I have a question in my textbook:
What was Franz expected to be prepared with for school that day?
Is "prepare with" a phrasal verb? Can I say : "I am preparing with mathematics tasks for school" ?
Please answer, sirs.
With in association with prepared in that way is creating an adverbial phrase. It can have a range of meanings. You might see on a menu:
Chicken prepared with soy sauce and ginger
This means that the chicken has been cooked (including the pre-cooking preparation) with those ingredients. In this, as in many cases, you wouldn't say it without the adverbial, so one might consider it a phrasal verb. As far as I'm aware, it's not generally considered as such.
Part of the trick here is that the order of adverbials can be confusing. In your example, the verb (the present progressive am preparing) has two adverbials - one of purpose, for school, and one that's an instrumental adjunct, with mathematics tasks. This is clearly an instrumental adjunct, as you are saying that you are using the tasks to prepare for school. Not all with clauses are instrumental adjuncts. They might me adverbials of manner, such as doing something with trepidation. They might be verb arguments, complements - though linguists actually vary in what examples of this they accept. One of the more common examples would be "I danced with Bob". To dance can be intransitive, and "I danced" is a perfectly valid sentence, but when you dance with someone they are (sometimes) an inherent part of that activity, and with Bob is therefore an optional argument of the verb. However, because your example is clearly two adverbials the order of them can matter.
A major reason that they matter is that those phrases could be things other than adverbials. For school could be an adjectival phrase. By putting it immediately after 'mathematics tasks', it invites the reader to see it as adjectivally modifying 'mathematics tasks' rather than 'preparing'. On the other hand, with mathematics tasks could be an adjectival, but would not be seen as potentially modifying 'school', so if you flip the adverbials around, the meaning is clear:
I am preparing for school with mathematics tasks.
That is a clear and correct, if slightly unnatural sentence. After all, what do you do with the mathematics tasks to prepare? Do you gather them up into a collection? Practice them? Complete them? The preposition by and a gerund would be more natural:
I am preparing for school by practising mathematics tasks.
I am preparing for school by collecting mathematics tasks.
The question you are trying to answer puts the adverbial elements in the other order, but there's no possibility of confusion there. On the other hand, I would actually prefer to order it like so:
What was Franz expected to be prepared for school that day with?
That emphasises that it is "school that day" that is prepared for, which highlights the possibility of different preparations for different days, and makes it more clear that the with is central to the question.
Which comes back to the menu example again. Sometimes, "prepared with" does begin to seem like a phrasal verb, and you see it that way on menus a lot. It is possible that some people see it more that way, and use it to more specifically mean physical objects at accompany a person. It is possible that the question setter meant what I would put as:
What was Franz expected to bring to school that day?
Without more context, it's impossible to be sure, but I've seen "prepared with" used in ways that support that specific meaning. If that was their intent, they did it in an ambiguous and confusing way.
In your example
I am preparing with mathematics tasks for school.
you mean you are preparing for school by way of using mathematics tasks.
It might better be expressed as
I am preparing for school by using mathematics tasks.
I am preparing for school by doing mathematics tasks.
I am preparing for school by practicing mathematics tasks.