A2: must, mustn´t, have to and don´t have to

In the affirmative have to / must both express the idea of obligation.

(It is necessary that you do something.)
However, must is only used in the present, and is never used after 'will' or 'may.'I must / have to get up early because I start work at 8 a.m.
I will must / have to leave work early if the snowstorm continues.
In the negative only the verb have to (do/does not have to) expresses the idea of obligation:
(It is not necessary that you do something.)You don't have to pay for children. They can come in for free.
In the negative must (must not / mustn't) is similar to an imperative: Do not do something:You mustn't smoke in the corridors. (= Don't smoke in the corridors.)

http://ww2.college-em.qc.ca/prof/epritchard/musthavt.htm

http://www.englishgrammarsecrets.com/musthaveto/exercise1.html

http://www.englishgrammarsecrets.com/musthaveto/exercise6.html

http://www.englishgrammarsecrets.com/musthaveto/exercise5.html