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There are a number of apps, but I use OneNote. OneNote is amazing for a number of reasons, but it's just amazing with iPad Pro!
 
GoodNotes also allows this. It is my personal favorite. But I present my notes via AirPlay and it has extra tools and features for that. Notability has voice recording if you are interested in that...
 
I found writing poor on OneNote, much better in notability (Apple pencil)

Down side in notability is I can't search handwriting like in OneNote.

How does good note organise/file notes?
 
I use Evernote which does not have lined paper but rather dot grid, when not in edit mode the dots are not shown.

I'm happy with this as I switched to dotgrid paper notebooks a while ago, they took a bit of getting used to but are more flexible than lines and less intrusive than squared.
 
Goodnotes has superior handwriting compared to notability - and it allows handwritten notes to be searched, and allows the pencil to connect as a "smart stylus" - something notability doesn't.

You can also buy the goodnote app for a Mac, and have your notes automatically sync.
 
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