I needn't have worn / didn't have to wear a hat to the ceremony, but I did because I had just bought a new one.
BOTH
It was wrong of them to use the machine without asking for permission first. // They ... permission before using the machine. (ASK)
should have asked for
I told you this would happen. You should listen / have listened to me in the first place!
should have listened
I can't find Lucy anywhere. Do you think she could / must have gone home?
could have
I didn't see the cats fighting last night, but I sure could / was able to hear them!
could
Were you able to / Could you do some grocery shopping before you arrived home today?
Were you able to
I didn't have time to practise before the music performance. // I ... practise before the music performance. (WAS)
wasn't able to
A: 'Where is Emma?' B: 'She might be playing / might play outside.'
might be playing
A: 'Did you know the smallest whale is only 2cm?' B: 'That couldn't / can't be true!'
can't
My boss missed the meeting today. She can't have / mustn't have been told.
mustn't have
A: 'It's taking Billy a long time to get here...' B: 'I think he might have taken / might be taking the bus.'
BOTH
Sarah left work. I think she can be feeling / may be feeling a bit sick.
may be feeling
I overslept, but I could / was able to catch my flight on time!
was able to
When I was young, I was able to / could touch my toes easily.
could
