问题 解答题

一条直线将平面分成2个部分,2条直线最多将平面分成4个部分,3条直线最多将平面分成7个部分,则6条直线最多将平面分成______个部分.

答案

由图可知,

(1)有一条直线时,最多分成2部分;

(2)有两条直线时,最多分成2+2=4部分;

(3)有三条直线时,最多分成1+1+2+3=7部分;

(4)设直线条数有n条,分成的平面最多有m个.有以下规律:

m=1+1+…+(n-1)+n=

n(n+1)
2
+1.

∴画6条直线最多可将平面分成

6×7
2
+1=22.

故答案为:22.

单项选择题
完形填空

阅读下面短文, 从短文后面各题的A、B、C、D四个选项中, 选出适合填入对应空白处的最佳选项, 并在答题卡上将该选项涂黑。

One afternoon, my son Adam asked me, “Are all people the same even if they are different in color?”

I thought for a minute, and then I said, “I’ll explain, 21 you can just wait until we make a quick 22 at the grocery store. I have something 23 to show you. ”

At grocery store, we 24 some apples --- red, green and yellow ones. Back home, I told Adam, “It’s time to 25 your question.” I put one apple of each 26 on the table. Then I looked at Adam, who had a 27 look on his face. 

“People are like apples. They come in all 28 colors, shapes and sizes. On the 29,  some of the apples may not 30 look as the others. ” As I was talking, Adam was 31 each one carefully. 

Then, I took each of the apples and peeled(削皮)them, 32 them back on the table, but 33 a different place. 

“Okay, Adam, tell me which is which.”

He said, “I 34 tell. They all look same now. ” “Take a bite of 35. See if that helps you 36 which one is which. ”

He took 37,  and then a huge smile came cross his face. . ”People are 38 like apples! They are all different, but once you 39 the outside, they’re pretty much the same on the inside. ”

He totally 40 it. I didn’t need to say or do anything else. 

21. A. although        B. so              C. because        D. if        

22. A. stop            B. start           C. turn           D. stay        

23. A. expressive      B. encouraging     C. informative    D. interesting     

24. A. bought          B. counted         C. saw            D. collected      

25. A. check           B. mention         C. answer         D. improve       

26. A. size            B. type            C. shape          D. class        

27. A. worried         B. satisfied       C. proud          D. curious       

28. A. ordinary        B. normal          C. different      D. regular       

29. A. outside         B. whole           C. table          D. inside        

30. A. still           B. even            C. only           D. ever        

31. A. examining       B. measuring       C. drawing        D. packing       

32. A. keeping         B. placing         C. pulling        D. giving        

33. A. on              B. toward          C. for            D. in         

34. A. mustn’t        B. can’t          C. shouldn’t     D. needn’t       

35. A. each one        B. each other      C. the other      D. one another    

36. A. admit           B. consider        C. decide         D. believe

37. A. big bites       B. deep breaths    C. a firm hold    D. close look 

38. A. just            B. always          C. merely         D. seldom

39. A. put away        B. get down        C. hand out       D. take off 

40. A. made            B. took           C. got           D. did