Tibees. .u are a fine physicist. .but u need to think like a 19th century mathematician to answer these questions. .roots. .powers. .were relatively straightforward back then. .just by using logarithmic tables! ..
"To solve this paper, one needs to be better at English than Math." That's the biggest problem with this. If they can use simpler language they should. It's an ARITHMETIC test.
@@13ivanogre13 That it filters out foreigners, non-native English speakers and people of the lower classes less used to the academic jargon was probably considered a feature, not a bug.
@@Shaeress I get the non-native English speakers part, but if people of lower classes don't know English that well, what makes you think they'd be better at Math?
That's the problem with English education nowadays. If for example I listen to people in the 50's being interviewed on the road, I am surprised about how clear and accurate they spoke.
Inaccurate. The 2080's mathematics student has automatic access to the full information on why exams in 2019 were the way they are through his or her cyborg brain's connection to the hive mind. They would never get the chance to be surprised.
@Salvador Luna Research neuralink, development of brain tech has already started. And flying cars isn't the only thing people in the 80s predicted, many things they predicted have come to fruition.
@Salvador Luna It's not like we don't have flying cars, we simply don't need them. Airplanes are literally flying cares since you can fly and also drive them.
It seems like it today but the question is how much time did they have at their disposal, what was the percentage that would give you a pass and who had to solve it. I can imagine that someone working in a bank can not afford any mistakes whatsoever. If you have yo do this by hand in a short amount of time and you're allowed to make one or two mistakes then this very simple exam becomes very very hard all of a sudden.
Narrative problems might be the most important though, since that's the way to apply your math skills the proper way, otherwise it's useless knowledge :( @@@ccricers
As an old American, I thought I might explain what some of these old American terms mean. The bu, pk, and qt are US dry measures; these three pretty specifically used in farming. There's 8 oz (ounces) in a cup, 2 c in a pint, 2 pt in a quart, 8 qt in a peck, 4 pk in a bushel. (1 oz is 28 cc) Pecks and bushels aren't used for liquid measure, and for liquids there's 4 qt in 1 gallon (gal). These US measures are not equal to the British measures of the same names. Gold is weighed in Troy ounces (31.1 grams), cotton is weighed in Imperial units (28.35 grams in an ounce). Qr as a unit of weight is not used anymore, but it's a quarter or 25 lb (pounds) - so a quarter of a hundredweight (cwt), which also has gone out of common use. In the cost of lumber question, the "feet" measure would be "board feet", which is actually a measure of volume equal to 144 cubic inches. The "M" is a symbol for 1000. There is a method for extracting roots that is somewhat akin to long division. I did learn it in school, but even then (at the dawn of pocket calculators) it was much easier to use a slide rule. Value of the mine - I believe the owner sold 3/4 of his interest, not 8/4. The print probably got blurred in the digitalization process. Potash (pot-ash) is potassium carbonate.
I'm a not-so-old American (at 36), and I knew a lot of these. I knew "qr" was a quarter but wasn't sure of its value and only recognized why "cwt" and "M" made sense after you spelled them out: Roman numerals, of course -- I should have realized that since it was a 19th Century document. To be fair, I wouldn't expect anyone but a woodworking geek to recognize board feet, which is the only reason I knew it.
I confirm bob's comments. 1866 is slightly before my time, but back when I was taking arithmetic tests I saw similar questions, with more emphasis on units used in more recent technologies (also with metric as well as English units). Pharmacists were still using drams, grains, etc. and lumber was still being sold by board feet, although the size of a "2 by 4" has since then shrunk a couple of times. "A bushel and a peck" was in the lyrics to a popular song, but not used as much in marketplaces. As to the computations, I have many times had to compute square roots to six places etc. and although calculators exist, often it was faster to do by pencil and paper than by hunting around for a calculator. I'm surprised there wasn't a question involving compound interest; maybe that required a higher level of education. Anyway, I've seen many cases where people we having trouble doing their job "because the register isn't working" and so forth. There is certainly less general knowledge of arithmetic, both its meaning and its details. If a cashier says (correctly) that I need to pay $18.27 and I give the cashier $20.30, quite often they seem puzzled by the extra change.
But it takes a country that uses the Imperial system put men on the Moon. [For those of you unable to recognize a joke: Joke (noun) 1) Something said or done to provoke laughter or cause amusement, as a witticism, a short and amusing anecdote, or a prankish act. 2) Something that is amusing or ridiculous, especially because of being ludicrously inadequate or a sham; a thing, situation, or person laughed at rather than taken seriously; farce.]
This test isn't strange, it contains pertinent arithmetic for the time. Being able to measure resources, relate distance and time, and change units of measurement would be critical skills.
Jesus Christ even with calculators my grades in this subject were abysmal. Without calculators, well... even God himself wouldn’t have the kind of juice it’d take for that kind of miracle.
@Edward Foyer No wonder we fear math tests more than saber tooth tigers. The amygdala is an evolutionary process to protect us from math tests and not from saber tooth tigers.
Calculus exam would be like "What is the summation over a continuous index, of the product of an infinitesimal width and the continuous index with our consideration limited by a lower value zero and an upper value 1?"
@Salvador Luna Physics was probably really basic stuff, like speed and maybe gravity, as we hadn't figured stuff like radiation etc. out back then. And chemistry was not far enough to be teached at schools at that time i think. And even if it was taught back then it was probably only daltons modell of the atoms, and stuff goes boom if you mix it.
its actually more of a practical arithmetic exam, like learning how to do your taxes or give change for money. it makes a lot of sense to teach practical, applicable math even by today standards, the units and the commonplace situations were slightly different
@CrAzYCaM 8 'Yet they were all much less intelligent' - er...university students in the 19th century were far more intelligent than those today. There were only a few subjects and so you had to be excellent at both mathematics and english just to get in. Kids today can get into a university with english and math skills which wouldn't even let them graduate highschool in 1890.
It's interesting to see how the importance we attribute to skills evolves with time. Calculating cube roots (as question 17 seems to ask) is not really considered an important skill today, because of the computing power we have. Instead, we would focus on the insight and the interpretation that the value or the cube root operation can have. But really if you don't have computers, suddenly you have no idea what the value of a cube root would be without an appropriate technique !
An English man an Irish man and a Scottish man walk into an exam hall in 1866.. The English man understood everything and got great score of 86% The Scottish man copied the English man and got a passing score of 62% The Irish man thought he was in a poetry exam. He got 100%
Just seeing that date Oct. 1, 1866 gives you such a profound feeling. You hear about things happening 200 years ago etc. but seeing a actual date in real life written by the people of that time is just mind boggling.
You kids of 1866 and your arithmetic tests....try and answer a common question from my alchemy test in 1466: "If you drink an invisibilty potion but you grow donkey ears instead, which ingredients are missing considering that on that day Venus is alligned with Jupiter but Mars is not alligned with Neptune?."
@@WhattheHectogon Yeah! ahah! You sure know a lot of things, probably more than you should for your own sake. You watch yourself man, it'd be a shame if somebody turned you into a newt by mistake one of these days....
Well it’s not that much tbh look at real tests. This one neither includes calculus or stochastic. Also the only hard part of this test is being able to speak English properly
A late 19th century phone can be used to solve every problem here, not a joke. They had a feature most don't know about unless they have actually seen one up close. Inside there is a fairly large electrical generator to produce current for the ringers. The whole unit weighs in around 20 lbs or 4.5 kilos. if you remove that section from the wall and slam the teacher in the back of the head, you will have successfully solved all your problems from the math exam.
@@zikomo8913 then when your wife goes into labor, that doctor will kindly give her ergot, whose constituent compounds include LSD and a few fatally toxic chemicals. What a simpler time it was; nowadays, we buy our LSD and fatal toxins seperately.
"What fun times they were, go to war and come back home to do some math problems." Except nobody actually went to war. All war is theatre and then reported as "fact" by the newspapers. Even D-Day (or the footage) was military exercises off the coast of Cornwall. Nobody actually "died".
"visit a doctor as soon as possible" So that he can prescribe loads of useless drugs that do little if any good? Another cliched response not discussing the real issues. If the RAF and American air force had complete dominance over the skies the Allies could have picked almost place to land troops. The Normandy landings were picked to that the war could be extended, with spook reporters like Ernest Hemingway giving people the "facts" (propaganda) along the way. This is true.
