Warning: this is probably a dumb question. I was told by someone who took the jlpt2 last year that you do not need to know every kanji for every vocabulary word.
For example, let's suppose the word あさい appears on the n4 test. The kanji in 浅い（あさい） isn't on the list of kanji one needs to learn for the n4 so you do not need to know it. When looking at an n3 list from http://www.tanos.co.uk/jlpt/jlpt3 I noticed a substantial amount of words on the n3 vocabulary list does not use kanji from the n3 kanji list. Thanks for your help!

what's the question?

I guess my question is, how does vocabulary of which you do not need to know kanji appear on the test? Are the words written in hiragana?

it's a mixture of hiragana and kanji with furigana (the hiragana written above the kanji) depending on the level I think. you can see some sample test papers for the different levels here:

http://www.jlpt.jp/e/samples/forlearners.html

I have not taken the N3 or other newer "Nx" tests but on the older tests less common kanji compounds were given with furigana or if the hiragana/katakana is commonly used in place of the kanji just the hiragana/katakana was used.

This is really exactly the same as how less common kanji would be treated in other reading materials.

I took the N3 in July. The vocabulary that we weren't expected to know had furigana above it. There was quite a bit of it in the reading comprehension sections. Test-takers aren't expected to know those words, but they're supposed to be able to figure them out from context. This is MUCH easier if you're already familiar with the rough meanings of the kanji, whether from having kanji in your native language or from having studied RtK. Many of those words are uncommon or technical and are unlikely to have ever come up in prep material, so being given the pronunciation doesn't help because you don't know the word anyway.

I think the reading part must be pretty hellish for people who've studied only the level-appropriate kanji and no more, like to the extent that they'd be lucky to scrape up a passing mark for that section.

I passed N3 pretty easily with only knowing the N3 kanji, and my knowledge of that was kinda shakey...