Section A
Directions: In Section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.
1. A. An appointment. B. A meeting. C. A picnic. D. A surprise party.
2. A. The class usually begins at three.
B. Professor Smith didn’t have class today.
C. The woman’s class was allowed to leave ahead of time.
D. The woman wasn’t with the others.
3. A. Write to a bookstore. B. Ask the owner of a bookstore.
C. Purchase another copy. D. Borrow another copy from his teacher.
4. A. The woman didn’t like living in Shanghai.
B. The man and the woman failed to live in Shanghai.
C. The man didn’t agree with the woman.
D. The man and the woman couldn’t get used to their life in Shanghai.
5. A. Happy. B. Regretful. C. Disappointed. D. Sad.
6. A. Go to a show. B. Prepare for her test.
C. Watch the show at home. D. Go to the cinema.
7. A. 7:00 am. B. 7:30 am. C. 8:00 am. D. 8:30 am.
8. A. Tom tells his mother some bad news.
B. Tom tells his mother a piece of good news.
C. Tom’s mother feels very sad at the news.
D. Tom’s mother will go to university.
9. A. He went to see the foreign student advisor.
B. He went to Washington.
C. He went to the Passport Office.
D. He reported it to the Passport Office.
10. A. At the airport. B. On the plane. C. In a shop. D. At the railway station.
Section B
Directions: In Section B. you will hear two short passages, and you will be asked three questions on each of the passages. The passages will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.
Questions 11 through 13 are based on the following passage.
11. A. None. B. Nine. C. Eight. D. Six.
12. A. Because an electric wire was cut.
B. Because someone damaged the electrical power system.
C. Because of a technical fault in the electrical power system.
D. Because it was windy that day.
13. A. They were hurt trying to restore the electricity.
B. They were beaten up by thieves.
C. They were involved in car accidents.
D. The policemen shot them.
Questions 14 through 16 are based on the following passage.
14. A. The streets of London were full of rich people.
B. Both his parents were dead.
C. The streets of London were covered with gold.
D. He was an orphan.
15. A. He sent goods to trade in Africa. B. He sold his cat.
C. He found a job with a rich merchant. D. He found some gold.
16. A. Because Dick became rich.
B. Because Dick was made Lord Mayor of London.
C. Because Dick traded a lot of goods.
D. Because Dick became a close friend of the King of England.
Section C
Directions: In Section C, you will hear two longer conversations. The conversations will be read twice. After you hear each conversation, you are required to fill in the numbered blanks with the information you have heard. Write your answers on your answer sheet.
Blanks 17 through 20 are based on the following conversation.
|
Paying
A Bill At The Restaurant |
|
Bill: Item 1: the cover charge Item 2: the 17 : $1.20 …… Item 4: the main course: $ 18 ....... Service: 19 % |
|
The man is going to pay by 20 . |
Complete the form. Write ONE WORD for each answer.
Blanks 21 through 24 are based on the following conversation.
|
Where does the conversation probably take
place? |
21 . |
|
What do Cindy and Steve have to do? |
They have to 22 their classes they missed. |
|
Why don’t they add extra days before
summer? |
Because 23 can’t be changed. |
|
When does the conversation probably take
place? |
Before 24 . |
Complete the form. Write NO MORE THAN THREE WORDS for each answer.
22、(本小题满分14分)
已知点P在曲线C:y=
(x>1)上,设曲线C在点P处的切线为l,若l与函数y=kx(k>0)的图像的交点为A,与x轴的交点为B,设点P的横坐标为t,A、B的横坐标分别为xA、xB,记f(t)=xA·xB.
(Ⅰ)求f(t)的解析式;
(Ⅱ)设数列{an}(n≥1,n∈N)满足a1=1,an=
(n≥2),数列{bn}满足bn=
,求an与bn;
(Ⅲ)在(Ⅱ)的条件下,当1<k<3时,证明不等式:a1+a2+…+an>
.
自贡市普高2010级第二次诊断性考试数学试卷(理)
21、(本小题满分12分)
已知F1、F2是椭圆
(a>b>0)的左、右焦点,点P
在椭圆上,线段PF2与y轴的交点M满足
.
(Ⅰ)求椭圆的标准方程;
(Ⅱ)过F2作不与x轴重合的直线l,l与圆x2+y2=a2+b2相交于A、B并与椭圆相交于C、D,当
=λ,且λ∈
时,求△F1CD的面积S的取值范围.
20、(本小题满分12分)
已知A、B、C是直线l上的三点,O是直线l外一点,向量
满足
=[f(x)+2f ′(1)]
-ln(x+1)
.
(Ⅰ)求函数y=f(x)的表达式;
(Ⅱ)若x>0,证明:f(x)>
;
(Ⅲ)若不等式
x2≤f(x2)+m2-2m-3对x∈[-1,1]恒成立,求实数m的取值范围.
19、(本小题满分12分)
如图,在直三棱柱ABC-A1B1C1中,∠ACB=90°,2AC=AA1=BC=2.
![]()
(Ⅰ)若D为AA1的中点,求证:平面B1CD⊥B1C1D;
(Ⅱ)若二面角B1-DC-C1的大小为60°,求AD的长.
18、(本小题满分12分)
把圆周4等分,A是其中一个分点,动点P在四个分点上按逆时针方向前进。投掷一个质地均匀的正四面体,它的四个面上分别写着1,2,3,4四个数字,P从A点出发,按照正四面体底面上所投掷的点数前进(数字为n就前进n个分点),转一周之前继续投掷.
(Ⅰ)求点P恰好返回到A点的概率:
(Ⅱ)在点P转一周能返回A点的所有结果中,用随机变量ζ表示点P返回A点时的投掷次数,求ζ的分布列和期望.
17、(本小题满分12分)
已知函数f(x)=sin(ωx+
)+sin(ωx-
)-2cos2
(x∈R,ω>0)
(Ⅰ)求函数f(x)的值域;
(Ⅱ)若x=
是函数f(x)的图像的一条对称轴且1<ω<5,求f(x)的单调递增区间.
16、下列四个命题中,真命题的序号有__________(写出所有真命题的序号).
(1)将函数y=|x+1|的图象按向量
=(-1,0)平移,得到的图象的对应函数表达式为 y=|x|
(2)圆x2+y2+4x-2y+1=0与直线y=
相交,所得弦长为2.
(3)若sin(α+β)=
,sin(α-β)=
,则tanα·cotβ=5.
(4)已知正方体ABCD-A1B1C1D1,P为底面ABCD内一动点,P到平面AA1D1D的距离与到直线CC1的距离相等,则P点的轨迹是抛物线的一部份.
15、有红、黄、蓝三种颜色的小球各5个,都分别标有字母A、B、C、D、E,现取出5个,要求字母各不相同且三种颜色齐备,则有_________种取法(用数字做答).
14、若实数x,y满足条件
则
的取值范围是__________.
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