As a child of the 60s, graduating in 1971, I can relate. It is "old math" - the simple basics. I took Alegra I in the 9th grade, Geometry in the 10th, and I was never required to go further. This math is what I call useful math. It can be used in solving everyday problems and it teaches you to figure out thought problems. I loved seeing this!
It could be some of these questions are answerable with a slide rule or common logarithm table, which were common before calculators. Like for #17, I think the cube root could be solved by computing antilog((1 / 3) * log(389017)), where the log and antilog involve looking up in tables.
To get the next time for the train to arrive, you must take the time and times it by the time you think it'll take, so you can time your timing correctly. Take the sum time and times it by a decimal to get the previous time, thus, confirming your timesing of the time is correct. You can also pull out a copy of the Times to get the train times, but it's good excercise to try timesing your timing, anyway. Don't forget to carry the decimals when you times the time with, or without the times in the Times as your guide.
Very informative. Real good explanation too. I liked how there's no apparent "cheat sheet" included to give conversion factors during the exam. Potash is literally pot ash but without the space between the words, and comes from burning down residue from stuff that was already burned down. Potash was and is still used as fertilizer due to it's high concentration of compounds. The word potassium comes from potash, and that's one important element for the fertilizer. :)
You were reading threes as eights in the numerators of some of the fractions. That was not at all your fault, as, owing to poor printing, they did indeed look like eights when not magnified several times.
In particular, Question 22, it must be "3/4 of his interest" in the mine. This is a straightforward exam with a calculator, but would be very punishing without one.
Re: Question 18. This is a bond. The issuer will pay John Smith $100 at the end of the bond period and the question is asking how much John Smith would have to give the bank to get such a bond, i.e. its "present value". "Present value" is still a term used in finance. It means the value right now of some future cash flow which will be discounted by a "discount rate." We're still missing some information. Probably New York where this test was issued had a standard discount rate for bank bonds that would be known to test takers. For modern folks, this is basically the same as a loan, just specified in the opposite direction. i.e. the amount specified is the amount that will be repaid instead of the amount loaned: instead of saying, "I will give you $100 now, and in the future you will have to pay me that amount plus an interest rate," you can say, "In the future, you will repay me $100, so I can give you $X discounted by the discount rate." So this is like a compound interest question and you'd solve it the same way, just by dividing by the rate instead of multiplying.
I was inclined to either say zero, because the bond has not matured; or apply "common" knowledge about US bonds, such as the purchase value being half the face value, and common models of economics, such as the bond's market value being as if it had a fixed risk-free interest rate, to arrive at the answer. The latter would definitely require a calculator though, as it requires computing fractional powers of 2.
How is every one of your videos a nice trip down the ASMR lane. The vibes on each one are so calming. I don't even realise that I've been through another 15ish minutes of intense science shit. Nice content man. I'm shook ;)
Gold is measured in Troy ounces, Cotton is measured in Avoirdupois ounces. A pound of Gold is NOT the same weight as a pound of Cotton. (Troy ounces are 12 troy oz. to 1 troy pound, avoirdupois is 16 oz per pound.) 1 troy pound = 12 troy oz = 0.823 lbs = 13.168 oz. 1 lb = 16 oz = 14.583 troy oz = 1.215 troy pounds. (Σ)
If i saw anyone who could actually solve for the square root of 0.0043046721 by hand I'd be insanely impressed. As a math major myself in my 3rd year of college I find this really interesting to look at. I really hope you find a calculus or even linear algebra exam from the 19th or early 20th century, I'd be really interested in that. Awesome video as usual!
I'm assuming a slide rule would have been allowed, which would make the question more of an ability to use a slide rule than a test on the math; akin to using a modern calculator to work out a standard deviation for example?
Actually, I just tried this on my own slide rule and I can only get that the answer would be ~0.066* with an uncertain 3rd significant figure, so that's the end of my slide rule theory! :)
There is a video on RUclips titled "Square root of 2 on the pepper grinder". It is an amusing demonstration of how to calculate a square root using a machine that can only add and subtract!
It's actually not that hard. The problem does require some effort and thinking to solve it by hand. You first factorize 43046721 to get 3^16. (repeated division) That means it is the square of 3^8 (6561). With some other knowledge of squares and square roots, one can figure out it is the square of 0.06561 :)
I feel like you've been reading 8/4 instead of 3/4 the entire time. 3/4 makes sense and the old font may have a 3 looking like an 8. You should really take a closer look at it just to make sure. 8/4 just makes no sense.
You can do the cubic root with some school tricks. So the answer is gonna be a two digit number (because 389017 is between 1000 and 10^6). Now we can write x = 10*a + b where a and b are between 1 and 10. This here you were probably taught at school (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3, applied to our x we have x^3 = 1000*a^3 + 300*a^2b + 30*a*b^2 + b^3. Here we can notice that only b^3 determines the last digit (7) and the only number that can get us that last digit is 3 (3^3 = 27). So b=3 and now x^3 = 1000*a^3 + 900*a^2 + 270*a + 27. Now we suspect that the first digit is solely determined by 1000*a^3. Again we check all the digits and we find a very promising candidate in 7^3 = 343. So now we check 73^3 and indeed we get 389017.
Here is how I did it. Since these are solid cubes, the length has to be an integer. The last digit of the cube root has to be 3 because 3 is the only digit that ends in 7 when cubed. Then bound the problem by trying 100^3=1000000, too big 50^3 = 5^3*10^3=225000, too small 70^3=49*7*1000=343000, too small 80^3 = 64*8*1000=512000 to large, the answer is between 70 and 80 ending with a 3, 73 it is.
When I was in school, we learned an algorithm for taking square roots. I forgot it long before most people reading this were born and had to look it up the last time I wanted to take a square root by hand.
I'm pretty sure that question 17 "What is the length of the side of a cubical box which contains 389,017 solid inches?" would be solved by the use of a slide rule, which has been around since the 17th century and is excellent for calculating roots and exponents. Likewise question 20.
i 'calculated' the root this way: 1. assumption result is an integer since it is an exam (risk involved) 2. 389 017 is roughly 400 000 = 400 * 10^3, so 7^3 * 10^3 is not far from result 3. the only digit yielding '7' on the last position when cubed is 3
I have problems I'd like to appear on the 2066 Regents Exam -- they require the student develop a software numerical algorithm to be solved: Example1: Given 3 overlapping spheres (of different radii), solve for their two points of intersection. Example2: Given two skew lines (extended lines in 3D), solve for the shortest bridging line segment between them, calculating its two endpoints. I'm convinced that high school maths will be advancing to this level in that timeframe, with algo-design tools as ordinary as were paper and pencil in 1866. (I aced the New York State Regents Geometry Exam in 1966, spurring me on to lifelong learning in spatial maths & CS.)
Cube root and Square root (or any root) e.g Cube root - get the logarithm of the number - divide by 3 - find the Antilog of the number. The used books of logarithms in those days.
The cube root of six digit perfect cubes are easily found by a technique. I don't know the name of the technique, but here in India people cram it for competitive exams for government jobs.
at 6:05 maybe it's asking about the scale of the weight you would use to weight each material? Presumably, gold is more valuable than cotton, therefore when exchanging one for the other, you would exchange grams of gold dust for tonnes of cotton. So you would use a scale with a grams counterweight to measure the amount of gold dust and a scale with a tonnes counterweight to measure the amount of cotton.
qr. = Quarter of a hundredweight (2 stone, 28 lb) cwt = Hundredweight (1/8 of a ton, 112 lb) bu. = Bushel (4 pecks = 8 gallons = 32 quarts = 64 pints) pk. = Peck (2 gallons = 8 quarts = 16 pints) qt. = Quart (2 pints) This paper looks like great fun. What was the allocated time?!
@@necrisro Before calculators we used numbers other than 10 which have more factors and are easier to divide, i.e. 8/12/16/24/36 - hence why a lot of imperial measurements use them.
@@MaciejBogdanStepien Not really, the bigger problem was the variation between national standards, and even variation on what what being measured. For example the hundredweight was just a hundred pounds when you were measuring agricultural products.
