问题 解答题
已知x=
3
+
2
y=
3
-
2
,求下列各式的值.
(1)x2-y2
(2)x2+y2
答案

(1)∵x=

3
+
2
,y=
3
-
2

∴x2-y2=(x+y)(x-y)=2

3
×2
2
)=4
6

(2)∵x=

3
+
2
,y=
3
-
2

∴x+y=2

3
,xy=1,

则x2+y2=(x+y)2-2xy=12-2=10.

阅读理解

When Babbage was working at Cambridge, a new idea occurred to him. He wanted to construct a calculating machine to work out the solutions(解法)to maths problems not only with correctness but also with a speed beyond the power of any human mind. His machine could solve problems involving(涉及)long rows of figures in one continuous operation(运算).

In 1822 Babbage exhibited his invention and won a prize from the government. After that, he immediately started to work on a larger machine designed to solve more difficult problems. Although he received some money left by his father, the money was not enough to support his design. He wrote to the government about his plan and was given £2500 to start with, a sum worth much more in those days than it is now.

Babbage continued his work in London for four years. Then his health broke down, and he had to take a long holiday abroad. When he returned to London in 1828, he was at the end of his resources. Many bills remained unpaid. His chief assistant and co-workers quarreled with him and left with many expensive tools. For one year no work was done. During this period, Babbage, whose mind was always active, suddenly thought of a completely new idea for the machine. He rushed to meet the government officials to explain his new idea. But this time, they were unwilling to help him. For eight years, they refused to say whether they wanted the machine or not, and their final answer was “No.”

From 1828 to 1839, Babbage held the position of professor at Cambridge very successfully. But his greatest work was the unfinished calculating machine which stood covered in dust in his house. It was the beginning of the modern computer.

60.The machine Babbage designed would solve difficult maths problems _________.

A.in one operation with few mistakes

B.in more than one operation without any mistakes

C.in more than one operation with slight mistakes

D.in one operation without any mistakes

61.Babbage failed to continue his research work in 1828 mainly because _______.

A.he was in poor health                B.he almost ran out of money

C.his co-workers argued with him         D.he spent all his money on his bills

62.Babage explained his new idea to the government officials, expecting that _________.

A.they would agree to his plan             B.they would pay for his new idea

C.they would support him with money    D.they would exhibit his new design

63.From the passage, we can infer that __________.

A.Babbage failed to be a famous scientist at Cambridge

B.Babbage always had new ideas but gave them up easily

C.Babbage always needed support from the government officials

D.Babbage was the first designer of the modern computer

阅读理解

Technology has totally transformed our ability to communicate with each other. Linking to each other both literally and figuratively, many of us connect through cell phones, email, instant messaging, blogs, and networking web sites, yet we may be less connected to each other than we think.

According to a study, Americans are becoming increasingly socially isolated(孤立的). The study suggests, for example, that one quarter of Americans say that they have no one to discuss important personal issues with, and that the number of close friends that Americans have has dropped from three to two. Meanwhile, the Boston Globe reports that this spreading isolation is experienced more sharply among those with less education, people of color, and older Americans. Unsurprisingly, those who are young, white, and well educated tend to have stronger social networks.

From my own experience I have to say that I’ve never felt more connected, thanks to a web of friends, family, and colleagues. One of my closest friends is someone I met through an online discussion group who lives hundreds of miles away from me. We have met face-to-face only twice, yet our regular electronic correspondence and cell phone calls maintain our close friendship. And, speaking of blogging, my blog has introduced me to people I would never have met otherwise and has led to enduring and important friendships.

On the other hand, I recently saw a scene unfold that proved to me how deeply disconnected we as Americans have become. I had just wrapped up a presentation on mediation at a family therapy (治疗) center.

As I was leaving, I noticed a mother and her teenage son who had just completed their session with their family therapist. After making their next appointment, they both took out their cell phones, placed calls, and began loud conversations with whoever was on the other end. I walked out behind them to the parking lot to my car. They both jumped into their cars, and, as I saw them drive off, they were still talking on their cell phones but not to each other.

小题1:What does the passage lead you to believe?

A.Americans are more socially isolated today.

B.Americans are more socially connected today.

C.Americans don’t make good use of technology.

D.Technology plays a bigger role in American society.小题2:Which of the following has nothing to do with the isolation among Americans?

A.Sex.

B.Education.

C.Skin color.

D.Age.小题3:What is true about the mother and son in the passage?

A.They came for therapy in the same car.

B.They were quite close to each other.

C.There was not much communication between them.

D.They preferred talking to each other on cell phones.小题4:What can we learn from the passage?

A.The writer is totally against the modern technology.

B.The mother and the son have finished their family therapist and get a better relationship.

C.As far as the writer is concerned, he has benefited a lot from the modern technology.

D.Those black and well-educated people have stronger social network than aged white people.