nauczyłaś

In a sentence

• Nauczyłaś się szybko korzystać z tego programu.

  You learned quickly how to use this program.

  The word "nauczyłaś" here means "you learned" and is used in second person singular feminine past tense, indicating the subject is female and the learning process is completed.

• Czy nauczyłaś ich, jak rozwiązywać takie problemy?

  Did you teach them how to solve such problems?

  In this sentence, "nauczyłaś" means "you taught" referring to teaching someone something. It's addressing the listener in a formal manner and denotes a completed action.

• Co nauczyłaś się na wczorajszym wykładzie?

  What did you learn at yesterday's lecture?

  Here "nauczyłaś" is used to inquire what the addressed person (a female) gained knowledge about during a particular event in the past.