For the discounting $100 question, it is asking you to find the present value of the $100 to be paid in 90 days. The thing is it doesn't give you a rate to discount by, it just says "bank." So I'm assuming at this time there was a standardized discount rate that was the "bank" rate. Possibly 5%? If so it would be about $94.50 You would have to solve for X to the power of Bank/4 (90days/360 year) = $100 Also, you would see this on any finance 101 exam today less the vague "bank" rate. :)
The cynic in me assumes the banks just used a nice round number like 20% when buying bonds like this from the public... :) I was pretty amused at the question though and wonder how many business school graduates today truly understand it.
This is the big difference between then and now: then, education was all about teaching practical things - how to figure out how to convert mixed units of measure, and actually come up with numeric results. Today, what is taught is more abstract. Note that there isn't even a hint of algebra or geometry in this test. I'm sure that the method of calculating square roots by hand was taught at the senior level; it was still being taught when I was in high school a long time ago. Note that the solution to the cube root problem is a whole number, so the intended method for solving this would be to estimate and then zero in on the solution.
Whether this was more "practical" than what is taught today is a matter of perspective I'd say. Geometry and vectorial math is about as practical as it gets and it has an important place in today's curriculum. Didn't see any optimisation problems or geometry in that exam.
Where you are reading "8/4", it is actually printed as "3/4", but the small printing has blurred this 🙂 So question #22 is indeed a reasonable situation.
im a highschooler in new york. the regents exam are final exams given by the state for certain subjects. almost all of math (except pre-calc, ap calc and pre-alg), all sciences, 11th grade english and world history and american history regents. it happens annually on june, January and august (schools usually chose btwn January and June, August are usually taken by those who fail) this is given every year, is mostly mandatory (you need to take a certain amt. of regents to graduate. e.g. physics in my school was voluntary) and is like a final exam. its only given in new york, or what i know of. all of these exams are found online
You made an error in reading the fractions for question 2. Zoom right in and look really closely, the numbers are 3 + 3/4 and 2 + 3/4 and not as you stated 3 + 8/4 ( = 5) and 2 + 8/4 (= 4) which would have been too easy
st0ox Most languages have that peculiarity. Spanish, Italian, French, Greek. I suspect German is poorly organized if you can’t understand something written 150 years ago
I disagree. I don't know. What kind exams could exist in Newton childhood times??? ''Evaluate the maximum force that our great Lord can made to put the plan planets walking around on Luminiferous aether?'' Answer: Infinity + infinity Jokes apart...It is interesting to investigate and discover.
@@buttup8148 Before Newton, theories about euclidian geometries, complex numbers, arithmetic, series, trigonometry already existed. Even in terms of physics, despite his genius, he followed results of Copernic, Galilée, Brahé and Kepler among others ^^
@@buttup8148 Well, technically, as my teacher of General Relativity claimed, complex numbers were developed in their algebric form by italians mathematicans of the 16th century, to resolve equations of the third degree for example. But indeed their 'geometrical form' was studied in Gauss Age :)
Anyway, let me tell you the basic methodology for the square roots and the cube roots. So what is the cube root of 889017? So here's the thing. You know that the cube root of a million is 100, right? So this is going to be slightly less than 100. But how much? Well, if you cube .9 you get .729, if you cube 1.1 you get 1.331. So when you cube (1+delta) for a small delta, you get about 1+3*delta, you see? So to get something that is 11% less than a million when you cube it, you should start from something that is about 3.66667% less than 100. But actually it should be more than 3.6667% but more like maybe a full 4%, because .9 doesn't turn to .7 after all, it turns into .729, since 1-delta cubed is not 1-3*delta exactly but 1-3*delta+3*delta^2-delta^3. So what is 4% less than 100? 96. So my estimate would be 96. Of course it's not 96 exactly because 96 to any integer problem will end in a 6 and this is the cube root of 889017, but I would certainly wager 96 is the closest integer to the answer, which is an irrational number. And what is the actual answer? About 96.17459. So indeed it was 3.83541% less than 100, not merely 3.66667% less than 100. But my estimate of 96 was very close. For the square root one on the last page, what is the square root of .0043046721? Well let's multiply it by 10 thousand so that the answer scales up by 100. So what is the square root of 43.046721? Well 42.25 is 6.5 squared, while 49 is 7 squared, and this is like 10% of the way from 6.5 to 7, so we're talking about about 6.55 then, or .0655 when you divide it by 100 again, but I'm not confident of that 5 at the end, it could be anything from .653 to .657... and what is the real answer...... Oh, it's .6561 exactly.... which is a familiar number to me, since I know 6561 is 9 to the 4th power. Apparently the people in the 19th century had their powers of 3 memorized to some ridiculous and useless level to be able to recognize 43046721 as 3^16. But there's the answer, it's asking for the square root of 3^16/10^10 and so the answer would be 3^8/10^5. You were also expected to be able to do (5/8)^7 so maybe it was common in the 19th century to memorize tables of the first 20 or so powers of the integers 2 to 10? That's pretty dumb.
Have a high school text book from WW2 years and it's full of problems about calculating artillery shell trajectories, plane and ship navigation problems, etc. The public education system had tailored the math curriculum to prepare boys to graduate, go into military service, and go right off to war.
I may be weird, but all of these questions make a lot of sense to me and none of them seems weird, only the examples are a bit dated, but it is all super easy stuff.
Not as much as I'd like. For Geometry, you are expected to know 2D transforms and how to apply them. There's still too much reliance on special cases and hand-computation.
9:38 The cube root of 389017 is 73 exactly, which I found by guessing and multiplying. First I guessed only multiples of ten. That quickly showed it was more than 70 and less than 80. Next I guessed 75, and finally 73.
You can always look at the last digit of 389017 which is 7. 3 is the only number that cubed will give you a number which last digit is 7. Therefore the fist digit of the cube root of 389017 is 3.
They want to know if we know that the first digit of each product must be entered in the same column of its multiplyer. The multiplyer in each of the columns (ones, tens, etc) produces its own product but since we haven't completed the problem with the final addition, the product in each line is called a 'partial product'
When I was at school ... a fair time back ... we used logarithm tables to do all the tricky stuff - those were the days (not really). We could also use our slide rules - what fun they were!
In India we still learn how to use log table but yaa calculator are much better but in Indian exams you can't use calculator for calculation so we are still stuck with log table😅😅😅😅
@David Seddon One time in college I realized I had forgotten my calculator, so I went to the library and borrowed an old book of mathematical tables and used the logarithm tables from the book. (For people who don't know what logarithm tables are: they allow you to do addition in place of multiplication, and subtraction in place of division. Thus, they are very helpful if you have to do a lot of multiplication and division, because then you only have to do addition, subtraction, and table lookups.)
This was very interesting. I have seen a couple of your presentations and I really like how you do it and communicate. Well done. My maths is very engineering orientated - so in short we learned maths in order to underpin our designs and methodologies. But I'm very interested in your opinion that arithmetic is less (not) important today - and in part you are correct. Checkout controllers at supermarkets cannot do maths - if their machine breaks down - its all over. However what is more important today in our wonderful world of technology and devices is a sense of scale. Whilst we can generate clever designs with extremely powerful computers and can produce efficient use of technology and resources, not to mention learning more about our universe etc etc I learned originally to have a sense of scale. In other words, when the answer is produced by our wonderful technology who is there to ask....does that make sense? A simple question, but unless you have a sense of calculation (broad brush - order of magnitude even) the question becomes rhetorical. You admitted yourself that to work out a share of a food bill can be a challenge in a restaurant. I have seen many failures in recent times related in may cases directly to noone asking a basic question.....does that make sense? Some Building collapses, bridge failures are often design failures due to this lack of.....does it make sense? and not necessarily an extraordinary event. Sorry for the ramble but it is easy to accept and answer on a calculator if you have no sense of scale. Keep up your presentations - they are excellent.
As a graduate from a high school in the state of New York. Yes, the Regents are still in existence (or they were when I graduated in 1997). They are the end of year exams given for most high school classes.
For #3, I would equate “figure” to “digit.” The partial product refers to each product you wrote beneath the line. 12 x 28 = 12 x 8 + 12 x 20 = 12 x 8 + 12 x 2 x 10 The figures are written one space to the left to signify the digit’s place, tens, hundreds, thousands, etc. I wondered as soon as I saw this if it was the same name from the regents exams I took in New York, and I was delighted to hear it was!
