Keep the preposition
The construction determines the preposition: denken an gives daran, while warten auf gives darauf. Replacing the noun does not remove this relationship.
Nora denkt an das Wochenende. Sie denkt daran.
Nora is thinking about the weekend. She is thinking about it.
A linking r makes vowel combinations easier to recognise
Combine da or wo with an and auf using an intervening r. With consonant-initial mit, join directly: damit, womit. These are single words.
Womit öffnest du die Dose?
What are you opening the tin with?
Wo- does not always ask where
The complete compound asks about the prepositional phrase. A question with worauf can ask about an awaited event, rather than a location.
Worauf freut sich Nora? — Auf das Konzert.
What is Nora looking forward to? — The concert.
A person keeps a person form
For ordinary references to named people, retain the preposition and use the appropriate personal pronoun. Grammatical gender alone does not decide the construction.
Nora denkt an ihren Bruder. Sie denkt an ihn.
Nora is thinking about her brother. She is thinking about him.
Damit has two different jobs
As a compound, damit refers to a thing used or involved. As a conjunction, it introduces a purpose clause meaning “so that”. Look at the sentence structure to tell the jobs apart.
Hier ist der Schlüssel. Damit öffne ich die Tür.
Here is the key. I open the door with it.
Practise this pattern
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References
Original teaching prose and examples, informed by these grammar references. A2 placement is an editorial curriculum choice, not a CEFR certification.