问题 填空题

平面α内有四个点,平面β内有五个点.从这九个点中,任取三点最多可确定 ______个平面;任取四点最多可确定 ______个四面体.(用数字作答)

答案

从9个点中取3时,确定的平面分以下几种情况:

①当三点均在平面α内时,确定的平面即为α,即满足条件的平面有1个;

②当三点均在平面β内时,确定的平面即为β,即满足条件的平面有1个;

③当三点在平面α内取两个点,在平面β内取一个点时,确定的平面个数有C42C51=30个,

④当三点在平面α内取一个点,在平面β内取两个点时,确定的平面个数有C41C52=40个,

故满足答案的平面共有72个;

从9个点中取3时,确定的四面体分以下几种情况:

①当四点在平面α内取三个点,在平面β内取一个点时,确定的平面个数有C43C51=20个,

②当四点在平面α内取二个点,在平面β内取两个点时,确定的平面个数有C42C52=60个,

③当四点在平面α内取一个点,在平面β内取三个点时,确定的平面个数有C41C53=40个,

故满足答案的四面体共有120个;

故答案:72,120

单项选择题
阅读理解

阅读理解。

     When a rather dirty, poorly dressed person kneels at your feet and puts out his hands to beg for a few

coins, do you hurry on, not knowing what to do, or do you feel sad and hurriedly hand over some money?

What should our attitude to beggars be? There can be no question that the world is full of terribly sad

stories. It must be terrible to have no idea where our next meal is going to come from. It seems cruel not

to give some money to beggars.

     Certainly, most of the world's great religions (宗教) order us to be open-hearted and share what we

have with those less fortunate than ourselves.But has the world changed? Maybe what was morally (道德

方面) right in the old days,when one knew exactly who in the village had suffered misfortune and needed

help,is no longer the best idea. Quite a few people will not give to beggars. Let us look at their arguments.

     First, some believe that many city beggars dress up on purpose to look pitiable and actually make a good

living from begging. Giving to beggars only encourages this sort of evil (恶行). Secondly, there is the worry

that the money you give will be spent on beer, wine or drugs.Thirdly,there is the opinion that there is no real

excuse for begging. One might be poor,but that is no reason for losing one's sense of pride and

self-dependence.

     Related to this is the opinion that the problem should be dealt with by the government rather than ordinary

people. Some people think beggars should go to the local government department and receive help.

     It is hard to come to any final conclusion; there are various cases and we must deal with them differently.

A few coins can save a life in some situations, and even if the money is wasted, that does not take away the

moral goodness of the giver.

1. What is mainly discussed in the passage?

A. Moral deeds of people.

B. Religious activities of the church.

C. Moral goodness of the giver.

D. Arguments on giving to beggars.

2. What can we infer from the sentence "But has the world changed?" in the second paragraph?

A. People no longer know who suffers misfortune in the village.

B. Some people will not do what was morally right in the past.

C. We don't meet with those who need help any more.

D. Now it is the government's duty to help the beggars.

3. Which of the following is NOT mentioned in the passage?

A. Some people dress up to pretend to be beggars.

B. Some beggars want money to help their children go to school.

C. Some beggars use the money to buy drugs.

D. Some beggars have no excuse for begging.

4. In the last paragraph,the writer thinks that it is hard to come to any final conclusion, because _____.

A. the cases can be so different

B. there are so many beggars

C. there is so much money wasted

D. there are so many different arguments