问题 填空题

方程xyz=2009的所有整数解有 ______组.

答案

这个2009可以看做是(整数)1×1×2009,1×7×287,7×7×41,1×49×41.

其中又有三个未知数一正两负和三正两种情况,

先说xyz在三正的情况下,有三个可能的解集,分别为1×1×2009,1×2009×1,2009×1×1,

在三未知数一正两负的情况下原本的 x、y、z就会出现3种可能;

如1×1×2009=1×(-1)×(-2009)=(-1)×(-1)×2009=(-1)×1×(-2009),

所以在一正两负的情况下原本的三个可能的解集就会衍生出9个可能的解集.

那么得出结论,1×1×2009这样的分组共有12个可能的解集,

在7×7×41时,也有类似的12个可能的解集.

但当1×7×287时,因为三个数值均不同,所以和上面两组不同,在三正的情况下有6个可能的解集,两正一负的情况下又有18个可能的解集.

同理1×49×41也有24个可能的解集.

综上所述,xyz=2009共有72组整数解.

阅读理解

Hi Hongbo,

I’m so glad to read about the changes talking place in your city. It’s really good news that you can travel by subway in Xi’an, though there’s only one line there. Here in London we have twelve lines. By the way, we don’t use the word “subway” here. It’s American English. We call it “the Underground”, instead.

The London Underground is very famous. It’s famous for several reasons. First of all, part of the underground railway today is the oldest in the world, which opened in 1863. Secondly, the London Underground is also the first line to have electric trains, in 1890. Thirdly but not the last, the London Underground is the second largest metro system in the world, after the Shanghai Metro. There are 270 stations in the Underground and it has 402 kilometres of tracks(轨道). What’s more, the city of London itself helps make the transportation system famous! I’ve got a few photos to help you build a clear picture of the Underground in my city. They are together with this mail.

In your email, you also said workers were building more lines. I’m sure your city is developing fast. Maybe you can send me a few photos of your city today. I really want to see the changes taking place there. I’m happy for you to live there in an ancient city with such a new look!

So much for now. I’ll write soon again. Best wishes!

小题1:Where is the writer from?

A.From London

B.From Shanghai

C.From Xi’an.

D.From New York小题2:The second paragraph mainly tells us        ?

A.when the first subway was opened in the world.

B.when the London Underground first used electric trains

C.why the London Underground is the oldest subway in the world.

D.why the London Underground is famous in the world小题3:In the email, the words “subway”, “underground”, and “metro” mean   .

A.three different things

B.two different things

C.almost the same thing

D.nothing like each other小题4:What does the writer want Hongbo to do?

A.To buy a good book about Xi’an for him.

B.To send him a few photos of Xi’an.

C.To post him some postcards of Xi’an.

D.To tell him more about Xi’an subway.

单项选择题 案例分析题