@@SathnimBandara for sure. In 1866 people could predict the motion of planets in the solar system with many decimal digits precision. Maths was really advanced back than, but this test wasn't about that.
50 odd years since i left school but there is nothing difficult about any of the questions, It's so bloody easy now with multiple choice questions you don't even have to think anymore.
What multiple choice questions? Once you pass algebra 2 almost nothing is multiple choice. Also, what about these questions are remotely harder than today's math? I would easily argue that even multiple choice trigonometry tests of today (grade 12 math), if they existed, would still be far more difficult than this test, or any grade 12 math test 50 years ago.
@@ENZOxDV9 actually no, good asmr gets hundreds of thousands of views, millions sometimes. pornhub videos are quickly forgotten, as are countless camsessions
@@electricalastro "Yeh gore log sochte kya hai apun ke JEE ko... sab saale humi se chori karre..." or "Saali JEE ke paper ko halke mein leri... akal wahi ghutne mein..." YES! not racist or sexist at all... BTW, Indians have set the bar pretty high internationally with "bobs and vegene" buddy... lets just not talk about standards okay...
#3: In the algorithm she was using (see 4:14), the partial products are the numbers you achieve by multiplying the first number by each digit of the second. "96" is the partial product of "12 x 8" while "24(0)" is the partial product of "12 x 2(0)". The question is asking where to align the "ones" digit of each partial product, and why. For the first partial product (96 in her example), it is below the ones digit, while the second partial product (24(x10)) begins under the tens column. The "ones" digit of the partial product is always aligned under the correct place value. This is done to preserve the value of the place digits used from the lower factor.
Toby, Sadly in US, there no Calculus even in prep school and so is the case with Bio, Chem, Physics too - Very primitive But they do extort (those Pvt schools) parents to the max with tutions going on $40k-$50k/yr
My video solving Q20 from this exam, the square root of a decimal by hand: ruclips.net/video/nAZvUnWbS8c/видео.html
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Tibees give me the maps.. Like Atari... Anywuu goo d Yob.
Tibees on the second exchange ill dress up a deer for a horse in majestic railway.. Be good.
Hola.. no me canso de decir eres una mujer muy preciosa. Best..
Tibees. .u are a fine physicist. .but u need to think like a 19th century mathematician to answer these questions. .roots. .powers. .were relatively straightforward back then. .just by using logarithmic tables! ..
To solve this paper, one needs to be better at English than Math.
"To solve this paper, one needs to be better at English than Math."
That's the biggest problem with this. If they can use simpler language they should.
It's an ARITHMETIC test.
@@13ivanogre13 That it filters out foreigners, non-native English speakers and people of the lower classes less used to the academic jargon was probably considered a feature, not a bug.
@@Shaeress I get the non-native English speakers part, but if people of lower classes don't know English that well, what makes you think they'd be better at Math?
That's the problem with English education nowadays.
If for example I listen to people in the 50's being interviewed on the road, I am surprised about how clear and accurate they spoke.
@@13ivanogre13 I'm non-native and I can understand the exam. It's not like we are stupid
only 1860s kids remember
I learned most of this in 90s middle school. Been scouring the comments and I'm baffled I seem to be the only one.
Only 3/4 of white male southerners will remember.
@@JackWitaPack *3/5ths of black males
Lol
jacob henke Hahah! Nice
it's weird to think that everyone who took this is dead
People who do current math exams will die too. Stay away from math exams.
Hubblebub Lumbubwub you’ve cracked the secret to eternal life
lol yeah
this is the mathematical proof that maths kill people.
*R.I.P.* to all of them ⚰️⚰️⚰️
In 2080
Mathematics student:I don't believe 2019 maths was like this
Inaccurate. The 2080's mathematics student has automatic access to the full information on why exams in 2019 were the way they are through his or her cyborg brain's connection to the hive mind. They would never get the chance to be surprised.
Listen to hear voice in low volume (sound) you'll hear s,see,se,sss. It feels like a girl hissing sound. Isn't that wierd.
@Salvador Luna Research neuralink, development of brain tech has already started. And flying cars isn't the only thing people in the 80s predicted, many things they predicted have come to fruition.
@Salvador Luna stfu
@Salvador Luna It's not like we don't have flying cars, we simply don't need them. Airplanes are literally flying cares since you can fly and also drive them.
You are such a nice and calm Person
You too
She truly represents the Aryan ideal, Uncle Addie.
ww could have been avoided if u were calm too sir
So are you, father.
Ok .. Adolf has commented! Thats it!
Very simple mathematics. The hardest part was understanding the terminology.
It seems like it today but the question is how much time did they have at their disposal, what was the percentage that would give you a pass and who had to solve it. I can imagine that someone working in a bank can not afford any mistakes whatsoever. If you have yo do this by hand in a short amount of time and you're allowed to make one or two mistakes then this very simple exam becomes very very hard all of a sudden.
Even in school narrative problems weren't my strongest suit, but I was fine with the other math problems usually.
Narrative problems might be the most important though, since that's the way to apply your math skills the proper way, otherwise it's useless knowledge :( @@@ccricers
barely hard
Idk if cube roots by hand is simple lol
This is a really weird ASMR video
She seems like an asmr person. does she make asmrs?
I think she just has to be quit to not disturb other people in her house
I was just about to comment the same thing
I was looking for the ASMR mention
She needs to get on that game. Using chalk writing equations...crumbling paper, scraping pens while doing physics.
As an old American, I thought I might explain what some of these old American terms mean.
The bu, pk, and qt are US dry measures; these three pretty specifically used in farming. There's 8 oz (ounces) in a cup, 2 c in a pint, 2 pt in a quart, 8 qt in a peck, 4 pk in a bushel. (1 oz is 28 cc) Pecks and bushels aren't used for liquid measure, and for liquids there's 4 qt in 1 gallon (gal). These US measures are not equal to the British measures of the same names.
Gold is weighed in Troy ounces (31.1 grams), cotton is weighed in Imperial units (28.35 grams in an ounce).
Qr as a unit of weight is not used anymore, but it's a quarter or 25 lb (pounds) - so a quarter of a hundredweight (cwt), which also has gone out of common use.
In the cost of lumber question, the "feet" measure would be "board feet", which is actually a measure of volume equal to 144 cubic inches. The "M" is a symbol for 1000.
There is a method for extracting roots that is somewhat akin to long division. I did learn it in school, but even then (at the dawn of pocket calculators) it was much easier to use a slide rule.
Value of the mine - I believe the owner sold 3/4 of his interest, not 8/4. The print probably got blurred in the digitalization process.
Potash (pot-ash) is potassium carbonate.
How many gills to a hogshead? How many minum to a teaspoon?
I'm a not-so-old American (at 36), and I knew a lot of these. I knew "qr" was a quarter but wasn't sure of its value and only recognized why "cwt" and "M" made sense after you spelled them out: Roman numerals, of course -- I should have realized that since it was a 19th Century document. To be fair, I wouldn't expect anyone but a woodworking geek to recognize board feet, which is the only reason I knew it.
I confirm bob's comments. 1866 is slightly before my time, but back when I was taking arithmetic tests I saw similar questions, with more emphasis on units used in more recent technologies (also with metric as well as English units). Pharmacists were still using drams, grains, etc. and lumber was still being sold by board feet, although the size of a "2 by 4" has since then shrunk a couple of times. "A bushel and a peck" was in the lyrics to a popular song, but not used as much in marketplaces. As to the computations, I have many times had to compute square roots to six places etc. and although calculators exist, often it was faster to do by pencil and paper than by hunting around for a calculator. I'm surprised there wasn't a question involving compound interest; maybe that required a higher level of education. Anyway, I've seen many cases where people we having trouble doing their job "because the register isn't working" and so forth. There is certainly less general knowledge of arithmetic, both its meaning and its details. If a cashier says (correctly) that I need to pay $18.27 and I give the cashier $20.30, quite often they seem puzzled by the extra change.
And thats why normal countrys use the metric system.
But it takes a country that uses the Imperial system put men on the Moon.
[For those of you unable to recognize a joke:
Joke (noun)
1) Something said or done to provoke laughter or cause amusement, as a witticism, a short and amusing anecdote, or a prankish act.
