IELTS Grammar: interesting 'article' question

 A student noticed something interesting in my video lesson about "discussion essays". In the lesson I wrote the following two phrases:

1. their determination will help them in competitive situations
2. more useful than a competitive determination to win

The student asked why I used the article "a" in the second phrase. Isn't "determination" an uncountable noun? The answer is, not always.

Sometimes we use "determination" as a countable noun. In the second sentence above, I'm writing about one specific type of determination: the determination to win. In this case it's correct to write "a determination".

Note:
People often ask me to make a lesson that explains how to use articles. The problem is that article use doesn't follow a set of simple 'rules'. I think it's best to learn gradually by reading lots of English and by noticing things like the example above.