第一节　 听力理解(5段共15小题；每小题2分，满分30分)

每段播放两遍。各段后有几个小题，各段播放前每小题有5秒钟的阅题时间。请根据各段播放内容及其相关小题，在5秒钟内从题中所给的A、B、C项中，选出最佳选项，并在答题卡上将该项涂黑。

听第一段材料，回答第1-3题。

1. Why did the man look worried?

A. He got an expensive telephone bill.　　　　　　　　 B. He couldn’t afford the telephone bill.

C. His wife forgot to call his son.

2. What is the woman going to do?

A. Ask Jack to pay for the bill.　　　　　　　　　　　　　 B. Ask her father to pay for the bill.

C. Use her father’s bill to pay for the bill.

3. What is the relationship between the two speakers?

A. Mother and son.　　　　　　　　　　　　　　　　　　　　　 B. Husband and wife.

C. Teacher and student.

听第二段材料，回答第4-6题。

4. According to the conversation, what is one problem with arm exercises?

A. They can damage arm muscles.　　　　　　　　　　　 B. They aren’t acceptable to most people.

C. They can raise one’s blood pressure.

5. According to the conversation, what are the experts now suggesting?

A. Exercising the entire body.　　　　　　　　　　　　　　　　　 B. Having your blood pressure taken daily.

C. Exercising your legs more than your arms.

6. What forms of exercise does the woman mention?

A. Wearing arm weights while you are swimming.

B. Jogging vigorously in one place for a long time.

C. Using bicycles that require you to use both your arms and legs.

听第三段材料，回答第7-9题。

7. When does this conversation take place?

A. Just before the term begins.　　　　　　　　　　　　　 B. After the first week of classes.

C. In the middle of the term.

8. Why has the woman come to see Dr Taylor?

A. She had promised that she would.　　　　　　　　　 B. She has been sick.

C. She needs his approval (赞成) for her courses.

9. What does Dr Taylor seem most worried about?

A. She already knew the material.　　　　　　　　　　　 B. She entered the hospital.

C. Her course load was too heavy.

听第四段材料，回答第10-12题。

10. What bothers Nancy about her neighbor’s son?

A. Noise from his room.　　　　　　　　　　　　　　　　　　　　　 B. Noise from his car and radio.

C. Noise from his feet.

11. When does the noise stop?

A. When Nancy’s neighbor’s son turns off his car.

B. When Nancy’s neighbor’s son turns off the light.

C. When Nancy’s neighbor’s son turns off the radio.

12. What suggestion does Nancy’s friend make?

A. Say hello to her neighbor.　　　　　　　　　　　　　　 B. Give a little gift to her neighbor.

C. Say ugly names to her neighbor.

听第五段材料，回答第13-15题。

13. Where will the man be working during the summer?

A. In his father’s restaurant.　　　　　　　　　　　　　　　 B. In his uncle’s restaurant.

C. In a hotel.

14. Where is the woman going to work in the summer?

A. On the coast.　　　　　　　　　　　　　 B. On a ship.　　　　　　　　　　　 C. In a factory.

15. Why can’t the woman visit the man in the month of July?

A. Because she will be working on a ship.　　　　　

B. Because he will be working for his grandparents.

C. Because she will be working in the lab.

21．(本小题满分14分)

设函数，其中为常数．

(1)证明：对任意，的图象恒过定点；

(2)当时，判断函数是否存在极值？若存在，求出极值；若不存在，说明理由；

(3)若对任意时，恒为定义域上的增函数，求的最大值．

湛江市2010年普通高考测试(一)

20．(本小题满分14分)

已知抛物线的方程为　 ，圆的方程为，直线()是、的公切线．是的焦点．

(1)求与的值；

(2)设是上的一动点，以为切点的的切

线交轴于点，设，

证明：点在一定直线上．

19．(本小题满分14分)

已知数列的前项和为，且，.

(1)求的值；

(2)求数列的通项公式；

(3)设，求数列的前项和.

18．(本小题满分14分)

如图，已知四棱锥中，底面是直角梯形，，，，，平面，．

(1)求证：平面

(2)求证：平面

(3)求二面角的平面角的正弦值．

17．(本题满分12分)

甲乙两人各有四张卡片，甲的卡片分别标有数字1、2、3、4，乙的卡片分别标有数字0、1、3、5．两人各自随机抽出一张，甲抽出卡片的数字记为a，乙抽出卡片的数字记为b，游戏规则是：若a 和b的积为奇数，则甲赢，否则乙赢．

　 (1)请你运用概率计算说明这个游戏是否公平？

(2)若已知甲抽出的数字是奇数，求甲赢的概率．

16．(本小题满分12分)

已知△的内角的对边分别为，其中，又向量m_，n_，m·n=1_．

(1)若，求,的值；

(2)若，求△的面积．

(二)选做题(14-15题，考生只能从中选做一题)

14. (坐标系与参数方程选做题)已知⊙的方程为，则⊙上的点到直线(为参数)的距离的最大值为　　　　　 ．

15.(几何证明选讲选做题)如图，是半圆的圆心，

直径，是圆的一条切线，割线

与半圆交于点，，则　　　　 ．

(一)必做题(9~13题)

　9．是虚数单位，则________.

10．已知直线与直线垂直，则的倾斜角　　　 . 　

11．在二项式的展开式中，的系数是　　　　 .　

12．已知点的距离相等，则

的最小值为　　 　；此时　　　　 .

13．利用如图算法在平面直角坐标系上打印一系列点，则打印

的点既在直线左上方，又在直线下

方的有________个.

8．数列中，，且，则前2010项的和等于

A．1005　　　 　　　　　　 B．2010 　　　　　　　　 C．1　　　 　　　　　 D．0