问题 解答题
△ABC中内角A,B,C的对边分别为a,b,c,向量
m
=(2sinB,-
3
),
n
=(cos2B,2cos2
B
2
-1)且
m
n

(Ⅰ)求锐角B的大小;
(Ⅱ)如果b=2,求△ABC的面积S△ABC的最大值.
答案

(Ⅰ)∵

m
=(2sinB,-
3
),
n
=(cos2B,2cos2
B
2
-1)且
m
n

∴2sinB(2cos2

B
2
-1)=-
3
cos2B,

∴2sinBcosB=-

3
cos2B,即sin2B=-
3
cos2B,

∴tan2B=-

3

又B为锐角,∴2B∈(0,π),

∴2B=

3

则B=

π
3
;…(6分)

(Ⅱ)∵B=

π
3
,b=2,

∴由余弦定理cosB=

a2+c2-b2
2ac
得:a2+c2-ac-4=0,

又a2+c2≥2ac,代入上式得:ac≤4(当且仅当a=c=2时等号成立),

∴S△ABC=

1
2
acsinB=
3
4
ac≤
3
(当且仅当a=c=2时等号成立),

则S△ABC的最大值为

3
.…(12分)

单项选择题
阅读理解

阅读理解。

     Many students want to find friends on the Internet as a way of practising their language skills and learning

more about new cultures. Traditional pen pals were the primary source for such contacts, and students could

write each other letters. With the Internet, finding friends has become much easier, and such relationships are

called key pals.

     However, care and consideration should be given when finding friends on the Internet:

     ◎Search the Internet for reputable (有信誉的) services. Look for reviews(评论) of such sites to learn more about other students' experiences. Don't join a service until you have done your research.

     ◎Check to see if you can use a nickname (绰号) instead of __________, to protect your identity(身份).

     ◎Never give personal information to anyone, including your home address, phone number, and birthday.

     ◎Stop contact with others if you feel uncomfortable with the topics of conversation. Again, if you protect

your identity, this will be easier to do. Tell your teachers, parents, or even local law enforcement if problem

arise.

     ◎Try to use the language you are studying in the classroom in your communication(交流) with others.

     ◎Ask proper questions that will also help you learn about other cultures. Remember that someone's

personal experience might help you to understand a whole culture. You have to talk to many different people,

and this will get you started.

1. Please give this passage a proper title. (Please answer with 10 words.)

___________________________________________________________________________

2. Please fill in the blank with proper words. (Please answer within 5 words.)

___________________________________________________________________________

3. Which sentence in the passage is the closest in meaning to the following one?

      Pen friends used to write letters to keep in touch with each other.

___________________________________________________________________________

4. Why do many students want to find friends on the Internet? (Please answer within 30 words.)

___________________________________________________________________________

5. Please translate the underlined sentence.

___________________________________________________________________________