[Grammar] Past of Modals

[atabitaraf]

I've copied this rule from my English Grammar Class note:

For making the past tense of the following modals we have a way in grammar.
would, could (possibility), must (conclusion), should, ought to, may, might, need (necessity)
For simple past: modal + have + p.p.
For past continuous: modal + have + been + ing form of the verb.

My question is, "Is this rule only for the mentioned modals or it's a general rule?"
I know some exceptions like could (p.t. of can that's about physical ability), or need (which is not always a modal), but I think the rule above works most of the time for the other modals, am I right?

Thanks,

 

[Barb_D]

Why don't you write a couple sentences you have doubts about and we'll look.

 

[atabitaraf]

With your help I just want to find a rule to teach. There is a question for me and some of my students that when the mentioned formula is used and for which modals. As I remember for example 'must' is used in some different uses: 1. strong possibility, 2. conclusion, 3. obligation, etc. (As you can see in the following examples.)
1. Ali must be at home.
2. I'm touching the window. It must be cold outside.
3. I must do this project till tomorrow.
If I want to interpret them for the past, how will they be?
1'. Ali must have been at home.
2'. It must have been cold outside.
3'. I must have done that project till the next day.

 

[Barb_D]

The "must" of obligation doesn't work in the past. It moves to "had" (or other words, like "was required to.")

1 and 2 are fine - the "must" is the must of a conclusion or strong possibility (I don't really see a difference between those two).
3 is the obligation. I had to work on the project till the next day.