Does using composite keys violate 2NF

You're on the right track. Look closely at your 2NF result - this is where the 3NF result will come from. Your next task would be to take the 2NF result and eliminate the fields that do not depend on the key.

There are numerous sources for how and why to do this, but I prefer Microsoft's explanation the best:

http://support.microsoft.com/kb/283878

From my answer on stack overflow: https://stackoverflow.com/a/29772759/2534472

Ok, let's have a look at your 2NF attempt:

Student

studentID | studentName | courseCode | modCode | resultCode

Course

courseCode | courseTitle

Module

modCode | modTitle | credits

Let's talk about Student first.

Your key cannot be studentID, because the resultCode depends on studentID and courseCode (you have one result for every course). But your studentName depends only on studentID, so a part of the key (studentID,courseCode). So 2NF is violated. You need to do something like this:

Student

studentID | studentName | courseCode | modCode

Course

courseCode | courseTitle

Module

modCode | modTitle | credits

Result

studentID | courseCode | resultCode

But please keep in mind, that this respects the 2NF, but still seems not correct, because modules and courses are now completely unrelated. So try this:

Student

studentID | studentName | modCode

Module

modCode | modTitle | credits

Course

courseCode | courseTitle | modCode

Result

studentID | courseCode | resultCode

A course belongs to a module (a module has many courses) - from my point of view. This is automatically in 2NF (because the key is always just one attribute (except for the result, but there is just one non-key-attribute always depending on both key attributes), so nothing can depend on a "part" of the key). And it is in 3NF, too, because every "physical" entity has it's logical representation in the data model (more a rule of thumb than a formalism).

Now let's have a look at your 3NF attempt. I think you've got the module<->course dependency the wrong way round, but let's just concentrate on the normalization.

Student

studentID | studentName | courseCode

Course

courseCode | courseTitle

Module

modCode | modTitle | credits | courseCode

Results

studentID | modCode | resultCode

This is correct 3NF, because there is simply no other key candidate than the key itself. So there can't be any transitive dependency.

To clarify this: a key candidate is one of the many minimal sets of possible keys. In your relation you have found at least one key candidate with one element (except for the results relation). So any other key candidate cannot have more than one element. That means, that you can simply look at every single attribute and decide "can this be a key or not?" And in your example you find, that no other attribute can be a key - so it's automatically in 2NF and 3NF.