Per @Pheonix2105's answer, in some contexts there might be an implied to [do something to/with] after the word "left". But I don't see that as particularly relevant to the general case. For example...
1: Tom has 10 apples. He gives 3 to Dick. How many are left?
We neither know nor care whether Tom's 7 apples are "to eat", "to give to Harry", or whatever. All that matters is they're remaining (not given away, eaten, or otherwise removed from the original 10 apples).
In such contexts, left is simply an "adjectival" use of the past participle of the verb to leave...
2: Tom has 10 apples. Dick takes 3. How many does he leave?
Note that the last sentence there could just as well have been "How many does this leave?" - it's not really important whether we think of Dick as the "subject" who "leaves" (doesn't take) the leftover apples. If we use this, it's just a demonstrative pronoun meaning this action which has just been described.
If you're interested, see here for some interesting information about "Participle Adjectives" (such as "interested" and "interesting" as used earlier in this sentence).
Note that there are certain limitations on how adjectival left = remaining can be used...
3: Tom sold 3 of his 10 tickets. How many are left unsold? (either left or unsold could be omitted)
4: There are 7 left
5: There are 7 unsold
6: There are 7 tickets left
7: There are 7 tickets unsold
8: There are 7 unsold tickets
9: *There are 7 left tickets (idiomatically unacceptable)
...where #9 is "unacceptable" even though the basic construction is okay with alternatives which are "synonymous" in context (such as unsold, remaining). Because we're more used to adjectival left before a noun meaning "levo" (on the left, not the right side), we would normally express #9 as...
10: There are 7 leftover tickets (or left-over)
I guess this is an intensifier of sorts that intensifies or makes the adjective along with the noun it precedes sound stronger. When used like that, there absolutely must be an adjective to go along with it. This is actually along the lines of how we use adverbs like so in English. You can't really say this is so (in other contexts you can, but they're not applicable here). You say this is so hot.
As to why It was such an okay test. does not work, my thinking would be that some adjectives are naturally unintensifiable. Alright falls into that category as well. They lack comparative and superlative properties unlike most adjectives in English which do have them. We almost never say more okay or most okay or, God forbid, okayer or okayest. But I can imagine that under certain, though very rare, circumstances they might make sense when used in a whimsical kind of way to intentionally make ourselves sound funny.
In the case of You are such a good student., such is an adverb that is similar in meaning to very and intensifies the adjective good. So, what the whole thing really says is that you're not just a good student, you're more than that.
And that's probably how I would explain it.
Best Answer
"How" is unnecessary in that sentence; it feels awkward and doesn't really add anything. The reader is more likely to trip over the word.
We could also swap "like" with "as":
Although, using "like" would still be perfectly acceptable.