1. MODAL VERBS to express certainty and possibility

2. To express certainty about the present
use must:
She’s been in over 15 films, so she MUST be very well known.
Note: we usually have a good reason for expressing this certainty, e.g.
She’s been in over 15 films.
use can’t or couldn’t for the negative (not mustn’t)
You can’t be tired. You’ve just got out of bed!
Mark couldn’t be coming to the party – he’s on holiday in America at the moment.

3. To express certainty about the past
use must have + past participle
You have a very big part in the play. It must have taken you ages to learn all the lines.
use can’t have and couldn’t have + past participle for the negative
She can’t have left her glasses at home – I saw her wearing them on the bus.
She couldn’t have stolen the money because she’s far too honest!

4. The following modal verbs do not change in reported speech: could, would, should, might, ought to and used to.
Would doesn’t change: ‘I would prefer to study in London.’ → She said that she would prefer to study in London.
Must usually changes to had to: ‘You must read this text for the next lesson.’ → My teacher told me I had to read the text for the following lesson.
Must does not change:
when it is negative: ‘You mustn’t tell Katya our secret.’ → Ana told Stefan he mustn’t tell Katya their secret.
when it expresses a deduction: ‘Arturo must still be asleep.’ → She said that Arturo must still be asleep.
  NOTE: If the reporting verb is in a present tense, no tense changes are necessary: ‘I’ll help you with your homework.’ → She says she’ll help me with my homework.

5. To express possibility about the present or future
use may, might or could
I may come and visit you next summer.
We might go to the cinema this evening if we finish all our work in time.
We’d better go out for a walk now because it could rain later.
use may not and might not (not mayn’t and mightn’t) for the negative (not can’t or couldn’t which express certainty)
Frankie is looking very pale. He may not be very well.
Don’t cook any dinner for me because I might not be back in time.

6. To express possibility about the past
use may have, could have, may not have, might not have + past participle
It is unlikely Sally to be late. She may have overslept, or she might not have remembered the appointment.