2) Something that is amusing or ridiculous, especially because of being ludicrously inadequate or a sham; a thing, situation, or person laughed at rather than taken seriously; farce.]
damn, you are so polite.
i bet, even when you curse somebody, he would say "thanks" in return.
😂
Whoever gets cursed by her would be lucky.
Fr
This test isn't strange, it contains pertinent arithmetic for the time. Being able to measure resources, relate distance and time, and change units of measurement would be critical skills.
Only 90's kids remember (1890)
They had advanced tech by then...
@@Yatukih_001 according to that time machine documentary, they had time travel back then
It’s sad to know that even in the 1800s I’d have still failed maths.
Maybe in the 1800s you'd be forced to learn it more thoroughly though because they didn't have calculators.
Jesus Christ even with calculators my grades in this subject were abysmal. Without calculators, well... even God himself wouldn’t have the kind of juice it’d take for that kind of miracle.
Yes, most of us would struggle to pass such papers, but people back then would struggle to do our calculator tests.
@Edward Foyer No wonder we fear math tests more than saber tooth tigers. The amygdala is an evolutionary process to protect us from math tests and not from saber tooth tigers.
yea but when you fail in the 1800s you will most likely end up homeless and hungry lol
Calculus exam would be like "What is the summation over a continuous index, of the product of an infinitesimal width and the continuous index with our consideration limited by a lower value zero and an upper value 1?"
Tell me why I can do calculus but I can't do these questions?
@@kevinmaldonado204
You simply are not used to it.
Kevin Maldonado I think the notation is just really wonky.
My two favorite physics channels in one place!
Calculus can be taught easier.
Convert meters per second to furlongs per fortnight.
😁 I took that SAME TEST in a different life and aced it! 😁 I am joking of course! 😁
Hector Pascal
Yep.
Meter = 1.0936 yards
Furlong = 220 yards
Fortnight = 2 weeks
Seconds in two weeks = 60×60×24×14 = 1,209,600
Yards in two weeks
1,322,818.56
÷ 220 = 6012.8 furlongs in two weeks.
😁
how is fortnite related to stupid maths. Anyways, dab and floss
@@infinitytoinfinitysquaredb7836 omg wow
My God. I can only begin to imagine the calculus and physics papers of the time.
@Salvador Luna Physics was probably really basic stuff, like speed and maybe gravity, as we hadn't figured stuff like radiation etc. out back then. And chemistry was not far enough to be teached at schools at that time i think. And even if it was taught back then it was probably only daltons modell of the atoms, and stuff goes boom if you mix it.
*t e x t*
This is more of an English exam than a math exam. This looks like some Shakespeare level stuff.
its actually more of a practical arithmetic exam, like learning how to do your taxes or give change for money. it makes a lot of sense to teach practical, applicable math even by today standards, the units and the commonplace situations were slightly different
hhhh. xd.
@@adaster98 You're judging this off one test, relax lol
@CrAzYCaM 8 'Yet they were all much less intelligent' - er...university students in the 19th century were far more intelligent than those today. There were only a few subjects and so you had to be excellent at both mathematics and english just to get in. Kids today can get into a university with english and math skills which wouldn't even let them graduate highschool in 1890.
"Shakespeare level stuff"
How does this have 235 upvotes? I just can't…
Australian Maths be like
Oi^2 = m8, carry the roo, divide by the boomerang. The remainder is shrimps on the barbie.
She's newzealandanise though
OI
Lmaooooo
@@Tombalino If you divide an orc by two and carry the Hobbit, how far can King Kong throw Bilbo? Give the distance in Wetas.
😂
EXAM 👏 REVIEW 👏
she kille*d it
\m/
I see I'm not the only 9 year old here
LvlAndFarm do you know
@@ferdelance. I just saw that you've got TSoP album cover and assumed you're a fan
It's interesting to see how the importance we attribute to skills evolves with time.
Calculating cube roots (as question 17 seems to ask) is not really considered an important skill today, because of the computing power we have. Instead, we would focus on the insight and the interpretation that the value or the cube root operation can have.
But really if you don't have computers, suddenly you have no idea what the value of a cube root would be without an appropriate technique !
Ahh the good ol times. I remember when I had to take the same exam. Time flies so fast
Lol, what side did you fight on in the Civil War?
@@unavailableusername9694 lool
LOL xD
Congratulations for remaining alive since 1866 to the time of youtube
Time flies? What are they?
An English man an Irish man and a Scottish man walk into an exam hall in 1866..
The English man understood everything and got great score of 86%
The Scottish man copied the English man and got a passing score of 62%
The Irish man thought he was in a poetry exam. He got 100%
The American man nuked the school the day before the test.
@@Megaman99X And then built a wall to keep the English, Irish, Scottish and "math" out.
But then needed math to build the wall..
@@Nightceasar 🤣🤣🤣🤣
The Irish man drank Scotch while watching the american blow the school thinking it was a play.
Except if the Scottish man was James Clerk Maxwell. Then the exam would fail him.
Just seeing that date Oct. 1, 1866 gives you such a profound feeling. You hear about things happening 200 years ago etc. but seeing a actual date in real life written by the people of that time is just mind boggling.
You kids of 1866 and your arithmetic tests....try and answer a common question from my alchemy test in 1466:
"If you drink an invisibilty potion but you grow donkey ears instead, which ingredients are missing considering that on that day Venus is alligned with Jupiter but Mars is not alligned with Neptune?."
That would be quite the exceptional alchemy test though, as Neptune wasn't known about until 1846 ;)
@@WhattheHectogon Yeah! ahah! You sure know a lot of things, probably more than you should for your own sake. You watch yourself man, it'd be a shame if somebody turned you into a newt by mistake one of these days....
@@fabb91 LMAOOO
@@knife979 Indeed.
I did not get this. Please kindly explain.
Thanks
In my generation, the 1950s, we had to be able to do all this as well. Comptometers started to be used in that decade.
Well it’s not that much tbh look at real tests. This one neither includes calculus or stochastic. Also the only hard part of this test is being able to speak English properly
A late 19th century phone can be used to solve every problem here, not a joke. They had a feature most don't know about unless they have actually seen one up close. Inside there is a fairly large electrical generator to produce current for the ringers. The whole unit weighs in around 20 lbs or 4.5 kilos. if you remove that section from the wall and slam the teacher in the back of the head, you will have successfully solved all your problems from the math exam.
M'Night Shyamalan plot twist right there
20lbs is about 9kg... I'm now looking nervously over my shoulder.
Except that is a very millennial way of thinking, to grab one’s phone and perpetrate violence upon a teacher.
@@dacanale ok boomer
Only 19th century kids will remember this.
What fun times they were, go to war and come back home to do some math problems.
@@46pi26 and then go to the doctor. the good doctor.
@@zikomo8913 then when your wife goes into labor, that doctor will kindly give her ergot, whose constituent compounds include LSD and a few fatally toxic chemicals. What a simpler time it was; nowadays, we buy our LSD and fatal toxins seperately.
"What fun times they were, go to war and come back home to do some math problems."
Except nobody actually went to war. All war is theatre and then reported as "fact" by the newspapers. Even D-Day (or the footage) was military exercises off the coast of Cornwall. Nobody actually "died".
@@nossasenhoradoo871 visit a doctor as soon as possible
"visit a doctor as soon as possible"
So that he can prescribe loads of useless drugs that do little if any good? Another cliched response not discussing the real issues. If the RAF and American air force had complete dominance over the skies the Allies could have picked almost place to land troops. The Normandy landings were picked to that the war could be extended, with spook reporters like Ernest Hemingway giving people the "facts" (propaganda) along the way. This is true.
This is not a math exam, it's a resistance test of how much does you can stand without your hand stop writing and get bleeding
I see you everywhere
@@ugh6201 where r u from?
Everytime I reread this comment it makes less sense
Your level of English is 'Cretin'.
@@Captain_Nemo-y7q Sorry, I'm a brazilian and I don't speak very well.
No wonder people became criminals and robbed others in hopes they could gather enough *money* and go to Tahiti.
Its a magical place
@@stirnermax2396 30 mins late, damn!
like they do today?
Alright Dutch.
@@ravenaxyz xD
And they wonder why Tom Sawyer went rogue painting all those fences...!
