Grammar / B1+ Grammar lessons and exercises / Past modal verbs of deduction

We use modal verbs + have + past participle to talk about how certain we are that something was or was not true in the past. These are called past modal verbs of deduction or speculation.
We use must have + past participle when we are quite sure something happened in the past.
✅ I can’t find my wallet! I must have dropped it in the taxi.
✅ You must have had a real scare when you saw the crocodile.
We use can’t/couldn’t have + past participle when we are quite sure something did NOT happen in the past.
✅ You can’t/couldn’t have seen John last night. He was in hospital.
✅ She can’t/couldn’t have passed the test. She didn’t even open the books.
We use may/might/could have + past participle to say that something was possible in the past.
✅ It’s been three days. They might/may have finished painting the house by now.
✅ If they left at 9, they might/may have already arrived.
Could have can also express a missed opportunity (something someone was able to do but didn’t).
✅ You could have called me to say you weren’t coming. I waited for hours.
We use should have / ought to have + past participle to talk about something that was expected to happen in the past — often used to express criticism or regret.
✅ You should/ought to have already packed your things. We’re going to be late.
✅ He should/ought to have studied more. Nobody fails if they study.