Have to vs. must

[aatish]

Test No. incompl/elem-7 "Modals", question 3

I ......... go now because I am already late for my class.

(a) must
(b) have
(c) have to

Test No. incompl/elem-7 "Modals", answer 3

I have to go now because I am already late for my class.

Correct answer: (c) have to

Your answer was: incorrect
I must go now because I am already late for my class.
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i think must go is the right option

[Alan]

I have to is not quite so strong as must and is better here because there is not any compulsion.
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English as a Second Language
You can read my ESL story Phrasal Verbs/take

[EscoDMV]

I disagree.

"Must" and "Have to" are very similar. There is a difference in American and British English on this topic. In American English we would NEVER say

"I must go now because I am already late for class"

In Am. English you would say:

"I have to go now because I am already late for class"

You can read more about this topic in Practical English Usage, written by Michael Swan for Oxford Press.