I am teaching Intermediate Level English to exam students in Spain and I have been asked when is it correct to use contractions. I am of the understanding that, in an oral or written exam, it would be more appropriate to use the full form. However, my query is, would it be incorrect to use a contraction? Would they lose points?
There are patterns, but not rules.
Contractions are extremely common and accepted in most speech, both social and business. However, in very formal speech (presentations to organizations, public speeches), they are often avoided.
Contractions are much less common in written English. In formal writing, scientific, business, educational, and most journalistic settings, full form is used. But in personal communications, and even some business communications to a small or close group, they may be wholly acceptable.
As others have said, some contractions are more acceptable than others. Isn't is commonly used where won't or can't wouldn't be acceptable (Oh, I just used a contraction in written form). Forms like would've are much less common in writing.
In written form, it is almost never wrong to use the full form. At most it will sound a bit stiff. If you or your students are unsure, write it out.
(All of the above is from a US perspective.)
I was taught that contractions are discouraged in writing, as Mitch noted, because you should not write in the same way as you would speak as it is too informal. However, as John pointed out, some contractions would be more appropriate to use in writing than others.
Unfortunately, there may not be clear distinctions between which ones are acceptable and which ones are not; this is something that can be recognized more with experience. As an attempt to offer an example (although some other readers may disagree with my opinions), I would typically write out "are not" and "do not" as I think "aren't" and "don't" sound too informal in writing, but I would probably use "won't" instead of "will not" as it seems to have a different connotation to me.