Ter- never changes shape, which makes it easy to spot and confusing to interpret, because it does three different jobs.
One: by accident
Something happened without anyone intending it.
Saya terjatuh. ‘I fell over.’
Kunci saya tertinggal di rumah. ‘I left my keys at home.’
Terbawa. ‘Taken by mistake.’
Compare with the deliberate versions: menjatuhkan is to drop something on purpose, meninggalkan is to leave something deliberately. The ter- form removes the intention, and that is often exactly what you want when explaining yourself.
Two: a finished state
The action is over and the result is what you see.
Pintunya terbuka. ‘The door is open.’
Sudah tertulis. ‘It is already written.’
This shades into the di- passive and the two overlap. The rough difference: dibuka points at someone having opened it, terbuka points at its current state.
Three: the most
Attached to an adjective, ter- is the superlative you met in A1 alongside paling.
terbesar ‘biggest’
terbaik ‘best’
termurah ‘cheapest’
This use belongs to writing and signage. In speech, paling wins.
Telling them apart
Look at what follows the prefix. A verb root gives you accident or state. An adjective gives you the superlative. There is no ambiguity in practice, only on paper.
The trap
Terlalu ‘too much’ is not a ter- form. Neither is terima ‘to receive’, as in terima kasih. Strip the prefix and you get lalu and ima, neither of which gives the right meaning.
Same test as with ber-: if removing the prefix leaves nonsense or an unrelated word, the prefix was never there.
What you’ll actually hear
Ter- survives in speech far better than me- does, especially for accidents, because there is no other short way to say it was not on purpose.
Maaf, terlambat. ‘Sorry, I’m late.’
Ketinggalan. ‘Left behind.’ A casual variant you will hear instead of tertinggal.