The problems we have been doing from Chapter one are difficult because they involve proving results using strict logical arguments. There is no possibility that simple mathematical symbol manipulation can work. When evaluating a solution I am looking for an argument that begins with the given facts, uses sound logic based on physical and mathematical principles, and flows to the correct conclusion. It is indeed possible that a solution that receives a low score may contain some correct physics, but that is not enough unless it fits correctly into the argument.
For those of you who are unhappy with your scores, I do recommend that you obtain a solution from me and write the essay discussing it. It is this careful analysis of the solution and its differences from your own that will help you to see how to construct these kind of proofs. This skill is particularly important for those who would like to do theory, but it is valuable for everyone.