aloha,
The term: "show the calculation" in the SEII can mean a few different things.
It could mean calculate the ASD or LRFD moment using the equations in the spec portion of the 13th edition. Of coourse, this is perfectly just fine.
Like you, I would like to do it the easier way. That would give me more time in order to complete the exam with time to review it. I would reference the table used when you list the ASD or LRFD moment for a specific shape.
Remember, most of what the SEII is testing you on is your thought proccess. As long as you can make it as easy as possible for the grader to see how you are thinking about something, the better.
I hope this helps!!