I grew up in New York and we still have Regents exams, but yeah they're in geometry, trigonometry, pre-calculus
And other subjects
As a child of the 60s, graduating in 1971, I can relate. It is "old math" - the simple basics. I took Alegra I in the 9th grade, Geometry in the 10th, and I was never required to go further. This math is what I call useful math. It can be used in solving everyday problems and it teaches you to figure out thought problems. I loved seeing this!
It could be some of these questions are answerable with a slide rule or common logarithm table, which were common before calculators.
Like for #17, I think the cube root could be solved by computing antilog((1 / 3) * log(389017)), where the log and antilog involve looking up in tables.
It's so funny to hear math professionals still refusing to say the word multiply.
To get the next time for the train to arrive, you must take the time and times it by the time you think it'll take, so you can time your timing correctly. Take the sum time and times it by a decimal to get the previous time, thus, confirming your timesing of the time is correct. You can also pull out a copy of the Times to get the train times, but it's good excercise to try timesing your timing, anyway. Don't forget to carry the decimals when you times the time with, or without the times in the Times as your guide.
...so how about the product?
10/10 for effort
Well done
Maybe Parthenogenesis
When I heard her say that, I couldn't help rolling my eyes. I wonder if her teachers also learned her to plus things to each other :-)
Very informative. Real good explanation too. I liked how there's no apparent "cheat sheet" included to give conversion factors during the exam.
Potash is literally pot ash but without the space between the words, and comes from burning down residue from stuff that was already burned down. Potash was and is still used as fertilizer due to it's high concentration of compounds. The word potassium comes from potash, and that's one important element for the fertilizer. :)
as a recent graduate from a public school in New York, the regents exams are still alive and well
You were reading threes as eights in the numerators of some of the fractions. That was not at all your fault, as, owing to poor printing, they did indeed look like eights when not magnified several times.
Lol oops
In particular, Question 22, it must be "3/4 of his interest" in the mine. This is a straightforward exam with a calculator, but would be very punishing without one.
Re: Question 18. This is a bond. The issuer will pay John Smith $100 at the end of the bond period and the question is asking how much John Smith would have to give the bank to get such a bond, i.e. its "present value". "Present value" is still a term used in finance. It means the value right now of some future cash flow which will be discounted by a "discount rate." We're still missing some information. Probably New York where this test was issued had a standard discount rate for bank bonds that would be known to test takers.
For modern folks, this is basically the same as a loan, just specified in the opposite direction. i.e. the amount specified is the amount that will be repaid instead of the amount loaned: instead of saying, "I will give you $100 now, and in the future you will have to pay me that amount plus an interest rate," you can say, "In the future, you will repay me $100, so I can give you $X discounted by the discount rate." So this is like a compound interest question and you'd solve it the same way, just by dividing by the rate instead of multiplying.
I was inclined to either say zero, because the bond has not matured; or apply "common" knowledge about US bonds, such as the purchase value being half the face value, and common models of economics, such as the bond's market value being as if it had a fixed risk-free interest rate, to arrive at the answer. The latter would definitely require a calculator though, as it requires computing fractional powers of 2.
How is every one of your videos a nice trip down the ASMR lane. The vibes on each one are so calming. I don't even realise that I've been through another 15ish minutes of intense science shit. Nice content man. I'm shook ;)
Gold is measured in Troy ounces, Cotton is measured in Avoirdupois ounces. A pound of Gold is NOT the same weight as a pound of Cotton. (Troy ounces are 12 troy oz. to 1 troy pound, avoirdupois is 16 oz per pound.)
1 troy pound = 12 troy oz = 0.823 lbs = 13.168 oz.
1 lb = 16 oz = 14.583 troy oz = 1.215 troy pounds.
(Σ)
I'm saving this to use as a double-trick question: "Which weighs more, a pound of gold or a pound of feathers?"
Probably more like troy ounces vs stones or hundredweights.
...metric system
Get with the program
Damn trick question got me.
@@WorBlux
Not necessarily. What matters is that you know that the troy ounces are smaller than Avoirdupois ones.
“Old school”
*I see what you did there*
Just watching it gave me anxiety
i live in new york.... can confirm we STILL have these regents exams to this day.................
If i saw anyone who could actually solve for the square root of 0.0043046721 by hand I'd be insanely impressed. As a math major myself in my 3rd year of college I find this really interesting to look at. I really hope you find a calculus or even linear algebra exam from the 19th or early 20th century, I'd be really interested in that.
Awesome video as usual!
I'm assuming a slide rule would have been allowed, which would make the question more of an ability to use a slide rule than a test on the math; akin to using a modern calculator to work out a standard deviation for example?
Actually, I just tried this on my own slide rule and I can only get that the answer would be ~0.066* with an uncertain 3rd significant figure, so that's the end of my slide rule theory! :)
There is a video on RUclips titled "Square root of 2 on the pepper grinder". It is an amusing demonstration of how to calculate a square root using a machine that can only add and subtract!
@@robertlozyniak3661 i will go and check it out!
It's actually not that hard. The problem does require some effort and thinking to solve it by hand.
You first factorize 43046721 to get 3^16. (repeated division)
That means it is the square of 3^8 (6561).
With some other knowledge of squares and square roots, one can figure out it is the square of 0.06561 :)
I feel like you've been reading 8/4 instead of 3/4 the entire time. 3/4 makes sense and the old font may have a 3 looking like an 8. You should really take a closer look at it just to make sure. 8/4 just makes no sense.
3 8/4 would be 5
it’s definitely an 8 in the exam
@@wongpakyin4860 yeah but 8/4 is not a fraction its a whole number (2) so why would they write a whole number as a fraction??
I live in New York and we still use regents exams. The current math exams we have are algebra 1, geometry, and algebra 2.
my videos will help for your exam.
Im from new york moved to Minnesota 3 years ago I remember doing regents exams in hs but I had no clue they were around in the 1800s
@@rachelkrats5569 I actually just moved to New York from Ohio less than two years ago.
this feels like asmr
It is if you have a thing for private teachers.
Its because it is.
this meme should die
You can do the cubic root with some school tricks. So the answer is gonna be a two digit number (because 389017 is between 1000 and 10^6). Now we can write x = 10*a + b where a and b are between 1 and 10.
This here you were probably taught at school (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3, applied to our x we have x^3 = 1000*a^3 + 300*a^2b + 30*a*b^2 + b^3.
Here we can notice that only b^3 determines the last digit (7) and the only number that can get us that last digit is 3 (3^3 = 27). So b=3 and now x^3 = 1000*a^3 + 900*a^2 + 270*a + 27.
Now we suspect that the first digit is solely determined by 1000*a^3. Again we check all the digits and we find a very promising candidate in 7^3 = 343. So now we check 73^3 and indeed we get 389017.
thanksforthefish42 looks like tok much effort
Thanks for the explanation! Got the 3 but didn't catch the 7.
Here is how I did it.
Since these are solid cubes, the length has to be an integer.
The last digit of the cube root has to be 3 because 3 is the only digit that ends in 7 when cubed.
Then bound the problem by trying
100^3=1000000, too big
50^3 = 5^3*10^3=225000, too small
70^3=49*7*1000=343000, too small
80^3 = 64*8*1000=512000 to large,
the answer is between 70 and 80 ending with a 3, 73 it is.
@@mzallocc that is how I solved the problem, too. Good stuff!
When I was in school, we learned an algorithm for taking square roots. I forgot it long before most people reading this were born and had to look it up the last time I wanted to take a square root by hand.
I'm pretty sure that question 17 "What is the length of the side of a cubical box which contains 389,017 solid inches?" would be solved by the use of a slide rule, which has been around since the 17th century and is excellent for calculating roots and exponents. Likewise question 20.
i 'calculated' the root this way:
1. assumption result is an integer since it is an exam (risk involved)
2. 389 017 is roughly 400 000 = 400 * 10^3, so 7^3 * 10^3 is not far from result
3. the only digit yielding '7' on the last position when cubed is 3
I have problems I'd like to appear on the 2066 Regents Exam -- they require the student develop a software numerical algorithm to be solved:
Example1: Given 3 overlapping spheres (of different radii), solve for their two points of intersection.
Example2: Given two skew lines (extended lines in 3D), solve for the shortest bridging line segment between them, calculating its two endpoints.
I'm convinced that high school maths will be advancing to this level in that timeframe, with algo-design tools as ordinary as were paper and pencil in 1866.
