Answer:
1. You do not have to drive me to the airport.
2. I'm looking forward to spending the weekend on my grandpa's farm.
3. She may be having a bath now.
4. If you had listened to me, you wouldn't have gotten into trouble.
5. Take a compass with you in case you get lost.
6. They must have reached an agreement.
7. Can you take care of the baby while I'm at the supermarket?
8. My parents want me to study abroad.
9. She went to the competition, but didn't win.
10. I don't mind lending you my earrings.
Explanation:
This type of question does not have a single explanation. It will vary according to what each sentence requires. What is most important is to know synonyms or similar expressions, as well as understanding some grammar rules.
For instance, "take care" and "look after" are synonyms. The same goes for "can't wait" and "look forward to", in certain contexts. When you say you don't mind doing something, it means it is ok for you to do it.
It is important to know how to use the modal verbs - can, may,might, and must - especially in the past, when they are accompanied by "have" and a participle.