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Where the hell is Hecla? 
I'm with OC here that the important part is putting the facts together.
You fail to take into account that these schools chatered to the well todo, they didnt have the shere numbers of students. Students who dont have parental support, no resources, no future. Its one big baby sitting service so that the serfs can work.
You have a better way to do things?
High School Entrance Exam - Midsummer, 1890
WRITTEN ARITHMETIC
1. Define concrete number, aliquot part, finite decimal, present worth and ratio.
2. Simplify: (6/7 of 1 1/4 of 14/15 + 3 1/2 of 2 10/21 - 2 2/3) x 3 6/7
3. Three men, A, B, and C, start together from the same place to walk around an island 60 miles in circumference; they walk in the same direction, A at the rate of 5 miles per hour, B at 4, and C at 3. In what time will all be together for the first time after starting, and how many miles will each have travelled?
4. If 5 tons of coal are equal to 9 cords of wood for fuel, and a family burns 31. 5 cords of wood in a year, how much will be saved by changing from wood to coal, when wood is worth $4.25 per cord and coal $6.80 per ton?
5. If a family of 9 people can live comfortably in England for $7,862.40 per year, what will it cost a family of 8 to live in Canada in the same style for 7 months, prices being supposed to be 3/5 of what they would be in England?
6. Find the compound interest on $500 for 1 year 6 months at 8% per annum, interest payable semi-annually.
7. What is the present worth of $600 due 8 mos. 18 days hence @ 9% per annum.
MENTAL ARITHMETIC
1. What will 3 1/2 cwt. of hay cost @ $25 per ton?
2. If 5 1/2 yards cost $.77, what will 4 2/7 yards cost?
3. Write a decimal equal in value to a unit.
4. What is the first prime number below 100?
5. What will 225 hats cost @ $.66 2/3 each?
6. If 3/8 of a ton cost $13.50, what will 5/9 of a ton cost?
7. What is the simple interest on $1, 250 for 2 years 8 months @ 2/3% per month?
8. What part of 2/3 of 3 1/2 is 5/9 of 4 1/2?
9. What is the brokerage on half a million dollars @ 1/8% ?
10. What is the true discount on $620, due 2 years 8 months hence at 9% per annum?
Other than focusing on different areas, it doesn't seem to much harder than my 8th grade education. The math is less advanced, and the test is quite shoddy because it relies on the unknown givens like the volume of a bushel of wheat. However, I bet that the students solved the exact same type of problem regularly in real life. Orthography has certainly changed, with some of it being lumped into other studies and the rest just forgotten.
Doesn't seem all that useful. Most of that is mere regurgitation. Remember school is not primarily there to put facts in your head. It is there to teach you how to think. And that test doesn't do that or at least reinforce that.
Which today is pretty useless. Any kid with a browser and internet connection can look up facts. If that kid cannot make connections to read between the lines to determine why and how, that kid hasn't learned squat.
Hell, I'm 20, and I couldn't answer all of these correctly. God only knows what I'd have been able to answer when I was 13.
this is a graduation test from a rural county, not from Phillips-Andover or Boston Prep. But then, George W. went the Phillips-Andover route, after failing in Texas schools, and then Daddy got him into Harvard and Yale, he couldn't get into U of Texas, so maybe the 'Ivy League' has always been pretty much of a joke, too.