Could you clarify for what parts of the homework Mathematica usage is allowed (e.g. when should we use Mathematica or not)?
You can use Mathematica for all your homework. But you have to include all steps of your computations. For example, if you use Mathematica for checking the result of an integral, you still have to include all integration steps. For example, if you compute a triple integral, we need to see how you compute the most inner integral, then the middle integral and finally the outer integral. If you draw something with Mathematica, we need to see your code. Just printing out the notebook you created is ok. It is often much easier to plot it by hand. In general, you have to acknowledge all use of Mathematica and document, what you do.