(I aced the New York State Regents Geometry Exam in 1966, spurring me on to lifelong learning in spatial maths & CS.)
Cube root and Square root (or any root) e.g Cube root - get the logarithm of the number - divide by 3 - find the Antilog of the number. The used books of logarithms in those days.
9:44
"excuse me? um...."
Lmao
389017 == 73^3 here's the answer :P (obtained by clever trial & error...)
The cube root of six digit perfect cubes are easily found by a technique. I don't know the name of the technique, but here in India people cram it for competitive exams for government jobs.
This question has me a little bit shook. SHOOK.
You lied on your 4k video.
I wonder if this was recommended because I subscribed to you .
Knowing Better ok
at 6:05 maybe it's asking about the scale of the weight you would use to weight each material? Presumably, gold is more valuable than cotton, therefore when exchanging one for the other, you would exchange grams of gold dust for tonnes of cotton. So you would use a scale with a grams counterweight to measure the amount of gold dust and a scale with a tonnes counterweight to measure the amount of cotton.
I find your videos fun. I actually went to school in Utica 1945 - 1952
qr. = Quarter of a hundredweight (2 stone, 28 lb)
cwt = Hundredweight (1/8 of a ton, 112 lb)
bu. = Bushel (4 pecks = 8 gallons = 32 quarts = 64 pints)
pk. = Peck (2 gallons = 8 quarts = 16 pints)
qt. = Quart (2 pints)
This paper looks like great fun. What was the allocated time?!
And i thought retarded units were a hassle today, i feel bad for those who didn't use metric system back in the day.
@@necrisro Before calculators we used numbers other than 10 which have more factors and are easier to divide, i.e. 8/12/16/24/36 - hence why a lot of imperial measurements use them.
So, basically, this is why people came up with the metric system.
@@MaciejBogdanStepien Yeah, they found out that a lot of people are just stupid can can't grasp base 12 or base 60 measurements.
@@MaciejBogdanStepien
Not really, the bigger problem was the variation between national standards, and even variation on what what being measured. For example the hundredweight was just a hundred pounds when you were measuring agricultural products.
For the discounting $100 question, it is asking you to find the present value of the $100 to be paid in 90 days. The thing is it doesn't give you a rate to discount by, it just says "bank." So I'm assuming at this time there was a standardized discount rate that was the "bank" rate. Possibly 5%? If so it would be about $94.50 You would have to solve for X to the power of Bank/4 (90days/360 year) = $100
Also, you would see this on any finance 101 exam today less the vague "bank" rate. :)
The cynic in me assumes the banks just used a nice round number like 20% when buying bonds like this from the public... :)
I was pretty amused at the question though and wonder how many business school graduates today truly understand it.
Honestly I think why I watch is because this is virtually an ASMR channel for geeks.
Nah, you like blondes.
@@uruiamnot lol'd
These all seem perfectly reasonable and easy arithmetic questions we should expect seniors in high school to successfully complete
This is the big difference between then and now: then, education was all about teaching practical things - how to figure out how to convert mixed units of measure, and actually come up with numeric results. Today, what is taught is more abstract. Note that there isn't even a hint of algebra or geometry in this test. I'm sure that the method of calculating square roots by hand was taught at the senior level; it was still being taught when I was in high school a long time ago. Note that the solution to the cube root problem is a whole number, so the intended method for solving this would be to estimate and then zero in on the solution.
Whether this was more "practical" than what is taught today is a matter of perspective I'd say. Geometry and vectorial math is about as practical as it gets and it has an important place in today's curriculum. Didn't see any optimisation problems or geometry in that exam.
This is great, it's like a math lesson and a history lesson all in one!
When I was in high school the regents exams were very much alive.
Some unintended ASMR is going on here! Listening to you explaining this is just so calming!
Clever work Toby, I will now watch your Video solving Q20.
Question 22: Do you think the print may not be clear, and it's actually 3/4 of his interest in the mine that was sold?
I'd say every time she said 8/4, it was really 3/4.
Where you are reading "8/4", it is actually printed as "3/4", but the small printing has blurred this 🙂 So question #22 is indeed a reasonable situation.
'Where you are reading "8/4", it is actually printed as "3/4",'
An earlier question too, not just #22
how can i send you some physics graduate test from Brasil?
lol Brazil...
@@aryeahzenter4378 lol what?
@@aryeahzenter4378 I don't get it...
@@jessica5497 BraSil -> BraZil
"How can i send you some physics graduate test from Brasil?"
Does this involve dip-thongs?
I love random videos in my RUclips feed. It's super refreshing.
im a highschooler in new york. the regents exam are final exams given by the state for certain subjects. almost all of math (except pre-calc, ap calc and pre-alg), all sciences, 11th grade english and world history and american history regents. it happens annually on june, January and august (schools usually chose btwn January and June, August are usually taken by those who fail) this is given every year, is mostly mandatory (you need to take a certain amt. of regents to graduate. e.g. physics in my school was voluntary) and is like a final exam. its only given in new york, or what i know of. all of these exams are found online
youtube's recommendation algorithm is so weird 🤨
True, I never searched anything math related before.
And now of course my recommendations is full of math, chess and physics video...
M3rk fan?
You made an error in reading the fractions for question 2. Zoom right in and look really closely, the numbers are 3 + 3/4 and 2 + 3/4 and not as you stated 3 + 8/4 ( = 5) and 2 + 8/4 (= 4) which would have been too easy
you guys are so lucky that you can read 150 years old English texts so easily. Try as German reading some of the old German fonts^^
st0ox Most languages have that peculiarity. Spanish, Italian, French, Greek. I suspect German is poorly organized if you can’t understand something written 150 years ago
@@gianfrancostefanoli7854
Ha!
No.
@@gianfrancostefanoli7854 It's not the language that changed a lot, it's the conventional script it is written in.
@@alenvaneci Fraktur was a font for Latin script, just weirdly ligatured.
Es ist wirklich nicht schwierig, die Schrift zu lesen. Man muss sich wirklich nur kurz daran gewöhnen.
Somewhere, someone must be having a chuckle going through these questions once again after 1866.
There's GOT to be someone alive still.
you make everything sound like it'll be okay thank you
HI, The 8/4 you keep seeing are really 3/4. The three is in a font that almost closes.
math is math, no matter the century, rigorous, demanding, deterministic
I disagree. I don't know. What kind exams could exist in Newton childhood times???
''Evaluate the maximum force that our great Lord can made to put the plan planets walking around on Luminiferous aether?'' Answer: Infinity + infinity
Jokes apart...It is interesting to investigate and discover.
Definitely not. Math is not THAT universal as you can think
@@buttup8148 Before Newton, theories about euclidian geometries, complex numbers, arithmetic, series, trigonometry already existed. Even in terms of physics, despite his genius, he followed results of Copernic, Galilée, Brahé and Kepler among others ^^
@@Shonras but the complex numbers were ''invented'' just in Gauss Age...
@@buttup8148 Well, technically, as my teacher of General Relativity claimed, complex numbers were developed in their algebric form by italians mathematicans of the 16th century, to resolve equations of the third degree for example. But indeed their 'geometrical form' was studied in Gauss Age :)
Anyway, let me tell you the basic methodology for the square roots and the cube roots. So what is the cube root of 889017? So here's the thing. You know that the cube root of a million is 100, right? So this is going to be slightly less than 100. But how much? Well, if you cube .9 you get .729, if you cube 1.1 you get 1.331. So when you cube (1+delta) for a small delta, you get about 1+3*delta, you see? So to get something that is 11% less than a million when you cube it, you should start from something that is about 3.66667% less than 100. But actually it should be more than 3.6667% but more like maybe a full 4%, because .9 doesn't turn to .7 after all, it turns into .729, since 1-delta cubed is not 1-3*delta exactly but 1-3*delta+3*delta^2-delta^3. So what is 4% less than 100? 96. So my estimate would be 96. Of course it's not 96 exactly because 96 to any integer problem will end in a 6 and this is the cube root of 889017, but I would certainly wager 96 is the closest integer to the answer, which is an irrational number. And what is the actual answer? About 96.17459. So indeed it was 3.83541% less than 100, not merely 3.66667% less than 100. But my estimate of 96 was very close.
