Wow. I sure hope that you got better information than what's on this thread sometime yesterday before your exam. The correct answer is that both the monothelite and the monophysite positions are indeed heretical positions.
The reason being that if Christ had only a single will (monothelite), he would not have had a completely human nature of his own. The divine would have taken on a humanity devoid of its own will and ability to reason, and would therefore have been an incomplete human. It must be maintained that Christ's person had both a purely divine and a purely human will in his divine and human natures respectively, although the divine will is seen as the dominant will that works through the human will so as not to create a division between them (although, as can be seen in Gethsemane, there were occasions of temporarily differing desires). This positions was given formal assent at the sixth ecumenical council in Constantinople in AD681.
Similarly, the more extreme monophysite position denies that Christ could have had a human nature that was the same in its essence as our own, and therefore speak of a humanity that was transmuted by the divine, and therefore became a single human-divine nature (monophysite). Each nature must be seen as complete within itself, a fully divine and a fully human nature coming together in the person of Christ.
So, to recap, dyothelite/dyophysite=good; monothelite/monophysite=bad.
Hope that wasn't a major part of your exam
