modals auxiliary

AUXILIARY USES EXAMPLE
May 1.      Polite request (May i borrow your pencil please?)
2.      Formal permission (We may have to wait an hour for dinner in this restaurant.)
3.      Less than 50% certainty  (She may be sick)
Might 1.      Less than 50% certainty (She might be sick.)
2.      Polite request (rare) (It might rain today.)
Should 1.      Advisability (I should be happy right now)
2.      90% certainty (You should study harder.)
Ought to 1.      Advisability (You ought to carry a rain coat, it going to rain.)
2.      90% certainty (You ought to stop smoking)
Had better 1.   Advisability with threat of bad result (You had better take your umbrella with you today)
Be supposed to 1.    Expectation (She is supposed to be ill)
Be to 1.      Strong expectation (To be closed for three years.)
Must 1.      Strong necessity (She must have been sleeping)
2.      Prohibition (negative) (You must study harder. )
3.      95% certainty (Martha must not have been hungry.)
Have to 1.      Necessity   (We may have to wait an hour for dinner in this restaurant.)
2.      Lack of necessity (negative) (She doesn't have to read "Grapes of Wrath." It's optional reading for extra credit.)
Have got to 1.     (Necessity (I’ve got to get a handphone.)

Will 1.      100% certainty (I will pick you up tonight).
2.      Willingness (Maria will probably do well on the test.)
3.      Polite request (I will hold a birthday party)
Be going to 1.      100% certainty (I’m going to kill you)
2.      Definite plan (I’m going to marry you)
Can 1.      Ability/possibility (It can get very cold here in winter.)
2.      Informal permission (I can run fast.)
3.      Informal polite request (You can go to the mosque tonight).
4.      Impossibility (negative only) (He can not speak English very well.)
Could 1.      Past ability (It could be rain today.)
2.      Polite request (She could be sick.)
3.      Suggestion (I could run fast.)  
4.      Less than 50% certainty (She could have been playing)

5.      Impossibility (negative only) (could not have passed)
Be able to 1.      Ability (I will be able to drive)
Would 1.      Polite request (Would you wait for me, please?)
2.      Preference (Would you shut the door?)
3.      Repeated action in the past (I would like to be able to speak Chinese.)
Used to 1.   Repeated action in the past (There used to be a cinema in the town but now there isn'tShall)   1.      Polite question to make a suggestion (You shall open a door for a women.)
2.      Future with “I” or “We” as subject (I shall marry you)