Hi, so one of my players is playing a mark of detection half-elf bard. She has an expanded spell list of course and her daily uses of her mark spells but are those spells also added to her known list? i.e. can she expend a spell slot to cast detect magic or does she have to learn it separately to use a slot on it?

https://www.dndbeyond.com/forums/dungeons-dragons-discussion/rules-game-mechanics/17215-racial-spells

Also:

Magical Detection

You can cast the detect magic and detect poison and disease spells with this trait. Starting at 3rd level, you can also cast the see invisibility spell with it. Once you cast any of these spells with this trait, you can’t cast that spell with it again until you finish a long rest. Intelligence is your spellcasting ability for these spells, and you don’t require material components for them.

She would have to learn the spell to be able to use spell slots for it.

If it had been worded that you had “learned” those spells you would not have to learn them again. But it only says you can cast them.