问题 填空题

给出以下四个命题:

(1)对于任意的a>0,b>0,则有algb=blga成立;

(2)直线y=x•tanα+b的倾斜角等于α;

(3)在空间如果两条直线与同一条直线垂直,那么这两条直线平行;

(4)在平面将单位向量的起点移到同一个点,终点的轨迹是一个半径为1的圆.

其中真命题的序号是______.

答案

(1)中,∵a>0,b>0,若algb=blga,则lgalgb=lgblga,即lgb•lga=lga•lgb成立,∴命题正确;

(2)中,直线y=x•tanα+b的斜率是k=tanα,当α∈[0,π)且α≠

π
2
时,倾斜角等于α,否则,命题不成立;

(3)中,在空间如果两条直线与同一条直线垂直,那么这两条直线不一定平行,也可能异面或相交,∴命题不成立;

(4)中,∵单位向量的模长是1,∴在平面内将单位向量的起点移到同一个点,终点的轨迹是一个半径为1的圆,命题正确;

∴正确的命题有(1)(4);

故答案为:(1)(4).

完形填空
完形填空
     The books in David's schoolbag felt like bricks as he ran down the street. What he wanted to do was
to play basketball with Eric,   1  his mother told him he would have to return his sister's books to the
library first.
      He had   2   set foot in a library and he wasn't about to do so today. He would just   3  the books in
the outside return box. But there was a   4  : it was locked.
     He went into the building, only a few minutes   5  closing time. He put the books into the return box.
And after a brief   6  in the toilet, he would be on his way to the playground to    7  Eric.
     David stepped out of the toilet and stopped in   8  - the library lights were off. The place was   9  .
The doors had been shut. They   10  be opened from the inside, he was trapped(被困) - in a library!
     He tried to   11  a telephone call, but was unable to  12 . What's more, the pay phones were on the
outside of the building.  13 the sun began to set, he searched for a light and found it.
 14  he could see. David wrote on a piece of paper: "  15  ! I'm TRAPPED inside!" and stuck it to the
glass door.  16 , someone passing by would see it.
      He was surprised to discover that this place was not so unpleasant  17  . Rows and rows of shelves
held books, videos and music. He saw a book about Michael Jordan and took it off the shelf. He settled
into a chair and started to   18  .
     He knew he had to   19  , but now, that didn't seem to be such a  20  thing.
( )1. A. but        
( )2. A. ever        
( )3. A. pass        
( )4. A. problem    
( )5. A. during      
( )6. A. rest        
( )7. A. visit      
( )8. A. delight    
( )9. A. lonely      
( )10. A. wouldn't  
( )11. A. make      
( )12. A. get on    
( )13. A. If        
( )14. A. On time    
( )15. A. Come      
( )16. A. Surely    
( )17. A. at most    
( )18. A. watch      
( )19. A. wait      
( )20. A. bad        
B. because        
B. nearly          
B. drop            
B. mistake        
B. after          
B. break          
B. meet            
B. anger          
B. empty          
B. shouldn't    
B. fix            
B. get up          
B. As              
B. Now and then    
B. Help            
B. Thankfully      
B. after all      
B. play            
B. stand          
B. cool            
                  
C. or          
C. never        
C. carry        
C. case        
C. over        
C. walk        
C. catch        
C. surprise    
C. noisy       
C. couldn't
C. use          
C. get through  
C. Though      
C. By the way  
C. Hello        
C. Truly        
C. in short    
C. read        
C. sleep        
C. strange      
D. since        
D. often        
D. take        
D. question    
D. before      
D. stop        
D. greet        
D. eagerness    
D. crowded      
D. needn't
D. pick        
D. get in      
D. Until        
D. At last      
D. Sorry        
D. Gradually    
D. as usual    
D. write        
D. work        
D. nice        
判断题