Usually one says "jusqu'à ..." (until) or "à partir de ..." (starting from). I think "jusqu'à partir de la troisième" might be grammatically correct in theory, meaning "until one leaves la troisième" but a native speaker would never say that as it is ambiguous.
If you mean "until leaving", I'd say (with increasing preference) jusqu'à la fin de la troisième, jusqu'au collège, jusqu'en troisième, jusqu'à la fin du collège.
While I'm at it, a few corrections: on peut entre should probably be on peut choisir entre, and obligatoire étudier should be obligatoire d'étudier. Again by the way, in current French collège one has Technologie as a mandatory class, and in the lycée one can choose between sciences économiques and several other subjects, but not Technologie which does not exist in the lycée général, so your last sentence is not correct with regard to current conditions in France.
Source: I am not quite a native speaker but I do have one kid in lycée and another in collège.