Is there a general rule of thumb of how many times your core keyterm should be mentioned when optimizing for a page?

[odegi]

In short, how much is too little and how much is too many?

[iboxsecurityltd]

Nothing is set in stone as far as number of times a keyword should be used. Although from experience I find 5 or 6 is more than sufficient.

But Mike is certainly correct up front for title and H1 and that would get you off to a good start. Other areas to pay attention to would be making sure you don't have conflicting or too similar keywords in your text also.

Recently saw a paragraph with 15 keywords and probably the same amount of synonyms of that keyword bunched into a few lines.

[MikeRoberts]

Write for people, not for search engines. If it sounds unnatural then it is. There's no magic number for keyword density.

Most like to make sure their core term for the page is up front in the title, used in the H1, and used in the meta description. As far as in the content of the page itself, just make it sound good. Good content is better for you than potentially stuffing a keyword to hope to rank. Also, Google (likely) uses Latent Semantic Indexing or at least understands semantically related words... so you can mix it up a bit with related terms and synonyms without fear they won't understand.