The document discusses the uses of the modal auxiliary verbs "have", "could", "might", "may", "must", "need", "should", and "ought to" in the past tense. It explains that they are used to: 1) Refer to past events or hypothetical past situations. 2) Express deductions, possibilities, impossibilities, or uncertainties about past events. 3) Indicate that an action was not actually performed due to external reasons or unfulfilled conditions.

2.  To refer to the PAST.
 To refer to Unreal Situations.
 To show that the activity was different from
what we wanted.
 To say how confident we are that
something has happened.

3. Subject + modal + have + Past participle
•I gone
•We should
can played
•They have
might visited
•The students won
•My son ought to
paid

4.  It expresses deduction, a logical conclusion,
probability:
 It’s very cold; it must have snowed in the mountains.
 I saw him leaving. He must have finished the test.

5.  It expresses past reference about something
that was not carried out.
 She could have called the doctor early in the
morning.
 They could have danced in the party.

6.  It expresses negative deduction, impossibility
or disbelief:
 She can’t have passed the exam. It was too
difficult.
 The boy couldn’t have given a better answer
than this one.
 Bryan can’t have missed the bus.

7.  It expresses the possibility that an action took place
in the past (past possibility).
 The little boy may have lost the key.
 The little boy might have lost the key.
 Our neighbours may have heard some noises when our
car was stolen.
 Our neighbours might have heard some noises when
our car was stolen.
With “may”, action is more probable than with might.

8.  The action was not performed because of
external reasons.
 I would have played football but I had a strong pain
in my leg.
 Past Unreal Conditional.
 I would have gone to Paris if I had had the money
for the plane ticket.

9.  It expresses an unnecessary action, which was
performed.
 I needn’t have knocked at the door in this way. I awoke
the baby.
 You needn’t have bought the flowers for me.
In contrast, “didn’t need to” shows that the
action was not necessary but it wasn’t
performed either.
I didn’t need to knock at the door because it was
open (so I didn’t knock)

10.  It expresses that a past duty or obligation was not
carried out.
 You should have locked the door before leaving the
house (but you didn’t lock it).
 Paul ought to have waited until the lights were green
before he crossed the street (but he didn’t wait).