So I bought this tapered full carbon fork for $60(used), and now I want to know if it is possible to use a carbon fork on either of these Aventon frames. I have read that you can use use certain types of bottom headsets, and people also say that only old bikes don't support tapered, so can someone point me in the right direction.

AVENTON MATARO FRAME 2016 (aventon main website)

or

AVENTON MATARO FRAME BLACK/WHITE (mrbikeshop website)

Your choices of forks and headsets is determined by the head tube diameter. There are adaptors which make it possible to use a fork made for a smaller headset with a frame made for larger, but the reverse isn't possible for the same reason that you can't put 10#s of potatoes in a bag made for 5.

Since the fork is tapered, you're limiting factor will be the diameter at the crown, because you can adapt the narrower upper bearing to the frame if necessary.

So, read the headset specs for the fork and frame, see if it's possible, and look for any adaptors you might need.

Is the fork the correct length?
Is the fork the correct offset?

Yeah, but more importantly...

Links to his desired frames aren't showing for me and I'm not interested enough to search - but as FBinNY hinted...does the frame he's interested in have a tapered head tube to fit his fork that he described as having a tapered steer tube?

If not - fork length & rake don't matter a bit...

A quick search reveals that his chosen frame has a 1-1/8" integrated headset. I'm going to guess that it is NOT compatible with his fork.

Buy first, research second is always the best way to do things.

No, you can't use a tapered fork on an Aventon Mataro.

You know the old saying "don't measure and make as many awkward cuts as needed and then scrap the project, hire a professional and realize how much money you wasted trying to do it yourself"

Or, maybe just buy a complete frameset (frame + fork) ?

This is what I love about BF.

A noob posts a question, and gets a few answers, then the Greek Chorus chimes in to let him know just how dumb he must be to get into his situation.

FWIW - as I read it, so far he only has the fork, so isn't out at all if he can score a frame to match, and knowing what to consider will get him there.

Building a bike around a used carbon fork that will only work on a tiny amount of track frames, FTW.

And there is no guarantee that the steer tube is long enough for his needs. :-/

The OP can always use the fork as a garden tool, just as I did with my Vilano fork. There are no bad decisions, just lack of creativity with solutions.