Expressing lack of necessity : do not, have to Expressing prohibition: must not

(a) I finished all of my homework this afternoon. I don’t have to study tonight.
(b) Tomorrow is a holiday. Mary doesn’t have to go to class
Don’t/doesn’t have to expresses the idea that something is not necessary
(c) Children, you must not play with matches!
(d) We must not use that door. The sign says Private: Do Not Enter
Must not expresses prohibition (Do Not Do This)
(e) You mustn’t play with matches
Must + not=mustn’t. (Note: the first “t” is not pronounced)

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Expressing necessity: have to, have got to, must

(a) I have a very important test tomorrow. I (have to/have got to/must) study tonight
Have to, have got to, and must have basically the same meaning. They express the idea that something is necessary.
(b) I’d like to go with you to the movie this evening, but I can’t. I have to go to a meeting.
(c) Bye now! I’ve get to go. My wife’s waiting for me. I’ll call you later.
(d) All passengers must present their passport at customs upon arrival.
Have to is used much more frequently in everyday speech and writing then must.
Have got to is typically used in informal conversation, as in (c).
Must is typically found in written instructions, as in (d). It is usually a strong, serious, “no nonsense” word.
(e) Do we have to bring pencils to the test?
(f) Why did he have to leave so early?
Questions: Have to is usually used in question, not must or have got to. Forms of do are used with have to in questions.
(g) I had to study last night
The Past form of have to, have got to, and must (meaning necessity) is had to
(h) I have to (“hafta”) go to downtown today
(i) Rita has to (“hasta”) go to the bank
(j) I’ve got to (“gotta”) study tonight

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Expressing advice : had better

(a) My clothes are dirty. I (should/ought to/had better) wash them
(b) You’re driving too past! You’d better slow down.
Had better has the same basic meaning as should and ought to:”This is a good idea. This is good advice.”
Had better usually implies a warning about possible bad and consequences. In (b): If you don’t slow down, there could be a bad result. You could get a speeding ticket or have an accident.
(c) You’d better not eat that meat. It looks spoiled.
Negative: had better not
(d) I’d better send my boss an e-mail right now.
In speaking, had is usually contracted:’d

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Expressing advice : Should and ought to

(a) My clothes are dirty I (should/ought to) wash them
(b) Incorrect: I should to wash them
(c) Incorrect: I ought washing them
Should and ought to have the same meaning. They mean: “This is good idea. This is good advice.”
Forms:
Should + simple form of a verb (no to)
Ought + to + simple form of a verb
(d) You need your sleep. You should not (shouldn't) stay up late.

Polite question, would you, could you, will you, can you

(a) Would you please open the door? Yes
(b) Could you please open the door? Yes. Of course
(c) Will you please open the door? Certainly. I'd be happy to
(d) Can you please open the door? Of course. I’d be glad to.
Sure. (Informal)
Okay. (Informal)
Uh-huh. (Meaning “yes”)
I’m sorry. I’d like to help, but my hands are full.
People use would you, could you, will you, and can you to ask polite questions. The questions ask for someone’s help or cooperation. (a), (b), (c) and (d) have basically the same meaning. The use of can, as in (d), is less formal than the others.
Note: may is not used when you is the subject of a polite question.
Incorrect: may you please open the door?

POLITE QUESTIONS: MAY I, COULD I, CAN I

(a) May I please borrow your pen? yes
(b) Could I please borrow your pen? yes. of course
(c) Can I please borrow your pen? yes certainly.
Sure (informal)
Okay. (informal)
Uh-Huh. (meaning yes)
I'm sorry, but I need to use it myself.
People use may I, could I, and can I to ask polite questions. The questions ask for someone's permission or agreement. (a), (b), and (c) have basically the same meaning.
Note: can I is less formal than may I and could I.
Please can come at the end of the question: may I borrow your pen, please?
Please can be omitted from the question: may I borrow your pen?

Using could to express possibility

(a): Why isn't Greg in class?
B: I don't know. He could be sick.
(b) Look at those dark clouds. It could start raining any minute.
Could can mean past ability. But that is not its only meaning. another meaning of could is possibility.
In (a): "He could be sick" has the same meaning as "He may/might be sick," i.e," it is possible that he is sick."
In (a): could expresses a present possibility
In (b): could expresses a future possibility.

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