What Can or Cannot Mate vs. Lone King

In my New Year's Goals I set about studying the Endgame. So far I am still living up to my goals and have seen some improvement. Before I give the possiblities I would like to pass along the following story.

Not sure where I found this so I cannot give credit.

"Many years ago, I was directing a scholastic tourney of 8 yr olds..Now kids playing notoriously fast, but one board in particular was maelstrom of pieces so, curious, I walked over to observe..y the time I got there, one of the players had K+Q and his oppo had a bare K...Thinking to myself that it would not be long in ending, I went about my business..Some minutes later, I notice they were still playing and returned to watch...The fella with the Queen apparently had forgotten(or did not know) that he required his K in support to effect mate..I watched fascinated for quite a few moves until, finally, the fella with the Queen said to his oppo, "Guess it is a draw, huh?" The oppo nodded and off they went. chatting happily, to record their first tourney draw."

That said, here are the endings you should know.