I have stated before that the 60's/70's was the golden age of high school mathematics and this test exemplifies that feeling. Also, this is 12th grade, like Dave mentioned in his previous comments. Maybe calculus deprived many students of ever knowing algebra?
What I like about most of these problems is that they require the student to think fundamentally. A simple example of what I mean is problem 35...
35. Three coins are tossed simultaneously, what is the probability that they will show two heads and a tail.
The best way to start probability problems is to remember that probability is the number of possible positive outcomes divided by the number of all possible outcomes. Simple, yes, but your typical student (not prone to problem solving) doesn't think this way. The first thing they do is try to remember a formula, and they fail.
These problems are not "too clever" but they are unique enough so as to require the student to think fundamentally. This is good for students heading towards pure math or for students heading towards applied math, like physics. When you compare this exam to the CA exam it should not be a mystery as to what happened to our best students or why MIT and Harvard have struggled so much recently in teaching a single physics course that it previously taught fine for many decades.