The past tense of 'must'

How to you express the meaning of ‘must’ in the past tense. Well, it is ‘had to;.

Look at the following sentences.

Sentence 1: [Present Tense]

I must wake up early in order not to miss the train.

Sentence 2: [Past Tense]

Yesterday I had to wake up early in order not to miss the train.

Actually, ‘have to’ can be used to replace ‘must’ in the present tense. Hence, instead of saying “You must hurry as they are waiting for you right now.”, we can express it as “You have to hurry as they are waiting for you right now.”