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).

单项选择题
阅读理解

三、阅读理解(40分)

Maps are our oldest literature(文献),older than books.People think a map was the first thing the human ever wrote to communicate each other.Perhaps one million years ago,with a stick in the mud of a lake bed,the earlier human drew some lines to stand for a lake,a river,a thick forest and some good hunting grounds beyond the forest.

It made so much sense that people took it for magic(魔术),they expressed the world in a picture.There was something so real about this new thing called "map" that it helped us believe we could get there.It not only strengthened belief that good hunting existed beyond the forest,but it strongly suggested that the future existed;it was a place we could go to and be there tomorrow.What a comfort.On maps all paths lead somewhere.

41.Which of the following statements is true?

A.Maps can't be used to communicate each other.

B.Maps have the same long history as books.

C.No matter how hard you study them,maps don't make any sense.

D.None of the above is true.

42.The earlier human used lines drawn in the mud to express_________.

A.the whole world                              B.real places

C.strong belief                                          D.great comfort

43.Now people regard some lines drawn by the earlier human as _________.

A.the beginning of maps           B.the chanting form of maps

C.real maps                      D.a part of maps

44.It can be concluded that _________.

A.maps are the most useful way of communicating each other

B.the first map showed somewhere far away

C.the first map showed somewhere very near

D.the first map showed all directions