It seems logical to me that the arithmetic questions were intended to produce a physiological response and served as a form of "control" question. What sort of agency administered this polygraph examination?

As best I can tell the polygrapher was a contracted tester, not directly in the employ of the city or department.

On both LAPD polygraphs I endured I was asked to perform arithmetic calculations (but only one for each test) and would concur with George's assessment that these were control questions.  I believe the "purpose" behind it is that the examiner assumes the mental calculations will induce stress in the examinee so they can "see" how you respond.  In addition to a math problem, I was also asked a "surprise" question which, I believe, is designed to produce the same effect. It's quite possible that your examiner just likes to use arithmetic questions (for controls) as part of his/her process.

As noted in "The Lie Behind the Lie Detector" performing mental calculations during other control questions can be utilized as a countermeasure.  When I was asked to perform an aritmetic calculation on my second exam, I constricted my anal spinchter and altered my breathing pattern in order to augment my response. 

With regards to the number of "charts", I went through seven:  one "diagnostic" and two sets of questions asked three times each.  The total "hook up" time for that exam was about an hour. However, my first exam lasted for nearly three. (And that's not counting the hour I was kept waiting for the examiner.)

As George pointed out, if you were spared the post-test interrogation, you should be in good shape.  Good Luck.