
meistern
to master
To successfully handle a difficult task, challenge, or situation, or to learn a skill perfectly.
Sie hat die schwierige Prüfung mit Bravour gemeistert.
She mastered the difficult exam with flying colors.
to master
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to master
To successfully handle a difficult task, challenge, or situation, or to learn a skill perfectly.
Sie hat die schwierige Prüfung mit Bravour gemeistert.
She mastered the difficult exam with flying colors.
The verb 'meistern' (to master) is derived directly from 'der Meister' (the master). So when you master a task, you become the 'Meister' (master) of that task—you have perfect command of it.
Er ist ein wahrer Meister seines Fachs.
He is a true master of his field.
'Meistern' (to master) always takes an accusative object. This object is the difficult thing that one overcomes.
Die Mannschaft hat die schwere Krise erfolgreich gemeistert.
The team successfully mastered the serious crisis.
'Meistern' (to master) is often used with abstract nouns for difficulties. Typical phrases are: 'eine Herausforderung meistern' (to master a challenge), 'eine Krise meistern' (to master a crisis), 'eine Aufgabe meistern' (to master a task), or 'sein Leben meistern' (to master one's life).
Es war nicht einfach, aber sie hat die Herausforderung gemeistert.
It wasn't easy, but she mastered the challenge.
to pass / consist / exist
For an exam, bestehen and meistern both indicate a successful outcome. Bestehen simply says that the requirements were met; meistern presents the performance as especially confident or impressive. So bestehen is appropriate for stating the bare result, while meistern is appropriate for a clearly assured success.

Nora hat die schwierige Prüfung ohne einen einzigen Fehler gemeistert.
Nora mastered the difficult exam without making a single mistake.
Nora hat die schwierige Prüfung knapp bestanden.
Nora narrowly passed the difficult exam.