There are an almost limitless amount of Hamlet passages, but a few that I'd personally pick (choose all of the major lines, and some of the minor ones directly surrounding what I've outlined to mimic the exam):
#1:
Hamlet's solilquy "O that this too too solid flesh would melt", act 1 scene 2
Closet scene, act 3 scene 4 (pick any part of it)
Death of Hamlet, act 5 scene 2 (pick any part of it)
#2:
The ghost, act 1 scene 5 (pick any part of it)
"What a piece of work is a man!", act 2 scene 2
"Alas poor Yorrick", act 5 scene 1
#3
The very opening "Who's there?", act 1 scene 1
Hamlet's soliloquy "O what a rogue and peasant slave am I!", act 2 scene 2
The death of Ophelia as recounted by Gertrude, act 4 scene 7
#4
"To thine own self be true", act 1 scene 3
Hamlet's soliloquy "To be or not to be", act 3 scene 1
Hamlet discusses fate - "There's a special providence in the fall of a sparrow", act 5 scene 1
#5
Rosencrantz and Guildenstern arrive in Denmark, act 2 scene 2 (pick any part of it)
Hamlet's soliloquy "Now might I do it pat", act 3 scene 3
Hamlet's re-emergence "Tis I, Hamlet the Dane!", act 5 scene 1
Not saying that you'll get passages this "good" on the exam (they always throw in some really obscure ones), and this is all assuming they don't repeat last year's passages (which is always a risk, believe it or not). Still, this should keep you occupied.