⅰ)所求椭圆M的方程为…3分

　　　 (Ⅱ)当≠，设直线AB的斜率为k = tan，焦点F ( 3 , 0 )，则直线AB的方程为　　　 y = k ( x – 3 )　　　　 有( 1 + 2k² )x² – 12k²x + 18( k² – 1 ) = 0

　　　　　　　 设点A ( x₁ , y₁ ) , B ( x₂ , y₂ )　　　　　　 有x₁ + x₂ =, x₁x₂ =

　　　　　　　 |AB| =　

又因为k = tan=代入**式得　 |AB| =

　　　　　　　 当=时，直线AB的方程为x = 3，此时|AB| =

　　　　　　　 而当=时，|AB| ==　　　　　　　 |AB| =

　　　　　　　 同理可得　　　 |CD| ==

　　　　　　　 有|AB| + |CD| =+=

　　　　　　　 因为sin2∈[0，1]，所以　 当且仅当sin2=1时，|AB|+|CD|有最小值是

21. 解：(Ⅰ)当a=1时，对函数求导数，得　 　　

 …2分

　　 令 　　　　　　

列表讨论的变化情况：

			(-1，3)	3
	+	0	-	0	+
		极大值6		极小值-26

所以，的极大值是，极小值是 ………………6分

(Ⅱ)的图像是一条开口向上的抛物线，关于x=a对称.

若上是增函数，从而 　　　　　

上的最小值是最大值是

由于是有 　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　…………8分

由　　　　　　　 ………10分

所以 　　　　　　

若a>1,则不恒成立.

所以使恒成立的a的取值范围是 　　　　　　　………………12分

17.解：(1)

---------------2分

　 令

　 --------------4分　

　 (2)由，

　　　　　　　　　　　　　　　　 ------------6分

　　 ---------8分　

由 　　　　 ---10分

　 (2)平面ABC，BCAC，AA₁//CC­₁，面ABC，

　　　 则BC平面AC₁，CC₁AC

　　　 如图建系，则

　　　 设平面C₁DB的法向量为　　　　 则

　　　 又平面BDC的法向量为

　　　 二面角C₁-BD-C的余弦值：　 8分

　 (3)设，

又面BDC₁，

　　　 解得

　　　 所以AA₁=2，点P位置是在线段AB₁上且 12分

20：(1)的解集有且只有一个元素或

　　　 又由得

　　　 当时，；当时，

　　　 (2)　　　 　　　　　　　　 ①

　　　　 　　　　　　　 　　 ②

　　　　 由式①-或②得

　　　　　　　 ．

22.设椭圆M：(a＞b＞0)的离心率为，长轴长为，设过右焦点F倾

斜角为的直线交椭圆M于A，B两点。

　　　 (Ⅰ)求椭圆M的方程；

(2)设过右焦点F且与直线AB垂直的直线交椭圆M于C，D，求|AB| + |CD|的最小

值。

2009-2010届高三数学试卷(文)

21. (本小题12分)已知函数.

(1)　　 设，求函数的极值；

(2)　 若，且当时，12a恒成立，试确定的取值范围.

20. 已知二次函数，不等式的解集有且只有一个元素，设数列的前项和

　　　 (1)求数列的通项公式； (2)设，求数列的前项和．

19．(本小题满分12分)

　 如图，三棱柱ABC-A₁B₁C₁中，AA₁面ABC，BCAC，BC=AC=2，D为AC的中点。

　 (1)求证：AB₁//面BDC₁；

　 (2)若AA₁=3，求二面角C₁-BD-C的余弦值；

　 (3)若在线段AB₁上存在点P，使得CP面BDC₁，试求AA₁的长及点P的位置。

18.甲、乙、丙三台机床各自独立的加工同一种零件，已知甲、乙、丙三台机床加工的零件是一等品的概率分别为0.7、0.6、0.8，乙、丙两台机床加工的零件数相等，甲机床加工的零件数是乙机床加工的零件数的二倍.

(1)从甲、乙、丙加工的零件中各取一件检验，求至少有一件一等品的概率；

(2)将三台机床加工的零件混合到一起，从中任意的抽取一件检验，求它是一等品的概率；

(3)将三台机床加工的零件混合到一起，从中任意的抽取4件检验，求一等品的个数不少于3个的概率。