No...Ratio and Proportion =
Larger driving pulley makes smaller driven pulley turn faster...
Let's say you have an 8" pulley driving a 4" one..that is a 2:1 ratio..
The smaller 4" driven pulley,makes two revolutions for every one the larger 8" driver makes..
Now if the small pulley were driving the larger one,then a larger driven pulley will slow it down..