I know that "have to" can mean "must" and that "must" can be used in the past, but in the below sentence I don't understand why "had to" is the correct answer.
When I was going to university, I _____ find a part time job to earn some pocket money, because my family was not rich.
- had to
- must
- should
In context of obligation/necessity (as in your sentence), must isn't usually used to talk about the past: instead, it's paraphrased with the past form of the periphrastic modal have to, which is had to.
It would be wrong to say that had to is the past form of must – since must doesn't have a true past form – but for all intents and purposes, you can think of it as such; i.e., whenever you wish to express the meaning of must when you're talking about obligation/necessity in the past, use had to (or have had to, which is blessed with the perfect aspect; e.g., He has had to visit the ER several times).
As the modal verb must cannot be conjugated as a "normal" verb can, other verbal forms need to be used in order for past or future actions to be verbalized.
Thus:
I must do my homework.
(Must is used for a present action)
I had to do my homework.
(Had to replaces must when referring to a past action)
I will have to do my homework.
(Will have to replaces must when referring to a future action)
So, in the context of your sentence, the verbal replacement that you need to use in lieu of must, according to the time frame in which the meaning of must takes place, is had to.
