Unnecessary words?

No. "which was" is not necessary.

Not only is it not necessary it's in the passive voice.
And the sentence makes no sense with or without it. "interpreted by the student" "when it was first published"? There's no link there.

I said I was bad at thinking of sentences. But I kinda meant this question in terms of structure so I'm not sure why content matters that much? My teachers always tell me it's best to use fewer rather than more words. I just wanted to know if it's ever better to keep the which is/was/were/are in sentences even if they can be taken out. Though by your responses, i guess taking them out is generally preferable. Here's another sentence if it helps.

The house we bought, (which was) built in 1945, is in excellent condition.

My general rule of thumb, as a tech writer, is if it aids comprehension or removes ambiguity stick it in. But fewer words is almost always better.

Just on passive voice - don't use 'which was' use 'that was' - but in both your examples it seems redundant.

Speaking of removing ambiguity (and clarifying the point I was making). It appears the document was highly controversial when it was first published - whether the student interpreted it or not. The sentence just doesn't scan.

I thought which was is for non essential information and that was for essential. Why is that was better here? I also don't see how it's redudant. It's just extra information. It's not repeating the same idea more than once.

Forgive me - I write for the web (Read Steve Krug's 'Don't Make Me Think' to get a sense of where I'm coming from).

The redundancy I was referring to was in this:

Provides no more meaning than:
The house we bought, built in 1945, is in excellent condition.
Therefore (which was) is redundant.

Also, I fucked up calling which vs that 'passive' - it's actually non-restrictive vs restrictive (I blame the Stoneleigh Marlborough Sauvignon Blanc). Non-restrictives can be dropped.
http://www.quickanddirtytips.com/education/grammar/which-versus-that-0

Thank you.