Harvard's entrance exam from 1869...

[ElNono]

"The New York Times remembers back to when 'college was a buyer's bazaar' and digs up 19th-century classified ads from Columbia, Harvard, Yale, and others. In compe ive efforts to attract students from the limited pool of qualified candidates, applications were taken as late as September for an October freshman class. Vassar offered lush room accommodations. The expectations were high: Latin, Greek, Virgil, Caesar's Commentaries; Harvard's entrance exam from 1869 is posted (PDF). Could any of us pass the exam today?"

[TE]

Holy , Greek Composition, Greek Grammar, Latin Grammar, and Latin translations?

[LnGrrrR]

Eh, there's a reason not many of us write in Latin now. It's great to understand origins of words, and word backbones, but back then it was a sign that you were erudite.

The math section is still relevant, obviously.

[mouse]

I can see the teachers pay hasn't changed any.

[Wild Cobra]

How about the math...

The 5th root question. I know how to calculate square roots longhand, but never learned 3rd roots plus.

[DarkReign]

I can see the teachers pay hasn't changed any.

At Harvard?

Really?

[LnGrrrR]

How about the math...

The 5th root question. I know how to calculate square roots longhand, but never learned 3rd roots plus.

I'd just start guessing at that point. "Let's try .5 times .5 times .5, and see what that gives us... ok, how about .3 cubed..."

[Wild Cobra]

I'd just start guessing at that point. "Let's try .5 times .5 times .5, and see what that gives us... ok, how about .3 cubed..."

There are ways of doing it that are not trial and error. I just never learned you to solve that one without trial and error.

I can do square roots though!

[LnGrrrR]

There are ways of doing it that are not trial and error. I just never learned you to solve that one without trial and error.

I can do square roots though!

Yeah, neither have I. Whenever I get stuck on a math problem, I try the "educated guess" method.

[RandomGuy]

"The New York Times remembers back to when 'college was a buyer's bazaar' and digs up 19th-century classified ads from Columbia, Harvard, Yale, and others. In compe ive efforts to attract students from the limited pool of qualified candidates, applications were taken as late as September for an October freshman class. Vassar offered lush room accommodations. The expectations were high: Latin, Greek, Virgil, Caesar's Commentaries; Harvard's entrance exam from 1869 is posted (PDF). Could any of us pass the exam today?"

"A man bought a watch, a chain, and a locket that together cost $216.
The watch and locket together cost three times as much as the chain, and the chain and locket together cost half as much as the watch. What was the price of each?"

[RandomGuy]

Took me a lot of scribbling, but I got it. whoot.

[Wild Cobra]

Originally Posted by question 7 from the algebra section

"A man bought a watch, a chain, and a locket that together cost $216.
The watch and locket together cost three times as much as the chain, and the chain and locket together cost half as much as the watch. What was the price of each?"

If you want someone to solve that simple problem, maybe you should put it in this thread:

48÷2(9+3) = ????

[LnGrrrR]

That question 7 looks like it's going to be easy, but is it a bit of a pain.

[elbamba]

I was looking for instructions to tell the test taker to read all the questions carefully, then return to the first page and begin the test. Then the last paragraph would say to write your name at the top and then submit the exam.

I was disappointed.

[baseline bum]

How about the math...

The 5th root question. I know how to calculate square roots longhand, but never learned 3rd roots plus.

The Newton-Raphson method applied to the polynomial f(x) = x^n - y can be used to find the nth root of y (assuming y > 0), and it converges very quickly. The algorithm from Heron of Alexandria for finding square roots is a special case of this method.

[RandomGuy]

If you want someone to solve that simple problem, maybe you should put it in this thread:

48÷2(9+3) = ????

Erk.... missed that one. Spaced out the "left to right" rule.

[Wild Cobra]

The Newton-Raphson method applied to the polynomial f(x) = x^n - y can be used to find the nth root of y (assuming y > 0), and it converges very quickly. The algorithm from Heron of Alexandria for finding square roots is a special case of this method.

Thanx, I'll look that up.

[Wild Cobra]

That question 7 looks like it's going to be easy, but is it a bit of a pain.

oops...

When I wrote the equation, I originally solved for:

the chain and locket together cost twice as much as the watch.

not:

the chain and locket together cost half as much as the watch.

Changes the answer dramatically, except the chain. It remained the same price!

[LnGrrrR]

For those curious about the number 7, answers/work below! (If I'm taking the time to answer it, I'm bragging. :p)





SPOILERS BELOW, HIGHLIGHT FOR ANSWER



The question gives three different equations.

a) (W+L) = 3C
b) 2(L+C) = W
c) W+C+L = 216

Since we know that 2(L+C) = W, we can insert that into the first equation. This gives us (2L + 2C + L) = 3C, which ultimately boils down to 3L=C.

Now that we know that 3L=C, we also know that W= 2(L+C) or W = 2(L+3L), or W=8L.

So C = 3L, and W=8L. Time to subs ute those into equation C.

8L + 3L + L = 216. From this we get that L equals 18. And due to the info above, that means that C = 54, and W = 144. Doublechecking by plugging those numbers into the equations above, we see that it works. Voila!

[LnGrrrR]

Hint...

Chain squared plus Watch squared equals Locket squared.

Yeah, just posted the answer. I was hoping I could guesstimate the answer quick, but I kept guessing wrong, so I actually had to do the work.

[baseline bum]

Thanx, I'll look that up.

It's a pretty interesting algorithm useful for finding roots of algebraic equations in many cases, but the one Heron of Alexandria came up with for square roots is essentially just smoothing out an oscillating signal by averaging.

[Wild Cobra]

Yeah, just posted the answer. I was hoping I could guesstimate the answer quick, but I kept guessing wrong, so I actually had to do the work.

You caught that before I caught my mistake and removed it...

What I posted before editing is true with the "twice" rather than "half."

[admiralsnackbar]

Believe it or not, the Ancient Greek part wasn't as scary as you'd think.

I only took 3 semesters of it in college (over 15 years ago) ( ), getting mediocre to bad grades on the reg, and I was still able to get a fair amount of it with stuff I learned in 101.

I think LnGrrr's right, though: the exam was really just a formality that any kid of aristocratic breeding back then could have breezed through on a ripping laudanum high... or whatever they were into then.

[Wild Cobra]

It's a pretty interesting algorithm useful for finding roots of algebraic equations in many cases, but the one Heron of Alexandria came up with for square roots is essentially just smoothing out an oscillating signal by averaging.

Well, I was hoping for a straightforward method like there is for solving square roots, with no guessing.

[Wild Cobra]

Believe it or not, the Ancient Greek part wasn't as scary as you'd think.

I only took 3 semesters of it in college (over 15 years ago) ( ), getting mediocre to bad grades on the reg, and I was still able to get a fair amount of it with stuff I learned in 101.

I think LnGrrr's right, though: the exam was really just a formality that any kid of aristocratic breeding back then could have breezed through on a ripping laudanum high... or whatever they were into then.

I wish I took Greek as a language. Sure would like to read revelations in the original tongue.