What is important about Holden's exam paper?
The exam is about ancient Egyptians, and they are a symbol of people stuck in the past, just like Holden.
Throughout the novel, Holden is obsessed with things stuck: the ducks in Central Park, the fish in Central Park, the waxworks in the museum, Jane's kings in the back row, his dead brother Allie. First, though, are the Egyptians. All of these are to reinforce that Holden is a conservative who doesn't want to grow up and enter the phony adult world. They also suggest that Holden never got over his brother's death. Since then, he has been living in denial and suffering from survivor's guilt. For Holden, Allie will be forever dead, always the same age, and he wants to be stuck with him--just like the Egyptians are forever stuck in history.
The only way dead people are brought back to life is by writing, as Holden does in the composition for Spencer, and as he is doing in the Catcher in the Rye itself.