Modal verbs for deduction in the past: Must/m ustn’t is used from the speaker's point of view to express a strong likelihood in the past m u st/m ustn't + have + past participle
OR
m ust/m ustn't + have + been + past participle
The prim e m in iste r m u stn 't have kept his promise about increasing alternative energy form s,
as I've seen nothing in the news about it. (I thinkit was likely he didn’t keep his promise)
Note: M ustn'tcan be replaced by couldn’tfo r the same meaning.
Might/may/could is used to express possibility in the past m ight/m ay/could + have + past participle (Also m ight/m ay/could + have + been+ verb(-/7ig))
A curb on the use of fossil fuels m ight have curtailed the pollution problem , (it was possible)
Note: Modal verbs of deduction [m ust/could/m ight/m ay +be) can also be used in the present, but it
is unlikely that you w ill see this in an IELTS exam.
Modal verbs for past ability: Could is used:
1 To express ability I could swim 100 metres, but I can’t now.
2 To say that something was allowed People could travel w ithout a passport 200 years ago. (it was allowed)
Could not (couldn't)is used:
1 To express inability I couldn’t com plete my essay on global w arm ing.
2 To say that something was not allowed He couldn't go into the monkey enclosure, (it was not allowed)
Grammar for IELTS
Had to is used to express a strong objective obligation in the past Unit 13 People had to travel to A ustralia on a ship before a ir tra ve l was invented, (it was necessary)