问题 选择题

某刺猬有2006根刺,当它蜷缩成球时滚到平面上,任意相邻的三根刺都可支撑住身体,且任意四根刺的刺尖不共面,问该刺猬蜷缩成球时,共有(  )种不同的支撑身体的方式。

A.2006

B.4008

C.4012

D.2008

答案

答案:B

解答:当有n根刺时有an种支撑法,n = 4,5, 6,…

则an+1=an+3-1=an+2或an+1=an+4-2=an+2,

∴{an}n = 4,5,6,…, 为等差数列,

∵a4 = 4

∴an=2n-4

A2006=4008  选B

评析:本题考察学生数学建模能力,从n到n + 1会增加多少种支撑,分两种情行讨论,一是所加剌穿过三剌尖确定的三角形,an+1=an+3-1=an+2,二是所加剌尖在两剌确定的平面上an+1=an+4-2

由递推式求数列通项。

阅读理解

beep …beep … There went the bell! Robbie opened his eyes. He had been sitting in the room for a whole day, and now it was time for him to do something.

Robbie looked out of the window. It was still snowing heavily and there was ice on the window. It was another cold day. Robbie was told to turn the heat on before the family got home. And he did it.

Then Robbie was told to do some cleaning work at once. It was an easy job for him, but a tough one for his master, Helen. He kept on working until every room was clean and tidy.

For now, he had to cook supper for the family.

The first thing Robbie did was to get the big pot(锅) in the kitchen. Then he put some water in the pot and put it on the stove. He used one of his hands to cut up a chicken and added the pieces to the water to make a good soup. Then he got some tomatoes, cabbages and carrots to make a vegetable salad.

At ten past eight he laid the table. Then he put some bread, the chicken soup and the salad on it. What a sweet smell! The moment he turned on the lights, the whole family came home.

“The soup smells great, Victor,” said Helen. “You really know how to tell Robbie what to do.”

Robbie is one robot that really saves the family a lot of work.

小题1:What is Robbie?

A.A cook.

B.A robot

C.A cleaner

D.A computer小题2:What do the underlined words “did it” in the second paragraph mean?

A.Looked out

B.got home

C.turned the heat on

D.did some cleaning小题3:What time did Robbie lay the table?

小题4:What can we learn from the passage?

A.The story happened on a rainy day.

B.Robbie didn’t have to be told what to do.

C.Helen found it easy to do cleaning work at home.

D.Victor and Helen felt comfortable when they got home.

单项选择题 共用题干题