问题 填空题
如图,在底面边长为2的正三棱锥V-ABC中,E是BC的中点,若△VAE的面积是
1
4
,则侧棱VA与底面所成角的大小为arcsin
3
12
.(结果用反三角函数值表示)
答案

在正三棱锥V-ABC中,E是BC的中点;

∴VA与底面所成角是∠VAE;

∵△VAE的面积是

1
4
,∴
1
4
=
1
2
VA•AE•sin∠VAE;

∵正三棱锥V-ABC的底面边长为2,∴AE=

3
,∴VAsin∠VAE=
3
6

即三棱锥的高为

3
6
,又顶点在底面上的投影是底面的中心,令为O,则AO=
2
3
3

∴VA=

(AO)2+(VO)2
=
(
3
6
)
2
+(
2
3
3
)
2
=
17
12

∴sin∠VAE=

3
6
VA
=
3
6
17
12
=
1
17
=
17
17
,则所求的角为arcsin
17
17

故选Arcsin

17
17

阅读理解

Last month when I was taking part in a US college interview, I was asked, “ what makes you special ? ” In fact I had answered questions likes this many times since I decided to go to college in the US .college paid special attention to different achievement . For example, a person who is very good at math can go to a famous college but also can be a good football player .

This experience made me think again that I must try to find where my own interests might lead me . To be honest, it was not easy . However, I never felt sorry to choose this way because it helped me understand myself . If I took the College Entrance Examination,as we call it gaokao in China, it could never possibly do .

When I entered high school, I took gaokao seriously because it seemed to me a great way to show how good at my lessons . However,as I grew older, I realized gaokao did make me work hard at my lessons, but the pressure also pushed many other activities out of my life, like guitar―playing . Although I had no time for it, I will still get to it in the future .

No doubt, gaokao provides a way of choosing those who are successful in their studies . But it is really important for all of us to rethink what “ talent ” really is today . This is because we now live in a world in which all of our other human qualities ( 品质)are needed for success, not just the high grade .

Ken Robinson once said, “ the society depends on different kinds of talents . ”  However, gaokao pays too attention  to a person’s grades but little to his other qualities. And it is these qualities that makes life colorful and fun .

As high school students, we can not change the present situation of eduction, but we are always free to think outside of the box . Although good school grade is still useful, I hope one day we will see our education also welcomes the amazing possibilities in different people .

小题1:The US College pay special attention to ________.

A.students’family background .

B.the different achievement

C.students’ideas about way of life .

D.the school a student is from .小题2:When at high school, the writer ________.

A.had a lot of activities .

B.did not work hard at her lessons .

C.did well in gaokao

D.had no time to play the guitar .小题3:From the passage, we know that the writer may ________.

A.go to college in America .

B.give up the US college interview .

C.become a good football player in the US.

D.change the present situation of eduction .小题4:Which of the following might be the best title for the passage?

A. My school life abroad.             B. Different exams in the US.

C My view on gaokao           D. The importance of school grades

单项选择题