Translation:These are all the formulas that you need for the test.
Can provet also mean for the (eg mathematical) proof instead of test in this case
how can "det här" be translated to "these"? shouldn't it be "de här" in the sentence?
We usually say it that way in Swedish, but in English they want the plural form. This has been quite a problem for us course-builders. For instance, in Swedish you say "Det här är mina skor", but in English they don't say "This is my shoes", and if we translate it into "These are my shoes", that doesn't work perfectly either.
In Swedish, we think like this: I am pointing to "something", therefore I think of it as "det här". It works like a formal subject, but with "här" added to make the meaning the same as with "this". In English, they don't do that. Hope this helps?
Yes, although I might be slightly more inclined to only use that in informal context.