You'd get some points for that but also the comment: 'Could do better'. A lot.

Queens are not genetically identical to their workers, the statement was fully inaccurate. That gives you a clue for the rest of the answer but it is worth stating clearly your answer to the question rather than beating around that bush. You know why they're not but didn't clearly state it. Workers have a mum and a dad, the dad introduces new genetics not in the queen's own cells.

As a card-carrying geneticist (lapsed) I had to look up Hamilton's rule. It is about kin selection theory. It is OK to look after other folk's babies when you're related to them unless your own output of babies is affected. Workers have little chance to make their own (sometimes there may be an opportunity to make a drone) so they might as well help mum out by looking after hers. In many cases they're half sisters and in some cases (when dad was the same) they will be full sibs. Much has been speculated about whether or not workers can discriminate (and discriminate against) half-sibs versus full sibs.

To score points on the Mendel thing I would think that you'd also have to describe the behaviour of single genes such as Aa (queen) x A (drone) to Aa and AA (queens or workers) in a 1:1 ratio and how that might differ for a different patriline (A1, A2, A3, whatever).

To get all the points, read the question carefully. You were asked: 1) was the statement accurate?, 2) work in Mendel's laws to your answer, 3) work in Hamilton's Rule to your answer. You need to address all three.

I say all this with very little knowledge of the various bee examination systems other than I managed to pass the SBA's Basic a few years ago.