The math here is surprisingly weak. I'm not sure about where you guys went to school, but this is fifth grade stuff. Sure, there's a lot of memorization, more classics. But wowzers. No math.
I very much doubt that most college students today, even in technical majors, could work out the geometry proofs. I was a calculus TA for two years in college (at an engineering school), and students don't know geometry anymore. Nor can they prove anything at all.
Not sure why this is, or was, getting downvoted. For most high school students, geometry consists of 1 semester in their entire high school career, and it mostly involves learning about triangles and polygons and learning the (n-2)/180 formula and a few, trivial proofs. The depth of Geometry on the Harvard test is not very deep per se, but it's easily out of reach for most high schoolers.
Now the students who do math contests and are AIME/USAMO level could probably do the geometry section here without a lot of trouble, but they are the exception.
If things continue as they are, expect this to change a bit. In particular, proofs like #4 on Geometry is going to be a requirement in 45 of the 50 states.
There's 2 trigonometric proofs, and a number of less than obvious geometric proofs, especially the latter ones pertaining to the circle. The rational equation in #8 on algebra going to involve solving a cubic. And although #7 in arithmetic wouldn't be too hard if you worked entirely in pence, it is still a trickier problem in the days before decimalization.
Granted, it's weird in this day of students taking 5+ AP classes to see no calculus, but the math isn't weak at all. Remember, there's no calculators here. Maybe a slide rule and a table of trig values/logarithms. But that's still a lot of work by hand.
It takes a lot of time, but the calculation was definitely something I had to do in elementary school.
In terms of proofs, they are pretty basic, and I learned that stuff in third grade. I mean, I went in and out of gifted programs, but I think the better question is how long does it take to get people to add integers correctly? Ten years?
I drove myself a lot as a child, and drove enough teachers crazy to have to switch schools about ten times before middle school, but I would be surprised if my experience is no longer strictly atypical for people seeking a world-class education.
Note: I didn't attend an Ivy-League, but I did end up skipping a few grades. All those were after elementary school, so it's likely I was ahead of students at the time -- ahead of average, not ahead of the expectations we should have for first class minds seeking a higher education in an age when this is exceptionally uncommon.
What age are Americans typically when they take SATS? The geometry stuff is not so bad if you can give visual proofs, pretty hellish otherwise. I think I had to know quite a lot of this stuff for A-level maths as well as Calculus, basic Statistics, Linear Algebra and Applied Maths. But we take these exams when we are 17 and it was 1 of 3 subjects we specialised in for 2 years. Also, regarding your point about calculators, our exam questions were set so that it generally wasn't practical to use a calculator to solve them. E.g. some questions specifically stated that you should give the answer as surd or fraction, it was generally easier / quicker to do the working out manually.
Traditionally, Americans applying to Ivy schools take the SATs sometime midway through their 3rd year of High School, when they're anywhere from 16-17. Many will take it this month.
Also, as you may know, many calculators today have a CAS, a Computer\Calculator Algebra System, that will gladly give responses as a surd or fraction (or even solve a differential equation). To my knowledge, College Board has yet to ban a calculator for a CAS.
Whoa! Calculators were nowhere near as fancy as that back then. We were allowed programmable graphic calculators but the invigilators pressed the hard reset button on the back as you went in to the exam to make sure you hadn't stored anything on it.
This math is much harder than the math on the current SAT test. There are no geometry proofs or trig/logarithms on the SAT. However, most admits into Harvard nowadays have either a solid AP Test score in Calculus and/or a SAT2 Math score, so that's sort of an unfair comparison.
I've seen this response to the document before and it often turns out the author of the response had missed a page so mistakenly thought there was little math.
There are communities of people who would indeed consider this an easy test but they tend to delve even more deeply into classics than a typical contemporary of the test.
