My 13 year old son (who is not allowed to visit SDMB) says his geography teacher is seeking an answer to this question.
How tall does a hill have to be before it’s considered a mountain? Are there other criteria involved beside height?
ivylass, we’re really not supposed to do homework for others here. If someone asked directly they’d usually get jumped on. But that doesn’t mean we can’t help, it should be via guidance, as you would do as a parent, rather than just spout the answer.
First hint, have him look up the definitions of hill and mountain in the dictionary. He can go to www.m-w.com or www.dictionary.com for this if you don’t have a suitable resource at home.
1000 feet – see “The Englishman Who Went Up A Hill but Came Down a Mountain.” 
In Great Britain and Ireland a mountain must be at least 610m ( 2000 ft) high.
Oh, how tall must a hill be. I’ve always thought a hill became a mountain when it graduated from college, got married, lost its virginity, or something. So why isn’t your son allowed to visit? 
This site says that a “mountain” has a relative elevation of greater than 300m.
Or: When it’s filling out an employment application.
No, this isn’t a homework assignment. The geography teacher herself doesn’t know the answer. (Although, now that I think about it, perhaps she should be doing the homework.)
Short answer, there is no accepted universal definition.
Long answer, every locality has their own general guidelines by which a given rise is called a hill, mountain, butte, bluff, knob, bald, etc. Many places have no such general rules, and rely on history and imagination. Unless you are asking about a specific geographic region, I don’t think you’ll find an answer.