Gene - "No Finny we must get back in time for my trigonometry exam."
Them waking up has importance to the story because Finny ignores Gene even though he has his test leaving early would have helped Gene get there earlier or have some study time.
Finally back at the Devon School
Gene - "Finny I'm barely going to make it back for my exam, I must hurry.
Gene had to rush to class and rush back to the school to take his exam which ended up pretty badly. The importance is how Finny is giving Gene trouble and this affects them in the long run.
Finny -"You take it too serious Gene."
Gene failed his trig exam so he went back to study and Finny said he taking this all too seriously. Gene thinks Finny is holding him back from his full potential. This is important because Gene will let loose or Finny will learn Gene's values.
Gene's trig exam
Gene-"This is all, Finny's fault that I failed I must talk to him about this! He's distracting me from my work."
After Gene failed his exam he told Finny he needed to study because of his poor grade although Finny could care less so he wanted to play blitz ball.
Finny "Gene you take this too seriously, lets play blitz ball and jump of the tree."
After Gene's test
Gene "Finny, I need to study to make up for this test."
Finny "Never mind Gene, you're smart just stay and study and don't come jump of the tree."
Finny told Gene to just study and not come along, I think this resulted in Gene feeling guilty. I think that Gene would've kept studying without Finny's comments.
*Gene thought*, then dropped his books and headed for the tree.
This is important because this is what happens when Finny convinced Gene to go. I think this will probably lead to something in the future that will hurt Gene or something like that.