For the square root one on the last page, what is the square root of .0043046721? Well let's multiply it by 10 thousand so that the answer scales up by 100. So what is the square root of 43.046721? Well 42.25 is 6.5 squared, while 49 is 7 squared, and this is like 10% of the way from 6.5 to 7, so we're talking about about 6.55 then, or .0655 when you divide it by 100 again, but I'm not confident of that 5 at the end, it could be anything from .653 to .657... and what is the real answer...... Oh, it's .6561 exactly.... which is a familiar number to me, since I know 6561 is 9 to the 4th power. Apparently the people in the 19th century had their powers of 3 memorized to some ridiculous and useless level to be able to recognize 43046721 as 3^16. But there's the answer, it's asking for the square root of 3^16/10^10 and so the answer would be 3^8/10^5. You were also expected to be able to do (5/8)^7 so maybe it was common in the 19th century to memorize tables of the first 20 or so powers of the integers 2 to 10? That's pretty dumb.
You solved a wrong problem. It was 389017, not 889017.
9:03: That Dr. is debit, not doctor as you said. Looks like it's mundane accountancy again, duh!
Have a high school text book from WW2 years and it's full of problems about calculating artillery shell trajectories, plane and ship navigation problems, etc. The public education system had tailored the math curriculum to prepare boys to graduate, go into military service, and go right off to war.
I may be weird, but all of these questions make a lot of sense to me and none of them seems weird, only the examples are a bit dated, but it is all super easy stuff.
*She definitely works out!*
As a New Yorker, I can confirm we still take Regents exams, but they're much more modern
Not as much as I'd like. For Geometry, you are expected to know 2D transforms and how to apply them. There's still too much reliance on special cases and hand-computation.
9:38 The cube root of 389017 is 73 exactly, which I found by guessing and multiplying. First I guessed only multiples of ten. That quickly showed it was more than 70 and less than 80. Next I guessed 75, and finally 73.
You can always look at the last digit of 389017 which is 7. 3 is the only number that cubed will give you a number which last digit is 7. Therefore the fist digit of the cube root of 389017 is 3.
@@kmki Good idea. (To be honest, I was afraid to assume the answer would be an integer.)
They want to know if we know that the first digit of each product must be entered in the same column of its multiplyer.
The multiplyer in each of the columns (ones, tens, etc) produces its own product but since we haven't completed the problem with the final addition, the product in each line is called a 'partial product'
Bruh the fact that this has “I’m shook” on the thumbnail has me dead for some reason.
When I was at school ... a fair time back ... we used logarithm tables to do all the tricky stuff - those were the days (not really).
We could also use our slide rules - what fun they were!
Our teacher showed us some of these old tools! My father also used these.
Jeez, that must have been tedious. I'm so thankful that our calculators can do logs now
In India we still learn how to use log table but yaa calculator are much better but in Indian exams you can't use calculator for calculation so we are still stuck with log table😅😅😅😅
@@khushipandey2482 Are you allowed to use an abacus?
@David Seddon One time in college I realized I had forgotten my calculator, so I went to the library and borrowed an old book of mathematical tables and used the logarithm tables from the book.
(For people who don't know what logarithm tables are: they allow you to do addition in place of multiplication, and subtraction in place of division. Thus, they are very helpful if you have to do a lot of multiplication and division, because then you only have to do addition, subtraction, and table lookups.)
This was very interesting. I have seen a couple of your presentations and I really like how you do it and communicate. Well done. My maths is very engineering orientated - so in short we learned maths in order to underpin our designs and methodologies. But I'm very interested in your opinion that arithmetic is less (not) important today - and in part you are correct. Checkout controllers at supermarkets cannot do maths - if their machine breaks down - its all over. However what is more important today in our wonderful world of technology and devices is a sense of scale. Whilst we can generate clever designs with extremely powerful computers and can produce efficient use of technology and resources, not to mention learning more about our universe etc etc I learned originally to have a sense of scale. In other words, when the answer is produced by our wonderful technology who is there to ask....does that make sense? A simple question, but unless you have a sense of calculation (broad brush - order of magnitude even) the question becomes rhetorical. You admitted yourself that to work out a share of a food bill can be a challenge in a restaurant. I have seen many failures in recent times related in may cases directly to noone asking a basic question.....does that make sense? Some Building collapses, bridge failures are often design failures due to this lack of.....does it make sense? and not necessarily an extraordinary event. Sorry for the ramble but it is easy to accept and answer on a calculator if you have no sense of scale.
Keep up your presentations - they are excellent.
As a graduate from a high school in the state of New York. Yes, the Regents are still in existence (or they were when I graduated in 1997). They are the end of year exams given for most high school classes.
For #3, I would equate “figure” to “digit.” The partial product refers to each product you wrote beneath the line. 12 x 28 = 12 x 8 + 12 x 20 = 12 x 8 + 12 x 2 x 10
The figures are written one space to the left to signify the digit’s place, tens, hundreds, thousands, etc.
I wondered as soon as I saw this if it was the same name from the regents exams I took in New York, and I was delighted to hear it was!
Don't they still use fractions in the USA? Has the math test changed for them?
Sadly it's been phased out. Part of the intentional dumbing down of the population. It's easier to control the purposely stupid.
I live in Ohio and we still use fractions
@@nero7469 We want the Toledo strip back...
I was taught ratios and fractions in 4th grade back in the 80s.
Here in Oklahoma USA we use fractions and the metric system. Although the metric system is much simpler.
the youtube search algorithms are mathematically 1000x more complex than this test.
Taylor Series for square roots?
Youmight wish to read the Wikipedia article titled "Methods of computing square roots".
@@robertlozyniak3661 I will but was the Taylor Series invented by 1866?
@@SathnimBandara for sure. In 1866 people could predict the motion of planets in the solar system with many decimal digits precision. Maths was really advanced back than, but this test wasn't about that.
@@zoltankurti damn straight
Taylor Series were invented at around 1715 I think
50 odd years since i left school but there is nothing difficult about any of the questions, It's so bloody easy now with multiple choice questions you don't even have to think anymore.
says a person who clearly knows what they're talking about since they haven't been in school for 50 years...
What multiple choice questions? Once you pass algebra 2 almost nothing is multiple choice. Also, what about these questions are remotely harder than today's math? I would easily argue that even multiple choice trigonometry tests of today (grade 12 math), if they existed, would still be far more difficult than this test, or any grade 12 math test 50 years ago.
love voices that are well, ASMR without trying.
who was here in 1880?
Maladddddyyy u know i am not absent! 👨
An 138 year old person
You should do asmr videos. You'd make bank.
math asmr ?
there's some girl that does asmr with C programs I forgot her name
@Alchemica Blackwood she'd make even more bank getting rammed by 2 dongs but not everybody wants to do that!
@@ENZOxDV9 actually no, good asmr gets hundreds of thousands of views, millions sometimes. pornhub videos are quickly forgotten, as are countless camsessions
@@iceberg789 That would definitely increase the flux over my cylindrical surface.
You should do a podcast!
so that Indians can mock, troll and hurl racist and sexist slurs at her like they did in the IIT-JEE video?
@@electricalastro "Yeh gore log sochte kya hai apun ke JEE ko... sab saale humi se chori karre..." or "Saali JEE ke paper ko halke mein leri... akal wahi ghutne mein..." YES! not racist or sexist at all... BTW, Indians have set the bar pretty high internationally with "bobs and vegene" buddy... lets just not talk about standards okay...
"They have a kinda nationalist ideology..."
Trump voters of India?
@@13ivanogre13 Worse, they think its alright to lynch someone because they eat beef.
@@davidb6927 How do you know he is an Indian citizen? His family might have moved to other counties several generations ago for all you know
#3: In the algorithm she was using (see 4:14), the partial products are the numbers you achieve by multiplying the first number by each digit of the second. "96" is the partial product of "12 x 8" while "24(0)" is the partial product of "12 x 2(0)". The question is asking where to align the "ones" digit of each partial product, and why. For the first partial product (96 in her example), it is below the ones digit, while the second partial product (24(x10)) begins under the tens column. The "ones" digit of the partial product is always aligned under the correct place value. This is done to preserve the value of the place digits used from the lower factor.
Toby, Sadly in US, there no Calculus even in prep school and so is the case with Bio, Chem, Physics too - Very primitive But they do extort (those Pvt schools) parents to the max with tutions going on $40k-$50k/yr