问题 选择题
能够把圆O:x2+y2=16的周长和面积同时分为相等的两部分的函数称为圆O的“和谐函数”,下列函数不是圆O的“和谐函数”的是(  )
A.f(x)=4x3+xB.f(x)=1n
5-x
5+x
C.f(x)=tan
x
2
D.f(x)=ex+e-x
答案

由“和谐函数”的定义知,若函数为“和谐函数”,则该函数为过原点的奇函数.

A中,f(0)=0,且f(x)为奇函数,故f(x)=4x3+x为“和谐函数”;

B中,f(0)=ln

5-0
5+0
=ln1=0,且f(-x)=ln
5+x
5-x
=ln(
5-x
5+x
)-1
=-ln
5-x
5+x
=f(x),所以f(x)为奇函数,

所以f(x)=ln

5-x
5+x
为“和谐函数”;

C中,f(0)=tan0=0,且f(-x)=tan

-x
2
=-tan
x
2
=f(x),f(x)为奇函数,

故f(x)=tan

x
2
为“和谐函数”;

D中,f(0)=e0+e-0=2,所以f(x)=ex+e-x的图象不过原点,故f(x))=ex+e-x不为“和谐函数”;

故选D.

单项选择题 A1/A2型题
单项选择题

I once went to a town in the north of England on business.

It was about 7:30 in the evening when I reached the hotel. The manageress, a strict old lady of about 60, showed me to my room. When I asked her what time dinner was, she said there was only one sitting at 6:30, and I had (21) it.

"Never mind," I said. "I’m not very hungry. I’ll just have a drink in the bar(酒吧)and a sandwich. "

"Bar! " she (22) her voice. "This is a respectable hotel, young man. If you want beer, you must go somewhere else. " She spoke (23) a glass of beer was a dangerous drug.

I went to a bar and had some beer and sandwiches and then went to the cinema. At about 11:30 I (24) Everything was in darkness. I knocked at the door, but nothing happened. The (25) sound was the church clock opposite, which suddenly struck the half-hour with such force that it made me jump. (26) a window opened upstairs. The old lady (27) and asked me what was going on. I explained who I was and she let me (28) after ten minutes’ wait. She was in her nightdress. She told me seriously that guests were (29) to be back in the hotel by 11 o’clock.

I went to bed but could not sleep. Every quarter of an hour the church clock struck and at midnight the whole hotel shook with the noise. Just before dawn, I finally (30) .

When I arrived at breakfast, everyone else had nearly (31) and there was not enough coffee to go round.

"Did you (32) well, young man" the old lady asked.

" (33) , I don’t think I could go through another night in that room," I replied. "I hardly slept at all. "

"That’s because you were (34) all night drinking!" she said angrily, putting (35) to the conversation.

22()

A.lost 

B.lowered 

C.dropped 

D.raised